LMFDB - Embedded newform 2070.2.d.h.829.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(829,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, 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("2070.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.d (of order $2$, degree $1$, 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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 10x^{12} + 55x^{10} + 58x^{8} + 495x^{6} + 810x^{4} + 729x^{2} + 6561 $ x^16 + x^14 + 10x^12 + 55x^10 + 58x^8 + 495x^6 + 810x^4 + 729x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			829.8
Root			$1.51276 + 0.843532i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.h.829.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(2.11238 - 0.733377i) q^{5} +2.29167i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.11238 - 0.733377i) q^{5} +2.29167i q^{7} +1.00000i q^{8} +(-0.733377 - 2.11238i) q^{10} -4.37040 q^{11} +3.75939i q^{13} +2.29167 q^{14} +1.00000 q^{16} -3.37413i q^{17} -3.46675 q^{19} +(-2.11238 + 0.733377i) q^{20} +4.37040i q^{22} +1.00000i q^{23} +(3.92432 - 3.09834i) q^{25} +3.75939 q^{26} -2.29167i q^{28} +6.30349 q^{29} +9.84863 q^{31} -1.00000i q^{32} -3.37413 q^{34} +(1.68066 + 4.84088i) q^{35} +6.51643i q^{37} +3.46675i q^{38} +(0.733377 + 2.11238i) q^{40} +2.54411 q^{41} +10.5283i q^{43} +4.37040 q^{44} +1.00000 q^{46} +8.78214i q^{47} +1.74825 q^{49} +(-3.09834 - 3.92432i) q^{50} -3.75939i q^{52} +1.46675i q^{53} +(-9.23195 + 3.20515i) q^{55} -2.29167 q^{56} -6.30349i q^{58} +2.54411 q^{59} -11.7899 q^{61} -9.84863i q^{62} -1.00000 q^{64} +(2.75705 + 7.94126i) q^{65} +6.37080i q^{67} +3.37413i q^{68} +(4.84088 - 1.68066i) q^{70} +4.69014 q^{71} +5.90542i q^{73} +6.51643 q^{74} +3.46675 q^{76} -10.0155i q^{77} -8.30763 q^{79} +(2.11238 - 0.733377i) q^{80} -2.54411i q^{82} +7.77439i q^{83} +(-2.47451 - 7.12745i) q^{85} +10.5283 q^{86} -4.37040i q^{88} +11.9565 q^{89} -8.61527 q^{91} -1.00000i q^{92} +8.78214 q^{94} +(-7.32311 + 2.54244i) q^{95} -6.30349i q^{97} -1.74825i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	2.11238	−	0.733377i	0.944686	−	0.327976i
$5$	2.11238	−	0.733377i	0.944686	−	0.327976i
$6$		0			0
$7$			2.29167i			0.866169i	0.901353	+	0.433085i	$0.142575\pi$
$7$			2.29167i			0.866169i	−0.901353	+	0.433085i	$0.857425\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.733377	−	2.11238i	−0.231914	−	0.667994i
$11$	−4.37040			−1.31772			−0.658862	−	0.752264i	$-0.728962\pi$
$11$	−4.37040			−1.31772			−0.658862	+	0.752264i	$0.728962\pi$
$12$		0			0
$13$			3.75939i			1.04267i	0.853353	+	0.521333i	$0.174565\pi$
$13$			3.75939i			1.04267i	−0.853353	+	0.521333i	$0.825435\pi$
$14$	2.29167			0.612474
$15$		0			0
$16$	1.00000			0.250000
$17$		−	3.37413i		−	0.818346i	−0.912457	−	0.409173i	$-0.865817\pi$
$17$		−	3.37413i		−	0.818346i	0.912457	−	0.409173i	$-0.134183\pi$
$18$		0			0
$19$	−3.46675			−0.795328			−0.397664	−	0.917531i	$-0.630179\pi$
$19$	−3.46675			−0.795328			−0.397664	+	0.917531i	$0.630179\pi$
$20$	−2.11238	+	0.733377i	−0.472343	+	0.163988i
$21$		0			0
$22$			4.37040i			0.931772i
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$		0			0
$25$	3.92432	−	3.09834i	0.784863	−	0.619669i
$26$	3.75939			0.737276
$27$		0			0
$28$		−	2.29167i		−	0.433085i
$29$	6.30349			1.17053			0.585265	−	0.810842i	$-0.300991\pi$
$29$	6.30349			1.17053			0.585265	+	0.810842i	$0.300991\pi$
$30$		0			0
$31$	9.84863			1.76887			0.884433	−	0.466666i	$-0.154545\pi$
$31$	9.84863			1.76887			0.884433	+	0.466666i	$0.154545\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−3.37413			−0.578658
$35$	1.68066	+	4.84088i	0.284083	+	0.818258i
$36$		0			0
$37$			6.51643i			1.07130i	0.844442	+	0.535648i	$0.179932\pi$
$37$			6.51643i			1.07130i	−0.844442	+	0.535648i	$0.820068\pi$
$38$			3.46675i			0.562382i
$39$		0			0
$40$	0.733377	+	2.11238i	0.115957	+	0.333997i
$41$	2.54411			0.397323			0.198661	−	0.980068i	$-0.436341\pi$
$41$	2.54411			0.397323			0.198661	+	0.980068i	$0.436341\pi$
$42$		0			0
$43$			10.5283i			1.60554i	0.596286	+	0.802772i	$0.296642\pi$
$43$			10.5283i			1.60554i	−0.596286	+	0.802772i	$0.703358\pi$
$44$	4.37040			0.658862
$45$		0			0
$46$	1.00000			0.147442
$47$			8.78214i			1.28101i	0.767955	+	0.640503i	$0.221274\pi$
$47$			8.78214i			1.28101i	−0.767955	+	0.640503i	$0.778726\pi$
$48$		0			0
$49$	1.74825			0.249751
$50$	−3.09834	−	3.92432i	−0.438172	−	0.554982i
$51$		0			0
$52$		−	3.75939i		−	0.521333i
$53$			1.46675i			0.201474i	0.994913	+	0.100737i	$0.0321201\pi$
$53$			1.46675i			0.201474i	−0.994913	+	0.100737i	$0.967880\pi$
$54$		0			0
$55$	−9.23195	+	3.20515i	−1.24484	+	0.432182i
$56$	−2.29167			−0.306237
$57$		0			0
$58$		−	6.30349i		−	0.827689i
$59$	2.54411			0.331215			0.165607	−	0.986192i	$-0.447042\pi$
$59$	2.54411			0.331215			0.165607	+	0.986192i	$0.447042\pi$
$60$		0			0
$61$	−11.7899			−1.50954			−0.754771	−	0.655989i	$-0.772252\pi$
$61$	−11.7899			−1.50954			−0.754771	+	0.655989i	$0.772252\pi$
$62$		−	9.84863i		−	1.25078i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.75705	+	7.94126i	0.341970	+	0.984992i
$66$		0			0
$67$			6.37080i			0.778317i	0.921171	+	0.389159i	$0.127234\pi$
$67$			6.37080i			0.778317i	−0.921171	+	0.389159i	$0.872766\pi$
$68$			3.37413i			0.409173i
$69$		0			0
$70$	4.84088	−	1.68066i	0.578596	−	0.200877i
$71$	4.69014			0.556617			0.278309	−	0.960492i	$-0.410226\pi$
$71$	4.69014			0.556617			0.278309	+	0.960492i	$0.410226\pi$
$72$		0			0
$73$			5.90542i			0.691177i	0.938386	+	0.345589i	$0.112321\pi$
$73$			5.90542i			0.691177i	−0.938386	+	0.345589i	$0.887679\pi$
$74$	6.51643			0.757520
$75$		0			0
$76$	3.46675			0.397664
$77$		−	10.0155i		−	1.14137i
$78$		0			0
$79$	−8.30763			−0.934682			−0.467341	−	0.884077i	$-0.654788\pi$
