LMFDB - Embedded newform 825.2.c.e.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.4
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.2.c.e.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421i q^{2} -1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} -0.828427i q^{7} -4.41421i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.41421i q^{2} -1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} -0.828427i q^{7} -4.41421i q^{8} -1.00000 q^{9} -1.00000 q^{11} +3.82843i q^{12} -5.65685i q^{13} +2.00000 q^{14} +3.00000 q^{16} +1.17157i q^{17} -2.41421i q^{18} +6.82843 q^{19} -0.828427 q^{21} -2.41421i q^{22} -4.00000i q^{23} -4.41421 q^{24} +13.6569 q^{26} +1.00000i q^{27} +3.17157i q^{28} +4.82843 q^{29} -1.58579i q^{32} +1.00000i q^{33} -2.82843 q^{34} +3.82843 q^{36} -11.6569i q^{37} +16.4853i q^{38} -5.65685 q^{39} +4.82843 q^{41} -2.00000i q^{42} -8.82843i q^{43} +3.82843 q^{44} +9.65685 q^{46} +4.00000i q^{47} -3.00000i q^{48} +6.31371 q^{49} +1.17157 q^{51} +21.6569i q^{52} +9.31371i q^{53} -2.41421 q^{54} -3.65685 q^{56} -6.82843i q^{57} +11.6569i q^{58} +4.00000 q^{59} -11.6569 q^{61} +0.828427i q^{63} +9.82843 q^{64} -2.41421 q^{66} +5.65685i q^{67} -4.48528i q^{68} -4.00000 q^{69} +2.34315 q^{71} +4.41421i q^{72} +11.3137i q^{73} +28.1421 q^{74} -26.1421 q^{76} +0.828427i q^{77} -13.6569i q^{78} -8.48528 q^{79} +1.00000 q^{81} +11.6569i q^{82} -10.0000i q^{83} +3.17157 q^{84} +21.3137 q^{86} -4.82843i q^{87} +4.41421i q^{88} -3.65685 q^{89} -4.68629 q^{91} +15.3137i q^{92} -9.65685 q^{94} -1.58579 q^{96} -11.6569i q^{97} +15.2426i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} - 4 q^{11} + 8 q^{14} + 12 q^{16} + 16 q^{19} + 8 q^{21} - 12 q^{24} + 32 q^{26} + 8 q^{29} + 4 q^{36} + 8 q^{41} + 4 q^{44} + 16 q^{46} - 20 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 16 q^{59} - 24 q^{61} + 28 q^{64} - 4 q^{66} - 16 q^{69} + 32 q^{71} + 56 q^{74} - 48 q^{76} + 4 q^{81} + 24 q^{84} + 40 q^{86} + 8 q^{89} - 64 q^{91} - 16 q^{94} - 12 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 - 4 * q^11 + 8 * q^14 + 12 * q^16 + 16 * q^19 + 8 * q^21 - 12 * q^24 + 32 * q^26 + 8 * q^29 + 4 * q^36 + 8 * q^41 + 4 * q^44 + 16 * q^46 - 20 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 16 * q^59 - 24 * q^61 + 28 * q^64 - 4 * q^66 - 16 * q^69 + 32 * q^71 + 56 * q^74 - 48 * q^76 + 4 * q^81 + 24 * q^84 + 40 * q^86 + 8 * q^89 - 64 * q^91 - 16 * q^94 - 12 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	2.41421i	1.70711i	0.521005	+	0.853553i	$0.325557\pi$
$2$	2.41421i	1.70711i	−0.521005	+	0.853553i	$0.674443\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−3.82843	−1.91421
$5$	0	0
$5$	0	0
$6$	2.41421	0.985599
$7$	− 0.828427i	− 0.313116i	−0.987669	−	0.156558i	$-0.949960\pi$
$7$	− 0.828427i	− 0.313116i	0.987669	−	0.156558i	$-0.0500398\pi$
$8$	− 4.41421i	− 1.56066i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.82843i	1.10517i
$13$	− 5.65685i	− 1.56893i	−0.620174	−	0.784465i	$-0.712938\pi$
$13$	− 5.65685i	− 1.56893i	0.620174	−	0.784465i	$-0.287062\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	3.00000	0.750000
$17$	1.17157i	0.284148i	0.989856	+	0.142074i	$0.0453771\pi$
$17$	1.17157i	0.284148i	−0.989856	+	0.142074i	$0.954623\pi$
$18$	− 2.41421i	− 0.569036i
$19$	6.82843	1.56655	0.783274	−	0.621676i	$-0.213548\pi$
$19$	6.82843	1.56655	0.783274	+	0.621676i	$0.213548\pi$
$20$	0	0
$21$	−0.828427	−0.180778
$22$	− 2.41421i	− 0.514712i
$23$	− 4.00000i	− 0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$	− 4.00000i	− 0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$	−4.41421	−0.901048
$25$	0	0
$26$	13.6569	2.67833
$27$	1.00000i	0.192450i
$28$	3.17157i	0.599371i
$29$	4.82843	0.896616	0.448308	−	0.893879i	$-0.352027\pi$
$29$	4.82843	0.896616	0.448308	+	0.893879i	$0.352027\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	− 1.58579i	− 0.280330i
$33$	1.00000i	0.174078i
$34$	−2.82843	−0.485071
$35$	0	0
$36$	3.82843	0.638071
$37$	− 11.6569i	− 1.91638i	−0.286141	−	0.958188i	$-0.592373\pi$
$37$	− 11.6569i	− 1.91638i	0.286141	−	0.958188i	$-0.407627\pi$
$38$	16.4853i	2.67427i
$39$	−5.65685	−0.905822
$40$	0	0
$41$	4.82843	0.754074	0.377037	−	0.926198i	$-0.376943\pi$
$41$	4.82843	0.754074	0.377037	+	0.926198i	$0.376943\pi$
$42$	− 2.00000i	− 0.308607i
$43$	− 8.82843i	− 1.34632i	−0.739496	−	0.673161i	$-0.764936\pi$
$43$	− 8.82843i	− 1.34632i	0.739496	−	0.673161i	$-0.235064\pi$
$44$	3.82843	0.577157
$45$	0	0
$46$	9.65685	1.42383
$47$	4.00000i	0.583460i	0.956501	+	0.291730i	$0.0942309\pi$
$47$	4.00000i	0.583460i	−0.956501	+	0.291730i	$0.905769\pi$
$48$	− 3.00000i	− 0.433013i
$49$	6.31371	0.901958
$50$	0	0
$51$	1.17157	0.164053
$52$	21.6569i	3.00327i
$53$	9.31371i	1.27934i	0.768651	+	0.639668i	$0.220928\pi$
$53$	9.31371i	1.27934i	−0.768651	+	0.639668i	$0.779072\pi$
$54$	−2.41421	−0.328533
$55$	0	0
$56$	−3.65685	−0.488668
$57$	− 6.82843i	− 0.904447i
$58$	11.6569i	1.53062i
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−11.6569	−1.49251	−0.746254	−	0.665662i	$-0.768149\pi$
$61$	−11.6569	−1.49251	−0.746254	+	0.665662i	$0.768149\pi$
$62$	0	0
$63$	0.828427i	0.104372i
$64$	9.82843	1.22855
$65$	0	0
$66$	−2.41421	−0.297169
$67$	5.65685i	0.691095i	0.938401	+	0.345547i	$0.112307\pi$
$67$	5.65685i	0.691095i	−0.938401	+	0.345547i	$0.887693\pi$
$68$	− 4.48528i	− 0.543920i
$69$	−4.00000	−0.481543
$70$	0	0
$71$	2.34315	0.278080	0.139040	−	0.990287i	$-0.455598\pi$
