LMFDB - Embedded newform 1840.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1840,4,Mod(1,1840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1840, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1840.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1840 = 2^{4} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1840.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:	$108.563514411$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+5.00000 q^{3} -5.00000 q^{5} -12.0000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q+5.00000 q^{3} -5.00000 q^{5} -12.0000 q^{7} -2.00000 q^{9} -22.0000 q^{11} +19.0000 q^{13} -25.0000 q^{15} +96.0000 q^{17} +98.0000 q^{19} -60.0000 q^{21} -23.0000 q^{23} +25.0000 q^{25} -145.000 q^{27} -227.000 q^{29} +285.000 q^{31} -110.000 q^{33} +60.0000 q^{35} -398.000 q^{37} +95.0000 q^{39} +271.000 q^{41} +100.000 q^{43} +10.0000 q^{45} +285.000 q^{47} -199.000 q^{49} +480.000 q^{51} +18.0000 q^{53} +110.000 q^{55} +490.000 q^{57} +352.000 q^{59} -478.000 q^{61} +24.0000 q^{63} -95.0000 q^{65} -330.000 q^{67} -115.000 q^{69} -835.000 q^{71} -1127.00 q^{73} +125.000 q^{75} +264.000 q^{77} -322.000 q^{79} -671.000 q^{81} -572.000 q^{83} -480.000 q^{85} -1135.00 q^{87} -504.000 q^{89} -228.000 q^{91} +1425.00 q^{93} -490.000 q^{95} +1712.00 q^{97} +44.0000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	5.00000	0.962250	0.481125	−	0.876652i	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	0	0
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	−12.0000	−0.647939	−0.323970	−	0.946068i	$-0.605018\pi$
$7$	−12.0000	−0.647939	−0.323970	+	0.946068i	$0.605018\pi$
$8$	0	0
$9$	−2.00000	−0.0740741
$10$	0	0
$11$	−22.0000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−22.0000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	19.0000	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$13$	19.0000	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$14$	0	0
$15$	−25.0000	−0.430331
$16$	0	0
$17$	96.0000	1.36961	0.684806	−	0.728725i	$-0.259887\pi$
$17$	96.0000	1.36961	0.684806	+	0.728725i	$0.259887\pi$
$18$	0	0
$19$	98.0000	1.18330	0.591651	−	0.806194i	$-0.298476\pi$
$19$	98.0000	1.18330	0.591651	+	0.806194i	$0.298476\pi$
$20$	0	0
$21$	−60.0000	−0.623480
$22$	0	0
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−145.000	−1.03353
$28$	0	0
$29$	−227.000	−1.45355	−0.726773	−	0.686878i	$-0.758981\pi$
$29$	−227.000	−1.45355	−0.726773	+	0.686878i	$0.758981\pi$
$30$	0	0
$31$	285.000	1.65121	0.825605	−	0.564248i	$-0.190834\pi$
$31$	285.000	1.65121	0.825605	+	0.564248i	$0.190834\pi$
$32$	0	0
$33$	−110.000	−0.580259
$34$	0	0
$35$	60.0000	0.289767
$36$	0	0
$37$	−398.000	−1.76840	−0.884200	−	0.467109i	$-0.845296\pi$
$37$	−398.000	−1.76840	−0.884200	+	0.467109i	$0.845296\pi$
$38$	0	0
$39$	95.0000	0.390056
$40$	0	0
$41$	271.000	1.03227	0.516135	−	0.856507i	$-0.327370\pi$
$41$	271.000	1.03227	0.516135	+	0.856507i	$0.327370\pi$
$42$	0	0
$43$	100.000	0.354648	0.177324	−	0.984153i	$-0.443256\pi$
$43$	100.000	0.354648	0.177324	+	0.984153i	$0.443256\pi$
$44$	0	0
$45$	10.0000	0.0331269
$46$	0	0
$47$	285.000	0.884500	0.442250	−	0.896892i	$-0.354180\pi$
$47$	285.000	0.884500	0.442250	+	0.896892i	$0.354180\pi$
$48$	0	0
$49$	−199.000	−0.580175
$50$	0	0
$51$	480.000	1.31791
$52$	0	0
$53$	18.0000	0.0466508	0.0233254	−	0.999728i	$-0.492575\pi$
$53$	18.0000	0.0466508	0.0233254	+	0.999728i	$0.492575\pi$
$54$	0	0
$55$	110.000	0.269680
$56$	0	0
$57$	490.000	1.13863
$58$	0	0
$59$	352.000	0.776720	0.388360	−	0.921508i	$-0.373042\pi$
$59$	352.000	0.776720	0.388360	+	0.921508i	$0.373042\pi$
$60$	0	0
$61$	−478.000	−1.00331	−0.501653	−	0.865069i	$-0.667274\pi$
$61$	−478.000	−1.00331	−0.501653	+	0.865069i	$0.667274\pi$
$62$	0	0
$63$	24.0000	0.0479955
$64$	0	0
$65$	−95.0000	−0.181282
$66$	0	0
$67$	−330.000	−0.601730	−0.300865	−	0.953667i	$-0.597275\pi$
$67$	−330.000	−0.601730	−0.300865	+	0.953667i	$0.597275\pi$
$68$	0	0
$69$	−115.000	−0.200643
$70$	0	0
$71$	−835.000	−1.39572	−0.697861	−	0.716233i	$-0.745865\pi$
$71$	−835.000	−1.39572	−0.697861	+	0.716233i	$0.745865\pi$
$72$	0	0
$73$	−1127.00	−1.80692	−0.903461	−	0.428669i	$-0.858983\pi$
$73$	−1127.00	−1.80692	−0.903461	+	0.428669i	$0.858983\pi$
$74$	0	0
$75$	125.000	0.192450
$76$	0	0
$77$	264.000	0.390722
$78$	0	0
$79$	−322.000	−0.458580	−0.229290	−	0.973358i	$-0.573640\pi$
