LMFDB - Embedded newform 1850.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
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	$\chi$	$=$	1850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} -3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} -1.00000 q^{11} +3.00000 q^{12} +2.00000 q^{13} +1.00000 q^{16} +7.00000 q^{17} -6.00000 q^{18} +5.00000 q^{19} +1.00000 q^{22} -6.00000 q^{23} -3.00000 q^{24} -2.00000 q^{26} +9.00000 q^{27} -4.00000 q^{31} -1.00000 q^{32} -3.00000 q^{33} -7.00000 q^{34} +6.00000 q^{36} -1.00000 q^{37} -5.00000 q^{38} +6.00000 q^{39} -3.00000 q^{41} +4.00000 q^{43} -1.00000 q^{44} +6.00000 q^{46} +4.00000 q^{47} +3.00000 q^{48} -7.00000 q^{49} +21.0000 q^{51} +2.00000 q^{52} -2.00000 q^{53} -9.00000 q^{54} +15.0000 q^{57} +4.00000 q^{59} -8.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} +3.00000 q^{66} +13.0000 q^{67} +7.00000 q^{68} -18.0000 q^{69} -6.00000 q^{71} -6.00000 q^{72} +7.00000 q^{73} +1.00000 q^{74} +5.00000 q^{76} -6.00000 q^{78} +14.0000 q^{79} +9.00000 q^{81} +3.00000 q^{82} -3.00000 q^{83} -4.00000 q^{86} +1.00000 q^{88} -7.00000 q^{89} -6.00000 q^{92} -12.0000 q^{93} -4.00000 q^{94} -3.00000 q^{96} +18.0000 q^{97} +7.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	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	$0.410544\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	−6.00000	−1.41421
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	0	0
$22$	1.00000	0.213201
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	−3.00000	−0.612372
$25$	0	0
$26$	−2.00000	−0.392232
$27$	9.00000	1.73205
$28$	0	0
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	−3.00000	−0.522233
$34$	−7.00000	−1.20049
$35$	0	0
$36$	6.00000	1.00000
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.00000	−0.811107
$39$	6.00000	0.960769
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	6.00000	0.884652
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	3.00000	0.433013
$49$	−7.00000	−1.00000
$50$	0	0
$51$	21.0000	2.94059
$52$	2.00000	0.277350
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−9.00000	−1.22474
$55$	0	0
$56$	0	0
$57$	15.0000	1.98680
$58$	0	0
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	7.00000	0.848875
$69$	−18.0000	−2.16695
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−6.00000	−0.707107
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	5.00000	0.573539
$77$	0	0
$78$	−6.00000	−0.679366
$79$	14.0000	1.57512	0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000	1.57512	0.787562	+	0.616236i	$0.211343\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	3.00000	0.331295
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	1.00000	0.106600
$89$	−7.00000	−0.741999	−0.370999	−	0.928633i	$-0.620985\pi$
$89$	−7.00000	−0.741999	−0.370999	+	0.928633i	$0.620985\pi$
$90$	0	0
$91$	0	0
$92$	−6.00000	−0.625543
$93$	−12.0000	−1.24434
$94$	−4.00000	−0.412568
$95$	0	0
$96$	−3.00000	−0.306186
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	7.00000	0.707107
$99$	−6.00000	−0.603023
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−21.0000	−2.07931
$103$	18.0000	1.77359	0.886796	−	0.462160i	$-0.152926\pi$
$103$	18.0000	1.77359	0.886796	+	0.462160i	$0.152926\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	2.00000	0.194257
$107$	−5.00000	−0.483368	−0.241684	−	0.970355i	$-0.577700\pi$
$107$	−5.00000	−0.483368	−0.241684	+	0.970355i	$0.577700\pi$
$108$	9.00000	0.866025
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	−3.00000	−0.284747
$112$	0	0
$113$	17.0000	1.59923	0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000	1.59923	0.799613	+	0.600516i	$0.205038\pi$
