LMFDB - Embedded newform 735.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(1,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	735.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -1.00000 q^{5} -2.41421 q^{6} +4.41421 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -1.00000 q^{5} -2.41421 q^{6} +4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} +2.82843 q^{11} -3.82843 q^{12} +4.82843 q^{13} +1.00000 q^{15} +3.00000 q^{16} +7.65685 q^{17} +2.41421 q^{18} +0.828427 q^{19} -3.82843 q^{20} +6.82843 q^{22} -7.65685 q^{23} -4.41421 q^{24} +1.00000 q^{25} +11.6569 q^{26} -1.00000 q^{27} +6.00000 q^{29} +2.41421 q^{30} -6.48528 q^{31} -1.58579 q^{32} -2.82843 q^{33} +18.4853 q^{34} +3.82843 q^{36} -3.65685 q^{37} +2.00000 q^{38} -4.82843 q^{39} -4.41421 q^{40} -11.6569 q^{41} +8.00000 q^{43} +10.8284 q^{44} -1.00000 q^{45} -18.4853 q^{46} -5.65685 q^{47} -3.00000 q^{48} +2.41421 q^{50} -7.65685 q^{51} +18.4853 q^{52} -8.48528 q^{53} -2.41421 q^{54} -2.82843 q^{55} -0.828427 q^{57} +14.4853 q^{58} -2.34315 q^{59} +3.82843 q^{60} -15.6569 q^{62} -9.82843 q^{64} -4.82843 q^{65} -6.82843 q^{66} +29.3137 q^{68} +7.65685 q^{69} -2.82843 q^{71} +4.41421 q^{72} +11.1716 q^{73} -8.82843 q^{74} -1.00000 q^{75} +3.17157 q^{76} -11.6569 q^{78} -8.00000 q^{79} -3.00000 q^{80} +1.00000 q^{81} -28.1421 q^{82} +1.65685 q^{83} -7.65685 q^{85} +19.3137 q^{86} -6.00000 q^{87} +12.4853 q^{88} +5.31371 q^{89} -2.41421 q^{90} -29.3137 q^{92} +6.48528 q^{93} -13.6569 q^{94} -0.828427 q^{95} +1.58579 q^{96} -6.48528 q^{97} +2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 8 q^{22} - 4 q^{23} - 6 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} - 6 q^{32} + 20 q^{34} + 2 q^{36} + 4 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{40} - 12 q^{41} + 16 q^{43} + 16 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 2 q^{54} + 4 q^{57} + 12 q^{58} - 16 q^{59} + 2 q^{60} - 20 q^{62} - 14 q^{64} - 4 q^{65} - 8 q^{66} + 36 q^{68} + 4 q^{69} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 2 q^{75} + 12 q^{76} - 12 q^{78} - 16 q^{79} - 6 q^{80} + 2 q^{81} - 28 q^{82} - 8 q^{83} - 4 q^{85} + 16 q^{86} - 12 q^{87} + 8 q^{88} - 12 q^{89} - 2 q^{90} - 36 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} + 6 q^{96} + 4 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 8 * q^22 - 4 * q^23 - 6 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 - 6 * q^32 + 20 * q^34 + 2 * q^36 + 4 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^40 - 12 * q^41 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 2 * q^54 + 4 * q^57 + 12 * q^58 - 16 * q^59 + 2 * q^60 - 20 * q^62 - 14 * q^64 - 4 * q^65 - 8 * q^66 + 36 * q^68 + 4 * q^69 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 2 * q^75 + 12 * q^76 - 12 * q^78 - 16 * q^79 - 6 * q^80 + 2 * q^81 - 28 * q^82 - 8 * q^83 - 4 * q^85 + 16 * q^86 - 12 * q^87 + 8 * q^88 - 12 * q^89 - 2 * q^90 - 36 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 + 6 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.41421	1.70711	0.853553	−	0.521005i	$-0.174443\pi$
$2$	2.41421	1.70711	0.853553	+	0.521005i	$0.174443\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.82843	1.91421
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.41421	−0.985599
$7$	0	0
$7$	0	0
$8$	4.41421	1.56066
$9$	1.00000	0.333333
$10$	−2.41421	−0.763441
$11$	2.82843	0.852803	0.426401	−	0.904534i	$-0.359781\pi$
$11$	2.82843	0.852803	0.426401	+	0.904534i	$0.359781\pi$
$12$	−3.82843	−1.10517
$13$	4.82843	1.33916	0.669582	−	0.742738i	$-0.266473\pi$
$13$	4.82843	1.33916	0.669582	+	0.742738i	$0.266473\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	3.00000	0.750000
$17$	7.65685	1.85706	0.928530	−	0.371257i	$-0.121073\pi$
$17$	7.65685	1.85706	0.928530	+	0.371257i	$0.121073\pi$
$18$	2.41421	0.569036
$19$	0.828427	0.190054	0.0950271	−	0.995475i	$-0.469706\pi$
$19$	0.828427	0.190054	0.0950271	+	0.995475i	$0.469706\pi$
$20$	−3.82843	−0.856062
$21$	0	0
$22$	6.82843	1.45583
$23$	−7.65685	−1.59656	−0.798282	−	0.602284i	$-0.794258\pi$
$23$	−7.65685	−1.59656	−0.798282	+	0.602284i	$0.794258\pi$
$24$	−4.41421	−0.901048
$25$	1.00000	0.200000
$26$	11.6569	2.28610
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	2.41421	0.440773
$31$	−6.48528	−1.16479	−0.582395	−	0.812906i	$-0.697884\pi$
$31$	−6.48528	−1.16479	−0.582395	+	0.812906i	$0.697884\pi$
$32$	−1.58579	−0.280330
$33$	−2.82843	−0.492366
$34$	18.4853	3.17020
$35$	0	0
$36$	3.82843	0.638071
$37$	−3.65685	−0.601183	−0.300592	−	0.953753i	$-0.597184\pi$
$37$	−3.65685	−0.601183	−0.300592	+	0.953753i	$0.597184\pi$
$38$	2.00000	0.324443
$39$	−4.82843	−0.773167
$40$	−4.41421	−0.697948
$41$	−11.6569	−1.82049	−0.910247	−	0.414065i	$-0.864109\pi$
$41$	−11.6569	−1.82049	−0.910247	+	0.414065i	$0.864109\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	10.8284	1.63245
$45$	−1.00000	−0.149071
$46$	−18.4853	−2.72551
$47$	−5.65685	−0.825137	−0.412568	−	0.910927i	$-0.635368\pi$
$47$	−5.65685	−0.825137	−0.412568	+	0.910927i	$0.635368\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	2.41421	0.341421
$51$	−7.65685	−1.07217
$52$	18.4853	2.56345
$53$	−8.48528	−1.16554	−0.582772	−	0.812636i	$-0.698032\pi$
$53$	−8.48528	−1.16554	−0.582772	+	0.812636i	$0.698032\pi$
$54$	−2.41421	−0.328533
$55$	−2.82843	−0.381385
$56$	0	0
$57$	−0.828427	−0.109728
$58$	14.4853	1.90201
