LMFDB - Embedded newform 245.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, 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("245.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.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:	$14.4554679514$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +6.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +6.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} +6.00000 q^{6} -15.0000 q^{8} +9.00000 q^{9} -5.00000 q^{10} -44.0000 q^{11} -42.0000 q^{12} +6.00000 q^{13} -30.0000 q^{15} +41.0000 q^{16} -24.0000 q^{17} +9.00000 q^{18} -114.000 q^{19} +35.0000 q^{20} -44.0000 q^{22} -52.0000 q^{23} -90.0000 q^{24} +25.0000 q^{25} +6.00000 q^{26} -108.000 q^{27} +146.000 q^{29} -30.0000 q^{30} -276.000 q^{31} +161.000 q^{32} -264.000 q^{33} -24.0000 q^{34} -63.0000 q^{36} -210.000 q^{37} -114.000 q^{38} +36.0000 q^{39} +75.0000 q^{40} +444.000 q^{41} +492.000 q^{43} +308.000 q^{44} -45.0000 q^{45} -52.0000 q^{46} -612.000 q^{47} +246.000 q^{48} +25.0000 q^{50} -144.000 q^{51} -42.0000 q^{52} +50.0000 q^{53} -108.000 q^{54} +220.000 q^{55} -684.000 q^{57} +146.000 q^{58} +294.000 q^{59} +210.000 q^{60} +450.000 q^{61} -276.000 q^{62} -167.000 q^{64} -30.0000 q^{65} -264.000 q^{66} -668.000 q^{67} +168.000 q^{68} -312.000 q^{69} -308.000 q^{71} -135.000 q^{72} +12.0000 q^{73} -210.000 q^{74} +150.000 q^{75} +798.000 q^{76} +36.0000 q^{78} +596.000 q^{79} -205.000 q^{80} -891.000 q^{81} +444.000 q^{82} -966.000 q^{83} +120.000 q^{85} +492.000 q^{86} +876.000 q^{87} +660.000 q^{88} -408.000 q^{89} -45.0000 q^{90} +364.000 q^{92} -1656.00 q^{93} -612.000 q^{94} +570.000 q^{95} +966.000 q^{96} -1200.00 q^{97} -396.000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	6.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	6.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	−7.00000	−0.875000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	6.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−15.0000	−0.662913
$9$	9.00000	0.333333
$10$	−5.00000	−0.158114
$11$	−44.0000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−44.0000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	−42.0000	−1.01036
$13$	6.00000	0.128008	0.0640039	−	0.997950i	$-0.479613\pi$
$13$	6.00000	0.128008	0.0640039	+	0.997950i	$0.479613\pi$
$14$	0	0
$15$	−30.0000	−0.516398
$16$	41.0000	0.640625
$17$	−24.0000	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$17$	−24.0000	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$18$	9.00000	0.117851
$19$	−114.000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−114.000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	35.0000	0.391312
$21$	0	0
$22$	−44.0000	−0.426401
$23$	−52.0000	−0.471424	−0.235712	−	0.971823i	$-0.575742\pi$
$23$	−52.0000	−0.471424	−0.235712	+	0.971823i	$0.575742\pi$
$24$	−90.0000	−0.765466
$25$	25.0000	0.200000
$26$	6.00000	0.0452576
$27$	−108.000	−0.769800
$28$	0	0
$29$	146.000	0.934880	0.467440	−	0.884025i	$-0.345176\pi$
$29$	146.000	0.934880	0.467440	+	0.884025i	$0.345176\pi$
$30$	−30.0000	−0.182574
$31$	−276.000	−1.59907	−0.799533	−	0.600622i	$-0.794920\pi$
$31$	−276.000	−1.59907	−0.799533	+	0.600622i	$0.794920\pi$
$32$	161.000	0.889408
$33$	−264.000	−1.39262
$34$	−24.0000	−0.121058
$35$	0	0
$36$	−63.0000	−0.291667
$37$	−210.000	−0.933075	−0.466538	−	0.884501i	$-0.654499\pi$
$37$	−210.000	−0.933075	−0.466538	+	0.884501i	$0.654499\pi$
$38$	−114.000	−0.486664
$39$	36.0000	0.147811
$40$	75.0000	0.296464
$41$	444.000	1.69125	0.845624	−	0.533779i	$-0.179229\pi$
$41$	444.000	1.69125	0.845624	+	0.533779i	$0.179229\pi$
$42$	0	0
$43$	492.000	1.74487	0.872434	−	0.488733i	$-0.162541\pi$
$43$	492.000	1.74487	0.872434	+	0.488733i	$0.162541\pi$
$44$	308.000	1.05529
$45$	−45.0000	−0.149071
$46$	−52.0000	−0.166674
$47$	−612.000	−1.89935	−0.949674	−	0.313239i	$-0.898586\pi$
$47$	−612.000	−1.89935	−0.949674	+	0.313239i	$0.898586\pi$
$48$	246.000	0.739730
$49$	0	0
$50$	25.0000	0.0707107
$51$	−144.000	−0.395373
$52$	−42.0000	−0.112007
$53$	50.0000	0.129585	0.0647927	−	0.997899i	$-0.479361\pi$
$53$	50.0000	0.129585	0.0647927	+	0.997899i	$0.479361\pi$
$54$	−108.000	−0.272166
$55$	220.000	0.539360
$56$	0	0
$57$	−684.000	−1.58944
$58$	146.000	0.330530
$59$	294.000	0.648738	0.324369	−	0.945931i	$-0.394848\pi$
$59$	294.000	0.648738	0.324369	+	0.945931i	$0.394848\pi$
$60$	210.000	0.451848
$61$	450.000	0.944534	0.472267	−	0.881455i	$-0.343436\pi$
$61$	450.000	0.944534	0.472267	+	0.881455i	$0.343436\pi$
$62$	−276.000	−0.565355
$63$	0	0
$64$	−167.000	−0.326172
$65$	−30.0000	−0.0572468
$66$	−264.000	−0.492366
$67$	−668.000	−1.21805	−0.609024	−	0.793152i	$-0.708439\pi$
$67$	−668.000	−1.21805	−0.609024	+	0.793152i	$0.708439\pi$
$68$	168.000	0.299603
$69$	−312.000	−0.544353
$70$	0	0
$71$	−308.000	−0.514829	−0.257415	−	0.966301i	$-0.582871\pi$
$71$	−308.000	−0.514829	−0.257415	+	0.966301i	$0.582871\pi$
$72$	−135.000	−0.220971
$73$	12.0000	0.0192396	0.00961982	−	0.999954i	$-0.496938\pi$
$73$	12.0000	0.0192396	0.00961982	+	0.999954i	$0.496938\pi$
