LMFDB - Embedded newform 190.4.a.h.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [190,4,Mod(1,190)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(190, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("190.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	190.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,6,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$11.2103629011$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.5468.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 23x - 40 $ x^3 - 23*x - 40
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.20569$ of defining polynomial
Character	$\chi$	$=$	190.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -0.794314 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.58863 q^{6} -22.9577 q^{7} +8.00000 q^{8} -26.3691 q^{9} -10.0000 q^{10} +53.3074 q^{11} -3.17726 q^{12} -73.3488 q^{13} -45.9154 q^{14} +3.97157 q^{15} +16.0000 q^{16} -139.402 q^{17} -52.7381 q^{18} -19.0000 q^{19} -20.0000 q^{20} +18.2356 q^{21} +106.615 q^{22} +99.1611 q^{23} -6.35452 q^{24} +25.0000 q^{25} -146.698 q^{26} +42.3918 q^{27} -91.8308 q^{28} +170.693 q^{29} +7.94314 q^{30} -274.774 q^{31} +32.0000 q^{32} -42.3428 q^{33} -278.804 q^{34} +114.788 q^{35} -105.476 q^{36} -47.0653 q^{37} -38.0000 q^{38} +58.2620 q^{39} -40.0000 q^{40} +62.0699 q^{41} +36.4713 q^{42} -224.192 q^{43} +213.230 q^{44} +131.845 q^{45} +198.322 q^{46} -376.852 q^{47} -12.7090 q^{48} +184.056 q^{49} +50.0000 q^{50} +110.729 q^{51} -293.395 q^{52} +551.425 q^{53} +84.7836 q^{54} -266.537 q^{55} -183.662 q^{56} +15.0920 q^{57} +341.386 q^{58} -100.804 q^{59} +15.8863 q^{60} +533.726 q^{61} -549.549 q^{62} +605.373 q^{63} +64.0000 q^{64} +366.744 q^{65} -84.6856 q^{66} +327.968 q^{67} -557.608 q^{68} -78.7651 q^{69} +229.577 q^{70} -344.315 q^{71} -210.953 q^{72} +543.970 q^{73} -94.1306 q^{74} -19.8579 q^{75} -76.0000 q^{76} -1223.81 q^{77} +116.524 q^{78} +130.821 q^{79} -80.0000 q^{80} +678.292 q^{81} +124.140 q^{82} +944.539 q^{83} +72.9425 q^{84} +697.009 q^{85} -448.385 q^{86} -135.584 q^{87} +426.459 q^{88} -717.584 q^{89} +263.691 q^{90} +1683.92 q^{91} +396.644 q^{92} +218.257 q^{93} -753.704 q^{94} +95.0000 q^{95} -25.4181 q^{96} -190.085 q^{97} +368.111 q^{98} -1405.67 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 15 q^{5} - 18 q^{6} - 11 q^{7} + 24 q^{8} - 8 q^{9} - 30 q^{10} - 68 q^{11} - 36 q^{12} - 121 q^{13} - 22 q^{14} + 45 q^{15} + 48 q^{16} - 103 q^{17} - 16 q^{18} - 57 q^{19}+ \cdots - 2164 q^{99}+O(q^{100}) $ 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 15 * q^5 - 18 * q^6 - 11 * q^7 + 24 * q^8 - 8 * q^9 - 30 * q^10 - 68 * q^11 - 36 * q^12 - 121 * q^13 - 22 * q^14 + 45 * q^15 + 48 * q^16 - 103 * q^17 - 16 * q^18 - 57 * q^19 - 60 * q^20 - 271 * q^21 - 136 * q^22 - 203 * q^23 - 72 * q^24 + 75 * q^25 - 242 * q^26 - 129 * q^27 - 44 * q^28 + 91 * q^29 + 90 * q^30 - 154 * q^31 + 96 * q^32 + 412 * q^33 - 206 * q^34 + 55 * q^35 - 32 * q^36 - 304 * q^37 - 114 * q^38 + 461 * q^39 - 120 * q^40 + 282 * q^41 - 542 * q^42 - 214 * q^43 - 272 * q^44 + 40 * q^45 - 406 * q^46 - 1144 * q^47 - 144 * q^48 + 1060 * q^49 + 150 * q^50 + 969 * q^51 - 484 * q^52 + 795 * q^53 - 258 * q^54 + 340 * q^55 - 88 * q^56 + 171 * q^57 + 182 * q^58 - 609 * q^59 + 180 * q^60 + 792 * q^61 - 308 * q^62 + 2686 * q^63 + 192 * q^64 + 605 * q^65 + 824 * q^66 - 865 * q^67 - 412 * q^68 + 1237 * q^69 + 110 * q^70 - 312 * q^71 - 64 * q^72 + 79 * q^73 - 608 * q^74 - 225 * q^75 - 228 * q^76 - 1680 * q^77 + 922 * q^78 + 1806 * q^79 - 240 * q^80 + 1499 * q^81 + 564 * q^82 - 34 * q^83 - 1084 * q^84 + 515 * q^85 - 428 * q^86 - 197 * q^87 - 544 * q^88 - 1010 * q^89 + 80 * q^90 + 113 * q^91 - 812 * q^92 + 718 * q^93 - 2288 * q^94 + 285 * q^95 - 288 * q^96 - 1120 * q^97 + 2120 * q^98 - 2164 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−0.794314	−0.152866	−0.0764329	−	0.997075i	$-0.524353\pi$
$3$	−0.794314	−0.152866	−0.0764329	+	0.997075i	$0.524353\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−1.58863	−0.108093
$7$	−22.9577	−1.23960	−0.619799	−	0.784760i	$-0.712786\pi$
$7$	−22.9577	−1.23960	−0.619799	+	0.784760i	$0.712786\pi$
$8$	8.00000	0.353553
$9$	−26.3691	−0.976632
$10$	−10.0000	−0.316228
$11$	53.3074	1.46116	0.730581	−	0.682826i	$-0.239249\pi$
$11$	53.3074	1.46116	0.730581	+	0.682826i	$0.239249\pi$
$12$	−3.17726	−0.0764329
$13$	−73.3488	−1.56487	−0.782435	−	0.622732i	$-0.786023\pi$
$13$	−73.3488	−1.56487	−0.782435	+	0.622732i	$0.786023\pi$
$14$	−45.9154	−0.876529
$15$	3.97157	0.0683637
$16$	16.0000	0.250000
$17$	−139.402	−1.98882	−0.994410	−	0.105592i	$-0.966326\pi$
$17$	−139.402	−1.98882	−0.994410	+	0.105592i	$0.966326\pi$
$18$	−52.7381	−0.690583
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−20.0000	−0.223607
$21$	18.2356	0.189492
$22$	106.615	1.03320
$23$	99.1611	0.898979	0.449489	−	0.893286i	$-0.351606\pi$
$23$	99.1611	0.898979	0.449489	+	0.893286i	$0.351606\pi$
$24$	−6.35452	−0.0540463
$25$	25.0000	0.200000
$26$	−146.698	−1.10653
$27$	42.3918	0.302160
$28$	−91.8308	−0.619799
$29$	170.693	1.09300	0.546498	−	0.837461i	$-0.315961\pi$
$29$	170.693	1.09300	0.546498	+	0.837461i	$0.315961\pi$
$30$	7.94314	0.0483404
$31$	−274.774	−1.59197	−0.795983	−	0.605319i	$-0.793045\pi$
$31$	−274.774	−1.59197	−0.795983	+	0.605319i	$0.793045\pi$
$32$	32.0000	0.176777
$33$	−42.3428	−0.223362
$34$	−278.804	−1.40631
$35$	114.788	0.554365
$36$	−105.476	−0.488316
$37$	−47.0653	−0.209121	−0.104561	−	0.994519i	$-0.533344\pi$
$37$	−47.0653	−0.209121	−0.104561	+	0.994519i	$0.533344\pi$
$38$	−38.0000	−0.162221
$39$	58.2620	0.239215
$40$	−40.0000	−0.158114
$41$	62.0699	0.236431	0.118216	−	0.992988i	$-0.462283\pi$
$41$	62.0699	0.236431	0.118216	+	0.992988i	$0.462283\pi$
$42$	36.4713	0.133991
$43$	−224.192	−0.795093	−0.397547	−	0.917582i	$-0.630138\pi$
$43$	−224.192	−0.795093	−0.397547	+	0.917582i	$0.630138\pi$
$44$	213.230	0.730581
$45$	131.845	0.436763
$46$	198.322	0.635674