$59$	−2.34315	−0.305052	−0.152526	−	0.988299i	$-0.548741\pi$
$59$	−2.34315	−0.305052	−0.152526	+	0.988299i	$0.548741\pi$
$60$	3.82843	0.494248
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−15.6569	−1.98842
$63$	0	0
$64$	−9.82843	−1.22855
$65$	−4.82843	−0.598893
$66$	−6.82843	−0.840521
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	29.3137	3.55481
$69$	7.65685	0.921777
$70$	0	0
$71$	−2.82843	−0.335673	−0.167836	−	0.985815i	$-0.553678\pi$
$71$	−2.82843	−0.335673	−0.167836	+	0.985815i	$0.553678\pi$
$72$	4.41421	0.520220
$73$	11.1716	1.30753	0.653767	−	0.756696i	$-0.273188\pi$
$73$	11.1716	1.30753	0.653767	+	0.756696i	$0.273188\pi$
$74$	−8.82843	−1.02628
$75$	−1.00000	−0.115470
$76$	3.17157	0.363804
$77$	0	0
$78$	−11.6569	−1.31988
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	−28.1421	−3.10778
$83$	1.65685	0.181863	0.0909317	−	0.995857i	$-0.471016\pi$
$83$	1.65685	0.181863	0.0909317	+	0.995857i	$0.471016\pi$
$84$	0	0
$85$	−7.65685	−0.830502
$86$	19.3137	2.08265
$87$	−6.00000	−0.643268
$88$	12.4853	1.33094
$89$	5.31371	0.563252	0.281626	−	0.959524i	$-0.409126\pi$
$89$	5.31371	0.563252	0.281626	+	0.959524i	$0.409126\pi$
$90$	−2.41421	−0.254480
$91$	0	0
$92$	−29.3137	−3.05617
$93$	6.48528	0.672492
$94$	−13.6569	−1.40860
$95$	−0.828427	−0.0849948
$96$	1.58579	0.161849
$97$	−6.48528	−0.658481	−0.329240	−	0.944246i	$-0.606793\pi$
$97$	−6.48528	−0.658481	−0.329240	+	0.944246i	$0.606793\pi$
$98$	0	0
$99$	2.82843	0.284268
$100$	3.82843	0.382843
$101$	−7.65685	−0.761885	−0.380943	−	0.924599i	$-0.624401\pi$
$101$	−7.65685	−0.761885	−0.380943	+	0.924599i	$0.624401\pi$
$102$	−18.4853	−1.83032
$103$	12.0000	1.18240	0.591198	−	0.806527i	$-0.298655\pi$
$103$	12.0000	1.18240	0.591198	+	0.806527i	$0.298655\pi$
$104$	21.3137	2.08998
$105$	0	0
$106$	−20.4853	−1.98971
$107$	5.31371	0.513696	0.256848	−	0.966452i	$-0.417316\pi$
$107$	5.31371	0.513696	0.256848	+	0.966452i	$0.417316\pi$
$108$	−3.82843	−0.368391
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−6.82843	−0.651065
$111$	3.65685	0.347093
$112$	0	0
$113$	2.82843	0.266076	0.133038	−	0.991111i	$-0.457527\pi$
$113$	2.82843	0.266076	0.133038	+	0.991111i	$0.457527\pi$
$114$	−2.00000	−0.187317
$115$	7.65685	0.714005
$116$	22.9706	2.13276
$117$	4.82843	0.446388
$118$	−5.65685	−0.520756
$119$	0	0
$120$	4.41421	0.402961
$121$	−3.00000	−0.272727
$122$	0	0
$123$	11.6569	1.05106
$124$	−24.8284	−2.22966
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	19.3137	1.71381	0.856907	−	0.515471i	$-0.172383\pi$
$127$	19.3137	1.71381	0.856907	+	0.515471i	$0.172383\pi$
$128$	−20.5563	−1.81694
$129$	−8.00000	−0.704361
$130$	−11.6569	−1.02237
$131$	−5.65685	−0.494242	−0.247121	−	0.968985i	$-0.579484\pi$
$131$	−5.65685	−0.494242	−0.247121	+	0.968985i	$0.579484\pi$
$132$	−10.8284	−0.942494
$133$	0	0
$134$	0	0
$135$	1.00000	0.0860663
$136$	33.7990	2.89824
$137$	13.1716	1.12532	0.562662	−	0.826687i	$-0.309777\pi$
$137$	13.1716	1.12532	0.562662	+	0.826687i	$0.309777\pi$
$138$	18.4853	1.57357
$139$	1.51472	0.128477	0.0642384	−	0.997935i	$-0.479538\pi$
$139$	1.51472	0.128477	0.0642384	+	0.997935i	$0.479538\pi$
$140$	0	0
$141$	5.65685	0.476393
$142$	−6.82843	−0.573029
$143$	13.6569	1.14204
$144$	3.00000	0.250000
$145$	−6.00000	−0.498273
$146$	26.9706	2.23210
$147$	0	0
$148$	−14.0000	−1.15079
$149$	−7.65685	−0.627274	−0.313637	−	0.949543i	$-0.601547\pi$
$149$	−7.65685	−0.627274	−0.313637	+	0.949543i	$0.601547\pi$
$150$	−2.41421	−0.197120
$151$	−16.9706	−1.38104	−0.690522	−	0.723311i	$-0.742619\pi$
$151$	−16.9706	−1.38104	−0.690522	+	0.723311i	$0.742619\pi$
$152$	3.65685	0.296610
$153$	7.65685	0.619020
$154$	0	0
$155$	6.48528	0.520910
$156$	−18.4853	−1.48001
$157$	−12.1421	−0.969048	−0.484524	−	0.874778i	$-0.661007\pi$
$157$	−12.1421	−0.969048	−0.484524	+	0.874778i	$0.661007\pi$
$158$	−19.3137	−1.53652
$159$	8.48528	0.672927
$160$	1.58579	0.125367
$161$	0	0
$162$	2.41421	0.189679
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−44.6274	−3.48482
$165$	2.82843	0.220193
$166$	4.00000	0.310460
$167$	−11.3137	−0.875481	−0.437741	−	0.899101i	$-0.644221\pi$
$167$	−11.3137	−0.875481	−0.437741	+	0.899101i	$0.644221\pi$
$168$	0	0
$169$	10.3137	0.793362
$170$	−18.4853	−1.41776
$171$	0.828427	0.0633514
$172$	30.6274	2.33532
$173$	−24.6274	−1.87239	−0.936194	−	0.351484i	$-0.885677\pi$
$173$	−24.6274	−1.87239	−0.936194	+	0.351484i	$0.885677\pi$
$174$	−14.4853	−1.09813
$175$	0	0
$176$	8.48528	0.639602
$177$	2.34315	0.176122
$178$	12.8284	0.961531
$179$	−1.17157	−0.0875675	−0.0437837	−	0.999041i	$-0.513941\pi$
$179$	−1.17157	−0.0875675	−0.0437837	+	0.999041i	$0.513941\pi$
$180$	−3.82843	−0.285354
$181$	−2.34315	−0.174165	−0.0870823	−	0.996201i	$-0.527754\pi$
$181$	−2.34315	−0.174165	−0.0870823	+	0.996201i	$0.527754\pi$
$182$	0	0
$183$	0	0
$184$	−33.7990	−2.49169
$185$	3.65685	0.268857
$186$	15.6569	1.14802
$187$	21.6569	1.58371
$188$	−21.6569	−1.57949
$189$	0	0
$190$	−2.00000	−0.145095
$191$	−9.17157	−0.663632	−0.331816	−	0.943344i	$-0.607661\pi$
$191$	−9.17157	−0.663632	−0.331816	+	0.943344i	$0.607661\pi$
$192$	9.82843	0.709306
$193$	15.6569	1.12701	0.563503	−	0.826114i	$-0.309454\pi$
$193$	15.6569	1.12701	0.563503	+	0.826114i	$0.309454\pi$
$194$	−15.6569	−1.12410
$195$	4.82843	0.345771
$196$	0	0
$197$	−3.51472	−0.250413	−0.125207	−	0.992131i	$-0.539959\pi$
$197$	−3.51472	−0.250413	−0.125207	+	0.992131i	$0.539959\pi$
$198$	6.82843	0.485275
