LMFDB - Embedded newform 3762.2.g.l.2089.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3762,2,Mod(2089,3762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3762, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3762.2089");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3762.g (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:	$30.0397212404$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 199 x^{16} - 414 x^{15} + 430 x^{14} + 184 x^{13} + 6939 x^{12} + \cdots + 64 $ x^20 - 2x^19 + 2x^18 + 199x^16 - 414x^15 + 430x^14 + 184x^13 + 6939x^12 - 14914x^11 + 16078x^10 + 10764x^9 + 7501x^8 - 14446x^7 + 21922x^6 + 21836x^5 + 10900x^4 - 80x^3 + 128x^2 + 128x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 1254)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2089.13
Root			$-0.196118 + 0.196118i$ of defining polynomial
Character	$\chi$	$=$	3762.2089
Dual form			3762.2.g.l.2089.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +1.28096 q^{5} -0.392237i q^{7} +1.00000 q^{8} +1.28096 q^{10} +(-3.22665 - 0.767284i) q^{11} -4.16029 q^{13} -0.392237i q^{14} +1.00000 q^{16} +7.31859i q^{17} +(3.16426 + 2.99791i) q^{19} +1.28096 q^{20} +(-3.22665 - 0.767284i) q^{22} -7.62219 q^{23} -3.35913 q^{25} -4.16029 q^{26} -0.392237i q^{28} -3.00432 q^{29} +2.68525i q^{31} +1.00000 q^{32} +7.31859i q^{34} -0.502441i q^{35} +9.08665i q^{37} +(3.16426 + 2.99791i) q^{38} +1.28096 q^{40} +0.825668 q^{41} -5.57398i q^{43} +(-3.22665 - 0.767284i) q^{44} -7.62219 q^{46} -9.65646 q^{47} +6.84615 q^{49} -3.35913 q^{50} -4.16029 q^{52} +4.43450i q^{53} +(-4.13322 - 0.982862i) q^{55} -0.392237i q^{56} -3.00432 q^{58} +6.49403i q^{59} -4.87403i q^{61} +2.68525i q^{62} +1.00000 q^{64} -5.32918 q^{65} +14.6118i q^{67} +7.31859i q^{68} -0.502441i q^{70} -8.75634i q^{71} +10.3074i q^{73} +9.08665i q^{74} +(3.16426 + 2.99791i) q^{76} +(-0.300957 + 1.26561i) q^{77} +15.4604 q^{79} +1.28096 q^{80} +0.825668 q^{82} -6.29838i q^{83} +9.37485i q^{85} -5.57398i q^{86} +(-3.22665 - 0.767284i) q^{88} +4.35469i q^{89} +1.63182i q^{91} -7.62219 q^{92} -9.65646 q^{94} +(4.05330 + 3.84021i) q^{95} -6.18155i q^{97} +6.84615 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} + 20 q^{4} - 4 q^{5} + 20 q^{8} - 4 q^{10} - 6 q^{11} + 4 q^{13} + 20 q^{16} + 2 q^{19} - 4 q^{20} - 6 q^{22} + 8 q^{23} + 32 q^{25} + 4 q^{26} - 4 q^{29} + 20 q^{32} + 2 q^{38} - 4 q^{40}+ \cdots - 36 q^{98}+O(q^{100}) $ 20 * q + 20 * q^2 + 20 * q^4 - 4 * q^5 + 20 * q^8 - 4 * q^10 - 6 * q^11 + 4 * q^13 + 20 * q^16 + 2 * q^19 - 4 * q^20 - 6 * q^22 + 8 * q^23 + 32 * q^25 + 4 * q^26 - 4 * q^29 + 20 * q^32 + 2 * q^38 - 4 * q^40 + 24 * q^41 - 6 * q^44 + 8 * q^46 - 8 * q^47 - 36 * q^49 + 32 * q^50 + 4 * q^52 + 8 * q^55 - 4 * q^58 + 20 * q^64 + 24 * q^65 + 2 * q^76 - 28 * q^77 + 24 * q^79 - 4 * q^80 + 24 * q^82 - 6 * q^88 + 8 * q^92 - 8 * q^94 - 32 * q^95 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3762\mathbb{Z}\right)^\times$.

$n$	$343$	$2377$	$2927$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	1.28096			0.572864			0.286432	−	0.958101i	$-0.407531\pi$
$5$	1.28096			0.572864			0.286432	+	0.958101i	$0.407531\pi$
$6$		0			0
$7$		−	0.392237i		−	0.148252i	−0.997249	−	0.0741258i	$-0.976383\pi$
$7$		−	0.392237i		−	0.148252i	0.997249	−	0.0741258i	$-0.0236166\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	1.28096			0.405076
$11$	−3.22665	−	0.767284i	−0.972872	−	0.231345i
$11$	−3.22665	−	0.767284i	−0.972872	−	0.231345i
$12$		0			0
$13$	−4.16029			−1.15386			−0.576928	−	0.816795i	$-0.695749\pi$
$13$	−4.16029			−1.15386			−0.576928	+	0.816795i	$0.695749\pi$
$14$		−	0.392237i		−	0.104830i
$15$		0			0
$16$	1.00000			0.250000
$17$			7.31859i			1.77502i	0.460789	+	0.887510i	$0.347566\pi$
$17$			7.31859i			1.77502i	−0.460789	+	0.887510i	$0.652434\pi$
$18$		0			0
$19$	3.16426	+	2.99791i	0.725931	+	0.687767i
$19$	3.16426	+	2.99791i	0.725931	+	0.687767i
$20$	1.28096			0.286432
$21$		0			0
$22$	−3.22665	−	0.767284i	−0.687924	−	0.163585i
$23$	−7.62219			−1.58934			−0.794668	−	0.607044i	$-0.792355\pi$
$23$	−7.62219			−1.58934			−0.794668	+	0.607044i	$0.792355\pi$
$24$		0			0
$25$	−3.35913			−0.671827
$26$	−4.16029			−0.815900
$27$		0			0
$28$		−	0.392237i		−	0.0741258i
$29$	−3.00432			−0.557888			−0.278944	−	0.960307i	$-0.589984\pi$
$29$	−3.00432			−0.557888			−0.278944	+	0.960307i	$0.589984\pi$
$30$		0			0
$31$			2.68525i			0.482285i	0.970490	+	0.241142i	$0.0775221\pi$
$31$			2.68525i			0.482285i	−0.970490	+	0.241142i	$0.922478\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$			7.31859i			1.25513i
$35$		−	0.502441i		−	0.0849280i
$36$		0			0
$37$			9.08665i			1.49384i	0.664917	+	0.746918i	$0.268467\pi$
$37$			9.08665i			1.49384i	−0.664917	+	0.746918i	$0.731533\pi$
$38$	3.16426	+	2.99791i	0.513311	+	0.486325i
$39$		0			0
$40$	1.28096			0.202538
