LMFDB - Embedded newform 1078.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,4,Mod(1,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, 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("1078.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1078.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:	$63.6040589862$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1078.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +1.00000 q^{5} -10.0000 q^{6} -8.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +5.00000 q^{3} +4.00000 q^{4} +1.00000 q^{5} -10.0000 q^{6} -8.00000 q^{8} -2.00000 q^{9} -2.00000 q^{10} -11.0000 q^{11} +20.0000 q^{12} +8.00000 q^{13} +5.00000 q^{15} +16.0000 q^{16} -22.0000 q^{17} +4.00000 q^{18} -54.0000 q^{19} +4.00000 q^{20} +22.0000 q^{22} +213.000 q^{23} -40.0000 q^{24} -124.000 q^{25} -16.0000 q^{26} -145.000 q^{27} +190.000 q^{29} -10.0000 q^{30} -163.000 q^{31} -32.0000 q^{32} -55.0000 q^{33} +44.0000 q^{34} -8.00000 q^{36} +31.0000 q^{37} +108.000 q^{38} +40.0000 q^{39} -8.00000 q^{40} -110.000 q^{41} +4.00000 q^{43} -44.0000 q^{44} -2.00000 q^{45} -426.000 q^{46} +80.0000 q^{47} +80.0000 q^{48} +248.000 q^{50} -110.000 q^{51} +32.0000 q^{52} -566.000 q^{53} +290.000 q^{54} -11.0000 q^{55} -270.000 q^{57} -380.000 q^{58} -645.000 q^{59} +20.0000 q^{60} -634.000 q^{61} +326.000 q^{62} +64.0000 q^{64} +8.00000 q^{65} +110.000 q^{66} -729.000 q^{67} -88.0000 q^{68} +1065.00 q^{69} +431.000 q^{71} +16.0000 q^{72} +918.000 q^{73} -62.0000 q^{74} -620.000 q^{75} -216.000 q^{76} -80.0000 q^{78} -254.000 q^{79} +16.0000 q^{80} -671.000 q^{81} +220.000 q^{82} -904.000 q^{83} -22.0000 q^{85} -8.00000 q^{86} +950.000 q^{87} +88.0000 q^{88} -901.000 q^{89} +4.00000 q^{90} +852.000 q^{92} -815.000 q^{93} -160.000 q^{94} -54.0000 q^{95} -160.000 q^{96} +89.0000 q^{97} +22.0000 q^{99} +O(q^{100})\)

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
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	4.00000	0.500000
$5$	1.00000	0.0894427	0.0447214	−	0.998999i	$-0.485760\pi$
$5$	1.00000	0.0894427	0.0447214	+	0.998999i	$0.485760\pi$
$6$	−10.0000	−0.680414
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	−2.00000	−0.0740741
$10$	−2.00000	−0.0632456
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	20.0000	0.481125
$13$	8.00000	0.170677	0.0853385	−	0.996352i	$-0.472803\pi$
$13$	8.00000	0.170677	0.0853385	+	0.996352i	$0.472803\pi$
$14$	0	0
$15$	5.00000	0.0860663
$16$	16.0000	0.250000
$17$	−22.0000	−0.313870	−0.156935	−	0.987609i	$-0.550161\pi$
$17$	−22.0000	−0.313870	−0.156935	+	0.987609i	$0.550161\pi$
$18$	4.00000	0.0523783
$19$	−54.0000	−0.652024	−0.326012	−	0.945366i	$-0.605705\pi$
$19$	−54.0000	−0.652024	−0.326012	+	0.945366i	$0.605705\pi$
$20$	4.00000	0.0447214
$21$	0	0
$22$	22.0000	0.213201
$23$	213.000	1.93102	0.965512	−	0.260357i	$-0.0838403\pi$
$23$	213.000	1.93102	0.965512	+	0.260357i	$0.0838403\pi$
$24$	−40.0000	−0.340207
$25$	−124.000	−0.992000
$26$	−16.0000	−0.120687
$27$	−145.000	−1.03353
$28$	0	0
$29$	190.000	1.21662	0.608312	−	0.793698i	$-0.291847\pi$
$29$	190.000	1.21662	0.608312	+	0.793698i	$0.291847\pi$
$30$	−10.0000	−0.0608581
$31$	−163.000	−0.944376	−0.472188	−	0.881498i	$-0.656536\pi$
$31$	−163.000	−0.944376	−0.472188	+	0.881498i	$0.656536\pi$
$32$	−32.0000	−0.176777
$33$	−55.0000	−0.290129
$34$	44.0000	0.221939
$35$	0	0
$36$	−8.00000	−0.0370370
$37$	31.0000	0.137740	0.0688698	−	0.997626i	$-0.478061\pi$
$37$	31.0000	0.137740	0.0688698	+	0.997626i	$0.478061\pi$
$38$	108.000	0.461050
$39$	40.0000	0.164234
$40$	−8.00000	−0.0316228
$41$	−110.000	−0.419003	−0.209501	−	0.977808i	$-0.567184\pi$
$41$	−110.000	−0.419003	−0.209501	+	0.977808i	$0.567184\pi$
$42$	0	0
$43$	4.00000	0.0141859	0.00709296	−	0.999975i	$-0.497742\pi$
$43$	4.00000	0.0141859	0.00709296	+	0.999975i	$0.497742\pi$
$44$	−44.0000	−0.150756
$45$	−2.00000	−0.00662539
$46$	−426.000	−1.36544
$47$	80.0000	0.248281	0.124140	−	0.992265i	$-0.460383\pi$
$47$	80.0000	0.248281	0.124140	+	0.992265i	$0.460383\pi$
$48$	80.0000	0.240563
$49$	0	0
$50$	248.000	0.701450
$51$	−110.000	−0.302021
$52$	32.0000	0.0853385
$53$	−566.000	−1.46691	−0.733454	−	0.679740i	$-0.762093\pi$
$53$	−566.000	−1.46691	−0.733454	+	0.679740i	$0.762093\pi$
$54$	290.000	0.730815
$55$	−11.0000	−0.0269680
$56$	0	0
$57$	−270.000	−0.627410
$58$	−380.000	−0.860284
$59$	−645.000	−1.42325	−0.711626	−	0.702559i	$-0.752041\pi$
$59$	−645.000	−1.42325	−0.711626	+	0.702559i	$0.752041\pi$
$60$	20.0000	0.0430331
$61$	−634.000	−1.33074	−0.665372	−	0.746512i	$-0.731727\pi$
$61$	−634.000	−1.33074	−0.665372	+	0.746512i	$0.731727\pi$
$62$	326.000	0.667775
$63$	0	0
$64$	64.0000	0.125000
$65$	8.00000	0.0152658
$66$	110.000	0.205152
$67$	−729.000	−1.32928	−0.664638	−	0.747165i	$-0.731414\pi$
$67$	−729.000	−1.32928	−0.664638	+	0.747165i	$0.731414\pi$
$68$	−88.0000	−0.156935
$69$	1065.00	1.85813
$70$	0	0
$71$	431.000	0.720427	0.360213	−	0.932870i	$-0.382704\pi$
$71$	431.000	0.720427	0.360213	+	0.932870i	$0.382704\pi$
$72$	16.0000	0.0261891
$73$	918.000	1.47183	0.735916	−	0.677073i	$-0.236752\pi$
