LMFDB - Embedded newform 5929.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, 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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 847)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30278 q^{2} -1.30278 q^{3} -0.302776 q^{4} +3.60555 q^{5} +1.69722 q^{6} +3.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q-1.30278 q^{2} -1.30278 q^{3} -0.302776 q^{4} +3.60555 q^{5} +1.69722 q^{6} +3.00000 q^{8} -1.30278 q^{9} -4.69722 q^{10} +0.394449 q^{12} +0.605551 q^{13} -4.69722 q^{15} -3.30278 q^{16} -6.30278 q^{17} +1.69722 q^{18} +3.00000 q^{19} -1.09167 q^{20} -6.30278 q^{23} -3.90833 q^{24} +8.00000 q^{25} -0.788897 q^{26} +5.60555 q^{27} +8.30278 q^{29} +6.11943 q^{30} -1.00000 q^{31} -1.69722 q^{32} +8.21110 q^{34} +0.394449 q^{36} +9.21110 q^{37} -3.90833 q^{38} -0.788897 q^{39} +10.8167 q^{40} -7.00000 q^{41} +5.30278 q^{43} -4.69722 q^{45} +8.21110 q^{46} -8.90833 q^{47} +4.30278 q^{48} -10.4222 q^{50} +8.21110 q^{51} -0.183346 q^{52} -2.09167 q^{53} -7.30278 q^{54} -3.90833 q^{57} -10.8167 q^{58} -10.3028 q^{59} +1.42221 q^{60} +0.697224 q^{61} +1.30278 q^{62} +8.81665 q^{64} +2.18335 q^{65} -9.51388 q^{67} +1.90833 q^{68} +8.21110 q^{69} -0.697224 q^{71} -3.90833 q^{72} +5.00000 q^{73} -12.0000 q^{74} -10.4222 q^{75} -0.908327 q^{76} +1.02776 q^{78} -4.69722 q^{79} -11.9083 q^{80} -3.39445 q^{81} +9.11943 q^{82} -3.00000 q^{83} -22.7250 q^{85} -6.90833 q^{86} -10.8167 q^{87} -17.7250 q^{89} +6.11943 q^{90} +1.90833 q^{92} +1.30278 q^{93} +11.6056 q^{94} +10.8167 q^{95} +2.21110 q^{96} -3.60555 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 + 3 * q^4 + 7 * q^6 + 6 * q^8 + q^9	$ 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9} - 13 q^{10} + 8 q^{12} - 6 q^{13} - 13 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} + 6 q^{19} - 13 q^{20} - 9 q^{23} + 3 q^{24} + 16 q^{25} - 16 q^{26} + 4 q^{27} + 13 q^{29} - 13 q^{30} - 2 q^{31} - 7 q^{32} + 2 q^{34} + 8 q^{36} + 4 q^{37} + 3 q^{38} - 16 q^{39} - 14 q^{41} + 7 q^{43} - 13 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} + 8 q^{50} + 2 q^{51} - 22 q^{52} - 15 q^{53} - 11 q^{54} + 3 q^{57} - 17 q^{59} - 26 q^{60} + 5 q^{61} - q^{62} - 4 q^{64} + 26 q^{65} - q^{67} - 7 q^{68} + 2 q^{69} - 5 q^{71} + 3 q^{72} + 10 q^{73} - 24 q^{74} + 8 q^{75} + 9 q^{76} - 34 q^{78} - 13 q^{79} - 13 q^{80} - 14 q^{81} - 7 q^{82} - 6 q^{83} - 13 q^{85} - 3 q^{86} - 3 q^{89} - 13 q^{90} - 7 q^{92} - q^{93} + 16 q^{94} - 10 q^{96}+O(q^{100}) $ 2 * q + q^2 + q^3 + 3 * q^4 + 7 * q^6 + 6 * q^8 + q^9 - 13 * q^10 + 8 * q^12 - 6 * q^13 - 13 * q^15 - 3 * q^16 - 9 * q^17 + 7 * q^18 + 6 * q^19 - 13 * q^20 - 9 * q^23 + 3 * q^24 + 16 * q^25 - 16 * q^26 + 4 * q^27 + 13 * q^29 - 13 * q^30 - 2 * q^31 - 7 * q^32 + 2 * q^34 + 8 * q^36 + 4 * q^37 + 3 * q^38 - 16 * q^39 - 14 * q^41 + 7 * q^43 - 13 * q^45 + 2 * q^46 - 7 * q^47 + 5 * q^48 + 8 * q^50 + 2 * q^51 - 22 * q^52 - 15 * q^53 - 11 * q^54 + 3 * q^57 - 17 * q^59 - 26 * q^60 + 5 * q^61 - q^62 - 4 * q^64 + 26 * q^65 - q^67 - 7 * q^68 + 2 * q^69 - 5 * q^71 + 3 * q^72 + 10 * q^73 - 24 * q^74 + 8 * q^75 + 9 * q^76 - 34 * q^78 - 13 * q^79 - 13 * q^80 - 14 * q^81 - 7 * q^82 - 6 * q^83 - 13 * q^85 - 3 * q^86 - 3 * q^89 - 13 * q^90 - 7 * q^92 - q^93 + 16 * q^94 - 10 * q^96

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 $

$2$	−1.30278	−0.921201	−0.460601	−	0.887607i	$-0.652366\pi$
$2$	−1.30278	−0.921201	−0.460601	+	0.887607i	$0.652366\pi$
$3$	−1.30278	−0.752158	−0.376079	−	0.926588i	$-0.622728\pi$
$3$	−1.30278	−0.752158	−0.376079	+	0.926588i	$0.622728\pi$
$4$	−0.302776	−0.151388
$5$	3.60555	1.61245	0.806226	−	0.591608i	$-0.201507\pi$
$5$	3.60555	1.61245	0.806226	+	0.591608i	$0.201507\pi$
$6$	1.69722	0.692889
$7$	0	0
$7$	0	0
$8$	3.00000	1.06066
$9$	−1.30278	−0.434259
$10$	−4.69722	−1.48539
$11$	0	0
$11$	0	0
$12$	0.394449	0.113868
$13$	0.605551	0.167950	0.0839749	−	0.996468i	$-0.473238\pi$
$13$	0.605551	0.167950	0.0839749	+	0.996468i	$0.473238\pi$
$14$	0	0
$15$	−4.69722	−1.21282
$16$	−3.30278	−0.825694
$17$	−6.30278	−1.52865	−0.764324	−	0.644833i	$-0.776927\pi$
$17$	−6.30278	−1.52865	−0.764324	+	0.644833i	$0.776927\pi$
$18$	1.69722	0.400040
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−1.09167	−0.244106
$21$	0	0
$22$	0	0
$23$	−6.30278	−1.31422	−0.657110	−	0.753795i	$-0.728221\pi$
$23$	−6.30278	−1.31422	−0.657110	+	0.753795i	$0.728221\pi$
$24$	−3.90833	−0.797784
$25$	8.00000	1.60000
$26$	−0.788897	−0.154716
$27$	5.60555	1.07879
$28$	0	0
$29$	8.30278	1.54179	0.770893	−	0.636964i	$-0.219810\pi$
$29$	8.30278	1.54179	0.770893	+	0.636964i	$0.219810\pi$
$30$	6.11943	1.11725
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	−1.69722	−0.300030
$33$	0	0
$34$	8.21110	1.40819
$35$	0	0
$36$	0.394449	0.0657415
$37$	9.21110	1.51430	0.757148	−	0.653243i	$-0.226592\pi$
$37$	9.21110	1.51430	0.757148	+	0.653243i	$0.226592\pi$
$38$	−3.90833	−0.634014
$39$	−0.788897	−0.126325
$40$	10.8167	1.71026
$41$	−7.00000	−1.09322	−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000	−1.09322	−0.546608	+	0.837389i	$0.684081\pi$
$42$	0	0
$43$	5.30278	0.808666	0.404333	−	0.914612i	$-0.367504\pi$
$43$	5.30278	0.808666	0.404333	+	0.914612i	$0.367504\pi$
$44$	0	0
$45$	−4.69722	−0.700221
$46$	8.21110	1.21066
$47$	−8.90833	−1.29941	−0.649707	−	0.760185i	$-0.725108\pi$
$47$	−8.90833	−1.29941	−0.649707	+	0.760185i	$0.725108\pi$
$48$	4.30278	0.621052
$49$	0	0
$50$	−10.4222	−1.47392
$51$	8.21110	1.14978
$52$	−0.183346	−0.0254255
