LMFDB - Embedded newform 4025.2.a.p.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:	$0$
Dimension:	$5$
Coefficient field:	5.5.2147108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 $ x^5 - 2x^4 - 9x^3 + 17x^2 + 16x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 161)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.69017$ 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)

$f(q)$	$=$	$q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} +O(q^{10})$	\(q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} -3.78810 q^{11} +1.41317 q^{12} -1.24125 q^{13} +2.69017 q^{14} +12.9523 q^{16} -5.98512 q^{17} +7.87463 q^{18} -3.38034 q^{19} -0.269842 q^{21} +10.1906 q^{22} +1.00000 q^{23} -2.34982 q^{24} +3.33918 q^{26} -1.59940 q^{27} -5.23702 q^{28} -7.02088 q^{29} +6.26984 q^{31} -17.4276 q^{32} -1.02219 q^{33} +16.1010 q^{34} -15.3297 q^{36} -4.84066 q^{37} +9.09369 q^{38} -0.334942 q^{39} -1.78094 q^{41} +0.725921 q^{42} -3.02219 q^{43} -19.8383 q^{44} -2.69017 q^{46} -3.90322 q^{47} +3.49508 q^{48} +1.00000 q^{49} -1.61504 q^{51} -6.50046 q^{52} +2.47403 q^{53} +4.30267 q^{54} +8.70812 q^{56} -0.912158 q^{57} +18.8873 q^{58} -2.89143 q^{59} -10.3518 q^{61} -16.8669 q^{62} +2.92719 q^{63} +20.9787 q^{64} +2.74986 q^{66} -11.4466 q^{67} -31.3442 q^{68} +0.269842 q^{69} +2.70157 q^{71} +25.4903 q^{72} +14.1893 q^{73} +13.0222 q^{74} -17.7029 q^{76} +3.78810 q^{77} +0.901051 q^{78} +3.31407 q^{79} +8.34997 q^{81} +4.79102 q^{82} -7.02219 q^{83} -1.41317 q^{84} +8.13020 q^{86} -1.89453 q^{87} +32.9872 q^{88} -1.59107 q^{89} +1.24125 q^{91} +5.23702 q^{92} +1.69187 q^{93} +10.5003 q^{94} -4.70271 q^{96} +11.6270 q^{97} -2.69017 q^{98} +11.0885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 12 q^{4} - 3 q^{6} - 5 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 12 * q^4 - 3 * q^6 - 5 * q^7 - 3 * q^8 + 11 * q^9	$ 5 q - 2 q^{2} + 12 q^{4} - 3 q^{6} - 5 q^{7} - 3 q^{8} + 11 q^{9} - 4 q^{11} - 3 q^{12} + 6 q^{13} + 2 q^{14} + 10 q^{16} + 12 q^{17} + 19 q^{18} + 6 q^{19} - 14 q^{22} + 5 q^{23} - 36 q^{24} + q^{26} - 12 q^{28} - 4 q^{29} + 30 q^{31} - 8 q^{32} + 22 q^{33} + 6 q^{34} - q^{36} - 4 q^{37} + 40 q^{38} + 16 q^{39} + 6 q^{41} + 3 q^{42} + 12 q^{43} - 26 q^{44} - 2 q^{46} - 10 q^{47} - 25 q^{48} + 5 q^{49} - 4 q^{51} + 21 q^{52} - 16 q^{53} + 33 q^{54} + 3 q^{56} - 6 q^{57} - 13 q^{58} + 22 q^{59} - 18 q^{61} - 15 q^{62} - 11 q^{63} + 25 q^{64} + 4 q^{66} + 2 q^{67} - 12 q^{68} + 4 q^{71} + 41 q^{72} + 2 q^{73} + 38 q^{74} + 10 q^{76} + 4 q^{77} - 41 q^{78} + 30 q^{79} - 3 q^{81} + 7 q^{82} - 8 q^{83} + 3 q^{84} + 8 q^{86} + 12 q^{87} - 4 q^{88} - 20 q^{89} - 6 q^{91} + 12 q^{92} + 26 q^{93} - 25 q^{94} - q^{96} + 12 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 12 * q^4 - 3 * q^6 - 5 * q^7 - 3 * q^8 + 11 * q^9 - 4 * q^11 - 3 * q^12 + 6 * q^13 + 2 * q^14 + 10 * q^16 + 12 * q^17 + 19 * q^18 + 6 * q^19 - 14 * q^22 + 5 * q^23 - 36 * q^24 + q^26 - 12 * q^28 - 4 * q^29 + 30 * q^31 - 8 * q^32 + 22 * q^33 + 6 * q^34 - q^36 - 4 * q^37 + 40 * q^38 + 16 * q^39 + 6 * q^41 + 3 * q^42 + 12 * q^43 - 26 * q^44 - 2 * q^46 - 10 * q^47 - 25 * q^48 + 5 * q^49 - 4 * q^51 + 21 * q^52 - 16 * q^53 + 33 * q^54 + 3 * q^56 - 6 * q^57 - 13 * q^58 + 22 * q^59 - 18 * q^61 - 15 * q^62 - 11 * q^63 + 25 * q^64 + 4 * q^66 + 2 * q^67 - 12 * q^68 + 4 * q^71 + 41 * q^72 + 2 * q^73 + 38 * q^74 + 10 * q^76 + 4 * q^77 - 41 * q^78 + 30 * q^79 - 3 * q^81 + 7 * q^82 - 8 * q^83 + 3 * q^84 + 8 * q^86 + 12 * q^87 - 4 * q^88 - 20 * q^89 - 6 * q^91 + 12 * q^92 + 26 * q^93 - 25 * q^94 - q^96 + 12 * q^97 - 2 * 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 $

$2$	−2.69017	−1.90224	−0.951119	−	0.308825i	$-0.900064\pi$
$2$	−2.69017	−1.90224	−0.951119	+	0.308825i	$0.900064\pi$
$3$	0.269842	0.155793	0.0778967	−	0.996961i	$-0.475180\pi$
$3$	0.269842	0.155793	0.0778967	+	0.996961i	$0.475180\pi$
$4$	5.23702	2.61851
$5$	0	0
$5$	0	0
$6$	−0.725921	−0.296356
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−8.70812	−3.07879
$9$	−2.92719	−0.975728
$10$	0	0
$11$	−3.78810	−1.14215	−0.571077	−	0.820896i	$-0.693474\pi$
$11$	−3.78810	−1.14215	−0.571077	+	0.820896i	$0.693474\pi$
$12$	1.41317	0.407946
$13$	−1.24125	−0.344261	−0.172131	−	0.985074i	$-0.555065\pi$
$13$	−1.24125	−0.344261	−0.172131	+	0.985074i	$0.555065\pi$
$14$	2.69017	0.718978
$15$	0	0
$16$	12.9523	3.23807
$17$	−5.98512	−1.45161	−0.725803	−	0.687903i	$-0.758532\pi$
$17$	−5.98512	−1.45161	−0.725803	+	0.687903i	$0.758532\pi$
$18$	7.87463	1.85607
$19$	−3.38034	−0.775503	−0.387752	−	0.921764i	$-0.626748\pi$
$19$	−3.38034	−0.775503	−0.387752	+	0.921764i	$0.626748\pi$
$20$	0	0
$21$	−0.269842	−0.0588844
$22$	10.1906	2.17265
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.34982	−0.479655
$25$	0	0
$26$	3.33918	0.654867
$27$	−1.59940	−0.307805
$28$	−5.23702	−0.989703
$29$	−7.02088	−1.30374	−0.651872	−	0.758329i	$-0.726016\pi$
$29$	−7.02088	−1.30374	−0.651872	+	0.758329i	$0.726016\pi$
$30$	0	0
$31$	6.26984	1.12610	0.563048	−	0.826424i	$-0.309628\pi$
$31$	6.26984	1.12610	0.563048	+	0.826424i	$0.309628\pi$
$32$	−17.4276	−3.08080
$33$	−1.02219	−0.177940
$34$	16.1010	2.76130
$35$	0	0
$36$	−15.3297	−2.55495
$37$	−4.84066	−0.795799	−0.397899	−	0.917429i	$-0.630261\pi$
$37$	−4.84066	−0.795799	−0.397899	+	0.917429i	$0.630261\pi$
$38$	9.09369	1.47519
$39$	−0.334942	−0.0536336
$40$	0	0
$41$	−1.78094	−0.278135	−0.139068	−	0.990283i	$-0.544411\pi$
$41$	−1.78094	−0.278135	−0.139068	+	0.990283i	$0.544411\pi$
$42$	0.725921	0.112012
$43$	−3.02219	−0.460879	−0.230440	−	0.973087i	$-0.574016\pi$
