LMFDB - Embedded newform 6025.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.895481 q^{2} +0.415795 q^{3} -1.19811 q^{4} -0.372337 q^{6} -2.78281 q^{7} +2.86385 q^{8} -2.82711 q^{9} +O(q^{10})$	\(q-0.895481 q^{2} +0.415795 q^{3} -1.19811 q^{4} -0.372337 q^{6} -2.78281 q^{7} +2.86385 q^{8} -2.82711 q^{9} -5.25192 q^{11} -0.498169 q^{12} -1.97077 q^{13} +2.49196 q^{14} -0.168298 q^{16} -6.98701 q^{17} +2.53163 q^{18} +8.09238 q^{19} -1.15708 q^{21} +4.70300 q^{22} -3.31341 q^{23} +1.19077 q^{24} +1.76479 q^{26} -2.42288 q^{27} +3.33413 q^{28} +1.04029 q^{29} -3.07919 q^{31} -5.57699 q^{32} -2.18372 q^{33} +6.25674 q^{34} +3.38720 q^{36} -5.38818 q^{37} -7.24658 q^{38} -0.819437 q^{39} -6.04412 q^{41} +1.03614 q^{42} -11.7746 q^{43} +6.29240 q^{44} +2.96709 q^{46} +5.22254 q^{47} -0.0699774 q^{48} +0.744051 q^{49} -2.90516 q^{51} +2.36121 q^{52} -4.91604 q^{53} +2.16965 q^{54} -7.96956 q^{56} +3.36477 q^{57} -0.931561 q^{58} -5.43925 q^{59} -9.07272 q^{61} +2.75736 q^{62} +7.86733 q^{63} +5.33069 q^{64} +1.95548 q^{66} -8.20241 q^{67} +8.37123 q^{68} -1.37770 q^{69} +5.40696 q^{71} -8.09643 q^{72} -8.17508 q^{73} +4.82501 q^{74} -9.69559 q^{76} +14.6151 q^{77} +0.733791 q^{78} -14.6865 q^{79} +7.47392 q^{81} +5.41240 q^{82} -10.2994 q^{83} +1.38631 q^{84} +10.5439 q^{86} +0.432548 q^{87} -15.0407 q^{88} +13.0800 q^{89} +5.48429 q^{91} +3.96984 q^{92} -1.28031 q^{93} -4.67669 q^{94} -2.31889 q^{96} -9.14323 q^{97} -0.666283 q^{98} +14.8478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	$ 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) $ 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * 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 $

$2$	−0.895481	−0.633201	−0.316600	−	0.948559i	$-0.602541\pi$
$2$	−0.895481	−0.633201	−0.316600	+	0.948559i	$0.602541\pi$
$3$	0.415795	0.240059	0.120030	−	0.992770i	$-0.461701\pi$
$3$	0.415795	0.240059	0.120030	+	0.992770i	$0.461701\pi$
$4$	−1.19811	−0.599057
$5$	0	0
$5$	0	0
$6$	−0.372337	−0.152006
$7$	−2.78281	−1.05180	−0.525902	−	0.850545i	$-0.676272\pi$
$7$	−2.78281	−1.05180	−0.525902	+	0.850545i	$0.676272\pi$
$8$	2.86385	1.01252
$9$	−2.82711	−0.942372
$10$	0	0
$11$	−5.25192	−1.58351	−0.791757	−	0.610836i	$-0.790833\pi$
$11$	−5.25192	−1.58351	−0.791757	+	0.610836i	$0.790833\pi$
$12$	−0.498169	−0.143809
$13$	−1.97077	−0.546594	−0.273297	−	0.961930i	$-0.588114\pi$
$13$	−1.97077	−0.546594	−0.273297	+	0.961930i	$0.588114\pi$
$14$	2.49196	0.666004
$15$	0	0
$16$	−0.168298	−0.0420744
$17$	−6.98701	−1.69460	−0.847299	−	0.531116i	$-0.821773\pi$
$17$	−6.98701	−1.69460	−0.847299	+	0.531116i	$0.821773\pi$
$18$	2.53163	0.596710
$19$	8.09238	1.85652	0.928260	−	0.371932i	$-0.121305\pi$
$19$	8.09238	1.85652	0.928260	+	0.371932i	$0.121305\pi$
$20$	0	0
$21$	−1.15708	−0.252495
$22$	4.70300	1.00268
$23$	−3.31341	−0.690893	−0.345447	−	0.938438i	$-0.612273\pi$
$23$	−3.31341	−0.690893	−0.345447	+	0.938438i	$0.612273\pi$
$24$	1.19077	0.243066
$25$	0	0
$26$	1.76479	0.346104
$27$	−2.42288	−0.466284
$28$	3.33413	0.630091
$29$	1.04029	0.193177	0.0965886	−	0.995324i	$-0.469207\pi$
$29$	1.04029	0.193177	0.0965886	+	0.995324i	$0.469207\pi$
$30$	0	0
$31$	−3.07919	−0.553039	−0.276520	−	0.961008i	$-0.589181\pi$
$31$	−3.07919	−0.553039	−0.276520	+	0.961008i	$0.589181\pi$
$32$	−5.57699	−0.985882
$33$	−2.18372	−0.380137
$34$	6.25674	1.07302
$35$	0	0
$36$	3.38720	0.564534
$37$	−5.38818	−0.885811	−0.442906	−	0.896568i	$-0.646052\pi$
$37$	−5.38818	−0.885811	−0.442906	+	0.896568i	$0.646052\pi$
$38$	−7.24658	−1.17555
$39$	−0.819437	−0.131215
$40$	0	0
$41$	−6.04412	−0.943933	−0.471967	−	0.881616i	$-0.656456\pi$
$41$	−6.04412	−0.943933	−0.471967	+	0.881616i	$0.656456\pi$
$42$	1.03614	0.159880
$43$	−11.7746	−1.79561	−0.897804	−	0.440396i	$-0.854838\pi$
$43$	−11.7746	−1.79561	−0.897804	+	0.440396i	$0.854838\pi$
$44$	6.29240	0.948614
$45$	0	0
$46$	2.96709	0.437474
$47$	5.22254	0.761786	0.380893	−	0.924619i	$-0.375617\pi$
$47$	5.22254	0.761786	0.380893	+	0.924619i	$0.375617\pi$
$48$	−0.0699774	−0.0101004
$49$	0.744051	0.106293
$50$	0	0
$51$	−2.90516	−0.406804
$52$	2.36121	0.327441
$53$	−4.91604	−0.675270	−0.337635	−	0.941277i	$-0.609627\pi$
$53$	−4.91604	−0.675270	−0.337635	+	0.941277i	$0.609627\pi$
$54$	2.16965	0.295252
$55$	0	0
$56$	−7.96956	−1.06498
$57$	3.36477	0.445675
$58$	−0.931561	−0.122320
$59$	−5.43925	−0.708130	−0.354065	−	0.935221i	$-0.615201\pi$
$59$	−5.43925	−0.708130	−0.354065	+	0.935221i	$0.615201\pi$
$60$	0	0
$61$	−9.07272	−1.16164	−0.580821	−	0.814031i	$-0.697268\pi$
$61$	−9.07272	−1.16164	−0.580821	+	0.814031i	$0.697268\pi$
$62$	2.75736	0.350185
$63$	7.86733	0.991191
$64$	5.33069	0.666336
$65$	0	0
$66$	1.95548	0.240703
$67$	−8.20241	−1.00208	−0.501042	−	0.865423i	$-0.667050\pi$
$67$	−8.20241	−1.00208	−0.501042	+	0.865423i	$0.667050\pi$
$68$	8.37123	1.01516
$69$	−1.37770	−0.165855
$70$	0	0
$71$	5.40696	0.641688	0.320844	−	0.947132i	$-0.396034\pi$
$71$	5.40696	0.641688	0.320844	+	0.947132i	$0.396034\pi$
$72$	−8.09643	−0.954174
$73$	−8.17508	−0.956821	−0.478411	−	0.878136i	$-0.658787\pi$
$73$	−8.17508	−0.956821	−0.478411	+	0.878136i	$0.658787\pi$
$74$	4.82501	0.560896
$75$	0	0
$76$	−9.69559	−1.11216
$77$	14.6151	1.66555
$78$	0.733791	0.0830855
$79$	−14.6865	−1.65236	−0.826180	−	0.563407i	$-0.809490\pi$
$79$	−14.6865	−1.65236	−0.826180	+	0.563407i	$0.809490\pi$
$80$	0	0
