LMFDB - Embedded newform 1175.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1175,2,Mod(1,1175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1175 = 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1175.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:	$9.38242223750$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.106069.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + 3x - 4 $ x^5 - 2x^4 - 4x^3 + 7x^2 + 3x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 235)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.901635$ of defining polynomial
Character	$\chi$	$=$	1175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.661191 q^{2} +1.28542 q^{3} -1.56283 q^{4} -0.849908 q^{6} -1.97026 q^{7} +2.35571 q^{8} -1.34770 q^{9} +O(q^{10})$	\(q-0.661191 q^{2} +1.28542 q^{3} -1.56283 q^{4} -0.849908 q^{6} -1.97026 q^{7} +2.35571 q^{8} -1.34770 q^{9} -5.48811 q^{11} -2.00889 q^{12} +2.68927 q^{13} +1.30272 q^{14} +1.56808 q^{16} +2.59615 q^{17} +0.891085 q^{18} +1.17015 q^{19} -2.53261 q^{21} +3.62869 q^{22} +5.74712 q^{23} +3.02808 q^{24} -1.77812 q^{26} -5.58861 q^{27} +3.07918 q^{28} +9.95830 q^{29} +8.23966 q^{31} -5.74822 q^{32} -7.05453 q^{33} -1.71655 q^{34} +2.10621 q^{36} +8.77353 q^{37} -0.773695 q^{38} +3.45684 q^{39} -2.19673 q^{41} +1.67454 q^{42} +8.57697 q^{44} -3.79994 q^{46} +1.00000 q^{47} +2.01564 q^{48} -3.11807 q^{49} +3.33715 q^{51} -4.20286 q^{52} +8.35935 q^{53} +3.69514 q^{54} -4.64137 q^{56} +1.50414 q^{57} -6.58434 q^{58} -14.6178 q^{59} -4.68168 q^{61} -5.44799 q^{62} +2.65531 q^{63} +0.664516 q^{64} +4.66439 q^{66} -2.99558 q^{67} -4.05734 q^{68} +7.38746 q^{69} +12.9319 q^{71} -3.17478 q^{72} +13.8622 q^{73} -5.80098 q^{74} -1.82875 q^{76} +10.8130 q^{77} -2.28563 q^{78} +4.80733 q^{79} -3.14063 q^{81} +1.45246 q^{82} -2.72639 q^{83} +3.95804 q^{84} +12.8006 q^{87} -12.9284 q^{88} +3.28100 q^{89} -5.29856 q^{91} -8.98175 q^{92} +10.5914 q^{93} -0.661191 q^{94} -7.38887 q^{96} +5.14374 q^{97} +2.06164 q^{98} +7.39631 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9} - q^{11} + 8 q^{12} + 11 q^{13} - 2 q^{14} + 4 q^{16} + 14 q^{17} + 6 q^{18} + 5 q^{19} - 13 q^{21} - 5 q^{22} + 6 q^{23} + 20 q^{24} - 11 q^{26} + 11 q^{27} - q^{28} - 16 q^{29} + 3 q^{31} + 3 q^{32} + 5 q^{33} + 28 q^{34} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 25 q^{39} - 24 q^{41} - 46 q^{42} + 21 q^{44} + 14 q^{46} + 5 q^{47} - 7 q^{48} + 24 q^{49} + 14 q^{51} - 15 q^{52} + 14 q^{53} + 46 q^{54} - 3 q^{56} + 3 q^{57} - 32 q^{58} + 10 q^{59} - 9 q^{61} - 13 q^{62} - 24 q^{63} + 16 q^{64} - 23 q^{66} - 4 q^{67} + 47 q^{68} - 26 q^{69} + 4 q^{71} - 5 q^{72} + 27 q^{73} + 14 q^{74} - 19 q^{76} + 33 q^{77} - q^{78} - 18 q^{79} + 9 q^{81} - 24 q^{82} - 17 q^{83} - 26 q^{84} - 18 q^{87} + 35 q^{88} + 4 q^{89} + 13 q^{91} + 6 q^{92} - 25 q^{93} + 4 q^{94} - 33 q^{96} + 30 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9 - q^11 + 8 * q^12 + 11 * q^13 - 2 * q^14 + 4 * q^16 + 14 * q^17 + 6 * q^18 + 5 * q^19 - 13 * q^21 - 5 * q^22 + 6 * q^23 + 20 * q^24 - 11 * q^26 + 11 * q^27 - q^28 - 16 * q^29 + 3 * q^31 + 3 * q^32 + 5 * q^33 + 28 * q^34 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 25 * q^39 - 24 * q^41 - 46 * q^42 + 21 * q^44 + 14 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 14 * q^51 - 15 * q^52 + 14 * q^53 + 46 * q^54 - 3 * q^56 + 3 * q^57 - 32 * q^58 + 10 * q^59 - 9 * q^61 - 13 * q^62 - 24 * q^63 + 16 * q^64 - 23 * q^66 - 4 * q^67 + 47 * q^68 - 26 * q^69 + 4 * q^71 - 5 * q^72 + 27 * q^73 + 14 * q^74 - 19 * q^76 + 33 * q^77 - q^78 - 18 * q^79 + 9 * q^81 - 24 * q^82 - 17 * q^83 - 26 * q^84 - 18 * q^87 + 35 * q^88 + 4 * q^89 + 13 * q^91 + 6 * q^92 - 25 * q^93 + 4 * q^94 - 33 * q^96 + 30 * q^97 + 11 * q^98 - 4 * 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 $

$2$	−0.661191	−0.467533	−0.233766	−	0.972293i	$-0.575105\pi$
$2$	−0.661191	−0.467533	−0.233766	+	0.972293i	$0.575105\pi$
$3$	1.28542	0.742137	0.371069	−	0.928605i	$-0.378991\pi$
$3$	1.28542	0.742137	0.371069	+	0.928605i	$0.378991\pi$
$4$	−1.56283	−0.781413
$5$	0	0
$5$	0	0
$6$	−0.849908	−0.346974
$7$	−1.97026	−0.744689	−0.372345	−	0.928095i	$-0.621446\pi$
$7$	−1.97026	−0.744689	−0.372345	+	0.928095i	$0.621446\pi$
$8$	2.35571	0.832869
$9$	−1.34770	−0.449232
$10$	0	0
$11$	−5.48811	−1.65473	−0.827364	−	0.561666i	$-0.810161\pi$
$11$	−5.48811	−1.65473	−0.827364	+	0.561666i	$0.810161\pi$
$12$	−2.00889	−0.579916
$13$	2.68927	0.745868	0.372934	−	0.927858i	$-0.378352\pi$
$13$	2.68927	0.745868	0.372934	+	0.927858i	$0.378352\pi$
$14$	1.30272	0.348167
$15$	0	0
$16$	1.56808	0.392019
$17$	2.59615	0.629660	0.314830	−	0.949148i	$-0.398053\pi$
$17$	2.59615	0.629660	0.314830	+	0.949148i	$0.398053\pi$
$18$	0.891085	0.210031
$19$	1.17015	0.268452	0.134226	−	0.990951i	$-0.457145\pi$
$19$	1.17015	0.268452	0.134226	+	0.990951i	$0.457145\pi$
$20$	0	0
$21$	−2.53261	−0.552662
$22$	3.62869	0.773640
$23$	5.74712	1.19836	0.599179	−	0.800615i	$-0.295494\pi$
$23$	5.74712	1.19836	0.599179	+	0.800615i	$0.295494\pi$
$24$	3.02808	0.618103
$25$	0	0
$26$	−1.77812	−0.348718
$27$	−5.58861	−1.07553
$28$	3.07918	0.581910
$29$	9.95830	1.84921	0.924605	−	0.380928i	$-0.124395\pi$
$29$	9.95830	1.84921	0.924605	+	0.380928i	$0.124395\pi$
$30$	0	0
$31$	8.23966	1.47989	0.739943	−	0.672670i	$-0.234852\pi$
$31$	8.23966	1.47989	0.739943	+	0.672670i	$0.234852\pi$
$32$	−5.74822	−1.01615
$33$	−7.05453	−1.22804
$34$	−1.71655	−0.294387
$35$	0	0
$36$	2.10621	0.351036
$37$	8.77353	1.44236	0.721180	−	0.692748i	$-0.243600\pi$
