LMFDB - Embedded newform 1859.4.a.h.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1859,4,Mod(1,1859)] 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("1859.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1859, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment:select newform

sage:traces = [17,0,-6,50,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$3.12700$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.12700 q^{2} -0.537604 q^{3} +1.77811 q^{4} +0.516265 q^{5} -1.68109 q^{6} +34.6419 q^{7} -19.4558 q^{8} -26.7110 q^{9} +1.61436 q^{10} -11.0000 q^{11} -0.955919 q^{12} +108.325 q^{14} -0.277546 q^{15} -75.0632 q^{16} +114.143 q^{17} -83.5252 q^{18} +122.906 q^{19} +0.917976 q^{20} -18.6236 q^{21} -34.3970 q^{22} -66.8837 q^{23} +10.4595 q^{24} -124.733 q^{25} +28.8752 q^{27} +61.5971 q^{28} +64.6641 q^{29} -0.867886 q^{30} -238.455 q^{31} -79.0758 q^{32} +5.91364 q^{33} +356.926 q^{34} +17.8844 q^{35} -47.4951 q^{36} -28.3793 q^{37} +384.328 q^{38} -10.0444 q^{40} +308.251 q^{41} -58.2360 q^{42} +246.199 q^{43} -19.5592 q^{44} -13.7899 q^{45} -209.145 q^{46} +165.153 q^{47} +40.3543 q^{48} +857.062 q^{49} -390.041 q^{50} -61.3639 q^{51} +79.9222 q^{53} +90.2927 q^{54} -5.67892 q^{55} -673.987 q^{56} -66.0749 q^{57} +202.205 q^{58} -267.584 q^{59} -0.493508 q^{60} +351.586 q^{61} -745.650 q^{62} -925.319 q^{63} +353.236 q^{64} +18.4919 q^{66} -615.576 q^{67} +202.960 q^{68} +35.9569 q^{69} +55.9245 q^{70} -470.973 q^{71} +519.684 q^{72} +65.0008 q^{73} -88.7419 q^{74} +67.0572 q^{75} +218.541 q^{76} -381.061 q^{77} +982.163 q^{79} -38.7525 q^{80} +705.673 q^{81} +963.899 q^{82} +1032.15 q^{83} -33.1149 q^{84} +58.9283 q^{85} +769.864 q^{86} -34.7637 q^{87} +214.014 q^{88} +1315.55 q^{89} -43.1211 q^{90} -118.927 q^{92} +128.195 q^{93} +516.434 q^{94} +63.4522 q^{95} +42.5114 q^{96} -448.542 q^{97} +2680.03 q^{98} +293.821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} + 24 q^{5} - 16 q^{6} + 62 q^{7} + 21 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 127 q^{12} + 148 q^{15} + 126 q^{16} - 74 q^{17} - 90 q^{18} + 159 q^{19} + 222 q^{20} + 184 q^{21}+ \cdots - 1485 q^{99}+O(q^{100}) $ 17 * q - 6 * q^3 + 50 * q^4 + 24 * q^5 - 16 * q^6 + 62 * q^7 + 21 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 127 * q^12 + 148 * q^15 + 126 * q^16 - 74 * q^17 - 90 * q^18 + 159 * q^19 + 222 * q^20 + 184 * q^21 - 215 * q^23 - 214 * q^24 + 95 * q^25 - 192 * q^27 + 358 * q^28 - 157 * q^29 + 829 * q^30 + 394 * q^31 + 553 * q^32 + 66 * q^33 + 702 * q^34 + 58 * q^35 - 700 * q^36 - 88 * q^37 - 1318 * q^38 + 733 * q^40 + 512 * q^41 + 337 * q^42 + 927 * q^43 - 550 * q^44 + 1482 * q^45 + 1361 * q^46 + 143 * q^47 - 178 * q^48 + 1835 * q^49 + 583 * q^50 - 568 * q^51 + 106 * q^53 + 67 * q^54 - 264 * q^55 + 2059 * q^56 - 1298 * q^57 + 1690 * q^58 + 266 * q^59 - 37 * q^60 - 624 * q^61 + 643 * q^62 + 2360 * q^63 - 1589 * q^64 + 176 * q^66 + 676 * q^67 - 413 * q^68 + 764 * q^69 + 1061 * q^70 + 763 * q^71 + 1366 * q^72 + 2374 * q^73 - 1649 * q^74 + 2420 * q^75 + 2101 * q^76 - 682 * q^77 + 2164 * q^79 + 1013 * q^80 + 537 * q^81 + 3152 * q^82 - 777 * q^83 + 3381 * q^84 + 1690 * q^85 - 2894 * q^86 - 4200 * q^87 - 231 * q^88 + 1687 * q^89 - 5399 * q^90 + 5542 * q^92 + 4310 * q^93 + 1777 * q^94 + 1124 * q^95 + 3465 * q^96 + 2047 * q^97 - 1553 * q^98 - 1485 * 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 $

$2$	3.12700	1.10556	0.552780	−	0.833327i	$-0.313567\pi$
$2$	3.12700	1.10556	0.552780	+	0.833327i	$0.313567\pi$
$3$	−0.537604	−0.103462	−0.0517309	−	0.998661i	$-0.516474\pi$
$3$	−0.537604	−0.103462	−0.0517309	+	0.998661i	$0.516474\pi$
$4$	1.77811	0.222264
$5$	0.516265	0.0461761	0.0230881	−	0.999733i	$-0.492650\pi$
$5$	0.516265	0.0461761	0.0230881	+	0.999733i	$0.492650\pi$
$6$	−1.68109	−0.114383
$7$	34.6419	1.87049	0.935244	−	0.354005i	$-0.115180\pi$
$7$	34.6419	1.87049	0.935244	+	0.354005i	$0.115180\pi$
$8$	−19.4558	−0.859834
$9$	−26.7110	−0.989296
$10$	1.61436	0.0510505
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−0.955919	−0.0229958
$13$	0	0
$13$	0	0
$14$	108.325	2.06794
$15$	−0.277546	−0.00477747
$16$	−75.0632	−1.17286
$17$	114.143	1.62846	0.814231	−	0.580541i	$-0.197159\pi$
$17$	114.143	1.62846	0.814231	+	0.580541i	$0.197159\pi$
$18$	−83.5252	−1.09373
$19$	122.906	1.48403	0.742017	−	0.670382i	$-0.233870\pi$
$19$	122.906	1.48403	0.742017	+	0.670382i	$0.233870\pi$
$20$	0.917976	0.0102633
$21$	−18.6236	−0.193524
$22$	−34.3970	−0.333339
$23$	−66.8837	−0.606357	−0.303179	−	0.952934i	$-0.598048\pi$
$23$	−66.8837	−0.606357	−0.303179	+	0.952934i	$0.598048\pi$
$24$	10.4595	0.0889601
$25$	−124.733	−0.997868
$26$	0	0
$27$	28.8752	0.205816
$28$	61.5971	0.415742
$29$	64.6641	0.414063	0.207031	−	0.978334i	$-0.433620\pi$
$29$	64.6641	0.414063	0.207031	+	0.978334i	$0.433620\pi$
$30$	−0.867886	−0.00528178
$31$	−238.455	−1.38154	−0.690772	−	0.723073i	$-0.742729\pi$
$31$	−238.455	−1.38154	−0.690772	+	0.723073i	$0.742729\pi$
$32$	−79.0758	−0.436836
$33$	5.91364	0.0311949
$34$	356.926	1.80036
$35$	17.8844	0.0863719
$36$	−47.4951	−0.219885
$37$	−28.3793	−0.126095	−0.0630476	−	0.998011i	$-0.520082\pi$
$37$	−28.3793	−0.126095	−0.0630476	+	0.998011i	$0.520082\pi$
$38$	384.328	1.64069
$39$	0	0
$40$	−10.0444	−0.0397038
$41$	308.251	1.17416	0.587082	−	0.809528i	$-0.300277\pi$
$41$	308.251	1.17416	0.587082	+	0.809528i	$0.300277\pi$
$42$	−58.2360	−0.213953
$43$	246.199	0.873140	0.436570	−	0.899670i	$-0.356193\pi$
$43$	246.199	0.873140	0.436570	+	0.899670i	$0.356193\pi$
$44$	−19.5592	−0.0670151
$45$	−13.7899	−0.0456819
$46$	−209.145	−0.670365
$47$	165.153	0.512555	0.256277	−	0.966603i	$-0.417504\pi$
$47$	165.153	0.512555	0.256277	+	0.966603i	$0.417504\pi$
$48$	40.3543	0.121347
$49$	857.062	2.49872