$81$	7.47392	0.830436
$82$	5.41240	0.597699
$83$	−10.2994	−1.13050	−0.565251	−	0.824919i	$-0.691221\pi$
$83$	−10.2994	−1.13050	−0.565251	+	0.824919i	$0.691221\pi$
$84$	1.38631	0.151259
$85$	0	0
$86$	10.5439	1.13698
$87$	0.432548	0.0463740
$88$	−15.0407	−1.60335
$89$	13.0800	1.38648	0.693238	−	0.720709i	$-0.256184\pi$
$89$	13.0800	1.38648	0.693238	+	0.720709i	$0.256184\pi$
$90$	0	0
$91$	5.48429	0.574910
$92$	3.96984	0.413884
$93$	−1.28031	−0.132762
$94$	−4.67669	−0.482363
$95$	0	0
$96$	−2.31889	−0.236670
$97$	−9.14323	−0.928354	−0.464177	−	0.885742i	$-0.653650\pi$
$97$	−9.14323	−0.928354	−0.464177	+	0.885742i	$0.653650\pi$
$98$	−0.666283	−0.0673048
$99$	14.8478	1.49226
$100$	0	0
$101$	−8.79525	−0.875161	−0.437580	−	0.899179i	$-0.644164\pi$
$101$	−8.79525	−0.875161	−0.437580	+	0.899179i	$0.644164\pi$
$102$	2.60152	0.257589
$103$	−11.7442	−1.15719	−0.578597	−	0.815614i	$-0.696400\pi$
$103$	−11.7442	−1.15719	−0.578597	+	0.815614i	$0.696400\pi$
$104$	−5.64400	−0.553440
$105$	0	0
$106$	4.40222	0.427582
$107$	8.99498	0.869577	0.434789	−	0.900533i	$-0.356823\pi$
$107$	8.99498	0.869577	0.434789	+	0.900533i	$0.356823\pi$
$108$	2.90289	0.279331
$109$	19.6720	1.88423	0.942117	−	0.335285i	$-0.108833\pi$
$109$	19.6720	1.88423	0.942117	+	0.335285i	$0.108833\pi$
$110$	0	0
$111$	−2.24038	−0.212647
$112$	0.468341	0.0442541
$113$	9.96010	0.936968	0.468484	−	0.883472i	$-0.344800\pi$
$113$	9.96010	0.936968	0.468484	+	0.883472i	$0.344800\pi$
$114$	−3.01309	−0.282202
$115$	0	0
$116$	−1.24639	−0.115724
$117$	5.57160	0.515095
$118$	4.87075	0.448389
$119$	19.4435	1.78239
$120$	0	0
$121$	16.5827	1.50752
$122$	8.12445	0.735553
$123$	−2.51312	−0.226600
$124$	3.68922	0.331302
$125$	0	0
$126$	−7.04505	−0.627623
$127$	0.609694	0.0541016	0.0270508	−	0.999634i	$-0.491388\pi$
$127$	0.609694	0.0541016	0.0270508	+	0.999634i	$0.491388\pi$
$128$	6.38046	0.563958
$129$	−4.89581	−0.431052
$130$	0	0
$131$	−11.1764	−0.976483	−0.488241	−	0.872709i	$-0.662361\pi$
$131$	−11.1764	−0.976483	−0.488241	+	0.872709i	$0.662361\pi$
$132$	2.61635	0.227724
$133$	−22.5196	−1.95270
$134$	7.34511	0.634521
$135$	0	0
$136$	−20.0098	−1.71582
$137$	0.594894	0.0508252	0.0254126	−	0.999677i	$-0.491910\pi$
$137$	0.594894	0.0508252	0.0254126	+	0.999677i	$0.491910\pi$
$138$	1.23370	0.105020
$139$	−1.09697	−0.0930434	−0.0465217	−	0.998917i	$-0.514814\pi$
$139$	−1.09697	−0.0930434	−0.0465217	+	0.998917i	$0.514814\pi$
$140$	0	0
$141$	2.17151	0.182874
$142$	−4.84183	−0.406317
$143$	10.3503	0.865539
$144$	0.475797	0.0396498
$145$	0	0
$146$	7.32063	0.605860
$147$	0.309372	0.0255166
$148$	6.45565	0.530651
$149$	−11.6658	−0.955701	−0.477851	−	0.878441i	$-0.658584\pi$
$149$	−11.6658	−0.955701	−0.477851	+	0.878441i	$0.658584\pi$
$150$	0	0
$151$	14.9663	1.21794	0.608969	−	0.793194i	$-0.291583\pi$
$151$	14.9663	1.21794	0.608969	+	0.793194i	$0.291583\pi$
$152$	23.1754	1.87977
$153$	19.7531	1.59694
$154$	−13.0876	−1.05463
$155$	0	0
$156$	0.981779	0.0786052
$157$	9.84157	0.785443	0.392722	−	0.919657i	$-0.371534\pi$
$157$	9.84157	0.785443	0.392722	+	0.919657i	$0.371534\pi$
$158$	13.1515	1.04628
$159$	−2.04407	−0.162105
$160$	0	0
$161$	9.22060	0.726685
$162$	−6.69276	−0.525833
$163$	20.8137	1.63026	0.815129	−	0.579280i	$-0.196666\pi$
$163$	20.8137	1.63026	0.815129	+	0.579280i	$0.196666\pi$
$164$	7.24154	0.565470
$165$	0	0
$166$	9.22288	0.715835
$167$	−12.1110	−0.937179	−0.468589	−	0.883416i	$-0.655238\pi$
$167$	−12.1110	−0.937179	−0.468589	+	0.883416i	$0.655238\pi$
$168$	−3.31370	−0.255658
$169$	−9.11605	−0.701235
$170$	0	0
$171$	−22.8781	−1.74953
$172$	14.1073	1.07567
$173$	16.5113	1.25533	0.627664	−	0.778485i	$-0.284011\pi$
$173$	16.5113	1.25533	0.627664	+	0.778485i	$0.284011\pi$
$174$	−0.387338	−0.0293640
$175$	0	0
$176$	0.883887	0.0666255
$177$	−2.26161	−0.169993
$178$	−11.7129	−0.877917
$179$	18.4242	1.37709	0.688543	−	0.725195i	$-0.258250\pi$
$179$	18.4242	1.37709	0.688543	+	0.725195i	$0.258250\pi$
$180$	0	0
$181$	5.24551	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$181$	5.24551	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$182$	−4.91108	−0.364034
$183$	−3.77239	−0.278863
$184$	−9.48911	−0.699546
$185$	0	0
$186$	1.14650	0.0840652
$187$	36.6952	2.68342
$188$	−6.25720	−0.456353
$189$	6.74244	0.490440
$190$	0	0
$191$	5.28853	0.382664	0.191332	−	0.981525i	$-0.438719\pi$
$191$	5.28853	0.382664	0.191332	+	0.981525i	$0.438719\pi$
$192$	2.21647	0.159960
$193$	10.0114	0.720639	0.360319	−	0.932829i	$-0.382668\pi$
$193$	10.0114	0.720639	0.360319	+	0.932829i	$0.382668\pi$
$194$	8.18759	0.587835
$195$	0	0
$196$	−0.891457	−0.0636755
$197$	−24.4928	−1.74504	−0.872521	−	0.488577i	$-0.837516\pi$
$197$	−24.4928	−1.74504	−0.872521	+	0.488577i	$0.837516\pi$
$198$	−13.2959	−0.944899
$199$	−23.5581	−1.66999	−0.834995	−	0.550257i	$-0.814530\pi$
$199$	−23.5581	−1.66999	−0.834995	+	0.550257i	$0.814530\pi$
$200$	0	0
$201$	−3.41052	−0.240560
$202$	7.87599	0.554152
$203$	−2.89494	−0.203185
$204$	3.48071	0.243699
$205$	0	0
$206$	10.5167	0.732736
$207$	9.36738	0.651078
$208$	0.331677	0.0229976
$209$	−42.5005	−2.93982
$210$	0	0
$211$	−2.17766	−0.149916	−0.0749580	−	0.997187i	$-0.523882\pi$
$211$	−2.17766	−0.149916	−0.0749580	+	0.997187i	$0.523882\pi$
$212$	5.88997	0.404525
$213$	2.24819	0.154043
$214$	−8.05483	−0.550617
$215$	0	0
$216$	−6.93878	−0.472124
$217$	8.56882	0.581689
