LMFDB - Embedded newform 1850.2.a.p.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)

$f(q)$

$=$

$q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000 q^{6} +4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{12} -2.00000 q^{13} +4.00000 q^{14} +1.00000 q^{16} +1.00000 q^{18} +5.00000 q^{19} +8.00000 q^{21} -3.00000 q^{23} +2.00000 q^{24} -2.00000 q^{26} -4.00000 q^{27} +4.00000 q^{28} +6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{36} -1.00000 q^{37} +5.00000 q^{38} -4.00000 q^{39} -9.00000 q^{41} +8.00000 q^{42} +7.00000 q^{43} -3.00000 q^{46} +6.00000 q^{47} +2.00000 q^{48} +9.00000 q^{49} -2.00000 q^{52} -9.00000 q^{53} -4.00000 q^{54} +4.00000 q^{56} +10.0000 q^{57} +6.00000 q^{58} +3.00000 q^{59} +2.00000 q^{61} -4.00000 q^{62} +4.00000 q^{63} +1.00000 q^{64} -2.00000 q^{67} -6.00000 q^{69} -6.00000 q^{71} +1.00000 q^{72} -11.0000 q^{73} -1.00000 q^{74} +5.00000 q^{76} -4.00000 q^{78} -1.00000 q^{79} -11.0000 q^{81} -9.00000 q^{82} +8.00000 q^{84} +7.00000 q^{86} +12.0000 q^{87} -6.00000 q^{89} -8.00000 q^{91} -3.00000 q^{92} -8.00000 q^{93} +6.00000 q^{94} +2.00000 q^{96} +4.00000 q^{97} +9.00000 q^{98} +O(q^{100})\)

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
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	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
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	2.00000	0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	4.00000	1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.00000	0.235702
$19$	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
$21$	8.00000	1.74574
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	2.00000	0.408248
$25$	0	0
$26$	−2.00000	−0.392232
$27$	−4.00000	−0.769800
$28$	4.00000	0.755929
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	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
$33$	0	0
$34$	0	0
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	5.00000	0.811107
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	8.00000	1.23443
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	0	0
$45$	0	0
$46$	−3.00000	−0.442326
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	2.00000	0.288675
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	−4.00000	−0.544331
$55$	0	0
$56$	4.00000	0.534522
$57$	10.0000	1.32453
$58$	6.00000	0.787839
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.00000	−0.508001
$63$	4.00000	0.503953
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.00000	0.117851
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	5.00000	0.573539
$77$	0	0
$78$	−4.00000	−0.452911
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	−9.00000	−0.993884
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	8.00000	0.872872
$85$	0	0
$86$	7.00000	0.754829
$87$	12.0000	1.28654
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	−3.00000	−0.312772
$93$	−8.00000	−0.829561
$94$	6.00000	0.618853
$95$	0	0
$96$	2.00000	0.204124
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	9.00000	0.909137
$99$	0	0
$100$	0	0
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−9.00000	−0.874157
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	−4.00000	−0.384900
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	4.00000	0.377964
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	10.0000	0.936586
$115$	0	0
$116$	6.00000	0.557086
$117$	−2.00000	−0.184900
$118$	3.00000	0.276172
