LMFDB - Embedded newform 770.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,6,Mod(1,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, 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("770.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	770.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:	$123.495541256$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	770.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} -30.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +120.000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +657.000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} -30.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +120.000 q^{6} -49.0000 q^{7} -64.0000 q^{8} +657.000 q^{9} -100.000 q^{10} +121.000 q^{11} -480.000 q^{12} +408.000 q^{13} +196.000 q^{14} -750.000 q^{15} +256.000 q^{16} -252.000 q^{17} -2628.00 q^{18} -372.000 q^{19} +400.000 q^{20} +1470.00 q^{21} -484.000 q^{22} -2314.00 q^{23} +1920.00 q^{24} +625.000 q^{25} -1632.00 q^{26} -12420.0 q^{27} -784.000 q^{28} +3266.00 q^{29} +3000.00 q^{30} -1808.00 q^{31} -1024.00 q^{32} -3630.00 q^{33} +1008.00 q^{34} -1225.00 q^{35} +10512.0 q^{36} -1542.00 q^{37} +1488.00 q^{38} -12240.0 q^{39} -1600.00 q^{40} -10570.0 q^{41} -5880.00 q^{42} -6564.00 q^{43} +1936.00 q^{44} +16425.0 q^{45} +9256.00 q^{46} +1722.00 q^{47} -7680.00 q^{48} +2401.00 q^{49} -2500.00 q^{50} +7560.00 q^{51} +6528.00 q^{52} -15006.0 q^{53} +49680.0 q^{54} +3025.00 q^{55} +3136.00 q^{56} +11160.0 q^{57} -13064.0 q^{58} +49148.0 q^{59} -12000.0 q^{60} +5666.00 q^{61} +7232.00 q^{62} -32193.0 q^{63} +4096.00 q^{64} +10200.0 q^{65} +14520.0 q^{66} -26318.0 q^{67} -4032.00 q^{68} +69420.0 q^{69} +4900.00 q^{70} -1612.00 q^{71} -42048.0 q^{72} +63332.0 q^{73} +6168.00 q^{74} -18750.0 q^{75} -5952.00 q^{76} -5929.00 q^{77} +48960.0 q^{78} -40360.0 q^{79} +6400.00 q^{80} +212949. q^{81} +42280.0 q^{82} +63972.0 q^{83} +23520.0 q^{84} -6300.00 q^{85} +26256.0 q^{86} -97980.0 q^{87} -7744.00 q^{88} +85830.0 q^{89} -65700.0 q^{90} -19992.0 q^{91} -37024.0 q^{92} +54240.0 q^{93} -6888.00 q^{94} -9300.00 q^{95} +30720.0 q^{96} +13526.0 q^{97} -9604.00 q^{98} +79497.0 q^{99} +O(q^{100})\)

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
$3$	−30.0000	−1.92450	−0.962250	−	0.272166i	$-0.912260\pi$
$3$	−30.0000	−1.92450	−0.962250	+	0.272166i	$0.912260\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	120.000	1.36083
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−64.0000	−0.353553
$9$	657.000	2.70370
$10$	−100.000	−0.316228
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−480.000	−0.962250
$13$	408.000	0.669579	0.334789	−	0.942293i	$-0.391335\pi$
$13$	408.000	0.669579	0.334789	+	0.942293i	$0.391335\pi$
$14$	196.000	0.267261
$15$	−750.000	−0.860663
$16$	256.000	0.250000
$17$	−252.000	−0.211484	−0.105742	−	0.994394i	$-0.533722\pi$
$17$	−252.000	−0.211484	−0.105742	+	0.994394i	$0.533722\pi$
$18$	−2628.00	−1.91181
$19$	−372.000	−0.236406	−0.118203	−	0.992989i	$-0.537713\pi$
$19$	−372.000	−0.236406	−0.118203	+	0.992989i	$0.537713\pi$
$20$	400.000	0.223607
$21$	1470.00	0.727393
$22$	−484.000	−0.213201
$23$	−2314.00	−0.912103	−0.456051	−	0.889953i	$-0.650737\pi$
$23$	−2314.00	−0.912103	−0.456051	+	0.889953i	$0.650737\pi$
$24$	1920.00	0.680414
$25$	625.000	0.200000
$26$	−1632.00	−0.473464
$27$	−12420.0	−3.27878
$28$	−784.000	−0.188982
$29$	3266.00	0.721143	0.360571	−	0.932732i	$-0.382582\pi$
$29$	3266.00	0.721143	0.360571	+	0.932732i	$0.382582\pi$
$30$	3000.00	0.608581
$31$	−1808.00	−0.337905	−0.168952	−	0.985624i	$-0.554038\pi$
$31$	−1808.00	−0.337905	−0.168952	+	0.985624i	$0.554038\pi$
$32$	−1024.00	−0.176777
$33$	−3630.00	−0.580259
$34$	1008.00	0.149542
$35$	−1225.00	−0.169031
$36$	10512.0	1.35185
$37$	−1542.00	−0.185174	−0.0925870	−	0.995705i	$-0.529514\pi$
$37$	−1542.00	−0.185174	−0.0925870	+	0.995705i	$0.529514\pi$
$38$	1488.00	0.167164
$39$	−12240.0	−1.28861
$40$	−1600.00	−0.158114
$41$	−10570.0	−0.982009	−0.491004	−	0.871157i	$-0.663370\pi$
$41$	−10570.0	−0.982009	−0.491004	+	0.871157i	$0.663370\pi$
$42$	−5880.00	−0.514344
$43$	−6564.00	−0.541374	−0.270687	−	0.962667i	$-0.587251\pi$
$43$	−6564.00	−0.541374	−0.270687	+	0.962667i	$0.587251\pi$
$44$	1936.00	0.150756
$45$	16425.0	1.20913
$46$	9256.00	0.644954
$47$	1722.00	0.113707	0.0568537	−	0.998383i	$-0.481893\pi$
$47$	1722.00	0.113707	0.0568537	+	0.998383i	$0.481893\pi$
$48$	−7680.00	−0.481125
$49$	2401.00	0.142857
$50$	−2500.00	−0.141421
$51$	7560.00	0.407002
$52$	6528.00	0.334789
$53$	−15006.0	−0.733796	−0.366898	−	0.930261i	$-0.619580\pi$
$53$	−15006.0	−0.733796	−0.366898	+	0.930261i	$0.619580\pi$
$54$	49680.0	2.31845
$55$	3025.00	0.134840
$56$	3136.00	0.133631
$57$	11160.0	0.454964
$58$	−13064.0	−0.509925
$59$	49148.0	1.83813	0.919064	−	0.394108i	$-0.128946\pi$
$59$	49148.0	1.83813	0.919064	+	0.394108i	$0.128946\pi$
$60$	−12000.0	−0.430331
$61$	5666.00	0.194963	0.0974815	−	0.995237i	$-0.468921\pi$
$61$	5666.00	0.194963	0.0974815	+	0.995237i	$0.468921\pi$
$62$	7232.00	0.238935
$63$	−32193.0	−1.02190
$64$	4096.00	0.125000
$65$	10200.0	0.299445
$66$	14520.0	0.410305
$67$	−26318.0	−0.716252	−0.358126	−	0.933673i	$-0.616584\pi$
$67$	−26318.0	−0.716252	−0.358126	+	0.933673i	$0.616584\pi$
$68$	−4032.00	−0.105742
$69$	69420.0	1.75534
$70$	4900.00	0.119523
$71$	−1612.00	−0.0379506	−0.0189753	−	0.999820i	$-0.506040\pi$
$71$	−1612.00	−0.0379506	−0.0189753	+	0.999820i	$0.506040\pi$
$72$	−42048.0	−0.955904