$73$	918.000	1.47183	0.735916	+	0.677073i	$0.236752\pi$
$74$	−62.0000	−0.0973967
$75$	−620.000	−0.954552
$76$	−216.000	−0.326012
$77$	0	0
$78$	−80.0000	−0.116131
$79$	−254.000	−0.361737	−0.180869	−	0.983507i	$-0.557891\pi$
$79$	−254.000	−0.361737	−0.180869	+	0.983507i	$0.557891\pi$
$80$	16.0000	0.0223607
$81$	−671.000	−0.920439
$82$	220.000	0.296280
$83$	−904.000	−1.19550	−0.597752	−	0.801681i	$-0.703939\pi$
$83$	−904.000	−1.19550	−0.597752	+	0.801681i	$0.703939\pi$
$84$	0	0
$85$	−22.0000	−0.0280734
$86$	−8.00000	−0.0100310
$87$	950.000	1.17070
$88$	88.0000	0.106600
$89$	−901.000	−1.07310	−0.536549	−	0.843869i	$-0.680273\pi$
$89$	−901.000	−1.07310	−0.536549	+	0.843869i	$0.680273\pi$
$90$	4.00000	0.00468486
$91$	0	0
$92$	852.000	0.965512
$93$	−815.000	−0.908726
$94$	−160.000	−0.175561
$95$	−54.0000	−0.0583188
$96$	−160.000	−0.170103
$97$	89.0000	0.0931606	0.0465803	−	0.998915i	$-0.485168\pi$
$97$	89.0000	0.0931606	0.0465803	+	0.998915i	$0.485168\pi$
$98$	0	0
$99$	22.0000	0.0223342
$100$	−496.000	−0.496000
$101$	−332.000	−0.327082	−0.163541	−	0.986537i	$-0.552292\pi$
$101$	−332.000	−0.327082	−0.163541	+	0.986537i	$0.552292\pi$
$102$	220.000	0.213561
$103$	−52.0000	−0.0497448	−0.0248724	−	0.999691i	$-0.507918\pi$
$103$	−52.0000	−0.0497448	−0.0248724	+	0.999691i	$0.507918\pi$
$104$	−64.0000	−0.0603434
$105$	0	0
$106$	1132.00	1.03726
$107$	366.000	0.330678	0.165339	−	0.986237i	$-0.447128\pi$
$107$	366.000	0.330678	0.165339	+	0.986237i	$0.447128\pi$
$108$	−580.000	−0.516764
$109$	−184.000	−0.161688	−0.0808441	−	0.996727i	$-0.525762\pi$
$109$	−184.000	−0.161688	−0.0808441	+	0.996727i	$0.525762\pi$
$110$	22.0000	0.0190693
$111$	155.000	0.132540
$112$	0	0
$113$	−1131.00	−0.941553	−0.470777	−	0.882252i	$-0.656026\pi$
$113$	−1131.00	−0.941553	−0.470777	+	0.882252i	$0.656026\pi$
$114$	540.000	0.443646
$115$	213.000	0.172716
$116$	760.000	0.608312
$117$	−16.0000	−0.0126427
$118$	1290.00	1.00639
$119$	0	0
$120$	−40.0000	−0.0304290
$121$	121.000	0.0909091
$122$	1268.00	0.940978
$123$	−550.000	−0.403186
$124$	−652.000	−0.472188
$125$	−249.000	−0.178170
$126$	0	0
$127$	2126.00	1.48545	0.742724	−	0.669597i	$-0.233533\pi$
$127$	2126.00	1.48545	0.742724	+	0.669597i	$0.233533\pi$
$128$	−128.000	−0.0883883
$129$	20.0000	0.0136504
$130$	−16.0000	−0.0107946
$131$	−2610.00	−1.74074	−0.870369	−	0.492399i	$-0.836120\pi$
$131$	−2610.00	−1.74074	−0.870369	+	0.492399i	$0.836120\pi$
$132$	−220.000	−0.145065
$133$	0	0
$134$	1458.00	0.939940
$135$	−145.000	−0.0924416
$136$	176.000	0.110970
$137$	349.000	0.217643	0.108821	−	0.994061i	$-0.465292\pi$
$137$	349.000	0.217643	0.108821	+	0.994061i	$0.465292\pi$
$138$	−2130.00	−1.31390
$139$	762.000	0.464978	0.232489	−	0.972599i	$-0.425313\pi$
$139$	762.000	0.464978	0.232489	+	0.972599i	$0.425313\pi$
$140$	0	0
$141$	400.000	0.238908
$142$	−862.000	−0.509419
$143$	−88.0000	−0.0514610
$144$	−32.0000	−0.0185185
$145$	190.000	0.108818
$146$	−1836.00	−1.04074
$147$	0	0
$148$	124.000	0.0688698
$149$	2486.00	1.36685	0.683426	−	0.730019i	$-0.260489\pi$
$149$	2486.00	1.36685	0.683426	+	0.730019i	$0.260489\pi$
$150$	1240.00	0.674971
$151$	722.000	0.389109	0.194555	−	0.980892i	$-0.437674\pi$
$151$	722.000	0.389109	0.194555	+	0.980892i	$0.437674\pi$
$152$	432.000	0.230525
$153$	44.0000	0.0232496
$154$	0	0
$155$	−163.000	−0.0844676
$156$	160.000	0.0821170
$157$	2049.00	1.04158	0.520790	−	0.853685i	$-0.325638\pi$
$157$	2049.00	1.04158	0.520790	+	0.853685i	$0.325638\pi$
$158$	508.000	0.255787
$159$	−2830.00	−1.41153
$160$	−32.0000	−0.0158114
$161$	0	0
$162$	1342.00	0.650849
$163$	964.000	0.463229	0.231614	−	0.972808i	$-0.425599\pi$
$163$	964.000	0.463229	0.231614	+	0.972808i	$0.425599\pi$
$164$	−440.000	−0.209501
$165$	−55.0000	−0.0259500
$166$	1808.00	0.845349
$167$	−1194.00	−0.553260	−0.276630	−	0.960976i	$-0.589218\pi$
$167$	−1194.00	−0.553260	−0.276630	+	0.960976i	$0.589218\pi$
$168$	0	0
$169$	−2133.00	−0.970869
$170$	44.0000	0.0198509
$171$	108.000	0.0482980
$172$	16.0000	0.00709296
$173$	−1572.00	−0.690849	−0.345425	−	0.938446i	$-0.612265\pi$
$173$	−1572.00	−0.690849	−0.345425	+	0.938446i	$0.612265\pi$
$174$	−1900.00	−0.827808
$175$	0	0
$176$	−176.000	−0.0753778
$177$	−3225.00	−1.36952
$178$	1802.00	0.758796
$179$	−3693.00	−1.54205	−0.771027	−	0.636802i	$-0.780257\pi$
$179$	−3693.00	−1.54205	−0.771027	+	0.636802i	$0.780257\pi$
$180$	−8.00000	−0.00331269
$181$	−125.000	−0.0513325	−0.0256662	−	0.999671i	$-0.508171\pi$
$181$	−125.000	−0.0513325	−0.0256662	+	0.999671i	$0.508171\pi$
$182$	0	0
$183$	−3170.00	−1.28051
$184$	−1704.00	−0.682720
$185$	31.0000	0.0123198
$186$	1630.00	0.642567
$187$	242.000	0.0946353
$188$	320.000	0.124140
$189$	0	0
$190$	108.000	0.0412376
$191$	−4445.00	−1.68392	−0.841961	−	0.539539i	$-0.818598\pi$
$191$	−4445.00	−1.68392	−0.841961	+	0.539539i	$0.818598\pi$
$192$	320.000	0.120281
$193$	−718.000	−0.267786	−0.133893	−	0.990996i	$-0.542748\pi$
$193$	−718.000	−0.267786	−0.133893	+	0.990996i	$0.542748\pi$
$194$	−178.000	−0.0658745
$195$	40.0000	0.0146895
$196$	0	0
$197$	18.0000	0.00650988	0.00325494	−	0.999995i	$-0.498964\pi$