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	−18.0000	−1.62301
$124$	−4.00000	−0.359211
$125$	0	0
$126$	4.00000	0.356348
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	14.0000	1.23263
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	20.0000	1.73422
$134$	−2.00000	−0.172774
$135$	0	0
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−6.00000	−0.510754
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	12.0000	1.01058
$142$	−6.00000	−0.503509
$143$	0	0
$144$	1.00000	0.0833333
$145$	0	0
$146$	−11.0000	−0.910366
$147$	18.0000	1.48461
$148$	−1.00000	−0.0821995
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	5.00000	0.405554
$153$	0	0
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	−1.00000	−0.0795557
$159$	−18.0000	−1.42749
$160$	0	0
$161$	−12.0000	−0.945732
$162$	−11.0000	−0.864242
$163$	7.00000	0.548282	0.274141	−	0.961689i	$-0.411606\pi$
$163$	7.00000	0.548282	0.274141	+	0.961689i	$0.411606\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	0	0
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	8.00000	0.617213
$169$	−9.00000	−0.692308
$170$	0	0
$171$	5.00000	0.382360
$172$	7.00000	0.533745
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	12.0000	0.909718
$175$	0	0
$176$	0	0
$177$	6.00000	0.450988
$178$	−6.00000	−0.449719
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	5.00000	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$182$	−8.00000	−0.592999
$183$	4.00000	0.295689
$184$	−3.00000	−0.221163
$185$	0	0
$186$	−8.00000	−0.586588
$187$	0	0
$188$	6.00000	0.437595
$189$	−16.0000	−1.16383
$190$	0	0
$191$	−9.00000	−0.651217	−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000	−0.651217	−0.325609	+	0.945505i	$0.605569\pi$
$192$	2.00000	0.144338
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	9.00000	0.642857
$197$	−27.0000	−1.92367	−0.961835	−	0.273629i	$-0.911776\pi$
$197$	−27.0000	−1.92367	−0.961835	+	0.273629i	$0.911776\pi$
$198$	0	0
$199$	−13.0000	−0.921546	−0.460773	−	0.887518i	$-0.652428\pi$
$199$	−13.0000	−0.921546	−0.460773	+	0.887518i	$0.652428\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	3.00000	0.211079
$203$	24.0000	1.68447
$204$	0	0
$205$	0	0
$206$	13.0000	0.905753
$207$	−3.00000	−0.208514
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−9.00000	−0.618123
$213$	−12.0000	−0.822226
$214$	18.0000	1.23045
$215$	0	0
$216$	−4.00000	−0.272166
$217$	−16.0000	−1.08615
$218$	−16.0000	−1.08366
$219$	−22.0000	−1.48662
$220$	0	0
$221$	0	0
$222$	−2.00000	−0.134231
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	4.00000	0.267261
$225$	0	0
$226$	−18.0000	−1.19734
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	10.0000	0.662266
$229$	−13.0000	−0.859064	−0.429532	−	0.903052i	$-0.641321\pi$
$229$	−13.0000	−0.859064	−0.429532	+	0.903052i	$0.641321\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	21.0000	1.37576	0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000	1.37576	0.687878	+	0.725826i	$0.258542\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	3.00000	0.195283
$237$	−2.00000	−0.129914
$238$	0	0
$239$	9.00000	0.582162	0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000	0.582162	0.291081	+	0.956698i	$0.405985\pi$
$240$	0	0
$241$	14.0000	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$242$	−11.0000	−0.707107
$243$	−10.0000	−0.641500
$244$	2.00000	0.128037
$245$	0	0
$246$	−18.0000	−1.14764
$247$	−10.0000	−0.636285
$248$	−4.00000	−0.254000
$249$	0	0
$250$	0	0
