LMFDB - Embedded newform 850.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(1,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, 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("850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$850 = 2 \cdot 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	850.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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{3} - x^{2} - 6x - 2$ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.12489$ of defining polynomial
Character	$\chi$	$=$	850.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.484862 q^{3} +1.00000 q^{4} +0.484862 q^{6} +2.64002 q^{7} +1.00000 q^{8} -2.76491 q^{9} +2.00000 q^{11} +0.484862 q^{12} +0.484862 q^{13} +2.64002 q^{14} +1.00000 q^{16} +1.00000 q^{17} -2.76491 q^{18} +5.76491 q^{19} +1.28005 q^{21} +2.00000 q^{22} -1.35998 q^{23} +0.484862 q^{24} +0.484862 q^{26} -2.79518 q^{27} +2.64002 q^{28} +8.15516 q^{29} -2.09461 q^{31} +1.00000 q^{32} +0.969724 q^{33} +1.00000 q^{34} -2.76491 q^{36} -11.1396 q^{37} +5.76491 q^{38} +0.235091 q^{39} -0.249771 q^{41} +1.28005 q^{42} +1.03028 q^{43} +2.00000 q^{44} -1.35998 q^{46} +6.01468 q^{47} +0.484862 q^{48} -0.0302761 q^{49} +0.484862 q^{51} +0.484862 q^{52} -7.70436 q^{53} -2.79518 q^{54} +2.64002 q^{56} +2.79518 q^{57} +8.15516 q^{58} +8.73463 q^{59} -11.3747 q^{61} -2.09461 q^{62} -7.29942 q^{63} +1.00000 q^{64} +0.969724 q^{66} -4.96972 q^{67} +1.00000 q^{68} -0.659401 q^{69} +8.34438 q^{71} -2.76491 q^{72} +0.484862 q^{73} -11.1396 q^{74} +5.76491 q^{76} +5.28005 q^{77} +0.235091 q^{78} +9.85952 q^{79} +6.93945 q^{81} -0.249771 q^{82} -17.5298 q^{83} +1.28005 q^{84} +1.03028 q^{86} +3.95413 q^{87} +2.00000 q^{88} -8.73463 q^{89} +1.28005 q^{91} -1.35998 q^{92} -1.01560 q^{93} +6.01468 q^{94} +0.484862 q^{96} +6.73463 q^{97} -0.0302761 q^{98} -5.52982 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$3 q + 3 q^{2} + q^{3} + 3 q^{4} + q^{6} + 3 q^{8} + 8 q^{9} + 6 q^{11} + q^{12} + q^{13} + 3 q^{16} + 3 q^{17} + 8 q^{18} + q^{19} - 12 q^{21} + 6 q^{22} - 12 q^{23} + q^{24} + q^{26} + 7 q^{27}+ \cdots + 16 q^{99}+O(q^{100})$ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + q^6 + 3 * q^8 + 8 * q^9 + 6 * q^11 + q^12 + q^13 + 3 * q^16 + 3 * q^17 + 8 * q^18 + q^19 - 12 * q^21 + 6 * q^22 - 12 * q^23 + q^24 + q^26 + 7 * q^27 + 17 * q^29 + 3 * q^31 + 3 * q^32 + 2 * q^33 + 3 * q^34 + 8 * q^36 + 8 * q^37 + q^38 + 17 * q^39 + 16 * q^41 - 12 * q^42 + 4 * q^43 + 6 * q^44 - 12 * q^46 - 15 * q^47 + q^48 - q^49 + q^51 + q^52 - 5 * q^53 + 7 * q^54 - 7 * q^57 + 17 * q^58 + 9 * q^59 - 9 * q^61 + 3 * q^62 - 28 * q^63 + 3 * q^64 + 2 * q^66 - 14 * q^67 + 3 * q^68 - 16 * q^69 - q^71 + 8 * q^72 + q^73 + 8 * q^74 + q^76 + 17 * q^78 + 4 * q^79 + 19 * q^81 + 16 * q^82 - 20 * q^83 - 12 * q^84 + 4 * q^86 - 23 * q^87 + 6 * q^88 - 9 * q^89 - 12 * q^91 - 12 * q^92 - 37 * q^93 - 15 * q^94 + q^96 + 3 * q^97 - q^98 + 16 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.484862	0.279935	0.139968	−	0.990156i	$-0.455300\pi$
$3$	0.484862	0.279935	0.139968	+	0.990156i	$0.455300\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.484862	0.197944
$7$	2.64002	0.997835	0.498918	−	0.866649i	$-0.333731\pi$
$7$	2.64002	0.997835	0.498918	+	0.866649i	$0.333731\pi$
$8$	1.00000	0.353553
$9$	−2.76491	−0.921636
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0.484862	0.139968
$13$	0.484862	0.134477	0.0672383	−	0.997737i	$-0.478581\pi$
$13$	0.484862	0.134477	0.0672383	+	0.997737i	$0.478581\pi$
$14$	2.64002	0.705576
$15$	0	0
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.76491	−0.651695
$19$	5.76491	1.32256	0.661280	−	0.750139i	$-0.270013\pi$
$19$	5.76491	1.32256	0.661280	+	0.750139i	$0.270013\pi$
$20$	0	0
$21$	1.28005	0.279329
$22$	2.00000	0.426401
$23$	−1.35998	−0.283575	−0.141787	−	0.989897i	$-0.545285\pi$
$23$	−1.35998	−0.283575	−0.141787	+	0.989897i	$0.545285\pi$
$24$	0.484862	0.0989720
$25$	0	0
$26$	0.484862	0.0950893
$27$	−2.79518	−0.537934
$28$	2.64002	0.498918
$29$	8.15516	1.51438	0.757188	−	0.653197i	$-0.226573\pi$
$29$	8.15516	1.51438	0.757188	+	0.653197i	$0.226573\pi$
$30$	0	0
$31$	−2.09461	−0.376203	−0.188101	−	0.982150i	$-0.560233\pi$
$31$	−2.09461	−0.376203	−0.188101	+	0.982150i	$0.560233\pi$
$32$	1.00000	0.176777
$33$	0.969724	0.168807
$34$	1.00000	0.171499
$35$	0	0
$36$	−2.76491	−0.460818
$37$	−11.1396	−1.83133	−0.915667	−	0.401939i	$-0.868337\pi$
$37$	−11.1396	−1.83133	−0.915667	+	0.401939i	$0.868337\pi$
$38$	5.76491	0.935192
$39$	0.235091	0.0376447
$40$	0	0
$41$	−0.249771	−0.0390077	−0.0195038	−	0.999810i	$-0.506209\pi$
$41$	−0.249771	−0.0390077	−0.0195038	+	0.999810i	$0.506209\pi$
$42$	1.28005	0.197516
$43$	1.03028	0.157116	0.0785578	−	0.996910i	$-0.474968\pi$
$43$	1.03028	0.157116	0.0785578	+	0.996910i	$0.474968\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	−1.35998	−0.200518
$47$	6.01468	0.877331	0.438666	−	0.898650i	$-0.355451\pi$
$47$	6.01468	0.877331	0.438666	+	0.898650i	$0.355451\pi$
$48$	0.484862	0.0699838
$49$	−0.0302761	−0.00432516
$50$	0	0
$51$	0.484862	0.0678943
$52$	0.484862	0.0672383
$53$	−7.70436	−1.05827	−0.529137	−	0.848536i	$-0.677484\pi$