$197$	18.0000	0.00650988	0.00325494	+	0.999995i	$0.498964\pi$
$198$	−44.0000	−0.0157926
$199$	520.000	0.185235	0.0926176	−	0.995702i	$-0.470477\pi$
$199$	520.000	0.185235	0.0926176	+	0.995702i	$0.470477\pi$
$200$	992.000	0.350725
$201$	−3645.00	−1.27910
$202$	664.000	0.231282
$203$	0	0
$204$	−440.000	−0.151011
$205$	−110.000	−0.0374767
$206$	104.000	0.0351749
$207$	−426.000	−0.143039
$208$	128.000	0.0426692
$209$	594.000	0.196593
$210$	0	0
$211$	630.000	0.205550	0.102775	−	0.994705i	$-0.467228\pi$
$211$	630.000	0.205550	0.102775	+	0.994705i	$0.467228\pi$
$212$	−2264.00	−0.733454
$213$	2155.00	0.693231
$214$	−732.000	−0.233825
$215$	4.00000	0.00126883
$216$	1160.00	0.365407
$217$	0	0
$218$	368.000	0.114331
$219$	4590.00	1.41627
$220$	−44.0000	−0.0134840
$221$	−176.000	−0.0535703
$222$	−310.000	−0.0937200
$223$	2077.00	0.623705	0.311852	−	0.950131i	$-0.399051\pi$
$223$	2077.00	0.623705	0.311852	+	0.950131i	$0.399051\pi$
$224$	0	0
$225$	248.000	0.0734815
$226$	2262.00	0.665779
$227$	−3708.00	−1.08418	−0.542089	−	0.840321i	$-0.682367\pi$
$227$	−3708.00	−1.08418	−0.542089	+	0.840321i	$0.682367\pi$
$228$	−1080.00	−0.313705
$229$	−1417.00	−0.408900	−0.204450	−	0.978877i	$-0.565541\pi$
$229$	−1417.00	−0.408900	−0.204450	+	0.978877i	$0.565541\pi$
$230$	−426.000	−0.122129
$231$	0	0
$232$	−1520.00	−0.430142
$233$	−3222.00	−0.905924	−0.452962	−	0.891530i	$-0.649633\pi$
$233$	−3222.00	−0.905924	−0.452962	+	0.891530i	$0.649633\pi$
$234$	32.0000	0.00893977
$235$	80.0000	0.0222069
$236$	−2580.00	−0.711626
$237$	−1270.00	−0.348082
$238$	0	0
$239$	4072.00	1.10207	0.551037	−	0.834481i	$-0.314232\pi$
$239$	4072.00	1.10207	0.551037	+	0.834481i	$0.314232\pi$
$240$	80.0000	0.0215166
$241$	−3732.00	−0.997507	−0.498754	−	0.866744i	$-0.666209\pi$
$241$	−3732.00	−0.997507	−0.498754	+	0.866744i	$0.666209\pi$
$242$	−242.000	−0.0642824
$243$	560.000	0.147835
$244$	−2536.00	−0.665372
$245$	0	0
$246$	1100.00	0.285095
$247$	−432.000	−0.111285
$248$	1304.00	0.333887
$249$	−4520.00	−1.15037
$250$	498.000	0.125985
$251$	−5101.00	−1.28276	−0.641379	−	0.767224i	$-0.721637\pi$
$251$	−5101.00	−1.28276	−0.641379	+	0.767224i	$0.721637\pi$
$252$	0	0
$253$	−2343.00	−0.582226
$254$	−4252.00	−1.05037
$255$	−110.000	−0.0270136
$256$	256.000	0.0625000
$257$	2478.00	0.601453	0.300726	−	0.953710i	$-0.402771\pi$
$257$	2478.00	0.601453	0.300726	+	0.953710i	$0.402771\pi$
$258$	−40.0000	−0.00965229
$259$	0	0
$260$	32.0000	0.00763291
$261$	−380.000	−0.0901203
$262$	5220.00	1.23089
$263$	2378.00	0.557543	0.278771	−	0.960357i	$-0.410073\pi$
$263$	2378.00	0.557543	0.278771	+	0.960357i	$0.410073\pi$
$264$	440.000	0.102576
$265$	−566.000	−0.131204
$266$	0	0
$267$	−4505.00	−1.03259
$268$	−2916.00	−0.664638
$269$	−8518.00	−1.93068	−0.965338	−	0.261004i	$-0.915946\pi$
$269$	−8518.00	−1.93068	−0.965338	+	0.261004i	$0.915946\pi$
$270$	290.000	0.0653661
$271$	3716.00	0.832955	0.416478	−	0.909146i	$-0.363264\pi$
$271$	3716.00	0.832955	0.416478	+	0.909146i	$0.363264\pi$
$272$	−352.000	−0.0784674
$273$	0	0
$274$	−698.000	−0.153897
$275$	1364.00	0.299099
$276$	4260.00	0.929065
$277$	2564.00	0.556158	0.278079	−	0.960558i	$-0.410302\pi$
$277$	2564.00	0.556158	0.278079	+	0.960558i	$0.410302\pi$
$278$	−1524.00	−0.328789
$279$	326.000	0.0699538
$280$	0	0
$281$	928.000	0.197010	0.0985051	−	0.995137i	$-0.468594\pi$
$281$	928.000	0.197010	0.0985051	+	0.995137i	$0.468594\pi$
$282$	−800.000	−0.168934
$283$	−9328.00	−1.95934	−0.979668	−	0.200626i	$-0.935702\pi$
$283$	−9328.00	−1.95934	−0.979668	+	0.200626i	$0.935702\pi$
$284$	1724.00	0.360213
$285$	−270.000	−0.0561173
$286$	176.000	0.0363885
$287$	0	0
$288$	64.0000	0.0130946
$289$	−4429.00	−0.901486
$290$	−380.000	−0.0769461
$291$	445.000	0.0896439
$292$	3672.00	0.735916
$293$	3982.00	0.793962	0.396981	−	0.917827i	$-0.370058\pi$
$293$	3982.00	0.793962	0.396981	+	0.917827i	$0.370058\pi$
$294$	0	0
$295$	−645.000	−0.127299
$296$	−248.000	−0.0486983
$297$	1595.00	0.311620
$298$	−4972.00	−0.966511
$299$	1704.00	0.329581
$300$	−2480.00	−0.477276
$301$	0	0
$302$	−1444.00	−0.275142
$303$	−1660.00	−0.314734
$304$	−864.000	−0.163006
$305$	−634.000	−0.119025
$306$	−88.0000	−0.0164400
$307$	−6584.00	−1.22400	−0.612001	−	0.790857i	$-0.709635\pi$
$307$	−6584.00	−1.22400	−0.612001	+	0.790857i	$0.709635\pi$
$308$	0	0
$309$	−260.000	−0.0478669
$310$	326.000	0.0597276
$311$	−3920.00	−0.714736	−0.357368	−	0.933964i	$-0.616326\pi$
$311$	−3920.00	−0.714736	−0.357368	+	0.933964i	$0.616326\pi$
$312$	−320.000	−0.0580655
$313$	−4293.00	−0.775255	−0.387627	−	0.921816i	$-0.626705\pi$
$313$	−4293.00	−0.775255	−0.387627	+	0.921816i	$0.626705\pi$
$314$	−4098.00	−0.736508
$315$	0	0
$316$	−1016.00	−0.180869
$317$	6493.00	1.15042	0.575210	−	0.818006i	$-0.304920\pi$
$317$	6493.00	1.15042	0.575210	+	0.818006i	$0.304920\pi$
$318$	5660.00	0.998104
$319$	−2090.00	−0.366826
$320$	64.0000	0.0111803
$321$	1830.00	0.318195
$322$	0	0
$323$	1188.00	0.204650
$324$	−2684.00	−0.460219
$325$	−992.000	−0.169312
$326$	−1928.00	−0.327552
$327$	−920.000	−0.155584
$328$	880.000	0.148140
$329$	0	0
$330$	110.000	0.0183494
