LMFDB - Embedded newform 4025.2.a.l.1.1

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			1.1
Root			$-1.50848$ 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)

$f(q)$	$=$	$q-2.50848 q^{2} -0.817356 q^{3} +4.29248 q^{4} +2.05032 q^{6} +1.00000 q^{7} -5.75064 q^{8} -2.33193 q^{9} +O(q^{10})$	\(q-2.50848 q^{2} -0.817356 q^{3} +4.29248 q^{4} +2.05032 q^{6} +1.00000 q^{7} -5.75064 q^{8} -2.33193 q^{9} +3.50848 q^{11} -3.50848 q^{12} +0.541840 q^{13} -2.50848 q^{14} +5.84041 q^{16} -0.856807 q^{17} +5.84960 q^{18} -3.98360 q^{19} -0.817356 q^{21} -8.80096 q^{22} +1.00000 q^{23} +4.70032 q^{24} -1.35920 q^{26} +4.35808 q^{27} +4.29248 q^{28} +0.916320 q^{29} +0.314967 q^{31} -3.14929 q^{32} -2.86768 q^{33} +2.14929 q^{34} -10.0098 q^{36} +3.44176 q^{37} +9.99279 q^{38} -0.442876 q^{39} -3.60745 q^{41} +2.05032 q^{42} -12.6839 q^{43} +15.0601 q^{44} -2.50848 q^{46} +9.91689 q^{47} -4.77369 q^{48} +1.00000 q^{49} +0.700316 q^{51} +2.32584 q^{52} -3.29248 q^{53} -10.9322 q^{54} -5.75064 q^{56} +3.25602 q^{57} -2.29857 q^{58} -6.76151 q^{59} -3.19184 q^{61} -0.790090 q^{62} -2.33193 q^{63} -3.78090 q^{64} +7.19351 q^{66} -0.788104 q^{67} -3.67783 q^{68} -0.817356 q^{69} -3.25303 q^{71} +13.4101 q^{72} +5.04621 q^{73} -8.63360 q^{74} -17.0995 q^{76} +3.50848 q^{77} +1.11095 q^{78} +6.73424 q^{79} +3.43369 q^{81} +9.04921 q^{82} +3.37306 q^{83} -3.50848 q^{84} +31.8174 q^{86} -0.748959 q^{87} -20.1760 q^{88} -4.40642 q^{89} +0.541840 q^{91} +4.29248 q^{92} -0.257440 q^{93} -24.8763 q^{94} +2.57409 q^{96} -15.3951 q^{97} -2.50848 q^{98} -8.18153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.50848	−1.77376	−0.886882	−	0.461996i	$-0.847133\pi$
$2$	−2.50848	−1.77376	−0.886882	+	0.461996i	$0.847133\pi$
$3$	−0.817356	−0.471901	−0.235950	−	0.971765i	$-0.575820\pi$
$3$	−0.817356	−0.471901	−0.235950	+	0.971765i	$0.575820\pi$
$4$	4.29248	2.14624
$5$	0	0
$5$	0	0
$6$	2.05032	0.837040
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.75064	−2.03316
$9$	−2.33193	−0.777310
$10$	0	0
$11$	3.50848	1.05785	0.528923	−	0.848670i	$-0.322596\pi$
$11$	3.50848	1.05785	0.528923	+	0.848670i	$0.322596\pi$
$12$	−3.50848	−1.01281
$13$	0.541840	0.150279	0.0751397	−	0.997173i	$-0.476060\pi$
$13$	0.541840	0.150279	0.0751397	+	0.997173i	$0.476060\pi$
$14$	−2.50848	−0.670420
$15$	0	0
$16$	5.84041	1.46010
$17$	−0.856807	−0.207806	−0.103903	−	0.994587i	$-0.533133\pi$
$17$	−0.856807	−0.207806	−0.103903	+	0.994587i	$0.533133\pi$
$18$	5.84960	1.37876
$19$	−3.98360	−0.913901	−0.456951	−	0.889492i	$-0.651058\pi$
$19$	−3.98360	−0.913901	−0.456951	+	0.889492i	$0.651058\pi$
$20$	0	0
$21$	−0.817356	−0.178362
$22$	−8.80096	−1.87637
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	4.70032	0.959448
$25$	0	0
$26$	−1.35920	−0.266560
$27$	4.35808	0.838713
$28$	4.29248	0.811202
$29$	0.916320	0.170156	0.0850781	−	0.996374i	$-0.472886\pi$
$29$	0.916320	0.170156	0.0850781	+	0.996374i	$0.472886\pi$
$30$	0	0
$31$	0.314967	0.0565698	0.0282849	−	0.999600i	$-0.490995\pi$
$31$	0.314967	0.0565698	0.0282849	+	0.999600i	$0.490995\pi$
$32$	−3.14929	−0.556720
$33$	−2.86768	−0.499198
$34$	2.14929	0.368599
$35$	0	0
$36$	−10.0098	−1.66829
$37$	3.44176	0.565822	0.282911	−	0.959146i	$-0.408700\pi$
$37$	3.44176	0.565822	0.282911	+	0.959146i	$0.408700\pi$
$38$	9.99279	1.62105
$39$	−0.442876	−0.0709169
$40$	0	0
$41$	−3.60745	−0.563388	−0.281694	−	0.959504i	$-0.590896\pi$
$41$	−3.60745	−0.563388	−0.281694	+	0.959504i	$0.590896\pi$
$42$	2.05032	0.316371
$43$	−12.6839	−1.93428	−0.967140	−	0.254245i	$-0.918173\pi$
$43$	−12.6839	−1.93428	−0.967140	+	0.254245i	$0.918173\pi$
$44$	15.0601	2.27039
$45$	0	0
$46$	−2.50848	−0.369855
$47$	9.91689	1.44653	0.723263	−	0.690572i	$-0.242641\pi$
$47$	9.91689	1.44653	0.723263	+	0.690572i	$0.242641\pi$
$48$	−4.77369	−0.689023
$49$	1.00000	0.142857
$50$	0	0
$51$	0.700316	0.0980639
$52$	2.32584	0.322536
$53$	−3.29248	−0.452257	−0.226128	−	0.974098i	$-0.572607\pi$
$53$	−3.29248	−0.452257	−0.226128	+	0.974098i	$0.572607\pi$
$54$	−10.9322	−1.48768
$55$	0	0
$56$	−5.75064	−0.768461
$57$	3.25602	0.431271
$58$	−2.29857	−0.301817
$59$	−6.76151	−0.880273	−0.440137	−	0.897931i	$-0.645070\pi$
$59$	−6.76151	−0.880273	−0.440137	+	0.897931i	$0.645070\pi$
$60$	0	0
$61$	−3.19184	−0.408673	−0.204336	−	0.978901i	$-0.565504\pi$
$61$	−3.19184	−0.408673	−0.204336	+	0.978901i	$0.565504\pi$
$62$	−0.790090	−0.100341
$63$	−2.33193	−0.293796
$64$	−3.78090	−0.472612
$65$	0	0
$66$	7.19351	0.885460
$67$	−0.788104	−0.0962823	−0.0481411	−	0.998841i	$-0.515330\pi$
$67$	−0.788104	−0.0962823	−0.0481411	+	0.998841i	$0.515330\pi$
$68$	−3.67783	−0.446002
$69$	−0.817356	−0.0983981
$70$	0	0
$71$	−3.25303	−0.386063	−0.193032	−	0.981193i	$-0.561832\pi$
$71$	−3.25303	−0.386063	−0.193032	+	0.981193i	$0.561832\pi$
$72$	13.4101	1.58039
$73$	5.04621	0.590615	0.295307	−	0.955402i	$-0.404578\pi$
$73$	5.04621	0.590615	0.295307	+	0.955402i	$0.404578\pi$
$74$	−8.63360	−1.00364
$75$	0	0
$76$	−17.0995	−1.96145
$77$	3.50848	0.399829
$78$	1.11095	0.125790
$79$	6.73424	0.757661	0.378831	−	0.925466i	$-0.376326\pi$
$79$	6.73424	0.757661	0.378831	+	0.925466i	$0.376326\pi$