$74$	−210.000	−0.329892
$75$	150.000	0.230940
$76$	798.000	1.20443
$77$	0	0
$78$	36.0000	0.0522589
$79$	596.000	0.848800	0.424400	−	0.905475i	$-0.360485\pi$
$79$	596.000	0.848800	0.424400	+	0.905475i	$0.360485\pi$
$80$	−205.000	−0.286496
$81$	−891.000	−1.22222
$82$	444.000	0.597946
$83$	−966.000	−1.27750	−0.638749	−	0.769415i	$-0.720548\pi$
$83$	−966.000	−1.27750	−0.638749	+	0.769415i	$0.720548\pi$
$84$	0	0
$85$	120.000	0.153127
$86$	492.000	0.616904
$87$	876.000	1.07951
$88$	660.000	0.799503
$89$	−408.000	−0.485932	−0.242966	−	0.970035i	$-0.578120\pi$
$89$	−408.000	−0.485932	−0.242966	+	0.970035i	$0.578120\pi$
$90$	−45.0000	−0.0527046
$91$	0	0
$92$	364.000	0.412496
$93$	−1656.00	−1.84644
$94$	−612.000	−0.671521
$95$	570.000	0.615587
$96$	966.000	1.02700
$97$	−1200.00	−1.25610	−0.628049	−	0.778174i	$-0.716146\pi$
$97$	−1200.00	−1.25610	−0.628049	+	0.778174i	$0.716146\pi$
$98$	0	0
$99$	−396.000	−0.402015
$100$	−175.000	−0.175000
$101$	1098.00	1.08173	0.540867	−	0.841108i	$-0.318096\pi$
$101$	1098.00	1.08173	0.540867	+	0.841108i	$0.318096\pi$
$102$	−144.000	−0.139786
$103$	972.000	0.929845	0.464922	−	0.885351i	$-0.346082\pi$
$103$	972.000	0.929845	0.464922	+	0.885351i	$0.346082\pi$
$104$	−90.0000	−0.0848579
$105$	0	0
$106$	50.0000	0.0458154
$107$	1516.00	1.36969	0.684847	−	0.728687i	$-0.259869\pi$
$107$	1516.00	1.36969	0.684847	+	0.728687i	$0.259869\pi$
$108$	756.000	0.673575
$109$	930.000	0.817228	0.408614	−	0.912707i	$-0.366012\pi$
$109$	930.000	0.817228	0.408614	+	0.912707i	$0.366012\pi$
$110$	220.000	0.190693
$111$	−1260.00	−1.07742
$112$	0	0
$113$	1694.00	1.41025	0.705124	−	0.709084i	$-0.250891\pi$
$113$	1694.00	1.41025	0.705124	+	0.709084i	$0.250891\pi$
$114$	−684.000	−0.561951
$115$	260.000	0.210827
$116$	−1022.00	−0.818020
$117$	54.0000	0.0426692
$118$	294.000	0.229364
$119$	0	0
$120$	450.000	0.342327
$121$	605.000	0.454545
$122$	450.000	0.333943
$123$	2664.00	1.95288
$124$	1932.00	1.39918
$125$	−125.000	−0.0894427
$126$	0	0
$127$	916.000	0.640015	0.320007	−	0.947415i	$-0.396315\pi$
$127$	916.000	0.640015	0.320007	+	0.947415i	$0.396315\pi$
$128$	−1455.00	−1.00473
$129$	2952.00	2.01480
$130$	−30.0000	−0.0202398
$131$	−1002.00	−0.668284	−0.334142	−	0.942523i	$-0.608446\pi$
$131$	−1002.00	−0.668284	−0.334142	+	0.942523i	$0.608446\pi$
$132$	1848.00	1.21854
$133$	0	0
$134$	−668.000	−0.430645
$135$	540.000	0.344265
$136$	360.000	0.226983
$137$	−274.000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−274.000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−312.000	−0.192458
$139$	−270.000	−0.164756	−0.0823781	−	0.996601i	$-0.526251\pi$
$139$	−270.000	−0.164756	−0.0823781	+	0.996601i	$0.526251\pi$
$140$	0	0
$141$	−3672.00	−2.19318
$142$	−308.000	−0.182020
$143$	−264.000	−0.154383
$144$	369.000	0.213542
$145$	−730.000	−0.418091
$146$	12.0000	0.00680224
$147$	0	0
$148$	1470.00	0.816441
$149$	−530.000	−0.291405	−0.145702	−	0.989328i	$-0.546544\pi$
$149$	−530.000	−0.291405	−0.145702	+	0.989328i	$0.546544\pi$
$150$	150.000	0.0816497
$151$	−3120.00	−1.68147	−0.840735	−	0.541447i	$-0.817877\pi$
$151$	−3120.00	−1.68147	−0.840735	+	0.541447i	$0.817877\pi$
$152$	1710.00	0.912495
$153$	−216.000	−0.114134
$154$	0	0
$155$	1380.00	0.715124
$156$	−252.000	−0.129334
$157$	−2106.00	−1.07055	−0.535277	−	0.844676i	$-0.679793\pi$
$157$	−2106.00	−1.07055	−0.535277	+	0.844676i	$0.679793\pi$
$158$	596.000	0.300096
$159$	300.000	0.149632
$160$	−805.000	−0.397755
$161$	0	0
$162$	−891.000	−0.432121
$163$	628.000	0.301772	0.150886	−	0.988551i	$-0.451787\pi$
$163$	628.000	0.301772	0.150886	+	0.988551i	$0.451787\pi$
$164$	−3108.00	−1.47984
$165$	1320.00	0.622799
$166$	−966.000	−0.451663
$167$	1284.00	0.594963	0.297482	−	0.954728i	$-0.403853\pi$
$167$	1284.00	0.594963	0.297482	+	0.954728i	$0.403853\pi$
$168$	0	0
$169$	−2161.00	−0.983614
$170$	120.000	0.0541387
$171$	−1026.00	−0.458831
$172$	−3444.00	−1.52676
$173$	−906.000	−0.398161	−0.199081	−	0.979983i	$-0.563796\pi$
$173$	−906.000	−0.398161	−0.199081	+	0.979983i	$0.563796\pi$
$174$	876.000	0.381663
$175$	0	0
$176$	−1804.00	−0.772623
$177$	1764.00	0.749098
$178$	−408.000	−0.171803
$179$	−2084.00	−0.870198	−0.435099	−	0.900383i	$-0.643287\pi$
$179$	−2084.00	−0.870198	−0.435099	+	0.900383i	$0.643287\pi$
$180$	315.000	0.130437
$181$	−4674.00	−1.91942	−0.959712	−	0.280986i	$-0.909339\pi$
$181$	−4674.00	−1.91942	−0.959712	+	0.280986i	$0.909339\pi$
$182$	0	0
$183$	2700.00	1.09065
$184$	780.000	0.312513
$185$	1050.00	0.417284
$186$	−1656.00	−0.652816
$187$	1056.00	0.412954
$188$	4284.00	1.66193
$189$	0	0
$190$	570.000	0.217643
$191$	2012.00	0.762216	0.381108	−	0.924531i	$-0.375543\pi$
$191$	2012.00	0.762216	0.381108	+	0.924531i	$0.375543\pi$
$192$	−1002.00	−0.376631
$193$	4206.00	1.56868	0.784338	−	0.620334i	$-0.213003\pi$
$193$	4206.00	1.56868	0.784338	+	0.620334i	$0.213003\pi$
$194$	−1200.00	−0.444098
$195$	−180.000	−0.0661029
$196$	0	0
$197$	−1574.00	−0.569253	−0.284627	−	0.958638i	$-0.591870\pi$
$197$	−1574.00	−0.569253	−0.284627	+	0.958638i	$0.591870\pi$
$198$	−396.000	−0.142134
$199$	−2724.00	−0.970348	−0.485174	−	0.874418i	$-0.661244\pi$