$251$	−27.0000	−1.70422	−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000	−1.70422	−0.852112	+	0.523359i	$0.824679\pi$
$252$	4.00000	0.251976
$253$	0	0
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	14.0000	0.871602
$259$	−4.00000	−0.248548
$260$	0	0
$261$	6.00000	0.371391
$262$	−12.0000	−0.741362
$263$	−6.00000	−0.369976	−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000	−0.369976	−0.184988	+	0.982741i	$0.559225\pi$
$264$	0	0
$265$	0	0
$266$	20.0000	1.22628
$267$	−12.0000	−0.734388
$268$	−2.00000	−0.122169
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	0	0
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	0	0
$273$	−16.0000	−0.968364
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−6.00000	−0.361158
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	14.0000	0.839664
$279$	−4.00000	−0.239474
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	12.0000	0.714590
$283$	19.0000	1.12943	0.564716	−	0.825285i	$-0.308986\pi$
$283$	19.0000	1.12943	0.564716	+	0.825285i	$0.308986\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	0	0
$287$	−36.0000	−2.12501
$288$	1.00000	0.0589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	8.00000	0.468968
$292$	−11.0000	−0.643726
$293$	3.00000	0.175262	0.0876309	−	0.996153i	$-0.472070\pi$
$293$	3.00000	0.175262	0.0876309	+	0.996153i	$0.472070\pi$
$294$	18.0000	1.04978
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	0	0
$298$	15.0000	0.868927
$299$	6.00000	0.346989
$300$	0	0
$301$	28.0000	1.61389
$302$	−4.00000	−0.230174
$303$	6.00000	0.344691
$304$	5.00000	0.286770
$305$	0	0
$306$	0	0
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	0	0
$309$	26.0000	1.47909
$310$	0	0
$311$	15.0000	0.850572	0.425286	−	0.905059i	$-0.360174\pi$
$311$	15.0000	0.850572	0.425286	+	0.905059i	$0.360174\pi$
$312$	−4.00000	−0.226455
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	13.0000	0.733632
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	−33.0000	−1.85346	−0.926732	−	0.375722i	$-0.877395\pi$
$317$	−33.0000	−1.85346	−0.926732	+	0.375722i	$0.877395\pi$
$318$	−18.0000	−1.00939
$319$	0	0
$320$	0	0
$321$	36.0000	2.00932
$322$	−12.0000	−0.668734
$323$	0	0
$324$	−11.0000	−0.611111
$325$	0	0
$326$	7.00000	0.387694
$327$	−32.0000	−1.76960
$328$	−9.00000	−0.496942
$329$	24.0000	1.32316
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	0	0
$333$	−1.00000	−0.0547997
$334$	3.00000	0.164153
$335$	0	0
$336$	8.00000	0.436436
$337$	25.0000	1.36184	0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000	1.36184	0.680918	+	0.732359i	$0.261581\pi$
$338$	−9.00000	−0.489535
$339$	−36.0000	−1.95525
$340$	0	0
$341$	0	0
$342$	5.00000	0.270369
$343$	8.00000	0.431959
$344$	7.00000	0.377415
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−15.0000	−0.805242	−0.402621	−	0.915367i	$-0.631901\pi$
$347$	−15.0000	−0.805242	−0.402621	+	0.915367i	$0.631901\pi$
$348$	12.0000	0.643268
$349$	−19.0000	−1.01705	−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000	−1.01705	−0.508523	+	0.861048i	$0.669808\pi$
$350$	0	0
$351$	8.00000	0.427008
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	6.00000	0.318896
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	30.0000	1.58334	0.791670	−	0.610949i	$-0.209212\pi$
$359$	30.0000	1.58334	0.791670	+	0.610949i	$0.209212\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	5.00000	0.262794
$363$	−22.0000	−1.15470
$364$	−8.00000	−0.419314
$365$	0	0