$79$	−322.000	−0.458580	−0.229290	+	0.973358i	$0.573640\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	0	0
$83$	−572.000	−0.756448	−0.378224	−	0.925714i	$-0.623465\pi$
$83$	−572.000	−0.756448	−0.378224	+	0.925714i	$0.623465\pi$
$84$	0	0
$85$	−480.000	−0.612510
$86$	0	0
$87$	−1135.00	−1.39868
$88$	0	0
$89$	−504.000	−0.600268	−0.300134	−	0.953897i	$-0.597031\pi$
$89$	−504.000	−0.600268	−0.300134	+	0.953897i	$0.597031\pi$
$90$	0	0
$91$	−228.000	−0.262647
$92$	0	0
$93$	1425.00	1.58888
$94$	0	0
$95$	−490.000	−0.529189
$96$	0	0
$97$	1712.00	1.79203	0.896017	−	0.444020i	$-0.146448\pi$
$97$	1712.00	1.79203	0.896017	+	0.444020i	$0.146448\pi$
$98$	0	0
$99$	44.0000	0.0446683
$100$	0	0
$101$	−1710.00	−1.68467	−0.842333	−	0.538957i	$-0.818819\pi$
$101$	−1710.00	−1.68467	−0.842333	+	0.538957i	$0.818819\pi$
$102$	0	0
$103$	−36.0000	−0.0344387	−0.0172193	−	0.999852i	$-0.505481\pi$
$103$	−36.0000	−0.0344387	−0.0172193	+	0.999852i	$0.505481\pi$
$104$	0	0
$105$	300.000	0.278829
$106$	0	0
$107$	−690.000	−0.623410	−0.311705	−	0.950179i	$-0.600900\pi$
$107$	−690.000	−0.623410	−0.311705	+	0.950179i	$0.600900\pi$
$108$	0	0
$109$	380.000	0.333921	0.166961	−	0.985964i	$-0.446605\pi$
$109$	380.000	0.333921	0.166961	+	0.985964i	$0.446605\pi$
$110$	0	0
$111$	−1990.00	−1.70164
$112$	0	0
$113$	−2172.00	−1.80818	−0.904091	−	0.427340i	$-0.859451\pi$
$113$	−2172.00	−1.80818	−0.904091	+	0.427340i	$0.859451\pi$
$114$	0	0
$115$	115.000	0.0932505
$116$	0	0
$117$	−38.0000	−0.0300265
$118$	0	0
$119$	−1152.00	−0.887426
$120$	0	0
$121$	−847.000	−0.636364
$122$	0	0
$123$	1355.00	0.993303
$124$	0	0
$125$	−125.000	−0.0894427
$126$	0	0
$127$	43.0000	0.0300444	0.0150222	−	0.999887i	$-0.495218\pi$
$127$	43.0000	0.0300444	0.0150222	+	0.999887i	$0.495218\pi$
$128$	0	0
$129$	500.000	0.341260
$130$	0	0
$131$	−1187.00	−0.791669	−0.395835	−	0.918322i	$-0.629545\pi$
$131$	−1187.00	−0.791669	−0.395835	+	0.918322i	$0.629545\pi$
$132$	0	0
$133$	−1176.00	−0.766708
$134$	0	0
$135$	725.000	0.462208
$136$	0	0
$137$	212.000	0.132207	0.0661036	−	0.997813i	$-0.478943\pi$
$137$	212.000	0.132207	0.0661036	+	0.997813i	$0.478943\pi$
$138$	0	0
$139$	1091.00	0.665737	0.332868	−	0.942973i	$-0.391984\pi$
$139$	1091.00	0.665737	0.332868	+	0.942973i	$0.391984\pi$
$140$	0	0
$141$	1425.00	0.851111
$142$	0	0
$143$	−418.000	−0.244440
$144$	0	0
$145$	1135.00	0.650046
$146$	0	0
$147$	−995.000	−0.558274
$148$	0	0
$149$	−1186.00	−0.652087	−0.326043	−	0.945355i	$-0.605716\pi$
$149$	−1186.00	−0.652087	−0.326043	+	0.945355i	$0.605716\pi$
$150$	0	0
$151$	−587.000	−0.316354	−0.158177	−	0.987411i	$-0.550562\pi$
$151$	−587.000	−0.316354	−0.158177	+	0.987411i	$0.550562\pi$
$152$	0	0
$153$	−192.000	−0.101453
$154$	0	0
$155$	−1425.00	−0.738444
$156$	0	0
$157$	644.000	0.327368	0.163684	−	0.986513i	$-0.447662\pi$
$157$	644.000	0.327368	0.163684	+	0.986513i	$0.447662\pi$
$158$	0	0
$159$	90.0000	0.0448897
$160$	0	0
$161$	276.000	0.135105
$162$	0	0
$163$	2779.00	1.33539	0.667693	−	0.744436i	$-0.267282\pi$
$163$	2779.00	1.33539	0.667693	+	0.744436i	$0.267282\pi$
$164$	0	0
$165$	550.000	0.259500
$166$	0	0
$167$	568.000	0.263193	0.131596	−	0.991303i	$-0.457990\pi$
$167$	568.000	0.263193	0.131596	+	0.991303i	$0.457990\pi$
$168$	0	0
$169$	−1836.00	−0.835685
$170$	0	0
$171$	−196.000	−0.0876520
$172$	0	0
$173$	−2578.00	−1.13296	−0.566479	−	0.824076i	$-0.691695\pi$
$173$	−2578.00	−1.13296	−0.566479	+	0.824076i	$0.691695\pi$
$174$	0	0
$175$	−300.000	−0.129588
$176$	0	0
$177$	1760.00	0.747399
$178$	0	0
$179$	−4141.00	−1.72912	−0.864561	−	0.502528i	$-0.832403\pi$
$179$	−4141.00	−1.72912	−0.864561	+	0.502528i	$0.832403\pi$
$180$	0	0
$181$	−1454.00	−0.597099	−0.298550	−	0.954394i	$-0.596503\pi$
$181$	−1454.00	−0.597099	−0.298550	+	0.954394i	$0.596503\pi$
$182$	0	0
$183$	−2390.00	−0.965431
$184$	0	0
$185$	1990.00	0.790852
$186$	0	0
$187$	−2112.00	−0.825908
$188$	0	0
$189$	1740.00	0.669663
$190$	0	0
$191$	3390.00	1.28425	0.642125	−	0.766600i	$-0.278053\pi$
$191$	3390.00	1.28425	0.642125	+	0.766600i	$0.278053\pi$
$192$	0	0
$193$	−2587.00	−0.964851	−0.482426	−	0.875937i	$-0.660244\pi$
$193$	−2587.00	−0.964851	−0.482426	+	0.875937i	$0.660244\pi$
$194$	0	0
$195$	−475.000	−0.174438
$196$	0	0
$197$	1641.00	0.593484	0.296742	−	0.954958i	$-0.404100\pi$
$197$	1641.00	0.593484	0.296742	+	0.954958i	$0.404100\pi$
$198$	0	0
$199$	406.000	0.144626	0.0723130	−	0.997382i	$-0.476962\pi$