$218$	−17.6159	−1.19310
$219$	−3.39916	−0.229694
$220$	0	0
$221$	13.7698	0.926258
$222$	2.00622	0.134648
$223$	−22.2653	−1.49100	−0.745498	−	0.666508i	$-0.767788\pi$
$223$	−22.2653	−1.49100	−0.745498	+	0.666508i	$0.767788\pi$
$224$	15.5197	1.03696
$225$	0	0
$226$	−8.91909	−0.593289
$227$	−6.26018	−0.415503	−0.207751	−	0.978182i	$-0.566614\pi$
$227$	−6.26018	−0.415503	−0.207751	+	0.978182i	$0.566614\pi$
$228$	−4.03138	−0.266984
$229$	8.83087	0.583560	0.291780	−	0.956485i	$-0.405752\pi$
$229$	8.83087	0.583560	0.291780	+	0.956485i	$0.405752\pi$
$230$	0	0
$231$	6.07689	0.399830
$232$	2.97924	0.195597
$233$	16.7224	1.09552	0.547760	−	0.836636i	$-0.315481\pi$
$233$	16.7224	1.09552	0.547760	+	0.836636i	$0.315481\pi$
$234$	−4.98926	−0.326158
$235$	0	0
$236$	6.51684	0.424210
$237$	−6.10657	−0.396664
$238$	−17.4113	−1.12861
$239$	16.7632	1.08432	0.542160	−	0.840275i	$-0.317607\pi$
$239$	16.7632	1.08432	0.542160	+	0.840275i	$0.317607\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−14.8495	−0.954560
$243$	10.3763	0.665638
$244$	10.8701	0.695890
$245$	0	0
$246$	2.25045	0.143483
$247$	−15.9482	−1.01476
$248$	−8.81835	−0.559966
$249$	−4.28242	−0.271387
$250$	0	0
$251$	−3.11807	−0.196811	−0.0984053	−	0.995146i	$-0.531374\pi$
$251$	−3.11807	−0.196811	−0.0984053	+	0.995146i	$0.531374\pi$
$252$	−9.42596	−0.593779
$253$	17.4018	1.09404
$254$	−0.545970	−0.0342572
$255$	0	0
$256$	−16.3750	−1.02343
$257$	−12.1075	−0.755243	−0.377622	−	0.925960i	$-0.623258\pi$
$257$	−12.1075	−0.755243	−0.377622	+	0.925960i	$0.623258\pi$
$258$	4.38411	0.272943
$259$	14.9943	0.931700
$260$	0	0
$261$	−2.94102	−0.182045
$262$	10.0082	0.618310
$263$	4.27379	0.263533	0.131767	−	0.991281i	$-0.457935\pi$
$263$	4.27379	0.263533	0.131767	+	0.991281i	$0.457935\pi$
$264$	−6.25385	−0.384898
$265$	0	0
$266$	20.1659	1.23645
$267$	5.43859	0.332836
$268$	9.82742	0.600305
$269$	16.0727	0.979967	0.489984	−	0.871732i	$-0.337003\pi$
$269$	16.0727	0.979967	0.489984	+	0.871732i	$0.337003\pi$
$270$	0	0
$271$	−26.2302	−1.59337	−0.796687	−	0.604392i	$-0.793416\pi$
$271$	−26.2302	−1.59337	−0.796687	+	0.604392i	$0.793416\pi$
$272$	1.17590	0.0712993
$273$	2.28034	0.138013
$274$	−0.532716	−0.0321826
$275$	0	0
$276$	1.65064	0.0993568
$277$	−7.65594	−0.460001	−0.230000	−	0.973191i	$-0.573873\pi$
$277$	−7.65594	−0.460001	−0.230000	+	0.973191i	$0.573873\pi$
$278$	0.982312	0.0589151
$279$	8.70523	0.521168
$280$	0	0
$281$	−15.3498	−0.915692	−0.457846	−	0.889031i	$-0.651379\pi$
$281$	−15.3498	−0.915692	−0.457846	+	0.889031i	$0.651379\pi$
$282$	−1.94454	−0.115796
$283$	−28.8983	−1.71782	−0.858911	−	0.512124i	$-0.828859\pi$
$283$	−28.8983	−1.71782	−0.858911	+	0.512124i	$0.828859\pi$
$284$	−6.47815	−0.384407
$285$	0	0
$286$	−9.26854	−0.548060
$287$	16.8197	0.992833
$288$	15.7668	0.929068
$289$	31.8183	1.87166
$290$	0	0
$291$	−3.80171	−0.222860
$292$	9.79468	0.573190
$293$	−7.28210	−0.425425	−0.212712	−	0.977115i	$-0.568230\pi$
$293$	−7.28210	−0.425425	−0.212712	+	0.977115i	$0.568230\pi$
$294$	−0.277037	−0.0161571
$295$	0	0
$296$	−15.4309	−0.896905
$297$	12.7248	0.738368
$298$	10.4465	0.605151
$299$	6.52998	0.377638
$300$	0	0
$301$	32.7665	1.88863
$302$	−13.4020	−0.771200
$303$	−3.65702	−0.210090
$304$	−1.36193	−0.0781120
$305$	0	0
$306$	−17.6885	−1.01118
$307$	−6.91285	−0.394537	−0.197269	−	0.980349i	$-0.563207\pi$
$307$	−6.91285	−0.394537	−0.197269	+	0.980349i	$0.563207\pi$
$308$	−17.5106	−0.997757
$309$	−4.88319	−0.277795
$310$	0	0
$311$	−1.69265	−0.0959817	−0.0479908	−	0.998848i	$-0.515282\pi$
$311$	−1.69265	−0.0959817	−0.0479908	+	0.998848i	$0.515282\pi$
$312$	−2.34675	−0.132858
$313$	30.1123	1.70205	0.851023	−	0.525129i	$-0.175983\pi$
$313$	30.1123	1.70205	0.851023	+	0.525129i	$0.175983\pi$
$314$	−8.81294	−0.497343
$315$	0	0
$316$	17.5961	0.989857
$317$	−9.03306	−0.507347	−0.253674	−	0.967290i	$-0.581639\pi$
$317$	−9.03306	−0.507347	−0.253674	+	0.967290i	$0.581639\pi$
$318$	1.83042	0.102645
$319$	−5.46352	−0.305899
$320$	0	0
$321$	3.74007	0.208750
$322$	−8.25687	−0.460137
$323$	−56.5415	−3.14606
$324$	−8.95460	−0.497478
$325$	0	0
$326$	−18.6383	−1.03228
$327$	8.17951	0.452328
$328$	−17.3095	−0.955755
$329$	−14.5334	−0.801250
$330$	0	0
$331$	−7.68276	−0.422283	−0.211141	−	0.977456i	$-0.567718\pi$
$331$	−7.68276	−0.422283	−0.211141	+	0.977456i	$0.567718\pi$
$332$	12.3398	0.677235
$333$	15.2330	0.834763
$334$	10.8452	0.593422
$335$	0	0
$336$	0.194734	0.0106236
$337$	10.8126	0.588997	0.294499	−	0.955652i	$-0.404847\pi$
$337$	10.8126	0.588997	0.294499	+	0.955652i	$0.404847\pi$
$338$	8.16325	0.444023
$339$	4.14136	0.224928
$340$	0	0
$341$	16.1717	0.875745
$342$	20.4869	1.10780
$343$	17.4091	0.940005
$344$	−33.7207	−1.81810
$345$	0	0
$346$	−14.7855	−0.794874
$347$	−28.1117	−1.50912	−0.754559	−	0.656233i	$-0.772149\pi$
$347$	−28.1117	−1.50912	−0.754559	+	0.656233i	$0.772149\pi$
$348$	−0.518241	−0.0277806
$349$	−8.15411	−0.436479	−0.218240	−	0.975895i	$-0.570031\pi$
$349$	−8.15411	−0.436479	−0.218240	+	0.975895i	$0.570031\pi$
$350$	0	0
$351$	4.77496	0.254868
$352$	29.2899	1.56116
$353$	25.8292	1.37475	0.687376	−	0.726302i	$-0.258763\pi$
$353$	25.8292	1.37475	0.687376	+	0.726302i	$0.258763\pi$
$354$	2.02523	0.107640
$355$	0	0
$356$	−15.6713	−0.830577
$357$	8.08453	0.427879
$358$	−16.4985	−0.871973
$359$	30.6101	1.61554	0.807771	−	0.589497i	$-0.200674\pi$
