LMFDB - Embedded newform 1773.4.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1773,4,Mod(1,1773)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1773, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1773.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1773 = 3^{2} \cdot 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1773.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:	$104.610386440$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	no (minimal twist has level 197)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1773.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.25705 q^{2} +2.60839 q^{4} +8.26136 q^{5} +15.5528 q^{7} -17.5608 q^{8} +26.9077 q^{10} -24.4046 q^{11} +44.1406 q^{13} +50.6562 q^{14} -78.0634 q^{16} +0.107242 q^{17} -94.4553 q^{19} +21.5488 q^{20} -79.4870 q^{22} -144.904 q^{23} -56.7499 q^{25} +143.768 q^{26} +40.5676 q^{28} -24.1713 q^{29} -259.045 q^{31} -113.770 q^{32} +0.349293 q^{34} +128.487 q^{35} -412.288 q^{37} -307.646 q^{38} -145.076 q^{40} +362.243 q^{41} +239.777 q^{43} -63.6566 q^{44} -471.959 q^{46} +62.5601 q^{47} -101.111 q^{49} -184.837 q^{50} +115.136 q^{52} +518.071 q^{53} -201.615 q^{55} -273.119 q^{56} -78.7271 q^{58} +292.939 q^{59} -535.519 q^{61} -843.724 q^{62} +253.951 q^{64} +364.661 q^{65} +566.243 q^{67} +0.279729 q^{68} +418.489 q^{70} -413.907 q^{71} -336.802 q^{73} -1342.84 q^{74} -246.376 q^{76} -379.559 q^{77} +492.451 q^{79} -644.910 q^{80} +1179.85 q^{82} -1180.14 q^{83} +0.885966 q^{85} +780.967 q^{86} +428.563 q^{88} -663.513 q^{89} +686.508 q^{91} -377.964 q^{92} +203.762 q^{94} -780.330 q^{95} -336.952 q^{97} -329.324 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{2} + 68 q^{4} + 31 q^{5} - 102 q^{7} + 93 q^{8} - 133 q^{10} + 100 q^{11} - 223 q^{13} + 55 q^{14} + 112 q^{16} + 114 q^{17} - 529 q^{19} + 441 q^{20} - 671 q^{22} + 208 q^{23} + 35 q^{25} + 408 q^{26}+ \cdots - 2932 q^{98}+O(q^{100}) $ 22 * q + 6 * q^2 + 68 * q^4 + 31 * q^5 - 102 * q^7 + 93 * q^8 - 133 * q^10 + 100 * q^11 - 223 * q^13 + 55 * q^14 + 112 * q^16 + 114 * q^17 - 529 * q^19 + 441 * q^20 - 671 * q^22 + 208 * q^23 + 35 * q^25 + 408 * q^26 - 1202 * q^28 + 2 * q^29 - 1261 * q^31 + 1020 * q^32 - 814 * q^34 + 968 * q^35 - 792 * q^37 + 184 * q^38 - 1914 * q^40 + 271 * q^41 - 1349 * q^43 + 998 * q^44 - 1371 * q^46 + 986 * q^47 - 40 * q^49 - 1631 * q^50 - 1382 * q^52 - 248 * q^53 - 566 * q^55 - 4800 * q^56 + 351 * q^58 + 1281 * q^59 + 510 * q^61 - 2237 * q^62 + 3185 * q^64 - 2558 * q^65 - 3070 * q^67 - 4625 * q^68 + 2087 * q^70 - 101 * q^71 - 3352 * q^73 - 4501 * q^74 - 334 * q^76 + 492 * q^77 - 1313 * q^79 - 3098 * q^80 - 1243 * q^82 + 2631 * q^83 + 84 * q^85 - 7448 * q^86 - 3285 * q^88 - 798 * q^89 - 3992 * q^91 - 5966 * q^92 + 3517 * q^94 - 284 * q^95 - 3693 * q^97 - 2932 * q^98

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 $

$2$	3.25705	1.15154	0.575771	−	0.817611i	$-0.304702\pi$
$2$	3.25705	1.15154	0.575771	+	0.817611i	$0.304702\pi$
$3$	0	0
$3$	0	0
$4$	2.60839	0.326048
$5$	8.26136	0.738919	0.369459	−	0.929247i	$-0.379543\pi$
$5$	8.26136	0.738919	0.369459	+	0.929247i	$0.379543\pi$
$6$	0	0
$7$	15.5528	0.839771	0.419885	−	0.907577i	$-0.362070\pi$
$7$	15.5528	0.839771	0.419885	+	0.907577i	$0.362070\pi$
$8$	−17.5608	−0.776084
$9$	0	0
$10$	26.9077	0.850896
$11$	−24.4046	−0.668933	−0.334466	−	0.942408i	$-0.608556\pi$
$11$	−24.4046	−0.668933	−0.334466	+	0.942408i	$0.608556\pi$
$12$	0	0
$13$	44.1406	0.941722	0.470861	−	0.882207i	$-0.343943\pi$
$13$	44.1406	0.941722	0.470861	+	0.882207i	$0.343943\pi$
$14$	50.6562	0.967031
$15$	0	0
$16$	−78.0634	−1.21974
$17$	0.107242	0.00153000	0.000765001	−	1.00000i	$-0.499756\pi$
$17$	0.107242	0.00153000	0.000765001		1.00000i	$0.499756\pi$
$18$	0	0
$19$	−94.4553	−1.14050	−0.570251	−	0.821470i	$-0.693154\pi$
$19$	−94.4553	−1.14050	−0.570251	+	0.821470i	$0.693154\pi$
$20$	21.5488	0.240923
$21$	0	0
$22$	−79.4870	−0.770304
$23$	−144.904	−1.31367	−0.656837	−	0.754033i	$-0.728106\pi$
$23$	−144.904	−1.31367	−0.656837	+	0.754033i	$0.728106\pi$
$24$	0	0
$25$	−56.7499	−0.453999
$26$	143.768	1.08443
$27$	0	0
$28$	40.5676	0.273806
$29$	−24.1713	−0.154776	−0.0773878	−	0.997001i	$-0.524658\pi$
$29$	−24.1713	−0.154776	−0.0773878	+	0.997001i	$0.524658\pi$
$30$	0	0
$31$	−259.045	−1.50084	−0.750418	−	0.660963i	$-0.770148\pi$
$31$	−259.045	−1.50084	−0.750418	+	0.660963i	$0.770148\pi$
$32$	−113.770	−0.628499
$33$	0	0
$34$	0.349293	0.00176186
$35$	128.487	0.620522
$36$	0	0
$37$	−412.288	−1.83188	−0.915941	−	0.401312i	$-0.868554\pi$
$37$	−412.288	−1.83188	−0.915941	+	0.401312i	$0.868554\pi$
$38$	−307.646	−1.31334
$39$	0	0
$40$	−145.076	−0.573463
$41$	362.243	1.37983	0.689914	−	0.723892i	$-0.257649\pi$
$41$	362.243	1.37983	0.689914	+	0.723892i	$0.257649\pi$
$42$	0	0
$43$	239.777	0.850365	0.425182	−	0.905108i	$-0.360210\pi$
$43$	239.777	0.850365	0.425182	+	0.905108i	$0.360210\pi$
$44$	−63.6566	−0.218104
$45$	0	0
$46$	−471.959	−1.51275
$47$	62.5601	0.194156	0.0970780	−	0.995277i	$-0.469050\pi$
$47$	62.5601	0.194156	0.0970780	+	0.995277i	$0.469050\pi$
$48$	0	0
$49$	−101.111	−0.294785
$50$	−184.837	−0.522799