$53$	−7.70436	−1.05827	−0.529137	+	0.848536i	$0.677484\pi$
$54$	−2.79518	−0.380376
$55$	0	0
$56$	2.64002	0.352788
$57$	2.79518	0.370231
$58$	8.15516	1.07083
$59$	8.73463	1.13715	0.568576	−	0.822631i	$-0.307494\pi$
$59$	8.73463	1.13715	0.568576	+	0.822631i	$0.307494\pi$
$60$	0	0
$61$	−11.3747	−1.45638	−0.728188	−	0.685378i	$-0.759637\pi$
$61$	−11.3747	−1.45638	−0.728188	+	0.685378i	$0.759637\pi$
$62$	−2.09461	−0.266016
$63$	−7.29942	−0.919641
$64$	1.00000	0.125000
$65$	0	0
$66$	0.969724	0.119365
$67$	−4.96972	−0.607148	−0.303574	−	0.952808i	$-0.598180\pi$
$67$	−4.96972	−0.607148	−0.303574	+	0.952808i	$0.598180\pi$
$68$	1.00000	0.121268
$69$	−0.659401	−0.0793825
$70$	0	0
$71$	8.34438	0.990296	0.495148	−	0.868809i	$-0.335114\pi$
$71$	8.34438	0.990296	0.495148	+	0.868809i	$0.335114\pi$
$72$	−2.76491	−0.325848
$73$	0.484862	0.0567488	0.0283744	−	0.999597i	$-0.490967\pi$
$73$	0.484862	0.0567488	0.0283744	+	0.999597i	$0.490967\pi$
$74$	−11.1396	−1.29495
$75$	0	0
$76$	5.76491	0.661280
$77$	5.28005	0.601717
$78$	0.235091	0.0266188
$79$	9.85952	1.10928	0.554641	−	0.832090i	$-0.312856\pi$
$79$	9.85952	1.10928	0.554641	+	0.832090i	$0.312856\pi$
$80$	0	0
$81$	6.93945	0.771050
$82$	−0.249771	−0.0275826
$83$	−17.5298	−1.92415	−0.962074	−	0.272790i	$-0.912054\pi$
$83$	−17.5298	−1.92415	−0.962074	+	0.272790i	$0.912054\pi$
$84$	1.28005	0.139665
$85$	0	0
$86$	1.03028	0.111098
$87$	3.95413	0.423927
$88$	2.00000	0.213201
$89$	−8.73463	−0.925869	−0.462935	−	0.886392i	$-0.653204\pi$
$89$	−8.73463	−0.925869	−0.462935	+	0.886392i	$0.653204\pi$
$90$	0	0
$91$	1.28005	0.134185
$92$	−1.35998	−0.141787
$93$	−1.01560	−0.105312
$94$	6.01468	0.620367
$95$	0	0
$96$	0.484862	0.0494860
$97$	6.73463	0.683798	0.341899	−	0.939737i	$-0.388930\pi$
$97$	6.73463	0.683798	0.341899	+	0.939737i	$0.388930\pi$
$98$	−0.0302761	−0.00305835
$99$	−5.52982	−0.555768
$100$	0	0
$101$	13.5298	1.34627	0.673134	−	0.739521i	$-0.264948\pi$
$101$	13.5298	1.34627	0.673134	+	0.739521i	$0.264948\pi$
$102$	0.484862	0.0480085
$103$	−11.2195	−1.10549	−0.552745	−	0.833351i	$-0.686420\pi$
$103$	−11.2195	−1.10549	−0.552745	+	0.833351i	$0.686420\pi$
$104$	0.484862	0.0475446
$105$	0	0
$106$	−7.70436	−0.748313
$107$	−19.4693	−1.88216	−0.941082	−	0.338177i	$-0.890190\pi$
$107$	−19.4693	−1.88216	−0.941082	+	0.338177i	$0.890190\pi$
$108$	−2.79518	−0.268967
$109$	−12.6547	−1.21210	−0.606050	−	0.795426i	$-0.707247\pi$
$109$	−12.6547	−1.21210	−0.606050	+	0.795426i	$0.707247\pi$
$110$	0	0
$111$	−5.40115	−0.512655
$112$	2.64002	0.249459
$113$	7.51514	0.706965	0.353482	−	0.935441i	$-0.384997\pi$
$113$	7.51514	0.706965	0.353482	+	0.935441i	$0.384997\pi$
$114$	2.79518	0.261793
$115$	0	0
$116$	8.15516	0.757188
$117$	−1.34060	−0.123938
$118$	8.73463	0.804088
$119$	2.64002	0.242011
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−11.3747	−1.02981
$123$	−0.121104	−0.0109196
$124$	−2.09461	−0.188101
$125$	0	0
$126$	−7.29942	−0.650284
$127$	−14.7952	−1.31286	−0.656430	−	0.754387i	$-0.727934\pi$
$127$	−14.7952	−1.31286	−0.656430	+	0.754387i	$0.727934\pi$
$128$	1.00000	0.0883883
$129$	0.499542	0.0439822
$130$	0	0
$131$	−2.49954	−0.218386	−0.109193	−	0.994021i	$-0.534827\pi$
$131$	−2.49954	−0.218386	−0.109193	+	0.994021i	$0.534827\pi$
$132$	0.969724	0.0844036
$133$	15.2195	1.31970
$134$	−4.96972	−0.429319
$135$	0	0
$136$	1.00000	0.0857493
$137$	2.06055	0.176045	0.0880224	−	0.996118i	$-0.471945\pi$
$137$	2.06055	0.176045	0.0880224	+	0.996118i	$0.471945\pi$
$138$	−0.659401	−0.0561319
$139$	−15.5904	−1.32236	−0.661179	−	0.750228i	$-0.729944\pi$
$139$	−15.5904	−1.32236	−0.661179	+	0.750228i	$0.729944\pi$
$140$	0	0
$141$	2.91629	0.245596
$142$	8.34438	0.700245
$143$	0.969724	0.0810924
$144$	−2.76491	−0.230409
$145$	0	0
$146$	0.484862	0.0401275
$147$	−0.0146797	−0.00121076
$148$	−11.1396	−0.915667
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	0	0
$151$	−15.8401	−1.28905	−0.644526	−	0.764582i	$-0.722945\pi$
$151$	−15.8401	−1.28905	−0.644526	+	0.764582i	$0.722945\pi$
$152$	5.76491	0.467596
$153$	−2.76491	−0.223530
$154$	5.28005	0.425478
$155$	0	0
$156$	0.235091	0.0188224
$157$	1.34060	0.106991	0.0534957	−	0.998568i	$-0.482964\pi$
$157$	1.34060	0.106991	0.0534957	+	0.998568i	$0.482964\pi$
$158$	9.85952	0.784381
$159$	−3.73555	−0.296248
$160$	0	0
$161$	−3.59037	−0.282961
$162$	6.93945	0.545215
$163$	16.2498	1.27278	0.636390	−	0.771367i	$-0.280427\pi$
$163$	16.2498	1.27278	0.636390	+	0.771367i	$0.280427\pi$
$164$	−0.249771	−0.0195038
$165$	0	0
$166$	−17.5298	−1.36058
$167$	−2.95035	−0.228305	−0.114152	−	0.993463i	$-0.536415\pi$
$167$	−2.95035	−0.228305	−0.114152	+	0.993463i	$0.536415\pi$
$168$	1.28005	0.0987578
$169$	−12.7649	−0.981916
$170$	0	0
$171$	−15.9394	−1.21892
$172$	1.03028	0.0785578
$173$	−6.14048	−0.466852	−0.233426	−	0.972375i	$-0.574994\pi$
$173$	−6.14048	−0.466852	−0.233426	+	0.972375i	$0.574994\pi$
$174$	3.95413	0.299762
$175$	0	0
$176$	2.00000	0.150756
$177$	4.23509	0.318329
$178$	−8.73463	−0.654688
$179$	−15.5904	−1.16528	−0.582639	−	0.812731i	$-0.697980\pi$
$179$	−15.5904	−1.16528	−0.582639	+	0.812731i	$0.697980\pi$
$180$	0	0
$181$	4.10929	0.305441	0.152721	−	0.988269i	$-0.451197\pi$