$199$	406.000	0.144626	0.0723130	+	0.997382i	$0.476962\pi$
$200$	0	0
$201$	−1650.00	−0.579015
$202$	0	0
$203$	2724.00	0.941809
$204$	0	0
$205$	−1355.00	−0.461645
$206$	0	0
$207$	46.0000	0.0154455
$208$	0	0
$209$	−2156.00	−0.713558
$210$	0	0
$211$	5060.00	1.65092	0.825462	−	0.564458i	$-0.190915\pi$
$211$	5060.00	1.65092	0.825462	+	0.564458i	$0.190915\pi$
$212$	0	0
$213$	−4175.00	−1.34303
$214$	0	0
$215$	−500.000	−0.158603
$216$	0	0
$217$	−3420.00	−1.06988
$218$	0	0
$219$	−5635.00	−1.73871
$220$	0	0
$221$	1824.00	0.555183
$222$	0	0
$223$	−3232.00	−0.970541	−0.485271	−	0.874364i	$-0.661279\pi$
$223$	−3232.00	−0.970541	−0.485271	+	0.874364i	$0.661279\pi$
$224$	0	0
$225$	−50.0000	−0.0148148
$226$	0	0
$227$	1472.00	0.430397	0.215198	−	0.976570i	$-0.430960\pi$
$227$	1472.00	0.430397	0.215198	+	0.976570i	$0.430960\pi$
$228$	0	0
$229$	−4048.00	−1.16812	−0.584060	−	0.811711i	$-0.698537\pi$
$229$	−4048.00	−1.16812	−0.584060	+	0.811711i	$0.698537\pi$
$230$	0	0
$231$	1320.00	0.375972
$232$	0	0
$233$	−2313.00	−0.650342	−0.325171	−	0.945655i	$-0.605422\pi$
$233$	−2313.00	−0.650342	−0.325171	+	0.945655i	$0.605422\pi$
$234$	0	0
$235$	−1425.00	−0.395561
$236$	0	0
$237$	−1610.00	−0.441269
$238$	0	0
$239$	−379.000	−0.102575	−0.0512876	−	0.998684i	$-0.516333\pi$
$239$	−379.000	−0.102575	−0.0512876	+	0.998684i	$0.516333\pi$
$240$	0	0
$241$	7242.00	1.93568	0.967839	−	0.251572i	$-0.0809474\pi$
$241$	7242.00	1.93568	0.967839	+	0.251572i	$0.0809474\pi$
$242$	0	0
$243$	560.000	0.147835
$244$	0	0
$245$	995.000	0.259462
$246$	0	0
$247$	1862.00	0.479661
$248$	0	0
$249$	−2860.00	−0.727892
$250$	0	0
$251$	1516.00	0.381231	0.190616	−	0.981665i	$-0.438952\pi$
$251$	1516.00	0.381231	0.190616	+	0.981665i	$0.438952\pi$
$252$	0	0
$253$	506.000	0.125739
$254$	0	0
$255$	−2400.00	−0.589388
$256$	0	0
$257$	6379.00	1.54829	0.774146	−	0.633007i	$-0.218180\pi$
$257$	6379.00	1.54829	0.774146	+	0.633007i	$0.218180\pi$
$258$	0	0
$259$	4776.00	1.14582
$260$	0	0
$261$	454.000	0.107670
$262$	0	0
$263$	−1182.00	−0.277130	−0.138565	−	0.990353i	$-0.544249\pi$
$263$	−1182.00	−0.277130	−0.138565	+	0.990353i	$0.544249\pi$
$264$	0	0
$265$	−90.0000	−0.0208629
$266$	0	0
$267$	−2520.00	−0.577609
$268$	0	0
$269$	1769.00	0.400958	0.200479	−	0.979698i	$-0.435750\pi$
$269$	1769.00	0.400958	0.200479	+	0.979698i	$0.435750\pi$
$270$	0	0
$271$	−2208.00	−0.494932	−0.247466	−	0.968897i	$-0.579598\pi$
$271$	−2208.00	−0.494932	−0.247466	+	0.968897i	$0.579598\pi$
$272$	0	0
$273$	−1140.00	−0.252732
$274$	0	0
$275$	−550.000	−0.120605
$276$	0	0
$277$	−5083.00	−1.10256	−0.551278	−	0.834322i	$-0.685860\pi$
$277$	−5083.00	−1.10256	−0.551278	+	0.834322i	$0.685860\pi$
$278$	0	0
$279$	−570.000	−0.122312
$280$	0	0
$281$	6924.00	1.46993	0.734967	−	0.678103i	$-0.237198\pi$
$281$	6924.00	1.46993	0.734967	+	0.678103i	$0.237198\pi$
$282$	0	0
$283$	−6638.00	−1.39430	−0.697152	−	0.716923i	$-0.745550\pi$
$283$	−6638.00	−1.39430	−0.697152	+	0.716923i	$0.745550\pi$
$284$	0	0
$285$	−2450.00	−0.509212
$286$	0	0
$287$	−3252.00	−0.668848
$288$	0	0
$289$	4303.00	0.875840
$290$	0	0
$291$	8560.00	1.72439
$292$	0	0
$293$	5272.00	1.05117	0.525586	−	0.850740i	$-0.323846\pi$
$293$	5272.00	1.05117	0.525586	+	0.850740i	$0.323846\pi$
$294$	0	0
$295$	−1760.00	−0.347360
$296$	0	0
$297$	3190.00	0.623241
$298$	0	0
$299$	−437.000	−0.0845230
$300$	0	0
$301$	−1200.00	−0.229790
$302$	0	0
$303$	−8550.00	−1.62107
$304$	0	0
$305$	2390.00	0.448692
$306$	0	0
$307$	2192.00	0.407505	0.203753	−	0.979022i	$-0.434686\pi$
$307$	2192.00	0.407505	0.203753	+	0.979022i	$0.434686\pi$
$308$	0	0
$309$	−180.000	−0.0331386
$310$	0	0
$311$	−8987.00	−1.63860	−0.819302	−	0.573362i	$-0.805639\pi$
$311$	−8987.00	−1.63860	−0.819302	+	0.573362i	$0.805639\pi$
$312$	0	0
$313$	4336.00	0.783020	0.391510	−	0.920174i	$-0.371953\pi$
$313$	4336.00	0.783020	0.391510	+	0.920174i	$0.371953\pi$
$314$	0	0
$315$	−120.000	−0.0214642
$316$	0	0
$317$	4554.00	0.806871	0.403436	−	0.915008i	$-0.367816\pi$
$317$	4554.00	0.806871	0.403436	+	0.915008i	$0.367816\pi$
$318$	0	0
$319$	4994.00	0.876521
$320$	0	0
$321$	−3450.00	−0.599876
$322$	0	0
$323$	9408.00	1.62067
$324$	0	0
$325$	475.000	0.0810716
$326$	0	0
$327$	1900.00	0.321316
$328$	0	0
$329$	−3420.00	−0.573102
$330$	0	0
$331$	−961.000	−0.159581	−0.0797905	−	0.996812i	$-0.525425\pi$
$331$	−961.000	−0.159581	−0.0797905	+	0.996812i	$0.525425\pi$
$332$	0	0
$333$	796.000	0.130993
$334$	0	0