$51$	0	0
$52$	115.136	0.307047
$53$	518.071	1.34269	0.671345	−	0.741145i	$-0.265717\pi$
$53$	518.071	1.34269	0.671345	+	0.741145i	$0.265717\pi$
$54$	0	0
$55$	−201.615	−0.494287
$56$	−273.119	−0.651732
$57$	0	0
$58$	−78.7271	−0.178231
$59$	292.939	0.646397	0.323199	−	0.946331i	$-0.395242\pi$
$59$	292.939	0.646397	0.323199	+	0.946331i	$0.395242\pi$
$60$	0	0
$61$	−535.519	−1.12404	−0.562018	−	0.827125i	$-0.689975\pi$
$61$	−535.519	−1.12404	−0.562018	+	0.827125i	$0.689975\pi$
$62$	−843.724	−1.72828
$63$	0	0
$64$	253.951	0.495998
$65$	364.661	0.695856
$66$	0	0
$67$	566.243	1.03250	0.516251	−	0.856438i	$-0.327327\pi$
$67$	566.243	1.03250	0.516251	+	0.856438i	$0.327327\pi$
$68$	0.279729	0.000498854 0
$69$	0	0
$70$	418.489	0.714557
$71$	−413.907	−0.691855	−0.345927	−	0.938261i	$-0.612436\pi$
$71$	−413.907	−0.691855	−0.345927	+	0.938261i	$0.612436\pi$
$72$	0	0
$73$	−336.802	−0.539996	−0.269998	−	0.962861i	$-0.587023\pi$
$73$	−336.802	−0.539996	−0.269998	+	0.962861i	$0.587023\pi$
$74$	−1342.84	−2.10949
$75$	0	0
$76$	−246.376	−0.371859
$77$	−379.559	−0.561750
$78$	0	0
$79$	492.451	0.701330	0.350665	−	0.936501i	$-0.385956\pi$
$79$	492.451	0.701330	0.350665	+	0.936501i	$0.385956\pi$
$80$	−644.910	−0.901289
$81$	0	0
$82$	1179.85	1.58893
$83$	−1180.14	−1.56068	−0.780342	−	0.625353i	$-0.784955\pi$
$83$	−1180.14	−1.56068	−0.780342	+	0.625353i	$0.784955\pi$
$84$	0	0
$85$	0.885966	0.00113055
$86$	780.967	0.979230
$87$	0	0
$88$	428.563	0.519148
$89$	−663.513	−0.790250	−0.395125	−	0.918627i	$-0.629299\pi$
$89$	−663.513	−0.790250	−0.395125	+	0.918627i	$0.629299\pi$
$90$	0	0
$91$	686.508	0.790831
$92$	−377.964	−0.428321
$93$	0	0
$94$	203.762	0.223579
$95$	−780.330	−0.842738
$96$	0	0
$97$	−336.952	−0.352704	−0.176352	−	0.984327i	$-0.556430\pi$
$97$	−336.952	−0.352704	−0.176352	+	0.984327i	$0.556430\pi$
$98$	−329.324	−0.339457
$99$	0	0
$100$	−148.026	−0.148026
$101$	1753.02	1.72705	0.863526	−	0.504304i	$-0.168251\pi$
$101$	1753.02	1.72705	0.863526	+	0.504304i	$0.168251\pi$
$102$	0	0
$103$	−1848.63	−1.76846	−0.884229	−	0.467054i	$-0.845315\pi$
$103$	−1848.63	−1.76846	−0.884229	+	0.467054i	$0.845315\pi$
$104$	−775.142	−0.730855
$105$	0	0
$106$	1687.38	1.54616
$107$	553.585	0.500160	0.250080	−	0.968225i	$-0.419543\pi$
$107$	553.585	0.500160	0.250080	+	0.968225i	$0.419543\pi$
$108$	0	0
$109$	−621.460	−0.546102	−0.273051	−	0.962000i	$-0.588033\pi$
$109$	−621.460	−0.546102	−0.273051	+	0.962000i	$0.588033\pi$
$110$	−656.671	−0.569192
$111$	0	0
$112$	−1214.10	−1.02430
$113$	−1439.42	−1.19832	−0.599158	−	0.800631i	$-0.704498\pi$
$113$	−1439.42	−1.19832	−0.599158	+	0.800631i	$0.704498\pi$
$114$	0	0
$115$	−1197.10	−0.970698
$116$	−63.0480	−0.0504643
$117$	0	0
$118$	954.118	0.744353
$119$	1.66791	0.00128485
$120$	0	0
$121$	−735.416	−0.552529
$122$	−1744.21	−1.29437
$123$	0	0
$124$	−675.690	−0.489345
$125$	−1501.50	−1.07439
$126$	0	0
$127$	−1650.07	−1.15292	−0.576458	−	0.817127i	$-0.695566\pi$
$127$	−1650.07	−1.15292	−0.576458	+	0.817127i	$0.695566\pi$
$128$	1737.30	1.19966
$129$	0	0
$130$	1187.72	0.801307
$131$	−386.313	−0.257652	−0.128826	−	0.991667i	$-0.541121\pi$
$131$	−386.313	−0.257652	−0.128826	+	0.991667i	$0.541121\pi$
$132$	0	0
$133$	−1469.04	−0.957761
$134$	1844.28	1.18897
$135$	0	0
$136$	−1.88325	−0.00118741
$137$	827.801	0.516232	0.258116	−	0.966114i	$-0.416898\pi$
$137$	827.801	0.516232	0.258116	+	0.966114i	$0.416898\pi$
$138$	0	0
$139$	−612.420	−0.373703	−0.186852	−	0.982388i	$-0.559828\pi$
$139$	−612.420	−0.373703	−0.186852	+	0.982388i	$0.559828\pi$
$140$	335.144	0.202320
$141$	0	0
$142$	−1348.12	−0.796700
$143$	−1077.23	−0.629949
$144$	0	0
$145$	−199.688	−0.114367
$146$	−1096.98	−0.621828
$147$	0	0
$148$	−1075.40	−0.597282
$149$	−348.305	−0.191505	−0.0957527	−	0.995405i	$-0.530526\pi$
$149$	−348.305	−0.191505	−0.0957527	+	0.995405i	$0.530526\pi$
$150$	0	0
$151$	−1645.16	−0.886629	−0.443315	−	0.896366i	$-0.646198\pi$
$151$	−1645.16	−0.886629	−0.443315	+	0.896366i	$0.646198\pi$
$152$	1658.71	0.885125
$153$	0	0
$154$	−1236.24	−0.646879
$155$	−2140.07	−1.10900
$156$	0	0
$157$	3601.58	1.83081	0.915405	−	0.402534i	$-0.131871\pi$
$157$	3601.58	1.83081	0.915405	+	0.402534i	$0.131871\pi$
$158$	1603.94	0.807611
$159$	0	0
$160$	−939.898	−0.464409
$161$	−2253.65	−1.10318
$162$	0	0
$163$	−2816.70	−1.35350	−0.676750	−	0.736212i	$-0.736612\pi$
$163$	−2816.70	−1.35350	−0.676750	+	0.736212i	$0.736612\pi$
$164$	944.870	0.449890
$165$	0	0
$166$	−3843.76	−1.79719
$167$	1898.52	0.879712	0.439856	−	0.898068i	$-0.355029\pi$
$167$	1898.52	0.879712	0.439856	+	0.898068i	$0.355029\pi$
$168$	0	0
$169$	−248.611	−0.113159
$170$	2.88564	0.00130187
$171$	0	0
$172$	625.431	0.277260
$173$	3232.44	1.42057	0.710283	−	0.703916i	$-0.248567\pi$
$173$	3232.44	1.42057	0.710283	+	0.703916i	$0.248567\pi$
$174$	0	0
$175$	−882.618	−0.381255
$176$	1905.11	0.815925
$177$	0	0
$178$	−2161.10	−0.910006
$179$	1366.73	0.570694	0.285347	−	0.958424i	$-0.407891\pi$
$179$	1366.73	0.570694	0.285347	+	0.958424i	$0.407891\pi$
$180$	0	0
$181$	2031.77	0.834368	0.417184	−	0.908822i	$-0.363017\pi$
$181$	2031.77	0.834368	0.417184	+	0.908822i	$0.363017\pi$
