LMFDB - Embedded newform 1859.4.a.i.1.2

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 = [17,4,-6,78,16] 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} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.61453$ 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)

$f(q)$	$=$	\(q-4.61453 q^{2} +3.68758 q^{3} +13.2939 q^{4} +19.7910 q^{5} -17.0165 q^{6} -18.7869 q^{7} -24.4287 q^{8} -13.4017 q^{9} -91.3259 q^{10} -11.0000 q^{11} +49.0223 q^{12} +86.6927 q^{14} +72.9808 q^{15} +6.37610 q^{16} +67.7750 q^{17} +61.8427 q^{18} +129.430 q^{19} +263.099 q^{20} -69.2783 q^{21} +50.7598 q^{22} -103.682 q^{23} -90.0830 q^{24} +266.682 q^{25} -148.985 q^{27} -249.751 q^{28} +269.826 q^{29} -336.772 q^{30} +75.1728 q^{31} +166.007 q^{32} -40.5634 q^{33} -312.750 q^{34} -371.811 q^{35} -178.161 q^{36} -9.87062 q^{37} -597.258 q^{38} -483.468 q^{40} +162.811 q^{41} +319.687 q^{42} -231.244 q^{43} -146.233 q^{44} -265.233 q^{45} +478.444 q^{46} +42.7253 q^{47} +23.5124 q^{48} +9.94786 q^{49} -1230.61 q^{50} +249.926 q^{51} -717.060 q^{53} +687.494 q^{54} -217.701 q^{55} +458.940 q^{56} +477.283 q^{57} -1245.12 q^{58} +583.309 q^{59} +970.198 q^{60} -341.669 q^{61} -346.887 q^{62} +251.777 q^{63} -817.054 q^{64} +187.181 q^{66} -697.923 q^{67} +900.993 q^{68} -382.336 q^{69} +1715.73 q^{70} +620.263 q^{71} +327.387 q^{72} +790.345 q^{73} +45.5483 q^{74} +983.412 q^{75} +1720.62 q^{76} +206.656 q^{77} -119.274 q^{79} +126.189 q^{80} -187.547 q^{81} -751.298 q^{82} +98.6344 q^{83} -920.977 q^{84} +1341.33 q^{85} +1067.08 q^{86} +995.007 q^{87} +268.716 q^{88} +455.102 q^{89} +1223.93 q^{90} -1378.34 q^{92} +277.206 q^{93} -197.157 q^{94} +2561.54 q^{95} +612.165 q^{96} +346.559 q^{97} -45.9047 q^{98} +147.419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19}+ \cdots - 1485 q^{99}+O(q^{100}) $ 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * 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 $

$2$	−4.61453	−1.63148	−0.815741	−	0.578417i	$-0.803671\pi$
$2$	−4.61453	−1.63148	−0.815741	+	0.578417i	$0.803671\pi$
$3$	3.68758	0.709676	0.354838	−	0.934928i	$-0.384536\pi$
$3$	3.68758	0.709676	0.354838	+	0.934928i	$0.384536\pi$
$4$	13.2939	1.66173
$5$	19.7910	1.77016	0.885079	−	0.465442i	$-0.154104\pi$
$5$	19.7910	1.77016	0.885079	+	0.465442i	$0.154104\pi$
$6$	−17.0165	−1.15782
$7$	−18.7869	−1.01440	−0.507199	−	0.861829i	$-0.669319\pi$
$7$	−18.7869	−1.01440	−0.507199	+	0.861829i	$0.669319\pi$
$8$	−24.4287	−1.07961
$9$	−13.4017	−0.496360
$10$	−91.3259	−2.88798
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	49.0223	1.17929
$13$	0	0
$13$	0	0
$14$	86.6927	1.65497
$15$	72.9808	1.25624
$16$	6.37610	0.0996265
$17$	67.7750	0.966933	0.483466	−	0.875363i	$-0.339378\pi$
$17$	67.7750	0.966933	0.483466	+	0.875363i	$0.339378\pi$
$18$	61.8427	0.809803
$19$	129.430	1.56280	0.781401	−	0.624029i	$-0.214505\pi$
$19$	129.430	1.56280	0.781401	+	0.624029i	$0.214505\pi$
$20$	263.099	2.94153
$21$	−69.2783	−0.719893
$22$	50.7598	0.491910
$23$	−103.682	−0.939966	−0.469983	−	0.882676i	$-0.655740\pi$
$23$	−103.682	−0.939966	−0.469983	+	0.882676i	$0.655740\pi$
$24$	−90.0830	−0.766171
$25$	266.682	2.13346
$26$	0	0
$27$	−148.985	−1.06193
$28$	−249.751	−1.68566
$29$	269.826	1.72778	0.863888	−	0.503684i	$-0.168022\pi$
$29$	269.826	1.72778	0.863888	+	0.503684i	$0.168022\pi$
$30$	−336.772	−2.04953
$31$	75.1728	0.435530	0.217765	−	0.976001i	$-0.430123\pi$
$31$	75.1728	0.435530	0.217765	+	0.976001i	$0.430123\pi$
$32$	166.007	0.917069
$33$	−40.5634	−0.213975
$34$	−312.750	−1.57753
$35$	−371.811	−1.79564
$36$	−178.161	−0.824819
$37$	−9.87062	−0.0438573	−0.0219286	−	0.999760i	$-0.506981\pi$
$37$	−9.87062	−0.0438573	−0.0219286	+	0.999760i	$0.506981\pi$
$38$	−597.258	−2.54968
$39$	0	0
$40$	−483.468	−1.91108
$41$	162.811	0.620168	0.310084	−	0.950709i	$-0.399643\pi$
$41$	162.811	0.620168	0.310084	+	0.950709i	$0.399643\pi$
$42$	319.687	1.17449
$43$	−231.244	−0.820101	−0.410051	−	0.912063i	$-0.634489\pi$
$43$	−231.244	−0.820101	−0.410051	+	0.912063i	$0.634489\pi$
$44$	−146.233	−0.501032
$45$	−265.233	−0.878636
$46$	478.444	1.53354
$47$	42.7253	0.132598	0.0662991	−	0.997800i	$-0.478881\pi$
$47$	42.7253	0.132598	0.0662991	+	0.997800i	$0.478881\pi$
$48$	23.5124	0.0707025
$49$	9.94786	0.0290025
$50$	−1230.61	−3.48070
$51$	249.926	0.686209
$52$	0	0
$53$	−717.060	−1.85841	−0.929205	−	0.369564i	$-0.879507\pi$
$53$	−717.060	−1.85841	−0.929205	+	0.369564i	$0.879507\pi$
$54$	687.494	1.73252
$55$	−217.701	−0.533722
$56$	458.940	1.09515
$57$	477.283	1.10908
$58$	−1245.12	−2.81884
$59$	583.309	1.28712	0.643562	−	0.765394i	$-0.277456\pi$
$59$	583.309	1.28712	0.643562	+	0.765394i	$0.277456\pi$
$60$	970.198	2.08753
$61$	−341.669	−0.717152	−0.358576	−	0.933501i	$-0.616738\pi$
$61$	−341.669	−0.717152	−0.358576	+	0.933501i	$0.616738\pi$
$62$	−346.887	−0.710559
$63$	251.777	0.503507
$64$	−817.054	−1.59581
$65$	0	0
$66$	187.181	0.349097
$67$	−697.923	−1.27261	−0.636305	−	0.771438i	$-0.719538\pi$
$67$	−697.923	−1.27261	−0.636305	+	0.771438i	$0.719538\pi$
$68$	900.993	1.60679
$69$	−382.336	−0.667071
$70$	1715.73	2.92956
$71$	620.263	1.03678	0.518392	−	0.855143i	$-0.326531\pi$
$71$	620.263	1.03678	0.518392	+	0.855143i	$0.326531\pi$
$72$	327.387	0.535875
$73$	790.345	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$73$	790.345	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$74$	45.5483	0.0715524
