LMFDB - Embedded newform 1850.2.a.l.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)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} -3.00000 q^{11} -4.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -3.00000 q^{18} -3.00000 q^{22} -8.00000 q^{23} -4.00000 q^{26} +1.00000 q^{28} -3.00000 q^{29} -7.00000 q^{31} +1.00000 q^{32} -3.00000 q^{34} -3.00000 q^{36} -1.00000 q^{37} +11.0000 q^{41} +11.0000 q^{43} -3.00000 q^{44} -8.00000 q^{46} +4.00000 q^{47} -6.00000 q^{49} -4.00000 q^{52} +11.0000 q^{53} +1.00000 q^{56} -3.00000 q^{58} -12.0000 q^{59} -15.0000 q^{61} -7.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} -4.00000 q^{67} -3.00000 q^{68} +6.00000 q^{71} -3.00000 q^{72} +2.00000 q^{73} -1.00000 q^{74} -3.00000 q^{77} -8.00000 q^{79} +9.00000 q^{81} +11.0000 q^{82} +12.0000 q^{83} +11.0000 q^{86} -3.00000 q^{88} -4.00000 q^{91} -8.00000 q^{92} +4.00000 q^{94} -1.00000 q^{97} -6.00000 q^{98} +9.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	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
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	−3.00000	−0.707107
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	0	0
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	0	0
$25$	0	0
$26$	−4.00000	−0.784465
$27$	0	0
$28$	1.00000	0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.00000	−0.514496
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0	0
$39$	0	0
$40$	0	0
$41$	11.0000	1.71791	0.858956	−	0.512050i	$-0.171114\pi$
$41$	11.0000	1.71791	0.858956	+	0.512050i	$0.171114\pi$
$42$	0	0
$43$	11.0000	1.67748	0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000	1.67748	0.838742	+	0.544529i	$0.183292\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	−8.00000	−1.17954
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	−4.00000	−0.554700
$53$	11.0000	1.51097	0.755483	−	0.655168i	$-0.227402\pi$
$53$	11.0000	1.51097	0.755483	+	0.655168i	$0.227402\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.00000	−0.393919
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	−15.0000	−1.92055	−0.960277	−	0.279050i	$-0.909981\pi$
$61$	−15.0000	−1.92055	−0.960277	+	0.279050i	$0.909981\pi$
$62$	−7.00000	−0.889001
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−3.00000	−0.353553
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	0	0
$77$	−3.00000	−0.341882
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	11.0000	1.21475
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	0	0
$86$	11.0000	1.18616
$87$	0	0
$88$	−3.00000	−0.319801
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	−4.00000	−0.419314
$92$	−8.00000	−0.834058
$93$	0	0
$94$	4.00000	0.412568
$95$	0	0
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−6.00000	−0.606092
$99$	9.00000	0.904534
$100$	0	0
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−4.00000	−0.392232
$105$	0	0
$106$	11.0000	1.06841
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	0	0
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−1.00000	−0.0940721	−0.0470360	−	0.998893i	$-0.514978\pi$
$113$	−1.00000	−0.0940721	−0.0470360	+	0.998893i	$0.514978\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	12.0000	1.10940
$118$	−12.0000	−1.10469
$119$	−3.00000	−0.275010
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−15.0000	−1.35804
$123$	0	0
$124$	−7.00000	−0.628619
$125$	0	0
$126$	−3.00000	−0.267261
$127$	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
$129$	0	0
$130$	0	0
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	0	0
$133$	0	0
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−3.00000	−0.257248