$182$	2235.99	0.910675
$183$	0	0
$184$	2544.62	1.01952
$185$	−3406.06	−1.35361
$186$	0	0
$187$	−2.61720	−0.00102347
$188$	163.181	0.0633042
$189$	0	0
$190$	−2541.57	−0.970448
$191$	−211.108	−0.0799750	−0.0399875	−	0.999200i	$-0.512732\pi$
$191$	−211.108	−0.0799750	−0.0399875	+	0.999200i	$0.512732\pi$
$192$	0	0
$193$	4031.89	1.50374	0.751871	−	0.659311i	$-0.229152\pi$
$193$	4031.89	1.50374	0.751871	+	0.659311i	$0.229152\pi$
$194$	−1097.47	−0.406153
$195$	0	0
$196$	−263.737	−0.0961140
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	0	0
$199$	−1075.38	−0.383075	−0.191537	−	0.981485i	$-0.561347\pi$
$199$	−1075.38	−0.383075	−0.191537	+	0.981485i	$0.561347\pi$
$200$	996.572	0.352341
$201$	0	0
$202$	5709.69	1.98877
$203$	−375.930	−0.129976
$204$	0	0
$205$	2992.62	1.01958
$206$	−6021.09	−2.03645
$207$	0	0
$208$	−3445.76	−1.14866
$209$	2305.14	0.762919
$210$	0	0
$211$	−2851.30	−0.930292	−0.465146	−	0.885234i	$-0.653998\pi$
$211$	−2851.30	−0.930292	−0.465146	+	0.885234i	$0.653998\pi$
$212$	1351.33	0.437781
$213$	0	0
$214$	1803.06	0.575955
$215$	1980.89	0.628350
$216$	0	0
$217$	−4028.87	−1.26036
$218$	−2024.13	−0.628859
$219$	0	0
$220$	−525.890	−0.161161
$221$	4.73372	0.00144084
$222$	0	0
$223$	1564.14	0.469697	0.234848	−	0.972032i	$-0.424541\pi$
$223$	1564.14	0.469697	0.234848	+	0.972032i	$0.424541\pi$
$224$	−1769.45	−0.527795
$225$	0	0
$226$	−4688.28	−1.37991
$227$	3686.82	1.07799	0.538994	−	0.842310i	$-0.318805\pi$
$227$	3686.82	1.07799	0.538994	+	0.842310i	$0.318805\pi$
$228$	0	0
$229$	5061.92	1.46070	0.730352	−	0.683071i	$-0.239356\pi$
$229$	5061.92	1.46070	0.730352	+	0.683071i	$0.239356\pi$
$230$	−3899.02	−1.11780
$231$	0	0
$232$	424.466	0.120119
$233$	−6768.75	−1.90316	−0.951578	−	0.307407i	$-0.900539\pi$
$233$	−6768.75	−1.90316	−0.951578	+	0.307407i	$0.900539\pi$
$234$	0	0
$235$	516.832	0.143466
$236$	764.098	0.210757
$237$	0	0
$238$	5.43248	0.00147956
$239$	−353.255	−0.0956074	−0.0478037	−	0.998857i	$-0.515222\pi$
$239$	−353.255	−0.0956074	−0.0478037	+	0.998857i	$0.515222\pi$
$240$	0	0
$241$	−2126.72	−0.568439	−0.284219	−	0.958759i	$-0.591734\pi$
$241$	−2126.72	−0.568439	−0.284219	+	0.958759i	$0.591734\pi$
$242$	−2395.29	−0.636260
$243$	0	0
$244$	−1396.84	−0.366490
$245$	−835.316	−0.217822
$246$	0	0
$247$	−4169.31	−1.07404
$248$	4549.04	1.16477
$249$	0	0
$250$	−4890.47	−1.23720
$251$	−6107.73	−1.53592	−0.767962	−	0.640496i	$-0.778729\pi$
$251$	−6107.73	−1.53592	−0.767962	+	0.640496i	$0.778729\pi$
$252$	0	0
$253$	3536.31	0.878759
$254$	−5374.38	−1.32763
$255$	0	0
$256$	3626.85	0.885462
$257$	2096.67	0.508897	0.254449	−	0.967086i	$-0.418106\pi$
$257$	2096.67	0.508897	0.254449	+	0.967086i	$0.418106\pi$
$258$	0	0
$259$	−6412.22	−1.53836
$260$	951.177	0.226883
$261$	0	0
$262$	−1258.24	−0.296696
$263$	−7932.84	−1.85992	−0.929962	−	0.367655i	$-0.880161\pi$
$263$	−7932.84	−1.85992	−0.929962	+	0.367655i	$0.880161\pi$
$264$	0	0
$265$	4279.97	0.992138
$266$	−4784.75	−1.10290
$267$	0	0
$268$	1476.98	0.336645
$269$	−736.004	−0.166821	−0.0834107	−	0.996515i	$-0.526581\pi$
$269$	−736.004	−0.166821	−0.0834107	+	0.996515i	$0.526581\pi$
$270$	0	0
$271$	4856.77	1.08866	0.544332	−	0.838870i	$-0.316783\pi$
$271$	4856.77	1.08866	0.544332	+	0.838870i	$0.316783\pi$
$272$	−8.37168	−0.00186621
$273$	0	0
$274$	2696.19	0.594463
$275$	1384.96	0.303695
$276$	0	0
$277$	−6677.85	−1.44849	−0.724247	−	0.689540i	$-0.757813\pi$
$277$	−6677.85	−1.44849	−0.724247	+	0.689540i	$0.757813\pi$
$278$	−1994.68	−0.430335
$279$	0	0
$280$	−2256.33	−0.481577
$281$	5626.19	1.19441	0.597207	−	0.802087i	$-0.296277\pi$
$281$	5626.19	1.19441	0.597207	+	0.802087i	$0.296277\pi$
$282$	0	0
$283$	−5348.60	−1.12347	−0.561733	−	0.827318i	$-0.689865\pi$
$283$	−5348.60	−1.12347	−0.561733	+	0.827318i	$0.689865\pi$
$284$	−1079.63	−0.225578
$285$	0	0
$286$	−3508.60	−0.725412
$287$	5633.89	1.15874
$288$	0	0
$289$	−4912.99	−0.999998
$290$	−650.393	−0.131698
$291$	0	0
$292$	−878.510	−0.176065
$293$	5889.11	1.17422	0.587108	−	0.809509i	$-0.300266\pi$
$293$	5889.11	1.17422	0.587108	+	0.809509i	$0.300266\pi$
$294$	0	0
$295$	2420.08	0.477635
$296$	7240.09	1.42169
$297$	0	0
$298$	−1134.45	−0.220526
$299$	−6396.13	−1.23712
$300$	0	0
$301$	3729.20	0.714112
$302$	−5358.36	−1.02099
$303$	0	0
$304$	7373.51	1.39112
$305$	−4424.12	−0.830572
$306$	0	0
$307$	−860.391	−0.159951	−0.0799757	−	0.996797i	$-0.525484\pi$
$307$	−860.391	−0.159951	−0.0799757	+	0.996797i	$0.525484\pi$
$308$	−990.036	−0.183158
$309$	0	0
$310$	−6970.31	−1.27705
$311$	4317.20	0.787158	0.393579	−	0.919291i	$-0.371237\pi$
$311$	4317.20	0.787158	0.393579	+	0.919291i	$0.371237\pi$
$312$	0	0
$313$	−2958.58	−0.534277	−0.267138	−	0.963658i	$-0.586078\pi$
$313$	−2958.58	−0.534277	−0.267138	+	0.963658i	$0.586078\pi$
$314$	11730.5	2.10825
$315$	0	0
$316$	1284.50	0.228667
$317$	−7104.45	−1.25876	−0.629378	−	0.777099i	$-0.716690\pi$
$317$	−7104.45	−1.25876	−0.629378	+	0.777099i	$0.716690\pi$
$318$	0	0
$319$	589.890	0.103534
$320$	2097.98	0.366502
$321$	0	0
$322$	−7340.27	−1.27036
$323$	−10.1296	−0.00174497
$324$	0	0
$325$	−2504.97	−0.427541
$326$	−9174.12	−1.55861
$327$	0	0
$328$	−6361.27	−1.07086
