LMFDB - Embedded newform 4025.2.a.t.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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 36x^{4} - 23x^{3} - 30x^{2} + 17x - 2 $ x^8 - x^7 - 11x^6 + 9x^5 + 36x^4 - 23x^3 - 30x^2 + 17x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.42061$ 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)

$f(q)$	$=$	$q-2.42061 q^{2} +0.490228 q^{3} +3.85934 q^{4} -1.18665 q^{6} -1.00000 q^{7} -4.50072 q^{8} -2.75968 q^{9} +O(q^{10})$	\(q-2.42061 q^{2} +0.490228 q^{3} +3.85934 q^{4} -1.18665 q^{6} -1.00000 q^{7} -4.50072 q^{8} -2.75968 q^{9} +0.841565 q^{11} +1.89195 q^{12} -4.60725 q^{13} +2.42061 q^{14} +3.17580 q^{16} +1.35669 q^{17} +6.68009 q^{18} +7.24152 q^{19} -0.490228 q^{21} -2.03710 q^{22} -1.00000 q^{23} -2.20638 q^{24} +11.1524 q^{26} -2.82355 q^{27} -3.85934 q^{28} -4.95190 q^{29} -7.41080 q^{31} +1.31407 q^{32} +0.412558 q^{33} -3.28400 q^{34} -10.6505 q^{36} +8.07664 q^{37} -17.5289 q^{38} -2.25860 q^{39} +10.1985 q^{41} +1.18665 q^{42} +11.6762 q^{43} +3.24788 q^{44} +2.42061 q^{46} +10.2672 q^{47} +1.55687 q^{48} +1.00000 q^{49} +0.665085 q^{51} -17.7809 q^{52} -8.95540 q^{53} +6.83471 q^{54} +4.50072 q^{56} +3.54999 q^{57} +11.9866 q^{58} +2.24165 q^{59} -8.83097 q^{61} +17.9386 q^{62} +2.75968 q^{63} -9.53246 q^{64} -0.998642 q^{66} +6.29272 q^{67} +5.23591 q^{68} -0.490228 q^{69} +9.82614 q^{71} +12.4205 q^{72} -11.8792 q^{73} -19.5504 q^{74} +27.9474 q^{76} -0.841565 q^{77} +5.46719 q^{78} -5.18255 q^{79} +6.89485 q^{81} -24.6866 q^{82} +1.89084 q^{83} -1.89195 q^{84} -28.2634 q^{86} -2.42756 q^{87} -3.78765 q^{88} -12.2386 q^{89} +4.60725 q^{91} -3.85934 q^{92} -3.63298 q^{93} -24.8530 q^{94} +0.644195 q^{96} +8.69991 q^{97} -2.42061 q^{98} -2.32245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	$ 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) $ 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.42061	−1.71163	−0.855814	−	0.517284i	$-0.826943\pi$
$2$	−2.42061	−1.71163	−0.855814	+	0.517284i	$0.826943\pi$
$3$	0.490228	0.283033	0.141517	−	0.989936i	$-0.454802\pi$
$3$	0.490228	0.283033	0.141517	+	0.989936i	$0.454802\pi$
$4$	3.85934	1.92967
$5$	0	0
$5$	0	0
$6$	−1.18665	−0.484447
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.50072	−1.59125
$9$	−2.75968	−0.919892
$10$	0	0
$11$	0.841565	0.253741	0.126871	−	0.991919i	$-0.459507\pi$
$11$	0.841565	0.253741	0.126871	+	0.991919i	$0.459507\pi$
$12$	1.89195	0.546160
$13$	−4.60725	−1.27782	−0.638911	−	0.769280i	$-0.720615\pi$
$13$	−4.60725	−1.27782	−0.638911	+	0.769280i	$0.720615\pi$
$14$	2.42061	0.646934
$15$	0	0
$16$	3.17580	0.793951
$17$	1.35669	0.329045	0.164522	−	0.986373i	$-0.447392\pi$
$17$	1.35669	0.329045	0.164522	+	0.986373i	$0.447392\pi$
$18$	6.68009	1.57451
$19$	7.24152	1.66132	0.830659	−	0.556782i	$-0.187964\pi$
$19$	7.24152	1.66132	0.830659	+	0.556782i	$0.187964\pi$
$20$	0	0
$21$	−0.490228	−0.106976
$22$	−2.03710	−0.434311
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.20638	−0.450375
$25$	0	0
$26$	11.1524	2.18716
$27$	−2.82355	−0.543393
$28$	−3.85934	−0.729346
$29$	−4.95190	−0.919545	−0.459773	−	0.888037i	$-0.652069\pi$
$29$	−4.95190	−0.919545	−0.459773	+	0.888037i	$0.652069\pi$
$30$	0	0
$31$	−7.41080	−1.33102	−0.665509	−	0.746390i	$-0.731786\pi$
$31$	−7.41080	−1.33102	−0.665509	+	0.746390i	$0.731786\pi$
$32$	1.31407	0.232297
$33$	0.412558	0.0718172
$34$	−3.28400	−0.563202
$35$	0	0
$36$	−10.6505	−1.77509
$37$	8.07664	1.32779	0.663896	−	0.747825i	$-0.268902\pi$
$37$	8.07664	1.32779	0.663896	+	0.747825i	$0.268902\pi$
$38$	−17.5289	−2.84356
$39$	−2.25860	−0.361666
$40$	0	0
$41$	10.1985	1.59274	0.796371	−	0.604809i	$-0.206751\pi$
$41$	10.1985	1.59274	0.796371	+	0.604809i	$0.206751\pi$
$42$	1.18665	0.183104
$43$	11.6762	1.78060	0.890301	−	0.455373i	$-0.150494\pi$
$43$	11.6762	1.78060	0.890301	+	0.455373i	$0.150494\pi$
$44$	3.24788	0.489637
$45$	0	0
$46$	2.42061	0.356899
$47$	10.2672	1.49763	0.748816	−	0.662778i	$-0.230623\pi$
$47$	10.2672	1.49763	0.748816	+	0.662778i	$0.230623\pi$
$48$	1.55687	0.224714
$49$	1.00000	0.142857
$50$	0	0
$51$	0.665085	0.0931306
$52$	−17.7809	−2.46577
$53$	−8.95540	−1.23012	−0.615059	−	0.788481i	$-0.710868\pi$
$53$	−8.95540	−1.23012	−0.615059	+	0.788481i	$0.710868\pi$
$54$	6.83471	0.930086
$55$	0	0
$56$	4.50072	0.601434
$57$	3.54999	0.470208
$58$	11.9866	1.57392
$59$	2.24165	0.291838	0.145919	−	0.989297i	$-0.453386\pi$
$59$	2.24165	0.291838	0.145919	+	0.989297i	$0.453386\pi$
$60$	0	0
$61$	−8.83097	−1.13069	−0.565345	−	0.824855i	$-0.691257\pi$
$61$	−8.83097	−1.13069	−0.565345	+	0.824855i	$0.691257\pi$
$62$	17.9386	2.27821
$63$	2.75968	0.347687
$64$	−9.53246	−1.19156
$65$	0	0
$66$	−0.998642	−0.122924
$67$	6.29272	0.768778	0.384389	−	0.923171i	$-0.374412\pi$
$67$	6.29272	0.768778	0.384389	+	0.923171i	$0.374412\pi$
$68$	5.23591	0.634947
$69$	−0.490228	−0.0590165
$70$	0	0
$71$	9.82614	1.16615	0.583074	−	0.812419i	$-0.301850\pi$
$71$	9.82614	1.16615	0.583074	+	0.812419i	$0.301850\pi$
$72$	12.4205	1.46377
$73$	−11.8792	−1.39036	−0.695179	−	0.718837i	$-0.744675\pi$
$73$	−11.8792	−1.39036	−0.695179	+	0.718837i	$0.744675\pi$
$74$	−19.5504	−2.27268
$75$	0	0
$76$	27.9474	3.20579
$77$	−0.841565	−0.0959052
$78$	5.46719	0.619038
$79$	−5.18255	−0.583083	−0.291541	−	0.956558i	$-0.594168\pi$
$79$	−5.18255	−0.583083	−0.291541	+	0.956558i	$0.594168\pi$