$75$	983.412	1.51406
$76$	1720.62	2.59696
$77$	206.656	0.305852
$78$	0	0
$79$	−119.274	−0.169866	−0.0849328	−	0.996387i	$-0.527068\pi$
$79$	−119.274	−0.169866	−0.0849328	+	0.996387i	$0.527068\pi$
$80$	126.189	0.176355
$81$	−187.547	−0.257266
$82$	−751.298	−1.01179
$83$	98.6344	0.130440	0.0652201	−	0.997871i	$-0.479225\pi$
$83$	98.6344	0.130440	0.0652201	+	0.997871i	$0.479225\pi$
$84$	−920.977	−1.19627
$85$	1341.33	1.71162
$86$	1067.08	1.33798
$87$	995.007	1.22616
$88$	268.716	0.325514
$89$	455.102	0.542030	0.271015	−	0.962575i	$-0.412641\pi$
$89$	455.102	0.542030	0.271015	+	0.962575i	$0.412641\pi$
$90$	1223.93	1.43348
$91$	0	0
$92$	−1378.34	−1.56197
$93$	277.206	0.309085
$94$	−197.157	−0.216332
$95$	2561.54	2.76641
$96$	612.165	0.650821
$97$	346.559	0.362761	0.181380	−	0.983413i	$-0.441943\pi$
$97$	346.559	0.362761	0.181380	+	0.983413i	$0.441943\pi$
$98$	−45.9047	−0.0473171
$99$	147.419	0.149658
$100$	3545.24	3.54524
$101$	1584.30	1.56083	0.780414	−	0.625264i	$-0.215009\pi$
$101$	1584.30	1.56083	0.780414	+	0.625264i	$0.215009\pi$
$102$	−1153.29	−1.11954
$103$	−430.743	−0.412062	−0.206031	−	0.978546i	$-0.566055\pi$
$103$	−430.743	−0.412062	−0.206031	+	0.978546i	$0.566055\pi$
$104$	0	0
$105$	−1371.08	−1.27432
$106$	3308.89	3.03196
$107$	446.381	0.403302	0.201651	−	0.979457i	$-0.435369\pi$
$107$	446.381	0.403302	0.201651	+	0.979457i	$0.435369\pi$
$108$	−1980.58	−1.76465
$109$	−1219.62	−1.07173	−0.535865	−	0.844303i	$-0.680015\pi$
$109$	−1219.62	−1.07173	−0.535865	+	0.844303i	$0.680015\pi$
$110$	1004.59	0.870759
$111$	−36.3987	−0.0311245
$112$	−119.787	−0.101061
$113$	−509.751	−0.424366	−0.212183	−	0.977230i	$-0.568057\pi$
$113$	−509.751	−0.424366	−0.212183	+	0.977230i	$0.568057\pi$
$114$	−2202.44	−1.80945
$115$	−2051.97	−1.66389
$116$	3587.04	2.87110
$117$	0	0
$118$	−2691.69	−2.09992
$119$	−1273.28	−0.980854
$120$	−1782.83	−1.35624
$121$	121.000	0.0909091
$122$	1576.64	1.17002
$123$	600.381	0.440118
$124$	999.337	0.723735
$125$	2804.02	2.00640
$126$	−1161.83	−0.821463
$127$	796.850	0.556764	0.278382	−	0.960470i	$-0.410202\pi$
$127$	796.850	0.556764	0.278382	+	0.960470i	$0.410202\pi$
$128$	2442.26	1.68646
$129$	−852.731	−0.582006
$130$	0	0
$131$	1834.53	1.22354	0.611770	−	0.791035i	$-0.290458\pi$
$131$	1834.53	1.22354	0.611770	+	0.791035i	$0.290458\pi$
$132$	−539.245	−0.355570
$133$	−2431.59	−1.58530
$134$	3220.58	2.07624
$135$	−2948.55	−1.87978
$136$	−1655.66	−1.04391
$137$	−387.717	−0.241788	−0.120894	−	0.992665i	$-0.538576\pi$
$137$	−387.717	−0.241788	−0.120894	+	0.992665i	$0.538576\pi$
$138$	1764.30	1.08831
$139$	−2736.11	−1.66960	−0.834798	−	0.550556i	$-0.814416\pi$
$139$	−2736.11	−1.66960	−0.834798	+	0.550556i	$0.814416\pi$
$140$	−4942.81	−2.98388
$141$	157.553	0.0941018
$142$	−2862.22	−1.69149
$143$	0	0
$144$	−85.4508	−0.0494507
$145$	5340.12	3.05843
$146$	−3647.07	−2.06735
$147$	36.6835	0.0205824
$148$	−131.219	−0.0728792
$149$	1496.72	0.822929	0.411465	−	0.911426i	$-0.365017\pi$
$149$	1496.72	0.822929	0.411465	+	0.911426i	$0.365017\pi$
$150$	−4537.98	−2.47017
$151$	−2527.52	−1.36216	−0.681080	−	0.732209i	$-0.738490\pi$
$151$	−2527.52	−1.36216	−0.681080	+	0.732209i	$0.738490\pi$
$152$	−3161.81	−1.68721
$153$	−908.303	−0.479947
$154$	−953.620	−0.498993
$155$	1487.74	0.770956
$156$	0	0
$157$	1946.37	0.989408	0.494704	−	0.869061i	$-0.335276\pi$
$157$	1946.37	0.989408	0.494704	+	0.869061i	$0.335276\pi$
$158$	550.394	0.277133
$159$	−2644.22	−1.31887
$160$	3285.44	1.62336
$161$	1947.87	0.953499
$162$	865.440	0.419725
$163$	962.612	0.462562	0.231281	−	0.972887i	$-0.425708\pi$
$163$	962.612	0.462562	0.231281	+	0.972887i	$0.425708\pi$
$164$	2164.40	1.03055
$165$	−802.789	−0.378770
$166$	−455.151	−0.212811
$167$	−1302.91	−0.603727	−0.301863	−	0.953351i	$-0.597609\pi$
$167$	−1302.91	−0.603727	−0.301863	+	0.953351i	$0.597609\pi$
$168$	1692.38	0.777202
$169$	0	0
$170$	−6189.62	−2.79248
$171$	−1734.58	−0.775713
$172$	−3074.13	−1.36279
$173$	1703.21	0.748514	0.374257	−	0.927325i	$-0.377898\pi$
$173$	1703.21	0.748514	0.374257	+	0.927325i	$0.377898\pi$
$174$	−4591.49	−2.00046
$175$	−5010.13	−2.16417
$176$	−70.1371	−0.0300385
$177$	2151.00	0.913441
$178$	−2100.08	−0.884313
$179$	959.537	0.400666	0.200333	−	0.979728i	$-0.435798\pi$
$179$	959.537	0.400666	0.200333	+	0.979728i	$0.435798\pi$
$180$	−3525.98	−1.46006
$181$	3296.59	1.35378	0.676888	−	0.736086i	$-0.263328\pi$
$181$	3296.59	1.35378	0.676888	+	0.736086i	$0.263328\pi$
$182$	0	0
$183$	−1259.93	−0.508945
$184$	2532.82	1.01479
$185$	−195.349	−0.0776343
$186$	−1279.17	−0.504267
$187$	−745.525	−0.291541
$188$	567.984	0.220343
$189$	2798.96	1.07722
$190$	−11820.3	−4.51334
$191$	1052.02	0.398543	0.199271	−	0.979944i	$-0.436143\pi$
$191$	1052.02	0.398543	0.199271	+	0.979944i	$0.436143\pi$
$192$	−3012.95	−1.13251
$193$	1543.16	0.575540	0.287770	−	0.957700i	$-0.407086\pi$
$193$	1543.16	0.575540	0.287770	+	0.957700i	$0.407086\pi$
$194$	−1599.21	−0.591838
$195$	0	0
$196$	132.246	0.0481944
$197$	−2564.36	−0.927427	−0.463713	−	0.885985i	$-0.653483\pi$
$197$	−2564.36	−0.927427	−0.463713	+	0.885985i	$0.653483\pi$
$198$	−680.269	−0.244165
$199$	618.993	0.220499	0.110249	−	0.993904i	$-0.464835\pi$
$199$	618.993	0.220499	0.110249	+	0.993904i	$0.464835\pi$
$200$	−6514.70	−2.30330
$201$	−2573.65	−0.903140