$80$	0	0
$81$	3.43369	0.381521
$82$	9.04921	0.999318
$83$	3.37306	0.370241	0.185121	−	0.982716i	$-0.440732\pi$
$83$	3.37306	0.370241	0.185121	+	0.982716i	$0.440732\pi$
$84$	−3.50848	−0.382807
$85$	0	0
$86$	31.8174	3.43096
$87$	−0.748959	−0.0802968
$88$	−20.1760	−2.15077
$89$	−4.40642	−0.467079	−0.233540	−	0.972347i	$-0.575031\pi$
$89$	−4.40642	−0.467079	−0.233540	+	0.972347i	$0.575031\pi$
$90$	0	0
$91$	0.541840	0.0568003
$92$	4.29248	0.447522
$93$	−0.257440	−0.0266953
$94$	−24.8763	−2.56580
$95$	0	0
$96$	2.57409	0.262717
$97$	−15.3951	−1.56314	−0.781568	−	0.623820i	$-0.785580\pi$
$97$	−15.3951	−1.56314	−0.781568	+	0.623820i	$0.785580\pi$
$98$	−2.50848	−0.253395
$99$	−8.18153	−0.822275
$100$	0	0
$101$	9.01895	0.897419	0.448709	−	0.893678i	$-0.351884\pi$
$101$	9.01895	0.897419	0.448709	+	0.893678i	$0.351884\pi$
$102$	−1.75673	−0.173942
$103$	−11.3428	−1.11764	−0.558820	−	0.829289i	$-0.688746\pi$
$103$	−11.3428	−1.11764	−0.558820	+	0.829289i	$0.688746\pi$
$104$	−3.11593	−0.305542
$105$	0	0
$106$	8.25912	0.802197
$107$	6.98970	0.675719	0.337860	−	0.941196i	$-0.390297\pi$
$107$	6.98970	0.675719	0.337860	+	0.941196i	$0.390297\pi$
$108$	18.7070	1.80008
$109$	−1.25855	−0.120548	−0.0602738	−	0.998182i	$-0.519197\pi$
$109$	−1.25855	−0.120548	−0.0602738	+	0.998182i	$0.519197\pi$
$110$	0	0
$111$	−2.81314	−0.267012
$112$	5.84041	0.551867
$113$	−4.70752	−0.442846	−0.221423	−	0.975178i	$-0.571070\pi$
$113$	−4.70752	−0.442846	−0.221423	+	0.975178i	$0.571070\pi$
$114$	−8.16767	−0.764972
$115$	0	0
$116$	3.93328	0.365196
$117$	−1.26353	−0.116814
$118$	16.9611	1.56140
$119$	−0.856807	−0.0785434
$120$	0	0
$121$	1.30944	0.119040
$122$	8.00666	0.724889
$123$	2.94857	0.265863
$124$	1.35199	0.121412
$125$	0	0
$126$	5.84960	0.521124
$127$	−13.1863	−1.17010	−0.585048	−	0.810999i	$-0.698924\pi$
$127$	−13.1863	−1.17010	−0.585048	+	0.810999i	$0.698924\pi$
$128$	15.7829	1.39502
$129$	10.3673	0.912788
$130$	0	0
$131$	17.0509	1.48974	0.744871	−	0.667208i	$-0.232511\pi$
$131$	17.0509	1.48974	0.744871	+	0.667208i	$0.232511\pi$
$132$	−12.3094	−1.07140
$133$	−3.98360	−0.345422
$134$	1.97694	0.170782
$135$	0	0
$136$	4.92719	0.422503
$137$	−18.7251	−1.59979	−0.799895	−	0.600141i	$-0.795111\pi$
$137$	−18.7251	−1.59979	−0.799895	+	0.600141i	$0.795111\pi$
$138$	2.05032	0.174535
$139$	−11.1067	−0.942061	−0.471031	−	0.882117i	$-0.656118\pi$
$139$	−11.1067	−0.942061	−0.471031	+	0.882117i	$0.656118\pi$
$140$	0	0
$141$	−8.10562	−0.682617
$142$	8.16015	0.684785
$143$	1.90104	0.158973
$144$	−13.6194	−1.13495
$145$	0	0
$146$	−12.6583	−1.04761
$147$	−0.817356	−0.0674144
$148$	14.7737	1.21439
$149$	−13.1738	−1.07924	−0.539618	−	0.841910i	$-0.681431\pi$
$149$	−13.1738	−1.07924	−0.539618	+	0.841910i	$0.681431\pi$
$150$	0	0
$151$	4.80395	0.390940	0.195470	−	0.980710i	$-0.437377\pi$
$151$	4.80395	0.390940	0.195470	+	0.980710i	$0.437377\pi$
$152$	22.9083	1.85811
$153$	1.99801	0.161530
$154$	−8.80096	−0.709201
$155$	0	0
$156$	−1.90104	−0.152205
$157$	18.7865	1.49933	0.749665	−	0.661818i	$-0.230215\pi$
$157$	18.7865	1.49933	0.749665	+	0.661818i	$0.230215\pi$
$158$	−16.8927	−1.34391
$159$	2.69113	0.213420
$160$	0	0
$161$	1.00000	0.0788110
$162$	−8.61333	−0.676727
$163$	−8.84960	−0.693154	−0.346577	−	0.938021i	$-0.612656\pi$
$163$	−8.84960	−0.693154	−0.346577	+	0.938021i	$0.612656\pi$
$164$	−15.4849	−1.20917
$165$	0	0
$166$	−8.46126	−0.656721
$167$	16.7251	1.29422	0.647112	−	0.762395i	$-0.275977\pi$
$167$	16.7251	1.29422	0.647112	+	0.762395i	$0.275977\pi$
$168$	4.70032	0.362637
$169$	−12.7064	−0.977416
$170$	0	0
$171$	9.28948	0.710385
$172$	−54.4454	−4.15143
$173$	−10.3253	−0.785017	−0.392509	−	0.919748i	$-0.628393\pi$
$173$	−10.3253	−0.785017	−0.392509	+	0.919748i	$0.628393\pi$
$174$	1.87875	0.142428
$175$	0	0
$176$	20.4910	1.54457
$177$	5.52656	0.415401
$178$	11.0534	0.828489
$179$	24.9770	1.86687	0.933433	−	0.358752i	$-0.116798\pi$
$179$	24.9770	1.86687	0.933433	+	0.358752i	$0.116798\pi$
$180$	0	0
$181$	1.81493	0.134902	0.0674512	−	0.997723i	$-0.478513\pi$
$181$	1.81493	0.134902	0.0674512	+	0.997723i	$0.478513\pi$
$182$	−1.35920	−0.100750
$183$	2.60886	0.192853
$184$	−5.75064	−0.423943
$185$	0	0
$186$	0.645784	0.0473512
$187$	−3.00609	−0.219827
$188$	42.5680	3.10459
$189$	4.35808	0.317004
$190$	0	0
$191$	13.1084	0.948492	0.474246	−	0.880392i	$-0.342721\pi$
$191$	13.1084	0.948492	0.474246	+	0.880392i	$0.342721\pi$
$192$	3.09034	0.223026
$193$	10.4607	0.752978	0.376489	−	0.926421i	$-0.377131\pi$
$193$	10.4607	0.752978	0.376489	+	0.926421i	$0.377131\pi$
$194$	38.6183	2.77263
$195$	0	0
$196$	4.29248	0.306606
$197$	14.3223	1.02042	0.510211	−	0.860049i	$-0.329567\pi$
$197$	14.3223	1.02042	0.510211	+	0.860049i	$0.329567\pi$
$198$	20.5232	1.45852
$199$	−14.7918	−1.04856	−0.524280	−	0.851546i	$-0.675666\pi$
$199$	−14.7918	−1.04856	−0.524280	+	0.851546i	$0.675666\pi$
$200$	0	0
$201$	0.644162	0.0454356
$202$	−22.6239	−1.59181
$203$	0.916320	0.0643130
$204$	3.00609	0.210469
$205$	0	0
$206$	28.4532	1.98243
$207$	−2.33193	−0.162080
$208$	3.16457	0.219423
$209$	−13.9764	−0.966768
$210$	0	0
