LMFDB - Embedded newform 770.6.a.c.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:	$0$
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)

$f(q)$

$=$

$q-4.00000 q^{2} +14.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -56.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} -47.0000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} +14.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -56.0000 q^{6} -49.0000 q^{7} -64.0000 q^{8} -47.0000 q^{9} -100.000 q^{10} -121.000 q^{11} +224.000 q^{12} -362.000 q^{13} +196.000 q^{14} +350.000 q^{15} +256.000 q^{16} -142.000 q^{17} +188.000 q^{18} +2466.00 q^{19} +400.000 q^{20} -686.000 q^{21} +484.000 q^{22} -2182.00 q^{23} -896.000 q^{24} +625.000 q^{25} +1448.00 q^{26} -4060.00 q^{27} -784.000 q^{28} -1024.00 q^{29} -1400.00 q^{30} -4800.00 q^{31} -1024.00 q^{32} -1694.00 q^{33} +568.000 q^{34} -1225.00 q^{35} -752.000 q^{36} +8556.00 q^{37} -9864.00 q^{38} -5068.00 q^{39} -1600.00 q^{40} -5928.00 q^{41} +2744.00 q^{42} +14908.0 q^{43} -1936.00 q^{44} -1175.00 q^{45} +8728.00 q^{46} +25724.0 q^{47} +3584.00 q^{48} +2401.00 q^{49} -2500.00 q^{50} -1988.00 q^{51} -5792.00 q^{52} +2616.00 q^{53} +16240.0 q^{54} -3025.00 q^{55} +3136.00 q^{56} +34524.0 q^{57} +4096.00 q^{58} -4532.00 q^{59} +5600.00 q^{60} -5730.00 q^{61} +19200.0 q^{62} +2303.00 q^{63} +4096.00 q^{64} -9050.00 q^{65} +6776.00 q^{66} -3064.00 q^{67} -2272.00 q^{68} -30548.0 q^{69} +4900.00 q^{70} +42300.0 q^{71} +3008.00 q^{72} +62034.0 q^{73} -34224.0 q^{74} +8750.00 q^{75} +39456.0 q^{76} +5929.00 q^{77} +20272.0 q^{78} +27510.0 q^{79} +6400.00 q^{80} -45419.0 q^{81} +23712.0 q^{82} -46336.0 q^{83} -10976.0 q^{84} -3550.00 q^{85} -59632.0 q^{86} -14336.0 q^{87} +7744.00 q^{88} +118654. q^{89} +4700.00 q^{90} +17738.0 q^{91} -34912.0 q^{92} -67200.0 q^{93} -102896. q^{94} +61650.0 q^{95} -14336.0 q^{96} +104188. q^{97} -9604.00 q^{98} +5687.00 q^{99} +O(q^{100})\)

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
$3$	14.0000	0.898100	0.449050	−	0.893507i	$-0.351762\pi$
$3$	14.0000	0.898100	0.449050	+	0.893507i	$0.351762\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−56.0000	−0.635053
$7$	−49.0000	−0.377964
$7$	−49.0000	−0.377964
$8$	−64.0000	−0.353553
$9$	−47.0000	−0.193416
$10$	−100.000	−0.316228
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	224.000	0.449050
$13$	−362.000	−0.594087	−0.297044	−	0.954864i	$-0.596001\pi$
$13$	−362.000	−0.594087	−0.297044	+	0.954864i	$0.596001\pi$
$14$	196.000	0.267261
$15$	350.000	0.401643
$16$	256.000	0.250000
$17$	−142.000	−0.119170	−0.0595849	−	0.998223i	$-0.518978\pi$
$17$	−142.000	−0.119170	−0.0595849	+	0.998223i	$0.518978\pi$
$18$	188.000	0.136766
$19$	2466.00	1.56714	0.783572	−	0.621301i	$-0.213395\pi$
$19$	2466.00	1.56714	0.783572	+	0.621301i	$0.213395\pi$
$20$	400.000	0.223607
$21$	−686.000	−0.339450
$22$	484.000	0.213201
$23$	−2182.00	−0.860073	−0.430036	−	0.902812i	$-0.641499\pi$
$23$	−2182.00	−0.860073	−0.430036	+	0.902812i	$0.641499\pi$
$24$	−896.000	−0.317526
$25$	625.000	0.200000
$26$	1448.00	0.420083
$27$	−4060.00	−1.07181
$28$	−784.000	−0.188982
$29$	−1024.00	−0.226102	−0.113051	−	0.993589i	$-0.536062\pi$
$29$	−1024.00	−0.226102	−0.113051	+	0.993589i	$0.536062\pi$
$30$	−1400.00	−0.284004
$31$	−4800.00	−0.897092	−0.448546	−	0.893760i	$-0.648058\pi$
$31$	−4800.00	−0.897092	−0.448546	+	0.893760i	$0.648058\pi$
$32$	−1024.00	−0.176777
$33$	−1694.00	−0.270787
$34$	568.000	0.0842657
$35$	−1225.00	−0.169031
$36$	−752.000	−0.0967078
$37$	8556.00	1.02746	0.513732	−	0.857951i	$-0.328263\pi$
$37$	8556.00	1.02746	0.513732	+	0.857951i	$0.328263\pi$
$38$	−9864.00	−1.10814
$39$	−5068.00	−0.533550
$40$	−1600.00	−0.158114
$41$	−5928.00	−0.550742	−0.275371	−	0.961338i	$-0.588801\pi$
$41$	−5928.00	−0.550742	−0.275371	+	0.961338i	$0.588801\pi$
$42$	2744.00	0.240027
$43$	14908.0	1.22956	0.614778	−	0.788700i	$-0.289246\pi$
$43$	14908.0	1.22956	0.614778	+	0.788700i	$0.289246\pi$
$44$	−1936.00	−0.150756
$45$	−1175.00	−0.0864981
$46$	8728.00	0.608163
$47$	25724.0	1.69861	0.849305	−	0.527902i	$-0.177021\pi$
$47$	25724.0	1.69861	0.849305	+	0.527902i	$0.177021\pi$
$48$	3584.00	0.224525
$49$	2401.00	0.142857
$50$	−2500.00	−0.141421
$51$	−1988.00	−0.107026
$52$	−5792.00	−0.297044
$53$	2616.00	0.127923	0.0639614	−	0.997952i	$-0.479627\pi$
$53$	2616.00	0.127923	0.0639614	+	0.997952i	$0.479627\pi$
$54$	16240.0	0.757882
$55$	−3025.00	−0.134840
$56$	3136.00	0.133631
$57$	34524.0	1.40745
$58$	4096.00	0.159878
$59$	−4532.00	−0.169496	−0.0847481	−	0.996402i	$-0.527009\pi$
$59$	−4532.00	−0.169496	−0.0847481	+	0.996402i	$0.527009\pi$
$60$	5600.00	0.200821
$61$	−5730.00	−0.197165	−0.0985825	−	0.995129i	$-0.531431\pi$
$61$	−5730.00	−0.197165	−0.0985825	+	0.995129i	$0.531431\pi$
$62$	19200.0	0.634340
$63$	2303.00	0.0731042
$64$	4096.00	0.125000
$65$	−9050.00	−0.265684
$66$	6776.00	0.191476
$67$	−3064.00	−0.0833877	−0.0416938	−	0.999130i	$-0.513275\pi$
$67$	−3064.00	−0.0833877	−0.0416938	+	0.999130i	$0.513275\pi$
$68$	−2272.00	−0.0595849
$69$	−30548.0	−0.772432
$70$	4900.00	0.119523
$71$	42300.0	0.995851	0.497926	−	0.867220i	$-0.334095\pi$
$71$	42300.0	0.995851	0.497926	+	0.867220i	$0.334095\pi$
$72$	3008.00	0.0683828
$73$	62034.0	1.36246	0.681228	−	0.732071i	$-0.261446\pi$
$73$	62034.0	1.36246	0.681228	+	0.732071i	$0.261446\pi$
$74$	−34224.0	−0.726527
$75$	8750.00	0.179620
$76$	39456.0	0.783572
$77$	5929.00	0.113961
