LMFDB - Embedded newform 10000.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10000,2,Mod(1,10000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10000, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("10000.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 10000 = 2^{4} \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	10000.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:	$79.8504020213$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.18625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 14x^{2} + 9x + 41 $ x^4 - x^3 - 14x^2 + 9x + 41
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1250)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.46831$ of defining polynomial
Character	$\chi$	$=$	10000.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.08634 q^{3} -4.14353 q^{7} +6.52550 q^{9} +O(q^{10})$	$q-3.08634 q^{3} -4.14353 q^{7} +6.52550 q^{9} +3.61184 q^{11} -2.37577 q^{13} +1.75774 q^{17} -1.28943 q^{19} +12.7883 q^{21} -2.23224 q^{23} -10.8809 q^{27} -1.43916 q^{29} -7.79691 q^{31} -11.1474 q^{33} -0.143531 q^{37} +7.33243 q^{39} +4.08634 q^{41} +11.7907 q^{43} +3.61184 q^{47} +10.1689 q^{49} -5.42497 q^{51} -9.61184 q^{53} +3.97962 q^{57} -6.47450 q^{59} +3.13970 q^{61} -27.0386 q^{63} -13.5585 q^{67} +6.88945 q^{69} +15.4559 q^{71} -5.78689 q^{73} -14.9658 q^{77} -8.19070 q^{79} +14.0056 q^{81} +10.5013 q^{83} +4.44173 q^{87} -5.64718 q^{89} +9.84408 q^{91} +24.0639 q^{93} -5.88325 q^{97} +23.5690 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 3 q^{7} + 17 q^{9}+O(q^{10}) $ 4 * q + q^3 - 3 * q^7 + 17 * q^9	$ 4 q + q^{3} - 3 q^{7} + 17 q^{9} - 8 q^{11} + 4 q^{13} - 2 q^{17} - 5 q^{19} - 7 q^{21} - 9 q^{23} + 10 q^{27} - 10 q^{29} - 18 q^{31} - 22 q^{33} + 13 q^{37} + 16 q^{39} + 3 q^{41} + 16 q^{43} - 8 q^{47} + 23 q^{49} - 13 q^{51} - 16 q^{53} - 15 q^{57} - 35 q^{59} + 8 q^{61} - 54 q^{63} - 23 q^{67} + 19 q^{69} + 17 q^{71} - q^{73} - 29 q^{77} - 10 q^{79} + 24 q^{81} + 11 q^{83} - 40 q^{87} - 5 q^{89} + 17 q^{91} + 38 q^{93} + 3 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + q^3 - 3 * q^7 + 17 * q^9 - 8 * q^11 + 4 * q^13 - 2 * q^17 - 5 * q^19 - 7 * q^21 - 9 * q^23 + 10 * q^27 - 10 * q^29 - 18 * q^31 - 22 * q^33 + 13 * q^37 + 16 * q^39 + 3 * q^41 + 16 * q^43 - 8 * q^47 + 23 * q^49 - 13 * q^51 - 16 * q^53 - 15 * q^57 - 35 * q^59 + 8 * q^61 - 54 * q^63 - 23 * q^67 + 19 * q^69 + 17 * q^71 - q^73 - 29 * q^77 - 10 * q^79 + 24 * q^81 + 11 * q^83 - 40 * q^87 - 5 * q^89 + 17 * q^91 + 38 * q^93 + 3 * q^97 - 4 * 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 $

$2$	0	0
$2$	0	0
$3$	−3.08634	−1.78190	−0.890950	−	0.454102i	$-0.849960\pi$
$3$	−3.08634	−1.78190	−0.890950	+	0.454102i	$0.849960\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−4.14353	−1.56611	−0.783054	−	0.621954i	$-0.786339\pi$
$7$	−4.14353	−1.56611	−0.783054	+	0.621954i	$0.786339\pi$
$8$	0	0
$9$	6.52550	2.17517
$10$	0	0
$11$	3.61184	1.08901	0.544505	−	0.838758i	$-0.316718\pi$
$11$	3.61184	1.08901	0.544505	+	0.838758i	$0.316718\pi$
$12$	0	0
$13$	−2.37577	−0.658920	−0.329460	−	0.944170i	$-0.606867\pi$
$13$	−2.37577	−0.658920	−0.329460	+	0.944170i	$0.606867\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1.75774	0.426314	0.213157	−	0.977018i	$-0.431625\pi$
$17$	1.75774	0.426314	0.213157	+	0.977018i	$0.431625\pi$
$18$	0	0
$19$	−1.28943	−0.295815	−0.147908	−	0.989001i	$-0.547254\pi$
$19$	−1.28943	−0.295815	−0.147908	+	0.989001i	$0.547254\pi$
$20$	0	0
$21$	12.7883	2.79065
$22$	0	0
$23$	−2.23224	−0.465454	−0.232727	−	0.972542i	$-0.574765\pi$
$23$	−2.23224	−0.465454	−0.232727	+	0.972542i	$0.574765\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−10.8809	−2.09403
$28$	0	0
$29$	−1.43916	−0.267245	−0.133622	−	0.991032i	$-0.542661\pi$
$29$	−1.43916	−0.267245	−0.133622	+	0.991032i	$0.542661\pi$
$30$	0	0
$31$	−7.79691	−1.40037	−0.700183	−	0.713963i	$-0.746898\pi$
$31$	−7.79691	−1.40037	−0.700183	+	0.713963i	$0.746898\pi$
$32$	0	0
$33$	−11.1474	−1.94051
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−0.143531	−0.0235964	−0.0117982	−	0.999930i	$-0.503756\pi$
$37$	−0.143531	−0.0235964	−0.0117982	+	0.999930i	$0.503756\pi$
$38$	0	0
$39$	7.33243	1.17413
$40$	0	0
$41$	4.08634	0.638179	0.319090	−	0.947725i	$-0.396623\pi$
$41$	4.08634	0.638179	0.319090	+	0.947725i	$0.396623\pi$
$42$	0	0
$43$	11.7907	1.79807	0.899034	−	0.437880i	$-0.144270\pi$
$43$	11.7907	1.79807	0.899034	+	0.437880i	$0.144270\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	3.61184	0.526841	0.263420	−	0.964681i	$-0.415149\pi$
$47$	3.61184	0.526841	0.263420	+	0.964681i	$0.415149\pi$
$48$	0	0
$49$	10.1689	1.45269
$50$	0	0
$51$	−5.42497	−0.759648
$52$	0	0
$53$	−9.61184	−1.32029	−0.660144	−	0.751139i	$-0.729505\pi$