$211$	−9.61731	−0.662083	−0.331041	−	0.943616i	$-0.607400\pi$
$211$	−9.61731	−0.662083	−0.331041	+	0.943616i	$0.607400\pi$
$212$	−14.1329	−0.970651
$213$	2.65888	0.182183
$214$	−17.5335	−1.19857
$215$	0	0
$216$	−25.0618	−1.70524
$217$	0.314967	0.0213814
$218$	3.15706	0.213823
$219$	−4.12455	−0.278711
$220$	0	0
$221$	−0.464253	−0.0312290
$222$	7.05672	0.473616
$223$	23.3606	1.56434	0.782172	−	0.623063i	$-0.214112\pi$
$223$	23.3606	1.56434	0.782172	+	0.623063i	$0.214112\pi$
$224$	−3.14929	−0.210420
$225$	0	0
$226$	11.8087	0.785505
$227$	2.21499	0.147014	0.0735072	−	0.997295i	$-0.476581\pi$
$227$	2.21499	0.147014	0.0735072	+	0.997295i	$0.476581\pi$
$228$	13.9764	0.925610
$229$	4.57708	0.302462	0.151231	−	0.988498i	$-0.451676\pi$
$229$	4.57708	0.302462	0.151231	+	0.988498i	$0.451676\pi$
$230$	0	0
$231$	−2.86768	−0.188679
$232$	−5.26942	−0.345955
$233$	9.60558	0.629283	0.314641	−	0.949211i	$-0.398116\pi$
$233$	9.60558	0.629283	0.314641	+	0.949211i	$0.398116\pi$
$234$	3.16955	0.207200
$235$	0	0
$236$	−29.0236	−1.88928
$237$	−5.50427	−0.357541
$238$	2.14929	0.139317
$239$	24.1497	1.56212	0.781059	−	0.624458i	$-0.214680\pi$
$239$	24.1497	1.56212	0.781059	+	0.624458i	$0.214680\pi$
$240$	0	0
$241$	22.0321	1.41921	0.709605	−	0.704600i	$-0.248873\pi$
$241$	22.0321	1.41921	0.709605	+	0.704600i	$0.248873\pi$
$242$	−3.28471	−0.211149
$243$	−15.8808	−1.01875
$244$	−13.7009	−0.877109
$245$	0	0
$246$	−7.39642	−0.471579
$247$	−2.15848	−0.137341
$248$	−1.81126	−0.115015
$249$	−2.75699	−0.174717
$250$	0	0
$251$	6.87519	0.433958	0.216979	−	0.976176i	$-0.430380\pi$
$251$	6.87519	0.433958	0.216979	+	0.976176i	$0.430380\pi$
$252$	−10.0098	−0.630555
$253$	3.50848	0.220576
$254$	33.0776	2.07547
$255$	0	0
$256$	−32.0293	−2.00183
$257$	−6.39921	−0.399172	−0.199586	−	0.979880i	$-0.563960\pi$
$257$	−6.39921	−0.399172	−0.199586	+	0.979880i	$0.563960\pi$
$258$	−26.0061	−1.61907
$259$	3.44176	0.213861
$260$	0	0
$261$	−2.13679	−0.132264
$262$	−42.7718	−2.64245
$263$	−27.8958	−1.72013	−0.860065	−	0.510185i	$-0.829577\pi$
$263$	−27.8958	−1.72013	−0.860065	+	0.510185i	$0.829577\pi$
$264$	16.4910	1.01495
$265$	0	0
$266$	9.99279	0.612698
$267$	3.60161	0.220415
$268$	−3.38292	−0.206645
$269$	−1.70442	−0.103921	−0.0519603	−	0.998649i	$-0.516547\pi$
$269$	−1.70442	−0.103921	−0.0519603	+	0.998649i	$0.516547\pi$
$270$	0	0
$271$	15.0575	0.914681	0.457340	−	0.889292i	$-0.348802\pi$
$271$	15.0575	0.914681	0.457340	+	0.889292i	$0.348802\pi$
$272$	−5.00411	−0.303419
$273$	−0.442876	−0.0268041
$274$	46.9714	2.83765
$275$	0	0
$276$	−3.50848	−0.211186
$277$	−14.8658	−0.893200	−0.446600	−	0.894734i	$-0.647365\pi$
$277$	−14.8658	−0.893200	−0.446600	+	0.894734i	$0.647365\pi$
$278$	27.8610	1.67099
$279$	−0.734482	−0.0439723
$280$	0	0
$281$	−25.5471	−1.52401	−0.762005	−	0.647571i	$-0.775785\pi$
$281$	−25.5471	−1.52401	−0.762005	+	0.647571i	$0.775785\pi$
$282$	20.3328	1.21080
$283$	−5.94968	−0.353672	−0.176836	−	0.984240i	$-0.556586\pi$
$283$	−5.94968	−0.353672	−0.176836	+	0.984240i	$0.556586\pi$
$284$	−13.9635	−0.828584
$285$	0	0
$286$	−4.76871	−0.281980
$287$	−3.60745	−0.212941
$288$	7.34391	0.432744
$289$	−16.2659	−0.956817
$290$	0	0
$291$	12.5833	0.737645
$292$	21.6608	1.26760
$293$	−14.4206	−0.842460	−0.421230	−	0.906954i	$-0.638401\pi$
$293$	−14.4206	−0.842460	−0.421230	+	0.906954i	$0.638401\pi$
$294$	2.05032	0.119577
$295$	0	0
$296$	−19.7923	−1.15041
$297$	15.2903	0.887230
$298$	33.0461	1.91431
$299$	0.541840	0.0313354
$300$	0	0
$301$	−12.6839	−0.731089
$302$	−12.0506	−0.693436
$303$	−7.37169	−0.423492
$304$	−23.2659	−1.33439
$305$	0	0
$306$	−5.01198	−0.286516
$307$	−27.3695	−1.56206	−0.781030	−	0.624493i	$-0.785306\pi$
$307$	−27.3695	−1.56206	−0.781030	+	0.624493i	$0.785306\pi$
$308$	15.0601	0.858128
$309$	9.27110	0.527415
$310$	0	0
$311$	22.3542	1.26759	0.633796	−	0.773500i	$-0.281496\pi$
$311$	22.3542	1.26759	0.633796	+	0.773500i	$0.281496\pi$
$312$	2.54682	0.144185
$313$	−17.4227	−0.984788	−0.492394	−	0.870372i	$-0.663878\pi$
$313$	−17.4227	−0.984788	−0.492394	+	0.870372i	$0.663878\pi$
$314$	−47.1257	−2.65946
$315$	0	0
$316$	28.9066	1.62612
$317$	8.00864	0.449810	0.224905	−	0.974381i	$-0.427793\pi$
$317$	8.00864	0.449810	0.224905	+	0.974381i	$0.427793\pi$
$318$	−6.75064	−0.378557
$319$	3.21489	0.179999
$320$	0	0
$321$	−5.71307	−0.318872
$322$	−2.50848	−0.139792
$323$	3.41318	0.189914
$324$	14.7390	0.818834
$325$	0	0
$326$	22.1991	1.22949
$327$	1.02869	0.0568864
$328$	20.7451	1.14546
$329$	9.91689	0.546736
$330$	0	0
$331$	−26.0528	−1.43199	−0.715995	−	0.698106i	$-0.754027\pi$
$331$	−26.0528	−1.43199	−0.715995	+	0.698106i	$0.754027\pi$
$332$	14.4788	0.794627
$333$	−8.02595	−0.439819
$334$	−41.9545	−2.29565
$335$	0	0
$336$	−4.77369	−0.260426
$337$	−29.8174	−1.62426	−0.812128	−	0.583479i	$-0.801691\pi$
$337$	−29.8174	−1.62426	−0.812128	+	0.583479i	$0.801691\pi$
$338$	31.8738	1.73371
$339$	3.84772	0.208979
$340$	0	0
$341$	1.10506	0.0598422
$342$	−23.3025	−1.26005
$343$	1.00000	0.0539949
$344$	72.9406	3.93270
$345$	0	0
$346$	25.9008	1.39244
$347$	−31.1746	−1.67354	−0.836770	−	0.547555i	$-0.815559\pi$
$347$	−31.1746	−1.67354	−0.836770	+	0.547555i	$0.815559\pi$