$78$	20272.0	0.377277
$79$	27510.0	0.495933	0.247966	−	0.968769i	$-0.420238\pi$
$79$	27510.0	0.495933	0.247966	+	0.968769i	$0.420238\pi$
$80$	6400.00	0.111803
$81$	−45419.0	−0.769175
$82$	23712.0	0.389434
$83$	−46336.0	−0.738284	−0.369142	−	0.929373i	$-0.620348\pi$
$83$	−46336.0	−0.738284	−0.369142	+	0.929373i	$0.620348\pi$
$84$	−10976.0	−0.169725
$85$	−3550.00	−0.0532943
$86$	−59632.0	−0.869427
$87$	−14336.0	−0.203063
$88$	7744.00	0.106600
$89$	118654.	1.58784	0.793921	−	0.608021i	$-0.208036\pi$
$89$	118654.	1.58784	0.793921	+	0.608021i	$0.208036\pi$
$90$	4700.00	0.0611634
$91$	17738.0	0.224544
$92$	−34912.0	−0.430036
$93$	−67200.0	−0.805679
$94$	−102896.	−1.20110
$95$	61650.0	0.700848
$96$	−14336.0	−0.158763
$97$	104188.	1.12432	0.562158	−	0.827030i	$-0.309971\pi$
$97$	104188.	1.12432	0.562158	+	0.827030i	$0.309971\pi$
$98$	−9604.00	−0.101015
$99$	5687.00	0.0583170
$100$	10000.0	0.100000
$101$	−33378.0	−0.325579	−0.162790	−	0.986661i	$-0.552049\pi$
$101$	−33378.0	−0.325579	−0.162790	+	0.986661i	$0.552049\pi$
$102$	7952.00	0.0756791
$103$	4096.00	0.0380423	0.0190212	−	0.999819i	$-0.493945\pi$
$103$	4096.00	0.0380423	0.0190212	+	0.999819i	$0.493945\pi$
$104$	23168.0	0.210042
$105$	−17150.0	−0.151807
$106$	−10464.0	−0.0904551
$107$	19700.0	0.166344	0.0831719	−	0.996535i	$-0.473495\pi$
$107$	19700.0	0.166344	0.0831719	+	0.996535i	$0.473495\pi$
$108$	−64960.0	−0.535904
$109$	209424.	1.68834	0.844171	−	0.536075i	$-0.180093\pi$
$109$	209424.	1.68834	0.844171	+	0.536075i	$0.180093\pi$
$110$	12100.0	0.0953463
$111$	119784.	0.922766
$112$	−12544.0	−0.0944911
$113$	−83726.0	−0.616828	−0.308414	−	0.951252i	$-0.599798\pi$
$113$	−83726.0	−0.616828	−0.308414	+	0.951252i	$0.599798\pi$
$114$	−138096.	−0.995220
$115$	−54550.0	−0.384636
$116$	−16384.0	−0.113051
$117$	17014.0	0.114906
$118$	18128.0	0.119852
$119$	6958.00	0.0450419
$120$	−22400.0	−0.142002
$121$	14641.0	0.0909091
$122$	22920.0	0.139417
$123$	−82992.0	−0.494622
$124$	−76800.0	−0.448546
$125$	15625.0	0.0894427
$126$	−9212.00	−0.0516925
$127$	37136.0	0.204308	0.102154	−	0.994769i	$-0.467427\pi$
$127$	37136.0	0.204308	0.102154	+	0.994769i	$0.467427\pi$
$128$	−16384.0	−0.0883883
$129$	208712.	1.10426
$130$	36200.0	0.187867
$131$	78118.0	0.397716	0.198858	−	0.980028i	$-0.436277\pi$
$131$	78118.0	0.397716	0.198858	+	0.980028i	$0.436277\pi$
$132$	−27104.0	−0.135394
$133$	−120834.	−0.592325
$134$	12256.0	0.0589640
$135$	−101500.	−0.479327
$136$	9088.00	0.0421329
$137$	−219982.	−1.00135	−0.500675	−	0.865635i	$-0.666915\pi$
$137$	−219982.	−1.00135	−0.500675	+	0.865635i	$0.666915\pi$
$138$	122192.	0.546192
$139$	−328226.	−1.44091	−0.720454	−	0.693503i	$-0.756066\pi$
$139$	−328226.	−1.44091	−0.720454	+	0.693503i	$0.756066\pi$
$140$	−19600.0	−0.0845154
$141$	360136.	1.52552
$142$	−169200.	−0.704173
$143$	43802.0	0.179124
$144$	−12032.0	−0.0483539
$145$	−25600.0	−0.101116
$146$	−248136.	−0.963402
$147$	33614.0	0.128300
$148$	136896.	0.513732
$149$	245656.	0.906487	0.453244	−	0.891387i	$-0.350267\pi$
$149$	245656.	0.906487	0.453244	+	0.891387i	$0.350267\pi$
$150$	−35000.0	−0.127011
$151$	−313330.	−1.11830	−0.559152	−	0.829065i	$-0.688873\pi$
$151$	−313330.	−1.11830	−0.559152	+	0.829065i	$0.688873\pi$
$152$	−157824.	−0.554069
$153$	6674.00	0.0230493
$154$	−23716.0	−0.0805823
$155$	−120000.	−0.401192
$156$	−81088.0	−0.266775
$157$	−288198.	−0.933129	−0.466565	−	0.884487i	$-0.654509\pi$
$157$	−288198.	−0.933129	−0.466565	+	0.884487i	$0.654509\pi$
$158$	−110040.	−0.350677
$159$	36624.0	0.114888
$160$	−25600.0	−0.0790569
$161$	106918.	0.325077
$162$	181676.	0.543889
$163$	137352.	0.404917	0.202458	−	0.979291i	$-0.435107\pi$
$163$	137352.	0.404917	0.202458	+	0.979291i	$0.435107\pi$
$164$	−94848.0	−0.275371
$165$	−42350.0	−0.121100
$166$	185344.	0.522045
$167$	227400.	0.630956	0.315478	−	0.948933i	$-0.397835\pi$
$167$	227400.	0.630956	0.315478	+	0.948933i	$0.397835\pi$
$168$	43904.0	0.120014
$169$	−240249.	−0.647060
$170$	14200.0	0.0376848
$171$	−115902.	−0.303110
$172$	238528.	0.614778
$173$	58386.0	0.148318	0.0741589	−	0.997246i	$-0.476373\pi$
$173$	58386.0	0.148318	0.0741589	+	0.997246i	$0.476373\pi$
$174$	57344.0	0.143587
$175$	−30625.0	−0.0755929
$176$	−30976.0	−0.0753778
$177$	−63448.0	−0.152225
$178$	−474616.	−1.12277
$179$	93164.0	0.217328	0.108664	−	0.994079i	$-0.465343\pi$
$179$	93164.0	0.217328	0.108664	+	0.994079i	$0.465343\pi$
$180$	−18800.0	−0.0432491
$181$	610390.	1.38488	0.692438	−	0.721477i	$-0.256537\pi$
$181$	610390.	1.38488	0.692438	+	0.721477i	$0.256537\pi$
$182$	−70952.0	−0.158776
$183$	−80220.0	−0.177074
$184$	139648.	0.304082
$185$	213900.	0.459496
$186$	268800.	0.569701
$187$	17182.0	0.0359310
$188$	411584.	0.849305
$189$	198940.	0.405105
$190$	−246600.	−0.495575
$191$	−47304.0	−0.0938241	−0.0469121	−	0.998899i	$-0.514938\pi$
$191$	−47304.0	−0.0938241	−0.0469121	+	0.998899i	$0.514938\pi$
$192$	57344.0	0.112263
$193$	307442.	0.594114	0.297057	−	0.954860i	$-0.403995\pi$
$193$	307442.	0.594114	0.297057	+	0.954860i	$0.403995\pi$
$194$	−416752.	−0.795011
$195$	−126700.	−0.238611
$196$	38416.0	0.0714286
$197$	286902.	0.526706	0.263353	−	0.964700i	$-0.415172\pi$
$197$	286902.	0.526706	0.263353	+	0.964700i	$0.415172\pi$
$198$	−22748.0	−0.0412364
$199$	−598496.	−1.07134	−0.535672	−	0.844426i	$-0.679941\pi$
$199$	−598496.	−1.07134	−0.535672	+	0.844426i	$0.679941\pi$
$200$	−40000.0	−0.0707107
$201$	−42896.0	−0.0748905
$202$	133512.	0.230219
