LMFDB - Embedded newform 5775.2.a.ce.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5775,2,Mod(1,5775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5775, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5775.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5775.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:	$46.1136071673$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.457904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 8x^{2} + 5x - 6 $ x^5 - 2x^4 - 5x^3 + 8x^2 + 5x - 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.58059$ of defining polynomial
Character	$\chi$	$=$	5775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58059 q^{2} +1.00000 q^{3} +4.65942 q^{4} -2.58059 q^{6} -1.00000 q^{7} -6.86286 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58059 q^{2} +1.00000 q^{3} +4.65942 q^{4} -2.58059 q^{6} -1.00000 q^{7} -6.86286 q^{8} +1.00000 q^{9} +1.00000 q^{11} +4.65942 q^{12} -4.47290 q^{13} +2.58059 q^{14} +8.39135 q^{16} -2.67845 q^{17} -2.58059 q^{18} -0.383468 q^{19} -1.00000 q^{21} -2.58059 q^{22} +0.698699 q^{23} -6.86286 q^{24} +11.5427 q^{26} +1.00000 q^{27} -4.65942 q^{28} -4.91196 q^{29} +7.97054 q^{31} -7.92888 q^{32} +1.00000 q^{33} +6.91196 q^{34} +4.65942 q^{36} +6.06630 q^{37} +0.989572 q^{38} -4.47290 q^{39} -2.14152 q^{41} +2.58059 q^{42} +1.16117 q^{43} +4.65942 q^{44} -1.80305 q^{46} -5.59340 q^{47} +8.39135 q^{48} +1.00000 q^{49} -2.67845 q^{51} -20.8411 q^{52} +5.32645 q^{53} -2.58059 q^{54} +6.86286 q^{56} -0.383468 q^{57} +12.6757 q^{58} +2.60383 q^{59} +15.5097 q^{61} -20.5687 q^{62} -1.00000 q^{63} +3.67845 q^{64} -2.58059 q^{66} -7.37504 q^{67} -12.4800 q^{68} +0.698699 q^{69} +0.538316 q^{71} -6.86286 q^{72} +6.84101 q^{73} -15.6546 q^{74} -1.78674 q^{76} -1.00000 q^{77} +11.5427 q^{78} +3.87047 q^{79} +1.00000 q^{81} +5.52638 q^{82} -0.126713 q^{83} -4.65942 q^{84} -2.99650 q^{86} -4.91196 q^{87} -6.86286 q^{88} -7.75107 q^{89} +4.47290 q^{91} +3.25553 q^{92} +7.97054 q^{93} +14.4342 q^{94} -7.92888 q^{96} +0.987463 q^{97} -2.58059 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9} + 5 q^{11} + 4 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{16} - 15 q^{17} - 2 q^{18} + 3 q^{19} - 5 q^{21} - 2 q^{22} - 6 q^{24} + 5 q^{27} - 4 q^{28} - 4 q^{29} + 16 q^{31} - 14 q^{32} + 5 q^{33} + 14 q^{34} + 4 q^{36} - 7 q^{37} + 2 q^{38} - 7 q^{39} - 5 q^{41} + 2 q^{42} - 16 q^{43} + 4 q^{44} - 10 q^{46} - 6 q^{47} - 2 q^{48} + 5 q^{49} - 15 q^{51} - 18 q^{52} - 11 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 28 q^{58} - 6 q^{59} + q^{61} - 26 q^{62} - 5 q^{63} + 20 q^{64} - 2 q^{66} - 9 q^{67} - 2 q^{68} - 21 q^{71} - 6 q^{72} - 17 q^{73} + 4 q^{74} - 26 q^{76} - 5 q^{77} - 8 q^{79} + 5 q^{81} - 14 q^{82} - 26 q^{83} - 4 q^{84} - 20 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{91} + 12 q^{92} + 16 q^{93} + 4 q^{94} - 14 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9 + 5 * q^11 + 4 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^16 - 15 * q^17 - 2 * q^18 + 3 * q^19 - 5 * q^21 - 2 * q^22 - 6 * q^24 + 5 * q^27 - 4 * q^28 - 4 * q^29 + 16 * q^31 - 14 * q^32 + 5 * q^33 + 14 * q^34 + 4 * q^36 - 7 * q^37 + 2 * q^38 - 7 * q^39 - 5 * q^41 + 2 * q^42 - 16 * q^43 + 4 * q^44 - 10 * q^46 - 6 * q^47 - 2 * q^48 + 5 * q^49 - 15 * q^51 - 18 * q^52 - 11 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 28 * q^58 - 6 * q^59 + q^61 - 26 * q^62 - 5 * q^63 + 20 * q^64 - 2 * q^66 - 9 * q^67 - 2 * q^68 - 21 * q^71 - 6 * q^72 - 17 * q^73 + 4 * q^74 - 26 * q^76 - 5 * q^77 - 8 * q^79 + 5 * q^81 - 14 * q^82 - 26 * q^83 - 4 * q^84 - 20 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^91 + 12 * q^92 + 16 * q^93 + 4 * q^94 - 14 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	−2.58059	−1.82475	−0.912375	−	0.409356i	$-0.865753\pi$
$2$	−2.58059	−1.82475	−0.912375	+	0.409356i	$0.865753\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.65942	2.32971
$5$	0	0
$5$	0	0
$6$	−2.58059	−1.05352
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.86286	−2.42639
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.65942	1.34506
$13$	−4.47290	−1.24056	−0.620280	−	0.784381i	$-0.712981\pi$
$13$	−4.47290	−1.24056	−0.620280	+	0.784381i	$0.712981\pi$
$14$	2.58059	0.689690
$15$	0	0
$16$	8.39135	2.09784
$17$	−2.67845	−0.649619	−0.324809	−	0.945779i	$-0.605300\pi$
$17$	−2.67845	−0.649619	−0.324809	+	0.945779i	$0.605300\pi$
$18$	−2.58059	−0.608250
$19$	−0.383468	−0.0879736	−0.0439868	−	0.999032i	$-0.514006\pi$
$19$	−0.383468	−0.0879736	−0.0439868	+	0.999032i	$0.514006\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	−2.58059	−0.550183
$23$	0.698699	0.145689	0.0728444	−	0.997343i	$-0.476792\pi$
$23$	0.698699	0.145689	0.0728444	+	0.997343i	$0.476792\pi$
$24$	−6.86286	−1.40088
$25$	0	0
$26$	11.5427	2.26371
$27$	1.00000	0.192450
$28$	−4.65942	−0.880548
$29$	−4.91196	−0.912128	−0.456064	−	0.889947i	$-0.650741\pi$
$29$	−4.91196	−0.912128	−0.456064	+	0.889947i	$0.650741\pi$
$30$	0	0
$31$	7.97054	1.43155	0.715776	−	0.698330i	$-0.246073\pi$
$31$	7.97054	1.43155	0.715776	+	0.698330i	$0.246073\pi$
$32$	−7.92888	−1.40164
$33$	1.00000	0.174078
$34$	6.91196	1.18539
$35$	0	0
$36$	4.65942	0.776570
$37$	6.06630	0.997293	0.498647	−	0.866805i	$-0.333831\pi$
$37$	6.06630	0.997293	0.498647	+	0.866805i	$0.333831\pi$
$38$	0.989572	0.160530
$39$	−4.47290	−0.716237
$40$	0	0
$41$	−2.14152	−0.334450	−0.167225	−	0.985919i	$-0.553481\pi$
$41$	−2.14152	−0.334450	−0.167225	+	0.985919i	$0.553481\pi$
$42$	2.58059	0.398193
$43$	1.16117	0.177077	0.0885384	−	0.996073i	$-0.471780\pi$
