LMFDB - Embedded newform 4025.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.825785$ of defining polynomial
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.174215 q^{2} +0.596155 q^{3} -1.96965 q^{4} -0.103859 q^{6} +1.00000 q^{7} +0.691574 q^{8} -2.64460 q^{9} +O(q^{10})$	\(q-0.174215 q^{2} +0.596155 q^{3} -1.96965 q^{4} -0.103859 q^{6} +1.00000 q^{7} +0.691574 q^{8} -2.64460 q^{9} +1.17422 q^{11} -1.17422 q^{12} +0.721925 q^{13} -0.174215 q^{14} +3.81882 q^{16} -6.01809 q^{17} +0.460730 q^{18} +3.19928 q^{19} +0.596155 q^{21} -0.204566 q^{22} +1.00000 q^{23} +0.412285 q^{24} -0.125771 q^{26} -3.36505 q^{27} -1.96965 q^{28} +0.556150 q^{29} +5.29617 q^{31} -2.04844 q^{32} +0.700014 q^{33} +1.04844 q^{34} +5.20893 q^{36} -3.92120 q^{37} -0.557364 q^{38} +0.430379 q^{39} -2.32652 q^{41} -0.103859 q^{42} -1.21301 q^{43} -2.31279 q^{44} -0.174215 q^{46} -2.29470 q^{47} +2.27660 q^{48} +1.00000 q^{49} -3.58771 q^{51} -1.42194 q^{52} +2.96965 q^{53} +0.586244 q^{54} +0.691574 q^{56} +1.90727 q^{57} -0.0968899 q^{58} +8.40968 q^{59} -1.23807 q^{61} -0.922674 q^{62} -2.64460 q^{63} -7.28076 q^{64} -0.121953 q^{66} -14.8381 q^{67} +11.8535 q^{68} +0.596155 q^{69} +9.58390 q^{71} -1.82894 q^{72} -15.0858 q^{73} +0.683134 q^{74} -6.30146 q^{76} +1.17422 q^{77} -0.0749787 q^{78} -6.89085 q^{79} +5.92771 q^{81} +0.405316 q^{82} +4.89883 q^{83} -1.17422 q^{84} +0.211324 q^{86} +0.331551 q^{87} +0.812057 q^{88} -8.44653 q^{89} +0.721925 q^{91} -1.96965 q^{92} +3.15734 q^{93} +0.399772 q^{94} -1.22119 q^{96} +9.09282 q^{97} -0.174215 q^{98} -3.10533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	$ 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * 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 $

$2$	−0.174215	−0.123189	−0.0615945	−	0.998101i	$-0.519619\pi$
$2$	−0.174215	−0.123189	−0.0615945	+	0.998101i	$0.519619\pi$
$3$	0.596155	0.344190	0.172095	−	0.985080i	$-0.444946\pi$
$3$	0.596155	0.344190	0.172095	+	0.985080i	$0.444946\pi$
$4$	−1.96965	−0.984824
$5$	0	0
$5$	0	0
$6$	−0.103859	−0.0424004
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.691574	0.244508
$9$	−2.64460	−0.881533
$10$	0	0
$11$	1.17422	0.354039	0.177020	−	0.984207i	$-0.443354\pi$
$11$	1.17422	0.354039	0.177020	+	0.984207i	$0.443354\pi$
$12$	−1.17422	−0.338967
$13$	0.721925	0.200226	0.100113	−	0.994976i	$-0.468080\pi$
$13$	0.721925	0.200226	0.100113	+	0.994976i	$0.468080\pi$
$14$	−0.174215	−0.0465610
$15$	0	0
$16$	3.81882	0.954704
$17$	−6.01809	−1.45960	−0.729801	−	0.683660i	$-0.760387\pi$
$17$	−6.01809	−1.45960	−0.729801	+	0.683660i	$0.760387\pi$
$18$	0.460730	0.108595
$19$	3.19928	0.733965	0.366982	−	0.930228i	$-0.380391\pi$
$19$	3.19928	0.733965	0.366982	+	0.930228i	$0.380391\pi$
$20$	0	0
$21$	0.596155	0.130092
$22$	−0.204566	−0.0436137
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.412285	0.0841574
$25$	0	0
$26$	−0.125771	−0.0246656
$27$	−3.36505	−0.647605
$28$	−1.96965	−0.372229
$29$	0.556150	0.103274	0.0516372	−	0.998666i	$-0.483556\pi$
$29$	0.556150	0.103274	0.0516372	+	0.998666i	$0.483556\pi$
$30$	0	0
$31$	5.29617	0.951220	0.475610	−	0.879656i	$-0.342227\pi$
$31$	5.29617	0.951220	0.475610	+	0.879656i	$0.342227\pi$
$32$	−2.04844	−0.362117
$33$	0.700014	0.121857
$34$	1.04844	0.179807
$35$	0	0
$36$	5.20893	0.868155
$37$	−3.92120	−0.644642	−0.322321	−	0.946630i	$-0.604463\pi$
$37$	−3.92120	−0.644642	−0.322321	+	0.946630i	$0.604463\pi$
$38$	−0.557364	−0.0904163
$39$	0.430379	0.0689158
$40$	0	0
$41$	−2.32652	−0.363341	−0.181671	−	0.983359i	$-0.558150\pi$
$41$	−2.32652	−0.363341	−0.181671	+	0.983359i	$0.558150\pi$
$42$	−0.103859	−0.0160258
$43$	−1.21301	−0.184982	−0.0924909	−	0.995714i	$-0.529483\pi$
$43$	−1.21301	−0.184982	−0.0924909	+	0.995714i	$0.529483\pi$
$44$	−2.31279	−0.348667
$45$	0	0
$46$	−0.174215	−0.0256867
$47$	−2.29470	−0.334716	−0.167358	−	0.985896i	$-0.553524\pi$
$47$	−2.29470	−0.334716	−0.167358	+	0.985896i	$0.553524\pi$
$48$	2.27660	0.328600
$49$	1.00000	0.142857
$50$	0	0
$51$	−3.58771	−0.502381
$52$	−1.42194	−0.197187
$53$	2.96965	0.407913	0.203956	−	0.978980i	$-0.434620\pi$
$53$	2.96965	0.407913	0.203956	+	0.978980i	$0.434620\pi$
$54$	0.586244	0.0797778
$55$	0	0
$56$	0.691574	0.0924155
$57$	1.90727	0.252623
$58$	−0.0968899	−0.0127223
$59$	8.40968	1.09485	0.547424	−	0.836856i	$-0.315609\pi$
$59$	8.40968	1.09485	0.547424	+	0.836856i	$0.315609\pi$
$60$	0	0
$61$	−1.23807	−0.158519	−0.0792593	−	0.996854i	$-0.525256\pi$
$61$	−1.23807	−0.158519	−0.0792593	+	0.996854i	$0.525256\pi$
$62$	−0.922674	−0.117180
$63$	−2.64460	−0.333188
$64$	−7.28076	−0.910095
$65$	0	0
$66$	−0.121953	−0.0150114
$67$	−14.8381	−1.81277	−0.906383	−	0.422458i	$-0.861167\pi$
$67$	−14.8381	−1.81277	−0.906383	+	0.422458i	$0.861167\pi$
$68$	11.8535	1.43745
$69$	0.596155	0.0717686
$70$	0	0
$71$	9.58390	1.13740	0.568700	−	0.822545i	$-0.307447\pi$
$71$	9.58390	1.13740	0.568700	+	0.822545i	$0.307447\pi$
$72$	−1.82894	−0.215542
$73$	−15.0858	−1.76566	−0.882832	−	0.469688i	$-0.844366\pi$
$73$	−15.0858	−1.76566	−0.882832	+	0.469688i	$0.844366\pi$
$74$	0.683134	0.0794128
$75$	0	0
$76$	−6.30146	−0.722827
$77$	1.17422	0.133814
$78$	−0.0749787	−0.00848966
$79$	−6.89085	−0.775282	−0.387641	−	0.921811i	$-0.626710\pi$
$79$	−6.89085	−0.775282	−0.387641	+	0.921811i	$0.626710\pi$
$80$	0	0
$81$	5.92771	0.658634
$82$	0.405316	0.0447596
$83$	4.89883	0.537716	0.268858	−	0.963180i	$-0.413354\pi$
