LMFDB - Embedded newform 1150.4.a.c.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
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)

$f(q)$

$=$

$q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.00000 q^{6} +32.0000 q^{7} -8.00000 q^{8} -26.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -2.00000 q^{6} +32.0000 q^{7} -8.00000 q^{8} -26.0000 q^{9} -30.0000 q^{11} +4.00000 q^{12} -19.0000 q^{13} -64.0000 q^{14} +16.0000 q^{16} +60.0000 q^{17} +52.0000 q^{18} -58.0000 q^{19} +32.0000 q^{21} +60.0000 q^{22} -23.0000 q^{23} -8.00000 q^{24} +38.0000 q^{26} -53.0000 q^{27} +128.000 q^{28} +85.0000 q^{29} -65.0000 q^{31} -32.0000 q^{32} -30.0000 q^{33} -120.000 q^{34} -104.000 q^{36} +34.0000 q^{37} +116.000 q^{38} -19.0000 q^{39} +143.000 q^{41} -64.0000 q^{42} +332.000 q^{43} -120.000 q^{44} +46.0000 q^{46} +561.000 q^{47} +16.0000 q^{48} +681.000 q^{49} +60.0000 q^{51} -76.0000 q^{52} +422.000 q^{53} +106.000 q^{54} -256.000 q^{56} -58.0000 q^{57} -170.000 q^{58} +392.000 q^{59} -246.000 q^{61} +130.000 q^{62} -832.000 q^{63} +64.0000 q^{64} +60.0000 q^{66} -894.000 q^{67} +240.000 q^{68} -23.0000 q^{69} -737.000 q^{71} +208.000 q^{72} -1041.00 q^{73} -68.0000 q^{74} -232.000 q^{76} -960.000 q^{77} +38.0000 q^{78} +1114.00 q^{79} +649.000 q^{81} -286.000 q^{82} +936.000 q^{83} +128.000 q^{84} -664.000 q^{86} +85.0000 q^{87} +240.000 q^{88} +824.000 q^{89} -608.000 q^{91} -92.0000 q^{92} -65.0000 q^{93} -1122.00 q^{94} -32.0000 q^{96} +868.000 q^{97} -1362.00 q^{98} +780.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	1.00000	0.192450	0.0962250	−	0.995360i	$-0.469323\pi$
$3$	1.00000	0.192450	0.0962250	+	0.995360i	$0.469323\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−2.00000	−0.136083
$7$	32.0000	1.72784	0.863919	−	0.503631i	$-0.168003\pi$
$7$	32.0000	1.72784	0.863919	+	0.503631i	$0.168003\pi$
$8$	−8.00000	−0.353553
$9$	−26.0000	−0.962963
$10$	0	0
$11$	−30.0000	−0.822304	−0.411152	−	0.911567i	$-0.634873\pi$
$11$	−30.0000	−0.822304	−0.411152	+	0.911567i	$0.634873\pi$
$12$	4.00000	0.0962250
$13$	−19.0000	−0.405358	−0.202679	−	0.979245i	$-0.564965\pi$
$13$	−19.0000	−0.405358	−0.202679	+	0.979245i	$0.564965\pi$
$14$	−64.0000	−1.22177
$15$	0	0
$16$	16.0000	0.250000
$17$	60.0000	0.856008	0.428004	−	0.903777i	$-0.359217\pi$
$17$	60.0000	0.856008	0.428004	+	0.903777i	$0.359217\pi$
$18$	52.0000	0.680918
$19$	−58.0000	−0.700322	−0.350161	−	0.936690i	$-0.613873\pi$
$19$	−58.0000	−0.700322	−0.350161	+	0.936690i	$0.613873\pi$
$20$	0	0
$21$	32.0000	0.332522
$22$	60.0000	0.581456
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−8.00000	−0.0680414
$25$	0	0
$26$	38.0000	0.286631
$27$	−53.0000	−0.377772
$28$	128.000	0.863919
$29$	85.0000	0.544279	0.272140	−	0.962258i	$-0.412269\pi$
$29$	85.0000	0.544279	0.272140	+	0.962258i	$0.412269\pi$
$30$	0	0
$31$	−65.0000	−0.376592	−0.188296	−	0.982112i	$-0.560296\pi$
$31$	−65.0000	−0.376592	−0.188296	+	0.982112i	$0.560296\pi$
$32$	−32.0000	−0.176777
$33$	−30.0000	−0.158252
$34$	−120.000	−0.605289
$35$	0	0
$36$	−104.000	−0.481481
$37$	34.0000	0.151069	0.0755347	−	0.997143i	$-0.475934\pi$
$37$	34.0000	0.151069	0.0755347	+	0.997143i	$0.475934\pi$
$38$	116.000	0.495202
$39$	−19.0000	−0.0780112
$40$	0	0
$41$	143.000	0.544704	0.272352	−	0.962198i	$-0.412199\pi$
$41$	143.000	0.544704	0.272352	+	0.962198i	$0.412199\pi$
$42$	−64.0000	−0.235129
$43$	332.000	1.17743	0.588715	−	0.808340i	$-0.299634\pi$
$43$	332.000	1.17743	0.588715	+	0.808340i	$0.299634\pi$
$44$	−120.000	−0.411152
$45$	0	0
$46$	46.0000	0.147442
$47$	561.000	1.74107	0.870535	−	0.492107i	$-0.163773\pi$
$47$	561.000	1.74107	0.870535	+	0.492107i	$0.163773\pi$
$48$	16.0000	0.0481125
$49$	681.000	1.98542
$50$	0	0
$51$	60.0000	0.164739
$52$	−76.0000	−0.202679
$53$	422.000	1.09370	0.546851	−	0.837230i	$-0.315827\pi$
$53$	422.000	1.09370	0.546851	+	0.837230i	$0.315827\pi$
$54$	106.000	0.267125
$55$	0	0
$56$	−256.000	−0.610883
$57$	−58.0000	−0.134777
$58$	−170.000	−0.384864
$59$	392.000	0.864984	0.432492	−	0.901638i	$-0.357634\pi$
$59$	392.000	0.864984	0.432492	+	0.901638i	$0.357634\pi$
$60$	0	0
$61$	−246.000	−0.516345	−0.258173	−	0.966099i	$-0.583120\pi$
$61$	−246.000	−0.516345	−0.258173	+	0.966099i	$0.583120\pi$
$62$	130.000	0.266291
$63$	−832.000	−1.66384
$64$	64.0000	0.125000
$65$	0	0
$66$	60.0000	0.111901
$67$	−894.000	−1.63014	−0.815071	−	0.579361i	$-0.803302\pi$
$67$	−894.000	−1.63014	−0.815071	+	0.579361i	$0.803302\pi$
$68$	240.000	0.428004
$69$	−23.0000	−0.0401286
$70$	0	0
$71$	−737.000	−1.23191	−0.615956	−	0.787780i	$-0.711230\pi$
$71$	−737.000	−1.23191	−0.615956	+	0.787780i	$0.711230\pi$
$72$	208.000	0.340459
$73$	−1041.00	−1.66904	−0.834519	−	0.550979i	$-0.814255\pi$
$73$	−1041.00	−1.66904	−0.834519	+	0.550979i	$0.814255\pi$
$74$	−68.0000	−0.106822
$75$	0	0
$76$	−232.000	−0.350161
$77$	−960.000	−1.42081
$78$	38.0000	0.0551622
$79$	1114.00	1.58652	0.793258	−	0.608885i	$-0.208383\pi$
