LMFDB - Embedded newform 2450.4.a.bn.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, 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("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2450.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:	$144.554679514$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} +14.0000 q^{6} +8.00000 q^{8} +22.0000 q^{9} -37.0000 q^{11} +28.0000 q^{12} -51.0000 q^{13} +16.0000 q^{16} -41.0000 q^{17} +44.0000 q^{18} +108.000 q^{19} -74.0000 q^{22} -70.0000 q^{23} +56.0000 q^{24} -102.000 q^{26} -35.0000 q^{27} -249.000 q^{29} +134.000 q^{31} +32.0000 q^{32} -259.000 q^{33} -82.0000 q^{34} +88.0000 q^{36} -334.000 q^{37} +216.000 q^{38} -357.000 q^{39} -206.000 q^{41} -376.000 q^{43} -148.000 q^{44} -140.000 q^{46} +287.000 q^{47} +112.000 q^{48} -287.000 q^{51} -204.000 q^{52} -6.00000 q^{53} -70.0000 q^{54} +756.000 q^{57} -498.000 q^{58} +2.00000 q^{59} +940.000 q^{61} +268.000 q^{62} +64.0000 q^{64} -518.000 q^{66} +106.000 q^{67} -164.000 q^{68} -490.000 q^{69} +456.000 q^{71} +176.000 q^{72} -650.000 q^{73} -668.000 q^{74} +432.000 q^{76} -714.000 q^{78} -1239.00 q^{79} -839.000 q^{81} -412.000 q^{82} -428.000 q^{83} -752.000 q^{86} -1743.00 q^{87} -296.000 q^{88} +220.000 q^{89} -280.000 q^{92} +938.000 q^{93} +574.000 q^{94} +224.000 q^{96} +1055.00 q^{97} -814.000 q^{99} +O(q^{100})\)

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	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	14.0000	0.952579
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	22.0000	0.814815
$10$	0	0
$11$	−37.0000	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$11$	−37.0000	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$12$	28.0000	0.673575
$13$	−51.0000	−1.08807	−0.544033	−	0.839064i	$-0.683103\pi$
$13$	−51.0000	−1.08807	−0.544033	+	0.839064i	$0.683103\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	0.250000
$17$	−41.0000	−0.584939	−0.292469	−	0.956275i	$-0.594477\pi$
$17$	−41.0000	−0.584939	−0.292469	+	0.956275i	$0.594477\pi$
$18$	44.0000	0.576161
$19$	108.000	1.30405	0.652024	−	0.758199i	$-0.273920\pi$
$19$	108.000	1.30405	0.652024	+	0.758199i	$0.273920\pi$
$20$	0	0
$21$	0	0
$22$	−74.0000	−0.717130
$23$	−70.0000	−0.634609	−0.317305	−	0.948324i	$-0.602778\pi$
$23$	−70.0000	−0.634609	−0.317305	+	0.948324i	$0.602778\pi$
$24$	56.0000	0.476290
$25$	0	0
$26$	−102.000	−0.769379
$27$	−35.0000	−0.249472
$28$	0	0
$29$	−249.000	−1.59442	−0.797209	−	0.603703i	$-0.793691\pi$
$29$	−249.000	−1.59442	−0.797209	+	0.603703i	$0.793691\pi$
$30$	0	0
$31$	134.000	0.776358	0.388179	−	0.921584i	$-0.373104\pi$
$31$	134.000	0.776358	0.388179	+	0.921584i	$0.373104\pi$
$32$	32.0000	0.176777
$33$	−259.000	−1.36625
$34$	−82.0000	−0.413614
$35$	0	0
$36$	88.0000	0.407407
$37$	−334.000	−1.48403	−0.742017	−	0.670381i	$-0.766131\pi$
$37$	−334.000	−1.48403	−0.742017	+	0.670381i	$0.766131\pi$
$38$	216.000	0.922101
$39$	−357.000	−1.46579
$40$	0	0
$41$	−206.000	−0.784678	−0.392339	−	0.919821i	$-0.628334\pi$
$41$	−206.000	−0.784678	−0.392339	+	0.919821i	$0.628334\pi$
$42$	0	0
$43$	−376.000	−1.33348	−0.666738	−	0.745292i	$-0.732310\pi$
$43$	−376.000	−1.33348	−0.666738	+	0.745292i	$0.732310\pi$
$44$	−148.000	−0.507087
$45$	0	0
$46$	−140.000	−0.448736
$47$	287.000	0.890708	0.445354	−	0.895355i	$-0.353078\pi$
$47$	287.000	0.890708	0.445354	+	0.895355i	$0.353078\pi$
$48$	112.000	0.336788
$49$	0	0
$50$	0	0
$51$	−287.000	−0.788001
$52$	−204.000	−0.544033
$53$	−6.00000	−0.0155503	−0.00777513	−	0.999970i	$-0.502475\pi$
$53$	−6.00000	−0.0155503	−0.00777513	+	0.999970i	$0.502475\pi$
$54$	−70.0000	−0.176404
$55$	0	0
$56$	0	0
$57$	756.000	1.75675
$58$	−498.000	−1.12742
$59$	2.00000	0.00441318	0.00220659	−	0.999998i	$-0.499298\pi$
$59$	2.00000	0.00441318	0.00220659	+	0.999998i	$0.499298\pi$
$60$	0	0
$61$	940.000	1.97303	0.986514	−	0.163679i	$-0.0523361\pi$
$61$	940.000	1.97303	0.986514	+	0.163679i	$0.0523361\pi$
$62$	268.000	0.548968
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	−518.000	−0.966082
$67$	106.000	0.193283	0.0966415	−	0.995319i	$-0.469190\pi$
$67$	106.000	0.193283	0.0966415	+	0.995319i	$0.469190\pi$
$68$	−164.000	−0.292469
$69$	−490.000	−0.854914
$70$	0	0
$71$	456.000	0.762215	0.381107	−	0.924531i	$-0.375543\pi$
$71$	456.000	0.762215	0.381107	+	0.924531i	$0.375543\pi$
$72$	176.000	0.288081
$73$	−650.000	−1.04215	−0.521074	−	0.853512i	$-0.674468\pi$
$73$	−650.000	−1.04215	−0.521074	+	0.853512i	$0.674468\pi$
$74$	−668.000	−1.04937
$75$	0	0
$76$	432.000	0.652024
$77$	0	0
$78$	−714.000	−1.03647
$79$	−1239.00	−1.76454	−0.882268	−	0.470747i	$-0.843984\pi$
$79$	−1239.00	−1.76454	−0.882268	+	0.470747i	$0.843984\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	−412.000	−0.554851