$181$	4.10929	0.305441	0.152721	+	0.988269i	$0.451197\pi$
$182$	1.28005	0.0948834
$183$	−5.51514	−0.407691
$184$	−1.35998	−0.100259
$185$	0	0
$186$	−1.01560	−0.0744671
$187$	2.00000	0.146254
$188$	6.01468	0.438666
$189$	−7.37935	−0.536769
$190$	0	0
$191$	6.06055	0.438526	0.219263	−	0.975666i	$-0.429635\pi$
$191$	6.06055	0.438526	0.219263	+	0.975666i	$0.429635\pi$
$192$	0.484862	0.0349919
$193$	12.5601	0.904095	0.452048	−	0.891994i	$-0.350694\pi$
$193$	12.5601	0.904095	0.452048	+	0.891994i	$0.350694\pi$
$194$	6.73463	0.483518
$195$	0	0
$196$	−0.0302761	−0.00216258
$197$	26.0487	1.85590	0.927948	−	0.372710i	$-0.121571\pi$
$197$	26.0487	1.85590	0.927948	+	0.372710i	$0.121571\pi$
$198$	−5.52982	−0.392987
$199$	3.37466	0.239223	0.119612	−	0.992821i	$-0.461835\pi$
$199$	3.37466	0.239223	0.119612	+	0.992821i	$0.461835\pi$
$200$	0	0
$201$	−2.40963	−0.169962
$202$	13.5298	0.951955
$203$	21.5298	1.51110
$204$	0.484862	0.0339471
$205$	0	0
$206$	−11.2195	−0.781699
$207$	3.76021	0.261353
$208$	0.484862	0.0336191
$209$	11.5298	0.797534
$210$	0	0
$211$	18.0294	1.24119	0.620596	−	0.784130i	$-0.286891\pi$
$211$	18.0294	1.24119	0.620596	+	0.784130i	$0.286891\pi$
$212$	−7.70436	−0.529137
$213$	4.04587	0.277219
$214$	−19.4693	−1.33089
$215$	0	0
$216$	−2.79518	−0.190188
$217$	−5.52982	−0.375388
$218$	−12.6547	−0.857085
$219$	0.235091	0.0158860
$220$	0	0
$221$	0.484862	0.0326153
$222$	−5.40115	−0.362502
$223$	−23.2947	−1.55993	−0.779965	−	0.625823i	$-0.784763\pi$
$223$	−23.2947	−1.55993	−0.779965	+	0.625823i	$0.784763\pi$
$224$	2.64002	0.176394
$225$	0	0
$226$	7.51514	0.499900
$227$	−17.4839	−1.16045	−0.580225	−	0.814456i	$-0.697035\pi$
$227$	−17.4839	−1.16045	−0.580225	+	0.814456i	$0.697035\pi$
$228$	2.79518	0.185116
$229$	0.719953	0.0475758	0.0237879	−	0.999717i	$-0.492427\pi$
$229$	0.719953	0.0475758	0.0237879	+	0.999717i	$0.492427\pi$
$230$	0	0
$231$	2.56009	0.168442
$232$	8.15516	0.535413
$233$	−11.0450	−0.723579	−0.361790	−	0.932260i	$-0.617834\pi$
$233$	−11.0450	−0.723579	−0.361790	+	0.932260i	$0.617834\pi$
$234$	−1.34060	−0.0876377
$235$	0	0
$236$	8.73463	0.568576
$237$	4.78051	0.310527
$238$	2.64002	0.171127
$239$	−5.59037	−0.361611	−0.180805	−	0.983519i	$-0.557870\pi$
$239$	−5.59037	−0.361611	−0.180805	+	0.983519i	$0.557870\pi$
$240$	0	0
$241$	−8.37088	−0.539215	−0.269608	−	0.962970i	$-0.586894\pi$
$241$	−8.37088	−0.539215	−0.269608	+	0.962970i	$0.586894\pi$
$242$	−7.00000	−0.449977
$243$	11.7502	0.753778
$244$	−11.3747	−0.728188
$245$	0	0
$246$	−0.121104	−0.00772133
$247$	2.79518	0.177853
$248$	−2.09461	−0.133008
$249$	−8.49954	−0.538637
$250$	0	0
$251$	19.4693	1.22889	0.614445	−	0.788960i	$-0.289380\pi$
$251$	19.4693	1.22889	0.614445	+	0.788960i	$0.289380\pi$
$252$	−7.29942	−0.459821
$253$	−2.71995	−0.171002
$254$	−14.7952	−0.928332
$255$	0	0
$256$	1.00000	0.0625000
$257$	13.9394	0.869519	0.434759	−	0.900547i	$-0.356833\pi$
$257$	13.9394	0.869519	0.434759	+	0.900547i	$0.356833\pi$
$258$	0.499542	0.0311001
$259$	−29.4087	−1.82737
$260$	0	0
$261$	−22.5483	−1.39570
$262$	−2.49954	−0.154422
$263$	−16.2645	−1.00291	−0.501454	−	0.865184i	$-0.667202\pi$
$263$	−16.2645	−1.00291	−0.501454	+	0.865184i	$0.667202\pi$
$264$	0.969724	0.0596824
$265$	0	0
$266$	15.2195	0.933167
$267$	−4.23509	−0.259183
$268$	−4.96972	−0.303574
$269$	10.4049	0.634400	0.317200	−	0.948359i	$-0.397257\pi$
$269$	10.4049	0.634400	0.317200	+	0.948359i	$0.397257\pi$
$270$	0	0
$271$	−24.0294	−1.45968	−0.729840	−	0.683618i	$-0.760405\pi$
$271$	−24.0294	−1.45968	−0.729840	+	0.683618i	$0.760405\pi$
$272$	1.00000	0.0606339
$273$	0.620646	0.0375632
$274$	2.06055	0.124483
$275$	0	0
$276$	−0.659401	−0.0396913
$277$	18.9503	1.13862	0.569308	−	0.822124i	$-0.307211\pi$
$277$	18.9503	1.13862	0.569308	+	0.822124i	$0.307211\pi$
$278$	−15.5904	−0.935048
$279$	5.79140	0.346722
$280$	0	0
$281$	19.6438	1.17185	0.585926	−	0.810365i	$-0.300731\pi$
$281$	19.6438	1.17185	0.585926	+	0.810365i	$0.300731\pi$
$282$	2.91629	0.173663
$283$	25.7943	1.53331	0.766655	−	0.642059i	$-0.221920\pi$
$283$	25.7943	1.53331	0.766655	+	0.642059i	$0.221920\pi$
$284$	8.34438	0.495148
$285$	0	0
$286$	0.969724	0.0573410
$287$	−0.659401	−0.0389232
$288$	−2.76491	−0.162924
$289$	1.00000	0.0588235
$290$	0	0
$291$	3.26537	0.191419
$292$	0.484862	0.0283744
$293$	−22.9239	−1.33923	−0.669613	−	0.742710i	$-0.733540\pi$
$293$	−22.9239	−1.33923	−0.669613	+	0.742710i	$0.733540\pi$
$294$	−0.0146797	−0.000856139 0
$295$	0	0
$296$	−11.1396	−0.647474
$297$	−5.59037	−0.324386
$298$	10.0000	0.579284
$299$	−0.659401	−0.0381341
$300$	0	0
$301$	2.71995	0.156775
$302$	−15.8401	−0.911498
$303$	6.56009	0.376868
$304$	5.76491	0.330640
$305$	0	0
$306$	−2.76491	−0.158059
$307$	−10.4702	−0.597565	−0.298782	−	0.954321i	$-0.596580\pi$
$307$	−10.4702	−0.597565	−0.298782	+	0.954321i	$0.596580\pi$
$308$	5.28005	0.300859
$309$	−5.43991	−0.309465
$310$	0	0
$311$	−9.73841	−0.552215	−0.276107	−	0.961127i	$-0.589045\pi$
$311$	−9.73841	−0.552215	−0.276107	+	0.961127i	$0.589045\pi$
$312$	0.235091	0.0133094
$313$	9.50046	0.536998	0.268499	−	0.963280i	$-0.413472\pi$
$313$	9.50046	0.536998	0.268499	+	0.963280i	$0.413472\pi$
$314$	1.34060	0.0756544
$315$	0	0
$316$	9.85952	0.554641
