LMFDB - Embedded newform 250.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(1,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("250.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	250.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.85410 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.85410 q^{7} +1.00000 q^{8} -2.85410 q^{9} -0.763932 q^{11} +0.381966 q^{12} -3.23607 q^{13} +3.85410 q^{14} +1.00000 q^{16} +5.23607 q^{17} -2.85410 q^{18} -2.76393 q^{19} +1.47214 q^{21} -0.763932 q^{22} +5.38197 q^{23} +0.381966 q^{24} -3.23607 q^{26} -2.23607 q^{27} +3.85410 q^{28} -3.61803 q^{29} -9.70820 q^{31} +1.00000 q^{32} -0.291796 q^{33} +5.23607 q^{34} -2.85410 q^{36} -10.9443 q^{37} -2.76393 q^{38} -1.23607 q^{39} +5.61803 q^{41} +1.47214 q^{42} -6.85410 q^{43} -0.763932 q^{44} +5.38197 q^{46} -7.32624 q^{47} +0.381966 q^{48} +7.85410 q^{49} +2.00000 q^{51} -3.23607 q^{52} +12.9443 q^{53} -2.23607 q^{54} +3.85410 q^{56} -1.05573 q^{57} -3.61803 q^{58} -7.23607 q^{59} +7.85410 q^{61} -9.70820 q^{62} -11.0000 q^{63} +1.00000 q^{64} -0.291796 q^{66} +2.47214 q^{67} +5.23607 q^{68} +2.05573 q^{69} -5.23607 q^{71} -2.85410 q^{72} -3.23607 q^{73} -10.9443 q^{74} -2.76393 q^{76} -2.94427 q^{77} -1.23607 q^{78} +13.4164 q^{79} +7.70820 q^{81} +5.61803 q^{82} +7.09017 q^{83} +1.47214 q^{84} -6.85410 q^{86} -1.38197 q^{87} -0.763932 q^{88} -3.09017 q^{89} -12.4721 q^{91} +5.38197 q^{92} -3.70820 q^{93} -7.32624 q^{94} +0.381966 q^{96} +4.18034 q^{97} +7.85410 q^{98} +2.18034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + q^7 + 2 * q^8 + q^9	$ 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + q^{9} - 6 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + q^{18} - 10 q^{19} - 6 q^{21} - 6 q^{22} + 13 q^{23} + 3 q^{24} - 2 q^{26} + q^{28} - 5 q^{29} - 6 q^{31} + 2 q^{32} - 14 q^{33} + 6 q^{34} + q^{36} - 4 q^{37} - 10 q^{38} + 2 q^{39} + 9 q^{41} - 6 q^{42} - 7 q^{43} - 6 q^{44} + 13 q^{46} + q^{47} + 3 q^{48} + 9 q^{49} + 4 q^{51} - 2 q^{52} + 8 q^{53} + q^{56} - 20 q^{57} - 5 q^{58} - 10 q^{59} + 9 q^{61} - 6 q^{62} - 22 q^{63} + 2 q^{64} - 14 q^{66} - 4 q^{67} + 6 q^{68} + 22 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} - 4 q^{74} - 10 q^{76} + 12 q^{77} + 2 q^{78} + 2 q^{81} + 9 q^{82} + 3 q^{83} - 6 q^{84} - 7 q^{86} - 5 q^{87} - 6 q^{88} + 5 q^{89} - 16 q^{91} + 13 q^{92} + 6 q^{93} + q^{94} + 3 q^{96} - 14 q^{97} + 9 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + q^7 + 2 * q^8 + q^9 - 6 * q^11 + 3 * q^12 - 2 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + q^18 - 10 * q^19 - 6 * q^21 - 6 * q^22 + 13 * q^23 + 3 * q^24 - 2 * q^26 + q^28 - 5 * q^29 - 6 * q^31 + 2 * q^32 - 14 * q^33 + 6 * q^34 + q^36 - 4 * q^37 - 10 * q^38 + 2 * q^39 + 9 * q^41 - 6 * q^42 - 7 * q^43 - 6 * q^44 + 13 * q^46 + q^47 + 3 * q^48 + 9 * q^49 + 4 * q^51 - 2 * q^52 + 8 * q^53 + q^56 - 20 * q^57 - 5 * q^58 - 10 * q^59 + 9 * q^61 - 6 * q^62 - 22 * q^63 + 2 * q^64 - 14 * q^66 - 4 * q^67 + 6 * q^68 + 22 * q^69 - 6 * q^71 + q^72 - 2 * q^73 - 4 * q^74 - 10 * q^76 + 12 * q^77 + 2 * q^78 + 2 * q^81 + 9 * q^82 + 3 * q^83 - 6 * q^84 - 7 * q^86 - 5 * q^87 - 6 * q^88 + 5 * q^89 - 16 * q^91 + 13 * q^92 + 6 * q^93 + q^94 + 3 * q^96 - 14 * q^97 + 9 * q^98 - 18 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0.381966	0.155937
$7$	3.85410	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$8$	1.00000	0.353553
$9$	−2.85410	−0.951367
$10$	0	0
$11$	−0.763932	−0.230334	−0.115167	−	0.993346i	$-0.536740\pi$
$11$	−0.763932	−0.230334	−0.115167	+	0.993346i	$0.536740\pi$
$12$	0.381966	0.110264
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	3.85410	1.03005
$15$	0	0
$16$	1.00000	0.250000
$17$	5.23607	1.26993	0.634967	−	0.772540i	$-0.281014\pi$
$17$	5.23607	1.26993	0.634967	+	0.772540i	$0.281014\pi$
$18$	−2.85410	−0.672718
$19$	−2.76393	−0.634089	−0.317045	−	0.948411i	$-0.602691\pi$
$19$	−2.76393	−0.634089	−0.317045	+	0.948411i	$0.602691\pi$
$20$	0	0
$21$	1.47214	0.321246
$22$	−0.763932	−0.162871
$23$	5.38197	1.12222	0.561109	−	0.827742i	$-0.310375\pi$
$23$	5.38197	1.12222	0.561109	+	0.827742i	$0.310375\pi$
$24$	0.381966	0.0779685
$25$	0	0
$26$	−3.23607	−0.634645
$27$	−2.23607	−0.430331
$28$	3.85410	0.728357
$29$	−3.61803	−0.671852	−0.335926	−	0.941888i	$-0.609049\pi$
$29$	−3.61803	−0.671852	−0.335926	+	0.941888i	$0.609049\pi$
$30$	0	0
$31$	−9.70820	−1.74364	−0.871822	−	0.489822i	$-0.837062\pi$
$31$	−9.70820	−1.74364	−0.871822	+	0.489822i	$0.837062\pi$
$32$	1.00000	0.176777
$33$	−0.291796	−0.0507952
$34$	5.23607	0.897978
$35$	0	0
$36$	−2.85410	−0.475684
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	−2.76393	−0.448369
$39$	−1.23607	−0.197929
$40$	0	0
$41$	5.61803	0.877390	0.438695	−	0.898636i	$-0.355441\pi$
$41$	5.61803	0.877390	0.438695	+	0.898636i	$0.355441\pi$
$42$	1.47214	0.227156
$43$	−6.85410	−1.04524	−0.522620	−	0.852566i	$-0.675045\pi$
$43$	−6.85410	−1.04524	−0.522620	+	0.852566i	$0.675045\pi$
$44$	−0.763932	−0.115167
$45$	0	0
$46$	5.38197	0.793528
$47$	−7.32624	−1.06864	−0.534321	−	0.845282i	$-0.679433\pi$
$47$	−7.32624	−1.06864	−0.534321	+	0.845282i	$0.679433\pi$
$48$	0.381966	0.0551320
$49$	7.85410	1.12201
$50$	0	0
$51$	2.00000	0.280056
$52$	−3.23607	−0.448762
$53$	12.9443	1.77803	0.889016	−	0.457876i	$-0.151390\pi$
$53$	12.9443	1.77803	0.889016	+	0.457876i	$0.151390\pi$
$54$	−2.23607	−0.304290
$55$	0	0
$56$	3.85410	0.515026
$57$	−1.05573	−0.139835
$58$	−3.61803	−0.475071
$59$	−7.23607	−0.942056	−0.471028	−	0.882118i	$-0.656117\pi$