$83$	4.89883	0.537716	0.268858	+	0.963180i	$0.413354\pi$
$84$	−1.17422	−0.128117
$85$	0	0
$86$	0.211324	0.0227877
$87$	0.331551	0.0355460
$88$	0.812057	0.0865656
$89$	−8.44653	−0.895331	−0.447665	−	0.894201i	$-0.647744\pi$
$89$	−8.44653	−0.895331	−0.447665	+	0.894201i	$0.647744\pi$
$90$	0	0
$91$	0.721925	0.0756783
$92$	−1.96965	−0.205350
$93$	3.15734	0.327400
$94$	0.399772	0.0412333
$95$	0	0
$96$	−1.22119	−0.124637
$97$	9.09282	0.923236	0.461618	−	0.887079i	$-0.347269\pi$
$97$	9.09282	0.923236	0.461618	+	0.887079i	$0.347269\pi$
$98$	−0.174215	−0.0175984
$99$	−3.10533	−0.312097
$100$	0	0
$101$	−9.56702	−0.951954	−0.475977	−	0.879458i	$-0.657905\pi$
$101$	−9.56702	−0.951954	−0.475977	+	0.879458i	$0.657905\pi$
$102$	0.625035	0.0618877
$103$	−2.92649	−0.288356	−0.144178	−	0.989552i	$-0.546054\pi$
$103$	−2.92649	−0.288356	−0.144178	+	0.989552i	$0.546054\pi$
$104$	0.499265	0.0489569
$105$	0	0
$106$	−0.517359	−0.0502503
$107$	3.86726	0.373862	0.186931	−	0.982373i	$-0.440146\pi$
$107$	3.86726	0.373862	0.186931	+	0.982373i	$0.440146\pi$
$108$	6.62798	0.637777
$109$	−4.33349	−0.415073	−0.207536	−	0.978227i	$-0.566545\pi$
$109$	−4.33349	−0.415073	−0.207536	+	0.978227i	$0.566545\pi$
$110$	0	0
$111$	−2.33764	−0.221879
$112$	3.81882	0.360844
$113$	−10.9696	−1.03194	−0.515969	−	0.856607i	$-0.672568\pi$
$113$	−10.9696	−1.03194	−0.515969	+	0.856607i	$0.672568\pi$
$114$	−0.332275	−0.0311204
$115$	0	0
$116$	−1.09542	−0.101707
$117$	−1.90920	−0.176506
$118$	−1.46510	−0.134873
$119$	−6.01809	−0.551678
$120$	0	0
$121$	−9.62122	−0.874656
$122$	0.215691	0.0195277
$123$	−1.38697	−0.125058
$124$	−10.4316	−0.936785
$125$	0	0
$126$	0.460730	0.0410451
$127$	4.67932	0.415222	0.207611	−	0.978211i	$-0.433431\pi$
$127$	4.67932	0.415222	0.207611	+	0.978211i	$0.433431\pi$
$128$	5.36531	0.474231
$129$	−0.723139	−0.0636689
$130$	0	0
$131$	3.04529	0.266068	0.133034	−	0.991111i	$-0.457528\pi$
$131$	3.04529	0.266068	0.133034	+	0.991111i	$0.457528\pi$
$132$	−1.37878	−0.120008
$133$	3.19928	0.277413
$134$	2.58503	0.223313
$135$	0	0
$136$	−4.16196	−0.356885
$137$	−8.46723	−0.723404	−0.361702	−	0.932294i	$-0.617804\pi$
$137$	−8.46723	−0.723404	−0.361702	+	0.932294i	$0.617804\pi$
$138$	−0.103859	−0.00884110
$139$	−10.8588	−0.921033	−0.460517	−	0.887651i	$-0.652336\pi$
$139$	−10.8588	−0.921033	−0.460517	+	0.887651i	$0.652336\pi$
$140$	0	0
$141$	−1.36800	−0.115206
$142$	−1.66966	−0.140115
$143$	0.847696	0.0708879
$144$	−10.0992	−0.841603
$145$	0	0
$146$	2.62819	0.217510
$147$	0.596155	0.0491700
$148$	7.72340	0.634859
$149$	−9.39881	−0.769981	−0.384990	−	0.922921i	$-0.625795\pi$
$149$	−9.39881	−0.769981	−0.384990	+	0.922921i	$0.625795\pi$
$150$	0	0
$151$	7.69573	0.626270	0.313135	−	0.949709i	$-0.398621\pi$
$151$	7.69573	0.626270	0.313135	+	0.949709i	$0.398621\pi$
$152$	2.21254	0.179461
$153$	15.9154	1.28669
$154$	−0.204566	−0.0164844
$155$	0	0
$156$	−0.847696	−0.0678700
$157$	−10.9102	−0.870726	−0.435363	−	0.900255i	$-0.643380\pi$
$157$	−10.9102	−0.870726	−0.435363	+	0.900255i	$0.643380\pi$
$158$	1.20049	0.0955061
$159$	1.77037	0.140399
$160$	0	0
$161$	1.00000	0.0788110
$162$	−1.03270	−0.0811364
$163$	−3.46073	−0.271065	−0.135533	−	0.990773i	$-0.543275\pi$
$163$	−3.46073	−0.271065	−0.135533	+	0.990773i	$0.543275\pi$
$164$	4.58243	0.357827
$165$	0	0
$166$	−0.853451	−0.0662406
$167$	6.46723	0.500449	0.250225	−	0.968188i	$-0.419495\pi$
$167$	6.46723	0.500449	0.250225	+	0.968188i	$0.419495\pi$
$168$	0.412285	0.0318085
$169$	−12.4788	−0.959910
$170$	0	0
$171$	−8.46081	−0.647014
$172$	2.38920	0.182175
$173$	11.7636	0.894371	0.447185	−	0.894441i	$-0.352426\pi$
$173$	11.7636	0.894371	0.447185	+	0.894441i	$0.352426\pi$
$174$	−0.0577613	−0.00437888
$175$	0	0
$176$	4.48411	0.338003
$177$	5.01347	0.376836
$178$	1.47152	0.110295
$179$	−4.60749	−0.344380	−0.172190	−	0.985064i	$-0.555084\pi$
$179$	−4.60749	−0.344380	−0.172190	+	0.985064i	$0.555084\pi$
$180$	0	0
$181$	−22.9382	−1.70498	−0.852490	−	0.522743i	$-0.824909\pi$
$181$	−22.9382	−1.70498	−0.852490	+	0.522743i	$0.824909\pi$
$182$	−0.125771	−0.00932273
$183$	−0.738081	−0.0545605
$184$	0.691574	0.0509835
$185$	0	0
$186$	−0.550057	−0.0403321
$187$	−7.06654	−0.516756
$188$	4.51975	0.329637
$189$	−3.36505	−0.244772
$190$	0	0
$191$	7.49880	0.542594	0.271297	−	0.962496i	$-0.412547\pi$
$191$	7.49880	0.542594	0.271297	+	0.962496i	$0.412547\pi$
$192$	−4.34046	−0.313246
$193$	−15.4882	−1.11487	−0.557433	−	0.830222i	$-0.688214\pi$
$193$	−15.4882	−1.11487	−0.557433	+	0.830222i	$0.688214\pi$
$194$	−1.58411	−0.113732
$195$	0	0
$196$	−1.96965	−0.140689
$197$	−19.2548	−1.37185	−0.685923	−	0.727674i	$-0.740601\pi$
$197$	−19.2548	−1.37185	−0.685923	+	0.727674i	$0.740601\pi$
$198$	0.540996	0.0384469
$199$	−9.56265	−0.677878	−0.338939	−	0.940808i	$-0.610068\pi$
$199$	−9.56265	−0.677878	−0.338939	+	0.940808i	$0.610068\pi$
$200$	0	0
$201$	−8.84582	−0.623936
$202$	1.66672	0.117270
$203$	0.556150	0.0390340
$204$	7.06654	0.494757
$205$	0	0
$206$	0.509840	0.0355222
$207$	−2.64460	−0.183812
$208$	2.75690	0.191157
$209$	3.75664	0.259852
$210$	0	0
$211$	25.7982	1.77602	0.888011	−	0.459823i	$-0.152087\pi$
$211$	25.7982	1.77602	0.888011	+	0.459823i	$0.152087\pi$
$212$	−5.84917	−0.401722
$213$	5.71349	0.391482
$214$	−0.673736	−0.0460557
$215$	0	0
$216$	−2.32718	−0.158345
$217$	5.29617	0.359527
$218$	0.754961	0.0511324
$219$	−8.99350	−0.607724
$220$	0	0