$47$	−376.852	−1.16956	−0.584782	−	0.811190i	$-0.698820\pi$
$47$	−376.852	−1.16956	−0.584782	+	0.811190i	$0.698820\pi$
$48$	−12.7090	−0.0382165
$49$	184.056	0.536606
$50$	50.0000	0.141421
$51$	110.729	0.304023
$52$	−293.395	−0.782435
$53$	551.425	1.42913	0.714567	−	0.699567i	$-0.246624\pi$
$53$	551.425	1.42913	0.714567	+	0.699567i	$0.246624\pi$
$54$	84.7836	0.213659
$55$	−266.537	−0.653451
$56$	−183.662	−0.438264
$57$	15.0920	0.0350698
$58$	341.386	0.772864
$59$	−100.804	−0.222433	−0.111217	−	0.993796i	$-0.535475\pi$
$59$	−100.804	−0.222433	−0.111217	+	0.993796i	$0.535475\pi$
$60$	15.8863	0.0341819
$61$	533.726	1.12027	0.560136	−	0.828401i	$-0.310749\pi$
$61$	533.726	1.12027	0.560136	+	0.828401i	$0.310749\pi$
$62$	−549.549	−1.12569
$63$	605.373	1.21063
$64$	64.0000	0.125000
$65$	366.744	0.699831
$66$	−84.6856	−0.157941
$67$	327.968	0.598025	0.299012	−	0.954249i	$-0.403343\pi$
$67$	327.968	0.598025	0.299012	+	0.954249i	$0.403343\pi$
$68$	−557.608	−0.994410
$69$	−78.7651	−0.137423
$70$	229.577	0.391996
$71$	−344.315	−0.575531	−0.287765	−	0.957701i	$-0.592912\pi$
$71$	−344.315	−0.575531	−0.287765	+	0.957701i	$0.592912\pi$
$72$	−210.953	−0.345292
$73$	543.970	0.872149	0.436074	−	0.899911i	$-0.356368\pi$
$73$	543.970	0.872149	0.436074	+	0.899911i	$0.356368\pi$
$74$	−94.1306	−0.147871
$75$	−19.8579	−0.0305732
$76$	−76.0000	−0.114708
$77$	−1223.81	−1.81125
$78$	116.524	0.169151
$79$	130.821	0.186310	0.0931548	−	0.995652i	$-0.470305\pi$
$79$	130.821	0.186310	0.0931548	+	0.995652i	$0.470305\pi$
$80$	−80.0000	−0.111803
$81$	678.292	0.930442
$82$	124.140	0.167182
$83$	944.539	1.24912	0.624558	−	0.780979i	$-0.285279\pi$
$83$	944.539	1.24912	0.624558	+	0.780979i	$0.285279\pi$
$84$	72.9425	0.0947462
$85$	697.009	0.889427
$86$	−448.385	−0.562216
$87$	−135.584	−0.167082
$88$	426.459	0.516599
$89$	−717.584	−0.854648	−0.427324	−	0.904098i	$-0.640544\pi$
$89$	−717.584	−0.854648	−0.427324	+	0.904098i	$0.640544\pi$
$90$	263.691	0.308838
$91$	1683.92	1.93981
$92$	396.644	0.449489
$93$	218.257	0.243357
$94$	−753.704	−0.827007
$95$	95.0000	0.102598
$96$	−25.4181	−0.0270231
$97$	−190.085	−0.198971	−0.0994856	−	0.995039i	$-0.531720\pi$
$97$	−190.085	−0.198971	−0.0994856	+	0.995039i	$0.531720\pi$
$98$	368.111	0.379437
$99$	−1405.67	−1.42702
$100$	100.000	0.100000
$101$	−583.088	−0.574450	−0.287225	−	0.957863i	$-0.592733\pi$
$101$	−583.088	−0.574450	−0.287225	+	0.957863i	$0.592733\pi$
$102$	221.458	0.214976
$103$	−1794.19	−1.71638	−0.858189	−	0.513333i	$-0.828410\pi$
$103$	−1794.19	−1.71638	−0.858189	+	0.513333i	$0.828410\pi$
$104$	−586.791	−0.553265
$105$	−91.1781	−0.0847436
$106$	1102.85	1.01055
$107$	258.601	0.233644	0.116822	−	0.993153i	$-0.462729\pi$
$107$	258.601	0.233644	0.116822	+	0.993153i	$0.462729\pi$
$108$	169.567	0.151080
$109$	−562.480	−0.494273	−0.247137	−	0.968981i	$-0.579490\pi$
$109$	−562.480	−0.494273	−0.247137	+	0.968981i	$0.579490\pi$
$110$	−533.074	−0.462060
$111$	37.3847	0.0319675
$112$	−367.323	−0.309900
$113$	−706.717	−0.588340	−0.294170	−	0.955753i	$-0.595043\pi$
$113$	−706.717	−0.588340	−0.294170	+	0.955753i	$0.595043\pi$
$114$	30.1839	0.0247981
$115$	−495.805	−0.402036
$116$	682.771	0.546498
$117$	1934.14	1.52830
$118$	−201.608	−0.157284
$119$	3200.35	2.46534
$120$	31.7726	0.0241702
$121$	1510.68	1.13499
$122$	1067.45	0.792151
$123$	−49.3030	−0.0361423
$124$	−1099.10	−0.795983
$125$	−125.000	−0.0894427
$126$	1210.75	0.856046
$127$	−2640.33	−1.84481	−0.922407	−	0.386219i	$-0.873781\pi$
$127$	−2640.33	−1.84481	−0.922407	+	0.386219i	$0.873781\pi$
$128$	128.000	0.0883883
$129$	178.079	0.121543
$130$	733.488	0.494855
$131$	360.905	0.240705	0.120353	−	0.992731i	$-0.461597\pi$
$131$	360.905	0.240705	0.120353	+	0.992731i	$0.461597\pi$
$132$	−169.371	−0.111681
$133$	436.196	0.284383
$134$	655.936	0.422867
$135$	−211.959	−0.135130
$136$	−1115.22	−0.703154
$137$	49.7951	0.0310532	0.0155266	−	0.999879i	$-0.495058\pi$
$137$	49.7951	0.0310532	0.0155266	+	0.999879i	$0.495058\pi$
$138$	−157.530	−0.0971729
$139$	2216.11	1.35229	0.676144	−	0.736769i	$-0.263650\pi$
$139$	2216.11	1.35229	0.676144	+	0.736769i	$0.263650\pi$
$140$	459.154	0.277183
$141$	299.339	0.178787
$142$	−688.630	−0.406962
$143$	−3910.03	−2.28653
$144$	−421.905	−0.244158
$145$	−853.464	−0.488802
$146$	1087.94	0.616702
$147$	−146.198	−0.0820287
$148$	−188.261	−0.104561
$149$	−3381.39	−1.85916	−0.929579	−	0.368624i	$-0.879829\pi$
$149$	−3381.39	−1.85916	−0.929579	+	0.368624i	$0.879829\pi$
$150$	−39.7157	−0.0216185
$151$	−653.981	−0.352452	−0.176226	−	0.984350i	$-0.556389\pi$
$151$	−653.981	−0.352452	−0.176226	+	0.984350i	$0.556389\pi$
$152$	−152.000	−0.0811107
$153$	3675.90	1.94234
$154$	−2447.63	−1.28075
$155$	1373.87	0.711949
$156$	233.048	0.119608
$157$	−2927.57	−1.48819	−0.744093	−	0.668076i	$-0.767118\pi$
$157$	−2927.57	−1.48819	−0.744093	+	0.668076i	$0.767118\pi$
$158$	261.641	0.131741
$159$	−438.005	−0.218466
$160$	−160.000	−0.0790569
$161$	−2276.51	−1.11437
$162$	1356.58	0.657922
$163$	−991.454	−0.476421	−0.238211	−	0.971214i	$-0.576561\pi$
$163$	−991.454	−0.476421	−0.238211	+	0.971214i	$0.576561\pi$
$164$	248.280	0.118216
$165$	211.714	0.0998904
$166$	1889.08	0.883258
$167$	−3679.78	−1.70509	−0.852545	−	0.522653i	$-0.824942\pi$
$167$	−3679.78	−1.70509	−0.852545	+	0.522653i	$0.824942\pi$
$168$	145.885	0.0669957
$169$	3183.05	1.44882
$170$	1394.02	0.628920
$171$	501.012	0.224055
$172$	−896.770	−0.397547
$173$	2017.51	0.886638	0.443319	−	0.896364i	$-0.353801\pi$
$173$	2017.51	0.886638	0.443319	+	0.896364i	$0.353801\pi$
$174$	−271.168	−0.118145
$175$	−573.942	−0.247920
$176$	852.918	0.365290
$177$	80.0700	0.0340024
$178$	−1435.17	−0.604328
$179$	−3045.55	−1.27170	−0.635852	−	0.771811i	$-0.719351\pi$
$179$	−3045.55	−1.27170	−0.635852	+	0.771811i	$0.719351\pi$
$180$	527.381	0.218382
$181$	2374.04	0.974924	0.487462	−	0.873144i	$-0.337923\pi$
$181$	2374.04	0.974924	0.487462	+	0.873144i	$0.337923\pi$
$182$	3367.84	1.37165
$183$	−423.946	−0.171251
$184$	793.289	0.317837