$114$	−15.0000	−1.40488
$115$	0	0
$116$	0	0
$117$	12.0000	1.10940
$118$	−4.00000	−0.368230
$119$	0	0
$120$	0	0
$121$	−10.0000	−0.909091
$122$	8.00000	0.724286
$123$	−9.00000	−0.811503
$124$	−4.00000	−0.359211
$125$	0	0
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	12.0000	1.05654
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.00000	−0.261116
$133$	0	0
$134$	−13.0000	−1.12303
$135$	0	0
$136$	−7.00000	−0.600245
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	18.0000	1.53226
$139$	−1.00000	−0.0848189	−0.0424094	−	0.999100i	$-0.513503\pi$
$139$	−1.00000	−0.0848189	−0.0424094	+	0.999100i	$0.513503\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	6.00000	0.503509
$143$	−2.00000	−0.167248
$144$	6.00000	0.500000
$145$	0	0
$146$	−7.00000	−0.579324
$147$	−21.0000	−1.73205
$148$	−1.00000	−0.0821995
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	−5.00000	−0.405554
$153$	42.0000	3.39550
$154$	0	0
$155$	0	0
$156$	6.00000	0.480384
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−14.0000	−1.11378
$159$	−6.00000	−0.475831
$160$	0	0
$161$	0	0
$162$	−9.00000	−0.707107
$163$	−1.00000	−0.0783260	−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000	−0.0783260	−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	3.00000	0.232845
$167$	2.00000	0.154765	0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000	0.154765	0.0773823	+	0.997001i	$0.475344\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	30.0000	2.29416
$172$	4.00000	0.304997
$173$	−8.00000	−0.608229	−0.304114	−	0.952636i	$-0.598361\pi$
$173$	−8.00000	−0.608229	−0.304114	+	0.952636i	$0.598361\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	12.0000	0.901975
$178$	7.00000	0.524672
$179$	13.0000	0.971666	0.485833	−	0.874052i	$-0.338516\pi$
$179$	13.0000	0.971666	0.485833	+	0.874052i	$0.338516\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	−24.0000	−1.77413
$184$	6.00000	0.442326
$185$	0	0
$186$	12.0000	0.879883
$187$	−7.00000	−0.511891
$188$	4.00000	0.291730
$189$	0	0
$190$	0	0
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	3.00000	0.216506
$193$	−25.0000	−1.79954	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−25.0000	−1.79954	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−18.0000	−1.29232
$195$	0	0
$196$	−7.00000	−0.500000
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	6.00000	0.426401
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	39.0000	2.75085
$202$	−6.00000	−0.422159
$203$	0	0
$204$	21.0000	1.47029
$205$	0	0
$206$	−18.0000	−1.25412
$207$	−36.0000	−2.50217
$208$	2.00000	0.138675
$209$	−5.00000	−0.345857
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	−2.00000	−0.137361
$213$	−18.0000	−1.23334
$214$	5.00000	0.341793
$215$	0	0
$216$	−9.00000	−0.612372
$217$	0	0
$218$	6.00000	0.406371
$219$	21.0000	1.41905
$220$	0	0
$221$	14.0000	0.941742
$222$	3.00000	0.201347
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	0	0
$226$	−17.0000	−1.13082
$227$	−28.0000	−1.85843	−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000	−1.85843	−0.929213	+	0.369546i	$0.879513\pi$
$228$	15.0000	0.993399
$229$	24.0000	1.58596	0.792982	−	0.609245i	$-0.208527\pi$
$229$	24.0000	1.58596	0.792982	+	0.609245i	$0.208527\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−12.0000	−0.784465
$235$	0	0
$236$	4.00000	0.260378
$237$	42.0000	2.72819
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	−8.00000	−0.512148
$245$	0	0
$246$	9.00000	0.573819
$247$	10.0000	0.636285
$248$	4.00000	0.254000
$249$	−9.00000	−0.570352
$250$	0	0
$251$	−1.00000	−0.0631194	−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000	−0.0631194	−0.0315597	+	0.999502i	$0.510047\pi$
