LMFDB - Embedded newform 1045.4.a.d.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1045,4,Mod(1,1045)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1045.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1045, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.a (trivial)

Newform invariants

comment:select newform

sage:traces = [22,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$61.6569959560$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	1045.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.86531 q^{2} -5.40234 q^{3} +0.209982 q^{4} +5.00000 q^{5} +15.4794 q^{6} -24.6494 q^{7} +22.3208 q^{8} +2.18531 q^{9} -14.3265 q^{10} -11.0000 q^{11} -1.13439 q^{12} +15.7098 q^{13} +70.6279 q^{14} -27.0117 q^{15} -65.6358 q^{16} -2.85422 q^{17} -6.26159 q^{18} -19.0000 q^{19} +1.04991 q^{20} +133.164 q^{21} +31.5184 q^{22} -124.821 q^{23} -120.585 q^{24} +25.0000 q^{25} -45.0134 q^{26} +134.057 q^{27} -5.17592 q^{28} +78.4342 q^{29} +77.3968 q^{30} -36.4439 q^{31} +9.50027 q^{32} +59.4258 q^{33} +8.17823 q^{34} -123.247 q^{35} +0.458876 q^{36} +35.0684 q^{37} +54.4408 q^{38} -84.8697 q^{39} +111.604 q^{40} +283.204 q^{41} -381.556 q^{42} -184.609 q^{43} -2.30980 q^{44} +10.9266 q^{45} +357.652 q^{46} +241.399 q^{47} +354.587 q^{48} +264.590 q^{49} -71.6327 q^{50} +15.4195 q^{51} +3.29878 q^{52} +181.351 q^{53} -384.116 q^{54} -55.0000 q^{55} -550.193 q^{56} +102.645 q^{57} -224.738 q^{58} +893.693 q^{59} -5.67197 q^{60} -225.438 q^{61} +104.423 q^{62} -53.8665 q^{63} +497.865 q^{64} +78.5490 q^{65} -170.273 q^{66} -374.295 q^{67} -0.599336 q^{68} +674.329 q^{69} +353.140 q^{70} +194.109 q^{71} +48.7779 q^{72} -19.3282 q^{73} -100.482 q^{74} -135.059 q^{75} -3.98966 q^{76} +271.143 q^{77} +243.178 q^{78} +782.604 q^{79} -328.179 q^{80} -783.228 q^{81} -811.467 q^{82} -42.2123 q^{83} +27.9621 q^{84} -14.2711 q^{85} +528.963 q^{86} -423.728 q^{87} -245.529 q^{88} +1127.29 q^{89} -31.3079 q^{90} -387.236 q^{91} -26.2103 q^{92} +196.882 q^{93} -691.683 q^{94} -95.0000 q^{95} -51.3237 q^{96} +862.657 q^{97} -758.133 q^{98} -24.0384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18}+ \cdots - 2299 q^{99}+O(q^{100}) $ 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * q^99

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 $

$2$	−2.86531	−1.01304	−0.506519	−	0.862229i	$-0.669068\pi$
$2$	−2.86531	−1.01304	−0.506519	+	0.862229i	$0.669068\pi$
$3$	−5.40234	−1.03968	−0.519841	−	0.854263i	$-0.674009\pi$
$3$	−5.40234	−1.03968	−0.519841	+	0.854263i	$0.674009\pi$
$4$	0.209982	0.0262478
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	15.4794	1.05324
$7$	−24.6494	−1.33094	−0.665470	−	0.746425i	$-0.731769\pi$
$7$	−24.6494	−1.33094	−0.665470	+	0.746425i	$0.731769\pi$
$8$	22.3208	0.986449
$9$	2.18531	0.0809374
$10$	−14.3265	−0.453045
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−1.13439	−0.0272893
$13$	15.7098	0.335163	0.167581	−	0.985858i	$-0.446404\pi$
$13$	15.7098	0.335163	0.167581	+	0.985858i	$0.446404\pi$
$14$	70.6279	1.34829
$15$	−27.0117	−0.464960
$16$	−65.6358	−1.02556
$17$	−2.85422	−0.0407206	−0.0203603	−	0.999793i	$-0.506481\pi$
$17$	−2.85422	−0.0407206	−0.0203603	+	0.999793i	$0.506481\pi$
$18$	−6.26159	−0.0819928
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	1.04991	0.0117384
$21$	133.164	1.38375
$22$	31.5184	0.305443
$23$	−124.821	−1.13161	−0.565806	−	0.824538i	$-0.691435\pi$
$23$	−124.821	−1.13161	−0.565806	+	0.824538i	$0.691435\pi$
$24$	−120.585	−1.02559
$25$	25.0000	0.200000
$26$	−45.0134	−0.339533
$27$	134.057	0.955532
$28$	−5.17592	−0.0349342
$29$	78.4342	0.502237	0.251118	−	0.967956i	$-0.419202\pi$
$29$	78.4342	0.502237	0.251118	+	0.967956i	$0.419202\pi$
$30$	77.3968	0.471022
$31$	−36.4439	−0.211146	−0.105573	−	0.994412i	$-0.533668\pi$
$31$	−36.4439	−0.211146	−0.105573	+	0.994412i	$0.533668\pi$
$32$	9.50027	0.0524821
$33$	59.4258	0.313476
$34$	8.17823	0.0412516
$35$	−123.247	−0.595214
$36$	0.458876	0.00212443
$37$	35.0684	0.155816	0.0779081	−	0.996961i	$-0.475176\pi$
$37$	35.0684	0.155816	0.0779081	+	0.996961i	$0.475176\pi$
$38$	54.4408	0.232407
$39$	−84.8697	−0.348462
$40$	111.604	0.441153
$41$	283.204	1.07876	0.539379	−	0.842063i	$-0.318659\pi$
$41$	283.204	1.07876	0.539379	+	0.842063i	$0.318659\pi$
$42$	−381.556	−1.40180
$43$	−184.609	−0.654713	−0.327357	−	0.944901i	$-0.606158\pi$
$43$	−184.609	−0.654713	−0.327357	+	0.944901i	$0.606158\pi$
$44$	−2.30980	−0.00791399
$45$	10.9266	0.0361963
$46$	357.652	1.14637
$47$	241.399	0.749185	0.374592	−	0.927190i	$-0.377783\pi$
$47$	241.399	0.749185	0.374592	+	0.927190i	$0.377783\pi$
$48$	354.587	1.06625
$49$	264.590	0.771401
$50$	−71.6327	−0.202608
$51$	15.4195	0.0423365
$52$	3.29878	0.00879727
$53$	181.351	0.470009	0.235005	−	0.971994i	$-0.424489\pi$
$53$	181.351	0.470009	0.235005	+	0.971994i	$0.424489\pi$
$54$	−384.116	−0.967991
$55$	−55.0000	−0.134840
$56$	−550.193	−1.31290
$57$	102.645	0.238519
$58$	−224.738	−0.508785
$59$	893.693	1.97202	0.986008	−	0.166697i	$-0.0533102\pi$
$59$	893.693	1.97202	0.986008	+	0.166697i	$0.0533102\pi$
$60$	−5.67197	−0.0122041
$61$	−225.438	−0.473187	−0.236593	−	0.971609i	$-0.576031\pi$
$61$	−225.438	−0.473187	−0.236593	+	0.971609i	$0.576031\pi$
$62$	104.423	0.213899
$63$	−53.8665	−0.107723
$64$	497.865	0.972392
$65$	78.5490	0.149889
$66$	−170.273	−0.317563
$67$	−374.295	−0.682498	−0.341249	−	0.939973i	$-0.610850\pi$
$67$	−374.295	−0.682498	−0.341249	+	0.939973i	$0.610850\pi$
$68$	−0.599336	−0.00106883
$69$	674.329	1.17652
$70$	353.140	0.602975
$71$	194.109	0.324457	0.162229	−	0.986753i	$-0.448132\pi$
$71$	194.109	0.324457	0.162229	+	0.986753i	$0.448132\pi$
$72$	48.7779	0.0798407
$73$	−19.3282	−0.0309889	−0.0154945	−	0.999880i	$-0.504932\pi$
$73$	−19.3282	−0.0309889	−0.0154945	+	0.999880i	$0.504932\pi$
