LMFDB - Embedded newform 2150.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2150,2,Mod(1,2150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2150, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("2150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2150 = 2 \cdot 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2150.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:	$17.1678364346$
Analytic rank:	$0$
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	$\chi$	$=$	2150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +6.00000 q^{9} +5.00000 q^{11} +3.00000 q^{12} +2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -6.00000 q^{18} -5.00000 q^{19} +12.0000 q^{21} -5.00000 q^{22} +2.00000 q^{23} -3.00000 q^{24} -2.00000 q^{26} +9.00000 q^{27} +4.00000 q^{28} -2.00000 q^{29} +6.00000 q^{31} -1.00000 q^{32} +15.0000 q^{33} +3.00000 q^{34} +6.00000 q^{36} -8.00000 q^{37} +5.00000 q^{38} +6.00000 q^{39} -7.00000 q^{41} -12.0000 q^{42} -1.00000 q^{43} +5.00000 q^{44} -2.00000 q^{46} +3.00000 q^{48} +9.00000 q^{49} -9.00000 q^{51} +2.00000 q^{52} -8.00000 q^{53} -9.00000 q^{54} -4.00000 q^{56} -15.0000 q^{57} +2.00000 q^{58} -12.0000 q^{59} -10.0000 q^{61} -6.00000 q^{62} +24.0000 q^{63} +1.00000 q^{64} -15.0000 q^{66} +3.00000 q^{67} -3.00000 q^{68} +6.00000 q^{69} -12.0000 q^{71} -6.00000 q^{72} +13.0000 q^{73} +8.00000 q^{74} -5.00000 q^{76} +20.0000 q^{77} -6.00000 q^{78} -12.0000 q^{79} +9.00000 q^{81} +7.00000 q^{82} +15.0000 q^{83} +12.0000 q^{84} +1.00000 q^{86} -6.00000 q^{87} -5.00000 q^{88} -15.0000 q^{89} +8.00000 q^{91} +2.00000 q^{92} +18.0000 q^{93} -3.00000 q^{96} -14.0000 q^{97} -9.00000 q^{98} +30.0000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.00000	1.73205	0.866025	−	0.500000i	$-0.166667\pi$
$3$	3.00000	1.73205	0.866025	+	0.500000i	$0.166667\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−3.00000	−1.22474
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	0	0
$11$	5.00000	1.50756	0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000	1.50756	0.753778	+	0.657129i	$0.228229\pi$
$12$	3.00000	0.866025
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−6.00000	−1.41421
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	12.0000	2.61861
$22$	−5.00000	−1.06600
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−3.00000	−0.612372
$25$	0	0
$26$	−2.00000	−0.392232
$27$	9.00000	1.73205
$28$	4.00000	0.755929
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	−1.00000	−0.176777
$33$	15.0000	2.61116
$34$	3.00000	0.514496
$35$	0	0
$36$	6.00000	1.00000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	5.00000	0.811107
$39$	6.00000	0.960769
$40$	0	0
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	−12.0000	−1.85164
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	5.00000	0.753778
$45$	0	0
$46$	−2.00000	−0.294884
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	3.00000	0.433013
$49$	9.00000	1.28571
$50$	0	0
$51$	−9.00000	−1.26025
$52$	2.00000	0.277350
$53$	−8.00000	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$53$	−8.00000	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$54$	−9.00000	−1.22474
$55$	0	0
$56$	−4.00000	−0.534522
$57$	−15.0000	−1.98680
$58$	2.00000	0.262613
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−6.00000	−0.762001
$63$	24.0000	3.02372
$64$	1.00000	0.125000
$65$	0	0
$66$	−15.0000	−1.84637
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−3.00000	−0.363803
$69$	6.00000	0.722315
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−6.00000	−0.707107
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	−5.00000	−0.573539
$77$	20.0000	2.27921
$78$	−6.00000	−0.679366
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	7.00000	0.773021
$83$	15.0000	1.64646	0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000	1.64646	0.823232	+	0.567705i	$0.192169\pi$
$84$	12.0000	1.30931
$85$	0	0
$86$	1.00000	0.107833
$87$	−6.00000	−0.643268
$88$	−5.00000	−0.533002
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	8.00000	0.838628
$92$	2.00000	0.208514
$93$	18.0000	1.86651
$94$	0	0
