LMFDB - Embedded newform 1150.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.11903$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.11903 q^{3} +1.00000 q^{4} -3.11903 q^{6} -4.50973 q^{7} -1.00000 q^{8} +6.72833 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.11903 q^{3} +1.00000 q^{4} -3.11903 q^{6} -4.50973 q^{7} -1.00000 q^{8} +6.72833 q^{9} +4.33763 q^{11} +3.11903 q^{12} +3.72833 q^{13} +4.50973 q^{14} +1.00000 q^{16} -1.11903 q^{17} -6.72833 q^{18} +4.50973 q^{19} -14.0660 q^{21} -4.33763 q^{22} +1.00000 q^{23} -3.11903 q^{24} -3.72833 q^{26} +11.6288 q^{27} -4.50973 q^{28} -8.23805 q^{29} +1.72833 q^{31} -1.00000 q^{32} +13.5292 q^{33} +1.11903 q^{34} +6.72833 q^{36} +0.781399 q^{37} -4.50973 q^{38} +11.6288 q^{39} +3.90043 q^{41} +14.0660 q^{42} -8.00000 q^{43} +4.33763 q^{44} -1.00000 q^{46} +11.4567 q^{47} +3.11903 q^{48} +13.3376 q^{49} -3.49027 q^{51} +3.72833 q^{52} +6.00000 q^{53} -11.6288 q^{54} +4.50973 q^{56} +14.0660 q^{57} +8.23805 q^{58} -2.23805 q^{59} +3.55623 q^{61} -1.72833 q^{62} -30.3429 q^{63} +1.00000 q^{64} -13.5292 q^{66} -2.43720 q^{67} -1.11903 q^{68} +3.11903 q^{69} +7.11903 q^{71} -6.72833 q^{72} +9.45665 q^{73} -0.781399 q^{74} +4.50973 q^{76} -19.5615 q^{77} -11.6288 q^{78} -14.9133 q^{79} +16.0854 q^{81} -3.90043 q^{82} -2.78140 q^{83} -14.0660 q^{84} +8.00000 q^{86} -25.6947 q^{87} -4.33763 q^{88} -7.69471 q^{89} -16.8137 q^{91} +1.00000 q^{92} +5.39070 q^{93} -11.4567 q^{94} -3.11903 q^{96} +0.642920 q^{97} -13.3376 q^{98} +29.1850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9} + 3 q^{11} - q^{12} + q^{13} + 3 q^{14} + 3 q^{16} + 7 q^{17} - 10 q^{18} + 3 q^{19} - 22 q^{21} - 3 q^{22} + 3 q^{23} + q^{24} - q^{26} + 14 q^{27} - 3 q^{28} - 4 q^{29} - 5 q^{31} - 3 q^{32} + 9 q^{33} - 7 q^{34} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + q^{41} + 22 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{46} + 14 q^{47} - q^{48} + 30 q^{49} - 21 q^{51} + q^{52} + 18 q^{53} - 14 q^{54} + 3 q^{56} + 22 q^{57} + 4 q^{58} + 14 q^{59} + q^{61} + 5 q^{62} - 8 q^{63} + 3 q^{64} - 9 q^{66} - 8 q^{67} + 7 q^{68} - q^{69} + 11 q^{71} - 10 q^{72} + 8 q^{73} - 2 q^{74} + 3 q^{76} + 24 q^{77} - 14 q^{78} - 4 q^{79} + 7 q^{81} - q^{82} - 8 q^{83} - 22 q^{84} + 24 q^{86} - 36 q^{87} - 3 q^{88} + 18 q^{89} + q^{91} + 3 q^{92} + 16 q^{93} - 14 q^{94} + q^{96} + 33 q^{97} - 30 q^{98} + 57 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9 + 3 * q^11 - q^12 + q^13 + 3 * q^14 + 3 * q^16 + 7 * q^17 - 10 * q^18 + 3 * q^19 - 22 * q^21 - 3 * q^22 + 3 * q^23 + q^24 - q^26 + 14 * q^27 - 3 * q^28 - 4 * q^29 - 5 * q^31 - 3 * q^32 + 9 * q^33 - 7 * q^34 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + q^41 + 22 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^46 + 14 * q^47 - q^48 + 30 * q^49 - 21 * q^51 + q^52 + 18 * q^53 - 14 * q^54 + 3 * q^56 + 22 * q^57 + 4 * q^58 + 14 * q^59 + q^61 + 5 * q^62 - 8 * q^63 + 3 * q^64 - 9 * q^66 - 8 * q^67 + 7 * q^68 - q^69 + 11 * q^71 - 10 * q^72 + 8 * q^73 - 2 * q^74 + 3 * q^76 + 24 * q^77 - 14 * q^78 - 4 * q^79 + 7 * q^81 - q^82 - 8 * q^83 - 22 * q^84 + 24 * q^86 - 36 * q^87 - 3 * q^88 + 18 * q^89 + q^91 + 3 * q^92 + 16 * q^93 - 14 * q^94 + q^96 + 33 * q^97 - 30 * q^98 + 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.11903	1.80077	0.900385	−	0.435093i	$-0.143285\pi$
$3$	3.11903	1.80077	0.900385	+	0.435093i	$0.143285\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−3.11903	−1.27334
$7$	−4.50973	−1.70452	−0.852258	−	0.523122i	$-0.824767\pi$
$7$	−4.50973	−1.70452	−0.852258	+	0.523122i	$0.824767\pi$
$8$	−1.00000	−0.353553
$9$	6.72833	2.24278
$10$	0	0
$11$	4.33763	1.30784	0.653922	−	0.756562i	$-0.273122\pi$
$11$	4.33763	1.30784	0.653922	+	0.756562i	$0.273122\pi$
$12$	3.11903	0.900385
$13$	3.72833	1.03405	0.517026	−	0.855970i	$-0.327039\pi$
$13$	3.72833	1.03405	0.517026	+	0.855970i	$0.327039\pi$
$14$	4.50973	1.20527
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.11903	−0.271404	−0.135702	−	0.990750i	$-0.543329\pi$
$17$	−1.11903	−0.271404	−0.135702	+	0.990750i	$0.543329\pi$
$18$	−6.72833	−1.58588
$19$	4.50973	1.03460	0.517301	−	0.855803i	$-0.326937\pi$
$19$	4.50973	1.03460	0.517301	+	0.855803i	$0.326937\pi$
$20$	0	0
$21$	−14.0660	−3.06944
$22$	−4.33763	−0.924785
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.11903	−0.636669
$25$	0	0
$26$	−3.72833	−0.731185
$27$	11.6288	2.23795
$28$	−4.50973	−0.852258
$29$	−8.23805	−1.52977	−0.764884	−	0.644168i	$-0.777204\pi$
$29$	−8.23805	−1.52977	−0.764884	+	0.644168i	$0.777204\pi$
$30$	0	0
$31$	1.72833	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$31$	1.72833	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$32$	−1.00000	−0.176777
$33$	13.5292	2.35513
$34$	1.11903	0.191911
$35$	0	0
$36$	6.72833	1.12139
$37$	0.781399	0.128461	0.0642306	−	0.997935i	$-0.479541\pi$
$37$	0.781399	0.128461	0.0642306	+	0.997935i	$0.479541\pi$
$38$	−4.50973	−0.731574
$39$	11.6288	1.86209
$40$	0	0
$41$	3.90043	0.609144	0.304572	−	0.952489i	$-0.401487\pi$
$41$	3.90043	0.609144	0.304572	+	0.952489i	$0.401487\pi$
$42$	14.0660	2.17042
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	4.33763	0.653922
$45$	0	0
$46$	−1.00000	−0.147442
$47$	11.4567	1.67112	0.835562	−	0.549396i	$-0.185142\pi$
$47$	11.4567	1.67112	0.835562	+	0.549396i	$0.185142\pi$
$48$	3.11903	0.450193
$49$	13.3376	1.90538
$50$	0	0
$51$	−3.49027	−0.488736
$52$	3.72833	0.517026
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−11.6288	−1.58247