$329$	972.984	0.163047
$330$	0	0
$331$	3426.72	0.569031	0.284516	−	0.958671i	$-0.408167\pi$
$331$	3426.72	0.569031	0.284516	+	0.958671i	$0.408167\pi$
$332$	−3078.25	−0.508858
$333$	0	0
$334$	6183.58	1.01303
$335$	4677.94	0.762935
$336$	0	0
$337$	5875.10	0.949665	0.474833	−	0.880076i	$-0.342509\pi$
$337$	5875.10	0.949665	0.474833	+	0.880076i	$0.342509\pi$
$338$	−809.740	−0.130308
$339$	0	0
$340$	2.31094	0.000368613 0
$341$	6321.90	1.00396
$342$	0	0
$343$	−6907.16	−1.08732
$344$	−4210.67	−0.659954
$345$	0	0
$346$	10528.2	1.63584
$347$	−4979.84	−0.770408	−0.385204	−	0.922831i	$-0.625869\pi$
$347$	−4979.84	−0.770408	−0.385204	+	0.922831i	$0.625869\pi$
$348$	0	0
$349$	5281.46	0.810057	0.405028	−	0.914304i	$-0.367262\pi$
$349$	5281.46	0.810057	0.405028	+	0.914304i	$0.367262\pi$
$350$	−2874.73	−0.439031
$351$	0	0
$352$	2776.52	0.420423
$353$	2372.59	0.357734	0.178867	−	0.983873i	$-0.442757\pi$
$353$	2372.59	0.357734	0.178867	+	0.983873i	$0.442757\pi$
$354$	0	0
$355$	−3419.43	−0.511225
$356$	−1730.70	−0.257659
$357$	0	0
$358$	4451.51	0.657178
$359$	−8710.91	−1.28062	−0.640312	−	0.768115i	$-0.721195\pi$
$359$	−8710.91	−1.28062	−0.640312	+	0.768115i	$0.721195\pi$
$360$	0	0
$361$	2062.81	0.300745
$362$	6617.60	0.960810
$363$	0	0
$364$	1790.68	0.257849
$365$	−2782.45	−0.399013
$366$	0	0
$367$	4737.76	0.673867	0.336934	−	0.941528i	$-0.390610\pi$
$367$	4737.76	0.673867	0.336934	+	0.941528i	$0.390610\pi$
$368$	11311.7	1.60234
$369$	0	0
$370$	−11093.7	−1.55874
$371$	8057.44	1.12755
$372$	0	0
$373$	6914.00	0.959767	0.479884	−	0.877332i	$-0.340679\pi$
$373$	6914.00	0.959767	0.479884	+	0.877332i	$0.340679\pi$
$374$	−8.52435	−0.00117857
$375$	0	0
$376$	−1098.60	−0.150681
$377$	−1066.93	−0.145756
$378$	0	0
$379$	−2277.50	−0.308673	−0.154337	−	0.988018i	$-0.549324\pi$
$379$	−2277.50	−0.308673	−0.154337	+	0.988018i	$0.549324\pi$
$380$	−2035.40	−0.274773
$381$	0	0
$382$	−687.589	−0.0920945
$383$	−1882.94	−0.251211	−0.125606	−	0.992080i	$-0.540087\pi$
$383$	−1882.94	−0.251211	−0.125606	+	0.992080i	$0.540087\pi$
$384$	0	0
$385$	−3135.68	−0.415088
$386$	13132.1	1.73162
$387$	0	0
$388$	−878.900	−0.114998
$389$	−4471.16	−0.582768	−0.291384	−	0.956606i	$-0.594116\pi$
$389$	−4471.16	−0.582768	−0.291384	+	0.956606i	$0.594116\pi$
$390$	0	0
$391$	−15.5398	−0.00200992
$392$	1775.59	0.228778
$393$	0	0
$394$	−641.639	−0.0820439
$395$	4068.32	0.518226
$396$	0	0
$397$	−6932.41	−0.876392	−0.438196	−	0.898879i	$-0.644382\pi$
$397$	−6932.41	−0.876392	−0.438196	+	0.898879i	$0.644382\pi$
$398$	−3502.58	−0.441127
$399$	0	0
$400$	4430.09	0.553761
$401$	−12031.6	−1.49833	−0.749163	−	0.662386i	$-0.769544\pi$
$401$	−12031.6	−1.49833	−0.749163	+	0.662386i	$0.769544\pi$
$402$	0	0
$403$	−11434.4	−1.41337
$404$	4572.56	0.563102
$405$	0	0
$406$	−1224.42	−0.149673
$407$	10061.7	1.22541
$408$	0	0
$409$	582.097	0.0703737	0.0351868	−	0.999381i	$-0.488797\pi$
$409$	582.097	0.0703737	0.0351868	+	0.999381i	$0.488797\pi$
$410$	9747.13	1.17409
$411$	0	0
$412$	−4821.94	−0.576602
$413$	4556.02	0.542825
$414$	0	0
$415$	−9749.53	−1.15322
$416$	−5021.89	−0.591871
$417$	0	0
$418$	7507.97	0.878533
$419$	−3174.96	−0.370184	−0.185092	−	0.982721i	$-0.559258\pi$
$419$	−3174.96	−0.370184	−0.185092	+	0.982721i	$0.559258\pi$
$420$	0	0
$421$	3185.72	0.368794	0.184397	−	0.982852i	$-0.440967\pi$
$421$	3185.72	0.368794	0.184397	+	0.982852i	$0.440967\pi$
$422$	−9286.84	−1.07127
$423$	0	0
$424$	−9097.73	−1.04204
$425$	−6.08598	−0.000694619 0
$426$	0	0
$427$	−8328.81	−0.943933
$428$	1443.96	0.163076
$429$	0	0
$430$	6451.85	0.723572
$431$	−5525.11	−0.617483	−0.308741	−	0.951146i	$-0.599908\pi$
$431$	−5525.11	−0.617483	−0.308741	+	0.951146i	$0.599908\pi$
$432$	0	0
$433$	13661.7	1.51626	0.758130	−	0.652104i	$-0.226113\pi$
$433$	13661.7	1.51626	0.758130	+	0.652104i	$0.226113\pi$
$434$	−13122.3	−1.45136
$435$	0	0
$436$	−1621.01	−0.178056
$437$	13686.9	1.49825
$438$	0	0
$439$	17008.5	1.84913	0.924567	−	0.381018i	$-0.124427\pi$
$439$	17008.5	1.84913	0.924567	+	0.381018i	$0.124427\pi$
$440$	3540.52	0.383608
$441$	0	0
$442$	15.4180	0.00165918
$443$	13969.8	1.49825	0.749123	−	0.662430i	$-0.230475\pi$
$443$	13969.8	1.49825	0.749123	+	0.662430i	$0.230475\pi$
$444$	0	0
$445$	−5481.52	−0.583930
$446$	5094.48	0.540876
$447$	0	0
$448$	3949.65	0.416525
$449$	14558.2	1.53016	0.765082	−	0.643933i	$-0.222698\pi$
$449$	14558.2	1.53016	0.765082	+	0.643933i	$0.222698\pi$
$450$	0	0
$451$	−8840.40	−0.923012
$452$	−3754.57	−0.390709
$453$	0	0
$454$	12008.2	1.24135
$455$	5671.49	0.584360
$456$	0	0
$457$	−2504.82	−0.256390	−0.128195	−	0.991749i	$-0.540918\pi$
$457$	−2504.82	−0.256390	−0.128195	+	0.991749i	$0.540918\pi$
$458$	16486.9	1.68206
$459$	0	0
$460$	−3122.50	−0.316494
$461$	10815.7	1.09271	0.546354	−	0.837554i	$-0.316015\pi$
$461$	10815.7	1.09271	0.546354	+	0.837554i	$0.316015\pi$
$462$	0	0
$463$	5724.41	0.574592	0.287296	−	0.957842i	$-0.407244\pi$
$463$	5724.41	0.574592	0.287296	+	0.957842i	$0.407244\pi$
$464$	1886.89	0.188786
$465$	0	0
$466$	−22046.2	−2.19156
$467$	12776.2	1.26597	0.632987	−	0.774162i	$-0.281829\pi$
$467$	12776.2	1.26597	0.632987	+	0.774162i	$0.281829\pi$
$468$	0	0
$469$	8806.65	0.867065
