LMFDB - Embedded newform 315.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,6,Mod(1,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("315.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	315.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:	$50.5209032411$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	315.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+8.00000 q^{2} +32.0000 q^{4} -25.0000 q^{5} +49.0000 q^{7} +O(q^{10})$

$q+8.00000 q^{2} +32.0000 q^{4} -25.0000 q^{5} +49.0000 q^{7} -200.000 q^{10} +453.000 q^{11} -969.000 q^{13} +392.000 q^{14} -1024.00 q^{16} -1637.00 q^{17} -1550.00 q^{19} -800.000 q^{20} +3624.00 q^{22} +1654.00 q^{23} +625.000 q^{25} -7752.00 q^{26} +1568.00 q^{28} +4985.00 q^{29} +1192.00 q^{31} -8192.00 q^{32} -13096.0 q^{34} -1225.00 q^{35} -11018.0 q^{37} -12400.0 q^{38} +1728.00 q^{41} -10814.0 q^{43} +14496.0 q^{44} +13232.0 q^{46} -26237.0 q^{47} +2401.00 q^{49} +5000.00 q^{50} -31008.0 q^{52} -25936.0 q^{53} -11325.0 q^{55} +39880.0 q^{58} +4580.00 q^{59} -12488.0 q^{61} +9536.00 q^{62} -32768.0 q^{64} +24225.0 q^{65} -15848.0 q^{67} -52384.0 q^{68} -9800.00 q^{70} -51792.0 q^{71} +4846.00 q^{73} -88144.0 q^{74} -49600.0 q^{76} +22197.0 q^{77} +62765.0 q^{79} +25600.0 q^{80} +13824.0 q^{82} +23644.0 q^{83} +40925.0 q^{85} -86512.0 q^{86} +147300. q^{89} -47481.0 q^{91} +52928.0 q^{92} -209896. q^{94} +38750.0 q^{95} -8343.00 q^{97} +19208.0 q^{98} +O(q^{100})$

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 $

$2$	8.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	8.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	0	0
$3$	0	0
$4$	32.0000	1.00000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	0	0
$9$	0	0
$10$	−200.000	−0.632456
$11$	453.000	1.12880	0.564399	−	0.825502i	$-0.309108\pi$
$11$	453.000	1.12880	0.564399	+	0.825502i	$0.309108\pi$
$12$	0	0
$13$	−969.000	−1.59025	−0.795125	−	0.606446i	$-0.792595\pi$
$13$	−969.000	−1.59025	−0.795125	+	0.606446i	$0.792595\pi$
$14$	392.000	0.534522
$15$	0	0
$16$	−1024.00	−1.00000
$17$	−1637.00	−1.37381	−0.686905	−	0.726748i	$-0.741031\pi$
$17$	−1637.00	−1.37381	−0.686905	+	0.726748i	$0.741031\pi$
$18$	0	0
$19$	−1550.00	−0.985026	−0.492513	−	0.870305i	$-0.663922\pi$
$19$	−1550.00	−0.985026	−0.492513	+	0.870305i	$0.663922\pi$
$20$	−800.000	−0.447214
$21$	0	0
$22$	3624.00	1.59636
$23$	1654.00	0.651952	0.325976	−	0.945378i	$-0.394307\pi$
$23$	1654.00	0.651952	0.325976	+	0.945378i	$0.394307\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	−7752.00	−2.24895
$27$	0	0
$28$	1568.00	0.377964
$29$	4985.00	1.10070	0.550352	−	0.834933i	$-0.314494\pi$
$29$	4985.00	1.10070	0.550352	+	0.834933i	$0.314494\pi$
$30$	0	0
$31$	1192.00	0.222778	0.111389	−	0.993777i	$-0.464470\pi$
$31$	1192.00	0.222778	0.111389	+	0.993777i	$0.464470\pi$
$32$	−8192.00	−1.41421
$33$	0	0
$34$	−13096.0	−1.94286
$35$	−1225.00	−0.169031
$36$	0	0
$37$	−11018.0	−1.32312	−0.661559	−	0.749893i	$-0.730105\pi$
$37$	−11018.0	−1.32312	−0.661559	+	0.749893i	$0.730105\pi$
$38$	−12400.0	−1.39304
$39$	0	0
$40$	0	0
$41$	1728.00	0.160540	0.0802702	−	0.996773i	$-0.474422\pi$
$41$	1728.00	0.160540	0.0802702	+	0.996773i	$0.474422\pi$
$42$	0	0
$43$	−10814.0	−0.891898	−0.445949	−	0.895058i	$-0.647134\pi$
$43$	−10814.0	−0.891898	−0.445949	+	0.895058i	$0.647134\pi$
$44$	14496.0	1.12880
$45$	0	0
$46$	13232.0	0.922000
$47$	−26237.0	−1.73249	−0.866243	−	0.499624i	$-0.833472\pi$
$47$	−26237.0	−1.73249	−0.866243	+	0.499624i	$0.833472\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	5000.00	0.282843
$51$	0	0
$52$	−31008.0	−1.59025
$53$	−25936.0	−1.26827	−0.634137	−	0.773220i	$-0.718645\pi$
$53$	−25936.0	−1.26827	−0.634137	+	0.773220i	$0.718645\pi$
$54$	0	0
$55$	−11325.0	−0.504814
$56$	0	0
$57$	0	0
$58$	39880.0	1.55663
$59$	4580.00	0.171291	0.0856457	−	0.996326i	$-0.472705\pi$
$59$	4580.00	0.171291	0.0856457	+	0.996326i	$0.472705\pi$
$60$	0	0
$61$	−12488.0	−0.429703	−0.214851	−	0.976647i	$-0.568927\pi$
$61$	−12488.0	−0.429703	−0.214851	+	0.976647i	$0.568927\pi$
$62$	9536.00	0.315055
$63$	0	0
$64$	−32768.0	−1.00000
$65$	24225.0	0.711181
$66$	0	0
$67$	−15848.0	−0.431308	−0.215654	−	0.976470i	$-0.569188\pi$
$67$	−15848.0	−0.431308	−0.215654	+	0.976470i	$0.569188\pi$
$68$	−52384.0	−1.37381
$69$	0	0
$70$	−9800.00	−0.239046
$71$	−51792.0	−1.21932	−0.609659	−	0.792664i	$-0.708694\pi$
$71$	−51792.0	−1.21932	−0.609659	+	0.792664i	$0.708694\pi$
$72$	0	0
$73$	4846.00	0.106433	0.0532165	−	0.998583i	$-0.483053\pi$
$73$	4846.00	0.106433	0.0532165	+	0.998583i	$0.483053\pi$
$74$	−88144.0	−1.87117
$75$	0	0
$76$	−49600.0	−0.985026
$77$	22197.0	0.426646
$78$	0	0
$79$	62765.0	1.13149	0.565744	−	0.824581i	$-0.308589\pi$
$79$	62765.0	1.13149	0.565744	+	0.824581i	$0.308589\pi$