$74$	−100.482	−0.157848
$75$	−135.059	−0.207936
$76$	−3.98966	−0.00602165
$77$	271.143	0.401293
$78$	243.178	0.353006
$79$	782.604	1.11455	0.557277	−	0.830326i	$-0.311846\pi$
$79$	782.604	1.11455	0.557277	+	0.830326i	$0.311846\pi$
$80$	−328.179	−0.458644
$81$	−783.228	−1.07439
$82$	−811.467	−1.09282
$83$	−42.2123	−0.0558241	−0.0279120	−	0.999610i	$-0.508886\pi$
$83$	−42.2123	−0.0558241	−0.0279120	+	0.999610i	$0.508886\pi$
$84$	27.9621	0.0363204
$85$	−14.2711	−0.0182108
$86$	528.963	0.663250
$87$	−423.728	−0.522166
$88$	−245.529	−0.297426
$89$	1127.29	1.34262	0.671308	−	0.741178i	$-0.265733\pi$
$89$	1127.29	1.34262	0.671308	+	0.741178i	$0.265733\pi$
$90$	−31.3079	−0.0366683
$91$	−387.236	−0.446081
$92$	−26.2103	−0.0297023
$93$	196.882	0.219524
$94$	−691.683	−0.758953
$95$	−95.0000	−0.102598
$96$	−51.3237	−0.0545646
$97$	862.657	0.902985	0.451492	−	0.892275i	$-0.350892\pi$
$97$	862.657	0.902985	0.451492	+	0.892275i	$0.350892\pi$
$98$	−758.133	−0.781459
$99$	−24.0384	−0.0244036
$100$	5.24955	0.00524955
$101$	1479.27	1.45735	0.728677	−	0.684858i	$-0.240136\pi$
$101$	1479.27	1.45735	0.728677	+	0.684858i	$0.240136\pi$
$102$	−44.1816	−0.0428885
$103$	−1042.75	−0.997530	−0.498765	−	0.866737i	$-0.666213\pi$
$103$	−1042.75	−0.997530	−0.498765	+	0.866737i	$0.666213\pi$
$104$	350.655	0.330621
$105$	665.821	0.618833
$106$	−519.627	−0.476138
$107$	992.678	0.896877	0.448438	−	0.893814i	$-0.351980\pi$
$107$	992.678	0.896877	0.448438	+	0.893814i	$0.351980\pi$
$108$	28.1497	0.0250806
$109$	612.648	0.538358	0.269179	−	0.963090i	$-0.413248\pi$
$109$	612.648	0.538358	0.269179	+	0.963090i	$0.413248\pi$
$110$	157.592	0.136598
$111$	−189.451	−0.161999
$112$	1617.88	1.36496
$113$	157.386	0.131024	0.0655118	−	0.997852i	$-0.479132\pi$
$113$	157.386	0.131024	0.0655118	+	0.997852i	$0.479132\pi$
$114$	−294.108	−0.241629
$115$	−624.107	−0.506072
$116$	16.4698	0.0131826
$117$	34.3308	0.0271272
$118$	−2560.71	−1.99773
$119$	70.3548	0.0541967
$120$	−602.923	−0.458659
$121$	121.000	0.0909091
$122$	645.949	0.479356
$123$	−1529.97	−1.12157
$124$	−7.65256	−0.00554210
$125$	125.000	0.0894427
$126$	154.344	0.109127
$127$	−1846.15	−1.28991	−0.644956	−	0.764219i	$-0.723125\pi$
$127$	−1846.15	−1.28991	−0.644956	+	0.764219i	$0.723125\pi$
$128$	−1502.54	−1.03755
$129$	997.324	0.680693
$130$	−225.067	−0.151844
$131$	−1708.88	−1.13973	−0.569867	−	0.821737i	$-0.693005\pi$
$131$	−1708.88	−1.13973	−0.569867	+	0.821737i	$0.693005\pi$
$132$	12.4783	0.00822803
$133$	468.338	0.305339
$134$	1072.47	0.691397
$135$	670.287	0.427327
$136$	−63.7085	−0.0401688
$137$	−776.404	−0.484180	−0.242090	−	0.970254i	$-0.577833\pi$
$137$	−776.404	−0.484180	−0.242090	+	0.970254i	$0.577833\pi$
$138$	−1932.16	−1.19186
$139$	−364.291	−0.222293	−0.111147	−	0.993804i	$-0.535452\pi$
$139$	−364.291	−0.222293	−0.111147	+	0.993804i	$0.535452\pi$
$140$	−25.8796	−0.0156230
$141$	−1304.12	−0.778914
$142$	−556.181	−0.328688
$143$	−172.808	−0.101055
$144$	−143.435	−0.0830061
$145$	392.171	0.224607
$146$	55.3811	0.0313930
$147$	−1429.41	−0.802011
$148$	7.36372	0.00408983
$149$	−513.164	−0.282148	−0.141074	−	0.989999i	$-0.545056\pi$
$149$	−513.164	−0.282148	−0.141074	+	0.989999i	$0.545056\pi$
$150$	386.984	0.210648
$151$	−625.414	−0.337056	−0.168528	−	0.985697i	$-0.553901\pi$
$151$	−625.414	−0.337056	−0.168528	+	0.985697i	$0.553901\pi$
$152$	−424.095	−0.226307
$153$	−6.23737	−0.00329582
$154$	−776.907	−0.406526
$155$	−182.220	−0.0944273
$156$	−17.8211	−0.00914636
$157$	−1848.81	−0.939815	−0.469908	−	0.882716i	$-0.655713\pi$
$157$	−1848.81	−0.939815	−0.469908	+	0.882716i	$0.655713\pi$
$158$	−2242.40	−1.12909
$159$	−979.721	−0.488660
$160$	47.5013	0.0234707
$161$	3076.77	1.50611
$162$	2244.19	1.08840
$163$	−2250.84	−1.08159	−0.540796	−	0.841154i	$-0.681877\pi$
$163$	−2250.84	−1.08159	−0.540796	+	0.841154i	$0.681877\pi$
$164$	59.4678	0.0283150
$165$	297.129	0.140191
$166$	120.951	0.0565520
$167$	−779.737	−0.361305	−0.180652	−	0.983547i	$-0.557821\pi$
$167$	−779.737	−0.361305	−0.180652	+	0.983547i	$0.557821\pi$
$168$	2972.33	1.36500
$169$	−1950.20	−0.887666
$170$	40.8911	0.0184483
$171$	−41.5209	−0.0185683
$172$	−38.7647	−0.0171848
$173$	−1282.63	−0.563678	−0.281839	−	0.959462i	$-0.590944\pi$
$173$	−1282.63	−0.563678	−0.281839	+	0.959462i	$0.590944\pi$
$174$	1214.11	0.528975
$175$	−616.234	−0.266188
$176$	721.993	0.309218
$177$	−4828.04	−2.05027
$178$	−3230.04	−1.36012
$179$	−1170.32	−0.488681	−0.244341	−	0.969689i	$-0.578572\pi$
$179$	−1170.32	−0.488681	−0.244341	+	0.969689i	$0.578572\pi$
$180$	2.29438	0.000950072 0
$181$	1134.03	0.465701	0.232850	−	0.972513i	$-0.425195\pi$
$181$	1134.03	0.465701	0.232850	+	0.972513i	$0.425195\pi$
$182$	1109.55	0.451898
$183$	1217.89	0.491963
$184$	−2786.11	−1.11628
$185$	175.342	0.0696832
$186$	−564.129	−0.222387
$187$	31.3965	0.0122777
$188$	50.6895	0.0196644
$189$	−3304.43	−1.27176
$190$	272.204	0.103936
$191$	−3388.15	−1.28355	−0.641775	−	0.766893i	$-0.721802\pi$
$191$	−3388.15	−1.28355	−0.641775	+	0.766893i	$0.721802\pi$
$192$	−2689.64	−1.01098
$193$	−3992.67	−1.48911	−0.744555	−	0.667561i	$-0.767338\pi$
$193$	−3992.67	−1.48911	−0.744555	+	0.667561i	$0.767338\pi$
$194$	−2471.78	−0.914759
$195$	−424.349	−0.155837
$196$	55.5592	0.0202475
$197$	3282.00	1.18697	0.593485	−	0.804845i	$-0.297752\pi$
$197$	3282.00	1.18697	0.593485	+	0.804845i	$0.297752\pi$
$198$	68.8774	0.0247218
$199$	−639.257	−0.227717	−0.113859	−	0.993497i	$-0.536321\pi$
$199$	−639.257	−0.227717	−0.113859	+	0.993497i	$0.536321\pi$
$200$	558.020	0.197290
$201$	2022.07	0.709580
$202$	−4238.56	−1.47636
$203$	−1933.35	−0.668447
$204$	3.23782	0.00111124
$205$	1416.02	0.482435
$206$	2987.81	1.01054
$207$	−272.774	−0.0915898
$208$	−1031.12	−0.343729
$209$	209.000	0.0691714
$210$	−1907.78	−0.626902