$73$	63332.0	1.39096	0.695482	−	0.718543i	$-0.255191\pi$
$73$	63332.0	1.39096	0.695482	+	0.718543i	$0.255191\pi$
$74$	6168.00	0.130938
$75$	−18750.0	−0.384900
$76$	−5952.00	−0.118203
$77$	−5929.00	−0.113961
$78$	48960.0	0.911182
$79$	−40360.0	−0.727584	−0.363792	−	0.931480i	$-0.618518\pi$
$79$	−40360.0	−0.727584	−0.363792	+	0.931480i	$0.618518\pi$
$80$	6400.00	0.111803
$81$	212949.	3.60631
$82$	42280.0	0.694385
$83$	63972.0	1.01928	0.509641	−	0.860387i	$-0.329778\pi$
$83$	63972.0	1.01928	0.509641	+	0.860387i	$0.329778\pi$
$84$	23520.0	0.363696
$85$	−6300.00	−0.0945787
$86$	26256.0	0.382809
$87$	−97980.0	−1.38784
$88$	−7744.00	−0.106600
$89$	85830.0	1.14859	0.574294	−	0.818649i	$-0.305277\pi$
$89$	85830.0	1.14859	0.574294	+	0.818649i	$0.305277\pi$
$90$	−65700.0	−0.854986
$91$	−19992.0	−0.253077
$92$	−37024.0	−0.456051
$93$	54240.0	0.650298
$94$	−6888.00	−0.0804032
$95$	−9300.00	−0.105724
$96$	30720.0	0.340207
$97$	13526.0	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$97$	13526.0	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$98$	−9604.00	−0.101015
$99$	79497.0	0.815197
$100$	10000.0	0.100000
$101$	−4866.00	−0.0474645	−0.0237322	−	0.999718i	$-0.507555\pi$
$101$	−4866.00	−0.0474645	−0.0237322	+	0.999718i	$0.507555\pi$
$102$	−30240.0	−0.287794
$103$	32938.0	0.305917	0.152959	−	0.988233i	$-0.451120\pi$
$103$	32938.0	0.305917	0.152959	+	0.988233i	$0.451120\pi$
$104$	−26112.0	−0.236732
$105$	36750.0	0.325300
$106$	60024.0	0.518872
$107$	−189696.	−1.60176	−0.800882	−	0.598822i	$-0.795636\pi$
$107$	−189696.	−1.60176	−0.800882	+	0.598822i	$0.795636\pi$
$108$	−198720.	−1.63939
$109$	52014.0	0.419328	0.209664	−	0.977773i	$-0.432763\pi$
$109$	52014.0	0.419328	0.209664	+	0.977773i	$0.432763\pi$
$110$	−12100.0	−0.0953463
$111$	46260.0	0.356368
$112$	−12544.0	−0.0944911
$113$	78590.0	0.578990	0.289495	−	0.957180i	$-0.406513\pi$
$113$	78590.0	0.578990	0.289495	+	0.957180i	$0.406513\pi$
$114$	−44640.0	−0.321708
$115$	−57850.0	−0.407905
$116$	52256.0	0.360571
$117$	268056.	1.81034
$118$	−196592.	−1.29975
$119$	12348.0	0.0799336
$120$	48000.0	0.304290
$121$	14641.0	0.0909091
$122$	−22664.0	−0.137860
$123$	317100.	1.88988
$124$	−28928.0	−0.168952
$125$	15625.0	0.0894427
$126$	128772.	0.722595
$127$	106172.	0.584118	0.292059	−	0.956400i	$-0.405660\pi$
$127$	106172.	0.584118	0.292059	+	0.956400i	$0.405660\pi$
$128$	−16384.0	−0.0883883
$129$	196920.	1.04187
$130$	−40800.0	−0.211739
$131$	−243500.	−1.23971	−0.619856	−	0.784716i	$-0.712809\pi$
$131$	−243500.	−1.23971	−0.619856	+	0.784716i	$0.712809\pi$
$132$	−58080.0	−0.290129
$133$	18228.0	0.0893532
$134$	105272.	0.506467
$135$	−310500.	−1.46631
$136$	16128.0	0.0747710
$137$	343614.	1.56412	0.782059	−	0.623205i	$-0.214170\pi$
$137$	343614.	1.56412	0.782059	+	0.623205i	$0.214170\pi$
$138$	−277680.	−1.24121
$139$	208508.	0.915347	0.457673	−	0.889120i	$-0.348683\pi$
$139$	208508.	0.915347	0.457673	+	0.889120i	$0.348683\pi$
$140$	−19600.0	−0.0845154
$141$	−51660.0	−0.218830
$142$	6448.00	0.0268352
$143$	49368.0	0.201886
$144$	168192.	0.675926
$145$	81650.0	0.322505
$146$	−253328.	−0.983560
$147$	−72030.0	−0.274929
$148$	−24672.0	−0.0925870
$149$	−182970.	−0.675172	−0.337586	−	0.941295i	$-0.609610\pi$
$149$	−182970.	−0.675172	−0.337586	+	0.941295i	$0.609610\pi$
$150$	75000.0	0.272166
$151$	437728.	1.56229	0.781146	−	0.624349i	$-0.214636\pi$
$151$	437728.	1.56229	0.781146	+	0.624349i	$0.214636\pi$
$152$	23808.0	0.0835822
$153$	−165564.	−0.571791
$154$	23716.0	0.0805823
$155$	−45200.0	−0.151116
$156$	−195840.	−0.644303
$157$	−266154.	−0.861755	−0.430878	−	0.902410i	$-0.641796\pi$
$157$	−266154.	−0.861755	−0.430878	+	0.902410i	$0.641796\pi$
$158$	161440.	0.514480
$159$	450180.	1.41219
$160$	−25600.0	−0.0790569
$161$	113386.	0.344742
$162$	−851796.	−2.55005
$163$	−628622.	−1.85319	−0.926596	−	0.376058i	$-0.877280\pi$
$163$	−628622.	−1.85319	−0.926596	+	0.376058i	$0.877280\pi$
$164$	−169120.	−0.491004
$165$	−90750.0	−0.259500
$166$	−255888.	−0.720742
$167$	−130628.	−0.362447	−0.181224	−	0.983442i	$-0.558006\pi$
$167$	−130628.	−0.362447	−0.181224	+	0.983442i	$0.558006\pi$
$168$	−94080.0	−0.257172
$169$	−204829.	−0.551664
$170$	25200.0	0.0668772
$171$	−244404.	−0.639172
$172$	−105024.	−0.270687
$173$	57924.0	0.147144	0.0735721	−	0.997290i	$-0.476560\pi$
$173$	57924.0	0.147144	0.0735721	+	0.997290i	$0.476560\pi$
$174$	391920.	0.981351
$175$	−30625.0	−0.0755929
$176$	30976.0	0.0753778
$177$	−1.47444e6	−3.53748
$178$	−343320.	−0.812174
$179$	−91680.0	−0.213866	−0.106933	−	0.994266i	$-0.534103\pi$
$179$	−91680.0	−0.213866	−0.106933	+	0.994266i	$0.534103\pi$
$180$	262800.	0.604567
$181$	377322.	0.856083	0.428041	−	0.903759i	$-0.359204\pi$
$181$	377322.	0.856083	0.428041	+	0.903759i	$0.359204\pi$
$182$	79968.0	0.178952
$183$	−169980.	−0.375206
$184$	148096.	0.322477
$185$	−38550.0	−0.0828123
$186$	−216960.	−0.459830
$187$	−30492.0	−0.0637649
$188$	27552.0	0.0568537
$189$	608580.	1.23926
$190$	37200.0	0.0747582
$191$	248464.	0.492811	0.246405	−	0.969167i	$-0.420751\pi$
$191$	248464.	0.492811	0.246405	+	0.969167i	$0.420751\pi$
$192$	−122880.	−0.240563
$193$	43244.0	0.0835666	0.0417833	−	0.999127i	$-0.486696\pi$
$193$	43244.0	0.0835666	0.0417833	+	0.999127i	$0.486696\pi$
$194$	−54104.0	−0.103211
$195$	−306000.	−0.576282
$196$	38416.0	0.0714286
$197$	−742060.	−1.36230	−0.681151	−	0.732143i	$-0.738520\pi$
$197$	−742060.	−1.36230	−0.681151	+	0.732143i	$0.738520\pi$
$198$	−317988.	−0.576432