$43$	−3.02219	−0.460879	−0.230440	+	0.973087i	$0.574016\pi$
$44$	−19.8383	−2.99074
$45$	0	0
$46$	−2.69017	−0.396644
$47$	−3.90322	−0.569343	−0.284671	−	0.958625i	$-0.591884\pi$
$47$	−3.90322	−0.569343	−0.284671	+	0.958625i	$0.591884\pi$
$48$	3.49508	0.504471
$49$	1.00000	0.142857
$50$	0	0
$51$	−1.61504	−0.226151
$52$	−6.50046	−0.901451
$53$	2.47403	0.339834	0.169917	−	0.985458i	$-0.445650\pi$
$53$	2.47403	0.339834	0.169917	+	0.985458i	$0.445650\pi$
$54$	4.30267	0.585519
$55$	0	0
$56$	8.70812	1.16367
$57$	−0.912158	−0.120818
$58$	18.8873	2.48003
$59$	−2.89143	−0.376433	−0.188216	−	0.982128i	$-0.560271\pi$
$59$	−2.89143	−0.376433	−0.188216	+	0.982128i	$0.560271\pi$
$60$	0	0
$61$	−10.3518	−1.32541	−0.662703	−	0.748882i	$-0.730591\pi$
$61$	−10.3518	−1.32541	−0.662703	+	0.748882i	$0.730591\pi$
$62$	−16.8669	−2.14210
$63$	2.92719	0.368791
$64$	20.9787	2.62234
$65$	0	0
$66$	2.74986	0.338484
$67$	−11.4466	−1.39843	−0.699213	−	0.714913i	$-0.746466\pi$
$67$	−11.4466	−1.39843	−0.699213	+	0.714913i	$0.746466\pi$
$68$	−31.3442	−3.80104
$69$	0.269842	0.0324852
$70$	0	0
$71$	2.70157	0.320617	0.160309	−	0.987067i	$-0.448751\pi$
$71$	2.70157	0.320617	0.160309	+	0.987067i	$0.448751\pi$
$72$	25.4903	3.00406
$73$	14.1893	1.66073	0.830367	−	0.557217i	$-0.188131\pi$
$73$	14.1893	1.66073	0.830367	+	0.557217i	$0.188131\pi$
$74$	13.0222	1.51380
$75$	0	0
$76$	−17.7029	−2.03066
$77$	3.78810	0.431694
$78$	0.901051	0.102024
$79$	3.31407	0.372862	0.186431	−	0.982468i	$-0.440308\pi$
$79$	3.31407	0.372862	0.186431	+	0.982468i	$0.440308\pi$
$80$	0	0
$81$	8.34997	0.927774
$82$	4.79102	0.529080
$83$	−7.02219	−0.770785	−0.385393	−	0.922753i	$-0.625934\pi$
$83$	−7.02219	−0.770785	−0.385393	+	0.922753i	$0.625934\pi$
$84$	−1.41317	−0.154189
$85$	0	0
$86$	8.13020	0.876702
$87$	−1.89453	−0.203115
$88$	32.9872	3.51645
$89$	−1.59107	−0.168653	−0.0843265	−	0.996438i	$-0.526874\pi$
$89$	−1.59107	−0.168653	−0.0843265	+	0.996438i	$0.526874\pi$
$90$	0	0
$91$	1.24125	0.130119
$92$	5.23702	0.545997
$93$	1.69187	0.175438
$94$	10.5003	1.08302
$95$	0	0
$96$	−4.70271	−0.479968
$97$	11.6270	1.18054	0.590270	−	0.807206i	$-0.299021\pi$
$97$	11.6270	1.18054	0.590270	+	0.807206i	$0.299021\pi$
$98$	−2.69017	−0.271748
$99$	11.0885	1.11443
$100$	0	0
$101$	−0.366626	−0.0364806	−0.0182403	−	0.999834i	$-0.505806\pi$
$101$	−0.366626	−0.0364806	−0.0182403	+	0.999834i	$0.505806\pi$
$102$	4.34473	0.430192
$103$	0.474030	0.0467076	0.0233538	−	0.999727i	$-0.492566\pi$
$103$	0.474030	0.0467076	0.0233538	+	0.999727i	$0.492566\pi$
$104$	10.8090	1.05991
$105$	0	0
$106$	−6.65556	−0.646445
$107$	5.74697	0.555580	0.277790	−	0.960642i	$-0.410398\pi$
$107$	5.74697	0.555580	0.277790	+	0.960642i	$0.410398\pi$
$108$	−8.37610	−0.805991
$109$	15.4877	1.48346	0.741728	−	0.670700i	$-0.234006\pi$
$109$	15.4877	1.48346	0.741728	+	0.670700i	$0.234006\pi$
$110$	0	0
$111$	−1.30621	−0.123980
$112$	−12.9523	−1.22388
$113$	4.48250	0.421678	0.210839	−	0.977521i	$-0.432380\pi$
$113$	4.48250	0.421678	0.210839	+	0.977521i	$0.432380\pi$
$114$	2.45386	0.229825
$115$	0	0
$116$	−36.7684	−3.41386
$117$	3.63337	0.335906
$118$	7.77845	0.716064
$119$	5.98512	0.548655
$120$	0	0
$121$	3.34968	0.304516
$122$	27.8480	2.52124
$123$	−0.480572	−0.0433317
$124$	32.8353	2.94869
$125$	0	0
$126$	−7.87463	−0.701527
$127$	2.13061	0.189061	0.0945307	−	0.995522i	$-0.469865\pi$
$127$	2.13061	0.189061	0.0945307	+	0.995522i	$0.469865\pi$
$128$	−21.5811	−1.90751
$129$	−0.815514	−0.0718020
$130$	0	0
$131$	−18.1242	−1.58352	−0.791760	−	0.610832i	$-0.790835\pi$
$131$	−18.1242	−1.58352	−0.791760	+	0.610832i	$0.790835\pi$
$132$	−5.35321	−0.465937
$133$	3.38034	0.293113
$134$	30.7933	2.66014
$135$	0	0
$136$	52.1192	4.46918
$137$	15.3062	1.30770	0.653849	−	0.756625i	$-0.273153\pi$
$137$	15.3062	1.30770	0.653849	+	0.756625i	$0.273153\pi$
$138$	−0.725921	−0.0617945
$139$	13.5273	1.14737	0.573687	−	0.819074i	$-0.305512\pi$
$139$	13.5273	1.14737	0.573687	+	0.819074i	$0.305512\pi$
$140$	0	0
$141$	−1.05325	−0.0886998
$142$	−7.26768	−0.609890
$143$	4.70198	0.393200
$144$	−37.9138	−3.15948
$145$	0	0
$146$	−38.1717	−3.15911
$147$	0.269842	0.0222562
$148$	−25.3506	−2.08381
$149$	5.75773	0.471691	0.235846	−	0.971791i	$-0.424214\pi$
$149$	5.75773	0.471691	0.235846	+	0.971791i	$0.424214\pi$
$150$	0	0
$151$	−9.57813	−0.779457	−0.389728	−	0.920930i	$-0.627431\pi$
$151$	−9.57813	−0.779457	−0.389728	+	0.920930i	$0.627431\pi$
$152$	29.4364	2.38761
$153$	17.5196	1.41637
$154$	−10.1906	−0.821184
$155$	0	0
$156$	−1.75410	−0.140440
$157$	5.03706	0.402001	0.201001	−	0.979591i	$-0.435581\pi$
$157$	5.03706	0.402001	0.201001	+	0.979591i	$0.435581\pi$
$158$	−8.91540	−0.709271
$159$	0.667598	0.0529439
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	−22.4628	−1.76485
$163$	7.35713	0.576255	0.288127	−	0.957592i	$-0.406967\pi$
$163$	7.35713	0.576255	0.288127	+	0.957592i	$0.406967\pi$
$164$	−9.32679	−0.728300
$165$	0	0
$166$	18.8909	1.46622
$167$	−20.9904	−1.62428	−0.812142	−	0.583460i	$-0.801698\pi$
$167$	−20.9904	−1.62428	−0.812142	+	0.583460i	$0.801698\pi$
$168$	2.34982	0.181292
$169$	−11.4593	−0.881484
$170$	0	0
$171$	9.89488	0.756681
$172$	−15.8272	−1.20682
$173$	12.3369	0.937955	0.468978	−	0.883210i	$-0.344622\pi$
$173$	12.3369	0.937955	0.468978	+	0.883210i	$0.344622\pi$
$174$	5.09660	0.386372
$175$	0	0
$176$	−49.0646	−3.69838
$177$	−0.780231	−0.0586457
$178$	4.28025	0.320818
$179$	−12.9082	−0.964807	−0.482404	−	0.875949i	$-0.660236\pi$
$179$	−12.9082	−0.964807	−0.482404	+	0.875949i	$0.660236\pi$
$180$	0	0
$181$	−5.86925	−0.436258	−0.218129	−	0.975920i	$-0.569995\pi$