$53$	−2.09167	−0.287313	−0.143657	−	0.989628i	$-0.545886\pi$
$53$	−2.09167	−0.287313	−0.143657	+	0.989628i	$0.545886\pi$
$54$	−7.30278	−0.993782
$55$	0	0
$56$	0	0
$57$	−3.90833	−0.517671
$58$	−10.8167	−1.42030
$59$	−10.3028	−1.34131	−0.670654	−	0.741771i	$-0.733986\pi$
$59$	−10.3028	−1.34131	−0.670654	+	0.741771i	$0.733986\pi$
$60$	1.42221	0.183606
$61$	0.697224	0.0892704	0.0446352	−	0.999003i	$-0.485787\pi$
$61$	0.697224	0.0892704	0.0446352	+	0.999003i	$0.485787\pi$
$62$	1.30278	0.165453
$63$	0	0
$64$	8.81665	1.10208
$65$	2.18335	0.270811
$66$	0	0
$67$	−9.51388	−1.16231	−0.581153	−	0.813795i	$-0.697398\pi$
$67$	−9.51388	−1.16231	−0.581153	+	0.813795i	$0.697398\pi$
$68$	1.90833	0.231419
$69$	8.21110	0.988501
$70$	0	0
$71$	−0.697224	−0.0827453	−0.0413727	−	0.999144i	$-0.513173\pi$
$71$	−0.697224	−0.0827453	−0.0413727	+	0.999144i	$0.513173\pi$
$72$	−3.90833	−0.460601
$73$	5.00000	0.585206	0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000	0.585206	0.292603	+	0.956234i	$0.405479\pi$
$74$	−12.0000	−1.39497
$75$	−10.4222	−1.20345
$76$	−0.908327	−0.104192
$77$	0	0
$78$	1.02776	0.116370
$79$	−4.69722	−0.528479	−0.264240	−	0.964457i	$-0.585121\pi$
$79$	−4.69722	−0.528479	−0.264240	+	0.964457i	$0.585121\pi$
$80$	−11.9083	−1.33139
$81$	−3.39445	−0.377161
$82$	9.11943	1.00707
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	0	0
$85$	−22.7250	−2.46487
$86$	−6.90833	−0.744944
$87$	−10.8167	−1.15967
$88$	0	0
$89$	−17.7250	−1.87884	−0.939422	−	0.342762i	$-0.888637\pi$
$89$	−17.7250	−1.87884	−0.939422	+	0.342762i	$0.888637\pi$
$90$	6.11943	0.645045
$91$	0	0
$92$	1.90833	0.198957
$93$	1.30278	0.135092
$94$	11.6056	1.19702
$95$	10.8167	1.10977
$96$	2.21110	0.225670
$97$	−3.60555	−0.366088	−0.183044	−	0.983105i	$-0.558595\pi$
$97$	−3.60555	−0.366088	−0.183044	+	0.983105i	$0.558595\pi$
$98$	0	0
$99$	0	0
$100$	−2.42221	−0.242221
$101$	1.69722	0.168880	0.0844401	−	0.996429i	$-0.473090\pi$
$101$	1.69722	0.168880	0.0844401	+	0.996429i	$0.473090\pi$
$102$	−10.6972	−1.05918
$103$	10.6972	1.05403	0.527014	−	0.849856i	$-0.323311\pi$
$103$	10.6972	1.05403	0.527014	+	0.849856i	$0.323311\pi$
$104$	1.81665	0.178138
$105$	0	0
$106$	2.72498	0.264674
$107$	19.6056	1.89534	0.947670	−	0.319251i	$-0.103431\pi$
$107$	19.6056	1.89534	0.947670	+	0.319251i	$0.103431\pi$
$108$	−1.69722	−0.163315
$109$	−8.00000	−0.766261	−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000	−0.766261	−0.383131	+	0.923694i	$0.625154\pi$
$110$	0	0
$111$	−12.0000	−1.13899
$112$	0	0
$113$	−14.3028	−1.34549	−0.672746	−	0.739874i	$-0.734885\pi$
$113$	−14.3028	−1.34549	−0.672746	+	0.739874i	$0.734885\pi$
$114$	5.09167	0.476879
$115$	−22.7250	−2.11912
$116$	−2.51388	−0.233408
$117$	−0.788897	−0.0729336
$118$	13.4222	1.23561
$119$	0	0
$120$	−14.0917	−1.28639
$121$	0	0
$122$	−0.908327	−0.0822361
$123$	9.11943	0.822271
$124$	0.302776	0.0271901
$125$	10.8167	0.967471
$126$	0	0
$127$	2.00000	0.177471	0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000	0.177471	0.0887357	+	0.996055i	$0.471717\pi$
$128$	−8.09167	−0.715210
$129$	−6.90833	−0.608244
$130$	−2.84441	−0.249471
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	0	0
$134$	12.3944	1.07072
$135$	20.2111	1.73949
$136$	−18.9083	−1.62138
$137$	15.1194	1.29174	0.645870	−	0.763447i	$-0.276495\pi$
$137$	15.1194	1.29174	0.645870	+	0.763447i	$0.276495\pi$
$138$	−10.6972	−0.910608
$139$	−14.3944	−1.22092	−0.610461	−	0.792047i	$-0.709016\pi$
$139$	−14.3944	−1.22092	−0.610461	+	0.792047i	$0.709016\pi$
$140$	0	0
$141$	11.6056	0.977364
$142$	0.908327	0.0762251
$143$	0	0
$144$	4.30278	0.358565
$145$	29.9361	2.48606
$146$	−6.51388	−0.539092
$147$	0	0
$148$	−2.78890	−0.229246
$149$	5.90833	0.484029	0.242015	−	0.970273i	$-0.422192\pi$
$149$	5.90833	0.484029	0.242015	+	0.970273i	$0.422192\pi$
$150$	13.5778	1.10862
$151$	14.2111	1.15648	0.578242	−	0.815866i	$-0.303739\pi$
$151$	14.2111	1.15648	0.578242	+	0.815866i	$0.303739\pi$
$152$	9.00000	0.729996
$153$	8.21110	0.663828
$154$	0	0
$155$	−3.60555	−0.289605
$156$	0.238859	0.0191240
$157$	7.21110	0.575509	0.287754	−	0.957704i	$-0.407091\pi$
$157$	7.21110	0.575509	0.287754	+	0.957704i	$0.407091\pi$
$158$	6.11943	0.486836
$159$	2.72498	0.216105
$160$	−6.11943	−0.483783
$161$	0	0
$162$	4.42221	0.347441
$163$	−18.8167	−1.47383	−0.736917	−	0.675983i	$-0.763719\pi$
$163$	−18.8167	−1.47383	−0.736917	+	0.675983i	$0.763719\pi$
$164$	2.11943	0.165500
$165$	0	0
$166$	3.90833	0.303345
$167$	−9.21110	−0.712777	−0.356388	−	0.934338i	$-0.615992\pi$
$167$	−9.21110	−0.712777	−0.356388	+	0.934338i	$0.615992\pi$
$168$	0	0
$169$	−12.6333	−0.971793
$170$	29.6056	2.27064
$171$	−3.90833	−0.298877
$172$	−1.60555	−0.122422
$173$	−2.30278	−0.175077	−0.0875384	−	0.996161i	$-0.527900\pi$
$173$	−2.30278	−0.175077	−0.0875384	+	0.996161i	$0.527900\pi$
$174$	14.0917	1.06829
$175$	0	0
$176$	0	0
$177$	13.4222	1.00887
$178$	23.0917	1.73079
$179$	−13.6056	−1.01693	−0.508463	−	0.861084i	$-0.669786\pi$
$179$	−13.6056	−1.01693	−0.508463	+	0.861084i	$0.669786\pi$
$180$	1.42221	0.106005
$181$	10.7889	0.801932	0.400966	−	0.916093i	$-0.368674\pi$
$181$	10.7889	0.801932	0.400966	+	0.916093i	$0.368674\pi$
$182$	0	0
$183$	−0.908327	−0.0671455
$184$	−18.9083	−1.39394
$185$	33.2111	2.44173
$186$	−1.69722	−0.124447
$187$	0	0
$188$	2.69722	0.196715
$189$	0	0
$190$	−14.0917	−1.02232
$191$	−5.18335	−0.375054	−0.187527	−	0.982259i	$-0.560047\pi$
$191$	−5.18335	−0.375054	−0.187527	+	0.982259i	$0.560047\pi$
$192$	−11.4861	−0.828939
$193$	23.1194	1.66417	0.832086	−	0.554646i	$-0.187146\pi$
