LMFDB - Embedded newform 1425.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1425,4,Mod(1,1425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1425, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1425.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1425 = 3 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1425.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:	$84.0777217582$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1425.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{6} -32.0000 q^{7} -21.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{6} -32.0000 q^{7} -21.0000 q^{8} +9.00000 q^{9} -12.0000 q^{11} +3.00000 q^{12} +10.0000 q^{13} -96.0000 q^{14} -71.0000 q^{16} +30.0000 q^{17} +27.0000 q^{18} +19.0000 q^{19} -96.0000 q^{21} -36.0000 q^{22} +48.0000 q^{23} -63.0000 q^{24} +30.0000 q^{26} +27.0000 q^{27} -32.0000 q^{28} +150.000 q^{29} +224.000 q^{31} -45.0000 q^{32} -36.0000 q^{33} +90.0000 q^{34} +9.00000 q^{36} -254.000 q^{37} +57.0000 q^{38} +30.0000 q^{39} -54.0000 q^{41} -288.000 q^{42} +196.000 q^{43} -12.0000 q^{44} +144.000 q^{46} +504.000 q^{47} -213.000 q^{48} +681.000 q^{49} +90.0000 q^{51} +10.0000 q^{52} -78.0000 q^{53} +81.0000 q^{54} +672.000 q^{56} +57.0000 q^{57} +450.000 q^{58} +132.000 q^{59} +230.000 q^{61} +672.000 q^{62} -288.000 q^{63} +433.000 q^{64} -108.000 q^{66} -740.000 q^{67} +30.0000 q^{68} +144.000 q^{69} -120.000 q^{71} -189.000 q^{72} -122.000 q^{73} -762.000 q^{74} +19.0000 q^{76} +384.000 q^{77} +90.0000 q^{78} +1184.00 q^{79} +81.0000 q^{81} -162.000 q^{82} -612.000 q^{83} -96.0000 q^{84} +588.000 q^{86} +450.000 q^{87} +252.000 q^{88} +1050.00 q^{89} -320.000 q^{91} +48.0000 q^{92} +672.000 q^{93} +1512.00 q^{94} -135.000 q^{96} +1006.00 q^{97} +2043.00 q^{98} -108.000 q^{99} +O(q^{100})\)

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 $

$2$	3.00000	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$2$	3.00000	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	9.00000	0.612372
$7$	−32.0000	−1.72784	−0.863919	−	0.503631i	$-0.831997\pi$
$7$	−32.0000	−1.72784	−0.863919	+	0.503631i	$0.831997\pi$
$8$	−21.0000	−0.928078
$9$	9.00000	0.333333
$10$	0	0
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	3.00000	0.0721688
$13$	10.0000	0.213346	0.106673	−	0.994294i	$-0.465980\pi$
$13$	10.0000	0.213346	0.106673	+	0.994294i	$0.465980\pi$
$14$	−96.0000	−1.83265
$15$	0	0
$16$	−71.0000	−1.10938
$17$	30.0000	0.428004	0.214002	−	0.976833i	$-0.431350\pi$
$17$	30.0000	0.428004	0.214002	+	0.976833i	$0.431350\pi$
$18$	27.0000	0.353553
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	0	0
$21$	−96.0000	−0.997567
$22$	−36.0000	−0.348874
$23$	48.0000	0.435161	0.217580	−	0.976042i	$-0.430184\pi$
$23$	48.0000	0.435161	0.217580	+	0.976042i	$0.430184\pi$
$24$	−63.0000	−0.535826
$25$	0	0
$26$	30.0000	0.226288
$27$	27.0000	0.192450
$28$	−32.0000	−0.215980
$29$	150.000	0.960493	0.480247	−	0.877134i	$-0.340547\pi$
$29$	150.000	0.960493	0.480247	+	0.877134i	$0.340547\pi$
$30$	0	0
$31$	224.000	1.29779	0.648897	−	0.760877i	$-0.275231\pi$
$31$	224.000	1.29779	0.648897	+	0.760877i	$0.275231\pi$
$32$	−45.0000	−0.248592
$33$	−36.0000	−0.189903
$34$	90.0000	0.453967
$35$	0	0
$36$	9.00000	0.0416667
$37$	−254.000	−1.12858	−0.564288	−	0.825578i	$-0.690849\pi$
$37$	−254.000	−1.12858	−0.564288	+	0.825578i	$0.690849\pi$
$38$	57.0000	0.243332
$39$	30.0000	0.123176
$40$	0	0
$41$	−54.0000	−0.205692	−0.102846	−	0.994697i	$-0.532795\pi$
$41$	−54.0000	−0.205692	−0.102846	+	0.994697i	$0.532795\pi$
$42$	−288.000	−1.05808
$43$	196.000	0.695110	0.347555	−	0.937660i	$-0.387012\pi$
$43$	196.000	0.695110	0.347555	+	0.937660i	$0.387012\pi$
$44$	−12.0000	−0.0411152
$45$	0	0
$46$	144.000	0.461557
$47$	504.000	1.56417	0.782085	−	0.623172i	$-0.214156\pi$
$47$	504.000	1.56417	0.782085	+	0.623172i	$0.214156\pi$
$48$	−213.000	−0.640498
$49$	681.000	1.98542
$50$	0	0
$51$	90.0000	0.247108
$52$	10.0000	0.0266683
$53$	−78.0000	−0.202153	−0.101077	−	0.994879i	$-0.532229\pi$
$53$	−78.0000	−0.202153	−0.101077	+	0.994879i	$0.532229\pi$
$54$	81.0000	0.204124
$55$	0	0
$56$	672.000	1.60357
$57$	57.0000	0.132453
$58$	450.000	1.01876
$59$	132.000	0.291270	0.145635	−	0.989338i	$-0.453477\pi$
$59$	132.000	0.291270	0.145635	+	0.989338i	$0.453477\pi$
$60$	0	0
$61$	230.000	0.482762	0.241381	−	0.970430i	$-0.422400\pi$
$61$	230.000	0.482762	0.241381	+	0.970430i	$0.422400\pi$
$62$	672.000	1.37652
$63$	−288.000	−0.575946
$64$	433.000	0.845703
$65$	0	0
$66$	−108.000	−0.201422
$67$	−740.000	−1.34933	−0.674667	−	0.738122i	$-0.735713\pi$
$67$	−740.000	−1.34933	−0.674667	+	0.738122i	$0.735713\pi$
$68$	30.0000	0.0535005
$69$	144.000	0.251240
$70$	0	0
$71$	−120.000	−0.200583	−0.100291	−	0.994958i	$-0.531978\pi$
$71$	−120.000	−0.200583	−0.100291	+	0.994958i	$0.531978\pi$
$72$	−189.000	−0.309359
$73$	−122.000	−0.195603	−0.0978015	−	0.995206i	$-0.531181\pi$