$181$	−5.86925	−0.436258	−0.218129	+	0.975920i	$0.569995\pi$
$182$	−3.33918	−0.247516
$183$	−2.79334	−0.206489
$184$	−8.70812	−0.641971
$185$	0	0
$186$	−4.55141	−0.333726
$187$	22.6722	1.65796
$188$	−20.4412	−1.49083
$189$	1.59940	0.116340
$190$	0	0
$191$	11.9343	0.863539	0.431769	−	0.901984i	$-0.357889\pi$
$191$	11.9343	0.863539	0.431769	+	0.901984i	$0.357889\pi$
$192$	5.66094	0.408543
$193$	−0.752900	−0.0541949	−0.0270975	−	0.999633i	$-0.508626\pi$
$193$	−0.752900	−0.0541949	−0.0270975	+	0.999633i	$0.508626\pi$
$194$	−31.2785	−2.24567
$195$	0	0
$196$	5.23702	0.374073
$197$	−25.4074	−1.81020	−0.905100	−	0.425200i	$-0.860204\pi$
$197$	−25.4074	−1.81020	−0.905100	+	0.425200i	$0.860204\pi$
$198$	−29.8298	−2.11991
$199$	15.1988	1.07741	0.538707	−	0.842493i	$-0.318913\pi$
$199$	15.1988	1.07741	0.538707	+	0.842493i	$0.318913\pi$
$200$	0	0
$201$	−3.08878	−0.217866
$202$	0.986286	0.0693948
$203$	7.02088	0.492769
$204$	−8.45798	−0.592177
$205$	0	0
$206$	−1.27522	−0.0888489
$207$	−2.92719	−0.203453
$208$	−16.0771	−1.11474
$209$	12.8051	0.885744
$210$	0	0
$211$	−24.2797	−1.67148	−0.835742	−	0.549123i	$-0.814962\pi$
$211$	−24.2797	−1.67148	−0.835742	+	0.549123i	$0.814962\pi$
$212$	12.9565	0.889858
$213$	0.728997	0.0499500
$214$	−15.4603	−1.05685
$215$	0	0
$216$	13.9278	0.947667
$217$	−6.26984	−0.425625
$218$	−41.6647	−2.82189
$219$	3.82887	0.258731
$220$	0	0
$221$	7.42905	0.499732
$222$	3.51393	0.235840
$223$	−17.7344	−1.18758	−0.593791	−	0.804619i	$-0.702369\pi$
$223$	−17.7344	−1.18758	−0.593791	+	0.804619i	$0.702369\pi$
$224$	17.4276	1.16443
$225$	0	0
$226$	−12.0587	−0.802133
$227$	15.7087	1.04263	0.521313	−	0.853366i	$-0.325442\pi$
$227$	15.7087	1.04263	0.521313	+	0.853366i	$0.325442\pi$
$228$	−4.77699	−0.316364
$229$	−4.51633	−0.298448	−0.149224	−	0.988803i	$-0.547678\pi$
$229$	−4.51633	−0.298448	−0.149224	+	0.988803i	$0.547678\pi$
$230$	0	0
$231$	1.02219	0.0672550
$232$	61.1386	4.01395
$233$	16.2641	1.06549	0.532747	−	0.846275i	$-0.321160\pi$
$233$	16.2641	1.06549	0.532747	+	0.846275i	$0.321160\pi$
$234$	−9.77439	−0.638972
$235$	0	0
$236$	−15.1425	−0.985692
$237$	0.894275	0.0580894
$238$	−16.1010	−1.04367
$239$	2.14756	0.138914	0.0694571	−	0.997585i	$-0.477873\pi$
$239$	2.14756	0.138914	0.0694571	+	0.997585i	$0.477873\pi$
$240$	0	0
$241$	12.4676	0.803111	0.401555	−	0.915835i	$-0.368470\pi$
$241$	12.4676	0.803111	0.401555	+	0.915835i	$0.368470\pi$
$242$	−9.01121	−0.579262
$243$	7.05139	0.452347
$244$	−54.2123	−3.47059
$245$	0	0
$246$	1.29282	0.0824271
$247$	4.19585	0.266976
$248$	−54.5985	−3.46701
$249$	−1.89488	−0.120083
$250$	0	0
$251$	4.91478	0.310218	0.155109	−	0.987897i	$-0.450427\pi$
$251$	4.91478	0.310218	0.155109	+	0.987897i	$0.450427\pi$
$252$	15.3297	0.965681
$253$	−3.78810	−0.238156
$254$	−5.73172	−0.359640
$255$	0	0
$256$	16.0993	1.00620
$257$	−28.4782	−1.77642	−0.888212	−	0.459433i	$-0.848052\pi$
$257$	−28.4782	−1.77642	−0.888212	+	0.459433i	$0.848052\pi$
$258$	2.19387	0.136584
$259$	4.84066	0.300784
$260$	0	0
$261$	20.5514	1.27210
$262$	48.7572	3.01223
$263$	−1.89322	−0.116741	−0.0583703	−	0.998295i	$-0.518590\pi$
$263$	−1.89322	−0.116741	−0.0583703	+	0.998295i	$0.518590\pi$
$264$	8.90134	0.547839
$265$	0	0
$266$	−9.09369	−0.557570
$267$	−0.429338	−0.0262750
$268$	−59.9461	−3.66179
$269$	−2.51156	−0.153133	−0.0765663	−	0.997064i	$-0.524396\pi$
$269$	−2.51156	−0.153133	−0.0765663	+	0.997064i	$0.524396\pi$
$270$	0	0
$271$	25.1098	1.52531	0.762656	−	0.646804i	$-0.223895\pi$
$271$	25.1098	1.52531	0.762656	+	0.646804i	$0.223895\pi$
$272$	−77.5211	−4.70041
$273$	0.334942	0.0202716
$274$	−41.1763	−2.48755
$275$	0	0
$276$	1.41317	0.0850627
$277$	−9.48643	−0.569984	−0.284992	−	0.958530i	$-0.591991\pi$
$277$	−9.48643	−0.569984	−0.284992	+	0.958530i	$0.591991\pi$
$278$	−36.3909	−2.18258
$279$	−18.3530	−1.09876
$280$	0	0
$281$	8.71197	0.519713	0.259856	−	0.965647i	$-0.416325\pi$
$281$	8.71197	0.519713	0.259856	+	0.965647i	$0.416325\pi$
$282$	2.83343	0.168728
$283$	−30.5543	−1.81627	−0.908133	−	0.418683i	$-0.862492\pi$
$283$	−30.5543	−1.81627	−0.908133	+	0.418683i	$0.862492\pi$
$284$	14.1482	0.839538
$285$	0	0
$286$	−12.6491	−0.747959
$287$	1.78094	0.105125
$288$	51.0139	3.00602
$289$	18.8217	1.10716
$290$	0	0
$291$	3.13745	0.183920
$292$	74.3096	4.34864
$293$	−12.7063	−0.742312	−0.371156	−	0.928570i	$-0.621039\pi$
$293$	−12.7063	−0.742312	−0.371156	+	0.928570i	$0.621039\pi$
$294$	−0.725921	−0.0423366
$295$	0	0
$296$	42.1530	2.45009
$297$	6.05870	0.351561
$298$	−15.4893	−0.897269
$299$	−1.24125	−0.0717835
$300$	0	0
$301$	3.02219	0.174196
$302$	25.7668	1.48271
$303$	−0.0989310	−0.00568344
$304$	−43.7832	−2.51114
$305$	0	0
$306$	−47.1306	−2.69428
$307$	−22.1153	−1.26219	−0.631094	−	0.775706i	$-0.717394\pi$
$307$	−22.1153	−1.26219	−0.631094	+	0.775706i	$0.717394\pi$
$308$	19.8383	1.13039
$309$	0.127913	0.00727673
$310$	0	0
$311$	21.3945	1.21317	0.606586	−	0.795018i	$-0.292539\pi$
$311$	21.3945	1.21317	0.606586	+	0.795018i	$0.292539\pi$
$312$	2.91672	0.165127
$313$	29.9051	1.69034	0.845169	−	0.534498i	$-0.179499\pi$
$313$	29.9051	1.69034	0.845169	+	0.534498i	$0.179499\pi$
$314$	−13.5506	−0.764702
$315$	0	0
$316$	17.3558	0.976341
$317$	−7.06103	−0.396587	−0.198294	−	0.980143i	$-0.563540\pi$
$317$	−7.06103	−0.396587	−0.198294	+	0.980143i	$0.563540\pi$
$318$	−1.79595	−0.100712
$319$	26.5958	1.48908
$320$	0	0
$321$	1.55077	0.0865557
$322$	2.69017	0.149917
$323$	20.2318	1.12573
$324$	43.7289	2.42938
$325$	0	0
$326$	−19.7919	−1.09617
$327$	4.17925	0.231113
$328$	15.5086	0.856320
$329$	3.90322	0.215191
$330$	0	0