$43$	1.16117	0.177077	0.0885384	+	0.996073i	$0.471780\pi$
$44$	4.65942	0.702434
$45$	0	0
$46$	−1.80305	−0.265845
$47$	−5.59340	−0.815881	−0.407940	−	0.913009i	$-0.633753\pi$
$47$	−5.59340	−0.815881	−0.407940	+	0.913009i	$0.633753\pi$
$48$	8.39135	1.21119
$49$	1.00000	0.142857
$50$	0	0
$51$	−2.67845	−0.375058
$52$	−20.8411	−2.89014
$53$	5.32645	0.731644	0.365822	−	0.930685i	$-0.380788\pi$
$53$	5.32645	0.731644	0.365822	+	0.930685i	$0.380788\pi$
$54$	−2.58059	−0.351173
$55$	0	0
$56$	6.86286	0.917088
$57$	−0.383468	−0.0507916
$58$	12.6757	1.66441
$59$	2.60383	0.338989	0.169495	−	0.985531i	$-0.445786\pi$
$59$	2.60383	0.338989	0.169495	+	0.985531i	$0.445786\pi$
$60$	0	0
$61$	15.5097	1.98582	0.992909	−	0.118873i	$-0.0379282\pi$
$61$	15.5097	1.98582	0.992909	+	0.118873i	$0.0379282\pi$
$62$	−20.5687	−2.61222
$63$	−1.00000	−0.125988
$64$	3.67845	0.459806
$65$	0	0
$66$	−2.58059	−0.317648
$67$	−7.37504	−0.901004	−0.450502	−	0.892775i	$-0.648755\pi$
$67$	−7.37504	−0.901004	−0.450502	+	0.892775i	$0.648755\pi$
$68$	−12.4800	−1.51342
$69$	0.698699	0.0841135
$70$	0	0
$71$	0.538316	0.0638864	0.0319432	−	0.999490i	$-0.489830\pi$
$71$	0.538316	0.0638864	0.0319432	+	0.999490i	$0.489830\pi$
$72$	−6.86286	−0.808796
$73$	6.84101	0.800680	0.400340	−	0.916367i	$-0.368892\pi$
$73$	6.84101	0.800680	0.400340	+	0.916367i	$0.368892\pi$
$74$	−15.6546	−1.81981
$75$	0	0
$76$	−1.78674	−0.204953
$77$	−1.00000	−0.113961
$78$	11.5427	1.30695
$79$	3.87047	0.435462	0.217731	−	0.976009i	$-0.430135\pi$
$79$	3.87047	0.435462	0.217731	+	0.976009i	$0.430135\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.52638	0.610287
$83$	−0.126713	−0.0139085	−0.00695427	−	0.999976i	$-0.502214\pi$
$83$	−0.126713	−0.0139085	−0.00695427	+	0.999976i	$0.502214\pi$
$84$	−4.65942	−0.508384
$85$	0	0
$86$	−2.99650	−0.323121
$87$	−4.91196	−0.526618
$88$	−6.86286	−0.731583
$89$	−7.75107	−0.821611	−0.410806	−	0.911723i	$-0.634753\pi$
$89$	−7.75107	−0.821611	−0.410806	+	0.911723i	$0.634753\pi$
$90$	0	0
$91$	4.47290	0.468887
$92$	3.25553	0.339413
$93$	7.97054	0.826507
$94$	14.4342	1.48878
$95$	0	0
$96$	−7.92888	−0.809238
$97$	0.987463	0.100262	0.0501309	−	0.998743i	$-0.484036\pi$
$97$	0.987463	0.100262	0.0501309	+	0.998743i	$0.484036\pi$
$98$	−2.58059	−0.260678
$99$	1.00000	0.100504
$100$	0	0
$101$	−10.3318	−1.02805	−0.514027	−	0.857774i	$-0.671847\pi$
$101$	−10.3318	−1.02805	−0.514027	+	0.857774i	$0.671847\pi$
$102$	6.91196	0.684386
$103$	−2.52710	−0.249003	−0.124501	−	0.992219i	$-0.539733\pi$
$103$	−2.52710	−0.249003	−0.124501	+	0.992219i	$0.539733\pi$
$104$	30.6969	3.01008
$105$	0	0
$106$	−13.7454	−1.33507
$107$	−1.03296	−0.0998598	−0.0499299	−	0.998753i	$-0.515900\pi$
$107$	−1.03296	−0.0998598	−0.0499299	+	0.998753i	$0.515900\pi$
$108$	4.65942	0.448353
$109$	−16.0803	−1.54022	−0.770108	−	0.637913i	$-0.779798\pi$
$109$	−16.0803	−1.54022	−0.770108	+	0.637913i	$0.779798\pi$
$110$	0	0
$111$	6.06630	0.575788
$112$	−8.39135	−0.792908
$113$	−1.61653	−0.152071	−0.0760353	−	0.997105i	$-0.524226\pi$
$113$	−1.61653	−0.152071	−0.0760353	+	0.997105i	$0.524226\pi$
$114$	0.989572	0.0926819
$115$	0	0
$116$	−22.8869	−2.12499
$117$	−4.47290	−0.413520
$118$	−6.71940	−0.618570
$119$	2.67845	0.245533
$120$	0	0
$121$	1.00000	0.0909091
$122$	−40.0242	−3.62362
$123$	−2.14152	−0.193095
$124$	37.1381	3.33510
$125$	0	0
$126$	2.58059	0.229897
$127$	−1.40466	−0.124644	−0.0623218	−	0.998056i	$-0.519851\pi$
$127$	−1.40466	−0.124644	−0.0623218	+	0.998056i	$0.519851\pi$
$128$	6.36521	0.562611
$129$	1.16117	0.102235
$130$	0	0
$131$	−9.37154	−0.818795	−0.409397	−	0.912356i	$-0.634261\pi$
$131$	−9.37154	−0.818795	−0.409397	+	0.912356i	$0.634261\pi$
$132$	4.65942	0.405550
$133$	0.383468	0.0332509
$134$	19.0319	1.64411
$135$	0	0
$136$	18.3818	1.57623
$137$	−13.4633	−1.15024	−0.575122	−	0.818068i	$-0.695045\pi$
$137$	−13.4633	−1.15024	−0.575122	+	0.818068i	$0.695045\pi$
$138$	−1.80305	−0.153486
$139$	4.58691	0.389056	0.194528	−	0.980897i	$-0.437682\pi$
$139$	4.58691	0.389056	0.194528	+	0.980897i	$0.437682\pi$
$140$	0	0
$141$	−5.59340	−0.471049
$142$	−1.38917	−0.116577
$143$	−4.47290	−0.374043
$144$	8.39135	0.699279
$145$	0	0
$146$	−17.6538	−1.46104
$147$	1.00000	0.0824786
$148$	28.2654	2.32340
$149$	15.7784	1.29262	0.646310	−	0.763075i	$-0.276311\pi$
$149$	15.7784	1.29262	0.646310	+	0.763075i	$0.276311\pi$
$150$	0	0
$151$	5.38374	0.438123	0.219061	−	0.975711i	$-0.429700\pi$
$151$	5.38374	0.438123	0.219061	+	0.975711i	$0.429700\pi$
$152$	2.63169	0.213458
$153$	−2.67845	−0.216540
$154$	2.58059	0.207949
$155$	0	0
$156$	−20.8411	−1.66862
$157$	−12.7925	−1.02095	−0.510477	−	0.859891i	$-0.670531\pi$
$157$	−12.7925	−1.02095	−0.510477	+	0.859891i	$0.670531\pi$
$158$	−9.98807	−0.794608
$159$	5.32645	0.422415
$160$	0	0
$161$	−0.698699	−0.0550652
$162$	−2.58059	−0.202750
$163$	7.86874	0.616328	0.308164	−	0.951333i	$-0.400286\pi$
$163$	7.86874	0.616328	0.308164	+	0.951333i	$0.400286\pi$
$164$	−9.97826	−0.779171
$165$	0	0
$166$	0.326993	0.0253796
$167$	−23.6418	−1.82946	−0.914729	−	0.404069i	$-0.867596\pi$
$167$	−23.6418	−1.82946	−0.914729	+	0.404069i	$0.867596\pi$
$168$	6.86286	0.529481
$169$	7.00683	0.538987
$170$	0	0
$171$	−0.383468	−0.0293245
$172$	5.41038	0.412538
$173$	−16.2680	−1.23683	−0.618415	−	0.785851i	$-0.712225\pi$
$173$	−16.2680	−1.23683	−0.618415	+	0.785851i	$0.712225\pi$
$174$	12.6757	0.960945
$175$	0	0
$176$	8.39135	0.632522
$177$	2.60383	0.195716
$178$	20.0023	1.49923
$179$	−22.8258	−1.70608	−0.853039	−	0.521848i	$-0.825243\pi$
$179$	−22.8258	−1.70608	−0.853039	+	0.521848i	$0.825243\pi$
$180$	0	0
