LMFDB - Embedded newform 320.8.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,8,Mod(1,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("320.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	320.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:	$99.9632081549$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	320.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+48.0000 q^{3} -125.000 q^{5} -1644.00 q^{7} +117.000 q^{9} -172.000 q^{11} -3862.00 q^{13} -6000.00 q^{15} -12254.0 q^{17} +25940.0 q^{19} -78912.0 q^{21} +12972.0 q^{23} +15625.0 q^{25} -99360.0 q^{27} +81610.0 q^{29} -156888. q^{31} -8256.00 q^{33} +205500. q^{35} -110126. q^{37} -185376. q^{39} +467882. q^{41} +499208. q^{43} -14625.0 q^{45} -396884. q^{47} +1.87919e6 q^{49} -588192. q^{51} +1.28050e6 q^{53} +21500.0 q^{55} +1.24512e6 q^{57} +1.33742e6 q^{59} +923978. q^{61} -192348. q^{63} +482750. q^{65} +797304. q^{67} +622656. q^{69} +5.10339e6 q^{71} -4.26748e6 q^{73} +750000. q^{75} +282768. q^{77} -960.000 q^{79} -5.02516e6 q^{81} -6.14083e6 q^{83} +1.53175e6 q^{85} +3.91728e6 q^{87} +2.01057e6 q^{89} +6.34913e6 q^{91} -7.53062e6 q^{93} -3.24250e6 q^{95} -4.88193e6 q^{97} -20124.0 q^{99} +O(q^{100})$

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
$3$	48.0000	1.02640	0.513200	−	0.858269i	$-0.328460\pi$
$3$	48.0000	1.02640	0.513200	+	0.858269i	$0.328460\pi$
$4$	0	0
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	0	0
$7$	−1644.00	−1.81158	−0.905792	−	0.423722i	$-0.860723\pi$
$7$	−1644.00	−1.81158	−0.905792	+	0.423722i	$0.860723\pi$
$8$	0	0
$9$	117.000	0.0534979
$10$	0	0
$11$	−172.000	−0.0389631	−0.0194816	−	0.999810i	$-0.506202\pi$
$11$	−172.000	−0.0389631	−0.0194816	+	0.999810i	$0.506202\pi$
$12$	0	0
$13$	−3862.00	−0.487540	−0.243770	−	0.969833i	$-0.578384\pi$
$13$	−3862.00	−0.487540	−0.243770	+	0.969833i	$0.578384\pi$
$14$	0	0
$15$	−6000.00	−0.459020
$16$	0	0
$17$	−12254.0	−0.604932	−0.302466	−	0.953160i	$-0.597810\pi$
$17$	−12254.0	−0.604932	−0.302466	+	0.953160i	$0.597810\pi$
$18$	0	0
$19$	25940.0	0.867626	0.433813	−	0.901003i	$-0.357168\pi$
$19$	25940.0	0.867626	0.433813	+	0.901003i	$0.357168\pi$
$20$	0	0
$21$	−78912.0	−1.85941
$22$	0	0
$23$	12972.0	0.222310	0.111155	−	0.993803i	$-0.464545\pi$
$23$	12972.0	0.222310	0.111155	+	0.993803i	$0.464545\pi$
$24$	0	0
$25$	15625.0	0.200000
$26$	0	0
$27$	−99360.0	−0.971490
$28$	0	0
$29$	81610.0	0.621370	0.310685	−	0.950513i	$-0.399442\pi$
$29$	81610.0	0.621370	0.310685	+	0.950513i	$0.399442\pi$
$30$	0	0
$31$	−156888.	−0.945853	−0.472927	−	0.881102i	$-0.656802\pi$
$31$	−156888.	−0.945853	−0.472927	+	0.881102i	$0.656802\pi$
$32$	0	0
$33$	−8256.00	−0.0399918
$34$	0	0
$35$	205500.	0.810165
$36$	0	0
$37$	−110126.	−0.357424	−0.178712	−	0.983901i	$-0.557193\pi$
$37$	−110126.	−0.357424	−0.178712	+	0.983901i	$0.557193\pi$
$38$	0	0
$39$	−185376.	−0.500412
$40$	0	0
$41$	467882.	1.06021	0.530106	−	0.847931i	$-0.322152\pi$
$41$	467882.	1.06021	0.530106	+	0.847931i	$0.322152\pi$
$42$	0	0
$43$	499208.	0.957507	0.478753	−	0.877949i	$-0.341089\pi$
$43$	499208.	0.957507	0.478753	+	0.877949i	$0.341089\pi$
$44$	0	0
$45$	−14625.0	−0.0239250
$46$	0	0
$47$	−396884.	−0.557598	−0.278799	−	0.960349i	$-0.589936\pi$
$47$	−396884.	−0.557598	−0.278799	+	0.960349i	$0.589936\pi$
$48$	0	0
$49$	1.87919e6	2.28184
$50$	0	0
$51$	−588192.	−0.620903
$52$	0	0
$53$	1.28050e6	1.18144	0.590722	−	0.806875i	$-0.298843\pi$
$53$	1.28050e6	1.18144	0.590722	+	0.806875i	$0.298843\pi$
$54$	0	0
$55$	21500.0	0.0174248
$56$	0	0
$57$	1.24512e6	0.890531
$58$	0	0
$59$	1.33742e6	0.847785	0.423893	−	0.905712i	$-0.360663\pi$
$59$	1.33742e6	0.847785	0.423893	+	0.905712i	$0.360663\pi$
$60$	0	0
$61$	923978.	0.521203	0.260602	−	0.965446i	$-0.416079\pi$
$61$	923978.	0.521203	0.260602	+	0.965446i	$0.416079\pi$
$62$	0	0
$63$	−192348.	−0.0969161
$64$	0	0
$65$	482750.	0.218035
$66$	0	0
$67$	797304.	0.323864	0.161932	−	0.986802i	$-0.448228\pi$
$67$	797304.	0.323864	0.161932	+	0.986802i	$0.448228\pi$
$68$	0	0
$69$	622656.	0.228179
$70$	0	0
$71$	5.10339e6	1.69221	0.846106	−	0.533015i	$-0.178941\pi$
$71$	5.10339e6	1.69221	0.846106	+	0.533015i	$0.178941\pi$
$72$	0	0
$73$	−4.26748e6	−1.28393	−0.641965	−	0.766734i	$-0.721881\pi$
$73$	−4.26748e6	−1.28393	−0.641965	+	0.766734i	$0.721881\pi$
$74$	0	0
$75$	750000.	0.205280
$76$	0	0
$77$	282768.	0.0705850
$78$	0	0
$79$	−960.000	−0.000219067 0	−0.000109533	−	1.00000i	$-0.500035\pi$
$79$	−960.000	−0.000219067 0	−0.000109533		1.00000i	$0.500035\pi$
$80$	0	0
$81$	−5.02516e6	−1.05064
$82$	0	0
$83$	−6.14083e6	−1.17884	−0.589419	−	0.807828i	$-0.700643\pi$