$80$	0	0
$81$	6.89485	0.766094
$82$	−24.6866	−2.72618
$83$	1.89084	0.207547	0.103774	−	0.994601i	$-0.466908\pi$
$83$	1.89084	0.207547	0.103774	+	0.994601i	$0.466908\pi$
$84$	−1.89195	−0.206429
$85$	0	0
$86$	−28.2634	−3.04773
$87$	−2.42756	−0.260262
$88$	−3.78765	−0.403765
$89$	−12.2386	−1.29729	−0.648647	−	0.761089i	$-0.724665\pi$
$89$	−12.2386	−1.29729	−0.648647	+	0.761089i	$0.724665\pi$
$90$	0	0
$91$	4.60725	0.482972
$92$	−3.85934	−0.402364
$93$	−3.63298	−0.376722
$94$	−24.8530	−2.56339
$95$	0	0
$96$	0.644195	0.0657479
$97$	8.69991	0.883342	0.441671	−	0.897177i	$-0.354386\pi$
$97$	8.69991	0.883342	0.441671	+	0.897177i	$0.354386\pi$
$98$	−2.42061	−0.244518
$99$	−2.32245	−0.233415
$100$	0	0
$101$	−9.65427	−0.960636	−0.480318	−	0.877094i	$-0.659479\pi$
$101$	−9.65427	−0.960636	−0.480318	+	0.877094i	$0.659479\pi$
$102$	−1.60991	−0.159405
$103$	−12.0327	−1.18561	−0.592807	−	0.805344i	$-0.701980\pi$
$103$	−12.0327	−1.18561	−0.592807	+	0.805344i	$0.701980\pi$
$104$	20.7360	2.03333
$105$	0	0
$106$	21.6775	2.10550
$107$	−9.85268	−0.952494	−0.476247	−	0.879311i	$-0.658003\pi$
$107$	−9.85268	−0.952494	−0.476247	+	0.879311i	$0.658003\pi$
$108$	−10.8970	−1.04857
$109$	−19.1234	−1.83169	−0.915846	−	0.401531i	$-0.868478\pi$
$109$	−19.1234	−1.83169	−0.915846	+	0.401531i	$0.868478\pi$
$110$	0	0
$111$	3.95939	0.375809
$112$	−3.17580	−0.300085
$113$	−12.5960	−1.18493	−0.592465	−	0.805596i	$-0.701845\pi$
$113$	−12.5960	−1.18493	−0.592465	+	0.805596i	$0.701845\pi$
$114$	−8.59313	−0.804821
$115$	0	0
$116$	−19.1111	−1.77442
$117$	12.7145	1.17546
$118$	−5.42616	−0.499518
$119$	−1.35669	−0.124367
$120$	0	0
$121$	−10.2918	−0.935615
$122$	21.3763	1.93532
$123$	4.99960	0.450798
$124$	−28.6008	−2.56842
$125$	0	0
$126$	−6.68009	−0.595110
$127$	−9.42176	−0.836046	−0.418023	−	0.908437i	$-0.637277\pi$
$127$	−9.42176	−0.836046	−0.418023	+	0.908437i	$0.637277\pi$
$128$	20.4462	1.80720
$129$	5.72399	0.503969
$130$	0	0
$131$	15.4588	1.35064	0.675320	−	0.737524i	$-0.264005\pi$
$131$	15.4588	1.35064	0.675320	+	0.737524i	$0.264005\pi$
$132$	1.59220	0.138583
$133$	−7.24152	−0.627919
$134$	−15.2322	−1.31586
$135$	0	0
$136$	−6.10607	−0.523591
$137$	20.7129	1.76962	0.884810	−	0.465951i	$-0.154288\pi$
$137$	20.7129	1.76962	0.884810	+	0.465951i	$0.154288\pi$
$138$	1.18665	0.101014
$139$	−0.0228216	−0.00193570	−0.000967850	−	1.00000i	$-0.500308\pi$
$139$	−0.0228216	−0.00193570	−0.000967850		1.00000i	$0.500308\pi$
$140$	0	0
$141$	5.03329	0.423879
$142$	−23.7852	−1.99601
$143$	−3.87730	−0.324236
$144$	−8.76419	−0.730349
$145$	0	0
$146$	28.7549	2.37978
$147$	0.490228	0.0404333
$148$	31.1705	2.56220
$149$	2.06568	0.169227	0.0846137	−	0.996414i	$-0.473034\pi$
$149$	2.06568	0.169227	0.0846137	+	0.996414i	$0.473034\pi$
$150$	0	0
$151$	−4.86307	−0.395751	−0.197876	−	0.980227i	$-0.563404\pi$
$151$	−4.86307	−0.395751	−0.197876	+	0.980227i	$0.563404\pi$
$152$	−32.5920	−2.64356
$153$	−3.74402	−0.302686
$154$	2.03710	0.164154
$155$	0	0
$156$	−8.71671	−0.697895
$157$	−7.29044	−0.581840	−0.290920	−	0.956747i	$-0.593961\pi$
$157$	−7.29044	−0.581840	−0.290920	+	0.956747i	$0.593961\pi$
$158$	12.5449	0.998021
$159$	−4.39018	−0.348164
$160$	0	0
$161$	1.00000	0.0788110
$162$	−16.6897	−1.31127
$163$	−8.85813	−0.693823	−0.346911	−	0.937898i	$-0.612770\pi$
$163$	−8.85813	−0.693823	−0.346911	+	0.937898i	$0.612770\pi$
$164$	39.3595	3.07346
$165$	0	0
$166$	−4.57699	−0.355243
$167$	−23.7995	−1.84166	−0.920828	−	0.389968i	$-0.872486\pi$
$167$	−23.7995	−1.84166	−0.920828	+	0.389968i	$0.872486\pi$
$168$	2.20638	0.170226
$169$	8.22680	0.632831
$170$	0	0
$171$	−19.9842	−1.52823
$172$	45.0623	3.43597
$173$	17.7483	1.34938	0.674688	−	0.738103i	$-0.264278\pi$
$173$	17.7483	1.34938	0.674688	+	0.738103i	$0.264278\pi$
$174$	5.87617	0.445471
$175$	0	0
$176$	2.67264	0.201458
$177$	1.09892	0.0825999
$178$	29.6250	2.22048
$179$	−6.15726	−0.460215	−0.230108	−	0.973165i	$-0.573908\pi$
$179$	−6.15726	−0.460215	−0.230108	+	0.973165i	$0.573908\pi$
$180$	0	0
$181$	−14.8164	−1.10129	−0.550646	−	0.834739i	$-0.685618\pi$
$181$	−14.8164	−1.10129	−0.550646	+	0.834739i	$0.685618\pi$
$182$	−11.1524	−0.826667
$183$	−4.32919	−0.320023
$184$	4.50072	0.331798
$185$	0	0
$186$	8.79401	0.644808
$187$	1.14174	0.0834923
$188$	39.6247	2.88993
$189$	2.82355	0.205383
$190$	0	0
$191$	−3.75655	−0.271814	−0.135907	−	0.990722i	$-0.543395\pi$
$191$	−3.75655	−0.271814	−0.135907	+	0.990722i	$0.543395\pi$
$192$	−4.67308	−0.337250
$193$	−1.52912	−0.110068	−0.0550342	−	0.998484i	$-0.517527\pi$
$193$	−1.52912	−0.110068	−0.0550342	+	0.998484i	$0.517527\pi$
$194$	−21.0590	−1.51195
$195$	0	0
$196$	3.85934	0.275667
$197$	−7.05742	−0.502820	−0.251410	−	0.967881i	$-0.580894\pi$
$197$	−7.05742	−0.502820	−0.251410	+	0.967881i	$0.580894\pi$
$198$	5.62173	0.399519
$199$	16.1017	1.14142	0.570708	−	0.821153i	$-0.306669\pi$
$199$	16.1017	1.14142	0.570708	+	0.821153i	$0.306669\pi$
$200$	0	0
$201$	3.08487	0.217590
$202$	23.3692	1.64425
$203$	4.95190	0.347555
$204$	2.56679	0.179711
$205$	0	0
$206$	29.1264	2.02933
$207$	2.75968	0.191811
$208$	−14.6317	−1.01453
$209$	6.09421	0.421545
$210$	0	0
$211$	4.33498	0.298432	0.149216	−	0.988805i	$-0.452325\pi$
$211$	4.33498	0.298432	0.149216	+	0.988805i	$0.452325\pi$
$212$	−34.5619	−2.37372
$213$	4.81704	0.330058
$214$	23.8495	1.63032
$215$	0	0
$216$	12.7080	0.864672
$217$	7.41080	0.503078