$181$	6.72605	0.499943	0.249972	−	0.968253i	$-0.419579\pi$
$181$	6.72605	0.499943	0.249972	+	0.968253i	$0.419579\pi$
$182$	−11.5427	−0.855602
$183$	15.5097	1.14651
$184$	−4.79507	−0.353497
$185$	0	0
$186$	−20.5687	−1.50817
$187$	−2.67845	−0.195867
$188$	−26.0620	−1.90077
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	−23.1885	−1.67786	−0.838932	−	0.544237i	$-0.816819\pi$
$191$	−23.1885	−1.67786	−0.838932	+	0.544237i	$0.816819\pi$
$192$	3.67845	0.265469
$193$	−20.5601	−1.47995	−0.739973	−	0.672637i	$-0.765162\pi$
$193$	−20.5601	−1.47995	−0.739973	+	0.672637i	$0.765162\pi$
$194$	−2.54823	−0.182952
$195$	0	0
$196$	4.65942	0.332816
$197$	−6.57078	−0.468148	−0.234074	−	0.972219i	$-0.575206\pi$
$197$	−6.57078	−0.468148	−0.234074	+	0.972219i	$0.575206\pi$
$198$	−2.58059	−0.183394
$199$	0.581407	0.0412149	0.0206074	−	0.999788i	$-0.493440\pi$
$199$	0.581407	0.0412149	0.0206074	+	0.999788i	$0.493440\pi$
$200$	0	0
$201$	−7.37504	−0.520195
$202$	26.6621	1.87594
$203$	4.91196	0.344752
$204$	−12.4800	−0.873775
$205$	0	0
$206$	6.52140	0.454367
$207$	0.698699	0.0485629
$208$	−37.5337	−2.60249
$209$	−0.383468	−0.0265250
$210$	0	0
$211$	−25.2684	−1.73955	−0.869775	−	0.493449i	$-0.835736\pi$
$211$	−25.2684	−1.73955	−0.869775	+	0.493449i	$0.835736\pi$
$212$	24.8182	1.70452
$213$	0.538316	0.0368848
$214$	2.66563	0.182219
$215$	0	0
$216$	−6.86286	−0.466958
$217$	−7.97054	−0.541076
$218$	41.4967	2.81051
$219$	6.84101	0.462273
$220$	0	0
$221$	11.9804	0.805891
$222$	−15.6546	−1.05067
$223$	−14.6659	−0.982103	−0.491051	−	0.871131i	$-0.663387\pi$
$223$	−14.6659	−0.982103	−0.491051	+	0.871131i	$0.663387\pi$
$224$	7.92888	0.529771
$225$	0	0
$226$	4.17160	0.277491
$227$	−18.4835	−1.22679	−0.613397	−	0.789775i	$-0.710197\pi$
$227$	−18.4835	−1.22679	−0.613397	+	0.789775i	$0.710197\pi$
$228$	−1.78674	−0.118330
$229$	−9.52255	−0.629268	−0.314634	−	0.949213i	$-0.601882\pi$
$229$	−9.52255	−0.629268	−0.314634	+	0.949213i	$0.601882\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	33.7101	2.21318
$233$	−14.2272	−0.932054	−0.466027	−	0.884770i	$-0.654315\pi$
$233$	−14.2272	−0.932054	−0.466027	+	0.884770i	$0.654315\pi$
$234$	11.5427	0.754570
$235$	0	0
$236$	12.1323	0.789747
$237$	3.87047	0.251414
$238$	−6.91196	−0.448036
$239$	−20.5625	−1.33008	−0.665039	−	0.746808i	$-0.731585\pi$
$239$	−20.5625	−1.33008	−0.665039	+	0.746808i	$0.731585\pi$
$240$	0	0
$241$	20.5897	1.32630	0.663149	−	0.748487i	$-0.269219\pi$
$241$	20.5897	1.32630	0.663149	+	0.748487i	$0.269219\pi$
$242$	−2.58059	−0.165886
$243$	1.00000	0.0641500
$244$	72.2664	4.62638
$245$	0	0
$246$	5.52638	0.352349
$247$	1.71521	0.109136
$248$	−54.7007	−3.47350
$249$	−0.126713	−0.00803010
$250$	0	0
$251$	−12.9629	−0.818213	−0.409107	−	0.912487i	$-0.634160\pi$
$251$	−12.9629	−0.818213	−0.409107	+	0.912487i	$0.634160\pi$
$252$	−4.65942	−0.293516
$253$	0.698699	0.0439268
$254$	3.62485	0.227443
$255$	0	0
$256$	−23.7829	−1.48643
$257$	21.3052	1.32898	0.664490	−	0.747297i	$-0.268649\pi$
$257$	21.3052	1.32898	0.664490	+	0.747297i	$0.268649\pi$
$258$	−2.99650	−0.186554
$259$	−6.06630	−0.376941
$260$	0	0
$261$	−4.91196	−0.304043
$262$	24.1840	1.49410
$263$	15.9278	0.982152	0.491076	−	0.871117i	$-0.336604\pi$
$263$	15.9278	0.982152	0.491076	+	0.871117i	$0.336604\pi$
$264$	−6.86286	−0.422380
$265$	0	0
$266$	−0.989572	−0.0606745
$267$	−7.75107	−0.474358
$268$	−34.3634	−2.09908
$269$	−2.72766	−0.166308	−0.0831541	−	0.996537i	$-0.526499\pi$
$269$	−2.72766	−0.166308	−0.0831541	+	0.996537i	$0.526499\pi$
$270$	0	0
$271$	−18.6534	−1.13311	−0.566556	−	0.824023i	$-0.691724\pi$
$271$	−18.6534	−1.13311	−0.566556	+	0.824023i	$0.691724\pi$
$272$	−22.4758	−1.36280
$273$	4.47290	0.270712
$274$	34.7431	2.09891
$275$	0	0
$276$	3.25553	0.195960
$277$	−18.5494	−1.11453	−0.557263	−	0.830336i	$-0.688148\pi$
$277$	−18.5494	−1.11453	−0.557263	+	0.830336i	$0.688148\pi$
$278$	−11.8369	−0.709930
$279$	7.97054	0.477184
$280$	0	0
$281$	22.9813	1.37095	0.685474	−	0.728098i	$-0.259595\pi$
$281$	22.9813	1.37095	0.685474	+	0.728098i	$0.259595\pi$
$282$	14.4342	0.859546
$283$	18.1196	1.07710	0.538549	−	0.842594i	$-0.318973\pi$
$283$	18.1196	1.07710	0.538549	+	0.842594i	$0.318973\pi$
$284$	2.50824	0.148837
$285$	0	0
$286$	11.5427	0.682534
$287$	2.14152	0.126410
$288$	−7.92888	−0.467214
$289$	−9.82592	−0.577995
$290$	0	0
$291$	0.987463	0.0578861
$292$	31.8751	1.86535
$293$	30.5562	1.78511	0.892557	−	0.450934i	$-0.148909\pi$
$293$	30.5562	1.78511	0.892557	+	0.450934i	$0.148909\pi$
$294$	−2.58059	−0.150503
$295$	0	0
$296$	−41.6321	−2.41982
$297$	1.00000	0.0580259
$298$	−40.7176	−2.35871
$299$	−3.12521	−0.180736
$300$	0	0
$301$	−1.16117	−0.0669287
$302$	−13.8932	−0.799464
$303$	−10.3318	−0.593548
$304$	−3.21781	−0.184554
$305$	0	0
$306$	6.91196	0.395131
$307$	29.0129	1.65585	0.827927	−	0.560836i	$-0.189520\pi$
$307$	29.0129	1.65585	0.827927	+	0.560836i	$0.189520\pi$
$308$	−4.65942	−0.265495
$309$	−2.52710	−0.143762
$310$	0	0
$311$	5.27106	0.298894	0.149447	−	0.988770i	$-0.452251\pi$
$311$	5.27106	0.298894	0.149447	+	0.988770i	$0.452251\pi$
$312$	30.6969	1.73787
$313$	−8.44975	−0.477608	−0.238804	−	0.971068i	$-0.576755\pi$
$313$	−8.44975	−0.477608	−0.238804	+	0.971068i	$0.576755\pi$
$314$	33.0122	1.86298
$315$	0	0
$316$	18.0341	1.01450
$317$	−15.0499	−0.845289	−0.422645	−	0.906295i	$-0.638898\pi$
$317$	−15.0499	−0.845289	−0.422645	+	0.906295i	$0.638898\pi$
$318$	−13.7454	−0.770801
$319$	−4.91196	−0.275017
$320$	0	0
$321$	−1.03296	−0.0576541
$322$	1.80305	0.100480
$323$	1.02710	0.0571493
$324$	4.65942	0.258857
$325$	0	0
$326$	−20.3060	−1.12464
$327$	−16.0803	−0.889245