$193$	23.1194	1.66417	0.832086	+	0.554646i	$0.187146\pi$
$194$	4.69722	0.337241
$195$	−2.84441	−0.203692
$196$	0	0
$197$	−3.39445	−0.241844	−0.120922	−	0.992662i	$-0.538585\pi$
$197$	−3.39445	−0.241844	−0.120922	+	0.992662i	$0.538585\pi$
$198$	0	0
$199$	9.42221	0.667922	0.333961	−	0.942587i	$-0.391615\pi$
$199$	9.42221	0.667922	0.333961	+	0.942587i	$0.391615\pi$
$200$	24.0000	1.69706
$201$	12.3944	0.874237
$202$	−2.21110	−0.155573
$203$	0	0
$204$	−2.48612	−0.174063
$205$	−25.2389	−1.76276
$206$	−13.9361	−0.970973
$207$	8.21110	0.570711
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	−2.51388	−0.173063	−0.0865313	−	0.996249i	$-0.527578\pi$
$211$	−2.51388	−0.173063	−0.0865313	+	0.996249i	$0.527578\pi$
$212$	0.633308	0.0434957
$213$	0.908327	0.0622375
$214$	−25.5416	−1.74599
$215$	19.1194	1.30393
$216$	16.8167	1.14423
$217$	0	0
$218$	10.4222	0.705881
$219$	−6.51388	−0.440167
$220$	0	0
$221$	−3.81665	−0.256736
$222$	15.6333	1.04924
$223$	−3.09167	−0.207034	−0.103517	−	0.994628i	$-0.533010\pi$
$223$	−3.09167	−0.207034	−0.103517	+	0.994628i	$0.533010\pi$
$224$	0	0
$225$	−10.4222	−0.694814
$226$	18.6333	1.23947
$227$	11.5139	0.764203	0.382101	−	0.924120i	$-0.375200\pi$
$227$	11.5139	0.764203	0.382101	+	0.924120i	$0.375200\pi$
$228$	1.18335	0.0783690
$229$	−4.60555	−0.304343	−0.152172	−	0.988354i	$-0.548627\pi$
$229$	−4.60555	−0.304343	−0.152172	+	0.988354i	$0.548627\pi$
$230$	29.6056	1.95213
$231$	0	0
$232$	24.9083	1.63531
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	1.02776	0.0671865
$235$	−32.1194	−2.09524
$236$	3.11943	0.203058
$237$	6.11943	0.397500
$238$	0	0
$239$	−13.3305	−0.862280	−0.431140	−	0.902285i	$-0.641889\pi$
$239$	−13.3305	−0.862280	−0.431140	+	0.902285i	$0.641889\pi$
$240$	15.5139	1.00142
$241$	−18.5139	−1.19258	−0.596292	−	0.802768i	$-0.703360\pi$
$241$	−18.5139	−1.19258	−0.596292	+	0.802768i	$0.703360\pi$
$242$	0	0
$243$	−12.3944	−0.795104
$244$	−0.211103	−0.0135145
$245$	0	0
$246$	−11.8806	−0.757478
$247$	1.81665	0.115591
$248$	−3.00000	−0.190500
$249$	3.90833	0.247680
$250$	−14.0917	−0.891236
$251$	−11.6056	−0.732536	−0.366268	−	0.930509i	$-0.619365\pi$
$251$	−11.6056	−0.732536	−0.366268	+	0.930509i	$0.619365\pi$
$252$	0	0
$253$	0	0
$254$	−2.60555	−0.163487
$255$	29.6056	1.85397
$256$	−7.09167	−0.443230
$257$	−24.5139	−1.52913	−0.764567	−	0.644544i	$-0.777047\pi$
$257$	−24.5139	−1.52913	−0.764567	+	0.644544i	$0.777047\pi$
$258$	9.00000	0.560316
$259$	0	0
$260$	−0.661064	−0.0409975
$261$	−10.8167	−0.669534
$262$	−7.81665	−0.482914
$263$	−30.2389	−1.86461	−0.932304	−	0.361676i	$-0.882205\pi$
$263$	−30.2389	−1.86461	−0.932304	+	0.361676i	$0.882205\pi$
$264$	0	0
$265$	−7.54163	−0.463279
$266$	0	0
$267$	23.0917	1.41319
$268$	2.88057	0.175959
$269$	9.11943	0.556021	0.278011	−	0.960578i	$-0.410325\pi$
$269$	9.11943	0.556021	0.278011	+	0.960578i	$0.410325\pi$
$270$	−26.3305	−1.60243
$271$	10.4861	0.636987	0.318493	−	0.947925i	$-0.396823\pi$
$271$	10.4861	0.636987	0.318493	+	0.947925i	$0.396823\pi$
$272$	20.8167	1.26220
$273$	0	0
$274$	−19.6972	−1.18995
$275$	0	0
$276$	−2.48612	−0.149647
$277$	−16.9361	−1.01759	−0.508795	−	0.860888i	$-0.669909\pi$
$277$	−16.9361	−1.01759	−0.508795	+	0.860888i	$0.669909\pi$
$278$	18.7527	1.12471
$279$	1.30278	0.0779951
$280$	0	0
$281$	13.6056	0.811639	0.405820	−	0.913953i	$-0.366986\pi$
$281$	13.6056	0.811639	0.405820	+	0.913953i	$0.366986\pi$
$282$	−15.1194	−0.900349
$283$	−11.6056	−0.689878	−0.344939	−	0.938625i	$-0.612100\pi$
$283$	−11.6056	−0.689878	−0.344939	+	0.938625i	$0.612100\pi$
$284$	0.211103	0.0125266
$285$	−14.0917	−0.834719
$286$	0	0
$287$	0	0
$288$	2.21110	0.130290
$289$	22.7250	1.33676
$290$	−39.0000	−2.29016
$291$	4.69722	0.275356
$292$	−1.51388	−0.0885930
$293$	16.8167	0.982439	0.491220	−	0.871036i	$-0.336551\pi$
$293$	16.8167	0.982439	0.491220	+	0.871036i	$0.336551\pi$
$294$	0	0
$295$	−37.1472	−2.16279
$296$	27.6333	1.60615
$297$	0	0
$298$	−7.69722	−0.445888
$299$	−3.81665	−0.220723
$300$	3.15559	0.182188
$301$	0	0
$302$	−18.5139	−1.06535
$303$	−2.21110	−0.127025
$304$	−9.90833	−0.568282
$305$	2.51388	0.143944
$306$	−10.6972	−0.611520
$307$	−26.6333	−1.52004	−0.760022	−	0.649898i	$-0.774812\pi$
$307$	−26.6333	−1.52004	−0.760022	+	0.649898i	$0.774812\pi$
$308$	0	0
$309$	−13.9361	−0.792796
$310$	4.69722	0.266784
$311$	−13.6056	−0.771500	−0.385750	−	0.922603i	$-0.626057\pi$
$311$	−13.6056	−0.771500	−0.385750	+	0.922603i	$0.626057\pi$
$312$	−2.36669	−0.133988
$313$	−11.6972	−0.661166	−0.330583	−	0.943777i	$-0.607245\pi$
$313$	−11.6972	−0.661166	−0.330583	+	0.943777i	$0.607245\pi$
$314$	−9.39445	−0.530159
$315$	0	0
$316$	1.42221	0.0800053
$317$	13.6972	0.769313	0.384656	−	0.923060i	$-0.374320\pi$
$317$	13.6972	0.769313	0.384656	+	0.923060i	$0.374320\pi$
$318$	−3.55004	−0.199076
$319$	0	0
$320$	31.7889	1.77705
$321$	−25.5416	−1.42560
$322$	0	0
$323$	−18.9083	−1.05209
$324$	1.02776	0.0570976
$325$	4.84441	0.268720
$326$	24.5139	1.35770
$327$	10.4222	0.576349
$328$	−21.0000	−1.15953
$329$	0	0
$330$	0	0
$331$	2.18335	0.120008	0.0600038	−	0.998198i	$-0.480889\pi$
$331$	2.18335	0.120008	0.0600038	+	0.998198i	$0.480889\pi$
$332$	0.908327	0.0498509
$333$	−12.0000	−0.657596
$334$	12.0000	0.656611
$335$	−34.3028	−1.87416
$336$	0	0
$337$	26.2111	1.42781	0.713905	−	0.700243i	$-0.246925\pi$
$337$	26.2111	1.42781	0.713905	+	0.700243i	$0.246925\pi$
$338$	16.4584	0.895217
$339$	18.6333	1.01202
$340$	6.88057	0.373151
$341$	0	0
$342$	5.09167	0.275326
$343$	0	0
$344$	15.9083	0.857720
$345$	29.6056	1.59391