$331$	16.2063	0.890777	0.445388	−	0.895338i	$-0.353066\pi$
$331$	16.2063	0.890777	0.445388	+	0.895338i	$0.353066\pi$
$332$	−36.7753	−2.01831
$333$	14.1695	0.776484
$334$	56.4677	3.08977
$335$	0	0
$336$	−3.49508	−0.190672
$337$	−5.21804	−0.284245	−0.142122	−	0.989849i	$-0.545393\pi$
$337$	−5.21804	−0.284245	−0.142122	+	0.989849i	$0.545393\pi$
$338$	30.8274	1.67679
$339$	1.20957	0.0656947
$340$	0	0
$341$	−23.7508	−1.28618
$342$	−26.6189	−1.43939
$343$	−1.00000	−0.0539949
$344$	26.3176	1.41895
$345$	0	0
$346$	−33.1883	−1.78421
$347$	−4.19094	−0.224982	−0.112491	−	0.993653i	$-0.535883\pi$
$347$	−4.19094	−0.224982	−0.112491	+	0.993653i	$0.535883\pi$
$348$	−9.92167	−0.531857
$349$	−18.6611	−0.998903	−0.499452	−	0.866342i	$-0.666465\pi$
$349$	−18.6611	−0.998903	−0.499452	+	0.866342i	$0.666465\pi$
$350$	0	0
$351$	1.98526	0.105966
$352$	66.0176	3.51875
$353$	11.5781	0.616241	0.308121	−	0.951347i	$-0.400300\pi$
$353$	11.5781	0.616241	0.308121	+	0.951347i	$0.400300\pi$
$354$	2.09895	0.111558
$355$	0	0
$356$	−8.33246	−0.441619
$357$	1.61504	0.0854769
$358$	34.7254	1.83529
$359$	29.4910	1.55647	0.778237	−	0.627970i	$-0.216114\pi$
$359$	29.4910	1.55647	0.778237	+	0.627970i	$0.216114\pi$
$360$	0	0
$361$	−7.57330	−0.398595
$362$	15.7893	0.829866
$363$	0.903884	0.0474416
$364$	6.50046	0.340716
$365$	0	0
$366$	7.51455	0.392792
$367$	24.7858	1.29381	0.646903	−	0.762572i	$-0.276064\pi$
$367$	24.7858	1.29381	0.646903	+	0.762572i	$0.276064\pi$
$368$	12.9523	0.675185
$369$	5.21313	0.271385
$370$	0	0
$371$	−2.47403	−0.128445
$372$	8.86033	0.459387
$373$	−17.1524	−0.888117	−0.444058	−	0.895998i	$-0.646462\pi$
$373$	−17.1524	−0.888117	−0.444058	+	0.895998i	$0.646462\pi$
$374$	−60.9922	−3.15383
$375$	0	0
$376$	33.9897	1.75288
$377$	8.71467	0.448829
$378$	−4.30267	−0.221305
$379$	32.8211	1.68591	0.842953	−	0.537986i	$-0.180815\pi$
$379$	32.8211	1.68591	0.842953	+	0.537986i	$0.180815\pi$
$380$	0	0
$381$	0.574930	0.0294545
$382$	−32.1054	−1.64266
$383$	8.42609	0.430553	0.215277	−	0.976553i	$-0.430935\pi$
$383$	8.42609	0.430553	0.215277	+	0.976553i	$0.430935\pi$
$384$	−5.82348	−0.297178
$385$	0	0
$386$	2.02543	0.103092
$387$	8.84650	0.449693
$388$	60.8906	3.09125
$389$	−25.3004	−1.28278	−0.641390	−	0.767215i	$-0.721642\pi$
$389$	−25.3004	−1.28278	−0.641390	+	0.767215i	$0.721642\pi$
$390$	0	0
$391$	−5.98512	−0.302681
$392$	−8.70812	−0.439827
$393$	−4.89068	−0.246702
$394$	68.3501	3.44343
$395$	0	0
$396$	58.0704	2.91815
$397$	−20.3650	−1.02209	−0.511045	−	0.859554i	$-0.670741\pi$
$397$	−20.3650	−1.02209	−0.511045	+	0.859554i	$0.670741\pi$
$398$	−40.8874	−2.04950
$399$	0.912158	0.0456650
$400$	0	0
$401$	4.10277	0.204883	0.102441	−	0.994739i	$-0.467335\pi$
$401$	4.10277	0.204883	0.102441	+	0.994739i	$0.467335\pi$
$402$	8.30934	0.414432
$403$	−7.78245	−0.387672
$404$	−1.92002	−0.0955248
$405$	0	0
$406$	−18.8873	−0.937363
$407$	18.3369	0.908925
$408$	14.0640	0.696269
$409$	−26.8449	−1.32739	−0.663697	−	0.748002i	$-0.731013\pi$
$409$	−26.8449	−1.32739	−0.663697	+	0.748002i	$0.731013\pi$
$410$	0	0
$411$	4.13026	0.203731
$412$	2.48250	0.122304
$413$	2.89143	0.142278
$414$	7.87463	0.387017
$415$	0	0
$416$	21.6321	1.06060
$417$	3.65025	0.178753
$418$	−34.4478	−1.68490
$419$	0.149494	0.00730327	0.00365163	−	0.999993i	$-0.498838\pi$
$419$	0.149494	0.00730327	0.00365163	+	0.999993i	$0.498838\pi$
$420$	0	0
$421$	−10.5269	−0.513049	−0.256524	−	0.966538i	$-0.582577\pi$
$421$	−10.5269	−0.513049	−0.256524	+	0.966538i	$0.582577\pi$
$422$	65.3165	3.17956
$423$	11.4254	0.555524
$424$	−21.5442	−1.04628
$425$	0	0
$426$	−1.96113	−0.0950168
$427$	10.3518	0.500956
$428$	30.0969	1.45479
$429$	1.26879	0.0612579
$430$	0	0
$431$	−2.28665	−0.110144	−0.0550720	−	0.998482i	$-0.517539\pi$
$431$	−2.28665	−0.110144	−0.0550720	+	0.998482i	$0.517539\pi$
$432$	−20.7160	−0.996697
$433$	20.4569	0.983094	0.491547	−	0.870851i	$-0.336432\pi$
$433$	20.4569	0.983094	0.491547	+	0.870851i	$0.336432\pi$
$434$	16.8669	0.809639
$435$	0	0
$436$	81.1096	3.88444
$437$	−3.38034	−0.161704
$438$	−10.3003	−0.492168
$439$	8.93821	0.426597	0.213299	−	0.976987i	$-0.431579\pi$
$439$	8.93821	0.426597	0.213299	+	0.976987i	$0.431579\pi$
$440$	0	0
$441$	−2.92719	−0.139390
$442$	−19.9854	−0.950609
$443$	6.71589	0.319082	0.159541	−	0.987191i	$-0.448999\pi$
$443$	6.71589	0.319082	0.159541	+	0.987191i	$0.448999\pi$
$444$	−6.84066	−0.324643
$445$	0	0
$446$	47.7085	2.25906
$447$	1.55368	0.0734864
$448$	−20.9787	−0.991151
$449$	39.7178	1.87440	0.937200	−	0.348792i	$-0.113408\pi$
$449$	39.7178	1.87440	0.937200	+	0.348792i	$0.113408\pi$
$450$	0	0
$451$	6.74636	0.317674
$452$	23.4749	1.10417
$453$	−2.58458	−0.121434
$454$	−42.2592	−1.98332
$455$	0	0
$456$	7.94318	0.371974
$457$	35.7388	1.67179	0.835895	−	0.548889i	$-0.184949\pi$
$457$	35.7388	1.67179	0.835895	+	0.548889i	$0.184949\pi$
$458$	12.1497	0.567719
$459$	9.57263	0.446812
$460$	0	0
$461$	−18.3516	−0.854720	−0.427360	−	0.904082i	$-0.640556\pi$
$461$	−18.3516	−0.854720	−0.427360	+	0.904082i	$0.640556\pi$
$462$	−2.74986	−0.127935
$463$	−11.1821	−0.519678	−0.259839	−	0.965652i	$-0.583670\pi$
$463$	−11.1821	−0.519678	−0.259839	+	0.965652i	$0.583670\pi$
$464$	−90.9365	−4.22162
$465$	0	0
$466$	−43.7531	−2.02682
$467$	−31.7231	−1.46797	−0.733984	−	0.679167i	$-0.762341\pi$
$467$	−31.7231	−1.46797	−0.733984	+	0.679167i	$0.762341\pi$
$468$	19.0280	0.879571
$469$	11.4466	0.528556
$470$	0	0
$471$	1.35921	0.0626292
$472$	25.1790	1.15896
$473$	11.4483	0.526395
$474$	−2.40575	−0.110500
$475$	0	0
$476$	31.3442	1.43666
$477$	−7.24194	−0.331586
$478$	−5.77731	−0.264248