$95$	0	0
$96$	−3.00000	−0.306186
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−9.00000	−0.909137
$99$	30.0000	3.01511
$100$	0	0
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	9.00000	0.891133
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	8.00000	0.777029
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	9.00000	0.866025
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	−24.0000	−2.27798
$112$	4.00000	0.377964
$113$	−7.00000	−0.658505	−0.329252	−	0.944242i	$-0.606797\pi$
$113$	−7.00000	−0.658505	−0.329252	+	0.944242i	$0.606797\pi$
$114$	15.0000	1.40488
$115$	0	0
$116$	−2.00000	−0.185695
$117$	12.0000	1.10940
$118$	12.0000	1.10469
$119$	−12.0000	−1.10004
$120$	0	0
$121$	14.0000	1.27273
$122$	10.0000	0.905357
$123$	−21.0000	−1.89351
$124$	6.00000	0.538816
$125$	0	0
$126$	−24.0000	−2.13809
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−3.00000	−0.264135
$130$	0	0
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	15.0000	1.30558
$133$	−20.0000	−1.73422
$134$	−3.00000	−0.259161
$135$	0	0
$136$	3.00000	0.257248
$137$	−5.00000	−0.427179	−0.213589	−	0.976924i	$-0.568515\pi$
$137$	−5.00000	−0.427179	−0.213589	+	0.976924i	$0.568515\pi$
$138$	−6.00000	−0.510754
$139$	21.0000	1.78120	0.890598	−	0.454791i	$-0.150286\pi$
$139$	21.0000	1.78120	0.890598	+	0.454791i	$0.150286\pi$
$140$	0	0
$141$	0	0
$142$	12.0000	1.00702
$143$	10.0000	0.836242
$144$	6.00000	0.500000
$145$	0	0
$146$	−13.0000	−1.07589
$147$	27.0000	2.22692
$148$	−8.00000	−0.657596
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	5.00000	0.405554
$153$	−18.0000	−1.45521
$154$	−20.0000	−1.61165
$155$	0	0
$156$	6.00000	0.480384
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	12.0000	0.954669
$159$	−24.0000	−1.90332
$160$	0	0
$161$	8.00000	0.630488
$162$	−9.00000	−0.707107
$163$	25.0000	1.95815	0.979076	−	0.203497i	$-0.0652307\pi$
$163$	25.0000	1.95815	0.979076	+	0.203497i	$0.0652307\pi$
$164$	−7.00000	−0.546608
$165$	0	0
$166$	−15.0000	−1.16423
$167$	14.0000	1.08335	0.541676	−	0.840587i	$-0.317790\pi$
$167$	14.0000	1.08335	0.541676	+	0.840587i	$0.317790\pi$
$168$	−12.0000	−0.925820
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−30.0000	−2.29416
$172$	−1.00000	−0.0762493
$173$	−16.0000	−1.21646	−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000	−1.21646	−0.608229	+	0.793762i	$0.708120\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	5.00000	0.376889
$177$	−36.0000	−2.70593
$178$	15.0000	1.12430
$179$	−1.00000	−0.0747435	−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000	−0.0747435	−0.0373718	+	0.999301i	$0.511899\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−8.00000	−0.592999
$183$	−30.0000	−2.21766
$184$	−2.00000	−0.147442
$185$	0	0
$186$	−18.0000	−1.31982
$187$	−15.0000	−1.09691
$188$	0	0
$189$	36.0000	2.61861
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	3.00000	0.216506
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	9.00000	0.642857
$197$	20.0000	1.42494	0.712470	−	0.701702i	$-0.247576\pi$
$197$	20.0000	1.42494	0.712470	+	0.701702i	$0.247576\pi$
$198$	−30.0000	−2.13201
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	0	0
$201$	9.00000	0.634811
$202$	−10.0000	−0.703598
$203$	−8.00000	−0.561490
$204$	−9.00000	−0.630126
$205$	0	0
$206$	−6.00000	−0.418040
$207$	12.0000	0.834058
$208$	2.00000	0.138675
$209$	−25.0000	−1.72929
$210$	0	0
$211$	25.0000	1.72107	0.860535	−	0.509390i	$-0.170129\pi$
$211$	25.0000	1.72107	0.860535	+	0.509390i	$0.170129\pi$
$212$	−8.00000	−0.549442
$213$	−36.0000	−2.46668
$214$	−9.00000	−0.615227
$215$	0	0
$216$	−9.00000	−0.612372
$217$	24.0000	1.62923
$218$	−2.00000	−0.135457
$219$	39.0000	2.63538
$220$	0	0
$221$	−6.00000	−0.403604
$222$	24.0000	1.61077
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	7.00000	0.465633
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	−15.0000	−0.993399
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	60.0000	3.94771
$232$	2.00000	0.131306
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	−12.0000	−0.784465
$235$	0	0
$236$	−12.0000	−0.781133
$237$	−36.0000	−2.33845
