LMFDB - Embedded newform 9025.2.a.cv.1.35

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:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 1805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
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)

$f(q)$	$=$	$q+2.42726 q^{2} -1.05699 q^{3} +3.89157 q^{4} -2.56557 q^{6} -4.52506 q^{7} +4.59133 q^{8} -1.88278 q^{9} +O(q^{10})$	\(q+2.42726 q^{2} -1.05699 q^{3} +3.89157 q^{4} -2.56557 q^{6} -4.52506 q^{7} +4.59133 q^{8} -1.88278 q^{9} +0.194403 q^{11} -4.11334 q^{12} +3.48815 q^{13} -10.9835 q^{14} +3.36119 q^{16} -6.60308 q^{17} -4.56999 q^{18} +4.78292 q^{21} +0.471865 q^{22} +1.18472 q^{23} -4.85297 q^{24} +8.46664 q^{26} +5.16103 q^{27} -17.6096 q^{28} -4.10574 q^{29} +5.06679 q^{31} -1.02419 q^{32} -0.205481 q^{33} -16.0274 q^{34} -7.32698 q^{36} +4.20787 q^{37} -3.68693 q^{39} +9.20454 q^{41} +11.6094 q^{42} +2.26312 q^{43} +0.756532 q^{44} +2.87562 q^{46} -5.95612 q^{47} -3.55273 q^{48} +13.4761 q^{49} +6.97936 q^{51} +13.5744 q^{52} +6.94598 q^{53} +12.5271 q^{54} -20.7760 q^{56} -9.96568 q^{58} +2.39041 q^{59} +4.79183 q^{61} +12.2984 q^{62} +8.51970 q^{63} -9.20835 q^{64} -0.498754 q^{66} +5.22583 q^{67} -25.6964 q^{68} -1.25223 q^{69} +5.85628 q^{71} -8.64448 q^{72} +6.54790 q^{73} +10.2136 q^{74} -0.879683 q^{77} -8.94912 q^{78} +5.47834 q^{79} +0.193213 q^{81} +22.3418 q^{82} -9.54544 q^{83} +18.6131 q^{84} +5.49318 q^{86} +4.33971 q^{87} +0.892567 q^{88} +14.4923 q^{89} -15.7841 q^{91} +4.61042 q^{92} -5.35552 q^{93} -14.4570 q^{94} +1.08255 q^{96} -7.41146 q^{97} +32.7101 q^{98} -0.366018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * q^99

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 $

$2$	2.42726	1.71633	0.858165	−	0.513375i	$-0.171605\pi$
$2$	2.42726	1.71633	0.858165	+	0.513375i	$0.171605\pi$
$3$	−1.05699	−0.610251	−0.305125	−	0.952312i	$-0.598698\pi$
$3$	−1.05699	−0.610251	−0.305125	+	0.952312i	$0.598698\pi$
$4$	3.89157	1.94579
$5$	0	0
$5$	0	0
$6$	−2.56557	−1.04739
$7$	−4.52506	−1.71031	−0.855156	−	0.518371i	$-0.826538\pi$
$7$	−4.52506	−1.71031	−0.855156	+	0.518371i	$0.826538\pi$
$8$	4.59133	1.62328
$9$	−1.88278	−0.627594
$10$	0	0
$11$	0.194403	0.0586146	0.0293073	−	0.999570i	$-0.490670\pi$
$11$	0.194403	0.0586146	0.0293073	+	0.999570i	$0.490670\pi$
$12$	−4.11334	−1.18742
$13$	3.48815	0.967440	0.483720	−	0.875223i	$-0.339285\pi$
$13$	3.48815	0.967440	0.483720	+	0.875223i	$0.339285\pi$
$14$	−10.9835	−2.93546
$15$	0	0
$16$	3.36119	0.840298
$17$	−6.60308	−1.60148	−0.800741	−	0.599010i	$-0.795561\pi$
$17$	−6.60308	−1.60148	−0.800741	+	0.599010i	$0.795561\pi$
$18$	−4.56999	−1.07716
$19$	0	0
$19$	0	0
$20$	0	0
$21$	4.78292	1.04372
$22$	0.471865	0.100602
$23$	1.18472	0.247031	0.123516	−	0.992343i	$-0.460583\pi$
$23$	1.18472	0.247031	0.123516	+	0.992343i	$0.460583\pi$
$24$	−4.85297	−0.990608
$25$	0	0
$26$	8.46664	1.66045
$27$	5.16103	0.993241
$28$	−17.6096	−3.32790
$29$	−4.10574	−0.762417	−0.381208	−	0.924489i	$-0.624492\pi$
$29$	−4.10574	−0.762417	−0.381208	+	0.924489i	$0.624492\pi$
$30$	0	0
$31$	5.06679	0.910023	0.455011	−	0.890486i	$-0.349635\pi$
$31$	5.06679	0.910023	0.455011	+	0.890486i	$0.349635\pi$
$32$	−1.02419	−0.181052
$33$	−0.205481	−0.0357696
$34$	−16.0274	−2.74867
$35$	0	0
$36$	−7.32698	−1.22116
$37$	4.20787	0.691770	0.345885	−	0.938277i	$-0.387579\pi$
$37$	4.20787	0.691770	0.345885	+	0.938277i	$0.387579\pi$
$38$	0	0
$39$	−3.68693	−0.590381
$40$	0	0
$41$	9.20454	1.43751	0.718754	−	0.695265i	$-0.244713\pi$
$41$	9.20454	1.43751	0.718754	+	0.695265i	$0.244713\pi$
$42$	11.6094	1.79137
$43$	2.26312	0.345123	0.172561	−	0.984999i	$-0.444796\pi$
$43$	2.26312	0.345123	0.172561	+	0.984999i	$0.444796\pi$
$44$	0.756532	0.114052
$45$	0	0
$46$	2.87562	0.423987
$47$	−5.95612	−0.868789	−0.434394	−	0.900723i	$-0.643038\pi$
$47$	−5.95612	−0.868789	−0.434394	+	0.900723i	$0.643038\pi$
$48$	−3.55273	−0.512793
$49$	13.4761	1.92516
$50$	0	0
$51$	6.97936	0.977306
$52$	13.5744	1.88243
$53$	6.94598	0.954104	0.477052	−	0.878875i	$-0.341705\pi$
$53$	6.94598	0.954104	0.477052	+	0.878875i	$0.341705\pi$
$54$	12.5271	1.70473
$55$	0	0
$56$	−20.7760	−2.77632
$57$	0	0
$58$	−9.96568	−1.30856
$59$	2.39041	0.311204	0.155602	−	0.987820i	$-0.450268\pi$
$59$	2.39041	0.311204	0.155602	+	0.987820i	$0.450268\pi$
$60$	0	0
$61$	4.79183	0.613531	0.306765	−	0.951785i	$-0.400753\pi$
$61$	4.79183	0.613531	0.306765	+	0.951785i	$0.400753\pi$
$62$	12.2984	1.56190
$63$	8.51970	1.07338
$64$	−9.20835	−1.15104
$65$	0	0
$66$	−0.498754	−0.0613924
$67$	5.22583	0.638437	0.319219	−	0.947681i	$-0.396580\pi$
$67$	5.22583	0.638437	0.319219	+	0.947681i	$0.396580\pi$
$68$	−25.6964	−3.11614
$69$	−1.25223	−0.150751
$70$	0	0
$71$	5.85628	0.695012	0.347506	−	0.937678i	$-0.387029\pi$
$71$	5.85628	0.695012	0.347506	+	0.937678i	$0.387029\pi$
$72$	−8.64448	−1.01876
$73$	6.54790	0.766374	0.383187	−	0.923671i	$-0.374827\pi$
$73$	6.54790	0.766374	0.383187	+	0.923671i	$0.374827\pi$
$74$	10.2136	1.18730
$75$	0	0
$76$	0	0
$77$	−0.879683	−0.100249
$78$	−8.94912	−1.01329