$203$	50176.0	0.0854586
$204$	−31808.0	−0.0535132
$205$	−148200.	−0.246300
$206$	−16384.0	−0.0269000
$207$	102554.	0.166352
$208$	−92672.0	−0.148522
$209$	−298386.	−0.472512
$210$	68600.0	0.107344
$211$	704620.	1.08955	0.544777	−	0.838581i	$-0.316614\pi$
$211$	704620.	1.08955	0.544777	+	0.838581i	$0.316614\pi$
$212$	41856.0	0.0639614
$213$	592200.	0.894374
$214$	−78800.0	−0.117623
$215$	372700.	0.549874
$216$	259840.	0.378941
$217$	235200.	0.339069
$218$	−837696.	−1.19384
$219$	868476.	1.22362
$220$	−48400.0	−0.0674200
$221$	51404.0	0.0707972
$222$	−479136.	−0.652494
$223$	442696.	0.596133	0.298067	−	0.954545i	$-0.403658\pi$
$223$	442696.	0.596133	0.298067	+	0.954545i	$0.403658\pi$
$224$	50176.0	0.0668153
$225$	−29375.0	−0.0386831
$226$	334904.	0.436163
$227$	1.35744e6	1.74847	0.874233	−	0.485506i	$-0.161365\pi$
$227$	1.35744e6	1.74847	0.874233	+	0.485506i	$0.161365\pi$
$228$	552384.	0.703727
$229$	−725142.	−0.913765	−0.456882	−	0.889527i	$-0.651034\pi$
$229$	−725142.	−0.913765	−0.456882	+	0.889527i	$0.651034\pi$
$230$	218200.	0.271979
$231$	83006.0	0.102348
$232$	65536.0	0.0799392
$233$	281206.	0.339340	0.169670	−	0.985501i	$-0.445730\pi$
$233$	281206.	0.339340	0.169670	+	0.985501i	$0.445730\pi$
$234$	−68056.0	−0.0812506
$235$	643100.	0.759642
$236$	−72512.0	−0.0847481
$237$	385140.	0.445397
$238$	−27832.0	−0.0318495
$239$	871474.	0.986869	0.493435	−	0.869783i	$-0.335741\pi$
$239$	871474.	0.986869	0.493435	+	0.869783i	$0.335741\pi$
$240$	89600.0	0.100411
$241$	1.00702e6	1.11686	0.558428	−	0.829553i	$-0.311405\pi$
$241$	1.00702e6	1.11686	0.558428	+	0.829553i	$0.311405\pi$
$242$	−58564.0	−0.0642824
$243$	350714.	0.381011
$244$	−91680.0	−0.0985825
$245$	60025.0	0.0638877
$246$	331968.	0.349751
$247$	−892692.	−0.931021
$248$	307200.	0.317170
$249$	−648704.	−0.663053
$250$	−62500.0	−0.0632456
$251$	−167260.	−0.167574	−0.0837872	−	0.996484i	$-0.526702\pi$
$251$	−167260.	−0.167574	−0.0837872	+	0.996484i	$0.526702\pi$
$252$	36848.0	0.0365521
$253$	264022.	0.259322
$254$	−148544.	−0.144468
$255$	−49700.0	−0.0478637
$256$	65536.0	0.0625000
$257$	−1.24902e6	−1.17960	−0.589802	−	0.807548i	$-0.700794\pi$
$257$	−1.24902e6	−1.17960	−0.589802	+	0.807548i	$0.700794\pi$
$258$	−834848.	−0.780833
$259$	−419244.	−0.388345
$260$	−144800.	−0.132842
$261$	48128.0	0.0437317
$262$	−312472.	−0.281228
$263$	−402248.	−0.358595	−0.179298	−	0.983795i	$-0.557383\pi$
$263$	−402248.	−0.358595	−0.179298	+	0.983795i	$0.557383\pi$
$264$	108416.	0.0957378
$265$	65400.0	0.0572088
$266$	483336.	0.418837
$267$	1.66116e6	1.42604
$268$	−49024.0	−0.0416938
$269$	−474174.	−0.399537	−0.199769	−	0.979843i	$-0.564019\pi$
$269$	−474174.	−0.399537	−0.199769	+	0.979843i	$0.564019\pi$
$270$	406000.	0.338935
$271$	2.04520e6	1.69166	0.845831	−	0.533452i	$-0.179105\pi$
$271$	2.04520e6	1.69166	0.845831	+	0.533452i	$0.179105\pi$
$272$	−36352.0	−0.0297924
$273$	248332.	0.201663
$274$	879928.	0.708061
$275$	−75625.0	−0.0603023
$276$	−488768.	−0.386216
$277$	1.67595e6	1.31238	0.656192	−	0.754594i	$-0.272166\pi$
$277$	1.67595e6	1.31238	0.656192	+	0.754594i	$0.272166\pi$
$278$	1.31290e6	1.01888
$279$	225600.	0.173512
$280$	78400.0	0.0597614
$281$	239118.	0.180654	0.0903268	−	0.995912i	$-0.471209\pi$
$281$	239118.	0.180654	0.0903268	+	0.995912i	$0.471209\pi$
$282$	−1.44054e6	−1.07871
$283$	907724.	0.673733	0.336866	−	0.941552i	$-0.390633\pi$
$283$	907724.	0.673733	0.336866	+	0.941552i	$0.390633\pi$
$284$	676800.	0.497926
$285$	863100.	0.629432
$286$	−175208.	−0.126660
$287$	290472.	0.208161
$288$	48128.0	0.0341914
$289$	−1.39969e6	−0.985799
$290$	102400.	0.0714998
$291$	1.45863e6	1.00975
$292$	992544.	0.681228
$293$	1.84061e6	1.25255	0.626273	−	0.779604i	$-0.284580\pi$
$293$	1.84061e6	1.25255	0.626273	+	0.779604i	$0.284580\pi$
$294$	−134456.	−0.0907218
$295$	−113300.	−0.0758010
$296$	−547584.	−0.363263
$297$	491260.	0.323162
$298$	−982624.	−0.640983
$299$	789884.	0.510958
$300$	140000.	0.0898100
$301$	−730492.	−0.464728
$302$	1.25332e6	0.790760
$303$	−467292.	−0.292403
$304$	631296.	0.391786
$305$	−143250.	−0.0881749
$306$	−26696.0	−0.0162983
$307$	1.42773e6	0.864569	0.432284	−	0.901737i	$-0.357708\pi$
$307$	1.42773e6	0.864569	0.432284	+	0.901737i	$0.357708\pi$
$308$	94864.0	0.0569803
$309$	57344.0	0.0341658
$310$	480000.	0.283685
$311$	3.30332e6	1.93664	0.968322	−	0.249706i	$-0.0803339\pi$
$311$	3.30332e6	1.93664	0.968322	+	0.249706i	$0.0803339\pi$
$312$	324352.	0.188638
$313$	−1.81492e6	−1.04712	−0.523559	−	0.851989i	$-0.675396\pi$
$313$	−1.81492e6	−1.04712	−0.523559	+	0.851989i	$0.675396\pi$
$314$	1.15279e6	0.659822
$315$	57575.0	0.0326932
$316$	440160.	0.247966
$317$	−450468.	−0.251777	−0.125888	−	0.992044i	$-0.540178\pi$
$317$	−450468.	−0.251777	−0.125888	+	0.992044i	$0.540178\pi$
$318$	−146496.	−0.0812378
$319$	123904.	0.0681724
$320$	102400.	0.0559017
$321$	275800.	0.149393
$322$	−427672.	−0.229864
$323$	−350172.	−0.186756
$324$	−726704.	−0.384587
$325$	−226250.	−0.118817
$326$	−549408.	−0.286320
$327$	2.93194e6	1.51630
$328$	379392.	0.194717
$329$	−1.26048e6	−0.642014
$330$	169400.	0.0856305
$331$	−2.45107e6	−1.22966	−0.614830	−	0.788659i	$-0.710776\pi$
$331$	−2.45107e6	−1.22966	−0.614830	+	0.788659i	$0.710776\pi$
$332$	−741376.	−0.369142
$333$	−402132.	−0.198728
$334$	−909600.	−0.446153
$335$	−76600.0	−0.0372921
$336$	−175616.	−0.0848625
$337$	−320690.	−0.153819	−0.0769096	−	0.997038i	$-0.524505\pi$
$337$	−320690.	−0.153819	−0.0769096	+	0.997038i	$0.524505\pi$