$71$	2.34315	0.278080	0.139040	+	0.990287i	$0.455598\pi$
$72$	4.41421i	0.520220i
$73$	11.3137i	1.32417i	0.749429	+	0.662085i	$0.230328\pi$
$73$	11.3137i	1.32417i	−0.749429	+	0.662085i	$0.769672\pi$
$74$	28.1421	3.27146
$75$	0	0
$76$	−26.1421	−2.99871
$77$	0.828427i	0.0944080i
$78$	− 13.6569i	− 1.54633i
$79$	−8.48528	−0.954669	−0.477334	−	0.878722i	$-0.658397\pi$
$79$	−8.48528	−0.954669	−0.477334	+	0.878722i	$0.658397\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	11.6569i	1.28728i
$83$	− 10.0000i	− 1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$	− 10.0000i	− 1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$	3.17157	0.346047
$85$	0	0
$86$	21.3137	2.29832
$87$	− 4.82843i	− 0.517662i
$88$	4.41421i	0.470557i
$89$	−3.65685	−0.387626	−0.193813	−	0.981039i	$-0.562085\pi$
$89$	−3.65685	−0.387626	−0.193813	+	0.981039i	$0.562085\pi$
$90$	0	0
$91$	−4.68629	−0.491257
$92$	15.3137i	1.59656i
$93$	0	0
$94$	−9.65685	−0.996028
$95$	0	0
$96$	−1.58579	−0.161849
$97$	− 11.6569i	− 1.18357i	−0.806094	−	0.591787i	$-0.798423\pi$
$97$	− 11.6569i	− 1.18357i	0.806094	−	0.591787i	$-0.201577\pi$
$98$	15.2426i	1.53974i
$99$	1.00000	0.100504
$100$	0	0
$101$	−0.828427	−0.0824316	−0.0412158	−	0.999150i	$-0.513123\pi$
$101$	−0.828427	−0.0824316	−0.0412158	+	0.999150i	$0.513123\pi$
$102$	2.82843i	0.280056i
$103$	− 3.31371i	− 0.326509i	−0.986584	−	0.163255i	$-0.947801\pi$
$103$	− 3.31371i	− 0.326509i	0.986584	−	0.163255i	$-0.0521992\pi$
$104$	−24.9706	−2.44857
$105$	0	0
$106$	−22.4853	−2.18396
$107$	− 17.3137i	− 1.67378i	−0.547372	−	0.836890i	$-0.684372\pi$
$107$	− 17.3137i	− 1.67378i	0.547372	−	0.836890i	$-0.315628\pi$
$108$	− 3.82843i	− 0.368391i
$109$	−17.3137	−1.65835	−0.829176	−	0.558987i	$-0.811190\pi$
$109$	−17.3137	−1.65835	−0.829176	+	0.558987i	$0.811190\pi$
$110$	0	0
$111$	−11.6569	−1.10642
$112$	− 2.48528i	− 0.234837i
$113$	− 18.9706i	− 1.78460i	−0.451442	−	0.892300i	$-0.649090\pi$
$113$	− 18.9706i	− 1.78460i	0.451442	−	0.892300i	$-0.350910\pi$
$114$	16.4853	1.54399
$115$	0	0
$116$	−18.4853	−1.71632
$117$	5.65685i	0.522976i
$118$	9.65685i	0.888985i
$119$	0.970563	0.0889713
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 28.1421i	− 2.54787i
$123$	− 4.82843i	− 0.435365i
$124$	0	0
$125$	0	0
$126$	−2.00000	−0.178174
$127$	14.4853i	1.28536i	0.766134	+	0.642680i	$0.222178\pi$
$127$	14.4853i	1.28536i	−0.766134	+	0.642680i	$0.777822\pi$
$128$	20.5563i	1.81694i
$129$	−8.82843	−0.777300
$130$	0	0
$131$	3.31371	0.289520	0.144760	−	0.989467i	$-0.453759\pi$
$131$	3.31371	0.289520	0.144760	+	0.989467i	$0.453759\pi$
$132$	− 3.82843i	− 0.333222i
$133$	− 5.65685i	− 0.490511i
$134$	−13.6569	−1.17977
$135$	0	0
$136$	5.17157	0.443459
$137$	13.3137i	1.13747i	0.822522	+	0.568733i	$0.192566\pi$
$137$	13.3137i	1.13747i	−0.822522	+	0.568733i	$0.807434\pi$
$138$	− 9.65685i	− 0.822046i
$139$	−0.485281	−0.0411610	−0.0205805	−	0.999788i	$-0.506551\pi$
$139$	−0.485281	−0.0411610	−0.0205805	+	0.999788i	$0.506551\pi$
$140$	0	0
$141$	4.00000	0.336861
$142$	5.65685i	0.474713i
$143$	5.65685i	0.473050i
$144$	−3.00000	−0.250000
$145$	0	0
$146$	−27.3137	−2.26050
$147$	− 6.31371i	− 0.520746i
$148$	44.6274i	3.66835i
$149$	−1.51472	−0.124091	−0.0620453	−	0.998073i	$-0.519762\pi$
$149$	−1.51472	−0.124091	−0.0620453	+	0.998073i	$0.519762\pi$
$150$	0	0
$151$	16.4853	1.34155	0.670777	−	0.741659i	$-0.265961\pi$
$151$	16.4853	1.34155	0.670777	+	0.741659i	$0.265961\pi$
$152$	− 30.1421i	− 2.44485i
$153$	− 1.17157i	− 0.0947161i
$154$	−2.00000	−0.161165
$155$	0	0
$156$	21.6569	1.73394
$157$	− 18.0000i	− 1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$	− 18.0000i	− 1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	− 20.4853i	− 1.62972i
$159$	9.31371	0.738625
$160$	0	0
$161$	−3.31371	−0.261157
$162$	2.41421i	0.189679i
$163$	− 7.31371i	− 0.572854i	−0.958102	−	0.286427i	$-0.907532\pi$
$163$	− 7.31371i	− 0.572854i	0.958102	−	0.286427i	$-0.0924676\pi$
$164$	−18.4853	−1.44346
$165$	0	0
$166$	24.1421	1.87379
$167$	13.3137i	1.03025i	0.857116	+	0.515123i	$0.172254\pi$
$167$	13.3137i	1.03025i	−0.857116	+	0.515123i	$0.827746\pi$
$168$	3.65685i	0.282132i
$169$	−19.0000	−1.46154
$170$	0	0
$171$	−6.82843	−0.522183
$172$	33.7990i	2.57715i
$173$	2.82843i	0.215041i	0.994203	+	0.107521i	$0.0342912\pi$
$173$	2.82843i	0.215041i	−0.994203	+	0.107521i	$0.965709\pi$
$174$	11.6569	0.883704
$175$	0	0
$176$	−3.00000	−0.226134
$177$	− 4.00000i	− 0.300658i
$178$	− 8.82843i	− 0.661719i
$179$	17.6569	1.31974	0.659868	−	0.751382i	$-0.270612\pi$
$179$	17.6569	1.31974	0.659868	+	0.751382i	$0.270612\pi$
$180$	0	0
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	− 11.3137i	− 0.838628i
$183$	11.6569i	0.861699i
$184$	−17.6569	−1.30168
$185$	0	0
$186$	0	0
$187$	− 1.17157i	− 0.0856739i
$188$	− 15.3137i	− 1.11687i
$189$	0.828427	0.0602592
$190$	0	0
$191$	5.65685	0.409316	0.204658	−	0.978834i	$-0.434392\pi$
$191$	5.65685	0.409316	0.204658	+	0.978834i	$0.434392\pi$
$192$	− 9.82843i	− 0.709306i
$193$	13.6569i	0.983042i	0.870866	+	0.491521i	$0.163559\pi$
$193$	13.6569i	0.983042i	−0.870866	+	0.491521i	$0.836441\pi$
$194$	28.1421	2.02049
$195$	0	0
$196$	−24.1716	−1.72654
$197$	8.48528i	0.604551i	0.953221	+	0.302276i	$0.0977463\pi$
$197$	8.48528i	0.604551i	−0.953221	+	0.302276i	$0.902254\pi$
$198$	2.41421i	0.171571i
$199$	21.6569	1.53521	0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569	1.53521	0.767607	+	0.640921i	$0.221447\pi$
$200$	0	0
$201$	5.65685	0.399004