$199$	−2724.00	−0.970348	−0.485174	+	0.874418i	$0.661244\pi$
$200$	−375.000	−0.132583
$201$	−4008.00	−1.40648
$202$	1098.00	0.382451
$203$	0	0
$204$	1008.00	0.345952
$205$	−2220.00	−0.756349
$206$	972.000	0.328750
$207$	−468.000	−0.157141
$208$	246.000	0.0820050
$209$	5016.00	1.66011
$210$	0	0
$211$	−180.000	−0.0587285	−0.0293642	−	0.999569i	$-0.509348\pi$
$211$	−180.000	−0.0587285	−0.0293642	+	0.999569i	$0.509348\pi$
$212$	−350.000	−0.113387
$213$	−1848.00	−0.594474
$214$	1516.00	0.484260
$215$	−2460.00	−0.780328
$216$	1620.00	0.510310
$217$	0	0
$218$	930.000	0.288934
$219$	72.0000	0.0222160
$220$	−1540.00	−0.471940
$221$	−144.000	−0.0438303
$222$	−1260.00	−0.380926
$223$	−4584.00	−1.37654	−0.688268	−	0.725457i	$-0.741628\pi$
$223$	−4584.00	−1.37654	−0.688268	+	0.725457i	$0.741628\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	1694.00	0.498598
$227$	−1686.00	−0.492968	−0.246484	−	0.969147i	$-0.579275\pi$
$227$	−1686.00	−0.492968	−0.246484	+	0.969147i	$0.579275\pi$
$228$	4788.00	1.39076
$229$	−4026.00	−1.16177	−0.580886	−	0.813985i	$-0.697294\pi$
$229$	−4026.00	−1.16177	−0.580886	+	0.813985i	$0.697294\pi$
$230$	260.000	0.0745387
$231$	0	0
$232$	−2190.00	−0.619744
$233$	−6074.00	−1.70782	−0.853908	−	0.520425i	$-0.825774\pi$
$233$	−6074.00	−1.70782	−0.853908	+	0.520425i	$0.825774\pi$
$234$	54.0000	0.0150859
$235$	3060.00	0.849414
$236$	−2058.00	−0.567646
$237$	3576.00	0.980110
$238$	0	0
$239$	3928.00	1.06310	0.531551	−	0.847027i	$-0.321610\pi$
$239$	3928.00	1.06310	0.531551	+	0.847027i	$0.321610\pi$
$240$	−1230.00	−0.330817
$241$	−1236.00	−0.330364	−0.165182	−	0.986263i	$-0.552821\pi$
$241$	−1236.00	−0.330364	−0.165182	+	0.986263i	$0.552821\pi$
$242$	605.000	0.160706
$243$	−2430.00	−0.641500
$244$	−3150.00	−0.826468
$245$	0	0
$246$	2664.00	0.690449
$247$	−684.000	−0.176202
$248$	4140.00	1.06004
$249$	−5796.00	−1.47513
$250$	−125.000	−0.0316228
$251$	−78.0000	−0.0196148	−0.00980740	−	0.999952i	$-0.503122\pi$
$251$	−78.0000	−0.0196148	−0.00980740	+	0.999952i	$0.503122\pi$
$252$	0	0
$253$	2288.00	0.568559
$254$	916.000	0.226279
$255$	720.000	0.176816
$256$	−119.000	−0.0290527
$257$	−3276.00	−0.795141	−0.397571	−	0.917572i	$-0.630147\pi$
$257$	−3276.00	−0.795141	−0.397571	+	0.917572i	$0.630147\pi$
$258$	2952.00	0.712339
$259$	0	0
$260$	210.000	0.0500910
$261$	1314.00	0.311627
$262$	−1002.00	−0.236274
$263$	2240.00	0.525188	0.262594	−	0.964906i	$-0.415422\pi$
$263$	2240.00	0.525188	0.262594	+	0.964906i	$0.415422\pi$
$264$	3960.00	0.923186
$265$	−250.000	−0.0579524
$266$	0	0
$267$	−2448.00	−0.561105
$268$	4676.00	1.06579
$269$	4494.00	1.01860	0.509301	−	0.860588i	$-0.329904\pi$
$269$	4494.00	1.01860	0.509301	+	0.860588i	$0.329904\pi$
$270$	540.000	0.121716
$271$	3216.00	0.720879	0.360439	−	0.932783i	$-0.382627\pi$
$271$	3216.00	0.720879	0.360439	+	0.932783i	$0.382627\pi$
$272$	−984.000	−0.219352
$273$	0	0
$274$	−274.000	−0.0604122
$275$	−1100.00	−0.241209
$276$	2184.00	0.476309
$277$	1514.00	0.328402	0.164201	−	0.986427i	$-0.447495\pi$
$277$	1514.00	0.328402	0.164201	+	0.986427i	$0.447495\pi$
$278$	−270.000	−0.0582501
$279$	−2484.00	−0.533022
$280$	0	0
$281$	−5690.00	−1.20796	−0.603980	−	0.796999i	$-0.706419\pi$
$281$	−5690.00	−1.20796	−0.603980	+	0.796999i	$0.706419\pi$
$282$	−3672.00	−0.775406
$283$	−7518.00	−1.57915	−0.789574	−	0.613656i	$-0.789698\pi$
$283$	−7518.00	−1.57915	−0.789574	+	0.613656i	$0.789698\pi$
$284$	2156.00	0.450476
$285$	3420.00	0.710819
$286$	−264.000	−0.0545827
$287$	0	0
$288$	1449.00	0.296469
$289$	−4337.00	−0.882760
$290$	−730.000	−0.147818
$291$	−7200.00	−1.45042
$292$	−84.0000	−0.0168347
$293$	−702.000	−0.139970	−0.0699851	−	0.997548i	$-0.522295\pi$
$293$	−702.000	−0.139970	−0.0699851	+	0.997548i	$0.522295\pi$
$294$	0	0
$295$	−1470.00	−0.290124
$296$	3150.00	0.618547
$297$	4752.00	0.928414
$298$	−530.000	−0.103027
$299$	−312.000	−0.0603459
$300$	−1050.00	−0.202073
$301$	0	0
$302$	−3120.00	−0.594489
$303$	6588.00	1.24908
$304$	−4674.00	−0.881817
$305$	−2250.00	−0.422409
$306$	−216.000	−0.0403526
$307$	−10374.0	−1.92858	−0.964292	−	0.264840i	$-0.914681\pi$
$307$	−10374.0	−1.92858	−0.964292	+	0.264840i	$0.914681\pi$
$308$	0	0
$309$	5832.00	1.07369
$310$	1380.00	0.252835
$311$	−2784.00	−0.507608	−0.253804	−	0.967256i	$-0.581682\pi$
$311$	−2784.00	−0.507608	−0.253804	+	0.967256i	$0.581682\pi$
$312$	−540.000	−0.0979855
$313$	6216.00	1.12252	0.561261	−	0.827639i	$-0.310317\pi$
$313$	6216.00	1.12252	0.561261	+	0.827639i	$0.310317\pi$
$314$	−2106.00	−0.378498
$315$	0	0
$316$	−4172.00	−0.742700
$317$	5066.00	0.897586	0.448793	−	0.893636i	$-0.351854\pi$
$317$	5066.00	0.897586	0.448793	+	0.893636i	$0.351854\pi$
$318$	300.000	0.0529030
$319$	−6424.00	−1.12751
$320$	835.000	0.145868
$321$	9096.00	1.58159
$322$	0	0
$323$	2736.00	0.471316
$324$	6237.00	1.06944
$325$	150.000	0.0256015
$326$	628.000	0.106692
$327$	5580.00	0.943654
$328$	−6660.00	−1.12115
$329$	0	0
$330$	1320.00	0.220193
$331$	−6468.00	−1.07406	−0.537029	−	0.843564i	$-0.680454\pi$
$331$	−6468.00	−1.07406	−0.537029	+	0.843564i	$0.680454\pi$