$79$	−8.30763			−0.934682			−0.467341	+	0.884077i	$0.654788\pi$
$80$	2.11238	−	0.733377i	0.236172	−	0.0819940i
$81$		0			0
$82$		−	2.54411i		−	0.280950i
$83$			7.77439i			0.853350i	0.904405	+	0.426675i	$0.140315\pi$
$83$			7.77439i			0.853350i	−0.904405	+	0.426675i	$0.859685\pi$
$84$		0			0
$85$	−2.47451	−	7.12745i	−0.268398	−	0.773080i
$86$	10.5283			1.13529
$87$		0			0
$88$		−	4.37040i		−	0.465886i
$89$	11.9565			1.26738			0.633692	−	0.773585i	$-0.281539\pi$
$89$	11.9565			1.26738			0.633692	+	0.773585i	$0.281539\pi$
$90$		0			0
$91$	−8.61527			−0.903126
$92$		−	1.00000i		−	0.104257i
$93$		0			0
$94$	8.78214			0.905809
$95$	−7.32311	+	2.54244i	−0.751335	+	0.260849i
$96$		0			0
$97$		−	6.30349i		−	0.640023i	−0.947414	−	0.320011i	$-0.896313\pi$
$97$		−	6.30349i		−	0.640023i	0.947414	−	0.320011i	$-0.103687\pi$
$98$		−	1.74825i		−	0.176600i
$99$		0			0
$100$	−3.92432	+	3.09834i	−0.392432	+	0.309834i
$101$	10.5956			1.05430			0.527149	−	0.849773i	$-0.323261\pi$
$101$	10.5956			1.05430			0.527149	+	0.849773i	$0.323261\pi$
$102$		0			0
$103$		−	1.06965i		−	0.105395i	−0.998611	−	0.0526976i	$-0.983218\pi$
$103$		−	1.06965i		−	0.105395i	0.998611	−	0.0526976i	$-0.0167820\pi$
$104$	−3.75939			−0.368638
$105$		0			0
$106$	1.46675			0.142464
$107$			19.4717i			1.88240i	0.337856	+	0.941198i	$0.390298\pi$
$107$			19.4717i			1.88240i	−0.337856	+	0.941198i	$0.609702\pi$
$108$		0			0
$109$	−10.8409			−1.03837			−0.519184	−	0.854662i	$-0.673764\pi$
$109$	−10.8409			−1.03837			−0.519184	+	0.854662i	$0.673764\pi$
$110$	3.20515	+	9.23195i	0.305599	+	0.880232i
$111$		0			0
$112$			2.29167i			0.216542i
$113$			6.30763i			0.593372i	0.954975	+	0.296686i	$0.0958815\pi$
$113$			6.30763i			0.593372i	−0.954975	+	0.296686i	$0.904118\pi$
$114$		0			0
$115$	0.733377	+	2.11238i	0.0683877	+	0.196981i
$116$	−6.30349			−0.585265
$117$		0			0
$118$		−	2.54411i		−	0.234204i
$119$	7.73238			0.708826
$120$		0			0
$121$	8.10038			0.736398
$122$			11.7899i			1.06741i
$123$		0			0
$124$	−9.84863			−0.884433
$125$	6.01740	−	9.42289i	0.538213	−	0.842809i
$126$		0			0
$127$		−	7.41197i		−	0.657706i	−0.944381	−	0.328853i	$-0.893338\pi$
$127$		−	7.41197i		−	0.657706i	0.944381	−	0.328853i	$-0.106662\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	7.94126	−	2.75705i	0.696495	−	0.241809i
$131$	10.7800			0.941855			0.470928	−	0.882172i	$-0.343919\pi$
$131$	10.7800			0.941855			0.470928	+	0.882172i	$0.343919\pi$
$132$		0			0
$133$		−	7.94465i		−	0.688889i
$134$	6.37080			0.550353
$135$		0			0
$136$	3.37413			0.289329
$137$		−	7.37413i		−	0.630014i	−0.949089	−	0.315007i	$-0.897993\pi$
$137$		−	7.37413i		−	0.630014i	0.949089	−	0.315007i	$-0.102007\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$	−1.68066	−	4.84088i	−0.142041	−	0.409129i
$141$		0			0
$142$		−	4.69014i		−	0.393588i
$143$		−	16.4300i		−	1.37395i
$144$		0			0
$145$	13.3154	−	4.62284i	1.10578	−	0.383906i
$146$	5.90542			0.488736
$147$		0			0
$148$		−	6.51643i		−	0.535648i
$149$	−13.8963			−1.13843			−0.569215	−	0.822189i	$-0.692753\pi$
$149$	−13.8963			−1.13843			−0.569215	+	0.822189i	$0.692753\pi$
$150$		0			0
$151$	0.899620			0.0732101			0.0366050	−	0.999330i	$-0.488346\pi$
$151$	0.899620			0.0732101			0.0366050	+	0.999330i	$0.488346\pi$
$152$		−	3.46675i		−	0.281191i
$153$		0			0
$154$	−10.0155			−0.807072
$155$	20.8041	−	7.22276i	1.67102	−	0.580146i
$156$		0			0
$157$			14.3265i			1.14338i	0.820471	+	0.571689i	$0.193711\pi$
$157$			14.3265i			1.14338i	−0.820471	+	0.571689i	$0.806289\pi$
$158$			8.30763i			0.660920i
$159$		0			0
$160$	−0.733377	−	2.11238i	−0.0579785	−	0.166998i
$161$	−2.29167			−0.180609
$162$		0			0
$163$			5.51409i			0.431897i	0.976405	+	0.215949i	$0.0692844\pi$
$163$			5.51409i			0.431897i	−0.976405	+	0.215949i	$0.930716\pi$
$164$	−2.54411			−0.198661
$165$		0			0
$166$	7.77439			0.603410
$167$		−	16.7821i		−	1.29864i	−0.760515	−	0.649321i	$-0.775053\pi$
$167$		−	16.7821i		−	1.29864i	0.760515	−	0.649321i	$-0.224947\pi$
$168$		0			0
$169$	−1.13298			−0.0871527
$170$	−7.12745	+	2.47451i	−0.546650	+	0.189786i
$171$		0			0
$172$		−	10.5283i		−	0.802772i
$173$			2.18525i			0.166142i	0.996544	+	0.0830709i	$0.0264728\pi$
$173$			2.18525i			0.166142i	−0.996544	+	0.0830709i	$0.973527\pi$
$174$		0			0
$175$	7.10038	+	8.99323i	0.536738	+	0.679825i
$176$	−4.37040			−0.329431
$177$		0			0
$178$		−	11.9565i		−	0.896176i
$179$	−18.8037			−1.40545			−0.702726	−	0.711460i	$-0.748034\pi$
$179$	−18.8037			−1.40545			−0.702726	+	0.711460i	$0.748034\pi$
$180$		0			0
$181$	19.6046			1.45720			0.728601	−	0.684939i	$-0.240171\pi$
$181$	19.6046			1.45720			0.728601	+	0.684939i	$0.240171\pi$
$182$			8.61527i			0.638606i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	4.77900	+	13.7652i	0.351359	+	1.01204i
$186$		0			0
$187$			14.7463i			1.07835i
$188$		−	8.78214i		−	0.640503i
$189$		0			0
$190$	2.54244	+	7.32311i	0.184448	+	0.531274i
$191$	13.0329			0.943025			0.471513	−	0.881859i	$-0.343708\pi$
$191$	13.0329			0.943025			0.471513	+	0.881859i	$0.343708\pi$
$192$		0			0
$193$			4.58334i			0.329916i	0.986301	+	0.164958i	$0.0527488\pi$
$193$			4.58334i			0.329916i	−0.986301	+	0.164958i	$0.947251\pi$
$194$	−6.30349			−0.452564
$195$		0			0
$196$	−1.74825			−0.124875
$197$		−	23.5643i		−	1.67889i	−0.543448	−	0.839443i	$-0.682882\pi$
$197$		−	23.5643i		−	1.67889i	0.543448	−	0.839443i	$-0.317118\pi$
$198$		0			0
$199$	−12.3076			−0.872465			−0.436233	−	0.899834i	$-0.643687\pi$
$199$	−12.3076			−0.872465			−0.436233	+	0.899834i	$0.643687\pi$
$200$	3.09834	+	3.92432i	0.219086	+	0.277491i
$201$		0			0
$202$		−	10.5956i		−	0.745501i
$203$			14.4455i			1.01388i
$204$		0			0
$205$	5.37413	−	1.86579i	0.375345	−	0.130312i
$206$	−1.06965			−0.0745257
$207$		0			0
$208$			3.75939i			0.260667i
$209$	15.1511			1.04802
