LMFDB - Embedded newform 350.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,6,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("350.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	350.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:	$56.1343369345$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} -13.0000 q^{3} +16.0000 q^{4} +52.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} -74.0000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} -13.0000 q^{3} +16.0000 q^{4} +52.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} -74.0000 q^{9} -175.000 q^{11} -208.000 q^{12} +999.000 q^{13} -196.000 q^{14} +256.000 q^{16} -1831.00 q^{17} +296.000 q^{18} -1308.00 q^{19} -637.000 q^{21} +700.000 q^{22} +4190.00 q^{23} +832.000 q^{24} -3996.00 q^{26} +4121.00 q^{27} +784.000 q^{28} -981.000 q^{29} -4514.00 q^{31} -1024.00 q^{32} +2275.00 q^{33} +7324.00 q^{34} -1184.00 q^{36} +578.000 q^{37} +5232.00 q^{38} -12987.0 q^{39} +19526.0 q^{41} +2548.00 q^{42} -10288.0 q^{43} -2800.00 q^{44} -16760.0 q^{46} +25687.0 q^{47} -3328.00 q^{48} +2401.00 q^{49} +23803.0 q^{51} +15984.0 q^{52} +29874.0 q^{53} -16484.0 q^{54} -3136.00 q^{56} +17004.0 q^{57} +3924.00 q^{58} +1354.00 q^{59} -13012.0 q^{61} +18056.0 q^{62} -3626.00 q^{63} +4096.00 q^{64} -9100.00 q^{66} -33026.0 q^{67} -29296.0 q^{68} -54470.0 q^{69} -21960.0 q^{71} +4736.00 q^{72} -83782.0 q^{73} -2312.00 q^{74} -20928.0 q^{76} -8575.00 q^{77} +51948.0 q^{78} -6417.00 q^{79} -35591.0 q^{81} -78104.0 q^{82} -7324.00 q^{83} -10192.0 q^{84} +41152.0 q^{86} +12753.0 q^{87} +11200.0 q^{88} -80836.0 q^{89} +48951.0 q^{91} +67040.0 q^{92} +58682.0 q^{93} -102748. q^{94} +13312.0 q^{96} -78575.0 q^{97} -9604.00 q^{98} +12950.0 q^{99} +O(q^{100})\)

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−13.0000	−0.833950	−0.416975	−	0.908918i	$-0.636910\pi$
$3$	−13.0000	−0.833950	−0.416975	+	0.908918i	$0.636910\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	52.0000	0.589692
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−64.0000	−0.353553
$9$	−74.0000	−0.304527
$10$	0	0
$11$	−175.000	−0.436070	−0.218035	−	0.975941i	$-0.569965\pi$
$11$	−175.000	−0.436070	−0.218035	+	0.975941i	$0.569965\pi$
$12$	−208.000	−0.416975
$13$	999.000	1.63948	0.819742	−	0.572733i	$-0.194117\pi$
$13$	999.000	1.63948	0.819742	+	0.572733i	$0.194117\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	−1831.00	−1.53662	−0.768309	−	0.640079i	$-0.778902\pi$
$17$	−1831.00	−1.53662	−0.768309	+	0.640079i	$0.778902\pi$
$18$	296.000	0.215333
$19$	−1308.00	−0.831235	−0.415617	−	0.909540i	$-0.636434\pi$
$19$	−1308.00	−0.831235	−0.415617	+	0.909540i	$0.636434\pi$
$20$	0	0
$21$	−637.000	−0.315204
$22$	700.000	0.308348
$23$	4190.00	1.65156	0.825780	−	0.563992i	$-0.190735\pi$
$23$	4190.00	1.65156	0.825780	+	0.563992i	$0.190735\pi$
$24$	832.000	0.294846
$25$	0	0
$26$	−3996.00	−1.15929
$27$	4121.00	1.08791
$28$	784.000	0.188982
$29$	−981.000	−0.216608	−0.108304	−	0.994118i	$-0.534542\pi$
$29$	−981.000	−0.216608	−0.108304	+	0.994118i	$0.534542\pi$
$30$	0	0
$31$	−4514.00	−0.843640	−0.421820	−	0.906680i	$-0.638609\pi$
$31$	−4514.00	−0.843640	−0.421820	+	0.906680i	$0.638609\pi$
$32$	−1024.00	−0.176777
$33$	2275.00	0.363661
$34$	7324.00	1.08655
$35$	0	0
$36$	−1184.00	−0.152263
$37$	578.000	0.0694102	0.0347051	−	0.999398i	$-0.488951\pi$
$37$	578.000	0.0694102	0.0347051	+	0.999398i	$0.488951\pi$
$38$	5232.00	0.587772
$39$	−12987.0	−1.36725
$40$	0	0
$41$	19526.0	1.81407	0.907034	−	0.421057i	$-0.138341\pi$
$41$	19526.0	1.81407	0.907034	+	0.421057i	$0.138341\pi$
$42$	2548.00	0.222883
$43$	−10288.0	−0.848516	−0.424258	−	0.905541i	$-0.639465\pi$
$43$	−10288.0	−0.848516	−0.424258	+	0.905541i	$0.639465\pi$
$44$	−2800.00	−0.218035
$45$	0	0
$46$	−16760.0	−1.16783
$47$	25687.0	1.69617	0.848084	−	0.529862i	$-0.177756\pi$
$47$	25687.0	1.69617	0.848084	+	0.529862i	$0.177756\pi$
$48$	−3328.00	−0.208488
$49$	2401.00	0.142857
$50$	0	0
$51$	23803.0	1.28146
$52$	15984.0	0.819742
$53$	29874.0	1.46084	0.730422	−	0.682996i	$-0.239324\pi$
$53$	29874.0	1.46084	0.730422	+	0.682996i	$0.239324\pi$
$54$	−16484.0	−0.769269
$55$	0	0
$56$	−3136.00	−0.133631
$57$	17004.0	0.693209
$58$	3924.00	0.153165
$59$	1354.00	0.0506394	0.0253197	−	0.999679i	$-0.491940\pi$
$59$	1354.00	0.0506394	0.0253197	+	0.999679i	$0.491940\pi$
$60$	0	0
$61$	−13012.0	−0.447733	−0.223867	−	0.974620i	$-0.571868\pi$
$61$	−13012.0	−0.447733	−0.223867	+	0.974620i	$0.571868\pi$
$62$	18056.0	0.596544
$63$	−3626.00	−0.115100
$64$	4096.00	0.125000
$65$	0	0
$66$	−9100.00	−0.257147
$67$	−33026.0	−0.898812	−0.449406	−	0.893328i	$-0.648364\pi$
$67$	−33026.0	−0.898812	−0.449406	+	0.893328i	$0.648364\pi$
$68$	−29296.0	−0.768309
$69$	−54470.0	−1.37732
$70$	0	0
$71$	−21960.0	−0.516995	−0.258498	−	0.966012i	$-0.583227\pi$
$71$	−21960.0	−0.516995	−0.258498	+	0.966012i	$0.583227\pi$
$72$	4736.00	0.107666
$73$	−83782.0	−1.84011	−0.920055	−	0.391790i	$-0.871856\pi$
$73$	−83782.0	−1.84011	−0.920055	+	0.391790i	$0.871856\pi$
$74$	−2312.00	−0.0490804
$75$	0	0
$76$	−20928.0	−0.415617
$77$	−8575.00	−0.164819
$78$	51948.0	0.966790