$338$	960996.	0.457541
$339$	−1.17216e6	−0.553974
$340$	−56800.0	−0.0266472
$341$	580800.	0.270483
$342$	463608.	0.214331
$343$	−117649.	−0.0539949
$344$	−954112.	−0.434714
$345$	−763700.	−0.345442
$346$	−233544.	−0.104877
$347$	−403364.	−0.179835	−0.0899173	−	0.995949i	$-0.528660\pi$
$347$	−403364.	−0.179835	−0.0899173	+	0.995949i	$0.528660\pi$
$348$	−229376.	−0.101531
$349$	−2.14797e6	−0.943986	−0.471993	−	0.881602i	$-0.656465\pi$
$349$	−2.14797e6	−0.943986	−0.471993	+	0.881602i	$0.656465\pi$
$350$	122500.	0.0534522
$351$	1.46972e6	0.636747
$352$	123904.	0.0533002
$353$	1.11092e6	0.474509	0.237255	−	0.971448i	$-0.423752\pi$
$353$	1.11092e6	0.474509	0.237255	+	0.971448i	$0.423752\pi$
$354$	253792.	0.107639
$355$	1.05750e6	0.445358
$356$	1.89846e6	0.793921
$357$	97412.0	0.0404522
$358$	−372656.	−0.153674
$359$	−2.07637e6	−0.850293	−0.425147	−	0.905125i	$-0.639777\pi$
$359$	−2.07637e6	−0.850293	−0.425147	+	0.905125i	$0.639777\pi$
$360$	75200.0	0.0305817
$361$	3.60506e6	1.45594
$362$	−2.44156e6	−0.979255
$363$	204974.	0.0816455
$364$	283808.	0.112272
$365$	1.55085e6	0.609309
$366$	320880.	0.125210
$367$	−2.78956e6	−1.08111	−0.540556	−	0.841308i	$-0.681786\pi$
$367$	−2.78956e6	−1.08111	−0.540556	+	0.841308i	$0.681786\pi$
$368$	−558592.	−0.215018
$369$	278616.	0.106522
$370$	−855600.	−0.324913
$371$	−128184.	−0.0483503
$372$	−1.07520e6	−0.402839
$373$	4.14552e6	1.54279	0.771395	−	0.636357i	$-0.219559\pi$
$373$	4.14552e6	1.54279	0.771395	+	0.636357i	$0.219559\pi$
$374$	−68728.0	−0.0254071
$375$	218750.	0.0803285
$376$	−1.64634e6	−0.600550
$377$	370688.	0.134324
$378$	−795760.	−0.286452
$379$	−1.78203e6	−0.637260	−0.318630	−	0.947879i	$-0.603223\pi$
$379$	−1.78203e6	−0.637260	−0.318630	+	0.947879i	$0.603223\pi$
$380$	986400.	0.350424
$381$	519904.	0.183489
$382$	189216.	0.0663437
$383$	2.04140e6	0.711101	0.355550	−	0.934657i	$-0.384293\pi$
$383$	2.04140e6	0.711101	0.355550	+	0.934657i	$0.384293\pi$
$384$	−229376.	−0.0793816
$385$	148225.	0.0509647
$386$	−1.22977e6	−0.420102
$387$	−700676.	−0.237815
$388$	1.66701e6	0.562158
$389$	4.46482e6	1.49599	0.747997	−	0.663702i	$-0.231016\pi$
$389$	4.46482e6	1.49599	0.747997	+	0.663702i	$0.231016\pi$
$390$	506800.	0.168723
$391$	309844.	0.102495
$392$	−153664.	−0.0505076
$393$	1.09365e6	0.357189
$394$	−1.14761e6	−0.372437
$395$	687750.	0.221788
$396$	90992.0	0.0291585
$397$	−1.14113e6	−0.363377	−0.181688	−	0.983356i	$-0.558156\pi$
$397$	−1.14113e6	−0.363377	−0.181688	+	0.983356i	$0.558156\pi$
$398$	2.39398e6	0.757554
$399$	−1.69168e6	−0.531967
$400$	160000.	0.0500000
$401$	457934.	0.142214	0.0711069	−	0.997469i	$-0.477347\pi$
$401$	457934.	0.142214	0.0711069	+	0.997469i	$0.477347\pi$
$402$	171584.	0.0529556
$403$	1.73760e6	0.532951
$404$	−534048.	−0.162790
$405$	−1.13548e6	−0.343985
$406$	−200704.	−0.0604284
$407$	−1.03528e6	−0.309792
$408$	127232.	0.0378395
$409$	3.87794e6	1.14629	0.573143	−	0.819455i	$-0.305724\pi$
$409$	3.87794e6	1.14629	0.573143	+	0.819455i	$0.305724\pi$
$410$	592800.	0.174160
$411$	−3.07975e6	−0.899312
$412$	65536.0	0.0190212
$413$	222068.	0.0640635
$414$	−410216.	−0.117628
$415$	−1.15840e6	−0.330171
$416$	370688.	0.105021
$417$	−4.59516e6	−1.29408
$418$	1.19354e6	0.334116
$419$	−3.33907e6	−0.929159	−0.464580	−	0.885531i	$-0.653795\pi$
$419$	−3.33907e6	−0.929159	−0.464580	+	0.885531i	$0.653795\pi$
$420$	−274400.	−0.0759033
$421$	3.85844e6	1.06098	0.530489	−	0.847692i	$-0.322008\pi$
$421$	3.85844e6	1.06098	0.530489	+	0.847692i	$0.322008\pi$
$422$	−2.81848e6	−0.770431
$423$	−1.20903e6	−0.328538
$424$	−167424.	−0.0452276
$425$	−88750.0	−0.0238340
$426$	−2.36880e6	−0.632418
$427$	280770.	0.0745214
$428$	315200.	0.0831719
$429$	613228.	0.160871
$430$	−1.49080e6	−0.388820
$431$	−361378.	−0.0937062	−0.0468531	−	0.998902i	$-0.514919\pi$
$431$	−361378.	−0.0937062	−0.0468531	+	0.998902i	$0.514919\pi$
$432$	−1.03936e6	−0.267952
$433$	3.48831e6	0.894120	0.447060	−	0.894504i	$-0.352471\pi$
$433$	3.48831e6	0.894120	0.447060	+	0.894504i	$0.352471\pi$
$434$	−940800.	−0.239758
$435$	−358400.	−0.0908123
$436$	3.35078e6	0.844171
$437$	−5.38081e6	−1.34786
$438$	−3.47390e6	−0.865232
$439$	6.01440e6	1.48947	0.744734	−	0.667361i	$-0.232576\pi$
$439$	6.01440e6	1.48947	0.744734	+	0.667361i	$0.232576\pi$
$440$	193600.	0.0476731
$441$	−112847.	−0.0276308
$442$	−205616.	−0.0500612
$443$	−6.05014e6	−1.46472	−0.732362	−	0.680915i	$-0.761582\pi$
$443$	−6.05014e6	−1.46472	−0.732362	+	0.680915i	$0.761582\pi$
$444$	1.91654e6	0.461383
$445$	2.96635e6	0.710105
$446$	−1.77078e6	−0.421530
$447$	3.43918e6	0.814117
$448$	−200704.	−0.0472456
$449$	−3.41295e6	−0.798939	−0.399469	−	0.916747i	$-0.630806\pi$
$449$	−3.41295e6	−0.798939	−0.399469	+	0.916747i	$0.630806\pi$
$450$	117500.	0.0273531
$451$	717288.	0.166055
$452$	−1.33962e6	−0.308414
$453$	−4.38662e6	−1.00435
$454$	−5.42978e6	−1.23635
$455$	443450.	0.100419
$456$	−2.20954e6	−0.497610
$457$	4.81633e6	1.07876	0.539381	−	0.842062i	$-0.318658\pi$
$457$	4.81633e6	1.07876	0.539381	+	0.842062i	$0.318658\pi$
$458$	2.90057e6	0.646129
$459$	576520.	0.127727
$460$	−872800.	−0.192318
$461$	1.76277e6	0.386317	0.193158	−	0.981168i	$-0.438127\pi$
$461$	1.76277e6	0.386317	0.193158	+	0.981168i	$0.438127\pi$
$462$	−332024.	−0.0723710
$463$	3.74639e6	0.812195	0.406097	−	0.913830i	$-0.366889\pi$
$463$	3.74639e6	0.812195	0.406097	+	0.913830i	$0.366889\pi$
$464$	−262144.	−0.0565256
$465$	−1.68000e6	−0.360310
