LMFDB - Embedded newform 8025.2.a.w.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1605)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.06150$ of defining polynomial
Character	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.514916 q^{2} -1.00000 q^{3} -1.73486 q^{4} -0.514916 q^{6} +1.81172 q^{7} -1.92314 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.514916 q^{2} -1.00000 q^{3} -1.73486 q^{4} -0.514916 q^{6} +1.81172 q^{7} -1.92314 q^{8} +1.00000 q^{9} +1.06150 q^{11} +1.73486 q^{12} -1.63791 q^{13} +0.932884 q^{14} +2.47947 q^{16} +6.28144 q^{17} +0.514916 q^{18} -7.69941 q^{19} -1.81172 q^{21} +0.546583 q^{22} +6.24978 q^{23} +1.92314 q^{24} -0.843388 q^{26} -1.00000 q^{27} -3.14309 q^{28} -1.20837 q^{29} +4.02605 q^{31} +5.12300 q^{32} -1.06150 q^{33} +3.23442 q^{34} -1.73486 q^{36} -3.43989 q^{37} -3.96455 q^{38} +1.63791 q^{39} +10.0461 q^{41} -0.932884 q^{42} -5.53122 q^{43} -1.84155 q^{44} +3.21811 q^{46} -1.69758 q^{47} -2.47947 q^{48} -3.71767 q^{49} -6.28144 q^{51} +2.84155 q^{52} +9.15879 q^{53} -0.514916 q^{54} -3.48419 q^{56} +7.69941 q^{57} -0.622207 q^{58} -7.38252 q^{59} -13.0252 q^{61} +2.07308 q^{62} +1.81172 q^{63} -2.32102 q^{64} -0.546583 q^{66} +14.2796 q^{67} -10.8974 q^{68} -6.24978 q^{69} +0.0182532 q^{71} -1.92314 q^{72} -2.32102 q^{73} -1.77125 q^{74} +13.3574 q^{76} +1.92314 q^{77} +0.843388 q^{78} -15.2634 q^{79} +1.00000 q^{81} +5.17292 q^{82} +7.72924 q^{83} +3.14309 q^{84} -2.84811 q^{86} +1.20837 q^{87} -2.04141 q^{88} +10.5200 q^{89} -2.96744 q^{91} -10.8425 q^{92} -4.02605 q^{93} -0.874110 q^{94} -5.12300 q^{96} -2.72363 q^{97} -1.91429 q^{98} +1.06150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{18} - 7 q^{19} - 8 q^{21} - 7 q^{22} + 16 q^{23} - 3 q^{24} + 6 q^{26} - 4 q^{27} + 9 q^{28} + q^{29} - 6 q^{31} + 4 q^{32} + 4 q^{33} - 15 q^{34} + 3 q^{36} + 8 q^{37} - 2 q^{38} - 9 q^{39} + 13 q^{41} + 6 q^{43} - 10 q^{44} + 14 q^{46} + 5 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{51} + 14 q^{52} + 5 q^{53} - 3 q^{54} + 23 q^{56} + 7 q^{57} + 3 q^{58} - 11 q^{59} + 6 q^{61} - 5 q^{62} + 8 q^{63} + q^{64} + 7 q^{66} + 50 q^{67} - 26 q^{68} - 16 q^{69} + 7 q^{71} + 3 q^{72} + q^{73} + 37 q^{74} + 9 q^{76} - 3 q^{77} - 6 q^{78} + q^{79} + 4 q^{81} + q^{82} + 9 q^{83} - 9 q^{84} + 22 q^{86} - q^{87} - 5 q^{88} - 10 q^{89} + 14 q^{91} + 2 q^{92} + 6 q^{93} - 32 q^{94} - 4 q^{96} + 23 q^{97} - 26 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^18 - 7 * q^19 - 8 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 + 6 * q^26 - 4 * q^27 + 9 * q^28 + q^29 - 6 * q^31 + 4 * q^32 + 4 * q^33 - 15 * q^34 + 3 * q^36 + 8 * q^37 - 2 * q^38 - 9 * q^39 + 13 * q^41 + 6 * q^43 - 10 * q^44 + 14 * q^46 + 5 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^51 + 14 * q^52 + 5 * q^53 - 3 * q^54 + 23 * q^56 + 7 * q^57 + 3 * q^58 - 11 * q^59 + 6 * q^61 - 5 * q^62 + 8 * q^63 + q^64 + 7 * q^66 + 50 * q^67 - 26 * q^68 - 16 * q^69 + 7 * q^71 + 3 * q^72 + q^73 + 37 * q^74 + 9 * q^76 - 3 * q^77 - 6 * q^78 + q^79 + 4 * q^81 + q^82 + 9 * q^83 - 9 * q^84 + 22 * q^86 - q^87 - 5 * q^88 - 10 * q^89 + 14 * q^91 + 2 * q^92 + 6 * q^93 - 32 * q^94 - 4 * q^96 + 23 * q^97 - 26 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.514916	0.364101	0.182050	−	0.983289i	$-0.441727\pi$
$2$	0.514916	0.364101	0.182050	+	0.983289i	$0.441727\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.73486	−0.867431
$5$	0	0
$5$	0	0
$6$	−0.514916	−0.210214
$7$	1.81172	0.684766	0.342383	−	0.939560i	$-0.388766\pi$
$7$	1.81172	0.684766	0.342383	+	0.939560i	$0.388766\pi$
$8$	−1.92314	−0.679933
$9$	1.00000	0.333333
$10$	0	0
$11$	1.06150	0.320054	0.160027	−	0.987113i	$-0.448842\pi$
$11$	1.06150	0.320054	0.160027	+	0.987113i	$0.448842\pi$
$12$	1.73486	0.500811
$13$	−1.63791	−0.454276	−0.227138	−	0.973863i	$-0.572937\pi$
$13$	−1.63791	−0.454276	−0.227138	+	0.973863i	$0.572937\pi$
$14$	0.932884	0.249324
$15$	0	0
$16$	2.47947	0.619867
$17$	6.28144	1.52347	0.761737	−	0.647886i	$-0.224347\pi$
$17$	6.28144	1.52347	0.761737	+	0.647886i	$0.224347\pi$
$18$	0.514916	0.121367
$19$	−7.69941	−1.76637	−0.883183	−	0.469028i	$-0.844604\pi$
$19$	−7.69941	−1.76637	−0.883183	+	0.469028i	$0.844604\pi$
$20$	0	0
$21$	−1.81172	−0.395350
$22$	0.546583	0.116532
$23$	6.24978	1.30317	0.651584	−	0.758576i	$-0.274105\pi$
$23$	6.24978	1.30317	0.651584	+	0.758576i	$0.274105\pi$
$24$	1.92314	0.392559
$25$	0	0
$26$	−0.843388	−0.165402
$27$	−1.00000	−0.192450
$28$	−3.14309	−0.593987
$29$	−1.20837	−0.224388	−0.112194	−	0.993686i	$-0.535788\pi$
$29$	−1.20837	−0.224388	−0.112194	+	0.993686i	$0.535788\pi$
$30$	0	0
$31$	4.02605	0.723100	0.361550	−	0.932353i	$-0.382248\pi$
$31$	4.02605	0.723100	0.361550	+	0.932353i	$0.382248\pi$
$32$	5.12300	0.905627
$33$	−1.06150	−0.184783
$34$	3.23442	0.554698
$35$	0	0
$36$	−1.73486	−0.289144
$37$	−3.43989	−0.565515	−0.282757	−	0.959191i	$-0.591249\pi$
$37$	−3.43989	−0.565515	−0.282757	+	0.959191i	$0.591249\pi$
$38$	−3.96455	−0.643135
$39$	1.63791	0.262276
$40$	0	0
$41$	10.0461	1.56894	0.784472	−	0.620165i	$-0.212934\pi$
$41$	10.0461	1.56894	0.784472	+	0.620165i	$0.212934\pi$
$42$	−0.932884	−0.143947
$43$	−5.53122	−0.843503	−0.421752	−	0.906711i	$-0.638585\pi$
$43$	−5.53122	−0.843503	−0.421752	+	0.906711i	$0.638585\pi$
$44$	−1.84155	−0.277625
$45$	0	0
$46$	3.21811	0.474485
$47$	−1.69758	−0.247617	−0.123809	−	0.992306i	$-0.539511\pi$
$47$	−1.69758	−0.247617	−0.123809	+	0.992306i	$0.539511\pi$
$48$	−2.47947	−0.357880
$49$	−3.71767	−0.531095
$50$	0	0
$51$	−6.28144	−0.879578