$185$	235.327	0.0935219
$186$	436.514	0.172080
$187$	−7431.15	−2.90599
$188$	−1507.41	−0.584782
$189$	−973.218	−0.374557
$190$	190.000	0.0725476
$191$	−1777.35	−0.673324	−0.336662	−	0.941626i	$-0.609298\pi$
$191$	−1777.35	−0.673324	−0.336662	+	0.941626i	$0.609298\pi$
$192$	−50.8361	−0.0191082
$193$	−2180.19	−0.813128	−0.406564	−	0.913622i	$-0.633273\pi$
$193$	−2180.19	−0.813128	−0.406564	+	0.913622i	$0.633273\pi$
$194$	−380.170	−0.140694
$195$	−291.310	−0.106980
$196$	736.223	0.268303
$197$	−2601.13	−0.940724	−0.470362	−	0.882473i	$-0.655877\pi$
$197$	−2601.13	−0.940724	−0.470362	+	0.882473i	$0.655877\pi$
$198$	−2811.33	−1.00905
$199$	412.217	0.146841	0.0734204	−	0.997301i	$-0.476609\pi$
$199$	412.217	0.146841	0.0734204	+	0.997301i	$0.476609\pi$
$200$	200.000	0.0707107
$201$	−260.510	−0.0914175
$202$	−1166.18	−0.406198
$203$	−3918.71	−1.35488
$204$	442.916	0.152011
$205$	−310.349	−0.105735
$206$	−3588.38	−1.21366
$207$	−2614.78	−0.877972
$208$	−1173.58	−0.391217
$209$	−1012.84	−0.335214
$210$	−182.356	−0.0599228
$211$	−1123.55	−0.366579	−0.183289	−	0.983059i	$-0.558675\pi$
$211$	−1123.55	−0.366579	−0.183289	+	0.983059i	$0.558675\pi$
$212$	2205.70	0.714567
$213$	273.494	0.0879790
$214$	517.201	0.165211
$215$	1120.96	0.355577
$216$	339.135	0.106830
$217$	6308.18	1.97340
$218$	−1124.96	−0.349504
$219$	−432.083	−0.133322
$220$	−1066.15	−0.326726
$221$	10225.0	3.11224
$222$	74.7693	0.0226045
$223$	6066.46	1.82170	0.910852	−	0.412732i	$-0.135426\pi$
$223$	6066.46	1.82170	0.910852	+	0.412732i	$0.135426\pi$
$224$	−734.646	−0.219132
$225$	−659.227	−0.195326
$226$	−1413.43	−0.416019
$227$	2994.36	0.875518	0.437759	−	0.899092i	$-0.355772\pi$
$227$	2994.36	0.875518	0.437759	+	0.899092i	$0.355772\pi$
$228$	60.3679	0.0175349
$229$	−1510.63	−0.435917	−0.217959	−	0.975958i	$-0.569940\pi$
$229$	−1510.63	−0.435917	−0.217959	+	0.975958i	$0.569940\pi$
$230$	−991.611	−0.284282
$231$	972.094	0.276879
$232$	1365.54	0.386432
$233$	−5805.95	−1.63245	−0.816223	−	0.577736i	$-0.803936\pi$
$233$	−5805.95	−1.63245	−0.816223	+	0.577736i	$0.803936\pi$
$234$	3868.28	1.08067
$235$	1884.26	0.523045
$236$	−403.216	−0.111217
$237$	−103.913	−0.0284804
$238$	6400.69	1.74326
$239$	−722.022	−0.195413	−0.0977066	−	0.995215i	$-0.531151\pi$
$239$	−722.022	−0.195413	−0.0977066	+	0.995215i	$0.531151\pi$
$240$	63.5452	0.0170909
$241$	5771.57	1.54265	0.771327	−	0.636439i	$-0.219593\pi$
$241$	5771.57	1.54265	0.771327	+	0.636439i	$0.219593\pi$
$242$	3021.35	0.802562
$243$	−1683.36	−0.444392
$244$	2134.90	0.560136
$245$	−920.278	−0.239977
$246$	−98.6060	−0.0255565
$247$	1393.63	0.359006
$248$	−2198.19	−0.562845
$249$	−750.261	−0.190947
$250$	−250.000	−0.0632456
$251$	727.300	0.182895	0.0914477	−	0.995810i	$-0.470851\pi$
$251$	727.300	0.182895	0.0914477	+	0.995810i	$0.470851\pi$
$252$	2421.49	0.605316
$253$	5286.02	1.31355
$254$	−5280.66	−1.30448
$255$	−553.645	−0.135963
$256$	256.000	0.0625000
$257$	2137.23	0.518743	0.259371	−	0.965778i	$-0.416485\pi$
$257$	2137.23	0.518743	0.259371	+	0.965778i	$0.416485\pi$
$258$	356.159	0.0859436
$259$	1080.51	0.259227
$260$	1466.98	0.349916
$261$	−4501.01	−1.06745
$262$	721.809	0.170204
$263$	2997.82	0.702865	0.351433	−	0.936213i	$-0.385695\pi$
$263$	2997.82	0.702865	0.351433	+	0.936213i	$0.385695\pi$
$264$	−338.743	−0.0789703
$265$	−2757.13	−0.639128
$266$	872.392	0.201089
$267$	569.987	0.130647
$268$	1311.87	0.299012
$269$	2601.91	0.589743	0.294872	−	0.955537i	$-0.404723\pi$
$269$	2601.91	0.589743	0.294872	+	0.955537i	$0.404723\pi$
$270$	−423.918	−0.0955513
$271$	−766.382	−0.171787	−0.0858937	−	0.996304i	$-0.527375\pi$
$271$	−766.382	−0.171787	−0.0858937	+	0.996304i	$0.527375\pi$
$272$	−2230.43	−0.497205
$273$	−1337.56	−0.296531
$274$	99.5903	0.0219579
$275$	1332.68	0.292232
$276$	−315.060	−0.0687116
$277$	−5989.96	−1.29928	−0.649642	−	0.760240i	$-0.725081\pi$
$277$	−5989.96	−1.29928	−0.649642	+	0.760240i	$0.725081\pi$
$278$	4432.22	0.956212
$279$	7245.54	1.55476
$280$	918.308	0.195998
$281$	−1442.46	−0.306228	−0.153114	−	0.988209i	$-0.548930\pi$
$281$	−1442.46	−0.306228	−0.153114	+	0.988209i	$0.548930\pi$
$282$	598.678	0.126421
$283$	−3000.34	−0.630217	−0.315109	−	0.949056i	$-0.602041\pi$
$283$	−3000.34	−0.630217	−0.315109	+	0.949056i	$0.602041\pi$
$284$	−1377.26	−0.287765
$285$	−75.4599	−0.0156837
$286$	−7820.07	−1.61682
$287$	−1424.98	−0.293080
$288$	−843.810	−0.172646
$289$	14519.9	2.95540
$290$	−1706.93	−0.345636
$291$	150.987	0.0304159
$292$	2175.88	0.436074
$293$	750.895	0.149719	0.0748597	−	0.997194i	$-0.476149\pi$
$293$	750.895	0.149719	0.0748597	+	0.997194i	$0.476149\pi$
$294$	−292.396	−0.0580030
$295$	504.019	0.0994751
$296$	−376.523	−0.0739356
$297$	2259.80	0.441504
$298$	−6762.79	−1.31462
$299$	−7273.35	−1.40679
$300$	−79.4314	−0.0152866
$301$	5146.94	0.985597
$302$	−1307.96	−0.249221
$303$	463.155	0.0878138
$304$	−304.000	−0.0573539
$305$	−2668.63	−0.501001
$306$	7351.79	1.37344
$307$	−339.570	−0.0631279	−0.0315640	−	0.999502i	$-0.510049\pi$
$307$	−339.570	−0.0631279	−0.0315640	+	0.999502i	$0.510049\pi$
$308$	−4895.26	−0.905627
$309$	1425.15	0.262376
$310$	2747.74	0.503424
$311$	9239.59	1.68466	0.842330	−	0.538963i	$-0.181184\pi$
$311$	9239.59	1.68466	0.842330	+	0.538963i	$0.181184\pi$
$312$	466.096	0.0845754
$313$	−713.175	−0.128789	−0.0643946	−	0.997925i	$-0.520512\pi$
$313$	−713.175	−0.128789	−0.0643946	+	0.997925i	$0.520512\pi$
$314$	−5855.13	−1.05231
$315$	−3026.86	−0.541411
$316$	523.282	0.0931548
$317$	1145.46	0.202951	0.101475	−	0.994838i	$-0.467644\pi$
$317$	1145.46	0.202951	0.101475	+	0.994838i	$0.467644\pi$
$318$	−876.010	−0.154479
$319$	9099.19	1.59704
$320$	−320.000	−0.0559017
$321$	−205.410	−0.0357161
$322$	−4553.02	−0.787981
$323$	2648.64	0.456266
$324$	2713.17	0.465221
$325$	−1833.72	−0.312974
$326$	−1982.91	−0.336881
$327$	446.786	0.0755575
$328$	496.559	0.0835911
$329$	8651.66	1.44979
$330$	423.428	0.0706332
$331$	−1030.08	−0.171052	−0.0855261	−	0.996336i	$-0.527257\pi$