$55$	0	0
$56$	4.50973	0.602637
$57$	14.0660	1.86308
$58$	8.23805	1.08171
$59$	−2.23805	−0.291370	−0.145685	−	0.989331i	$-0.546539\pi$
$59$	−2.23805	−0.291370	−0.145685	+	0.989331i	$0.546539\pi$
$60$	0	0
$61$	3.55623	0.455329	0.227664	−	0.973740i	$-0.426891\pi$
$61$	3.55623	0.455329	0.227664	+	0.973740i	$0.426891\pi$
$62$	−1.72833	−0.219498
$63$	−30.3429	−3.82285
$64$	1.00000	0.125000
$65$	0	0
$66$	−13.5292	−1.66533
$67$	−2.43720	−0.297752	−0.148876	−	0.988856i	$-0.547565\pi$
$67$	−2.43720	−0.297752	−0.148876	+	0.988856i	$0.547565\pi$
$68$	−1.11903	−0.135702
$69$	3.11903	0.375487
$70$	0	0
$71$	7.11903	0.844873	0.422437	−	0.906393i	$-0.361175\pi$
$71$	7.11903	0.844873	0.422437	+	0.906393i	$0.361175\pi$
$72$	−6.72833	−0.792941
$73$	9.45665	1.10682	0.553409	−	0.832910i	$-0.313327\pi$
$73$	9.45665	1.10682	0.553409	+	0.832910i	$0.313327\pi$
$74$	−0.781399	−0.0908357
$75$	0	0
$76$	4.50973	0.517301
$77$	−19.5615	−2.22924
$78$	−11.6288	−1.31670
$79$	−14.9133	−1.67788	−0.838939	−	0.544225i	$-0.816824\pi$
$79$	−14.9133	−1.67788	−0.838939	+	0.544225i	$0.816824\pi$
$80$	0	0
$81$	16.0854	1.78727
$82$	−3.90043	−0.430730
$83$	−2.78140	−0.305298	−0.152649	−	0.988280i	$-0.548780\pi$
$83$	−2.78140	−0.305298	−0.152649	+	0.988280i	$0.548780\pi$
$84$	−14.0660	−1.53472
$85$	0	0
$86$	8.00000	0.862662
$87$	−25.6947	−2.75476
$88$	−4.33763	−0.462393
$89$	−7.69471	−0.815637	−0.407819	−	0.913063i	$-0.633710\pi$
$89$	−7.69471	−0.815637	−0.407819	+	0.913063i	$0.633710\pi$
$90$	0	0
$91$	−16.8137	−1.76256
$92$	1.00000	0.104257
$93$	5.39070	0.558989
$94$	−11.4567	−1.18166
$95$	0	0
$96$	−3.11903	−0.318334
$97$	0.642920	0.0652786	0.0326393	−	0.999467i	$-0.489609\pi$
$97$	0.642920	0.0652786	0.0326393	+	0.999467i	$0.489609\pi$
$98$	−13.3376	−1.34730
$99$	29.1850	2.93320
$100$	0	0
$101$	−8.23805	−0.819717	−0.409858	−	0.912149i	$-0.634422\pi$
$101$	−8.23805	−0.819717	−0.409858	+	0.912149i	$0.634422\pi$
$102$	3.49027	0.345589
$103$	−12.3376	−1.21566	−0.607831	−	0.794066i	$-0.707960\pi$
$103$	−12.3376	−1.21566	−0.607831	+	0.794066i	$0.707960\pi$
$104$	−3.72833	−0.365593
$105$	0	0
$106$	−6.00000	−0.582772
$107$	15.9328	1.54028	0.770139	−	0.637876i	$-0.220187\pi$
$107$	15.9328	1.54028	0.770139	+	0.637876i	$0.220187\pi$
$108$	11.6288	1.11898
$109$	−1.49027	−0.142742	−0.0713712	−	0.997450i	$-0.522737\pi$
$109$	−1.49027	−0.142742	−0.0713712	+	0.997450i	$0.522737\pi$
$110$	0	0
$111$	2.43720	0.231329
$112$	−4.50973	−0.426129
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−14.0660	−1.31740
$115$	0	0
$116$	−8.23805	−0.764884
$117$	25.0854	2.31915
$118$	2.23805	0.206030
$119$	5.04650	0.462612
$120$	0	0
$121$	7.81502	0.710456
$122$	−3.55623	−0.321966
$123$	12.1655	1.09693
$124$	1.72833	0.155208
$125$	0	0
$126$	30.3429	2.70316
$127$	0.675256	0.0599193	0.0299597	−	0.999551i	$-0.490462\pi$
$127$	0.675256	0.0599193	0.0299597	+	0.999551i	$0.490462\pi$
$128$	−1.00000	−0.0883883
$129$	−24.9522	−2.19692
$130$	0	0
$131$	−13.6947	−1.19651	−0.598256	−	0.801305i	$-0.704139\pi$
$131$	−13.6947	−1.19651	−0.598256	+	0.801305i	$0.704139\pi$
$132$	13.5292	1.17756
$133$	−20.3376	−1.76350
$134$	2.43720	0.210542
$135$	0	0
$136$	1.11903	0.0959557
$137$	−7.52918	−0.643261	−0.321631	−	0.946865i	$-0.604231\pi$
$137$	−7.52918	−0.643261	−0.321631	+	0.946865i	$0.604231\pi$
$138$	−3.11903	−0.265509
$139$	4.67526	0.396550	0.198275	−	0.980146i	$-0.436466\pi$
$139$	4.67526	0.396550	0.198275	+	0.980146i	$0.436466\pi$
$140$	0	0
$141$	35.7336	3.00931
$142$	−7.11903	−0.597415
$143$	16.1721	1.35238
$144$	6.72833	0.560694
$145$	0	0
$146$	−9.45665	−0.782638
$147$	41.6004	3.43114
$148$	0.781399	0.0642306
$149$	7.52918	0.616814	0.308407	−	0.951254i	$-0.400204\pi$
$149$	7.52918	0.616814	0.308407	+	0.951254i	$0.400204\pi$
$150$	0	0
$151$	−13.3571	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$151$	−13.3571	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$152$	−4.50973	−0.365787
$153$	−7.52918	−0.608698
$154$	19.5615	1.57631
$155$	0	0
$156$	11.6288	0.931045
$157$	−16.2381	−1.29594	−0.647969	−	0.761667i	$-0.724381\pi$
$157$	−16.2381	−1.29594	−0.647969	+	0.761667i	$0.724381\pi$
$158$	14.9133	1.18644
$159$	18.7142	1.48413
$160$	0	0
$161$	−4.50973	−0.355416
$162$	−16.0854	−1.26379
$163$	3.29112	0.257781	0.128890	−	0.991659i	$-0.458858\pi$
$163$	3.29112	0.257781	0.128890	+	0.991659i	$0.458858\pi$
$164$	3.90043	0.304572
$165$	0	0
$166$	2.78140	0.215878
$167$	−22.9133	−1.77309	−0.886543	−	0.462647i	$-0.846900\pi$
$167$	−22.9133	−1.77309	−0.886543	+	0.462647i	$0.846900\pi$
$168$	14.0660	1.08521
$169$	0.900425	0.0692635
$170$	0	0
$171$	30.3429	2.32038
$172$	−8.00000	−0.609994
$173$	−0.575681	−0.0437683	−0.0218841	−	0.999761i	$-0.506966\pi$
$173$	−0.575681	−0.0437683	−0.0218841	+	0.999761i	$0.506966\pi$
$174$	25.6947	1.94791
$175$	0	0
$176$	4.33763	0.326961
$177$	−6.98055	−0.524690
$178$	7.69471	0.576743
$179$	5.01945	0.375171	0.187586	−	0.982248i	$-0.439934\pi$
$179$	5.01945	0.375171	0.187586	+	0.982248i	$0.439934\pi$
$180$	0	0
$181$	−11.5292	−0.856957	−0.428479	−	0.903552i	$-0.640950\pi$
$181$	−11.5292	−0.856957	−0.428479	+	0.903552i	$0.640950\pi$
$182$	16.8137	1.24632
$183$	11.0920	0.819942
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−5.39070	−0.395265
$187$	−4.85392	−0.354954
$188$	11.4567	0.835562
$189$	−52.4425	−3.81463
$190$	0	0
$191$	−18.7142	−1.35411	−0.677055	−	0.735933i	$-0.736744\pi$
$191$	−18.7142	−1.35411	−0.677055	+	0.735933i	$0.736744\pi$
$192$	3.11903	0.225096