$79$	5.47834	0.616362	0.308181	−	0.951328i	$-0.400280\pi$
$79$	5.47834	0.616362	0.308181	+	0.951328i	$0.400280\pi$
$80$	0	0
$81$	0.193213	0.0214681
$82$	22.3418	2.46724
$83$	−9.54544	−1.04775	−0.523874	−	0.851796i	$-0.675514\pi$
$83$	−9.54544	−1.04775	−0.523874	+	0.851796i	$0.675514\pi$
$84$	18.6131	2.03085
$85$	0	0
$86$	5.49318	0.592345
$87$	4.33971	0.465265
$88$	0.892567	0.0951480
$89$	14.4923	1.53618	0.768091	−	0.640341i	$-0.221207\pi$
$89$	14.4923	1.53618	0.768091	+	0.640341i	$0.221207\pi$
$90$	0	0
$91$	−15.7841	−1.65462
$92$	4.61042	0.480670
$93$	−5.35552	−0.555342
$94$	−14.4570	−1.49113
$95$	0	0
$96$	1.08255	0.110487
$97$	−7.41146	−0.752520	−0.376260	−	0.926514i	$-0.622790\pi$
$97$	−7.41146	−0.752520	−0.376260	+	0.926514i	$0.622790\pi$
$98$	32.7101	3.30422
$99$	−0.366018	−0.0367862
$100$	0	0
$101$	−12.2199	−1.21593	−0.607963	−	0.793965i	$-0.708013\pi$
$101$	−12.2199	−1.21593	−0.607963	+	0.793965i	$0.708013\pi$
$102$	16.9407	1.67738
$103$	10.1826	1.00332	0.501660	−	0.865065i	$-0.332723\pi$
$103$	10.1826	1.00332	0.501660	+	0.865065i	$0.332723\pi$
$104$	16.0153	1.57043
$105$	0	0
$106$	16.8597	1.63756
$107$	−0.779264	−0.0753343	−0.0376671	−	0.999290i	$-0.511993\pi$
$107$	−0.779264	−0.0753343	−0.0376671	+	0.999290i	$0.511993\pi$
$108$	20.0845	1.93263
$109$	−3.46937	−0.332305	−0.166153	−	0.986100i	$-0.553134\pi$
$109$	−3.46937	−0.332305	−0.166153	+	0.986100i	$0.553134\pi$
$110$	0	0
$111$	−4.44766	−0.422153
$112$	−15.2096	−1.43717
$113$	14.5203	1.36595	0.682976	−	0.730441i	$-0.260685\pi$
$113$	14.5203	1.36595	0.682976	+	0.730441i	$0.260685\pi$
$114$	0	0
$115$	0	0
$116$	−15.9778	−1.48350
$117$	−6.56743	−0.607159
$118$	5.80213	0.534129
$119$	29.8793	2.73903
$120$	0	0
$121$	−10.9622	−0.996564
$122$	11.6310	1.05302
$123$	−9.72906	−0.877240
$124$	19.7178	1.77071
$125$	0	0
$126$	20.6795	1.84228
$127$	18.7617	1.66484	0.832418	−	0.554149i	$-0.186956\pi$
$127$	18.7617	1.66484	0.832418	+	0.554149i	$0.186956\pi$
$128$	−20.3027	−1.79452
$129$	−2.39209	−0.210612
$130$	0	0
$131$	14.0733	1.22959	0.614795	−	0.788687i	$-0.289239\pi$
$131$	14.0733	1.22959	0.614795	+	0.788687i	$0.289239\pi$
$132$	−0.799643	−0.0696000
$133$	0	0
$134$	12.6844	1.09577
$135$	0	0
$136$	−30.3169	−2.59966
$137$	−6.71499	−0.573700	−0.286850	−	0.957975i	$-0.592608\pi$
$137$	−6.71499	−0.573700	−0.286850	+	0.957975i	$0.592608\pi$
$138$	−3.03949	−0.258738
$139$	−6.33776	−0.537562	−0.268781	−	0.963201i	$-0.586621\pi$
$139$	−6.33776	−0.537562	−0.268781	+	0.963201i	$0.586621\pi$
$140$	0	0
$141$	6.29553	0.530179
$142$	14.2147	1.19287
$143$	0.678106	0.0567061
$144$	−6.32839	−0.527366
$145$	0	0
$146$	15.8934	1.31535
$147$	−14.2441	−1.17483
$148$	16.3752	1.34604
$149$	6.51608	0.533818	0.266909	−	0.963722i	$-0.413998\pi$
$149$	6.51608	0.533818	0.266909	+	0.963722i	$0.413998\pi$
$150$	0	0
$151$	15.0078	1.22132	0.610660	−	0.791893i	$-0.290904\pi$
$151$	15.0078	1.22132	0.610660	+	0.791893i	$0.290904\pi$
$152$	0	0
$153$	12.4322	1.00508
$154$	−2.13522	−0.172061
$155$	0	0
$156$	−14.3479	−1.14876
$157$	−15.9224	−1.27074	−0.635371	−	0.772207i	$-0.719153\pi$
$157$	−15.9224	−1.27074	−0.635371	+	0.772207i	$0.719153\pi$
$158$	13.2973	1.05788
$159$	−7.34180	−0.582243
$160$	0	0
$161$	−5.36092	−0.422500
$162$	0.468978	0.0368464
$163$	−17.6799	−1.38480	−0.692400	−	0.721514i	$-0.743447\pi$
$163$	−17.6799	−1.38480	−0.692400	+	0.721514i	$0.743447\pi$
$164$	35.8201	2.79708
$165$	0	0
$166$	−23.1692	−1.79828
$167$	−12.5103	−0.968075	−0.484038	−	0.875047i	$-0.660830\pi$
$167$	−12.5103	−0.968075	−0.484038	+	0.875047i	$0.660830\pi$
$168$	21.9600	1.69425
$169$	−0.832781	−0.0640601
$170$	0	0
$171$	0	0
$172$	8.80710	0.671535
$173$	−6.09199	−0.463166	−0.231583	−	0.972815i	$-0.574390\pi$
$173$	−6.09199	−0.463166	−0.231583	+	0.972815i	$0.574390\pi$
$174$	10.5336	0.798549
$175$	0	0
$176$	0.653425	0.0492538
$177$	−2.52662	−0.189913
$178$	35.1765	2.63659
$179$	5.35886	0.400540	0.200270	−	0.979741i	$-0.435818\pi$
$179$	5.35886	0.400540	0.200270	+	0.979741i	$0.435818\pi$
$180$	0	0
$181$	15.8763	1.18007	0.590037	−	0.807376i	$-0.299113\pi$
$181$	15.8763	1.18007	0.590037	+	0.807376i	$0.299113\pi$
$182$	−38.3121	−2.83988
$183$	−5.06489	−0.374408
$184$	5.43944	0.401001
$185$	0	0
$186$	−12.9992	−0.953150
$187$	−1.28366	−0.0938703
$188$	−23.1787	−1.69048
$189$	−23.3540	−1.69875
$190$	0	0
$191$	22.2361	1.60895	0.804475	−	0.593987i	$-0.202447\pi$
$191$	22.2361	1.60895	0.804475	+	0.593987i	$0.202447\pi$
$192$	9.73309	0.702425
$193$	−14.4423	−1.03958	−0.519791	−	0.854293i	$-0.673990\pi$
$193$	−14.4423	−1.03958	−0.519791	+	0.854293i	$0.673990\pi$
$194$	−17.9895	−1.29157
$195$	0	0
$196$	52.4434	3.74596
$197$	−10.7740	−0.767613	−0.383806	−	0.923414i	$-0.625387\pi$
$197$	−10.7740	−0.767613	−0.383806	+	0.923414i	$0.625387\pi$
$198$	−0.888419	−0.0631372
$199$	2.09938	0.148821	0.0744105	−	0.997228i	$-0.476293\pi$
$199$	2.09938	0.148821	0.0744105	+	0.997228i	$0.476293\pi$
$200$	0	0
$201$	−5.52363	−0.389607
$202$	−29.6609	−2.08693
$203$	18.5787	1.30397
$204$	27.1607	1.90163
$205$	0	0
$206$	24.7157	1.72203
$207$	−2.23057	−0.155035
$208$	11.7244	0.812938