$479$	−9.81725	−0.448562	−0.224281	−	0.974525i	$-0.572003\pi$
$479$	−9.81725	−0.448562	−0.224281	+	0.974525i	$0.572003\pi$
$480$	0	0
$481$	6.00847	0.273963
$482$	−33.5400	−1.52771
$483$	−0.269842	−0.0122782
$484$	17.5423	0.797378
$485$	0	0
$486$	−18.9694	−0.860471
$487$	36.2778	1.64390	0.821952	−	0.569557i	$-0.192885\pi$
$487$	36.2778	1.64390	0.821952	+	0.569557i	$0.192885\pi$
$488$	90.1443	4.08064
$489$	1.98526	0.0897767
$490$	0	0
$491$	−17.6053	−0.794514	−0.397257	−	0.917707i	$-0.630038\pi$
$491$	−17.6053	−0.794514	−0.397257	+	0.917707i	$0.630038\pi$
$492$	−2.51676	−0.113464
$493$	42.0208	1.89252
$494$	−11.2876	−0.507851
$495$	0	0
$496$	81.2089	3.64639
$497$	−2.70157	−0.121182
$498$	5.09755	0.228427
$499$	12.1142	0.542308	0.271154	−	0.962536i	$-0.412595\pi$
$499$	12.1142	0.542308	0.271154	+	0.962536i	$0.412595\pi$
$500$	0	0
$501$	−5.66408	−0.253053
$502$	−13.2216	−0.590109
$503$	−10.2723	−0.458020	−0.229010	−	0.973424i	$-0.573549\pi$
$503$	−10.2723	−0.458020	−0.229010	+	0.973424i	$0.573549\pi$
$504$	−25.4903	−1.13543
$505$	0	0
$506$	10.1906	0.453029
$507$	−3.09220	−0.137329
$508$	11.1581	0.495059
$509$	−6.45082	−0.285928	−0.142964	−	0.989728i	$-0.545663\pi$
$509$	−6.45082	−0.285928	−0.142964	+	0.989728i	$0.545663\pi$
$510$	0	0
$511$	−14.1893	−0.627698
$512$	−0.147625	−0.00652419
$513$	5.40653	0.238704
$514$	76.6113	3.37918
$515$	0	0
$516$	−4.27086	−0.188014
$517$	14.7858	0.650277
$518$	−13.0222	−0.572162
$519$	3.32901	0.146127
$520$	0	0
$521$	34.4858	1.51085	0.755425	−	0.655235i	$-0.227430\pi$
$521$	34.4858	1.51085	0.755425	+	0.655235i	$0.227430\pi$
$522$	−55.2868	−2.41984
$523$	25.7852	1.12751	0.563753	−	0.825943i	$-0.309357\pi$
$523$	25.7852	1.12751	0.563753	+	0.825943i	$0.309357\pi$
$524$	−94.9168	−4.14646
$525$	0	0
$526$	5.09307	0.222068
$527$	−37.5258	−1.63465
$528$	−13.2397	−0.576183
$529$	1.00000	0.0434783
$530$	0	0
$531$	8.46376	0.367296
$532$	17.7029	0.767518
$533$	2.21059	0.0957513
$534$	1.15499	0.0499814
$535$	0	0
$536$	99.6785	4.30546
$537$	−3.48319	−0.150311
$538$	6.75653	0.291295
$539$	−3.78810	−0.163165
$540$	0	0
$541$	−21.1475	−0.909203	−0.454601	−	0.890695i	$-0.650218\pi$
$541$	−21.1475	−0.909203	−0.454601	+	0.890695i	$0.650218\pi$
$542$	−67.5496	−2.90151
$543$	−1.58377	−0.0679661
$544$	104.307	4.47211
$545$	0	0
$546$	−0.901051	−0.0385614
$547$	3.97188	0.169825	0.0849126	−	0.996388i	$-0.472939\pi$
$547$	3.97188	0.169825	0.0849126	+	0.996388i	$0.472939\pi$
$548$	80.1589	3.42422
$549$	30.3015	1.29324
$550$	0	0
$551$	23.7329	1.01106
$552$	−2.34982	−0.100015
$553$	−3.31407	−0.140928
$554$	25.5201	1.08425
$555$	0	0
$556$	70.8429	3.00441
$557$	13.5585	0.574491	0.287246	−	0.957857i	$-0.407260\pi$
$557$	13.5585	0.574491	0.287246	+	0.957857i	$0.407260\pi$
$558$	49.3727	2.09011
$559$	3.75130	0.158663
$560$	0	0
$561$	6.11792	0.258299
$562$	−23.4367	−0.988617
$563$	32.4740	1.36862	0.684309	−	0.729193i	$-0.260104\pi$
$563$	32.4740	1.36862	0.684309	+	0.729193i	$0.260104\pi$
$564$	−5.51590	−0.232261
$565$	0	0
$566$	82.1963	3.45497
$567$	−8.34997	−0.350666
$568$	−23.5256	−0.987111
$569$	−26.7707	−1.12228	−0.561142	−	0.827719i	$-0.689638\pi$
$569$	−26.7707	−1.12228	−0.561142	+	0.827719i	$0.689638\pi$
$570$	0	0
$571$	5.30884	0.222168	0.111084	−	0.993811i	$-0.464568\pi$
$571$	5.30884	0.222168	0.111084	+	0.993811i	$0.464568\pi$
$572$	24.6244	1.02960
$573$	3.22039	0.134534
$574$	−4.79102	−0.199973
$575$	0	0
$576$	−61.4086	−2.55869
$577$	−43.9737	−1.83065	−0.915325	−	0.402717i	$-0.868066\pi$
$577$	−43.9737	−1.83065	−0.915325	+	0.402717i	$0.868066\pi$
$578$	−50.6336	−2.10608
$579$	−0.203164	−0.00844321
$580$	0	0
$581$	7.02219	0.291329
$582$	−8.44026	−0.349860
$583$	−9.37187	−0.388143
$584$	−123.562	−5.11304
$585$	0	0
$586$	34.1822	1.41205
$587$	34.5314	1.42526	0.712631	−	0.701539i	$-0.247503\pi$
$587$	34.5314	1.42526	0.712631	+	0.701539i	$0.247503\pi$
$588$	1.41317	0.0582780
$589$	−21.1942	−0.873292
$590$	0	0
$591$	−6.85597	−0.282017
$592$	−62.6976	−2.57686
$593$	−2.06074	−0.0846245	−0.0423123	−	0.999104i	$-0.513472\pi$
$593$	−2.06074	−0.0846245	−0.0423123	+	0.999104i	$0.513472\pi$
$594$	−16.2989	−0.668753
$595$	0	0
$596$	30.1533	1.23513
$597$	4.10128	0.167854
$598$	3.33918	0.136549
$599$	−28.2627	−1.15478	−0.577392	−	0.816467i	$-0.695930\pi$
$599$	−28.2627	−1.15478	−0.577392	+	0.816467i	$0.695930\pi$
$600$	0	0
$601$	−25.0036	−1.01992	−0.509959	−	0.860199i	$-0.670340\pi$
$601$	−25.0036	−1.01992	−0.509959	+	0.860199i	$0.670340\pi$
$602$	−8.13020	−0.331362
$603$	33.5064	1.36448
$604$	−50.1608	−2.04101
$605$	0	0
$606$	0.266141	0.0108113
$607$	29.0255	1.17811	0.589054	−	0.808093i	$-0.299500\pi$
$607$	29.0255	1.17811	0.589054	+	0.808093i	$0.299500\pi$
$608$	58.9114	2.38917
$609$	1.89453	0.0767701
$610$	0	0
$611$	4.84487	0.196003
$612$	91.7502	3.70878
$613$	25.2180	1.01855	0.509274	−	0.860605i	$-0.329914\pi$
$613$	25.2180	1.01855	0.509274	+	0.860605i	$0.329914\pi$
$614$	59.4940	2.40098
$615$	0	0
$616$	−32.9872	−1.32909
$617$	−41.7462	−1.68064	−0.840319	−	0.542093i	$-0.817632\pi$
$617$	−41.7462	−1.68064	−0.840319	+	0.542093i	$0.817632\pi$
$618$	−0.344109	−0.0138421
$619$	−0.503782	−0.0202487	−0.0101243	−	0.999949i	$-0.503223\pi$
$619$	−0.503782	−0.0202487	−0.0101243	+	0.999949i	$0.503223\pi$
$620$	0	0
$621$	−1.59940	−0.0641819
$622$	−57.5549	−2.30774
$623$	1.59107	0.0637449
$624$	−4.33827	−0.173670
$625$	0	0
$626$	−80.4499	−3.21543
$627$	3.45534	0.137993
$628$	26.3792	1.05264
$629$	28.9719	1.15519
$630$	0	0
$631$	−17.6868	−0.704102	−0.352051	−	0.935981i	$-0.614516\pi$
$631$	−17.6868	−0.704102	−0.352051	+	0.935981i	$0.614516\pi$
$632$	−28.8593	−1.14796