$348$	−3.21489	−0.172336
$349$	−1.97075	−0.105492	−0.0527459	−	0.998608i	$-0.516797\pi$
$349$	−1.97075	−0.105492	−0.0527459	+	0.998608i	$0.516797\pi$
$350$	0	0
$351$	2.36138	0.126041
$352$	−11.0492	−0.588925
$353$	8.17722	0.435230	0.217615	−	0.976035i	$-0.430172\pi$
$353$	8.17722	0.435230	0.217615	+	0.976035i	$0.430172\pi$
$354$	−13.8633	−0.736824
$355$	0	0
$356$	−18.9145	−1.00246
$357$	0.700316	0.0370647
$358$	−62.6542	−3.31138
$359$	−12.3064	−0.649509	−0.324755	−	0.945798i	$-0.605282\pi$
$359$	−12.3064	−0.649509	−0.324755	+	0.945798i	$0.605282\pi$
$360$	0	0
$361$	−3.13090	−0.164784
$362$	−4.55271	−0.239285
$363$	−1.07028	−0.0561751
$364$	2.32584	0.121907
$365$	0	0
$366$	−6.54429	−0.342075
$367$	−36.8034	−1.92112	−0.960561	−	0.278069i	$-0.910306\pi$
$367$	−36.8034	−1.92112	−0.960561	+	0.278069i	$0.910306\pi$
$368$	5.84041	0.304452
$369$	8.41231	0.437927
$370$	0	0
$371$	−3.29248	−0.170937
$372$	−1.10506	−0.0572945
$373$	18.6234	0.964283	0.482142	−	0.876093i	$-0.339859\pi$
$373$	18.6234	0.964283	0.482142	+	0.876093i	$0.339859\pi$
$374$	7.54073	0.389922
$375$	0	0
$376$	−57.0284	−2.94102
$377$	0.496499	0.0255710
$378$	−10.9322	−0.562290
$379$	−17.5845	−0.903256	−0.451628	−	0.892206i	$-0.649157\pi$
$379$	−17.5845	−0.903256	−0.451628	+	0.892206i	$0.649157\pi$
$380$	0	0
$381$	10.7779	0.552169
$382$	−32.8822	−1.68240
$383$	−16.1214	−0.823764	−0.411882	−	0.911237i	$-0.635128\pi$
$383$	−16.1214	−0.823764	−0.411882	+	0.911237i	$0.635128\pi$
$384$	−12.9002	−0.658312
$385$	0	0
$386$	−26.2405	−1.33561
$387$	29.5780	1.50353
$388$	−66.0832	−3.35486
$389$	−22.3119	−1.13126	−0.565629	−	0.824660i	$-0.691366\pi$
$389$	−22.3119	−1.13126	−0.565629	+	0.824660i	$0.691366\pi$
$390$	0	0
$391$	−0.856807	−0.0433306
$392$	−5.75064	−0.290451
$393$	−13.9366	−0.703010
$394$	−35.9272	−1.80999
$395$	0	0
$396$	−35.1190	−1.76480
$397$	30.1165	1.51150	0.755752	−	0.654858i	$-0.227272\pi$
$397$	30.1165	1.51150	0.755752	+	0.654858i	$0.227272\pi$
$398$	37.1049	1.85990
$399$	3.25602	0.163005
$400$	0	0
$401$	−11.2492	−0.561757	−0.280879	−	0.959743i	$-0.590626\pi$
$401$	−11.2492	−0.561757	−0.280879	+	0.959743i	$0.590626\pi$
$402$	−1.61587	−0.0805921
$403$	0.170662	0.00850128
$404$	38.7136	1.92608
$405$	0	0
$406$	−2.29857	−0.114076
$407$	12.0754	0.598553
$408$	−4.02727	−0.199379
$409$	−12.6669	−0.626336	−0.313168	−	0.949698i	$-0.601390\pi$
$409$	−12.6669	−0.626336	−0.313168	+	0.949698i	$0.601390\pi$
$410$	0	0
$411$	15.3050	0.754941
$412$	−48.6887	−2.39872
$413$	−6.76151	−0.332712
$414$	5.84960	0.287492
$415$	0	0
$416$	−1.70641	−0.0836636
$417$	9.07815	0.444559
$418$	35.0595	1.71482
$419$	−18.6714	−0.912156	−0.456078	−	0.889940i	$-0.650746\pi$
$419$	−18.6714	−0.912156	−0.456078	+	0.889940i	$0.650746\pi$
$420$	0	0
$421$	−16.1723	−0.788192	−0.394096	−	0.919069i	$-0.628942\pi$
$421$	−16.1723	−0.788192	−0.394096	+	0.919069i	$0.628942\pi$
$422$	24.1248	1.17438
$423$	−23.1255	−1.12440
$424$	18.9338	0.919509
$425$	0	0
$426$	−6.66975	−0.323150
$427$	−3.19184	−0.154464
$428$	30.0031	1.45026
$429$	−1.55382	−0.0750193
$430$	0	0
$431$	3.79673	0.182882	0.0914410	−	0.995810i	$-0.470853\pi$
$431$	3.79673	0.182882	0.0914410	+	0.995810i	$0.470853\pi$
$432$	25.4530	1.22461
$433$	−32.6028	−1.56679	−0.783395	−	0.621524i	$-0.786514\pi$
$433$	−32.6028	−1.56679	−0.783395	+	0.621524i	$0.786514\pi$
$434$	−0.790090	−0.0379255
$435$	0	0
$436$	−5.40231	−0.258724
$437$	−3.98360	−0.190562
$438$	10.3464	0.494368
$439$	−28.5319	−1.36175	−0.680877	−	0.732398i	$-0.738401\pi$
$439$	−28.5319	−1.36175	−0.680877	+	0.732398i	$0.738401\pi$
$440$	0	0
$441$	−2.33193	−0.111044
$442$	1.16457	0.0553929
$443$	13.0072	0.617992	0.308996	−	0.951063i	$-0.400007\pi$
$443$	13.0072	0.617992	0.308996	+	0.951063i	$0.400007\pi$
$444$	−12.0754	−0.573071
$445$	0	0
$446$	−58.5997	−2.77478
$447$	10.7676	0.509292
$448$	−3.78090	−0.178631
$449$	9.41571	0.444355	0.222177	−	0.975006i	$-0.428684\pi$
$449$	9.41571	0.444355	0.222177	+	0.975006i	$0.428684\pi$
$450$	0	0
$451$	−12.6567	−0.595979
$452$	−20.2069	−0.950454
$453$	−3.92654	−0.184485
$454$	−5.55627	−0.260769
$455$	0	0
$456$	−18.7242	−0.876841
$457$	−4.21246	−0.197051	−0.0985253	−	0.995135i	$-0.531413\pi$
$457$	−4.21246	−0.197051	−0.0985253	+	0.995135i	$0.531413\pi$
$458$	−11.4815	−0.536496
$459$	−3.73404	−0.174290
$460$	0	0
$461$	−13.4911	−0.628342	−0.314171	−	0.949366i	$-0.601727\pi$
$461$	−13.4911	−0.628342	−0.314171	+	0.949366i	$0.601727\pi$
$462$	7.19351	0.334673
$463$	−14.4738	−0.672655	−0.336327	−	0.941745i	$-0.609185\pi$
$463$	−14.4738	−0.672655	−0.336327	+	0.941745i	$0.609185\pi$
$464$	5.35168	0.248446
$465$	0	0
$466$	−24.0954	−1.11620
$467$	−36.1865	−1.67451	−0.837256	−	0.546811i	$-0.815842\pi$
$467$	−36.1865	−1.67451	−0.837256	+	0.546811i	$0.815842\pi$
$468$	−5.42369	−0.250710
$469$	−0.788104	−0.0363913
$470$	0	0
$471$	−15.3553	−0.707534
$472$	38.8830	1.78973
$473$	−44.5013	−2.04617
$474$	13.8074	0.634193
$475$	0	0
$476$	−3.67783	−0.168573
$477$	7.67783	0.351544
$478$	−60.5792	−2.77083
$479$	−29.4649	−1.34629	−0.673144	−	0.739512i	$-0.735056\pi$
$479$	−29.4649	−1.34629	−0.673144	+	0.739512i	$0.735056\pi$
