LMFDB - Embedded newform 1058.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1058,4,Mod(1,1058)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1058, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1058.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1058 = 2 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1058.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:	$62.4240207861$
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	$\chi$	$=$	1058.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} -18.0000 q^{5} +14.0000 q^{6} +30.0000 q^{7} +8.00000 q^{8} +22.0000 q^{9} -36.0000 q^{10} +6.00000 q^{11} +28.0000 q^{12} +79.0000 q^{13} +60.0000 q^{14} -126.000 q^{15} +16.0000 q^{16} -102.000 q^{17} +44.0000 q^{18} +36.0000 q^{19} -72.0000 q^{20} +210.000 q^{21} +12.0000 q^{22} +56.0000 q^{24} +199.000 q^{25} +158.000 q^{26} -35.0000 q^{27} +120.000 q^{28} +33.0000 q^{29} -252.000 q^{30} +43.0000 q^{31} +32.0000 q^{32} +42.0000 q^{33} -204.000 q^{34} -540.000 q^{35} +88.0000 q^{36} +354.000 q^{37} +72.0000 q^{38} +553.000 q^{39} -144.000 q^{40} +375.000 q^{41} +420.000 q^{42} -96.0000 q^{43} +24.0000 q^{44} -396.000 q^{45} -129.000 q^{47} +112.000 q^{48} +557.000 q^{49} +398.000 q^{50} -714.000 q^{51} +316.000 q^{52} +300.000 q^{53} -70.0000 q^{54} -108.000 q^{55} +240.000 q^{56} +252.000 q^{57} +66.0000 q^{58} -324.000 q^{59} -504.000 q^{60} -120.000 q^{61} +86.0000 q^{62} +660.000 q^{63} +64.0000 q^{64} -1422.00 q^{65} +84.0000 q^{66} -582.000 q^{67} -408.000 q^{68} -1080.00 q^{70} +147.000 q^{71} +176.000 q^{72} +637.000 q^{73} +708.000 q^{74} +1393.00 q^{75} +144.000 q^{76} +180.000 q^{77} +1106.00 q^{78} +468.000 q^{79} -288.000 q^{80} -839.000 q^{81} +750.000 q^{82} -978.000 q^{83} +840.000 q^{84} +1836.00 q^{85} -192.000 q^{86} +231.000 q^{87} +48.0000 q^{88} +252.000 q^{89} -792.000 q^{90} +2370.00 q^{91} +301.000 q^{93} -258.000 q^{94} -648.000 q^{95} +224.000 q^{96} +1170.00 q^{97} +1114.00 q^{98} +132.000 q^{99} +O(q^{100})\)

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
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	4.00000	0.500000
$5$	−18.0000	−1.60997	−0.804984	−	0.593296i	$-0.797826\pi$
$5$	−18.0000	−1.60997	−0.804984	+	0.593296i	$0.797826\pi$
$6$	14.0000	0.952579
$7$	30.0000	1.61985	0.809924	−	0.586535i	$-0.199508\pi$
$7$	30.0000	1.61985	0.809924	+	0.586535i	$0.199508\pi$
$8$	8.00000	0.353553
$9$	22.0000	0.814815
$10$	−36.0000	−1.13842
$11$	6.00000	0.164461	0.0822304	−	0.996613i	$-0.473796\pi$
$11$	6.00000	0.164461	0.0822304	+	0.996613i	$0.473796\pi$
$12$	28.0000	0.673575
$13$	79.0000	1.68544	0.842718	−	0.538356i	$-0.180954\pi$
$13$	79.0000	1.68544	0.842718	+	0.538356i	$0.180954\pi$
$14$	60.0000	1.14541
$15$	−126.000	−2.16887
$16$	16.0000	0.250000
$17$	−102.000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−102.000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	44.0000	0.576161
$19$	36.0000	0.434682	0.217341	−	0.976096i	$-0.430262\pi$
$19$	36.0000	0.434682	0.217341	+	0.976096i	$0.430262\pi$
$20$	−72.0000	−0.804984
$21$	210.000	2.18218
$22$	12.0000	0.116291
$23$	0	0
$23$	0	0
$24$	56.0000	0.476290
$25$	199.000	1.59200
$26$	158.000	1.19178
$27$	−35.0000	−0.249472
$28$	120.000	0.809924
$29$	33.0000	0.211308	0.105654	−	0.994403i	$-0.466306\pi$
$29$	33.0000	0.211308	0.105654	+	0.994403i	$0.466306\pi$
$30$	−252.000	−1.53362
$31$	43.0000	0.249130	0.124565	−	0.992211i	$-0.460246\pi$
$31$	43.0000	0.249130	0.124565	+	0.992211i	$0.460246\pi$
$32$	32.0000	0.176777
$33$	42.0000	0.221553
$34$	−204.000	−1.02899
$35$	−540.000	−2.60790
$36$	88.0000	0.407407
$37$	354.000	1.57290	0.786449	−	0.617655i	$-0.211917\pi$
$37$	354.000	1.57290	0.786449	+	0.617655i	$0.211917\pi$
$38$	72.0000	0.307367
$39$	553.000	2.27054
$40$	−144.000	−0.569210
$41$	375.000	1.42842	0.714209	−	0.699932i	$-0.246786\pi$
$41$	375.000	1.42842	0.714209	+	0.699932i	$0.246786\pi$
$42$	420.000	1.54303
$43$	−96.0000	−0.340462	−0.170231	−	0.985404i	$-0.554451\pi$
$43$	−96.0000	−0.340462	−0.170231	+	0.985404i	$0.554451\pi$
$44$	24.0000	0.0822304
$45$	−396.000	−1.31183
$46$	0	0
$47$	−129.000	−0.400353	−0.200176	−	0.979760i	$-0.564152\pi$
$47$	−129.000	−0.400353	−0.200176	+	0.979760i	$0.564152\pi$
$48$	112.000	0.336788
$49$	557.000	1.62391
$50$	398.000	1.12571
$51$	−714.000	−1.96039
$52$	316.000	0.842718
$53$	300.000	0.777513	0.388756	−	0.921341i	$-0.372905\pi$
$53$	300.000	0.777513	0.388756	+	0.921341i	$0.372905\pi$
$54$	−70.0000	−0.176404
$55$	−108.000	−0.264777
$56$	240.000	0.572703
$57$	252.000	0.585583
$58$	66.0000	0.149418
$59$	−324.000	−0.714936	−0.357468	−	0.933925i	$-0.616360\pi$
$59$	−324.000	−0.714936	−0.357468	+	0.933925i	$0.616360\pi$
$60$	−504.000	−1.08444
$61$	−120.000	−0.251876	−0.125938	−	0.992038i	$-0.540194\pi$
$61$	−120.000	−0.251876	−0.125938	+	0.992038i	$0.540194\pi$
$62$	86.0000	0.176161
$63$	660.000	1.31988
$64$	64.0000	0.125000
$65$	−1422.00	−2.71350
$66$	84.0000	0.156662
$67$	−582.000	−1.06123	−0.530617	−	0.847612i	$-0.678040\pi$
$67$	−582.000	−1.06123	−0.530617	+	0.847612i	$0.678040\pi$
$68$	−408.000	−0.727607
$69$	0	0
$70$	−1080.00	−1.84407
$71$	147.000	0.245714	0.122857	−	0.992424i	$-0.460794\pi$