$346$	3.00000	0.161281
$347$	2.39445	0.128541	0.0642704	−	0.997933i	$-0.479528\pi$
$347$	2.39445	0.128541	0.0642704	+	0.997933i	$0.479528\pi$
$348$	3.27502	0.175559
$349$	8.30278	0.444437	0.222219	−	0.974997i	$-0.428670\pi$
$349$	8.30278	0.444437	0.222219	+	0.974997i	$0.428670\pi$
$350$	0	0
$351$	3.39445	0.181182
$352$	0	0
$353$	−15.9083	−0.846715	−0.423357	−	0.905963i	$-0.639149\pi$
$353$	−15.9083	−0.846715	−0.423357	+	0.905963i	$0.639149\pi$
$354$	−17.4861	−0.929377
$355$	−2.51388	−0.133423
$356$	5.36669	0.284434
$357$	0	0
$358$	17.7250	0.936794
$359$	12.9361	0.682740	0.341370	−	0.939929i	$-0.389109\pi$
$359$	12.9361	0.682740	0.341370	+	0.939929i	$0.389109\pi$
$360$	−14.0917	−0.742696
$361$	−10.0000	−0.526316
$362$	−14.0555	−0.738741
$363$	0	0
$364$	0	0
$365$	18.0278	0.943616
$366$	1.18335	0.0618545
$367$	−25.6333	−1.33805	−0.669024	−	0.743241i	$-0.733288\pi$
$367$	−25.6333	−1.33805	−0.669024	+	0.743241i	$0.733288\pi$
$368$	20.8167	1.08514
$369$	9.11943	0.474739
$370$	−43.2666	−2.24932
$371$	0	0
$372$	−0.394449	−0.0204512
$373$	5.11943	0.265074	0.132537	−	0.991178i	$-0.457688\pi$
$373$	5.11943	0.265074	0.132537	+	0.991178i	$0.457688\pi$
$374$	0	0
$375$	−14.0917	−0.727691
$376$	−26.7250	−1.37824
$377$	5.02776	0.258943
$378$	0	0
$379$	5.81665	0.298781	0.149391	−	0.988778i	$-0.452269\pi$
$379$	5.81665	0.298781	0.149391	+	0.988778i	$0.452269\pi$
$380$	−3.27502	−0.168005
$381$	−2.60555	−0.133486
$382$	6.75274	0.345500
$383$	4.63331	0.236751	0.118375	−	0.992969i	$-0.462231\pi$
$383$	4.63331	0.236751	0.118375	+	0.992969i	$0.462231\pi$
$384$	10.5416	0.537951
$385$	0	0
$386$	−30.1194	−1.53304
$387$	−6.90833	−0.351170
$388$	1.09167	0.0554213
$389$	13.8167	0.700532	0.350266	−	0.936650i	$-0.386091\pi$
$389$	13.8167	0.700532	0.350266	+	0.936650i	$0.386091\pi$
$390$	3.70563	0.187642
$391$	39.7250	2.00898
$392$	0	0
$393$	−7.81665	−0.394298
$394$	4.42221	0.222787
$395$	−16.9361	−0.852147
$396$	0	0
$397$	−15.7889	−0.792422	−0.396211	−	0.918159i	$-0.629675\pi$
$397$	−15.7889	−0.792422	−0.396211	+	0.918159i	$0.629675\pi$
$398$	−12.2750	−0.615291
$399$	0	0
$400$	−26.4222	−1.32111
$401$	−6.78890	−0.339021	−0.169511	−	0.985528i	$-0.554219\pi$
$401$	−6.78890	−0.339021	−0.169511	+	0.985528i	$0.554219\pi$
$402$	−16.1472	−0.805348
$403$	−0.605551	−0.0301647
$404$	−0.513878	−0.0255664
$405$	−12.2389	−0.608154
$406$	0	0
$407$	0	0
$408$	24.6333	1.21953
$409$	−13.3944	−0.662313	−0.331156	−	0.943576i	$-0.607439\pi$
$409$	−13.3944	−0.662313	−0.331156	+	0.943576i	$0.607439\pi$
$410$	32.8806	1.62386
$411$	−19.6972	−0.971592
$412$	−3.23886	−0.159567
$413$	0	0
$414$	−10.6972	−0.525740
$415$	−10.8167	−0.530969
$416$	−1.02776	−0.0503899
$417$	18.7527	0.918325
$418$	0	0
$419$	9.57779	0.467906	0.233953	−	0.972248i	$-0.424834\pi$
$419$	9.57779	0.467906	0.233953	+	0.972248i	$0.424834\pi$
$420$	0	0
$421$	−0.183346	−0.00893575	−0.00446787	−	0.999990i	$-0.501422\pi$
$421$	−0.183346	−0.00893575	−0.00446787	+	0.999990i	$0.501422\pi$
$422$	3.27502	0.159425
$423$	11.6056	0.564281
$424$	−6.27502	−0.304742
$425$	−50.4222	−2.44584
$426$	−1.18335	−0.0573333
$427$	0	0
$428$	−5.93608	−0.286931
$429$	0	0
$430$	−24.9083	−1.20119
$431$	22.1194	1.06546	0.532728	−	0.846287i	$-0.321167\pi$
$431$	22.1194	1.06546	0.532728	+	0.846287i	$0.321167\pi$
$432$	−18.5139	−0.890749
$433$	32.1472	1.54490	0.772448	−	0.635079i	$-0.219032\pi$
$433$	32.1472	1.54490	0.772448	+	0.635079i	$0.219032\pi$
$434$	0	0
$435$	−39.0000	−1.86991
$436$	2.42221	0.116003
$437$	−18.9083	−0.904508
$438$	8.48612	0.405483
$439$	4.72498	0.225511	0.112756	−	0.993623i	$-0.464032\pi$
$439$	4.72498	0.225511	0.112756	+	0.993623i	$0.464032\pi$
$440$	0	0
$441$	0	0
$442$	4.97224	0.236506
$443$	−19.9361	−0.947192	−0.473596	−	0.880742i	$-0.657044\pi$
$443$	−19.9361	−0.947192	−0.473596	+	0.880742i	$0.657044\pi$
$444$	3.63331	0.172429
$445$	−63.9083	−3.02955
$446$	4.02776	0.190720
$447$	−7.69722	−0.364066
$448$	0	0
$449$	0.669468	0.0315941	0.0157971	−	0.999875i	$-0.494971\pi$
$449$	0.669468	0.0315941	0.0157971	+	0.999875i	$0.494971\pi$
$450$	13.5778	0.640063
$451$	0	0
$452$	4.33053	0.203691
$453$	−18.5139	−0.869858
$454$	−15.0000	−0.703985
$455$	0	0
$456$	−11.7250	−0.549073
$457$	−4.11943	−0.192699	−0.0963494	−	0.995348i	$-0.530717\pi$
$457$	−4.11943	−0.192699	−0.0963494	+	0.995348i	$0.530717\pi$
$458$	6.00000	0.280362
$459$	−35.3305	−1.64909
$460$	6.88057	0.320808
$461$	−18.9083	−0.880649	−0.440324	−	0.897839i	$-0.645137\pi$
$461$	−18.9083	−0.880649	−0.440324	+	0.897839i	$0.645137\pi$
$462$	0	0
$463$	−9.18335	−0.426786	−0.213393	−	0.976966i	$-0.568452\pi$
$463$	−9.18335	−0.426786	−0.213393	+	0.976966i	$0.568452\pi$
$464$	−27.4222	−1.27304
$465$	4.69722	0.217829
$466$	−23.4500	−1.08630
$467$	−40.5416	−1.87604	−0.938022	−	0.346577i	$-0.887344\pi$
$467$	−40.5416	−1.87604	−0.938022	+	0.346577i	$0.887344\pi$
$468$	0.238859	0.0110413
$469$	0	0
$470$	41.8444	1.93014
$471$	−9.39445	−0.432873
$472$	−30.9083	−1.42267
$473$	0	0
$474$	−7.97224	−0.366177
$475$	24.0000	1.10120
$476$	0	0
$477$	2.72498	0.124768
$478$	17.3667	0.794334
$479$	−14.6333	−0.668613	−0.334306	−	0.942464i	$-0.608502\pi$
$479$	−14.6333	−0.668613	−0.334306	+	0.942464i	$0.608502\pi$
$480$	7.97224	0.363881
$481$	5.57779	0.254326
$482$	24.1194	1.09861
$483$	0	0
$484$	0	0
$485$	−13.0000	−0.590300
$486$	16.1472	0.732451
$487$	18.8167	0.852664	0.426332	−	0.904567i	$-0.359806\pi$
$487$	18.8167	0.852664	0.426332	+	0.904567i	$0.359806\pi$
$488$	2.09167	0.0946856
$489$	24.5139	1.10856
$490$	0	0