$359$	30.6101	1.61554	0.807771	+	0.589497i	$0.200674\pi$
$360$	0	0
$361$	46.4866	2.44667
$362$	−4.69726	−0.246882
$363$	6.89499	0.361893
$364$	−6.57081	−0.344404
$365$	0	0
$366$	3.37810	0.176576
$367$	32.1757	1.67956	0.839780	−	0.542927i	$-0.182684\pi$
$367$	32.1757	1.67956	0.839780	+	0.542927i	$0.182684\pi$
$368$	0.557639	0.0290690
$369$	17.0874	0.889536
$370$	0	0
$371$	13.6804	0.710252
$372$	1.53396	0.0795321
$373$	−30.4349	−1.57586	−0.787930	−	0.615764i	$-0.788847\pi$
$373$	−30.4349	−1.57586	−0.787930	+	0.615764i	$0.788847\pi$
$374$	−32.8599	−1.69914
$375$	0	0
$376$	14.9566	0.771326
$377$	−2.05018	−0.105589
$378$	−6.03773	−0.310547
$379$	−3.66260	−0.188135	−0.0940675	−	0.995566i	$-0.529987\pi$
$379$	−3.66260	−0.188135	−0.0940675	+	0.995566i	$0.529987\pi$
$380$	0	0
$381$	0.253508	0.0129876
$382$	−4.73578	−0.242303
$383$	−12.6946	−0.648662	−0.324331	−	0.945944i	$-0.605139\pi$
$383$	−12.6946	−0.648662	−0.324331	+	0.945944i	$0.605139\pi$
$384$	2.65296	0.135383
$385$	0	0
$386$	−8.96505	−0.456309
$387$	33.2881	1.69213
$388$	10.9546	0.556137
$389$	14.1093	0.715368	0.357684	−	0.933843i	$-0.383566\pi$
$389$	14.1093	0.715368	0.357684	+	0.933843i	$0.383566\pi$
$390$	0	0
$391$	23.1508	1.17079
$392$	2.13085	0.107624
$393$	−4.64707	−0.234414
$394$	21.9329	1.10496
$395$	0	0
$396$	−17.7893	−0.893947
$397$	4.33930	0.217783	0.108892	−	0.994054i	$-0.465270\pi$
$397$	4.33930	0.217783	0.108892	+	0.994054i	$0.465270\pi$
$398$	21.0958	1.05744
$399$	−9.36353	−0.468763
$400$	0	0
$401$	−27.3792	−1.36725	−0.683625	−	0.729834i	$-0.739597\pi$
$401$	−27.3792	−1.36725	−0.683625	+	0.729834i	$0.739597\pi$
$402$	3.05406	0.152323
$403$	6.06839	0.302288
$404$	10.5377	0.524271
$405$	0	0
$406$	2.59236	0.128657
$407$	28.2983	1.40269
$408$	−8.31995	−0.411899
$409$	6.26389	0.309729	0.154865	−	0.987936i	$-0.450506\pi$
$409$	6.26389	0.309729	0.154865	+	0.987936i	$0.450506\pi$
$410$	0	0
$411$	0.247354	0.0122011
$412$	14.0709	0.693225
$413$	15.1364	0.744814
$414$	−8.38832	−0.412263
$415$	0	0
$416$	10.9910	0.538878
$417$	−0.456112	−0.0223359
$418$	38.0584	1.86150
$419$	20.1470	0.984246	0.492123	−	0.870526i	$-0.336221\pi$
$419$	20.1470	0.984246	0.492123	+	0.870526i	$0.336221\pi$
$420$	0	0
$421$	−39.0656	−1.90394	−0.951971	−	0.306187i	$-0.900947\pi$
$421$	−39.0656	−1.90394	−0.951971	+	0.306187i	$0.900947\pi$
$422$	1.95005	0.0949270
$423$	−14.7647	−0.717885
$424$	−14.0788	−0.683727
$425$	0	0
$426$	−2.01321	−0.0975402
$427$	25.2477	1.22182
$428$	−10.7770	−0.520926
$429$	4.30362	0.207781
$430$	0	0
$431$	−9.40024	−0.452794	−0.226397	−	0.974035i	$-0.572695\pi$
$431$	−9.40024	−0.452794	−0.226397	+	0.974035i	$0.572695\pi$
$432$	0.407766	0.0196187
$433$	−17.1249	−0.822972	−0.411486	−	0.911416i	$-0.634990\pi$
$433$	−17.1249	−0.822972	−0.411486	+	0.911416i	$0.634990\pi$
$434$	−7.67322	−0.368326
$435$	0	0
$436$	−23.5693	−1.12876
$437$	−26.8134	−1.28266
$438$	3.04388	0.145442
$439$	23.8747	1.13948	0.569740	−	0.821825i	$-0.307044\pi$
$439$	23.8747	1.13948	0.569740	+	0.821825i	$0.307044\pi$
$440$	0	0
$441$	−2.10352	−0.100167
$442$	−12.3306	−0.586507
$443$	20.4473	0.971483	0.485741	−	0.874103i	$-0.338550\pi$
$443$	20.4473	0.971483	0.485741	+	0.874103i	$0.338550\pi$
$444$	2.68423	0.127388
$445$	0	0
$446$	19.9382	0.944100
$447$	−4.85059	−0.229425
$448$	−14.8343	−0.700855
$449$	−21.2110	−1.00101	−0.500505	−	0.865734i	$-0.666852\pi$
$449$	−21.2110	−1.00101	−0.500505	+	0.865734i	$0.666852\pi$
$450$	0	0
$451$	31.7432	1.49473
$452$	−11.9333	−0.561297
$453$	6.22290	0.292377
$454$	5.60587	0.263097
$455$	0	0
$456$	9.63620	0.451256
$457$	−35.6703	−1.66858	−0.834292	−	0.551323i	$-0.814123\pi$
$457$	−35.6703	−1.66858	−0.834292	+	0.551323i	$0.814123\pi$
$458$	−7.90788	−0.369511
$459$	16.9287	0.790165
$460$	0	0
$461$	31.5155	1.46782	0.733912	−	0.679244i	$-0.237692\pi$
$461$	31.5155	1.46782	0.733912	+	0.679244i	$0.237692\pi$
$462$	−5.44174	−0.253173
$463$	−15.8124	−0.734864	−0.367432	−	0.930050i	$-0.619763\pi$
$463$	−15.8124	−0.734864	−0.367432	+	0.930050i	$0.619763\pi$
$464$	−0.175079	−0.00812782
$465$	0	0
$466$	−14.9746	−0.693684
$467$	−26.8482	−1.24239	−0.621193	−	0.783657i	$-0.713352\pi$
$467$	−26.8482	−1.24239	−0.621193	+	0.783657i	$0.713352\pi$
$468$	−6.67541	−0.308571
$469$	22.8258	1.05400
$470$	0	0
$471$	4.09208	0.188553
$472$	−15.5772	−0.716999
$473$	61.8392	2.84337
$474$	5.46832	0.251168
$475$	0	0
$476$	−23.2956	−1.06775
$477$	13.8982	0.636355
$478$	−15.0111	−0.686592
$479$	−25.6730	−1.17303	−0.586514	−	0.809939i	$-0.699500\pi$
$479$	−25.6730	−1.17303	−0.586514	+	0.809939i	$0.699500\pi$
$480$	0	0
$481$	10.6189	0.484179
$482$	−0.895481	−0.0407881
$483$	3.83388	0.174447
$484$	−19.8679	−0.903087
$485$	0	0
$486$	−9.29176	−0.421483
$487$	−4.29727	−0.194728	−0.0973639	−	0.995249i	$-0.531041\pi$
$487$	−4.29727	−0.194728	−0.0973639	+	0.995249i	$0.531041\pi$
$488$	−25.9829	−1.17619
$489$	8.65424	0.391358
$490$	0	0
$491$	36.8507	1.66305	0.831524	−	0.555489i	$-0.187469\pi$
$491$	36.8507	1.66305	0.831524	+	0.555489i	$0.187469\pi$
$492$	3.01100	0.135746
$493$	−7.26852	−0.327358
$494$	14.2814	0.642549
$495$	0	0
$496$	0.518221	0.0232688
$497$	−15.0466	−0.674930
$498$	3.83483	0.171843
$499$	37.6961	1.68751	0.843754	−	0.536730i	$-0.180341\pi$
$499$	37.6961	1.68751	0.843754	+	0.536730i	$0.180341\pi$
$500$	0	0
$501$	−5.03570	−0.224979
$502$	2.79217	0.124621
$503$	23.9213	1.06660	0.533299	−	0.845927i	$-0.320952\pi$