$199$	0.828427	0.0587256	0.0293628	−	0.999569i	$-0.490652\pi$
$199$	0.828427	0.0587256	0.0293628	+	0.999569i	$0.490652\pi$
$200$	4.41421	0.312132
$201$	0	0
$202$	−18.4853	−1.30062
$203$	0	0
$204$	−29.3137	−2.05237
$205$	11.6569	0.814150
$206$	28.9706	2.01847
$207$	−7.65685	−0.532188
$208$	14.4853	1.00437
$209$	2.34315	0.162079
$210$	0	0
$211$	−9.65685	−0.664805	−0.332403	−	0.943138i	$-0.607859\pi$
$211$	−9.65685	−0.664805	−0.332403	+	0.943138i	$0.607859\pi$
$212$	−32.4853	−2.23110
$213$	2.82843	0.193801
$214$	12.8284	0.876933
$215$	−8.00000	−0.545595
$216$	−4.41421	−0.300349
$217$	0	0
$218$	14.4853	0.981067
$219$	−11.1716	−0.754905
$220$	−10.8284	−0.730052
$221$	36.9706	2.48691
$222$	8.82843	0.592525
$223$	20.9706	1.40429	0.702146	−	0.712033i	$-0.252225\pi$
$223$	20.9706	1.40429	0.702146	+	0.712033i	$0.252225\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	6.82843	0.454220
$227$	−28.9706	−1.92284	−0.961422	−	0.275078i	$-0.911296\pi$
$227$	−28.9706	−1.92284	−0.961422	+	0.275078i	$0.911296\pi$
$228$	−3.17157	−0.210043
$229$	15.3137	1.01196	0.505979	−	0.862546i	$-0.331131\pi$
$229$	15.3137	1.01196	0.505979	+	0.862546i	$0.331131\pi$
$230$	18.4853	1.21888
$231$	0	0
$232$	26.4853	1.73884
$233$	14.8284	0.971443	0.485721	−	0.874114i	$-0.338557\pi$
$233$	14.8284	0.971443	0.485721	+	0.874114i	$0.338557\pi$
$234$	11.6569	0.762032
$235$	5.65685	0.369012
$236$	−8.97056	−0.583934
$237$	8.00000	0.519656
$238$	0	0
$239$	−2.14214	−0.138563	−0.0692816	−	0.997597i	$-0.522071\pi$
$239$	−2.14214	−0.138563	−0.0692816	+	0.997597i	$0.522071\pi$
$240$	3.00000	0.193649
$241$	21.6569	1.39504	0.697520	−	0.716565i	$-0.254287\pi$
$241$	21.6569	1.39504	0.697520	+	0.716565i	$0.254287\pi$
$242$	−7.24264	−0.465575
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	0	0
$246$	28.1421	1.79428
$247$	4.00000	0.254514
$248$	−28.6274	−1.81784
$249$	−1.65685	−0.104999
$250$	−2.41421	−0.152688
$251$	−29.6569	−1.87192	−0.935962	−	0.352101i	$-0.885467\pi$
$251$	−29.6569	−1.87192	−0.935962	+	0.352101i	$0.885467\pi$
$252$	0	0
$253$	−21.6569	−1.36155
$254$	46.6274	2.92566
$255$	7.65685	0.479491
$256$	−29.9706	−1.87316
$257$	0.343146	0.0214048	0.0107024	−	0.999943i	$-0.496593\pi$
$257$	0.343146	0.0214048	0.0107024	+	0.999943i	$0.496593\pi$
$258$	−19.3137	−1.20242
$259$	0	0
$260$	−18.4853	−1.14641
$261$	6.00000	0.371391
$262$	−13.6569	−0.843723
$263$	−2.68629	−0.165644	−0.0828219	−	0.996564i	$-0.526393\pi$
$263$	−2.68629	−0.165644	−0.0828219	+	0.996564i	$0.526393\pi$
$264$	−12.4853	−0.768416
$265$	8.48528	0.521247
$266$	0	0
$267$	−5.31371	−0.325194
$268$	0	0
$269$	−0.343146	−0.0209220	−0.0104610	−	0.999945i	$-0.503330\pi$
$269$	−0.343146	−0.0209220	−0.0104610	+	0.999945i	$0.503330\pi$
$270$	2.41421	0.146924
$271$	22.4853	1.36588	0.682942	−	0.730473i	$-0.260700\pi$
$271$	22.4853	1.36588	0.682942	+	0.730473i	$0.260700\pi$
$272$	22.9706	1.39279
$273$	0	0
$274$	31.7990	1.92105
$275$	2.82843	0.170561
$276$	29.3137	1.76448
$277$	21.3137	1.28062	0.640308	−	0.768118i	$-0.278807\pi$
$277$	21.3137	1.28062	0.640308	+	0.768118i	$0.278807\pi$
$278$	3.65685	0.219324
$279$	−6.48528	−0.388264
$280$	0	0
$281$	12.3431	0.736330	0.368165	−	0.929760i	$-0.379986\pi$
$281$	12.3431	0.736330	0.368165	+	0.929760i	$0.379986\pi$
$282$	13.6569	0.813254
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	−10.8284	−0.642549
$285$	0.828427	0.0490718
$286$	32.9706	1.94959
$287$	0	0
$288$	−1.58579	−0.0934434
$289$	41.6274	2.44867
$290$	−14.4853	−0.850605
$291$	6.48528	0.380174
$292$	42.7696	2.50290
$293$	12.3431	0.721094	0.360547	−	0.932741i	$-0.382590\pi$
$293$	12.3431	0.721094	0.360547	+	0.932741i	$0.382590\pi$
$294$	0	0
$295$	2.34315	0.136423
$296$	−16.1421	−0.938243
$297$	−2.82843	−0.164122
$298$	−18.4853	−1.07082
$299$	−36.9706	−2.13806
$300$	−3.82843	−0.221034
$301$	0	0
$302$	−40.9706	−2.35759
$303$	7.65685	0.439875
$304$	2.48528	0.142541
$305$	0	0
$306$	18.4853	1.05673
$307$	28.9706	1.65344	0.826719	−	0.562616i	$-0.190205\pi$
$307$	28.9706	1.65344	0.826719	+	0.562616i	$0.190205\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	15.6569	0.889250
$311$	−9.65685	−0.547590	−0.273795	−	0.961788i	$-0.588279\pi$
$311$	−9.65685	−0.547590	−0.273795	+	0.961788i	$0.588279\pi$
$312$	−21.3137	−1.20665
$313$	−2.48528	−0.140476	−0.0702382	−	0.997530i	$-0.522376\pi$
$313$	−2.48528	−0.140476	−0.0702382	+	0.997530i	$0.522376\pi$
$314$	−29.3137	−1.65427
$315$	0	0
$316$	−30.6274	−1.72293
$317$	22.1421	1.24363	0.621813	−	0.783166i	$-0.286396\pi$
$317$	22.1421	1.24363	0.621813	+	0.783166i	$0.286396\pi$
$318$	20.4853	1.14876
$319$	16.9706	0.950169
$320$	9.82843	0.549426
$321$	−5.31371	−0.296582
$322$	0	0
$323$	6.34315	0.352942
$324$	3.82843	0.212690
$325$	4.82843	0.267833
$326$	−28.9706	−1.60453
$327$	−6.00000	−0.331801
$328$	−51.4558	−2.84117
$329$	0	0
$330$	6.82843	0.375893
$331$	1.65685	0.0910689	0.0455345	−	0.998963i	$-0.485501\pi$
$331$	1.65685	0.0910689	0.0455345	+	0.998963i	$0.485501\pi$
$332$	6.34315	0.348125
$333$	−3.65685	−0.200394
$334$	−27.3137	−1.49454
$335$	0	0
$336$	0	0
$337$	−6.97056	−0.379711	−0.189855	−	0.981812i	$-0.560802\pi$
$337$	−6.97056	−0.379711	−0.189855	+	0.981812i	$0.560802\pi$
$338$	24.8995	1.35435
$339$	−2.82843	−0.153619
$340$	−29.3137	−1.58976
$341$	−18.3431	−0.993337
$342$	2.00000	0.108148
$343$	0	0
$344$	35.3137	1.90399
$345$	−7.65685	−0.412231
$346$	−59.4558	−3.19637
$347$	−22.9706	−1.23312	−0.616562	−	0.787306i	$-0.711475\pi$