$50$	−390.041	−1.10320
$51$	−61.3639	−0.168484
$52$	0	0
$53$	79.9222	0.207135	0.103568	−	0.994622i	$-0.466974\pi$
$53$	79.9222	0.207135	0.103568	+	0.994622i	$0.466974\pi$
$54$	90.2927	0.227542
$55$	−5.67892	−0.0139226
$56$	−673.987	−1.60831
$57$	−66.0749	−0.153541
$58$	202.205	0.457772
$59$	−267.584	−0.590448	−0.295224	−	0.955428i	$-0.595394\pi$
$59$	−267.584	−0.590448	−0.295224	+	0.955428i	$0.595394\pi$
$60$	−0.493508	−0.00106186
$61$	351.586	0.737966	0.368983	−	0.929436i	$-0.379706\pi$
$61$	351.586	0.737966	0.368983	+	0.929436i	$0.379706\pi$
$62$	−745.650	−1.52738
$63$	−925.319	−1.85046
$64$	353.236	0.689914
$65$	0	0
$66$	18.4919	0.0344879
$67$	−615.576	−1.12246	−0.561228	−	0.827661i	$-0.689671\pi$
$67$	−615.576	−1.12246	−0.561228	+	0.827661i	$0.689671\pi$
$68$	202.960	0.361948
$69$	35.9569	0.0627349
$70$	55.9245	0.0954893
$71$	−470.973	−0.787243	−0.393621	−	0.919273i	$-0.628778\pi$
$71$	−470.973	−0.787243	−0.393621	+	0.919273i	$0.628778\pi$
$72$	519.684	0.850630
$73$	65.0008	0.104216	0.0521080	−	0.998641i	$-0.483406\pi$
$73$	65.0008	0.104216	0.0521080	+	0.998641i	$0.483406\pi$
$74$	−88.7419	−0.139406
$75$	67.0572	0.103241
$76$	218.541	0.329847
$77$	−381.061	−0.563973
$78$	0	0
$79$	982.163	1.39876	0.699380	−	0.714750i	$-0.253460\pi$
$79$	982.163	1.39876	0.699380	+	0.714750i	$0.253460\pi$
$80$	−38.7525	−0.0541583
$81$	705.673	0.968002
$82$	963.899	1.29811
$83$	1032.15	1.36498	0.682489	−	0.730896i	$-0.260897\pi$
$83$	1032.15	1.36498	0.682489	+	0.730896i	$0.260897\pi$
$84$	−33.1149	−0.0430134
$85$	58.9283	0.0751961
$86$	769.864	0.965309
$87$	−34.7637	−0.0428397
$88$	214.014	0.259250
$89$	1315.55	1.56683	0.783417	−	0.621497i	$-0.213475\pi$
$89$	1315.55	1.56683	0.783417	+	0.621497i	$0.213475\pi$
$90$	−43.1211	−0.0505041
$91$	0	0
$92$	−118.927	−0.134771
$93$	128.195	0.142937
$94$	516.434	0.566660
$95$	63.4522	0.0685269
$96$	42.5114	0.0451959
$97$	−448.542	−0.469510	−0.234755	−	0.972055i	$-0.575429\pi$
$97$	−448.542	−0.469510	−0.234755	+	0.972055i	$0.575429\pi$
$98$	2680.03	2.76249
$99$	293.821	0.298284
$100$	−221.790	−0.221790
$101$	135.044	0.133043	0.0665215	−	0.997785i	$-0.478810\pi$
$101$	135.044	0.133043	0.0665215	+	0.997785i	$0.478810\pi$
$102$	−191.885	−0.186269
$103$	−1497.31	−1.43238	−0.716188	−	0.697907i	$-0.754115\pi$
$103$	−1497.31	−1.43238	−0.716188	+	0.697907i	$0.754115\pi$
$104$	0	0
$105$	−9.61472	−0.00893620
$106$	249.917	0.229000
$107$	553.293	0.499895	0.249948	−	0.968259i	$-0.419587\pi$
$107$	553.293	0.499895	0.249948	+	0.968259i	$0.419587\pi$
$108$	51.3433	0.0457455
$109$	110.399	0.0970116	0.0485058	−	0.998823i	$-0.484554\pi$
$109$	110.399	0.0970116	0.0485058	+	0.998823i	$0.484554\pi$
$110$	−17.7580	−0.0153923
$111$	15.2568	0.0130461
$112$	−2600.33	−2.19382
$113$	1318.93	1.09801	0.549003	−	0.835820i	$-0.315007\pi$
$113$	1318.93	1.09801	0.549003	+	0.835820i	$0.315007\pi$
$114$	−206.616	−0.169749
$115$	−34.5297	−0.0279992
$116$	114.980	0.0920312
$117$	0	0
$118$	−836.734	−0.652776
$119$	3954.15	3.04602
$120$	5.39989	0.00410783
$121$	121.000	0.0909091
$122$	1099.41	0.815866
$123$	−165.717	−0.121481
$124$	−424.000	−0.307067
$125$	−128.929	−0.0922538
$126$	−2893.47	−2.04580
$127$	−431.583	−0.301550	−0.150775	−	0.988568i	$-0.548177\pi$
$127$	−431.583	−0.301550	−0.150775	+	0.988568i	$0.548177\pi$
$128$	1737.17	1.19958
$129$	−132.358	−0.0903367
$130$	0	0
$131$	2721.05	1.81480	0.907400	−	0.420268i	$-0.138064\pi$
$131$	2721.05	1.81480	0.907400	+	0.420268i	$0.138064\pi$
$132$	10.5151	0.00693351
$133$	4257.71	2.77586
$134$	−1924.90	−1.24094
$135$	14.9073	0.00950380
$136$	−2220.76	−1.40021
$137$	164.939	0.102859	0.0514294	−	0.998677i	$-0.483622\pi$
$137$	164.939	0.102859	0.0514294	+	0.998677i	$0.483622\pi$
$138$	112.437	0.0693572
$139$	−374.908	−0.228772	−0.114386	−	0.993436i	$-0.536490\pi$
$139$	−374.908	−0.228772	−0.114386	+	0.993436i	$0.536490\pi$
$140$	31.8005	0.0191973
$141$	−88.7870	−0.0530299
$142$	−1472.73	−0.870345
$143$	0	0
$144$	2005.01	1.16031
$145$	33.3838	0.0191198
$146$	203.257	0.115217
$147$	−460.759	−0.258522
$148$	−50.4615	−0.0280264
$149$	774.264	0.425706	0.212853	−	0.977084i	$-0.431724\pi$
$149$	774.264	0.425706	0.212853	+	0.977084i	$0.431724\pi$
$150$	209.688	0.114139
$151$	1331.32	0.717491	0.358746	−	0.933435i	$-0.383205\pi$
$151$	1331.32	0.717491	0.358746	+	0.933435i	$0.383205\pi$
$152$	−2391.24	−1.27602
$153$	−3048.88	−1.61103
$154$	−1191.58	−0.623506
$155$	−123.106	−0.0637944
$156$	0	0
$157$	2022.51	1.02811	0.514057	−	0.857756i	$-0.328142\pi$
$157$	2022.51	1.02811	0.514057	+	0.857756i	$0.328142\pi$
$158$	3071.22	1.54641
$159$	−42.9665	−0.0214306
$160$	−40.8241	−0.0201714
$161$	−2316.98	−1.13418
$162$	2206.64	1.07018
$163$	−2759.81	−1.32616	−0.663082	−	0.748546i	$-0.730752\pi$
$163$	−2759.81	−1.32616	−0.663082	+	0.748546i	$0.730752\pi$
$164$	548.104	0.260974
$165$	3.05301	0.00144046
$166$	3227.53	1.50907
$167$	−442.781	−0.205170	−0.102585	−	0.994724i	$-0.532711\pi$
$167$	−442.781	−0.205170	−0.102585	+	0.994724i	$0.532711\pi$
$168$	362.338	0.166399
$169$	0	0
$170$	184.269	0.0831338
$171$	−3282.95	−1.46815
$172$	437.770	0.194068
$173$	−3165.97	−1.39135	−0.695677	−	0.718354i	$-0.744896\pi$
$173$	−3165.97	−1.39135	−0.695677	+	0.718354i	$0.744896\pi$
$174$	−108.706	−0.0473619
$175$	−4321.01	−1.86650
$176$	825.695	0.353631
$177$	143.854	0.0610889
$178$	4113.73	1.73223
$179$	1984.97	0.828849	0.414424	−	0.910084i	$-0.363983\pi$
$179$	1984.97	0.828849	0.414424	+	0.910084i	$0.363983\pi$
$180$	−24.5201	−0.0101534
$181$	−765.845	−0.314502	−0.157251	−	0.987559i	$-0.550263\pi$
$181$	−765.845	−0.314502	−0.157251	+	0.987559i	$0.550263\pi$
$182$	0	0
$183$	−189.014	−0.0763513
$184$	1301.28	0.521367
$185$	−14.6512	−0.00582259
$186$	400.864	0.158026
$187$	−1255.58	−0.491000
$188$	293.661	0.113922