$252$	0	0
$253$	6.00000	0.377217
$254$	4.00000	0.250982
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−12.0000	−0.747087
$259$	0	0
$260$	0	0
$261$	0	0
$262$	12.0000	0.741362
$263$	−14.0000	−0.863277	−0.431638	−	0.902047i	$-0.642064\pi$
$263$	−14.0000	−0.863277	−0.431638	+	0.902047i	$0.642064\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	0	0
$267$	−21.0000	−1.28518
$268$	13.0000	0.794101
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	7.00000	0.424437
$273$	0	0
$274$	15.0000	0.906183
$275$	0	0
$276$	−18.0000	−1.08347
$277$	20.0000	1.20168	0.600842	−	0.799368i	$-0.294832\pi$
$277$	20.0000	1.20168	0.600842	+	0.799368i	$0.294832\pi$
$278$	1.00000	0.0599760
$279$	−24.0000	−1.43684
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	−12.0000	−0.714590
$283$	7.00000	0.416107	0.208053	−	0.978117i	$-0.433287\pi$
$283$	7.00000	0.416107	0.208053	+	0.978117i	$0.433287\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	−6.00000	−0.353553
$289$	32.0000	1.88235
$290$	0	0
$291$	54.0000	3.16554
$292$	7.00000	0.409644
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	21.0000	1.22474
$295$	0	0
$296$	1.00000	0.0581238
$297$	−9.00000	−0.522233
$298$	22.0000	1.27443
$299$	−12.0000	−0.693978
$300$	0	0
$301$	0	0
$302$	18.0000	1.03578
$303$	18.0000	1.03407
$304$	5.00000	0.286770
$305$	0	0
$306$	−42.0000	−2.40098
$307$	7.00000	0.399511	0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000	0.399511	0.199756	+	0.979846i	$0.435985\pi$
$308$	0	0
$309$	54.0000	3.07195
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	−6.00000	−0.339683
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	14.0000	0.787562
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	6.00000	0.336463
$319$	0	0
$320$	0	0
$321$	−15.0000	−0.837218
$322$	0	0
$323$	35.0000	1.94745
$324$	9.00000	0.500000
$325$	0	0
$326$	1.00000	0.0553849
$327$	−18.0000	−0.995402
$328$	3.00000	0.165647
$329$	0	0
$330$	0	0
$331$	−19.0000	−1.04433	−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000	−1.04433	−0.522167	+	0.852843i	$0.674876\pi$
$332$	−3.00000	−0.164646
$333$	−6.00000	−0.328798
$334$	−2.00000	−0.109435
$335$	0	0
$336$	0	0
$337$	31.0000	1.68868	0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000	1.68868	0.844339	+	0.535810i	$0.179994\pi$
$338$	9.00000	0.489535
$339$	51.0000	2.76994
$340$	0	0
$341$	4.00000	0.216612
$342$	−30.0000	−1.62221
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	8.00000	0.430083
$347$	−23.0000	−1.23470	−0.617352	−	0.786687i	$-0.711795\pi$
$347$	−23.0000	−1.23470	−0.617352	+	0.786687i	$0.711795\pi$
$348$	0	0
$349$	−12.0000	−0.642345	−0.321173	−	0.947021i	$-0.604077\pi$
$349$	−12.0000	−0.642345	−0.321173	+	0.947021i	$0.604077\pi$
$350$	0	0
$351$	18.0000	0.960769
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−7.00000	−0.370999
$357$	0	0
$358$	−13.0000	−0.687071
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	2.00000	0.105118
$363$	−30.0000	−1.57459
$364$	0	0
$365$	0	0
$366$	24.0000	1.25450
$367$	26.0000	1.35719	0.678594	−	0.734513i	$-0.262589\pi$
$367$	26.0000	1.35719	0.678594	+	0.734513i	$0.262589\pi$
$368$	−6.00000	−0.312772
$369$	−18.0000	−0.937043
$370$	0	0
$371$	0	0
$372$	−12.0000	−0.622171
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	7.00000	0.361961
$375$	0	0
$376$	−4.00000	−0.206284
$377$	0	0
$378$	0	0
$379$	−19.0000	−0.975964	−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000	−0.975964	−0.487982	+	0.872854i	$0.662267\pi$
$380$	0	0
$381$	−12.0000	−0.614779
$382$	−6.00000	−0.306987
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	−3.00000	−0.153093
$385$	0	0
$386$	25.0000	1.27247
$387$	24.0000	1.21999
$388$	18.0000	0.913812