$328$	14.6970	0.811505
$329$	5.59340	0.308374
$330$	0	0
$331$	−13.3064	−0.731384	−0.365692	−	0.930736i	$-0.619168\pi$
$331$	−13.3064	−0.731384	−0.365692	+	0.930736i	$0.619168\pi$
$332$	−0.590408	−0.0324029
$333$	6.06630	0.332431
$334$	61.0097	3.33830
$335$	0	0
$336$	−8.39135	−0.457786
$337$	35.2035	1.91766	0.958829	−	0.283984i	$-0.0916562\pi$
$337$	35.2035	1.91766	0.958829	+	0.283984i	$0.0916562\pi$
$338$	−18.0817	−0.983516
$339$	−1.61653	−0.0877980
$340$	0	0
$341$	7.97054	0.431629
$342$	0.989572	0.0535099
$343$	−1.00000	−0.0539949
$344$	−7.96895	−0.429657
$345$	0	0
$346$	41.9809	2.25691
$347$	15.6063	0.837791	0.418896	−	0.908034i	$-0.362417\pi$
$347$	15.6063	0.837791	0.418896	+	0.908034i	$0.362417\pi$
$348$	−22.8869	−1.22687
$349$	7.13392	0.381870	0.190935	−	0.981603i	$-0.438848\pi$
$349$	7.13392	0.381870	0.190935	+	0.981603i	$0.438848\pi$
$350$	0	0
$351$	−4.47290	−0.238746
$352$	−7.92888	−0.422611
$353$	20.9153	1.11321	0.556605	−	0.830778i	$-0.312104\pi$
$353$	20.9153	1.11321	0.556605	+	0.830778i	$0.312104\pi$
$354$	−6.71940	−0.357132
$355$	0	0
$356$	−36.1155	−1.91412
$357$	2.67845	0.141758
$358$	58.9038	3.11316
$359$	−25.1061	−1.32505	−0.662524	−	0.749040i	$-0.730515\pi$
$359$	−25.1061	−1.32505	−0.662524	+	0.749040i	$0.730515\pi$
$360$	0	0
$361$	−18.8530	−0.992261
$362$	−17.3571	−0.912271
$363$	1.00000	0.0524864
$364$	20.8411	1.09237
$365$	0	0
$366$	−40.0242	−2.09210
$367$	13.7654	0.718550	0.359275	−	0.933232i	$-0.383024\pi$
$367$	13.7654	0.718550	0.359275	+	0.933232i	$0.383024\pi$
$368$	5.86303	0.305631
$369$	−2.14152	−0.111483
$370$	0	0
$371$	−5.32645	−0.276535
$372$	37.1381	1.92552
$373$	15.2741	0.790864	0.395432	−	0.918495i	$-0.370595\pi$
$373$	15.2741	0.790864	0.395432	+	0.918495i	$0.370595\pi$
$374$	6.91196	0.357409
$375$	0	0
$376$	38.3867	1.97964
$377$	21.9707	1.13155
$378$	2.58059	0.132731
$379$	9.32815	0.479155	0.239577	−	0.970877i	$-0.422991\pi$
$379$	9.32815	0.479155	0.239577	+	0.970877i	$0.422991\pi$
$380$	0	0
$381$	−1.40466	−0.0719631
$382$	59.8400	3.06168
$383$	27.7946	1.42024	0.710120	−	0.704081i	$-0.248641\pi$
$383$	27.7946	1.42024	0.710120	+	0.704081i	$0.248641\pi$
$384$	6.36521	0.324824
$385$	0	0
$386$	53.0570	2.70053
$387$	1.16117	0.0590256
$388$	4.60101	0.233581
$389$	−22.1942	−1.12529	−0.562647	−	0.826698i	$-0.690217\pi$
$389$	−22.1942	−1.12529	−0.562647	+	0.826698i	$0.690217\pi$
$390$	0	0
$391$	−1.87143	−0.0946422
$392$	−6.86286	−0.346627
$393$	−9.37154	−0.472731
$394$	16.9564	0.854253
$395$	0	0
$396$	4.65942	0.234145
$397$	−5.79447	−0.290816	−0.145408	−	0.989372i	$-0.546449\pi$
$397$	−5.79447	−0.290816	−0.145408	+	0.989372i	$0.546449\pi$
$398$	−1.50037	−0.0752068
$399$	0.383468	0.0191974
$400$	0	0
$401$	26.0760	1.30217	0.651087	−	0.759003i	$-0.274313\pi$
$401$	26.0760	1.30217	0.651087	+	0.759003i	$0.274313\pi$
$402$	19.0319	0.949226
$403$	−35.6514	−1.77592
$404$	−48.1403	−2.39507
$405$	0	0
$406$	−12.6757	−0.629086
$407$	6.06630	0.300695
$408$	18.3818	0.910035
$409$	0.128618	0.00635973	0.00317987	−	0.999995i	$-0.498988\pi$
$409$	0.128618	0.00635973	0.00317987	+	0.999995i	$0.498988\pi$
$410$	0	0
$411$	−13.4633	−0.664094
$412$	−11.7748	−0.580104
$413$	−2.60383	−0.128126
$414$	−1.80305	−0.0886152
$415$	0	0
$416$	35.4651	1.73882
$417$	4.58691	0.224622
$418$	0.989572	0.0484015
$419$	−29.4131	−1.43692	−0.718462	−	0.695566i	$-0.755154\pi$
$419$	−29.4131	−1.43692	−0.718462	+	0.695566i	$0.755154\pi$
$420$	0	0
$421$	14.1586	0.690049	0.345025	−	0.938594i	$-0.387871\pi$
$421$	14.1586	0.690049	0.345025	+	0.938594i	$0.387871\pi$
$422$	65.2073	3.17424
$423$	−5.59340	−0.271960
$424$	−36.5547	−1.77525
$425$	0	0
$426$	−1.38917	−0.0673056
$427$	−15.5097	−0.750569
$428$	−4.81298	−0.232644
$429$	−4.47290	−0.215954
$430$	0	0
$431$	22.7272	1.09473	0.547365	−	0.836894i	$-0.315631\pi$
$431$	22.7272	1.09473	0.547365	+	0.836894i	$0.315631\pi$
$432$	8.39135	0.403729
$433$	−6.77471	−0.325572	−0.162786	−	0.986661i	$-0.552048\pi$
$433$	−6.77471	−0.325572	−0.162786	+	0.986661i	$0.552048\pi$
$434$	20.5687	0.987328
$435$	0	0
$436$	−74.9250	−3.58826
$437$	−0.267929	−0.0128168
$438$	−17.6538	−0.843532
$439$	−27.6162	−1.31805	−0.659025	−	0.752121i	$-0.729031\pi$
$439$	−27.6162	−1.31805	−0.659025	+	0.752121i	$0.729031\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−30.9165	−1.47055
$443$	−14.6125	−0.694261	−0.347130	−	0.937817i	$-0.612844\pi$
$443$	−14.6125	−0.694261	−0.347130	+	0.937817i	$0.612844\pi$
$444$	28.2654	1.34142
$445$	0	0
$446$	37.8467	1.79209
$447$	15.7784	0.746294
$448$	−3.67845	−0.173790
$449$	16.0951	0.759577	0.379788	−	0.925073i	$-0.375997\pi$
$449$	16.0951	0.759577	0.379788	+	0.925073i	$0.375997\pi$
$450$	0	0
$451$	−2.14152	−0.100840
$452$	−7.53210	−0.354280
$453$	5.38374	0.252950
$454$	47.6983	2.23859
$455$	0	0
$456$	2.63169	0.123240
$457$	−19.2327	−0.899670	−0.449835	−	0.893112i	$-0.648517\pi$
$457$	−19.2327	−0.899670	−0.449835	+	0.893112i	$0.648517\pi$
$458$	24.5738	1.14826
$459$	−2.67845	−0.125019
$460$	0	0
$461$	−19.3672	−0.902019	−0.451009	−	0.892519i	$-0.648936\pi$
$461$	−19.3672	−0.902019	−0.451009	+	0.892519i	$0.648936\pi$
$462$	2.58059	0.120060
$463$	−28.3022	−1.31531	−0.657657	−	0.753317i	$-0.728452\pi$
$463$	−28.3022	−1.31531	−0.657657	+	0.753317i	$0.728452\pi$
$464$	−41.2180	−1.91350
$465$	0	0
$466$	36.7145	1.70077
$467$	−14.9259	−0.690688	−0.345344	−	0.938476i	$-0.612238\pi$
$467$	−14.9259	−0.690688	−0.345344	+	0.938476i	$0.612238\pi$
$468$	−20.8411	−0.963381
$469$	7.37504	0.340548
$470$	0	0
$471$	−12.7925	−0.589448
$472$	−17.8697	−0.822519
$473$	1.16117	0.0533907
$474$	−9.98807	−0.458767
$475$	0	0
$476$	12.4800	0.572020