$73$	−122.000	−0.195603	−0.0978015	+	0.995206i	$0.531181\pi$
$74$	−762.000	−1.19704
$75$	0	0
$76$	19.0000	0.0286770
$77$	384.000	0.568323
$78$	90.0000	0.130647
$79$	1184.00	1.68621	0.843104	−	0.537751i	$-0.180726\pi$
$79$	1184.00	1.68621	0.843104	+	0.537751i	$0.180726\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−162.000	−0.218170
$83$	−612.000	−0.809346	−0.404673	−	0.914461i	$-0.632615\pi$
$83$	−612.000	−0.809346	−0.404673	+	0.914461i	$0.632615\pi$
$84$	−96.0000	−0.124696
$85$	0	0
$86$	588.000	0.737275
$87$	450.000	0.554541
$88$	252.000	0.305265
$89$	1050.00	1.25056	0.625280	−	0.780401i	$-0.284985\pi$
$89$	1050.00	1.25056	0.625280	+	0.780401i	$0.284985\pi$
$90$	0	0
$91$	−320.000	−0.368628
$92$	48.0000	0.0543951
$93$	672.000	0.749281
$94$	1512.00	1.65905
$95$	0	0
$96$	−135.000	−0.143525
$97$	1006.00	1.05303	0.526515	−	0.850166i	$-0.323499\pi$
$97$	1006.00	1.05303	0.526515	+	0.850166i	$0.323499\pi$
$98$	2043.00	2.10586
$99$	−108.000	−0.109640
$100$	0	0
$101$	−642.000	−0.632489	−0.316244	−	0.948678i	$-0.602422\pi$
$101$	−642.000	−0.632489	−0.316244	+	0.948678i	$0.602422\pi$
$102$	270.000	0.262098
$103$	−1472.00	−1.40816	−0.704080	−	0.710121i	$-0.748640\pi$
$103$	−1472.00	−1.40816	−0.704080	+	0.710121i	$0.748640\pi$
$104$	−210.000	−0.198002
$105$	0	0
$106$	−234.000	−0.214416
$107$	2052.00	1.85397	0.926983	−	0.375104i	$-0.122393\pi$
$107$	2052.00	1.85397	0.926983	+	0.375104i	$0.122393\pi$
$108$	27.0000	0.0240563
$109$	1334.00	1.17224	0.586119	−	0.810225i	$-0.300655\pi$
$109$	1334.00	1.17224	0.586119	+	0.810225i	$0.300655\pi$
$110$	0	0
$111$	−762.000	−0.651584
$112$	2272.00	1.91682
$113$	414.000	0.344653	0.172327	−	0.985040i	$-0.444872\pi$
$113$	414.000	0.344653	0.172327	+	0.985040i	$0.444872\pi$
$114$	171.000	0.140488
$115$	0	0
$116$	150.000	0.120062
$117$	90.0000	0.0711154
$118$	396.000	0.308939
$119$	−960.000	−0.739521
$120$	0	0
$121$	−1187.00	−0.891811
$122$	690.000	0.512046
$123$	−162.000	−0.118756
$124$	224.000	0.162224
$125$	0	0
$126$	−864.000	−0.610883
$127$	−1496.00	−1.04526	−0.522632	−	0.852558i	$-0.675050\pi$
$127$	−1496.00	−1.04526	−0.522632	+	0.852558i	$0.675050\pi$
$128$	1659.00	1.14560
$129$	588.000	0.401322
$130$	0	0
$131$	1404.00	0.936397	0.468199	−	0.883623i	$-0.344903\pi$
$131$	1404.00	0.936397	0.468199	+	0.883623i	$0.344903\pi$
$132$	−36.0000	−0.0237379
$133$	−608.000	−0.396393
$134$	−2220.00	−1.43119
$135$	0	0
$136$	−630.000	−0.397221
$137$	−138.000	−0.0860594	−0.0430297	−	0.999074i	$-0.513701\pi$
$137$	−138.000	−0.0860594	−0.0430297	+	0.999074i	$0.513701\pi$
$138$	432.000	0.266480
$139$	−124.000	−0.0756658	−0.0378329	−	0.999284i	$-0.512045\pi$
$139$	−124.000	−0.0756658	−0.0378329	+	0.999284i	$0.512045\pi$
$140$	0	0
$141$	1512.00	0.903074
$142$	−360.000	−0.212750
$143$	−120.000	−0.0701742
$144$	−639.000	−0.369792
$145$	0	0
$146$	−366.000	−0.207468
$147$	2043.00	1.14628
$148$	−254.000	−0.141072
$149$	2670.00	1.46802	0.734010	−	0.679139i	$-0.237647\pi$
$149$	2670.00	1.46802	0.734010	+	0.679139i	$0.237647\pi$
$150$	0	0
$151$	−376.000	−0.202639	−0.101319	−	0.994854i	$-0.532306\pi$
$151$	−376.000	−0.202639	−0.101319	+	0.994854i	$0.532306\pi$
$152$	−399.000	−0.212916
$153$	270.000	0.142668
$154$	1152.00	0.602797
$155$	0	0
$156$	30.0000	0.0153969
$157$	682.000	0.346685	0.173342	−	0.984862i	$-0.444543\pi$
$157$	682.000	0.346685	0.173342	+	0.984862i	$0.444543\pi$
$158$	3552.00	1.78849
$159$	−234.000	−0.116713
$160$	0	0
$161$	−1536.00	−0.751887
$162$	243.000	0.117851
$163$	−3524.00	−1.69338	−0.846690	−	0.532086i	$-0.821408\pi$
$163$	−3524.00	−1.69338	−0.846690	+	0.532086i	$0.821408\pi$
$164$	−54.0000	−0.0257115
$165$	0	0
$166$	−1836.00	−0.858441
$167$	912.000	0.422591	0.211295	−	0.977422i	$-0.432232\pi$
$167$	912.000	0.422591	0.211295	+	0.977422i	$0.432232\pi$
$168$	2016.00	0.925820
$169$	−2097.00	−0.954483
$170$	0	0
$171$	171.000	0.0764719
$172$	196.000	0.0868887
$173$	−3990.00	−1.75349	−0.876746	−	0.480954i	$-0.840290\pi$
$173$	−3990.00	−1.75349	−0.876746	+	0.480954i	$0.840290\pi$
$174$	1350.00	0.588180
$175$	0	0
$176$	852.000	0.364897
$177$	396.000	0.168165
$178$	3150.00	1.32642
$179$	2316.00	0.967072	0.483536	−	0.875324i	$-0.339352\pi$
$179$	2316.00	0.967072	0.483536	+	0.875324i	$0.339352\pi$
$180$	0	0
$181$	−3346.00	−1.37407	−0.687034	−	0.726625i	$-0.741088\pi$
$181$	−3346.00	−1.37407	−0.687034	+	0.726625i	$0.741088\pi$
$182$	−960.000	−0.390989
$183$	690.000	0.278723
$184$	−1008.00	−0.403863
$185$	0	0
$186$	2016.00	0.794733
$187$	−360.000	−0.140780
$188$	504.000	0.195521
$189$	−864.000	−0.332522
$190$	0	0
$191$	960.000	0.363681	0.181841	−	0.983328i	$-0.441794\pi$
$191$	960.000	0.363681	0.181841	+	0.983328i	$0.441794\pi$
$192$	1299.00	0.488267
$193$	3214.00	1.19870	0.599349	−	0.800488i	$-0.295426\pi$
$193$	3214.00	1.19870	0.599349	+	0.800488i	$0.295426\pi$
$194$	3018.00	1.11691
$195$	0	0
$196$	681.000	0.248178
$197$	−990.000	−0.358044	−0.179022	−	0.983845i	$-0.557293\pi$