$199$	−131040.	−0.234569	−0.117285	−	0.993098i	$-0.537419\pi$
$199$	−131040.	−0.234569	−0.117285	+	0.993098i	$0.537419\pi$
$200$	−40000.0	−0.0707107
$201$	789540.	1.37843
$202$	19464.0	0.0335625
$203$	−160034.	−0.272566
$204$	120960.	0.203501
$205$	−264250.	−0.439168
$206$	−131752.	−0.216316
$207$	−1.52030e6	−2.46606
$208$	104448.	0.167395
$209$	−45012.0	−0.0712792
$210$	−147000.	−0.230022
$211$	−278340.	−0.430397	−0.215199	−	0.976570i	$-0.569040\pi$
$211$	−278340.	−0.430397	−0.215199	+	0.976570i	$0.569040\pi$
$212$	−240096.	−0.366898
$213$	48360.0	0.0730361
$214$	758784.	1.13262
$215$	−164100.	−0.242110
$216$	794880.	1.15922
$217$	88592.0	0.127716
$218$	−208056.	−0.296510
$219$	−1.89996e6	−2.67691
$220$	48400.0	0.0674200
$221$	−102816.	−0.141605
$222$	−185040.	−0.251990
$223$	−1.16205e6	−1.56481	−0.782407	−	0.622768i	$-0.786008\pi$
$223$	−1.16205e6	−1.56481	−0.782407	+	0.622768i	$0.786008\pi$
$224$	50176.0	0.0668153
$225$	410625.	0.540741
$226$	−314360.	−0.409408
$227$	−67892.0	−0.0874488	−0.0437244	−	0.999044i	$-0.513922\pi$
$227$	−67892.0	−0.0874488	−0.0437244	+	0.999044i	$0.513922\pi$
$228$	178560.	0.227482
$229$	−915442.	−1.15357	−0.576783	−	0.816898i	$-0.695692\pi$
$229$	−915442.	−1.15357	−0.576783	+	0.816898i	$0.695692\pi$
$230$	231400.	0.288432
$231$	177870.	0.219317
$232$	−209024.	−0.254962
$233$	−698784.	−0.843244	−0.421622	−	0.906772i	$-0.638539\pi$
$233$	−698784.	−0.843244	−0.421622	+	0.906772i	$0.638539\pi$
$234$	−1.07222e6	−1.28011
$235$	43050.0	0.0508515
$236$	786368.	0.919064
$237$	1.21080e6	1.40024
$238$	−49392.0	−0.0565216
$239$	−446832.	−0.505999	−0.252999	−	0.967466i	$-0.581417\pi$
$239$	−446832.	−0.505999	−0.252999	+	0.967466i	$0.581417\pi$
$240$	−192000.	−0.215166
$241$	−249946.	−0.277207	−0.138603	−	0.990348i	$-0.544261\pi$
$241$	−249946.	−0.277207	−0.138603	+	0.990348i	$0.544261\pi$
$242$	−58564.0	−0.0642824
$243$	−3.37041e6	−3.66157
$244$	90656.0	0.0974815
$245$	60025.0	0.0638877
$246$	−1.26840e6	−1.33634
$247$	−151776.	−0.158293
$248$	115712.	0.119467
$249$	−1.91916e6	−1.96161
$250$	−62500.0	−0.0632456
$251$	−466328.	−0.467205	−0.233602	−	0.972332i	$-0.575051\pi$
$251$	−466328.	−0.467205	−0.233602	+	0.972332i	$0.575051\pi$
$252$	−515088.	−0.510952
$253$	−279994.	−0.275009
$254$	−424688.	−0.413034
$255$	189000.	0.182017
$256$	65536.0	0.0625000
$257$	−420302.	−0.396943	−0.198472	−	0.980107i	$-0.563598\pi$
$257$	−420302.	−0.396943	−0.198472	+	0.980107i	$0.563598\pi$
$258$	−787680.	−0.736717
$259$	75558.0	0.0699892
$260$	163200.	0.149722
$261$	2.14576e6	1.94976
$262$	974000.	0.876609
$263$	4620.00	0.00411863	0.00205931	−	0.999998i	$-0.499344\pi$
$263$	4620.00	0.00411863	0.00205931	+	0.999998i	$0.499344\pi$
$264$	232320.	0.205152
$265$	−375150.	−0.328163
$266$	−72912.0	−0.0631822
$267$	−2.57490e6	−2.21046
$268$	−421088.	−0.358126
$269$	−92606.0	−0.0780294	−0.0390147	−	0.999239i	$-0.512422\pi$
$269$	−92606.0	−0.0780294	−0.0390147	+	0.999239i	$0.512422\pi$
$270$	1.24200e6	1.03684
$271$	1.58017e6	1.30701	0.653507	−	0.756921i	$-0.273297\pi$
$271$	1.58017e6	1.30701	0.653507	+	0.756921i	$0.273297\pi$
$272$	−64512.0	−0.0528711
$273$	599760.	0.487047
$274$	−1.37446e6	−1.10600
$275$	75625.0	0.0603023
$276$	1.11072e6	0.877671
$277$	1.16680e6	0.913686	0.456843	−	0.889547i	$-0.348980\pi$
$277$	1.16680e6	0.913686	0.456843	+	0.889547i	$0.348980\pi$
$278$	−834032.	−0.647248
$279$	−1.18786e6	−0.913594
$280$	78400.0	0.0597614
$281$	1.61649e6	1.22126	0.610630	−	0.791916i	$-0.290916\pi$
$281$	1.61649e6	1.22126	0.610630	+	0.791916i	$0.290916\pi$
$282$	206640.	0.154736
$283$	2.33086e6	1.73002	0.865008	−	0.501758i	$-0.167313\pi$
$283$	2.33086e6	1.73002	0.865008	+	0.501758i	$0.167313\pi$
$284$	−25792.0	−0.0189753
$285$	279000.	0.203466
$286$	−197472.	−0.142755
$287$	517930.	0.371164
$288$	−672768.	−0.477952
$289$	−1.35635e6	−0.955274
$290$	−326600.	−0.228045
$291$	−405780.	−0.280904
$292$	1.01331e6	0.695482
$293$	1.80812e6	1.23043	0.615217	−	0.788358i	$-0.289068\pi$
$293$	1.80812e6	1.23043	0.615217	+	0.788358i	$0.289068\pi$
$294$	288120.	0.194404
$295$	1.22870e6	0.822036
$296$	98688.0	0.0654689
$297$	−1.50282e6	−0.988589
$298$	731880.	0.477418
$299$	−944112.	−0.610725
$300$	−300000.	−0.192450
$301$	321636.	0.204620
$302$	−1.75091e6	−1.10471
$303$	145980.	0.0913454
$304$	−95232.0	−0.0591016
$305$	141650.	0.0871901
$306$	662256.	0.404317
$307$	1.39262e6	0.843306	0.421653	−	0.906757i	$-0.361450\pi$
$307$	1.39262e6	0.843306	0.421653	+	0.906757i	$0.361450\pi$
$308$	−94864.0	−0.0569803
$309$	−988140.	−0.588738
$310$	180800.	0.106855
$311$	−357084.	−0.209348	−0.104674	−	0.994507i	$-0.533380\pi$
$311$	−357084.	−0.209348	−0.104674	+	0.994507i	$0.533380\pi$
$312$	783360.	0.455591
$313$	−588262.	−0.339399	−0.169699	−	0.985496i	$-0.554280\pi$
$313$	−588262.	−0.339399	−0.169699	+	0.985496i	$0.554280\pi$
$314$	1.06462e6	0.609353
$315$	−804825.	−0.457009
$316$	−645760.	−0.363792
$317$	2.12263e6	1.18639	0.593193	−	0.805060i	$-0.297867\pi$
$317$	2.12263e6	1.18639	0.593193	+	0.805060i	$0.297867\pi$
$318$	−1.80072e6	−0.998570
$319$	395186.	0.217433
$320$	102400.	0.0559017
$321$	5.69088e6	3.08260
$322$	−453544.	−0.243770
$323$	93744.0	0.0499962
$324$	3.40718e6	1.80316
$325$	255000.	0.133916
$326$	2.51449e6	1.31041
$327$	−1.56042e6	−0.806997
$328$	676480.	0.347193
$329$	−84378.0	−0.0429773
$330$	363000.	0.183494
$331$	2.27216e6	1.13990	0.569952	−	0.821678i	$-0.306962\pi$
$331$	2.27216e6	1.13990	0.569952	+	0.821678i	$0.306962\pi$
$332$	1.02355e6	0.509641
$333$	−1.01309e6	−0.500656