$238$	12.0000	0.777844
$239$	6.00000	0.388108	0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000	0.388108	0.194054	+	0.980991i	$0.437836\pi$
$240$	0	0
$241$	−17.0000	−1.09507	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000	−1.09507	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	−10.0000	−0.640184
$245$	0	0
$246$	21.0000	1.33891
$247$	−10.0000	−0.636285
$248$	−6.00000	−0.381000
$249$	45.0000	2.85176
$250$	0	0
$251$	−13.0000	−0.820553	−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000	−0.820553	−0.410276	+	0.911961i	$0.634568\pi$
$252$	24.0000	1.51186
$253$	10.0000	0.628695
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	3.00000	0.186772
$259$	−32.0000	−1.98838
$260$	0	0
$261$	−12.0000	−0.742781
$262$	8.00000	0.494242
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	−15.0000	−0.923186
$265$	0	0
$266$	20.0000	1.22628
$267$	−45.0000	−2.75396
$268$	3.00000	0.183254
$269$	28.0000	1.70719	0.853595	−	0.520937i	$-0.174417\pi$
$269$	28.0000	1.70719	0.853595	+	0.520937i	$0.174417\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−3.00000	−0.181902
$273$	24.0000	1.45255
$274$	5.00000	0.302061
$275$	0	0
$276$	6.00000	0.361158
$277$	20.0000	1.20168	0.600842	−	0.799368i	$-0.294832\pi$
$277$	20.0000	1.20168	0.600842	+	0.799368i	$0.294832\pi$
$278$	−21.0000	−1.25950
$279$	36.0000	2.15526
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	11.0000	0.653882	0.326941	−	0.945045i	$-0.393982\pi$
$283$	11.0000	0.653882	0.326941	+	0.945045i	$0.393982\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−10.0000	−0.591312
$287$	−28.0000	−1.65279
$288$	−6.00000	−0.353553
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−42.0000	−2.46208
$292$	13.0000	0.760767
$293$	26.0000	1.51894	0.759468	−	0.650545i	$-0.225459\pi$
$293$	26.0000	1.51894	0.759468	+	0.650545i	$0.225459\pi$
$294$	−27.0000	−1.57467
$295$	0	0
$296$	8.00000	0.464991
$297$	45.0000	2.61116
$298$	14.0000	0.810998
$299$	4.00000	0.231326
$300$	0	0
$301$	−4.00000	−0.230556
$302$	−6.00000	−0.345261
$303$	30.0000	1.72345
$304$	−5.00000	−0.286770
$305$	0	0
$306$	18.0000	1.02899
$307$	13.0000	0.741949	0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000	0.741949	0.370975	+	0.928643i	$0.379024\pi$
$308$	20.0000	1.13961
$309$	18.0000	1.02398
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	−6.00000	−0.339683
$313$	−2.00000	−0.113047	−0.0565233	−	0.998401i	$-0.518002\pi$
$313$	−2.00000	−0.113047	−0.0565233	+	0.998401i	$0.518002\pi$
$314$	4.00000	0.225733
$315$	0	0
$316$	−12.0000	−0.675053
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	24.0000	1.34585
$319$	−10.0000	−0.559893
$320$	0	0
$321$	27.0000	1.50699
$322$	−8.00000	−0.445823
$323$	15.0000	0.834622
$324$	9.00000	0.500000
$325$	0	0
$326$	−25.0000	−1.38462
$327$	6.00000	0.331801
$328$	7.00000	0.386510
$329$	0	0
$330$	0	0
$331$	3.00000	0.164895	0.0824475	−	0.996595i	$-0.473726\pi$
$331$	3.00000	0.164895	0.0824475	+	0.996595i	$0.473726\pi$
$332$	15.0000	0.823232
$333$	−48.0000	−2.63038
$334$	−14.0000	−0.766046
$335$	0	0
$336$	12.0000	0.654654
$337$	−9.00000	−0.490261	−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000	−0.490261	−0.245131	+	0.969490i	$0.578831\pi$
$338$	9.00000	0.489535
$339$	−21.0000	−1.14056
$340$	0	0
$341$	30.0000	1.62459
$342$	30.0000	1.62221
$343$	8.00000	0.431959
$344$	1.00000	0.0539164
$345$	0	0
$346$	16.0000	0.860165
$347$	−1.00000	−0.0536828	−0.0268414	−	0.999640i	$-0.508545\pi$
$347$	−1.00000	−0.0536828	−0.0268414	+	0.999640i	$0.508545\pi$
$348$	−6.00000	−0.321634
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	18.0000	0.960769
$352$	−5.00000	−0.266501
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	36.0000	1.91338
$355$	0	0
$356$	−15.0000	−0.794998
$357$	−36.0000	−1.90532
$358$	1.00000	0.0528516
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	2.00000	0.105118
$363$	42.0000	2.20443
$364$	8.00000	0.419314
$365$	0	0
$366$	30.0000	1.56813
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	2.00000	0.104257
$369$	−42.0000	−2.18643
$370$	0	0
$371$	−32.0000	−1.66136
$372$	18.0000	0.933257