$83$	−6.14083e6	−1.17884	−0.589419	+	0.807828i	$0.700643\pi$
$84$	0	0
$85$	1.53175e6	0.270534
$86$	0	0
$87$	3.91728e6	0.637775
$88$	0	0
$89$	2.01057e6	0.302311	0.151156	−	0.988510i	$-0.451701\pi$
$89$	2.01057e6	0.302311	0.151156	+	0.988510i	$0.451701\pi$
$90$	0	0
$91$	6.34913e6	0.883221
$92$	0	0
$93$	−7.53062e6	−0.970824
$94$	0	0
$95$	−3.24250e6	−0.388014
$96$	0	0
$97$	−4.88193e6	−0.543114	−0.271557	−	0.962422i	$-0.587539\pi$
$97$	−4.88193e6	−0.543114	−0.271557	+	0.962422i	$0.587539\pi$
$98$	0	0
$99$	−20124.0	−0.00208445
$100$	0	0
$101$	−9.72670e6	−0.939379	−0.469689	−	0.882832i	$-0.655634\pi$
$101$	−9.72670e6	−0.939379	−0.469689	+	0.882832i	$0.655634\pi$
$102$	0	0
$103$	1.63151e7	1.47115	0.735577	−	0.677441i	$-0.236911\pi$
$103$	1.63151e7	1.47115	0.735577	+	0.677441i	$0.236911\pi$
$104$	0	0
$105$	9.86400e6	0.831554
$106$	0	0
$107$	4.08974e6	0.322740	0.161370	−	0.986894i	$-0.448409\pi$
$107$	4.08974e6	0.322740	0.161370	+	0.986894i	$0.448409\pi$
$108$	0	0
$109$	2.68318e7	1.98453	0.992263	−	0.124158i	$-0.0396228\pi$
$109$	2.68318e7	1.98453	0.992263	+	0.124158i	$0.0396228\pi$
$110$	0	0
$111$	−5.28605e6	−0.366860
$112$	0	0
$113$	−1.74810e7	−1.13971	−0.569853	−	0.821747i	$-0.693000\pi$
$113$	−1.74810e7	−1.13971	−0.569853	+	0.821747i	$0.693000\pi$
$114$	0	0
$115$	−1.62150e6	−0.0994202
$116$	0	0
$117$	−451854.	−0.0260824
$118$	0	0
$119$	2.01456e7	1.09589
$120$	0	0
$121$	−1.94576e7	−0.998482
$122$	0	0
$123$	2.24583e7	1.08820
$124$	0	0
$125$	−1.95312e6	−0.0894427
$126$	0	0
$127$	−1.25018e7	−0.541575	−0.270787	−	0.962639i	$-0.587284\pi$
$127$	−1.25018e7	−0.541575	−0.270787	+	0.962639i	$0.587284\pi$
$128$	0	0
$129$	2.39620e7	0.982786
$130$	0	0
$131$	7.75619e6	0.301439	0.150719	−	0.988577i	$-0.451841\pi$
$131$	7.75619e6	0.301439	0.150719	+	0.988577i	$0.451841\pi$
$132$	0	0
$133$	−4.26454e7	−1.57178
$134$	0	0
$135$	1.24200e7	0.434464
$136$	0	0
$137$	3.61720e7	1.20185	0.600926	−	0.799305i	$-0.294799\pi$
$137$	3.61720e7	1.20185	0.600926	+	0.799305i	$0.294799\pi$
$138$	0	0
$139$	−1.09092e7	−0.344542	−0.172271	−	0.985050i	$-0.555110\pi$
$139$	−1.09092e7	−0.344542	−0.172271	+	0.985050i	$0.555110\pi$
$140$	0	0
$141$	−1.90504e7	−0.572319
$142$	0	0
$143$	664264.	0.0189961
$144$	0	0
$145$	−1.02012e7	−0.277885
$146$	0	0
$147$	9.02013e7	2.34208
$148$	0	0
$149$	3.64580e7	0.902904	0.451452	−	0.892295i	$-0.350906\pi$
$149$	3.64580e7	0.902904	0.451452	+	0.892295i	$0.350906\pi$
$150$	0	0
$151$	7.18955e6	0.169935	0.0849674	−	0.996384i	$-0.472921\pi$
$151$	7.18955e6	0.169935	0.0849674	+	0.996384i	$0.472921\pi$
$152$	0	0
$153$	−1.43372e6	−0.0323626
$154$	0	0
$155$	1.96110e7	0.422998
$156$	0	0
$157$	−8.79932e7	−1.81468	−0.907341	−	0.420396i	$-0.861891\pi$
$157$	−8.79932e7	−1.81468	−0.907341	+	0.420396i	$0.861891\pi$
$158$	0	0
$159$	6.14639e7	1.21264
$160$	0	0
$161$	−2.13260e7	−0.402734
$162$	0	0
$163$	5.48875e7	0.992697	0.496349	−	0.868123i	$-0.334674\pi$
$163$	5.48875e7	0.992697	0.496349	+	0.868123i	$0.334674\pi$
$164$	0	0
$165$	1.03200e6	0.0178849
$166$	0	0
$167$	8.61460e6	0.143129	0.0715644	−	0.997436i	$-0.477201\pi$
$167$	8.61460e6	0.143129	0.0715644	+	0.997436i	$0.477201\pi$
$168$	0	0
$169$	−4.78335e7	−0.762304
$170$	0	0
$171$	3.03498e6	0.0464162
$172$	0	0
$173$	5.12524e7	0.752580	0.376290	−	0.926502i	$-0.377200\pi$
$173$	5.12524e7	0.752580	0.376290	+	0.926502i	$0.377200\pi$
$174$	0	0
$175$	−2.56875e7	−0.362317
$176$	0	0
$177$	6.41962e7	0.870167
$178$	0	0
$179$	5.01627e7	0.653725	0.326862	−	0.945072i	$-0.394009\pi$
$179$	5.01627e7	0.653725	0.326862	+	0.945072i	$0.394009\pi$
$180$	0	0
$181$	−6.90817e7	−0.865940	−0.432970	−	0.901408i	$-0.642534\pi$
$181$	−6.90817e7	−0.865940	−0.432970	+	0.901408i	$0.642534\pi$
$182$	0	0
$183$	4.43509e7	0.534963
$184$	0	0
$185$	1.37658e7	0.159845
$186$	0	0
$187$	2.10769e6	0.0235701
$188$	0	0
$189$	1.63348e8	1.75994
$190$	0	0
$191$	1.54745e8	1.60695	0.803473	−	0.595342i	$-0.202983\pi$
$191$	1.54745e8	1.60695	0.803473	+	0.595342i	$0.202983\pi$
$192$	0	0
$193$	−1.59406e7	−0.159607	−0.0798037	−	0.996811i	$-0.525429\pi$
$193$	−1.59406e7	−0.159607	−0.0798037	+	0.996811i	$0.525429\pi$
$194$	0	0
$195$	2.31720e7	0.223791
$196$	0	0
$197$	1.68188e8	1.56734	0.783670	−	0.621177i	$-0.213345\pi$
$197$	1.68188e8	1.56734	0.783670	+	0.621177i	$0.213345\pi$
$198$	0	0
$199$	1.77773e8	1.59911	0.799556	−	0.600591i	$-0.205068\pi$
$199$	1.77773e8	1.59911	0.799556	+	0.600591i	$0.205068\pi$
$200$	0	0
$201$	3.82706e7	0.332414
$202$	0	0
$203$	−1.34167e8	−1.12566
$204$	0	0
$205$	−5.84852e7	−0.474141
$206$	0	0
$207$	1.51772e6	0.0118931
$208$	0	0
$209$	−4.46168e6	−0.0338054
$210$	0	0
$211$	1.61996e8	1.18718	0.593590	−	0.804767i	$-0.297710\pi$