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	0	0
$391$	−42.0000	−2.12403
$392$	7.00000	0.353553
$393$	−36.0000	−1.81596
$394$	−8.00000	−0.403034
$395$	0	0
$396$	−6.00000	−0.301511
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	0	0
$401$	23.0000	1.14857	0.574283	−	0.818657i	$-0.305281\pi$
$401$	23.0000	1.14857	0.574283	+	0.818657i	$0.305281\pi$
$402$	−39.0000	−1.94514
$403$	−8.00000	−0.398508
$404$	6.00000	0.298511
$405$	0	0
$406$	0	0
$407$	1.00000	0.0495682
$408$	−21.0000	−1.03965
$409$	11.0000	0.543915	0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000	0.543915	0.271957	+	0.962309i	$0.412329\pi$
$410$	0	0
$411$	−45.0000	−2.21969
$412$	18.0000	0.886796
$413$	0	0
$414$	36.0000	1.76930
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	−3.00000	−0.146911
$418$	5.00000	0.244558
$419$	−17.0000	−0.830504	−0.415252	−	0.909706i	$-0.636307\pi$
$419$	−17.0000	−0.830504	−0.415252	+	0.909706i	$0.636307\pi$
$420$	0	0
$421$	24.0000	1.16969	0.584844	−	0.811146i	$-0.301156\pi$
$421$	24.0000	1.16969	0.584844	+	0.811146i	$0.301156\pi$
$422$	−13.0000	−0.632830
$423$	24.0000	1.16692
$424$	2.00000	0.0971286
$425$	0	0
$426$	18.0000	0.872103
$427$	0	0
$428$	−5.00000	−0.241684
$429$	−6.00000	−0.289683
$430$	0	0
$431$	−38.0000	−1.83040	−0.915198	−	0.403005i	$-0.867966\pi$
$431$	−38.0000	−1.83040	−0.915198	+	0.403005i	$0.867966\pi$
$432$	9.00000	0.433013
$433$	−11.0000	−0.528626	−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000	−0.528626	−0.264313	+	0.964437i	$0.585145\pi$
$434$	0	0
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−30.0000	−1.43509
$438$	−21.0000	−1.00342
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	−42.0000	−2.00000
$442$	−14.0000	−0.665912
$443$	−15.0000	−0.712672	−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000	−0.712672	−0.356336	+	0.934358i	$0.615974\pi$
$444$	−3.00000	−0.142374
$445$	0	0
$446$	16.0000	0.757622
$447$	−66.0000	−3.12169
$448$	0	0
$449$	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
$451$	3.00000	0.141264
$452$	17.0000	0.799613
$453$	−54.0000	−2.53714
$454$	28.0000	1.31411
$455$	0	0
$456$	−15.0000	−0.702439
$457$	−21.0000	−0.982339	−0.491169	−	0.871064i	$-0.663430\pi$
$457$	−21.0000	−0.982339	−0.491169	+	0.871064i	$0.663430\pi$
$458$	−24.0000	−1.12145
$459$	63.0000	2.94059
$460$	0	0
$461$	4.00000	0.186299	0.0931493	−	0.995652i	$-0.470307\pi$
$461$	4.00000	0.186299	0.0931493	+	0.995652i	$0.470307\pi$
$462$	0	0
$463$	26.0000	1.20832	0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000	1.20832	0.604161	+	0.796862i	$0.293508\pi$
$464$	0	0
$465$	0	0
$466$	−14.0000	−0.648537
$467$	4.00000	0.185098	0.0925490	−	0.995708i	$-0.470499\pi$
$467$	4.00000	0.185098	0.0925490	+	0.995708i	$0.470499\pi$
$468$	12.0000	0.554700
$469$	0	0
$470$	0	0
$471$	−36.0000	−1.65879
$472$	−4.00000	−0.184115
$473$	−4.00000	−0.183920
$474$	−42.0000	−1.92912
$475$	0	0
$476$	0	0
$477$	−12.0000	−0.549442
$478$	−12.0000	−0.548867
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	25.0000	1.13872
$483$	0	0
$484$	−10.0000	−0.454545
$485$	0	0
$486$	0	0
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	8.00000	0.362143
$489$	−3.00000	−0.135665
$490$	0	0
$491$	44.0000	1.98569	0.992846	−	0.119401i	$-0.0380974\pi$
$491$	44.0000	1.98569	0.992846	+	0.119401i	$0.0380974\pi$
$492$	−9.00000	−0.405751
$493$	0	0
$494$	−10.0000	−0.449921
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	9.00000	0.403300
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	1.00000	0.0446322
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	0	0
$506$	−6.00000	−0.266733
$507$	−27.0000	−1.19911
$508$	−4.00000	−0.177471