$59$	−7.23607	−0.942056	−0.471028	+	0.882118i	$0.656117\pi$
$60$	0	0
$61$	7.85410	1.00561	0.502807	−	0.864398i	$-0.332301\pi$
$61$	7.85410	1.00561	0.502807	+	0.864398i	$0.332301\pi$
$62$	−9.70820	−1.23294
$63$	−11.0000	−1.38587
$64$	1.00000	0.125000
$65$	0	0
$66$	−0.291796	−0.0359176
$67$	2.47214	0.302019	0.151010	−	0.988532i	$-0.451748\pi$
$67$	2.47214	0.302019	0.151010	+	0.988532i	$0.451748\pi$
$68$	5.23607	0.634967
$69$	2.05573	0.247481
$70$	0	0
$71$	−5.23607	−0.621407	−0.310703	−	0.950507i	$-0.600565\pi$
$71$	−5.23607	−0.621407	−0.310703	+	0.950507i	$0.600565\pi$
$72$	−2.85410	−0.336359
$73$	−3.23607	−0.378753	−0.189377	−	0.981905i	$-0.560647\pi$
$73$	−3.23607	−0.378753	−0.189377	+	0.981905i	$0.560647\pi$
$74$	−10.9443	−1.27225
$75$	0	0
$76$	−2.76393	−0.317045
$77$	−2.94427	−0.335531
$78$	−1.23607	−0.139957
$79$	13.4164	1.50946	0.754732	−	0.656033i	$-0.227767\pi$
$79$	13.4164	1.50946	0.754732	+	0.656033i	$0.227767\pi$
$80$	0	0
$81$	7.70820	0.856467
$82$	5.61803	0.620408
$83$	7.09017	0.778247	0.389124	−	0.921186i	$-0.372778\pi$
$83$	7.09017	0.778247	0.389124	+	0.921186i	$0.372778\pi$
$84$	1.47214	0.160623
$85$	0	0
$86$	−6.85410	−0.739097
$87$	−1.38197	−0.148162
$88$	−0.763932	−0.0814354
$89$	−3.09017	−0.327557	−0.163779	−	0.986497i	$-0.552368\pi$
$89$	−3.09017	−0.327557	−0.163779	+	0.986497i	$0.552368\pi$
$90$	0	0
$91$	−12.4721	−1.30744
$92$	5.38197	0.561109
$93$	−3.70820	−0.384523
$94$	−7.32624	−0.755644
$95$	0	0
$96$	0.381966	0.0389842
$97$	4.18034	0.424449	0.212225	−	0.977221i	$-0.431929\pi$
$97$	4.18034	0.424449	0.212225	+	0.977221i	$0.431929\pi$
$98$	7.85410	0.793384
$99$	2.18034	0.219132
$100$	0	0
$101$	10.6180	1.05653	0.528267	−	0.849078i	$-0.322842\pi$
$101$	10.6180	1.05653	0.528267	+	0.849078i	$0.322842\pi$
$102$	2.00000	0.198030
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−3.23607	−0.317323
$105$	0	0
$106$	12.9443	1.25726
$107$	4.38197	0.423621	0.211810	−	0.977311i	$-0.432064\pi$
$107$	4.38197	0.423621	0.211810	+	0.977311i	$0.432064\pi$
$108$	−2.23607	−0.215166
$109$	3.61803	0.346545	0.173272	−	0.984874i	$-0.444566\pi$
$109$	3.61803	0.346545	0.173272	+	0.984874i	$0.444566\pi$
$110$	0	0
$111$	−4.18034	−0.396780
$112$	3.85410	0.364178
$113$	2.29180	0.215594	0.107797	−	0.994173i	$-0.465620\pi$
$113$	2.29180	0.215594	0.107797	+	0.994173i	$0.465620\pi$
$114$	−1.05573	−0.0988780
$115$	0	0
$116$	−3.61803	−0.335926
$117$	9.23607	0.853875
$118$	−7.23607	−0.666134
$119$	20.1803	1.84993
$120$	0	0
$121$	−10.4164	−0.946946
$122$	7.85410	0.711077
$123$	2.14590	0.193489
$124$	−9.70820	−0.871822
$125$	0	0
$126$	−11.0000	−0.979958
$127$	10.5623	0.937253	0.468627	−	0.883396i	$-0.344749\pi$
$127$	10.5623	0.937253	0.468627	+	0.883396i	$0.344749\pi$
$128$	1.00000	0.0883883
$129$	−2.61803	−0.230505
$130$	0	0
$131$	−12.4721	−1.08970	−0.544848	−	0.838535i	$-0.683413\pi$
$131$	−12.4721	−1.08970	−0.544848	+	0.838535i	$0.683413\pi$
$132$	−0.291796	−0.0253976
$133$	−10.6525	−0.923687
$134$	2.47214	0.213560
$135$	0	0
$136$	5.23607	0.448989
$137$	10.7639	0.919625	0.459812	−	0.888016i	$-0.347917\pi$
$137$	10.7639	0.919625	0.459812	+	0.888016i	$0.347917\pi$
$138$	2.05573	0.174995
$139$	−13.4164	−1.13796	−0.568982	−	0.822350i	$-0.692663\pi$
$139$	−13.4164	−1.13796	−0.568982	+	0.822350i	$0.692663\pi$
$140$	0	0
$141$	−2.79837	−0.235666
$142$	−5.23607	−0.439401
$143$	2.47214	0.206730
$144$	−2.85410	−0.237842
$145$	0	0
$146$	−3.23607	−0.267819
$147$	3.00000	0.247436
$148$	−10.9443	−0.899614
$149$	13.0902	1.07239	0.536194	−	0.844095i	$-0.319861\pi$
$149$	13.0902	1.07239	0.536194	+	0.844095i	$0.319861\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	−2.76393	−0.224184
$153$	−14.9443	−1.20817
$154$	−2.94427	−0.237256
$155$	0	0
$156$	−1.23607	−0.0989646
$157$	10.7639	0.859055	0.429528	−	0.903054i	$-0.358680\pi$
$157$	10.7639	0.859055	0.429528	+	0.903054i	$0.358680\pi$
$158$	13.4164	1.06735
$159$	4.94427	0.392106
$160$	0	0
$161$	20.7426	1.63475
$162$	7.70820	0.605614
$163$	13.2705	1.03943	0.519713	−	0.854341i	$-0.326039\pi$
$163$	13.2705	1.03943	0.519713	+	0.854341i	$0.326039\pi$
$164$	5.61803	0.438695
$165$	0	0
$166$	7.09017	0.550304
$167$	−5.61803	−0.434737	−0.217368	−	0.976090i	$-0.569747\pi$
$167$	−5.61803	−0.434737	−0.217368	+	0.976090i	$0.569747\pi$
$168$	1.47214	0.113578
$169$	−2.52786	−0.194451
$170$	0	0
$171$	7.88854	0.603252
$172$	−6.85410	−0.522620
$173$	10.1803	0.773997	0.386998	−	0.922080i	$-0.373512\pi$
$173$	10.1803	0.773997	0.386998	+	0.922080i	$0.373512\pi$
$174$	−1.38197	−0.104767
$175$	0	0
$176$	−0.763932	−0.0575835
$177$	−2.76393	−0.207750
$178$	−3.09017	−0.231618
$179$	−10.6525	−0.796203	−0.398102	−	0.917341i	$-0.630331\pi$
$179$	−10.6525	−0.796203	−0.398102	+	0.917341i	$0.630331\pi$
$180$	0	0
$181$	4.56231	0.339114	0.169557	−	0.985520i	$-0.445766\pi$
$181$	4.56231	0.339114	0.169557	+	0.985520i	$0.445766\pi$
$182$	−12.4721	−0.924496
$183$	3.00000	0.221766
$184$	5.38197	0.396764
$185$	0	0
$186$	−3.70820	−0.271899
$187$	−4.00000	−0.292509
$188$	−7.32624	−0.534321
$189$	−8.61803	−0.626870
$190$	0	0
$191$	14.7639	1.06828	0.534140	−	0.845396i	$-0.320635\pi$
$191$	14.7639	1.06828	0.534140	+	0.845396i	$0.320635\pi$
$192$	0.381966	0.0275660
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	4.18034	0.300131
$195$	0	0
$196$	7.85410	0.561007
$197$	−3.70820	−0.264199	−0.132099	−	0.991236i	$-0.542172\pi$
$197$	−3.70820	−0.264199	−0.132099	+	0.991236i	$0.542172\pi$
$198$	2.18034	0.154950