$202$	−7310.79	−2.54646
$203$	−5069.20	−1.75265
$204$	3322.49	1.14030
$205$	3222.20	1.09779
$206$	1987.68	0.672271
$207$	1389.52	0.466562
$208$	0	0
$209$	−1423.73	−0.471203
$210$	6326.90	2.07904
$211$	−102.673	−0.0334990	−0.0167495	−	0.999860i	$-0.505332\pi$
$211$	−102.673	−0.0334990	−0.0167495	+	0.999860i	$0.505332\pi$
$212$	−9532.51	−3.08818
$213$	2287.27	0.735780
$214$	−2059.84	−0.657980
$215$	−4576.54	−1.45171
$216$	3639.51	1.14647
$217$	−1412.26	−0.441800
$218$	5627.98	1.74851
$219$	2914.46	0.899274
$220$	−2894.08	−0.886905
$221$	0	0
$222$	167.963	0.0507790
$223$	4471.33	1.34270	0.671350	−	0.741140i	$-0.265715\pi$
$223$	4471.33	1.34270	0.671350	+	0.741140i	$0.265715\pi$
$224$	−3118.76	−0.930272
$225$	−3574.00	−1.05896
$226$	2352.26	0.692345
$227$	310.802	0.0908752	0.0454376	−	0.998967i	$-0.485532\pi$
$227$	310.802	0.0908752	0.0454376	+	0.998967i	$0.485532\pi$
$228$	6344.94	1.84300
$229$	4163.95	1.20158	0.600789	−	0.799408i	$-0.294853\pi$
$229$	4163.95	1.20158	0.600789	+	0.799408i	$0.294853\pi$
$230$	9468.86	2.71460
$231$	762.061	0.217056
$232$	−6591.52	−1.86532
$233$	−1678.18	−0.471849	−0.235925	−	0.971771i	$-0.575812\pi$
$233$	−1678.18	−0.471849	−0.235925	+	0.971771i	$0.575812\pi$
$234$	0	0
$235$	845.574	0.234720
$236$	7754.43	2.13886
$237$	−439.833	−0.120549
$238$	5875.60	1.60025
$239$	6855.31	1.85537	0.927685	−	0.373364i	$-0.121796\pi$
$239$	6855.31	1.85537	0.927685	+	0.373364i	$0.121796\pi$
$240$	465.333	0.125155
$241$	2819.47	0.753602	0.376801	−	0.926294i	$-0.377024\pi$
$241$	2819.47	0.753602	0.376801	+	0.926294i	$0.377024\pi$
$242$	−558.358	−0.148317
$243$	3330.99	0.879355
$244$	−4542.11	−1.19172
$245$	196.878	0.0513390
$246$	−2770.47	−0.718045
$247$	0	0
$248$	−1836.38	−0.470201
$249$	363.723	0.0925702
$250$	−12939.2	−3.27340
$251$	−2693.44	−0.677325	−0.338662	−	0.940908i	$-0.609974\pi$
$251$	−2693.44	−0.677325	−0.338662	+	0.940908i	$0.609974\pi$
$252$	3347.09	0.836695
$253$	1140.50	0.283410
$254$	−3677.09	−0.908351
$255$	4946.28	1.21470
$256$	−4733.45	−1.15563
$257$	1225.71	0.297500	0.148750	−	0.988875i	$-0.452475\pi$
$257$	1225.71	0.297500	0.148750	+	0.988875i	$0.452475\pi$
$258$	3934.95	0.949532
$259$	185.438	0.0444887
$260$	0	0
$261$	−3616.14	−0.857600
$262$	−8465.50	−1.99619
$263$	2300.15	0.539291	0.269646	−	0.962960i	$-0.413093\pi$
$263$	2300.15	0.539291	0.269646	+	0.962960i	$0.413093\pi$
$264$	990.913	0.231009
$265$	−14191.3	−3.28968
$266$	11220.6	2.58639
$267$	1678.23	0.384666
$268$	−9278.10	−2.11474
$269$	−4183.92	−0.948321	−0.474160	−	0.880438i	$-0.657248\pi$
$269$	−4183.92	−0.948321	−0.474160	+	0.880438i	$0.657248\pi$
$270$	13606.2	3.06683
$271$	−3308.84	−0.741689	−0.370845	−	0.928695i	$-0.620932\pi$
$271$	−3308.84	−0.741689	−0.370845	+	0.928695i	$0.620932\pi$
$272$	432.140	0.0963322
$273$	0	0
$274$	1789.13	0.394473
$275$	−2933.50	−0.643261
$276$	−5082.73	−1.10849
$277$	656.952	0.142500	0.0712499	−	0.997458i	$-0.477301\pi$
$277$	656.952	0.142500	0.0712499	+	0.997458i	$0.477301\pi$
$278$	12625.9	2.72392
$279$	−1007.45	−0.216180
$280$	9082.87	1.93859
$281$	7566.29	1.60629	0.803144	−	0.595785i	$-0.203159\pi$
$281$	7566.29	1.60629	0.803144	+	0.595785i	$0.203159\pi$
$282$	−727.033	−0.153525
$283$	2773.07	0.582479	0.291240	−	0.956650i	$-0.405932\pi$
$283$	2773.07	0.582479	0.291240	+	0.956650i	$0.405932\pi$
$284$	8245.70	1.72286
$285$	9445.89	1.96325
$286$	0	0
$287$	−3058.72	−0.629097
$288$	−2224.78	−0.455197
$289$	−319.546	−0.0650409
$290$	−24642.1	−4.98978
$291$	1277.97	0.257442
$292$	10506.7	2.10569
$293$	4758.11	0.948709	0.474354	−	0.880334i	$-0.342682\pi$
$293$	4758.11	0.948709	0.474354	+	0.880334i	$0.342682\pi$
$294$	−169.277	−0.0335798
$295$	11544.2	2.27841
$296$	241.127	0.0473487
$297$	1638.83	0.320184
$298$	−6906.68	−1.34259
$299$	0	0
$300$	13073.4	2.51597
$301$	4344.36	0.831909
$302$	11663.3	2.22234
$303$	5842.23	1.10768
$304$	825.257	0.155697
$305$	−6761.96	−1.26947
$306$	4191.39	0.783025
$307$	769.035	0.142968	0.0714840	−	0.997442i	$-0.477227\pi$
$307$	769.035	0.142968	0.0714840	+	0.997442i	$0.477227\pi$
$308$	2747.26	0.508245
$309$	−1588.40	−0.292430
$310$	−6865.22	−1.25780
$311$	804.126	0.146617	0.0733084	−	0.997309i	$-0.476644\pi$
$311$	804.126	0.146617	0.0733084	+	0.997309i	$0.476644\pi$
$312$	0	0
$313$	7233.90	1.30634	0.653170	−	0.757211i	$-0.273439\pi$
$313$	7233.90	1.30634	0.653170	+	0.757211i	$0.273439\pi$
$314$	−8981.57	−1.61420
$315$	4982.91	0.891286
$316$	−1585.61	−0.282271
$317$	−2161.28	−0.382932	−0.191466	−	0.981499i	$-0.561324\pi$
$317$	−2161.28	−0.382932	−0.191466	+	0.981499i	$0.561324\pi$
$318$	12201.8	2.15171
$319$	−2968.09	−0.520944
$320$	−16170.3	−2.82483
$321$	1646.07	0.286214
$322$	−8988.48	−1.55562
$323$	8772.11	1.51112
$324$	−2493.22	−0.427507
$325$	0	0
$326$	−4442.00	−0.754661
$327$	−4497.46	−0.760581
$328$	−3977.28	−0.669538
$329$	−802.675	−0.134507
$330$	3704.49	0.617956
$331$	−3564.76	−0.591955	−0.295978	−	0.955195i	$-0.595645\pi$
$331$	−3564.76	−0.591955	−0.295978	+	0.955195i	$0.595645\pi$
$332$	1311.23	0.216757
$333$	132.283	0.0217690
$334$	6012.33	0.984970
$335$	−13812.6	−2.25272
$336$	−441.725	−0.0717205
$337$	9469.23	1.53063	0.765315	−	0.643656i	$-0.222583\pi$
$337$	9469.23	1.53063	0.765315	+	0.643656i	$0.222583\pi$
$338$	0	0
$339$	−1879.75	−0.301162
$340$	17831.5	2.84426
$341$	−826.900	−0.131317
$342$	8004.29	1.26556