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	15.0000	0.775632
$375$	0	0
$376$	0	0
$377$	−4.00000	−0.206010
$378$	−36.0000	−1.85164
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	0	0
$381$	24.0000	1.22956
$382$	6.00000	0.306987
$383$	−20.0000	−1.02195	−0.510976	−	0.859595i	$-0.670716\pi$
$383$	−20.0000	−1.02195	−0.510976	+	0.859595i	$0.670716\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	−13.0000	−0.661683
$387$	−6.00000	−0.304997
$388$	−14.0000	−0.710742
$389$	36.0000	1.82527	0.912636	−	0.408773i	$-0.134043\pi$
$389$	36.0000	1.82527	0.912636	+	0.408773i	$0.134043\pi$
$390$	0	0
$391$	−6.00000	−0.303433
$392$	−9.00000	−0.454569
$393$	−24.0000	−1.21064
$394$	−20.0000	−1.00759
$395$	0	0
$396$	30.0000	1.50756
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	−20.0000	−1.00251
$399$	−60.0000	−3.00376
$400$	0	0
$401$	−15.0000	−0.749064	−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000	−0.749064	−0.374532	+	0.927214i	$0.622197\pi$
$402$	−9.00000	−0.448879
$403$	12.0000	0.597763
$404$	10.0000	0.497519
$405$	0	0
$406$	8.00000	0.397033
$407$	−40.0000	−1.98273
$408$	9.00000	0.445566
$409$	−33.0000	−1.63174	−0.815872	−	0.578232i	$-0.803743\pi$
$409$	−33.0000	−1.63174	−0.815872	+	0.578232i	$0.803743\pi$
$410$	0	0
$411$	−15.0000	−0.739895
$412$	6.00000	0.295599
$413$	−48.0000	−2.36193
$414$	−12.0000	−0.589768
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	63.0000	3.08512
$418$	25.0000	1.22279
$419$	7.00000	0.341972	0.170986	−	0.985273i	$-0.445305\pi$
$419$	7.00000	0.341972	0.170986	+	0.985273i	$0.445305\pi$
$420$	0	0
$421$	30.0000	1.46211	0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000	1.46211	0.731055	+	0.682318i	$0.239028\pi$
$422$	−25.0000	−1.21698
$423$	0	0
$424$	8.00000	0.388514
$425$	0	0
$426$	36.0000	1.74421
$427$	−40.0000	−1.93574
$428$	9.00000	0.435031
$429$	30.0000	1.44841
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	9.00000	0.433013
$433$	−29.0000	−1.39365	−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000	−1.39365	−0.696826	+	0.717241i	$0.745405\pi$
$434$	−24.0000	−1.15204
$435$	0	0
$436$	2.00000	0.0957826
$437$	−10.0000	−0.478365
$438$	−39.0000	−1.86349
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	54.0000	2.57143
$442$	6.00000	0.285391
$443$	−29.0000	−1.37783	−0.688916	−	0.724841i	$-0.741913\pi$
$443$	−29.0000	−1.37783	−0.688916	+	0.724841i	$0.741913\pi$
$444$	−24.0000	−1.13899
$445$	0	0
$446$	−8.00000	−0.378811
$447$	−42.0000	−1.98653
$448$	4.00000	0.188982
$449$	15.0000	0.707894	0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000	0.707894	0.353947	+	0.935266i	$0.384839\pi$
$450$	0	0
$451$	−35.0000	−1.64809
$452$	−7.00000	−0.329252
$453$	18.0000	0.845714
$454$	20.0000	0.938647
$455$	0	0
$456$	15.0000	0.702439
$457$	27.0000	1.26301	0.631503	−	0.775373i	$-0.282438\pi$
$457$	27.0000	1.26301	0.631503	+	0.775373i	$0.282438\pi$
$458$	2.00000	0.0934539
$459$	−27.0000	−1.26025
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	−60.0000	−2.79145
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	−2.00000	−0.0928477
$465$	0	0
$466$	26.0000	1.20443
$467$	32.0000	1.48078	0.740392	−	0.672176i	$-0.234640\pi$
$467$	32.0000	1.48078	0.740392	+	0.672176i	$0.234640\pi$
$468$	12.0000	0.554700
$469$	12.0000	0.554109
$470$	0	0
$471$	−12.0000	−0.552931
$472$	12.0000	0.552345
$473$	−5.00000	−0.229900
$474$	36.0000	1.65353
$475$	0	0
$476$	−12.0000	−0.550019
$477$	−48.0000	−2.19777
$478$	−6.00000	−0.274434
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	0	0
$481$	−16.0000	−0.729537
$482$	17.0000	0.774329
$483$	24.0000	1.09204
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	18.0000	0.815658	0.407829	−	0.913058i	$-0.366286\pi$
$487$	18.0000	0.815658	0.407829	+	0.913058i	$0.366286\pi$
$488$	10.0000	0.452679
$489$	75.0000	3.39162
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	−21.0000	−0.946753
$493$	6.00000	0.270226
$494$	10.0000	0.449921
$495$	0	0
$496$	6.00000	0.269408
$497$	−48.0000	−2.15309
$498$	−45.0000	−2.01650
$499$	−8.00000	−0.358129	−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000	−0.358129	−0.179065	+	0.983837i	$0.557307\pi$