$209$	0	0
$210$	0	0
$211$	−6.30512	−0.434062	−0.217031	−	0.976165i	$-0.569637\pi$
$211$	−6.30512	−0.434062	−0.217031	+	0.976165i	$0.569637\pi$
$212$	27.0308	1.85648
$213$	−6.19000	−0.424132
$214$	−1.89147	−0.129298
$215$	0	0
$216$	23.6960	1.61231
$217$	−22.9275	−1.55642
$218$	−8.42105	−0.570346
$219$	−6.92103	−0.467680
$220$	0	0
$221$	−23.0326	−1.54934
$222$	−10.7956	−0.724553
$223$	−12.6960	−0.850187	−0.425094	−	0.905149i	$-0.639759\pi$
$223$	−12.6960	−0.850187	−0.425094	+	0.905149i	$0.639759\pi$
$224$	4.63450	0.309656
$225$	0	0
$226$	35.2444	2.34442
$227$	10.8208	0.718201	0.359101	−	0.933299i	$-0.383084\pi$
$227$	10.8208	0.718201	0.359101	+	0.933299i	$0.383084\pi$
$228$	0	0
$229$	1.66903	0.110293	0.0551463	−	0.998478i	$-0.482437\pi$
$229$	1.66903	0.110293	0.0551463	+	0.998478i	$0.482437\pi$
$230$	0	0
$231$	0.929812	0.0611772
$232$	−18.8508	−1.23762
$233$	10.3979	0.681192	0.340596	−	0.940210i	$-0.389371\pi$
$233$	10.3979	0.681192	0.340596	+	0.940210i	$0.389371\pi$
$234$	−15.9408	−1.04209
$235$	0	0
$236$	9.30244	0.605537
$237$	−5.79053	−0.376135
$238$	72.5248	4.70108
$239$	9.94852	0.643516	0.321758	−	0.946822i	$-0.395726\pi$
$239$	9.94852	0.643516	0.321758	+	0.946822i	$0.395726\pi$
$240$	0	0
$241$	−5.01351	−0.322949	−0.161474	−	0.986877i	$-0.551625\pi$
$241$	−5.01351	−0.322949	−0.161474	+	0.986877i	$0.551625\pi$
$242$	−26.6081	−1.71043
$243$	−15.6873	−1.00634
$244$	18.6478	1.19380
$245$	0	0
$246$	−23.6149	−1.50563
$247$	0	0
$248$	23.2633	1.47722
$249$	10.0894	0.639389
$250$	0	0
$251$	24.2323	1.52953	0.764766	−	0.644308i	$-0.222855\pi$
$251$	24.2323	1.52953	0.764766	+	0.644308i	$0.222855\pi$
$252$	33.1550	2.08857
$253$	0.230313	0.0144796
$254$	45.5396	2.85741
$255$	0	0
$256$	−30.8630	−1.92894
$257$	13.2309	0.825323	0.412662	−	0.910884i	$-0.364599\pi$
$257$	13.2309	0.825323	0.412662	+	0.910884i	$0.364599\pi$
$258$	−5.80621	−0.361479
$259$	−19.0409	−1.18314
$260$	0	0
$261$	7.73021	0.478488
$262$	34.1595	2.11038
$263$	14.8787	0.917461	0.458730	−	0.888575i	$-0.348304\pi$
$263$	14.8787	0.917461	0.458730	+	0.888575i	$0.348304\pi$
$264$	−0.943430	−0.0580641
$265$	0	0
$266$	0	0
$267$	−15.3182	−0.937456
$268$	20.3367	1.24226
$269$	−3.82602	−0.233277	−0.116638	−	0.993174i	$-0.537212\pi$
$269$	−3.82602	−0.233277	−0.116638	+	0.993174i	$0.537212\pi$
$270$	0	0
$271$	−20.6532	−1.25459	−0.627297	−	0.778780i	$-0.715839\pi$
$271$	−20.6532	−1.25459	−0.627297	+	0.778780i	$0.715839\pi$
$272$	−22.1942	−1.34572
$273$	16.6836	1.00974
$274$	−16.2990	−0.984659
$275$	0	0
$276$	−4.87315	−0.293329
$277$	12.9777	0.779757	0.389879	−	0.920866i	$-0.372517\pi$
$277$	12.9777	0.779757	0.389879	+	0.920866i	$0.372517\pi$
$278$	−15.3834	−0.922633
$279$	−9.53966	−0.571125
$280$	0	0
$281$	12.4242	0.741165	0.370582	−	0.928800i	$-0.379158\pi$
$281$	12.4242	0.741165	0.370582	+	0.928800i	$0.379158\pi$
$282$	15.2809	0.909962
$283$	19.2541	1.14454	0.572268	−	0.820066i	$-0.306064\pi$
$283$	19.2541	1.14454	0.572268	+	0.820066i	$0.306064\pi$
$284$	22.7901	1.35235
$285$	0	0
$286$	1.64594	0.0973264
$287$	−41.6511	−2.45859
$288$	1.92832	0.113627
$289$	26.6007	1.56475
$290$	0	0
$291$	7.83381	0.459226
$292$	25.4816	1.49120
$293$	−13.2897	−0.776395	−0.388197	−	0.921576i	$-0.626902\pi$
$293$	−13.2897	−0.776395	−0.388197	+	0.921576i	$0.626902\pi$
$294$	−34.5741	−2.01640
$295$	0	0
$296$	19.3197	1.12294
$297$	1.00332	0.0582184
$298$	15.8162	0.916208
$299$	4.13248	0.238988
$300$	0	0
$301$	−10.2408	−0.590267
$302$	36.4278	2.09619
$303$	12.9163	0.742020
$304$	0	0
$305$	0	0
$306$	30.1760	1.72505
$307$	15.3103	0.873802	0.436901	−	0.899510i	$-0.356076\pi$
$307$	15.3103	0.873802	0.436901	+	0.899510i	$0.356076\pi$
$308$	−3.42335	−0.195064
$309$	−10.7628	−0.612276
$310$	0	0
$311$	25.6272	1.45319	0.726594	−	0.687067i	$-0.241102\pi$
$311$	25.6272	1.45319	0.726594	+	0.687067i	$0.241102\pi$
$312$	−16.9279	−0.958354
$313$	−4.64058	−0.262301	−0.131150	−	0.991362i	$-0.541867\pi$
$313$	−4.64058	−0.262301	−0.131150	+	0.991362i	$0.541867\pi$
$314$	−38.6476	−2.18101
$315$	0	0
$316$	21.3194	1.19931
$317$	−7.58665	−0.426109	−0.213054	−	0.977040i	$-0.568341\pi$
$317$	−7.58665	−0.426109	−0.213054	+	0.977040i	$0.568341\pi$
$318$	−17.8204	−0.999320
$319$	−0.798167	−0.0446888
$320$	0	0
$321$	0.823670	0.0459728
$322$	−13.0123	−0.725149
$323$	0	0
$324$	0.751903	0.0417724
$325$	0	0
$326$	−42.9137	−2.37677
$327$	3.66707	0.202790
$328$	42.2611	2.33348
$329$	26.9518	1.48590
$330$	0	0
$331$	7.17378	0.394307	0.197153	−	0.980373i	$-0.436830\pi$
$331$	7.17378	0.394307	0.197153	+	0.980373i	$0.436830\pi$
$332$	−37.1468	−2.03869
$333$	−7.92250	−0.434150
$334$	−30.3657	−1.66154
$335$	0	0
$336$	16.0763	0.877035
$337$	−8.16394	−0.444718	−0.222359	−	0.974965i	$-0.571376\pi$
$337$	−8.16394	−0.444718	−0.222359	+	0.974965i	$0.571376\pi$
$338$	−2.02137	−0.109948
$339$	−15.3477	−0.833573
$340$	0	0
$341$	0.984998	0.0533406
$342$	0	0
$343$	−29.3050	−1.58232
$344$	10.3907	0.560231
$345$	0	0
$346$	−14.7868	−0.794945
$347$	3.02384	0.162328	0.0811642	−	0.996701i	$-0.474136\pi$
$347$	3.02384	0.162328	0.0811642	+	0.996701i	$0.474136\pi$