$470$	1683.35	0.165207
$471$	0	0
$472$	−5144.24	−0.501658
$473$	−5851.66	−0.568837
$474$	0	0
$475$	5360.33	0.517787
$476$	4.35056	0.000418923 0
$477$	0	0
$478$	−1150.57	−0.110096
$479$	−890.206	−0.0849155	−0.0424578	−	0.999098i	$-0.513519\pi$
$479$	−890.206	−0.0849155	−0.0424578	+	0.999098i	$0.513519\pi$
$480$	0	0
$481$	−18198.6	−1.72512
$482$	−6926.82	−0.654581
$483$	0	0
$484$	−1918.25	−0.180151
$485$	−2783.68	−0.260619
$486$	0	0
$487$	8592.42	0.799507	0.399753	−	0.916623i	$-0.369096\pi$
$487$	8592.42	0.799507	0.399753	+	0.916623i	$0.369096\pi$
$488$	9404.13	0.872346
$489$	0	0
$490$	−2720.67	−0.250831
$491$	14000.1	1.28680	0.643398	−	0.765532i	$-0.277524\pi$
$491$	14000.1	1.28680	0.643398	+	0.765532i	$0.277524\pi$
$492$	0	0
$493$	−2.59218	−0.000236807 0
$494$	−13579.7	−1.23680
$495$	0	0
$496$	20222.0	1.83063
$497$	−6437.40	−0.581000
$498$	0	0
$499$	6167.22	0.553272	0.276636	−	0.960975i	$-0.410780\pi$
$499$	6167.22	0.553272	0.276636	+	0.960975i	$0.410780\pi$
$500$	−3916.49	−0.350302
$501$	0	0
$502$	−19893.2	−1.76868
$503$	−6449.42	−0.571701	−0.285850	−	0.958274i	$-0.592276\pi$
$503$	−6449.42	−0.571701	−0.285850	+	0.958274i	$0.592276\pi$
$504$	0	0
$505$	14482.4	1.27615
$506$	11518.0	1.01193
$507$	0	0
$508$	−4304.03	−0.375906
$509$	1949.07	0.169727	0.0848633	−	0.996393i	$-0.472955\pi$
$509$	1949.07	0.169727	0.0848633	+	0.996393i	$0.472955\pi$
$510$	0	0
$511$	−5238.21	−0.453473
$512$	−2085.52	−0.180015
$513$	0	0
$514$	6828.96	0.586016
$515$	−15272.2	−1.30675
$516$	0	0
$517$	−1526.75	−0.129877
$518$	−20884.9	−1.77149
$519$	0	0
$520$	−6403.73	−0.540042
$521$	−13798.7	−1.16033	−0.580163	−	0.814500i	$-0.697011\pi$
$521$	−13798.7	−1.16033	−0.580163	+	0.814500i	$0.697011\pi$
$522$	0	0
$523$	21367.6	1.78650	0.893250	−	0.449561i	$-0.148419\pi$
$523$	21367.6	1.78650	0.893250	+	0.449561i	$0.148419\pi$
$524$	−1007.65	−0.0840068
$525$	0	0
$526$	−25837.7	−2.14178
$527$	−27.7806	−0.00229628
$528$	0	0
$529$	8830.06	0.725739
$530$	13940.1	1.14249
$531$	0	0
$532$	−3831.83	−0.312276
$533$	15989.6	1.29941
$534$	0	0
$535$	4573.37	0.369578
$536$	−9943.66	−0.801307
$537$	0	0
$538$	−2397.20	−0.192102
$539$	2467.58	0.197191
$540$	0	0
$541$	−18713.8	−1.48719	−0.743595	−	0.668630i	$-0.766881\pi$
$541$	−18713.8	−1.48719	−0.743595	+	0.668630i	$0.766881\pi$
$542$	15818.8	1.25364
$543$	0	0
$544$	−12.2010	−0.000961604 0
$545$	−5134.11	−0.403525
$546$	0	0
$547$	−12519.0	−0.978561	−0.489280	−	0.872127i	$-0.662740\pi$
$547$	−12519.0	−0.978561	−0.489280	+	0.872127i	$0.662740\pi$
$548$	2159.22	0.168317
$549$	0	0
$550$	4510.88	0.349717
$551$	2283.11	0.176522
$552$	0	0
$553$	7658.98	0.588957
$554$	−21750.1	−1.66800
$555$	0	0
$556$	−1597.43	−0.121845
$557$	1180.39	0.0897931	0.0448965	−	0.998992i	$-0.485704\pi$
$557$	1180.39	0.0897931	0.0448965	+	0.998992i	$0.485704\pi$
$558$	0	0
$559$	10583.9	0.800807
$560$	−10030.1	−0.756876
$561$	0	0
$562$	18324.8	1.37542
$563$	15586.9	1.16680	0.583401	−	0.812184i	$-0.301721\pi$
$563$	15586.9	1.16680	0.583401	+	0.812184i	$0.301721\pi$
$564$	0	0
$565$	−11891.6	−0.885458
$566$	−17420.7	−1.29372
$567$	0	0
$568$	7268.52	0.536937
$569$	2743.60	0.202140	0.101070	−	0.994879i	$-0.467773\pi$
$569$	2743.60	0.202140	0.101070	+	0.994879i	$0.467773\pi$
$570$	0	0
$571$	1194.38	0.0875360	0.0437680	−	0.999042i	$-0.486064\pi$
$571$	1194.38	0.0875360	0.0437680	+	0.999042i	$0.486064\pi$
$572$	−2809.84	−0.205394
$573$	0	0
$574$	18349.9	1.33434
$575$	8223.27	0.596407
$576$	0	0
$577$	20968.2	1.51285	0.756427	−	0.654078i	$-0.226943\pi$
$577$	20968.2	1.51285	0.756427	+	0.654078i	$0.226943\pi$
$578$	−16001.9	−1.15154
$579$	0	0
$580$	−520.862	−0.0372890
$581$	−18354.4	−1.31062
$582$	0	0
$583$	−12643.3	−0.898169
$584$	5914.51	0.419082
$585$	0	0
$586$	19181.1	1.35216
$587$	3915.64	0.275325	0.137663	−	0.990479i	$-0.456041\pi$
$587$	3915.64	0.275325	0.137663	+	0.990479i	$0.456041\pi$
$588$	0	0
$589$	24468.2	1.71171
$590$	7882.31	0.550016
$591$	0	0
$592$	32184.6	2.23442
$593$	6327.58	0.438183	0.219091	−	0.975704i	$-0.429691\pi$
$593$	6327.58	0.438183	0.219091	+	0.975704i	$0.429691\pi$
$594$	0	0
$595$	13.7792	0.000949400 0
$596$	−908.515	−0.0624400
$597$	0	0
$598$	−20832.5	−1.42459
$599$	1631.72	0.111303	0.0556513	−	0.998450i	$-0.482276\pi$
$599$	1631.72	0.111303	0.0556513	+	0.998450i	$0.482276\pi$
$600$	0	0
$601$	1445.94	0.0981384	0.0490692	−	0.998795i	$-0.484375\pi$
$601$	1445.94	0.0981384	0.0490692	+	0.998795i	$0.484375\pi$
$602$	12146.2	0.822329
$603$	0	0
$604$	−4291.20	−0.289084
$605$	−6075.54	−0.408274
$606$	0	0
$607$	11038.7	0.738131	0.369065	−	0.929403i	$-0.379678\pi$
$607$	11038.7	0.738131	0.369065	+	0.929403i	$0.379678\pi$
$608$	10746.2	0.716804
$609$	0	0
$610$	−14409.6	−0.956438
$611$	2761.44	0.182841
$612$	0	0
$613$	20856.3	1.37419	0.687096	−	0.726567i	$-0.258885\pi$
$613$	20856.3	1.37419	0.687096	+	0.726567i	$0.258885\pi$
$614$	−2802.34	−0.184191
$615$	0	0
$616$	6665.35	0.435965
$617$	−5712.03	−0.372703	−0.186351	−	0.982483i	$-0.559666\pi$
$617$	−5712.03	−0.372703	−0.186351	+	0.982483i	$0.559666\pi$
$618$	0	0
$619$	−25250.3	−1.63957	−0.819787	−	0.572669i	$-0.805908\pi$
$619$	−25250.3	−1.63957	−0.819787	+	0.572669i	$0.805908\pi$