$37$	8.77353	1.44236	0.721180	+	0.692748i	$0.243600\pi$
$38$	−0.773695	−0.125510
$39$	3.45684	0.553537
$40$	0	0
$41$	−2.19673	−0.343072	−0.171536	−	0.985178i	$-0.554873\pi$
$41$	−2.19673	−0.343072	−0.171536	+	0.985178i	$0.554873\pi$
$42$	1.67454	0.258387
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	8.57697	1.29303
$45$	0	0
$46$	−3.79994	−0.560271
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	2.01564	0.290932
$49$	−3.11807	−0.445438
$50$	0	0
$51$	3.33715	0.467294
$52$	−4.20286	−0.582831
$53$	8.35935	1.14824	0.574122	−	0.818770i	$-0.305343\pi$
$53$	8.35935	1.14824	0.574122	+	0.818770i	$0.305343\pi$
$54$	3.69514	0.502845
$55$	0	0
$56$	−4.64137	−0.620229
$57$	1.50414	0.199228
$58$	−6.58434	−0.864566
$59$	−14.6178	−1.90308	−0.951540	−	0.307526i	$-0.900499\pi$
$59$	−14.6178	−1.90308	−0.951540	+	0.307526i	$0.900499\pi$
$60$	0	0
$61$	−4.68168	−0.599428	−0.299714	−	0.954029i	$-0.596891\pi$
$61$	−4.68168	−0.599428	−0.299714	+	0.954029i	$0.596891\pi$
$62$	−5.44799	−0.691895
$63$	2.65531	0.334538
$64$	0.664516	0.0830645
$65$	0	0
$66$	4.66439	0.574147
$67$	−2.99558	−0.365968	−0.182984	−	0.983116i	$-0.558576\pi$
$67$	−2.99558	−0.365968	−0.182984	+	0.983116i	$0.558576\pi$
$68$	−4.05734	−0.492024
$69$	7.38746	0.889346
$70$	0	0
$71$	12.9319	1.53473	0.767366	−	0.641209i	$-0.221567\pi$
$71$	12.9319	1.53473	0.767366	+	0.641209i	$0.221567\pi$
$72$	−3.17478	−0.374151
$73$	13.8622	1.62245	0.811225	−	0.584734i	$-0.198801\pi$
$73$	13.8622	1.62245	0.811225	+	0.584734i	$0.198801\pi$
$74$	−5.80098	−0.674351
$75$	0	0
$76$	−1.82875	−0.209772
$77$	10.8130	1.23226
$78$	−2.28563	−0.258797
$79$	4.80733	0.540867	0.270434	−	0.962739i	$-0.412833\pi$
$79$	4.80733	0.540867	0.270434	+	0.962739i	$0.412833\pi$
$80$	0	0
$81$	−3.14063	−0.348958
$82$	1.45246	0.160397
$83$	−2.72639	−0.299261	−0.149630	−	0.988742i	$-0.547808\pi$
$83$	−2.72639	−0.299261	−0.149630	+	0.988742i	$0.547808\pi$
$84$	3.95804	0.431857
$85$	0	0
$86$	0	0
$87$	12.8006	1.37237
$88$	−12.9284	−1.37817
$89$	3.28100	0.347785	0.173892	−	0.984765i	$-0.444365\pi$
$89$	3.28100	0.347785	0.173892	+	0.984765i	$0.444365\pi$
$90$	0	0
$91$	−5.29856	−0.555440
$92$	−8.98175	−0.936412
$93$	10.5914	1.09828
$94$	−0.661191	−0.0681967
$95$	0	0
$96$	−7.38887	−0.754124
$97$	5.14374	0.522268	0.261134	−	0.965303i	$-0.415904\pi$
$97$	5.14374	0.522268	0.261134	+	0.965303i	$0.415904\pi$
$98$	2.06164	0.208257
$99$	7.39631	0.743357
$100$	0	0
$101$	−14.3549	−1.42837	−0.714184	−	0.699958i	$-0.753202\pi$
$101$	−14.3549	−1.42837	−0.714184	+	0.699958i	$0.753202\pi$
$102$	−2.20649	−0.218475
$103$	−16.0237	−1.57887	−0.789433	−	0.613837i	$-0.789625\pi$
$103$	−16.0237	−1.57887	−0.789433	+	0.613837i	$0.789625\pi$
$104$	6.33513	0.621211
$105$	0	0
$106$	−5.52713	−0.536842
$107$	13.4301	1.29834	0.649169	−	0.760644i	$-0.275117\pi$
$107$	13.4301	1.29834	0.649169	+	0.760644i	$0.275117\pi$
$108$	8.73403	0.840433
$109$	6.90230	0.661120	0.330560	−	0.943785i	$-0.392762\pi$
$109$	6.90230	0.661120	0.330560	+	0.943785i	$0.392762\pi$
$110$	0	0
$111$	11.2777	1.07043
$112$	−3.08952	−0.291933
$113$	2.90562	0.273338	0.136669	−	0.990617i	$-0.456360\pi$
$113$	2.90562	0.273338	0.136669	+	0.990617i	$0.456360\pi$
$114$	−0.994523	−0.0931457
$115$	0	0
$116$	−15.5631	−1.44500
$117$	−3.62431	−0.335068
$118$	9.66518	0.889752
$119$	−5.11510	−0.468901
$120$	0	0
$121$	19.1194	1.73813
$122$	3.09549	0.280252
$123$	−2.82372	−0.254606
$124$	−12.8771	−1.15640
$125$	0	0
$126$	−1.75567	−0.156408
$127$	−7.03490	−0.624246	−0.312123	−	0.950042i	$-0.601040\pi$
$127$	−7.03490	−0.624246	−0.312123	+	0.950042i	$0.601040\pi$
$128$	11.0571	0.977316
$129$	0	0
$130$	0	0
$131$	−2.27824	−0.199051	−0.0995254	−	0.995035i	$-0.531732\pi$
$131$	−2.27824	−0.199051	−0.0995254	+	0.995035i	$0.531732\pi$
$132$	11.0250	0.959603
$133$	−2.30551	−0.199913
$134$	1.98065	0.171102
$135$	0	0
$136$	6.11578	0.524424
$137$	2.91395	0.248955	0.124478	−	0.992222i	$-0.460274\pi$
$137$	2.91395	0.248955	0.124478	+	0.992222i	$0.460274\pi$
$138$	−4.88452	−0.415798
$139$	−9.29138	−0.788085	−0.394042	−	0.919092i	$-0.628924\pi$
$139$	−9.29138	−0.788085	−0.394042	+	0.919092i	$0.628924\pi$
$140$	0	0
$141$	1.28542	0.108252
$142$	−8.55045	−0.717538
$143$	−14.7590	−1.23421
$144$	−2.11329	−0.176108
$145$	0	0
$146$	−9.16558	−0.758549
$147$	−4.00802	−0.330576
$148$	−13.7115	−1.12708
$149$	−3.63518	−0.297805	−0.148903	−	0.988852i	$-0.547574\pi$
$149$	−3.63518	−0.297805	−0.148903	+	0.988852i	$0.547574\pi$
$150$	0	0
$151$	12.9406	1.05309	0.526544	−	0.850148i	$-0.323487\pi$
$151$	12.9406	1.05309	0.526544	+	0.850148i	$0.323487\pi$
$152$	2.75654	0.223585
$153$	−3.49883	−0.282863
$154$	−7.14947	−0.576121
$155$	0	0
$156$	−5.40243	−0.432541
$157$	11.6045	0.926138	0.463069	−	0.886322i	$-0.346748\pi$
$157$	11.6045	0.926138	0.463069	+	0.886322i	$0.346748\pi$
$158$	−3.17857	−0.252873
$159$	10.7453	0.852155
$160$	0	0
$161$	−11.3233	−0.892404
$162$	2.07655	0.163150
$163$	9.62351	0.753772	0.376886	−	0.926260i	$-0.376995\pi$
$163$	9.62351	0.753772	0.376886	+	0.926260i	$0.376995\pi$
$164$	3.43311	0.268081
$165$	0	0
$166$	1.80267	0.139914
$167$	0.677617	0.0524356	0.0262178	−	0.999656i	$-0.491654\pi$
$167$	0.677617	0.0524356	0.0262178	+	0.999656i	$0.491654\pi$
$168$	−5.96610	−0.460295
$169$	−5.76785	−0.443680
$170$	0	0
$171$	−1.57701	−0.120597
$172$	0	0
$173$	16.8474	1.28088	0.640442	−	0.768006i	$-0.278751\pi$
$173$	16.8474	1.28088	0.640442	+	0.768006i	$0.278751\pi$
$174$	−8.46364	−0.641627
$175$	0	0
$176$	−8.60579	−0.648686
$177$	−18.7900	−1.41235
$178$	−2.16937	−0.162601
$179$	−7.94385	−0.593751	−0.296876	−	0.954916i	$-0.595945\pi$