$509$	−36.0000	−1.59567	−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000	−1.59567	−0.797836	+	0.602875i	$0.794022\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	45.0000	1.98680
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	12.0000	0.528271
$517$	−4.00000	−0.175920
$518$	0	0
$519$	−24.0000	−1.05348
$520$	0	0
$521$	−35.0000	−1.53338	−0.766689	−	0.642019i	$-0.778097\pi$
$521$	−35.0000	−1.53338	−0.766689	+	0.642019i	$0.778097\pi$
$522$	0	0
$523$	45.0000	1.96771	0.983856	−	0.178960i	$-0.0572733\pi$
$523$	45.0000	1.96771	0.983856	+	0.178960i	$0.0572733\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	14.0000	0.610429
$527$	−28.0000	−1.21970
$528$	−3.00000	−0.130558
$529$	13.0000	0.565217
$530$	0	0
$531$	24.0000	1.04151
$532$	0	0
$533$	−6.00000	−0.259889
$534$	21.0000	0.908759
$535$	0	0
$536$	−13.0000	−0.561514
$537$	39.0000	1.68297
$538$	4.00000	0.172452
$539$	7.00000	0.301511
$540$	0	0
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−16.0000	−0.687259
$543$	−6.00000	−0.257485
$544$	−7.00000	−0.300123
$545$	0	0
$546$	0	0
$547$	−11.0000	−0.470326	−0.235163	−	0.971956i	$-0.575562\pi$
$547$	−11.0000	−0.470326	−0.235163	+	0.971956i	$0.575562\pi$
$548$	−15.0000	−0.640768
$549$	−48.0000	−2.04859
$550$	0	0
$551$	0	0
$552$	18.0000	0.766131
$553$	0	0
$554$	−20.0000	−0.849719
$555$	0	0
$556$	−1.00000	−0.0424094
$557$	−40.0000	−1.69485	−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000	−1.69485	−0.847427	+	0.530912i	$0.821850\pi$
$558$	24.0000	1.01600
$559$	8.00000	0.338364
$560$	0	0
$561$	−21.0000	−0.886621
$562$	22.0000	0.928014
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−7.00000	−0.294232
$567$	0	0
$568$	6.00000	0.251754
$569$	39.0000	1.63497	0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000	1.63497	0.817483	+	0.575953i	$0.195369\pi$
$570$	0	0
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−2.00000	−0.0836242
$573$	18.0000	0.751961
$574$	0	0
$575$	0	0
$576$	6.00000	0.250000
$577$	−11.0000	−0.457936	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000	−0.457936	−0.228968	+	0.973434i	$0.573535\pi$
$578$	−32.0000	−1.33102
$579$	−75.0000	−3.11689
$580$	0	0
$581$	0	0
$582$	−54.0000	−2.23837
$583$	2.00000	0.0828315
$584$	−7.00000	−0.289662
$585$	0	0
$586$	24.0000	0.991431
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	−21.0000	−0.866025
$589$	−20.0000	−0.824086
$590$	0	0
$591$	24.0000	0.987228
$592$	−1.00000	−0.0410997
$593$	−41.0000	−1.68367	−0.841834	−	0.539736i	$-0.818524\pi$
$593$	−41.0000	−1.68367	−0.841834	+	0.539736i	$0.818524\pi$
$594$	9.00000	0.369274
$595$	0	0
$596$	−22.0000	−0.901155
$597$	48.0000	1.96451
$598$	12.0000	0.490716
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	0	0
$603$	78.0000	3.17641
$604$	−18.0000	−0.732410
$605$	0	0
$606$	−18.0000	−0.731200
$607$	18.0000	0.730597	0.365299	−	0.930890i	$-0.380967\pi$
$607$	18.0000	0.730597	0.365299	+	0.930890i	$0.380967\pi$
$608$	−5.00000	−0.202777
$609$	0	0
$610$	0	0
$611$	8.00000	0.323645
$612$	42.0000	1.69775
$613$	42.0000	1.69636	0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000	1.69636	0.848182	+	0.529705i	$0.177697\pi$
$614$	−7.00000	−0.282497
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	−54.0000	−2.17220
$619$	40.0000	1.60774	0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000	1.60774	0.803868	+	0.594808i	$0.202772\pi$
$620$	0	0
$621$	−54.0000	−2.16695
$622$	24.0000	0.962312
$623$	0	0
$624$	6.00000	0.240192
$625$	0	0
$626$	10.0000	0.399680
$627$	−15.0000	−0.599042
$628$	−12.0000	−0.478852
$629$	−7.00000	−0.279108
$630$	0	0
$631$	30.0000	1.19428	0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000	1.19428	0.597141	+	0.802137i	$0.296303\pi$
$632$	−14.0000	−0.556890
