LMFDB - Embedded newform 1890.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1890.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.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:	$15.0917259820$
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	$\chi$	$=$	1890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -1.00000 q^{10} +2.00000 q^{11} +1.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} +6.00000 q^{19} +1.00000 q^{20} -2.00000 q^{22} -6.00000 q^{23} +1.00000 q^{25} -1.00000 q^{28} +3.00000 q^{29} +5.00000 q^{31} -1.00000 q^{32} +2.00000 q^{34} -1.00000 q^{35} +5.00000 q^{37} -6.00000 q^{38} -1.00000 q^{40} -5.00000 q^{41} +4.00000 q^{43} +2.00000 q^{44} +6.00000 q^{46} +1.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} +2.00000 q^{53} +2.00000 q^{55} +1.00000 q^{56} -3.00000 q^{58} -7.00000 q^{59} +7.00000 q^{61} -5.00000 q^{62} +1.00000 q^{64} +6.00000 q^{67} -2.00000 q^{68} +1.00000 q^{70} +13.0000 q^{71} +5.00000 q^{73} -5.00000 q^{74} +6.00000 q^{76} -2.00000 q^{77} -8.00000 q^{79} +1.00000 q^{80} +5.00000 q^{82} +4.00000 q^{83} -2.00000 q^{85} -4.00000 q^{86} -2.00000 q^{88} +2.00000 q^{89} -6.00000 q^{92} -1.00000 q^{94} +6.00000 q^{95} +2.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−1.00000	−0.316228
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−1.00000	−0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	−1.00000	−0.169031
$36$	0	0
$37$	5.00000	0.821995	0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000	0.821995	0.410997	+	0.911636i	$0.365181\pi$
$38$	−6.00000	−0.973329
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	6.00000	0.884652
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	0	0
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0	0
$55$	2.00000	0.269680
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.00000	−0.393919
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	0	0
$61$	7.00000	0.896258	0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000	0.896258	0.448129	+	0.893969i	$0.352090\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	6.00000	0.733017	0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000	0.733017	0.366508	+	0.930415i	$0.380553\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	1.00000	0.119523
$71$	13.0000	1.54282	0.771408	−	0.636341i	$-0.219553\pi$
$71$	13.0000	1.54282	0.771408	+	0.636341i	$0.219553\pi$
$72$	0	0
$73$	5.00000	0.585206	0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000	0.585206	0.292603	+	0.956234i	$0.405479\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	6.00000	0.688247
$77$	−2.00000	−0.227921
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	5.00000	0.552158
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	−4.00000	−0.431331
$87$	0	0
$88$	−2.00000	−0.213201
$89$	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
$92$	−6.00000	−0.625543
$93$	0	0
$94$	−1.00000	−0.103142
$95$	6.00000	0.615587
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	0	0
$105$	0	0
$106$	−2.00000	−0.194257
$107$	9.00000	0.870063	0.435031	−	0.900415i	$-0.356737\pi$
$107$	9.00000	0.870063	0.435031	+	0.900415i	$0.356737\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−5.00000	−0.470360	−0.235180	−	0.971952i	$-0.575568\pi$
$113$	−5.00000	−0.470360	−0.235180	+	0.971952i	$0.575568\pi$
$114$	0	0
$115$	−6.00000	−0.559503
$116$	3.00000	0.278543
$117$	0	0
$118$	7.00000	0.644402
$119$	2.00000	0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−7.00000	−0.633750
$123$	0	0
$124$	5.00000	0.449013
$125$	1.00000	0.0894427
$126$	0	0
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	13.0000	1.13582	0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000	1.13582	0.567908	+	0.823092i	$0.307753\pi$