$79$	1114.00	1.58652	0.793258	+	0.608885i	$0.208383\pi$
$80$	0	0
$81$	649.000	0.890261
$82$	−286.000	−0.385164
$83$	936.000	1.23782	0.618912	−	0.785461i	$-0.287574\pi$
$83$	936.000	1.23782	0.618912	+	0.785461i	$0.287574\pi$
$84$	128.000	0.166261
$85$	0	0
$86$	−664.000	−0.832569
$87$	85.0000	0.104747
$88$	240.000	0.290728
$89$	824.000	0.981391	0.490696	−	0.871331i	$-0.336743\pi$
$89$	824.000	0.981391	0.490696	+	0.871331i	$0.336743\pi$
$90$	0	0
$91$	−608.000	−0.700393
$92$	−92.0000	−0.104257
$93$	−65.0000	−0.0724751
$94$	−1122.00	−1.23112
$95$	0	0
$96$	−32.0000	−0.0340207
$97$	868.000	0.908578	0.454289	−	0.890854i	$-0.349893\pi$
$97$	868.000	0.908578	0.454289	+	0.890854i	$0.349893\pi$
$98$	−1362.00	−1.40391
$99$	780.000	0.791848
$100$	0	0
$101$	50.0000	0.0492593	0.0246296	−	0.999697i	$-0.492159\pi$
$101$	50.0000	0.0492593	0.0246296	+	0.999697i	$0.492159\pi$
$102$	−120.000	−0.116488
$103$	−440.000	−0.420917	−0.210459	−	0.977603i	$-0.567496\pi$
$103$	−440.000	−0.420917	−0.210459	+	0.977603i	$0.567496\pi$
$104$	152.000	0.143316
$105$	0	0
$106$	−844.000	−0.773363
$107$	318.000	0.287310	0.143655	−	0.989628i	$-0.454114\pi$
$107$	318.000	0.287310	0.143655	+	0.989628i	$0.454114\pi$
$108$	−212.000	−0.188886
$109$	−828.000	−0.727596	−0.363798	−	0.931478i	$-0.618520\pi$
$109$	−828.000	−0.727596	−0.363798	+	0.931478i	$0.618520\pi$
$110$	0	0
$111$	34.0000	0.0290733
$112$	512.000	0.431959
$113$	−208.000	−0.173159	−0.0865796	−	0.996245i	$-0.527594\pi$
$113$	−208.000	−0.173159	−0.0865796	+	0.996245i	$0.527594\pi$
$114$	116.000	0.0953017
$115$	0	0
$116$	340.000	0.272140
$117$	494.000	0.390345
$118$	−784.000	−0.611636
$119$	1920.00	1.47904
$120$	0	0
$121$	−431.000	−0.323817
$122$	492.000	0.365111
$123$	143.000	0.104828
$124$	−260.000	−0.188296
$125$	0	0
$126$	1664.00	1.17652
$127$	495.000	0.345859	0.172930	−	0.984934i	$-0.444677\pi$
$127$	495.000	0.345859	0.172930	+	0.984934i	$0.444677\pi$
$128$	−128.000	−0.0883883
$129$	332.000	0.226597
$130$	0	0
$131$	335.000	0.223428	0.111714	−	0.993740i	$-0.464366\pi$
$131$	335.000	0.223428	0.111714	+	0.993740i	$0.464366\pi$
$132$	−120.000	−0.0791262
$133$	−1856.00	−1.21004
$134$	1788.00	1.15268
$135$	0	0
$136$	−480.000	−0.302645
$137$	652.000	0.406599	0.203300	−	0.979117i	$-0.434833\pi$
$137$	652.000	0.406599	0.203300	+	0.979117i	$0.434833\pi$
$138$	46.0000	0.0283752
$139$	−1999.00	−1.21981	−0.609903	−	0.792476i	$-0.708792\pi$
$139$	−1999.00	−1.21981	−0.609903	+	0.792476i	$0.708792\pi$
$140$	0	0
$141$	561.000	0.335069
$142$	1474.00	0.871094
$143$	570.000	0.333327
$144$	−416.000	−0.240741
$145$	0	0
$146$	2082.00	1.18019
$147$	681.000	0.382095
$148$	136.000	0.0755347
$149$	1870.00	1.02816	0.514082	−	0.857741i	$-0.328133\pi$
$149$	1870.00	1.02816	0.514082	+	0.857741i	$0.328133\pi$
$150$	0	0
$151$	1463.00	0.788459	0.394229	−	0.919012i	$-0.371012\pi$
$151$	1463.00	0.788459	0.394229	+	0.919012i	$0.371012\pi$
$152$	464.000	0.247601
$153$	−1560.00	−0.824304
$154$	1920.00	1.00466
$155$	0	0
$156$	−76.0000	−0.0390056
$157$	3004.00	1.52704	0.763520	−	0.645784i	$-0.223469\pi$
$157$	3004.00	1.52704	0.763520	+	0.645784i	$0.223469\pi$
$158$	−2228.00	−1.12184
$159$	422.000	0.210483
$160$	0	0
$161$	−736.000	−0.360279
$162$	−1298.00	−0.629509
$163$	4047.00	1.94470	0.972348	−	0.233536i	$-0.0750296\pi$
$163$	4047.00	1.94470	0.972348	+	0.233536i	$0.0750296\pi$
$164$	572.000	0.272352
$165$	0	0
$166$	−1872.00	−0.875273
$167$	2112.00	0.978632	0.489316	−	0.872107i	$-0.337247\pi$
$167$	2112.00	0.978632	0.489316	+	0.872107i	$0.337247\pi$
$168$	−256.000	−0.117564
$169$	−1836.00	−0.835685
$170$	0	0
$171$	1508.00	0.674384
$172$	1328.00	0.588715
$173$	−342.000	−0.150299	−0.0751496	−	0.997172i	$-0.523943\pi$
$173$	−342.000	−0.150299	−0.0751496	+	0.997172i	$0.523943\pi$
$174$	−170.000	−0.0740671
$175$	0	0
$176$	−480.000	−0.205576
$177$	392.000	0.166466
$178$	−1648.00	−0.693948
$179$	1689.00	0.705261	0.352631	−	0.935763i	$-0.385287\pi$
$179$	1689.00	0.705261	0.352631	+	0.935763i	$0.385287\pi$
$180$	0	0
$181$	−194.000	−0.0796680	−0.0398340	−	0.999206i	$-0.512683\pi$
$181$	−194.000	−0.0796680	−0.0398340	+	0.999206i	$0.512683\pi$
$182$	1216.00	0.495252
$183$	−246.000	−0.0993707
$184$	184.000	0.0737210
$185$	0	0
$186$	130.000	0.0512476
$187$	−1800.00	−0.703899
$188$	2244.00	0.870535
$189$	−1696.00	−0.652729
$190$	0	0
$191$	−298.000	−0.112893	−0.0564464	−	0.998406i	$-0.517977\pi$
$191$	−298.000	−0.112893	−0.0564464	+	0.998406i	$0.517977\pi$
$192$	64.0000	0.0240563
$193$	−2301.00	−0.858184	−0.429092	−	0.903261i	$-0.641166\pi$
$193$	−2301.00	−0.858184	−0.429092	+	0.903261i	$0.641166\pi$
$194$	−1736.00	−0.642462
$195$	0	0
$196$	2724.00	0.992711
$197$	535.000	0.193488	0.0967441	−	0.995309i	$-0.469157\pi$
$197$	535.000	0.193488	0.0967441	+	0.995309i	$0.469157\pi$
$198$	−1560.00	−0.559921
$199$	278.000	0.0990296	0.0495148	−	0.998773i	$-0.484232\pi$
$199$	278.000	0.0990296	0.0495148	+	0.998773i	$0.484232\pi$