$620$	−5582.12	−0.361586
$621$	0	0
$622$	14061.3	0.906445
$623$	−10319.5	−0.663629
$624$	0	0
$625$	−5310.71	−0.339885
$626$	−9636.24	−0.615242
$627$	0	0
$628$	9394.30	0.596932
$629$	−44.2146	−0.00280278
$630$	0	0
$631$	−16775.7	−1.05837	−0.529183	−	0.848508i	$-0.677501\pi$
$631$	−16775.7	−1.05837	−0.529183	+	0.848508i	$0.677501\pi$
$632$	−8647.82	−0.544291
$633$	0	0
$634$	−23139.6	−1.44951
$635$	−13631.9	−0.851912
$636$	0	0
$637$	−4463.10	−0.277605
$638$	1921.30	0.119224
$639$	0	0
$640$	14352.4	0.886452
$641$	−9988.54	−0.615482	−0.307741	−	0.951470i	$-0.599573\pi$
$641$	−9988.54	−0.615482	−0.307741	+	0.951470i	$0.599573\pi$
$642$	0	0
$643$	26304.1	1.61327	0.806634	−	0.591051i	$-0.201287\pi$
$643$	26304.1	1.61327	0.806634	+	0.591051i	$0.201287\pi$
$644$	−5878.40	−0.359691
$645$	0	0
$646$	−32.9926	−0.00200941
$647$	−7956.48	−0.483464	−0.241732	−	0.970343i	$-0.577716\pi$
$647$	−7956.48	−0.483464	−0.241732	+	0.970343i	$0.577716\pi$
$648$	0	0
$649$	−7149.06	−0.432396
$650$	−8158.82	−0.492331
$651$	0	0
$652$	−7347.03	−0.441306
$653$	−2872.28	−0.172130	−0.0860652	−	0.996290i	$-0.527429\pi$
$653$	−2872.28	−0.172130	−0.0860652	+	0.996290i	$0.527429\pi$
$654$	0	0
$655$	−3191.47	−0.190384
$656$	−28278.0	−1.68303
$657$	0	0
$658$	3169.06	0.187755
$659$	15107.1	0.893004	0.446502	−	0.894783i	$-0.352670\pi$
$659$	15107.1	0.893004	0.446502	+	0.894783i	$0.352670\pi$
$660$	0	0
$661$	−13750.5	−0.809127	−0.404563	−	0.914510i	$-0.632576\pi$
$661$	−13750.5	−0.809127	−0.404563	+	0.914510i	$0.632576\pi$
$662$	11161.0	0.655263
$663$	0	0
$664$	20724.1	1.21122
$665$	−12136.3	−0.707707
$666$	0	0
$667$	3502.50	0.203325
$668$	4952.07	0.286829
$669$	0	0
$670$	15236.3	0.878551
$671$	13069.1	0.751905
$672$	0	0
$673$	3385.45	0.193907	0.0969535	−	0.995289i	$-0.469090\pi$
$673$	3385.45	0.193907	0.0969535	+	0.995289i	$0.469090\pi$
$674$	19135.5	1.09358
$675$	0	0
$676$	−648.474	−0.0368954
$677$	20705.6	1.17545	0.587727	−	0.809059i	$-0.300023\pi$
$677$	20705.6	1.17545	0.587727	+	0.809059i	$0.300023\pi$
$678$	0	0
$679$	−5240.53	−0.296190
$680$	−15.5582	−0.000877399 0
$681$	0	0
$682$	20590.7	1.15610
$683$	−2748.19	−0.153963	−0.0769814	−	0.997033i	$-0.524528\pi$
$683$	−2748.19	−0.153963	−0.0769814	+	0.997033i	$0.524528\pi$
$684$	0	0
$685$	6838.77	0.381454
$686$	−22497.0	−1.25210
$687$	0	0
$688$	−18717.8	−1.03722
$689$	22868.0	1.26444
$690$	0	0
$691$	−28050.7	−1.54428	−0.772142	−	0.635450i	$-0.780815\pi$
$691$	−28050.7	−1.54428	−0.772142	+	0.635450i	$0.780815\pi$
$692$	8431.45	0.463173
$693$	0	0
$694$	−16219.6	−0.887157
$695$	−5059.42	−0.276136
$696$	0	0
$697$	38.8477	0.00211114
$698$	17202.0	0.932814
$699$	0	0
$700$	−2302.21	−0.124308
$701$	15551.0	0.837877	0.418939	−	0.908015i	$-0.362402\pi$
$701$	15551.0	0.837877	0.418939	+	0.908015i	$0.362402\pi$
$702$	0	0
$703$	38942.8	2.08927
$704$	−6197.57	−0.331790
$705$	0	0
$706$	7727.64	0.411945
$707$	27264.4	1.45033
$708$	0	0
$709$	−4368.81	−0.231416	−0.115708	−	0.993283i	$-0.536914\pi$
$709$	−4368.81	−0.231416	−0.115708	+	0.993283i	$0.536914\pi$
$710$	−11137.3	−0.588696
$711$	0	0
$712$	11651.8	0.613300
$713$	37536.6	1.97161
$714$	0	0
$715$	−8899.40	−0.465481
$716$	3564.96	0.186074
$717$	0	0
$718$	−28371.9	−1.47469
$719$	8550.59	0.443510	0.221755	−	0.975102i	$-0.428822\pi$
$719$	8550.59	0.443510	0.221755	+	0.975102i	$0.428822\pi$
$720$	0	0
$721$	−28751.4	−1.48510
$722$	6718.68	0.346320
$723$	0	0
$724$	5299.65	0.272044
$725$	1371.72	0.0702680
$726$	0	0
$727$	−16852.9	−0.859750	−0.429875	−	0.902888i	$-0.641442\pi$
$727$	−16852.9	−0.859750	−0.429875	+	0.902888i	$0.641442\pi$
$728$	−12055.6	−0.613751
$729$	0	0
$730$	−9062.57	−0.459480
$731$	25.7142	0.00130106
$732$	0	0
$733$	−18457.9	−0.930095	−0.465048	−	0.885286i	$-0.653963\pi$
$733$	−18457.9	−0.930095	−0.465048	+	0.885286i	$0.653963\pi$
$734$	15431.1	0.775986
$735$	0	0
$736$	16485.7	0.825642
$737$	−13818.9	−0.690674
$738$	0	0
$739$	11329.5	0.563955	0.281978	−	0.959421i	$-0.409010\pi$
$739$	11329.5	0.563955	0.281978	+	0.959421i	$0.409010\pi$
$740$	−8884.31	−0.441343
$741$	0	0
$742$	26243.5	1.29842
$743$	1810.71	0.0894059	0.0447029	−	0.999000i	$-0.485766\pi$
$743$	1810.71	0.0894059	0.0447029	+	0.999000i	$0.485766\pi$
$744$	0	0
$745$	−2877.48	−0.141507
$746$	22519.2	1.10521
$747$	0	0
$748$	−6.82666	−0.000333700 0
$749$	8609.79	0.420020
$750$	0	0
$751$	11058.7	0.537332	0.268666	−	0.963233i	$-0.413417\pi$
$751$	11058.7	0.537332	0.268666	+	0.963233i	$0.413417\pi$
$752$	−4883.66	−0.236820
$753$	0	0
$754$	−3475.06	−0.167844
$755$	−13591.2	−0.655147
$756$	0	0
$757$	−18384.6	−0.882692	−0.441346	−	0.897337i	$-0.645499\pi$
$757$	−18384.6	−0.882692	−0.441346	+	0.897337i	$0.645499\pi$
$758$	−7417.92	−0.355450
$759$	0	0
$760$	13703.2	0.654035
$761$	3179.76	0.151467	0.0757335	−	0.997128i	$-0.475870\pi$
$761$	3179.76	0.151467	0.0757335	+	0.997128i	$0.475870\pi$
$762$	0	0
$763$	−9665.43	−0.458600
$764$	−550.650	−0.0260757
$765$	0	0
$766$	−6132.85	−0.289280
$767$	12930.5	0.608726
$768$	0	0
$769$	2596.88	0.121776	0.0608881	−	0.998145i	$-0.480607\pi$
$769$	2596.88	0.121776	0.0608881	+	0.998145i	$0.480607\pi$
$770$	−10213.1	−0.477991
