LMFDB - Embedded newform 1386.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,4,Mod(1,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1386.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1386.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:	$81.7766472680$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1386.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} +13.0000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} +13.0000 q^{5} -7.00000 q^{7} -8.00000 q^{8} -26.0000 q^{10} -11.0000 q^{11} -67.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -8.00000 q^{17} +21.0000 q^{19} +52.0000 q^{20} +22.0000 q^{22} +194.000 q^{23} +44.0000 q^{25} +134.000 q^{26} -28.0000 q^{28} +221.000 q^{29} +88.0000 q^{31} -32.0000 q^{32} +16.0000 q^{34} -91.0000 q^{35} -347.000 q^{37} -42.0000 q^{38} -104.000 q^{40} -292.000 q^{41} -458.000 q^{43} -44.0000 q^{44} -388.000 q^{46} -221.000 q^{47} +49.0000 q^{49} -88.0000 q^{50} -268.000 q^{52} +642.000 q^{53} -143.000 q^{55} +56.0000 q^{56} -442.000 q^{58} -273.000 q^{59} -530.000 q^{61} -176.000 q^{62} +64.0000 q^{64} -871.000 q^{65} +561.000 q^{67} -32.0000 q^{68} +182.000 q^{70} -604.000 q^{71} +703.000 q^{73} +694.000 q^{74} +84.0000 q^{76} +77.0000 q^{77} +552.000 q^{79} +208.000 q^{80} +584.000 q^{82} +144.000 q^{83} -104.000 q^{85} +916.000 q^{86} +88.0000 q^{88} -750.000 q^{89} +469.000 q^{91} +776.000 q^{92} +442.000 q^{94} +273.000 q^{95} -1370.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	13.0000	1.16276	0.581378	−	0.813634i	$-0.302514\pi$
$5$	13.0000	1.16276	0.581378	+	0.813634i	$0.302514\pi$
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	−26.0000	−0.822192
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	0	0
$13$	−67.0000	−1.42942	−0.714710	−	0.699421i	$-0.753441\pi$
$13$	−67.0000	−1.42942	−0.714710	+	0.699421i	$0.753441\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−8.00000	−0.114134	−0.0570672	−	0.998370i	$-0.518175\pi$
$17$	−8.00000	−0.114134	−0.0570672	+	0.998370i	$0.518175\pi$
$18$	0	0
$19$	21.0000	0.253565	0.126782	−	0.991931i	$-0.459535\pi$
$19$	21.0000	0.253565	0.126782	+	0.991931i	$0.459535\pi$
$20$	52.0000	0.581378
$21$	0	0
$22$	22.0000	0.213201
$23$	194.000	1.75877	0.879387	−	0.476108i	$-0.157953\pi$
$23$	194.000	1.75877	0.879387	+	0.476108i	$0.157953\pi$
$24$	0	0
$25$	44.0000	0.352000
$26$	134.000	1.01075
$27$	0	0
$28$	−28.0000	−0.188982
$29$	221.000	1.41513	0.707563	−	0.706650i	$-0.249794\pi$
$29$	221.000	1.41513	0.707563	+	0.706650i	$0.249794\pi$
$30$	0	0
$31$	88.0000	0.509847	0.254924	−	0.966961i	$-0.417950\pi$
$31$	88.0000	0.509847	0.254924	+	0.966961i	$0.417950\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	16.0000	0.0807052
$35$	−91.0000	−0.439480
$36$	0	0
$37$	−347.000	−1.54180	−0.770898	−	0.636959i	$-0.780192\pi$
$37$	−347.000	−1.54180	−0.770898	+	0.636959i	$0.780192\pi$
$38$	−42.0000	−0.179297
$39$	0	0
$40$	−104.000	−0.411096
$41$	−292.000	−1.11226	−0.556131	−	0.831095i	$-0.687715\pi$
$41$	−292.000	−1.11226	−0.556131	+	0.831095i	$0.687715\pi$
$42$	0	0
$43$	−458.000	−1.62429	−0.812144	−	0.583458i	$-0.801699\pi$
$43$	−458.000	−1.62429	−0.812144	+	0.583458i	$0.801699\pi$
$44$	−44.0000	−0.150756
$45$	0	0
$46$	−388.000	−1.24364
$47$	−221.000	−0.685876	−0.342938	−	0.939358i	$-0.611422\pi$
$47$	−221.000	−0.685876	−0.342938	+	0.939358i	$0.611422\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−88.0000	−0.248902
$51$	0	0
$52$	−268.000	−0.714710
$53$	642.000	1.66388	0.831939	−	0.554868i	$-0.187231\pi$
$53$	642.000	1.66388	0.831939	+	0.554868i	$0.187231\pi$
$54$	0	0
$55$	−143.000	−0.350584
$56$	56.0000	0.133631
$57$	0	0
$58$	−442.000	−1.00065
$59$	−273.000	−0.602400	−0.301200	−	0.953561i	$-0.597387\pi$
$59$	−273.000	−0.602400	−0.301200	+	0.953561i	$0.597387\pi$
$60$	0	0
$61$	−530.000	−1.11245	−0.556226	−	0.831031i	$-0.687751\pi$
$61$	−530.000	−1.11245	−0.556226	+	0.831031i	$0.687751\pi$
$62$	−176.000	−0.360516
$63$	0	0
$64$	64.0000	0.125000
$65$	−871.000	−1.66207
$66$	0	0
$67$	561.000	1.02294	0.511471	−	0.859301i	$-0.329101\pi$
$67$	561.000	1.02294	0.511471	+	0.859301i	$0.329101\pi$
$68$	−32.0000	−0.0570672
$69$	0	0
$70$	182.000	0.310759
$71$	−604.000	−1.00960	−0.504800	−	0.863236i	$-0.668434\pi$
$71$	−604.000	−1.00960	−0.504800	+	0.863236i	$0.668434\pi$
$72$	0	0
$73$	703.000	1.12712	0.563561	−	0.826074i	$-0.309431\pi$
$73$	703.000	1.12712	0.563561	+	0.826074i	$0.309431\pi$
$74$	694.000	1.09021
$75$	0	0
$76$	84.0000	0.126782
$77$	77.0000	0.113961
$78$	0	0
$79$	552.000	0.786137	0.393069	−	0.919509i	$-0.371413\pi$
$79$	552.000	0.786137	0.393069	+	0.919509i	$0.371413\pi$
$80$	208.000	0.290689