$79$	−6417.00	−0.115682	−0.0578408	−	0.998326i	$-0.518422\pi$
$79$	−6417.00	−0.115682	−0.0578408	+	0.998326i	$0.518422\pi$
$80$	0	0
$81$	−35591.0	−0.602737
$82$	−78104.0	−1.28274
$83$	−7324.00	−0.116695	−0.0583476	−	0.998296i	$-0.518583\pi$
$83$	−7324.00	−0.116695	−0.0583476	+	0.998296i	$0.518583\pi$
$84$	−10192.0	−0.157602
$85$	0	0
$86$	41152.0	0.599991
$87$	12753.0	0.180640
$88$	11200.0	0.154174
$89$	−80836.0	−1.08176	−0.540879	−	0.841101i	$-0.681908\pi$
$89$	−80836.0	−1.08176	−0.540879	+	0.841101i	$0.681908\pi$
$90$	0	0
$91$	48951.0	0.619667
$92$	67040.0	0.825780
$93$	58682.0	0.703554
$94$	−102748.	−1.19937
$95$	0	0
$96$	13312.0	0.147423
$97$	−78575.0	−0.847920	−0.423960	−	0.905681i	$-0.639360\pi$
$97$	−78575.0	−0.847920	−0.423960	+	0.905681i	$0.639360\pi$
$98$	−9604.00	−0.101015
$99$	12950.0	0.132795
$100$	0	0
$101$	−86000.0	−0.838871	−0.419435	−	0.907785i	$-0.637772\pi$
$101$	−86000.0	−0.838871	−0.419435	+	0.907785i	$0.637772\pi$
$102$	−95212.0	−0.906132
$103$	55039.0	0.511184	0.255592	−	0.966785i	$-0.417730\pi$
$103$	55039.0	0.511184	0.255592	+	0.966785i	$0.417730\pi$
$104$	−63936.0	−0.579645
$105$	0	0
$106$	−119496.	−1.03297
$107$	29568.0	0.249668	0.124834	−	0.992178i	$-0.460160\pi$
$107$	29568.0	0.249668	0.124834	+	0.992178i	$0.460160\pi$
$108$	65936.0	0.543955
$109$	11917.0	0.0960729	0.0480364	−	0.998846i	$-0.484704\pi$
$109$	11917.0	0.0960729	0.0480364	+	0.998846i	$0.484704\pi$
$110$	0	0
$111$	−7514.00	−0.0578847
$112$	12544.0	0.0944911
$113$	−129546.	−0.954394	−0.477197	−	0.878796i	$-0.658347\pi$
$113$	−129546.	−0.954394	−0.477197	+	0.878796i	$0.658347\pi$
$114$	−68016.0	−0.490173
$115$	0	0
$116$	−15696.0	−0.108304
$117$	−73926.0	−0.499267
$118$	−5416.00	−0.0358075
$119$	−89719.0	−0.580787
$120$	0	0
$121$	−130426.	−0.809843
$122$	52048.0	0.316595
$123$	−253838.	−1.51284
$124$	−72224.0	−0.421820
$125$	0	0
$126$	14504.0	0.0813882
$127$	−220114.	−1.21098	−0.605492	−	0.795851i	$-0.707024\pi$
$127$	−220114.	−1.21098	−0.605492	+	0.795851i	$0.707024\pi$
$128$	−16384.0	−0.0883883
$129$	133744.	0.707620
$130$	0	0
$131$	69738.0	0.355051	0.177526	−	0.984116i	$-0.443191\pi$
$131$	69738.0	0.355051	0.177526	+	0.984116i	$0.443191\pi$
$132$	36400.0	0.181830
$133$	−64092.0	−0.314177
$134$	132104.	0.635556
$135$	0	0
$136$	117184.	0.543277
$137$	226152.	1.02944	0.514718	−	0.857360i	$-0.327897\pi$
$137$	226152.	1.02944	0.514718	+	0.857360i	$0.327897\pi$
$138$	217880.	0.973912
$139$	−410066.	−1.80018	−0.900092	−	0.435700i	$-0.856501\pi$
$139$	−410066.	−1.80018	−0.900092	+	0.435700i	$0.856501\pi$
$140$	0	0
$141$	−333931.	−1.41452
$142$	87840.0	0.365571
$143$	−174825.	−0.714930
$144$	−18944.0	−0.0761317
$145$	0	0
$146$	335128.	1.30115
$147$	−31213.0	−0.119136
$148$	9248.00	0.0347051
$149$	−357158.	−1.31794	−0.658969	−	0.752170i	$-0.729007\pi$
$149$	−357158.	−1.31794	−0.658969	+	0.752170i	$0.729007\pi$
$150$	0	0
$151$	−187217.	−0.668195	−0.334097	−	0.942539i	$-0.608431\pi$
$151$	−187217.	−0.668195	−0.334097	+	0.942539i	$0.608431\pi$
$152$	83712.0	0.293886
$153$	135494.	0.467941
$154$	34300.0	0.116545
$155$	0	0
$156$	−207792.	−0.683624
$157$	35074.0	0.113563	0.0567814	−	0.998387i	$-0.481916\pi$
$157$	35074.0	0.113563	0.0567814	+	0.998387i	$0.481916\pi$
$158$	25668.0	0.0817992
$159$	−388362.	−1.21827
$160$	0	0
$161$	205310.	0.624231
$162$	142364.	0.426199
$163$	338206.	0.997039	0.498520	−	0.866878i	$-0.333877\pi$
$163$	338206.	0.997039	0.498520	+	0.866878i	$0.333877\pi$
$164$	312416.	0.907034
$165$	0	0
$166$	29296.0	0.0825160
$167$	−340713.	−0.945361	−0.472680	−	0.881234i	$-0.656713\pi$
$167$	−340713.	−0.945361	−0.472680	+	0.881234i	$0.656713\pi$
$168$	40768.0	0.111441
$169$	626708.	1.68791
$170$	0	0
$171$	96792.0	0.253133
$172$	−164608.	−0.424258
$173$	−434183.	−1.10295	−0.551477	−	0.834190i	$-0.685936\pi$
$173$	−434183.	−1.10295	−0.551477	+	0.834190i	$0.685936\pi$
$174$	−51012.0	−0.127732
$175$	0	0
$176$	−44800.0	−0.109018
$177$	−17602.0	−0.0422308
$178$	323344.	0.764918
$179$	−473252.	−1.10398	−0.551988	−	0.833852i	$-0.686131\pi$
$179$	−473252.	−1.10398	−0.551988	+	0.833852i	$0.686131\pi$
$180$	0	0
$181$	157670.	0.357728	0.178864	−	0.983874i	$-0.442758\pi$
$181$	157670.	0.357728	0.178864	+	0.983874i	$0.442758\pi$
$182$	−195804.	−0.438170
$183$	169156.	0.373387
$184$	−268160.	−0.583915
$185$	0	0
$186$	−234728.	−0.497488
$187$	320425.	0.670073
$188$	410992.	0.848084
$189$	201929.	0.411192
$190$	0	0
$191$	459729.	0.911840	0.455920	−	0.890021i	$-0.349310\pi$
$191$	459729.	0.911840	0.455920	+	0.890021i	$0.349310\pi$
$192$	−53248.0	−0.104244
$193$	−341164.	−0.659280	−0.329640	−	0.944107i	$-0.606927\pi$
$193$	−341164.	−0.659280	−0.329640	+	0.944107i	$0.606927\pi$
$194$	314300.	0.599570
$195$	0	0
$196$	38416.0	0.0714286
$197$	−442742.	−0.812803	−0.406401	−	0.913695i	$-0.633217\pi$
$197$	−442742.	−0.812803	−0.406401	+	0.913695i	$0.633217\pi$
$198$	−51800.0	−0.0939003
$199$	264030.	0.472629	0.236315	−	0.971677i	$-0.424060\pi$
$199$	264030.	0.472629	0.236315	+	0.971677i	$0.424060\pi$
$200$	0	0
$201$	429338.	0.749565
$202$	344000.	0.593171
$203$	−48069.0	−0.0818700
$204$	380848.	0.640732
$205$	0	0