$71$	147.000	0.245714	0.122857	+	0.992424i	$0.460794\pi$
$72$	176.000	0.288081
$73$	637.000	1.02130	0.510652	−	0.859787i	$-0.329404\pi$
$73$	637.000	1.02130	0.510652	+	0.859787i	$0.329404\pi$
$74$	708.000	1.11221
$75$	1393.00	2.14466
$76$	144.000	0.217341
$77$	180.000	0.266401
$78$	1106.00	1.60551
$79$	468.000	0.666508	0.333254	−	0.942837i	$-0.391853\pi$
$79$	468.000	0.666508	0.333254	+	0.942837i	$0.391853\pi$
$80$	−288.000	−0.402492
$81$	−839.000	−1.15089
$82$	750.000	1.01004
$83$	−978.000	−1.29337	−0.646683	−	0.762759i	$-0.723844\pi$
$83$	−978.000	−1.29337	−0.646683	+	0.762759i	$0.723844\pi$
$84$	840.000	1.09109
$85$	1836.00	2.34285
$86$	−192.000	−0.240743
$87$	231.000	0.284664
$88$	48.0000	0.0581456
$89$	252.000	0.300134	0.150067	−	0.988676i	$-0.452051\pi$
$89$	252.000	0.300134	0.150067	+	0.988676i	$0.452051\pi$
$90$	−792.000	−0.927601
$91$	2370.00	2.73015
$92$	0	0
$93$	301.000	0.335616
$94$	−258.000	−0.283092
$95$	−648.000	−0.699825
$96$	224.000	0.238145
$97$	1170.00	1.22470	0.612348	−	0.790588i	$-0.290225\pi$
$97$	1170.00	1.22470	0.612348	+	0.790588i	$0.290225\pi$
$98$	1114.00	1.14828
$99$	132.000	0.134005
$100$	796.000	0.796000
$101$	1098.00	1.08173	0.540867	−	0.841108i	$-0.318096\pi$
$101$	1098.00	1.08173	0.540867	+	0.841108i	$0.318096\pi$
$102$	−1428.00	−1.38621
$103$	66.0000	0.0631376	0.0315688	−	0.999502i	$-0.489950\pi$
$103$	66.0000	0.0631376	0.0315688	+	0.999502i	$0.489950\pi$
$104$	632.000	0.595891
$105$	−3780.00	−3.51324
$106$	600.000	0.549784
$107$	1416.00	1.27934	0.639672	−	0.768648i	$-0.279070\pi$
$107$	1416.00	1.27934	0.639672	+	0.768648i	$0.279070\pi$
$108$	−140.000	−0.124736
$109$	192.000	0.168718	0.0843590	−	0.996435i	$-0.473116\pi$
$109$	192.000	0.168718	0.0843590	+	0.996435i	$0.473116\pi$
$110$	−216.000	−0.187225
$111$	2478.00	2.11893
$112$	480.000	0.404962
$113$	882.000	0.734262	0.367131	−	0.930169i	$-0.380340\pi$
$113$	882.000	0.734262	0.367131	+	0.930169i	$0.380340\pi$
$114$	504.000	0.414070
$115$	0	0
$116$	132.000	0.105654
$117$	1738.00	1.37332
$118$	−648.000	−0.505536
$119$	−3060.00	−2.35722
$120$	−1008.00	−0.766812
$121$	−1295.00	−0.972953
$122$	−240.000	−0.178103
$123$	2625.00	1.92429
$124$	172.000	0.124565
$125$	−1332.00	−0.953102
$126$	1320.00	0.933293
$127$	−551.000	−0.384987	−0.192493	−	0.981298i	$-0.561657\pi$
$127$	−551.000	−0.384987	−0.192493	+	0.981298i	$0.561657\pi$
$128$	128.000	0.0883883
$129$	−672.000	−0.458653
$130$	−2844.00	−1.91873
$131$	−321.000	−0.214091	−0.107045	−	0.994254i	$-0.534139\pi$
$131$	−321.000	−0.214091	−0.107045	+	0.994254i	$0.534139\pi$
$132$	168.000	0.110777
$133$	1080.00	0.704119
$134$	−1164.00	−0.750405
$135$	630.000	0.401643
$136$	−816.000	−0.514496
$137$	−2112.00	−1.31708	−0.658541	−	0.752545i	$-0.728826\pi$
$137$	−2112.00	−1.31708	−0.658541	+	0.752545i	$0.728826\pi$
$138$	0	0
$139$	−763.000	−0.465589	−0.232794	−	0.972526i	$-0.574787\pi$
$139$	−763.000	−0.465589	−0.232794	+	0.972526i	$0.574787\pi$
$140$	−2160.00	−1.30395
$141$	−903.000	−0.539336
$142$	294.000	0.173746
$143$	474.000	0.277188
$144$	352.000	0.203704
$145$	−594.000	−0.340200
$146$	1274.00	0.722171
$147$	3899.00	2.18765
$148$	1416.00	0.786449
$149$	2208.00	1.21400	0.607001	−	0.794701i	$-0.292372\pi$
$149$	2208.00	1.21400	0.607001	+	0.794701i	$0.292372\pi$
$150$	2786.00	1.51651
$151$	−3193.00	−1.72081	−0.860406	−	0.509609i	$-0.829790\pi$
$151$	−3193.00	−1.72081	−0.860406	+	0.509609i	$0.829790\pi$
$152$	288.000	0.153683
$153$	−2244.00	−1.18573
$154$	360.000	0.188374
$155$	−774.000	−0.401091
$156$	2212.00	1.13527
$157$	516.000	0.262301	0.131151	−	0.991362i	$-0.458133\pi$
$157$	516.000	0.262301	0.131151	+	0.991362i	$0.458133\pi$
$158$	936.000	0.471292
$159$	2100.00	1.04743
$160$	−576.000	−0.284605
$161$	0	0
$162$	−1678.00	−0.813803
$163$	421.000	0.202302	0.101151	−	0.994871i	$-0.467747\pi$
$163$	421.000	0.202302	0.101151	+	0.994871i	$0.467747\pi$
$164$	1500.00	0.714209
$165$	−756.000	−0.356694
$166$	−1956.00	−0.914548
$167$	−1584.00	−0.733974	−0.366987	−	0.930226i	$-0.619611\pi$
$167$	−1584.00	−0.733974	−0.366987	+	0.930226i	$0.619611\pi$
$168$	1680.00	0.771517
$169$	4044.00	1.84069
$170$	3672.00	1.65664
$171$	792.000	0.354186
$172$	−384.000	−0.170231
$173$	2070.00	0.909706	0.454853	−	0.890566i	$-0.349692\pi$
$173$	2070.00	0.909706	0.454853	+	0.890566i	$0.349692\pi$
$174$	462.000	0.201288
$175$	5970.00	2.57880
$176$	96.0000	0.0411152
$177$	−2268.00	−0.963126
$178$	504.000	0.212227
$179$	−591.000	−0.246779	−0.123389	−	0.992358i	$-0.539376\pi$
$179$	−591.000	−0.246779	−0.123389	+	0.992358i	$0.539376\pi$
$180$	−1584.00	−0.655913
$181$	−2958.00	−1.21473	−0.607366	−	0.794422i	$-0.707774\pi$
$181$	−2958.00	−1.21473	−0.607366	+	0.794422i	$0.707774\pi$
$182$	4740.00	1.93051
$183$	−840.000	−0.339315
$184$	0	0
$185$	−6372.00	−2.53232
$186$	602.000	0.237316
$187$	−612.000	−0.239326
$188$	−516.000	−0.200176
$189$	−1050.00	−0.404107
$190$	−1296.00	−0.494851
$191$	−4650.00	−1.76158	−0.880791	−	0.473505i	$-0.842989\pi$
$191$	−4650.00	−1.76158	−0.880791	+	0.473505i	$0.842989\pi$
$192$	448.000	0.168394
$193$	−3283.00	−1.22443	−0.612216	−	0.790690i	$-0.709722\pi$
$193$	−3283.00	−1.22443	−0.612216	+	0.790690i	$0.709722\pi$
$194$	2340.00	0.865991