$221$	−4.34461	−0.292250
$222$	0.407254	0.0273331
$223$	−10.1314	−0.678445	−0.339223	−	0.940706i	$-0.610164\pi$
$223$	−10.1314	−0.678445	−0.339223	+	0.940706i	$0.610164\pi$
$224$	−2.04844	−0.136867
$225$	0	0
$226$	1.91108	0.127123
$227$	−19.2627	−1.27851	−0.639257	−	0.768993i	$-0.720758\pi$
$227$	−19.2627	−1.27851	−0.639257	+	0.768993i	$0.720758\pi$
$228$	−3.75664	−0.248790
$229$	12.2700	0.810823	0.405411	−	0.914134i	$-0.367128\pi$
$229$	12.2700	0.810823	0.405411	+	0.914134i	$0.367128\pi$
$230$	0	0
$231$	0.700014	0.0460575
$232$	0.384619	0.0252515
$233$	−26.8663	−1.76007	−0.880036	−	0.474907i	$-0.842482\pi$
$233$	−26.8663	−1.76007	−0.880036	+	0.474907i	$0.842482\pi$
$234$	0.332613	0.0217436
$235$	0	0
$236$	−16.5641	−1.07823
$237$	−4.10801	−0.266844
$238$	1.04844	0.0679606
$239$	30.1134	1.94787	0.973936	−	0.226821i	$-0.0728333\pi$
$239$	30.1134	1.94787	0.973936	+	0.226821i	$0.0728333\pi$
$240$	0	0
$241$	−22.4960	−1.44909	−0.724547	−	0.689225i	$-0.757951\pi$
$241$	−22.4960	−1.44909	−0.724547	+	0.689225i	$0.757951\pi$
$242$	1.67616	0.107748
$243$	13.6290	0.874300
$244$	2.43856	0.156113
$245$	0	0
$246$	0.241631	0.0154058
$247$	2.30964	0.146959
$248$	3.66269	0.232581
$249$	2.92046	0.185076
$250$	0	0
$251$	5.30192	0.334654	0.167327	−	0.985901i	$-0.446486\pi$
$251$	5.30192	0.334654	0.167327	+	0.985901i	$0.446486\pi$
$252$	5.20893	0.328132
$253$	1.17422	0.0738223
$254$	−0.815209	−0.0511508
$255$	0	0
$256$	13.6268	0.851675
$257$	0.110829	0.00691331	0.00345666	−	0.999994i	$-0.498900\pi$
$257$	0.110829	0.00691331	0.00345666	+	0.999994i	$0.498900\pi$
$258$	0.125982	0.00784330
$259$	−3.92120	−0.243652
$260$	0	0
$261$	−1.47079	−0.0910398
$262$	−0.530537	−0.0327767
$263$	−2.37488	−0.146442	−0.0732208	−	0.997316i	$-0.523328\pi$
$263$	−2.37488	−0.146442	−0.0732208	+	0.997316i	$0.523328\pi$
$264$	0.484112	0.0297950
$265$	0	0
$266$	−0.557364	−0.0341742
$267$	−5.03544	−0.308164
$268$	29.2259	1.78526
$269$	−15.3943	−0.938605	−0.469303	−	0.883037i	$-0.655495\pi$
$269$	−15.3943	−0.938605	−0.469303	+	0.883037i	$0.655495\pi$
$270$	0	0
$271$	−6.73902	−0.409366	−0.204683	−	0.978828i	$-0.565616\pi$
$271$	−6.73902	−0.409366	−0.204683	+	0.978828i	$0.565616\pi$
$272$	−22.9820	−1.39349
$273$	0.430379	0.0260477
$274$	1.47512	0.0891154
$275$	0	0
$276$	−1.17422	−0.0706795
$277$	23.8929	1.43558	0.717792	−	0.696258i	$-0.245153\pi$
$277$	23.8929	1.43558	0.717792	+	0.696258i	$0.245153\pi$
$278$	1.89177	0.113461
$279$	−14.0062	−0.838532
$280$	0	0
$281$	−20.0022	−1.19323	−0.596616	−	0.802527i	$-0.703488\pi$
$281$	−20.0022	−1.19323	−0.596616	+	0.802527i	$0.703488\pi$
$282$	0.238326	0.0141921
$283$	−8.10386	−0.481724	−0.240862	−	0.970559i	$-0.577430\pi$
$283$	−8.10386	−0.481724	−0.240862	+	0.970559i	$0.577430\pi$
$284$	−18.8769	−1.12014
$285$	0	0
$286$	−0.147682	−0.00873260
$287$	−2.32652	−0.137330
$288$	5.41732	0.319218
$289$	19.2175	1.13044
$290$	0	0
$291$	5.42073	0.317769
$292$	29.7138	1.73887
$293$	−12.6642	−0.739848	−0.369924	−	0.929062i	$-0.620616\pi$
$293$	−12.6642	−0.739848	−0.369924	+	0.929062i	$0.620616\pi$
$294$	−0.103859	−0.00605720
$295$	0	0
$296$	−2.71180	−0.157620
$297$	−3.95130	−0.229278
$298$	1.63742	0.0948531
$299$	0.721925	0.0417500
$300$	0	0
$301$	−1.21301	−0.0699165
$302$	−1.34071	−0.0771495
$303$	−5.70342	−0.327653
$304$	12.2175	0.700719
$305$	0	0
$306$	−2.77272	−0.158506
$307$	0.934010	0.0533068	0.0266534	−	0.999645i	$-0.491515\pi$
$307$	0.934010	0.0533068	0.0266534	+	0.999645i	$0.491515\pi$
$308$	−2.31279	−0.131784
$309$	−1.74464	−0.0992492
$310$	0	0
$311$	−6.64246	−0.376660	−0.188330	−	0.982106i	$-0.560307\pi$
$311$	−6.64246	−0.376660	−0.188330	+	0.982106i	$0.560307\pi$
$312$	0.297639	0.0168505
$313$	17.1671	0.970340	0.485170	−	0.874420i	$-0.338758\pi$
$313$	17.1671	0.970340	0.485170	+	0.874420i	$0.338758\pi$
$314$	1.90072	0.107264
$315$	0	0
$316$	13.5726	0.763516
$317$	−13.6998	−0.769455	−0.384728	−	0.923030i	$-0.625705\pi$
$317$	−13.6998	−0.769455	−0.384728	+	0.923030i	$0.625705\pi$
$318$	−0.308426	−0.0172957
$319$	0.653039	0.0365632
$320$	0	0
$321$	2.30549	0.128680
$322$	−0.174215	−0.00970865
$323$	−19.2536	−1.07130
$324$	−11.6755	−0.648639
$325$	0	0
$326$	0.602913	0.0333922
$327$	−2.58343	−0.142864
$328$	−1.60896	−0.0888400
$329$	−2.29470	−0.126511
$330$	0	0
$331$	−17.0456	−0.936913	−0.468456	−	0.883487i	$-0.655190\pi$
$331$	−17.0456	−0.936913	−0.468456	+	0.883487i	$0.655190\pi$
$332$	−9.64897	−0.529556
$333$	10.3700	0.568273
$334$	−1.12669	−0.0616498
$335$	0	0
$336$	2.27660	0.124199
$337$	1.78868	0.0974354	0.0487177	−	0.998813i	$-0.484487\pi$
$337$	1.78868	0.0974354	0.0487177	+	0.998813i	$0.484487\pi$
$338$	2.17400	0.118250
$339$	−6.53961	−0.355183
$340$	0	0
$341$	6.21884	0.336769
$342$	1.47400	0.0797050
$343$	1.00000	0.0539949
$344$	−0.838884	−0.0452296
$345$	0	0
$346$	−2.04940	−0.110177
$347$	−12.2525	−0.657751	−0.328876	−	0.944373i	$-0.606670\pi$
$347$	−12.2525	−0.657751	−0.328876	+	0.944373i	$0.606670\pi$
$348$	−0.653039	−0.0350066
$349$	−17.4343	−0.933235	−0.466618	−	0.884459i	$-0.654528\pi$
$349$	−17.4343	−0.933235	−0.466618	+	0.884459i	$0.654528\pi$
$350$	0	0
$351$	−2.42932	−0.129667
$352$	−2.40532	−0.128204
$353$	−25.2370	−1.34323	−0.671615	−	0.740900i	$-0.734399\pi$
$353$	−25.2370	−1.34323	−0.671615	+	0.740900i	$0.734399\pi$
$354$	−0.873424	−0.0464220
$355$	0	0
$356$	16.6367	0.881744
$357$	−3.58771	−0.189882
$358$	0.802696	0.0424238