$332$	6762.00	1.11781
$333$	−1890.00	−0.311025
$334$	1284.00	0.210351
$335$	3340.00	0.544727
$336$	0	0
$337$	−3438.00	−0.555726	−0.277863	−	0.960621i	$-0.589626\pi$
$337$	−3438.00	−0.555726	−0.277863	+	0.960621i	$0.589626\pi$
$338$	−2161.00	−0.347760
$339$	10164.0	1.62842
$340$	−840.000	−0.133986
$341$	12144.0	1.92855
$342$	−1026.00	−0.162221
$343$	0	0
$344$	−7380.00	−1.15669
$345$	1560.00	0.243442
$346$	−906.000	−0.140771
$347$	2212.00	0.342209	0.171104	−	0.985253i	$-0.445266\pi$
$347$	2212.00	0.342209	0.171104	+	0.985253i	$0.445266\pi$
$348$	−6132.00	−0.944568
$349$	2910.00	0.446329	0.223164	−	0.974781i	$-0.428361\pi$
$349$	2910.00	0.446329	0.223164	+	0.974781i	$0.428361\pi$
$350$	0	0
$351$	−648.000	−0.0985404
$352$	−7084.00	−1.07267
$353$	8364.00	1.26111	0.630554	−	0.776146i	$-0.282828\pi$
$353$	8364.00	1.26111	0.630554	+	0.776146i	$0.282828\pi$
$354$	1764.00	0.264846
$355$	1540.00	0.230239
$356$	2856.00	0.425190
$357$	0	0
$358$	−2084.00	−0.307662
$359$	−6712.00	−0.986757	−0.493379	−	0.869815i	$-0.664238\pi$
$359$	−6712.00	−0.986757	−0.493379	+	0.869815i	$0.664238\pi$
$360$	675.000	0.0988212
$361$	6137.00	0.894737
$362$	−4674.00	−0.678619
$363$	3630.00	0.524864
$364$	0	0
$365$	−60.0000	−0.00860423
$366$	2700.00	0.385605
$367$	456.000	0.0648583	0.0324292	−	0.999474i	$-0.489676\pi$
$367$	456.000	0.0648583	0.0324292	+	0.999474i	$0.489676\pi$
$368$	−2132.00	−0.302006
$369$	3996.00	0.563749
$370$	1050.00	0.147532
$371$	0	0
$372$	11592.0	1.61564
$373$	−2558.00	−0.355089	−0.177545	−	0.984113i	$-0.556815\pi$
$373$	−2558.00	−0.355089	−0.177545	+	0.984113i	$0.556815\pi$
$374$	1056.00	0.146001
$375$	−750.000	−0.103280
$376$	9180.00	1.25910
$377$	876.000	0.119672
$378$	0	0
$379$	2004.00	0.271606	0.135803	−	0.990736i	$-0.456639\pi$
$379$	2004.00	0.271606	0.135803	+	0.990736i	$0.456639\pi$
$380$	−3990.00	−0.538639
$381$	5496.00	0.739025
$382$	2012.00	0.269484
$383$	11340.0	1.51292	0.756458	−	0.654042i	$-0.226928\pi$
$383$	11340.0	1.51292	0.756458	+	0.654042i	$0.226928\pi$
$384$	−8730.00	−1.16016
$385$	0	0
$386$	4206.00	0.554611
$387$	4428.00	0.581622
$388$	8400.00	1.09909
$389$	10522.0	1.37143	0.685715	−	0.727870i	$-0.259489\pi$
$389$	10522.0	1.37143	0.685715	+	0.727870i	$0.259489\pi$
$390$	−180.000	−0.0233709
$391$	1248.00	0.161417
$392$	0	0
$393$	−6012.00	−0.771667
$394$	−1574.00	−0.201261
$395$	−2980.00	−0.379595
$396$	2772.00	0.351763
$397$	−2898.00	−0.366364	−0.183182	−	0.983079i	$-0.558640\pi$
$397$	−2898.00	−0.366364	−0.183182	+	0.983079i	$0.558640\pi$
$398$	−2724.00	−0.343070
$399$	0	0
$400$	1025.00	0.128125
$401$	3026.00	0.376836	0.188418	−	0.982089i	$-0.439664\pi$
$401$	3026.00	0.376836	0.188418	+	0.982089i	$0.439664\pi$
$402$	−4008.00	−0.497266
$403$	−1656.00	−0.204693
$404$	−7686.00	−0.946517
$405$	4455.00	0.546594
$406$	0	0
$407$	9240.00	1.12533
$408$	2160.00	0.262098
$409$	−8940.00	−1.08082	−0.540409	−	0.841402i	$-0.681730\pi$
$409$	−8940.00	−1.08082	−0.540409	+	0.841402i	$0.681730\pi$
$410$	−2220.00	−0.267410
$411$	−1644.00	−0.197305
$412$	−6804.00	−0.813614
$413$	0	0
$414$	−468.000	−0.0555578
$415$	4830.00	0.571314
$416$	966.000	0.113851
$417$	−1620.00	−0.190244
$418$	5016.00	0.586939
$419$	2994.00	0.349085	0.174542	−	0.984650i	$-0.444155\pi$
$419$	2994.00	0.349085	0.174542	+	0.984650i	$0.444155\pi$
$420$	0	0
$421$	15766.0	1.82515	0.912575	−	0.408910i	$-0.134091\pi$
$421$	15766.0	1.82515	0.912575	+	0.408910i	$0.134091\pi$
$422$	−180.000	−0.0207637
$423$	−5508.00	−0.633116
$424$	−750.000	−0.0859038
$425$	−600.000	−0.0684806
$426$	−1848.00	−0.210178
$427$	0	0
$428$	−10612.0	−1.19848
$429$	−1584.00	−0.178266
$430$	−2460.00	−0.275888
$431$	14720.0	1.64510	0.822549	−	0.568694i	$-0.192551\pi$
$431$	14720.0	1.64510	0.822549	+	0.568694i	$0.192551\pi$
$432$	−4428.00	−0.493153
$433$	4440.00	0.492778	0.246389	−	0.969171i	$-0.420756\pi$
$433$	4440.00	0.492778	0.246389	+	0.969171i	$0.420756\pi$
$434$	0	0
$435$	−4380.00	−0.482770
$436$	−6510.00	−0.715074
$437$	5928.00	0.648912
$438$	72.0000	0.00785455
$439$	−1488.00	−0.161773	−0.0808865	−	0.996723i	$-0.525775\pi$
$439$	−1488.00	−0.161773	−0.0808865	+	0.996723i	$0.525775\pi$
$440$	−3300.00	−0.357548
$441$	0	0
$442$	−144.000	−0.0154963
$443$	−5828.00	−0.625049	−0.312524	−	0.949910i	$-0.601175\pi$
$443$	−5828.00	−0.625049	−0.312524	+	0.949910i	$0.601175\pi$
$444$	8820.00	0.942745
$445$	2040.00	0.217315
$446$	−4584.00	−0.486679
$447$	−3180.00	−0.336485
$448$	0	0
$449$	−6958.00	−0.731333	−0.365666	−	0.930746i	$-0.619159\pi$
$449$	−6958.00	−0.731333	−0.365666	+	0.930746i	$0.619159\pi$
$450$	225.000	0.0235702
$451$	−19536.0	−2.03972
$452$	−11858.0	−1.23397
$453$	−18720.0	−1.94159
$454$	−1686.00	−0.174291
$455$	0	0
$456$	10260.0	1.05366
$457$	18102.0	1.85290	0.926451	−	0.376416i	$-0.122844\pi$
$457$	18102.0	1.85290	0.926451	+	0.376416i	$0.122844\pi$
$458$	−4026.00	−0.410748
$459$	2592.00	0.263582
$460$	−1820.00	−0.184474
$461$	2574.00	0.260050	0.130025	−	0.991511i	$-0.458494\pi$
$461$	2574.00	0.260050	0.130025	+	0.991511i	$0.458494\pi$
$462$	0	0
$463$	−12832.0	−1.28802	−0.644010	−	0.765017i	$-0.722731\pi$
