LMFDB - Embedded newform 600.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,4,Mod(1,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, 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("600.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	600.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:	$35.4011460034$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	600.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} -10.0000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} -10.0000 q^{7} +9.00000 q^{9} -14.0000 q^{11} +82.0000 q^{13} -18.0000 q^{17} -136.000 q^{19} +30.0000 q^{21} +140.000 q^{23} -27.0000 q^{27} +112.000 q^{29} +72.0000 q^{31} +42.0000 q^{33} -26.0000 q^{37} -246.000 q^{39} -446.000 q^{41} -396.000 q^{43} +144.000 q^{47} -243.000 q^{49} +54.0000 q^{51} -158.000 q^{53} +408.000 q^{57} -342.000 q^{59} +314.000 q^{61} -90.0000 q^{63} +152.000 q^{67} -420.000 q^{69} -932.000 q^{71} +548.000 q^{73} +140.000 q^{77} -512.000 q^{79} +81.0000 q^{81} -284.000 q^{83} -336.000 q^{87} -810.000 q^{89} -820.000 q^{91} -216.000 q^{93} -1304.00 q^{97} -126.000 q^{99} +O(q^{100})$

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−10.0000	−0.539949	−0.269975	−	0.962867i	$-0.587015\pi$
$7$	−10.0000	−0.539949	−0.269975	+	0.962867i	$0.587015\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	−14.0000	−0.383742	−0.191871	−	0.981420i	$-0.561455\pi$
$11$	−14.0000	−0.383742	−0.191871	+	0.981420i	$0.561455\pi$
$12$	0	0
$13$	82.0000	1.74944	0.874720	−	0.484629i	$-0.161046\pi$
$13$	82.0000	1.74944	0.874720	+	0.484629i	$0.161046\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−18.0000	−0.256802	−0.128401	−	0.991722i	$-0.540985\pi$
$17$	−18.0000	−0.256802	−0.128401	+	0.991722i	$0.540985\pi$
$18$	0	0
$19$	−136.000	−1.64213	−0.821067	−	0.570832i	$-0.806621\pi$
$19$	−136.000	−1.64213	−0.821067	+	0.570832i	$0.806621\pi$
$20$	0	0
$21$	30.0000	0.311740
$22$	0	0
$23$	140.000	1.26922	0.634609	−	0.772833i	$-0.281161\pi$
$23$	140.000	1.26922	0.634609	+	0.772833i	$0.281161\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−27.0000	−0.192450
$28$	0	0
$29$	112.000	0.717168	0.358584	−	0.933497i	$-0.383260\pi$
$29$	112.000	0.717168	0.358584	+	0.933497i	$0.383260\pi$
$30$	0	0
$31$	72.0000	0.417148	0.208574	−	0.978007i	$-0.433118\pi$
$31$	72.0000	0.417148	0.208574	+	0.978007i	$0.433118\pi$
$32$	0	0
$33$	42.0000	0.221553
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−26.0000	−0.115524	−0.0577618	−	0.998330i	$-0.518396\pi$
$37$	−26.0000	−0.115524	−0.0577618	+	0.998330i	$0.518396\pi$
$38$	0	0
$39$	−246.000	−1.01004
$40$	0	0
$41$	−446.000	−1.69887	−0.849433	−	0.527697i	$-0.823056\pi$
$41$	−446.000	−1.69887	−0.849433	+	0.527697i	$0.823056\pi$
$42$	0	0
$43$	−396.000	−1.40441	−0.702203	−	0.711977i	$-0.747800\pi$
$43$	−396.000	−1.40441	−0.702203	+	0.711977i	$0.747800\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	144.000	0.446906	0.223453	−	0.974715i	$-0.428267\pi$
$47$	144.000	0.446906	0.223453	+	0.974715i	$0.428267\pi$
$48$	0	0
$49$	−243.000	−0.708455
$50$	0	0
$51$	54.0000	0.148265
$52$	0	0
$53$	−158.000	−0.409490	−0.204745	−	0.978815i	$-0.565637\pi$
$53$	−158.000	−0.409490	−0.204745	+	0.978815i	$0.565637\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	408.000	0.948086
$58$	0	0
$59$	−342.000	−0.754654	−0.377327	−	0.926080i	$-0.623157\pi$
$59$	−342.000	−0.754654	−0.377327	+	0.926080i	$0.623157\pi$
$60$	0	0
$61$	314.000	0.659075	0.329538	−	0.944142i	$-0.393107\pi$
$61$	314.000	0.659075	0.329538	+	0.944142i	$0.393107\pi$
$62$	0	0
$63$	−90.0000	−0.179983
$64$	0	0
$65$	0	0
$66$	0	0
$67$	152.000	0.277161	0.138580	−	0.990351i	$-0.455746\pi$
$67$	152.000	0.277161	0.138580	+	0.990351i	$0.455746\pi$
$68$	0	0
$69$	−420.000	−0.732783
$70$	0	0
$71$	−932.000	−1.55786	−0.778930	−	0.627111i	$-0.784237\pi$
$71$	−932.000	−1.55786	−0.778930	+	0.627111i	$0.784237\pi$
$72$	0	0
$73$	548.000	0.878610	0.439305	−	0.898338i	$-0.355225\pi$
$73$	548.000	0.878610	0.439305	+	0.898338i	$0.355225\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	140.000	0.207201
$78$	0	0
$79$	−512.000	−0.729171	−0.364585	−	0.931170i	$-0.618789\pi$
$79$	−512.000	−0.729171	−0.364585	+	0.931170i	$0.618789\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	0	0
$83$	−284.000	−0.375579	−0.187789	−	0.982209i	$-0.560132\pi$