$199$	−11.7082	−0.829973	−0.414986	−	0.909828i	$-0.636214\pi$
$199$	−11.7082	−0.829973	−0.414986	+	0.909828i	$0.636214\pi$
$200$	0	0
$201$	0.944272	0.0666038
$202$	10.6180	0.747082
$203$	−13.9443	−0.978696
$204$	2.00000	0.140028
$205$	0	0
$206$	4.00000	0.278693
$207$	−15.3607	−1.06764
$208$	−3.23607	−0.224381
$209$	2.11146	0.146052
$210$	0	0
$211$	−18.0000	−1.23917	−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000	−1.23917	−0.619586	+	0.784929i	$0.712699\pi$
$212$	12.9443	0.889016
$213$	−2.00000	−0.137038
$214$	4.38197	0.299545
$215$	0	0
$216$	−2.23607	−0.152145
$217$	−37.4164	−2.53999
$218$	3.61803	0.245044
$219$	−1.23607	−0.0835257
$220$	0	0
$221$	−16.9443	−1.13980
$222$	−4.18034	−0.280566
$223$	−22.3820	−1.49881	−0.749404	−	0.662113i	$-0.769660\pi$
$223$	−22.3820	−1.49881	−0.749404	+	0.662113i	$0.769660\pi$
$224$	3.85410	0.257513
$225$	0	0
$226$	2.29180	0.152448
$227$	−11.6738	−0.774815	−0.387407	−	0.921909i	$-0.626629\pi$
$227$	−11.6738	−0.774815	−0.387407	+	0.921909i	$0.626629\pi$
$228$	−1.05573	−0.0699173
$229$	−4.14590	−0.273969	−0.136984	−	0.990573i	$-0.543741\pi$
$229$	−4.14590	−0.273969	−0.136984	+	0.990573i	$0.543741\pi$
$230$	0	0
$231$	−1.12461	−0.0739940
$232$	−3.61803	−0.237536
$233$	1.23607	0.0809775	0.0404888	−	0.999180i	$-0.487109\pi$
$233$	1.23607	0.0809775	0.0404888	+	0.999180i	$0.487109\pi$
$234$	9.23607	0.603781
$235$	0	0
$236$	−7.23607	−0.471028
$237$	5.12461	0.332879
$238$	20.1803	1.30810
$239$	13.4164	0.867835	0.433918	−	0.900953i	$-0.357131\pi$
$239$	13.4164	0.867835	0.433918	+	0.900953i	$0.357131\pi$
$240$	0	0
$241$	−11.0902	−0.714381	−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902	−0.714381	−0.357190	+	0.934032i	$0.616265\pi$
$242$	−10.4164	−0.669592
$243$	9.65248	0.619207
$244$	7.85410	0.502807
$245$	0	0
$246$	2.14590	0.136817
$247$	8.94427	0.569110
$248$	−9.70820	−0.616472
$249$	2.70820	0.171625
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−11.0000	−0.692935
$253$	−4.11146	−0.258485
$254$	10.5623	0.662738
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.9443	−1.30647	−0.653234	−	0.757156i	$-0.726588\pi$
$257$	−20.9443	−1.30647	−0.653234	+	0.757156i	$0.726588\pi$
$258$	−2.61803	−0.162992
$259$	−42.1803	−2.62096
$260$	0	0
$261$	10.3262	0.639178
$262$	−12.4721	−0.770531
$263$	17.6180	1.08637	0.543187	−	0.839612i	$-0.317217\pi$
$263$	17.6180	1.08637	0.543187	+	0.839612i	$0.317217\pi$
$264$	−0.291796	−0.0179588
$265$	0	0
$266$	−10.6525	−0.653145
$267$	−1.18034	−0.0722356
$268$	2.47214	0.151010
$269$	−24.4721	−1.49209	−0.746046	−	0.665894i	$-0.768050\pi$
$269$	−24.4721	−1.49209	−0.746046	+	0.665894i	$0.768050\pi$
$270$	0	0
$271$	9.88854	0.600686	0.300343	−	0.953831i	$-0.402899\pi$
$271$	9.88854	0.600686	0.300343	+	0.953831i	$0.402899\pi$
$272$	5.23607	0.317483
$273$	−4.76393	−0.288326
$274$	10.7639	0.650273
$275$	0	0
$276$	2.05573	0.123740
$277$	10.7639	0.646742	0.323371	−	0.946272i	$-0.395184\pi$
$277$	10.7639	0.646742	0.323371	+	0.946272i	$0.395184\pi$
$278$	−13.4164	−0.804663
$279$	27.7082	1.65885
$280$	0	0
$281$	−11.0902	−0.661584	−0.330792	−	0.943704i	$-0.607316\pi$
$281$	−11.0902	−0.661584	−0.330792	+	0.943704i	$0.607316\pi$
$282$	−2.79837	−0.166641
$283$	−22.8328	−1.35727	−0.678635	−	0.734476i	$-0.737428\pi$
$283$	−22.8328	−1.35727	−0.678635	+	0.734476i	$0.737428\pi$
$284$	−5.23607	−0.310703
$285$	0	0
$286$	2.47214	0.146180
$287$	21.6525	1.27811
$288$	−2.85410	−0.168180
$289$	10.4164	0.612730
$290$	0	0
$291$	1.59675	0.0936030
$292$	−3.23607	−0.189377
$293$	0.180340	0.0105356	0.00526778	−	0.999986i	$-0.498323\pi$
$293$	0.180340	0.0105356	0.00526778	+	0.999986i	$0.498323\pi$
$294$	3.00000	0.174964
$295$	0	0
$296$	−10.9443	−0.636123
$297$	1.70820	0.0991200
$298$	13.0902	0.758293
$299$	−17.4164	−1.00722
$300$	0	0
$301$	−26.4164	−1.52262
$302$	2.00000	0.115087
$303$	4.05573	0.232995
$304$	−2.76393	−0.158522
$305$	0	0
$306$	−14.9443	−0.854307
$307$	−21.2705	−1.21397	−0.606986	−	0.794712i	$-0.707622\pi$
$307$	−21.2705	−1.21397	−0.606986	+	0.794712i	$0.707622\pi$
$308$	−2.94427	−0.167765
$309$	1.52786	0.0869171
$310$	0	0
$311$	−9.70820	−0.550502	−0.275251	−	0.961372i	$-0.588761\pi$
$311$	−9.70820	−0.550502	−0.275251	+	0.961372i	$0.588761\pi$
$312$	−1.23607	−0.0699786
$313$	27.4164	1.54967	0.774833	−	0.632165i	$-0.217834\pi$
$313$	27.4164	1.54967	0.774833	+	0.632165i	$0.217834\pi$
$314$	10.7639	0.607444
$315$	0	0
$316$	13.4164	0.754732
$317$	12.4721	0.700505	0.350252	−	0.936655i	$-0.386096\pi$
$317$	12.4721	0.700505	0.350252	+	0.936655i	$0.386096\pi$
$318$	4.94427	0.277261
$319$	2.76393	0.154750
$320$	0	0
$321$	1.67376	0.0934203
$322$	20.7426	1.15594
$323$	−14.4721	−0.805251
$324$	7.70820	0.428234
$325$	0	0
$326$	13.2705	0.734986
$327$	1.38197	0.0764229
$328$	5.61803	0.310204
$329$	−28.2361	−1.55670
$330$	0	0
$331$	5.41641	0.297713	0.148856	−	0.988859i	$-0.452441\pi$
$331$	5.41641	0.297713	0.148856	+	0.988859i	$0.452441\pi$
$332$	7.09017	0.389124
$333$	31.2361	1.71173
$334$	−5.61803	−0.307405
$335$	0	0
$336$	1.47214	0.0803116
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−2.52786	−0.137498
$339$	0.875388	0.0475446
$340$	0	0
$341$	7.41641	0.401621
$342$	7.88854	0.426564
$343$	3.29180	0.177740
$344$	−6.85410	−0.369548
$345$	0	0
$346$	10.1803	0.547298
$347$	16.6180	0.892103	0.446051	−	0.895007i	$-0.352830\pi$
$347$	16.6180	0.892103	0.446051	+	0.895007i	$0.352830\pi$
$348$	−1.38197	−0.0740812
$349$	15.8541	0.848651	0.424325	−	0.905510i	$-0.360511\pi$
$349$	15.8541	0.848651	0.424325	+	0.905510i	$0.360511\pi$