$503$	23.9213	1.06660	0.533299	+	0.845927i	$0.320952\pi$
$504$	22.5309	1.00360
$505$	0	0
$506$	−15.5829	−0.692746
$507$	−3.79041	−0.168338
$508$	−0.730483	−0.0324099
$509$	−25.9118	−1.14852	−0.574261	−	0.818672i	$-0.694711\pi$
$509$	−25.9118	−1.14852	−0.574261	+	0.818672i	$0.694711\pi$
$510$	0	0
$511$	22.7497	1.00639
$512$	1.90255	0.0840818
$513$	−19.6069	−0.865666
$514$	10.8420	0.478221
$515$	0	0
$516$	5.86574	0.258225
$517$	−27.4284	−1.20630
$518$	−13.4271	−0.589954
$519$	6.86529	0.301353
$520$	0	0
$521$	−34.4794	−1.51057	−0.755285	−	0.655396i	$-0.772502\pi$
$521$	−34.4794	−1.51057	−0.755285	+	0.655396i	$0.772502\pi$
$522$	2.63363	0.115271
$523$	−33.0412	−1.44479	−0.722395	−	0.691480i	$-0.756959\pi$
$523$	−33.0412	−1.44479	−0.722395	+	0.691480i	$0.756959\pi$
$524$	13.3905	0.584969
$525$	0	0
$526$	−3.82710	−0.166869
$527$	21.5143	0.937180
$528$	0.367516	0.0159941
$529$	−12.0213	−0.522666
$530$	0	0
$531$	15.3774	0.667322
$532$	26.9810	1.16978
$533$	11.9116	0.515948
$534$	−4.87016	−0.210752
$535$	0	0
$536$	−23.4905	−1.01463
$537$	7.66067	0.330583
$538$	−14.3928	−0.620516
$539$	−3.90769	−0.168316
$540$	0	0
$541$	−23.1289	−0.994390	−0.497195	−	0.867639i	$-0.665637\pi$
$541$	−23.1289	−0.994390	−0.497195	+	0.867639i	$0.665637\pi$
$542$	23.4887	1.00893
$543$	2.18106	0.0935981
$544$	38.9665	1.67068
$545$	0	0
$546$	−2.04200	−0.0873897
$547$	20.1732	0.862543	0.431271	−	0.902222i	$-0.358065\pi$
$547$	20.1732	0.862543	0.431271	+	0.902222i	$0.358065\pi$
$548$	−0.712750	−0.0304472
$549$	25.6496	1.09470
$550$	0	0
$551$	8.41843	0.358637
$552$	−3.94552	−0.167933
$553$	40.8698	1.73796
$554$	6.85575	0.291273
$555$	0	0
$556$	1.31429	0.0557382
$557$	10.5030	0.445027	0.222513	−	0.974930i	$-0.428574\pi$
$557$	10.5030	0.445027	0.222513	+	0.974930i	$0.428574\pi$
$558$	−7.79537	−0.330004
$559$	23.2050	0.981469
$560$	0	0
$561$	15.2577	0.644180
$562$	13.7455	0.579817
$563$	38.2113	1.61042	0.805208	−	0.592993i	$-0.202054\pi$
$563$	38.2113	1.61042	0.805208	+	0.592993i	$0.202054\pi$
$564$	−2.60171	−0.109552
$565$	0	0
$566$	25.8778	1.08773
$567$	−20.7985	−0.873456
$568$	15.4847	0.649724
$569$	−4.30872	−0.180631	−0.0903155	−	0.995913i	$-0.528788\pi$
$569$	−4.30872	−0.180631	−0.0903155	+	0.995913i	$0.528788\pi$
$570$	0	0
$571$	2.64175	0.110554	0.0552769	−	0.998471i	$-0.482396\pi$
$571$	2.64175	0.110554	0.0552769	+	0.998471i	$0.482396\pi$
$572$	−12.4009	−0.518507
$573$	2.19894	0.0918622
$574$	−15.0617	−0.628663
$575$	0	0
$576$	−15.0705	−0.627936
$577$	9.62250	0.400590	0.200295	−	0.979736i	$-0.435810\pi$
$577$	9.62250	0.400590	0.200295	+	0.979736i	$0.435810\pi$
$578$	−28.4927	−1.18514
$579$	4.16270	0.172996
$580$	0	0
$581$	28.6612	1.18907
$582$	3.40436	0.141115
$583$	25.8187	1.06930
$584$	−23.4122	−0.968804
$585$	0	0
$586$	6.52098	0.269379
$587$	0.267800	0.0110533	0.00552664	−	0.999985i	$-0.498241\pi$
$587$	0.267800	0.0110533	0.00552664	+	0.999985i	$0.498241\pi$
$588$	−0.370663	−0.0152859
$589$	−24.9180	−1.02673
$590$	0	0
$591$	−10.1840	−0.418914
$592$	0.906819	0.0372700
$593$	−6.91291	−0.283879	−0.141940	−	0.989875i	$-0.545334\pi$
$593$	−6.91291	−0.283879	−0.141940	+	0.989875i	$0.545334\pi$
$594$	−11.3948	−0.467535
$595$	0	0
$596$	13.9770	0.572519
$597$	−9.79534	−0.400897
$598$	−5.84747	−0.239121
$599$	−38.5224	−1.57398	−0.786992	−	0.616963i	$-0.788363\pi$
$599$	−38.5224	−1.57398	−0.786992	+	0.616963i	$0.788363\pi$
$600$	0	0
$601$	−23.0744	−0.941226	−0.470613	−	0.882340i	$-0.655967\pi$
$601$	−23.0744	−0.941226	−0.470613	+	0.882340i	$0.655967\pi$
$602$	−29.3418	−1.19588
$603$	23.1892	0.944336
$604$	−17.9313	−0.729614
$605$	0	0
$606$	3.27479	0.133029
$607$	−7.17183	−0.291096	−0.145548	−	0.989351i	$-0.546494\pi$
$607$	−7.17183	−0.291096	−0.145548	+	0.989351i	$0.546494\pi$
$608$	−45.1312	−1.83031
$609$	−1.20370	−0.0487764
$610$	0	0
$611$	−10.2924	−0.416388
$612$	−23.6664	−0.956658
$613$	−18.4684	−0.745932	−0.372966	−	0.927845i	$-0.621659\pi$
$613$	−18.4684	−0.745932	−0.372966	+	0.927845i	$0.621659\pi$
$614$	6.19033	0.249821
$615$	0	0
$616$	41.8555	1.68641
$617$	39.4184	1.58693	0.793463	−	0.608618i	$-0.208276\pi$
$617$	39.4184	1.58693	0.793463	+	0.608618i	$0.208276\pi$
$618$	4.37281	0.175900
$619$	19.2131	0.772238	0.386119	−	0.922449i	$-0.373815\pi$
$619$	19.2131	0.772238	0.386119	+	0.922449i	$0.373815\pi$
$620$	0	0
$621$	8.02801	0.322153
$622$	1.51574	0.0607757
$623$	−36.3992	−1.45830
$624$	0.137910	0.00552080
$625$	0	0
$626$	−26.9650	−1.07774
$627$	−17.6715	−0.705732
$628$	−11.7913	−0.470525
$629$	37.6473	1.50109
$630$	0	0
$631$	−41.4698	−1.65089	−0.825444	−	0.564484i	$-0.809075\pi$
$631$	−41.4698	−1.65089	−0.825444	+	0.564484i	$0.809075\pi$
$632$	−42.0599	−1.67305
$633$	−0.905459	−0.0359888
$634$	8.08893	0.321253
$635$	0	0
$636$	2.44902	0.0971100
$637$	−1.46636	−0.0580991
$638$	4.89248	0.193695
$639$	−15.2861	−0.604708
$640$	0	0
$641$	2.01618	0.0796344	0.0398172	−	0.999207i	$-0.487322\pi$
$641$	2.01618	0.0796344	0.0398172	+	0.999207i	$0.487322\pi$
$642$	−3.34916	−0.132181
$643$	−23.3800	−0.922017	−0.461009	−	0.887396i	$-0.652512\pi$
$643$	−23.3800	−0.922017	−0.461009	+	0.887396i	$0.652512\pi$
$644$	−11.0473	−0.435325
$645$	0	0
$646$	50.6319	1.99209
$647$	3.24784	0.127686	0.0638429	−	0.997960i	$-0.479664\pi$
$647$	3.24784	0.127686	0.0638429	+	0.997960i	$0.479664\pi$
$648$	21.4042	0.840836
$649$	28.5665	1.12133
$650$	0	0