$179$	−7.94385	−0.593751	−0.296876	+	0.954916i	$0.595945\pi$
$180$	0	0
$181$	6.03048	0.448242	0.224121	−	0.974561i	$-0.428049\pi$
$181$	6.03048	0.448242	0.224121	+	0.974561i	$0.428049\pi$
$182$	3.50336	0.259686
$183$	−6.01793	−0.444858
$184$	13.5385	0.998075
$185$	0	0
$186$	−7.00295	−0.513481
$187$	−14.2480	−1.04192
$188$	−1.56283	−0.113981
$189$	11.0110	0.800935
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	0.854182	0.0616453
$193$	−3.79889	−0.273450	−0.136725	−	0.990609i	$-0.543658\pi$
$193$	−3.79889	−0.273450	−0.136725	+	0.990609i	$0.543658\pi$
$194$	−3.40100	−0.244177
$195$	0	0
$196$	4.87300	0.348071
$197$	16.9762	1.20951	0.604753	−	0.796413i	$-0.293272\pi$
$197$	16.9762	1.20951	0.604753	+	0.796413i	$0.293272\pi$
$198$	−4.89037	−0.347544
$199$	−5.64034	−0.399833	−0.199917	−	0.979813i	$-0.564067\pi$
$199$	−5.64034	−0.399833	−0.199917	+	0.979813i	$0.564067\pi$
$200$	0	0
$201$	−3.85057	−0.271598
$202$	9.49135	0.667809
$203$	−19.6205	−1.37709
$204$	−5.21538	−0.365150
$205$	0	0
$206$	10.5948	0.738172
$207$	−7.74537	−0.538340
$208$	4.21698	0.292395
$209$	−6.42194	−0.444215
$210$	0	0
$211$	28.0259	1.92938	0.964691	−	0.263383i	$-0.0848383\pi$
$211$	28.0259	1.92938	0.964691	+	0.263383i	$0.0848383\pi$
$212$	−13.0642	−0.897253
$213$	16.6229	1.13898
$214$	−8.87987	−0.607015
$215$	0	0
$216$	−13.1652	−0.895775
$217$	−16.2343	−1.10205
$218$	−4.56374	−0.309095
$219$	17.8188	1.20408
$220$	0	0
$221$	6.98175	0.469643
$222$	−7.45670	−0.500461
$223$	20.4874	1.37194	0.685970	−	0.727630i	$-0.259378\pi$
$223$	20.4874	1.37194	0.685970	+	0.727630i	$0.259378\pi$
$224$	11.3255	0.756717
$225$	0	0
$226$	−1.92117	−0.127795
$227$	−20.5828	−1.36613	−0.683063	−	0.730359i	$-0.739353\pi$
$227$	−20.5828	−1.36613	−0.683063	+	0.730359i	$0.739353\pi$
$228$	−2.35071	−0.155679
$229$	4.32681	0.285923	0.142962	−	0.989728i	$-0.454337\pi$
$229$	4.32681	0.285923	0.142962	+	0.989728i	$0.454337\pi$
$230$	0	0
$231$	13.8993	0.914505
$232$	23.4589	1.54015
$233$	−16.8570	−1.10434	−0.552169	−	0.833732i	$-0.686200\pi$
$233$	−16.8570	−1.10434	−0.552169	+	0.833732i	$0.686200\pi$
$234$	2.39637	0.156655
$235$	0	0
$236$	22.8451	1.48709
$237$	6.17944	0.401398
$238$	3.38206	0.219226
$239$	−14.3104	−0.925664	−0.462832	−	0.886446i	$-0.653167\pi$
$239$	−14.3104	−0.925664	−0.462832	+	0.886446i	$0.653167\pi$
$240$	0	0
$241$	10.1750	0.655430	0.327715	−	0.944777i	$-0.393721\pi$
$241$	10.1750	0.655430	0.327715	+	0.944777i	$0.393721\pi$
$242$	−12.6416	−0.812631
$243$	12.7288	0.816554
$244$	7.31665	0.468401
$245$	0	0
$246$	1.86702	0.119037
$247$	3.14686	0.200230
$248$	19.4102	1.23255
$249$	−3.50456	−0.222092
$250$	0	0
$251$	−5.99964	−0.378694	−0.189347	−	0.981910i	$-0.560637\pi$
$251$	−5.99964	−0.378694	−0.189347	+	0.981910i	$0.560637\pi$
$252$	−4.14980	−0.261413
$253$	−31.5408	−1.98296
$254$	4.65141	0.291856
$255$	0	0
$256$	−8.63987	−0.539992
$257$	−9.79975	−0.611291	−0.305646	−	0.952145i	$-0.598872\pi$
$257$	−9.79975	−0.611291	−0.305646	+	0.952145i	$0.598872\pi$
$258$	0	0
$259$	−17.2862	−1.07411
$260$	0	0
$261$	−13.4208	−0.830724
$262$	1.50635	0.0930628
$263$	−14.9106	−0.919429	−0.459715	−	0.888067i	$-0.652048\pi$
$263$	−14.9106	−0.919429	−0.459715	+	0.888067i	$0.652048\pi$
$264$	−16.6184	−1.02279
$265$	0	0
$266$	1.52438	0.0934659
$267$	4.21746	0.258104
$268$	4.68156	0.285972
$269$	−19.7026	−1.20129	−0.600645	−	0.799516i	$-0.705089\pi$
$269$	−19.7026	−1.20129	−0.600645	+	0.799516i	$0.705089\pi$
$270$	0	0
$271$	10.1119	0.614257	0.307128	−	0.951668i	$-0.400632\pi$
$271$	10.1119	0.614257	0.307128	+	0.951668i	$0.400632\pi$
$272$	4.07097	0.246839
$273$	−6.81087	−0.412213
$274$	−1.92668	−0.116395
$275$	0	0
$276$	−11.5453	−0.694946
$277$	−17.6696	−1.06166	−0.530832	−	0.847477i	$-0.678120\pi$
$277$	−17.6696	−1.06166	−0.530832	+	0.847477i	$0.678120\pi$
$278$	6.14338	0.368455
$279$	−11.1046	−0.664812
$280$	0	0
$281$	22.3404	1.33272	0.666358	−	0.745632i	$-0.267852\pi$
$281$	22.3404	1.33272	0.666358	+	0.745632i	$0.267852\pi$
$282$	−0.849908	−0.0506113
$283$	3.04686	0.181117	0.0905586	−	0.995891i	$-0.471135\pi$
$283$	3.04686	0.181117	0.0905586	+	0.995891i	$0.471135\pi$
$284$	−20.2103	−1.19926
$285$	0	0
$286$	9.75852	0.577033
$287$	4.32813	0.255482
$288$	7.74685	0.456488
$289$	−10.2600	−0.603529
$290$	0	0
$291$	6.61187	0.387594
$292$	−21.6642	−1.26780
$293$	−26.5093	−1.54869	−0.774344	−	0.632765i	$-0.781920\pi$
$293$	−26.5093	−1.54869	−0.774344	+	0.632765i	$0.781920\pi$
$294$	2.65007	0.154555
$295$	0	0
$296$	20.6679	1.20130
$297$	30.6709	1.77971
$298$	2.40355	0.139234
$299$	15.4555	0.893817
$300$	0	0
$301$	0	0
$302$	−8.55619	−0.492354
$303$	−18.4521	−1.06005
$304$	1.83489	0.105238
$305$	0	0
$306$	2.31339	0.132248
$307$	7.93018	0.452600	0.226300	−	0.974058i	$-0.427337\pi$
$307$	7.93018	0.452600	0.226300	+	0.974058i	$0.427337\pi$
$308$	−16.8989	−0.962903
$309$	−20.5972	−1.17174
$310$	0	0
$311$	−26.6885	−1.51337	−0.756684	−	0.653780i	$-0.773182\pi$
$311$	−26.6885	−1.51337	−0.756684	+	0.653780i	$0.773182\pi$
$312$	8.14330	0.461024
$313$	15.0690	0.851749	0.425874	−	0.904782i	$-0.359967\pi$
$313$	15.0690	0.851749	0.425874	+	0.904782i	$0.359967\pi$
$314$	−7.67278	−0.433000
$315$	0	0
$316$	−7.51303	−0.422641
$317$	−1.89507	−0.106438	−0.0532190	−	0.998583i	$-0.516948\pi$
$317$	−1.89507	−0.106438	−0.0532190	+	0.998583i	$0.516948\pi$
$318$	−7.10468	−0.398410
$319$	−54.6523	−3.05994
$320$	0	0
$321$	17.2633	0.963545
$322$	7.48689	0.417228
$323$	3.03790	0.169033
$324$	4.90825	0.272681
$325$	0	0
$326$	−6.36298	−0.352413
$327$	8.87235	0.490642
$328$	−5.17486	−0.285734
$329$	−1.97026	−0.108624
