LMFDB - Embedded newform 1150.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,4,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1150.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:	$67.8521965066$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} +4.00000 q^{6} -21.0000 q^{7} -8.00000 q^{8} -23.0000 q^{9} +47.0000 q^{11} -8.00000 q^{12} -57.0000 q^{13} +42.0000 q^{14} +16.0000 q^{16} +84.0000 q^{17} +46.0000 q^{18} -5.00000 q^{19} +42.0000 q^{21} -94.0000 q^{22} -23.0000 q^{23} +16.0000 q^{24} +114.000 q^{26} +100.000 q^{27} -84.0000 q^{28} +285.000 q^{29} +82.0000 q^{31} -32.0000 q^{32} -94.0000 q^{33} -168.000 q^{34} -92.0000 q^{36} +54.0000 q^{37} +10.0000 q^{38} +114.000 q^{39} -53.0000 q^{41} -84.0000 q^{42} -197.000 q^{43} +188.000 q^{44} +46.0000 q^{46} +124.000 q^{47} -32.0000 q^{48} +98.0000 q^{49} -168.000 q^{51} -228.000 q^{52} +148.000 q^{53} -200.000 q^{54} +168.000 q^{56} +10.0000 q^{57} -570.000 q^{58} +30.0000 q^{59} -578.000 q^{61} -164.000 q^{62} +483.000 q^{63} +64.0000 q^{64} +188.000 q^{66} -296.000 q^{67} +336.000 q^{68} +46.0000 q^{69} +422.000 q^{71} +184.000 q^{72} -487.000 q^{73} -108.000 q^{74} -20.0000 q^{76} -987.000 q^{77} -228.000 q^{78} -405.000 q^{79} +421.000 q^{81} +106.000 q^{82} -397.000 q^{83} +168.000 q^{84} +394.000 q^{86} -570.000 q^{87} -376.000 q^{88} +730.000 q^{89} +1197.00 q^{91} -92.0000 q^{92} -164.000 q^{93} -248.000 q^{94} +64.0000 q^{96} +64.0000 q^{97} -196.000 q^{98} -1081.00 q^{99} +O(q^{100})\)

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
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	4.00000	0.272166
$7$	−21.0000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−21.0000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−8.00000	−0.353553
$9$	−23.0000	−0.851852
$10$	0	0
$11$	47.0000	1.28828	0.644138	−	0.764909i	$-0.277216\pi$
$11$	47.0000	1.28828	0.644138	+	0.764909i	$0.277216\pi$
$12$	−8.00000	−0.192450
$13$	−57.0000	−1.21607	−0.608037	−	0.793909i	$-0.708043\pi$
$13$	−57.0000	−1.21607	−0.608037	+	0.793909i	$0.708043\pi$
$14$	42.0000	0.801784
$15$	0	0
$16$	16.0000	0.250000
$17$	84.0000	1.19841	0.599206	−	0.800595i	$-0.295483\pi$
$17$	84.0000	1.19841	0.599206	+	0.800595i	$0.295483\pi$
$18$	46.0000	0.602350
$19$	−5.00000	−0.0603726	−0.0301863	−	0.999544i	$-0.509610\pi$
$19$	−5.00000	−0.0603726	−0.0301863	+	0.999544i	$0.509610\pi$
$20$	0	0
$21$	42.0000	0.436436
$22$	−94.0000	−0.910949
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	16.0000	0.136083
$25$	0	0
$26$	114.000	0.859894
$27$	100.000	0.712778
$28$	−84.0000	−0.566947
$29$	285.000	1.82494	0.912468	−	0.409147i	$-0.134174\pi$
$29$	285.000	1.82494	0.912468	+	0.409147i	$0.134174\pi$
$30$	0	0
$31$	82.0000	0.475085	0.237542	−	0.971377i	$-0.423658\pi$
$31$	82.0000	0.475085	0.237542	+	0.971377i	$0.423658\pi$
$32$	−32.0000	−0.176777
$33$	−94.0000	−0.495858
$34$	−168.000	−0.847405
$35$	0	0
$36$	−92.0000	−0.425926
$37$	54.0000	0.239934	0.119967	−	0.992778i	$-0.461721\pi$
$37$	54.0000	0.239934	0.119967	+	0.992778i	$0.461721\pi$
$38$	10.0000	0.0426898
$39$	114.000	0.468067
$40$	0	0
$41$	−53.0000	−0.201883	−0.100942	−	0.994892i	$-0.532186\pi$
$41$	−53.0000	−0.201883	−0.100942	+	0.994892i	$0.532186\pi$
$42$	−84.0000	−0.308607
$43$	−197.000	−0.698656	−0.349328	−	0.937000i	$-0.613590\pi$
$43$	−197.000	−0.698656	−0.349328	+	0.937000i	$0.613590\pi$
$44$	188.000	0.644138
$45$	0	0
$46$	46.0000	0.147442
$47$	124.000	0.384835	0.192418	−	0.981313i	$-0.438367\pi$
$47$	124.000	0.384835	0.192418	+	0.981313i	$0.438367\pi$
$48$	−32.0000	−0.0962250
$49$	98.0000	0.285714
$50$	0	0
$51$	−168.000	−0.461269
$52$	−228.000	−0.608037
$53$	148.000	0.383573	0.191786	−	0.981437i	$-0.438572\pi$
$53$	148.000	0.383573	0.191786	+	0.981437i	$0.438572\pi$
$54$	−200.000	−0.504010
$55$	0	0
$56$	168.000	0.400892
$57$	10.0000	0.0232374
$58$	−570.000	−1.29043
$59$	30.0000	0.0661978	0.0330989	−	0.999452i	$-0.489462\pi$
$59$	30.0000	0.0661978	0.0330989	+	0.999452i	$0.489462\pi$
$60$	0	0
$61$	−578.000	−1.21320	−0.606601	−	0.795006i	$-0.707467\pi$
$61$	−578.000	−1.21320	−0.606601	+	0.795006i	$0.707467\pi$
$62$	−164.000	−0.335936
$63$	483.000	0.965909
$64$	64.0000	0.125000
$65$	0	0
$66$	188.000	0.350624
$67$	−296.000	−0.539734	−0.269867	−	0.962898i	$-0.586980\pi$
$67$	−296.000	−0.539734	−0.269867	+	0.962898i	$0.586980\pi$
$68$	336.000	0.599206
$69$	46.0000	0.0802572
$70$	0	0
$71$	422.000	0.705383	0.352691	−	0.935740i	$-0.385267\pi$
$71$	422.000	0.705383	0.352691	+	0.935740i	$0.385267\pi$
$72$	184.000	0.301175
$73$	−487.000	−0.780809	−0.390404	−	0.920643i	$-0.627665\pi$
$73$	−487.000	−0.780809	−0.390404	+	0.920643i	$0.627665\pi$
$74$	−108.000	−0.169659
$75$	0	0
$76$	−20.0000	−0.0301863
$77$	−987.000	−1.46077
$78$	−228.000	−0.330973
$79$	−405.000	−0.576786	−0.288393	−	0.957512i	$-0.593121\pi$