$53$	−9.61184	−1.32029	−0.660144	+	0.751139i	$0.729505\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	3.97962	0.527113
$58$	0	0
$59$	−6.47450	−0.842908	−0.421454	−	0.906850i	$-0.638480\pi$
$59$	−6.47450	−0.842908	−0.421454	+	0.906850i	$0.638480\pi$
$60$	0	0
$61$	3.13970	0.401998	0.200999	−	0.979591i	$-0.435581\pi$
$61$	3.13970	0.401998	0.200999	+	0.979591i	$0.435581\pi$
$62$	0	0
$63$	−27.0386	−3.40654
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−13.5585	−1.65643	−0.828216	−	0.560409i	$-0.810644\pi$
$67$	−13.5585	−1.65643	−0.828216	+	0.560409i	$0.810644\pi$
$68$	0	0
$69$	6.88945	0.829392
$70$	0	0
$71$	15.4559	1.83428	0.917140	−	0.398566i	$-0.130492\pi$
$71$	15.4559	1.83428	0.917140	+	0.398566i	$0.130492\pi$
$72$	0	0
$73$	−5.78689	−0.677304	−0.338652	−	0.940912i	$-0.609971\pi$
$73$	−5.78689	−0.677304	−0.338652	+	0.940912i	$0.609971\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−14.9658	−1.70551
$78$	0	0
$79$	−8.19070	−0.921525	−0.460763	−	0.887523i	$-0.652424\pi$
$79$	−8.19070	−0.921525	−0.460763	+	0.887523i	$0.652424\pi$
$80$	0	0
$81$	14.0056	1.55618
$82$	0	0
$83$	10.5013	1.15267	0.576333	−	0.817215i	$-0.304483\pi$
$83$	10.5013	1.15267	0.576333	+	0.817215i	$0.304483\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	4.44173	0.476203
$88$	0	0
$89$	−5.64718	−0.598600	−0.299300	−	0.954159i	$-0.596753\pi$
$89$	−5.64718	−0.598600	−0.299300	+	0.954159i	$0.596753\pi$
$90$	0	0
$91$	9.84408	1.03194
$92$	0	0
$93$	24.0639	2.49531
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−5.88325	−0.597354	−0.298677	−	0.954354i	$-0.596545\pi$
$97$	−5.88325	−0.597354	−0.298677	+	0.954354i	$0.596545\pi$
$98$	0	0
$99$	23.5690	2.36878
$100$	0	0
$101$	5.14736	0.512182	0.256091	−	0.966653i	$-0.417565\pi$
$101$	5.14736	0.512182	0.256091	+	0.966653i	$0.417565\pi$
$102$	0	0
$103$	8.25665	0.813552	0.406776	−	0.913528i	$-0.366653\pi$
$103$	8.25665	0.813552	0.406776	+	0.913528i	$0.366653\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	17.4064	1.68274	0.841369	−	0.540461i	$-0.181750\pi$
$107$	17.4064	1.68274	0.841369	+	0.540461i	$0.181750\pi$
$108$	0	0
$109$	5.49746	0.526561	0.263280	−	0.964719i	$-0.415196\pi$
$109$	5.49746	0.526561	0.263280	+	0.964719i	$0.415196\pi$
$110$	0	0
$111$	0.442986	0.0420464
$112$	0	0
$113$	6.51131	0.612533	0.306266	−	0.951946i	$-0.400920\pi$
$113$	6.51131	0.612533	0.306266	+	0.951946i	$0.400920\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−15.5031	−1.43326
$118$	0	0
$119$	−7.28323	−0.667653
$120$	0	0
$121$	2.04537	0.185943
$122$	0	0
$123$	−12.6118	−1.13717
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−2.91986	−0.259095	−0.129548	−	0.991573i	$-0.541353\pi$
$127$	−2.91986	−0.259095	−0.129548	+	0.991573i	$0.541353\pi$
$128$	0	0
$129$	−36.3902	−3.20397
$130$	0	0
$131$	7.48013	0.653542	0.326771	−	0.945104i	$-0.394039\pi$
$131$	7.48013	0.653542	0.326771	+	0.945104i	$0.394039\pi$
$132$	0	0
$133$	5.34279	0.463279
$134$	0	0
$135$	0	0
$136$	0	0
$137$	17.8809	1.52767	0.763834	−	0.645413i	$-0.223315\pi$
$137$	17.8809	1.52767	0.763834	+	0.645413i	$0.223315\pi$
$138$	0	0
$139$	4.36574	0.370298	0.185149	−	0.982711i	$-0.440723\pi$
$139$	4.36574	0.370298	0.185149	+	0.982711i	$0.440723\pi$
$140$	0	0
$141$	−11.1474	−0.938777
$142$	0	0
$143$	−8.58089	−0.717570
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−31.3845	−2.58855
$148$	0	0
$149$	13.0678	1.07055	0.535276	−	0.844677i	$-0.320208\pi$
$149$	13.0678	1.07055	0.535276	+	0.844677i	$0.320208\pi$
$150$	0	0
$151$	−0.811097	−0.0660061	−0.0330031	−	0.999455i	$-0.510507\pi$
$151$	−0.811097	−0.0660061	−0.0330031	+	0.999455i	$0.510507\pi$
$152$	0	0
$153$	11.4701	0.927303
$154$	0	0
$155$	0	0
$156$	0	0
$157$	11.3796	0.908191	0.454095	−	0.890953i	$-0.349963\pi$
$157$	11.3796	0.908191	0.454095	+	0.890953i	$0.349963\pi$
$158$	0	0
$159$	29.6654	2.35262
$160$	0	0
$161$	9.24935	0.728951
$162$	0	0
$163$	6.63605	0.519776	0.259888	−	0.965639i	$-0.416314\pi$
$163$	6.63605	0.519776	0.259888	+	0.965639i	$0.416314\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	8.26905	0.639878	0.319939	−	0.947438i	$-0.396338\pi$
$167$	8.26905	0.639878	0.319939	+	0.947438i	$0.396338\pi$
$168$	0	0
$169$	−7.35572	−0.565824
$170$	0	0
$171$	−8.41417	−0.643447
$172$	0	0
$173$	−12.4902	−0.949609	−0.474804	−	0.880091i	$-0.657481\pi$
$173$	−12.4902	−0.949609	−0.474804	+	0.880091i	$0.657481\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	19.9825	1.50198
$178$	0	0
$179$	−18.7860	−1.40413	−0.702065	−	0.712113i	$-0.747738\pi$
$179$	−18.7860	−1.40413	−0.702065	+	0.712113i	$0.747738\pi$
$180$	0	0
$181$	−9.74298	−0.724190	−0.362095	−	0.932141i	$-0.617938\pi$
$181$	−9.74298	−0.724190	−0.362095	+	0.932141i	$0.617938\pi$
$182$	0	0