$197$	−990.000	−0.358044	−0.179022	+	0.983845i	$0.557293\pi$
$198$	−324.000	−0.116291
$199$	3560.00	1.26815	0.634075	−	0.773272i	$-0.281381\pi$
$199$	3560.00	1.26815	0.634075	+	0.773272i	$0.281381\pi$
$200$	0	0
$201$	−2220.00	−0.779038
$202$	−1926.00	−0.670856
$203$	−4800.00	−1.65958
$204$	90.0000	0.0308885
$205$	0	0
$206$	−4416.00	−1.49358
$207$	432.000	0.145054
$208$	−710.000	−0.236681
$209$	−228.000	−0.0754598
$210$	0	0
$211$	−2740.00	−0.893978	−0.446989	−	0.894539i	$-0.647504\pi$
$211$	−2740.00	−0.893978	−0.446989	+	0.894539i	$0.647504\pi$
$212$	−78.0000	−0.0252692
$213$	−360.000	−0.115807
$214$	6156.00	1.96643
$215$	0	0
$216$	−567.000	−0.178609
$217$	−7168.00	−2.24238
$218$	4002.00	1.24335
$219$	−366.000	−0.112931
$220$	0	0
$221$	300.000	0.0913130
$222$	−2286.00	−0.691109
$223$	3448.00	1.03540	0.517702	−	0.855561i	$-0.326788\pi$
$223$	3448.00	1.03540	0.517702	+	0.855561i	$0.326788\pi$
$224$	1440.00	0.429527
$225$	0	0
$226$	1242.00	0.365560
$227$	−5124.00	−1.49820	−0.749101	−	0.662456i	$-0.769514\pi$
$227$	−5124.00	−1.49820	−0.749101	+	0.662456i	$0.769514\pi$
$228$	57.0000	0.0165567
$229$	−3010.00	−0.868587	−0.434293	−	0.900771i	$-0.643002\pi$
$229$	−3010.00	−0.868587	−0.434293	+	0.900771i	$0.643002\pi$
$230$	0	0
$231$	1152.00	0.328121
$232$	−3150.00	−0.891412
$233$	3510.00	0.986900	0.493450	−	0.869774i	$-0.335736\pi$
$233$	3510.00	0.986900	0.493450	+	0.869774i	$0.335736\pi$
$234$	270.000	0.0754293
$235$	0	0
$236$	132.000	0.0364088
$237$	3552.00	0.973532
$238$	−2880.00	−0.784381
$239$	5280.00	1.42902	0.714508	−	0.699627i	$-0.246651\pi$
$239$	5280.00	1.42902	0.714508	+	0.699627i	$0.246651\pi$
$240$	0	0
$241$	1106.00	0.295617	0.147809	−	0.989016i	$-0.452778\pi$
$241$	1106.00	0.295617	0.147809	+	0.989016i	$0.452778\pi$
$242$	−3561.00	−0.945908
$243$	243.000	0.0641500
$244$	230.000	0.0603453
$245$	0	0
$246$	−486.000	−0.125960
$247$	190.000	0.0489450
$248$	−4704.00	−1.20445
$249$	−1836.00	−0.467276
$250$	0	0
$251$	−2844.00	−0.715186	−0.357593	−	0.933878i	$-0.616402\pi$
$251$	−2844.00	−0.715186	−0.357593	+	0.933878i	$0.616402\pi$
$252$	−288.000	−0.0719932
$253$	−576.000	−0.143134
$254$	−4488.00	−1.10867
$255$	0	0
$256$	1513.00	0.369385
$257$	4014.00	0.974266	0.487133	−	0.873328i	$-0.338043\pi$
$257$	4014.00	0.974266	0.487133	+	0.873328i	$0.338043\pi$
$258$	1764.00	0.425666
$259$	8128.00	1.95000
$260$	0	0
$261$	1350.00	0.320164
$262$	4212.00	0.993199
$263$	5472.00	1.28296	0.641479	−	0.767141i	$-0.278321\pi$
$263$	5472.00	1.28296	0.641479	+	0.767141i	$0.278321\pi$
$264$	756.000	0.176245
$265$	0	0
$266$	−1824.00	−0.420438
$267$	3150.00	0.722011
$268$	−740.000	−0.168667
$269$	1734.00	0.393025	0.196513	−	0.980501i	$-0.437038\pi$
$269$	1734.00	0.393025	0.196513	+	0.980501i	$0.437038\pi$
$270$	0	0
$271$	5456.00	1.22298	0.611492	−	0.791251i	$-0.290570\pi$
$271$	5456.00	1.22298	0.611492	+	0.791251i	$0.290570\pi$
$272$	−2130.00	−0.474817
$273$	−960.000	−0.212827
$274$	−414.000	−0.0912798
$275$	0	0
$276$	144.000	0.0314050
$277$	−830.000	−0.180036	−0.0900178	−	0.995940i	$-0.528692\pi$
$277$	−830.000	−0.180036	−0.0900178	+	0.995940i	$0.528692\pi$
$278$	−372.000	−0.0802557
$279$	2016.00	0.432598
$280$	0	0
$281$	3450.00	0.732419	0.366210	−	0.930532i	$-0.380655\pi$
$281$	3450.00	0.732419	0.366210	+	0.930532i	$0.380655\pi$
$282$	4536.00	0.957854
$283$	−1964.00	−0.412536	−0.206268	−	0.978496i	$-0.566132\pi$
$283$	−1964.00	−0.412536	−0.206268	+	0.978496i	$0.566132\pi$
$284$	−120.000	−0.0250729
$285$	0	0
$286$	−360.000	−0.0744309
$287$	1728.00	0.355403
$288$	−405.000	−0.0828641
$289$	−4013.00	−0.816813
$290$	0	0
$291$	3018.00	0.607967
$292$	−122.000	−0.0244504
$293$	2466.00	0.491690	0.245845	−	0.969309i	$-0.420935\pi$
$293$	2466.00	0.491690	0.245845	+	0.969309i	$0.420935\pi$
$294$	6129.00	1.21582
$295$	0	0
$296$	5334.00	1.04741
$297$	−324.000	−0.0633010
$298$	8010.00	1.55707
$299$	480.000	0.0928399
$300$	0	0
$301$	−6272.00	−1.20104
$302$	−1128.00	−0.214931
$303$	−1926.00	−0.365168
$304$	−1349.00	−0.254508
$305$	0	0
$306$	810.000	0.151322
$307$	7468.00	1.38834	0.694171	−	0.719810i	$-0.255771\pi$
$307$	7468.00	1.38834	0.694171	+	0.719810i	$0.255771\pi$
$308$	384.000	0.0710404
$309$	−4416.00	−0.813001
$310$	0	0
$311$	−3768.00	−0.687021	−0.343511	−	0.939149i	$-0.611616\pi$
$311$	−3768.00	−0.687021	−0.343511	+	0.939149i	$0.611616\pi$
$312$	−630.000	−0.114316
$313$	6838.00	1.23485	0.617423	−	0.786632i	$-0.288177\pi$
$313$	6838.00	1.23485	0.617423	+	0.786632i	$0.288177\pi$
$314$	2046.00	0.367715
$315$	0	0
$316$	1184.00	0.210776
$317$	−7014.00	−1.24273	−0.621365	−	0.783521i	$-0.713422\pi$
$317$	−7014.00	−1.24273	−0.621365	+	0.783521i	$0.713422\pi$
$318$	−702.000	−0.123793
$319$	−1800.00	−0.315927
$320$	0	0
$321$	6156.00	1.07039
$322$	−4608.00	−0.797496
$323$	570.000	0.0981909
$324$	81.0000	0.0138889
$325$	0	0
$326$	−10572.0	−1.79610
$327$	4002.00	0.676792
$328$	1134.00	0.190898
$329$	−16128.0	−2.70263
$330$	0	0