$193$	−23.4956	−1.69125	−0.845624	−	0.533780i	$-0.820771\pi$
$193$	−23.4956	−1.69125	−0.845624	+	0.533780i	$0.820771\pi$
$194$	−0.642920	−0.0461590
$195$	0	0
$196$	13.3376	0.952688
$197$	18.1385	1.29231	0.646157	−	0.763205i	$-0.276375\pi$
$197$	18.1385	1.29231	0.646157	+	0.763205i	$0.276375\pi$
$198$	−29.1850	−2.07409
$199$	−23.2575	−1.64868	−0.824340	−	0.566094i	$-0.808454\pi$
$199$	−23.2575	−1.64868	−0.824340	+	0.566094i	$0.808454\pi$
$200$	0	0
$201$	−7.60170	−0.536183
$202$	8.23805	0.579627
$203$	37.1514	2.60751
$204$	−3.49027	−0.244368
$205$	0	0
$206$	12.3376	0.859603
$207$	6.72833	0.467651
$208$	3.72833	0.258513
$209$	19.5615	1.35310
$210$	0	0
$211$	4.34420	0.299067	0.149533	−	0.988757i	$-0.452223\pi$
$211$	4.34420	0.299067	0.149533	+	0.988757i	$0.452223\pi$
$212$	6.00000	0.412082
$213$	22.2044	1.52142
$214$	−15.9328	−1.08914
$215$	0	0
$216$	−11.6288	−0.791236
$217$	−7.79428	−0.529110
$218$	1.49027	0.100934
$219$	29.4956	1.99313
$220$	0	0
$221$	−4.17210	−0.280646
$222$	−2.43720	−0.163574
$223$	−12.4761	−0.835462	−0.417731	−	0.908571i	$-0.637175\pi$
$223$	−12.4761	−0.835462	−0.417731	+	0.908571i	$0.637175\pi$
$224$	4.50973	0.301319
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−15.9328	−1.05749	−0.528747	−	0.848779i	$-0.677338\pi$
$227$	−15.9328	−1.05749	−0.528747	+	0.848779i	$0.677338\pi$
$228$	14.0660	0.931541
$229$	−3.56280	−0.235436	−0.117718	−	0.993047i	$-0.537558\pi$
$229$	−3.56280	−0.235436	−0.117718	+	0.993047i	$0.537558\pi$
$230$	0	0
$231$	−61.0129	−4.01435
$232$	8.23805	0.540855
$233$	27.4956	1.80129	0.900647	−	0.434552i	$-0.143093\pi$
$233$	27.4956	1.80129	0.900647	+	0.434552i	$0.143093\pi$
$234$	−25.0854	−1.63988
$235$	0	0
$236$	−2.23805	−0.145685
$237$	−46.5150	−3.02147
$238$	−5.04650	−0.327116
$239$	10.0389	0.649363	0.324681	−	0.945823i	$-0.394743\pi$
$239$	10.0389	0.649363	0.324681	+	0.945823i	$0.394743\pi$
$240$	0	0
$241$	−23.6947	−1.52631	−0.763155	−	0.646215i	$-0.776351\pi$
$241$	−23.6947	−1.52631	−0.763155	+	0.646215i	$0.776351\pi$
$242$	−7.81502	−0.502368
$243$	15.2846	0.980505
$244$	3.55623	0.227664
$245$	0	0
$246$	−12.1655	−0.775646
$247$	16.8137	1.06983
$248$	−1.72833	−0.109749
$249$	−8.67526	−0.549772
$250$	0	0
$251$	12.4425	0.785363	0.392681	−	0.919675i	$-0.371548\pi$
$251$	12.4425	0.785363	0.392681	+	0.919675i	$0.371548\pi$
$252$	−30.3429	−1.91142
$253$	4.33763	0.272704
$254$	−0.675256	−0.0423693
$255$	0	0
$256$	1.00000	0.0625000
$257$	−5.45665	−0.340377	−0.170188	−	0.985412i	$-0.554438\pi$
$257$	−5.45665	−0.340377	−0.170188	+	0.985412i	$0.554438\pi$
$258$	24.9522	1.55346
$259$	−3.52389	−0.218964
$260$	0	0
$261$	−55.4283	−3.43093
$262$	13.6947	0.846062
$263$	−0.138479	−0.00853895	−0.00426948	−	0.999991i	$-0.501359\pi$
$263$	−0.138479	−0.00853895	−0.00426948	+	0.999991i	$0.501359\pi$
$264$	−13.5292	−0.832663
$265$	0	0
$266$	20.3376	1.24698
$267$	−24.0000	−1.46878
$268$	−2.43720	−0.148876
$269$	14.6753	0.894766	0.447383	−	0.894342i	$-0.352356\pi$
$269$	14.6753	0.894766	0.447383	+	0.894342i	$0.352356\pi$
$270$	0	0
$271$	−8.31058	−0.504832	−0.252416	−	0.967619i	$-0.581225\pi$
$271$	−8.31058	−0.504832	−0.252416	+	0.967619i	$0.581225\pi$
$272$	−1.11903	−0.0678510
$273$	−52.4425	−3.17396
$274$	7.52918	0.454854
$275$	0	0
$276$	3.11903	0.187743
$277$	−12.9133	−0.775886	−0.387943	−	0.921683i	$-0.626814\pi$
$277$	−12.9133	−0.775886	−0.387943	+	0.921683i	$0.626814\pi$
$278$	−4.67526	−0.280403
$279$	11.6288	0.696195
$280$	0	0
$281$	2.67526	0.159592	0.0797962	−	0.996811i	$-0.474573\pi$
$281$	2.67526	0.159592	0.0797962	+	0.996811i	$0.474573\pi$
$282$	−35.7336	−2.12791
$283$	−0.742495	−0.0441367	−0.0220684	−	0.999756i	$-0.507025\pi$
$283$	−0.742495	−0.0441367	−0.0220684	+	0.999756i	$0.507025\pi$
$284$	7.11903	0.422437
$285$	0	0
$286$	−16.1721	−0.956276
$287$	−17.5898	−1.03830
$288$	−6.72833	−0.396470
$289$	−15.7478	−0.926340
$290$	0	0
$291$	2.00528	0.117552
$292$	9.45665	0.553409
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−41.6004	−2.42619
$295$	0	0
$296$	−0.781399	−0.0454179
$297$	50.4412	2.92690
$298$	−7.52918	−0.436154
$299$	3.72833	0.215615
$300$	0	0
$301$	36.0778	2.07949
$302$	13.3571	0.768614
$303$	−25.6947	−1.47612
$304$	4.50973	0.258651
$305$	0	0
$306$	7.52918	0.430414
$307$	−30.5084	−1.74121	−0.870604	−	0.491984i	$-0.836272\pi$
$307$	−30.5084	−1.74121	−0.870604	+	0.491984i	$0.836272\pi$
$308$	−19.5615	−1.11462
$309$	−38.4814	−2.18913
$310$	0	0
$311$	5.56280	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$311$	5.56280	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$312$	−11.6288	−0.658348
$313$	−4.07252	−0.230193	−0.115096	−	0.993354i	$-0.536718\pi$
$313$	−4.07252	−0.230193	−0.115096	+	0.993354i	$0.536718\pi$
$314$	16.2381	0.916366
$315$	0	0
$316$	−14.9133	−0.838939
$317$	6.16553	0.346291	0.173145	−	0.984896i	$-0.444607\pi$
$317$	6.16553	0.346291	0.173145	+	0.984896i	$0.444607\pi$
$318$	−18.7142	−1.04944
$319$	−35.7336	−2.00070
$320$	0	0
$321$	49.6947	2.77369
$322$	4.50973	0.251317
$323$	−5.04650	−0.280795
$324$	16.0854	0.893634
$325$	0	0
$326$	−3.29112	−0.182279
$327$	−4.64820	−0.257046
$328$	−3.90043	−0.215365
$329$	−51.6664	−2.84846
$330$	0	0
$331$	27.5886	1.51640	0.758202	−	0.652019i	$-0.226078\pi$
$331$	27.5886	1.51640	0.758202	+	0.652019i	$0.226078\pi$
$332$	−2.78140	−0.152649
$333$	5.25751	0.288110
$334$	22.9133	1.25376
$335$	0	0
$336$	−14.0660	−0.767361
$337$	17.4230	0.949093	0.474547	−	0.880230i	$-0.342612\pi$
$337$	17.4230	0.949093	0.474547	+	0.880230i	$0.342612\pi$
$338$	−0.900425	−0.0489767