$331$	−1030.08	−0.171052	−0.0855261	+	0.996336i	$0.527257\pi$
$332$	3778.15	0.624558
$333$	1241.07	0.204235
$334$	−7359.57	−1.20568
$335$	−1639.84	−0.267445
$336$	291.770	0.0473731
$337$	7214.68	1.16620	0.583099	−	0.812401i	$-0.301840\pi$
$337$	7214.68	1.16620	0.583099	+	0.812401i	$0.301840\pi$
$338$	6366.11	1.02447
$339$	561.356	0.0899371
$340$	2788.04	0.444713
$341$	−14647.5	−2.32612
$342$	1002.02	0.158431
$343$	3648.99	0.574423
$344$	−1793.54	−0.281108
$345$	393.825	0.0614575
$346$	4035.02	0.626948
$347$	−1463.81	−0.226459	−0.113229	−	0.993569i	$-0.536120\pi$
$347$	−1463.81	−0.226459	−0.113229	+	0.993569i	$0.536120\pi$
$348$	−542.335	−0.0835409
$349$	−10644.8	−1.63267	−0.816336	−	0.577578i	$-0.803998\pi$
$349$	−10644.8	−1.63267	−0.816336	+	0.577578i	$0.803998\pi$
$350$	−1147.88	−0.175306
$351$	−3109.39	−0.472840
$352$	1705.84	0.258299
$353$	−3372.46	−0.508492	−0.254246	−	0.967140i	$-0.581827\pi$
$353$	−3372.46	−0.508492	−0.254246	+	0.967140i	$0.581827\pi$
$354$	160.140	0.0240433
$355$	1721.58	0.257385
$356$	−2870.33	−0.427324
$357$	−2542.08	−0.376866
$358$	−6091.10	−0.899230
$359$	−10388.6	−1.52728	−0.763638	−	0.645645i	$-0.776589\pi$
$359$	−10388.6	−1.52728	−0.763638	+	0.645645i	$0.776589\pi$
$360$	1054.76	0.154419
$361$	361.000	0.0526316
$362$	4748.08	0.689375
$363$	−1199.95	−0.173502
$364$	6735.68	0.969906
$365$	−2719.85	−0.390037
$366$	−847.892	−0.121093
$367$	−430.531	−0.0612358	−0.0306179	−	0.999531i	$-0.509748\pi$
$367$	−430.531	−0.0612358	−0.0306179	+	0.999531i	$0.509748\pi$
$368$	1586.58	0.224745
$369$	−1636.72	−0.230906
$370$	470.653	0.0661300
$371$	−12659.4	−1.77155
$372$	873.029	0.121679
$373$	−375.132	−0.0520740	−0.0260370	−	0.999661i	$-0.508289\pi$
$373$	−375.132	−0.0520740	−0.0260370	+	0.999661i	$0.508289\pi$
$374$	−14862.3	−2.05484
$375$	99.2893	0.0136727
$376$	−3014.82	−0.413504
$377$	−12520.1	−1.71040
$378$	−1946.44	−0.264852
$379$	2575.31	0.349036	0.174518	−	0.984654i	$-0.444163\pi$
$379$	2575.31	0.349036	0.174518	+	0.984654i	$0.444163\pi$
$380$	380.000	0.0512989
$381$	2097.25	0.282009
$382$	−3554.71	−0.476112
$383$	9007.80	1.20177	0.600884	−	0.799336i	$-0.294815\pi$
$383$	9007.80	1.20177	0.600884	+	0.799336i	$0.294815\pi$
$384$	−101.672	−0.0135116
$385$	6119.07	0.810018
$386$	−4360.39	−0.574968
$387$	5911.74	0.776514
$388$	−760.340	−0.0994856
$389$	3716.86	0.484453	0.242227	−	0.970220i	$-0.422122\pi$
$389$	3716.86	0.484453	0.242227	+	0.970220i	$0.422122\pi$
$390$	−582.620	−0.0756465
$391$	−13823.2	−1.78791
$392$	1472.45	0.189719
$393$	−286.672	−0.0367956
$394$	−5202.26	−0.665193
$395$	−654.103	−0.0833202
$396$	−5622.66	−0.713509
$397$	14192.2	1.79418	0.897088	−	0.441851i	$-0.145678\pi$
$397$	14192.2	1.79418	0.897088	+	0.441851i	$0.145678\pi$
$398$	824.435	0.103832
$399$	−346.477	−0.0434725
$400$	400.000	0.0500000
$401$	−9736.11	−1.21246	−0.606232	−	0.795288i	$-0.707320\pi$
$401$	−9736.11	−1.21246	−0.606232	+	0.795288i	$0.707320\pi$
$402$	−521.019	−0.0646420
$403$	20154.4	2.49122
$404$	−2332.35	−0.287225
$405$	−3391.46	−0.416106
$406$	−7837.43	−0.958042
$407$	−2508.93	−0.305560
$408$	885.831	0.107488
$409$	15847.0	1.91585	0.957925	−	0.287020i	$-0.0926646\pi$
$409$	15847.0	1.91585	0.957925	+	0.287020i	$0.0926646\pi$
$410$	−620.699	−0.0747662
$411$	−39.5530	−0.00474697
$412$	−7176.77	−0.858189
$413$	2314.22	0.275728
$414$	−5229.57	−0.620820
$415$	−4722.69	−0.558621
$416$	−2347.16	−0.276633
$417$	−1760.29	−0.206719
$418$	−2025.68	−0.237032
$419$	−15104.2	−1.76107	−0.880536	−	0.473979i	$-0.842817\pi$
$419$	−15104.2	−1.76107	−0.880536	+	0.473979i	$0.842817\pi$
$420$	−364.713	−0.0423718
$421$	1317.72	0.152546	0.0762729	−	0.997087i	$-0.475698\pi$
$421$	1317.72	0.152546	0.0762729	+	0.997087i	$0.475698\pi$
$422$	−2247.09	−0.259210
$423$	9937.24	1.14223
$424$	4411.40	0.505275
$425$	−3485.05	−0.397764
$426$	546.989	0.0622106
$427$	−12253.1	−1.38869
$428$	1034.40	0.116822
$429$	3105.80	0.349532
$430$	2241.92	0.251431
$431$	−16162.6	−1.80632	−0.903159	−	0.429306i	$-0.858758\pi$
$431$	−16162.6	−1.80632	−0.903159	+	0.429306i	$0.858758\pi$
$432$	678.269	0.0755399
$433$	10551.5	1.17107	0.585536	−	0.810647i	$-0.300884\pi$
$433$	10551.5	1.17107	0.585536	+	0.810647i	$0.300884\pi$
$434$	12616.4	1.39540
$435$	677.919	0.0747212
$436$	−2249.92	−0.247137
$437$	−1884.06	−0.206240
$438$	−864.166	−0.0942727
$439$	−12039.2	−1.30889	−0.654443	−	0.756112i	$-0.727097\pi$
$439$	−12039.2	−1.30889	−0.654443	+	0.756112i	$0.727097\pi$
$440$	−2132.30	−0.231030
$441$	−4853.38	−0.524066
$442$	20449.9	2.20069
$443$	4159.65	0.446120	0.223060	−	0.974805i	$-0.428395\pi$
$443$	4159.65	0.446120	0.223060	+	0.974805i	$0.428395\pi$
$444$	149.539	0.0159838
$445$	3587.92	0.382210
$446$	12132.9	1.28814
$447$	2685.89	0.284202
$448$	−1469.29	−0.154950
$449$	14827.6	1.55848	0.779242	−	0.626724i	$-0.215605\pi$
$449$	14827.6	1.55848	0.779242	+	0.626724i	$0.215605\pi$
$450$	−1318.45	−0.138117
$451$	3308.78	0.345465
$452$	−2826.87	−0.294170
$453$	519.466	0.0538778
$454$	5988.72	0.619085
$455$	−8419.60	−0.867510
$456$	120.736	0.0123991
$457$	14972.2	1.53254	0.766270	−	0.642518i	$-0.222110\pi$
$457$	14972.2	1.53254	0.766270	+	0.642518i	$0.222110\pi$
$458$	−3021.26	−0.308240
$459$	−5909.50	−0.600941
$460$	−1983.22	−0.201018
$461$	−6764.28	−0.683392	−0.341696	−	0.939810i	$-0.611001\pi$
$461$	−6764.28	−0.683392	−0.341696	+	0.939810i	$0.611001\pi$
$462$	1944.19	0.195783
$463$	−12092.4	−1.21378	−0.606890	−	0.794786i	$-0.707583\pi$
$463$	−12092.4	−1.21378	−0.606890	+	0.794786i	$0.707583\pi$
$464$	2731.09	0.273249
$465$	−1091.29	−0.108833
$466$	−11611.9	−1.15431
$467$	3436.72	0.340541	0.170270	−	0.985397i	$-0.445536\pi$
$467$	3436.72	0.340541	0.170270	+	0.985397i	$0.445536\pi$
$468$	7736.56	0.764151
$469$	−7529.38	−0.741311
$470$	3768.52	0.369849
$471$	2325.41	0.227493
$472$	−806.431	−0.0786419
$473$	−11951.1	−1.16176
$474$	−207.825	−0.0201387
$475$	−475.000	−0.0458831
$476$	12801.4	1.23267
$477$	−14540.6	−1.39574
$478$	−1444.04	−0.138178