$137$	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
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	0	0
$141$	0	0
$142$	6.00000	0.503509
$143$	12.0000	1.00349
$144$	−3.00000	−0.250000
$145$	0	0
$146$	2.00000	0.165521
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	−14.0000	−1.13930	−0.569652	−	0.821886i	$-0.692922\pi$
$151$	−14.0000	−1.13930	−0.569652	+	0.821886i	$0.692922\pi$
$152$	0	0
$153$	9.00000	0.727607
$154$	−3.00000	−0.241747
$155$	0	0
$156$	0	0
$157$	−5.00000	−0.399043	−0.199522	−	0.979893i	$-0.563939\pi$
$157$	−5.00000	−0.399043	−0.199522	+	0.979893i	$0.563939\pi$
$158$	−8.00000	−0.636446
$159$	0	0
$160$	0	0
$161$	−8.00000	−0.630488
$162$	9.00000	0.707107
$163$	3.00000	0.234978	0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000	0.234978	0.117489	+	0.993074i	$0.462515\pi$
$164$	11.0000	0.858956
$165$	0	0
$166$	12.0000	0.931381
$167$	−14.0000	−1.08335	−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000	−1.08335	−0.541676	+	0.840587i	$0.682210\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	0	0
$172$	11.0000	0.838742
$173$	−13.0000	−0.988372	−0.494186	−	0.869356i	$-0.664534\pi$
$173$	−13.0000	−0.988372	−0.494186	+	0.869356i	$0.664534\pi$
$174$	0	0
$175$	0	0
$176$	−3.00000	−0.226134
$177$	0	0
$178$	0	0
$179$	10.0000	0.747435	0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000	0.747435	0.373718	+	0.927543i	$0.378083\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	−4.00000	−0.296500
$183$	0	0
$184$	−8.00000	−0.589768
$185$	0	0
$186$	0	0
$187$	9.00000	0.658145
$188$	4.00000	0.291730
$189$	0	0
$190$	0	0
$191$	−17.0000	−1.23008	−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000	−1.23008	−0.615038	+	0.788497i	$0.710860\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−1.00000	−0.0717958
$195$	0	0
$196$	−6.00000	−0.428571
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	9.00000	0.639602
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	0	0
$202$	14.0000	0.985037
$203$	−3.00000	−0.210559
$204$	0	0
$205$	0	0
$206$	0	0
$207$	24.0000	1.66812
$208$	−4.00000	−0.277350
$209$	0	0
$210$	0	0
$211$	−1.00000	−0.0688428	−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000	−0.0688428	−0.0344214	+	0.999407i	$0.510959\pi$
$212$	11.0000	0.755483
$213$	0	0
$214$	−10.0000	−0.683586
$215$	0	0
$216$	0	0
$217$	−7.00000	−0.475191
$218$	−11.0000	−0.745014
$219$	0	0
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	11.0000	0.736614	0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000	0.736614	0.368307	+	0.929704i	$0.379937\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−1.00000	−0.0665190
$227$	17.0000	1.12833	0.564165	−	0.825662i	$-0.309198\pi$
$227$	17.0000	1.12833	0.564165	+	0.825662i	$0.309198\pi$
$228$	0	0
$229$	20.0000	1.32164	0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000	1.32164	0.660819	+	0.750546i	$0.270209\pi$
$230$	0	0
$231$	0	0
$232$	−3.00000	−0.196960
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	12.0000	0.784465
$235$	0	0
$236$	−12.0000	−0.781133
$237$	0	0
$238$	−3.00000	−0.194461
$239$	−17.0000	−1.09964	−0.549819	−	0.835284i	$-0.685303\pi$
$239$	−17.0000	−1.09964	−0.549819	+	0.835284i	$0.685303\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−2.00000	−0.128565
$243$	0	0
$244$	−15.0000	−0.960277
$245$	0	0
$246$	0	0
$247$	0	0
$248$	−7.00000	−0.444500
$249$	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	$0.282565\pi$
$252$	−3.00000	−0.188982
$253$	24.0000	1.50887
$254$	16.0000	1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	−1.00000	−0.0621370
$260$	0	0
$261$	9.00000	0.557086
$262$	−10.0000	−0.617802