$83$	−284.000	−0.375579	−0.187789	+	0.982209i	$0.560132\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−336.000	−0.414057
$88$	0	0
$89$	−810.000	−0.964717	−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000	−0.964717	−0.482359	+	0.875974i	$0.660220\pi$
$90$	0	0
$91$	−820.000	−0.944608
$92$	0	0
$93$	−216.000	−0.240840
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1304.00	−1.36496	−0.682480	−	0.730904i	$-0.739099\pi$
$97$	−1304.00	−1.36496	−0.682480	+	0.730904i	$0.739099\pi$
$98$	0	0
$99$	−126.000	−0.127914
$100$	0	0
$101$	936.000	0.922133	0.461067	−	0.887365i	$-0.347467\pi$
$101$	936.000	0.922133	0.461067	+	0.887365i	$0.347467\pi$
$102$	0	0
$103$	−1450.00	−1.38711	−0.693557	−	0.720402i	$-0.743957\pi$
$103$	−1450.00	−1.38711	−0.693557	+	0.720402i	$0.743957\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−1292.00	−1.16731	−0.583656	−	0.812001i	$-0.698378\pi$
$107$	−1292.00	−1.16731	−0.583656	+	0.812001i	$0.698378\pi$
$108$	0	0
$109$	−2142.00	−1.88226	−0.941130	−	0.338044i	$-0.890235\pi$
$109$	−2142.00	−1.88226	−0.941130	+	0.338044i	$0.890235\pi$
$110$	0	0
$111$	78.0000	0.0666976
$112$	0	0
$113$	1418.00	1.18048	0.590240	−	0.807228i	$-0.299033\pi$
$113$	1418.00	1.18048	0.590240	+	0.807228i	$0.299033\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	738.000	0.583146
$118$	0	0
$119$	180.000	0.138660
$120$	0	0
$121$	−1135.00	−0.852742
$122$	0	0
$123$	1338.00	0.980841
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−1674.00	−1.16963	−0.584817	−	0.811165i	$-0.698834\pi$
$127$	−1674.00	−1.16963	−0.584817	+	0.811165i	$0.698834\pi$
$128$	0	0
$129$	1188.00	0.810834
$130$	0	0
$131$	1134.00	0.756321	0.378160	−	0.925740i	$-0.376557\pi$
$131$	1134.00	0.756321	0.378160	+	0.925740i	$0.376557\pi$
$132$	0	0
$133$	1360.00	0.886669
$134$	0	0
$135$	0	0
$136$	0	0
$137$	2866.00	1.78729	0.893646	−	0.448773i	$-0.148139\pi$
$137$	2866.00	1.78729	0.893646	+	0.448773i	$0.148139\pi$
$138$	0	0
$139$	−764.000	−0.466199	−0.233099	−	0.972453i	$-0.574887\pi$
$139$	−764.000	−0.466199	−0.233099	+	0.972453i	$0.574887\pi$
$140$	0	0
$141$	−432.000	−0.258021
$142$	0	0
$143$	−1148.00	−0.671333
$144$	0	0
$145$	0	0
$146$	0	0
$147$	729.000	0.409027
$148$	0	0
$149$	−3060.00	−1.68245	−0.841225	−	0.540686i	$-0.818165\pi$
$149$	−3060.00	−1.68245	−0.841225	+	0.540686i	$0.818165\pi$
$150$	0	0
$151$	−1304.00	−0.702768	−0.351384	−	0.936231i	$-0.614289\pi$
$151$	−1304.00	−0.702768	−0.351384	+	0.936231i	$0.614289\pi$
$152$	0	0
$153$	−162.000	−0.0856008
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1582.00	−0.804187	−0.402093	−	0.915599i	$-0.631717\pi$
$157$	−1582.00	−0.804187	−0.402093	+	0.915599i	$0.631717\pi$
$158$	0	0
$159$	474.000	0.236419
$160$	0	0
$161$	−1400.00	−0.685313
$162$	0	0
$163$	−3232.00	−1.55307	−0.776533	−	0.630077i	$-0.783024\pi$
$163$	−3232.00	−1.55307	−0.776533	+	0.630077i	$0.783024\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	2988.00	1.38454	0.692271	−	0.721638i	$-0.256610\pi$
$167$	2988.00	1.38454	0.692271	+	0.721638i	$0.256610\pi$
$168$	0	0
$169$	4527.00	2.06054
$170$	0	0
$171$	−1224.00	−0.547378
$172$	0	0
$173$	918.000	0.403435	0.201717	−	0.979444i	$-0.435348\pi$
$173$	918.000	0.403435	0.201717	+	0.979444i	$0.435348\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1026.00	0.435700
$178$	0	0
$179$	−1238.00	−0.516941	−0.258471	−	0.966019i	$-0.583219\pi$
$179$	−1238.00	−0.516941	−0.258471	+	0.966019i	$0.583219\pi$
$180$	0	0
$181$	1450.00	0.595457	0.297728	−	0.954651i	$-0.403771\pi$
$181$	1450.00	0.595457	0.297728	+	0.954651i	$0.403771\pi$
$182$	0	0
$183$	−942.000	−0.380517
$184$	0	0
$185$	0	0
$186$	0	0
$187$	252.000	0.0985458
$188$	0	0
$189$	270.000	0.103913
$190$	0	0
$191$	4860.00	1.84114	0.920569	−	0.390581i	$-0.127726\pi$
$191$	4860.00	1.84114	0.920569	+	0.390581i	$0.127726\pi$
$192$	0	0
$193$	1412.00	0.526622	0.263311	−	0.964711i	$-0.415186\pi$
$193$	1412.00	0.526622	0.263311	+	0.964711i	$0.415186\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	1170.00	0.423142	0.211571	−	0.977363i	$-0.432142\pi$
$197$	1170.00	0.423142	0.211571	+	0.977363i	$0.432142\pi$
$198$	0	0
$199$	2080.00	0.740941	0.370471	−	0.928844i	$-0.379196\pi$
$199$	2080.00	0.740941	0.370471	+	0.928844i	$0.379196\pi$
$200$	0	0
$201$	−456.000	−0.160019
$202$	0	0
$203$	−1120.00	−0.387234
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1260.00	0.423073
$208$	0	0
$209$	1904.00	0.630155
$210$	0	0
$211$	2692.00	0.878317	0.439159	−	0.898410i	$-0.355277\pi$