$359$	10.1124	0.533711	0.266856	−	0.963737i	$-0.414015\pi$
$359$	10.1124	0.533711	0.266856	+	0.963737i	$0.414015\pi$
$360$	0	0
$361$	−8.76461	−0.461296
$362$	3.99618	0.210035
$363$	−5.73573	−0.301048
$364$	−1.42194	−0.0745299
$365$	0	0
$366$	0.128585	0.00672125
$367$	−21.3541	−1.11467	−0.557336	−	0.830287i	$-0.688177\pi$
$367$	−21.3541	−1.11467	−0.557336	+	0.830287i	$0.688177\pi$
$368$	3.81882	0.199069
$369$	6.15271	0.320297
$370$	0	0
$371$	2.96965	0.154176
$372$	−6.21884	−0.322432
$373$	−12.7317	−0.659220	−0.329610	−	0.944117i	$-0.606917\pi$
$373$	−12.7317	−0.659220	−0.329610	+	0.944117i	$0.606917\pi$
$374$	1.23110	0.0636587
$375$	0	0
$376$	−1.58695	−0.0818409
$377$	0.401498	0.0206782
$378$	0.586244	0.0301532
$379$	32.1968	1.65384	0.826918	−	0.562322i	$-0.190092\pi$
$379$	32.1968	1.65384	0.826918	+	0.562322i	$0.190092\pi$
$380$	0	0
$381$	2.78960	0.142915
$382$	−1.30641	−0.0668416
$383$	31.0505	1.58661	0.793304	−	0.608825i	$-0.208359\pi$
$383$	31.0505	1.58661	0.793304	+	0.608825i	$0.208359\pi$
$384$	3.19856	0.163226
$385$	0	0
$386$	2.69829	0.137339
$387$	3.20792	0.163068
$388$	−17.9097	−0.909225
$389$	−4.52827	−0.229592	−0.114796	−	0.993389i	$-0.536622\pi$
$389$	−4.52827	−0.229592	−0.114796	+	0.993389i	$0.536622\pi$
$390$	0	0
$391$	−6.01809	−0.304348
$392$	0.691574	0.0349298
$393$	1.81547	0.0915781
$394$	3.35448	0.168996
$395$	0	0
$396$	6.11641	0.307361
$397$	14.6499	0.735257	0.367628	−	0.929973i	$-0.380170\pi$
$397$	14.6499	0.735257	0.367628	+	0.929973i	$0.380170\pi$
$398$	1.66596	0.0835071
$399$	1.90727	0.0954827
$400$	0	0
$401$	22.8613	1.14164	0.570820	−	0.821076i	$-0.306626\pi$
$401$	22.8613	1.14164	0.570820	+	0.821076i	$0.306626\pi$
$402$	1.54108	0.0768620
$403$	3.82344	0.190459
$404$	18.8437	0.937507
$405$	0	0
$406$	−0.0968899	−0.00480856
$407$	−4.60434	−0.228229
$408$	−2.48117	−0.122836
$409$	−24.7804	−1.22531	−0.612655	−	0.790350i	$-0.709898\pi$
$409$	−24.7804	−1.22531	−0.612655	+	0.790350i	$0.709898\pi$
$410$	0	0
$411$	−5.04778	−0.248989
$412$	5.76416	0.283980
$413$	8.40968	0.413813
$414$	0.460730	0.0226436
$415$	0	0
$416$	−1.47882	−0.0725053
$417$	−6.47354	−0.317010
$418$	−0.654465	−0.0320109
$419$	−21.2911	−1.04014	−0.520070	−	0.854124i	$-0.674094\pi$
$419$	−21.2911	−1.04014	−0.520070	+	0.854124i	$0.674094\pi$
$420$	0	0
$421$	−14.4634	−0.704904	−0.352452	−	0.935830i	$-0.614652\pi$
$421$	−14.4634	−0.704904	−0.352452	+	0.935830i	$0.614652\pi$
$422$	−4.49444	−0.218786
$423$	6.06856	0.295063
$424$	2.05373	0.0997381
$425$	0	0
$426$	−0.995377	−0.0482262
$427$	−1.23807	−0.0599144
$428$	−7.61714	−0.368189
$429$	0.505358	0.0243989
$430$	0	0
$431$	26.3309	1.26831	0.634157	−	0.773204i	$-0.281347\pi$
$431$	26.3309	1.26831	0.634157	+	0.773204i	$0.281347\pi$
$432$	−12.8505	−0.618271
$433$	4.99714	0.240147	0.120074	−	0.992765i	$-0.461687\pi$
$433$	4.99714	0.240147	0.120074	+	0.992765i	$0.461687\pi$
$434$	−0.922674	−0.0442898
$435$	0	0
$436$	8.53545	0.408774
$437$	3.19928	0.153042
$438$	1.56681	0.0748649
$439$	26.8145	1.27979	0.639894	−	0.768463i	$-0.278978\pi$
$439$	26.8145	1.27979	0.639894	+	0.768463i	$0.278978\pi$
$440$	0	0
$441$	−2.64460	−0.125933
$442$	0.756899	0.0360020
$443$	−6.63516	−0.315246	−0.157623	−	0.987499i	$-0.550383\pi$
$443$	−6.63516	−0.315246	−0.157623	+	0.987499i	$0.550383\pi$
$444$	4.60434	0.218512
$445$	0	0
$446$	1.76504	0.0835770
$447$	−5.60315	−0.265020
$448$	−7.28076	−0.343984
$449$	−8.82734	−0.416588	−0.208294	−	0.978066i	$-0.566791\pi$
$449$	−8.82734	−0.416588	−0.208294	+	0.978066i	$0.566791\pi$
$450$	0	0
$451$	−2.73184	−0.128637
$452$	21.6064	1.01628
$453$	4.58784	0.215556
$454$	3.35587	0.157499
$455$	0	0
$456$	1.31902	0.0617685
$457$	21.6890	1.01457	0.507284	−	0.861779i	$-0.330650\pi$
$457$	21.6890	1.01457	0.507284	+	0.861779i	$0.330650\pi$
$458$	−2.13762	−0.0998844
$459$	20.2512	0.945246
$460$	0	0
$461$	21.4317	0.998173	0.499086	−	0.866552i	$-0.333669\pi$
$461$	21.4317	0.998173	0.499086	+	0.866552i	$0.333669\pi$
$462$	−0.121953	−0.00567378
$463$	7.22468	0.335759	0.167880	−	0.985807i	$-0.446308\pi$
$463$	7.22468	0.335759	0.167880	+	0.985807i	$0.446308\pi$
$464$	2.12383	0.0985964
$465$	0	0
$466$	4.68053	0.216821
$467$	−28.6810	−1.32720	−0.663600	−	0.748087i	$-0.730972\pi$
$467$	−28.6810	−1.32720	−0.663600	+	0.748087i	$0.730972\pi$
$468$	3.76046	0.173827
$469$	−14.8381	−0.685161
$470$	0	0
$471$	−6.50414	−0.299695
$472$	5.81592	0.267699
$473$	−1.42433	−0.0654908
$474$	0.715680	0.0328723
$475$	0	0
$476$	11.8535	0.543306
$477$	−7.85353	−0.359589
$478$	−5.24622	−0.239956
$479$	27.6145	1.26174	0.630870	−	0.775888i	$-0.282698\pi$
$479$	27.6145	1.26174	0.630870	+	0.775888i	$0.282698\pi$
$480$	0	0
$481$	−2.83082	−0.129074
$482$	3.91915	0.178512
$483$	0.596155	0.0271260
$484$	18.9504	0.861383
$485$	0	0
$486$	−2.37438	−0.107704
$487$	−8.72314	−0.395283	−0.197642	−	0.980274i	$-0.563328\pi$
$487$	−8.72314	−0.395283	−0.197642	+	0.980274i	$0.563328\pi$
$488$	−0.856217	−0.0387591
$489$	−2.06313	−0.0932980
$490$	0	0
$491$	23.5791	1.06411	0.532054	−	0.846710i	$-0.321420\pi$
$491$	23.5791	1.06411	0.532054	+	0.846710i	$0.321420\pi$
$492$	2.73184	0.123161
$493$	−3.34696	−0.150740
$494$	−0.402375	−0.0181037
$495$	0	0
$496$	20.2251	0.908133
$497$	9.58390	0.429897
$498$	−0.508789	−0.0227994
$499$	−22.3220	−0.999269	−0.499635	−	0.866236i	$-0.666532\pi$
$499$	−22.3220	−0.999269	−0.499635	+	0.866236i	$0.666532\pi$
$500$	0	0