$491$	−16.3028	−0.735734	−0.367867	−	0.929878i	$-0.619912\pi$
$491$	−16.3028	−0.735734	−0.367867	+	0.929878i	$0.619912\pi$
$492$	−2.76114	−0.124482
$493$	−52.3305	−2.35685
$494$	−2.36669	−0.106483
$495$	0	0
$496$	3.30278	0.148299
$497$	0	0
$498$	−5.09167	−0.228163
$499$	−7.90833	−0.354025	−0.177013	−	0.984209i	$-0.556643\pi$
$499$	−7.90833	−0.354025	−0.177013	+	0.984209i	$0.556643\pi$
$500$	−3.27502	−0.146463
$501$	12.0000	0.536120
$502$	15.1194	0.674813
$503$	−34.4222	−1.53481	−0.767405	−	0.641163i	$-0.778452\pi$
$503$	−34.4222	−1.53481	−0.767405	+	0.641163i	$0.778452\pi$
$504$	0	0
$505$	6.11943	0.272311
$506$	0	0
$507$	16.4584	0.730942
$508$	−0.605551	−0.0268670
$509$	−18.6972	−0.828740	−0.414370	−	0.910109i	$-0.635998\pi$
$509$	−18.6972	−0.828740	−0.414370	+	0.910109i	$0.635998\pi$
$510$	−38.5694	−1.70788
$511$	0	0
$512$	25.4222	1.12351
$513$	16.8167	0.742473
$514$	31.9361	1.40864
$515$	38.5694	1.69957
$516$	2.09167	0.0920808
$517$	0	0
$518$	0	0
$519$	3.00000	0.131685
$520$	6.55004	0.287238
$521$	21.4222	0.938524	0.469262	−	0.883059i	$-0.344520\pi$
$521$	21.4222	0.938524	0.469262	+	0.883059i	$0.344520\pi$
$522$	14.0917	0.616776
$523$	−9.54163	−0.417227	−0.208613	−	0.977998i	$-0.566895\pi$
$523$	−9.54163	−0.417227	−0.208613	+	0.977998i	$0.566895\pi$
$524$	−1.81665	−0.0793609
$525$	0	0
$526$	39.3944	1.71768
$527$	6.30278	0.274553
$528$	0	0
$529$	16.7250	0.727173
$530$	9.82506	0.426773
$531$	13.4222	0.582474
$532$	0	0
$533$	−4.23886	−0.183605
$534$	−30.0833	−1.30183
$535$	70.6888	3.05614
$536$	−28.5416	−1.23281
$537$	17.7250	0.764889
$538$	−11.8806	−0.512208
$539$	0	0
$540$	−6.11943	−0.263338
$541$	−39.6056	−1.70278	−0.851388	−	0.524537i	$-0.824239\pi$
$541$	−39.6056	−1.70278	−0.851388	+	0.524537i	$0.824239\pi$
$542$	−13.6611	−0.586793
$543$	−14.0555	−0.603180
$544$	10.6972	0.458640
$545$	−28.8444	−1.23556
$546$	0	0
$547$	16.9361	0.724135	0.362067	−	0.932152i	$-0.382071\pi$
$547$	16.9361	0.724135	0.362067	+	0.932152i	$0.382071\pi$
$548$	−4.57779	−0.195554
$549$	−0.908327	−0.0387664
$550$	0	0
$551$	24.9083	1.06113
$552$	24.6333	1.04846
$553$	0	0
$554$	22.0639	0.937406
$555$	−43.2666	−1.83657
$556$	4.35829	0.184833
$557$	−43.2389	−1.83209	−0.916045	−	0.401076i	$-0.868636\pi$
$557$	−43.2389	−1.83209	−0.916045	+	0.401076i	$0.868636\pi$
$558$	−1.69722	−0.0718492
$559$	3.21110	0.135815
$560$	0	0
$561$	0	0
$562$	−17.7250	−0.747683
$563$	−3.30278	−0.139195	−0.0695977	−	0.997575i	$-0.522172\pi$
$563$	−3.30278	−0.139195	−0.0695977	+	0.997575i	$0.522172\pi$
$564$	−3.51388	−0.147961
$565$	−51.5694	−2.16954
$566$	15.1194	0.635517
$567$	0	0
$568$	−2.09167	−0.0877647
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	18.3583	0.768944
$571$	−31.8444	−1.33265	−0.666324	−	0.745663i	$-0.732133\pi$
$571$	−31.8444	−1.33265	−0.666324	+	0.745663i	$0.732133\pi$
$572$	0	0
$573$	6.75274	0.282100
$574$	0	0
$575$	−50.4222	−2.10275
$576$	−11.4861	−0.478588
$577$	12.2111	0.508355	0.254177	−	0.967158i	$-0.418195\pi$
$577$	12.2111	0.508355	0.254177	+	0.967158i	$0.418195\pi$
$578$	−29.6056	−1.23143
$579$	−30.1194	−1.25172
$580$	−9.06392	−0.376359
$581$	0	0
$582$	−6.11943	−0.253659
$583$	0	0
$584$	15.0000	0.620704
$585$	−2.84441	−0.117602
$586$	−21.9083	−0.905025
$587$	6.39445	0.263927	0.131964	−	0.991255i	$-0.457872\pi$
$587$	6.39445	0.263927	0.131964	+	0.991255i	$0.457872\pi$
$588$	0	0
$589$	−3.00000	−0.123613
$590$	48.3944	1.99237
$591$	4.42221	0.181905
$592$	−30.4222	−1.25034
$593$	−15.3944	−0.632174	−0.316087	−	0.948730i	$-0.602369\pi$
$593$	−15.3944	−0.632174	−0.316087	+	0.948730i	$0.602369\pi$
$594$	0	0
$595$	0	0
$596$	−1.78890	−0.0732761
$597$	−12.2750	−0.502383
$598$	4.97224	0.203330
$599$	−29.2111	−1.19353	−0.596767	−	0.802415i	$-0.703548\pi$
$599$	−29.2111	−1.19353	−0.596767	+	0.802415i	$0.703548\pi$
$600$	−31.2666	−1.27645
$601$	−15.8167	−0.645175	−0.322587	−	0.946540i	$-0.604553\pi$
$601$	−15.8167	−0.645175	−0.322587	+	0.946540i	$0.604553\pi$
$602$	0	0
$603$	12.3944	0.504741
$604$	−4.30278	−0.175077
$605$	0	0
$606$	2.88057	0.117015
$607$	−33.5416	−1.36141	−0.680706	−	0.732556i	$-0.738327\pi$
$607$	−33.5416	−1.36141	−0.680706	+	0.732556i	$0.738327\pi$
$608$	−5.09167	−0.206495
$609$	0	0
$610$	−3.27502	−0.132602
$611$	−5.39445	−0.218236
$612$	−2.48612	−0.100496
$613$	39.0555	1.57744	0.788719	−	0.614754i	$-0.210745\pi$
$613$	39.0555	1.57744	0.788719	+	0.614754i	$0.210745\pi$
$614$	34.6972	1.40027
$615$	32.8806	1.32587
$616$	0	0
$617$	−21.6333	−0.870924	−0.435462	−	0.900207i	$-0.643415\pi$
$617$	−21.6333	−0.870924	−0.435462	+	0.900207i	$0.643415\pi$
$618$	18.1556	0.730325
$619$	−18.1833	−0.730850	−0.365425	−	0.930841i	$-0.619076\pi$
$619$	−18.1833	−0.730850	−0.365425	+	0.930841i	$0.619076\pi$
$620$	1.09167	0.0438426
$621$	−35.3305	−1.41777
$622$	17.7250	0.710707
$623$	0	0
$624$	2.60555	0.104306
$625$	−1.00000	−0.0400000
$626$	15.2389	0.609067
$627$	0	0
$628$	−2.18335	−0.0871250
$629$	−58.0555	−2.31482
$630$	0	0
$631$	41.0555	1.63439	0.817197	−	0.576358i	$-0.195527\pi$
$631$	41.0555	1.63439	0.817197	+	0.576358i	$0.195527\pi$
$632$	−14.0917	−0.560537
$633$	3.27502	0.130170
$634$	−17.8444	−0.708692
$635$	7.21110	0.286164
$636$	−0.825058	−0.0327157
$637$	0	0
$638$	0	0
$639$	0.908327	0.0359329
$640$	−29.1749	−1.15324
$641$	−7.18335	−0.283725	−0.141863	−	0.989886i	$-0.545309\pi$
$641$	−7.18335	−0.283725	−0.141863	+	0.989886i	$0.545309\pi$
$642$	33.2750	1.31326
$643$	−49.2389	−1.94179	−0.970896	−	0.239503i	$-0.923015\pi$
$643$	−49.2389	−1.94179	−0.970896	+	0.239503i	$0.923015\pi$
$644$	0	0
$645$	−24.9083	−0.980764