$331$	3269.00	0.542841	0.271421	−	0.962461i	$-0.412507\pi$
$331$	3269.00	0.542841	0.271421	+	0.962461i	$0.412507\pi$
$332$	−3616.00	−0.597752
$333$	−62.0000	−0.0102029
$334$	2388.00	0.391214
$335$	−729.000	−0.118894
$336$	0	0
$337$	11114.0	1.79649	0.898247	−	0.439492i	$-0.144842\pi$
$337$	11114.0	1.79649	0.898247	+	0.439492i	$0.144842\pi$
$338$	4266.00	0.686508
$339$	−5655.00	−0.906010
$340$	−88.0000	−0.0140367
$341$	1793.00	0.284740
$342$	−216.000	−0.0341519
$343$	0	0
$344$	−32.0000	−0.00501548
$345$	1065.00	0.166196
$346$	3144.00	0.488504
$347$	−6342.00	−0.981142	−0.490571	−	0.871401i	$-0.663212\pi$
$347$	−6342.00	−0.981142	−0.490571	+	0.871401i	$0.663212\pi$
$348$	3800.00	0.585349
$349$	1790.00	0.274546	0.137273	−	0.990533i	$-0.456166\pi$
$349$	1790.00	0.274546	0.137273	+	0.990533i	$0.456166\pi$
$350$	0	0
$351$	−1160.00	−0.176399
$352$	352.000	0.0533002
$353$	6939.00	1.04625	0.523124	−	0.852256i	$-0.324766\pi$
$353$	6939.00	1.04625	0.523124	+	0.852256i	$0.324766\pi$
$354$	6450.00	0.968400
$355$	431.000	0.0644369
$356$	−3604.00	−0.536549
$357$	0	0
$358$	7386.00	1.09040
$359$	2332.00	0.342836	0.171418	−	0.985198i	$-0.445165\pi$
$359$	2332.00	0.342836	0.171418	+	0.985198i	$0.445165\pi$
$360$	16.0000	0.00234243
$361$	−3943.00	−0.574865
$362$	250.000	0.0362975
$363$	605.000	0.0874773
$364$	0	0
$365$	918.000	0.131645
$366$	6340.00	0.905457
$367$	−11039.0	−1.57011	−0.785056	−	0.619425i	$-0.787366\pi$
$367$	−11039.0	−1.57011	−0.785056	+	0.619425i	$0.787366\pi$
$368$	3408.00	0.482756
$369$	220.000	0.0310372
$370$	−62.0000	−0.00871142
$371$	0	0
$372$	−3260.00	−0.454363
$373$	364.000	0.0505287	0.0252644	−	0.999681i	$-0.491957\pi$
$373$	364.000	0.0505287	0.0252644	+	0.999681i	$0.491957\pi$
$374$	−484.000	−0.0669172
$375$	−1245.00	−0.171444
$376$	−640.000	−0.0877805
$377$	1520.00	0.207650
$378$	0	0
$379$	6145.00	0.832843	0.416421	−	0.909172i	$-0.363284\pi$
$379$	6145.00	0.832843	0.416421	+	0.909172i	$0.363284\pi$
$380$	−216.000	−0.0291594
$381$	10630.0	1.42937
$382$	8890.00	1.19071
$383$	12381.0	1.65180	0.825900	−	0.563816i	$-0.190667\pi$
$383$	12381.0	1.65180	0.825900	+	0.563816i	$0.190667\pi$
$384$	−640.000	−0.0850517
$385$	0	0
$386$	1436.00	0.189354
$387$	−8.00000	−0.00105081
$388$	356.000	0.0465803
$389$	12061.0	1.57202	0.786012	−	0.618212i	$-0.212143\pi$
$389$	12061.0	1.57202	0.786012	+	0.618212i	$0.212143\pi$
$390$	−80.0000	−0.0103871
$391$	−4686.00	−0.606090
$392$	0	0
$393$	−13050.0	−1.67503
$394$	−36.0000	−0.00460318
$395$	−254.000	−0.0323548
$396$	88.0000	0.0111671
$397$	774.000	0.0978487	0.0489244	−	0.998802i	$-0.484421\pi$
$397$	774.000	0.0978487	0.0489244	+	0.998802i	$0.484421\pi$
$398$	−1040.00	−0.130981
$399$	0	0
$400$	−1984.00	−0.248000
$401$	5154.00	0.641842	0.320921	−	0.947106i	$-0.396008\pi$
$401$	5154.00	0.641842	0.320921	+	0.947106i	$0.396008\pi$
$402$	7290.00	0.904458
$403$	−1304.00	−0.161183
$404$	−1328.00	−0.163541
$405$	−671.000	−0.0823266
$406$	0	0
$407$	−341.000	−0.0415301
$408$	880.000	0.106781
$409$	5266.00	0.636643	0.318321	−	0.947983i	$-0.396881\pi$
$409$	5266.00	0.636643	0.318321	+	0.947983i	$0.396881\pi$
$410$	220.000	0.0265001
$411$	1745.00	0.209427
$412$	−208.000	−0.0248724
$413$	0	0
$414$	852.000	0.101144
$415$	−904.000	−0.106929
$416$	−256.000	−0.0301717
$417$	3810.00	0.447426
$418$	−1188.00	−0.139012
$419$	8280.00	0.965404	0.482702	−	0.875785i	$-0.339655\pi$
$419$	8280.00	0.965404	0.482702	+	0.875785i	$0.339655\pi$
$420$	0	0
$421$	−2610.00	−0.302146	−0.151073	−	0.988523i	$-0.548273\pi$
$421$	−2610.00	−0.302146	−0.151073	+	0.988523i	$0.548273\pi$
$422$	−1260.00	−0.145346
$423$	−160.000	−0.0183912
$424$	4528.00	0.518630
$425$	2728.00	0.311359
$426$	−4310.00	−0.490188
$427$	0	0
$428$	1464.00	0.165339
$429$	−440.000	−0.0495184
$430$	−8.00000	−0.000897196 0
$431$	−10636.0	−1.18867	−0.594337	−	0.804216i	$-0.702585\pi$
$431$	−10636.0	−1.18867	−0.594337	+	0.804216i	$0.702585\pi$
$432$	−2320.00	−0.258382
$433$	13317.0	1.47800	0.739000	−	0.673705i	$-0.235298\pi$
$433$	13317.0	1.47800	0.739000	+	0.673705i	$0.235298\pi$
$434$	0	0
$435$	950.000	0.104710
$436$	−736.000	−0.0808441
$437$	−11502.0	−1.25907
$438$	−9180.00	−1.00146
$439$	14822.0	1.61142	0.805712	−	0.592307i	$-0.201783\pi$
$439$	14822.0	1.61142	0.805712	+	0.592307i	$0.201783\pi$
$440$	88.0000	0.00953463
$441$	0	0
$442$	352.000	0.0378799
$443$	−11637.0	−1.24806	−0.624030	−	0.781400i	$-0.714506\pi$
$443$	−11637.0	−1.24806	−0.624030	+	0.781400i	$0.714506\pi$
$444$	620.000	0.0662700
$445$	−901.000	−0.0959809
$446$	−4154.00	−0.441026
$447$	12430.0	1.31525
$448$	0	0
$449$	−15489.0	−1.62800	−0.813999	−	0.580866i	$-0.802714\pi$
$449$	−15489.0	−1.62800	−0.813999	+	0.580866i	$0.802714\pi$
$450$	−496.000	−0.0519593
$451$	1210.00	0.126334
$452$	−4524.00	−0.470777
$453$	3610.00	0.374421
$454$	7416.00	0.766630
$455$	0	0
$456$	2160.00	0.221823
$457$	16888.0	1.72864	0.864319	−	0.502944i	$-0.167750\pi$
$457$	16888.0	1.72864	0.864319	+	0.502944i	$0.167750\pi$
$458$	2834.00	0.289136
$459$	3190.00	0.324393
$460$	852.000	0.0863581
$461$	4938.00	0.498884	0.249442	−	0.968390i	$-0.419753\pi$