$334$	522512.	0.256289
$335$	−657950.	−0.320318
$336$	376320.	0.181848
$337$	2.79664e6	1.34141	0.670706	−	0.741723i	$-0.265991\pi$
$337$	2.79664e6	1.34141	0.670706	+	0.741723i	$0.265991\pi$
$338$	819316.	0.390085
$339$	−2.35770e6	−1.11427
$340$	−100800.	−0.0472893
$341$	−218768.	−0.101882
$342$	977616.	0.451963
$343$	−117649.	−0.0539949
$344$	420096.	0.191405
$345$	1.73550e6	0.785013
$346$	−231696.	−0.104047
$347$	−1.90724e6	−0.850319	−0.425159	−	0.905119i	$-0.639782\pi$
$347$	−1.90724e6	−0.850319	−0.425159	+	0.905119i	$0.639782\pi$
$348$	−1.56768e6	−0.693920
$349$	−3.24525e6	−1.42621	−0.713106	−	0.701056i	$-0.752712\pi$
$349$	−3.24525e6	−1.42621	−0.713106	+	0.701056i	$0.752712\pi$
$350$	122500.	0.0534522
$351$	−5.06736e6	−2.19540
$352$	−123904.	−0.0533002
$353$	1.09466e6	0.467565	0.233782	−	0.972289i	$-0.424890\pi$
$353$	1.09466e6	0.467565	0.233782	+	0.972289i	$0.424890\pi$
$354$	5.89776e6	2.50138
$355$	−40300.0	−0.0169720
$356$	1.37328e6	0.574294
$357$	−370440.	−0.153832
$358$	366720.	0.151226
$359$	−2.23717e6	−0.916141	−0.458071	−	0.888916i	$-0.651459\pi$
$359$	−2.23717e6	−0.916141	−0.458071	+	0.888916i	$0.651459\pi$
$360$	−1.05120e6	−0.427493
$361$	−2.33772e6	−0.944112
$362$	−1.50929e6	−0.605342
$363$	−439230.	−0.174955
$364$	−319872.	−0.126539
$365$	1.58330e6	0.622058
$366$	679920.	0.265311
$367$	−3.02340e6	−1.17174	−0.585869	−	0.810406i	$-0.699247\pi$
$367$	−3.02340e6	−1.17174	−0.585869	+	0.810406i	$0.699247\pi$
$368$	−592384.	−0.228026
$369$	−6.94449e6	−2.65506
$370$	154200.	0.0585572
$371$	735294.	0.277349
$372$	867840.	0.325149
$373$	−4.71113e6	−1.75329	−0.876644	−	0.481140i	$-0.840223\pi$
$373$	−4.71113e6	−1.75329	−0.876644	+	0.481140i	$0.840223\pi$
$374$	121968.	0.0450886
$375$	−468750.	−0.172133
$376$	−110208.	−0.0402016
$377$	1.33253e6	0.482862
$378$	−2.43432e6	−0.876291
$379$	3.98875e6	1.42639	0.713195	−	0.700965i	$-0.247247\pi$
$379$	3.98875e6	1.42639	0.713195	+	0.700965i	$0.247247\pi$
$380$	−148800.	−0.0528620
$381$	−3.18516e6	−1.12414
$382$	−993856.	−0.348470
$383$	−2.84077e6	−0.989555	−0.494777	−	0.869020i	$-0.664750\pi$
$383$	−2.84077e6	−0.989555	−0.494777	+	0.869020i	$0.664750\pi$
$384$	491520.	0.170103
$385$	−148225.	−0.0509647
$386$	−172976.	−0.0590905
$387$	−4.31255e6	−1.46372
$388$	216416.	0.0729810
$389$	4.65507e6	1.55974	0.779871	−	0.625941i	$-0.215285\pi$
$389$	4.65507e6	1.55974	0.779871	+	0.625941i	$0.215285\pi$
$390$	1.22400e6	0.407493
$391$	583128.	0.192895
$392$	−153664.	−0.0505076
$393$	7.30500e6	2.38583
$394$	2.96824e6	0.963293
$395$	−1.00900e6	−0.325386
$396$	1.27195e6	0.407599
$397$	3.13185e6	0.997296	0.498648	−	0.866805i	$-0.333830\pi$
$397$	3.13185e6	0.997296	0.498648	+	0.866805i	$0.333830\pi$
$398$	524160.	0.165866
$399$	−546840.	−0.171960
$400$	160000.	0.0500000
$401$	−3.44205e6	−1.06895	−0.534474	−	0.845185i	$-0.679490\pi$
$401$	−3.44205e6	−1.06895	−0.534474	+	0.845185i	$0.679490\pi$
$402$	−3.15816e6	−0.974696
$403$	−737664.	−0.226254
$404$	−77856.0	−0.0237322
$405$	5.32372e6	1.61279
$406$	640136.	0.192733
$407$	−186582.	−0.0558321
$408$	−483840.	−0.143897
$409$	−877862.	−0.259488	−0.129744	−	0.991547i	$-0.541416\pi$
$409$	−877862.	−0.259488	−0.129744	+	0.991547i	$0.541416\pi$
$410$	1.05700e6	0.310538
$411$	−1.03084e7	−3.01015
$412$	527008.	0.152959
$413$	−2.40825e6	−0.694747
$414$	6.08119e6	1.74376
$415$	1.59930e6	0.455837
$416$	−417792.	−0.118366
$417$	−6.25524e6	−1.76159
$418$	180048.	0.0504020
$419$	4.46068e6	1.24127	0.620635	−	0.784100i	$-0.286875\pi$
$419$	4.46068e6	1.24127	0.620635	+	0.784100i	$0.286875\pi$
$420$	588000.	0.162650
$421$	2.61236e6	0.718336	0.359168	−	0.933273i	$-0.383061\pi$
$421$	2.61236e6	0.718336	0.359168	+	0.933273i	$0.383061\pi$
$422$	1.11336e6	0.304337
$423$	1.13135e6	0.307431
$424$	960384.	0.259436
$425$	−157500.	−0.0422969
$426$	−193440.	−0.0516443
$427$	−277634.	−0.0736891
$428$	−3.03514e6	−0.800882
$429$	−1.48104e6	−0.388529
$430$	656400.	0.171198
$431$	−1.52080e6	−0.394347	−0.197174	−	0.980369i	$-0.563176\pi$
$431$	−1.52080e6	−0.394347	−0.197174	+	0.980369i	$0.563176\pi$
$432$	−3.17952e6	−0.819695
$433$	−756874.	−0.194001	−0.0970005	−	0.995284i	$-0.530925\pi$
$433$	−756874.	−0.194001	−0.0970005	+	0.995284i	$0.530925\pi$
$434$	−354368.	−0.0903088
$435$	−2.44950e6	−0.620661
$436$	832224.	0.209664
$437$	860808.	0.215627
$438$	7.59984e6	1.89286
$439$	−4.26853e6	−1.05710	−0.528551	−	0.848902i	$-0.677264\pi$
$439$	−4.26853e6	−1.05710	−0.528551	+	0.848902i	$0.677264\pi$
$440$	−193600.	−0.0476731
$441$	1.57746e6	0.386243
$442$	411264.	0.100130
$443$	4.60981e6	1.11602	0.558012	−	0.829833i	$-0.311564\pi$
$443$	4.60981e6	1.11602	0.558012	+	0.829833i	$0.311564\pi$
$444$	740160.	0.178184
$445$	2.14575e6	0.513664
$446$	4.64820e6	1.10649
$447$	5.48910e6	1.29937
$448$	−200704.	−0.0472456
$449$	−3.23241e6	−0.756678	−0.378339	−	0.925667i	$-0.623505\pi$
$449$	−3.23241e6	−0.756678	−0.378339	+	0.925667i	$0.623505\pi$
$450$	−1.64250e6	−0.382361
$451$	−1.27897e6	−0.296087
$452$	1.25744e6	0.289495
$453$	−1.31318e7	−3.00663
$454$	271568.	0.0618357
$455$	−499800.	−0.113179
$456$	−714240.	−0.160854
$457$	−7.61229e6	−1.70500	−0.852501	−	0.522726i	$-0.824915\pi$
$457$	−7.61229e6	−1.70500	−0.852501	+	0.522726i	$0.824915\pi$
$458$	3.66177e6	0.815694
$459$	3.12984e6	0.693411
$460$	−925600.	−0.203952
$461$	2.33481e6	0.511682	0.255841	−	0.966719i	$-0.417648\pi$
$461$	2.33481e6	0.511682	0.255841	+	0.966719i	$0.417648\pi$
$462$	−711480.	−0.155081
$463$	−6.83196e6	−1.48113	−0.740565	−	0.671985i	$-0.765442\pi$