$646$	24.6333	0.969185
$647$	−3.39445	−0.133450	−0.0667248	−	0.997771i	$-0.521255\pi$
$647$	−3.39445	−0.133450	−0.0667248	+	0.997771i	$0.521255\pi$
$648$	−10.1833	−0.400040
$649$	0	0
$650$	−6.31118	−0.247545
$651$	0	0
$652$	5.69722	0.223121
$653$	14.8167	0.579820	0.289910	−	0.957054i	$-0.406375\pi$
$653$	14.8167	0.579820	0.289910	+	0.957054i	$0.406375\pi$
$654$	−13.5778	−0.530934
$655$	21.6333	0.845283
$656$	23.1194	0.902662
$657$	−6.51388	−0.254131
$658$	0	0
$659$	−38.6333	−1.50494	−0.752470	−	0.658627i	$-0.771138\pi$
$659$	−38.6333	−1.50494	−0.752470	+	0.658627i	$0.771138\pi$
$660$	0	0
$661$	14.6972	0.571656	0.285828	−	0.958281i	$-0.407731\pi$
$661$	14.6972	0.571656	0.285828	+	0.958281i	$0.407731\pi$
$662$	−2.84441	−0.110551
$663$	4.97224	0.193106
$664$	−9.00000	−0.349268
$665$	0	0
$666$	15.6333	0.605778
$667$	−52.3305	−2.02625
$668$	2.78890	0.107906
$669$	4.02776	0.155722
$670$	44.6888	1.72648
$671$	0	0
$672$	0	0
$673$	20.4222	0.787218	0.393609	−	0.919278i	$-0.371226\pi$
$673$	20.4222	0.787218	0.393609	+	0.919278i	$0.371226\pi$
$674$	−34.1472	−1.31530
$675$	44.8444	1.72606
$676$	3.82506	0.147118
$677$	−6.69722	−0.257395	−0.128698	−	0.991684i	$-0.541080\pi$
$677$	−6.69722	−0.257395	−0.128698	+	0.991684i	$0.541080\pi$
$678$	−24.2750	−0.932276
$679$	0	0
$680$	−68.1749	−2.61439
$681$	−15.0000	−0.574801
$682$	0	0
$683$	19.3028	0.738600	0.369300	−	0.929310i	$-0.379597\pi$
$683$	19.3028	0.738600	0.369300	+	0.929310i	$0.379597\pi$
$684$	1.18335	0.0452464
$685$	54.5139	2.08287
$686$	0	0
$687$	6.00000	0.228914
$688$	−17.5139	−0.667710
$689$	−1.26662	−0.0482542
$690$	−38.5694	−1.46831
$691$	−19.0278	−0.723850	−0.361925	−	0.932207i	$-0.617880\pi$
$691$	−19.0278	−0.723850	−0.361925	+	0.932207i	$0.617880\pi$
$692$	0.697224	0.0265045
$693$	0	0
$694$	−3.11943	−0.118412
$695$	−51.8999	−1.96868
$696$	−32.4500	−1.23001
$697$	44.1194	1.67114
$698$	−10.8167	−0.409416
$699$	−23.4500	−0.886959
$700$	0	0
$701$	−5.88057	−0.222106	−0.111053	−	0.993814i	$-0.535422\pi$
$701$	−5.88057	−0.222106	−0.111053	+	0.993814i	$0.535422\pi$
$702$	−4.42221	−0.166905
$703$	27.6333	1.04221
$704$	0	0
$705$	41.8444	1.57595
$706$	20.7250	0.779995
$707$	0	0
$708$	−4.06392	−0.152731
$709$	−14.3305	−0.538194	−0.269097	−	0.963113i	$-0.586725\pi$
$709$	−14.3305	−0.538194	−0.269097	+	0.963113i	$0.586725\pi$
$710$	3.27502	0.122909
$711$	6.11943	0.229497
$712$	−53.1749	−1.99282
$713$	6.30278	0.236041
$714$	0	0
$715$	0	0
$716$	4.11943	0.153950
$717$	17.3667	0.648571
$718$	−16.8528	−0.628941
$719$	29.2389	1.09043	0.545213	−	0.838298i	$-0.316449\pi$
$719$	29.2389	1.09043	0.545213	+	0.838298i	$0.316449\pi$
$720$	15.5139	0.578168
$721$	0	0
$722$	13.0278	0.484843
$723$	24.1194	0.897011
$724$	−3.26662	−0.121403
$725$	66.4222	2.46686
$726$	0	0
$727$	1.11943	0.0415173	0.0207587	−	0.999785i	$-0.493392\pi$
$727$	1.11943	0.0415173	0.0207587	+	0.999785i	$0.493392\pi$
$728$	0	0
$729$	26.3305	0.975205
$730$	−23.4861	−0.869260
$731$	−33.4222	−1.23616
$732$	0.275019	0.0101650
$733$	21.2111	0.783450	0.391725	−	0.920082i	$-0.371878\pi$
$733$	21.2111	0.783450	0.391725	+	0.920082i	$0.371878\pi$
$734$	33.3944	1.23261
$735$	0	0
$736$	10.6972	0.394305
$737$	0	0
$738$	−11.8806	−0.437330
$739$	−17.8806	−0.657747	−0.328874	−	0.944374i	$-0.606669\pi$
$739$	−17.8806	−0.657747	−0.328874	+	0.944374i	$0.606669\pi$
$740$	−10.0555	−0.369648
$741$	−2.36669	−0.0869426
$742$	0	0
$743$	−1.93608	−0.0710280	−0.0355140	−	0.999369i	$-0.511307\pi$
$743$	−1.93608	−0.0710280	−0.0355140	+	0.999369i	$0.511307\pi$
$744$	3.90833	0.143286
$745$	21.3028	0.780473
$746$	−6.66947	−0.244187
$747$	3.90833	0.142998
$748$	0	0
$749$	0	0
$750$	18.3583	0.670350
$751$	−35.6333	−1.30028	−0.650139	−	0.759815i	$-0.725289\pi$
$751$	−35.6333	−1.30028	−0.650139	+	0.759815i	$0.725289\pi$
$752$	29.4222	1.07292
$753$	15.1194	0.550983
$754$	−6.55004	−0.238538
$755$	51.2389	1.86477
$756$	0	0
$757$	−2.18335	−0.0793551	−0.0396775	−	0.999213i	$-0.512633\pi$
$757$	−2.18335	−0.0793551	−0.0396775	+	0.999213i	$0.512633\pi$
$758$	−7.57779	−0.275238
$759$	0	0
$760$	32.4500	1.17708
$761$	−42.0000	−1.52250	−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000	−1.52250	−0.761249	+	0.648459i	$0.775414\pi$
$762$	3.39445	0.122968
$763$	0	0
$764$	1.56939	0.0567786
$765$	29.6056	1.07039
$766$	−6.03616	−0.218095
$767$	−6.23886	−0.225272
$768$	9.23886	0.333379
$769$	−0.330532	−0.0119193	−0.00595964	−	0.999982i	$-0.501897\pi$
$769$	−0.330532	−0.0119193	−0.00595964	+	0.999982i	$0.501897\pi$
$770$	0	0
$771$	31.9361	1.15015
$772$	−7.00000	−0.251936
$773$	12.6333	0.454388	0.227194	−	0.973849i	$-0.427045\pi$
$773$	12.6333	0.454388	0.227194	+	0.973849i	$0.427045\pi$
$774$	9.00000	0.323498
$775$	−8.00000	−0.287368
$776$	−10.8167	−0.388295
$777$	0	0
$778$	−18.0000	−0.645331
$779$	−21.0000	−0.752403
$780$	0.861218	0.0308366
$781$	0	0
$782$	−51.7527	−1.85067
$783$	46.5416	1.66326
$784$	0	0
$785$	26.0000	0.927980
$786$	10.1833	0.363228
$787$	40.5139	1.44416	0.722082	−	0.691808i	$-0.243185\pi$
$787$	40.5139	1.44416	0.722082	+	0.691808i	$0.243185\pi$
$788$	1.02776	0.0366123
$789$	39.3944	1.40248
$790$	22.0639	0.784999
$791$	0	0
$792$	0	0
$793$	0.422205	0.0149929
$794$	20.5694	0.729980
$795$	9.82506	0.348459
$796$	−2.85281	−0.101115
$797$	−14.6333	−0.518338	−0.259169	−	0.965832i	$-0.583449\pi$
$797$	−14.6333	−0.518338	−0.259169	+	0.965832i	$0.583449\pi$
$798$	0	0
$799$	56.1472	1.98634
$800$	−13.5778	−0.480048
$801$	23.0917	0.815904
$802$	8.84441	0.312307
$803$	0	0
$804$	−3.75274	−0.132349
$805$	0	0
$806$	0.788897	0.0277877