$211$	1636.22	0.533849	0.266924	−	0.963717i	$-0.413993\pi$
$211$	1636.22	0.533849	0.266924	+	0.963717i	$0.413993\pi$
$212$	38.0805	0.0123367
$213$	−1048.64	−0.337332
$214$	−2844.33	−0.908571
$215$	−923.047	−0.292797
$216$	2992.27	0.942584
$217$	898.319	0.281022
$218$	−1755.43	−0.545378
$219$	104.417	0.0322186
$220$	−11.5490	−0.00353925
$221$	−44.8393	−0.0136480
$222$	542.836	0.164112
$223$	−1451.71	−0.435934	−0.217967	−	0.975956i	$-0.569943\pi$
$223$	−1451.71	−0.435934	−0.217967	+	0.975956i	$0.569943\pi$
$224$	−234.175	−0.0698505
$225$	54.6328	0.0161875
$226$	−450.960	−0.132732
$227$	3007.04	0.879226	0.439613	−	0.898187i	$-0.355116\pi$
$227$	3007.04	0.879226	0.439613	+	0.898187i	$0.355116\pi$
$228$	21.5535	0.00626059
$229$	5945.81	1.71577	0.857883	−	0.513845i	$-0.171779\pi$
$229$	5945.81	1.71577	0.857883	+	0.513845i	$0.171779\pi$
$230$	1788.26	0.512671
$231$	−1464.81	−0.417217
$232$	1750.71	0.495431
$233$	−6162.43	−1.73268	−0.866340	−	0.499455i	$-0.833533\pi$
$233$	−6162.43	−1.73268	−0.866340	+	0.499455i	$0.833533\pi$
$234$	−98.3683	−0.0274809
$235$	1207.00	0.335046
$236$	187.660	0.0517610
$237$	−4227.89	−1.15878
$238$	−201.588	−0.0549034
$239$	−1029.81	−0.278714	−0.139357	−	0.990242i	$-0.544504\pi$
$239$	−1029.81	−0.278714	−0.139357	+	0.990242i	$0.544504\pi$
$240$	1772.93	0.476843
$241$	−2891.72	−0.772913	−0.386456	−	0.922308i	$-0.626301\pi$
$241$	−2891.72	−0.772913	−0.386456	+	0.922308i	$0.626301\pi$
$242$	−346.702	−0.0920944
$243$	611.714	0.161487
$244$	−47.3379	−0.0124201
$245$	1322.95	0.344981
$246$	4383.83	1.13619
$247$	−298.486	−0.0768916
$248$	−813.457	−0.208285
$249$	228.045	0.0580393
$250$	−358.163	−0.0906090
$251$	4386.15	1.10299	0.551497	−	0.834177i	$-0.314057\pi$
$251$	4386.15	1.10299	0.551497	+	0.834177i	$0.314057\pi$
$252$	−11.3110	−0.00282748
$253$	1373.04	0.341194
$254$	5289.77	1.30673
$255$	77.0975	0.0189335
$256$	322.312	0.0786895
$257$	−2376.80	−0.576890	−0.288445	−	0.957497i	$-0.593138\pi$
$257$	−2376.80	−0.576890	−0.288445	+	0.957497i	$0.593138\pi$
$258$	−2857.64	−0.689569
$259$	−864.412	−0.207382
$260$	16.4939	0.00393426
$261$	171.403	0.0406498
$262$	4896.45	1.15459
$263$	−4766.85	−1.11763	−0.558814	−	0.829293i	$-0.688744\pi$
$263$	−4766.85	−1.11763	−0.558814	+	0.829293i	$0.688744\pi$
$264$	1326.43	0.309228
$265$	906.756	0.210195
$266$	−1341.93	−0.309320
$267$	−6090.02	−1.39589
$268$	−78.5951	−0.0179140
$269$	−2775.89	−0.629179	−0.314590	−	0.949228i	$-0.601867\pi$
$269$	−2775.89	−0.629179	−0.314590	+	0.949228i	$0.601867\pi$
$270$	−1920.58	−0.432899
$271$	5280.64	1.18368	0.591838	−	0.806057i	$-0.298403\pi$
$271$	5280.64	1.18368	0.591838	+	0.806057i	$0.298403\pi$
$272$	187.339	0.0417614
$273$	2091.98	0.463783
$274$	2224.64	0.490493
$275$	−275.000	−0.0603023
$276$	141.597	0.0308809
$277$	−2656.63	−0.576251	−0.288126	−	0.957593i	$-0.593032\pi$
$277$	−2656.63	−0.576251	−0.288126	+	0.957593i	$0.593032\pi$
$278$	1043.81	0.225192
$279$	−79.6413	−0.0170896
$280$	−2750.96	−0.587149
$281$	6754.91	1.43404	0.717018	−	0.697055i	$-0.245507\pi$
$281$	6754.91	1.43404	0.717018	+	0.697055i	$0.245507\pi$
$282$	3736.71	0.789070
$283$	927.744	0.194872	0.0974358	−	0.995242i	$-0.468936\pi$
$283$	927.744	0.194872	0.0974358	+	0.995242i	$0.468936\pi$
$284$	40.7593	0.00851627
$285$	513.223	0.106669
$286$	495.147	0.102373
$287$	−6980.80	−1.43576
$288$	20.7610	0.00424776
$289$	−4904.85	−0.998342
$290$	−1123.69	−0.227536
$291$	−4660.37	−0.938817
$292$	−4.05857	−0.000813390 0
$293$	219.315	0.0437288	0.0218644	−	0.999761i	$-0.493040\pi$
$293$	219.315	0.0437288	0.0218644	+	0.999761i	$0.493040\pi$
$294$	4095.69	0.812468
$295$	4468.47	0.881912
$296$	782.753	0.153705
$297$	−1474.63	−0.288104
$298$	1470.37	0.285827
$299$	−1960.92	−0.379274
$300$	−28.3599	−0.00545786
$301$	4550.50	0.871384
$302$	1792.00	0.341451
$303$	−7991.52	−1.51518
$304$	1247.08	0.235279
$305$	−1127.19	−0.211615
$306$	17.8720	0.00333880
$307$	1264.66	0.235107	0.117553	−	0.993067i	$-0.462495\pi$
$307$	1264.66	0.235107	0.117553	+	0.993067i	$0.462495\pi$
$308$	56.9351	0.0105331
$309$	5633.31	1.03711
$310$	522.115	0.0956585
$311$	−2868.32	−0.522983	−0.261491	−	0.965206i	$-0.584214\pi$
$311$	−2868.32	−0.522983	−0.261491	+	0.965206i	$0.584214\pi$
$312$	−1894.36	−0.343740
$313$	6070.20	1.09619	0.548096	−	0.836415i	$-0.315353\pi$
$313$	6070.20	1.09619	0.548096	+	0.836415i	$0.315353\pi$
$314$	5297.40	0.952069
$315$	−269.332	−0.0481751
$316$	164.333	0.0292546
$317$	976.721	0.173054	0.0865270	−	0.996250i	$-0.472423\pi$
$317$	976.721	0.173054	0.0865270	+	0.996250i	$0.472423\pi$
$318$	2807.20	0.495032
$319$	−862.776	−0.151430
$320$	2489.32	0.434867
$321$	−5362.79	−0.932466
$322$	−8815.89	−1.52575
$323$	54.2302	0.00934196
$324$	−164.464	−0.0282002
$325$	392.745	0.0670325
$326$	6449.35	1.09569
$327$	−3309.74	−0.559721
$328$	6321.35	1.06414
$329$	−5950.33	−0.997120
$330$	−851.365	−0.142019
$331$	−4617.48	−0.766767	−0.383383	−	0.923589i	$-0.625241\pi$
$331$	−4617.48	−0.766767	−0.383383	+	0.923589i	$0.625241\pi$
$332$	−8.86382	−0.00146526
$333$	76.6353	0.0126114
$334$	2234.19	0.366016
$335$	−1871.47	−0.305222
$336$	−8740.34	−1.41912
$337$	253.846	0.0410322	0.0205161	−	0.999790i	$-0.493469\pi$
$337$	253.846	0.0410322	0.0205161	+	0.999790i	$0.493469\pi$
$338$	5587.93	0.899240
$339$	−850.256	−0.136223
$340$	−2.99668	−0.000477993 0
$341$	400.883	0.0636628
$342$	118.970	0.0188104
$343$	1932.74	0.304252
$344$	−4120.63	−0.645841
$345$	3371.64	0.526154
$346$	3675.12	0.571028
$347$	−10223.5	−1.58164	−0.790818	−	0.612051i	$-0.790345\pi$
$347$	−10223.5	−1.58164	−0.790818	+	0.612051i	$0.790345\pi$
$348$	−88.9753	−0.0137057
$349$	−579.251	−0.0888440	−0.0444220	−	0.999013i	$-0.514145\pi$
$349$	−579.251	−0.0888440	−0.0444220	+	0.999013i	$0.514145\pi$
$350$	1765.70	0.269659
$351$	2106.02	0.320259