$189$	1000.29	0.384977
$190$	198.415	0.0757607
$191$	3877.18	1.46881	0.734406	−	0.678710i	$-0.237461\pi$
$191$	3877.18	1.46881	0.734406	+	0.678710i	$0.237461\pi$
$192$	−189.901	−0.0713798
$193$	1012.82	0.377745	0.188872	−	0.982002i	$-0.439517\pi$
$193$	1012.82	0.377745	0.188872	+	0.982002i	$0.439517\pi$
$194$	−1402.59	−0.519072
$195$	0	0
$196$	1523.95	0.555376
$197$	−2328.30	−0.842054	−0.421027	−	0.907048i	$-0.638330\pi$
$197$	−2328.30	−0.842054	−0.421027	+	0.907048i	$0.638330\pi$
$198$	918.777	0.329771
$199$	2807.36	1.00004	0.500022	−	0.866013i	$-0.333325\pi$
$199$	2807.36	1.00004	0.500022	+	0.866013i	$0.333325\pi$
$200$	2426.79	0.858001
$201$	330.936	0.116131
$202$	422.281	0.147087
$203$	2240.09	0.774499
$204$	−109.112	−0.0374478
$205$	159.139	0.0542183
$206$	−4682.10	−1.58358
$207$	1786.53	0.599867
$208$	0	0
$209$	−1351.97	−0.447453
$210$	−30.0652	−0.00987951
$211$	2050.64	0.669062	0.334531	−	0.942385i	$-0.391422\pi$
$211$	2050.64	0.669062	0.334531	+	0.942385i	$0.391422\pi$
$212$	142.111	0.0460387
$213$	253.197	0.0814496
$214$	1730.14	0.552665
$215$	127.104	0.0403183
$216$	−561.791	−0.176968
$217$	−8260.55	−2.58416
$218$	345.216	0.107252
$219$	−34.9447	−0.0107824
$220$	−10.0977	−0.00309450
$221$	0	0
$222$	47.7080	0.0144232
$223$	5976.81	1.79478	0.897392	−	0.441234i	$-0.145459\pi$
$223$	5976.81	1.79478	0.897392	+	0.441234i	$0.145459\pi$
$224$	−2739.34	−0.817096
$225$	3331.75	0.987186
$226$	4124.30	1.21391
$227$	2086.97	0.610207	0.305104	−	0.952319i	$-0.401309\pi$
$227$	2086.97	0.610207	0.305104	+	0.952319i	$0.401309\pi$
$228$	−117.488	−0.0341266
$229$	3653.93	1.05440	0.527202	−	0.849740i	$-0.323241\pi$
$229$	3653.93	1.05440	0.527202	+	0.849740i	$0.323241\pi$
$230$	−107.974	−0.0309549
$231$	204.860	0.0583497
$232$	−1258.09	−0.356026
$233$	−558.289	−0.156973	−0.0784866	−	0.996915i	$-0.525009\pi$
$233$	−558.289	−0.156973	−0.0784866	+	0.996915i	$0.525009\pi$
$234$	0	0
$235$	85.2628	0.0236678
$236$	−475.794	−0.131235
$237$	−528.015	−0.144718
$238$	12364.6	3.36756
$239$	−2105.54	−0.569857	−0.284929	−	0.958549i	$-0.591970\pi$
$239$	−2105.54	−0.569857	−0.284929	+	0.958549i	$0.591970\pi$
$240$	20.8335	0.00560332
$241$	5423.33	1.44957	0.724787	−	0.688973i	$-0.241938\pi$
$241$	5423.33	1.44957	0.724787	+	0.688973i	$0.241938\pi$
$242$	378.367	0.100505
$243$	−1159.00	−0.305968
$244$	625.158	0.164023
$245$	442.471	0.115381
$246$	−518.196	−0.134305
$247$	0	0
$248$	4639.35	1.18790
$249$	−554.888	−0.141223
$250$	−403.160	−0.101992
$251$	−7030.87	−1.76807	−0.884033	−	0.467424i	$-0.845182\pi$
$251$	−7030.87	−1.76807	−0.884033	+	0.467424i	$0.845182\pi$
$252$	−1645.32	−0.411291
$253$	735.721	0.182824
$254$	−1349.56	−0.333382
$255$	−31.6801	−0.00777993
$256$	2606.25	0.636292
$257$	−6109.03	−1.48276	−0.741382	−	0.671083i	$-0.765829\pi$
$257$	−6109.03	−1.48276	−0.741382	+	0.671083i	$0.765829\pi$
$258$	−413.882	−0.0998727
$259$	−983.112	−0.235860
$260$	0	0
$261$	−1727.24	−0.409631
$262$	8508.70	2.00637
$263$	5612.35	1.31587	0.657933	−	0.753077i	$-0.271431\pi$
$263$	5612.35	1.31587	0.657933	+	0.753077i	$0.271431\pi$
$264$	−115.055	−0.0268225
$265$	41.2611	0.00956470
$266$	13313.8	3.06889
$267$	−707.246	−0.162108
$268$	−1094.56	−0.249481
$269$	−5299.19	−1.20111	−0.600553	−	0.799585i	$-0.705053\pi$
$269$	−5299.19	−1.20111	−0.600553	+	0.799585i	$0.705053\pi$
$270$	46.6150	0.0105070
$271$	2702.76	0.605834	0.302917	−	0.953017i	$-0.402039\pi$
$271$	2702.76	0.605834	0.302917	+	0.953017i	$0.402039\pi$
$272$	−8567.97	−1.90996
$273$	0	0
$274$	515.762	0.113717
$275$	1372.07	0.300868
$276$	63.9354	0.0139437
$277$	268.441	0.0582276	0.0291138	−	0.999576i	$-0.490731\pi$
$277$	268.441	0.0582276	0.0291138	+	0.999576i	$0.490731\pi$
$278$	−1172.34	−0.252921
$279$	6369.38	1.36676
$280$	−347.956	−0.0742655
$281$	−6782.10	−1.43981	−0.719904	−	0.694073i	$-0.755814\pi$
$281$	−6782.10	−1.43981	−0.719904	+	0.694073i	$0.755814\pi$
$282$	−277.637	−0.0586277
$283$	3606.17	0.757473	0.378736	−	0.925505i	$-0.376359\pi$
$283$	3606.17	0.757473	0.378736	+	0.925505i	$0.376359\pi$
$284$	−837.443	−0.174976
$285$	−34.1121	−0.00708993
$286$	0	0
$287$	10678.4	2.19626
$288$	2112.19	0.432160
$289$	8115.72	1.65189
$290$	104.391	0.0211381
$291$	241.138	0.0485764
$292$	115.579	0.0231634
$293$	629.575	0.125530	0.0627648	−	0.998028i	$-0.480008\pi$
$293$	629.575	0.125530	0.0627648	+	0.998028i	$0.480008\pi$
$294$	−1440.79	−0.285812
$295$	−138.144	−0.0272646
$296$	552.142	0.108421
$297$	−317.627	−0.0620559
$298$	2421.12	0.470644
$299$	0	0
$300$	119.235	0.0229468
$301$	8528.81	1.63320
$302$	4163.03	0.793230
$303$	−72.5999	−0.0137649
$304$	−9225.74	−1.74057
$305$	181.511	0.0340764
$306$	−9533.85	−1.78109
$307$	−6511.32	−1.21049	−0.605246	−	0.796039i	$-0.706925\pi$
$307$	−6511.32	−1.21049	−0.605246	+	0.796039i	$0.706925\pi$
$308$	−677.569	−0.125351
$309$	804.962	0.148196
$310$	−384.953	−0.0705285
$311$	566.158	0.103228	0.0516140	−	0.998667i	$-0.483563\pi$
$311$	566.158	0.103228	0.0516140	+	0.998667i	$0.483563\pi$
$312$	0	0
$313$	−8279.52	−1.49516	−0.747581	−	0.664170i	$-0.768785\pi$
$313$	−8279.52	−1.49516	−0.747581	+	0.664170i	$0.768785\pi$
$314$	6324.38	1.13664
$315$	−477.710	−0.0854473
$316$	1746.40	0.310894
$317$	7529.92	1.33414	0.667070	−	0.744995i	$-0.267548\pi$
$317$	7529.92	1.33414	0.667070	+	0.744995i	$0.267548\pi$
$318$	−134.356	−0.0236928
$319$	−711.305	−0.124845
$320$	182.363	0.0318576
$321$	−297.452	−0.0517201
$322$	−7245.19	−1.25391
$323$	14028.9	2.41669
$324$	1254.77	0.215152
$325$	0	0
$326$	−8629.91	−1.46616
$327$	−59.3507	−0.0100370
$328$	−5997.27	−1.00959
$329$	5721.22	0.958727
$330$	9.54674	0.00159252
$331$	4350.95	0.722507	0.361253	−	0.932468i	$-0.382349\pi$
$331$	4350.95	0.722507	0.361253	+	0.932468i	$0.382349\pi$
$332$	1835.28	0.303385
$333$	758.038	0.124745