$350$	0	0
$351$	7.23607	0.386233
$352$	−0.763932	−0.0407177
$353$	−35.5967	−1.89462	−0.947312	−	0.320313i	$-0.896212\pi$
$353$	−35.5967	−1.89462	−0.947312	+	0.320313i	$0.896212\pi$
$354$	−2.76393	−0.146901
$355$	0	0
$356$	−3.09017	−0.163779
$357$	7.70820	0.407961
$358$	−10.6525	−0.563001
$359$	30.6525	1.61778	0.808888	−	0.587963i	$-0.200070\pi$
$359$	30.6525	1.61778	0.808888	+	0.587963i	$0.200070\pi$
$360$	0	0
$361$	−11.3607	−0.597931
$362$	4.56231	0.239789
$363$	−3.97871	−0.208828
$364$	−12.4721	−0.653718
$365$	0	0
$366$	3.00000	0.156813
$367$	−7.85410	−0.409981	−0.204990	−	0.978764i	$-0.565716\pi$
$367$	−7.85410	−0.409981	−0.204990	+	0.978764i	$0.565716\pi$
$368$	5.38197	0.280554
$369$	−16.0344	−0.834720
$370$	0	0
$371$	49.8885	2.59008
$372$	−3.70820	−0.192261
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	−7.32624	−0.377822
$377$	11.7082	0.603003
$378$	−8.61803	−0.443264
$379$	−5.52786	−0.283947	−0.141974	−	0.989870i	$-0.545345\pi$
$379$	−5.52786	−0.283947	−0.141974	+	0.989870i	$0.545345\pi$
$380$	0	0
$381$	4.03444	0.206691
$382$	14.7639	0.755388
$383$	−0.673762	−0.0344276	−0.0172138	−	0.999852i	$-0.505480\pi$
$383$	−0.673762	−0.0344276	−0.0172138	+	0.999852i	$0.505480\pi$
$384$	0.381966	0.0194921
$385$	0	0
$386$	14.0000	0.712581
$387$	19.5623	0.994408
$388$	4.18034	0.212225
$389$	7.03444	0.356660	0.178330	−	0.983971i	$-0.442930\pi$
$389$	7.03444	0.356660	0.178330	+	0.983971i	$0.442930\pi$
$390$	0	0
$391$	28.1803	1.42514
$392$	7.85410	0.396692
$393$	−4.76393	−0.240309
$394$	−3.70820	−0.186817
$395$	0	0
$396$	2.18034	0.109566
$397$	−2.65248	−0.133124	−0.0665620	−	0.997782i	$-0.521203\pi$
$397$	−2.65248	−0.133124	−0.0665620	+	0.997782i	$0.521203\pi$
$398$	−11.7082	−0.586879
$399$	−4.06888	−0.203699
$400$	0	0
$401$	−22.7984	−1.13850	−0.569248	−	0.822166i	$-0.692766\pi$
$401$	−22.7984	−1.13850	−0.569248	+	0.822166i	$0.692766\pi$
$402$	0.944272	0.0470960
$403$	31.4164	1.56496
$404$	10.6180	0.528267
$405$	0	0
$406$	−13.9443	−0.692043
$407$	8.36068	0.414424
$408$	2.00000	0.0990148
$409$	29.9230	1.47960	0.739798	−	0.672829i	$-0.234921\pi$
$409$	29.9230	1.47960	0.739798	+	0.672829i	$0.234921\pi$
$410$	0	0
$411$	4.11146	0.202803
$412$	4.00000	0.197066
$413$	−27.8885	−1.37231
$414$	−15.3607	−0.754936
$415$	0	0
$416$	−3.23607	−0.158661
$417$	−5.12461	−0.250953
$418$	2.11146	0.103275
$419$	8.94427	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$419$	8.94427	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$420$	0	0
$421$	−18.4508	−0.899239	−0.449620	−	0.893220i	$-0.648440\pi$
$421$	−18.4508	−0.899239	−0.449620	+	0.893220i	$0.648440\pi$
$422$	−18.0000	−0.876226
$423$	20.9098	1.01667
$424$	12.9443	0.628629
$425$	0	0
$426$	−2.00000	−0.0969003
$427$	30.2705	1.46489
$428$	4.38197	0.211810
$429$	0.944272	0.0455899
$430$	0	0
$431$	−10.3607	−0.499056	−0.249528	−	0.968368i	$-0.580276\pi$
$431$	−10.3607	−0.499056	−0.249528	+	0.968368i	$0.580276\pi$
$432$	−2.23607	−0.107583
$433$	−2.58359	−0.124160	−0.0620798	−	0.998071i	$-0.519773\pi$
$433$	−2.58359	−0.124160	−0.0620798	+	0.998071i	$0.519773\pi$
$434$	−37.4164	−1.79605
$435$	0	0
$436$	3.61803	0.173272
$437$	−14.8754	−0.711586
$438$	−1.23607	−0.0590616
$439$	8.29180	0.395746	0.197873	−	0.980228i	$-0.436597\pi$
$439$	8.29180	0.395746	0.197873	+	0.980228i	$0.436597\pi$
$440$	0	0
$441$	−22.4164	−1.06745
$442$	−16.9443	−0.805957
$443$	3.67376	0.174546	0.0872729	−	0.996184i	$-0.472185\pi$
$443$	3.67376	0.174546	0.0872729	+	0.996184i	$0.472185\pi$
$444$	−4.18034	−0.198390
$445$	0	0
$446$	−22.3820	−1.05982
$447$	5.00000	0.236492
$448$	3.85410	0.182089
$449$	13.4164	0.633159	0.316580	−	0.948566i	$-0.397466\pi$
$449$	13.4164	0.633159	0.316580	+	0.948566i	$0.397466\pi$
$450$	0	0
$451$	−4.29180	−0.202093
$452$	2.29180	0.107797
$453$	0.763932	0.0358927
$454$	−11.6738	−0.547877
$455$	0	0
$456$	−1.05573	−0.0494390
$457$	28.0000	1.30978	0.654892	−	0.755722i	$-0.272714\pi$
$457$	28.0000	1.30978	0.654892	+	0.755722i	$0.272714\pi$
$458$	−4.14590	−0.193725
$459$	−11.7082	−0.546492
$460$	0	0
$461$	−14.9098	−0.694420	−0.347210	−	0.937787i	$-0.612871\pi$
$461$	−14.9098	−0.694420	−0.347210	+	0.937787i	$0.612871\pi$
$462$	−1.12461	−0.0523217
$463$	−0.145898	−0.00678046	−0.00339023	−	0.999994i	$-0.501079\pi$
$463$	−0.145898	−0.00678046	−0.00339023	+	0.999994i	$0.501079\pi$
$464$	−3.61803	−0.167963
$465$	0	0
$466$	1.23607	0.0572597
$467$	5.56231	0.257393	0.128696	−	0.991684i	$-0.458921\pi$
$467$	5.56231	0.257393	0.128696	+	0.991684i	$0.458921\pi$
$468$	9.23607	0.426937
$469$	9.52786	0.439956
$470$	0	0
$471$	4.11146	0.189446
$472$	−7.23607	−0.333067
$473$	5.23607	0.240755
$474$	5.12461	0.235381
$475$	0	0
$476$	20.1803	0.924964
$477$	−36.9443	−1.69156
$478$	13.4164	0.613652
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	35.4164	1.61485
$482$	−11.0902	−0.505143
$483$	7.92299	0.360508
$484$	−10.4164	−0.473473
$485$	0	0
$486$	9.65248	0.437845
$487$	−41.3951	−1.87579	−0.937896	−	0.346917i	$-0.887229\pi$
$487$	−41.3951	−1.87579	−0.937896	+	0.346917i	$0.887229\pi$
$488$	7.85410	0.355538
$489$	5.06888	0.229223
$490$	0	0
$491$	−7.34752	−0.331589	−0.165795	−	0.986160i	$-0.553019\pi$
$491$	−7.34752	−0.331589	−0.165795	+	0.986160i	$0.553019\pi$
$492$	2.14590	0.0967446
$493$	−18.9443	−0.853207
$494$	8.94427	0.402422
$495$	0	0
$496$	−9.70820	−0.435911
$497$	−20.1803	−0.905212
$498$	2.70820	0.121358
$499$	−31.7082	−1.41945	−0.709727	−	0.704477i	$-0.751182\pi$
$499$	−31.7082	−1.41945	−0.709727	+	0.704477i	$0.751182\pi$
$500$	0	0