$52$	2.84155	0.394053
$53$	9.15879	1.25806	0.629028	−	0.777382i	$-0.283453\pi$
$53$	9.15879	1.25806	0.629028	+	0.777382i	$0.283453\pi$
$54$	−0.514916	−0.0700712
$55$	0	0
$56$	−3.48419	−0.465595
$57$	7.69941	1.01981
$58$	−0.622207	−0.0816998
$59$	−7.38252	−0.961122	−0.480561	−	0.876961i	$-0.659567\pi$
$59$	−7.38252	−0.961122	−0.480561	+	0.876961i	$0.659567\pi$
$60$	0	0
$61$	−13.0252	−1.66770	−0.833850	−	0.551990i	$-0.813868\pi$
$61$	−13.0252	−1.66770	−0.833850	+	0.551990i	$0.813868\pi$
$62$	2.07308	0.263281
$63$	1.81172	0.228255
$64$	−2.32102	−0.290128
$65$	0	0
$66$	−0.546583	−0.0672797
$67$	14.2796	1.74453	0.872266	−	0.489032i	$-0.162650\pi$
$67$	14.2796	1.74453	0.872266	+	0.489032i	$0.162650\pi$
$68$	−10.8974	−1.32151
$69$	−6.24978	−0.752385
$70$	0	0
$71$	0.0182532	0.00216625	0.00108313	−	0.999999i	$-0.499655\pi$
$71$	0.0182532	0.00216625	0.00108313	+	0.999999i	$0.499655\pi$
$72$	−1.92314	−0.226644
$73$	−2.32102	−0.271655	−0.135827	−	0.990733i	$-0.543369\pi$
$73$	−2.32102	−0.271655	−0.135827	+	0.990733i	$0.543369\pi$
$74$	−1.77125	−0.205904
$75$	0	0
$76$	13.3574	1.53220
$77$	1.92314	0.219162
$78$	0.843388	0.0954949
$79$	−15.2634	−1.71726	−0.858631	−	0.512594i	$-0.828685\pi$
$79$	−15.2634	−1.71726	−0.858631	+	0.512594i	$0.828685\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.17292	0.571253
$83$	7.72924	0.848395	0.424197	−	0.905570i	$-0.360556\pi$
$83$	7.72924	0.848395	0.424197	+	0.905570i	$0.360556\pi$
$84$	3.14309	0.342939
$85$	0	0
$86$	−2.84811	−0.307120
$87$	1.20837	0.129550
$88$	−2.04141	−0.217615
$89$	10.5200	1.11512	0.557558	−	0.830138i	$-0.311738\pi$
$89$	10.5200	1.11512	0.557558	+	0.830138i	$0.311738\pi$
$90$	0	0
$91$	−2.96744	−0.311073
$92$	−10.8425	−1.13041
$93$	−4.02605	−0.417482
$94$	−0.874110	−0.0901576
$95$	0	0
$96$	−5.12300	−0.522864
$97$	−2.72363	−0.276543	−0.138271	−	0.990394i	$-0.544155\pi$
$97$	−2.72363	−0.276543	−0.138271	+	0.990394i	$0.544155\pi$
$98$	−1.91429	−0.193372
$99$	1.06150	0.106685
$100$	0	0
$101$	0.0182532	0.00181626	0.000908130	−	1.00000i	$-0.499711\pi$
$101$	0.0182532	0.00181626	0.000908130		1.00000i	$0.499711\pi$
$102$	−3.23442	−0.320255
$103$	5.62940	0.554682	0.277341	−	0.960772i	$-0.410547\pi$
$103$	5.62940	0.554682	0.277341	+	0.960772i	$0.410547\pi$
$104$	3.14994	0.308877
$105$	0	0
$106$	4.71601	0.458059
$107$	1.00000	0.0966736
$107$	1.00000	0.0966736
$108$	1.73486	0.166937
$109$	−14.8350	−1.42094	−0.710470	−	0.703728i	$-0.751518\pi$
$109$	−14.8350	−1.42094	−0.710470	+	0.703728i	$0.751518\pi$
$110$	0	0
$111$	3.43989	0.326500
$112$	4.49210	0.424464
$113$	10.5140	0.989076	0.494538	−	0.869156i	$-0.335337\pi$
$113$	10.5140	0.989076	0.494538	+	0.869156i	$0.335337\pi$
$114$	3.96455	0.371314
$115$	0	0
$116$	2.09635	0.194641
$117$	−1.63791	−0.151425
$118$	−3.80138	−0.349945
$119$	11.3802	1.04322
$120$	0	0
$121$	−9.87322	−0.897565
$122$	−6.70686	−0.607211
$123$	−10.0461	−0.905830
$124$	−6.98464	−0.627239
$125$	0	0
$126$	0.932884	0.0831079
$127$	6.10958	0.542138	0.271069	−	0.962560i	$-0.412623\pi$
$127$	6.10958	0.542138	0.271069	+	0.962560i	$0.412623\pi$
$128$	−11.4411	−1.01126
$129$	5.53122	0.486997
$130$	0	0
$131$	−12.9096	−1.12792	−0.563959	−	0.825803i	$-0.690722\pi$
$131$	−12.9096	−1.12792	−0.563959	+	0.825803i	$0.690722\pi$
$132$	1.84155	0.160287
$133$	−13.9492	−1.20955
$134$	7.35280	0.635185
$135$	0	0
$136$	−12.0801	−1.03586
$137$	−2.14125	−0.182939	−0.0914697	−	0.995808i	$-0.529156\pi$
$137$	−2.14125	−0.182939	−0.0914697	+	0.995808i	$0.529156\pi$
$138$	−3.21811	−0.273944
$139$	18.8271	1.59690	0.798448	−	0.602063i	$-0.205654\pi$
$139$	18.8271	1.59690	0.798448	+	0.602063i	$0.205654\pi$
$140$	0	0
$141$	1.69758	0.142962
$142$	0.00939886	0.000788735 0
$143$	−1.73864	−0.145393
$144$	2.47947	0.206622
$145$	0	0
$146$	−1.19513	−0.0989097
$147$	3.71767	0.306628
$148$	5.96773	0.490545
$149$	22.0471	1.80617	0.903084	−	0.429465i	$-0.141298\pi$
$149$	22.0471	1.80617	0.903084	+	0.429465i	$0.141298\pi$
$150$	0	0
$151$	21.8454	1.77775	0.888876	−	0.458147i	$-0.151487\pi$
$151$	21.8454	1.77775	0.888876	+	0.458147i	$0.151487\pi$
$152$	14.8070	1.20101
$153$	6.28144	0.507825
$154$	0.990256	0.0797971
$155$	0	0
$156$	−2.84155	−0.227506
$157$	9.72239	0.775931	0.387966	−	0.921674i	$-0.373178\pi$
$157$	9.72239	0.775931	0.387966	+	0.921674i	$0.373178\pi$
$158$	−7.85935	−0.625256
$159$	−9.15879	−0.726339
$160$	0	0
$161$	11.3229	0.892366
$162$	0.514916	0.0404556
$163$	20.2297	1.58451	0.792256	−	0.610189i	$-0.208907\pi$
$163$	20.2297	1.58451	0.792256	+	0.610189i	$0.208907\pi$
$164$	−17.4287	−1.36095
$165$	0	0
$166$	3.97991	0.308901
$167$	−6.94630	−0.537521	−0.268760	−	0.963207i	$-0.586614\pi$
$167$	−6.94630	−0.537521	−0.268760	+	0.963207i	$0.586614\pi$
$168$	3.48419	0.268811
$169$	−10.3172	−0.793634
$170$	0	0
$171$	−7.69941	−0.588789
$172$	9.59590	0.731681
$173$	−19.7090	−1.49845	−0.749225	−	0.662315i	$-0.769574\pi$
$173$	−19.7090	−1.49845	−0.749225	+	0.662315i	$0.769574\pi$
$174$	0.622207	0.0471694
$175$	0	0
$176$	2.63195	0.198391
$177$	7.38252	0.554904
$178$	5.41691	0.406015
$179$	−4.93105	−0.368564	−0.184282	−	0.982873i	$-0.558996\pi$
$179$	−4.93105	−0.368564	−0.184282	+	0.982873i	$0.558996\pi$
$180$	0	0
$181$	−9.31346	−0.692264	−0.346132	−	0.938186i	$-0.612505\pi$
$181$	−9.31346	−0.692264	−0.346132	+	0.938186i	$0.612505\pi$
$182$	−1.52798	−0.113262
$183$	13.0252	0.962848
$184$	−12.0192	−0.886067
$185$	0	0
$186$	−2.07308	−0.152005
$187$	6.66775	0.487594
$188$	2.94506	0.214791
$189$	−1.81172	−0.131783
$190$	0	0
$191$	−12.7568	−0.923048	−0.461524	−	0.887128i	$-0.652697\pi$