$771$	0	0
$772$	10516.7	0.490292
$773$	−38095.1	−1.77255	−0.886277	−	0.463156i	$-0.846717\pi$
$773$	−38095.1	−1.77255	−0.886277	+	0.463156i	$0.846717\pi$
$774$	0	0
$775$	14700.8	0.681379
$776$	5917.13	0.273728
$777$	0	0
$778$	−14562.8	−0.671081
$779$	−34215.8	−1.57370
$780$	0	0
$781$	10101.2	0.462804
$782$	−50.6138	−0.00231451
$783$	0	0
$784$	7893.08	0.359561
$785$	29753.9	1.35282
$786$	0	0
$787$	2242.72	0.101581	0.0507905	−	0.998709i	$-0.483826\pi$
$787$	2242.72	0.101581	0.0507905	+	0.998709i	$0.483826\pi$
$788$	−513.852	−0.0232300
$789$	0	0
$790$	13250.7	0.596759
$791$	−22387.1	−1.00631
$792$	0	0
$793$	−23638.1	−1.05853
$794$	−22579.2	−1.00920
$795$	0	0
$796$	−2805.01	−0.124901
$797$	−16110.3	−0.716006	−0.358003	−	0.933720i	$-0.616542\pi$
$797$	−16110.3	−0.716006	−0.358003	+	0.933720i	$0.616542\pi$
$798$	0	0
$799$	6.70908	0.000297059 0
$800$	6456.46	0.285338
$801$	0	0
$802$	−39187.5	−1.72538
$803$	8219.52	0.361221
$804$	0	0
$805$	−18618.2	−0.815164
$806$	−37242.5	−1.62756
$807$	0	0
$808$	−30784.4	−1.34034
$809$	−35408.8	−1.53882	−0.769412	−	0.638753i	$-0.779451\pi$
$809$	−35408.8	−1.53882	−0.769412	+	0.638753i	$0.779451\pi$
$810$	0	0
$811$	−29961.3	−1.29727	−0.648633	−	0.761101i	$-0.724659\pi$
$811$	−29961.3	−1.29727	−0.648633	+	0.761101i	$0.724659\pi$
$812$	−980.571	−0.0423784
$813$	0	0
$814$	32771.5	1.41111
$815$	−23269.7	−1.00013
$816$	0	0
$817$	−22648.2	−0.969843
$818$	1895.92	0.0810382
$819$	0	0
$820$	7805.91	0.332432
$821$	−41220.1	−1.75224	−0.876122	−	0.482090i	$-0.839878\pi$
$821$	−41220.1	−1.75224	−0.876122	+	0.482090i	$0.839878\pi$
$822$	0	0
$823$	−6327.55	−0.268001	−0.134000	−	0.990981i	$-0.542782\pi$
$823$	−6327.55	−0.268001	−0.134000	+	0.990981i	$0.542782\pi$
$824$	32463.4	1.37247
$825$	0	0
$826$	14839.2	0.625086
$827$	26605.5	1.11870	0.559350	−	0.828932i	$-0.311051\pi$
$827$	26605.5	1.11870	0.559350	+	0.828932i	$0.311051\pi$
$828$	0	0
$829$	37088.6	1.55385	0.776925	−	0.629593i	$-0.216778\pi$
$829$	37088.6	1.55385	0.776925	+	0.629593i	$0.216778\pi$
$830$	−31754.7	−1.32798
$831$	0	0
$832$	11209.5	0.467093
$833$	−10.8434	−0.000451021 0
$834$	0	0
$835$	15684.4	0.650036
$836$	6012.70	0.248748
$837$	0	0
$838$	−10341.0	−0.426282
$839$	−11211.3	−0.461333	−0.230667	−	0.973033i	$-0.574091\pi$
$839$	−11211.3	−0.461333	−0.230667	+	0.973033i	$0.574091\pi$
$840$	0	0
$841$	−23804.7	−0.976045
$842$	10376.0	0.424682
$843$	0	0
$844$	−7437.29	−0.303320
$845$	−2053.87	−0.0836156
$846$	0	0
$847$	−11437.8	−0.463998
$848$	−40442.4	−1.63773
$849$	0	0
$850$	−19.8223	−0.000799883 0
$851$	59742.0	2.40650
$852$	0	0
$853$	−36808.1	−1.47748	−0.738738	−	0.673993i	$-0.764578\pi$
$853$	−36808.1	−1.47748	−0.738738	+	0.673993i	$0.764578\pi$
$854$	−27127.4	−1.08698
$855$	0	0
$856$	−9721.38	−0.388166
$857$	3442.46	0.137214	0.0686068	−	0.997644i	$-0.478145\pi$
$857$	3442.46	0.137214	0.0686068	+	0.997644i	$0.478145\pi$
$858$	0	0
$859$	−6614.42	−0.262725	−0.131363	−	0.991334i	$-0.541935\pi$
$859$	−6614.42	−0.262725	−0.131363	+	0.991334i	$0.541935\pi$
$860$	5166.91	0.204872
$861$	0	0
$862$	−17995.6	−0.711057
$863$	47138.8	1.85935	0.929677	−	0.368376i	$-0.120086\pi$
$863$	47138.8	1.85935	0.929677	+	0.368376i	$0.120086\pi$
$864$	0	0
$865$	26704.4	1.04968
$866$	44496.9	1.74604
$867$	0	0
$868$	−10508.9	−0.410938
$869$	−12018.1	−0.469143
$870$	0	0
$871$	24994.3	0.972329
$872$	10913.3	0.423821
$873$	0	0
$874$	44579.0	1.72529
$875$	−23352.5	−0.902239
$876$	0	0
$877$	31400.3	1.20902	0.604510	−	0.796597i	$-0.293369\pi$
$877$	31400.3	1.20902	0.604510	+	0.796597i	$0.293369\pi$
$878$	55397.5	2.12936
$879$	0	0
$880$	15738.8	0.602902
$881$	−27904.8	−1.06712	−0.533562	−	0.845761i	$-0.679147\pi$
$881$	−27904.8	−1.06712	−0.533562	+	0.845761i	$0.679147\pi$
$882$	0	0
$883$	27053.5	1.03106	0.515529	−	0.856872i	$-0.327596\pi$
$883$	27053.5	1.03106	0.515529	+	0.856872i	$0.327596\pi$
$884$	12.3474	0.000469782 0
$885$	0	0
$886$	45500.2	1.72529
$887$	−38756.4	−1.46709	−0.733546	−	0.679639i	$-0.762136\pi$
$887$	−38756.4	−1.46709	−0.733546	+	0.679639i	$0.762136\pi$
$888$	0	0
$889$	−25663.2	−0.968186
$890$	−17853.6	−0.672420
$891$	0	0
$892$	4079.87	0.153144
$893$	−5909.14	−0.221435
$894$	0	0
$895$	11291.1	0.421697
$896$	27019.8	1.00744
$897$	0	0
$898$	47416.8	1.76205
$899$	6261.46	0.232293
$900$	0	0
$901$	55.5590	0.00205432
$902$	−28793.6	−1.06289
$903$	0	0
$904$	25277.4	0.929993
$905$	16785.2	0.616530
$906$	0	0
$907$	−23050.6	−0.843861	−0.421930	−	0.906628i	$-0.638647\pi$
$907$	−23050.6	−0.843861	−0.421930	+	0.906628i	$0.638647\pi$
$908$	9616.66	0.351476
$909$	0	0
$910$	18472.3	0.672914
$911$	−5461.95	−0.198642	−0.0993209	−	0.995055i	$-0.531667\pi$
$911$	−5461.95	−0.198642	−0.0993209	+	0.995055i	$0.531667\pi$
$912$	0	0
$913$	28800.7	1.04399
$914$	−8158.32	−0.295244
$915$	0	0
$916$	13203.4	0.476260
$917$	−6008.24	−0.216368
$918$	0	0
$919$	−16139.2	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$919$	−16139.2	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$920$	21022.0	0.753343
$921$	0	0
$922$	35227.4	1.25830
$923$	−18270.1	−0.651535
$924$	0	0
$925$	23397.3	0.831673
$926$	18644.7	0.661666
$927$	0	0
$928$	2749.98	0.0972762