$331$	3092.00	0.513449	0.256725	−	0.966485i	$-0.417357\pi$
$331$	3092.00	0.513449	0.256725	+	0.966485i	$0.417357\pi$
$332$	−612.000	−0.101168
$333$	−2286.00	−0.376192
$334$	2736.00	0.448225
$335$	0	0
$336$	6816.00	1.10668
$337$	10270.0	1.66007	0.830033	−	0.557714i	$-0.188321\pi$
$337$	10270.0	1.66007	0.830033	+	0.557714i	$0.188321\pi$
$338$	−6291.00	−1.01238
$339$	1242.00	0.198986
$340$	0	0
$341$	−2688.00	−0.426872
$342$	513.000	0.0811107
$343$	−10816.0	−1.70265
$344$	−4116.00	−0.645116
$345$	0	0
$346$	−11970.0	−1.85986
$347$	−396.000	−0.0612634	−0.0306317	−	0.999531i	$-0.509752\pi$
$347$	−396.000	−0.0612634	−0.0306317	+	0.999531i	$0.509752\pi$
$348$	450.000	0.0693176
$349$	−5146.00	−0.789281	−0.394640	−	0.918836i	$-0.629131\pi$
$349$	−5146.00	−0.789281	−0.394640	+	0.918836i	$0.629131\pi$
$350$	0	0
$351$	270.000	0.0410585
$352$	540.000	0.0817673
$353$	9582.00	1.44475	0.722377	−	0.691499i	$-0.243049\pi$
$353$	9582.00	1.44475	0.722377	+	0.691499i	$0.243049\pi$
$354$	1188.00	0.178366
$355$	0	0
$356$	1050.00	0.156320
$357$	−2880.00	−0.426963
$358$	6948.00	1.02574
$359$	4968.00	0.730365	0.365182	−	0.930936i	$-0.381007\pi$
$359$	4968.00	0.730365	0.365182	+	0.930936i	$0.381007\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	−10038.0	−1.45742
$363$	−3561.00	−0.514887
$364$	−320.000	−0.0460785
$365$	0	0
$366$	2070.00	0.295630
$367$	−4088.00	−0.581449	−0.290725	−	0.956807i	$-0.593896\pi$
$367$	−4088.00	−0.581449	−0.290725	+	0.956807i	$0.593896\pi$
$368$	−3408.00	−0.482756
$369$	−486.000	−0.0685641
$370$	0	0
$371$	2496.00	0.349288
$372$	672.000	0.0936602
$373$	−2990.00	−0.415057	−0.207529	−	0.978229i	$-0.566542\pi$
$373$	−2990.00	−0.415057	−0.207529	+	0.978229i	$0.566542\pi$
$374$	−1080.00	−0.149319
$375$	0	0
$376$	−10584.0	−1.45167
$377$	1500.00	0.204918
$378$	−2592.00	−0.352693
$379$	4436.00	0.601219	0.300610	−	0.953747i	$-0.402810\pi$
$379$	4436.00	0.601219	0.300610	+	0.953747i	$0.402810\pi$
$380$	0	0
$381$	−4488.00	−0.603483
$382$	2880.00	0.385742
$383$	9048.00	1.20713	0.603566	−	0.797313i	$-0.293746\pi$
$383$	9048.00	1.20713	0.603566	+	0.797313i	$0.293746\pi$
$384$	4977.00	0.661410
$385$	0	0
$386$	9642.00	1.27141
$387$	1764.00	0.231703
$388$	1006.00	0.131629
$389$	−8034.00	−1.04715	−0.523573	−	0.851981i	$-0.675401\pi$
$389$	−8034.00	−1.04715	−0.523573	+	0.851981i	$0.675401\pi$
$390$	0	0
$391$	1440.00	0.186250
$392$	−14301.0	−1.84263
$393$	4212.00	0.540629
$394$	−2970.00	−0.379763
$395$	0	0
$396$	−108.000	−0.0137051
$397$	−11366.0	−1.43688	−0.718442	−	0.695587i	$-0.755145\pi$
$397$	−11366.0	−1.43688	−0.718442	+	0.695587i	$0.755145\pi$
$398$	10680.0	1.34508
$399$	−1824.00	−0.228858
$400$	0	0
$401$	−8382.00	−1.04383	−0.521917	−	0.852997i	$-0.674783\pi$
$401$	−8382.00	−1.04383	−0.521917	+	0.852997i	$0.674783\pi$
$402$	−6660.00	−0.826295
$403$	2240.00	0.276879
$404$	−642.000	−0.0790611
$405$	0	0
$406$	−14400.0	−1.76025
$407$	3048.00	0.371213
$408$	−1890.00	−0.229336
$409$	−6550.00	−0.791874	−0.395937	−	0.918278i	$-0.629580\pi$
$409$	−6550.00	−0.791874	−0.395937	+	0.918278i	$0.629580\pi$
$410$	0	0
$411$	−414.000	−0.0496864
$412$	−1472.00	−0.176020
$413$	−4224.00	−0.503267
$414$	1296.00	0.153852
$415$	0	0
$416$	−450.000	−0.0530362
$417$	−372.000	−0.0436857
$418$	−684.000	−0.0800372
$419$	−11412.0	−1.33058	−0.665290	−	0.746585i	$-0.731692\pi$
$419$	−11412.0	−1.33058	−0.665290	+	0.746585i	$0.731692\pi$
$420$	0	0
$421$	−8098.00	−0.937464	−0.468732	−	0.883340i	$-0.655289\pi$
$421$	−8098.00	−0.937464	−0.468732	+	0.883340i	$0.655289\pi$
$422$	−8220.00	−0.948207
$423$	4536.00	0.521390
$424$	1638.00	0.187614
$425$	0	0
$426$	−1080.00	−0.122831
$427$	−7360.00	−0.834134
$428$	2052.00	0.231746
$429$	−360.000	−0.0405151
$430$	0	0
$431$	10368.0	1.15872	0.579361	−	0.815071i	$-0.303302\pi$
$431$	10368.0	1.15872	0.579361	+	0.815071i	$0.303302\pi$
$432$	−1917.00	−0.213499
$433$	4606.00	0.511201	0.255601	−	0.966782i	$-0.417727\pi$
$433$	4606.00	0.511201	0.255601	+	0.966782i	$0.417727\pi$
$434$	−21504.0	−2.37840
$435$	0	0
$436$	1334.00	0.146530
$437$	912.000	0.0998327
$438$	−1098.00	−0.119782
$439$	9944.00	1.08110	0.540548	−	0.841313i	$-0.318217\pi$
$439$	9944.00	1.08110	0.540548	+	0.841313i	$0.318217\pi$
$440$	0	0
$441$	6129.00	0.661808
$442$	900.000	0.0968521
$443$	14532.0	1.55855	0.779273	−	0.626684i	$-0.215588\pi$
$443$	14532.0	1.55855	0.779273	+	0.626684i	$0.215588\pi$
$444$	−762.000	−0.0814480
$445$	0	0
$446$	10344.0	1.09821
$447$	8010.00	0.847562
$448$	−13856.0	−1.46124
$449$	16050.0	1.68696	0.843481	−	0.537158i	$-0.180502\pi$
$449$	16050.0	1.68696	0.843481	+	0.537158i	$0.180502\pi$
$450$	0	0
$451$	648.000	0.0676566
$452$	414.000	0.0430817
$453$	−1128.00	−0.116994
$454$	−15372.0	−1.58908
$455$	0	0
$456$	−1197.00	−0.122927
$457$	10918.0	1.11755	0.558777	−	0.829318i	$-0.311271\pi$
$457$	10918.0	1.11755	0.558777	+	0.829318i	$0.311271\pi$
$458$	−9030.00	−0.921276
$459$	810.000	0.0823694
$460$	0	0