$79$	−405.000	−0.576786	−0.288393	+	0.957512i	$0.593121\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	106.000	0.142753
$83$	−397.000	−0.525017	−0.262509	−	0.964930i	$-0.584550\pi$
$83$	−397.000	−0.525017	−0.262509	+	0.964930i	$0.584550\pi$
$84$	168.000	0.218218
$85$	0	0
$86$	394.000	0.494025
$87$	−570.000	−0.702419
$88$	−376.000	−0.455474
$89$	730.000	0.869436	0.434718	−	0.900567i	$-0.356848\pi$
$89$	730.000	0.869436	0.434718	+	0.900567i	$0.356848\pi$
$90$	0	0
$91$	1197.00	1.37890
$92$	−92.0000	−0.104257
$93$	−164.000	−0.182860
$94$	−248.000	−0.272120
$95$	0	0
$96$	64.0000	0.0680414
$97$	64.0000	0.0669919	0.0334960	−	0.999439i	$-0.489336\pi$
$97$	64.0000	0.0669919	0.0334960	+	0.999439i	$0.489336\pi$
$98$	−196.000	−0.202031
$99$	−1081.00	−1.09742
$100$	0	0
$101$	1002.00	0.987156	0.493578	−	0.869702i	$-0.335689\pi$
$101$	1002.00	0.987156	0.493578	+	0.869702i	$0.335689\pi$
$102$	336.000	0.326166
$103$	−1807.00	−1.72863	−0.864316	−	0.502950i	$-0.832248\pi$
$103$	−1807.00	−1.72863	−0.864316	+	0.502950i	$0.832248\pi$
$104$	456.000	0.429947
$105$	0	0
$106$	−296.000	−0.271227
$107$	1664.00	1.50341	0.751705	−	0.659499i	$-0.229232\pi$
$107$	1664.00	1.50341	0.751705	+	0.659499i	$0.229232\pi$
$108$	400.000	0.356389
$109$	470.000	0.413008	0.206504	−	0.978446i	$-0.433791\pi$
$109$	470.000	0.413008	0.206504	+	0.978446i	$0.433791\pi$
$110$	0	0
$111$	−108.000	−0.0923505
$112$	−336.000	−0.283473
$113$	−992.000	−0.825836	−0.412918	−	0.910768i	$-0.635490\pi$
$113$	−992.000	−0.825836	−0.412918	+	0.910768i	$0.635490\pi$
$114$	−20.0000	−0.0164313
$115$	0	0
$116$	1140.00	0.912468
$117$	1311.00	1.03591
$118$	−60.0000	−0.0468089
$119$	−1764.00	−1.35887
$120$	0	0
$121$	878.000	0.659654
$122$	1156.00	0.857863
$123$	106.000	0.0777049
$124$	328.000	0.237542
$125$	0	0
$126$	−966.000	−0.683001
$127$	2274.00	1.58886	0.794429	−	0.607358i	$-0.207770\pi$
$127$	2274.00	1.58886	0.794429	+	0.607358i	$0.207770\pi$
$128$	−128.000	−0.0883883
$129$	394.000	0.268913
$130$	0	0
$131$	1802.00	1.20184	0.600922	−	0.799308i	$-0.294800\pi$
$131$	1802.00	1.20184	0.600922	+	0.799308i	$0.294800\pi$
$132$	−376.000	−0.247929
$133$	105.000	0.0684561
$134$	592.000	0.381649
$135$	0	0
$136$	−672.000	−0.423702
$137$	−106.000	−0.0661036	−0.0330518	−	0.999454i	$-0.510523\pi$
$137$	−106.000	−0.0661036	−0.0330518	+	0.999454i	$0.510523\pi$
$138$	−92.0000	−0.0567504
$139$	−2700.00	−1.64756	−0.823781	−	0.566909i	$-0.808139\pi$
$139$	−2700.00	−1.64756	−0.823781	+	0.566909i	$0.808139\pi$
$140$	0	0
$141$	−248.000	−0.148123
$142$	−844.000	−0.498781
$143$	−2679.00	−1.56664
$144$	−368.000	−0.212963
$145$	0	0
$146$	974.000	0.552115
$147$	−196.000	−0.109971
$148$	216.000	0.119967
$149$	−890.000	−0.489340	−0.244670	−	0.969606i	$-0.578680\pi$
$149$	−890.000	−0.489340	−0.244670	+	0.969606i	$0.578680\pi$
$150$	0	0
$151$	−3398.00	−1.83129	−0.915647	−	0.401984i	$-0.868321\pi$
$151$	−3398.00	−1.83129	−0.915647	+	0.401984i	$0.868321\pi$
$152$	40.0000	0.0213449
$153$	−1932.00	−1.02087
$154$	1974.00	1.03292
$155$	0	0
$156$	456.000	0.234033
$157$	−2976.00	−1.51281	−0.756403	−	0.654105i	$-0.773045\pi$
$157$	−2976.00	−1.51281	−0.756403	+	0.654105i	$0.773045\pi$
$158$	810.000	0.407849
$159$	−296.000	−0.147637
$160$	0	0
$161$	483.000	0.236433
$162$	−842.000	−0.408357
$163$	−512.000	−0.246030	−0.123015	−	0.992405i	$-0.539256\pi$
$163$	−512.000	−0.246030	−0.123015	+	0.992405i	$0.539256\pi$
$164$	−212.000	−0.100942
$165$	0	0
$166$	794.000	0.371243
$167$	−1426.00	−0.660762	−0.330381	−	0.943848i	$-0.607177\pi$
$167$	−1426.00	−0.660762	−0.330381	+	0.943848i	$0.607177\pi$
$168$	−336.000	−0.154303
$169$	1052.00	0.478835
$170$	0	0
$171$	115.000	0.0514285
$172$	−788.000	−0.349328
$173$	−1047.00	−0.460127	−0.230063	−	0.973176i	$-0.573893\pi$
$173$	−1047.00	−0.460127	−0.230063	+	0.973176i	$0.573893\pi$
$174$	1140.00	0.496685
$175$	0	0
$176$	752.000	0.322069
$177$	−60.0000	−0.0254795
$178$	−1460.00	−0.614784
$179$	−1380.00	−0.576235	−0.288117	−	0.957595i	$-0.593029\pi$
$179$	−1380.00	−0.576235	−0.288117	+	0.957595i	$0.593029\pi$
$180$	0	0
$181$	1332.00	0.546999	0.273499	−	0.961872i	$-0.411819\pi$
$181$	1332.00	0.546999	0.273499	+	0.961872i	$0.411819\pi$
$182$	−2394.00	−0.975028
$183$	1156.00	0.466962
$184$	184.000	0.0737210
$185$	0	0
$186$	328.000	0.129302
$187$	3948.00	1.54388
$188$	496.000	0.192418
$189$	−2100.00	−0.808214
$190$	0	0
$191$	1297.00	0.491349	0.245674	−	0.969352i	$-0.420991\pi$
$191$	1297.00	0.491349	0.245674	+	0.969352i	$0.420991\pi$
$192$	−128.000	−0.0481125
$193$	−3902.00	−1.45530	−0.727648	−	0.685951i	$-0.759387\pi$
$193$	−3902.00	−1.45530	−0.727648	+	0.685951i	$0.759387\pi$
$194$	−128.000	−0.0473704
$195$	0	0
$196$	392.000	0.142857
$197$	149.000	0.0538874	0.0269437	−	0.999637i	$-0.491423\pi$
$197$	149.000	0.0538874	0.0269437	+	0.999637i	$0.491423\pi$
$198$	2162.00	0.775993
$199$	−525.000	−0.187016	−0.0935082	−	0.995619i	$-0.529808\pi$
$199$	−525.000	−0.187016	−0.0935082	+	0.995619i	$0.529808\pi$