$183$	−9.69019	−0.716319
$184$	0	0
$185$	0	0
$186$	0	0
$187$	6.34866	0.464260
$188$	0	0
$189$	45.0853	3.27947
$190$	0	0
$191$	0.399296	0.0288921	0.0144460	−	0.999896i	$-0.495402\pi$
$191$	0.399296	0.0288921	0.0144460	+	0.999896i	$0.495402\pi$
$192$	0	0
$193$	−8.13733	−0.585738	−0.292869	−	0.956153i	$-0.594610\pi$
$193$	−8.13733	−0.585738	−0.292869	+	0.956153i	$0.594610\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	18.0819	1.28828	0.644142	−	0.764906i	$-0.277214\pi$
$197$	18.0819	1.28828	0.644142	+	0.764906i	$0.277214\pi$
$198$	0	0
$199$	−19.4940	−1.38189	−0.690946	−	0.722907i	$-0.742806\pi$
$199$	−19.4940	−1.38189	−0.690946	+	0.722907i	$0.742806\pi$
$200$	0	0
$201$	41.8461	2.95159
$202$	0	0
$203$	5.96319	0.418534
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−14.5665	−1.01244
$208$	0	0
$209$	−4.65721	−0.322146
$210$	0	0
$211$	27.5829	1.89888	0.949442	−	0.313942i	$-0.101650\pi$
$211$	27.5829	1.89888	0.949442	+	0.313942i	$0.101650\pi$
$212$	0	0
$213$	−47.7022	−3.26850
$214$	0	0
$215$	0	0
$216$	0	0
$217$	32.3067	2.19312
$218$	0	0
$219$	17.8603	1.20689
$220$	0	0
$221$	−4.17598	−0.280907
$222$	0	0
$223$	−24.8647	−1.66506	−0.832530	−	0.553979i	$-0.813109\pi$
$223$	−24.8647	−1.66506	−0.832530	+	0.553979i	$0.813109\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	23.2251	1.54151	0.770753	−	0.637134i	$-0.219880\pi$
$227$	23.2251	1.54151	0.770753	+	0.637134i	$0.219880\pi$
$228$	0	0
$229$	−4.69198	−0.310055	−0.155027	−	0.987910i	$-0.549547\pi$
$229$	−4.69198	−0.310055	−0.155027	+	0.987910i	$0.549547\pi$
$230$	0	0
$231$	46.1894	3.03904
$232$	0	0
$233$	22.4574	1.47123	0.735616	−	0.677399i	$-0.236893\pi$
$233$	22.4574	1.47123	0.735616	+	0.677399i	$0.236893\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	25.2793	1.64207
$238$	0	0
$239$	23.6882	1.53226	0.766130	−	0.642686i	$-0.222180\pi$
$239$	23.6882	1.53226	0.766130	+	0.642686i	$0.222180\pi$
$240$	0	0
$241$	15.2694	0.983587	0.491794	−	0.870712i	$-0.336341\pi$
$241$	15.2694	0.983587	0.491794	+	0.870712i	$0.336341\pi$
$242$	0	0
$243$	−10.5835	−0.678930
$244$	0	0
$245$	0	0
$246$	0	0
$247$	3.06339	0.194919
$248$	0	0
$249$	−32.4105	−2.05393
$250$	0	0
$251$	12.1373	0.766102	0.383051	−	0.923727i	$-0.374873\pi$
$251$	12.1373	0.766102	0.383051	+	0.923727i	$0.374873\pi$
$252$	0	0
$253$	−8.06248	−0.506884
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0.256450	0.0159969	0.00799846	−	0.999968i	$-0.497454\pi$
$257$	0.256450	0.0159969	0.00799846	+	0.999968i	$0.497454\pi$
$258$	0	0
$259$	0.594726	0.0369545
$260$	0	0
$261$	−9.39121	−0.581302
$262$	0	0
$263$	0.430594	0.0265516	0.0132758	−	0.999912i	$-0.495774\pi$
$263$	0.430594	0.0265516	0.0132758	+	0.999912i	$0.495774\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	17.4291	1.06665
$268$	0	0
$269$	−28.4785	−1.73637	−0.868184	−	0.496243i	$-0.834712\pi$
$269$	−28.4785	−1.73637	−0.868184	+	0.496243i	$0.834712\pi$
$270$	0	0
$271$	−22.7044	−1.37919	−0.689596	−	0.724194i	$-0.742212\pi$
$271$	−22.7044	−1.37919	−0.689596	+	0.724194i	$0.742212\pi$
$272$	0	0
$273$	−30.3822	−1.83881
$274$	0	0
$275$	0	0
$276$	0	0
$277$	1.27413	0.0765554	0.0382777	−	0.999267i	$-0.487813\pi$
$277$	1.27413	0.0765554	0.0382777	+	0.999267i	$0.487813\pi$
$278$	0	0
$279$	−50.8787	−3.04603
$280$	0	0
$281$	9.62749	0.574328	0.287164	−	0.957881i	$-0.407288\pi$
$281$	9.62749	0.574328	0.287164	+	0.957881i	$0.407288\pi$
$282$	0	0
$283$	11.0778	0.658506	0.329253	−	0.944242i	$-0.393203\pi$
$283$	11.0778	0.658506	0.329253	+	0.944242i	$0.393203\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−16.9319	−0.999457
$288$	0	0
$289$	−13.9104	−0.818257
$290$	0	0
$291$	18.1577	1.06442
$292$	0	0
$293$	−2.42497	−0.141668	−0.0708342	−	0.997488i	$-0.522566\pi$
$293$	−2.42497	−0.141668	−0.0708342	+	0.997488i	$0.522566\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−39.3000	−2.28042
$298$	0	0
$299$	5.30328	0.306697
$300$	0	0
$301$	−48.8552	−2.81597
$302$	0	0
$303$	−15.8865	−0.912656
$304$	0	0
$305$	0	0
$306$	0	0
$307$	24.8927	1.42070	0.710351	−	0.703848i	$-0.248536\pi$
$307$	24.8927	1.42070	0.710351	+	0.703848i	$0.248536\pi$
$308$	0	0
$309$	−25.4828	−1.44967
$310$	0	0
$311$	0.600349	0.0340427	0.0170213	−	0.999855i	$-0.494582\pi$
$311$	0.600349	0.0340427	0.0170213	+	0.999855i	$0.494582\pi$
$312$	0	0
$313$	−16.4783	−0.931410	−0.465705	−	0.884940i	$-0.654199\pi$
$313$	−16.4783	−0.931410	−0.465705	+	0.884940i	$0.654199\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−10.2579	−0.576142	−0.288071	−	0.957609i	$-0.593014\pi$
$317$	−10.2579	−0.576142	−0.288071	+	0.957609i	$0.593014\pi$
$318$	0	0
$319$	−5.19800	−0.291032
$320$	0	0
$321$	−53.7220	−2.99847
$322$	0	0
$323$	−2.26648	−0.126110
$324$	0	0
$325$	0	0
$326$	0	0
$327$	−16.9670	−0.938278