$352$	−104.503	−0.0158239
$353$	4122.14	0.621528	0.310764	−	0.950487i	$-0.399415\pi$
$353$	4122.14	0.621528	0.310764	+	0.950487i	$0.399415\pi$
$354$	13833.8	2.07700
$355$	970.543	0.145102
$356$	236.711	0.0352407
$357$	−380.081	−0.0563473
$358$	3353.33	0.495053
$359$	10583.6	1.55594	0.777971	−	0.628300i	$-0.216249\pi$
$359$	10583.6	1.55594	0.777971	+	0.628300i	$0.216249\pi$
$360$	243.889	0.0357058
$361$	361.000	0.0526316
$362$	−3249.35	−0.471773
$363$	−653.684	−0.0945165
$364$	−81.3127	−0.0117086
$365$	−96.6409	−0.0138587
$366$	−3489.64	−0.498378
$367$	7227.69	1.02802	0.514009	−	0.857785i	$-0.328160\pi$
$367$	7227.69	1.02802	0.514009	+	0.857785i	$0.328160\pi$
$368$	8192.75	1.16053
$369$	618.890	0.0873119
$370$	−502.408	−0.0705918
$371$	−4470.19	−0.625554
$372$	41.3418	0.00576202
$373$	10193.5	1.41502	0.707509	−	0.706704i	$-0.249819\pi$
$373$	10193.5	1.41502	0.707509	+	0.706704i	$0.249819\pi$
$374$	−89.9605	−0.0124378
$375$	−675.293	−0.0929919
$376$	5388.22	0.739033
$377$	1232.19	0.168331
$378$	9468.20	1.28834
$379$	4698.54	0.636801	0.318401	−	0.947956i	$-0.396854\pi$
$379$	4698.54	0.636801	0.318401	+	0.947956i	$0.396854\pi$
$380$	−19.9483	−0.00269296
$381$	9973.51	1.34110
$382$	9708.09	1.30029
$383$	−10690.1	−1.42621	−0.713104	−	0.701058i	$-0.752711\pi$
$383$	−10690.1	−1.42621	−0.713104	+	0.701058i	$0.752711\pi$
$384$	8117.22	1.07872
$385$	1355.71	0.179464
$386$	11440.2	1.50853
$387$	−403.429	−0.0529908
$388$	181.142	0.0237013
$389$	−900.057	−0.117313	−0.0586564	−	0.998278i	$-0.518682\pi$
$389$	−900.057	−0.117313	−0.0586564	+	0.998278i	$0.518682\pi$
$390$	1215.89	0.157869
$391$	356.268	0.0460800
$392$	5905.87	0.760947
$393$	9231.93	1.18496
$394$	−9403.94	−1.20245
$395$	3913.02	0.498444
$396$	−5.04764	−0.000640539 0
$397$	12280.1	1.55244	0.776222	−	0.630459i	$-0.217133\pi$
$397$	12280.1	1.55244	0.776222	+	0.630459i	$0.217133\pi$
$398$	1831.67	0.230686
$399$	−2530.12	−0.317455
$400$	−1640.89	−0.205112
$401$	214.314	0.0266891	0.0133445	−	0.999911i	$-0.495752\pi$
$401$	214.314	0.0266891	0.0133445	+	0.999911i	$0.495752\pi$
$402$	−5793.84	−0.718833
$403$	−572.527	−0.0707682
$404$	310.620	0.0382523
$405$	−3916.14	−0.480480
$406$	5539.65	0.677163
$407$	−385.752	−0.0469804
$408$	344.175	0.0417628
$409$	−3725.68	−0.450423	−0.225212	−	0.974310i	$-0.572307\pi$
$409$	−3725.68	−0.450423	−0.225212	+	0.974310i	$0.572307\pi$
$410$	−4057.34	−0.488726
$411$	4194.40	0.503393
$412$	−218.959	−0.0261829
$413$	−22029.0	−2.62464
$414$	781.581	0.0927840
$415$	−211.061	−0.0249653
$416$	149.247	0.0175900
$417$	1968.03	0.231114
$418$	−598.849	−0.0700734
$419$	−1154.92	−0.134658	−0.0673288	−	0.997731i	$-0.521448\pi$
$419$	−1154.92	−0.134658	−0.0673288	+	0.997731i	$0.521448\pi$
$420$	139.810	0.0162430
$421$	−13171.3	−1.52478	−0.762390	−	0.647118i	$-0.775974\pi$
$421$	−13171.3	−1.52478	−0.762390	+	0.647118i	$0.775974\pi$
$422$	−4688.27	−0.540809
$423$	527.532	0.0606371
$424$	4047.90	0.463640
$425$	−71.3556	−0.00814413
$426$	3004.68	0.341730
$427$	5556.90	0.629783
$428$	208.444	0.0235410
$429$	933.567	0.105065
$430$	2644.81	0.296615
$431$	−12741.0	−1.42393	−0.711964	−	0.702216i	$-0.752194\pi$
$431$	−12741.0	−1.42393	−0.711964	+	0.702216i	$0.752194\pi$
$432$	−8798.96	−0.979955
$433$	2297.04	0.254939	0.127470	−	0.991842i	$-0.459314\pi$
$433$	2297.04	0.254939	0.127470	+	0.991842i	$0.459314\pi$
$434$	−2573.96	−0.284687
$435$	−2118.64	−0.233520
$436$	128.645	0.0141307
$437$	2371.61	0.259610
$438$	−299.188	−0.0326387
$439$	−6341.99	−0.689492	−0.344746	−	0.938696i	$-0.612035\pi$
$439$	−6341.99	−0.689492	−0.344746	+	0.938696i	$0.612035\pi$
$440$	−1227.64	−0.133013
$441$	578.212	0.0624352
$442$	128.478	0.0138260
$443$	−3358.12	−0.360156	−0.180078	−	0.983652i	$-0.557635\pi$
$443$	−3358.12	−0.360156	−0.180078	+	0.983652i	$0.557635\pi$
$444$	−39.7814	−0.00425212
$445$	5636.47	0.600436
$446$	4159.58	0.441619
$447$	2772.29	0.293344
$448$	−12272.0	−1.29420
$449$	−4885.02	−0.513449	−0.256724	−	0.966485i	$-0.582643\pi$
$449$	−4885.02	−0.513449	−0.256724	+	0.966485i	$0.582643\pi$
$450$	−156.540	−0.0163986
$451$	−3115.25	−0.325258
$452$	33.0483	0.00343908
$453$	3378.70	0.350431
$454$	−8616.10	−0.890690
$455$	−1936.18	−0.199494
$456$	2291.11	0.235287
$457$	−10150.7	−1.03902	−0.519509	−	0.854465i	$-0.673885\pi$
$457$	−10150.7	−1.03902	−0.519509	+	0.854465i	$0.673885\pi$
$458$	−17036.6	−1.73814
$459$	−382.630	−0.0389099
$460$	−131.051	−0.0132833
$461$	−6286.30	−0.635103	−0.317551	−	0.948241i	$-0.602861\pi$
$461$	−6286.30	−0.635103	−0.317551	+	0.948241i	$0.602861\pi$
$462$	4197.12	0.422657
$463$	−14797.5	−1.48531	−0.742654	−	0.669675i	$-0.766433\pi$
$463$	−14797.5	−1.48531	−0.742654	+	0.669675i	$0.766433\pi$
$464$	−5148.09	−0.515073
$465$	984.412	0.0981743
$466$	17657.3	1.75527
$467$	−5866.50	−0.581305	−0.290652	−	0.956829i	$-0.593872\pi$
$467$	−5866.50	−0.581305	−0.290652	+	0.956829i	$0.593872\pi$
$468$	7.20885	0.000712028 0
$469$	9226.12	0.908364
$470$	−3458.41	−0.339414
$471$	9987.90	0.977109
$472$	19947.9	1.94529
$473$	2030.70	0.197404
$474$	12114.2	1.17389
$475$	−475.000	−0.0458831
$476$	14.7732	0.00142254
$477$	396.309	0.0380414
$478$	2950.72	0.282349
$479$	8325.91	0.794197	0.397099	−	0.917776i	$-0.370017\pi$
$479$	8325.91	0.794197	0.397099	+	0.917776i	$0.370017\pi$
$480$	−256.619	−0.0244020
$481$	550.917	0.0522238
$482$	8285.66	0.782991
$483$	−16621.8	−1.56587
$484$	25.4078	0.00238616
$485$	4313.28	0.403827
$486$	−1752.75	−0.163593
$487$	4987.16	0.464044	0.232022	−	0.972710i	$-0.425466\pi$
$487$	4987.16	0.464044	0.232022	+	0.972710i	$0.425466\pi$
$488$	−5031.95	−0.466774
$489$	12159.8	1.12451
$490$	−3790.66	−0.349479
$491$	17441.5	1.60311	0.801553	−	0.597923i	$-0.204007\pi$
$491$	17441.5	1.60311	0.801553	+	0.597923i	$0.204007\pi$
$492$	−321.266	−0.0294386
$493$	−223.869	−0.0204514