$211$	1.61996e8	1.18718	0.593590	+	0.804767i	$0.297710\pi$
$212$	0	0
$213$	2.44963e8	1.73689
$214$	0	0
$215$	−6.24010e7	−0.428210
$216$	0	0
$217$	2.57924e8	1.71349
$218$	0	0
$219$	−2.04839e8	−1.31783
$220$	0	0
$221$	4.73249e7	0.294929
$222$	0	0
$223$	1.75932e7	0.106237	0.0531187	−	0.998588i	$-0.483084\pi$
$223$	1.75932e7	0.106237	0.0531187	+	0.998588i	$0.483084\pi$
$224$	0	0
$225$	1.82812e6	0.0106996
$226$	0	0
$227$	2.03036e8	1.15208	0.576039	−	0.817422i	$-0.304597\pi$
$227$	2.03036e8	1.15208	0.576039	+	0.817422i	$0.304597\pi$
$228$	0	0
$229$	−1.59559e8	−0.878005	−0.439003	−	0.898486i	$-0.644668\pi$
$229$	−1.59559e8	−0.878005	−0.439003	+	0.898486i	$0.644668\pi$
$230$	0	0
$231$	1.35729e7	0.0724485
$232$	0	0
$233$	−1.94985e7	−0.100985	−0.0504924	−	0.998724i	$-0.516079\pi$
$233$	−1.94985e7	−0.100985	−0.0504924	+	0.998724i	$0.516079\pi$
$234$	0	0
$235$	4.96105e7	0.249365
$236$	0	0
$237$	−46080.0	−0.000224850 0
$238$	0	0
$239$	−1.60220e8	−0.759146	−0.379573	−	0.925162i	$-0.623929\pi$
$239$	−1.60220e8	−0.759146	−0.379573	+	0.925162i	$0.623929\pi$
$240$	0	0
$241$	−3.78779e8	−1.74311	−0.871557	−	0.490294i	$-0.836890\pi$
$241$	−3.78779e8	−1.74311	−0.871557	+	0.490294i	$0.836890\pi$
$242$	0	0
$243$	−2.39073e7	−0.106883
$244$	0	0
$245$	−2.34899e8	−1.02047
$246$	0	0
$247$	−1.00180e8	−0.423002
$248$	0	0
$249$	−2.94760e8	−1.20996
$250$	0	0
$251$	−1.61304e8	−0.643855	−0.321927	−	0.946764i	$-0.604331\pi$
$251$	−1.61304e8	−0.643855	−0.321927	+	0.946764i	$0.604331\pi$
$252$	0	0
$253$	−2.23118e6	−0.00866191
$254$	0	0
$255$	7.35240e7	0.277676
$256$	0	0
$257$	2.27387e8	0.835603	0.417801	−	0.908538i	$-0.362801\pi$
$257$	2.27387e8	0.835603	0.417801	+	0.908538i	$0.362801\pi$
$258$	0	0
$259$	1.81047e8	0.647504
$260$	0	0
$261$	9.54837e6	0.0332420
$262$	0	0
$263$	4.57728e8	1.55154	0.775768	−	0.631018i	$-0.217363\pi$
$263$	4.57728e8	1.55154	0.775768	+	0.631018i	$0.217363\pi$
$264$	0	0
$265$	−1.60062e8	−0.528358
$266$	0	0
$267$	9.65074e7	0.310292
$268$	0	0
$269$	−4.67286e8	−1.46369	−0.731847	−	0.681469i	$-0.761341\pi$
$269$	−4.67286e8	−1.46369	−0.731847	+	0.681469i	$0.761341\pi$
$270$	0	0
$271$	−4.45932e7	−0.136106	−0.0680528	−	0.997682i	$-0.521679\pi$
$271$	−4.45932e7	−0.136106	−0.0680528	+	0.997682i	$0.521679\pi$
$272$	0	0
$273$	3.04758e8	0.906538
$274$	0	0
$275$	−2.68750e6	−0.00779263
$276$	0	0
$277$	−3.16657e8	−0.895179	−0.447590	−	0.894239i	$-0.647717\pi$
$277$	−3.16657e8	−0.895179	−0.447590	+	0.894239i	$0.647717\pi$
$278$	0	0
$279$	−1.83559e7	−0.0506012
$280$	0	0
$281$	−2.25818e8	−0.607136	−0.303568	−	0.952810i	$-0.598178\pi$
$281$	−2.25818e8	−0.607136	−0.303568	+	0.952810i	$0.598178\pi$
$282$	0	0
$283$	−2.08210e7	−0.0546072	−0.0273036	−	0.999627i	$-0.508692\pi$
$283$	−2.08210e7	−0.0546072	−0.0273036	+	0.999627i	$0.508692\pi$
$284$	0	0
$285$	−1.55640e8	−0.398258
$286$	0	0
$287$	−7.69198e8	−1.92066
$288$	0	0
$289$	−2.60178e8	−0.634057
$290$	0	0
$291$	−2.34333e8	−0.557452
$292$	0	0
$293$	1.78825e8	0.415329	0.207665	−	0.978200i	$-0.433414\pi$
$293$	1.78825e8	0.415329	0.207665	+	0.978200i	$0.433414\pi$
$294$	0	0
$295$	−1.67178e8	−0.379141
$296$	0	0
$297$	1.70899e7	0.0378523
$298$	0	0
$299$	−5.00979e7	−0.108385
$300$	0	0
$301$	−8.20698e8	−1.73461
$302$	0	0
$303$	−4.66882e8	−0.964179
$304$	0	0
$305$	−1.15497e8	−0.233089
$306$	0	0
$307$	8.55159e7	0.168680	0.0843398	−	0.996437i	$-0.473122\pi$
$307$	8.55159e7	0.168680	0.0843398	+	0.996437i	$0.473122\pi$
$308$	0	0
$309$	7.83122e8	1.50999
$310$	0	0
$311$	−4.84706e8	−0.913728	−0.456864	−	0.889537i	$-0.651027\pi$
$311$	−4.84706e8	−0.913728	−0.456864	+	0.889537i	$0.651027\pi$
$312$	0	0
$313$	5.70821e8	1.05219	0.526096	−	0.850425i	$-0.323655\pi$
$313$	5.70821e8	1.05219	0.526096	+	0.850425i	$0.323655\pi$
$314$	0	0
$315$	2.40435e7	0.0433422
$316$	0	0
$317$	5.50191e8	0.970076	0.485038	−	0.874493i	$-0.338806\pi$
$317$	5.50191e8	0.970076	0.485038	+	0.874493i	$0.338806\pi$
$318$	0	0
$319$	−1.40369e7	−0.0242105
$320$	0	0
$321$	1.96308e8	0.331261
$322$	0	0
$323$	−3.17869e8	−0.524855
$324$	0	0
$325$	−6.03438e7	−0.0975081
$326$	0	0
$327$	1.28792e9	2.03692
$328$	0	0
$329$	6.52477e8	1.01014
$330$	0	0
$331$	9.39839e8	1.42448	0.712238	−	0.701938i	$-0.247681\pi$
$331$	9.39839e8	1.42448	0.712238	+	0.701938i	$0.247681\pi$
$332$	0	0
$333$	−1.28847e7	−0.0191215
$334$	0	0
$335$	−9.96630e7	−0.144836
$336$	0	0
$337$	5.33632e8	0.759516	0.379758	−	0.925086i	$-0.376007\pi$
$337$	5.33632e8	0.759516	0.379758	+	0.925086i	$0.376007\pi$
$338$	0	0
$339$	−8.39090e8	−1.16979
$340$	0	0
$341$	2.69847e7	0.0368534
$342$	0	0
$343$	−1.73549e9	−2.32216
$344$	0	0
$345$	−7.78320e7	−0.102045
$346$	0	0