$263$	31.0000	1.91154	0.955771	−	0.294112i	$-0.0950239\pi$
$263$	31.0000	1.91154	0.955771	+	0.294112i	$0.0950239\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−4.00000	−0.244339
$269$	−16.0000	−0.975537	−0.487769	−	0.872973i	$-0.662189\pi$
$269$	−16.0000	−0.975537	−0.487769	+	0.872973i	$0.662189\pi$
$270$	0	0
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	1.00000	0.0599760
$279$	21.0000	1.25724
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−8.00000	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	12.0000	0.709575
$287$	11.0000	0.649309
$288$	−3.00000	−0.176777
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	2.00000	0.117041
$293$	−15.0000	−0.876309	−0.438155	−	0.898900i	$-0.644368\pi$
$293$	−15.0000	−0.876309	−0.438155	+	0.898900i	$0.644368\pi$
$294$	0	0
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	0	0
$298$	−4.00000	−0.231714
$299$	32.0000	1.85061
$300$	0	0
$301$	11.0000	0.634029
$302$	−14.0000	−0.805609
$303$	0	0
$304$	0	0
$305$	0	0
$306$	9.00000	0.514496
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	−3.00000	−0.170941
$309$	0	0
$310$	0	0
$311$	3.00000	0.170114	0.0850572	−	0.996376i	$-0.472893\pi$
$311$	3.00000	0.170114	0.0850572	+	0.996376i	$0.472893\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	−5.00000	−0.282166
$315$	0	0
$316$	−8.00000	−0.450035
$317$	−21.0000	−1.17948	−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000	−1.17948	−0.589739	+	0.807594i	$0.700769\pi$
$318$	0	0
$319$	9.00000	0.503903
$320$	0	0
$321$	0	0
$322$	−8.00000	−0.445823
$323$	0	0
$324$	9.00000	0.500000
$325$	0	0
$326$	3.00000	0.166155
$327$	0	0
$328$	11.0000	0.607373
$329$	4.00000	0.220527
$330$	0	0
$331$	2.00000	0.109930	0.0549650	−	0.998488i	$-0.482495\pi$
$331$	2.00000	0.109930	0.0549650	+	0.998488i	$0.482495\pi$
$332$	12.0000	0.658586
$333$	3.00000	0.164399
$334$	−14.0000	−0.766046
$335$	0	0
$336$	0	0
$337$	−28.0000	−1.52526	−0.762629	−	0.646837i	$-0.776092\pi$
$337$	−28.0000	−1.52526	−0.762629	+	0.646837i	$0.776092\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	0	0
$341$	21.0000	1.13721
$342$	0	0
$343$	−13.0000	−0.701934
$344$	11.0000	0.593080
$345$	0	0
$346$	−13.0000	−0.698884
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−6.00000	−0.321173	−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000	−0.321173	−0.160586	+	0.987022i	$0.551338\pi$
$350$	0	0
$351$	0	0
$352$	−3.00000	−0.159901
$353$	−3.00000	−0.159674	−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000	−0.159674	−0.0798369	+	0.996808i	$0.525440\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	10.0000	0.528516
$359$	−14.0000	−0.738892	−0.369446	−	0.929252i	$-0.620452\pi$
$359$	−14.0000	−0.738892	−0.369446	+	0.929252i	$0.620452\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	−16.0000	−0.840941
$363$	0	0
$364$	−4.00000	−0.209657
$365$	0	0
$366$	0	0
$367$	13.0000	0.678594	0.339297	−	0.940679i	$-0.389811\pi$
$367$	13.0000	0.678594	0.339297	+	0.940679i	$0.389811\pi$
$368$	−8.00000	−0.417029
$369$	−33.0000	−1.71791
$370$	0	0
$371$	11.0000	0.571092
$372$	0	0
$373$	38.0000	1.96757	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	38.0000	1.96757	0.983783	+	0.179364i	$0.0574041\pi$
$374$	9.00000	0.465379
$375$	0	0
$376$	4.00000	0.206284
$377$	12.0000	0.618031
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0	0
$382$	−17.0000	−0.869796
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−33.0000	−1.67748
$388$	−1.00000	−0.0507673
$389$	23.0000	1.16615	0.583073	−	0.812420i	$-0.301850\pi$
$389$	23.0000	1.16615	0.583073	+	0.812420i	$0.301850\pi$
$390$	0	0
