LMFDB - Embedded newform 1078.4.a.e.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:	$0$
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)

$f(q)$

$=$

$q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} -3.00000 q^{5} -14.0000 q^{6} +8.00000 q^{8} +22.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -7.00000 q^{3} +4.00000 q^{4} -3.00000 q^{5} -14.0000 q^{6} +8.00000 q^{8} +22.0000 q^{9} -6.00000 q^{10} -11.0000 q^{11} -28.0000 q^{12} +16.0000 q^{13} +21.0000 q^{15} +16.0000 q^{16} -6.00000 q^{17} +44.0000 q^{18} -14.0000 q^{19} -12.0000 q^{20} -22.0000 q^{22} -51.0000 q^{23} -56.0000 q^{24} -116.000 q^{25} +32.0000 q^{26} +35.0000 q^{27} +54.0000 q^{29} +42.0000 q^{30} -95.0000 q^{31} +32.0000 q^{32} +77.0000 q^{33} -12.0000 q^{34} +88.0000 q^{36} -193.000 q^{37} -28.0000 q^{38} -112.000 q^{39} -24.0000 q^{40} -102.000 q^{41} +284.000 q^{43} -44.0000 q^{44} -66.0000 q^{45} -102.000 q^{46} +72.0000 q^{47} -112.000 q^{48} -232.000 q^{50} +42.0000 q^{51} +64.0000 q^{52} -102.000 q^{53} +70.0000 q^{54} +33.0000 q^{55} +98.0000 q^{57} +108.000 q^{58} +63.0000 q^{59} +84.0000 q^{60} +790.000 q^{61} -190.000 q^{62} +64.0000 q^{64} -48.0000 q^{65} +154.000 q^{66} -433.000 q^{67} -24.0000 q^{68} +357.000 q^{69} +135.000 q^{71} +176.000 q^{72} +238.000 q^{73} -386.000 q^{74} +812.000 q^{75} -56.0000 q^{76} -224.000 q^{78} +770.000 q^{79} -48.0000 q^{80} -839.000 q^{81} -204.000 q^{82} +1008.00 q^{83} +18.0000 q^{85} +568.000 q^{86} -378.000 q^{87} -88.0000 q^{88} +639.000 q^{89} -132.000 q^{90} -204.000 q^{92} +665.000 q^{93} +144.000 q^{94} +42.0000 q^{95} -224.000 q^{96} -11.0000 q^{97} -242.000 q^{99} +O(q^{100})\)

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
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	4.00000	0.500000
$5$	−3.00000	−0.268328	−0.134164	−	0.990959i	$-0.542835\pi$
$5$	−3.00000	−0.268328	−0.134164	+	0.990959i	$0.542835\pi$
$6$	−14.0000	−0.952579
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	22.0000	0.814815
$10$	−6.00000	−0.189737
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−28.0000	−0.673575
$13$	16.0000	0.341354	0.170677	−	0.985327i	$-0.445405\pi$
$13$	16.0000	0.341354	0.170677	+	0.985327i	$0.445405\pi$
$14$	0	0
$15$	21.0000	0.361478
$16$	16.0000	0.250000
$17$	−6.00000	−0.0856008	−0.0428004	−	0.999084i	$-0.513628\pi$
$17$	−6.00000	−0.0856008	−0.0428004	+	0.999084i	$0.513628\pi$
$18$	44.0000	0.576161
$19$	−14.0000	−0.169043	−0.0845216	−	0.996422i	$-0.526936\pi$
$19$	−14.0000	−0.169043	−0.0845216	+	0.996422i	$0.526936\pi$
$20$	−12.0000	−0.134164
$21$	0	0
$22$	−22.0000	−0.213201
$23$	−51.0000	−0.462358	−0.231179	−	0.972911i	$-0.574258\pi$
$23$	−51.0000	−0.462358	−0.231179	+	0.972911i	$0.574258\pi$
$24$	−56.0000	−0.476290
$25$	−116.000	−0.928000
$26$	32.0000	0.241374
$27$	35.0000	0.249472
$28$	0	0
$29$	54.0000	0.345778	0.172889	−	0.984941i	$-0.444690\pi$
$29$	54.0000	0.345778	0.172889	+	0.984941i	$0.444690\pi$
$30$	42.0000	0.255604
$31$	−95.0000	−0.550403	−0.275202	−	0.961387i	$-0.588745\pi$
$31$	−95.0000	−0.550403	−0.275202	+	0.961387i	$0.588745\pi$
$32$	32.0000	0.176777
$33$	77.0000	0.406181
$34$	−12.0000	−0.0605289
$35$	0	0
$36$	88.0000	0.407407
$37$	−193.000	−0.857541	−0.428770	−	0.903414i	$-0.641053\pi$
$37$	−193.000	−0.857541	−0.428770	+	0.903414i	$0.641053\pi$
$38$	−28.0000	−0.119532
$39$	−112.000	−0.459855
$40$	−24.0000	−0.0948683
$41$	−102.000	−0.388530	−0.194265	−	0.980949i	$-0.562232\pi$
$41$	−102.000	−0.388530	−0.194265	+	0.980949i	$0.562232\pi$
$42$	0	0
$43$	284.000	1.00720	0.503600	−	0.863937i	$-0.332009\pi$
$43$	284.000	1.00720	0.503600	+	0.863937i	$0.332009\pi$
$44$	−44.0000	−0.150756
$45$	−66.0000	−0.218638
$46$	−102.000	−0.326937
$47$	72.0000	0.223453	0.111726	−	0.993739i	$-0.464362\pi$
$47$	72.0000	0.223453	0.111726	+	0.993739i	$0.464362\pi$
$48$	−112.000	−0.336788
$49$	0	0
$50$	−232.000	−0.656195
$51$	42.0000	0.115317
$52$	64.0000	0.170677
$53$	−102.000	−0.264354	−0.132177	−	0.991226i	$-0.542197\pi$
$53$	−102.000	−0.264354	−0.132177	+	0.991226i	$0.542197\pi$
$54$	70.0000	0.176404
$55$	33.0000	0.0809040
$56$	0	0
$57$	98.0000	0.227727
$58$	108.000	0.244502
$59$	63.0000	0.139015	0.0695076	−	0.997581i	$-0.477857\pi$
$59$	63.0000	0.139015	0.0695076	+	0.997581i	$0.477857\pi$
$60$	84.0000	0.180739
$61$	790.000	1.65818	0.829091	−	0.559113i	$-0.188858\pi$
$61$	790.000	1.65818	0.829091	+	0.559113i	$0.188858\pi$
$62$	−190.000	−0.389194
$63$	0	0
$64$	64.0000	0.125000
$65$	−48.0000	−0.0915949
$66$	154.000	0.287213
$67$	−433.000	−0.789543	−0.394771	−	0.918779i	$-0.629176\pi$
$67$	−433.000	−0.789543	−0.394771	+	0.918779i	$0.629176\pi$
$68$	−24.0000	−0.0428004
$69$	357.000	0.622866
$70$	0	0
$71$	135.000	0.225656	0.112828	−	0.993615i	$-0.464009\pi$
$71$	135.000	0.225656	0.112828	+	0.993615i	$0.464009\pi$
$72$	176.000	0.288081
$73$	238.000	0.381586	0.190793	−	0.981630i	$-0.438894\pi$
$73$	238.000	0.381586	0.190793	+	0.981630i	$0.438894\pi$
$74$	−386.000	−0.606373
$75$	812.000	1.25016
$76$	−56.0000	−0.0845216