$210$		0			0
$211$	20.4300			1.40646			0.703230	−	0.710962i	$-0.251740\pi$
$211$	20.4300			1.40646			0.703230	+	0.710962i	$0.251740\pi$
$212$		−	1.46675i		−	0.100737i
$213$		0			0
$214$	19.4717			1.33105
$215$	7.72118	+	22.2397i	0.526580	+	1.51674i
$216$		0			0
$217$			22.5698i			1.53214i
$218$			10.8409i			0.734237i
$219$		0			0
$220$	9.23195	−	3.20515i	0.622418	−	0.216091i
$221$	12.6846			0.853262
$222$		0			0
$223$		−	15.9750i		−	1.06977i	−0.844925	−	0.534884i	$-0.820355\pi$
$223$		−	15.9750i		−	1.06977i	0.844925	−	0.534884i	$-0.179645\pi$
$224$	2.29167			0.153119
$225$		0			0
$226$	6.30763			0.419578
$227$		−	21.6046i		−	1.43395i	−0.697099	−	0.716975i	$-0.745526\pi$
$227$		−	21.6046i		−	1.43395i	0.697099	−	0.716975i	$-0.254474\pi$
$228$		0			0
$229$	−21.7744			−1.43889			−0.719446	−	0.694548i	$-0.755604\pi$
$229$	−21.7744			−1.43889			−0.719446	+	0.694548i	$0.755604\pi$
$230$	2.11238	−	0.733377i	0.139286	−	0.0483574i
$231$		0			0
$232$			6.30349i			0.413845i
$233$		−	12.0339i		−	0.788366i	−0.919032	−	0.394183i	$-0.871028\pi$
$233$		−	12.0339i		−	0.788366i	0.919032	−	0.394183i	$-0.128972\pi$
$234$		0			0
$235$	6.44062	+	18.5512i	0.420140	+	1.21015i
$236$	−2.54411			−0.165607
$237$		0			0
$238$		−	7.73238i		−	0.501216i
$239$	−17.4748			−1.13035			−0.565177	−	0.824970i	$-0.691192\pi$
$239$	−17.4748			−1.13035			−0.565177	+	0.824970i	$0.691192\pi$
$240$		0			0
$241$	23.7495			1.52984			0.764921	−	0.644124i	$-0.222778\pi$
$241$	23.7495			1.52984			0.764921	+	0.644124i	$0.222778\pi$
$242$		−	8.10038i		−	0.520712i
$243$		0			0
$244$	11.7899			0.754771
$245$	3.69298	−	1.28213i	0.235936	−	0.0819122i
$246$		0			0
$247$		−	13.0329i		−	0.829261i
$248$			9.84863i			0.625389i
$249$		0			0
$250$	−9.42289	−	6.01740i	−0.595956	−	0.380574i
$251$	−20.8436			−1.31563			−0.657817	−	0.753177i	$-0.728520\pi$
$251$	−20.8436			−1.31563			−0.657817	+	0.753177i	$0.728520\pi$
$252$		0			0
$253$		−	4.37040i		−	0.274765i
$254$	−7.41197			−0.465068
$255$		0			0
$256$	1.00000			0.0625000
$257$			10.9490i			0.682981i	0.939885	+	0.341490i	$0.110932\pi$
$257$			10.9490i			0.682981i	−0.939885	+	0.341490i	$0.889068\pi$
$258$		0			0
$259$	−14.9335			−0.927923
$260$	−2.75705	−	7.94126i	−0.170985	−	0.492496i
$261$		0			0
$262$		−	10.7800i		−	0.665992i
$263$		−	18.8160i		−	1.16025i	−0.814529	−	0.580123i	$-0.803004\pi$
$263$		−	18.8160i		−	1.16025i	0.814529	−	0.580123i	$-0.196996\pi$
$264$		0			0
$265$	1.07568	+	3.09834i	0.0660787	+	0.190330i
$266$	−7.94465			−0.487118
$267$		0			0
$268$		−	6.37080i		−	0.389159i
$269$	−11.5263			−0.702772			−0.351386	−	0.936231i	$-0.614290\pi$
$269$	−11.5263			−0.702772			−0.351386	+	0.936231i	$0.614290\pi$
$270$		0			0
$271$	−20.3125			−1.23390			−0.616949	−	0.787003i	$-0.711632\pi$
$271$	−20.3125			−1.23390			−0.616949	+	0.787003i	$0.711632\pi$
$272$		−	3.37413i		−	0.204586i
$273$		0			0
$274$	−7.37413			−0.445487
$275$	−17.1508	+	13.5410i	−1.03423	+	0.816553i
$276$		0			0
$277$		−	23.1025i		−	1.38809i	−0.719930	−	0.694047i	$-0.755826\pi$
$277$		−	23.1025i		−	1.38809i	0.719930	−	0.694047i	$-0.244174\pi$
$278$			8.00000i			0.479808i
$279$		0			0
$280$	−4.84088	+	1.68066i	−0.289298	+	0.100438i
$281$	−4.72897			−0.282107			−0.141053	−	0.990002i	$-0.545049\pi$
$281$	−4.72897			−0.282107			−0.141053	+	0.990002i	$0.545049\pi$
$282$		0			0
$283$			13.6760i			0.812952i	0.913662	+	0.406476i	$0.133242\pi$
$283$			13.6760i			0.812952i	−0.913662	+	0.406476i	$0.866758\pi$
$284$	−4.69014			−0.278309
$285$		0			0
$286$	−16.4300			−0.971527
$287$			5.83025i			0.344149i
$288$		0			0
$289$	5.61527			0.330310
$290$	−4.62284	−	13.3154i	−0.271462	−	0.781906i
$291$		0			0
$292$		−	5.90542i		−	0.345589i
$293$		−	21.1640i		−	1.23642i	−0.786015	−	0.618208i	$-0.787859\pi$
$293$		−	21.1640i		−	1.23642i	0.786015	−	0.618208i	$-0.212141\pi$
$294$		0			0
$295$	5.37413	−	1.86579i	0.312894	−	0.108630i
$296$	−6.51643			−0.378760
$297$		0			0
$298$			13.8963i			0.804992i
$299$	−3.75939			−0.217411
$300$		0			0
$301$	−24.1273			−1.39067
$302$		−	0.899620i		−	0.0517673i
$303$		0			0
$304$	−3.46675			−0.198832
$305$	−24.9048	+	8.64644i	−1.42604	+	0.495093i
$306$		0			0
$307$		−	13.0329i		−	0.743825i	−0.928268	−	0.371912i	$-0.878702\pi$
$307$		−	13.0329i		−	0.743825i	0.928268	−	0.371912i	$-0.121298\pi$
$308$			10.0155i			0.570686i
$309$		0			0
$310$	−7.22276	−	20.8041i	−0.410225	−	1.18159i
$311$	13.3964			0.759639			0.379820	−	0.925061i	$-0.375986\pi$
$311$	13.3964			0.759639			0.379820	+	0.925061i	$0.375986\pi$
$312$		0			0
$313$		−	26.4293i		−	1.49387i	−0.664897	−	0.746935i	$-0.731525\pi$
$313$		−	26.4293i		−	1.49387i	0.664897	−	0.746935i	$-0.268475\pi$
$314$	14.3265			0.808490
$315$		0			0
$316$	8.30763			0.467341
$317$			19.3790i			1.08843i	0.838944	+	0.544217i	$0.183173\pi$
$317$			19.3790i			1.08843i	−0.838944	+	0.544217i	$0.816827\pi$
$318$		0			0
$319$	−27.5488			−1.54244
$320$	−2.11238	+	0.733377i	−0.118086	+	0.0409970i
$321$		0			0
$322$			2.29167i			0.127710i
$323$			11.6973i			0.650853i
$324$		0			0
$325$	11.6479	+	14.7530i	0.646108	+	0.818350i
$326$	5.51409			0.305397
$327$		0			0
$328$			2.54411i			0.140475i
$329$	−20.1258			−1.10957
$330$		0			0
$331$	14.5630			0.800455			0.400227	−	0.916416i	$-0.368931\pi$
$331$	14.5630			0.800455			0.400227	+	0.916416i	$0.368931\pi$
$332$		−	7.77439i		−	0.426675i
$333$		0			0
$334$	−16.7821			−0.918278
$335$	4.67220	+	13.4576i	0.255269	+	0.735265i
$336$		0			0
$337$		−	26.3503i		−	1.43539i	−0.696358	−	0.717695i	$-0.745197\pi$
$337$		−	26.3503i		−	1.43539i	0.696358	−	0.717695i	$-0.254803\pi$
$338$			1.13298i			0.0616263i
$339$		0			0
$340$	2.47451	+	7.12745i	0.134199	+	0.386540i
$341$	−43.0424			−2.33088
$342$		0			0
$343$			20.0481i			1.08250i
$344$	−10.5283			−0.567646
$345$		0			0