$348$	16.8883	0.905307
$349$	23.1629	1.23988	0.619940	−	0.784650i	$-0.287157\pi$
$349$	23.1629	1.23988	0.619940	+	0.784650i	$0.287157\pi$
$350$	0	0
$351$	18.0025	0.960901
$352$	−0.199105	−0.0106123
$353$	2.14345	0.114084	0.0570421	−	0.998372i	$-0.481833\pi$
$353$	2.14345	0.114084	0.0570421	+	0.998372i	$0.481833\pi$
$354$	−6.13276	−0.325953
$355$	0	0
$356$	56.3979	2.98908
$357$	−31.5820	−1.67150
$358$	13.0073	0.687458
$359$	−6.89505	−0.363907	−0.181953	−	0.983307i	$-0.558242\pi$
$359$	−6.89505	−0.363907	−0.181953	+	0.983307i	$0.558242\pi$
$360$	0	0
$361$	0	0
$362$	38.5358	2.02540
$363$	11.5869	0.608154
$364$	−61.4250	−3.21954
$365$	0	0
$366$	−12.2938	−0.642607
$367$	12.3423	0.644263	0.322132	−	0.946695i	$-0.395601\pi$
$367$	12.3423	0.644263	0.322132	+	0.946695i	$0.395601\pi$
$368$	3.98207	0.207580
$369$	−17.3301	−0.902171
$370$	0	0
$371$	−31.4310	−1.63181
$372$	−20.8414	−1.08058
$373$	−21.5626	−1.11647	−0.558234	−	0.829683i	$-0.688521\pi$
$373$	−21.5626	−1.11647	−0.558234	+	0.829683i	$0.688521\pi$
$374$	−3.11576	−0.161112
$375$	0	0
$376$	−27.3465	−1.41029
$377$	−14.3215	−0.737592
$378$	−56.6860	−2.91562
$379$	28.3040	1.45388	0.726939	−	0.686703i	$-0.240942\pi$
$379$	28.3040	1.45388	0.726939	+	0.686703i	$0.240942\pi$
$380$	0	0
$381$	−19.8309	−1.01597
$382$	53.9728	2.76149
$383$	−8.08490	−0.413119	−0.206560	−	0.978434i	$-0.566227\pi$
$383$	−8.08490	−0.413119	−0.206560	+	0.978434i	$0.566227\pi$
$384$	21.4596	1.09511
$385$	0	0
$386$	−35.0552	−1.78426
$387$	−4.26097	−0.216597
$388$	−28.8422	−1.46424
$389$	1.83534	0.0930556	0.0465278	−	0.998917i	$-0.485184\pi$
$389$	1.83534	0.0930556	0.0465278	+	0.998917i	$0.485184\pi$
$390$	0	0
$391$	−7.82280	−0.395616
$392$	61.8735	3.12508
$393$	−14.8753	−0.750359
$394$	−26.1512	−1.31748
$395$	0	0
$396$	−1.42438	−0.0715780
$397$	4.86954	0.244395	0.122198	−	0.992506i	$-0.461006\pi$
$397$	4.86954	0.244395	0.122198	+	0.992506i	$0.461006\pi$
$398$	5.09573	0.255426
$399$	0	0
$400$	0	0
$401$	−18.0028	−0.899016	−0.449508	−	0.893276i	$-0.648401\pi$
$401$	−18.0028	−0.899016	−0.449508	+	0.893276i	$0.648401\pi$
$402$	−13.4073	−0.668693
$403$	17.6737	0.880392
$404$	−47.5547	−2.36593
$405$	0	0
$406$	45.0953	2.23804
$407$	0.818021	0.0405478
$408$	32.0446	1.58644
$409$	11.3247	0.559969	0.279985	−	0.960005i	$-0.409671\pi$
$409$	11.3247	0.559969	0.279985	+	0.960005i	$0.409671\pi$
$410$	0	0
$411$	7.09765	0.350101
$412$	39.6262	1.95224
$413$	−10.8167	−0.532256
$414$	−5.41416	−0.266091
$415$	0	0
$416$	−3.57252	−0.175157
$417$	6.69892	0.328048
$418$	0	0
$419$	−3.64977	−0.178303	−0.0891514	−	0.996018i	$-0.528416\pi$
$419$	−3.64977	−0.178303	−0.0891514	+	0.996018i	$0.528416\pi$
$420$	0	0
$421$	−14.5023	−0.706799	−0.353400	−	0.935472i	$-0.614974\pi$
$421$	−14.5023	−0.706799	−0.353400	+	0.935472i	$0.614974\pi$
$422$	−15.3041	−0.744994
$423$	11.2141	0.545247
$424$	31.8913	1.54878
$425$	0	0
$426$	−15.0247	−0.727950
$427$	−21.6833	−1.04933
$428$	−3.03256	−0.146584
$429$	−0.716749	−0.0346049
$430$	0	0
$431$	−0.227835	−0.0109744	−0.00548721	−	0.999985i	$-0.501747\pi$
$431$	−0.227835	−0.0109744	−0.00548721	+	0.999985i	$0.501747\pi$
$432$	17.3472	0.834618
$433$	33.0508	1.58832	0.794160	−	0.607709i	$-0.207911\pi$
$433$	33.0508	1.58832	0.794160	+	0.607709i	$0.207911\pi$
$434$	−55.6510	−2.67133
$435$	0	0
$436$	−13.5013	−0.646595
$437$	0	0
$438$	−16.7991	−0.802693
$439$	−29.8555	−1.42493	−0.712464	−	0.701709i	$-0.752421\pi$
$439$	−29.8555	−1.42493	−0.712464	+	0.701709i	$0.752421\pi$
$440$	0	0
$441$	−25.3727	−1.20822
$442$	−55.9059	−2.65917
$443$	16.1507	0.767342	0.383671	−	0.923470i	$-0.374660\pi$
$443$	16.1507	0.767342	0.383671	+	0.923470i	$0.374660\pi$
$444$	−17.3084	−0.821419
$445$	0	0
$446$	−30.8164	−1.45920
$447$	−6.88740	−0.325763
$448$	41.6683	1.96864
$449$	−23.8916	−1.12752	−0.563758	−	0.825940i	$-0.690645\pi$
$449$	−23.8916	−1.12752	−0.563758	+	0.825940i	$0.690645\pi$
$450$	0	0
$451$	1.78939	0.0842589
$452$	56.5067	2.65785
$453$	−15.8631	−0.745311
$454$	26.2648	1.23267
$455$	0	0
$456$	0	0
$457$	−15.1145	−0.707027	−0.353514	−	0.935429i	$-0.615013\pi$
$457$	−15.1145	−0.707027	−0.353514	+	0.935429i	$0.615013\pi$
$458$	4.05116	0.189298
$459$	−34.0787	−1.59066
$460$	0	0
$461$	25.2228	1.17474	0.587372	−	0.809317i	$-0.300162\pi$
$461$	25.2228	1.17474	0.587372	+	0.809317i	$0.300162\pi$
$462$	2.25689	0.105000
$463$	−40.2723	−1.87161	−0.935807	−	0.352513i	$-0.885327\pi$
$463$	−40.2723	−1.87161	−0.935807	+	0.352513i	$0.885327\pi$
$464$	−13.8002	−0.640657
$465$	0	0
$466$	25.2385	1.16915
$467$	20.5304	0.950035	0.475017	−	0.879976i	$-0.342442\pi$
$467$	20.5304	0.950035	0.475017	+	0.879976i	$0.342442\pi$
$468$	−25.5576	−1.18140
$469$	−23.6472	−1.09193
$470$	0	0
$471$	16.8297	0.775472
$472$	10.9751	0.505172
$473$	0.439957	0.0202292
$474$	−14.0551	−0.645572
$475$	0	0
$476$	116.278	5.32957
$477$	−13.0778	−0.598790
$478$	24.1476	1.10449
$479$	−21.6877	−0.990936	−0.495468	−	0.868626i	$-0.665003\pi$
$479$	−21.6877	−0.990936	−0.495468	+	0.868626i	$0.665003\pi$
$480$	0	0
$481$	14.6777	0.669245
$482$	−12.1691	−0.554286
$483$	5.66642	0.257831