$202$	− 2.00000i	− 0.140720i
$203$	− 4.00000i	− 0.280745i
$204$	−4.48528	−0.314033
$205$	0	0
$206$	8.00000	0.557386
$207$	4.00000i	0.278019i
$208$	− 16.9706i	− 1.17670i
$209$	−6.82843	−0.472332
$210$	0	0
$211$	1.17157	0.0806544	0.0403272	−	0.999187i	$-0.487160\pi$
$211$	1.17157	0.0806544	0.0403272	+	0.999187i	$0.487160\pi$
$212$	− 35.6569i	− 2.44892i
$213$	− 2.34315i	− 0.160550i
$214$	41.7990	2.85732
$215$	0	0
$216$	4.41421	0.300349
$217$	0	0
$218$	− 41.7990i	− 2.83098i
$219$	11.3137	0.764510
$220$	0	0
$221$	6.62742	0.445808
$222$	− 28.1421i	− 1.88878i
$223$	− 6.34315i	− 0.424768i	−0.977186	−	0.212384i	$-0.931877\pi$
$223$	− 6.34315i	− 0.424768i	0.977186	−	0.212384i	$-0.0681228\pi$
$224$	−1.31371	−0.0877758
$225$	0	0
$226$	45.7990	3.04650
$227$	14.0000i	0.929213i	0.885517	+	0.464606i	$0.153804\pi$
$227$	14.0000i	0.929213i	−0.885517	+	0.464606i	$0.846196\pi$
$228$	26.1421i	1.73131i
$229$	2.00000	0.132164	0.0660819	−	0.997814i	$-0.478950\pi$
$229$	2.00000	0.132164	0.0660819	+	0.997814i	$0.478950\pi$
$230$	0	0
$231$	0.828427	0.0545065
$232$	− 21.3137i	− 1.39931i
$233$	− 18.8284i	− 1.23349i	−0.787163	−	0.616746i	$-0.788451\pi$
$233$	− 18.8284i	− 1.23349i	0.787163	−	0.616746i	$-0.211549\pi$
$234$	−13.6569	−0.892776
$235$	0	0
$236$	−15.3137	−0.996838
$237$	8.48528i	0.551178i
$238$	2.34315i	0.151884i
$239$	−17.6569	−1.14213	−0.571063	−	0.820906i	$-0.693469\pi$
$239$	−17.6569	−1.14213	−0.571063	+	0.820906i	$0.693469\pi$
$240$	0	0
$241$	−12.3431	−0.795092	−0.397546	−	0.917582i	$-0.630138\pi$
$241$	−12.3431	−0.795092	−0.397546	+	0.917582i	$0.630138\pi$
$242$	2.41421i	0.155192i
$243$	− 1.00000i	− 0.0641500i
$244$	44.6274	2.85698
$245$	0	0
$246$	11.6569	0.743214
$247$	− 38.6274i	− 2.45780i
$248$	0	0
$249$	−10.0000	−0.633724
$250$	0	0
$251$	20.9706	1.32365	0.661825	−	0.749658i	$-0.269782\pi$
$251$	20.9706	1.32365	0.661825	+	0.749658i	$0.269782\pi$
$252$	− 3.17157i	− 0.199790i
$253$	4.00000i	0.251478i
$254$	−34.9706	−2.19425
$255$	0	0
$256$	−29.9706	−1.87316
$257$	16.3431i	1.01946i	0.860335	+	0.509729i	$0.170254\pi$
$257$	16.3431i	1.01946i	−0.860335	+	0.509729i	$0.829746\pi$
$258$	− 21.3137i	− 1.32693i
$259$	−9.65685	−0.600048
$260$	0	0
$261$	−4.82843	−0.298872
$262$	8.00000i	0.494242i
$263$	18.0000i	1.10993i	0.831875	+	0.554964i	$0.187268\pi$
$263$	18.0000i	1.10993i	−0.831875	+	0.554964i	$0.812732\pi$
$264$	4.41421	0.271676
$265$	0	0
$266$	13.6569	0.837355
$267$	3.65685i	0.223796i
$268$	− 21.6569i	− 1.32290i
$269$	−20.6274	−1.25768	−0.628838	−	0.777536i	$-0.716469\pi$
$269$	−20.6274	−1.25768	−0.628838	+	0.777536i	$0.716469\pi$
$270$	0	0
$271$	−11.7990	−0.716738	−0.358369	−	0.933580i	$-0.616667\pi$
$271$	−11.7990	−0.716738	−0.358369	+	0.933580i	$0.616667\pi$
$272$	3.51472i	0.213111i
$273$	4.68629i	0.283627i
$274$	−32.1421	−1.94178
$275$	0	0
$276$	15.3137	0.921777
$277$	2.34315i	0.140786i	0.997519	+	0.0703930i	$0.0224253\pi$
$277$	2.34315i	0.140786i	−0.997519	+	0.0703930i	$0.977575\pi$
$278$	− 1.17157i	− 0.0702663i
$279$	0	0
$280$	0	0
$281$	−11.1716	−0.666440	−0.333220	−	0.942849i	$-0.608135\pi$
$281$	−11.1716	−0.666440	−0.333220	+	0.942849i	$0.608135\pi$
$282$	9.65685i	0.575057i
$283$	− 8.82843i	− 0.524796i	−0.964960	−	0.262398i	$-0.915487\pi$
$283$	− 8.82843i	− 0.524796i	0.964960	−	0.262398i	$-0.0845132\pi$
$284$	−8.97056	−0.532305
$285$	0	0
$286$	−13.6569	−0.807547
$287$	− 4.00000i	− 0.236113i
$288$	1.58579i	0.0934434i
$289$	15.6274	0.919260
$290$	0	0
$291$	−11.6569	−0.683337
$292$	− 43.3137i	− 2.53474i
$293$	− 6.82843i	− 0.398921i	−0.979906	−	0.199460i	$-0.936081\pi$
$293$	− 6.82843i	− 0.398921i	0.979906	−	0.199460i	$-0.0639190\pi$
$294$	15.2426	0.888969
$295$	0	0
$296$	−51.4558	−2.99081
$297$	− 1.00000i	− 0.0580259i
$298$	− 3.65685i	− 0.211836i
$299$	−22.6274	−1.30858
$300$	0	0
$301$	−7.31371	−0.421555
$302$	39.7990i	2.29017i
$303$	0.828427i	0.0475919i
$304$	20.4853	1.17491
$305$	0	0
$306$	2.82843	0.161690
$307$	3.17157i	0.181011i	0.995896	+	0.0905056i	$0.0288483\pi$
$307$	3.17157i	0.181011i	−0.995896	+	0.0905056i	$0.971152\pi$
$308$	− 3.17157i	− 0.180717i
$309$	−3.31371	−0.188510
$310$	0	0
$311$	−3.31371	−0.187903	−0.0939516	−	0.995577i	$-0.529950\pi$
$311$	−3.31371	−0.187903	−0.0939516	+	0.995577i	$0.529950\pi$
$312$	24.9706i	1.41368i
$313$	15.6569i	0.884978i	0.896774	+	0.442489i	$0.145904\pi$
$313$	15.6569i	0.884978i	−0.896774	+	0.442489i	$0.854096\pi$
$314$	43.4558	2.45236
$315$	0	0
$316$	32.4853	1.82744
$317$	26.2843i	1.47627i	0.674652	+	0.738136i	$0.264294\pi$
$317$	26.2843i	1.47627i	−0.674652	+	0.738136i	$0.735706\pi$
$318$	22.4853i	1.26091i
$319$	−4.82843	−0.270340
$320$	0	0
$321$	−17.3137	−0.966357
$322$	− 8.00000i	− 0.445823i
$323$	8.00000i	0.445132i
$324$	−3.82843	−0.212690
$325$	0	0
$326$	17.6569	0.977923
$327$	17.3137i	0.957450i
$328$	− 21.3137i	− 1.17685i
$329$	3.31371	0.182691
$330$	0	0
$331$	6.34315	0.348651	0.174325	−	0.984688i	$-0.444226\pi$
$331$	6.34315	0.348651	0.174325	+	0.984688i	$0.444226\pi$
$332$	38.2843i	2.10112i
$333$	11.6569i	0.638792i
$334$	−32.1421	−1.75874
$335$	0	0
$336$	−2.48528	−0.135583
$337$	− 3.31371i	− 0.180509i	−0.995919	−	0.0902546i	$-0.971232\pi$
$337$	− 3.31371i	− 0.180509i	0.995919	−	0.0902546i	$-0.0287681\pi$
$338$	− 45.8701i	− 2.49500i
$339$	−18.9706	−1.03034
$340$	0	0
$341$	0	0
$342$	− 16.4853i	− 0.891422i
$343$	− 11.0294i	− 0.595534i
$344$	−38.9706	−2.10115
$345$	0	0
$346$	−6.82843	−0.367099
$347$	29.3137i	1.57364i	0.617181	+	0.786821i	$0.288275\pi$