$200$	0	0
$201$	592.000	0.207744
$202$	−2004.00	−0.698024
$203$	−5985.00	−2.06928
$204$	−672.000	−0.230634
$205$	0	0
$206$	3614.00	1.22233
$207$	529.000	0.177623
$208$	−912.000	−0.304018
$209$	−235.000	−0.0777765
$210$	0	0
$211$	−3518.00	−1.14782	−0.573908	−	0.818920i	$-0.694573\pi$
$211$	−3518.00	−1.14782	−0.573908	+	0.818920i	$0.694573\pi$
$212$	592.000	0.191786
$213$	−844.000	−0.271502
$214$	−3328.00	−1.06307
$215$	0	0
$216$	−800.000	−0.252005
$217$	−1722.00	−0.538696
$218$	−940.000	−0.292041
$219$	974.000	0.300533
$220$	0	0
$221$	−4788.00	−1.45736
$222$	216.000	0.0653017
$223$	2968.00	0.891264	0.445632	−	0.895216i	$-0.352979\pi$
$223$	2968.00	0.891264	0.445632	+	0.895216i	$0.352979\pi$
$224$	672.000	0.200446
$225$	0	0
$226$	1984.00	0.583954
$227$	−4036.00	−1.18008	−0.590041	−	0.807373i	$-0.700889\pi$
$227$	−4036.00	−1.18008	−0.590041	+	0.807373i	$0.700889\pi$
$228$	40.0000	0.0116187
$229$	−4190.00	−1.20910	−0.604548	−	0.796569i	$-0.706646\pi$
$229$	−4190.00	−1.20910	−0.604548	+	0.796569i	$0.706646\pi$
$230$	0	0
$231$	1974.00	0.562250
$232$	−2280.00	−0.645213
$233$	−977.000	−0.274701	−0.137351	−	0.990522i	$-0.543859\pi$
$233$	−977.000	−0.274701	−0.137351	+	0.990522i	$0.543859\pi$
$234$	−2622.00	−0.732502
$235$	0	0
$236$	120.000	0.0330989
$237$	810.000	0.222005
$238$	3528.00	0.960867
$239$	−3740.00	−1.01222	−0.506110	−	0.862469i	$-0.668917\pi$
$239$	−3740.00	−1.01222	−0.506110	+	0.862469i	$0.668917\pi$
$240$	0	0
$241$	3692.00	0.986816	0.493408	−	0.869798i	$-0.335751\pi$
$241$	3692.00	0.986816	0.493408	+	0.869798i	$0.335751\pi$
$242$	−1756.00	−0.466446
$243$	−3542.00	−0.935059
$244$	−2312.00	−0.606601
$245$	0	0
$246$	−212.000	−0.0549456
$247$	285.000	0.0734175
$248$	−656.000	−0.167968
$249$	794.000	0.202079
$250$	0	0
$251$	−6468.00	−1.62652	−0.813260	−	0.581900i	$-0.802309\pi$
$251$	−6468.00	−1.62652	−0.813260	+	0.581900i	$0.802309\pi$
$252$	1932.00	0.482955
$253$	−1081.00	−0.268624
$254$	−4548.00	−1.12349
$255$	0	0
$256$	256.000	0.0625000
$257$	−5586.00	−1.35582	−0.677909	−	0.735146i	$-0.737114\pi$
$257$	−5586.00	−1.35582	−0.677909	+	0.735146i	$0.737114\pi$
$258$	−788.000	−0.190150
$259$	−1134.00	−0.272059
$260$	0	0
$261$	−6555.00	−1.55458
$262$	−3604.00	−0.849832
$263$	6208.00	1.45552	0.727760	−	0.685832i	$-0.240562\pi$
$263$	6208.00	1.45552	0.727760	+	0.685832i	$0.240562\pi$
$264$	752.000	0.175312
$265$	0	0
$266$	−210.000	−0.0484057
$267$	−1460.00	−0.334646
$268$	−1184.00	−0.269867
$269$	−7895.00	−1.78947	−0.894734	−	0.446600i	$-0.852635\pi$
$269$	−7895.00	−1.78947	−0.894734	+	0.446600i	$0.852635\pi$
$270$	0	0
$271$	−68.0000	−0.0152425	−0.00762123	−	0.999971i	$-0.502426\pi$
$271$	−68.0000	−0.0152425	−0.00762123	+	0.999971i	$0.502426\pi$
$272$	1344.00	0.299603
$273$	−2394.00	−0.530738
$274$	212.000	0.0467423
$275$	0	0
$276$	184.000	0.0401286
$277$	5289.00	1.14724	0.573620	−	0.819122i	$-0.305539\pi$
$277$	5289.00	1.14724	0.573620	+	0.819122i	$0.305539\pi$
$278$	5400.00	1.16500
$279$	−1886.00	−0.404702
$280$	0	0
$281$	−3408.00	−0.723503	−0.361751	−	0.932275i	$-0.617821\pi$
$281$	−3408.00	−0.723503	−0.361751	+	0.932275i	$0.617821\pi$
$282$	496.000	0.104739
$283$	1828.00	0.383969	0.191985	−	0.981398i	$-0.438508\pi$
$283$	1828.00	0.383969	0.191985	+	0.981398i	$0.438508\pi$
$284$	1688.00	0.352691
$285$	0	0
$286$	5358.00	1.10778
$287$	1113.00	0.228914
$288$	736.000	0.150588
$289$	2143.00	0.436190
$290$	0	0
$291$	−128.000	−0.0257852
$292$	−1948.00	−0.390404
$293$	6388.00	1.27369	0.636845	−	0.770992i	$-0.280239\pi$
$293$	6388.00	1.27369	0.636845	+	0.770992i	$0.280239\pi$
$294$	392.000	0.0777616
$295$	0	0
$296$	−432.000	−0.0848294
$297$	4700.00	0.918255
$298$	1780.00	0.346016
$299$	1311.00	0.253569
$300$	0	0
$301$	4137.00	0.792202
$302$	6796.00	1.29492
$303$	−2004.00	−0.379956
$304$	−80.0000	−0.0150931
$305$	0	0
$306$	3864.00	0.721863
$307$	−5016.00	−0.932502	−0.466251	−	0.884652i	$-0.654396\pi$
$307$	−5016.00	−0.932502	−0.466251	+	0.884652i	$0.654396\pi$
$308$	−3948.00	−0.730384
$309$	3614.00	0.665350
$310$	0	0
$311$	5542.00	1.01048	0.505238	−	0.862980i	$-0.331405\pi$
$311$	5542.00	1.01048	0.505238	+	0.862980i	$0.331405\pi$
$312$	−912.000	−0.165487
$313$	3838.00	0.693088	0.346544	−	0.938034i	$-0.387355\pi$
$313$	3838.00	0.693088	0.346544	+	0.938034i	$0.387355\pi$
$314$	5952.00	1.06972
$315$	0	0
$316$	−1620.00	−0.288393
$317$	−9771.00	−1.73121	−0.865606	−	0.500726i	$-0.833066\pi$
$317$	−9771.00	−1.73121	−0.865606	+	0.500726i	$0.833066\pi$
$318$	592.000	0.104395
$319$	13395.0	2.35102
$320$	0	0
$321$	−3328.00	−0.578663
$322$	−966.000	−0.167183
$323$	−420.000	−0.0723512
$324$	1684.00	0.288752
$325$	0	0
$326$	1024.00	0.173970
$327$	−940.000	−0.158967
$328$	424.000	0.0713765
$329$	−2604.00	−0.436362
$330$	0	0
$331$	3982.00	0.661240	0.330620	−	0.943764i	$-0.392742\pi$
$331$	3982.00	0.661240	0.330620	+	0.943764i	$0.392742\pi$
$332$	−1588.00	−0.262509