$334$	−1384.57	−0.226828
$335$	−317.800	−0.0518307
$336$	1397.95	0.226977
$337$	−5453.18	−0.881465	−0.440733	−	0.897638i	$-0.645281\pi$
$337$	−5453.18	−0.881465	−0.440733	+	0.897638i	$0.645281\pi$
$338$	0	0
$339$	−709.063	−0.113602
$340$	104.781	0.0167134
$341$	2623.01	0.416551
$342$	−10265.8	−1.62313
$343$	17808.1	2.80334
$344$	−4790.01	−0.750756
$345$	18.5633	0.00289685
$346$	−9899.99	−1.53823
$347$	1498.28	0.231792	0.115896	−	0.993261i	$-0.463026\pi$
$347$	1498.28	0.231792	0.115896	+	0.993261i	$0.463026\pi$
$348$	−61.8137	−0.00952172
$349$	7113.63	1.09107	0.545536	−	0.838087i	$-0.316326\pi$
$349$	7113.63	1.09107	0.545536	+	0.838087i	$0.316326\pi$
$350$	−13511.8	−2.06353
$351$	0	0
$352$	869.834	0.131711
$353$	−4106.43	−0.619160	−0.309580	−	0.950873i	$-0.600188\pi$
$353$	−4106.43	−0.619160	−0.309580	+	0.950873i	$0.600188\pi$
$354$	449.831	0.0675375
$355$	−243.147	−0.0363518
$356$	2339.20	0.348251
$357$	−2125.76	−0.315147
$358$	6207.01	0.916342
$359$	−4321.68	−0.635347	−0.317674	−	0.948200i	$-0.602902\pi$
$359$	−4321.68	−0.635347	−0.317674	+	0.948200i	$0.602902\pi$
$360$	268.295	0.0392788
$361$	8246.95	1.20235
$362$	−2394.79	−0.347700
$363$	−65.0500	−0.00940563
$364$	0	0
$365$	33.5576	0.00481229
$366$	−591.045	−0.0844110
$367$	−11419.3	−1.62420	−0.812101	−	0.583517i	$-0.801676\pi$
$367$	−11419.3	−1.62420	−0.812101	+	0.583517i	$0.801676\pi$
$368$	5020.51	0.711174
$369$	−8233.68	−1.16159
$370$	−45.8143	−0.00643723
$371$	2768.66	0.387444
$372$	227.944	0.0317698
$373$	−2823.25	−0.391910	−0.195955	−	0.980613i	$-0.562781\pi$
$373$	−2823.25	−0.391910	−0.195955	+	0.980613i	$0.562781\pi$
$374$	−3926.19	−0.542830
$375$	69.3125	0.00954476
$376$	−3213.19	−0.440712
$377$	0	0
$378$	3127.91	0.425615
$379$	−4642.00	−0.629138	−0.314569	−	0.949235i	$-0.601860\pi$
$379$	−4642.00	−0.629138	−0.314569	+	0.949235i	$0.601860\pi$
$380$	112.825	0.0152311
$381$	232.021	0.0311989
$382$	12123.9	1.62386
$383$	−4881.73	−0.651291	−0.325646	−	0.945492i	$-0.605582\pi$
$383$	−4881.73	−0.651291	−0.325646	+	0.945492i	$0.605582\pi$
$384$	−933.911	−0.124111
$385$	−196.728	−0.0260421
$386$	3167.10	0.417620
$387$	−6576.22	−0.863794
$388$	−797.557	−0.104355
$389$	−438.111	−0.0571031	−0.0285515	−	0.999592i	$-0.509089\pi$
$389$	−438.111	−0.0571031	−0.0285515	+	0.999592i	$0.509089\pi$
$390$	0	0
$391$	−7634.34	−0.987430
$392$	−16674.8	−2.14849
$393$	−1462.84	−0.187763
$394$	−7280.59	−0.930941
$395$	507.057	0.0645893
$396$	522.446	0.0662977
$397$	−283.017	−0.0357789	−0.0178895	−	0.999840i	$-0.505695\pi$
$397$	−283.017	−0.0357789	−0.0178895	+	0.999840i	$0.505695\pi$
$398$	8778.62	1.10561
$399$	−2288.96	−0.287196
$400$	9362.89	1.17036
$401$	1345.05	0.167502	0.0837512	−	0.996487i	$-0.473310\pi$
$401$	1345.05	0.167502	0.0837512	+	0.996487i	$0.473310\pi$
$402$	1034.84	0.128390
$403$	0	0
$404$	240.122	0.0295706
$405$	364.314	0.0446986
$406$	7004.75	0.856256
$407$	312.172	0.0380191
$408$	1193.89	0.144868
$409$	781.457	0.0944757	0.0472378	−	0.998884i	$-0.484958\pi$
$409$	781.457	0.0944757	0.0472378	+	0.998884i	$0.484958\pi$
$410$	497.628	0.0599416
$411$	−88.6716	−0.0106420
$412$	−2662.39	−0.318366
$413$	−9269.62	−1.10443
$414$	5586.47	0.663189
$415$	532.863	0.0630295
$416$	0	0
$417$	201.552	0.0236692
$418$	−4227.60	−0.494686
$419$	−11667.2	−1.36033	−0.680164	−	0.733060i	$-0.738092\pi$
$419$	−11667.2	−1.36033	−0.680164	+	0.733060i	$0.738092\pi$
$420$	−17.0960	−0.00198619
$421$	9402.48	1.08848	0.544239	−	0.838930i	$-0.316819\pi$
$421$	9402.48	1.08848	0.544239	+	0.838930i	$0.316819\pi$
$422$	6412.35	0.739688
$423$	−4411.40	−0.507068
$424$	−1554.95	−0.178102
$425$	−14237.5	−1.62499
$426$	791.746	0.0900475
$427$	12179.6	1.38036
$428$	983.816	0.111109
$429$	0	0
$430$	397.454	0.0445743
$431$	−5286.19	−0.590782	−0.295391	−	0.955376i	$-0.595450\pi$
$431$	−5286.19	−0.590782	−0.295391	+	0.955376i	$0.595450\pi$
$432$	−2167.47	−0.241394
$433$	−5444.60	−0.604274	−0.302137	−	0.953264i	$-0.597700\pi$
$433$	−5444.60	−0.604274	−0.302137	+	0.953264i	$0.597700\pi$
$434$	−25830.7	−2.85695
$435$	−17.9473	−0.00197817
$436$	196.301	0.0215622
$437$	−8220.43	−0.899854
$438$	−109.272	−0.0119206
$439$	13175.2	1.43238	0.716192	−	0.697903i	$-0.245883\pi$
$439$	13175.2	1.43238	0.716192	+	0.697903i	$0.245883\pi$
$440$	110.488	0.0119712
$441$	−22893.0	−2.47197
$442$	0	0
$443$	−4445.06	−0.476729	−0.238365	−	0.971176i	$-0.576611\pi$
$443$	−4445.06	−0.476729	−0.238365	+	0.971176i	$0.576611\pi$
$444$	27.1283	0.00289967
$445$	679.173	0.0723504
$446$	18689.5	1.98424
$447$	−416.247	−0.0440443
$448$	12236.8	1.29047
$449$	14969.1	1.57335	0.786675	−	0.617367i	$-0.211801\pi$
$449$	14969.1	1.57335	0.786675	+	0.617367i	$0.211801\pi$
$450$	10418.4	1.09139
$451$	−3390.76	−0.354023
$452$	2345.21	0.244047
$453$	−715.722	−0.0742330
$454$	6525.95	0.674621
$455$	0	0
$456$	1285.54	0.132020
$457$	2194.92	0.224669	0.112335	−	0.993670i	$-0.464167\pi$
$457$	2194.92	0.224669	0.112335	+	0.993670i	$0.464167\pi$
$458$	11425.8	1.16571
$459$	3295.92	0.335164
$460$	−61.3977	−0.00622322
$461$	3512.47	0.354864	0.177432	−	0.984133i	$-0.443221\pi$
$461$	3512.47	0.354864	0.177432	+	0.984133i	$0.443221\pi$
$462$	640.596	0.0645091
$463$	−11381.4	−1.14242	−0.571209	−	0.820805i	$-0.693525\pi$
$463$	−11381.4	−1.14242	−0.571209	+	0.820805i	$0.693525\pi$
$464$	−4853.90	−0.485639
$465$	66.1824	0.00660029
$466$	−1745.77	−0.173543
$467$	−17611.1	−1.74506	−0.872531	−	0.488559i	$-0.837523\pi$
$467$	−17611.1	−1.74506	−0.872531	+	0.488559i	$0.837523\pi$
$468$	0	0
$469$	−21324.7	−2.09954
$470$	266.617	0.0261662
$471$	−1087.31	−0.106371
$472$	5206.07	0.507688
$473$	−2708.19	−0.263262
$474$	−1651.10	−0.159995
$475$	−15330.5	−1.48087
$476$	7030.91	0.677019
$477$	−2134.80	−0.204918
$478$	−6584.01	−0.630012
$479$	−2937.43	−0.280198	−0.140099	−	0.990138i	$-0.544742\pi$