$206$	−220156.	−0.361462
$207$	−310060.	−0.502944
$208$	255744.	0.409871
$209$	228900.	0.362477
$210$	0	0
$211$	292911.	0.452928	0.226464	−	0.974019i	$-0.427283\pi$
$211$	292911.	0.452928	0.226464	+	0.974019i	$0.427283\pi$
$212$	477984.	0.730422
$213$	285480.	0.431148
$214$	−118272.	−0.176542
$215$	0	0
$216$	−263744.	−0.384634
$217$	−221186.	−0.318866
$218$	−47668.0	−0.0679338
$219$	1.08917e6	1.53456
$220$	0	0
$221$	−1.82917e6	−2.51926
$222$	30056.0	0.0409307
$223$	−230833.	−0.310839	−0.155420	−	0.987849i	$-0.549673\pi$
$223$	−230833.	−0.310839	−0.155420	+	0.987849i	$0.549673\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	518184.	0.674859
$227$	1.02839e6	1.32462	0.662311	−	0.749229i	$-0.269576\pi$
$227$	1.02839e6	1.32462	0.662311	+	0.749229i	$0.269576\pi$
$228$	272064.	0.346604
$229$	−416134.	−0.524378	−0.262189	−	0.965017i	$-0.584444\pi$
$229$	−416134.	−0.524378	−0.262189	+	0.965017i	$0.584444\pi$
$230$	0	0
$231$	111475.	0.137451
$232$	62784.0	0.0765824
$233$	−742784.	−0.896340	−0.448170	−	0.893948i	$-0.647924\pi$
$233$	−742784.	−0.896340	−0.448170	+	0.893948i	$0.647924\pi$
$234$	295704.	0.353035
$235$	0	0
$236$	21664.0	0.0253197
$237$	83421.0	0.0964727
$238$	358876.	0.410679
$239$	1.20642e6	1.36617	0.683083	−	0.730341i	$-0.260639\pi$
$239$	1.20642e6	1.36617	0.683083	+	0.730341i	$0.260639\pi$
$240$	0	0
$241$	284290.	0.315296	0.157648	−	0.987495i	$-0.449609\pi$
$241$	284290.	0.315296	0.157648	+	0.987495i	$0.449609\pi$
$242$	521704.	0.572645
$243$	−538720.	−0.585258
$244$	−208192.	−0.223867
$245$	0	0
$246$	1.01535e6	1.06974
$247$	−1.30669e6	−1.36280
$248$	288896.	0.298272
$249$	95212.0	0.0973180
$250$	0	0
$251$	1.18858e6	1.19082	0.595408	−	0.803423i	$-0.296990\pi$
$251$	1.18858e6	1.19082	0.595408	+	0.803423i	$0.296990\pi$
$252$	−58016.0	−0.0575501
$253$	−733250.	−0.720196
$254$	880456.	0.856295
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.06840e6	1.00902	0.504512	−	0.863404i	$-0.331672\pi$
$257$	1.06840e6	1.00902	0.504512	+	0.863404i	$0.331672\pi$
$258$	−534976.	−0.500363
$259$	28322.0	0.0262346
$260$	0	0
$261$	72594.0	0.0659629
$262$	−278952.	−0.251059
$263$	−932680.	−0.831464	−0.415732	−	0.909487i	$-0.636475\pi$
$263$	−932680.	−0.831464	−0.415732	+	0.909487i	$0.636475\pi$
$264$	−145600.	−0.128574
$265$	0	0
$266$	256368.	0.222157
$267$	1.05087e6	0.902132
$268$	−528416.	−0.449406
$269$	−1.27006e6	−1.07015	−0.535074	−	0.844805i	$-0.679716\pi$
$269$	−1.27006e6	−1.07015	−0.535074	+	0.844805i	$0.679716\pi$
$270$	0	0
$271$	−1.37088e6	−1.13390	−0.566950	−	0.823752i	$-0.691877\pi$
$271$	−1.37088e6	−1.13390	−0.566950	+	0.823752i	$0.691877\pi$
$272$	−468736.	−0.384155
$273$	−636363.	−0.516771
$274$	−904608.	−0.727921
$275$	0	0
$276$	−871520.	−0.688660
$277$	−401650.	−0.314520	−0.157260	−	0.987557i	$-0.550266\pi$
$277$	−401650.	−0.314520	−0.157260	+	0.987557i	$0.550266\pi$
$278$	1.64026e6	1.27292
$279$	334036.	0.256911
$280$	0	0
$281$	470439.	0.355416	0.177708	−	0.984083i	$-0.443132\pi$
$281$	470439.	0.355416	0.177708	+	0.984083i	$0.443132\pi$
$282$	1.33572e6	1.00022
$283$	−1.94834e6	−1.44610	−0.723052	−	0.690794i	$-0.757261\pi$
$283$	−1.94834e6	−1.44610	−0.723052	+	0.690794i	$0.757261\pi$
$284$	−351360.	−0.258498
$285$	0	0
$286$	699300.	0.505532
$287$	956774.	0.685653
$288$	75776.0	0.0538332
$289$	1.93270e6	1.36120
$290$	0	0
$291$	1.02148e6	0.707123
$292$	−1.34051e6	−0.920055
$293$	254481.	0.173175	0.0865877	−	0.996244i	$-0.472404\pi$
$293$	254481.	0.173175	0.0865877	+	0.996244i	$0.472404\pi$
$294$	124852.	0.0842417
$295$	0	0
$296$	−36992.0	−0.0245402
$297$	−721175.	−0.474405
$298$	1.42863e6	0.931922
$299$	4.18581e6	2.70771
$300$	0	0
$301$	−504112.	−0.320709
$302$	748868.	0.472485
$303$	1.11800e6	0.699577
$304$	−334848.	−0.207809
$305$	0	0
$306$	−541976.	−0.330885
$307$	888813.	0.538226	0.269113	−	0.963109i	$-0.413270\pi$
$307$	888813.	0.538226	0.269113	+	0.963109i	$0.413270\pi$
$308$	−137200.	−0.0824095
$309$	−715507.	−0.426302
$310$	0	0
$311$	2.30050e6	1.34872	0.674358	−	0.738405i	$-0.264420\pi$
$311$	2.30050e6	1.34872	0.674358	+	0.738405i	$0.264420\pi$
$312$	831168.	0.483395
$313$	3.05980e6	1.76535	0.882676	−	0.469981i	$-0.155739\pi$
$313$	3.05980e6	1.76535	0.882676	+	0.469981i	$0.155739\pi$
$314$	−140296.	−0.0803010
$315$	0	0
$316$	−102672.	−0.0578408
$317$	−1.63196e6	−0.912137	−0.456069	−	0.889945i	$-0.650743\pi$
$317$	−1.63196e6	−0.912137	−0.456069	+	0.889945i	$0.650743\pi$
$318$	1.55345e6	0.861448
$319$	171675.	0.0944562
$320$	0	0
$321$	−384384.	−0.208211
$322$	−821240.	−0.441398
$323$	2.39495e6	1.27729
$324$	−569456.	−0.301368
$325$	0	0
$326$	−1.35282e6	−0.705013
$327$	−154921.	−0.0801200
$328$	−1.24966e6	−0.641370
$329$	1.25866e6	0.641091
$330$	0	0
$331$	−1.58673e6	−0.796038	−0.398019	−	0.917377i	$-0.630302\pi$
$331$	−1.58673e6	−0.796038	−0.398019	+	0.917377i	$0.630302\pi$
$332$	−117184.	−0.0583476
$333$	−42772.0	−0.0211373
$334$	1.36285e6	0.668471
$335$	0	0
$336$	−163072.	−0.0788009
$337$	−3.65685e6	−1.75401	−0.877007	−	0.480478i	$-0.840463\pi$
$337$	−3.65685e6	−1.75401	−0.877007	+	0.480478i	$0.840463\pi$
$338$	−2.50683e6	−1.19353
$339$	1.68410e6	0.795918
$340$	0	0
