LMFDB - Embedded newform 2175.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2175,4,Mod(1,2175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2175, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2175.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2175.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$128.329154262$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-4.88324$ of defining polynomial
Character	$\chi$	$=$	2175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.88324 q^{2} +3.00000 q^{3} +15.8460 q^{4} -14.6497 q^{6} -5.48750 q^{7} -38.3141 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-4.88324 q^{2} +3.00000 q^{3} +15.8460 q^{4} -14.6497 q^{6} -5.48750 q^{7} -38.3141 q^{8} +9.00000 q^{9} +50.1324 q^{11} +47.5381 q^{12} +20.7349 q^{13} +26.7968 q^{14} +60.3288 q^{16} +18.8027 q^{17} -43.9492 q^{18} +78.8346 q^{19} -16.4625 q^{21} -244.809 q^{22} +6.33763 q^{23} -114.942 q^{24} -101.254 q^{26} +27.0000 q^{27} -86.9552 q^{28} +29.0000 q^{29} +310.950 q^{31} +11.9130 q^{32} +150.397 q^{33} -91.8182 q^{34} +142.614 q^{36} +338.745 q^{37} -384.969 q^{38} +62.2047 q^{39} +353.526 q^{41} +80.3904 q^{42} -507.609 q^{43} +794.400 q^{44} -30.9482 q^{46} +112.771 q^{47} +180.986 q^{48} -312.887 q^{49} +56.4081 q^{51} +328.566 q^{52} +144.849 q^{53} -131.848 q^{54} +210.249 q^{56} +236.504 q^{57} -141.614 q^{58} -342.739 q^{59} +357.486 q^{61} -1518.44 q^{62} -49.3875 q^{63} -540.804 q^{64} -734.426 q^{66} +183.087 q^{67} +297.949 q^{68} +19.0129 q^{69} -594.034 q^{71} -344.827 q^{72} +622.609 q^{73} -1654.17 q^{74} +1249.22 q^{76} -275.102 q^{77} -303.761 q^{78} -1275.18 q^{79} +81.0000 q^{81} -1726.35 q^{82} +739.108 q^{83} -260.866 q^{84} +2478.78 q^{86} +87.0000 q^{87} -1920.78 q^{88} +906.113 q^{89} -113.783 q^{91} +100.426 q^{92} +932.849 q^{93} -550.688 q^{94} +35.7390 q^{96} -76.0665 q^{97} +1527.90 q^{98} +451.192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9} + 76 q^{11} + 66 q^{12} - 30 q^{13} + 89 q^{14} + 138 q^{16} + 140 q^{17} + 18 q^{18} + 90 q^{19} + 150 q^{21} - 61 q^{22} - 34 q^{23} + 99 q^{24} - 241 q^{26} + 189 q^{27} + 57 q^{28} + 203 q^{29} + 524 q^{31} + 6 q^{32} + 228 q^{33} + 255 q^{34} + 198 q^{36} + 28 q^{37} - 222 q^{38} - 90 q^{39} + 1532 q^{41} + 267 q^{42} + 464 q^{43} + 1475 q^{44} + 72 q^{46} + 360 q^{47} + 414 q^{48} + 569 q^{49} + 420 q^{51} + 205 q^{52} - 282 q^{53} + 54 q^{54} + 1102 q^{56} + 270 q^{57} + 58 q^{58} + 766 q^{59} + 1200 q^{61} - 2856 q^{62} + 450 q^{63} + 701 q^{64} - 183 q^{66} - 1546 q^{67} - 1801 q^{68} - 102 q^{69} + 1802 q^{71} + 297 q^{72} + 220 q^{73} + 1594 q^{74} + 1960 q^{76} - 3222 q^{77} - 723 q^{78} + 1298 q^{79} + 567 q^{81} - 856 q^{82} - 1652 q^{83} + 171 q^{84} + 7628 q^{86} + 609 q^{87} - 550 q^{88} + 2846 q^{89} - 816 q^{91} - 472 q^{92} + 1572 q^{93} + 745 q^{94} + 18 q^{96} - 1110 q^{97} + 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9 + 76 * q^11 + 66 * q^12 - 30 * q^13 + 89 * q^14 + 138 * q^16 + 140 * q^17 + 18 * q^18 + 90 * q^19 + 150 * q^21 - 61 * q^22 - 34 * q^23 + 99 * q^24 - 241 * q^26 + 189 * q^27 + 57 * q^28 + 203 * q^29 + 524 * q^31 + 6 * q^32 + 228 * q^33 + 255 * q^34 + 198 * q^36 + 28 * q^37 - 222 * q^38 - 90 * q^39 + 1532 * q^41 + 267 * q^42 + 464 * q^43 + 1475 * q^44 + 72 * q^46 + 360 * q^47 + 414 * q^48 + 569 * q^49 + 420 * q^51 + 205 * q^52 - 282 * q^53 + 54 * q^54 + 1102 * q^56 + 270 * q^57 + 58 * q^58 + 766 * q^59 + 1200 * q^61 - 2856 * q^62 + 450 * q^63 + 701 * q^64 - 183 * q^66 - 1546 * q^67 - 1801 * q^68 - 102 * q^69 + 1802 * q^71 + 297 * q^72 + 220 * q^73 + 1594 * q^74 + 1960 * q^76 - 3222 * q^77 - 723 * q^78 + 1298 * q^79 + 567 * q^81 - 856 * q^82 - 1652 * q^83 + 171 * q^84 + 7628 * q^86 + 609 * q^87 - 550 * q^88 + 2846 * q^89 - 816 * q^91 - 472 * q^92 + 1572 * q^93 + 745 * q^94 + 18 * q^96 - 1110 * q^97 + 761 * q^98 + 684 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−4.88324	−1.72649	−0.863243	−	0.504788i	$-0.831571\pi$
$2$	−4.88324	−1.72649	−0.863243	+	0.504788i	$0.831571\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	15.8460	1.98076
$5$	0	0
$5$	0	0
$6$	−14.6497	−0.996787
$7$	−5.48750	−0.296297	−0.148149	−	0.988965i	$-0.547331\pi$
$7$	−5.48750	−0.296297	−0.148149	+	0.988965i	$0.547331\pi$
$8$	−38.3141	−1.69326
$9$	9.00000	0.333333
$10$	0	0
$11$	50.1324	1.37413	0.687067	−	0.726594i	$-0.258898\pi$
$11$	50.1324	1.37413	0.687067	+	0.726594i	$0.258898\pi$
$12$	47.5381	1.14359
$13$	20.7349	0.442371	0.221186	−	0.975232i	$-0.429007\pi$
$13$	20.7349	0.442371	0.221186	+	0.975232i	$0.429007\pi$
$14$	26.7968	0.511553
$15$	0	0
$16$	60.3288	0.942637
$17$	18.8027	0.268255	0.134127	−	0.990964i	$-0.457177\pi$
$17$	18.8027	0.268255	0.134127	+	0.990964i	$0.457177\pi$
$18$	−43.9492	−0.575496
$19$	78.8346	0.951890	0.475945	−	0.879475i	$-0.342106\pi$
$19$	78.8346	0.951890	0.475945	+	0.879475i	$0.342106\pi$
$20$	0	0
$21$	−16.4625	−0.171067
$22$	−244.809	−2.37243
$23$	6.33763	0.0574559	0.0287280	−	0.999587i	$-0.490854\pi$
$23$	6.33763	0.0574559	0.0287280	+	0.999587i	$0.490854\pi$
$24$	−114.942	−0.977605
$25$	0	0
$26$	−101.254	−0.763748
$27$	27.0000	0.192450
$28$	−86.9552	−0.586892
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	310.950	1.80156	0.900778	−	0.434280i	$-0.142997\pi$
$31$	310.950	1.80156	0.900778	+	0.434280i	$0.142997\pi$
$32$	11.9130	0.0658106
$33$	150.397	0.793357
$34$	−91.8182	−0.463138
$35$	0	0
$36$	142.614	0.660252
$37$	338.745	1.50512	0.752558	−	0.658525i	$-0.228820\pi$
$37$	338.745	1.50512	0.752558	+	0.658525i	$0.228820\pi$
$38$	−384.969	−1.64343
$39$	62.2047	0.255403
$40$	0	0