$480$	0	0
$481$	1.86489	0.0850315
$482$	−55.2670	−2.51734
$483$	−0.817356	−0.0371910
$484$	5.62074	0.255488
$485$	0	0
$486$	39.8367	1.80703
$487$	2.36727	0.107271	0.0536357	−	0.998561i	$-0.482919\pi$
$487$	2.36727	0.107271	0.0536357	+	0.998561i	$0.482919\pi$
$488$	18.3551	0.830896
$489$	7.23327	0.327100
$490$	0	0
$491$	−14.2619	−0.643632	−0.321816	−	0.946802i	$-0.604293\pi$
$491$	−14.2619	−0.643632	−0.321816	+	0.946802i	$0.604293\pi$
$492$	12.6567	0.570606
$493$	−0.785110	−0.0353596
$494$	5.41450	0.243610
$495$	0	0
$496$	1.83954	0.0825977
$497$	−3.25303	−0.145918
$498$	6.91586	0.309907
$499$	−6.13811	−0.274780	−0.137390	−	0.990517i	$-0.543871\pi$
$499$	−6.13811	−0.274780	−0.137390	+	0.990517i	$0.543871\pi$
$500$	0	0
$501$	−13.6703	−0.610745
$502$	−17.2463	−0.769739
$503$	−4.15463	−0.185246	−0.0926229	−	0.995701i	$-0.529525\pi$
$503$	−4.15463	−0.185246	−0.0926229	+	0.995701i	$0.529525\pi$
$504$	13.4101	0.597333
$505$	0	0
$506$	−8.80096	−0.391250
$507$	10.3857	0.461243
$508$	−56.6019	−2.51130
$509$	−17.7266	−0.785717	−0.392859	−	0.919599i	$-0.628514\pi$
$509$	−17.7266	−0.785717	−0.392859	+	0.919599i	$0.628514\pi$
$510$	0	0
$511$	5.04621	0.223231
$512$	48.7791	2.15575
$513$	−17.3609	−0.766501
$514$	16.0523	0.708037
$515$	0	0
$516$	44.5013	1.95906
$517$	34.7932	1.53020
$518$	−8.63360	−0.379339
$519$	8.43943	0.370450
$520$	0	0
$521$	−1.64137	−0.0719097	−0.0359549	−	0.999353i	$-0.511447\pi$
$521$	−1.64137	−0.0719097	−0.0359549	+	0.999353i	$0.511447\pi$
$522$	5.36011	0.234605
$523$	10.9325	0.478046	0.239023	−	0.971014i	$-0.423173\pi$
$523$	10.9325	0.478046	0.239023	+	0.971014i	$0.423173\pi$
$524$	73.1906	3.19734
$525$	0	0
$526$	69.9761	3.05110
$527$	−0.269866	−0.0117556
$528$	−16.7484	−0.728881
$529$	1.00000	0.0434783
$530$	0	0
$531$	15.7674	0.684245
$532$	−17.0995	−0.741359
$533$	−1.95466	−0.0846657
$534$	−9.03458	−0.390964
$535$	0	0
$536$	4.53210	0.195757
$537$	−20.4151	−0.880975
$538$	4.27552	0.184331
$539$	3.50848	0.151121
$540$	0	0
$541$	29.1080	1.25145	0.625725	−	0.780044i	$-0.284803\pi$
$541$	29.1080	1.25145	0.625725	+	0.780044i	$0.284803\pi$
$542$	−37.7716	−1.62243
$543$	−1.48344	−0.0636605
$544$	2.69833	0.115690
$545$	0	0
$546$	1.11095	0.0475441
$547$	11.3355	0.484670	0.242335	−	0.970193i	$-0.422087\pi$
$547$	11.3355	0.484670	0.242335	+	0.970193i	$0.422087\pi$
$548$	−80.3769	−3.43353
$549$	7.44314	0.317665
$550$	0	0
$551$	−3.65025	−0.155506
$552$	4.70032	0.200059
$553$	6.73424	0.286369
$554$	37.2906	1.58433
$555$	0	0
$556$	−47.6754	−2.02189
$557$	36.5791	1.54990	0.774952	−	0.632020i	$-0.217774\pi$
$557$	36.5791	1.54990	0.774952	+	0.632020i	$0.217774\pi$
$558$	1.84243	0.0779964
$559$	−6.87266	−0.290682
$560$	0	0
$561$	2.45705	0.103737
$562$	64.0844	2.70324
$563$	−27.4270	−1.15591	−0.577956	−	0.816068i	$-0.696150\pi$
$563$	−27.4270	−1.15591	−0.577956	+	0.816068i	$0.696150\pi$
$564$	−34.7932	−1.46506
$565$	0	0
$566$	14.9247	0.627330
$567$	3.43369	0.144201
$568$	18.7070	0.784927
$569$	33.7226	1.41373	0.706863	−	0.707351i	$-0.250110\pi$
$569$	33.7226	1.41373	0.706863	+	0.707351i	$0.250110\pi$
$570$	0	0
$571$	−23.9542	−1.00245	−0.501225	−	0.865317i	$-0.667117\pi$
$571$	−23.9542	−1.00245	−0.501225	+	0.865317i	$0.667117\pi$
$572$	8.16015	0.341193
$573$	−10.7142	−0.447594
$574$	9.04921	0.377707
$575$	0	0
$576$	8.81679	0.367366
$577$	−9.86403	−0.410645	−0.205323	−	0.978694i	$-0.565824\pi$
$577$	−9.86403	−0.410645	−0.205323	+	0.978694i	$0.565824\pi$
$578$	40.8027	1.69717
$579$	−8.55012	−0.355331
$580$	0	0
$581$	3.37306	0.139938
$582$	−31.5649	−1.30841
$583$	−11.5516	−0.478418
$584$	−29.0189	−1.20081
$585$	0	0
$586$	36.1738	1.49433
$587$	−40.1041	−1.65527	−0.827636	−	0.561265i	$-0.810315\pi$
$587$	−40.1041	−1.65527	−0.827636	+	0.561265i	$0.810315\pi$
$588$	−3.50848	−0.144687
$589$	−1.25470	−0.0516992
$590$	0	0
$591$	−11.7064	−0.481537
$592$	20.1013	0.826159
$593$	12.6878	0.521024	0.260512	−	0.965471i	$-0.416109\pi$
$593$	12.6878	0.521024	0.260512	+	0.965471i	$0.416109\pi$
$594$	−38.3553	−1.57374
$595$	0	0
$596$	−56.5481	−2.31630
$597$	12.0901	0.494816
$598$	−1.35920	−0.0555817
$599$	21.7401	0.888278	0.444139	−	0.895958i	$-0.353510\pi$
$599$	21.7401	0.888278	0.444139	+	0.895958i	$0.353510\pi$
$600$	0	0
$601$	4.04779	0.165113	0.0825564	−	0.996586i	$-0.473692\pi$
$601$	4.04779	0.165113	0.0825564	+	0.996586i	$0.473692\pi$
$602$	31.8174	1.29678
$603$	1.83780	0.0748412
$604$	20.6209	0.839051
$605$	0	0
$606$	18.4917	0.751176
$607$	31.7697	1.28949	0.644747	−	0.764396i	$-0.276963\pi$
$607$	31.7697	1.28949	0.644747	+	0.764396i	$0.276963\pi$
$608$	12.5455	0.508787
$609$	−0.748959	−0.0303494
$610$	0	0
$611$	5.37337	0.217383
$612$	8.57643	0.346682
$613$	−10.2630	−0.414517	−0.207259	−	0.978286i	$-0.566454\pi$
$613$	−10.2630	−0.414517	−0.207259	+	0.978286i	$0.566454\pi$
$614$	68.6559	2.77073
$615$	0	0
$616$	−20.1760	−0.812914
$617$	26.1681	1.05349	0.526745	−	0.850024i	$-0.323412\pi$
$617$	26.1681	1.05349	0.526745	+	0.850024i	$0.323412\pi$
$618$	−23.2564	−0.935509
$619$	43.7567	1.75873	0.879364	−	0.476149i	$-0.157968\pi$
$619$	43.7567	1.75873	0.879364	+	0.476149i	$0.157968\pi$