$651$	3.56287	0.139640
$652$	−24.9372	−0.976616
$653$	10.8929	0.426270	0.213135	−	0.977023i	$-0.431633\pi$
$653$	10.8929	0.426270	0.213135	+	0.977023i	$0.431633\pi$
$654$	−7.32460	−0.286414
$655$	0	0
$656$	1.01721	0.0397155
$657$	23.1119	0.901681
$658$	13.0143	0.507352
$659$	−11.2886	−0.439740	−0.219870	−	0.975529i	$-0.570563\pi$
$659$	−11.2886	−0.439740	−0.219870	+	0.975529i	$0.570563\pi$
$660$	0	0
$661$	−46.6521	−1.81456	−0.907279	−	0.420529i	$-0.861844\pi$
$661$	−46.6521	−1.81456	−0.907279	+	0.420529i	$0.861844\pi$
$662$	6.87977	0.267390
$663$	5.72542	0.222357
$664$	−29.4958	−1.14466
$665$	0	0
$666$	−13.6409	−0.528573
$667$	−3.44691	−0.133465
$668$	14.5104	0.561423
$669$	−9.25780	−0.357927
$670$	0	0
$671$	47.6492	1.83948
$672$	6.45303	0.248931
$673$	6.21011	0.239382	0.119691	−	0.992811i	$-0.461810\pi$
$673$	6.21011	0.239382	0.119691	+	0.992811i	$0.461810\pi$
$674$	−9.68244	−0.372954
$675$	0	0
$676$	10.9221	0.420079
$677$	33.4448	1.28539	0.642694	−	0.766123i	$-0.277817\pi$
$677$	33.4448	1.28539	0.642694	+	0.766123i	$0.277817\pi$
$678$	−3.70851	−0.142424
$679$	25.4439	0.976447
$680$	0	0
$681$	−2.60295	−0.0997453
$682$	−14.4814	−0.554523
$683$	1.61182	0.0616747	0.0308373	−	0.999524i	$-0.490183\pi$
$683$	1.61182	0.0616747	0.0308373	+	0.999524i	$0.490183\pi$
$684$	27.4105	1.04807
$685$	0	0
$686$	−15.5896	−0.595212
$687$	3.67183	0.140089
$688$	1.98164	0.0755492
$689$	9.68840	0.369099
$690$	0	0
$691$	29.6594	1.12830	0.564148	−	0.825673i	$-0.309205\pi$
$691$	29.6594	1.12830	0.564148	+	0.825673i	$0.309205\pi$
$692$	−19.7824	−0.752012
$693$	−41.3186	−1.56956
$694$	25.1735	0.955574
$695$	0	0
$696$	1.23875	0.0469548
$697$	42.2303	1.59959
$698$	7.30185	0.276379
$699$	6.95308	0.262990
$700$	0	0
$701$	4.56478	0.172409	0.0862047	−	0.996277i	$-0.472526\pi$
$701$	4.56478	0.172409	0.0862047	+	0.996277i	$0.472526\pi$
$702$	−4.27588	−0.161383
$703$	−43.6032	−1.64453
$704$	−27.9964	−1.05515
$705$	0	0
$706$	−23.1296	−0.870494
$707$	24.4756	0.920498
$708$	2.70967	0.101836
$709$	−37.9291	−1.42446	−0.712229	−	0.701947i	$-0.752314\pi$
$709$	−37.9291	−1.42446	−0.712229	+	0.701947i	$0.752314\pi$
$710$	0	0
$711$	41.5204	1.55714
$712$	37.4591	1.40384
$713$	10.2026	0.382091
$714$	−7.23954	−0.270933
$715$	0	0
$716$	−22.0742	−0.824953
$717$	6.97005	0.260301
$718$	−27.4108	−1.02296
$719$	10.4558	0.389934	0.194967	−	0.980810i	$-0.437540\pi$
$719$	10.4558	0.389934	0.194967	+	0.980810i	$0.437540\pi$
$720$	0	0
$721$	32.6820	1.21714
$722$	−41.6279	−1.54923
$723$	0.415795	0.0154636
$724$	−6.28472	−0.233570
$725$	0	0
$726$	−6.17433	−0.229151
$727$	−7.12081	−0.264096	−0.132048	−	0.991243i	$-0.542155\pi$
$727$	−7.12081	−0.264096	−0.132048	+	0.991243i	$0.542155\pi$
$728$	15.7062	0.582110
$729$	−18.1074	−0.670643
$730$	0	0
$731$	82.2691	3.04283
$732$	4.51975	0.167055
$733$	46.0113	1.69946	0.849732	−	0.527214i	$-0.176763\pi$
$733$	46.0113	1.69946	0.849732	+	0.527214i	$0.176763\pi$
$734$	−28.8128	−1.06350
$735$	0	0
$736$	18.4789	0.681140
$737$	43.0784	1.58681
$738$	−15.3015	−0.563255
$739$	−26.7095	−0.982526	−0.491263	−	0.871011i	$-0.663465\pi$
$739$	−26.7095	−0.982526	−0.491263	+	0.871011i	$0.663465\pi$
$740$	0	0
$741$	−6.63120	−0.243603
$742$	−12.2506	−0.449732
$743$	−6.46665	−0.237239	−0.118619	−	0.992940i	$-0.537847\pi$
$743$	−6.46665	−0.237239	−0.118619	+	0.992940i	$0.537847\pi$
$744$	−3.66662	−0.134425
$745$	0	0
$746$	27.2539	0.997836
$747$	29.1175	1.06535
$748$	−43.9650	−1.60752
$749$	−25.0313	−0.914625
$750$	0	0
$751$	24.6570	0.899748	0.449874	−	0.893092i	$-0.351469\pi$
$751$	24.6570	0.899748	0.449874	+	0.893092i	$0.351469\pi$
$752$	−0.878942	−0.0320517
$753$	−1.29648	−0.0472462
$754$	1.83590	0.0668594
$755$	0	0
$756$	−8.07820	−0.293801
$757$	−28.4323	−1.03339	−0.516695	−	0.856169i	$-0.672838\pi$
$757$	−28.4323	−1.03339	−0.516695	+	0.856169i	$0.672838\pi$
$758$	3.27979	0.119127
$759$	7.23556	0.262634
$760$	0	0
$761$	−15.6167	−0.566106	−0.283053	−	0.959104i	$-0.591347\pi$
$761$	−15.6167	−0.566106	−0.283053	+	0.959104i	$0.591347\pi$
$762$	−0.227012	−0.00822376
$763$	−54.7434	−1.98185
$764$	−6.33626	−0.229238
$765$	0	0
$766$	11.3677	0.410733
$767$	10.7195	0.387060
$768$	−6.80862	−0.245685
$769$	−27.0051	−0.973827	−0.486914	−	0.873450i	$-0.661877\pi$
$769$	−27.0051	−0.973827	−0.486914	+	0.873450i	$0.661877\pi$
$770$	0	0
$771$	−5.03423	−0.181303
$772$	−11.9948	−0.431703
$773$	11.1324	0.400403	0.200201	−	0.979755i	$-0.435840\pi$
$773$	11.1324	0.400403	0.200201	+	0.979755i	$0.435840\pi$
$774$	−29.8089	−1.07146
$775$	0	0
$776$	−26.1848	−0.939981
$777$	6.23455	0.223663
$778$	−12.6346	−0.452972
$779$	−48.9113	−1.75243
$780$	0	0
$781$	−28.3969	−1.01612
$782$	−20.7311	−0.741343
$783$	−2.52050	−0.0900755
$784$	−0.125222	−0.00447222
$785$	0	0
$786$	4.16137	0.148431
$787$	−13.2232	−0.471357	−0.235678	−	0.971831i	$-0.575731\pi$
$787$	−13.2232	−0.471357	−0.235678	+	0.971831i	$0.575731\pi$
$788$	29.3452	1.04538
$789$	1.77702	0.0632636
$790$	0	0
$791$	−27.7171	−0.985507
$792$	42.5218	1.51095
$793$	17.8803	0.634947
$794$	−3.88576	−0.137900
$795$	0	0
$796$	28.2253	1.00042
$797$	−11.4439	−0.405363	−0.202681	−	0.979245i	$-0.564966\pi$
$797$	−11.4439	−0.405363	−0.202681	+	0.979245i	$0.564966\pi$
$798$	8.38487	0.296821
$799$	−36.4899	−1.29092
$800$	0	0
$801$	−36.9786	−1.30657
$802$	24.5175	0.865744
$803$	42.9349	1.51514
$804$	4.08619	0.144109
$805$	0	0