$132$	0	0
$133$	−6.00000	−0.520266
$134$	−6.00000	−0.518321
$135$	0	0
$136$	2.00000	0.171499
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	22.0000	1.86602	0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000	1.86602	0.933008	+	0.359856i	$0.117174\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	−13.0000	−1.09094
$143$	0	0
$144$	0	0
$145$	3.00000	0.249136
$146$	−5.00000	−0.413803
$147$	0	0
$148$	5.00000	0.410997
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	2.00000	0.161165
$155$	5.00000	0.401610
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	6.00000	0.472866
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−4.00000	−0.310460
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	2.00000	0.153393
$171$	0	0
$172$	4.00000	0.304997
$173$	7.00000	0.532200	0.266100	−	0.963945i	$-0.414265\pi$
$173$	7.00000	0.532200	0.266100	+	0.963945i	$0.414265\pi$
$174$	0	0
$175$	−1.00000	−0.0755929
$176$	2.00000	0.150756
$177$	0	0
$178$	−2.00000	−0.149906
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	25.0000	1.85824	0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000	1.85824	0.929118	+	0.369784i	$0.120568\pi$
$182$	0	0
$183$	0	0
$184$	6.00000	0.442326
$185$	5.00000	0.367607
$186$	0	0
$187$	−4.00000	−0.292509
$188$	1.00000	0.0729325
$189$	0	0
$190$	−6.00000	−0.435286
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	0	0
$203$	−3.00000	−0.210559
$204$	0	0
$205$	−5.00000	−0.349215
$206$	8.00000	0.557386
$207$	0	0
$208$	0	0
$209$	12.0000	0.830057
$210$	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
$213$	0	0
$214$	−9.00000	−0.615227
$215$	4.00000	0.272798
$216$	0	0
$217$	−5.00000	−0.339422
$218$	0	0
$219$	0	0
$220$	2.00000	0.134840
$221$	0	0
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	5.00000	0.332595
$227$	−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
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	6.00000	0.395628
$231$	0	0
$232$	−3.00000	−0.196960
$233$	−21.0000	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$234$	0	0
$235$	1.00000	0.0652328
$236$	−7.00000	−0.455661
$237$	0	0
$238$	−2.00000	−0.129641
$239$	11.0000	0.711531	0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000	0.711531	0.355765	+	0.934575i	$0.384220\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	7.00000	0.448129
$245$	1.00000	0.0638877
$246$	0	0
$247$	0	0
$248$	−5.00000	−0.317500
$249$	0	0
$250$	−1.00000	−0.0632456
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.0000	−1.24757	−0.623783	−	0.781598i	$-0.714405\pi$
$257$	−20.0000	−1.24757	−0.623783	+	0.781598i	$0.714405\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	0	0
$262$	−13.0000	−0.803143
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	6.00000	0.367884
$267$	0	0
$268$	6.00000	0.366508
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	9.00000	0.543710
$275$	2.00000	0.120605
$276$	0	0
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	−22.0000	−1.31947
$279$	0	0
$280$	1.00000	0.0597614
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	13.0000	0.771408
$285$	0	0
$286$	0	0
$287$	5.00000	0.295141
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−3.00000	−0.176166
$291$	0	0
$292$	5.00000	0.292603
$293$	17.0000	0.993151	0.496575	−	0.867994i	$-0.334591\pi$
$293$	17.0000	0.993151	0.496575	+	0.867994i	$0.334591\pi$
$294$	0	0
$295$	−7.00000	−0.407556
$296$	−5.00000	−0.290619
$297$	0	0
$298$	6.00000	0.347571
$299$	0	0
$300$	0	0
$301$	−4.00000	−0.230556
$302$	4.00000	0.230174
$303$	0	0
$304$	6.00000	0.344124
$305$	7.00000	0.400819
$306$	0	0
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	−5.00000	−0.283981
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	1.00000	0.0559017
$321$	0	0