$41$	0.825668			0.128948			0.0644739	−	0.997919i	$-0.479463\pi$
$41$	0.825668			0.128948			0.0644739	+	0.997919i	$0.479463\pi$
$42$		0			0
$43$		−	5.57398i		−	0.850023i	−0.905188	−	0.425012i	$-0.860270\pi$
$43$		−	5.57398i		−	0.850023i	0.905188	−	0.425012i	$-0.139730\pi$
$44$	−3.22665	−	0.767284i	−0.486436	−	0.115672i
$45$		0			0
$46$	−7.62219			−1.12383
$47$	−9.65646			−1.40854			−0.704270	−	0.709932i	$-0.748726\pi$
$47$	−9.65646			−1.40854			−0.704270	+	0.709932i	$0.748726\pi$
$48$		0			0
$49$	6.84615			0.978021
$50$	−3.35913			−0.475053
$51$		0			0
$52$	−4.16029			−0.576928
$53$			4.43450i			0.609125i	0.952492	+	0.304563i	$0.0985103\pi$
$53$			4.43450i			0.609125i	−0.952492	+	0.304563i	$0.901490\pi$
$54$		0			0
$55$	−4.13322	−	0.982862i	−0.557323	−	0.132529i
$56$		−	0.392237i		−	0.0524149i
$57$		0			0
$58$	−3.00432			−0.394486
$59$			6.49403i			0.845450i	0.906258	+	0.422725i	$0.138926\pi$
$59$			6.49403i			0.845450i	−0.906258	+	0.422725i	$0.861074\pi$
$60$		0			0
$61$		−	4.87403i		−	0.624056i	−0.950073	−	0.312028i	$-0.898992\pi$
$61$		−	4.87403i		−	0.624056i	0.950073	−	0.312028i	$-0.101008\pi$
$62$			2.68525i			0.341027i
$63$		0			0
$64$	1.00000			0.125000
$65$	−5.32918			−0.661003
$66$		0			0
$67$			14.6118i			1.78512i	0.450932	+	0.892559i	$0.351092\pi$
$67$			14.6118i			1.78512i	−0.450932	+	0.892559i	$0.648908\pi$
$68$			7.31859i			0.887510i
$69$		0			0
$70$		−	0.502441i		−	0.0600532i
$71$		−	8.75634i		−	1.03919i	−0.854414	−	0.519593i	$-0.826083\pi$
$71$		−	8.75634i		−	1.03919i	0.854414	−	0.519593i	$-0.173917\pi$
$72$		0			0
$73$			10.3074i			1.20639i	0.797594	+	0.603195i	$0.206106\pi$
$73$			10.3074i			1.20639i	−0.797594	+	0.603195i	$0.793894\pi$
$74$			9.08665i			1.05630i
$75$		0			0
$76$	3.16426	+	2.99791i	0.362966	+	0.343884i
$77$	−0.300957	+	1.26561i	−0.0342972	+	0.144230i
$78$		0			0
$79$	15.4604			1.73943			0.869713	−	0.493558i	$-0.164304\pi$
$79$	15.4604			1.73943			0.869713	+	0.493558i	$0.164304\pi$
$80$	1.28096			0.143216
$81$		0			0
$82$	0.825668			0.0911798
$83$		−	6.29838i		−	0.691337i	−0.938357	−	0.345669i	$-0.887652\pi$
$83$		−	6.29838i		−	0.691337i	0.938357	−	0.345669i	$-0.112348\pi$
$84$		0			0
$85$			9.37485i			1.01685i
$86$		−	5.57398i		−	0.601057i
$87$		0			0
$88$	−3.22665	−	0.767284i	−0.343962	−	0.0817927i
$89$			4.35469i			0.461596i	0.973002	+	0.230798i	$0.0741337\pi$
$89$			4.35469i			0.461596i	−0.973002	+	0.230798i	$0.925866\pi$
$90$		0			0
$91$			1.63182i			0.171061i
$92$	−7.62219			−0.794668
$93$		0			0
$94$	−9.65646			−0.995988
$95$	4.05330	+	3.84021i	0.415860	+	0.393997i
$96$		0			0
$97$		−	6.18155i		−	0.627641i	−0.949482	−	0.313821i	$-0.898391\pi$
$97$		−	6.18155i		−	0.627641i	0.949482	−	0.313821i	$-0.101609\pi$
$98$	6.84615			0.691566
$99$		0			0
$100$	−3.35913			−0.335913
$101$		−	16.5100i		−	1.64281i	−0.570349	−	0.821403i	$-0.693192\pi$
$101$		−	16.5100i		−	1.64281i	0.570349	−	0.821403i	$-0.306808\pi$
$102$		0			0
$103$		−	5.61416i		−	0.553180i	−0.960988	−	0.276590i	$-0.910796\pi$
$103$		−	5.61416i		−	0.553180i	0.960988	−	0.276590i	$-0.0892043\pi$
$104$	−4.16029			−0.407950
$105$		0			0
$106$			4.43450i			0.430717i
$107$	2.31418			0.223720			0.111860	−	0.993724i	$-0.464319\pi$
$107$	2.31418			0.223720			0.111860	+	0.993724i	$0.464319\pi$
$108$		0			0
$109$	14.1894			1.35910			0.679548	−	0.733631i	$-0.262176\pi$
$109$	14.1894			1.35910			0.679548	+	0.733631i	$0.262176\pi$
$110$	−4.13322	−	0.982862i	−0.394087	−	0.0937123i
$111$		0			0
$112$		−	0.392237i		−	0.0370629i
$113$			8.73342i			0.821571i	0.911732	+	0.410786i	$0.134746\pi$
$113$			8.73342i			0.821571i	−0.911732	+	0.410786i	$0.865254\pi$
$114$		0			0
$115$	−9.76374			−0.910474
$116$	−3.00432			−0.278944
$117$		0			0
$118$			6.49403i			0.597824i
$119$	2.87062			0.263149
$120$		0			0
$121$	9.82255	+	4.95151i	0.892959	+	0.450138i
$122$		−	4.87403i		−	0.441274i
$123$		0			0
$124$			2.68525i			0.241142i
$125$	−10.7077			−0.957730
$126$		0			0
$127$	−11.8120			−1.04815			−0.524073	−	0.851674i	$-0.675588\pi$
$127$	−11.8120			−1.04815			−0.524073	+	0.851674i	$0.675588\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−5.32918			−0.467400
$131$		−	6.40399i		−	0.559519i	−0.960070	−	0.279760i	$-0.909745\pi$
$131$		−	6.40399i		−	0.559519i	0.960070	−	0.279760i	$-0.0902548\pi$
$132$		0			0
$133$	1.17589	−	1.24114i	0.101963	−	0.107621i
$134$			14.6118i			1.26227i
$135$		0			0
$136$			7.31859i			0.627564i
$137$	−10.5157			−0.898416			−0.449208	−	0.893427i	$-0.648294\pi$
$137$	−10.5157			−0.898416			−0.449208	+	0.893427i	$0.648294\pi$
$138$		0			0
$139$			9.62814i			0.816648i	0.912837	+	0.408324i	$0.133887\pi$
$139$			9.62814i			0.816648i	−0.912837	+	0.408324i	$0.866113\pi$
$140$		−	0.502441i		−	0.0424640i
$141$		0			0
$142$		−	8.75634i		−	0.734816i
$143$	13.4238	+	3.19212i	1.12255	+	0.266939i
$144$		0			0