$347$	−22.9706	−1.23312	−0.616562	+	0.787306i	$0.711475\pi$
$348$	−22.9706	−1.23135
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	0	0
$351$	−4.82843	−0.257722
$352$	−4.48528	−0.239066
$353$	25.3137	1.34731	0.673656	−	0.739045i	$-0.264723\pi$
$353$	25.3137	1.34731	0.673656	+	0.739045i	$0.264723\pi$
$354$	5.65685	0.300658
$355$	2.82843	0.150117
$356$	20.3431	1.07818
$357$	0	0
$358$	−2.82843	−0.149487
$359$	−15.7990	−0.833839	−0.416919	−	0.908943i	$-0.636890\pi$
$359$	−15.7990	−0.833839	−0.416919	+	0.908943i	$0.636890\pi$
$360$	−4.41421	−0.232649
$361$	−18.3137	−0.963879
$362$	−5.65685	−0.297318
$363$	3.00000	0.157459
$364$	0	0
$365$	−11.1716	−0.584747
$366$	0	0
$367$	12.9706	0.677058	0.338529	−	0.940956i	$-0.390071\pi$
$367$	12.9706	0.677058	0.338529	+	0.940956i	$0.390071\pi$
$368$	−22.9706	−1.19742
$369$	−11.6569	−0.606832
$370$	8.82843	0.458968
$371$	0	0
$372$	24.8284	1.28729
$373$	−24.6274	−1.27516	−0.637580	−	0.770384i	$-0.720064\pi$
$373$	−24.6274	−1.27516	−0.637580	+	0.770384i	$0.720064\pi$
$374$	52.2843	2.70356
$375$	1.00000	0.0516398
$376$	−24.9706	−1.28776
$377$	28.9706	1.49206
$378$	0	0
$379$	−20.9706	−1.07719	−0.538593	−	0.842566i	$-0.681044\pi$
$379$	−20.9706	−1.07719	−0.538593	+	0.842566i	$0.681044\pi$
$380$	−3.17157	−0.162698
$381$	−19.3137	−0.989471
$382$	−22.1421	−1.13289
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	20.5563	1.04901
$385$	0	0
$386$	37.7990	1.92392
$387$	8.00000	0.406663
$388$	−24.8284	−1.26047
$389$	−11.6569	−0.591026	−0.295513	−	0.955339i	$-0.595491\pi$
$389$	−11.6569	−0.591026	−0.295513	+	0.955339i	$0.595491\pi$
$390$	11.6569	0.590268
$391$	−58.6274	−2.96492
$392$	0	0
$393$	5.65685	0.285351
$394$	−8.48528	−0.427482
$395$	8.00000	0.402524
$396$	10.8284	0.544149
$397$	24.8284	1.24610	0.623052	−	0.782181i	$-0.285893\pi$
$397$	24.8284	1.24610	0.623052	+	0.782181i	$0.285893\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	3.00000	0.150000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	−31.3137	−1.55985
$404$	−29.3137	−1.45841
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−10.3431	−0.512691
$408$	−33.7990	−1.67330
$409$	−12.0000	−0.593362	−0.296681	−	0.954977i	$-0.595880\pi$
$409$	−12.0000	−0.593362	−0.296681	+	0.954977i	$0.595880\pi$
$410$	28.1421	1.38984
$411$	−13.1716	−0.649706
$412$	45.9411	2.26336
$413$	0	0
$414$	−18.4853	−0.908502
$415$	−1.65685	−0.0813318
$416$	−7.65685	−0.375408
$417$	−1.51472	−0.0741761
$418$	5.65685	0.276686
$419$	0.686292	0.0335275	0.0167638	−	0.999859i	$-0.494664\pi$
$419$	0.686292	0.0335275	0.0167638	+	0.999859i	$0.494664\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	−23.3137	−1.13489
$423$	−5.65685	−0.275046
$424$	−37.4558	−1.81902
$425$	7.65685	0.371412
$426$	6.82843	0.330838
$427$	0	0
$428$	20.3431	0.983323
$429$	−13.6569	−0.659359
$430$	−19.3137	−0.931390
$431$	−10.8284	−0.521587	−0.260793	−	0.965395i	$-0.583984\pi$
$431$	−10.8284	−0.521587	−0.260793	+	0.965395i	$0.583984\pi$
$432$	−3.00000	−0.144338
$433$	−7.17157	−0.344644	−0.172322	−	0.985041i	$-0.555127\pi$
$433$	−7.17157	−0.344644	−0.172322	+	0.985041i	$0.555127\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	22.9706	1.10009
$437$	−6.34315	−0.303434
$438$	−26.9706	−1.28870
$439$	13.5147	0.645022	0.322511	−	0.946566i	$-0.395473\pi$
$439$	13.5147	0.645022	0.322511	+	0.946566i	$0.395473\pi$
$440$	−12.4853	−0.595212
$441$	0	0
$442$	89.2548	4.24542
$443$	23.6569	1.12397	0.561986	−	0.827147i	$-0.310038\pi$
$443$	23.6569	1.12397	0.561986	+	0.827147i	$0.310038\pi$
$444$	14.0000	0.664411
$445$	−5.31371	−0.251894
$446$	50.6274	2.39728
$447$	7.65685	0.362157
$448$	0	0
$449$	−12.6274	−0.595925	−0.297962	−	0.954578i	$-0.596307\pi$
$449$	−12.6274	−0.595925	−0.297962	+	0.954578i	$0.596307\pi$
$450$	2.41421	0.113807
$451$	−32.9706	−1.55252
$452$	10.8284	0.509326
$453$	16.9706	0.797347
$454$	−69.9411	−3.28250
$455$	0	0
$456$	−3.65685	−0.171248
$457$	16.3431	0.764500	0.382250	−	0.924059i	$-0.375149\pi$
$457$	16.3431	0.764500	0.382250	+	0.924059i	$0.375149\pi$
$458$	36.9706	1.72752
$459$	−7.65685	−0.357391
$460$	29.3137	1.36676
$461$	−13.3137	−0.620081	−0.310041	−	0.950723i	$-0.600343\pi$
$461$	−13.3137	−0.620081	−0.310041	+	0.950723i	$0.600343\pi$
$462$	0	0
$463$	38.6274	1.79517	0.897584	−	0.440843i	$-0.145321\pi$
$463$	38.6274	1.79517	0.897584	+	0.440843i	$0.145321\pi$
$464$	18.0000	0.835629
$465$	−6.48528	−0.300748
$466$	35.7990	1.65836
$467$	24.2843	1.12374	0.561871	−	0.827225i	$-0.310082\pi$
$467$	24.2843	1.12374	0.561871	+	0.827225i	$0.310082\pi$
$468$	18.4853	0.854482
$469$	0	0
$470$	13.6569	0.629944
$471$	12.1421	0.559480
$472$	−10.3431	−0.476082
$473$	22.6274	1.04041
$474$	19.3137	0.887108
$475$	0.828427	0.0380108
$476$	0	0
$477$	−8.48528	−0.388514
$478$	−5.17157	−0.236542
$479$	14.3431	0.655355	0.327678	−	0.944790i	$-0.393734\pi$
$479$	14.3431	0.655355	0.327678	+	0.944790i	$0.393734\pi$
$480$	−1.58579	−0.0723809
$481$	−17.6569	−0.805083
$482$	52.2843	2.38148
$483$	0	0
$484$	−11.4853	−0.522058
$485$	6.48528	0.294481
$486$	−2.41421	−0.109511
$487$	29.9411	1.35676	0.678381	−	0.734710i	$-0.262682\pi$
$487$	29.9411	1.35676	0.678381	+	0.734710i	$0.262682\pi$
$488$	0	0
$489$	12.0000	0.542659
$490$	0	0
$491$	18.1421	0.818743	0.409372	−	0.912368i	$-0.365748\pi$
$491$	18.1421	0.818743	0.409372	+	0.912368i	$0.365748\pi$
$492$	44.6274	2.01196
$493$	45.9411	2.06908
$494$	9.65685	0.434482