$83$	−428.000	−0.566013	−0.283007	−	0.959118i	$-0.591332\pi$
$83$	−428.000	−0.566013	−0.283007	+	0.959118i	$0.591332\pi$
$84$	0	0
$85$	0	0
$86$	−752.000	−0.942910
$87$	−1743.00	−2.14792
$88$	−296.000	−0.358565
$89$	220.000	0.262022	0.131011	−	0.991381i	$-0.458178\pi$
$89$	220.000	0.262022	0.131011	+	0.991381i	$0.458178\pi$
$90$	0	0
$91$	0	0
$92$	−280.000	−0.317305
$93$	938.000	1.04587
$94$	574.000	0.629825
$95$	0	0
$96$	224.000	0.238145
$97$	1055.00	1.10432	0.552160	−	0.833738i	$-0.313804\pi$
$97$	1055.00	1.10432	0.552160	+	0.833738i	$0.313804\pi$
$98$	0	0
$99$	−814.000	−0.826364
$100$	0	0
$101$	−1960.00	−1.93096	−0.965482	−	0.260471i	$-0.916122\pi$
$101$	−1960.00	−1.93096	−0.965482	+	0.260471i	$0.916122\pi$
$102$	−574.000	−0.557201
$103$	−1825.00	−1.74585	−0.872925	−	0.487854i	$-0.837780\pi$
$103$	−1825.00	−1.74585	−0.872925	+	0.487854i	$0.837780\pi$
$104$	−408.000	−0.384689
$105$	0	0
$106$	−12.0000	−0.0109957
$107$	−144.000	−0.130103	−0.0650514	−	0.997882i	$-0.520721\pi$
$107$	−144.000	−0.130103	−0.0650514	+	0.997882i	$0.520721\pi$
$108$	−140.000	−0.124736
$109$	1681.00	1.47716	0.738581	−	0.674165i	$-0.235496\pi$
$109$	1681.00	1.47716	0.738581	+	0.674165i	$0.235496\pi$
$110$	0	0
$111$	−2338.00	−1.99922
$112$	0	0
$113$	798.000	0.664332	0.332166	−	0.943221i	$-0.392221\pi$
$113$	798.000	0.664332	0.332166	+	0.943221i	$0.392221\pi$
$114$	1512.00	1.24221
$115$	0	0
$116$	−996.000	−0.797209
$117$	−1122.00	−0.886572
$118$	4.00000	0.00312059
$119$	0	0
$120$	0	0
$121$	38.0000	0.0285500
$122$	1880.00	1.39514
$123$	−1442.00	−1.05708
$124$	536.000	0.388179
$125$	0	0
$126$	0	0
$127$	434.000	0.303238	0.151619	−	0.988439i	$-0.451551\pi$
$127$	434.000	0.303238	0.151619	+	0.988439i	$0.451551\pi$
$128$	128.000	0.0883883
$129$	−2632.00	−1.79639
$130$	0	0
$131$	1290.00	0.860365	0.430183	−	0.902742i	$-0.358449\pi$
$131$	1290.00	0.860365	0.430183	+	0.902742i	$0.358449\pi$
$132$	−1036.00	−0.683123
$133$	0	0
$134$	212.000	0.136672
$135$	0	0
$136$	−328.000	−0.206807
$137$	192.000	0.119735	0.0598674	−	0.998206i	$-0.480932\pi$
$137$	192.000	0.119735	0.0598674	+	0.998206i	$0.480932\pi$
$138$	−980.000	−0.604516
$139$	−1402.00	−0.855511	−0.427756	−	0.903894i	$-0.640696\pi$
$139$	−1402.00	−0.855511	−0.427756	+	0.903894i	$0.640696\pi$
$140$	0	0
$141$	2009.00	1.19992
$142$	912.000	0.538967
$143$	1887.00	1.10349
$144$	352.000	0.203704
$145$	0	0
$146$	−1300.00	−0.736909
$147$	0	0
$148$	−1336.00	−0.742017
$149$	−302.000	−0.166046	−0.0830228	−	0.996548i	$-0.526457\pi$
$149$	−302.000	−0.166046	−0.0830228	+	0.996548i	$0.526457\pi$
$150$	0	0
$151$	−3167.00	−1.70680	−0.853400	−	0.521257i	$-0.825463\pi$
$151$	−3167.00	−1.70680	−0.853400	+	0.521257i	$0.825463\pi$
$152$	864.000	0.461050
$153$	−902.000	−0.476617
$154$	0	0
$155$	0	0
$156$	−1428.00	−0.732894
$157$	470.000	0.238918	0.119459	−	0.992839i	$-0.461884\pi$
$157$	470.000	0.238918	0.119459	+	0.992839i	$0.461884\pi$
$158$	−2478.00	−1.24772
$159$	−42.0000	−0.0209485
$160$	0	0
$161$	0	0
$162$	−1678.00	−0.813803
$163$	−2390.00	−1.14846	−0.574231	−	0.818693i	$-0.694699\pi$
$163$	−2390.00	−1.14846	−0.574231	+	0.818693i	$0.694699\pi$
$164$	−824.000	−0.392339
$165$	0	0
$166$	−856.000	−0.400232
$167$	2631.00	1.21912	0.609560	−	0.792740i	$-0.291346\pi$
$167$	2631.00	1.21912	0.609560	+	0.792740i	$0.291346\pi$
$168$	0	0
$169$	404.000	0.183887
$170$	0	0
$171$	2376.00	1.06256
$172$	−1504.00	−0.666738
$173$	2243.00	0.985735	0.492867	−	0.870104i	$-0.335949\pi$
$173$	2243.00	0.985735	0.492867	+	0.870104i	$0.335949\pi$
$174$	−3486.00	−1.51881
$175$	0	0
$176$	−592.000	−0.253544
$177$	14.0000	0.00594522
$178$	440.000	0.185277
$179$	52.0000	0.0217132	0.0108566	−	0.999941i	$-0.496544\pi$
$179$	52.0000	0.0217132	0.0108566	+	0.999941i	$0.496544\pi$
$180$	0	0
$181$	−2462.00	−1.01104	−0.505522	−	0.862814i	$-0.668700\pi$
$181$	−2462.00	−1.01104	−0.505522	+	0.862814i	$0.668700\pi$
$182$	0	0
$183$	6580.00	2.65797
$184$	−560.000	−0.224368
$185$	0	0
$186$	1876.00	0.739543
$187$	1517.00	0.593230
$188$	1148.00	0.445354
$189$	0	0
$190$	0	0
$191$	3159.00	1.19674	0.598370	−	0.801220i	$-0.295815\pi$
$191$	3159.00	1.19674	0.598370	+	0.801220i	$0.295815\pi$
$192$	448.000	0.168394
$193$	2060.00	0.768301	0.384150	−	0.923271i	$-0.374494\pi$
$193$	2060.00	0.768301	0.384150	+	0.923271i	$0.374494\pi$
$194$	2110.00	0.780872
$195$	0	0
$196$	0	0
$197$	1738.00	0.628565	0.314283	−	0.949329i	$-0.398236\pi$
$197$	1738.00	0.628565	0.314283	+	0.949329i	$0.398236\pi$
$198$	−1628.00	−0.584328
$199$	894.000	0.318462	0.159231	−	0.987241i	$-0.449099\pi$
$199$	894.000	0.318462	0.159231	+	0.987241i	$0.449099\pi$
$200$	0	0
$201$	742.000	0.260381
$202$	−3920.00	−1.36540
$203$	0	0
$204$	−1148.00	−0.394000
$205$	0	0
$206$	−3650.00	−1.23450