$347$	−1.07934e9	−1.38677	−0.693385	−	0.720567i	$-0.743882\pi$
$347$	−1.07934e9	−1.38677	−0.693385	+	0.720567i	$0.743882\pi$
$348$	0	0
$349$	4.27217e8	0.537972	0.268986	−	0.963144i	$-0.413311\pi$
$349$	4.27217e8	0.537972	0.268986	+	0.963144i	$0.413311\pi$
$350$	0	0
$351$	3.83728e8	0.473641
$352$	0	0
$353$	−1.48966e9	−1.80250	−0.901250	−	0.433299i	$-0.857350\pi$
$353$	−1.48966e9	−1.80250	−0.901250	+	0.433299i	$0.857350\pi$
$354$	0	0
$355$	−6.37924e8	−0.756780
$356$	0	0
$357$	9.66988e8	1.12482
$358$	0	0
$359$	8.41275e8	0.959638	0.479819	−	0.877367i	$-0.340702\pi$
$359$	8.41275e8	0.959638	0.479819	+	0.877367i	$0.340702\pi$
$360$	0	0
$361$	−2.20988e8	−0.247226
$362$	0	0
$363$	−9.33964e8	−1.02484
$364$	0	0
$365$	5.33435e8	0.574191
$366$	0	0
$367$	−7.50462e8	−0.792496	−0.396248	−	0.918143i	$-0.629688\pi$
$367$	−7.50462e8	−0.792496	−0.396248	+	0.918143i	$0.629688\pi$
$368$	0	0
$369$	5.47422e7	0.0567192
$370$	0	0
$371$	−2.10514e9	−2.14029
$372$	0	0
$373$	−1.71074e8	−0.170688	−0.0853439	−	0.996352i	$-0.527199\pi$
$373$	−1.71074e8	−0.170688	−0.0853439	+	0.996352i	$0.527199\pi$
$374$	0	0
$375$	−9.37500e7	−0.0918040
$376$	0	0
$377$	−3.15178e8	−0.302943
$378$	0	0
$379$	−4.66239e7	−0.0439918	−0.0219959	−	0.999758i	$-0.507002\pi$
$379$	−4.66239e7	−0.0439918	−0.0219959	+	0.999758i	$0.507002\pi$
$380$	0	0
$381$	−6.00085e8	−0.555872
$382$	0	0
$383$	−4.42266e8	−0.402242	−0.201121	−	0.979566i	$-0.564458\pi$
$383$	−4.42266e8	−0.402242	−0.201121	+	0.979566i	$0.564458\pi$
$384$	0	0
$385$	−3.53460e7	−0.0315666
$386$	0	0
$387$	5.84073e7	0.0512247
$388$	0	0
$389$	4.64033e8	0.399691	0.199846	−	0.979827i	$-0.435956\pi$
$389$	4.64033e8	0.399691	0.199846	+	0.979827i	$0.435956\pi$
$390$	0	0
$391$	−1.58959e8	−0.134483
$392$	0	0
$393$	3.72297e8	0.309397
$394$	0	0
$395$	120000.	9.79696e−5 0
$396$	0	0
$397$	3.17792e8	0.254904	0.127452	−	0.991845i	$-0.459320\pi$
$397$	3.17792e8	0.254904	0.127452	+	0.991845i	$0.459320\pi$
$398$	0	0
$399$	−2.04698e9	−1.61327
$400$	0	0
$401$	−1.19563e9	−0.925958	−0.462979	−	0.886369i	$-0.653219\pi$
$401$	−1.19563e9	−0.925958	−0.462979	+	0.886369i	$0.653219\pi$
$402$	0	0
$403$	6.05901e8	0.461142
$404$	0	0
$405$	6.28145e8	0.469859
$406$	0	0
$407$	1.89417e7	0.0139264
$408$	0	0
$409$	2.21305e9	1.59941	0.799704	−	0.600395i	$-0.204990\pi$
$409$	2.21305e9	1.59941	0.799704	+	0.600395i	$0.204990\pi$
$410$	0	0
$411$	1.73626e9	1.23358
$412$	0	0
$413$	−2.19872e9	−1.53583
$414$	0	0
$415$	7.67604e8	0.527192
$416$	0	0
$417$	−5.23643e8	−0.353638
$418$	0	0
$419$	8.02299e8	0.532828	0.266414	−	0.963859i	$-0.414161\pi$
$419$	8.02299e8	0.532828	0.266414	+	0.963859i	$0.414161\pi$
$420$	0	0
$421$	−3.44713e7	−0.0225149	−0.0112575	−	0.999937i	$-0.503583\pi$
$421$	−3.44713e7	−0.0225149	−0.0112575	+	0.999937i	$0.503583\pi$
$422$	0	0
$423$	−4.64354e7	−0.0298303
$424$	0	0
$425$	−1.91469e8	−0.120986
$426$	0	0
$427$	−1.51902e9	−0.944204
$428$	0	0
$429$	3.18847e7	0.0194976
$430$	0	0
$431$	1.72692e9	1.03897	0.519485	−	0.854480i	$-0.326124\pi$
$431$	1.72692e9	1.03897	0.519485	+	0.854480i	$0.326124\pi$
$432$	0	0
$433$	4.88308e8	0.289059	0.144529	−	0.989501i	$-0.453833\pi$
$433$	4.88308e8	0.289059	0.144529	+	0.989501i	$0.453833\pi$
$434$	0	0
$435$	−4.89660e8	−0.285221
$436$	0	0
$437$	3.36494e8	0.192882
$438$	0	0
$439$	−2.88640e9	−1.62828	−0.814142	−	0.580665i	$-0.802793\pi$
$439$	−2.88640e9	−1.62828	−0.814142	+	0.580665i	$0.802793\pi$
$440$	0	0
$441$	2.19866e8	0.122074
$442$	0	0
$443$	−9.26583e8	−0.506374	−0.253187	−	0.967417i	$-0.581479\pi$
$443$	−9.26583e8	−0.506374	−0.253187	+	0.967417i	$0.581479\pi$
$444$	0	0
$445$	−2.51321e8	−0.135198
$446$	0	0
$447$	1.74999e9	0.926741
$448$	0	0
$449$	1.35535e9	0.706627	0.353313	−	0.935505i	$-0.385055\pi$
$449$	1.35535e9	0.706627	0.353313	+	0.935505i	$0.385055\pi$
$450$	0	0
$451$	−8.04757e7	−0.0413092
$452$	0	0
$453$	3.45098e8	0.174421
$454$	0	0
$455$	−7.93641e8	−0.394988
$456$	0	0
$457$	4.63429e7	0.0227131	0.0113566	−	0.999936i	$-0.496385\pi$
$457$	4.63429e7	0.0227131	0.0113566	+	0.999936i	$0.496385\pi$
$458$	0	0
$459$	1.21756e9	0.587686
$460$	0	0
$461$	1.52117e8	0.0723144	0.0361572	−	0.999346i	$-0.488488\pi$
$461$	1.52117e8	0.0723144	0.0361572	+	0.999346i	$0.488488\pi$
$462$	0	0
$463$	1.63450e9	0.765337	0.382668	−	0.923886i	$-0.375005\pi$
$463$	1.63450e9	0.765337	0.382668	+	0.923886i	$0.375005\pi$
$464$	0	0
$465$	9.41328e8	0.434166
$466$	0	0
$467$	1.11380e9	0.506057	0.253029	−	0.967459i	$-0.418573\pi$
$467$	1.11380e9	0.506057	0.253029	+	0.967459i	$0.418573\pi$
$468$	0	0
$469$	−1.31077e9	−0.586706
$470$	0	0
$471$	−4.22367e9	−1.86259
$472$	0	0
$473$	−8.58638e7	−0.0373075
$474$	0	0