$322$	−6.00000	−0.334367
$323$	−12.0000	−0.667698
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	5.00000	0.276079
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	−11.0000	−0.604615	−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000	−0.604615	−0.302307	+	0.953211i	$0.597757\pi$
$332$	4.00000	0.219529
$333$	0	0
$334$	3.00000	0.164153
$335$	6.00000	0.327815
$336$	0	0
$337$	−8.00000	−0.435788	−0.217894	−	0.975972i	$-0.569919\pi$
$337$	−8.00000	−0.435788	−0.217894	+	0.975972i	$0.569919\pi$
$338$	13.0000	0.707107
$339$	0	0
$340$	−2.00000	−0.108465
$341$	10.0000	0.541530
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−7.00000	−0.376322
$347$	−25.0000	−1.34207	−0.671035	−	0.741426i	$-0.734150\pi$
$347$	−25.0000	−1.34207	−0.671035	+	0.741426i	$0.734150\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	13.0000	0.689968
$356$	2.00000	0.106000
$357$	0	0
$358$	−18.0000	−0.951330
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−25.0000	−1.31397
$363$	0	0
$364$	0	0
$365$	5.00000	0.261712
$366$	0	0
$367$	−14.0000	−0.730794	−0.365397	−	0.930852i	$-0.619067\pi$
$367$	−14.0000	−0.730794	−0.365397	+	0.930852i	$0.619067\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	−5.00000	−0.259938
$371$	−2.00000	−0.103835
$372$	0	0
$373$	−31.0000	−1.60512	−0.802560	−	0.596572i	$-0.796529\pi$
$373$	−31.0000	−1.60512	−0.802560	+	0.596572i	$0.796529\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	0	0
$378$	0	0
$379$	−21.0000	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$380$	6.00000	0.307794
$381$	0	0
$382$	−24.0000	−1.22795
$383$	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
$385$	−2.00000	−0.101929
$386$	10.0000	0.508987
$387$	0	0
$388$	2.00000	0.101535
$389$	−29.0000	−1.47036	−0.735179	−	0.677873i	$-0.762902\pi$
$389$	−29.0000	−1.47036	−0.735179	+	0.677873i	$0.762902\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−10.0000	−0.503793
$395$	−8.00000	−0.402524
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	1.00000	0.0500000
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	3.00000	0.148888
$407$	10.0000	0.495682
$408$	0	0
$409$	18.0000	0.890043	0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000	0.890043	0.445021	+	0.895520i	$0.353196\pi$
$410$	5.00000	0.246932
$411$	0	0
$412$	−8.00000	−0.394132
$413$	7.00000	0.344447
$414$	0	0
$415$	4.00000	0.196352
$416$	0	0
$417$	0	0
$418$	−12.0000	−0.586939
$419$	−27.0000	−1.31904	−0.659518	−	0.751689i	$-0.729240\pi$
$419$	−27.0000	−1.31904	−0.659518	+	0.751689i	$0.729240\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	−13.0000	−0.632830
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	−7.00000	−0.338754
$428$	9.00000	0.435031
$429$	0	0
$430$	−4.00000	−0.192897
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	0	0
$433$	17.0000	0.816968	0.408484	−	0.912766i	$-0.366058\pi$
$433$	17.0000	0.816968	0.408484	+	0.912766i	$0.366058\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	0	0
$437$	−36.0000	−1.72211
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	0	0
$443$	17.0000	0.807694	0.403847	−	0.914826i	$-0.367673\pi$
$443$	17.0000	0.807694	0.403847	+	0.914826i	$0.367673\pi$
$444$	0	0
$445$	2.00000	0.0948091
$446$	2.00000	0.0947027
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	−5.00000	−0.235180
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	0	0
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	−6.00000	−0.279751
$461$	32.0000	1.49039	0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000	1.49039	0.745194	+	0.666847i	$0.232357\pi$
$462$	0	0
$463$	−7.00000	−0.325318	−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000	−0.325318	−0.162659	+	0.986682i	$0.552007\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	21.0000	0.972806