$500$	0	0
$501$	42.0000	1.87642
$502$	13.0000	0.580218
$503$	14.0000	0.624229	0.312115	−	0.950044i	$-0.398963\pi$
$503$	14.0000	0.624229	0.312115	+	0.950044i	$0.398963\pi$
$504$	−24.0000	−1.06904
$505$	0	0
$506$	−10.0000	−0.444554
$507$	−27.0000	−1.19911
$508$	8.00000	0.354943
$509$	−16.0000	−0.709188	−0.354594	−	0.935020i	$-0.615381\pi$
$509$	−16.0000	−0.709188	−0.354594	+	0.935020i	$0.615381\pi$
$510$	0	0
$511$	52.0000	2.30034
$512$	−1.00000	−0.0441942
$513$	−45.0000	−1.98680
$514$	6.00000	0.264649
$515$	0	0
$516$	−3.00000	−0.132068
$517$	0	0
$518$	32.0000	1.40600
$519$	−48.0000	−2.10697
$520$	0	0
$521$	−33.0000	−1.44576	−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000	−1.44576	−0.722878	+	0.690976i	$0.757181\pi$
$522$	12.0000	0.525226
$523$	7.00000	0.306089	0.153044	−	0.988219i	$-0.451092\pi$
$523$	7.00000	0.306089	0.153044	+	0.988219i	$0.451092\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−30.0000	−1.30806
$527$	−18.0000	−0.784092
$528$	15.0000	0.652791
$529$	−19.0000	−0.826087
$530$	0	0
$531$	−72.0000	−3.12453
$532$	−20.0000	−0.867110
$533$	−14.0000	−0.606407
$534$	45.0000	1.94734
$535$	0	0
$536$	−3.00000	−0.129580
$537$	−3.00000	−0.129460
$538$	−28.0000	−1.20717
$539$	45.0000	1.93829
$540$	0	0
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	−20.0000	−0.859074
$543$	−6.00000	−0.257485
$544$	3.00000	0.128624
$545$	0	0
$546$	−24.0000	−1.02711
$547$	−39.0000	−1.66752	−0.833760	−	0.552127i	$-0.813816\pi$
$547$	−39.0000	−1.66752	−0.833760	+	0.552127i	$0.813816\pi$
$548$	−5.00000	−0.213589
$549$	−60.0000	−2.56074
$550$	0	0
$551$	10.0000	0.426014
$552$	−6.00000	−0.255377
$553$	−48.0000	−2.04117
$554$	−20.0000	−0.849719
$555$	0	0
$556$	21.0000	0.890598
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−36.0000	−1.52400
$559$	−2.00000	−0.0845910
$560$	0	0
$561$	−45.0000	−1.89990
$562$	6.00000	0.253095
$563$	−20.0000	−0.842900	−0.421450	−	0.906852i	$-0.638479\pi$
$563$	−20.0000	−0.842900	−0.421450	+	0.906852i	$0.638479\pi$
$564$	0	0
$565$	0	0
$566$	−11.0000	−0.462364
$567$	36.0000	1.51186
$568$	12.0000	0.503509
$569$	−23.0000	−0.964210	−0.482105	−	0.876113i	$-0.660128\pi$
$569$	−23.0000	−0.964210	−0.482105	+	0.876113i	$0.660128\pi$
$570$	0	0
$571$	4.00000	0.167395	0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000	0.167395	0.0836974	+	0.996491i	$0.473327\pi$
$572$	10.0000	0.418121
$573$	−18.0000	−0.751961
$574$	28.0000	1.16870
$575$	0	0
$576$	6.00000	0.250000
$577$	45.0000	1.87337	0.936687	−	0.350167i	$-0.113875\pi$
$577$	45.0000	1.87337	0.936687	+	0.350167i	$0.113875\pi$
$578$	8.00000	0.332756
$579$	39.0000	1.62078
$580$	0	0
$581$	60.0000	2.48922
$582$	42.0000	1.74096
$583$	−40.0000	−1.65663
$584$	−13.0000	−0.537944
$585$	0	0
$586$	−26.0000	−1.07405
$587$	5.00000	0.206372	0.103186	−	0.994662i	$-0.467096\pi$
$587$	5.00000	0.206372	0.103186	+	0.994662i	$0.467096\pi$
$588$	27.0000	1.11346
$589$	−30.0000	−1.23613
$590$	0	0
$591$	60.0000	2.46807
$592$	−8.00000	−0.328798
$593$	−3.00000	−0.123195	−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000	−0.123195	−0.0615976	+	0.998101i	$0.519620\pi$
$594$	−45.0000	−1.84637
$595$	0	0
$596$	−14.0000	−0.573462
$597$	60.0000	2.45564
$598$	−4.00000	−0.163572
$599$	2.00000	0.0817178	0.0408589	−	0.999165i	$-0.486991\pi$
$599$	2.00000	0.0817178	0.0408589	+	0.999165i	$0.486991\pi$
$600$	0	0
$601$	−3.00000	−0.122373	−0.0611863	−	0.998126i	$-0.519488\pi$
$601$	−3.00000	−0.122373	−0.0611863	+	0.998126i	$0.519488\pi$
$602$	4.00000	0.163028
$603$	18.0000	0.733017
$604$	6.00000	0.244137
$605$	0	0
$606$	−30.0000	−1.21867
$607$	−18.0000	−0.730597	−0.365299	−	0.930890i	$-0.619033\pi$
$607$	−18.0000	−0.730597	−0.365299	+	0.930890i	$0.619033\pi$
$608$	5.00000	0.202777
$609$	−24.0000	−0.972529
$610$	0	0
$611$	0	0
$612$	−18.0000	−0.727607
$613$	16.0000	0.646234	0.323117	−	0.946359i	$-0.395269\pi$
$613$	16.0000	0.646234	0.323117	+	0.946359i	$0.395269\pi$
$614$	−13.0000	−0.524637
$615$	0	0
$616$	−20.0000	−0.805823
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−18.0000	−0.724066
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	18.0000	0.722315