$366$	4.00000	0.209083
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	−3.00000	−0.156386
$369$	−9.00000	−0.468521
$370$	0	0
$371$	−36.0000	−1.86903
$372$	−8.00000	−0.414781
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	6.00000	0.309426
$377$	−12.0000	−0.618031
$378$	−16.0000	−0.822951
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	0	0
$381$	32.0000	1.63941
$382$	−9.00000	−0.460480
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	2.00000	0.102062
$385$	0	0
$386$	4.00000	0.203595
$387$	7.00000	0.355830
$388$	4.00000	0.203069
$389$	−36.0000	−1.82527	−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000	−1.82527	−0.912636	+	0.408773i	$0.865957\pi$
$390$	0	0
$391$	0	0
$392$	9.00000	0.454569
$393$	−24.0000	−1.21064
$394$	−27.0000	−1.36024
$395$	0	0
$396$	0	0
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	−13.0000	−0.651631
$399$	40.0000	2.00250
$400$	0	0
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−4.00000	−0.199502
$403$	8.00000	0.398508
$404$	3.00000	0.149256
$405$	0	0
$406$	24.0000	1.19110
$407$	0	0
$408$	0	0
$409$	20.0000	0.988936	0.494468	−	0.869196i	$-0.335363\pi$
$409$	20.0000	0.988936	0.494468	+	0.869196i	$0.335363\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	13.0000	0.640464
$413$	12.0000	0.590481
$414$	−3.00000	−0.147442
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	28.0000	1.37117
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	2.00000	0.0973585
$423$	6.00000	0.291730
$424$	−9.00000	−0.437079
$425$	0	0
$426$	−12.0000	−0.581402
$427$	8.00000	0.387147
$428$	18.0000	0.870063
$429$	0	0
$430$	0	0
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	−4.00000	−0.192450
$433$	−26.0000	−1.24948	−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000	−1.24948	−0.624740	+	0.780833i	$0.714795\pi$
$434$	−16.0000	−0.768025
$435$	0	0
$436$	−16.0000	−0.766261
$437$	−15.0000	−0.717547
$438$	−22.0000	−1.05120
$439$	−7.00000	−0.334092	−0.167046	−	0.985949i	$-0.553423\pi$
$439$	−7.00000	−0.334092	−0.167046	+	0.985949i	$0.553423\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	0	0
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−2.00000	−0.0949158
$445$	0	0
$446$	−2.00000	−0.0947027
$447$	30.0000	1.41895
$448$	4.00000	0.188982
$449$	6.00000	0.283158	0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000	0.283158	0.141579	+	0.989927i	$0.454782\pi$
$450$	0	0
$451$	0	0
$452$	−18.0000	−0.846649
$453$	−8.00000	−0.375873
$454$	9.00000	0.422391
$455$	0	0
$456$	10.0000	0.468293
$457$	28.0000	1.30978	0.654892	−	0.755722i	$-0.272714\pi$
$457$	28.0000	1.30978	0.654892	+	0.755722i	$0.272714\pi$
$458$	−13.0000	−0.607450
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	21.0000	0.972806
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	−2.00000	−0.0924500
$469$	−8.00000	−0.369406
$470$	0	0
$471$	26.0000	1.19802
$472$	3.00000	0.138086
$473$	0	0
$474$	−2.00000	−0.0918630
$475$	0	0
$476$	0	0
$477$	−9.00000	−0.412082
$478$	9.00000	0.411650
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	14.0000	0.637683
$483$	−24.0000	−1.09204
$484$	−11.0000	−0.500000
$485$	0	0
$486$	−10.0000	−0.453609
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	2.00000	0.0905357
$489$	14.0000	0.633102
$490$	0	0
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	−18.0000	−0.811503
$493$	0	0
$494$	−10.0000	−0.449921
$495$	0	0
$496$	−4.00000	−0.179605
$497$	−24.0000	−1.07655
$498$	0	0