$633$	−6.55168	−0.260406
$634$	18.9954	0.754403
$635$	0	0
$636$	3.49622	0.138634
$637$	−1.24125	−0.0491802
$638$	−71.5471	−2.83258
$639$	−7.90799	−0.312835
$640$	0	0
$641$	−37.4714	−1.48003	−0.740015	−	0.672590i	$-0.765182\pi$
$641$	−37.4714	−1.48003	−0.740015	+	0.672590i	$0.765182\pi$
$642$	−4.17184	−0.164650
$643$	−0.178907	−0.00705539	−0.00352770	−	0.999994i	$-0.501123\pi$
$643$	−0.178907	−0.00705539	−0.00352770	+	0.999994i	$0.501123\pi$
$644$	−5.23702	−0.206367
$645$	0	0
$646$	−54.4269	−2.14140
$647$	−2.94235	−0.115676	−0.0578379	−	0.998326i	$-0.518421\pi$
$647$	−2.94235	−0.115676	−0.0578379	+	0.998326i	$0.518421\pi$
$648$	−72.7125	−2.85642
$649$	10.9530	0.429944
$650$	0	0
$651$	−1.69187	−0.0663095
$652$	38.5294	1.50893
$653$	−44.1719	−1.72858	−0.864290	−	0.502994i	$-0.832232\pi$
$653$	−44.1719	−1.72858	−0.864290	+	0.502994i	$0.832232\pi$
$654$	−11.2429	−0.439631
$655$	0	0
$656$	−23.0672	−0.900623
$657$	−41.5347	−1.62042
$658$	−10.5003	−0.409345
$659$	13.9282	0.542564	0.271282	−	0.962500i	$-0.412552\pi$
$659$	13.9282	0.542564	0.271282	+	0.962500i	$0.412552\pi$
$660$	0	0
$661$	−2.15327	−0.0837525	−0.0418763	−	0.999123i	$-0.513334\pi$
$661$	−2.15327	−0.0837525	−0.0418763	+	0.999123i	$0.513334\pi$
$662$	−43.5976	−1.69447
$663$	2.00467	0.0778549
$664$	61.1501	2.37308
$665$	0	0
$666$	−38.1184	−1.47706
$667$	−7.02088	−0.271849
$668$	−109.927	−4.25320
$669$	−4.78548	−0.185017
$670$	0	0
$671$	39.2134	1.51382
$672$	4.70271	0.181411
$673$	2.96276	0.114206	0.0571030	−	0.998368i	$-0.481814\pi$
$673$	2.96276	0.114206	0.0571030	+	0.998368i	$0.481814\pi$
$674$	14.0374	0.540701
$675$	0	0
$676$	−60.0125	−2.30817
$677$	−9.59927	−0.368930	−0.184465	−	0.982839i	$-0.559055\pi$
$677$	−9.59927	−0.368930	−0.184465	+	0.982839i	$0.559055\pi$
$678$	−3.25394	−0.124967
$679$	−11.6270	−0.446202
$680$	0	0
$681$	4.23888	0.162434
$682$	63.8936	2.44661
$683$	24.1908	0.925636	0.462818	−	0.886453i	$-0.346838\pi$
$683$	24.1908	0.925636	0.462818	+	0.886453i	$0.346838\pi$
$684$	51.8196	1.98137
$685$	0	0
$686$	2.69017	0.102711
$687$	−1.21870	−0.0464962
$688$	−39.1443	−1.49236
$689$	−3.07089	−0.116992
$690$	0	0
$691$	30.4784	1.15945	0.579726	−	0.814811i	$-0.303159\pi$
$691$	30.4784	1.15945	0.579726	+	0.814811i	$0.303159\pi$
$692$	64.6084	2.45604
$693$	−11.0885	−0.421216
$694$	11.2743	0.427968
$695$	0	0
$696$	16.4978	0.625347
$697$	10.6591	0.403743
$698$	50.2014	1.90015
$699$	4.38873	0.165997
$700$	0	0
$701$	17.4101	0.657570	0.328785	−	0.944405i	$-0.393361\pi$
$701$	17.4101	0.657570	0.328785	+	0.944405i	$0.393361\pi$
$702$	−5.34070	−0.201572
$703$	16.3631	0.617145
$704$	−79.4694	−2.99512
$705$	0	0
$706$	−31.1471	−1.17224
$707$	0.366626	0.0137884
$708$	−4.08608	−0.153564
$709$	13.6465	0.512504	0.256252	−	0.966610i	$-0.417512\pi$
$709$	13.6465	0.512504	0.256252	+	0.966610i	$0.417512\pi$
$710$	0	0
$711$	−9.70089	−0.363812
$712$	13.8552	0.519247
$713$	6.26984	0.234807
$714$	−4.34473	−0.162597
$715$	0	0
$716$	−67.6007	−2.52636
$717$	0.579503	0.0216419
$718$	−79.3358	−2.96078
$719$	−29.8264	−1.11234	−0.556169	−	0.831069i	$-0.687729\pi$
$719$	−29.8264	−1.11234	−0.556169	+	0.831069i	$0.687729\pi$
$720$	0	0
$721$	−0.474030	−0.0176538
$722$	20.3735	0.758222
$723$	3.36429	0.125119
$724$	−30.7373	−1.14234
$725$	0	0
$726$	−2.43160	−0.0902452
$727$	−6.92789	−0.256941	−0.128471	−	0.991713i	$-0.541007\pi$
$727$	−6.92789	−0.256941	−0.128471	+	0.991713i	$0.541007\pi$
$728$	−10.8090	−0.400607
$729$	−23.1471	−0.857302
$730$	0	0
$731$	18.0882	0.669015
$732$	−14.6288	−0.540694
$733$	10.8092	0.399246	0.199623	−	0.979873i	$-0.436028\pi$
$733$	10.8092	0.399246	0.199623	+	0.979873i	$0.436028\pi$
$734$	−66.6779	−2.46113
$735$	0	0
$736$	−17.4276	−0.642391
$737$	43.3609	1.59722
$738$	−14.0242	−0.516238
$739$	34.5455	1.27078	0.635388	−	0.772193i	$-0.280840\pi$
$739$	34.5455	1.27078	0.635388	+	0.772193i	$0.280840\pi$
$740$	0	0
$741$	1.13222	0.0415931
$742$	6.65556	0.244333
$743$	−19.7750	−0.725475	−0.362737	−	0.931891i	$-0.618158\pi$
$743$	−19.7750	−0.725475	−0.362737	+	0.931891i	$0.618158\pi$
$744$	−14.7330	−0.540137
$745$	0	0
$746$	46.1428	1.68941
$747$	20.5552	0.752077
$748$	118.735	4.34137
$749$	−5.74697	−0.209990
$750$	0	0
$751$	−31.0704	−1.13378	−0.566888	−	0.823795i	$-0.691853\pi$
$751$	−31.0704	−1.13378	−0.566888	+	0.823795i	$0.691853\pi$
$752$	−50.5556	−1.84357
$753$	1.32622	0.0483300
$754$	−23.4440	−0.853779
$755$	0	0
$756$	8.37610	0.304636
$757$	−8.32104	−0.302433	−0.151217	−	0.988501i	$-0.548319\pi$
$757$	−8.32104	−0.302433	−0.151217	+	0.988501i	$0.548319\pi$
$758$	−88.2944	−3.20700
$759$	−1.02219	−0.0371031
$760$	0	0
$761$	−3.82034	−0.138487	−0.0692436	−	0.997600i	$-0.522059\pi$
$761$	−3.82034	−0.138487	−0.0692436	+	0.997600i	$0.522059\pi$
$762$	−1.54666	−0.0560295
$763$	−15.4877	−0.560694
$764$	62.5004	2.26118
$765$	0	0
$766$	−22.6676	−0.819014
$767$	3.58900	0.129591
$768$	4.34426	0.156760
$769$	8.05891	0.290612	0.145306	−	0.989387i	$-0.453583\pi$
$769$	8.05891	0.290612	0.145306	+	0.989387i	$0.453583\pi$
$770$	0	0
$771$	−7.68463	−0.276755
$772$	−3.94295	−0.141910
$773$	20.3254	0.731054	0.365527	−	0.930801i	$-0.380889\pi$
$773$	20.3254	0.731054	0.365527	+	0.930801i	$0.380889\pi$
$774$	−23.7986	−0.855423
$775$	0	0
$776$	−101.249	−3.63463
$777$	1.30621	0.0468601
$778$	68.0623	2.44015
$779$	6.02017	0.215695
$780$	0	0
$781$	−10.2338	−0.366194
$782$	16.1010	0.575771
$783$	11.2292	0.401299
$784$	12.9523	0.462582
$785$	0	0
$786$	13.1567	0.469286
$787$	47.7951	1.70371	0.851856	−	0.523775i	$-0.175477\pi$
$787$	47.7951	1.70371	0.851856	+	0.523775i	$0.175477\pi$
$788$	−133.059	−4.74002