$41$	353.526	1.34662	0.673312	−	0.739359i	$-0.264871\pi$
$41$	353.526	1.34662	0.673312	+	0.739359i	$0.264871\pi$
$42$	80.3904	0.295345
$43$	−507.609	−1.80022	−0.900112	−	0.435658i	$-0.856516\pi$
$43$	−507.609	−1.80022	−0.900112	+	0.435658i	$0.856516\pi$
$44$	794.400	2.72183
$45$	0	0
$46$	−30.9482	−0.0991969
$47$	112.771	0.349986	0.174993	−	0.984570i	$-0.444010\pi$
$47$	112.771	0.349986	0.174993	+	0.984570i	$0.444010\pi$
$48$	180.986	0.544232
$49$	−312.887	−0.912208
$50$	0	0
$51$	56.4081	0.154877
$52$	328.566	0.876230
$53$	144.849	0.375406	0.187703	−	0.982226i	$-0.439896\pi$
$53$	144.849	0.375406	0.187703	+	0.982226i	$0.439896\pi$
$54$	−131.848	−0.332262
$55$	0	0
$56$	210.249	0.501709
$57$	236.504	0.549574
$58$	−141.614	−0.320600
$59$	−342.739	−0.756285	−0.378142	−	0.925747i	$-0.623437\pi$
$59$	−342.739	−0.756285	−0.378142	+	0.925747i	$0.623437\pi$
$60$	0	0
$61$	357.486	0.750350	0.375175	−	0.926954i	$-0.377583\pi$
$61$	357.486	0.750350	0.375175	+	0.926954i	$0.377583\pi$
$62$	−1518.44	−3.11036
$63$	−49.3875	−0.0987657
$64$	−540.804	−1.05626
$65$	0	0
$66$	−734.426	−1.36972
$67$	183.087	0.333844	0.166922	−	0.985970i	$-0.446617\pi$
$67$	183.087	0.333844	0.166922	+	0.985970i	$0.446617\pi$
$68$	297.949	0.531347
$69$	19.0129	0.0331722
$70$	0	0
$71$	−594.034	−0.992942	−0.496471	−	0.868053i	$-0.665371\pi$
$71$	−594.034	−0.992942	−0.496471	+	0.868053i	$0.665371\pi$
$72$	−344.827	−0.564421
$73$	622.609	0.998231	0.499115	−	0.866536i	$-0.333658\pi$
$73$	622.609	0.998231	0.499115	+	0.866536i	$0.333658\pi$
$74$	−1654.17	−2.59856
$75$	0	0
$76$	1249.22	1.88546
$77$	−275.102	−0.407152
$78$	−303.761	−0.440950
$79$	−1275.18	−1.81607	−0.908034	−	0.418897i	$-0.862417\pi$
$79$	−1275.18	−1.81607	−0.908034	+	0.418897i	$0.862417\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−1726.35	−2.32493
$83$	739.108	0.977441	0.488720	−	0.872440i	$-0.337464\pi$
$83$	739.108	0.977441	0.488720	+	0.872440i	$0.337464\pi$
$84$	−260.866	−0.338842
$85$	0	0
$86$	2478.78	3.10806
$87$	87.0000	0.107211
$88$	−1920.78	−2.32677
$89$	906.113	1.07919	0.539594	−	0.841925i	$-0.318578\pi$
$89$	906.113	1.07919	0.539594	+	0.841925i	$0.318578\pi$
$90$	0	0
$91$	−113.783	−0.131073
$92$	100.426	0.113806
$93$	932.849	1.04013
$94$	−550.688	−0.604246
$95$	0	0
$96$	35.7390	0.0379958
$97$	−76.0665	−0.0796225	−0.0398112	−	0.999207i	$-0.512676\pi$
$97$	−76.0665	−0.0796225	−0.0398112	+	0.999207i	$0.512676\pi$
$98$	1527.90	1.57491
$99$	451.192	0.458045
$100$	0	0
$101$	653.553	0.643871	0.321935	−	0.946762i	$-0.395667\pi$
$101$	653.553	0.643871	0.321935	+	0.946762i	$0.395667\pi$
$102$	−275.455	−0.267393
$103$	−969.801	−0.927741	−0.463871	−	0.885903i	$-0.653540\pi$
$103$	−969.801	−0.927741	−0.463871	+	0.885903i	$0.653540\pi$
$104$	−794.440	−0.749050
$105$	0	0
$106$	−707.332	−0.648133
$107$	1267.53	1.14520	0.572601	−	0.819835i	$-0.305935\pi$
$107$	1267.53	1.14520	0.572601	+	0.819835i	$0.305935\pi$
$108$	427.843	0.381197
$109$	−808.142	−0.710146	−0.355073	−	0.934838i	$-0.615544\pi$
$109$	−808.142	−0.710146	−0.355073	+	0.934838i	$0.615544\pi$
$110$	0	0
$111$	1016.23	0.868980
$112$	−331.054	−0.279301
$113$	1220.10	1.01572	0.507862	−	0.861438i	$-0.330436\pi$
$113$	1220.10	1.01572	0.507862	+	0.861438i	$0.330436\pi$
$114$	−1154.91	−0.948832
$115$	0	0
$116$	459.535	0.367817
$117$	186.614	0.147457
$118$	1673.68	1.30572
$119$	−103.180	−0.0794831
$120$	0	0
$121$	1182.26	0.888247
$122$	−1745.69	−1.29547
$123$	1060.58	0.777473
$124$	4927.32	3.56844
$125$	0	0
$126$	241.171	0.170518
$127$	−814.733	−0.569258	−0.284629	−	0.958638i	$-0.591870\pi$
$127$	−814.733	−0.569258	−0.284629	+	0.958638i	$0.591870\pi$
$128$	2545.57	1.75781
$129$	−1522.83	−1.03936
$130$	0	0
$131$	−1493.91	−0.996363	−0.498181	−	0.867073i	$-0.665999\pi$
$131$	−1493.91	−0.996363	−0.498181	+	0.867073i	$0.665999\pi$
$132$	2383.20	1.57145
$133$	−432.605	−0.282042
$134$	−894.056	−0.576378
$135$	0	0
$136$	−720.410	−0.454225
$137$	1608.72	1.00323	0.501615	−	0.865091i	$-0.332739\pi$
$137$	1608.72	1.00323	0.501615	+	0.865091i	$0.332739\pi$
$138$	−92.8445	−0.0572714
$139$	51.5725	0.0314700	0.0157350	−	0.999876i	$-0.494991\pi$
$139$	51.5725	0.0314700	0.0157350	+	0.999876i	$0.494991\pi$
$140$	0	0
$141$	338.313	0.202064
$142$	2900.81	1.71430
$143$	1039.49	0.607878
$144$	542.959	0.314212
$145$	0	0
$146$	−3040.35	−1.72343
$147$	−938.662	−0.526664
$148$	5367.77	2.98127
$149$	−608.330	−0.334472	−0.167236	−	0.985917i	$-0.553484\pi$
$149$	−608.330	−0.334472	−0.167236	+	0.985917i	$0.553484\pi$
$150$	0	0
$151$	−341.568	−0.184082	−0.0920412	−	0.995755i	$-0.529339\pi$
$151$	−341.568	−0.184082	−0.0920412	+	0.995755i	$0.529339\pi$
$152$	−3020.48	−1.61180
$153$	169.224	0.0894182
$154$	1343.39	0.702943
$155$	0	0
$156$	985.699	0.505891
$157$	358.378	0.182176	0.0910882	−	0.995843i	$-0.470965\pi$
$157$	358.378	0.182176	0.0910882	+	0.995843i	$0.470965\pi$
$158$	6227.03	3.13542
$159$	434.547	0.216741
$160$	0	0
$161$	−34.7777	−0.0170240
$162$	−395.543	−0.191832
$163$	1667.36	0.801213	0.400606	−	0.916250i	$-0.368799\pi$
$163$	1667.36	0.801213	0.400606	+	0.916250i	$0.368799\pi$
$164$	5602.00	2.66733
$165$	0	0
$166$	−3609.24	−1.68754
$167$	1832.30	0.849029	0.424514	−	0.905421i	$-0.360445\pi$
$167$	1832.30	0.849029	0.424514	+	0.905421i	$0.360445\pi$
$168$	630.746	0.289662
$169$	−1767.06	−0.804308
$170$	0	0
$171$	709.512	0.317297
$172$	−8043.60	−3.56580
$173$	−2034.77	−0.894224	−0.447112	−	0.894478i	$-0.647547\pi$
$173$	−2034.77	−0.894224	−0.447112	+	0.894478i	$0.647547\pi$
$174$	−424.842	−0.185099
$175$	0	0
$176$	3024.43	1.29531
$177$	−1028.22	−0.436641
$178$	−4424.77	−1.86320
$179$	−332.198	−0.138713	−0.0693566	−	0.997592i	$-0.522095\pi$