$501$	3.85547	0.172250
$502$	−0.923677	−0.0412257
$503$	21.5870	0.962519	0.481259	−	0.876578i	$-0.340179\pi$
$503$	21.5870	0.962519	0.481259	+	0.876578i	$0.340179\pi$
$504$	−1.82894	−0.0814673
$505$	0	0
$506$	−0.204566	−0.00909409
$507$	−7.43931	−0.330391
$508$	−9.21661	−0.408921
$509$	43.7057	1.93722	0.968610	−	0.248585i	$-0.0799656\pi$
$509$	43.7057	1.93722	0.968610	+	0.248585i	$0.0799656\pi$
$510$	0	0
$511$	−15.0858	−0.667359
$512$	−13.1046	−0.579148
$513$	−10.7657	−0.475319
$514$	−0.0193081	−0.000851644 0
$515$	0	0
$516$	1.42433	0.0627027
$517$	−2.69447	−0.118503
$518$	0.683134	0.0300152
$519$	7.01293	0.307834
$520$	0	0
$521$	8.97662	0.393273	0.196636	−	0.980476i	$-0.436998\pi$
$521$	8.97662	0.393273	0.196636	+	0.980476i	$0.436998\pi$
$522$	0.256235	0.0112151
$523$	−22.7975	−0.996863	−0.498432	−	0.866929i	$-0.666090\pi$
$523$	−22.7975	−0.996863	−0.498432	+	0.866929i	$0.666090\pi$
$524$	−5.99816	−0.262031
$525$	0	0
$526$	0.413741	0.0180400
$527$	−31.8728	−1.38840
$528$	2.67322	0.116337
$529$	1.00000	0.0434783
$530$	0	0
$531$	−22.2402	−0.965144
$532$	−6.30146	−0.273203
$533$	−1.67957	−0.0727504
$534$	0.877252	0.0379624
$535$	0	0
$536$	−10.2617	−0.443236
$537$	−2.74678	−0.118532
$538$	2.68192	0.115626
$539$	1.17422	0.0505770
$540$	0	0
$541$	−43.9512	−1.88961	−0.944804	−	0.327635i	$-0.893748\pi$
$541$	−43.9512	−1.88961	−0.944804	+	0.327635i	$0.893748\pi$
$542$	1.17404	0.0504294
$543$	−13.6747	−0.586837
$544$	12.3277	0.528547
$545$	0	0
$546$	−0.0749787	−0.00320879
$547$	41.4774	1.77345	0.886724	−	0.462300i	$-0.152976\pi$
$547$	41.4774	1.77345	0.886724	+	0.462300i	$0.152976\pi$
$548$	16.6775	0.712426
$549$	3.27420	0.139739
$550$	0	0
$551$	1.77928	0.0757998
$552$	0.412285	0.0175480
$553$	−6.89085	−0.293029
$554$	−4.16251	−0.176848
$555$	0	0
$556$	21.3881	0.907056
$557$	30.3545	1.28616	0.643081	−	0.765798i	$-0.277656\pi$
$557$	30.3545	1.28616	0.643081	+	0.765798i	$0.277656\pi$
$558$	2.44010	0.103298
$559$	−0.875700	−0.0370382
$560$	0	0
$561$	−4.21275	−0.177862
$562$	3.48470	0.146993
$563$	−7.51949	−0.316909	−0.158454	−	0.987366i	$-0.550651\pi$
$563$	−7.51949	−0.316909	−0.158454	+	0.987366i	$0.550651\pi$
$564$	2.69447	0.113458
$565$	0	0
$566$	1.41182	0.0593431
$567$	5.92771	0.248940
$568$	6.62798	0.278104
$569$	0.125221	0.00524955	0.00262478	−	0.999997i	$-0.499165\pi$
$569$	0.125221	0.00524955	0.00262478	+	0.999997i	$0.499165\pi$
$570$	0	0
$571$	8.31788	0.348093	0.174046	−	0.984737i	$-0.444316\pi$
$571$	8.31788	0.348093	0.174046	+	0.984737i	$0.444316\pi$
$572$	−1.66966	−0.0698121
$573$	4.47044	0.186755
$574$	0.405316	0.0169175
$575$	0	0
$576$	19.2547	0.802279
$577$	4.61706	0.192211	0.0961054	−	0.995371i	$-0.469361\pi$
$577$	4.61706	0.192211	0.0961054	+	0.995371i	$0.469361\pi$
$578$	−3.34798	−0.139258
$579$	−9.23338	−0.383726
$580$	0	0
$581$	4.89883	0.203238
$582$	−0.944374	−0.0391456
$583$	3.48701	0.144417
$584$	−10.4330	−0.431720
$585$	0	0
$586$	2.20629	0.0911411
$587$	10.3803	0.428440	0.214220	−	0.976785i	$-0.431279\pi$
$587$	10.3803	0.428440	0.214220	+	0.976785i	$0.431279\pi$
$588$	−1.17422	−0.0484238
$589$	16.9439	0.698162
$590$	0	0
$591$	−11.4788	−0.472176
$592$	−14.9744	−0.615442
$593$	22.4904	0.923571	0.461785	−	0.886992i	$-0.347209\pi$
$593$	22.4904	0.923571	0.461785	+	0.886992i	$0.347209\pi$
$594$	0.688377	0.0282445
$595$	0	0
$596$	18.5124	0.758296
$597$	−5.70082	−0.233319
$598$	−0.125771	−0.00514314
$599$	−28.3772	−1.15946	−0.579730	−	0.814808i	$-0.696842\pi$
$599$	−28.3772	−1.15946	−0.579730	+	0.814808i	$0.696842\pi$
$600$	0	0
$601$	−2.53008	−0.103204	−0.0516021	−	0.998668i	$-0.516433\pi$
$601$	−2.53008	−0.103204	−0.0516021	+	0.998668i	$0.516433\pi$
$602$	0.211324	0.00861294
$603$	39.2409	1.59801
$604$	−15.1579	−0.616766
$605$	0	0
$606$	0.993624	0.0403632
$607$	22.3618	0.907636	0.453818	−	0.891094i	$-0.350062\pi$
$607$	22.3618	0.907636	0.453818	+	0.891094i	$0.350062\pi$
$608$	−6.55355	−0.265781
$609$	0.331551	0.0134351
$610$	0	0
$611$	−1.65660	−0.0670189
$612$	−31.3478	−1.26716
$613$	−22.7601	−0.919270	−0.459635	−	0.888108i	$-0.652020\pi$
$613$	−22.7601	−0.919270	−0.459635	+	0.888108i	$0.652020\pi$
$614$	−0.162719	−0.00656681
$615$	0	0
$616$	0.812057	0.0327187
$617$	25.3972	1.02245	0.511227	−	0.859446i	$-0.329191\pi$
$617$	25.3972	1.02245	0.511227	+	0.859446i	$0.329191\pi$
$618$	0.303944	0.0122264
$619$	−48.2862	−1.94079	−0.970394	−	0.241529i	$-0.922351\pi$
$619$	−48.2862	−1.94079	−0.970394	+	0.241529i	$0.922351\pi$
$620$	0	0
$621$	−3.36505	−0.135035
$622$	1.15722	0.0464003
$623$	−8.44653	−0.338403
$624$	1.64354	0.0657942
$625$	0	0
$626$	−2.99077	−0.119535
$627$	2.23954	0.0894386
$628$	21.4892	0.857512
$629$	23.5982	0.940921
$630$	0	0
$631$	−10.4465	−0.415870	−0.207935	−	0.978143i	$-0.566674\pi$
$631$	−10.4465	−0.415870	−0.207935	+	0.978143i	$0.566674\pi$
$632$	−4.76554	−0.189563
$633$	15.3797	0.611289
$634$	2.38671	0.0947883
$635$	0	0
$636$	−3.48701	−0.138269
$637$	0.721925	0.0286037
$638$	−0.113770	−0.00450418
$639$	−25.3456	−1.00266
$640$	0	0
$641$	24.8980	0.983411	0.491706	−	0.870761i	$-0.336374\pi$
$641$	24.8980	0.983411	0.491706	+	0.870761i	$0.336374\pi$
$642$	−0.401651	−0.0158519
$643$	−1.39642	−0.0550695	−0.0275348	−	0.999621i	$-0.508766\pi$
$643$	−1.39642	−0.0550695	−0.0275348	+	0.999621i	$0.508766\pi$
$644$	−1.96965	−0.0776150
$645$	0	0
$646$	3.35427	0.131972
$647$	25.7481	1.01226	0.506131	−	0.862457i	$-0.331075\pi$