$317$	13.0790	0.734591	0.367295	−	0.930104i	$-0.380284\pi$
$317$	13.0790	0.734591	0.367295	+	0.930104i	$0.380284\pi$
$318$	−3.73555	−0.209479
$319$	16.3103	0.913203
$320$	0	0
$321$	−9.43991	−0.526884
$322$	−3.59037	−0.200083
$323$	5.76491	0.320768
$324$	6.93945	0.385525
$325$	0	0
$326$	16.2498	0.899992
$327$	−6.13578	−0.339310
$328$	−0.249771	−0.0137913
$329$	15.8789	0.875432
$330$	0	0
$331$	24.8851	1.36781	0.683904	−	0.729572i	$-0.260281\pi$
$331$	24.8851	1.36781	0.683904	+	0.729572i	$0.260281\pi$
$332$	−17.5298	−0.962074
$333$	30.7999	1.68782
$334$	−2.95035	−0.161436
$335$	0	0
$336$	1.28005	0.0698323
$337$	27.5445	1.50044	0.750222	−	0.661186i	$-0.229947\pi$
$337$	27.5445	1.50044	0.750222	+	0.661186i	$0.229947\pi$
$338$	−12.7649	−0.694320
$339$	3.64380	0.197904
$340$	0	0
$341$	−4.18922	−0.226859
$342$	−15.9394	−0.861907
$343$	−18.5601	−1.00215
$344$	1.03028	0.0555488
$345$	0	0
$346$	−6.14048	−0.330114
$347$	4.48486	0.240760	0.120380	−	0.992728i	$-0.461589\pi$
$347$	4.48486	0.240760	0.120380	+	0.992728i	$0.461589\pi$
$348$	3.95413	0.211963
$349$	34.2186	1.83168	0.915839	−	0.401545i	$-0.131527\pi$
$349$	34.2186	1.83168	0.915839	+	0.401545i	$0.131527\pi$
$350$	0	0
$351$	−1.35528	−0.0723394
$352$	2.00000	0.106600
$353$	−4.90917	−0.261289	−0.130644	−	0.991429i	$-0.541705\pi$
$353$	−4.90917	−0.261289	−0.130644	+	0.991429i	$0.541705\pi$
$354$	4.23509	0.225093
$355$	0	0
$356$	−8.73463	−0.462935
$357$	1.28005	0.0677473
$358$	−15.5904	−0.823977
$359$	−13.7796	−0.727259	−0.363629	−	0.931544i	$-0.618463\pi$
$359$	−13.7796	−0.727259	−0.363629	+	0.931544i	$0.618463\pi$
$360$	0	0
$361$	14.2342	0.749167
$362$	4.10929	0.215979
$363$	−3.39403	−0.178141
$364$	1.28005	0.0670927
$365$	0	0
$366$	−5.51514	−0.288281
$367$	−4.39025	−0.229169	−0.114585	−	0.993413i	$-0.536554\pi$
$367$	−4.39025	−0.229169	−0.114585	+	0.993413i	$0.536554\pi$
$368$	−1.35998	−0.0708937
$369$	0.690594	0.0359509
$370$	0	0
$371$	−20.3397	−1.05598
$372$	−1.01560	−0.0526562
$373$	0.220411	0.0114125	0.00570623	−	0.999984i	$-0.498184\pi$
$373$	0.220411	0.0114125	0.00570623	+	0.999984i	$0.498184\pi$
$374$	2.00000	0.103418
$375$	0	0
$376$	6.01468	0.310183
$377$	3.95413	0.203648
$378$	−7.37935	−0.379553
$379$	26.3103	1.35147	0.675735	−	0.737144i	$-0.263826\pi$
$379$	26.3103	1.35147	0.675735	+	0.737144i	$0.263826\pi$
$380$	0	0
$381$	−7.17362	−0.367516
$382$	6.06055	0.310085
$383$	36.1433	1.84684	0.923419	−	0.383793i	$-0.125382\pi$
$383$	36.1433	1.84684	0.923419	+	0.383793i	$0.125382\pi$
$384$	0.484862	0.0247430
$385$	0	0
$386$	12.5601	0.639292
$387$	−2.84862	−0.144803
$388$	6.73463	0.341899
$389$	3.77959	0.191633	0.0958164	−	0.995399i	$-0.469454\pi$
$389$	3.77959	0.191633	0.0958164	+	0.995399i	$0.469454\pi$
$390$	0	0
$391$	−1.35998	−0.0687770
$392$	−0.0302761	−0.00152917
$393$	−1.21193	−0.0611339
$394$	26.0487	1.31232
$395$	0	0
$396$	−5.52982	−0.277884
$397$	−12.2304	−0.613826	−0.306913	−	0.951738i	$-0.599296\pi$
$397$	−12.2304	−0.613826	−0.306913	+	0.951738i	$0.599296\pi$
$398$	3.37466	0.169156
$399$	7.37935	0.369430
$400$	0	0
$401$	−11.7796	−0.588245	−0.294122	−	0.955768i	$-0.595027\pi$
$401$	−11.7796	−0.588245	−0.294122	+	0.955768i	$0.595027\pi$
$402$	−2.40963	−0.120181
$403$	−1.01560	−0.0505905
$404$	13.5298	0.673134
$405$	0	0
$406$	21.5298	1.06851
$407$	−22.2791	−1.10434
$408$	0.484862	0.0240042
$409$	−15.7649	−0.779525	−0.389762	−	0.920916i	$-0.627443\pi$
$409$	−15.7649	−0.779525	−0.389762	+	0.920916i	$0.627443\pi$
$410$	0	0
$411$	0.999083	0.0492811
$412$	−11.2195	−0.552745
$413$	23.0596	1.13469
$414$	3.76021	0.184804
$415$	0	0
$416$	0.484862	0.0237723
$417$	−7.55918	−0.370175
$418$	11.5298	0.563942
$419$	18.1892	0.888601	0.444301	−	0.895878i	$-0.353452\pi$
$419$	18.1892	0.888601	0.444301	+	0.895878i	$0.353452\pi$
$420$	0	0
$421$	9.03028	0.440109	0.220054	−	0.975488i	$-0.429377\pi$
$421$	9.03028	0.440109	0.220054	+	0.975488i	$0.429377\pi$
$422$	18.0294	0.877655
$423$	−16.6300	−0.808580
$424$	−7.70436	−0.374157
$425$	0	0
$426$	4.04587	0.196023
$427$	−30.0294	−1.45322
$428$	−19.4693	−0.941082
$429$	0.470182	0.0227006
$430$	0	0
$431$	20.4196	0.983578	0.491789	−	0.870714i	$-0.336343\pi$
$431$	20.4196	0.983578	0.491789	+	0.870714i	$0.336343\pi$
$432$	−2.79518	−0.134483
$433$	−11.5904	−0.556998	−0.278499	−	0.960437i	$-0.589837\pi$
$433$	−11.5904	−0.556998	−0.278499	+	0.960437i	$0.589837\pi$
$434$	−5.52982	−0.265440
$435$	0	0
$436$	−12.6547	−0.606050
$437$	−7.84014	−0.375045
$438$	0.235091	0.0112331
$439$	−2.01938	−0.0963796	−0.0481898	−	0.998838i	$-0.515345\pi$
$439$	−2.01938	−0.0963796	−0.0481898	+	0.998838i	$0.515345\pi$
$440$	0	0
$441$	0.0837106	0.00398622
$442$	0.484862	0.0230625
$443$	27.4087	1.30223	0.651114	−	0.758980i	$-0.274302\pi$
$443$	27.4087	1.30223	0.651114	+	0.758980i	$0.274302\pi$
$444$	−5.40115	−0.256327
$445$	0	0
$446$	−23.2947	−1.10304
$447$	4.84862	0.229332
$448$	2.64002	0.124729
$449$	29.7190	1.40253	0.701264	−	0.712902i	$-0.252619\pi$
$449$	29.7190	1.40253	0.701264	+	0.712902i	$0.252619\pi$
$450$	0	0
$451$	−0.499542	−0.0235225
$452$	7.51514	0.353482
$453$	−7.68028	−0.360851
$454$	−17.4839	−0.820562
$455$	0	0
$456$	2.79518	0.130897
$457$	−39.4693	−1.84629	−0.923147	−	0.384447i	$-0.874392\pi$