$343$	6257.02	0.984978
$344$	5648.99	0.885388
$345$	−7566.80	−1.18082
$346$	−7859.53	−1.22119
$347$	3030.03	0.468763	0.234381	−	0.972145i	$-0.424694\pi$
$347$	3030.03	0.468763	0.234381	+	0.972145i	$0.424694\pi$
$348$	13227.5	2.03755
$349$	11320.6	1.73633	0.868165	−	0.496276i	$-0.165300\pi$
$349$	11320.6	1.73633	0.868165	+	0.496276i	$0.165300\pi$
$350$	23119.4	3.53081
$351$	0	0
$352$	−1826.08	−0.276507
$353$	−9960.80	−1.50187	−0.750935	−	0.660376i	$-0.770397\pi$
$353$	−9960.80	−1.50187	−0.750935	+	0.660376i	$0.770397\pi$
$354$	−9925.85	−1.49026
$355$	12275.6	1.83527
$356$	6050.07	0.900710
$357$	−4695.34	−0.696088
$358$	−4427.81	−0.653679
$359$	−9822.94	−1.44411	−0.722054	−	0.691837i	$-0.756802\pi$
$359$	−9822.94	−1.44411	−0.722054	+	0.691837i	$0.756802\pi$
$360$	6479.31	0.948582
$361$	9893.08	1.44235
$362$	−15212.2	−2.20866
$363$	446.198	0.0645160
$364$	0	0
$365$	15641.7	2.24308
$366$	5814.00	0.830335
$367$	−2451.62	−0.348701	−0.174351	−	0.984684i	$-0.555783\pi$
$367$	−2451.62	−0.348701	−0.174351	+	0.984684i	$0.555783\pi$
$368$	−661.087	−0.0936455
$369$	−2181.96	−0.307827
$370$	901.444	0.126659
$371$	13471.3	1.88517
$372$	3685.14	0.513617
$373$	7431.12	1.03155	0.515776	−	0.856724i	$-0.327504\pi$
$373$	7431.12	1.03155	0.515776	+	0.856724i	$0.327504\pi$
$374$	3440.25	0.475644
$375$	10340.1	1.42389
$376$	−1043.72	−0.143154
$377$	0	0
$378$	−12915.9	−1.75747
$379$	−6225.63	−0.843771	−0.421886	−	0.906649i	$-0.638632\pi$
$379$	−6225.63	−0.843771	−0.421886	+	0.906649i	$0.638632\pi$
$380$	34052.8	4.59703
$381$	2938.45	0.395122
$382$	−4854.58	−0.650215
$383$	5098.87	0.680261	0.340131	−	0.940378i	$-0.389529\pi$
$383$	5098.87	0.680261	0.340131	+	0.940378i	$0.389529\pi$
$384$	9006.04	1.19684
$385$	4089.92	0.541407
$386$	−7120.96	−0.938983
$387$	3099.07	0.407066
$388$	4607.12	0.602812
$389$	−2672.32	−0.348308	−0.174154	−	0.984718i	$-0.555719\pi$
$389$	−2672.32	−0.348308	−0.174154	+	0.984718i	$0.555719\pi$
$390$	0	0
$391$	−7027.06	−0.908884
$392$	−243.014	−0.0313113
$393$	6764.99	0.868317
$394$	11833.3	1.51308
$395$	−2360.55	−0.300689
$396$	1959.77	0.248692
$397$	−400.284	−0.0506038	−0.0253019	−	0.999680i	$-0.508055\pi$
$397$	−400.284	−0.0506038	−0.0253019	+	0.999680i	$0.508055\pi$
$398$	−2856.36	−0.359740
$399$	−8966.68	−1.12505
$400$	1700.39	0.212549
$401$	−8939.46	−1.11325	−0.556627	−	0.830762i	$-0.687905\pi$
$401$	−8939.46	−1.11325	−0.556627	+	0.830762i	$0.687905\pi$
$402$	11876.2	1.47346
$403$	0	0
$404$	21061.5	2.59368
$405$	−3711.73	−0.455401
$406$	23392.0	2.85942
$407$	108.577	0.0132235
$408$	−6105.38	−0.740836
$409$	−9481.18	−1.14624	−0.573122	−	0.819470i	$-0.694268\pi$
$409$	−9481.18	−1.14624	−0.573122	+	0.819470i	$0.694268\pi$
$410$	−14868.9	−1.79103
$411$	−1429.74	−0.171591
$412$	−5726.24	−0.684737
$413$	−10958.6	−1.30566
$414$	−6411.98	−0.761187
$415$	1952.07	0.230900
$416$	0	0
$417$	−10089.6	−1.18487
$418$	6569.83	0.768759
$419$	12413.7	1.44737	0.723687	−	0.690128i	$-0.242446\pi$
$419$	12413.7	1.44737	0.723687	+	0.690128i	$0.242446\pi$
$420$	−18227.0	−2.11759
$421$	13243.0	1.53307	0.766536	−	0.642201i	$-0.221979\pi$
$421$	13243.0	1.53307	0.766536	+	0.642201i	$0.221979\pi$
$422$	473.786	0.0546529
$423$	−572.592	−0.0658165
$424$	17516.9	2.00635
$425$	18074.4	2.06291
$426$	−10554.7	−1.20041
$427$	6418.91	0.727477
$428$	5934.14	0.670181
$429$	0	0
$430$	21118.6	2.36844
$431$	−6005.50	−0.671171	−0.335585	−	0.942010i	$-0.608934\pi$
$431$	−6005.50	−0.671171	−0.335585	+	0.942010i	$0.608934\pi$
$432$	−949.941	−0.105796
$433$	−9921.49	−1.10115	−0.550573	−	0.834787i	$-0.685591\pi$
$433$	−9921.49	−1.10115	−0.550573	+	0.834787i	$0.685591\pi$
$434$	6516.93	0.720790
$435$	19692.1	2.17050
$436$	−16213.5	−1.78093
$437$	−13419.6	−1.46898
$438$	−13448.9	−1.46715
$439$	−4889.28	−0.531555	−0.265777	−	0.964034i	$-0.585629\pi$
$439$	−4889.28	−0.531555	−0.265777	+	0.964034i	$0.585629\pi$
$440$	5318.15	0.576211
$441$	−133.319	−0.0143957
$442$	0	0
$443$	−10568.8	−1.13349	−0.566747	−	0.823892i	$-0.691798\pi$
$443$	−10568.8	−1.13349	−0.566747	+	0.823892i	$0.691798\pi$
$444$	−483.880	−0.0517206
$445$	9006.90	0.959479
$446$	−20633.1	−2.19059
$447$	5519.30	0.584013
$448$	15349.9	1.61878
$449$	−15760.7	−1.65656	−0.828280	−	0.560315i	$-0.810680\pi$
$449$	−15760.7	−1.65656	−0.828280	+	0.560315i	$0.810680\pi$
$450$	16492.3	1.72768
$451$	−1790.93	−0.186988
$452$	−6776.56	−0.705183
$453$	−9320.42	−0.966692
$454$	−1434.21	−0.148261
$455$	0	0
$456$	−11659.4	−1.19737
$457$	1098.13	0.112404	0.0562018	−	0.998419i	$-0.482101\pi$
$457$	1098.13	0.112404	0.0562018	+	0.998419i	$0.482101\pi$
$458$	−19214.7	−1.96035
$459$	−10097.4	−1.02682
$460$	−27278.6	−2.76494
$461$	−257.041	−0.0259687	−0.0129843	−	0.999916i	$-0.504133\pi$
$461$	−257.041	−0.0259687	−0.0129843	+	0.999916i	$0.504133\pi$
$462$	−3516.55	−0.354123
$463$	−14489.1	−1.45435	−0.727177	−	0.686450i	$-0.759168\pi$
$463$	−14489.1	−1.45435	−0.727177	+	0.686450i	$0.759168\pi$
$464$	1720.44	0.172132
$465$	5486.17	0.547129
$466$	7743.99	0.769814
$467$	8855.29	0.877461	0.438730	−	0.898619i	$-0.355428\pi$
$467$	8855.29	0.877461	0.438730	+	0.898619i	$0.355428\pi$
$468$	0	0
$469$	13111.8	1.29093
$470$	−3901.92	−0.382941
$471$	7177.40	0.702159
$472$	−14249.5	−1.38959
$473$	2543.68	0.247270
$474$	2029.62	0.196674
$475$	34516.6	3.33417
$476$	−16926.9	−1.62992
$477$	9609.85	0.922442
$478$	−31634.0	−3.02700