$341$	789950.	0.367886
$342$	−387168.	−0.178992
$343$	117649.	0.0539949
$344$	658432.	0.299996
$345$	0	0
$346$	1.73673e6	0.779907
$347$	−3.94519e6	−1.75891	−0.879455	−	0.475981i	$-0.842093\pi$
$347$	−3.94519e6	−1.75891	−0.879455	+	0.475981i	$0.842093\pi$
$348$	204048.	0.0903201
$349$	−2.34913e6	−1.03239	−0.516194	−	0.856472i	$-0.672652\pi$
$349$	−2.34913e6	−1.03239	−0.516194	+	0.856472i	$0.672652\pi$
$350$	0	0
$351$	4.11688e6	1.78361
$352$	179200.	0.0770870
$353$	−1.20368e6	−0.514133	−0.257066	−	0.966394i	$-0.582756\pi$
$353$	−1.20368e6	−0.514133	−0.257066	+	0.966394i	$0.582756\pi$
$354$	70408.0	0.0298617
$355$	0	0
$356$	−1.29338e6	−0.540879
$357$	1.16635e6	0.484348
$358$	1.89301e6	0.780629
$359$	−1.45916e6	−0.597541	−0.298771	−	0.954325i	$-0.596577\pi$
$359$	−1.45916e6	−0.597541	−0.298771	+	0.954325i	$0.596577\pi$
$360$	0	0
$361$	−765235.	−0.309049
$362$	−630680.	−0.252952
$363$	1.69554e6	0.675369
$364$	783216.	0.309833
$365$	0	0
$366$	−676624.	−0.264025
$367$	1.74617e6	0.676738	0.338369	−	0.941013i	$-0.390125\pi$
$367$	1.74617e6	0.676738	0.338369	+	0.941013i	$0.390125\pi$
$368$	1.07264e6	0.412890
$369$	−1.44492e6	−0.552432
$370$	0	0
$371$	1.46383e6	0.552147
$372$	938912.	0.351777
$373$	−3.52940e6	−1.31350	−0.656749	−	0.754109i	$-0.728069\pi$
$373$	−3.52940e6	−1.31350	−0.656749	+	0.754109i	$0.728069\pi$
$374$	−1.28170e6	−0.473813
$375$	0	0
$376$	−1.64397e6	−0.599686
$377$	−980019.	−0.355125
$378$	−807716.	−0.290756
$379$	−1.65860e6	−0.593120	−0.296560	−	0.955014i	$-0.595839\pi$
$379$	−1.65860e6	−0.593120	−0.296560	+	0.955014i	$0.595839\pi$
$380$	0	0
$381$	2.86148e6	1.00990
$382$	−1.83892e6	−0.644768
$383$	916264.	0.319171	0.159586	−	0.987184i	$-0.448984\pi$
$383$	916264.	0.319171	0.159586	+	0.987184i	$0.448984\pi$
$384$	212992.	0.0737115
$385$	0	0
$386$	1.36466e6	0.466181
$387$	761312.	0.258396
$388$	−1.25720e6	−0.423960
$389$	−4.93387e6	−1.65315	−0.826577	−	0.562823i	$-0.809715\pi$
$389$	−4.93387e6	−1.65315	−0.826577	+	0.562823i	$0.809715\pi$
$390$	0	0
$391$	−7.67189e6	−2.53782
$392$	−153664.	−0.0505076
$393$	−906594.	−0.296095
$394$	1.77097e6	0.574738
$395$	0	0
$396$	207200.	0.0663975
$397$	3.37638e6	1.07517	0.537583	−	0.843211i	$-0.319337\pi$
$397$	3.37638e6	1.07517	0.537583	+	0.843211i	$0.319337\pi$
$398$	−1.05612e6	−0.334199
$399$	833196.	0.262008
$400$	0	0
$401$	−968123.	−0.300656	−0.150328	−	0.988636i	$-0.548033\pi$
$401$	−968123.	−0.300656	−0.150328	+	0.988636i	$0.548033\pi$
$402$	−1.71735e6	−0.530022
$403$	−4.50949e6	−1.38313
$404$	−1.37600e6	−0.419435
$405$	0	0
$406$	192276.	0.0578909
$407$	−101150.	−0.0302677
$408$	−1.52339e6	−0.453066
$409$	−2.94872e6	−0.871615	−0.435807	−	0.900040i	$-0.643537\pi$
$409$	−2.94872e6	−0.871615	−0.435807	+	0.900040i	$0.643537\pi$
$410$	0	0
$411$	−2.93998e6	−0.858498
$412$	880624.	0.255592
$413$	66346.0	0.0191399
$414$	1.24024e6	0.355635
$415$	0	0
$416$	−1.02298e6	−0.289823
$417$	5.33086e6	1.50126
$418$	−915600.	−0.256310
$419$	−468274.	−0.130306	−0.0651531	−	0.997875i	$-0.520754\pi$
$419$	−468274.	−0.130306	−0.0651531	+	0.997875i	$0.520754\pi$
$420$	0	0
$421$	1.35104e6	0.371505	0.185752	−	0.982597i	$-0.440528\pi$
$421$	1.35104e6	0.371505	0.185752	+	0.982597i	$0.440528\pi$
$422$	−1.17164e6	−0.320269
$423$	−1.90084e6	−0.516528
$424$	−1.91194e6	−0.516486
$425$	0	0
$426$	−1.14192e6	−0.304868
$427$	−637588.	−0.169227
$428$	473088.	0.124834
$429$	2.27272e6	0.596216
$430$	0	0
$431$	−1.79673e6	−0.465897	−0.232948	−	0.972489i	$-0.574837\pi$
$431$	−1.79673e6	−0.465897	−0.232948	+	0.972489i	$0.574837\pi$
$432$	1.05498e6	0.271978
$433$	728294.	0.186675	0.0933377	−	0.995635i	$-0.470246\pi$
$433$	728294.	0.186675	0.0933377	+	0.995635i	$0.470246\pi$
$434$	884744.	0.225472
$435$	0	0
$436$	190672.	0.0480364
$437$	−5.48052e6	−1.37283
$438$	−4.35666e6	−1.08510
$439$	39798.0	0.00985598	0.00492799	−	0.999988i	$-0.498431\pi$
$439$	39798.0	0.00985598	0.00492799	+	0.999988i	$0.498431\pi$
$440$	0	0
$441$	−177674.	−0.0435038
$442$	7.31668e6	1.78139
$443$	7.58227e6	1.83565	0.917825	−	0.396984i	$-0.129943\pi$
$443$	7.58227e6	1.83565	0.917825	+	0.396984i	$0.129943\pi$
$444$	−120224.	−0.0289423
$445$	0	0
$446$	923332.	0.219796
$447$	4.64305e6	1.09909
$448$	200704.	0.0472456
$449$	−4.19676e6	−0.982422	−0.491211	−	0.871041i	$-0.663446\pi$
$449$	−4.19676e6	−0.982422	−0.491211	+	0.871041i	$0.663446\pi$
$450$	0	0
$451$	−3.41705e6	−0.791061
$452$	−2.07274e6	−0.477197
$453$	2.43382e6	0.557241
$454$	−4.11355e6	−0.936649
$455$	0	0
$456$	−1.08826e6	−0.245086
$457$	−2.98399e6	−0.668354	−0.334177	−	0.942510i	$-0.608458\pi$
$457$	−2.98399e6	−0.668354	−0.334177	+	0.942510i	$0.608458\pi$
$458$	1.66454e6	0.370791
$459$	−7.54555e6	−1.67170
$460$	0	0
$461$	3.56857e6	0.782064	0.391032	−	0.920377i	$-0.372118\pi$
$461$	3.56857e6	0.782064	0.391032	+	0.920377i	$0.372118\pi$
$462$	−445900.	−0.0971925
$463$	−2.43883e6	−0.528724	−0.264362	−	0.964423i	$-0.585161\pi$
$463$	−2.43883e6	−0.528724	−0.264362	+	0.964423i	$0.585161\pi$
$464$	−251136.	−0.0541519
$465$	0	0
$466$	2.97114e6	0.633808
$467$	5.63060e6	1.19471	0.597355	−	0.801977i	$-0.296218\pi$
$467$	5.63060e6	1.19471	0.597355	+	0.801977i	$0.296218\pi$