$633$	39.0000	1.55011
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	−6.00000	−0.237915
$637$	−14.0000	−0.554700
$638$	0	0
$639$	−36.0000	−1.42414
$640$	0	0
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	15.0000	0.592003
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	0	0
$645$	0	0
$646$	−35.0000	−1.37706
$647$	38.0000	1.49393	0.746967	−	0.664861i	$-0.231509\pi$
$647$	38.0000	1.49393	0.746967	+	0.664861i	$0.231509\pi$
$648$	−9.00000	−0.353553
$649$	−4.00000	−0.157014
$650$	0	0
$651$	0	0
$652$	−1.00000	−0.0391630
$653$	40.0000	1.56532	0.782660	−	0.622449i	$-0.213862\pi$
$653$	40.0000	1.56532	0.782660	+	0.622449i	$0.213862\pi$
$654$	18.0000	0.703856
$655$	0	0
$656$	−3.00000	−0.117130
$657$	42.0000	1.63858
$658$	0	0
$659$	5.00000	0.194772	0.0973862	−	0.995247i	$-0.468952\pi$
$659$	5.00000	0.194772	0.0973862	+	0.995247i	$0.468952\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	19.0000	0.738456
$663$	42.0000	1.63114
$664$	3.00000	0.116423
$665$	0	0
$666$	6.00000	0.232495
$667$	0	0
$668$	2.00000	0.0773823
$669$	−48.0000	−1.85579
$670$	0	0
$671$	8.00000	0.308837
$672$	0	0
$673$	46.0000	1.77317	0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000	1.77317	0.886585	+	0.462566i	$0.153071\pi$
$674$	−31.0000	−1.19408
$675$	0	0
$676$	−9.00000	−0.346154
$677$	8.00000	0.307465	0.153732	−	0.988113i	$-0.450871\pi$
$677$	8.00000	0.307465	0.153732	+	0.988113i	$0.450871\pi$
$678$	−51.0000	−1.95864
$679$	0	0
$680$	0	0
$681$	−84.0000	−3.21889
$682$	−4.00000	−0.153168
$683$	9.00000	0.344375	0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000	0.344375	0.172188	+	0.985064i	$0.444916\pi$
$684$	30.0000	1.14708
$685$	0	0
$686$	0	0
$687$	72.0000	2.74697
$688$	4.00000	0.152499
$689$	−4.00000	−0.152388
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	−8.00000	−0.304114
$693$	0	0
$694$	23.0000	0.873068
$695$	0	0
$696$	0	0
$697$	−21.0000	−0.795432
$698$	12.0000	0.454207
$699$	42.0000	1.58859
$700$	0	0
$701$	50.0000	1.88847	0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000	1.88847	0.944237	+	0.329267i	$0.106802\pi$
$702$	−18.0000	−0.679366
$703$	−5.00000	−0.188579
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	6.00000	0.225813
$707$	0	0
$708$	12.0000	0.450988
$709$	24.0000	0.901339	0.450669	−	0.892691i	$-0.351185\pi$
$709$	24.0000	0.901339	0.450669	+	0.892691i	$0.351185\pi$
$710$	0	0
$711$	84.0000	3.15025
$712$	7.00000	0.262336
$713$	24.0000	0.898807
$714$	0	0
$715$	0	0
$716$	13.0000	0.485833
$717$	36.0000	1.34444
$718$	6.00000	0.223918
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	0	0
$722$	−6.00000	−0.223297
$723$	−75.0000	−2.78928
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	30.0000	1.11340
$727$	−20.0000	−0.741759	−0.370879	−	0.928681i	$-0.620944\pi$
$727$	−20.0000	−0.741759	−0.370879	+	0.928681i	$0.620944\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	28.0000	1.03562
$732$	−24.0000	−0.887066
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−26.0000	−0.959678
$735$	0	0
$736$	6.00000	0.221163
$737$	−13.0000	−0.478861
$738$	18.0000	0.662589
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	30.0000	1.10208
$742$	0	0
$743$	54.0000	1.98107	0.990534	−	0.137268i	$-0.0438322\pi$
$743$	54.0000	1.98107	0.990534	+	0.137268i	$0.0438322\pi$
$744$	12.0000	0.439941
$745$	0	0
$746$	32.0000	1.17160
$747$	−18.0000	−0.658586
$748$	−7.00000	−0.255945
$749$	0	0
$750$	0	0
$751$	−4.00000	−0.145962	−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000	−0.145962	−0.0729810	+	0.997333i	$0.523251\pi$
$752$	4.00000	0.145865
$753$	−3.00000	−0.109326
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	19.0000	0.690111
$759$	18.0000	0.653359