$495$	−2.82843	−0.127128
$496$	−19.4558	−0.873593
$497$	0	0
$498$	−4.00000	−0.179244
$499$	4.97056	0.222513	0.111256	−	0.993792i	$-0.464512\pi$
$499$	4.97056	0.222513	0.111256	+	0.993792i	$0.464512\pi$
$500$	−3.82843	−0.171212
$501$	11.3137	0.505459
$502$	−71.5980	−3.19557
$503$	−4.68629	−0.208951	−0.104476	−	0.994527i	$-0.533316\pi$
$503$	−4.68629	−0.208951	−0.104476	+	0.994527i	$0.533316\pi$
$504$	0	0
$505$	7.65685	0.340726
$506$	−52.2843	−2.32432
$507$	−10.3137	−0.458048
$508$	73.9411	3.28061
$509$	28.3431	1.25629	0.628144	−	0.778097i	$-0.283815\pi$
$509$	28.3431	1.25629	0.628144	+	0.778097i	$0.283815\pi$
$510$	18.4853	0.818542
$511$	0	0
$512$	−31.2426	−1.38074
$513$	−0.828427	−0.0365760
$514$	0.828427	0.0365404
$515$	−12.0000	−0.528783
$516$	−30.6274	−1.34830
$517$	−16.0000	−0.703679
$518$	0	0
$519$	24.6274	1.08102
$520$	−21.3137	−0.934668
$521$	−22.2843	−0.976292	−0.488146	−	0.872762i	$-0.662327\pi$
$521$	−22.2843	−0.976292	−0.488146	+	0.872762i	$0.662327\pi$
$522$	14.4853	0.634004
$523$	−36.2843	−1.58660	−0.793300	−	0.608831i	$-0.791639\pi$
$523$	−36.2843	−1.58660	−0.793300	+	0.608831i	$0.791639\pi$
$524$	−21.6569	−0.946084
$525$	0	0
$526$	−6.48528	−0.282772
$527$	−49.6569	−2.16309
$528$	−8.48528	−0.369274
$529$	35.6274	1.54902
$530$	20.4853	0.889824
$531$	−2.34315	−0.101684
$532$	0	0
$533$	−56.2843	−2.43794
$534$	−12.8284	−0.555140
$535$	−5.31371	−0.229732
$536$	0	0
$537$	1.17157	0.0505571
$538$	−0.828427	−0.0357160
$539$	0	0
$540$	3.82843	0.164749
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	54.2843	2.33171
$543$	2.34315	0.100554
$544$	−12.1421	−0.520590
$545$	−6.00000	−0.257012
$546$	0	0
$547$	−27.3137	−1.16785	−0.583925	−	0.811808i	$-0.698484\pi$
$547$	−27.3137	−1.16785	−0.583925	+	0.811808i	$0.698484\pi$
$548$	50.4264	2.15411
$549$	0	0
$550$	6.82843	0.291165
$551$	4.97056	0.211753
$552$	33.7990	1.43858
$553$	0	0
$554$	51.4558	2.18615
$555$	−3.65685	−0.155225
$556$	5.79899	0.245932
$557$	26.8284	1.13676	0.568378	−	0.822767i	$-0.307571\pi$
$557$	26.8284	1.13676	0.568378	+	0.822767i	$0.307571\pi$
$558$	−15.6569	−0.662807
$559$	38.6274	1.63377
$560$	0	0
$561$	−21.6569	−0.914353
$562$	29.7990	1.25699
$563$	−8.68629	−0.366084	−0.183042	−	0.983105i	$-0.558594\pi$
$563$	−8.68629	−0.366084	−0.183042	+	0.983105i	$0.558594\pi$
$564$	21.6569	0.911918
$565$	−2.82843	−0.118993
$566$	0	0
$567$	0	0
$568$	−12.4853	−0.523871
$569$	10.6863	0.447993	0.223996	−	0.974590i	$-0.428090\pi$
$569$	10.6863	0.447993	0.223996	+	0.974590i	$0.428090\pi$
$570$	2.00000	0.0837708
$571$	−16.6863	−0.698300	−0.349150	−	0.937067i	$-0.613530\pi$
$571$	−16.6863	−0.698300	−0.349150	+	0.937067i	$0.613530\pi$
$572$	52.2843	2.18612
$573$	9.17157	0.383148
$574$	0	0
$575$	−7.65685	−0.319313
$576$	−9.82843	−0.409518
$577$	−18.4853	−0.769552	−0.384776	−	0.923010i	$-0.625721\pi$
$577$	−18.4853	−0.769552	−0.384776	+	0.923010i	$0.625721\pi$
$578$	100.497	4.18014
$579$	−15.6569	−0.650677
$580$	−22.9706	−0.953801
$581$	0	0
$582$	15.6569	0.648997
$583$	−24.0000	−0.993978
$584$	49.3137	2.04062
$585$	−4.82843	−0.199631
$586$	29.7990	1.23098
$587$	8.68629	0.358522	0.179261	−	0.983802i	$-0.442629\pi$
$587$	8.68629	0.358522	0.179261	+	0.983802i	$0.442629\pi$
$588$	0	0
$589$	−5.37258	−0.221373
$590$	5.65685	0.232889
$591$	3.51472	0.144576
$592$	−10.9706	−0.450887
$593$	4.62742	0.190025	0.0950126	−	0.995476i	$-0.469711\pi$
$593$	4.62742	0.190025	0.0950126	+	0.995476i	$0.469711\pi$
$594$	−6.82843	−0.280174
$595$	0	0
$596$	−29.3137	−1.20074
$597$	−0.828427	−0.0339053
$598$	−89.2548	−3.64990
$599$	−44.4853	−1.81762	−0.908810	−	0.417211i	$-0.863008\pi$
$599$	−44.4853	−1.81762	−0.908810	+	0.417211i	$0.863008\pi$
$600$	−4.41421	−0.180210
$601$	−33.6569	−1.37289	−0.686446	−	0.727181i	$-0.740830\pi$
$601$	−33.6569	−1.37289	−0.686446	+	0.727181i	$0.740830\pi$
$602$	0	0
$603$	0	0
$604$	−64.9706	−2.64361
$605$	3.00000	0.121967
$606$	18.4853	0.750913
$607$	3.02944	0.122961	0.0614805	−	0.998108i	$-0.480418\pi$
$607$	3.02944	0.122961	0.0614805	+	0.998108i	$0.480418\pi$
$608$	−1.31371	−0.0532779
$609$	0	0
$610$	0	0
$611$	−27.3137	−1.10499
$612$	29.3137	1.18494
$613$	−23.9411	−0.966973	−0.483486	−	0.875352i	$-0.660630\pi$
$613$	−23.9411	−0.966973	−0.483486	+	0.875352i	$0.660630\pi$
$614$	69.9411	2.82259
$615$	−11.6569	−0.470050
$616$	0	0
$617$	13.4558	0.541712	0.270856	−	0.962620i	$-0.412693\pi$
$617$	13.4558	0.541712	0.270856	+	0.962620i	$0.412693\pi$
$618$	−28.9706	−1.16537
$619$	48.1421	1.93500	0.967498	−	0.252879i	$-0.0813775\pi$
$619$	48.1421	1.93500	0.967498	+	0.252879i	$0.0813775\pi$
$620$	24.8284	0.997134
$621$	7.65685	0.307259
$622$	−23.3137	−0.934795
$623$	0	0
$624$	−14.4853	−0.579875
$625$	1.00000	0.0400000
$626$	−6.00000	−0.239808
$627$	−2.34315	−0.0935762
$628$	−46.4853	−1.85496
$629$	−28.0000	−1.11643
$630$	0	0
$631$	3.31371	0.131917	0.0659583	−	0.997822i	$-0.478990\pi$
$631$	3.31371	0.131917	0.0659583	+	0.997822i	$0.478990\pi$
$632$	−35.3137	−1.40470
$633$	9.65685	0.383825
$634$	53.4558	2.12300
$635$	−19.3137	−0.766441
$636$	32.4853	1.28813
$637$	0	0
$638$	40.9706	1.62204
$639$	−2.82843	−0.111891
$640$	20.5563	0.812561
$641$	−34.2843	−1.35415	−0.677074	−	0.735915i	$-0.736752\pi$
$641$	−34.2843	−1.35415	−0.677074	+	0.735915i	$0.736752\pi$
$642$	−12.8284	−0.506298
$643$	−4.97056	−0.196020	−0.0980099	−	0.995185i	$-0.531248\pi$
$643$	−4.97056	−0.196020	−0.0980099	+	0.995185i	$0.531248\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	15.3137	0.602510