$647$	25.7481	1.01226	0.506131	+	0.862457i	$0.331075\pi$
$648$	4.09945	0.161042
$649$	9.87478	0.387619
$650$	0	0
$651$	3.15734	0.123746
$652$	6.81642	0.266952
$653$	−7.95236	−0.311200	−0.155600	−	0.987820i	$-0.549731\pi$
$653$	−7.95236	−0.311200	−0.155600	+	0.987820i	$0.549731\pi$
$654$	0.450073	0.0175993
$655$	0	0
$656$	−8.88455	−0.346883
$657$	39.8960	1.55649
$658$	0.399772	0.0155847
$659$	9.94173	0.387275	0.193637	−	0.981073i	$-0.437971\pi$
$659$	9.94173	0.387275	0.193637	+	0.981073i	$0.437971\pi$
$660$	0	0
$661$	39.5802	1.53949	0.769747	−	0.638350i	$-0.220383\pi$
$661$	39.5802	1.53949	0.769747	+	0.638350i	$0.220383\pi$
$662$	2.96961	0.115417
$663$	−2.59006	−0.100590
$664$	3.38790	0.131476
$665$	0	0
$666$	−1.80662	−0.0700050
$667$	0.556150	0.0215342
$668$	−12.7382	−0.492855
$669$	−6.03985	−0.233514
$670$	0	0
$671$	−1.45376	−0.0561218
$672$	−1.22119	−0.0471084
$673$	5.74115	0.221305	0.110653	−	0.993859i	$-0.464706\pi$
$673$	5.74115	0.221305	0.110653	+	0.993859i	$0.464706\pi$
$674$	−0.311615	−0.0120030
$675$	0	0
$676$	24.5789	0.945342
$677$	7.67945	0.295145	0.147573	−	0.989051i	$-0.452854\pi$
$677$	7.67945	0.295145	0.147573	+	0.989051i	$0.452854\pi$
$678$	1.13930	0.0437546
$679$	9.09282	0.348950
$680$	0	0
$681$	−11.4836	−0.440052
$682$	−1.08342	−0.0414862
$683$	35.3019	1.35079	0.675395	−	0.737456i	$-0.263973\pi$
$683$	35.3019	1.35079	0.675395	+	0.737456i	$0.263973\pi$
$684$	16.6648	0.637196
$685$	0	0
$686$	−0.174215	−0.00665158
$687$	7.31480	0.279077
$688$	−4.63225	−0.176603
$689$	2.14386	0.0816747
$690$	0	0
$691$	−27.8750	−1.06041	−0.530207	−	0.847868i	$-0.677886\pi$
$691$	−27.8750	−1.06041	−0.530207	+	0.847868i	$0.677886\pi$
$692$	−23.1702	−0.880798
$693$	−3.10533	−0.117962
$694$	2.13458	0.0810276
$695$	0	0
$696$	0.229292	0.00869130
$697$	14.0012	0.530334
$698$	3.03732	0.114964
$699$	−16.0165	−0.605799
$700$	0	0
$701$	−45.1399	−1.70491	−0.852456	−	0.522800i	$-0.824888\pi$
$701$	−45.1399	−1.70491	−0.852456	+	0.522800i	$0.824888\pi$
$702$	0.423225	0.0159736
$703$	−12.5450	−0.473145
$704$	−8.54918	−0.322209
$705$	0	0
$706$	4.39668	0.165471
$707$	−9.56702	−0.359805
$708$	−9.87478	−0.371117
$709$	2.77399	0.104179	0.0520897	−	0.998642i	$-0.483412\pi$
$709$	2.77399	0.104179	0.0520897	+	0.998642i	$0.483412\pi$
$710$	0	0
$711$	18.2235	0.683436
$712$	−5.84141	−0.218916
$713$	5.29617	0.198343
$714$	0.625035	0.0233914
$715$	0	0
$716$	9.07514	0.339154
$717$	17.9522	0.670438
$718$	−1.76173	−0.0657473
$719$	−2.30704	−0.0860380	−0.0430190	−	0.999074i	$-0.513698\pi$
$719$	−2.30704	−0.0860380	−0.0430190	+	0.999074i	$0.513698\pi$
$720$	0	0
$721$	−2.92649	−0.108988
$722$	1.52693	0.0568265
$723$	−13.4111	−0.498764
$724$	45.1801	1.67911
$725$	0	0
$726$	0.999253	0.0370858
$727$	37.4857	1.39027	0.695135	−	0.718880i	$-0.255345\pi$
$727$	37.4857	1.39027	0.695135	+	0.718880i	$0.255345\pi$
$728$	0.499265	0.0185040
$729$	−9.65813	−0.357709
$730$	0	0
$731$	7.29999	0.270000
$732$	1.45376	0.0537325
$733$	−5.11909	−0.189078	−0.0945390	−	0.995521i	$-0.530138\pi$
$733$	−5.11909	−0.189078	−0.0945390	+	0.995521i	$0.530138\pi$
$734$	3.72021	0.137315
$735$	0	0
$736$	−2.04844	−0.0755067
$737$	−17.4232	−0.641790
$738$	−1.07190	−0.0394571
$739$	20.6970	0.761350	0.380675	−	0.924709i	$-0.375692\pi$
$739$	20.6970	0.761350	0.380675	+	0.924709i	$0.375692\pi$
$740$	0	0
$741$	1.37690	0.0505818
$742$	−0.517359	−0.0189928
$743$	−5.91932	−0.217159	−0.108579	−	0.994088i	$-0.534630\pi$
$743$	−5.91932	−0.217159	−0.108579	+	0.994088i	$0.534630\pi$
$744$	2.18353	0.0800522
$745$	0	0
$746$	2.21805	0.0812087
$747$	−12.9554	−0.474014
$748$	13.9186	0.508914
$749$	3.86726	0.141307
$750$	0	0
$751$	−24.2071	−0.883330	−0.441665	−	0.897180i	$-0.645612\pi$
$751$	−24.2071	−0.883330	−0.441665	+	0.897180i	$0.645612\pi$
$752$	−8.76303	−0.319555
$753$	3.16077	0.115185
$754$	−0.0699472	−0.00254733
$755$	0	0
$756$	6.62798	0.241057
$757$	20.2899	0.737451	0.368725	−	0.929538i	$-0.379794\pi$
$757$	20.2899	0.737451	0.368725	+	0.929538i	$0.379794\pi$
$758$	−5.60917	−0.203734
$759$	0.700014	0.0254089
$760$	0	0
$761$	−29.7815	−1.07958	−0.539789	−	0.841800i	$-0.681496\pi$
$761$	−29.7815	−1.07958	−0.539789	+	0.841800i	$0.681496\pi$
$762$	−0.485991	−0.0176056
$763$	−4.33349	−0.156883
$764$	−14.7700	−0.534360
$765$	0	0
$766$	−5.40948	−0.195453
$767$	6.07116	0.219217
$768$	8.12368	0.293138
$769$	18.2916	0.659612	0.329806	−	0.944049i	$-0.393017\pi$
$769$	18.2916	0.659612	0.329806	+	0.944049i	$0.393017\pi$
$770$	0	0
$771$	0.0660711	0.00237949
$772$	30.5064	1.09795
$773$	−16.8609	−0.606445	−0.303223	−	0.952920i	$-0.598063\pi$
$773$	−16.8609	−0.606445	−0.303223	+	0.952920i	$0.598063\pi$
$774$	−0.558869	−0.0200881
$775$	0	0
$776$	6.28836	0.225739
$777$	−2.33764	−0.0838625
$778$	0.788895	0.0282833
$779$	−7.44319	−0.266680
$780$	0	0
$781$	11.2536	0.402684
$782$	1.04844	0.0374923
$783$	−1.87147	−0.0668810
$784$	3.81882	0.136386
$785$	0	0
$786$	−0.316282	−0.0112814
$787$	35.7572	1.27461	0.637303	−	0.770613i	$-0.280050\pi$
$787$	35.7572	1.27461	0.637303	+	0.770613i	$0.280050\pi$
$788$	37.9251	1.35103
$789$	−1.41580	−0.0504037
$790$	0	0
$791$	−10.9696	−0.390036
$792$	−2.14757	−0.0763104
$793$	−0.893794	−0.0317395
$794$	−2.55224	−0.0905755
$795$	0	0
$796$	18.8351	0.667591
$797$	42.1705	1.49376	0.746878	−	0.664962i	$-0.231552\pi$
$797$	42.1705	1.49376	0.746878	+	0.664962i	$0.231552\pi$
$798$	−0.332275	−0.0117624