$346$	2.18525			0.117480
$347$		−	13.6818i		−	0.734475i	−0.930127	−	0.367238i	$-0.880304\pi$
$347$		−	13.6818i		−	0.734475i	0.930127	−	0.367238i	$-0.119696\pi$
$348$		0			0
$349$	6.61527			0.354107			0.177054	−	0.984201i	$-0.443343\pi$
$349$	6.61527			0.354107			0.177054	+	0.984201i	$0.443343\pi$
$350$	8.99323	−	7.10038i	0.480709	−	0.379531i
$351$		0			0
$352$			4.37040i			0.232943i
$353$			12.6492i			0.673247i	0.941639	+	0.336623i	$0.109285\pi$
$353$			12.6492i			0.673247i	−0.941639	+	0.336623i	$0.890715\pi$
$354$		0			0
$355$	9.90737	−	3.43964i	0.525829	−	0.182557i
$356$	−11.9565			−0.633692
$357$		0			0
$358$			18.8037i			0.993805i
$359$	−25.3486			−1.33785			−0.668924	−	0.743331i	$-0.733245\pi$
$359$	−25.3486			−1.33785			−0.668924	+	0.743331i	$0.733245\pi$
$360$		0			0
$361$	−6.98162			−0.367454
$362$		−	19.6046i		−	1.03040i
$363$		0			0
$364$	8.61527			0.451563
$365$	4.33090	+	12.4745i	0.226690	+	0.652946i
$366$		0			0
$367$			15.1123i			0.788854i	0.918927	+	0.394427i	$0.129057\pi$
$367$			15.1123i			0.788854i	−0.918927	+	0.394427i	$0.870943\pi$
$368$			1.00000i			0.0521286i
$369$		0			0
$370$	13.7652	−	4.77900i	0.715619	−	0.248448i
$371$	−3.36131			−0.174511
$372$		0			0
$373$			27.3593i			1.41661i	0.705905	+	0.708306i	$0.250541\pi$
$373$			27.3593i			1.41661i	−0.705905	+	0.708306i	$0.749459\pi$
$374$	14.7463			0.762512
$375$		0			0
$376$	−8.78214			−0.452904
$377$			23.6973i			1.22047i
$378$		0			0
$379$	4.08202			0.209679			0.104840	−	0.994489i	$-0.466567\pi$
$379$	4.08202			0.209679			0.104840	+	0.994489i	$0.466567\pi$
$380$	7.32311	−	2.54244i	0.375668	−	0.130424i
$381$		0			0
$382$		−	13.0329i		−	0.666819i
$383$		−	29.5643i		−	1.51066i	−0.655342	−	0.755332i	$-0.727476\pi$
$383$		−	29.5643i		−	1.51066i	0.655342	−	0.755332i	$-0.272524\pi$
$384$		0			0
$385$	−7.34514	−	21.1566i	−0.374343	−	1.07824i
$386$	4.58334			0.233286
$387$		0			0
$388$			6.30349i			0.320011i
$389$	27.4982			1.39422			0.697108	−	0.716966i	$-0.254470\pi$
$389$	27.4982			1.39422			0.697108	+	0.716966i	$0.254470\pi$
$390$		0			0
$391$	3.37413			0.170637
$392$			1.74825i			0.0883001i
$393$		0			0
$394$	−23.5643			−1.18715
$395$	−17.5489	+	6.09263i	−0.882981	+	0.306553i
$396$		0			0
$397$		−	3.11990i		−	0.156583i	−0.996931	−	0.0782916i	$-0.975053\pi$
$397$		−	3.11990i		−	0.156583i	0.996931	−	0.0782916i	$-0.0249465\pi$
$398$			12.3076i			0.616926i
$399$		0			0
$400$	3.92432	−	3.09834i	0.196216	−	0.154917i
$401$	−23.0637			−1.15174			−0.575872	−	0.817540i	$-0.695337\pi$
$401$	−23.0637			−1.15174			−0.575872	+	0.817540i	$0.695337\pi$
$402$		0			0
$403$			37.0248i			1.84434i
$404$	−10.5956			−0.527149
$405$		0			0
$406$	14.4455			0.716919
$407$		−	28.4794i		−	1.41167i
$408$		0			0
$409$	−20.7483			−1.02594			−0.512968	−	0.858408i	$-0.671454\pi$
$409$	−20.7483			−1.02594			−0.512968	+	0.858408i	$0.671454\pi$
$410$	−1.86579	−	5.37413i	−0.0921448	−	0.265409i
$411$		0			0
$412$			1.06965i			0.0526976i
$413$			5.83025i			0.286888i
$414$		0			0
$415$	5.70156	+	16.4225i	0.279878	+	0.806148i
$416$	3.75939			0.184319
$417$		0			0
$418$		−	15.1511i		−	0.741064i
$419$	7.09222			0.346478			0.173239	−	0.984880i	$-0.444577\pi$
$419$	7.09222			0.346478			0.173239	+	0.984880i	$0.444577\pi$
$420$		0			0
$421$	38.0869			1.85624			0.928122	−	0.372277i	$-0.121423\pi$
$421$	38.0869			1.85624			0.928122	+	0.372277i	$0.121423\pi$
$422$		−	20.4300i		−	0.994518i
$423$		0			0
$424$	−1.46675			−0.0712319
$425$	−10.4542	−	13.2411i	−0.507104	−	0.642290i
$426$		0			0
$427$		−	27.0185i		−	1.30752i
$428$		−	19.4717i		−	0.941198i
$429$		0			0
$430$	22.2397	−	7.72118i	1.07249	−	0.372348i
$431$	20.8429			1.00397			0.501984	−	0.864877i	$-0.332604\pi$
$431$	20.8429			1.00397			0.501984	+	0.864877i	$0.332604\pi$
$432$		0			0
$433$		−	37.7487i		−	1.81409i	−0.421037	−	0.907044i	$-0.638334\pi$
$433$		−	37.7487i		−	1.81409i	0.421037	−	0.907044i	$-0.361666\pi$
$434$	22.5698			1.08339
$435$		0			0
$436$	10.8409			0.519184
$437$		−	3.46675i		−	0.165837i
$438$		0			0
$439$	−25.5643			−1.22012			−0.610058	−	0.792357i	$-0.708854\pi$
$439$	−25.5643			−1.22012			−0.610058	+	0.792357i	$0.708854\pi$
$440$	−3.20515	−	9.23195i	−0.152799	−	0.440116i
$441$		0			0
$442$		−	12.6846i		−	0.603347i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$	25.2566	−	8.76860i	1.19728	−	0.415672i
$446$	−15.9750			−0.756440
$447$		0			0
$448$		−	2.29167i		−	0.108271i
$449$	8.48408			0.400389			0.200194	−	0.979756i	$-0.435843\pi$
$449$	8.48408			0.400389			0.200194	+	0.979756i	$0.435843\pi$
$450$		0			0
$451$	−11.1188			−0.523562
$452$		−	6.30763i		−	0.296686i
$453$		0			0
$454$	−21.6046			−1.01396
$455$	−18.1987	+	6.31824i	−0.853170	+	0.296204i
$456$		0			0
$457$			35.8872i			1.67873i	0.543566	+	0.839366i	$0.317074\pi$
$457$			35.8872i			1.67873i	−0.543566	+	0.839366i	$0.682926\pi$
$458$			21.7744i			1.01745i
$459$		0			0
$460$	−0.733377	−	2.11238i	−0.0341939	−	0.0984903i
$461$	−15.3356			−0.714248			−0.357124	−	0.934057i	$-0.616243\pi$
$461$	−15.3356			−0.714248			−0.357124	+	0.934057i	$0.616243\pi$
$462$		0			0
$463$			18.1489i			0.843450i	0.906724	+	0.421725i	$0.138575\pi$
$463$			18.1489i			0.843450i	−0.906724	+	0.421725i	$0.861425\pi$
$464$	6.30349			0.292632
$465$		0			0
$466$	−12.0339			−0.557459
$467$		−	5.97515i		−	0.276497i	−0.990398	−	0.138248i	$-0.955853\pi$
$467$		−	5.97515i		−	0.276497i	0.990398	−	0.138248i	$-0.0441472\pi$
$468$		0			0
$469$	−14.5998			−0.674154
$470$	18.5512	−	6.44062i	0.855705	−	0.297084i
$471$		0			0
$472$			2.54411i			0.117102i
$473$		−	46.0127i		−	2.11567i
$474$		0			0
$475$	−13.6046	+	10.7412i	−0.624224	+	0.492840i
$476$	−7.73238			−0.354413
$477$		0			0
$478$			17.4748i			0.799281i
$479$	−4.58334			−0.209418			−0.104709	−	0.994503i	$-0.533391\pi$