$463$	−6.83196e6	−1.48113	−0.740565	+	0.671985i	$0.765442\pi$
$464$	836096.	0.180286
$465$	1.35600e6	0.290822
$466$	2.79514e6	0.596263
$467$	8.80454e6	1.86816	0.934081	−	0.357062i	$-0.116222\pi$
$467$	8.80454e6	1.86816	0.934081	+	0.357062i	$0.116222\pi$
$468$	4.28890e6	0.905172
$469$	1.28958e6	0.270718
$470$	−172200.	−0.0359574
$471$	7.98462e6	1.65845
$472$	−3.14547e6	−0.649876
$473$	−794244.	−0.163230
$474$	−4.84320e6	−0.990117
$475$	−232500.	−0.0472812
$476$	197568.	0.0399668
$477$	−9.85894e6	−1.98397
$478$	1.78733e6	0.357795
$479$	−6.50013e6	−1.29444	−0.647222	−	0.762302i	$-0.724069\pi$
$479$	−6.50013e6	−1.29444	−0.647222	+	0.762302i	$0.724069\pi$
$480$	768000.	0.152145
$481$	−629136.	−0.123989
$482$	999784.	0.196015
$483$	−3.40158e6	−0.663457
$484$	234256.	0.0454545
$485$	338150.	0.0652762
$486$	1.34816e7	2.58912
$487$	−7.33128e6	−1.40074	−0.700370	−	0.713780i	$-0.746981\pi$
$487$	−7.33128e6	−1.40074	−0.700370	+	0.713780i	$0.746981\pi$
$488$	−362624.	−0.0689298
$489$	1.88587e7	3.56647
$490$	−240100.	−0.0451754
$491$	−4.83491e6	−0.905075	−0.452537	−	0.891745i	$-0.649481\pi$
$491$	−4.83491e6	−0.905075	−0.452537	+	0.891745i	$0.649481\pi$
$492$	5.07360e6	0.944938
$493$	−823032.	−0.152510
$494$	607104.	0.111930
$495$	1.98742e6	0.364567
$496$	−462848.	−0.0844762
$497$	78988.0	0.0143440
$498$	7.67664e6	1.38707
$499$	−1.16132e6	−0.208785	−0.104392	−	0.994536i	$-0.533290\pi$
$499$	−1.16132e6	−0.208785	−0.104392	+	0.994536i	$0.533290\pi$
$500$	250000.	0.0447214
$501$	3.91884e6	0.697531
$502$	1.86531e6	0.330364
$503$	7.62958e6	1.34456	0.672280	−	0.740297i	$-0.265315\pi$
$503$	7.62958e6	1.34456	0.672280	+	0.740297i	$0.265315\pi$
$504$	2.06035e6	0.361298
$505$	−121650.	−0.0212268
$506$	1.11998e6	0.194461
$507$	6.14487e6	1.06168
$508$	1.69875e6	0.292059
$509$	−2.26934e6	−0.388244	−0.194122	−	0.980977i	$-0.562186\pi$
$509$	−2.26934e6	−0.388244	−0.194122	+	0.980977i	$0.562186\pi$
$510$	−756000.	−0.128705
$511$	−3.10327e6	−0.525735
$512$	−262144.	−0.0441942
$513$	4.62024e6	0.775124
$514$	1.68121e6	0.280681
$515$	823450.	0.136810
$516$	3.15072e6	0.520937
$517$	208362.	0.0342841
$518$	−302232.	−0.0494898
$519$	−1.73772e6	−0.283179
$520$	−652800.	−0.105870
$521$	−3.64009e6	−0.587513	−0.293757	−	0.955880i	$-0.594906\pi$
$521$	−3.64009e6	−0.587513	−0.293757	+	0.955880i	$0.594906\pi$
$522$	−8.58305e6	−1.37869
$523$	4.57653e6	0.731614	0.365807	−	0.930691i	$-0.380793\pi$
$523$	4.57653e6	0.731614	0.365807	+	0.930691i	$0.380793\pi$
$524$	−3.89600e6	−0.619856
$525$	918750.	0.145479
$526$	−18480.0	−0.00291231
$527$	455616.	0.0714615
$528$	−929280.	−0.145065
$529$	−1.08175e6	−0.168069
$530$	1.50060e6	0.232047
$531$	3.22902e7	4.96975
$532$	291648.	0.0446766
$533$	−4.31256e6	−0.657532
$534$	1.02996e7	1.56303
$535$	−4.74240e6	−0.716331
$536$	1.68435e6	0.253233
$537$	2.75040e6	0.411586
$538$	370424.	0.0551751
$539$	290521.	0.0430730
$540$	−4.96800e6	−0.733157
$541$	−2.11753e6	−0.311054	−0.155527	−	0.987832i	$-0.549708\pi$
$541$	−2.11753e6	−0.311054	−0.155527	+	0.987832i	$0.549708\pi$
$542$	−6.32067e6	−0.924198
$543$	−1.13197e7	−1.64753
$544$	258048.	0.0373855
$545$	1.30035e6	0.187529
$546$	−2.39904e6	−0.344394
$547$	2.68109e6	0.383128	0.191564	−	0.981480i	$-0.438644\pi$
$547$	2.68109e6	0.383128	0.191564	+	0.981480i	$0.438644\pi$
$548$	5.49782e6	0.782059
$549$	3.72256e6	0.527122
$550$	−302500.	−0.0426401
$551$	−1.21495e6	−0.170483
$552$	−4.44288e6	−0.620607
$553$	1.97764e6	0.275001
$554$	−4.66720e6	−0.646074
$555$	1.15650e6	0.159372
$556$	3.33613e6	0.457673
$557$	−8.29520e6	−1.13289	−0.566447	−	0.824098i	$-0.691682\pi$
$557$	−8.29520e6	−1.13289	−0.566447	+	0.824098i	$0.691682\pi$
$558$	4.75142e6	0.646009
$559$	−2.67811e6	−0.362493
$560$	−313600.	−0.0422577
$561$	914760.	0.122716
$562$	−6.46598e6	−0.863562
$563$	−8.86912e6	−1.17926	−0.589630	−	0.807674i	$-0.700726\pi$
$563$	−8.86912e6	−1.17926	−0.589630	+	0.807674i	$0.700726\pi$
$564$	−826560.	−0.109415
$565$	1.96475e6	0.258932
$566$	−9.32344e6	−1.22331
$567$	−1.04345e7	−1.36306
$568$	103168.	0.0134176
$569$	−1.07719e7	−1.39480	−0.697400	−	0.716682i	$-0.745660\pi$
$569$	−1.07719e7	−1.39480	−0.697400	+	0.716682i	$0.745660\pi$
$570$	−1.11600e6	−0.143872
$571$	−1.09048e7	−1.39967	−0.699837	−	0.714302i	$-0.746744\pi$
$571$	−1.09048e7	−1.39967	−0.699837	+	0.714302i	$0.746744\pi$
$572$	789888.	0.100943
$573$	−7.45392e6	−0.948414
$574$	−2.07172e6	−0.262453
$575$	−1.44625e6	−0.182421
$576$	2.69107e6	0.337963
$577$	1.42687e6	0.178421	0.0892103	−	0.996013i	$-0.471566\pi$
$577$	1.42687e6	0.178421	0.0892103	+	0.996013i	$0.471566\pi$
$578$	5.42541e6	0.675481
$579$	−1.29732e6	−0.160824
$580$	1.30640e6	0.161252
$581$	−3.13463e6	−0.385253
$582$	1.62312e6	0.198629
$583$	−1.81573e6	−0.221248
$584$	−4.05325e6	−0.491780
$585$	6.70140e6	0.809610
$586$	−7.23248e6	−0.870048
$587$	−1.12230e7	−1.34436	−0.672178	−	0.740389i	$-0.734641\pi$
$587$	−1.12230e7	−1.34436	−0.672178	+	0.740389i	$0.734641\pi$
$588$	−1.15248e6	−0.137464
$589$	672576.	0.0798828
$590$	−4.91480e6	−0.581267
$591$	2.22618e7	2.62175
$592$	−394752.	−0.0462935
$593$	1.61719e7	1.88853	0.944265	−	0.329186i	$-0.106774\pi$
$593$	1.61719e7	1.88853	0.944265	+	0.329186i	$0.106774\pi$
$594$	6.01128e6	0.699038
$595$	308700.	0.0357474
$596$	−2.92752e6	−0.337586
$597$	3.93120e6	0.451429
$598$	3.77645e6	0.431848
$599$	1.30381e7	1.48473	0.742363	−	0.669998i	$-0.233705\pi$
$599$	1.30381e7	1.48473	0.742363	+	0.669998i	$0.233705\pi$
$600$	1.20000e6	0.136083