$335$	1650.00	0.269102
$336$	0	0
$337$	−400.000	−0.0646569	−0.0323285	−	0.999477i	$-0.510292\pi$
$337$	−400.000	−0.0646569	−0.0323285	+	0.999477i	$0.510292\pi$
$338$	0	0
$339$	−10860.0	−1.73992
$340$	0	0
$341$	−6270.00	−0.995717
$342$	0	0
$343$	6504.00	1.02386
$344$	0	0
$345$	575.000	0.0897303
$346$	0	0
$347$	12684.0	1.96228	0.981142	−	0.193287i	$-0.0619147\pi$
$347$	12684.0	1.96228	0.981142	+	0.193287i	$0.0619147\pi$
$348$	0	0
$349$	−3631.00	−0.556914	−0.278457	−	0.960449i	$-0.589823\pi$
$349$	−3631.00	−0.556914	−0.278457	+	0.960449i	$0.589823\pi$
$350$	0	0
$351$	−2755.00	−0.418949
$352$	0	0
$353$	−6539.00	−0.985937	−0.492969	−	0.870047i	$-0.664088\pi$
$353$	−6539.00	−0.985937	−0.492969	+	0.870047i	$0.664088\pi$
$354$	0	0
$355$	4175.00	0.624186
$356$	0	0
$357$	−5760.00	−0.853926
$358$	0	0
$359$	−7262.00	−1.06761	−0.533807	−	0.845606i	$-0.679239\pi$
$359$	−7262.00	−1.06761	−0.533807	+	0.845606i	$0.679239\pi$
$360$	0	0
$361$	2745.00	0.400204
$362$	0	0
$363$	−4235.00	−0.612341
$364$	0	0
$365$	5635.00	0.808080
$366$	0	0
$367$	−11884.0	−1.69030	−0.845150	−	0.534530i	$-0.820489\pi$
$367$	−11884.0	−1.69030	−0.845150	+	0.534530i	$0.820489\pi$
$368$	0	0
$369$	−542.000	−0.0764645
$370$	0	0
$371$	−216.000	−0.0302268
$372$	0	0
$373$	−1902.00	−0.264026	−0.132013	−	0.991248i	$-0.542144\pi$
$373$	−1902.00	−0.264026	−0.132013	+	0.991248i	$0.542144\pi$
$374$	0	0
$375$	−625.000	−0.0860663
$376$	0	0
$377$	−4313.00	−0.589206
$378$	0	0
$379$	2472.00	0.335035	0.167517	−	0.985869i	$-0.446425\pi$
$379$	2472.00	0.335035	0.167517	+	0.985869i	$0.446425\pi$
$380$	0	0
$381$	215.000	0.0289102
$382$	0	0
$383$	−9088.00	−1.21247	−0.606234	−	0.795286i	$-0.707320\pi$
$383$	−9088.00	−1.21247	−0.606234	+	0.795286i	$0.707320\pi$
$384$	0	0
$385$	−1320.00	−0.174736
$386$	0	0
$387$	−200.000	−0.0262702
$388$	0	0
$389$	−4480.00	−0.583920	−0.291960	−	0.956430i	$-0.594307\pi$
$389$	−4480.00	−0.583920	−0.291960	+	0.956430i	$0.594307\pi$
$390$	0	0
$391$	−2208.00	−0.285584
$392$	0	0
$393$	−5935.00	−0.761784
$394$	0	0
$395$	1610.00	0.205083
$396$	0	0
$397$	−11237.0	−1.42058	−0.710288	−	0.703911i	$-0.751435\pi$
$397$	−11237.0	−1.42058	−0.710288	+	0.703911i	$0.751435\pi$
$398$	0	0
$399$	−5880.00	−0.737765
$400$	0	0
$401$	−6458.00	−0.804232	−0.402116	−	0.915589i	$-0.631725\pi$
$401$	−6458.00	−0.804232	−0.402116	+	0.915589i	$0.631725\pi$
$402$	0	0
$403$	5415.00	0.669331
$404$	0	0
$405$	3355.00	0.411633
$406$	0	0
$407$	8756.00	1.06639
$408$	0	0
$409$	2261.00	0.273348	0.136674	−	0.990616i	$-0.456359\pi$
$409$	2261.00	0.273348	0.136674	+	0.990616i	$0.456359\pi$
$410$	0	0
$411$	1060.00	0.127216
$412$	0	0
$413$	−4224.00	−0.503267
$414$	0	0
$415$	2860.00	0.338294
$416$	0	0
$417$	5455.00	0.640606
$418$	0	0
$419$	612.000	0.0713560	0.0356780	−	0.999363i	$-0.488641\pi$
$419$	612.000	0.0713560	0.0356780	+	0.999363i	$0.488641\pi$
$420$	0	0
$421$	−4292.00	−0.496863	−0.248431	−	0.968649i	$-0.579915\pi$
$421$	−4292.00	−0.496863	−0.248431	+	0.968649i	$0.579915\pi$
$422$	0	0
$423$	−570.000	−0.0655186
$424$	0	0
$425$	2400.00	0.273923
$426$	0	0
$427$	5736.00	0.650081
$428$	0	0
$429$	−2090.00	−0.235212
$430$	0	0
$431$	5132.00	0.573549	0.286775	−	0.957998i	$-0.407417\pi$
$431$	5132.00	0.573549	0.286775	+	0.957998i	$0.407417\pi$
$432$	0	0
$433$	15982.0	1.77378	0.886889	−	0.461983i	$-0.152862\pi$
$433$	15982.0	1.77378	0.886889	+	0.461983i	$0.152862\pi$
$434$	0	0
$435$	5675.00	0.625507
$436$	0	0
$437$	−2254.00	−0.246736
$438$	0	0
$439$	3323.00	0.361271	0.180636	−	0.983550i	$-0.442185\pi$
$439$	3323.00	0.361271	0.180636	+	0.983550i	$0.442185\pi$
$440$	0	0
$441$	398.000	0.0429759
$442$	0	0
$443$	−8699.00	−0.932962	−0.466481	−	0.884531i	$-0.654478\pi$
$443$	−8699.00	−0.932962	−0.466481	+	0.884531i	$0.654478\pi$
$444$	0	0
$445$	2520.00	0.268448
$446$	0	0
$447$	−5930.00	−0.627471
$448$	0	0
$449$	6966.00	0.732173	0.366087	−	0.930581i	$-0.380697\pi$
$449$	6966.00	0.732173	0.366087	+	0.930581i	$0.380697\pi$
$450$	0	0
$451$	−5962.00	−0.622483
$452$	0	0
$453$	−2935.00	−0.304411
$454$	0	0
$455$	1140.00	0.117459
$456$	0	0
$457$	−9020.00	−0.923277	−0.461639	−	0.887068i	$-0.652738\pi$
$457$	−9020.00	−0.923277	−0.461639	+	0.887068i	$0.652738\pi$
$458$	0	0
$459$	−13920.0	−1.41553
$460$	0	0
$461$	−17847.0	−1.80308	−0.901538	−	0.432701i	$-0.857561\pi$
$461$	−17847.0	−1.80308	−0.901538	+	0.432701i	$0.857561\pi$
$462$	0	0
$463$	11360.0	1.14027	0.570134	−	0.821552i	$-0.306891\pi$