$200$	0	0
$201$	−894.000	−0.313721
$202$	−100.000	−0.0348316
$203$	2720.00	0.940426
$204$	240.000	0.0823694
$205$	0	0
$206$	880.000	0.297634
$207$	598.000	0.200792
$208$	−304.000	−0.101339
$209$	1740.00	0.575877
$210$	0	0
$211$	−2444.00	−0.797402	−0.398701	−	0.917081i	$-0.630539\pi$
$211$	−2444.00	−0.797402	−0.398701	+	0.917081i	$0.630539\pi$
$212$	1688.00	0.546851
$213$	−737.000	−0.237082
$214$	−636.000	−0.203159
$215$	0	0
$216$	424.000	0.133563
$217$	−2080.00	−0.650689
$218$	1656.00	0.514488
$219$	−1041.00	−0.321207
$220$	0	0
$221$	−1140.00	−0.346990
$222$	−68.0000	−0.0205579
$223$	5368.00	1.61196	0.805982	−	0.591940i	$-0.201638\pi$
$223$	5368.00	1.61196	0.805982	+	0.591940i	$0.201638\pi$
$224$	−1024.00	−0.305441
$225$	0	0
$226$	416.000	0.122442
$227$	5780.00	1.69001	0.845005	−	0.534759i	$-0.179598\pi$
$227$	5780.00	1.69001	0.845005	+	0.534759i	$0.179598\pi$
$228$	−232.000	−0.0673885
$229$	−1064.00	−0.307035	−0.153518	−	0.988146i	$-0.549060\pi$
$229$	−1064.00	−0.307035	−0.153518	+	0.988146i	$0.549060\pi$
$230$	0	0
$231$	−960.000	−0.273434
$232$	−680.000	−0.192432
$233$	2833.00	0.796549	0.398275	−	0.917266i	$-0.369609\pi$
$233$	2833.00	0.796549	0.398275	+	0.917266i	$0.369609\pi$
$234$	−988.000	−0.276015
$235$	0	0
$236$	1568.00	0.432492
$237$	1114.00	0.305325
$238$	−3840.00	−1.04584
$239$	6831.00	1.84879	0.924395	−	0.381437i	$-0.124571\pi$
$239$	6831.00	1.84879	0.924395	+	0.381437i	$0.124571\pi$
$240$	0	0
$241$	−1794.00	−0.479509	−0.239755	−	0.970834i	$-0.577067\pi$
$241$	−1794.00	−0.479509	−0.239755	+	0.970834i	$0.577067\pi$
$242$	862.000	0.228973
$243$	2080.00	0.549103
$244$	−984.000	−0.258173
$245$	0	0
$246$	−286.000	−0.0741248
$247$	1102.00	0.283881
$248$	520.000	0.133145
$249$	936.000	0.238219
$250$	0	0
$251$	−6672.00	−1.67782	−0.838910	−	0.544270i	$-0.816807\pi$
$251$	−6672.00	−1.67782	−0.838910	+	0.544270i	$0.816807\pi$
$252$	−3328.00	−0.831922
$253$	690.000	0.171462
$254$	−990.000	−0.244560
$255$	0	0
$256$	256.000	0.0625000
$257$	−291.000	−0.0706307	−0.0353153	−	0.999376i	$-0.511244\pi$
$257$	−291.000	−0.0706307	−0.0353153	+	0.999376i	$0.511244\pi$
$258$	−664.000	−0.160228
$259$	1088.00	0.261023
$260$	0	0
$261$	−2210.00	−0.524121
$262$	−670.000	−0.157988
$263$	5306.00	1.24404	0.622019	−	0.783002i	$-0.286313\pi$
$263$	5306.00	1.24404	0.622019	+	0.783002i	$0.286313\pi$
$264$	240.000	0.0559507
$265$	0	0
$266$	3712.00	0.855629
$267$	824.000	0.188869
$268$	−3576.00	−0.815071
$269$	7785.00	1.76453	0.882267	−	0.470749i	$-0.156016\pi$
$269$	7785.00	1.76453	0.882267	+	0.470749i	$0.156016\pi$
$270$	0	0
$271$	3440.00	0.771089	0.385544	−	0.922689i	$-0.374014\pi$
$271$	3440.00	0.771089	0.385544	+	0.922689i	$0.374014\pi$
$272$	960.000	0.214002
$273$	−608.000	−0.134791
$274$	−1304.00	−0.287509
$275$	0	0
$276$	−92.0000	−0.0200643
$277$	7643.00	1.65785	0.828923	−	0.559363i	$-0.188954\pi$
$277$	7643.00	1.65785	0.828923	+	0.559363i	$0.188954\pi$
$278$	3998.00	0.862533
$279$	1690.00	0.362644
$280$	0	0
$281$	5408.00	1.14809	0.574047	−	0.818823i	$-0.305373\pi$
$281$	5408.00	1.14809	0.574047	+	0.818823i	$0.305373\pi$
$282$	−1122.00	−0.236930
$283$	−4402.00	−0.924635	−0.462318	−	0.886714i	$-0.652982\pi$
$283$	−4402.00	−0.924635	−0.462318	+	0.886714i	$0.652982\pi$
$284$	−2948.00	−0.615956
$285$	0	0
$286$	−1140.00	−0.235698
$287$	4576.00	0.941159
$288$	832.000	0.170229
$289$	−1313.00	−0.267250
$290$	0	0
$291$	868.000	0.174856
$292$	−4164.00	−0.834519
$293$	−9808.00	−1.95560	−0.977798	−	0.209551i	$-0.932800\pi$
$293$	−9808.00	−1.95560	−0.977798	+	0.209551i	$0.932800\pi$
$294$	−1362.00	−0.270182
$295$	0	0
$296$	−272.000	−0.0534111
$297$	1590.00	0.310644
$298$	−3740.00	−0.727021
$299$	437.000	0.0845230
$300$	0	0
$301$	10624.0	2.03441
$302$	−2926.00	−0.557524
$303$	50.0000	0.00947995
$304$	−928.000	−0.175080
$305$	0	0
$306$	3120.00	0.582871
$307$	3288.00	0.611258	0.305629	−	0.952151i	$-0.401133\pi$
$307$	3288.00	0.611258	0.305629	+	0.952151i	$0.401133\pi$
$308$	−3840.00	−0.710404
$309$	−440.000	−0.0810056
$310$	0	0
$311$	3919.00	0.714553	0.357277	−	0.933999i	$-0.383705\pi$
$311$	3919.00	0.714553	0.357277	+	0.933999i	$0.383705\pi$
$312$	152.000	0.0275811
$313$	−5112.00	−0.923154	−0.461577	−	0.887100i	$-0.652716\pi$
$313$	−5112.00	−0.923154	−0.461577	+	0.887100i	$0.652716\pi$
$314$	−6008.00	−1.07978
$315$	0	0
$316$	4456.00	0.793258
$317$	−8058.00	−1.42770	−0.713852	−	0.700296i	$-0.753051\pi$
$317$	−8058.00	−1.42770	−0.713852	+	0.700296i	$0.753051\pi$
$318$	−844.000	−0.148834
$319$	−2550.00	−0.447563
$320$	0	0
$321$	318.000	0.0552929
$322$	1472.00	0.254756
$323$	−3480.00	−0.599481
$324$	2596.00	0.445130
$325$	0	0
$326$	−8094.00	−1.37511
$327$	−828.000	−0.140026
$328$	−1144.00	−0.192582
$329$	17952.0	3.00829
$330$	0	0
$331$	−2555.00	−0.424276	−0.212138	−	0.977240i	$-0.568043\pi$
$331$	−2555.00	−0.424276	−0.212138	+	0.977240i	$0.568043\pi$
$332$	3744.00	0.618912
$333$	−884.000	−0.145474