$207$	−1540.00	−0.517089
$208$	−816.000	−0.272016
$209$	−3996.00	−1.32253
$210$	0	0
$211$	−4083.00	−1.33216	−0.666079	−	0.745881i	$-0.732029\pi$
$211$	−4083.00	−1.33216	−0.666079	+	0.745881i	$0.732029\pi$
$212$	−24.0000	−0.00777513
$213$	3192.00	1.02682
$214$	−288.000	−0.0919966
$215$	0	0
$216$	−280.000	−0.0882018
$217$	0	0
$218$	3362.00	1.04451
$219$	−4550.00	−1.40393
$220$	0	0
$221$	2091.00	0.636452
$222$	−4676.00	−1.41366
$223$	−377.000	−0.113210	−0.0566049	−	0.998397i	$-0.518028\pi$
$223$	−377.000	−0.113210	−0.0566049	+	0.998397i	$0.518028\pi$
$224$	0	0
$225$	0	0
$226$	1596.00	0.469754
$227$	2551.00	0.745885	0.372942	−	0.927855i	$-0.378349\pi$
$227$	2551.00	0.745885	0.372942	+	0.927855i	$0.378349\pi$
$228$	3024.00	0.878374
$229$	−74.0000	−0.0213540	−0.0106770	−	0.999943i	$-0.503399\pi$
$229$	−74.0000	−0.0213540	−0.0106770	+	0.999943i	$0.503399\pi$
$230$	0	0
$231$	0	0
$232$	−1992.00	−0.563712
$233$	1888.00	0.530845	0.265423	−	0.964132i	$-0.414488\pi$
$233$	1888.00	0.530845	0.265423	+	0.964132i	$0.414488\pi$
$234$	−2244.00	−0.626901
$235$	0	0
$236$	8.00000	0.00220659
$237$	−8673.00	−2.37710
$238$	0	0
$239$	4997.00	1.35242	0.676211	−	0.736708i	$-0.263621\pi$
$239$	4997.00	1.35242	0.676211	+	0.736708i	$0.263621\pi$
$240$	0	0
$241$	3830.00	1.02370	0.511851	−	0.859074i	$-0.328960\pi$
$241$	3830.00	1.02370	0.511851	+	0.859074i	$0.328960\pi$
$242$	76.0000	0.0201879
$243$	−4928.00	−1.30095
$244$	3760.00	0.986514
$245$	0	0
$246$	−2884.00	−0.747468
$247$	−5508.00	−1.41889
$248$	1072.00	0.274484
$249$	−2996.00	−0.762505
$250$	0	0
$251$	3390.00	0.852490	0.426245	−	0.904608i	$-0.359836\pi$
$251$	3390.00	0.852490	0.426245	+	0.904608i	$0.359836\pi$
$252$	0	0
$253$	2590.00	0.643604
$254$	868.000	0.214422
$255$	0	0
$256$	256.000	0.0625000
$257$	−7170.00	−1.74028	−0.870141	−	0.492803i	$-0.835972\pi$
$257$	−7170.00	−1.74028	−0.870141	+	0.492803i	$0.835972\pi$
$258$	−5264.00	−1.27024
$259$	0	0
$260$	0	0
$261$	−5478.00	−1.29916
$262$	2580.00	0.608370
$263$	−7672.00	−1.79877	−0.899384	−	0.437160i	$-0.855984\pi$
$263$	−7672.00	−1.79877	−0.899384	+	0.437160i	$0.855984\pi$
$264$	−2072.00	−0.483041
$265$	0	0
$266$	0	0
$267$	1540.00	0.352983
$268$	424.000	0.0966415
$269$	54.0000	0.0122395	0.00611977	−	0.999981i	$-0.498052\pi$
$269$	54.0000	0.0122395	0.00611977	+	0.999981i	$0.498052\pi$
$270$	0	0
$271$	−2932.00	−0.657219	−0.328609	−	0.944466i	$-0.606580\pi$
$271$	−2932.00	−0.657219	−0.328609	+	0.944466i	$0.606580\pi$
$272$	−656.000	−0.146235
$273$	0	0
$274$	384.000	0.0846653
$275$	0	0
$276$	−1960.00	−0.427457
$277$	3254.00	0.705826	0.352913	−	0.935656i	$-0.385191\pi$
$277$	3254.00	0.705826	0.352913	+	0.935656i	$0.385191\pi$
$278$	−2804.00	−0.604938
$279$	2948.00	0.632588
$280$	0	0
$281$	3327.00	0.706307	0.353153	−	0.935565i	$-0.385109\pi$
$281$	3327.00	0.706307	0.353153	+	0.935565i	$0.385109\pi$
$282$	4018.00	0.848470
$283$	−4627.00	−0.971896	−0.485948	−	0.873988i	$-0.661526\pi$
$283$	−4627.00	−0.971896	−0.485948	+	0.873988i	$0.661526\pi$
$284$	1824.00	0.381107
$285$	0	0
$286$	3774.00	0.780284
$287$	0	0
$288$	704.000	0.144040
$289$	−3232.00	−0.657847
$290$	0	0
$291$	7385.00	1.48769
$292$	−2600.00	−0.521074
$293$	4083.00	0.814100	0.407050	−	0.913406i	$-0.366557\pi$
$293$	4083.00	0.814100	0.407050	+	0.913406i	$0.366557\pi$
$294$	0	0
$295$	0	0
$296$	−2672.00	−0.524685
$297$	1295.00	0.253008
$298$	−604.000	−0.117412
$299$	3570.00	0.690496
$300$	0	0
$301$	0	0
$302$	−6334.00	−1.20689
$303$	−13720.0	−2.60130
$304$	1728.00	0.326012
$305$	0	0
$306$	−1804.00	−0.337019
$307$	4089.00	0.760168	0.380084	−	0.924952i	$-0.375895\pi$
$307$	4089.00	0.760168	0.380084	+	0.924952i	$0.375895\pi$
$308$	0	0
$309$	−12775.0	−2.35192
$310$	0	0
$311$	4008.00	0.730781	0.365390	−	0.930854i	$-0.380935\pi$
$311$	4008.00	0.730781	0.365390	+	0.930854i	$0.380935\pi$
$312$	−2856.00	−0.518234
$313$	−7355.00	−1.32821	−0.664104	−	0.747640i	$-0.731187\pi$
$313$	−7355.00	−1.32821	−0.664104	+	0.747640i	$0.731187\pi$
$314$	940.000	0.168940
$315$	0	0
$316$	−4956.00	−0.882268
$317$	−1684.00	−0.298369	−0.149184	−	0.988809i	$-0.547665\pi$
$317$	−1684.00	−0.298369	−0.149184	+	0.988809i	$0.547665\pi$
$318$	−84.0000	−0.0148128
$319$	9213.00	1.61702
$320$	0	0
$321$	−1008.00	−0.175268
$322$	0	0
$323$	−4428.00	−0.762788
$324$	−3356.00	−0.575446
$325$	0	0
$326$	−4780.00	−0.812085
$327$	11767.0	1.98996
$328$	−1648.00	−0.277426
$329$	0	0
$330$	0	0
$331$	−1460.00	−0.242444	−0.121222	−	0.992625i	$-0.538681\pi$
$331$	−1460.00	−0.242444	−0.121222	+	0.992625i	$0.538681\pi$
$332$	−1712.00	−0.283007
$333$	−7348.00	−1.20921
$334$	5262.00	0.862047
$335$	0	0
$336$	0	0
$337$	7514.00	1.21458	0.607290	−	0.794480i	$-0.292256\pi$
$337$	7514.00	1.21458	0.607290	+	0.794480i	$0.292256\pi$