$391$	24.0000	1.21373
$392$	−6.00000	−0.303046
$393$	0	0
$394$	2.00000	0.100759
$395$	0	0
$396$	9.00000	0.452267
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	0	0
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	0	0
$403$	28.0000	1.39478
$404$	14.0000	0.696526
$405$	0	0
$406$	−3.00000	−0.148888
$407$	3.00000	0.148704
$408$	0	0
$409$	−4.00000	−0.197787	−0.0988936	−	0.995098i	$-0.531530\pi$
$409$	−4.00000	−0.197787	−0.0988936	+	0.995098i	$0.531530\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−12.0000	−0.590481
$414$	24.0000	1.17954
$415$	0	0
$416$	−4.00000	−0.196116
$417$	0	0
$418$	0	0
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	−30.0000	−1.46211	−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000	−1.46211	−0.731055	+	0.682318i	$0.760972\pi$
$422$	−1.00000	−0.0486792
$423$	−12.0000	−0.583460
$424$	11.0000	0.534207
$425$	0	0
$426$	0	0
$427$	−15.0000	−0.725901
$428$	−10.0000	−0.483368
$429$	0	0
$430$	0	0
$431$	23.0000	1.10787	0.553936	−	0.832560i	$-0.313125\pi$
$431$	23.0000	1.10787	0.553936	+	0.832560i	$0.313125\pi$
$432$	0	0
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	−11.0000	−0.526804
$437$	0	0
$438$	0	0
$439$	7.00000	0.334092	0.167046	−	0.985949i	$-0.446577\pi$
$439$	7.00000	0.334092	0.167046	+	0.985949i	$0.446577\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	12.0000	0.570782
$443$	34.0000	1.61539	0.807694	−	0.589601i	$-0.200715\pi$
$443$	34.0000	1.61539	0.807694	+	0.589601i	$0.200715\pi$
$444$	0	0
$445$	0	0
$446$	11.0000	0.520865
$447$	0	0
$448$	1.00000	0.0472456
$449$	36.0000	1.69895	0.849473	−	0.527633i	$-0.176920\pi$
$449$	36.0000	1.69895	0.849473	+	0.527633i	$0.176920\pi$
$450$	0	0
$451$	−33.0000	−1.55391
$452$	−1.00000	−0.0470360
$453$	0	0
$454$	17.0000	0.797850
$455$	0	0
$456$	0	0
$457$	−37.0000	−1.73079	−0.865393	−	0.501093i	$-0.832931\pi$
$457$	−37.0000	−1.73079	−0.865393	+	0.501093i	$0.832931\pi$
$458$	20.0000	0.934539
$459$	0	0
$460$	0	0
$461$	3.00000	0.139724	0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000	0.139724	0.0698620	+	0.997557i	$0.477744\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	6.00000	0.277945
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	12.0000	0.554700
$469$	−4.00000	−0.184703
$470$	0	0
$471$	0	0
$472$	−12.0000	−0.552345
$473$	−33.0000	−1.51734
$474$	0	0
$475$	0	0
$476$	−3.00000	−0.137505
$477$	−33.0000	−1.51097
$478$	−17.0000	−0.777562
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	−14.0000	−0.637683
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	36.0000	1.63132	0.815658	−	0.578535i	$-0.196375\pi$
$487$	36.0000	1.63132	0.815658	+	0.578535i	$0.196375\pi$
$488$	−15.0000	−0.679018
$489$	0	0
$490$	0	0
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	0	0
$493$	9.00000	0.405340
$494$	0	0
$495$	0	0
$496$	−7.00000	−0.314309
$497$	6.00000	0.269137
$498$	0	0
$499$	−18.0000	−0.805791	−0.402895	−	0.915246i	$-0.631996\pi$
$499$	−18.0000	−0.805791	−0.402895	+	0.915246i	$0.631996\pi$
$500$	0	0
$501$	0	0
$502$	20.0000	0.892644
$503$	−26.0000	−1.15928	−0.579641	−	0.814872i	$-0.696807\pi$
$503$	−26.0000	−1.15928	−0.579641	+	0.814872i	$0.696807\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	24.0000	1.06693
$507$	0	0
$508$	16.0000	0.709885
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	1.00000	0.0441942
$513$	0	0
$514$	6.00000	0.264649
$515$	0	0
$516$	0	0
$517$	−12.0000	−0.527759
$518$	−1.00000	−0.0439375
$519$	0	0
$520$	0	0
$521$	−7.00000	−0.306676	−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000	−0.306676	−0.153338	+	0.988174i	$0.549002\pi$
$522$	9.00000	0.393919