$191$	−12.7568	−0.923048	−0.461524	+	0.887128i	$0.652697\pi$
$192$	2.32102	0.167505
$193$	−16.5874	−1.19399	−0.596995	−	0.802245i	$-0.703639\pi$
$193$	−16.5874	−1.19399	−0.596995	+	0.802245i	$0.703639\pi$
$194$	−1.40244	−0.100689
$195$	0	0
$196$	6.44964	0.460688
$197$	−11.5859	−0.825459	−0.412729	−	0.910854i	$-0.635425\pi$
$197$	−11.5859	−0.825459	−0.412729	+	0.910854i	$0.635425\pi$
$198$	0.546583	0.0388439
$199$	15.8851	1.12607	0.563034	−	0.826434i	$-0.309634\pi$
$199$	15.8851	1.12607	0.563034	+	0.826434i	$0.309634\pi$
$200$	0	0
$201$	−14.2796	−1.00721
$202$	0.00939886	0.000661301 0
$203$	−2.18922	−0.153653
$204$	10.8974	0.762973
$205$	0	0
$206$	2.89867	0.201960
$207$	6.24978	0.434390
$208$	−4.06115	−0.281590
$209$	−8.17292	−0.565333
$210$	0	0
$211$	4.62255	0.318230	0.159115	−	0.987260i	$-0.449136\pi$
$211$	4.62255	0.318230	0.159115	+	0.987260i	$0.449136\pi$
$212$	−15.8892	−1.09128
$213$	−0.0182532	−0.00125069
$214$	0.514916	0.0351989
$215$	0	0
$216$	1.92314	0.130853
$217$	7.29408	0.495154
$218$	−7.63880	−0.517365
$219$	2.32102	0.156840
$220$	0	0
$221$	−10.2885	−0.692077
$222$	1.77125	0.118879
$223$	19.3601	1.29645	0.648225	−	0.761449i	$-0.275511\pi$
$223$	19.3601	1.29645	0.648225	+	0.761449i	$0.275511\pi$
$224$	9.28144	0.620143
$225$	0	0
$226$	5.41384	0.360123
$227$	10.6808	0.708911	0.354455	−	0.935073i	$-0.384666\pi$
$227$	10.6808	0.708911	0.354455	+	0.935073i	$0.384666\pi$
$228$	−13.3574	−0.884616
$229$	18.5639	1.22674	0.613370	−	0.789796i	$-0.289813\pi$
$229$	18.5639	1.22674	0.613370	+	0.789796i	$0.289813\pi$
$230$	0	0
$231$	−1.92314	−0.126533
$232$	2.32386	0.152569
$233$	−16.3959	−1.07413	−0.537067	−	0.843540i	$-0.680468\pi$
$233$	−16.3959	−1.07413	−0.537067	+	0.843540i	$0.680468\pi$
$234$	−0.843388	−0.0551340
$235$	0	0
$236$	12.8076	0.833707
$237$	15.2634	0.991462
$238$	5.85986	0.379838
$239$	20.1026	1.30033	0.650165	−	0.759793i	$-0.274700\pi$
$239$	20.1026	1.30033	0.650165	+	0.759793i	$0.274700\pi$
$240$	0	0
$241$	−17.4439	−1.12366	−0.561830	−	0.827252i	$-0.689903\pi$
$241$	−17.4439	−1.12366	−0.561830	+	0.827252i	$0.689903\pi$
$242$	−5.08388	−0.326804
$243$	−1.00000	−0.0641500
$244$	22.5968	1.44661
$245$	0	0
$246$	−5.17292	−0.329813
$247$	12.6110	0.802417
$248$	−7.74266	−0.491659
$249$	−7.72924	−0.489821
$250$	0	0
$251$	24.7061	1.55944	0.779719	−	0.626130i	$-0.215362\pi$
$251$	24.7061	1.55944	0.779719	+	0.626130i	$0.215362\pi$
$252$	−3.14309	−0.197996
$253$	6.63413	0.417084
$254$	3.14592	0.197393
$255$	0	0
$256$	−1.24918	−0.0780736
$257$	−10.0615	−0.627619	−0.313810	−	0.949486i	$-0.601605\pi$
$257$	−10.0615	−0.627619	−0.313810	+	0.949486i	$0.601605\pi$
$258$	2.84811	0.177316
$259$	−6.23212	−0.387245
$260$	0	0
$261$	−1.20837	−0.0747960
$262$	−6.64737	−0.410676
$263$	−0.845336	−0.0521256	−0.0260628	−	0.999660i	$-0.508297\pi$
$263$	−0.845336	−0.0521256	−0.0260628	+	0.999660i	$0.508297\pi$
$264$	2.04141	0.125640
$265$	0	0
$266$	−7.18266	−0.440397
$267$	−10.5200	−0.643813
$268$	−24.7731	−1.51326
$269$	14.3708	0.876205	0.438102	−	0.898925i	$-0.355651\pi$
$269$	14.3708	0.876205	0.438102	+	0.898925i	$0.355651\pi$
$270$	0	0
$271$	1.93956	0.117820	0.0589099	−	0.998263i	$-0.481238\pi$
$271$	1.93956	0.117820	0.0589099	+	0.998263i	$0.481238\pi$
$272$	15.5746	0.944351
$273$	2.96744	0.179598
$274$	−1.10256	−0.0666084
$275$	0	0
$276$	10.8425	0.652642
$277$	14.5560	0.874587	0.437294	−	0.899319i	$-0.355937\pi$
$277$	14.5560	0.874587	0.437294	+	0.899319i	$0.355937\pi$
$278$	9.69440	0.581431
$279$	4.02605	0.241033
$280$	0	0
$281$	27.8928	1.66394	0.831971	−	0.554819i	$-0.187212\pi$
$281$	27.8928	1.66394	0.831971	+	0.554819i	$0.187212\pi$
$282$	0.874110	0.0520525
$283$	−12.8302	−0.762677	−0.381338	−	0.924436i	$-0.624537\pi$
$283$	−12.8302	−0.762677	−0.381338	+	0.924436i	$0.624537\pi$
$284$	−0.0316667	−0.00187908
$285$	0	0
$286$	−0.895255	−0.0529376
$287$	18.2008	1.07436
$288$	5.12300	0.301876
$289$	22.4565	1.32097
$290$	0	0
$291$	2.72363	0.159662
$292$	4.02665	0.235642
$293$	20.4845	1.19672	0.598360	−	0.801228i	$-0.295819\pi$
$293$	20.4845	1.19672	0.598360	+	0.801228i	$0.295819\pi$
$294$	1.91429	0.111643
$295$	0	0
$296$	6.61539	0.384512
$297$	−1.06150	−0.0615944
$298$	11.3524	0.657627
$299$	−10.2366	−0.591998
$300$	0	0
$301$	−10.0210	−0.577603
$302$	11.2485	0.647281
$303$	−0.0182532	−0.00104862
$304$	−19.0904	−1.09491
$305$	0	0
$306$	3.23442	0.184899
$307$	−16.3620	−0.933827	−0.466914	−	0.884303i	$-0.654634\pi$
$307$	−16.3620	−0.933827	−0.466914	+	0.884303i	$0.654634\pi$
$308$	−3.33638	−0.190108
$309$	−5.62940	−0.320246
$310$	0	0
$311$	−25.1742	−1.42750	−0.713749	−	0.700401i	$-0.753004\pi$
$311$	−25.1742	−1.42750	−0.713749	+	0.700401i	$0.753004\pi$
$312$	−3.14994	−0.178330
$313$	18.9738	1.07246	0.536230	−	0.844072i	$-0.319848\pi$
$313$	18.9738	1.07246	0.536230	+	0.844072i	$0.319848\pi$
$314$	5.00622	0.282517
$315$	0	0
$316$	26.4798	1.48961
$317$	14.8005	0.831281	0.415641	−	0.909529i	$-0.363557\pi$
$317$	14.8005	0.831281	0.415641	+	0.909529i	$0.363557\pi$
$318$	−4.71601	−0.264461
$319$	−1.28268	−0.0718163
$320$	0	0
$321$	−1.00000	−0.0558146
$322$	5.83032	0.324911
$323$	−48.3634	−2.69101
$324$	−1.73486	−0.0963812
$325$	0	0
$326$	10.4166	0.576922
$327$	14.8350	0.820380
$328$	−19.3201	−1.06678
$329$	−3.07554	−0.169560
$330$	0	0
$331$	18.4136	1.01211	0.506053	−	0.862503i	$-0.331104\pi$
$331$	18.4136	1.01211	0.506053	+	0.862503i	$0.331104\pi$
$332$	−13.4092	−0.735924
$333$	−3.43989	−0.188505
$334$	−3.57676	−0.195712
$335$	0	0
$336$	−4.49210	−0.245064
$337$	14.5958	0.795083	0.397542	−	0.917584i	$-0.369863\pi$