$477$	5.32645	0.243881
$478$	53.0633	2.42706
$479$	4.12542	0.188495	0.0942477	−	0.995549i	$-0.469955\pi$
$479$	4.12542	0.188495	0.0942477	+	0.995549i	$0.469955\pi$
$480$	0	0
$481$	−27.1339	−1.23720
$482$	−53.1335	−2.42016
$483$	−0.698699	−0.0317919
$484$	4.65942	0.211792
$485$	0	0
$486$	−2.58059	−0.117058
$487$	−22.6403	−1.02593	−0.512965	−	0.858410i	$-0.671453\pi$
$487$	−22.6403	−1.02593	−0.512965	+	0.858410i	$0.671453\pi$
$488$	−106.441	−4.81837
$489$	7.86874	0.355837
$490$	0	0
$491$	−9.95172	−0.449115	−0.224557	−	0.974461i	$-0.572094\pi$
$491$	−9.95172	−0.449115	−0.224557	+	0.974461i	$0.572094\pi$
$492$	−9.97826	−0.449855
$493$	13.1564	0.592536
$494$	−4.42625	−0.199147
$495$	0	0
$496$	66.8836	3.00316
$497$	−0.538316	−0.0241468
$498$	0.326993	0.0146529
$499$	38.3094	1.71497	0.857483	−	0.514513i	$-0.172027\pi$
$499$	38.3094	1.71497	0.857483	+	0.514513i	$0.172027\pi$
$500$	0	0
$501$	−23.6418	−1.05624
$502$	33.4520	1.49303
$503$	30.5045	1.36013	0.680064	−	0.733153i	$-0.261952\pi$
$503$	30.5045	1.36013	0.680064	+	0.733153i	$0.261952\pi$
$504$	6.86286	0.305696
$505$	0	0
$506$	−1.80305	−0.0801554
$507$	7.00683	0.311184
$508$	−6.54491	−0.290384
$509$	5.90744	0.261843	0.130921	−	0.991393i	$-0.458206\pi$
$509$	5.90744	0.261843	0.130921	+	0.991393i	$0.458206\pi$
$510$	0	0
$511$	−6.84101	−0.302628
$512$	48.6433	2.14975
$513$	−0.383468	−0.0169305
$514$	−54.9798	−2.42506
$515$	0	0
$516$	5.41038	0.238179
$517$	−5.59340	−0.245997
$518$	15.6546	0.687824
$519$	−16.2680	−0.714085
$520$	0	0
$521$	−8.27734	−0.362637	−0.181319	−	0.983424i	$-0.558036\pi$
$521$	−8.27734	−0.362637	−0.181319	+	0.983424i	$0.558036\pi$
$522$	12.6757	0.554802
$523$	3.58938	0.156953	0.0784764	−	0.996916i	$-0.474994\pi$
$523$	3.58938	0.156953	0.0784764	+	0.996916i	$0.474994\pi$
$524$	−43.6659	−1.90755
$525$	0	0
$526$	−41.1031	−1.79218
$527$	−21.3487	−0.929963
$528$	8.39135	0.365187
$529$	−22.5118	−0.978775
$530$	0	0
$531$	2.60383	0.112996
$532$	1.78674	0.0774649
$533$	9.57882	0.414905
$534$	20.0023	0.865584
$535$	0	0
$536$	50.6138	2.18619
$537$	−22.8258	−0.985004
$538$	7.03895	0.303471
$539$	1.00000	0.0430730
$540$	0	0
$541$	−17.6944	−0.760741	−0.380371	−	0.924834i	$-0.624204\pi$
$541$	−17.6944	−0.760741	−0.380371	+	0.924834i	$0.624204\pi$
$542$	48.1366	2.06764
$543$	6.72605	0.288642
$544$	21.2371	0.910533
$545$	0	0
$546$	−11.5427	−0.493982
$547$	−44.9896	−1.92362	−0.961808	−	0.273726i	$-0.911744\pi$
$547$	−44.9896	−1.92362	−0.961808	+	0.273726i	$0.911744\pi$
$548$	−62.7310	−2.67973
$549$	15.5097	0.661940
$550$	0	0
$551$	1.88358	0.0802432
$552$	−4.79507	−0.204092
$553$	−3.87047	−0.164589
$554$	47.8683	2.03373
$555$	0	0
$556$	21.3723	0.906388
$557$	34.9250	1.47982	0.739910	−	0.672706i	$-0.234868\pi$
$557$	34.9250	1.47982	0.739910	+	0.672706i	$0.234868\pi$
$558$	−20.5687	−0.870741
$559$	−5.19380	−0.219674
$560$	0	0
$561$	−2.67845	−0.113084
$562$	−59.3051	−2.50163
$563$	34.5246	1.45504	0.727518	−	0.686088i	$-0.240674\pi$
$563$	34.5246	1.45504	0.727518	+	0.686088i	$0.240674\pi$
$564$	−26.0620	−1.09741
$565$	0	0
$566$	−46.7591	−1.96543
$567$	−1.00000	−0.0419961
$568$	−3.69439	−0.155013
$569$	−17.6143	−0.738432	−0.369216	−	0.929344i	$-0.620374\pi$
$569$	−17.6143	−0.738432	−0.369216	+	0.929344i	$0.620374\pi$
$570$	0	0
$571$	−15.6231	−0.653806	−0.326903	−	0.945058i	$-0.606005\pi$
$571$	−15.6231	−0.653806	−0.326903	+	0.945058i	$0.606005\pi$
$572$	−20.8411	−0.871411
$573$	−23.1885	−0.968715
$574$	−5.52638	−0.230667
$575$	0	0
$576$	3.67845	0.153269
$577$	−44.0026	−1.83185	−0.915925	−	0.401349i	$-0.868542\pi$
$577$	−44.0026	−1.83185	−0.915925	+	0.401349i	$0.868542\pi$
$578$	25.3566	1.05470
$579$	−20.5601	−0.854447
$580$	0	0
$581$	0.126713	0.00525693
$582$	−2.54823	−0.105628
$583$	5.32645	0.220599
$584$	−46.9489	−1.94276
$585$	0	0
$586$	−78.8530	−3.25739
$587$	10.3531	0.427319	0.213660	−	0.976908i	$-0.431462\pi$
$587$	10.3531	0.427319	0.213660	+	0.976908i	$0.431462\pi$
$588$	4.65942	0.192151
$589$	−3.05645	−0.125939
$590$	0	0
$591$	−6.57078	−0.270286
$592$	50.9044	2.09216
$593$	−41.4876	−1.70369	−0.851846	−	0.523792i	$-0.824517\pi$
$593$	−41.4876	−1.70369	−0.851846	+	0.523792i	$0.824517\pi$
$594$	−2.58059	−0.105883
$595$	0	0
$596$	73.5183	3.01143
$597$	0.581407	0.0237954
$598$	8.06487	0.329797
$599$	−35.2867	−1.44177	−0.720887	−	0.693053i	$-0.756265\pi$
$599$	−35.2867	−1.44177	−0.720887	+	0.693053i	$0.756265\pi$
$600$	0	0
$601$	−28.6354	−1.16806	−0.584031	−	0.811731i	$-0.698525\pi$
$601$	−28.6354	−1.16806	−0.584031	+	0.811731i	$0.698525\pi$
$602$	2.99650	0.122128
$603$	−7.37504	−0.300335
$604$	25.0851	1.02070
$605$	0	0
$606$	26.6621	1.08308
$607$	3.40672	0.138275	0.0691373	−	0.997607i	$-0.477975\pi$
$607$	3.40672	0.138275	0.0691373	+	0.997607i	$0.477975\pi$
$608$	3.04047	0.123307
$609$	4.91196	0.199043
$610$	0	0
$611$	25.0187	1.01215
$612$	−12.4800	−0.504474
$613$	−15.2442	−0.615708	−0.307854	−	0.951434i	$-0.599611\pi$
$613$	−15.2442	−0.615708	−0.307854	+	0.951434i	$0.599611\pi$
$614$	−74.8703	−3.02152
$615$	0	0
$616$	6.86286	0.276512
$617$	0.804164	0.0323744	0.0161872	−	0.999869i	$-0.494847\pi$
$617$	0.804164	0.0323744	0.0161872	+	0.999869i	$0.494847\pi$
$618$	6.52140	0.262329
$619$	3.89036	0.156367	0.0781834	−	0.996939i	$-0.475088\pi$
$619$	3.89036	0.156367	0.0781834	+	0.996939i	$0.475088\pi$
$620$	0	0
$621$	0.698699	0.0280378
$622$	−13.6024	−0.545407
$623$	7.75107	0.310540
$624$	−37.5337	−1.50255
$625$	0	0
$626$	21.8053	0.871515
$627$	−0.383468	−0.0153142
$628$	−59.6057	−2.37853
$629$	−16.2483	−0.647860
$630$	0	0
$631$	9.27226	0.369123	0.184561	−	0.982821i	$-0.440914\pi$