$77$	0	0
$78$	−224.000	−0.325167
$79$	770.000	1.09660	0.548302	−	0.836280i	$-0.315274\pi$
$79$	770.000	1.09660	0.548302	+	0.836280i	$0.315274\pi$
$80$	−48.0000	−0.0670820
$81$	−839.000	−1.15089
$82$	−204.000	−0.274732
$83$	1008.00	1.33304	0.666520	−	0.745487i	$-0.267783\pi$
$83$	1008.00	1.33304	0.666520	+	0.745487i	$0.267783\pi$
$84$	0	0
$85$	18.0000	0.0229691
$86$	568.000	0.712198
$87$	−378.000	−0.465814
$88$	−88.0000	−0.106600
$89$	639.000	0.761055	0.380527	−	0.924770i	$-0.375742\pi$
$89$	639.000	0.761055	0.380527	+	0.924770i	$0.375742\pi$
$90$	−132.000	−0.154600
$91$	0	0
$92$	−204.000	−0.231179
$93$	665.000	0.741476
$94$	144.000	0.158005
$95$	42.0000	0.0453590
$96$	−224.000	−0.238145
$97$	−11.0000	−0.0115142	−0.00575712	−	0.999983i	$-0.501833\pi$
$97$	−11.0000	−0.0115142	−0.00575712	+	0.999983i	$0.501833\pi$
$98$	0	0
$99$	−242.000	−0.245676
$100$	−464.000	−0.464000
$101$	−1692.00	−1.66693	−0.833467	−	0.552570i	$-0.813647\pi$
$101$	−1692.00	−1.66693	−0.833467	+	0.552570i	$0.813647\pi$
$102$	84.0000	0.0815416
$103$	532.000	0.508927	0.254464	−	0.967082i	$-0.418101\pi$
$103$	532.000	0.508927	0.254464	+	0.967082i	$0.418101\pi$
$104$	128.000	0.120687
$105$	0	0
$106$	−204.000	−0.186927
$107$	1350.00	1.21971	0.609857	−	0.792511i	$-0.291227\pi$
$107$	1350.00	1.21971	0.609857	+	0.792511i	$0.291227\pi$
$108$	140.000	0.124736
$109$	1616.00	1.42004	0.710022	−	0.704180i	$-0.248685\pi$
$109$	1616.00	1.42004	0.710022	+	0.704180i	$0.248685\pi$
$110$	66.0000	0.0572078
$111$	1351.00	1.15524
$112$	0	0
$113$	597.000	0.497000	0.248500	−	0.968632i	$-0.420062\pi$
$113$	597.000	0.497000	0.248500	+	0.968632i	$0.420062\pi$
$114$	196.000	0.161027
$115$	153.000	0.124064
$116$	216.000	0.172889
$117$	352.000	0.278140
$118$	126.000	0.0982986
$119$	0	0
$120$	168.000	0.127802
$121$	121.000	0.0909091
$122$	1580.00	1.17251
$123$	714.000	0.523408
$124$	−380.000	−0.275202
$125$	723.000	0.517337
$126$	0	0
$127$	302.000	0.211009	0.105505	−	0.994419i	$-0.466354\pi$
$127$	302.000	0.211009	0.105505	+	0.994419i	$0.466354\pi$
$128$	128.000	0.0883883
$129$	−1988.00	−1.35685
$130$	−96.0000	−0.0647674
$131$	462.000	0.308131	0.154065	−	0.988061i	$-0.450763\pi$
$131$	462.000	0.308131	0.154065	+	0.988061i	$0.450763\pi$
$132$	308.000	0.203091
$133$	0	0
$134$	−866.000	−0.558291
$135$	−105.000	−0.0669405
$136$	−48.0000	−0.0302645
$137$	3021.00	1.88395	0.941976	−	0.335680i	$-0.108966\pi$
$137$	3021.00	1.88395	0.941976	+	0.335680i	$0.108966\pi$
$138$	714.000	0.440433
$139$	1594.00	0.972671	0.486336	−	0.873772i	$-0.338333\pi$
$139$	1594.00	0.972671	0.486336	+	0.873772i	$0.338333\pi$
$140$	0	0
$141$	−504.000	−0.301025
$142$	270.000	0.159563
$143$	−176.000	−0.102922
$144$	352.000	0.203704
$145$	−162.000	−0.0927818
$146$	476.000	0.269822
$147$	0	0
$148$	−772.000	−0.428770
$149$	2814.00	1.54719	0.773597	−	0.633678i	$-0.218456\pi$
$149$	2814.00	1.54719	0.773597	+	0.633678i	$0.218456\pi$
$150$	1624.00	0.883994
$151$	2450.00	1.32039	0.660193	−	0.751096i	$-0.270475\pi$
$151$	2450.00	1.32039	0.660193	+	0.751096i	$0.270475\pi$
$152$	−112.000	−0.0597658
$153$	−132.000	−0.0697488
$154$	0	0
$155$	285.000	0.147689
$156$	−448.000	−0.229928
$157$	−3899.00	−1.98200	−0.991000	−	0.133860i	$-0.957263\pi$
$157$	−3899.00	−1.98200	−0.991000	+	0.133860i	$0.957263\pi$
$158$	1540.00	0.775417
$159$	714.000	0.356125
$160$	−96.0000	−0.0474342
$161$	0	0
$162$	−1678.00	−0.813803
$163$	−124.000	−0.0595855	−0.0297927	−	0.999556i	$-0.509485\pi$
$163$	−124.000	−0.0595855	−0.0297927	+	0.999556i	$0.509485\pi$
$164$	−408.000	−0.194265
$165$	−231.000	−0.108990
$166$	2016.00	0.942602
$167$	30.0000	0.0139010	0.00695051	−	0.999976i	$-0.497788\pi$
$167$	30.0000	0.0139010	0.00695051	+	0.999976i	$0.497788\pi$
$168$	0	0
$169$	−1941.00	−0.883477
$170$	36.0000	0.0162416
$171$	−308.000	−0.137739
$172$	1136.00	0.503600
$173$	−2268.00	−0.996722	−0.498361	−	0.866970i	$-0.666065\pi$
$173$	−2268.00	−0.996722	−0.498361	+	0.866970i	$0.666065\pi$
$174$	−756.000	−0.329381
$175$	0	0
$176$	−176.000	−0.0753778
$177$	−441.000	−0.187275
$178$	1278.00	0.538147
$179$	1731.00	0.722799	0.361399	−	0.932411i	$-0.382299\pi$
$179$	1731.00	0.722799	0.361399	+	0.932411i	$0.382299\pi$
$180$	−264.000	−0.109319
$181$	−785.000	−0.322368	−0.161184	−	0.986924i	$-0.551531\pi$
$181$	−785.000	−0.322368	−0.161184	+	0.986924i	$0.551531\pi$
$182$	0	0
$183$	−5530.00	−2.23382
$184$	−408.000	−0.163468
$185$	579.000	0.230102
$186$	1330.00	0.524303
$187$	66.0000	0.0258096
$188$	288.000	0.111726
$189$	0	0
$190$	84.0000	0.0320737
$191$	51.0000	0.0193206	0.00966029	−	0.999953i	$-0.496925\pi$
$191$	51.0000	0.0193206	0.00966029	+	0.999953i	$0.496925\pi$
$192$	−448.000	−0.168394
$193$	1226.00	0.457251	0.228625	−	0.973514i	$-0.426577\pi$
$193$	1226.00	0.457251	0.228625	+	0.973514i	$0.426577\pi$
$194$	−22.0000	−0.00814179
$195$	336.000	0.123392
$196$	0	0
$197$	2754.00	0.996012	0.498006	−	0.867174i	$-0.334066\pi$
$197$	2754.00	0.996012	0.498006	+	0.867174i	$0.334066\pi$
$198$	−484.000	−0.173719
