LMFDB - Embedded newform 1850.2.a.k.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 370)
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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{8} -3.00000 q^{9} -4.00000 q^{11} -2.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} -3.00000 q^{18} -4.00000 q^{19} -4.00000 q^{22} -2.00000 q^{26} -6.00000 q^{29} -4.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} -3.00000 q^{36} +1.00000 q^{37} -4.00000 q^{38} -6.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} +8.00000 q^{47} -7.00000 q^{49} -2.00000 q^{52} -10.0000 q^{53} -6.00000 q^{58} +4.00000 q^{59} +10.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +8.00000 q^{67} +2.00000 q^{68} -3.00000 q^{72} -10.0000 q^{73} +1.00000 q^{74} -4.00000 q^{76} -4.00000 q^{79} +9.00000 q^{81} -6.00000 q^{82} -4.00000 q^{86} -4.00000 q^{88} +2.00000 q^{89} +8.00000 q^{94} -6.00000 q^{97} -7.00000 q^{98} +12.0000 q^{99} +O(q^{100})$

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
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−3.00000	−0.707107
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	0	0
$22$	−4.00000	−0.852803
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	−2.00000	−0.392232
$27$	0	0
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	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
$34$	2.00000	0.342997
$35$	0	0
$36$	−3.00000	−0.500000
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	−4.00000	−0.648886
$39$	0	0
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	0	0
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−6.00000	−0.787839
$59$	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
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−3.00000	−0.353553
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−4.00000	−0.458831
$77$	0	0
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	−4.00000	−0.426401
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	8.00000	0.825137
$95$	0	0
$96$	0	0
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	−7.00000	−0.707107
$99$	12.0000	1.20605
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	−10.0000	−0.971286
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	0	0
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	0	0
$116$	−6.00000	−0.557086
$117$	6.00000	0.554700
$118$	4.00000	0.368230
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	10.0000	0.905357
$123$	0	0
$124$	−4.00000	−0.359211
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	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
$133$	0	0
$134$	8.00000	0.691095
$135$	0	0
$136$	2.00000	0.171499
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	8.00000	0.668994
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−10.0000	−0.827606
$147$	0	0
$148$	1.00000	0.0821995
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	−4.00000	−0.324443
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	0	0
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	−4.00000	−0.318223
$159$	0	0
$160$	0	0
$161$	0	0
$162$	9.00000	0.707107
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	0	0
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	12.0000	0.917663
$172$	−4.00000	−0.304997
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	0	0
$176$	−4.00000	−0.301511
$177$	0	0
$178$	2.00000	0.149906
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	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
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−8.00000	−0.585018
$188$	8.00000	0.583460
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−6.00000	−0.430775
$195$	0	0
$196$	−7.00000	−0.500000
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	12.0000	0.852803
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	0	0
$201$	0	0
$202$	6.00000	0.422159
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−2.00000	−0.138675
$209$	16.0000	1.10674
$210$	0	0
$211$	28.0000	1.92760	0.963800	−	0.266627i	$-0.0859092\pi$
$211$	28.0000	1.92760	0.963800	+	0.266627i	$0.0859092\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	8.00000	0.546869
$215$	0	0
$216$	0	0
$217$	0	0
$218$	18.0000	1.21911
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	0	0