$195$	−9954.00	−3.65549
$196$	2228.00	0.811953
$197$	−1959.00	−0.708492	−0.354246	−	0.935152i	$-0.615262\pi$
$197$	−1959.00	−0.708492	−0.354246	+	0.935152i	$0.615262\pi$
$198$	264.000	0.0947559
$199$	4518.00	1.60941	0.804705	−	0.593675i	$-0.202324\pi$
$199$	4518.00	1.60941	0.804705	+	0.593675i	$0.202324\pi$
$200$	1592.00	0.562857
$201$	−4074.00	−1.42964
$202$	2196.00	0.764901
$203$	990.000	0.342288
$204$	−2856.00	−0.980196
$205$	−6750.00	−2.29971
$206$	132.000	0.0446450
$207$	0	0
$208$	1264.00	0.421359
$209$	216.000	0.0714882
$210$	−7560.00	−2.48424
$211$	−5636.00	−1.83885	−0.919427	−	0.393260i	$-0.871347\pi$
$211$	−5636.00	−1.83885	−0.919427	+	0.393260i	$0.871347\pi$
$212$	1200.00	0.388756
$213$	1029.00	0.331014
$214$	2832.00	0.904633
$215$	1728.00	0.548133
$216$	−280.000	−0.0882018
$217$	1290.00	0.403553
$218$	384.000	0.119302
$219$	4459.00	1.37585
$220$	−432.000	−0.132388
$221$	−8058.00	−2.45267
$222$	4956.00	1.49831
$223$	3044.00	0.914087	0.457043	−	0.889444i	$-0.348908\pi$
$223$	3044.00	0.914087	0.457043	+	0.889444i	$0.348908\pi$
$224$	960.000	0.286351
$225$	4378.00	1.29719
$226$	1764.00	0.519201
$227$	−3726.00	−1.08944	−0.544721	−	0.838617i	$-0.683364\pi$
$227$	−3726.00	−1.08944	−0.544721	+	0.838617i	$0.683364\pi$
$228$	1008.00	0.292791
$229$	−4512.00	−1.30201	−0.651007	−	0.759071i	$-0.725653\pi$
$229$	−4512.00	−1.30201	−0.651007	+	0.759071i	$0.725653\pi$
$230$	0	0
$231$	1260.00	0.358883
$232$	264.000	0.0747088
$233$	3039.00	0.854470	0.427235	−	0.904141i	$-0.359488\pi$
$233$	3039.00	0.854470	0.427235	+	0.904141i	$0.359488\pi$
$234$	3476.00	0.971082
$235$	2322.00	0.644556
$236$	−1296.00	−0.357468
$237$	3276.00	0.897886
$238$	−6120.00	−1.66681
$239$	−5361.00	−1.45094	−0.725469	−	0.688255i	$-0.758377\pi$
$239$	−5361.00	−1.45094	−0.725469	+	0.688255i	$0.758377\pi$
$240$	−2016.00	−0.542218
$241$	2130.00	0.569317	0.284658	−	0.958629i	$-0.408120\pi$
$241$	2130.00	0.569317	0.284658	+	0.958629i	$0.408120\pi$
$242$	−2590.00	−0.687981
$243$	−4928.00	−1.30095
$244$	−480.000	−0.125938
$245$	−10026.0	−2.61444
$246$	5250.00	1.36068
$247$	2844.00	0.732629
$248$	344.000	0.0880807
$249$	−6846.00	−1.74236
$250$	−2664.00	−0.673945
$251$	1038.00	0.261028	0.130514	−	0.991446i	$-0.458337\pi$
$251$	1038.00	0.261028	0.130514	+	0.991446i	$0.458337\pi$
$252$	2640.00	0.659938
$253$	0	0
$254$	−1102.00	−0.272227
$255$	12852.0	3.15617
$256$	256.000	0.0625000
$257$	723.000	0.175484	0.0877422	−	0.996143i	$-0.472035\pi$
$257$	723.000	0.175484	0.0877422	+	0.996143i	$0.472035\pi$
$258$	−1344.00	−0.324317
$259$	10620.0	2.54786
$260$	−5688.00	−1.35675
$261$	726.000	0.172177
$262$	−642.000	−0.151385
$263$	−3252.00	−0.762460	−0.381230	−	0.924480i	$-0.624499\pi$
$263$	−3252.00	−0.762460	−0.381230	+	0.924480i	$0.624499\pi$
$264$	336.000	0.0783309
$265$	−5400.00	−1.25177
$266$	2160.00	0.497888
$267$	1764.00	0.404326
$268$	−2328.00	−0.530617
$269$	−4215.00	−0.955365	−0.477682	−	0.878533i	$-0.658523\pi$
$269$	−4215.00	−0.955365	−0.477682	+	0.878533i	$0.658523\pi$
$270$	1260.00	0.284004
$271$	−3728.00	−0.835645	−0.417823	−	0.908529i	$-0.637207\pi$
$271$	−3728.00	−0.835645	−0.417823	+	0.908529i	$0.637207\pi$
$272$	−1632.00	−0.363803
$273$	16590.0	3.67792
$274$	−4224.00	−0.931318
$275$	1194.00	0.261821
$276$	0	0
$277$	−8507.00	−1.84526	−0.922628	−	0.385690i	$-0.873963\pi$
$277$	−8507.00	−1.84526	−0.922628	+	0.385690i	$0.873963\pi$
$278$	−1526.00	−0.329221
$279$	946.000	0.202995
$280$	−4320.00	−0.922033
$281$	−2010.00	−0.426714	−0.213357	−	0.976974i	$-0.568440\pi$
$281$	−2010.00	−0.426714	−0.213357	+	0.976974i	$0.568440\pi$
$282$	−1806.00	−0.381368
$283$	9438.00	1.98244	0.991221	−	0.132218i	$-0.0422100\pi$
$283$	9438.00	1.98244	0.991221	+	0.132218i	$0.0422100\pi$
$284$	588.000	0.122857
$285$	−4536.00	−0.942770
$286$	948.000	0.196001
$287$	11250.0	2.31382
$288$	704.000	0.144040
$289$	5491.00	1.11765
$290$	−1188.00	−0.240558
$291$	8190.00	1.64985
$292$	2548.00	0.510652
$293$	−12.0000	−0.00239265	−0.00119633	−	0.999999i	$-0.500381\pi$
$293$	−12.0000	−0.00239265	−0.00119633	+	0.999999i	$0.500381\pi$
$294$	7798.00	1.54690
$295$	5832.00	1.15102
$296$	2832.00	0.556104
$297$	−210.000	−0.0410284
$298$	4416.00	0.858430
$299$	0	0
$300$	5572.00	1.07233
$301$	−2880.00	−0.551496
$302$	−6386.00	−1.21680
$303$	7686.00	1.45726
$304$	576.000	0.108671
$305$	2160.00	0.405512
$306$	−4488.00	−0.838438
$307$	−10028.0	−1.86426	−0.932131	−	0.362122i	$-0.882052\pi$
$307$	−10028.0	−1.86426	−0.932131	+	0.362122i	$0.882052\pi$
$308$	720.000	0.133201
$309$	462.000	0.0850559
$310$	−1548.00	−0.283614
$311$	7251.00	1.32208	0.661039	−	0.750351i	$-0.270116\pi$
$311$	7251.00	1.32208	0.661039	+	0.750351i	$0.270116\pi$
$312$	4424.00	0.802755
$313$	4452.00	0.803968	0.401984	−	0.915647i	$-0.368321\pi$
$313$	4452.00	0.803968	0.401984	+	0.915647i	$0.368321\pi$
$314$	1032.00	0.185475
$315$	−11880.0	−2.12496
$316$	1872.00	0.333254
$317$	3294.00	0.583626	0.291813	−	0.956475i	$-0.405741\pi$
$317$	3294.00	0.583626	0.291813	+	0.956475i	$0.405741\pi$
$318$	4200.00	0.740642
$319$	198.000	0.0347519
$320$	−1152.00	−0.201246
$321$	9912.00	1.72347
$322$	0	0
$323$	−3672.00	−0.632556
$324$	−3356.00	−0.575446
$325$	15721.0	2.68321
$326$	842.000	0.143049