$338$	808.000	0.130028
$339$	5586.00	0.894955
$340$	0	0
$341$	−4958.00	−0.787363
$342$	4752.00	0.751341
$343$	0	0
$344$	−3008.00	−0.471455
$345$	0	0
$346$	4486.00	0.697020
$347$	−2862.00	−0.442767	−0.221384	−	0.975187i	$-0.571057\pi$
$347$	−2862.00	−0.442767	−0.221384	+	0.975187i	$0.571057\pi$
$348$	−6972.00	−1.07396
$349$	6368.00	0.976708	0.488354	−	0.872646i	$-0.337597\pi$
$349$	6368.00	0.976708	0.488354	+	0.872646i	$0.337597\pi$
$350$	0	0
$351$	1785.00	0.271442
$352$	−1184.00	−0.179282
$353$	3635.00	0.548078	0.274039	−	0.961719i	$-0.411640\pi$
$353$	3635.00	0.548078	0.274039	+	0.961719i	$0.411640\pi$
$354$	28.0000	0.00420391
$355$	0	0
$356$	880.000	0.131011
$357$	0	0
$358$	104.000	0.0153535
$359$	7116.00	1.04615	0.523075	−	0.852286i	$-0.324785\pi$
$359$	7116.00	1.04615	0.523075	+	0.852286i	$0.324785\pi$
$360$	0	0
$361$	4805.00	0.700539
$362$	−4924.00	−0.714916
$363$	266.000	0.0384611
$364$	0	0
$365$	0	0
$366$	13160.0	1.87947
$367$	319.000	0.0453724	0.0226862	−	0.999743i	$-0.492778\pi$
$367$	319.000	0.0453724	0.0226862	+	0.999743i	$0.492778\pi$
$368$	−1120.00	−0.158652
$369$	−4532.00	−0.639367
$370$	0	0
$371$	0	0
$372$	3752.00	0.522936
$373$	−11652.0	−1.61747	−0.808737	−	0.588171i	$-0.799848\pi$
$373$	−11652.0	−1.61747	−0.808737	+	0.588171i	$0.799848\pi$
$374$	3034.00	0.419477
$375$	0	0
$376$	2296.00	0.314913
$377$	12699.0	1.73483
$378$	0	0
$379$	7748.00	1.05010	0.525050	−	0.851071i	$-0.324047\pi$
$379$	7748.00	1.05010	0.525050	+	0.851071i	$0.324047\pi$
$380$	0	0
$381$	3038.00	0.408508
$382$	6318.00	0.846223
$383$	−8680.00	−1.15803	−0.579017	−	0.815315i	$-0.696564\pi$
$383$	−8680.00	−1.15803	−0.579017	+	0.815315i	$0.696564\pi$
$384$	896.000	0.119072
$385$	0	0
$386$	4120.00	0.543271
$387$	−8272.00	−1.08654
$388$	4220.00	0.552160
$389$	−1711.00	−0.223011	−0.111505	−	0.993764i	$-0.535567\pi$
$389$	−1711.00	−0.223011	−0.111505	+	0.993764i	$0.535567\pi$
$390$	0	0
$391$	2870.00	0.371208
$392$	0	0
$393$	9030.00	1.15904
$394$	3476.00	0.444463
$395$	0	0
$396$	−3256.00	−0.413182
$397$	−1589.00	−0.200881	−0.100440	−	0.994943i	$-0.532025\pi$
$397$	−1589.00	−0.200881	−0.100440	+	0.994943i	$0.532025\pi$
$398$	1788.00	0.225187
$399$	0	0
$400$	0	0
$401$	−5147.00	−0.640970	−0.320485	−	0.947254i	$-0.603846\pi$
$401$	−5147.00	−0.640970	−0.320485	+	0.947254i	$0.603846\pi$
$402$	1484.00	0.184117
$403$	−6834.00	−0.844729
$404$	−7840.00	−0.965482
$405$	0	0
$406$	0	0
$407$	12358.0	1.50507
$408$	−2296.00	−0.278600
$409$	9100.00	1.10016	0.550081	−	0.835111i	$-0.314597\pi$
$409$	9100.00	1.10016	0.550081	+	0.835111i	$0.314597\pi$
$410$	0	0
$411$	1344.00	0.161301
$412$	−7300.00	−0.872925
$413$	0	0
$414$	−3080.00	−0.365637
$415$	0	0
$416$	−1632.00	−0.192345
$417$	−9814.00	−1.15250
$418$	−7992.00	−0.935171
$419$	−2618.00	−0.305245	−0.152623	−	0.988285i	$-0.548772\pi$
$419$	−2618.00	−0.305245	−0.152623	+	0.988285i	$0.548772\pi$
$420$	0	0
$421$	−3695.00	−0.427751	−0.213876	−	0.976861i	$-0.568609\pi$
$421$	−3695.00	−0.427751	−0.213876	+	0.976861i	$0.568609\pi$
$422$	−8166.00	−0.941978
$423$	6314.00	0.725762
$424$	−48.0000	−0.00549784
$425$	0	0
$426$	6384.00	0.726070
$427$	0	0
$428$	−576.000	−0.0650514
$429$	13209.0	1.48657
$430$	0	0
$431$	15779.0	1.76345	0.881726	−	0.471762i	$-0.156382\pi$
$431$	15779.0	1.76345	0.881726	+	0.471762i	$0.156382\pi$
$432$	−560.000	−0.0623681
$433$	−7238.00	−0.803317	−0.401658	−	0.915790i	$-0.631566\pi$
$433$	−7238.00	−0.803317	−0.401658	+	0.915790i	$0.631566\pi$
$434$	0	0
$435$	0	0
$436$	6724.00	0.738581
$437$	−7560.00	−0.827560
$438$	−9100.00	−0.992728
$439$	2646.00	0.287669	0.143834	−	0.989602i	$-0.454057\pi$
$439$	2646.00	0.287669	0.143834	+	0.989602i	$0.454057\pi$
$440$	0	0
$441$	0	0
$442$	4182.00	0.450039
$443$	5688.00	0.610034	0.305017	−	0.952347i	$-0.401338\pi$
$443$	5688.00	0.610034	0.305017	+	0.952347i	$0.401338\pi$
$444$	−9352.00	−0.999609
$445$	0	0
$446$	−754.000	−0.0800514
$447$	−2114.00	−0.223689
$448$	0	0
$449$	−3285.00	−0.345276	−0.172638	−	0.984985i	$-0.555229\pi$
$449$	−3285.00	−0.345276	−0.172638	+	0.984985i	$0.555229\pi$
$450$	0	0
$451$	7622.00	0.795800
$452$	3192.00	0.332166
$453$	−22169.0	−2.29932
$454$	5102.00	0.527420
$455$	0	0
$456$	6048.00	0.621104
$457$	14834.0	1.51839	0.759196	−	0.650862i	$-0.225592\pi$
$457$	14834.0	1.51839	0.759196	+	0.650862i	$0.225592\pi$
$458$	−148.000	−0.0150995
$459$	1435.00	0.145926
$460$	0	0
$461$	9972.00	1.00747	0.503734	−	0.863859i	$-0.331959\pi$
$461$	9972.00	1.00747	0.503734	+	0.863859i	$0.331959\pi$
$462$	0	0
$463$	−9096.00	−0.913017	−0.456509	−	0.889719i	$-0.650900\pi$
$463$	−9096.00	−0.913017	−0.456509	+	0.889719i	$0.650900\pi$
$464$	−3984.00	−0.398605
$465$	0	0
$466$	3776.00	0.375364
$467$	−15867.0	−1.57224	−0.786121	−	0.618072i	$-0.787914\pi$