$463$	−12832.0	−1.28802	−0.644010	+	0.765017i	$0.722731\pi$
$464$	5986.00	0.598907
$465$	8280.00	0.825754
$466$	−6074.00	−0.603804
$467$	7170.00	0.710467	0.355233	−	0.934778i	$-0.384401\pi$
$467$	7170.00	0.710467	0.355233	+	0.934778i	$0.384401\pi$
$468$	−378.000	−0.0373356
$469$	0	0
$470$	3060.00	0.300313
$471$	−12636.0	−1.23617
$472$	−4410.00	−0.430057
$473$	−21648.0	−2.10439
$474$	3576.00	0.346521
$475$	−2850.00	−0.275299
$476$	0	0
$477$	450.000	0.0431951
$478$	3928.00	0.375863
$479$	−10164.0	−0.969530	−0.484765	−	0.874644i	$-0.661095\pi$
$479$	−10164.0	−0.969530	−0.484765	+	0.874644i	$0.661095\pi$
$480$	−4830.00	−0.459288
$481$	−1260.00	−0.119441
$482$	−1236.00	−0.116801
$483$	0	0
$484$	−4235.00	−0.397727
$485$	6000.00	0.561744
$486$	−2430.00	−0.226805
$487$	10212.0	0.950205	0.475103	−	0.879930i	$-0.342411\pi$
$487$	10212.0	0.950205	0.475103	+	0.879930i	$0.342411\pi$
$488$	−6750.00	−0.626144
$489$	3768.00	0.348456
$490$	0	0
$491$	−7972.00	−0.732732	−0.366366	−	0.930471i	$-0.619398\pi$
$491$	−7972.00	−0.732732	−0.366366	+	0.930471i	$0.619398\pi$
$492$	−18648.0	−1.70877
$493$	−3504.00	−0.320106
$494$	−684.000	−0.0622968
$495$	1980.00	0.179787
$496$	−11316.0	−1.02440
$497$	0	0
$498$	−5796.00	−0.521536
$499$	−1548.00	−0.138874	−0.0694369	−	0.997586i	$-0.522120\pi$
$499$	−1548.00	−0.138874	−0.0694369	+	0.997586i	$0.522120\pi$
$500$	875.000	0.0782624
$501$	7704.00	0.687005
$502$	−78.0000	−0.00693488
$503$	1368.00	0.121265	0.0606323	−	0.998160i	$-0.480688\pi$
$503$	1368.00	0.121265	0.0606323	+	0.998160i	$0.480688\pi$
$504$	0	0
$505$	−5490.00	−0.483766
$506$	2288.00	0.201016
$507$	−12966.0	−1.13578
$508$	−6412.00	−0.560013
$509$	−8274.00	−0.720508	−0.360254	−	0.932854i	$-0.617310\pi$
$509$	−8274.00	−0.720508	−0.360254	+	0.932854i	$0.617310\pi$
$510$	720.000	0.0625140
$511$	0	0
$512$	11521.0	0.994455
$513$	12312.0	1.05963
$514$	−3276.00	−0.281125
$515$	−4860.00	−0.415839
$516$	−20664.0	−1.76295
$517$	26928.0	2.29070
$518$	0	0
$519$	−5436.00	−0.459757
$520$	450.000	0.0379496
$521$	20268.0	1.70433	0.852166	−	0.523271i	$-0.175289\pi$
$521$	20268.0	1.70433	0.852166	+	0.523271i	$0.175289\pi$
$522$	1314.00	0.110177
$523$	−1302.00	−0.108858	−0.0544288	−	0.998518i	$-0.517334\pi$
$523$	−1302.00	−0.108858	−0.0544288	+	0.998518i	$0.517334\pi$
$524$	7014.00	0.584748
$525$	0	0
$526$	2240.00	0.185682
$527$	6624.00	0.547526
$528$	−10824.0	−0.892148
$529$	−9463.00	−0.777760
$530$	−250.000	−0.0204893
$531$	2646.00	0.216246
$532$	0	0
$533$	2664.00	0.216493
$534$	−2448.00	−0.198381
$535$	−7580.00	−0.612546
$536$	10020.0	0.807459
$537$	−12504.0	−1.00482
$538$	4494.00	0.360130
$539$	0	0
$540$	−3780.00	−0.301232
$541$	−8314.00	−0.660715	−0.330357	−	0.943856i	$-0.607169\pi$
$541$	−8314.00	−0.660715	−0.330357	+	0.943856i	$0.607169\pi$
$542$	3216.00	0.254869
$543$	−28044.0	−2.21636
$544$	−3864.00	−0.304536
$545$	−4650.00	−0.365475
$546$	0	0
$547$	−9484.00	−0.741328	−0.370664	−	0.928767i	$-0.620870\pi$
$547$	−9484.00	−0.741328	−0.370664	+	0.928767i	$0.620870\pi$
$548$	1918.00	0.149513
$549$	4050.00	0.314845
$550$	−1100.00	−0.0852803
$551$	−16644.0	−1.28686
$552$	4680.00	0.360859
$553$	0	0
$554$	1514.00	0.116108
$555$	6300.00	0.481838
$556$	1890.00	0.144162
$557$	23218.0	1.76621	0.883104	−	0.469177i	$-0.155449\pi$
$557$	23218.0	1.76621	0.883104	+	0.469177i	$0.155449\pi$
$558$	−2484.00	−0.188452
$559$	2952.00	0.223357
$560$	0	0
$561$	6336.00	0.476838
$562$	−5690.00	−0.427079
$563$	5334.00	0.399292	0.199646	−	0.979868i	$-0.436021\pi$
$563$	5334.00	0.399292	0.199646	+	0.979868i	$0.436021\pi$
$564$	25704.0	1.91903
$565$	−8470.00	−0.630682
$566$	−7518.00	−0.558313
$567$	0	0
$568$	4620.00	0.341287
$569$	−182.000	−0.0134092	−0.00670460	−	0.999978i	$-0.502134\pi$
$569$	−182.000	−0.0134092	−0.00670460	+	0.999978i	$0.502134\pi$
$570$	3420.00	0.251312
$571$	14164.0	1.03808	0.519041	−	0.854749i	$-0.326289\pi$
$571$	14164.0	1.03808	0.519041	+	0.854749i	$0.326289\pi$
$572$	1848.00	0.135085
$573$	12072.0	0.880131
$574$	0	0
$575$	−1300.00	−0.0942848
$576$	−1503.00	−0.108724
$577$	−13740.0	−0.991341	−0.495670	−	0.868511i	$-0.665078\pi$
$577$	−13740.0	−0.991341	−0.495670	+	0.868511i	$0.665078\pi$
$578$	−4337.00	−0.312103
$579$	25236.0	1.81135
$580$	5110.00	0.365830
$581$	0	0
$582$	−7200.00	−0.512800
$583$	−2200.00	−0.156286
$584$	−180.000	−0.0127542
$585$	−270.000	−0.0190823
$586$	−702.000	−0.0494870
$587$	9174.00	0.645062	0.322531	−	0.946559i	$-0.395466\pi$
$587$	9174.00	0.645062	0.322531	+	0.946559i	$0.395466\pi$
$588$	0	0
$589$	31464.0	2.20111
$590$	−1470.00	−0.102574
$591$	−9444.00	−0.657317
$592$	−8610.00	−0.597751
$593$	14580.0	1.00966	0.504830	−	0.863219i	$-0.331555\pi$
$593$	14580.0	1.00966	0.504830	+	0.863219i	$0.331555\pi$
$594$	4752.00	0.328244
$595$	0	0
$596$	3710.00	0.254979
$597$	−16344.0	−1.12046
$598$	−312.000	−0.0213355
$599$	1988.00	0.135605	0.0678026	−	0.997699i	$-0.478401\pi$
$599$	1988.00	0.135605	0.0678026	+	0.997699i	$0.478401\pi$
$600$	−2250.00	−0.153093
$601$	−7800.00	−0.529399	−0.264699	−	0.964331i	$-0.585273\pi$
$601$	−7800.00	−0.529399	−0.264699	+	0.964331i	$0.585273\pi$