$501$	−2.14590	−0.0958717
$502$	12.0000	0.535586
$503$	−31.8541	−1.42030	−0.710152	−	0.704048i	$-0.751374\pi$
$503$	−31.8541	−1.42030	−0.710152	+	0.704048i	$0.751374\pi$
$504$	−11.0000	−0.489979
$505$	0	0
$506$	−4.11146	−0.182777
$507$	−0.965558	−0.0428819
$508$	10.5623	0.468627
$509$	13.4164	0.594672	0.297336	−	0.954773i	$-0.403902\pi$
$509$	13.4164	0.594672	0.297336	+	0.954773i	$0.403902\pi$
$510$	0	0
$511$	−12.4721	−0.551735
$512$	1.00000	0.0441942
$513$	6.18034	0.272869
$514$	−20.9443	−0.923812
$515$	0	0
$516$	−2.61803	−0.115253
$517$	5.59675	0.246145
$518$	−42.1803	−1.85330
$519$	3.88854	0.170688
$520$	0	0
$521$	−36.0902	−1.58114	−0.790570	−	0.612372i	$-0.790215\pi$
$521$	−36.0902	−1.58114	−0.790570	+	0.612372i	$0.790215\pi$
$522$	10.3262	0.451967
$523$	25.5066	1.11532	0.557662	−	0.830068i	$-0.311698\pi$
$523$	25.5066	1.11532	0.557662	+	0.830068i	$0.311698\pi$
$524$	−12.4721	−0.544848
$525$	0	0
$526$	17.6180	0.768183
$527$	−50.8328	−2.21431
$528$	−0.291796	−0.0126988
$529$	5.96556	0.259372
$530$	0	0
$531$	20.6525	0.896241
$532$	−10.6525	−0.461843
$533$	−18.1803	−0.787478
$534$	−1.18034	−0.0510783
$535$	0	0
$536$	2.47214	0.106780
$537$	−4.06888	−0.175585
$538$	−24.4721	−1.05507
$539$	−6.00000	−0.258438
$540$	0	0
$541$	−25.6869	−1.10437	−0.552183	−	0.833723i	$-0.686205\pi$
$541$	−25.6869	−1.10437	−0.552183	+	0.833723i	$0.686205\pi$
$542$	9.88854	0.424749
$543$	1.74265	0.0747841
$544$	5.23607	0.224495
$545$	0	0
$546$	−4.76393	−0.203877
$547$	−37.8541	−1.61852	−0.809262	−	0.587448i	$-0.800133\pi$
$547$	−37.8541	−1.61852	−0.809262	+	0.587448i	$0.800133\pi$
$548$	10.7639	0.459812
$549$	−22.4164	−0.956709
$550$	0	0
$551$	10.0000	0.426014
$552$	2.05573	0.0874976
$553$	51.7082	2.19886
$554$	10.7639	0.457316
$555$	0	0
$556$	−13.4164	−0.568982
$557$	−20.2918	−0.859791	−0.429895	−	0.902879i	$-0.641450\pi$
$557$	−20.2918	−0.859791	−0.429895	+	0.902879i	$0.641450\pi$
$558$	27.7082	1.17298
$559$	22.1803	0.938128
$560$	0	0
$561$	−1.52786	−0.0645065
$562$	−11.0902	−0.467811
$563$	−44.9443	−1.89418	−0.947088	−	0.320975i	$-0.895989\pi$
$563$	−44.9443	−1.89418	−0.947088	+	0.320975i	$0.895989\pi$
$564$	−2.79837	−0.117833
$565$	0	0
$566$	−22.8328	−0.959735
$567$	29.7082	1.24763
$568$	−5.23607	−0.219701
$569$	8.49342	0.356063	0.178031	−	0.984025i	$-0.443027\pi$
$569$	8.49342	0.356063	0.178031	+	0.984025i	$0.443027\pi$
$570$	0	0
$571$	24.3607	1.01946	0.509731	−	0.860334i	$-0.329745\pi$
$571$	24.3607	1.01946	0.509731	+	0.860334i	$0.329745\pi$
$572$	2.47214	0.103365
$573$	5.63932	0.235586
$574$	21.6525	0.903757
$575$	0	0
$576$	−2.85410	−0.118921
$577$	11.4164	0.475271	0.237636	−	0.971354i	$-0.423628\pi$
$577$	11.4164	0.475271	0.237636	+	0.971354i	$0.423628\pi$
$578$	10.4164	0.433265
$579$	5.34752	0.222236
$580$	0	0
$581$	27.3262	1.13368
$582$	1.59675	0.0661873
$583$	−9.88854	−0.409542
$584$	−3.23607	−0.133909
$585$	0	0
$586$	0.180340	0.00744977
$587$	−29.8885	−1.23363	−0.616816	−	0.787107i	$-0.711578\pi$
$587$	−29.8885	−1.23363	−0.616816	+	0.787107i	$0.711578\pi$
$588$	3.00000	0.123718
$589$	26.8328	1.10563
$590$	0	0
$591$	−1.41641	−0.0582632
$592$	−10.9443	−0.449807
$593$	2.94427	0.120907	0.0604534	−	0.998171i	$-0.480745\pi$
$593$	2.94427	0.120907	0.0604534	+	0.998171i	$0.480745\pi$
$594$	1.70820	0.0700885
$595$	0	0
$596$	13.0902	0.536194
$597$	−4.47214	−0.183032
$598$	−17.4164	−0.712210
$599$	−24.4721	−0.999904	−0.499952	−	0.866053i	$-0.666649\pi$
$599$	−24.4721	−0.999904	−0.499952	+	0.866053i	$0.666649\pi$
$600$	0	0
$601$	−8.85410	−0.361166	−0.180583	−	0.983560i	$-0.557799\pi$
$601$	−8.85410	−0.361166	−0.180583	+	0.983560i	$0.557799\pi$
$602$	−26.4164	−1.07665
$603$	−7.05573	−0.287331
$604$	2.00000	0.0813788
$605$	0	0
$606$	4.05573	0.164753
$607$	31.4164	1.27515	0.637576	−	0.770387i	$-0.279937\pi$
$607$	31.4164	1.27515	0.637576	+	0.770387i	$0.279937\pi$
$608$	−2.76393	−0.112092
$609$	−5.32624	−0.215830
$610$	0	0
$611$	23.7082	0.959131
$612$	−14.9443	−0.604086
$613$	10.8328	0.437533	0.218767	−	0.975777i	$-0.429797\pi$
$613$	10.8328	0.437533	0.218767	+	0.975777i	$0.429797\pi$
$614$	−21.2705	−0.858408
$615$	0	0
$616$	−2.94427	−0.118628
$617$	34.1803	1.37605	0.688024	−	0.725688i	$-0.258478\pi$
$617$	34.1803	1.37605	0.688024	+	0.725688i	$0.258478\pi$
$618$	1.52786	0.0614597
$619$	6.18034	0.248409	0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034	0.248409	0.124204	+	0.992257i	$0.460362\pi$
$620$	0	0
$621$	−12.0344	−0.482926
$622$	−9.70820	−0.389264
$623$	−11.9098	−0.477157
$624$	−1.23607	−0.0494823
$625$	0	0
$626$	27.4164	1.09578
$627$	0.806504	0.0322087
$628$	10.7639	0.429528
$629$	−57.3050	−2.28490
$630$	0	0
$631$	10.2918	0.409710	0.204855	−	0.978792i	$-0.434328\pi$
$631$	10.2918	0.409710	0.204855	+	0.978792i	$0.434328\pi$
$632$	13.4164	0.533676
$633$	−6.87539	−0.273272
$634$	12.4721	0.495332
$635$	0	0
$636$	4.94427	0.196053
$637$	−25.4164	−1.00703
$638$	2.76393	0.109425
$639$	14.9443	0.591186
$640$	0	0
$641$	40.0902	1.58347	0.791733	−	0.610867i	$-0.209179\pi$
$641$	40.0902	1.58347	0.791733	+	0.610867i	$0.209179\pi$
$642$	1.67376	0.0660581
$643$	−14.2148	−0.560576	−0.280288	−	0.959916i	$-0.590430\pi$
$643$	−14.2148	−0.560576	−0.280288	+	0.959916i	$0.590430\pi$
$644$	20.7426	0.817375
$645$	0	0
$646$	−14.4721	−0.569399
$647$	16.9443	0.666148	0.333074	−	0.942901i	$-0.391914\pi$
$647$	16.9443	0.666148	0.333074	+	0.942901i	$0.391914\pi$
$648$	7.70820	0.302807
$649$	5.52786	0.216988
$650$	0	0
$651$	−14.2918	−0.560140
$652$	13.2705	0.519713