$461$	4938.00	0.498884	0.249442	+	0.968390i	$0.419753\pi$
$462$	0	0
$463$	−8645.00	−0.867748	−0.433874	−	0.900974i	$-0.642854\pi$
$463$	−8645.00	−0.867748	−0.433874	+	0.900974i	$0.642854\pi$
$464$	3040.00	0.304156
$465$	−815.000	−0.0812790
$466$	6444.00	0.640585
$467$	2075.00	0.205609	0.102805	−	0.994702i	$-0.467218\pi$
$467$	2075.00	0.205609	0.102805	+	0.994702i	$0.467218\pi$
$468$	−64.0000	−0.00632137
$469$	0	0
$470$	−160.000	−0.0157027
$471$	10245.0	1.00226
$472$	5160.00	0.503195
$473$	−44.0000	−0.00427721
$474$	2540.00	0.246131
$475$	6696.00	0.646807
$476$	0	0
$477$	1132.00	0.108660
$478$	−8144.00	−0.779284
$479$	16472.0	1.57124	0.785621	−	0.618708i	$-0.212344\pi$
$479$	16472.0	1.57124	0.785621	+	0.618708i	$0.212344\pi$
$480$	−160.000	−0.0152145
$481$	248.000	0.0235090
$482$	7464.00	0.705344
$483$	0	0
$484$	484.000	0.0454545
$485$	89.0000	0.00833254
$486$	−1120.00	−0.104535
$487$	9133.00	0.849806	0.424903	−	0.905239i	$-0.360308\pi$
$487$	9133.00	0.849806	0.424903	+	0.905239i	$0.360308\pi$
$488$	5072.00	0.470489
$489$	4820.00	0.445742
$490$	0	0
$491$	354.000	0.0325373	0.0162686	−	0.999868i	$-0.494821\pi$
$491$	354.000	0.0325373	0.0162686	+	0.999868i	$0.494821\pi$
$492$	−2200.00	−0.201593
$493$	−4180.00	−0.381862
$494$	864.000	0.0786907
$495$	22.0000	0.00199763
$496$	−2608.00	−0.236094
$497$	0	0
$498$	9040.00	0.813438
$499$	8956.00	0.803458	0.401729	−	0.915759i	$-0.368409\pi$
$499$	8956.00	0.803458	0.401729	+	0.915759i	$0.368409\pi$
$500$	−996.000	−0.0890849
$501$	−5970.00	−0.532375
$502$	10202.0	0.907047
$503$	20804.0	1.84414	0.922072	−	0.387018i	$-0.126495\pi$
$503$	20804.0	1.84414	0.922072	+	0.387018i	$0.126495\pi$
$504$	0	0
$505$	−332.000	−0.0292551
$506$	4686.00	0.411696
$507$	−10665.0	−0.934219
$508$	8504.00	0.742724
$509$	−6241.00	−0.543472	−0.271736	−	0.962372i	$-0.587598\pi$
$509$	−6241.00	−0.543472	−0.271736	+	0.962372i	$0.587598\pi$
$510$	220.000	0.0191015
$511$	0	0
$512$	−512.000	−0.0441942
$513$	7830.00	0.673885
$514$	−4956.00	−0.425291
$515$	−52.0000	−0.00444931
$516$	80.0000	0.00682520
$517$	−880.000	−0.0748595
$518$	0	0
$519$	−7860.00	−0.664770
$520$	−64.0000	−0.00539728
$521$	−12867.0	−1.08198	−0.540992	−	0.841028i	$-0.681951\pi$
$521$	−12867.0	−1.08198	−0.540992	+	0.841028i	$0.681951\pi$
$522$	760.000	0.0637247
$523$	12532.0	1.04777	0.523887	−	0.851788i	$-0.324481\pi$
$523$	12532.0	1.04777	0.523887	+	0.851788i	$0.324481\pi$
$524$	−10440.0	−0.870369
$525$	0	0
$526$	−4756.00	−0.394242
$527$	3586.00	0.296411
$528$	−880.000	−0.0725324
$529$	33202.0	2.72886
$530$	1132.00	0.0927754
$531$	1290.00	0.105426
$532$	0	0
$533$	−880.000	−0.0715141
$534$	9010.00	0.730151
$535$	366.000	0.0295767
$536$	5832.00	0.469970
$537$	−18465.0	−1.48384
$538$	17036.0	1.36519
$539$	0	0
$540$	−580.000	−0.0462208
$541$	−4404.00	−0.349987	−0.174993	−	0.984570i	$-0.555990\pi$
$541$	−4404.00	−0.349987	−0.174993	+	0.984570i	$0.555990\pi$
$542$	−7432.00	−0.588988
$543$	−625.000	−0.0493947
$544$	704.000	0.0554848
$545$	−184.000	−0.0144618
$546$	0	0
$547$	−1904.00	−0.148828	−0.0744142	−	0.997227i	$-0.523709\pi$
$547$	−1904.00	−0.148828	−0.0744142	+	0.997227i	$0.523709\pi$
$548$	1396.00	0.108821
$549$	1268.00	0.0985736
$550$	−2728.00	−0.211495
$551$	−10260.0	−0.793268
$552$	−8520.00	−0.656948
$553$	0	0
$554$	−5128.00	−0.393263
$555$	155.000	0.0118547
$556$	3048.00	0.232489
$557$	7250.00	0.551512	0.275756	−	0.961228i	$-0.411072\pi$
$557$	7250.00	0.551512	0.275756	+	0.961228i	$0.411072\pi$
$558$	−652.000	−0.0494648
$559$	32.0000	0.00242121
$560$	0	0
$561$	1210.00	0.0910628
$562$	−1856.00	−0.139307
$563$	9612.00	0.719534	0.359767	−	0.933042i	$-0.382856\pi$
$563$	9612.00	0.719534	0.359767	+	0.933042i	$0.382856\pi$
$564$	1600.00	0.119454
$565$	−1131.00	−0.0842151
$566$	18656.0	1.38546
$567$	0	0
$568$	−3448.00	−0.254709
$569$	2.00000	0.000147354 0	7.36769e−5	−	1.00000i	$-0.499977\pi$
$569$	2.00000	0.000147354 0	7.36769e−5		1.00000i	$0.499977\pi$
$570$	540.000	0.0396809
$571$	14900.0	1.09202	0.546012	−	0.837777i	$-0.316145\pi$
$571$	14900.0	1.09202	0.546012	+	0.837777i	$0.316145\pi$
$572$	−352.000	−0.0257305
$573$	−22225.0	−1.62035
$574$	0	0
$575$	−26412.0	−1.91558
$576$	−128.000	−0.00925926
$577$	−12187.0	−0.879292	−0.439646	−	0.898171i	$-0.644896\pi$
$577$	−12187.0	−0.879292	−0.439646	+	0.898171i	$0.644896\pi$
$578$	8858.00	0.637447
$579$	−3590.00	−0.257678
$580$	760.000	0.0544091
$581$	0	0
$582$	−890.000	−0.0633878
$583$	6226.00	0.442289
$584$	−7344.00	−0.520371
$585$	−16.0000	−0.00113080
$586$	−7964.00	−0.561416
$587$	−21788.0	−1.53201	−0.766003	−	0.642838i	$-0.777757\pi$
$587$	−21788.0	−1.53201	−0.766003	+	0.642838i	$0.777757\pi$
$588$	0	0
$589$	8802.00	0.615756
$590$	1290.00	0.0900143
$591$	90.0000	0.00626414
$592$	496.000	0.0344349
$593$	1750.00	0.121187	0.0605935	−	0.998163i	$-0.480701\pi$
$593$	1750.00	0.121187	0.0605935	+	0.998163i	$0.480701\pi$
$594$	−3190.00	−0.220349
$595$	0	0
$596$	9944.00	0.683426
$597$	2600.00	0.178243
$598$	−3408.00	−0.233049
$599$	−22104.0	−1.50775	−0.753877	−	0.657015i	$-0.771819\pi$
$599$	−22104.0	−1.50775	−0.753877	+	0.657015i	$0.771819\pi$
$600$	4960.00	0.337485