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−10.0000	−0.436852
$525$	0	0
$526$	31.0000	1.35166
$527$	21.0000	0.914774
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	36.0000	1.56227
$532$	0	0
$533$	−44.0000	−1.90585
$534$	0	0
$535$	0	0
$536$	−4.00000	−0.172774
$537$	0	0
$538$	−16.0000	−0.689809
$539$	18.0000	0.775315
$540$	0	0
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	22.0000	0.944981
$543$	0	0
$544$	−3.00000	−0.128624
$545$	0	0
$546$	0	0
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	6.00000	0.256307
$549$	45.0000	1.92055
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−8.00000	−0.340195
$554$	0	0
$555$	0	0
$556$	1.00000	0.0424094
$557$	−6.00000	−0.254228	−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000	−0.254228	−0.127114	+	0.991888i	$0.540571\pi$
$558$	21.0000	0.889001
$559$	−44.0000	−1.86100
$560$	0	0
$561$	0	0
$562$	6.00000	0.253095
$563$	−19.0000	−0.800755	−0.400377	−	0.916350i	$-0.631121\pi$
$563$	−19.0000	−0.800755	−0.400377	+	0.916350i	$0.631121\pi$
$564$	0	0
$565$	0	0
$566$	−8.00000	−0.336265
$567$	9.00000	0.377964
$568$	6.00000	0.251754
$569$	14.0000	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$569$	14.0000	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$570$	0	0
$571$	7.00000	0.292941	0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000	0.292941	0.146470	+	0.989215i	$0.453209\pi$
$572$	12.0000	0.501745
$573$	0	0
$574$	11.0000	0.459131
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	12.0000	0.497844
$582$	0	0
$583$	−33.0000	−1.36672
$584$	2.00000	0.0827606
$585$	0	0
$586$	−15.0000	−0.619644
$587$	15.0000	0.619116	0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000	0.619116	0.309558	+	0.950881i	$0.399819\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−1.00000	−0.0410997
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	0	0
$595$	0	0
$596$	−4.00000	−0.163846
$597$	0	0
$598$	32.0000	1.30858
$599$	−32.0000	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$599$	−32.0000	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$600$	0	0
$601$	−47.0000	−1.91717	−0.958585	−	0.284807i	$-0.908071\pi$
$601$	−47.0000	−1.91717	−0.958585	+	0.284807i	$0.908071\pi$
$602$	11.0000	0.448327
$603$	12.0000	0.488678
$604$	−14.0000	−0.569652
$605$	0	0
$606$	0	0
$607$	−42.0000	−1.70473	−0.852364	−	0.522949i	$-0.824832\pi$
$607$	−42.0000	−1.70473	−0.852364	+	0.522949i	$0.824832\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−16.0000	−0.647291
$612$	9.00000	0.363803
$613$	−15.0000	−0.605844	−0.302922	−	0.953015i	$-0.597962\pi$
$613$	−15.0000	−0.605844	−0.302922	+	0.953015i	$0.597962\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	−3.00000	−0.120873
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	0	0
$619$	−35.0000	−1.40677	−0.703384	−	0.710810i	$-0.748329\pi$
$619$	−35.0000	−1.40677	−0.703384	+	0.710810i	$0.748329\pi$
$620$	0	0
$621$	0	0
$622$	3.00000	0.120289
$623$	0	0
$624$	0	0
$625$	0	0
$626$	−14.0000	−0.559553
$627$	0	0
$628$	−5.00000	−0.199522
$629$	3.00000	0.119618
$630$	0	0
$631$	37.0000	1.47295	0.736473	−	0.676467i	$-0.236490\pi$
$631$	37.0000	1.47295	0.736473	+	0.676467i	$0.236490\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	−21.0000	−0.834017
$635$	0	0
$636$	0	0
$637$	24.0000	0.950915
$638$	9.00000	0.356313
$639$	−18.0000	−0.712069
$640$	0	0
$641$	−25.0000	−0.987441	−0.493720	−	0.869621i	$-0.664363\pi$
$641$	−25.0000	−0.987441	−0.493720	+	0.869621i	$0.664363\pi$
$642$	0	0
$643$	7.00000	0.276053	0.138027	−	0.990429i	$-0.455924\pi$
$643$	7.00000	0.276053	0.138027	+	0.990429i	$0.455924\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	0	0