$463$	11360.0	1.14027	0.570134	+	0.821552i	$0.306891\pi$
$464$	0	0
$465$	−7125.00	−0.710568
$466$	0	0
$467$	534.000	0.0529134	0.0264567	−	0.999650i	$-0.491578\pi$
$467$	534.000	0.0529134	0.0264567	+	0.999650i	$0.491578\pi$
$468$	0	0
$469$	3960.00	0.389884
$470$	0	0
$471$	3220.00	0.315010
$472$	0	0
$473$	−2200.00	−0.213861
$474$	0	0
$475$	2450.00	0.236660
$476$	0	0
$477$	−36.0000	−0.00345561
$478$	0	0
$479$	−3428.00	−0.326992	−0.163496	−	0.986544i	$-0.552277\pi$
$479$	−3428.00	−0.326992	−0.163496	+	0.986544i	$0.552277\pi$
$480$	0	0
$481$	−7562.00	−0.716835
$482$	0	0
$483$	1380.00	0.130005
$484$	0	0
$485$	−8560.00	−0.801422
$486$	0	0
$487$	−6949.00	−0.646590	−0.323295	−	0.946298i	$-0.604791\pi$
$487$	−6949.00	−0.646590	−0.323295	+	0.946298i	$0.604791\pi$
$488$	0	0
$489$	13895.0	1.28498
$490$	0	0
$491$	9571.00	0.879701	0.439850	−	0.898071i	$-0.355031\pi$
$491$	9571.00	0.879701	0.439850	+	0.898071i	$0.355031\pi$
$492$	0	0
$493$	−21792.0	−1.99080
$494$	0	0
$495$	−220.000	−0.0199763
$496$	0	0
$497$	10020.0	0.904343
$498$	0	0
$499$	−10679.0	−0.958031	−0.479016	−	0.877806i	$-0.659006\pi$
$499$	−10679.0	−0.958031	−0.479016	+	0.877806i	$0.659006\pi$
$500$	0	0
$501$	2840.00	0.253257
$502$	0	0
$503$	9514.00	0.843356	0.421678	−	0.906746i	$-0.361441\pi$
$503$	9514.00	0.843356	0.421678	+	0.906746i	$0.361441\pi$
$504$	0	0
$505$	8550.00	0.753406
$506$	0	0
$507$	−9180.00	−0.804138
$508$	0	0
$509$	6977.00	0.607564	0.303782	−	0.952742i	$-0.401751\pi$
$509$	6977.00	0.607564	0.303782	+	0.952742i	$0.401751\pi$
$510$	0	0
$511$	13524.0	1.17078
$512$	0	0
$513$	−14210.0	−1.22298
$514$	0	0
$515$	180.000	0.0154015
$516$	0	0
$517$	−6270.00	−0.533374
$518$	0	0
$519$	−12890.0	−1.09019
$520$	0	0
$521$	−13172.0	−1.10763	−0.553816	−	0.832639i	$-0.686829\pi$
$521$	−13172.0	−1.10763	−0.553816	+	0.832639i	$0.686829\pi$
$522$	0	0
$523$	1512.00	0.126415	0.0632076	−	0.998000i	$-0.479867\pi$
$523$	1512.00	0.126415	0.0632076	+	0.998000i	$0.479867\pi$
$524$	0	0
$525$	−1500.00	−0.124696
$526$	0	0
$527$	27360.0	2.26152
$528$	0	0
$529$	529.000	0.0434783
$530$	0	0
$531$	−704.000	−0.0575348
$532$	0	0
$533$	5149.00	0.418439
$534$	0	0
$535$	3450.00	0.278797
$536$	0	0
$537$	−20705.0	−1.66385
$538$	0	0
$539$	4378.00	0.349859
$540$	0	0
$541$	10589.0	0.841510	0.420755	−	0.907174i	$-0.361765\pi$
$541$	10589.0	0.841510	0.420755	+	0.907174i	$0.361765\pi$
$542$	0	0
$543$	−7270.00	−0.574559
$544$	0	0
$545$	−1900.00	−0.149334
$546$	0	0
$547$	3227.00	0.252242	0.126121	−	0.992015i	$-0.459747\pi$
$547$	3227.00	0.252242	0.126121	+	0.992015i	$0.459747\pi$
$548$	0	0
$549$	956.000	0.0743189
$550$	0	0
$551$	−22246.0	−1.71998
$552$	0	0
$553$	3864.00	0.297132
$554$	0	0
$555$	9950.00	0.760998
$556$	0	0
$557$	−1888.00	−0.143621	−0.0718107	−	0.997418i	$-0.522878\pi$
$557$	−1888.00	−0.143621	−0.0718107	+	0.997418i	$0.522878\pi$
$558$	0	0
$559$	1900.00	0.143759
$560$	0	0
$561$	−10560.0	−0.794730
$562$	0	0
$563$	−14388.0	−1.07705	−0.538527	−	0.842608i	$-0.681019\pi$
$563$	−14388.0	−1.07705	−0.538527	+	0.842608i	$0.681019\pi$
$564$	0	0
$565$	10860.0	0.808644
$566$	0	0
$567$	8052.00	0.596388
$568$	0	0
$569$	−18234.0	−1.34343	−0.671713	−	0.740812i	$-0.734441\pi$
$569$	−18234.0	−1.34343	−0.671713	+	0.740812i	$0.734441\pi$
$570$	0	0
$571$	−2024.00	−0.148339	−0.0741697	−	0.997246i	$-0.523631\pi$
$571$	−2024.00	−0.148339	−0.0741697	+	0.997246i	$0.523631\pi$
$572$	0	0
$573$	16950.0	1.23577
$574$	0	0
$575$	−575.000	−0.0417029
$576$	0	0
$577$	7085.00	0.511183	0.255591	−	0.966785i	$-0.417730\pi$
$577$	7085.00	0.511183	0.255591	+	0.966785i	$0.417730\pi$
$578$	0	0
$579$	−12935.0	−0.928429
$580$	0	0
$581$	6864.00	0.490132
$582$	0	0
$583$	−396.000	−0.0281315
$584$	0	0
$585$	190.000	0.0134283
$586$	0	0
$587$	1421.00	0.0999164	0.0499582	−	0.998751i	$-0.484091\pi$
$587$	1421.00	0.0999164	0.0499582	+	0.998751i	$0.484091\pi$
$588$	0	0
$589$	27930.0	1.95388
$590$	0	0
$591$	8205.00	0.571081
$592$	0	0
$593$	−8202.00	−0.567986	−0.283993	−	0.958826i	$-0.591659\pi$
$593$	−8202.00	−0.567986	−0.283993	+	0.958826i	$0.591659\pi$
$594$	0	0
$595$	5760.00	0.396869
$596$	0	0
$597$	2030.00	0.139166
$598$	0	0
$599$	−16304.0	−1.11213	−0.556063	−	0.831140i	$-0.687689\pi$
$599$	−16304.0	−1.11213	−0.556063	+	0.831140i	$0.687689\pi$
$600$	0	0
$601$	18829.0	1.27795	0.638977	−	0.769225i	$-0.279358\pi$
$601$	18829.0	1.27795	0.638977	+	0.769225i	$0.279358\pi$
$602$	0	0