$484$	−42.6602	−1.93910
$485$	0	0
$486$	−38.0771	−1.72721
$487$	−6.84733	−0.310282	−0.155141	−	0.987892i	$-0.549583\pi$
$487$	−6.84733	−0.310282	−0.155141	+	0.987892i	$0.549583\pi$
$488$	22.0009	0.995933
$489$	18.6874	0.845075
$490$	0	0
$491$	25.4609	1.14904	0.574518	−	0.818492i	$-0.305190\pi$
$491$	25.4609	1.14904	0.574518	+	0.818492i	$0.305190\pi$
$492$	−37.8614	−1.70692
$493$	27.1105	1.22100
$494$	0	0
$495$	0	0
$496$	17.0305	0.764690
$497$	−26.5000	−1.18869
$498$	24.4895	1.09740
$499$	−43.7606	−1.95899	−0.979496	−	0.201465i	$-0.935430\pi$
$499$	−43.7606	−1.95899	−0.979496	+	0.201465i	$0.935430\pi$
$500$	0	0
$501$	13.2232	0.590769
$502$	58.8181	2.62518
$503$	1.49740	0.0667657	0.0333828	−	0.999443i	$-0.489372\pi$
$503$	1.49740	0.0667657	0.0333828	+	0.999443i	$0.489372\pi$
$504$	39.1168	1.74240
$505$	0	0
$506$	0.559028	0.0248518
$507$	0.880237	0.0390927
$508$	73.0127	3.23941
$509$	28.0342	1.24259	0.621297	−	0.783575i	$-0.286606\pi$
$509$	28.0342	1.24259	0.621297	+	0.783575i	$0.286606\pi$
$510$	0	0
$511$	−29.6296	−1.31074
$512$	−34.3072	−1.51618
$513$	0	0
$514$	32.1149	1.41653
$515$	0	0
$516$	−9.30898	−0.409805
$517$	−1.15788	−0.0509237
$518$	−46.2170	−2.03066
$519$	6.43915	0.282647
$520$	0	0
$521$	5.17980	0.226931	0.113466	−	0.993542i	$-0.463805\pi$
$521$	5.17980	0.226931	0.113466	+	0.993542i	$0.463805\pi$
$522$	18.7632	0.821243
$523$	−24.3654	−1.06543	−0.532713	−	0.846296i	$-0.678828\pi$
$523$	−24.3654	−1.06543	−0.532713	+	0.846296i	$0.678828\pi$
$524$	54.7673	2.39252
$525$	0	0
$526$	36.1145	1.57466
$527$	−33.4564	−1.45739
$528$	−0.690661	−0.0300571
$529$	−21.5964	−0.938976
$530$	0	0
$531$	−4.50061	−0.195310
$532$	0	0
$533$	32.1069	1.39070
$534$	−37.1811	−1.60898
$535$	0	0
$536$	23.9935	1.03636
$537$	−5.66423	−0.244430
$538$	−9.28673	−0.400379
$539$	2.61980	0.112843
$540$	0	0
$541$	24.8099	1.06666	0.533330	−	0.845907i	$-0.320940\pi$
$541$	24.8099	1.06666	0.533330	+	0.845907i	$0.320940\pi$
$542$	−50.1307	−2.15330
$543$	−16.7810	−0.720141
$544$	6.76279	0.289952
$545$	0	0
$546$	40.4953	1.73304
$547$	9.73496	0.416237	0.208118	−	0.978104i	$-0.433266\pi$
$547$	9.73496	0.416237	0.208118	+	0.978104i	$0.433266\pi$
$548$	−26.1319	−1.11630
$549$	−9.02197	−0.385048
$550$	0	0
$551$	0	0
$552$	−5.74941	−0.244711
$553$	−24.7898	−1.05417
$554$	31.5003	1.33832
$555$	0	0
$556$	−24.6639	−1.04598
$557$	17.7327	0.751359	0.375679	−	0.926750i	$-0.377409\pi$
$557$	17.7327	0.751359	0.375679	+	0.926750i	$0.377409\pi$
$558$	−23.1552	−0.980238
$559$	7.89412	0.333886
$560$	0	0
$561$	1.35681	0.0572844
$562$	30.1567	1.27208
$563$	30.7541	1.29613	0.648065	−	0.761585i	$-0.275578\pi$
$563$	30.7541	1.29613	0.648065	+	0.761585i	$0.275578\pi$
$564$	24.4995	1.03162
$565$	0	0
$566$	46.7346	1.96440
$567$	−0.874300	−0.0367172
$568$	26.8881	1.12820
$569$	34.2367	1.43528	0.717639	−	0.696415i	$-0.245223\pi$
$569$	34.2367	1.43528	0.717639	+	0.696415i	$0.245223\pi$
$570$	0	0
$571$	−36.7211	−1.53673	−0.768366	−	0.640011i	$-0.778930\pi$
$571$	−36.7211	−1.53673	−0.768366	+	0.640011i	$0.778930\pi$
$572$	2.63890	0.110338
$573$	−23.5033	−0.981863
$574$	−101.098	−4.21974
$575$	0	0
$576$	17.3373	0.722388
$577$	−41.5983	−1.73176	−0.865880	−	0.500252i	$-0.833241\pi$
$577$	−41.5983	−1.73176	−0.865880	+	0.500252i	$0.833241\pi$
$578$	64.5667	2.68562
$579$	15.2653	0.634406
$580$	0	0
$581$	43.1937	1.79197
$582$	19.0147	0.788183
$583$	1.35032	0.0559244
$584$	30.0636	1.24404
$585$	0	0
$586$	−32.2576	−1.33255
$587$	13.3401	0.550604	0.275302	−	0.961358i	$-0.411222\pi$
$587$	13.3401	0.550604	0.275302	+	0.961358i	$0.411222\pi$
$588$	−55.4319	−2.28597
$589$	0	0
$590$	0	0
$591$	11.3879	0.468436
$592$	14.1435	0.581293
$593$	5.69252	0.233764	0.116882	−	0.993146i	$-0.462710\pi$
$593$	5.69252	0.233764	0.116882	+	0.993146i	$0.462710\pi$
$594$	2.43531	0.0999220
$595$	0	0
$596$	25.3578	1.03870
$597$	−2.21901	−0.0908181
$598$	10.0306	0.410182
$599$	42.1070	1.72044	0.860222	−	0.509919i	$-0.170325\pi$
$599$	42.1070	1.72044	0.860222	+	0.509919i	$0.170325\pi$
$600$	0	0
$601$	36.0751	1.47153	0.735767	−	0.677235i	$-0.236822\pi$
$601$	36.0751	1.47153	0.735767	+	0.677235i	$0.236822\pi$
$602$	−24.8569	−1.01309
$603$	−9.83910	−0.400679
$604$	58.4041	2.37643
$605$	0	0
$606$	31.3511	1.27355
$607$	32.4019	1.31515	0.657577	−	0.753388i	$-0.271582\pi$
$607$	32.4019	1.31515	0.657577	+	0.753388i	$0.271582\pi$
$608$	0	0
$609$	−19.6374	−0.795749
$610$	0	0
$611$	−20.7759	−0.840501
$612$	48.3807	1.95567
$613$	−25.1069	−1.01406	−0.507030	−	0.861929i	$-0.669257\pi$
$613$	−25.1069	−1.01406	−0.507030	+	0.861929i	$0.669257\pi$
$614$	37.1619	1.49973
$615$	0	0
$616$	−4.03892	−0.162733
$617$	−11.0213	−0.443703	−0.221851	−	0.975080i	$-0.571210\pi$
$617$	−11.0213	−0.443703	−0.221851	+	0.975080i	$0.571210\pi$
$618$	−26.1242	−1.05087
$619$	−15.0846	−0.606302	−0.303151	−	0.952942i	$-0.598039\pi$
$619$	−15.0846	−0.606302	−0.303151	+	0.952942i	$0.598039\pi$
$620$	0	0
$621$	6.11437	0.245361
$622$	62.2039	2.49415
$623$	−65.5785	−2.62735
$624$	−12.3925	−0.496096
$625$	0	0
$626$	−11.2639	−0.450195
$627$	0	0
$628$	−61.9630	−2.47259