$145$	−3.84842			−0.319594
$146$			10.3074i			0.853046i
$147$		0			0
$148$			9.08665i			0.746918i
$149$			1.79326i			0.146910i	0.997299	+	0.0734549i	$0.0234025\pi$
$149$			1.79326i			0.146910i	−0.997299	+	0.0734549i	$0.976598\pi$
$150$		0			0
$151$	19.0044			1.54656			0.773280	−	0.634065i	$-0.218615\pi$
$151$	19.0044			1.54656			0.773280	+	0.634065i	$0.218615\pi$
$152$	3.16426	+	2.99791i	0.256656	+	0.243162i
$153$		0			0
$154$	−0.300957	+	1.26561i	−0.0242518	+	0.101986i
$155$			3.43971i			0.276284i
$156$		0			0
$157$	7.84764			0.626310			0.313155	−	0.949702i	$-0.398614\pi$
$157$	7.84764			0.626310			0.313155	+	0.949702i	$0.398614\pi$
$158$	15.4604			1.22996
$159$		0			0
$160$	1.28096			0.101269
$161$			2.98970i			0.235622i
$162$		0			0
$163$	−14.6344			−1.14625			−0.573127	−	0.819467i	$-0.694270\pi$
$163$	−14.6344			−1.14625			−0.573127	+	0.819467i	$0.694270\pi$
$164$	0.825668			0.0644739
$165$		0			0
$166$		−	6.29838i		−	0.488849i
$167$	−17.8960			−1.38484			−0.692418	−	0.721497i	$-0.743455\pi$
$167$	−17.8960			−1.38484			−0.692418	+	0.721497i	$0.743455\pi$
$168$		0			0
$169$	4.30801			0.331385
$170$			9.37485i			0.719018i
$171$		0			0
$172$		−	5.57398i		−	0.425012i
$173$	−7.95773			−0.605015			−0.302507	−	0.953147i	$-0.597824\pi$
$173$	−7.95773			−0.605015			−0.302507	+	0.953147i	$0.597824\pi$
$174$		0			0
$175$			1.31758i			0.0995994i
$176$	−3.22665	−	0.767284i	−0.243218	−	0.0578362i
$177$		0			0
$178$			4.35469i			0.326398i
$179$			2.64141i			0.197428i	0.995116	+	0.0987139i	$0.0314729\pi$
$179$			2.64141i			0.197428i	−0.995116	+	0.0987139i	$0.968527\pi$
$180$		0			0
$181$		−	7.86248i		−	0.584414i	−0.956355	−	0.292207i	$-0.905610\pi$
$181$		−	7.86248i		−	0.584414i	0.956355	−	0.292207i	$-0.0943895\pi$
$182$			1.63182i			0.120958i
$183$		0			0
$184$	−7.62219			−0.561915
$185$			11.6397i			0.855765i
$186$		0			0
$187$	5.61544	−	23.6145i	0.410642	−	1.72687i
$188$	−9.65646			−0.704270
$189$		0			0
$190$	4.05330	+	3.84021i	0.294057	+	0.278598i
$191$	−4.82045			−0.348796			−0.174398	−	0.984675i	$-0.555798\pi$
$191$	−4.82045			−0.348796			−0.174398	+	0.984675i	$0.555798\pi$
$192$		0			0
$193$	−1.00099			−0.0720527			−0.0360263	−	0.999351i	$-0.511470\pi$
$193$	−1.00099			−0.0720527			−0.0360263	+	0.999351i	$0.511470\pi$
$194$		−	6.18155i		−	0.443809i
$195$		0			0
$196$	6.84615			0.489011
$197$		−	14.3961i		−	1.02568i	−0.858485	−	0.512839i	$-0.828594\pi$
$197$		−	14.3961i		−	1.02568i	0.858485	−	0.512839i	$-0.171406\pi$
$198$		0			0
$199$	9.58482			0.679450			0.339725	−	0.940525i	$-0.389666\pi$
$199$	9.58482			0.679450			0.339725	+	0.940525i	$0.389666\pi$
$200$	−3.35913			−0.237527
$201$		0			0
$202$		−	16.5100i		−	1.16164i
$203$			1.17840i			0.0827078i
$204$		0			0
$205$	1.05765			0.0738695
$206$		−	5.61416i		−	0.391157i
$207$		0			0
$208$	−4.16029			−0.288464
$209$	−7.90972	−	12.1011i	−0.547127	−	0.837050i
$210$		0			0
$211$	−6.83304			−0.470406			−0.235203	−	0.971946i	$-0.575575\pi$
$211$	−6.83304			−0.470406			−0.235203	+	0.971946i	$0.575575\pi$
$212$			4.43450i			0.304563i
$213$		0			0
$214$	2.31418			0.158194
$215$		−	7.14006i		−	0.486948i
$216$		0			0
$217$	1.05325			0.0714995
$218$	14.1894			0.961025
$219$		0			0
$220$	−4.13322	−	0.982862i	−0.278662	−	0.0662646i
$221$		−	30.4475i		−	2.04812i
$222$		0			0
$223$		−	29.3935i		−	1.96834i	−0.177239	−	0.984168i	$-0.556716\pi$
$223$		−	29.3935i		−	1.96834i	0.177239	−	0.984168i	$-0.443284\pi$
$224$		−	0.392237i		−	0.0262074i
$225$		0			0
$226$			8.73342i			0.580939i
$227$	24.3018			1.61297			0.806485	−	0.591255i	$-0.201367\pi$
$227$	24.3018			1.61297			0.806485	+	0.591255i	$0.201367\pi$
$228$		0			0
$229$	−19.5240			−1.29018			−0.645090	−	0.764106i	$-0.723180\pi$
$229$	−19.5240			−1.29018			−0.645090	+	0.764106i	$0.723180\pi$
$230$	−9.76374			−0.643802
$231$		0			0
$232$	−3.00432			−0.197243
$233$			9.93903i			0.651127i	0.945520	+	0.325564i	$0.105554\pi$
$233$			9.93903i			0.651127i	−0.945520	+	0.325564i	$0.894446\pi$
$234$		0			0
$235$	−12.3696			−0.806902
$236$			6.49403i			0.422725i
$237$		0			0
$238$	2.87062			0.186075
$239$			4.70511i			0.304348i	0.988354	+	0.152174i	$0.0486274\pi$
$239$			4.70511i			0.304348i	−0.988354	+	0.152174i	$0.951373\pi$
$240$		0			0
$241$	−18.6944			−1.20421			−0.602107	−	0.798415i	$-0.705672\pi$
$241$	−18.6944			−1.20421			−0.602107	+	0.798415i	$0.705672\pi$
$242$	9.82255	+	4.95151i	0.631417	+	0.318295i
$243$		0			0
$244$		−	4.87403i		−	0.312028i
$245$	8.76967			0.560273
$246$		0			0
$247$	−13.1642	−	12.4722i	−0.837621	−	0.793585i
$248$			2.68525i			0.170513i
$249$		0			0
$250$	−10.7077			−0.677217
$251$	−7.50024			−0.473411			−0.236705	−	0.971581i	$-0.576068\pi$
$251$	−7.50024			−0.473411			−0.236705	+	0.971581i	$0.576068\pi$
$252$		0			0
$253$	24.5941	+	5.84838i	1.54622	+	0.367685i
$254$	−11.8120			−0.741151
$255$		0			0