$647$	19.3137	0.759300	0.379650	−	0.925130i	$-0.376044\pi$
$647$	19.3137	0.759300	0.379650	+	0.925130i	$0.376044\pi$
$648$	4.41421	0.173407
$649$	−6.62742	−0.260149
$650$	11.6569	0.457219
$651$	0	0
$652$	−45.9411	−1.79919
$653$	19.7990	0.774794	0.387397	−	0.921913i	$-0.373374\pi$
$653$	19.7990	0.774794	0.387397	+	0.921913i	$0.373374\pi$
$654$	−14.4853	−0.566419
$655$	5.65685	0.221032
$656$	−34.9706	−1.36537
$657$	11.1716	0.435845
$658$	0	0
$659$	43.1127	1.67943	0.839716	−	0.543026i	$-0.182721\pi$
$659$	43.1127	1.67943	0.839716	+	0.543026i	$0.182721\pi$
$660$	10.8284	0.421496
$661$	19.3137	0.751216	0.375608	−	0.926779i	$-0.377434\pi$
$661$	19.3137	0.751216	0.375608	+	0.926779i	$0.377434\pi$
$662$	4.00000	0.155464
$663$	−36.9706	−1.43582
$664$	7.31371	0.283827
$665$	0	0
$666$	−8.82843	−0.342095
$667$	−45.9411	−1.77885
$668$	−43.3137	−1.67586
$669$	−20.9706	−0.810769
$670$	0	0
$671$	0	0
$672$	0	0
$673$	22.9706	0.885450	0.442725	−	0.896657i	$-0.354012\pi$
$673$	22.9706	0.885450	0.442725	+	0.896657i	$0.354012\pi$
$674$	−16.8284	−0.648207
$675$	−1.00000	−0.0384900
$676$	39.4853	1.51866
$677$	15.6569	0.601742	0.300871	−	0.953665i	$-0.402723\pi$
$677$	15.6569	0.601742	0.300871	+	0.953665i	$0.402723\pi$
$678$	−6.82843	−0.262244
$679$	0	0
$680$	−33.7990	−1.29613
$681$	28.9706	1.11015
$682$	−44.2843	−1.69573
$683$	−16.3431	−0.625353	−0.312677	−	0.949860i	$-0.601226\pi$
$683$	−16.3431	−0.625353	−0.312677	+	0.949860i	$0.601226\pi$
$684$	3.17157	0.121268
$685$	−13.1716	−0.503260
$686$	0	0
$687$	−15.3137	−0.584254
$688$	24.0000	0.914991
$689$	−40.9706	−1.56085
$690$	−18.4853	−0.703723
$691$	6.48528	0.246712	0.123356	−	0.992362i	$-0.460634\pi$
$691$	6.48528	0.246712	0.123356	+	0.992362i	$0.460634\pi$
$692$	−94.2843	−3.58415
$693$	0	0
$694$	−55.4558	−2.10508
$695$	−1.51472	−0.0574566
$696$	−26.4853	−1.00392
$697$	−89.2548	−3.38077
$698$	−38.6274	−1.46207
$699$	−14.8284	−0.560863
$700$	0	0
$701$	12.6274	0.476931	0.238465	−	0.971151i	$-0.423356\pi$
$701$	12.6274	0.476931	0.238465	+	0.971151i	$0.423356\pi$
$702$	−11.6569	−0.439960
$703$	−3.02944	−0.114257
$704$	−27.7990	−1.04771
$705$	−5.65685	−0.213049
$706$	61.1127	2.30001
$707$	0	0
$708$	8.97056	0.337134
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	6.82843	0.256266
$711$	−8.00000	−0.300023
$712$	23.4558	0.879045
$713$	49.6569	1.85966
$714$	0	0
$715$	−13.6569	−0.510737
$716$	−4.48528	−0.167623
$717$	2.14214	0.0799995
$718$	−38.1421	−1.42345
$719$	9.65685	0.360140	0.180070	−	0.983654i	$-0.442368\pi$
$719$	9.65685	0.360140	0.180070	+	0.983654i	$0.442368\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	−44.2132	−1.64545
$723$	−21.6569	−0.805427
$724$	−8.97056	−0.333388
$725$	6.00000	0.222834
$726$	7.24264	0.268800
$727$	10.3431	0.383606	0.191803	−	0.981433i	$-0.438567\pi$
$727$	10.3431	0.383606	0.191803	+	0.981433i	$0.438567\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−26.9706	−0.998225
$731$	61.2548	2.26559
$732$	0	0
$733$	3.45584	0.127645	0.0638223	−	0.997961i	$-0.479671\pi$
$733$	3.45584	0.127645	0.0638223	+	0.997961i	$0.479671\pi$
$734$	31.3137	1.15581
$735$	0	0
$736$	12.1421	0.447565
$737$	0	0
$738$	−28.1421	−1.03593
$739$	−29.9411	−1.10140	−0.550701	−	0.834703i	$-0.685640\pi$
$739$	−29.9411	−1.10140	−0.550701	+	0.834703i	$0.685640\pi$
$740$	14.0000	0.514650
$741$	−4.00000	−0.146944
$742$	0	0
$743$	−29.3137	−1.07542	−0.537708	−	0.843131i	$-0.680710\pi$
$743$	−29.3137	−1.07542	−0.537708	+	0.843131i	$0.680710\pi$
$744$	28.6274	1.04953
$745$	7.65685	0.280525
$746$	−59.4558	−2.17683
$747$	1.65685	0.0606211
$748$	82.9117	3.03155
$749$	0	0
$750$	2.41421	0.0881546
$751$	−37.6569	−1.37412	−0.687059	−	0.726602i	$-0.741099\pi$
$751$	−37.6569	−1.37412	−0.687059	+	0.726602i	$0.741099\pi$
$752$	−16.9706	−0.618853
$753$	29.6569	1.08076
$754$	69.9411	2.54711
$755$	16.9706	0.617622
$756$	0	0
$757$	−4.34315	−0.157854	−0.0789272	−	0.996880i	$-0.525149\pi$
$757$	−4.34315	−0.157854	−0.0789272	+	0.996880i	$0.525149\pi$
$758$	−50.6274	−1.83887
$759$	21.6569	0.786094
$760$	−3.65685	−0.132648
$761$	−9.31371	−0.337622	−0.168811	−	0.985648i	$-0.553993\pi$
$761$	−9.31371	−0.337622	−0.168811	+	0.985648i	$0.553993\pi$
$762$	−46.6274	−1.68913
$763$	0	0
$764$	−35.1127	−1.27033
$765$	−7.65685	−0.276834
$766$	0	0
$767$	−11.3137	−0.408514
$768$	29.9706	1.08147
$769$	−3.02944	−0.109244	−0.0546222	−	0.998507i	$-0.517395\pi$
$769$	−3.02944	−0.109244	−0.0546222	+	0.998507i	$0.517395\pi$
$770$	0	0
$771$	−0.343146	−0.0123581
$772$	59.9411	2.15733
$773$	−32.6274	−1.17353	−0.586763	−	0.809758i	$-0.699598\pi$
$773$	−32.6274	−1.17353	−0.586763	+	0.809758i	$0.699598\pi$
$774$	19.3137	0.694217
$775$	−6.48528	−0.232958
$776$	−28.6274	−1.02766
$777$	0	0
$778$	−28.1421	−1.00894
$779$	−9.65685	−0.345993
$780$	18.4853	0.661879
$781$	−8.00000	−0.286263
$782$	−141.539	−5.06143
$783$	−6.00000	−0.214423
$784$	0	0
$785$	12.1421	0.433371
$786$	13.6569	0.487124
$787$	−13.6569	−0.486814	−0.243407	−	0.969924i	$-0.578265\pi$
$787$	−13.6569	−0.486814	−0.243407	+	0.969924i	$0.578265\pi$
$788$	−13.4558	−0.479345
$789$	2.68629	0.0956345
$790$	19.3137	0.687151
$791$	0	0
$792$	12.4853	0.443645
$793$	0	0
$794$	59.9411	2.12723
$795$	−8.48528	−0.300942
$796$	3.17157	0.112413
$797$	7.37258	0.261150	0.130575	−	0.991438i	$-0.458318\pi$
$797$	7.37258	0.261150	0.130575	+	0.991438i	$0.458318\pi$
$798$	0	0