$334$	−4224.00	−0.691997
$335$	0	0
$336$	512.000	0.0831306
$337$	6272.00	1.01382	0.506910	−	0.861999i	$-0.330787\pi$
$337$	6272.00	1.01382	0.506910	+	0.861999i	$0.330787\pi$
$338$	3672.00	0.590919
$339$	−208.000	−0.0333245
$340$	0	0
$341$	1950.00	0.309673
$342$	−3016.00	−0.476861
$343$	10816.0	1.70265
$344$	−2656.00	−0.416285
$345$	0	0
$346$	684.000	0.106278
$347$	−6844.00	−1.05880	−0.529402	−	0.848371i	$-0.677584\pi$
$347$	−6844.00	−1.05880	−0.529402	+	0.848371i	$0.677584\pi$
$348$	340.000	0.0523733
$349$	4057.00	0.622253	0.311126	−	0.950369i	$-0.399294\pi$
$349$	4057.00	0.622253	0.311126	+	0.950369i	$0.399294\pi$
$350$	0	0
$351$	1007.00	0.153133
$352$	960.000	0.145364
$353$	7155.00	1.07882	0.539408	−	0.842044i	$-0.318648\pi$
$353$	7155.00	1.07882	0.539408	+	0.842044i	$0.318648\pi$
$354$	−784.000	−0.117709
$355$	0	0
$356$	3296.00	0.490696
$357$	1920.00	0.284642
$358$	−3378.00	−0.498695
$359$	−5434.00	−0.798873	−0.399437	−	0.916761i	$-0.630794\pi$
$359$	−5434.00	−0.798873	−0.399437	+	0.916761i	$0.630794\pi$
$360$	0	0
$361$	−3495.00	−0.509549
$362$	388.000	0.0563338
$363$	−431.000	−0.0623185
$364$	−2432.00	−0.350196
$365$	0	0
$366$	492.000	0.0702657
$367$	2944.00	0.418734	0.209367	−	0.977837i	$-0.432860\pi$
$367$	2944.00	0.418734	0.209367	+	0.977837i	$0.432860\pi$
$368$	−368.000	−0.0521286
$369$	−3718.00	−0.524529
$370$	0	0
$371$	13504.0	1.88974
$372$	−260.000	−0.0362376
$373$	5962.00	0.827616	0.413808	−	0.910364i	$-0.364199\pi$
$373$	5962.00	0.827616	0.413808	+	0.910364i	$0.364199\pi$
$374$	3600.00	0.497731
$375$	0	0
$376$	−4488.00	−0.615561
$377$	−1615.00	−0.220628
$378$	3392.00	0.461549
$379$	−5856.00	−0.793674	−0.396837	−	0.917889i	$-0.629892\pi$
$379$	−5856.00	−0.793674	−0.396837	+	0.917889i	$0.629892\pi$
$380$	0	0
$381$	495.000	0.0665607
$382$	596.000	0.0798273
$383$	−6456.00	−0.861322	−0.430661	−	0.902514i	$-0.641719\pi$
$383$	−6456.00	−0.861322	−0.430661	+	0.902514i	$0.641719\pi$
$384$	−128.000	−0.0170103
$385$	0	0
$386$	4602.00	0.606828
$387$	−8632.00	−1.13382
$388$	3472.00	0.454289
$389$	−152.000	−0.0198116	−0.00990579	−	0.999951i	$-0.503153\pi$
$389$	−152.000	−0.0198116	−0.00990579	+	0.999951i	$0.503153\pi$
$390$	0	0
$391$	−1380.00	−0.178490
$392$	−5448.00	−0.701953
$393$	335.000	0.0429988
$394$	−1070.00	−0.136817
$395$	0	0
$396$	3120.00	0.395924
$397$	−11603.0	−1.46685	−0.733423	−	0.679773i	$-0.762079\pi$
$397$	−11603.0	−1.46685	−0.733423	+	0.679773i	$0.762079\pi$
$398$	−556.000	−0.0700245
$399$	−1856.00	−0.232873
$400$	0	0
$401$	602.000	0.0749687	0.0374843	−	0.999297i	$-0.488066\pi$
$401$	602.000	0.0749687	0.0374843	+	0.999297i	$0.488066\pi$
$402$	1788.00	0.221834
$403$	1235.00	0.152654
$404$	200.000	0.0246296
$405$	0	0
$406$	−5440.00	−0.664982
$407$	−1020.00	−0.124225
$408$	−480.000	−0.0582440
$409$	3629.00	0.438735	0.219367	−	0.975642i	$-0.429601\pi$
$409$	3629.00	0.438735	0.219367	+	0.975642i	$0.429601\pi$
$410$	0	0
$411$	652.000	0.0782501
$412$	−1760.00	−0.210459
$413$	12544.0	1.49455
$414$	−1196.00	−0.141981
$415$	0	0
$416$	608.000	0.0716578
$417$	−1999.00	−0.234752
$418$	−3480.00	−0.407207
$419$	92.0000	0.0107267	0.00536336	−	0.999986i	$-0.498293\pi$
$419$	92.0000	0.0107267	0.00536336	+	0.999986i	$0.498293\pi$
$420$	0	0
$421$	−8280.00	−0.958533	−0.479267	−	0.877669i	$-0.659097\pi$
$421$	−8280.00	−0.958533	−0.479267	+	0.877669i	$0.659097\pi$
$422$	4888.00	0.563849
$423$	−14586.0	−1.67659
$424$	−3376.00	−0.386682
$425$	0	0
$426$	1474.00	0.167642
$427$	−7872.00	−0.892161
$428$	1272.00	0.143655
$429$	570.000	0.0641489
$430$	0	0
$431$	−15372.0	−1.71797	−0.858983	−	0.512004i	$-0.828903\pi$
$431$	−15372.0	−1.71797	−0.858983	+	0.512004i	$0.828903\pi$
$432$	−848.000	−0.0944431
$433$	11342.0	1.25880	0.629402	−	0.777080i	$-0.283300\pi$
$433$	11342.0	1.25880	0.629402	+	0.777080i	$0.283300\pi$
$434$	4160.00	0.460107
$435$	0	0
$436$	−3312.00	−0.363798
$437$	1334.00	0.146027
$438$	2082.00	0.227127
$439$	4593.00	0.499344	0.249672	−	0.968330i	$-0.419677\pi$
$439$	4593.00	0.499344	0.249672	+	0.968330i	$0.419677\pi$
$440$	0	0
$441$	−17706.0	−1.91189
$442$	2280.00	0.245359
$443$	−967.000	−0.103710	−0.0518550	−	0.998655i	$-0.516513\pi$
$443$	−967.000	−0.103710	−0.0518550	+	0.998655i	$0.516513\pi$
$444$	136.000	0.0145367
$445$	0	0
$446$	−10736.0	−1.13983
$447$	1870.00	0.197870
$448$	2048.00	0.215980
$449$	−11210.0	−1.17825	−0.589123	−	0.808043i	$-0.700527\pi$
$449$	−11210.0	−1.17825	−0.589123	+	0.808043i	$0.700527\pi$
$450$	0	0
$451$	−4290.00	−0.447912
$452$	−832.000	−0.0865796
$453$	1463.00	0.151739
$454$	−11560.0	−1.19502
$455$	0	0
$456$	464.000	0.0476509
$457$	72.0000	0.00736984	0.00368492	−	0.999993i	$-0.498827\pi$
$457$	72.0000	0.00736984	0.00368492	+	0.999993i	$0.498827\pi$
$458$	2128.00	0.217107
$459$	−3180.00	−0.323376
$460$	0	0
$461$	5137.00	0.518989	0.259495	−	0.965745i	$-0.416444\pi$
$461$	5137.00	0.518989	0.259495	+	0.965745i	$0.416444\pi$
$462$	1920.00	0.193347