$799$	13.8097	0.488552
$800$	0	0
$801$	22.3377	0.789264
$802$	−3.98279	−0.140637
$803$	−17.7140	−0.625115
$804$	17.4232	0.614467
$805$	0	0
$806$	−0.666102	−0.0234624
$807$	−9.17737	−0.323059
$808$	−6.61630	−0.232761
$809$	−54.1750	−1.90469	−0.952346	−	0.305020i	$-0.901337\pi$
$809$	−54.1750	−1.90469	−0.952346	+	0.305020i	$0.901337\pi$
$810$	0	0
$811$	−7.85022	−0.275658	−0.137829	−	0.990456i	$-0.544013\pi$
$811$	−7.85022	−0.275658	−0.137829	+	0.990456i	$0.544013\pi$
$812$	−1.09542	−0.0384417
$813$	−4.01750	−0.140900
$814$	0.802147	0.0281152
$815$	0	0
$816$	−13.7008	−0.479625
$817$	−3.88075	−0.135770
$818$	4.31712	0.150945
$819$	−1.90920	−0.0667130
$820$	0	0
$821$	34.4168	1.20116	0.600578	−	0.799567i	$-0.294937\pi$
$821$	34.4168	1.20116	0.600578	+	0.799567i	$0.294937\pi$
$822$	0.879401	0.0306726
$823$	−41.8654	−1.45934	−0.729668	−	0.683801i	$-0.760326\pi$
$823$	−41.8654	−1.45934	−0.729668	+	0.683801i	$0.760326\pi$
$824$	−2.02389	−0.0705054
$825$	0	0
$826$	−1.46510	−0.0509772
$827$	−7.62651	−0.265200	−0.132600	−	0.991170i	$-0.542333\pi$
$827$	−7.62651	−0.265200	−0.132600	+	0.991170i	$0.542333\pi$
$828$	5.20893	0.181023
$829$	2.82037	0.0979554	0.0489777	−	0.998800i	$-0.484404\pi$
$829$	2.82037	0.0979554	0.0489777	+	0.998800i	$0.484404\pi$
$830$	0	0
$831$	14.2438	0.494114
$832$	−5.25616	−0.182225
$833$	−6.01809	−0.208515
$834$	1.12779	0.0390522
$835$	0	0
$836$	−7.39927	−0.255909
$837$	−17.8219	−0.616015
$838$	3.70925	0.128134
$839$	42.4484	1.46548	0.732740	−	0.680509i	$-0.238241\pi$
$839$	42.4484	1.46548	0.732740	+	0.680509i	$0.238241\pi$
$840$	0	0
$841$	−28.6907	−0.989334
$842$	2.51975	0.0868363
$843$	−11.9244	−0.410699
$844$	−50.8134	−1.74907
$845$	0	0
$846$	−1.05724	−0.0363485
$847$	−9.62122	−0.330589
$848$	11.3405	0.389436
$849$	−4.83115	−0.165805
$850$	0	0
$851$	−3.92120	−0.134417
$852$	−11.2536	−0.385541
$853$	−37.3761	−1.27973	−0.639866	−	0.768486i	$-0.721010\pi$
$853$	−37.3761	−1.27973	−0.639866	+	0.768486i	$0.721010\pi$
$854$	0.215691	0.00738079
$855$	0	0
$856$	2.67450	0.0914124
$857$	24.1143	0.823727	0.411864	−	0.911245i	$-0.364878\pi$
$857$	24.1143	0.823727	0.411864	+	0.911245i	$0.364878\pi$
$858$	−0.0880411	−0.00300567
$859$	−15.2902	−0.521695	−0.260847	−	0.965380i	$-0.584002\pi$
$859$	−15.2902	−0.521695	−0.260847	+	0.965380i	$0.584002\pi$
$860$	0	0
$861$	−1.38697	−0.0472677
$862$	−4.58725	−0.156242
$863$	4.00055	0.136180	0.0680901	−	0.997679i	$-0.478309\pi$
$863$	4.00055	0.136180	0.0680901	+	0.997679i	$0.478309\pi$
$864$	6.89313	0.234509
$865$	0	0
$866$	−0.870579	−0.0295835
$867$	11.4566	0.389086
$868$	−10.4316	−0.354071
$869$	−8.09135	−0.274480
$870$	0	0
$871$	−10.7120	−0.362963
$872$	−2.99693	−0.101489
$873$	−24.0469	−0.813863
$874$	−0.557364	−0.0188531
$875$	0	0
$876$	17.7140	0.598502
$877$	24.9032	0.840921	0.420461	−	0.907311i	$-0.361869\pi$
$877$	24.9032	0.840921	0.420461	+	0.907311i	$0.361869\pi$
$878$	−4.67151	−0.157656
$879$	−7.54980	−0.254648
$880$	0	0
$881$	−20.1237	−0.677985	−0.338993	−	0.940789i	$-0.610086\pi$
$881$	−20.1237	−0.677985	−0.338993	+	0.940789i	$0.610086\pi$
$882$	0.460730	0.0155136
$883$	−30.3303	−1.02070	−0.510348	−	0.859968i	$-0.670483\pi$
$883$	−30.3303	−1.02070	−0.510348	+	0.859968i	$0.670483\pi$
$884$	8.55736	0.287815
$885$	0	0
$886$	1.15595	0.0388348
$887$	24.0672	0.808096	0.404048	−	0.914738i	$-0.367603\pi$
$887$	24.0672	0.808096	0.404048	+	0.914738i	$0.367603\pi$
$888$	−1.61665	−0.0542514
$889$	4.67932	0.156939
$890$	0	0
$891$	6.96040	0.233182
$892$	19.9552	0.668150
$893$	−7.34138	−0.245670
$894$	0.976155	0.0326475
$895$	0	0
$896$	5.36531	0.179242
$897$	0.430379	0.0143699
$898$	1.53786	0.0513190
$899$	2.94546	0.0982367
$900$	0	0
$901$	−17.8716	−0.595390
$902$	0.475928	0.0158467
$903$	−0.723139	−0.0240646
$904$	−7.58633	−0.252317
$905$	0	0
$906$	−0.799273	−0.0265541
$907$	−22.3417	−0.741843	−0.370922	−	0.928664i	$-0.620958\pi$
$907$	−22.3417	−0.741843	−0.370922	+	0.928664i	$0.620958\pi$
$908$	37.9408	1.25911
$909$	25.3009	0.839179
$910$	0	0
$911$	−59.5221	−1.97206	−0.986028	−	0.166578i	$-0.946728\pi$
$911$	−59.5221	−1.97206	−0.986028	+	0.166578i	$0.946728\pi$
$912$	7.28349	0.241181
$913$	5.75228	0.190373
$914$	−3.77855	−0.124983
$915$	0	0
$916$	−24.1675	−0.798518
$917$	3.04529	0.100564
$918$	−3.52807	−0.116444
$919$	20.3269	0.670522	0.335261	−	0.942125i	$-0.391175\pi$
$919$	20.3269	0.670522	0.335261	+	0.942125i	$0.391175\pi$
$920$	0	0
$921$	0.556815	0.0183477
$922$	−3.73373	−0.122964
$923$	6.91886	0.227737
$924$	−1.37878	−0.0453586
$925$	0	0
$926$	−1.25865	−0.0413618
$927$	7.73940	0.254195
$928$	−1.13924	−0.0373974
$929$	27.8194	0.912723	0.456362	−	0.889794i	$-0.349152\pi$
$929$	27.8194	0.912723	0.456362	+	0.889794i	$0.349152\pi$
$930$	0	0
$931$	3.19928	0.104852
$932$	52.9173	1.73336
$933$	−3.95994	−0.129642
$934$	4.99668	0.163496
$935$	0	0
$936$	−1.32036	−0.0431572
$937$	−14.6270	−0.477844	−0.238922	−	0.971039i	$-0.576794\pi$
$937$	−14.6270	−0.477844	−0.238922	+	0.971039i	$0.576794\pi$
$938$	2.58503	0.0844042
$939$	10.2342	0.333981
$940$	0	0
$941$	−29.6197	−0.965576	−0.482788	−	0.875737i	$-0.660376\pi$
$941$	−29.6197	−0.965576	−0.482788	+	0.875737i	$0.660376\pi$
$942$	1.13312	0.0369191
$943$	−2.32652	−0.0757619
$944$	32.1150	1.04525
$945$	0	0
$946$	0.248140	0.00806774
$947$	−2.68088	−0.0871169	−0.0435585	−	0.999051i	$-0.513869\pi$
$947$	−2.68088	−0.0871169	−0.0435585	+	0.999051i	$0.513869\pi$