$179$	−332.198	−0.138713	−0.0693566	+	0.997592i	$0.522095\pi$
$180$	0	0
$181$	−843.391	−0.346347	−0.173173	−	0.984891i	$-0.555402\pi$
$181$	−843.391	−0.346347	−0.173173	+	0.984891i	$0.555402\pi$
$182$	555.629	0.226296
$183$	1072.46	0.433215
$184$	−242.821	−0.0972879
$185$	0	0
$186$	−4555.33	−1.79577
$187$	942.625	0.368618
$188$	1786.97	0.693236
$189$	−148.163	−0.0570224
$190$	0	0
$191$	2438.81	0.923908	0.461954	−	0.886904i	$-0.347148\pi$
$191$	2438.81	0.923908	0.461954	+	0.886904i	$0.347148\pi$
$192$	−1622.41	−0.609831
$193$	−4095.03	−1.52729	−0.763645	−	0.645637i	$-0.776592\pi$
$193$	−4095.03	−1.52729	−0.763645	+	0.645637i	$0.776592\pi$
$194$	371.451	0.137467
$195$	0	0
$196$	−4958.03	−1.80686
$197$	−3226.76	−1.16699	−0.583495	−	0.812117i	$-0.698315\pi$
$197$	−3226.76	−1.16699	−0.583495	+	0.812117i	$0.698315\pi$
$198$	−2203.28	−0.790809
$199$	−4218.74	−1.50281	−0.751404	−	0.659842i	$-0.770623\pi$
$199$	−4218.74	−1.50281	−0.751404	+	0.659842i	$0.770623\pi$
$200$	0	0
$201$	549.260	0.192745
$202$	−3191.46	−1.11163
$203$	−159.138	−0.0550210
$204$	893.846	0.306773
$205$	0	0
$206$	4735.77	1.60173
$207$	57.0387	0.0191520
$208$	1250.91	0.416996
$209$	3952.17	1.30803
$210$	0	0
$211$	−2798.33	−0.913010	−0.456505	−	0.889721i	$-0.650899\pi$
$211$	−2798.33	−0.913010	−0.456505	+	0.889721i	$0.650899\pi$
$212$	2295.28	0.743588
$213$	−1782.10	−0.573276
$214$	−6189.64	−1.97717
$215$	0	0
$216$	−1034.48	−0.325868
$217$	−1706.34	−0.533796
$218$	3946.35	1.22606
$219$	1867.83	0.576329
$220$	0	0
$221$	389.872	0.118668
$222$	−4962.52	−1.50028
$223$	−2496.01	−0.749529	−0.374764	−	0.927120i	$-0.622276\pi$
$223$	−2496.01	−0.749529	−0.374764	+	0.927120i	$0.622276\pi$
$224$	−65.3725	−0.0194995
$225$	0	0
$226$	−5958.02	−1.75364
$227$	−3409.57	−0.996920	−0.498460	−	0.866913i	$-0.666101\pi$
$227$	−3409.57	−0.996920	−0.498460	+	0.866913i	$0.666101\pi$
$228$	3747.65	1.08857
$229$	4794.47	1.38353	0.691763	−	0.722125i	$-0.256834\pi$
$229$	4794.47	1.38353	0.691763	+	0.722125i	$0.256834\pi$
$230$	0	0
$231$	−825.305	−0.235069
$232$	−1111.11	−0.314431
$233$	−1989.36	−0.559345	−0.279672	−	0.960095i	$-0.590226\pi$
$233$	−1989.36	−0.559345	−0.279672	+	0.960095i	$0.590226\pi$
$234$	−911.282	−0.254583
$235$	0	0
$236$	−5431.06	−1.49802
$237$	−3825.55	−1.04851
$238$	503.852	0.137226
$239$	2574.69	0.696832	0.348416	−	0.937340i	$-0.386720\pi$
$239$	2574.69	0.696832	0.348416	+	0.937340i	$0.386720\pi$
$240$	0	0
$241$	−3683.44	−0.984528	−0.492264	−	0.870446i	$-0.663831\pi$
$241$	−3683.44	−0.984528	−0.492264	+	0.870446i	$0.663831\pi$
$242$	−5773.24	−1.53355
$243$	243.000	0.0641500
$244$	5664.73	1.48626
$245$	0	0
$246$	−5179.06	−1.34230
$247$	1634.63	0.421089
$248$	−11913.8	−3.05050
$249$	2217.32	0.564326
$250$	0	0
$251$	4631.27	1.16463	0.582317	−	0.812962i	$-0.302146\pi$
$251$	4631.27	1.16463	0.582317	+	0.812962i	$0.302146\pi$
$252$	−782.597	−0.195631
$253$	317.720	0.0789522
$254$	3978.54	0.982817
$255$	0	0
$256$	−8104.22	−1.97857
$257$	1609.98	0.390770	0.195385	−	0.980727i	$-0.437404\pi$
$257$	1609.98	0.390770	0.195385	+	0.980727i	$0.437404\pi$
$258$	7436.33	1.79444
$259$	−1858.86	−0.445962
$260$	0	0
$261$	261.000	0.0618984
$262$	7295.12	1.72021
$263$	2868.22	0.672479	0.336239	−	0.941777i	$-0.390845\pi$
$263$	2868.22	0.672479	0.336239	+	0.941777i	$0.390845\pi$
$264$	−5762.34	−1.34336
$265$	0	0
$266$	2112.52	0.486942
$267$	2718.34	0.623070
$268$	2901.20	0.661264
$269$	−554.047	−0.125579	−0.0627896	−	0.998027i	$-0.520000\pi$
$269$	−554.047	−0.125579	−0.0627896	+	0.998027i	$0.520000\pi$
$270$	0	0
$271$	−1826.02	−0.409309	−0.204655	−	0.978834i	$-0.565607\pi$
$271$	−1826.02	−0.409309	−0.204655	+	0.978834i	$0.565607\pi$
$272$	1134.35	0.252867
$273$	−341.348	−0.0756752
$274$	−7855.79	−1.73206
$275$	0	0
$276$	301.279	0.0657060
$277$	−1470.00	−0.318859	−0.159429	−	0.987209i	$-0.550965\pi$
$277$	−1470.00	−0.318859	−0.159429	+	0.987209i	$0.550965\pi$
$278$	−251.841	−0.0543325
$279$	2798.55	0.600519
$280$	0	0
$281$	7826.43	1.66151	0.830757	−	0.556635i	$-0.187908\pi$
$281$	7826.43	1.66151	0.830757	+	0.556635i	$0.187908\pi$
$282$	−1652.06	−0.348861
$283$	6796.87	1.42767	0.713837	−	0.700312i	$-0.246956\pi$
$283$	6796.87	1.42767	0.713837	+	0.700312i	$0.246956\pi$
$284$	−9413.10	−1.96678
$285$	0	0
$286$	−5076.08	−1.04949
$287$	−1939.98	−0.399001
$288$	107.217	0.0219369
$289$	−4559.46	−0.928039
$290$	0	0
$291$	−228.199	−0.0459701
$292$	9865.89	1.97725
$293$	−3631.49	−0.724074	−0.362037	−	0.932164i	$-0.617919\pi$
$293$	−3631.49	−0.724074	−0.362037	+	0.932164i	$0.617919\pi$
$294$	4583.71	0.909277
$295$	0	0
$296$	−12978.7	−2.54856
$297$	1353.57	0.264452
$298$	2970.62	0.577461
$299$	131.410	0.0254169
$300$	0	0
$301$	2785.50	0.533401
$302$	1667.96	0.317816
$303$	1960.66	0.371739
$304$	4756.00	0.897287
$305$	0	0
$306$	−826.364	−0.154379
$307$	9080.77	1.68817	0.844083	−	0.536213i	$-0.180146\pi$
$307$	9080.77	1.68817	0.844083	+	0.536213i	$0.180146\pi$
$308$	−4359.27	−0.806469
$309$	−2909.40	−0.535632
$310$	0	0
$311$	2657.69	0.484577	0.242289	−	0.970204i	$-0.422102\pi$
$311$	2657.69	0.484577	0.242289	+	0.970204i	$0.422102\pi$
$312$	−2383.32	−0.432464
$313$	530.474	0.0957960	0.0478980	−	0.998852i	$-0.484748\pi$
$313$	530.474	0.0957960	0.0478980	+	0.998852i	$0.484748\pi$
$314$	−1750.05	−0.314525
$315$	0	0
$316$	−20206.6	−3.59719
$317$	−2393.66	−0.424106	−0.212053	−	0.977258i	$-0.568015\pi$
$317$	−2393.66	−0.424106	−0.212053	+	0.977258i	$0.568015\pi$
$318$	−2122.00	−0.374200
$319$	1453.84	0.255170
$320$	0	0
$321$	3802.58	0.661182
$322$	169.828	0.0293918
$323$	1482.31	0.255349
$324$	1283.53	0.220084
$325$	0	0