$479$	−4.58334			−0.209418			−0.104709	+	0.994503i	$0.533391\pi$
$480$		0			0
$481$	−24.4978			−1.11700
$482$		−	23.7495i		−	1.08176i
$483$		0			0
$484$	−8.10038			−0.368199
$485$	−4.62284	−	13.3154i	−0.209912	−	0.604621i
$486$		0			0
$487$			33.9826i			1.53990i	0.638106	+	0.769949i	$0.279718\pi$
$487$			33.9826i			1.53990i	−0.638106	+	0.769949i	$0.720282\pi$
$488$		−	11.7899i		−	0.533703i
$489$		0			0
$490$	−1.28213	−	3.69298i	−0.0579207	−	0.166832i
$491$	19.8690			0.896677			0.448339	−	0.893864i	$-0.352016\pi$
$491$	19.8690			0.896677			0.448339	+	0.893864i	$0.352016\pi$
$492$		0			0
$493$		−	21.2688i		−	0.957898i
$494$	−13.0329			−0.586376
$495$		0			0
$496$	9.84863			0.442217
$497$			10.7483i			0.482125i
$498$		0			0
$499$	28.1951			1.26218			0.631092	−	0.775708i	$-0.282607\pi$
$499$	28.1951			1.26218			0.631092	+	0.775708i	$0.282607\pi$
$500$	−6.01740	+	9.42289i	−0.269106	+	0.421404i
$501$		0			0
$502$			20.8436i			0.930294i
$503$		−	14.9335i		−	0.665852i	−0.942953	−	0.332926i	$-0.891964\pi$
$503$		−	14.9335i		−	0.665852i	0.942953	−	0.332926i	$-0.108036\pi$
$504$		0			0
$505$	22.3819	−	7.77054i	0.995981	−	0.345785i
$506$	−4.37040			−0.194288
$507$		0			0
$508$			7.41197i			0.328853i
$509$	32.9518			1.46056			0.730281	−	0.683147i	$-0.239389\pi$
$509$	32.9518			1.46056			0.730281	+	0.683147i	$0.239389\pi$
$510$		0			0
$511$	−13.5333			−0.598677
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	10.9490			0.482940
$515$	−0.784453	−	2.25950i	−0.0345671	−	0.0995654i
$516$		0			0
$517$		−	38.3815i		−	1.68801i
$518$			14.9335i			0.656141i
$519$		0			0
$520$	−7.94126	+	2.75705i	−0.348247	+	0.120905i
$521$	−17.2570			−0.756041			−0.378021	−	0.925797i	$-0.623395\pi$
$521$	−17.2570			−0.756041			−0.378021	+	0.925797i	$0.623395\pi$
$522$		0			0
$523$		−	6.79668i		−	0.297198i	−0.988898	−	0.148599i	$-0.952524\pi$
$523$		−	6.79668i		−	0.297198i	0.988898	−	0.148599i	$-0.0474764\pi$
$524$	−10.7800			−0.470928
$525$		0			0
$526$	−18.8160			−0.820418
$527$		−	33.2305i		−	1.44754i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	3.09834	−	1.07568i	0.134583	−	0.0467247i
$531$		0			0
$532$			7.94465i			0.344444i
$533$			9.56428i			0.414275i
$534$		0			0
$535$	14.2801	+	41.1316i	0.617381	+	1.77827i
$536$	−6.37080			−0.275177
$537$		0			0
$538$			11.5263i			0.496935i
$539$	−7.64056			−0.329102
$540$		0			0
$541$	−22.6153			−0.972306			−0.486153	−	0.873874i	$-0.661600\pi$
$541$	−22.6153			−0.972306			−0.486153	+	0.873874i	$0.661600\pi$
$542$			20.3125i			0.872498i
$543$		0			0
$544$	−3.37413			−0.144664
$545$	−22.9001	+	7.95045i	−0.980932	+	0.340560i
$546$		0			0
$547$			2.57866i			0.110256i	0.998479	+	0.0551278i	$0.0175566\pi$
$547$			2.57866i			0.110256i	−0.998479	+	0.0551278i	$0.982443\pi$
$548$			7.37413i			0.315007i
$549$		0			0
$550$	13.5410	+	17.1508i	0.577390	+	0.731314i
$551$	−21.8527			−0.930955
$552$		0			0
$553$		−	19.0383i		−	0.809593i
$554$	−23.1025			−0.981531
$555$		0			0
$556$	8.00000			0.339276
$557$			29.2815i			1.24070i	0.784326	+	0.620348i	$0.213009\pi$
$557$			29.2815i			1.24070i	−0.784326	+	0.620348i	$0.786991\pi$
$558$		0			0
$559$	−39.5798			−1.67405
$560$	1.68066	+	4.84088i	0.0710207	+	0.204565i
$561$		0			0
$562$			4.72897i			0.199480i
$563$			1.17463i			0.0495045i	0.999694	+	0.0247523i	$0.00787970\pi$
$563$			1.17463i			0.0495045i	−0.999694	+	0.0247523i	$0.992120\pi$
$564$		0			0
$565$	4.62587	+	13.3241i	0.194612	+	0.560551i
$566$	13.6760			0.574844
$567$		0			0
$568$			4.69014i			0.196794i
$569$	8.30389			0.348117			0.174059	−	0.984735i	$-0.444312\pi$
$569$	8.30389			0.348117			0.174059	+	0.984735i	$0.444312\pi$
$570$		0			0
$571$	9.78499			0.409489			0.204745	−	0.978815i	$-0.434364\pi$
$571$	9.78499			0.409489			0.204745	+	0.978815i	$0.434364\pi$
$572$			16.4300i			0.686973i
$573$		0			0
$574$	5.83025			0.243350
$575$	3.09834	+	3.92432i	0.129210	+	0.163655i
$576$		0			0
$577$		−	3.18360i		−	0.132535i	−0.997802	−	0.0662674i	$-0.978891\pi$
$577$		−	3.18360i		−	0.132535i	0.997802	−	0.0662674i	$-0.0211090\pi$
$578$		−	5.61527i		−	0.233564i
$579$		0			0
$580$	−13.3154	+	4.62284i	−0.552891	+	0.191953i
$581$	−17.8163			−0.739146
$582$		0			0
$583$		−	6.41030i		−	0.265487i
$584$	−5.90542			−0.244368
$585$		0			0
$586$	−21.1640			−0.874278
$587$			9.74954i			0.402406i	0.979550	+	0.201203i	$0.0644852\pi$
$587$			9.74954i			0.402406i	−0.979550	+	0.201203i	$0.935515\pi$
$588$		0			0
$589$	−34.1428			−1.40683
$590$	−1.86579	−	5.37413i	−0.0768133	−	0.221249i
$591$		0			0
$592$			6.51643i			0.267824i
$593$		−	6.91800i		−	0.284088i	−0.989860	−	0.142044i	$-0.954633\pi$
$593$		−	6.91800i		−	0.284088i	0.989860	−	0.142044i	$-0.0453675\pi$
$594$		0			0
$595$	16.3337	−	5.67075i	0.669618	−	0.232478i
$596$	13.8963			0.569215
$597$		0			0
$598$			3.75939i			0.153733i
$599$	−34.1603			−1.39575			−0.697876	−	0.716219i	$-0.745871\pi$
$599$	−34.1603			−1.39575			−0.697876	+	0.716219i	$0.745871\pi$
$600$		0			0
$601$	−1.64787			−0.0672182			−0.0336091	−	0.999435i	$-0.510700\pi$
$601$	−1.64787			−0.0672182			−0.0336091	+	0.999435i	$0.510700\pi$
$602$			24.1273i			0.983355i
$603$		0			0
$604$	−0.899620			−0.0366050
$605$	17.1111	−	5.94063i	0.695665	−	0.241521i
$606$		0			0
$607$			44.6849i			1.81371i	0.421447	+	0.906853i	$0.361522\pi$
$607$			44.6849i			1.81371i	−0.421447	+	0.906853i	$0.638478\pi$
$608$			3.46675i			0.140595i
$609$		0			0
$610$	8.64644	+	24.9048i	0.350084	+	1.00836i
$611$	−33.0155			−1.33566
$612$		0			0
$613$			6.94231i			0.280397i	0.990123	+	0.140199i	$0.0447741\pi$
$613$			6.94231i			0.280397i	−0.990123	+	0.140199i	$0.955226\pi$
$614$	−13.0329			−0.525964
$615$		0			0
$616$	10.0155			0.403536
$617$			42.0049i			1.69105i	0.533933	+	0.845527i	$0.320713\pi$
$617$			42.0049i			1.69105i	−0.533933	+	0.845527i	$0.679287\pi$
$618$		0			0