$327$	1344.00	0.227289
$328$	3000.00	0.505022
$329$	−3870.00	−0.648511
$330$	−1512.00	−0.252221
$331$	3445.00	0.572067	0.286034	−	0.958220i	$-0.407663\pi$
$331$	3445.00	0.572067	0.286034	+	0.958220i	$0.407663\pi$
$332$	−3912.00	−0.646683
$333$	7788.00	1.28162
$334$	−3168.00	−0.518998
$335$	10476.0	1.70855
$336$	3360.00	0.545545
$337$	3900.00	0.630405	0.315203	−	0.949024i	$-0.397928\pi$
$337$	3900.00	0.630405	0.315203	+	0.949024i	$0.397928\pi$
$338$	8088.00	1.30157
$339$	6174.00	0.989161
$340$	7344.00	1.17142
$341$	258.000	0.0409721
$342$	1584.00	0.250447
$343$	6420.00	1.01063
$344$	−768.000	−0.120371
$345$	0	0
$346$	4140.00	0.643259
$347$	5256.00	0.813132	0.406566	−	0.913621i	$-0.366726\pi$
$347$	5256.00	0.813132	0.406566	+	0.913621i	$0.366726\pi$
$348$	924.000	0.142332
$349$	−547.000	−0.0838975	−0.0419488	−	0.999120i	$-0.513357\pi$
$349$	−547.000	−0.0838975	−0.0419488	+	0.999120i	$0.513357\pi$
$350$	11940.0	1.82349
$351$	−2765.00	−0.420469
$352$	192.000	0.0290728
$353$	−6591.00	−0.993778	−0.496889	−	0.867814i	$-0.665524\pi$
$353$	−6591.00	−0.993778	−0.496889	+	0.867814i	$0.665524\pi$
$354$	−4536.00	−0.681033
$355$	−2646.00	−0.395592
$356$	1008.00	0.150067
$357$	−21420.0	−3.17554
$358$	−1182.00	−0.174499
$359$	−12180.0	−1.79063	−0.895315	−	0.445435i	$-0.853049\pi$
$359$	−12180.0	−1.79063	−0.895315	+	0.445435i	$0.853049\pi$
$360$	−3168.00	−0.463801
$361$	−5563.00	−0.811051
$362$	−5916.00	−0.858945
$363$	−9065.00	−1.31071
$364$	9480.00	1.36507
$365$	−11466.0	−1.64427
$366$	−1680.00	−0.239932
$367$	6114.00	0.869614	0.434807	−	0.900524i	$-0.356817\pi$
$367$	6114.00	0.869614	0.434807	+	0.900524i	$0.356817\pi$
$368$	0	0
$369$	8250.00	1.16390
$370$	−12744.0	−1.79062
$371$	9000.00	1.25945
$372$	1204.00	0.167808
$373$	−4230.00	−0.587188	−0.293594	−	0.955930i	$-0.594851\pi$
$373$	−4230.00	−0.587188	−0.293594	+	0.955930i	$0.594851\pi$
$374$	−1224.00	−0.169229
$375$	−9324.00	−1.28397
$376$	−1032.00	−0.141546
$377$	2607.00	0.356147
$378$	−2100.00	−0.285747
$379$	−6684.00	−0.905895	−0.452947	−	0.891537i	$-0.649627\pi$
$379$	−6684.00	−0.905895	−0.452947	+	0.891537i	$0.649627\pi$
$380$	−2592.00	−0.349913
$381$	−3857.00	−0.518635
$382$	−9300.00	−1.24563
$383$	−12336.0	−1.64580	−0.822898	−	0.568189i	$-0.807644\pi$
$383$	−12336.0	−1.64580	−0.822898	+	0.568189i	$0.807644\pi$
$384$	896.000	0.119072
$385$	−3240.00	−0.428898
$386$	−6566.00	−0.865805
$387$	−2112.00	−0.277413
$388$	4680.00	0.612348
$389$	−516.000	−0.0672551	−0.0336276	−	0.999434i	$-0.510706\pi$
$389$	−516.000	−0.0672551	−0.0336276	+	0.999434i	$0.510706\pi$
$390$	−19908.0	−2.58482
$391$	0	0
$392$	4456.00	0.574138
$393$	−2247.00	−0.288413
$394$	−3918.00	−0.500980
$395$	−8424.00	−1.07306
$396$	528.000	0.0670025
$397$	−4453.00	−0.562946	−0.281473	−	0.959569i	$-0.590823\pi$
$397$	−4453.00	−0.562946	−0.281473	+	0.959569i	$0.590823\pi$
$398$	9036.00	1.13802
$399$	7560.00	0.948555
$400$	3184.00	0.398000
$401$	3522.00	0.438604	0.219302	−	0.975657i	$-0.429622\pi$
$401$	3522.00	0.438604	0.219302	+	0.975657i	$0.429622\pi$
$402$	−8148.00	−1.01091
$403$	3397.00	0.419892
$404$	4392.00	0.540867
$405$	15102.0	1.85290
$406$	1980.00	0.242034
$407$	2124.00	0.258680
$408$	−5712.00	−0.693103
$409$	−3247.00	−0.392552	−0.196276	−	0.980549i	$-0.562885\pi$
$409$	−3247.00	−0.392552	−0.196276	+	0.980549i	$0.562885\pi$
$410$	−13500.0	−1.62614
$411$	−14784.0	−1.77431
$412$	264.000	0.0315688
$413$	−9720.00	−1.15809
$414$	0	0
$415$	17604.0	2.08228
$416$	2528.00	0.297946
$417$	−5341.00	−0.627218
$418$	432.000	0.0505498
$419$	−5940.00	−0.692573	−0.346286	−	0.938129i	$-0.612557\pi$
$419$	−5940.00	−0.692573	−0.346286	+	0.938129i	$0.612557\pi$
$420$	−15120.0	−1.75662
$421$	11562.0	1.33847	0.669237	−	0.743049i	$-0.266621\pi$
$421$	11562.0	1.33847	0.669237	+	0.743049i	$0.266621\pi$
$422$	−11272.0	−1.30027
$423$	−2838.00	−0.326213
$424$	2400.00	0.274892
$425$	−20298.0	−2.31670
$426$	2058.00	0.234062
$427$	−3600.00	−0.408000
$428$	5664.00	0.639672
$429$	3318.00	0.373414
$430$	3456.00	0.387589
$431$	3204.00	0.358077	0.179039	−	0.983842i	$-0.442701\pi$
$431$	3204.00	0.358077	0.179039	+	0.983842i	$0.442701\pi$
$432$	−560.000	−0.0623681
$433$	−14478.0	−1.60686	−0.803428	−	0.595402i	$-0.796993\pi$
$433$	−14478.0	−1.60686	−0.803428	+	0.595402i	$0.796993\pi$
$434$	2580.00	0.285355
$435$	−4158.00	−0.458301
$436$	768.000	0.0843590
$437$	0	0
$438$	8918.00	0.972873
$439$	−4579.00	−0.497822	−0.248911	−	0.968526i	$-0.580073\pi$
$439$	−4579.00	−0.497822	−0.248911	+	0.968526i	$0.580073\pi$
$440$	−864.000	−0.0936127
$441$	12254.0	1.32318
$442$	−16116.0	−1.73430
$443$	−3057.00	−0.327861	−0.163931	−	0.986472i	$-0.552417\pi$
$443$	−3057.00	−0.327861	−0.163931	+	0.986472i	$0.552417\pi$
$444$	9912.00	1.05947
$445$	−4536.00	−0.483207
$446$	6088.00	0.646357
$447$	15456.0	1.63544
$448$	1920.00	0.202481
$449$	2034.00	0.213787	0.106894	−	0.994270i	$-0.465910\pi$
$449$	2034.00	0.213787	0.106894	+	0.994270i	$0.465910\pi$
$450$	8756.00	0.917248
$451$	2250.00	0.234919
$452$	3528.00	0.367131
$453$	−22351.0	−2.31819
$454$	−7452.00	−0.770352
$455$	−42660.0	−4.39545
$456$	2016.00	0.207035
$457$	3210.00	0.328572	0.164286	−	0.986413i	$-0.447468\pi$