$479$	13749.1	1.31151	0.655756	−	0.754973i	$-0.272350\pi$
$479$	13749.1	1.31151	0.655756	+	0.754973i	$0.272350\pi$
$480$	127.090	0.0120851
$481$	3452.19	0.327248
$482$	11543.1	1.09082
$483$	1808.26	0.170350
$484$	6042.71	0.567497
$485$	950.425	0.0889827
$486$	−3366.71	−0.314233
$487$	6265.57	0.582999	0.291499	−	0.956571i	$-0.405846\pi$
$487$	6265.57	0.582999	0.291499	+	0.956571i	$0.405846\pi$
$488$	4269.80	0.396076
$489$	787.526	0.0728285
$490$	−1840.56	−0.169690
$491$	−184.155	−0.0169263	−0.00846314	−	0.999964i	$-0.502694\pi$
$491$	−184.155	−0.0169263	−0.00846314	+	0.999964i	$0.502694\pi$
$492$	−197.212	−0.0180711
$493$	−23794.9	−2.17377
$494$	2787.26	0.253855
$495$	7028.33	0.638182
$496$	−4396.39	−0.397991
$497$	7904.68	0.713427
$498$	−1500.52	−0.135020
$499$	670.487	0.0601506	0.0300753	−	0.999548i	$-0.490425\pi$
$499$	670.487	0.0601506	0.0300753	+	0.999548i	$0.490425\pi$
$500$	−500.000	−0.0447214
$501$	2922.91	0.260650
$502$	1454.60	0.129327
$503$	−8875.83	−0.786786	−0.393393	−	0.919370i	$-0.628699\pi$
$503$	−8875.83	−0.786786	−0.393393	+	0.919370i	$0.628699\pi$
$504$	4842.98	0.428023
$505$	2915.44	0.256902
$506$	10572.0	0.928823
$507$	−2528.34	−0.221475
$508$	−10561.3	−0.922407
$509$	12882.1	1.12179	0.560893	−	0.827888i	$-0.310458\pi$
$509$	12882.1	1.12179	0.560893	+	0.827888i	$0.310458\pi$
$510$	−1107.29	−0.0961404
$511$	−12488.3	−1.08111
$512$	512.000	0.0441942
$513$	−805.445	−0.0693202
$514$	4274.47	0.366807
$515$	8970.96	0.767588
$516$	712.317	0.0607713
$517$	−20089.0	−1.70892
$518$	2161.02	0.183301
$519$	−1602.54	−0.135537
$520$	2933.95	0.247428
$521$	11785.0	0.990996	0.495498	−	0.868609i	$-0.334986\pi$
$521$	11785.0	0.990996	0.495498	+	0.868609i	$0.334986\pi$
$522$	−9002.02	−0.754804
$523$	51.4550	0.00430204	0.00215102	−	0.999998i	$-0.499315\pi$
$523$	51.4550	0.00430204	0.00215102	+	0.999998i	$0.499315\pi$
$524$	1443.62	0.120353
$525$	455.891	0.0378985
$526$	5995.64	0.497001
$527$	38304.1	3.16613
$528$	−677.485	−0.0558404
$529$	−2334.08	−0.191837
$530$	−5514.25	−0.451932
$531$	2658.10	0.217235
$532$	1744.78	0.142192
$533$	−4552.75	−0.369984
$534$	1139.97	0.0923811
$535$	−1293.00	−0.104489
$536$	2623.74	0.211434
$537$	2419.12	0.194400
$538$	5203.81	0.417012
$539$	9811.53	0.784067
$540$	−847.836	−0.0675649
$541$	4414.29	0.350804	0.175402	−	0.984497i	$-0.443877\pi$
$541$	4414.29	0.350804	0.175402	+	0.984497i	$0.443877\pi$
$542$	−1532.76	−0.121472
$543$	−1885.74	−0.149033
$544$	−4460.86	−0.351577
$545$	2812.40	0.221046
$546$	−2675.12	−0.209679
$547$	11425.2	0.893067	0.446533	−	0.894767i	$-0.352658\pi$
$547$	11425.2	0.893067	0.446533	+	0.894767i	$0.352658\pi$
$548$	199.181	0.0155266
$549$	−14073.8	−1.09409
$550$	2665.37	0.206639
$551$	−3243.16	−0.250750
$552$	−630.121	−0.0485864
$553$	−3003.34	−0.230949
$554$	−11979.9	−0.918732
$555$	−186.923	−0.0142963
$556$	8864.44	0.676144
$557$	19442.2	1.47898	0.739491	−	0.673166i	$-0.235066\pi$
$557$	19442.2	1.47898	0.739491	+	0.673166i	$0.235066\pi$
$558$	14491.1	1.09938
$559$	16444.3	1.24422
$560$	1836.62	0.138591
$561$	5902.67	0.444226
$562$	−2884.93	−0.216536
$563$	−9459.96	−0.708153	−0.354076	−	0.935217i	$-0.615205\pi$
$563$	−9459.96	−0.708153	−0.354076	+	0.935217i	$0.615205\pi$
$564$	1197.36	0.0893933
$565$	3533.59	0.263114
$566$	−6000.67	−0.445631
$567$	−15572.0	−1.15338
$568$	−2754.52	−0.203481
$569$	−19606.0	−1.44451	−0.722256	−	0.691626i	$-0.756895\pi$
$569$	−19606.0	−1.44451	−0.722256	+	0.691626i	$0.756895\pi$
$570$	−150.920	−0.0110901
$571$	5156.19	0.377898	0.188949	−	0.981987i	$-0.439492\pi$
$571$	5156.19	0.377898	0.188949	+	0.981987i	$0.439492\pi$
$572$	−15640.1	−1.14326
$573$	1411.78	0.102928
$574$	−2849.96	−0.207239
$575$	2479.03	0.179796
$576$	−1687.62	−0.122079
$577$	−17093.9	−1.23332	−0.616662	−	0.787228i	$-0.711515\pi$
$577$	−17093.9	−1.23332	−0.616662	+	0.787228i	$0.711515\pi$
$578$	29039.8	2.08978
$579$	1731.76	0.124300
$580$	−3413.86	−0.244401
$581$	−21684.4	−1.54840
$582$	301.975	0.0215073
$583$	29395.0	2.08820
$584$	4351.76	0.308351
$585$	−9670.70	−0.683477
$586$	1501.79	0.105868
$587$	−10003.2	−0.703366	−0.351683	−	0.936119i	$-0.614390\pi$
$587$	−10003.2	−0.703366	−0.351683	+	0.936119i	$0.614390\pi$
$588$	−584.792	−0.0410143
$589$	5220.71	0.365222
$590$	1008.04	0.0703395
$591$	2066.11	0.143805
$592$	−753.045	−0.0522803
$593$	−5615.44	−0.388868	−0.194434	−	0.980916i	$-0.562287\pi$
$593$	−5615.44	−0.388868	−0.194434	+	0.980916i	$0.562287\pi$
$594$	4519.59	0.312191
$595$	−16001.7	−1.10253
$596$	−13525.6	−0.929579
$597$	−327.430	−0.0224470
$598$	−14546.7	−0.994747
$599$	−2294.71	−0.156526	−0.0782631	−	0.996933i	$-0.524937\pi$
$599$	−2294.71	−0.156526	−0.0782631	+	0.996933i	$0.524937\pi$
$600$	−158.863	−0.0108093
$601$	−11049.3	−0.749935	−0.374967	−	0.927038i	$-0.622346\pi$
$601$	−11049.3	−0.749935	−0.374967	+	0.927038i	$0.622346\pi$
$602$	10293.9	0.696922
$603$	−8648.20	−0.584050
$604$	−2615.92	−0.176226
$605$	−7553.38	−0.507585
$606$	926.311	0.0620937
$607$	3081.49	0.206053	0.103026	−	0.994679i	$-0.467147\pi$
$607$	3081.49	0.206053	0.103026	+	0.994679i	$0.467147\pi$
$608$	−608.000	−0.0405554
$609$	3112.69	0.207114
$610$	−5337.26	−0.354261
$611$	27641.7	1.83022
$612$	14703.6	0.971172
$613$	−8913.61	−0.587304	−0.293652	−	0.955912i	$-0.594871\pi$
$613$	−8913.61	−0.587304	−0.293652	+	0.955912i	$0.594871\pi$
$614$	−679.140	−0.0446382
$615$	246.515	0.0161633
$616$	−9790.52	−0.640375
$617$	17711.0	1.15562	0.577811	−	0.816170i	$-0.303907\pi$
$617$	17711.0	1.15562	0.577811	+	0.816170i	$0.303907\pi$
$618$	2850.31	0.185528
$619$	−9489.11	−0.616154	−0.308077	−	0.951361i	$-0.599685\pi$
$619$	−9489.11	−0.616154	−0.308077	+	0.951361i	$0.599685\pi$
$620$	5495.49	0.355974
$621$	4203.62	0.271635
$622$	18479.2	1.19123
$623$	16474.1	1.05942
$624$	932.193	0.0598038
$625$	625.000	0.0400000
$626$	−1426.35	−0.0910677
$627$	804.514	0.0512427
$628$	−11710.3	−0.744093
$629$	6560.99	0.415905
$630$	−6053.73	−0.382835
$631$	−8443.93	−0.532722	−0.266361	−	0.963873i	$-0.585821\pi$