$80$	25600.0	0.447214
$81$	0	0
$82$	13824.0	0.227038
$83$	23644.0	0.376726	0.188363	−	0.982099i	$-0.439682\pi$
$83$	23644.0	0.376726	0.188363	+	0.982099i	$0.439682\pi$
$84$	0	0
$85$	40925.0	0.614386
$86$	−86512.0	−1.26133
$87$	0	0
$88$	0	0
$89$	147300.	1.97119	0.985593	−	0.169133i	$-0.0540967\pi$
$89$	147300.	1.97119	0.985593	+	0.169133i	$0.0540967\pi$
$90$	0	0
$91$	−47481.0	−0.601058
$92$	52928.0	0.651952
$93$	0	0
$94$	−209896.	−2.45010
$95$	38750.0	0.440517
$96$	0	0
$97$	−8343.00	−0.0900312	−0.0450156	−	0.998986i	$-0.514334\pi$
$97$	−8343.00	−0.0900312	−0.0450156	+	0.998986i	$0.514334\pi$
$98$	19208.0	0.202031
$99$	0	0
$100$	20000.0	0.200000
$101$	11878.0	0.115862	0.0579308	−	0.998321i	$-0.481550\pi$
$101$	11878.0	0.115862	0.0579308	+	0.998321i	$0.481550\pi$
$102$	0	0
$103$	−132439.	−1.23005	−0.615025	−	0.788508i	$-0.710854\pi$
$103$	−132439.	−1.23005	−0.615025	+	0.788508i	$0.710854\pi$
$104$	0	0
$105$	0	0
$106$	−207488.	−1.79361
$107$	−136842.	−1.15547	−0.577737	−	0.816223i	$-0.696064\pi$
$107$	−136842.	−1.15547	−0.577737	+	0.816223i	$0.696064\pi$
$108$	0	0
$109$	109485.	0.882650	0.441325	−	0.897347i	$-0.354509\pi$
$109$	109485.	0.882650	0.441325	+	0.897347i	$0.354509\pi$
$110$	−90600.0	−0.713915
$111$	0	0
$112$	−50176.0	−0.377964
$113$	200934.	1.48033	0.740163	−	0.672428i	$-0.234748\pi$
$113$	200934.	1.48033	0.740163	+	0.672428i	$0.234748\pi$
$114$	0	0
$115$	−41350.0	−0.291562
$116$	159520.	1.10070
$117$	0	0
$118$	36640.0	0.242243
$119$	−80213.0	−0.519251
$120$	0	0
$121$	44158.0	0.274186
$122$	−99904.0	−0.607692
$123$	0	0
$124$	38144.0	0.222778
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	330692.	1.81934	0.909671	−	0.415329i	$-0.136334\pi$
$127$	330692.	1.81934	0.909671	+	0.415329i	$0.136334\pi$
$128$	0	0
$129$	0	0
$130$	193800.	1.00576
$131$	−43982.0	−0.223922	−0.111961	−	0.993713i	$-0.535713\pi$
$131$	−43982.0	−0.223922	−0.111961	+	0.993713i	$0.535713\pi$
$132$	0	0
$133$	−75950.0	−0.372305
$134$	−126784.	−0.609962
$135$	0	0
$136$	0	0
$137$	99748.0	0.454049	0.227025	−	0.973889i	$-0.427100\pi$
$137$	99748.0	0.454049	0.227025	+	0.973889i	$0.427100\pi$
$138$	0	0
$139$	258930.	1.13670	0.568349	−	0.822787i	$-0.307582\pi$
$139$	258930.	1.13670	0.568349	+	0.822787i	$0.307582\pi$
$140$	−39200.0	−0.169031
$141$	0	0
$142$	−414336.	−1.72438
$143$	−438957.	−1.79507
$144$	0	0
$145$	−124625.	−0.492249
$146$	38768.0	0.150519
$147$	0	0
$148$	−352576.	−1.32312
$149$	498430.	1.83924	0.919620	−	0.392809i	$-0.128497\pi$
$149$	498430.	1.83924	0.919620	+	0.392809i	$0.128497\pi$
$150$	0	0
$151$	−245803.	−0.877293	−0.438647	−	0.898660i	$-0.644542\pi$
$151$	−245803.	−0.877293	−0.438647	+	0.898660i	$0.644542\pi$
$152$	0	0
$153$	0	0
$154$	177576.	0.603368
$155$	−29800.0	−0.0996293
$156$	0	0
$157$	−85478.0	−0.276761	−0.138381	−	0.990379i	$-0.544190\pi$
$157$	−85478.0	−0.276761	−0.138381	+	0.990379i	$0.544190\pi$
$158$	502120.	1.60017
$159$	0	0
$160$	204800.	0.632456
$161$	81046.0	0.246415
$162$	0	0
$163$	193026.	0.569045	0.284523	−	0.958669i	$-0.408165\pi$
$163$	193026.	0.569045	0.284523	+	0.958669i	$0.408165\pi$
$164$	55296.0	0.160540
$165$	0	0
$166$	189152.	0.532771
$167$	157783.	0.437793	0.218897	−	0.975748i	$-0.429754\pi$
$167$	157783.	0.437793	0.218897	+	0.975748i	$0.429754\pi$
$168$	0	0
$169$	567668.	1.52889
$170$	327400.	0.868873
$171$	0	0
$172$	−346048.	−0.891898
$173$	265659.	0.674853	0.337427	−	0.941352i	$-0.390444\pi$
$173$	265659.	0.674853	0.337427	+	0.941352i	$0.390444\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	−463872.	−1.12880
$177$	0	0
$178$	1.17840e6	2.78768
$179$	−183660.	−0.428432	−0.214216	−	0.976786i	$-0.568720\pi$
$179$	−183660.	−0.428432	−0.214216	+	0.976786i	$0.568720\pi$
$180$	0	0
$181$	−635048.	−1.44082	−0.720411	−	0.693548i	$-0.756047\pi$
$181$	−635048.	−1.44082	−0.720411	+	0.693548i	$0.756047\pi$
$182$	−379848.	−0.850024
$183$	0	0
$184$	0	0
$185$	275450.	0.591716
$186$	0	0
$187$	−741561.	−1.55075
$188$	−839584.	−1.73249
$189$	0	0
$190$	310000.	0.622985
$191$	226613.	0.449471	0.224735	−	0.974420i	$-0.427848\pi$
$191$	226613.	0.449471	0.224735	+	0.974420i	$0.427848\pi$
$192$	0	0
$193$	46476.0	0.0898122	0.0449061	−	0.998991i	$-0.485701\pi$
$193$	46476.0	0.0898122	0.0449061	+	0.998991i	$0.485701\pi$
$194$	−66744.0	−0.127323
$195$	0	0
$196$	76832.0	0.142857
$197$	−204972.	−0.376295	−0.188148	−	0.982141i	$-0.560248\pi$
$197$	−204972.	−0.376295	−0.188148	+	0.982141i	$0.560248\pi$
$198$	0	0
$199$	−953020.	−1.70596	−0.852981	−	0.521942i	$-0.825208\pi$
$199$	−953020.	−1.70596	−0.852981	+	0.521942i	$0.825208\pi$
$200$	0	0
$201$	0	0
$202$	95024.0	0.163853
$203$	244265.	0.416027
$204$	0	0
$205$	−43200.0	−0.0717958
$206$	−1.05951e6	−1.73955
$207$	0	0
$208$	992256.	1.59025