$620$	0	0
$621$	4.35808	0.174884
$622$	−56.0752	−2.24841
$623$	−4.40642	−0.176539
$624$	−2.58658	−0.103546
$625$	0	0
$626$	43.7045	1.74678
$627$	11.4237	0.456218
$628$	80.6408	3.21792
$629$	−2.94893	−0.117581
$630$	0	0
$631$	−6.40642	−0.255036	−0.127518	−	0.991836i	$-0.540701\pi$
$631$	−6.40642	−0.255036	−0.127518	+	0.991836i	$0.540701\pi$
$632$	−38.7262	−1.54044
$633$	7.86076	0.312437
$634$	−20.0895	−0.797857
$635$	0	0
$636$	11.5516	0.458051
$637$	0.541840	0.0214685
$638$	−8.06449	−0.319276
$639$	7.58583	0.300091
$640$	0	0
$641$	−39.3613	−1.55468	−0.777339	−	0.629082i	$-0.783431\pi$
$641$	−39.3613	−1.55468	−0.777339	+	0.629082i	$0.783431\pi$
$642$	14.3311	0.565604
$643$	41.6534	1.64265	0.821324	−	0.570462i	$-0.193236\pi$
$643$	41.6534	1.64265	0.821324	+	0.570462i	$0.193236\pi$
$644$	4.29248	0.169147
$645$	0	0
$646$	−8.56190	−0.336863
$647$	9.36686	0.368249	0.184125	−	0.982903i	$-0.441055\pi$
$647$	9.36686	0.368249	0.184125	+	0.982903i	$0.441055\pi$
$648$	−19.7459	−0.775691
$649$	−23.7226	−0.931194
$650$	0	0
$651$	−0.257440	−0.0100899
$652$	−37.9867	−1.48767
$653$	7.37174	0.288479	0.144239	−	0.989543i	$-0.453926\pi$
$653$	7.37174	0.288479	0.144239	+	0.989543i	$0.453926\pi$
$654$	−2.58044	−0.100903
$655$	0	0
$656$	−21.0690	−0.822605
$657$	−11.7674	−0.459091
$658$	−24.8763	−0.969780
$659$	−24.4032	−0.950613	−0.475307	−	0.879820i	$-0.657663\pi$
$659$	−24.4032	−0.950613	−0.475307	+	0.879820i	$0.657663\pi$
$660$	0	0
$661$	−28.0839	−1.09234	−0.546169	−	0.837675i	$-0.683914\pi$
$661$	−28.0839	−1.09234	−0.546169	+	0.837675i	$0.683914\pi$
$662$	65.3529	2.54001
$663$	0.379460	0.0147370
$664$	−19.3972	−0.752759
$665$	0	0
$666$	20.1329	0.780136
$667$	0.916320	0.0354800
$668$	71.7919	2.77771
$669$	−19.0939	−0.738215
$670$	0	0
$671$	−11.1985	−0.432313
$672$	2.57409	0.0992975
$673$	12.6286	0.486797	0.243399	−	0.969926i	$-0.421738\pi$
$673$	12.6286	0.486797	0.243399	+	0.969926i	$0.421738\pi$
$674$	74.7963	2.88105
$675$	0	0
$676$	−54.5420	−2.09777
$677$	−14.4125	−0.553919	−0.276959	−	0.960882i	$-0.589327\pi$
$677$	−14.4125	−0.553919	−0.276959	+	0.960882i	$0.589327\pi$
$678$	−9.65193	−0.370680
$679$	−15.3951	−0.590810
$680$	0	0
$681$	−1.81044	−0.0693761
$682$	−2.77201	−0.106146
$683$	−50.6830	−1.93933	−0.969666	−	0.244433i	$-0.921398\pi$
$683$	−50.6830	−1.93933	−0.969666	+	0.244433i	$0.921398\pi$
$684$	39.8749	1.52465
$685$	0	0
$686$	−2.50848	−0.0957743
$687$	−3.74110	−0.142732
$688$	−74.0793	−2.82425
$689$	−1.78400	−0.0679649
$690$	0	0
$691$	33.0879	1.25872	0.629362	−	0.777112i	$-0.283316\pi$
$691$	33.0879	1.25872	0.629362	+	0.777112i	$0.283316\pi$
$692$	−44.3211	−1.68483
$693$	−8.18153	−0.310791
$694$	78.2009	2.96846
$695$	0	0
$696$	4.30699	0.163256
$697$	3.09089	0.117076
$698$	4.94359	0.187117
$699$	−7.85118	−0.296959
$700$	0	0
$701$	−36.8895	−1.39330	−0.696649	−	0.717412i	$-0.745326\pi$
$701$	−36.8895	−1.39330	−0.696649	+	0.717412i	$0.745326\pi$
$702$	−5.92349	−0.223568
$703$	−13.7106	−0.517106
$704$	−13.2652	−0.499951
$705$	0	0
$706$	−20.5124	−0.771995
$707$	9.01895	0.339192
$708$	23.7226	0.891551
$709$	−18.4348	−0.692334	−0.346167	−	0.938173i	$-0.612517\pi$
$709$	−18.4348	−0.692334	−0.346167	+	0.938173i	$0.612517\pi$
$710$	0	0
$711$	−15.7038	−0.588938
$712$	25.3397	0.949646
$713$	0.314967	0.0117956
$714$	−1.75673	−0.0657440
$715$	0	0
$716$	107.213	4.00674
$717$	−19.7389	−0.737164
$718$	30.8705	1.15208
$719$	21.6203	0.806301	0.403151	−	0.915134i	$-0.367915\pi$
$719$	21.6203	0.806301	0.403151	+	0.915134i	$0.367915\pi$
$720$	0	0
$721$	−11.3428	−0.422428
$722$	7.85381	0.292289
$723$	−18.0080	−0.669726
$724$	7.79053	0.289533
$725$	0	0
$726$	2.68477	0.0996413
$727$	14.4447	0.535723	0.267861	−	0.963457i	$-0.413683\pi$
$727$	14.4447	0.535723	0.267861	+	0.963457i	$0.413683\pi$
$728$	−3.11593	−0.115484
$729$	2.67920	0.0992296
$730$	0	0
$731$	10.8677	0.401956
$732$	11.1985	0.413908
$733$	39.7963	1.46991	0.734955	−	0.678116i	$-0.237203\pi$
$733$	39.7963	1.46991	0.734955	+	0.678116i	$0.237203\pi$
$734$	92.3207	3.40762
$735$	0	0
$736$	−3.14929	−0.116084
$737$	−2.76505	−0.101852
$738$	−21.1021	−0.776780
$739$	−51.1491	−1.88155	−0.940775	−	0.339030i	$-0.889901\pi$
$739$	−51.1491	−1.88155	−0.940775	+	0.339030i	$0.889901\pi$
$740$	0	0
$741$	1.76424	0.0648111
$742$	8.25912	0.303202
$743$	11.9870	0.439759	0.219879	−	0.975527i	$-0.429434\pi$
$743$	11.9870	0.439759	0.219879	+	0.975527i	$0.429434\pi$
$744$	1.48045	0.0542758
$745$	0	0
$746$	−46.7164	−1.71041
$747$	−7.86574	−0.287792
$748$	−12.9036	−0.471802
$749$	6.98970	0.255398
$750$	0	0
$751$	−33.3499	−1.21696	−0.608478	−	0.793571i	$-0.708220\pi$
$751$	−33.3499	−1.21696	−0.608478	+	0.793571i	$0.708220\pi$
$752$	57.9187	2.11208
$753$	−5.61947	−0.204785
$754$	−1.24546	−0.0453569
$755$	0	0
$756$	18.7070	0.680366
$757$	17.9791	0.653461	0.326730	−	0.945118i	$-0.394053\pi$
$757$	17.9791	0.653461	0.326730	+	0.945118i	$0.394053\pi$
$758$	44.1104	1.60216
$759$	−2.86768	−0.104090
$760$	0	0
$761$	−29.8968	−1.08376	−0.541880	−	0.840456i	$-0.682287\pi$
$761$	−29.8968	−1.08376	−0.541880	+	0.840456i	$0.682287\pi$
$762$	−27.0362	−0.979417
$763$	−1.25855	−0.0455627