$461$	16182.0	1.63486	0.817430	−	0.576027i	$-0.195398\pi$
$461$	16182.0	1.63486	0.817430	+	0.576027i	$0.195398\pi$
$462$	3456.00	0.348025
$463$	−3560.00	−0.357337	−0.178669	−	0.983909i	$-0.557179\pi$
$463$	−3560.00	−0.357337	−0.178669	+	0.983909i	$0.557179\pi$
$464$	−10650.0	−1.06555
$465$	0	0
$466$	10530.0	1.04677
$467$	3372.00	0.334128	0.167064	−	0.985946i	$-0.446571\pi$
$467$	3372.00	0.334128	0.167064	+	0.985946i	$0.446571\pi$
$468$	90.0000	0.00888943
$469$	23680.0	2.33143
$470$	0	0
$471$	2046.00	0.200159
$472$	−2772.00	−0.270321
$473$	−2352.00	−0.228637
$474$	10656.0	1.03259
$475$	0	0
$476$	−960.000	−0.0924402
$477$	−702.000	−0.0673844
$478$	15840.0	1.51570
$479$	−2448.00	−0.233511	−0.116756	−	0.993161i	$-0.537249\pi$
$479$	−2448.00	−0.233511	−0.116756	+	0.993161i	$0.537249\pi$
$480$	0	0
$481$	−2540.00	−0.240778
$482$	3318.00	0.313549
$483$	−4608.00	−0.434102
$484$	−1187.00	−0.111476
$485$	0	0
$486$	729.000	0.0680414
$487$	4048.00	0.376658	0.188329	−	0.982106i	$-0.439693\pi$
$487$	4048.00	0.376658	0.188329	+	0.982106i	$0.439693\pi$
$488$	−4830.00	−0.448041
$489$	−10572.0	−0.977674
$490$	0	0
$491$	−5580.00	−0.512876	−0.256438	−	0.966561i	$-0.582549\pi$
$491$	−5580.00	−0.512876	−0.256438	+	0.966561i	$0.582549\pi$
$492$	−162.000	−0.0148446
$493$	4500.00	0.411095
$494$	570.000	0.0519140
$495$	0	0
$496$	−15904.0	−1.43974
$497$	3840.00	0.346575
$498$	−5508.00	−0.495621
$499$	476.000	0.0427028	0.0213514	−	0.999772i	$-0.493203\pi$
$499$	476.000	0.0427028	0.0213514	+	0.999772i	$0.493203\pi$
$500$	0	0
$501$	2736.00	0.243983
$502$	−8532.00	−0.758569
$503$	−2832.00	−0.251039	−0.125520	−	0.992091i	$-0.540060\pi$
$503$	−2832.00	−0.251039	−0.125520	+	0.992091i	$0.540060\pi$
$504$	6048.00	0.534522
$505$	0	0
$506$	−1728.00	−0.151816
$507$	−6291.00	−0.551071
$508$	−1496.00	−0.130658
$509$	−2346.00	−0.204292	−0.102146	−	0.994769i	$-0.532571\pi$
$509$	−2346.00	−0.204292	−0.102146	+	0.994769i	$0.532571\pi$
$510$	0	0
$511$	3904.00	0.337970
$512$	−8733.00	−0.753804
$513$	513.000	0.0441511
$514$	12042.0	1.03337
$515$	0	0
$516$	588.000	0.0501652
$517$	−6048.00	−0.514489
$518$	24384.0	2.06828
$519$	−11970.0	−1.01238
$520$	0	0
$521$	−3990.00	−0.335518	−0.167759	−	0.985828i	$-0.553653\pi$
$521$	−3990.00	−0.335518	−0.167759	+	0.985828i	$0.553653\pi$
$522$	4050.00	0.339586
$523$	−3020.00	−0.252496	−0.126248	−	0.991999i	$-0.540294\pi$
$523$	−3020.00	−0.252496	−0.126248	+	0.991999i	$0.540294\pi$
$524$	1404.00	0.117050
$525$	0	0
$526$	16416.0	1.36078
$527$	6720.00	0.555461
$528$	2556.00	0.210674
$529$	−9863.00	−0.810635
$530$	0	0
$531$	1188.00	0.0970900
$532$	−608.000	−0.0495491
$533$	−540.000	−0.0438837
$534$	9450.00	0.765808
$535$	0	0
$536$	15540.0	1.25229
$537$	6948.00	0.558340
$538$	5202.00	0.416866
$539$	−8172.00	−0.653048
$540$	0	0
$541$	5894.00	0.468397	0.234199	−	0.972189i	$-0.424753\pi$
$541$	5894.00	0.468397	0.234199	+	0.972189i	$0.424753\pi$
$542$	16368.0	1.29717
$543$	−10038.0	−0.793318
$544$	−1350.00	−0.106398
$545$	0	0
$546$	−2880.00	−0.225737
$547$	22780.0	1.78063	0.890313	−	0.455349i	$-0.150486\pi$
$547$	22780.0	1.78063	0.890313	+	0.455349i	$0.150486\pi$
$548$	−138.000	−0.0107574
$549$	2070.00	0.160921
$550$	0	0
$551$	2850.00	0.220352
$552$	−3024.00	−0.233170
$553$	−37888.0	−2.91349
$554$	−2490.00	−0.190957
$555$	0	0
$556$	−124.000	−0.00945822
$557$	−9366.00	−0.712478	−0.356239	−	0.934395i	$-0.615941\pi$
$557$	−9366.00	−0.712478	−0.356239	+	0.934395i	$0.615941\pi$
$558$	6048.00	0.458839
$559$	1960.00	0.148299
$560$	0	0
$561$	−1080.00	−0.0812792
$562$	10350.0	0.776848
$563$	−19332.0	−1.44715	−0.723576	−	0.690245i	$-0.757503\pi$
$563$	−19332.0	−1.44715	−0.723576	+	0.690245i	$0.757503\pi$
$564$	1512.00	0.112884
$565$	0	0
$566$	−5892.00	−0.437560
$567$	−2592.00	−0.191982
$568$	2520.00	0.186156
$569$	−21222.0	−1.56357	−0.781786	−	0.623547i	$-0.785691\pi$
$569$	−21222.0	−1.56357	−0.781786	+	0.623547i	$0.785691\pi$
$570$	0	0
$571$	−26524.0	−1.94395	−0.971974	−	0.235086i	$-0.924463\pi$
$571$	−26524.0	−1.94395	−0.971974	+	0.235086i	$0.924463\pi$
$572$	−120.000	−0.00877177
$573$	2880.00	0.209972
$574$	5184.00	0.376962
$575$	0	0
$576$	3897.00	0.281901
$577$	−5186.00	−0.374170	−0.187085	−	0.982344i	$-0.559904\pi$
$577$	−5186.00	−0.374170	−0.187085	+	0.982344i	$0.559904\pi$
$578$	−12039.0	−0.866361
$579$	9642.00	0.692069
$580$	0	0
$581$	19584.0	1.39842
$582$	9054.00	0.644846
$583$	936.000	0.0664926
$584$	2562.00	0.181535
$585$	0	0
$586$	7398.00	0.521516
$587$	12516.0	0.880052	0.440026	−	0.897985i	$-0.354969\pi$
$587$	12516.0	0.880052	0.440026	+	0.897985i	$0.354969\pi$
$588$	2043.00	0.143286
$589$	4256.00	0.297734
$590$	0	0
$591$	−2970.00	−0.206717
$592$	18034.0	1.25201
$593$	−15042.0	−1.04165	−0.520827	−	0.853662i	$-0.674376\pi$
$593$	−15042.0	−1.04165	−0.520827	+	0.853662i	$0.674376\pi$
$594$	−972.000	−0.0671408
$595$	0	0
$596$	2670.00	0.183502
$597$	10680.0	0.732166
$598$	1440.00	0.0984715
$599$	6600.00	0.450198	0.225099	−	0.974336i	$-0.427729\pi$