$647$	2.00000	0.0786281	0.0393141	−	0.999227i	$-0.487483\pi$
$647$	2.00000	0.0786281	0.0393141	+	0.999227i	$0.487483\pi$
$648$	9.00000	0.353553
$649$	36.0000	1.41312
$650$	0	0
$651$	0	0
$652$	3.00000	0.117489
$653$	38.0000	1.48705	0.743527	−	0.668705i	$-0.233151\pi$
$653$	38.0000	1.48705	0.743527	+	0.668705i	$0.233151\pi$
$654$	0	0
$655$	0	0
$656$	11.0000	0.429478
$657$	−6.00000	−0.234082
$658$	4.00000	0.155936
$659$	48.0000	1.86981	0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000	1.86981	0.934907	+	0.354892i	$0.115482\pi$
$660$	0	0
$661$	−25.0000	−0.972387	−0.486194	−	0.873851i	$-0.661615\pi$
$661$	−25.0000	−0.972387	−0.486194	+	0.873851i	$0.661615\pi$
$662$	2.00000	0.0777322
$663$	0	0
$664$	12.0000	0.465690
$665$	0	0
$666$	3.00000	0.116248
$667$	24.0000	0.929284
$668$	−14.0000	−0.541676
$669$	0	0
$670$	0	0
$671$	45.0000	1.73721
$672$	0	0
$673$	0	0		−	1.00000i	$-0.5\pi$
$673$	0	0			1.00000i	$0.5\pi$
$674$	−28.0000	−1.07852
$675$	0	0
$676$	3.00000	0.115385
$677$	−42.0000	−1.61419	−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000	−1.61419	−0.807096	+	0.590421i	$0.798962\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	0	0
$682$	21.0000	0.804132
$683$	13.0000	0.497431	0.248716	−	0.968577i	$-0.419992\pi$
$683$	13.0000	0.497431	0.248716	+	0.968577i	$0.419992\pi$
$684$	0	0
$685$	0	0
$686$	−13.0000	−0.496342
$687$	0	0
$688$	11.0000	0.419371
$689$	−44.0000	−1.67627
$690$	0	0
$691$	−41.0000	−1.55971	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	−41.0000	−1.55971	−0.779857	+	0.625958i	$0.784708\pi$
$692$	−13.0000	−0.494186
$693$	9.00000	0.341882
$694$	12.0000	0.455514
$695$	0	0
$696$	0	0
$697$	−33.0000	−1.24996
$698$	−6.00000	−0.227103
$699$	0	0
$700$	0	0
$701$	−22.0000	−0.830929	−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000	−0.830929	−0.415464	+	0.909610i	$0.636381\pi$
$702$	0	0
$703$	0	0
$704$	−3.00000	−0.113067
$705$	0	0
$706$	−3.00000	−0.112906
$707$	14.0000	0.526524
$708$	0	0
$709$	29.0000	1.08912	0.544559	−	0.838723i	$-0.316697\pi$
$709$	29.0000	1.08912	0.544559	+	0.838723i	$0.316697\pi$
$710$	0	0
$711$	24.0000	0.900070
$712$	0	0
$713$	56.0000	2.09722
$714$	0	0
$715$	0	0
$716$	10.0000	0.373718
$717$	0	0
$718$	−14.0000	−0.522475
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	0	0
$721$	0	0
$722$	−19.0000	−0.707107
$723$	0	0
$724$	−16.0000	−0.594635
$725$	0	0
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−4.00000	−0.148250
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−33.0000	−1.22055
$732$	0	0
$733$	1.00000	0.0369358	0.0184679	−	0.999829i	$-0.494121\pi$
$733$	1.00000	0.0369358	0.0184679	+	0.999829i	$0.494121\pi$
$734$	13.0000	0.479839
$735$	0	0
$736$	−8.00000	−0.294884
$737$	12.0000	0.442026
$738$	−33.0000	−1.21475
$739$	−15.0000	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$740$	0	0
$741$	0	0
$742$	11.0000	0.403823
$743$	−13.0000	−0.476924	−0.238462	−	0.971152i	$-0.576643\pi$
$743$	−13.0000	−0.476924	−0.238462	+	0.971152i	$0.576643\pi$
$744$	0	0
$745$	0	0
$746$	38.0000	1.39128
$747$	−36.0000	−1.31717
$748$	9.00000	0.329073
$749$	−10.0000	−0.365392
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	12.0000	0.437014
$755$	0	0
$756$	0	0
$757$	−28.0000	−1.01768	−0.508839	−	0.860862i	$-0.669925\pi$
$757$	−28.0000	−1.01768	−0.508839	+	0.860862i	$0.669925\pi$
$758$	12.0000	0.435860
$759$	0	0
$760$	0	0
$761$	7.00000	0.253750	0.126875	−	0.991919i	$-0.459505\pi$
$761$	7.00000	0.253750	0.126875	+	0.991919i	$0.459505\pi$
$762$	0	0
$763$	−11.0000	−0.398227
$764$	−17.0000	−0.615038
$765$	0	0
$766$	−16.0000	−0.578103
$767$	48.0000	1.73318