$339$	18.7142	1.01641
$340$	0	0
$341$	7.49684	0.405977
$342$	−30.3429	−1.64076
$343$	−28.5810	−1.54323
$344$	8.00000	0.431331
$345$	0	0
$346$	0.575681	0.0309488
$347$	−4.88097	−0.262024	−0.131012	−	0.991381i	$-0.541823\pi$
$347$	−4.88097	−0.262024	−0.131012	+	0.991381i	$0.541823\pi$
$348$	−25.6947	−1.37738
$349$	24.0389	1.28677	0.643387	−	0.765542i	$-0.277529\pi$
$349$	24.0389	1.28677	0.643387	+	0.765542i	$0.277529\pi$
$350$	0	0
$351$	43.3558	2.31416
$352$	−4.33763	−0.231196
$353$	14.3442	0.763464	0.381732	−	0.924273i	$-0.375328\pi$
$353$	14.3442	0.763464	0.381732	+	0.924273i	$0.375328\pi$
$354$	6.98055	0.371012
$355$	0	0
$356$	−7.69471	−0.407819
$357$	15.7402	0.833059
$358$	−5.01945	−0.265286
$359$	26.7814	1.41347	0.706734	−	0.707479i	$-0.250168\pi$
$359$	26.7814	1.41347	0.706734	+	0.707479i	$0.250168\pi$
$360$	0	0
$361$	1.33763	0.0704015
$362$	11.5292	0.605960
$363$	24.3752	1.27937
$364$	−16.8137	−0.881279
$365$	0	0
$366$	−11.0920	−0.579787
$367$	20.4761	1.06884	0.534422	−	0.845218i	$-0.320529\pi$
$367$	20.4761	1.06884	0.534422	+	0.845218i	$0.320529\pi$
$368$	1.00000	0.0521286
$369$	26.2433	1.36617
$370$	0	0
$371$	−27.0584	−1.40480
$372$	5.39070	0.279495
$373$	3.89386	0.201616	0.100808	−	0.994906i	$-0.467857\pi$
$373$	3.89386	0.201616	0.100808	+	0.994906i	$0.467857\pi$
$374$	4.85392	0.250990
$375$	0	0
$376$	−11.4567	−0.590832
$377$	−30.7142	−1.58186
$378$	52.4425	2.69735
$379$	−30.3765	−1.56034	−0.780169	−	0.625569i	$-0.784867\pi$
$379$	−30.3765	−1.56034	−0.780169	+	0.625569i	$0.784867\pi$
$380$	0	0
$381$	2.10614	0.107901
$382$	18.7142	0.957500
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−3.11903	−0.159167
$385$	0	0
$386$	23.4956	1.19589
$387$	−53.8266	−2.73616
$388$	0.642920	0.0326393
$389$	−18.6818	−0.947206	−0.473603	−	0.880738i	$-0.657047\pi$
$389$	−18.6818	−0.947206	−0.473603	+	0.880738i	$0.657047\pi$
$390$	0	0
$391$	−1.11903	−0.0565916
$392$	−13.3376	−0.673652
$393$	−42.7142	−2.15464
$394$	−18.1385	−0.913803
$395$	0	0
$396$	29.1850	1.46660
$397$	28.5757	1.43417	0.717086	−	0.696985i	$-0.245475\pi$
$397$	28.5757	1.43417	0.717086	+	0.696985i	$0.245475\pi$
$398$	23.2575	1.16579
$399$	−63.4336	−3.17565
$400$	0	0
$401$	12.1061	0.604552	0.302276	−	0.953220i	$-0.402254\pi$
$401$	12.1061	0.604552	0.302276	+	0.953220i	$0.402254\pi$
$402$	7.60170	0.379138
$403$	6.44377	0.320987
$404$	−8.23805	−0.409858
$405$	0	0
$406$	−37.1514	−1.84379
$407$	3.38942	0.168007
$408$	3.49027	0.172794
$409$	25.2911	1.25057	0.625283	−	0.780398i	$-0.284984\pi$
$409$	25.2911	1.25057	0.625283	+	0.780398i	$0.284984\pi$
$410$	0	0
$411$	−23.4837	−1.15837
$412$	−12.3376	−0.607831
$413$	10.0930	0.496644
$414$	−6.72833	−0.330679
$415$	0	0
$416$	−3.72833	−0.182796
$417$	14.5822	0.714096
$418$	−19.5615	−0.956785
$419$	−17.3505	−0.847628	−0.423814	−	0.905749i	$-0.639309\pi$
$419$	−17.3505	−0.847628	−0.423814	+	0.905749i	$0.639309\pi$
$420$	0	0
$421$	21.4230	1.04409	0.522047	−	0.852916i	$-0.325168\pi$
$421$	21.4230	1.04409	0.522047	+	0.852916i	$0.325168\pi$
$422$	−4.34420	−0.211472
$423$	77.0841	3.74796
$424$	−6.00000	−0.291386
$425$	0	0
$426$	−22.2044	−1.07581
$427$	−16.0376	−0.776115
$428$	15.9328	0.770139
$429$	50.4412	2.43532
$430$	0	0
$431$	22.5822	1.08775	0.543874	−	0.839167i	$-0.316957\pi$
$431$	22.5822	1.08775	0.543874	+	0.839167i	$0.316957\pi$
$432$	11.6288	0.559489
$433$	−1.01417	−0.0487378	−0.0243689	−	0.999703i	$-0.507758\pi$
$433$	−1.01417	−0.0487378	−0.0243689	+	0.999703i	$0.507758\pi$
$434$	7.79428	0.374138
$435$	0	0
$436$	−1.49027	−0.0713712
$437$	4.50973	0.215729
$438$	−29.4956	−1.40935
$439$	−26.7478	−1.27660	−0.638301	−	0.769787i	$-0.720362\pi$
$439$	−26.7478	−1.27660	−0.638301	+	0.769787i	$0.720362\pi$
$440$	0	0
$441$	89.7399	4.27333
$442$	4.17210	0.198446
$443$	−10.2044	−0.484827	−0.242414	−	0.970173i	$-0.577939\pi$
$443$	−10.2044	−0.484827	−0.242414	+	0.970173i	$0.577939\pi$
$444$	2.43720	0.115665
$445$	0	0
$446$	12.4761	0.590761
$447$	23.4837	1.11074
$448$	−4.50973	−0.213065
$449$	38.7867	1.83046	0.915228	−	0.402936i	$-0.132010\pi$
$449$	38.7867	1.83046	0.915228	+	0.402936i	$0.132010\pi$
$450$	0	0
$451$	16.9186	0.796665
$452$	6.00000	0.282216
$453$	−41.6611	−1.95741
$454$	15.9328	0.747762
$455$	0	0
$456$	−14.0660	−0.658699
$457$	−34.9522	−1.63500	−0.817498	−	0.575932i	$-0.804639\pi$
$457$	−34.9522	−1.63500	−0.817498	+	0.575932i	$0.804639\pi$
$458$	3.56280	0.166479
$459$	−13.0129	−0.607389
$460$	0	0
$461$	16.3700	0.762425	0.381213	−	0.924487i	$-0.375507\pi$
$461$	16.3700	0.762425	0.381213	+	0.924487i	$0.375507\pi$
$462$	61.0129	2.83858
$463$	−29.2186	−1.35790	−0.678952	−	0.734183i	$-0.737565\pi$
$463$	−29.2186	−1.35790	−0.678952	+	0.734183i	$0.737565\pi$
$464$	−8.23805	−0.382442
$465$	0	0
$466$	−27.4956	−1.27371
$467$	−24.2770	−1.12340	−0.561702	−	0.827340i	$-0.689853\pi$
$467$	−24.2770	−1.12340	−0.561702	+	0.827340i	$0.689853\pi$
$468$	25.0854	1.15957
$469$	10.9911	0.507523
$470$	0	0
$471$	−50.6469	−2.33369
$472$	2.23805	0.103015
$473$	−34.7010	−1.59555
$474$	46.5150	2.13651
$475$	0	0
$476$	5.04650	0.231306
$477$	40.3700	1.84841
$478$	−10.0389	−0.459169
$479$	24.6080	1.12437	0.562185	−	0.827012i	$-0.309961\pi$
$479$	24.6080	1.12437	0.562185	+	0.827012i	$0.309961\pi$
$480$	0	0
$481$	2.91331	0.132835
$482$	23.6947	1.07926
$483$	−14.0660	−0.640023
$484$	7.81502	0.355228
$485$	0	0
$486$	−15.2846	−0.693322
$487$	30.2381	1.37022	0.685108	−	0.728441i	$-0.259755\pi$
$487$	30.2381	1.37022	0.685108	+	0.728441i	$0.259755\pi$
$488$	−3.55623	−0.160983