$806$	−5.43413	−0.191409
$807$	6.68293	0.235250
$808$	−25.1883	−0.886121
$809$	−31.3092	−1.10077	−0.550387	−	0.834909i	$-0.685520\pi$
$809$	−31.3092	−1.10077	−0.550387	+	0.834909i	$0.685520\pi$
$810$	0	0
$811$	41.4545	1.45567	0.727833	−	0.685754i	$-0.240528\pi$
$811$	41.4545	1.45567	0.727833	+	0.685754i	$0.240528\pi$
$812$	3.46846	0.121719
$813$	−10.9064	−0.382504
$814$	−25.3406	−0.888187
$815$	0	0
$816$	0.488932	0.0171161
$817$	−95.2844	−3.33358
$818$	−5.60919	−0.196121
$819$	−15.5047	−0.541779
$820$	0	0
$821$	0.690877	0.0241118	0.0120559	−	0.999927i	$-0.496162\pi$
$821$	0.690877	0.0241118	0.0120559	+	0.999927i	$0.496162\pi$
$822$	−0.221501	−0.00772572
$823$	−8.14976	−0.284083	−0.142041	−	0.989861i	$-0.545367\pi$
$823$	−8.14976	−0.284083	−0.142041	+	0.989861i	$0.545367\pi$
$824$	−33.6337	−1.17169
$825$	0	0
$826$	−13.5544	−0.471617
$827$	−9.90749	−0.344517	−0.172259	−	0.985052i	$-0.555106\pi$
$827$	−9.90749	−0.344517	−0.172259	+	0.985052i	$0.555106\pi$
$828$	−11.2232	−0.390033
$829$	−23.7776	−0.825831	−0.412916	−	0.910769i	$-0.635490\pi$
$829$	−23.7776	−0.825831	−0.412916	+	0.910769i	$0.635490\pi$
$830$	0	0
$831$	−3.18330	−0.110427
$832$	−10.5056	−0.364215
$833$	−5.19869	−0.180124
$834$	0.408440	0.0141431
$835$	0	0
$836$	50.9205	1.76112
$837$	7.46053	0.257874
$838$	−18.0413	−0.623226
$839$	24.8900	0.859298	0.429649	−	0.902996i	$-0.358637\pi$
$839$	24.8900	0.859298	0.429649	+	0.902996i	$0.358637\pi$
$840$	0	0
$841$	−27.9178	−0.962683
$842$	34.9826	1.20558
$843$	−6.38237	−0.219821
$844$	2.60908	0.0898082
$845$	0	0
$846$	13.2215	0.454566
$847$	−46.1465	−1.58561
$848$	0.827359	0.0284116
$849$	−12.0157	−0.412379
$850$	0	0
$851$	17.8532	0.612001
$852$	−2.69358	−0.0922805
$853$	−26.9790	−0.923745	−0.461872	−	0.886946i	$-0.652822\pi$
$853$	−26.9790	−0.923745	−0.461872	+	0.886946i	$0.652822\pi$
$854$	−22.6088	−0.773658
$855$	0	0
$856$	25.7603	0.880468
$857$	−37.6700	−1.28678	−0.643392	−	0.765537i	$-0.722473\pi$
$857$	−37.6700	−1.28678	−0.643392	+	0.765537i	$0.722473\pi$
$858$	−3.85381	−0.131567
$859$	46.3768	1.58236	0.791178	−	0.611586i	$-0.209468\pi$
$859$	46.3768	1.58236	0.791178	+	0.611586i	$0.209468\pi$
$860$	0	0
$861$	6.99353	0.238339
$862$	8.41774	0.286709
$863$	15.2943	0.520624	0.260312	−	0.965525i	$-0.416175\pi$
$863$	15.2943	0.520624	0.260312	+	0.965525i	$0.416175\pi$
$864$	13.5124	0.459702
$865$	0	0
$866$	15.3351	0.521107
$867$	13.2299	0.449311
$868$	−10.2664	−0.348465
$869$	77.1323	2.61653
$870$	0	0
$871$	16.1651	0.547733
$872$	56.3376	1.90783
$873$	25.8489	0.874854
$874$	24.0109	0.812180
$875$	0	0
$876$	4.07258	0.137600
$877$	−11.8646	−0.400638	−0.200319	−	0.979731i	$-0.564198\pi$
$877$	−11.8646	−0.400638	−0.200319	+	0.979731i	$0.564198\pi$
$878$	−21.3794	−0.721519
$879$	−3.02786	−0.102127
$880$	0	0
$881$	−3.23133	−0.108866	−0.0544331	−	0.998517i	$-0.517335\pi$
$881$	−3.23133	−0.108866	−0.0544331	+	0.998517i	$0.517335\pi$
$882$	1.88366	0.0634261
$883$	7.06622	0.237797	0.118899	−	0.992906i	$-0.462064\pi$
$883$	7.06622	0.237797	0.118899	+	0.992906i	$0.462064\pi$
$884$	−16.4978	−0.554881
$885$	0	0
$886$	−18.3102	−0.615144
$887$	−34.5130	−1.15883	−0.579416	−	0.815032i	$-0.696719\pi$
$887$	−34.5130	−1.15883	−0.579416	+	0.815032i	$0.696719\pi$
$888$	−6.41611	−0.215310
$889$	−1.69667	−0.0569043
$890$	0	0
$891$	−39.2524	−1.31501
$892$	26.6764	0.893191
$893$	42.2628	1.41427
$894$	4.34361	0.145272
$895$	0	0
$896$	−17.7556	−0.593174
$897$	2.71513	0.0906556
$898$	18.9941	0.633840
$899$	−3.20326	−0.106835
$900$	0	0
$901$	34.3484	1.14431
$902$	−28.4255	−0.946465
$903$	13.6241	0.453383
$904$	28.5242	0.948702
$905$	0	0
$906$	−5.57249	−0.185134
$907$	−0.164530	−0.00546313	−0.00273157	−	0.999996i	$-0.500869\pi$
$907$	−0.164530	−0.00546313	−0.00273157	+	0.999996i	$0.500869\pi$
$908$	7.50040	0.248910
$909$	24.8652	0.824726
$910$	0	0
$911$	43.6397	1.44585	0.722924	−	0.690928i	$-0.242798\pi$
$911$	43.6397	1.44585	0.722924	+	0.690928i	$0.242798\pi$
$912$	−0.566284	−0.0187515
$913$	54.0914	1.79016
$914$	31.9420	1.05655
$915$	0	0
$916$	−10.5804	−0.349586
$917$	31.1017	1.02707
$918$	−15.1593	−0.500333
$919$	37.5717	1.23938	0.619689	−	0.784848i	$-0.287259\pi$
$919$	37.5717	1.23938	0.619689	+	0.784848i	$0.287259\pi$
$920$	0	0
$921$	−2.87433	−0.0947123
$922$	−28.2216	−0.929428
$923$	−10.6559	−0.350743
$924$	−7.28080	−0.239521
$925$	0	0
$926$	14.1597	0.465317
$927$	33.2023	1.09051
$928$	−5.80169	−0.190450
$929$	−33.7566	−1.10752	−0.553759	−	0.832677i	$-0.686807\pi$
$929$	−33.7566	−1.10752	−0.553759	+	0.832677i	$0.686807\pi$
$930$	0	0
$931$	6.02114	0.197335
$932$	−20.0353	−0.656279
$933$	−0.703797	−0.0230413
$934$	24.0421	0.786680
$935$	0	0
$936$	15.9562	0.521546
$937$	−44.5489	−1.45535	−0.727674	−	0.685923i	$-0.759399\pi$
$937$	−44.5489	−1.45535	−0.727674	+	0.685923i	$0.759399\pi$
$938$	−20.4401	−0.667392
$939$	12.5205	0.408592
$940$	0	0
$941$	−6.78223	−0.221094	−0.110547	−	0.993871i	$-0.535260\pi$
$941$	−6.78223	−0.221094	−0.110547	+	0.993871i	$0.535260\pi$
$942$	−3.66438	−0.119392
$943$	20.0266	0.652157
$944$	0.915414	0.0297942
$945$	0	0
$946$	−55.3758	−1.80042
$947$	−28.9902	−0.942056	−0.471028	−	0.882118i	$-0.656117\pi$
$947$	−28.9902	−0.942056	−0.471028	+	0.882118i	$0.656117\pi$
$948$	7.31636	0.237624
$949$	16.1112	0.522993
$950$	0	0
$951$	−3.75590	−0.121793
$952$	55.6834	1.80471
$953$	10.0178	0.324509	0.162254	−	0.986749i	$-0.448124\pi$