$199$	1744.00	0.621251	0.310625	−	0.950532i	$-0.399462\pi$
$199$	1744.00	0.621251	0.310625	+	0.950532i	$0.399462\pi$
$200$	−928.000	−0.328098
$201$	3031.00	1.06363
$202$	−3384.00	−1.17870
$203$	0	0
$204$	168.000	0.0576586
$205$	306.000	0.104253
$206$	1064.00	0.359866
$207$	−1122.00	−0.376736
$208$	256.000	0.0853385
$209$	154.000	0.0509684
$210$	0	0
$211$	−4210.00	−1.37359	−0.686797	−	0.726849i	$-0.740984\pi$
$211$	−4210.00	−1.37359	−0.686797	+	0.726849i	$0.740984\pi$
$212$	−408.000	−0.132177
$213$	−945.000	−0.303992
$214$	2700.00	0.862468
$215$	−852.000	−0.270260
$216$	280.000	0.0882018
$217$	0	0
$218$	3232.00	1.00412
$219$	−1666.00	−0.514054
$220$	132.000	0.0404520
$221$	−96.0000	−0.0292202
$222$	2702.00	0.816876
$223$	5497.00	1.65070	0.825351	−	0.564621i	$-0.190978\pi$
$223$	5497.00	1.65070	0.825351	+	0.564621i	$0.190978\pi$
$224$	0	0
$225$	−2552.00	−0.756148
$226$	1194.00	0.351432
$227$	3732.00	1.09120	0.545598	−	0.838047i	$-0.316303\pi$
$227$	3732.00	1.09120	0.545598	+	0.838047i	$0.316303\pi$
$228$	392.000	0.113863
$229$	3883.00	1.12051	0.560253	−	0.828322i	$-0.310704\pi$
$229$	3883.00	1.12051	0.560253	+	0.828322i	$0.310704\pi$
$230$	306.000	0.0877263
$231$	0	0
$232$	432.000	0.122251
$233$	−222.000	−0.0624193	−0.0312097	−	0.999513i	$-0.509936\pi$
$233$	−222.000	−0.0624193	−0.0312097	+	0.999513i	$0.509936\pi$
$234$	704.000	0.196675
$235$	−216.000	−0.0599587
$236$	252.000	0.0695076
$237$	−5390.00	−1.47729
$238$	0	0
$239$	−2304.00	−0.623571	−0.311785	−	0.950153i	$-0.600927\pi$
$239$	−2304.00	−0.623571	−0.311785	+	0.950153i	$0.600927\pi$
$240$	336.000	0.0903696
$241$	1276.00	0.341056	0.170528	−	0.985353i	$-0.445453\pi$
$241$	1276.00	0.341056	0.170528	+	0.985353i	$0.445453\pi$
$242$	242.000	0.0642824
$243$	4928.00	1.30095
$244$	3160.00	0.829091
$245$	0	0
$246$	1428.00	0.370106
$247$	−224.000	−0.0577036
$248$	−760.000	−0.194597
$249$	−7056.00	−1.79581
$250$	1446.00	0.365812
$251$	255.000	0.0641253	0.0320627	−	0.999486i	$-0.489792\pi$
$251$	255.000	0.0641253	0.0320627	+	0.999486i	$0.489792\pi$
$252$	0	0
$253$	561.000	0.139406
$254$	604.000	0.149206
$255$	−126.000	−0.0309428
$256$	256.000	0.0625000
$257$	−2370.00	−0.575239	−0.287620	−	0.957745i	$-0.592864\pi$
$257$	−2370.00	−0.575239	−0.287620	+	0.957745i	$0.592864\pi$
$258$	−3976.00	−0.959438
$259$	0	0
$260$	−192.000	−0.0457974
$261$	1188.00	0.281745
$262$	924.000	0.217881
$263$	2466.00	0.578175	0.289088	−	0.957303i	$-0.406648\pi$
$263$	2466.00	0.578175	0.289088	+	0.957303i	$0.406648\pi$
$264$	616.000	0.143607
$265$	306.000	0.0709337
$266$	0	0
$267$	−4473.00	−1.02526
$268$	−1732.00	−0.394771
$269$	−6774.00	−1.53538	−0.767692	−	0.640820i	$-0.778595\pi$
$269$	−6774.00	−1.53538	−0.767692	+	0.640820i	$0.778595\pi$
$270$	−210.000	−0.0473340
$271$	4876.00	1.09297	0.546487	−	0.837468i	$-0.315965\pi$
$271$	4876.00	1.09297	0.546487	+	0.837468i	$0.315965\pi$
$272$	−96.0000	−0.0214002
$273$	0	0
$274$	6042.00	1.33216
$275$	1276.00	0.279803
$276$	1428.00	0.311433
$277$	−3268.00	−0.708863	−0.354432	−	0.935082i	$-0.615326\pi$
$277$	−3268.00	−0.708863	−0.354432	+	0.935082i	$0.615326\pi$
$278$	3188.00	0.687782
$279$	−2090.00	−0.448477
$280$	0	0
$281$	5928.00	1.25849	0.629243	−	0.777208i	$-0.283365\pi$
$281$	5928.00	1.25849	0.629243	+	0.777208i	$0.283365\pi$
$282$	−1008.00	−0.212856
$283$	−2672.00	−0.561251	−0.280625	−	0.959817i	$-0.590542\pi$
$283$	−2672.00	−0.561251	−0.280625	+	0.959817i	$0.590542\pi$
$284$	540.000	0.112828
$285$	−294.000	−0.0611055
$286$	−352.000	−0.0727769
$287$	0	0
$288$	704.000	0.144040
$289$	−4877.00	−0.992673
$290$	−324.000	−0.0656067
$291$	77.0000	0.0155114
$292$	952.000	0.190793
$293$	−5322.00	−1.06114	−0.530571	−	0.847641i	$-0.678022\pi$
$293$	−5322.00	−1.06114	−0.530571	+	0.847641i	$0.678022\pi$
$294$	0	0
$295$	−189.000	−0.0373017
$296$	−1544.00	−0.303186
$297$	−385.000	−0.0752187
$298$	5628.00	1.09403
$299$	−816.000	−0.157828
$300$	3248.00	0.625078
$301$	0	0
$302$	4900.00	0.933653
$303$	11844.0	2.24561
$304$	−224.000	−0.0422608
$305$	−2370.00	−0.444937
$306$	−264.000	−0.0493199
$307$	−2816.00	−0.523510	−0.261755	−	0.965134i	$-0.584301\pi$
$307$	−2816.00	−0.523510	−0.261755	+	0.965134i	$0.584301\pi$
$308$	0	0
$309$	−3724.00	−0.685602
$310$	570.000	0.104432
$311$	−8760.00	−1.59722	−0.798608	−	0.601852i	$-0.794430\pi$
$311$	−8760.00	−1.59722	−0.798608	+	0.601852i	$0.794430\pi$
$312$	−896.000	−0.162583
$313$	−1337.00	−0.241443	−0.120722	−	0.992686i	$-0.538521\pi$
$313$	−1337.00	−0.241443	−0.120722	+	0.992686i	$0.538521\pi$
$314$	−7798.00	−1.40149
$315$	0	0
$316$	3080.00	0.548302
$317$	4269.00	0.756375	0.378188	−	0.925729i	$-0.376547\pi$
$317$	4269.00	0.756375	0.378188	+	0.925729i	$0.376547\pi$
$318$	1428.00	0.251818
$319$	−594.000	−0.104256
$320$	−192.000	−0.0335410
$321$	−9450.00	−1.64314
$322$	0	0
$323$	84.0000	0.0144702
$324$	−3356.00	−0.575446
$325$	−1856.00	−0.316776
$326$	−248.000	−0.0421333
$327$	−11312.0	−1.91301
$328$	−816.000	−0.137366
$329$	0	0
$330$	−462.000	−0.0770675
$331$	−4843.00	−0.804216	−0.402108	−	0.915592i	$-0.631722\pi$