$807$	−11.8806	−0.418216
$808$	5.09167	0.179124
$809$	18.9083	0.664781	0.332391	−	0.943142i	$-0.392145\pi$
$809$	18.9083	0.664781	0.332391	+	0.943142i	$0.392145\pi$
$810$	15.9445	0.560232
$811$	−16.8444	−0.591487	−0.295744	−	0.955267i	$-0.595567\pi$
$811$	−16.8444	−0.591487	−0.295744	+	0.955267i	$0.595567\pi$
$812$	0	0
$813$	−13.6611	−0.479114
$814$	0	0
$815$	−67.8444	−2.37649
$816$	−27.1194	−0.949370
$817$	15.9083	0.556562
$818$	17.4500	0.610124
$819$	0	0
$820$	7.64171	0.266860
$821$	1.42221	0.0496353	0.0248177	−	0.999692i	$-0.492099\pi$
$821$	1.42221	0.0496353	0.0248177	+	0.999692i	$0.492099\pi$
$822$	25.6611	0.895032
$823$	20.7889	0.724655	0.362328	−	0.932051i	$-0.381982\pi$
$823$	20.7889	0.724655	0.362328	+	0.932051i	$0.381982\pi$
$824$	32.0917	1.11797
$825$	0	0
$826$	0	0
$827$	−35.8167	−1.24547	−0.622734	−	0.782434i	$-0.713978\pi$
$827$	−35.8167	−1.24547	−0.622734	+	0.782434i	$0.713978\pi$
$828$	−2.48612	−0.0863987
$829$	−45.7250	−1.58809	−0.794047	−	0.607856i	$-0.792030\pi$
$829$	−45.7250	−1.58809	−0.794047	+	0.607856i	$0.792030\pi$
$830$	14.0917	0.489129
$831$	22.0639	0.765389
$832$	5.33894	0.185094
$833$	0	0
$834$	−24.4306	−0.845963
$835$	−33.2111	−1.14932
$836$	0	0
$837$	−5.60555	−0.193756
$838$	−12.4777	−0.431036
$839$	−27.7889	−0.959379	−0.479690	−	0.877438i	$-0.659251\pi$
$839$	−27.7889	−0.959379	−0.479690	+	0.877438i	$0.659251\pi$
$840$	0	0
$841$	39.9361	1.37711
$842$	0.238859	0.00823162
$843$	−17.7250	−0.610481
$844$	0.761141	0.0261996
$845$	−45.5500	−1.56697
$846$	−15.1194	−0.519817
$847$	0	0
$848$	6.90833	0.237233
$849$	15.1194	0.518897
$850$	65.6888	2.25311
$851$	−58.0555	−1.99012
$852$	−0.275019	−0.00942200
$853$	13.2750	0.454528	0.227264	−	0.973833i	$-0.427022\pi$
$853$	13.2750	0.454528	0.227264	+	0.973833i	$0.427022\pi$
$854$	0	0
$855$	−14.0917	−0.481925
$856$	58.8167	2.01031
$857$	40.3583	1.37861	0.689306	−	0.724470i	$-0.257915\pi$
$857$	40.3583	1.37861	0.689306	+	0.724470i	$0.257915\pi$
$858$	0	0
$859$	21.6972	0.740300	0.370150	−	0.928972i	$-0.379306\pi$
$859$	21.6972	0.740300	0.370150	+	0.928972i	$0.379306\pi$
$860$	−5.78890	−0.197400
$861$	0	0
$862$	−28.8167	−0.981499
$863$	2.57779	0.0877492	0.0438746	−	0.999037i	$-0.486030\pi$
$863$	2.57779	0.0877492	0.0438746	+	0.999037i	$0.486030\pi$
$864$	−9.51388	−0.323669
$865$	−8.30278	−0.282303
$866$	−41.8806	−1.42316
$867$	−29.6056	−1.00546
$868$	0	0
$869$	0	0
$870$	50.8082	1.72256
$871$	−5.76114	−0.195209
$872$	−24.0000	−0.812743
$873$	4.69722	0.158977
$874$	24.6333	0.833234
$875$	0	0
$876$	1.97224	0.0666359
$877$	−25.0555	−0.846065	−0.423032	−	0.906115i	$-0.639034\pi$
$877$	−25.0555	−0.846065	−0.423032	+	0.906115i	$0.639034\pi$
$878$	−6.15559	−0.207741
$879$	−21.9083	−0.738950
$880$	0	0
$881$	5.33053	0.179590	0.0897951	−	0.995960i	$-0.471379\pi$
$881$	5.33053	0.179590	0.0897951	+	0.995960i	$0.471379\pi$
$882$	0	0
$883$	24.7250	0.832062	0.416031	−	0.909350i	$-0.363421\pi$
$883$	24.7250	0.832062	0.416031	+	0.909350i	$0.363421\pi$
$884$	1.15559	0.0388667
$885$	48.3944	1.62676
$886$	25.9722	0.872555
$887$	−18.8806	−0.633948	−0.316974	−	0.948434i	$-0.602667\pi$
$887$	−18.8806	−0.633948	−0.316974	+	0.948434i	$0.602667\pi$
$888$	−36.0000	−1.20808
$889$	0	0
$890$	83.2582	2.79082
$891$	0	0
$892$	0.936083	0.0313424
$893$	−26.7250	−0.894317
$894$	10.0278	0.335378
$895$	−49.0555	−1.63974
$896$	0	0
$897$	4.97224	0.166018
$898$	−0.872167	−0.0291046
$899$	−8.30278	−0.276913
$900$	3.15559	0.105186
$901$	13.1833	0.439201
$902$	0	0
$903$	0	0
$904$	−42.9083	−1.42711
$905$	38.8999	1.29308
$906$	24.1194	0.801314
$907$	7.60555	0.252538	0.126269	−	0.991996i	$-0.459700\pi$
$907$	7.60555	0.252538	0.126269	+	0.991996i	$0.459700\pi$
$908$	−3.48612	−0.115691
$909$	−2.21110	−0.0733376
$910$	0	0
$911$	14.4500	0.478749	0.239374	−	0.970927i	$-0.423058\pi$
$911$	14.4500	0.478749	0.239374	+	0.970927i	$0.423058\pi$
$912$	12.9083	0.427437
$913$	0	0
$914$	5.36669	0.177514
$915$	−3.27502	−0.108269
$916$	1.39445	0.0460739
$917$	0	0
$918$	46.0278	1.51914
$919$	−45.4777	−1.50017	−0.750086	−	0.661341i	$-0.769988\pi$
$919$	−45.4777	−1.50017	−0.750086	+	0.661341i	$0.769988\pi$
$920$	−68.1749	−2.24766
$921$	34.6972	1.14331
$922$	24.6333	0.811255
$923$	−0.422205	−0.0138971
$924$	0	0
$925$	73.6888	2.42287
$926$	11.9638	0.393156
$927$	−13.9361	−0.457721
$928$	−14.0917	−0.462582
$929$	−15.6333	−0.512912	−0.256456	−	0.966556i	$-0.582555\pi$
$929$	−15.6333	−0.512912	−0.256456	+	0.966556i	$0.582555\pi$
$930$	−6.11943	−0.200664
$931$	0	0
$932$	−5.44996	−0.178519
$933$	17.7250	0.580290
$934$	52.8167	1.72821
$935$	0	0
$936$	−2.36669	−0.0773578
$937$	−24.3944	−0.796932	−0.398466	−	0.917183i	$-0.630457\pi$
$937$	−24.3944	−0.796932	−0.398466	+	0.917183i	$0.630457\pi$
$938$	0	0
$939$	15.2389	0.497301
$940$	9.72498	0.317194
$941$	−8.57779	−0.279628	−0.139814	−	0.990178i	$-0.544650\pi$
$941$	−8.57779	−0.279628	−0.139814	+	0.990178i	$0.544650\pi$
$942$	12.2389	0.398764
$943$	44.1194	1.43673
$944$	34.0278	1.10751
$945$	0	0
$946$	0	0
$947$	−32.6611	−1.06134	−0.530671	−	0.847578i	$-0.678060\pi$
$947$	−32.6611	−1.06134	−0.530671	+	0.847578i	$0.678060\pi$
$948$	−1.85281	−0.0601766
$949$	3.02776	0.0982851
$950$	−31.2666	−1.01442
$951$	−17.8444	−0.578645
$952$	0	0
$953$	30.0278	0.972694	0.486347	−	0.873766i	$-0.338329\pi$
$953$	30.0278	0.972694	0.486347	+	0.873766i	$0.338329\pi$
$954$	−3.55004	−0.114937
$955$	−18.6888	−0.604756
$956$	4.03616	0.130539
$957$	0	0
$958$	19.0639	0.615927
$959$	0	0
$960$	−41.4138	−1.33662
$961$	−30.0000	−0.967742
$962$	−7.26662	−0.234285