$653$	42.9443	1.68054	0.840270	−	0.542169i	$-0.182397\pi$
$653$	42.9443	1.68054	0.840270	+	0.542169i	$0.182397\pi$
$654$	1.38197	0.0540391
$655$	0	0
$656$	5.61803	0.219347
$657$	9.23607	0.360333
$658$	−28.2361	−1.10076
$659$	−0.652476	−0.0254169	−0.0127084	−	0.999919i	$-0.504045\pi$
$659$	−0.652476	−0.0254169	−0.0127084	+	0.999919i	$0.504045\pi$
$660$	0	0
$661$	28.3820	1.10393	0.551965	−	0.833867i	$-0.313878\pi$
$661$	28.3820	1.10393	0.551965	+	0.833867i	$0.313878\pi$
$662$	5.41641	0.210515
$663$	−6.47214	−0.251357
$664$	7.09017	0.275152
$665$	0	0
$666$	31.2361	1.21037
$667$	−19.4721	−0.753964
$668$	−5.61803	−0.217368
$669$	−8.54915	−0.330529
$670$	0	0
$671$	−6.00000	−0.231627
$672$	1.47214	0.0567889
$673$	7.81966	0.301426	0.150713	−	0.988578i	$-0.451843\pi$
$673$	7.81966	0.301426	0.150713	+	0.988578i	$0.451843\pi$
$674$	18.0000	0.693334
$675$	0	0
$676$	−2.52786	−0.0972255
$677$	22.4721	0.863674	0.431837	−	0.901952i	$-0.357866\pi$
$677$	22.4721	0.863674	0.431837	+	0.901952i	$0.357866\pi$
$678$	0.875388	0.0336191
$679$	16.1115	0.618301
$680$	0	0
$681$	−4.45898	−0.170868
$682$	7.41641	0.283989
$683$	43.7984	1.67590	0.837949	−	0.545748i	$-0.183755\pi$
$683$	43.7984	1.67590	0.837949	+	0.545748i	$0.183755\pi$
$684$	7.88854	0.301626
$685$	0	0
$686$	3.29180	0.125681
$687$	−1.58359	−0.0604178
$688$	−6.85410	−0.261310
$689$	−41.8885	−1.59583
$690$	0	0
$691$	−18.0000	−0.684752	−0.342376	−	0.939563i	$-0.611232\pi$
$691$	−18.0000	−0.684752	−0.342376	+	0.939563i	$0.611232\pi$
$692$	10.1803	0.386998
$693$	8.40325	0.319213
$694$	16.6180	0.630812
$695$	0	0
$696$	−1.38197	−0.0523833
$697$	29.4164	1.11423
$698$	15.8541	0.600087
$699$	0.472136	0.0178578
$700$	0	0
$701$	−46.9443	−1.77306	−0.886530	−	0.462670i	$-0.846891\pi$
$701$	−46.9443	−1.77306	−0.886530	+	0.462670i	$0.846891\pi$
$702$	7.23607	0.273108
$703$	30.2492	1.14087
$704$	−0.763932	−0.0287918
$705$	0	0
$706$	−35.5967	−1.33970
$707$	40.9230	1.53907
$708$	−2.76393	−0.103875
$709$	17.9656	0.674711	0.337355	−	0.941377i	$-0.390468\pi$
$709$	17.9656	0.674711	0.337355	+	0.941377i	$0.390468\pi$
$710$	0	0
$711$	−38.2918	−1.43605
$712$	−3.09017	−0.115809
$713$	−52.2492	−1.95675
$714$	7.70820	0.288472
$715$	0	0
$716$	−10.6525	−0.398102
$717$	5.12461	0.191382
$718$	30.6525	1.14394
$719$	−22.3607	−0.833913	−0.416956	−	0.908927i	$-0.636903\pi$
$719$	−22.3607	−0.833913	−0.416956	+	0.908927i	$0.636903\pi$
$720$	0	0
$721$	15.4164	0.574137
$722$	−11.3607	−0.422801
$723$	−4.23607	−0.157541
$724$	4.56231	0.169557
$725$	0	0
$726$	−3.97871	−0.147664
$727$	28.8541	1.07014	0.535070	−	0.844808i	$-0.320285\pi$
$727$	28.8541	1.07014	0.535070	+	0.844808i	$0.320285\pi$
$728$	−12.4721	−0.462248
$729$	−19.4377	−0.719915
$730$	0	0
$731$	−35.8885	−1.32739
$732$	3.00000	0.110883
$733$	−30.0689	−1.11062	−0.555310	−	0.831644i	$-0.687400\pi$
$733$	−30.0689	−1.11062	−0.555310	+	0.831644i	$0.687400\pi$
$734$	−7.85410	−0.289900
$735$	0	0
$736$	5.38197	0.198382
$737$	−1.88854	−0.0695654
$738$	−16.0344	−0.590236
$739$	−36.8328	−1.35492	−0.677459	−	0.735561i	$-0.736919\pi$
$739$	−36.8328	−1.35492	−0.677459	+	0.735561i	$0.736919\pi$
$740$	0	0
$741$	3.41641	0.125505
$742$	49.8885	1.83147
$743$	−40.7214	−1.49392	−0.746961	−	0.664868i	$-0.768488\pi$
$743$	−40.7214	−1.49392	−0.746961	+	0.664868i	$0.768488\pi$
$744$	−3.70820	−0.135949
$745$	0	0
$746$	−6.00000	−0.219676
$747$	−20.2361	−0.740399
$748$	−4.00000	−0.146254
$749$	16.8885	0.617094
$750$	0	0
$751$	52.2492	1.90660	0.953301	−	0.302023i	$-0.0976620\pi$
$751$	52.2492	1.90660	0.953301	+	0.302023i	$0.0976620\pi$
$752$	−7.32624	−0.267160
$753$	4.58359	0.167035
$754$	11.7082	0.426388
$755$	0	0
$756$	−8.61803	−0.313435
$757$	−17.1246	−0.622405	−0.311202	−	0.950344i	$-0.600732\pi$
$757$	−17.1246	−0.622405	−0.311202	+	0.950344i	$0.600732\pi$
$758$	−5.52786	−0.200781
$759$	−1.57044	−0.0570032
$760$	0	0
$761$	−13.8541	−0.502211	−0.251105	−	0.967960i	$-0.580794\pi$
$761$	−13.8541	−0.502211	−0.251105	+	0.967960i	$0.580794\pi$
$762$	4.03444	0.146152
$763$	13.9443	0.504817
$764$	14.7639	0.534140
$765$	0	0
$766$	−0.673762	−0.0243440
$767$	23.4164	0.845517
$768$	0.381966	0.0137830
$769$	−20.8541	−0.752018	−0.376009	−	0.926616i	$-0.622704\pi$
$769$	−20.8541	−0.752018	−0.376009	+	0.926616i	$0.622704\pi$
$770$	0	0
$771$	−8.00000	−0.288113
$772$	14.0000	0.503871
$773$	−8.36068	−0.300713	−0.150356	−	0.988632i	$-0.548042\pi$
$773$	−8.36068	−0.300713	−0.150356	+	0.988632i	$0.548042\pi$
$774$	19.5623	0.703153
$775$	0	0
$776$	4.18034	0.150065
$777$	−16.1115	−0.577995
$778$	7.03444	0.252197
$779$	−15.5279	−0.556343
$780$	0	0
$781$	4.00000	0.143131
$782$	28.1803	1.00773
$783$	8.09017	0.289119
$784$	7.85410	0.280504
$785$	0	0
$786$	−4.76393	−0.169924
$787$	22.6738	0.808232	0.404116	−	0.914708i	$-0.367579\pi$
$787$	22.6738	0.808232	0.404116	+	0.914708i	$0.367579\pi$
$788$	−3.70820	−0.132099
$789$	6.72949	0.239576
$790$	0	0
$791$	8.83282	0.314059
$792$	2.18034	0.0774750
$793$	−25.4164	−0.902563
$794$	−2.65248	−0.0941328
$795$	0	0
$796$	−11.7082	−0.414986
$797$	27.5967	0.977527	0.488763	−	0.872416i	$-0.337448\pi$
$797$	27.5967	0.977527	0.488763	+	0.872416i	$0.337448\pi$
$798$	−4.06888	−0.144037
$799$	−38.3607	−1.35710
$800$	0	0
$801$	8.81966	0.311627
$802$	−22.7984	−0.805039
$803$	2.47214	0.0872398
$804$	0.944272	0.0333019
$805$	0	0
$806$	31.4164	1.10660
$807$	−9.34752	−0.329048
$808$	10.6180	0.373541
$809$	0.326238	0.0114699	0.00573496	−	0.999984i	$-0.498174\pi$
$809$	0.326238	0.0114699	0.00573496	+	0.999984i	$0.498174\pi$
$810$	0	0