$467$	−15867.0	−1.57224	−0.786121	+	0.618072i	$0.787914\pi$
$468$	−4488.00	−0.443286
$469$	0	0
$470$	0	0
$471$	3290.00	0.321858
$472$	16.0000	0.00156030
$473$	13912.0	1.35238
$474$	−17346.0	−1.68086
$475$	0	0
$476$	0	0
$477$	−132.000	−0.0126706
$478$	9994.00	0.956307
$479$	−242.000	−0.0230841	−0.0115420	−	0.999933i	$-0.503674\pi$
$479$	−242.000	−0.0230841	−0.0115420	+	0.999933i	$0.503674\pi$
$480$	0	0
$481$	17034.0	1.61473
$482$	7660.00	0.723866
$483$	0	0
$484$	152.000	0.0142750
$485$	0	0
$486$	−9856.00	−0.919912
$487$	−3558.00	−0.331064	−0.165532	−	0.986204i	$-0.552934\pi$
$487$	−3558.00	−0.331064	−0.165532	+	0.986204i	$0.552934\pi$
$488$	7520.00	0.697571
$489$	−16730.0	−1.54715
$490$	0	0
$491$	1473.00	0.135388	0.0676941	−	0.997706i	$-0.478436\pi$
$491$	1473.00	0.135388	0.0676941	+	0.997706i	$0.478436\pi$
$492$	−5768.00	−0.528540
$493$	10209.0	0.932637
$494$	−11016.0	−1.00331
$495$	0	0
$496$	2144.00	0.194090
$497$	0	0
$498$	−5992.00	−0.539173
$499$	603.000	0.0540962	0.0270481	−	0.999634i	$-0.491389\pi$
$499$	603.000	0.0540962	0.0270481	+	0.999634i	$0.491389\pi$
$500$	0	0
$501$	18417.0	1.64234
$502$	6780.00	0.602801
$503$	−18387.0	−1.62989	−0.814946	−	0.579537i	$-0.803234\pi$
$503$	−18387.0	−1.62989	−0.814946	+	0.579537i	$0.803234\pi$
$504$	0	0
$505$	0	0
$506$	5180.00	0.455097
$507$	2828.00	0.247724
$508$	1736.00	0.151619
$509$	−9018.00	−0.785296	−0.392648	−	0.919689i	$-0.628441\pi$
$509$	−9018.00	−0.785296	−0.392648	+	0.919689i	$0.628441\pi$
$510$	0	0
$511$	0	0
$512$	512.000	0.0441942
$513$	−3780.00	−0.325324
$514$	−14340.0	−1.23056
$515$	0	0
$516$	−10528.0	−0.898196
$517$	−10619.0	−0.903333
$518$	0	0
$519$	15701.0	1.32793
$520$	0	0
$521$	−4624.00	−0.388831	−0.194416	−	0.980919i	$-0.562281\pi$
$521$	−4624.00	−0.388831	−0.194416	+	0.980919i	$0.562281\pi$
$522$	−10956.0	−0.918642
$523$	5876.00	0.491280	0.245640	−	0.969361i	$-0.421002\pi$
$523$	5876.00	0.491280	0.245640	+	0.969361i	$0.421002\pi$
$524$	5160.00	0.430183
$525$	0	0
$526$	−15344.0	−1.27192
$527$	−5494.00	−0.454122
$528$	−4144.00	−0.341561
$529$	−7267.00	−0.597271
$530$	0	0
$531$	44.0000	0.00359593
$532$	0	0
$533$	10506.0	0.853781
$534$	3080.00	0.249597
$535$	0	0
$536$	848.000	0.0683359
$537$	364.000	0.0292509
$538$	108.000	0.00865467
$539$	0	0
$540$	0	0
$541$	−8537.00	−0.678437	−0.339218	−	0.940708i	$-0.610163\pi$
$541$	−8537.00	−0.678437	−0.339218	+	0.940708i	$0.610163\pi$
$542$	−5864.00	−0.464724
$543$	−17234.0	−1.36203
$544$	−1312.00	−0.103404
$545$	0	0
$546$	0	0
$547$	−13060.0	−1.02085	−0.510425	−	0.859922i	$-0.670512\pi$
$547$	−13060.0	−1.02085	−0.510425	+	0.859922i	$0.670512\pi$
$548$	768.000	0.0598674
$549$	20680.0	1.60765
$550$	0	0
$551$	−26892.0	−2.07920
$552$	−3920.00	−0.302258
$553$	0	0
$554$	6508.00	0.499095
$555$	0	0
$556$	−5608.00	−0.427756
$557$	21372.0	1.62578	0.812891	−	0.582416i	$-0.197892\pi$
$557$	21372.0	1.62578	0.812891	+	0.582416i	$0.197892\pi$
$558$	5896.00	0.447307
$559$	19176.0	1.45091
$560$	0	0
$561$	10619.0	0.799170
$562$	6654.00	0.499434
$563$	12704.0	0.950994	0.475497	−	0.879717i	$-0.342268\pi$
$563$	12704.0	0.950994	0.475497	+	0.879717i	$0.342268\pi$
$564$	8036.00	0.599959
$565$	0	0
$566$	−9254.00	−0.687234
$567$	0	0
$568$	3648.00	0.269484
$569$	8762.00	0.645557	0.322779	−	0.946474i	$-0.395383\pi$
$569$	8762.00	0.645557	0.322779	+	0.946474i	$0.395383\pi$
$570$	0	0
$571$	−24764.0	−1.81496	−0.907479	−	0.420097i	$-0.861996\pi$
$571$	−24764.0	−1.81496	−0.907479	+	0.420097i	$0.861996\pi$
$572$	7548.00	0.551744
$573$	22113.0	1.61219
$574$	0	0
$575$	0	0
$576$	1408.00	0.101852
$577$	−1811.00	−0.130664	−0.0653318	−	0.997864i	$-0.520811\pi$
$577$	−1811.00	−0.130664	−0.0653318	+	0.997864i	$0.520811\pi$
$578$	−6464.00	−0.465168
$579$	14420.0	1.03502
$580$	0	0
$581$	0	0
$582$	14770.0	1.05195
$583$	222.000	0.0157707
$584$	−5200.00	−0.368455
$585$	0	0
$586$	8166.00	0.575656
$587$	−10548.0	−0.741674	−0.370837	−	0.928698i	$-0.620929\pi$
$587$	−10548.0	−0.741674	−0.370837	+	0.928698i	$0.620929\pi$
$588$	0	0
$589$	14472.0	1.01241
$590$	0	0
$591$	12166.0	0.846772
$592$	−5344.00	−0.371009
$593$	−17439.0	−1.20765	−0.603823	−	0.797119i	$-0.706357\pi$
$593$	−17439.0	−1.20765	−0.603823	+	0.797119i	$0.706357\pi$
$594$	2590.00	0.178904
$595$	0	0
$596$	−1208.00	−0.0830228
$597$	6258.00	0.429017
$598$	7140.00	0.488255
$599$	2451.00	0.167187	0.0835936	−	0.996500i	$-0.473360\pi$
$599$	2451.00	0.167187	0.0835936	+	0.996500i	$0.473360\pi$
$600$	0	0
$601$	7792.00	0.528856	0.264428	−	0.964405i	$-0.414817\pi$
$601$	7792.00	0.528856	0.264428	+	0.964405i	$0.414817\pi$
$602$	0	0
$603$	2332.00	0.157490
$604$	−12668.0	−0.853400
$605$	0	0
$606$	−27440.0	−1.83940
$607$	1937.00	0.129523	0.0647615	−	0.997901i	$-0.479371\pi$