$622$	−18.0000	−0.721734
$623$	−60.0000	−2.40385
$624$	6.00000	0.240192
$625$	0	0
$626$	2.00000	0.0799361
$627$	−75.0000	−2.99521
$628$	−4.00000	−0.159617
$629$	24.0000	0.956943
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	12.0000	0.477334
$633$	75.0000	2.98098
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	−24.0000	−0.951662
$637$	18.0000	0.713186
$638$	10.0000	0.395904
$639$	−72.0000	−2.84828
$640$	0	0
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	−27.0000	−1.06561
$643$	−12.0000	−0.473234	−0.236617	−	0.971603i	$-0.576039\pi$
$643$	−12.0000	−0.473234	−0.236617	+	0.971603i	$0.576039\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	−15.0000	−0.590167
$647$	26.0000	1.02217	0.511083	−	0.859532i	$-0.329245\pi$
$647$	26.0000	1.02217	0.511083	+	0.859532i	$0.329245\pi$
$648$	−9.00000	−0.353553
$649$	−60.0000	−2.35521
$650$	0	0
$651$	72.0000	2.82190
$652$	25.0000	0.979076
$653$	−36.0000	−1.40879	−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000	−1.40879	−0.704394	+	0.709809i	$0.748781\pi$
$654$	−6.00000	−0.234619
$655$	0	0
$656$	−7.00000	−0.273304
$657$	78.0000	3.04307
$658$	0	0
$659$	11.0000	0.428499	0.214250	−	0.976779i	$-0.431269\pi$
$659$	11.0000	0.428499	0.214250	+	0.976779i	$0.431269\pi$
$660$	0	0
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−3.00000	−0.116598
$663$	−18.0000	−0.699062
$664$	−15.0000	−0.582113
$665$	0	0
$666$	48.0000	1.85996
$667$	−4.00000	−0.154881
$668$	14.0000	0.541676
$669$	24.0000	0.927894
$670$	0	0
$671$	−50.0000	−1.93023
$672$	−12.0000	−0.462910
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	9.00000	0.346667
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	21.0000	0.806500
$679$	−56.0000	−2.14908
$680$	0	0
$681$	−60.0000	−2.29920
$682$	−30.0000	−1.14876
$683$	−23.0000	−0.880071	−0.440035	−	0.897980i	$-0.645034\pi$
$683$	−23.0000	−0.880071	−0.440035	+	0.897980i	$0.645034\pi$
$684$	−30.0000	−1.14708
$685$	0	0
$686$	−8.00000	−0.305441
$687$	−6.00000	−0.228914
$688$	−1.00000	−0.0381246
$689$	−16.0000	−0.609551
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	−16.0000	−0.608229
$693$	120.000	4.55842
$694$	1.00000	0.0379595
$695$	0	0
$696$	6.00000	0.227429
$697$	21.0000	0.795432
$698$	26.0000	0.984115
$699$	−78.0000	−2.95023
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	−18.0000	−0.679366
$703$	40.0000	1.50863
$704$	5.00000	0.188445
$705$	0	0
$706$	−14.0000	−0.526897
$707$	40.0000	1.50435
$708$	−36.0000	−1.35296
$709$	−10.0000	−0.375558	−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000	−0.375558	−0.187779	+	0.982211i	$0.560129\pi$
$710$	0	0
$711$	−72.0000	−2.70021
$712$	15.0000	0.562149
$713$	12.0000	0.449404
$714$	36.0000	1.34727
$715$	0	0
$716$	−1.00000	−0.0373718
$717$	18.0000	0.672222
$718$	0	0
$719$	2.00000	0.0745874	0.0372937	−	0.999304i	$-0.488126\pi$
$719$	2.00000	0.0745874	0.0372937	+	0.999304i	$0.488126\pi$
$720$	0	0
$721$	24.0000	0.893807
$722$	−6.00000	−0.223297
$723$	−51.0000	−1.89671
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	−42.0000	−1.55877
$727$	12.0000	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$728$	−8.00000	−0.296500
$729$	−27.0000	−1.00000
$730$	0	0
$731$	3.00000	0.110959
$732$	−30.0000	−1.10883
$733$	34.0000	1.25582	0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000	1.25582	0.627909	+	0.778287i	$0.283911\pi$
$734$	−4.00000	−0.147643
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	15.0000	0.552532
$738$	42.0000	1.54604
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	0	0
$741$	−30.0000	−1.10208
$742$	32.0000	1.17476
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−18.0000	−0.659912
$745$	0	0
$746$	36.0000	1.31805
$747$	90.0000	3.29293
$748$	−15.0000	−0.548454
$749$	36.0000	1.31541
$750$	0	0
$751$	22.0000	0.802791	0.401396	−	0.915905i	$-0.368525\pi$
$751$	22.0000	0.802791	0.401396	+	0.915905i	$0.368525\pi$
$752$	0	0
$753$	−39.0000	−1.42124
$754$	4.00000	0.145671
$755$	0	0
$756$	36.0000	1.30931
$757$	8.00000	0.290765	0.145382	−	0.989376i	$-0.453559\pi$
$757$	8.00000	0.290765	0.145382	+	0.989376i	$0.453559\pi$