$768$	0	0
$769$	−44.0000	−1.58668	−0.793340	−	0.608778i	$-0.791660\pi$
$769$	−44.0000	−1.58668	−0.793340	+	0.608778i	$0.791660\pi$
$770$	0	0
$771$	0	0
$772$	−14.0000	−0.503871
$773$	−51.0000	−1.83434	−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000	−1.83434	−0.917171	+	0.398493i	$0.869533\pi$
$774$	−33.0000	−1.18616
$775$	0	0
$776$	−1.00000	−0.0358979
$777$	0	0
$778$	23.0000	0.824590
$779$	0	0
$780$	0	0
$781$	−18.0000	−0.644091
$782$	24.0000	0.858238
$783$	0	0
$784$	−6.00000	−0.214286
$785$	0	0
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	0	0
$791$	−1.00000	−0.0355559
$792$	9.00000	0.319801
$793$	60.0000	2.13066
$794$	14.0000	0.496841
$795$	0	0
$796$	16.0000	0.567105
$797$	12.0000	0.425062	0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000	0.425062	0.212531	+	0.977154i	$0.431829\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	0	0
$801$	0	0
$802$	10.0000	0.353112
$803$	−6.00000	−0.211735
$804$	0	0
$805$	0	0
$806$	28.0000	0.986258
$807$	0	0
$808$	14.0000	0.492518
$809$	−12.0000	−0.421898	−0.210949	−	0.977497i	$-0.567655\pi$
$809$	−12.0000	−0.421898	−0.210949	+	0.977497i	$0.567655\pi$
$810$	0	0
$811$	0	0		−	1.00000i	$-0.5\pi$
$811$	0	0			1.00000i	$0.5\pi$
$812$	−3.00000	−0.105279
$813$	0	0
$814$	3.00000	0.105150
$815$	0	0
$816$	0	0
$817$	0	0
$818$	−4.00000	−0.139857
$819$	12.0000	0.419314
$820$	0	0
$821$	−14.0000	−0.488603	−0.244302	−	0.969699i	$-0.578559\pi$
$821$	−14.0000	−0.488603	−0.244302	+	0.969699i	$0.578559\pi$
$822$	0	0
$823$	40.0000	1.39431	0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000	1.39431	0.697156	+	0.716919i	$0.254448\pi$
$824$	0	0
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−3.00000	−0.104320	−0.0521601	−	0.998639i	$-0.516611\pi$
$827$	−3.00000	−0.104320	−0.0521601	+	0.998639i	$0.516611\pi$
$828$	24.0000	0.834058
$829$	−23.0000	−0.798823	−0.399412	−	0.916772i	$-0.630786\pi$
$829$	−23.0000	−0.798823	−0.399412	+	0.916772i	$0.630786\pi$
$830$	0	0
$831$	0	0
$832$	−4.00000	−0.138675
$833$	18.0000	0.623663
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	20.0000	0.690889
$839$	−12.0000	−0.414286	−0.207143	−	0.978311i	$-0.566417\pi$
$839$	−12.0000	−0.414286	−0.207143	+	0.978311i	$0.566417\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−30.0000	−1.03387
$843$	0	0
$844$	−1.00000	−0.0344214
$845$	0	0
$846$	−12.0000	−0.412568
$847$	−2.00000	−0.0687208
$848$	11.0000	0.377742
$849$	0	0
$850$	0	0
$851$	8.00000	0.274236
$852$	0	0
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	−15.0000	−0.513289
$855$	0	0
$856$	−10.0000	−0.341793
$857$	−17.0000	−0.580709	−0.290354	−	0.956919i	$-0.593773\pi$
$857$	−17.0000	−0.580709	−0.290354	+	0.956919i	$0.593773\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	0	0
$861$	0	0
$862$	23.0000	0.783383
$863$	−39.0000	−1.32758	−0.663788	−	0.747921i	$-0.731052\pi$
$863$	−39.0000	−1.32758	−0.663788	+	0.747921i	$0.731052\pi$
$864$	0	0
$865$	0	0
$866$	−16.0000	−0.543702
$867$	0	0
$868$	−7.00000	−0.237595
$869$	24.0000	0.814144
$870$	0	0
$871$	16.0000	0.542139
$872$	−11.0000	−0.372507
$873$	3.00000	0.101535
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−1.00000	−0.0337676	−0.0168838	−	0.999857i	$-0.505375\pi$
$877$	−1.00000	−0.0337676	−0.0168838	+	0.999857i	$0.505375\pi$
$878$	7.00000	0.236239
$879$	0	0
$880$	0	0
$881$	39.0000	1.31394	0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000	1.31394	0.656972	+	0.753915i	$0.271837\pi$
$882$	18.0000	0.606092
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	34.0000	1.14225
$887$	7.00000	0.235037	0.117518	−	0.993071i	$-0.462506\pi$