$799$	−43.3137	−1.53233
$800$	−1.58579	−0.0560660
$801$	5.31371	0.187751
$802$	72.4264	2.55747
$803$	31.5980	1.11507
$804$	0	0
$805$	0	0
$806$	−75.5980	−2.66283
$807$	0.343146	0.0120793
$808$	−33.7990	−1.18904
$809$	3.65685	0.128568	0.0642841	−	0.997932i	$-0.479524\pi$
$809$	3.65685	0.128568	0.0642841	+	0.997932i	$0.479524\pi$
$810$	−2.41421	−0.0848268
$811$	43.4558	1.52594	0.762971	−	0.646433i	$-0.223740\pi$
$811$	43.4558	1.52594	0.762971	+	0.646433i	$0.223740\pi$
$812$	0	0
$813$	−22.4853	−0.788593
$814$	−24.9706	−0.875218
$815$	12.0000	0.420342
$816$	−22.9706	−0.804131
$817$	6.62742	0.231864
$818$	−28.9706	−1.01293
$819$	0	0
$820$	44.6274	1.55846
$821$	−44.6274	−1.55751	−0.778754	−	0.627330i	$-0.784148\pi$
$821$	−44.6274	−1.55751	−0.778754	+	0.627330i	$0.784148\pi$
$822$	−31.7990	−1.10912
$823$	−41.9411	−1.46198	−0.730988	−	0.682390i	$-0.760940\pi$
$823$	−41.9411	−1.46198	−0.730988	+	0.682390i	$0.760940\pi$
$824$	52.9706	1.84532
$825$	−2.82843	−0.0984732
$826$	0	0
$827$	5.31371	0.184776	0.0923879	−	0.995723i	$-0.470550\pi$
$827$	5.31371	0.184776	0.0923879	+	0.995723i	$0.470550\pi$
$828$	−29.3137	−1.01872
$829$	−47.5980	−1.65315	−0.826573	−	0.562829i	$-0.809713\pi$
$829$	−47.5980	−1.65315	−0.826573	+	0.562829i	$0.809713\pi$
$830$	−4.00000	−0.138842
$831$	−21.3137	−0.739364
$832$	−47.4558	−1.64524
$833$	0	0
$834$	−3.65685	−0.126627
$835$	11.3137	0.391527
$836$	8.97056	0.310253
$837$	6.48528	0.224164
$838$	1.65685	0.0572351
$839$	46.6274	1.60976	0.804879	−	0.593439i	$-0.202230\pi$
$839$	46.6274	1.60976	0.804879	+	0.593439i	$0.202230\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−14.4853	−0.499196
$843$	−12.3431	−0.425121
$844$	−36.9706	−1.27258
$845$	−10.3137	−0.354802
$846$	−13.6569	−0.469532
$847$	0	0
$848$	−25.4558	−0.874157
$849$	0	0
$850$	18.4853	0.634040
$851$	28.0000	0.959828
$852$	10.8284	0.370976
$853$	−10.4853	−0.359009	−0.179505	−	0.983757i	$-0.557449\pi$
$853$	−10.4853	−0.359009	−0.179505	+	0.983757i	$0.557449\pi$
$854$	0	0
$855$	−0.828427	−0.0283316
$856$	23.4558	0.801704
$857$	−44.6274	−1.52444	−0.762222	−	0.647316i	$-0.775891\pi$
$857$	−44.6274	−1.52444	−0.762222	+	0.647316i	$0.775891\pi$
$858$	−32.9706	−1.12560
$859$	45.7990	1.56264	0.781321	−	0.624130i	$-0.214546\pi$
$859$	45.7990	1.56264	0.781321	+	0.624130i	$0.214546\pi$
$860$	−30.6274	−1.04439
$861$	0	0
$862$	−26.1421	−0.890405
$863$	46.9706	1.59890	0.799448	−	0.600735i	$-0.205125\pi$
$863$	46.9706	1.59890	0.799448	+	0.600735i	$0.205125\pi$
$864$	1.58579	0.0539496
$865$	24.6274	0.837357
$866$	−17.3137	−0.588344
$867$	−41.6274	−1.41374
$868$	0	0
$869$	−22.6274	−0.767583
$870$	14.4853	0.491097
$871$	0	0
$872$	26.4853	0.896905
$873$	−6.48528	−0.219494
$874$	−15.3137	−0.517994
$875$	0	0
$876$	−42.7696	−1.44505
$877$	27.9411	0.943505	0.471752	−	0.881731i	$-0.343622\pi$
$877$	27.9411	0.943505	0.471752	+	0.881731i	$0.343622\pi$
$878$	32.6274	1.10112
$879$	−12.3431	−0.416324
$880$	−8.48528	−0.286039
$881$	43.2548	1.45729	0.728646	−	0.684890i	$-0.240150\pi$
$881$	43.2548	1.45729	0.728646	+	0.684890i	$0.240150\pi$
$882$	0	0
$883$	28.0000	0.942275	0.471138	−	0.882060i	$-0.343844\pi$
$883$	28.0000	0.942275	0.471138	+	0.882060i	$0.343844\pi$
$884$	141.539	4.76048
$885$	−2.34315	−0.0787640
$886$	57.1127	1.91874
$887$	7.02944	0.236025	0.118013	−	0.993012i	$-0.462348\pi$
$887$	7.02944	0.236025	0.118013	+	0.993012i	$0.462348\pi$
$888$	16.1421	0.541695
$889$	0	0
$890$	−12.8284	−0.430010
$891$	2.82843	0.0947559
$892$	80.2843	2.68812
$893$	−4.68629	−0.156821
$894$	18.4853	0.618240
$895$	1.17157	0.0391614
$896$	0	0
$897$	36.9706	1.23441
$898$	−30.4853	−1.01731
$899$	−38.9117	−1.29778
$900$	3.82843	0.127614
$901$	−64.9706	−2.16448
$902$	−79.5980	−2.65032
$903$	0	0
$904$	12.4853	0.415254
$905$	2.34315	0.0778888
$906$	40.9706	1.36116
$907$	−39.3137	−1.30539	−0.652695	−	0.757621i	$-0.726362\pi$
$907$	−39.3137	−1.30539	−0.652695	+	0.757621i	$0.726362\pi$
$908$	−110.912	−3.68073
$909$	−7.65685	−0.253962
$910$	0	0
$911$	−7.79899	−0.258392	−0.129196	−	0.991619i	$-0.541240\pi$
$911$	−7.79899	−0.258392	−0.129196	+	0.991619i	$0.541240\pi$
$912$	−2.48528	−0.0822959
$913$	4.68629	0.155094
$914$	39.4558	1.30508
$915$	0	0
$916$	58.6274	1.93710
$917$	0	0
$918$	−18.4853	−0.610105
$919$	44.2843	1.46080	0.730402	−	0.683018i	$-0.239333\pi$
$919$	44.2843	1.46080	0.730402	+	0.683018i	$0.239333\pi$
$920$	33.7990	1.11432
$921$	−28.9706	−0.954612
$922$	−32.1421	−1.05854
$923$	−13.6569	−0.449521
$924$	0	0
$925$	−3.65685	−0.120237
$926$	93.2548	3.06454
$927$	12.0000	0.394132
$928$	−9.51472	−0.312336
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	−15.6569	−0.513408
$931$	0	0
$932$	56.7696	1.85955
$933$	9.65685	0.316151
$934$	58.6274	1.91835
$935$	−21.6569	−0.708255
$936$	21.3137	0.696660
$937$	−15.4558	−0.504920	−0.252460	−	0.967607i	$-0.581240\pi$
$937$	−15.4558	−0.504920	−0.252460	+	0.967607i	$0.581240\pi$
$938$	0	0
$939$	2.48528	0.0811041
$940$	21.6569	0.706369
$941$	0.627417	0.0204532	0.0102266	−	0.999948i	$-0.496745\pi$
$941$	0.627417	0.0204532	0.0102266	+	0.999948i	$0.496745\pi$
$942$	29.3137	0.955092
$943$	89.2548	2.90654
$944$	−7.02944	−0.228789
$945$	0	0
$946$	54.6274	1.77609
$947$	−12.3431	−0.401098	−0.200549	−	0.979684i	$-0.564273\pi$
$947$	−12.3431	−0.401098	−0.200549	+	0.979684i	$0.564273\pi$
$948$	30.6274	0.994732
$949$	53.9411	1.75100
$950$	2.00000	0.0648886
$951$	−22.1421	−0.718008
$952$	0	0