$226$	−14.0000	−0.931266
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	0	0
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	0	0
$231$	0	0
$232$	−6.00000	−0.393919
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	6.00000	0.392232
$235$	0	0
$236$	4.00000	0.260378
$237$	0	0
$238$	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
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	10.0000	0.640184
$245$	0	0
$246$	0	0
$247$	8.00000	0.509028
$248$	−4.00000	−0.254000
$249$	0	0
$250$	0	0
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	0	0
$253$	0	0
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	18.0000	1.11417
$262$	−12.0000	−0.741362
$263$	32.0000	1.97320	0.986602	−	0.163144i	$-0.0521635\pi$
$263$	32.0000	1.97320	0.986602	+	0.163144i	$0.0521635\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	8.00000	0.488678
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−4.00000	−0.239904
$279$	12.0000	0.718421
$280$	0	0
$281$	2.00000	0.119310	0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000	0.119310	0.0596550	+	0.998219i	$0.481000\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	8.00000	0.473050
$287$	0	0
$288$	−3.00000	−0.176777
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	−10.0000	−0.585206
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	0	0
$296$	1.00000	0.0581238
$297$	0	0
$298$	−10.0000	−0.579284
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−24.0000	−1.38104
$303$	0	0
$304$	−4.00000	−0.229416
$305$	0	0
$306$	−6.00000	−0.342997
$307$	32.0000	1.82634	0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000	1.82634	0.913168	+	0.407583i	$0.133628\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0	0
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	−4.00000	−0.225018
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	24.0000	1.34374
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−8.00000	−0.445132
$324$	9.00000	0.500000
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	0	0
$333$	−3.00000	−0.164399
$334$	16.0000	0.875481
$335$	0	0
$336$	0	0
$337$	−34.0000	−1.85210	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−34.0000	−1.85210	−0.926049	+	0.377403i	$0.876817\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	0	0
$341$	16.0000	0.866449
$342$	12.0000	0.648886
$343$	0	0
$344$	−4.00000	−0.215666
$345$	0	0
$346$	14.0000	0.752645
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	0	0
$349$	−18.0000	−0.963518	−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000	−0.963518	−0.481759	+	0.876304i	$0.660002\pi$
$350$	0	0
$351$	0	0
$352$	−4.00000	−0.213201
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	4.00000	0.211407
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−2.00000	−0.105118
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	0	0
$369$	18.0000	0.937043
$370$	0	0
$371$	0	0
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	8.00000	0.412568
$377$	12.0000	0.618031
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	0	0
$382$	−12.0000	−0.613973
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	12.0000	0.609994
$388$	−6.00000	−0.304604
$389$	−14.0000	−0.709828	−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000	−0.709828	−0.354914	+	0.934899i	$0.615490\pi$
$390$	0	0
$391$	0	0
$392$	−7.00000	−0.353553
$393$	0	0
$394$	−2.00000	−0.100759
$395$	0	0
$396$	12.0000	0.603023
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−20.0000	−1.00251
$399$	0	0
$400$	0	0
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	0	0
$403$	8.00000	0.398508
$404$	6.00000	0.298511
$405$	0	0
$406$	0	0
$407$	−4.00000	−0.198273
$408$	0	0
$409$	2.00000	0.0988936	0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000	0.0988936	0.0494468	+	0.998777i	$0.484254\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	16.0000	0.782586
$419$	28.0000	1.36789	0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000	1.36789	0.683945	+	0.729534i	$0.260263\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	28.0000	1.36302
$423$	−24.0000	−1.16692
$424$	−10.0000	−0.485643
$425$	0	0
$426$	0	0
$427$	0	0
$428$	8.00000	0.386695
$429$	0	0
$430$	0	0
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	0	0
$435$	0	0
$436$	18.0000	0.862044
$437$	0	0