$331$	−4843.00	−0.804216	−0.402108	+	0.915592i	$0.631722\pi$
$332$	4032.00	0.666520
$333$	−4246.00	−0.698737
$334$	60.0000	0.00982950
$335$	1299.00	0.211857
$336$	0	0
$337$	−3790.00	−0.612624	−0.306312	−	0.951931i	$-0.599095\pi$
$337$	−3790.00	−0.612624	−0.306312	+	0.951931i	$0.599095\pi$
$338$	−3882.00	−0.624713
$339$	−4179.00	−0.669534
$340$	72.0000	0.0114846
$341$	1045.00	0.165953
$342$	−616.000	−0.0973961
$343$	0	0
$344$	2272.00	0.356099
$345$	−1071.00	−0.167132
$346$	−4536.00	−0.704789
$347$	1722.00	0.266403	0.133201	−	0.991089i	$-0.457474\pi$
$347$	1722.00	0.266403	0.133201	+	0.991089i	$0.457474\pi$
$348$	−1512.00	−0.232907
$349$	3166.00	0.485593	0.242797	−	0.970077i	$-0.421935\pi$
$349$	3166.00	0.485593	0.242797	+	0.970077i	$0.421935\pi$
$350$	0	0
$351$	560.000	0.0851584
$352$	−352.000	−0.0533002
$353$	4167.00	0.628292	0.314146	−	0.949375i	$-0.398282\pi$
$353$	4167.00	0.628292	0.314146	+	0.949375i	$0.398282\pi$
$354$	−882.000	−0.132423
$355$	−405.000	−0.0605498
$356$	2556.00	0.380527
$357$	0	0
$358$	3462.00	0.511096
$359$	1380.00	0.202879	0.101440	−	0.994842i	$-0.467655\pi$
$359$	1380.00	0.202879	0.101440	+	0.994842i	$0.467655\pi$
$360$	−528.000	−0.0773001
$361$	−6663.00	−0.971424
$362$	−1570.00	−0.227949
$363$	−847.000	−0.122468
$364$	0	0
$365$	−714.000	−0.102390
$366$	−11060.0	−1.57955
$367$	−755.000	−0.107386	−0.0536930	−	0.998557i	$-0.517099\pi$
$367$	−755.000	−0.107386	−0.0536930	+	0.998557i	$0.517099\pi$
$368$	−816.000	−0.115590
$369$	−2244.00	−0.316580
$370$	1158.00	0.162707
$371$	0	0
$372$	2660.00	0.370738
$373$	−8596.00	−1.19325	−0.596627	−	0.802518i	$-0.703493\pi$
$373$	−8596.00	−1.19325	−0.596627	+	0.802518i	$0.703493\pi$
$374$	132.000	0.0182502
$375$	−5061.00	−0.696930
$376$	576.000	0.0790025
$377$	864.000	0.118033
$378$	0	0
$379$	−11287.0	−1.52975	−0.764874	−	0.644180i	$-0.777199\pi$
$379$	−11287.0	−1.52975	−0.764874	+	0.644180i	$0.777199\pi$
$380$	168.000	0.0226795
$381$	−2114.00	−0.284261
$382$	102.000	0.0136617
$383$	1185.00	0.158096	0.0790479	−	0.996871i	$-0.474812\pi$
$383$	1185.00	0.158096	0.0790479	+	0.996871i	$0.474812\pi$
$384$	−896.000	−0.119072
$385$	0	0
$386$	2452.00	0.323325
$387$	6248.00	0.820681
$388$	−44.0000	−0.00575712
$389$	−11643.0	−1.51754	−0.758771	−	0.651358i	$-0.774200\pi$
$389$	−11643.0	−1.51754	−0.758771	+	0.651358i	$0.774200\pi$
$390$	672.000	0.0872514
$391$	306.000	0.0395782
$392$	0	0
$393$	−3234.00	−0.415099
$394$	5508.00	0.704287
$395$	−2310.00	−0.294250
$396$	−968.000	−0.122838
$397$	3382.00	0.427551	0.213775	−	0.976883i	$-0.431424\pi$
$397$	3382.00	0.427551	0.213775	+	0.976883i	$0.431424\pi$
$398$	3488.00	0.439291
$399$	0	0
$400$	−1856.00	−0.232000
$401$	−7566.00	−0.942214	−0.471107	−	0.882076i	$-0.656146\pi$
$401$	−7566.00	−0.942214	−0.471107	+	0.882076i	$0.656146\pi$
$402$	6062.00	0.752102
$403$	−1520.00	−0.187882
$404$	−6768.00	−0.833467
$405$	2517.00	0.308817
$406$	0	0
$407$	2123.00	0.258558
$408$	336.000	0.0407708
$409$	−86.0000	−0.0103971	−0.00519857	−	0.999986i	$-0.501655\pi$
$409$	−86.0000	−0.0103971	−0.00519857	+	0.999986i	$0.501655\pi$
$410$	612.000	0.0737184
$411$	−21147.0	−2.53797
$412$	2128.00	0.254464
$413$	0	0
$414$	−2244.00	−0.266393
$415$	−3024.00	−0.357692
$416$	512.000	0.0603434
$417$	−11158.0	−1.31033
$418$	308.000	0.0360401
$419$	12672.0	1.47749	0.738744	−	0.673986i	$-0.235419\pi$
$419$	12672.0	1.47749	0.738744	+	0.673986i	$0.235419\pi$
$420$	0	0
$421$	12398.0	1.43525	0.717627	−	0.696428i	$-0.245229\pi$
$421$	12398.0	1.43525	0.717627	+	0.696428i	$0.245229\pi$
$422$	−8420.00	−0.971278
$423$	1584.00	0.182073
$424$	−816.000	−0.0934634
$425$	696.000	0.0794376
$426$	−1890.00	−0.214955
$427$	0	0
$428$	5400.00	0.609857
$429$	1232.00	0.138652
$430$	−1704.00	−0.191103
$431$	12372.0	1.38269	0.691344	−	0.722526i	$-0.257019\pi$
$431$	12372.0	1.38269	0.691344	+	0.722526i	$0.257019\pi$
$432$	560.000	0.0623681
$433$	14929.0	1.65691	0.828455	−	0.560056i	$-0.189220\pi$
$433$	14929.0	1.65691	0.828455	+	0.560056i	$0.189220\pi$
$434$	0	0
$435$	1134.00	0.124991
$436$	6464.00	0.710022
$437$	714.000	0.0781585
$438$	−3332.00	−0.363491
$439$	−9146.00	−0.994339	−0.497169	−	0.867653i	$-0.665627\pi$
$439$	−9146.00	−0.994339	−0.497169	+	0.867653i	$0.665627\pi$
$440$	264.000	0.0286039
$441$	0	0
$442$	−192.000	−0.0206618
$443$	−11253.0	−1.20688	−0.603438	−	0.797410i	$-0.706203\pi$
$443$	−11253.0	−1.20688	−0.603438	+	0.797410i	$0.706203\pi$
$444$	5404.00	0.577618
$445$	−1917.00	−0.204212
$446$	10994.0	1.16722
$447$	−19698.0	−2.08430
$448$	0	0
$449$	6711.00	0.705371	0.352686	−	0.935742i	$-0.385269\pi$
$449$	6711.00	0.705371	0.352686	+	0.935742i	$0.385269\pi$
$450$	−5104.00	−0.534677
$451$	1122.00	0.117146
$452$	2388.00	0.248500
$453$	−17150.0	−1.77876
$454$	7464.00	0.771592
$455$	0	0
$456$	784.000	0.0805135
$457$	16952.0	1.73519	0.867594	−	0.497273i	$-0.165665\pi$
$457$	16952.0	1.73519	0.867594	+	0.497273i	$0.165665\pi$
$458$	7766.00	0.792317
$459$	−210.000	−0.0213550
$460$	612.000	0.0620318
$461$	5850.00	0.591023	0.295512	−	0.955339i	$-0.404510\pi$