$758$	5.00000	0.181608
$759$	30.0000	1.08893
$760$	0	0
$761$	43.0000	1.55875	0.779374	−	0.626559i	$-0.215537\pi$
$761$	43.0000	1.55875	0.779374	+	0.626559i	$0.215537\pi$
$762$	−24.0000	−0.869428
$763$	8.00000	0.289619
$764$	−6.00000	−0.217072
$765$	0	0
$766$	20.0000	0.722629
$767$	−24.0000	−0.866590
$768$	3.00000	0.108253
$769$	−23.0000	−0.829401	−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000	−0.829401	−0.414701	+	0.909958i	$0.636114\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	13.0000	0.467880
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	6.00000	0.215666
$775$	0	0
$776$	14.0000	0.502571
$777$	−96.0000	−3.44398
$778$	−36.0000	−1.29066
$779$	35.0000	1.25401
$780$	0	0
$781$	−60.0000	−2.14697
$782$	6.00000	0.214560
$783$	−18.0000	−0.643268
$784$	9.00000	0.321429
$785$	0	0
$786$	24.0000	0.856052
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	20.0000	0.712470
$789$	90.0000	3.20408
$790$	0	0
$791$	−28.0000	−0.995565
$792$	−30.0000	−1.06600
$793$	−20.0000	−0.710221
$794$	8.00000	0.283909
$795$	0	0
$796$	20.0000	0.708881
$797$	38.0000	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$798$	60.0000	2.12398
$799$	0	0
$800$	0	0
$801$	−90.0000	−3.17999
$802$	15.0000	0.529668
$803$	65.0000	2.29380
$804$	9.00000	0.317406
$805$	0	0
$806$	−12.0000	−0.422682
$807$	84.0000	2.95694
$808$	−10.0000	−0.351799
$809$	−22.0000	−0.773479	−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000	−0.773479	−0.386739	+	0.922189i	$0.626399\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	−8.00000	−0.280745
$813$	60.0000	2.10429
$814$	40.0000	1.40200
$815$	0	0
$816$	−9.00000	−0.315063
$817$	5.00000	0.174928
$818$	33.0000	1.15382
$819$	48.0000	1.67726
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	15.0000	0.523185
$823$	−50.0000	−1.74289	−0.871445	−	0.490493i	$-0.836817\pi$
$823$	−50.0000	−1.74289	−0.871445	+	0.490493i	$0.836817\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	48.0000	1.67013
$827$	−9.00000	−0.312961	−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000	−0.312961	−0.156480	+	0.987681i	$0.550015\pi$
$828$	12.0000	0.417029
$829$	−8.00000	−0.277851	−0.138926	−	0.990303i	$-0.544365\pi$
$829$	−8.00000	−0.277851	−0.138926	+	0.990303i	$0.544365\pi$
$830$	0	0
$831$	60.0000	2.08138
$832$	2.00000	0.0693375
$833$	−27.0000	−0.935495
$834$	−63.0000	−2.18151
$835$	0	0
$836$	−25.0000	−0.864643
$837$	54.0000	1.86651
$838$	−7.00000	−0.241811
$839$	−30.0000	−1.03572	−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000	−1.03572	−0.517858	+	0.855467i	$0.673270\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−30.0000	−1.03387
$843$	−18.0000	−0.619953
$844$	25.0000	0.860535
$845$	0	0
$846$	0	0
$847$	56.0000	1.92418
$848$	−8.00000	−0.274721
$849$	33.0000	1.13256
$850$	0	0
$851$	−16.0000	−0.548473
$852$	−36.0000	−1.23334
$853$	−50.0000	−1.71197	−0.855984	−	0.517003i	$-0.827048\pi$
$853$	−50.0000	−1.71197	−0.855984	+	0.517003i	$0.827048\pi$
$854$	40.0000	1.36877
$855$	0	0
$856$	−9.00000	−0.307614
$857$	33.0000	1.12726	0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000	1.12726	0.563629	+	0.826028i	$0.309405\pi$
$858$	−30.0000	−1.02418
$859$	35.0000	1.19418	0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000	1.19418	0.597092	+	0.802173i	$0.296323\pi$
$860$	0	0
$861$	−84.0000	−2.86271
$862$	−12.0000	−0.408722
$863$	−4.00000	−0.136162	−0.0680808	−	0.997680i	$-0.521688\pi$
$863$	−4.00000	−0.136162	−0.0680808	+	0.997680i	$0.521688\pi$
$864$	−9.00000	−0.306186
$865$	0	0
$866$	29.0000	0.985460
$867$	−24.0000	−0.815083
$868$	24.0000	0.814613
$869$	−60.0000	−2.03536
$870$	0	0
$871$	6.00000	0.203302
$872$	−2.00000	−0.0677285
$873$	−84.0000	−2.84297
$874$	10.0000	0.338255
$875$	0	0
$876$	39.0000	1.31769
$877$	4.00000	0.135070	0.0675352	−	0.997717i	$-0.478487\pi$
$877$	4.00000	0.135070	0.0675352	+	0.997717i	$0.478487\pi$
$878$	−24.0000	−0.809961
$879$	78.0000	2.63087
$880$	0	0
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	−54.0000	−1.81827
$883$	−15.0000	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$883$	−15.0000	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$884$	−6.00000	−0.201802