$601$	1.49635e7	1.68984	0.844922	−	0.534889i	$-0.179647\pi$
$601$	1.49635e7	1.68984	0.844922	+	0.534889i	$0.179647\pi$
$602$	−1.28654e6	−0.144688
$603$	−1.72909e7	−1.93653
$604$	7.00365e6	0.781146
$605$	366025.	0.0406558
$606$	−583920.	−0.0645910
$607$	−9.42025e6	−1.03775	−0.518873	−	0.854852i	$-0.673648\pi$
$607$	−9.42025e6	−1.03775	−0.518873	+	0.854852i	$0.673648\pi$
$608$	380928.	0.0417911
$609$	4.80102e6	0.524554
$610$	−566600.	−0.0616527
$611$	702576.	0.0761360
$612$	−2.64902e6	−0.285896
$613$	−9.78788e6	−1.05205	−0.526027	−	0.850468i	$-0.676319\pi$
$613$	−9.78788e6	−1.05205	−0.526027	+	0.850468i	$0.676319\pi$
$614$	−5.57046e6	−0.596308
$615$	7.92750e6	0.845179
$616$	379456.	0.0402911
$617$	−6.32025e6	−0.668377	−0.334188	−	0.942506i	$-0.608462\pi$
$617$	−6.32025e6	−0.668377	−0.334188	+	0.942506i	$0.608462\pi$
$618$	3.95256e6	0.416301
$619$	4.34338e6	0.455619	0.227809	−	0.973706i	$-0.426844\pi$
$619$	4.34338e6	0.455619	0.227809	+	0.973706i	$0.426844\pi$
$620$	−723200.	−0.0755578
$621$	2.87399e7	2.99058
$622$	1.42834e6	0.148032
$623$	−4.20567e6	−0.434125
$624$	−3.13344e6	−0.322151
$625$	390625.	0.0400000
$626$	2.35305e6	0.239991
$627$	1.35036e6	0.137177
$628$	−4.25846e6	−0.430878
$629$	388584.	0.0391614
$630$	3.21930e6	0.323154
$631$	−1.37745e7	−1.37721	−0.688607	−	0.725135i	$-0.741777\pi$
$631$	−1.37745e7	−1.37721	−0.688607	+	0.725135i	$0.741777\pi$
$632$	2.58304e6	0.257240
$633$	8.35020e6	0.828300
$634$	−8.49052e6	−0.838902
$635$	2.65430e6	0.261226
$636$	7.20288e6	0.706095
$637$	979608.	0.0956541
$638$	−1.58074e6	−0.153748
$639$	−1.05908e6	−0.102607
$640$	−409600.	−0.0395285
$641$	534418.	0.0513731	0.0256866	−	0.999670i	$-0.491823\pi$
$641$	534418.	0.0513731	0.0256866	+	0.999670i	$0.491823\pi$
$642$	−2.27635e7	−2.17973
$643$	−1.02103e7	−0.973896	−0.486948	−	0.873431i	$-0.661890\pi$
$643$	−1.02103e7	−0.973896	−0.486948	+	0.873431i	$0.661890\pi$
$644$	1.81418e6	0.172371
$645$	4.92300e6	0.465941
$646$	−374976.	−0.0353527
$647$	1.28819e7	1.20981	0.604906	−	0.796297i	$-0.293211\pi$
$647$	1.28819e7	1.20981	0.604906	+	0.796297i	$0.293211\pi$
$648$	−1.36287e7	−1.27502
$649$	5.94691e6	0.554217
$650$	−1.02000e6	−0.0946928
$651$	−2.65776e6	−0.245789
$652$	−1.00580e7	−0.926596
$653$	1.31579e7	1.20755	0.603774	−	0.797156i	$-0.293663\pi$
$653$	1.31579e7	1.20755	0.603774	+	0.797156i	$0.293663\pi$
$654$	6.24168e6	0.570633
$655$	−6.08750e6	−0.554416
$656$	−2.70592e6	−0.245502
$657$	4.16091e7	3.76076
$658$	337512.	0.0303896
$659$	4.97763e6	0.446487	0.223244	−	0.974763i	$-0.428335\pi$
$659$	4.97763e6	0.446487	0.223244	+	0.974763i	$0.428335\pi$
$660$	−1.45200e6	−0.129750
$661$	−2.04072e7	−1.81669	−0.908344	−	0.418223i	$-0.862653\pi$
$661$	−2.04072e7	−1.81669	−0.908344	+	0.418223i	$0.862653\pi$
$662$	−9.08862e6	−0.806034
$663$	3.08448e6	0.272520
$664$	−4.09421e6	−0.360371
$665$	455700.	0.0399599
$666$	4.05238e6	0.354017
$667$	−7.55752e6	−0.657756
$668$	−2.09005e6	−0.181224
$669$	3.48615e7	3.01149
$670$	2.63180e6	0.226499
$671$	685586.	0.0587835
$672$	−1.50528e6	−0.128586
$673$	−1.99669e7	−1.69931	−0.849656	−	0.527338i	$-0.823190\pi$
$673$	−1.99669e7	−1.69931	−0.849656	+	0.527338i	$0.823190\pi$
$674$	−1.11866e7	−0.948522
$675$	−7.76250e6	−0.655756
$676$	−3.27726e6	−0.275832
$677$	−7.24632e6	−0.607639	−0.303820	−	0.952730i	$-0.598262\pi$
$677$	−7.24632e6	−0.607639	−0.303820	+	0.952730i	$0.598262\pi$
$678$	9.43080e6	0.787906
$679$	−662774.	−0.0551685
$680$	403200.	0.0334386
$681$	2.03676e6	0.168295
$682$	875072.	0.0720415
$683$	−5.95187e6	−0.488204	−0.244102	−	0.969750i	$-0.578493\pi$
$683$	−5.95187e6	−0.488204	−0.244102	+	0.969750i	$0.578493\pi$
$684$	−3.91046e6	−0.319586
$685$	8.59035e6	0.699495
$686$	470596.	0.0381802
$687$	2.74633e7	2.22004
$688$	−1.68038e6	−0.135344
$689$	−6.12245e6	−0.491334
$690$	−6.94200e6	−0.555088
$691$	−1.51691e7	−1.20855	−0.604276	−	0.796775i	$-0.706538\pi$
$691$	−1.51691e7	−1.20855	−0.604276	+	0.796775i	$0.706538\pi$
$692$	926784.	0.0735721
$693$	−3.89535e6	−0.308116
$694$	7.62896e6	0.601266
$695$	5.21270e6	0.409356
$696$	6.27072e6	0.490675
$697$	2.66364e6	0.207679
$698$	1.29810e7	1.00848
$699$	2.09635e7	1.62282
$700$	−490000.	−0.0377964
$701$	1.99923e7	1.53662	0.768311	−	0.640076i	$-0.221097\pi$
$701$	1.99923e7	1.53662	0.768311	+	0.640076i	$0.221097\pi$
$702$	2.02694e7	1.55238
$703$	573624.	0.0437763
$704$	495616.	0.0376889
$705$	−1.29150e6	−0.0978637
$706$	−4.37863e6	−0.330618
$707$	238434.	0.0179399
$708$	−2.35910e7	−1.76874
$709$	−1.78290e7	−1.33202	−0.666010	−	0.745943i	$-0.731999\pi$
$709$	−1.78290e7	−1.33202	−0.666010	+	0.745943i	$0.731999\pi$
$710$	161200.	0.0120010
$711$	−2.65165e7	−1.96717
$712$	−5.49312e6	−0.406087
$713$	4.18371e6	0.308204
$714$	1.48176e6	0.108776
$715$	1.23420e6	0.0902860
$716$	−1.46688e6	−0.106933
$717$	1.34050e7	0.973795
$718$	8.94867e6	0.647810
$719$	−1.33999e7	−0.966669	−0.483334	−	0.875436i	$-0.660574\pi$
$719$	−1.33999e7	−0.966669	−0.483334	+	0.875436i	$0.660574\pi$
$720$	4.20480e6	0.302283
$721$	−1.61396e6	−0.115626
$722$	9.35086e6	0.667588
$723$	7.49838e6	0.533484
$724$	6.03715e6	0.428041
$725$	2.04125e6	0.144229
$726$	1.75692e6	0.123712
$727$	4.14717e6	0.291015	0.145508	−	0.989357i	$-0.453519\pi$
$727$	4.14717e6	0.291015	0.145508	+	0.989357i	$0.453519\pi$
$728$	1.27949e6	0.0894762
$729$	4.93657e7	3.44038
$730$	−6.33320e6	−0.439862
$731$	1.65413e6	0.114492
$732$	−2.71968e6	−0.187603
$733$	3.73584e6	0.256820	0.128410	−	0.991721i	$-0.459013\pi$
$733$	3.73584e6	0.256820	0.128410	+	0.991721i	$0.459013\pi$