$461$	5850.00	0.591023	0.295512	+	0.955339i	$0.404510\pi$
$462$	0	0
$463$	−4957.00	−0.497562	−0.248781	−	0.968560i	$-0.580030\pi$
$463$	−4957.00	−0.497562	−0.248781	+	0.968560i	$0.580030\pi$
$464$	864.000	0.0864444
$465$	−1995.00	−0.198959
$466$	−444.000	−0.0441371
$467$	−3753.00	−0.371880	−0.185940	−	0.982561i	$-0.559533\pi$
$467$	−3753.00	−0.371880	−0.185940	+	0.982561i	$0.559533\pi$
$468$	1408.00	0.139070
$469$	0	0
$470$	−432.000	−0.0423972
$471$	27293.0	2.67005
$472$	504.000	0.0491493
$473$	−3124.00	−0.303682
$474$	−10780.0	−1.04460
$475$	1624.00	0.156872
$476$	0	0
$477$	−2244.00	−0.215400
$478$	−4608.00	−0.440931
$479$	16272.0	1.55216	0.776082	−	0.630632i	$-0.217204\pi$
$479$	16272.0	1.55216	0.776082	+	0.630632i	$0.217204\pi$
$480$	672.000	0.0639010
$481$	−3088.00	−0.292725
$482$	2552.00	0.241163
$483$	0	0
$484$	484.000	0.0454545
$485$	33.0000	0.00308959
$486$	9856.00	0.919912
$487$	10613.0	0.987517	0.493759	−	0.869599i	$-0.335623\pi$
$487$	10613.0	0.987517	0.493759	+	0.869599i	$0.335623\pi$
$488$	6320.00	0.586256
$489$	868.000	0.0802706
$490$	0	0
$491$	11562.0	1.06270	0.531350	−	0.847152i	$-0.321685\pi$
$491$	11562.0	1.06270	0.531350	+	0.847152i	$0.321685\pi$
$492$	2856.00	0.261704
$493$	−324.000	−0.0295988
$494$	−448.000	−0.0408026
$495$	726.000	0.0659218
$496$	−1520.00	−0.137601
$497$	0	0
$498$	−14112.0	−1.26983
$499$	−9604.00	−0.861591	−0.430796	−	0.902449i	$-0.641767\pi$
$499$	−9604.00	−0.861591	−0.430796	+	0.902449i	$0.641767\pi$
$500$	2892.00	0.258668
$501$	−210.000	−0.0187268
$502$	510.000	0.0453435
$503$	15852.0	1.40518	0.702590	−	0.711595i	$-0.252027\pi$
$503$	15852.0	1.40518	0.702590	+	0.711595i	$0.252027\pi$
$504$	0	0
$505$	5076.00	0.447285
$506$	1122.00	0.0985751
$507$	13587.0	1.19018
$508$	1208.00	0.105505
$509$	−15669.0	−1.36447	−0.682236	−	0.731132i	$-0.738992\pi$
$509$	−15669.0	−1.36447	−0.682236	+	0.731132i	$0.738992\pi$
$510$	−252.000	−0.0218799
$511$	0	0
$512$	512.000	0.0441942
$513$	−490.000	−0.0421716
$514$	−4740.00	−0.406756
$515$	−1596.00	−0.136560
$516$	−7952.00	−0.678425
$517$	−792.000	−0.0673735
$518$	0	0
$519$	15876.0	1.34273
$520$	−384.000	−0.0323837
$521$	2817.00	0.236881	0.118441	−	0.992961i	$-0.462211\pi$
$521$	2817.00	0.236881	0.118441	+	0.992961i	$0.462211\pi$
$522$	2376.00	0.199224
$523$	12364.0	1.03373	0.516864	−	0.856067i	$-0.327099\pi$
$523$	12364.0	1.03373	0.516864	+	0.856067i	$0.327099\pi$
$524$	1848.00	0.154065
$525$	0	0
$526$	4932.00	0.408832
$527$	570.000	0.0471150
$528$	1232.00	0.101545
$529$	−9566.00	−0.786225
$530$	612.000	0.0501577
$531$	1386.00	0.113272
$532$	0	0
$533$	−1632.00	−0.132626
$534$	−8946.00	−0.724965
$535$	−4050.00	−0.327284
$536$	−3464.00	−0.279146
$537$	−12117.0	−0.973719
$538$	−13548.0	−1.08568
$539$	0	0
$540$	−420.000	−0.0334702
$541$	2372.00	0.188503	0.0942516	−	0.995548i	$-0.469954\pi$
$541$	2372.00	0.188503	0.0942516	+	0.995548i	$0.469954\pi$
$542$	9752.00	0.772849
$543$	5495.00	0.434278
$544$	−192.000	−0.0151322
$545$	−4848.00	−0.381038
$546$	0	0
$547$	−12832.0	−1.00303	−0.501514	−	0.865149i	$-0.667224\pi$
$547$	−12832.0	−1.00303	−0.501514	+	0.865149i	$0.667224\pi$
$548$	12084.0	0.941976
$549$	17380.0	1.35111
$550$	2552.00	0.197850
$551$	−756.000	−0.0584513
$552$	2856.00	0.220216
$553$	0	0
$554$	−6536.00	−0.501242
$555$	−4053.00	−0.309982
$556$	6376.00	0.486336
$557$	−14166.0	−1.07762	−0.538809	−	0.842428i	$-0.681125\pi$
$557$	−14166.0	−1.07762	−0.538809	+	0.842428i	$0.681125\pi$
$558$	−4180.00	−0.317121
$559$	4544.00	0.343812
$560$	0	0
$561$	−462.000	−0.0347694
$562$	11856.0	0.889885
$563$	18540.0	1.38786	0.693932	−	0.720040i	$-0.255877\pi$
$563$	18540.0	1.38786	0.693932	+	0.720040i	$0.255877\pi$
$564$	−2016.00	−0.150512
$565$	−1791.00	−0.133359
$566$	−5344.00	−0.396864
$567$	0	0
$568$	1080.00	0.0797813
$569$	−21894.0	−1.61308	−0.806541	−	0.591177i	$-0.798663\pi$
$569$	−21894.0	−1.61308	−0.806541	+	0.591177i	$0.798663\pi$
$570$	−588.000	−0.0432081
$571$	23204.0	1.70063	0.850313	−	0.526278i	$-0.176413\pi$
$571$	23204.0	1.70063	0.850313	+	0.526278i	$0.176413\pi$
$572$	−704.000	−0.0514610
$573$	−357.000	−0.0260277
$574$	0	0
$575$	5916.00	0.429068
$576$	1408.00	0.101852
$577$	−18479.0	−1.33326	−0.666630	−	0.745389i	$-0.732264\pi$
$577$	−18479.0	−1.33326	−0.666630	+	0.745389i	$0.732264\pi$
$578$	−9754.00	−0.701925
$579$	−8582.00	−0.615986
$580$	−648.000	−0.0463909
$581$	0	0
$582$	154.000	0.0109682
$583$	1122.00	0.0797058
$584$	1904.00	0.134911
$585$	−1056.00	−0.0746329
$586$	−10644.0	−0.750341
$587$	1116.00	0.0784706	0.0392353	−	0.999230i	$-0.487508\pi$
$587$	1116.00	0.0784706	0.0392353	+	0.999230i	$0.487508\pi$
$588$	0	0
$589$	1330.00	0.0930419
$590$	−378.000	−0.0263763
$591$	−19278.0	−1.34178
$592$	−3088.00	−0.214385
$593$	3654.00	0.253038	0.126519	−	0.991964i	$-0.459619\pi$
$593$	3654.00	0.253038	0.126519	+	0.991964i	$0.459619\pi$
$594$	−770.000	−0.0531877
$595$	0	0
$596$	11256.0	0.773597
$597$	−12208.0	−0.836918
$598$	−1632.00	−0.111601
$599$	10248.0	0.699035	0.349517	−	0.936930i	$-0.386346\pi$