$218$	46.2903	3.13517
$219$	−5.82353	−0.393517
$220$	0	0
$221$	−6.25060	−0.420461
$222$	−9.58413	−0.643245
$223$	−4.71222	−0.315554	−0.157777	−	0.987475i	$-0.550433\pi$
$223$	−4.71222	−0.315554	−0.157777	+	0.987475i	$0.550433\pi$
$224$	−1.31407	−0.0878002
$225$	0	0
$226$	30.4899	2.02816
$227$	−8.03745	−0.533464	−0.266732	−	0.963771i	$-0.585944\pi$
$227$	−8.03745	−0.533464	−0.266732	+	0.963771i	$0.585944\pi$
$228$	13.7006	0.907345
$229$	−7.88819	−0.521266	−0.260633	−	0.965438i	$-0.583931\pi$
$229$	−7.88819	−0.521266	−0.260633	+	0.965438i	$0.583931\pi$
$230$	0	0
$231$	−0.412558	−0.0271444
$232$	22.2871	1.46322
$233$	−16.2507	−1.06462	−0.532311	−	0.846549i	$-0.678676\pi$
$233$	−16.2507	−1.06462	−0.532311	+	0.846549i	$0.678676\pi$
$234$	−30.7769	−2.01195
$235$	0	0
$236$	8.65129	0.563151
$237$	−2.54063	−0.165032
$238$	3.28400	0.212870
$239$	24.4814	1.58357	0.791784	−	0.610802i	$-0.209153\pi$
$239$	24.4814	1.58357	0.791784	+	0.610802i	$0.209153\pi$
$240$	0	0
$241$	−2.43005	−0.156533	−0.0782666	−	0.996932i	$-0.524939\pi$
$241$	−2.43005	−0.156533	−0.0782666	+	0.996932i	$0.524939\pi$
$242$	24.9123	1.60142
$243$	11.8507	0.760223
$244$	−34.0817	−2.18186
$245$	0	0
$246$	−12.1021	−0.771599
$247$	−33.3635	−2.12287
$248$	33.3539	2.11798
$249$	0.926944	0.0587427
$250$	0	0
$251$	19.5610	1.23468	0.617340	−	0.786697i	$-0.288210\pi$
$251$	19.5610	1.23468	0.617340	+	0.786697i	$0.288210\pi$
$252$	10.6505	0.670920
$253$	−0.841565	−0.0529087
$254$	22.8064	1.43100
$255$	0	0
$256$	−30.4273	−1.90170
$257$	−0.424651	−0.0264890	−0.0132445	−	0.999912i	$-0.504216\pi$
$257$	−0.424651	−0.0264890	−0.0132445	+	0.999912i	$0.504216\pi$
$258$	−13.8555	−0.862607
$259$	−8.07664	−0.501858
$260$	0	0
$261$	13.6657	0.845883
$262$	−37.4197	−2.31179
$263$	−11.8213	−0.728934	−0.364467	−	0.931216i	$-0.618749\pi$
$263$	−11.8213	−0.728934	−0.364467	+	0.931216i	$0.618749\pi$
$264$	−1.85681	−0.114279
$265$	0	0
$266$	17.5289	1.07476
$267$	−5.99972	−0.367177
$268$	24.2857	1.48349
$269$	14.5287	0.885831	0.442916	−	0.896563i	$-0.353944\pi$
$269$	14.5287	0.885831	0.442916	+	0.896563i	$0.353944\pi$
$270$	0	0
$271$	−2.49715	−0.151691	−0.0758455	−	0.997120i	$-0.524166\pi$
$271$	−2.49715	−0.151691	−0.0758455	+	0.997120i	$0.524166\pi$
$272$	4.30857	0.261245
$273$	2.25860	0.136697
$274$	−50.1377	−3.02893
$275$	0	0
$276$	−1.89195	−0.113882
$277$	−32.5937	−1.95836	−0.979182	−	0.202984i	$-0.934936\pi$
$277$	−32.5937	−1.95836	−0.979182	+	0.202984i	$0.934936\pi$
$278$	0.0552420	0.00331320
$279$	20.4514	1.22439
$280$	0	0
$281$	13.8113	0.823911	0.411956	−	0.911204i	$-0.364846\pi$
$281$	13.8113	0.823911	0.411956	+	0.911204i	$0.364846\pi$
$282$	−12.1836	−0.725523
$283$	−14.2987	−0.849971	−0.424985	−	0.905200i	$-0.639721\pi$
$283$	−14.2987	−0.849971	−0.424985	+	0.905200i	$0.639721\pi$
$284$	37.9224	2.25028
$285$	0	0
$286$	9.38543	0.554972
$287$	−10.1985	−0.602000
$288$	−3.62642	−0.213689
$289$	−15.1594	−0.891730
$290$	0	0
$291$	4.26493	0.250015
$292$	−45.8459	−2.68293
$293$	−14.0191	−0.819005	−0.409502	−	0.912309i	$-0.634298\pi$
$293$	−14.0191	−0.819005	−0.409502	+	0.912309i	$0.634298\pi$
$294$	−1.18665	−0.0692067
$295$	0	0
$296$	−36.3507	−2.11284
$297$	−2.37620	−0.137881
$298$	−5.00021	−0.289654
$299$	4.60725	0.266444
$300$	0	0
$301$	−11.6762	−0.673004
$302$	11.7716	0.677379
$303$	−4.73279	−0.271892
$304$	22.9976	1.31900
$305$	0	0
$306$	9.06279	0.518085
$307$	−4.79018	−0.273390	−0.136695	−	0.990613i	$-0.543648\pi$
$307$	−4.79018	−0.273390	−0.136695	+	0.990613i	$0.543648\pi$
$308$	−3.24788	−0.185065
$309$	−5.89875	−0.335568
$310$	0	0
$311$	−25.6269	−1.45317	−0.726584	−	0.687077i	$-0.758893\pi$
$311$	−25.6269	−1.45317	−0.726584	+	0.687077i	$0.758893\pi$
$312$	10.1653	0.575499
$313$	−11.5473	−0.652691	−0.326345	−	0.945251i	$-0.605817\pi$
$313$	−11.5473	−0.652691	−0.326345	+	0.945251i	$0.605817\pi$
$314$	17.6473	0.995893
$315$	0	0
$316$	−20.0012	−1.12516
$317$	−1.54699	−0.0868879	−0.0434439	−	0.999056i	$-0.513833\pi$
$317$	−1.54699	−0.0868879	−0.0434439	+	0.999056i	$0.513833\pi$
$318$	10.6269	0.595927
$319$	−4.16735	−0.233327
$320$	0	0
$321$	−4.83006	−0.269587
$322$	−2.42061	−0.134895
$323$	9.82447	0.546648
$324$	26.6095	1.47831
$325$	0	0
$326$	21.4421	1.18757
$327$	−9.37483	−0.518429
$328$	−45.9007	−2.53444
$329$	−10.2672	−0.566052
$330$	0	0
$331$	17.6438	0.969791	0.484896	−	0.874572i	$-0.338858\pi$
$331$	17.6438	0.969791	0.484896	+	0.874572i	$0.338858\pi$
$332$	7.29740	0.400497
$333$	−22.2889	−1.22143
$334$	57.6091	3.15223
$335$	0	0
$336$	−1.55687	−0.0849340
$337$	7.99390	0.435456	0.217728	−	0.976010i	$-0.430136\pi$
$337$	7.99390	0.435456	0.217728	+	0.976010i	$0.430136\pi$
$338$	−19.9138	−1.08317
$339$	−6.17490	−0.335374
$340$	0	0
$341$	−6.23667	−0.337734
$342$	48.3740	2.61577
$343$	−1.00000	−0.0539949
$344$	−52.5513	−2.83337
$345$	0	0
$346$	−42.9616	−2.30963
$347$	24.4144	1.31063	0.655316	−	0.755355i	$-0.272536\pi$
$347$	24.4144	1.31063	0.655316	+	0.755355i	$0.272536\pi$
$348$	−9.36877	−0.502219
$349$	19.0300	1.01865	0.509327	−	0.860573i	$-0.329894\pi$
$349$	19.0300	1.01865	0.509327	+	0.860573i	$0.329894\pi$
$350$	0	0
$351$	13.0088	0.694360
$352$	1.10588	0.0589435
$353$	10.7755	0.573521	0.286760	−	0.958002i	$-0.407422\pi$
$353$	10.7755	0.573521	0.286760	+	0.958002i	$0.407422\pi$
$354$	−2.66005	−0.141380
$355$	0	0
$356$	−47.2331	−2.50335
$357$	−0.665085	−0.0352000
$358$	14.9043	0.787717