$330$	0	0
$331$	1.41772	0.0779250	0.0389625	−	0.999241i	$-0.487595\pi$
$331$	1.41772	0.0779250	0.0389625	+	0.999241i	$0.487595\pi$
$332$	4.26088	0.233846
$333$	−11.8241	−0.647954
$334$	−0.448035	−0.0245154
$335$	0	0
$336$	−3.97134	−0.216654
$337$	2.80596	0.152850	0.0764252	−	0.997075i	$-0.475649\pi$
$337$	2.80596	0.152850	0.0764252	+	0.997075i	$0.475649\pi$
$338$	3.81365	0.207435
$339$	3.73495	0.202854
$340$	0	0
$341$	−45.2202	−2.44881
$342$	1.04271	0.0563831
$343$	19.9352	1.07640
$344$	0	0
$345$	0	0
$346$	−11.1394	−0.598856
$347$	−11.7063	−0.628428	−0.314214	−	0.949352i	$-0.601741\pi$
$347$	−11.7063	−0.628428	−0.314214	+	0.949352i	$0.601741\pi$
$348$	−20.0051	−1.07239
$349$	−9.19958	−0.492442	−0.246221	−	0.969214i	$-0.579189\pi$
$349$	−9.19958	−0.492442	−0.246221	+	0.969214i	$0.579189\pi$
$350$	0	0
$351$	−15.0293	−0.802203
$352$	31.5469	1.68145
$353$	−21.5894	−1.14909	−0.574544	−	0.818474i	$-0.694821\pi$
$353$	−21.5894	−1.14909	−0.574544	+	0.818474i	$0.694821\pi$
$354$	12.4238	0.660318
$355$	0	0
$356$	−5.12763	−0.271764
$357$	−6.57505	−0.347989
$358$	5.25240	0.277598
$359$	−18.0566	−0.952990	−0.476495	−	0.879177i	$-0.658093\pi$
$359$	−18.0566	−0.952990	−0.476495	+	0.879177i	$0.658093\pi$
$360$	0	0
$361$	−17.6307	−0.927934
$362$	−3.98730	−0.209568
$363$	24.5764	1.28993
$364$	8.28073	0.434028
$365$	0	0
$366$	3.97900	0.207986
$367$	17.9389	0.936405	0.468203	−	0.883621i	$-0.344902\pi$
$367$	17.9389	0.936405	0.468203	+	0.883621i	$0.344902\pi$
$368$	9.01193	0.469779
$369$	2.96053	0.154119
$370$	0	0
$371$	−16.4701	−0.855085
$372$	−16.5525	−0.858209
$373$	−35.4121	−1.83357	−0.916784	−	0.399383i	$-0.869224\pi$
$373$	−35.4121	−1.83357	−0.916784	+	0.399383i	$0.869224\pi$
$374$	9.42064	0.487130
$375$	0	0
$376$	2.35571	0.121486
$377$	26.7805	1.37927
$378$	−7.28040	−0.374463
$379$	31.7356	1.63015	0.815074	−	0.579357i	$-0.196696\pi$
$379$	31.7356	1.63015	0.815074	+	0.579357i	$0.196696\pi$
$380$	0	0
$381$	−9.04280	−0.463277
$382$	−7.93430	−0.405954
$383$	18.1405	0.926936	0.463468	−	0.886114i	$-0.346605\pi$
$383$	18.1405	0.926936	0.463468	+	0.886114i	$0.346605\pi$
$384$	14.2130	0.725302
$385$	0	0
$386$	2.51179	0.127847
$387$	0	0
$388$	−8.03877	−0.408107
$389$	−4.53371	−0.229868	−0.114934	−	0.993373i	$-0.536666\pi$
$389$	−4.53371	−0.229868	−0.114934	+	0.993373i	$0.536666\pi$
$390$	0	0
$391$	14.9204	0.754557
$392$	−7.34526	−0.370992
$393$	−2.92850	−0.147723
$394$	−11.2245	−0.565484
$395$	0	0
$396$	−11.5591	−0.580869
$397$	18.4012	0.923528	0.461764	−	0.887003i	$-0.347217\pi$
$397$	18.4012	0.923528	0.461764	+	0.887003i	$0.347217\pi$
$398$	3.72934	0.186935
$399$	−2.96355	−0.148363
$400$	0	0
$401$	38.7219	1.93368	0.966840	−	0.255381i	$-0.0822009\pi$
$401$	38.7219	1.93368	0.966840	+	0.255381i	$0.0822009\pi$
$402$	2.54596	0.126981
$403$	22.1586	1.10380
$404$	22.4342	1.11615
$405$	0	0
$406$	12.9729	0.643833
$407$	−48.1501	−2.38671
$408$	7.86135	0.389195
$409$	23.3457	1.15437	0.577185	−	0.816614i	$-0.304151\pi$
$409$	23.3457	1.15437	0.577185	+	0.816614i	$0.304151\pi$
$410$	0	0
$411$	3.74565	0.184759
$412$	25.0423	1.23375
$413$	28.8010	1.41720
$414$	5.12117	0.251692
$415$	0	0
$416$	−15.4585	−0.757915
$417$	−11.9433	−0.584867
$418$	4.24613	0.207685
$419$	9.64519	0.471198	0.235599	−	0.971850i	$-0.424295\pi$
$419$	9.64519	0.471198	0.235599	+	0.971850i	$0.424295\pi$
$420$	0	0
$421$	5.18898	0.252895	0.126448	−	0.991973i	$-0.459642\pi$
$421$	5.18898	0.252895	0.126448	+	0.991973i	$0.459642\pi$
$422$	−18.5305	−0.902050
$423$	−1.34770	−0.0655272
$424$	19.6922	0.956337
$425$	0	0
$426$	−10.9909	−0.532512
$427$	9.22414	0.446387
$428$	−20.9889	−1.01454
$429$	−18.9715	−0.915953
$430$	0	0
$431$	−11.6029	−0.558892	−0.279446	−	0.960161i	$-0.590151\pi$
$431$	−11.6029	−0.558892	−0.279446	+	0.960161i	$0.590151\pi$
$432$	−8.76338	−0.421628
$433$	32.1115	1.54318	0.771590	−	0.636121i	$-0.219462\pi$
$433$	32.1115	1.54318	0.771590	+	0.636121i	$0.219462\pi$
$434$	10.7340	0.515247
$435$	0	0
$436$	−10.7871	−0.516608
$437$	6.72501	0.321701
$438$	−11.7816	−0.562947
$439$	13.3521	0.637260	0.318630	−	0.947879i	$-0.396777\pi$
$439$	13.3521	0.637260	0.318630	+	0.947879i	$0.396777\pi$
$440$	0	0
$441$	4.20221	0.200105
$442$	−4.61627	−0.219574
$443$	−15.9570	−0.758141	−0.379071	−	0.925368i	$-0.623756\pi$
$443$	−15.9570	−0.758141	−0.379071	+	0.925368i	$0.623756\pi$
$444$	−17.6250	−0.836447
$445$	0	0
$446$	−13.5461	−0.641427
$447$	−4.67273	−0.221013
$448$	−1.30927	−0.0618572
$449$	−4.14951	−0.195827	−0.0979137	−	0.995195i	$-0.531217\pi$
$449$	−4.14951	−0.195827	−0.0979137	+	0.995195i	$0.531217\pi$
$450$	0	0
$451$	12.0559	0.567690
$452$	−4.54098	−0.213590
$453$	16.6341	0.781537
$454$	13.6091	0.638709
$455$	0	0
$456$	3.54331	0.165931
$457$	33.3824	1.56156	0.780782	−	0.624803i	$-0.214821\pi$
$457$	33.3824	1.56156	0.780782	+	0.624803i	$0.214821\pi$
$458$	−2.86085	−0.133679
$459$	−14.5089	−0.677217
$460$	0	0
$461$	−25.1368	−1.17074	−0.585368	−	0.810768i	$-0.699050\pi$
$461$	−25.1368	−1.17074	−0.585368	+	0.810768i	$0.699050\pi$
$462$	−9.19008	−0.427561
$463$	−5.67249	−0.263623	−0.131811	−	0.991275i	$-0.542079\pi$
$463$	−5.67249	−0.263623	−0.131811	+	0.991275i	$0.542079\pi$
$464$	15.6154	0.724926
$465$	0	0
$466$	11.1457	0.516315
$467$	−24.6367	−1.14005	−0.570026	−	0.821627i	$-0.693067\pi$
$467$	−24.6367	−1.14005	−0.570026	+	0.821627i	$0.693067\pi$
$468$	5.66417	0.261827
$469$	5.90207	0.272532
$470$	0	0
$471$	14.9166	0.687322
$472$	−34.4354	−1.58502
$473$	0	0
$474$	−4.08579	−0.187667
$475$	0	0
$476$	7.99402	0.366405
$477$	−11.2659	−0.515828
$478$	9.46192	0.432778