$607$	1937.00	0.129523	0.0647615	+	0.997901i	$0.479371\pi$
$608$	3456.00	0.230525
$609$	0	0
$610$	0	0
$611$	−14637.0	−0.969148
$612$	−3608.00	−0.238308
$613$	5036.00	0.331814	0.165907	−	0.986141i	$-0.446945\pi$
$613$	5036.00	0.331814	0.165907	+	0.986141i	$0.446945\pi$
$614$	8178.00	0.537520
$615$	0	0
$616$	0	0
$617$	−27286.0	−1.78038	−0.890189	−	0.455592i	$-0.849428\pi$
$617$	−27286.0	−1.78038	−0.890189	+	0.455592i	$0.849428\pi$
$618$	−25550.0	−1.66306
$619$	−28538.0	−1.85305	−0.926526	−	0.376231i	$-0.877220\pi$
$619$	−28538.0	−1.85305	−0.926526	+	0.376231i	$0.877220\pi$
$620$	0	0
$621$	2450.00	0.158317
$622$	8016.00	0.516740
$623$	0	0
$624$	−5712.00	−0.366447
$625$	0	0
$626$	−14710.0	−0.939185
$627$	−27972.0	−1.78165
$628$	1880.00	0.119459
$629$	13694.0	0.868069
$630$	0	0
$631$	25007.0	1.57768	0.788838	−	0.614602i	$-0.210683\pi$
$631$	25007.0	1.57768	0.788838	+	0.614602i	$0.210683\pi$
$632$	−9912.00	−0.623858
$633$	−28581.0	−1.79462
$634$	−3368.00	−0.210978
$635$	0	0
$636$	−168.000	−0.0104743
$637$	0	0
$638$	18426.0	1.14340
$639$	10032.0	0.621064
$640$	0	0
$641$	−12130.0	−0.747436	−0.373718	−	0.927542i	$-0.621917\pi$
$641$	−12130.0	−0.747436	−0.373718	+	0.927542i	$0.621917\pi$
$642$	−2016.00	−0.123933
$643$	−14385.0	−0.882254	−0.441127	−	0.897445i	$-0.645421\pi$
$643$	−14385.0	−0.882254	−0.441127	+	0.897445i	$0.645421\pi$
$644$	0	0
$645$	0	0
$646$	−8856.00	−0.539373
$647$	2208.00	0.134166	0.0670830	−	0.997747i	$-0.478631\pi$
$647$	2208.00	0.134166	0.0670830	+	0.997747i	$0.478631\pi$
$648$	−6712.00	−0.406902
$649$	−74.0000	−0.00447574
$650$	0	0
$651$	0	0
$652$	−9560.00	−0.574231
$653$	22448.0	1.34527	0.672633	−	0.739977i	$-0.265163\pi$
$653$	22448.0	1.34527	0.672633	+	0.739977i	$0.265163\pi$
$654$	23534.0	1.40711
$655$	0	0
$656$	−3296.00	−0.196169
$657$	−14300.0	−0.849157
$658$	0	0
$659$	8791.00	0.519649	0.259825	−	0.965656i	$-0.416335\pi$
$659$	8791.00	0.519649	0.259825	+	0.965656i	$0.416335\pi$
$660$	0	0
$661$	13180.0	0.775556	0.387778	−	0.921753i	$-0.373243\pi$
$661$	13180.0	0.775556	0.387778	+	0.921753i	$0.373243\pi$
$662$	−2920.00	−0.171434
$663$	14637.0	0.857397
$664$	−3424.00	−0.200116
$665$	0	0
$666$	−14696.0	−0.855043
$667$	17430.0	1.01183
$668$	10524.0	0.609560
$669$	−2639.00	−0.152511
$670$	0	0
$671$	−34780.0	−2.00099
$672$	0	0
$673$	−7164.00	−0.410330	−0.205165	−	0.978727i	$-0.565773\pi$
$673$	−7164.00	−0.410330	−0.205165	+	0.978727i	$0.565773\pi$
$674$	15028.0	0.858838
$675$	0	0
$676$	1616.00	0.0919436
$677$	−12335.0	−0.700255	−0.350127	−	0.936702i	$-0.613862\pi$
$677$	−12335.0	−0.700255	−0.350127	+	0.936702i	$0.613862\pi$
$678$	11172.0	0.632829
$679$	0	0
$680$	0	0
$681$	17857.0	1.00482
$682$	−9916.00	−0.556750
$683$	−15436.0	−0.864776	−0.432388	−	0.901688i	$-0.642329\pi$
$683$	−15436.0	−0.864776	−0.432388	+	0.901688i	$0.642329\pi$
$684$	9504.00	0.531279
$685$	0	0
$686$	0	0
$687$	−518.000	−0.0287670
$688$	−6016.00	−0.333369
$689$	306.000	0.0169197
$690$	0	0
$691$	19184.0	1.05614	0.528071	−	0.849200i	$-0.322916\pi$
$691$	19184.0	1.05614	0.528071	+	0.849200i	$0.322916\pi$
$692$	8972.00	0.492867
$693$	0	0
$694$	−5724.00	−0.313084
$695$	0	0
$696$	−13944.0	−0.759405
$697$	8446.00	0.458989
$698$	12736.0	0.690637
$699$	13216.0	0.715129
$700$	0	0
$701$	32975.0	1.77667	0.888337	−	0.459192i	$-0.151861\pi$
$701$	32975.0	1.77667	0.888337	+	0.459192i	$0.151861\pi$
$702$	3570.00	0.191939
$703$	−36072.0	−1.93525
$704$	−2368.00	−0.126772
$705$	0	0
$706$	7270.00	0.387550
$707$	0	0
$708$	56.0000	0.00297261
$709$	−31497.0	−1.66840	−0.834199	−	0.551463i	$-0.814070\pi$
$709$	−31497.0	−1.66840	−0.834199	+	0.551463i	$0.814070\pi$
$710$	0	0
$711$	−27258.0	−1.43777
$712$	1760.00	0.0926387
$713$	−9380.00	−0.492684
$714$	0	0
$715$	0	0
$716$	208.000	0.0108566
$717$	34979.0	1.82192
$718$	14232.0	0.739740
$719$	18610.0	0.965279	0.482640	−	0.875819i	$-0.339678\pi$
$719$	18610.0	0.965279	0.482640	+	0.875819i	$0.339678\pi$
$720$	0	0
$721$	0	0
$722$	9610.00	0.495356
$723$	26810.0	1.37908
$724$	−9848.00	−0.505522
$725$	0	0
$726$	532.000	0.0271961
$727$	17508.0	0.893172	0.446586	−	0.894741i	$-0.352640\pi$
$727$	17508.0	0.893172	0.446586	+	0.894741i	$0.352640\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	15416.0	0.780002
$732$	26320.0	1.32898
$733$	4685.00	0.236077	0.118038	−	0.993009i	$-0.462339\pi$
$733$	4685.00	0.236077	0.118038	+	0.993009i	$0.462339\pi$
$734$	638.000	0.0320831
$735$	0	0
$736$	−2240.00	−0.112184
$737$	−3922.00	−0.196023
$738$	−9064.00	−0.452101
$739$	−25925.0	−1.29048	−0.645241	−	0.763979i	$-0.723243\pi$
$739$	−25925.0	−1.29048	−0.645241	+	0.763979i	$0.723243\pi$
$740$	0	0
$741$	−38556.0	−1.91146
$742$	0	0
$743$	25578.0	1.26294	0.631471	−	0.775400i	$-0.282452\pi$
$743$	25578.0	1.26294	0.631471	+	0.775400i	$0.282452\pi$