$602$	0	0
$603$	−6012.00	−0.406016
$604$	21840.0	1.47129
$605$	−3025.00	−0.203279
$606$	6588.00	0.441616
$607$	24288.0	1.62408	0.812042	−	0.583598i	$-0.198356\pi$
$607$	24288.0	1.62408	0.812042	+	0.583598i	$0.198356\pi$
$608$	−18354.0	−1.22426
$609$	0	0
$610$	−2250.00	−0.149344
$611$	−3672.00	−0.243131
$612$	1512.00	0.0998676
$613$	−9866.00	−0.650055	−0.325028	−	0.945704i	$-0.605374\pi$
$613$	−9866.00	−0.650055	−0.325028	+	0.945704i	$0.605374\pi$
$614$	−10374.0	−0.681858
$615$	−13320.0	−0.873356
$616$	0	0
$617$	22858.0	1.49146	0.745728	−	0.666250i	$-0.232102\pi$
$617$	22858.0	1.49146	0.745728	+	0.666250i	$0.232102\pi$
$618$	5832.00	0.379608
$619$	−19074.0	−1.23853	−0.619264	−	0.785183i	$-0.712569\pi$
$619$	−19074.0	−1.23853	−0.619264	+	0.785183i	$0.712569\pi$
$620$	−9660.00	−0.625734
$621$	5616.00	0.362902
$622$	−2784.00	−0.179467
$623$	0	0
$624$	1476.00	0.0946912
$625$	625.000	0.0400000
$626$	6216.00	0.396871
$627$	30096.0	1.91694
$628$	14742.0	0.936735
$629$	5040.00	0.319488
$630$	0	0
$631$	22084.0	1.39326	0.696632	−	0.717428i	$-0.254681\pi$
$631$	22084.0	1.39326	0.696632	+	0.717428i	$0.254681\pi$
$632$	−8940.00	−0.562681
$633$	−1080.00	−0.0678138
$634$	5066.00	0.317345
$635$	−4580.00	−0.286223
$636$	−2100.00	−0.130928
$637$	0	0
$638$	−6424.00	−0.398634
$639$	−2772.00	−0.171610
$640$	7275.00	0.449328
$641$	−16622.0	−1.02423	−0.512114	−	0.858918i	$-0.671137\pi$
$641$	−16622.0	−1.02423	−0.512114	+	0.858918i	$0.671137\pi$
$642$	9096.00	0.559175
$643$	−12906.0	−0.791544	−0.395772	−	0.918349i	$-0.629523\pi$
$643$	−12906.0	−0.791544	−0.395772	+	0.918349i	$0.629523\pi$
$644$	0	0
$645$	−14760.0	−0.901046
$646$	2736.00	0.166635
$647$	3156.00	0.191770	0.0958850	−	0.995392i	$-0.469432\pi$
$647$	3156.00	0.191770	0.0958850	+	0.995392i	$0.469432\pi$
$648$	13365.0	0.810227
$649$	−12936.0	−0.782407
$650$	150.000	0.00905151
$651$	0	0
$652$	−4396.00	−0.264050
$653$	−3658.00	−0.219217	−0.109608	−	0.993975i	$-0.534960\pi$
$653$	−3658.00	−0.219217	−0.109608	+	0.993975i	$0.534960\pi$
$654$	5580.00	0.333632
$655$	5010.00	0.298865
$656$	18204.0	1.08346
$657$	108.000	0.00641321
$658$	0	0
$659$	−12316.0	−0.728017	−0.364009	−	0.931396i	$-0.618592\pi$
$659$	−12316.0	−0.728017	−0.364009	+	0.931396i	$0.618592\pi$
$660$	−9240.00	−0.544949
$661$	32298.0	1.90052	0.950262	−	0.311451i	$-0.100815\pi$
$661$	32298.0	1.90052	0.950262	+	0.311451i	$0.100815\pi$
$662$	−6468.00	−0.379737
$663$	−864.000	−0.0506108
$664$	14490.0	0.846869
$665$	0	0
$666$	−1890.00	−0.109964
$667$	−7592.00	−0.440725
$668$	−8988.00	−0.520593
$669$	−27504.0	−1.58949
$670$	3340.00	0.192590
$671$	−19800.0	−1.13915
$672$	0	0
$673$	−23274.0	−1.33306	−0.666528	−	0.745480i	$-0.732220\pi$
$673$	−23274.0	−1.33306	−0.666528	+	0.745480i	$0.732220\pi$
$674$	−3438.00	−0.196479
$675$	−2700.00	−0.153960
$676$	15127.0	0.860662
$677$	4518.00	0.256486	0.128243	−	0.991743i	$-0.459066\pi$
$677$	4518.00	0.256486	0.128243	+	0.991743i	$0.459066\pi$
$678$	10164.0	0.575732
$679$	0	0
$680$	−1800.00	−0.101510
$681$	−10116.0	−0.569230
$682$	12144.0	0.681844
$683$	−19636.0	−1.10007	−0.550037	−	0.835140i	$-0.685386\pi$
$683$	−19636.0	−1.10007	−0.550037	+	0.835140i	$0.685386\pi$
$684$	7182.00	0.401478
$685$	1370.00	0.0764161
$686$	0	0
$687$	−24156.0	−1.34150
$688$	20172.0	1.11781
$689$	300.000	0.0165879
$690$	1560.00	0.0860698
$691$	−17226.0	−0.948347	−0.474174	−	0.880431i	$-0.657253\pi$
$691$	−17226.0	−0.948347	−0.474174	+	0.880431i	$0.657253\pi$
$692$	6342.00	0.348391
$693$	0	0
$694$	2212.00	0.120989
$695$	1350.00	0.0736812
$696$	−13140.0	−0.715618
$697$	−10656.0	−0.579089
$698$	2910.00	0.157801
$699$	−36444.0	−1.97202
$700$	0	0
$701$	21362.0	1.15097	0.575486	−	0.817812i	$-0.304813\pi$
$701$	21362.0	1.15097	0.575486	+	0.817812i	$0.304813\pi$
$702$	−648.000	−0.0348393
$703$	23940.0	1.28437
$704$	7348.00	0.393378
$705$	18360.0	0.980819
$706$	8364.00	0.445869
$707$	0	0
$708$	−12348.0	−0.655461
$709$	8658.00	0.458615	0.229307	−	0.973354i	$-0.426354\pi$
$709$	8658.00	0.458615	0.229307	+	0.973354i	$0.426354\pi$
$710$	1540.00	0.0814016
$711$	5364.00	0.282933
$712$	6120.00	0.322130
$713$	14352.0	0.753838
$714$	0	0
$715$	1320.00	0.0690422
$716$	14588.0	0.761423
$717$	23568.0	1.22756
$718$	−6712.00	−0.348871
$719$	29484.0	1.52930	0.764651	−	0.644445i	$-0.222912\pi$
$719$	29484.0	1.52930	0.764651	+	0.644445i	$0.222912\pi$
$720$	−1845.00	−0.0954987
$721$	0	0
$722$	6137.00	0.316337
$723$	−7416.00	−0.381472
$724$	32718.0	1.67950
$725$	3650.00	0.186976
$726$	3630.00	0.185567
$727$	−28260.0	−1.44169	−0.720843	−	0.693099i	$-0.756245\pi$
$727$	−28260.0	−1.44169	−0.720843	+	0.693099i	$0.756245\pi$
$728$	0	0
$729$	9477.00	0.481481
$730$	−60.0000	−0.00304205
$731$	−11808.0	−0.597448
$732$	−18900.0	−0.954323
$733$	−10950.0	−0.551770	−0.275885	−	0.961191i	$-0.588971\pi$
$733$	−10950.0	−0.551770	−0.275885	+	0.961191i	$0.588971\pi$
$734$	456.000	0.0229309
$735$	0	0
$736$	−8372.00	−0.419288
$737$	29392.0	1.46902
$738$	3996.00	0.199315
$739$	−9772.00	−0.486426	−0.243213	−	0.969973i	$-0.578201\pi$
$739$	−9772.00	−0.486426	−0.243213	+	0.969973i	$0.578201\pi$