$326$	−8142.12	−1.38328
$327$	−2424.43	−0.410003
$328$	−13545.1	−2.28019
$329$	−618.830	−0.103700
$330$	0	0
$331$	−7984.54	−1.32589	−0.662945	−	0.748668i	$-0.730694\pi$
$331$	−7984.54	−1.32589	−0.662945	+	0.748668i	$0.730694\pi$
$332$	11711.9	1.93607
$333$	3048.70	0.501706
$334$	−8947.57	−1.46584
$335$	0	0
$336$	−993.163	−0.161254
$337$	−9704.45	−1.56865	−0.784325	−	0.620350i	$-0.786990\pi$
$337$	−9704.45	−1.56865	−0.784325	+	0.620350i	$0.786990\pi$
$338$	8629.00	1.38863
$339$	3660.29	0.586429
$340$	0	0
$341$	15588.7	2.47558
$342$	−3464.72	−0.547808
$343$	3599.18	0.566582
$344$	19448.6	3.04825
$345$	0	0
$346$	9936.27	1.54387
$347$	−5514.04	−0.853053	−0.426526	−	0.904475i	$-0.640263\pi$
$347$	−5514.04	−0.853053	−0.426526	+	0.904475i	$0.640263\pi$
$348$	1378.61	0.212359
$349$	2521.06	0.386674	0.193337	−	0.981132i	$-0.438069\pi$
$349$	2521.06	0.386674	0.193337	+	0.981132i	$0.438069\pi$
$350$	0	0
$351$	559.842	0.0851344
$352$	597.227	0.0904326
$353$	−5721.03	−0.862606	−0.431303	−	0.902207i	$-0.641946\pi$
$353$	−5721.03	−0.862606	−0.431303	+	0.902207i	$0.641946\pi$
$354$	5021.03	0.753855
$355$	0	0
$356$	14358.3	2.13761
$357$	−309.540	−0.0458896
$358$	1622.20	0.239486
$359$	6403.95	0.941470	0.470735	−	0.882275i	$-0.343989\pi$
$359$	6403.95	0.941470	0.470735	+	0.882275i	$0.343989\pi$
$360$	0	0
$361$	−644.098	−0.0939055
$362$	4118.48	0.597963
$363$	3546.77	0.512830
$364$	−1803.01	−0.259624
$365$	0	0
$366$	−5237.06	−0.747939
$367$	−13350.7	−1.89891	−0.949456	−	0.313899i	$-0.898365\pi$
$367$	−13350.7	−1.89891	−0.949456	+	0.313899i	$0.898365\pi$
$368$	382.341	0.0541601
$369$	3181.74	0.448874
$370$	0	0
$371$	−794.858	−0.111232
$372$	14782.0	2.06024
$373$	1367.05	0.189767	0.0948837	−	0.995488i	$-0.469752\pi$
$373$	1367.05	0.189767	0.0948837	+	0.995488i	$0.469752\pi$
$374$	−4603.07	−0.636414
$375$	0	0
$376$	−4320.72	−0.592617
$377$	601.312	0.0821463
$378$	723.513	0.0984484
$379$	9882.96	1.33945	0.669727	−	0.742607i	$-0.266411\pi$
$379$	9882.96	1.33945	0.669727	+	0.742607i	$0.266411\pi$
$380$	0	0
$381$	−2444.20	−0.328662
$382$	−11909.3	−1.59511
$383$	−13225.8	−1.76450	−0.882252	−	0.470777i	$-0.843974\pi$
$383$	−13225.8	−1.76450	−0.882252	+	0.470777i	$0.843974\pi$
$384$	7636.72	1.01487
$385$	0	0
$386$	19997.0	2.63684
$387$	−4568.48	−0.600075
$388$	−1205.35	−0.157713
$389$	−8442.16	−1.10035	−0.550173	−	0.835051i	$-0.685438\pi$
$389$	−8442.16	−1.10035	−0.550173	+	0.835051i	$0.685438\pi$
$390$	0	0
$391$	119.165	0.0154128
$392$	11988.0	1.54461
$393$	−4481.73	−0.575250
$394$	15757.0	2.01479
$395$	0	0
$396$	7149.60	0.907275
$397$	2268.55	0.286789	0.143394	−	0.989666i	$-0.454198\pi$
$397$	2268.55	0.286789	0.143394	+	0.989666i	$0.454198\pi$
$398$	20601.1	2.59458
$399$	−1297.82	−0.162837
$400$	0	0
$401$	8294.00	1.03287	0.516437	−	0.856325i	$-0.327258\pi$
$401$	8294.00	1.03287	0.516437	+	0.856325i	$0.327258\pi$
$402$	−2682.17	−0.332772
$403$	6447.51	0.796957
$404$	10356.2	1.27535
$405$	0	0
$406$	777.107	0.0949930
$407$	16982.1	2.06823
$408$	−2161.23	−0.262247
$409$	9913.01	1.19845	0.599226	−	0.800580i	$-0.295475\pi$
$409$	9913.01	1.19845	0.599226	+	0.800580i	$0.295475\pi$
$410$	0	0
$411$	4826.17	0.579216
$412$	−15367.5	−1.83763
$413$	1880.78	0.224085
$414$	−278.534	−0.0330656
$415$	0	0
$416$	247.015	0.0291127
$417$	154.718	0.0181692
$418$	−19299.4	−2.25829
$419$	−13332.1	−1.55446	−0.777228	−	0.629219i	$-0.783375\pi$
$419$	−13332.1	−1.55446	−0.777228	+	0.629219i	$0.783375\pi$
$420$	0	0
$421$	−2848.13	−0.329714	−0.164857	−	0.986317i	$-0.552716\pi$
$421$	−2848.13	−0.329714	−0.164857	+	0.986317i	$0.552716\pi$
$422$	13664.9	1.57630
$423$	1014.94	0.116662
$424$	−5549.76	−0.635661
$425$	0	0
$426$	8702.44	0.989752
$427$	−1961.70	−0.222326
$428$	20085.3	2.26836
$429$	3118.47	0.350958
$430$	0	0
$431$	12669.7	1.41595	0.707977	−	0.706235i	$-0.249608\pi$
$431$	12669.7	1.41595	0.707977	+	0.706235i	$0.249608\pi$
$432$	1628.88	0.181411
$433$	14545.6	1.61436	0.807178	−	0.590308i	$-0.200994\pi$
$433$	14545.6	1.61436	0.807178	+	0.590308i	$0.200994\pi$
$434$	8332.45	0.921591
$435$	0	0
$436$	−12805.9	−1.40663
$437$	499.625	0.0546917
$438$	−9121.05	−0.995024
$439$	11489.4	1.24911	0.624557	−	0.780979i	$-0.285280\pi$
$439$	11489.4	1.24911	0.624557	+	0.780979i	$0.285280\pi$
$440$	0	0
$441$	−2815.99	−0.304069
$442$	−1903.84	−0.204879
$443$	11125.7	1.19322	0.596611	−	0.802531i	$-0.296514\pi$
$443$	11125.7	1.19322	0.596611	+	0.802531i	$0.296514\pi$
$444$	16103.3	1.72124
$445$	0	0
$446$	12188.6	1.29405
$447$	−1824.99	−0.193107
$448$	2967.66	0.312966
$449$	−6676.79	−0.701776	−0.350888	−	0.936418i	$-0.614120\pi$
$449$	−6676.79	−0.701776	−0.350888	+	0.936418i	$0.614120\pi$
$450$	0	0
$451$	17723.1	1.85044
$452$	19333.7	2.01190
$453$	−1024.70	−0.106280
$454$	16649.7	1.72117
$455$	0	0
$456$	−9061.44	−0.930572
$457$	10826.9	1.10823	0.554114	−	0.832441i	$-0.313057\pi$
$457$	10826.9	1.10823	0.554114	+	0.832441i	$0.313057\pi$
$458$	−23412.6	−2.38864
$459$	507.673	0.0516256
$460$	0	0
$461$	−4114.21	−0.415657	−0.207829	−	0.978165i	$-0.566640\pi$
$461$	−4114.21	−0.415657	−0.207829	+	0.978165i	$0.566640\pi$
$462$	4030.16	0.405844
$463$	6107.19	0.613014	0.306507	−	0.951868i	$-0.400840\pi$
$463$	6107.19	0.613014	0.306507	+	0.951868i	$0.400840\pi$
$464$	1749.54	0.175043
$465$	0	0
$466$	9714.53	0.965701
$467$	1409.31	0.139647	0.0698235	−	0.997559i	$-0.477756\pi$
$467$	1409.31	0.139647	0.0698235	+	0.997559i	$0.477756\pi$
$468$	2957.10	0.292077
$469$	−1004.69	−0.0989172
$470$	0	0
$471$	1075.13	0.105180
$472$	13131.7	1.28059
$473$	−25447.7	−2.47375
$474$	18681.1	1.81023
$475$	0	0
$476$	−1634.99	−0.157437
$477$	1303.64	0.125135