$499$	−43.0000	−1.92494	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−43.0000	−1.92494	−0.962472	+	0.271380i	$0.912520\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	−27.0000	−1.20507
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	4.00000	0.178174
$505$	0	0
$506$	0	0
$507$	−18.0000	−0.799408
$508$	16.0000	0.709885
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	0	0
$511$	−44.0000	−1.94645
$512$	1.00000	0.0441942
$513$	−20.0000	−0.883022
$514$	0	0
$515$	0	0
$516$	14.0000	0.616316
$517$	0	0
$518$	−4.00000	−0.175750
$519$	−12.0000	−0.526742
$520$	0	0
$521$	−33.0000	−1.44576	−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000	−1.44576	−0.722878	+	0.690976i	$0.757181\pi$
$522$	6.00000	0.262613
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−6.00000	−0.261612
$527$	0	0
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	3.00000	0.130189
$532$	20.0000	0.867110
$533$	18.0000	0.779667
$534$	−12.0000	−0.519291
$535$	0	0
$536$	−2.00000	−0.0863868
$537$	−24.0000	−1.03568
$538$	−21.0000	−0.905374
$539$	0	0
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	−16.0000	−0.687259
$543$	10.0000	0.429141
$544$	0	0
$545$	0	0
$546$	−16.0000	−0.684737
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−6.00000	−0.256307
$549$	2.00000	0.0853579
$550$	0	0
$551$	30.0000	1.27804
$552$	−6.00000	−0.255377
$553$	−4.00000	−0.170097
$554$	22.0000	0.934690
$555$	0	0
$556$	14.0000	0.593732
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−4.00000	−0.169334
$559$	−14.0000	−0.592137
$560$	0	0
$561$	0	0
$562$	12.0000	0.506189
$563$	−45.0000	−1.89652	−0.948262	−	0.317489i	$-0.897160\pi$
$563$	−45.0000	−1.89652	−0.948262	+	0.317489i	$0.897160\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	19.0000	0.798630
$567$	−44.0000	−1.84783
$568$	−6.00000	−0.251754
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	0	0
$573$	−18.0000	−0.751961
$574$	−36.0000	−1.50261
$575$	0	0
$576$	1.00000	0.0416667
$577$	40.0000	1.66522	0.832611	−	0.553858i	$-0.186845\pi$
$577$	40.0000	1.66522	0.832611	+	0.553858i	$0.186845\pi$
$578$	−17.0000	−0.707107
$579$	8.00000	0.332469
$580$	0	0
$581$	0	0
$582$	8.00000	0.331611
$583$	0	0
$584$	−11.0000	−0.455183
$585$	0	0
$586$	3.00000	0.123929
$587$	3.00000	0.123823	0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000	0.123823	0.0619116	+	0.998082i	$0.480280\pi$
$588$	18.0000	0.742307
$589$	−20.0000	−0.824086
$590$	0	0
$591$	−54.0000	−2.22126
$592$	−1.00000	−0.0410997
$593$	−15.0000	−0.615976	−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000	−0.615976	−0.307988	+	0.951390i	$0.599656\pi$
$594$	0	0
$595$	0	0
$596$	15.0000	0.614424
$597$	−26.0000	−1.06411
$598$	6.00000	0.245358
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	0	0
$601$	−37.0000	−1.50926	−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000	−1.50926	−0.754631	+	0.656150i	$0.772184\pi$
$602$	28.0000	1.14119
$603$	−2.00000	−0.0814463
$604$	−4.00000	−0.162758
$605$	0	0
$606$	6.00000	0.243733
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	5.00000	0.202777
$609$	48.0000	1.94506
$610$	0	0
$611$	−12.0000	−0.485468
$612$	0	0
$613$	25.0000	1.00974	0.504870	−	0.863195i	$-0.331540\pi$
$613$	25.0000	1.00974	0.504870	+	0.863195i	$0.331540\pi$
$614$	−32.0000	−1.29141
$615$	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	$0.618017\pi$
$618$	26.0000	1.04587
$619$	−46.0000	−1.84890	−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000	−1.84890	−0.924448	+	0.381308i	$0.875474\pi$