$328$	0	0
$329$	−14.9658	−0.825089
$330$	0	0
$331$	−24.7736	−1.36168	−0.680840	−	0.732432i	$-0.738385\pi$
$331$	−24.7736	−1.36168	−0.680840	+	0.732432i	$0.738385\pi$
$332$	0	0
$333$	−0.936613	−0.0513261
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−27.2428	−1.48401	−0.742005	−	0.670394i	$-0.766125\pi$
$337$	−27.2428	−1.48401	−0.742005	+	0.670394i	$0.766125\pi$
$338$	0	0
$339$	−20.0961	−1.09147
$340$	0	0
$341$	−28.1612	−1.52501
$342$	0	0
$343$	−13.1302	−0.708966
$344$	0	0
$345$	0	0
$346$	0	0
$347$	3.16266	0.169780	0.0848901	−	0.996390i	$-0.472946\pi$
$347$	3.16266	0.169780	0.0848901	+	0.996390i	$0.472946\pi$
$348$	0	0
$349$	5.15772	0.276086	0.138043	−	0.990426i	$-0.455919\pi$
$349$	5.15772	0.276086	0.138043	+	0.990426i	$0.455919\pi$
$350$	0	0
$351$	25.8505	1.37980
$352$	0	0
$353$	−29.9104	−1.59197	−0.795984	−	0.605318i	$-0.793046\pi$
$353$	−29.9104	−1.59197	−0.795984	+	0.605318i	$0.793046\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	22.4785	1.18969
$358$	0	0
$359$	−19.9204	−1.05136	−0.525679	−	0.850683i	$-0.676189\pi$
$359$	−19.9204	−1.05136	−0.525679	+	0.850683i	$0.676189\pi$
$360$	0	0
$361$	−17.3374	−0.912493
$362$	0	0
$363$	−6.31271	−0.331332
$364$	0	0
$365$	0	0
$366$	0	0
$367$	5.13497	0.268043	0.134022	−	0.990978i	$-0.457211\pi$
$367$	5.13497	0.268043	0.134022	+	0.990978i	$0.457211\pi$
$368$	0	0
$369$	26.6654	1.38815
$370$	0	0
$371$	39.8270	2.06771
$372$	0	0
$373$	−7.69707	−0.398539	−0.199270	−	0.979945i	$-0.563857\pi$
$373$	−7.69707	−0.398539	−0.199270	+	0.979945i	$0.563857\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	3.41911	0.176093
$378$	0	0
$379$	−15.1583	−0.778629	−0.389315	−	0.921105i	$-0.627288\pi$
$379$	−15.1583	−0.778629	−0.389315	+	0.921105i	$0.627288\pi$
$380$	0	0
$381$	9.01167	0.461682
$382$	0	0
$383$	−21.7450	−1.11112	−0.555559	−	0.831477i	$-0.687496\pi$
$383$	−21.7450	−1.11112	−0.555559	+	0.831477i	$0.687496\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	76.9403	3.91109
$388$	0	0
$389$	20.8188	1.05555	0.527776	−	0.849383i	$-0.323026\pi$
$389$	20.8188	1.05555	0.527776	+	0.849383i	$0.323026\pi$
$390$	0	0
$391$	−3.92369	−0.198429
$392$	0	0
$393$	−23.0862	−1.16455
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−33.6958	−1.69114	−0.845572	−	0.533861i	$-0.820740\pi$
$397$	−33.6958	−1.69114	−0.845572	+	0.533861i	$0.820740\pi$
$398$	0	0
$399$	−16.4897	−0.825516
$400$	0	0
$401$	9.90510	0.494637	0.247318	−	0.968934i	$-0.420451\pi$
$401$	9.90510	0.494637	0.247318	+	0.968934i	$0.420451\pi$
$402$	0	0
$403$	18.5237	0.922730
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−0.518412	−0.0256967
$408$	0	0
$409$	−1.86557	−0.0922463	−0.0461232	−	0.998936i	$-0.514687\pi$
$409$	−1.86557	−0.0922463	−0.0461232	+	0.998936i	$0.514687\pi$
$410$	0	0
$411$	−55.1865	−2.72215
$412$	0	0
$413$	26.8273	1.32009
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−13.4742	−0.659833
$418$	0	0
$419$	20.0920	0.981557	0.490778	−	0.871284i	$-0.336712\pi$
$419$	20.0920	0.981557	0.490778	+	0.871284i	$0.336712\pi$
$420$	0	0
$421$	27.5107	1.34079	0.670396	−	0.742004i	$-0.266124\pi$
$421$	27.5107	1.34079	0.670396	+	0.742004i	$0.266124\pi$
$422$	0	0
$423$	23.5690	1.14597
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−13.0095	−0.629572
$428$	0	0
$429$	26.4836	1.27864
$430$	0	0
$431$	−9.66248	−0.465425	−0.232713	−	0.972546i	$-0.574760\pi$
$431$	−9.66248	−0.465425	−0.232713	+	0.972546i	$0.574760\pi$
$432$	0	0
$433$	−18.3849	−0.883522	−0.441761	−	0.897133i	$-0.645646\pi$
$433$	−18.3849	−0.883522	−0.441761	+	0.897133i	$0.645646\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	2.87831	0.137688
$438$	0	0
$439$	−36.0836	−1.72218	−0.861088	−	0.508456i	$-0.830217\pi$
$439$	−36.0836	−1.72218	−0.861088	+	0.508456i	$0.830217\pi$
$440$	0	0
$441$	66.3568	3.15985
$442$	0	0
$443$	−6.50580	−0.309100	−0.154550	−	0.987985i	$-0.549393\pi$
$443$	−6.50580	−0.309100	−0.154550	+	0.987985i	$0.549393\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−40.3315	−1.90762
$448$	0	0
$449$	−13.0495	−0.615845	−0.307923	−	0.951411i	$-0.599634\pi$
$449$	−13.0495	−0.615845	−0.307923	+	0.951411i	$0.599634\pi$
$450$	0	0
$451$	14.7592	0.694984
$452$	0	0
$453$	2.50332	0.117616
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−9.75953	−0.456532	−0.228266	−	0.973599i	$-0.573306\pi$
$457$	−9.75953	−0.456532	−0.228266	+	0.973599i	$0.573306\pi$
$458$	0	0
$459$	−19.1257	−0.892712
$460$	0	0
$461$	31.5039	1.46728	0.733640	−	0.679538i	$-0.237820\pi$
$461$	31.5039	1.46728	0.733640	+	0.679538i	$0.237820\pi$
$462$	0	0
$463$	−10.9075	−0.506913	−0.253456	−	0.967347i	$-0.581567\pi$
$463$	−10.9075	−0.506913	−0.253456	+	0.967347i	$0.581567\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	5.83992	0.270239	0.135120	−	0.990829i	$-0.456858\pi$