$467$	−2.00000	−0.0925490	−0.0462745	−	0.998929i	$-0.514735\pi$
$467$	−2.00000	−0.0925490	−0.0462745	+	0.998929i	$0.514735\pi$
$468$	0	0
$469$	−6.00000	−0.277054
$470$	−1.00000	−0.0461266
$471$	0	0
$472$	7.00000	0.322201
$473$	8.00000	0.367840
$474$	0	0
$475$	6.00000	0.275299
$476$	2.00000	0.0916698
$477$	0	0
$478$	−11.0000	−0.503128
$479$	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
$481$	0	0
$482$	14.0000	0.637683
$483$	0	0
$484$	−7.00000	−0.318182
$485$	2.00000	0.0908153
$486$	0	0
$487$	5.00000	0.226572	0.113286	−	0.993562i	$-0.463862\pi$
$487$	5.00000	0.226572	0.113286	+	0.993562i	$0.463862\pi$
$488$	−7.00000	−0.316875
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	0	0
$495$	0	0
$496$	5.00000	0.224507
$497$	−13.0000	−0.583130
$498$	0	0
$499$	−39.0000	−1.74588	−0.872940	−	0.487828i	$-0.837789\pi$
$499$	−39.0000	−1.74588	−0.872940	+	0.487828i	$0.837789\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	−24.0000	−1.07117
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	7.00000	0.310575
$509$	−4.00000	−0.177297	−0.0886484	−	0.996063i	$-0.528255\pi$
$509$	−4.00000	−0.177297	−0.0886484	+	0.996063i	$0.528255\pi$
$510$	0	0
$511$	−5.00000	−0.221187
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	20.0000	0.882162
$515$	−8.00000	−0.352522
$516$	0	0
$517$	2.00000	0.0879599
$518$	5.00000	0.219687
$519$	0	0
$520$	0	0
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	13.0000	0.567908
$525$	0	0
$526$	−28.0000	−1.22086
$527$	−10.0000	−0.435607
$528$	0	0
$529$	13.0000	0.565217
$530$	−2.00000	−0.0868744
$531$	0	0
$532$	−6.00000	−0.260133
$533$	0	0
$534$	0	0
$535$	9.00000	0.389104
$536$	−6.00000	−0.259161
$537$	0	0
$538$	6.00000	0.258678
$539$	2.00000	0.0861461
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	−3.00000	−0.128861
$543$	0	0
$544$	2.00000	0.0857493
$545$	0	0
$546$	0	0
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	−9.00000	−0.384461
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	18.0000	0.766826
$552$	0	0
$553$	8.00000	0.340195
$554$	−30.0000	−1.27458
$555$	0	0
$556$	22.0000	0.933008
$557$	−22.0000	−0.932170	−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000	−0.932170	−0.466085	+	0.884740i	$0.654336\pi$
$558$	0	0
$559$	0	0
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−10.0000	−0.421825
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	−5.00000	−0.210352
$566$	13.0000	0.546431
$567$	0	0
$568$	−13.0000	−0.545468
$569$	−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
$571$	−45.0000	−1.88319	−0.941596	−	0.336746i	$-0.890674\pi$
$571$	−45.0000	−1.88319	−0.941596	+	0.336746i	$0.890674\pi$
$572$	0	0
$573$	0	0
$574$	−5.00000	−0.208696
$575$	−6.00000	−0.250217
$576$	0	0
$577$	7.00000	0.291414	0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000	0.291414	0.145707	+	0.989328i	$0.453454\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	3.00000	0.124568
$581$	−4.00000	−0.165948
$582$	0	0
$583$	4.00000	0.165663
$584$	−5.00000	−0.206901
$585$	0	0
$586$	−17.0000	−0.702264
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	0	0
$589$	30.0000	1.23613
$590$	7.00000	0.288185
$591$	0	0
$592$	5.00000	0.205499
$593$	12.0000	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$594$	0	0
$595$	2.00000	0.0819920
$596$	−6.00000	−0.245770
$597$	0	0
$598$	0	0
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	36.0000	1.46847	0.734235	−	0.678895i	$-0.237541\pi$
$601$	36.0000	1.46847	0.734235	+	0.678895i	$0.237541\pi$
$602$	4.00000	0.163028
$603$	0	0
$604$	−4.00000	−0.162758
$605$	−7.00000	−0.284590
$606$	0	0
$607$	−44.0000	−1.78590	−0.892952	−	0.450151i	$-0.851370\pi$
$607$	−44.0000	−1.78590	−0.892952	+	0.450151i	$0.851370\pi$
$608$	−6.00000	−0.243332