$256$	1.00000			0.0625000
$257$			13.0530i			0.814226i	0.913378	+	0.407113i	$0.133464\pi$
$257$			13.0530i			0.814226i	−0.913378	+	0.407113i	$0.866536\pi$
$258$		0			0
$259$	3.56412			0.221463
$260$	−5.32918			−0.330502
$261$		0			0
$262$		−	6.40399i		−	0.395640i
$263$			27.6548i			1.70527i	0.522508	+	0.852634i	$0.324996\pi$
$263$			27.6548i			1.70527i	−0.522508	+	0.852634i	$0.675004\pi$
$264$		0			0
$265$			5.68043i			0.348946i
$266$	1.17589	−	1.24114i	0.0720984	−	0.0760992i
$267$		0			0
$268$			14.6118i			0.892559i
$269$			16.8086i			1.02484i	0.858736	+	0.512418i	$0.171250\pi$
$269$			16.8086i			1.02484i	−0.858736	+	0.512418i	$0.828750\pi$
$270$		0			0
$271$		−	9.95751i		−	0.604875i	−0.953169	−	0.302438i	$-0.902200\pi$
$271$		−	9.95751i		−	0.604875i	0.953169	−	0.302438i	$-0.0978004\pi$
$272$			7.31859i			0.443755i
$273$		0			0
$274$	−10.5157			−0.635276
$275$	10.8388	+	2.57741i	0.653601	+	0.155424i
$276$		0			0
$277$			11.4686i			0.689083i	0.938771	+	0.344542i	$0.111966\pi$
$277$			11.4686i			0.689083i	−0.938771	+	0.344542i	$0.888034\pi$
$278$			9.62814i			0.577458i
$279$		0			0
$280$		−	0.502441i		−	0.0300266i
$281$	12.2517			0.730873			0.365437	−	0.930836i	$-0.380920\pi$
$281$	12.2517			0.730873			0.365437	+	0.930836i	$0.380920\pi$
$282$		0			0
$283$		−	27.0812i		−	1.60981i	−0.593405	−	0.804904i	$-0.702217\pi$
$283$		−	27.0812i		−	1.60981i	0.593405	−	0.804904i	$-0.297783\pi$
$284$		−	8.75634i		−	0.519593i
$285$		0			0
$286$	13.4238	+	3.19212i	0.793766	+	0.188754i
$287$		−	0.323858i		−	0.0191167i
$288$		0			0
$289$	−36.5618			−2.15069
$290$	−3.84842			−0.225987
$291$		0			0
$292$			10.3074i			0.603195i
$293$	−9.60892			−0.561359			−0.280679	−	0.959802i	$-0.590560\pi$
$293$	−9.60892			−0.561359			−0.280679	+	0.959802i	$0.590560\pi$
$294$		0			0
$295$			8.31861i			0.484328i
$296$			9.08665i			0.528151i
$297$		0			0
$298$			1.79326i			0.103881i
$299$	31.7105			1.83387
$300$		0			0
$301$	−2.18632			−0.126017
$302$	19.0044			1.09358
$303$		0			0
$304$	3.16426	+	2.99791i	0.181483	+	0.171942i
$305$		−	6.24345i		−	0.357499i
$306$		0			0
$307$	2.13570			0.121891			0.0609453	−	0.998141i	$-0.480588\pi$
$307$	2.13570			0.121891			0.0609453	+	0.998141i	$0.480588\pi$
$308$	−0.300957	+	1.26561i	−0.0171486	+	0.0721149i
$309$		0			0
$310$			3.43971i			0.195362i
$311$	16.6337			0.943209			0.471605	−	0.881810i	$-0.343675\pi$
$311$	16.6337			0.943209			0.471605	+	0.881810i	$0.343675\pi$
$312$		0			0
$313$	−32.0516			−1.81166			−0.905831	−	0.423639i	$-0.860753\pi$
$313$	−32.0516			−1.81166			−0.905831	+	0.423639i	$0.860753\pi$
$314$	7.84764			0.442868
$315$		0			0
$316$	15.4604			0.869713
$317$			34.7556i			1.95207i	0.217621	+	0.976033i	$0.430170\pi$
$317$			34.7556i			1.95207i	−0.217621	+	0.976033i	$0.569830\pi$
$318$		0			0
$319$	9.69389	+	2.30517i	0.542754	+	0.129065i
$320$	1.28096			0.0716080
$321$		0			0
$322$			2.98970i			0.166610i
$323$	−21.9405	+	23.1579i	−1.22080	+	1.28854i
$324$		0			0
$325$	13.9750			0.775192
$326$	−14.6344			−0.810524
$327$		0			0
$328$	0.825668			0.0455899
$329$			3.78762i			0.208818i
$330$		0			0
$331$			26.8731i			1.47708i	0.674211	+	0.738539i	$0.264484\pi$
$331$			26.8731i			1.47708i	−0.674211	+	0.738539i	$0.735516\pi$
$332$		−	6.29838i		−	0.345669i
$333$		0			0
$334$	−17.8960			−0.979227
$335$			18.7172i			1.02263i
$336$		0			0
$337$	6.33466			0.345071			0.172536	−	0.985003i	$-0.444804\pi$
$337$	6.33466			0.345071			0.172536	+	0.985003i	$0.444804\pi$
$338$	4.30801			0.234325
$339$		0			0
$340$			9.37485i			0.508423i
$341$	2.06035	−	8.66436i	0.111574	−	0.469201i
$342$		0			0
$343$		−	5.43097i		−	0.293245i
$344$		−	5.57398i		−	0.300529i
$345$		0			0
$346$	−7.95773			−0.427810
$347$			17.1780i			0.922162i	0.887358	+	0.461081i	$0.152538\pi$
$347$			17.1780i			0.922162i	−0.887358	+	0.461081i	$0.847462\pi$
$348$		0			0
$349$			33.1259i			1.77319i	0.462547	+	0.886595i	$0.346936\pi$
$349$			33.1259i			1.77319i	−0.462547	+	0.886595i	$0.653064\pi$
$350$			1.31758i			0.0704274i
$351$		0			0
$352$	−3.22665	−	0.767284i	−0.171981	−	0.0408964i
$353$	0.856028			0.0455618			0.0227809	−	0.999740i	$-0.492748\pi$
$353$	0.856028			0.0455618			0.0227809	+	0.999740i	$0.492748\pi$
$354$		0			0
$355$		−	11.2166i		−	0.595313i
$356$			4.35469i			0.230798i
$357$		0			0
$358$			2.64141i			0.139603i
$359$		−	32.3606i		−	1.70793i	−0.520331	−	0.853965i	$-0.674191\pi$
$359$		−	32.3606i		−	1.70793i	0.520331	−	0.853965i	$-0.325809\pi$
$360$		0			0
$361$	1.02511	+	18.9723i	0.0539529	+	0.998543i
$362$		−	7.86248i		−	0.413243i
$363$		0			0
$364$			1.63182i			0.0855306i
$365$			13.2034i			0.691097i
$366$		0			0
$367$	−1.85564			−0.0968637			−0.0484318	−	0.998826i	$-0.515422\pi$
$367$	−1.85564			−0.0968637			−0.0484318	+	0.998826i	$0.515422\pi$
$368$	−7.62219			−0.397334
$369$		0			0
$370$			11.6397i			0.605117i