$467$	5.83992	0.270239	0.135120	+	0.990829i	$0.456858\pi$
$468$	0	0
$469$	56.1800	2.59415
$470$	0	0
$471$	−35.1213	−1.61830
$472$	0	0
$473$	42.5861	1.95811
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−62.7220	−2.87184
$478$	0	0
$479$	42.6368	1.94812	0.974062	−	0.226280i	$-0.0726564\pi$
$479$	42.6368	1.94812	0.974062	+	0.226280i	$0.0726564\pi$
$480$	0	0
$481$	0.340997	0.0155481
$482$	0	0
$483$	−28.5466	−1.29892
$484$	0	0
$485$	0	0
$486$	0	0
$487$	10.8783	0.492943	0.246472	−	0.969150i	$-0.420729\pi$
$487$	10.8783	0.492943	0.246472	+	0.969150i	$0.420729\pi$
$488$	0	0
$489$	−20.4811	−0.926188
$490$	0	0
$491$	−1.26464	−0.0570726	−0.0285363	−	0.999593i	$-0.509085\pi$
$491$	−1.26464	−0.0570726	−0.0285363	+	0.999593i	$0.509085\pi$
$492$	0	0
$493$	−2.52966	−0.113930
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−64.0421	−2.87268
$498$	0	0
$499$	−29.1995	−1.30715	−0.653574	−	0.756863i	$-0.726731\pi$
$499$	−29.1995	−1.30715	−0.653574	+	0.756863i	$0.726731\pi$
$500$	0	0
$501$	−25.5211	−1.14020
$502$	0	0
$503$	−37.8976	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$503$	−37.8976	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	22.7023	1.00824
$508$	0	0
$509$	16.1615	0.716348	0.358174	−	0.933655i	$-0.383399\pi$
$509$	16.1615	0.716348	0.358174	+	0.933655i	$0.383399\pi$
$510$	0	0
$511$	23.9781	1.06073
$512$	0	0
$513$	14.0301	0.619445
$514$	0	0
$515$	0	0
$516$	0	0
$517$	13.0454	0.573735
$518$	0	0
$519$	38.5489	1.69211
$520$	0	0
$521$	29.9676	1.31290	0.656452	−	0.754368i	$-0.272057\pi$
$521$	29.9676	1.31290	0.656452	+	0.754368i	$0.272057\pi$
$522$	0	0
$523$	0.417312	0.0182478	0.00912389	−	0.999958i	$-0.497096\pi$
$523$	0.417312	0.0182478	0.00912389	+	0.999958i	$0.497096\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−13.7049	−0.596995
$528$	0	0
$529$	−18.0171	−0.783353
$530$	0	0
$531$	−42.2493	−1.83347
$532$	0	0
$533$	−9.70820	−0.420509
$534$	0	0
$535$	0	0
$536$	0	0
$537$	57.9799	2.50202
$538$	0	0
$539$	36.7282	1.58200
$540$	0	0
$541$	−28.1098	−1.20854	−0.604268	−	0.796781i	$-0.706534\pi$
$541$	−28.1098	−1.20854	−0.604268	+	0.796781i	$0.706534\pi$
$542$	0	0
$543$	30.0701	1.29043
$544$	0	0
$545$	0	0
$546$	0	0
$547$	3.71024	0.158638	0.0793192	−	0.996849i	$-0.474725\pi$
$547$	3.71024	0.158638	0.0793192	+	0.996849i	$0.474725\pi$
$548$	0	0
$549$	20.4881	0.874411
$550$	0	0
$551$	1.85569	0.0790551
$552$	0	0
$553$	33.9384	1.44321
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−7.60059	−0.322047	−0.161024	−	0.986951i	$-0.551480\pi$
$557$	−7.60059	−0.322047	−0.161024	+	0.986951i	$0.551480\pi$
$558$	0	0
$559$	−28.0120	−1.18478
$560$	0	0
$561$	−19.5941	−0.827264
$562$	0	0
$563$	25.1708	1.06082	0.530412	−	0.847740i	$-0.322037\pi$
$563$	25.1708	1.06082	0.530412	+	0.847740i	$0.322037\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−58.0327	−2.43715
$568$	0	0
$569$	−15.0182	−0.629597	−0.314798	−	0.949159i	$-0.601937\pi$
$569$	−15.0182	−0.629597	−0.314798	+	0.949159i	$0.601937\pi$
$570$	0	0
$571$	−2.96813	−0.124212	−0.0621062	−	0.998070i	$-0.519782\pi$
$571$	−2.96813	−0.124212	−0.0621062	+	0.998070i	$0.519782\pi$
$572$	0	0
$573$	−1.23236	−0.0514828
$574$	0	0
$575$	0	0
$576$	0	0
$577$	21.1337	0.879808	0.439904	−	0.898045i	$-0.355012\pi$
$577$	21.1337	0.879808	0.439904	+	0.898045i	$0.355012\pi$
$578$	0	0
$579$	25.1146	1.04373
$580$	0	0
$581$	−43.5124	−1.80520
$582$	0	0
$583$	−34.7164	−1.43781
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−31.1696	−1.28651	−0.643254	−	0.765653i	$-0.722416\pi$
$587$	−31.1696	−1.28651	−0.643254	+	0.765653i	$0.722416\pi$
$588$	0	0
$589$	10.0536	0.414250
$590$	0	0
$591$	−55.8070	−2.29559
$592$	0	0
$593$	−19.0213	−0.781110	−0.390555	−	0.920580i	$-0.627717\pi$
$593$	−19.0213	−0.781110	−0.390555	+	0.920580i	$0.627717\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	60.1651	2.46239
$598$	0	0
$599$	23.1384	0.945411	0.472706	−	0.881220i	$-0.343277\pi$
$599$	23.1384	0.945411	0.472706	+	0.881220i	$0.343277\pi$
$600$	0	0
$601$	−19.6077	−0.799814	−0.399907	−	0.916556i	$-0.630958\pi$
$601$	−19.6077	−0.799814	−0.399907	+	0.916556i	$0.630958\pi$
$602$	0	0
$603$	−88.4758	−3.60301
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−15.5656	−0.631787	−0.315893	−	0.948795i	$-0.602304\pi$
$607$	−15.5656	−0.631787	−0.315893	+	0.948795i	$0.602304\pi$
$608$	0	0
$609$	−18.4044	−0.745785
$610$	0	0
$611$	−8.58089	−0.347146
$612$	0	0
$613$	−22.7995	−0.920862	−0.460431	−	0.887695i	$-0.652305\pi$
$613$	−22.7995	−0.920862	−0.460431	+	0.887695i	$0.652305\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	20.7321	0.834641	0.417321	−	0.908759i	$-0.362969\pi$
$617$	20.7321	0.834641	0.417321	+	0.908759i	$0.362969\pi$
$618$	0	0