$457$	−39.4693	−1.84629	−0.923147	+	0.384447i	$0.874392\pi$
$458$	0.719953	0.0336412
$459$	−2.79518	−0.130468
$460$	0	0
$461$	14.6888	0.684124	0.342062	−	0.939677i	$-0.388875\pi$
$461$	14.6888	0.684124	0.342062	+	0.939677i	$0.388875\pi$
$462$	2.56009	0.119106
$463$	−35.1055	−1.63149	−0.815746	−	0.578411i	$-0.803673\pi$
$463$	−35.1055	−1.63149	−0.815746	+	0.578411i	$0.803673\pi$
$464$	8.15516	0.378594
$465$	0	0
$466$	−11.0450	−0.511648
$467$	9.96881	0.461301	0.230651	−	0.973037i	$-0.425915\pi$
$467$	9.96881	0.461301	0.230651	+	0.973037i	$0.425915\pi$
$468$	−1.34060	−0.0619692
$469$	−13.1202	−0.605834
$470$	0	0
$471$	0.650006	0.0299507
$472$	8.73463	0.402044
$473$	2.06055	0.0947443
$474$	4.78051	0.219576
$475$	0	0
$476$	2.64002	0.121005
$477$	21.3018	0.975344
$478$	−5.59037	−0.255698
$479$	−2.28383	−0.104351	−0.0521754	−	0.998638i	$-0.516615\pi$
$479$	−2.28383	−0.104351	−0.0521754	+	0.998638i	$0.516615\pi$
$480$	0	0
$481$	−5.40115	−0.246271
$482$	−8.37088	−0.381283
$483$	−1.74083	−0.0792107
$484$	−7.00000	−0.318182
$485$	0	0
$486$	11.7502	0.533001
$487$	10.8292	0.490720	0.245360	−	0.969432i	$-0.421094\pi$
$487$	10.8292	0.490720	0.245360	+	0.969432i	$0.421094\pi$
$488$	−11.3747	−0.514906
$489$	7.87890	0.356296
$490$	0	0
$491$	24.7952	1.11899	0.559496	−	0.828833i	$-0.310995\pi$
$491$	24.7952	1.11899	0.559496	+	0.828833i	$0.310995\pi$
$492$	−0.121104	−0.00545981
$493$	8.15516	0.367290
$494$	2.79518	0.125761
$495$	0	0
$496$	−2.09461	−0.0940507
$497$	22.0294	0.988152
$498$	−8.49954	−0.380874
$499$	5.15138	0.230607	0.115304	−	0.993330i	$-0.463216\pi$
$499$	5.15138	0.230607	0.115304	+	0.993330i	$0.463216\pi$
$500$	0	0
$501$	−1.43051	−0.0639105
$502$	19.4693	0.868956
$503$	29.0109	1.29353	0.646766	−	0.762688i	$-0.276121\pi$
$503$	29.0109	1.29353	0.646766	+	0.762688i	$0.276121\pi$
$504$	−7.29942	−0.325142
$505$	0	0
$506$	−2.71995	−0.120917
$507$	−6.18922	−0.274873
$508$	−14.7952	−0.656430
$509$	−27.4693	−1.21755	−0.608777	−	0.793341i	$-0.708340\pi$
$509$	−27.4693	−1.21755	−0.608777	+	0.793341i	$0.708340\pi$
$510$	0	0
$511$	1.28005	0.0566259
$512$	1.00000	0.0441942
$513$	−16.1140	−0.711450
$514$	13.9394	0.614843
$515$	0	0
$516$	0.499542	0.0219911
$517$	12.0294	0.529051
$518$	−29.4087	−1.29214
$519$	−2.97729	−0.130688
$520$	0	0
$521$	5.68968	0.249269	0.124635	−	0.992203i	$-0.460224\pi$
$521$	5.68968	0.249269	0.124635	+	0.992203i	$0.460224\pi$
$522$	−22.5483	−0.986911
$523$	−7.52982	−0.329256	−0.164628	−	0.986356i	$-0.552642\pi$
$523$	−7.52982	−0.329256	−0.164628	+	0.986356i	$0.552642\pi$
$524$	−2.49954	−0.109193
$525$	0	0
$526$	−16.2645	−0.709164
$527$	−2.09461	−0.0912426
$528$	0.969724	0.0422018
$529$	−21.1505	−0.919585
$530$	0	0
$531$	−24.1505	−1.04804
$532$	15.2195	0.659849
$533$	−0.121104	−0.00524561
$534$	−4.23509	−0.183270
$535$	0	0
$536$	−4.96972	−0.214659
$537$	−7.55918	−0.326203
$538$	10.4049	0.448588
$539$	−0.0605522	−0.00260817
$540$	0	0
$541$	26.0100	1.11826	0.559128	−	0.829081i	$-0.311136\pi$
$541$	26.0100	1.11826	0.559128	+	0.829081i	$0.311136\pi$
$542$	−24.0294	−1.03215
$543$	1.99244	0.0855037
$544$	1.00000	0.0428746
$545$	0	0
$546$	0.620646	0.0265612
$547$	11.5833	0.495264	0.247632	−	0.968854i	$-0.420348\pi$
$547$	11.5833	0.495264	0.247632	+	0.968854i	$0.420348\pi$
$548$	2.06055	0.0880224
$549$	31.4499	1.34225
$550$	0	0
$551$	47.0138	2.00285
$552$	−0.659401	−0.0280660
$553$	26.0294	1.10688
$554$	18.9503	0.805123
$555$	0	0
$556$	−15.5904	−0.661179
$557$	−5.95413	−0.252284	−0.126142	−	0.992012i	$-0.540260\pi$
$557$	−5.95413	−0.252284	−0.126142	+	0.992012i	$0.540260\pi$
$558$	5.79140	0.245170
$559$	0.499542	0.0211284
$560$	0	0
$561$	0.969724	0.0409418
$562$	19.6438	0.828624
$563$	34.5289	1.45522	0.727610	−	0.685991i	$-0.240631\pi$
$563$	34.5289	1.45522	0.727610	+	0.685991i	$0.240631\pi$
$564$	2.91629	0.122798
$565$	0	0
$566$	25.7943	1.08421
$567$	18.3203	0.769380
$568$	8.34438	0.350122
$569$	12.7952	0.536402	0.268201	−	0.963363i	$-0.413571\pi$
$569$	12.7952	0.536402	0.268201	+	0.963363i	$0.413571\pi$
$570$	0	0
$571$	−4.22041	−0.176619	−0.0883094	−	0.996093i	$-0.528146\pi$
$571$	−4.22041	−0.176619	−0.0883094	+	0.996093i	$0.528146\pi$
$572$	0.969724	0.0405462
$573$	2.93853	0.122759
$574$	−0.659401	−0.0275229
$575$	0	0
$576$	−2.76491	−0.115205
$577$	35.5592	1.48035	0.740174	−	0.672415i	$-0.234743\pi$
$577$	35.5592	1.48035	0.740174	+	0.672415i	$0.234743\pi$
$578$	1.00000	0.0415945
$579$	6.08991	0.253088
$580$	0	0
$581$	−46.2791	−1.91998
$582$	3.26537	0.135354
$583$	−15.4087	−0.638164
$584$	0.484862	0.0200637
$585$	0	0
$586$	−22.9239	−0.946976
$587$	43.6803	1.80288	0.901439	−	0.432906i	$-0.142512\pi$
$587$	43.6803	1.80288	0.901439	+	0.432906i	$0.142512\pi$
$588$	−0.0146797	−0.000605382 0
$589$	−12.0752	−0.497551
$590$	0	0
$591$	12.6300	0.519530
$592$	−11.1396	−0.457833
$593$	−20.1505	−0.827480	−0.413740	−	0.910395i	$-0.635778\pi$
$593$	−20.1505	−0.827480	−0.413740	+	0.910395i	$0.635778\pi$
$594$	−5.59037	−0.229376
$595$	0	0
$596$	10.0000	0.409616
$597$	1.63624	0.0669669
$598$	−0.659401	−0.0269649
$599$	33.4986	1.36872	0.684358	−	0.729146i	$-0.260082\pi$
$599$	33.4986	1.36872	0.684358	+	0.729146i	$0.260082\pi$
$600$	0	0