$371$	1.73937			0.0903038
$372$		0			0
$373$	27.9173			1.44551			0.722753	−	0.691107i	$-0.242877\pi$
$373$	27.9173			1.44551			0.722753	+	0.691107i	$0.242877\pi$
$374$	5.61544	−	23.6145i	0.290367	−	1.22108i
$375$		0			0
$376$	−9.65646			−0.497994
$377$	12.4988			0.643723
$378$		0			0
$379$		−	5.41292i		−	0.278043i	−0.990289	−	0.139021i	$-0.955604\pi$
$379$		−	5.41292i		−	0.278043i	0.990289	−	0.139021i	$-0.0443957\pi$
$380$	4.05330	+	3.84021i	0.207930	+	0.196999i
$381$		0			0
$382$	−4.82045			−0.246636
$383$		−	8.83675i		−	0.451537i	−0.974181	−	0.225768i	$-0.927511\pi$
$383$		−	8.83675i		−	0.451537i	0.974181	−	0.225768i	$-0.0724893\pi$
$384$		0			0
$385$	−0.385515	+	1.62120i	−0.0196477	+	0.0826241i
$386$	−1.00099			−0.0509489
$387$		0			0
$388$		−	6.18155i		−	0.313821i
$389$	−31.7505			−1.60981			−0.804906	−	0.593402i	$-0.797785\pi$
$389$	−31.7505			−1.60981			−0.804906	+	0.593402i	$0.797785\pi$
$390$		0			0
$391$		−	55.7837i		−	2.82110i
$392$	6.84615			0.345783
$393$		0			0
$394$		−	14.3961i		−	0.725264i
$395$	19.8041			0.996455
$396$		0			0
$397$	−17.1766			−0.862066			−0.431033	−	0.902336i	$-0.641851\pi$
$397$	−17.1766			−0.862066			−0.431033	+	0.902336i	$0.641851\pi$
$398$	9.58482			0.480444
$399$		0			0
$400$	−3.35913			−0.167957
$401$			10.1717i			0.507948i	0.967211	+	0.253974i	$0.0817378\pi$
$401$			10.1717i			0.507948i	−0.967211	+	0.253974i	$0.918262\pi$
$402$		0			0
$403$		−	11.1714i		−	0.556488i
$404$		−	16.5100i		−	0.821403i
$405$		0			0
$406$			1.17840i			0.0584833i
$407$	6.97204	−	29.3194i	0.345591	−	1.45331i
$408$		0			0
$409$	15.0584			0.744592			0.372296	−	0.928114i	$-0.378571\pi$
$409$	15.0584			0.744592			0.372296	+	0.928114i	$0.378571\pi$
$410$	1.05765			0.0522336
$411$		0			0
$412$		−	5.61416i		−	0.276590i
$413$	2.54720			0.125339
$414$		0			0
$415$		−	8.06800i		−	0.396042i
$416$	−4.16029			−0.203975
$417$		0			0
$418$	−7.90972	−	12.1011i	−0.386877	−	0.591883i
$419$	12.2679			0.599325			0.299662	−	0.954045i	$-0.403126\pi$
$419$	12.2679			0.599325			0.299662	+	0.954045i	$0.403126\pi$
$420$		0			0
$421$		−	33.4918i		−	1.63229i	−0.577848	−	0.816144i	$-0.696108\pi$
$421$		−	33.4918i		−	1.63229i	0.577848	−	0.816144i	$-0.303892\pi$
$422$	−6.83304			−0.332627
$423$		0			0
$424$			4.43450i			0.215358i
$425$		−	24.5841i		−	1.19251i
$426$		0			0
$427$	−1.91177			−0.0925172
$428$	2.31418			0.111860
$429$		0			0
$430$		−	7.14006i		−	0.344324i
$431$	9.17278			0.441837			0.220919	−	0.975292i	$-0.429095\pi$
$431$	9.17278			0.441837			0.220919	+	0.975292i	$0.429095\pi$
$432$		0			0
$433$			38.9700i			1.87278i	0.350960	+	0.936390i	$0.385855\pi$
$433$			38.9700i			1.87278i	−0.350960	+	0.936390i	$0.614145\pi$
$434$	1.05325			0.0505578
$435$		0			0
$436$	14.1894			0.679548
$437$	−24.1186	−	22.8506i	−1.15375	−	1.09309i
$438$		0			0
$439$	−14.9980			−0.715818			−0.357909	−	0.933757i	$-0.616510\pi$
$439$	−14.9980			−0.715818			−0.357909	+	0.933757i	$0.616510\pi$
$440$	−4.13322	−	0.982862i	−0.197044	−	0.0468561i
$441$		0			0
$442$		−	30.4475i		−	1.44824i
$443$	21.6446			1.02837			0.514183	−	0.857681i	$-0.328095\pi$
$443$	21.6446			1.02837			0.514183	+	0.857681i	$0.328095\pi$
$444$		0			0
$445$			5.57820i			0.264432i
$446$		−	29.3935i		−	1.39182i
$447$		0			0
$448$		−	0.392237i		−	0.0185315i
$449$		−	28.0549i		−	1.32399i	−0.749508	−	0.661996i	$-0.769710\pi$
$449$		−	28.0549i		−	1.32399i	0.749508	−	0.661996i	$-0.230290\pi$
$450$		0			0
$451$	−2.66414	−	0.633522i	−0.125450	−	0.0298314i
$452$			8.73342i			0.410786i
$453$		0			0
$454$	24.3018			1.14054
$455$			2.09030i			0.0979948i
$456$		0			0
$457$		−	13.6597i		−	0.638975i	−0.947591	−	0.319487i	$-0.896489\pi$
$457$		−	13.6597i		−	0.638975i	0.947591	−	0.319487i	$-0.103511\pi$
$458$	−19.5240			−0.912295
$459$		0			0
$460$	−9.76374			−0.455237
$461$			29.8154i			1.38864i	0.719665	+	0.694321i	$0.244295\pi$
$461$			29.8154i			1.38864i	−0.719665	+	0.694321i	$0.755705\pi$
$462$		0			0
$463$	10.2461			0.476179			0.238089	−	0.971243i	$-0.423479\pi$
$463$	10.2461			0.476179			0.238089	+	0.971243i	$0.423479\pi$
$464$	−3.00432			−0.139472
$465$		0			0
$466$			9.93903i			0.460417i
$467$	27.9949			1.29545			0.647725	−	0.761875i	$-0.275721\pi$
$467$	27.9949			1.29545			0.647725	+	0.761875i	$0.275721\pi$
$468$		0			0
$469$	5.73129			0.264646
$470$	−12.3696			−0.570566
$471$		0			0
$472$			6.49403i			0.298912i
$473$	−4.27682	+	17.9853i	−0.196648	+	0.826964i
$474$		0			0
$475$	−10.6292	−	10.0704i	−0.487700	−	0.462060i
$476$	2.87062			0.131575
$477$		0			0
$478$			4.70511i			0.215207i
$479$			34.9593i			1.59733i	0.601776	+	0.798665i	$0.294460\pi$
$479$			34.9593i			1.59733i	−0.601776	+	0.798665i	$0.705540\pi$
$480$		0			0
$481$		−	37.8031i		−	1.72367i
$482$	−18.6944			−0.851508
$483$		0			0
$484$	9.82255	+	4.95151i	0.446480	+	0.225069i
$485$		−	7.91834i		−	0.359553i
$486$		0			0