$629$	−27.7849	−1.10786
$630$	0	0
$631$	−43.2378	−1.72127	−0.860635	−	0.509223i	$-0.829933\pi$
$631$	−43.2378	−1.72127	−0.860635	+	0.509223i	$0.829933\pi$
$632$	25.1529	1.00053
$633$	6.66442	0.264887
$634$	−18.4147	−0.731343
$635$	0	0
$636$	−28.5712	−1.13292
$637$	47.0069	1.86248
$638$	−1.93736	−0.0767006
$639$	−11.0261	−0.436185
$640$	0	0
$641$	−29.9485	−1.18290	−0.591448	−	0.806343i	$-0.701444\pi$
$641$	−29.9485	−1.18290	−0.591448	+	0.806343i	$0.701444\pi$
$642$	1.99926	0.0789044
$643$	31.5665	1.24486	0.622430	−	0.782675i	$-0.286145\pi$
$643$	31.5665	1.24486	0.622430	+	0.782675i	$0.286145\pi$
$644$	−20.8624	−0.822095
$645$	0	0
$646$	0	0
$647$	−17.5232	−0.688907	−0.344453	−	0.938803i	$-0.611936\pi$
$647$	−17.5232	−0.688907	−0.344453	+	0.938803i	$0.611936\pi$
$648$	0.887105	0.0348488
$649$	0.464701	0.0182411
$650$	0	0
$651$	24.2341	0.949808
$652$	−68.8028	−2.69452
$653$	31.0328	1.21441	0.607203	−	0.794547i	$-0.292291\pi$
$653$	31.0328	1.21441	0.607203	+	0.794547i	$0.292291\pi$
$654$	8.90093	0.348054
$655$	0	0
$656$	30.9382	1.20794
$657$	−12.3283	−0.480972
$658$	65.4189	2.55029
$659$	47.0487	1.83276	0.916379	−	0.400311i	$-0.131098\pi$
$659$	47.0487	1.83276	0.916379	+	0.400311i	$0.131098\pi$
$660$	0	0
$661$	−11.9223	−0.463723	−0.231861	−	0.972749i	$-0.574482\pi$
$661$	−11.9223	−0.463723	−0.231861	+	0.972749i	$0.574482\pi$
$662$	17.4126	0.676760
$663$	24.3451	0.945485
$664$	−43.8263	−1.70079
$665$	0	0
$666$	−19.2299	−0.745145
$667$	−4.86415	−0.188341
$668$	−48.6847	−1.88367
$669$	13.4195	0.518827
$670$	0	0
$671$	0.931544	0.0359619
$672$	−4.89860	−0.188968
$673$	−27.0397	−1.04230	−0.521152	−	0.853464i	$-0.674497\pi$
$673$	−27.0397	−1.04230	−0.521152	+	0.853464i	$0.674497\pi$
$674$	−19.8160	−0.763283
$675$	0	0
$676$	−3.24083	−0.124647
$677$	20.0588	0.770924	0.385462	−	0.922724i	$-0.374042\pi$
$677$	20.0588	0.770924	0.385462	+	0.922724i	$0.374042\pi$
$678$	−37.2528	−1.43069
$679$	33.5373	1.28704
$680$	0	0
$681$	−11.4374	−0.438283
$682$	2.39084	0.0915501
$683$	−39.5059	−1.51165	−0.755825	−	0.654773i	$-0.772764\pi$
$683$	−39.5059	−1.51165	−0.755825	+	0.654773i	$0.772764\pi$
$684$	0	0
$685$	0	0
$686$	−71.1306	−2.71578
$687$	−1.76414	−0.0673061
$688$	7.60679	0.290006
$689$	24.2287	0.923038
$690$	0	0
$691$	−22.2396	−0.846035	−0.423018	−	0.906121i	$-0.639029\pi$
$691$	−22.2396	−0.846035	−0.423018	+	0.906121i	$0.639029\pi$
$692$	−23.7074	−0.901222
$693$	1.65625	0.0629158
$694$	7.33964	0.278609
$695$	0	0
$696$	19.9250	0.755256
$697$	−60.7783	−2.30214
$698$	56.2222	2.12804
$699$	−10.9905	−0.415698
$700$	0	0
$701$	−28.0887	−1.06090	−0.530448	−	0.847717i	$-0.677976\pi$
$701$	−28.0887	−1.06090	−0.530448	+	0.847717i	$0.677976\pi$
$702$	43.6966	1.64922
$703$	0	0
$704$	−1.79013	−0.0674680
$705$	0	0
$706$	5.20270	0.195806
$707$	55.2958	2.07961
$708$	−9.83254	−0.369529
$709$	−39.9125	−1.49894	−0.749472	−	0.662036i	$-0.769693\pi$
$709$	−39.9125	−1.49894	−0.749472	+	0.662036i	$0.769693\pi$
$710$	0	0
$711$	−10.3145	−0.386825
$712$	66.5390	2.49365
$713$	6.00272	0.224804
$714$	−76.6576	−2.86884
$715$	0	0
$716$	20.8544	0.779365
$717$	−10.5154	−0.392706
$718$	−16.7361	−0.624584
$719$	6.17844	0.230417	0.115208	−	0.993341i	$-0.463246\pi$
$719$	6.17844	0.230417	0.115208	+	0.993341i	$0.463246\pi$
$720$	0	0
$721$	−46.0767	−1.71599
$722$	0	0
$723$	5.29921	0.197080
$724$	61.7837	2.29617
$725$	0	0
$726$	28.1244	1.04379
$727$	−9.21771	−0.341866	−0.170933	−	0.985283i	$-0.554678\pi$
$727$	−9.21771	−0.341866	−0.170933	+	0.985283i	$0.554678\pi$
$728$	−72.4700	−2.68592
$729$	16.0016	0.592653
$730$	0	0
$731$	−14.9436	−0.552708
$732$	−19.7104	−0.728518
$733$	20.5865	0.760381	0.380190	−	0.924908i	$-0.375858\pi$
$733$	20.5865	0.760381	0.380190	+	0.924908i	$0.375858\pi$
$734$	29.9579	1.10577
$735$	0	0
$736$	−1.21337	−0.0447255
$737$	1.01592	0.0374217
$738$	−42.0647	−1.54842
$739$	−14.4627	−0.532021	−0.266010	−	0.963970i	$-0.585706\pi$
$739$	−14.4627	−0.532021	−0.266010	+	0.963970i	$0.585706\pi$
$740$	0	0
$741$	0	0
$742$	−76.2910	−2.80073
$743$	−4.23224	−0.155266	−0.0776329	−	0.996982i	$-0.524736\pi$
$743$	−4.23224	−0.155266	−0.0776329	+	0.996982i	$0.524736\pi$
$744$	−24.5890	−0.901476
$745$	0	0
$746$	−52.3379	−1.91623
$747$	17.9720	0.657560
$748$	−4.99544	−0.182651
$749$	3.52621	0.128845
$750$	0	0
$751$	22.0045	0.802956	0.401478	−	0.915869i	$-0.368497\pi$
$751$	22.0045	0.802956	0.401478	+	0.915869i	$0.368497\pi$
$752$	−20.0197	−0.730042
$753$	−25.6132	−0.933398
$754$	−34.7618	−1.26595
$755$	0	0
$756$	−90.8836	−3.30541
$757$	−1.19032	−0.0432628	−0.0216314	−	0.999766i	$-0.506886\pi$
$757$	−1.19032	−0.0432628	−0.0216314	+	0.999766i	$0.506886\pi$
$758$	68.7010	2.49533
$759$	−0.243437	−0.00883620
$760$	0	0
$761$	−19.5355	−0.708161	−0.354080	−	0.935215i	$-0.615206\pi$
$761$	−19.5355	−0.708161	−0.354080	+	0.935215i	$0.615206\pi$
$762$	−48.1346	−1.74373
$763$	15.6991	0.568346
$764$	86.5335	3.13067
$765$	0	0
$766$	−19.6241	−0.709049
$767$	8.33810	0.301071
$768$	32.6218	1.17714
$769$	53.9907	1.94696	0.973478	−	0.228780i	$-0.0734738\pi$
$769$	53.9907	1.94696	0.973478	+	0.228780i	$0.0734738\pi$