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	12.0000	0.434714
$763$	0	0
$764$	6.00000	0.217072
$765$	0	0
$766$	36.0000	1.30073
$767$	8.00000	0.288863
$768$	3.00000	0.108253
$769$	−21.0000	−0.757279	−0.378640	−	0.925544i	$-0.623608\pi$
$769$	−21.0000	−0.757279	−0.378640	+	0.925544i	$0.623608\pi$
$770$	0	0
$771$	6.00000	0.216085
$772$	−25.0000	−0.899770
$773$	−22.0000	−0.791285	−0.395643	−	0.918405i	$-0.629478\pi$
$773$	−22.0000	−0.791285	−0.395643	+	0.918405i	$0.629478\pi$
$774$	−24.0000	−0.862662
$775$	0	0
$776$	−18.0000	−0.646162
$777$	0	0
$778$	8.00000	0.286814
$779$	−15.0000	−0.537431
$780$	0	0
$781$	6.00000	0.214697
$782$	42.0000	1.50192
$783$	0	0
$784$	−7.00000	−0.250000
$785$	0	0
$786$	36.0000	1.28408
$787$	24.0000	0.855508	0.427754	−	0.903895i	$-0.359305\pi$
$787$	24.0000	0.855508	0.427754	+	0.903895i	$0.359305\pi$
$788$	8.00000	0.284988
$789$	−42.0000	−1.49524
$790$	0	0
$791$	0	0
$792$	6.00000	0.213201
$793$	−16.0000	−0.568177
$794$	2.00000	0.0709773
$795$	0	0
$796$	16.0000	0.567105
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	28.0000	0.990569
$800$	0	0
$801$	−42.0000	−1.48400
$802$	−23.0000	−0.812158
$803$	−7.00000	−0.247025
$804$	39.0000	1.37542
$805$	0	0
$806$	8.00000	0.281788
$807$	−12.0000	−0.422420
$808$	−6.00000	−0.211079
$809$	−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
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	0	0
$813$	48.0000	1.68343
$814$	−1.00000	−0.0350500
$815$	0	0
$816$	21.0000	0.735147
$817$	20.0000	0.699711
$818$	−11.0000	−0.384606
$819$	0	0
$820$	0	0
$821$	0	0		−	1.00000i	$-0.5\pi$
$821$	0	0			1.00000i	$0.5\pi$
$822$	45.0000	1.56956
$823$	−34.0000	−1.18517	−0.592583	−	0.805510i	$-0.701892\pi$
$823$	−34.0000	−1.18517	−0.592583	+	0.805510i	$0.701892\pi$
$824$	−18.0000	−0.627060
$825$	0	0
$826$	0	0
$827$	−33.0000	−1.14752	−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000	−1.14752	−0.573761	+	0.819023i	$0.694516\pi$
$828$	−36.0000	−1.25109
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	0	0
$831$	60.0000	2.08138
$832$	2.00000	0.0693375
$833$	−49.0000	−1.69775
$834$	3.00000	0.103882
$835$	0	0
$836$	−5.00000	−0.172929
$837$	−36.0000	−1.24434
$838$	17.0000	0.587255
$839$	−6.00000	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−24.0000	−0.827095
$843$	−66.0000	−2.27316
$844$	13.0000	0.447478
$845$	0	0
$846$	−24.0000	−0.825137
$847$	0	0
$848$	−2.00000	−0.0686803
$849$	21.0000	0.720718
$850$	0	0
$851$	6.00000	0.205677
$852$	−18.0000	−0.616670
$853$	−20.0000	−0.684787	−0.342393	−	0.939557i	$-0.611238\pi$
$853$	−20.0000	−0.684787	−0.342393	+	0.939557i	$0.611238\pi$
$854$	0	0
$855$	0	0
$856$	5.00000	0.170896
$857$	−9.00000	−0.307434	−0.153717	−	0.988115i	$-0.549124\pi$
$857$	−9.00000	−0.307434	−0.153717	+	0.988115i	$0.549124\pi$
$858$	6.00000	0.204837
$859$	41.0000	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$859$	41.0000	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$860$	0	0
$861$	0	0
$862$	38.0000	1.29429
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	−9.00000	−0.306186
$865$	0	0
$866$	11.0000	0.373795
$867$	96.0000	3.26033
$868$	0	0
$869$	−14.0000	−0.474917
$870$	0	0
$871$	26.0000	0.880976
$872$	6.00000	0.203186
$873$	108.000	3.65525
$874$	30.0000	1.01477
$875$	0	0
$876$	21.0000	0.709524
$877$	−42.0000	−1.41824	−0.709120	−	0.705088i	$-0.750907\pi$
$877$	−42.0000	−1.41824	−0.709120	+	0.705088i	$0.750907\pi$
$878$	32.0000	1.07995
$879$	−72.0000	−2.42850
$880$	0	0
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	42.0000	1.41421
$883$	−7.00000	−0.235569	−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000	−0.235569	−0.117784	+	0.993039i	$0.537579\pi$