$359$	15.1540	0.799797	0.399898	−	0.916559i	$-0.369045\pi$
$359$	15.1540	0.799797	0.399898	+	0.916559i	$0.369045\pi$
$360$	0	0
$361$	33.4396	1.75998
$362$	35.8646	1.88500
$363$	−5.04531	−0.264810
$364$	17.7809	0.931975
$365$	0	0
$366$	10.4793	0.547760
$367$	21.4907	1.12180	0.560902	−	0.827882i	$-0.310454\pi$
$367$	21.4907	1.12180	0.560902	+	0.827882i	$0.310454\pi$
$368$	−3.17580	−0.165550
$369$	−28.1446	−1.46515
$370$	0	0
$371$	8.95540	0.464941
$372$	−14.0209	−0.726949
$373$	7.62209	0.394657	0.197328	−	0.980337i	$-0.436773\pi$
$373$	7.62209	0.394657	0.197328	+	0.980337i	$0.436773\pi$
$374$	−2.76370	−0.142908
$375$	0	0
$376$	−46.2100	−2.38310
$377$	22.8147	1.17502
$378$	−6.83471	−0.351540
$379$	−27.8972	−1.43298	−0.716492	−	0.697595i	$-0.754253\pi$
$379$	−27.8972	−1.43298	−0.716492	+	0.697595i	$0.754253\pi$
$380$	0	0
$381$	−4.61881	−0.236629
$382$	9.09312	0.465245
$383$	7.51140	0.383815	0.191907	−	0.981413i	$-0.438533\pi$
$383$	7.51140	0.383815	0.191907	+	0.981413i	$0.438533\pi$
$384$	10.0233	0.511499
$385$	0	0
$386$	3.70140	0.188396
$387$	−32.2225	−1.63796
$388$	33.5759	1.70456
$389$	−37.4182	−1.89718	−0.948590	−	0.316507i	$-0.897490\pi$
$389$	−37.4182	−1.89718	−0.948590	+	0.316507i	$0.897490\pi$
$390$	0	0
$391$	−1.35669	−0.0686106
$392$	−4.50072	−0.227321
$393$	7.57833	0.382276
$394$	17.0832	0.860641
$395$	0	0
$396$	−8.96310	−0.450413
$397$	−29.9389	−1.50259	−0.751295	−	0.659967i	$-0.770570\pi$
$397$	−29.9389	−1.50259	−0.751295	+	0.659967i	$0.770570\pi$
$398$	−38.9758	−1.95368
$399$	−3.54999	−0.177722
$400$	0	0
$401$	−12.8187	−0.640135	−0.320067	−	0.947395i	$-0.603706\pi$
$401$	−12.8187	−0.640135	−0.320067	+	0.947395i	$0.603706\pi$
$402$	−7.46724	−0.372432
$403$	34.1434	1.70081
$404$	−37.2591	−1.85371
$405$	0	0
$406$	−11.9866	−0.594885
$407$	6.79702	0.336916
$408$	−2.99336	−0.148194
$409$	−34.7647	−1.71900	−0.859502	−	0.511132i	$-0.829226\pi$
$409$	−34.7647	−1.71900	−0.859502	+	0.511132i	$0.829226\pi$
$410$	0	0
$411$	10.1540	0.500861
$412$	−46.4381	−2.28784
$413$	−2.24165	−0.110304
$414$	−6.68009	−0.328309
$415$	0	0
$416$	−6.05427	−0.296835
$417$	−0.0111878	−0.000547867 0
$418$	−14.7517	−0.721528
$419$	24.5813	1.20087	0.600437	−	0.799672i	$-0.294993\pi$
$419$	24.5813	1.20087	0.600437	+	0.799672i	$0.294993\pi$
$420$	0	0
$421$	−34.2908	−1.67123	−0.835616	−	0.549313i	$-0.814889\pi$
$421$	−34.2908	−1.67123	−0.835616	+	0.549313i	$0.814889\pi$
$422$	−10.4933	−0.510805
$423$	−28.3343	−1.37766
$424$	40.3057	1.95742
$425$	0	0
$426$	−11.6602	−0.564937
$427$	8.83097	0.427361
$428$	−38.0248	−1.83800
$429$	−1.90076	−0.0917696
$430$	0	0
$431$	−3.65912	−0.176254	−0.0881268	−	0.996109i	$-0.528088\pi$
$431$	−3.65912	−0.176254	−0.0881268	+	0.996109i	$0.528088\pi$
$432$	−8.96705	−0.431427
$433$	11.1281	0.534784	0.267392	−	0.963588i	$-0.413838\pi$
$433$	11.1281	0.534784	0.267392	+	0.963588i	$0.413838\pi$
$434$	−17.9386	−0.861082
$435$	0	0
$436$	−73.8037	−3.53456
$437$	−7.24152	−0.346409
$438$	14.0965	0.673555
$439$	3.10986	0.148426	0.0742128	−	0.997242i	$-0.476356\pi$
$439$	3.10986	0.148426	0.0742128	+	0.997242i	$0.476356\pi$
$440$	0	0
$441$	−2.75968	−0.131413
$442$	15.1302	0.719672
$443$	−14.5375	−0.690699	−0.345350	−	0.938474i	$-0.612240\pi$
$443$	−14.5375	−0.690699	−0.345350	+	0.938474i	$0.612240\pi$
$444$	15.2806	0.725187
$445$	0	0
$446$	11.4064	0.540110
$447$	1.01266	0.0478970
$448$	9.53246	0.450366
$449$	4.39307	0.207322	0.103661	−	0.994613i	$-0.466944\pi$
$449$	4.39307	0.207322	0.103661	+	0.994613i	$0.466944\pi$
$450$	0	0
$451$	8.58272	0.404144
$452$	−48.6121	−2.28652
$453$	−2.38401	−0.112011
$454$	19.4555	0.913092
$455$	0	0
$456$	−15.9775	−0.748216
$457$	−3.25412	−0.152221	−0.0761107	−	0.997099i	$-0.524250\pi$
$457$	−3.25412	−0.152221	−0.0761107	+	0.997099i	$0.524250\pi$
$458$	19.0942	0.892214
$459$	−3.83068	−0.178801
$460$	0	0
$461$	4.92591	0.229422	0.114711	−	0.993399i	$-0.463406\pi$
$461$	4.92591	0.229422	0.114711	+	0.993399i	$0.463406\pi$
$462$	0.998642	0.0464610
$463$	−38.1528	−1.77311	−0.886555	−	0.462623i	$-0.846909\pi$
$463$	−38.1528	−1.77311	−0.886555	+	0.462623i	$0.846909\pi$
$464$	−15.7263	−0.730074
$465$	0	0
$466$	39.3366	1.82223
$467$	0.0875451	0.00405111	0.00202555	−	0.999998i	$-0.499355\pi$
$467$	0.0875451	0.00405111	0.00202555	+	0.999998i	$0.499355\pi$
$468$	49.0697	2.26825
$469$	−6.29272	−0.290571
$470$	0	0
$471$	−3.57397	−0.164680
$472$	−10.0890	−0.464386
$473$	9.82627	0.451812
$474$	6.14987	0.282473
$475$	0	0
$476$	−5.23591	−0.239988
$477$	24.7140	1.13158
$478$	−59.2597	−2.71048
$479$	−3.34469	−0.152823	−0.0764114	−	0.997076i	$-0.524346\pi$
$479$	−3.34469	−0.152823	−0.0764114	+	0.997076i	$0.524346\pi$
$480$	0	0
$481$	−37.2112	−1.69668
$482$	5.88220	0.267927
$483$	0.490228	0.0223061
$484$	−39.7194	−1.80543
$485$	0	0
$486$	−28.6859	−1.30122
$487$	13.9729	0.633174	0.316587	−	0.948564i	$-0.397463\pi$
$487$	13.9729	0.633174	0.316587	+	0.948564i	$0.397463\pi$
$488$	39.7457	1.79920
$489$	−4.34250	−0.196375
$490$	0	0
$491$	20.3448	0.918149	0.459075	−	0.888398i	$-0.348181\pi$
$491$	20.3448	0.918149	0.459075	+	0.888398i	$0.348181\pi$
$492$	19.2951	0.869891
$493$	−6.71818	−0.302572
$494$	80.7599	3.63356
$495$	0	0
$496$	−23.5352	−1.05676
$497$	−9.82614	−0.440762
$498$	−2.24377	−0.100546
$499$	−23.2598	−1.04125	−0.520627	−	0.853784i	$-0.674302\pi$
$499$	−23.2598	−1.04125	−0.520627	+	0.853784i	$0.674302\pi$