$744$	7504.00	0.369771
$745$	0	0
$746$	−23304.0	−1.14373
$747$	−9416.00	−0.461196
$748$	6068.00	0.296615
$749$	0	0
$750$	0	0
$751$	−4291.00	−0.208496	−0.104248	−	0.994551i	$-0.533244\pi$
$751$	−4291.00	−0.208496	−0.104248	+	0.994551i	$0.533244\pi$
$752$	4592.00	0.222677
$753$	23730.0	1.14843
$754$	25398.0	1.22671
$755$	0	0
$756$	0	0
$757$	−31528.0	−1.51374	−0.756872	−	0.653563i	$-0.773274\pi$
$757$	−31528.0	−1.51374	−0.756872	+	0.653563i	$0.773274\pi$
$758$	15496.0	0.742533
$759$	18130.0	0.867032
$760$	0	0
$761$	23154.0	1.10293	0.551466	−	0.834197i	$-0.314068\pi$
$761$	23154.0	1.10293	0.551466	+	0.834197i	$0.314068\pi$
$762$	6076.00	0.288859
$763$	0	0
$764$	12636.0	0.598370
$765$	0	0
$766$	−17360.0	−0.818854
$767$	−102.000	−0.00480183
$768$	1792.00	0.0841969
$769$	−13992.0	−0.656131	−0.328065	−	0.944655i	$-0.606397\pi$
$769$	−13992.0	−0.656131	−0.328065	+	0.944655i	$0.606397\pi$
$770$	0	0
$771$	−50190.0	−2.34442
$772$	8240.00	0.384150
$773$	21681.0	1.00881	0.504406	−	0.863467i	$-0.331712\pi$
$773$	21681.0	1.00881	0.504406	+	0.863467i	$0.331712\pi$
$774$	−16544.0	−0.768297
$775$	0	0
$776$	8440.00	0.390436
$777$	0	0
$778$	−3422.00	−0.157692
$779$	−22248.0	−1.02326
$780$	0	0
$781$	−16872.0	−0.773019
$782$	5740.00	0.262483
$783$	8715.00	0.397763
$784$	0	0
$785$	0	0
$786$	18060.0	0.819566
$787$	16903.0	0.765600	0.382800	−	0.923831i	$-0.374960\pi$
$787$	16903.0	0.765600	0.382800	+	0.923831i	$0.374960\pi$
$788$	6952.00	0.314283
$789$	−53704.0	−2.42321
$790$	0	0
$791$	0	0
$792$	−6512.00	−0.292164
$793$	−47940.0	−2.14678
$794$	−3178.00	−0.142044
$795$	0	0
$796$	3576.00	0.159231
$797$	−18905.0	−0.840213	−0.420106	−	0.907475i	$-0.638007\pi$
$797$	−18905.0	−0.840213	−0.420106	+	0.907475i	$0.638007\pi$
$798$	0	0
$799$	−11767.0	−0.521009
$800$	0	0
$801$	4840.00	0.213499
$802$	−10294.0	−0.453234
$803$	24050.0	1.05692
$804$	2968.00	0.130191
$805$	0	0
$806$	−13668.0	−0.597314
$807$	378.000	0.0164885
$808$	−15680.0	−0.682699
$809$	−5571.00	−0.242109	−0.121054	−	0.992646i	$-0.538628\pi$
$809$	−5571.00	−0.242109	−0.121054	+	0.992646i	$0.538628\pi$
$810$	0	0
$811$	−10894.0	−0.471689	−0.235845	−	0.971791i	$-0.575786\pi$
$811$	−10894.0	−0.471689	−0.235845	+	0.971791i	$0.575786\pi$
$812$	0	0
$813$	−20524.0	−0.885373
$814$	24716.0	1.06424
$815$	0	0
$816$	−4592.00	−0.197000
$817$	−40608.0	−1.73892
$818$	18200.0	0.777932
$819$	0	0
$820$	0	0
$821$	−30731.0	−1.30636	−0.653179	−	0.757204i	$-0.726565\pi$
$821$	−30731.0	−1.30636	−0.653179	+	0.757204i	$0.726565\pi$
$822$	2688.00	0.114057
$823$	1038.00	0.0439640	0.0219820	−	0.999758i	$-0.493002\pi$
$823$	1038.00	0.0439640	0.0219820	+	0.999758i	$0.493002\pi$
$824$	−14600.0	−0.617251
$825$	0	0
$826$	0	0
$827$	7958.00	0.334615	0.167308	−	0.985905i	$-0.446493\pi$
$827$	7958.00	0.334615	0.167308	+	0.985905i	$0.446493\pi$
$828$	−6160.00	−0.258544
$829$	30666.0	1.28477	0.642385	−	0.766382i	$-0.277945\pi$
$829$	30666.0	1.28477	0.642385	+	0.766382i	$0.277945\pi$
$830$	0	0
$831$	22778.0	0.950854
$832$	−3264.00	−0.136008
$833$	0	0
$834$	−19628.0	−0.814943
$835$	0	0
$836$	−15984.0	−0.661266
$837$	−4690.00	−0.193680
$838$	−5236.00	−0.215841
$839$	5354.00	0.220311	0.110155	−	0.993914i	$-0.464865\pi$
$839$	5354.00	0.220311	0.110155	+	0.993914i	$0.464865\pi$
$840$	0	0
$841$	37612.0	1.54217
$842$	−7390.00	−0.302466
$843$	23289.0	0.951502
$844$	−16332.0	−0.666079
$845$	0	0
$846$	12628.0	0.513191
$847$	0	0
$848$	−96.0000	−0.00388756
$849$	−32389.0	−1.30929
$850$	0	0
$851$	23380.0	0.941782
$852$	12768.0	0.513409
$853$	42890.0	1.72160	0.860800	−	0.508943i	$-0.169963\pi$
$853$	42890.0	1.72160	0.860800	+	0.508943i	$0.169963\pi$
$854$	0	0
$855$	0	0
$856$	−1152.00	−0.0459983
$857$	−22950.0	−0.914769	−0.457385	−	0.889269i	$-0.651214\pi$
$857$	−22950.0	−0.914769	−0.457385	+	0.889269i	$0.651214\pi$
$858$	26418.0	1.05116
$859$	2824.00	0.112170	0.0560848	−	0.998426i	$-0.482138\pi$
$859$	2824.00	0.112170	0.0560848	+	0.998426i	$0.482138\pi$
$860$	0	0
$861$	0	0
$862$	31558.0	1.24695
$863$	−4866.00	−0.191936	−0.0959679	−	0.995384i	$-0.530595\pi$
$863$	−4866.00	−0.191936	−0.0959679	+	0.995384i	$0.530595\pi$
$864$	−1120.00	−0.0441009
$865$	0	0
$866$	−14476.0	−0.568031
$867$	−22624.0	−0.886218
$868$	0	0
$869$	45843.0	1.78955
$870$	0	0
$871$	−5406.00	−0.210305
$872$	13448.0	0.522255
$873$	23210.0	0.899816
$874$	−15120.0	−0.585173
$875$	0	0
$876$	−18200.0	−0.701965
$877$	−10676.0	−0.411064	−0.205532	−	0.978650i	$-0.565892\pi$
$877$	−10676.0	−0.411064	−0.205532	+	0.978650i	$0.565892\pi$
$878$	5292.00	0.203413
$879$	28581.0	1.09672
$880$	0	0
$881$	29856.0	1.14174	0.570871	−	0.821040i	$-0.306606\pi$
$881$	29856.0	1.14174	0.570871	+	0.821040i	$0.306606\pi$
$882$	0	0
$883$	−1944.00	−0.0740893	−0.0370446	−	0.999314i	$-0.511794\pi$