$631$	9.27226	0.369123	0.184561	+	0.982821i	$0.440914\pi$
$632$	−26.5625	−1.05660
$633$	−25.2684	−1.00433
$634$	38.8377	1.54244
$635$	0	0
$636$	24.8182	0.984104
$637$	−4.47290	−0.177223
$638$	12.6757	0.501837
$639$	0.538316	0.0212955
$640$	0	0
$641$	−32.7169	−1.29224	−0.646119	−	0.763237i	$-0.723609\pi$
$641$	−32.7169	−1.29224	−0.646119	+	0.763237i	$0.723609\pi$
$642$	2.66563	0.105204
$643$	26.4650	1.04368	0.521839	−	0.853044i	$-0.325246\pi$
$643$	26.4650	1.04368	0.521839	+	0.853044i	$0.325246\pi$
$644$	−3.25553	−0.128286
$645$	0	0
$646$	−2.65052	−0.104283
$647$	28.2903	1.11221	0.556104	−	0.831113i	$-0.312296\pi$
$647$	28.2903	1.11221	0.556104	+	0.831113i	$0.312296\pi$
$648$	−6.86286	−0.269599
$649$	2.60383	0.102209
$650$	0	0
$651$	−7.97054	−0.312390
$652$	36.6638	1.43586
$653$	−6.03829	−0.236296	−0.118148	−	0.992996i	$-0.537696\pi$
$653$	−6.03829	−0.236296	−0.118148	+	0.992996i	$0.537696\pi$
$654$	41.4967	1.62265
$655$	0	0
$656$	−17.9703	−0.701622
$657$	6.84101	0.266893
$658$	−14.4342	−0.562705
$659$	−24.7961	−0.965920	−0.482960	−	0.875642i	$-0.660438\pi$
$659$	−24.7961	−0.965920	−0.482960	+	0.875642i	$0.660438\pi$
$660$	0	0
$661$	10.8962	0.423813	0.211906	−	0.977290i	$-0.432033\pi$
$661$	10.8962	0.423813	0.211906	+	0.977290i	$0.432033\pi$
$662$	34.3382	1.33459
$663$	11.9804	0.465281
$664$	0.869612	0.0337475
$665$	0	0
$666$	−15.6546	−0.606603
$667$	−3.43198	−0.132887
$668$	−110.157	−4.26210
$669$	−14.6659	−0.567017
$670$	0	0
$671$	15.5097	0.598747
$672$	7.92888	0.305863
$673$	19.3682	0.746589	0.373295	−	0.927713i	$-0.378228\pi$
$673$	19.3682	0.746589	0.373295	+	0.927713i	$0.378228\pi$
$674$	−90.8457	−3.49925
$675$	0	0
$676$	32.6478	1.25568
$677$	−37.1635	−1.42831	−0.714154	−	0.699989i	$-0.753188\pi$
$677$	−37.1635	−1.42831	−0.714154	+	0.699989i	$0.753188\pi$
$678$	4.17160	0.160209
$679$	−0.987463	−0.0378954
$680$	0	0
$681$	−18.4835	−0.708290
$682$	−20.5687	−0.787615
$683$	11.6821	0.447003	0.223501	−	0.974704i	$-0.428251\pi$
$683$	11.6821	0.447003	0.223501	+	0.974704i	$0.428251\pi$
$684$	−1.78674	−0.0683176
$685$	0	0
$686$	2.58059	0.0985272
$687$	−9.52255	−0.363308
$688$	9.74379	0.371478
$689$	−23.8247	−0.907647
$690$	0	0
$691$	−24.9883	−0.950598	−0.475299	−	0.879824i	$-0.657660\pi$
$691$	−24.9883	−0.950598	−0.475299	+	0.879824i	$0.657660\pi$
$692$	−75.7993	−2.88146
$693$	−1.00000	−0.0379869
$694$	−40.2734	−1.52876
$695$	0	0
$696$	33.7101	1.27778
$697$	5.73596	0.217265
$698$	−18.4097	−0.696817
$699$	−14.2272	−0.538122
$700$	0	0
$701$	12.7611	0.481981	0.240990	−	0.970527i	$-0.422528\pi$
$701$	12.7611	0.481981	0.240990	+	0.970527i	$0.422528\pi$
$702$	11.5427	0.435651
$703$	−2.32623	−0.0877354
$704$	3.67845	0.138637
$705$	0	0
$706$	−53.9737	−2.03133
$707$	10.3318	0.388568
$708$	12.1323	0.455960
$709$	−6.98967	−0.262502	−0.131251	−	0.991349i	$-0.541899\pi$
$709$	−6.98967	−0.262502	−0.131251	+	0.991349i	$0.541899\pi$
$710$	0	0
$711$	3.87047	0.145154
$712$	53.1945	1.99355
$713$	5.56901	0.208561
$714$	−6.91196	−0.258674
$715$	0	0
$716$	−106.355	−3.97467
$717$	−20.5625	−0.767921
$718$	64.7884	2.41788
$719$	25.7134	0.958948	0.479474	−	0.877556i	$-0.340827\pi$
$719$	25.7134	0.958948	0.479474	+	0.877556i	$0.340827\pi$
$720$	0	0
$721$	2.52710	0.0941141
$722$	48.6516	1.81063
$723$	20.5897	0.765739
$724$	31.3395	1.16472
$725$	0	0
$726$	−2.58059	−0.0957745
$727$	−23.9290	−0.887479	−0.443740	−	0.896156i	$-0.646348\pi$
$727$	−23.9290	−0.887479	−0.443740	+	0.896156i	$0.646348\pi$
$728$	−30.6969	−1.13770
$729$	1.00000	0.0370370
$730$	0	0
$731$	−3.11013	−0.115032
$732$	72.2664	2.67104
$733$	−22.9063	−0.846064	−0.423032	−	0.906115i	$-0.639034\pi$
$733$	−22.9063	−0.846064	−0.423032	+	0.906115i	$0.639034\pi$
$734$	−35.5229	−1.31117
$735$	0	0
$736$	−5.53990	−0.204203
$737$	−7.37504	−0.271663
$738$	5.52638	0.203429
$739$	−47.5758	−1.75010	−0.875052	−	0.484028i	$-0.839173\pi$
$739$	−47.5758	−1.75010	−0.875052	+	0.484028i	$0.839173\pi$
$740$	0	0
$741$	1.71521	0.0630099
$742$	13.7454	0.504608
$743$	9.21998	0.338248	0.169124	−	0.985595i	$-0.445906\pi$
$743$	9.21998	0.338248	0.169124	+	0.985595i	$0.445906\pi$
$744$	−54.7007	−2.00543
$745$	0	0
$746$	−39.4162	−1.44313
$747$	−0.126713	−0.00463618
$748$	−12.4800	−0.456314
$749$	1.03296	0.0377434
$750$	0	0
$751$	−3.77758	−0.137846	−0.0689229	−	0.997622i	$-0.521956\pi$
$751$	−3.77758	−0.137846	−0.0689229	+	0.997622i	$0.521956\pi$
$752$	−46.9362	−1.71159
$753$	−12.9629	−0.472396
$754$	−56.6973	−2.06479
$755$	0	0
$756$	−4.65942	−0.169461
$757$	46.1974	1.67907	0.839537	−	0.543303i	$-0.182826\pi$
$757$	46.1974	1.67907	0.839537	+	0.543303i	$0.182826\pi$
$758$	−24.0721	−0.874338
$759$	0.698699	0.0253612
$760$	0	0
$761$	37.5804	1.36229	0.681145	−	0.732149i	$-0.261482\pi$
$761$	37.5804	1.36229	0.681145	+	0.732149i	$0.261482\pi$
$762$	3.62485	0.131315
$763$	16.0803	0.582147
$764$	−108.045	−3.90893
$765$	0	0
$766$	−71.7264	−2.59158
$767$	−11.6467	−0.420536
$768$	−23.7829	−0.858190
$769$	0.780815	0.0281569	0.0140785	−	0.999901i	$-0.495519\pi$
$769$	0.780815	0.0281569	0.0140785	+	0.999901i	$0.495519\pi$
$770$	0	0
$771$	21.3052	0.767288
$772$	−95.7980	−3.44784
$773$	−5.08079	−0.182743	−0.0913716	−	0.995817i	$-0.529125\pi$
$773$	−5.08079	−0.182743	−0.0913716	+	0.995817i	$0.529125\pi$
$774$	−2.99650	−0.107707
$775$	0	0
$776$	−6.77682	−0.243274
$777$	−6.06630	−0.217627
$778$	57.2741	2.05338
$779$	0.821206	0.0294227
$780$	0	0
$781$	0.538316	0.0192625
$782$	4.82938	0.172698
$783$	−4.91196	−0.175539
$784$	8.39135	0.299691
$785$	0	0
$786$	24.1840	0.862616
$787$	52.7254	1.87946	0.939729	−	0.341920i	$-0.111077\pi$