$789$	−0.510869	−0.0181874
$790$	0	0
$791$	−4.48250	−0.159379
$792$	−96.5597	−3.43110
$793$	12.8491	0.456286
$794$	54.7853	1.94426
$795$	0	0
$796$	79.5964	2.82122
$797$	7.57090	0.268175	0.134088	−	0.990969i	$-0.457190\pi$
$797$	7.57090	0.268175	0.134088	+	0.990969i	$0.457190\pi$
$798$	−2.45386	−0.0868657
$799$	23.3612	0.826461
$800$	0	0
$801$	4.65736	0.164560
$802$	−11.0372	−0.389735
$803$	−53.7505	−1.89681
$804$	−16.1760	−0.570483
$805$	0	0
$806$	20.9361	0.737444
$807$	−0.677725	−0.0238571
$808$	3.19262	0.112316
$809$	8.55279	0.300700	0.150350	−	0.988633i	$-0.451960\pi$
$809$	8.55279	0.300700	0.150350	+	0.988633i	$0.451960\pi$
$810$	0	0
$811$	−45.0023	−1.58024	−0.790122	−	0.612950i	$-0.789983\pi$
$811$	−45.0023	−1.58024	−0.790122	+	0.612950i	$0.789983\pi$
$812$	36.7684	1.29032
$813$	6.77568	0.237634
$814$	−49.3293	−1.72899
$815$	0	0
$816$	−20.9185	−0.732293
$817$	10.2160	0.357413
$818$	72.2173	2.52502
$819$	−3.63337	−0.126960
$820$	0	0
$821$	41.4358	1.44612	0.723060	−	0.690785i	$-0.242735\pi$
$821$	41.4358	1.44612	0.723060	+	0.690785i	$0.242735\pi$
$822$	−11.1111	−0.387544
$823$	19.1508	0.667553	0.333777	−	0.942652i	$-0.391677\pi$
$823$	19.1508	0.667553	0.333777	+	0.942652i	$0.391677\pi$
$824$	−4.12791	−0.143803
$825$	0	0
$826$	−7.77845	−0.270647
$827$	32.2820	1.12256	0.561278	−	0.827627i	$-0.310310\pi$
$827$	32.2820	1.12256	0.561278	+	0.827627i	$0.310310\pi$
$828$	−15.3297	−0.532744
$829$	9.85700	0.342348	0.171174	−	0.985241i	$-0.445244\pi$
$829$	9.85700	0.342348	0.171174	+	0.985241i	$0.445244\pi$
$830$	0	0
$831$	−2.55984	−0.0887998
$832$	−26.0399	−0.902770
$833$	−5.98512	−0.207372
$834$	−9.81979	−0.340031
$835$	0	0
$836$	67.0603	2.31933
$837$	−10.0280	−0.346619
$838$	−0.402165	−0.0138925
$839$	11.7098	0.404267	0.202133	−	0.979358i	$-0.435213\pi$
$839$	11.7098	0.404267	0.202133	+	0.979358i	$0.435213\pi$
$840$	0	0
$841$	20.2927	0.699748
$842$	28.3191	0.975941
$843$	2.35086	0.0809678
$844$	−127.153	−4.37679
$845$	0	0
$846$	−30.7364	−1.05674
$847$	−3.34968	−0.115096
$848$	32.0444	1.10041
$849$	−8.24484	−0.282962
$850$	0	0
$851$	−4.84066	−0.165936
$852$	3.81777	0.130795
$853$	29.2441	1.00130	0.500650	−	0.865650i	$-0.333094\pi$
$853$	29.2441	1.00130	0.500650	+	0.865650i	$0.333094\pi$
$854$	−27.8480	−0.952938
$855$	0	0
$856$	−50.0453	−1.71051
$857$	−38.6873	−1.32153	−0.660766	−	0.750592i	$-0.729768\pi$
$857$	−38.6873	−1.32153	−0.660766	+	0.750592i	$0.729768\pi$
$858$	−3.41327	−0.116527
$859$	−49.3913	−1.68521	−0.842604	−	0.538534i	$-0.818979\pi$
$859$	−49.3913	−1.68521	−0.842604	+	0.538534i	$0.818979\pi$
$860$	0	0
$861$	0.480572	0.0163778
$862$	6.15148	0.209520
$863$	2.32156	0.0790267	0.0395134	−	0.999219i	$-0.487419\pi$
$863$	2.32156	0.0790267	0.0395134	+	0.999219i	$0.487419\pi$
$864$	27.8738	0.948287
$865$	0	0
$866$	−55.0325	−1.87008
$867$	5.07889	0.172488
$868$	−32.8353	−1.11450
$869$	−12.5540	−0.425865
$870$	0	0
$871$	14.2081	0.481424
$872$	−134.869	−4.56725
$873$	−34.0343	−1.15189
$874$	9.09369	0.307599
$875$	0	0
$876$	20.0519	0.677490
$877$	−36.2775	−1.22500	−0.612502	−	0.790469i	$-0.709837\pi$
$877$	−36.2775	−1.22500	−0.612502	+	0.790469i	$0.709837\pi$
$878$	−24.0453	−0.811490
$879$	−3.42871	−0.115647
$880$	0	0
$881$	30.1252	1.01494	0.507472	−	0.861668i	$-0.330580\pi$
$881$	30.1252	1.01494	0.507472	+	0.861668i	$0.330580\pi$
$882$	7.87463	0.265152
$883$	−1.94158	−0.0653394	−0.0326697	−	0.999466i	$-0.510401\pi$
$883$	−1.94158	−0.0653394	−0.0326697	+	0.999466i	$0.510401\pi$
$884$	38.9060	1.30855
$885$	0	0
$886$	−18.0669	−0.606969
$887$	−52.3596	−1.75806	−0.879031	−	0.476765i	$-0.841809\pi$
$887$	−52.3596	−1.75806	−0.879031	+	0.476765i	$0.841809\pi$
$888$	11.3747	0.381709
$889$	−2.13061	−0.0714585
$890$	0	0
$891$	−31.6305	−1.05966
$892$	−92.8752	−3.10969
$893$	13.1942	0.441527
$894$	−4.17965	−0.139789
$895$	0	0
$896$	21.5811	0.720972
$897$	−0.334942	−0.0111834
$898$	−106.848	−3.56555
$899$	−44.0198	−1.46814
$900$	0	0
$901$	−14.8074	−0.493305
$902$	−18.1489	−0.604291
$903$	0.815514	0.0271386
$904$	−39.0342	−1.29826
$905$	0	0
$906$	6.95296	0.230997
$907$	−9.62846	−0.319708	−0.159854	−	0.987141i	$-0.551102\pi$
$907$	−9.62846	−0.319708	−0.159854	+	0.987141i	$0.551102\pi$
$908$	82.2669	2.73012
$909$	1.07318	0.0355952
$910$	0	0
$911$	−24.6036	−0.815154	−0.407577	−	0.913171i	$-0.633626\pi$
$911$	−24.6036	−0.815154	−0.407577	+	0.913171i	$0.633626\pi$
$912$	−11.8145	−0.391219
$913$	26.6007	0.880356
$914$	−96.1434	−3.18014
$915$	0	0
$916$	−23.6521	−0.781488
$917$	18.1242	0.598514
$918$	−25.7520	−0.849943
$919$	18.4685	0.609220	0.304610	−	0.952477i	$-0.401474\pi$
$919$	18.4685	0.609220	0.304610	+	0.952477i	$0.401474\pi$
$920$	0	0
$921$	−5.96765	−0.196641
$922$	49.3690	1.62588
$923$	−3.35333	−0.110376
$924$	5.35321	0.176108
$925$	0	0
$926$	30.0819	0.988551
$927$	−1.38757	−0.0455739
$928$	122.357	4.01657
$929$	21.6032	0.708778	0.354389	−	0.935098i	$-0.384689\pi$
$929$	21.6032	0.708778	0.354389	+	0.935098i	$0.384689\pi$
$930$	0	0
$931$	−3.38034	−0.110786
$932$	85.1751	2.79000
$933$	5.77314	0.189004
$934$	85.3404	2.79242
$935$	0	0
$936$	−31.6399	−1.03418
$937$	−4.95446	−0.161855	−0.0809276	−	0.996720i	$-0.525788\pi$
$937$	−4.95446	−0.161855	−0.0809276	+	0.996720i	$0.525788\pi$
$938$	−30.7933	−1.00544
$939$	8.06967	0.263344
$940$	0	0
$941$	−37.1398	−1.21072	−0.605361	−	0.795951i	$-0.706971\pi$
$941$	−37.1398	−1.21072	−0.605361	+	0.795951i	$0.706971\pi$
$942$	−3.65651	−0.119136
$943$	−1.78094	−0.0579953
$944$	−37.4507	−1.21892
$945$	0	0
$946$	−30.7980	−1.00133
$947$	11.0644	0.359543	0.179772	−	0.983708i	$-0.442464\pi$