$494$	855.255	0.0778942
$495$	−120.192	−0.0109136
$496$	2392.02	0.216542
$497$	−4784.65	−0.431833
$498$	−653.419	−0.0587960
$499$	−6307.04	−0.565815	−0.282908	−	0.959147i	$-0.591299\pi$
$499$	−6307.04	−0.565815	−0.282908	+	0.959147i	$0.591299\pi$
$500$	26.2478	0.00234767
$501$	4212.41	0.375642
$502$	−12567.7	−1.11738
$503$	−16431.8	−1.45658	−0.728290	−	0.685269i	$-0.759684\pi$
$503$	−16431.8	−1.45658	−0.728290	+	0.685269i	$0.759684\pi$
$504$	−1202.34	−0.106263
$505$	7396.34	0.651748
$506$	−3934.17	−0.345643
$507$	10535.7	0.922890
$508$	−387.657	−0.0338573
$509$	1049.12	0.0913582	0.0456791	−	0.998956i	$-0.485455\pi$
$509$	1049.12	0.0913582	0.0456791	+	0.998956i	$0.485455\pi$
$510$	−220.908	−0.0191803
$511$	476.427	0.0412444
$512$	11096.8	0.957838
$513$	−2547.09	−0.219214
$514$	6810.26	0.584412
$515$	−5213.77	−0.446109
$516$	209.420	0.0178667
$517$	−2655.39	−0.225888
$518$	2476.81	0.210086
$519$	6929.19	0.586046
$520$	1753.28	0.147858
$521$	919.399	0.0773121	0.0386561	−	0.999253i	$-0.487692\pi$
$521$	919.399	0.0773121	0.0386561	+	0.999253i	$0.487692\pi$
$522$	−491.122	−0.0411798
$523$	−2325.98	−0.194471	−0.0972353	−	0.995261i	$-0.531000\pi$
$523$	−2325.98	−0.194471	−0.0972353	+	0.995261i	$0.531000\pi$
$524$	−358.833	−0.0299154
$525$	3329.11	0.276751
$526$	13658.5	1.13220
$527$	104.019	0.00859799
$528$	−3900.46	−0.321488
$529$	3413.41	0.280546
$530$	−2598.13	−0.212935
$531$	1953.00	0.159610
$532$	98.3425	0.00801445
$533$	4449.09	0.361560
$534$	17449.8	1.41409
$535$	4963.39	0.401095
$536$	−8354.55	−0.673249
$537$	6322.48	0.508073
$538$	7953.78	0.637383
$539$	−2910.50	−0.232586
$540$	140.748	0.0112164
$541$	12146.9	0.965315	0.482658	−	0.875809i	$-0.339672\pi$
$541$	12146.9	0.965315	0.482658	+	0.875809i	$0.339672\pi$
$542$	−15130.6	−1.19911
$543$	−6126.42	−0.484180
$544$	−27.1159	−0.00213710
$545$	3063.24	0.240761
$546$	−5994.18	−0.469830
$547$	24387.9	1.90631	0.953153	−	0.302489i	$-0.0978174\pi$
$547$	24387.9	1.90631	0.953153	+	0.302489i	$0.0978174\pi$
$548$	−163.031	−0.0127086
$549$	−492.652	−0.0382985
$550$	787.959	0.0610885
$551$	−1490.25	−0.115221
$552$	15051.5	1.16057
$553$	−19290.7	−1.48341
$554$	7612.07	0.583765
$555$	−947.257	−0.0724483
$556$	−76.4946	−0.00583470
$557$	22481.2	1.71016	0.855081	−	0.518495i	$-0.173508\pi$
$557$	22481.2	1.71016	0.855081	+	0.518495i	$0.173508\pi$
$558$	228.197	0.0173124
$559$	−2900.18	−0.219436
$560$	8089.39	0.610427
$561$	−169.614	−0.0127649
$562$	−19354.9	−1.45273
$563$	−3671.71	−0.274856	−0.137428	−	0.990512i	$-0.543884\pi$
$563$	−3671.71	−0.274856	−0.137428	+	0.990512i	$0.543884\pi$
$564$	−273.842	−0.0204447
$565$	786.932	0.0585956
$566$	−2658.27	−0.197412
$567$	19306.1	1.42994
$568$	4332.66	0.320060
$569$	−20719.3	−1.52654	−0.763268	−	0.646082i	$-0.776407\pi$
$569$	−20719.3	−1.52654	−0.763268	+	0.646082i	$0.776407\pi$
$570$	−1470.54	−0.108060
$571$	−25461.0	−1.86604	−0.933020	−	0.359825i	$-0.882836\pi$
$571$	−25461.0	−1.86604	−0.933020	+	0.359825i	$0.882836\pi$
$572$	−36.2865	−0.00265248
$573$	18304.0	1.33448
$574$	20002.1	1.45448
$575$	−3120.54	−0.226322
$576$	1087.99	0.0787030
$577$	2249.96	0.162335	0.0811675	−	0.996700i	$-0.474135\pi$
$577$	2249.96	0.162335	0.0811675	+	0.996700i	$0.474135\pi$
$578$	14053.9	1.01136
$579$	21569.7	1.54820
$580$	82.3488	0.00589543
$581$	1040.51	0.0742985
$582$	13353.4	0.951058
$583$	−1994.86	−0.141713
$584$	−431.420	−0.0305690
$585$	171.654	0.0121317
$586$	−628.405	−0.0442990
$587$	20807.9	1.46309	0.731545	−	0.681793i	$-0.238800\pi$
$587$	20807.9	1.46309	0.731545	+	0.681793i	$0.238800\pi$
$588$	−300.150	−0.0210510
$589$	692.434	0.0484402
$590$	−12803.5	−0.893412
$591$	−17730.5	−1.23407
$592$	−2301.74	−0.159799
$593$	−4305.09	−0.298126	−0.149063	−	0.988828i	$-0.547626\pi$
$593$	−4305.09	−0.298126	−0.149063	+	0.988828i	$0.547626\pi$
$594$	4225.27	0.291860
$595$	351.774	0.0242375
$596$	−107.755	−0.00740575
$597$	3453.48	0.236753
$598$	5618.64	0.384220
$599$	12864.0	0.877478	0.438739	−	0.898614i	$-0.355425\pi$
$599$	12864.0	0.877478	0.438739	+	0.898614i	$0.355425\pi$
$600$	−3014.61	−0.205119
$601$	11768.5	0.798745	0.399373	−	0.916789i	$-0.369228\pi$
$601$	11768.5	0.798745	0.399373	+	0.916789i	$0.369228\pi$
$602$	−13038.6	−0.882746
$603$	−817.950	−0.0552396
$604$	−131.326	−0.00884697
$605$	605.000	0.0406558
$606$	22898.1	1.53494
$607$	−3220.98	−0.215380	−0.107690	−	0.994185i	$-0.534345\pi$
$607$	−3220.98	−0.215380	−0.107690	+	0.994185i	$0.534345\pi$
$608$	−180.505	−0.0120402
$609$	10444.6	0.694972
$610$	3229.75	0.214375
$611$	3792.33	0.251099
$612$	−1.30973	−8.65080e−5 0
$613$	−1679.94	−0.110689	−0.0553444	−	0.998467i	$-0.517626\pi$
$613$	−1679.94	−0.110689	−0.0553444	+	0.998467i	$0.517626\pi$
$614$	−3623.63	−0.238172
$615$	−7649.84	−0.501579
$616$	6052.12	0.395855
$617$	−9030.96	−0.589259	−0.294629	−	0.955612i	$-0.595196\pi$
$617$	−9030.96	−0.589259	−0.294629	+	0.955612i	$0.595196\pi$
$618$	−16141.2	−1.05064
$619$	5124.00	0.332716	0.166358	−	0.986065i	$-0.446799\pi$
$619$	5124.00	0.332716	0.166358	+	0.986065i	$0.446799\pi$
$620$	−38.2628	−0.00247850
$621$	−16733.3	−1.08129
$622$	8218.62	0.529802
$623$	−27787.0	−1.78694
$624$	5570.49	0.357369
$625$	625.000	0.0400000
$626$	−17393.0	−1.11049
$627$	−1129.09	−0.0719163
$628$	−388.217	−0.0246680
$629$	−100.093	−0.00634494
$630$	771.720	0.0488033
$631$	4464.55	0.281666	0.140833	−	0.990033i	$-0.455022\pi$
$631$	4464.55	0.281666	0.140833	+	0.990033i	$0.455022\pi$
$632$	17468.3	1.09945
$633$	−8839.42	−0.555032
$634$	−2798.61	−0.175310
$635$	−9230.73	−0.576867
$636$	−205.724	−0.0128262
$637$	4156.66	0.258545
$638$	2472.12	0.153405
$639$	424.188	0.0262607
$640$	−7512.69	−0.464008
$641$	226.866	0.0139792	0.00698961	−	0.999976i	$-0.497775\pi$
$641$	226.866	0.0139792	0.00698961	+	0.999976i	$0.497775\pi$