$347$	29.3137i	1.57364i	−0.617181	+	0.786821i	$0.711725\pi$
$348$	18.4853i	0.990915i
$349$	−10.9706	−0.587241	−0.293620	−	0.955922i	$-0.594860\pi$
$349$	−10.9706	−0.587241	−0.293620	+	0.955922i	$0.594860\pi$
$350$	0	0
$351$	5.65685	0.301941
$352$	1.58579i	0.0845227i
$353$	26.0000i	1.38384i	0.721974	+	0.691920i	$0.243235\pi$
$353$	26.0000i	1.38384i	−0.721974	+	0.691920i	$0.756765\pi$
$354$	9.65685	0.513256
$355$	0	0
$356$	14.0000	0.741999
$357$	− 0.970563i	− 0.0513676i
$358$	42.6274i	2.25293i
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	27.6274	1.45407
$362$	− 33.7990i	− 1.77644i
$363$	− 1.00000i	− 0.0524864i
$364$	17.9411	0.940370
$365$	0	0
$366$	−28.1421	−1.47101
$367$	− 9.65685i	− 0.504084i	−0.967716	−	0.252042i	$-0.918898\pi$
$367$	− 9.65685i	− 0.504084i	0.967716	−	0.252042i	$-0.0811021\pi$
$368$	− 12.0000i	− 0.625543i
$369$	−4.82843	−0.251358
$370$	0	0
$371$	7.71573	0.400581
$372$	0	0
$373$	10.6274i	0.550267i	0.961406	+	0.275133i	$0.0887220\pi$
$373$	10.6274i	0.550267i	−0.961406	+	0.275133i	$0.911278\pi$
$374$	2.82843	0.146254
$375$	0	0
$376$	17.6569	0.910583
$377$	− 27.3137i	− 1.40673i
$378$	2.00000i	0.102869i
$379$	23.3137	1.19754	0.598772	−	0.800919i	$-0.295655\pi$
$379$	23.3137	1.19754	0.598772	+	0.800919i	$0.295655\pi$
$380$	0	0
$381$	14.4853	0.742103
$382$	13.6569i	0.698745i
$383$	− 8.00000i	− 0.408781i	−0.978889	−	0.204390i	$-0.934479\pi$
$383$	− 8.00000i	− 0.408781i	0.978889	−	0.204390i	$-0.0655212\pi$
$384$	20.5563	1.04901
$385$	0	0
$386$	−32.9706	−1.67816
$387$	8.82843i	0.448774i
$388$	44.6274i	2.26561i
$389$	23.6569	1.19945	0.599725	−	0.800206i	$-0.295277\pi$
$389$	23.6569	1.19945	0.599725	+	0.800206i	$0.295277\pi$
$390$	0	0
$391$	4.68629	0.236996
$392$	− 27.8701i	− 1.40765i
$393$	− 3.31371i	− 0.167154i
$394$	−20.4853	−1.03203
$395$	0	0
$396$	−3.82843	−0.192386
$397$	14.9706i	0.751351i	0.926751	+	0.375676i	$0.122589\pi$
$397$	14.9706i	0.751351i	−0.926751	+	0.375676i	$0.877411\pi$
$398$	52.2843i	2.62077i
$399$	−5.65685	−0.283197
$400$	0	0
$401$	−6.68629	−0.333897	−0.166949	−	0.985966i	$-0.553391\pi$
$401$	−6.68629	−0.333897	−0.166949	+	0.985966i	$0.553391\pi$
$402$	13.6569i	0.681142i
$403$	0	0
$404$	3.17157	0.157792
$405$	0	0
$406$	9.65685	0.479262
$407$	11.6569i	0.577809i
$408$	− 5.17157i	− 0.256031i
$409$	19.6569	0.971969	0.485984	−	0.873967i	$-0.338461\pi$
$409$	19.6569	0.971969	0.485984	+	0.873967i	$0.338461\pi$
$410$	0	0
$411$	13.3137	0.656717
$412$	12.6863i	0.625009i
$413$	− 3.31371i	− 0.163057i
$414$	−9.65685	−0.474608
$415$	0	0
$416$	−8.97056	−0.439818
$417$	0.485281i	0.0237643i
$418$	− 16.4853i	− 0.806321i
$419$	36.9706	1.80613	0.903065	−	0.429504i	$-0.141311\pi$
$419$	36.9706	1.80613	0.903065	+	0.429504i	$0.141311\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	2.82843i	0.137686i
$423$	− 4.00000i	− 0.194487i
$424$	41.1127	1.99661
$425$	0	0
$426$	5.65685	0.274075
$427$	9.65685i	0.467328i
$428$	66.2843i	3.20397i
$429$	5.65685	0.273115
$430$	0	0
$431$	21.6569	1.04317	0.521587	−	0.853198i	$-0.325340\pi$
$431$	21.6569	1.04317	0.521587	+	0.853198i	$0.325340\pi$
$432$	3.00000i	0.144338i
$433$	− 15.6569i	− 0.752420i	−0.926534	−	0.376210i	$-0.877227\pi$
$433$	− 15.6569i	− 0.752420i	0.926534	−	0.376210i	$-0.122773\pi$
$434$	0	0
$435$	0	0
$436$	66.2843	3.17444
$437$	− 27.3137i	− 1.30659i
$438$	27.3137i	1.30510i
$439$	20.4853	0.977709	0.488855	−	0.872365i	$-0.337415\pi$
$439$	20.4853	0.977709	0.488855	+	0.872365i	$0.337415\pi$
$440$	0	0
$441$	−6.31371	−0.300653
$442$	16.0000i	0.761042i
$443$	12.0000i	0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$	12.0000i	0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$	44.6274	2.11792
$445$	0	0
$446$	15.3137	0.725125
$447$	1.51472i	0.0716437i
$448$	− 8.14214i	− 0.384680i
$449$	−30.9706	−1.46159	−0.730796	−	0.682596i	$-0.760851\pi$
$449$	−30.9706	−1.46159	−0.730796	+	0.682596i	$0.760851\pi$
$450$	0	0
$451$	−4.82843	−0.227362
$452$	72.6274i	3.41611i
$453$	− 16.4853i	− 0.774546i
$454$	−33.7990	−1.58627
$455$	0	0
$456$	−30.1421	−1.41153
$457$	23.3137i	1.09057i	0.838251	+	0.545285i	$0.183578\pi$
$457$	23.3137i	1.09057i	−0.838251	+	0.545285i	$0.816422\pi$
$458$	4.82843i	0.225618i
$459$	−1.17157	−0.0546843
$460$	0	0
$461$	0.142136	0.00661992	0.00330996	−	0.999995i	$-0.498946\pi$
$461$	0.142136	0.00661992	0.00330996	+	0.999995i	$0.498946\pi$
$462$	2.00000i	0.0930484i
$463$	4.97056i	0.231002i	0.993307	+	0.115501i	$0.0368473\pi$
$463$	4.97056i	0.231002i	−0.993307	+	0.115501i	$0.963153\pi$
$464$	14.4853	0.672462
$465$	0	0
$466$	45.4558	2.10570
$467$	22.6274i	1.04707i	0.852004	+	0.523536i	$0.175387\pi$
$467$	22.6274i	1.04707i	−0.852004	+	0.523536i	$0.824613\pi$
$468$	− 21.6569i	− 1.00109i
$469$	4.68629	0.216393
$470$	0	0
$471$	−18.0000	−0.829396
$472$	− 17.6569i	− 0.812723i
$473$	8.82843i	0.405932i
$474$	−20.4853	−0.940920
$475$	0	0
$476$	−3.71573	−0.170310
$477$	− 9.31371i	− 0.426445i
$478$	− 42.6274i	− 1.94973i
$479$	−36.9706	−1.68923	−0.844614	−	0.535376i	$-0.820170\pi$
$479$	−36.9706	−1.68923	−0.844614	+	0.535376i	$0.820170\pi$
$480$	0	0
$481$	−65.9411	−3.00666
$482$	− 29.7990i	− 1.35731i
$483$	3.31371i	0.150779i
$484$	−3.82843	−0.174019
$485$	0	0
$486$	2.41421	0.109511
$487$	12.9706i	0.587752i	0.955844	+	0.293876i	$0.0949453\pi$
$487$	12.9706i	0.587752i	−0.955844	+	0.293876i	$0.905055\pi$
$488$	51.4558i	2.32930i
$489$	−7.31371	−0.330737
$490$	0	0
$491$	14.3431	0.647297	0.323649	−	0.946177i	$-0.395090\pi$
$491$	14.3431	0.647297	0.323649	+	0.946177i	$0.395090\pi$