$619$	13.8445			0.556457			0.278229	−	0.960515i	$-0.410253\pi$
$619$	13.8445			0.556457			0.278229	+	0.960515i	$0.410253\pi$
$620$	−20.8041	+	7.22276i	−0.835512	+	0.290073i
$621$		0			0
$622$		−	13.3964i		−	0.537146i
$623$			27.4003i			1.09777i
$624$		0			0
$625$	5.80052	−	24.3178i	0.232021	−	0.972711i
$626$	−26.4293			−1.05633
$627$		0			0
$628$		−	14.3265i		−	0.571689i
$629$	21.9873			0.876690
$630$		0			0
$631$	−11.1734			−0.444805			−0.222402	−	0.974955i	$-0.571390\pi$
$631$	−11.1734			−0.444805			−0.222402	+	0.974955i	$0.571390\pi$
$632$		−	8.30763i		−	0.330460i
$633$		0			0
$634$	19.3790			0.769640
$635$	−5.43577	−	15.6569i	−0.215712	−	0.621325i
$636$		0			0
$637$			6.57236i			0.260406i
$638$			27.5488i			1.09067i
$639$		0			0
$640$	0.733377	+	2.11238i	0.0289893	+	0.0834992i
$641$	7.45214			0.294342			0.147171	−	0.989111i	$-0.452983\pi$
$641$	7.45214			0.294342			0.147171	+	0.989111i	$0.452983\pi$
$642$		0			0
$643$			32.4365i			1.27917i	0.768720	+	0.639586i	$0.220894\pi$
$643$			32.4365i			1.27917i	−0.768720	+	0.639586i	$0.779106\pi$
$644$	2.29167			0.0903044
$645$		0			0
$646$	11.6973			0.460223
$647$			7.66626i			0.301392i	0.988580	+	0.150696i	$0.0481514\pi$
$647$			7.66626i			0.301392i	−0.988580	+	0.150696i	$0.951849\pi$
$648$		0			0
$649$	−11.1188			−0.436450
$650$	14.7530	−	11.6479i	0.578661	−	0.456867i
$651$		0			0
$652$		−	5.51409i		−	0.215949i
$653$			6.43001i			0.251626i	0.992054	+	0.125813i	$0.0401539\pi$
$653$			6.43001i			0.251626i	−0.992054	+	0.125813i	$0.959846\pi$
$654$		0			0
$655$	22.7715	−	7.90582i	0.889758	−	0.308906i
$656$	2.54411			0.0993307
$657$		0			0
$658$			20.1258i			0.784584i
$659$	30.7139			1.19644			0.598222	−	0.801330i	$-0.295874\pi$
$659$	30.7139			1.19644			0.598222	+	0.801330i	$0.295874\pi$
$660$		0			0
$661$	22.2044			0.863651			0.431826	−	0.901957i	$-0.357870\pi$
$661$	22.2044			0.863651			0.431826	+	0.901957i	$0.357870\pi$
$662$		−	14.5630i		−	0.566007i
$663$		0			0
$664$	−7.77439			−0.301705
$665$	−5.82642	−	16.7821i	−0.225939	−	0.650784i
$666$		0			0
$667$			6.30349i			0.244072i
$668$			16.7821i			0.649321i
$669$		0			0
$670$	13.4576	−	4.67220i	0.519911	−	0.180503i
$671$	51.5265			1.98916
$672$		0			0
$673$		−	21.5169i		−	0.829417i	−0.909954	−	0.414709i	$-0.863883\pi$
$673$		−	21.5169i		−	0.829417i	0.909954	−	0.414709i	$-0.136117\pi$
$674$	−26.3503			−1.01497
$675$		0			0
$676$	1.13298			0.0435763
$677$			12.5488i			0.482288i	0.970489	+	0.241144i	$0.0775226\pi$
$677$			12.5488i			0.482288i	−0.970489	+	0.241144i	$0.922477\pi$
$678$		0			0
$679$	14.4455			0.554368
$680$	7.12745	−	2.47451i	0.273325	−	0.0948930i
$681$		0			0
$682$			43.0424i			1.64818i
$683$		−	31.6166i		−	1.20977i	−0.796311	−	0.604887i	$-0.793218\pi$
$683$		−	31.6166i		−	1.20977i	0.796311	−	0.604887i	$-0.206782\pi$
$684$		0			0
$685$	−5.40801	−	15.5770i	−0.206630	−	0.595166i
$686$	20.0481			0.765440
$687$		0			0
$688$			10.5283i			0.401386i
$689$	−5.51409			−0.210070
$690$		0			0
$691$	16.8005			0.639122			0.319561	−	0.947566i	$-0.396465\pi$
$691$	16.8005			0.639122			0.319561	+	0.947566i	$0.396465\pi$
$692$		−	2.18525i		−	0.0830709i
$693$		0			0
$694$	−13.6818			−0.519353
$695$	−16.8991	+	5.86702i	−0.641018	+	0.222549i
$696$		0			0
$697$		−	8.58414i		−	0.325148i
$698$		−	6.61527i		−	0.250392i
$699$		0			0
$700$	−7.10038	−	8.99323i	−0.268369	−	0.339912i
$701$	−40.5311			−1.53084			−0.765419	−	0.643532i	$-0.777468\pi$
$701$	−40.5311			−1.53084			−0.765419	+	0.643532i	$0.777468\pi$
$702$		0			0
$703$		−	22.5909i		−	0.852031i
$704$	4.37040			0.164716
$705$		0			0
$706$	12.6492			0.476057
$707$			24.2815i			0.913201i
$708$		0			0
$709$	−3.10685			−0.116680			−0.0583401	−	0.998297i	$-0.518581\pi$
$709$	−3.10685			−0.116680			−0.0583401	+	0.998297i	$0.518581\pi$
$710$	−3.43964	−	9.90737i	−0.129087	−	0.371817i
$711$		0			0
$712$			11.9565i			0.448088i
$713$			9.84863i			0.368834i
$714$		0			0
$715$	−12.0494	−	34.7065i	−0.450622	−	1.29795i
$716$	18.8037			0.702726
$717$		0			0
$718$			25.3486i			0.946001i
$719$	−8.59089			−0.320386			−0.160193	−	0.987086i	$-0.551212\pi$
$719$	−8.59089			−0.320386			−0.160193	+	0.987086i	$0.551212\pi$
$720$		0			0
$721$	2.45127			0.0912902
$722$			6.98162i			0.259829i
$723$		0			0
$724$	−19.6046			−0.728601
$725$	24.7369	−	19.5304i	0.918706	−	0.725341i
$726$		0			0
$727$		−	4.44445i		−	0.164835i	−0.996598	−	0.0824177i	$-0.973736\pi$
$727$		−	4.44445i		−	0.164835i	0.996598	−	0.0824177i	$-0.0262642\pi$
$728$		−	8.61527i		−	0.319303i
$729$		0			0
$730$	12.4745	−	4.33090i	0.461702	−	0.160294i
$731$	35.5237			1.31389
$732$		0			0
$733$			20.6937i			0.764338i	0.924092	+	0.382169i	$0.124823\pi$
$733$			20.6937i			0.764338i	−0.924092	+	0.382169i	$0.875177\pi$
$734$	15.1123			0.557804
$735$		0			0
$736$	1.00000			0.0368605
$737$		−	27.8429i		−	1.02561i
$738$		0			0
$739$	29.5275			1.08619			0.543094	−	0.839672i	$-0.317253\pi$
$739$	29.5275			1.08619			0.543094	+	0.839672i	$0.317253\pi$
$740$	−4.77900	−	13.7652i	−0.175680	−	0.506019i
$741$		0			0
$742$			3.36131i			0.123398i
$743$		−	14.1330i		−	0.518489i	−0.965812	−	0.259244i	$-0.916526\pi$
$743$		−	14.1330i		−	0.518489i	0.965812	−	0.259244i	$-0.0834735\pi$
$744$		0			0
$745$	−29.3543	+	10.1912i	−1.07546	+	0.373378i
$746$	27.3593			1.00170
$747$		0			0
$748$		−	14.7463i		−	0.539177i
$749$	−44.6226			−1.63047
$750$		0			0
$751$	39.8874			1.45551			0.727756	−	0.685836i	$-0.240563\pi$
$751$	39.8874			1.45551			0.727756	+	0.685836i	$0.240563\pi$
$752$			8.78214i			0.320252i
$753$		0			0
$754$	23.6973			0.863004
$755$	1.90034	−	0.659761i	0.0691605	−	0.0240111i
$756$		0			0
$757$			40.1009i			1.45749i	0.684783	+	0.728747i	$0.259897\pi$
$757$			40.1009i			1.45749i	−0.684783	+	0.728747i	$0.740103\pi$
$758$		−	4.08202i		−	0.148266i