$81$	0	0
$82$	584.000	0.786488
$83$	144.000	0.190434	0.0952172	−	0.995457i	$-0.469645\pi$
$83$	144.000	0.190434	0.0952172	+	0.995457i	$0.469645\pi$
$84$	0	0
$85$	−104.000	−0.132710
$86$	916.000	1.14854
$87$	0	0
$88$	88.0000	0.106600
$89$	−750.000	−0.893257	−0.446628	−	0.894720i	$-0.647375\pi$
$89$	−750.000	−0.893257	−0.446628	+	0.894720i	$0.647375\pi$
$90$	0	0
$91$	469.000	0.540270
$92$	776.000	0.879387
$93$	0	0
$94$	442.000	0.484987
$95$	273.000	0.294834
$96$	0	0
$97$	−1370.00	−1.43405	−0.717023	−	0.697050i	$-0.754496\pi$
$97$	−1370.00	−1.43405	−0.717023	+	0.697050i	$0.754496\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	176.000	0.176000
$101$	−1980.00	−1.95067	−0.975333	−	0.220736i	$-0.929154\pi$
$101$	−1980.00	−1.95067	−0.975333	+	0.220736i	$0.929154\pi$
$102$	0	0
$103$	−666.000	−0.637116	−0.318558	−	0.947903i	$-0.603199\pi$
$103$	−666.000	−0.637116	−0.318558	+	0.947903i	$0.603199\pi$
$104$	536.000	0.505376
$105$	0	0
$106$	−1284.00	−1.17654
$107$	−1439.00	−1.30013	−0.650063	−	0.759881i	$-0.725257\pi$
$107$	−1439.00	−1.30013	−0.650063	+	0.759881i	$0.725257\pi$
$108$	0	0
$109$	−956.000	−0.840075	−0.420038	−	0.907507i	$-0.637983\pi$
$109$	−956.000	−0.840075	−0.420038	+	0.907507i	$0.637983\pi$
$110$	286.000	0.247900
$111$	0	0
$112$	−112.000	−0.0944911
$113$	2302.00	1.91641	0.958203	−	0.286088i	$-0.0923550\pi$
$113$	2302.00	1.91641	0.958203	+	0.286088i	$0.0923550\pi$
$114$	0	0
$115$	2522.00	2.04502
$116$	884.000	0.707563
$117$	0	0
$118$	546.000	0.425961
$119$	56.0000	0.0431388
$120$	0	0
$121$	121.000	0.0909091
$122$	1060.00	0.786622
$123$	0	0
$124$	352.000	0.254924
$125$	−1053.00	−0.753465
$126$	0	0
$127$	608.000	0.424813	0.212407	−	0.977181i	$-0.431870\pi$
$127$	608.000	0.424813	0.212407	+	0.977181i	$0.431870\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	1742.00	1.17526
$131$	192.000	0.128054	0.0640272	−	0.997948i	$-0.479606\pi$
$131$	192.000	0.128054	0.0640272	+	0.997948i	$0.479606\pi$
$132$	0	0
$133$	−147.000	−0.0958385
$134$	−1122.00	−0.723329
$135$	0	0
$136$	64.0000	0.0403526
$137$	1212.00	0.755826	0.377913	−	0.925841i	$-0.376642\pi$
$137$	1212.00	0.755826	0.377913	+	0.925841i	$0.376642\pi$
$138$	0	0
$139$	−1876.00	−1.14475	−0.572375	−	0.819992i	$-0.693978\pi$
$139$	−1876.00	−1.14475	−0.572375	+	0.819992i	$0.693978\pi$
$140$	−364.000	−0.219740
$141$	0	0
$142$	1208.00	0.713895
$143$	737.000	0.430986
$144$	0	0
$145$	2873.00	1.64545
$146$	−1406.00	−0.796996
$147$	0	0
$148$	−1388.00	−0.770898
$149$	265.000	0.145702	0.0728512	−	0.997343i	$-0.476790\pi$
$149$	265.000	0.145702	0.0728512	+	0.997343i	$0.476790\pi$
$150$	0	0
$151$	−1728.00	−0.931276	−0.465638	−	0.884975i	$-0.654175\pi$
$151$	−1728.00	−0.931276	−0.465638	+	0.884975i	$0.654175\pi$
$152$	−168.000	−0.0896487
$153$	0	0
$154$	−154.000	−0.0805823
$155$	1144.00	0.592828
$156$	0	0
$157$	−884.000	−0.449369	−0.224684	−	0.974432i	$-0.572135\pi$
$157$	−884.000	−0.449369	−0.224684	+	0.974432i	$0.572135\pi$
$158$	−1104.00	−0.555883
$159$	0	0
$160$	−416.000	−0.205548
$161$	−1358.00	−0.664754
$162$	0	0
$163$	673.000	0.323395	0.161698	−	0.986840i	$-0.448303\pi$
$163$	673.000	0.323395	0.161698	+	0.986840i	$0.448303\pi$
$164$	−1168.00	−0.556131
$165$	0	0
$166$	−288.000	−0.134657
$167$	−1846.00	−0.855376	−0.427688	−	0.903926i	$-0.640672\pi$
$167$	−1846.00	−0.855376	−0.427688	+	0.903926i	$0.640672\pi$
$168$	0	0
$169$	2292.00	1.04324
$170$	208.000	0.0938404
$171$	0	0
$172$	−1832.00	−0.812144
$173$	2816.00	1.23755	0.618776	−	0.785567i	$-0.287629\pi$
$173$	2816.00	1.23755	0.618776	+	0.785567i	$0.287629\pi$
$174$	0	0
$175$	−308.000	−0.133043
$176$	−176.000	−0.0753778
$177$	0	0
$178$	1500.00	0.631628
$179$	−2800.00	−1.16917	−0.584586	−	0.811332i	$-0.698743\pi$
$179$	−2800.00	−1.16917	−0.584586	+	0.811332i	$0.698743\pi$
$180$	0	0
$181$	2042.00	0.838567	0.419284	−	0.907855i	$-0.362281\pi$
$181$	2042.00	0.838567	0.419284	+	0.907855i	$0.362281\pi$
$182$	−938.000	−0.382028
$183$	0	0
$184$	−1552.00	−0.621820
$185$	−4511.00	−1.79273
$186$	0	0
$187$	88.0000	0.0344128
$188$	−884.000	−0.342938
$189$	0	0
$190$	−546.000	−0.208479
$191$	−3992.00	−1.51231	−0.756154	−	0.654393i	$-0.772924\pi$
$191$	−3992.00	−1.51231	−0.756154	+	0.654393i	$0.772924\pi$
$192$	0	0
$193$	1526.00	0.569139	0.284570	−	0.958655i	$-0.408149\pi$
$193$	1526.00	0.569139	0.284570	+	0.958655i	$0.408149\pi$
$194$	2740.00	1.01402
$195$	0	0
$196$	196.000	0.0714286
$197$	−354.000	−0.128028	−0.0640138	−	0.997949i	$-0.520390\pi$
$197$	−354.000	−0.128028	−0.0640138	+	0.997949i	$0.520390\pi$
$198$	0	0
$199$	1474.00	0.525071	0.262535	−	0.964922i	$-0.415441\pi$
$199$	1474.00	0.525071	0.262535	+	0.964922i	$0.415441\pi$