$603$	660.000	0.0445726
$604$	0	0
$605$	4235.00	0.284590
$606$	0	0
$607$	6556.00	0.438385	0.219193	−	0.975682i	$-0.429658\pi$
$607$	6556.00	0.438385	0.219193	+	0.975682i	$0.429658\pi$
$608$	0	0
$609$	13620.0	0.906257
$610$	0	0
$611$	5415.00	0.358539
$612$	0	0
$613$	−8208.00	−0.540812	−0.270406	−	0.962746i	$-0.587158\pi$
$613$	−8208.00	−0.540812	−0.270406	+	0.962746i	$0.587158\pi$
$614$	0	0
$615$	−6775.00	−0.444218
$616$	0	0
$617$	−5874.00	−0.383271	−0.191636	−	0.981466i	$-0.561379\pi$
$617$	−5874.00	−0.383271	−0.191636	+	0.981466i	$0.561379\pi$
$618$	0	0
$619$	−23864.0	−1.54956	−0.774778	−	0.632233i	$-0.782138\pi$
$619$	−23864.0	−1.54956	−0.774778	+	0.632233i	$0.782138\pi$
$620$	0	0
$621$	3335.00	0.215506
$622$	0	0
$623$	6048.00	0.388937
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−10780.0	−0.686622
$628$	0	0
$629$	−38208.0	−2.42202
$630$	0	0
$631$	23120.0	1.45863	0.729313	−	0.684180i	$-0.239840\pi$
$631$	23120.0	1.45863	0.729313	+	0.684180i	$0.239840\pi$
$632$	0	0
$633$	25300.0	1.58860
$634$	0	0
$635$	−215.000	−0.0134362
$636$	0	0
$637$	−3781.00	−0.235178
$638$	0	0
$639$	1670.00	0.103387
$640$	0	0
$641$	17264.0	1.06379	0.531893	−	0.846811i	$-0.321481\pi$
$641$	17264.0	1.06379	0.531893	+	0.846811i	$0.321481\pi$
$642$	0	0
$643$	−1130.00	−0.0693046	−0.0346523	−	0.999399i	$-0.511032\pi$
$643$	−1130.00	−0.0693046	−0.0346523	+	0.999399i	$0.511032\pi$
$644$	0	0
$645$	−2500.00	−0.152616
$646$	0	0
$647$	−17075.0	−1.03754	−0.518769	−	0.854914i	$-0.673610\pi$
$647$	−17075.0	−1.03754	−0.518769	+	0.854914i	$0.673610\pi$
$648$	0	0
$649$	−7744.00	−0.468380
$650$	0	0
$651$	−17100.0	−1.02950
$652$	0	0
$653$	6059.00	0.363104	0.181552	−	0.983381i	$-0.441888\pi$
$653$	6059.00	0.363104	0.181552	+	0.983381i	$0.441888\pi$
$654$	0	0
$655$	5935.00	0.354045
$656$	0	0
$657$	2254.00	0.133846
$658$	0	0
$659$	980.000	0.0579293	0.0289646	−	0.999580i	$-0.490779\pi$
$659$	980.000	0.0579293	0.0289646	+	0.999580i	$0.490779\pi$
$660$	0	0
$661$	31126.0	1.83156	0.915780	−	0.401680i	$-0.131574\pi$
$661$	31126.0	1.83156	0.915780	+	0.401680i	$0.131574\pi$
$662$	0	0
$663$	9120.00	0.534225
$664$	0	0
$665$	5880.00	0.342882
$666$	0	0
$667$	5221.00	0.303085
$668$	0	0
$669$	−16160.0	−0.933904
$670$	0	0
$671$	10516.0	0.605016
$672$	0	0
$673$	23399.0	1.34022	0.670108	−	0.742264i	$-0.266248\pi$
$673$	23399.0	1.34022	0.670108	+	0.742264i	$0.266248\pi$
$674$	0	0
$675$	−3625.00	−0.206706
$676$	0	0
$677$	7106.00	0.403406	0.201703	−	0.979447i	$-0.435352\pi$
$677$	7106.00	0.403406	0.201703	+	0.979447i	$0.435352\pi$
$678$	0	0
$679$	−20544.0	−1.16113
$680$	0	0
$681$	7360.00	0.414150
$682$	0	0
$683$	−4281.00	−0.239836	−0.119918	−	0.992784i	$-0.538263\pi$
$683$	−4281.00	−0.239836	−0.119918	+	0.992784i	$0.538263\pi$
$684$	0	0
$685$	−1060.00	−0.0591248
$686$	0	0
$687$	−20240.0	−1.12402
$688$	0	0
$689$	342.000	0.0189103
$690$	0	0
$691$	−29036.0	−1.59853	−0.799263	−	0.600981i	$-0.794777\pi$
$691$	−29036.0	−1.59853	−0.799263	+	0.600981i	$0.794777\pi$
$692$	0	0
$693$	−528.000	−0.0289424
$694$	0	0
$695$	−5455.00	−0.297727
$696$	0	0
$697$	26016.0	1.41381
$698$	0	0
$699$	−11565.0	−0.625792
$700$	0	0
$701$	5740.00	0.309268	0.154634	−	0.987972i	$-0.450580\pi$
$701$	5740.00	0.309268	0.154634	+	0.987972i	$0.450580\pi$
$702$	0	0
$703$	−39004.0	−2.09255
$704$	0	0
$705$	−7125.00	−0.380628
$706$	0	0
$707$	20520.0	1.09156
$708$	0	0
$709$	−13432.0	−0.711494	−0.355747	−	0.934582i	$-0.615774\pi$
$709$	−13432.0	−0.711494	−0.355747	+	0.934582i	$0.615774\pi$
$710$	0	0
$711$	644.000	0.0339689
$712$	0	0
$713$	−6555.00	−0.344301
$714$	0	0
$715$	2090.00	0.109317
$716$	0	0
$717$	−1895.00	−0.0987030
$718$	0	0
$719$	2768.00	0.143573	0.0717865	−	0.997420i	$-0.477130\pi$
$719$	2768.00	0.143573	0.0717865	+	0.997420i	$0.477130\pi$
$720$	0	0
$721$	432.000	0.0223142
$722$	0	0
$723$	36210.0	1.86261
$724$	0	0
$725$	−5675.00	−0.290709
$726$	0	0
$727$	−22378.0	−1.14161	−0.570807	−	0.821084i	$-0.693370\pi$
$727$	−22378.0	−1.14161	−0.570807	+	0.821084i	$0.693370\pi$
$728$	0	0
$729$	20917.0	1.06269
$730$	0	0
$731$	9600.00	0.485730
$732$	0	0
$733$	13368.0	0.673613	0.336807	−	0.941574i	$-0.390653\pi$
$733$	13368.0	0.673613	0.336807	+	0.941574i	$0.390653\pi$
$734$	0	0
$735$	4975.00	0.249668
$736$	0	0
$737$	7260.00	0.362857
$738$	0	0
$739$	25803.0	1.28441	0.642205	−	0.766533i	$-0.278020\pi$
$739$	25803.0	1.28441	0.642205	+	0.766533i	$0.278020\pi$
$740$	0	0