$884$	14.0000	0.470871
$885$	0	0
$886$	15.0000	0.503935
$887$	−52.0000	−1.74599	−0.872995	−	0.487730i	$-0.837825\pi$
$887$	−52.0000	−1.74599	−0.872995	+	0.487730i	$0.837825\pi$
$888$	3.00000	0.100673
$889$	0	0
$890$	0	0
$891$	−9.00000	−0.301511
$892$	−16.0000	−0.535720
$893$	20.0000	0.669274
$894$	66.0000	2.20737
$895$	0	0
$896$	0	0
$897$	−36.0000	−1.20201
$898$	−15.0000	−0.500556
$899$	0	0
$900$	0	0
$901$	−14.0000	−0.466408
$902$	−3.00000	−0.0998891
$903$	0	0
$904$	−17.0000	−0.565412
$905$	0	0
$906$	54.0000	1.79403
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−28.0000	−0.929213
$909$	36.0000	1.19404
$910$	0	0
$911$	30.0000	0.993944	0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000	0.993944	0.496972	+	0.867766i	$0.334445\pi$
$912$	15.0000	0.496700
$913$	3.00000	0.0992855
$914$	21.0000	0.694618
$915$	0	0
$916$	24.0000	0.792982
$917$	0	0
$918$	−63.0000	−2.07931
$919$	14.0000	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$920$	0	0
$921$	21.0000	0.691974
$922$	−4.00000	−0.131733
$923$	−12.0000	−0.394985
$924$	0	0
$925$	0	0
$926$	−26.0000	−0.854413
$927$	108.000	3.54719
$928$	0	0
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−35.0000	−1.14708
$932$	14.0000	0.458585
$933$	−72.0000	−2.35717
$934$	−4.00000	−0.130884
$935$	0	0
$936$	−12.0000	−0.392232
$937$	7.00000	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$938$	0	0
$939$	−30.0000	−0.979013
$940$	0	0
$941$	−24.0000	−0.782378	−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000	−0.782378	−0.391189	+	0.920310i	$0.627936\pi$
$942$	36.0000	1.17294
$943$	18.0000	0.586161
$944$	4.00000	0.130189
$945$	0	0
$946$	4.00000	0.130051
$947$	56.0000	1.81976	0.909878	−	0.414876i	$-0.136175\pi$
$947$	56.0000	1.81976	0.909878	+	0.414876i	$0.136175\pi$
$948$	42.0000	1.36410
$949$	14.0000	0.454459
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	9.00000	0.291539	0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000	0.291539	0.145769	+	0.989319i	$0.453434\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	−4.00000	−0.129234
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	2.00000	0.0644826
$963$	−30.0000	−0.966736
$964$	−25.0000	−0.805196
$965$	0	0
$966$	0	0
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	10.0000	0.321412
$969$	105.000	3.37309
$970$	0	0
$971$	15.0000	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$972$	0	0
$973$	0	0
$974$	16.0000	0.512673
$975$	0	0
$976$	−8.00000	−0.256074
$977$	43.0000	1.37569	0.687846	−	0.725857i	$-0.258556\pi$
$977$	43.0000	1.37569	0.687846	+	0.725857i	$0.258556\pi$
$978$	3.00000	0.0959294
$979$	7.00000	0.223721
$980$	0	0
$981$	−36.0000	−1.14939
$982$	−44.0000	−1.40410
$983$	42.0000	1.33959	0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000	1.33959	0.669796	+	0.742545i	$0.266382\pi$
$984$	9.00000	0.286910
$985$	0	0
$986$	0	0
$987$	0	0
$988$	10.0000	0.318142
$989$	−24.0000	−0.763156
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	4.00000	0.127000
$993$	−57.0000	−1.80884
$994$	0	0
$995$	0	0
$996$	−9.00000	−0.285176
$997$	10.0000	0.316703	0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000	0.316703	0.158352	+	0.987383i	$0.449382\pi$
$998$	−16.0000	−0.506471
$999$	−9.00000	−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.g.1.1	✓	1
5.2	odd	4		1850.2.b.a.149.1		2
5.3	odd	4		1850.2.b.a.149.2		2
5.4	even	2		1850.2.a.h.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.g.1.1	✓	1	1.1	even	1	trivial
1850.2.a.h.1.1	yes	1	5.4	even	2
1850.2.b.a.149.1		2	5.2	odd	4
1850.2.b.a.149.2		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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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