$479$	13509.7	1.28867	0.644336	−	0.764743i	$-0.277134\pi$
$479$	13509.7	1.28867	0.644336	+	0.764743i	$0.277134\pi$
$480$	12115.3	1.15206
$481$	0	0
$482$	−13010.5	−1.22949
$483$	7182.92	0.676675
$484$	1608.56	0.151067
$485$	6858.74	0.642143
$486$	−15371.0	−1.43465
$487$	16750.5	1.55860	0.779298	−	0.626654i	$-0.215576\pi$
$487$	16750.5	1.55860	0.779298	+	0.626654i	$0.215576\pi$
$488$	8346.55	0.774243
$489$	3549.71	0.328269
$490$	−908.497	−0.0837586
$491$	4829.42	0.443888	0.221944	−	0.975059i	$-0.428760\pi$
$491$	4829.42	0.443888	0.221944	+	0.975059i	$0.428760\pi$
$492$	7981.39	0.731359
$493$	18287.5	1.67064
$494$	0	0
$495$	2917.56	0.264919
$496$	479.309	0.0433903
$497$	−11652.8	−1.05171
$498$	−1678.41	−0.151027
$499$	8964.56	0.804226	0.402113	−	0.915590i	$-0.368276\pi$
$499$	8964.56	0.804226	0.402113	+	0.915590i	$0.368276\pi$
$500$	37276.3	3.33410
$501$	−4804.60	−0.428450
$502$	12429.0	1.10504
$503$	12006.7	1.06432	0.532158	−	0.846645i	$-0.321381\pi$
$503$	12006.7	1.06432	0.532158	+	0.846645i	$0.321381\pi$
$504$	−6150.60	−0.543590
$505$	31354.8	2.76291
$506$	−5262.88	−0.462379
$507$	0	0
$508$	10593.2	0.925194
$509$	13634.7	1.18733	0.593663	−	0.804714i	$-0.297681\pi$
$509$	13634.7	1.18733	0.593663	+	0.804714i	$0.297681\pi$
$510$	−22824.7	−1.98176
$511$	−14848.1	−1.28541
$512$	2304.56	0.198922
$513$	−19283.1	−1.65959
$514$	−5656.06	−0.485366
$515$	−8524.81	−0.729414
$516$	−11336.1	−0.967139
$517$	−469.978	−0.0399799
$518$	−855.711	−0.0725826
$519$	6280.74	0.531202
$520$	0	0
$521$	16044.5	1.34918	0.674591	−	0.738192i	$-0.264320\pi$
$521$	16044.5	1.34918	0.674591	+	0.738192i	$0.264320\pi$
$522$	16686.8	1.39916
$523$	−6594.48	−0.551351	−0.275675	−	0.961251i	$-0.588901\pi$
$523$	−6594.48	−0.551351	−0.275675	+	0.961251i	$0.588901\pi$
$524$	24388.0	2.03320
$525$	−18475.3	−1.53586
$526$	−10614.1	−0.879844
$527$	5094.84	0.421128
$528$	−258.636	−0.0213176
$529$	−1417.03	−0.116465
$530$	65486.2	5.36705
$531$	−7817.35	−0.638878
$532$	−32325.2	−2.63435
$533$	0	0
$534$	−7744.22	−0.627575
$535$	8834.31	0.713908
$536$	17049.4	1.37392
$537$	3538.37	0.284343
$538$	19306.8	1.54717
$539$	−109.426	−0.00874458
$540$	−39197.7	−3.12370
$541$	−6092.77	−0.484193	−0.242097	−	0.970252i	$-0.577835\pi$
$541$	−6092.77	−0.484193	−0.242097	+	0.970252i	$0.577835\pi$
$542$	15268.7	1.21005
$543$	12156.4	0.960742
$544$	11251.1	0.886744
$545$	−24137.5	−1.89713
$546$	0	0
$547$	1980.28	0.154791	0.0773954	−	0.997000i	$-0.475340\pi$
$547$	1980.28	0.154791	0.0773954	+	0.997000i	$0.475340\pi$
$548$	−5154.27	−0.401787
$549$	4578.96	0.355966
$550$	13536.7	1.04947
$551$	34923.6	2.70017
$552$	9339.99	0.720175
$553$	2240.79	0.172311
$554$	−3031.52	−0.232486
$555$	−720.366	−0.0550952
$556$	−36373.5	−2.77442
$557$	4042.44	0.307511	0.153756	−	0.988109i	$-0.450863\pi$
$557$	4042.44	0.307511	0.153756	+	0.988109i	$0.450863\pi$
$558$	4648.88	0.352694
$559$	0	0
$560$	−2370.70	−0.178894
$561$	−2749.19	−0.206900
$562$	−34914.8	−2.62063
$563$	195.731	0.0146520	0.00732601	−	0.999973i	$-0.497668\pi$
$563$	195.731	0.0146520	0.00732601	+	0.999973i	$0.497668\pi$
$564$	2094.49	0.156372
$565$	−10088.5	−0.751194
$566$	−12796.4	−0.950305
$567$	3523.42	0.260970
$568$	−15152.2	−1.11932
$569$	−5398.85	−0.397771	−0.198885	−	0.980023i	$-0.563732\pi$
$569$	−5398.85	−0.397771	−0.198885	+	0.980023i	$0.563732\pi$
$570$	−43588.3	−3.20301
$571$	−11551.6	−0.846618	−0.423309	−	0.905985i	$-0.639132\pi$
$571$	−11551.6	−0.846618	−0.423309	+	0.905985i	$0.639132\pi$
$572$	0	0
$573$	3879.42	0.282836
$574$	14114.6	1.02636
$575$	−27650.1	−2.00538
$576$	10949.9	0.792096
$577$	4928.61	0.355599	0.177800	−	0.984067i	$-0.443102\pi$
$577$	4928.61	0.355599	0.177800	+	0.984067i	$0.443102\pi$
$578$	1474.55	0.106113
$579$	5690.54	0.408447
$580$	70990.9	5.08231
$581$	−1853.04	−0.132318
$582$	−5897.21	−0.420013
$583$	7887.66	0.560332
$584$	−19307.1	−1.36804
$585$	0	0
$586$	−21956.4	−1.54780
$587$	−22142.3	−1.55692	−0.778459	−	0.627696i	$-0.783998\pi$
$587$	−22142.3	−1.55692	−0.778459	+	0.627696i	$0.783998\pi$
$588$	487.666	0.0342024
$589$	9729.60	0.680647
$590$	−53271.2	−3.71719
$591$	−9456.29	−0.658172
$592$	−62.9361	−0.00436935
$593$	6962.36	0.482141	0.241071	−	0.970508i	$-0.422501\pi$
$593$	6962.36	0.482141	0.241071	+	0.970508i	$0.422501\pi$
$594$	−7562.44	−0.522375
$595$	−25199.5	−1.73627
$596$	19897.3	1.36749
$597$	2282.59	0.156482
$598$	0	0
$599$	−4050.44	−0.276288	−0.138144	−	0.990412i	$-0.544114\pi$
$599$	−4050.44	−0.276288	−0.138144	+	0.990412i	$0.544114\pi$
$600$	−24023.5	−1.63459
$601$	5193.94	0.352521	0.176261	−	0.984344i	$-0.443600\pi$
$601$	5193.94	0.352521	0.176261	+	0.984344i	$0.443600\pi$
$602$	−20047.2	−1.35724
$603$	9353.37	0.631673
$604$	−33600.5	−2.26355
$605$	2394.71	0.160923
$606$	−26959.1	−1.80716
$607$	−11147.8	−0.745428	−0.372714	−	0.927946i	$-0.621573\pi$
$607$	−11147.8	−0.745428	−0.372714	+	0.927946i	$0.621573\pi$
$608$	21486.3	1.43320
$609$	−18693.1	−1.24381
$610$	31203.3	2.07112
$611$	0	0
$612$	−12074.9	−0.797545
$613$	26142.9	1.72251	0.861257	−	0.508170i	$-0.169678\pi$
$613$	26142.9	1.72251	0.861257	+	0.508170i	$0.169678\pi$
$614$	−3548.73	−0.233250
$615$	11882.1	0.779078
$616$	−5048.34	−0.330201
$617$	8866.64	0.578537	0.289269	−	0.957248i	$-0.406588\pi$
$617$	8866.64	0.578537	0.289269	+	0.957248i	$0.406588\pi$
$618$	7329.72	0.477095