$200$	−352.000	−0.124451
$201$	0	0
$202$	3960.00	1.37933
$203$	−1547.00	−0.534868
$204$	0	0
$205$	−3796.00	−1.29329
$206$	1332.00	0.450509
$207$	0	0
$208$	−1072.00	−0.357355
$209$	−231.000	−0.0764527
$210$	0	0
$211$	−590.000	−0.192499	−0.0962495	−	0.995357i	$-0.530685\pi$
$211$	−590.000	−0.192499	−0.0962495	+	0.995357i	$0.530685\pi$
$212$	2568.00	0.831939
$213$	0	0
$214$	2878.00	0.919327
$215$	−5954.00	−1.88865
$216$	0	0
$217$	−616.000	−0.192704
$218$	1912.00	0.594023
$219$	0	0
$220$	−572.000	−0.175292
$221$	536.000	0.163146
$222$	0	0
$223$	−2714.00	−0.814991	−0.407495	−	0.913207i	$-0.633598\pi$
$223$	−2714.00	−0.814991	−0.407495	+	0.913207i	$0.633598\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	−4604.00	−1.35510
$227$	3326.00	0.972486	0.486243	−	0.873824i	$-0.338367\pi$
$227$	3326.00	0.972486	0.486243	+	0.873824i	$0.338367\pi$
$228$	0	0
$229$	−1294.00	−0.373406	−0.186703	−	0.982416i	$-0.559780\pi$
$229$	−1294.00	−0.373406	−0.186703	+	0.982416i	$0.559780\pi$
$230$	−5044.00	−1.44605
$231$	0	0
$232$	−1768.00	−0.500323
$233$	−3390.00	−0.953160	−0.476580	−	0.879131i	$-0.658124\pi$
$233$	−3390.00	−0.953160	−0.476580	+	0.879131i	$0.658124\pi$
$234$	0	0
$235$	−2873.00	−0.797506
$236$	−1092.00	−0.301200
$237$	0	0
$238$	−112.000	−0.0305037
$239$	−5209.00	−1.40980	−0.704900	−	0.709307i	$-0.749008\pi$
$239$	−5209.00	−1.40980	−0.704900	+	0.709307i	$0.749008\pi$
$240$	0	0
$241$	−2511.00	−0.671152	−0.335576	−	0.942013i	$-0.608931\pi$
$241$	−2511.00	−0.671152	−0.335576	+	0.942013i	$0.608931\pi$
$242$	−242.000	−0.0642824
$243$	0	0
$244$	−2120.00	−0.556226
$245$	637.000	0.166108
$246$	0	0
$247$	−1407.00	−0.362450
$248$	−704.000	−0.180258
$249$	0	0
$250$	2106.00	0.532781
$251$	−4215.00	−1.05995	−0.529977	−	0.848012i	$-0.677799\pi$
$251$	−4215.00	−1.05995	−0.529977	+	0.848012i	$0.677799\pi$
$252$	0	0
$253$	−2134.00	−0.530290
$254$	−1216.00	−0.300388
$255$	0	0
$256$	256.000	0.0625000
$257$	6945.00	1.68567	0.842835	−	0.538172i	$-0.180885\pi$
$257$	6945.00	1.68567	0.842835	+	0.538172i	$0.180885\pi$
$258$	0	0
$259$	2429.00	0.582744
$260$	−3484.00	−0.831033
$261$	0	0
$262$	−384.000	−0.0905481
$263$	57.0000	0.0133641	0.00668207	−	0.999978i	$-0.497873\pi$
$263$	57.0000	0.0133641	0.00668207	+	0.999978i	$0.497873\pi$
$264$	0	0
$265$	8346.00	1.93468
$266$	294.000	0.0677680
$267$	0	0
$268$	2244.00	0.511471
$269$	−2502.00	−0.567099	−0.283550	−	0.958958i	$-0.591512\pi$
$269$	−2502.00	−0.567099	−0.283550	+	0.958958i	$0.591512\pi$
$270$	0	0
$271$	565.000	0.126647	0.0633234	−	0.997993i	$-0.479830\pi$
$271$	565.000	0.126647	0.0633234	+	0.997993i	$0.479830\pi$
$272$	−128.000	−0.0285336
$273$	0	0
$274$	−2424.00	−0.534450
$275$	−484.000	−0.106132
$276$	0	0
$277$	−7164.00	−1.55395	−0.776973	−	0.629534i	$-0.783246\pi$
$277$	−7164.00	−1.55395	−0.776973	+	0.629534i	$0.783246\pi$
$278$	3752.00	0.809460
$279$	0	0
$280$	728.000	0.155380
$281$	6985.00	1.48288	0.741442	−	0.671017i	$-0.234142\pi$
$281$	6985.00	1.48288	0.741442	+	0.671017i	$0.234142\pi$
$282$	0	0
$283$	−6435.00	−1.35166	−0.675832	−	0.737055i	$-0.736216\pi$
$283$	−6435.00	−1.35166	−0.675832	+	0.737055i	$0.736216\pi$
$284$	−2416.00	−0.504800
$285$	0	0
$286$	−1474.00	−0.304753
$287$	2044.00	0.420395
$288$	0	0
$289$	−4849.00	−0.986973
$290$	−5746.00	−1.16351
$291$	0	0
$292$	2812.00	0.563561
$293$	−8400.00	−1.67486	−0.837429	−	0.546547i	$-0.815942\pi$
$293$	−8400.00	−1.67486	−0.837429	+	0.546547i	$0.815942\pi$
$294$	0	0
$295$	−3549.00	−0.700443
$296$	2776.00	0.545107
$297$	0	0
$298$	−530.000	−0.103027
$299$	−12998.0	−2.51403
$300$	0	0
$301$	3206.00	0.613923
$302$	3456.00	0.658511
$303$	0	0
$304$	336.000	0.0633912
$305$	−6890.00	−1.29351
$306$	0	0
$307$	−6364.00	−1.18310	−0.591552	−	0.806267i	$-0.701484\pi$
$307$	−6364.00	−1.18310	−0.591552	+	0.806267i	$0.701484\pi$
$308$	308.000	0.0569803
$309$	0	0
$310$	−2288.00	−0.419192
$311$	7456.00	1.35946	0.679728	−	0.733464i	$-0.262098\pi$
$311$	7456.00	1.35946	0.679728	+	0.733464i	$0.262098\pi$
$312$	0	0
$313$	10204.0	1.84270	0.921349	−	0.388738i	$-0.127089\pi$
$313$	10204.0	1.84270	0.921349	+	0.388738i	$0.127089\pi$
$314$	1768.00	0.317752
$315$	0	0
$316$	2208.00	0.393069
$317$	−9666.00	−1.71261	−0.856304	−	0.516472i	$-0.827245\pi$
$317$	−9666.00	−1.71261	−0.856304	+	0.516472i	$0.827245\pi$
$318$	0	0
$319$	−2431.00	−0.426677
$320$	832.000	0.145344
$321$	0	0
$322$	2716.00	0.470052
$323$	−168.000	−0.0289405
$324$	0	0
$325$	−2948.00	−0.503156
$326$	−1346.00	−0.228675
$327$	0	0
$328$	2336.00	0.393244
$329$	1547.00	0.259237
$330$	0	0
$331$	−11228.0	−1.86449	−0.932246	−	0.361826i	$-0.882154\pi$
$331$	−11228.0	−1.86449	−0.932246	+	0.361826i	$0.882154\pi$