$211$	2692.00	0.878317	0.439159	+	0.898410i	$0.355277\pi$
$212$	0	0
$213$	2796.00	0.899431
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−720.000	−0.225239
$218$	0	0
$219$	−1644.00	−0.507266
$220$	0	0
$221$	−1476.00	−0.449260
$222$	0	0
$223$	846.000	0.254046	0.127023	−	0.991900i	$-0.459458\pi$
$223$	846.000	0.254046	0.127023	+	0.991900i	$0.459458\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−2884.00	−0.843250	−0.421625	−	0.906770i	$-0.638540\pi$
$227$	−2884.00	−0.843250	−0.421625	+	0.906770i	$0.638540\pi$
$228$	0	0
$229$	3150.00	0.908986	0.454493	−	0.890750i	$-0.349820\pi$
$229$	3150.00	0.908986	0.454493	+	0.890750i	$0.349820\pi$
$230$	0	0
$231$	−420.000	−0.119628
$232$	0	0
$233$	4014.00	1.12861	0.564304	−	0.825567i	$-0.309144\pi$
$233$	4014.00	1.12861	0.564304	+	0.825567i	$0.309144\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	1536.00	0.420987
$238$	0	0
$239$	4900.00	1.32617	0.663085	−	0.748544i	$-0.269247\pi$
$239$	4900.00	1.32617	0.663085	+	0.748544i	$0.269247\pi$
$240$	0	0
$241$	−2314.00	−0.618497	−0.309249	−	0.950981i	$-0.600078\pi$
$241$	−2314.00	−0.618497	−0.309249	+	0.950981i	$0.600078\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−11152.0	−2.87281
$248$	0	0
$249$	852.000	0.216841
$250$	0	0
$251$	−2002.00	−0.503447	−0.251723	−	0.967799i	$-0.580997\pi$
$251$	−2002.00	−0.503447	−0.251723	+	0.967799i	$0.580997\pi$
$252$	0	0
$253$	−1960.00	−0.487052
$254$	0	0
$255$	0	0
$256$	0	0
$257$	450.000	0.109223	0.0546113	−	0.998508i	$-0.482608\pi$
$257$	450.000	0.109223	0.0546113	+	0.998508i	$0.482608\pi$
$258$	0	0
$259$	260.000	0.0623769
$260$	0	0
$261$	1008.00	0.239056
$262$	0	0
$263$	−180.000	−0.0422026	−0.0211013	−	0.999777i	$-0.506717\pi$
$263$	−180.000	−0.0422026	−0.0211013	+	0.999777i	$0.506717\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	2430.00	0.556980
$268$	0	0
$269$	2448.00	0.554859	0.277430	−	0.960746i	$-0.410517\pi$
$269$	2448.00	0.554859	0.277430	+	0.960746i	$0.410517\pi$
$270$	0	0
$271$	6776.00	1.51887	0.759433	−	0.650586i	$-0.225476\pi$
$271$	6776.00	1.51887	0.759433	+	0.650586i	$0.225476\pi$
$272$	0	0
$273$	2460.00	0.545370
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−6426.00	−1.39387	−0.696933	−	0.717136i	$-0.745453\pi$
$277$	−6426.00	−1.39387	−0.696933	+	0.717136i	$0.745453\pi$
$278$	0	0
$279$	648.000	0.139049
$280$	0	0
$281$	2718.00	0.577019	0.288509	−	0.957477i	$-0.406840\pi$
$281$	2718.00	0.577019	0.288509	+	0.957477i	$0.406840\pi$
$282$	0	0
$283$	−6048.00	−1.27038	−0.635188	−	0.772358i	$-0.719077\pi$
$283$	−6048.00	−1.27038	−0.635188	+	0.772358i	$0.719077\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	4460.00	0.917301
$288$	0	0
$289$	−4589.00	−0.934053
$290$	0	0
$291$	3912.00	0.788060
$292$	0	0
$293$	−1246.00	−0.248437	−0.124219	−	0.992255i	$-0.539642\pi$
$293$	−1246.00	−0.248437	−0.124219	+	0.992255i	$0.539642\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	378.000	0.0738511
$298$	0	0
$299$	11480.0	2.22042
$300$	0	0
$301$	3960.00	0.758308
$302$	0	0
$303$	−2808.00	−0.532394
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−1244.00	−0.231267	−0.115633	−	0.993292i	$-0.536890\pi$
$307$	−1244.00	−0.231267	−0.115633	+	0.993292i	$0.536890\pi$
$308$	0	0
$309$	4350.00	0.800851
$310$	0	0
$311$	−6372.00	−1.16181	−0.580905	−	0.813971i	$-0.697301\pi$
$311$	−6372.00	−1.16181	−0.580905	+	0.813971i	$0.697301\pi$
$312$	0	0
$313$	−5500.00	−0.993222	−0.496611	−	0.867973i	$-0.665422\pi$
$313$	−5500.00	−0.993222	−0.496611	+	0.867973i	$0.665422\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−378.000	−0.0669735	−0.0334867	−	0.999439i	$-0.510661\pi$
$317$	−378.000	−0.0669735	−0.0334867	+	0.999439i	$0.510661\pi$
$318$	0	0
$319$	−1568.00	−0.275207
$320$	0	0
$321$	3876.00	0.673948
$322$	0	0
$323$	2448.00	0.421704
$324$	0	0
$325$	0	0
$326$	0	0
$327$	6426.00	1.08672
$328$	0	0
$329$	−1440.00	−0.241306
$330$	0	0
$331$	−11888.0	−1.97409	−0.987045	−	0.160446i	$-0.948707\pi$
$331$	−11888.0	−1.97409	−0.987045	+	0.160446i	$0.948707\pi$
$332$	0	0
$333$	−234.000	−0.0385079
$334$	0	0
$335$	0	0
$336$	0	0
$337$	9116.00	1.47353	0.736766	−	0.676148i	$-0.236352\pi$
$337$	9116.00	1.47353	0.736766	+	0.676148i	$0.236352\pi$
$338$	0	0
$339$	−4254.00	−0.681550
$340$	0	0
$341$	−1008.00	−0.160077
$342$	0	0
$343$	5860.00	0.922479
$344$	0	0
$345$	0	0
$346$	0	0
$347$	4676.00	0.723403	0.361701	−	0.932294i	$-0.382196\pi$