$609$	0	0
$610$	−7.00000	−0.283422
$611$	0	0
$612$	0	0
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	2.00000	0.0805823
$617$	7.00000	0.281809	0.140905	−	0.990023i	$-0.454999\pi$
$617$	7.00000	0.281809	0.140905	+	0.990023i	$0.454999\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	5.00000	0.200805
$621$	0	0
$622$	6.00000	0.240578
$623$	−2.00000	−0.0801283
$624$	0	0
$625$	1.00000	0.0400000
$626$	22.0000	0.879297
$627$	0	0
$628$	22.0000	0.877896
$629$	−10.0000	−0.398726
$630$	0	0
$631$	−46.0000	−1.83123	−0.915616	−	0.402055i	$-0.868296\pi$
$631$	−46.0000	−1.83123	−0.915616	+	0.402055i	$0.868296\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	10.0000	0.397151
$635$	7.00000	0.277787
$636$	0	0
$637$	0	0
$638$	−6.00000	−0.237542
$639$	0	0
$640$	−1.00000	−0.0395285
$641$	−20.0000	−0.789953	−0.394976	−	0.918691i	$-0.629247\pi$
$641$	−20.0000	−0.789953	−0.394976	+	0.918691i	$0.629247\pi$
$642$	0	0
$643$	43.0000	1.69575	0.847877	−	0.530193i	$-0.177880\pi$
$643$	43.0000	1.69575	0.847877	+	0.530193i	$0.177880\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	12.0000	0.472134
$647$	−7.00000	−0.275198	−0.137599	−	0.990488i	$-0.543939\pi$
$647$	−7.00000	−0.275198	−0.137599	+	0.990488i	$0.543939\pi$
$648$	0	0
$649$	−14.0000	−0.549548
$650$	0	0
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	0	0
$655$	13.0000	0.507952
$656$	−5.00000	−0.195217
$657$	0	0
$658$	1.00000	0.0389841
$659$	32.0000	1.24654	0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000	1.24654	0.623272	+	0.782006i	$0.285803\pi$
$660$	0	0
$661$	7.00000	0.272268	0.136134	−	0.990690i	$-0.456532\pi$
$661$	7.00000	0.272268	0.136134	+	0.990690i	$0.456532\pi$
$662$	11.0000	0.427527
$663$	0	0
$664$	−4.00000	−0.155230
$665$	−6.00000	−0.232670
$666$	0	0
$667$	−18.0000	−0.696963
$668$	−3.00000	−0.116073
$669$	0	0
$670$	−6.00000	−0.231800
$671$	14.0000	0.540464
$672$	0	0
$673$	−2.00000	−0.0770943	−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000	−0.0770943	−0.0385472	+	0.999257i	$0.512273\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−27.0000	−1.03769	−0.518847	−	0.854867i	$-0.673639\pi$
$677$	−27.0000	−1.03769	−0.518847	+	0.854867i	$0.673639\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	2.00000	0.0766965
$681$	0	0
$682$	−10.0000	−0.382920
$683$	−47.0000	−1.79841	−0.899203	−	0.437533i	$-0.855852\pi$
$683$	−47.0000	−1.79841	−0.899203	+	0.437533i	$0.855852\pi$
$684$	0	0
$685$	−9.00000	−0.343872
$686$	1.00000	0.0381802
$687$	0	0
$688$	4.00000	0.152499
$689$	0	0
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	7.00000	0.266100
$693$	0	0
$694$	25.0000	0.948987
$695$	22.0000	0.834508
$696$	0	0
$697$	10.0000	0.378777
$698$	26.0000	0.984115
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	−1.00000	−0.0377695	−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000	−0.0377695	−0.0188847	+	0.999822i	$0.506012\pi$
$702$	0	0
$703$	30.0000	1.13147
$704$	2.00000	0.0753778
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	−13.0000	−0.487881
$711$	0	0
$712$	−2.00000	−0.0749532
$713$	−30.0000	−1.12351
$714$	0	0
$715$	0	0
$716$	18.0000	0.672692
$717$	0	0
$718$	32.0000	1.19423
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	−17.0000	−0.632674
$723$	0	0
$724$	25.0000	0.929118
$725$	3.00000	0.111417
$726$	0	0
$727$	24.0000	0.890111	0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000	0.890111	0.445055	+	0.895503i	$0.353184\pi$
$728$	0	0
$729$	0	0
$730$	−5.00000	−0.185058
$731$	−8.00000	−0.295891
$732$	0	0
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	6.00000	0.221163
$737$	12.0000	0.442026
$738$	0	0
$739$	25.0000	0.919640	0.459820	−	0.888012i	$-0.347914\pi$
$739$	25.0000	0.919640	0.459820	+	0.888012i	$0.347914\pi$