$764$	56.2676	2.03569
$765$	0	0
$766$	40.4402	1.46116
$767$	−3.66366	−0.132287
$768$	26.1793	0.944664
$769$	6.44703	0.232486	0.116243	−	0.993221i	$-0.462915\pi$
$769$	6.44703	0.232486	0.116243	+	0.993221i	$0.462915\pi$
$770$	0	0
$771$	5.23043	0.188369
$772$	44.9024	1.61607
$773$	31.1639	1.12089	0.560444	−	0.828192i	$-0.310630\pi$
$773$	31.1639	1.12089	0.560444	+	0.828192i	$0.310630\pi$
$774$	−74.1959	−2.66692
$775$	0	0
$776$	88.5317	3.17810
$777$	−2.81314	−0.100921
$778$	55.9690	2.00658
$779$	14.3706	0.514881
$780$	0	0
$781$	−11.4132	−0.408396
$782$	2.14929	0.0768583
$783$	3.99340	0.142712
$784$	5.84041	0.208586
$785$	0	0
$786$	34.9598	1.24697
$787$	−14.3398	−0.511160	−0.255580	−	0.966788i	$-0.582266\pi$
$787$	−14.3398	−0.511160	−0.255580	+	0.966788i	$0.582266\pi$
$788$	61.4781	2.19007
$789$	22.8008	0.811730
$790$	0	0
$791$	−4.70752	−0.167380
$792$	47.0490	1.67181
$793$	−1.72946	−0.0614151
$794$	−75.5467	−2.68105
$795$	0	0
$796$	−63.4933	−2.25046
$797$	12.8167	0.453990	0.226995	−	0.973896i	$-0.427110\pi$
$797$	12.8167	0.453990	0.226995	+	0.973896i	$0.427110\pi$
$798$	−8.16767	−0.289132
$799$	−8.49686	−0.300597
$800$	0	0
$801$	10.2755	0.363066
$802$	28.2184	0.996425
$803$	17.7045	0.624780
$804$	2.76505	0.0975158
$805$	0	0
$806$	−0.428102	−0.0150793
$807$	1.39312	0.0490402
$808$	−51.8647	−1.82459
$809$	45.2722	1.59169	0.795843	−	0.605503i	$-0.207028\pi$
$809$	45.2722	1.59169	0.795843	+	0.605503i	$0.207028\pi$
$810$	0	0
$811$	−51.5019	−1.80848	−0.904239	−	0.427027i	$-0.859561\pi$
$811$	−51.5019	−1.80848	−0.904239	+	0.427027i	$0.859561\pi$
$812$	3.93328	0.138031
$813$	−12.3074	−0.431638
$814$	−30.2908	−1.06169
$815$	0	0
$816$	4.09014	0.143183
$817$	50.5277	1.76774
$818$	31.7746	1.11097
$819$	−1.26353	−0.0441514
$820$	0	0
$821$	−31.3886	−1.09547	−0.547734	−	0.836652i	$-0.684510\pi$
$821$	−31.3886	−1.09547	−0.547734	+	0.836652i	$0.684510\pi$
$822$	−38.3924	−1.33909
$823$	34.2009	1.19217	0.596084	−	0.802922i	$-0.296723\pi$
$823$	34.2009	1.19217	0.596084	+	0.802922i	$0.296723\pi$
$824$	65.2283	2.27234
$825$	0	0
$826$	16.9611	0.590153
$827$	−12.4751	−0.433803	−0.216901	−	0.976194i	$-0.569595\pi$
$827$	−12.4751	−0.433803	−0.216901	+	0.976194i	$0.569595\pi$
$828$	−10.0098	−0.347863
$829$	−11.0668	−0.384367	−0.192183	−	0.981359i	$-0.561557\pi$
$829$	−11.0668	−0.384367	−0.192183	+	0.981359i	$0.561557\pi$
$830$	0	0
$831$	12.1507	0.421502
$832$	−2.04864	−0.0710239
$833$	−0.856807	−0.0296866
$834$	−22.7724	−0.788543
$835$	0	0
$836$	−59.9934	−2.07491
$837$	1.37265	0.0474459
$838$	46.8368	1.61795
$839$	−17.4038	−0.600846	−0.300423	−	0.953806i	$-0.597128\pi$
$839$	−17.4038	−0.600846	−0.300423	+	0.953806i	$0.597128\pi$
$840$	0	0
$841$	−28.1604	−0.971047
$842$	40.5680	1.39807
$843$	20.8811	0.719182
$844$	−41.2821	−1.42099
$845$	0	0
$846$	58.0098	1.99442
$847$	1.30944	0.0449929
$848$	−19.2294	−0.660341
$849$	4.86300	0.166898
$850$	0	0
$851$	3.44176	0.117982
$852$	11.4132	0.391009
$853$	24.9701	0.854961	0.427480	−	0.904025i	$-0.359401\pi$
$853$	24.9701	0.854961	0.427480	+	0.904025i	$0.359401\pi$
$854$	8.00666	0.273982
$855$	0	0
$856$	−40.1952	−1.37384
$857$	12.2388	0.418068	0.209034	−	0.977908i	$-0.432968\pi$
$857$	12.2388	0.418068	0.209034	+	0.977908i	$0.432968\pi$
$858$	3.89773	0.133066
$859$	−31.1201	−1.06180	−0.530901	−	0.847434i	$-0.678146\pi$
$859$	−31.1201	−1.06180	−0.530901	+	0.847434i	$0.678146\pi$
$860$	0	0
$861$	2.94857	0.100487
$862$	−9.52402	−0.324390
$863$	−28.3634	−0.965502	−0.482751	−	0.875758i	$-0.660362\pi$
$863$	−28.3634	−0.965502	−0.482751	+	0.875758i	$0.660362\pi$
$864$	−13.7248	−0.466929
$865$	0	0
$866$	81.7835	2.77912
$867$	13.2950	0.451522
$868$	1.35199	0.0458895
$869$	23.6270	0.801490
$870$	0	0
$871$	−0.427027	−0.0144692
$872$	7.23748	0.245092
$873$	35.9003	1.21504
$874$	9.99279	0.338011
$875$	0	0
$876$	−17.7045	−0.598181
$877$	−0.437656	−0.0147786	−0.00738929	−	0.999973i	$-0.502352\pi$
$877$	−0.437656	−0.0147786	−0.00738929	+	0.999973i	$0.502352\pi$
$878$	71.5718	2.41543
$879$	11.7868	0.397557
$880$	0	0
$881$	30.4661	1.02643	0.513214	−	0.858261i	$-0.328455\pi$
$881$	30.4661	1.02643	0.513214	+	0.858261i	$0.328455\pi$
$882$	5.84960	0.196966
$883$	−21.2473	−0.715028	−0.357514	−	0.933908i	$-0.616376\pi$
$883$	−21.2473	−0.715028	−0.357514	+	0.933908i	$0.616376\pi$
$884$	−1.99279	−0.0670249
$885$	0	0
$886$	−32.6284	−1.09617
$887$	−35.4964	−1.19185	−0.595927	−	0.803039i	$-0.703215\pi$
$887$	−35.4964	−1.19185	−0.595927	+	0.803039i	$0.703215\pi$
$888$	16.1774	0.542877
$889$	−13.1863	−0.442255
$890$	0	0
$891$	12.0470	0.403590
$892$	100.275	3.35746
$893$	−39.5049	−1.32198
$894$	−27.0104	−0.903364
$895$	0	0
$896$	15.7829	0.527269
$897$	−0.442876	−0.0147872
$898$	−23.6191	−0.788181
$899$	0.288611	0.00962571
$900$	0	0
$901$	2.82102	0.0939818
$902$	31.7490	1.05713
$903$	10.3673	0.345001
$904$	27.0713	0.900377
$905$	0	0
$906$	9.84965	0.327233
$907$	−4.00055	−0.132836	−0.0664180	−	0.997792i	$-0.521157\pi$
$907$	−4.00055	−0.132836	−0.0664180	+	0.997792i	$0.521157\pi$
$908$	9.50781	0.315528
$909$	−21.0316	−0.697573
$910$	0	0
$911$	1.20704	0.0399910	0.0199955	−	0.999800i	$-0.493635\pi$