$492$	18.4853i	0.833381i
$493$	5.65685i	0.254772i
$494$	93.2548	4.19573
$495$	0	0
$496$	0	0
$497$	− 1.94113i	− 0.0870714i
$498$	− 24.1421i	− 1.08183i
$499$	22.3431	1.00022	0.500108	−	0.865963i	$-0.333294\pi$
$499$	22.3431	1.00022	0.500108	+	0.865963i	$0.333294\pi$
$500$	0	0
$501$	13.3137	0.594813
$502$	50.6274i	2.25961i
$503$	17.3137i	0.771980i	0.922503	+	0.385990i	$0.126140\pi$
$503$	17.3137i	0.771980i	−0.922503	+	0.385990i	$0.873860\pi$
$504$	3.65685	0.162889
$505$	0	0
$506$	−9.65685	−0.429300
$507$	19.0000i	0.843820i
$508$	− 55.4558i	− 2.46046i
$509$	−18.6863	−0.828255	−0.414128	−	0.910219i	$-0.635913\pi$
$509$	−18.6863	−0.828255	−0.414128	+	0.910219i	$0.635913\pi$
$510$	0	0
$511$	9.37258	0.414619
$512$	− 31.2426i	− 1.38074i
$513$	6.82843i	0.301482i
$514$	−39.4558	−1.74032
$515$	0	0
$516$	33.7990	1.48792
$517$	− 4.00000i	− 0.175920i
$518$	− 23.3137i	− 1.02435i
$519$	2.82843	0.124154
$520$	0	0
$521$	−32.6274	−1.42943	−0.714717	−	0.699414i	$-0.753444\pi$
$521$	−32.6274	−1.42943	−0.714717	+	0.699414i	$0.753444\pi$
$522$	− 11.6569i	− 0.510207i
$523$	− 9.51472i	− 0.416050i	−0.978124	−	0.208025i	$-0.933297\pi$
$523$	− 9.51472i	− 0.416050i	0.978124	−	0.208025i	$-0.0667035\pi$
$524$	−12.6863	−0.554203
$525$	0	0
$526$	−43.4558	−1.89476
$527$	0	0
$528$	3.00000i	0.130558i
$529$	7.00000	0.304348
$530$	0	0
$531$	−4.00000	−0.173585
$532$	21.6569i	0.938944i
$533$	− 27.3137i	− 1.18309i
$534$	−8.82843	−0.382043
$535$	0	0
$536$	24.9706	1.07856
$537$	− 17.6569i	− 0.761950i
$538$	− 49.7990i	− 2.14699i
$539$	−6.31371	−0.271951
$540$	0	0
$541$	17.3137	0.744374	0.372187	−	0.928158i	$-0.378608\pi$
$541$	17.3137	0.744374	0.372187	+	0.928158i	$0.378608\pi$
$542$	− 28.4853i	− 1.22355i
$543$	14.0000i	0.600798i
$544$	1.85786	0.0796553
$545$	0	0
$546$	−11.3137	−0.484182
$547$	8.14214i	0.348133i	0.984734	+	0.174066i	$0.0556907\pi$
$547$	8.14214i	0.348133i	−0.984734	+	0.174066i	$0.944309\pi$
$548$	− 50.9706i	− 2.17735i
$549$	11.6569	0.497502
$550$	0	0
$551$	32.9706	1.40459
$552$	17.6569i	0.751526i
$553$	7.02944i	0.298922i
$554$	−5.65685	−0.240337
$555$	0	0
$556$	1.85786	0.0787910
$557$	− 5.17157i	− 0.219127i	−0.993980	−	0.109563i	$-0.965055\pi$
$557$	− 5.17157i	− 0.219127i	0.993980	−	0.109563i	$-0.0349452\pi$
$558$	0	0
$559$	−49.9411	−2.11228
$560$	0	0
$561$	−1.17157	−0.0494638
$562$	− 26.9706i	− 1.13768i
$563$	31.6569i	1.33418i	0.744978	+	0.667089i	$0.232460\pi$
$563$	31.6569i	1.33418i	−0.744978	+	0.667089i	$0.767540\pi$
$564$	−15.3137	−0.644823
$565$	0	0
$566$	21.3137	0.895882
$567$	− 0.828427i	− 0.0347907i
$568$	− 10.3431i	− 0.433989i
$569$	35.4558	1.48639	0.743193	−	0.669077i	$-0.233310\pi$
$569$	35.4558	1.48639	0.743193	+	0.669077i	$0.233310\pi$
$570$	0	0
$571$	−16.4853	−0.689888	−0.344944	−	0.938623i	$-0.612102\pi$
$571$	−16.4853	−0.689888	−0.344944	+	0.938623i	$0.612102\pi$
$572$	− 21.6569i	− 0.905519i
$573$	− 5.65685i	− 0.236318i
$574$	9.65685	0.403069
$575$	0	0
$576$	−9.82843	−0.409518
$577$	− 14.0000i	− 0.582828i	−0.956597	−	0.291414i	$-0.905874\pi$
$577$	− 14.0000i	− 0.582828i	0.956597	−	0.291414i	$-0.0941257\pi$
$578$	37.7279i	1.56927i
$579$	13.6569	0.567559
$580$	0	0
$581$	−8.28427	−0.343689
$582$	− 28.1421i	− 1.16653i
$583$	− 9.31371i	− 0.385734i
$584$	49.9411	2.06658
$585$	0	0
$586$	16.4853	0.681001
$587$	− 14.6274i	− 0.603738i	−0.953349	−	0.301869i	$-0.902389\pi$
$587$	− 14.6274i	− 0.603738i	0.953349	−	0.301869i	$-0.0976105\pi$
$588$	24.1716i	0.996819i
$589$	0	0
$590$	0	0
$591$	8.48528	0.349038
$592$	− 34.9706i	− 1.43728i
$593$	− 22.8284i	− 0.937451i	−0.883344	−	0.468726i	$-0.844713\pi$
$593$	− 22.8284i	− 0.937451i	0.883344	−	0.468726i	$-0.155287\pi$
$594$	2.41421	0.0990564
$595$	0	0
$596$	5.79899	0.237536
$597$	− 21.6569i	− 0.886356i
$598$	− 54.6274i	− 2.23388i
$599$	−27.3137	−1.11601	−0.558004	−	0.829838i	$-0.688433\pi$
$599$	−27.3137	−1.11601	−0.558004	+	0.829838i	$0.688433\pi$
$600$	0	0
$601$	−5.31371	−0.216751	−0.108375	−	0.994110i	$-0.534565\pi$
$601$	−5.31371	−0.216751	−0.108375	+	0.994110i	$0.534565\pi$
$602$	− 17.6569i	− 0.719640i
$603$	− 5.65685i	− 0.230365i
$604$	−63.1127	−2.56802
$605$	0	0
$606$	−2.00000	−0.0812444
$607$	− 1.51472i	− 0.0614805i	−0.999527	−	0.0307403i	$-0.990214\pi$
$607$	− 1.51472i	− 0.0614805i	0.999527	−	0.0307403i	$-0.00978647\pi$
$608$	− 10.8284i	− 0.439151i
$609$	−4.00000	−0.162088
$610$	0	0
$611$	22.6274	0.915407
$612$	4.48528i	0.181307i
$613$	− 45.9411i	− 1.85554i	−0.373147	−	0.927772i	$-0.621721\pi$
$613$	− 45.9411i	− 1.85554i	0.373147	−	0.927772i	$-0.378279\pi$
$614$	−7.65685	−0.309005
$615$	0	0
$616$	3.65685	0.147339
$617$	− 0.343146i	− 0.0138145i	−0.999976	−	0.00690726i	$-0.997801\pi$
$617$	− 0.343146i	− 0.0138145i	0.999976	−	0.00690726i	$-0.00219867\pi$
$618$	− 8.00000i	− 0.321807i
$619$	14.3431	0.576500	0.288250	−	0.957555i	$-0.406927\pi$
$619$	14.3431	0.576500	0.288250	+	0.957555i	$0.406927\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	− 8.00000i	− 0.320771i
$623$	3.02944i	0.121372i
$624$	−16.9706	−0.679366
$625$	0	0
$626$	−37.7990	−1.51075
$627$	6.82843i	0.272701i
$628$	68.9117i	2.74988i
$629$	13.6569	0.544534
$630$	0	0
$631$	45.6569	1.81757	0.908785	−	0.417264i	$-0.137011\pi$
$631$	45.6569	1.81757	0.908785	+	0.417264i	$0.137011\pi$
$632$	37.4558i	1.48991i
$633$	− 1.17157i	− 0.0465658i
$634$	−63.4558	−2.52015
$635$	0	0
$636$	−35.6569	−1.41389
$637$	− 35.7157i	− 1.41511i
$638$	− 11.6569i	− 0.461499i
$639$	−2.34315	−0.0926934
$640$	0	0