$619$	−40.5160	−1.62848	−0.814238	−	0.580531i	$-0.802845\pi$
$619$	−40.5160	−1.62848	−0.814238	+	0.580531i	$0.802845\pi$
$620$	0	0
$621$	24.2887	0.974673
$622$	0	0
$623$	23.3993	0.937472
$624$	0	0
$625$	0	0
$626$	0	0
$627$	14.3737	0.574032
$628$	0	0
$629$	−0.252290	−0.0100595
$630$	0	0
$631$	−10.5206	−0.418817	−0.209408	−	0.977828i	$-0.567154\pi$
$631$	−10.5206	−0.418817	−0.209408	+	0.977828i	$0.567154\pi$
$632$	0	0
$633$	−85.1302	−3.38362
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−24.1588	−0.957208
$638$	0	0
$639$	100.858	3.98986
$640$	0	0
$641$	9.84297	0.388774	0.194387	−	0.980925i	$-0.437728\pi$
$641$	9.84297	0.388774	0.194387	+	0.980925i	$0.437728\pi$
$642$	0	0
$643$	5.83971	0.230296	0.115148	−	0.993348i	$-0.463266\pi$
$643$	5.83971	0.230296	0.115148	+	0.993348i	$0.463266\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−33.2862	−1.30861	−0.654307	−	0.756229i	$-0.727040\pi$
$647$	−33.2862	−1.30861	−0.654307	+	0.756229i	$0.727040\pi$
$648$	0	0
$649$	−23.3849	−0.917936
$650$	0	0
$651$	−99.7096	−3.90793
$652$	0	0
$653$	−4.83588	−0.189243	−0.0946213	−	0.995513i	$-0.530164\pi$
$653$	−4.83588	−0.189243	−0.0946213	+	0.995513i	$0.530164\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−37.7623	−1.47325
$658$	0	0
$659$	0.989974	0.0385639	0.0192820	−	0.999814i	$-0.493862\pi$
$659$	0.989974	0.0385639	0.0192820	+	0.999814i	$0.493862\pi$
$660$	0	0
$661$	−3.84611	−0.149596	−0.0747982	−	0.997199i	$-0.523831\pi$
$661$	−3.84611	−0.149596	−0.0747982	+	0.997199i	$0.523831\pi$
$662$	0	0
$663$	12.8885	0.500547
$664$	0	0
$665$	0	0
$666$	0	0
$667$	3.21254	0.124390
$668$	0	0
$669$	76.7408	2.96697
$670$	0	0
$671$	11.3401	0.437779
$672$	0	0
$673$	22.9896	0.886184	0.443092	−	0.896476i	$-0.353881\pi$
$673$	22.9896	0.886184	0.443092	+	0.896476i	$0.353881\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−48.3851	−1.85959	−0.929795	−	0.368077i	$-0.880016\pi$
$677$	−48.3851	−1.85959	−0.929795	+	0.368077i	$0.880016\pi$
$678$	0	0
$679$	24.3774	0.935520
$680$	0	0
$681$	−71.6807	−2.74681
$682$	0	0
$683$	−1.16230	−0.0444742	−0.0222371	−	0.999753i	$-0.507079\pi$
$683$	−1.16230	−0.0444742	−0.0222371	+	0.999753i	$0.507079\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	14.4811	0.552487
$688$	0	0
$689$	22.8355	0.869964
$690$	0	0
$691$	−20.1818	−0.767751	−0.383876	−	0.923385i	$-0.625411\pi$
$691$	−20.1818	−0.767751	−0.383876	+	0.923385i	$0.625411\pi$
$692$	0	0
$693$	−97.6590	−3.70976
$694$	0	0
$695$	0	0
$696$	0	0
$697$	7.18271	0.272064
$698$	0	0
$699$	−69.3111	−2.62159
$700$	0	0
$701$	23.2210	0.877044	0.438522	−	0.898720i	$-0.355502\pi$
$701$	23.2210	0.877044	0.438522	+	0.898720i	$0.355502\pi$
$702$	0	0
$703$	0.185073	0.00698018
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−21.3283	−0.802131
$708$	0	0
$709$	28.8835	1.08474	0.542370	−	0.840139i	$-0.317527\pi$
$709$	28.8835	1.08474	0.542370	+	0.840139i	$0.317527\pi$
$710$	0	0
$711$	−53.4484	−2.00447
$712$	0	0
$713$	17.4046	0.651806
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−73.1097	−2.73033
$718$	0	0
$719$	12.5359	0.467509	0.233755	−	0.972296i	$-0.424899\pi$
$719$	12.5359	0.467509	0.233755	+	0.972296i	$0.424899\pi$
$720$	0	0
$721$	−34.2117	−1.27411
$722$	0	0
$723$	−47.1265	−1.75265
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−45.3556	−1.68215	−0.841073	−	0.540922i	$-0.818075\pi$
$727$	−45.3556	−1.68215	−0.841073	+	0.540922i	$0.818075\pi$
$728$	0	0
$729$	−9.35269	−0.346396
$730$	0	0
$731$	20.7250	0.766540
$732$	0	0
$733$	5.71383	0.211045	0.105523	−	0.994417i	$-0.466348\pi$
$733$	5.71383	0.211045	0.105523	+	0.994417i	$0.466348\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−48.9710	−1.80387
$738$	0	0
$739$	10.5636	0.388587	0.194293	−	0.980943i	$-0.437759\pi$
$739$	10.5636	0.388587	0.194293	+	0.980943i	$0.437759\pi$
$740$	0	0
$741$	−9.45466	−0.347325
$742$	0	0
$743$	−35.5690	−1.30490	−0.652451	−	0.757831i	$-0.726259\pi$
$743$	−35.5690	−1.30490	−0.652451	+	0.757831i	$0.726259\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	68.5261	2.50724
$748$	0	0
$749$	−72.1239	−2.63535
$750$	0	0
$751$	−3.65009	−0.133194	−0.0665968	−	0.997780i	$-0.521214\pi$
$751$	−3.65009	−0.133194	−0.0665968	+	0.997780i	$0.521214\pi$
$752$	0	0
$753$	−37.4599	−1.36512
$754$	0	0
$755$	0	0
$756$	0	0
$757$	34.9362	1.26978	0.634890	−	0.772603i	$-0.281046\pi$
$757$	34.9362	1.26978	0.634890	+	0.772603i	$0.281046\pi$
$758$	0	0
$759$	24.8836	0.903216
$760$	0	0
$761$	−19.2676	−0.698449	−0.349225	−	0.937039i	$-0.613555\pi$
$761$	−19.2676	−0.698449	−0.349225	+	0.937039i	$0.613555\pi$
$762$	0	0
$763$	−22.7789	−0.824651
$764$	0	0
$765$	0	0
$766$	0	0
$767$	15.3819	0.555409
$768$	0	0
$769$	−12.0821	−0.435693	−0.217847	−	0.975983i	$-0.569903\pi$