$479$	−2937.43	−0.280198	−0.140099	+	0.990138i	$0.544742\pi$
$480$	21.9472	0.00208697
$481$	0	0
$482$	16958.7	1.60259
$483$	1245.62	0.117345
$484$	215.151	0.0202058
$485$	−231.566	−0.0216802
$486$	−3624.20	−0.338266
$487$	9265.77	0.862160	0.431080	−	0.902314i	$-0.358133\pi$
$487$	9265.77	0.862160	0.431080	+	0.902314i	$0.358133\pi$
$488$	−6840.39	−0.634528
$489$	1483.68	0.137208
$490$	1383.61	0.127561
$491$	−18767.8	−1.72501	−0.862506	−	0.506046i	$-0.831106\pi$
$491$	−18767.8	−1.72501	−0.862506	+	0.506046i	$0.831106\pi$
$492$	−294.663	−0.0270009
$493$	7380.99	0.674286
$494$	0	0
$495$	151.689	0.0137736
$496$	17899.2	1.62036
$497$	−16315.4	−1.47253
$498$	−1735.13	−0.156131
$499$	9803.34	0.879475	0.439737	−	0.898126i	$-0.355072\pi$
$499$	9803.34	0.879475	0.439737	+	0.898126i	$0.355072\pi$
$500$	−229.249	−0.0205047
$501$	238.041	0.0212273
$502$	−21985.5	−1.95470
$503$	2887.20	0.255932	0.127966	−	0.991779i	$-0.459155\pi$
$503$	2887.20	0.255932	0.127966	+	0.991779i	$0.459155\pi$
$504$	18002.9	1.59109
$505$	69.7183	0.00614341
$506$	2300.60	0.202123
$507$	0	0
$508$	−767.403	−0.0670236
$509$	1606.06	0.139857	0.0699285	−	0.997552i	$-0.477723\pi$
$509$	1606.06	0.139857	0.0699285	+	0.997552i	$0.477723\pi$
$510$	−99.0634	−0.00860118
$511$	2251.75	0.194935
$512$	−5747.65	−0.496119
$513$	3548.95	0.305438
$514$	−19102.9	−1.63929
$515$	−773.011	−0.0661416
$516$	−235.347	−0.0200786
$517$	−1816.69	−0.154541
$518$	−3074.19	−0.260757
$519$	1702.04	0.143952
$520$	0	0
$521$	−4621.78	−0.388644	−0.194322	−	0.980938i	$-0.562251\pi$
$521$	−4621.78	−0.388644	−0.194322	+	0.980938i	$0.562251\pi$
$522$	−5401.08	−0.452871
$523$	5965.88	0.498795	0.249398	−	0.968401i	$-0.419767\pi$
$523$	5965.88	0.498795	0.249398	+	0.968401i	$0.419767\pi$
$524$	4838.32	0.403365
$525$	2322.99	0.193111
$526$	17549.8	1.45477
$527$	−27218.1	−2.24979
$528$	−443.897	−0.0365874
$529$	−7693.57	−0.632331
$530$	129.023	0.0105744
$531$	7147.43	0.584128
$532$	7570.68	0.616974
$533$	0	0
$534$	−2211.55	−0.179220
$535$	285.646	0.0230832
$536$	11976.5	0.965126
$537$	−1067.13	−0.0857543
$538$	−16570.6	−1.32790
$539$	−9427.68	−0.753393
$540$	26.5068	0.00211235
$541$	8397.55	0.667355	0.333677	−	0.942687i	$-0.391710\pi$
$541$	8397.55	0.667355	0.333677	+	0.942687i	$0.391710\pi$
$542$	8451.53	0.669786
$543$	411.721	0.0325389
$544$	−9025.98	−0.711371
$545$	56.9949	0.00447962
$546$	0	0
$547$	20935.8	1.63647	0.818237	−	0.574882i	$-0.194952\pi$
$547$	20935.8	1.63647	0.818237	+	0.574882i	$0.194952\pi$
$548$	293.279	0.0228618
$549$	−9391.19	−0.730066
$550$	4290.45	0.332628
$551$	7947.63	0.614483
$552$	−699.572	−0.0539416
$553$	34024.0	2.61636
$554$	839.414	0.0643741
$555$	7.87655	0.000602416 0
$556$	−666.628	−0.0508477
$557$	−8477.52	−0.644891	−0.322445	−	0.946588i	$-0.604505\pi$
$557$	−8477.52	−0.644891	−0.322445	+	0.946588i	$0.604505\pi$
$558$	19917.0	1.51103
$559$	0	0
$560$	−1342.46	−0.101302
$561$	675.003	0.0507998
$562$	−21207.6	−1.59180
$563$	−2282.30	−0.170848	−0.0854241	−	0.996345i	$-0.527225\pi$
$563$	−2282.30	−0.170848	−0.0854241	+	0.996345i	$0.527225\pi$
$564$	−157.873	−0.0117866
$565$	680.919	0.0507017
$566$	11276.5	0.837432
$567$	24445.9	1.81063
$568$	9163.18	0.676898
$569$	−23523.0	−1.73310	−0.866551	−	0.499089i	$-0.833668\pi$
$569$	−23523.0	−1.73310	−0.866551	+	0.499089i	$0.833668\pi$
$570$	−106.669	−0.00783834
$571$	11920.3	0.873643	0.436821	−	0.899548i	$-0.356104\pi$
$571$	11920.3	0.873643	0.436821	+	0.899548i	$0.356104\pi$
$572$	0	0
$573$	−2084.39	−0.151966
$574$	33391.3	2.42809
$575$	8342.64	0.605064
$576$	−9435.28	−0.682529
$577$	−17452.3	−1.25918	−0.629592	−	0.776926i	$-0.716778\pi$
$577$	−17452.3	−1.25918	−0.629592	+	0.776926i	$0.716778\pi$
$578$	25377.8	1.82626
$579$	−544.498	−0.0390822
$580$	59.3601	0.00424965
$581$	35755.7	2.55317
$582$	754.037	0.0537042
$583$	−879.144	−0.0624536
$584$	−1264.64	−0.0896085
$585$	0	0
$586$	1968.68	0.138781
$587$	−5180.08	−0.364233	−0.182117	−	0.983277i	$-0.558295\pi$
$587$	−5180.08	−0.364233	−0.182117	+	0.983277i	$0.558295\pi$
$588$	−819.281	−0.0574602
$589$	−29307.7	−2.05026
$590$	−431.977	−0.0301427
$591$	1251.70	0.0871204
$592$	2130.24	0.147892
$593$	−5440.59	−0.376759	−0.188380	−	0.982096i	$-0.560324\pi$
$593$	−5440.59	−0.376759	−0.188380	+	0.982096i	$0.560324\pi$
$594$	−993.220	−0.0686066
$595$	2041.39	0.140653
$596$	1376.73	0.0946190
$597$	−1509.25	−0.103466
$598$	0	0
$599$	−17258.2	−1.17721	−0.588607	−	0.808419i	$-0.700324\pi$
$599$	−17258.2	−1.17721	−0.588607	+	0.808419i	$0.700324\pi$
$600$	−1304.65	−0.0887704
$601$	8501.72	0.577025	0.288513	−	0.957476i	$-0.406839\pi$
$601$	8501.72	0.577025	0.288513	+	0.957476i	$0.406839\pi$
$602$	26669.6	1.80560
$603$	16442.6	1.11044
$604$	2367.23	0.159472
$605$	62.4681	0.00419783
$606$	−227.020	−0.0152179
$607$	−14312.1	−0.957017	−0.478508	−	0.878083i	$-0.658822\pi$
$607$	−14312.1	−0.957017	−0.478508	+	0.878083i	$0.658822\pi$
$608$	−9718.91	−0.648279
$609$	−1204.28	−0.0801312
$610$	567.585	0.0376735
$611$	0	0
$612$	−5421.25	−0.358074
$613$	−27491.1	−1.81135	−0.905673	−	0.423976i	$-0.860634\pi$
$613$	−27491.1	−1.81135	−0.905673	+	0.423976i	$0.860634\pi$
$614$	−20360.9	−1.33827
$615$	−85.5538	−0.00560953
$616$	7413.86	0.484923
$617$	−27892.3	−1.81994	−0.909970	−	0.414674i	$-0.863896\pi$
$617$	−27892.3	−1.81994	−0.909970	+	0.414674i	$0.863896\pi$
$618$	2517.11	0.163840
$619$	−2742.28	−0.178064	−0.0890319	−	0.996029i	$-0.528377\pi$
$619$	−2742.28	−0.178064	−0.0890319	+	0.996029i	$0.528377\pi$
$620$	−218.896	−0.0141792
$621$	−1931.28	−0.124798
$622$	1770.37	0.114125
$623$	45573.2	2.93074
$624$	0	0
$625$	15525.1	0.993608
$626$	−25890.0	−1.65299
$627$	726.823	0.0462943
$628$	3596.25	0.228512
$629$	−3239.31	−0.205341
$630$	−1493.80	−0.0944672