$740$	5.00000	0.183804
$741$	0	0
$742$	2.00000	0.0734223
$743$	42.0000	1.54083	0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000	1.54083	0.770415	+	0.637542i	$0.220049\pi$
$744$	0	0
$745$	−6.00000	−0.219823
$746$	31.0000	1.13499
$747$	0	0
$748$	−4.00000	−0.146254
$749$	−9.00000	−0.328853
$750$	0	0
$751$	−10.0000	−0.364905	−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000	−0.364905	−0.182453	+	0.983215i	$0.558404\pi$
$752$	1.00000	0.0364662
$753$	0	0
$754$	0	0
$755$	−4.00000	−0.145575
$756$	0	0
$757$	7.00000	0.254419	0.127210	−	0.991876i	$-0.459398\pi$
$757$	7.00000	0.254419	0.127210	+	0.991876i	$0.459398\pi$
$758$	21.0000	0.762754
$759$	0	0
$760$	−6.00000	−0.217643
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	0	0
$763$	0	0
$764$	24.0000	0.868290
$765$	0	0
$766$	−24.0000	−0.867155
$767$	0	0
$768$	0	0
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	2.00000	0.0720750
$771$	0	0
$772$	−10.0000	−0.359908
$773$	−33.0000	−1.18693	−0.593464	−	0.804861i	$-0.702240\pi$
$773$	−33.0000	−1.18693	−0.593464	+	0.804861i	$0.702240\pi$
$774$	0	0
$775$	5.00000	0.179605
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	29.0000	1.03970
$779$	−30.0000	−1.07486
$780$	0	0
$781$	26.0000	0.930353
$782$	−12.0000	−0.429119
$783$	0	0
$784$	1.00000	0.0357143
$785$	22.0000	0.785214
$786$	0	0
$787$	49.0000	1.74666	0.873331	−	0.487128i	$-0.161955\pi$
$787$	49.0000	1.74666	0.873331	+	0.487128i	$0.161955\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	8.00000	0.284627
$791$	5.00000	0.177780
$792$	0	0
$793$	0	0
$794$	2.00000	0.0709773
$795$	0	0
$796$	8.00000	0.283552
$797$	−9.00000	−0.318796	−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000	−0.318796	−0.159398	+	0.987214i	$0.550955\pi$
$798$	0	0
$799$	−2.00000	−0.0707549
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	16.0000	0.564980
$803$	10.0000	0.352892
$804$	0	0
$805$	6.00000	0.211472
$806$	0	0
$807$	0	0
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	−10.0000	−0.350500
$815$	−4.00000	−0.140114
$816$	0	0
$817$	24.0000	0.839654
$818$	−18.0000	−0.629355
$819$	0	0
$820$	−5.00000	−0.174608
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	0	0
$823$	−29.0000	−1.01088	−0.505438	−	0.862863i	$-0.668669\pi$
$823$	−29.0000	−1.01088	−0.505438	+	0.862863i	$0.668669\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−7.00000	−0.243561
$827$	−23.0000	−0.799788	−0.399894	−	0.916561i	$-0.630953\pi$
$827$	−23.0000	−0.799788	−0.399894	+	0.916561i	$0.630953\pi$
$828$	0	0
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	0	0
$833$	−2.00000	−0.0692959
$834$	0	0
$835$	−3.00000	−0.103819
$836$	12.0000	0.415029
$837$	0	0
$838$	27.0000	0.932700
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	34.0000	1.17172
$843$	0	0
$844$	13.0000	0.447478
$845$	−13.0000	−0.447214
$846$	0	0
$847$	7.00000	0.240523
$848$	2.00000	0.0686803
$849$	0	0
$850$	2.00000	0.0685994
$851$	−30.0000	−1.02839
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	7.00000	0.239535
$855$	0	0
$856$	−9.00000	−0.307614
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	0	0
$859$	−18.0000	−0.614152	−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000	−0.614152	−0.307076	+	0.951685i	$0.599351\pi$
$860$	4.00000	0.136399
$861$	0	0
$862$	−15.0000	−0.510902
$863$	−16.0000	−0.544646	−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000	−0.544646	−0.272323	+	0.962206i	$0.587792\pi$
$864$	0	0
$865$	7.00000	0.238007
$866$	−17.0000	−0.577684
$867$	0	0
$868$	−5.00000	−0.169711
$869$	−16.0000	−0.542763
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	36.0000	1.21772
$875$	−1.00000	−0.0338062
$876$	0	0
$877$	−1.00000	−0.0337676	−0.0168838	−	0.999857i	$-0.505375\pi$