$337$	14.5958	0.795083	0.397542	+	0.917584i	$0.369863\pi$
$338$	−5.31251	−0.288963
$339$	−10.5140	−0.571044
$340$	0	0
$341$	4.27365	0.231431
$342$	−3.96455	−0.214378
$343$	−19.4174	−1.04844
$344$	10.6373	0.573526
$345$	0	0
$346$	−10.1485	−0.545587
$347$	0.271101	0.0145534	0.00727672	−	0.999974i	$-0.497684\pi$
$347$	0.271101	0.0145534	0.00727672	+	0.999974i	$0.497684\pi$
$348$	−2.09635	−0.112376
$349$	20.8235	1.11465	0.557327	−	0.830293i	$-0.311827\pi$
$349$	20.8235	1.11465	0.557327	+	0.830293i	$0.311827\pi$
$350$	0	0
$351$	1.63791	0.0874254
$352$	5.43806	0.289849
$353$	−1.10256	−0.0586836	−0.0293418	−	0.999569i	$-0.509341\pi$
$353$	−1.10256	−0.0586836	−0.0293418	+	0.999569i	$0.509341\pi$
$354$	3.80138	0.202041
$355$	0	0
$356$	−18.2507	−0.967286
$357$	−11.3802	−0.602305
$358$	−2.53908	−0.134194
$359$	−9.11271	−0.480950	−0.240475	−	0.970655i	$-0.577303\pi$
$359$	−9.11271	−0.480950	−0.240475	+	0.970655i	$0.577303\pi$
$360$	0	0
$361$	40.2810	2.12005
$362$	−4.79565	−0.252054
$363$	9.87322	0.518210
$364$	5.14810	0.269834
$365$	0	0
$366$	6.70686	0.350573
$367$	33.6561	1.75683	0.878417	−	0.477894i	$-0.158600\pi$
$367$	33.6561	1.75683	0.878417	+	0.477894i	$0.158600\pi$
$368$	15.4961	0.807791
$369$	10.0461	0.522981
$370$	0	0
$371$	16.5932	0.861475
$372$	6.98464	0.362137
$373$	2.56702	0.132915	0.0664575	−	0.997789i	$-0.478830\pi$
$373$	2.56702	0.132915	0.0664575	+	0.997789i	$0.478830\pi$
$374$	3.43333	0.177533
$375$	0	0
$376$	3.26468	0.168363
$377$	1.97920	0.101934
$378$	−0.932884	−0.0479824
$379$	10.7646	0.552939	0.276470	−	0.961023i	$-0.410835\pi$
$379$	10.7646	0.552939	0.276470	+	0.961023i	$0.410835\pi$
$380$	0	0
$381$	−6.10958	−0.313003
$382$	−6.56867	−0.336083
$383$	33.2567	1.69934	0.849669	−	0.527317i	$-0.176802\pi$
$383$	33.2567	1.69934	0.849669	+	0.527317i	$0.176802\pi$
$384$	11.4411	0.583853
$385$	0	0
$386$	−8.54114	−0.434733
$387$	−5.53122	−0.281168
$388$	4.72512	0.239881
$389$	32.3312	1.63926	0.819628	−	0.572897i	$-0.194180\pi$
$389$	32.3312	1.63926	0.819628	+	0.572897i	$0.194180\pi$
$390$	0	0
$391$	39.2576	1.98534
$392$	7.14959	0.361109
$393$	12.9096	0.651204
$394$	−5.96575	−0.300550
$395$	0	0
$396$	−1.84155	−0.0925415
$397$	−11.6949	−0.586948	−0.293474	−	0.955967i	$-0.594811\pi$
$397$	−11.6949	−0.586948	−0.293474	+	0.955967i	$0.594811\pi$
$398$	8.17952	0.410002
$399$	13.9492	0.698333
$400$	0	0
$401$	22.6786	1.13252	0.566258	−	0.824228i	$-0.308391\pi$
$401$	22.6786	1.13252	0.566258	+	0.824228i	$0.308391\pi$
$402$	−7.35280	−0.366724
$403$	−6.59432	−0.328487
$404$	−0.0316667	−0.00157548
$405$	0	0
$406$	−1.12727	−0.0559453
$407$	−3.65144	−0.180995
$408$	12.0801	0.598054
$409$	−1.83092	−0.0905331	−0.0452666	−	0.998975i	$-0.514414\pi$
$409$	−1.83092	−0.0905331	−0.0452666	+	0.998975i	$0.514414\pi$
$410$	0	0
$411$	2.14125	0.105620
$412$	−9.76624	−0.481148
$413$	−13.3751	−0.658144
$414$	3.21811	0.158162
$415$	0	0
$416$	−8.39103	−0.411404
$417$	−18.8271	−0.921969
$418$	−4.20837	−0.205838
$419$	−18.1720	−0.887762	−0.443881	−	0.896086i	$-0.646399\pi$
$419$	−18.1720	−0.887762	−0.443881	+	0.896086i	$0.646399\pi$
$420$	0	0
$421$	−33.9563	−1.65493	−0.827464	−	0.561519i	$-0.810217\pi$
$421$	−33.9563	−1.65493	−0.827464	+	0.561519i	$0.810217\pi$
$422$	2.38023	0.115868
$423$	−1.69758	−0.0825391
$424$	−17.6136	−0.855394
$425$	0	0
$426$	−0.00939886	−0.000455376 0
$427$	−23.5980	−1.14199
$428$	−1.73486	−0.0838577
$429$	1.73864	0.0839425
$430$	0	0
$431$	20.8664	1.00510	0.502549	−	0.864549i	$-0.332396\pi$
$431$	20.8664	1.00510	0.502549	+	0.864549i	$0.332396\pi$
$432$	−2.47947	−0.119293
$433$	6.27099	0.301364	0.150682	−	0.988582i	$-0.451853\pi$
$433$	6.27099	0.301364	0.150682	+	0.988582i	$0.451853\pi$
$434$	3.75584	0.180286
$435$	0	0
$436$	25.7368	1.23257
$437$	−48.1196	−2.30187
$438$	1.19513	0.0571056
$439$	−26.2510	−1.25289	−0.626445	−	0.779466i	$-0.715491\pi$
$439$	−26.2510	−1.25289	−0.626445	+	0.779466i	$0.715491\pi$
$440$	0	0
$441$	−3.71767	−0.177032
$442$	−5.29770	−0.251986
$443$	23.5537	1.11907	0.559534	−	0.828807i	$-0.310980\pi$
$443$	23.5537	1.11907	0.559534	+	0.828807i	$0.310980\pi$
$444$	−5.96773	−0.283216
$445$	0	0
$446$	9.96885	0.472039
$447$	−22.0471	−1.04279
$448$	−4.20504	−0.198670
$449$	30.5501	1.44175	0.720873	−	0.693067i	$-0.243741\pi$
$449$	30.5501	1.44175	0.720873	+	0.693067i	$0.243741\pi$
$450$	0	0
$451$	10.6640	0.502146
$452$	−18.2404	−0.857955
$453$	−21.8454	−1.02639
$454$	5.49972	0.258115
$455$	0	0
$456$	−14.8070	−0.693404
$457$	34.7311	1.62465	0.812326	−	0.583204i	$-0.198201\pi$
$457$	34.7311	1.62465	0.812326	+	0.583204i	$0.198201\pi$
$458$	9.55887	0.446657
$459$	−6.28144	−0.293193
$460$	0	0
$461$	24.0503	1.12014	0.560068	−	0.828447i	$-0.310775\pi$
$461$	24.0503	1.12014	0.560068	+	0.828447i	$0.310775\pi$
$462$	−0.990256	−0.0460709
$463$	37.5139	1.74342	0.871710	−	0.490023i	$-0.163012\pi$
$463$	37.5139	1.74342	0.871710	+	0.490023i	$0.163012\pi$
$464$	−2.99611	−0.139091
$465$	0	0
$466$	−8.44253	−0.391093
$467$	−5.01376	−0.232009	−0.116005	−	0.993249i	$-0.537009\pi$
$467$	−5.01376	−0.232009	−0.116005	+	0.993249i	$0.537009\pi$
$468$	2.84155	0.131351
$469$	25.8707	1.19460
$470$	0	0
$471$	−9.72239	−0.447984
$472$	14.1976	0.653498
$473$	−5.87139	−0.269967
$474$	7.85935	0.360992
$475$	0	0
$476$	−19.7431	−0.904924
$477$	9.15879	0.419352
$478$	10.3512	0.473451
$479$	30.6850	1.40203	0.701017	−	0.713145i	$-0.252730\pi$
$479$	30.6850	1.40203	0.701017	+	0.713145i	$0.252730\pi$
$480$	0	0
$481$	5.63424	0.256899
$482$	−8.98215	−0.409126
$483$	−11.3229	−0.515208
$484$	17.1287	0.778576
$485$	0	0