$948$	8.09135	0.262795
$949$	−10.8909	−0.353532
$950$	0	0
$951$	−8.16717	−0.264839
$952$	−4.16196	−0.134890
$953$	25.6941	0.832314	0.416157	−	0.909293i	$-0.363377\pi$
$953$	25.6941	0.832314	0.416157	+	0.909293i	$0.363377\pi$
$954$	1.36821	0.0442973
$955$	0	0
$956$	−59.3128	−1.91831
$957$	0.389313	0.0125847
$958$	−4.81088	−0.155432
$959$	−8.46723	−0.273421
$960$	0	0
$961$	−2.95060	−0.0951805
$962$	0.493172	0.0159005
$963$	−10.2274	−0.329572
$964$	44.3092	1.42710
$965$	0	0
$966$	−0.103859	−0.00334162
$967$	45.7344	1.47072	0.735360	−	0.677677i	$-0.237013\pi$
$967$	45.7344	1.47072	0.735360	+	0.677677i	$0.237013\pi$
$968$	−6.65379	−0.213861
$969$	−11.4781	−0.368730
$970$	0	0
$971$	16.2728	0.522219	0.261109	−	0.965309i	$-0.415912\pi$
$971$	16.2728	0.522219	0.261109	+	0.965309i	$0.415912\pi$
$972$	−26.8443	−0.861032
$973$	−10.8588	−0.348118
$974$	1.51971	0.0486945
$975$	0	0
$976$	−4.72796	−0.151338
$977$	−0.364375	−0.0116574	−0.00582870	−	0.999983i	$-0.501855\pi$
$977$	−0.364375	−0.0116574	−0.00582870	+	0.999983i	$0.501855\pi$
$978$	0.359429	0.0114933
$979$	−9.91805	−0.316982
$980$	0	0
$981$	11.4603	0.365901
$982$	−4.10784	−0.131086
$983$	−28.6938	−0.915190	−0.457595	−	0.889161i	$-0.651289\pi$
$983$	−28.6938	−0.915190	−0.457595	+	0.889161i	$0.651289\pi$
$984$	−0.959190	−0.0305778
$985$	0	0
$986$	0.583092	0.0185694
$987$	−1.36800	−0.0435438
$988$	−4.54918	−0.144729
$989$	−1.21301	−0.0385714
$990$	0	0
$991$	−52.2867	−1.66094	−0.830471	−	0.557063i	$-0.811928\pi$
$991$	−52.2867	−1.66094	−0.830471	+	0.557063i	$0.811928\pi$
$992$	−10.8489	−0.344453
$993$	−10.1618	−0.322476
$994$	−1.66966	−0.0529585
$995$	0	0
$996$	−5.75228	−0.182268
$997$	42.9033	1.35876	0.679380	−	0.733787i	$-0.262249\pi$
$997$	42.9033	1.35876	0.679380	+	0.733787i	$0.262249\pi$
$998$	3.88883	0.123099
$999$	13.1951	0.417473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.l.1.3		4
5.4	even	2		805.2.a.j.1.2	✓	4
15.14	odd	2		7245.2.a.bc.1.3		4
35.34	odd	2		5635.2.a.w.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.j.1.2	✓	4	5.4	even	2
4025.2.a.l.1.3		4	1.1	even	1	trivial
5635.2.a.w.1.2		4	35.34	odd	2
7245.2.a.bc.1.3		4	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.174215 q^{2} +0.596155 q^{3} -1.96965 q^{4} -0.103859 q^{6} +1.00000 q^{7} +0.691574 q^{8} -2.64460 q^{9} +O(q^{10})\)	\(q-0.174215 q^{2} +0.596155 q^{3} -1.96965 q^{4} -0.103859 q^{6} +1.00000 q^{7} +0.691574 q^{8} -2.64460 q^{9} +1.17422 q^{11} -1.17422 q^{12} +0.721925 q^{13} -0.174215 q^{14} +3.81882 q^{16} -6.01809 q^{17} +0.460730 q^{18} +3.19928 q^{19} +0.596155 q^{21} -0.204566 q^{22} +1.00000 q^{23} +0.412285 q^{24} -0.125771 q^{26} -3.36505 q^{27} -1.96965 q^{28} +0.556150 q^{29} +5.29617 q^{31} -2.04844 q^{32} +0.700014 q^{33} +1.04844 q^{34} +5.20893 q^{36} -3.92120 q^{37} -0.557364 q^{38} +0.430379 q^{39} -2.32652 q^{41} -0.103859 q^{42} -1.21301 q^{43} -2.31279 q^{44} -0.174215 q^{46} -2.29470 q^{47} +2.27660 q^{48} +1.00000 q^{49} -3.58771 q^{51} -1.42194 q^{52} +2.96965 q^{53} +0.586244 q^{54} +0.691574 q^{56} +1.90727 q^{57} -0.0968899 q^{58} +8.40968 q^{59} -1.23807 q^{61} -0.922674 q^{62} -2.64460 q^{63} -7.28076 q^{64} -0.121953 q^{66} -14.8381 q^{67} +11.8535 q^{68} +0.596155 q^{69} +9.58390 q^{71} -1.82894 q^{72} -15.0858 q^{73} +0.683134 q^{74} -6.30146 q^{76} +1.17422 q^{77} -0.0749787 q^{78} -6.89085 q^{79} +5.92771 q^{81} +0.405316 q^{82} +4.89883 q^{83} -1.17422 q^{84} +0.211324 q^{86} +0.331551 q^{87} +0.812057 q^{88} -8.44653 q^{89} +0.721925 q^{91} -1.96965 q^{92} +3.15734 q^{93} +0.399772 q^{94} -1.22119 q^{96} +9.09282 q^{97} -0.174215 q^{98} -3.10533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9} + 7 q^{11} - 7 q^{12} + 5 q^{13} - 3 q^{14} + q^{16} - 5 q^{17} - 2 q^{18} + 8 q^{19} - 6 q^{21} - 14 q^{22} + 4 q^{23} + 6 q^{24} - 11 q^{26} - 15 q^{27} + 3 q^{28} - 2 q^{29} - 10 q^{33} - 4 q^{34} + q^{36} - 13 q^{37} + 13 q^{38} - 13 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + 15 q^{44} - 3 q^{46} - 4 q^{47} + 23 q^{48} + 4 q^{49} - 10 q^{51} + 5 q^{52} + q^{53} + 14 q^{54} - 6 q^{56} - 19 q^{57} + 16 q^{58} - 7 q^{59} - 7 q^{61} + 15 q^{62} + 6 q^{63} + 23 q^{66} - 15 q^{67} + 11 q^{68} - 6 q^{69} + 17 q^{72} - 3 q^{73} - 2 q^{74} - 22 q^{76} + 7 q^{77} + 31 q^{78} - 14 q^{79} + 28 q^{81} - 6 q^{82} - 3 q^{83} - 7 q^{84} + 16 q^{86} + 14 q^{87} - 13 q^{88} - 11 q^{89} + 5 q^{91} + 3 q^{92} + 23 q^{93} - 19 q^{94} - 15 q^{96} - 9 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 6 * q^3 + 3 * q^4 + 4 * q^6 + 4 * q^7 - 6 * q^8 + 6 * q^9 + 7 * q^11 - 7 * q^12 + 5 * q^13 - 3 * q^14 + q^16 - 5 * q^17 - 2 * q^18 + 8 * q^19 - 6 * q^21 - 14 * q^22 + 4 * q^23 + 6 * q^24 - 11 * q^26 - 15 * q^27 + 3 * q^28 - 2 * q^29 - 10 * q^33 - 4 * q^34 + q^36 - 13 * q^37 + 13 * q^38 - 13 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + 15 * q^44 - 3 * q^46 - 4 * q^47 + 23 * q^48 + 4 * q^49 - 10 * q^51 + 5 * q^52 + q^53 + 14 * q^54 - 6 * q^56 - 19 * q^57 + 16 * q^58 - 7 * q^59 - 7 * q^61 + 15 * q^62 + 6 * q^63 + 23 * q^66 - 15 * q^67 + 11 * q^68 - 6 * q^69 + 17 * q^72 - 3 * q^73 - 2 * q^74 - 22 * q^76 + 7 * q^77 + 31 * q^78 - 14 * q^79 + 28 * q^81 - 6 * q^82 - 3 * q^83 - 7 * q^84 + 16 * q^86 + 14 * q^87 - 13 * q^88 - 11 * q^89 + 5 * q^91 + 3 * q^92 + 23 * q^93 - 19 * q^94 - 15 * q^96 - 9 * q^97 - 3 * q^98 + 8 * q^99

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