$489$	10.2651	0.464204
$490$	0	0
$491$	12.3311	0.556493	0.278246	−	0.960510i	$-0.410247\pi$
$491$	12.3311	0.556493	0.278246	+	0.960510i	$0.410247\pi$
$492$	12.1655	0.548464
$493$	9.21860	0.415185
$494$	−16.8137	−0.756486
$495$	0	0
$496$	1.72833	0.0776042
$497$	−32.1049	−1.44010
$498$	8.67526	0.388748
$499$	−26.9133	−1.20481	−0.602403	−	0.798192i	$-0.705790\pi$
$499$	−26.9133	−1.20481	−0.602403	+	0.798192i	$0.705790\pi$
$500$	0	0
$501$	−71.4672	−3.19292
$502$	−12.4425	−0.555335
$503$	−20.5097	−0.914483	−0.457242	−	0.889342i	$-0.651163\pi$
$503$	−20.5097	−0.914483	−0.457242	+	0.889342i	$0.651163\pi$
$504$	30.3429	1.35158
$505$	0	0
$506$	−4.33763	−0.192831
$507$	2.80845	0.124728
$508$	0.675256	0.0299597
$509$	−36.7142	−1.62733	−0.813663	−	0.581336i	$-0.802530\pi$
$509$	−36.7142	−1.62733	−0.813663	+	0.581336i	$0.802530\pi$
$510$	0	0
$511$	−42.6469	−1.88659
$512$	−1.00000	−0.0441942
$513$	52.4425	2.31539
$514$	5.45665	0.240683
$515$	0	0
$516$	−24.9522	−1.09846
$517$	49.6947	2.18557
$518$	3.52389	0.154831
$519$	−1.79557	−0.0788166
$520$	0	0
$521$	−4.91331	−0.215256	−0.107628	−	0.994191i	$-0.534326\pi$
$521$	−4.91331	−0.215256	−0.107628	+	0.994191i	$0.534326\pi$
$522$	55.4283	2.42603
$523$	0.344196	0.0150506	0.00752531	−	0.999972i	$-0.497605\pi$
$523$	0.344196	0.0150506	0.00752531	+	0.999972i	$0.497605\pi$
$524$	−13.6947	−0.598256
$525$	0	0
$526$	0.138479	0.00603795
$527$	−1.93404	−0.0842483
$528$	13.5292	0.588782
$529$	1.00000	0.0434783
$530$	0	0
$531$	−15.0584	−0.653477
$532$	−20.3376	−0.881748
$533$	14.5421	0.629887
$534$	24.0000	1.03858
$535$	0	0
$536$	2.43720	0.105271
$537$	15.6558	0.675598
$538$	−14.6753	−0.632695
$539$	57.8537	2.49193
$540$	0	0
$541$	−6.13191	−0.263631	−0.131816	−	0.991274i	$-0.542081\pi$
$541$	−6.13191	−0.263631	−0.131816	+	0.991274i	$0.542081\pi$
$542$	8.31058	0.356970
$543$	−35.9598	−1.54318
$544$	1.11903	0.0479779
$545$	0	0
$546$	52.4425	2.24433
$547$	9.18498	0.392721	0.196361	−	0.980532i	$-0.437088\pi$
$547$	9.18498	0.392721	0.196361	+	0.980532i	$0.437088\pi$
$548$	−7.52918	−0.321631
$549$	23.9275	1.02120
$550$	0	0
$551$	−37.1514	−1.58270
$552$	−3.11903	−0.132755
$553$	67.2549	2.85997
$554$	12.9133	0.548634
$555$	0	0
$556$	4.67526	0.198275
$557$	4.30529	0.182421	0.0912105	−	0.995832i	$-0.470926\pi$
$557$	4.30529	0.182421	0.0912105	+	0.995832i	$0.470926\pi$
$558$	−11.6288	−0.492284
$559$	−29.8266	−1.26153
$560$	0	0
$561$	−15.1395	−0.639191
$562$	−2.67526	−0.112849
$563$	−11.1256	−0.468888	−0.234444	−	0.972130i	$-0.575327\pi$
$563$	−11.1256	−0.468888	−0.234444	+	0.972130i	$0.575327\pi$
$564$	35.7336	1.50466
$565$	0	0
$566$	0.742495	0.0312094
$567$	−72.5408	−3.04643
$568$	−7.11903	−0.298708
$569$	−16.0389	−0.672386	−0.336193	−	0.941793i	$-0.609139\pi$
$569$	−16.0389	−0.672386	−0.336193	+	0.941793i	$0.609139\pi$
$570$	0	0
$571$	17.9004	0.749109	0.374555	−	0.927205i	$-0.377796\pi$
$571$	17.9004	0.749109	0.374555	+	0.927205i	$0.377796\pi$
$572$	16.1721	0.676189
$573$	−58.3700	−2.43844
$574$	17.5898	0.734186
$575$	0	0
$576$	6.72833	0.280347
$577$	9.12559	0.379903	0.189952	−	0.981793i	$-0.439167\pi$
$577$	9.12559	0.379903	0.189952	+	0.981793i	$0.439167\pi$
$578$	15.7478	0.655021
$579$	−73.2833	−3.04555
$580$	0	0
$581$	12.5433	0.520386
$582$	−2.00528	−0.0831217
$583$	26.0258	1.07788
$584$	−9.45665	−0.391319
$585$	0	0
$586$	−6.00000	−0.247858
$587$	33.6340	1.38823	0.694113	−	0.719866i	$-0.255797\pi$
$587$	33.6340	1.38823	0.694113	+	0.719866i	$0.255797\pi$
$588$	41.6004	1.71557
$589$	7.79428	0.321158
$590$	0	0
$591$	56.5744	2.32716
$592$	0.781399	0.0321153
$593$	17.4567	0.716859	0.358429	−	0.933557i	$-0.383312\pi$
$593$	17.4567	0.716859	0.358429	+	0.933557i	$0.383312\pi$
$594$	−50.4412	−2.06963
$595$	0	0
$596$	7.52918	0.308407
$597$	−72.5408	−2.96890
$598$	−3.72833	−0.152463
$599$	−11.5951	−0.473764	−0.236882	−	0.971538i	$-0.576126\pi$
$599$	−11.5951	−0.473764	−0.236882	+	0.971538i	$0.576126\pi$
$600$	0	0
$601$	−31.6611	−1.29148	−0.645741	−	0.763556i	$-0.723452\pi$
$601$	−31.6611	−1.29148	−0.645741	+	0.763556i	$0.723452\pi$
$602$	−36.0778	−1.47042
$603$	−16.3983	−0.667790
$604$	−13.3571	−0.543492
$605$	0	0
$606$	25.6947	1.04378
$607$	36.0778	1.46435	0.732177	−	0.681115i	$-0.238505\pi$
$607$	36.0778	1.46435	0.732177	+	0.681115i	$0.238505\pi$
$608$	−4.50973	−0.182894
$609$	115.876	4.69554
$610$	0	0
$611$	42.7142	1.72803
$612$	−7.52918	−0.304349
$613$	32.0389	1.29404	0.647020	−	0.762473i	$-0.276015\pi$
$613$	32.0389	1.29404	0.647020	+	0.762473i	$0.276015\pi$
$614$	30.5084	1.23122
$615$	0	0
$616$	19.5615	0.788156
$617$	13.3960	0.539302	0.269651	−	0.962958i	$-0.413092\pi$
$617$	13.3960	0.539302	0.269651	+	0.962958i	$0.413092\pi$
$618$	38.4814	1.54795
$619$	37.1309	1.49242	0.746208	−	0.665713i	$-0.231872\pi$
$619$	37.1309	1.49242	0.746208	+	0.665713i	$0.231872\pi$
$620$	0	0
$621$	11.6288	0.466646
$622$	−5.56280	−0.223048
$623$	34.7010	1.39027
$624$	11.6288	0.465523
$625$	0	0
$626$	4.07252	0.162771
$627$	61.0129	2.43662
$628$	−16.2381	−0.647969
$629$	−0.874406	−0.0348648
$630$	0	0
$631$	11.1125	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$631$	11.1125	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$632$	14.9133	0.593220
$633$	13.5497	0.538551
$634$	−6.16553	−0.244864
$635$	0	0
$636$	18.7142	0.742065
$637$	49.7270	1.97026
$638$	35.7336	1.41471
$639$	47.8991	1.89486
$640$	0	0
$641$	12.3831	0.489103	0.244552	−	0.969636i	$-0.421359\pi$
$641$	12.3831	0.489103	0.244552	+	0.969636i	$0.421359\pi$
$642$	−49.6947	−1.96129