$347$	4676.00	0.723403	0.361701	+	0.932294i	$0.382196\pi$
$348$	0	0
$349$	11906.0	1.82611	0.913057	−	0.407833i	$-0.133715\pi$
$349$	11906.0	1.82611	0.913057	+	0.407833i	$0.133715\pi$
$350$	0	0
$351$	−2214.00	−0.336680
$352$	0	0
$353$	2142.00	0.322966	0.161483	−	0.986875i	$-0.448372\pi$
$353$	2142.00	0.322966	0.161483	+	0.986875i	$0.448372\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−540.000	−0.0800555
$358$	0	0
$359$	9824.00	1.44426	0.722132	−	0.691755i	$-0.243162\pi$
$359$	9824.00	1.44426	0.722132	+	0.691755i	$0.243162\pi$
$360$	0	0
$361$	11637.0	1.69660
$362$	0	0
$363$	3405.00	0.492331
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−5354.00	−0.761516	−0.380758	−	0.924675i	$-0.624337\pi$
$367$	−5354.00	−0.761516	−0.380758	+	0.924675i	$0.624337\pi$
$368$	0	0
$369$	−4014.00	−0.566289
$370$	0	0
$371$	1580.00	0.221104
$372$	0	0
$373$	−7694.00	−1.06804	−0.534022	−	0.845471i	$-0.679320\pi$
$373$	−7694.00	−1.06804	−0.534022	+	0.845471i	$0.679320\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	9184.00	1.25464
$378$	0	0
$379$	−6004.00	−0.813733	−0.406866	−	0.913488i	$-0.633379\pi$
$379$	−6004.00	−0.813733	−0.406866	+	0.913488i	$0.633379\pi$
$380$	0	0
$381$	5022.00	0.675288
$382$	0	0
$383$	−9432.00	−1.25836	−0.629181	−	0.777259i	$-0.716610\pi$
$383$	−9432.00	−1.25836	−0.629181	+	0.777259i	$0.716610\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−3564.00	−0.468135
$388$	0	0
$389$	−6156.00	−0.802369	−0.401185	−	0.915997i	$-0.631401\pi$
$389$	−6156.00	−0.802369	−0.401185	+	0.915997i	$0.631401\pi$
$390$	0	0
$391$	−2520.00	−0.325938
$392$	0	0
$393$	−3402.00	−0.436662
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−7866.00	−0.994416	−0.497208	−	0.867631i	$-0.665641\pi$
$397$	−7866.00	−0.994416	−0.497208	+	0.867631i	$0.665641\pi$
$398$	0	0
$399$	−4080.00	−0.511918
$400$	0	0
$401$	−2074.00	−0.258281	−0.129140	−	0.991626i	$-0.541222\pi$
$401$	−2074.00	−0.258281	−0.129140	+	0.991626i	$0.541222\pi$
$402$	0	0
$403$	5904.00	0.729775
$404$	0	0
$405$	0	0
$406$	0	0
$407$	364.000	0.0443312
$408$	0	0
$409$	−2746.00	−0.331983	−0.165991	−	0.986127i	$-0.553082\pi$
$409$	−2746.00	−0.331983	−0.165991	+	0.986127i	$0.553082\pi$
$410$	0	0
$411$	−8598.00	−1.03189
$412$	0	0
$413$	3420.00	0.407475
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2292.00	0.269160
$418$	0	0
$419$	−6426.00	−0.749238	−0.374619	−	0.927179i	$-0.622226\pi$
$419$	−6426.00	−0.749238	−0.374619	+	0.927179i	$0.622226\pi$
$420$	0	0
$421$	−10610.0	−1.22827	−0.614133	−	0.789203i	$-0.710494\pi$
$421$	−10610.0	−1.22827	−0.614133	+	0.789203i	$0.710494\pi$
$422$	0	0
$423$	1296.00	0.148969
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−3140.00	−0.355867
$428$	0	0
$429$	3444.00	0.387594
$430$	0	0
$431$	8384.00	0.936991	0.468495	−	0.883466i	$-0.344796\pi$
$431$	8384.00	0.936991	0.468495	+	0.883466i	$0.344796\pi$
$432$	0	0
$433$	−1980.00	−0.219752	−0.109876	−	0.993945i	$-0.535045\pi$
$433$	−1980.00	−0.219752	−0.109876	+	0.993945i	$0.535045\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−19040.0	−2.08423
$438$	0	0
$439$	864.000	0.0939327	0.0469664	−	0.998896i	$-0.485045\pi$
$439$	864.000	0.0939327	0.0469664	+	0.998896i	$0.485045\pi$
$440$	0	0
$441$	−2187.00	−0.236152
$442$	0	0
$443$	13212.0	1.41698	0.708489	−	0.705722i	$-0.249377\pi$
$443$	13212.0	1.41698	0.708489	+	0.705722i	$0.249377\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	9180.00	0.971363
$448$	0	0
$449$	−16290.0	−1.71219	−0.856094	−	0.516820i	$-0.827116\pi$
$449$	−16290.0	−1.71219	−0.856094	+	0.516820i	$0.827116\pi$
$450$	0	0
$451$	6244.00	0.651926
$452$	0	0
$453$	3912.00	0.405743
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−6336.00	−0.648546	−0.324273	−	0.945964i	$-0.605120\pi$
$457$	−6336.00	−0.648546	−0.324273	+	0.945964i	$0.605120\pi$
$458$	0	0
$459$	486.000	0.0494217
$460$	0	0
$461$	−13716.0	−1.38572	−0.692861	−	0.721071i	$-0.743650\pi$
$461$	−13716.0	−1.38572	−0.692861	+	0.721071i	$0.743650\pi$
$462$	0	0
$463$	14626.0	1.46809	0.734047	−	0.679098i	$-0.237629\pi$
$463$	14626.0	1.46809	0.734047	+	0.679098i	$0.237629\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	5796.00	0.574319	0.287159	−	0.957883i	$-0.407289\pi$
$467$	5796.00	0.574319	0.287159	+	0.957883i	$0.407289\pi$
$468$	0	0
$469$	−1520.00	−0.149653
$470$	0	0
$471$	4746.00	0.464298
$472$	0	0
$473$	5544.00	0.538929