$333$	−1242.00	−0.204388
$334$	2852.00	0.467229
$335$	0	0
$336$	672.000	0.109109
$337$	−536.000	−0.0866403	−0.0433201	−	0.999061i	$-0.513794\pi$
$337$	−536.000	−0.0866403	−0.0433201	+	0.999061i	$0.513794\pi$
$338$	−2104.00	−0.338587
$339$	1984.00	0.317865
$340$	0	0
$341$	3854.00	0.612040
$342$	−230.000	−0.0363654
$343$	5145.00	0.809924
$344$	1576.00	0.247012
$345$	0	0
$346$	2094.00	0.325359
$347$	8024.00	1.24136	0.620679	−	0.784065i	$-0.286857\pi$
$347$	8024.00	1.24136	0.620679	+	0.784065i	$0.286857\pi$
$348$	−2280.00	−0.351209
$349$	−4675.00	−0.717040	−0.358520	−	0.933522i	$-0.616719\pi$
$349$	−4675.00	−0.717040	−0.358520	+	0.933522i	$0.616719\pi$
$350$	0	0
$351$	−5700.00	−0.866791
$352$	−1504.00	−0.227737
$353$	−10347.0	−1.56010	−0.780050	−	0.625717i	$-0.784806\pi$
$353$	−10347.0	−1.56010	−0.780050	+	0.625717i	$0.784806\pi$
$354$	120.000	0.0180167
$355$	0	0
$356$	2920.00	0.434718
$357$	3528.00	0.523030
$358$	2760.00	0.407460
$359$	12715.0	1.86928	0.934641	−	0.355593i	$-0.115721\pi$
$359$	12715.0	1.86928	0.934641	+	0.355593i	$0.115721\pi$
$360$	0	0
$361$	−6834.00	−0.996355
$362$	−2664.00	−0.386787
$363$	−1756.00	−0.253901
$364$	4788.00	0.689449
$365$	0	0
$366$	−2312.00	−0.330192
$367$	7999.00	1.13772	0.568862	−	0.822433i	$-0.307384\pi$
$367$	7999.00	1.13772	0.568862	+	0.822433i	$0.307384\pi$
$368$	−368.000	−0.0521286
$369$	1219.00	0.171975
$370$	0	0
$371$	−3108.00	−0.434931
$372$	−656.000	−0.0914301
$373$	3588.00	0.498069	0.249034	−	0.968495i	$-0.419887\pi$
$373$	3588.00	0.498069	0.249034	+	0.968495i	$0.419887\pi$
$374$	−7896.00	−1.09169
$375$	0	0
$376$	−992.000	−0.136060
$377$	−16245.0	−2.21926
$378$	4200.00	0.571494
$379$	−2060.00	−0.279195	−0.139598	−	0.990208i	$-0.544581\pi$
$379$	−2060.00	−0.279195	−0.139598	+	0.990208i	$0.544581\pi$
$380$	0	0
$381$	−4548.00	−0.611551
$382$	−2594.00	−0.347436
$383$	9943.00	1.32654	0.663268	−	0.748382i	$-0.269169\pi$
$383$	9943.00	1.32654	0.663268	+	0.748382i	$0.269169\pi$
$384$	256.000	0.0340207
$385$	0	0
$386$	7804.00	1.02905
$387$	4531.00	0.595152
$388$	256.000	0.0334960
$389$	−14580.0	−1.90035	−0.950174	−	0.311720i	$-0.899095\pi$
$389$	−14580.0	−1.90035	−0.950174	+	0.311720i	$0.899095\pi$
$390$	0	0
$391$	−1932.00	−0.249886
$392$	−784.000	−0.101015
$393$	−3604.00	−0.462590
$394$	−298.000	−0.0381041
$395$	0	0
$396$	−4324.00	−0.548710
$397$	14594.0	1.84497	0.922483	−	0.386037i	$-0.126156\pi$
$397$	14594.0	1.84497	0.922483	+	0.386037i	$0.126156\pi$
$398$	1050.00	0.132241
$399$	−210.000	−0.0263487
$400$	0	0
$401$	9702.00	1.20822	0.604108	−	0.796902i	$-0.293529\pi$
$401$	9702.00	1.20822	0.604108	+	0.796902i	$0.293529\pi$
$402$	−1184.00	−0.146897
$403$	−4674.00	−0.577738
$404$	4008.00	0.493578
$405$	0	0
$406$	11970.0	1.46320
$407$	2538.00	0.309101
$408$	1344.00	0.163083
$409$	−14315.0	−1.73064	−0.865319	−	0.501221i	$-0.832884\pi$
$409$	−14315.0	−1.73064	−0.865319	+	0.501221i	$0.832884\pi$
$410$	0	0
$411$	212.000	0.0254433
$412$	−7228.00	−0.864316
$413$	−630.000	−0.0750612
$414$	−1058.00	−0.125599
$415$	0	0
$416$	1824.00	0.214973
$417$	5400.00	0.634147
$418$	470.000	0.0549963
$419$	−975.000	−0.113680	−0.0568399	−	0.998383i	$-0.518102\pi$
$419$	−975.000	−0.113680	−0.0568399	+	0.998383i	$0.518102\pi$
$420$	0	0
$421$	−11138.0	−1.28939	−0.644695	−	0.764440i	$-0.723015\pi$
$421$	−11138.0	−1.28939	−0.644695	+	0.764440i	$0.723015\pi$
$422$	7036.00	0.811628
$423$	−2852.00	−0.327823
$424$	−1184.00	−0.135613
$425$	0	0
$426$	1688.00	0.191981
$427$	12138.0	1.37564
$428$	6656.00	0.751705
$429$	5358.00	0.602999
$430$	0	0
$431$	−9568.00	−1.06931	−0.534657	−	0.845069i	$-0.679559\pi$
$431$	−9568.00	−1.06931	−0.534657	+	0.845069i	$0.679559\pi$
$432$	1600.00	0.178195
$433$	−1762.00	−0.195557	−0.0977787	−	0.995208i	$-0.531174\pi$
$433$	−1762.00	−0.195557	−0.0977787	+	0.995208i	$0.531174\pi$
$434$	3444.00	0.380915
$435$	0	0
$436$	1880.00	0.206504
$437$	115.000	0.0125885
$438$	−1948.00	−0.212509
$439$	4080.00	0.443571	0.221786	−	0.975095i	$-0.428811\pi$
$439$	4080.00	0.443571	0.221786	+	0.975095i	$0.428811\pi$
$440$	0	0
$441$	−2254.00	−0.243386
$442$	9576.00	1.03051
$443$	−9582.00	−1.02766	−0.513831	−	0.857891i	$-0.671774\pi$
$443$	−9582.00	−1.02766	−0.513831	+	0.857891i	$0.671774\pi$
$444$	−432.000	−0.0461753
$445$	0	0
$446$	−5936.00	−0.630219
$447$	1780.00	0.188347
$448$	−1344.00	−0.141737
$449$	−3290.00	−0.345801	−0.172901	−	0.984939i	$-0.555314\pi$
$449$	−3290.00	−0.345801	−0.172901	+	0.984939i	$0.555314\pi$
$450$	0	0
$451$	−2491.00	−0.260081
$452$	−3968.00	−0.412918
$453$	6796.00	0.704865
$454$	8072.00	0.834444
$455$	0	0
$456$	−80.0000	−0.00821567
$457$	484.000	0.0495417	0.0247709	−	0.999693i	$-0.492114\pi$
$457$	484.000	0.0495417	0.0247709	+	0.999693i	$0.492114\pi$
$458$	8380.00	0.854960
$459$	8400.00	0.854201
$460$	0	0
$461$	−10243.0	−1.03485	−0.517423	−	0.855730i	$-0.673109\pi$
$461$	−10243.0	−1.03485	−0.517423	+	0.855730i	$0.673109\pi$