$642$	15366.0	0.944624
$643$	1961.31	0.120290	0.0601450	−	0.998190i	$-0.480844\pi$
$643$	1961.31	0.120290	0.0601450	+	0.998190i	$0.480844\pi$
$644$	646.066	0.0395319
$645$	4986.62	0.304415
$646$	−155.386	−0.00946376
$647$	−9631.33	−0.585234	−0.292617	−	0.956230i	$-0.594526\pi$
$647$	−9631.33	−0.585234	−0.292617	+	0.956230i	$0.594526\pi$
$648$	−17482.3	−1.05983
$649$	−9830.63	−0.594585
$650$	−1125.34	−0.0679066
$651$	−4853.03	−0.292174
$652$	−472.636	−0.0283893
$653$	−25646.6	−1.53695	−0.768475	−	0.639880i	$-0.778984\pi$
$653$	−25646.6	−1.53695	−0.768475	+	0.639880i	$0.778984\pi$
$654$	9483.41	0.567019
$655$	−8544.38	−0.509704
$656$	−18588.3	−1.10633
$657$	−42.2381	−0.00250816
$658$	17049.5	1.01012
$659$	−3861.23	−0.228243	−0.114122	−	0.993467i	$-0.536405\pi$
$659$	−3861.23	−0.228243	−0.114122	+	0.993467i	$0.536405\pi$
$660$	62.3917	0.00367969
$661$	10936.0	0.643514	0.321757	−	0.946822i	$-0.395727\pi$
$661$	10936.0	0.643514	0.321757	+	0.946822i	$0.395727\pi$
$662$	13230.5	0.776764
$663$	242.237	0.0141896
$664$	−942.211	−0.0550676
$665$	2341.69	0.136552
$666$	−219.584	−0.0127758
$667$	−9790.27	−0.568337
$668$	−163.731	−0.00948344
$669$	7842.61	0.453233
$670$	5362.34	0.309202
$671$	2479.82	0.142671
$672$	1265.10	0.0726222
$673$	−9654.32	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$673$	−9654.32	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$674$	−727.346	−0.0415672
$675$	3351.44	0.191106
$676$	−409.507	−0.0232992
$677$	17353.5	0.985153	0.492577	−	0.870269i	$-0.336055\pi$
$677$	17353.5	0.985153	0.492577	+	0.870269i	$0.336055\pi$
$678$	2436.24	0.137999
$679$	−21263.9	−1.20182
$680$	−318.543	−0.0179640
$681$	−16245.1	−0.914115
$682$	−1148.65	−0.0644929
$683$	−21838.7	−1.22348	−0.611739	−	0.791059i	$-0.709530\pi$
$683$	−21838.7	−1.22348	−0.611739	+	0.791059i	$0.709530\pi$
$684$	−8.71864	−0.000487377 0
$685$	−3882.02	−0.216532
$686$	−5537.90	−0.308219
$687$	−32121.3	−1.78385
$688$	12117.0	0.671447
$689$	2848.99	0.157530
$690$	−9660.79	−0.533014
$691$	−1641.38	−0.0903634	−0.0451817	−	0.998979i	$-0.514387\pi$
$691$	−1641.38	−0.0903634	−0.0451817	+	0.998979i	$0.514387\pi$
$692$	−269.329	−0.0147953
$693$	592.531	0.0324797
$694$	29293.5	1.60226
$695$	−1821.46	−0.0994126
$696$	−9457.95	−0.515090
$697$	−808.329	−0.0439277
$698$	1659.73	0.0900025
$699$	33291.6	1.80143
$700$	−129.398	−0.00698684
$701$	22238.3	1.19819	0.599094	−	0.800679i	$-0.295528\pi$
$701$	22238.3	1.19819	0.599094	+	0.800679i	$0.295528\pi$
$702$	−6034.38	−0.324435
$703$	−666.299	−0.0357467
$704$	−5476.51	−0.293187
$705$	−6520.61	−0.348341
$706$	−11811.2	−0.629632
$707$	−36463.0	−1.93965
$708$	−1013.80	−0.0538149
$709$	12132.4	0.642656	0.321328	−	0.946968i	$-0.395871\pi$
$709$	12132.4	0.642656	0.321328	+	0.946968i	$0.395871\pi$
$710$	−2780.90	−0.146994
$711$	1710.23	0.0902092
$712$	25162.1	1.32442
$713$	4548.98	0.238935
$714$	1089.05	0.0570820
$715$	−864.039	−0.0451933
$716$	−245.746	−0.0128268
$717$	5563.38	0.289774
$718$	−30325.4	−1.57623
$719$	−15636.8	−0.811064	−0.405532	−	0.914081i	$-0.632914\pi$
$719$	−15636.8	−0.811064	−0.405532	+	0.914081i	$0.632914\pi$
$720$	−717.173	−0.0371215
$721$	25703.2	1.32765
$722$	−1034.38	−0.0533178
$723$	15622.1	0.803583
$724$	238.126	0.0122236
$725$	1960.85	0.100447
$726$	1873.00	0.0957489
$727$	−13738.4	−0.700865	−0.350433	−	0.936588i	$-0.613965\pi$
$727$	−13738.4	−0.700865	−0.350433	+	0.936588i	$0.613965\pi$
$728$	−8643.42	−0.440037
$729$	17842.5	0.906491
$730$	276.906	0.0140394
$731$	526.917	0.0266604
$732$	255.736	0.0129129
$733$	−4300.29	−0.216691	−0.108346	−	0.994113i	$-0.534555\pi$
$733$	−4300.29	−0.216691	−0.108346	+	0.994113i	$0.534555\pi$
$734$	−20709.5	−1.04142
$735$	−7147.04	−0.358670
$736$	−1185.84	−0.0593893
$737$	4117.24	0.205781
$738$	−1773.31	−0.0884504
$739$	21800.8	1.08519	0.542594	−	0.839995i	$-0.317442\pi$
$739$	21800.8	1.08519	0.542594	+	0.839995i	$0.317442\pi$
$740$	36.8186	0.00182903
$741$	1612.53	0.0799428
$742$	12808.5	0.633711
$743$	−10460.3	−0.516487	−0.258244	−	0.966080i	$-0.583144\pi$
$743$	−10460.3	−0.516487	−0.258244	+	0.966080i	$0.583144\pi$
$744$	4394.57	0.216550
$745$	−2565.82	−0.126180
$746$	−29207.6	−1.43347
$747$	−92.2470	−0.00451826
$748$	6.59269	0.000322263 0
$749$	−24468.9	−1.19369
$750$	1934.92	0.0942044
$751$	−27336.4	−1.32825	−0.664126	−	0.747620i	$-0.731196\pi$
$751$	−27336.4	−1.32825	−0.664126	+	0.747620i	$0.731196\pi$
$752$	−15844.4	−0.768333
$753$	−23695.5	−1.14676
$754$	−3530.59	−0.170526
$755$	−3127.07	−0.150736
$756$	−693.871	−0.0333807
$757$	−19433.5	−0.933055	−0.466528	−	0.884507i	$-0.654495\pi$
$757$	−19433.5	−0.933055	−0.466528	+	0.884507i	$0.654495\pi$
$758$	−13462.8	−0.645104
$759$	−7417.61	−0.354733
$760$	−2120.48	−0.101208
$761$	−34363.5	−1.63690	−0.818448	−	0.574581i	$-0.805165\pi$
$761$	−34363.5	−1.63690	−0.818448	+	0.574581i	$0.805165\pi$
$762$	−28577.2	−1.35858
$763$	−15101.4	−0.716523
$764$	−711.451	−0.0336903
$765$	−31.1868	−0.00147394
$766$	30630.4	1.44480
$767$	14039.7	0.660946
$768$	−1741.24	−0.0818120
$769$	29604.2	1.38824	0.694119	−	0.719861i	$-0.255794\pi$
$769$	29604.2	1.38824	0.694119	+	0.719861i	$0.255794\pi$
$770$	−3884.54	−0.181804
$771$	12840.3	0.599782
$772$	−838.388	−0.0390858
$773$	−14030.2	−0.652824	−0.326412	−	0.945228i	$-0.605840\pi$
$773$	−14030.2	−0.652824	−0.326412	+	0.945228i	$0.605840\pi$
$774$	1155.95	0.0536818
$775$	−911.098	−0.0422292
$776$	19255.2	0.890748
$777$	4669.85	0.215611
$778$	2578.94	0.118842
$779$	−5380.88	−0.247484
$780$	−89.1056	−0.00409037
$781$	−2135.19	−0.0978275
$782$	−1020.82	−0.0466808
$783$	10514.7	0.479903
$784$	−17366.6	−0.791117
$785$	−9244.04	−0.420298
$786$	−26452.3	−1.20041
$787$	5177.93	0.234528	0.117264	−	0.993101i	$-0.462588\pi$
$787$	5177.93	0.234528	0.117264	+	0.993101i	$0.462588\pi$
$788$	689.161	0.0311553