$929$	44343.7	1.56606	0.783030	−	0.621983i	$-0.213673\pi$
$929$	44343.7	1.56606	0.783030	+	0.621983i	$0.213673\pi$
$930$	0	0
$931$	9550.49	0.336203
$932$	−17655.5	−0.620521
$933$	0	0
$934$	41612.6	1.45782
$935$	−21.6216	−0.000756260 0
$936$	0	0
$937$	−6439.87	−0.224526	−0.112263	−	0.993679i	$-0.535810\pi$
$937$	−6439.87	−0.224526	−0.112263	+	0.993679i	$0.535810\pi$
$938$	28683.7	0.998461
$939$	0	0
$940$	1348.10	0.0467767
$941$	−11377.8	−0.394162	−0.197081	−	0.980387i	$-0.563146\pi$
$941$	−11377.8	−0.394162	−0.197081	+	0.980387i	$0.563146\pi$
$942$	0	0
$943$	−52490.4	−1.81264
$944$	−22867.8	−0.788437
$945$	0	0
$946$	−19059.2	−0.655039
$947$	−2029.00	−0.0696236	−0.0348118	−	0.999394i	$-0.511083\pi$
$947$	−2029.00	−0.0696236	−0.0348118	+	0.999394i	$0.511083\pi$
$948$	0	0
$949$	−14866.6	−0.508526
$950$	17458.9	0.596253
$951$	0	0
$952$	−29.2898	−0.000997152 0
$953$	18497.6	0.628747	0.314373	−	0.949299i	$-0.398206\pi$
$953$	18497.6	0.628747	0.314373	+	0.949299i	$0.398206\pi$
$954$	0	0
$955$	−1744.04	−0.0590950
$956$	−921.426	−0.0311726
$957$	0	0
$958$	−2899.45	−0.0977838
$959$	12874.6	0.433517
$960$	0	0
$961$	37313.5	1.25251
$962$	−59273.8	−1.98655
$963$	0	0
$964$	−5547.29	−0.185338
$965$	33308.9	1.11114
$966$	0	0
$967$	−12880.3	−0.428339	−0.214170	−	0.976796i	$-0.568705\pi$
$967$	−12880.3	−0.428339	−0.214170	+	0.976796i	$0.568705\pi$
$968$	12914.5	0.428809
$969$	0	0
$970$	−9066.59	−0.300114
$971$	−11969.8	−0.395600	−0.197800	−	0.980242i	$-0.563380\pi$
$971$	−11969.8	−0.395600	−0.197800	+	0.980242i	$0.563380\pi$
$972$	0	0
$973$	−9524.82	−0.313825
$974$	27986.0	0.920665
$975$	0	0
$976$	41804.5	1.37103
$977$	5543.99	0.181544	0.0907718	−	0.995872i	$-0.471067\pi$
$977$	5543.99	0.181544	0.0907718	+	0.995872i	$0.471067\pi$
$978$	0	0
$979$	16192.8	0.528624
$980$	−2178.83	−0.0710205
$981$	0	0
$982$	45599.2	1.48180
$983$	47280.6	1.53410	0.767048	−	0.641590i	$-0.221725\pi$
$983$	47280.6	1.53410	0.767048	+	0.641590i	$0.221725\pi$
$984$	0	0
$985$	−1627.49	−0.0526458
$986$	−8.44285	−0.000272693 0
$987$	0	0
$988$	−10875.2	−0.350187
$989$	−34744.6	−1.11710
$990$	0	0
$991$	−19940.0	−0.639167	−0.319584	−	0.947558i	$-0.603543\pi$
$991$	−19940.0	−0.639167	−0.319584	+	0.947558i	$0.603543\pi$
$992$	29471.7	0.943274
$993$	0	0
$994$	−20966.9	−0.669045
$995$	−8884.13	−0.283061
$996$	0	0
$997$	−11334.5	−0.360047	−0.180024	−	0.983662i	$-0.557617\pi$
$997$	−11334.5	−0.360047	−0.180024	+	0.983662i	$0.557617\pi$
$998$	20087.0	0.637116
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1773.4.a.c.1.17		22
3.2	odd	2		197.4.a.a.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.a.1.6	✓	22	3.2	odd	2
1773.4.a.c.1.17		22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1773 = 3^{2} \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1773.a (trivial)

\(f(q)\)	\(=\)	\(q+3.25705 q^{2} +2.60839 q^{4} +8.26136 q^{5} +15.5528 q^{7} -17.5608 q^{8} +26.9077 q^{10} -24.4046 q^{11} +44.1406 q^{13} +50.6562 q^{14} -78.0634 q^{16} +0.107242 q^{17} -94.4553 q^{19} +21.5488 q^{20} -79.4870 q^{22} -144.904 q^{23} -56.7499 q^{25} +143.768 q^{26} +40.5676 q^{28} -24.1713 q^{29} -259.045 q^{31} -113.770 q^{32} +0.349293 q^{34} +128.487 q^{35} -412.288 q^{37} -307.646 q^{38} -145.076 q^{40} +362.243 q^{41} +239.777 q^{43} -63.6566 q^{44} -471.959 q^{46} +62.5601 q^{47} -101.111 q^{49} -184.837 q^{50} +115.136 q^{52} +518.071 q^{53} -201.615 q^{55} -273.119 q^{56} -78.7271 q^{58} +292.939 q^{59} -535.519 q^{61} -843.724 q^{62} +253.951 q^{64} +364.661 q^{65} +566.243 q^{67} +0.279729 q^{68} +418.489 q^{70} -413.907 q^{71} -336.802 q^{73} -1342.84 q^{74} -246.376 q^{76} -379.559 q^{77} +492.451 q^{79} -644.910 q^{80} +1179.85 q^{82} -1180.14 q^{83} +0.885966 q^{85} +780.967 q^{86} +428.563 q^{88} -663.513 q^{89} +686.508 q^{91} -377.964 q^{92} +203.762 q^{94} -780.330 q^{95} -336.952 q^{97} -329.324 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{2} + 68 q^{4} + 31 q^{5} - 102 q^{7} + 93 q^{8} - 133 q^{10} + 100 q^{11} - 223 q^{13} + 55 q^{14} + 112 q^{16} + 114 q^{17} - 529 q^{19} + 441 q^{20} - 671 q^{22} + 208 q^{23} + 35 q^{25} + 408 q^{26}+ \cdots - 2932 q^{98}+O(q^{100}) \) 22 * q + 6 * q^2 + 68 * q^4 + 31 * q^5 - 102 * q^7 + 93 * q^8 - 133 * q^10 + 100 * q^11 - 223 * q^13 + 55 * q^14 + 112 * q^16 + 114 * q^17 - 529 * q^19 + 441 * q^20 - 671 * q^22 + 208 * q^23 + 35 * q^25 + 408 * q^26 - 1202 * q^28 + 2 * q^29 - 1261 * q^31 + 1020 * q^32 - 814 * q^34 + 968 * q^35 - 792 * q^37 + 184 * q^38 - 1914 * q^40 + 271 * q^41 - 1349 * q^43 + 998 * q^44 - 1371 * q^46 + 986 * q^47 - 40 * q^49 - 1631 * q^50 - 1382 * q^52 - 248 * q^53 - 566 * q^55 - 4800 * q^56 + 351 * q^58 + 1281 * q^59 + 510 * q^61 - 2237 * q^62 + 3185 * q^64 - 2558 * q^65 - 3070 * q^67 - 4625 * q^68 + 2087 * q^70 - 101 * q^71 - 3352 * q^73 - 4501 * q^74 - 334 * q^76 + 492 * q^77 - 1313 * q^79 - 3098 * q^80 - 1243 * q^82 + 2631 * q^83 + 84 * q^85 - 7448 * q^86 - 3285 * q^88 - 798 * q^89 - 3992 * q^91 - 5966 * q^92 + 3517 * q^94 - 284 * q^95 - 3693 * q^97 - 2932 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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