$479$	7.33652	0.335214	0.167607	−	0.985854i	$-0.446396\pi$
$479$	7.33652	0.335214	0.167607	+	0.985854i	$0.446396\pi$
$480$	0	0
$481$	23.5944	1.07581
$482$	−6.72763	−0.306435
$483$	−14.5552	−0.662286
$484$	−29.8803	−1.35819
$485$	0	0
$486$	−8.41618	−0.381766
$487$	34.2728	1.55305	0.776525	−	0.630086i	$-0.216981\pi$
$487$	34.2728	1.55305	0.776525	+	0.630086i	$0.216981\pi$
$488$	−11.0287	−0.499245
$489$	12.3703	0.559402
$490$	0	0
$491$	−16.8377	−0.759875	−0.379938	−	0.925012i	$-0.624055\pi$
$491$	−16.8377	−0.759875	−0.379938	+	0.925012i	$0.624055\pi$
$492$	4.41298	0.198953
$493$	25.8533	1.16437
$494$	−2.08067	−0.0936139
$495$	0	0
$496$	12.9204	0.580144
$497$	−25.4792	−1.14290
$498$	2.31718	0.103835
$499$	5.19616	0.232612	0.116306	−	0.993213i	$-0.462895\pi$
$499$	5.19616	0.232612	0.116306	+	0.993213i	$0.462895\pi$
$500$	0	0
$501$	0.871023	0.0389144
$502$	3.96691	0.177052
$503$	−1.95988	−0.0873865	−0.0436933	−	0.999045i	$-0.513912\pi$
$503$	−1.95988	−0.0873865	−0.0436933	+	0.999045i	$0.513912\pi$
$504$	6.25515	0.278627
$505$	0	0
$506$	20.8545	0.927097
$507$	−7.41410	−0.329272
$508$	10.9943	0.487794
$509$	3.32018	0.147165	0.0735823	−	0.997289i	$-0.476557\pi$
$509$	3.32018	0.147165	0.0735823	+	0.997289i	$0.476557\pi$
$510$	0	0
$511$	−27.3122	−1.20822
$512$	−16.4015	−0.724852
$513$	−6.53954	−0.288728
$514$	6.47951	0.285799
$515$	0	0
$516$	0	0
$517$	−5.48811	−0.241367
$518$	11.4295	0.502182
$519$	21.6560	0.950593
$520$	0	0
$521$	−35.9237	−1.57384	−0.786922	−	0.617052i	$-0.788327\pi$
$521$	−35.9237	−1.57384	−0.786922	+	0.617052i	$0.788327\pi$
$522$	8.87369	0.388391
$523$	−2.57749	−0.112706	−0.0563530	−	0.998411i	$-0.517947\pi$
$523$	−2.57749	−0.112706	−0.0563530	+	0.998411i	$0.517947\pi$
$524$	3.56050	0.155541
$525$	0	0
$526$	9.85878	0.429863
$527$	21.3914	0.931824
$528$	−11.0620	−0.481414
$529$	10.0294	0.436060
$530$	0	0
$531$	19.7004	0.854924
$532$	3.60311	0.156215
$533$	−5.90759	−0.255886
$534$	−2.78855	−0.120672
$535$	0	0
$536$	−7.05671	−0.304803
$537$	−10.2112	−0.440645
$538$	13.0272	0.561642
$539$	17.1123	0.737079
$540$	0	0
$541$	13.7791	0.592408	0.296204	−	0.955125i	$-0.404279\pi$
$541$	13.7791	0.592408	0.296204	+	0.955125i	$0.404279\pi$
$542$	−6.68593	−0.287185
$543$	7.75169	0.332657
$544$	−14.9233	−0.639829
$545$	0	0
$546$	4.50329	0.192723
$547$	29.0402	1.24167	0.620834	−	0.783942i	$-0.286794\pi$
$547$	29.0402	1.24167	0.620834	+	0.783942i	$0.286794\pi$
$548$	−4.55399	−0.194537
$549$	6.30948	0.269282
$550$	0	0
$551$	11.6527	0.496424
$552$	17.4027	0.740709
$553$	−9.47171	−0.402778
$554$	11.6830	0.496363
$555$	0	0
$556$	14.5208	0.615820
$557$	13.2516	0.561488	0.280744	−	0.959783i	$-0.409419\pi$
$557$	13.2516	0.561488	0.280744	+	0.959783i	$0.409419\pi$
$558$	7.34223	0.310822
$559$	0	0
$560$	0	0
$561$	−18.3146	−0.773244
$562$	−14.7713	−0.623088
$563$	−28.4195	−1.19774	−0.598869	−	0.800847i	$-0.704383\pi$
$563$	−28.4195	−1.19774	−0.598869	+	0.800847i	$0.704383\pi$
$564$	−2.00889	−0.0845894
$565$	0	0
$566$	−2.01456	−0.0846783
$567$	6.18786	0.259866
$568$	30.4638	1.27823
$569$	24.3435	1.02053	0.510267	−	0.860016i	$-0.329547\pi$
$569$	24.3435	1.02053	0.510267	+	0.860016i	$0.329547\pi$
$570$	0	0
$571$	9.39895	0.393334	0.196667	−	0.980470i	$-0.436988\pi$
$571$	9.39895	0.393334	0.196667	+	0.980470i	$0.436988\pi$
$572$	23.0657	0.964427
$573$	15.4250	0.644390
$574$	−2.86172	−0.119446
$575$	0	0
$576$	−0.895566	−0.0373152
$577$	2.63459	0.109679	0.0548397	−	0.998495i	$-0.482535\pi$
$577$	2.63459	0.109679	0.0548397	+	0.998495i	$0.482535\pi$
$578$	6.78382	0.282170
$579$	−4.88317	−0.202938
$580$	0	0
$581$	5.37171	0.222856
$582$	−4.37171	−0.181213
$583$	−45.8770	−1.90003
$584$	32.6554	1.35129
$585$	0	0
$586$	17.5277	0.724062
$587$	37.3867	1.54312	0.771558	−	0.636159i	$-0.219478\pi$
$587$	37.3867	1.54312	0.771558	+	0.636159i	$0.219478\pi$
$588$	6.26385	0.258317
$589$	9.64166	0.397278
$590$	0	0
$591$	21.8216	0.897620
$592$	13.7576	0.565433
$593$	−9.23138	−0.379087	−0.189544	−	0.981872i	$-0.560701\pi$
$593$	−9.23138	−0.379087	−0.189544	+	0.981872i	$0.560701\pi$
$594$	−20.2794	−0.832072
$595$	0	0
$596$	5.68115	0.232709
$597$	−7.25021	−0.296731
$598$	−10.2191	−0.417889
$599$	23.5812	0.963502	0.481751	−	0.876308i	$-0.340001\pi$
$599$	23.5812	0.963502	0.481751	+	0.876308i	$0.340001\pi$
$600$	0	0
$601$	−27.5664	−1.12446	−0.562228	−	0.826982i	$-0.690056\pi$
$601$	−27.5664	−1.12446	−0.562228	+	0.826982i	$0.690056\pi$
$602$	0	0
$603$	4.03713	0.164404
$604$	−20.2239	−0.822897
$605$	0	0
$606$	12.2004	0.495606
$607$	−28.9049	−1.17321	−0.586607	−	0.809872i	$-0.699537\pi$
$607$	−28.9049	−1.17321	−0.586607	+	0.809872i	$0.699537\pi$
$608$	−6.72630	−0.272787
$609$	−25.2205	−1.02199
$610$	0	0
$611$	2.68927	0.108796
$612$	5.46806	0.221033
$613$	39.6309	1.60068	0.800338	−	0.599550i	$-0.204654\pi$
$613$	39.6309	1.60068	0.800338	+	0.599550i	$0.204654\pi$
$614$	−5.24337	−0.211605
$615$	0	0
$616$	25.4723	1.02631
$617$	−15.7105	−0.632481	−0.316241	−	0.948679i	$-0.602421\pi$
$617$	−15.7105	−0.632481	−0.316241	+	0.948679i	$0.602421\pi$
$618$	13.6187	0.547825
$619$	−5.95350	−0.239291	−0.119646	−	0.992817i	$-0.538176\pi$
$619$	−5.95350	−0.239291	−0.119646	+	0.992817i	$0.538176\pi$
$620$	0	0
$621$	−32.1184	−1.28887
$622$	17.6462	0.707549
$623$	−6.46442	−0.258992
$624$	5.42059	0.216997
$625$	0	0
$626$	−9.96348	−0.398221
$627$	−8.25488	−0.329668
$628$	−18.1358	−0.723696
$629$	22.7774	0.908196
$630$	0	0
$631$	−32.1972	−1.28175	−0.640874	−	0.767646i	$-0.721428\pi$
$631$	−32.1972	−1.28175	−0.640874	+	0.767646i	$0.721428\pi$
$632$	11.3247	0.450472
$633$	36.0250	1.43187
$634$	1.25301	0.0497632