$631$	−8443.93	−0.532722	−0.266361	+	0.963873i	$0.585821\pi$
$632$	1046.56	0.0658704
$633$	892.449	0.0560374
$634$	2290.92	0.143508
$635$	13201.7	0.825026
$636$	−1752.02	−0.109233
$637$	−13500.3	−0.839718
$638$	18198.4	1.12928
$639$	9079.27	0.562082
$640$	−640.000	−0.0395285
$641$	2397.17	0.147711	0.0738554	−	0.997269i	$-0.476470\pi$
$641$	2397.17	0.147711	0.0738554	+	0.997269i	$0.476470\pi$
$642$	−410.820	−0.0252551
$643$	−19474.3	−1.19439	−0.597193	−	0.802097i	$-0.703718\pi$
$643$	−19474.3	−1.19439	−0.597193	+	0.802097i	$0.703718\pi$
$644$	−9106.04	−0.557187
$645$	−890.396	−0.0543555
$646$	5297.27	0.322629
$647$	−27920.1	−1.69652	−0.848262	−	0.529577i	$-0.822351\pi$
$647$	−27920.1	−1.69652	−0.848262	+	0.529577i	$0.822351\pi$
$648$	5426.34	0.328961
$649$	−5373.59	−0.325011
$650$	−3667.44	−0.221306
$651$	−5010.68	−0.301665
$652$	−3965.81	−0.238211
$653$	−465.094	−0.0278722	−0.0139361	−	0.999903i	$-0.504436\pi$
$653$	−465.094	−0.0278722	−0.0139361	+	0.999903i	$0.504436\pi$
$654$	893.572	0.0534272
$655$	−1804.52	−0.107647
$656$	993.118	0.0591079
$657$	−14344.0	−0.851768
$658$	17303.3	1.02516
$659$	8363.60	0.494385	0.247192	−	0.968966i	$-0.420492\pi$
$659$	8363.60	0.494385	0.247192	+	0.968966i	$0.420492\pi$
$660$	846.856	0.0499452
$661$	27046.1	1.59149	0.795743	−	0.605635i	$-0.207081\pi$
$661$	27046.1	1.59149	0.795743	+	0.605635i	$0.207081\pi$
$662$	−2060.16	−0.120952
$663$	−8121.84	−0.475756
$664$	7556.31	0.441629
$665$	−2180.98	−0.127180
$666$	2482.14	0.144416
$667$	16926.1	0.982580
$668$	−14719.1	−0.852545
$669$	−4818.68	−0.278477
$670$	−3279.68	−0.189112
$671$	28451.5	1.63690
$672$	583.540	0.0334978
$673$	−3938.39	−0.225578	−0.112789	−	0.993619i	$-0.535978\pi$
$673$	−3938.39	−0.225578	−0.112789	+	0.993619i	$0.535978\pi$
$674$	14429.4	0.824626
$675$	1059.80	0.0604319
$676$	12732.2	0.724409
$677$	−7796.77	−0.442621	−0.221310	−	0.975203i	$-0.571033\pi$
$677$	−7796.77	−0.442621	−0.221310	+	0.975203i	$0.571033\pi$
$678$	1122.71	0.0635951
$679$	4363.91	0.246645
$680$	5576.08	0.314460
$681$	−2378.46	−0.133837
$682$	−29295.0	−1.64481
$683$	21022.7	1.17776	0.588880	−	0.808221i	$-0.299569\pi$
$683$	21022.7	1.17776	0.588880	+	0.808221i	$0.299569\pi$
$684$	2004.05	0.112027
$685$	−248.976	−0.0138874
$686$	7297.99	0.406179
$687$	1199.91	0.0666369
$688$	−3587.08	−0.198773
$689$	−40446.4	−2.23641
$690$	787.651	0.0434570
$691$	−4955.79	−0.272832	−0.136416	−	0.990652i	$-0.543558\pi$
$691$	−4955.79	−0.272832	−0.136416	+	0.990652i	$0.543558\pi$
$692$	8070.03	0.443319
$693$	32270.8	1.76893
$694$	−2927.61	−0.160131
$695$	−11080.6	−0.604762
$696$	−1084.67	−0.0590723
$697$	−8652.66	−0.470219
$698$	−21289.6	−1.15447
$699$	4611.75	0.249545
$700$	−2295.77	−0.123960
$701$	−34916.0	−1.88126	−0.940628	−	0.339440i	$-0.889762\pi$
$701$	−34916.0	−1.88126	−0.940628	+	0.339440i	$0.889762\pi$
$702$	−6218.78	−0.334349
$703$	894.241	0.0479757
$704$	3411.67	0.182645
$705$	−1496.70	−0.0799558
$706$	−6744.91	−0.359558
$707$	13386.4	0.712088
$708$	320.280	0.0170012
$709$	−21741.3	−1.15164	−0.575820	−	0.817576i	$-0.695317\pi$
$709$	−21741.3	−1.15164	−0.575820	+	0.817576i	$0.695317\pi$
$710$	3443.15	0.181999
$711$	−3449.62	−0.181956
$712$	−5740.67	−0.302164
$713$	−27246.9	−1.43114
$714$	−5084.16	−0.266485
$715$	19550.2	1.02257
$716$	−12182.2	−0.635852
$717$	573.513	0.0298720
$718$	−20777.3	−1.07995
$719$	−22241.1	−1.15362	−0.576810	−	0.816879i	$-0.695703\pi$
$719$	−22241.1	−1.15362	−0.576810	+	0.816879i	$0.695703\pi$
$720$	2109.53	0.109191
$721$	41190.5	2.12762
$722$	722.000	0.0372161
$723$	−4584.44	−0.235819
$724$	9496.17	0.487462
$725$	4267.32	0.218599
$726$	−2399.90	−0.122684
$727$	2988.44	0.152456	0.0762278	−	0.997090i	$-0.475712\pi$
$727$	2988.44	0.152456	0.0762278	+	0.997090i	$0.475712\pi$
$728$	13471.4	0.685827
$729$	−16976.8	−0.862510
$730$	−5439.70	−0.275798
$731$	31252.8	1.58130
$732$	−1695.78	−0.0856256
$733$	−12240.9	−0.616816	−0.308408	−	0.951254i	$-0.599796\pi$
$733$	−12240.9	−0.616816	−0.308408	+	0.951254i	$0.599796\pi$
$734$	−861.062	−0.0433003
$735$	730.990	0.0366843
$736$	3173.15	0.158919
$737$	17483.1	0.873811
$738$	−3273.45	−0.163276
$739$	19051.6	0.948340	0.474170	−	0.880433i	$-0.342748\pi$
$739$	19051.6	0.948340	0.474170	+	0.880433i	$0.342748\pi$
$740$	941.306	0.0467610
$741$	−1106.98	−0.0548797
$742$	−25318.9	−1.25268
$743$	−21009.1	−1.03735	−0.518673	−	0.854973i	$-0.673574\pi$
$743$	−21009.1	−1.03735	−0.518673	+	0.854973i	$0.673574\pi$
$744$	1746.06	0.0860398
$745$	16907.0	0.831441
$746$	−750.264	−0.0368219
$747$	−24906.6	−1.21993
$748$	−29724.6	−1.45299
$749$	−5936.87	−0.289624
$750$	198.579	0.00966809
$751$	−17060.4	−0.828951	−0.414475	−	0.910061i	$-0.636035\pi$
$751$	−17060.4	−0.828951	−0.414475	+	0.910061i	$0.636035\pi$
$752$	−6029.63	−0.292391
$753$	−577.705	−0.0279585
$754$	−25040.2	−1.20943
$755$	3269.90	0.157621
$756$	−3892.87	−0.187278
$757$	21029.9	1.00970	0.504850	−	0.863207i	$-0.331548\pi$
$757$	21029.9	1.00970	0.504850	+	0.863207i	$0.331548\pi$
$758$	5150.61	0.246806
$759$	−4198.76	−0.200798
$760$	760.000	0.0362738
$761$	25781.2	1.22808	0.614040	−	0.789275i	$-0.289543\pi$
$761$	25781.2	1.22808	0.614040	+	0.789275i	$0.289543\pi$
$762$	4194.50	0.199411
$763$	12913.2	0.612701
$764$	−7109.42	−0.336662
$765$	−18379.5	−0.868643
$766$	18015.6	0.849778
$767$	7393.85	0.348079
$768$	−203.344	−0.00955412
$769$	−26905.2	−1.26167	−0.630835	−	0.775917i	$-0.717288\pi$
$769$	−26905.2	−1.26167	−0.630835	+	0.775917i	$0.717288\pi$
$770$	12238.1	0.572769
$771$	−1697.63	−0.0792981
$772$	−8720.77	−0.406564
$773$	−10683.7	−0.497111	−0.248556	−	0.968618i	$-0.579956\pi$
$773$	−10683.7	−0.497111	−0.248556	+	0.968618i	$0.579956\pi$
$774$	11823.5	0.549078
$775$	−6869.36	−0.318393
$776$	−1520.68	−0.0703470
$777$	−858.266	−0.0396269
$778$	7433.72	0.342560
$779$	−1179.33	−0.0542411
$780$	−1165.24	−0.0534901
$781$	−18354.5	−0.840943
$782$	−27646.5	−1.26424
$783$	7235.98	0.330259
$784$	2944.89	0.134151
$785$	14637.8	0.665537