$631$	17616.5	1.11141	0.555706	−	0.831379i	$-0.312448\pi$
$631$	17616.5	1.11141	0.555706	+	0.831379i	$0.312448\pi$
$632$	−19108.8	−1.20270
$633$	−1102.43	−0.0692224
$634$	23546.0	1.47497
$635$	−222.811	−0.0139244
$636$	−76.3992	−0.00476325
$637$	0	0
$638$	−2224.25	−0.138023
$639$	12580.2	0.778816
$640$	896.842	0.0553919
$641$	13061.4	0.804826	0.402413	−	0.915458i	$-0.368172\pi$
$641$	13061.4	0.804826	0.402413	+	0.915458i	$0.368172\pi$
$642$	−930.132	−0.0571797
$643$	−18121.0	−1.11139	−0.555694	−	0.831387i	$-0.687547\pi$
$643$	−18121.0	−1.11139	−0.555694	+	0.831387i	$0.687547\pi$
$644$	−4119.85	−0.252088
$645$	−68.3316	−0.00417140
$646$	43868.5	2.67180
$647$	−5095.41	−0.309615	−0.154808	−	0.987945i	$-0.549476\pi$
$647$	−5095.41	−0.309615	−0.154808	+	0.987945i	$0.549476\pi$
$648$	−13729.5	−0.832321
$649$	2943.42	0.178027
$650$	0	0
$651$	4440.90	0.267362
$652$	−4907.25	−0.294759
$653$	11717.1	0.702186	0.351093	−	0.936341i	$-0.385810\pi$
$653$	11717.1	0.702186	0.351093	+	0.936341i	$0.385810\pi$
$654$	−185.589	−0.0110965
$655$	1404.78	0.0838005
$656$	−23138.3	−1.37713
$657$	−1736.23	−0.103100
$658$	17890.2	1.05993
$659$	−31395.5	−1.85583	−0.927917	−	0.372786i	$-0.878403\pi$
$659$	−31395.5	−1.85583	−0.927917	+	0.372786i	$0.878403\pi$
$660$	5.42858	0.000320163 0
$661$	−32211.0	−1.89540	−0.947701	−	0.319158i	$-0.896600\pi$
$661$	−32211.0	−1.89540	−0.947701	+	0.319158i	$0.896600\pi$
$662$	13605.4	0.798775
$663$	0	0
$664$	−20081.3	−1.17366
$665$	2198.11	0.128179
$666$	2370.38	0.137914
$667$	−4324.98	−0.251070
$668$	−787.314	−0.0456019
$669$	−3213.16	−0.185692
$670$	−993.760	−0.0573020
$671$	−3867.44	−0.222505
$672$	1472.68	0.0845383
$673$	−542.400	−0.0310668	−0.0155334	−	0.999879i	$-0.504945\pi$
$673$	−542.400	−0.0310668	−0.0155334	+	0.999879i	$0.504945\pi$
$674$	−17052.1	−0.974513
$675$	−3601.71	−0.205377
$676$	0	0
$677$	−12012.5	−0.681944	−0.340972	−	0.940073i	$-0.610756\pi$
$677$	−12012.5	−0.681944	−0.340972	+	0.940073i	$0.610756\pi$
$678$	−2217.24	−0.125594
$679$	−15538.3	−0.878213
$680$	−1146.50	−0.0646562
$681$	−1121.96	−0.0631332
$682$	8202.14	0.460523
$683$	−14999.1	−0.840297	−0.420149	−	0.907455i	$-0.638022\pi$
$683$	−14999.1	−0.840297	−0.420149	+	0.907455i	$0.638022\pi$
$684$	−5837.44	−0.326316
$685$	85.1520	0.00474962
$686$	55685.8	3.09926
$687$	−1964.36	−0.109091
$688$	−18480.5	−1.02407
$689$	0	0
$690$	58.0474	0.00320265
$691$	−29172.2	−1.60602	−0.803012	−	0.595963i	$-0.796770\pi$
$691$	−29172.2	−1.60602	−0.803012	+	0.595963i	$0.796770\pi$
$692$	−5629.45	−0.309248
$693$	10178.5	0.557936
$694$	4685.11	0.256260
$695$	−193.552	−0.0105638
$696$	676.356	0.0368351
$697$	35184.8	1.91208
$698$	22244.3	1.20625
$699$	300.138	0.0162407
$700$	−7683.23	−0.414855
$701$	−21053.3	−1.13434	−0.567170	−	0.823601i	$-0.691962\pi$
$701$	−21053.3	−1.13434	−0.567170	+	0.823601i	$0.691962\pi$
$702$	0	0
$703$	−3487.99	−0.187130
$704$	−3885.59	−0.208017
$705$	−45.8376	−0.00244872
$706$	−12840.8	−0.684519
$707$	4678.17	0.248855
$708$	255.789	0.0135779
$709$	−3195.28	−0.169254	−0.0846271	−	0.996413i	$-0.526970\pi$
$709$	−3195.28	−0.169254	−0.0846271	+	0.996413i	$0.526970\pi$
$710$	−760.320	−0.0401892
$711$	−26234.5	−1.38379
$712$	−25595.2	−1.34722
$713$	15948.8	0.837709
$714$	−6647.26	−0.348414
$715$	0	0
$716$	3529.50	0.184223
$717$	1131.94	0.0589585
$718$	−13513.9	−0.702415
$719$	−25450.5	−1.32009	−0.660044	−	0.751227i	$-0.729462\pi$
$719$	−25450.5	−1.32009	−0.660044	+	0.751227i	$0.729462\pi$
$720$	1035.12	0.0535786
$721$	−51869.8	−2.67924
$722$	25788.2	1.32928
$723$	−2915.60	−0.149976
$724$	−1361.76	−0.0699023
$725$	−8065.78	−0.413180
$726$	−203.411	−0.0103985
$727$	12657.0	0.645697	0.322848	−	0.946451i	$-0.395360\pi$
$727$	12657.0	0.645697	0.322848	+	0.946451i	$0.395360\pi$
$728$	0	0
$729$	−18430.1	−0.936346
$730$	104.935	0.00532028
$731$	28102.0	1.42188
$732$	−336.087	−0.0169701
$733$	−14254.0	−0.718259	−0.359129	−	0.933288i	$-0.616926\pi$
$733$	−14254.0	−0.718259	−0.359129	+	0.933288i	$0.616926\pi$
$734$	−35708.1	−1.79565
$735$	−237.874	−0.0119376
$736$	5288.88	0.264879
$737$	6771.33	0.338433
$738$	−25746.7	−1.28421
$739$	21152.9	1.05294	0.526471	−	0.850193i	$-0.323515\pi$
$739$	21152.9	1.05294	0.526471	+	0.850193i	$0.323515\pi$
$740$	−26.0515	−0.00129415
$741$	0	0
$742$	8657.59	0.428342
$743$	−8087.83	−0.399345	−0.199673	−	0.979863i	$-0.563988\pi$
$743$	−8087.83	−0.399345	−0.199673	+	0.979863i	$0.563988\pi$
$744$	−2494.13	−0.122902
$745$	399.725	0.0196575
$746$	−8828.30	−0.433280
$747$	−27569.8	−1.35037
$748$	−2232.56	−0.109131
$749$	19167.1	0.935048
$750$	216.740	0.0105523
$751$	34946.5	1.69802	0.849012	−	0.528373i	$-0.177198\pi$
$751$	34946.5	1.69802	0.849012	+	0.528373i	$0.177198\pi$
$752$	−12396.9	−0.601156
$753$	3779.82	0.182928
$754$	0	0
$755$	687.313	0.0331310
$756$	1778.63	0.0855664
$757$	30668.7	1.47249	0.736243	−	0.676717i	$-0.236598\pi$
$757$	30668.7	1.47249	0.736243	+	0.676717i	$0.236598\pi$
$758$	−14515.5	−0.695551
$759$	−395.526	−0.0189153
$760$	−1234.52	−0.0589218
$761$	−21593.1	−1.02858	−0.514290	−	0.857616i	$-0.671944\pi$
$761$	−21593.1	−1.02858	−0.514290	+	0.857616i	$0.671944\pi$
$762$	725.528	0.0344923
$763$	3824.42	0.181459
$764$	6894.06	0.326464
$765$	−1574.03	−0.0743912
$766$	−15265.1	−0.720042
$767$	0	0
$768$	−1401.13	−0.0658319
$769$	36796.0	1.72548	0.862742	−	0.505644i	$-0.168745\pi$
$769$	36796.0	1.72548	0.862742	+	0.505644i	$0.168745\pi$
$770$	−615.169	−0.0287911
$771$	3284.23	0.153410
$772$	1800.91	0.0839590
$773$	−3681.07	−0.171279	−0.0856397	−	0.996326i	$-0.527293\pi$
$773$	−3681.07	−0.171279	−0.0856397	+	0.996326i	$0.527293\pi$
$774$	−20563.8	−0.954976
$775$	29743.4	1.37860
$776$	8726.75	0.403701
$777$	528.525	0.0244025
$778$	−1369.97	−0.0631309
$779$	37886.0	1.74250
$780$	0	0
$781$	5180.71	0.237363