$332$	576.000	0.0952172
$333$	0	0
$334$	3692.00	0.604842
$335$	7293.00	1.18943
$336$	0	0
$337$	2274.00	0.367575	0.183787	−	0.982966i	$-0.441164\pi$
$337$	2274.00	0.367575	0.183787	+	0.982966i	$0.441164\pi$
$338$	−4584.00	−0.737683
$339$	0	0
$340$	−416.000	−0.0663552
$341$	−968.000	−0.153725
$342$	0	0
$343$	−343.000	−0.0539949
$344$	3664.00	0.574272
$345$	0	0
$346$	−5632.00	−0.875081
$347$	2008.00	0.310649	0.155324	−	0.987864i	$-0.450358\pi$
$347$	2008.00	0.310649	0.155324	+	0.987864i	$0.450358\pi$
$348$	0	0
$349$	1721.00	0.263963	0.131981	−	0.991252i	$-0.457866\pi$
$349$	1721.00	0.263963	0.131981	+	0.991252i	$0.457866\pi$
$350$	616.000	0.0940760
$351$	0	0
$352$	352.000	0.0533002
$353$	2055.00	0.309849	0.154924	−	0.987926i	$-0.450487\pi$
$353$	2055.00	0.309849	0.154924	+	0.987926i	$0.450487\pi$
$354$	0	0
$355$	−7852.00	−1.17392
$356$	−3000.00	−0.446628
$357$	0	0
$358$	5600.00	0.826730
$359$	−1304.00	−0.191706	−0.0958530	−	0.995395i	$-0.530558\pi$
$359$	−1304.00	−0.191706	−0.0958530	+	0.995395i	$0.530558\pi$
$360$	0	0
$361$	−6418.00	−0.935705
$362$	−4084.00	−0.592957
$363$	0	0
$364$	1876.00	0.270135
$365$	9139.00	1.31057
$366$	0	0
$367$	−1754.00	−0.249477	−0.124738	−	0.992190i	$-0.539809\pi$
$367$	−1754.00	−0.249477	−0.124738	+	0.992190i	$0.539809\pi$
$368$	3104.00	0.439693
$369$	0	0
$370$	9022.00	1.26765
$371$	−4494.00	−0.628886
$372$	0	0
$373$	11348.0	1.57527	0.787637	−	0.616140i	$-0.211304\pi$
$373$	11348.0	1.57527	0.787637	+	0.616140i	$0.211304\pi$
$374$	−176.000	−0.0243335
$375$	0	0
$376$	1768.00	0.242494
$377$	−14807.0	−2.02281
$378$	0	0
$379$	−8945.00	−1.21233	−0.606166	−	0.795338i	$-0.707293\pi$
$379$	−8945.00	−1.21233	−0.606166	+	0.795338i	$0.707293\pi$
$380$	1092.00	0.147417
$381$	0	0
$382$	7984.00	1.06936
$383$	5560.00	0.741783	0.370891	−	0.928676i	$-0.379052\pi$
$383$	5560.00	0.741783	0.370891	+	0.928676i	$0.379052\pi$
$384$	0	0
$385$	1001.00	0.132508
$386$	−3052.00	−0.402442
$387$	0	0
$388$	−5480.00	−0.717023
$389$	12372.0	1.61256	0.806279	−	0.591535i	$-0.201478\pi$
$389$	12372.0	1.61256	0.806279	+	0.591535i	$0.201478\pi$
$390$	0	0
$391$	−1552.00	−0.200737
$392$	−392.000	−0.0505076
$393$	0	0
$394$	708.000	0.0905293
$395$	7176.00	0.914085
$396$	0	0
$397$	−3984.00	−0.503655	−0.251828	−	0.967772i	$-0.581032\pi$
$397$	−3984.00	−0.503655	−0.251828	+	0.967772i	$0.581032\pi$
$398$	−2948.00	−0.371281
$399$	0	0
$400$	704.000	0.0880000
$401$	414.000	0.0515565	0.0257783	−	0.999668i	$-0.491794\pi$
$401$	414.000	0.0515565	0.0257783	+	0.999668i	$0.491794\pi$
$402$	0	0
$403$	−5896.00	−0.728786
$404$	−7920.00	−0.975333
$405$	0	0
$406$	3094.00	0.378208
$407$	3817.00	0.464869
$408$	0	0
$409$	4534.00	0.548146	0.274073	−	0.961709i	$-0.411629\pi$
$409$	4534.00	0.548146	0.274073	+	0.961709i	$0.411629\pi$
$410$	7592.00	0.914493
$411$	0	0
$412$	−2664.00	−0.318558
$413$	1911.00	0.227686
$414$	0	0
$415$	1872.00	0.221429
$416$	2144.00	0.252688
$417$	0	0
$418$	462.000	0.0540602
$419$	5285.00	0.616203	0.308102	−	0.951353i	$-0.400306\pi$
$419$	5285.00	0.616203	0.308102	+	0.951353i	$0.400306\pi$
$420$	0	0
$421$	9019.00	1.04408	0.522042	−	0.852920i	$-0.325171\pi$
$421$	9019.00	1.04408	0.522042	+	0.852920i	$0.325171\pi$
$422$	1180.00	0.136117
$423$	0	0
$424$	−5136.00	−0.588269
$425$	−352.000	−0.0401753
$426$	0	0
$427$	3710.00	0.420467
$428$	−5756.00	−0.650063
$429$	0	0
$430$	11908.0	1.33548
$431$	−4447.00	−0.496994	−0.248497	−	0.968633i	$-0.579937\pi$
$431$	−4447.00	−0.496994	−0.248497	+	0.968633i	$0.579937\pi$
$432$	0	0
$433$	−3508.00	−0.389339	−0.194669	−	0.980869i	$-0.562363\pi$
$433$	−3508.00	−0.389339	−0.194669	+	0.980869i	$0.562363\pi$
$434$	1232.00	0.136262
$435$	0	0
$436$	−3824.00	−0.420038
$437$	4074.00	0.445963
$438$	0	0
$439$	−13187.0	−1.43367	−0.716835	−	0.697243i	$-0.754410\pi$
$439$	−13187.0	−1.43367	−0.716835	+	0.697243i	$0.754410\pi$
$440$	1144.00	0.123950
$441$	0	0
$442$	−1072.00	−0.115362
$443$	8016.00	0.859710	0.429855	−	0.902898i	$-0.358565\pi$
$443$	8016.00	0.859710	0.429855	+	0.902898i	$0.358565\pi$
$444$	0	0
$445$	−9750.00	−1.03864
$446$	5428.00	0.576285
$447$	0	0
$448$	−448.000	−0.0472456
$449$	5724.00	0.601631	0.300815	−	0.953682i	$-0.402741\pi$
$449$	5724.00	0.601631	0.300815	+	0.953682i	$0.402741\pi$
$450$	0	0
$451$	3212.00	0.335360
$452$	9208.00	0.958203
$453$	0	0
$454$	−6652.00	−0.687652
$455$	6097.00	0.628202
$456$	0	0
$457$	2306.00	0.236040	0.118020	−	0.993011i	$-0.462345\pi$
$457$	2306.00	0.236040	0.118020	+	0.993011i	$0.462345\pi$
$458$	2588.00	0.264038
$459$	0	0
$460$	10088.0	1.02251
$461$	16068.0	1.62334	0.811672	−	0.584114i	$-0.198558\pi$
$461$	16068.0	1.62334	0.811672	+	0.584114i	$0.198558\pi$