$787$	52.7254	1.87946	0.939729	+	0.341920i	$0.111077\pi$
$788$	−30.6160	−1.09065
$789$	15.9278	0.567046
$790$	0	0
$791$	1.61653	0.0574773
$792$	−6.86286	−0.243861
$793$	−69.3735	−2.46353
$794$	14.9531	0.530666
$795$	0	0
$796$	2.70902	0.0960187
$797$	−47.3890	−1.67861	−0.839303	−	0.543664i	$-0.817037\pi$
$797$	−47.3890	−1.67861	−0.839303	+	0.543664i	$0.817037\pi$
$798$	−0.989572	−0.0350305
$799$	14.9816	0.530012
$800$	0	0
$801$	−7.75107	−0.273870
$802$	−67.2914	−2.37614
$803$	6.84101	0.241414
$804$	−34.3634	−1.21190
$805$	0	0
$806$	92.0016	3.24062
$807$	−2.72766	−0.0960181
$808$	70.9058	2.49446
$809$	−46.4923	−1.63458	−0.817291	−	0.576225i	$-0.804525\pi$
$809$	−46.4923	−1.63458	−0.817291	+	0.576225i	$0.804525\pi$
$810$	0	0
$811$	−20.3789	−0.715602	−0.357801	−	0.933798i	$-0.616473\pi$
$811$	−20.3789	−0.715602	−0.357801	+	0.933798i	$0.616473\pi$
$812$	22.8869	0.803172
$813$	−18.6534	−0.654202
$814$	−15.6546	−0.548693
$815$	0	0
$816$	−22.4758	−0.786810
$817$	−0.445272	−0.0155781
$818$	−0.331909	−0.0116049
$819$	4.47290	0.156296
$820$	0	0
$821$	23.7694	0.829558	0.414779	−	0.909922i	$-0.363859\pi$
$821$	23.7694	0.829558	0.414779	+	0.909922i	$0.363859\pi$
$822$	34.7431	1.21180
$823$	33.8632	1.18040	0.590198	−	0.807258i	$-0.299050\pi$
$823$	33.8632	1.18040	0.590198	+	0.807258i	$0.299050\pi$
$824$	17.3431	0.604177
$825$	0	0
$826$	6.71940	0.233798
$827$	−17.0357	−0.592391	−0.296195	−	0.955127i	$-0.595718\pi$
$827$	−17.0357	−0.592391	−0.296195	+	0.955127i	$0.595718\pi$
$828$	3.25553	0.113138
$829$	12.9745	0.450622	0.225311	−	0.974287i	$-0.427660\pi$
$829$	12.9745	0.450622	0.225311	+	0.974287i	$0.427660\pi$
$830$	0	0
$831$	−18.5494	−0.643472
$832$	−16.4533	−0.570416
$833$	−2.67845	−0.0928027
$834$	−11.8369	−0.409878
$835$	0	0
$836$	−1.78674	−0.0617956
$837$	7.97054	0.275502
$838$	75.9030	2.62203
$839$	13.8196	0.477107	0.238554	−	0.971129i	$-0.423327\pi$
$839$	13.8196	0.477107	0.238554	+	0.971129i	$0.423327\pi$
$840$	0	0
$841$	−4.87264	−0.168022
$842$	−36.5375	−1.25917
$843$	22.9813	0.791517
$844$	−117.736	−4.05265
$845$	0	0
$846$	14.4342	0.496259
$847$	−1.00000	−0.0343604
$848$	44.6961	1.53487
$849$	18.1196	0.621862
$850$	0	0
$851$	4.23852	0.145294
$852$	2.50824	0.0859309
$853$	25.5797	0.875832	0.437916	−	0.899016i	$-0.355717\pi$
$853$	25.5797	0.875832	0.437916	+	0.899016i	$0.355717\pi$
$854$	40.0242	1.36960
$855$	0	0
$856$	7.08904	0.242298
$857$	19.7978	0.676280	0.338140	−	0.941096i	$-0.390202\pi$
$857$	19.7978	0.676280	0.338140	+	0.941096i	$0.390202\pi$
$858$	11.5427	0.394061
$859$	31.8025	1.08509	0.542543	−	0.840028i	$-0.317462\pi$
$859$	31.8025	1.08509	0.542543	+	0.840028i	$0.317462\pi$
$860$	0	0
$861$	2.14152	0.0729829
$862$	−58.6494	−1.99761
$863$	21.6367	0.736521	0.368261	−	0.929723i	$-0.379953\pi$
$863$	21.6367	0.736521	0.368261	+	0.929723i	$0.379953\pi$
$864$	−7.92888	−0.269746
$865$	0	0
$866$	17.4827	0.594087
$867$	−9.82592	−0.333706
$868$	−37.1381	−1.26055
$869$	3.87047	0.131297
$870$	0	0
$871$	32.9878	1.11775
$872$	110.357	3.73716
$873$	0.987463	0.0334206
$874$	0.691412	0.0233874
$875$	0	0
$876$	31.8751	1.07696
$877$	−45.6877	−1.54276	−0.771381	−	0.636373i	$-0.780434\pi$
$877$	−45.6877	−1.54276	−0.771381	+	0.636373i	$0.780434\pi$
$878$	71.2660	2.40511
$879$	30.5562	1.03064
$880$	0	0
$881$	−1.63954	−0.0552376	−0.0276188	−	0.999619i	$-0.508792\pi$
$881$	−1.63954	−0.0552376	−0.0276188	+	0.999619i	$0.508792\pi$
$882$	−2.58059	−0.0868928
$883$	−15.9908	−0.538132	−0.269066	−	0.963122i	$-0.586715\pi$
$883$	−15.9908	−0.538132	−0.269066	+	0.963122i	$0.586715\pi$
$884$	55.8218	1.87749
$885$	0	0
$886$	37.7088	1.26685
$887$	−3.35261	−0.112569	−0.0562847	−	0.998415i	$-0.517925\pi$
$887$	−3.35261	−0.112569	−0.0562847	+	0.998415i	$0.517925\pi$
$888$	−41.6321	−1.39708
$889$	1.40466	0.0471109
$890$	0	0
$891$	1.00000	0.0335013
$892$	−68.3347	−2.28801
$893$	2.14489	0.0717760
$894$	−40.7176	−1.36180
$895$	0	0
$896$	−6.36521	−0.212647
$897$	−3.12521	−0.104348
$898$	−41.5349	−1.38604
$899$	−39.1510	−1.30576
$900$	0	0
$901$	−14.2666	−0.475290
$902$	5.52638	0.184008
$903$	−1.16117	−0.0386413
$904$	11.0940	0.368982
$905$	0	0
$906$	−13.8932	−0.461571
$907$	−4.40888	−0.146394	−0.0731972	−	0.997317i	$-0.523320\pi$
$907$	−4.40888	−0.146394	−0.0731972	+	0.997317i	$0.523320\pi$
$908$	−86.1224	−2.85807
$909$	−10.3318	−0.342685
$910$	0	0
$911$	22.9224	0.759452	0.379726	−	0.925099i	$-0.376018\pi$
$911$	22.9224	0.759452	0.379726	+	0.925099i	$0.376018\pi$
$912$	−3.21781	−0.106552
$913$	−0.126713	−0.00419358
$914$	49.6317	1.64167
$915$	0	0
$916$	−44.3696	−1.46601
$917$	9.37154	0.309475
$918$	6.91196	0.228129
$919$	−51.8152	−1.70922	−0.854612	−	0.519267i	$-0.826205\pi$
$919$	−51.8152	−1.70922	−0.854612	+	0.519267i	$0.826205\pi$
$920$	0	0
$921$	29.0129	0.956008
$922$	49.9786	1.64596
$923$	−2.40783	−0.0792549
$924$	−4.65942	−0.153284
$925$	0	0
$926$	73.0362	2.40012
$927$	−2.52710	−0.0830009
$928$	38.9464	1.27848
$929$	30.5209	1.00136	0.500679	−	0.865633i	$-0.333084\pi$
$929$	30.5209	1.00136	0.500679	+	0.865633i	$0.333084\pi$
$930$	0	0
$931$	−0.383468	−0.0125677
$932$	−66.2905	−2.17142
$933$	5.27106	0.172567
$934$	38.5175	1.26033
$935$	0	0
$936$	30.6969	1.00336
$937$	−0.0648455	−0.00211841	−0.00105920	−	0.999999i	$-0.500337\pi$
$937$	−0.0648455	−0.00211841	−0.00105920	+	0.999999i	$0.500337\pi$
$938$	−19.0319	−0.621414
$939$	−8.44975	−0.275747
$940$	0	0
$941$	−41.3056	−1.34653	−0.673263	−	0.739403i	$-0.735108\pi$
$941$	−41.3056	−1.34653	−0.673263	+	0.739403i	$0.735108\pi$
$942$	33.0122	1.07559
$943$	−1.49628	−0.0487256
$944$	21.8496	0.711145
$945$	0	0
$946$	−2.99650	−0.0974246