$641$	6.97056	0.275321	0.137660	−	0.990479i	$-0.456042\pi$
$641$	6.97056	0.275321	0.137660	+	0.990479i	$0.456042\pi$
$642$	− 41.7990i	− 1.64967i
$643$	37.9411i	1.49625i	0.663557	+	0.748126i	$0.269046\pi$
$643$	37.9411i	1.49625i	−0.663557	+	0.748126i	$0.730954\pi$
$644$	12.6863	0.499910
$645$	0	0
$646$	−19.3137	−0.759888
$647$	− 4.68629i	− 0.184237i	−0.995748	−	0.0921186i	$-0.970636\pi$
$647$	− 4.68629i	− 0.184237i	0.995748	−	0.0921186i	$-0.0293639\pi$
$648$	− 4.41421i	− 0.173407i
$649$	−4.00000	−0.157014
$650$	0	0
$651$	0	0
$652$	28.0000i	1.09656i
$653$	6.97056i	0.272779i	0.990655	+	0.136390i	$0.0435499\pi$
$653$	6.97056i	0.272779i	−0.990655	+	0.136390i	$0.956450\pi$
$654$	−41.7990	−1.63447
$655$	0	0
$656$	14.4853	0.565555
$657$	− 11.3137i	− 0.441390i
$658$	8.00000i	0.311872i
$659$	15.3137	0.596537	0.298269	−	0.954482i	$-0.403591\pi$
$659$	15.3137	0.596537	0.298269	+	0.954482i	$0.403591\pi$
$660$	0	0
$661$	9.31371	0.362261	0.181131	−	0.983459i	$-0.442024\pi$
$661$	9.31371	0.362261	0.181131	+	0.983459i	$0.442024\pi$
$662$	15.3137i	0.595184i
$663$	− 6.62742i	− 0.257388i
$664$	−44.1421	−1.71305
$665$	0	0
$666$	−28.1421	−1.09049
$667$	− 19.3137i	− 0.747830i
$668$	− 50.9706i	− 1.97211i
$669$	−6.34315	−0.245240
$670$	0	0
$671$	11.6569	0.450008
$672$	1.31371i	0.0506774i
$673$	18.3431i	0.707076i	0.935420	+	0.353538i	$0.115022\pi$
$673$	18.3431i	0.707076i	−0.935420	+	0.353538i	$0.884978\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	72.7401	2.79770
$677$	− 29.4558i	− 1.13208i	−0.824378	−	0.566040i	$-0.808475\pi$
$677$	− 29.4558i	− 1.13208i	0.824378	−	0.566040i	$-0.191525\pi$
$678$	− 45.7990i	− 1.75890i
$679$	−9.65685	−0.370596
$680$	0	0
$681$	14.0000	0.536481
$682$	0	0
$683$	24.0000i	0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$	24.0000i	0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	26.1421	0.999570
$685$	0	0
$686$	26.6274	1.01664
$687$	− 2.00000i	− 0.0763048i
$688$	− 26.4853i	− 1.00974i
$689$	52.6863	2.00719
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	− 10.8284i	− 0.411635i
$693$	− 0.828427i	− 0.0314693i
$694$	−70.7696	−2.68638
$695$	0	0
$696$	−21.3137	−0.807894
$697$	5.65685i	0.214269i
$698$	− 26.4853i	− 1.00248i
$699$	−18.8284	−0.712157
$700$	0	0
$701$	36.1421	1.36507	0.682535	−	0.730853i	$-0.260878\pi$
$701$	36.1421	1.36507	0.682535	+	0.730853i	$0.260878\pi$
$702$	13.6569i	0.515445i
$703$	− 79.5980i	− 3.00209i
$704$	−9.82843	−0.370423
$705$	0	0
$706$	−62.7696	−2.36236
$707$	0.686292i	0.0258106i
$708$	15.3137i	0.575524i
$709$	−6.68629	−0.251109	−0.125554	−	0.992087i	$-0.540071\pi$
$709$	−6.68629	−0.251109	−0.125554	+	0.992087i	$0.540071\pi$
$710$	0	0
$711$	8.48528	0.318223
$712$	16.1421i	0.604952i
$713$	0	0
$714$	2.34315	0.0876900
$715$	0	0
$716$	−67.5980	−2.52626
$717$	17.6569i	0.659407i
$718$	− 28.9706i	− 1.08117i
$719$	47.5980	1.77511	0.887553	−	0.460706i	$-0.152404\pi$
$719$	47.5980	1.77511	0.887553	+	0.460706i	$0.152404\pi$
$720$	0	0
$721$	−2.74517	−0.102235
$722$	66.6985i	2.48226i
$723$	12.3431i	0.459047i
$724$	53.5980	1.99195
$725$	0	0
$726$	2.41421	0.0895999
$727$	− 33.9411i	− 1.25881i	−0.777079	−	0.629403i	$-0.783299\pi$
$727$	− 33.9411i	− 1.25881i	0.777079	−	0.629403i	$-0.216701\pi$
$728$	20.6863i	0.766685i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	10.3431	0.382555
$732$	− 44.6274i	− 1.64948i
$733$	− 6.34315i	− 0.234289i	−0.993115	−	0.117145i	$-0.962626\pi$
$733$	− 6.34315i	− 0.234289i	0.993115	−	0.117145i	$-0.0373741\pi$
$734$	23.3137	0.860525
$735$	0	0
$736$	−6.34315	−0.233811
$737$	− 5.65685i	− 0.208373i
$738$	− 11.6569i	− 0.429095i
$739$	15.1127	0.555930	0.277965	−	0.960591i	$-0.410340\pi$
$739$	15.1127	0.555930	0.277965	+	0.960591i	$0.410340\pi$
$740$	0	0
$741$	−38.6274	−1.41901
$742$	18.6274i	0.683834i
$743$	36.3431i	1.33330i	0.745371	+	0.666650i	$0.232273\pi$
$743$	36.3431i	1.33330i	−0.745371	+	0.666650i	$0.767727\pi$
$744$	0	0
$745$	0	0
$746$	−25.6569	−0.939364
$747$	10.0000i	0.365881i
$748$	4.48528i	0.163998i
$749$	−14.3431	−0.524087
$750$	0	0
$751$	20.2843	0.740184	0.370092	−	0.928995i	$-0.379326\pi$
$751$	20.2843	0.740184	0.370092	+	0.928995i	$0.379326\pi$
$752$	12.0000i	0.437595i
$753$	− 20.9706i	− 0.764210i
$754$	65.9411	2.40143
$755$	0	0
$756$	−3.17157	−0.115349
$757$	36.6274i	1.33125i	0.746288	+	0.665623i	$0.231834\pi$
$757$	36.6274i	1.33125i	−0.746288	+	0.665623i	$0.768166\pi$
$758$	56.2843i	2.04434i
$759$	4.00000	0.145191
$760$	0	0
$761$	−28.8284	−1.04503	−0.522515	−	0.852630i	$-0.675006\pi$
$761$	−28.8284	−1.04503	−0.522515	+	0.852630i	$0.675006\pi$
$762$	34.9706i	1.26685i
$763$	14.3431i	0.519257i
$764$	−21.6569	−0.783517
$765$	0	0
$766$	19.3137	0.697833
$767$	− 22.6274i	− 0.817029i
$768$	29.9706i	1.08147i
$769$	−10.6863	−0.385358	−0.192679	−	0.981262i	$-0.561718\pi$
$769$	−10.6863	−0.385358	−0.192679	+	0.981262i	$0.561718\pi$
$770$	0	0
$771$	16.3431	0.588584
$772$	− 52.2843i	− 1.88175i
$773$	3.65685i	0.131528i	0.997835	+	0.0657640i	$0.0209484\pi$
$773$	3.65685i	0.131528i	−0.997835	+	0.0657640i	$0.979052\pi$
$774$	−21.3137	−0.766105
$775$	0	0
$776$	−51.4558	−1.84716
$777$	9.65685i	0.346438i
$778$	57.1127i	2.04759i
$779$	32.9706	1.18129
$780$	0	0
$781$	−2.34315	−0.0838443
$782$	11.3137i	0.404577i
$783$	4.82843i	0.172554i
$784$	18.9411	0.676469
$785$	0	0
$786$	8.00000	0.285351
$787$	20.1421i	0.717990i	0.933340	+	0.358995i	$0.116880\pi$
$787$	20.1421i	0.717990i	−0.933340	+	0.358995i	$0.883120\pi$
$788$	− 32.4853i	− 1.15724i
$789$	18.0000	0.640817