$462$	−3948.00	−0.397571
$463$	6208.00	0.623132	0.311566	−	0.950224i	$-0.399146\pi$
$463$	6208.00	0.623132	0.311566	+	0.950224i	$0.399146\pi$
$464$	4560.00	0.456234
$465$	0	0
$466$	1954.00	0.194243
$467$	6089.00	0.603352	0.301676	−	0.953411i	$-0.402454\pi$
$467$	6089.00	0.603352	0.301676	+	0.953411i	$0.402454\pi$
$468$	5244.00	0.517957
$469$	6216.00	0.612000
$470$	0	0
$471$	5952.00	0.582280
$472$	−240.000	−0.0234044
$473$	−9259.00	−0.900062
$474$	−1620.00	−0.156981
$475$	0	0
$476$	−7056.00	−0.679435
$477$	−3404.00	−0.326747
$478$	7480.00	0.715747
$479$	8145.00	0.776941	0.388470	−	0.921461i	$-0.373004\pi$
$479$	8145.00	0.776941	0.388470	+	0.921461i	$0.373004\pi$
$480$	0	0
$481$	−3078.00	−0.291777
$482$	−7384.00	−0.697784
$483$	−966.000	−0.0910032
$484$	3512.00	0.329827
$485$	0	0
$486$	7084.00	0.661187
$487$	−1096.00	−0.101980	−0.0509902	−	0.998699i	$-0.516238\pi$
$487$	−1096.00	−0.101980	−0.0509902	+	0.998699i	$0.516238\pi$
$488$	4624.00	0.428932
$489$	1024.00	0.0946971
$490$	0	0
$491$	−15318.0	−1.40793	−0.703963	−	0.710237i	$-0.748588\pi$
$491$	−15318.0	−1.40793	−0.703963	+	0.710237i	$0.748588\pi$
$492$	424.000	0.0388524
$493$	23940.0	2.18703
$494$	−570.000	−0.0519140
$495$	0	0
$496$	1312.00	0.118771
$497$	−8862.00	−0.799829
$498$	−1588.00	−0.142892
$499$	−7440.00	−0.667455	−0.333728	−	0.942670i	$-0.608307\pi$
$499$	−7440.00	−0.667455	−0.333728	+	0.942670i	$0.608307\pi$
$500$	0	0
$501$	2852.00	0.254327
$502$	12936.0	1.15012
$503$	−6147.00	−0.544893	−0.272447	−	0.962171i	$-0.587833\pi$
$503$	−6147.00	−0.544893	−0.272447	+	0.962171i	$0.587833\pi$
$504$	−3864.00	−0.341500
$505$	0	0
$506$	2162.00	0.189946
$507$	−2104.00	−0.184304
$508$	9096.00	0.794429
$509$	1590.00	0.138459	0.0692294	−	0.997601i	$-0.477946\pi$
$509$	1590.00	0.138459	0.0692294	+	0.997601i	$0.477946\pi$
$510$	0	0
$511$	10227.0	0.885354
$512$	−512.000	−0.0441942
$513$	−500.000	−0.0430322
$514$	11172.0	0.958708
$515$	0	0
$516$	1576.00	0.134456
$517$	5828.00	0.495774
$518$	2268.00	0.192375
$519$	2094.00	0.177103
$520$	0	0
$521$	−16638.0	−1.39909	−0.699543	−	0.714590i	$-0.746613\pi$
$521$	−16638.0	−1.39909	−0.699543	+	0.714590i	$0.746613\pi$
$522$	13110.0	1.09925
$523$	4453.00	0.372306	0.186153	−	0.982521i	$-0.440398\pi$
$523$	4453.00	0.372306	0.186153	+	0.982521i	$0.440398\pi$
$524$	7208.00	0.600922
$525$	0	0
$526$	−12416.0	−1.02921
$527$	6888.00	0.569347
$528$	−1504.00	−0.123964
$529$	529.000	0.0434783
$530$	0	0
$531$	−690.000	−0.0563907
$532$	420.000	0.0342280
$533$	3021.00	0.245505
$534$	2920.00	0.236631
$535$	0	0
$536$	2368.00	0.190825
$537$	2760.00	0.221793
$538$	15790.0	1.26534
$539$	4606.00	0.368079
$540$	0	0
$541$	18077.0	1.43658	0.718291	−	0.695743i	$-0.244925\pi$
$541$	18077.0	1.43658	0.718291	+	0.695743i	$0.244925\pi$
$542$	136.000	0.0107780
$543$	−2664.00	−0.210540
$544$	−2688.00	−0.211851
$545$	0	0
$546$	4788.00	0.375288
$547$	6644.00	0.519336	0.259668	−	0.965698i	$-0.416387\pi$
$547$	6644.00	0.519336	0.259668	+	0.965698i	$0.416387\pi$
$548$	−424.000	−0.0330518
$549$	13294.0	1.03347
$550$	0	0
$551$	−1425.00	−0.110176
$552$	−368.000	−0.0283752
$553$	8505.00	0.654013
$554$	−10578.0	−0.811220
$555$	0	0
$556$	−10800.0	−0.823781
$557$	6954.00	0.528995	0.264498	−	0.964386i	$-0.414794\pi$
$557$	6954.00	0.528995	0.264498	+	0.964386i	$0.414794\pi$
$558$	3772.00	0.286168
$559$	11229.0	0.849617
$560$	0	0
$561$	−7896.00	−0.594241
$562$	6816.00	0.511594
$563$	−77.0000	−0.00576406	−0.00288203	−	0.999996i	$-0.500917\pi$
$563$	−77.0000	−0.00576406	−0.00288203	+	0.999996i	$0.500917\pi$
$564$	−992.000	−0.0740616
$565$	0	0
$566$	−3656.00	−0.271507
$567$	−8841.00	−0.654827
$568$	−3376.00	−0.249391
$569$	14820.0	1.09189	0.545946	−	0.837820i	$-0.316170\pi$
$569$	14820.0	1.09189	0.545946	+	0.837820i	$0.316170\pi$
$570$	0	0
$571$	2492.00	0.182639	0.0913196	−	0.995822i	$-0.470892\pi$
$571$	2492.00	0.182639	0.0913196	+	0.995822i	$0.470892\pi$
$572$	−10716.0	−0.783319
$573$	−2594.00	−0.189120
$574$	−2226.00	−0.161867
$575$	0	0
$576$	−1472.00	−0.106481
$577$	5929.00	0.427777	0.213889	−	0.976858i	$-0.431387\pi$
$577$	5929.00	0.427777	0.213889	+	0.976858i	$0.431387\pi$
$578$	−4286.00	−0.308433
$579$	7804.00	0.560144
$580$	0	0
$581$	8337.00	0.595313
$582$	256.000	0.0182329
$583$	6956.00	0.494148
$584$	3896.00	0.276058
$585$	0	0
$586$	−12776.0	−0.900634
$587$	7274.00	0.511465	0.255733	−	0.966748i	$-0.417683\pi$
$587$	7274.00	0.511465	0.255733	+	0.966748i	$0.417683\pi$
$588$	−784.000	−0.0549857
$589$	−410.000	−0.0286821
$590$	0	0
$591$	−298.000	−0.0207413
$592$	864.000	0.0599834
$593$	5823.00	0.403241	0.201621	−	0.979464i	$-0.435379\pi$
$593$	5823.00	0.403241	0.201621	+	0.979464i	$0.435379\pi$
$594$	−9400.00	−0.649304
$595$	0	0
$596$	−3560.00	−0.244670
$597$	1050.00	0.0719826
$598$	−2622.00	−0.179300
$599$	10430.0	0.711449	0.355725	−	0.934591i	$-0.384234\pi$
$599$	10430.0	0.711449	0.355725	+	0.934591i	$0.384234\pi$