$486$	−0.514916	−0.0233571
$487$	−5.11474	−0.231771	−0.115886	−	0.993263i	$-0.536971\pi$
$487$	−5.11474	−0.231771	−0.115886	+	0.993263i	$0.536971\pi$
$488$	25.0492	1.13392
$489$	−20.2297	−0.914818
$490$	0	0
$491$	−36.1206	−1.63010	−0.815050	−	0.579390i	$-0.803291\pi$
$491$	−36.1206	−1.63010	−0.815050	+	0.579390i	$0.803291\pi$
$492$	17.4287	0.785745
$493$	−7.59029	−0.341849
$494$	6.49359	0.292161
$495$	0	0
$496$	9.98246	0.448226
$497$	0.0330697	0.00148338
$498$	−3.97991	−0.178344
$499$	−16.6984	−0.747523	−0.373762	−	0.927525i	$-0.621932\pi$
$499$	−16.6984	−0.747523	−0.373762	+	0.927525i	$0.621932\pi$
$500$	0	0
$501$	6.94630	0.310338
$502$	12.7216	0.567792
$503$	−19.4922	−0.869112	−0.434556	−	0.900645i	$-0.643095\pi$
$503$	−19.4922	−0.869112	−0.434556	+	0.900645i	$0.643095\pi$
$504$	−3.48419	−0.155198
$505$	0	0
$506$	3.41602	0.151861
$507$	10.3172	0.458205
$508$	−10.5993	−0.470267
$509$	6.17275	0.273602	0.136801	−	0.990599i	$-0.456318\pi$
$509$	6.17275	0.273602	0.136801	+	0.990599i	$0.456318\pi$
$510$	0	0
$511$	−4.20504	−0.186020
$512$	22.2390	0.982836
$513$	7.69941	0.339937
$514$	−5.18083	−0.228516
$515$	0	0
$516$	−9.59590	−0.422436
$517$	−1.80198	−0.0792509
$518$	−3.20902	−0.140996
$519$	19.7090	0.865131
$520$	0	0
$521$	−18.0093	−0.789000	−0.394500	−	0.918896i	$-0.629082\pi$
$521$	−18.0093	−0.789000	−0.394500	+	0.918896i	$0.629082\pi$
$522$	−0.622207	−0.0272333
$523$	−20.4416	−0.893850	−0.446925	−	0.894571i	$-0.647481\pi$
$523$	−20.4416	−0.893850	−0.446925	+	0.894571i	$0.647481\pi$
$524$	22.3964	0.978391
$525$	0	0
$526$	−0.435277	−0.0189790
$527$	25.2894	1.10162
$528$	−2.63195	−0.114541
$529$	16.0597	0.698249
$530$	0	0
$531$	−7.38252	−0.320374
$532$	24.1999	1.04920
$533$	−16.4547	−0.712732
$534$	−5.41691	−0.234413
$535$	0	0
$536$	−27.4617	−1.18616
$537$	4.93105	0.212791
$538$	7.39977	0.319027
$539$	−3.94630	−0.169979
$540$	0	0
$541$	25.7585	1.10745	0.553723	−	0.832701i	$-0.313207\pi$
$541$	25.7585	1.10745	0.553723	+	0.832701i	$0.313207\pi$
$542$	0.998710	0.0428983
$543$	9.31346	0.399679
$544$	32.1798	1.37970
$545$	0	0
$546$	1.52798	0.0653917
$547$	−12.4111	−0.530661	−0.265331	−	0.964158i	$-0.585481\pi$
$547$	−12.4111	−0.530661	−0.265331	+	0.964158i	$0.585481\pi$
$548$	3.71477	0.158687
$549$	−13.0252	−0.555900
$550$	0	0
$551$	9.30371	0.396351
$552$	12.0192	0.511571
$553$	−27.6530	−1.17592
$554$	7.49514	0.318438
$555$	0	0
$556$	−32.6625	−1.38520
$557$	−20.5959	−0.872676	−0.436338	−	0.899783i	$-0.643725\pi$
$557$	−20.5959	−0.872676	−0.436338	+	0.899783i	$0.643725\pi$
$558$	2.07308	0.0877604
$559$	9.05966	0.383183
$560$	0	0
$561$	−6.66775	−0.281512
$562$	14.3624	0.605843
$563$	5.36876	0.226266	0.113133	−	0.993580i	$-0.463911\pi$
$563$	5.36876	0.226266	0.113133	+	0.993580i	$0.463911\pi$
$564$	−2.94506	−0.124010
$565$	0	0
$566$	−6.60648	−0.277691
$567$	1.81172	0.0760851
$568$	−0.0351034	−0.00147291
$569$	−19.2821	−0.808349	−0.404175	−	0.914682i	$-0.632441\pi$
$569$	−19.2821	−0.808349	−0.404175	+	0.914682i	$0.632441\pi$
$570$	0	0
$571$	32.9393	1.37847	0.689234	−	0.724539i	$-0.257947\pi$
$571$	32.9393	1.37847	0.689234	+	0.724539i	$0.257947\pi$
$572$	3.01631	0.126118
$573$	12.7568	0.532922
$574$	9.37189	0.391175
$575$	0	0
$576$	−2.32102	−0.0967092
$577$	−0.00200220	−8.33527e−5 0	−4.16763e−5	−	1.00000i	$-0.500013\pi$
$577$	−0.00200220	−8.33527e−5 0	−4.16763e−5		1.00000i	$0.500013\pi$
$578$	11.5632	0.480967
$579$	16.5874	0.689351
$580$	0	0
$581$	14.0032	0.580952
$582$	1.40244	0.0581330
$583$	9.72205	0.402646
$584$	4.46365	0.184707
$585$	0	0
$586$	10.5478	0.435726
$587$	38.3296	1.58203	0.791016	−	0.611796i	$-0.209553\pi$
$587$	38.3296	1.58203	0.791016	+	0.611796i	$0.209553\pi$
$588$	−6.44964	−0.265978
$589$	−30.9982	−1.27726
$590$	0	0
$591$	11.5859	0.476579
$592$	−8.52910	−0.350544
$593$	36.6557	1.50527	0.752634	−	0.658439i	$-0.228783\pi$
$593$	36.6557	1.50527	0.752634	+	0.658439i	$0.228783\pi$
$594$	−0.546583	−0.0224266
$595$	0	0
$596$	−38.2486	−1.56673
$597$	−15.8851	−0.650136
$598$	−5.27099	−0.215547
$599$	41.4027	1.69167	0.845835	−	0.533445i	$-0.179103\pi$
$599$	41.4027	1.69167	0.845835	+	0.533445i	$0.179103\pi$
$600$	0	0
$601$	−9.58940	−0.391160	−0.195580	−	0.980688i	$-0.562659\pi$
$601$	−9.58940	−0.391160	−0.195580	+	0.980688i	$0.562659\pi$
$602$	−5.15999	−0.210306
$603$	14.2796	0.581511
$604$	−37.8987	−1.54208
$605$	0	0
$606$	−0.00939886	−0.000381802 0
$607$	−25.8100	−1.04760	−0.523798	−	0.851842i	$-0.675486\pi$
$607$	−25.8100	−1.04760	−0.523798	+	0.851842i	$0.675486\pi$
$608$	−39.4441	−1.59967
$609$	2.18922	0.0887118
$610$	0	0
$611$	2.78049	0.112486
$612$	−10.8974	−0.440503
$613$	−4.79679	−0.193741	−0.0968703	−	0.995297i	$-0.530883\pi$
$613$	−4.79679	−0.193741	−0.0968703	+	0.995297i	$0.530883\pi$
$614$	−8.42504	−0.340007
$615$	0	0
$616$	−3.69847	−0.149016
$617$	−6.24233	−0.251307	−0.125653	−	0.992074i	$-0.540103\pi$
$617$	−6.24233	−0.251307	−0.125653	+	0.992074i	$0.540103\pi$
$618$	−2.89867	−0.116602
$619$	−41.7252	−1.67708	−0.838538	−	0.544843i	$-0.816589\pi$
$619$	−41.7252	−1.67708	−0.838538	+	0.544843i	$0.816589\pi$
$620$	0	0
$621$	−6.24978	−0.250795
$622$	−12.9626	−0.519753
$623$	19.0593	0.763594
$624$	4.06115	0.162576
$625$	0	0
$626$	9.76989	0.390483
$627$	8.17292	0.326395
$628$	−16.8670	−0.673067
$629$	−21.6075	−0.861547
$630$	0	0
$631$	14.6202	0.582020	0.291010	−	0.956720i	$-0.406009\pi$
$631$	14.6202	0.582020	0.291010	+	0.956720i	$0.406009\pi$
$632$	29.3536	1.16762
$633$	−4.62255	−0.183730
$634$	7.62104	0.302670
$635$	0	0
$636$	15.8892	0.630049
$637$	6.08922	0.241264
$638$	−0.660472	−0.0261484