$790$	0	0
$791$	−15.7157	−0.558787
$792$	− 4.41421i	− 0.156852i
$793$	65.9411i	2.34164i
$794$	−36.1421	−1.28264
$795$	0	0
$796$	−82.9117	−2.93873
$797$	− 34.9706i	− 1.23872i	−0.785107	−	0.619360i	$-0.787392\pi$
$797$	− 34.9706i	− 1.23872i	0.785107	−	0.619360i	$-0.212608\pi$
$798$	− 13.6569i	− 0.483447i
$799$	−4.68629	−0.165789
$800$	0	0
$801$	3.65685	0.129209
$802$	− 16.1421i	− 0.569999i
$803$	− 11.3137i	− 0.399252i
$804$	−21.6569	−0.763778
$805$	0	0
$806$	0	0
$807$	20.6274i	0.726119i
$808$	3.65685i	0.128648i
$809$	−28.4264	−0.999419	−0.499710	−	0.866193i	$-0.666560\pi$
$809$	−28.4264	−0.999419	−0.499710	+	0.866193i	$0.666560\pi$
$810$	0	0
$811$	0.485281	0.0170405	0.00852027	−	0.999964i	$-0.497288\pi$
$811$	0.485281	0.0170405	0.00852027	+	0.999964i	$0.497288\pi$
$812$	15.3137i	0.537406i
$813$	11.7990i	0.413809i
$814$	−28.1421	−0.986381
$815$	0	0
$816$	3.51472	0.123040
$817$	− 60.2843i	− 2.10908i
$818$	47.4558i	1.65925i
$819$	4.68629	0.163752
$820$	0	0
$821$	−12.8284	−0.447715	−0.223858	−	0.974622i	$-0.571865\pi$
$821$	−12.8284	−0.447715	−0.223858	+	0.974622i	$0.571865\pi$
$822$	32.1421i	1.12109i
$823$	16.0000i	0.557725i	0.960331	+	0.278862i	$0.0899574\pi$
$823$	16.0000i	0.557725i	−0.960331	+	0.278862i	$0.910043\pi$
$824$	−14.6274	−0.509570
$825$	0	0
$826$	8.00000	0.278356
$827$	− 41.3137i	− 1.43662i	−0.695724	−	0.718309i	$-0.744916\pi$
$827$	− 41.3137i	− 1.43662i	0.695724	−	0.718309i	$-0.255084\pi$
$828$	− 15.3137i	− 0.532188i
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	0	0
$831$	2.34315	0.0812828
$832$	− 55.5980i	− 1.92751i
$833$	7.39697i	0.256290i
$834$	−1.17157	−0.0405683
$835$	0	0
$836$	26.1421	0.904145
$837$	0	0
$838$	89.2548i	3.08326i
$839$	22.6274	0.781185	0.390593	−	0.920564i	$-0.372270\pi$
$839$	22.6274	0.781185	0.390593	+	0.920564i	$0.372270\pi$
$840$	0	0
$841$	−5.68629	−0.196079
$842$	− 14.4853i	− 0.499196i
$843$	11.1716i	0.384769i
$844$	−4.48528	−0.154390
$845$	0	0
$846$	9.65685	0.332009
$847$	− 0.828427i	− 0.0284651i
$848$	27.9411i	0.959502i
$849$	−8.82843	−0.302991
$850$	0	0
$851$	−46.6274	−1.59837
$852$	8.97056i	0.307326i
$853$	− 8.68629i	− 0.297413i	−0.988881	−	0.148706i	$-0.952489\pi$
$853$	− 8.68629i	− 0.297413i	0.988881	−	0.148706i	$-0.0475110\pi$
$854$	−23.3137	−0.797779
$855$	0	0
$856$	−76.4264	−2.61220
$857$	28.4853i	0.973039i	0.873670	+	0.486519i	$0.161734\pi$
$857$	28.4853i	0.973039i	−0.873670	+	0.486519i	$0.838266\pi$
$858$	13.6569i	0.466237i
$859$	52.9706	1.80733	0.903666	−	0.428238i	$-0.140865\pi$
$859$	52.9706	1.80733	0.903666	+	0.428238i	$0.140865\pi$
$860$	0	0
$861$	−4.00000	−0.136320
$862$	52.2843i	1.78081i
$863$	− 20.6863i	− 0.704170i	−0.935968	−	0.352085i	$-0.885473\pi$
$863$	− 20.6863i	− 0.704170i	0.935968	−	0.352085i	$-0.114527\pi$
$864$	1.58579	0.0539496
$865$	0	0
$866$	37.7990	1.28446
$867$	− 15.6274i	− 0.530735i
$868$	0	0
$869$	8.48528	0.287843
$870$	0	0
$871$	32.0000	1.08428
$872$	76.4264i	2.58812i
$873$	11.6569i	0.394525i
$874$	65.9411	2.23049
$875$	0	0
$876$	−43.3137	−1.46343
$877$	− 2.62742i	− 0.0887216i	−0.999016	−	0.0443608i	$-0.985875\pi$
$877$	− 2.62742i	− 0.0887216i	0.999016	−	0.0443608i	$-0.0141251\pi$
$878$	49.4558i	1.66905i
$879$	−6.82843	−0.230317
$880$	0	0
$881$	−46.9706	−1.58248	−0.791239	−	0.611507i	$-0.790564\pi$
$881$	−46.9706	−1.58248	−0.791239	+	0.611507i	$0.790564\pi$
$882$	− 15.2426i	− 0.513246i
$883$	− 5.37258i	− 0.180802i	−0.995905	−	0.0904009i	$-0.971185\pi$
$883$	− 5.37258i	− 0.180802i	0.995905	−	0.0904009i	$-0.0288148\pi$
$884$	−25.3726	−0.853372
$885$	0	0
$886$	−28.9706	−0.973285
$887$	15.6569i	0.525706i	0.964836	+	0.262853i	$0.0846634\pi$
$887$	15.6569i	0.525706i	−0.964836	+	0.262853i	$0.915337\pi$
$888$	51.4558i	1.72675i
$889$	12.0000	0.402467
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	24.2843i	0.813098i
$893$	27.3137i	0.914018i
$894$	−3.65685	−0.122304
$895$	0	0
$896$	17.0294	0.568914
$897$	22.6274i	0.755507i
$898$	− 74.7696i	− 2.49509i
$899$	0	0
$900$	0	0
$901$	−10.9117	−0.363521
$902$	− 11.6569i	− 0.388131i
$903$	7.31371i	0.243385i
$904$	−83.7401	−2.78515
$905$	0	0
$906$	39.7990	1.32223
$907$	− 40.9706i	− 1.36041i	−0.733024	−	0.680203i	$-0.761892\pi$
$907$	− 40.9706i	− 1.36041i	0.733024	−	0.680203i	$-0.238108\pi$
$908$	− 53.5980i	− 1.77871i
$909$	0.828427	0.0274772
$910$	0	0
$911$	−48.9706	−1.62247	−0.811234	−	0.584722i	$-0.801203\pi$
$911$	−48.9706	−1.62247	−0.811234	+	0.584722i	$0.801203\pi$
$912$	− 20.4853i	− 0.678335i
$913$	10.0000i	0.330952i
$914$	−56.2843	−1.86172
$915$	0	0
$916$	−7.65685	−0.252990
$917$	− 2.74517i	− 0.0906534i
$918$	− 2.82843i	− 0.0933520i
$919$	−11.5147	−0.379836	−0.189918	−	0.981800i	$-0.560822\pi$
$919$	−11.5147	−0.379836	−0.189918	+	0.981800i	$0.560822\pi$
$920$	0	0
$921$	3.17157	0.104507
$922$	0.343146i	0.0113009i
$923$	− 13.2548i	− 0.436288i
$924$	−3.17157	−0.104337
$925$	0	0
$926$	−12.0000	−0.394344
$927$	3.31371i	0.108836i
$928$	− 7.65685i	− 0.251349i
$929$	45.5980	1.49602	0.748011	−	0.663687i	$-0.231009\pi$
$929$	45.5980	1.49602	0.748011	+	0.663687i	$0.231009\pi$
$930$	0	0
$931$	43.1127	1.41296
$932$	72.0833i	2.36117i
$933$	3.31371i	0.108486i
$934$	−54.6274	−1.78746
$935$	0	0
$936$	24.9706	0.816188
$937$	− 11.0294i	− 0.360316i	−0.983638	−	0.180158i	$-0.942339\pi$
$937$	− 11.0294i	− 0.360316i	0.983638	−	0.180158i	$-0.0576609\pi$
$938$	11.3137i	0.369406i
$939$	15.6569	0.510942
$940$	0	0
$941$	−34.7696	−1.13346	−0.566728	−	0.823905i	$-0.691791\pi$