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−1422.00	−0.136497
$478$	0	0
$479$	−8348.00	−0.796305	−0.398152	−	0.917319i	$-0.630348\pi$
$479$	−8348.00	−0.796305	−0.398152	+	0.917319i	$0.630348\pi$
$480$	0	0
$481$	−2132.00	−0.202102
$482$	0	0
$483$	4200.00	0.395666
$484$	0	0
$485$	0	0
$486$	0	0
$487$	1898.00	0.176605	0.0883025	−	0.996094i	$-0.471856\pi$
$487$	1898.00	0.176605	0.0883025	+	0.996094i	$0.471856\pi$
$488$	0	0
$489$	9696.00	0.896663
$490$	0	0
$491$	16654.0	1.53072	0.765361	−	0.643601i	$-0.222560\pi$
$491$	16654.0	1.53072	0.765361	+	0.643601i	$0.222560\pi$
$492$	0	0
$493$	−2016.00	−0.184171
$494$	0	0
$495$	0	0
$496$	0	0
$497$	9320.00	0.841165
$498$	0	0
$499$	−10600.0	−0.950944	−0.475472	−	0.879731i	$-0.657723\pi$
$499$	−10600.0	−0.950944	−0.475472	+	0.879731i	$0.657723\pi$
$500$	0	0
$501$	−8964.00	−0.799365
$502$	0	0
$503$	10048.0	0.890692	0.445346	−	0.895359i	$-0.353081\pi$
$503$	10048.0	0.890692	0.445346	+	0.895359i	$0.353081\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−13581.0	−1.18965
$508$	0	0
$509$	−15088.0	−1.31388	−0.656939	−	0.753944i	$-0.728149\pi$
$509$	−15088.0	−1.31388	−0.656939	+	0.753944i	$0.728149\pi$
$510$	0	0
$511$	−5480.00	−0.474405
$512$	0	0
$513$	3672.00	0.316029
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−2016.00	−0.171496
$518$	0	0
$519$	−2754.00	−0.232923
$520$	0	0
$521$	8582.00	0.721659	0.360829	−	0.932632i	$-0.382494\pi$
$521$	8582.00	0.721659	0.360829	+	0.932632i	$0.382494\pi$
$522$	0	0
$523$	−16928.0	−1.41532	−0.707658	−	0.706556i	$-0.750248\pi$
$523$	−16928.0	−1.41532	−0.707658	+	0.706556i	$0.750248\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−1296.00	−0.107125
$528$	0	0
$529$	7433.00	0.610915
$530$	0	0
$531$	−3078.00	−0.251551
$532$	0	0
$533$	−36572.0	−2.97206
$534$	0	0
$535$	0	0
$536$	0	0
$537$	3714.00	0.298456
$538$	0	0
$539$	3402.00	0.271864
$540$	0	0
$541$	−11150.0	−0.886092	−0.443046	−	0.896499i	$-0.646102\pi$
$541$	−11150.0	−0.886092	−0.443046	+	0.896499i	$0.646102\pi$
$542$	0	0
$543$	−4350.00	−0.343787
$544$	0	0
$545$	0	0
$546$	0	0
$547$	19628.0	1.53425	0.767123	−	0.641500i	$-0.221688\pi$
$547$	19628.0	1.53425	0.767123	+	0.641500i	$0.221688\pi$
$548$	0	0
$549$	2826.00	0.219692
$550$	0	0
$551$	−15232.0	−1.17769
$552$	0	0
$553$	5120.00	0.393715
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−8694.00	−0.661358	−0.330679	−	0.943743i	$-0.607278\pi$
$557$	−8694.00	−0.661358	−0.330679	+	0.943743i	$0.607278\pi$
$558$	0	0
$559$	−32472.0	−2.45692
$560$	0	0
$561$	−756.000	−0.0568954
$562$	0	0
$563$	828.000	0.0619823	0.0309912	−	0.999520i	$-0.490134\pi$
$563$	828.000	0.0619823	0.0309912	+	0.999520i	$0.490134\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−810.000	−0.0599944
$568$	0	0
$569$	−17514.0	−1.29038	−0.645189	−	0.764023i	$-0.723221\pi$
$569$	−17514.0	−1.29038	−0.645189	+	0.764023i	$0.723221\pi$
$570$	0	0
$571$	−5552.00	−0.406907	−0.203454	−	0.979085i	$-0.565217\pi$
$571$	−5552.00	−0.406907	−0.203454	+	0.979085i	$0.565217\pi$
$572$	0	0
$573$	−14580.0	−1.06298
$574$	0	0
$575$	0	0
$576$	0	0
$577$	12896.0	0.930446	0.465223	−	0.885193i	$-0.345974\pi$
$577$	12896.0	0.930446	0.465223	+	0.885193i	$0.345974\pi$
$578$	0	0
$579$	−4236.00	−0.304045
$580$	0	0
$581$	2840.00	0.202794
$582$	0	0
$583$	2212.00	0.157138
$584$	0	0
$585$	0	0
$586$	0	0
$587$	1588.00	0.111659	0.0558295	−	0.998440i	$-0.482220\pi$
$587$	1588.00	0.111659	0.0558295	+	0.998440i	$0.482220\pi$
$588$	0	0
$589$	−9792.00	−0.685012
$590$	0	0
$591$	−3510.00	−0.244301
$592$	0	0
$593$	−22262.0	−1.54164	−0.770819	−	0.637055i	$-0.780152\pi$
$593$	−22262.0	−1.54164	−0.770819	+	0.637055i	$0.780152\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−6240.00	−0.427783
$598$	0	0
$599$	4640.00	0.316503	0.158251	−	0.987399i	$-0.449414\pi$
$599$	4640.00	0.316503	0.158251	+	0.987399i	$0.449414\pi$
$600$	0	0
$601$	−2574.00	−0.174702	−0.0873508	−	0.996178i	$-0.527840\pi$
$601$	−2574.00	−0.174702	−0.0873508	+	0.996178i	$0.527840\pi$
$602$	0	0
$603$	1368.00	0.0923868
$604$	0	0
$605$	0	0
$606$	0	0
$607$	11170.0	0.746913	0.373457	−	0.927648i	$-0.378172\pi$
$607$	11170.0	0.746913	0.373457	+	0.927648i	$0.378172\pi$
$608$	0	0
$609$	3360.00	0.223570
$610$	0	0
$611$	11808.0	0.781834
$612$	0	0
$613$	3646.00	0.240229	0.120115	−	0.992760i	$-0.461674\pi$
$613$	3646.00	0.240229	0.120115	+	0.992760i	$0.461674\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	7646.00	0.498892	0.249446	−	0.968389i	$-0.419751\pi$