$438$	0	0
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	21.0000	1.00000
$442$	−4.00000	−0.190261
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	0	0
$446$	16.0000	0.757622
$447$	0	0
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	−14.0000	−0.658505
$453$	0	0
$454$	−20.0000	−0.938647
$455$	0	0
$456$	0	0
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	−18.0000	−0.841085
$459$	0	0
$460$	0	0
$461$	10.0000	0.465746	0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000	0.465746	0.232873	+	0.972507i	$0.425187\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	22.0000	1.01913
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	6.00000	0.277350
$469$	0	0
$470$	0	0
$471$	0	0
$472$	4.00000	0.184115
$473$	16.0000	0.735681
$474$	0	0
$475$	0	0
$476$	0	0
$477$	30.0000	1.37361
$478$	12.0000	0.548867
$479$	28.0000	1.27935	0.639676	−	0.768644i	$-0.279068\pi$
$479$	28.0000	1.27935	0.639676	+	0.768644i	$0.279068\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	2.00000	0.0910975
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	−12.0000	−0.540453
$494$	8.00000	0.359937
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	0	0
$501$	0	0
$502$	20.0000	0.892644
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−14.0000	−0.617514
$515$	0	0
$516$	0	0
$517$	−32.0000	−1.40736
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−38.0000	−1.66481	−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000	−1.66481	−0.832405	+	0.554168i	$0.813037\pi$
$522$	18.0000	0.787839
$523$	−12.0000	−0.524723	−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000	−0.524723	−0.262362	+	0.964970i	$0.584501\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	32.0000	1.39527
$527$	−8.00000	−0.348485
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−12.0000	−0.520756
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	0	0
$536$	8.00000	0.345547
$537$	0	0
$538$	14.0000	0.603583
$539$	28.0000	1.20605
$540$	0	0
$541$	−6.00000	−0.257960	−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000	−0.257960	−0.128980	+	0.991647i	$0.541170\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	2.00000	0.0857493
$545$	0	0
$546$	0	0
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	6.00000	0.256307
$549$	−30.0000	−1.28037
$550$	0	0
$551$	24.0000	1.02243
$552$	0	0
$553$	0	0
$554$	22.0000	0.934690
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	12.0000	0.508001
$559$	8.00000	0.338364
$560$	0	0
$561$	0	0
$562$	2.00000	0.0843649
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	0	0
$566$	−4.00000	−0.168133
$567$	0	0
$568$	0	0
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	0	0
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−46.0000	−1.91501	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−46.0000	−1.91501	−0.957503	+	0.288425i	$0.906868\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	40.0000	1.65663
$584$	−10.0000	−0.413803
$585$	0	0
$586$	−18.0000	−0.743573
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	0	0
$591$	0	0
$592$	1.00000	0.0410997
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	0	0
$595$	0	0
$596$	−10.0000	−0.409616
$597$	0	0
$598$	0	0
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	−24.0000	−0.977356
$604$	−24.0000	−0.976546
$605$	0	0
$606$	0	0
$607$	−24.0000	−0.974130	−0.487065	−	0.873366i	$-0.661933\pi$
$607$	−24.0000	−0.974130	−0.487065	+	0.873366i	$0.661933\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	0	0
$611$	−16.0000	−0.647291
$612$	−6.00000	−0.242536
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	0	0
$622$	12.0000	0.481156
$623$	0	0
$624$	0	0
$625$	0	0
$626$	10.0000	0.399680
$627$	0	0
$628$	6.00000	0.239426
$629$	2.00000	0.0797452
$630$	0	0
$631$	−36.0000	−1.43314	−0.716569	−	0.697517i	$-0.754288\pi$
$631$	−36.0000	−1.43314	−0.716569	+	0.697517i	$0.754288\pi$
$632$	−4.00000	−0.159111
$633$	0	0
$634$	−2.00000	−0.0794301
$635$	0	0
$636$	0	0
$637$	14.0000	0.554700
$638$	24.0000	0.950169
$639$	0	0
$640$	0	0
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	0	0
$643$	44.0000	1.73519	0.867595	−	0.497271i	$-0.165665\pi$
$643$	44.0000	1.73519	0.867595	+	0.497271i	$0.165665\pi$
$644$	0	0
$645$	0	0
$646$	−8.00000	−0.314756
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	9.00000	0.353553