$953$	10.0178	0.324509	0.162254	+	0.986749i	$0.448124\pi$
$954$	−12.4456	−0.402941
$955$	0	0
$956$	−20.0842	−0.649569
$957$	−2.27171	−0.0734338
$958$	22.9897	0.742763
$959$	−1.65548	−0.0534582
$960$	0	0
$961$	−21.5186	−0.694148
$962$	−9.50901	−0.306583
$963$	−25.4298	−0.819465
$964$	−1.19811	−0.0385886
$965$	0	0
$966$	−3.43317	−0.110460
$967$	5.58965	0.179751	0.0898755	−	0.995953i	$-0.471353\pi$
$967$	5.58965	0.179751	0.0898755	+	0.995953i	$0.471353\pi$
$968$	47.4903	1.52640
$969$	−23.5097	−0.755240
$970$	0	0
$971$	−17.7973	−0.571144	−0.285572	−	0.958357i	$-0.592184\pi$
$971$	−17.7973	−0.571144	−0.285572	+	0.958357i	$0.592184\pi$
$972$	−12.4320	−0.398755
$973$	3.05265	0.0978634
$974$	3.84812	0.123302
$975$	0	0
$976$	1.52692	0.0488755
$977$	−8.88618	−0.284294	−0.142147	−	0.989846i	$-0.545401\pi$
$977$	−8.88618	−0.284294	−0.142147	+	0.989846i	$0.545401\pi$
$978$	−7.74971	−0.247808
$979$	−68.6950	−2.19550
$980$	0	0
$981$	−55.6149	−1.77565
$982$	−32.9991	−1.05304
$983$	−10.2895	−0.328184	−0.164092	−	0.986445i	$-0.552469\pi$
$983$	−10.2895	−0.328184	−0.164092	+	0.986445i	$0.552469\pi$
$984$	−7.19719	−0.229438
$985$	0	0
$986$	6.50882	0.207283
$987$	−6.04290	−0.192347
$988$	19.1078	0.607900
$989$	39.0140	1.24057
$990$	0	0
$991$	7.83347	0.248838	0.124419	−	0.992230i	$-0.460293\pi$
$991$	7.83347	0.248838	0.124419	+	0.992230i	$0.460293\pi$
$992$	17.1726	0.545232
$993$	−3.19445	−0.101373
$994$	13.4739	0.427366
$995$	0	0
$996$	5.13083	0.162576
$997$	22.6268	0.716598	0.358299	−	0.933607i	$-0.383357\pi$
$997$	22.6268	0.716598	0.358299	+	0.933607i	$0.383357\pi$
$998$	−33.7561	−1.06853
$999$	13.0549	0.413040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.k.1.9		25
5.4	even	2		1205.2.a.d.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.d.1.17	✓	25	5.4	even	2
6025.2.a.k.1.9		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.895481 q^{2} +0.415795 q^{3} -1.19811 q^{4} -0.372337 q^{6} -2.78281 q^{7} +2.86385 q^{8} -2.82711 q^{9} +O(q^{10})\)	\(q-0.895481 q^{2} +0.415795 q^{3} -1.19811 q^{4} -0.372337 q^{6} -2.78281 q^{7} +2.86385 q^{8} -2.82711 q^{9} -5.25192 q^{11} -0.498169 q^{12} -1.97077 q^{13} +2.49196 q^{14} -0.168298 q^{16} -6.98701 q^{17} +2.53163 q^{18} +8.09238 q^{19} -1.15708 q^{21} +4.70300 q^{22} -3.31341 q^{23} +1.19077 q^{24} +1.76479 q^{26} -2.42288 q^{27} +3.33413 q^{28} +1.04029 q^{29} -3.07919 q^{31} -5.57699 q^{32} -2.18372 q^{33} +6.25674 q^{34} +3.38720 q^{36} -5.38818 q^{37} -7.24658 q^{38} -0.819437 q^{39} -6.04412 q^{41} +1.03614 q^{42} -11.7746 q^{43} +6.29240 q^{44} +2.96709 q^{46} +5.22254 q^{47} -0.0699774 q^{48} +0.744051 q^{49} -2.90516 q^{51} +2.36121 q^{52} -4.91604 q^{53} +2.16965 q^{54} -7.96956 q^{56} +3.36477 q^{57} -0.931561 q^{58} -5.43925 q^{59} -9.07272 q^{61} +2.75736 q^{62} +7.86733 q^{63} +5.33069 q^{64} +1.95548 q^{66} -8.20241 q^{67} +8.37123 q^{68} -1.37770 q^{69} +5.40696 q^{71} -8.09643 q^{72} -8.17508 q^{73} +4.82501 q^{74} -9.69559 q^{76} +14.6151 q^{77} +0.733791 q^{78} -14.6865 q^{79} +7.47392 q^{81} +5.41240 q^{82} -10.2994 q^{83} +1.38631 q^{84} +10.5439 q^{86} +0.432548 q^{87} -15.0407 q^{88} +13.0800 q^{89} +5.48429 q^{91} +3.96984 q^{92} -1.28031 q^{93} -4.67669 q^{94} -2.31889 q^{96} -9.14323 q^{97} -0.666283 q^{98} +14.8478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9}+O(q^{10}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9	\( 25 q + 4 q^{2} - 9 q^{3} + 36 q^{4} + 7 q^{6} - 7 q^{7} + 15 q^{8} + 36 q^{9} + 10 q^{11} - 22 q^{12} - 10 q^{13} + 13 q^{14} + 54 q^{16} - q^{17} + 13 q^{18} + 50 q^{19} + 9 q^{21} - 11 q^{22} + 31 q^{23} + 22 q^{24} + 8 q^{26} - 42 q^{27} - 14 q^{28} + 4 q^{29} + 34 q^{31} + 44 q^{32} - 28 q^{33} + 33 q^{34} + 83 q^{36} - 14 q^{37} + 10 q^{38} + 23 q^{39} + 11 q^{41} - 23 q^{42} - 49 q^{43} + 20 q^{44} + 27 q^{46} + 28 q^{47} - 30 q^{48} + 66 q^{49} + 49 q^{51} - 39 q^{52} + 16 q^{53} + 5 q^{54} + 51 q^{56} - 10 q^{57} + 8 q^{58} + 30 q^{59} + 35 q^{61} + 18 q^{62} + 73 q^{64} - 13 q^{66} - 37 q^{67} - 11 q^{68} - 4 q^{69} + 12 q^{71} + 90 q^{72} - 36 q^{73} - 12 q^{74} + 57 q^{76} + 31 q^{77} + 9 q^{78} + 16 q^{79} + 65 q^{81} + 11 q^{82} - 43 q^{83} - 62 q^{84} - 9 q^{86} + 22 q^{87} - 20 q^{88} + 38 q^{89} + 86 q^{91} + 119 q^{92} - 10 q^{93} - 18 q^{94} - 34 q^{96} - 17 q^{97} + 32 q^{98} + 26 q^{99}+O(q^{100}) \) 25 * q + 4 * q^2 - 9 * q^3 + 36 * q^4 + 7 * q^6 - 7 * q^7 + 15 * q^8 + 36 * q^9 + 10 * q^11 - 22 * q^12 - 10 * q^13 + 13 * q^14 + 54 * q^16 - q^17 + 13 * q^18 + 50 * q^19 + 9 * q^21 - 11 * q^22 + 31 * q^23 + 22 * q^24 + 8 * q^26 - 42 * q^27 - 14 * q^28 + 4 * q^29 + 34 * q^31 + 44 * q^32 - 28 * q^33 + 33 * q^34 + 83 * q^36 - 14 * q^37 + 10 * q^38 + 23 * q^39 + 11 * q^41 - 23 * q^42 - 49 * q^43 + 20 * q^44 + 27 * q^46 + 28 * q^47 - 30 * q^48 + 66 * q^49 + 49 * q^51 - 39 * q^52 + 16 * q^53 + 5 * q^54 + 51 * q^56 - 10 * q^57 + 8 * q^58 + 30 * q^59 + 35 * q^61 + 18 * q^62 + 73 * q^64 - 13 * q^66 - 37 * q^67 - 11 * q^68 - 4 * q^69 + 12 * q^71 + 90 * q^72 - 36 * q^73 - 12 * q^74 + 57 * q^76 + 31 * q^77 + 9 * q^78 + 16 * q^79 + 65 * q^81 + 11 * q^82 - 43 * q^83 - 62 * q^84 - 9 * q^86 + 22 * q^87 - 20 * q^88 + 38 * q^89 + 86 * q^91 + 119 * q^92 - 10 * q^93 - 18 * q^94 - 34 * q^96 - 17 * q^97 + 32 * q^98 + 26 * q^99

Introduction

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