$617$	7646.00	0.498892	0.249446	+	0.968389i	$0.419751\pi$
$618$	0	0
$619$	26668.0	1.73163	0.865814	−	0.500366i	$-0.166801\pi$
$619$	26668.0	1.73163	0.865814	+	0.500366i	$0.166801\pi$
$620$	0	0
$621$	−3780.00	−0.244261
$622$	0	0
$623$	8100.00	0.520898
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−5712.00	−0.363820
$628$	0	0
$629$	468.000	0.0296667
$630$	0	0
$631$	7712.00	0.486545	0.243272	−	0.969958i	$-0.421779\pi$
$631$	7712.00	0.486545	0.243272	+	0.969958i	$0.421779\pi$
$632$	0	0
$633$	−8076.00	−0.507097
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−19926.0	−1.23940
$638$	0	0
$639$	−8388.00	−0.519287
$640$	0	0
$641$	−22302.0	−1.37422	−0.687111	−	0.726553i	$-0.741121\pi$
$641$	−22302.0	−1.37422	−0.687111	+	0.726553i	$0.741121\pi$
$642$	0	0
$643$	−2232.00	−0.136892	−0.0684459	−	0.997655i	$-0.521804\pi$
$643$	−2232.00	−0.136892	−0.0684459	+	0.997655i	$0.521804\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−9464.00	−0.575067	−0.287533	−	0.957771i	$-0.592835\pi$
$647$	−9464.00	−0.575067	−0.287533	+	0.957771i	$0.592835\pi$
$648$	0	0
$649$	4788.00	0.289592
$650$	0	0
$651$	2160.00	0.130042
$652$	0	0
$653$	4878.00	0.292329	0.146165	−	0.989260i	$-0.453307\pi$
$653$	4878.00	0.292329	0.146165	+	0.989260i	$0.453307\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	4932.00	0.292870
$658$	0	0
$659$	10206.0	0.603292	0.301646	−	0.953420i	$-0.402464\pi$
$659$	10206.0	0.603292	0.301646	+	0.953420i	$0.402464\pi$
$660$	0	0
$661$	20906.0	1.23018	0.615090	−	0.788457i	$-0.289120\pi$
$661$	20906.0	1.23018	0.615090	+	0.788457i	$0.289120\pi$
$662$	0	0
$663$	4428.00	0.259380
$664$	0	0
$665$	0	0
$666$	0	0
$667$	15680.0	0.910243
$668$	0	0
$669$	−2538.00	−0.146674
$670$	0	0
$671$	−4396.00	−0.252915
$672$	0	0
$673$	6812.00	0.390168	0.195084	−	0.980787i	$-0.437502\pi$
$673$	6812.00	0.390168	0.195084	+	0.980787i	$0.437502\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−10026.0	−0.569174	−0.284587	−	0.958650i	$-0.591856\pi$
$677$	−10026.0	−0.569174	−0.284587	+	0.958650i	$0.591856\pi$
$678$	0	0
$679$	13040.0	0.737009
$680$	0	0
$681$	8652.00	0.486851
$682$	0	0
$683$	21236.0	1.18971	0.594856	−	0.803832i	$-0.297209\pi$
$683$	21236.0	1.18971	0.594856	+	0.803832i	$0.297209\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−9450.00	−0.524803
$688$	0	0
$689$	−12956.0	−0.716378
$690$	0	0
$691$	−11520.0	−0.634213	−0.317107	−	0.948390i	$-0.602711\pi$
$691$	−11520.0	−0.634213	−0.317107	+	0.948390i	$0.602711\pi$
$692$	0	0
$693$	1260.00	0.0690670
$694$	0	0
$695$	0	0
$696$	0	0
$697$	8028.00	0.436273
$698$	0	0
$699$	−12042.0	−0.651603
$700$	0	0
$701$	−400.000	−0.0215518	−0.0107759	−	0.999942i	$-0.503430\pi$
$701$	−400.000	−0.0215518	−0.0107759	+	0.999942i	$0.503430\pi$
$702$	0	0
$703$	3536.00	0.189705
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−9360.00	−0.497905
$708$	0	0
$709$	−5930.00	−0.314113	−0.157056	−	0.987590i	$-0.550200\pi$
$709$	−5930.00	−0.314113	−0.157056	+	0.987590i	$0.550200\pi$
$710$	0	0
$711$	−4608.00	−0.243057
$712$	0	0
$713$	10080.0	0.529452
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−14700.0	−0.765665
$718$	0	0
$719$	7160.00	0.371381	0.185691	−	0.982608i	$-0.440548\pi$
$719$	7160.00	0.371381	0.185691	+	0.982608i	$0.440548\pi$
$720$	0	0
$721$	14500.0	0.748971
$722$	0	0
$723$	6942.00	0.357090
$724$	0	0
$725$	0	0
$726$	0	0
$727$	8874.00	0.452708	0.226354	−	0.974045i	$-0.427319\pi$
$727$	8874.00	0.452708	0.226354	+	0.974045i	$0.427319\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	7128.00	0.360655
$732$	0	0
$733$	−5562.00	−0.280269	−0.140134	−	0.990132i	$-0.544753\pi$
$733$	−5562.00	−0.280269	−0.140134	+	0.990132i	$0.544753\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−2128.00	−0.106358
$738$	0	0
$739$	−12096.0	−0.602109	−0.301055	−	0.953607i	$-0.597339\pi$
$739$	−12096.0	−0.602109	−0.301055	+	0.953607i	$0.597339\pi$
$740$	0	0
$741$	33456.0	1.65862
$742$	0	0
$743$	−21312.0	−1.05230	−0.526152	−	0.850391i	$-0.676366\pi$
$743$	−21312.0	−1.05230	−0.526152	+	0.850391i	$0.676366\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−2556.00	−0.125193
$748$	0	0
$749$	12920.0	0.630289
$750$	0	0
$751$	−6832.00	−0.331962	−0.165981	−	0.986129i	$-0.553079\pi$
$751$	−6832.00	−0.331962	−0.165981	+	0.986129i	$0.553079\pi$
$752$	0	0
$753$	6006.00	0.290665
$754$	0	0
$755$	0	0
$756$	0	0