$466$	−1.12482e6	−0.239949
$467$	1.32735e6	0.281640	0.140820	−	0.990035i	$-0.455026\pi$
$467$	1.32735e6	0.281640	0.140820	+	0.990035i	$0.455026\pi$
$468$	272224.	0.0574529
$469$	150136.	0.0315176
$470$	−2.57240e6	−0.537148
$471$	−4.03477e6	−0.838044
$472$	290048.	0.0599259
$473$	−1.80387e6	−0.370725
$474$	−1.54056e6	−0.314944
$475$	1.54125e6	0.313429
$476$	111328.	0.0225210
$477$	−122952.	−0.0247423
$478$	−3.48590e6	−0.697822
$479$	−7.57681e6	−1.50885	−0.754427	−	0.656383i	$-0.772085\pi$
$479$	−7.57681e6	−1.50885	−0.754427	+	0.656383i	$0.772085\pi$
$480$	−358400.	−0.0710011
$481$	−3.09727e6	−0.610403
$482$	−4.02810e6	−0.789737
$483$	1.49685e6	0.291952
$484$	234256.	0.0454545
$485$	2.60470e6	0.502809
$486$	−1.40286e6	−0.269415
$487$	1.32211e6	0.252608	0.126304	−	0.991992i	$-0.459689\pi$
$487$	1.32211e6	0.252608	0.126304	+	0.991992i	$0.459689\pi$
$488$	366720.	0.0697084
$489$	1.92293e6	0.363656
$490$	−240100.	−0.0451754
$491$	−9.74663e6	−1.82453	−0.912264	−	0.409602i	$-0.865668\pi$
$491$	−9.74663e6	−1.82453	−0.912264	+	0.409602i	$0.865668\pi$
$492$	−1.32787e6	−0.247311
$493$	145408.	0.0269446
$494$	3.57077e6	0.658331
$495$	142175.	0.0260802
$496$	−1.22880e6	−0.224273
$497$	−2.07270e6	−0.376396
$498$	2.59482e6	0.468849
$499$	−3.43656e6	−0.617834	−0.308917	−	0.951089i	$-0.599967\pi$
$499$	−3.43656e6	−0.617834	−0.308917	+	0.951089i	$0.599967\pi$
$500$	250000.	0.0447214
$501$	3.18360e6	0.566662
$502$	669040.	0.118493
$503$	462416.	0.0814916	0.0407458	−	0.999170i	$-0.487027\pi$
$503$	462416.	0.0814916	0.0407458	+	0.999170i	$0.487027\pi$
$504$	−147392.	−0.0258463
$505$	−834450.	−0.145604
$506$	−1.05609e6	−0.183368
$507$	−3.36349e6	−0.581125
$508$	594176.	0.102154
$509$	−6.50143e6	−1.11228	−0.556141	−	0.831088i	$-0.687718\pi$
$509$	−6.50143e6	−1.11228	−0.556141	+	0.831088i	$0.687718\pi$
$510$	198800.	0.0338447
$511$	−3.03967e6	−0.514960
$512$	−262144.	−0.0441942
$513$	−1.00120e7	−1.67968
$514$	4.99608e6	0.834107
$515$	102400.	0.0170130
$516$	3.33939e6	0.552132
$517$	−3.11260e6	−0.512150
$518$	1.67698e6	0.274601
$519$	817404.	0.133204
$520$	579200.	0.0939334
$521$	5.45480e6	0.880409	0.440204	−	0.897898i	$-0.354906\pi$
$521$	5.45480e6	0.880409	0.440204	+	0.897898i	$0.354906\pi$
$522$	−192512.	−0.0309230
$523$	−3.69741e6	−0.591076	−0.295538	−	0.955331i	$-0.595499\pi$
$523$	−3.69741e6	−0.591076	−0.295538	+	0.955331i	$0.595499\pi$
$524$	1.24989e6	0.198858
$525$	−428750.	−0.0678900
$526$	1.60899e6	0.253565
$527$	681600.	0.106906
$528$	−433664.	−0.0676969
$529$	−1.67522e6	−0.260275
$530$	−261600.	−0.0404528
$531$	213004.	0.0327832
$532$	−1.93334e6	−0.296162
$533$	2.14594e6	0.327189
$534$	−6.64462e6	−1.00836
$535$	492500.	0.0743912
$536$	196096.	0.0294820
$537$	1.30430e6	0.195182
$538$	1.89670e6	0.282515
$539$	−290521.	−0.0430730
$540$	−1.62400e6	−0.239663
$541$	−584548.	−0.0858671	−0.0429336	−	0.999078i	$-0.513670\pi$
$541$	−584548.	−0.0858671	−0.0429336	+	0.999078i	$0.513670\pi$
$542$	−8.18082e6	−1.19619
$543$	8.54546e6	1.24376
$544$	145408.	0.0210664
$545$	5.23560e6	0.755049
$546$	−993328.	−0.142597
$547$	1.02792e6	0.146890	0.0734451	−	0.997299i	$-0.476601\pi$
$547$	1.02792e6	0.146890	0.0734451	+	0.997299i	$0.476601\pi$
$548$	−3.51971e6	−0.500675
$549$	269310.	0.0381348
$550$	302500.	0.0426401
$551$	−2.52518e6	−0.354335
$552$	1.95507e6	0.273096
$553$	−1.34799e6	−0.187445
$554$	−6.70378e6	−0.927995
$555$	2.99460e6	0.412673
$556$	−5.25162e6	−0.720454
$557$	−5.88350e6	−0.803522	−0.401761	−	0.915745i	$-0.631602\pi$
$557$	−5.88350e6	−0.803522	−0.401761	+	0.915745i	$0.631602\pi$
$558$	−902400.	−0.122691
$559$	−5.39670e6	−0.730463
$560$	−313600.	−0.0422577
$561$	240548.	0.0322697
$562$	−956472.	−0.127741
$563$	4.26246e6	0.566747	0.283374	−	0.959010i	$-0.408546\pi$
$563$	4.26246e6	0.566747	0.283374	+	0.959010i	$0.408546\pi$
$564$	5.76218e6	0.762761
$565$	−2.09315e6	−0.275854
$566$	−3.63090e6	−0.476401
$567$	2.22553e6	0.290721
$568$	−2.70720e6	−0.352087
$569$	−1.29766e7	−1.68027	−0.840135	−	0.542377i	$-0.817524\pi$
$569$	−1.29766e7	−1.68027	−0.840135	+	0.542377i	$0.817524\pi$
$570$	−3.45240e6	−0.445076
$571$	−440576.	−0.0565497	−0.0282749	−	0.999600i	$-0.509001\pi$
$571$	−440576.	−0.0565497	−0.0282749	+	0.999600i	$0.509001\pi$
$572$	700832.	0.0895620
$573$	−662256.	−0.0842635
$574$	−1.16189e6	−0.147192
$575$	−1.36375e6	−0.172015
$576$	−192512.	−0.0241770
$577$	4.19229e6	0.524218	0.262109	−	0.965038i	$-0.415582\pi$
$577$	4.19229e6	0.524218	0.262109	+	0.965038i	$0.415582\pi$
$578$	5.59877e6	0.697065
$579$	4.30419e6	0.533574
$580$	−409600.	−0.0505580
$581$	2.27046e6	0.279045
$582$	−5.83453e6	−0.714000
$583$	−316536.	−0.0385702
$584$	−3.97018e6	−0.481701
$585$	425350.	0.0513874
$586$	−7.36246e6	−0.885684
$587$	−5.90140e6	−0.706903	−0.353451	−	0.935453i	$-0.614992\pi$
$587$	−5.90140e6	−0.706903	−0.353451	+	0.935453i	$0.614992\pi$
$588$	537824.	0.0641500
$589$	−1.18368e7	−1.40587
$590$	453200.	0.0535994
$591$	4.01663e6	0.473035
$592$	2.19034e6	0.256866
$593$	5.56896e6	0.650336	0.325168	−	0.945656i	$-0.394579\pi$
$593$	5.56896e6	0.650336	0.325168	+	0.945656i	$0.394579\pi$
$594$	−1.96504e6	−0.228510
$595$	173950.	0.0201434
$596$	3.93050e6	0.453244
$597$	−8.37894e6	−0.962174
$598$	−3.15954e6	−0.361302
$599$	−4.58235e6	−0.521820	−0.260910	−	0.965363i	$-0.584023\pi$
$599$	−4.58235e6	−0.521820	−0.260910	+	0.965363i	$0.584023\pi$
$600$	−560000.	−0.0635053
$601$	5.62707e6	0.635471	0.317736	−	0.948179i	$-0.397078\pi$