$619$	14375.9	0.933464	0.466732	−	0.884399i	$-0.345431\pi$
$619$	14375.9	0.933464	0.466732	+	0.884399i	$0.345431\pi$
$620$	19777.8	1.28112
$621$	15447.0	0.998178
$622$	−3710.66	−0.239203
$623$	−8549.96	−0.549834
$624$	0	0
$625$	22159.1	1.41818
$626$	−33381.1	−2.13127
$627$	−5250.12	−0.334401
$628$	25874.8	1.64413
$629$	−668.982	−0.0424071
$630$	−22993.8	−1.45412
$631$	−16861.7	−1.06379	−0.531897	−	0.846809i	$-0.678521\pi$
$631$	−16861.7	−1.06379	−0.531897	+	0.846809i	$0.678521\pi$
$632$	2913.71	0.183388
$633$	−378.614	−0.0237734
$634$	9973.28	0.624747
$635$	15770.4	0.985560
$636$	−35151.9	−2.19161
$637$	0	0
$638$	13696.3	0.849911
$639$	−8312.60	−0.514618
$640$	48334.7	2.98531
$641$	17281.8	1.06488	0.532442	−	0.846467i	$-0.321275\pi$
$641$	17281.8	1.06488	0.532442	+	0.846467i	$0.321275\pi$
$642$	−7595.83	−0.466952
$643$	−5058.54	−0.310248	−0.155124	−	0.987895i	$-0.549578\pi$
$643$	−5058.54	−0.310248	−0.155124	+	0.987895i	$0.549578\pi$
$644$	25894.7	1.58446
$645$	−16876.4	−1.03024
$646$	−40479.2	−2.46537
$647$	4595.03	0.279211	0.139605	−	0.990207i	$-0.455417\pi$
$647$	4595.03	0.279211	0.139605	+	0.990207i	$0.455417\pi$
$648$	4581.53	0.277746
$649$	−6416.40	−0.388083
$650$	0	0
$651$	−5207.84	−0.313535
$652$	12796.8	0.768655
$653$	−11986.5	−0.718326	−0.359163	−	0.933275i	$-0.616938\pi$
$653$	−11986.5	−0.718326	−0.359163	+	0.933275i	$0.616938\pi$
$654$	20753.7	1.24088
$655$	36307.2	2.16586
$656$	1038.10	0.0617852
$657$	−10592.0	−0.628969
$658$	3703.97	0.219446
$659$	−27151.2	−1.60495	−0.802475	−	0.596686i	$-0.796484\pi$
$659$	−27151.2	−1.60495	−0.802475	+	0.596686i	$0.796484\pi$
$660$	−10672.2	−0.629415
$661$	9477.81	0.557707	0.278853	−	0.960334i	$-0.410046\pi$
$661$	9477.81	0.557707	0.278853	+	0.960334i	$0.410046\pi$
$662$	16449.7	0.965765
$663$	0	0
$664$	−2409.51	−0.140824
$665$	−48123.4	−2.80623
$666$	−610.426	−0.0355158
$667$	−27976.2	−1.62405
$668$	−17320.8	−1.00323
$669$	16488.4	0.952882
$670$	63738.4	3.67527
$671$	3758.36	0.216229
$672$	−11500.7	−0.660192
$673$	−12835.8	−0.735192	−0.367596	−	0.929986i	$-0.619819\pi$
$673$	−12835.8	−0.735192	−0.367596	+	0.929986i	$0.619819\pi$
$674$	−43696.1	−2.49719
$675$	−39731.6	−2.26558
$676$	0	0
$677$	−25666.5	−1.45708	−0.728541	−	0.685002i	$-0.759801\pi$
$677$	−25666.5	−1.45708	−0.728541	+	0.685002i	$0.759801\pi$
$678$	8674.15	0.491340
$679$	−6510.78	−0.367984
$680$	−32767.1	−1.84788
$681$	1146.11	0.0644919
$682$	3815.76	0.214242
$683$	−34230.6	−1.91771	−0.958856	−	0.283892i	$-0.908374\pi$
$683$	−34230.6	−1.91771	−0.958856	+	0.283892i	$0.908374\pi$
$684$	−23059.3	−1.28903
$685$	−7673.30	−0.428003
$686$	−28873.2	−1.60697
$687$	15354.9	0.852731
$688$	−1474.43	−0.0817039
$689$	0	0
$690$	34917.2	1.92649
$691$	31496.4	1.73398	0.866988	−	0.498328i	$-0.166053\pi$
$691$	31496.4	1.73398	0.866988	+	0.498328i	$0.166053\pi$
$692$	22642.3	1.24383
$693$	−2769.55	−0.151813
$694$	−13982.2	−0.764778
$695$	−54150.2	−2.95545
$696$	−24306.8	−1.32377
$697$	11034.6	0.599661
$698$	−52239.3	−2.83279
$699$	−6188.41	−0.334860
$700$	−66604.0	−3.59628
$701$	−27292.4	−1.47050	−0.735249	−	0.677797i	$-0.762935\pi$
$701$	−27292.4	−1.47050	−0.735249	+	0.677797i	$0.762935\pi$
$702$	0	0
$703$	−1277.55	−0.0685403
$704$	8987.59	0.481154
$705$	3118.12	0.166575
$706$	45964.4	2.45027
$707$	−29764.1	−1.58330
$708$	28595.1	1.51790
$709$	−9950.79	−0.527094	−0.263547	−	0.964647i	$-0.584892\pi$
$709$	−9950.79	−0.527094	−0.263547	+	0.964647i	$0.584892\pi$
$710$	−56646.1	−2.99421
$711$	1598.48	0.0843146
$712$	−11117.6	−0.585180
$713$	−7794.07	−0.409383
$714$	21666.8	1.13566
$715$	0	0
$716$	12756.0	0.665800
$717$	25279.5	1.31671
$718$	45328.2	2.35604
$719$	18426.3	0.955753	0.477876	−	0.878427i	$-0.341407\pi$
$719$	18426.3	0.955753	0.477876	+	0.878427i	$0.341407\pi$
$720$	−1691.15	−0.0875355
$721$	8092.32	0.417994
$722$	−45651.9	−2.35317
$723$	10397.0	0.534813
$724$	43824.4	2.24962
$725$	71957.8	3.68613
$726$	−2058.99	−0.105257
$727$	−18460.9	−0.941781	−0.470891	−	0.882192i	$-0.656067\pi$
$727$	−18460.9	−0.941781	−0.470891	+	0.882192i	$0.656067\pi$
$728$	0	0
$729$	17347.1	0.881323
$730$	−72179.0	−3.65954
$731$	−15672.6	−0.792983
$732$	−16749.4	−0.845732
$733$	24975.1	1.25849	0.629247	−	0.777205i	$-0.283363\pi$
$733$	24975.1	1.25849	0.629247	+	0.777205i	$0.283363\pi$
$734$	11313.1	0.568900
$735$	726.003	0.0364340
$736$	−17212.0	−0.862013
$737$	7677.15	0.383706
$738$	10068.7	0.502214
$739$	−8876.13	−0.441832	−0.220916	−	0.975293i	$-0.570905\pi$
$739$	−8876.13	−0.441832	−0.220916	+	0.975293i	$0.570905\pi$
$740$	−2596.95	−0.129008
$741$	0	0
$742$	−62163.9	−3.07562
$743$	−35601.7	−1.75788	−0.878938	−	0.476937i	$-0.841747\pi$
$743$	−35601.7	−1.75788	−0.878938	+	0.476937i	$0.841747\pi$
$744$	−6771.79	−0.333691
$745$	29621.6	1.45671
$746$	−34291.1	−1.68296
$747$	−1321.87	−0.0647454
$748$	−9910.92	−0.484464
$749$	−8386.12	−0.409109
$750$	−47714.5	−2.32305
$751$	37294.6	1.81212	0.906058	−	0.423153i	$-0.139077\pi$
$751$	37294.6	1.81212	0.906058	+	0.423153i	$0.139077\pi$
$752$	272.420	0.0132103
$753$	−9932.29	−0.480681
$754$	0	0
$755$	−50021.9	−2.41124
$756$	37209.1	1.79005
$757$	2656.35	0.127538	0.0637692	−	0.997965i	$-0.479688\pi$
$757$	2656.35	0.127538	0.0637692	+	0.997965i	$0.479688\pi$
$758$	28728.4	1.37660
$759$	4205.70	0.201129
$760$	−62575.2	−2.98663
$761$	13669.7	0.651152	0.325576	−	0.945516i	$-0.394442\pi$