$475$	4.05312e8	0.173525
$476$	0	0
$477$	1.49818e8	0.0632049
$478$	0	0
$479$	1.27745e9	0.531091	0.265546	−	0.964098i	$-0.414448\pi$
$479$	1.27745e9	0.531091	0.265546	+	0.964098i	$0.414448\pi$
$480$	0	0
$481$	4.25307e8	0.174259
$482$	0	0
$483$	−1.02365e9	−0.413366
$484$	0	0
$485$	6.10242e8	0.242888
$486$	0	0
$487$	9.79673e8	0.384352	0.192176	−	0.981360i	$-0.438445\pi$
$487$	9.79673e8	0.384352	0.192176	+	0.981360i	$0.438445\pi$
$488$	0	0
$489$	2.63460e9	1.01890
$490$	0	0
$491$	4.92125e9	1.87625	0.938124	−	0.346298i	$-0.112562\pi$
$491$	4.92125e9	1.87625	0.938124	+	0.346298i	$0.112562\pi$
$492$	0	0
$493$	−1.00005e9	−0.375887
$494$	0	0
$495$	2.51550e6	0.000932194 0
$496$	0	0
$497$	−8.38998e9	−3.06559
$498$	0	0
$499$	3.65786e9	1.31788	0.658940	−	0.752196i	$-0.271005\pi$
$499$	3.65786e9	1.31788	0.658940	+	0.752196i	$0.271005\pi$
$500$	0	0
$501$	4.13501e8	0.146908
$502$	0	0
$503$	−3.88358e9	−1.36064	−0.680322	−	0.732914i	$-0.738160\pi$
$503$	−3.88358e9	−1.36064	−0.680322	+	0.732914i	$0.738160\pi$
$504$	0	0
$505$	1.21584e9	0.420103
$506$	0	0
$507$	−2.29601e9	−0.782430
$508$	0	0
$509$	−3.90072e9	−1.31109	−0.655545	−	0.755156i	$-0.727561\pi$
$509$	−3.90072e9	−1.31109	−0.655545	+	0.755156i	$0.727561\pi$
$510$	0	0
$511$	7.01573e9	2.32595
$512$	0	0
$513$	−2.57740e9	−0.842890
$514$	0	0
$515$	−2.03938e9	−0.657920
$516$	0	0
$517$	6.82640e7	0.0217258
$518$	0	0
$519$	2.46011e9	0.772448
$520$	0	0
$521$	2.88399e9	0.893431	0.446716	−	0.894676i	$-0.352594\pi$
$521$	2.88399e9	0.893431	0.446716	+	0.894676i	$0.352594\pi$
$522$	0	0
$523$	−8.77188e8	−0.268125	−0.134062	−	0.990973i	$-0.542802\pi$
$523$	−8.77188e8	−0.268125	−0.134062	+	0.990973i	$0.542802\pi$
$524$	0	0
$525$	−1.23300e9	−0.371882
$526$	0	0
$527$	1.92251e9	0.572177
$528$	0	0
$529$	−3.23655e9	−0.950578
$530$	0	0
$531$	1.56478e8	0.0453548
$532$	0	0
$533$	−1.80696e9	−0.516896
$534$	0	0
$535$	−5.11218e8	−0.144334
$536$	0	0
$537$	2.40781e9	0.670983
$538$	0	0
$539$	−3.23221e8	−0.0889077
$540$	0	0
$541$	6.53485e8	0.177437	0.0887187	−	0.996057i	$-0.471723\pi$
$541$	6.53485e8	0.177437	0.0887187	+	0.996057i	$0.471723\pi$
$542$	0	0
$543$	−3.31592e9	−0.888801
$544$	0	0
$545$	−3.35397e9	−0.887507
$546$	0	0
$547$	4.59299e9	1.19988	0.599942	−	0.800043i	$-0.295190\pi$
$547$	4.59299e9	1.19988	0.599942	+	0.800043i	$0.295190\pi$
$548$	0	0
$549$	1.08105e8	0.0278833
$550$	0	0
$551$	2.11696e9	0.539117
$552$	0	0
$553$	1.57824e6	0.000396858 0
$554$	0	0
$555$	6.60756e8	0.164065
$556$	0	0
$557$	−6.83164e9	−1.67507	−0.837533	−	0.546387i	$-0.816003\pi$
$557$	−6.83164e9	−1.67507	−0.837533	+	0.546387i	$0.816003\pi$
$558$	0	0
$559$	−1.92794e9	−0.466823
$560$	0	0
$561$	1.01169e8	0.0241923
$562$	0	0
$563$	−3.42509e9	−0.808897	−0.404449	−	0.914561i	$-0.632537\pi$
$563$	−3.42509e9	−0.808897	−0.404449	+	0.914561i	$0.632537\pi$
$564$	0	0
$565$	2.18513e9	0.509692
$566$	0	0
$567$	8.26136e9	1.90332
$568$	0	0
$569$	−7.50930e9	−1.70886	−0.854430	−	0.519566i	$-0.826094\pi$
$569$	−7.50930e9	−1.70886	−0.854430	+	0.519566i	$0.826094\pi$
$570$	0	0
$571$	1.35841e8	0.0305355	0.0152677	−	0.999883i	$-0.495140\pi$
$571$	1.35841e8	0.0305355	0.0152677	+	0.999883i	$0.495140\pi$
$572$	0	0
$573$	7.42778e9	1.64937
$574$	0	0
$575$	2.02688e8	0.0444621
$576$	0	0
$577$	1.63775e9	0.354922	0.177461	−	0.984128i	$-0.443212\pi$
$577$	1.63775e9	0.354922	0.177461	+	0.984128i	$0.443212\pi$
$578$	0	0
$579$	−7.65147e8	−0.163821
$580$	0	0
$581$	1.00955e10	2.13556
$582$	0	0
$583$	−2.20246e8	−0.0460328
$584$	0	0
$585$	5.64818e7	0.0116644
$586$	0	0
$587$	5.97205e9	1.21868	0.609341	−	0.792909i	$-0.291434\pi$
$587$	5.97205e9	1.21868	0.609341	+	0.792909i	$0.291434\pi$
$588$	0	0
$589$	−4.06967e9	−0.820647
$590$	0	0
$591$	8.07303e9	1.60872
$592$	0	0
$593$	8.31347e9	1.63716	0.818579	−	0.574394i	$-0.194762\pi$
$593$	8.31347e9	1.63716	0.818579	+	0.574394i	$0.194762\pi$
$594$	0	0
$595$	−2.51820e9	−0.490095
$596$	0	0
$597$	8.53308e9	1.64133
$598$	0	0
$599$	9.78368e9	1.85998	0.929990	−	0.367585i	$-0.119815\pi$
$599$	9.78368e9	1.85998	0.929990	+	0.367585i	$0.119815\pi$
$600$	0	0
$601$	5.40159e9	1.01499	0.507494	−	0.861655i	$-0.330572\pi$
$601$	5.40159e9	1.01499	0.507494	+	0.861655i	$0.330572\pi$
$602$	0	0
$603$	9.32846e7	0.0173260
$604$	0	0
$605$	2.43220e9	0.446535
$606$	0	0
$607$	−2.84439e9	−0.516214	−0.258107	−	0.966116i	$-0.583099\pi$
$607$	−2.84439e9	−0.516214	−0.258107	+	0.966116i	$0.583099\pi$
$608$	0	0
$609$	−6.44001e9	−1.15538
$610$	0	0
$611$	1.53277e9	0.271851
$612$	0	0
$613$	7.02106e9	1.23109	0.615547	−	0.788101i	$-0.288935\pi$
$613$	7.02106e9	1.23109	0.615547	+	0.788101i	$0.288935\pi$
$614$	0	0
$615$	−2.80729e9	−0.486659
$616$	0	0