$500$	0	0
$501$	−11.6672	−0.521250
$502$	−47.3495	−2.11331
$503$	−17.4599	−0.778496	−0.389248	−	0.921133i	$-0.627265\pi$
$503$	−17.4599	−0.778496	−0.389248	+	0.921133i	$0.627265\pi$
$504$	−12.4205	−0.553255
$505$	0	0
$506$	2.03710	0.0905600
$507$	4.03300	0.179112
$508$	−36.3617	−1.61329
$509$	−16.9089	−0.749473	−0.374736	−	0.927131i	$-0.622267\pi$
$509$	−16.9089	−0.749473	−0.374736	+	0.927131i	$0.622267\pi$
$510$	0	0
$511$	11.8792	0.525506
$512$	32.7600	1.44780
$513$	−20.4468	−0.902749
$514$	1.02791	0.0453393
$515$	0	0
$516$	22.0908	0.972493
$517$	8.64055	0.380011
$518$	19.5504	0.858994
$519$	8.70069	0.381918
$520$	0	0
$521$	−27.3078	−1.19637	−0.598187	−	0.801356i	$-0.704112\pi$
$521$	−27.3078	−1.19637	−0.598187	+	0.801356i	$0.704112\pi$
$522$	−33.0792	−1.44784
$523$	−24.1096	−1.05424	−0.527120	−	0.849791i	$-0.676728\pi$
$523$	−24.1096	−1.05424	−0.527120	+	0.849791i	$0.676728\pi$
$524$	59.6607	2.60629
$525$	0	0
$526$	28.6148	1.24766
$527$	−10.0541	−0.437965
$528$	1.31020	0.0570193
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.18623	−0.268460
$532$	−27.9474	−1.21168
$533$	−46.9872	−2.03524
$534$	14.5230	0.628470
$535$	0	0
$536$	−28.3218	−1.22331
$537$	−3.01846	−0.130256
$538$	−35.1683	−1.51621
$539$	0.841565	0.0362488
$540$	0	0
$541$	23.8363	1.02480	0.512402	−	0.858746i	$-0.328756\pi$
$541$	23.8363	1.02480	0.512402	+	0.858746i	$0.328756\pi$
$542$	6.04462	0.259639
$543$	−7.26339	−0.311702
$544$	1.78279	0.0764363
$545$	0	0
$546$	−5.46719	−0.233974
$547$	4.34654	0.185845	0.0929223	−	0.995673i	$-0.470379\pi$
$547$	4.34654	0.185845	0.0929223	+	0.995673i	$0.470379\pi$
$548$	79.9380	3.41478
$549$	24.3706	1.04011
$550$	0	0
$551$	−35.8593	−1.52766
$552$	2.20638	0.0939097
$553$	5.18255	0.220385
$554$	78.8965	3.35199
$555$	0	0
$556$	−0.0880761	−0.00373526
$557$	20.6847	0.876437	0.438218	−	0.898868i	$-0.355610\pi$
$557$	20.6847	0.876437	0.438218	+	0.898868i	$0.355610\pi$
$558$	−49.5048	−2.09571
$559$	−53.7952	−2.27529
$560$	0	0
$561$	0.559712	0.0236311
$562$	−33.4317	−1.41023
$563$	−21.3970	−0.901774	−0.450887	−	0.892581i	$-0.648892\pi$
$563$	−21.3970	−0.901774	−0.450887	+	0.892581i	$0.648892\pi$
$564$	19.4251	0.817946
$565$	0	0
$566$	34.6116	1.45483
$567$	−6.89485	−0.289556
$568$	−44.2247	−1.85563
$569$	−8.14928	−0.341636	−0.170818	−	0.985303i	$-0.554641\pi$
$569$	−8.14928	−0.341636	−0.170818	+	0.985303i	$0.554641\pi$
$570$	0	0
$571$	−4.79434	−0.200637	−0.100318	−	0.994955i	$-0.531986\pi$
$571$	−4.79434	−0.200637	−0.100318	+	0.994955i	$0.531986\pi$
$572$	−14.9638	−0.625669
$573$	−1.84156	−0.0769324
$574$	24.6866	1.03040
$575$	0	0
$576$	26.3065	1.09610
$577$	−12.6407	−0.526238	−0.263119	−	0.964763i	$-0.584751\pi$
$577$	−12.6407	−0.526238	−0.263119	+	0.964763i	$0.584751\pi$
$578$	36.6949	1.52631
$579$	−0.749617	−0.0311530
$580$	0	0
$581$	−1.89084	−0.0784454
$582$	−10.3237	−0.427932
$583$	−7.53655	−0.312132
$584$	53.4651	2.21240
$585$	0	0
$586$	33.9347	1.40183
$587$	−0.0250666	−0.00103461	−0.000517306	−	1.00000i	$-0.500165\pi$
$587$	−0.0250666	−0.00103461	−0.000517306		1.00000i	$0.500165\pi$
$588$	1.89195	0.0780228
$589$	−53.6654	−2.21124
$590$	0	0
$591$	−3.45974	−0.142315
$592$	25.6498	1.05420
$593$	−20.9146	−0.858859	−0.429430	−	0.903100i	$-0.641285\pi$
$593$	−20.9146	−0.858859	−0.429430	+	0.903100i	$0.641285\pi$
$594$	5.75185	0.236001
$595$	0	0
$596$	7.97217	0.326553
$597$	7.89348	0.323059
$598$	−11.1524	−0.456054
$599$	20.4880	0.837116	0.418558	−	0.908190i	$-0.362536\pi$
$599$	20.4880	0.837116	0.418558	+	0.908190i	$0.362536\pi$
$600$	0	0
$601$	9.56660	0.390230	0.195115	−	0.980780i	$-0.437492\pi$
$601$	9.56660	0.390230	0.195115	+	0.980780i	$0.437492\pi$
$602$	28.2634	1.15193
$603$	−17.3659	−0.707193
$604$	−18.7682	−0.763669
$605$	0	0
$606$	11.4562	0.465377
$607$	19.1764	0.778345	0.389173	−	0.921165i	$-0.372761\pi$
$607$	19.1764	0.778345	0.389173	+	0.921165i	$0.372761\pi$
$608$	9.51588	0.385920
$609$	2.42756	0.0983697
$610$	0	0
$611$	−47.3038	−1.91371
$612$	−14.4494	−0.584083
$613$	−29.0395	−1.17290	−0.586448	−	0.809987i	$-0.699474\pi$
$613$	−29.0395	−1.17290	−0.586448	+	0.809987i	$0.699474\pi$
$614$	11.5951	0.467942
$615$	0	0
$616$	3.78765	0.152609
$617$	−5.38704	−0.216874	−0.108437	−	0.994103i	$-0.534585\pi$
$617$	−5.38704	−0.216874	−0.108437	+	0.994103i	$0.534585\pi$
$618$	14.2785	0.574367
$619$	−0.166112	−0.00667662	−0.00333831	−	0.999994i	$-0.501063\pi$
$619$	−0.166112	−0.00667662	−0.00333831	+	0.999994i	$0.501063\pi$
$620$	0	0
$621$	2.82355	0.113305
$622$	62.0327	2.48728
$623$	12.2386	0.490331
$624$	−7.17288	−0.287145
$625$	0	0
$626$	27.9514	1.11716
$627$	2.98755	0.119311
$628$	−28.1362	−1.12276
$629$	10.9575	0.436903
$630$	0	0
$631$	−45.7545	−1.82146	−0.910728	−	0.413007i	$-0.864479\pi$
$631$	−45.7545	−1.82146	−0.910728	+	0.413007i	$0.864479\pi$
$632$	23.3252	0.927828
$633$	2.12513	0.0844662
$634$	3.74467	0.148720
$635$	0	0
$636$	−16.9432	−0.671841
$637$	−4.60725	−0.182546
$638$	10.0875	0.399368
$639$	−27.1170	−1.07273
$640$	0	0
$641$	−19.1601	−0.756779	−0.378390	−	0.925646i	$-0.623522\pi$
$641$	−19.1601	−0.756779	−0.378390	+	0.925646i	$0.623522\pi$
$642$	11.6917	0.461433
$643$	−22.2863	−0.878887	−0.439443	−	0.898270i	$-0.644824\pi$
$643$	−22.2863	−0.878887	−0.439443	+	0.898270i	$0.644824\pi$
$644$	3.85934	0.152079
$645$	0	0
$646$	−23.7812	−0.935658
$647$	7.39416	0.290695	0.145347	−	0.989381i	$-0.453570\pi$