$643$	37.4956	1.47868	0.739340	−	0.673332i	$-0.235138\pi$
$643$	37.4956	1.47868	0.739340	+	0.673332i	$0.235138\pi$
$644$	−4.50973	−0.177708
$645$	0	0
$646$	5.04650	0.198552
$647$	−14.5691	−0.572771	−0.286385	−	0.958114i	$-0.592454\pi$
$647$	−14.5691	−0.572771	−0.286385	+	0.958114i	$0.592454\pi$
$648$	−16.0854	−0.631894
$649$	−9.70784	−0.381066
$650$	0	0
$651$	−24.3106	−0.952807
$652$	3.29112	0.128890
$653$	4.41672	0.172840	0.0864198	−	0.996259i	$-0.472457\pi$
$653$	4.41672	0.172840	0.0864198	+	0.996259i	$0.472457\pi$
$654$	4.64820	0.181759
$655$	0	0
$656$	3.90043	0.152286
$657$	63.6275	2.48234
$658$	51.6664	2.01416
$659$	−31.8655	−1.24130	−0.620652	−	0.784086i	$-0.713132\pi$
$659$	−31.8655	−1.24130	−0.620652	+	0.784086i	$0.713132\pi$
$660$	0	0
$661$	33.1190	1.28818	0.644090	−	0.764949i	$-0.277236\pi$
$661$	33.1190	1.28818	0.644090	+	0.764949i	$0.277236\pi$
$662$	−27.5886	−1.07226
$663$	−13.0129	−0.505379
$664$	2.78140	0.107939
$665$	0	0
$666$	−5.25751	−0.203724
$667$	−8.23805	−0.318979
$668$	−22.9133	−0.886543
$669$	−38.9133	−1.50448
$670$	0	0
$671$	15.4256	0.595499
$672$	14.0660	0.542606
$673$	−19.3505	−0.745907	−0.372954	−	0.927850i	$-0.621655\pi$
$673$	−19.3505	−0.745907	−0.372954	+	0.927850i	$0.621655\pi$
$674$	−17.4230	−0.671110
$675$	0	0
$676$	0.900425	0.0346317
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	−18.7142	−0.718713
$679$	−2.89939	−0.111268
$680$	0	0
$681$	−49.6947	−1.90431
$682$	−7.49684	−0.287069
$683$	−38.3495	−1.46740	−0.733701	−	0.679472i	$-0.762209\pi$
$683$	−38.3495	−1.46740	−0.733701	+	0.679472i	$0.762209\pi$
$684$	30.3429	1.16019
$685$	0	0
$686$	28.5810	1.09123
$687$	−11.1125	−0.423967
$688$	−8.00000	−0.304997
$689$	22.3700	0.852228
$690$	0	0
$691$	−21.0195	−0.799618	−0.399809	−	0.916599i	$-0.630923\pi$
$691$	−21.0195	−0.799618	−0.399809	+	0.916599i	$0.630923\pi$
$692$	−0.575681	−0.0218841
$693$	−131.616	−4.99969
$694$	4.88097	0.185279
$695$	0	0
$696$	25.6947	0.973955
$697$	−4.36468	−0.165324
$698$	−24.0389	−0.909886
$699$	85.7594	3.24372
$700$	0	0
$701$	19.3169	0.729589	0.364794	−	0.931088i	$-0.381139\pi$
$701$	19.3169	0.729589	0.364794	+	0.931088i	$0.381139\pi$
$702$	−43.3558	−1.63636
$703$	3.52389	0.132906
$704$	4.33763	0.163481
$705$	0	0
$706$	−14.3442	−0.539851
$707$	37.1514	1.39722
$708$	−6.98055	−0.262345
$709$	12.2315	0.459363	0.229682	−	0.973266i	$-0.426232\pi$
$709$	12.2315	0.459363	0.229682	+	0.973266i	$0.426232\pi$
$710$	0	0
$711$	−100.342	−3.76311
$712$	7.69471	0.288371
$713$	1.72833	0.0647264
$714$	−15.7402	−0.589061
$715$	0	0
$716$	5.01945	0.187586
$717$	31.3116	1.16935
$718$	−26.7814	−0.999473
$719$	−40.6416	−1.51568	−0.757839	−	0.652442i	$-0.773745\pi$
$719$	−40.6416	−1.51568	−0.757839	+	0.652442i	$0.773745\pi$
$720$	0	0
$721$	55.6393	2.07212
$722$	−1.33763	−0.0497814
$723$	−73.9044	−2.74854
$724$	−11.5292	−0.428479
$725$	0	0
$726$	−24.3752	−0.904650
$727$	23.4501	0.869716	0.434858	−	0.900499i	$-0.356799\pi$
$727$	23.4501	0.869716	0.434858	+	0.900499i	$0.356799\pi$
$728$	16.8137	0.623158
$729$	−0.583281	−0.0216030
$730$	0	0
$731$	8.95221	0.331110
$732$	11.0920	0.409971
$733$	12.5150	0.462252	0.231126	−	0.972924i	$-0.425759\pi$
$733$	12.5150	0.462252	0.231126	+	0.972924i	$0.425759\pi$
$734$	−20.4761	−0.755787
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−10.5717	−0.389413
$738$	−26.2433	−0.966031
$739$	−21.3505	−0.785391	−0.392696	−	0.919668i	$-0.628457\pi$
$739$	−21.3505	−0.785391	−0.392696	+	0.919668i	$0.628457\pi$
$740$	0	0
$741$	52.4425	1.92652
$742$	27.0584	0.993343
$743$	−24.9858	−0.916641	−0.458321	−	0.888787i	$-0.651549\pi$
$743$	−24.9858	−0.916641	−0.458321	+	0.888787i	$0.651549\pi$
$744$	−5.39070	−0.197633
$745$	0	0
$746$	−3.89386	−0.142564
$747$	−18.7142	−0.684715
$748$	−4.85392	−0.177477
$749$	−71.8524	−2.62543
$750$	0	0
$751$	−33.6275	−1.22708	−0.613542	−	0.789662i	$-0.710256\pi$
$751$	−33.6275	−1.22708	−0.613542	+	0.789662i	$0.710256\pi$
$752$	11.4567	0.417781
$753$	38.8085	1.41426
$754$	30.7142	1.11854
$755$	0	0
$756$	−52.4425	−1.90731
$757$	37.1230	1.34926	0.674630	−	0.738156i	$-0.264303\pi$
$757$	37.1230	1.34926	0.674630	+	0.738156i	$0.264303\pi$
$758$	30.3765	1.10333
$759$	13.5292	0.491078
$760$	0	0
$761$	−3.87337	−0.140410	−0.0702048	−	0.997533i	$-0.522365\pi$
$761$	−3.87337	−0.140410	−0.0702048	+	0.997533i	$0.522365\pi$
$762$	−2.10614	−0.0762975
$763$	6.72073	0.243307
$764$	−18.7142	−0.677055
$765$	0	0
$766$	0	0
$767$	−8.34420	−0.301291
$768$	3.11903	0.112548
$769$	23.1645	0.835333	0.417667	−	0.908600i	$-0.362848\pi$
$769$	23.1645	0.835333	0.417667	+	0.908600i	$0.362848\pi$
$770$	0	0
$771$	−17.0195	−0.612941
$772$	−23.4956	−0.845624
$773$	8.78140	0.315845	0.157922	−	0.987452i	$-0.449520\pi$
$773$	8.78140	0.315845	0.157922	+	0.987452i	$0.449520\pi$
$774$	53.8266	1.93476
$775$	0	0
$776$	−0.642920	−0.0230795
$777$	−10.9911	−0.394304
$778$	18.6818	0.669776
$779$	17.5898	0.630222
$780$	0	0
$781$	30.8797	1.10496
$782$	1.11903	0.0400163
$783$	−95.7983	−3.42355
$784$	13.3376	0.476344
$785$	0	0
$786$	42.7142	1.52356
$787$	−49.6275	−1.76903	−0.884514	−	0.466513i	$-0.845510\pi$
$787$	−49.6275	−1.76903	−0.884514	+	0.466513i	$0.845510\pi$
$788$	18.1385	0.646157
$789$	−0.431918	−0.0153767
$790$	0	0
$791$	−27.0584	−0.962084
$792$	−29.1850	−1.03704
$793$	13.2588	0.470833
$794$	−28.5757	−1.01411
$795$	0	0
$796$	−23.2575	−0.824340
$797$	−18.3311	−0.649319	−0.324660	−	0.945831i	$-0.605250\pi$
$797$	−18.3311	−0.649319	−0.324660	+	0.945831i	$0.605250\pi$
$798$	63.4336	2.24553
$799$	−12.8203	−0.453550