$601$	−3792.00	−0.257369	−0.128685	−	0.991686i	$-0.541075\pi$
$601$	−3792.00	−0.257369	−0.128685	+	0.991686i	$0.541075\pi$
$602$	0	0
$603$	1458.00	0.0984649
$604$	2888.00	0.194555
$605$	121.000	0.00813116
$606$	3320.00	0.222551
$607$	25414.0	1.69938	0.849689	−	0.527284i	$-0.176790\pi$
$607$	25414.0	1.69938	0.849689	+	0.527284i	$0.176790\pi$
$608$	1728.00	0.115263
$609$	0	0
$610$	1268.00	0.0841636
$611$	640.000	0.0423758
$612$	176.000	0.0116248
$613$	−14416.0	−0.949848	−0.474924	−	0.880027i	$-0.657524\pi$
$613$	−14416.0	−0.949848	−0.474924	+	0.880027i	$0.657524\pi$
$614$	13168.0	0.865500
$615$	−550.000	−0.0360620
$616$	0	0
$617$	17858.0	1.16521	0.582606	−	0.812755i	$-0.302033\pi$
$617$	17858.0	1.16521	0.582606	+	0.812755i	$0.302033\pi$
$618$	520.000	0.0338470
$619$	−10279.0	−0.667444	−0.333722	−	0.942672i	$-0.608305\pi$
$619$	−10279.0	−0.667444	−0.333722	+	0.942672i	$0.608305\pi$
$620$	−652.000	−0.0422338
$621$	−30885.0	−1.99577
$622$	7840.00	0.505394
$623$	0	0
$624$	640.000	0.0410585
$625$	15251.0	0.976064
$626$	8586.00	0.548188
$627$	2970.00	0.189171
$628$	8196.00	0.520790
$629$	−682.000	−0.0432323
$630$	0	0
$631$	−11067.0	−0.698210	−0.349105	−	0.937084i	$-0.613514\pi$
$631$	−11067.0	−0.698210	−0.349105	+	0.937084i	$0.613514\pi$
$632$	2032.00	0.127893
$633$	3150.00	0.197790
$634$	−12986.0	−0.813470
$635$	2126.00	0.132863
$636$	−11320.0	−0.705766
$637$	0	0
$638$	4180.00	0.259385
$639$	−862.000	−0.0533649
$640$	−128.000	−0.00790569
$641$	7239.00	0.446058	0.223029	−	0.974812i	$-0.428406\pi$
$641$	7239.00	0.446058	0.223029	+	0.974812i	$0.428406\pi$
$642$	−3660.00	−0.224998
$643$	17611.0	1.08011	0.540054	−	0.841630i	$-0.318404\pi$
$643$	17611.0	1.08011	0.540054	+	0.841630i	$0.318404\pi$
$644$	0	0
$645$	20.0000	0.00122093
$646$	−2376.00	−0.144710
$647$	−17225.0	−1.04665	−0.523327	−	0.852132i	$-0.675309\pi$
$647$	−17225.0	−1.04665	−0.523327	+	0.852132i	$0.675309\pi$
$648$	5368.00	0.325424
$649$	7095.00	0.429127
$650$	1984.00	0.119721
$651$	0	0
$652$	3856.00	0.231614
$653$	−17757.0	−1.06414	−0.532071	−	0.846700i	$-0.678586\pi$
$653$	−17757.0	−1.06414	−0.532071	+	0.846700i	$0.678586\pi$
$654$	1840.00	0.110015
$655$	−2610.00	−0.155696
$656$	−1760.00	−0.104751
$657$	−1836.00	−0.109025
$658$	0	0
$659$	13114.0	0.775188	0.387594	−	0.921830i	$-0.373306\pi$
$659$	13114.0	0.775188	0.387594	+	0.921830i	$0.373306\pi$
$660$	−220.000	−0.0129750
$661$	19101.0	1.12397	0.561984	−	0.827148i	$-0.310038\pi$
$661$	19101.0	1.12397	0.561984	+	0.827148i	$0.310038\pi$
$662$	−6538.00	−0.383847
$663$	−880.000	−0.0515481
$664$	7232.00	0.422675
$665$	0	0
$666$	124.000	0.00721457
$667$	40470.0	2.34933
$668$	−4776.00	−0.276630
$669$	10385.0	0.600160
$670$	1458.00	0.0840708
$671$	6974.00	0.401234
$672$	0	0
$673$	464.000	0.0265764	0.0132882	−	0.999912i	$-0.495770\pi$
$673$	464.000	0.0265764	0.0132882	+	0.999912i	$0.495770\pi$
$674$	−22228.0	−1.27031
$675$	17980.0	1.02526
$676$	−8532.00	−0.485435
$677$	20014.0	1.13619	0.568095	−	0.822963i	$-0.307681\pi$
$677$	20014.0	1.13619	0.568095	+	0.822963i	$0.307681\pi$
$678$	11310.0	0.640646
$679$	0	0
$680$	176.000	0.00992543
$681$	−18540.0	−1.04325
$682$	−3586.00	−0.201342
$683$	−5620.00	−0.314851	−0.157426	−	0.987531i	$-0.550319\pi$
$683$	−5620.00	−0.314851	−0.157426	+	0.987531i	$0.550319\pi$
$684$	432.000	0.0241490
$685$	349.000	0.0194666
$686$	0	0
$687$	−7085.00	−0.393464
$688$	64.0000	0.00354648
$689$	−4528.00	−0.250367
$690$	−2130.00	−0.117518
$691$	32303.0	1.77838	0.889192	−	0.457533i	$-0.151267\pi$
$691$	32303.0	1.77838	0.889192	+	0.457533i	$0.151267\pi$
$692$	−6288.00	−0.345425
$693$	0	0
$694$	12684.0	0.693772
$695$	762.000	0.0415889
$696$	−7600.00	−0.413904
$697$	2420.00	0.131512
$698$	−3580.00	−0.194133
$699$	−16110.0	−0.871726
$700$	0	0
$701$	−18000.0	−0.969830	−0.484915	−	0.874561i	$-0.661149\pi$
$701$	−18000.0	−0.969830	−0.484915	+	0.874561i	$0.661149\pi$
$702$	2320.00	0.124733
$703$	−1674.00	−0.0898095
$704$	−704.000	−0.0376889
$705$	400.000	0.0213686
$706$	−13878.0	−0.739809
$707$	0	0
$708$	−12900.0	−0.684762
$709$	−14933.0	−0.791002	−0.395501	−	0.918465i	$-0.629429\pi$
$709$	−14933.0	−0.791002	−0.395501	+	0.918465i	$0.629429\pi$
$710$	−862.000	−0.0455638
$711$	508.000	0.0267953
$712$	7208.00	0.379398
$713$	−34719.0	−1.82361
$714$	0	0
$715$	−88.0000	−0.00460282
$716$	−14772.0	−0.771027
$717$	20360.0	1.06047
$718$	−4664.00	−0.242422
$719$	185.000	0.00959574	0.00479787	−	0.999988i	$-0.498473\pi$
$719$	185.000	0.00959574	0.00479787	+	0.999988i	$0.498473\pi$
$720$	−32.0000	−0.00165635
$721$	0	0
$722$	7886.00	0.406491
$723$	−18660.0	−0.959852
$724$	−500.000	−0.0256662
$725$	−23560.0	−1.20689
$726$	−1210.00	−0.0618558
$727$	−32551.0	−1.66059	−0.830296	−	0.557323i	$-0.811828\pi$
$727$	−32551.0	−1.66059	−0.830296	+	0.557323i	$0.811828\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	−1836.00	−0.0930869
$731$	−88.0000	−0.00445253
$732$	−12680.0	−0.640254
$733$	−36244.0	−1.82633	−0.913167	−	0.407586i	$-0.866371\pi$
$733$	−36244.0	−1.82633	−0.913167	+	0.407586i	$0.866371\pi$
$734$	22078.0	1.11024
$735$	0	0
$736$	−6816.00	−0.341360