$761$	13669.7	0.651152	0.325576	+	0.945516i	$0.394442\pi$
$762$	−13559.6	−0.644634
$763$	22912.9	1.08716
$764$	13985.4	0.662272
$765$	−17976.2	−0.849582
$766$	−23528.9	−1.10983
$767$	0	0
$768$	−17455.0	−0.820121
$769$	624.543	0.0292868	0.0146434	−	0.999893i	$-0.495339\pi$
$769$	624.543	0.0292868	0.0146434	+	0.999893i	$0.495339\pi$
$770$	−18873.1	−0.883296
$771$	4519.89	0.211128
$772$	20514.6	0.956394
$773$	−17576.4	−0.817826	−0.408913	−	0.912573i	$-0.634092\pi$
$773$	−17576.4	−0.817826	−0.408913	+	0.912573i	$0.634092\pi$
$774$	−14300.7	−0.664121
$775$	20047.2	0.929184
$776$	−8466.01	−0.391639
$777$	683.820	0.0315726
$778$	12331.5	0.568259
$779$	21072.7	0.969200
$780$	0	0
$781$	−6822.89	−0.312602
$782$	32426.5	1.48283
$783$	−40200.0	−1.83478
$784$	63.4285	0.00288942
$785$	38520.5	1.75141
$786$	−31217.2	−1.41664
$787$	21207.3	0.960557	0.480279	−	0.877116i	$-0.340536\pi$
$787$	21207.3	0.960557	0.480279	+	0.877116i	$0.340536\pi$
$788$	−34090.3	−1.54114
$789$	8482.01	0.382722
$790$	10892.8	0.490568
$791$	9576.64	0.430475
$792$	−3601.26	−0.161572
$793$	0	0
$794$	1847.12	0.0825591
$795$	−52331.6	−2.33461
$796$	8228.81	0.366410
$797$	21481.3	0.954712	0.477356	−	0.878710i	$-0.341595\pi$
$797$	21481.3	0.954712	0.477356	+	0.878710i	$0.341595\pi$
$798$	41377.0	1.83550
$799$	2895.71	0.128214
$800$	44271.1	1.95653
$801$	−6099.15	−0.269042
$802$	41251.4	1.81626
$803$	−8693.79	−0.382064
$804$	−34213.7	−1.50078
$805$	38550.1	1.68784
$806$	0	0
$807$	−15428.6	−0.673000
$808$	−38702.4	−1.68508
$809$	−4674.16	−0.203133	−0.101566	−	0.994829i	$-0.532385\pi$
$809$	−4674.16	−0.203133	−0.101566	+	0.994829i	$0.532385\pi$
$810$	17127.9	0.742979
$811$	10381.5	0.449499	0.224749	−	0.974417i	$-0.427844\pi$
$811$	10381.5	0.449499	0.224749	+	0.974417i	$0.427844\pi$
$812$	−67389.3	−2.91244
$813$	−12201.6	−0.526359
$814$	−501.031	−0.0215739
$815$	19051.0	0.818807
$816$	1593.55	0.0683646
$817$	−29929.8	−1.28166
$818$	43751.2	1.87008
$819$	0	0
$820$	42835.5	1.82424
$821$	41246.0	1.75335	0.876673	−	0.481087i	$-0.159758\pi$
$821$	41246.0	1.75335	0.876673	+	0.481087i	$0.159758\pi$
$822$	6597.58	0.279948
$823$	−22899.1	−0.969882	−0.484941	−	0.874547i	$-0.661159\pi$
$823$	−22899.1	−0.969882	−0.484941	+	0.874547i	$0.661159\pi$
$824$	10522.5	0.444865
$825$	−10817.5	−0.456507
$826$	50568.6	2.13015
$827$	18630.2	0.783358	0.391679	−	0.920102i	$-0.371894\pi$
$827$	18630.2	0.783358	0.391679	+	0.920102i	$0.371894\pi$
$828$	18472.1	0.775302
$829$	−17105.3	−0.716638	−0.358319	−	0.933599i	$-0.616650\pi$
$829$	−17105.3	−0.716638	−0.358319	+	0.933599i	$0.616650\pi$
$830$	−9007.88	−0.376709
$831$	2422.57	0.101129
$832$	0	0
$833$	674.216	0.0280435
$834$	46558.9	1.93310
$835$	−25785.9	−1.06869
$836$	−18926.9	−0.783013
$837$	−11199.6	−0.462503
$838$	−57283.5	−2.36137
$839$	−16211.0	−0.667065	−0.333532	−	0.942739i	$-0.608241\pi$
$839$	−16211.0	−0.667065	−0.333532	+	0.942739i	$0.608241\pi$
$840$	33493.8	1.37577
$841$	48417.3	1.98521
$842$	−61110.1	−2.50118
$843$	27901.3	1.13994
$844$	−1364.92	−0.0556664
$845$	0	0
$846$	2642.24	0.107379
$847$	−2273.22	−0.0922180
$848$	−4572.05	−0.185147
$849$	10225.9	0.413371
$850$	−83404.8	−3.36560
$851$	1023.41	0.0412244
$852$	30406.7	1.22267
$853$	25403.3	1.01969	0.509843	−	0.860267i	$-0.329703\pi$
$853$	25403.3	1.01969	0.509843	+	0.860267i	$0.329703\pi$
$854$	−29620.2	−1.18687
$855$	−34329.1	−1.37313
$856$	−10904.5	−0.435408
$857$	26314.5	1.04887	0.524437	−	0.851449i	$-0.324276\pi$
$857$	26314.5	1.04887	0.524437	+	0.851449i	$0.324276\pi$
$858$	0	0
$859$	37876.6	1.50446	0.752231	−	0.658900i	$-0.228978\pi$
$859$	37876.6	1.50446	0.752231	+	0.658900i	$0.228978\pi$
$860$	−60839.9	−2.41235
$861$	−11279.3	−0.446455
$862$	27712.5	1.09500
$863$	−7130.65	−0.281263	−0.140632	−	0.990062i	$-0.544913\pi$
$863$	−7130.65	−0.281263	−0.140632	+	0.990062i	$0.544913\pi$
$864$	−24732.5	−0.973863
$865$	33708.2	1.32499
$866$	45783.0	1.79650
$867$	−1178.35	−0.0461579
$868$	−18774.5	−0.734155
$869$	1312.01	0.0512164
$870$	−90870.0	−3.54113
$871$	0	0
$872$	29793.8	1.15705
$873$	−4644.50	−0.180060
$874$	61924.9	2.39661
$875$	−52678.9	−2.03528
$876$	38744.5	1.49435
$877$	498.556	0.0191962	0.00959809	−	0.999954i	$-0.496945\pi$
$877$	498.556	0.0191962	0.00959809	+	0.999954i	$0.496945\pi$
$878$	22561.7	0.867222
$879$	17545.9	0.673275
$880$	−1388.08	−0.0531729
$881$	2371.51	0.0906903	0.0453452	−	0.998971i	$-0.485561\pi$
$881$	2371.51	0.0906903	0.0453452	+	0.998971i	$0.485561\pi$
$882$	615.202	0.0234863
$883$	−32108.2	−1.22370	−0.611849	−	0.790974i	$-0.709574\pi$
$883$	−32108.2	−1.22370	−0.611849	+	0.790974i	$0.709574\pi$
$884$	0	0
$885$	42570.3	1.61693
$886$	48769.9	1.84927
$887$	−24899.9	−0.942566	−0.471283	−	0.881982i	$-0.656209\pi$
$887$	−24899.9	−0.942566	−0.471283	+	0.881982i	$0.656209\pi$
$888$	889.175	0.0336022
$889$	−14970.4	−0.564780
$890$	−41562.6	−1.56537
$891$	2063.01	0.0775686
$892$	59441.3	2.23121
$893$	5529.92	0.207225
$894$	−25469.0	−0.952807
$895$	18990.1	0.709241
$896$	−45882.5	−1.71074
$897$	0	0
$898$	72728.4	2.70265
$899$	20283.6	0.752498
$900$	−47512.3	−1.75972
$901$	−48598.8	−1.79696
$902$	8264.28	0.305067
$903$	16020.2	0.590385
$904$	12452.6	0.458148
$905$	65242.7	2.39640
$906$	43009.4	1.57714
$907$	−15807.4	−0.578696	−0.289348	−	0.957224i	$-0.593438\pi$
$907$	−15807.4	−0.578696	−0.289348	+	0.957224i	$0.593438\pi$