$487$		−	5.81207i		−	0.263370i	−0.991292	−	0.131685i	$-0.957961\pi$
$487$		−	5.81207i		−	0.263370i	0.991292	−	0.131685i	$-0.0420388\pi$
$488$		−	4.87403i		−	0.220637i
$489$		0			0
$490$	8.76967			0.396173
$491$		−	14.0518i		−	0.634150i	−0.948400	−	0.317075i	$-0.897299\pi$
$491$		−	14.0518i		−	0.634150i	0.948400	−	0.317075i	$-0.102701\pi$
$492$		0			0
$493$		−	21.9874i		−	0.990262i
$494$	−13.1642	−	12.4722i	−0.592287	−	0.561149i
$495$		0			0
$496$			2.68525i			0.120571i
$497$	−3.43456			−0.154061
$498$		0			0
$499$	7.99077			0.357716			0.178858	−	0.983875i	$-0.442760\pi$
$499$	7.99077			0.357716			0.178858	+	0.983875i	$0.442760\pi$
$500$	−10.7077			−0.478865
$501$		0			0
$502$	−7.50024			−0.334752
$503$		−	12.1803i		−	0.543093i	−0.962425	−	0.271546i	$-0.912465\pi$
$503$		−	12.1803i		−	0.543093i	0.962425	−	0.271546i	$-0.0875351\pi$
$504$		0			0
$505$		−	21.1487i		−	0.941104i
$506$	24.5941	+	5.84838i	1.09334	+	0.259992i
$507$		0			0
$508$	−11.8120			−0.524073
$509$			7.44144i			0.329836i	0.986307	+	0.164918i	$0.0527359\pi$
$509$			7.44144i			0.329836i	−0.986307	+	0.164918i	$0.947264\pi$
$510$		0			0
$511$	4.04294			0.178849
$512$	1.00000			0.0441942
$513$		0			0
$514$			13.0530i			0.575745i
$515$		−	7.19153i		−	0.316897i
$516$		0			0
$517$	31.1580	+	7.40925i	1.37033	+	0.325858i
$518$	3.56412			0.156598
$519$		0			0
$520$	−5.32918			−0.233700
$521$		−	23.7435i		−	1.04022i	−0.854098	−	0.520111i	$-0.825890\pi$
$521$		−	23.7435i		−	1.04022i	0.854098	−	0.520111i	$-0.174110\pi$
$522$		0			0
$523$	−22.1470			−0.968422			−0.484211	−	0.874951i	$-0.660893\pi$
$523$	−22.1470			−0.968422			−0.484211	+	0.874951i	$0.660893\pi$
$524$		−	6.40399i		−	0.279760i
$525$		0			0
$526$			27.6548i			1.20581i
$527$	−19.6522			−0.856065
$528$		0			0
$529$	35.0978			1.52599
$530$			5.68043i			0.246742i
$531$		0			0
$532$	1.17589	−	1.24114i	0.0509813	−	0.0538103i
$533$	−3.43502			−0.148787
$534$		0			0
$535$	2.96438			0.128161
$536$			14.6118i			0.631134i
$537$		0			0
$538$			16.8086i			0.724669i
$539$	−22.0901	−	5.25294i	−0.951490	−	0.226260i
$540$		0			0
$541$			32.6100i			1.40202i	0.713154	+	0.701008i	$0.247266\pi$
$541$			32.6100i			1.40202i	−0.713154	+	0.701008i	$0.752734\pi$
$542$		−	9.95751i		−	0.427712i
$543$		0			0
$544$			7.31859i			0.313782i
$545$	18.1761			0.778577
$546$		0			0
$547$	43.5283			1.86113			0.930567	−	0.366121i	$-0.119314\pi$
$547$	43.5283			1.86113			0.930567	+	0.366121i	$0.119314\pi$
$548$	−10.5157			−0.449208
$549$		0			0
$550$	10.8388	+	2.57741i	0.462166	+	0.109901i
$551$	−9.50645	−	9.00667i	−0.404989	−	0.383697i
$552$		0			0
$553$		−	6.06412i		−	0.257873i
$554$			11.4686i			0.487255i
$555$		0			0
$556$			9.62814i			0.408324i
$557$		−	14.0929i		−	0.597136i	−0.954388	−	0.298568i	$-0.903491\pi$
$557$		−	14.0929i		−	0.597136i	0.954388	−	0.298568i	$-0.0965090\pi$
$558$		0			0
$559$			23.1894i			0.980805i
$560$		−	0.502441i		−	0.0212320i
$561$		0			0
$562$	12.2517			0.516806
$563$	−4.40278			−0.185555			−0.0927775	−	0.995687i	$-0.529575\pi$
$563$	−4.40278			−0.185555			−0.0927775	+	0.995687i	$0.529575\pi$
$564$		0			0
$565$			11.1872i			0.470649i
$566$		−	27.0812i		−	1.13831i
$567$		0			0
$568$		−	8.75634i		−	0.367408i
$569$	15.7550			0.660485			0.330242	−	0.943896i	$-0.392870\pi$
$569$	15.7550			0.660485			0.330242	+	0.943896i	$0.392870\pi$
$570$		0			0
$571$			7.86435i			0.329113i	0.986368	+	0.164556i	$0.0526192\pi$
$571$			7.86435i			0.329113i	−0.986368	+	0.164556i	$0.947381\pi$
$572$	13.4238	+	3.19212i	0.561277	+	0.133469i
$573$		0			0
$574$		−	0.323858i		−	0.0135176i
$575$	25.6040			1.06776
$576$		0			0
$577$	18.9389			0.788437			0.394218	−	0.919017i	$-0.371015\pi$
$577$	18.9389			0.788437			0.394218	+	0.919017i	$0.371015\pi$
$578$	−36.5618			−1.52077
$579$		0			0
$580$	−3.84842			−0.159797
$581$	−2.47046			−0.102492
$582$		0			0
$583$	3.40252	−	14.3086i	0.140918	−	0.592601i
$584$			10.3074i			0.426523i
$585$		0			0
$586$	−9.60892			−0.396941
$587$	−32.3029			−1.33328			−0.666642	−	0.745378i	$-0.732269\pi$
$587$	−32.3029			−1.33328			−0.666642	+	0.745378i	$0.732269\pi$
$588$		0			0
$589$	−8.05013	+	8.49683i	−0.331700	+	0.350106i
$590$			8.31861i			0.342472i
$591$		0			0
$592$			9.08665i			0.373459i
$593$		−	5.01688i		−	0.206018i	−0.994680	−	0.103009i	$-0.967153\pi$
$593$		−	5.01688i		−	0.206018i	0.994680	−	0.103009i	$-0.0328471\pi$
$594$		0			0
$595$	3.67716			0.150749
$596$			1.79326i			0.0734549i
$597$		0			0
$598$	31.7105			1.29674
$599$		−	26.8152i		−	1.09564i	−0.836597	−	0.547819i	$-0.815458\pi$
$599$		−	26.8152i		−	1.09564i	0.836597	−	0.547819i	$-0.184542\pi$
$600$		0			0
$601$	7.45857			0.304241			0.152121	−	0.988362i	$-0.451390\pi$
$601$	7.45857			0.304241			0.152121	+	0.988362i	$0.451390\pi$
$602$	−2.18632			−0.0891077
$603$		0			0
$604$	19.0044			0.773280
$605$	12.5823	+	6.34271i	0.511544	+	0.257868i