$639$	0.0182532	0.000722085 0
$640$	0	0
$641$	27.7341	1.09543	0.547717	−	0.836664i	$-0.315497\pi$
$641$	27.7341	1.09543	0.547717	+	0.836664i	$0.315497\pi$
$642$	−0.514916	−0.0203221
$643$	−7.73775	−0.305147	−0.152574	−	0.988292i	$-0.548756\pi$
$643$	−7.73775	−0.305147	−0.152574	+	0.988292i	$0.548756\pi$
$644$	−19.6436	−0.774066
$645$	0	0
$646$	−24.9031	−0.979800
$647$	−39.6336	−1.55816	−0.779079	−	0.626926i	$-0.784313\pi$
$647$	−39.6336	−1.55816	−0.779079	+	0.626926i	$0.784313\pi$
$648$	−1.92314	−0.0755481
$649$	−7.83654	−0.307611
$650$	0	0
$651$	−7.29408	−0.285878
$652$	−35.0957	−1.37445
$653$	−12.3236	−0.482261	−0.241131	−	0.970493i	$-0.577518\pi$
$653$	−12.3236	−0.482261	−0.241131	+	0.970493i	$0.577518\pi$
$654$	7.63880	0.298701
$655$	0	0
$656$	24.9091	0.972536
$657$	−2.32102	−0.0905516
$658$	−1.58364	−0.0617369
$659$	33.8822	1.31986	0.659932	−	0.751325i	$-0.270585\pi$
$659$	33.8822	1.31986	0.659932	+	0.751325i	$0.270585\pi$
$660$	0	0
$661$	11.8192	0.459713	0.229856	−	0.973225i	$-0.426174\pi$
$661$	11.8192	0.459713	0.229856	+	0.973225i	$0.426174\pi$
$662$	9.48148	0.368508
$663$	10.2885	0.399571
$664$	−14.8644	−0.576851
$665$	0	0
$666$	−1.77125	−0.0686347
$667$	−7.55202	−0.292415
$668$	12.0509	0.466262
$669$	−19.3601	−0.748506
$670$	0	0
$671$	−13.8262	−0.533754
$672$	−9.28144	−0.358039
$673$	−5.03791	−0.194197	−0.0970986	−	0.995275i	$-0.530956\pi$
$673$	−5.03791	−0.194197	−0.0970986	+	0.995275i	$0.530956\pi$
$674$	7.51561	0.289490
$675$	0	0
$676$	17.8990	0.688422
$677$	15.9225	0.611951	0.305975	−	0.952039i	$-0.401017\pi$
$677$	15.9225	0.611951	0.305975	+	0.952039i	$0.401017\pi$
$678$	−5.41384	−0.207917
$679$	−4.93445	−0.189367
$680$	0	0
$681$	−10.6808	−0.409290
$682$	2.20057	0.0842642
$683$	−18.3037	−0.700372	−0.350186	−	0.936680i	$-0.613882\pi$
$683$	−18.3037	−0.700372	−0.350186	+	0.936680i	$0.613882\pi$
$684$	13.3574	0.510733
$685$	0	0
$686$	−9.99834	−0.381739
$687$	−18.5639	−0.708259
$688$	−13.7145	−0.522860
$689$	−15.0013	−0.571504
$690$	0	0
$691$	−20.5611	−0.782179	−0.391090	−	0.920353i	$-0.627902\pi$
$691$	−20.5611	−0.782179	−0.391090	+	0.920353i	$0.627902\pi$
$692$	34.1925	1.29980
$693$	1.92314	0.0730541
$694$	0.139594	0.00529892
$695$	0	0
$696$	−2.32386	−0.0880856
$697$	63.1043	2.39024
$698$	10.7223	0.405846
$699$	16.3959	0.620151
$700$	0	0
$701$	−24.7577	−0.935087	−0.467543	−	0.883970i	$-0.654861\pi$
$701$	−24.7577	−0.935087	−0.467543	+	0.883970i	$0.654861\pi$
$702$	0.843388	0.0318316
$703$	26.4851	0.998906
$704$	−2.46376	−0.0928565
$705$	0	0
$706$	−0.567728	−0.0213667
$707$	0.0330697	0.00124371
$708$	−12.8076	−0.481341
$709$	9.85573	0.370140	0.185070	−	0.982725i	$-0.440749\pi$
$709$	9.85573	0.370140	0.185070	+	0.982725i	$0.440749\pi$
$710$	0	0
$711$	−15.2634	−0.572421
$712$	−20.2314	−0.758204
$713$	25.1619	0.942321
$714$	−5.85986	−0.219300
$715$	0	0
$716$	8.55469	0.319704
$717$	−20.1026	−0.750746
$718$	−4.69228	−0.175114
$719$	12.7315	0.474806	0.237403	−	0.971411i	$-0.423704\pi$
$719$	12.7315	0.474806	0.237403	+	0.971411i	$0.423704\pi$
$720$	0	0
$721$	10.1989	0.379827
$722$	20.7413	0.771912
$723$	17.4439	0.648746
$724$	16.1576	0.600491
$725$	0	0
$726$	5.08388	0.188680
$727$	36.7216	1.36193	0.680964	−	0.732317i	$-0.261561\pi$
$727$	36.7216	1.36193	0.680964	+	0.732317i	$0.261561\pi$
$728$	5.70681	0.211508
$729$	1.00000	0.0370370
$730$	0	0
$731$	−34.7441	−1.28506
$732$	−22.5968	−0.835204
$733$	−8.37197	−0.309226	−0.154613	−	0.987975i	$-0.549413\pi$
$733$	−8.37197	−0.309226	−0.154613	+	0.987975i	$0.549413\pi$
$734$	17.3301	0.639665
$735$	0	0
$736$	32.0176	1.18018
$737$	15.1578	0.558344
$738$	5.17292	0.190418
$739$	1.58036	0.0581347	0.0290673	−	0.999577i	$-0.490746\pi$
$739$	1.58036	0.0581347	0.0290673	+	0.999577i	$0.490746\pi$
$740$	0	0
$741$	−12.6110	−0.463276
$742$	8.54409	0.313664
$743$	36.4125	1.33584	0.667922	−	0.744231i	$-0.267184\pi$
$743$	36.4125	1.33584	0.667922	+	0.744231i	$0.267184\pi$
$744$	7.74266	0.283860
$745$	0	0
$746$	1.32180	0.0483945
$747$	7.72924	0.282798
$748$	−11.5676	−0.422954
$749$	1.81172	0.0661989
$750$	0	0
$751$	1.53044	0.0558467	0.0279234	−	0.999610i	$-0.491111\pi$
$751$	1.53044	0.0558467	0.0279234	+	0.999610i	$0.491111\pi$
$752$	−4.20909	−0.153490
$753$	−24.7061	−0.900342
$754$	1.01912	0.0371142
$755$	0	0
$756$	3.14309	0.114313
$757$	2.11810	0.0769838	0.0384919	−	0.999259i	$-0.487745\pi$
$757$	2.11810	0.0769838	0.0384919	+	0.999259i	$0.487745\pi$
$758$	5.54286	0.201326
$759$	−6.63413	−0.240804
$760$	0	0
$761$	−17.7911	−0.644928	−0.322464	−	0.946582i	$-0.604511\pi$
$761$	−17.7911	−0.644928	−0.322464	+	0.946582i	$0.604511\pi$
$762$	−3.14592	−0.113965
$763$	−26.8770	−0.973012
$764$	22.1313	0.800681
$765$	0	0
$766$	17.1244	0.618730
$767$	12.0919	0.436614
$768$	1.24918	0.0450758
$769$	26.3213	0.949171	0.474586	−	0.880209i	$-0.342598\pi$
$769$	26.3213	0.949171	0.474586	+	0.880209i	$0.342598\pi$
$770$	0	0
$771$	10.0615	0.362356
$772$	28.7769	1.03570
$773$	34.0185	1.22356	0.611780	−	0.791028i	$-0.290454\pi$
$773$	34.0185	1.22356	0.611780	+	0.791028i	$0.290454\pi$
$774$	−2.84811	−0.102373
$775$	0	0
$776$	5.23792	0.188030
$777$	6.23212	0.223576
$778$	16.6478	0.596854
$779$	−77.3494	−2.77133
$780$	0	0
$781$	0.0193757	0.000693318 0
$782$	20.2144	0.722865
$783$	1.20837	0.0431835
$784$	−9.21783	−0.329208
$785$	0	0
$786$	6.64737	0.237104
$787$	42.0867	1.50023	0.750115	−	0.661308i	$-0.229998\pi$
$787$	42.0867	1.50023	0.750115	+	0.661308i	$0.229998\pi$
$788$	20.0999	0.716028
$789$	0.845336	0.0300947
$790$	0	0
$791$	19.0485	0.677286
$792$	−2.04141	−0.0725384