$740$	−7350.00	−0.365123
$741$	−4104.00	−0.203460
$742$	0	0
$743$	7844.00	0.387306	0.193653	−	0.981070i	$-0.437966\pi$
$743$	7844.00	0.387306	0.193653	+	0.981070i	$0.437966\pi$
$744$	24840.0	1.22403
$745$	2650.00	0.130320
$746$	−2558.00	−0.125543
$747$	−8694.00	−0.425832
$748$	−7392.00	−0.361335
$749$	0	0
$750$	−750.000	−0.0365148
$751$	1800.00	0.0874606	0.0437303	−	0.999043i	$-0.486076\pi$
$751$	1800.00	0.0874606	0.0437303	+	0.999043i	$0.486076\pi$
$752$	−25092.0	−1.21677
$753$	−468.000	−0.0226492
$754$	876.000	0.0423104
$755$	15600.0	0.751976
$756$	0	0
$757$	−11274.0	−0.541295	−0.270648	−	0.962678i	$-0.587238\pi$
$757$	−11274.0	−0.541295	−0.270648	+	0.962678i	$0.587238\pi$
$758$	2004.00	0.0960271
$759$	13728.0	0.656515
$760$	−8550.00	−0.408080
$761$	22668.0	1.07978	0.539891	−	0.841735i	$-0.318465\pi$
$761$	22668.0	1.07978	0.539891	+	0.841735i	$0.318465\pi$
$762$	5496.00	0.261285
$763$	0	0
$764$	−14084.0	−0.666939
$765$	1080.00	0.0510425
$766$	11340.0	0.534897
$767$	1764.00	0.0830435
$768$	−714.000	−0.0335472
$769$	−15468.0	−0.725345	−0.362673	−	0.931917i	$-0.618136\pi$
$769$	−15468.0	−0.725345	−0.362673	+	0.931917i	$0.618136\pi$
$770$	0	0
$771$	−19656.0	−0.918150
$772$	−29442.0	−1.37259
$773$	28986.0	1.34871	0.674356	−	0.738407i	$-0.264421\pi$
$773$	28986.0	1.34871	0.674356	+	0.738407i	$0.264421\pi$
$774$	4428.00	0.205635
$775$	−6900.00	−0.319813
$776$	18000.0	0.832683
$777$	0	0
$778$	10522.0	0.484874
$779$	−50616.0	−2.32799
$780$	1260.00	0.0578400
$781$	13552.0	0.620907
$782$	1248.00	0.0570696
$783$	−15768.0	−0.719671
$784$	0	0
$785$	10530.0	0.478767
$786$	−6012.00	−0.272826
$787$	20562.0	0.931329	0.465665	−	0.884961i	$-0.345815\pi$
$787$	20562.0	0.931329	0.465665	+	0.884961i	$0.345815\pi$
$788$	11018.0	0.498096
$789$	13440.0	0.606434
$790$	−2980.00	−0.134207
$791$	0	0
$792$	5940.00	0.266501
$793$	2700.00	0.120908
$794$	−2898.00	−0.129529
$795$	−1500.00	−0.0669176
$796$	19068.0	0.849054
$797$	−20826.0	−0.925589	−0.462795	−	0.886465i	$-0.653153\pi$
$797$	−20826.0	−0.925589	−0.462795	+	0.886465i	$0.653153\pi$
$798$	0	0
$799$	14688.0	0.650343
$800$	4025.00	0.177882
$801$	−3672.00	−0.161977
$802$	3026.00	0.133232
$803$	−528.000	−0.0232039
$804$	28056.0	1.23067
$805$	0	0
$806$	−1656.00	−0.0723699
$807$	26964.0	1.17618
$808$	−16470.0	−0.717095
$809$	−4250.00	−0.184700	−0.0923498	−	0.995727i	$-0.529438\pi$
$809$	−4250.00	−0.184700	−0.0923498	+	0.995727i	$0.529438\pi$
$810$	4455.00	0.193250
$811$	24342.0	1.05396	0.526981	−	0.849877i	$-0.323324\pi$
$811$	24342.0	1.05396	0.526981	+	0.849877i	$0.323324\pi$
$812$	0	0
$813$	19296.0	0.832399
$814$	9240.00	0.397865
$815$	−3140.00	−0.134956
$816$	−5904.00	−0.253286
$817$	−56088.0	−2.40180
$818$	−8940.00	−0.382127
$819$	0	0
$820$	15540.0	0.661805
$821$	−2138.00	−0.0908852	−0.0454426	−	0.998967i	$-0.514470\pi$
$821$	−2138.00	−0.0908852	−0.0454426	+	0.998967i	$0.514470\pi$
$822$	−1644.00	−0.0697580
$823$	9560.00	0.404910	0.202455	−	0.979292i	$-0.435108\pi$
$823$	9560.00	0.404910	0.202455	+	0.979292i	$0.435108\pi$
$824$	−14580.0	−0.616406
$825$	−6600.00	−0.278524
$826$	0	0
$827$	7748.00	0.325785	0.162893	−	0.986644i	$-0.447918\pi$
$827$	7748.00	0.325785	0.162893	+	0.986644i	$0.447918\pi$
$828$	3276.00	0.137499
$829$	−5334.00	−0.223471	−0.111736	−	0.993738i	$-0.535641\pi$
$829$	−5334.00	−0.223471	−0.111736	+	0.993738i	$0.535641\pi$
$830$	4830.00	0.201990
$831$	9084.00	0.379206
$832$	−1002.00	−0.0417525
$833$	0	0
$834$	−1620.00	−0.0672614
$835$	−6420.00	−0.266076
$836$	−35112.0	−1.45260
$837$	29808.0	1.23096
$838$	2994.00	0.123420
$839$	−36444.0	−1.49963	−0.749813	−	0.661650i	$-0.769857\pi$
$839$	−36444.0	−1.49963	−0.749813	+	0.661650i	$0.769857\pi$
$840$	0	0
$841$	−3073.00	−0.125999
$842$	15766.0	0.645288
$843$	−34140.0	−1.39483
$844$	1260.00	0.0513874
$845$	10805.0	0.439886
$846$	−5508.00	−0.223840
$847$	0	0
$848$	2050.00	0.0830157
$849$	−45108.0	−1.82344
$850$	−600.000	−0.0242116
$851$	10920.0	0.439874
$852$	12936.0	0.520164
$853$	21030.0	0.844142	0.422071	−	0.906563i	$-0.361303\pi$
$853$	21030.0	0.844142	0.422071	+	0.906563i	$0.361303\pi$
$854$	0	0
$855$	5130.00	0.205196
$856$	−22740.0	−0.907987
$857$	−32328.0	−1.28857	−0.644284	−	0.764786i	$-0.722845\pi$
$857$	−32328.0	−1.28857	−0.644284	+	0.764786i	$0.722845\pi$
$858$	−1584.00	−0.0630267
$859$	−43518.0	−1.72854	−0.864269	−	0.503029i	$-0.832219\pi$
$859$	−43518.0	−1.72854	−0.864269	+	0.503029i	$0.832219\pi$
$860$	17220.0	0.682787
$861$	0	0
$862$	14720.0	0.581630
$863$	−5032.00	−0.198484	−0.0992418	−	0.995063i	$-0.531642\pi$
$863$	−5032.00	−0.198484	−0.0992418	+	0.995063i	$0.531642\pi$
$864$	−17388.0	−0.684666
$865$	4530.00	0.178063
$866$	4440.00	0.174223
$867$	−26022.0	−1.01932
$868$	0	0
$869$	−26224.0	−1.02369
$870$	−4380.00	−0.170685
$871$	−4008.00	−0.155920
$872$	−13950.0	−0.541751
$873$	−10800.0	−0.418699
$874$	5928.00	0.229425
$875$	0	0
$876$	−504.000	−0.0194390
$877$	4286.00	0.165026	0.0825131	−	0.996590i	$-0.473705\pi$
$877$	4286.00	0.165026	0.0825131	+	0.996590i	$0.473705\pi$
$878$	−1488.00	−0.0571954
$879$	−4212.00	−0.161624