$606$		0			0
$607$	9.97458			0.404856			0.202428	−	0.979297i	$-0.435117\pi$
$607$	9.97458			0.404856			0.202428	+	0.979297i	$0.435117\pi$
$608$	3.16426	+	2.99791i	0.128328	+	0.121581i
$609$		0			0
$610$		−	6.24345i		−	0.252790i
$611$	40.1737			1.62525
$612$		0			0
$613$		−	14.8691i		−	0.600557i	−0.953852	−	0.300279i	$-0.902920\pi$
$613$		−	14.8691i		−	0.600557i	0.953852	−	0.300279i	$-0.0970796\pi$
$614$	2.13570			0.0861897
$615$		0			0
$616$	−0.300957	+	1.26561i	−0.0121259	+	0.0509929i
$617$	−35.3162			−1.42178			−0.710888	−	0.703305i	$-0.751707\pi$
$617$	−35.3162			−1.42178			−0.710888	+	0.703305i	$0.751707\pi$
$618$		0			0
$619$	39.0066			1.56781			0.783904	−	0.620882i	$-0.213225\pi$
$619$	39.0066			1.56781			0.783904	+	0.620882i	$0.213225\pi$
$620$			3.43971i			0.138142i
$621$		0			0
$622$	16.6337			0.666950
$623$	1.70807			0.0684324
$624$		0			0
$625$	3.07944			0.123178
$626$	−32.0516			−1.28104
$627$		0			0
$628$	7.84764			0.313155
$629$	−66.5015			−2.65159
$630$		0			0
$631$	−18.8570			−0.750684			−0.375342	−	0.926886i	$-0.622475\pi$
$631$	−18.8570			−0.750684			−0.375342	+	0.926886i	$0.622475\pi$
$632$	15.4604			0.614980
$633$		0			0
$634$			34.7556i			1.38032i
$635$	−15.1307			−0.600445
$636$		0			0
$637$	−28.4820			−1.12850
$638$	9.69389	+	2.30517i	0.383785	+	0.0912624i
$639$		0			0
$640$	1.28096			0.0506345
$641$		−	8.61956i		−	0.340452i	−0.985405	−	0.170226i	$-0.945550\pi$
$641$		−	8.61956i		−	0.340452i	0.985405	−	0.170226i	$-0.0544498\pi$
$642$		0			0
$643$	−42.5257			−1.67705			−0.838526	−	0.544862i	$-0.816582\pi$
$643$	−42.5257			−1.67705			−0.838526	+	0.544862i	$0.816582\pi$
$644$			2.98970i			0.117811i
$645$		0			0
$646$	−21.9405	+	23.1579i	−0.863236	+	0.911137i
$647$	−15.0890			−0.593211			−0.296606	−	0.955000i	$-0.595855\pi$
$647$	−15.0890			−0.593211			−0.296606	+	0.955000i	$0.595855\pi$
$648$		0			0
$649$	4.98276	−	20.9540i	0.195591	−	0.822515i
$650$	13.9750			0.548143
$651$		0			0
$652$	−14.6344			−0.573127
$653$	22.9868			0.899541			0.449771	−	0.893144i	$-0.351506\pi$
$653$	22.9868			0.899541			0.449771	+	0.893144i	$0.351506\pi$
$654$		0			0
$655$		−	8.20328i		−	0.320529i
$656$	0.825668			0.0322369
$657$		0			0
$658$			3.78762i			0.147657i
$659$	−27.0408			−1.05336			−0.526679	−	0.850064i	$-0.676563\pi$
$659$	−27.0408			−1.05336			−0.526679	+	0.850064i	$0.676563\pi$
$660$		0			0
$661$		−	34.0283i		−	1.32355i	−0.749704	−	0.661773i	$-0.769804\pi$
$661$		−	34.0283i		−	1.32355i	0.749704	−	0.661773i	$-0.230196\pi$
$662$			26.8731i			1.04445i
$663$		0			0
$664$		−	6.29838i		−	0.244425i
$665$	1.50627	−	1.58985i	0.0584107	−	0.0616519i
$666$		0			0
$667$	22.8995			0.886672
$668$	−17.8960			−0.692418
$669$		0			0
$670$			18.7172i			0.723108i
$671$	−3.73976	+	15.7268i	−0.144372	+	0.607126i
$672$		0			0
$673$	−9.68072			−0.373164			−0.186582	−	0.982439i	$-0.559741\pi$
$673$	−9.68072			−0.373164			−0.186582	+	0.982439i	$0.559741\pi$
$674$	6.33466			0.244002
$675$		0			0
$676$	4.30801			0.165693
$677$	19.1039			0.734224			0.367112	−	0.930177i	$-0.380347\pi$
$677$	19.1039			0.734224			0.367112	+	0.930177i	$0.380347\pi$
$678$		0			0
$679$	−2.42463			−0.0930488
$680$			9.37485i			0.359509i
$681$		0			0
$682$	2.06035	−	8.66436i	0.0788948	−	0.331776i
$683$		−	34.2778i		−	1.31160i	−0.754933	−	0.655802i	$-0.772331\pi$
$683$		−	34.2778i		−	1.31160i	0.754933	−	0.655802i	$-0.227669\pi$
$684$		0			0
$685$	−13.4702			−0.514671
$686$		−	5.43097i		−	0.207355i
$687$		0			0
$688$		−	5.57398i		−	0.212506i
$689$		−	18.4488i		−	0.702843i
$690$		0			0
$691$	36.8018			1.40001			0.700003	−	0.714140i	$-0.253182\pi$
$691$	36.8018			1.40001			0.700003	+	0.714140i	$0.253182\pi$
$692$	−7.95773			−0.302507
$693$		0			0
$694$			17.1780i			0.652067i
$695$			12.3333i			0.467829i
$696$		0			0
$697$			6.04273i			0.228885i
$698$			33.1259i			1.25383i
$699$		0			0
$700$			1.31758i			0.0497997i
$701$		−	12.5960i		−	0.475743i	−0.971297	−	0.237872i	$-0.923550\pi$
$701$		−	12.5960i		−	0.475743i	0.971297	−	0.237872i	$-0.0764498\pi$
$702$		0			0
$703$	−27.2409	+	28.7525i	−1.02741	+	1.08442i
$704$	−3.22665	−	0.767284i	−0.121609	−	0.0289181i
$705$		0			0
$706$	0.856028			0.0322170
$707$	−6.47583			−0.243549
$708$		0			0
$709$	18.5468			0.696541			0.348271	−	0.937394i	$-0.386769\pi$
$709$	18.5468			0.696541			0.348271	+	0.937394i	$0.386769\pi$
$710$		−	11.2166i		−	0.420950i
$711$		0			0
$712$			4.35469i			0.163199i
$713$		−	20.4675i		−	0.766513i
$714$		0			0
$715$	17.1954	+	4.08899i	0.643071	+	0.152920i
$716$			2.64141i			0.0987139i
$717$		0			0
$718$		−	32.3606i		−	1.20769i
$719$	25.2658			0.942256			0.471128	−	0.882065i	$-0.343847\pi$
$719$	25.2658			0.942256			0.471128	+	0.882065i	$0.343847\pi$
$720$		0			0
$721$	−2.20208			−0.0820098
$722$	1.02511	+	18.9723i	0.0381505	+	0.706077i
$723$		0			0
$724$		−	7.86248i		−	0.292207i