$800$	0	0
$801$	−51.7725	−1.82929
$802$	−12.1061	−0.427483
$803$	41.0195	1.44755
$804$	−7.60170	−0.268091
$805$	0	0
$806$	−6.44377	−0.226972
$807$	45.7725	1.61127
$808$	8.23805	0.289814
$809$	−1.93933	−0.0681832	−0.0340916	−	0.999419i	$-0.510854\pi$
$809$	−1.93933	−0.0681832	−0.0340916	+	0.999419i	$0.510854\pi$
$810$	0	0
$811$	−5.41775	−0.190243	−0.0951215	−	0.995466i	$-0.530324\pi$
$811$	−5.41775	−0.190243	−0.0951215	+	0.995466i	$0.530324\pi$
$812$	37.1514	1.30376
$813$	−25.9209	−0.909086
$814$	−3.38942	−0.118799
$815$	0	0
$816$	−3.49027	−0.122184
$817$	−36.0778	−1.26220
$818$	−25.2911	−0.884283
$819$	−113.128	−3.95302
$820$	0	0
$821$	37.8655	1.32152	0.660758	−	0.750599i	$-0.270235\pi$
$821$	37.8655	1.32152	0.660758	+	0.750599i	$0.270235\pi$
$822$	23.4837	0.819088
$823$	−43.7336	−1.52446	−0.762229	−	0.647308i	$-0.775895\pi$
$823$	−43.7336	−1.52446	−0.762229	+	0.647308i	$0.775895\pi$
$824$	12.3376	0.429802
$825$	0	0
$826$	−10.0930	−0.351181
$827$	−28.1991	−0.980581	−0.490290	−	0.871559i	$-0.663109\pi$
$827$	−28.1991	−0.980581	−0.490290	+	0.871559i	$0.663109\pi$
$828$	6.72833	0.233826
$829$	1.12559	0.0390935	0.0195468	−	0.999809i	$-0.493778\pi$
$829$	1.12559	0.0390935	0.0195468	+	0.999809i	$0.493778\pi$
$830$	0	0
$831$	−40.2770	−1.39719
$832$	3.72833	0.129256
$833$	−14.9252	−0.517126
$834$	−14.5822	−0.504942
$835$	0	0
$836$	19.5615	0.676549
$837$	20.0983	0.694699
$838$	17.3505	0.599364
$839$	39.9328	1.37863	0.689316	−	0.724461i	$-0.257911\pi$
$839$	39.9328	1.37863	0.689316	+	0.724461i	$0.257911\pi$
$840$	0	0
$841$	38.8655	1.34019
$842$	−21.4230	−0.738287
$843$	8.34420	0.287389
$844$	4.34420	0.149533
$845$	0	0
$846$	−77.0841	−2.65021
$847$	−35.2436	−1.21098
$848$	6.00000	0.206041
$849$	−2.31586	−0.0794801
$850$	0	0
$851$	0.781399	0.0267860
$852$	22.2044	0.760711
$853$	−47.9921	−1.64322	−0.821610	−	0.570050i	$-0.806924\pi$
$853$	−47.9921	−1.64322	−0.821610	+	0.570050i	$0.806924\pi$
$854$	16.0376	0.548796
$855$	0	0
$856$	−15.9328	−0.544571
$857$	43.4283	1.48348	0.741742	−	0.670686i	$-0.234000\pi$
$857$	43.4283	1.48348	0.741742	+	0.670686i	$0.234000\pi$
$858$	−50.4412	−1.72203
$859$	32.5433	1.11036	0.555182	−	0.831729i	$-0.312648\pi$
$859$	32.5433	1.11036	0.555182	+	0.831729i	$0.312648\pi$
$860$	0	0
$861$	−54.8632	−1.86973
$862$	−22.5822	−0.769154
$863$	−46.1036	−1.56938	−0.784692	−	0.619886i	$-0.787179\pi$
$863$	−46.1036	−1.56938	−0.784692	+	0.619886i	$0.787179\pi$
$864$	−11.6288	−0.395618
$865$	0	0
$866$	1.01417	0.0344628
$867$	−49.1177	−1.66813
$868$	−7.79428	−0.264555
$869$	−64.6884	−2.19440
$870$	0	0
$871$	−9.08669	−0.307891
$872$	1.49027	0.0504670
$873$	4.32578	0.146405
$874$	−4.50973	−0.152544
$875$	0	0
$876$	29.4956	0.996563
$877$	24.0996	0.813785	0.406892	−	0.913476i	$-0.366612\pi$
$877$	24.0996	0.813785	0.406892	+	0.913476i	$0.366612\pi$
$878$	26.7478	0.902694
$879$	18.7142	0.631213
$880$	0	0
$881$	2.34420	0.0789780	0.0394890	−	0.999220i	$-0.487427\pi$
$881$	2.34420	0.0789780	0.0394890	+	0.999220i	$0.487427\pi$
$882$	−89.7399	−3.02170
$883$	41.0505	1.38146	0.690730	−	0.723113i	$-0.257289\pi$
$883$	41.0505	1.38146	0.690730	+	0.723113i	$0.257289\pi$
$884$	−4.17210	−0.140323
$885$	0	0
$886$	10.2044	0.342825
$887$	−54.7788	−1.83929	−0.919647	−	0.392747i	$-0.871525\pi$
$887$	−54.7788	−1.83929	−0.919647	+	0.392747i	$0.871525\pi$
$888$	−2.43720	−0.0817872
$889$	−3.04522	−0.102133
$890$	0	0
$891$	69.7725	2.33747
$892$	−12.4761	−0.417731
$893$	51.6664	1.72895
$894$	−23.4837	−0.785413
$895$	0	0
$896$	4.50973	0.150659
$897$	11.6288	0.388273
$898$	−38.7867	−1.29433
$899$	−14.2381	−0.474866
$900$	0	0
$901$	−6.71416	−0.223681
$902$	−16.9186	−0.563328
$903$	112.528	3.74469
$904$	−6.00000	−0.199557
$905$	0	0
$906$	41.6611	1.38410
$907$	10.1061	0.335569	0.167784	−	0.985824i	$-0.446339\pi$
$907$	10.1061	0.335569	0.167784	+	0.985824i	$0.446339\pi$
$908$	−15.9328	−0.528747
$909$	−55.4283	−1.83844
$910$	0	0
$911$	−25.4178	−0.842128	−0.421064	−	0.907031i	$-0.638343\pi$
$911$	−25.4178	−0.842128	−0.421064	+	0.907031i	$0.638343\pi$
$912$	14.0660	0.465770
$913$	−12.0647	−0.399282
$914$	34.9522	1.15612
$915$	0	0
$916$	−3.56280	−0.117718
$917$	61.7594	2.03947
$918$	13.0129	0.429489
$919$	23.6017	0.778548	0.389274	−	0.921122i	$-0.372726\pi$
$919$	23.6017	0.778548	0.389274	+	0.921122i	$0.372726\pi$
$920$	0	0
$921$	−95.1566	−3.13552
$922$	−16.3700	−0.539116
$923$	26.5421	0.873643
$924$	−61.0129	−2.00718
$925$	0	0
$926$	29.2186	0.960183
$927$	−83.0116	−2.72646
$928$	8.23805	0.270427
$929$	−7.08669	−0.232507	−0.116253	−	0.993220i	$-0.537088\pi$
$929$	−7.08669	−0.232507	−0.116253	+	0.993220i	$0.537088\pi$
$930$	0	0
$931$	60.1490	1.97131
$932$	27.4956	0.900647
$933$	17.3505	0.568030
$934$	24.2770	0.794366
$935$	0	0
$936$	−25.0854	−0.819942
$937$	−27.3169	−0.892404	−0.446202	−	0.894932i	$-0.647224\pi$
$937$	−27.3169	−0.892404	−0.446202	+	0.894932i	$0.647224\pi$
$938$	−10.9911	−0.358873
$939$	−12.7023	−0.414524
$940$	0	0
$941$	55.8979	1.82222	0.911109	−	0.412165i	$-0.135227\pi$
$941$	55.8979	1.82222	0.911109	+	0.412165i	$0.135227\pi$
$942$	50.6469	1.65017
$943$	3.90043	0.127015
$944$	−2.23805	−0.0728424
$945$	0	0
$946$	34.7010	1.12823
$947$	−37.5939	−1.22164	−0.610818	−	0.791771i	$-0.709159\pi$
$947$	−37.5939	−1.22164	−0.610818	+	0.791771i	$0.709159\pi$
$948$	−46.5150	−1.51074
$949$	35.2575	1.14451
$950$	0	0
$951$	19.2305	0.623590
$952$	−5.04650	−0.163558
$953$	29.3828	0.951804	0.475902	−	0.879498i	$-0.342122\pi$
$953$	29.3828	0.951804	0.475902	+	0.879498i	$0.342122\pi$