$649$	−16.0000	−0.628055
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	−34.0000	−1.33052	−0.665261	−	0.746611i	$-0.731680\pi$
$653$	−34.0000	−1.33052	−0.665261	+	0.746611i	$0.731680\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	30.0000	1.17041
$658$	0	0
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−3.00000	−0.116248
$667$	0	0
$668$	16.0000	0.619059
$669$	0	0
$670$	0	0
$671$	−40.0000	−1.54418
$672$	0	0
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	−34.0000	−1.30963
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−2.00000	−0.0768662	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000	−0.0768662	−0.0384331	+	0.999261i	$0.512237\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	16.0000	0.612672
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	12.0000	0.458831
$685$	0	0
$686$	0	0
$687$	0	0
$688$	−4.00000	−0.152499
$689$	20.0000	0.761939
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	14.0000	0.532200
$693$	0	0
$694$	−4.00000	−0.151838
$695$	0	0
$696$	0	0
$697$	−12.0000	−0.454532
$698$	−18.0000	−0.681310
$699$	0	0
$700$	0	0
$701$	50.0000	1.88847	0.944237	−	0.329267i	$-0.106802\pi$
$701$	50.0000	1.88847	0.944237	+	0.329267i	$0.106802\pi$
$702$	0	0
$703$	−4.00000	−0.150863
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−6.00000	−0.225813
$707$	0	0
$708$	0	0
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	0	0
$711$	12.0000	0.450035
$712$	2.00000	0.0749532
$713$	0	0
$714$	0	0
$715$	0	0
$716$	4.00000	0.149487
$717$	0	0
$718$	0	0
$719$	32.0000	1.19340	0.596699	−	0.802465i	$-0.296479\pi$
$719$	32.0000	1.19340	0.596699	+	0.802465i	$0.296479\pi$
$720$	0	0
$721$	0	0
$722$	−3.00000	−0.111648
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	0	0
$727$	−16.0000	−0.593407	−0.296704	−	0.954970i	$-0.595887\pi$
$727$	−16.0000	−0.593407	−0.296704	+	0.954970i	$0.595887\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−8.00000	−0.295891
$732$	0	0
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	0	0
$737$	−32.0000	−1.17874
$738$	18.0000	0.662589
$739$	36.0000	1.32428	0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000	1.32428	0.662141	+	0.749380i	$0.269648\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	0	0
$746$	14.0000	0.512576
$747$	0	0
$748$	−8.00000	−0.292509
$749$	0	0
$750$	0	0
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	8.00000	0.291730
$753$	0	0
$754$	12.0000	0.437014
$755$	0	0
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−28.0000	−1.01701
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	0	0
$764$	−12.0000	−0.434145
$765$	0	0
$766$	24.0000	0.867155
$767$	−8.00000	−0.288863
$768$	0	0
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	0	0
$772$	−14.0000	−0.503871
$773$	22.0000	0.791285	0.395643	−	0.918405i	$-0.370522\pi$
$773$	22.0000	0.791285	0.395643	+	0.918405i	$0.370522\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	−6.00000	−0.215387
$777$	0	0
$778$	−14.0000	−0.501924
$779$	24.0000	0.859889
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−7.00000	−0.250000
$785$	0	0
$786$	0	0
$787$	−48.0000	−1.71102	−0.855508	−	0.517790i	$-0.826755\pi$
$787$	−48.0000	−1.71102	−0.855508	+	0.517790i	$0.826755\pi$
$788$	−2.00000	−0.0712470
$789$	0	0
$790$	0	0
$791$	0	0
$792$	12.0000	0.426401
$793$	−20.0000	−0.710221
$794$	−34.0000	−1.20661
$795$	0	0
$796$	−20.0000	−0.708881
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	16.0000	0.566039
$800$	0	0
$801$	−6.00000	−0.212000
$802$	−22.0000	−0.776847
$803$	40.0000	1.41157
$804$	0	0
$805$	0	0
$806$	8.00000	0.281788
$807$	0	0
$808$	6.00000	0.211079
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	0	0
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	0	0
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	16.0000	0.559769
$818$	2.00000	0.0699284
$819$	0	0
$820$	0	0
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	−8.00000	−0.278862	−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000	−0.278862	−0.139431	+	0.990232i	$0.544527\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	−14.0000	−0.486240	−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000	−0.486240	−0.243120	+	0.969996i	$0.578171\pi$
$830$	0	0