$953$	6.14214	0.198963	0.0994816	−	0.995039i	$-0.468282\pi$
$953$	6.14214	0.198963	0.0994816	+	0.995039i	$0.468282\pi$
$954$	−20.4853	−0.663235
$955$	9.17157	0.296785
$956$	−8.20101	−0.265240
$957$	−16.9706	−0.548580
$958$	34.6274	1.11876
$959$	0	0
$960$	−9.82843	−0.317211
$961$	11.0589	0.356738
$962$	−42.6274	−1.37436
$963$	5.31371	0.171232
$964$	82.9117	2.67041
$965$	−15.6569	−0.504012
$966$	0	0
$967$	5.37258	0.172771	0.0863853	−	0.996262i	$-0.472468\pi$
$967$	5.37258	0.172771	0.0863853	+	0.996262i	$0.472468\pi$
$968$	−13.2426	−0.425635
$969$	−6.34315	−0.203771
$970$	15.6569	0.502711
$971$	−39.3137	−1.26164	−0.630818	−	0.775930i	$-0.717281\pi$
$971$	−39.3137	−1.26164	−0.630818	+	0.775930i	$0.717281\pi$
$972$	−3.82843	−0.122797
$973$	0	0
$974$	72.2843	2.31614
$975$	−4.82843	−0.154633
$976$	0	0
$977$	−20.4853	−0.655382	−0.327691	−	0.944785i	$-0.606271\pi$
$977$	−20.4853	−0.655382	−0.327691	+	0.944785i	$0.606271\pi$
$978$	28.9706	0.926376
$979$	15.0294	0.480343
$980$	0	0
$981$	6.00000	0.191565
$982$	43.7990	1.39768
$983$	−21.6569	−0.690746	−0.345373	−	0.938465i	$-0.612248\pi$
$983$	−21.6569	−0.690746	−0.345373	+	0.938465i	$0.612248\pi$
$984$	51.4558	1.64035
$985$	3.51472	0.111988
$986$	110.912	3.53215
$987$	0	0
$988$	15.3137	0.487194
$989$	−61.2548	−1.94779
$990$	−6.82843	−0.217022
$991$	16.9706	0.539088	0.269544	−	0.962988i	$-0.413127\pi$
$991$	16.9706	0.539088	0.269544	+	0.962988i	$0.413127\pi$
$992$	10.2843	0.326526
$993$	−1.65685	−0.0525787
$994$	0	0
$995$	−0.828427	−0.0262629
$996$	−6.34315	−0.200990
$997$	55.4558	1.75630	0.878152	−	0.478382i	$-0.158776\pi$
$997$	55.4558	1.75630	0.878152	+	0.478382i	$0.158776\pi$
$998$	12.0000	0.379853
$999$	3.65685	0.115698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.a.l.1.2	✓	2
3.2	odd	2		2205.2.a.r.1.1		2
5.4	even	2		3675.2.a.t.1.1		2
7.2	even	3		735.2.i.h.361.1		4
7.3	odd	6		735.2.i.g.226.1		4
7.4	even	3		735.2.i.h.226.1		4
7.5	odd	6		735.2.i.g.361.1		4
7.6	odd	2		735.2.a.m.1.2	yes	2
21.20	even	2		2205.2.a.o.1.1		2
35.34	odd	2		3675.2.a.s.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.a.l.1.2	✓	2	1.1	even	1	trivial
735.2.a.m.1.2	yes	2	7.6	odd	2
735.2.i.g.226.1		4	7.3	odd	6
735.2.i.g.361.1		4	7.5	odd	6
735.2.i.h.226.1		4	7.4	even	3
735.2.i.h.361.1		4	7.2	even	3
2205.2.a.o.1.1		2	21.20	even	2
2205.2.a.r.1.1		2	3.2	odd	2
3675.2.a.s.1.1		2	35.34	odd	2
3675.2.a.t.1.1		2	5.4	even	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -1.00000 q^{5} -2.41421 q^{6} +4.41421 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} -1.00000 q^{5} -2.41421 q^{6} +4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} +2.82843 q^{11} -3.82843 q^{12} +4.82843 q^{13} +1.00000 q^{15} +3.00000 q^{16} +7.65685 q^{17} +2.41421 q^{18} +0.828427 q^{19} -3.82843 q^{20} +6.82843 q^{22} -7.65685 q^{23} -4.41421 q^{24} +1.00000 q^{25} +11.6569 q^{26} -1.00000 q^{27} +6.00000 q^{29} +2.41421 q^{30} -6.48528 q^{31} -1.58579 q^{32} -2.82843 q^{33} +18.4853 q^{34} +3.82843 q^{36} -3.65685 q^{37} +2.00000 q^{38} -4.82843 q^{39} -4.41421 q^{40} -11.6569 q^{41} +8.00000 q^{43} +10.8284 q^{44} -1.00000 q^{45} -18.4853 q^{46} -5.65685 q^{47} -3.00000 q^{48} +2.41421 q^{50} -7.65685 q^{51} +18.4853 q^{52} -8.48528 q^{53} -2.41421 q^{54} -2.82843 q^{55} -0.828427 q^{57} +14.4853 q^{58} -2.34315 q^{59} +3.82843 q^{60} -15.6569 q^{62} -9.82843 q^{64} -4.82843 q^{65} -6.82843 q^{66} +29.3137 q^{68} +7.65685 q^{69} -2.82843 q^{71} +4.41421 q^{72} +11.1716 q^{73} -8.82843 q^{74} -1.00000 q^{75} +3.17157 q^{76} -11.6569 q^{78} -8.00000 q^{79} -3.00000 q^{80} +1.00000 q^{81} -28.1421 q^{82} +1.65685 q^{83} -7.65685 q^{85} +19.3137 q^{86} -6.00000 q^{87} +12.4853 q^{88} +5.31371 q^{89} -2.41421 q^{90} -29.3137 q^{92} +6.48528 q^{93} -13.6569 q^{94} -0.828427 q^{95} +1.58579 q^{96} -6.48528 q^{97} +2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} + 4 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 8 q^{22} - 4 q^{23} - 6 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} - 6 q^{32} + 20 q^{34} + 2 q^{36} + 4 q^{37} + 4 q^{38} - 4 q^{39} - 6 q^{40} - 12 q^{41} + 16 q^{43} + 16 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 2 q^{54} + 4 q^{57} + 12 q^{58} - 16 q^{59} + 2 q^{60} - 20 q^{62} - 14 q^{64} - 4 q^{65} - 8 q^{66} + 36 q^{68} + 4 q^{69} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 2 q^{75} + 12 q^{76} - 12 q^{78} - 16 q^{79} - 6 q^{80} + 2 q^{81} - 28 q^{82} - 8 q^{83} - 4 q^{85} + 16 q^{86} - 12 q^{87} + 8 q^{88} - 12 q^{89} - 2 q^{90} - 36 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} + 6 q^{96} + 4 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 + 4 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 8 * q^22 - 4 * q^23 - 6 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 - 6 * q^32 + 20 * q^34 + 2 * q^36 + 4 * q^37 + 4 * q^38 - 4 * q^39 - 6 * q^40 - 12 * q^41 + 16 * q^43 + 16 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 2 * q^54 + 4 * q^57 + 12 * q^58 - 16 * q^59 + 2 * q^60 - 20 * q^62 - 14 * q^64 - 4 * q^65 - 8 * q^66 + 36 * q^68 + 4 * q^69 + 6 * q^72 + 28 * q^73 - 12 * q^74 - 2 * q^75 + 12 * q^76 - 12 * q^78 - 16 * q^79 - 6 * q^80 + 2 * q^81 - 28 * q^82 - 8 * q^83 - 4 * q^85 + 16 * q^86 - 12 * q^87 + 8 * q^88 - 12 * q^89 - 2 * q^90 - 36 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 + 6 * q^96 + 4 * q^97

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