$468$	−1.18282e6	−0.249633
$469$	−1.61827e6	−0.339719
$470$	0	0
$471$	−455962.	−0.0947058
$472$	−86656.0	−0.0179037
$473$	1.80040e6	0.370012
$474$	−333684.	−0.0682165
$475$	0	0
$476$	−1.43550e6	−0.290394
$477$	−2.21068e6	−0.444866
$478$	−4.82568e6	−0.966025
$479$	−3.29963e6	−0.657092	−0.328546	−	0.944488i	$-0.606559\pi$
$479$	−3.29963e6	−0.657092	−0.328546	+	0.944488i	$0.606559\pi$
$480$	0	0
$481$	577422.	0.113797
$482$	−1.13716e6	−0.222948
$483$	−2.66903e6	−0.520578
$484$	−2.08682e6	−0.404921
$485$	0	0
$486$	2.15488e6	0.413840
$487$	5.50873e6	1.05252	0.526258	−	0.850325i	$-0.323595\pi$
$487$	5.50873e6	1.05252	0.526258	+	0.850325i	$0.323595\pi$
$488$	832768.	0.158298
$489$	−4.39668e6	−0.831481
$490$	0	0
$491$	−5.35920e6	−1.00322	−0.501610	−	0.865094i	$-0.667259\pi$
$491$	−5.35920e6	−1.00322	−0.501610	+	0.865094i	$0.667259\pi$
$492$	−4.06141e6	−0.756421
$493$	1.79621e6	0.332843
$494$	5.22677e6	0.963642
$495$	0	0
$496$	−1.15558e6	−0.210910
$497$	−1.07604e6	−0.195406
$498$	−380848.	−0.0688142
$499$	5.19932e6	0.934750	0.467375	−	0.884059i	$-0.345200\pi$
$499$	5.19932e6	0.934750	0.467375	+	0.884059i	$0.345200\pi$
$500$	0	0
$501$	4.42927e6	0.788384
$502$	−4.75433e6	−0.842034
$503$	9.68428e6	1.70666	0.853331	−	0.521369i	$-0.174579\pi$
$503$	9.68428e6	1.70666	0.853331	+	0.521369i	$0.174579\pi$
$504$	232064.	0.0406941
$505$	0	0
$506$	2.93300e6	0.509256
$507$	−8.14720e6	−1.40763
$508$	−3.52182e6	−0.605492
$509$	−548814.	−0.0938925	−0.0469462	−	0.998897i	$-0.514949\pi$
$509$	−548814.	−0.0938925	−0.0469462	+	0.998897i	$0.514949\pi$
$510$	0	0
$511$	−4.10532e6	−0.695496
$512$	−262144.	−0.0441942
$513$	−5.39027e6	−0.904309
$514$	−4.27361e6	−0.713488
$515$	0	0
$516$	2.13990e6	0.353810
$517$	−4.49522e6	−0.739648
$518$	−113288.	−0.0185507
$519$	5.64438e6	0.919809
$520$	0	0
$521$	−1.06748e7	−1.72293	−0.861463	−	0.507821i	$-0.830451\pi$
$521$	−1.06748e7	−1.72293	−0.861463	+	0.507821i	$0.830451\pi$
$522$	−290376.	−0.0466428
$523$	8.80599e6	1.40774	0.703872	−	0.710327i	$-0.251453\pi$
$523$	8.80599e6	1.40774	0.703872	+	0.710327i	$0.251453\pi$
$524$	1.11581e6	0.177526
$525$	0	0
$526$	3.73072e6	0.587934
$527$	8.26513e6	1.29635
$528$	582400.	0.0909152
$529$	1.11198e7	1.72765
$530$	0	0
$531$	−100196.	−0.0154211
$532$	−1.02547e6	−0.157089
$533$	1.95065e7	2.97414
$534$	−4.20347e6	−0.637904
$535$	0	0
$536$	2.11366e6	0.317778
$537$	6.15228e6	0.920662
$538$	5.08025e6	0.756710
$539$	−420175.	−0.0622957
$540$	0	0
$541$	4.15108e6	0.609773	0.304887	−	0.952389i	$-0.401381\pi$
$541$	4.15108e6	0.609773	0.304887	+	0.952389i	$0.401381\pi$
$542$	5.48350e6	0.801789
$543$	−2.04971e6	−0.298327
$544$	1.87494e6	0.271638
$545$	0	0
$546$	2.54545e6	0.365412
$547$	8.80209e6	1.25782	0.628909	−	0.777479i	$-0.283502\pi$
$547$	8.80209e6	1.25782	0.628909	+	0.777479i	$0.283502\pi$
$548$	3.61843e6	0.514718
$549$	962888.	0.136347
$550$	0	0
$551$	1.28315e6	0.180052
$552$	3.48608e6	0.486956
$553$	−314433.	−0.0437235
$554$	1.60660e6	0.222399
$555$	0	0
$556$	−6.56106e6	−0.900092
$557$	−4.64668e6	−0.634606	−0.317303	−	0.948324i	$-0.602777\pi$
$557$	−4.64668e6	−0.634606	−0.317303	+	0.948324i	$0.602777\pi$
$558$	−1.33614e6	−0.181664
$559$	−1.02777e7	−1.39113
$560$	0	0
$561$	−4.16552e6	−0.558808
$562$	−1.88176e6	−0.251317
$563$	−7.42856e6	−0.987720	−0.493860	−	0.869542i	$-0.664414\pi$
$563$	−7.42856e6	−0.987720	−0.493860	+	0.869542i	$0.664414\pi$
$564$	−5.34290e6	−0.707260
$565$	0	0
$566$	7.79337e6	1.02255
$567$	−1.74396e6	−0.227813
$568$	1.40544e6	0.182785
$569$	−3.34317e6	−0.432891	−0.216445	−	0.976295i	$-0.569446\pi$
$569$	−3.34317e6	−0.432891	−0.216445	+	0.976295i	$0.569446\pi$
$570$	0	0
$571$	−1.06783e6	−0.137060	−0.0685300	−	0.997649i	$-0.521831\pi$
$571$	−1.06783e6	−0.137060	−0.0685300	+	0.997649i	$0.521831\pi$
$572$	−2.79720e6	−0.357465
$573$	−5.97648e6	−0.760429
$574$	−3.82710e6	−0.484830
$575$	0	0
$576$	−303104.	−0.0380658
$577$	3.59408e6	0.449416	0.224708	−	0.974426i	$-0.427857\pi$
$577$	3.59408e6	0.449416	0.224708	+	0.974426i	$0.427857\pi$
$578$	−7.73082e6	−0.962511
$579$	4.43513e6	0.549807
$580$	0	0
$581$	−358876.	−0.0441067
$582$	−4.08590e6	−0.500012
$583$	−5.22795e6	−0.637030
$584$	5.36205e6	0.650577
$585$	0	0
$586$	−1.01792e6	−0.122454
$587$	9.79969e6	1.17386	0.586931	−	0.809637i	$-0.300336\pi$
$587$	9.79969e6	1.17386	0.586931	+	0.809637i	$0.300336\pi$
$588$	−499408.	−0.0595679
$589$	5.90431e6	0.701263
$590$	0	0
$591$	5.75565e6	0.677837
$592$	147968.	0.0173526
$593$	1.45482e7	1.69892	0.849459	−	0.527655i	$-0.176929\pi$
$593$	1.45482e7	1.69892	0.849459	+	0.527655i	$0.176929\pi$
$594$	2.88470e6	0.335455
$595$	0	0
$596$	−5.71453e6	−0.658969
$597$	−3.43239e6	−0.394149
$598$	−1.67432e7	−1.91464
$599$	1.37702e6	0.156810	0.0784050	−	0.996922i	$-0.475017\pi$
$599$	1.37702e6	0.156810	0.0784050	+	0.996922i	$0.475017\pi$
$600$	0	0
$601$	−1.01084e7	−1.14155	−0.570776	−	0.821106i	$-0.693357\pi$
$601$	−1.01084e7	−1.14155	−0.570776	+	0.821106i	$0.693357\pi$
$602$	2.01645e6	0.226775
$603$	2.44392e6	0.273712
$604$	−2.99547e6	−0.334097
$605$	0	0
$606$	−4.47200e6	−0.494675
$607$	−129767.	−0.0142953	−0.00714764	−	0.999974i	$-0.502275\pi$