$769$	−12.0821	−0.435693	−0.217847	+	0.975983i	$0.569903\pi$
$770$	0	0
$771$	−0.791493	−0.0285049
$772$	0	0
$773$	29.1329	1.04784	0.523919	−	0.851768i	$-0.324469\pi$
$773$	29.1329	1.04784	0.523919	+	0.851768i	$0.324469\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−1.83553	−0.0658492
$778$	0	0
$779$	−5.26905	−0.188783
$780$	0	0
$781$	55.8243	1.99755
$782$	0	0
$783$	15.6593	0.559618
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−19.1073	−0.681100	−0.340550	−	0.940226i	$-0.610613\pi$
$787$	−19.1073	−0.681100	−0.340550	+	0.940226i	$0.610613\pi$
$788$	0	0
$789$	−1.32896	−0.0473122
$790$	0	0
$791$	−26.9798	−0.959292
$792$	0	0
$793$	−7.45921	−0.264884
$794$	0	0
$795$	0	0
$796$	0	0
$797$	35.0417	1.24124	0.620620	−	0.784111i	$-0.286881\pi$
$797$	35.0417	1.24124	0.620620	+	0.784111i	$0.286881\pi$
$798$	0	0
$799$	6.34866	0.224599
$800$	0	0
$801$	−36.8507	−1.30205
$802$	0	0
$803$	−20.9013	−0.737591
$804$	0	0
$805$	0	0
$806$	0	0
$807$	87.8945	3.09403
$808$	0	0
$809$	−32.4768	−1.14182	−0.570912	−	0.821011i	$-0.693410\pi$
$809$	−32.4768	−1.14182	−0.570912	+	0.821011i	$0.693410\pi$
$810$	0	0
$811$	−4.69782	−0.164963	−0.0824815	−	0.996593i	$-0.526285\pi$
$811$	−4.69782	−0.164963	−0.0824815	+	0.996593i	$0.526285\pi$
$812$	0	0
$813$	70.0734	2.45758
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−15.2033	−0.531896
$818$	0	0
$819$	64.2375	2.24464
$820$	0	0
$821$	35.6203	1.24316	0.621578	−	0.783352i	$-0.286492\pi$
$821$	35.6203	1.24316	0.621578	+	0.783352i	$0.286492\pi$
$822$	0	0
$823$	53.9927	1.88207	0.941034	−	0.338311i	$-0.109855\pi$
$823$	53.9927	1.88207	0.941034	+	0.338311i	$0.109855\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−10.5259	−0.366020	−0.183010	−	0.983111i	$-0.558584\pi$
$827$	−10.5259	−0.366020	−0.183010	+	0.983111i	$0.558584\pi$
$828$	0	0
$829$	7.41293	0.257462	0.128731	−	0.991680i	$-0.458910\pi$
$829$	7.41293	0.257462	0.128731	+	0.991680i	$0.458910\pi$
$830$	0	0
$831$	−3.93241	−0.136414
$832$	0	0
$833$	17.8742	0.619303
$834$	0	0
$835$	0	0
$836$	0	0
$837$	84.8373	2.93241
$838$	0	0
$839$	−52.0335	−1.79640	−0.898198	−	0.439591i	$-0.855124\pi$
$839$	−52.0335	−1.79640	−0.898198	+	0.439591i	$0.855124\pi$
$840$	0	0
$841$	−26.9288	−0.928580
$842$	0	0
$843$	−29.7137	−1.02339
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−8.47506	−0.291207
$848$	0	0
$849$	−34.1898	−1.17339
$850$	0	0
$851$	0.320396	0.0109830
$852$	0	0
$853$	12.1920	0.417445	0.208722	−	0.977975i	$-0.433070\pi$
$853$	12.1920	0.417445	0.208722	+	0.977975i	$0.433070\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	45.4882	1.55385	0.776924	−	0.629595i	$-0.216779\pi$
$857$	45.4882	1.55385	0.776924	+	0.629595i	$0.216779\pi$
$858$	0	0
$859$	−8.89965	−0.303652	−0.151826	−	0.988407i	$-0.548515\pi$
$859$	−8.89965	−0.303652	−0.151826	+	0.988407i	$0.548515\pi$
$860$	0	0
$861$	52.2575	1.78093
$862$	0	0
$863$	−37.3335	−1.27085	−0.635424	−	0.772164i	$-0.719175\pi$
$863$	−37.3335	−1.27085	−0.635424	+	0.772164i	$0.719175\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	42.9321	1.45805
$868$	0	0
$869$	−29.5835	−1.00355
$870$	0	0
$871$	32.2118	1.09146
$872$	0	0
$873$	−38.3911	−1.29934
$874$	0	0
$875$	0	0
$876$	0	0
$877$	15.1529	0.511676	0.255838	−	0.966720i	$-0.417649\pi$
$877$	15.1529	0.511676	0.255838	+	0.966720i	$0.417649\pi$
$878$	0	0
$879$	7.48429	0.252439
$880$	0	0
$881$	−1.72350	−0.0580661	−0.0290331	−	0.999578i	$-0.509243\pi$
$881$	−1.72350	−0.0580661	−0.0290331	+	0.999578i	$0.509243\pi$
$882$	0	0
$883$	−12.4980	−0.420592	−0.210296	−	0.977638i	$-0.567443\pi$
$883$	−12.4980	−0.420592	−0.210296	+	0.977638i	$0.567443\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−8.78195	−0.294869	−0.147434	−	0.989072i	$-0.547102\pi$
$887$	−8.78195	−0.294869	−0.147434	+	0.989072i	$0.547102\pi$
$888$	0	0
$889$	12.0985	0.405771
$890$	0	0
$891$	50.5860	1.69470
$892$	0	0
$893$	−4.65721	−0.155848
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−16.3677	−0.546503
$898$	0	0
$899$	11.2210	0.374241
$900$	0	0
$901$	−16.8951	−0.562856
$902$	0	0
$903$	150.784	5.01777
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−19.6142	−0.651279	−0.325639	−	0.945494i	$-0.605580\pi$
$907$	−19.6142	−0.651279	−0.325639	+	0.945494i	$0.605580\pi$
$908$	0	0
$909$	33.5891	1.11408
$910$	0	0
$911$	−31.2884	−1.03663	−0.518315	−	0.855190i	$-0.673441\pi$
$911$	−31.2884	−1.03663	−0.518315	+	0.855190i	$0.673441\pi$
$912$	0	0
$913$	37.9289	1.25526
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−30.9941	−1.02352
$918$	0	0
$919$	33.4235	1.10254	0.551269	−	0.834327i	$-0.314144\pi$
$919$	33.4235	1.10254	0.551269	+	0.834327i	$0.314144\pi$
$920$	0	0
$921$	−76.8274	−2.53155
$922$	0	0
$923$	−36.7197	−1.20864
$924$	0	0
$925$	0	0
$926$	0	0
$927$	53.8788	1.76961