$620$	0	0
$621$	12.0000	0.481543
$622$	15.0000	0.601445
$623$	−24.0000	−0.961540
$624$	−4.00000	−0.160128
$625$	0	0
$626$	22.0000	0.879297
$627$	0	0
$628$	13.0000	0.518756
$629$	0	0
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	−1.00000	−0.0397779
$633$	4.00000	0.158986
$634$	−33.0000	−1.31060
$635$	0	0
$636$	−18.0000	−0.713746
$637$	−18.0000	−0.713186
$638$	0	0
$639$	−6.00000	−0.237356
$640$	0	0
$641$	−21.0000	−0.829450	−0.414725	−	0.909947i	$-0.636122\pi$
$641$	−21.0000	−0.829450	−0.414725	+	0.909947i	$0.636122\pi$
$642$	36.0000	1.42081
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	−12.0000	−0.472866
$645$	0	0
$646$	0	0
$647$	27.0000	1.06148	0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000	1.06148	0.530740	+	0.847535i	$0.321914\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	0	0
$651$	−32.0000	−1.25418
$652$	7.00000	0.274141
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	−32.0000	−1.25130
$655$	0	0
$656$	−9.00000	−0.351391
$657$	−11.0000	−0.429151
$658$	24.0000	0.935617
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	8.00000	0.310929
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−1.00000	−0.0387492
$667$	−18.0000	−0.696963
$668$	3.00000	0.116073
$669$	−4.00000	−0.154649
$670$	0	0
$671$	0	0
$672$	8.00000	0.308607
$673$	37.0000	1.42625	0.713123	−	0.701039i	$-0.247280\pi$
$673$	37.0000	1.42625	0.713123	+	0.701039i	$0.247280\pi$
$674$	25.0000	0.962964
$675$	0	0
$676$	−9.00000	−0.346154
$677$	39.0000	1.49889	0.749446	−	0.662066i	$-0.230320\pi$
$677$	39.0000	1.49889	0.749446	+	0.662066i	$0.230320\pi$
$678$	−36.0000	−1.38257
$679$	16.0000	0.614024
$680$	0	0
$681$	18.0000	0.689761
$682$	0	0
$683$	48.0000	1.83667	0.918334	−	0.395805i	$-0.129534\pi$
$683$	48.0000	1.83667	0.918334	+	0.395805i	$0.129534\pi$
$684$	5.00000	0.191180
$685$	0	0
$686$	8.00000	0.305441
$687$	−26.0000	−0.991962
$688$	7.00000	0.266872
$689$	18.0000	0.685745
$690$	0	0
$691$	−10.0000	−0.380418	−0.190209	−	0.981744i	$-0.560917\pi$
$691$	−10.0000	−0.380418	−0.190209	+	0.981744i	$0.560917\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−15.0000	−0.569392
$695$	0	0
$696$	12.0000	0.454859
$697$	0	0
$698$	−19.0000	−0.719161
$699$	42.0000	1.58859
$700$	0	0
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	8.00000	0.301941
$703$	−5.00000	−0.188579
$704$	0	0
$705$	0	0
$706$	−12.0000	−0.451626
$707$	12.0000	0.451306
$708$	6.00000	0.225494
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	−6.00000	−0.224860
$713$	12.0000	0.449404
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	18.0000	0.672222
$718$	30.0000	1.11959
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	0	0
$721$	52.0000	1.93658
$722$	6.00000	0.223297
$723$	28.0000	1.04133
$724$	5.00000	0.185824
$725$	0	0
$726$	−22.0000	−0.816497
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	−8.00000	−0.296500
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	4.00000	0.147844
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−2.00000	−0.0738213
$735$	0	0
$736$	−3.00000	−0.110581
$737$	0	0
$738$	−9.00000	−0.331295
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	0	0
$741$	−20.0000	−0.734718
$742$	−36.0000	−1.32160
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	−8.00000	−0.293294
$745$	0	0
$746$	−14.0000	−0.512576
$747$	0	0
$748$	0	0
$749$	72.0000	2.63082
$750$	0	0
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	6.00000	0.218797
$753$	−54.0000	−1.96787