$463$	19528.0	1.96014	0.980068	−	0.198661i	$-0.0636594\pi$
$463$	19528.0	1.96014	0.980068	+	0.198661i	$0.0636594\pi$
$464$	1360.00	0.136070
$465$	0	0
$466$	−5666.00	−0.563245
$467$	−14874.0	−1.47385	−0.736924	−	0.675976i	$-0.763722\pi$
$467$	−14874.0	−1.47385	−0.736924	+	0.675976i	$0.763722\pi$
$468$	1976.00	0.195172
$469$	−28608.0	−2.81662
$470$	0	0
$471$	3004.00	0.293879
$472$	−3136.00	−0.305818
$473$	−9960.00	−0.968206
$474$	−2228.00	−0.215898
$475$	0	0
$476$	7680.00	0.739521
$477$	−10972.0	−1.05319
$478$	−13662.0	−1.30729
$479$	10568.0	1.00807	0.504034	−	0.863684i	$-0.331849\pi$
$479$	10568.0	1.00807	0.504034	+	0.863684i	$0.331849\pi$
$480$	0	0
$481$	−646.000	−0.0612371
$482$	3588.00	0.339064
$483$	−736.000	−0.0693357
$484$	−1724.00	−0.161908
$485$	0	0
$486$	−4160.00	−0.388275
$487$	9311.00	0.866369	0.433184	−	0.901305i	$-0.357390\pi$
$487$	9311.00	0.866369	0.433184	+	0.901305i	$0.357390\pi$
$488$	1968.00	0.182556
$489$	4047.00	0.374257
$490$	0	0
$491$	−16511.0	−1.51758	−0.758789	−	0.651336i	$-0.774209\pi$
$491$	−16511.0	−1.51758	−0.758789	+	0.651336i	$0.774209\pi$
$492$	572.000	0.0524141
$493$	5100.00	0.465908
$494$	−2204.00	−0.200734
$495$	0	0
$496$	−1040.00	−0.0941479
$497$	−23584.0	−2.12855
$498$	−1872.00	−0.168446
$499$	2331.00	0.209118	0.104559	−	0.994519i	$-0.466657\pi$
$499$	2331.00	0.209118	0.104559	+	0.994519i	$0.466657\pi$
$500$	0	0
$501$	2112.00	0.188338
$502$	13344.0	1.18640
$503$	−17062.0	−1.51244	−0.756220	−	0.654318i	$-0.772956\pi$
$503$	−17062.0	−1.51244	−0.756220	+	0.654318i	$0.772956\pi$
$504$	6656.00	0.588258
$505$	0	0
$506$	−1380.00	−0.121242
$507$	−1836.00	−0.160828
$508$	1980.00	0.172930
$509$	17169.0	1.49509	0.747547	−	0.664209i	$-0.231232\pi$
$509$	17169.0	1.49509	0.747547	+	0.664209i	$0.231232\pi$
$510$	0	0
$511$	−33312.0	−2.88383
$512$	−512.000	−0.0441942
$513$	3074.00	0.264562
$514$	582.000	0.0499434
$515$	0	0
$516$	1328.00	0.113298
$517$	−16830.0	−1.43169
$518$	−2176.00	−0.184571
$519$	−342.000	−0.0289251
$520$	0	0
$521$	−10060.0	−0.845944	−0.422972	−	0.906143i	$-0.639013\pi$
$521$	−10060.0	−0.845944	−0.422972	+	0.906143i	$0.639013\pi$
$522$	4420.00	0.370609
$523$	−15244.0	−1.27452	−0.637260	−	0.770649i	$-0.719932\pi$
$523$	−15244.0	−1.27452	−0.637260	+	0.770649i	$0.719932\pi$
$524$	1340.00	0.111714
$525$	0	0
$526$	−10612.0	−0.879668
$527$	−3900.00	−0.322366
$528$	−480.000	−0.0395631
$529$	529.000	0.0434783
$530$	0	0
$531$	−10192.0	−0.832948
$532$	−7424.00	−0.605021
$533$	−2717.00	−0.220800
$534$	−1648.00	−0.133550
$535$	0	0
$536$	7152.00	0.576342
$537$	1689.00	0.135728
$538$	−15570.0	−1.24771
$539$	−20430.0	−1.63262
$540$	0	0
$541$	16389.0	1.30244	0.651218	−	0.758891i	$-0.274258\pi$
$541$	16389.0	1.30244	0.651218	+	0.758891i	$0.274258\pi$
$542$	−6880.00	−0.545242
$543$	−194.000	−0.0153321
$544$	−1920.00	−0.151322
$545$	0	0
$546$	1216.00	0.0953113
$547$	−17913.0	−1.40019	−0.700096	−	0.714049i	$-0.746859\pi$
$547$	−17913.0	−1.40019	−0.700096	+	0.714049i	$0.746859\pi$
$548$	2608.00	0.203300
$549$	6396.00	0.497222
$550$	0	0
$551$	−4930.00	−0.381171
$552$	184.000	0.0141876
$553$	35648.0	2.74124
$554$	−15286.0	−1.17227
$555$	0	0
$556$	−7996.00	−0.609903
$557$	18224.0	1.38631	0.693156	−	0.720788i	$-0.256220\pi$
$557$	18224.0	1.38631	0.693156	+	0.720788i	$0.256220\pi$
$558$	−3380.00	−0.256428
$559$	−6308.00	−0.477281
$560$	0	0
$561$	−1800.00	−0.135465
$562$	−10816.0	−0.811825
$563$	4860.00	0.363809	0.181905	−	0.983316i	$-0.441774\pi$
$563$	4860.00	0.363809	0.181905	+	0.983316i	$0.441774\pi$
$564$	2244.00	0.167534
$565$	0	0
$566$	8804.00	0.653816
$567$	20768.0	1.53823
$568$	5896.00	0.435547
$569$	−12438.0	−0.916394	−0.458197	−	0.888851i	$-0.651505\pi$
$569$	−12438.0	−0.916394	−0.458197	+	0.888851i	$0.651505\pi$
$570$	0	0
$571$	7948.00	0.582510	0.291255	−	0.956645i	$-0.405927\pi$
$571$	7948.00	0.582510	0.291255	+	0.956645i	$0.405927\pi$
$572$	2280.00	0.166664
$573$	−298.000	−0.0217262
$574$	−9152.00	−0.665500
$575$	0	0
$576$	−1664.00	−0.120370
$577$	−9061.00	−0.653751	−0.326876	−	0.945067i	$-0.605996\pi$
$577$	−9061.00	−0.653751	−0.326876	+	0.945067i	$0.605996\pi$
$578$	2626.00	0.188974
$579$	−2301.00	−0.165158
$580$	0	0
$581$	29952.0	2.13876
$582$	−1736.00	−0.123642
$583$	−12660.0	−0.899354
$584$	8328.00	0.590094
$585$	0	0
$586$	19616.0	1.38281
$587$	−8559.00	−0.601819	−0.300909	−	0.953653i	$-0.597290\pi$
$587$	−8559.00	−0.601819	−0.300909	+	0.953653i	$0.597290\pi$
$588$	2724.00	0.191047
$589$	3770.00	0.263735
$590$	0	0
$591$	535.000	0.0372368
$592$	544.000	0.0377673
$593$	8850.00	0.612860	0.306430	−	0.951893i	$-0.400865\pi$
$593$	8850.00	0.612860	0.306430	+	0.951893i	$0.400865\pi$
$594$	−3180.00	−0.219658
$595$	0	0
$596$	7480.00	0.514082
$597$	278.000	0.0190583
$598$	−874.000	−0.0597668
$599$	−7952.00	−0.542421	−0.271210	−	0.962520i	$-0.587424\pi$
$599$	−7952.00	−0.542421	−0.271210	+	0.962520i	$0.587424\pi$
$600$	0	0
$601$	27085.0	1.83830	0.919152	−	0.393904i	$-0.128876\pi$