$478$	−12572.8	−1.20307
$479$	12633.9	1.20513	0.602566	−	0.798069i	$-0.294145\pi$
$479$	12633.9	1.20513	0.602566	+	0.798069i	$0.294145\pi$
$480$	0	0
$481$	7023.84	0.665821
$482$	17987.1	1.69977
$483$	−104.333	−0.00982883
$484$	18734.1	1.75940
$485$	0	0
$486$	−1186.63	−0.110754
$487$	17024.7	1.58411	0.792056	−	0.610449i	$-0.209011\pi$
$487$	17024.7	1.58411	0.792056	+	0.610449i	$0.209011\pi$
$488$	−13696.7	−1.27054
$489$	5002.08	0.462580
$490$	0	0
$491$	−3792.47	−0.348578	−0.174289	−	0.984695i	$-0.555763\pi$
$491$	−3792.47	−0.348578	−0.174289	+	0.984695i	$0.555763\pi$
$492$	16806.0	1.53998
$493$	545.279	0.0498136
$494$	−7982.29	−0.727004
$495$	0	0
$496$	18759.2	1.69821
$497$	3259.76	0.294206
$498$	−10827.7	−0.974301
$499$	6484.19	0.581708	0.290854	−	0.956767i	$-0.406061\pi$
$499$	6484.19	0.581708	0.290854	+	0.956767i	$0.406061\pi$
$500$	0	0
$501$	5496.91	0.490187
$502$	−22615.6	−2.01073
$503$	8781.60	0.778434	0.389217	−	0.921146i	$-0.372746\pi$
$503$	8781.60	0.778434	0.389217	+	0.921146i	$0.372746\pi$
$504$	1892.24	0.167236
$505$	0	0
$506$	−1551.51	−0.136310
$507$	−5301.19	−0.464367
$508$	−12910.3	−1.12756
$509$	21343.3	1.85860	0.929299	−	0.369328i	$-0.120412\pi$
$509$	21343.3	1.85860	0.929299	+	0.369328i	$0.120412\pi$
$510$	0	0
$511$	−3416.57	−0.295773
$512$	19210.3	1.65817
$513$	2128.54	0.183191
$514$	−7861.93	−0.674659
$515$	0	0
$516$	−24130.8	−2.05872
$517$	5653.48	0.480928
$518$	9077.28	0.769947
$519$	−6104.31	−0.516280
$520$	0	0
$521$	7007.06	0.589223	0.294611	−	0.955617i	$-0.404810\pi$
$521$	7007.06	0.589223	0.294611	+	0.955617i	$0.404810\pi$
$522$	−1274.53	−0.106867
$523$	5901.85	0.493441	0.246721	−	0.969087i	$-0.420647\pi$
$523$	5901.85	0.493441	0.246721	+	0.969087i	$0.420647\pi$
$524$	−23672.6	−1.97355
$525$	0	0
$526$	−14006.2	−1.16103
$527$	5846.70	0.483276
$528$	9073.28	0.747848
$529$	−12126.8	−0.996699
$530$	0	0
$531$	−3084.65	−0.252095
$532$	−6855.08	−0.558657
$533$	7330.34	0.595707
$534$	−13274.3	−1.07572
$535$	0	0
$536$	−7014.80	−0.565286
$537$	−996.595	−0.0800861
$538$	2705.54	0.216811
$539$	−15685.8	−1.25350
$540$	0	0
$541$	7826.71	0.621990	0.310995	−	0.950412i	$-0.399338\pi$
$541$	7826.71	0.621990	0.310995	+	0.950412i	$0.399338\pi$
$542$	8916.90	0.706667
$543$	−2530.17	−0.199963
$544$	223.997	0.0176540
$545$	0	0
$546$	1666.89	0.130652
$547$	−4256.78	−0.332737	−0.166368	−	0.986064i	$-0.553204\pi$
$547$	−4256.78	−0.332737	−0.166368	+	0.986064i	$0.553204\pi$
$548$	25491.9	1.98716
$549$	3217.37	0.250117
$550$	0	0
$551$	2286.20	0.176762
$552$	−728.462	−0.0561692
$553$	6997.57	0.538096
$554$	7178.38	0.550506
$555$	0	0
$556$	817.221	0.0623343
$557$	11138.6	0.847324	0.423662	−	0.905820i	$-0.360744\pi$
$557$	11138.6	0.847324	0.423662	+	0.905820i	$0.360744\pi$
$558$	−13666.0	−1.03679
$559$	−10525.2	−0.796368
$560$	0	0
$561$	2827.88	0.212822
$562$	−38218.3	−2.86858
$563$	−16458.1	−1.23202	−0.616009	−	0.787739i	$-0.711252\pi$
$563$	−16458.1	−1.23202	−0.616009	+	0.787739i	$0.711252\pi$
$564$	5360.92	0.400240
$565$	0	0
$566$	−33190.7	−2.46486
$567$	−444.488	−0.0329219
$568$	22759.9	1.68131
$569$	2449.68	0.180485	0.0902423	−	0.995920i	$-0.471236\pi$
$569$	2449.68	0.180485	0.0902423	+	0.995920i	$0.471236\pi$
$570$	0	0
$571$	156.880	0.0114978	0.00574888	−	0.999983i	$-0.498170\pi$
$571$	156.880	0.0114978	0.00574888	+	0.999983i	$0.498170\pi$
$572$	16471.8	1.20406
$573$	7316.44	0.533419
$574$	9473.37	0.688869
$575$	0	0
$576$	−4867.24	−0.352086
$577$	20318.3	1.46597	0.732984	−	0.680246i	$-0.238127\pi$
$577$	20318.3	1.46597	0.732984	+	0.680246i	$0.238127\pi$
$578$	22264.9	1.60225
$579$	−12285.1	−0.881781
$580$	0	0
$581$	−4055.85	−0.289613
$582$	1114.35	0.0793667
$583$	7261.62	0.515859
$584$	−23854.7	−1.69027
$585$	0	0
$586$	17733.4	1.25010
$587$	9510.91	0.668752	0.334376	−	0.942440i	$-0.391475\pi$
$587$	9510.91	0.668752	0.334376	+	0.942440i	$0.391475\pi$
$588$	−14874.1	−1.04319
$589$	24513.6	1.71488
$590$	0	0
$591$	−9680.27	−0.673762
$592$	20436.1	1.41878
$593$	15977.2	1.10641	0.553207	−	0.833044i	$-0.313404\pi$
$593$	15977.2	1.10641	0.553207	+	0.833044i	$0.313404\pi$
$594$	−6609.83	−0.456574
$595$	0	0
$596$	−9639.62	−0.662507
$597$	−12656.2	−0.867647
$598$	−641.707	−0.0438819
$599$	−4002.17	−0.272995	−0.136498	−	0.990640i	$-0.543585\pi$
$599$	−4002.17	−0.272995	−0.136498	+	0.990640i	$0.543585\pi$
$600$	0	0
$601$	−1574.81	−0.106885	−0.0534425	−	0.998571i	$-0.517019\pi$
$601$	−1574.81	−0.106885	−0.0534425	+	0.998571i	$0.517019\pi$
$602$	−13602.3	−0.920910
$603$	1647.78	0.111281
$604$	−5412.51	−0.364622
$605$	0	0
$606$	−9574.37	−0.641802
$607$	8803.52	0.588672	0.294336	−	0.955702i	$-0.404902\pi$
$607$	8803.52	0.588672	0.294336	+	0.955702i	$0.404902\pi$
$608$	939.156	0.0626444
$609$	−477.413	−0.0317664
$610$	0	0
$611$	2338.29	0.154824
$612$	2681.54	0.177116
$613$	−16874.2	−1.11181	−0.555907	−	0.831245i	$-0.687629\pi$
$613$	−16874.2	−1.11181	−0.555907	+	0.831245i	$0.687629\pi$
$614$	−44343.6	−2.91460
$615$	0	0
$616$	10540.3	0.689415
$617$	−4592.02	−0.299624	−0.149812	−	0.988715i	$-0.547867\pi$
$617$	−4592.02	−0.299624	−0.149812	+	0.988715i	$0.547867\pi$
$618$	14207.3	0.924761
$619$	4982.48	0.323526	0.161763	−	0.986830i	$-0.448282\pi$
$619$	4982.48	0.323526	0.161763	+	0.986830i	$0.448282\pi$
$620$	0	0
$621$	171.116	0.0110574
$622$	−12978.1	−0.836616
$623$	−4972.30	−0.319761
$624$	3752.74	0.240753
$625$	0	0
$626$	−2590.43	−0.165391
$627$	11856.5	0.755189
$628$	5678.88	0.360847
$629$	6369.32	0.403755
$630$	0	0
$631$	20584.3	1.29865	0.649325	−	0.760511i	$-0.275051\pi$
$631$	20584.3	1.29865	0.649325	+	0.760511i	$0.275051\pi$
$632$	48857.6	3.07508