$607$	−129767.	−0.0142953	−0.00714764	+	0.999974i	$0.502275\pi$
$608$	1.33939e6	0.146943
$609$	624897.	0.0682756
$610$	0	0
$611$	2.56613e7	2.78084
$612$	2.16790e6	0.233971
$613$	−1.04293e7	−1.12099	−0.560495	−	0.828158i	$-0.689389\pi$
$613$	−1.04293e7	−1.12099	−0.560495	+	0.828158i	$0.689389\pi$
$614$	−3.55525e6	−0.380583
$615$	0	0
$616$	548800.	0.0582723
$617$	−8.03825e6	−0.850058	−0.425029	−	0.905180i	$-0.639736\pi$
$617$	−8.03825e6	−0.850058	−0.425029	+	0.905180i	$0.639736\pi$
$618$	2.86203e6	0.301441
$619$	−5.14119e6	−0.539309	−0.269654	−	0.962957i	$-0.586909\pi$
$619$	−5.14119e6	−0.539309	−0.269654	+	0.962957i	$0.586909\pi$
$620$	0	0
$621$	1.72670e7	1.79675
$622$	−9.20198e6	−0.953686
$623$	−3.96096e6	−0.408866
$624$	−3.32467e6	−0.341812
$625$	0	0
$626$	−1.22392e7	−1.24829
$627$	−2.97570e6	−0.302288
$628$	561184.	0.0567814
$629$	−1.05832e6	−0.106657
$630$	0	0
$631$	−1.32603e7	−1.32580	−0.662902	−	0.748707i	$-0.730675\pi$
$631$	−1.32603e7	−1.32580	−0.662902	+	0.748707i	$0.730675\pi$
$632$	410688.	0.0408996
$633$	−3.80784e6	−0.377720
$634$	6.52782e6	0.644979
$635$	0	0
$636$	−6.21379e6	−0.609136
$637$	2.39860e6	0.234212
$638$	−686700.	−0.0667906
$639$	1.62504e6	0.157439
$640$	0	0
$641$	3.06366e6	0.294507	0.147254	−	0.989099i	$-0.452957\pi$
$641$	3.06366e6	0.294507	0.147254	+	0.989099i	$0.452957\pi$
$642$	1.53754e6	0.147227
$643$	1.78735e7	1.70483	0.852415	−	0.522866i	$-0.175137\pi$
$643$	1.78735e7	1.70483	0.852415	+	0.522866i	$0.175137\pi$
$644$	3.28496e6	0.312116
$645$	0	0
$646$	−9.57979e6	−0.903181
$647$	−3.24341e6	−0.304608	−0.152304	−	0.988334i	$-0.548669\pi$
$647$	−3.24341e6	−0.304608	−0.152304	+	0.988334i	$0.548669\pi$
$648$	2.27782e6	0.213100
$649$	−236950.	−0.0220823
$650$	0	0
$651$	2.87542e6	0.265918
$652$	5.41130e6	0.498520
$653$	−1.88072e7	−1.72600	−0.863001	−	0.505202i	$-0.831418\pi$
$653$	−1.88072e7	−1.72600	−0.863001	+	0.505202i	$0.831418\pi$
$654$	619684.	0.0566534
$655$	0	0
$656$	4.99866e6	0.453517
$657$	6.19987e6	0.560362
$658$	−5.03465e6	−0.453320
$659$	9.35310e6	0.838962	0.419481	−	0.907764i	$-0.362212\pi$
$659$	9.35310e6	0.838962	0.419481	+	0.907764i	$0.362212\pi$
$660$	0	0
$661$	1.46906e6	0.130778	0.0653892	−	0.997860i	$-0.479171\pi$
$661$	1.46906e6	0.130778	0.0653892	+	0.997860i	$0.479171\pi$
$662$	6.34693e6	0.562884
$663$	2.37792e7	2.10094
$664$	468736.	0.0412580
$665$	0	0
$666$	171088.	0.0149463
$667$	−4.11039e6	−0.357741
$668$	−5.45141e6	−0.472680
$669$	3.00083e6	0.259224
$670$	0	0
$671$	2.27710e6	0.195243
$672$	652288.	0.0557207
$673$	−1.23008e7	−1.04687	−0.523437	−	0.852065i	$-0.675350\pi$
$673$	−1.23008e7	−1.04687	−0.523437	+	0.852065i	$0.675350\pi$
$674$	1.46274e7	1.24027
$675$	0	0
$676$	1.00273e7	0.843953
$677$	−4.87477e6	−0.408773	−0.204387	−	0.978890i	$-0.565520\pi$
$677$	−4.87477e6	−0.408773	−0.204387	+	0.978890i	$0.565520\pi$
$678$	−6.73639e6	−0.562799
$679$	−3.85018e6	−0.320484
$680$	0	0
$681$	−1.33690e7	−1.10467
$682$	−3.15980e6	−0.260135
$683$	−1.92627e6	−0.158003	−0.0790014	−	0.996875i	$-0.525173\pi$
$683$	−1.92627e6	−0.158003	−0.0790014	+	0.996875i	$0.525173\pi$
$684$	1.54867e6	0.126567
$685$	0	0
$686$	−470596.	−0.0381802
$687$	5.40974e6	0.437305
$688$	−2.63373e6	−0.212129
$689$	2.98441e7	2.39503
$690$	0	0
$691$	2.14791e7	1.71128	0.855640	−	0.517572i	$-0.173164\pi$
$691$	2.14791e7	1.71128	0.855640	+	0.517572i	$0.173164\pi$
$692$	−6.94693e6	−0.551477
$693$	634550.	0.0501918
$694$	1.57807e7	1.24374
$695$	0	0
$696$	−816192.	−0.0638659
$697$	−3.57521e7	−2.78753
$698$	9.39651e6	0.730009
$699$	9.65619e6	0.747503
$700$	0	0
$701$	−57037.0	−0.00438391	−0.00219196	−	0.999998i	$-0.500698\pi$
$701$	−57037.0	−0.00438391	−0.00219196	+	0.999998i	$0.500698\pi$
$702$	−1.64675e7	−1.26120
$703$	−756024.	−0.0576962
$704$	−716800.	−0.0545088
$705$	0	0
$706$	4.81473e6	0.363547
$707$	−4.21400e6	−0.317063
$708$	−281632.	−0.0211154
$709$	−6.60254e6	−0.493282	−0.246641	−	0.969107i	$-0.579327\pi$
$709$	−6.60254e6	−0.493282	−0.246641	+	0.969107i	$0.579327\pi$
$710$	0	0
$711$	474858.	0.0352281
$712$	5.17350e6	0.382459
$713$	−1.89137e7	−1.39332
$714$	−4.66539e6	−0.342486
$715$	0	0
$716$	−7.57203e6	−0.551988
$717$	−1.56834e7	−1.13931
$718$	5.83666e6	0.422526
$719$	−1.53592e7	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$719$	−1.53592e7	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$720$	0	0
$721$	2.69691e6	0.193209
$722$	3.06094e6	0.218530
$723$	−3.69577e6	−0.262942
$724$	2.52272e6	0.178864
$725$	0	0
$726$	−6.78215e6	−0.477558
$727$	3.98812e6	0.279854	0.139927	−	0.990162i	$-0.455313\pi$
$727$	3.98812e6	0.279854	0.139927	+	0.990162i	$0.455313\pi$
$728$	−3.13286e6	−0.219085
$729$	1.56520e7	1.09081
$730$	0	0
$731$	1.88373e7	1.30384
$732$	2.70650e6	0.186694
$733$	1.55266e7	1.06737	0.533687	−	0.845682i	$-0.320806\pi$
$733$	1.55266e7	1.06737	0.533687	+	0.845682i	$0.320806\pi$
$734$	−6.98467e6	−0.478526
$735$	0	0
$736$	−4.29056e6	−0.291957
$737$	5.77955e6	0.391945
$738$	5.77970e6	0.390629
$739$	1.18859e7	0.800612	0.400306	−	0.916382i	$-0.368904\pi$
$739$	1.18859e7	0.800612	0.400306	+	0.916382i	$0.368904\pi$
$740$	0	0
$741$	1.69870e7	1.13650
$742$	−5.85530e6	−0.390427