$601$	5.62707e6	0.635471	0.317736	+	0.948179i	$0.397078\pi$
$602$	2.92197e6	0.328613
$603$	144008.	0.0161285
$604$	−5.01328e6	−0.559152
$605$	366025.	0.0406558
$606$	1.86917e6	0.206760
$607$	−2.68046e6	−0.295283	−0.147641	−	0.989041i	$-0.547168\pi$
$607$	−2.68046e6	−0.295283	−0.147641	+	0.989041i	$0.547168\pi$
$608$	−2.52518e6	−0.277035
$609$	702464.	0.0767504
$610$	573000.	0.0623491
$611$	−9.31209e6	−1.00912
$612$	106784.	0.0115246
$613$	1.42075e7	1.52710	0.763548	−	0.645751i	$-0.223456\pi$
$613$	1.42075e7	1.52710	0.763548	+	0.645751i	$0.223456\pi$
$614$	−5.71091e6	−0.611342
$615$	−2.07480e6	−0.221202
$616$	−379456.	−0.0402911
$617$	1.05318e6	0.111376	0.0556879	−	0.998448i	$-0.482265\pi$
$617$	1.05318e6	0.111376	0.0556879	+	0.998448i	$0.482265\pi$
$618$	−229376.	−0.0241589
$619$	−6.30748e6	−0.661651	−0.330826	−	0.943692i	$-0.607327\pi$
$619$	−6.30748e6	−0.661651	−0.330826	+	0.943692i	$0.607327\pi$
$620$	−1.92000e6	−0.200596
$621$	8.85892e6	0.921832
$622$	−1.32133e7	−1.36941
$623$	−5.81405e6	−0.600148
$624$	−1.29741e6	−0.133387
$625$	390625.	0.0400000
$626$	7.25966e6	0.740424
$627$	−4.17740e6	−0.424363
$628$	−4.61117e6	−0.466565
$629$	−1.21495e6	−0.122443
$630$	−230300.	−0.0231176
$631$	−1.35177e7	−1.35154	−0.675772	−	0.737111i	$-0.736190\pi$
$631$	−1.35177e7	−1.35154	−0.675772	+	0.737111i	$0.736190\pi$
$632$	−1.76064e6	−0.175339
$633$	9.86468e6	0.978529
$634$	1.80187e6	0.178033
$635$	928400.	0.0913694
$636$	585984.	0.0574438
$637$	−869162.	−0.0848696
$638$	−495616.	−0.0482052
$639$	−1.98810e6	−0.192613
$640$	−409600.	−0.0395285
$641$	−1.50685e7	−1.44852	−0.724261	−	0.689526i	$-0.757819\pi$
$641$	−1.50685e7	−1.44852	−0.724261	+	0.689526i	$0.757819\pi$
$642$	−1.10320e6	−0.105637
$643$	−1.50920e6	−0.143953	−0.0719764	−	0.997406i	$-0.522931\pi$
$643$	−1.50920e6	−0.143953	−0.0719764	+	0.997406i	$0.522931\pi$
$644$	1.71069e6	0.162538
$645$	5.21780e6	0.493842
$646$	1.40069e6	0.132057
$647$	1.23759e6	0.116230	0.0581148	−	0.998310i	$-0.481491\pi$
$647$	1.23759e6	0.116230	0.0581148	+	0.998310i	$0.481491\pi$
$648$	2.90682e6	0.271944
$649$	548372.	0.0511050
$650$	905000.	0.0840166
$651$	3.29280e6	0.304518
$652$	2.19763e6	0.202458
$653$	4.43599e6	0.407106	0.203553	−	0.979064i	$-0.434751\pi$
$653$	4.43599e6	0.407106	0.203553	+	0.979064i	$0.434751\pi$
$654$	−1.17277e7	−1.07219
$655$	1.95295e6	0.177864
$656$	−1.51757e6	−0.137686
$657$	−2.91560e6	−0.263520
$658$	5.04190e6	0.453973
$659$	2.20136e6	0.197459	0.0987296	−	0.995114i	$-0.468522\pi$
$659$	2.20136e6	0.197459	0.0987296	+	0.995114i	$0.468522\pi$
$660$	−677600.	−0.0605499
$661$	6.43879e6	0.573193	0.286596	−	0.958051i	$-0.407476\pi$
$661$	6.43879e6	0.573193	0.286596	+	0.958051i	$0.407476\pi$
$662$	9.80427e6	0.869502
$663$	719656.	0.0635830
$664$	2.96550e6	0.261023
$665$	−3.02085e6	−0.264896
$666$	1.60853e6	0.140522
$667$	2.23437e6	0.194464
$668$	3.63840e6	0.315478
$669$	6.19774e6	0.535388
$670$	306400.	0.0263695
$671$	693330.	0.0594475
$672$	702464.	0.0600069
$673$	−1.15085e7	−0.979451	−0.489725	−	0.871877i	$-0.662903\pi$
$673$	−1.15085e7	−0.979451	−0.489725	+	0.871877i	$0.662903\pi$
$674$	1.28276e6	0.108767
$675$	−2.53750e6	−0.214361
$676$	−3.84398e6	−0.323530
$677$	4.23537e6	0.355156	0.177578	−	0.984107i	$-0.443174\pi$
$677$	4.23537e6	0.355156	0.177578	+	0.984107i	$0.443174\pi$
$678$	4.68866e6	0.391719
$679$	−5.10521e6	−0.424951
$680$	227200.	0.0188424
$681$	1.90042e7	1.57030
$682$	−2.32320e6	−0.191261
$683$	1.40042e7	1.14870	0.574349	−	0.818610i	$-0.305255\pi$
$683$	1.40042e7	1.14870	0.574349	+	0.818610i	$0.305255\pi$
$684$	−1.85443e6	−0.151555
$685$	−5.49955e6	−0.447817
$686$	470596.	0.0381802
$687$	−1.01520e7	−0.820652
$688$	3.81645e6	0.307389
$689$	−946992.	−0.0759973
$690$	3.05480e6	0.244264
$691$	7.02922e6	0.560031	0.280016	−	0.959995i	$-0.409660\pi$
$691$	7.02922e6	0.560031	0.280016	+	0.959995i	$0.409660\pi$
$692$	934176.	0.0741589
$693$	−278663.	−0.0220418
$694$	1.61346e6	0.127162
$695$	−8.20565e6	−0.644393
$696$	917504.	0.0717935
$697$	841776.	0.0656318
$698$	8.59190e6	0.667499
$699$	3.93688e6	0.304761
$700$	−490000.	−0.0377964
$701$	−1.12546e7	−0.865039	−0.432519	−	0.901625i	$-0.642375\pi$
$701$	−1.12546e7	−0.865039	−0.432519	+	0.901625i	$0.642375\pi$
$702$	−5.87888e6	−0.450248
$703$	2.10991e7	1.61018
$704$	−495616.	−0.0376889
$705$	9.00340e6	0.682235
$706$	−4.44366e6	−0.335529
$707$	1.63552e6	0.123057
$708$	−1.01517e6	−0.0761123
$709$	−8.20381e6	−0.612914	−0.306457	−	0.951884i	$-0.599144\pi$
$709$	−8.20381e6	−0.612914	−0.306457	+	0.951884i	$0.599144\pi$
$710$	−4.23000e6	−0.314916
$711$	−1.29297e6	−0.0959212
$712$	−7.59386e6	−0.561387
$713$	1.04736e7	0.771564
$714$	−389648.	−0.0286040
$715$	1.09505e6	0.0801067
$716$	1.49062e6	0.108664
$717$	1.22006e7	0.886308
$718$	8.30548e6	0.601248
$719$	6.40477e6	0.462042	0.231021	−	0.972949i	$-0.425793\pi$
$719$	6.40477e6	0.462042	0.231021	+	0.972949i	$0.425793\pi$
$720$	−300800.	−0.0216245
$721$	−200704.	−0.0143786
$722$	−1.44202e7	−1.02951
$723$	1.40983e7	1.00305
$724$	9.76624e6	0.692438
$725$	−640000.	−0.0452205
$726$	−819896.	−0.0577321
$727$	8.55986e6	0.600663	0.300331	−	0.953835i	$-0.402903\pi$
$727$	8.55986e6	0.600663	0.300331	+	0.953835i	$0.402903\pi$
$728$	−1.13523e6	−0.0793882
$729$	1.59468e7	1.11136
$730$	−6.20340e6	−0.430847
$731$	−2.11694e6	−0.146526
$732$	−1.28352e6	−0.0885370
$733$	2.13193e7	1.46559	0.732797	−	0.680448i	$-0.238215\pi$
$733$	2.13193e7	1.46559	0.732797	+	0.680448i	$0.238215\pi$