$599$	10248.0	0.699035	0.349517	+	0.936930i	$0.386346\pi$
$600$	6496.00	0.441997
$601$	−18848.0	−1.27924	−0.639622	−	0.768689i	$-0.720909\pi$
$601$	−18848.0	−1.27924	−0.639622	+	0.768689i	$0.720909\pi$
$602$	0	0
$603$	−9526.00	−0.643331
$604$	9800.00	0.660193
$605$	−363.000	−0.0243935
$606$	23688.0	1.58789
$607$	13198.0	0.882521	0.441261	−	0.897379i	$-0.354531\pi$
$607$	13198.0	0.882521	0.441261	+	0.897379i	$0.354531\pi$
$608$	−448.000	−0.0298829
$609$	0	0
$610$	−4740.00	−0.314618
$611$	1152.00	0.0762765
$612$	−528.000	−0.0348744
$613$	1712.00	0.112801	0.0564005	−	0.998408i	$-0.482038\pi$
$613$	1712.00	0.112801	0.0564005	+	0.998408i	$0.482038\pi$
$614$	−5632.00	−0.370178
$615$	−2142.00	−0.140445
$616$	0	0
$617$	20994.0	1.36983	0.684916	−	0.728622i	$-0.259839\pi$
$617$	20994.0	1.36983	0.684916	+	0.728622i	$0.259839\pi$
$618$	−7448.00	−0.484794
$619$	−25691.0	−1.66819	−0.834094	−	0.551622i	$-0.814009\pi$
$619$	−25691.0	−1.66819	−0.834094	+	0.551622i	$0.814009\pi$
$620$	1140.00	0.0738444
$621$	−1785.00	−0.115346
$622$	−17520.0	−1.12940
$623$	0	0
$624$	−1792.00	−0.114964
$625$	12331.0	0.789184
$626$	−2674.00	−0.170726
$627$	−1078.00	−0.0686622
$628$	−15596.0	−0.991000
$629$	1158.00	0.0734062
$630$	0	0
$631$	25445.0	1.60531	0.802654	−	0.596445i	$-0.203421\pi$
$631$	25445.0	1.60531	0.802654	+	0.596445i	$0.203421\pi$
$632$	6160.00	0.387708
$633$	29470.0	1.85044
$634$	8538.00	0.534838
$635$	−906.000	−0.0566197
$636$	2856.00	0.178063
$637$	0	0
$638$	−1188.00	−0.0737200
$639$	2970.00	0.183868
$640$	−384.000	−0.0237171
$641$	19095.0	1.17661	0.588305	−	0.808639i	$-0.299795\pi$
$641$	19095.0	1.17661	0.588305	+	0.808639i	$0.299795\pi$
$642$	−18900.0	−1.16187
$643$	24391.0	1.49594	0.747968	−	0.663735i	$-0.231030\pi$
$643$	24391.0	1.49594	0.747968	+	0.663735i	$0.231030\pi$
$644$	0	0
$645$	5964.00	0.364081
$646$	168.000	0.0102320
$647$	5691.00	0.345806	0.172903	−	0.984939i	$-0.444685\pi$
$647$	5691.00	0.345806	0.172903	+	0.984939i	$0.444685\pi$
$648$	−6712.00	−0.406902
$649$	−693.000	−0.0419147
$650$	−3712.00	−0.223995
$651$	0	0
$652$	−496.000	−0.0297927
$653$	−25749.0	−1.54309	−0.771544	−	0.636176i	$-0.780515\pi$
$653$	−25749.0	−1.54309	−0.771544	+	0.636176i	$0.780515\pi$
$654$	−22624.0	−1.35270
$655$	−1386.00	−0.0826802
$656$	−1632.00	−0.0971325
$657$	5236.00	0.310922
$658$	0	0
$659$	−9030.00	−0.533777	−0.266888	−	0.963727i	$-0.585995\pi$
$659$	−9030.00	−0.533777	−0.266888	+	0.963727i	$0.585995\pi$
$660$	−924.000	−0.0544949
$661$	−28895.0	−1.70028	−0.850140	−	0.526557i	$-0.823483\pi$
$661$	−28895.0	−1.70028	−0.850140	+	0.526557i	$0.823483\pi$
$662$	−9686.00	−0.568666
$663$	672.000	0.0393640
$664$	8064.00	0.471301
$665$	0	0
$666$	−8492.00	−0.494082
$667$	−2754.00	−0.159873
$668$	120.000	0.00695051
$669$	−38479.0	−2.22374
$670$	2598.00	0.149805
$671$	−8690.00	−0.499961
$672$	0	0
$673$	16856.0	0.965455	0.482727	−	0.875771i	$-0.339646\pi$
$673$	16856.0	0.965455	0.482727	+	0.875771i	$0.339646\pi$
$674$	−7580.00	−0.433191
$675$	−4060.00	−0.231510
$676$	−7764.00	−0.441739
$677$	19470.0	1.10531	0.552654	−	0.833411i	$-0.313615\pi$
$677$	19470.0	1.10531	0.552654	+	0.833411i	$0.313615\pi$
$678$	−8358.00	−0.473432
$679$	0	0
$680$	144.000	0.00812081
$681$	−26124.0	−1.47001
$682$	2090.00	0.117346
$683$	−14820.0	−0.830266	−0.415133	−	0.909761i	$-0.636265\pi$
$683$	−14820.0	−0.830266	−0.415133	+	0.909761i	$0.636265\pi$
$684$	−1232.00	−0.0688694
$685$	−9063.00	−0.505517
$686$	0	0
$687$	−27181.0	−1.50949
$688$	4544.00	0.251800
$689$	−1632.00	−0.0902384
$690$	−2142.00	−0.118181
$691$	18451.0	1.01579	0.507894	−	0.861420i	$-0.330424\pi$
$691$	18451.0	1.01579	0.507894	+	0.861420i	$0.330424\pi$
$692$	−9072.00	−0.498361
$693$	0	0
$694$	3444.00	0.188375
$695$	−4782.00	−0.260995
$696$	−3024.00	−0.164690
$697$	612.000	0.0332585
$698$	6332.00	0.343366
$699$	1554.00	0.0840882
$700$	0	0
$701$	6288.00	0.338794	0.169397	−	0.985548i	$-0.445818\pi$
$701$	6288.00	0.338794	0.169397	+	0.985548i	$0.445818\pi$
$702$	1120.00	0.0602161
$703$	2702.00	0.144961
$704$	−704.000	−0.0376889
$705$	1512.00	0.0807734
$706$	8334.00	0.444269
$707$	0	0
$708$	−1764.00	−0.0936373
$709$	−17629.0	−0.933810	−0.466905	−	0.884308i	$-0.654631\pi$
$709$	−17629.0	−0.933810	−0.466905	+	0.884308i	$0.654631\pi$
$710$	−810.000	−0.0428152
$711$	16940.0	0.893530
$712$	5112.00	0.269073
$713$	4845.00	0.254483
$714$	0	0
$715$	528.000	0.0276169
$716$	6924.00	0.361399
$717$	16128.0	0.840044
$718$	2760.00	0.143457
$719$	−2067.00	−0.107213	−0.0536065	−	0.998562i	$-0.517072\pi$
$719$	−2067.00	−0.107213	−0.0536065	+	0.998562i	$0.517072\pi$
$720$	−1056.00	−0.0546594
$721$	0	0
$722$	−13326.0	−0.686901
$723$	−8932.00	−0.459453
$724$	−3140.00	−0.161184
$725$	−6264.00	−0.320882
$726$	−1694.00	−0.0865981
$727$	−11315.0	−0.577235	−0.288618	−	0.957444i	$-0.593196\pi$
$727$	−11315.0	−0.577235	−0.288618	+	0.957444i	$0.593196\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	−1428.00	−0.0724009
$731$	−1704.00	−0.0862171
$732$	−22120.0	−1.11691