$600$	0	0
$601$	−18998.0	−1.28943	−0.644713	−	0.764425i	$-0.723023\pi$
$601$	−18998.0	−1.28943	−0.644713	+	0.764425i	$0.723023\pi$
$602$	−8274.00	−0.560171
$603$	6808.00	0.459773
$604$	−13592.0	−0.915647
$605$	0	0
$606$	4008.00	0.268670
$607$	−26416.0	−1.76638	−0.883190	−	0.469016i	$-0.844609\pi$
$607$	−26416.0	−1.76638	−0.883190	+	0.469016i	$0.844609\pi$
$608$	160.000	0.0106725
$609$	11970.0	0.796468
$610$	0	0
$611$	−7068.00	−0.467988
$612$	−7728.00	−0.510434
$613$	−27262.0	−1.79625	−0.898125	−	0.439739i	$-0.855071\pi$
$613$	−27262.0	−1.79625	−0.898125	+	0.439739i	$0.855071\pi$
$614$	10032.0	0.659379
$615$	0	0
$616$	7896.00	0.516459
$617$	25584.0	1.66932	0.834662	−	0.550762i	$-0.185663\pi$
$617$	25584.0	1.66932	0.834662	+	0.550762i	$0.185663\pi$
$618$	−7228.00	−0.470474
$619$	−3640.00	−0.236355	−0.118178	−	0.992992i	$-0.537705\pi$
$619$	−3640.00	−0.236355	−0.118178	+	0.992992i	$0.537705\pi$
$620$	0	0
$621$	−2300.00	−0.148625
$622$	−11084.0	−0.714514
$623$	−15330.0	−0.985848
$624$	1824.00	0.117017
$625$	0	0
$626$	−7676.00	−0.490087
$627$	470.000	0.0299362
$628$	−11904.0	−0.756403
$629$	4536.00	0.287539
$630$	0	0
$631$	19937.0	1.25781	0.628906	−	0.777481i	$-0.283503\pi$
$631$	19937.0	1.25781	0.628906	+	0.777481i	$0.283503\pi$
$632$	3240.00	0.203924
$633$	7036.00	0.441794
$634$	19542.0	1.22415
$635$	0	0
$636$	−1184.00	−0.0738186
$637$	−5586.00	−0.347450
$638$	−26790.0	−1.66242
$639$	−9706.00	−0.600882
$640$	0	0
$641$	−14048.0	−0.865620	−0.432810	−	0.901485i	$-0.642478\pi$
$641$	−14048.0	−0.865620	−0.432810	+	0.901485i	$0.642478\pi$
$642$	6656.00	0.409177
$643$	13423.0	0.823253	0.411626	−	0.911353i	$-0.364961\pi$
$643$	13423.0	0.823253	0.411626	+	0.911353i	$0.364961\pi$
$644$	1932.00	0.118217
$645$	0	0
$646$	840.000	0.0511600
$647$	9024.00	0.548331	0.274165	−	0.961683i	$-0.411598\pi$
$647$	9024.00	0.548331	0.274165	+	0.961683i	$0.411598\pi$
$648$	−3368.00	−0.204178
$649$	1410.00	0.0852810
$650$	0	0
$651$	3444.00	0.207344
$652$	−2048.00	−0.123015
$653$	11263.0	0.674970	0.337485	−	0.941331i	$-0.390424\pi$
$653$	11263.0	0.674970	0.337485	+	0.941331i	$0.390424\pi$
$654$	1880.00	0.112406
$655$	0	0
$656$	−848.000	−0.0504708
$657$	11201.0	0.665133
$658$	5208.00	0.308555
$659$	7425.00	0.438903	0.219451	−	0.975623i	$-0.429573\pi$
$659$	7425.00	0.438903	0.219451	+	0.975623i	$0.429573\pi$
$660$	0	0
$661$	2032.00	0.119570	0.0597849	−	0.998211i	$-0.480959\pi$
$661$	2032.00	0.119570	0.0597849	+	0.998211i	$0.480959\pi$
$662$	−7964.00	−0.467567
$663$	9576.00	0.560937
$664$	3176.00	0.185622
$665$	0	0
$666$	2484.00	0.144524
$667$	−6555.00	−0.380526
$668$	−5704.00	−0.330381
$669$	−5936.00	−0.343048
$670$	0	0
$671$	−27166.0	−1.56294
$672$	−1344.00	−0.0771517
$673$	11903.0	0.681764	0.340882	−	0.940106i	$-0.389274\pi$
$673$	11903.0	0.681764	0.340882	+	0.940106i	$0.389274\pi$
$674$	1072.00	0.0612639
$675$	0	0
$676$	4208.00	0.239417
$677$	18654.0	1.05898	0.529491	−	0.848315i	$-0.322383\pi$
$677$	18654.0	1.05898	0.529491	+	0.848315i	$0.322383\pi$
$678$	−3968.00	−0.224764
$679$	−1344.00	−0.0759617
$680$	0	0
$681$	8072.00	0.454214
$682$	−7708.00	−0.432778
$683$	−23302.0	−1.30546	−0.652728	−	0.757592i	$-0.726375\pi$
$683$	−23302.0	−1.30546	−0.652728	+	0.757592i	$0.726375\pi$
$684$	460.000	0.0257142
$685$	0	0
$686$	−10290.0	−0.572703
$687$	8380.00	0.465381
$688$	−3152.00	−0.174664
$689$	−8436.00	−0.466453
$690$	0	0
$691$	16472.0	0.906837	0.453419	−	0.891298i	$-0.350204\pi$
$691$	16472.0	0.906837	0.453419	+	0.891298i	$0.350204\pi$
$692$	−4188.00	−0.230063
$693$	22701.0	1.24436
$694$	−16048.0	−0.877772
$695$	0	0
$696$	4560.00	0.248342
$697$	−4452.00	−0.241939
$698$	9350.00	0.507024
$699$	1954.00	0.105733
$700$	0	0
$701$	−19008.0	−1.02414	−0.512070	−	0.858944i	$-0.671121\pi$
$701$	−19008.0	−1.02414	−0.512070	+	0.858944i	$0.671121\pi$
$702$	11400.0	0.612913
$703$	−270.000	−0.0144854
$704$	3008.00	0.161034
$705$	0	0
$706$	20694.0	1.10316
$707$	−21042.0	−1.11933
$708$	−240.000	−0.0127398
$709$	−35870.0	−1.90004	−0.950018	−	0.312194i	$-0.898936\pi$
$709$	−35870.0	−1.90004	−0.950018	+	0.312194i	$0.898936\pi$
$710$	0	0
$711$	9315.00	0.491336
$712$	−5840.00	−0.307392
$713$	−1886.00	−0.0990621
$714$	−7056.00	−0.369838
$715$	0	0
$716$	−5520.00	−0.288117
$717$	7480.00	0.389604
$718$	−25430.0	−1.32178
$719$	37610.0	1.95079	0.975394	−	0.220470i	$-0.0707590\pi$
$719$	37610.0	1.95079	0.975394	+	0.220470i	$0.0707590\pi$
$720$	0	0
$721$	37947.0	1.96008
$722$	13668.0	0.704529
$723$	−7384.00	−0.379826
$724$	5328.00	0.273499
$725$	0	0
$726$	3512.00	0.179535
$727$	−26176.0	−1.33537	−0.667685	−	0.744444i	$-0.732715\pi$
$727$	−26176.0	−1.33537	−0.667685	+	0.744444i	$0.732715\pi$
$728$	−9576.00	−0.487514
$729$	−4283.00	−0.217599
$730$	0	0
$731$	−16548.0	−0.837278
$732$	4624.00	0.233481
$733$	17238.0	0.868622	0.434311	−	0.900763i	$-0.356992\pi$
$733$	17238.0	0.868622	0.434311	+	0.900763i	$0.356992\pi$