$617$	3.35166e9	0.574462	0.287231	−	0.957861i	$-0.407265\pi$
$617$	3.35166e9	0.574462	0.287231	+	0.957861i	$0.407265\pi$
$618$	0	0
$619$	3.92362e9	0.664921	0.332461	−	0.943117i	$-0.392121\pi$
$619$	3.92362e9	0.664921	0.332461	+	0.943117i	$0.392121\pi$
$620$	0	0
$621$	−1.28890e9	−0.215972
$622$	0	0
$623$	−3.30538e9	−0.547662
$624$	0	0
$625$	2.44141e8	0.0400000
$626$	0	0
$627$	−2.14161e8	−0.0346979
$628$	0	0
$629$	1.34948e9	0.216217
$630$	0	0
$631$	−6.81545e8	−0.107992	−0.0539960	−	0.998541i	$-0.517196\pi$
$631$	−6.81545e8	−0.107992	−0.0539960	+	0.998541i	$0.517196\pi$
$632$	0	0
$633$	7.77583e9	1.21852
$634$	0	0
$635$	1.56272e9	0.242200
$636$	0	0
$637$	−7.25744e9	−1.11249
$638$	0	0
$639$	5.97097e8	0.0905298
$640$	0	0
$641$	9.65199e9	1.44748	0.723742	−	0.690071i	$-0.242421\pi$
$641$	9.65199e9	1.44748	0.723742	+	0.690071i	$0.242421\pi$
$642$	0	0
$643$	5.07826e9	0.753315	0.376657	−	0.926353i	$-0.377073\pi$
$643$	5.07826e9	0.753315	0.376657	+	0.926353i	$0.377073\pi$
$644$	0	0
$645$	−2.99525e9	−0.439515
$646$	0	0
$647$	−2.08330e9	−0.302404	−0.151202	−	0.988503i	$-0.548314\pi$
$647$	−2.08330e9	−0.302404	−0.151202	+	0.988503i	$0.548314\pi$
$648$	0	0
$649$	−2.30036e8	−0.0330324
$650$	0	0
$651$	1.23803e10	1.75873
$652$	0	0
$653$	−6.84881e9	−0.962540	−0.481270	−	0.876572i	$-0.659824\pi$
$653$	−6.84881e9	−0.962540	−0.481270	+	0.876572i	$0.659824\pi$
$654$	0	0
$655$	−9.69524e8	−0.134807
$656$	0	0
$657$	−4.99295e8	−0.0686876
$658$	0	0
$659$	−6.99913e9	−0.952676	−0.476338	−	0.879262i	$-0.658036\pi$
$659$	−6.99913e9	−0.952676	−0.476338	+	0.879262i	$0.658036\pi$
$660$	0	0
$661$	1.99594e9	0.268809	0.134404	−	0.990927i	$-0.457088\pi$
$661$	1.99594e9	0.268809	0.134404	+	0.990927i	$0.457088\pi$
$662$	0	0
$663$	2.27160e9	0.302715
$664$	0	0
$665$	5.33067e9	0.702920
$666$	0	0
$667$	1.05864e9	0.138137
$668$	0	0
$669$	8.44472e8	0.109042
$670$	0	0
$671$	−1.58924e8	−0.0203077
$672$	0	0
$673$	−1.17939e10	−1.49144	−0.745718	−	0.666261i	$-0.767894\pi$
$673$	−1.17939e10	−1.49144	−0.745718	+	0.666261i	$0.767894\pi$
$674$	0	0
$675$	−1.55250e9	−0.194298
$676$	0	0
$677$	−7.80222e9	−0.966402	−0.483201	−	0.875509i	$-0.660526\pi$
$677$	−7.80222e9	−0.966402	−0.483201	+	0.875509i	$0.660526\pi$
$678$	0	0
$679$	8.02590e9	0.983897
$680$	0	0
$681$	9.74572e9	1.18249
$682$	0	0
$683$	−4.51153e9	−0.541815	−0.270908	−	0.962605i	$-0.587324\pi$
$683$	−4.51153e9	−0.541815	−0.270908	+	0.962605i	$0.587324\pi$
$684$	0	0
$685$	−4.52150e9	−0.537484
$686$	0	0
$687$	−7.65883e9	−0.901185
$688$	0	0
$689$	−4.94528e9	−0.576002
$690$	0	0
$691$	1.06331e10	1.22599	0.612997	−	0.790086i	$-0.289964\pi$
$691$	1.06331e10	1.22599	0.612997	+	0.790086i	$0.289964\pi$
$692$	0	0
$693$	3.30839e7	0.00377615
$694$	0	0
$695$	1.36365e9	0.154084
$696$	0	0
$697$	−5.73343e9	−0.641356
$698$	0	0
$699$	−9.35929e8	−0.103651
$700$	0	0
$701$	4.38514e9	0.480807	0.240403	−	0.970673i	$-0.422720\pi$
$701$	4.38514e9	0.480807	0.240403	+	0.970673i	$0.422720\pi$
$702$	0	0
$703$	−2.85667e9	−0.310110
$704$	0	0
$705$	2.38130e9	0.255949
$706$	0	0
$707$	1.59907e10	1.70176
$708$	0	0
$709$	5.98805e9	0.630992	0.315496	−	0.948927i	$-0.397829\pi$
$709$	5.98805e9	0.630992	0.315496	+	0.948927i	$0.397829\pi$
$710$	0	0
$711$	−112320.	−1.17196e−5 0
$712$	0	0
$713$	−2.03515e9	−0.210273
$714$	0	0
$715$	−8.30330e7	−0.00849532
$716$	0	0
$717$	−7.69058e9	−0.779188
$718$	0	0
$719$	−1.17768e10	−1.18161	−0.590807	−	0.806813i	$-0.701191\pi$
$719$	−1.17768e10	−1.18161	−0.590807	+	0.806813i	$0.701191\pi$
$720$	0	0
$721$	−2.68219e10	−2.66512
$722$	0	0
$723$	−1.81814e10	−1.78913
$724$	0	0
$725$	1.27516e9	0.124274
$726$	0	0
$727$	8.41051e9	0.811805	0.405902	−	0.913916i	$-0.366957\pi$
$727$	8.41051e9	0.811805	0.405902	+	0.913916i	$0.366957\pi$
$728$	0	0
$729$	9.84247e9	0.940931
$730$	0	0
$731$	−6.11729e9	−0.579227
$732$	0	0
$733$	−1.44084e10	−1.35130	−0.675650	−	0.737223i	$-0.736137\pi$
$733$	−1.44084e10	−1.35130	−0.675650	+	0.737223i	$0.736137\pi$
$734$	0	0
$735$	−1.12752e10	−1.04741
$736$	0	0
$737$	−1.37136e8	−0.0126187
$738$	0	0
$739$	−8.21708e9	−0.748966	−0.374483	−	0.927234i	$-0.622180\pi$
$739$	−8.21708e9	−0.748966	−0.374483	+	0.927234i	$0.622180\pi$
$740$	0	0
$741$	−4.80865e9	−0.434170
$742$	0	0
$743$	−1.72531e10	−1.54314	−0.771570	−	0.636144i	$-0.780528\pi$
$743$	−1.72531e10	−1.54314	−0.771570	+	0.636144i	$0.780528\pi$
$744$	0	0
$745$	−4.55726e9	−0.403791
$746$	0	0
$747$	−7.18477e8	−0.0630654
$748$	0	0
$749$	−6.72354e9	−0.584671
$750$	0	0
$751$	1.58498e10	1.36548	0.682739	−	0.730662i	$-0.260789\pi$
$751$	1.58498e10	1.36548	0.682739	+	0.730662i	$0.260789\pi$
$752$	0	0
$753$	−7.74260e9	−0.660853
$754$	0	0