$928$	0	0
$929$	11.0696	0.363181	0.181591	−	0.983374i	$-0.441875\pi$
$929$	11.0696	0.363181	0.181591	+	0.983374i	$0.441875\pi$
$930$	0	0
$931$	−13.1120	−0.429729
$932$	0	0
$933$	−1.85288	−0.0606606
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−32.2151	−1.05242	−0.526211	−	0.850354i	$-0.676388\pi$
$937$	−32.2151	−1.05242	−0.526211	+	0.850354i	$0.676388\pi$
$938$	0	0
$939$	50.8577	1.65968
$940$	0	0
$941$	−47.4812	−1.54784	−0.773922	−	0.633281i	$-0.781708\pi$
$941$	−47.4812	−1.54784	−0.773922	+	0.633281i	$0.781708\pi$
$942$	0	0
$943$	−9.12169	−0.297043
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−11.9584	−0.388597	−0.194298	−	0.980942i	$-0.562243\pi$
$947$	−11.9584	−0.388597	−0.194298	+	0.980942i	$0.562243\pi$
$948$	0	0
$949$	13.7483	0.446289
$950$	0	0
$951$	31.6594	1.02663
$952$	0	0
$953$	26.2962	0.851817	0.425908	−	0.904766i	$-0.359955\pi$
$953$	26.2962	0.851817	0.425908	+	0.904766i	$0.359955\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	16.0428	0.518590
$958$	0	0
$959$	−74.0900	−2.39249
$960$	0	0
$961$	29.7918	0.961027
$962$	0	0
$963$	113.585	3.66024
$964$	0	0
$965$	0	0
$966$	0	0
$967$	6.67792	0.214748	0.107374	−	0.994219i	$-0.465756\pi$
$967$	6.67792	0.214748	0.107374	+	0.994219i	$0.465756\pi$
$968$	0	0
$969$	6.99512	0.224716
$970$	0	0
$971$	−9.76066	−0.313235	−0.156617	−	0.987659i	$-0.550059\pi$
$971$	−9.76066	−0.313235	−0.156617	+	0.987659i	$0.550059\pi$
$972$	0	0
$973$	−18.0896	−0.579926
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−22.7577	−0.728084	−0.364042	−	0.931382i	$-0.618604\pi$
$977$	−22.7577	−0.728084	−0.364042	+	0.931382i	$0.618604\pi$
$978$	0	0
$979$	−20.3967	−0.651882
$980$	0	0
$981$	35.8736	1.14536
$982$	0	0
$983$	12.0681	0.384913	0.192456	−	0.981306i	$-0.438355\pi$
$983$	12.0681	0.384913	0.192456	+	0.981306i	$0.438355\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	46.1894	1.47023
$988$	0	0
$989$	−26.3197	−0.836917
$990$	0	0
$991$	−58.6951	−1.86451	−0.932255	−	0.361801i	$-0.882162\pi$
$991$	−58.6951	−1.86451	−0.932255	+	0.361801i	$0.882162\pi$
$992$	0	0
$993$	76.4597	2.42638
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−11.9876	−0.379651	−0.189826	−	0.981818i	$-0.560792\pi$
$997$	−11.9876	−0.379651	−0.189826	+	0.981818i	$0.560792\pi$
$998$	0	0
$999$	1.56175	0.0494115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10000.2.a.v.1.1		4
4.3	odd	2		1250.2.a.g.1.4	✓	4
5.4	even	2		10000.2.a.u.1.4		4
20.3	even	4		1250.2.b.d.1249.8		8
20.7	even	4		1250.2.b.d.1249.1		8
20.19	odd	2		1250.2.a.j.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1250.2.a.g.1.4	✓	4	4.3	odd	2
1250.2.a.j.1.1	yes	4	20.19	odd	2
1250.2.b.d.1249.1		8	20.7	even	4
1250.2.b.d.1249.8		8	20.3	even	4
10000.2.a.u.1.4		4	5.4	even	2
10000.2.a.v.1.1		4	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 10000 = 2^{4} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10000.a (trivial)

\(f(q)\)	\(=\)	\(q-3.08634 q^{3} -4.14353 q^{7} +6.52550 q^{9} +O(q^{10})\)	\(q-3.08634 q^{3} -4.14353 q^{7} +6.52550 q^{9} +3.61184 q^{11} -2.37577 q^{13} +1.75774 q^{17} -1.28943 q^{19} +12.7883 q^{21} -2.23224 q^{23} -10.8809 q^{27} -1.43916 q^{29} -7.79691 q^{31} -11.1474 q^{33} -0.143531 q^{37} +7.33243 q^{39} +4.08634 q^{41} +11.7907 q^{43} +3.61184 q^{47} +10.1689 q^{49} -5.42497 q^{51} -9.61184 q^{53} +3.97962 q^{57} -6.47450 q^{59} +3.13970 q^{61} -27.0386 q^{63} -13.5585 q^{67} +6.88945 q^{69} +15.4559 q^{71} -5.78689 q^{73} -14.9658 q^{77} -8.19070 q^{79} +14.0056 q^{81} +10.5013 q^{83} +4.44173 q^{87} -5.64718 q^{89} +9.84408 q^{91} +24.0639 q^{93} -5.88325 q^{97} +23.5690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 3 q^{7} + 17 q^{9}+O(q^{10}) \) 4 * q + q^3 - 3 * q^7 + 17 * q^9	\( 4 q + q^{3} - 3 q^{7} + 17 q^{9} - 8 q^{11} + 4 q^{13} - 2 q^{17} - 5 q^{19} - 7 q^{21} - 9 q^{23} + 10 q^{27} - 10 q^{29} - 18 q^{31} - 22 q^{33} + 13 q^{37} + 16 q^{39} + 3 q^{41} + 16 q^{43} - 8 q^{47} + 23 q^{49} - 13 q^{51} - 16 q^{53} - 15 q^{57} - 35 q^{59} + 8 q^{61} - 54 q^{63} - 23 q^{67} + 19 q^{69} + 17 q^{71} - q^{73} - 29 q^{77} - 10 q^{79} + 24 q^{81} + 11 q^{83} - 40 q^{87} - 5 q^{89} + 17 q^{91} + 38 q^{93} + 3 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + q^3 - 3 * q^7 + 17 * q^9 - 8 * q^11 + 4 * q^13 - 2 * q^17 - 5 * q^19 - 7 * q^21 - 9 * q^23 + 10 * q^27 - 10 * q^29 - 18 * q^31 - 22 * q^33 + 13 * q^37 + 16 * q^39 + 3 * q^41 + 16 * q^43 - 8 * q^47 + 23 * q^49 - 13 * q^51 - 16 * q^53 - 15 * q^57 - 35 * q^59 + 8 * q^61 - 54 * q^63 - 23 * q^67 + 19 * q^69 + 17 * q^71 - q^73 - 29 * q^77 - 10 * q^79 + 24 * q^81 + 11 * q^83 - 40 * q^87 - 5 * q^89 + 17 * q^91 + 38 * q^93 + 3 * q^97 - 4 * q^99

Introduction

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