$601$	7.93945	0.323857	0.161928	−	0.986803i	$-0.448229\pi$
$601$	7.93945	0.323857	0.161928	+	0.986803i	$0.448229\pi$
$602$	2.71995	0.110857
$603$	13.7408	0.559570
$604$	−15.8401	−0.644526
$605$	0	0
$606$	6.56009	0.266486
$607$	−38.9797	−1.58214	−0.791069	−	0.611727i	$-0.790475\pi$
$607$	−38.9797	−1.58214	−0.791069	+	0.611727i	$0.790475\pi$
$608$	5.76491	0.233798
$609$	10.4390	0.423009
$610$	0	0
$611$	2.91629	0.117980
$612$	−2.76491	−0.111765
$613$	−28.5142	−1.15168	−0.575839	−	0.817563i	$-0.695325\pi$
$613$	−28.5142	−1.15168	−0.575839	+	0.817563i	$0.695325\pi$
$614$	−10.4702	−0.422542
$615$	0	0
$616$	5.28005	0.212739
$617$	1.07615	0.0433241	0.0216621	−	0.999765i	$-0.493104\pi$
$617$	1.07615	0.0433241	0.0216621	+	0.999765i	$0.493104\pi$
$618$	−5.43991	−0.218825
$619$	−0.719953	−0.0289374	−0.0144687	−	0.999895i	$-0.504606\pi$
$619$	−0.719953	−0.0289374	−0.0144687	+	0.999895i	$0.504606\pi$
$620$	0	0
$621$	3.80139	0.152544
$622$	−9.73841	−0.390475
$623$	−23.0596	−0.923865
$624$	0.235091	0.00941118
$625$	0	0
$626$	9.50046	0.379715
$627$	5.59037	0.223258
$628$	1.34060	0.0534957
$629$	−11.1396	−0.444164
$630$	0	0
$631$	3.81078	0.151705	0.0758524	−	0.997119i	$-0.475832\pi$
$631$	3.81078	0.151705	0.0758524	+	0.997119i	$0.475832\pi$
$632$	9.85952	0.392191
$633$	8.74175	0.347453
$634$	13.0790	0.519434
$635$	0	0
$636$	−3.73555	−0.148124
$637$	−0.0146797	−0.000581632 0
$638$	16.3103	0.645732
$639$	−23.0715	−0.912692
$640$	0	0
$641$	35.7796	1.41321	0.706604	−	0.707609i	$-0.250226\pi$
$641$	35.7796	1.41321	0.706604	+	0.707609i	$0.250226\pi$
$642$	−9.43991	−0.372563
$643$	−11.3094	−0.445999	−0.223000	−	0.974819i	$-0.571585\pi$
$643$	−11.3094	−0.445999	−0.223000	+	0.974819i	$0.571585\pi$
$644$	−3.59037	−0.141480
$645$	0	0
$646$	5.76491	0.226817
$647$	−49.4528	−1.94419	−0.972094	−	0.234591i	$-0.924625\pi$
$647$	−49.4528	−1.94419	−0.972094	+	0.234591i	$0.924625\pi$
$648$	6.93945	0.272607
$649$	17.4693	0.685729
$650$	0	0
$651$	−2.68120	−0.105084
$652$	16.2498	0.636390
$653$	46.1311	1.80525	0.902624	−	0.430429i	$-0.141638\pi$
$653$	46.1311	1.80525	0.902624	+	0.430429i	$0.141638\pi$
$654$	−6.13578	−0.239928
$655$	0	0
$656$	−0.249771	−0.00975191
$657$	−1.34060	−0.0523018
$658$	15.8789	0.619024
$659$	−23.6732	−0.922176	−0.461088	−	0.887355i	$-0.652541\pi$
$659$	−23.6732	−0.922176	−0.461088	+	0.887355i	$0.652541\pi$
$660$	0	0
$661$	−32.1287	−1.24966	−0.624830	−	0.780761i	$-0.714832\pi$
$661$	−32.1287	−1.24966	−0.624830	+	0.780761i	$0.714832\pi$
$662$	24.8851	0.967187
$663$	0.235091	0.00913018
$664$	−17.5298	−0.680289
$665$	0	0
$666$	30.7999	1.19347
$667$	−11.0908	−0.429439
$668$	−2.95035	−0.114152
$669$	−11.2947	−0.436679
$670$	0	0
$671$	−22.7493	−0.878227
$672$	1.28005	0.0493789
$673$	47.7631	1.84113	0.920566	−	0.390588i	$-0.127728\pi$
$673$	47.7631	1.84113	0.920566	+	0.390588i	$0.127728\pi$
$674$	27.5445	1.06097
$675$	0	0
$676$	−12.7649	−0.490958
$677$	−8.82168	−0.339045	−0.169522	−	0.985526i	$-0.554222\pi$
$677$	−8.82168	−0.339045	−0.169522	+	0.985526i	$0.554222\pi$
$678$	3.64380	0.139939
$679$	17.7796	0.682318
$680$	0	0
$681$	−8.47730	−0.324851
$682$	−4.18922	−0.160413
$683$	−28.5142	−1.09107	−0.545533	−	0.838089i	$-0.683673\pi$
$683$	−28.5142	−1.09107	−0.545533	+	0.838089i	$0.683673\pi$
$684$	−15.9394	−0.609460
$685$	0	0
$686$	−18.5601	−0.708628
$687$	0.349078	0.0133182
$688$	1.03028	0.0392789
$689$	−3.73555	−0.142313
$690$	0	0
$691$	−50.4078	−1.91760	−0.958801	−	0.284077i	$-0.908313\pi$
$691$	−50.4078	−1.91760	−0.958801	+	0.284077i	$0.908313\pi$
$692$	−6.14048	−0.233426
$693$	−14.5988	−0.554564
$694$	4.48486	0.170243
$695$	0	0
$696$	3.95413	0.149881
$697$	−0.249771	−0.00946075
$698$	34.2186	1.29519
$699$	−5.35528	−0.202555
$700$	0	0
$701$	10.4702	0.395453	0.197727	−	0.980257i	$-0.436644\pi$
$701$	10.4702	0.395453	0.197727	+	0.980257i	$0.436644\pi$
$702$	−1.35528	−0.0511517
$703$	−64.2186	−2.42205
$704$	2.00000	0.0753778
$705$	0	0
$706$	−4.90917	−0.184759
$707$	35.7190	1.34335
$708$	4.23509	0.159164
$709$	−5.90539	−0.221782	−0.110891	−	0.993833i	$-0.535370\pi$
$709$	−5.90539	−0.221782	−0.110891	+	0.993833i	$0.535370\pi$
$710$	0	0
$711$	−27.2607	−1.02235
$712$	−8.73463	−0.327344
$713$	2.84862	0.106682
$714$	1.28005	0.0479046
$715$	0	0
$716$	−15.5904	−0.582639
$717$	−2.71056	−0.101228
$718$	−13.7796	−0.514250
$719$	−43.8354	−1.63479	−0.817393	−	0.576080i	$-0.804582\pi$
$719$	−43.8354	−1.63479	−0.817393	+	0.576080i	$0.804582\pi$
$720$	0	0
$721$	−29.6197	−1.10310
$722$	14.2342	0.529741
$723$	−4.05872	−0.150945
$724$	4.10929	0.152721
$725$	0	0
$726$	−3.39403	−0.125964
$727$	−6.60597	−0.245002	−0.122501	−	0.992468i	$-0.539091\pi$
$727$	−6.60597	−0.245002	−0.122501	+	0.992468i	$0.539091\pi$
$728$	1.28005	0.0474417
$729$	−15.1211	−0.560041
$730$	0	0
$731$	1.03028	0.0381061
$732$	−5.51514	−0.203845
$733$	44.6188	1.64803	0.824017	−	0.566565i	$-0.191728\pi$
$733$	44.6188	1.64803	0.824017	+	0.566565i	$0.191728\pi$
$734$	−4.39025	−0.162047
$735$	0	0
$736$	−1.35998	−0.0501294
$737$	−9.93945	−0.366124
$738$	0.690594	0.0254211
$739$	34.4149	1.26597	0.632987	−	0.774163i	$-0.281829\pi$
$739$	34.4149	1.26597	0.632987	+	0.774163i	$0.281829\pi$
$740$	0	0
$741$	1.35528	0.0497874