$793$	21.3341	0.757596
$794$	−6.02187	−0.213708
$795$	0	0
$796$	−27.5585	−0.976786
$797$	−10.6404	−0.376902	−0.188451	−	0.982083i	$-0.560347\pi$
$797$	−10.6404	−0.376902	−0.188451	+	0.982083i	$0.560347\pi$
$798$	7.18266	0.254263
$799$	−10.6632	−0.377238
$800$	0	0
$801$	10.5200	0.371706
$802$	11.6776	0.412350
$803$	−2.46376	−0.0869442
$804$	24.7731	0.873681
$805$	0	0
$806$	−3.39552	−0.119602
$807$	−14.3708	−0.505877
$808$	−0.0351034	−0.00123493
$809$	−22.5260	−0.791973	−0.395987	−	0.918256i	$-0.629597\pi$
$809$	−22.5260	−0.791973	−0.395987	+	0.918256i	$0.629597\pi$
$810$	0	0
$811$	−24.8426	−0.872342	−0.436171	−	0.899864i	$-0.643666\pi$
$811$	−24.8426	−0.872342	−0.436171	+	0.899864i	$0.643666\pi$
$812$	3.79800	0.133284
$813$	−1.93956	−0.0680233
$814$	−1.88019	−0.0659005
$815$	0	0
$816$	−15.5746	−0.545221
$817$	42.5872	1.48994
$818$	−0.942770	−0.0329632
$819$	−2.96744	−0.103691
$820$	0	0
$821$	−43.6730	−1.52420	−0.762100	−	0.647460i	$-0.775831\pi$
$821$	−43.6730	−1.52420	−0.762100	+	0.647460i	$0.775831\pi$
$822$	1.10256	0.0384564
$823$	−42.9691	−1.49781	−0.748904	−	0.662679i	$-0.769420\pi$
$823$	−42.9691	−1.49781	−0.748904	+	0.662679i	$0.769420\pi$
$824$	−10.8261	−0.377146
$825$	0	0
$826$	−6.88704	−0.239631
$827$	2.07280	0.0720782	0.0360391	−	0.999350i	$-0.488526\pi$
$827$	2.07280	0.0720782	0.0360391	+	0.999350i	$0.488526\pi$
$828$	−10.8425	−0.376803
$829$	−37.1830	−1.29142	−0.645710	−	0.763583i	$-0.723438\pi$
$829$	−37.1830	−1.29142	−0.645710	+	0.763583i	$0.723438\pi$
$830$	0	0
$831$	−14.5560	−0.504943
$832$	3.80163	0.131798
$833$	−23.3523	−0.809110
$834$	−9.69440	−0.335689
$835$	0	0
$836$	14.1789	0.490387
$837$	−4.02605	−0.139161
$838$	−9.35707	−0.323235
$839$	46.6134	1.60927	0.804637	−	0.593767i	$-0.202360\pi$
$839$	46.6134	1.60927	0.804637	+	0.593767i	$0.202360\pi$
$840$	0	0
$841$	−27.5399	−0.949650
$842$	−17.4846	−0.602560
$843$	−27.8928	−0.960678
$844$	−8.01949	−0.276042
$845$	0	0
$846$	−0.874110	−0.0300525
$847$	−17.8875	−0.614623
$848$	22.7089	0.779828
$849$	12.8302	0.440332
$850$	0	0
$851$	−21.4986	−0.736961
$852$	0.0316667	0.00108488
$853$	−19.9996	−0.684774	−0.342387	−	0.939559i	$-0.611235\pi$
$853$	−19.9996	−0.684774	−0.342387	+	0.939559i	$0.611235\pi$
$854$	−12.1510	−0.415798
$855$	0	0
$856$	−1.92314	−0.0657316
$857$	−0.901676	−0.0308007	−0.0154003	−	0.999881i	$-0.504902\pi$
$857$	−0.901676	−0.0308007	−0.0154003	+	0.999881i	$0.504902\pi$
$858$	0.895255	0.0305635
$859$	−31.1413	−1.06253	−0.531264	−	0.847206i	$-0.678283\pi$
$859$	−31.1413	−1.06253	−0.531264	+	0.847206i	$0.678283\pi$
$860$	0	0
$861$	−18.2008	−0.620282
$862$	10.7444	0.365957
$863$	16.1870	0.551010	0.275505	−	0.961300i	$-0.411155\pi$
$863$	16.1870	0.551010	0.275505	+	0.961300i	$0.411155\pi$
$864$	−5.12300	−0.174288
$865$	0	0
$866$	3.22903	0.109727
$867$	−22.4565	−0.762664
$868$	−12.6542	−0.429512
$869$	−16.2020	−0.549616
$870$	0	0
$871$	−23.3888	−0.792498
$872$	28.5299	0.966143
$873$	−2.72363	−0.0921808
$874$	−24.7776	−0.838114
$875$	0	0
$876$	−4.02665	−0.136048
$877$	−30.3771	−1.02576	−0.512881	−	0.858459i	$-0.671422\pi$
$877$	−30.3771	−1.02576	−0.512881	+	0.858459i	$0.671422\pi$
$878$	−13.5170	−0.456178
$879$	−20.4845	−0.690926
$880$	0	0
$881$	−20.9943	−0.707315	−0.353657	−	0.935375i	$-0.615062\pi$
$881$	−20.9943	−0.707315	−0.353657	+	0.935375i	$0.615062\pi$
$882$	−1.91429	−0.0644574
$883$	47.0350	1.58285	0.791427	−	0.611264i	$-0.209338\pi$
$883$	47.0350	1.58285	0.791427	+	0.611264i	$0.209338\pi$
$884$	17.8491	0.600329
$885$	0	0
$886$	12.1282	0.407453
$887$	−41.6975	−1.40007	−0.700033	−	0.714110i	$-0.746832\pi$
$887$	−41.6975	−1.40007	−0.700033	+	0.714110i	$0.746832\pi$
$888$	−6.61539	−0.221998
$889$	11.0689	0.371238
$890$	0	0
$891$	1.06150	0.0355615
$892$	−33.5872	−1.12458
$893$	13.0704	0.437383
$894$	−11.3524	−0.379681
$895$	0	0
$896$	−20.7281	−0.692478
$897$	10.2366	0.341790
$898$	15.7307	0.524941
$899$	−4.86494	−0.162255
$900$	0	0
$901$	57.5304	1.91662
$902$	5.49105	0.182832
$903$	10.0210	0.333479
$904$	−20.2199	−0.672505
$905$	0	0
$906$	−11.2485	−0.373708
$907$	17.6504	0.586071	0.293035	−	0.956102i	$-0.405335\pi$
$907$	17.6504	0.586071	0.293035	+	0.956102i	$0.405335\pi$
$908$	−18.5297	−0.614931
$909$	0.0182532	0.000605420 0
$910$	0	0
$911$	−13.3742	−0.443107	−0.221554	−	0.975148i	$-0.571113\pi$
$911$	−13.3742	−0.443107	−0.221554	+	0.975148i	$0.571113\pi$
$912$	19.0904	0.632148
$913$	8.20458	0.271532
$914$	17.8836	0.591537
$915$	0	0
$916$	−32.2059	−1.06411
$917$	−23.3886	−0.772360
$918$	−3.23442	−0.106752
$919$	−16.1133	−0.531530	−0.265765	−	0.964038i	$-0.585625\pi$
$919$	−16.1133	−0.531530	−0.265765	+	0.964038i	$0.585625\pi$
$920$	0	0
$921$	16.3620	0.539145
$922$	12.3839	0.407842
$923$	−0.0298971	−0.000984076 0
$924$	3.33638	0.109759
$925$	0	0
$926$	19.3165	0.634780
$927$	5.62940	0.184894
$928$	−6.19046	−0.203212
$929$	4.10333	0.134626	0.0673130	−	0.997732i	$-0.478557\pi$
$929$	4.10333	0.134626	0.0673130	+	0.997732i	$0.478557\pi$
$930$	0	0
$931$	28.6238	0.938109
$932$	28.4447	0.931736
$933$	25.1742	0.824167
$934$	−2.58166	−0.0844747
$935$	0	0
$936$	3.14994	0.102959
$937$	12.1518	0.396981	0.198491	−	0.980103i	$-0.436396\pi$
$937$	12.1518	0.396981	0.198491	+	0.980103i	$0.436396\pi$
$938$	13.3212	0.434953
$939$	−18.9738	−0.619185
$940$	0	0
$941$	32.5394	1.06075	0.530377	−	0.847762i	$-0.322050\pi$
$941$	32.5394	1.06075	0.530377	+	0.847762i	$0.322050\pi$
$942$	−5.00622	−0.163111
$943$	62.7861	2.04460
$944$	−18.3047	−0.595768
$945$	0	0
$946$	−3.02327	−0.0982950
$947$	−4.86139	−0.157974	−0.0789869	−	0.996876i	$-0.525169\pi$