$941$	−34.7696	−1.13346	−0.566728	+	0.823905i	$0.691791\pi$
$942$	− 43.4558i	− 1.41587i
$943$	− 19.3137i	− 0.628941i
$944$	12.0000	0.390567
$945$	0	0
$946$	−21.3137	−0.692968
$947$	− 6.62742i	− 0.215362i	−0.994185	−	0.107681i	$-0.965657\pi$
$947$	− 6.62742i	− 0.215362i	0.994185	−	0.107681i	$-0.0343425\pi$
$948$	− 32.4853i	− 1.05507i
$949$	64.0000	2.07753
$950$	0	0
$951$	26.2843	0.852326
$952$	− 4.28427i	− 0.138854i
$953$	− 11.7990i	− 0.382207i	−0.981570	−	0.191103i	$-0.938793\pi$
$953$	− 11.7990i	− 0.382207i	0.981570	−	0.191103i	$-0.0612066\pi$
$954$	22.4853	0.727988
$955$	0	0
$956$	67.5980	2.18627
$957$	4.82843i	0.156081i
$958$	− 89.2548i	− 2.88369i
$959$	11.0294	0.356159
$960$	0	0
$961$	−31.0000	−1.00000
$962$	− 159.196i	− 5.13268i
$963$	17.3137i	0.557926i
$964$	47.2548	1.52198
$965$	0	0
$966$	−8.00000	−0.257396
$967$	− 11.4558i	− 0.368395i	−0.982889	−	0.184198i	$-0.941031\pi$
$967$	− 11.4558i	− 0.368395i	0.982889	−	0.184198i	$-0.0589686\pi$
$968$	− 4.41421i	− 0.141878i
$969$	8.00000	0.256997
$970$	0	0
$971$	−34.6274	−1.11125	−0.555623	−	0.831434i	$-0.687520\pi$
$971$	−34.6274	−1.11125	−0.555623	+	0.831434i	$0.687520\pi$
$972$	3.82843i	0.122797i
$973$	0.402020i	0.0128882i
$974$	−31.3137	−1.00336
$975$	0	0
$976$	−34.9706	−1.11938
$977$	− 2.68629i	− 0.0859421i	−0.999076	−	0.0429710i	$-0.986318\pi$
$977$	− 2.68629i	− 0.0859421i	0.999076	−	0.0429710i	$-0.0136823\pi$
$978$	− 17.6569i	− 0.564604i
$979$	3.65685	0.116874
$980$	0	0
$981$	17.3137	0.552784
$982$	34.6274i	1.10501i
$983$	− 30.6274i	− 0.976863i	−0.872602	−	0.488431i	$-0.837569\pi$
$983$	− 30.6274i	− 0.976863i	0.872602	−	0.488431i	$-0.162431\pi$
$984$	−21.3137	−0.679456
$985$	0	0
$986$	−13.6569	−0.434923
$987$	− 3.31371i	− 0.105477i
$988$	147.882i	4.70476i
$989$	−35.3137	−1.12291
$990$	0	0
$991$	−30.6274	−0.972912	−0.486456	−	0.873705i	$-0.661711\pi$
$991$	−30.6274	−0.972912	−0.486456	+	0.873705i	$0.661711\pi$
$992$	0	0
$993$	− 6.34315i	− 0.201294i
$994$	4.68629	0.148640
$995$	0	0
$996$	38.2843	1.21308
$997$	39.3137i	1.24508i	0.782589	+	0.622539i	$0.213899\pi$
$997$	39.3137i	1.24508i	−0.782589	+	0.622539i	$0.786101\pi$
$998$	53.9411i	1.70748i
$999$	11.6569	0.368807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.c.e.199.4		4
3.2	odd	2		2475.2.c.m.199.1		4
5.2	odd	4		165.2.a.a.1.1	✓	2
5.3	odd	4		825.2.a.g.1.2		2
5.4	even	2	inner	825.2.c.e.199.1		4
15.2	even	4		495.2.a.d.1.2		2
15.8	even	4		2475.2.a.m.1.1		2
15.14	odd	2		2475.2.c.m.199.4		4
20.7	even	4		2640.2.a.bb.1.1		2
35.27	even	4		8085.2.a.ba.1.1		2
55.32	even	4		1815.2.a.k.1.2		2
55.43	even	4		9075.2.a.v.1.1		2
60.47	odd	4		7920.2.a.cg.1.1		2
165.32	odd	4		5445.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.a.a.1.1	✓	2	5.2	odd	4
495.2.a.d.1.2		2	15.2	even	4
825.2.a.g.1.2		2	5.3	odd	4
825.2.c.e.199.1		4	5.4	even	2	inner
825.2.c.e.199.4		4	1.1	even	1	trivial
1815.2.a.k.1.2		2	55.32	even	4
2475.2.a.m.1.1		2	15.8	even	4
2475.2.c.m.199.1		4	3.2	odd	2
2475.2.c.m.199.4		4	15.14	odd	2
2640.2.a.bb.1.1		2	20.7	even	4
5445.2.a.m.1.1		2	165.32	odd	4
7920.2.a.cg.1.1		2	60.47	odd	4
8085.2.a.ba.1.1		2	35.27	even	4
9075.2.a.v.1.1		2	55.43	even	4

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.41421i q^{2} -1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} -0.828427i q^{7} -4.41421i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.41421i q^{2} -1.00000i q^{3} -3.82843 q^{4} +2.41421 q^{6} -0.828427i q^{7} -4.41421i q^{8} -1.00000 q^{9} -1.00000 q^{11} +3.82843i q^{12} -5.65685i q^{13} +2.00000 q^{14} +3.00000 q^{16} +1.17157i q^{17} -2.41421i q^{18} +6.82843 q^{19} -0.828427 q^{21} -2.41421i q^{22} -4.00000i q^{23} -4.41421 q^{24} +13.6569 q^{26} +1.00000i q^{27} +3.17157i q^{28} +4.82843 q^{29} -1.58579i q^{32} +1.00000i q^{33} -2.82843 q^{34} +3.82843 q^{36} -11.6569i q^{37} +16.4853i q^{38} -5.65685 q^{39} +4.82843 q^{41} -2.00000i q^{42} -8.82843i q^{43} +3.82843 q^{44} +9.65685 q^{46} +4.00000i q^{47} -3.00000i q^{48} +6.31371 q^{49} +1.17157 q^{51} +21.6569i q^{52} +9.31371i q^{53} -2.41421 q^{54} -3.65685 q^{56} -6.82843i q^{57} +11.6569i q^{58} +4.00000 q^{59} -11.6569 q^{61} +0.828427i q^{63} +9.82843 q^{64} -2.41421 q^{66} +5.65685i q^{67} -4.48528i q^{68} -4.00000 q^{69} +2.34315 q^{71} +4.41421i q^{72} +11.3137i q^{73} +28.1421 q^{74} -26.1421 q^{76} +0.828427i q^{77} -13.6569i q^{78} -8.48528 q^{79} +1.00000 q^{81} +11.6569i q^{82} -10.0000i q^{83} +3.17157 q^{84} +21.3137 q^{86} -4.82843i q^{87} +4.41421i q^{88} -3.65685 q^{89} -4.68629 q^{91} +15.3137i q^{92} -9.65685 q^{94} -1.58579 q^{96} -11.6569i q^{97} +15.2426i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} - 4 q^{11} + 8 q^{14} + 12 q^{16} + 16 q^{19} + 8 q^{21} - 12 q^{24} + 32 q^{26} + 8 q^{29} + 4 q^{36} + 8 q^{41} + 4 q^{44} + 16 q^{46} - 20 q^{49} + 16 q^{51} - 4 q^{54} + 8 q^{56} + 16 q^{59} - 24 q^{61} + 28 q^{64} - 4 q^{66} - 16 q^{69} + 32 q^{71} + 56 q^{74} - 48 q^{76} + 4 q^{81} + 24 q^{84} + 40 q^{86} + 8 q^{89} - 64 q^{91} - 16 q^{94} - 12 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 - 4 * q^11 + 8 * q^14 + 12 * q^16 + 16 * q^19 + 8 * q^21 - 12 * q^24 + 32 * q^26 + 8 * q^29 + 4 * q^36 + 8 * q^41 + 4 * q^44 + 16 * q^46 - 20 * q^49 + 16 * q^51 - 4 * q^54 + 8 * q^56 + 16 * q^59 - 24 * q^61 + 28 * q^64 - 4 * q^66 - 16 * q^69 + 32 * q^71 + 56 * q^74 - 48 * q^76 + 4 * q^81 + 24 * q^84 + 40 * q^86 + 8 * q^89 - 64 * q^91 - 16 * q^94 - 12 * q^96 + 4 * q^99

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