$633$	−8394.99	−0.527126
$634$	11688.8	0.732213
$635$	0	0
$636$	6885.84	0.429310
$637$	−6487.69	−0.403535
$638$	−7099.45	−0.440548
$639$	−5346.31	−0.330981
$640$	0	0
$641$	4840.03	0.298237	0.149118	−	0.988819i	$-0.452356\pi$
$641$	4840.03	0.298237	0.149118	+	0.988819i	$0.452356\pi$
$642$	−18568.9	−1.14152
$643$	−1340.16	−0.0821941	−0.0410970	−	0.999155i	$-0.513085\pi$
$643$	−1340.16	−0.0821941	−0.0410970	+	0.999155i	$0.513085\pi$
$644$	−551.090	−0.0337205
$645$	0	0
$646$	−7238.46	−0.440856
$647$	−15752.3	−0.957169	−0.478585	−	0.878041i	$-0.658850\pi$
$647$	−15752.3	−0.957169	−0.478585	+	0.878041i	$0.658850\pi$
$648$	−3103.44	−0.188140
$649$	−17182.3	−1.03924
$650$	0	0
$651$	−5119.01	−0.308187
$652$	26421.1	1.58701
$653$	−2290.66	−0.137275	−0.0686373	−	0.997642i	$-0.521865\pi$
$653$	−2290.66	−0.137275	−0.0686373	+	0.997642i	$0.521865\pi$
$654$	11839.1	0.707865
$655$	0	0
$656$	21327.8	1.26938
$657$	5603.48	0.332744
$658$	3021.90	0.179036
$659$	−3003.49	−0.177541	−0.0887704	−	0.996052i	$-0.528294\pi$
$659$	−3003.49	−0.177541	−0.0887704	+	0.996052i	$0.528294\pi$
$660$	0	0
$661$	8104.71	0.476909	0.238454	−	0.971154i	$-0.423359\pi$
$661$	8104.71	0.476909	0.238454	+	0.971154i	$0.423359\pi$
$662$	38990.4	2.28913
$663$	1169.62	0.0685131
$664$	−28318.3	−1.65506
$665$	0	0
$666$	−14887.6	−0.866188
$667$	183.791	0.0106693
$668$	29034.7	1.68172
$669$	−7488.02	−0.432741
$670$	0	0
$671$	17921.6	1.03108
$672$	−196.118	−0.0112580
$673$	−5747.03	−0.329170	−0.164585	−	0.986363i	$-0.552629\pi$
$673$	−5747.03	−0.329170	−0.164585	+	0.986363i	$0.552629\pi$
$674$	47389.2	2.70825
$675$	0	0
$676$	−28001.0	−1.59314
$677$	−25714.2	−1.45979	−0.729895	−	0.683559i	$-0.760431\pi$
$677$	−25714.2	−1.45979	−0.729895	+	0.683559i	$0.760431\pi$
$678$	−17874.1	−1.01246
$679$	417.415	0.0235919
$680$	0	0
$681$	−10228.7	−0.575572
$682$	−76123.2	−4.27406
$683$	−4007.09	−0.224490	−0.112245	−	0.993681i	$-0.535804\pi$
$683$	−4007.09	−0.224490	−0.112245	+	0.993681i	$0.535804\pi$
$684$	11243.0	0.628487
$685$	0	0
$686$	−17575.7	−0.978196
$687$	14383.4	0.798779
$688$	−30623.4	−1.69696
$689$	3003.43	0.166069
$690$	0	0
$691$	−27863.7	−1.53399	−0.766993	−	0.641655i	$-0.778248\pi$
$691$	−27863.7	−1.53399	−0.766993	+	0.641655i	$0.778248\pi$
$692$	−32243.1	−1.77124
$693$	−2475.91	−0.135717
$694$	26926.4	1.47278
$695$	0	0
$696$	−3333.33	−0.181537
$697$	6647.26	0.361238
$698$	−12311.0	−0.667588
$699$	−5968.08	−0.322938
$700$	0	0
$701$	12916.0	0.695906	0.347953	−	0.937512i	$-0.386877\pi$
$701$	12916.0	0.695906	0.347953	+	0.937512i	$0.386877\pi$
$702$	−2733.85	−0.146983
$703$	26704.8	1.43271
$704$	−27111.8	−1.45144
$705$	0	0
$706$	27937.2	1.48928
$707$	−3586.37	−0.190777
$708$	−16293.2	−0.864880
$709$	−30250.8	−1.60239	−0.801193	−	0.598406i	$-0.795801\pi$
$709$	−30250.8	−1.60239	−0.801193	+	0.598406i	$0.795801\pi$
$710$	0	0
$711$	−11476.7	−0.605356
$712$	−34716.9	−1.82735
$713$	1970.68	0.103510
$714$	1511.56	0.0792277
$715$	0	0
$716$	−5264.03	−0.274757
$717$	7724.07	0.402316
$718$	−31272.1	−1.62544
$719$	6161.35	0.319582	0.159791	−	0.987151i	$-0.448918\pi$
$719$	6161.35	0.319582	0.159791	+	0.987151i	$0.448918\pi$
$720$	0	0
$721$	5321.78	0.274887
$722$	3145.29	0.162127
$723$	−11050.3	−0.568417
$724$	−13364.4	−0.686029
$725$	0	0
$726$	−17319.7	−0.885393
$727$	35454.3	1.80870	0.904352	−	0.426786i	$-0.140354\pi$
$727$	35454.3	1.80870	0.904352	+	0.426786i	$0.140354\pi$
$728$	4359.49	0.221941
$729$	729.000	0.0370370
$730$	0	0
$731$	−9544.43	−0.482919
$732$	16994.2	0.858092
$733$	26681.1	1.34446	0.672231	−	0.740342i	$-0.265336\pi$
$733$	26681.1	1.34446	0.672231	+	0.740342i	$0.265336\pi$
$734$	65194.7	3.27845
$735$	0	0
$736$	75.5001	0.00378121
$737$	9178.57	0.458747
$738$	−15537.2	−0.774976
$739$	−28886.6	−1.43791	−0.718953	−	0.695059i	$-0.755378\pi$
$739$	−28886.6	−1.43791	−0.718953	+	0.695059i	$0.755378\pi$
$740$	0	0
$741$	4903.89	0.243116
$742$	3881.48	0.192040
$743$	16398.0	0.809669	0.404834	−	0.914390i	$-0.367329\pi$
$743$	16398.0	0.809669	0.404834	+	0.914390i	$0.367329\pi$
$744$	−35741.3	−1.76121
$745$	0	0
$746$	−6675.64	−0.327631
$747$	6651.97	0.325814
$748$	14936.9	0.730142
$749$	−6955.56	−0.339320
$750$	0	0
$751$	−5905.21	−0.286930	−0.143465	−	0.989655i	$-0.545824\pi$
$751$	−5905.21	−0.286930	−0.143465	+	0.989655i	$0.545824\pi$
$752$	6803.33	0.329910
$753$	13893.8	0.672402
$754$	−2936.35	−0.141824
$755$	0	0
$756$	−2347.79	−0.112947
$757$	12439.0	0.597229	0.298614	−	0.954374i	$-0.403476\pi$
$757$	12439.0	0.597229	0.298614	+	0.954374i	$0.403476\pi$
$758$	−48260.9	−2.31255
$759$	953.161	0.0455831
$760$	0	0
$761$	14270.0	0.679748	0.339874	−	0.940471i	$-0.389616\pi$
$761$	14270.0	0.679748	0.339874	+	0.940471i	$0.389616\pi$
$762$	11935.6	0.567430
$763$	4434.68	0.210414
$764$	38645.6	1.83004
$765$	0	0
$766$	64584.6	3.04639
$767$	−7106.66	−0.334559
$768$	−24312.7	−1.14233
$769$	−15143.9	−0.710147	−0.355074	−	0.934838i	$-0.615544\pi$
$769$	−15143.9	−0.710147	−0.355074	+	0.934838i	$0.615544\pi$
$770$	0	0
$771$	4829.95	0.225611
$772$	−64890.1	−3.02519
$773$	40617.2	1.88991	0.944955	−	0.327202i	$-0.106106\pi$
$773$	40617.2	1.88991	0.944955	+	0.327202i	$0.106106\pi$
$774$	22309.0	1.03602
$775$	0	0
$776$	2914.42	0.134822
$777$	−5576.59	−0.257476
$778$	41225.1	1.89973
$779$	27870.1	1.28184
$780$	0	0
$781$	−29780.4	−1.36444
$782$	−581.910	−0.0266100
$783$	783.000	0.0357371
$784$	−18876.1	−0.859881
$785$	0	0
$786$	21885.4	0.993162
$787$	−43878.2	−1.98741	−0.993703	−	0.112048i	$-0.964259\pi$
$787$	−43878.2	−1.98741	−0.993703	+	0.112048i	$0.964259\pi$
$788$	−51131.3	−2.31152
$789$	8604.66	0.388256
$790$	0	0
$791$	−6695.27	−0.300956