$601$	27085.0	1.83830	0.919152	+	0.393904i	$0.128876\pi$
$602$	−21248.0	−1.43854
$603$	23244.0	1.56977
$604$	5852.00	0.394229
$605$	0	0
$606$	−100.000	−0.00670334
$607$	5204.00	0.347980	0.173990	−	0.984747i	$-0.444334\pi$
$607$	5204.00	0.347980	0.173990	+	0.984747i	$0.444334\pi$
$608$	1856.00	0.123801
$609$	2720.00	0.180985
$610$	0	0
$611$	−10659.0	−0.705756
$612$	−6240.00	−0.412152
$613$	4348.00	0.286483	0.143241	−	0.989688i	$-0.454247\pi$
$613$	4348.00	0.286483	0.143241	+	0.989688i	$0.454247\pi$
$614$	−6576.00	−0.432224
$615$	0	0
$616$	7680.00	0.502331
$617$	4066.00	0.265301	0.132651	−	0.991163i	$-0.457651\pi$
$617$	4066.00	0.265301	0.132651	+	0.991163i	$0.457651\pi$
$618$	880.000	0.0572796
$619$	−6080.00	−0.394791	−0.197396	−	0.980324i	$-0.563248\pi$
$619$	−6080.00	−0.394791	−0.197396	+	0.980324i	$0.563248\pi$
$620$	0	0
$621$	1219.00	0.0787710
$622$	−7838.00	−0.505266
$623$	26368.0	1.69568
$624$	−304.000	−0.0195028
$625$	0	0
$626$	10224.0	0.652769
$627$	1740.00	0.110828
$628$	12016.0	0.763520
$629$	2040.00	0.129317
$630$	0	0
$631$	21200.0	1.33749	0.668747	−	0.743490i	$-0.266831\pi$
$631$	21200.0	1.33749	0.668747	+	0.743490i	$0.266831\pi$
$632$	−8912.00	−0.560918
$633$	−2444.00	−0.153460
$634$	16116.0	1.00954
$635$	0	0
$636$	1688.00	0.105241
$637$	−12939.0	−0.804807
$638$	5100.00	0.316475
$639$	19162.0	1.18629
$640$	0	0
$641$	14016.0	0.863649	0.431824	−	0.901958i	$-0.357870\pi$
$641$	14016.0	0.863649	0.431824	+	0.901958i	$0.357870\pi$
$642$	−636.000	−0.0390980
$643$	−23894.0	−1.46545	−0.732727	−	0.680522i	$-0.761753\pi$
$643$	−23894.0	−1.46545	−0.732727	+	0.680522i	$0.761753\pi$
$644$	−2944.00	−0.180140
$645$	0	0
$646$	6960.00	0.423897
$647$	−27111.0	−1.64736	−0.823681	−	0.567053i	$-0.808083\pi$
$647$	−27111.0	−1.64736	−0.823681	+	0.567053i	$0.808083\pi$
$648$	−5192.00	−0.314755
$649$	−11760.0	−0.711279
$650$	0	0
$651$	−2080.00	−0.125225
$652$	16188.0	0.972348
$653$	−7819.00	−0.468578	−0.234289	−	0.972167i	$-0.575276\pi$
$653$	−7819.00	−0.468578	−0.234289	+	0.972167i	$0.575276\pi$
$654$	1656.00	0.0990133
$655$	0	0
$656$	2288.00	0.136176
$657$	27066.0	1.60722
$658$	−35904.0	−2.12718
$659$	−8712.00	−0.514979	−0.257490	−	0.966281i	$-0.582895\pi$
$659$	−8712.00	−0.514979	−0.257490	+	0.966281i	$0.582895\pi$
$660$	0	0
$661$	−12746.0	−0.750018	−0.375009	−	0.927021i	$-0.622360\pi$
$661$	−12746.0	−0.750018	−0.375009	+	0.927021i	$0.622360\pi$
$662$	5110.00	0.300009
$663$	−1140.00	−0.0667782
$664$	−7488.00	−0.437637
$665$	0	0
$666$	1768.00	0.102866
$667$	−1955.00	−0.113490
$668$	8448.00	0.489316
$669$	5368.00	0.310223
$670$	0	0
$671$	7380.00	0.424593
$672$	−1024.00	−0.0587822
$673$	14937.0	0.855541	0.427770	−	0.903887i	$-0.359299\pi$
$673$	14937.0	0.855541	0.427770	+	0.903887i	$0.359299\pi$
$674$	−12544.0	−0.716880
$675$	0	0
$676$	−7344.00	−0.417843
$677$	−8226.00	−0.466988	−0.233494	−	0.972358i	$-0.575016\pi$
$677$	−8226.00	−0.466988	−0.233494	+	0.972358i	$0.575016\pi$
$678$	416.000	0.0235640
$679$	27776.0	1.56987
$680$	0	0
$681$	5780.00	0.325242
$682$	−3900.00	−0.218972
$683$	−5797.00	−0.324767	−0.162384	−	0.986728i	$-0.551918\pi$
$683$	−5797.00	−0.324767	−0.162384	+	0.986728i	$0.551918\pi$
$684$	6032.00	0.337192
$685$	0	0
$686$	−21632.0	−1.20396
$687$	−1064.00	−0.0590890
$688$	5312.00	0.294358
$689$	−8018.00	−0.443340
$690$	0	0
$691$	16892.0	0.929959	0.464980	−	0.885321i	$-0.346062\pi$
$691$	16892.0	0.929959	0.464980	+	0.885321i	$0.346062\pi$
$692$	−1368.00	−0.0751496
$693$	24960.0	1.36818
$694$	13688.0	0.748688
$695$	0	0
$696$	−680.000	−0.0370335
$697$	8580.00	0.466271
$698$	−8114.00	−0.439999
$699$	2833.00	0.153296
$700$	0	0
$701$	−19008.0	−1.02414	−0.512070	−	0.858944i	$-0.671121\pi$
$701$	−19008.0	−1.02414	−0.512070	+	0.858944i	$0.671121\pi$
$702$	−2014.00	−0.108281
$703$	−1972.00	−0.105797
$704$	−1920.00	−0.102788
$705$	0	0
$706$	−14310.0	−0.762838
$707$	1600.00	0.0851120
$708$	1568.00	0.0832331
$709$	−29484.0	−1.56177	−0.780885	−	0.624675i	$-0.785232\pi$
$709$	−29484.0	−1.56177	−0.780885	+	0.624675i	$0.785232\pi$
$710$	0	0
$711$	−28964.0	−1.52776
$712$	−6592.00	−0.346974
$713$	1495.00	0.0785248
$714$	−3840.00	−0.201272
$715$	0	0
$716$	6756.00	0.352631
$717$	6831.00	0.355800
$718$	10868.0	0.564889
$719$	13760.0	0.713715	0.356858	−	0.934159i	$-0.383848\pi$
$719$	13760.0	0.713715	0.356858	+	0.934159i	$0.383848\pi$
$720$	0	0
$721$	−14080.0	−0.727277
$722$	6990.00	0.360306
$723$	−1794.00	−0.0922816
$724$	−776.000	−0.0398340
$725$	0	0
$726$	862.000	0.0440659
$727$	30554.0	1.55871	0.779357	−	0.626580i	$-0.215546\pi$
$727$	30554.0	1.55871	0.779357	+	0.626580i	$0.215546\pi$
$728$	4864.00	0.247626
$729$	−15443.0	−0.784586
$730$	0	0
$731$	19920.0	1.00789
$732$	−984.000	−0.0496854
$733$	−37404.0	−1.88479	−0.942393	−	0.334508i	$-0.891430\pi$
$733$	−37404.0	−1.88479	−0.942393	+	0.334508i	$0.891430\pi$
$734$	−5888.00	−0.296090
$735$	0	0
$736$	736.000	0.0368605