$209$	−702150.	−1.11190
$210$	0	0
$211$	−223523.	−0.345634	−0.172817	−	0.984954i	$-0.555287\pi$
$211$	−223523.	−0.345634	−0.172817	+	0.984954i	$0.555287\pi$
$212$	−829952.	−1.26827
$213$	0	0
$214$	−1.09474e6	−1.63409
$215$	270350.	0.398869
$216$	0	0
$217$	58408.0	0.0842021
$218$	875880.	1.24826
$219$	0	0
$220$	−362400.	−0.504814
$221$	1.58625e6	2.18470
$222$	0	0
$223$	1.01480e6	1.36653	0.683264	−	0.730171i	$-0.260560\pi$
$223$	1.01480e6	1.36653	0.683264	+	0.730171i	$0.260560\pi$
$224$	−401408.	−0.534522
$225$	0	0
$226$	1.60747e6	2.09350
$227$	−999797.	−1.28780	−0.643898	−	0.765111i	$-0.722684\pi$
$227$	−999797.	−1.28780	−0.643898	+	0.765111i	$0.722684\pi$
$228$	0	0
$229$	−851120.	−1.07251	−0.536256	−	0.844055i	$-0.680162\pi$
$229$	−851120.	−1.07251	−0.536256	+	0.844055i	$0.680162\pi$
$230$	−330800.	−0.412331
$231$	0	0
$232$	0	0
$233$	−1.09270e6	−1.31859	−0.659295	−	0.751885i	$-0.729145\pi$
$233$	−1.09270e6	−1.31859	−0.659295	+	0.751885i	$0.729145\pi$
$234$	0	0
$235$	655925.	0.774791
$236$	146560.	0.171291
$237$	0	0
$238$	−641704.	−0.734332
$239$	−765905.	−0.867322	−0.433661	−	0.901076i	$-0.642778\pi$
$239$	−765905.	−0.867322	−0.433661	+	0.901076i	$0.642778\pi$
$240$	0	0
$241$	−1.21094e6	−1.34301	−0.671505	−	0.741000i	$-0.734352\pi$
$241$	−1.21094e6	−1.34301	−0.671505	+	0.741000i	$0.734352\pi$
$242$	353264.	0.387758
$243$	0	0
$244$	−399616.	−0.429703
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	1.50195e6	1.56644
$248$	0	0
$249$	0	0
$250$	−125000.	−0.126491
$251$	−278262.	−0.278785	−0.139393	−	0.990237i	$-0.544515\pi$
$251$	−278262.	−0.278785	−0.139393	+	0.990237i	$0.544515\pi$
$252$	0	0
$253$	749262.	0.735923
$254$	2.64554e6	2.57294
$255$	0	0
$256$	1.04858e6	1.00000
$257$	352998.	0.333380	0.166690	−	0.986009i	$-0.446692\pi$
$257$	352998.	0.333380	0.166690	+	0.986009i	$0.446692\pi$
$258$	0	0
$259$	−539882.	−0.500091
$260$	775200.	0.711181
$261$	0	0
$262$	−351856.	−0.316674
$263$	1.55809e6	1.38901	0.694503	−	0.719490i	$-0.255624\pi$
$263$	1.55809e6	1.38901	0.694503	+	0.719490i	$0.255624\pi$
$264$	0	0
$265$	648400.	0.567190
$266$	−607600.	−0.526519
$267$	0	0
$268$	−507136.	−0.431308
$269$	1.21963e6	1.02766	0.513828	−	0.857893i	$-0.328227\pi$
$269$	1.21963e6	1.02766	0.513828	+	0.857893i	$0.328227\pi$
$270$	0	0
$271$	405792.	0.335645	0.167823	−	0.985817i	$-0.446326\pi$
$271$	405792.	0.335645	0.167823	+	0.985817i	$0.446326\pi$
$272$	1.67629e6	1.37381
$273$	0	0
$274$	797984.	0.642122
$275$	283125.	0.225760
$276$	0	0
$277$	652442.	0.510908	0.255454	−	0.966821i	$-0.417775\pi$
$277$	652442.	0.510908	0.255454	+	0.966821i	$0.417775\pi$
$278$	2.07144e6	1.60753
$279$	0	0
$280$	0	0
$281$	−118827.	−0.0897737	−0.0448869	−	0.998992i	$-0.514293\pi$
$281$	−118827.	−0.0897737	−0.0448869	+	0.998992i	$0.514293\pi$
$282$	0	0
$283$	1.48801e6	1.10443	0.552217	−	0.833700i	$-0.313782\pi$
$283$	1.48801e6	1.10443	0.552217	+	0.833700i	$0.313782\pi$
$284$	−1.65734e6	−1.21932
$285$	0	0
$286$	−3.51166e6	−2.53862
$287$	84672.0	0.0606785
$288$	0	0
$289$	1.25991e6	0.887351
$290$	−997000.	−0.696146
$291$	0	0
$292$	155072.	0.106433
$293$	−1.89580e6	−1.29010	−0.645050	−	0.764140i	$-0.723164\pi$
$293$	−1.89580e6	−1.29010	−0.645050	+	0.764140i	$0.723164\pi$
$294$	0	0
$295$	−114500.	−0.0766038
$296$	0	0
$297$	0	0
$298$	3.98744e6	2.60108
$299$	−1.60273e6	−1.03677
$300$	0	0
$301$	−529886.	−0.337106
$302$	−1.96642e6	−1.24068
$303$	0	0
$304$	1.58720e6	0.985026
$305$	312200.	0.192169
$306$	0	0
$307$	−821853.	−0.497678	−0.248839	−	0.968545i	$-0.580049\pi$
$307$	−821853.	−0.497678	−0.248839	+	0.968545i	$0.580049\pi$
$308$	710304.	0.426646
$309$	0	0
$310$	−238400.	−0.140897
$311$	2.09600e6	1.22882	0.614412	−	0.788985i	$-0.289393\pi$
$311$	2.09600e6	1.22882	0.614412	+	0.788985i	$0.289393\pi$
$312$	0	0
$313$	394571.	0.227648	0.113824	−	0.993501i	$-0.463690\pi$
$313$	394571.	0.227648	0.113824	+	0.993501i	$0.463690\pi$
$314$	−683824.	−0.391399
$315$	0	0
$316$	2.00848e6	1.13149
$317$	−321422.	−0.179650	−0.0898250	−	0.995958i	$-0.528631\pi$
$317$	−321422.	−0.179650	−0.0898250	+	0.995958i	$0.528631\pi$
$318$	0	0
$319$	2.25820e6	1.24247
$320$	819200.	0.447214
$321$	0	0
$322$	648368.	0.348483
$323$	2.53735e6	1.35324
$324$	0	0
$325$	−605625.	−0.318050
$326$	1.54421e6	0.804752
$327$	0	0
$328$	0	0
$329$	−1.28561e6	−0.654818
$330$	0	0
$331$	−2.23259e6	−1.12005	−0.560027	−	0.828475i	$-0.689209\pi$
$331$	−2.23259e6	−1.12005	−0.560027	+	0.828475i	$0.689209\pi$
$332$	756608.	0.376726
$333$	0	0
$334$	1.26226e6	0.619133
$335$	396200.	0.192887
$336$	0	0
$337$	−3.65656e6	−1.75387	−0.876936	−	0.480608i	$-0.840416\pi$
$337$	−3.65656e6	−1.75387	−0.876936	+	0.480608i	$0.840416\pi$
$338$	4.54134e6	2.16218
$339$	0	0
$340$	1.30960e6	0.614386
$341$	539976.	0.251471