$755$	−8.98694e8	−0.0759972
$756$	0	0
$757$	−7.13856e9	−0.598102	−0.299051	−	0.954237i	$-0.596670\pi$
$757$	−7.13856e9	−0.598102	−0.299051	+	0.954237i	$0.596670\pi$
$758$	0	0
$759$	−1.07097e8	−0.00889059
$760$	0	0
$761$	−2.59993e9	−0.213853	−0.106926	−	0.994267i	$-0.534101\pi$
$761$	−2.59993e9	−0.213853	−0.106926	+	0.994267i	$0.534101\pi$
$762$	0	0
$763$	−4.41114e10	−3.59514
$764$	0	0
$765$	1.79215e8	0.0144730
$766$	0	0
$767$	−5.16512e9	−0.413329
$768$	0	0
$769$	−4.96477e9	−0.393692	−0.196846	−	0.980434i	$-0.563070\pi$
$769$	−4.96477e9	−0.393692	−0.196846	+	0.980434i	$0.563070\pi$
$770$	0	0
$771$	1.09146e10	0.857663
$772$	0	0
$773$	1.49681e10	1.16557	0.582786	−	0.812626i	$-0.301963\pi$
$773$	1.49681e10	1.16557	0.582786	+	0.812626i	$0.301963\pi$
$774$	0	0
$775$	−2.45138e9	−0.189171
$776$	0	0
$777$	8.69026e9	0.664598
$778$	0	0
$779$	1.21369e10	0.919867
$780$	0	0
$781$	−8.77783e8	−0.0659339
$782$	0	0
$783$	−8.10877e9	−0.603655
$784$	0	0
$785$	1.09992e10	0.811550
$786$	0	0
$787$	9.79990e9	0.716655	0.358328	−	0.933596i	$-0.383347\pi$
$787$	9.79990e9	0.716655	0.358328	+	0.933596i	$0.383347\pi$
$788$	0	0
$789$	2.19709e10	1.59250
$790$	0	0
$791$	2.87388e10	2.06467
$792$	0	0
$793$	−3.56840e9	−0.254108
$794$	0	0
$795$	−7.68299e9	−0.542307
$796$	0	0
$797$	−3.93169e9	−0.275090	−0.137545	−	0.990495i	$-0.543921\pi$
$797$	−3.93169e9	−0.275090	−0.137545	+	0.990495i	$0.543921\pi$
$798$	0	0
$799$	4.86342e9	0.337309
$800$	0	0
$801$	2.35237e8	0.0161730
$802$	0	0
$803$	7.34006e8	0.0500259
$804$	0	0
$805$	2.66575e9	0.180108
$806$	0	0
$807$	−2.24297e10	−1.50234
$808$	0	0
$809$	1.26324e10	0.838816	0.419408	−	0.907798i	$-0.362238\pi$
$809$	1.26324e10	0.838816	0.419408	+	0.907798i	$0.362238\pi$
$810$	0	0
$811$	−1.16653e10	−0.767934	−0.383967	−	0.923347i	$-0.625442\pi$
$811$	−1.16653e10	−0.767934	−0.383967	+	0.923347i	$0.625442\pi$
$812$	0	0
$813$	−2.14047e9	−0.139699
$814$	0	0
$815$	−6.86094e9	−0.443948
$816$	0	0
$817$	1.29495e10	0.830758
$818$	0	0
$819$	7.42848e8	0.0472505
$820$	0	0
$821$	8.17500e9	0.515569	0.257784	−	0.966202i	$-0.417008\pi$
$821$	8.17500e9	0.515569	0.257784	+	0.966202i	$0.417008\pi$
$822$	0	0
$823$	−1.75211e10	−1.09563	−0.547813	−	0.836601i	$-0.684540\pi$
$823$	−1.75211e10	−1.09563	−0.547813	+	0.836601i	$0.684540\pi$
$824$	0	0
$825$	−1.29000e8	−0.00799836
$826$	0	0
$827$	−1.22225e10	−0.751437	−0.375718	−	0.926734i	$-0.622604\pi$
$827$	−1.22225e10	−0.751437	−0.375718	+	0.926734i	$0.622604\pi$
$828$	0	0
$829$	1.06634e10	0.650063	0.325032	−	0.945703i	$-0.394625\pi$
$829$	1.06634e10	0.650063	0.325032	+	0.945703i	$0.394625\pi$
$830$	0	0
$831$	−1.51995e10	−0.918812
$832$	0	0
$833$	−2.30276e10	−1.38036
$834$	0	0
$835$	−1.07682e9	−0.0640092
$836$	0	0
$837$	1.55884e10	0.918887
$838$	0	0
$839$	−2.31400e9	−0.135268	−0.0676342	−	0.997710i	$-0.521545\pi$
$839$	−2.31400e9	−0.135268	−0.0676342	+	0.997710i	$0.521545\pi$
$840$	0	0
$841$	−1.05897e10	−0.613899
$842$	0	0
$843$	−1.08392e10	−0.623164
$844$	0	0
$845$	5.97918e9	0.340913
$846$	0	0
$847$	3.19883e10	1.80883
$848$	0	0
$849$	−9.99410e8	−0.0560488
$850$	0	0
$851$	−1.42855e9	−0.0794590
$852$	0	0
$853$	4.22377e9	0.233012	0.116506	−	0.993190i	$-0.462831\pi$
$853$	4.22377e9	0.233012	0.116506	+	0.993190i	$0.462831\pi$
$854$	0	0
$855$	−3.79372e8	−0.0207579
$856$	0	0
$857$	−3.52104e9	−0.191090	−0.0955450	−	0.995425i	$-0.530459\pi$
$857$	−3.52104e9	−0.191090	−0.0955450	+	0.995425i	$0.530459\pi$
$858$	0	0
$859$	−2.44930e10	−1.31846	−0.659229	−	0.751943i	$-0.729117\pi$
$859$	−2.44930e10	−1.31846	−0.659229	+	0.751943i	$0.729117\pi$
$860$	0	0
$861$	−3.69215e10	−1.97137
$862$	0	0
$863$	−5.40573e9	−0.286297	−0.143148	−	0.989701i	$-0.545723\pi$
$863$	−5.40573e9	−0.286297	−0.143148	+	0.989701i	$0.545723\pi$
$864$	0	0
$865$	−6.40655e9	−0.336564
$866$	0	0
$867$	−1.24886e10	−0.650797
$868$	0	0
$869$	165120.	8.53553e−6 0
$870$	0	0
$871$	−3.07919e9	−0.157897
$872$	0	0
$873$	−5.71186e8	−0.0290555
$874$	0	0
$875$	3.21094e9	0.162033
$876$	0	0
$877$	2.89155e10	1.44755	0.723773	−	0.690039i	$-0.242406\pi$
$877$	2.89155e10	1.44755	0.723773	+	0.690039i	$0.242406\pi$
$878$	0	0
$879$	8.58362e9	0.426294
$880$	0	0
$881$	7.80643e8	0.0384624	0.0192312	−	0.999815i	$-0.493878\pi$
$881$	7.80643e8	0.0384624	0.0192312	+	0.999815i	$0.493878\pi$
$882$	0	0
$883$	1.36907e10	0.669211	0.334605	−	0.942358i	$-0.391397\pi$
$883$	1.36907e10	0.669211	0.334605	+	0.942358i	$0.391397\pi$
$884$	0	0
$885$	−8.02452e9	−0.389151
$886$	0	0
$887$	3.58403e9	0.172441	0.0862203	−	0.996276i	$-0.472521\pi$
$887$	3.58403e9	0.172441	0.0862203	+	0.996276i	$0.472521\pi$
$888$	0	0
$889$	2.05529e10	0.981108
$890$	0	0