$792$	−17287.0	−0.775590
$793$	7412.43	0.331933
$794$	−11077.9	−0.495137
$795$	0	0
$796$	−66850.4	−2.97670
$797$	−14556.0	−0.646925	−0.323463	−	0.946241i	$-0.604847\pi$
$797$	−14556.0	−0.646925	−0.323463	+	0.946241i	$0.604847\pi$
$798$	6337.55	0.281136
$799$	2120.40	0.0938853
$800$	0	0
$801$	8155.02	0.359730
$802$	−40501.6	−1.78324
$803$	31212.9	1.37170
$804$	8703.59	0.381781
$805$	0	0
$806$	−31484.8	−1.37593
$807$	−1662.14	−0.0725032
$808$	−25040.3	−1.09024
$809$	−14030.7	−0.609755	−0.304878	−	0.952392i	$-0.598616\pi$
$809$	−14030.7	−0.609755	−0.304878	+	0.952392i	$0.598616\pi$
$810$	0	0
$811$	30195.7	1.30741	0.653707	−	0.756747i	$-0.273213\pi$
$811$	30195.7	1.30741	0.653707	+	0.756747i	$0.273213\pi$
$812$	−2521.70	−0.108983
$813$	−5478.06	−0.236315
$814$	−82927.7	−3.57078
$815$	0	0
$816$	3403.04	0.145993
$817$	−40017.2	−1.71362
$818$	−48407.6	−2.06911
$819$	−1024.05	−0.0436911
$820$	0	0
$821$	31237.5	1.32789	0.663944	−	0.747782i	$-0.268881\pi$
$821$	31237.5	1.32789	0.663944	+	0.747782i	$0.268881\pi$
$822$	−23567.4	−1.00001
$823$	22306.9	0.944798	0.472399	−	0.881385i	$-0.343388\pi$
$823$	22306.9	0.944798	0.472399	+	0.881385i	$0.343388\pi$
$824$	37157.1	1.57091
$825$	0	0
$826$	−9184.30	−0.386880
$827$	−41561.9	−1.74758	−0.873790	−	0.486304i	$-0.838345\pi$
$827$	−41561.9	−1.74758	−0.873790	+	0.486304i	$0.838345\pi$
$828$	903.837	0.0379354
$829$	42423.6	1.77736	0.888681	−	0.458527i	$-0.151623\pi$
$829$	42423.6	1.77736	0.888681	+	0.458527i	$0.151623\pi$
$830$	0	0
$831$	−4410.01	−0.184093
$832$	−11213.5	−0.467259
$833$	−5883.13	−0.244704
$834$	−755.524	−0.0313689
$835$	0	0
$836$	62626.3	2.59088
$837$	8395.64	0.346710
$838$	65104.0	2.68375
$839$	−31547.4	−1.29814	−0.649068	−	0.760730i	$-0.724841\pi$
$839$	−31547.4	−1.29814	−0.649068	+	0.760730i	$0.724841\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	13908.1	0.569247
$843$	23479.3	0.959276
$844$	−44342.5	−1.80845
$845$	0	0
$846$	−4956.19	−0.201415
$847$	−6487.63	−0.263185
$848$	8738.56	0.353872
$849$	20390.6	0.824268
$850$	0	0
$851$	2146.84	0.0864779
$852$	−28239.3	−1.13552
$853$	5030.77	0.201935	0.100967	−	0.994890i	$-0.467806\pi$
$853$	5030.77	0.201935	0.100967	+	0.994890i	$0.467806\pi$
$854$	9579.46	0.383844
$855$	0	0
$856$	−48564.2	−1.93912
$857$	16655.5	0.663875	0.331937	−	0.943301i	$-0.392298\pi$
$857$	16655.5	0.663875	0.331937	+	0.943301i	$0.392298\pi$
$858$	−15228.2	−0.605925
$859$	33206.7	1.31897	0.659486	−	0.751717i	$-0.270774\pi$
$859$	33206.7	1.31897	0.659486	+	0.751717i	$0.270774\pi$
$860$	0	0
$861$	−5819.93	−0.230363
$862$	−61869.0	−2.44463
$863$	12156.5	0.479504	0.239752	−	0.970834i	$-0.422934\pi$
$863$	12156.5	0.479504	0.239752	+	0.970834i	$0.422934\pi$
$864$	321.651	0.0126653
$865$	0	0
$866$	−71029.6	−2.78716
$867$	−13678.4	−0.535804
$868$	−27038.7	−1.05732
$869$	−63928.0	−2.49552
$870$	0	0
$871$	3796.28	0.147683
$872$	30963.3	1.20246
$873$	−684.598	−0.0265408
$874$	−2439.79	−0.0944246
$875$	0	0
$876$	29597.7	1.14157
$877$	−10910.0	−0.420075	−0.210037	−	0.977693i	$-0.567359\pi$
$877$	−10910.0	−0.420075	−0.210037	+	0.977693i	$0.567359\pi$
$878$	−56105.7	−2.15658
$879$	−10894.5	−0.418044
$880$	0	0
$881$	−10796.4	−0.412871	−0.206435	−	0.978460i	$-0.566186\pi$
$881$	−10796.4	−0.412871	−0.206435	+	0.978460i	$0.566186\pi$
$882$	13751.1	0.524972
$883$	23778.3	0.906232	0.453116	−	0.891452i	$-0.350312\pi$
$883$	23778.3	0.906232	0.453116	+	0.891452i	$0.350312\pi$
$884$	6177.94	0.235053
$885$	0	0
$886$	−54329.4	−2.06008
$887$	26229.5	0.992897	0.496449	−	0.868066i	$-0.334637\pi$
$887$	26229.5	0.992897	0.496449	+	0.868066i	$0.334637\pi$
$888$	−38936.2	−1.47141
$889$	4470.85	0.168670
$890$	0	0
$891$	4060.72	0.152682
$892$	−39551.8	−1.48463
$893$	8890.26	0.333148
$894$	8911.86	0.333397
$895$	0	0
$896$	−13968.8	−0.520833
$897$	394.230	0.0146744
$898$	32604.4	1.21161
$899$	9017.54	0.334540
$900$	0	0
$901$	2723.55	0.100704
$902$	−86546.3	−3.19476
$903$	8356.51	0.307959
$904$	−46746.9	−1.71989
$905$	0	0
$906$	5003.88	0.183491
$907$	−53019.1	−1.94098	−0.970491	−	0.241136i	$-0.922480\pi$
$907$	−53019.1	−1.94098	−0.970491	+	0.241136i	$0.922480\pi$
$908$	−54028.1	−1.97465
$909$	5881.98	0.214624
$910$	0	0
$911$	−16886.9	−0.614147	−0.307074	−	0.951686i	$-0.599350\pi$
$911$	−16886.9	−0.614147	−0.307074	+	0.951686i	$0.599350\pi$
$912$	14268.0	0.518049
$913$	37053.2	1.34314
$914$	−52870.3	−1.91334
$915$	0	0
$916$	75973.4	2.74043
$917$	8197.83	0.295219
$918$	−2479.09	−0.0891309
$919$	−54865.8	−1.96937	−0.984687	−	0.174330i	$-0.944224\pi$
$919$	−54865.8	−1.96937	−0.984687	+	0.174330i	$0.944224\pi$
$920$	0	0
$921$	27242.3	0.974663
$922$	20090.7	0.717626
$923$	−12317.2	−0.439249
$924$	−13077.8	−0.465615
$925$	0	0
$926$	−29822.9	−1.05836
$927$	−8728.21	−0.309247
$928$	345.477	0.0122207
$929$	27835.6	0.983053	0.491527	−	0.870863i	$-0.336439\pi$
$929$	27835.6	0.983053	0.491527	+	0.870863i	$0.336439\pi$
$930$	0	0
$931$	−24666.4	−0.868322
$932$	−31523.5	−1.10793
$933$	7973.06	0.279771
$934$	−6882.01	−0.241099
$935$	0	0
$936$	−7149.96	−0.249683
$937$	38996.7	1.35962	0.679811	−	0.733387i	$-0.262062\pi$
$937$	38996.7	1.35962	0.679811	+	0.733387i	$0.262062\pi$
$938$	4906.13	0.170779
$939$	1591.42	0.0553079
$940$	0	0
$941$	15686.8	0.543437	0.271718	−	0.962377i	$-0.412408\pi$
$941$	15686.8	0.543437	0.271718	+	0.962377i	$0.412408\pi$
$942$	−5250.14	−0.181591
$943$	2240.52	0.0773715
$944$	−20677.0	−0.712902
$945$	0	0
$946$	124267.	4.27090
$947$	54527.1	1.87106	0.935530	−	0.353248i	$-0.114923\pi$
$947$	54527.1	1.87106	0.935530	+	0.353248i	$0.114923\pi$
$948$	−60619.8	−2.07684
$949$	12909.7	0.441589
$950$	0	0
$951$	−7180.99	−0.244858