$647$	7.39416	0.290695	0.145347	+	0.989381i	$0.453570\pi$
$648$	−31.0318	−1.21904
$649$	1.88650	0.0740514
$650$	0	0
$651$	3.63298	0.142388
$652$	−34.1865	−1.33885
$653$	20.2423	0.792142	0.396071	−	0.918220i	$-0.370373\pi$
$653$	20.2423	0.792142	0.396071	+	0.918220i	$0.370373\pi$
$654$	22.6928	0.887357
$655$	0	0
$656$	32.3885	1.26456
$657$	32.7828	1.27898
$658$	24.8530	0.968869
$659$	4.09548	0.159537	0.0797687	−	0.996813i	$-0.474582\pi$
$659$	4.09548	0.159537	0.0797687	+	0.996813i	$0.474582\pi$
$660$	0	0
$661$	−30.4201	−1.18321	−0.591603	−	0.806230i	$-0.701505\pi$
$661$	−30.4201	−1.18321	−0.591603	+	0.806230i	$0.701505\pi$
$662$	−42.7087	−1.65992
$663$	−3.06422	−0.119004
$664$	−8.51016	−0.330258
$665$	0	0
$666$	53.9527	2.09063
$667$	4.95190	0.191738
$668$	−91.8501	−3.55379
$669$	−2.31006	−0.0893122
$670$	0	0
$671$	−7.43184	−0.286903
$672$	−0.644195	−0.0248504
$673$	17.3707	0.669591	0.334796	−	0.942291i	$-0.391333\pi$
$673$	17.3707	0.669591	0.334796	+	0.942291i	$0.391333\pi$
$674$	−19.3501	−0.745338
$675$	0	0
$676$	31.7500	1.22115
$677$	−36.5884	−1.40621	−0.703103	−	0.711088i	$-0.748203\pi$
$677$	−36.5884	−1.40621	−0.703103	+	0.711088i	$0.748203\pi$
$678$	14.9470	0.574036
$679$	−8.69991	−0.333872
$680$	0	0
$681$	−3.94018	−0.150988
$682$	15.0965	0.578076
$683$	−29.8118	−1.14072	−0.570358	−	0.821396i	$-0.693196\pi$
$683$	−29.8118	−1.14072	−0.570358	+	0.821396i	$0.693196\pi$
$684$	−77.1259	−2.94898
$685$	0	0
$686$	2.42061	0.0924192
$687$	−3.86701	−0.147536
$688$	37.0813	1.41371
$689$	41.2598	1.57187
$690$	0	0
$691$	−9.58316	−0.364560	−0.182280	−	0.983247i	$-0.558348\pi$
$691$	−9.58316	−0.364560	−0.182280	+	0.983247i	$0.558348\pi$
$692$	68.4965	2.60385
$693$	2.32245	0.0882225
$694$	−59.0976	−2.24331
$695$	0	0
$696$	10.9258	0.414140
$697$	13.8362	0.524083
$698$	−46.0642	−1.74356
$699$	−7.96656	−0.301323
$700$	0	0
$701$	33.7113	1.27326	0.636628	−	0.771171i	$-0.280329\pi$
$701$	33.7113	1.27326	0.636628	+	0.771171i	$0.280329\pi$
$702$	−31.4893	−1.18849
$703$	58.4871	2.20588
$704$	−8.02218	−0.302347
$705$	0	0
$706$	−26.0832	−0.981654
$707$	9.65427	0.363086
$708$	4.24110	0.159390
$709$	25.2647	0.948836	0.474418	−	0.880300i	$-0.342659\pi$
$709$	25.2647	0.948836	0.474418	+	0.880300i	$0.342659\pi$
$710$	0	0
$711$	14.3022	0.536373
$712$	55.0827	2.06431
$713$	7.41080	0.277537
$714$	1.60991	0.0602494
$715$	0	0
$716$	−23.7629	−0.888063
$717$	12.0014	0.448202
$718$	−36.6818	−1.36895
$719$	−3.68698	−0.137501	−0.0687506	−	0.997634i	$-0.521901\pi$
$719$	−3.68698	−0.137501	−0.0687506	+	0.997634i	$0.521901\pi$
$720$	0	0
$721$	12.0327	0.448120
$722$	−80.9440	−3.01243
$723$	−1.19128	−0.0443041
$724$	−57.1813	−2.12513
$725$	0	0
$726$	12.2127	0.453256
$727$	8.41763	0.312193	0.156096	−	0.987742i	$-0.450109\pi$
$727$	8.41763	0.312193	0.156096	+	0.987742i	$0.450109\pi$
$728$	−20.7360	−0.768526
$729$	−14.8750	−0.550926
$730$	0	0
$731$	15.8409	0.585898
$732$	−16.7078	−0.617537
$733$	41.0364	1.51571	0.757856	−	0.652422i	$-0.226247\pi$
$733$	41.0364	1.51571	0.757856	+	0.652422i	$0.226247\pi$
$734$	−52.0205	−1.92011
$735$	0	0
$736$	−1.31407	−0.0484374
$737$	5.29573	0.195071
$738$	68.1271	2.50779
$739$	−0.204454	−0.00752095	−0.00376048	−	0.999993i	$-0.501197\pi$
$739$	−0.204454	−0.00752095	−0.00376048	+	0.999993i	$0.501197\pi$
$740$	0	0
$741$	−16.3557	−0.600842
$742$	−21.6775	−0.795806
$743$	48.6317	1.78412	0.892062	−	0.451913i	$-0.149258\pi$
$743$	48.6317	1.78412	0.892062	+	0.451913i	$0.149258\pi$
$744$	16.3510	0.599458
$745$	0	0
$746$	−18.4501	−0.675506
$747$	−5.21812	−0.190921
$748$	4.40636	0.161112
$749$	9.85268	0.360009
$750$	0	0
$751$	−20.5438	−0.749654	−0.374827	−	0.927095i	$-0.622298\pi$
$751$	−20.5438	−0.749654	−0.374827	+	0.927095i	$0.622298\pi$
$752$	32.6067	1.18905
$753$	9.58934	0.349455
$754$	−55.2254	−2.01119
$755$	0	0
$756$	10.8970	0.396322
$757$	−8.12809	−0.295420	−0.147710	−	0.989031i	$-0.547190\pi$
$757$	−8.12809	−0.295420	−0.147710	+	0.989031i	$0.547190\pi$
$758$	67.5282	2.45274
$759$	−0.412558	−0.0149749
$760$	0	0
$761$	27.8698	1.01028	0.505139	−	0.863038i	$-0.331441\pi$
$761$	27.8698	1.01028	0.505139	+	0.863038i	$0.331441\pi$
$762$	11.1803	0.405020
$763$	19.1234	0.692314
$764$	−14.4978	−0.524511
$765$	0	0
$766$	−18.1822	−0.656948
$767$	−10.3279	−0.372917
$768$	−14.9163	−0.538245
$769$	4.31474	0.155593	0.0777967	−	0.996969i	$-0.475211\pi$
$769$	4.31474	0.155593	0.0777967	+	0.996969i	$0.475211\pi$
$770$	0	0
$771$	−0.208175	−0.00749726
$772$	−5.90139	−0.212396
$773$	−16.8379	−0.605618	−0.302809	−	0.953051i	$-0.597924\pi$
$773$	−16.8379	−0.605618	−0.302809	+	0.953051i	$0.597924\pi$
$774$	77.9980	2.80358
$775$	0	0
$776$	−39.1558	−1.40561
$777$	−3.95939	−0.142042
$778$	90.5749	3.24727
$779$	73.8528	2.64605
$780$	0	0
$781$	8.26933	0.295900
$782$	3.28400	0.117436
$783$	13.9820	0.499674
$784$	3.17580	0.113422
$785$	0	0
$786$	−18.3441	−0.654314
$787$	−27.3563	−0.975147	−0.487574	−	0.873082i	$-0.662118\pi$
$787$	−27.3563	−0.975147	−0.487574	+	0.873082i	$0.662118\pi$
$788$	−27.2370	−0.970276
$789$	−5.79514	−0.206312
$790$	0	0
$791$	12.5960	0.447861
$792$	10.4527	0.371420
$793$	40.6865	1.44482
$794$	72.4702	2.57187
$795$	0	0
$796$	62.1417	2.20255
$797$	26.0292	0.922002	0.461001	−	0.887400i	$-0.347490\pi$
$797$	26.0292	0.922002	0.461001	+	0.887400i	$0.347490\pi$
$798$	8.59313	0.304194
$799$	13.9294	0.492788
$800$	0	0