$737$	26820.0	1.34047
$738$	7436.00	0.370898
$739$	6873.00	0.342121	0.171060	−	0.985261i	$-0.445281\pi$
$739$	6873.00	0.342121	0.171060	+	0.985261i	$0.445281\pi$
$740$	0	0
$741$	1102.00	0.0546329
$742$	−27008.0	−1.33625
$743$	−25216.0	−1.24507	−0.622534	−	0.782593i	$-0.713897\pi$
$743$	−25216.0	−1.24507	−0.622534	+	0.782593i	$0.713897\pi$
$744$	520.000	0.0256238
$745$	0	0
$746$	−11924.0	−0.585213
$747$	−24336.0	−1.19198
$748$	−7200.00	−0.351949
$749$	10176.0	0.496426
$750$	0	0
$751$	−27556.0	−1.33893	−0.669463	−	0.742846i	$-0.733476\pi$
$751$	−27556.0	−1.33893	−0.669463	+	0.742846i	$0.733476\pi$
$752$	8976.00	0.435267
$753$	−6672.00	−0.322897
$754$	3230.00	0.156008
$755$	0	0
$756$	−6784.00	−0.326365
$757$	30550.0	1.46679	0.733394	−	0.679804i	$-0.237935\pi$
$757$	30550.0	1.46679	0.733394	+	0.679804i	$0.237935\pi$
$758$	11712.0	0.561212
$759$	690.000	0.0329979
$760$	0	0
$761$	10125.0	0.482301	0.241150	−	0.970488i	$-0.422475\pi$
$761$	10125.0	0.482301	0.241150	+	0.970488i	$0.422475\pi$
$762$	−990.000	−0.0470655
$763$	−26496.0	−1.25717
$764$	−1192.00	−0.0564464
$765$	0	0
$766$	12912.0	0.609046
$767$	−7448.00	−0.350628
$768$	256.000	0.0120281
$769$	−35210.0	−1.65111	−0.825556	−	0.564320i	$-0.809138\pi$
$769$	−35210.0	−1.65111	−0.825556	+	0.564320i	$0.809138\pi$
$770$	0	0
$771$	−291.000	−0.0135929
$772$	−9204.00	−0.429092
$773$	−15696.0	−0.730331	−0.365166	−	0.930943i	$-0.618988\pi$
$773$	−15696.0	−0.730331	−0.365166	+	0.930943i	$0.618988\pi$
$774$	17264.0	0.801733
$775$	0	0
$776$	−6944.00	−0.321231
$777$	1088.00	0.0502340
$778$	304.000	0.0140089
$779$	−8294.00	−0.381468
$780$	0	0
$781$	22110.0	1.01301
$782$	2760.00	0.126212
$783$	−4505.00	−0.205614
$784$	10896.0	0.496356
$785$	0	0
$786$	−670.000	−0.0304047
$787$	−9356.00	−0.423768	−0.211884	−	0.977295i	$-0.567960\pi$
$787$	−9356.00	−0.423768	−0.211884	+	0.977295i	$0.567960\pi$
$788$	2140.00	0.0967441
$789$	5306.00	0.239415
$790$	0	0
$791$	−6656.00	−0.299191
$792$	−6240.00	−0.279961
$793$	4674.00	0.209305
$794$	23206.0	1.03722
$795$	0	0
$796$	1112.00	0.0495148
$797$	31110.0	1.38265	0.691325	−	0.722544i	$-0.257027\pi$
$797$	31110.0	1.38265	0.691325	+	0.722544i	$0.257027\pi$
$798$	3712.00	0.164666
$799$	33660.0	1.49037
$800$	0	0
$801$	−21424.0	−0.945043
$802$	−1204.00	−0.0530109
$803$	31230.0	1.37246
$804$	−3576.00	−0.156860
$805$	0	0
$806$	−2470.00	−0.107943
$807$	7785.00	0.339585
$808$	−400.000	−0.0174158
$809$	20890.0	0.907853	0.453927	−	0.891039i	$-0.350023\pi$
$809$	20890.0	0.907853	0.453927	+	0.891039i	$0.350023\pi$
$810$	0	0
$811$	6291.00	0.272388	0.136194	−	0.990682i	$-0.456513\pi$
$811$	6291.00	0.272388	0.136194	+	0.990682i	$0.456513\pi$
$812$	10880.0	0.470213
$813$	3440.00	0.148396
$814$	2040.00	0.0878402
$815$	0	0
$816$	960.000	0.0411847
$817$	−19256.0	−0.824580
$818$	−7258.00	−0.310232
$819$	15808.0	0.674452
$820$	0	0
$821$	36210.0	1.53927	0.769633	−	0.638486i	$-0.220439\pi$
$821$	36210.0	1.53927	0.769633	+	0.638486i	$0.220439\pi$
$822$	−1304.00	−0.0553312
$823$	−40867.0	−1.73090	−0.865452	−	0.500992i	$-0.832969\pi$
$823$	−40867.0	−1.73090	−0.865452	+	0.500992i	$0.832969\pi$
$824$	3520.00	0.148817
$825$	0	0
$826$	−25088.0	−1.05681
$827$	−2088.00	−0.0877955	−0.0438977	−	0.999036i	$-0.513978\pi$
$827$	−2088.00	−0.0877955	−0.0438977	+	0.999036i	$0.513978\pi$
$828$	2392.00	0.100396
$829$	−25942.0	−1.08686	−0.543428	−	0.839456i	$-0.682874\pi$
$829$	−25942.0	−1.08686	−0.543428	+	0.839456i	$0.682874\pi$
$830$	0	0
$831$	7643.00	0.319053
$832$	−1216.00	−0.0506697
$833$	40860.0	1.69954
$834$	3998.00	0.165995
$835$	0	0
$836$	6960.00	0.287939
$837$	3445.00	0.142266
$838$	−184.000	−0.00758493
$839$	19636.0	0.807998	0.403999	−	0.914760i	$-0.367620\pi$
$839$	19636.0	0.807998	0.403999	+	0.914760i	$0.367620\pi$
$840$	0	0
$841$	−17164.0	−0.703760
$842$	16560.0	0.677785
$843$	5408.00	0.220951
$844$	−9776.00	−0.398701
$845$	0	0
$846$	29172.0	1.18552
$847$	−13792.0	−0.559503
$848$	6752.00	0.273425
$849$	−4402.00	−0.177946
$850$	0	0
$851$	−782.000	−0.0315001
$852$	−2948.00	−0.118541
$853$	15954.0	0.640392	0.320196	−	0.947351i	$-0.396251\pi$
$853$	15954.0	0.640392	0.320196	+	0.947351i	$0.396251\pi$
$854$	15744.0	0.630853
$855$	0	0
$856$	−2544.00	−0.101580
$857$	36353.0	1.44900	0.724501	−	0.689274i	$-0.242070\pi$
$857$	36353.0	1.44900	0.724501	+	0.689274i	$0.242070\pi$
$858$	−1140.00	−0.0453601
$859$	−34173.0	−1.35735	−0.678677	−	0.734437i	$-0.737447\pi$
$859$	−34173.0	−1.35735	−0.678677	+	0.734437i	$0.737447\pi$
$860$	0	0
$861$	4576.00	0.181126
$862$	30744.0	1.21479
$863$	−9129.00	−0.360087	−0.180043	−	0.983659i	$-0.557624\pi$
$863$	−9129.00	−0.360087	−0.180043	+	0.983659i	$0.557624\pi$
$864$	1696.00	0.0667814
$865$	0	0
$866$	−22684.0	−0.890108
$867$	−1313.00	−0.0514323
$868$	−8320.00	−0.325345
$869$	−33420.0	−1.30460
$870$	0	0
$871$	16986.0	0.660791
$872$	6624.00	0.257244
$873$	−22568.0	−0.874927
$874$	−2668.00	−0.103257
$875$	0	0
$876$	−4164.00	−0.160603