$880$	9020.00	0.345527
$881$	19080.0	0.729650	0.364825	−	0.931076i	$-0.381129\pi$
$881$	19080.0	0.729650	0.364825	+	0.931076i	$0.381129\pi$
$882$	0	0
$883$	26580.0	1.01301	0.506505	−	0.862237i	$-0.330937\pi$
$883$	26580.0	1.01301	0.506505	+	0.862237i	$0.330937\pi$
$884$	1008.00	0.0383515
$885$	−8820.00	−0.335007
$886$	−5828.00	−0.220988
$887$	12588.0	0.476509	0.238255	−	0.971203i	$-0.423425\pi$
$887$	12588.0	0.476509	0.238255	+	0.971203i	$0.423425\pi$
$888$	18900.0	0.714237
$889$	0	0
$890$	2040.00	0.0768325
$891$	39204.0	1.47406
$892$	32088.0	1.20447
$893$	69768.0	2.61444
$894$	−3180.00	−0.118965
$895$	10420.0	0.389164
$896$	0	0
$897$	−1872.00	−0.0696815
$898$	−6958.00	−0.258565
$899$	−40296.0	−1.49494
$900$	−1575.00	−0.0583333
$901$	−1200.00	−0.0443705
$902$	−19536.0	−0.721150
$903$	0	0
$904$	−25410.0	−0.934872
$905$	23370.0	0.858392
$906$	−18720.0	−0.686457
$907$	−19332.0	−0.707727	−0.353864	−	0.935297i	$-0.615132\pi$
$907$	−19332.0	−0.707727	−0.353864	+	0.935297i	$0.615132\pi$
$908$	11802.0	0.431347
$909$	9882.00	0.360578
$910$	0	0
$911$	−43640.0	−1.58711	−0.793555	−	0.608498i	$-0.791772\pi$
$911$	−43640.0	−1.58711	−0.793555	+	0.608498i	$0.791772\pi$
$912$	−28044.0	−1.01823
$913$	42504.0	1.54072
$914$	18102.0	0.655099
$915$	−13500.0	−0.487755
$916$	28182.0	1.01655
$917$	0	0
$918$	2592.00	0.0931904
$919$	9084.00	0.326065	0.163032	−	0.986621i	$-0.447872\pi$
$919$	9084.00	0.326065	0.163032	+	0.986621i	$0.447872\pi$
$920$	−3900.00	−0.139760
$921$	−62244.0	−2.22694
$922$	2574.00	0.0919416
$923$	−1848.00	−0.0659021
$924$	0	0
$925$	−5250.00	−0.186615
$926$	−12832.0	−0.455384
$927$	8748.00	0.309948
$928$	23506.0	0.831489
$929$	−48228.0	−1.70324	−0.851620	−	0.524160i	$-0.824379\pi$
$929$	−48228.0	−1.70324	−0.851620	+	0.524160i	$0.824379\pi$
$930$	8280.00	0.291948
$931$	0	0
$932$	42518.0	1.49434
$933$	−16704.0	−0.586135
$934$	7170.00	0.251188
$935$	−5280.00	−0.184679
$936$	−810.000	−0.0282860
$937$	39204.0	1.36685	0.683425	−	0.730021i	$-0.260490\pi$
$937$	39204.0	1.36685	0.683425	+	0.730021i	$0.260490\pi$
$938$	0	0
$939$	37296.0	1.29618
$940$	−21420.0	−0.743238
$941$	4770.00	0.165247	0.0826236	−	0.996581i	$-0.473670\pi$
$941$	4770.00	0.165247	0.0826236	+	0.996581i	$0.473670\pi$
$942$	−12636.0	−0.437052
$943$	−23088.0	−0.797295
$944$	12054.0	0.415598
$945$	0	0
$946$	−21648.0	−0.744014
$947$	56236.0	1.92970	0.964849	−	0.262804i	$-0.0846473\pi$
$947$	56236.0	1.92970	0.964849	+	0.262804i	$0.0846473\pi$
$948$	−25032.0	−0.857597
$949$	72.0000	0.00246282
$950$	−2850.00	−0.0973329
$951$	30396.0	1.03644
$952$	0	0
$953$	−52814.0	−1.79519	−0.897594	−	0.440824i	$-0.854686\pi$
$953$	−52814.0	−1.79519	−0.897594	+	0.440824i	$0.854686\pi$
$954$	450.000	0.0152718
$955$	−10060.0	−0.340873
$956$	−27496.0	−0.930214
$957$	−38544.0	−1.30193
$958$	−10164.0	−0.342781
$959$	0	0
$960$	5010.00	0.168434
$961$	46385.0	1.55701
$962$	−1260.00	−0.0422287
$963$	13644.0	0.456565
$964$	8652.00	0.289069
$965$	−21030.0	−0.701533
$966$	0	0
$967$	−39364.0	−1.30906	−0.654530	−	0.756036i	$-0.727133\pi$
$967$	−39364.0	−1.30906	−0.654530	+	0.756036i	$0.727133\pi$
$968$	−9075.00	−0.301324
$969$	16416.0	0.544229
$970$	6000.00	0.198607
$971$	−29322.0	−0.969091	−0.484546	−	0.874766i	$-0.661015\pi$
$971$	−29322.0	−0.969091	−0.484546	+	0.874766i	$0.661015\pi$
$972$	17010.0	0.561313
$973$	0	0
$974$	10212.0	0.335948
$975$	900.000	0.0295621
$976$	18450.0	0.605092
$977$	−35882.0	−1.17499	−0.587496	−	0.809227i	$-0.699886\pi$
$977$	−35882.0	−1.17499	−0.587496	+	0.809227i	$0.699886\pi$
$978$	3768.00	0.123198
$979$	17952.0	0.586056
$980$	0	0
$981$	8370.00	0.272409
$982$	−7972.00	−0.259060
$983$	−32580.0	−1.05711	−0.528556	−	0.848899i	$-0.677266\pi$
$983$	−32580.0	−1.05711	−0.528556	+	0.848899i	$0.677266\pi$
$984$	−39960.0	−1.29459
$985$	7870.00	0.254578
$986$	−3504.00	−0.113175
$987$	0	0
$988$	4788.00	0.154177
$989$	−25584.0	−0.822572
$990$	1980.00	0.0635642
$991$	−30036.0	−0.962790	−0.481395	−	0.876504i	$-0.659870\pi$
$991$	−30036.0	−0.962790	−0.481395	+	0.876504i	$0.659870\pi$
$992$	−44436.0	−1.42222
$993$	−38808.0	−1.24022
$994$	0	0
$995$	13620.0	0.433953
$996$	40572.0	1.29074
$997$	−25134.0	−0.798397	−0.399198	−	0.916865i	$-0.630712\pi$
$997$	−25134.0	−0.798397	−0.399198	+	0.916865i	$0.630712\pi$
$998$	−1548.00	−0.0490993
$999$	22680.0	0.718282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.c.1.1	yes	1
3.2	odd	2		2205.4.a.n.1.1		1
5.4	even	2		1225.4.a.f.1.1		1
7.2	even	3		245.4.e.c.116.1		2
7.3	odd	6		245.4.e.d.226.1		2
7.4	even	3		245.4.e.c.226.1		2
7.5	odd	6		245.4.e.d.116.1		2
7.6	odd	2		245.4.a.b.1.1	✓	1
21.20	even	2		2205.4.a.k.1.1		1
35.34	odd	2		1225.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.a.b.1.1	✓	1	7.6	odd	2
245.4.a.c.1.1	yes	1	1.1	even	1	trivial
245.4.e.c.116.1		2	7.2	even	3
245.4.e.c.226.1		2	7.4	even	3
245.4.e.d.116.1		2	7.5	odd	6
245.4.e.d.226.1		2	7.3	odd	6
1225.4.a.f.1.1		1	5.4	even	2
1225.4.a.g.1.1		1	35.34	odd	2
2205.4.a.k.1.1		1	21.20	even	2
2205.4.a.n.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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