$743$	−1.22759e6	−0.0815798	−0.0407899	−	0.999168i	$-0.512987\pi$
$743$	−1.22759e6	−0.0815798	−0.0407899	+	0.999168i	$0.512987\pi$
$744$	−3.75565e6	−0.248744
$745$	0	0
$746$	1.41176e7	0.928783
$747$	541976.	0.0355368
$748$	5.12680e6	0.335037
$749$	1.44883e6	0.0943656
$750$	0	0
$751$	−1.60580e7	−1.03894	−0.519472	−	0.854488i	$-0.673871\pi$
$751$	−1.60580e7	−1.03894	−0.519472	+	0.854488i	$0.673871\pi$
$752$	6.57587e6	0.424042
$753$	−1.54516e7	−0.993082
$754$	3.92008e6	0.251111
$755$	0	0
$756$	3.23086e6	0.205596
$757$	2.56513e6	0.162693	0.0813466	−	0.996686i	$-0.474078\pi$
$757$	2.56513e6	0.162693	0.0813466	+	0.996686i	$0.474078\pi$
$758$	6.63438e6	0.419399
$759$	9.53225e6	0.600608
$760$	0	0
$761$	−1.84665e7	−1.15590	−0.577952	−	0.816071i	$-0.696148\pi$
$761$	−1.84665e7	−1.15590	−0.577952	+	0.816071i	$0.696148\pi$
$762$	−1.14459e7	−0.714107
$763$	583933.	0.0363121
$764$	7.35566e6	0.455920
$765$	0	0
$766$	−3.66506e6	−0.225688
$767$	1.35265e6	0.0830225
$768$	−851968.	−0.0521219
$769$	1.65360e7	1.00836	0.504180	−	0.863599i	$-0.331795\pi$
$769$	1.65360e7	1.00836	0.504180	+	0.863599i	$0.331795\pi$
$770$	0	0
$771$	−1.38892e7	−0.841477
$772$	−5.45862e6	−0.329640
$773$	9.95201e6	0.599049	0.299524	−	0.954089i	$-0.403172\pi$
$773$	9.95201e6	0.599049	0.299524	+	0.954089i	$0.403172\pi$
$774$	−3.04525e6	−0.182713
$775$	0	0
$776$	5.02880e6	0.299785
$777$	−368186.	−0.0218784
$778$	1.97355e7	1.16896
$779$	−2.55400e7	−1.50792
$780$	0	0
$781$	3.84300e6	0.225446
$782$	3.06876e7	1.79451
$783$	−4.04270e6	−0.235650
$784$	614656.	0.0357143
$785$	0	0
$786$	3.62638e6	0.209371
$787$	3.02239e7	1.73946	0.869729	−	0.493530i	$-0.164294\pi$
$787$	3.02239e7	1.73946	0.869729	+	0.493530i	$0.164294\pi$
$788$	−7.08387e6	−0.406401
$789$	1.21248e7	0.693399
$790$	0	0
$791$	−6.34775e6	−0.360727
$792$	−828800.	−0.0469501
$793$	−1.29990e7	−0.734052
$794$	−1.35055e7	−0.760257
$795$	0	0
$796$	4.22448e6	0.236315
$797$	1.30485e7	0.727638	0.363819	−	0.931470i	$-0.381473\pi$
$797$	1.30485e7	0.727638	0.363819	+	0.931470i	$0.381473\pi$
$798$	−3.33278e6	−0.185268
$799$	−4.70329e7	−2.60636
$800$	0	0
$801$	5.98186e6	0.329424
$802$	3.87249e6	0.212596
$803$	1.46619e7	0.802417
$804$	6.86941e6	0.374782
$805$	0	0
$806$	1.80379e7	0.978024
$807$	1.65108e7	0.892451
$808$	5.50400e6	0.296586
$809$	2.55706e7	1.37363	0.686814	−	0.726833i	$-0.259009\pi$
$809$	2.55706e7	1.37363	0.686814	+	0.726833i	$0.259009\pi$
$810$	0	0
$811$	−1.47936e7	−0.789810	−0.394905	−	0.918722i	$-0.629223\pi$
$811$	−1.47936e7	−0.789810	−0.394905	+	0.918722i	$0.629223\pi$
$812$	−769104.	−0.0409350
$813$	1.78214e7	0.945617
$814$	404600.	0.0214025
$815$	0	0
$816$	6.09357e6	0.320366
$817$	1.34567e7	0.705316
$818$	1.17949e7	0.616325
$819$	−3.62237e6	−0.188705
$820$	0	0
$821$	2.64112e7	1.36751	0.683754	−	0.729713i	$-0.260346\pi$
$821$	2.64112e7	1.36751	0.683754	+	0.729713i	$0.260346\pi$
$822$	1.17599e7	0.607050
$823$	−569430.	−0.0293049	−0.0146525	−	0.999893i	$-0.504664\pi$
$823$	−569430.	−0.0293049	−0.0146525	+	0.999893i	$0.504664\pi$
$824$	−3.52250e6	−0.180731
$825$	0	0
$826$	−265384.	−0.0135340
$827$	2.73601e7	1.39109	0.695544	−	0.718483i	$-0.255163\pi$
$827$	2.73601e7	1.39109	0.695544	+	0.718483i	$0.255163\pi$
$828$	−4.96096e6	−0.251472
$829$	−1.32254e7	−0.668380	−0.334190	−	0.942506i	$-0.608463\pi$
$829$	−1.32254e7	−0.668380	−0.334190	+	0.942506i	$0.608463\pi$
$830$	0	0
$831$	5.22145e6	0.262294
$832$	4.09190e6	0.204935
$833$	−4.39623e6	−0.219517
$834$	−2.13234e7	−1.06155
$835$	0	0
$836$	3.66240e6	0.181238
$837$	−1.86022e7	−0.917805
$838$	1.87310e6	0.0921404
$839$	−2.87296e6	−0.140904	−0.0704522	−	0.997515i	$-0.522444\pi$
$839$	−2.87296e6	−0.140904	−0.0704522	+	0.997515i	$0.522444\pi$
$840$	0	0
$841$	−1.95488e7	−0.953081
$842$	−5.40418e6	−0.262694
$843$	−6.11571e6	−0.296400
$844$	4.68658e6	0.226464
$845$	0	0
$846$	7.60335e6	0.365241
$847$	−6.39087e6	−0.306092
$848$	7.64774e6	0.365211
$849$	2.53285e7	1.20598
$850$	0	0
$851$	2.42182e6	0.114635
$852$	4.56768e6	0.215574
$853$	1.97720e7	0.930416	0.465208	−	0.885201i	$-0.345979\pi$
$853$	1.97720e7	0.930416	0.465208	+	0.885201i	$0.345979\pi$
$854$	2.55035e6	0.119662
$855$	0	0
$856$	−1.89235e6	−0.0882709
$857$	−6.01876e6	−0.279934	−0.139967	−	0.990156i	$-0.544700\pi$
$857$	−6.01876e6	−0.279934	−0.139967	+	0.990156i	$0.544700\pi$
$858$	−9.09090e6	−0.421588
$859$	−308056.	−0.0142445	−0.00712224	−	0.999975i	$-0.502267\pi$
$859$	−308056.	−0.0142445	−0.00712224	+	0.999975i	$0.502267\pi$
$860$	0	0
$861$	−1.24381e7	−0.571801
$862$	7.18692e6	0.329439
$863$	−3.62988e7	−1.65907	−0.829536	−	0.558453i	$-0.811395\pi$
$863$	−3.62988e7	−1.65907	−0.829536	+	0.558453i	$0.811395\pi$
$864$	−4.21990e6	−0.192317
$865$	0	0
$866$	−2.91318e6	−0.131999
$867$	−2.51252e7	−1.13517
$868$	−3.53898e6	−0.159433
$869$	1.12298e6	0.0504453
$870$	0	0
$871$	−3.29930e7	−1.47359
$872$	−762688.	−0.0339669
$873$	5.81455e6	0.258214
$874$	2.19221e7	0.970741
$875$	0	0
$876$	1.74267e7	0.767280
$877$	−716828.	−0.0314714	−0.0157357	−	0.999876i	$-0.505009\pi$
$877$	−716828.	−0.0314714	−0.0157357	+	0.999876i	$0.505009\pi$
$878$	−159192.	−0.00696923
$879$	−3.30825e6	−0.144420