$789$	25752.1	1.16198
$790$	−11212.0	−0.504943
$791$	−3879.47	−0.174385
$792$	−536.557	−0.0240729
$793$	−3541.59	−0.158595
$794$	−35186.2	−1.57269
$795$	−4898.61	−0.218535
$796$	−134.232	−0.00597706
$797$	−14756.6	−0.655839	−0.327920	−	0.944706i	$-0.606348\pi$
$797$	−14756.6	−0.655839	−0.327920	+	0.944706i	$0.606348\pi$
$798$	7249.57	0.321594
$799$	−689.007	−0.0305073
$800$	237.507	0.0104964
$801$	2463.49	0.108668
$802$	−614.075	−0.0270371
$803$	212.610	0.00934351
$804$	424.598	0.0186249
$805$	15383.8	0.673552
$806$	1640.46	0.0716909
$807$	14996.3	0.654146
$808$	33018.4	1.43760
$809$	18484.2	0.803300	0.401650	−	0.915793i	$-0.368437\pi$
$809$	18484.2	0.803300	0.401650	+	0.915793i	$0.368437\pi$
$810$	11220.9	0.486745
$811$	13100.5	0.567225	0.283613	−	0.958939i	$-0.408467\pi$
$811$	13100.5	0.567225	0.283613	+	0.958939i	$0.408467\pi$
$812$	−405.969	−0.0175452
$813$	−28527.8	−1.23065
$814$	1105.30	0.0475929
$815$	−11254.2	−0.483702
$816$	−1012.07	−0.0434186
$817$	3507.58	0.150202
$818$	10675.2	0.456296
$819$	−846.232	−0.0361047
$820$	297.339	0.0126628
$821$	−9049.11	−0.384672	−0.192336	−	0.981329i	$-0.561606\pi$
$821$	−9049.11	−0.384672	−0.192336	+	0.981329i	$0.561606\pi$
$822$	−12018.2	−0.509957
$823$	−17347.8	−0.734760	−0.367380	−	0.930071i	$-0.619745\pi$
$823$	−17347.8	−0.734760	−0.367380	+	0.930071i	$0.619745\pi$
$824$	−23275.1	−0.984012
$825$	1485.64	0.0626951
$826$	63119.7	2.65886
$827$	−24928.7	−1.04819	−0.524097	−	0.851659i	$-0.675597\pi$
$827$	−24928.7	−1.04819	−0.524097	+	0.851659i	$0.675597\pi$
$828$	−57.2776	−0.00240403
$829$	−15992.3	−0.670008	−0.335004	−	0.942217i	$-0.608738\pi$
$829$	−15992.3	−0.670008	−0.335004	+	0.942217i	$0.608738\pi$
$830$	604.756	0.0252908
$831$	14352.0	0.599118
$832$	7821.36	0.325910
$833$	−755.200	−0.0314119
$834$	−5639.00	−0.234128
$835$	−3898.69	−0.161580
$836$	43.8862	0.00181559
$837$	−4885.58	−0.201757
$838$	3309.20	0.136413
$839$	−44443.3	−1.82879	−0.914394	−	0.404825i	$-0.867332\pi$
$839$	−44443.3	−1.82879	−0.914394	+	0.404825i	$0.867332\pi$
$840$	14861.7	0.610447
$841$	−18237.1	−0.747758
$842$	37739.9	1.54466
$843$	−36492.3	−1.49094
$844$	343.577	0.0140123
$845$	−9751.01	−0.396976
$846$	−1511.54	−0.0614278
$847$	−2982.57	−0.120995
$848$	−11903.1	−0.482022
$849$	−5011.99	−0.202604
$850$	204.456	0.00825032
$851$	−4377.28	−0.176324
$852$	−220.196	−0.00885421
$853$	−1727.71	−0.0693501	−0.0346751	−	0.999399i	$-0.511040\pi$
$853$	−1727.71	−0.0693501	−0.0346751	+	0.999399i	$0.511040\pi$
$854$	−15922.2	−0.637995
$855$	−207.605	−0.00830401
$856$	22157.4	0.884723
$857$	18972.0	0.756211	0.378105	−	0.925763i	$-0.376576\pi$
$857$	18972.0	0.756211	0.378105	+	0.925763i	$0.376576\pi$
$858$	−2674.96	−0.106435
$859$	6078.00	0.241419	0.120709	−	0.992688i	$-0.461483\pi$
$859$	6078.00	0.241419	0.120709	+	0.992688i	$0.461483\pi$
$860$	−193.823	−0.00768526
$861$	37712.7	1.49274
$862$	36506.9	1.44249
$863$	−10.0005	−0.000394463 0	−0.000197231	−	1.00000i	$-0.500063\pi$
$863$	−10.0005	−0.000394463 0	−0.000197231		1.00000i	$0.500063\pi$
$864$	1273.58	0.0501483
$865$	−6413.13	−0.252085
$866$	−6581.72	−0.258263
$867$	26497.7	1.03796
$868$	188.631	0.00737620
$869$	−8608.64	−0.336051
$870$	6070.56	0.236565
$871$	−5880.09	−0.228748
$872$	13674.8	0.531063
$873$	1885.17	0.0730853
$874$	−6795.39	−0.262995
$875$	−3081.17	−0.119043
$876$	21.9258	0.000845666 0
$877$	−6962.23	−0.268070	−0.134035	−	0.990977i	$-0.542794\pi$
$877$	−6962.23	−0.268070	−0.134035	+	0.990977i	$0.542794\pi$
$878$	18171.8	0.698482
$879$	−1184.82	−0.0454640
$880$	3609.97	0.138286
$881$	−11580.3	−0.442851	−0.221425	−	0.975177i	$-0.571071\pi$
$881$	−11580.3	−0.442851	−0.221425	+	0.975177i	$0.571071\pi$
$882$	−1656.76	−0.0632493
$883$	−22409.0	−0.854046	−0.427023	−	0.904241i	$-0.640438\pi$
$883$	−22409.0	−0.854046	−0.427023	+	0.904241i	$0.640438\pi$
$884$	−9.41544	−0.000358230 0
$885$	−24140.2	−0.916908
$886$	9622.04	0.364852
$887$	38324.7	1.45075	0.725376	−	0.688353i	$-0.241666\pi$
$887$	38324.7	1.45075	0.725376	+	0.688353i	$0.241666\pi$
$888$	−4228.70	−0.159804
$889$	45506.3	1.71680
$890$	−16150.2	−0.608265
$891$	8615.51	0.323940
$892$	−304.832	−0.0114423
$893$	−4586.58	−0.171875
$894$	−7943.46	−0.297169
$895$	−5851.61	−0.218545
$896$	37036.6	1.38092
$897$	10593.6	0.394324
$898$	13997.1	0.520143
$899$	−2858.45	−0.106045
$900$	11.4719	0.000424885 0
$901$	−517.617	−0.0191391
$902$	8926.14	0.329499
$903$	−24583.4	−0.905962
$904$	3512.99	0.129248
$905$	5670.15	0.208268
$906$	−9681.02	−0.355000
$907$	−28746.8	−1.05240	−0.526198	−	0.850362i	$-0.676383\pi$
$907$	−28746.8	−1.05240	−0.526198	+	0.850362i	$0.676383\pi$
$908$	631.425	0.0230777
$909$	3232.66	0.117954
$910$	5547.76	0.202095
$911$	−22477.0	−0.817450	−0.408725	−	0.912658i	$-0.634026\pi$
$911$	−22477.0	−0.817450	−0.408725	+	0.912658i	$0.634026\pi$
$912$	−6737.15	−0.244616
$913$	464.335	0.0168316
$914$	29085.0	1.05257
$915$	6089.47	0.220013
$916$	1248.51	0.0450350
$917$	42122.7	1.51692
$918$	1096.35	0.0394172
$919$	−11936.1	−0.428439	−0.214219	−	0.976786i	$-0.568721\pi$
$919$	−11936.1	−0.428439	−0.214219	+	0.976786i	$0.568721\pi$
$920$	−13930.6	−0.499215
$921$	−6832.11	−0.244436
$922$	18012.2	0.643384
$923$	3049.41	0.108746
$924$	−307.583	−0.0109510
$925$	876.709	0.0311633
$926$	42399.4	1.50468
$927$	−2278.74	−0.0807375
$928$	745.146	0.0263584
$929$	−38488.9	−1.35929	−0.679645	−	0.733541i	$-0.737866\pi$
$929$	−38488.9	−1.35929	−0.679645	+	0.733541i	$0.737866\pi$
$930$	−2820.64	−0.0994543
$931$	−5027.22	−0.176971
$932$	−1294.00	−0.0454789
$933$	15495.7	0.543735
$934$	16809.3	0.588884
$935$	156.982	0.00549077
$936$	766.291	0.0267596
$937$	−27212.3	−0.948760	−0.474380	−	0.880320i	$-0.657328\pi$
$937$	−27212.3	−0.948760	−0.474380	+	0.880320i	$0.657328\pi$
$938$	−26435.7	−0.920208
$939$	−32793.3	−1.13969