$599$	6600.00	0.450198	0.225099	+	0.974336i	$0.427729\pi$
$600$	0	0
$601$	−23830.0	−1.61738	−0.808690	−	0.588234i	$-0.799823\pi$
$601$	−23830.0	−1.61738	−0.808690	+	0.588234i	$0.799823\pi$
$602$	−18816.0	−1.27389
$603$	−6660.00	−0.449778
$604$	−376.000	−0.0253298
$605$	0	0
$606$	−5778.00	−0.387319
$607$	4552.00	0.304382	0.152191	−	0.988351i	$-0.451367\pi$
$607$	4552.00	0.304382	0.152191	+	0.988351i	$0.451367\pi$
$608$	−855.000	−0.0570310
$609$	−14400.0	−0.958157
$610$	0	0
$611$	5040.00	0.333710
$612$	270.000	0.0178335
$613$	6802.00	0.448173	0.224087	−	0.974569i	$-0.428060\pi$
$613$	6802.00	0.448173	0.224087	+	0.974569i	$0.428060\pi$
$614$	22404.0	1.47256
$615$	0	0
$616$	−8064.00	−0.527448
$617$	13686.0	0.892995	0.446497	−	0.894785i	$-0.352671\pi$
$617$	13686.0	0.892995	0.446497	+	0.894785i	$0.352671\pi$
$618$	−13248.0	−0.862318
$619$	24836.0	1.61267	0.806335	−	0.591459i	$-0.201448\pi$
$619$	24836.0	1.61267	0.806335	+	0.591459i	$0.201448\pi$
$620$	0	0
$621$	1296.00	0.0837467
$622$	−11304.0	−0.728696
$623$	−33600.0	−2.16076
$624$	−2130.00	−0.136648
$625$	0	0
$626$	20514.0	1.30975
$627$	−684.000	−0.0435667
$628$	682.000	0.0433356
$629$	−7620.00	−0.483035
$630$	0	0
$631$	30056.0	1.89621	0.948107	−	0.317953i	$-0.102995\pi$
$631$	30056.0	1.89621	0.948107	+	0.317953i	$0.102995\pi$
$632$	−24864.0	−1.56493
$633$	−8220.00	−0.516138
$634$	−21042.0	−1.31811
$635$	0	0
$636$	−234.000	−0.0145892
$637$	6810.00	0.423582
$638$	−5400.00	−0.335091
$639$	−1080.00	−0.0668609
$640$	0	0
$641$	−3438.00	−0.211845	−0.105923	−	0.994374i	$-0.533780\pi$
$641$	−3438.00	−0.211845	−0.105923	+	0.994374i	$0.533780\pi$
$642$	18468.0	1.13532
$643$	5596.00	0.343211	0.171606	−	0.985166i	$-0.445105\pi$
$643$	5596.00	0.343211	0.171606	+	0.985166i	$0.445105\pi$
$644$	−1536.00	−0.0939858
$645$	0	0
$646$	1710.00	0.104147
$647$	−1968.00	−0.119583	−0.0597914	−	0.998211i	$-0.519044\pi$
$647$	−1968.00	−0.119583	−0.0597914	+	0.998211i	$0.519044\pi$
$648$	−1701.00	−0.103120
$649$	−1584.00	−0.0958050
$650$	0	0
$651$	−21504.0	−1.29464
$652$	−3524.00	−0.211673
$653$	12138.0	0.727407	0.363703	−	0.931515i	$-0.381512\pi$
$653$	12138.0	0.727407	0.363703	+	0.931515i	$0.381512\pi$
$654$	12006.0	0.717847
$655$	0	0
$656$	3834.00	0.228190
$657$	−1098.00	−0.0652010
$658$	−48384.0	−2.86657
$659$	−2004.00	−0.118459	−0.0592297	−	0.998244i	$-0.518864\pi$
$659$	−2004.00	−0.118459	−0.0592297	+	0.998244i	$0.518864\pi$
$660$	0	0
$661$	24590.0	1.44696	0.723480	−	0.690346i	$-0.242542\pi$
$661$	24590.0	1.44696	0.723480	+	0.690346i	$0.242542\pi$
$662$	9276.00	0.544595
$663$	900.000	0.0527196
$664$	12852.0	0.751136
$665$	0	0
$666$	−6858.00	−0.399012
$667$	7200.00	0.417969
$668$	912.000	0.0528239
$669$	10344.0	0.597791
$670$	0	0
$671$	−2760.00	−0.158791
$672$	4320.00	0.247988
$673$	−11762.0	−0.673688	−0.336844	−	0.941561i	$-0.609359\pi$
$673$	−11762.0	−0.673688	−0.336844	+	0.941561i	$0.609359\pi$
$674$	30810.0	1.76077
$675$	0	0
$676$	−2097.00	−0.119310
$677$	−21438.0	−1.21703	−0.608515	−	0.793542i	$-0.708234\pi$
$677$	−21438.0	−1.21703	−0.608515	+	0.793542i	$0.708234\pi$
$678$	3726.00	0.211056
$679$	−32192.0	−1.81946
$680$	0	0
$681$	−15372.0	−0.864987
$682$	−8064.00	−0.452766
$683$	−25644.0	−1.43666	−0.718331	−	0.695701i	$-0.755094\pi$
$683$	−25644.0	−1.43666	−0.718331	+	0.695701i	$0.755094\pi$
$684$	171.000	0.00955899
$685$	0	0
$686$	−32448.0	−1.80593
$687$	−9030.00	−0.501479
$688$	−13916.0	−0.771137
$689$	−780.000	−0.0431286
$690$	0	0
$691$	12332.0	0.678917	0.339458	−	0.940621i	$-0.389756\pi$
$691$	12332.0	0.678917	0.339458	+	0.940621i	$0.389756\pi$
$692$	−3990.00	−0.219186
$693$	3456.00	0.189441
$694$	−1188.00	−0.0649796
$695$	0	0
$696$	−9450.00	−0.514657
$697$	−1620.00	−0.0880371
$698$	−15438.0	−0.837159
$699$	10530.0	0.569787
$700$	0	0
$701$	−1050.00	−0.0565734	−0.0282867	−	0.999600i	$-0.509005\pi$
$701$	−1050.00	−0.0565734	−0.0282867	+	0.999600i	$0.509005\pi$
$702$	810.000	0.0435491
$703$	−4826.00	−0.258913
$704$	−5196.00	−0.278170
$705$	0	0
$706$	28746.0	1.53239
$707$	20544.0	1.09284
$708$	396.000	0.0210206
$709$	13790.0	0.730457	0.365229	−	0.930918i	$-0.380991\pi$
$709$	13790.0	0.730457	0.365229	+	0.930918i	$0.380991\pi$
$710$	0	0
$711$	10656.0	0.562069
$712$	−22050.0	−1.16062
$713$	10752.0	0.564748
$714$	−8640.00	−0.452863
$715$	0	0
$716$	2316.00	0.120884
$717$	15840.0	0.825043
$718$	14904.0	0.774669
$719$	−20160.0	−1.04568	−0.522838	−	0.852432i	$-0.675127\pi$
$719$	−20160.0	−1.04568	−0.522838	+	0.852432i	$0.675127\pi$
$720$	0	0
$721$	47104.0	2.43307
$722$	1083.00	0.0558242
$723$	3318.00	0.170675
$724$	−3346.00	−0.171758
$725$	0	0
$726$	−10683.0	−0.546120
$727$	36976.0	1.88633	0.943166	−	0.332321i	$-0.107832\pi$
$727$	36976.0	1.88633	0.943166	+	0.332321i	$0.107832\pi$
$728$	6720.00	0.342115
$729$	729.000	0.0370370
$730$	0	0
$731$	5880.00	0.297510
$732$	690.000	0.0348403
$733$	970.000	0.0488783	0.0244391	−	0.999701i	$-0.492220\pi$