$741$	9310.00	0.461554
$742$	0	0
$743$	16812.0	0.830111	0.415055	−	0.909796i	$-0.363762\pi$
$743$	16812.0	0.830111	0.415055	+	0.909796i	$0.363762\pi$
$744$	0	0
$745$	5930.00	0.291622
$746$	0	0
$747$	1144.00	0.0560332
$748$	0	0
$749$	8280.00	0.403931
$750$	0	0
$751$	18052.0	0.877133	0.438566	−	0.898699i	$-0.355486\pi$
$751$	18052.0	0.877133	0.438566	+	0.898699i	$0.355486\pi$
$752$	0	0
$753$	7580.00	0.366840
$754$	0	0
$755$	2935.00	0.141478
$756$	0	0
$757$	−20946.0	−1.00567	−0.502837	−	0.864381i	$-0.667710\pi$
$757$	−20946.0	−1.00567	−0.502837	+	0.864381i	$0.667710\pi$
$758$	0	0
$759$	2530.00	0.120992
$760$	0	0
$761$	19805.0	0.943404	0.471702	−	0.881758i	$-0.343640\pi$
$761$	19805.0	0.943404	0.471702	+	0.881758i	$0.343640\pi$
$762$	0	0
$763$	−4560.00	−0.216361
$764$	0	0
$765$	960.000	0.0453711
$766$	0	0
$767$	6688.00	0.314850
$768$	0	0
$769$	14098.0	0.661101	0.330551	−	0.943788i	$-0.392766\pi$
$769$	14098.0	0.661101	0.330551	+	0.943788i	$0.392766\pi$
$770$	0	0
$771$	31895.0	1.48984
$772$	0	0
$773$	6480.00	0.301513	0.150756	−	0.988571i	$-0.451829\pi$
$773$	6480.00	0.301513	0.150756	+	0.988571i	$0.451829\pi$
$774$	0	0
$775$	7125.00	0.330242
$776$	0	0
$777$	23880.0	1.10256
$778$	0	0
$779$	26558.0	1.22149
$780$	0	0
$781$	18370.0	0.841652
$782$	0	0
$783$	32915.0	1.50228
$784$	0	0
$785$	−3220.00	−0.146403
$786$	0	0
$787$	−196.000	−0.00887757	−0.00443878	−	0.999990i	$-0.501413\pi$
$787$	−196.000	−0.00887757	−0.00443878	+	0.999990i	$0.501413\pi$
$788$	0	0
$789$	−5910.00	−0.266669
$790$	0	0
$791$	26064.0	1.17159
$792$	0	0
$793$	−9082.00	−0.406698
$794$	0	0
$795$	−450.000	−0.0200753
$796$	0	0
$797$	10826.0	0.481150	0.240575	−	0.970631i	$-0.422664\pi$
$797$	10826.0	0.481150	0.240575	+	0.970631i	$0.422664\pi$
$798$	0	0
$799$	27360.0	1.21142
$800$	0	0
$801$	1008.00	0.0444643
$802$	0	0
$803$	24794.0	1.08962
$804$	0	0
$805$	−1380.00	−0.0604206
$806$	0	0
$807$	8845.00	0.385822
$808$	0	0
$809$	−14110.0	−0.613203	−0.306601	−	0.951838i	$-0.599192\pi$
$809$	−14110.0	−0.613203	−0.306601	+	0.951838i	$0.599192\pi$
$810$	0	0
$811$	−33775.0	−1.46239	−0.731196	−	0.682167i	$-0.761038\pi$
$811$	−33775.0	−1.46239	−0.731196	+	0.682167i	$0.761038\pi$
$812$	0	0
$813$	−11040.0	−0.476248
$814$	0	0
$815$	−13895.0	−0.597203
$816$	0	0
$817$	9800.00	0.419656
$818$	0	0
$819$	456.000	0.0194553
$820$	0	0
$821$	−2310.00	−0.0981968	−0.0490984	−	0.998794i	$-0.515635\pi$
$821$	−2310.00	−0.0981968	−0.0490984	+	0.998794i	$0.515635\pi$
$822$	0	0
$823$	−16967.0	−0.718630	−0.359315	−	0.933216i	$-0.616990\pi$
$823$	−16967.0	−0.718630	−0.359315	+	0.933216i	$0.616990\pi$
$824$	0	0
$825$	−2750.00	−0.116052
$826$	0	0
$827$	21888.0	0.920339	0.460169	−	0.887831i	$-0.347789\pi$
$827$	21888.0	0.920339	0.460169	+	0.887831i	$0.347789\pi$
$828$	0	0
$829$	−45830.0	−1.92007	−0.960037	−	0.279872i	$-0.909708\pi$
$829$	−45830.0	−1.92007	−0.960037	+	0.279872i	$0.909708\pi$
$830$	0	0
$831$	−25415.0	−1.06093
$832$	0	0
$833$	−19104.0	−0.794615
$834$	0	0
$835$	−2840.00	−0.117703
$836$	0	0
$837$	−41325.0	−1.70657
$838$	0	0
$839$	35304.0	1.45272	0.726358	−	0.687316i	$-0.241211\pi$
$839$	35304.0	1.45272	0.726358	+	0.687316i	$0.241211\pi$
$840$	0	0
$841$	27140.0	1.11280
$842$	0	0
$843$	34620.0	1.41444
$844$	0	0
$845$	9180.00	0.373730
$846$	0	0
$847$	10164.0	0.412325
$848$	0	0
$849$	−33190.0	−1.34167
$850$	0	0
$851$	9154.00	0.368737
$852$	0	0
$853$	−15522.0	−0.623052	−0.311526	−	0.950238i	$-0.600840\pi$
$853$	−15522.0	−0.623052	−0.311526	+	0.950238i	$0.600840\pi$
$854$	0	0
$855$	980.000	0.0391992
$856$	0	0
$857$	39399.0	1.57041	0.785207	−	0.619234i	$-0.212557\pi$
$857$	39399.0	1.57041	0.785207	+	0.619234i	$0.212557\pi$
$858$	0	0
$859$	40825.0	1.62157	0.810786	−	0.585342i	$-0.199040\pi$
$859$	40825.0	1.62157	0.810786	+	0.585342i	$0.199040\pi$
$860$	0	0
$861$	−16260.0	−0.643600
$862$	0	0
$863$	−48061.0	−1.89573	−0.947865	−	0.318671i	$-0.896763\pi$
$863$	−48061.0	−1.89573	−0.947865	+	0.318671i	$0.896763\pi$
$864$	0	0
$865$	12890.0	0.506674
$866$	0	0
$867$	21515.0	0.842777
$868$	0	0
$869$	7084.00	0.276534
$870$	0	0
$871$	−6270.00	−0.243916
$872$	0	0
$873$	−3424.00	−0.132743
$874$	0	0
$875$	1500.00	0.0579534
$876$	0	0
$877$	16006.0	0.616288	0.308144	−	0.951340i	$-0.400292\pi$
$877$	16006.0	0.616288	0.308144	+	0.951340i	$0.400292\pi$
$878$	0	0
$879$	26360.0	1.01149
$880$	0	0
$881$	−9632.00	−0.368343	−0.184172	−	0.982894i	$-0.558960\pi$