$742$	−20.3397	−0.746693
$743$	−28.0412	−1.02873	−0.514365	−	0.857571i	$-0.671973\pi$
$743$	−28.0412	−1.02873	−0.514365	+	0.857571i	$0.671973\pi$
$744$	−1.01560	−0.0372336
$745$	0	0
$746$	0.220411	0.00806983
$747$	48.4683	1.77336
$748$	2.00000	0.0731272
$749$	−51.3993	−1.87809
$750$	0	0
$751$	−47.4040	−1.72980	−0.864899	−	0.501947i	$-0.832617\pi$
$751$	−47.4040	−1.72980	−0.864899	+	0.501947i	$0.832617\pi$
$752$	6.01468	0.219333
$753$	9.43991	0.344009
$754$	3.95413	0.144001
$755$	0	0
$756$	−7.37935	−0.268385
$757$	−35.9759	−1.30757	−0.653784	−	0.756682i	$-0.726819\pi$
$757$	−35.9759	−1.30757	−0.653784	+	0.756682i	$0.726819\pi$
$758$	26.3103	0.955634
$759$	−1.31880	−0.0478695
$760$	0	0
$761$	13.1807	0.477801	0.238901	−	0.971044i	$-0.423213\pi$
$761$	13.1807	0.477801	0.238901	+	0.971044i	$0.423213\pi$
$762$	−7.17362	−0.259873
$763$	−33.4087	−1.20948
$764$	6.06055	0.219263
$765$	0	0
$766$	36.1433	1.30591
$767$	4.23509	0.152920
$768$	0.484862	0.0174959
$769$	−6.11399	−0.220476	−0.110238	−	0.993905i	$-0.535161\pi$
$769$	−6.11399	−0.220476	−0.110238	+	0.993905i	$0.535161\pi$
$770$	0	0
$771$	6.75871	0.243409
$772$	12.5601	0.452048
$773$	−44.5601	−1.60272	−0.801358	−	0.598186i	$-0.795889\pi$
$773$	−44.5601	−1.60272	−0.801358	+	0.598186i	$0.795889\pi$
$774$	−2.84862	−0.102392
$775$	0	0
$776$	6.73463	0.241759
$777$	−14.2592	−0.511545
$778$	3.77959	0.135505
$779$	−1.43991	−0.0515900
$780$	0	0
$781$	16.6888	0.597171
$782$	−1.35998	−0.0486327
$783$	−22.7952	−0.814633
$784$	−0.0302761	−0.00108129
$785$	0	0
$786$	−1.21193	−0.0432282
$787$	26.3856	0.940543	0.470272	−	0.882522i	$-0.344156\pi$
$787$	26.3856	0.940543	0.470272	+	0.882522i	$0.344156\pi$
$788$	26.0487	0.927948
$789$	−7.88601	−0.280750
$790$	0	0
$791$	19.8401	0.705434
$792$	−5.52982	−0.196494
$793$	−5.51514	−0.195848
$794$	−12.2304	−0.434040
$795$	0	0
$796$	3.37466	0.119612
$797$	−12.4390	−0.440612	−0.220306	−	0.975431i	$-0.570706\pi$
$797$	−12.4390	−0.440612	−0.220306	+	0.975431i	$0.570706\pi$
$798$	7.37935	0.261226
$799$	6.01468	0.212784
$800$	0	0
$801$	24.1505	0.853315
$802$	−11.7796	−0.415952
$803$	0.969724	0.0342208
$804$	−2.40963	−0.0849811
$805$	0	0
$806$	−1.01560	−0.0357729
$807$	5.04496	0.177591
$808$	13.5298	0.475977
$809$	5.96125	0.209586	0.104793	−	0.994494i	$-0.466582\pi$
$809$	5.96125	0.209586	0.104793	+	0.994494i	$0.466582\pi$
$810$	0	0
$811$	−27.8089	−0.976504	−0.488252	−	0.872703i	$-0.662365\pi$
$811$	−27.8089	−0.976504	−0.488252	+	0.872703i	$0.662365\pi$
$812$	21.5298	0.755548
$813$	−11.6509	−0.408616
$814$	−22.2791	−0.780883
$815$	0	0
$816$	0.484862	0.0169736
$817$	5.93945	0.207795
$818$	−15.7649	−0.551207
$819$	−3.53921	−0.123670
$820$	0	0
$821$	−9.05677	−0.316083	−0.158042	−	0.987432i	$-0.550518\pi$
$821$	−9.05677	−0.316083	−0.158042	+	0.987432i	$0.550518\pi$
$822$	0.999083	0.0348470
$823$	6.54828	0.228259	0.114129	−	0.993466i	$-0.463592\pi$
$823$	6.54828	0.228259	0.114129	+	0.993466i	$0.463592\pi$
$824$	−11.2195	−0.390850
$825$	0	0
$826$	23.0596	0.802347
$827$	−15.7115	−0.546341	−0.273171	−	0.961966i	$-0.588072\pi$
$827$	−15.7115	−0.546341	−0.273171	+	0.961966i	$0.588072\pi$
$828$	3.76021	0.130676
$829$	−1.87890	−0.0652567	−0.0326284	−	0.999468i	$-0.510388\pi$
$829$	−1.87890	−0.0652567	−0.0326284	+	0.999468i	$0.510388\pi$
$830$	0	0
$831$	9.18830	0.318739
$832$	0.484862	0.0168096
$833$	−0.0302761	−0.00104900
$834$	−7.55918	−0.261753
$835$	0	0
$836$	11.5298	0.398767
$837$	5.85482	0.202372
$838$	18.1892	0.628336
$839$	−48.6841	−1.68076	−0.840380	−	0.541997i	$-0.817668\pi$
$839$	−48.6841	−1.68076	−0.840380	+	0.541997i	$0.817668\pi$
$840$	0	0
$841$	37.5067	1.29333
$842$	9.03028	0.311204
$843$	9.52453	0.328042
$844$	18.0294	0.620596
$845$	0	0
$846$	−16.6300	−0.571753
$847$	−18.4802	−0.634986
$848$	−7.70436	−0.264569
$849$	12.5067	0.429227
$850$	0	0
$851$	15.1495	0.519320
$852$	4.04587	0.138609
$853$	−35.9494	−1.23089	−0.615443	−	0.788182i	$-0.711023\pi$
$853$	−35.9494	−1.23089	−0.615443	+	0.788182i	$0.711023\pi$
$854$	−30.0294	−1.02758
$855$	0	0
$856$	−19.4693	−0.665446
$857$	13.4158	0.458276	0.229138	−	0.973394i	$-0.426409\pi$
$857$	13.4158	0.458276	0.229138	+	0.973394i	$0.426409\pi$
$858$	0.470182	0.0160518
$859$	−23.8860	−0.814980	−0.407490	−	0.913210i	$-0.633596\pi$
$859$	−23.8860	−0.814980	−0.407490	+	0.913210i	$0.633596\pi$
$860$	0	0
$861$	−0.319718	−0.0108960
$862$	20.4196	0.695495
$863$	15.5979	0.530960	0.265480	−	0.964116i	$-0.414470\pi$
$863$	15.5979	0.530960	0.265480	+	0.964116i	$0.414470\pi$
$864$	−2.79518	−0.0950941
$865$	0	0
$866$	−11.5904	−0.393857
$867$	0.484862	0.0164668
$868$	−5.52982	−0.187694
$869$	19.7190	0.668922
$870$	0	0
$871$	−2.40963	−0.0816472
$872$	−12.6547	−0.428542
$873$	−18.6206	−0.630213
$874$	−7.84014	−0.265197
$875$	0	0
$876$	0.235091	0.00794299
$877$	−33.3893	−1.12748	−0.563739	−	0.825953i	$-0.690638\pi$
$877$	−33.3893	−1.12748	−0.563739	+	0.825953i	$0.690638\pi$
$878$	−2.01938	−0.0681507
$879$	−11.1149	−0.374896
$880$	0	0
$881$	−35.1202	−1.18323	−0.591615	−	0.806221i	$-0.701509\pi$
$881$	−35.1202	−1.18323	−0.591615	+	0.806221i	$0.701509\pi$
$882$	0.0837106	0.00281868
$883$	22.2110	0.747460	0.373730	−	0.927537i	$-0.378079\pi$