$963$	−25.5416	−0.823068
$964$	5.60555	0.180543
$965$	83.3583	2.68340
$966$	0	0
$967$	22.4861	0.723105	0.361552	−	0.932352i	$-0.382247\pi$
$967$	22.4861	0.723105	0.361552	+	0.932352i	$0.382247\pi$
$968$	0	0
$969$	24.6333	0.791336
$970$	16.9361	0.543785
$971$	49.6333	1.59281	0.796404	−	0.604765i	$-0.206733\pi$
$971$	49.6333	1.59281	0.796404	+	0.604765i	$0.206733\pi$
$972$	3.75274	0.120369
$973$	0	0
$974$	−24.5139	−0.785475
$975$	−6.31118	−0.202120
$976$	−2.30278	−0.0737101
$977$	3.97224	0.127083	0.0635417	−	0.997979i	$-0.479760\pi$
$977$	3.97224	0.127083	0.0635417	+	0.997979i	$0.479760\pi$
$978$	−31.9361	−1.02120
$979$	0	0
$980$	0	0
$981$	10.4222	0.332755
$982$	21.2389	0.677759
$983$	41.7250	1.33082	0.665410	−	0.746478i	$-0.268257\pi$
$983$	41.7250	1.33082	0.665410	+	0.746478i	$0.268257\pi$
$984$	27.3583	0.872150
$985$	−12.2389	−0.389962
$986$	68.1749	2.17113
$987$	0	0
$988$	−0.550039	−0.0174991
$989$	−33.4222	−1.06276
$990$	0	0
$991$	−11.2750	−0.358163	−0.179081	−	0.983834i	$-0.557313\pi$
$991$	−11.2750	−0.358163	−0.179081	+	0.983834i	$0.557313\pi$
$992$	1.69722	0.0538869
$993$	−2.84441	−0.0902646
$994$	0	0
$995$	33.9722	1.07699
$996$	−1.18335	−0.0374958
$997$	−49.3028	−1.56143	−0.780717	−	0.624884i	$-0.785146\pi$
$997$	−49.3028	−1.56143	−0.780717	+	0.624884i	$0.785146\pi$
$998$	10.3028	0.326129
$999$	51.6333	1.63361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.p.1.1		2
7.6	odd	2		847.2.a.g.1.1	yes	2
11.10	odd	2		5929.2.a.k.1.2		2
21.20	even	2		7623.2.a.bc.1.2		2
77.6	even	10		847.2.f.r.729.1		8
77.13	even	10		847.2.f.r.323.1		8
77.20	odd	10		847.2.f.o.323.2		8
77.27	odd	10		847.2.f.o.729.2		8
77.41	even	10		847.2.f.r.372.2		8
77.48	odd	10		847.2.f.o.148.1		8
77.62	even	10		847.2.f.r.148.2		8
77.69	odd	10		847.2.f.o.372.1		8
77.76	even	2		847.2.a.e.1.2	✓	2
231.230	odd	2		7623.2.a.bs.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.e.1.2	✓	2	77.76	even	2
847.2.a.g.1.1	yes	2	7.6	odd	2
847.2.f.o.148.1		8	77.48	odd	10
847.2.f.o.323.2		8	77.20	odd	10
847.2.f.o.372.1		8	77.69	odd	10
847.2.f.o.729.2		8	77.27	odd	10
847.2.f.r.148.2		8	77.62	even	10
847.2.f.r.323.1		8	77.13	even	10
847.2.f.r.372.2		8	77.41	even	10
847.2.f.r.729.1		8	77.6	even	10
5929.2.a.k.1.2		2	11.10	odd	2
5929.2.a.p.1.1		2	1.1	even	1	trivial
7623.2.a.bc.1.2		2	21.20	even	2
7623.2.a.bs.1.1		2	231.230	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-1.30278 q^{2} -1.30278 q^{3} -0.302776 q^{4} +3.60555 q^{5} +1.69722 q^{6} +3.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q-1.30278 q^{2} -1.30278 q^{3} -0.302776 q^{4} +3.60555 q^{5} +1.69722 q^{6} +3.00000 q^{8} -1.30278 q^{9} -4.69722 q^{10} +0.394449 q^{12} +0.605551 q^{13} -4.69722 q^{15} -3.30278 q^{16} -6.30278 q^{17} +1.69722 q^{18} +3.00000 q^{19} -1.09167 q^{20} -6.30278 q^{23} -3.90833 q^{24} +8.00000 q^{25} -0.788897 q^{26} +5.60555 q^{27} +8.30278 q^{29} +6.11943 q^{30} -1.00000 q^{31} -1.69722 q^{32} +8.21110 q^{34} +0.394449 q^{36} +9.21110 q^{37} -3.90833 q^{38} -0.788897 q^{39} +10.8167 q^{40} -7.00000 q^{41} +5.30278 q^{43} -4.69722 q^{45} +8.21110 q^{46} -8.90833 q^{47} +4.30278 q^{48} -10.4222 q^{50} +8.21110 q^{51} -0.183346 q^{52} -2.09167 q^{53} -7.30278 q^{54} -3.90833 q^{57} -10.8167 q^{58} -10.3028 q^{59} +1.42221 q^{60} +0.697224 q^{61} +1.30278 q^{62} +8.81665 q^{64} +2.18335 q^{65} -9.51388 q^{67} +1.90833 q^{68} +8.21110 q^{69} -0.697224 q^{71} -3.90833 q^{72} +5.00000 q^{73} -12.0000 q^{74} -10.4222 q^{75} -0.908327 q^{76} +1.02776 q^{78} -4.69722 q^{79} -11.9083 q^{80} -3.39445 q^{81} +9.11943 q^{82} -3.00000 q^{83} -22.7250 q^{85} -6.90833 q^{86} -10.8167 q^{87} -17.7250 q^{89} +6.11943 q^{90} +1.90833 q^{92} +1.30278 q^{93} +11.6056 q^{94} +10.8167 q^{95} +2.21110 q^{96} -3.60555 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 + 3 * q^4 + 7 * q^6 + 6 * q^8 + q^9	\( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9} - 13 q^{10} + 8 q^{12} - 6 q^{13} - 13 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} + 6 q^{19} - 13 q^{20} - 9 q^{23} + 3 q^{24} + 16 q^{25} - 16 q^{26} + 4 q^{27} + 13 q^{29} - 13 q^{30} - 2 q^{31} - 7 q^{32} + 2 q^{34} + 8 q^{36} + 4 q^{37} + 3 q^{38} - 16 q^{39} - 14 q^{41} + 7 q^{43} - 13 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} + 8 q^{50} + 2 q^{51} - 22 q^{52} - 15 q^{53} - 11 q^{54} + 3 q^{57} - 17 q^{59} - 26 q^{60} + 5 q^{61} - q^{62} - 4 q^{64} + 26 q^{65} - q^{67} - 7 q^{68} + 2 q^{69} - 5 q^{71} + 3 q^{72} + 10 q^{73} - 24 q^{74} + 8 q^{75} + 9 q^{76} - 34 q^{78} - 13 q^{79} - 13 q^{80} - 14 q^{81} - 7 q^{82} - 6 q^{83} - 13 q^{85} - 3 q^{86} - 3 q^{89} - 13 q^{90} - 7 q^{92} - q^{93} + 16 q^{94} - 10 q^{96}+O(q^{100}) \) 2 * q + q^2 + q^3 + 3 * q^4 + 7 * q^6 + 6 * q^8 + q^9 - 13 * q^10 + 8 * q^12 - 6 * q^13 - 13 * q^15 - 3 * q^16 - 9 * q^17 + 7 * q^18 + 6 * q^19 - 13 * q^20 - 9 * q^23 + 3 * q^24 + 16 * q^25 - 16 * q^26 + 4 * q^27 + 13 * q^29 - 13 * q^30 - 2 * q^31 - 7 * q^32 + 2 * q^34 + 8 * q^36 + 4 * q^37 + 3 * q^38 - 16 * q^39 - 14 * q^41 + 7 * q^43 - 13 * q^45 + 2 * q^46 - 7 * q^47 + 5 * q^48 + 8 * q^50 + 2 * q^51 - 22 * q^52 - 15 * q^53 - 11 * q^54 + 3 * q^57 - 17 * q^59 - 26 * q^60 + 5 * q^61 - q^62 - 4 * q^64 + 26 * q^65 - q^67 - 7 * q^68 + 2 * q^69 - 5 * q^71 + 3 * q^72 + 10 * q^73 - 24 * q^74 + 8 * q^75 + 9 * q^76 - 34 * q^78 - 13 * q^79 - 13 * q^80 - 14 * q^81 - 7 * q^82 - 6 * q^83 - 13 * q^85 - 3 * q^86 - 3 * q^89 - 13 * q^90 - 7 * q^92 - q^93 + 16 * q^94 - 10 * q^96

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