$770$	0	0
$771$	−13.9849	−0.503654
$772$	−56.2034	−2.02280
$773$	−17.3893	−0.625451	−0.312725	−	0.949844i	$-0.601242\pi$
$773$	−17.3893	−0.625451	−0.312725	+	0.949844i	$0.601242\pi$
$774$	−10.3425	−0.371752
$775$	0	0
$776$	−34.0285	−1.22155
$777$	20.1259	0.722013
$778$	4.45485	0.159714
$779$	0	0
$780$	0	0
$781$	1.13848	0.0407379
$782$	−18.9879	−0.679007
$783$	−21.1898	−0.757263
$784$	45.2959	1.61771
$785$	0	0
$786$	−36.1061	−1.28786
$787$	48.0664	1.71338	0.856691	−	0.515830i	$-0.172516\pi$
$787$	48.0664	1.71338	0.856691	+	0.515830i	$0.172516\pi$
$788$	−41.9276	−1.49361
$789$	−15.7266	−0.559881
$790$	0	0
$791$	−65.7050	−2.33620
$792$	−1.68051	−0.0597143
$793$	16.7146	0.593554
$794$	11.8196	0.419463
$795$	0	0
$796$	8.16988	0.289574
$797$	−27.1546	−0.961866	−0.480933	−	0.876757i	$-0.659702\pi$
$797$	−27.1546	−0.961866	−0.480933	+	0.876757i	$0.659702\pi$
$798$	0	0
$799$	39.3287	1.39135
$800$	0	0
$801$	−27.2859	−0.964098
$802$	−43.6974	−1.54301
$803$	1.27293	0.0449207
$804$	−21.4956	−0.758091
$805$	0	0
$806$	42.8987	1.51104
$807$	4.04405	0.142357
$808$	−56.1057	−1.97379
$809$	−2.22424	−0.0782001	−0.0391001	−	0.999235i	$-0.512449\pi$
$809$	−2.22424	−0.0782001	−0.0391001	+	0.999235i	$0.512449\pi$
$810$	0	0
$811$	−16.5337	−0.580577	−0.290289	−	0.956939i	$-0.593751\pi$
$811$	−16.5337	−0.580577	−0.290289	+	0.956939i	$0.593751\pi$
$812$	72.3004	2.53725
$813$	21.8301	0.765617
$814$	1.98555	0.0695934
$815$	0	0
$816$	23.4590	0.821229
$817$	0	0
$818$	27.4879	0.961091
$819$	29.7180	1.03843
$820$	0	0
$821$	40.6846	1.41990	0.709952	−	0.704250i	$-0.248717\pi$
$821$	40.6846	1.41990	0.709952	+	0.704250i	$0.248717\pi$
$822$	17.2278	0.600889
$823$	−15.8784	−0.553486	−0.276743	−	0.960944i	$-0.589255\pi$
$823$	−15.8784	−0.553486	−0.276743	+	0.960944i	$0.589255\pi$
$824$	46.7516	1.62867
$825$	0	0
$826$	−26.2550	−0.913527
$827$	−2.03295	−0.0706926	−0.0353463	−	0.999375i	$-0.511253\pi$
$827$	−2.03295	−0.0706926	−0.0353463	+	0.999375i	$0.511253\pi$
$828$	−8.68042	−0.301665
$829$	17.2280	0.598354	0.299177	−	0.954198i	$-0.403288\pi$
$829$	17.2280	0.598354	0.299177	+	0.954198i	$0.403288\pi$
$830$	0	0
$831$	−13.7173	−0.475847
$832$	−32.1201	−1.11357
$833$	−88.9841	−3.08312
$834$	16.2600	0.563038
$835$	0	0
$836$	0	0
$837$	26.1499	0.903871
$838$	−8.85893	−0.306026
$839$	0.456894	0.0157737	0.00788687	−	0.999969i	$-0.497490\pi$
$839$	0.456894	0.0157737	0.00788687	+	0.999969i	$0.497490\pi$
$840$	0	0
$841$	−12.1429	−0.418721
$842$	−35.2008	−1.21310
$843$	−13.1322	−0.452296
$844$	−24.5368	−0.844592
$845$	0	0
$846$	27.2194	0.935823
$847$	49.6046	1.70444
$848$	23.3468	0.801732
$849$	−20.3513	−0.698454
$850$	0	0
$851$	4.98514	0.170889
$852$	−24.0888	−0.825270
$853$	29.8966	1.02364	0.511820	−	0.859093i	$-0.328971\pi$
$853$	29.8966	1.02364	0.511820	+	0.859093i	$0.328971\pi$
$854$	−52.6309	−1.80099
$855$	0	0
$856$	−3.57786	−0.122289
$857$	15.6100	0.533226	0.266613	−	0.963804i	$-0.414095\pi$
$857$	15.6100	0.533226	0.266613	+	0.963804i	$0.414095\pi$
$858$	−1.73973	−0.0593935
$859$	35.1240	1.19842	0.599208	−	0.800594i	$-0.295482\pi$
$859$	35.1240	1.19842	0.599208	+	0.800594i	$0.295482\pi$
$860$	0	0
$861$	44.0246	1.50035
$862$	−0.553014	−0.0188357
$863$	15.1704	0.516406	0.258203	−	0.966091i	$-0.416870\pi$
$863$	15.1704	0.516406	0.258203	+	0.966091i	$0.416870\pi$
$864$	−5.28586	−0.179829
$865$	0	0
$866$	80.2227	2.72608
$867$	−28.1165	−0.954888
$868$	−89.2241	−3.02846
$869$	1.06500	0.0361278
$870$	0	0
$871$	18.2285	0.617649
$872$	−15.9290	−0.539425
$873$	13.9542	0.472277
$874$	0	0
$875$	0	0
$876$	−26.9337	−0.910006
$877$	−29.3157	−0.989922	−0.494961	−	0.868915i	$-0.664818\pi$
$877$	−29.3157	−0.989922	−0.494961	+	0.868915i	$0.664818\pi$
$878$	−72.4671	−2.44564
$879$	14.0471	0.473795
$880$	0	0
$881$	29.7218	1.00135	0.500676	−	0.865634i	$-0.333085\pi$
$881$	29.7218	1.00135	0.500676	+	0.865634i	$0.333085\pi$
$882$	−61.5859	−2.07371
$883$	49.1965	1.65559	0.827797	−	0.561027i	$-0.189594\pi$
$883$	49.1965	1.65559	0.827797	+	0.561027i	$0.189594\pi$
$884$	−89.6329	−3.01468
$885$	0	0
$886$	39.2018	1.31701
$887$	45.2035	1.51779	0.758893	−	0.651215i	$-0.225741\pi$
$887$	45.2035	1.51779	0.758893	+	0.651215i	$0.225741\pi$
$888$	−20.4207	−0.685273
$889$	−84.8980	−2.84739
$890$	0	0
$891$	0.0375611	0.00125835
$892$	−49.4074	−1.65428
$893$	0	0
$894$	−16.7175	−0.559117
$895$	0	0
$896$	91.8707	3.06918
$897$	−4.36797	−0.145842
$898$	−57.9911	−1.93519
$899$	−20.8029	−0.693816
$900$	0	0
$901$	−45.8649	−1.52798
$902$	4.34330	0.144616
$903$	10.8243	0.360211
$904$	66.6673	2.21732
$905$	0	0
$906$	−38.5037	−1.27920
$907$	−52.8789	−1.75581	−0.877907	−	0.478831i	$-0.841061\pi$
$907$	−52.8789	−1.75581	−0.877907	+	0.478831i	$0.841061\pi$
$908$	42.1099	1.39747
$909$	23.0074	0.763108
$910$	0	0
$911$	13.9927	0.463597	0.231799	−	0.972764i	$-0.425539\pi$
$911$	13.9927	0.463597	0.231799	+	0.972764i	$0.425539\pi$
$912$	0	0
$913$	−1.85566	−0.0614133
$914$	−36.6868	−1.21349
$915$	0	0
$916$	6.49515	0.214606
$917$	−63.6825	−2.10298
$918$	−82.7177	−2.73009