$883$	22.2110	0.747460	0.373730	+	0.927537i	$0.378079\pi$
$884$	0.484862	0.0163077
$885$	0	0
$886$	27.4087	0.920814
$887$	5.17076	0.173617	0.0868085	−	0.996225i	$-0.472333\pi$
$887$	5.17076	0.173617	0.0868085	+	0.996225i	$0.472333\pi$
$888$	−5.40115	−0.181251
$889$	−39.0596	−1.31002
$890$	0	0
$891$	13.8789	0.464960
$892$	−23.2947	−0.779965
$893$	34.6741	1.16032
$894$	4.84862	0.162162
$895$	0	0
$896$	2.64002	0.0881970
$897$	−0.319718	−0.0106751
$898$	29.7190	0.991737
$899$	−17.0819	−0.569713
$900$	0	0
$901$	−7.70436	−0.256669
$902$	−0.499542	−0.0166329
$903$	1.31880	0.0438870
$904$	7.51514	0.249950
$905$	0	0
$906$	−7.68028	−0.255160
$907$	3.85482	0.127997	0.0639986	−	0.997950i	$-0.479615\pi$
$907$	3.85482	0.127997	0.0639986	+	0.997950i	$0.479615\pi$
$908$	−17.4839	−0.580225
$909$	−37.4087	−1.24077
$910$	0	0
$911$	−22.6400	−0.750097	−0.375049	−	0.927005i	$-0.622374\pi$
$911$	−22.6400	−0.750097	−0.375049	+	0.927005i	$0.622374\pi$
$912$	2.79518	0.0925578
$913$	−35.0596	−1.16030
$914$	−39.4693	−1.30553
$915$	0	0
$916$	0.719953	0.0237879
$917$	−6.59885	−0.217913
$918$	−2.79518	−0.0922549
$919$	31.5298	1.04007	0.520036	−	0.854144i	$-0.325918\pi$
$919$	31.5298	1.04007	0.520036	+	0.854144i	$0.325918\pi$
$920$	0	0
$921$	−5.07659	−0.167279
$922$	14.6888	0.483749
$923$	4.04587	0.133172
$924$	2.56009	0.0842209
$925$	0	0
$926$	−35.1055	−1.15364
$927$	31.0209	1.01886
$928$	8.15516	0.267706
$929$	−11.1589	−0.366113	−0.183057	−	0.983102i	$-0.558599\pi$
$929$	−11.1589	−0.366113	−0.183057	+	0.983102i	$0.558599\pi$
$930$	0	0
$931$	−0.174539	−0.00572028
$932$	−11.0450	−0.361790
$933$	−4.72179	−0.154584
$934$	9.96881	0.326189
$935$	0	0
$936$	−1.34060	−0.0438189
$937$	−24.5307	−0.801384	−0.400692	−	0.916213i	$-0.631230\pi$
$937$	−24.5307	−0.801384	−0.400692	+	0.916213i	$0.631230\pi$
$938$	−13.1202	−0.428389
$939$	4.60641	0.150325
$940$	0	0
$941$	35.3747	1.15318	0.576590	−	0.817033i	$-0.304383\pi$
$941$	35.3747	1.15318	0.576590	+	0.817033i	$0.304383\pi$
$942$	0.650006	0.0211783
$943$	0.339682	0.0110616
$944$	8.73463	0.284288
$945$	0	0
$946$	2.06055	0.0669943
$947$	2.23509	0.0726307	0.0363154	−	0.999340i	$-0.488438\pi$
$947$	2.23509	0.0726307	0.0363154	+	0.999340i	$0.488438\pi$
$948$	4.78051	0.155264
$949$	0.235091	0.00763138
$950$	0	0
$951$	6.34152	0.205638
$952$	2.64002	0.0855637
$953$	−5.65092	−0.183051	−0.0915257	−	0.995803i	$-0.529174\pi$
$953$	−5.65092	−0.183051	−0.0915257	+	0.995803i	$0.529174\pi$
$954$	21.3018	0.689673
$955$	0	0
$956$	−5.59037	−0.180805
$957$	7.90826	0.255638
$958$	−2.28383	−0.0737871
$959$	5.43991	0.175664
$960$	0	0
$961$	−26.6126	−0.858471
$962$	−5.40115	−0.174140
$963$	53.8307	1.73467
$964$	−8.37088	−0.269608
$965$	0	0
$966$	−1.74083	−0.0560104
$967$	−40.9991	−1.31844	−0.659221	−	0.751949i	$-0.729114\pi$
$967$	−40.9991	−1.31844	−0.659221	+	0.751949i	$0.729114\pi$
$968$	−7.00000	−0.224989
$969$	2.79518	0.0897943
$970$	0	0
$971$	−45.3846	−1.45646	−0.728231	−	0.685332i	$-0.759657\pi$
$971$	−45.3846	−1.45646	−0.728231	+	0.685332i	$0.759657\pi$
$972$	11.7502	0.376889
$973$	−41.1589	−1.31950
$974$	10.8292	0.346991
$975$	0	0
$976$	−11.3747	−0.364094
$977$	4.72752	0.151247	0.0756233	−	0.997136i	$-0.475905\pi$
$977$	4.72752	0.151247	0.0756233	+	0.997136i	$0.475905\pi$
$978$	7.87890	0.251939
$979$	−17.4693	−0.558320
$980$	0	0
$981$	34.9891	1.11712
$982$	24.7952	0.791246
$983$	−14.3297	−0.457046	−0.228523	−	0.973538i	$-0.573390\pi$
$983$	−14.3297	−0.457046	−0.228523	+	0.973538i	$0.573390\pi$
$984$	−0.121104	−0.00386067
$985$	0	0
$986$	8.15516	0.259713
$987$	7.69907	0.245064
$988$	2.79518	0.0889267
$989$	−1.40115	−0.0445540
$990$	0	0
$991$	16.8827	0.536296	0.268148	−	0.963378i	$-0.413588\pi$
$991$	16.8827	0.536296	0.268148	+	0.963378i	$0.413588\pi$
$992$	−2.09461	−0.0665039
$993$	12.0658	0.382898
$994$	22.0294	0.698729
$995$	0	0
$996$	−8.49954	−0.269318
$997$	−18.5189	−0.586500	−0.293250	−	0.956036i	$-0.594737\pi$
$997$	−18.5189	−0.586500	−0.293250	+	0.956036i	$0.594737\pi$
$998$	5.15138	0.163064
$999$	31.1371	0.985136

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.a.q.1.2		3
3.2	odd	2		7650.2.a.dj.1.3		3
4.3	odd	2		6800.2.a.bk.1.2		3
5.2	odd	4		170.2.c.b.69.5	yes	6
5.3	odd	4		170.2.c.b.69.2	✓	6
5.4	even	2		850.2.a.p.1.2		3
15.2	even	4		1530.2.d.g.919.1		6
15.8	even	4		1530.2.d.g.919.4		6
15.14	odd	2		7650.2.a.do.1.1		3
20.3	even	4		1360.2.e.c.1089.3		6
20.7	even	4		1360.2.e.c.1089.4		6
20.19	odd	2		6800.2.a.bp.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.c.b.69.2	✓	6	5.3	odd	4
170.2.c.b.69.5	yes	6	5.2	odd	4
850.2.a.p.1.2		3	5.4	even	2
850.2.a.q.1.2		3	1.1	even	1	trivial
1360.2.e.c.1089.3		6	20.3	even	4
1360.2.e.c.1089.4		6	20.7	even	4
1530.2.d.g.919.1		6	15.2	even	4
1530.2.d.g.919.4		6	15.8	even	4
6800.2.a.bk.1.2		3	4.3	odd	2
6800.2.a.bp.1.2		3	20.19	odd	2
7650.2.a.dj.1.3		3	3.2	odd	2
7650.2.a.do.1.1		3	15.14	odd	2

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

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Groups

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	850.2.a.q.1.2

Level	$850$
Weight	$2$
Character	850.1
Self dual	yes
Analytic conductor	$6.787$
Analytic rank	$0$
Dimension	$3$
CM	no
Inner twists	$1$