$635$	0	0
$636$	−16.7930	−0.665885
$637$	−8.38531	−0.332238
$638$	36.1356	1.43062
$639$	−17.4283	−0.689451
$640$	0	0
$641$	3.21726	0.127074	0.0635371	−	0.997979i	$-0.479762\pi$
$641$	3.21726	0.127074	0.0635371	+	0.997979i	$0.479762\pi$
$642$	−11.4144	−0.450489
$643$	20.0551	0.790894	0.395447	−	0.918489i	$-0.370590\pi$
$643$	20.0551	0.790894	0.395447	+	0.918489i	$0.370590\pi$
$644$	17.6964	0.697336
$645$	0	0
$646$	−2.00863	−0.0790286
$647$	−2.54481	−0.100047	−0.0500233	−	0.998748i	$-0.515930\pi$
$647$	−2.54481	−0.100047	−0.0500233	+	0.998748i	$0.515930\pi$
$648$	−7.39840	−0.290637
$649$	80.2243	3.14908
$650$	0	0
$651$	−20.8679	−0.817876
$652$	−15.0399	−0.589007
$653$	37.1283	1.45294	0.726471	−	0.687197i	$-0.241159\pi$
$653$	37.1283	1.45294	0.726471	+	0.687197i	$0.241159\pi$
$654$	−5.86632	−0.229391
$655$	0	0
$656$	−3.44464	−0.134491
$657$	−18.6821	−0.728857
$658$	1.30272	0.0507853
$659$	−25.9376	−1.01039	−0.505193	−	0.863006i	$-0.668579\pi$
$659$	−25.9376	−1.01039	−0.505193	+	0.863006i	$0.668579\pi$
$660$	0	0
$661$	−22.7219	−0.883781	−0.441890	−	0.897069i	$-0.645692\pi$
$661$	−22.7219	−0.883781	−0.441890	+	0.897069i	$0.645692\pi$
$662$	−0.937385	−0.0364325
$663$	8.97448	0.348540
$664$	−6.42259	−0.249245
$665$	0	0
$666$	7.81796	0.302940
$667$	57.2315	2.21601
$668$	−1.05900	−0.0409739
$669$	26.3350	1.01817
$670$	0	0
$671$	25.6936	0.991890
$672$	14.5580	0.561588
$673$	−10.4265	−0.401911	−0.200955	−	0.979600i	$-0.564405\pi$
$673$	−10.4265	−0.401911	−0.200955	+	0.979600i	$0.564405\pi$
$674$	−1.85528	−0.0714625
$675$	0	0
$676$	9.01414	0.346698
$677$	19.3163	0.742387	0.371194	−	0.928556i	$-0.378949\pi$
$677$	19.3163	0.742387	0.371194	+	0.928556i	$0.378949\pi$
$678$	−2.46951	−0.0948411
$679$	−10.1345	−0.388927
$680$	0	0
$681$	−26.4575	−1.01385
$682$	29.8992	1.14490
$683$	1.26749	0.0484993	0.0242497	−	0.999706i	$-0.492280\pi$
$683$	1.26749	0.0484993	0.0242497	+	0.999706i	$0.492280\pi$
$684$	2.46460	0.0942362
$685$	0	0
$686$	−13.1810	−0.503253
$687$	5.56176	0.212194
$688$	0	0
$689$	22.4805	0.856439
$690$	0	0
$691$	12.7917	0.486620	0.243310	−	0.969949i	$-0.421767\pi$
$691$	12.7917	0.486620	0.243310	+	0.969949i	$0.421767\pi$
$692$	−26.3296	−1.00090
$693$	−14.5727	−0.553570
$694$	7.74011	0.293810
$695$	0	0
$696$	30.1545	1.14300
$697$	−5.70305	−0.216018
$698$	6.08268	0.230233
$699$	−21.6683	−0.819571
$700$	0	0
$701$	43.6461	1.64849	0.824246	−	0.566233i	$-0.191600\pi$
$701$	43.6461	1.64849	0.824246	+	0.566233i	$0.191600\pi$
$702$	9.93722	0.375056
$703$	10.2664	0.387204
$704$	−3.64694	−0.137449
$705$	0	0
$706$	14.2747	0.537236
$707$	28.2830	1.06369
$708$	29.3656	1.10363
$709$	27.8095	1.04441	0.522203	−	0.852821i	$-0.325110\pi$
$709$	27.8095	1.04441	0.522203	+	0.852821i	$0.325110\pi$
$710$	0	0
$711$	−6.47883	−0.242975
$712$	7.72907	0.289659
$713$	47.3543	1.77343
$714$	4.34737	0.162696
$715$	0	0
$716$	12.4149	0.463965
$717$	−18.3949	−0.686970
$718$	11.9388	0.445554
$719$	30.0083	1.11912	0.559560	−	0.828790i	$-0.310970\pi$
$719$	30.0083	1.11912	0.559560	+	0.828790i	$0.310970\pi$
$720$	0	0
$721$	31.5710	1.17576
$722$	11.6573	0.433839
$723$	13.0792	0.486419
$724$	−9.42459	−0.350262
$725$	0	0
$726$	−16.2497	−0.603084
$727$	−12.0282	−0.446101	−0.223051	−	0.974807i	$-0.571602\pi$
$727$	−12.0282	−0.446101	−0.223051	+	0.974807i	$0.571602\pi$
$728$	−12.4819	−0.462609
$729$	25.7838	0.954954
$730$	0	0
$731$	0	0
$732$	9.40497	0.347618
$733$	27.9925	1.03393	0.516964	−	0.856007i	$-0.327062\pi$
$733$	27.9925	1.03393	0.516964	+	0.856007i	$0.327062\pi$
$734$	−11.8611	−0.437800
$735$	0	0
$736$	−33.0357	−1.21771
$737$	16.4401	0.605577
$738$	−1.95747	−0.0720556
$739$	−39.3991	−1.44932	−0.724659	−	0.689108i	$-0.758003\pi$
$739$	−39.3991	−1.44932	−0.724659	+	0.689108i	$0.758003\pi$
$740$	0	0
$741$	4.04503	0.148598
$742$	10.8899	0.399780
$743$	42.3258	1.55278	0.776391	−	0.630252i	$-0.217048\pi$
$743$	42.3258	1.55278	0.776391	+	0.630252i	$0.217048\pi$
$744$	24.9503	0.914722
$745$	0	0
$746$	23.4142	0.857253
$747$	3.67435	0.134437
$748$	22.2671	0.814166
$749$	−26.4608	−0.966858
$750$	0	0
$751$	−53.5724	−1.95489	−0.977443	−	0.211199i	$-0.932263\pi$
$751$	−53.5724	−1.95489	−0.977443	+	0.211199i	$0.932263\pi$
$752$	1.56808	0.0571819
$753$	−7.71205	−0.281043
$754$	−17.7070	−0.644853
$755$	0	0
$756$	−17.2083	−0.625861
$757$	−15.9981	−0.581463	−0.290731	−	0.956805i	$-0.593899\pi$
$757$	−15.9981	−0.581463	−0.290731	+	0.956805i	$0.593899\pi$
$758$	−20.9833	−0.762147
$759$	−40.5432	−1.47163
$760$	0	0
$761$	6.57969	0.238514	0.119257	−	0.992863i	$-0.461949\pi$
$761$	6.57969	0.238514	0.119257	+	0.992863i	$0.461949\pi$
$762$	5.97902	0.216597
$763$	−13.5993	−0.492329
$764$	−18.7539	−0.678493
$765$	0	0
$766$	−11.9943	−0.433373
$767$	−39.3112	−1.41945
$768$	−11.1059	−0.400748
$769$	−23.9076	−0.862130	−0.431065	−	0.902321i	$-0.641862\pi$
$769$	−23.9076	−0.862130	−0.431065	+	0.902321i	$0.641862\pi$
$770$	0	0
$771$	−12.5968	−0.453662
$772$	5.93701	0.213678
$773$	−30.4348	−1.09466	−0.547332	−	0.836916i	$-0.684356\pi$
$773$	−30.4348	−1.09466	−0.547332	+	0.836916i	$0.684356\pi$
$774$	0	0
$775$	0	0
$776$	12.1172	0.434981
$777$	−22.2200	−0.797137
$778$	2.99765	0.107471
$779$	−2.57051	−0.0920982
$780$	0	0
$781$	−70.9716	−2.53957
$782$	−9.86524	−0.352780
$783$	−55.6531	−1.98888
$784$	−4.88937	−0.174620
$785$	0	0
$786$	1.93630	0.0690654
$787$	−45.0681	−1.60650	−0.803252	−	0.595640i	$-0.796899\pi$
$787$	−45.0681	−1.60650	−0.803252	+	0.595640i	$0.796899\pi$
$788$	−26.5309	−0.945124
$789$	−19.1664	−0.682343
$790$	0	0
$791$	−5.72484	−0.203552
$792$	17.4236	0.619119