$457$	3210.00	0.328572	0.164286	+	0.986413i	$0.447468\pi$
$458$	−9024.00	−0.920663
$459$	3570.00	0.363036
$460$	0	0
$461$	−8835.00	−0.892596	−0.446298	−	0.894884i	$-0.647258\pi$
$461$	−8835.00	−0.892596	−0.446298	+	0.894884i	$0.647258\pi$
$462$	2520.00	0.253768
$463$	1532.00	0.153776	0.0768878	−	0.997040i	$-0.475502\pi$
$463$	1532.00	0.153776	0.0768878	+	0.997040i	$0.475502\pi$
$464$	528.000	0.0528271
$465$	−5418.00	−0.540331
$466$	6078.00	0.604202
$467$	−10356.0	−1.02616	−0.513082	−	0.858340i	$-0.671496\pi$
$467$	−10356.0	−1.02616	−0.513082	+	0.858340i	$0.671496\pi$
$468$	6952.00	0.686659
$469$	−17460.0	−1.71904
$470$	4644.00	0.455770
$471$	3612.00	0.353359
$472$	−2592.00	−0.252768
$473$	−576.000	−0.0559926
$474$	6552.00	0.634902
$475$	7164.00	0.692014
$476$	−12240.0	−1.17861
$477$	6600.00	0.633529
$478$	−10722.0	−1.02597
$479$	−4614.00	−0.440123	−0.220062	−	0.975486i	$-0.570626\pi$
$479$	−4614.00	−0.440123	−0.220062	+	0.975486i	$0.570626\pi$
$480$	−4032.00	−0.383406
$481$	27966.0	2.65102
$482$	4260.00	0.402568
$483$	0	0
$484$	−5180.00	−0.486476
$485$	−21060.0	−1.97172
$486$	−9856.00	−0.919912
$487$	−5731.00	−0.533257	−0.266629	−	0.963799i	$-0.585910\pi$
$487$	−5731.00	−0.533257	−0.266629	+	0.963799i	$0.585910\pi$
$488$	−960.000	−0.0890516
$489$	2947.00	0.272532
$490$	−20052.0	−1.84869
$491$	18129.0	1.66629	0.833147	−	0.553052i	$-0.186537\pi$
$491$	18129.0	1.66629	0.833147	+	0.553052i	$0.186537\pi$
$492$	10500.0	0.962147
$493$	−3366.00	−0.307499
$494$	5688.00	0.518047
$495$	−2376.00	−0.215744
$496$	688.000	0.0622825
$497$	4410.00	0.398019
$498$	−13692.0	−1.23203
$499$	15307.0	1.37322	0.686609	−	0.727027i	$-0.259099\pi$
$499$	15307.0	1.37322	0.686609	+	0.727027i	$0.259099\pi$
$500$	−5328.00	−0.476551
$501$	−11088.0	−0.988773
$502$	2076.00	0.184575
$503$	−2868.00	−0.254230	−0.127115	−	0.991888i	$-0.540572\pi$
$503$	−2868.00	−0.254230	−0.127115	+	0.991888i	$0.540572\pi$
$504$	5280.00	0.466647
$505$	−19764.0	−1.74156
$506$	0	0
$507$	28308.0	2.47969
$508$	−2204.00	−0.192493
$509$	9093.00	0.791827	0.395914	−	0.918288i	$-0.370428\pi$
$509$	9093.00	0.791827	0.395914	+	0.918288i	$0.370428\pi$
$510$	25704.0	2.23175
$511$	19110.0	1.65436
$512$	512.000	0.0441942
$513$	−1260.00	−0.108441
$514$	1446.00	0.124086
$515$	−1188.00	−0.101650
$516$	−2688.00	−0.229327
$517$	−774.000	−0.0658423
$518$	21240.0	1.80161
$519$	14490.0	1.22551
$520$	−11376.0	−0.959367
$521$	14700.0	1.23612	0.618060	−	0.786131i	$-0.287919\pi$
$521$	14700.0	1.23612	0.618060	+	0.786131i	$0.287919\pi$
$522$	1452.00	0.121748
$523$	−10626.0	−0.888418	−0.444209	−	0.895923i	$-0.646515\pi$
$523$	−10626.0	−0.888418	−0.444209	+	0.895923i	$0.646515\pi$
$524$	−1284.00	−0.107045
$525$	41790.0	3.47403
$526$	−6504.00	−0.539140
$527$	−4386.00	−0.362537
$528$	672.000	0.0553883
$529$	0	0
$530$	−10800.0	−0.885136
$531$	−7128.00	−0.582540
$532$	4320.00	0.352060
$533$	29625.0	2.40751
$534$	3528.00	0.285902
$535$	−25488.0	−2.05971
$536$	−4656.00	−0.375203
$537$	−4137.00	−0.332448
$538$	−8430.00	−0.675545
$539$	3342.00	0.267069
$540$	2520.00	0.200821
$541$	1901.00	0.151073	0.0755364	−	0.997143i	$-0.475933\pi$
$541$	1901.00	0.151073	0.0755364	+	0.997143i	$0.475933\pi$
$542$	−7456.00	−0.590890
$543$	−20706.0	−1.63643
$544$	−3264.00	−0.257248
$545$	−3456.00	−0.271631
$546$	33180.0	2.60068
$547$	−5483.00	−0.428585	−0.214293	−	0.976770i	$-0.568745\pi$
$547$	−5483.00	−0.428585	−0.214293	+	0.976770i	$0.568745\pi$
$548$	−8448.00	−0.658541
$549$	−2640.00	−0.205232
$550$	2388.00	0.185136
$551$	1188.00	0.0918521
$552$	0	0
$553$	14040.0	1.07964
$554$	−17014.0	−1.30479
$555$	−44604.0	−3.41141
$556$	−3052.00	−0.232794
$557$	10308.0	0.784136	0.392068	−	0.919936i	$-0.371760\pi$
$557$	10308.0	0.784136	0.392068	+	0.919936i	$0.371760\pi$
$558$	1892.00	0.143539
$559$	−7584.00	−0.573827
$560$	−8640.00	−0.651976
$561$	−4284.00	−0.322408
$562$	−4020.00	−0.301732
$563$	18288.0	1.36900	0.684500	−	0.729013i	$-0.260020\pi$
$563$	18288.0	1.36900	0.684500	+	0.729013i	$0.260020\pi$
$564$	−3612.00	−0.269668
$565$	−15876.0	−1.18214
$566$	18876.0	1.40180
$567$	−25170.0	−1.86427
$568$	1176.00	0.0868730
$569$	4962.00	0.365585	0.182792	−	0.983152i	$-0.441486\pi$
$569$	4962.00	0.365585	0.182792	+	0.983152i	$0.441486\pi$
$570$	−9072.00	−0.666639
$571$	−3126.00	−0.229105	−0.114553	−	0.993417i	$-0.536543\pi$
$571$	−3126.00	−0.229105	−0.114553	+	0.993417i	$0.536543\pi$
$572$	1896.00	0.138594
$573$	−32550.0	−2.37312
$574$	22500.0	1.63612
$575$	0	0
$576$	1408.00	0.101852
$577$	5537.00	0.399494	0.199747	−	0.979847i	$-0.435988\pi$
$577$	5537.00	0.399494	0.199747	+	0.979847i	$0.435988\pi$
$578$	10982.0	0.790296
$579$	−22981.0	−1.64950
$580$	−2376.00	−0.170100
$581$	−29340.0	−2.09506
$582$	16380.0	1.16662
$583$	1800.00	0.127870
$584$	5096.00	0.361086
$585$	−31284.0	−2.21100
$586$	−24.0000	−0.00169186
$587$	−8709.00	−0.612366	−0.306183	−	0.951973i	$-0.599052\pi$
$587$	−8709.00	−0.612366	−0.306183	+	0.951973i	$0.599052\pi$
$588$	15596.0	1.09382
$589$	1548.00	0.108292
$590$	11664.0	0.813897
$591$	−13713.0	−0.954446
$592$	5664.00	0.393225
$593$	9198.00	0.636959	0.318479	−	0.947930i	$-0.396828\pi$
$593$	9198.00	0.636959	0.318479	+	0.947930i	$0.396828\pi$
$594$	−420.000	−0.0290115