$954$	−40.3700	−1.30703
$955$	0	0
$956$	10.0389	0.324681
$957$	−111.454	−3.60280
$958$	−24.6080	−0.795049
$959$	33.9545	1.09645
$960$	0	0
$961$	−28.0129	−0.903641
$962$	−2.91331	−0.0939289
$963$	107.201	3.45450
$964$	−23.6947	−0.763155
$965$	0	0
$966$	14.0660	0.452565
$967$	49.2292	1.58310	0.791552	−	0.611102i	$-0.209274\pi$
$967$	49.2292	1.58310	0.791552	+	0.611102i	$0.209274\pi$
$968$	−7.81502	−0.251184
$969$	−15.7402	−0.505647
$970$	0	0
$971$	9.62347	0.308832	0.154416	−	0.988006i	$-0.450650\pi$
$971$	9.62347	0.308832	0.154416	+	0.988006i	$0.450650\pi$
$972$	15.2846	0.490252
$973$	−21.0841	−0.675926
$974$	−30.2381	−0.968890
$975$	0	0
$976$	3.55623	0.113832
$977$	−18.9858	−0.607411	−0.303705	−	0.952766i	$-0.598224\pi$
$977$	−18.9858	−0.607411	−0.303705	+	0.952766i	$0.598224\pi$
$978$	−10.2651	−0.328242
$979$	−33.3768	−1.06673
$980$	0	0
$981$	−10.0271	−0.320139
$982$	−12.3311	−0.393500
$983$	−4.33763	−0.138349	−0.0691744	−	0.997605i	$-0.522037\pi$
$983$	−4.33763	−0.138349	−0.0691744	+	0.997605i	$0.522037\pi$
$984$	−12.1655	−0.387823
$985$	0	0
$986$	−9.21860	−0.293580
$987$	−161.149	−5.12942
$988$	16.8137	0.534916
$989$	−8.00000	−0.254385
$990$	0	0
$991$	1.96766	0.0625049	0.0312524	−	0.999512i	$-0.490050\pi$
$991$	1.96766	0.0625049	0.0312524	+	0.999512i	$0.490050\pi$
$992$	−1.72833	−0.0548744
$993$	86.0495	2.73070
$994$	32.1049	1.01830
$995$	0	0
$996$	−8.67526	−0.274886
$997$	−3.96110	−0.125449	−0.0627246	−	0.998031i	$-0.519979\pi$
$997$	−3.96110	−0.125449	−0.0627246	+	0.998031i	$0.519979\pi$
$998$	26.9133	0.851926
$999$	9.08669	0.287490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.q.1.3		3
4.3	odd	2		9200.2.a.cf.1.1		3
5.2	odd	4		1150.2.b.j.599.1		6
5.3	odd	4		1150.2.b.j.599.6		6
5.4	even	2		230.2.a.d.1.1	✓	3
15.14	odd	2		2070.2.a.z.1.3		3
20.19	odd	2		1840.2.a.r.1.3		3
40.19	odd	2		7360.2.a.ce.1.1		3
40.29	even	2		7360.2.a.bz.1.3		3
115.114	odd	2		5290.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.1	✓	3	5.4	even	2
1150.2.a.q.1.3		3	1.1	even	1	trivial
1150.2.b.j.599.1		6	5.2	odd	4
1150.2.b.j.599.6		6	5.3	odd	4
1840.2.a.r.1.3		3	20.19	odd	2
2070.2.a.z.1.3		3	15.14	odd	2
5290.2.a.r.1.1		3	115.114	odd	2
7360.2.a.bz.1.3		3	40.29	even	2
7360.2.a.ce.1.1		3	40.19	odd	2
9200.2.a.cf.1.1		3	4.3	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.11903 q^{3} +1.00000 q^{4} -3.11903 q^{6} -4.50973 q^{7} -1.00000 q^{8} +6.72833 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.11903 q^{3} +1.00000 q^{4} -3.11903 q^{6} -4.50973 q^{7} -1.00000 q^{8} +6.72833 q^{9} +4.33763 q^{11} +3.11903 q^{12} +3.72833 q^{13} +4.50973 q^{14} +1.00000 q^{16} -1.11903 q^{17} -6.72833 q^{18} +4.50973 q^{19} -14.0660 q^{21} -4.33763 q^{22} +1.00000 q^{23} -3.11903 q^{24} -3.72833 q^{26} +11.6288 q^{27} -4.50973 q^{28} -8.23805 q^{29} +1.72833 q^{31} -1.00000 q^{32} +13.5292 q^{33} +1.11903 q^{34} +6.72833 q^{36} +0.781399 q^{37} -4.50973 q^{38} +11.6288 q^{39} +3.90043 q^{41} +14.0660 q^{42} -8.00000 q^{43} +4.33763 q^{44} -1.00000 q^{46} +11.4567 q^{47} +3.11903 q^{48} +13.3376 q^{49} -3.49027 q^{51} +3.72833 q^{52} +6.00000 q^{53} -11.6288 q^{54} +4.50973 q^{56} +14.0660 q^{57} +8.23805 q^{58} -2.23805 q^{59} +3.55623 q^{61} -1.72833 q^{62} -30.3429 q^{63} +1.00000 q^{64} -13.5292 q^{66} -2.43720 q^{67} -1.11903 q^{68} +3.11903 q^{69} +7.11903 q^{71} -6.72833 q^{72} +9.45665 q^{73} -0.781399 q^{74} +4.50973 q^{76} -19.5615 q^{77} -11.6288 q^{78} -14.9133 q^{79} +16.0854 q^{81} -3.90043 q^{82} -2.78140 q^{83} -14.0660 q^{84} +8.00000 q^{86} -25.6947 q^{87} -4.33763 q^{88} -7.69471 q^{89} -16.8137 q^{91} +1.00000 q^{92} +5.39070 q^{93} -11.4567 q^{94} -3.11903 q^{96} +0.642920 q^{97} -13.3376 q^{98} +29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9} + 3 q^{11} - q^{12} + q^{13} + 3 q^{14} + 3 q^{16} + 7 q^{17} - 10 q^{18} + 3 q^{19} - 22 q^{21} - 3 q^{22} + 3 q^{23} + q^{24} - q^{26} + 14 q^{27} - 3 q^{28} - 4 q^{29} - 5 q^{31} - 3 q^{32} + 9 q^{33} - 7 q^{34} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 14 q^{39} + q^{41} + 22 q^{42} - 24 q^{43} + 3 q^{44} - 3 q^{46} + 14 q^{47} - q^{48} + 30 q^{49} - 21 q^{51} + q^{52} + 18 q^{53} - 14 q^{54} + 3 q^{56} + 22 q^{57} + 4 q^{58} + 14 q^{59} + q^{61} + 5 q^{62} - 8 q^{63} + 3 q^{64} - 9 q^{66} - 8 q^{67} + 7 q^{68} - q^{69} + 11 q^{71} - 10 q^{72} + 8 q^{73} - 2 q^{74} + 3 q^{76} + 24 q^{77} - 14 q^{78} - 4 q^{79} + 7 q^{81} - q^{82} - 8 q^{83} - 22 q^{84} + 24 q^{86} - 36 q^{87} - 3 q^{88} + 18 q^{89} + q^{91} + 3 q^{92} + 16 q^{93} - 14 q^{94} + q^{96} + 33 q^{97} - 30 q^{98} + 57 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9 + 3 * q^11 - q^12 + q^13 + 3 * q^14 + 3 * q^16 + 7 * q^17 - 10 * q^18 + 3 * q^19 - 22 * q^21 - 3 * q^22 + 3 * q^23 + q^24 - q^26 + 14 * q^27 - 3 * q^28 - 4 * q^29 - 5 * q^31 - 3 * q^32 + 9 * q^33 - 7 * q^34 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + q^41 + 22 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^46 + 14 * q^47 - q^48 + 30 * q^49 - 21 * q^51 + q^52 + 18 * q^53 - 14 * q^54 + 3 * q^56 + 22 * q^57 + 4 * q^58 + 14 * q^59 + q^61 + 5 * q^62 - 8 * q^63 + 3 * q^64 - 9 * q^66 - 8 * q^67 + 7 * q^68 - q^69 + 11 * q^71 - 10 * q^72 + 8 * q^73 - 2 * q^74 + 3 * q^76 + 24 * q^77 - 14 * q^78 - 4 * q^79 + 7 * q^81 - q^82 - 8 * q^83 - 22 * q^84 + 24 * q^86 - 36 * q^87 - 3 * q^88 + 18 * q^89 + q^91 + 3 * q^92 + 16 * q^93 - 14 * q^94 + q^96 + 33 * q^97 - 30 * q^98 + 57 * q^99

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