$940$	253.447	0.00879420
$941$	−15596.4	−0.540306	−0.270153	−	0.962817i	$-0.587074\pi$
$941$	−15596.4	−0.540306	−0.270153	+	0.962817i	$0.587074\pi$
$942$	−28618.4	−0.989849
$943$	−35350.0	−1.22074
$944$	−58658.2	−2.02242
$945$	−16522.1	−0.568747
$946$	−5818.59	−0.199977
$947$	−48748.2	−1.67276	−0.836380	−	0.548150i	$-0.815332\pi$
$947$	−48748.2	−1.67276	−0.836380	+	0.548150i	$0.815332\pi$
$948$	−887.782	−0.0304154
$949$	−303.642	−0.0103863
$950$	1361.02	0.0464814
$951$	−5276.58	−0.179921
$952$	1570.37	0.0534623
$953$	10573.1	0.359388	0.179694	−	0.983723i	$-0.442489\pi$
$953$	10573.1	0.359388	0.179694	+	0.983723i	$0.442489\pi$
$954$	−1135.55	−0.0385374
$955$	−16940.8	−0.574021
$956$	−216.241	−0.00731563
$957$	4661.01	0.157439
$958$	−23856.3	−0.804552
$959$	19137.9	0.644414
$960$	−13448.2	−0.452123
$961$	−28462.8	−0.955417
$962$	−1578.55	−0.0529048
$963$	2169.31	0.0725909
$964$	−607.209	−0.0202872
$965$	−19963.3	−0.665950
$966$	47626.4	1.58629
$967$	34987.8	1.16353	0.581764	−	0.813358i	$-0.302363\pi$
$967$	34987.8	1.16353	0.581764	+	0.813358i	$0.302363\pi$
$968$	2700.82	0.0896772
$969$	−292.970	−0.00971266
$970$	−12358.9	−0.409093
$971$	11577.6	0.382640	0.191320	−	0.981528i	$-0.438723\pi$
$971$	11577.6	0.382640	0.191320	+	0.981528i	$0.438723\pi$
$972$	128.449	0.00423868
$973$	8979.54	0.295859
$974$	−14289.7	−0.470095
$975$	−2121.74	−0.0696925
$976$	14796.8	0.485281
$977$	−23084.9	−0.755938	−0.377969	−	0.925818i	$-0.623377\pi$
$977$	−23084.9	−0.755938	−0.377969	+	0.925818i	$0.623377\pi$
$978$	−34841.6	−1.13917
$979$	−12400.2	−0.404814
$980$	277.796	0.00905497
$981$	1338.83	0.0435734
$982$	−49975.3	−1.62401
$983$	52632.0	1.70773	0.853866	−	0.520493i	$-0.174252\pi$
$983$	52632.0	1.70773	0.853866	+	0.520493i	$0.174252\pi$
$984$	−34150.1	−1.10637
$985$	16410.0	0.530829
$986$	641.452	0.0207181
$987$	32145.7	1.03669
$988$	−62.6767	−0.00201823
$989$	23043.2	0.740882
$990$	344.387	0.0110559
$991$	−10382.8	−0.332816	−0.166408	−	0.986057i	$-0.553217\pi$
$991$	−10382.8	−0.332816	−0.166408	+	0.986057i	$0.553217\pi$
$992$	−346.227	−0.0110814
$993$	24945.2	0.797193
$994$	13709.5	0.437463
$995$	−3196.28	−0.101838
$996$	47.8854	0.00152340
$997$	18002.2	0.571852	0.285926	−	0.958252i	$-0.407699\pi$
$997$	18002.2	0.571852	0.285926	+	0.958252i	$0.407699\pi$
$998$	18071.6	0.573193
$999$	4701.18	0.148887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.d.1.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.a.d.1.7	✓	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.86531 q^{2} -5.40234 q^{3} +0.209982 q^{4} +5.00000 q^{5} +15.4794 q^{6} -24.6494 q^{7} +22.3208 q^{8} +2.18531 q^{9} -14.3265 q^{10} -11.0000 q^{11} -1.13439 q^{12} +15.7098 q^{13} +70.6279 q^{14} -27.0117 q^{15} -65.6358 q^{16} -2.85422 q^{17} -6.26159 q^{18} -19.0000 q^{19} +1.04991 q^{20} +133.164 q^{21} +31.5184 q^{22} -124.821 q^{23} -120.585 q^{24} +25.0000 q^{25} -45.0134 q^{26} +134.057 q^{27} -5.17592 q^{28} +78.4342 q^{29} +77.3968 q^{30} -36.4439 q^{31} +9.50027 q^{32} +59.4258 q^{33} +8.17823 q^{34} -123.247 q^{35} +0.458876 q^{36} +35.0684 q^{37} +54.4408 q^{38} -84.8697 q^{39} +111.604 q^{40} +283.204 q^{41} -381.556 q^{42} -184.609 q^{43} -2.30980 q^{44} +10.9266 q^{45} +357.652 q^{46} +241.399 q^{47} +354.587 q^{48} +264.590 q^{49} -71.6327 q^{50} +15.4195 q^{51} +3.29878 q^{52} +181.351 q^{53} -384.116 q^{54} -55.0000 q^{55} -550.193 q^{56} +102.645 q^{57} -224.738 q^{58} +893.693 q^{59} -5.67197 q^{60} -225.438 q^{61} +104.423 q^{62} -53.8665 q^{63} +497.865 q^{64} +78.5490 q^{65} -170.273 q^{66} -374.295 q^{67} -0.599336 q^{68} +674.329 q^{69} +353.140 q^{70} +194.109 q^{71} +48.7779 q^{72} -19.3282 q^{73} -100.482 q^{74} -135.059 q^{75} -3.98966 q^{76} +271.143 q^{77} +243.178 q^{78} +782.604 q^{79} -328.179 q^{80} -783.228 q^{81} -811.467 q^{82} -42.2123 q^{83} +27.9621 q^{84} -14.2711 q^{85} +528.963 q^{86} -423.728 q^{87} -245.529 q^{88} +1127.29 q^{89} -31.3079 q^{90} -387.236 q^{91} -26.2103 q^{92} +196.882 q^{93} -691.683 q^{94} -95.0000 q^{95} -51.3237 q^{96} +862.657 q^{97} -758.133 q^{98} -24.0384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 4 q^{2} - 21 q^{3} + 74 q^{4} + 110 q^{5} - 9 q^{6} - 41 q^{7} - 78 q^{8} + 209 q^{9} - 20 q^{10} - 242 q^{11} - 196 q^{12} - q^{13} - 63 q^{14} - 105 q^{15} + 6 q^{16} + 187 q^{17} - 361 q^{18}+ \cdots - 2299 q^{99}+O(q^{100}) \) 22 * q - 4 * q^2 - 21 * q^3 + 74 * q^4 + 110 * q^5 - 9 * q^6 - 41 * q^7 - 78 * q^8 + 209 * q^9 - 20 * q^10 - 242 * q^11 - 196 * q^12 - q^13 - 63 * q^14 - 105 * q^15 + 6 * q^16 + 187 * q^17 - 361 * q^18 - 418 * q^19 + 370 * q^20 - 107 * q^21 + 44 * q^22 - 361 * q^23 + 208 * q^24 + 550 * q^25 - 365 * q^26 - 1467 * q^27 - 773 * q^28 - 319 * q^29 - 45 * q^30 - 402 * q^31 - 873 * q^32 + 231 * q^33 - 717 * q^34 - 205 * q^35 + 725 * q^36 - 838 * q^37 + 76 * q^38 - 607 * q^39 - 390 * q^40 - 392 * q^41 - 1350 * q^42 - 610 * q^43 - 814 * q^44 + 1045 * q^45 - 605 * q^46 - 1866 * q^47 - 1637 * q^48 + 379 * q^49 - 100 * q^50 - 2659 * q^51 - 638 * q^52 - 1303 * q^53 + 2338 * q^54 - 1210 * q^55 + 727 * q^56 + 399 * q^57 + 44 * q^58 - 2417 * q^59 - 980 * q^60 + 918 * q^61 - 1634 * q^62 - 374 * q^63 - 1716 * q^64 - 5 * q^65 + 99 * q^66 - 2339 * q^67 + 4940 * q^68 + 127 * q^69 - 315 * q^70 - 2370 * q^71 - 3306 * q^72 + 2207 * q^73 + 2051 * q^74 - 525 * q^75 - 1406 * q^76 + 451 * q^77 + 1380 * q^78 + 586 * q^79 + 30 * q^80 + 1950 * q^81 - 1566 * q^82 - 2870 * q^83 + 3076 * q^84 + 935 * q^85 - 1246 * q^86 - 1811 * q^87 + 858 * q^88 - 1768 * q^89 - 1805 * q^90 - 2195 * q^91 - 6728 * q^92 - 2916 * q^93 + 672 * q^94 - 2090 * q^95 + 6022 * q^96 - 4022 * q^97 + 1162 * q^98 - 2299 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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