$891$	8.64327e8	0.0409361
$892$	0	0
$893$	−1.02952e10	−0.483786
$894$	0	0
$895$	−6.27033e9	−0.292355
$896$	0	0
$897$	−2.40470e9	−0.111247
$898$	0	0
$899$	−1.28036e10	−0.587725
$900$	0	0
$901$	−1.56912e10	−0.714694
$902$	0	0
$903$	−3.93935e10	−1.78040
$904$	0	0
$905$	8.63521e9	0.387260
$906$	0	0
$907$	3.01108e10	1.33998	0.669988	−	0.742372i	$-0.266299\pi$
$907$	3.01108e10	1.33998	0.669988	+	0.742372i	$0.266299\pi$
$908$	0	0
$909$	−1.13802e9	−0.0502548
$910$	0	0
$911$	−2.48800e10	−1.09027	−0.545137	−	0.838347i	$-0.683523\pi$
$911$	−2.48800e10	−1.09027	−0.545137	+	0.838347i	$0.683523\pi$
$912$	0	0
$913$	1.05622e9	0.0459312
$914$	0	0
$915$	−5.54387e9	−0.239243
$916$	0	0
$917$	−1.27512e10	−0.546082
$918$	0	0
$919$	1.08420e10	0.460794	0.230397	−	0.973097i	$-0.425997\pi$
$919$	1.08420e10	0.460794	0.230397	+	0.973097i	$0.425997\pi$
$920$	0	0
$921$	4.10477e9	0.173133
$922$	0	0
$923$	−1.97093e10	−0.825021
$924$	0	0
$925$	−1.72072e9	−0.0714848
$926$	0	0
$927$	1.90886e9	0.0787037
$928$	0	0
$929$	1.07045e10	0.438038	0.219019	−	0.975721i	$-0.429714\pi$
$929$	1.07045e10	0.438038	0.219019	+	0.975721i	$0.429714\pi$
$930$	0	0
$931$	4.87463e10	1.97978
$932$	0	0
$933$	−2.32659e10	−0.937851
$934$	0	0
$935$	−2.63461e8	−0.0105409
$936$	0	0
$937$	3.42787e10	1.36124	0.680621	−	0.732635i	$-0.261710\pi$
$937$	3.42787e10	1.36124	0.680621	+	0.732635i	$0.261710\pi$
$938$	0	0
$939$	2.73994e10	1.07997
$940$	0	0
$941$	3.73695e9	0.146202	0.0731010	−	0.997325i	$-0.476710\pi$
$941$	3.73695e9	0.146202	0.0731010	+	0.997325i	$0.476710\pi$
$942$	0	0
$943$	6.06937e9	0.235696
$944$	0	0
$945$	−2.04185e10	−0.787068
$946$	0	0
$947$	−3.32150e10	−1.27089	−0.635447	−	0.772145i	$-0.719184\pi$
$947$	−3.32150e10	−1.27089	−0.635447	+	0.772145i	$0.719184\pi$
$948$	0	0
$949$	1.64810e10	0.625968
$950$	0	0
$951$	2.64091e10	0.995686
$952$	0	0
$953$	4.69895e10	1.75864	0.879318	−	0.476235i	$-0.157999\pi$
$953$	4.69895e10	1.75864	0.879318	+	0.476235i	$0.157999\pi$
$954$	0	0
$955$	−1.93432e10	−0.718648
$956$	0	0
$957$	−6.73772e8	−0.0248497
$958$	0	0
$959$	−5.94668e10	−2.17726
$960$	0	0
$961$	−2.89877e9	−0.105361
$962$	0	0
$963$	4.78500e8	0.0172659
$964$	0	0
$965$	1.99257e9	0.0713786
$966$	0	0
$967$	−1.42294e10	−0.506050	−0.253025	−	0.967460i	$-0.581425\pi$
$967$	−1.42294e10	−0.506050	−0.253025	+	0.967460i	$0.581425\pi$
$968$	0	0
$969$	−1.52577e10	−0.538711
$970$	0	0
$971$	−5.45474e8	−0.0191208	−0.00956041	−	0.999954i	$-0.503043\pi$
$971$	−5.45474e8	−0.0191208	−0.00956041	+	0.999954i	$0.503043\pi$
$972$	0	0
$973$	1.79348e10	0.624167
$974$	0	0
$975$	−2.89650e9	−0.100082
$976$	0	0
$977$	−1.97916e10	−0.678968	−0.339484	−	0.940612i	$-0.610252\pi$
$977$	−1.97916e10	−0.678968	−0.339484	+	0.940612i	$0.610252\pi$
$978$	0	0
$979$	−3.45818e8	−0.0117790
$980$	0	0
$981$	3.13932e9	0.106168
$982$	0	0
$983$	−4.71503e10	−1.58324	−0.791620	−	0.611013i	$-0.790762\pi$
$983$	−4.71503e10	−1.58324	−0.791620	+	0.611013i	$0.790762\pi$
$984$	0	0
$985$	−2.10235e10	−0.700936
$986$	0	0
$987$	3.13189e10	1.03680
$988$	0	0
$989$	6.47573e9	0.212864
$990$	0	0
$991$	3.87968e10	1.26631	0.633153	−	0.774027i	$-0.281761\pi$
$991$	3.87968e10	1.26631	0.633153	+	0.774027i	$0.281761\pi$
$992$	0	0
$993$	4.51123e10	1.46208
$994$	0	0
$995$	−2.22216e10	−0.715145
$996$	0	0
$997$	5.66394e10	1.81003	0.905015	−	0.425380i	$-0.139860\pi$
$997$	5.66394e10	1.81003	0.905015	+	0.425380i	$0.139860\pi$
$998$	0	0
$999$	1.09421e10	0.347234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.8.a.h.1.1		1
4.3	odd	2		320.8.a.a.1.1		1
8.3	odd	2		80.8.a.d.1.1		1
8.5	even	2		5.8.a.a.1.1	✓	1
24.5	odd	2		45.8.a.f.1.1		1
40.3	even	4		400.8.c.e.49.2		2
40.13	odd	4		25.8.b.a.24.2		2
40.19	odd	2		400.8.a.e.1.1		1
40.27	even	4		400.8.c.e.49.1		2
40.29	even	2		25.8.a.a.1.1		1
40.37	odd	4		25.8.b.a.24.1		2
56.13	odd	2		245.8.a.a.1.1		1
88.21	odd	2		605.8.a.c.1.1		1
120.29	odd	2		225.8.a.b.1.1		1
120.53	even	4		225.8.b.b.199.1		2
120.77	even	4		225.8.b.b.199.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.8.a.a.1.1	✓	1	8.5	even	2
25.8.a.a.1.1		1	40.29	even	2
25.8.b.a.24.1		2	40.37	odd	4
25.8.b.a.24.2		2	40.13	odd	4
45.8.a.f.1.1		1	24.5	odd	2
80.8.a.d.1.1		1	8.3	odd	2
225.8.a.b.1.1		1	120.29	odd	2
225.8.b.b.199.1		2	120.53	even	4
225.8.b.b.199.2		2	120.77	even	4
245.8.a.a.1.1		1	56.13	odd	2
320.8.a.a.1.1		1	4.3	odd	2
320.8.a.h.1.1		1	1.1	even	1	trivial
400.8.a.e.1.1		1	40.19	odd	2
400.8.c.e.49.1		2	40.27	even	4
400.8.c.e.49.2		2	40.3	even	4
605.8.a.c.1.1		1	88.21	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	320.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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