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	−14.0000	−0.485071
$834$	0	0
$835$	0	0
$836$	16.0000	0.553372
$837$	0	0
$838$	28.0000	0.967244
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−6.00000	−0.206774
$843$	0	0
$844$	28.0000	0.963800
$845$	0	0
$846$	−24.0000	−0.825137
$847$	0	0
$848$	−10.0000	−0.343401
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	0	0
$855$	0	0
$856$	8.00000	0.273434
$857$	18.0000	0.614868	0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000	0.614868	0.307434	+	0.951569i	$0.400530\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	0	0
$861$	0	0
$862$	−20.0000	−0.681203
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	0	0
$866$	14.0000	0.475739
$867$	0	0
$868$	0	0
$869$	16.0000	0.542763
$870$	0	0
$871$	−16.0000	−0.542139
$872$	18.0000	0.609557
$873$	18.0000	0.609208
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−42.0000	−1.41824	−0.709120	−	0.705088i	$-0.750907\pi$
$877$	−42.0000	−1.41824	−0.709120	+	0.705088i	$0.750907\pi$
$878$	−20.0000	−0.674967
$879$	0	0
$880$	0	0
$881$	−30.0000	−1.01073	−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000	−1.01073	−0.505363	+	0.862907i	$0.668641\pi$
$882$	21.0000	0.707107
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	24.0000	0.806296
$887$	−56.0000	−1.88030	−0.940148	−	0.340766i	$-0.889313\pi$
$887$	−56.0000	−1.88030	−0.940148	+	0.340766i	$0.889313\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−36.0000	−1.20605
$892$	16.0000	0.535720
$893$	−32.0000	−1.07084
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−6.00000	−0.200223
$899$	24.0000	0.800445
$900$	0	0
$901$	−20.0000	−0.666297
$902$	24.0000	0.799113
$903$	0	0
$904$	−14.0000	−0.465633
$905$	0	0
$906$	0	0
$907$	20.0000	0.664089	0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000	0.664089	0.332045	+	0.943264i	$0.392262\pi$
$908$	−20.0000	−0.663723
$909$	−18.0000	−0.597022
$910$	0	0
$911$	−36.0000	−1.19273	−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000	−1.19273	−0.596367	+	0.802712i	$0.703390\pi$
$912$	0	0
$913$	0	0
$914$	18.0000	0.595387
$915$	0	0
$916$	−18.0000	−0.594737
$917$	0	0
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	0	0
$922$	10.0000	0.329332
$923$	0	0
$924$	0	0
$925$	0	0
$926$	40.0000	1.31448
$927$	0	0
$928$	−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
$931$	28.0000	0.917663
$932$	22.0000	0.720634
$933$	0	0
$934$	−28.0000	−0.916188
$935$	0	0
$936$	6.00000	0.196116
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−42.0000	−1.36916	−0.684580	−	0.728937i	$-0.740015\pi$
$941$	−42.0000	−1.36916	−0.684580	+	0.728937i	$0.740015\pi$
$942$	0	0
$943$	0	0
$944$	4.00000	0.130189
$945$	0	0
$946$	16.0000	0.520205
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	20.0000	0.649227
$950$	0	0
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	30.0000	0.971286
$955$	0	0
$956$	12.0000	0.388108
$957$	0	0
$958$	28.0000	0.904639
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−2.00000	−0.0644826
$963$	−24.0000	−0.773389
$964$	2.00000	0.0644157
$965$	0	0
$966$	0	0
$967$	8.00000	0.257263	0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000	0.257263	0.128631	+	0.991692i	$0.458942\pi$
$968$	5.00000	0.160706
$969$	0	0
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	0	0
$974$	16.0000	0.512673
$975$	0	0
$976$	10.0000	0.320092
$977$	50.0000	1.59964	0.799821	−	0.600239i	$-0.204928\pi$
$977$	50.0000	1.59964	0.799821	+	0.600239i	$0.204928\pi$
$978$	0	0
$979$	−8.00000	−0.255681
$980$	0	0
$981$	−54.0000	−1.72409
$982$	20.0000	0.638226
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	0	0
$986$	−12.0000	−0.382158
$987$	0	0
$988$	8.00000	0.254514
$989$	0	0
$990$	0	0
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−20.0000	−0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.k.1.1		1
5.2	odd	4		1850.2.b.d.149.2		2
5.3	odd	4		1850.2.b.d.149.1		2
5.4	even	2		370.2.a.b.1.1	✓	1
15.14	odd	2		3330.2.a.w.1.1		1
20.19	odd	2		2960.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.a.b.1.1	✓	1	5.4	even	2
1850.2.a.k.1.1		1	1.1	even	1	trivial
1850.2.b.d.149.1		2	5.3	odd	4
1850.2.b.d.149.2		2	5.2	odd	4
2960.2.a.g.1.1		1	20.19	odd	2
3330.2.a.w.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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