$754$	−12.0000	−0.437014
$755$	0	0
$756$	−16.0000	−0.581914
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	0	0
$761$	45.0000	1.63125	0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000	1.63125	0.815624	+	0.578582i	$0.196394\pi$
$762$	32.0000	1.15924
$763$	−64.0000	−2.31696
$764$	−9.00000	−0.325609
$765$	0	0
$766$	15.0000	0.541972
$767$	−6.00000	−0.216647
$768$	2.00000	0.0721688
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	0	0
$772$	4.00000	0.143963
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	7.00000	0.251610
$775$	0	0
$776$	4.00000	0.143592
$777$	−8.00000	−0.286998
$778$	−36.0000	−1.29066
$779$	−45.0000	−1.61229
$780$	0	0
$781$	0	0
$782$	0	0
$783$	−24.0000	−0.857690
$784$	9.00000	0.321429
$785$	0	0
$786$	−24.0000	−0.856052
$787$	−20.0000	−0.712923	−0.356462	−	0.934310i	$-0.616017\pi$
$787$	−20.0000	−0.712923	−0.356462	+	0.934310i	$0.616017\pi$
$788$	−27.0000	−0.961835
$789$	−12.0000	−0.427211
$790$	0	0
$791$	−72.0000	−2.56003
$792$	0	0
$793$	−4.00000	−0.142044
$794$	25.0000	0.887217
$795$	0	0
$796$	−13.0000	−0.460773
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	40.0000	1.41598
$799$	0	0
$800$	0	0
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	0	0
$804$	−4.00000	−0.141069
$805$	0	0
$806$	8.00000	0.281788
$807$	−42.0000	−1.47847
$808$	3.00000	0.105540
$809$	12.0000	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	24.0000	0.842235
$813$	−32.0000	−1.12229
$814$	0	0
$815$	0	0
$816$	0	0
$817$	35.0000	1.22449
$818$	20.0000	0.699284
$819$	−8.00000	−0.279543
$820$	0	0
$821$	33.0000	1.15171	0.575854	−	0.817553i	$-0.304670\pi$
$821$	33.0000	1.15171	0.575854	+	0.817553i	$0.304670\pi$
$822$	−12.0000	−0.418548
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	13.0000	0.452876
$825$	0	0
$826$	12.0000	0.417533
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	−3.00000	−0.104257
$829$	56.0000	1.94496	0.972480	−	0.232986i	$-0.0748495\pi$
$829$	56.0000	1.94496	0.972480	+	0.232986i	$0.0748495\pi$
$830$	0	0
$831$	44.0000	1.52634
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	28.0000	0.969561
$835$	0	0
$836$	0	0
$837$	16.0000	0.553041
$838$	12.0000	0.414533
$839$	−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
$841$	7.00000	0.241379
$842$	26.0000	0.896019
$843$	24.0000	0.826604
$844$	2.00000	0.0688428
$845$	0	0
$846$	6.00000	0.206284
$847$	−44.0000	−1.51186
$848$	−9.00000	−0.309061
$849$	38.0000	1.30416
$850$	0	0
$851$	3.00000	0.102839
$852$	−12.0000	−0.411113
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	8.00000	0.273754
$855$	0	0
$856$	18.0000	0.615227
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	0	0
$859$	5.00000	0.170598	0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000	0.170598	0.0852989	+	0.996355i	$0.472815\pi$
$860$	0	0
$861$	−72.0000	−2.45375
$862$	15.0000	0.510902
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	−4.00000	−0.136083
$865$	0	0
$866$	−26.0000	−0.883516
$867$	−34.0000	−1.15470
$868$	−16.0000	−0.543075
$869$	0	0
$870$	0	0
$871$	4.00000	0.135535
$872$	−16.0000	−0.541828
$873$	4.00000	0.135379
$874$	−15.0000	−0.507383
$875$	0	0
$876$	−22.0000	−0.743311
$877$	25.0000	0.844190	0.422095	−	0.906552i	$-0.361295\pi$
$877$	25.0000	0.844190	0.422095	+	0.906552i	$0.361295\pi$
$878$	−7.00000	−0.236239
$879$	6.00000	0.202375
$880$	0	0
$881$	−39.0000	−1.31394	−0.656972	−	0.753915i	$-0.728163\pi$
$881$	−39.0000	−1.31394	−0.656972	+	0.753915i	$0.728163\pi$