$342$	0	0
$343$	117649.	0.0539949
$344$	0	0
$345$	0	0
$346$	2.12527e6	0.954386
$347$	1.88962e6	0.842462	0.421231	−	0.906953i	$-0.361598\pi$
$347$	1.88962e6	0.842462	0.421231	+	0.906953i	$0.361598\pi$
$348$	0	0
$349$	−2.69329e6	−1.18364	−0.591820	−	0.806070i	$-0.701590\pi$
$349$	−2.69329e6	−1.18364	−0.591820	+	0.806070i	$0.701590\pi$
$350$	245000.	0.106904
$351$	0	0
$352$	−3.71098e6	−1.59636
$353$	1.57468e6	0.672598	0.336299	−	0.941755i	$-0.390825\pi$
$353$	1.57468e6	0.672598	0.336299	+	0.941755i	$0.390825\pi$
$354$	0	0
$355$	1.29480e6	0.545295
$356$	4.71360e6	1.97119
$357$	0	0
$358$	−1.46928e6	−0.605894
$359$	−4.05576e6	−1.66087	−0.830436	−	0.557114i	$-0.811909\pi$
$359$	−4.05576e6	−1.66087	−0.830436	+	0.557114i	$0.811909\pi$
$360$	0	0
$361$	−73599.0	−0.0297238
$362$	−5.08038e6	−2.03763
$363$	0	0
$364$	−1.51939e6	−0.601058
$365$	−121150.	−0.0475983
$366$	0	0
$367$	−4.90628e6	−1.90146	−0.950731	−	0.310018i	$-0.899665\pi$
$367$	−4.90628e6	−1.90146	−0.950731	+	0.310018i	$0.899665\pi$
$368$	−1.69370e6	−0.651952
$369$	0	0
$370$	2.20360e6	0.836813
$371$	−1.27086e6	−0.479363
$372$	0	0
$373$	−3.45336e6	−1.28520	−0.642599	−	0.766202i	$-0.722144\pi$
$373$	−3.45336e6	−1.28520	−0.642599	+	0.766202i	$0.722144\pi$
$374$	−5.93249e6	−2.19310
$375$	0	0
$376$	0	0
$377$	−4.83046e6	−1.75039
$378$	0	0
$379$	−4.23466e6	−1.51433	−0.757165	−	0.653224i	$-0.773416\pi$
$379$	−4.23466e6	−1.51433	−0.757165	+	0.653224i	$0.773416\pi$
$380$	1.24000e6	0.440517
$381$	0	0
$382$	1.81290e6	0.635648
$383$	1.86460e6	0.649516	0.324758	−	0.945797i	$-0.394717\pi$
$383$	1.86460e6	0.649516	0.324758	+	0.945797i	$0.394717\pi$
$384$	0	0
$385$	−554925.	−0.190802
$386$	371808.	0.127014
$387$	0	0
$388$	−266976.	−0.0900312
$389$	4.81502e6	1.61333	0.806666	−	0.591008i	$-0.201270\pi$
$389$	4.81502e6	1.61333	0.806666	+	0.591008i	$0.201270\pi$
$390$	0	0
$391$	−2.70760e6	−0.895658
$392$	0	0
$393$	0	0
$394$	−1.63978e6	−0.532162
$395$	−1.56912e6	−0.506017
$396$	0	0
$397$	1.21376e6	0.386505	0.193253	−	0.981149i	$-0.438096\pi$
$397$	1.21376e6	0.386505	0.193253	+	0.981149i	$0.438096\pi$
$398$	−7.62416e6	−2.41259
$399$	0	0
$400$	−640000.	−0.200000
$401$	−5.90442e6	−1.83365	−0.916824	−	0.399291i	$-0.869256\pi$
$401$	−5.90442e6	−1.83365	−0.916824	+	0.399291i	$0.869256\pi$
$402$	0	0
$403$	−1.15505e6	−0.354272
$404$	380096.	0.115862
$405$	0	0
$406$	1.95412e6	0.588351
$407$	−4.99115e6	−1.49353
$408$	0	0
$409$	4.84289e6	1.43152	0.715758	−	0.698348i	$-0.246081\pi$
$409$	4.84289e6	1.43152	0.715758	+	0.698348i	$0.246081\pi$
$410$	−345600.	−0.101535
$411$	0	0
$412$	−4.23805e6	−1.23005
$413$	224420.	0.0647420
$414$	0	0
$415$	−591100.	−0.168477
$416$	7.93805e6	2.24895
$417$	0	0
$418$	−5.61720e6	−1.57246
$419$	−270360.	−0.0752328	−0.0376164	−	0.999292i	$-0.511977\pi$
$419$	−270360.	−0.0752328	−0.0376164	+	0.999292i	$0.511977\pi$
$420$	0	0
$421$	3.13648e6	0.862456	0.431228	−	0.902243i	$-0.358080\pi$
$421$	3.13648e6	0.862456	0.431228	+	0.902243i	$0.358080\pi$
$422$	−1.78818e6	−0.488800
$423$	0	0
$424$	0	0
$425$	−1.02312e6	−0.274762
$426$	0	0
$427$	−611912.	−0.162412
$428$	−4.37894e6	−1.15547
$429$	0	0
$430$	2.16280e6	0.564086
$431$	1.87703e6	0.486719	0.243360	−	0.969936i	$-0.421750\pi$
$431$	1.87703e6	0.486719	0.243360	+	0.969936i	$0.421750\pi$
$432$	0	0
$433$	3.20357e6	0.821134	0.410567	−	0.911830i	$-0.365331\pi$
$433$	3.20357e6	0.821134	0.410567	+	0.911830i	$0.365331\pi$
$434$	467264.	0.119080
$435$	0	0
$436$	3.50352e6	0.882650
$437$	−2.56370e6	−0.642190
$438$	0	0
$439$	−6.27209e6	−1.55328	−0.776642	−	0.629942i	$-0.783079\pi$
$439$	−6.27209e6	−1.55328	−0.776642	+	0.629942i	$0.783079\pi$
$440$	0	0
$441$	0	0
$442$	1.26900e7	3.08963
$443$	−724986.	−0.175517	−0.0877587	−	0.996142i	$-0.527970\pi$
$443$	−724986.	−0.175517	−0.0877587	+	0.996142i	$0.527970\pi$
$444$	0	0
$445$	−3.68250e6	−0.881541
$446$	8.11841e6	1.93256
$447$	0	0
$448$	−1.60563e6	−0.377964
$449$	875985.	0.205060	0.102530	−	0.994730i	$-0.467306\pi$
$449$	875985.	0.205060	0.102530	+	0.994730i	$0.467306\pi$
$450$	0	0
$451$	782784.	0.181218
$452$	6.42989e6	1.48033
$453$	0	0
$454$	−7.99838e6	−1.82122
$455$	1.18702e6	0.268801
$456$	0	0
$457$	−832668.	−0.186501	−0.0932505	−	0.995643i	$-0.529726\pi$
$457$	−832668.	−0.186501	−0.0932505	+	0.995643i	$0.529726\pi$
$458$	−6.80896e6	−1.51676
$459$	0	0
$460$	−1.32320e6	−0.291562
$461$	−5.92115e6	−1.29764	−0.648820	−	0.760942i	$-0.724737\pi$
$461$	−5.92115e6	−1.29764	−0.648820	+	0.760942i	$0.724737\pi$
$462$	0	0
$463$	682776.	0.148022	0.0740109	−	0.997257i	$-0.476420\pi$
$463$	682776.	0.148022	0.0740109	+	0.997257i	$0.476420\pi$
$464$	−5.10464e6	−1.10070
$465$	0	0
$466$	−8.74157e6	−1.86477
$467$	5.41667e6	1.14932	0.574659	−	0.818393i	$-0.305135\pi$