$801$	33.7747	1.19337
$802$	31.0290	1.09567
$803$	−9.99714	−0.352791
$804$	11.9055	0.419876
$805$	0	0
$806$	−82.6478	−2.91115
$807$	7.12238	0.250720
$808$	43.4512	1.52861
$809$	27.7725	0.976428	0.488214	−	0.872724i	$-0.337649\pi$
$809$	27.7725	0.976428	0.488214	+	0.872724i	$0.337649\pi$
$810$	0	0
$811$	46.6033	1.63646	0.818231	−	0.574889i	$-0.194955\pi$
$811$	46.6033	1.63646	0.818231	+	0.574889i	$0.194955\pi$
$812$	19.1111	0.670667
$813$	−1.22417	−0.0429336
$814$	−16.4529	−0.576674
$815$	0	0
$816$	2.11218	0.0739411
$817$	84.5533	2.95815
$818$	84.1517	2.94230
$819$	−12.7145	−0.444282
$820$	0	0
$821$	22.7527	0.794076	0.397038	−	0.917802i	$-0.370038\pi$
$821$	22.7527	0.794076	0.397038	+	0.917802i	$0.370038\pi$
$822$	−24.5789	−0.857288
$823$	30.6727	1.06918	0.534591	−	0.845111i	$-0.320466\pi$
$823$	30.6727	1.06918	0.534591	+	0.845111i	$0.320466\pi$
$824$	54.1557	1.88660
$825$	0	0
$826$	5.42616	0.188800
$827$	−16.2579	−0.565341	−0.282671	−	0.959217i	$-0.591220\pi$
$827$	−16.2579	−0.565341	−0.282671	+	0.959217i	$0.591220\pi$
$828$	10.6505	0.370131
$829$	−40.5331	−1.40777	−0.703887	−	0.710312i	$-0.748554\pi$
$829$	−40.5331	−1.40777	−0.703887	+	0.710312i	$0.748554\pi$
$830$	0	0
$831$	−15.9783	−0.554282
$832$	43.9185	1.52260
$833$	1.35669	0.0470064
$834$	0.0270812	0.000937744 0
$835$	0	0
$836$	23.5196	0.813442
$837$	20.9248	0.723266
$838$	−59.5016	−2.05545
$839$	10.7129	0.369849	0.184925	−	0.982753i	$-0.440796\pi$
$839$	10.7129	0.369849	0.184925	+	0.982753i	$0.440796\pi$
$840$	0	0
$841$	−4.47866	−0.154437
$842$	83.0046	2.86053
$843$	6.77067	0.233194
$844$	16.7301	0.575875
$845$	0	0
$846$	68.5861	2.35804
$847$	10.2918	0.353629
$848$	−28.4406	−0.976653
$849$	−7.00963	−0.240570
$850$	0	0
$851$	−8.07664	−0.276864
$852$	18.5906	0.636903
$853$	−36.1743	−1.23858	−0.619292	−	0.785161i	$-0.712580\pi$
$853$	−36.1743	−1.23858	−0.619292	+	0.785161i	$0.712580\pi$
$854$	−21.3763	−0.731482
$855$	0	0
$856$	44.3442	1.51565
$857$	19.6448	0.671053	0.335526	−	0.942031i	$-0.391086\pi$
$857$	19.6448	0.671053	0.335526	+	0.942031i	$0.391086\pi$
$858$	4.60100	0.157075
$859$	−39.1879	−1.33707	−0.668537	−	0.743679i	$-0.733079\pi$
$859$	−39.1879	−1.33707	−0.668537	+	0.743679i	$0.733079\pi$
$860$	0	0
$861$	−4.99960	−0.170386
$862$	8.85729	0.301680
$863$	1.99011	0.0677440	0.0338720	−	0.999426i	$-0.489216\pi$
$863$	1.99011	0.0677440	0.0338720	+	0.999426i	$0.489216\pi$
$864$	−3.71035	−0.126229
$865$	0	0
$866$	−26.9368	−0.915351
$867$	−7.43156	−0.252389
$868$	28.6008	0.970773
$869$	−4.36146	−0.147952
$870$	0	0
$871$	−28.9922	−0.982362
$872$	86.0692	2.91467
$873$	−24.0089	−0.812579
$874$	17.5289	0.592923
$875$	0	0
$876$	−22.4749	−0.759358
$877$	37.7430	1.27449	0.637246	−	0.770661i	$-0.280074\pi$
$877$	37.7430	1.27449	0.637246	+	0.770661i	$0.280074\pi$
$878$	−7.52776	−0.254049
$879$	−6.87255	−0.231805
$880$	0	0
$881$	−14.2322	−0.479497	−0.239748	−	0.970835i	$-0.577065\pi$
$881$	−14.2322	−0.479497	−0.239748	+	0.970835i	$0.577065\pi$
$882$	6.68009	0.224930
$883$	28.1181	0.946249	0.473124	−	0.880996i	$-0.343126\pi$
$883$	28.1181	0.946249	0.473124	+	0.880996i	$0.343126\pi$
$884$	−24.1232	−0.811350
$885$	0	0
$886$	35.1897	1.18222
$887$	−12.1996	−0.409621	−0.204811	−	0.978802i	$-0.565658\pi$
$887$	−12.1996	−0.409621	−0.204811	+	0.978802i	$0.565658\pi$
$888$	−17.8201	−0.598004
$889$	9.42176	0.315996
$890$	0	0
$891$	5.80246	0.194390
$892$	−18.1861	−0.608914
$893$	74.3504	2.48804
$894$	−2.45124	−0.0819817
$895$	0	0
$896$	−20.4462	−0.683059
$897$	2.25860	0.0754126
$898$	−10.6339	−0.354858
$899$	36.6975	1.22393
$900$	0	0
$901$	−12.1497	−0.404764
$902$	−20.7754	−0.691745
$903$	−5.72399	−0.190482
$904$	56.6910	1.88551
$905$	0	0
$906$	5.77076	0.191721
$907$	16.4394	0.545862	0.272931	−	0.962034i	$-0.412007\pi$
$907$	16.4394	0.545862	0.272931	+	0.962034i	$0.412007\pi$
$908$	−31.0192	−1.02941
$909$	26.6427	0.883682
$910$	0	0
$911$	2.17147	0.0719440	0.0359720	−	0.999353i	$-0.488547\pi$
$911$	2.17147	0.0719440	0.0359720	+	0.999353i	$0.488547\pi$
$912$	11.2741	0.373322
$913$	1.59127	0.0526633
$914$	7.87695	0.260546
$915$	0	0
$916$	−30.4432	−1.00587
$917$	−15.4588	−0.510494
$918$	9.27256	0.306040
$919$	−30.5983	−1.00934	−0.504672	−	0.863311i	$-0.668387\pi$
$919$	−30.5983	−1.00934	−0.504672	+	0.863311i	$0.668387\pi$
$920$	0	0
$921$	−2.34828	−0.0773784
$922$	−11.9237	−0.392686
$923$	−45.2715	−1.49013
$924$	−1.59220	−0.0523796
$925$	0	0
$926$	92.3529	3.03490
$927$	33.2063	1.09064
$928$	−6.50716	−0.213608
$929$	−18.0032	−0.590667	−0.295334	−	0.955394i	$-0.595431\pi$
$929$	−18.0032	−0.590667	−0.295334	+	0.955394i	$0.595431\pi$
$930$	0	0
$931$	7.24152	0.237331
$932$	−62.7171	−2.05437
$933$	−12.5630	−0.411295
$934$	−0.211912	−0.00693398
$935$	0	0
$936$	−57.2246	−1.87044
$937$	6.60317	0.215716	0.107858	−	0.994166i	$-0.465601\pi$
$937$	6.60317	0.215716	0.107858	+	0.994166i	$0.465601\pi$
$938$	15.2322	0.497349
$939$	−5.66080	−0.184733
$940$	0	0
$941$	14.5797	0.475284	0.237642	−	0.971353i	$-0.423626\pi$
$941$	14.5797	0.475284	0.237642	+	0.971353i	$0.423626\pi$
$942$	8.65118	0.281871
$943$	−10.1985	−0.332110
$944$	7.11904	0.231705
$945$	0	0
$946$	−23.7855	−0.773334
$947$	−9.77865	−0.317763	−0.158882	−	0.987298i	$-0.550789\pi$
$947$	−9.77865	−0.317763	−0.158882	+	0.987298i	$0.550789\pi$
$948$	−9.80515	−0.318457
$949$	54.7306	1.77663
$950$	0	0
$951$	−0.758380	−0.0245921