$462$	0	0
$463$	−16187.0	−1.62478	−0.812391	−	0.583114i	$-0.801834\pi$
$463$	−16187.0	−1.62478	−0.812391	+	0.583114i	$0.801834\pi$
$464$	3536.00	0.353782
$465$	0	0
$466$	6780.00	0.673986
$467$	13503.0	1.33800	0.668998	−	0.743264i	$-0.266723\pi$
$467$	13503.0	1.33800	0.668998	+	0.743264i	$0.266723\pi$
$468$	0	0
$469$	−3927.00	−0.386635
$470$	5746.00	0.563922
$471$	0	0
$472$	2184.00	0.212980
$473$	5038.00	0.489741
$474$	0	0
$475$	924.000	0.0892548
$476$	224.000	0.0215694
$477$	0	0
$478$	10418.0	0.996879
$479$	1588.00	0.151477	0.0757386	−	0.997128i	$-0.475869\pi$
$479$	1588.00	0.151477	0.0757386	+	0.997128i	$0.475869\pi$
$480$	0	0
$481$	23249.0	2.20387
$482$	5022.00	0.474576
$483$	0	0
$484$	484.000	0.0454545
$485$	−17810.0	−1.66744
$486$	0	0
$487$	−19096.0	−1.77684	−0.888421	−	0.459029i	$-0.848197\pi$
$487$	−19096.0	−1.77684	−0.888421	+	0.459029i	$0.848197\pi$
$488$	4240.00	0.393311
$489$	0	0
$490$	−1274.00	−0.117456
$491$	3705.00	0.340538	0.170269	−	0.985398i	$-0.445536\pi$
$491$	3705.00	0.340538	0.170269	+	0.985398i	$0.445536\pi$
$492$	0	0
$493$	−1768.00	−0.161515
$494$	2814.00	0.256291
$495$	0	0
$496$	1408.00	0.127462
$497$	4228.00	0.381593
$498$	0	0
$499$	−3673.00	−0.329511	−0.164756	−	0.986334i	$-0.552684\pi$
$499$	−3673.00	−0.329511	−0.164756	+	0.986334i	$0.552684\pi$
$500$	−4212.00	−0.376733
$501$	0	0
$502$	8430.00	0.749501
$503$	7326.00	0.649404	0.324702	−	0.945816i	$-0.394736\pi$
$503$	7326.00	0.649404	0.324702	+	0.945816i	$0.394736\pi$
$504$	0	0
$505$	−25740.0	−2.26815
$506$	4268.00	0.374972
$507$	0	0
$508$	2432.00	0.212407
$509$	−3470.00	−0.302171	−0.151086	−	0.988521i	$-0.548277\pi$
$509$	−3470.00	−0.302171	−0.151086	+	0.988521i	$0.548277\pi$
$510$	0	0
$511$	−4921.00	−0.426012
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−13890.0	−1.19195
$515$	−8658.00	−0.740810
$516$	0	0
$517$	2431.00	0.206799
$518$	−4858.00	−0.412062
$519$	0	0
$520$	6968.00	0.587629
$521$	−6379.00	−0.536409	−0.268204	−	0.963362i	$-0.586430\pi$
$521$	−6379.00	−0.536409	−0.268204	+	0.963362i	$0.586430\pi$
$522$	0	0
$523$	3671.00	0.306925	0.153462	−	0.988154i	$-0.450958\pi$
$523$	3671.00	0.306925	0.153462	+	0.988154i	$0.450958\pi$
$524$	768.000	0.0640272
$525$	0	0
$526$	−114.000	−0.00944988
$527$	−704.000	−0.0581911
$528$	0	0
$529$	25469.0	2.09329
$530$	−16692.0	−1.36803
$531$	0	0
$532$	−588.000	−0.0479192
$533$	19564.0	1.58989
$534$	0	0
$535$	−18707.0	−1.51173
$536$	−4488.00	−0.361664
$537$	0	0
$538$	5004.00	0.401000
$539$	−539.000	−0.0430730
$540$	0	0
$541$	9572.00	0.760688	0.380344	−	0.924845i	$-0.375806\pi$
$541$	9572.00	0.760688	0.380344	+	0.924845i	$0.375806\pi$
$542$	−1130.00	−0.0895529
$543$	0	0
$544$	256.000	0.0201763
$545$	−12428.0	−0.976802
$546$	0	0
$547$	8760.00	0.684736	0.342368	−	0.939566i	$-0.388771\pi$
$547$	8760.00	0.684736	0.342368	+	0.939566i	$0.388771\pi$
$548$	4848.00	0.377913
$549$	0	0
$550$	968.000	0.0750467
$551$	4641.00	0.358826
$552$	0	0
$553$	−3864.00	−0.297132
$554$	14328.0	1.09881
$555$	0	0
$556$	−7504.00	−0.572375
$557$	−23651.0	−1.79915	−0.899574	−	0.436769i	$-0.856123\pi$
$557$	−23651.0	−1.79915	−0.899574	+	0.436769i	$0.856123\pi$
$558$	0	0
$559$	30686.0	2.32179
$560$	−1456.00	−0.109870
$561$	0	0
$562$	−13970.0	−1.04856
$563$	−5198.00	−0.389111	−0.194556	−	0.980891i	$-0.562326\pi$
$563$	−5198.00	−0.389111	−0.194556	+	0.980891i	$0.562326\pi$
$564$	0	0
$565$	29926.0	2.22831
$566$	12870.0	0.955771
$567$	0	0
$568$	4832.00	0.356948
$569$	−18306.0	−1.34873	−0.674365	−	0.738398i	$-0.735583\pi$
$569$	−18306.0	−1.34873	−0.674365	+	0.738398i	$0.735583\pi$
$570$	0	0
$571$	−13676.0	−1.00232	−0.501158	−	0.865356i	$-0.667093\pi$
$571$	−13676.0	−1.00232	−0.501158	+	0.865356i	$0.667093\pi$
$572$	2948.00	0.215493
$573$	0	0
$574$	−4088.00	−0.297265
$575$	8536.00	0.619088
$576$	0	0
$577$	−6712.00	−0.484271	−0.242135	−	0.970242i	$-0.577848\pi$
$577$	−6712.00	−0.484271	−0.242135	+	0.970242i	$0.577848\pi$
$578$	9698.00	0.697896
$579$	0	0
$580$	11492.0	0.822723
$581$	−1008.00	−0.0719774
$582$	0	0
$583$	−7062.00	−0.501678
$584$	−5624.00	−0.398498
$585$	0	0
$586$	16800.0	1.18430
$587$	−24891.0	−1.75019	−0.875095	−	0.483951i	$-0.839201\pi$
$587$	−24891.0	−1.75019	−0.875095	+	0.483951i	$0.839201\pi$
$588$	0	0
$589$	1848.00	0.129279
$590$	7098.00	0.495288
$591$	0	0
$592$	−5552.00	−0.385449
$593$	−7896.00	−0.546796	−0.273398	−	0.961901i	$-0.588148\pi$
$593$	−7896.00	−0.546796	−0.273398	+	0.961901i	$0.588148\pi$
$594$	0	0
$595$	728.000	0.0501598
$596$	1060.00	0.0728512
$597$	0	0
$598$	25996.0	1.77768
$599$	4320.00	0.294675	0.147338	−	0.989086i	$-0.452930\pi$
$599$	4320.00	0.294675	0.147338	+	0.989086i	$0.452930\pi$