$911$	1.20704	0.0399910	0.0199955	+	0.999800i	$0.493635\pi$
$912$	19.0165	0.629699
$913$	11.8343	0.391659
$914$	10.5669	0.349521
$915$	0	0
$916$	19.6470	0.649156
$917$	17.0509	0.563070
$918$	9.36676	0.309149
$919$	−52.0360	−1.71651	−0.858255	−	0.513223i	$-0.828451\pi$
$919$	−52.0360	−1.71651	−0.858255	+	0.513223i	$0.828451\pi$
$920$	0	0
$921$	22.3706	0.737137
$922$	33.8421	1.11453
$923$	−1.76262	−0.0580173
$924$	−12.3094	−0.404951
$925$	0	0
$926$	36.3073	1.19313
$927$	26.4506	0.868752
$928$	−2.88575	−0.0947295
$929$	55.5209	1.82158	0.910792	−	0.412866i	$-0.135472\pi$
$929$	55.5209	1.82158	0.910792	+	0.412866i	$0.135472\pi$
$930$	0	0
$931$	−3.98360	−0.130557
$932$	41.2317	1.35059
$933$	−18.2714	−0.598177
$934$	90.7732	2.97019
$935$	0	0
$936$	7.26612	0.237501
$937$	58.3946	1.90767	0.953834	−	0.300335i	$-0.0970984\pi$
$937$	58.3946	1.90767	0.953834	+	0.300335i	$0.0970984\pi$
$938$	1.97694	0.0645495
$939$	14.2405	0.464722
$940$	0	0
$941$	−11.4587	−0.373543	−0.186772	−	0.982403i	$-0.559802\pi$
$941$	−11.4587	−0.373543	−0.186772	+	0.982403i	$0.559802\pi$
$942$	38.5185	1.25500
$943$	−3.60745	−0.117475
$944$	−39.4900	−1.28529
$945$	0	0
$946$	111.631	3.62943
$947$	−56.4647	−1.83486	−0.917428	−	0.397902i	$-0.869738\pi$
$947$	−56.4647	−1.83486	−0.917428	+	0.397902i	$0.869738\pi$
$948$	−23.6270	−0.767368
$949$	2.73424	0.0887572
$950$	0	0
$951$	−6.54591	−0.212266
$952$	4.92719	0.159691
$953$	19.7983	0.641331	0.320665	−	0.947193i	$-0.396094\pi$
$953$	19.7983	0.641331	0.320665	+	0.947193i	$0.396094\pi$
$954$	−19.2597	−0.623555
$955$	0	0
$956$	103.662	3.35268
$957$	−2.62771	−0.0849418
$958$	73.9122	2.38800
$959$	−18.7251	−0.604663
$960$	0	0
$961$	−30.9008	−0.996800
$962$	−4.67803	−0.150826
$963$	−16.2995	−0.525243
$964$	94.5721	3.04596
$965$	0	0
$966$	2.05032	0.0659680
$967$	−1.83834	−0.0591172	−0.0295586	−	0.999563i	$-0.509410\pi$
$967$	−1.83834	−0.0591172	−0.0295586	+	0.999563i	$0.509410\pi$
$968$	−7.53012	−0.242027
$969$	−2.78978	−0.0896207
$970$	0	0
$971$	0.673597	0.0216168	0.0108084	−	0.999942i	$-0.496560\pi$
$971$	0.673597	0.0216168	0.0108084	+	0.999942i	$0.496560\pi$
$972$	−68.1679	−2.18649
$973$	−11.1067	−0.356066
$974$	−5.93826	−0.190274
$975$	0	0
$976$	−18.6416	−0.596704
$977$	−29.2316	−0.935201	−0.467600	−	0.883940i	$-0.654881\pi$
$977$	−29.2316	−0.935201	−0.467600	+	0.883940i	$0.654881\pi$
$978$	−18.1445	−0.580198
$979$	−15.4598	−0.494099
$980$	0	0
$981$	2.93486	0.0937028
$982$	35.7758	1.14165
$983$	30.2475	0.964746	0.482373	−	0.875966i	$-0.339775\pi$
$983$	30.2475	0.964746	0.482373	+	0.875966i	$0.339775\pi$
$984$	−16.9561	−0.540542
$985$	0	0
$986$	1.96943	0.0627195
$987$	−8.10562	−0.258005
$988$	−9.26521	−0.294766
$989$	−12.6839	−0.403325
$990$	0	0
$991$	−9.06295	−0.287894	−0.143947	−	0.989585i	$-0.545980\pi$
$991$	−9.06295	−0.287894	−0.143947	+	0.989585i	$0.545980\pi$
$992$	−0.991922	−0.0314936
$993$	21.2944	0.675757
$994$	8.16015	0.258824
$995$	0	0
$996$	−11.8343	−0.374985
$997$	5.02466	0.159133	0.0795663	−	0.996830i	$-0.474646\pi$
$997$	5.02466	0.159133	0.0795663	+	0.996830i	$0.474646\pi$
$998$	15.3973	0.487394
$999$	14.9995	0.474563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.l.1.1		4
5.4	even	2		805.2.a.j.1.4	✓	4
15.14	odd	2		7245.2.a.bc.1.1		4
35.34	odd	2		5635.2.a.w.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.j.1.4	✓	4	5.4	even	2
4025.2.a.l.1.1		4	1.1	even	1	trivial
5635.2.a.w.1.4		4	35.34	odd	2
7245.2.a.bc.1.1		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)

\(f(q)\)	\(=\)	\(q-2.50848 q^{2} -0.817356 q^{3} +4.29248 q^{4} +2.05032 q^{6} +1.00000 q^{7} -5.75064 q^{8} -2.33193 q^{9} +O(q^{10})\)	\(q-2.50848 q^{2} -0.817356 q^{3} +4.29248 q^{4} +2.05032 q^{6} +1.00000 q^{7} -5.75064 q^{8} -2.33193 q^{9} +3.50848 q^{11} -3.50848 q^{12} +0.541840 q^{13} -2.50848 q^{14} +5.84041 q^{16} -0.856807 q^{17} +5.84960 q^{18} -3.98360 q^{19} -0.817356 q^{21} -8.80096 q^{22} +1.00000 q^{23} +4.70032 q^{24} -1.35920 q^{26} +4.35808 q^{27} +4.29248 q^{28} +0.916320 q^{29} +0.314967 q^{31} -3.14929 q^{32} -2.86768 q^{33} +2.14929 q^{34} -10.0098 q^{36} +3.44176 q^{37} +9.99279 q^{38} -0.442876 q^{39} -3.60745 q^{41} +2.05032 q^{42} -12.6839 q^{43} +15.0601 q^{44} -2.50848 q^{46} +9.91689 q^{47} -4.77369 q^{48} +1.00000 q^{49} +0.700316 q^{51} +2.32584 q^{52} -3.29248 q^{53} -10.9322 q^{54} -5.75064 q^{56} +3.25602 q^{57} -2.29857 q^{58} -6.76151 q^{59} -3.19184 q^{61} -0.790090 q^{62} -2.33193 q^{63} -3.78090 q^{64} +7.19351 q^{66} -0.788104 q^{67} -3.67783 q^{68} -0.817356 q^{69} -3.25303 q^{71} +13.4101 q^{72} +5.04621 q^{73} -8.63360 q^{74} -17.0995 q^{76} +3.50848 q^{77} +1.11095 q^{78} +6.73424 q^{79} +3.43369 q^{81} +9.04921 q^{82} +3.37306 q^{83} -3.50848 q^{84} +31.8174 q^{86} -0.748959 q^{87} -20.1760 q^{88} -4.40642 q^{89} +0.541840 q^{91} +4.29248 q^{92} -0.257440 q^{93} -24.8763 q^{94} +2.57409 q^{96} -15.3951 q^{97} -2.50848 q^{98} -8.18153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} + 3 q^{4} + 4 q^{6} + 4 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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