$737$	8019.00	0.400792
$738$	−440.000	−0.0219466
$739$	32258.0	1.60572	0.802862	−	0.596165i	$-0.203310\pi$
$739$	32258.0	1.60572	0.802862	+	0.596165i	$0.203310\pi$
$740$	124.000	0.00615991
$741$	−2160.00	−0.107084
$742$	0	0
$743$	−9232.00	−0.455840	−0.227920	−	0.973680i	$-0.573192\pi$
$743$	−9232.00	−0.455840	−0.227920	+	0.973680i	$0.573192\pi$
$744$	6520.00	0.321283
$745$	2486.00	0.122255
$746$	−728.000	−0.0357292
$747$	1808.00	0.0885559
$748$	968.000	0.0473176
$749$	0	0
$750$	2490.00	0.121229
$751$	−26681.0	−1.29641	−0.648205	−	0.761466i	$-0.724480\pi$
$751$	−26681.0	−1.29641	−0.648205	+	0.761466i	$0.724480\pi$
$752$	1280.00	0.0620702
$753$	−25505.0	−1.23433
$754$	−3040.00	−0.146831
$755$	722.000	0.0348030
$756$	0	0
$757$	1062.00	0.0509895	0.0254947	−	0.999675i	$-0.491884\pi$
$757$	1062.00	0.0509895	0.0254947	+	0.999675i	$0.491884\pi$
$758$	−12290.0	−0.588909
$759$	−11715.0	−0.560247
$760$	432.000	0.0206188
$761$	−24748.0	−1.17886	−0.589431	−	0.807819i	$-0.700648\pi$
$761$	−24748.0	−1.17886	−0.589431	+	0.807819i	$0.700648\pi$
$762$	−21260.0	−1.01072
$763$	0	0
$764$	−17780.0	−0.841961
$765$	44.0000	0.00207951
$766$	−24762.0	−1.16800
$767$	−5160.00	−0.242916
$768$	1280.00	0.0601407
$769$	14612.0	0.685204	0.342602	−	0.939481i	$-0.388692\pi$
$769$	14612.0	0.685204	0.342602	+	0.939481i	$0.388692\pi$
$770$	0	0
$771$	12390.0	0.578748
$772$	−2872.00	−0.133893
$773$	−8962.00	−0.417000	−0.208500	−	0.978022i	$-0.566858\pi$
$773$	−8962.00	−0.417000	−0.208500	+	0.978022i	$0.566858\pi$
$774$	16.0000	0.000743034 0
$775$	20212.0	0.936821
$776$	−712.000	−0.0329373
$777$	0	0
$778$	−24122.0	−1.11159
$779$	5940.00	0.273200
$780$	160.000	0.00734477
$781$	−4741.00	−0.217217
$782$	9372.00	0.428570
$783$	−27550.0	−1.25742
$784$	0	0
$785$	2049.00	0.0931617
$786$	26100.0	1.18442
$787$	38182.0	1.72940	0.864702	−	0.502285i	$-0.167507\pi$
$787$	38182.0	1.72940	0.864702	+	0.502285i	$0.167507\pi$
$788$	72.0000	0.00325494
$789$	11890.0	0.536496
$790$	508.000	0.0228783
$791$	0	0
$792$	−176.000	−0.00789632
$793$	−5072.00	−0.227127
$794$	−1548.00	−0.0691895
$795$	−2830.00	−0.126251
$796$	2080.00	0.0926176
$797$	20297.0	0.902079	0.451039	−	0.892504i	$-0.351053\pi$
$797$	20297.0	0.902079	0.451039	+	0.892504i	$0.351053\pi$
$798$	0	0
$799$	−1760.00	−0.0779278
$800$	3968.00	0.175362
$801$	1802.00	0.0794888
$802$	−10308.0	−0.453851
$803$	−10098.0	−0.443774
$804$	−14580.0	−0.639548
$805$	0	0
$806$	2608.00	0.113974
$807$	−42590.0	−1.85779
$808$	2656.00	0.115641
$809$	−29522.0	−1.28299	−0.641495	−	0.767128i	$-0.721685\pi$
$809$	−29522.0	−1.28299	−0.641495	+	0.767128i	$0.721685\pi$
$810$	1342.00	0.0582137
$811$	−42294.0	−1.83125	−0.915625	−	0.402034i	$-0.868303\pi$
$811$	−42294.0	−1.83125	−0.915625	+	0.402034i	$0.868303\pi$
$812$	0	0
$813$	18580.0	0.801512
$814$	682.000	0.0293662
$815$	964.000	0.0414325
$816$	−1760.00	−0.0755053
$817$	−216.000	−0.00924955
$818$	−10532.0	−0.450175
$819$	0	0
$820$	−440.000	−0.0187384
$821$	16546.0	0.703361	0.351681	−	0.936120i	$-0.385610\pi$
$821$	16546.0	0.703361	0.351681	+	0.936120i	$0.385610\pi$
$822$	−3490.00	−0.148087
$823$	−16263.0	−0.688812	−0.344406	−	0.938821i	$-0.611920\pi$
$823$	−16263.0	−0.688812	−0.344406	+	0.938821i	$0.611920\pi$
$824$	416.000	0.0175874
$825$	6820.00	0.287808
$826$	0	0
$827$	3744.00	0.157426	0.0787132	−	0.996897i	$-0.474919\pi$
$827$	3744.00	0.157426	0.0787132	+	0.996897i	$0.474919\pi$
$828$	−1704.00	−0.0715194
$829$	17205.0	0.720813	0.360407	−	0.932795i	$-0.382638\pi$
$829$	17205.0	0.720813	0.360407	+	0.932795i	$0.382638\pi$
$830$	1808.00	0.0756104
$831$	12820.0	0.535164
$832$	512.000	0.0213346
$833$	0	0
$834$	−7620.00	−0.316378
$835$	−1194.00	−0.0494851
$836$	2376.00	0.0982963
$837$	23635.0	0.976040
$838$	−16560.0	−0.682644
$839$	42513.0	1.74936	0.874679	−	0.484702i	$-0.161072\pi$
$839$	42513.0	1.74936	0.874679	+	0.484702i	$0.161072\pi$
$840$	0	0
$841$	11711.0	0.480175
$842$	5220.00	0.213650
$843$	4640.00	0.189573
$844$	2520.00	0.102775
$845$	−2133.00	−0.0868372
$846$	320.000	0.0130045
$847$	0	0
$848$	−9056.00	−0.366727
$849$	−46640.0	−1.88537
$850$	−5456.00	−0.220164
$851$	6603.00	0.265979
$852$	8620.00	0.346615
$853$	−24774.0	−0.994426	−0.497213	−	0.867628i	$-0.665643\pi$
$853$	−24774.0	−0.994426	−0.497213	+	0.867628i	$0.665643\pi$
$854$	0	0
$855$	108.000	0.00431991
$856$	−2928.00	−0.116912
$857$	33364.0	1.32986	0.664931	−	0.746904i	$-0.268461\pi$
$857$	33364.0	1.32986	0.664931	+	0.746904i	$0.268461\pi$
$858$	880.000	0.0350148
$859$	−19825.0	−0.787451	−0.393725	−	0.919228i	$-0.628814\pi$
$859$	−19825.0	−0.787451	−0.393725	+	0.919228i	$0.628814\pi$
$860$	16.0000	0.000634413 0
$861$	0	0
$862$	21272.0	0.840519
$863$	−11460.0	−0.452031	−0.226016	−	0.974124i	$-0.572570\pi$
$863$	−11460.0	−0.452031	−0.226016	+	0.974124i	$0.572570\pi$
$864$	4640.00	0.182704
$865$	−1572.00	−0.0617914
$866$	−26634.0	−1.04510
$867$	−22145.0	−0.867455
$868$	0	0
$869$	2794.00	0.109068
$870$	−1900.00	−0.0740414
$871$	−5832.00	−0.226877
$872$	1472.00	0.0571654
$873$	−178.000	−0.00690079
$874$	23004.0	0.890300
$875$	0	0
$876$	18360.0	0.708136