$883$	−1944.00	−0.0740893	−0.0370446	+	0.999314i	$0.511794\pi$
$884$	8364.00	0.318226
$885$	0	0
$886$	11376.0	0.431359
$887$	14628.0	0.553732	0.276866	−	0.960909i	$-0.410704\pi$
$887$	14628.0	0.553732	0.276866	+	0.960909i	$0.410704\pi$
$888$	−18704.0	−0.706830
$889$	0	0
$890$	0	0
$891$	31043.0	1.16720
$892$	−1508.00	−0.0566049
$893$	30996.0	1.16152
$894$	−4228.00	−0.158172
$895$	0	0
$896$	0	0
$897$	24990.0	0.930203
$898$	−6570.00	−0.244147
$899$	−33366.0	−1.23784
$900$	0	0
$901$	246.000	0.00909595
$902$	15244.0	0.562716
$903$	0	0
$904$	6384.00	0.234877
$905$	0	0
$906$	−44338.0	−1.62586
$907$	−12858.0	−0.470720	−0.235360	−	0.971908i	$-0.575627\pi$
$907$	−12858.0	−0.470720	−0.235360	+	0.971908i	$0.575627\pi$
$908$	10204.0	0.372942
$909$	−43120.0	−1.57338
$910$	0	0
$911$	−18324.0	−0.666412	−0.333206	−	0.942854i	$-0.608130\pi$
$911$	−18324.0	−0.666412	−0.333206	+	0.942854i	$0.608130\pi$
$912$	12096.0	0.439187
$913$	15836.0	0.574036
$914$	29668.0	1.07367
$915$	0	0
$916$	−296.000	−0.0106770
$917$	0	0
$918$	2870.00	0.103185
$919$	−14751.0	−0.529478	−0.264739	−	0.964320i	$-0.585286\pi$
$919$	−14751.0	−0.529478	−0.264739	+	0.964320i	$0.585286\pi$
$920$	0	0
$921$	28623.0	1.02406
$922$	19944.0	0.712387
$923$	−23256.0	−0.829340
$924$	0	0
$925$	0	0
$926$	−18192.0	−0.645601
$927$	−40150.0	−1.42254
$928$	−7968.00	−0.281856
$929$	47922.0	1.69243	0.846216	−	0.532840i	$-0.178875\pi$
$929$	47922.0	1.69243	0.846216	+	0.532840i	$0.178875\pi$
$930$	0	0
$931$	0	0
$932$	7552.00	0.265423
$933$	28056.0	0.984472
$934$	−31734.0	−1.11174
$935$	0	0
$936$	−8976.00	−0.313451
$937$	44987.0	1.56848	0.784238	−	0.620461i	$-0.213054\pi$
$937$	44987.0	1.56848	0.784238	+	0.620461i	$0.213054\pi$
$938$	0	0
$939$	−51485.0	−1.78930
$940$	0	0
$941$	20356.0	0.705193	0.352597	−	0.935775i	$-0.385299\pi$
$941$	20356.0	0.705193	0.352597	+	0.935775i	$0.385299\pi$
$942$	6580.00	0.227588
$943$	14420.0	0.497964
$944$	32.0000	0.00110330
$945$	0	0
$946$	27824.0	0.956275
$947$	−27786.0	−0.953457	−0.476728	−	0.879051i	$-0.658177\pi$
$947$	−27786.0	−0.953457	−0.476728	+	0.879051i	$0.658177\pi$
$948$	−34692.0	−1.18855
$949$	33150.0	1.13392
$950$	0	0
$951$	−11788.0	−0.401948
$952$	0	0
$953$	−48674.0	−1.65447	−0.827233	−	0.561859i	$-0.810086\pi$
$953$	−48674.0	−1.65447	−0.827233	+	0.561859i	$0.810086\pi$
$954$	−264.000	−0.00895945
$955$	0	0
$956$	19988.0	0.676211
$957$	64491.0	2.17837
$958$	−484.000	−0.0163229
$959$	0	0
$960$	0	0
$961$	−11835.0	−0.397268
$962$	34068.0	1.14178
$963$	−3168.00	−0.106010
$964$	15320.0	0.511851
$965$	0	0
$966$	0	0
$967$	−11168.0	−0.371395	−0.185697	−	0.982607i	$-0.559454\pi$
$967$	−11168.0	−0.371395	−0.185697	+	0.982607i	$0.559454\pi$
$968$	304.000	0.0100939
$969$	−30996.0	−1.02759
$970$	0	0
$971$	−20094.0	−0.664106	−0.332053	−	0.943261i	$-0.607741\pi$
$971$	−20094.0	−0.664106	−0.332053	+	0.943261i	$0.607741\pi$
$972$	−19712.0	−0.650476
$973$	0	0
$974$	−7116.00	−0.234098
$975$	0	0
$976$	15040.0	0.493257
$977$	49104.0	1.60796	0.803980	−	0.594657i	$-0.202712\pi$
$977$	49104.0	1.60796	0.803980	+	0.594657i	$0.202712\pi$
$978$	−33460.0	−1.09400
$979$	−8140.00	−0.265736
$980$	0	0
$981$	36982.0	1.20361
$982$	2946.00	0.0957338
$983$	−27751.0	−0.900427	−0.450213	−	0.892921i	$-0.648652\pi$
$983$	−27751.0	−0.900427	−0.450213	+	0.892921i	$0.648652\pi$
$984$	−11536.0	−0.373734
$985$	0	0
$986$	20418.0	0.659474
$987$	0	0
$988$	−22032.0	−0.709445
$989$	26320.0	0.846236
$990$	0	0
$991$	37600.0	1.20525	0.602625	−	0.798024i	$-0.294121\pi$
$991$	37600.0	1.20525	0.602625	+	0.798024i	$0.294121\pi$
$992$	4288.00	0.137242
$993$	−10220.0	−0.326608
$994$	0	0
$995$	0	0
$996$	−11984.0	−0.381253
$997$	10911.0	0.346595	0.173297	−	0.984870i	$-0.444558\pi$
$997$	10911.0	0.346595	0.173297	+	0.984870i	$0.444558\pi$
$998$	1206.00	0.0382518
$999$	11690.0	0.370225

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.4.a.bn.1.1		1
5.2	odd	4		490.4.c.a.99.2		2
5.3	odd	4		490.4.c.a.99.1		2
5.4	even	2		2450.4.a.c.1.1		1
7.6	odd	2		350.4.a.m.1.1		1
35.13	even	4		70.4.c.a.29.1	✓	2
35.27	even	4		70.4.c.a.29.2	yes	2
35.34	odd	2		350.4.a.i.1.1		1
105.62	odd	4		630.4.g.a.379.1		2
105.83	odd	4		630.4.g.a.379.2		2
140.27	odd	4		560.4.g.c.449.1		2
140.83	odd	4		560.4.g.c.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.c.a.29.1	✓	2	35.13	even	4
70.4.c.a.29.2	yes	2	35.27	even	4
350.4.a.i.1.1		1	35.34	odd	2
350.4.a.m.1.1		1	7.6	odd	2
490.4.c.a.99.1		2	5.3	odd	4
490.4.c.a.99.2		2	5.2	odd	4
560.4.g.c.449.1		2	140.27	odd	4
560.4.g.c.449.2		2	140.83	odd	4
630.4.g.a.379.1		2	105.62	odd	4
630.4.g.a.379.2		2	105.83	odd	4
2450.4.a.c.1.1		1	5.4	even	2
2450.4.a.bn.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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