$734$	1.11582e7	0.764461
$735$	840350.	0.0573775
$736$	2.23437e6	0.152041
$737$	370744.	0.0251423
$738$	−1.11446e6	−0.0753226
$739$	3.61217e6	0.243309	0.121654	−	0.992573i	$-0.461180\pi$
$739$	3.61217e6	0.243309	0.121654	+	0.992573i	$0.461180\pi$
$740$	3.42240e6	0.229748
$741$	−1.24977e7	−0.836150
$742$	512736.	0.0341888
$743$	2.23599e7	1.48593	0.742963	−	0.669333i	$-0.233420\pi$
$743$	2.23599e7	1.48593	0.742963	+	0.669333i	$0.233420\pi$
$744$	4.30080e6	0.284850
$745$	6.14140e6	0.405393
$746$	−1.65821e7	−1.09092
$747$	2.17779e6	0.142796
$748$	274912.	0.0179655
$749$	−965300.	−0.0628721
$750$	−875000.	−0.0568009
$751$	8.98941e6	0.581609	0.290805	−	0.956782i	$-0.406077\pi$
$751$	8.98941e6	0.581609	0.290805	+	0.956782i	$0.406077\pi$
$752$	6.58534e6	0.424653
$753$	−2.34164e6	−0.150499
$754$	−1.48275e6	−0.0949817
$755$	−7.83325e6	−0.500120
$756$	3.18304e6	0.202552
$757$	−2.73403e7	−1.73406	−0.867029	−	0.498258i	$-0.833973\pi$
$757$	−2.73403e7	−1.73406	−0.867029	+	0.498258i	$0.833973\pi$
$758$	7.12811e6	0.450611
$759$	3.69631e6	0.232897
$760$	−3.94560e6	−0.247787
$761$	−9.26592e6	−0.579999	−0.289999	−	0.957027i	$-0.593655\pi$
$761$	−9.26592e6	−0.579999	−0.289999	+	0.957027i	$0.593655\pi$
$762$	−2.07962e6	−0.129747
$763$	−1.02618e7	−0.638133
$764$	−756864.	−0.0469121
$765$	166850.	0.0103080
$766$	−8.16560e6	−0.502824
$767$	1.64058e6	0.100695
$768$	917504.	0.0561313
$769$	−1.19487e7	−0.728626	−0.364313	−	0.931277i	$-0.618696\pi$
$769$	−1.19487e7	−0.728626	−0.364313	+	0.931277i	$0.618696\pi$
$770$	−592900.	−0.0360375
$771$	−1.74863e7	−1.05940
$772$	4.91907e6	0.297057
$773$	1.15709e7	0.696495	0.348248	−	0.937403i	$-0.386777\pi$
$773$	1.15709e7	0.696495	0.348248	+	0.937403i	$0.386777\pi$
$774$	2.80270e6	0.168161
$775$	−3.00000e6	−0.179418
$776$	−6.66803e6	−0.397506
$777$	−5.86942e6	−0.348773
$778$	−1.78593e7	−1.05783
$779$	−1.46184e7	−0.863093
$780$	−2.02720e6	−0.119305
$781$	−5.11830e6	−0.300260
$782$	−1.23938e6	−0.0724747
$783$	4.15744e6	0.242338
$784$	614656.	0.0357143
$785$	−7.20495e6	−0.417308
$786$	−4.37461e6	−0.252571
$787$	2.44124e7	1.40499	0.702497	−	0.711687i	$-0.252068\pi$
$787$	2.44124e7	1.40499	0.702497	+	0.711687i	$0.252068\pi$
$788$	4.59043e6	0.263353
$789$	−5.63147e6	−0.322055
$790$	−2.75100e6	−0.156828
$791$	4.10257e6	0.233139
$792$	−363968.	−0.0206182
$793$	2.07426e6	0.117133
$794$	4.56450e6	0.256946
$795$	915600.	0.0513793
$796$	−9.57594e6	−0.535672
$797$	2.45124e7	1.36691	0.683456	−	0.729992i	$-0.260476\pi$
$797$	2.45124e7	1.36691	0.683456	+	0.729992i	$0.260476\pi$
$798$	6.76670e6	0.376158
$799$	−3.65281e6	−0.202423
$800$	−640000.	−0.0353553
$801$	−5.57674e6	−0.307114
$802$	−1.83174e6	−0.100560
$803$	−7.50611e6	−0.410796
$804$	−686336.	−0.0374452
$805$	2.67295e6	0.145379
$806$	−6.95040e6	−0.376853
$807$	−6.63844e6	−0.358824
$808$	2.13619e6	0.115110
$809$	−720906.	−0.0387264	−0.0193632	−	0.999813i	$-0.506164\pi$
$809$	−720906.	−0.0387264	−0.0193632	+	0.999813i	$0.506164\pi$
$810$	4.54190e6	0.243234
$811$	3.44309e7	1.83822	0.919108	−	0.394005i	$-0.128911\pi$
$811$	3.44309e7	1.83822	0.919108	+	0.394005i	$0.128911\pi$
$812$	802816.	0.0427293
$813$	2.86329e7	1.51928
$814$	4.14110e6	0.219056
$815$	3.43380e6	0.181084
$816$	−508928.	−0.0267566
$817$	3.67631e7	1.92689
$818$	−1.55118e7	−0.810547
$819$	−833686.	−0.0434303
$820$	−2.37120e6	−0.123150
$821$	−2.61540e7	−1.35419	−0.677097	−	0.735894i	$-0.736762\pi$
$821$	−2.61540e7	−1.35419	−0.677097	+	0.735894i	$0.736762\pi$
$822$	1.23190e7	0.635910
$823$	−9.94226e6	−0.511665	−0.255832	−	0.966721i	$-0.582350\pi$
$823$	−9.94226e6	−0.511665	−0.255832	+	0.966721i	$0.582350\pi$
$824$	−262144.	−0.0134500
$825$	−1.05875e6	−0.0541575
$826$	−888272.	−0.0452998
$827$	2.71170e7	1.37873	0.689363	−	0.724416i	$-0.257890\pi$
$827$	2.71170e7	1.37873	0.689363	+	0.724416i	$0.257890\pi$
$828$	1.64086e6	0.0831758
$829$	1.98027e7	1.00078	0.500390	−	0.865800i	$-0.333190\pi$
$829$	1.98027e7	1.00078	0.500390	+	0.865800i	$0.333190\pi$
$830$	4.63360e6	0.233466
$831$	2.34632e7	1.17865
$832$	−1.48275e6	−0.0742609
$833$	−340942.	−0.0170243
$834$	1.83807e7	0.915052
$835$	5.68500e6	0.282172
$836$	−4.77418e6	−0.236256
$837$	1.94880e7	0.961510
$838$	1.33563e7	0.657015
$839$	−3.13891e7	−1.53948	−0.769739	−	0.638359i	$-0.779614\pi$
$839$	−3.13891e7	−1.53948	−0.769739	+	0.638359i	$0.779614\pi$
$840$	1.09760e6	0.0536718
$841$	−1.94626e7	−0.948878
$842$	−1.54338e7	−0.750225
$843$	3.34765e6	0.162245
$844$	1.12739e7	0.544777
$845$	−6.00622e6	−0.289374
$846$	4.83611e6	0.232311
$847$	−717409.	−0.0343604
$848$	669696.	0.0319807
$849$	1.27081e7	0.605080
$850$	355000.	0.0168531
$851$	−1.86692e7	−0.883693
$852$	9.47520e6	0.447187
$853$	−3.56154e7	−1.67597	−0.837983	−	0.545697i	$-0.816265\pi$
$853$	−3.56154e7	−1.67597	−0.837983	+	0.545697i	$0.816265\pi$
$854$	−1.12308e6	−0.0526946
$855$	−2.89755e6	−0.135555
$856$	−1.26080e6	−0.0588114
$857$	−1.98405e7	−0.922787	−0.461394	−	0.887196i	$-0.652650\pi$
$857$	−1.98405e7	−0.922787	−0.461394	+	0.887196i	$0.652650\pi$
$858$	−2.45291e6	−0.113753
$859$	4.29726e7	1.98705	0.993525	−	0.113616i	$-0.0362434\pi$
$859$	4.29726e7	1.98705	0.993525	+	0.113616i	$0.0362434\pi$
$860$	5.96320e6	0.274937
$861$	4.06661e6	0.186950
$862$	1.44551e6	0.0662603
$863$	−4.04186e7	−1.84737	−0.923686	−	0.383151i	$-0.874839\pi$
$863$	−4.04186e7	−1.84737	−0.923686	+	0.383151i	$0.874839\pi$
$864$	4.15744e6	0.189471
$865$	1.45965e6	0.0663298
$866$	−1.39532e7	−0.632238