$877$	−37862.0	−1.45782	−0.728910	−	0.684609i	$-0.759973\pi$
$877$	−37862.0	−1.45782	−0.728910	+	0.684609i	$0.759973\pi$
$878$	−29644.0	−1.13945
$879$	19910.0	0.763990
$880$	−176.000	−0.00674200
$881$	14705.0	0.562343	0.281171	−	0.959658i	$-0.409277\pi$
$881$	14705.0	0.562343	0.281171	+	0.959658i	$0.409277\pi$
$882$	0	0
$883$	15212.0	0.579756	0.289878	−	0.957064i	$-0.406385\pi$
$883$	15212.0	0.579756	0.289878	+	0.957064i	$0.406385\pi$
$884$	−704.000	−0.0267852
$885$	−3225.00	−0.122494
$886$	23274.0	0.882512
$887$	−25698.0	−0.972778	−0.486389	−	0.873742i	$-0.661686\pi$
$887$	−25698.0	−0.972778	−0.486389	+	0.873742i	$0.661686\pi$
$888$	−1240.00	−0.0468600
$889$	0	0
$890$	1802.00	0.0678687
$891$	7381.00	0.277523
$892$	8308.00	0.311852
$893$	−4320.00	−0.161885
$894$	−24860.0	−0.930025
$895$	−3693.00	−0.137926
$896$	0	0
$897$	8520.00	0.317140
$898$	30978.0	1.15117
$899$	−30970.0	−1.14895
$900$	992.000	0.0367407
$901$	12452.0	0.460418
$902$	−2420.00	−0.0893317
$903$	0	0
$904$	9048.00	0.332889
$905$	−125.000	−0.00459132
$906$	−7220.00	−0.264755
$907$	29016.0	1.06225	0.531125	−	0.847294i	$-0.321770\pi$
$907$	29016.0	1.06225	0.531125	+	0.847294i	$0.321770\pi$
$908$	−14832.0	−0.542089
$909$	664.000	0.0242283
$910$	0	0
$911$	−1048.00	−0.0381139	−0.0190570	−	0.999818i	$-0.506066\pi$
$911$	−1048.00	−0.0381139	−0.0190570	+	0.999818i	$0.506066\pi$
$912$	−4320.00	−0.156853
$913$	9944.00	0.360458
$914$	−33776.0	−1.22233
$915$	−3170.00	−0.114532
$916$	−5668.00	−0.204450
$917$	0	0
$918$	−6380.00	−0.229381
$919$	−28804.0	−1.03390	−0.516951	−	0.856015i	$-0.672933\pi$
$919$	−28804.0	−1.03390	−0.516951	+	0.856015i	$0.672933\pi$
$920$	−1704.00	−0.0610644
$921$	−32920.0	−1.17780
$922$	−9876.00	−0.352764
$923$	3448.00	0.122960
$924$	0	0
$925$	−3844.00	−0.136638
$926$	17290.0	0.613590
$927$	104.000	0.00368480
$928$	−6080.00	−0.215071
$929$	−24546.0	−0.866876	−0.433438	−	0.901183i	$-0.642700\pi$
$929$	−24546.0	−0.866876	−0.433438	+	0.901183i	$0.642700\pi$
$930$	1630.00	0.0574729
$931$	0	0
$932$	−12888.0	−0.452962
$933$	−19600.0	−0.687755
$934$	−4150.00	−0.145388
$935$	242.000	0.00846443
$936$	128.000	0.00446988
$937$	−50584.0	−1.76361	−0.881807	−	0.471610i	$-0.843673\pi$
$937$	−50584.0	−1.76361	−0.881807	+	0.471610i	$0.843673\pi$
$938$	0	0
$939$	−21465.0	−0.745989
$940$	320.000	0.0111035
$941$	9174.00	0.317815	0.158907	−	0.987293i	$-0.449203\pi$
$941$	9174.00	0.317815	0.158907	+	0.987293i	$0.449203\pi$
$942$	−20490.0	−0.708705
$943$	−23430.0	−0.809105
$944$	−10320.0	−0.355813
$945$	0	0
$946$	88.0000	0.00302445
$947$	27919.0	0.958021	0.479010	−	0.877809i	$-0.340996\pi$
$947$	27919.0	0.958021	0.479010	+	0.877809i	$0.340996\pi$
$948$	−5080.00	−0.174041
$949$	7344.00	0.251208
$950$	−13392.0	−0.457362
$951$	32465.0	1.10699
$952$	0	0
$953$	33348.0	1.13352	0.566762	−	0.823882i	$-0.308196\pi$
$953$	33348.0	1.13352	0.566762	+	0.823882i	$0.308196\pi$
$954$	−2264.00	−0.0768341
$955$	−4445.00	−0.150614
$956$	16288.0	0.551037
$957$	−10450.0	−0.352979
$958$	−32944.0	−1.11104
$959$	0	0
$960$	320.000	0.0107583
$961$	−3222.00	−0.108153
$962$	−496.000	−0.0166234
$963$	−732.000	−0.0244947
$964$	−14928.0	−0.498754
$965$	−718.000	−0.0239515
$966$	0	0
$967$	36302.0	1.20723	0.603616	−	0.797275i	$-0.293726\pi$
$967$	36302.0	1.20723	0.603616	+	0.797275i	$0.293726\pi$
$968$	−968.000	−0.0321412
$969$	5940.00	0.196925
$970$	−178.000	−0.00589200
$971$	18709.0	0.618332	0.309166	−	0.951008i	$-0.399950\pi$
$971$	18709.0	0.618332	0.309166	+	0.951008i	$0.399950\pi$
$972$	2240.00	0.0739177
$973$	0	0
$974$	−18266.0	−0.600904
$975$	−4960.00	−0.162920
$976$	−10144.0	−0.332686
$977$	−17479.0	−0.572367	−0.286184	−	0.958175i	$-0.592387\pi$
$977$	−17479.0	−0.572367	−0.286184	+	0.958175i	$0.592387\pi$
$978$	−9640.00	−0.315187
$979$	9911.00	0.323552
$980$	0	0
$981$	368.000	0.0119769
$982$	−708.000	−0.0230073
$983$	−34127.0	−1.10731	−0.553653	−	0.832747i	$-0.686767\pi$
$983$	−34127.0	−1.10731	−0.553653	+	0.832747i	$0.686767\pi$
$984$	4400.00	0.142548
$985$	18.0000	0.000582262 0
$986$	8360.00	0.270017
$987$	0	0
$988$	−1728.00	−0.0556427
$989$	852.000	0.0273934
$990$	−44.0000	−0.00141254
$991$	52840.0	1.69376	0.846881	−	0.531783i	$-0.178478\pi$
$991$	52840.0	1.69376	0.846881	+	0.531783i	$0.178478\pi$
$992$	5216.00	0.166944
$993$	16345.0	0.522349
$994$	0	0
$995$	520.000	0.0165679
$996$	−18080.0	−0.575187
$997$	53956.0	1.71395	0.856973	−	0.515362i	$-0.172342\pi$
$997$	53956.0	1.71395	0.856973	+	0.515362i	$0.172342\pi$
$998$	−17912.0	−0.568131
$999$	−4495.00	−0.142358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.4.a.c.1.1		1
7.6	odd	2		154.4.a.a.1.1	✓	1
21.20	even	2		1386.4.a.k.1.1		1
28.27	even	2		1232.4.a.g.1.1		1
77.76	even	2		1694.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.a.1.1	✓	1	7.6	odd	2
1078.4.a.c.1.1		1	1.1	even	1	trivial
1232.4.a.g.1.1		1	28.27	even	2
1386.4.a.k.1.1		1	21.20	even	2
1694.4.a.e.1.1		1	77.76	even	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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1078.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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