$734$	1.20936e7	0.828543
$735$	−1.80075e6	−0.122952
$736$	2.36954e6	0.161239
$737$	−3.18448e6	−0.215958
$738$	2.77780e7	1.87741
$739$	6.32442e6	0.426000	0.213000	−	0.977052i	$-0.431677\pi$
$739$	6.32442e6	0.426000	0.213000	+	0.977052i	$0.431677\pi$
$740$	−616800.	−0.0414062
$741$	4.55328e6	0.304634
$742$	−2.94118e6	−0.196115
$743$	−1.86241e7	−1.23766	−0.618832	−	0.785524i	$-0.712394\pi$
$743$	−1.86241e7	−1.23766	−0.618832	+	0.785524i	$0.712394\pi$
$744$	−3.47136e6	−0.229915
$745$	−4.57425e6	−0.301946
$746$	1.88445e7	1.23976
$747$	4.20296e7	2.75584
$748$	−487872.	−0.0318825
$749$	9.29510e6	0.605410
$750$	1.87500e6	0.121716
$751$	−1.60975e6	−0.104150	−0.0520749	−	0.998643i	$-0.516583\pi$
$751$	−1.60975e6	−0.104150	−0.0520749	+	0.998643i	$0.516583\pi$
$752$	440832.	0.0284268
$753$	1.39898e7	0.899136
$754$	−5.33011e6	−0.341435
$755$	1.09432e7	0.698678
$756$	9.73728e6	0.619631
$757$	2.03712e7	1.29204	0.646022	−	0.763319i	$-0.276431\pi$
$757$	2.03712e7	1.29204	0.646022	+	0.763319i	$0.276431\pi$
$758$	−1.59550e7	−1.00861
$759$	8.39982e6	0.529256
$760$	595200.	0.0373791
$761$	−2.95071e6	−0.184699	−0.0923496	−	0.995727i	$-0.529438\pi$
$761$	−2.95071e6	−0.184699	−0.0923496	+	0.995727i	$0.529438\pi$
$762$	1.27406e7	0.794884
$763$	−2.54869e6	−0.158491
$764$	3.97542e6	0.246405
$765$	−4.13910e6	−0.255713
$766$	1.13631e7	0.699721
$767$	2.00524e7	1.23077
$768$	−1.96608e6	−0.120281
$769$	1.40749e6	0.0858279	0.0429139	−	0.999079i	$-0.486336\pi$
$769$	1.40749e6	0.0858279	0.0429139	+	0.999079i	$0.486336\pi$
$770$	592900.	0.0360375
$771$	1.26091e7	0.763918
$772$	691904.	0.0417833
$773$	1.63720e7	0.985489	0.492744	−	0.870174i	$-0.335994\pi$
$773$	1.63720e7	0.985489	0.492744	+	0.870174i	$0.335994\pi$
$774$	1.72502e7	1.03500
$775$	−1.13000e6	−0.0675809
$776$	−865664.	−0.0516054
$777$	−2.26674e6	−0.134694
$778$	−1.86203e7	−1.10290
$779$	3.93204e6	0.232153
$780$	−4.89600e6	−0.288141
$781$	−195052.	−0.0114426
$782$	−2.33251e6	−0.136398
$783$	−4.05637e7	−2.36447
$784$	614656.	0.0357143
$785$	−6.65385e6	−0.385389
$786$	−2.92200e7	−1.68703
$787$	3.09871e6	0.178338	0.0891691	−	0.996017i	$-0.471579\pi$
$787$	3.09871e6	0.178338	0.0891691	+	0.996017i	$0.471579\pi$
$788$	−1.18730e7	−0.681151
$789$	−138600.	−0.00792630
$790$	4.03600e6	0.230082
$791$	−3.85091e6	−0.218838
$792$	−5.08781e6	−0.288216
$793$	2.31173e6	0.130543
$794$	−1.25274e7	−0.705195
$795$	1.12545e7	0.631551
$796$	−2.09664e6	−0.117285
$797$	8.82884e6	0.492332	0.246166	−	0.969228i	$-0.420829\pi$
$797$	8.82884e6	0.492332	0.246166	+	0.969228i	$0.420829\pi$
$798$	2.18736e6	0.121594
$799$	−433944.	−0.0240473
$800$	−640000.	−0.0353553
$801$	5.63903e7	3.10544
$802$	1.37682e7	0.755860
$803$	7.66317e6	0.419392
$804$	1.26326e7	0.689214
$805$	2.83465e6	0.154174
$806$	2.95066e6	0.159986
$807$	2.77818e6	0.150168
$808$	311424.	0.0167812
$809$	−2.79472e7	−1.50130	−0.750650	−	0.660700i	$-0.770259\pi$
$809$	−2.79472e7	−1.50130	−0.750650	+	0.660700i	$0.770259\pi$
$810$	−2.12949e7	−1.14042
$811$	−1.18672e7	−0.633570	−0.316785	−	0.948497i	$-0.602603\pi$
$811$	−1.18672e7	−0.633570	−0.316785	+	0.948497i	$0.602603\pi$
$812$	−2.56054e6	−0.136283
$813$	−4.74050e7	−2.51535
$814$	746328.	0.0394792
$815$	−1.57156e7	−0.828773
$816$	1.93536e6	0.101750
$817$	2.44181e6	0.127984
$818$	3.51145e6	0.183486
$819$	−1.31347e7	−0.684245
$820$	−4.22800e6	−0.219584
$821$	−2.44927e7	−1.26817	−0.634086	−	0.773262i	$-0.718624\pi$
$821$	−2.44927e7	−1.26817	−0.634086	+	0.773262i	$0.718624\pi$
$822$	4.12337e7	2.12849
$823$	−2.39807e7	−1.23414	−0.617068	−	0.786910i	$-0.711679\pi$
$823$	−2.39807e7	−1.23414	−0.617068	+	0.786910i	$0.711679\pi$
$824$	−2.10803e6	−0.108158
$825$	−2.26875e6	−0.116052
$826$	9.63301e6	0.491260
$827$	1.36460e7	0.693812	0.346906	−	0.937900i	$-0.387232\pi$
$827$	1.36460e7	0.693812	0.346906	+	0.937900i	$0.387232\pi$
$828$	−2.43248e7	−1.23303
$829$	−1.74552e7	−0.882141	−0.441071	−	0.897472i	$-0.645401\pi$
$829$	−1.74552e7	−0.882141	−0.441071	+	0.897472i	$0.645401\pi$
$830$	−6.39720e6	−0.322326
$831$	−3.50040e7	−1.75839
$832$	1.67117e6	0.0836974
$833$	−605052.	−0.0302121
$834$	2.50210e7	1.24563
$835$	−3.26570e6	−0.162091
$836$	−720192.	−0.0356396
$837$	2.24554e7	1.10791
$838$	−1.78427e7	−0.877710
$839$	−2.32008e7	−1.13789	−0.568943	−	0.822377i	$-0.692648\pi$
$839$	−2.32008e7	−1.13789	−0.568943	+	0.822377i	$0.692648\pi$
$840$	−2.35200e6	−0.115011
$841$	−9.84439e6	−0.479953
$842$	−1.04494e7	−0.507940
$843$	−4.84948e7	−2.35032
$844$	−4.45344e6	−0.215199
$845$	−5.12072e6	−0.246712
$846$	−4.52542e6	−0.217387
$847$	−717409.	−0.0343604
$848$	−3.84154e6	−0.183449
$849$	−6.99258e7	−3.32942
$850$	630000.	0.0299084
$851$	3.56819e6	0.168898
$852$	773760.	0.0365180
$853$	−4.00053e7	−1.88254	−0.941271	−	0.337651i	$-0.890368\pi$
$853$	−4.00053e7	−1.88254	−0.941271	+	0.337651i	$0.890368\pi$
$854$	1.11054e6	0.0521060
$855$	−6.11010e6	−0.285847
$856$	1.21405e7	0.566309
$857$	9.04931e6	0.420885	0.210442	−	0.977606i	$-0.432510\pi$
$857$	9.04931e6	0.420885	0.210442	+	0.977606i	$0.432510\pi$
$858$	5.92416e6	0.274732
$859$	−1.16671e7	−0.539485	−0.269743	−	0.962932i	$-0.586939\pi$
$859$	−1.16671e7	−0.539485	−0.269743	+	0.962932i	$0.586939\pi$
$860$	−2.62560e6	−0.121055
$861$	−1.55379e7	−0.714306
$862$	6.08320e6	0.278846
$863$	−3.23449e7	−1.47835	−0.739177	−	0.673511i	$-0.764785\pi$
$863$	−3.23449e7	−1.47835	−0.739177	+	0.673511i	$0.764785\pi$
$864$	1.27181e7	0.579612
$865$	1.44810e6	0.0658049
$866$	3.02750e6	0.137179
$867$	4.06906e7	1.83843
$868$	1.41747e6	0.0638580