$882$	9.00000	0.303046
$883$	−32.0000	−1.07689	−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000	−1.07689	−0.538443	+	0.842662i	$0.680987\pi$
$884$	0	0
$885$	0	0
$886$	−24.0000	−0.806296
$887$	30.0000	1.00730	0.503651	−	0.863907i	$-0.331990\pi$
$887$	30.0000	1.00730	0.503651	+	0.863907i	$0.331990\pi$
$888$	−2.00000	−0.0671156
$889$	64.0000	2.14649
$890$	0	0
$891$	0	0
$892$	−2.00000	−0.0669650
$893$	30.0000	1.00391
$894$	30.0000	1.00335
$895$	0	0
$896$	4.00000	0.133631
$897$	12.0000	0.400668
$898$	6.00000	0.200223
$899$	−24.0000	−0.800445
$900$	0	0
$901$	0	0
$902$	0	0
$903$	56.0000	1.86356
$904$	−18.0000	−0.598671
$905$	0	0
$906$	−8.00000	−0.265782
$907$	37.0000	1.22856	0.614282	−	0.789086i	$-0.289446\pi$
$907$	37.0000	1.22856	0.614282	+	0.789086i	$0.289446\pi$
$908$	9.00000	0.298675
$909$	3.00000	0.0995037
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	10.0000	0.331133
$913$	0	0
$914$	28.0000	0.926158
$915$	0	0
$916$	−13.0000	−0.429532
$917$	−48.0000	−1.58510
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	−64.0000	−2.10887
$922$	0	0
$923$	12.0000	0.394985
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	13.0000	0.426976
$928$	6.00000	0.196960
$929$	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
$932$	21.0000	0.687878
$933$	30.0000	0.982156
$934$	−12.0000	−0.392652
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−8.00000	−0.261209
$939$	44.0000	1.43589
$940$	0	0
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	26.0000	0.847126
$943$	27.0000	0.879241
$944$	3.00000	0.0976417
$945$	0	0
$946$	0	0
$947$	−33.0000	−1.07236	−0.536178	−	0.844105i	$-0.680132\pi$
$947$	−33.0000	−1.07236	−0.536178	+	0.844105i	$0.680132\pi$
$948$	−2.00000	−0.0649570
$949$	22.0000	0.714150
$950$	0	0
$951$	−66.0000	−2.14020
$952$	0	0
$953$	−9.00000	−0.291539	−0.145769	−	0.989319i	$-0.546566\pi$
$953$	−9.00000	−0.291539	−0.145769	+	0.989319i	$0.546566\pi$
$954$	−9.00000	−0.291386
$955$	0	0
$956$	9.00000	0.291081
$957$	0	0
$958$	24.0000	0.775405
$959$	−24.0000	−0.775000
$960$	0	0
$961$	−15.0000	−0.483871
$962$	2.00000	0.0644826
$963$	18.0000	0.580042
$964$	14.0000	0.450910
$965$	0	0
$966$	−24.0000	−0.772187
$967$	31.0000	0.996893	0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000	0.996893	0.498446	+	0.866921i	$0.333904\pi$
$968$	−11.0000	−0.353553
$969$	0	0
$970$	0	0
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	−10.0000	−0.320750
$973$	56.0000	1.79528
$974$	16.0000	0.512673
$975$	0	0
$976$	2.00000	0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	14.0000	0.447671
$979$	0	0
$980$	0	0
$981$	−16.0000	−0.510841
$982$	−18.0000	−0.574403
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	−18.0000	−0.573819
$985$	0	0
$986$	0	0
$987$	48.0000	1.52786
$988$	−10.0000	−0.318142
$989$	−21.0000	−0.667761
$990$	0	0
$991$	−13.0000	−0.412959	−0.206479	−	0.978451i	$-0.566201\pi$
$991$	−13.0000	−0.412959	−0.206479	+	0.978451i	$0.566201\pi$
$992$	−4.00000	−0.127000
$993$	16.0000	0.507745
$994$	−24.0000	−0.761234
$995$	0	0
$996$	0	0
$997$	28.0000	0.886769	0.443384	−	0.896332i	$-0.353778\pi$
$997$	28.0000	0.886769	0.443384	+	0.896332i	$0.353778\pi$
$998$	−43.0000	−1.36114
$999$	4.00000	0.126554

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.a.1.1	✓	1	5.4	even	2
1850.2.a.p.1.1	yes	1	1.1	even	1	trivial
1850.2.b.f.149.1		2	5.3	odd	4
1850.2.b.f.149.2		2	5.2	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

Related objects

Downloads

Learn more