$880$	0	0
$881$	−1.24338e7	−0.539716	−0.269858	−	0.962900i	$-0.586977\pi$
$881$	−1.24338e7	−0.539716	−0.269858	+	0.962900i	$0.586977\pi$
$882$	710696.	0.0307618
$883$	−2.44142e7	−1.05376	−0.526880	−	0.849940i	$-0.676638\pi$
$883$	−2.44142e7	−1.05376	−0.526880	+	0.849940i	$0.676638\pi$
$884$	−2.92667e7	−1.25963
$885$	0	0
$886$	−3.03291e7	−1.29800
$887$	2.56721e7	1.09560	0.547801	−	0.836609i	$-0.315465\pi$
$887$	2.56721e7	1.09560	0.547801	+	0.836609i	$0.315465\pi$
$888$	480896.	0.0204653
$889$	−1.07856e7	−0.457709
$890$	0	0
$891$	6.22842e6	0.262835
$892$	−3.69333e6	−0.155420
$893$	−3.35986e7	−1.40991
$894$	−1.85722e7	−0.777177
$895$	0	0
$896$	−802816.	−0.0334077
$897$	−5.44155e7	−2.25809
$898$	1.67870e7	0.694677
$899$	4.42823e6	0.182739
$900$	0	0
$901$	−5.46993e7	−2.24476
$902$	1.36682e7	0.559365
$903$	6.55346e6	0.267455
$904$	8.29094e6	0.337429
$905$	0	0
$906$	−9.73528e6	−0.394029
$907$	4.51473e7	1.82227	0.911137	−	0.412104i	$-0.135206\pi$
$907$	4.51473e7	1.82227	0.911137	+	0.412104i	$0.135206\pi$
$908$	1.64542e7	0.662311
$909$	6.36400e6	0.255459
$910$	0	0
$911$	4.80689e7	1.91897	0.959484	−	0.281761i	$-0.0909187\pi$
$911$	4.80689e7	1.91897	0.959484	+	0.281761i	$0.0909187\pi$
$912$	4.35302e6	0.173302
$913$	1.28170e6	0.0508873
$914$	1.19360e7	0.472598
$915$	0	0
$916$	−6.65814e6	−0.262189
$917$	3.41716e6	0.134197
$918$	3.01822e7	1.18207
$919$	2.18989e7	0.855330	0.427665	−	0.903937i	$-0.359336\pi$
$919$	2.18989e7	0.855330	0.427665	+	0.903937i	$0.359336\pi$
$920$	0	0
$921$	−1.15546e7	−0.448854
$922$	−1.42743e7	−0.553003
$923$	−2.19380e7	−0.847605
$924$	1.78360e6	0.0687254
$925$	0	0
$926$	9.75533e6	0.373865
$927$	−4.07289e6	−0.155669
$928$	1.00454e6	0.0382912
$929$	−1.39883e6	−0.0531774	−0.0265887	−	0.999646i	$-0.508464\pi$
$929$	−1.39883e6	−0.0531774	−0.0265887	+	0.999646i	$0.508464\pi$
$930$	0	0
$931$	−3.14051e6	−0.118748
$932$	−1.18845e7	−0.448170
$933$	−2.99064e7	−1.12476
$934$	−2.25224e7	−0.844788
$935$	0	0
$936$	4.73126e6	0.176517
$937$	1.41701e7	0.527259	0.263629	−	0.964624i	$-0.415080\pi$
$937$	1.41701e7	0.527259	0.263629	+	0.964624i	$0.415080\pi$
$938$	6.47310e6	0.240218
$939$	−3.97773e7	−1.47222
$940$	0	0
$941$	3.30822e7	1.21792	0.608962	−	0.793199i	$-0.291586\pi$
$941$	3.30822e7	1.21792	0.608962	+	0.793199i	$0.291586\pi$
$942$	1.82385e6	0.0669671
$943$	8.18139e7	2.99604
$944$	346624.	0.0126599
$945$	0	0
$946$	−7.20160e6	−0.261638
$947$	−1.91693e7	−0.694596	−0.347298	−	0.937755i	$-0.612901\pi$
$947$	−1.91693e7	−0.694596	−0.347298	+	0.937755i	$0.612901\pi$
$948$	1.33474e6	0.0482364
$949$	−8.36982e7	−3.01683
$950$	0	0
$951$	2.12154e7	0.760677
$952$	5.74202e6	0.205339
$953$	4.02398e7	1.43524	0.717619	−	0.696436i	$-0.245232\pi$
$953$	4.02398e7	1.43524	0.717619	+	0.696436i	$0.245232\pi$
$954$	8.84270e6	0.314568
$955$	0	0
$956$	1.93027e7	0.683083
$957$	−2.23178e6	−0.0787718
$958$	1.31985e7	0.464634
$959$	1.10814e7	0.389090
$960$	0	0
$961$	−8.25295e6	−0.288271
$962$	−2.30969e6	−0.0804666
$963$	−2.18803e6	−0.0760305
$964$	4.54864e6	0.157648
$965$	0	0
$966$	1.06761e7	0.368104
$967$	−2.32923e6	−0.0801026	−0.0400513	−	0.999198i	$-0.512752\pi$
$967$	−2.32923e6	−0.0801026	−0.0400513	+	0.999198i	$0.512752\pi$
$968$	8.34726e6	0.286323
$969$	−3.11343e7	−1.06520
$970$	0	0
$971$	−4.35760e7	−1.48320	−0.741599	−	0.670844i	$-0.765932\pi$
$971$	−4.35760e7	−1.48320	−0.741599	+	0.670844i	$0.765932\pi$
$972$	−8.61952e6	−0.292629
$973$	−2.00932e7	−0.680405
$974$	−2.20349e7	−0.744241
$975$	0	0
$976$	−3.33107e6	−0.111933
$977$	−4.40436e7	−1.47620	−0.738102	−	0.674689i	$-0.764278\pi$
$977$	−4.40436e7	−1.47620	−0.738102	+	0.674689i	$0.764278\pi$
$978$	1.75867e7	0.587946
$979$	1.41463e7	0.471722
$980$	0	0
$981$	−881858.	−0.0292568
$982$	2.14368e7	0.709383
$983$	−1.96132e7	−0.647387	−0.323693	−	0.946162i	$-0.604925\pi$
$983$	−1.96132e7	−0.647387	−0.323693	+	0.946162i	$0.604925\pi$
$984$	1.62456e7	0.534871
$985$	0	0
$986$	−7.18484e6	−0.235356
$987$	−1.63626e7	−0.534638
$988$	−2.09071e7	−0.681398
$989$	−4.31067e7	−1.40137
$990$	0	0
$991$	−4.13805e7	−1.33848	−0.669239	−	0.743047i	$-0.733380\pi$
$991$	−4.13805e7	−1.33848	−0.669239	+	0.743047i	$0.733380\pi$
$992$	4.62234e6	0.149136
$993$	2.06275e7	0.663856
$994$	4.30416e6	0.138173
$995$	0	0
$996$	1.52339e6	0.0486590
$997$	−5.75096e7	−1.83233	−0.916163	−	0.400806i	$-0.868730\pi$
$997$	−5.75096e7	−1.83233	−0.916163	+	0.400806i	$0.868730\pi$
$998$	−2.07973e7	−0.660968
$999$	2.38194e6	0.0755121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.6.a.a.1.1		1
5.2	odd	4		70.6.c.c.29.1	✓	2
5.3	odd	4		70.6.c.c.29.2	yes	2
5.4	even	2		350.6.a.m.1.1		1
15.2	even	4		630.6.g.a.379.2		2
15.8	even	4		630.6.g.a.379.1		2
20.3	even	4		560.6.g.c.449.2		2
20.7	even	4		560.6.g.c.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.c.c.29.1	✓	2	5.2	odd	4
70.6.c.c.29.2	yes	2	5.3	odd	4
350.6.a.a.1.1		1	1.1	even	1	trivial
350.6.a.m.1.1		1	5.4	even	2
560.6.g.c.449.1		2	20.7	even	4
560.6.g.c.449.2		2	20.3	even	4
630.6.g.a.379.1		2	15.8	even	4
630.6.g.a.379.2		2	15.2	even	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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