$467$	5.41667e6	1.14932	0.574659	+	0.818393i	$0.305135\pi$
$468$	0	0
$469$	−776552.	−0.163019
$470$	5.24740e6	1.09572
$471$	0	0
$472$	0	0
$473$	−4.89874e6	−1.00677
$474$	0	0
$475$	−968750.	−0.197005
$476$	−2.56682e6	−0.519251
$477$	0	0
$478$	−6.12724e6	−1.22658
$479$	−1.98599e6	−0.395493	−0.197746	−	0.980253i	$-0.563362\pi$
$479$	−1.98599e6	−0.395493	−0.197746	+	0.980253i	$0.563362\pi$
$480$	0	0
$481$	1.06764e7	2.10409
$482$	−9.68750e6	−1.89930
$483$	0	0
$484$	1.41306e6	0.274186
$485$	208575.	0.0402632
$486$	0	0
$487$	−1.06974e6	−0.204388	−0.102194	−	0.994764i	$-0.532586\pi$
$487$	−1.06974e6	−0.204388	−0.102194	+	0.994764i	$0.532586\pi$
$488$	0	0
$489$	0	0
$490$	−480200.	−0.0903508
$491$	−4.59246e6	−0.859689	−0.429844	−	0.902903i	$-0.641432\pi$
$491$	−4.59246e6	−0.859689	−0.429844	+	0.902903i	$0.641432\pi$
$492$	0	0
$493$	−8.16045e6	−1.51216
$494$	1.20156e7	2.21528
$495$	0	0
$496$	−1.22061e6	−0.222778
$497$	−2.53781e6	−0.460859
$498$	0	0
$499$	1.96066e6	0.352492	0.176246	−	0.984346i	$-0.443605\pi$
$499$	1.96066e6	0.352492	0.176246	+	0.984346i	$0.443605\pi$
$500$	−500000.	−0.0894427
$501$	0	0
$502$	−2.22610e6	−0.394262
$503$	−3.51483e6	−0.619419	−0.309709	−	0.950831i	$-0.600232\pi$
$503$	−3.51483e6	−0.619419	−0.309709	+	0.950831i	$0.600232\pi$
$504$	0	0
$505$	−296950.	−0.0518149
$506$	5.99410e6	1.04075
$507$	0	0
$508$	1.05821e7	1.81934
$509$	1.45211e6	0.248431	0.124215	−	0.992255i	$-0.460359\pi$
$509$	1.45211e6	0.248431	0.124215	+	0.992255i	$0.460359\pi$
$510$	0	0
$511$	237454.	0.0402279
$512$	8.38861e6	1.41421
$513$	0	0
$514$	2.82398e6	0.471470
$515$	3.31098e6	0.550095
$516$	0	0
$517$	−1.18854e7	−1.95563
$518$	−4.31906e6	−0.707236
$519$	0	0
$520$	0	0
$521$	4.24240e6	0.684726	0.342363	−	0.939568i	$-0.388773\pi$
$521$	4.24240e6	0.684726	0.342363	+	0.939568i	$0.388773\pi$
$522$	0	0
$523$	−7.56012e6	−1.20858	−0.604289	−	0.796765i	$-0.706543\pi$
$523$	−7.56012e6	−1.20858	−0.604289	+	0.796765i	$0.706543\pi$
$524$	−1.40742e6	−0.223922
$525$	0	0
$526$	1.24648e7	1.96435
$527$	−1.95130e6	−0.306054
$528$	0	0
$529$	−3.70063e6	−0.574958
$530$	5.18720e6	0.802127
$531$	0	0
$532$	−2.43040e6	−0.372305
$533$	−1.67443e6	−0.255299
$534$	0	0
$535$	3.42105e6	0.516743
$536$	0	0
$537$	0	0
$538$	9.75704e6	1.45332
$539$	1.08765e6	0.161257
$540$	0	0
$541$	1.24065e6	0.182245	0.0911224	−	0.995840i	$-0.470955\pi$
$541$	1.24065e6	0.182245	0.0911224	+	0.995840i	$0.470955\pi$
$542$	3.24634e6	0.474674
$543$	0	0
$544$	1.34103e7	1.94286
$545$	−2.73712e6	−0.394733
$546$	0	0
$547$	−1.85057e6	−0.264446	−0.132223	−	0.991220i	$-0.542211\pi$
$547$	−1.85057e6	−0.264446	−0.132223	+	0.991220i	$0.542211\pi$
$548$	3.19194e6	0.454049
$549$	0	0
$550$	2.26500e6	0.319272
$551$	−7.72675e6	−1.08422
$552$	0	0
$553$	3.07548e6	0.427662
$554$	5.21954e6	0.722533
$555$	0	0
$556$	8.28576e6	1.13670
$557$	−7.77555e6	−1.06192	−0.530962	−	0.847396i	$-0.678169\pi$
$557$	−7.77555e6	−1.06192	−0.530962	+	0.847396i	$0.678169\pi$
$558$	0	0
$559$	1.04788e7	1.41834
$560$	1.25440e6	0.169031
$561$	0	0
$562$	−950616.	−0.126959
$563$	−8.37716e6	−1.11385	−0.556924	−	0.830564i	$-0.688018\pi$
$563$	−8.37716e6	−1.11385	−0.556924	+	0.830564i	$0.688018\pi$
$564$	0	0
$565$	−5.02335e6	−0.662022
$566$	1.19041e7	1.56191
$567$	0	0
$568$	0	0
$569$	6.15591e6	0.797098	0.398549	−	0.917147i	$-0.369514\pi$
$569$	6.15591e6	0.797098	0.398549	+	0.917147i	$0.369514\pi$
$570$	0	0
$571$	7.21513e6	0.926092	0.463046	−	0.886334i	$-0.346757\pi$
$571$	7.21513e6	0.926092	0.463046	+	0.886334i	$0.346757\pi$
$572$	−1.40466e7	−1.79507
$573$	0	0
$574$	677376.	0.0858124
$575$	1.03375e6	0.130390
$576$	0	0
$577$	1.36699e7	1.70933	0.854666	−	0.519177i	$-0.173762\pi$
$577$	1.36699e7	1.70933	0.854666	+	0.519177i	$0.173762\pi$
$578$	1.00793e7	1.25490
$579$	0	0
$580$	−3.98800e6	−0.492249
$581$	1.15856e6	0.142389
$582$	0	0
$583$	−1.17490e7	−1.43163
$584$	0	0
$585$	0	0
$586$	−1.51664e7	−1.82448
$587$	1.00686e7	1.20608	0.603040	−	0.797711i	$-0.293956\pi$
$587$	1.00686e7	1.20608	0.603040	+	0.797711i	$0.293956\pi$
$588$	0	0
$589$	−1.84760e6	−0.219442
$590$	−916000.	−0.108334
$591$	0	0
$592$	1.12824e7	1.32312
$593$	−9.80615e6	−1.14515	−0.572574	−	0.819853i	$-0.694055\pi$
$593$	−9.80615e6	−1.14515	−0.572574	+	0.819853i	$0.694055\pi$
$594$	0	0
$595$	2.00532e6	0.232216
$596$	1.59498e7	1.83924
$597$	0	0
$598$	−1.28218e7	−1.46621
$599$	−8.26257e6	−0.940911	−0.470455	−	0.882424i	$-0.655910\pi$
$599$	−8.26257e6	−0.940911	−0.470455	+	0.882424i	$0.655910\pi$
$600$	0	0
$601$	−3.59492e6	−0.405978	−0.202989	−	0.979181i	$-0.565066\pi$
$601$	−3.59492e6	−0.405978	−0.202989	+	0.979181i	$0.565066\pi$
$602$	−4.23909e6	−0.476740
$603$	0	0
$604$	−7.86570e6	−0.877293
$605$	−1.10395e6	−0.122620
$606$	0	0
$607$	−1.32969e7	−1.46480	−0.732401	−	0.680873i	$-0.761600\pi$