$908$	4131.77	0.151011
$909$	−21232.3	−0.774733
$910$	0	0
$911$	6529.29	0.237459	0.118729	−	0.992927i	$-0.462118\pi$
$911$	6529.29	0.237459	0.118729	+	0.992927i	$0.462118\pi$
$912$	3043.21	0.110494
$913$	−1084.98	−0.0393292
$914$	−5067.36	−0.183385
$915$	−24935.3	−0.900913
$916$	55355.0	1.99670
$917$	−34465.2	−1.24116
$918$	46594.9	1.67523
$919$	−592.657	−0.0212731	−0.0106365	−	0.999943i	$-0.503386\pi$
$919$	−592.657	−0.0212731	−0.0106365	+	0.999943i	$0.503386\pi$
$920$	50127.0	1.79634
$921$	2835.88	0.101461
$922$	1186.12	0.0423675
$923$	0	0
$924$	10130.7	0.360689
$925$	−2632.32	−0.0935676
$926$	66860.4	2.37275
$927$	5772.70	0.204531
$928$	44793.1	1.58449
$929$	6338.23	0.223843	0.111922	−	0.993717i	$-0.464299\pi$
$929$	6338.23	0.223843	0.111922	+	0.993717i	$0.464299\pi$
$930$	−25316.1	−0.892631
$931$	1287.55	0.0453252
$932$	−22309.4	−0.784088
$933$	2965.28	0.104050
$934$	−40863.0	−1.43156
$935$	−14754.7	−0.516074
$936$	0	0
$937$	−19414.2	−0.676877	−0.338438	−	0.940989i	$-0.609899\pi$
$937$	−19414.2	−0.676877	−0.338438	+	0.940989i	$0.609899\pi$
$938$	−60504.8	−2.10613
$939$	26675.6	0.927078
$940$	11241.0	0.390042
$941$	29467.4	1.02084	0.510419	−	0.859926i	$-0.329490\pi$
$941$	29467.4	1.02084	0.510419	+	0.859926i	$0.329490\pi$
$942$	−33120.3	−1.14556
$943$	−16880.6	−0.582936
$944$	3719.23	0.128232
$945$	55394.1	1.90685
$946$	−11737.9	−0.403416
$947$	36382.4	1.24844	0.624218	−	0.781250i	$-0.285418\pi$
$947$	36382.4	1.24844	0.624218	+	0.781250i	$0.285418\pi$
$948$	−5847.08	−0.200321
$949$	0	0
$950$	−159278.	−5.43964
$951$	−7969.90	−0.271758
$952$	31104.7	1.05894
$953$	15865.6	0.539284	0.269642	−	0.962961i	$-0.413095\pi$
$953$	15865.6	0.539284	0.269642	+	0.962961i	$0.413095\pi$
$954$	−44344.9	−1.50495
$955$	20820.5	0.705483
$956$	91133.7	3.08313
$957$	−10945.1	−0.369701
$958$	−62340.9	−2.10245
$959$	7284.01	0.245269
$960$	−59629.2	−2.00471
$961$	−24140.1	−0.810314
$962$	0	0
$963$	−5982.28	−0.200183
$964$	37481.7	1.25229
$965$	30540.6	1.01880
$966$	−33145.8	−1.10398
$967$	−54819.1	−1.82302	−0.911512	−	0.411273i	$-0.865084\pi$
$967$	−54819.1	−1.82302	−0.911512	+	0.411273i	$0.865084\pi$
$968$	−2955.88	−0.0981462
$969$	32347.9	1.07241
$970$	−31649.9	−1.04765
$971$	18825.3	0.622177	0.311088	−	0.950381i	$-0.399306\pi$
$971$	18825.3	0.622177	0.311088	+	0.950381i	$0.399306\pi$
$972$	44281.8	1.46125
$973$	51403.0	1.69363
$974$	−77295.5	−2.54282
$975$	0	0
$976$	−2178.52	−0.0714474
$977$	−33592.0	−1.10000	−0.550002	−	0.835163i	$-0.685373\pi$
$977$	−33592.0	−1.10000	−0.550002	+	0.835163i	$0.685373\pi$
$978$	−16380.2	−0.535565
$979$	−5006.12	−0.163428
$980$	2617.27	0.0853117
$981$	16345.1	0.531965
$982$	−22285.5	−0.724195
$983$	−52254.5	−1.69548	−0.847741	−	0.530411i	$-0.822038\pi$
$983$	−52254.5	−1.69548	−0.847741	+	0.530411i	$0.822038\pi$
$984$	−14666.5	−0.475155
$985$	−50751.2	−1.64169
$986$	−84388.1	−2.72562
$987$	−2959.93	−0.0954566
$988$	0	0
$989$	23975.8	0.770867
$990$	−13463.2	−0.432210
$991$	−11333.3	−0.363285	−0.181642	−	0.983365i	$-0.558141\pi$
$991$	−11333.3	−0.363285	−0.181642	+	0.983365i	$0.558141\pi$
$992$	12479.2	0.399411
$993$	−13145.4	−0.420096
$994$	53772.3	1.71585
$995$	12250.5	0.390317
$996$	4835.28	0.153827
$997$	2785.34	0.0884781	0.0442390	−	0.999021i	$-0.485914\pi$
$997$	2785.34	0.0884781	0.0442390	+	0.999021i	$0.485914\pi$
$998$	−41367.2	−1.31208
$999$	1470.57	0.0465734

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.i.1.2		17
13.3	even	3		143.4.e.a.100.16	✓	34
13.9	even	3		143.4.e.a.133.16	yes	34
13.12	even	2		1859.4.a.f.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.16	✓	34	13.3	even	3
143.4.e.a.133.16	yes	34	13.9	even	3
1859.4.a.f.1.16		17	13.12	even	2
1859.4.a.i.1.2		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)

\(f(q)\)	\(=\)	\(q-4.61453 q^{2} +3.68758 q^{3} +13.2939 q^{4} +19.7910 q^{5} -17.0165 q^{6} -18.7869 q^{7} -24.4287 q^{8} -13.4017 q^{9} -91.3259 q^{10} -11.0000 q^{11} +49.0223 q^{12} +86.6927 q^{14} +72.9808 q^{15} +6.37610 q^{16} +67.7750 q^{17} +61.8427 q^{18} +129.430 q^{19} +263.099 q^{20} -69.2783 q^{21} +50.7598 q^{22} -103.682 q^{23} -90.0830 q^{24} +266.682 q^{25} -148.985 q^{27} -249.751 q^{28} +269.826 q^{29} -336.772 q^{30} +75.1728 q^{31} +166.007 q^{32} -40.5634 q^{33} -312.750 q^{34} -371.811 q^{35} -178.161 q^{36} -9.87062 q^{37} -597.258 q^{38} -483.468 q^{40} +162.811 q^{41} +319.687 q^{42} -231.244 q^{43} -146.233 q^{44} -265.233 q^{45} +478.444 q^{46} +42.7253 q^{47} +23.5124 q^{48} +9.94786 q^{49} -1230.61 q^{50} +249.926 q^{51} -717.060 q^{53} +687.494 q^{54} -217.701 q^{55} +458.940 q^{56} +477.283 q^{57} -1245.12 q^{58} +583.309 q^{59} +970.198 q^{60} -341.669 q^{61} -346.887 q^{62} +251.777 q^{63} -817.054 q^{64} +187.181 q^{66} -697.923 q^{67} +900.993 q^{68} -382.336 q^{69} +1715.73 q^{70} +620.263 q^{71} +327.387 q^{72} +790.345 q^{73} +45.5483 q^{74} +983.412 q^{75} +1720.62 q^{76} +206.656 q^{77} -119.274 q^{79} +126.189 q^{80} -187.547 q^{81} -751.298 q^{82} +98.6344 q^{83} -920.977 q^{84} +1341.33 q^{85} +1067.08 q^{86} +995.007 q^{87} +268.716 q^{88} +455.102 q^{89} +1223.93 q^{90} -1378.34 q^{92} +277.206 q^{93} -197.157 q^{94} +2561.54 q^{95} +612.165 q^{96} +346.559 q^{97} -45.9047 q^{98} +147.419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19}+ \cdots - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more