$877$	8106.00	0.312110	0.156055	−	0.987748i	$-0.450122\pi$
$877$	8106.00	0.312110	0.156055	+	0.987748i	$0.450122\pi$
$878$	−9186.00	−0.353089
$879$	−9808.00	−0.376355
$880$	0	0
$881$	14124.0	0.540124	0.270062	−	0.962843i	$-0.412956\pi$
$881$	14124.0	0.540124	0.270062	+	0.962843i	$0.412956\pi$
$882$	35412.0	1.35191
$883$	1700.00	0.0647900	0.0323950	−	0.999475i	$-0.489687\pi$
$883$	1700.00	0.0647900	0.0323950	+	0.999475i	$0.489687\pi$
$884$	−4560.00	−0.173495
$885$	0	0
$886$	1934.00	0.0733341
$887$	−26711.0	−1.01112	−0.505562	−	0.862790i	$-0.668715\pi$
$887$	−26711.0	−1.01112	−0.505562	+	0.862790i	$0.668715\pi$
$888$	−272.000	−0.0102790
$889$	15840.0	0.597589
$890$	0	0
$891$	−19470.0	−0.732065
$892$	21472.0	0.805982
$893$	−32538.0	−1.21931
$894$	−3740.00	−0.139915
$895$	0	0
$896$	−4096.00	−0.152721
$897$	437.000	0.0162664
$898$	22420.0	0.833146
$899$	−5525.00	−0.204971
$900$	0	0
$901$	25320.0	0.936217
$902$	8580.00	0.316721
$903$	10624.0	0.391522
$904$	1664.00	0.0612210
$905$	0	0
$906$	−2926.00	−0.107296
$907$	18758.0	0.686714	0.343357	−	0.939205i	$-0.388436\pi$
$907$	18758.0	0.686714	0.343357	+	0.939205i	$0.388436\pi$
$908$	23120.0	0.845005
$909$	−1300.00	−0.0474348
$910$	0	0
$911$	20298.0	0.738203	0.369101	−	0.929389i	$-0.379666\pi$
$911$	20298.0	0.738203	0.369101	+	0.929389i	$0.379666\pi$
$912$	−928.000	−0.0336942
$913$	−28080.0	−1.01787
$914$	−144.000	−0.00521127
$915$	0	0
$916$	−4256.00	−0.153518
$917$	10720.0	0.386048
$918$	6360.00	0.228662
$919$	39276.0	1.40979	0.704894	−	0.709312i	$-0.250994\pi$
$919$	39276.0	1.40979	0.704894	+	0.709312i	$0.250994\pi$
$920$	0	0
$921$	3288.00	0.117637
$922$	−10274.0	−0.366981
$923$	14003.0	0.499366
$924$	−3840.00	−0.136717
$925$	0	0
$926$	−39056.0	−1.38603
$927$	11440.0	0.405328
$928$	−2720.00	−0.0962159
$929$	−51265.0	−1.81050	−0.905248	−	0.424884i	$-0.860315\pi$
$929$	−51265.0	−1.81050	−0.905248	+	0.424884i	$0.860315\pi$
$930$	0	0
$931$	−39498.0	−1.39043
$932$	11332.0	0.398275
$933$	3919.00	0.137516
$934$	29748.0	1.04217
$935$	0	0
$936$	−3952.00	−0.138008
$937$	−12182.0	−0.424726	−0.212363	−	0.977191i	$-0.568116\pi$
$937$	−12182.0	−0.424726	−0.212363	+	0.977191i	$0.568116\pi$
$938$	57216.0	1.99165
$939$	−5112.00	−0.177661
$940$	0	0
$941$	33192.0	1.14987	0.574935	−	0.818199i	$-0.305027\pi$
$941$	33192.0	1.14987	0.574935	+	0.818199i	$0.305027\pi$
$942$	−6008.00	−0.207804
$943$	−3289.00	−0.113579
$944$	6272.00	0.216246
$945$	0	0
$946$	19920.0	0.684625
$947$	−18127.0	−0.622015	−0.311008	−	0.950407i	$-0.600666\pi$
$947$	−18127.0	−0.622015	−0.311008	+	0.950407i	$0.600666\pi$
$948$	4456.00	0.152663
$949$	19779.0	0.676558
$950$	0	0
$951$	−8058.00	−0.274762
$952$	−15360.0	−0.522921
$953$	31722.0	1.07825	0.539127	−	0.842224i	$-0.318754\pi$
$953$	31722.0	1.07825	0.539127	+	0.842224i	$0.318754\pi$
$954$	21944.0	0.744720
$955$	0	0
$956$	27324.0	0.924395
$957$	−2550.00	−0.0861335
$958$	−21136.0	−0.712811
$959$	20864.0	0.702538
$960$	0	0
$961$	−25566.0	−0.858179
$962$	1292.00	0.0433012
$963$	−8268.00	−0.276669
$964$	−7176.00	−0.239755
$965$	0	0
$966$	1472.00	0.0490278
$967$	1459.00	0.0485194	0.0242597	−	0.999706i	$-0.492277\pi$
$967$	1459.00	0.0485194	0.0242597	+	0.999706i	$0.492277\pi$
$968$	3448.00	0.114486
$969$	−3480.00	−0.115370
$970$	0	0
$971$	−29626.0	−0.979139	−0.489569	−	0.871964i	$-0.662846\pi$
$971$	−29626.0	−0.979139	−0.489569	+	0.871964i	$0.662846\pi$
$972$	8320.00	0.274552
$973$	−63968.0	−2.10763
$974$	−18622.0	−0.612615
$975$	0	0
$976$	−3936.00	−0.129086
$977$	40202.0	1.31645	0.658227	−	0.752819i	$-0.271307\pi$
$977$	40202.0	1.31645	0.658227	+	0.752819i	$0.271307\pi$
$978$	−8094.00	−0.264640
$979$	−24720.0	−0.807002
$980$	0	0
$981$	21528.0	0.700648
$982$	33022.0	1.07309
$983$	9278.00	0.301040	0.150520	−	0.988607i	$-0.451905\pi$
$983$	9278.00	0.301040	0.150520	+	0.988607i	$0.451905\pi$
$984$	−1144.00	−0.0370624
$985$	0	0
$986$	−10200.0	−0.329446
$987$	17952.0	0.578945
$988$	4408.00	0.141940
$989$	−7636.00	−0.245511
$990$	0	0
$991$	37264.0	1.19448	0.597240	−	0.802062i	$-0.296264\pi$
$991$	37264.0	1.19448	0.597240	+	0.802062i	$0.296264\pi$
$992$	2080.00	0.0665726
$993$	−2555.00	−0.0816520
$994$	47168.0	1.50511
$995$	0	0
$996$	3744.00	0.119110
$997$	41930.0	1.33193	0.665966	−	0.745982i	$-0.268020\pi$
$997$	41930.0	1.33193	0.665966	+	0.745982i	$0.268020\pi$
$998$	−4662.00	−0.147869
$999$	−1802.00	−0.0570698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.4.a.c.1.1		1
5.2	odd	4		1150.4.b.d.599.1		2
5.3	odd	4		1150.4.b.d.599.2		2
5.4	even	2		230.4.a.d.1.1	✓	1
15.14	odd	2		2070.4.a.a.1.1		1
20.19	odd	2		1840.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.d.1.1	✓	1	5.4	even	2
1150.4.a.c.1.1		1	1.1	even	1	trivial
1150.4.b.d.599.1		2	5.2	odd	4
1150.4.b.d.599.2		2	5.3	odd	4
1840.4.a.e.1.1		1	20.19	odd	2
2070.4.a.a.1.1		1	15.14	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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