$885$	0	0
$886$	29.0000	0.974274
$887$	14.0000	0.470074	0.235037	−	0.971986i	$-0.424479\pi$
$887$	14.0000	0.470074	0.235037	+	0.971986i	$0.424479\pi$
$888$	24.0000	0.805387
$889$	32.0000	1.07325
$890$	0	0
$891$	45.0000	1.50756
$892$	8.00000	0.267860
$893$	0	0
$894$	42.0000	1.40469
$895$	0	0
$896$	−4.00000	−0.133631
$897$	12.0000	0.400668
$898$	−15.0000	−0.500556
$899$	−12.0000	−0.400222
$900$	0	0
$901$	24.0000	0.799556
$902$	35.0000	1.16537
$903$	−12.0000	−0.399335
$904$	7.00000	0.232817
$905$	0	0
$906$	−18.0000	−0.598010
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	−20.0000	−0.663723
$909$	60.0000	1.99007
$910$	0	0
$911$	−2.00000	−0.0662630	−0.0331315	−	0.999451i	$-0.510548\pi$
$911$	−2.00000	−0.0662630	−0.0331315	+	0.999451i	$0.510548\pi$
$912$	−15.0000	−0.496700
$913$	75.0000	2.48214
$914$	−27.0000	−0.893081
$915$	0	0
$916$	−2.00000	−0.0660819
$917$	−32.0000	−1.05673
$918$	27.0000	0.891133
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	39.0000	1.28509
$922$	−18.0000	−0.592798
$923$	−24.0000	−0.789970
$924$	60.0000	1.97386
$925$	0	0
$926$	−22.0000	−0.722965
$927$	36.0000	1.18240
$928$	2.00000	0.0656532
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	0	0
$931$	−45.0000	−1.47482
$932$	−26.0000	−0.851658
$933$	54.0000	1.76788
$934$	−32.0000	−1.04707
$935$	0	0
$936$	−12.0000	−0.392232
$937$	−47.0000	−1.53542	−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000	−1.53542	−0.767712	+	0.640796i	$0.778605\pi$
$938$	−12.0000	−0.391814
$939$	−6.00000	−0.195803
$940$	0	0
$941$	50.0000	1.62995	0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000	1.62995	0.814977	+	0.579494i	$0.196750\pi$
$942$	12.0000	0.390981
$943$	−14.0000	−0.455903
$944$	−12.0000	−0.390567
$945$	0	0
$946$	5.00000	0.162564
$947$	−28.0000	−0.909878	−0.454939	−	0.890523i	$-0.650339\pi$
$947$	−28.0000	−0.909878	−0.454939	+	0.890523i	$0.650339\pi$
$948$	−36.0000	−1.16923
$949$	26.0000	0.843996
$950$	0	0
$951$	6.00000	0.194563
$952$	12.0000	0.388922
$953$	23.0000	0.745043	0.372522	−	0.928024i	$-0.378493\pi$
$953$	23.0000	0.745043	0.372522	+	0.928024i	$0.378493\pi$
$954$	48.0000	1.55406
$955$	0	0
$956$	6.00000	0.194054
$957$	−30.0000	−0.969762
$958$	20.0000	0.646171
$959$	−20.0000	−0.645834
$960$	0	0
$961$	5.00000	0.161290
$962$	16.0000	0.515861
$963$	54.0000	1.74013
$964$	−17.0000	−0.547533
$965$	0	0
$966$	−24.0000	−0.772187
$967$	60.0000	1.92947	0.964735	−	0.263223i	$-0.0847856\pi$
$967$	60.0000	1.92947	0.964735	+	0.263223i	$0.0847856\pi$
$968$	−14.0000	−0.449977
$969$	45.0000	1.44561
$970$	0	0
$971$	−3.00000	−0.0962746	−0.0481373	−	0.998841i	$-0.515328\pi$
$971$	−3.00000	−0.0962746	−0.0481373	+	0.998841i	$0.515328\pi$
$972$	0	0
$973$	84.0000	2.69292
$974$	−18.0000	−0.576757
$975$	0	0
$976$	−10.0000	−0.320092
$977$	25.0000	0.799821	0.399910	−	0.916554i	$-0.369041\pi$
$977$	25.0000	0.799821	0.399910	+	0.916554i	$0.369041\pi$
$978$	−75.0000	−2.39824
$979$	−75.0000	−2.39701
$980$	0	0
$981$	12.0000	0.383131
$982$	12.0000	0.382935
$983$	14.0000	0.446531	0.223265	−	0.974758i	$-0.428328\pi$
$983$	14.0000	0.446531	0.223265	+	0.974758i	$0.428328\pi$
$984$	21.0000	0.669456
$985$	0	0
$986$	−6.00000	−0.191079
$987$	0	0
$988$	−10.0000	−0.318142
$989$	−2.00000	−0.0635963
$990$	0	0
$991$	52.0000	1.65183	0.825917	−	0.563791i	$-0.190658\pi$
$991$	52.0000	1.65183	0.825917	+	0.563791i	$0.190658\pi$
$992$	−6.00000	−0.190500
$993$	9.00000	0.285606
$994$	48.0000	1.52247
$995$	0	0
$996$	45.0000	1.42588
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	8.00000	0.253236
$999$	−72.0000	−2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2150.2.a.i.1.1	✓	1
5.2	odd	4		2150.2.b.b.1549.1		2
5.3	odd	4		2150.2.b.b.1549.2		2
5.4	even	2		2150.2.a.j.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2150.2.a.i.1.1	✓	1	1.1	even	1	trivial
2150.2.a.j.1.1	yes	1	5.4	even	2
2150.2.b.b.1549.1		2	5.2	odd	4
2150.2.b.b.1549.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 2150 = 2 \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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