$595$	55080.0	3.79506
$596$	8832.00	0.607001
$597$	31626.0	2.16812
$598$	0	0
$599$	−20448.0	−1.39480	−0.697398	−	0.716684i	$-0.745659\pi$
$599$	−20448.0	−1.39480	−0.697398	+	0.716684i	$0.745659\pi$
$600$	11144.0	0.758253
$601$	14933.0	1.01353	0.506764	−	0.862085i	$-0.330842\pi$
$601$	14933.0	1.01353	0.506764	+	0.862085i	$0.330842\pi$
$602$	−5760.00	−0.389967
$603$	−12804.0	−0.864708
$604$	−12772.0	−0.860406
$605$	23310.0	1.56642
$606$	15372.0	1.03044
$607$	−23056.0	−1.54170	−0.770852	−	0.637014i	$-0.780169\pi$
$607$	−23056.0	−1.54170	−0.770852	+	0.637014i	$0.780169\pi$
$608$	1152.00	0.0768417
$609$	6930.00	0.461113
$610$	4320.00	0.286740
$611$	−10191.0	−0.674769
$612$	−8976.00	−0.592865
$613$	2442.00	0.160900	0.0804498	−	0.996759i	$-0.474364\pi$
$613$	2442.00	0.160900	0.0804498	+	0.996759i	$0.474364\pi$
$614$	−20056.0	−1.31823
$615$	−47250.0	−3.09806
$616$	1440.00	0.0941871
$617$	12180.0	0.794730	0.397365	−	0.917661i	$-0.369925\pi$
$617$	12180.0	0.794730	0.397365	+	0.917661i	$0.369925\pi$
$618$	924.000	0.0601436
$619$	−12516.0	−0.812699	−0.406349	−	0.913718i	$-0.633198\pi$
$619$	−12516.0	−0.812699	−0.406349	+	0.913718i	$0.633198\pi$
$620$	−3096.00	−0.200546
$621$	0	0
$622$	14502.0	0.934851
$623$	7560.00	0.486172
$624$	8848.00	0.567634
$625$	−899.000	−0.0575360
$626$	8904.00	0.568491
$627$	1512.00	0.0963054
$628$	2064.00	0.131151
$629$	−36108.0	−2.28890
$630$	−23760.0	−1.50257
$631$	−22308.0	−1.40740	−0.703698	−	0.710499i	$-0.748469\pi$
$631$	−22308.0	−1.40740	−0.703698	+	0.710499i	$0.748469\pi$
$632$	3744.00	0.235646
$633$	−39452.0	−2.47721
$634$	6588.00	0.412686
$635$	9918.00	0.619817
$636$	8400.00	0.523713
$637$	44003.0	2.73699
$638$	396.000	0.0245733
$639$	3234.00	0.200211
$640$	−2304.00	−0.142302
$641$	7572.00	0.466577	0.233289	−	0.972408i	$-0.425051\pi$
$641$	7572.00	0.466577	0.233289	+	0.972408i	$0.425051\pi$
$642$	19824.0	1.21868
$643$	−16254.0	−0.996882	−0.498441	−	0.866924i	$-0.666094\pi$
$643$	−16254.0	−0.996882	−0.498441	+	0.866924i	$0.666094\pi$
$644$	0	0
$645$	12096.0	0.738418
$646$	−7344.00	−0.447285
$647$	2895.00	0.175911	0.0879553	−	0.996124i	$-0.471967\pi$
$647$	2895.00	0.175911	0.0879553	+	0.996124i	$0.471967\pi$
$648$	−6712.00	−0.406902
$649$	−1944.00	−0.117579
$650$	31442.0	1.89732
$651$	9030.00	0.543646
$652$	1684.00	0.101151
$653$	22107.0	1.32483	0.662415	−	0.749137i	$-0.269532\pi$
$653$	22107.0	1.32483	0.662415	+	0.749137i	$0.269532\pi$
$654$	2688.00	0.160717
$655$	5778.00	0.344680
$656$	6000.00	0.357105
$657$	14014.0	0.832174
$658$	−7740.00	−0.458566
$659$	−9906.00	−0.585558	−0.292779	−	0.956180i	$-0.594580\pi$
$659$	−9906.00	−0.585558	−0.292779	+	0.956180i	$0.594580\pi$
$660$	−3024.00	−0.178347
$661$	19992.0	1.17640	0.588199	−	0.808716i	$-0.299837\pi$
$661$	19992.0	1.17640	0.588199	+	0.808716i	$0.299837\pi$
$662$	6890.00	0.404513
$663$	−56406.0	−3.30411
$664$	−7824.00	−0.457274
$665$	−19440.0	−1.13361
$666$	15576.0	0.906243
$667$	0	0
$668$	−6336.00	−0.366987
$669$	21308.0	1.23141
$670$	20952.0	1.20813
$671$	−720.000	−0.0414237
$672$	6720.00	0.385758
$673$	1771.00	0.101437	0.0507184	−	0.998713i	$-0.483849\pi$
$673$	1771.00	0.101437	0.0507184	+	0.998713i	$0.483849\pi$
$674$	7800.00	0.445764
$675$	−6965.00	−0.397160
$676$	16176.0	0.920346
$677$	23112.0	1.31206	0.656031	−	0.754734i	$-0.272234\pi$
$677$	23112.0	1.31206	0.656031	+	0.754734i	$0.272234\pi$
$678$	12348.0	0.699443
$679$	35100.0	1.98382
$680$	14688.0	0.828322
$681$	−26082.0	−1.46764
$682$	516.000	0.0289716
$683$	−9219.00	−0.516479	−0.258240	−	0.966081i	$-0.583142\pi$
$683$	−9219.00	−0.516479	−0.258240	+	0.966081i	$0.583142\pi$
$684$	3168.00	0.177093
$685$	38016.0	2.12046
$686$	12840.0	0.714626
$687$	−31584.0	−1.75401
$688$	−1536.00	−0.0851155
$689$	23700.0	1.31045
$690$	0	0
$691$	8836.00	0.486450	0.243225	−	0.969970i	$-0.421795\pi$
$691$	8836.00	0.486450	0.243225	+	0.969970i	$0.421795\pi$
$692$	8280.00	0.454853
$693$	3960.00	0.217068
$694$	10512.0	0.574971
$695$	13734.0	0.749583
$696$	1848.00	0.100644
$697$	−38250.0	−2.07865
$698$	−1094.00	−0.0593245
$699$	21273.0	1.15110
$700$	23880.0	1.28940
$701$	−25146.0	−1.35485	−0.677426	−	0.735591i	$-0.736905\pi$
$701$	−25146.0	−1.35485	−0.677426	+	0.735591i	$0.736905\pi$
$702$	−5530.00	−0.297317
$703$	12744.0	0.683711
$704$	384.000	0.0205576
$705$	16254.0	0.868314
$706$	−13182.0	−0.702707
$707$	32940.0	1.75224
$708$	−9072.00	−0.481563
$709$	−13446.0	−0.712236	−0.356118	−	0.934441i	$-0.615900\pi$
$709$	−13446.0	−0.712236	−0.356118	+	0.934441i	$0.615900\pi$
$710$	−5292.00	−0.279726
$711$	10296.0	0.543080
$712$	2016.00	0.106113
$713$	0	0
$714$	−42840.0	−2.24544
$715$	−8532.00	−0.446264
$716$	−2364.00	−0.123389
$717$	−37527.0	−1.95463
$718$	−24360.0	−1.26617
$719$	20736.0	1.07555	0.537776	−	0.843088i	$-0.319265\pi$
$719$	20736.0	1.07555	0.537776	+	0.843088i	$0.319265\pi$
$720$	−6336.00	−0.327957
$721$	1980.00	0.102273
$722$	−11126.0	−0.573500
$723$	14910.0	0.766956
$724$	−11832.0	−0.607366
$725$	6567.00	0.336403
$726$	−18130.0	−0.926815
$727$	−3438.00	−0.175390	−0.0876949	−	0.996147i	$-0.527950\pi$
$727$	−3438.00	−0.175390	−0.0876949	+	0.996147i	$0.527950\pi$
$728$	18960.0	0.965253
$729$	−11843.0	−0.601687
$730$	−22932.0	−1.16267