$867$	−1.95957e7	−0.885346
$868$	3.76320e6	0.169534
$869$	−3.32871e6	−0.149529
$870$	1.43360e6	0.0642140
$871$	1.10917e6	0.0495395
$872$	−1.34031e7	−0.596919
$873$	−4.89684e6	−0.217460
$874$	2.15232e7	0.953080
$875$	−765625.	−0.0338062
$876$	1.38956e7	0.611811
$877$	−2.06571e7	−0.906924	−0.453462	−	0.891276i	$-0.649811\pi$
$877$	−2.06571e7	−0.906924	−0.453462	+	0.891276i	$0.649811\pi$
$878$	−2.40576e7	−1.05321
$879$	2.57686e7	1.12491
$880$	−774400.	−0.0337100
$881$	2.78230e7	1.20771	0.603857	−	0.797093i	$-0.293630\pi$
$881$	2.78230e7	1.20771	0.603857	+	0.797093i	$0.293630\pi$
$882$	451388.	0.0195379
$883$	1.10636e7	0.477523	0.238761	−	0.971078i	$-0.423259\pi$
$883$	1.10636e7	0.477523	0.238761	+	0.971078i	$0.423259\pi$
$884$	822464.	0.0353986
$885$	−1.58620e6	−0.0680769
$886$	2.42005e7	1.03572
$887$	−1.51778e7	−0.647738	−0.323869	−	0.946102i	$-0.604984\pi$
$887$	−1.51778e7	−0.647738	−0.323869	+	0.946102i	$0.604984\pi$
$888$	−7.66618e6	−0.326247
$889$	−1.81966e6	−0.0772212
$890$	−1.18654e7	−0.502120
$891$	5.49570e6	0.231915
$892$	7.08314e6	0.298067
$893$	6.34354e7	2.66197
$894$	−1.37567e7	−0.575667
$895$	2.32910e6	0.0971920
$896$	802816.	0.0334077
$897$	1.10584e7	0.458892
$898$	1.36518e7	0.564935
$899$	4.91520e6	0.202835
$900$	−470000.	−0.0193416
$901$	−371472.	−0.0152445
$902$	−2.86915e6	−0.117419
$903$	−1.02269e7	−0.417373
$904$	5.35846e6	0.218082
$905$	1.52598e7	0.619335
$906$	1.75465e7	0.710182
$907$	−1.31128e7	−0.529271	−0.264636	−	0.964349i	$-0.585252\pi$
$907$	−1.31128e7	−0.529271	−0.264636	+	0.964349i	$0.585252\pi$
$908$	2.17191e7	0.874233
$909$	1.56877e6	0.0629721
$910$	−1.77380e6	−0.0710070
$911$	−4.31290e7	−1.72176	−0.860882	−	0.508805i	$-0.830088\pi$
$911$	−4.31290e7	−1.72176	−0.860882	+	0.508805i	$0.830088\pi$
$912$	8.83814e6	0.351863
$913$	5.60666e6	0.222601
$914$	−1.92653e7	−0.762799
$915$	−2.00550e6	−0.0791899
$916$	−1.16023e7	−0.456882
$917$	−3.82778e6	−0.150322
$918$	−2.30608e6	−0.0903166
$919$	4.19933e6	0.164018	0.0820090	−	0.996632i	$-0.473866\pi$
$919$	4.19933e6	0.164018	0.0820090	+	0.996632i	$0.473866\pi$
$920$	3.49120e6	0.135989
$921$	1.99882e7	0.776470
$922$	−7.05108e6	−0.273167
$923$	−1.53126e7	−0.591623
$924$	1.32810e6	0.0511740
$925$	5.34750e6	0.205493
$926$	−1.49855e7	−0.574308
$927$	−192512.	−0.00735798
$928$	1.04858e6	0.0399696
$929$	−5.04998e7	−1.91977	−0.959887	−	0.280386i	$-0.909538\pi$
$929$	−5.04998e7	−1.91977	−0.959887	+	0.280386i	$0.909538\pi$
$930$	6.72000e6	0.254778
$931$	5.92087e6	0.223878
$932$	4.49930e6	0.169670
$933$	4.62465e7	1.73930
$934$	−5.30942e6	−0.199150
$935$	429550.	0.0160688
$936$	−1.08890e6	−0.0406253
$937$	−4.25211e6	−0.158218	−0.0791090	−	0.996866i	$-0.525208\pi$
$937$	−4.25211e6	−0.158218	−0.0791090	+	0.996866i	$0.525208\pi$
$938$	−600544.	−0.0222863
$939$	−2.54088e7	−0.940417
$940$	1.02896e7	0.379821
$941$	−4.20480e7	−1.54800	−0.774000	−	0.633186i	$-0.781747\pi$
$941$	−4.20480e7	−1.54800	−0.774000	+	0.633186i	$0.781747\pi$
$942$	1.61391e7	0.592586
$943$	1.29349e7	0.473679
$944$	−1.16019e6	−0.0423740
$945$	4.97350e6	0.181168
$946$	7.21547e6	0.262142
$947$	2.02326e7	0.733122	0.366561	−	0.930394i	$-0.380535\pi$
$947$	2.02326e7	0.733122	0.366561	+	0.930394i	$0.380535\pi$
$948$	6.16224e6	0.222699
$949$	−2.24563e7	−0.809418
$950$	−6.16500e6	−0.221628
$951$	−6.30655e6	−0.226121
$952$	−445312.	−0.0159247
$953$	−2.61419e7	−0.932404	−0.466202	−	0.884678i	$-0.654378\pi$
$953$	−2.61419e7	−0.932404	−0.466202	+	0.884678i	$0.654378\pi$
$954$	491808.	0.0174954
$955$	−1.18260e6	−0.0419594
$956$	1.39436e7	0.493435
$957$	1.73466e6	0.0612257
$958$	3.03072e7	1.06692
$959$	1.07791e7	0.378475
$960$	1.43360e6	0.0502053
$961$	−5.58915e6	−0.195226
$962$	1.23891e7	0.431620
$963$	−925900.	−0.0321735
$964$	1.61124e7	0.558428
$965$	7.68605e6	0.265696
$966$	−5.98741e6	−0.206441
$967$	−1.14106e7	−0.392413	−0.196207	−	0.980563i	$-0.562862\pi$
$967$	−1.14106e7	−0.392413	−0.196207	+	0.980563i	$0.562862\pi$
$968$	−937024.	−0.0321412
$969$	−4.90241e6	−0.167726
$970$	−1.04188e7	−0.355540
$971$	9.05291e6	0.308134	0.154067	−	0.988060i	$-0.450763\pi$
$971$	9.05291e6	0.308134	0.154067	+	0.988060i	$0.450763\pi$
$972$	5.61142e6	0.190505
$973$	1.60831e7	0.544612
$974$	−5.28846e6	−0.178621
$975$	−3.16750e6	−0.106710
$976$	−1.46688e6	−0.0492913
$977$	5.21061e7	1.74643	0.873217	−	0.487332i	$-0.162030\pi$
$977$	5.21061e7	1.74643	0.873217	+	0.487332i	$0.162030\pi$
$978$	−7.69171e6	−0.257144
$979$	−1.43571e7	−0.478752
$980$	960400.	0.0319438
$981$	−9.84293e6	−0.326552
$982$	3.89865e7	1.29014
$983$	−5.11635e7	−1.68879	−0.844396	−	0.535719i	$-0.820041\pi$
$983$	−5.11635e7	−1.68879	−0.844396	+	0.535719i	$0.820041\pi$
$984$	5.31149e6	0.174875
$985$	7.17255e6	0.235550
$986$	−581632.	−0.0190527
$987$	−1.76467e7	−0.576593
$988$	−1.42831e7	−0.465510
$989$	−3.25293e7	−1.05751
$990$	−568700.	−0.0184415
$991$	2.01442e7	0.651576	0.325788	−	0.945443i	$-0.394370\pi$
$991$	2.01442e7	0.651576	0.325788	+	0.945443i	$0.394370\pi$
$992$	4.91520e6	0.158585
$993$	−3.43150e7	−1.10436
$994$	8.29080e6	0.266152
$995$	−1.49624e7	−0.479119
$996$	−1.03793e7	−0.331526
$997$	−2.40284e7	−0.765575	−0.382787	−	0.923837i	$-0.625036\pi$
$997$	−2.40284e7	−0.765575	−0.382787	+	0.923837i	$0.625036\pi$
$998$	1.37462e7	0.436875
$999$	−3.47374e7	−1.10124

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.6.a.c.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

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