$759$		0			0
$760$	−2.54244	−	7.32311i	−0.0922239	−	0.265637i
$761$	−10.2541			−0.371710			−0.185855	−	0.982577i	$-0.559506\pi$
$761$	−10.2541			−0.371710			−0.185855	+	0.982577i	$0.559506\pi$
$762$		0			0
$763$		−	24.8437i		−	0.899403i
$764$	−13.0329			−0.471513
$765$		0			0
$766$	−29.5643			−1.06820
$767$			9.56428i			0.345346i
$768$		0			0
$769$	20.2970			0.731930			0.365965	−	0.930629i	$-0.380739\pi$
$769$	20.2970			0.731930			0.365965	+	0.930629i	$0.380739\pi$
$770$	−21.1566	+	7.34514i	−0.762430	+	0.264700i
$771$		0			0
$772$		−	4.58334i		−	0.164958i
$773$		−	45.4766i		−	1.63568i	−0.575447	−	0.817839i	$-0.695172\pi$
$773$		−	45.4766i		−	1.63568i	0.575447	−	0.817839i	$-0.304828\pi$
$774$		0			0
$775$	38.6492	−	30.5145i	1.38832	−	1.09611i
$776$	6.30349			0.226282
$777$		0			0
$778$		−	27.4982i		−	0.985859i
$779$	−8.81979			−0.316002
$780$		0			0
$781$	−20.4978			−0.733469
$782$		−	3.37413i		−	0.120659i
$783$		0			0
$784$	1.74825			0.0624376
$785$	10.5067	+	30.2630i	0.375000	+	1.08013i
$786$		0			0
$787$		−	10.6849i		−	0.380876i	−0.981699	−	0.190438i	$-0.939009\pi$
$787$		−	10.6849i		−	0.380876i	0.981699	−	0.190438i	$-0.0609908\pi$
$788$			23.5643i			0.839443i
$789$		0			0
$790$	6.09263	+	17.5489i	0.216766	+	0.624362i
$791$	−14.4550			−0.513961
$792$		0			0
$793$		−	44.3228i		−	1.57395i
$794$	−3.11990			−0.110721
$795$		0			0
$796$	12.3076			0.436233
$797$		−	34.5430i		−	1.22358i	−0.791021	−	0.611789i	$-0.790450\pi$
$797$		−	34.5430i		−	1.22358i	0.791021	−	0.611789i	$-0.209550\pi$
$798$		0			0
$799$	29.6321			1.04831
$800$	−3.09834	−	3.92432i	−0.109543	−	0.138746i
$801$		0			0
$802$			23.0637i			0.814406i
$803$		−	25.8090i		−	0.910781i
$804$		0			0
$805$	−4.84088	+	1.68066i	−0.170619	+	0.0592354i
$806$	37.0248			1.30414
$807$		0			0
$808$			10.5956i			0.372751i
$809$	−38.9640			−1.36990			−0.684950	−	0.728590i	$-0.740176\pi$
$809$	−38.9640			−1.36990			−0.684950	+	0.728590i	$0.740176\pi$
$810$		0			0
$811$	−8.76376			−0.307737			−0.153869	−	0.988091i	$-0.549173\pi$
$811$	−8.76376			−0.307737			−0.153869	+	0.988091i	$0.549173\pi$
$812$		−	14.4455i		−	0.506938i
$813$		0			0
$814$	−28.4794			−0.998203
$815$	4.04391	+	11.6479i	0.141652	+	0.408007i
$816$		0			0
$817$		−	36.4989i		−	1.27693i
$818$			20.7483i			0.725446i
$819$		0			0
$820$	−5.37413	+	1.86579i	−0.187673	+	0.0651562i
$821$	32.9518			1.15002			0.575012	−	0.818145i	$-0.304997\pi$
$821$	32.9518			1.15002			0.575012	+	0.818145i	$0.304997\pi$
$822$		0			0
$823$		−	18.4833i		−	0.644286i	−0.946691	−	0.322143i	$-0.895597\pi$
$823$		−	18.4833i		−	0.644286i	0.946691	−	0.322143i	$-0.104403\pi$
$824$	1.06965			0.0372629
$825$		0			0
$826$	5.83025			0.202860
$827$		−	8.84088i		−	0.307428i	−0.988115	−	0.153714i	$-0.950877\pi$
$827$		−	8.84088i		−	0.307428i	0.988115	−	0.153714i	$-0.0491234\pi$
$828$		0			0
$829$	10.6830			0.371037			0.185519	−	0.982641i	$-0.440603\pi$
$829$	10.6830			0.371037			0.185519	+	0.982641i	$0.440603\pi$
$830$	16.4225	−	5.70156i	0.570033	−	0.197904i
$831$		0			0
$832$		−	3.75939i		−	0.130333i
$833$		−	5.89883i		−	0.204382i
$834$		0			0
$835$	−12.3076	−	35.4503i	−0.425923	−	1.22681i
$836$	−15.1511			−0.524012
$837$		0			0
$838$		−	7.09222i		−	0.244997i
$839$	51.8488			1.79002			0.895009	−	0.446048i	$-0.147169\pi$
$839$	51.8488			1.79002			0.895009	+	0.446048i	$0.147169\pi$
$840$		0			0
$841$	10.7340			0.370139
$842$		−	38.0869i		−	1.31256i
$843$		0			0
$844$	−20.4300			−0.703230
$845$	−2.39330	+	0.830905i	−0.0823319	+	0.0285840i
$846$		0			0
$847$			18.5634i			0.637846i
$848$			1.46675i			0.0503685i
$849$		0			0
$850$	−13.2411	+	10.4542i	−0.454167	+	0.358576i
$851$	−6.51643			−0.223380
$852$		0			0
$853$		−	49.5250i		−	1.69570i	−0.530233	−	0.847852i	$-0.677896\pi$
$853$		−	49.5250i		−	1.69570i	0.530233	−	0.847852i	$-0.322104\pi$
$854$	−27.0185			−0.924555
$855$		0			0
$856$	−19.4717			−0.665527
$857$			17.8331i			0.609168i	0.952485	+	0.304584i	$0.0985174\pi$
$857$			17.8331i			0.609168i	−0.952485	+	0.304584i	$0.901483\pi$
$858$		0			0
$859$	−51.3945			−1.75356			−0.876779	−	0.480893i	$-0.840313\pi$
$859$	−51.3945			−1.75356			−0.876779	+	0.480893i	$0.840313\pi$
$860$	−7.72118	−	22.2397i	−0.263290	−	0.758368i
$861$		0			0
$862$		−	20.8429i		−	0.709912i
$863$			25.2305i			0.858857i	0.903101	+	0.429429i	$0.141285\pi$
$863$			25.2305i			0.858857i	−0.903101	+	0.429429i	$0.858715\pi$
$864$		0			0
$865$	1.60261	+	4.61609i	0.0544905	+	0.156952i
$866$	−37.7487			−1.28275
$867$		0			0
$868$		−	22.5698i		−	0.766069i
$869$	36.3077			1.23165
$870$		0			0
$871$	−23.9503			−0.811525
$872$		−	10.8409i		−	0.367119i
$873$		0			0
$874$	−3.46675			−0.117265
$875$	21.5941	+	13.7899i	0.730015	+	0.466183i
$876$		0			0
$877$		−	3.33217i		−	0.112519i	−0.998416	−	0.0562597i	$-0.982083\pi$
$877$		−	3.33217i		−	0.112519i	0.998416	−	0.0562597i	$-0.0179175\pi$
$878$			25.5643i			0.862753i
$879$		0			0
$880$	−9.23195	+	3.20515i	−0.311209	+	0.108046i
$881$	22.7020			0.764848			0.382424	−	0.923987i	$-0.375089\pi$
$881$	22.7020			0.764848			0.382424	+	0.923987i	$0.375089\pi$
$882$		0			0
$883$			51.7832i			1.74264i	0.490711	+	0.871322i	$0.336737\pi$
$883$			51.7832i			1.74264i	−0.490711	+	0.871322i	$0.663263\pi$
$884$	−12.6846			−0.426631
$885$		0			0
$886$	4.00000			0.134383
$887$		−	4.75113i		−	0.159527i	−0.996814	−	0.0797637i	$-0.974583\pi$
$887$		−	4.75113i		−	0.159527i	0.996814	−	0.0797637i	$-0.0254166\pi$
$888$		0			0
$889$	16.9858			0.569685
$890$	−8.76860	−	25.2566i	−0.293924	−	0.846605i
$891$		0			0
$892$			15.9750i			0.534884i
$893$		−	30.4455i		−	1.01882i
$894$		0			0
$895$	−39.7205	+	13.7902i	−1.32771	+	0.460955i
$896$	−2.29167			−0.0765593
$897$		0			0
$898$		−	8.48408i		−	0.283117i
$899$	62.0808			2.07051
$900$		0			0
$901$	4.94901			0.164876
$902$			11.1188i			0.370214i