$811$	−13.1246	−0.460867	−0.230434	−	0.973088i	$-0.574014\pi$
$811$	−13.1246	−0.460867	−0.230434	+	0.973088i	$0.574014\pi$
$812$	−13.9443	−0.489348
$813$	3.77709	0.132468
$814$	8.36068	0.293042
$815$	0	0
$816$	2.00000	0.0700140
$817$	18.9443	0.662776
$818$	29.9230	1.04623
$819$	35.5967	1.24385
$820$	0	0
$821$	33.3820	1.16504	0.582519	−	0.812817i	$-0.302067\pi$
$821$	33.3820	1.16504	0.582519	+	0.812817i	$0.302067\pi$
$822$	4.11146	0.143404
$823$	29.5279	1.02928	0.514638	−	0.857407i	$-0.327926\pi$
$823$	29.5279	1.02928	0.514638	+	0.857407i	$0.327926\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	−27.8885	−0.970367
$827$	5.88854	0.204765	0.102382	−	0.994745i	$-0.467353\pi$
$827$	5.88854	0.204765	0.102382	+	0.994745i	$0.467353\pi$
$828$	−15.3607	−0.533821
$829$	27.0344	0.938945	0.469472	−	0.882947i	$-0.344444\pi$
$829$	27.0344	0.938945	0.469472	+	0.882947i	$0.344444\pi$
$830$	0	0
$831$	4.11146	0.142625
$832$	−3.23607	−0.112190
$833$	41.1246	1.42488
$834$	−5.12461	−0.177451
$835$	0	0
$836$	2.11146	0.0730262
$837$	21.7082	0.750345
$838$	8.94427	0.308975
$839$	25.7771	0.889924	0.444962	−	0.895549i	$-0.353217\pi$
$839$	25.7771	0.889924	0.444962	+	0.895549i	$0.353217\pi$
$840$	0	0
$841$	−15.9098	−0.548615
$842$	−18.4508	−0.635858
$843$	−4.23607	−0.145898
$844$	−18.0000	−0.619586
$845$	0	0
$846$	20.9098	0.718895
$847$	−40.1459	−1.37943
$848$	12.9443	0.444508
$849$	−8.72136	−0.299316
$850$	0	0
$851$	−58.9017	−2.01912
$852$	−2.00000	−0.0685189
$853$	−21.5279	−0.737100	−0.368550	−	0.929608i	$-0.620146\pi$
$853$	−21.5279	−0.737100	−0.368550	+	0.929608i	$0.620146\pi$
$854$	30.2705	1.03584
$855$	0	0
$856$	4.38197	0.149773
$857$	−26.0689	−0.890496	−0.445248	−	0.895407i	$-0.646885\pi$
$857$	−26.0689	−0.890496	−0.445248	+	0.895407i	$0.646885\pi$
$858$	0.944272	0.0322369
$859$	−50.2492	−1.71448	−0.857241	−	0.514916i	$-0.827823\pi$
$859$	−50.2492	−1.71448	−0.857241	+	0.514916i	$0.827823\pi$
$860$	0	0
$861$	8.27051	0.281858
$862$	−10.3607	−0.352886
$863$	34.3262	1.16848	0.584239	−	0.811581i	$-0.301393\pi$
$863$	34.3262	1.16848	0.584239	+	0.811581i	$0.301393\pi$
$864$	−2.23607	−0.0760726
$865$	0	0
$866$	−2.58359	−0.0877940
$867$	3.97871	0.135124
$868$	−37.4164	−1.27000
$869$	−10.2492	−0.347681
$870$	0	0
$871$	−8.00000	−0.271070
$872$	3.61803	0.122522
$873$	−11.9311	−0.403807
$874$	−14.8754	−0.503168
$875$	0	0
$876$	−1.23607	−0.0417629
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	8.29180	0.279835
$879$	0.0688837	0.00232339
$880$	0	0
$881$	21.2705	0.716622	0.358311	−	0.933602i	$-0.383353\pi$
$881$	21.2705	0.716622	0.358311	+	0.933602i	$0.383353\pi$
$882$	−22.4164	−0.754800
$883$	−45.2705	−1.52347	−0.761737	−	0.647886i	$-0.775653\pi$
$883$	−45.2705	−1.52347	−0.761737	+	0.647886i	$0.775653\pi$
$884$	−16.9443	−0.569898
$885$	0	0
$886$	3.67376	0.123422
$887$	8.72949	0.293108	0.146554	−	0.989203i	$-0.453182\pi$
$887$	8.72949	0.293108	0.146554	+	0.989203i	$0.453182\pi$
$888$	−4.18034	−0.140283
$889$	40.7082	1.36531
$890$	0	0
$891$	−5.88854	−0.197274
$892$	−22.3820	−0.749404
$893$	20.2492	0.677614
$894$	5.00000	0.167225
$895$	0	0
$896$	3.85410	0.128757
$897$	−6.65248	−0.222120
$898$	13.4164	0.447711
$899$	35.1246	1.17147
$900$	0	0
$901$	67.7771	2.25798
$902$	−4.29180	−0.142901
$903$	−10.0902	−0.335780
$904$	2.29180	0.0762240
$905$	0	0
$906$	0.763932	0.0253799
$907$	19.3820	0.643568	0.321784	−	0.946813i	$-0.395718\pi$
$907$	19.3820	0.643568	0.321784	+	0.946813i	$0.395718\pi$
$908$	−11.6738	−0.387407
$909$	−30.3050	−1.00515
$910$	0	0
$911$	−36.5410	−1.21066	−0.605329	−	0.795975i	$-0.706958\pi$
$911$	−36.5410	−1.21066	−0.605329	+	0.795975i	$0.706958\pi$
$912$	−1.05573	−0.0349587
$913$	−5.41641	−0.179257
$914$	28.0000	0.926158
$915$	0	0
$916$	−4.14590	−0.136984
$917$	−48.0689	−1.58737
$918$	−11.7082	−0.386428
$919$	−56.4296	−1.86144	−0.930720	−	0.365733i	$-0.880818\pi$
$919$	−56.4296	−1.86144	−0.930720	+	0.365733i	$0.880818\pi$
$920$	0	0
$921$	−8.12461	−0.267715
$922$	−14.9098	−0.491029
$923$	16.9443	0.557728
$924$	−1.12461	−0.0369970
$925$	0	0
$926$	−0.145898	−0.00479451
$927$	−11.4164	−0.374964
$928$	−3.61803	−0.118768
$929$	35.4508	1.16310	0.581552	−	0.813509i	$-0.302446\pi$
$929$	35.4508	1.16310	0.581552	+	0.813509i	$0.302446\pi$
$930$	0	0
$931$	−21.7082	−0.711458
$932$	1.23607	0.0404888
$933$	−3.70820	−0.121401
$934$	5.56231	0.182004
$935$	0	0
$936$	9.23607	0.301890
$937$	−52.0000	−1.69877	−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000	−1.69877	−0.849383	+	0.527777i	$0.823026\pi$
$938$	9.52786	0.311096
$939$	10.4721	0.341745
$940$	0	0
$941$	8.83282	0.287942	0.143971	−	0.989582i	$-0.454013\pi$
$941$	8.83282	0.287942	0.143971	+	0.989582i	$0.454013\pi$
$942$	4.11146	0.133958
$943$	30.2361	0.984622
$944$	−7.23607	−0.235514
$945$	0	0
$946$	5.23607	0.170239
$947$	−6.27051	−0.203764	−0.101882	−	0.994796i	$-0.532486\pi$
$947$	−6.27051	−0.203764	−0.101882	+	0.994796i	$0.532486\pi$
$948$	5.12461	0.166440
$949$	10.4721	0.339940
$950$	0	0
$951$	4.76393	0.154481
$952$	20.1803	0.654049
$953$	−4.94427	−0.160161	−0.0800803	−	0.996788i	$-0.525518\pi$
$953$	−4.94427	−0.160161	−0.0800803	+	0.996788i	$0.525518\pi$
$954$	−36.9443	−1.19611
$955$	0	0
$956$	13.4164	0.433918
$957$	1.05573	0.0341268
$958$	30.0000	0.969256
$959$	41.4853	1.33963
$960$	0	0
$961$	63.2492	2.04030
$962$	35.4164	1.14187
$963$	−12.5066	−0.403019
$964$	−11.0902	−0.357190
$965$	0	0
$966$	7.92299	0.254918
$967$	−52.4508	−1.68671	−0.843353	−	0.537360i	$-0.819422\pi$