$607$	−1.32969e7	−1.46480	−0.732401	+	0.680873i	$0.761600\pi$
$608$	1.26976e7	1.39304
$609$	0	0
$610$	2.49760e6	0.271768
$611$	2.54237e7	2.75508
$612$	0	0
$613$	2.50327e6	0.269064	0.134532	−	0.990909i	$-0.457047\pi$
$613$	2.50327e6	0.269064	0.134532	+	0.990909i	$0.457047\pi$
$614$	−6.57482e6	−0.703823
$615$	0	0
$616$	0	0
$617$	−1.88254e6	−0.199082	−0.0995409	−	0.995033i	$-0.531737\pi$
$617$	−1.88254e6	−0.199082	−0.0995409	+	0.995033i	$0.531737\pi$
$618$	0	0
$619$	8.21487e6	0.861736	0.430868	−	0.902415i	$-0.358208\pi$
$619$	8.21487e6	0.861736	0.430868	+	0.902415i	$0.358208\pi$
$620$	−953600.	−0.0996293
$621$	0	0
$622$	1.67680e7	1.73782
$623$	7.21770e6	0.745038
$624$	0	0
$625$	390625.	0.0400000
$626$	3.15657e6	0.321943
$627$	0	0
$628$	−2.73530e6	−0.276761
$629$	1.80365e7	1.81771
$630$	0	0
$631$	1.61155e7	1.61128	0.805638	−	0.592408i	$-0.201823\pi$
$631$	1.61155e7	1.61128	0.805638	+	0.592408i	$0.201823\pi$
$632$	0	0
$633$	0	0
$634$	−2.57138e6	−0.254064
$635$	−8.26730e6	−0.813635
$636$	0	0
$637$	−2.32657e6	−0.227179
$638$	1.80656e7	1.75712
$639$	0	0
$640$	0	0
$641$	8.50544e6	0.817620	0.408810	−	0.912619i	$-0.365944\pi$
$641$	8.50544e6	0.817620	0.408810	+	0.912619i	$0.365944\pi$
$642$	0	0
$643$	−1.32191e7	−1.26088	−0.630440	−	0.776238i	$-0.717126\pi$
$643$	−1.32191e7	−1.26088	−0.630440	+	0.776238i	$0.717126\pi$
$644$	2.59347e6	0.246415
$645$	0	0
$646$	2.02988e7	1.91377
$647$	−1.89115e6	−0.177609	−0.0888047	−	0.996049i	$-0.528305\pi$
$647$	−1.89115e6	−0.177609	−0.0888047	+	0.996049i	$0.528305\pi$
$648$	0	0
$649$	2.07474e6	0.193353
$650$	−4.84500e6	−0.449791
$651$	0	0
$652$	6.17683e6	0.569045
$653$	−4.90587e6	−0.450228	−0.225114	−	0.974332i	$-0.572275\pi$
$653$	−4.90587e6	−0.450228	−0.225114	+	0.974332i	$0.572275\pi$
$654$	0	0
$655$	1.09955e6	0.100141
$656$	−1.76947e6	−0.160540
$657$	0	0
$658$	−1.02849e7	−0.926052
$659$	−1.36367e7	−1.22319	−0.611597	−	0.791169i	$-0.709473\pi$
$659$	−1.36367e7	−1.22319	−0.611597	+	0.791169i	$0.709473\pi$
$660$	0	0
$661$	−2.22345e6	−0.197935	−0.0989677	−	0.995091i	$-0.531554\pi$
$661$	−2.22345e6	−0.197935	−0.0989677	+	0.995091i	$0.531554\pi$
$662$	−1.78607e7	−1.58399
$663$	0	0
$664$	0	0
$665$	1.89875e6	0.166500
$666$	0	0
$667$	8.24519e6	0.717606
$668$	5.04906e6	0.437793
$669$	0	0
$670$	3.16960e6	0.272783
$671$	−5.65706e6	−0.485048
$672$	0	0
$673$	4.88484e6	0.415731	0.207865	−	0.978157i	$-0.433348\pi$
$673$	4.88484e6	0.415731	0.207865	+	0.978157i	$0.433348\pi$
$674$	−2.92525e7	−2.48035
$675$	0	0
$676$	1.81654e7	1.52889
$677$	1.98785e7	1.66691	0.833453	−	0.552590i	$-0.186360\pi$
$677$	1.98785e7	1.66691	0.833453	+	0.552590i	$0.186360\pi$
$678$	0	0
$679$	−408807.	−0.0340286
$680$	0	0
$681$	0	0
$682$	4.31981e6	0.355634
$683$	−4.27870e6	−0.350962	−0.175481	−	0.984483i	$-0.556148\pi$
$683$	−4.27870e6	−0.350962	−0.175481	+	0.984483i	$0.556148\pi$
$684$	0	0
$685$	−2.49370e6	−0.203057
$686$	941192.	0.0763604
$687$	0	0
$688$	1.10735e7	0.891898
$689$	2.51320e7	2.01687
$690$	0	0
$691$	9.48925e6	0.756026	0.378013	−	0.925800i	$-0.376607\pi$
$691$	9.48925e6	0.756026	0.378013	+	0.925800i	$0.376607\pi$
$692$	8.50109e6	0.674853
$693$	0	0
$694$	1.51169e7	1.19142
$695$	−6.47325e6	−0.508347
$696$	0	0
$697$	−2.82874e6	−0.220552
$698$	−2.15463e7	−1.67392
$699$	0	0
$700$	980000.	0.0755929
$701$	5.86385e6	0.450700	0.225350	−	0.974278i	$-0.427647\pi$
$701$	5.86385e6	0.450700	0.225350	+	0.974278i	$0.427647\pi$
$702$	0	0
$703$	1.70779e7	1.30331
$704$	−1.48439e7	−1.12880
$705$	0	0
$706$	1.25974e7	0.951197
$707$	582022.	0.0437916
$708$	0	0
$709$	−2.66670e6	−0.199232	−0.0996161	−	0.995026i	$-0.531761\pi$
$709$	−2.66670e6	−0.199232	−0.0996161	+	0.995026i	$0.531761\pi$
$710$	1.03584e7	0.771164
$711$	0	0
$712$	0	0
$713$	1.97157e6	0.145241
$714$	0	0
$715$	1.09739e7	0.802781
$716$	−5.87712e6	−0.428432
$717$	0	0
$718$	−3.24461e7	−2.34883
$719$	4.46629e6	0.322199	0.161100	−	0.986938i	$-0.448496\pi$
$719$	4.46629e6	0.322199	0.161100	+	0.986938i	$0.448496\pi$
$720$	0	0
$721$	−6.48951e6	−0.464915
$722$	−588792.	−0.0420358
$723$	0	0
$724$	−2.03215e7	−1.44082
$725$	3.11562e6	0.220141
$726$	0	0
$727$	−7.47757e6	−0.524716	−0.262358	−	0.964971i	$-0.584500\pi$
$727$	−7.47757e6	−0.524716	−0.262358	+	0.964971i	$0.584500\pi$
$728$	0	0
$729$	0	0
$730$	−969200.	−0.0673141
$731$	1.77025e7	1.22530
$732$	0	0
$733$	−4.39751e6	−0.302306	−0.151153	−	0.988510i	$-0.548299\pi$
$733$	−4.39751e6	−0.302306	−0.151153	+	0.988510i	$0.548299\pi$
$734$	−3.92503e7	−2.68907
$735$	0	0
$736$	−1.35496e7	−0.922000
$737$	−7.17914e6	−0.486860
$738$	0	0
$739$	2.84036e7	1.91321	0.956603	−	0.291395i	$-0.0941195\pi$
$739$	2.84036e7	1.91321	0.956603	+	0.291395i	$0.0941195\pi$
$740$	8.81440e6	0.591716
$741$	0	0
$742$	−1.01669e7	−0.677921