$793$	−12.5903	−0.447094
$794$	−12.1667	−0.431780
$795$	0	0
$796$	8.81487	0.312435
$797$	−20.2327	−0.716679	−0.358340	−	0.933591i	$-0.616657\pi$
$797$	−20.2327	−0.716679	−0.358340	+	0.933591i	$0.616657\pi$
$798$	1.95947	0.0693646
$799$	2.59615	0.0918453
$800$	0	0
$801$	−4.42179	−0.156236
$802$	−25.6026	−0.904059
$803$	−76.0774	−2.68471
$804$	6.01777	0.212231
$805$	0	0
$806$	−14.6511	−0.516063
$807$	−25.3261	−0.891522
$808$	−33.8160	−1.18964
$809$	29.2093	1.02694	0.513472	−	0.858106i	$-0.328359\pi$
$809$	29.2093	1.02694	0.513472	+	0.858106i	$0.328359\pi$
$810$	0	0
$811$	−4.07681	−0.143156	−0.0715781	−	0.997435i	$-0.522804\pi$
$811$	−4.07681	−0.143156	−0.0715781	+	0.997435i	$0.522804\pi$
$812$	30.6634	1.07607
$813$	12.9981	0.455863
$814$	31.8364	1.11587
$815$	0	0
$816$	5.23290	0.183188
$817$	0	0
$818$	−15.4360	−0.539706
$819$	7.14085	0.249521
$820$	0	0
$821$	4.37491	0.152685	0.0763427	−	0.997082i	$-0.475676\pi$
$821$	4.37491	0.152685	0.0763427	+	0.997082i	$0.475676\pi$
$822$	−2.47659	−0.0863809
$823$	6.56418	0.228813	0.114407	−	0.993434i	$-0.463503\pi$
$823$	6.56418	0.228813	0.114407	+	0.993434i	$0.463503\pi$
$824$	−37.7473	−1.31499
$825$	0	0
$826$	−19.0429	−0.662589
$827$	10.0948	0.351031	0.175516	−	0.984477i	$-0.443841\pi$
$827$	10.0948	0.351031	0.175516	+	0.984477i	$0.443841\pi$
$828$	12.1047	0.420666
$829$	49.2733	1.71133	0.855665	−	0.517529i	$-0.173148\pi$
$829$	49.2733	1.71133	0.855665	+	0.517529i	$0.173148\pi$
$830$	0	0
$831$	−22.7129	−0.787900
$832$	1.78706	0.0619552
$833$	−8.09498	−0.280474
$834$	7.89682	0.273445
$835$	0	0
$836$	10.0364	0.347115
$837$	−46.0483	−1.59166
$838$	−6.37732	−0.220301
$839$	−17.3880	−0.600300	−0.300150	−	0.953892i	$-0.597037\pi$
$839$	−17.3880	−0.600300	−0.300150	+	0.953892i	$0.597037\pi$
$840$	0	0
$841$	70.1677	2.41958
$842$	−3.43091	−0.118237
$843$	28.7168	0.989058
$844$	−43.7996	−1.50764
$845$	0	0
$846$	0.891085	0.0306361
$847$	−37.6702	−1.29436
$848$	13.1081	0.450134
$849$	3.91650	0.134414
$850$	0	0
$851$	50.4225	1.72846
$852$	−25.9787	−0.890016
$853$	−23.4978	−0.804550	−0.402275	−	0.915519i	$-0.631780\pi$
$853$	−23.4978	−0.804550	−0.402275	+	0.915519i	$0.631780\pi$
$854$	−6.09892	−0.208701
$855$	0	0
$856$	31.6374	1.08135
$857$	14.7161	0.502691	0.251346	−	0.967897i	$-0.419127\pi$
$857$	14.7161	0.502691	0.251346	+	0.967897i	$0.419127\pi$
$858$	12.5438	0.428238
$859$	−20.9957	−0.716366	−0.358183	−	0.933651i	$-0.616604\pi$
$859$	−20.9957	−0.716366	−0.358183	+	0.933651i	$0.616604\pi$
$860$	0	0
$861$	5.56347	0.189603
$862$	7.67174	0.261300
$863$	−17.4899	−0.595363	−0.297681	−	0.954665i	$-0.596213\pi$
$863$	−17.4899	−0.595363	−0.297681	+	0.954665i	$0.596213\pi$
$864$	32.1246	1.09290
$865$	0	0
$866$	−21.2318	−0.721487
$867$	−13.1884	−0.447901
$868$	25.3714	0.861160
$869$	−26.3832	−0.894988
$870$	0	0
$871$	−8.05590	−0.272964
$872$	16.2598	0.550627
$873$	−6.93220	−0.234619
$874$	−4.44652	−0.150406
$875$	0	0
$876$	−27.8476	−0.940885
$877$	45.7885	1.54617	0.773083	−	0.634304i	$-0.218713\pi$
$877$	45.7885	1.54617	0.773083	+	0.634304i	$0.218713\pi$
$878$	−8.82828	−0.297940
$879$	−34.0755	−1.14934
$880$	0	0
$881$	−53.7028	−1.80929	−0.904647	−	0.426163i	$-0.859865\pi$
$881$	−53.7028	−1.80929	−0.904647	+	0.426163i	$0.859865\pi$
$882$	−2.77846	−0.0935557
$883$	−44.0325	−1.48181	−0.740906	−	0.671609i	$-0.765604\pi$
$883$	−44.0325	−1.48181	−0.740906	+	0.671609i	$0.765604\pi$
$884$	−10.9113	−0.366985
$885$	0	0
$886$	10.5506	0.354456
$887$	54.1039	1.81663	0.908315	−	0.418287i	$-0.137369\pi$
$887$	54.1039	1.81663	0.908315	+	0.418287i	$0.137369\pi$
$888$	26.5669	0.891527
$889$	13.8606	0.464870
$890$	0	0
$891$	17.2361	0.577431
$892$	−32.0183	−1.07205
$893$	1.17015	0.0391577
$894$	3.08957	0.103331
$895$	0	0
$896$	−21.7853	−0.727796
$897$	19.8668	0.663335
$898$	2.74362	0.0915557
$899$	82.0530	2.73662
$900$	0	0
$901$	21.7021	0.723003
$902$	−7.97126	−0.265414
$903$	0	0
$904$	6.84481	0.227655
$905$	0	0
$906$	−10.9983	−0.365394
$907$	5.01535	0.166532	0.0832660	−	0.996527i	$-0.473465\pi$
$907$	5.01535	0.166532	0.0832660	+	0.996527i	$0.473465\pi$
$908$	32.1673	1.06751
$909$	19.3461	0.641669
$910$	0	0
$911$	−42.4032	−1.40488	−0.702441	−	0.711742i	$-0.747906\pi$
$911$	−42.4032	−1.40488	−0.702441	+	0.711742i	$0.747906\pi$
$912$	2.35861	0.0781013
$913$	14.9628	0.495195
$914$	−22.0722	−0.730083
$915$	0	0
$916$	−6.76205	−0.223424
$917$	4.48873	0.148231
$918$	9.59316	0.316621
$919$	−8.06353	−0.265991	−0.132996	−	0.991117i	$-0.542460\pi$
$919$	−8.06353	−0.265991	−0.132996	+	0.991117i	$0.542460\pi$
$920$	0	0
$921$	10.1936	0.335891
$922$	16.6202	0.547358
$923$	34.7773	1.14471
$924$	−21.7221	−0.714606
$925$	0	0
$926$	3.75060	0.123252
$927$	21.5951	0.709277
$928$	−57.2425	−1.87908
$929$	−51.7173	−1.69679	−0.848395	−	0.529363i	$-0.822431\pi$
$929$	−51.7173	−1.69679	−0.848395	+	0.529363i	$0.822431\pi$
$930$	0	0
$931$	−3.64862	−0.119579
$932$	26.3446	0.862945
$933$	−34.3060	−1.12313
$934$	16.2896	0.533011
$935$	0	0
$936$	−8.53783	−0.279068
$937$	−12.4087	−0.405375	−0.202687	−	0.979243i	$-0.564968\pi$
$937$	−12.4087	−0.405375	−0.202687	+	0.979243i	$0.564968\pi$
$938$	−3.90240	−0.127418
$939$	19.3700	0.632115
$940$	0	0
$941$	4.58645	0.149514	0.0747570	−	0.997202i	$-0.476182\pi$
$941$	4.58645	0.149514	0.0747570	+	0.997202i	$0.476182\pi$
$942$	−9.86274	−0.321345
$943$	−12.6249	−0.411122
$944$	−22.9219	−0.746044
$945$	0	0
$946$	0	0
$947$	−20.9590	−0.681074	−0.340537	−	0.940231i	$-0.610609\pi$
$947$	−20.9590	−0.681074	−0.340537	+	0.940231i	$0.610609\pi$
$948$	−9.65739	−0.313658
$949$	37.2792	1.21013
$950$	0	0
$951$	−2.43597	−0.0789916