$952$	6.10607	0.197899
$953$	−11.5144	−0.372989	−0.186495	−	0.982456i	$-0.559713\pi$
$953$	−11.5144	−0.372989	−0.186495	+	0.982456i	$0.559713\pi$
$954$	−59.8229	−1.93684
$955$	0	0
$956$	94.4818	3.05576
$957$	−2.04295	−0.0660392
$958$	8.09618	0.261576
$959$	−20.7129	−0.668854
$960$	0	0
$961$	23.9199	0.771610
$962$	90.0736	2.90409
$963$	27.1902	0.876192
$964$	−9.37838	−0.302057
$965$	0	0
$966$	−1.18665	−0.0381798
$967$	55.3038	1.77845	0.889225	−	0.457470i	$-0.151244\pi$
$967$	55.3038	1.77845	0.889225	+	0.457470i	$0.151244\pi$
$968$	46.3204	1.48879
$969$	4.81623	0.154719
$970$	0	0
$971$	−52.5632	−1.68683	−0.843416	−	0.537261i	$-0.819459\pi$
$971$	−52.5632	−1.68683	−0.843416	+	0.537261i	$0.819459\pi$
$972$	45.7358	1.46698
$973$	0.0228216	0.000731626 0
$974$	−33.8229	−1.08376
$975$	0	0
$976$	−28.0454	−0.897712
$977$	−44.1258	−1.41171	−0.705854	−	0.708357i	$-0.749437\pi$
$977$	−44.1258	−1.41171	−0.705854	+	0.708357i	$0.749437\pi$
$978$	10.5115	0.336120
$979$	−10.2996	−0.329177
$980$	0	0
$981$	52.7744	1.68496
$982$	−49.2468	−1.57153
$983$	9.12363	0.290999	0.145499	−	0.989358i	$-0.453521\pi$
$983$	9.12363	0.290999	0.145499	+	0.989358i	$0.453521\pi$
$984$	−22.5018	−0.717331
$985$	0	0
$986$	16.2621	0.517890
$987$	−5.03329	−0.160211
$988$	−128.761	−4.09643
$989$	−11.6762	−0.371281
$990$	0	0
$991$	16.0132	0.508676	0.254338	−	0.967115i	$-0.418142\pi$
$991$	16.0132	0.508676	0.254338	+	0.967115i	$0.418142\pi$
$992$	−9.73833	−0.309192
$993$	8.64948	0.274483
$994$	23.7852	0.754421
$995$	0	0
$996$	3.57739	0.113354
$997$	50.9272	1.61288	0.806440	−	0.591316i	$-0.201391\pi$
$997$	50.9272	1.61288	0.806440	+	0.591316i	$0.201391\pi$
$998$	56.3029	1.78224
$999$	−22.8048	−0.721513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.t.1.1		8
5.4	even	2		805.2.a.m.1.8	✓	8
15.14	odd	2		7245.2.a.bp.1.1		8
35.34	odd	2		5635.2.a.bb.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.m.1.8	✓	8	5.4	even	2
4025.2.a.t.1.1		8	1.1	even	1	trivial
5635.2.a.bb.1.8		8	35.34	odd	2
7245.2.a.bp.1.1		8	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)

\(f(q)\)	\(=\)	\(q-2.42061 q^{2} +0.490228 q^{3} +3.85934 q^{4} -1.18665 q^{6} -1.00000 q^{7} -4.50072 q^{8} -2.75968 q^{9} +O(q^{10})\)	\(q-2.42061 q^{2} +0.490228 q^{3} +3.85934 q^{4} -1.18665 q^{6} -1.00000 q^{7} -4.50072 q^{8} -2.75968 q^{9} +0.841565 q^{11} +1.89195 q^{12} -4.60725 q^{13} +2.42061 q^{14} +3.17580 q^{16} +1.35669 q^{17} +6.68009 q^{18} +7.24152 q^{19} -0.490228 q^{21} -2.03710 q^{22} -1.00000 q^{23} -2.20638 q^{24} +11.1524 q^{26} -2.82355 q^{27} -3.85934 q^{28} -4.95190 q^{29} -7.41080 q^{31} +1.31407 q^{32} +0.412558 q^{33} -3.28400 q^{34} -10.6505 q^{36} +8.07664 q^{37} -17.5289 q^{38} -2.25860 q^{39} +10.1985 q^{41} +1.18665 q^{42} +11.6762 q^{43} +3.24788 q^{44} +2.42061 q^{46} +10.2672 q^{47} +1.55687 q^{48} +1.00000 q^{49} +0.665085 q^{51} -17.7809 q^{52} -8.95540 q^{53} +6.83471 q^{54} +4.50072 q^{56} +3.54999 q^{57} +11.9866 q^{58} +2.24165 q^{59} -8.83097 q^{61} +17.9386 q^{62} +2.75968 q^{63} -9.53246 q^{64} -0.998642 q^{66} +6.29272 q^{67} +5.23591 q^{68} -0.490228 q^{69} +9.82614 q^{71} +12.4205 q^{72} -11.8792 q^{73} -19.5504 q^{74} +27.9474 q^{76} -0.841565 q^{77} +5.46719 q^{78} -5.18255 q^{79} +6.89485 q^{81} -24.6866 q^{82} +1.89084 q^{83} -1.89195 q^{84} -28.2634 q^{86} -2.42756 q^{87} -3.78765 q^{88} -12.2386 q^{89} +4.60725 q^{91} -3.85934 q^{92} -3.63298 q^{93} -24.8530 q^{94} +0.644195 q^{96} +8.69991 q^{97} -2.42061 q^{98} -2.32245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9	\( 8 q - q^{2} - 7 q^{3} + 7 q^{4} + q^{6} - 8 q^{7} - 3 q^{8} + 9 q^{9} + 6 q^{11} - 8 q^{12} - 8 q^{13} + q^{14} + q^{16} - 4 q^{17} + 11 q^{18} + 7 q^{21} + 8 q^{22} - 8 q^{23} - 8 q^{24} + 2 q^{26} - 28 q^{27} - 7 q^{28} - 3 q^{29} - 16 q^{31} - 12 q^{32} - 5 q^{33} - 4 q^{34} - 14 q^{36} + 7 q^{37} - 11 q^{38} + 16 q^{39} + 7 q^{41} - q^{42} + 10 q^{43} + 7 q^{44} + q^{46} - 19 q^{47} + 6 q^{48} + 8 q^{49} + 7 q^{51} - 18 q^{52} + q^{53} - 25 q^{54} + 3 q^{56} + 25 q^{57} + 9 q^{58} + 21 q^{59} - 7 q^{61} - 18 q^{62} - 9 q^{63} - 37 q^{64} - 43 q^{66} - 11 q^{67} + 17 q^{68} + 7 q^{69} + 8 q^{71} - 4 q^{72} + 3 q^{73} + 12 q^{74} + 8 q^{76} - 6 q^{77} + 50 q^{78} - 15 q^{79} + 28 q^{81} - 41 q^{82} - 25 q^{83} + 8 q^{84} - 12 q^{86} - 21 q^{87} + 29 q^{88} + q^{89} + 8 q^{91} - 7 q^{92} + 5 q^{93} - 36 q^{94} + 30 q^{96} - 10 q^{97} - q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q - q^2 - 7 * q^3 + 7 * q^4 + q^6 - 8 * q^7 - 3 * q^8 + 9 * q^9 + 6 * q^11 - 8 * q^12 - 8 * q^13 + q^14 + q^16 - 4 * q^17 + 11 * q^18 + 7 * q^21 + 8 * q^22 - 8 * q^23 - 8 * q^24 + 2 * q^26 - 28 * q^27 - 7 * q^28 - 3 * q^29 - 16 * q^31 - 12 * q^32 - 5 * q^33 - 4 * q^34 - 14 * q^36 + 7 * q^37 - 11 * q^38 + 16 * q^39 + 7 * q^41 - q^42 + 10 * q^43 + 7 * q^44 + q^46 - 19 * q^47 + 6 * q^48 + 8 * q^49 + 7 * q^51 - 18 * q^52 + q^53 - 25 * q^54 + 3 * q^56 + 25 * q^57 + 9 * q^58 + 21 * q^59 - 7 * q^61 - 18 * q^62 - 9 * q^63 - 37 * q^64 - 43 * q^66 - 11 * q^67 + 17 * q^68 + 7 * q^69 + 8 * q^71 - 4 * q^72 + 3 * q^73 + 12 * q^74 + 8 * q^76 - 6 * q^77 + 50 * q^78 - 15 * q^79 + 28 * q^81 - 41 * q^82 - 25 * q^83 + 8 * q^84 - 12 * q^86 - 21 * q^87 + 29 * q^88 + q^89 + 8 * q^91 - 7 * q^92 + 5 * q^93 - 36 * q^94 + 30 * q^96 - 10 * q^97 - q^98 - 18 * q^99

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