$881$	−9632.00	−0.368343	−0.184172	+	0.982894i	$0.558960\pi$
$882$	0	0
$883$	−49052.0	−1.86946	−0.934729	−	0.355362i	$-0.884358\pi$
$883$	−49052.0	−1.86946	−0.934729	+	0.355362i	$0.884358\pi$
$884$	0	0
$885$	−8800.00	−0.334247
$886$	0	0
$887$	−27963.0	−1.05852	−0.529259	−	0.848460i	$-0.677530\pi$
$887$	−27963.0	−1.05852	−0.529259	+	0.848460i	$0.677530\pi$
$888$	0	0
$889$	−516.000	−0.0194669
$890$	0	0
$891$	14762.0	0.555046
$892$	0	0
$893$	27930.0	1.04663
$894$	0	0
$895$	20705.0	0.773287
$896$	0	0
$897$	−2185.00	−0.0813322
$898$	0	0
$899$	−64695.0	−2.40011
$900$	0	0
$901$	1728.00	0.0638935
$902$	0	0
$903$	−6000.00	−0.221116
$904$	0	0
$905$	7270.00	0.267031
$906$	0	0
$907$	17110.0	0.626382	0.313191	−	0.949690i	$-0.398602\pi$
$907$	17110.0	0.626382	0.313191	+	0.949690i	$0.398602\pi$
$908$	0	0
$909$	3420.00	0.124790
$910$	0	0
$911$	4390.00	0.159657	0.0798283	−	0.996809i	$-0.474563\pi$
$911$	4390.00	0.159657	0.0798283	+	0.996809i	$0.474563\pi$
$912$	0	0
$913$	12584.0	0.456155
$914$	0	0
$915$	11950.0	0.431754
$916$	0	0
$917$	14244.0	0.512953
$918$	0	0
$919$	47576.0	1.70771	0.853856	−	0.520509i	$-0.174258\pi$
$919$	47576.0	1.70771	0.853856	+	0.520509i	$0.174258\pi$
$920$	0	0
$921$	10960.0	0.392122
$922$	0	0
$923$	−15865.0	−0.565767
$924$	0	0
$925$	−9950.00	−0.353680
$926$	0	0
$927$	72.0000	0.00255101
$928$	0	0
$929$	1143.00	0.0403666	0.0201833	−	0.999796i	$-0.493575\pi$
$929$	1143.00	0.0403666	0.0201833	+	0.999796i	$0.493575\pi$
$930$	0	0
$931$	−19502.0	−0.686522
$932$	0	0
$933$	−44935.0	−1.57675
$934$	0	0
$935$	10560.0	0.369357
$936$	0	0
$937$	−50494.0	−1.76048	−0.880239	−	0.474531i	$-0.842618\pi$
$937$	−50494.0	−1.76048	−0.880239	+	0.474531i	$0.842618\pi$
$938$	0	0
$939$	21680.0	0.753461
$940$	0	0
$941$	−16444.0	−0.569670	−0.284835	−	0.958577i	$-0.591939\pi$
$941$	−16444.0	−0.569670	−0.284835	+	0.958577i	$0.591939\pi$
$942$	0	0
$943$	−6233.00	−0.215243
$944$	0	0
$945$	−8700.00	−0.299483
$946$	0	0
$947$	4949.00	0.169821	0.0849107	−	0.996389i	$-0.472939\pi$
$947$	4949.00	0.169821	0.0849107	+	0.996389i	$0.472939\pi$
$948$	0	0
$949$	−21413.0	−0.732450
$950$	0	0
$951$	22770.0	0.776412
$952$	0	0
$953$	4718.00	0.160368	0.0801842	−	0.996780i	$-0.474449\pi$
$953$	4718.00	0.160368	0.0801842	+	0.996780i	$0.474449\pi$
$954$	0	0
$955$	−16950.0	−0.574334
$956$	0	0
$957$	24970.0	0.843433
$958$	0	0
$959$	−2544.00	−0.0856622
$960$	0	0
$961$	51434.0	1.72649
$962$	0	0
$963$	1380.00	0.0461785
$964$	0	0
$965$	12935.0	0.431495
$966$	0	0
$967$	−47793.0	−1.58937	−0.794684	−	0.607023i	$-0.792364\pi$
$967$	−47793.0	−1.58937	−0.794684	+	0.607023i	$0.792364\pi$
$968$	0	0
$969$	47040.0	1.55949
$970$	0	0
$971$	17858.0	0.590206	0.295103	−	0.955465i	$-0.404646\pi$
$971$	17858.0	0.590206	0.295103	+	0.955465i	$0.404646\pi$
$972$	0	0
$973$	−13092.0	−0.431357
$974$	0	0
$975$	2375.00	0.0780112
$976$	0	0
$977$	−41238.0	−1.35038	−0.675190	−	0.737644i	$-0.735938\pi$
$977$	−41238.0	−1.35038	−0.675190	+	0.737644i	$0.735938\pi$
$978$	0	0
$979$	11088.0	0.361976
$980$	0	0
$981$	−760.000	−0.0247349
$982$	0	0
$983$	19158.0	0.621613	0.310806	−	0.950473i	$-0.399401\pi$
$983$	19158.0	0.621613	0.310806	+	0.950473i	$0.399401\pi$
$984$	0	0
$985$	−8205.00	−0.265414
$986$	0	0
$987$	−17100.0	−0.551468
$988$	0	0
$989$	−2300.00	−0.0739492
$990$	0	0
$991$	48816.0	1.56477	0.782387	−	0.622792i	$-0.214002\pi$
$991$	48816.0	1.56477	0.782387	+	0.622792i	$0.214002\pi$
$992$	0	0
$993$	−4805.00	−0.153557
$994$	0	0
$995$	−2030.00	−0.0646787
$996$	0	0
$997$	31550.0	1.00221	0.501103	−	0.865388i	$-0.332928\pi$
$997$	31550.0	1.00221	0.501103	+	0.865388i	$0.332928\pi$
$998$	0	0
$999$	57710.0	1.82769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1840.4.a.g.1.1		1
4.3	odd	2		230.4.a.a.1.1	✓	1
12.11	even	2		2070.4.a.o.1.1		1
20.3	even	4		1150.4.b.h.599.2		2
20.7	even	4		1150.4.b.h.599.1		2
20.19	odd	2		1150.4.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.a.1.1	✓	1	4.3	odd	2
1150.4.a.i.1.1		1	20.19	odd	2
1150.4.b.h.599.1		2	20.7	even	4
1150.4.b.h.599.2		2	20.3	even	4
1840.4.a.g.1.1		1	1.1	even	1	trivial
2070.4.a.o.1.1		1	12.11	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:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)

Introduction

L-functions

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Fields

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Groups

Database

Properties

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