$782$	−23872.5	−1.09166
$783$	1867.19	0.0852209
$784$	−64333.8	−2.93066
$785$	1044.15	0.0474743
$786$	−4574.31	−0.207583
$787$	14395.5	0.652027	0.326013	−	0.945365i	$-0.394295\pi$
$787$	14395.5	0.652027	0.326013	+	0.945365i	$0.394295\pi$
$788$	−4139.98	−0.187158
$789$	−3017.22	−0.136142
$790$	1585.56	0.0714074
$791$	45690.3	2.05381
$792$	−5716.53	−0.256475
$793$	0	0
$794$	−884.994	−0.0395558
$795$	−22.1821	−0.000989582 0
$796$	4991.81	0.222274
$797$	1602.22	0.0712090	0.0356045	−	0.999366i	$-0.488664\pi$
$797$	1602.22	0.0712090	0.0356045	+	0.999366i	$0.488664\pi$
$798$	−7157.57	−0.317513
$799$	18851.2	0.834676
$800$	9863.40	0.435905
$801$	−35139.7	−1.55006
$802$	4205.96	0.185184
$803$	−715.009	−0.0314223
$804$	588.440	0.0258118
$805$	−1196.18	−0.0523722
$806$	0	0
$807$	2848.87	0.124269
$808$	−2627.38	−0.114395
$809$	25997.2	1.12980	0.564902	−	0.825158i	$-0.308914\pi$
$809$	25997.2	1.12980	0.564902	+	0.825158i	$0.308914\pi$
$810$	1139.21	0.0494170
$811$	−2200.08	−0.0952594	−0.0476297	−	0.998865i	$-0.515167\pi$
$811$	−2200.08	−0.0952594	−0.0476297	+	0.998865i	$0.515167\pi$
$812$	3983.13	0.172143
$813$	−1453.01	−0.0626807
$814$	976.161	0.0420325
$815$	−1424.79	−0.0612372
$816$	4606.17	0.197608
$817$	30259.4	1.29577
$818$	2443.61	0.104449
$819$	0	0
$820$	282.967	0.0120508
$821$	−20651.3	−0.877873	−0.438937	−	0.898518i	$-0.644645\pi$
$821$	−20651.3	−0.877873	−0.438937	+	0.898518i	$0.644645\pi$
$822$	−277.276	−0.0117653
$823$	−13474.0	−0.570687	−0.285343	−	0.958425i	$-0.592108\pi$
$823$	−13474.0	−0.570687	−0.285343	+	0.958425i	$0.592108\pi$
$824$	29131.5	1.23161
$825$	−737.629	−0.0311284
$826$	−28986.1	−1.22101
$827$	−1640.46	−0.0689775	−0.0344888	−	0.999405i	$-0.510980\pi$
$827$	−1640.46	−0.0689775	−0.0344888	+	0.999405i	$0.510980\pi$
$828$	3176.65	0.133329
$829$	−29646.3	−1.24205	−0.621024	−	0.783791i	$-0.713283\pi$
$829$	−29646.3	−1.24205	−0.621024	+	0.783791i	$0.713283\pi$
$830$	1666.26	0.0696829
$831$	−144.315	−0.00602434
$832$	0	0
$833$	97828.0	4.06907
$834$	630.252	0.0261677
$835$	−228.592	−0.00947397
$836$	−2403.95	−0.0994526
$837$	−6885.45	−0.284344
$838$	−36483.2	−1.50393
$839$	6135.11	0.252452	0.126226	−	0.992001i	$-0.459713\pi$
$839$	6135.11	0.252452	0.126226	+	0.992001i	$0.459713\pi$
$840$	187.062	0.00768365
$841$	−20207.6	−0.828552
$842$	29401.5	1.20338
$843$	3646.08	0.148965
$844$	3646.27	0.148708
$845$	0	0
$846$	−13794.4	−0.560594
$847$	4191.67	0.170044
$848$	−5999.22	−0.242941
$849$	−1938.69	−0.0783696
$850$	−44520.6	−1.79652
$851$	1898.11	0.0764588
$852$	450.212	0.0181033
$853$	−14949.8	−0.600085	−0.300043	−	0.953926i	$-0.597001\pi$
$853$	−14949.8	−0.600085	−0.300043	+	0.953926i	$0.597001\pi$
$854$	38085.5	1.52607
$855$	−1694.87	−0.0677934
$856$	−10764.8	−0.429827
$857$	3174.24	0.126523	0.0632613	−	0.997997i	$-0.479850\pi$
$857$	3174.24	0.126523	0.0632613	+	0.997997i	$0.479850\pi$
$858$	0	0
$859$	21283.9	0.845400	0.422700	−	0.906270i	$-0.361082\pi$
$859$	21283.9	0.845400	0.422700	+	0.906270i	$0.361082\pi$
$860$	226.005	0.00896129
$861$	−5740.74	−0.227229
$862$	−16529.9	−0.653145
$863$	44304.5	1.74756	0.873779	−	0.486323i	$-0.161662\pi$
$863$	44304.5	1.74756	0.873779	+	0.486323i	$0.161662\pi$
$864$	−2283.33	−0.0899080
$865$	−1634.48	−0.0642474
$866$	−17025.3	−0.668062
$867$	−4363.04	−0.170907
$868$	−14688.2	−0.574365
$869$	−10803.8	−0.421742
$870$	−56.1211	−0.00218699
$871$	0	0
$872$	−2147.90	−0.0834139
$873$	11981.0	0.464484
$874$	−25705.2	−0.994843
$875$	−4466.33	−0.172560
$876$	−62.1355	−0.00239653
$877$	−31517.6	−1.21354	−0.606770	−	0.794877i	$-0.707535\pi$
$877$	−31517.6	−1.21354	−0.606770	+	0.794877i	$0.707535\pi$
$878$	41198.7	1.58359
$879$	−338.462	−0.0129875
$880$	426.278	0.0163293
$881$	−25267.4	−0.966267	−0.483134	−	0.875547i	$-0.660501\pi$
$881$	−25267.4	−0.966267	−0.483134	+	0.875547i	$0.660501\pi$
$882$	−71586.2	−2.73292
$883$	19500.1	0.743184	0.371592	−	0.928396i	$-0.378812\pi$
$883$	19500.1	0.743184	0.371592	+	0.928396i	$0.378812\pi$
$884$	0	0
$885$	74.2668	0.00282085
$886$	−13899.7	−0.527053
$887$	−14200.9	−0.537564	−0.268782	−	0.963201i	$-0.586621\pi$
$887$	−14200.9	−0.537564	−0.268782	+	0.963201i	$0.586621\pi$
$888$	−296.834	−0.0112174
$889$	−14950.9	−0.564045
$890$	2123.77	0.0799877
$891$	−7762.40	−0.291863
$892$	10627.4	0.398916
$893$	20298.4	0.760648
$894$	−1301.60	−0.0486937
$895$	1024.77	0.0382730
$896$	60179.0	2.24379
$897$	0	0
$898$	46808.2	1.73943
$899$	−15419.5	−0.572046
$900$	5924.23	0.219416
$901$	9122.60	0.337312
$902$	−10602.9	−0.391394
$903$	−4585.12	−0.168974
$904$	−25660.9	−0.944104
$905$	−395.379	−0.0145225
$906$	−2238.06	−0.0820690
$907$	170.034	0.00622480	0.00311240	−	0.999995i	$-0.499009\pi$
$907$	170.034	0.00622480	0.00311240	+	0.999995i	$0.499009\pi$
$908$	3710.86	0.135627
$909$	−3607.15	−0.131619
$910$	0	0
$911$	−23915.6	−0.869770	−0.434885	−	0.900486i	$-0.643211\pi$
$911$	−23915.6	−0.869770	−0.434885	+	0.900486i	$0.643211\pi$
$912$	4959.79	0.180082
$913$	−11353.7	−0.411557
$914$	6863.50	0.248386
$915$	−97.5812	−0.00352561
$916$	6497.09	0.234356
$917$	94262.2	3.39456
$918$	10306.3	0.370544
$919$	2914.50	0.104614	0.0523071	−	0.998631i	$-0.483343\pi$
$919$	2914.50	0.104614	0.0523071	+	0.998631i	$0.483343\pi$
$920$	671.804	0.0240747
$921$	3500.51	0.125240
$922$	10983.5	0.392323
$923$	0	0
$924$	364.263	0.0129690
$925$	3539.85	0.125826
$926$	−35589.7	−1.26301
$927$	39994.7	1.41704
$928$	−5113.37	−0.180878
$929$	10396.7	0.367172	0.183586	−	0.983004i	$-0.441229\pi$
$929$	10396.7	0.367172	0.183586	+	0.983004i	$0.441229\pi$
$930$	206.952	0.00729702
$931$	105338.	3.70819
$932$	−992.700	−0.0348895
$933$	−304.369	−0.0106802
$934$	−55069.8	−1.92927
$935$	−648.211	−0.0226725
$936$	0	0
$937$	7615.33	0.265509	0.132755	−	0.991149i	$-0.457618\pi$
$937$	7615.33	0.265509	0.132755	+	0.991149i	$0.457618\pi$