$869$	−4.88356e6	−0.219375
$870$	9.79800e6	0.438873
$871$	−1.07377e7	−0.479587
$872$	−3.32890e6	−0.148255
$873$	8.88658e6	0.394638
$874$	−3.44323e6	−0.152471
$875$	−765625.	−0.0338062
$876$	−3.03994e7	−1.33846
$877$	−3.70377e7	−1.62609	−0.813045	−	0.582200i	$-0.802192\pi$
$877$	−3.70377e7	−1.62609	−0.813045	+	0.582200i	$0.802192\pi$
$878$	1.70741e7	0.747484
$879$	−5.42436e7	−2.36797
$880$	774400.	0.0337100
$881$	−2.86459e7	−1.24343	−0.621716	−	0.783242i	$-0.713564\pi$
$881$	−2.86459e7	−1.24343	−0.621716	+	0.783242i	$0.713564\pi$
$882$	−6.30983e6	−0.273115
$883$	−1.97543e7	−0.852630	−0.426315	−	0.904575i	$-0.640189\pi$
$883$	−1.97543e7	−0.852630	−0.426315	+	0.904575i	$0.640189\pi$
$884$	−1.64506e6	−0.0708027
$885$	−3.68610e7	−1.58201
$886$	−1.84392e7	−0.789148
$887$	3.55832e7	1.51857	0.759287	−	0.650756i	$-0.225548\pi$
$887$	3.55832e7	1.51857	0.759287	+	0.650756i	$0.225548\pi$
$888$	−2.96064e6	−0.125995
$889$	−5.20243e6	−0.220776
$890$	−8.58300e6	−0.363215
$891$	2.57668e7	1.08734
$892$	−1.85928e7	−0.782407
$893$	−640584.	−0.0268811
$894$	−2.19564e7	−0.918792
$895$	−2.29200e6	−0.0956438
$896$	802816.	0.0334077
$897$	2.83234e7	1.17534
$898$	1.29297e7	0.535052
$899$	−5.90493e6	−0.243677
$900$	6.57000e6	0.270370
$901$	3.78151e6	0.155186
$902$	5.11588e6	0.209365
$903$	−9.64908e6	−0.393792
$904$	−5.02976e6	−0.204704
$905$	9.43305e6	0.382852
$906$	5.25274e7	2.12601
$907$	1.15095e7	0.464556	0.232278	−	0.972649i	$-0.425382\pi$
$907$	1.15095e7	0.464556	0.232278	+	0.972649i	$0.425382\pi$
$908$	−1.08627e6	−0.0437244
$909$	−3.19696e6	−0.128330
$910$	1.99920e6	0.0800300
$911$	−4.80704e7	−1.91903	−0.959514	−	0.281661i	$-0.909115\pi$
$911$	−4.80704e7	−1.91903	−0.959514	+	0.281661i	$0.909115\pi$
$912$	2.85696e6	0.113741
$913$	7.74061e6	0.307325
$914$	3.04492e7	1.20562
$915$	−4.24950e6	−0.167797
$916$	−1.46471e7	−0.576783
$917$	1.19315e7	0.468567
$918$	−1.25194e7	−0.490315
$919$	1.21446e7	0.474344	0.237172	−	0.971468i	$-0.423780\pi$
$919$	1.21446e7	0.474344	0.237172	+	0.971468i	$0.423780\pi$
$920$	3.70240e6	0.144216
$921$	−4.17785e7	−1.62294
$922$	−9.33926e6	−0.361814
$923$	−657696.	−0.0254110
$924$	2.84592e6	0.109659
$925$	−963750.	−0.0370348
$926$	2.73278e7	1.04732
$927$	2.16403e7	0.827110
$928$	−3.34438e6	−0.127481
$929$	3.47049e7	1.31932	0.659662	−	0.751562i	$-0.270699\pi$
$929$	3.47049e7	1.31932	0.659662	+	0.751562i	$0.270699\pi$
$930$	−5.42400e6	−0.205642
$931$	−893172.	−0.0337723
$932$	−1.11805e7	−0.421622
$933$	1.07125e7	0.402891
$934$	−3.52182e7	−1.32099
$935$	−762300.	−0.0285165
$936$	−1.71556e7	−0.640053
$937$	1.92802e6	0.0717400	0.0358700	−	0.999356i	$-0.488580\pi$
$937$	1.92802e6	0.0717400	0.0358700	+	0.999356i	$0.488580\pi$
$938$	−5.15833e6	−0.191426
$939$	1.76479e7	0.653173
$940$	688800.	0.0254257
$941$	3.54329e7	1.30446	0.652232	−	0.758019i	$-0.273833\pi$
$941$	3.54329e7	1.30446	0.652232	+	0.758019i	$0.273833\pi$
$942$	−3.19385e7	−1.17270
$943$	2.44590e7	0.895693
$944$	1.25819e7	0.459532
$945$	1.52145e7	0.554215
$946$	3.17698e6	0.115421
$947$	7.75322e6	0.280936	0.140468	−	0.990085i	$-0.455139\pi$
$947$	7.75322e6	0.280936	0.140468	+	0.990085i	$0.455139\pi$
$948$	1.93728e7	0.700118
$949$	2.58395e7	0.931361
$950$	930000.	0.0334329
$951$	−6.36789e7	−2.28320
$952$	−790272.	−0.0282608
$953$	3.09769e7	1.10486	0.552429	−	0.833560i	$-0.313701\pi$
$953$	3.09769e7	1.10486	0.552429	+	0.833560i	$0.313701\pi$
$954$	3.94358e7	1.40288
$955$	6.21160e6	0.220392
$956$	−7.14931e6	−0.252999
$957$	−1.18556e7	−0.418449
$958$	2.60005e7	0.915310
$959$	−1.68371e7	−0.591181
$960$	−3.07200e6	−0.107583
$961$	−2.53603e7	−0.885820
$962$	2.51654e6	0.0876732
$963$	−1.24630e8	−4.33070
$964$	−3.99914e6	−0.138603
$965$	1.08110e6	0.0373721
$966$	1.36063e7	0.469135
$967$	−7.32493e6	−0.251905	−0.125953	−	0.992036i	$-0.540199\pi$
$967$	−7.32493e6	−0.251905	−0.125953	+	0.992036i	$0.540199\pi$
$968$	−937024.	−0.0321412
$969$	−2.81232e6	−0.0962178
$970$	−1.35260e6	−0.0461573
$971$	−2.00669e7	−0.683018	−0.341509	−	0.939878i	$-0.610938\pi$
$971$	−2.00669e7	−0.683018	−0.341509	+	0.939878i	$0.610938\pi$
$972$	−5.39266e7	−1.83078
$973$	−1.02169e7	−0.345969
$974$	2.93251e7	0.990472
$975$	−7.65000e6	−0.257721
$976$	1.45050e6	0.0487407
$977$	8.51401e6	0.285363	0.142681	−	0.989769i	$-0.454428\pi$
$977$	8.51401e6	0.285363	0.142681	+	0.989769i	$0.454428\pi$
$978$	−7.54346e7	−2.52188
$979$	1.03854e7	0.346312
$980$	960400.	0.0319438
$981$	3.41732e7	1.13374
$982$	1.93396e7	0.639985
$983$	−4.16577e6	−0.137503	−0.0687515	−	0.997634i	$-0.521902\pi$
$983$	−4.16577e6	−0.137503	−0.0687515	+	0.997634i	$0.521902\pi$
$984$	−2.02944e7	−0.668172
$985$	−1.85515e7	−0.609240
$986$	3.29213e6	0.107841
$987$	2.53134e6	0.0827099
$988$	−2.42842e6	−0.0791463
$989$	1.51891e7	0.493789
$990$	−7.94970e6	−0.257788
$991$	−3.21760e7	−1.04075	−0.520376	−	0.853937i	$-0.674208\pi$
$991$	−3.21760e7	−1.04075	−0.520376	+	0.853937i	$0.674208\pi$
$992$	1.85139e6	0.0597337
$993$	−6.81647e7	−2.19375
$994$	−315952.	−0.0101427
$995$	−3.27600e6	−0.104903
$996$	−3.07066e7	−0.980805
$997$	2.15411e7	0.686326	0.343163	−	0.939276i	$-0.388502\pi$
$997$	2.15411e7	0.686326	0.343163	+	0.939276i	$0.388502\pi$
$998$	4.64526e6	0.147633
$999$	1.91516e7	0.607145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.6.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.6.a.a.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	770.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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