$743$	1.96012e7	1.30260	0.651299	−	0.758821i	$-0.274224\pi$
$743$	1.96012e7	1.30260	0.651299	+	0.758821i	$0.274224\pi$
$744$	0	0
$745$	−1.24608e7	−0.822533
$746$	−2.76269e7	−1.81755
$747$	0	0
$748$	−2.37300e7	−1.55075
$749$	−6.70526e6	−0.436728
$750$	0	0
$751$	−2.60344e6	−0.168441	−0.0842206	−	0.996447i	$-0.526840\pi$
$751$	−2.60344e6	−0.168441	−0.0842206	+	0.996447i	$0.526840\pi$
$752$	2.68667e7	1.73249
$753$	0	0
$754$	−3.86437e7	−2.47543
$755$	6.14508e6	0.392337
$756$	0	0
$757$	−2.98869e7	−1.89558	−0.947789	−	0.318899i	$-0.896687\pi$
$757$	−2.98869e7	−1.89558	−0.947789	+	0.318899i	$0.896687\pi$
$758$	−3.38773e7	−2.14159
$759$	0	0
$760$	0	0
$761$	−1.21470e7	−0.760338	−0.380169	−	0.924917i	$-0.624134\pi$
$761$	−1.21470e7	−0.760338	−0.380169	+	0.924917i	$0.624134\pi$
$762$	0	0
$763$	5.36476e6	0.333610
$764$	7.25162e6	0.449471
$765$	0	0
$766$	1.49168e7	0.918554
$767$	−4.43802e6	−0.272396
$768$	0	0
$769$	4.53845e6	0.276753	0.138376	−	0.990380i	$-0.455812\pi$
$769$	4.53845e6	0.276753	0.138376	+	0.990380i	$0.455812\pi$
$770$	−4.43940e6	−0.269834
$771$	0	0
$772$	1.48723e6	0.0898122
$773$	−1.93330e7	−1.16372	−0.581861	−	0.813288i	$-0.697675\pi$
$773$	−1.93330e7	−1.16372	−0.581861	+	0.813288i	$0.697675\pi$
$774$	0	0
$775$	745000.	0.0445556
$776$	0	0
$777$	0	0
$778$	3.85201e7	2.28160
$779$	−2.67840e6	−0.158136
$780$	0	0
$781$	−2.34618e7	−1.37636
$782$	−2.16608e7	−1.26665
$783$	0	0
$784$	−2.45862e6	−0.142857
$785$	2.13695e6	0.123771
$786$	0	0
$787$	1.66392e7	0.957627	0.478814	−	0.877917i	$-0.341067\pi$
$787$	1.66392e7	0.957627	0.478814	+	0.877917i	$0.341067\pi$
$788$	−6.55910e6	−0.376295
$789$	0	0
$790$	−1.25530e7	−0.715616
$791$	9.84577e6	0.559511
$792$	0	0
$793$	1.21009e7	0.683335
$794$	9.71006e6	0.546601
$795$	0	0
$796$	−3.04966e7	−1.70596
$797$	−1.80409e7	−1.00603	−0.503017	−	0.864276i	$-0.667777\pi$
$797$	−1.80409e7	−1.00603	−0.503017	+	0.864276i	$0.667777\pi$
$798$	0	0
$799$	4.29500e7	2.38010
$800$	−5.12000e6	−0.282843
$801$	0	0
$802$	−4.72353e7	−2.59317
$803$	2.19524e6	0.120141
$804$	0	0
$805$	−2.02615e6	−0.110200
$806$	−9.24038e6	−0.501017
$807$	0	0
$808$	0	0
$809$	−2.33891e7	−1.25644	−0.628220	−	0.778036i	$-0.716216\pi$
$809$	−2.33891e7	−1.25644	−0.628220	+	0.778036i	$0.716216\pi$
$810$	0	0
$811$	−2.29037e7	−1.22279	−0.611397	−	0.791324i	$-0.709392\pi$
$811$	−2.29037e7	−1.22279	−0.611397	+	0.791324i	$0.709392\pi$
$812$	7.81648e6	0.416027
$813$	0	0
$814$	−3.99292e7	−2.11218
$815$	−4.82565e6	−0.254485
$816$	0	0
$817$	1.67617e7	0.878543
$818$	3.87431e7	2.02447
$819$	0	0
$820$	−1.38240e6	−0.0717958
$821$	1.80745e7	0.935853	0.467926	−	0.883767i	$-0.345001\pi$
$821$	1.80745e7	0.935853	0.467926	+	0.883767i	$0.345001\pi$
$822$	0	0
$823$	1.17989e7	0.607216	0.303608	−	0.952797i	$-0.401809\pi$
$823$	1.17989e7	0.607216	0.303608	+	0.952797i	$0.401809\pi$
$824$	0	0
$825$	0	0
$826$	1.79536e6	0.0915591
$827$	−2.57650e6	−0.130999	−0.0654993	−	0.997853i	$-0.520864\pi$
$827$	−2.57650e6	−0.130999	−0.0654993	+	0.997853i	$0.520864\pi$
$828$	0	0
$829$	−3.84340e7	−1.94236	−0.971178	−	0.238356i	$-0.923392\pi$
$829$	−3.84340e7	−1.94236	−0.971178	+	0.238356i	$0.923392\pi$
$830$	−4.72880e6	−0.238263
$831$	0	0
$832$	3.17522e7	1.59025
$833$	−3.93044e6	−0.196258
$834$	0	0
$835$	−3.94458e6	−0.195787
$836$	−2.24688e7	−1.11190
$837$	0	0
$838$	−2.16288e6	−0.106395
$839$	1.24222e7	0.609247	0.304623	−	0.952473i	$-0.401469\pi$
$839$	1.24222e7	0.609247	0.304623	+	0.952473i	$0.401469\pi$
$840$	0	0
$841$	4.33908e6	0.211547
$842$	2.50918e7	1.21970
$843$	0	0
$844$	−7.15274e6	−0.345634
$845$	−1.41917e7	−0.683743
$846$	0	0
$847$	2.16374e6	0.103633
$848$	2.65585e7	1.26827
$849$	0	0
$850$	−8.18500e6	−0.388572
$851$	−1.82238e7	−0.862610
$852$	0	0
$853$	7.92067e6	0.372726	0.186363	−	0.982481i	$-0.440330\pi$
$853$	7.92067e6	0.372726	0.186363	+	0.982481i	$0.440330\pi$
$854$	−4.89530e6	−0.229686
$855$	0	0
$856$	0	0
$857$	−1.48983e7	−0.692924	−0.346462	−	0.938064i	$-0.612617\pi$
$857$	−1.48983e7	−0.692924	−0.346462	+	0.938064i	$0.612617\pi$
$858$	0	0
$859$	−1.38740e7	−0.641534	−0.320767	−	0.947158i	$-0.603941\pi$
$859$	−1.38740e7	−0.641534	−0.320767	+	0.947158i	$0.603941\pi$
$860$	8.65120e6	0.398869
$861$	0	0
$862$	1.50163e7	0.688325
$863$	−1.25500e7	−0.573610	−0.286805	−	0.957989i	$-0.592593\pi$
$863$	−1.25500e7	−0.573610	−0.286805	+	0.957989i	$0.592593\pi$
$864$	0	0
$865$	−6.64147e6	−0.301804
$866$	2.56285e7	1.16126
$867$	0	0
$868$	1.86906e6	0.0842021
$869$	2.84325e7	1.27722
$870$	0	0
$871$	1.53567e7	0.685887
$872$	0	0
$873$	0	0
$874$	−2.05096e7	−0.908194
$875$	−765625.	−0.0338062
$876$	0	0
$877$	−2.86002e7	−1.25565	−0.627827	−	0.778353i	$-0.716056\pi$
$877$	−2.86002e7	−1.25565	−0.627827	+	0.778353i	$0.716056\pi$
$878$	−5.01767e7	−2.19668
$879$	0	0