$938$	−66682.3	−2.32117
$939$	4451.10	0.154692
$940$	151.607	0.00526050
$941$	14371.4	0.497868	0.248934	−	0.968520i	$-0.419920\pi$
$941$	14371.4	0.497868	0.248934	+	0.968520i	$0.419920\pi$
$942$	−3400.01	−0.117599
$943$	−20617.0	−0.711962
$944$	20085.7	0.692515
$945$	516.416	0.0177767
$946$	−8468.51	−0.291052
$947$	2477.84	0.0850252	0.0425126	−	0.999096i	$-0.486464\pi$
$947$	2477.84	0.0850252	0.0425126	+	0.999096i	$0.486464\pi$
$948$	−938.868	−0.0321656
$949$	0	0
$950$	−47938.5	−1.63719
$951$	−4048.11	−0.138033
$952$	−76931.2	−2.61907
$953$	−48096.8	−1.63485	−0.817423	−	0.576038i	$-0.804598\pi$
$953$	−48096.8	−1.63485	−0.817423	+	0.576038i	$0.804598\pi$
$954$	−6675.52	−0.226549
$955$	2001.65	0.0678241
$956$	−3743.88	−0.126659
$957$	382.400	0.0129167
$958$	−9185.34	−0.309775
$959$	5713.79	0.192396
$960$	−98.0392	−0.00329604
$961$	27070.0	0.908664
$962$	0	0
$963$	−14779.0	−0.494544
$964$	9643.29	0.322188
$965$	522.886	0.0174428
$966$	3895.04	0.129732
$967$	−12384.4	−0.411847	−0.205923	−	0.978568i	$-0.566020\pi$
$967$	−12384.4	−0.411847	−0.205923	+	0.978568i	$0.566020\pi$
$968$	−2354.16	−0.0781668
$969$	−7542.01	−0.250035
$970$	−724.107	−0.0239687
$971$	36035.0	1.19096	0.595478	−	0.803372i	$-0.296963\pi$
$971$	36035.0	1.19096	0.595478	+	0.803372i	$0.296963\pi$
$972$	−2060.84	−0.0680055
$973$	−12987.5	−0.427915
$974$	28974.0	0.953170
$975$	0	0
$976$	−26391.1	−0.865533
$977$	20510.4	0.671633	0.335817	−	0.941927i	$-0.390988\pi$
$977$	20510.4	0.671633	0.335817	+	0.941927i	$0.390988\pi$
$978$	4639.47	0.151691
$979$	−14471.1	−0.472418
$980$	786.762	0.0256451
$981$	−2948.85	−0.0959732
$982$	−58687.0	−1.90711
$983$	−668.979	−0.0217061	−0.0108531	−	0.999941i	$-0.503455\pi$
$983$	−668.979	−0.0217061	−0.0108531	+	0.999941i	$0.503455\pi$
$984$	3224.16	0.104454
$985$	−1202.02	−0.0388828
$986$	23080.3	0.745464
$987$	−3075.75	−0.0991917
$988$	0	0
$989$	−16466.7	−0.529435
$990$	474.332	0.0152275
$991$	23395.2	0.749923	0.374961	−	0.927040i	$-0.377656\pi$
$991$	23395.2	0.749923	0.374961	+	0.927040i	$0.377656\pi$
$992$	18856.1	0.603508
$993$	−2339.09	−0.0747519
$994$	−51018.2	−1.62797
$995$	1449.34	0.0461782
$996$	−986.652	−0.0313888
$997$	50642.3	1.60868	0.804342	−	0.594166i	$-0.202518\pi$
$997$	50642.3	1.60868	0.804342	+	0.594166i	$0.202518\pi$
$998$	30655.0	0.972312
$999$	−819.458	−0.0259525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.h.1.13		17
13.4	even	6		143.4.e.b.133.13	yes	34
13.10	even	6		143.4.e.b.100.13	✓	34
13.12	even	2		1859.4.a.g.1.5		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.13	✓	34	13.10	even	6
143.4.e.b.133.13	yes	34	13.4	even	6
1859.4.a.g.1.5		17	13.12	even	2
1859.4.a.h.1.13		17	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+3.12700 q^{2} -0.537604 q^{3} +1.77811 q^{4} +0.516265 q^{5} -1.68109 q^{6} +34.6419 q^{7} -19.4558 q^{8} -26.7110 q^{9} +1.61436 q^{10} -11.0000 q^{11} -0.955919 q^{12} +108.325 q^{14} -0.277546 q^{15} -75.0632 q^{16} +114.143 q^{17} -83.5252 q^{18} +122.906 q^{19} +0.917976 q^{20} -18.6236 q^{21} -34.3970 q^{22} -66.8837 q^{23} +10.4595 q^{24} -124.733 q^{25} +28.8752 q^{27} +61.5971 q^{28} +64.6641 q^{29} -0.867886 q^{30} -238.455 q^{31} -79.0758 q^{32} +5.91364 q^{33} +356.926 q^{34} +17.8844 q^{35} -47.4951 q^{36} -28.3793 q^{37} +384.328 q^{38} -10.0444 q^{40} +308.251 q^{41} -58.2360 q^{42} +246.199 q^{43} -19.5592 q^{44} -13.7899 q^{45} -209.145 q^{46} +165.153 q^{47} +40.3543 q^{48} +857.062 q^{49} -390.041 q^{50} -61.3639 q^{51} +79.9222 q^{53} +90.2927 q^{54} -5.67892 q^{55} -673.987 q^{56} -66.0749 q^{57} +202.205 q^{58} -267.584 q^{59} -0.493508 q^{60} +351.586 q^{61} -745.650 q^{62} -925.319 q^{63} +353.236 q^{64} +18.4919 q^{66} -615.576 q^{67} +202.960 q^{68} +35.9569 q^{69} +55.9245 q^{70} -470.973 q^{71} +519.684 q^{72} +65.0008 q^{73} -88.7419 q^{74} +67.0572 q^{75} +218.541 q^{76} -381.061 q^{77} +982.163 q^{79} -38.7525 q^{80} +705.673 q^{81} +963.899 q^{82} +1032.15 q^{83} -33.1149 q^{84} +58.9283 q^{85} +769.864 q^{86} -34.7637 q^{87} +214.014 q^{88} +1315.55 q^{89} -43.1211 q^{90} -118.927 q^{92} +128.195 q^{93} +516.434 q^{94} +63.4522 q^{95} +42.5114 q^{96} -448.542 q^{97} +2680.03 q^{98} +293.821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} + 24 q^{5} - 16 q^{6} + 62 q^{7} + 21 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 127 q^{12} + 148 q^{15} + 126 q^{16} - 74 q^{17} - 90 q^{18} + 159 q^{19} + 222 q^{20} + 184 q^{21}+ \cdots - 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 + 24 * q^5 - 16 * q^6 + 62 * q^7 + 21 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 127 * q^12 + 148 * q^15 + 126 * q^16 - 74 * q^17 - 90 * q^18 + 159 * q^19 + 222 * q^20 + 184 * q^21 - 215 * q^23 - 214 * q^24 + 95 * q^25 - 192 * q^27 + 358 * q^28 - 157 * q^29 + 829 * q^30 + 394 * q^31 + 553 * q^32 + 66 * q^33 + 702 * q^34 + 58 * q^35 - 700 * q^36 - 88 * q^37 - 1318 * q^38 + 733 * q^40 + 512 * q^41 + 337 * q^42 + 927 * q^43 - 550 * q^44 + 1482 * q^45 + 1361 * q^46 + 143 * q^47 - 178 * q^48 + 1835 * q^49 + 583 * q^50 - 568 * q^51 + 106 * q^53 + 67 * q^54 - 264 * q^55 + 2059 * q^56 - 1298 * q^57 + 1690 * q^58 + 266 * q^59 - 37 * q^60 - 624 * q^61 + 643 * q^62 + 2360 * q^63 - 1589 * q^64 + 176 * q^66 + 676 * q^67 - 413 * q^68 + 764 * q^69 + 1061 * q^70 + 763 * q^71 + 1366 * q^72 + 2374 * q^73 - 1649 * q^74 + 2420 * q^75 + 2101 * q^76 - 682 * q^77 + 2164 * q^79 + 1013 * q^80 + 537 * q^81 + 3152 * q^82 - 777 * q^83 + 3381 * q^84 + 1690 * q^85 - 2894 * q^86 - 4200 * q^87 - 231 * q^88 + 1687 * q^89 - 5399 * q^90 + 5542 * q^92 + 4310 * q^93 + 1777 * q^94 + 1124 * q^95 + 3465 * q^96 + 2047 * q^97 - 1553 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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