$600$	0	0
$601$	−9457.00	−0.641862	−0.320931	−	0.947103i	$-0.603996\pi$
$601$	−9457.00	−0.641862	−0.320931	+	0.947103i	$0.603996\pi$
$602$	−6412.00	−0.434109
$603$	0	0
$604$	−6912.00	−0.465638
$605$	1573.00	0.105705
$606$	0	0
$607$	28961.0	1.93656	0.968279	−	0.249871i	$-0.0803884\pi$
$607$	28961.0	1.93656	0.968279	+	0.249871i	$0.0803884\pi$
$608$	−672.000	−0.0448243
$609$	0	0
$610$	13780.0	0.914649
$611$	14807.0	0.980404
$612$	0	0
$613$	244.000	0.0160768	0.00803839	−	0.999968i	$-0.497441\pi$
$613$	244.000	0.0160768	0.00803839	+	0.999968i	$0.497441\pi$
$614$	12728.0	0.836580
$615$	0	0
$616$	−616.000	−0.0402911
$617$	19062.0	1.24377	0.621886	−	0.783108i	$-0.286367\pi$
$617$	19062.0	1.24377	0.621886	+	0.783108i	$0.286367\pi$
$618$	0	0
$619$	−18148.0	−1.17840	−0.589200	−	0.807987i	$-0.700557\pi$
$619$	−18148.0	−1.17840	−0.589200	+	0.807987i	$0.700557\pi$
$620$	4576.00	0.296414
$621$	0	0
$622$	−14912.0	−0.961281
$623$	5250.00	0.337619
$624$	0	0
$625$	−19189.0	−1.22810
$626$	−20408.0	−1.30298
$627$	0	0
$628$	−3536.00	−0.224684
$629$	2776.00	0.175972
$630$	0	0
$631$	8016.00	0.505724	0.252862	−	0.967502i	$-0.418628\pi$
$631$	8016.00	0.505724	0.252862	+	0.967502i	$0.418628\pi$
$632$	−4416.00	−0.277942
$633$	0	0
$634$	19332.0	1.21100
$635$	7904.00	0.493954
$636$	0	0
$637$	−3283.00	−0.204203
$638$	4862.00	0.301706
$639$	0	0
$640$	−1664.00	−0.102774
$641$	19476.0	1.20009	0.600043	−	0.799967i	$-0.295150\pi$
$641$	19476.0	1.20009	0.600043	+	0.799967i	$0.295150\pi$
$642$	0	0
$643$	5206.00	0.319292	0.159646	−	0.987174i	$-0.448965\pi$
$643$	5206.00	0.319292	0.159646	+	0.987174i	$0.448965\pi$
$644$	−5432.00	−0.332377
$645$	0	0
$646$	336.000	0.0204640
$647$	−13227.0	−0.803720	−0.401860	−	0.915701i	$-0.631636\pi$
$647$	−13227.0	−0.803720	−0.401860	+	0.915701i	$0.631636\pi$
$648$	0	0
$649$	3003.00	0.181630
$650$	5896.00	0.355785
$651$	0	0
$652$	2692.00	0.161698
$653$	11768.0	0.705233	0.352617	−	0.935768i	$-0.385292\pi$
$653$	11768.0	0.705233	0.352617	+	0.935768i	$0.385292\pi$
$654$	0	0
$655$	2496.00	0.148896
$656$	−4672.00	−0.278065
$657$	0	0
$658$	−3094.00	−0.183308
$659$	8189.00	0.484064	0.242032	−	0.970268i	$-0.422186\pi$
$659$	8189.00	0.484064	0.242032	+	0.970268i	$0.422186\pi$
$660$	0	0
$661$	−30562.0	−1.79837	−0.899186	−	0.437566i	$-0.855840\pi$
$661$	−30562.0	−1.79837	−0.899186	+	0.437566i	$0.855840\pi$
$662$	22456.0	1.31839
$663$	0	0
$664$	−1152.00	−0.0673287
$665$	−1911.00	−0.111437
$666$	0	0
$667$	42874.0	2.48889
$668$	−7384.00	−0.427688
$669$	0	0
$670$	−14586.0	−0.841054
$671$	5830.00	0.335417
$672$	0	0
$673$	17626.0	1.00956	0.504779	−	0.863249i	$-0.331574\pi$
$673$	17626.0	1.00956	0.504779	+	0.863249i	$0.331574\pi$
$674$	−4548.00	−0.259915
$675$	0	0
$676$	9168.00	0.521620
$677$	−13610.0	−0.772636	−0.386318	−	0.922366i	$-0.626253\pi$
$677$	−13610.0	−0.772636	−0.386318	+	0.922366i	$0.626253\pi$
$678$	0	0
$679$	9590.00	0.542018
$680$	832.000	0.0469202
$681$	0	0
$682$	1936.00	0.108700
$683$	5328.00	0.298492	0.149246	−	0.988800i	$-0.452315\pi$
$683$	5328.00	0.298492	0.149246	+	0.988800i	$0.452315\pi$
$684$	0	0
$685$	15756.0	0.878841
$686$	686.000	0.0381802
$687$	0	0
$688$	−7328.00	−0.406072
$689$	−43014.0	−2.37838
$690$	0	0
$691$	−6222.00	−0.342541	−0.171271	−	0.985224i	$-0.554787\pi$
$691$	−6222.00	−0.342541	−0.171271	+	0.985224i	$0.554787\pi$
$692$	11264.0	0.618776
$693$	0	0
$694$	−4016.00	−0.219662
$695$	−24388.0	−1.33106
$696$	0	0
$697$	2336.00	0.126947
$698$	−3442.00	−0.186650
$699$	0	0
$700$	−1232.00	−0.0665217
$701$	2034.00	0.109591	0.0547954	−	0.998498i	$-0.482549\pi$
$701$	2034.00	0.109591	0.0547954	+	0.998498i	$0.482549\pi$
$702$	0	0
$703$	−7287.00	−0.390945
$704$	−704.000	−0.0376889
$705$	0	0
$706$	−4110.00	−0.219096
$707$	13860.0	0.737283
$708$	0	0
$709$	18591.0	0.984767	0.492383	−	0.870378i	$-0.336126\pi$
$709$	18591.0	0.984767	0.492383	+	0.870378i	$0.336126\pi$
$710$	15704.0	0.830085
$711$	0	0
$712$	6000.00	0.315814
$713$	17072.0	0.896706
$714$	0	0
$715$	9581.00	0.501132
$716$	−11200.0	−0.584586
$717$	0	0
$718$	2608.00	0.135557
$719$	−9619.00	−0.498927	−0.249463	−	0.968384i	$-0.580254\pi$
$719$	−9619.00	−0.498927	−0.249463	+	0.968384i	$0.580254\pi$
$720$	0	0
$721$	4662.00	0.240807
$722$	12836.0	0.661643
$723$	0	0
$724$	8168.00	0.419284
$725$	9724.00	0.498125
$726$	0	0
$727$	27818.0	1.41914	0.709568	−	0.704637i	$-0.248890\pi$
$727$	27818.0	1.41914	0.709568	+	0.704637i	$0.248890\pi$
$728$	−3752.00	−0.191014
$729$	0	0
$730$	−18278.0	−0.926711
$731$	3664.00	0.185387
$732$	0	0
$733$	10982.0	0.553383	0.276691	−	0.960959i	$-0.410762\pi$
$733$	10982.0	0.553383	0.276691	+	0.960959i	$0.410762\pi$