$952$	−12.0497	−0.390533
$953$	−25.9878	−0.841828	−0.420914	−	0.907100i	$-0.638291\pi$
$953$	−25.9878	−0.841828	−0.420914	+	0.907100i	$0.638291\pi$
$954$	7.44889	0.241167
$955$	0	0
$956$	22.3647	0.723326
$957$	−70.2511	−2.27090
$958$	−4.85084	−0.156724
$959$	−5.74124	−0.185394
$960$	0	0
$961$	36.8919	1.19006
$962$	−15.6004	−0.502977
$963$	−18.0997	−0.583255
$964$	−15.9018	−0.512162
$965$	0	0
$966$	9.62379	0.309640
$967$	−52.6946	−1.69455	−0.847273	−	0.531158i	$-0.821757\pi$
$967$	−52.6946	−1.69455	−0.847273	+	0.531158i	$0.821757\pi$
$968$	45.0397	1.44763
$969$	3.90497	0.125446
$970$	0	0
$971$	2.70624	0.0868474	0.0434237	−	0.999057i	$-0.486173\pi$
$971$	2.70624	0.0868474	0.0434237	+	0.999057i	$0.486173\pi$
$972$	−19.8929	−0.638066
$973$	18.3065	0.586878
$974$	−22.6609	−0.726102
$975$	0	0
$976$	−7.34124	−0.234987
$977$	−6.03925	−0.193213	−0.0966064	−	0.995323i	$-0.530799\pi$
$977$	−6.03925	−0.193213	−0.0966064	+	0.995323i	$0.530799\pi$
$978$	−8.17910	−0.261539
$979$	−18.0065	−0.575489
$980$	0	0
$981$	−9.30220	−0.296996
$982$	11.1329	0.355267
$983$	−12.1525	−0.387604	−0.193802	−	0.981041i	$-0.562082\pi$
$983$	−12.1525	−0.387604	−0.193802	+	0.981041i	$0.562082\pi$
$984$	−6.65186	−0.212054
$985$	0	0
$986$	−17.0940	−0.544382
$987$	−2.53261	−0.0806140
$988$	−4.91799	−0.156462
$989$	0	0
$990$	0	0
$991$	−48.7512	−1.54863	−0.774317	−	0.632798i	$-0.781906\pi$
$991$	−48.7512	−1.54863	−0.774317	+	0.632798i	$0.781906\pi$
$992$	−47.3633	−1.50379
$993$	1.82237	0.0578311
$994$	16.8466	0.534343
$995$	0	0
$996$	5.47702	0.173546
$997$	42.8523	1.35715	0.678573	−	0.734533i	$-0.262599\pi$
$997$	42.8523	1.35715	0.678573	+	0.734533i	$0.262599\pi$
$998$	−3.43566	−0.108754
$999$	−49.0319	−1.55130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1175.2.a.g.1.2		5
5.2	odd	4		1175.2.c.f.424.5		10
5.3	odd	4		1175.2.c.f.424.6		10
5.4	even	2		235.2.a.d.1.4	✓	5
15.14	odd	2		2115.2.a.r.1.2		5
20.19	odd	2		3760.2.a.bg.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
235.2.a.d.1.4	✓	5	5.4	even	2
1175.2.a.g.1.2		5	1.1	even	1	trivial
1175.2.c.f.424.5		10	5.2	odd	4
1175.2.c.f.424.6		10	5.3	odd	4
2115.2.a.r.1.2		5	15.14	odd	2
3760.2.a.bg.1.3		5	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1175 = 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1175.a (trivial)

\(f(q)\)	\(=\)	\(q-0.661191 q^{2} +1.28542 q^{3} -1.56283 q^{4} -0.849908 q^{6} -1.97026 q^{7} +2.35571 q^{8} -1.34770 q^{9} +O(q^{10})\)	\(q-0.661191 q^{2} +1.28542 q^{3} -1.56283 q^{4} -0.849908 q^{6} -1.97026 q^{7} +2.35571 q^{8} -1.34770 q^{9} -5.48811 q^{11} -2.00889 q^{12} +2.68927 q^{13} +1.30272 q^{14} +1.56808 q^{16} +2.59615 q^{17} +0.891085 q^{18} +1.17015 q^{19} -2.53261 q^{21} +3.62869 q^{22} +5.74712 q^{23} +3.02808 q^{24} -1.77812 q^{26} -5.58861 q^{27} +3.07918 q^{28} +9.95830 q^{29} +8.23966 q^{31} -5.74822 q^{32} -7.05453 q^{33} -1.71655 q^{34} +2.10621 q^{36} +8.77353 q^{37} -0.773695 q^{38} +3.45684 q^{39} -2.19673 q^{41} +1.67454 q^{42} +8.57697 q^{44} -3.79994 q^{46} +1.00000 q^{47} +2.01564 q^{48} -3.11807 q^{49} +3.33715 q^{51} -4.20286 q^{52} +8.35935 q^{53} +3.69514 q^{54} -4.64137 q^{56} +1.50414 q^{57} -6.58434 q^{58} -14.6178 q^{59} -4.68168 q^{61} -5.44799 q^{62} +2.65531 q^{63} +0.664516 q^{64} +4.66439 q^{66} -2.99558 q^{67} -4.05734 q^{68} +7.38746 q^{69} +12.9319 q^{71} -3.17478 q^{72} +13.8622 q^{73} -5.80098 q^{74} -1.82875 q^{76} +10.8130 q^{77} -2.28563 q^{78} +4.80733 q^{79} -3.14063 q^{81} +1.45246 q^{82} -2.72639 q^{83} +3.95804 q^{84} +12.8006 q^{87} -12.9284 q^{88} +3.28100 q^{89} -5.29856 q^{91} -8.98175 q^{92} +10.5914 q^{93} -0.661191 q^{94} -7.38887 q^{96} +5.14374 q^{97} +2.06164 q^{98} +7.39631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + q^{6} + 5 q^{7} + 12 q^{8} + 4 q^{9} - q^{11} + 8 q^{12} + 11 q^{13} - 2 q^{14} + 4 q^{16} + 14 q^{17} + 6 q^{18} + 5 q^{19} - 13 q^{21} - 5 q^{22} + 6 q^{23} + 20 q^{24} - 11 q^{26} + 11 q^{27} - q^{28} - 16 q^{29} + 3 q^{31} + 3 q^{32} + 5 q^{33} + 28 q^{34} + 9 q^{36} + 16 q^{37} + 5 q^{38} + 25 q^{39} - 24 q^{41} - 46 q^{42} + 21 q^{44} + 14 q^{46} + 5 q^{47} - 7 q^{48} + 24 q^{49} + 14 q^{51} - 15 q^{52} + 14 q^{53} + 46 q^{54} - 3 q^{56} + 3 q^{57} - 32 q^{58} + 10 q^{59} - 9 q^{61} - 13 q^{62} - 24 q^{63} + 16 q^{64} - 23 q^{66} - 4 q^{67} + 47 q^{68} - 26 q^{69} + 4 q^{71} - 5 q^{72} + 27 q^{73} + 14 q^{74} - 19 q^{76} + 33 q^{77} - q^{78} - 18 q^{79} + 9 q^{81} - 24 q^{82} - 17 q^{83} - 26 q^{84} - 18 q^{87} + 35 q^{88} + 4 q^{89} + 13 q^{91} + 6 q^{92} - 25 q^{93} + 4 q^{94} - 33 q^{96} + 30 q^{97} + 11 q^{98} - 4 q^{99}+O(q^{100}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + q^6 + 5 * q^7 + 12 * q^8 + 4 * q^9 - q^11 + 8 * q^12 + 11 * q^13 - 2 * q^14 + 4 * q^16 + 14 * q^17 + 6 * q^18 + 5 * q^19 - 13 * q^21 - 5 * q^22 + 6 * q^23 + 20 * q^24 - 11 * q^26 + 11 * q^27 - q^28 - 16 * q^29 + 3 * q^31 + 3 * q^32 + 5 * q^33 + 28 * q^34 + 9 * q^36 + 16 * q^37 + 5 * q^38 + 25 * q^39 - 24 * q^41 - 46 * q^42 + 21 * q^44 + 14 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 14 * q^51 - 15 * q^52 + 14 * q^53 + 46 * q^54 - 3 * q^56 + 3 * q^57 - 32 * q^58 + 10 * q^59 - 9 * q^61 - 13 * q^62 - 24 * q^63 + 16 * q^64 - 23 * q^66 - 4 * q^67 + 47 * q^68 - 26 * q^69 + 4 * q^71 - 5 * q^72 + 27 * q^73 + 14 * q^74 - 19 * q^76 + 33 * q^77 - q^78 - 18 * q^79 + 9 * q^81 - 24 * q^82 - 17 * q^83 - 26 * q^84 - 18 * q^87 + 35 * q^88 + 4 * q^89 + 13 * q^91 + 6 * q^92 - 25 * q^93 + 4 * q^94 - 33 * q^96 + 30 * q^97 + 11 * q^98 - 4 * q^99

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