$786$	−573.343	−0.0260184
$787$	6017.52	0.272556	0.136278	−	0.990671i	$-0.456486\pi$
$787$	6017.52	0.272556	0.136278	+	0.990671i	$0.456486\pi$
$788$	−10404.5	−0.470362
$789$	−2381.21	−0.107444
$790$	−1308.21	−0.0589163
$791$	16224.6	0.729305
$792$	−11245.3	−0.504527
$793$	−39148.1	−1.75308
$794$	28384.5	1.26867
$795$	2190.02	0.0977008
$796$	1648.87	0.0734204
$797$	36703.4	1.63124	0.815621	−	0.578587i	$-0.196396\pi$
$797$	36703.4	1.63124	0.815621	+	0.578587i	$0.196396\pi$
$798$	−692.954	−0.0307397
$799$	52533.9	2.32605
$800$	800.000	0.0353553
$801$	18922.0	0.834677
$802$	−19472.2	−0.857341
$803$	28997.6	1.27435
$804$	−1042.04	−0.0457088
$805$	11382.5	0.498363
$806$	40308.8	1.76156
$807$	−2066.73	−0.0901516
$808$	−4664.71	−0.203099
$809$	3237.98	0.140718	0.0703592	−	0.997522i	$-0.477585\pi$
$809$	3237.98	0.140718	0.0703592	+	0.997522i	$0.477585\pi$
$810$	−6782.92	−0.294232
$811$	−25947.0	−1.12346	−0.561728	−	0.827322i	$-0.689863\pi$
$811$	−25947.0	−1.12346	−0.561728	+	0.827322i	$0.689863\pi$
$812$	−15674.9	−0.677438
$813$	608.748	0.0262604
$814$	−5017.86	−0.216064
$815$	4957.27	0.213062
$816$	1771.66	0.0760056
$817$	4259.66	0.182407
$818$	31693.9	1.35471
$819$	−44403.4	−1.89448
$820$	−1241.40	−0.0528677
$821$	11190.8	0.475713	0.237856	−	0.971300i	$-0.423555\pi$
$821$	11190.8	0.475713	0.237856	+	0.971300i	$0.423555\pi$
$822$	−79.1060	−0.00335662
$823$	14476.1	0.613129	0.306564	−	0.951850i	$-0.400821\pi$
$823$	14476.1	0.613129	0.306564	+	0.951850i	$0.400821\pi$
$824$	−14353.5	−0.606832
$825$	−1058.57	−0.0446724
$826$	4628.45	0.194969
$827$	−21055.8	−0.885349	−0.442674	−	0.896682i	$-0.645970\pi$
$827$	−21055.8	−0.885349	−0.442674	+	0.896682i	$0.645970\pi$
$828$	−10459.1	−0.438986
$829$	11156.5	0.467407	0.233704	−	0.972308i	$-0.424915\pi$
$829$	11156.5	0.467407	0.233704	+	0.972308i	$0.424915\pi$
$830$	−9445.39	−0.395005
$831$	4757.91	0.198616
$832$	−4694.33	−0.195609
$833$	−25657.7	−1.06721
$834$	−3520.58	−0.146172
$835$	18398.9	0.762540
$836$	−4051.36	−0.167607
$837$	−11648.2	−0.481028
$838$	−30208.4	−1.24527
$839$	−39171.2	−1.61185	−0.805923	−	0.592021i	$-0.798330\pi$
$839$	−39171.2	−1.61185	−0.805923	+	0.592021i	$0.798330\pi$
$840$	−729.425	−0.0299614
$841$	4747.05	0.194639
$842$	2635.44	0.107866
$843$	1145.77	0.0468118
$844$	−4494.18	−0.183289
$845$	−15915.3	−0.647931
$846$	19874.5	0.807682
$847$	−34681.7	−1.40694
$848$	8822.80	0.357283
$849$	2383.21	0.0963388
$850$	−6970.09	−0.281261
$851$	−4667.05	−0.187996
$852$	1093.98	0.0439895
$853$	−30337.0	−1.21773	−0.608863	−	0.793275i	$-0.708374\pi$
$853$	−30337.0	−1.21773	−0.608863	+	0.793275i	$0.708374\pi$
$854$	−24506.2	−0.981950
$855$	−2505.06	−0.100200
$856$	2068.80	0.0826055
$857$	22146.0	0.882724	0.441362	−	0.897329i	$-0.354496\pi$
$857$	22146.0	0.882724	0.441362	+	0.897329i	$0.354496\pi$
$858$	6211.59	0.247157
$859$	35168.0	1.39687	0.698437	−	0.715671i	$-0.253879\pi$
$859$	35168.0	1.39687	0.698437	+	0.715671i	$0.253879\pi$
$860$	4483.85	0.177788
$861$	1131.88	0.0448020
$862$	−32325.1	−1.27726
$863$	3982.75	0.157097	0.0785483	−	0.996910i	$-0.474972\pi$
$863$	3982.75	0.157097	0.0785483	+	0.996910i	$0.474972\pi$
$864$	1356.54	0.0534148
$865$	−10087.5	−0.396516
$866$	21103.0	0.828073
$867$	−11533.4	−0.451780
$868$	25232.7	0.986699
$869$	6973.70	0.272229
$870$	1355.84	0.0528359
$871$	−24056.1	−0.935831
$872$	−4499.84	−0.174752
$873$	5012.36	0.194322
$874$	−3768.12	−0.145834
$875$	2869.71	0.110873
$876$	−1728.33	−0.0666609
$877$	22118.0	0.851621	0.425810	−	0.904812i	$-0.359989\pi$
$877$	22118.0	0.851621	0.425810	+	0.904812i	$0.359989\pi$
$878$	−24078.4	−0.925522
$879$	−596.447	−0.0228870
$880$	−4264.59	−0.163363
$881$	44513.2	1.70225	0.851127	−	0.524959i	$-0.175919\pi$
$881$	44513.2	1.70225	0.851127	+	0.524959i	$0.175919\pi$
$882$	−9706.75	−0.370571
$883$	−14433.7	−0.550093	−0.275047	−	0.961431i	$-0.588693\pi$
$883$	−14433.7	−0.550093	−0.275047	+	0.961431i	$0.588693\pi$
$884$	40899.9	1.55612
$885$	−400.350	−0.0152063
$886$	8319.30	0.315454
$887$	19559.0	0.740392	0.370196	−	0.928954i	$-0.379291\pi$
$887$	19559.0	0.740392	0.370196	+	0.928954i	$0.379291\pi$
$888$	299.077	0.0113022
$889$	60615.9	2.28683
$890$	7175.84	0.270264
$891$	36158.0	1.35953
$892$	24265.8	0.910852
$893$	7160.19	0.268317
$894$	5371.78	0.200961
$895$	15227.7	0.568723
$896$	−2938.58	−0.109566
$897$	5777.33	0.215049
$898$	29655.3	1.10201
$899$	−46902.0	−1.74001
$900$	−2636.91	−0.0976632
$901$	−76869.7	−2.84229
$902$	6617.57	0.244280
$903$	−4088.29	−0.150664
$904$	−5653.74	−0.208009
$905$	−11870.2	−0.435999
$906$	1038.93	0.0380974
$907$	−23674.9	−0.866715	−0.433358	−	0.901222i	$-0.642671\pi$
$907$	−23674.9	−0.866715	−0.433358	+	0.901222i	$0.642671\pi$
$908$	11977.4	0.437759
$909$	15375.5	0.561026
$910$	−16839.2	−0.613422
$911$	−6452.53	−0.234667	−0.117334	−	0.993093i	$-0.537435\pi$
$911$	−6452.53	−0.234667	−0.117334	+	0.993093i	$0.537435\pi$
$912$	241.472	0.00876746
$913$	50350.9	1.82516
$914$	29944.4	1.08367
$915$	2119.73	0.0765859
$916$	−6042.51	−0.217959
$917$	−8285.54	−0.298378
$918$	−11819.0	−0.424929
$919$	−5928.94	−0.212816	−0.106408	−	0.994323i	$-0.533935\pi$
$919$	−5928.94	−0.212816	−0.106408	+	0.994323i	$0.533935\pi$
$920$	−3966.44	−0.142141
$921$	269.725	0.00965010
$922$	−13528.6	−0.483231
$923$	25255.1	0.900631
$924$	3888.37	0.138440
$925$	−1176.63	−0.0418243
$926$	−24184.8	−0.858273
$927$	47311.2	1.67627
$928$	5462.17	0.193216
$929$	39057.4	1.37937	0.689684	−	0.724111i	$-0.257750\pi$
$929$	39057.4	1.37937	0.689684	+	0.724111i	$0.257750\pi$
$930$	−2182.57	−0.0769563
$931$	−3497.06	−0.123106
$932$	−23223.8	−0.816223
$933$	−7339.14	−0.257527
$934$	6873.44	0.240799
$935$	37155.7	1.29960
$936$	15473.1	0.540336
$937$	11163.3	0.389208	0.194604	−	0.980882i	$-0.437658\pi$
$937$	11163.3	0.389208	0.194604	+	0.980882i	$0.437658\pi$
$938$	−15058.8	−0.524186
$939$	566.485	0.0196875
$940$	7537.04	0.261523
$941$	7071.91	0.244992	0.122496	−	0.992469i	$-0.460910\pi$
$941$	7071.91	0.244992	0.122496	+	0.992469i	$0.460910\pi$