$947$	11.0644	0.359543	0.179772	+	0.983708i	$0.442464\pi$
$948$	4.68333	0.152107
$949$	−17.6125	−0.571726
$950$	0	0
$951$	−1.90536	−0.0617857
$952$	−52.1192	−1.68919
$953$	−19.3888	−0.628065	−0.314033	−	0.949412i	$-0.601680\pi$
$953$	−19.3888	−0.628065	−0.314033	+	0.949412i	$0.601680\pi$
$954$	19.4821	0.630755
$955$	0	0
$956$	11.2468	0.363748
$957$	7.17665	0.231988
$958$	26.4101	0.853271
$959$	−15.3062	−0.494263
$960$	0	0
$961$	8.31092	0.268094
$962$	−16.1638	−0.521142
$963$	−16.8224	−0.542095
$964$	65.2932	2.10295
$965$	0	0
$966$	0.725921	0.0233561
$967$	32.5154	1.04563	0.522813	−	0.852448i	$-0.324883\pi$
$967$	32.5154	1.04563	0.522813	+	0.852448i	$0.324883\pi$
$968$	−29.1694	−0.937540
$969$	5.45938	0.175381
$970$	0	0
$971$	1.32316	0.0424622	0.0212311	−	0.999775i	$-0.493241\pi$
$971$	1.32316	0.0424622	0.0212311	+	0.999775i	$0.493241\pi$
$972$	36.9282	1.18447
$973$	−13.5273	−0.433667
$974$	−97.5934	−3.12709
$975$	0	0
$976$	−134.079	−4.29176
$977$	31.6195	1.01160	0.505799	−	0.862651i	$-0.331198\pi$
$977$	31.6195	1.01160	0.505799	+	0.862651i	$0.331198\pi$
$978$	−5.34070	−0.170777
$979$	6.02713	0.192628
$980$	0	0
$981$	−45.3355	−1.44745
$982$	47.3611	1.51135
$983$	12.1696	0.388149	0.194074	−	0.980987i	$-0.437830\pi$
$983$	12.1696	0.388149	0.194074	+	0.980987i	$0.437830\pi$
$984$	4.18488	0.133409
$985$	0	0
$986$	−113.043	−3.60003
$987$	1.05325	0.0335254
$988$	21.9737	0.699078
$989$	−3.02219	−0.0961000
$990$	0	0
$991$	2.18738	0.0694844	0.0347422	−	0.999396i	$-0.488939\pi$
$991$	2.18738	0.0694844	0.0347422	+	0.999396i	$0.488939\pi$
$992$	−109.269	−3.46928
$993$	4.37313	0.138777
$994$	7.26768	0.230517
$995$	0	0
$996$	−9.92353	−0.314439
$997$	3.78052	0.119730	0.0598652	−	0.998206i	$-0.480933\pi$
$997$	3.78052	0.119730	0.0598652	+	0.998206i	$0.480933\pi$
$998$	−32.5894	−1.03160
$999$	7.74216	0.244951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.p.1.1		5
5.4	even	2		161.2.a.d.1.5	✓	5
15.14	odd	2		1449.2.a.r.1.1		5
20.19	odd	2		2576.2.a.bd.1.3		5
35.34	odd	2		1127.2.a.h.1.5		5
115.114	odd	2		3703.2.a.j.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.5	✓	5	5.4	even	2
1127.2.a.h.1.5		5	35.34	odd	2
1449.2.a.r.1.1		5	15.14	odd	2
2576.2.a.bd.1.3		5	20.19	odd	2
3703.2.a.j.1.5		5	115.114	odd	2
4025.2.a.p.1.1		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} +O(q^{10})\)	\(q-2.69017 q^{2} +0.269842 q^{3} +5.23702 q^{4} -0.725921 q^{6} -1.00000 q^{7} -8.70812 q^{8} -2.92719 q^{9} -3.78810 q^{11} +1.41317 q^{12} -1.24125 q^{13} +2.69017 q^{14} +12.9523 q^{16} -5.98512 q^{17} +7.87463 q^{18} -3.38034 q^{19} -0.269842 q^{21} +10.1906 q^{22} +1.00000 q^{23} -2.34982 q^{24} +3.33918 q^{26} -1.59940 q^{27} -5.23702 q^{28} -7.02088 q^{29} +6.26984 q^{31} -17.4276 q^{32} -1.02219 q^{33} +16.1010 q^{34} -15.3297 q^{36} -4.84066 q^{37} +9.09369 q^{38} -0.334942 q^{39} -1.78094 q^{41} +0.725921 q^{42} -3.02219 q^{43} -19.8383 q^{44} -2.69017 q^{46} -3.90322 q^{47} +3.49508 q^{48} +1.00000 q^{49} -1.61504 q^{51} -6.50046 q^{52} +2.47403 q^{53} +4.30267 q^{54} +8.70812 q^{56} -0.912158 q^{57} +18.8873 q^{58} -2.89143 q^{59} -10.3518 q^{61} -16.8669 q^{62} +2.92719 q^{63} +20.9787 q^{64} +2.74986 q^{66} -11.4466 q^{67} -31.3442 q^{68} +0.269842 q^{69} +2.70157 q^{71} +25.4903 q^{72} +14.1893 q^{73} +13.0222 q^{74} -17.7029 q^{76} +3.78810 q^{77} +0.901051 q^{78} +3.31407 q^{79} +8.34997 q^{81} +4.79102 q^{82} -7.02219 q^{83} -1.41317 q^{84} +8.13020 q^{86} -1.89453 q^{87} +32.9872 q^{88} -1.59107 q^{89} +1.24125 q^{91} +5.23702 q^{92} +1.69187 q^{93} +10.5003 q^{94} -4.70271 q^{96} +11.6270 q^{97} -2.69017 q^{98} +11.0885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 12 q^{4} - 3 q^{6} - 5 q^{7} - 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 12 * q^4 - 3 * q^6 - 5 * q^7 - 3 * q^8 + 11 * q^9	\( 5 q - 2 q^{2} + 12 q^{4} - 3 q^{6} - 5 q^{7} - 3 q^{8} + 11 q^{9} - 4 q^{11} - 3 q^{12} + 6 q^{13} + 2 q^{14} + 10 q^{16} + 12 q^{17} + 19 q^{18} + 6 q^{19} - 14 q^{22} + 5 q^{23} - 36 q^{24} + q^{26} - 12 q^{28} - 4 q^{29} + 30 q^{31} - 8 q^{32} + 22 q^{33} + 6 q^{34} - q^{36} - 4 q^{37} + 40 q^{38} + 16 q^{39} + 6 q^{41} + 3 q^{42} + 12 q^{43} - 26 q^{44} - 2 q^{46} - 10 q^{47} - 25 q^{48} + 5 q^{49} - 4 q^{51} + 21 q^{52} - 16 q^{53} + 33 q^{54} + 3 q^{56} - 6 q^{57} - 13 q^{58} + 22 q^{59} - 18 q^{61} - 15 q^{62} - 11 q^{63} + 25 q^{64} + 4 q^{66} + 2 q^{67} - 12 q^{68} + 4 q^{71} + 41 q^{72} + 2 q^{73} + 38 q^{74} + 10 q^{76} + 4 q^{77} - 41 q^{78} + 30 q^{79} - 3 q^{81} + 7 q^{82} - 8 q^{83} + 3 q^{84} + 8 q^{86} + 12 q^{87} - 4 q^{88} - 20 q^{89} - 6 q^{91} + 12 q^{92} + 26 q^{93} - 25 q^{94} - q^{96} + 12 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 12 * q^4 - 3 * q^6 - 5 * q^7 - 3 * q^8 + 11 * q^9 - 4 * q^11 - 3 * q^12 + 6 * q^13 + 2 * q^14 + 10 * q^16 + 12 * q^17 + 19 * q^18 + 6 * q^19 - 14 * q^22 + 5 * q^23 - 36 * q^24 + q^26 - 12 * q^28 - 4 * q^29 + 30 * q^31 - 8 * q^32 + 22 * q^33 + 6 * q^34 - q^36 - 4 * q^37 + 40 * q^38 + 16 * q^39 + 6 * q^41 + 3 * q^42 + 12 * q^43 - 26 * q^44 - 2 * q^46 - 10 * q^47 - 25 * q^48 + 5 * q^49 - 4 * q^51 + 21 * q^52 - 16 * q^53 + 33 * q^54 + 3 * q^56 - 6 * q^57 - 13 * q^58 + 22 * q^59 - 18 * q^61 - 15 * q^62 - 11 * q^63 + 25 * q^64 + 4 * q^66 + 2 * q^67 - 12 * q^68 + 4 * q^71 + 41 * q^72 + 2 * q^73 + 38 * q^74 + 10 * q^76 + 4 * q^77 - 41 * q^78 + 30 * q^79 - 3 * q^81 + 7 * q^82 - 8 * q^83 + 3 * q^84 + 8 * q^86 + 12 * q^87 - 4 * q^88 - 20 * q^89 - 6 * q^91 + 12 * q^92 + 26 * q^93 - 25 * q^94 - q^96 + 12 * q^97 - 2 * q^98 - 8 * q^99

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