$734$	3508.00	0.176407
$735$	0	0
$736$	−6208.00	−0.310910
$737$	−6171.00	−0.308428
$738$	0	0
$739$	1914.00	0.0952742	0.0476371	−	0.998865i	$-0.484831\pi$
$739$	1914.00	0.0952742	0.0476371	+	0.998865i	$0.484831\pi$
$740$	−18044.0	−0.896366
$741$	0	0
$742$	8988.00	0.444690
$743$	2049.00	0.101172	0.0505858	−	0.998720i	$-0.483891\pi$
$743$	2049.00	0.101172	0.0505858	+	0.998720i	$0.483891\pi$
$744$	0	0
$745$	3445.00	0.169416
$746$	−22696.0	−1.11389
$747$	0	0
$748$	352.000	0.0172064
$749$	10073.0	0.491401
$750$	0	0
$751$	−7415.00	−0.360289	−0.180145	−	0.983640i	$-0.557657\pi$
$751$	−7415.00	−0.360289	−0.180145	+	0.983640i	$0.557657\pi$
$752$	−3536.00	−0.171469
$753$	0	0
$754$	29614.0	1.43034
$755$	−22464.0	−1.08285
$756$	0	0
$757$	8141.00	0.390871	0.195436	−	0.980717i	$-0.437388\pi$
$757$	8141.00	0.390871	0.195436	+	0.980717i	$0.437388\pi$
$758$	17890.0	0.857248
$759$	0	0
$760$	−2184.00	−0.104239
$761$	−27564.0	−1.31300	−0.656501	−	0.754325i	$-0.727964\pi$
$761$	−27564.0	−1.31300	−0.656501	+	0.754325i	$0.727964\pi$
$762$	0	0
$763$	6692.00	0.317519
$764$	−15968.0	−0.756154
$765$	0	0
$766$	−11120.0	−0.524519
$767$	18291.0	0.861082
$768$	0	0
$769$	−12095.0	−0.567174	−0.283587	−	0.958947i	$-0.591524\pi$
$769$	−12095.0	−0.567174	−0.283587	+	0.958947i	$0.591524\pi$
$770$	−2002.00	−0.0936975
$771$	0	0
$772$	6104.00	0.284570
$773$	20925.0	0.973635	0.486818	−	0.873504i	$-0.338158\pi$
$773$	20925.0	0.973635	0.486818	+	0.873504i	$0.338158\pi$
$774$	0	0
$775$	3872.00	0.179466
$776$	10960.0	0.507012
$777$	0	0
$778$	−24744.0	−1.14025
$779$	−6132.00	−0.282030
$780$	0	0
$781$	6644.00	0.304406
$782$	3104.00	0.141942
$783$	0	0
$784$	784.000	0.0357143
$785$	−11492.0	−0.522506
$786$	0	0
$787$	−10789.0	−0.488674	−0.244337	−	0.969690i	$-0.578570\pi$
$787$	−10789.0	−0.488674	−0.244337	+	0.969690i	$0.578570\pi$
$788$	−1416.00	−0.0640138
$789$	0	0
$790$	−14352.0	−0.646356
$791$	−16114.0	−0.724334
$792$	0	0
$793$	35510.0	1.59016
$794$	7968.00	0.356138
$795$	0	0
$796$	5896.00	0.262535
$797$	11011.0	0.489372	0.244686	−	0.969602i	$-0.421315\pi$
$797$	11011.0	0.489372	0.244686	+	0.969602i	$0.421315\pi$
$798$	0	0
$799$	1768.00	0.0782820
$800$	−1408.00	−0.0622254
$801$	0	0
$802$	−828.000	−0.0364560
$803$	−7733.00	−0.339840
$804$	0	0
$805$	−17654.0	−0.772946
$806$	11792.0	0.515329
$807$	0	0
$808$	15840.0	0.689665
$809$	35205.0	1.52997	0.764983	−	0.644051i	$-0.222748\pi$
$809$	35205.0	1.52997	0.764983	+	0.644051i	$0.222748\pi$
$810$	0	0
$811$	32951.0	1.42672	0.713358	−	0.700800i	$-0.247174\pi$
$811$	32951.0	1.42672	0.713358	+	0.700800i	$0.247174\pi$
$812$	−6188.00	−0.267434
$813$	0	0
$814$	−7634.00	−0.328712
$815$	8749.00	0.376030
$816$	0	0
$817$	−9618.00	−0.411862
$818$	−9068.00	−0.387598
$819$	0	0
$820$	−15184.0	−0.646644
$821$	−477.000	−0.0202770	−0.0101385	−	0.999949i	$-0.503227\pi$
$821$	−477.000	−0.0202770	−0.0101385	+	0.999949i	$0.503227\pi$
$822$	0	0
$823$	20921.0	0.886100	0.443050	−	0.896497i	$-0.353896\pi$
$823$	20921.0	0.886100	0.443050	+	0.896497i	$0.353896\pi$
$824$	5328.00	0.225254
$825$	0	0
$826$	−3822.00	−0.160998
$827$	29965.0	1.25996	0.629979	−	0.776612i	$-0.283064\pi$
$827$	29965.0	1.25996	0.629979	+	0.776612i	$0.283064\pi$
$828$	0	0
$829$	9232.00	0.386780	0.193390	−	0.981122i	$-0.438052\pi$
$829$	9232.00	0.386780	0.193390	+	0.981122i	$0.438052\pi$
$830$	−3744.00	−0.156574
$831$	0	0
$832$	−4288.00	−0.178677
$833$	−392.000	−0.0163049
$834$	0	0
$835$	−23998.0	−0.994593
$836$	−924.000	−0.0382263
$837$	0	0
$838$	−10570.0	−0.435721
$839$	27435.0	1.12892	0.564459	−	0.825461i	$-0.309085\pi$
$839$	27435.0	1.12892	0.564459	+	0.825461i	$0.309085\pi$
$840$	0	0
$841$	24452.0	1.00258
$842$	−18038.0	−0.738279
$843$	0	0
$844$	−2360.00	−0.0962495
$845$	29796.0	1.21303
$846$	0	0
$847$	−847.000	−0.0343604
$848$	10272.0	0.415969
$849$	0	0
$850$	704.000	0.0284082
$851$	−67318.0	−2.71167
$852$	0	0
$853$	7214.00	0.289569	0.144785	−	0.989463i	$-0.453751\pi$
$853$	7214.00	0.289569	0.144785	+	0.989463i	$0.453751\pi$
$854$	−7420.00	−0.297315
$855$	0	0
$856$	11512.0	0.459664
$857$	−28298.0	−1.12794	−0.563968	−	0.825797i	$-0.690726\pi$
$857$	−28298.0	−1.12794	−0.563968	+	0.825797i	$0.690726\pi$
$858$	0	0
$859$	−31460.0	−1.24959	−0.624797	−	0.780787i	$-0.714818\pi$
$859$	−31460.0	−1.24959	−0.624797	+	0.780787i	$0.714818\pi$
$860$	−23816.0	−0.944324
$861$	0	0
$862$	8894.00	0.351428
$863$	3014.00	0.118885	0.0594425	−	0.998232i	$-0.481068\pi$
$863$	3014.00	0.118885	0.0594425	+	0.998232i	$0.481068\pi$
$864$	0	0
$865$	36608.0	1.43897
$866$	7016.00	0.275304
$867$	0	0
$868$	−2464.00	−0.0963521
$869$	−6072.00	−0.237029
$870$	0	0
$871$	−37587.0	−1.46221