$734$	−15998.0	−0.804492
$735$	0	0
$736$	736.000	0.0368605
$737$	−13912.0	−0.695326
$738$	−2438.00	−0.121604
$739$	−5910.00	−0.294185	−0.147093	−	0.989123i	$-0.546992\pi$
$739$	−5910.00	−0.294185	−0.147093	+	0.989123i	$0.546992\pi$
$740$	0	0
$741$	−570.000	−0.0282584
$742$	6216.00	0.307543
$743$	31203.0	1.54068	0.770341	−	0.637632i	$-0.220086\pi$
$743$	31203.0	1.54068	0.770341	+	0.637632i	$0.220086\pi$
$744$	1312.00	0.0646509
$745$	0	0
$746$	−7176.00	−0.352188
$747$	9131.00	0.447237
$748$	15792.0	0.771942
$749$	−34944.0	−1.70471
$750$	0	0
$751$	−36643.0	−1.78046	−0.890228	−	0.455516i	$-0.849455\pi$
$751$	−36643.0	−1.78046	−0.890228	+	0.455516i	$0.849455\pi$
$752$	1984.00	0.0962088
$753$	12936.0	0.626048
$754$	32490.0	1.56925
$755$	0	0
$756$	−8400.00	−0.404107
$757$	−846.000	−0.0406187	−0.0203094	−	0.999794i	$-0.506465\pi$
$757$	−846.000	−0.0406187	−0.0203094	+	0.999794i	$0.506465\pi$
$758$	4120.00	0.197421
$759$	2162.00	0.103393
$760$	0	0
$761$	−11303.0	−0.538414	−0.269207	−	0.963082i	$-0.586762\pi$
$761$	−11303.0	−0.538414	−0.269207	+	0.963082i	$0.586762\pi$
$762$	9096.00	0.432432
$763$	−9870.00	−0.468307
$764$	5188.00	0.245674
$765$	0	0
$766$	−19886.0	−0.938003
$767$	−1710.00	−0.0805013
$768$	−512.000	−0.0240563
$769$	−31830.0	−1.49261	−0.746306	−	0.665603i	$-0.768175\pi$
$769$	−31830.0	−1.49261	−0.746306	+	0.665603i	$0.768175\pi$
$770$	0	0
$771$	11172.0	0.521854
$772$	−15608.0	−0.727648
$773$	−15562.0	−0.724096	−0.362048	−	0.932159i	$-0.617922\pi$
$773$	−15562.0	−0.724096	−0.362048	+	0.932159i	$0.617922\pi$
$774$	−9062.00	−0.420836
$775$	0	0
$776$	−512.000	−0.0236852
$777$	2268.00	0.104716
$778$	29160.0	1.34375
$779$	265.000	0.0121882
$780$	0	0
$781$	19834.0	0.908728
$782$	3864.00	0.176696
$783$	28500.0	1.30078
$784$	1568.00	0.0714286
$785$	0	0
$786$	7208.00	0.327100
$787$	−24771.0	−1.12197	−0.560985	−	0.827826i	$-0.689578\pi$
$787$	−24771.0	−1.12197	−0.560985	+	0.827826i	$0.689578\pi$
$788$	596.000	0.0269437
$789$	−12416.0	−0.560230
$790$	0	0
$791$	20832.0	0.936410
$792$	8648.00	0.387997
$793$	32946.0	1.47534
$794$	−29188.0	−1.30459
$795$	0	0
$796$	−2100.00	−0.0935082
$797$	−24486.0	−1.08825	−0.544127	−	0.839003i	$-0.683139\pi$
$797$	−24486.0	−1.08825	−0.544127	+	0.839003i	$0.683139\pi$
$798$	420.000	0.0186314
$799$	10416.0	0.461191
$800$	0	0
$801$	−16790.0	−0.740631
$802$	−19404.0	−0.854338
$803$	−22889.0	−1.00590
$804$	2368.00	0.103872
$805$	0	0
$806$	9348.00	0.408523
$807$	15790.0	0.688766
$808$	−8016.00	−0.349012
$809$	24705.0	1.07365	0.536824	−	0.843694i	$-0.319624\pi$
$809$	24705.0	1.07365	0.536824	+	0.843694i	$0.319624\pi$
$810$	0	0
$811$	6392.00	0.276761	0.138381	−	0.990379i	$-0.455810\pi$
$811$	6392.00	0.276761	0.138381	+	0.990379i	$0.455810\pi$
$812$	−23940.0	−1.03464
$813$	136.000	0.00586682
$814$	−5076.00	−0.218567
$815$	0	0
$816$	−2688.00	−0.115317
$817$	985.000	0.0421797
$818$	28630.0	1.22375
$819$	−27531.0	−1.17462
$820$	0	0
$821$	39047.0	1.65987	0.829933	−	0.557863i	$-0.188379\pi$
$821$	39047.0	1.65987	0.829933	+	0.557863i	$0.188379\pi$
$822$	−424.000	−0.0179911
$823$	14348.0	0.607703	0.303852	−	0.952719i	$-0.401727\pi$
$823$	14348.0	0.607703	0.303852	+	0.952719i	$0.401727\pi$
$824$	14456.0	0.611163
$825$	0	0
$826$	1260.00	0.0530763
$827$	23749.0	0.998590	0.499295	−	0.866432i	$-0.333592\pi$
$827$	23749.0	0.998590	0.499295	+	0.866432i	$0.333592\pi$
$828$	2116.00	0.0888117
$829$	25125.0	1.05263	0.526313	−	0.850291i	$-0.323574\pi$
$829$	25125.0	1.05263	0.526313	+	0.850291i	$0.323574\pi$
$830$	0	0
$831$	−10578.0	−0.441573
$832$	−3648.00	−0.152009
$833$	8232.00	0.342403
$834$	−10800.0	−0.448409
$835$	0	0
$836$	−940.000	−0.0388883
$837$	8200.00	0.338630
$838$	1950.00	0.0803838
$839$	−32295.0	−1.32890	−0.664450	−	0.747333i	$-0.731334\pi$
$839$	−32295.0	−1.32890	−0.664450	+	0.747333i	$0.731334\pi$
$840$	0	0
$841$	56836.0	2.33039
$842$	22276.0	0.911736
$843$	6816.00	0.278476
$844$	−14072.0	−0.573908
$845$	0	0
$846$	5704.00	0.231806
$847$	−18438.0	−0.747978
$848$	2368.00	0.0958932
$849$	−3656.00	−0.147790
$850$	0	0
$851$	−1242.00	−0.0500296
$852$	−3376.00	−0.135751
$853$	−29257.0	−1.17437	−0.587187	−	0.809451i	$-0.699765\pi$
$853$	−29257.0	−1.17437	−0.587187	+	0.809451i	$0.699765\pi$
$854$	−24276.0	−0.972726
$855$	0	0
$856$	−13312.0	−0.531536
$857$	−11766.0	−0.468984	−0.234492	−	0.972118i	$-0.575343\pi$
$857$	−11766.0	−0.468984	−0.234492	+	0.972118i	$0.575343\pi$
$858$	−10716.0	−0.426385
$859$	−32390.0	−1.28653	−0.643267	−	0.765642i	$-0.722421\pi$
$859$	−32390.0	−1.28653	−0.643267	+	0.765642i	$0.722421\pi$
$860$	0	0
$861$	−2226.00	−0.0881090
$862$	19136.0	0.756119
$863$	−16332.0	−0.644204	−0.322102	−	0.946705i	$-0.604389\pi$
$863$	−16332.0	−0.644204	−0.322102	+	0.946705i	$0.604389\pi$
$864$	−3200.00	−0.126003
$865$	0	0
$866$	3524.00	0.138280
$867$	−4286.00	−0.167889
$868$	−6888.00	−0.269348
$869$	−19035.0	−0.743059
$870$	0	0
$871$	16872.0	0.656356