$880$	1.15968e7	0.504814
$881$	−4.09608e7	−1.77799	−0.888993	−	0.457922i	$-0.848594\pi$
$881$	−4.09608e7	−1.77799	−0.888993	+	0.457922i	$0.848594\pi$
$882$	0	0
$883$	1.30504e7	0.563279	0.281639	−	0.959520i	$-0.409122\pi$
$883$	1.30504e7	0.563279	0.281639	+	0.959520i	$0.409122\pi$
$884$	5.07601e7	2.18470
$885$	0	0
$886$	−5.79989e6	−0.248219
$887$	−2.53595e7	−1.08226	−0.541129	−	0.840939i	$-0.682003\pi$
$887$	−2.53595e7	−1.08226	−0.541129	+	0.840939i	$0.682003\pi$
$888$	0	0
$889$	1.62039e7	0.687647
$890$	−2.94600e7	−1.24669
$891$	0	0
$892$	3.24736e7	1.36653
$893$	4.06674e7	1.70654
$894$	0	0
$895$	4.59150e6	0.191601
$896$	0	0
$897$	0	0
$898$	7.00788e6	0.289999
$899$	5.94212e6	0.245212
$900$	0	0
$901$	4.24572e7	1.74237
$902$	6.26227e6	0.256281
$903$	0	0
$904$	0	0
$905$	1.58762e7	0.644355
$906$	0	0
$907$	1.98595e7	0.801585	0.400793	−	0.916169i	$-0.368735\pi$
$907$	1.98595e7	0.801585	0.400793	+	0.916169i	$0.368735\pi$
$908$	−3.19935e7	−1.28780
$909$	0	0
$910$	9.49620e6	0.380142
$911$	1.99344e7	0.795808	0.397904	−	0.917427i	$-0.369738\pi$
$911$	1.99344e7	0.795808	0.397904	+	0.917427i	$0.369738\pi$
$912$	0	0
$913$	1.07107e7	0.425248
$914$	−6.66134e6	−0.263752
$915$	0	0
$916$	−2.72358e7	−1.07251
$917$	−2.15512e6	−0.0846346
$918$	0	0
$919$	−1.10695e7	−0.432355	−0.216178	−	0.976354i	$-0.569359\pi$
$919$	−1.10695e7	−0.432355	−0.216178	+	0.976354i	$0.569359\pi$
$920$	0	0
$921$	0	0
$922$	−4.73692e7	−1.83514
$923$	5.01864e7	1.93902
$924$	0	0
$925$	−6.88625e6	−0.264624
$926$	5.46221e6	0.209334
$927$	0	0
$928$	−4.08371e7	−1.55663
$929$	3.25682e7	1.23810	0.619048	−	0.785353i	$-0.287519\pi$
$929$	3.25682e7	1.23810	0.619048	+	0.785353i	$0.287519\pi$
$930$	0	0
$931$	−3.72155e6	−0.140718
$932$	−3.49663e7	−1.31859
$933$	0	0
$934$	4.33334e7	1.62538
$935$	1.85390e7	0.693518
$936$	0	0
$937$	3.15690e7	1.17466	0.587329	−	0.809348i	$-0.300179\pi$
$937$	3.15690e7	1.17466	0.587329	+	0.809348i	$0.300179\pi$
$938$	−6.21242e6	−0.230544
$939$	0	0
$940$	2.09896e7	0.774791
$941$	3.67997e7	1.35479	0.677393	−	0.735622i	$-0.263110\pi$
$941$	3.67997e7	1.35479	0.677393	+	0.735622i	$0.263110\pi$
$942$	0	0
$943$	2.85811e6	0.104665
$944$	−4.68992e6	−0.171291
$945$	0	0
$946$	−3.91899e7	−1.42379
$947$	−1.88453e7	−0.682853	−0.341426	−	0.939909i	$-0.610910\pi$
$947$	−1.88453e7	−0.682853	−0.341426	+	0.939909i	$0.610910\pi$
$948$	0	0
$949$	−4.69577e6	−0.169255
$950$	−7.75000e6	−0.278607
$951$	0	0
$952$	0	0
$953$	1.25120e7	0.446265	0.223133	−	0.974788i	$-0.428372\pi$
$953$	1.25120e7	0.446265	0.223133	+	0.974788i	$0.428372\pi$
$954$	0	0
$955$	−5.66532e6	−0.201009
$956$	−2.45090e7	−0.867322
$957$	0	0
$958$	−1.58879e7	−0.559311
$959$	4.88765e6	0.171614
$960$	0	0
$961$	−2.72083e7	−0.950370
$962$	8.54115e7	2.97563
$963$	0	0
$964$	−3.87500e7	−1.34301
$965$	−1.16190e6	−0.0401652
$966$	0	0
$967$	−3.42344e7	−1.17733	−0.588663	−	0.808379i	$-0.700346\pi$
$967$	−3.42344e7	−1.17733	−0.588663	+	0.808379i	$0.700346\pi$
$968$	0	0
$969$	0	0
$970$	1.66860e6	0.0569407
$971$	2.62027e7	0.891864	0.445932	−	0.895067i	$-0.352872\pi$
$971$	2.62027e7	0.891864	0.445932	+	0.895067i	$0.352872\pi$
$972$	0	0
$973$	1.26876e7	0.429632
$974$	−8.55790e6	−0.289048
$975$	0	0
$976$	1.27877e7	0.429703
$977$	8.01114e6	0.268508	0.134254	−	0.990947i	$-0.457136\pi$
$977$	8.01114e6	0.268508	0.134254	+	0.990947i	$0.457136\pi$
$978$	0	0
$979$	6.67269e7	2.22507
$980$	−1.92080e6	−0.0638877
$981$	0	0
$982$	−3.67397e7	−1.21578
$983$	4.60126e7	1.51877	0.759387	−	0.650639i	$-0.225499\pi$
$983$	4.60126e7	1.51877	0.759387	+	0.650639i	$0.225499\pi$
$984$	0	0
$985$	5.12430e6	0.168284
$986$	−6.52836e7	−2.13851
$987$	0	0
$988$	4.80624e7	1.56644
$989$	−1.78864e7	−0.581475
$990$	0	0
$991$	−3.75828e7	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$991$	−3.75828e7	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$992$	−9.76486e6	−0.315055
$993$	0	0
$994$	−2.03025e7	−0.651753
$995$	2.38255e7	0.762929
$996$	0	0
$997$	2.22066e7	0.707529	0.353765	−	0.935334i	$-0.384901\pi$
$997$	2.22066e7	0.707529	0.353765	+	0.935334i	$0.384901\pi$
$998$	1.56852e7	0.498500
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.6.a.a.1.1		1
3.2	odd	2		35.6.a.a.1.1	✓	1
12.11	even	2		560.6.a.c.1.1		1
15.2	even	4		175.6.b.b.99.1		2
15.8	even	4		175.6.b.b.99.2		2
15.14	odd	2		175.6.a.a.1.1		1
21.20	even	2		245.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.a.1.1	✓	1	3.2	odd	2
175.6.a.a.1.1		1	15.14	odd	2
175.6.b.b.99.1		2	15.2	even	4
175.6.b.b.99.2		2	15.8	even	4
245.6.a.a.1.1		1	21.20	even	2
315.6.a.a.1.1		1	1.1	even	1	trivial
560.6.a.c.1.1		1	12.11	even	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	315.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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