$877$	−1.00000	−0.0337676	−0.0168838	+	0.999857i	$0.505375\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	2.00000	0.0674200
$881$	43.0000	1.44871	0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000	1.44871	0.724353	+	0.689429i	$0.242138\pi$
$882$	0	0
$883$	−24.0000	−0.807664	−0.403832	−	0.914833i	$-0.632322\pi$
$883$	−24.0000	−0.807664	−0.403832	+	0.914833i	$0.632322\pi$
$884$	0	0
$885$	0	0
$886$	−17.0000	−0.571126
$887$	13.0000	0.436497	0.218249	−	0.975893i	$-0.429966\pi$
$887$	13.0000	0.436497	0.218249	+	0.975893i	$0.429966\pi$
$888$	0	0
$889$	−7.00000	−0.234772
$890$	−2.00000	−0.0670402
$891$	0	0
$892$	−2.00000	−0.0669650
$893$	6.00000	0.200782
$894$	0	0
$895$	18.0000	0.601674
$896$	1.00000	0.0334077
$897$	0	0
$898$	24.0000	0.800890
$899$	15.0000	0.500278
$900$	0	0
$901$	−4.00000	−0.133259
$902$	10.0000	0.332964
$903$	0	0
$904$	5.00000	0.166298
$905$	25.0000	0.831028
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	−20.0000	−0.663723
$909$	0	0
$910$	0	0
$911$	45.0000	1.49092	0.745458	−	0.666552i	$-0.232231\pi$
$911$	45.0000	1.49092	0.745458	+	0.666552i	$0.232231\pi$
$912$	0	0
$913$	8.00000	0.264761
$914$	8.00000	0.264616
$915$	0	0
$916$	−14.0000	−0.462573
$917$	−13.0000	−0.429298
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	6.00000	0.197814
$921$	0	0
$922$	−32.0000	−1.05386
$923$	0	0
$924$	0	0
$925$	5.00000	0.164399
$926$	7.00000	0.230034
$927$	0	0
$928$	−3.00000	−0.0984798
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	−21.0000	−0.687878
$933$	0	0
$934$	2.00000	0.0654420
$935$	−4.00000	−0.130814
$936$	0	0
$937$	−7.00000	−0.228680	−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000	−0.228680	−0.114340	+	0.993442i	$0.536475\pi$
$938$	6.00000	0.195907
$939$	0	0
$940$	1.00000	0.0326164
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	0	0
$943$	30.0000	0.976934
$944$	−7.00000	−0.227831
$945$	0	0
$946$	−8.00000	−0.260102
$947$	52.0000	1.68977	0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000	1.68977	0.844886	+	0.534946i	$0.179668\pi$
$948$	0	0
$949$	0	0
$950$	−6.00000	−0.194666
$951$	0	0
$952$	−2.00000	−0.0648204
$953$	−30.0000	−0.971795	−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000	−0.971795	−0.485898	+	0.874016i	$0.661507\pi$
$954$	0	0
$955$	24.0000	0.776622
$956$	11.0000	0.355765
$957$	0	0
$958$	−24.0000	−0.775405
$959$	9.00000	0.290625
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	0	0
$964$	−14.0000	−0.450910
$965$	−10.0000	−0.321911
$966$	0	0
$967$	37.0000	1.18984	0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000	1.18984	0.594920	+	0.803785i	$0.297184\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−2.00000	−0.0642161
$971$	27.0000	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$972$	0	0
$973$	−22.0000	−0.705288
$974$	−5.00000	−0.160210
$975$	0	0
$976$	7.00000	0.224065
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	4.00000	0.127841
$980$	1.00000	0.0319438
$981$	0	0
$982$	−12.0000	−0.382935
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	6.00000	0.191079
$987$	0	0
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	10.0000	0.317660	0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000	0.317660	0.158830	+	0.987306i	$0.449228\pi$
$992$	−5.00000	−0.158750
$993$	0	0
$994$	13.0000	0.412335
$995$	8.00000	0.253617
$996$	0	0
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	39.0000	1.23452
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.a.h.1.1	✓	1
3.2	odd	2		1890.2.a.n.1.1	yes	1
5.4	even	2		9450.2.a.ds.1.1		1
15.14	odd	2		9450.2.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.h.1.1	✓	1	1.1	even	1	trivial
1890.2.a.n.1.1	yes	1	3.2	odd	2
9450.2.a.bg.1.1		1	15.14	odd	2
9450.2.a.ds.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more