$872$	−3760.00	−0.146020
$873$	−1472.00	−0.0570672
$874$	−230.000	−0.00890145
$875$	0	0
$876$	3896.00	0.150267
$877$	−42226.0	−1.62585	−0.812925	−	0.582368i	$-0.802126\pi$
$877$	−42226.0	−1.62585	−0.812925	+	0.582368i	$0.802126\pi$
$878$	−8160.00	−0.313652
$879$	−12776.0	−0.490243
$880$	0	0
$881$	−7158.00	−0.273733	−0.136867	−	0.990589i	$-0.543703\pi$
$881$	−7158.00	−0.273733	−0.136867	+	0.990589i	$0.543703\pi$
$882$	4508.00	0.172100
$883$	−28672.0	−1.09274	−0.546370	−	0.837544i	$-0.683991\pi$
$883$	−28672.0	−1.09274	−0.546370	+	0.837544i	$0.683991\pi$
$884$	−19152.0	−0.728678
$885$	0	0
$886$	19164.0	0.726667
$887$	−5536.00	−0.209561	−0.104781	−	0.994495i	$-0.533414\pi$
$887$	−5536.00	−0.209561	−0.104781	+	0.994495i	$0.533414\pi$
$888$	864.000	0.0326508
$889$	−47754.0	−1.80159
$890$	0	0
$891$	19787.0	0.743984
$892$	11872.0	0.445632
$893$	−620.000	−0.0232335
$894$	−3560.00	−0.133181
$895$	0	0
$896$	2688.00	0.100223
$897$	−2622.00	−0.0975987
$898$	6580.00	0.244518
$899$	23370.0	0.867000
$900$	0	0
$901$	12432.0	0.459678
$902$	4982.00	0.183905
$903$	−8274.00	−0.304919
$904$	7936.00	0.291977
$905$	0	0
$906$	−13592.0	−0.498415
$907$	−451.000	−0.0165107	−0.00825535	−	0.999966i	$-0.502628\pi$
$907$	−451.000	−0.0165107	−0.00825535	+	0.999966i	$0.502628\pi$
$908$	−16144.0	−0.590041
$909$	−23046.0	−0.840910
$910$	0	0
$911$	−21013.0	−0.764206	−0.382103	−	0.924120i	$-0.624800\pi$
$911$	−21013.0	−0.764206	−0.382103	+	0.924120i	$0.624800\pi$
$912$	160.000	0.00580935
$913$	−18659.0	−0.676367
$914$	−968.000	−0.0350313
$915$	0	0
$916$	−16760.0	−0.604548
$917$	−37842.0	−1.36276
$918$	−16800.0	−0.604012
$919$	28800.0	1.03376	0.516879	−	0.856058i	$-0.327094\pi$
$919$	28800.0	1.03376	0.516879	+	0.856058i	$0.327094\pi$
$920$	0	0
$921$	10032.0	0.358920
$922$	20486.0	0.731747
$923$	−24054.0	−0.857797
$924$	7896.00	0.281125
$925$	0	0
$926$	−12416.0	−0.440621
$927$	41561.0	1.47254
$928$	−9120.00	−0.322606
$929$	39555.0	1.39694	0.698470	−	0.715639i	$-0.253865\pi$
$929$	39555.0	1.39694	0.698470	+	0.715639i	$0.253865\pi$
$930$	0	0
$931$	−490.000	−0.0172493
$932$	−3908.00	−0.137351
$933$	−11084.0	−0.388932
$934$	−12178.0	−0.426634
$935$	0	0
$936$	−10488.0	−0.366251
$937$	−38756.0	−1.35123	−0.675615	−	0.737254i	$-0.736122\pi$
$937$	−38756.0	−1.35123	−0.675615	+	0.737254i	$0.736122\pi$
$938$	−12432.0	−0.432750
$939$	−7676.00	−0.266770
$940$	0	0
$941$	−3968.00	−0.137463	−0.0687317	−	0.997635i	$-0.521895\pi$
$941$	−3968.00	−0.137463	−0.0687317	+	0.997635i	$0.521895\pi$
$942$	−11904.0	−0.411734
$943$	1219.00	0.0420955
$944$	480.000	0.0165494
$945$	0	0
$946$	18518.0	0.636440
$947$	32374.0	1.11089	0.555445	−	0.831553i	$-0.312548\pi$
$947$	32374.0	1.11089	0.555445	+	0.831553i	$0.312548\pi$
$948$	3240.00	0.111002
$949$	27759.0	0.949521
$950$	0	0
$951$	19542.0	0.666344
$952$	14112.0	0.480433
$953$	−23122.0	−0.785934	−0.392967	−	0.919553i	$-0.628551\pi$
$953$	−23122.0	−0.785934	−0.392967	+	0.919553i	$0.628551\pi$
$954$	6808.00	0.231045
$955$	0	0
$956$	−14960.0	−0.506110
$957$	−26790.0	−0.904909
$958$	−16290.0	−0.549380
$959$	2226.00	0.0749544
$960$	0	0
$961$	−23067.0	−0.774294
$962$	6156.00	0.206317
$963$	−38272.0	−1.28068
$964$	14768.0	0.493408
$965$	0	0
$966$	1932.00	0.0643489
$967$	−16916.0	−0.562546	−0.281273	−	0.959628i	$-0.590757\pi$
$967$	−16916.0	−0.562546	−0.281273	+	0.959628i	$0.590757\pi$
$968$	−7024.00	−0.233223
$969$	840.000	0.0278480
$970$	0	0
$971$	32277.0	1.06675	0.533377	−	0.845878i	$-0.320923\pi$
$971$	32277.0	1.06675	0.533377	+	0.845878i	$0.320923\pi$
$972$	−14168.0	−0.467530
$973$	56700.0	1.86816
$974$	2192.00	0.0721111
$975$	0	0
$976$	−9248.00	−0.303300
$977$	−48076.0	−1.57430	−0.787148	−	0.616764i	$-0.788443\pi$
$977$	−48076.0	−1.57430	−0.787148	+	0.616764i	$0.788443\pi$
$978$	−2048.00	−0.0669610
$979$	34310.0	1.12007
$980$	0	0
$981$	−10810.0	−0.351821
$982$	30636.0	0.995554
$983$	−37287.0	−1.20984	−0.604919	−	0.796287i	$-0.706794\pi$
$983$	−37287.0	−1.20984	−0.604919	+	0.796287i	$0.706794\pi$
$984$	−848.000	−0.0274728
$985$	0	0
$986$	−47880.0	−1.54646
$987$	5208.00	0.167956
$988$	1140.00	0.0367087
$989$	4531.00	0.145680
$990$	0	0
$991$	4872.00	0.156170	0.0780849	−	0.996947i	$-0.475119\pi$
$991$	4872.00	0.156170	0.0780849	+	0.996947i	$0.475119\pi$
$992$	−2624.00	−0.0839840
$993$	−7964.00	−0.254511
$994$	17724.0	0.565565
$995$	0	0
$996$	3176.00	0.101040
$997$	−24751.0	−0.786231	−0.393115	−	0.919489i	$-0.628603\pi$
$997$	−24751.0	−0.786231	−0.393115	+	0.919489i	$0.628603\pi$
$998$	14880.0	0.471962
$999$	5400.00	0.171019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.a.1.1	✓	1
5.2	odd	4		1150.4.b.g.599.1		2
5.3	odd	4		1150.4.b.g.599.2		2
5.4	even	2		1150.4.a.h.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.4.a.a.1.1	✓	1	1.1	even	1	trivial
1150.4.a.h.1.1	yes	1	5.4	even	2
1150.4.b.g.599.1		2	5.2	odd	4
1150.4.b.g.599.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more