$919$	28.2198	0.930884	0.465442	−	0.885078i	$-0.345895\pi$
$919$	28.2198	0.930884	0.465442	+	0.885078i	$0.345895\pi$
$920$	0	0
$921$	−16.1827	−0.533238
$922$	61.2223	2.01625
$923$	20.4276	0.672382
$924$	3.61843	0.119038
$925$	0	0
$926$	−97.7512	−3.21231
$927$	−19.1716	−0.629677
$928$	4.20504	0.138037
$929$	−22.9113	−0.751696	−0.375848	−	0.926681i	$-0.622649\pi$
$929$	−22.9113	−0.751696	−0.375848	+	0.926681i	$0.622649\pi$
$930$	0	0
$931$	0	0
$932$	40.4643	1.32545
$933$	−27.0876	−0.886809
$934$	49.8326	1.63057
$935$	0	0
$936$	−30.1533	−0.985590
$937$	48.7586	1.59287	0.796437	−	0.604722i	$-0.206716\pi$
$937$	48.7586	1.59287	0.796437	+	0.604722i	$0.206716\pi$
$938$	−57.3978	−1.87410
$939$	4.90502	0.160069
$940$	0	0
$941$	5.26228	0.171545	0.0857727	−	0.996315i	$-0.472664\pi$
$941$	5.26228	0.171545	0.0857727	+	0.996315i	$0.472664\pi$
$942$	40.8500	1.33096
$943$	10.9048	0.355109
$944$	8.03461	0.261504
$945$	0	0
$946$	1.06789	0.0347200
$947$	−55.3080	−1.79727	−0.898634	−	0.438700i	$-0.855439\pi$
$947$	−55.3080	−1.79727	−0.898634	+	0.438700i	$0.855439\pi$
$948$	−22.5343	−0.731879
$949$	22.8401	0.741421
$950$	0	0
$951$	8.01898	0.260033
$952$	137.186	4.44622
$953$	−15.8248	−0.512616	−0.256308	−	0.966595i	$-0.582506\pi$
$953$	−15.8248	−0.512616	−0.256308	+	0.966595i	$0.582506\pi$
$954$	−31.7431	−1.02772
$955$	0	0
$956$	38.7154	1.25215
$957$	0.843651	0.0272713
$958$	−52.6416	−1.70077
$959$	30.3857	0.981206
$960$	0	0
$961$	−5.32763	−0.171859
$962$	35.6265	1.14865
$963$	1.46718	0.0472793
$964$	−19.5104	−0.628389
$965$	0	0
$966$	13.7538	0.442523
$967$	42.2128	1.35747	0.678736	−	0.734382i	$-0.262528\pi$
$967$	42.2128	1.35747	0.678736	+	0.734382i	$0.262528\pi$
$968$	−50.3311	−1.61770
$969$	0	0
$970$	0	0
$971$	10.0408	0.322224	0.161112	−	0.986936i	$-0.448492\pi$
$971$	10.0408	0.322224	0.161112	+	0.986936i	$0.448492\pi$
$972$	−61.0483	−1.95813
$973$	28.6787	0.919398
$974$	−16.6202	−0.532546
$975$	0	0
$976$	16.1063	0.515549
$977$	−47.5795	−1.52220	−0.761102	−	0.648632i	$-0.775341\pi$
$977$	−47.5795	−1.52220	−0.761102	+	0.648632i	$0.775341\pi$
$978$	45.3592	1.45043
$979$	2.81734	0.0900427
$980$	0	0
$981$	6.53207	0.208553
$982$	61.8002	1.97212
$983$	−48.8895	−1.55933	−0.779667	−	0.626194i	$-0.784612\pi$
$983$	−48.8895	−1.55933	−0.779667	+	0.626194i	$0.784612\pi$
$984$	−44.6694	−1.42401
$985$	0	0
$986$	65.8042	2.09563
$987$	−28.4876	−0.906771
$988$	0	0
$989$	2.68116	0.0852561
$990$	0	0
$991$	−7.28600	−0.231447	−0.115724	−	0.993281i	$-0.536919\pi$
$991$	−7.28600	−0.231447	−0.115724	+	0.993281i	$0.536919\pi$
$992$	−5.18934	−0.164762
$993$	−7.58258	−0.240626
$994$	−64.3223	−2.04018
$995$	0	0
$996$	39.2636	1.24411
$997$	20.4024	0.646151	0.323075	−	0.946373i	$-0.395283\pi$
$997$	20.4024	0.646151	0.323075	+	0.946373i	$0.395283\pi$
$998$	−106.218	−3.36227
$999$	21.7169	0.687094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cv.1.35		40
5.2	odd	4		1805.2.b.m.1084.36	yes	40
5.3	odd	4		1805.2.b.m.1084.5	✓	40
5.4	even	2	inner	9025.2.a.cv.1.6		40
19.18	odd	2	inner	9025.2.a.cv.1.5		40
95.18	even	4		1805.2.b.m.1084.35	yes	40
95.37	even	4		1805.2.b.m.1084.6	yes	40
95.94	odd	2	inner	9025.2.a.cv.1.36		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.5	✓	40	5.3	odd	4
1805.2.b.m.1084.6	yes	40	95.37	even	4
1805.2.b.m.1084.35	yes	40	95.18	even	4
1805.2.b.m.1084.36	yes	40	5.2	odd	4
9025.2.a.cv.1.5		40	19.18	odd	2	inner
9025.2.a.cv.1.6		40	5.4	even	2	inner
9025.2.a.cv.1.35		40	1.1	even	1	trivial
9025.2.a.cv.1.36		40	95.94	odd	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.42726 q^{2} -1.05699 q^{3} +3.89157 q^{4} -2.56557 q^{6} -4.52506 q^{7} +4.59133 q^{8} -1.88278 q^{9} +O(q^{10})\)	\(q+2.42726 q^{2} -1.05699 q^{3} +3.89157 q^{4} -2.56557 q^{6} -4.52506 q^{7} +4.59133 q^{8} -1.88278 q^{9} +0.194403 q^{11} -4.11334 q^{12} +3.48815 q^{13} -10.9835 q^{14} +3.36119 q^{16} -6.60308 q^{17} -4.56999 q^{18} +4.78292 q^{21} +0.471865 q^{22} +1.18472 q^{23} -4.85297 q^{24} +8.46664 q^{26} +5.16103 q^{27} -17.6096 q^{28} -4.10574 q^{29} +5.06679 q^{31} -1.02419 q^{32} -0.205481 q^{33} -16.0274 q^{34} -7.32698 q^{36} +4.20787 q^{37} -3.68693 q^{39} +9.20454 q^{41} +11.6094 q^{42} +2.26312 q^{43} +0.756532 q^{44} +2.87562 q^{46} -5.95612 q^{47} -3.55273 q^{48} +13.4761 q^{49} +6.97936 q^{51} +13.5744 q^{52} +6.94598 q^{53} +12.5271 q^{54} -20.7760 q^{56} -9.96568 q^{58} +2.39041 q^{59} +4.79183 q^{61} +12.2984 q^{62} +8.51970 q^{63} -9.20835 q^{64} -0.498754 q^{66} +5.22583 q^{67} -25.6964 q^{68} -1.25223 q^{69} +5.85628 q^{71} -8.64448 q^{72} +6.54790 q^{73} +10.2136 q^{74} -0.879683 q^{77} -8.94912 q^{78} +5.47834 q^{79} +0.193213 q^{81} +22.3418 q^{82} -9.54544 q^{83} +18.6131 q^{84} +5.49318 q^{86} +4.33971 q^{87} +0.892567 q^{88} +14.4923 q^{89} -15.7841 q^{91} +4.61042 q^{92} -5.35552 q^{93} -14.4570 q^{94} +1.08255 q^{96} -7.41146 q^{97} +32.7101 q^{98} -0.366018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * q^99

Introduction

L-functions

Modular forms

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Database

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