$947$	−4.86139	−0.157974	−0.0789869	+	0.996876i	$0.525169\pi$
$948$	−26.4798	−0.860024
$949$	3.80163	0.123406
$950$	0	0
$951$	−14.8005	−0.479940
$952$	−21.8858	−0.709322
$953$	−25.8363	−0.836919	−0.418459	−	0.908235i	$-0.637430\pi$
$953$	−25.8363	−0.836919	−0.418459	+	0.908235i	$0.637430\pi$
$954$	4.71601	0.152686
$955$	0	0
$956$	−34.8753	−1.12795
$957$	1.28268	0.0414631
$958$	15.8002	0.510481
$959$	−3.87935	−0.125271
$960$	0	0
$961$	−14.7909	−0.477126
$962$	2.90116	0.0935372
$963$	1.00000	0.0322245
$964$	30.2628	0.974698
$965$	0	0
$966$	−5.83032	−0.187587
$967$	5.96461	0.191809	0.0959044	−	0.995391i	$-0.469426\pi$
$967$	5.96461	0.191809	0.0959044	+	0.995391i	$0.469426\pi$
$968$	18.9876	0.610284
$969$	48.3634	1.55366
$970$	0	0
$971$	9.29672	0.298346	0.149173	−	0.988811i	$-0.452339\pi$
$971$	9.29672	0.298346	0.149173	+	0.988811i	$0.452339\pi$
$972$	1.73486	0.0556457
$973$	34.1095	1.09350
$974$	−2.63366	−0.0843880
$975$	0	0
$976$	−32.2955	−1.03375
$977$	3.29207	0.105323	0.0526613	−	0.998612i	$-0.483230\pi$
$977$	3.29207	0.105323	0.0526613	+	0.998612i	$0.483230\pi$
$978$	−10.4166	−0.333086
$979$	11.1670	0.356897
$980$	0	0
$981$	−14.8350	−0.473647
$982$	−18.5991	−0.593521
$983$	21.2471	0.677677	0.338839	−	0.940844i	$-0.389966\pi$
$983$	21.2471	0.677677	0.338839	+	0.940844i	$0.389966\pi$
$984$	19.3201	0.615903
$985$	0	0
$986$	−3.90836	−0.124468
$987$	3.07554	0.0978955
$988$	−21.8783	−0.696041
$989$	−34.5689	−1.09923
$990$	0	0
$991$	7.12394	0.226299	0.113150	−	0.993578i	$-0.463906\pi$
$991$	7.12394	0.226299	0.113150	+	0.993578i	$0.463906\pi$
$992$	20.6254	0.654859
$993$	−18.4136	−0.584339
$994$	0.0170281	0.000540099 0
$995$	0	0
$996$	13.4092	0.424886
$997$	−30.3383	−0.960824	−0.480412	−	0.877043i	$-0.659513\pi$
$997$	−30.3383	−0.960824	−0.480412	+	0.877043i	$0.659513\pi$
$998$	−8.59828	−0.272174
$999$	3.43989	0.108833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.w.1.2		4
5.4	even	2		1605.2.a.g.1.3	✓	4
15.14	odd	2		4815.2.a.j.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1605.2.a.g.1.3	✓	4	5.4	even	2
4815.2.a.j.1.2		4	15.14	odd	2
8025.2.a.w.1.2		4	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:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.514916 q^{2} -1.00000 q^{3} -1.73486 q^{4} -0.514916 q^{6} +1.81172 q^{7} -1.92314 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.514916 q^{2} -1.00000 q^{3} -1.73486 q^{4} -0.514916 q^{6} +1.81172 q^{7} -1.92314 q^{8} +1.00000 q^{9} +1.06150 q^{11} +1.73486 q^{12} -1.63791 q^{13} +0.932884 q^{14} +2.47947 q^{16} +6.28144 q^{17} +0.514916 q^{18} -7.69941 q^{19} -1.81172 q^{21} +0.546583 q^{22} +6.24978 q^{23} +1.92314 q^{24} -0.843388 q^{26} -1.00000 q^{27} -3.14309 q^{28} -1.20837 q^{29} +4.02605 q^{31} +5.12300 q^{32} -1.06150 q^{33} +3.23442 q^{34} -1.73486 q^{36} -3.43989 q^{37} -3.96455 q^{38} +1.63791 q^{39} +10.0461 q^{41} -0.932884 q^{42} -5.53122 q^{43} -1.84155 q^{44} +3.21811 q^{46} -1.69758 q^{47} -2.47947 q^{48} -3.71767 q^{49} -6.28144 q^{51} +2.84155 q^{52} +9.15879 q^{53} -0.514916 q^{54} -3.48419 q^{56} +7.69941 q^{57} -0.622207 q^{58} -7.38252 q^{59} -13.0252 q^{61} +2.07308 q^{62} +1.81172 q^{63} -2.32102 q^{64} -0.546583 q^{66} +14.2796 q^{67} -10.8974 q^{68} -6.24978 q^{69} +0.0182532 q^{71} -1.92314 q^{72} -2.32102 q^{73} -1.77125 q^{74} +13.3574 q^{76} +1.92314 q^{77} +0.843388 q^{78} -15.2634 q^{79} +1.00000 q^{81} +5.17292 q^{82} +7.72924 q^{83} +3.14309 q^{84} -2.84811 q^{86} +1.20837 q^{87} -2.04141 q^{88} +10.5200 q^{89} -2.96744 q^{91} -10.8425 q^{92} -4.02605 q^{93} -0.874110 q^{94} -5.12300 q^{96} -2.72363 q^{97} -1.91429 q^{98} +1.06150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + 3 q^{2} - 4 q^{3} + 3 q^{4} - 3 q^{6} + 8 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{11} - 3 q^{12} + 9 q^{13} - 3 q^{16} + 6 q^{17} + 3 q^{18} - 7 q^{19} - 8 q^{21} - 7 q^{22} + 16 q^{23} - 3 q^{24} + 6 q^{26} - 4 q^{27} + 9 q^{28} + q^{29} - 6 q^{31} + 4 q^{32} + 4 q^{33} - 15 q^{34} + 3 q^{36} + 8 q^{37} - 2 q^{38} - 9 q^{39} + 13 q^{41} + 6 q^{43} - 10 q^{44} + 14 q^{46} + 5 q^{47} + 3 q^{48} + 2 q^{49} - 6 q^{51} + 14 q^{52} + 5 q^{53} - 3 q^{54} + 23 q^{56} + 7 q^{57} + 3 q^{58} - 11 q^{59} + 6 q^{61} - 5 q^{62} + 8 q^{63} + q^{64} + 7 q^{66} + 50 q^{67} - 26 q^{68} - 16 q^{69} + 7 q^{71} + 3 q^{72} + q^{73} + 37 q^{74} + 9 q^{76} - 3 q^{77} - 6 q^{78} + q^{79} + 4 q^{81} + q^{82} + 9 q^{83} - 9 q^{84} + 22 q^{86} - q^{87} - 5 q^{88} - 10 q^{89} + 14 q^{91} + 2 q^{92} + 6 q^{93} - 32 q^{94} - 4 q^{96} + 23 q^{97} - 26 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 - 4 * q^3 + 3 * q^4 - 3 * q^6 + 8 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^11 - 3 * q^12 + 9 * q^13 - 3 * q^16 + 6 * q^17 + 3 * q^18 - 7 * q^19 - 8 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 + 6 * q^26 - 4 * q^27 + 9 * q^28 + q^29 - 6 * q^31 + 4 * q^32 + 4 * q^33 - 15 * q^34 + 3 * q^36 + 8 * q^37 - 2 * q^38 - 9 * q^39 + 13 * q^41 + 6 * q^43 - 10 * q^44 + 14 * q^46 + 5 * q^47 + 3 * q^48 + 2 * q^49 - 6 * q^51 + 14 * q^52 + 5 * q^53 - 3 * q^54 + 23 * q^56 + 7 * q^57 + 3 * q^58 - 11 * q^59 + 6 * q^61 - 5 * q^62 + 8 * q^63 + q^64 + 7 * q^66 + 50 * q^67 - 26 * q^68 - 16 * q^69 + 7 * q^71 + 3 * q^72 + q^73 + 37 * q^74 + 9 * q^76 - 3 * q^77 - 6 * q^78 + q^79 + 4 * q^81 + q^82 + 9 * q^83 - 9 * q^84 + 22 * q^86 - q^87 - 5 * q^88 - 10 * q^89 + 14 * q^91 + 2 * q^92 + 6 * q^93 - 32 * q^94 - 4 * q^96 + 23 * q^97 - 26 * q^98 - 4 * q^99

Introduction

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