$757$	7174.00	0.344443	0.172222	−	0.985058i	$-0.444905\pi$
$757$	7174.00	0.344443	0.172222	+	0.985058i	$0.444905\pi$
$758$	0	0
$759$	5880.00	0.281200
$760$	0	0
$761$	−15394.0	−0.733288	−0.366644	−	0.930361i	$-0.619493\pi$
$761$	−15394.0	−0.733288	−0.366644	+	0.930361i	$0.619493\pi$
$762$	0	0
$763$	21420.0	1.01633
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−28044.0	−1.32022
$768$	0	0
$769$	9730.00	0.456271	0.228136	−	0.973629i	$-0.426737\pi$
$769$	9730.00	0.456271	0.228136	+	0.973629i	$0.426737\pi$
$770$	0	0
$771$	−1350.00	−0.0630597
$772$	0	0
$773$	24206.0	1.12630	0.563150	−	0.826355i	$-0.309589\pi$
$773$	24206.0	1.12630	0.563150	+	0.826355i	$0.309589\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−780.000	−0.0360133
$778$	0	0
$779$	60656.0	2.78976
$780$	0	0
$781$	13048.0	0.597816
$782$	0	0
$783$	−3024.00	−0.138019
$784$	0	0
$785$	0	0
$786$	0	0
$787$	31312.0	1.41824	0.709118	−	0.705089i	$-0.249093\pi$
$787$	31312.0	1.41824	0.709118	+	0.705089i	$0.249093\pi$
$788$	0	0
$789$	540.000	0.0243657
$790$	0	0
$791$	−14180.0	−0.637399
$792$	0	0
$793$	25748.0	1.15301
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−10746.0	−0.477595	−0.238797	−	0.971069i	$-0.576753\pi$
$797$	−10746.0	−0.477595	−0.238797	+	0.971069i	$0.576753\pi$
$798$	0	0
$799$	−2592.00	−0.114766
$800$	0	0
$801$	−7290.00	−0.321572
$802$	0	0
$803$	−7672.00	−0.337159
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−7344.00	−0.320348
$808$	0	0
$809$	30546.0	1.32749	0.663745	−	0.747959i	$-0.268966\pi$
$809$	30546.0	1.32749	0.663745	+	0.747959i	$0.268966\pi$
$810$	0	0
$811$	−2628.00	−0.113787	−0.0568937	−	0.998380i	$-0.518120\pi$
$811$	−2628.00	−0.113787	−0.0568937	+	0.998380i	$0.518120\pi$
$812$	0	0
$813$	−20328.0	−0.876918
$814$	0	0
$815$	0	0
$816$	0	0
$817$	53856.0	2.30622
$818$	0	0
$819$	−7380.00	−0.314869
$820$	0	0
$821$	26280.0	1.11715	0.558574	−	0.829455i	$-0.311349\pi$
$821$	26280.0	1.11715	0.558574	+	0.829455i	$0.311349\pi$
$822$	0	0
$823$	26146.0	1.10740	0.553701	−	0.832715i	$-0.313215\pi$
$823$	26146.0	1.10740	0.553701	+	0.832715i	$0.313215\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−29268.0	−1.23065	−0.615325	−	0.788273i	$-0.710975\pi$
$827$	−29268.0	−1.23065	−0.615325	+	0.788273i	$0.710975\pi$
$828$	0	0
$829$	6202.00	0.259836	0.129918	−	0.991525i	$-0.458529\pi$
$829$	6202.00	0.259836	0.129918	+	0.991525i	$0.458529\pi$
$830$	0	0
$831$	19278.0	0.804749
$832$	0	0
$833$	4374.00	0.181933
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1944.00	−0.0802801
$838$	0	0
$839$	4680.00	0.192576	0.0962882	−	0.995353i	$-0.469303\pi$
$839$	4680.00	0.192576	0.0962882	+	0.995353i	$0.469303\pi$
$840$	0	0
$841$	−11845.0	−0.485670
$842$	0	0
$843$	−8154.00	−0.333142
$844$	0	0
$845$	0	0
$846$	0	0
$847$	11350.0	0.460438
$848$	0	0
$849$	18144.0	0.733452
$850$	0	0
$851$	−3640.00	−0.146625
$852$	0	0
$853$	−12122.0	−0.486576	−0.243288	−	0.969954i	$-0.578226\pi$
$853$	−12122.0	−0.486576	−0.243288	+	0.969954i	$0.578226\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	26006.0	1.03658	0.518289	−	0.855205i	$-0.326569\pi$
$857$	26006.0	1.03658	0.518289	+	0.855205i	$0.326569\pi$
$858$	0	0
$859$	−17684.0	−0.702410	−0.351205	−	0.936299i	$-0.614228\pi$
$859$	−17684.0	−0.702410	−0.351205	+	0.936299i	$0.614228\pi$
$860$	0	0
$861$	−13380.0	−0.529604
$862$	0	0
$863$	−15084.0	−0.594977	−0.297489	−	0.954725i	$-0.596149\pi$
$863$	−15084.0	−0.594977	−0.297489	+	0.954725i	$0.596149\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	13767.0	0.539275
$868$	0	0
$869$	7168.00	0.279813
$870$	0	0
$871$	12464.0	0.484875
$872$	0	0
$873$	−11736.0	−0.454987
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−17614.0	−0.678201	−0.339101	−	0.940750i	$-0.610123\pi$
$877$	−17614.0	−0.678201	−0.339101	+	0.940750i	$0.610123\pi$
$878$	0	0
$879$	3738.00	0.143435
$880$	0	0
$881$	−3298.00	−0.126121	−0.0630604	−	0.998010i	$-0.520086\pi$
$881$	−3298.00	−0.126121	−0.0630604	+	0.998010i	$0.520086\pi$
$882$	0	0
$883$	−9496.00	−0.361909	−0.180955	−	0.983491i	$-0.557919\pi$
$883$	−9496.00	−0.361909	−0.180955	+	0.983491i	$0.557919\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	50220.0	1.90104	0.950520	−	0.310663i	$-0.100551\pi$
$887$	50220.0	1.90104	0.950520	+	0.310663i	$0.100551\pi$
$888$	0	0
$889$	16740.0	0.631543
$890$	0	0
$891$	−1134.00	−0.0426380
$892$	0	0
$893$	−19584.0	−0.733879