$731$	9792.00	0.495445
$732$	−3360.00	−0.169657
$733$	−26934.0	−1.35720	−0.678602	−	0.734507i	$-0.737414\pi$
$733$	−26934.0	−1.35720	−0.678602	+	0.734507i	$0.737414\pi$
$734$	12228.0	0.614910
$735$	−70182.0	−3.52204
$736$	0	0
$737$	−3492.00	−0.174531
$738$	16500.0	0.822999
$739$	9461.00	0.470945	0.235473	−	0.971881i	$-0.424336\pi$
$739$	9461.00	0.470945	0.235473	+	0.971881i	$0.424336\pi$
$740$	−25488.0	−1.26616
$741$	19908.0	0.986962
$742$	18000.0	0.890567
$743$	24006.0	1.18532	0.592661	−	0.805452i	$-0.298077\pi$
$743$	24006.0	1.18532	0.592661	+	0.805452i	$0.298077\pi$
$744$	2408.00	0.118658
$745$	−39744.0	−1.95451
$746$	−8460.00	−0.415205
$747$	−21516.0	−1.05385
$748$	−2448.00	−0.119663
$749$	42480.0	2.07234
$750$	−18648.0	−0.907905
$751$	1284.00	0.0623886	0.0311943	−	0.999513i	$-0.490069\pi$
$751$	1284.00	0.0623886	0.0311943	+	0.999513i	$0.490069\pi$
$752$	−2064.00	−0.100088
$753$	7266.00	0.351644
$754$	5214.00	0.251834
$755$	57474.0	2.77045
$756$	−4200.00	−0.202054
$757$	11850.0	0.568951	0.284475	−	0.958683i	$-0.408181\pi$
$757$	11850.0	0.568951	0.284475	+	0.958683i	$0.408181\pi$
$758$	−13368.0	−0.640564
$759$	0	0
$760$	−5184.00	−0.247426
$761$	24765.0	1.17967	0.589836	−	0.807523i	$-0.299192\pi$
$761$	24765.0	1.17967	0.589836	+	0.807523i	$0.299192\pi$
$762$	−7714.00	−0.366731
$763$	5760.00	0.273298
$764$	−18600.0	−0.880791
$765$	40392.0	1.90899
$766$	−24672.0	−1.16375
$767$	−25596.0	−1.20498
$768$	1792.00	0.0841969
$769$	3906.00	0.183165	0.0915826	−	0.995797i	$-0.470807\pi$
$769$	3906.00	0.183165	0.0915826	+	0.995797i	$0.470807\pi$
$770$	−6480.00	−0.303277
$771$	5061.00	0.236404
$772$	−13132.0	−0.612216
$773$	26820.0	1.24793	0.623964	−	0.781453i	$-0.285521\pi$
$773$	26820.0	1.24793	0.623964	+	0.781453i	$0.285521\pi$
$774$	−4224.00	−0.196161
$775$	8557.00	0.396615
$776$	9360.00	0.432995
$777$	74340.0	3.43235
$778$	−1032.00	−0.0475565
$779$	13500.0	0.620908
$780$	−39816.0	−1.82775
$781$	882.000	0.0404103
$782$	0	0
$783$	−1155.00	−0.0527156
$784$	8912.00	0.405977
$785$	−9288.00	−0.422297
$786$	−4494.00	−0.203939
$787$	−25284.0	−1.14521	−0.572603	−	0.819833i	$-0.694066\pi$
$787$	−25284.0	−1.14521	−0.572603	+	0.819833i	$0.694066\pi$
$788$	−7836.00	−0.354246
$789$	−22764.0	−1.02715
$790$	−16848.0	−0.758766
$791$	26460.0	1.18939
$792$	1056.00	0.0473779
$793$	−9480.00	−0.424520
$794$	−8906.00	−0.398063
$795$	−37800.0	−1.68632
$796$	18072.0	0.804705
$797$	8124.00	0.361063	0.180531	−	0.983569i	$-0.442218\pi$
$797$	8124.00	0.361063	0.180531	+	0.983569i	$0.442218\pi$
$798$	15120.0	0.670730
$799$	13158.0	0.582599
$800$	6368.00	0.281428
$801$	5544.00	0.244554
$802$	7044.00	0.310140
$803$	3822.00	0.167964
$804$	−16296.0	−0.714820
$805$	0	0
$806$	6794.00	0.296909
$807$	−29505.0	−1.28702
$808$	8784.00	0.382451
$809$	37530.0	1.63101	0.815503	−	0.578752i	$-0.196460\pi$
$809$	37530.0	1.63101	0.815503	+	0.578752i	$0.196460\pi$
$810$	30204.0	1.31020
$811$	8395.00	0.363487	0.181744	−	0.983346i	$-0.441826\pi$
$811$	8395.00	0.363487	0.181744	+	0.983346i	$0.441826\pi$
$812$	3960.00	0.171144
$813$	−26096.0	−1.12574
$814$	4248.00	0.182914
$815$	−7578.00	−0.325700
$816$	−11424.0	−0.490098
$817$	−3456.00	−0.147993
$818$	−6494.00	−0.277576
$819$	52140.0	2.22457
$820$	−27000.0	−1.14985
$821$	40194.0	1.70862	0.854312	−	0.519761i	$-0.173979\pi$
$821$	40194.0	1.70862	0.854312	+	0.519761i	$0.173979\pi$
$822$	−29568.0	−1.25463
$823$	19303.0	0.817570	0.408785	−	0.912631i	$-0.365953\pi$
$823$	19303.0	0.817570	0.408785	+	0.912631i	$0.365953\pi$
$824$	528.000	0.0223225
$825$	8358.00	0.352713
$826$	−19440.0	−0.818891
$827$	6876.00	0.289120	0.144560	−	0.989496i	$-0.453823\pi$
$827$	6876.00	0.289120	0.144560	+	0.989496i	$0.453823\pi$
$828$	0	0
$829$	−28618.0	−1.19897	−0.599484	−	0.800387i	$-0.704627\pi$
$829$	−28618.0	−1.19897	−0.599484	+	0.800387i	$0.704627\pi$
$830$	35208.0	1.47239
$831$	−59549.0	−2.48584
$832$	5056.00	0.210679
$833$	−56814.0	−2.36313
$834$	−10682.0	−0.443510
$835$	28512.0	1.18167
$836$	864.000	0.0357441
$837$	−1505.00	−0.0621510
$838$	−11880.0	−0.489723
$839$	11802.0	0.485638	0.242819	−	0.970072i	$-0.421928\pi$
$839$	11802.0	0.485638	0.242819	+	0.970072i	$0.421928\pi$
$840$	−30240.0	−1.24212
$841$	−23300.0	−0.955349
$842$	23124.0	0.946444
$843$	−14070.0	−0.574848
$844$	−22544.0	−0.919427
$845$	−72792.0	−2.96346
$846$	−5676.00	−0.230668
$847$	−38850.0	−1.57604
$848$	4800.00	0.194378
$849$	66066.0	2.67065
$850$	−40596.0	−1.63815
$851$	0	0
$852$	4116.00	0.165507
$853$	−20374.0	−0.817811	−0.408905	−	0.912577i	$-0.634089\pi$
$853$	−20374.0	−0.817811	−0.408905	+	0.912577i	$0.634089\pi$
$854$	−7200.00	−0.288500
$855$	−14256.0	−0.570228
$856$	11328.0	0.452317
$857$	25527.0	1.01749	0.508743	−	0.860918i	$-0.330110\pi$
$857$	25527.0	1.01749	0.508743	+	0.860918i	$0.330110\pi$
$858$	6636.00	0.264043
$859$	41735.0	1.65772	0.828859	−	0.559458i	$-0.188990\pi$
$859$	41735.0	1.65772	0.828859	+	0.559458i	$0.188990\pi$
$860$	6912.00	0.274067
$861$	78750.0	3.11706
$862$	6408.00	0.253199
$863$	3513.00	0.138568	0.0692838	−	0.997597i	$-0.477929\pi$
$863$	3513.00	0.138568	0.0692838	+	0.997597i	$0.477929\pi$
$864$	−1120.00	−0.0441009
$865$	−37260.0	−1.46460
$866$	−28956.0	−1.13622
$867$	38437.0	1.50564