$942$	4650.82	0.160862
$943$	6154.92	0.212547
$944$	−1612.86	−0.0556083
$945$	4866.09	0.167507
$946$	−23902.2	−0.821488
$947$	11977.8	0.411010	0.205505	−	0.978656i	$-0.434116\pi$
$947$	11977.8	0.411010	0.205505	+	0.978656i	$0.434116\pi$
$948$	−415.651	−0.0142402
$949$	−39899.6	−1.36480
$950$	−950.000	−0.0324443
$951$	−909.854	−0.0310242
$952$	25602.8	0.871629
$953$	10362.5	0.352228	0.176114	−	0.984370i	$-0.443647\pi$
$953$	10362.5	0.352228	0.176114	+	0.984370i	$0.443647\pi$
$954$	−29081.1	−0.986935
$955$	8886.77	0.301120
$956$	−2888.09	−0.0977066
$957$	−7227.62	−0.244133
$958$	27498.3	0.927378
$959$	−1143.18	−0.0384935
$960$	254.181	0.00854546
$961$	45709.9	1.53435
$962$	6904.37	0.231399
$963$	−6819.05	−0.228184
$964$	23086.3	0.771327
$965$	10901.0	0.363642
$966$	3616.53	0.120455
$967$	−47698.3	−1.58622	−0.793110	−	0.609079i	$-0.791539\pi$
$967$	−47698.3	−1.58622	−0.793110	+	0.609079i	$0.791539\pi$
$968$	12085.4	0.401281
$969$	−2103.85	−0.0697476
$970$	1900.85	0.0629202
$971$	1174.76	0.0388259	0.0194130	−	0.999812i	$-0.493820\pi$
$971$	1174.76	0.0388259	0.0194130	+	0.999812i	$0.493820\pi$
$972$	−6733.43	−0.222196
$973$	−50876.8	−1.67630
$974$	12531.1	0.412242
$975$	1456.55	0.0478430
$976$	8539.61	0.280068
$977$	58282.8	1.90853	0.954264	−	0.298964i	$-0.0966411\pi$
$977$	58282.8	1.90853	0.954264	+	0.298964i	$0.0966411\pi$
$978$	1575.05	0.0514976
$979$	−38252.5	−1.24878
$980$	−3681.11	−0.119989
$981$	14832.1	0.482723
$982$	−368.310	−0.0119687
$983$	49969.4	1.62134	0.810669	−	0.585504i	$-0.199103\pi$
$983$	49969.4	1.62134	0.810669	+	0.585504i	$0.199103\pi$
$984$	−394.424	−0.0127782
$985$	13005.6	0.420705
$986$	−47589.8	−1.53709
$987$	−6872.14	−0.221624
$988$	5574.51	0.179503
$989$	−22231.2	−0.714772
$990$	14056.7	0.451263
$991$	−3449.31	−0.110566	−0.0552830	−	0.998471i	$-0.517606\pi$
$991$	−3449.31	−0.110566	−0.0552830	+	0.998471i	$0.517606\pi$
$992$	−8792.78	−0.281422
$993$	818.207	0.0261481
$994$	15809.4	0.504469
$995$	−2061.09	−0.0656692
$996$	−3001.04	−0.0954736
$997$	−49274.3	−1.56523	−0.782614	−	0.622508i	$-0.786114\pi$
$997$	−49274.3	−1.56523	−0.782614	+	0.622508i	$0.786114\pi$
$998$	1340.97	0.0425329
$999$	−1995.18	−0.0631880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.4.a.h.1.2	✓	3
3.2	odd	2		1710.4.a.x.1.1		3
4.3	odd	2		1520.4.a.p.1.2		3
5.2	odd	4		950.4.b.j.799.5		6
5.3	odd	4		950.4.b.j.799.2		6
5.4	even	2		950.4.a.m.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.4.a.h.1.2	✓	3	1.1	even	1	trivial
950.4.a.m.1.2		3	5.4	even	2
950.4.b.j.799.2		6	5.3	odd	4
950.4.b.j.799.5		6	5.2	odd	4
1520.4.a.p.1.2		3	4.3	odd	2
1710.4.a.x.1.1		3	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	190.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -0.794314 q^{3} +4.00000 q^{4} -5.00000 q^{5} -1.58863 q^{6} -22.9577 q^{7} +8.00000 q^{8} -26.3691 q^{9} -10.0000 q^{10} +53.3074 q^{11} -3.17726 q^{12} -73.3488 q^{13} -45.9154 q^{14} +3.97157 q^{15} +16.0000 q^{16} -139.402 q^{17} -52.7381 q^{18} -19.0000 q^{19} -20.0000 q^{20} +18.2356 q^{21} +106.615 q^{22} +99.1611 q^{23} -6.35452 q^{24} +25.0000 q^{25} -146.698 q^{26} +42.3918 q^{27} -91.8308 q^{28} +170.693 q^{29} +7.94314 q^{30} -274.774 q^{31} +32.0000 q^{32} -42.3428 q^{33} -278.804 q^{34} +114.788 q^{35} -105.476 q^{36} -47.0653 q^{37} -38.0000 q^{38} +58.2620 q^{39} -40.0000 q^{40} +62.0699 q^{41} +36.4713 q^{42} -224.192 q^{43} +213.230 q^{44} +131.845 q^{45} +198.322 q^{46} -376.852 q^{47} -12.7090 q^{48} +184.056 q^{49} +50.0000 q^{50} +110.729 q^{51} -293.395 q^{52} +551.425 q^{53} +84.7836 q^{54} -266.537 q^{55} -183.662 q^{56} +15.0920 q^{57} +341.386 q^{58} -100.804 q^{59} +15.8863 q^{60} +533.726 q^{61} -549.549 q^{62} +605.373 q^{63} +64.0000 q^{64} +366.744 q^{65} -84.6856 q^{66} +327.968 q^{67} -557.608 q^{68} -78.7651 q^{69} +229.577 q^{70} -344.315 q^{71} -210.953 q^{72} +543.970 q^{73} -94.1306 q^{74} -19.8579 q^{75} -76.0000 q^{76} -1223.81 q^{77} +116.524 q^{78} +130.821 q^{79} -80.0000 q^{80} +678.292 q^{81} +124.140 q^{82} +944.539 q^{83} +72.9425 q^{84} +697.009 q^{85} -448.385 q^{86} -135.584 q^{87} +426.459 q^{88} -717.584 q^{89} +263.691 q^{90} +1683.92 q^{91} +396.644 q^{92} +218.257 q^{93} -753.704 q^{94} +95.0000 q^{95} -25.4181 q^{96} -190.085 q^{97} +368.111 q^{98} -1405.67 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} - 9 q^{3} + 12 q^{4} - 15 q^{5} - 18 q^{6} - 11 q^{7} + 24 q^{8} - 8 q^{9} - 30 q^{10} - 68 q^{11} - 36 q^{12} - 121 q^{13} - 22 q^{14} + 45 q^{15} + 48 q^{16} - 103 q^{17} - 16 q^{18} - 57 q^{19}+ \cdots - 2164 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 - 9 * q^3 + 12 * q^4 - 15 * q^5 - 18 * q^6 - 11 * q^7 + 24 * q^8 - 8 * q^9 - 30 * q^10 - 68 * q^11 - 36 * q^12 - 121 * q^13 - 22 * q^14 + 45 * q^15 + 48 * q^16 - 103 * q^17 - 16 * q^18 - 57 * q^19 - 60 * q^20 - 271 * q^21 - 136 * q^22 - 203 * q^23 - 72 * q^24 + 75 * q^25 - 242 * q^26 - 129 * q^27 - 44 * q^28 + 91 * q^29 + 90 * q^30 - 154 * q^31 + 96 * q^32 + 412 * q^33 - 206 * q^34 + 55 * q^35 - 32 * q^36 - 304 * q^37 - 114 * q^38 + 461 * q^39 - 120 * q^40 + 282 * q^41 - 542 * q^42 - 214 * q^43 - 272 * q^44 + 40 * q^45 - 406 * q^46 - 1144 * q^47 - 144 * q^48 + 1060 * q^49 + 150 * q^50 + 969 * q^51 - 484 * q^52 + 795 * q^53 - 258 * q^54 + 340 * q^55 - 88 * q^56 + 171 * q^57 + 182 * q^58 - 609 * q^59 + 180 * q^60 + 792 * q^61 - 308 * q^62 + 2686 * q^63 + 192 * q^64 + 605 * q^65 + 824 * q^66 - 865 * q^67 - 412 * q^68 + 1237 * q^69 + 110 * q^70 - 312 * q^71 - 64 * q^72 + 79 * q^73 - 608 * q^74 - 225 * q^75 - 228 * q^76 - 1680 * q^77 + 922 * q^78 + 1806 * q^79 - 240 * q^80 + 1499 * q^81 + 564 * q^82 - 34 * q^83 - 1084 * q^84 + 515 * q^85 - 428 * q^86 - 197 * q^87 - 544 * q^88 - 1010 * q^89 + 80 * q^90 + 113 * q^91 - 812 * q^92 + 718 * q^93 - 2288 * q^94 + 285 * q^95 - 288 * q^96 - 1120 * q^97 + 2120 * q^98 - 2164 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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