$947$	−29.6670	−0.964049	−0.482025	−	0.876158i	$-0.660098\pi$
$947$	−29.6670	−0.964049	−0.482025	+	0.876158i	$0.660098\pi$
$948$	18.0341	0.585721
$949$	−30.5992	−0.993291
$950$	0	0
$951$	−15.0499	−0.488028
$952$	−18.3818	−0.595758
$953$	12.3109	0.398789	0.199394	−	0.979919i	$-0.436103\pi$
$953$	12.3109	0.398789	0.199394	+	0.979919i	$0.436103\pi$
$954$	−13.7454	−0.445022
$955$	0	0
$956$	−95.8094	−3.09870
$957$	−4.91196	−0.158781
$958$	−10.6460	−0.343957
$959$	13.4633	0.434751
$960$	0	0
$961$	32.5296	1.04934
$962$	70.0214	2.25758
$963$	−1.03296	−0.0332866
$964$	95.9360	3.08989
$965$	0	0
$966$	1.80305	0.0580122
$967$	18.8123	0.604964	0.302482	−	0.953155i	$-0.402185\pi$
$967$	18.8123	0.604964	0.302482	+	0.953155i	$0.402185\pi$
$968$	−6.86286	−0.220581
$969$	1.02710	0.0329952
$970$	0	0
$971$	27.6424	0.887087	0.443543	−	0.896253i	$-0.353721\pi$
$971$	27.6424	0.887087	0.443543	+	0.896253i	$0.353721\pi$
$972$	4.65942	0.149451
$973$	−4.58691	−0.147049
$974$	58.4252	1.87206
$975$	0	0
$976$	130.148	4.16593
$977$	−55.4690	−1.77461	−0.887305	−	0.461182i	$-0.847425\pi$
$977$	−55.4690	−1.77461	−0.887305	+	0.461182i	$0.847425\pi$
$978$	−20.3060	−0.649313
$979$	−7.75107	−0.247725
$980$	0	0
$981$	−16.0803	−0.513406
$982$	25.6813	0.819522
$983$	17.0969	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$983$	17.0969	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$984$	14.6970	0.468522
$985$	0	0
$986$	−33.9513	−1.08123
$987$	5.59340	0.178040
$988$	7.99190	0.254256
$989$	0.811308	0.0257981
$990$	0	0
$991$	17.8478	0.566953	0.283476	−	0.958979i	$-0.408512\pi$
$991$	17.8478	0.566953	0.283476	+	0.958979i	$0.408512\pi$
$992$	−63.1975	−2.00652
$993$	−13.3064	−0.422265
$994$	1.38917	0.0440618
$995$	0	0
$996$	−0.590408	−0.0187078
$997$	−28.1335	−0.890998	−0.445499	−	0.895282i	$-0.646974\pi$
$997$	−28.1335	−0.890998	−0.445499	+	0.895282i	$0.646974\pi$
$998$	−98.8607	−3.12938
$999$	6.06630	0.191929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5775.2.a.ce.1.1	✓	5
5.4	even	2		5775.2.a.cl.1.5	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5775.2.a.ce.1.1	✓	5	1.1	even	1	trivial
5775.2.a.cl.1.5	yes	5	5.4	even	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:	\( N \)	\(=\)	\( 5775 = 3 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5775.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58059 q^{2} +1.00000 q^{3} +4.65942 q^{4} -2.58059 q^{6} -1.00000 q^{7} -6.86286 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58059 q^{2} +1.00000 q^{3} +4.65942 q^{4} -2.58059 q^{6} -1.00000 q^{7} -6.86286 q^{8} +1.00000 q^{9} +1.00000 q^{11} +4.65942 q^{12} -4.47290 q^{13} +2.58059 q^{14} +8.39135 q^{16} -2.67845 q^{17} -2.58059 q^{18} -0.383468 q^{19} -1.00000 q^{21} -2.58059 q^{22} +0.698699 q^{23} -6.86286 q^{24} +11.5427 q^{26} +1.00000 q^{27} -4.65942 q^{28} -4.91196 q^{29} +7.97054 q^{31} -7.92888 q^{32} +1.00000 q^{33} +6.91196 q^{34} +4.65942 q^{36} +6.06630 q^{37} +0.989572 q^{38} -4.47290 q^{39} -2.14152 q^{41} +2.58059 q^{42} +1.16117 q^{43} +4.65942 q^{44} -1.80305 q^{46} -5.59340 q^{47} +8.39135 q^{48} +1.00000 q^{49} -2.67845 q^{51} -20.8411 q^{52} +5.32645 q^{53} -2.58059 q^{54} +6.86286 q^{56} -0.383468 q^{57} +12.6757 q^{58} +2.60383 q^{59} +15.5097 q^{61} -20.5687 q^{62} -1.00000 q^{63} +3.67845 q^{64} -2.58059 q^{66} -7.37504 q^{67} -12.4800 q^{68} +0.698699 q^{69} +0.538316 q^{71} -6.86286 q^{72} +6.84101 q^{73} -15.6546 q^{74} -1.78674 q^{76} -1.00000 q^{77} +11.5427 q^{78} +3.87047 q^{79} +1.00000 q^{81} +5.52638 q^{82} -0.126713 q^{83} -4.65942 q^{84} -2.99650 q^{86} -4.91196 q^{87} -6.86286 q^{88} -7.75107 q^{89} +4.47290 q^{91} +3.25553 q^{92} +7.97054 q^{93} +14.4342 q^{94} -7.92888 q^{96} +0.987463 q^{97} -2.58059 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} + 5 q^{3} + 4 q^{4} - 2 q^{6} - 5 q^{7} - 6 q^{8} + 5 q^{9} + 5 q^{11} + 4 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{16} - 15 q^{17} - 2 q^{18} + 3 q^{19} - 5 q^{21} - 2 q^{22} - 6 q^{24} + 5 q^{27} - 4 q^{28} - 4 q^{29} + 16 q^{31} - 14 q^{32} + 5 q^{33} + 14 q^{34} + 4 q^{36} - 7 q^{37} + 2 q^{38} - 7 q^{39} - 5 q^{41} + 2 q^{42} - 16 q^{43} + 4 q^{44} - 10 q^{46} - 6 q^{47} - 2 q^{48} + 5 q^{49} - 15 q^{51} - 18 q^{52} - 11 q^{53} - 2 q^{54} + 6 q^{56} + 3 q^{57} + 28 q^{58} - 6 q^{59} + q^{61} - 26 q^{62} - 5 q^{63} + 20 q^{64} - 2 q^{66} - 9 q^{67} - 2 q^{68} - 21 q^{71} - 6 q^{72} - 17 q^{73} + 4 q^{74} - 26 q^{76} - 5 q^{77} - 8 q^{79} + 5 q^{81} - 14 q^{82} - 26 q^{83} - 4 q^{84} - 20 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{91} + 12 q^{92} + 16 q^{93} + 4 q^{94} - 14 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 5 * q^3 + 4 * q^4 - 2 * q^6 - 5 * q^7 - 6 * q^8 + 5 * q^9 + 5 * q^11 + 4 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^16 - 15 * q^17 - 2 * q^18 + 3 * q^19 - 5 * q^21 - 2 * q^22 - 6 * q^24 + 5 * q^27 - 4 * q^28 - 4 * q^29 + 16 * q^31 - 14 * q^32 + 5 * q^33 + 14 * q^34 + 4 * q^36 - 7 * q^37 + 2 * q^38 - 7 * q^39 - 5 * q^41 + 2 * q^42 - 16 * q^43 + 4 * q^44 - 10 * q^46 - 6 * q^47 - 2 * q^48 + 5 * q^49 - 15 * q^51 - 18 * q^52 - 11 * q^53 - 2 * q^54 + 6 * q^56 + 3 * q^57 + 28 * q^58 - 6 * q^59 + q^61 - 26 * q^62 - 5 * q^63 + 20 * q^64 - 2 * q^66 - 9 * q^67 - 2 * q^68 - 21 * q^71 - 6 * q^72 - 17 * q^73 + 4 * q^74 - 26 * q^76 - 5 * q^77 - 8 * q^79 + 5 * q^81 - 14 * q^82 - 26 * q^83 - 4 * q^84 - 20 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^91 + 12 * q^92 + 16 * q^93 + 4 * q^94 - 14 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

Introduction

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