$967$	−52.4508	−1.68671	−0.843353	+	0.537360i	$0.819422\pi$
$968$	−10.4164	−0.334796
$969$	−5.52786	−0.177581
$970$	0	0
$971$	46.7214	1.49936	0.749680	−	0.661801i	$-0.230207\pi$
$971$	46.7214	1.49936	0.749680	+	0.661801i	$0.230207\pi$
$972$	9.65248	0.309603
$973$	−51.7082	−1.65769
$974$	−41.3951	−1.32639
$975$	0	0
$976$	7.85410	0.251404
$977$	−29.2361	−0.935345	−0.467672	−	0.883902i	$-0.654907\pi$
$977$	−29.2361	−0.935345	−0.467672	+	0.883902i	$0.654907\pi$
$978$	5.06888	0.162085
$979$	2.36068	0.0754477
$980$	0	0
$981$	−10.3262	−0.329691
$982$	−7.34752	−0.234469
$983$	7.41641	0.236547	0.118273	−	0.992981i	$-0.462264\pi$
$983$	7.41641	0.236547	0.118273	+	0.992981i	$0.462264\pi$
$984$	2.14590	0.0684087
$985$	0	0
$986$	−18.9443	−0.603309
$987$	−10.7852	−0.343297
$988$	8.94427	0.284555
$989$	−36.8885	−1.17299
$990$	0	0
$991$	24.3607	0.773842	0.386921	−	0.922113i	$-0.373539\pi$
$991$	24.3607	0.773842	0.386921	+	0.922113i	$0.373539\pi$
$992$	−9.70820	−0.308236
$993$	2.06888	0.0656540
$994$	−20.1803	−0.640082
$995$	0	0
$996$	2.70820	0.0858127
$997$	−0.291796	−0.00924127	−0.00462064	−	0.999989i	$-0.501471\pi$
$997$	−0.291796	−0.00924127	−0.00462064	+	0.999989i	$0.501471\pi$
$998$	−31.7082	−1.00371
$999$	24.4721	0.774264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.a.d.1.1	yes	2
3.2	odd	2		2250.2.a.f.1.2		2
4.3	odd	2		2000.2.a.b.1.2		2
5.2	odd	4		250.2.b.b.249.4		4
5.3	odd	4		250.2.b.b.249.1		4
5.4	even	2		250.2.a.a.1.2	✓	2
8.3	odd	2		8000.2.a.w.1.1		2
8.5	even	2		8000.2.a.b.1.2		2
15.2	even	4		2250.2.c.h.1999.2		4
15.8	even	4		2250.2.c.h.1999.3		4
15.14	odd	2		2250.2.a.m.1.1		2
20.3	even	4		2000.2.c.d.1249.2		4
20.7	even	4		2000.2.c.d.1249.3		4
20.19	odd	2		2000.2.a.k.1.1		2
40.19	odd	2		8000.2.a.a.1.2		2
40.29	even	2		8000.2.a.x.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.a.a.1.2	✓	2	5.4	even	2
250.2.a.d.1.1	yes	2	1.1	even	1	trivial
250.2.b.b.249.1		4	5.3	odd	4
250.2.b.b.249.4		4	5.2	odd	4
2000.2.a.b.1.2		2	4.3	odd	2
2000.2.a.k.1.1		2	20.19	odd	2
2000.2.c.d.1249.2		4	20.3	even	4
2000.2.c.d.1249.3		4	20.7	even	4
2250.2.a.f.1.2		2	3.2	odd	2
2250.2.a.m.1.1		2	15.14	odd	2
2250.2.c.h.1999.2		4	15.2	even	4
2250.2.c.h.1999.3		4	15.8	even	4
8000.2.a.a.1.2		2	40.19	odd	2
8000.2.a.b.1.2		2	8.5	even	2
8000.2.a.w.1.1		2	8.3	odd	2
8000.2.a.x.1.1		2	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.85410 q^{7} +1.00000 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.381966 q^{3} +1.00000 q^{4} +0.381966 q^{6} +3.85410 q^{7} +1.00000 q^{8} -2.85410 q^{9} -0.763932 q^{11} +0.381966 q^{12} -3.23607 q^{13} +3.85410 q^{14} +1.00000 q^{16} +5.23607 q^{17} -2.85410 q^{18} -2.76393 q^{19} +1.47214 q^{21} -0.763932 q^{22} +5.38197 q^{23} +0.381966 q^{24} -3.23607 q^{26} -2.23607 q^{27} +3.85410 q^{28} -3.61803 q^{29} -9.70820 q^{31} +1.00000 q^{32} -0.291796 q^{33} +5.23607 q^{34} -2.85410 q^{36} -10.9443 q^{37} -2.76393 q^{38} -1.23607 q^{39} +5.61803 q^{41} +1.47214 q^{42} -6.85410 q^{43} -0.763932 q^{44} +5.38197 q^{46} -7.32624 q^{47} +0.381966 q^{48} +7.85410 q^{49} +2.00000 q^{51} -3.23607 q^{52} +12.9443 q^{53} -2.23607 q^{54} +3.85410 q^{56} -1.05573 q^{57} -3.61803 q^{58} -7.23607 q^{59} +7.85410 q^{61} -9.70820 q^{62} -11.0000 q^{63} +1.00000 q^{64} -0.291796 q^{66} +2.47214 q^{67} +5.23607 q^{68} +2.05573 q^{69} -5.23607 q^{71} -2.85410 q^{72} -3.23607 q^{73} -10.9443 q^{74} -2.76393 q^{76} -2.94427 q^{77} -1.23607 q^{78} +13.4164 q^{79} +7.70820 q^{81} +5.61803 q^{82} +7.09017 q^{83} +1.47214 q^{84} -6.85410 q^{86} -1.38197 q^{87} -0.763932 q^{88} -3.09017 q^{89} -12.4721 q^{91} +5.38197 q^{92} -3.70820 q^{93} -7.32624 q^{94} +0.381966 q^{96} +4.18034 q^{97} +7.85410 q^{98} +2.18034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + q^7 + 2 * q^8 + q^9	\( 2 q + 2 q^{2} + 3 q^{3} + 2 q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + q^{9} - 6 q^{11} + 3 q^{12} - 2 q^{13} + q^{14} + 2 q^{16} + 6 q^{17} + q^{18} - 10 q^{19} - 6 q^{21} - 6 q^{22} + 13 q^{23} + 3 q^{24} - 2 q^{26} + q^{28} - 5 q^{29} - 6 q^{31} + 2 q^{32} - 14 q^{33} + 6 q^{34} + q^{36} - 4 q^{37} - 10 q^{38} + 2 q^{39} + 9 q^{41} - 6 q^{42} - 7 q^{43} - 6 q^{44} + 13 q^{46} + q^{47} + 3 q^{48} + 9 q^{49} + 4 q^{51} - 2 q^{52} + 8 q^{53} + q^{56} - 20 q^{57} - 5 q^{58} - 10 q^{59} + 9 q^{61} - 6 q^{62} - 22 q^{63} + 2 q^{64} - 14 q^{66} - 4 q^{67} + 6 q^{68} + 22 q^{69} - 6 q^{71} + q^{72} - 2 q^{73} - 4 q^{74} - 10 q^{76} + 12 q^{77} + 2 q^{78} + 2 q^{81} + 9 q^{82} + 3 q^{83} - 6 q^{84} - 7 q^{86} - 5 q^{87} - 6 q^{88} + 5 q^{89} - 16 q^{91} + 13 q^{92} + 6 q^{93} + q^{94} + 3 q^{96} - 14 q^{97} + 9 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 + 2 * q^4 + 3 * q^6 + q^7 + 2 * q^8 + q^9 - 6 * q^11 + 3 * q^12 - 2 * q^13 + q^14 + 2 * q^16 + 6 * q^17 + q^18 - 10 * q^19 - 6 * q^21 - 6 * q^22 + 13 * q^23 + 3 * q^24 - 2 * q^26 + q^28 - 5 * q^29 - 6 * q^31 + 2 * q^32 - 14 * q^33 + 6 * q^34 + q^36 - 4 * q^37 - 10 * q^38 + 2 * q^39 + 9 * q^41 - 6 * q^42 - 7 * q^43 - 6 * q^44 + 13 * q^46 + q^47 + 3 * q^48 + 9 * q^49 + 4 * q^51 - 2 * q^52 + 8 * q^53 + q^56 - 20 * q^57 - 5 * q^58 - 10 * q^59 + 9 * q^61 - 6 * q^62 - 22 * q^63 + 2 * q^64 - 14 * q^66 - 4 * q^67 + 6 * q^68 + 22 * q^69 - 6 * q^71 + q^72 - 2 * q^73 - 4 * q^74 - 10 * q^76 + 12 * q^77 + 2 * q^78 + 2 * q^81 + 9 * q^82 + 3 * q^83 - 6 * q^84 - 7 * q^86 - 5 * q^87 - 6 * q^88 + 5 * q^89 - 16 * q^91 + 13 * q^92 + 6 * q^93 + q^94 + 3 * q^96 - 14 * q^97 + 9 * q^98 - 18 * q^99

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