$903$		0			0
$904$	−6.30763			−0.209789
$905$	41.4125	−	14.3776i	1.37660	−	0.477927i
$906$		0			0
$907$			14.2585i			0.473446i	0.971577	+	0.236723i	$0.0760733\pi$
$907$			14.2585i			0.473446i	−0.971577	+	0.236723i	$0.923927\pi$
$908$			21.6046i			0.716975i
$909$		0			0
$910$	6.31824	+	18.1987i	0.209448	+	0.603282i
$911$	−5.79187			−0.191893			−0.0959466	−	0.995386i	$-0.530588\pi$
$911$	−5.79187			−0.191893			−0.0959466	+	0.995386i	$0.530588\pi$
$912$		0			0
$913$		−	33.9772i		−	1.12448i
$914$	35.8872			1.18704
$915$		0			0
$916$	21.7744			0.719446
$917$			24.7043i			0.815806i
$918$		0			0
$919$	−52.6879			−1.73801			−0.869007	−	0.494799i	$-0.835242\pi$
$919$	−52.6879			−1.73801			−0.869007	+	0.494799i	$0.835242\pi$
$920$	−2.11238	+	0.733377i	−0.0696432	+	0.0241787i
$921$		0			0
$922$			15.3356i			0.505050i
$923$			17.6321i			0.580366i
$924$		0			0
$925$	20.1902	+	25.5725i	0.663848	+	0.840820i
$926$	18.1489			0.596409
$927$		0			0
$928$		−	6.30349i		−	0.206922i
$929$	−42.3684			−1.39006			−0.695031	−	0.718980i	$-0.744609\pi$
$929$	−42.3684			−1.39006			−0.695031	+	0.718980i	$0.744609\pi$
$930$		0			0
$931$	−6.06076			−0.198634
$932$			12.0339i			0.394183i
$933$		0			0
$934$	−5.97515			−0.195513
$935$	10.8146	+	31.1498i	0.353675	+	1.01871i
$936$		0			0
$937$		−	17.1194i		−	0.559267i	−0.960107	−	0.279633i	$-0.909787\pi$
$937$		−	17.1194i		−	0.559267i	0.960107	−	0.279633i	$-0.0902129\pi$
$938$			14.5998i			0.476699i
$939$		0			0
$940$	−6.44062	−	18.5512i	−0.210070	−	0.605075i
$941$	52.4900			1.71113			0.855563	−	0.517698i	$-0.173211\pi$
$941$	52.4900			1.71113			0.855563	+	0.517698i	$0.173211\pi$
$942$		0			0
$943$			2.54411i			0.0828475i
$944$	2.54411			0.0828036
$945$		0			0
$946$	−46.0127			−1.49600
$947$		−	9.64500i		−	0.313420i	−0.987645	−	0.156710i	$-0.949911\pi$
$947$		−	9.64500i		−	0.313420i	0.987645	−	0.156710i	$-0.0500889\pi$
$948$		0			0
$949$	−22.2008			−0.720667
$950$	10.7412	+	13.6046i	0.348490	+	0.441393i
$951$		0			0
$952$			7.73238i			0.250608i
$953$		−	24.2921i		−	0.786899i	−0.919346	−	0.393450i	$-0.871282\pi$
$953$		−	24.2921i		−	0.786899i	0.919346	−	0.393450i	$-0.128718\pi$
$954$		0			0
$955$	27.5304	−	9.55800i	0.890863	−	0.309290i
$956$	17.4748			0.565177
$957$		0			0
$958$			4.58334i			0.148081i
$959$	16.8991			0.545699
$960$		0			0
$961$	65.9956			2.12889
$962$			24.4978i			0.789840i
$963$		0			0
$964$	−23.7495			−0.764921
$965$	3.36131	+	9.68176i	0.108205	+	0.311667i
$966$		0			0
$967$		−	52.2814i		−	1.68126i	−0.541613	−	0.840628i	$-0.682186\pi$
$967$		−	52.2814i		−	1.68126i	0.541613	−	0.840628i	$-0.317814\pi$
$968$			8.10038i			0.260356i
$969$		0			0
$970$	−13.3154	+	4.62284i	−0.427531	+	0.148430i
$971$	11.5979			0.372194			0.186097	−	0.982531i	$-0.440416\pi$
$971$	11.5979			0.372194			0.186097	+	0.982531i	$0.440416\pi$
$972$		0			0
$973$		−	18.3334i		−	0.587740i
$974$	33.9826			1.08887
$975$		0			0
$976$	−11.7899			−0.377385
$977$			44.8706i			1.43554i	0.696281	+	0.717769i	$0.254837\pi$
$977$			44.8706i			1.43554i	−0.696281	+	0.717769i	$0.745163\pi$
$978$		0			0
$979$	−52.2546			−1.67006
$980$	−3.69298	+	1.28213i	−0.117968	+	0.0409561i
$981$		0			0
$982$		−	19.8690i		−	0.634047i
$983$			40.5656i			1.29384i	0.762558	+	0.646920i	$0.223943\pi$
$983$			40.5656i			1.29384i	−0.762558	+	0.646920i	$0.776057\pi$
$984$		0			0
$985$	−17.2815	−	49.7768i	−0.550634	−	1.58602i
$986$	−21.2688			−0.677336
$987$		0			0
$988$			13.0329i			0.414631i
$989$	−10.5283			−0.334779
$990$		0			0
$991$	25.2799			0.803043			0.401522	−	0.915849i	$-0.368481\pi$
$991$	25.2799			0.803043			0.401522	+	0.915849i	$0.368481\pi$
$992$		−	9.84863i		−	0.312694i
$993$		0			0
$994$	10.7483			0.340914
$995$	−25.9984	+	9.02613i	−0.824206	+	0.286148i
$996$		0			0
$997$		−	48.4596i		−	1.53473i	−0.641209	−	0.767366i	$-0.721567\pi$
$997$		−	48.4596i		−	1.53473i	0.641209	−	0.767366i	$-0.278433\pi$
$998$		−	28.1951i		−	0.892499i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.h.829.8	yes	16
3.2	odd	2	inner	2070.2.d.h.829.9	yes	16
5.4	even	2	inner	2070.2.d.h.829.16	yes	16
15.14	odd	2	inner	2070.2.d.h.829.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.d.h.829.1	✓	16	15.14	odd	2	inner
2070.2.d.h.829.8	yes	16	1.1	even	1	trivial
2070.2.d.h.829.9	yes	16	3.2	odd	2	inner
2070.2.d.h.829.16	yes	16	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.11238 - 0.733377i) q^{5} +2.29167i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(2.11238 - 0.733377i) q^{5} +2.29167i q^{7} +1.00000i q^{8} +(-0.733377 - 2.11238i) q^{10} -4.37040 q^{11} +3.75939i q^{13} +2.29167 q^{14} +1.00000 q^{16} -3.37413i q^{17} -3.46675 q^{19} +(-2.11238 + 0.733377i) q^{20} +4.37040i q^{22} +1.00000i q^{23} +(3.92432 - 3.09834i) q^{25} +3.75939 q^{26} -2.29167i q^{28} +6.30349 q^{29} +9.84863 q^{31} -1.00000i q^{32} -3.37413 q^{34} +(1.68066 + 4.84088i) q^{35} +6.51643i q^{37} +3.46675i q^{38} +(0.733377 + 2.11238i) q^{40} +2.54411 q^{41} +10.5283i q^{43} +4.37040 q^{44} +1.00000 q^{46} +8.78214i q^{47} +1.74825 q^{49} +(-3.09834 - 3.92432i) q^{50} -3.75939i q^{52} +1.46675i q^{53} +(-9.23195 + 3.20515i) q^{55} -2.29167 q^{56} -6.30349i q^{58} +2.54411 q^{59} -11.7899 q^{61} -9.84863i q^{62} -1.00000 q^{64} +(2.75705 + 7.94126i) q^{65} +6.37080i q^{67} +3.37413i q^{68} +(4.84088 - 1.68066i) q^{70} +4.69014 q^{71} +5.90542i q^{73} +6.51643 q^{74} +3.46675 q^{76} -10.0155i q^{77} -8.30763 q^{79} +(2.11238 - 0.733377i) q^{80} -2.54411i q^{82} +7.77439i q^{83} +(-2.47451 - 7.12745i) q^{85} +10.5283 q^{86} -4.37040i q^{88} +11.9565 q^{89} -8.61527 q^{91} -1.00000i q^{92} +8.78214 q^{94} +(-7.32311 + 2.54244i) q^{95} -6.30349i q^{97} -1.74825i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

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