$868$	5160.00	0.201776
$869$	2808.00	0.109614
$870$	−8316.00	−0.324068
$871$	−45978.0	−1.78864
$872$	1536.00	0.0596508
$873$	25740.0	0.997900
$874$	0	0
$875$	−39960.0	−1.54388
$876$	17836.0	0.687925
$877$	3526.00	0.135763	0.0678817	−	0.997693i	$-0.478376\pi$
$877$	3526.00	0.135763	0.0678817	+	0.997693i	$0.478376\pi$
$878$	−9158.00	−0.352013
$879$	−84.0000	−0.00322326
$880$	−1728.00	−0.0661942
$881$	−7818.00	−0.298973	−0.149486	−	0.988764i	$-0.547762\pi$
$881$	−7818.00	−0.298973	−0.149486	+	0.988764i	$0.547762\pi$
$882$	24508.0	0.935632
$883$	4804.00	0.183089	0.0915444	−	0.995801i	$-0.470820\pi$
$883$	4804.00	0.183089	0.0915444	+	0.995801i	$0.470820\pi$
$884$	−32232.0	−1.22633
$885$	40824.0	1.55060
$886$	−6114.00	−0.231833
$887$	−38613.0	−1.46167	−0.730833	−	0.682556i	$-0.760868\pi$
$887$	−38613.0	−1.46167	−0.730833	+	0.682556i	$0.760868\pi$
$888$	19824.0	0.749155
$889$	−16530.0	−0.623620
$890$	−9072.00	−0.341679
$891$	−5034.00	−0.189276
$892$	12176.0	0.457043
$893$	−4644.00	−0.174026
$894$	30912.0	1.15643
$895$	10638.0	0.397306
$896$	3840.00	0.143176
$897$	0	0
$898$	4068.00	0.151170
$899$	1419.00	0.0526433
$900$	17512.0	0.648593
$901$	−30600.0	−1.13145
$902$	4500.00	0.166113
$903$	−20160.0	−0.742949
$904$	7056.00	0.259601
$905$	53244.0	1.95568
$906$	−44702.0	−1.63921
$907$	−47160.0	−1.72649	−0.863243	−	0.504789i	$-0.831570\pi$
$907$	−47160.0	−1.72649	−0.863243	+	0.504789i	$0.831570\pi$
$908$	−14904.0	−0.544721
$909$	24156.0	0.881412
$910$	−85320.0	−3.10806
$911$	−20544.0	−0.747149	−0.373575	−	0.927600i	$-0.621868\pi$
$911$	−20544.0	−0.747149	−0.373575	+	0.927600i	$0.621868\pi$
$912$	4032.00	0.146396
$913$	−5868.00	−0.212708
$914$	6420.00	0.232336
$915$	15120.0	0.546286
$916$	−18048.0	−0.651007
$917$	−9630.00	−0.346795
$918$	7140.00	0.256705
$919$	42606.0	1.52932	0.764658	−	0.644436i	$-0.222908\pi$
$919$	42606.0	1.52932	0.764658	+	0.644436i	$0.222908\pi$
$920$	0	0
$921$	−70196.0	−2.51144
$922$	−17670.0	−0.631161
$923$	11613.0	0.414135
$924$	5040.00	0.179441
$925$	70446.0	2.50405
$926$	3064.00	0.108736
$927$	1452.00	0.0514455
$928$	1056.00	0.0373544
$929$	23559.0	0.832019	0.416010	−	0.909360i	$-0.363428\pi$
$929$	23559.0	0.832019	0.416010	+	0.909360i	$0.363428\pi$
$930$	−10836.0	−0.382071
$931$	20052.0	0.705884
$932$	12156.0	0.427235
$933$	50757.0	1.78104
$934$	−20712.0	−0.725607
$935$	11016.0	0.385307
$936$	13904.0	0.485541
$937$	44382.0	1.54738	0.773691	−	0.633563i	$-0.218408\pi$
$937$	44382.0	1.54738	0.773691	+	0.633563i	$0.218408\pi$
$938$	−34920.0	−1.21554
$939$	31164.0	1.08307
$940$	9288.00	0.322278
$941$	25098.0	0.869470	0.434735	−	0.900558i	$-0.356842\pi$
$941$	25098.0	0.869470	0.434735	+	0.900558i	$0.356842\pi$
$942$	7224.00	0.249863
$943$	0	0
$944$	−5184.00	−0.178734
$945$	18900.0	0.650600
$946$	−1152.00	−0.0395928
$947$	30507.0	1.04683	0.523413	−	0.852079i	$-0.324658\pi$
$947$	30507.0	1.04683	0.523413	+	0.852079i	$0.324658\pi$
$948$	13104.0	0.448943
$949$	50323.0	1.72134
$950$	14328.0	0.489328
$951$	23058.0	0.786232
$952$	−24480.0	−0.833405
$953$	−45492.0	−1.54631	−0.773153	−	0.634219i	$-0.781322\pi$
$953$	−45492.0	−1.54631	−0.773153	+	0.634219i	$0.781322\pi$
$954$	13200.0	0.447973
$955$	83700.0	2.83609
$956$	−21444.0	−0.725469
$957$	1386.00	0.0468161
$958$	−9228.00	−0.311214
$959$	−63360.0	−2.13347
$960$	−8064.00	−0.271109
$961$	−27942.0	−0.937934
$962$	55932.0	1.87455
$963$	31152.0	1.04243
$964$	8520.00	0.284658
$965$	59094.0	1.97130
$966$	0	0
$967$	42181.0	1.40274	0.701370	−	0.712797i	$-0.252572\pi$
$967$	42181.0	1.40274	0.701370	+	0.712797i	$0.252572\pi$
$968$	−10360.0	−0.343991
$969$	−25704.0	−0.852148
$970$	−42120.0	−1.39422
$971$	−55128.0	−1.82198	−0.910990	−	0.412429i	$-0.864680\pi$
$971$	−55128.0	−1.82198	−0.910990	+	0.412429i	$0.864680\pi$
$972$	−19712.0	−0.650476
$973$	−22890.0	−0.754183
$974$	−11462.0	−0.377070
$975$	110047.	3.61469
$976$	−1920.00	−0.0629690
$977$	−24294.0	−0.795531	−0.397766	−	0.917487i	$-0.630214\pi$
$977$	−24294.0	−0.795531	−0.397766	+	0.917487i	$0.630214\pi$
$978$	5894.00	0.192709
$979$	1512.00	0.0493603
$980$	−40104.0	−1.30722
$981$	4224.00	0.137474
$982$	36258.0	1.17825
$983$	34320.0	1.11357	0.556784	−	0.830657i	$-0.312035\pi$
$983$	34320.0	1.11357	0.556784	+	0.830657i	$0.312035\pi$
$984$	21000.0	0.680341
$985$	35262.0	1.14065
$986$	−6732.00	−0.217435
$987$	−27090.0	−0.873642
$988$	11376.0	0.366315
$989$	0	0
$990$	−4752.00	−0.152554
$991$	−31232.0	−1.00113	−0.500564	−	0.865700i	$-0.666874\pi$
$991$	−31232.0	−1.00113	−0.500564	+	0.865700i	$0.666874\pi$
$992$	1376.00	0.0440404
$993$	24115.0	0.770661
$994$	8820.00	0.281442
$995$	−81324.0	−2.59110
$996$	−27384.0	−0.871180
$997$	17606.0	0.559265	0.279633	−	0.960107i	$-0.409787\pi$
$997$	17606.0	0.559265	0.279633	+	0.960107i	$0.409787\pi$
$998$	30614.0	0.971011
$999$	−12390.0	−0.392395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1058.4.a.c.1.1	✓	1
23.22	odd	2		1058.4.a.d.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1058.4.a.c.1.1	✓	1	1.1	even	1	trivial
1058.4.a.d.1.1	yes	1	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1058.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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