$733$	970.000	0.0488783	0.0244391	+	0.999701i	$0.492220\pi$
$734$	−12264.0	−0.616720
$735$	0	0
$736$	−2160.00	−0.108178
$737$	8880.00	0.443825
$738$	−1458.00	−0.0727232
$739$	17900.0	0.891018	0.445509	−	0.895278i	$-0.353023\pi$
$739$	17900.0	0.891018	0.445509	+	0.895278i	$0.353023\pi$
$740$	0	0
$741$	570.000	0.0282584
$742$	7488.00	0.370476
$743$	−2496.00	−0.123243	−0.0616214	−	0.998100i	$-0.519627\pi$
$743$	−2496.00	−0.123243	−0.0616214	+	0.998100i	$0.519627\pi$
$744$	−14112.0	−0.695391
$745$	0	0
$746$	−8970.00	−0.440235
$747$	−5508.00	−0.269782
$748$	−360.000	−0.0175975
$749$	−65664.0	−3.20335
$750$	0	0
$751$	−9520.00	−0.462570	−0.231285	−	0.972886i	$-0.574293\pi$
$751$	−9520.00	−0.462570	−0.231285	+	0.972886i	$0.574293\pi$
$752$	−35784.0	−1.73525
$753$	−8532.00	−0.412913
$754$	4500.00	0.217348
$755$	0	0
$756$	−864.000	−0.0415653
$757$	6466.00	0.310450	0.155225	−	0.987879i	$-0.450390\pi$
$757$	6466.00	0.310450	0.155225	+	0.987879i	$0.450390\pi$
$758$	13308.0	0.637689
$759$	−1728.00	−0.0826382
$760$	0	0
$761$	−30198.0	−1.43847	−0.719236	−	0.694766i	$-0.755508\pi$
$761$	−30198.0	−1.43847	−0.719236	+	0.694766i	$0.755508\pi$
$762$	−13464.0	−0.640091
$763$	−42688.0	−2.02544
$764$	960.000	0.0454602
$765$	0	0
$766$	27144.0	1.28036
$767$	1320.00	0.0621414
$768$	4539.00	0.213264
$769$	−14590.0	−0.684173	−0.342086	−	0.939669i	$-0.611134\pi$
$769$	−14590.0	−0.684173	−0.342086	+	0.939669i	$0.611134\pi$
$770$	0	0
$771$	12042.0	0.562493
$772$	3214.00	0.149837
$773$	34818.0	1.62007	0.810036	−	0.586379i	$-0.199447\pi$
$773$	34818.0	1.62007	0.810036	+	0.586379i	$0.199447\pi$
$774$	5292.00	0.245758
$775$	0	0
$776$	−21126.0	−0.977293
$777$	24384.0	1.12583
$778$	−24102.0	−1.11067
$779$	−1026.00	−0.0471890
$780$	0	0
$781$	1440.00	0.0659760
$782$	4320.00	0.197548
$783$	4050.00	0.184847
$784$	−48351.0	−2.20258
$785$	0	0
$786$	12636.0	0.573424
$787$	1804.00	0.0817099	0.0408549	−	0.999165i	$-0.486992\pi$
$787$	1804.00	0.0817099	0.0408549	+	0.999165i	$0.486992\pi$
$788$	−990.000	−0.0447554
$789$	16416.0	0.740716
$790$	0	0
$791$	−13248.0	−0.595505
$792$	2268.00	0.101755
$793$	2300.00	0.102995
$794$	−34098.0	−1.52405
$795$	0	0
$796$	3560.00	0.158519
$797$	−35718.0	−1.58745	−0.793724	−	0.608278i	$-0.791861\pi$
$797$	−35718.0	−1.58745	−0.793724	+	0.608278i	$0.791861\pi$
$798$	−5472.00	−0.242740
$799$	15120.0	0.669471
$800$	0	0
$801$	9450.00	0.416853
$802$	−25146.0	−1.10715
$803$	1464.00	0.0643380
$804$	−2220.00	−0.0973798
$805$	0	0
$806$	6720.00	0.293675
$807$	5202.00	0.226913
$808$	13482.0	0.586999
$809$	−44838.0	−1.94860	−0.974302	−	0.225247i	$-0.927681\pi$
$809$	−44838.0	−1.94860	−0.974302	+	0.225247i	$0.927681\pi$
$810$	0	0
$811$	17588.0	0.761527	0.380763	−	0.924673i	$-0.375661\pi$
$811$	17588.0	0.761527	0.380763	+	0.924673i	$0.375661\pi$
$812$	−4800.00	−0.207447
$813$	16368.0	0.706090
$814$	9144.00	0.393731
$815$	0	0
$816$	−6390.00	−0.274136
$817$	3724.00	0.159469
$818$	−19650.0	−0.839910
$819$	−2880.00	−0.122876
$820$	0	0
$821$	−33522.0	−1.42500	−0.712501	−	0.701672i	$-0.752437\pi$
$821$	−33522.0	−1.42500	−0.712501	+	0.701672i	$0.752437\pi$
$822$	−1242.00	−0.0527004
$823$	3904.00	0.165352	0.0826761	−	0.996576i	$-0.473653\pi$
$823$	3904.00	0.165352	0.0826761	+	0.996576i	$0.473653\pi$
$824$	30912.0	1.30688
$825$	0	0
$826$	−12672.0	−0.533796
$827$	−11628.0	−0.488930	−0.244465	−	0.969658i	$-0.578612\pi$
$827$	−11628.0	−0.488930	−0.244465	+	0.969658i	$0.578612\pi$
$828$	432.000	0.0181317
$829$	−19738.0	−0.826935	−0.413467	−	0.910519i	$-0.635682\pi$
$829$	−19738.0	−0.826935	−0.413467	+	0.910519i	$0.635682\pi$
$830$	0	0
$831$	−2490.00	−0.103944
$832$	4330.00	0.180428
$833$	20430.0	0.849769
$834$	−1116.00	−0.0463356
$835$	0	0
$836$	−228.000	−0.00943247
$837$	6048.00	0.249760
$838$	−34236.0	−1.41129
$839$	−31752.0	−1.30656	−0.653278	−	0.757118i	$-0.726607\pi$
$839$	−31752.0	−1.30656	−0.653278	+	0.757118i	$0.726607\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	−24294.0	−0.994331
$843$	10350.0	0.422862
$844$	−2740.00	−0.111747
$845$	0	0
$846$	13608.0	0.553017
$847$	37984.0	1.54090
$848$	5538.00	0.224264
$849$	−5892.00	−0.238178
$850$	0	0
$851$	−12192.0	−0.491112
$852$	−360.000	−0.0144758
$853$	10978.0	0.440656	0.220328	−	0.975426i	$-0.429287\pi$
$853$	10978.0	0.440656	0.220328	+	0.975426i	$0.429287\pi$
$854$	−22080.0	−0.884733
$855$	0	0
$856$	−43092.0	−1.72062
$857$	−3450.00	−0.137514	−0.0687571	−	0.997633i	$-0.521903\pi$
$857$	−3450.00	−0.137514	−0.0687571	+	0.997633i	$0.521903\pi$
$858$	−1080.00	−0.0429727
$859$	−46348.0	−1.84095	−0.920473	−	0.390805i	$-0.872197\pi$
$859$	−46348.0	−1.84095	−0.920473	+	0.390805i	$0.872197\pi$
$860$	0	0
$861$	5184.00	0.205192
$862$	31104.0	1.22901
$863$	47736.0	1.88291	0.941456	−	0.337137i	$-0.109459\pi$
$863$	47736.0	1.88291	0.941456	+	0.337137i	$0.109459\pi$
$864$	−1215.00	−0.0478416
$865$	0	0
$866$	13818.0	0.542211
$867$	−12039.0	−0.471587
$868$	−7168.00	−0.280297
$869$	−14208.0	−0.554630