$872$	7648.00	0.297011
$873$	0	0
$874$	−8148.00	−0.315343
$875$	7371.00	0.284783
$876$	0	0
$877$	25564.0	0.984304	0.492152	−	0.870509i	$-0.336210\pi$
$877$	25564.0	0.984304	0.492152	+	0.870509i	$0.336210\pi$
$878$	26374.0	1.01376
$879$	0	0
$880$	−2288.00	−0.0876460
$881$	3945.00	0.150863	0.0754316	−	0.997151i	$-0.475967\pi$
$881$	3945.00	0.150863	0.0754316	+	0.997151i	$0.475967\pi$
$882$	0	0
$883$	−2693.00	−0.102635	−0.0513175	−	0.998682i	$-0.516342\pi$
$883$	−2693.00	−0.102635	−0.0513175	+	0.998682i	$0.516342\pi$
$884$	2144.00	0.0815730
$885$	0	0
$886$	−16032.0	−0.607907
$887$	−14500.0	−0.548887	−0.274443	−	0.961603i	$-0.588494\pi$
$887$	−14500.0	−0.548887	−0.274443	+	0.961603i	$0.588494\pi$
$888$	0	0
$889$	−4256.00	−0.160564
$890$	19500.0	0.734429
$891$	0	0
$892$	−10856.0	−0.407495
$893$	−4641.00	−0.173914
$894$	0	0
$895$	−36400.0	−1.35946
$896$	896.000	0.0334077
$897$	0	0
$898$	−11448.0	−0.425417
$899$	19448.0	0.721498
$900$	0	0
$901$	−5136.00	−0.189906
$902$	−6424.00	−0.237135
$903$	0	0
$904$	−18416.0	−0.677552
$905$	26546.0	0.975049
$906$	0	0
$907$	18908.0	0.692205	0.346102	−	0.938197i	$-0.387505\pi$
$907$	18908.0	0.692205	0.346102	+	0.938197i	$0.387505\pi$
$908$	13304.0	0.486243
$909$	0	0
$910$	−12194.0	−0.444206
$911$	42894.0	1.55998	0.779990	−	0.625792i	$-0.215224\pi$
$911$	42894.0	1.55998	0.779990	+	0.625792i	$0.215224\pi$
$912$	0	0
$913$	−1584.00	−0.0574181
$914$	−4612.00	−0.166905
$915$	0	0
$916$	−5176.00	−0.186703
$917$	−1344.00	−0.0484000
$918$	0	0
$919$	−16050.0	−0.576105	−0.288053	−	0.957615i	$-0.593008\pi$
$919$	−16050.0	−0.576105	−0.288053	+	0.957615i	$0.593008\pi$
$920$	−20176.0	−0.723025
$921$	0	0
$922$	−32136.0	−1.14788
$923$	40468.0	1.44314
$924$	0	0
$925$	−15268.0	−0.542712
$926$	32374.0	1.14889
$927$	0	0
$928$	−7072.00	−0.250161
$929$	17595.0	0.621392	0.310696	−	0.950509i	$-0.399438\pi$
$929$	17595.0	0.621392	0.310696	+	0.950509i	$0.399438\pi$
$930$	0	0
$931$	1029.00	0.0362235
$932$	−13560.0	−0.476580
$933$	0	0
$934$	−27006.0	−0.946106
$935$	1144.00	0.0400137
$936$	0	0
$937$	55242.0	1.92602	0.963008	−	0.269472i	$-0.0868491\pi$
$937$	55242.0	1.92602	0.963008	+	0.269472i	$0.0868491\pi$
$938$	7854.00	0.273393
$939$	0	0
$940$	−11492.0	−0.398753
$941$	27020.0	0.936054	0.468027	−	0.883714i	$-0.344965\pi$
$941$	27020.0	0.936054	0.468027	+	0.883714i	$0.344965\pi$
$942$	0	0
$943$	−56648.0	−1.95622
$944$	−4368.00	−0.150600
$945$	0	0
$946$	−10076.0	−0.346299
$947$	6874.00	0.235876	0.117938	−	0.993021i	$-0.462372\pi$
$947$	6874.00	0.235876	0.117938	+	0.993021i	$0.462372\pi$
$948$	0	0
$949$	−47101.0	−1.61113
$950$	−1848.00	−0.0631127
$951$	0	0
$952$	−448.000	−0.0152519
$953$	−5615.00	−0.190858	−0.0954290	−	0.995436i	$-0.530422\pi$
$953$	−5615.00	−0.190858	−0.0954290	+	0.995436i	$0.530422\pi$
$954$	0	0
$955$	−51896.0	−1.75845
$956$	−20836.0	−0.704900
$957$	0	0
$958$	−3176.00	−0.107111
$959$	−8484.00	−0.285675
$960$	0	0
$961$	−22047.0	−0.740056
$962$	−46498.0	−1.55837
$963$	0	0
$964$	−10044.0	−0.335576
$965$	19838.0	0.661770
$966$	0	0
$967$	10562.0	0.351242	0.175621	−	0.984458i	$-0.443807\pi$
$967$	10562.0	0.351242	0.175621	+	0.984458i	$0.443807\pi$
$968$	−968.000	−0.0321412
$969$	0	0
$970$	35620.0	1.17906
$971$	31669.0	1.04666	0.523330	−	0.852130i	$-0.324690\pi$
$971$	31669.0	1.04666	0.523330	+	0.852130i	$0.324690\pi$
$972$	0	0
$973$	13132.0	0.432675
$974$	38192.0	1.25642
$975$	0	0
$976$	−8480.00	−0.278113
$977$	−24134.0	−0.790292	−0.395146	−	0.918618i	$-0.629306\pi$
$977$	−24134.0	−0.790292	−0.395146	+	0.918618i	$0.629306\pi$
$978$	0	0
$979$	8250.00	0.269327
$980$	2548.00	0.0830540
$981$	0	0
$982$	−7410.00	−0.240797
$983$	2868.00	0.0930570	0.0465285	−	0.998917i	$-0.485184\pi$
$983$	2868.00	0.0930570	0.0465285	+	0.998917i	$0.485184\pi$
$984$	0	0
$985$	−4602.00	−0.148865
$986$	3536.00	0.114208
$987$	0	0
$988$	−5628.00	−0.181225
$989$	−88852.0	−2.85675
$990$	0	0
$991$	−1271.00	−0.0407413	−0.0203707	−	0.999792i	$-0.506485\pi$
$991$	−1271.00	−0.0407413	−0.0203707	+	0.999792i	$0.506485\pi$
$992$	−2816.00	−0.0901291
$993$	0	0
$994$	−8456.00	−0.269827
$995$	19162.0	0.610529
$996$	0	0
$997$	8706.00	0.276551	0.138276	−	0.990394i	$-0.455844\pi$
$997$	8706.00	0.276551	0.138276	+	0.990394i	$0.455844\pi$
$998$	7346.00	0.233000
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.4.a.f.1.1		1
3.2	odd	2		462.4.a.i.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.4.a.i.1.1	✓	1	3.2	odd	2
1386.4.a.f.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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1386.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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