$887$	7.00000	0.235037	0.117518	+	0.993071i	$0.462506\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	−27.0000	−0.904534
$892$	11.0000	0.368307
$893$	0	0
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	36.0000	1.20134
$899$	21.0000	0.700389
$900$	0	0
$901$	−33.0000	−1.09939
$902$	−33.0000	−1.09878
$903$	0	0
$904$	−1.00000	−0.0332595
$905$	0	0
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	17.0000	0.564165
$909$	−42.0000	−1.39305
$910$	0	0
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	0	0
$913$	−36.0000	−1.19143
$914$	−37.0000	−1.22385
$915$	0	0
$916$	20.0000	0.660819
$917$	−10.0000	−0.330229
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	0	0
$922$	3.00000	0.0987997
$923$	−24.0000	−0.789970
$924$	0	0
$925$	0	0
$926$	−4.00000	−0.131448
$927$	0	0
$928$	−3.00000	−0.0984798
$929$	−15.0000	−0.492134	−0.246067	−	0.969253i	$-0.579138\pi$
$929$	−15.0000	−0.492134	−0.246067	+	0.969253i	$0.579138\pi$
$930$	0	0
$931$	0	0
$932$	6.00000	0.196537
$933$	0	0
$934$	3.00000	0.0981630
$935$	0	0
$936$	12.0000	0.392232
$937$	28.0000	0.914720	0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000	0.914720	0.457360	+	0.889282i	$0.348795\pi$
$938$	−4.00000	−0.130605
$939$	0	0
$940$	0	0
$941$	26.0000	0.847576	0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000	0.847576	0.423788	+	0.905761i	$0.360700\pi$
$942$	0	0
$943$	−88.0000	−2.86567
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−33.0000	−1.07292
$947$	37.0000	1.20234	0.601169	−	0.799122i	$-0.294702\pi$
$947$	37.0000	1.20234	0.601169	+	0.799122i	$0.294702\pi$
$948$	0	0
$949$	−8.00000	−0.259691
$950$	0	0
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	−33.0000	−1.06841
$955$	0	0
$956$	−17.0000	−0.549819
$957$	0	0
$958$	−36.0000	−1.16311
$959$	6.00000	0.193750
$960$	0	0
$961$	18.0000	0.580645
$962$	4.00000	0.128965
$963$	30.0000	0.966736
$964$	−14.0000	−0.450910
$965$	0	0
$966$	0	0
$967$	−34.0000	−1.09337	−0.546683	−	0.837340i	$-0.684110\pi$
$967$	−34.0000	−1.09337	−0.546683	+	0.837340i	$0.684110\pi$
$968$	−2.00000	−0.0642824
$969$	0	0
$970$	0	0
$971$	−1.00000	−0.0320915	−0.0160458	−	0.999871i	$-0.505108\pi$
$971$	−1.00000	−0.0320915	−0.0160458	+	0.999871i	$0.505108\pi$
$972$	0	0
$973$	1.00000	0.0320585
$974$	36.0000	1.15351
$975$	0	0
$976$	−15.0000	−0.480138
$977$	33.0000	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	33.0000	1.05361
$982$	−36.0000	−1.14881
$983$	−11.0000	−0.350846	−0.175423	−	0.984493i	$-0.556129\pi$
$983$	−11.0000	−0.350846	−0.175423	+	0.984493i	$0.556129\pi$
$984$	0	0
$985$	0	0
$986$	9.00000	0.286618
$987$	0	0
$988$	0	0
$989$	−88.0000	−2.79824
$990$	0	0
$991$	−45.0000	−1.42947	−0.714736	−	0.699394i	$-0.753453\pi$
$991$	−45.0000	−1.42947	−0.714736	+	0.699394i	$0.753453\pi$
$992$	−7.00000	−0.222250
$993$	0	0
$994$	6.00000	0.190308
$995$	0	0
$996$	0	0
$997$	−44.0000	−1.39349	−0.696747	−	0.717317i	$-0.745370\pi$
$997$	−44.0000	−1.39349	−0.696747	+	0.717317i	$0.745370\pi$
$998$	−18.0000	−0.569780
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.l.1.1		1
5.2	odd	4		370.2.b.b.149.2	yes	2
5.3	odd	4		370.2.b.b.149.1	✓	2
5.4	even	2		1850.2.a.d.1.1		1
15.2	even	4		3330.2.d.c.1999.1		2
15.8	even	4		3330.2.d.c.1999.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.b.149.1	✓	2	5.3	odd	4
370.2.b.b.149.2	yes	2	5.2	odd	4
1850.2.a.d.1.1		1	5.4	even	2
1850.2.a.l.1.1		1	1.1	even	1	trivial
3330.2.d.c.1999.1		2	15.2	even	4
3330.2.d.c.1999.2		2	15.8	even	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)

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L-functions

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