$870$	0	0
$871$	−7400.00	−0.287875
$872$	−28014.0	−1.08793
$873$	9054.00	0.351010
$874$	2736.00	0.105889
$875$	0	0
$876$	−366.000	−0.0141164
$877$	33706.0	1.29780	0.648900	−	0.760874i	$-0.275229\pi$
$877$	33706.0	1.29780	0.648900	+	0.760874i	$0.275229\pi$
$878$	29832.0	1.14668
$879$	7398.00	0.283878
$880$	0	0
$881$	−33774.0	−1.29157	−0.645786	−	0.763518i	$-0.723470\pi$
$881$	−33774.0	−1.29157	−0.645786	+	0.763518i	$0.723470\pi$
$882$	18387.0	0.701953
$883$	22444.0	0.855380	0.427690	−	0.903925i	$-0.359327\pi$
$883$	22444.0	0.855380	0.427690	+	0.903925i	$0.359327\pi$
$884$	300.000	0.0114141
$885$	0	0
$886$	43596.0	1.65309
$887$	−30240.0	−1.14471	−0.572356	−	0.820005i	$-0.693971\pi$
$887$	−30240.0	−1.14471	−0.572356	+	0.820005i	$0.693971\pi$
$888$	16002.0	0.604721
$889$	47872.0	1.80605
$890$	0	0
$891$	−972.000	−0.0365468
$892$	3448.00	0.129426
$893$	9576.00	0.358845
$894$	24030.0	0.898975
$895$	0	0
$896$	−53088.0	−1.97940
$897$	1440.00	0.0536011
$898$	48150.0	1.78929
$899$	33600.0	1.24652
$900$	0	0
$901$	−2340.00	−0.0865224
$902$	1944.00	0.0717607
$903$	−18816.0	−0.693419
$904$	−8694.00	−0.319865
$905$	0	0
$906$	−3384.00	−0.124090
$907$	−38972.0	−1.42673	−0.713365	−	0.700793i	$-0.752830\pi$
$907$	−38972.0	−1.42673	−0.713365	+	0.700793i	$0.752830\pi$
$908$	−5124.00	−0.187275
$909$	−5778.00	−0.210830
$910$	0	0
$911$	16128.0	0.586547	0.293274	−	0.956029i	$-0.405255\pi$
$911$	16128.0	0.586547	0.293274	+	0.956029i	$0.405255\pi$
$912$	−4047.00	−0.146940
$913$	7344.00	0.266211
$914$	32754.0	1.18535
$915$	0	0
$916$	−3010.00	−0.108573
$917$	−44928.0	−1.61794
$918$	2430.00	0.0873660
$919$	23576.0	0.846246	0.423123	−	0.906072i	$-0.360934\pi$
$919$	23576.0	0.846246	0.423123	+	0.906072i	$0.360934\pi$
$920$	0	0
$921$	22404.0	0.801560
$922$	48546.0	1.73403
$923$	−1200.00	−0.0427936
$924$	1152.00	0.0410152
$925$	0	0
$926$	−10680.0	−0.379014
$927$	−13248.0	−0.469387
$928$	−6750.00	−0.238771
$929$	54882.0	1.93823	0.969117	−	0.246600i	$-0.0793134\pi$
$929$	54882.0	1.93823	0.969117	+	0.246600i	$0.0793134\pi$
$930$	0	0
$931$	12939.0	0.455487
$932$	3510.00	0.123363
$933$	−11304.0	−0.396652
$934$	10116.0	0.354396
$935$	0	0
$936$	−1890.00	−0.0660006
$937$	−33146.0	−1.15564	−0.577819	−	0.816165i	$-0.696096\pi$
$937$	−33146.0	−1.15564	−0.577819	+	0.816165i	$0.696096\pi$
$938$	71040.0	2.47286
$939$	20514.0	0.712938
$940$	0	0
$941$	−33786.0	−1.17045	−0.585224	−	0.810871i	$-0.698994\pi$
$941$	−33786.0	−1.17045	−0.585224	+	0.810871i	$0.698994\pi$
$942$	6138.00	0.212300
$943$	−2592.00	−0.0895092
$944$	−9372.00	−0.323128
$945$	0	0
$946$	−7056.00	−0.242506
$947$	18060.0	0.619716	0.309858	−	0.950783i	$-0.399718\pi$
$947$	18060.0	0.619716	0.309858	+	0.950783i	$0.399718\pi$
$948$	3552.00	0.121692
$949$	−1220.00	−0.0417312
$950$	0	0
$951$	−21042.0	−0.717491
$952$	20160.0	0.686333
$953$	−26202.0	−0.890625	−0.445313	−	0.895375i	$-0.646907\pi$
$953$	−26202.0	−0.890625	−0.445313	+	0.895375i	$0.646907\pi$
$954$	−2106.00	−0.0714720
$955$	0	0
$956$	5280.00	0.178627
$957$	−5400.00	−0.182400
$958$	−7344.00	−0.247676
$959$	4416.00	0.148697
$960$	0	0
$961$	20385.0	0.684267
$962$	−7620.00	−0.255383
$963$	18468.0	0.617989
$964$	1106.00	0.0369521
$965$	0	0
$966$	−13824.0	−0.460435
$967$	−13856.0	−0.460785	−0.230392	−	0.973098i	$-0.574001\pi$
$967$	−13856.0	−0.460785	−0.230392	+	0.973098i	$0.574001\pi$
$968$	24927.0	0.827670
$969$	1710.00	0.0566905
$970$	0	0
$971$	16644.0	0.550084	0.275042	−	0.961432i	$-0.411308\pi$
$971$	16644.0	0.550084	0.275042	+	0.961432i	$0.411308\pi$
$972$	243.000	0.00801875
$973$	3968.00	0.130738
$974$	12144.0	0.399506
$975$	0	0
$976$	−16330.0	−0.535564
$977$	40446.0	1.32444	0.662222	−	0.749308i	$-0.269613\pi$
$977$	40446.0	1.32444	0.662222	+	0.749308i	$0.269613\pi$
$978$	−31716.0	−1.03698
$979$	−12600.0	−0.411336
$980$	0	0
$981$	12006.0	0.390746
$982$	−16740.0	−0.543987
$983$	−17232.0	−0.559120	−0.279560	−	0.960128i	$-0.590189\pi$
$983$	−17232.0	−0.559120	−0.279560	+	0.960128i	$0.590189\pi$
$984$	3402.00	0.110215
$985$	0	0
$986$	13500.0	0.436032
$987$	−48384.0	−1.56036
$988$	190.000	0.00611812
$989$	9408.00	0.302484
$990$	0	0
$991$	48992.0	1.57042	0.785208	−	0.619232i	$-0.212556\pi$
$991$	48992.0	1.57042	0.785208	+	0.619232i	$0.212556\pi$
$992$	−10080.0	−0.322621
$993$	9276.00	0.296440
$994$	11520.0	0.367598
$995$	0	0
$996$	−1836.00	−0.0584095
$997$	−7310.00	−0.232207	−0.116103	−	0.993237i	$-0.537040\pi$
$997$	−7310.00	−0.232207	−0.116103	+	0.993237i	$0.537040\pi$
$998$	1428.00	0.0452931
$999$	−6858.00	−0.217195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1425.4.a.f.1.1		1
5.4	even	2		285.4.a.a.1.1	✓	1
15.14	odd	2		855.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.4.a.a.1.1	✓	1	5.4	even	2
855.4.a.f.1.1		1	15.14	odd	2
1425.4.a.f.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1425.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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