$733$	23644.0	1.19142	0.595710	−	0.803199i	$-0.296871\pi$
$733$	23644.0	1.19142	0.595710	+	0.803199i	$0.296871\pi$
$734$	−1510.00	−0.0759334
$735$	0	0
$736$	−1632.00	−0.0817341
$737$	4763.00	0.238056
$738$	−4488.00	−0.223856
$739$	−862.000	−0.0429082	−0.0214541	−	0.999770i	$-0.506830\pi$
$739$	−862.000	−0.0429082	−0.0214541	+	0.999770i	$0.506830\pi$
$740$	2316.00	0.115051
$741$	1568.00	0.0777354
$742$	0	0
$743$	9072.00	0.447940	0.223970	−	0.974596i	$-0.428098\pi$
$743$	9072.00	0.447940	0.223970	+	0.974596i	$0.428098\pi$
$744$	5320.00	0.262151
$745$	−8442.00	−0.415156
$746$	−17192.0	−0.843759
$747$	22176.0	1.08618
$748$	264.000	0.0129048
$749$	0	0
$750$	−10122.0	−0.492804
$751$	9407.00	0.457079	0.228539	−	0.973535i	$-0.426605\pi$
$751$	9407.00	0.457079	0.228539	+	0.973535i	$0.426605\pi$
$752$	1152.00	0.0558632
$753$	−1785.00	−0.0863865
$754$	1728.00	0.0834616
$755$	−7350.00	−0.354297
$756$	0	0
$757$	−15946.0	−0.765611	−0.382805	−	0.923829i	$-0.625042\pi$
$757$	−15946.0	−0.765611	−0.382805	+	0.923829i	$0.625042\pi$
$758$	−22574.0	−1.08169
$759$	−3927.00	−0.187801
$760$	336.000	0.0160368
$761$	8220.00	0.391557	0.195778	−	0.980648i	$-0.437277\pi$
$761$	8220.00	0.391557	0.195778	+	0.980648i	$0.437277\pi$
$762$	−4228.00	−0.201003
$763$	0	0
$764$	204.000	0.00966029
$765$	396.000	0.0187156
$766$	2370.00	0.111791
$767$	1008.00	0.0474534
$768$	−1792.00	−0.0841969
$769$	−14372.0	−0.673950	−0.336975	−	0.941514i	$-0.609404\pi$
$769$	−14372.0	−0.673950	−0.336975	+	0.941514i	$0.609404\pi$
$770$	0	0
$771$	16590.0	0.774934
$772$	4904.00	0.228625
$773$	−14082.0	−0.655232	−0.327616	−	0.944811i	$-0.606245\pi$
$773$	−14082.0	−0.655232	−0.327616	+	0.944811i	$0.606245\pi$
$774$	12496.0	0.580309
$775$	11020.0	0.510774
$776$	−88.0000	−0.00407090
$777$	0	0
$778$	−23286.0	−1.07306
$779$	1428.00	0.0656783
$780$	1344.00	0.0616961
$781$	−1485.00	−0.0680377
$782$	612.000	0.0279860
$783$	1890.00	0.0862619
$784$	0	0
$785$	11697.0	0.531827
$786$	−6468.00	−0.293519
$787$	12742.0	0.577132	0.288566	−	0.957460i	$-0.406821\pi$
$787$	12742.0	0.577132	0.288566	+	0.957460i	$0.406821\pi$
$788$	11016.0	0.498006
$789$	−17262.0	−0.778889
$790$	−4620.00	−0.208066
$791$	0	0
$792$	−1936.00	−0.0868596
$793$	12640.0	0.566027
$794$	6764.00	0.302324
$795$	−2142.00	−0.0955584
$796$	6976.00	0.310625
$797$	−7131.00	−0.316930	−0.158465	−	0.987365i	$-0.550654\pi$
$797$	−7131.00	−0.316930	−0.158465	+	0.987365i	$0.550654\pi$
$798$	0	0
$799$	−432.000	−0.0191277
$800$	−3712.00	−0.164049
$801$	14058.0	0.620119
$802$	−15132.0	−0.666246
$803$	−2618.00	−0.115053
$804$	12124.0	0.531817
$805$	0	0
$806$	−3040.00	−0.132853
$807$	47418.0	2.06839
$808$	−13536.0	−0.589350
$809$	21966.0	0.954615	0.477307	−	0.878736i	$-0.341613\pi$
$809$	21966.0	0.954615	0.477307	+	0.878736i	$0.341613\pi$
$810$	5034.00	0.218366
$811$	10978.0	0.475326	0.237663	−	0.971348i	$-0.423619\pi$
$811$	10978.0	0.475326	0.237663	+	0.971348i	$0.423619\pi$
$812$	0	0
$813$	−34132.0	−1.47240
$814$	4246.00	0.182828
$815$	372.000	0.0159885
$816$	672.000	0.0288293
$817$	−3976.00	−0.170260
$818$	−172.000	−0.00735188
$819$	0	0
$820$	1224.00	0.0521267
$821$	−27534.0	−1.17045	−0.585227	−	0.810869i	$-0.698995\pi$
$821$	−27534.0	−1.17045	−0.585227	+	0.810869i	$0.698995\pi$
$822$	−42294.0	−1.79461
$823$	−19591.0	−0.829768	−0.414884	−	0.909874i	$-0.636178\pi$
$823$	−19591.0	−0.829768	−0.414884	+	0.909874i	$0.636178\pi$
$824$	4256.00	0.179933
$825$	−8932.00	−0.376936
$826$	0	0
$827$	12744.0	0.535855	0.267928	−	0.963439i	$-0.413661\pi$
$827$	12744.0	0.535855	0.267928	+	0.963439i	$0.413661\pi$
$828$	−4488.00	−0.188368
$829$	−23567.0	−0.987353	−0.493677	−	0.869646i	$-0.664347\pi$
$829$	−23567.0	−0.987353	−0.493677	+	0.869646i	$0.664347\pi$
$830$	−6048.00	−0.252927
$831$	22876.0	0.954945
$832$	1024.00	0.0426692
$833$	0	0
$834$	−22316.0	−0.926547
$835$	−90.0000	−0.00373003
$836$	616.000	0.0254842
$837$	−3325.00	−0.137310
$838$	25344.0	1.04474
$839$	−30219.0	−1.24348	−0.621738	−	0.783226i	$-0.713573\pi$
$839$	−30219.0	−1.24348	−0.621738	+	0.783226i	$0.713573\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	24796.0	1.01488
$843$	−41496.0	−1.69537
$844$	−16840.0	−0.686797
$845$	5823.00	0.237062
$846$	3168.00	0.128745
$847$	0	0
$848$	−1632.00	−0.0660886
$849$	18704.0	0.756089
$850$	1392.00	0.0561708
$851$	9843.00	0.396491
$852$	−3780.00	−0.151996
$853$	−8654.00	−0.347371	−0.173685	−	0.984801i	$-0.555568\pi$
$853$	−8654.00	−0.347371	−0.173685	+	0.984801i	$0.555568\pi$
$854$	0	0
$855$	924.000	0.0369592
$856$	10800.0	0.431234
$857$	43284.0	1.72527	0.862633	−	0.505830i	$-0.168814\pi$
$857$	43284.0	1.72527	0.862633	+	0.505830i	$0.168814\pi$
$858$	2464.00	0.0980415
$859$	21931.0	0.871101	0.435551	−	0.900164i	$-0.356554\pi$
$859$	21931.0	0.871101	0.435551	+	0.900164i	$0.356554\pi$
$860$	−3408.00	−0.135130
$861$	0	0
$862$	24744.0	0.977708
$863$	−22404.0	−0.883709	−0.441855	−	0.897087i	$-0.645679\pi$
$863$	−22404.0	−0.883709	−0.441855	+	0.897087i	$0.645679\pi$
$864$	1120.00	0.0441009
$865$	6804.00	0.267448
$866$	29858.0	1.17161