$952$	3953.25	0.134586
$953$	−48998.7	−1.66550	−0.832752	−	0.553647i	$-0.813236\pi$
$953$	−48998.7	−1.66550	−0.832752	+	0.553647i	$0.813236\pi$
$954$	−6365.99	−0.216044
$955$	0	0
$956$	40798.6	1.38025
$957$	4361.52	0.147323
$958$	−61694.4	−2.08064
$959$	−8827.88	−0.297254
$960$	0	0
$961$	66898.8	2.24560
$962$	−34299.1	−1.14953
$963$	11407.7	0.381734
$964$	−58368.0	−1.95011
$965$	0	0
$966$	509.484	0.0169693
$967$	18866.1	0.627395	0.313698	−	0.949523i	$-0.398432\pi$
$967$	18866.1	0.627395	0.313698	+	0.949523i	$0.398432\pi$
$968$	−45297.1	−1.50403
$969$	4446.92	0.147426
$970$	0	0
$971$	49921.4	1.64990	0.824950	−	0.565205i	$-0.191203\pi$
$971$	49921.4	1.64990	0.824950	+	0.565205i	$0.191203\pi$
$972$	3850.59	0.127066
$973$	−283.004	−0.00932446
$974$	−83135.6	−2.73495
$975$	0	0
$976$	21566.7	0.707308
$977$	2591.52	0.0848618	0.0424309	−	0.999099i	$-0.486490\pi$
$977$	2591.52	0.0848618	0.0424309	+	0.999099i	$0.486490\pi$
$978$	−24426.4	−0.798639
$979$	45425.6	1.48295
$980$	0	0
$981$	−7273.28	−0.236715
$982$	18519.6	0.601815
$983$	−18566.6	−0.602423	−0.301211	−	0.953557i	$-0.597391\pi$
$983$	−18566.6	−0.602423	−0.301211	+	0.953557i	$0.597391\pi$
$984$	−40635.2	−1.31647
$985$	0	0
$986$	−2662.73	−0.0860026
$987$	−1856.49	−0.0598711
$988$	25902.4	0.834074
$989$	−3217.04	−0.103434
$990$	0	0
$991$	−34558.3	−1.10775	−0.553875	−	0.832600i	$-0.686851\pi$
$991$	−34558.3	−1.10775	−0.553875	+	0.832600i	$0.686851\pi$
$992$	3704.34	0.118561
$993$	−23953.6	−0.765503
$994$	−15918.2	−0.507943
$995$	0	0
$996$	35135.8	1.11779
$997$	11238.6	0.357000	0.178500	−	0.983940i	$-0.442876\pi$
$997$	11238.6	0.357000	0.178500	+	0.983940i	$0.442876\pi$
$998$	−31663.9	−1.00431
$999$	9146.11	0.289660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.4.a.n.1.1		7
5.4	even	2		435.4.a.i.1.7	✓	7
15.14	odd	2		1305.4.a.n.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.7	✓	7	5.4	even	2
1305.4.a.n.1.1		7	15.14	odd	2
2175.4.a.n.1.1		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

\(f(q)\)	\(=\)	\(q-4.88324 q^{2} +3.00000 q^{3} +15.8460 q^{4} -14.6497 q^{6} -5.48750 q^{7} -38.3141 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-4.88324 q^{2} +3.00000 q^{3} +15.8460 q^{4} -14.6497 q^{6} -5.48750 q^{7} -38.3141 q^{8} +9.00000 q^{9} +50.1324 q^{11} +47.5381 q^{12} +20.7349 q^{13} +26.7968 q^{14} +60.3288 q^{16} +18.8027 q^{17} -43.9492 q^{18} +78.8346 q^{19} -16.4625 q^{21} -244.809 q^{22} +6.33763 q^{23} -114.942 q^{24} -101.254 q^{26} +27.0000 q^{27} -86.9552 q^{28} +29.0000 q^{29} +310.950 q^{31} +11.9130 q^{32} +150.397 q^{33} -91.8182 q^{34} +142.614 q^{36} +338.745 q^{37} -384.969 q^{38} +62.2047 q^{39} +353.526 q^{41} +80.3904 q^{42} -507.609 q^{43} +794.400 q^{44} -30.9482 q^{46} +112.771 q^{47} +180.986 q^{48} -312.887 q^{49} +56.4081 q^{51} +328.566 q^{52} +144.849 q^{53} -131.848 q^{54} +210.249 q^{56} +236.504 q^{57} -141.614 q^{58} -342.739 q^{59} +357.486 q^{61} -1518.44 q^{62} -49.3875 q^{63} -540.804 q^{64} -734.426 q^{66} +183.087 q^{67} +297.949 q^{68} +19.0129 q^{69} -594.034 q^{71} -344.827 q^{72} +622.609 q^{73} -1654.17 q^{74} +1249.22 q^{76} -275.102 q^{77} -303.761 q^{78} -1275.18 q^{79} +81.0000 q^{81} -1726.35 q^{82} +739.108 q^{83} -260.866 q^{84} +2478.78 q^{86} +87.0000 q^{87} -1920.78 q^{88} +906.113 q^{89} -113.783 q^{91} +100.426 q^{92} +932.849 q^{93} -550.688 q^{94} +35.7390 q^{96} -76.0665 q^{97} +1527.90 q^{98} +451.192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9	\( 7 q + 2 q^{2} + 21 q^{3} + 22 q^{4} + 6 q^{6} + 50 q^{7} + 33 q^{8} + 63 q^{9} + 76 q^{11} + 66 q^{12} - 30 q^{13} + 89 q^{14} + 138 q^{16} + 140 q^{17} + 18 q^{18} + 90 q^{19} + 150 q^{21} - 61 q^{22} - 34 q^{23} + 99 q^{24} - 241 q^{26} + 189 q^{27} + 57 q^{28} + 203 q^{29} + 524 q^{31} + 6 q^{32} + 228 q^{33} + 255 q^{34} + 198 q^{36} + 28 q^{37} - 222 q^{38} - 90 q^{39} + 1532 q^{41} + 267 q^{42} + 464 q^{43} + 1475 q^{44} + 72 q^{46} + 360 q^{47} + 414 q^{48} + 569 q^{49} + 420 q^{51} + 205 q^{52} - 282 q^{53} + 54 q^{54} + 1102 q^{56} + 270 q^{57} + 58 q^{58} + 766 q^{59} + 1200 q^{61} - 2856 q^{62} + 450 q^{63} + 701 q^{64} - 183 q^{66} - 1546 q^{67} - 1801 q^{68} - 102 q^{69} + 1802 q^{71} + 297 q^{72} + 220 q^{73} + 1594 q^{74} + 1960 q^{76} - 3222 q^{77} - 723 q^{78} + 1298 q^{79} + 567 q^{81} - 856 q^{82} - 1652 q^{83} + 171 q^{84} + 7628 q^{86} + 609 q^{87} - 550 q^{88} + 2846 q^{89} - 816 q^{91} - 472 q^{92} + 1572 q^{93} + 745 q^{94} + 18 q^{96} - 1110 q^{97} + 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 21 * q^3 + 22 * q^4 + 6 * q^6 + 50 * q^7 + 33 * q^8 + 63 * q^9 + 76 * q^11 + 66 * q^12 - 30 * q^13 + 89 * q^14 + 138 * q^16 + 140 * q^17 + 18 * q^18 + 90 * q^19 + 150 * q^21 - 61 * q^22 - 34 * q^23 + 99 * q^24 - 241 * q^26 + 189 * q^27 + 57 * q^28 + 203 * q^29 + 524 * q^31 + 6 * q^32 + 228 * q^33 + 255 * q^34 + 198 * q^36 + 28 * q^37 - 222 * q^38 - 90 * q^39 + 1532 * q^41 + 267 * q^42 + 464 * q^43 + 1475 * q^44 + 72 * q^46 + 360 * q^47 + 414 * q^48 + 569 * q^49 + 420 * q^51 + 205 * q^52 - 282 * q^53 + 54 * q^54 + 1102 * q^56 + 270 * q^57 + 58 * q^58 + 766 * q^59 + 1200 * q^61 - 2856 * q^62 + 450 * q^63 + 701 * q^64 - 183 * q^66 - 1546 * q^67 - 1801 * q^68 - 102 * q^69 + 1802 * q^71 + 297 * q^72 + 220 * q^73 + 1594 * q^74 + 1960 * q^76 - 3222 * q^77 - 723 * q^78 + 1298 * q^79 + 567 * q^81 - 856 * q^82 - 1652 * q^83 + 171 * q^84 + 7628 * q^86 + 609 * q^87 - 550 * q^88 + 2846 * q^89 - 816 * q^91 - 472 * q^92 + 1572 * q^93 + 745 * q^94 + 18 * q^96 - 1110 * q^97 + 761 * q^98 + 684 * q^99

Introduction

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