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−34440.0	−1.28196
$898$	0	0
$899$	8064.00	0.299165
$900$	0	0
$901$	2844.00	0.105158
$902$	0	0
$903$	−11880.0	−0.437809
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−20636.0	−0.755465	−0.377733	−	0.925915i	$-0.623296\pi$
$907$	−20636.0	−0.755465	−0.377733	+	0.925915i	$0.623296\pi$
$908$	0	0
$909$	8424.00	0.307378
$910$	0	0
$911$	13680.0	0.497518	0.248759	−	0.968565i	$-0.419977\pi$
$911$	13680.0	0.497518	0.248759	+	0.968565i	$0.419977\pi$
$912$	0	0
$913$	3976.00	0.144125
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−11340.0	−0.408375
$918$	0	0
$919$	21456.0	0.770150	0.385075	−	0.922885i	$-0.374176\pi$
$919$	21456.0	0.770150	0.385075	+	0.922885i	$0.374176\pi$
$920$	0	0
$921$	3732.00	0.133522
$922$	0	0
$923$	−76424.0	−2.72538
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−13050.0	−0.462371
$928$	0	0
$929$	16510.0	0.583074	0.291537	−	0.956560i	$-0.405833\pi$
$929$	16510.0	0.583074	0.291537	+	0.956560i	$0.405833\pi$
$930$	0	0
$931$	33048.0	1.16338
$932$	0	0
$933$	19116.0	0.670771
$934$	0	0
$935$	0	0
$936$	0	0
$937$	36296.0	1.26546	0.632731	−	0.774371i	$-0.281934\pi$
$937$	36296.0	1.26546	0.632731	+	0.774371i	$0.281934\pi$
$938$	0	0
$939$	16500.0	0.573437
$940$	0	0
$941$	13540.0	0.469066	0.234533	−	0.972108i	$-0.424644\pi$
$941$	13540.0	0.469066	0.234533	+	0.972108i	$0.424644\pi$
$942$	0	0
$943$	−62440.0	−2.15623
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−32940.0	−1.13031	−0.565156	−	0.824984i	$-0.691184\pi$
$947$	−32940.0	−1.13031	−0.565156	+	0.824984i	$0.691184\pi$
$948$	0	0
$949$	44936.0	1.53708
$950$	0	0
$951$	1134.00	0.0386672
$952$	0	0
$953$	22482.0	0.764180	0.382090	−	0.924125i	$-0.375204\pi$
$953$	22482.0	0.764180	0.382090	+	0.924125i	$0.375204\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	4704.00	0.158891
$958$	0	0
$959$	−28660.0	−0.965047
$960$	0	0
$961$	−24607.0	−0.825988
$962$	0	0
$963$	−11628.0	−0.389104
$964$	0	0
$965$	0	0
$966$	0	0
$967$	9566.00	0.318120	0.159060	−	0.987269i	$-0.449154\pi$
$967$	9566.00	0.318120	0.159060	+	0.987269i	$0.449154\pi$
$968$	0	0
$969$	−7344.00	−0.243471
$970$	0	0
$971$	10062.0	0.332549	0.166274	−	0.986080i	$-0.446826\pi$
$971$	10062.0	0.332549	0.166274	+	0.986080i	$0.446826\pi$
$972$	0	0
$973$	7640.00	0.251724
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−48506.0	−1.58838	−0.794189	−	0.607671i	$-0.792104\pi$
$977$	−48506.0	−1.58838	−0.794189	+	0.607671i	$0.792104\pi$
$978$	0	0
$979$	11340.0	0.370202
$980$	0	0
$981$	−19278.0	−0.627420
$982$	0	0
$983$	41144.0	1.33498	0.667492	−	0.744617i	$-0.267368\pi$
$983$	41144.0	1.33498	0.667492	+	0.744617i	$0.267368\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	4320.00	0.139318
$988$	0	0
$989$	−55440.0	−1.78250
$990$	0	0
$991$	16120.0	0.516719	0.258360	−	0.966049i	$-0.416818\pi$
$991$	16120.0	0.516719	0.258360	+	0.966049i	$0.416818\pi$
$992$	0	0
$993$	35664.0	1.13974
$994$	0	0
$995$	0	0
$996$	0	0
$997$	36666.0	1.16472	0.582359	−	0.812932i	$-0.302130\pi$
$997$	36666.0	1.16472	0.582359	+	0.812932i	$0.302130\pi$
$998$	0	0
$999$	702.000	0.0222325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.4.a.c.1.1		1
3.2	odd	2		1800.4.a.i.1.1		1
4.3	odd	2		1200.4.a.bg.1.1		1
5.2	odd	4		120.4.f.b.49.2	yes	2
5.3	odd	4		120.4.f.b.49.1	✓	2
5.4	even	2		600.4.a.p.1.1		1
15.2	even	4		360.4.f.b.289.2		2
15.8	even	4		360.4.f.b.289.1		2
15.14	odd	2		1800.4.a.x.1.1		1
20.3	even	4		240.4.f.c.49.2		2
20.7	even	4		240.4.f.c.49.1		2
20.19	odd	2		1200.4.a.e.1.1		1
40.3	even	4		960.4.f.e.769.1		2
40.13	odd	4		960.4.f.f.769.2		2
40.27	even	4		960.4.f.e.769.2		2
40.37	odd	4		960.4.f.f.769.1		2
60.23	odd	4		720.4.f.e.289.1		2
60.47	odd	4		720.4.f.e.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.f.b.49.1	✓	2	5.3	odd	4
120.4.f.b.49.2	yes	2	5.2	odd	4
240.4.f.c.49.1		2	20.7	even	4
240.4.f.c.49.2		2	20.3	even	4
360.4.f.b.289.1		2	15.8	even	4
360.4.f.b.289.2		2	15.2	even	4
600.4.a.c.1.1		1	1.1	even	1	trivial
600.4.a.p.1.1		1	5.4	even	2
720.4.f.e.289.1		2	60.23	odd	4
720.4.f.e.289.2		2	60.47	odd	4
960.4.f.e.769.1		2	40.3	even	4
960.4.f.e.769.2		2	40.27	even	4
960.4.f.f.769.1		2	40.37	odd	4
960.4.f.f.769.2		2	40.13	odd	4
1200.4.a.e.1.1		1	20.19	odd	2
1200.4.a.bg.1.1		1	4.3	odd	2
1800.4.a.i.1.1		1	3.2	odd	2
1800.4.a.x.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	600.a (trivial)

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