$867$	34139.0	1.33728
$868$	0	0
$869$	−8470.00	−0.330639
$870$	2268.00	0.0883821
$871$	−6928.00	−0.269514
$872$	12928.0	0.502061
$873$	−242.000	−0.00938197
$874$	1428.00	0.0552664
$875$	0	0
$876$	−6664.00	−0.257027
$877$	4826.00	0.185818	0.0929090	−	0.995675i	$-0.470383\pi$
$877$	4826.00	0.185818	0.0929090	+	0.995675i	$0.470383\pi$
$878$	−18292.0	−0.703104
$879$	37254.0	1.42952
$880$	528.000	0.0202260
$881$	−40203.0	−1.53743	−0.768714	−	0.639593i	$-0.779103\pi$
$881$	−40203.0	−1.53743	−0.768714	+	0.639593i	$0.779103\pi$
$882$	0	0
$883$	−41716.0	−1.58987	−0.794935	−	0.606695i	$-0.792495\pi$
$883$	−41716.0	−1.58987	−0.794935	+	0.606695i	$0.792495\pi$
$884$	−384.000	−0.0146101
$885$	1323.00	0.0502510
$886$	−22506.0	−0.853390
$887$	44358.0	1.67914	0.839569	−	0.543253i	$-0.182807\pi$
$887$	44358.0	1.67914	0.839569	+	0.543253i	$0.182807\pi$
$888$	10808.0	0.408438
$889$	0	0
$890$	−3834.00	−0.144400
$891$	9229.00	0.347007
$892$	21988.0	0.825351
$893$	−1008.00	−0.0377732
$894$	−39396.0	−1.47382
$895$	−5193.00	−0.193947
$896$	0	0
$897$	5712.00	0.212618
$898$	13422.0	0.498773
$899$	−5130.00	−0.190317
$900$	−10208.0	−0.378074
$901$	612.000	0.0226289
$902$	2244.00	0.0828348
$903$	0	0
$904$	4776.00	0.175716
$905$	2355.00	0.0865004
$906$	−34300.0	−1.25777
$907$	29384.0	1.07572	0.537861	−	0.843034i	$-0.319233\pi$
$907$	29384.0	1.07572	0.537861	+	0.843034i	$0.319233\pi$
$908$	14928.0	0.545598
$909$	−37224.0	−1.35824
$910$	0	0
$911$	5160.00	0.187660	0.0938301	−	0.995588i	$-0.470089\pi$
$911$	5160.00	0.187660	0.0938301	+	0.995588i	$0.470089\pi$
$912$	1568.00	0.0569317
$913$	−11088.0	−0.401927
$914$	33904.0	1.22696
$915$	16590.0	0.599397
$916$	15532.0	0.560253
$917$	0	0
$918$	−420.000	−0.0151003
$919$	10436.0	0.374594	0.187297	−	0.982303i	$-0.440027\pi$
$919$	10436.0	0.374594	0.187297	+	0.982303i	$0.440027\pi$
$920$	1224.00	0.0438631
$921$	19712.0	0.705247
$922$	11700.0	0.417916
$923$	2160.00	0.0770285
$924$	0	0
$925$	22388.0	0.795798
$926$	−9914.00	−0.351830
$927$	11704.0	0.414682
$928$	1728.00	0.0611254
$929$	−40626.0	−1.43476	−0.717382	−	0.696680i	$-0.754660\pi$
$929$	−40626.0	−1.43476	−0.717382	+	0.696680i	$0.754660\pi$
$930$	−3990.00	−0.140685
$931$	0	0
$932$	−888.000	−0.0312097
$933$	61320.0	2.15169
$934$	−7506.00	−0.262959
$935$	−198.000	−0.00692545
$936$	2816.00	0.0983374
$937$	2608.00	0.0909281	0.0454641	−	0.998966i	$-0.485523\pi$
$937$	2608.00	0.0909281	0.0454641	+	0.998966i	$0.485523\pi$
$938$	0	0
$939$	9359.00	0.325260
$940$	−864.000	−0.0299793
$941$	57150.0	1.97985	0.989924	−	0.141600i	$-0.0452248\pi$
$941$	57150.0	1.97985	0.989924	+	0.141600i	$0.0452248\pi$
$942$	54586.0	1.88801
$943$	5202.00	0.179640
$944$	1008.00	0.0347538
$945$	0	0
$946$	−6248.00	−0.214736
$947$	−657.000	−0.0225445	−0.0112722	−	0.999936i	$-0.503588\pi$
$947$	−657.000	−0.0225445	−0.0112722	+	0.999936i	$0.503588\pi$
$948$	−21560.0	−0.738646
$949$	3808.00	0.130256
$950$	3248.00	0.110925
$951$	−29883.0	−1.01895
$952$	0	0
$953$	5508.00	0.187221	0.0936105	−	0.995609i	$-0.470159\pi$
$953$	5508.00	0.187221	0.0936105	+	0.995609i	$0.470159\pi$
$954$	−4488.00	−0.152311
$955$	−153.000	−0.00518426
$956$	−9216.00	−0.311785
$957$	4158.00	0.140448
$958$	32544.0	1.09755
$959$	0	0
$960$	1344.00	0.0451848
$961$	−20766.0	−0.697056
$962$	−6176.00	−0.206988
$963$	29700.0	0.993841
$964$	5104.00	0.170528
$965$	−3678.00	−0.122693
$966$	0	0
$967$	−1690.00	−0.0562014	−0.0281007	−	0.999605i	$-0.508946\pi$
$967$	−1690.00	−0.0562014	−0.0281007	+	0.999605i	$0.508946\pi$
$968$	968.000	0.0321412
$969$	−588.000	−0.0194936
$970$	66.0000	0.00218467
$971$	−7263.00	−0.240042	−0.120021	−	0.992771i	$-0.538296\pi$
$971$	−7263.00	−0.240042	−0.120021	+	0.992771i	$0.538296\pi$
$972$	19712.0	0.650476
$973$	0	0
$974$	21226.0	0.698280
$975$	12992.0	0.426746
$976$	12640.0	0.414546
$977$	1569.00	0.0513785	0.0256892	−	0.999670i	$-0.491822\pi$
$977$	1569.00	0.0513785	0.0256892	+	0.999670i	$0.491822\pi$
$978$	1736.00	0.0567599
$979$	−7029.00	−0.229467
$980$	0	0
$981$	35552.0	1.15707
$982$	23124.0	0.751442
$983$	9261.00	0.300488	0.150244	−	0.988649i	$-0.451994\pi$
$983$	9261.00	0.300488	0.150244	+	0.988649i	$0.451994\pi$
$984$	5712.00	0.185053
$985$	−8262.00	−0.267258
$986$	−648.000	−0.0209295
$987$	0	0
$988$	−896.000	−0.0288518
$989$	−14484.0	−0.465687
$990$	1452.00	0.0466137
$991$	19400.0	0.621858	0.310929	−	0.950433i	$-0.399360\pi$
$991$	19400.0	0.621858	0.310929	+	0.950433i	$0.399360\pi$
$992$	−3040.00	−0.0972985
$993$	33901.0	1.08340
$994$	0	0
$995$	−5232.00	−0.166699
$996$	−28224.0	−0.897903
$997$	20740.0	0.658819	0.329409	−	0.944187i	$-0.393150\pi$
$997$	20740.0	0.658819	0.329409	+	0.944187i	$0.393150\pi$
$998$	−19208.0	−0.609237
$999$	−6755.00	−0.213933

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.4.a.e.1.1	✓	1	7.6	odd	2
1078.4.a.e.1.1		1	1.1	even	1	trivial
1232.4.a.b.1.1		1	28.27	even	2
1386.4.a.b.1.1		1	21.20	even	2
1694.4.a.d.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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