$725$	10.0919			0.374804
$726$		0			0
$727$	18.9714			0.703609			0.351805	−	0.936073i	$-0.385568\pi$
$727$	18.9714			0.703609			0.351805	+	0.936073i	$0.385568\pi$
$728$			1.63182i			0.0604792i
$729$		0			0
$730$			13.2034i			0.488680i
$731$	40.7937			1.50881
$732$		0			0
$733$		−	27.5546i		−	1.01775i	−0.860840	−	0.508876i	$-0.830061\pi$
$733$		−	27.5546i		−	1.01775i	0.860840	−	0.508876i	$-0.169939\pi$
$734$	−1.85564			−0.0684930
$735$		0			0
$736$	−7.62219			−0.280958
$737$	11.2114	−	47.1472i	0.412978	−	1.73669i
$738$		0			0
$739$			24.2374i			0.891588i	0.895136	+	0.445794i	$0.147079\pi$
$739$			24.2374i			0.891588i	−0.895136	+	0.445794i	$0.852921\pi$
$740$			11.6397i			0.427882i
$741$		0			0
$742$	1.73937			0.0638544
$743$	41.9694			1.53971			0.769853	−	0.638221i	$-0.220329\pi$
$743$	41.9694			1.53971			0.769853	+	0.638221i	$0.220329\pi$
$744$		0			0
$745$			2.29710i			0.0841594i
$746$	27.9173			1.02213
$747$		0			0
$748$	5.61544	−	23.6145i	0.205321	−	0.863433i
$749$		−	0.907707i		−	0.0331669i
$750$		0			0
$751$		−	13.5234i		−	0.493476i	−0.969082	−	0.246738i	$-0.920641\pi$
$751$		−	13.5234i		−	0.493476i	0.969082	−	0.246738i	$-0.0793587\pi$
$752$	−9.65646			−0.352135
$753$		0			0
$754$	12.4988			0.455181
$755$	24.3440			0.885968
$756$		0			0
$757$	−14.3267			−0.520712			−0.260356	−	0.965513i	$-0.583840\pi$
$757$	−14.3267			−0.520712			−0.260356	+	0.965513i	$0.583840\pi$
$758$		−	5.41292i		−	0.196606i
$759$		0			0
$760$	4.05330	+	3.84021i	0.147029	+	0.139299i
$761$			26.9287i			0.976164i	0.872798	+	0.488082i	$0.162303\pi$
$761$			26.9287i			0.976164i	−0.872798	+	0.488082i	$0.837697\pi$
$762$		0			0
$763$		−	5.56559i		−	0.201488i
$764$	−4.82045			−0.174398
$765$		0			0
$766$		−	8.83675i		−	0.319285i
$767$		−	27.0170i		−	0.975528i
$768$		0			0
$769$			9.78202i			0.352748i	0.984323	+	0.176374i	$0.0564369\pi$
$769$			9.78202i			0.352748i	−0.984323	+	0.176374i	$0.943563\pi$
$770$	−0.385515	+	1.62120i	−0.0138930	+	0.0584241i
$771$		0			0
$772$	−1.00099			−0.0360263
$773$		−	0.265027i		−	0.00953238i	−0.999989	−	0.00476619i	$-0.998483\pi$
$773$		−	0.265027i		−	0.00953238i	0.999989	−	0.00476619i	$-0.00151713\pi$
$774$		0			0
$775$		−	9.02011i		−	0.324012i
$776$		−	6.18155i		−	0.221905i
$777$		0			0
$778$	−31.7505			−1.13831
$779$	2.61263	+	2.47528i	0.0936072	+	0.0886860i
$780$		0			0
$781$	−6.71860	+	28.2537i	−0.240410	+	1.01100i
$782$		−	55.7837i		−	1.99482i
$783$		0			0
$784$	6.84615			0.244505
$785$	10.0525			0.358791
$786$		0			0
$787$	−18.1212			−0.645952			−0.322976	−	0.946407i	$-0.604683\pi$
$787$	−18.1212			−0.645952			−0.322976	+	0.946407i	$0.604683\pi$
$788$		−	14.3961i		−	0.512839i
$789$		0			0
$790$	19.8041			0.704600
$791$	3.42557			0.121799
$792$		0			0
$793$			20.2774i			0.720071i
$794$	−17.1766			−0.609573
$795$		0			0
$796$	9.58482			0.339725
$797$			23.4980i			0.832341i	0.909287	+	0.416171i	$0.136628\pi$
$797$			23.4980i			0.832341i	−0.909287	+	0.416171i	$0.863372\pi$
$798$		0			0
$799$		−	70.6717i		−	2.50019i
$800$	−3.35913			−0.118763
$801$		0			0
$802$			10.1717i			0.359174i
$803$	7.90870	−	33.2584i	0.279092	−	1.17366i
$804$		0			0
$805$			3.82970i			0.134979i
$806$		−	11.1714i		−	0.393496i
$807$		0			0
$808$		−	16.5100i		−	0.580819i
$809$		−	16.4267i		−	0.577533i	−0.957400	−	0.288766i	$-0.906755\pi$
$809$		−	16.4267i		−	0.577533i	0.957400	−	0.288766i	$-0.0932451\pi$
$810$		0			0
$811$	−5.50789			−0.193408			−0.0967040	−	0.995313i	$-0.530830\pi$
$811$	−5.50789			−0.193408			−0.0967040	+	0.995313i	$0.530830\pi$
$812$			1.17840i			0.0413539i
$813$		0			0
$814$	6.97204	−	29.3194i	0.244370	−	1.02765i
$815$	−18.7461			−0.656647
$816$		0			0
$817$	16.7103	−	17.6375i	0.584618	−	0.617059i
$818$	15.0584			0.526506
$819$		0			0
$820$	1.05765			0.0369348
$821$		−	18.9098i		−	0.659956i	−0.943989	−	0.329978i	$-0.892959\pi$
$821$		−	18.9098i		−	0.659956i	0.943989	−	0.329978i	$-0.107041\pi$
$822$		0			0
$823$	−13.2282			−0.461106			−0.230553	−	0.973060i	$-0.574054\pi$
$823$	−13.2282			−0.461106			−0.230553	+	0.973060i	$0.574054\pi$
$824$		−	5.61416i		−	0.195579i
$825$		0			0
$826$	2.54720			0.0886283
$827$	21.5619			0.749782			0.374891	−	0.927069i	$-0.377680\pi$
$827$	21.5619			0.749782			0.374891	+	0.927069i	$0.377680\pi$
$828$		0			0
$829$			48.9602i			1.70046i	0.526414	+	0.850228i	$0.323536\pi$
$829$			48.9602i			1.70046i	−0.526414	+	0.850228i	$0.676464\pi$
$830$		−	8.06800i		−	0.280044i
$831$		0			0
$832$	−4.16029			−0.144232
$833$			50.1042i			1.73601i
$834$		0			0
$835$	−22.9242			−0.793323
$836$	−7.90972	−	12.1011i	−0.273563	−	0.418525i
$837$		0			0
$838$	12.2679			0.423787
$839$			9.21919i			0.318282i	0.987256	+	0.159141i	$0.0508724\pi$
$839$			9.21919i			0.318282i	−0.987256	+	0.159141i	$0.949128\pi$
$840$		0			0
$841$	−19.9741			−0.688761
$842$		−	33.4918i		−	1.15420i
$843$		0			0
$844$	−6.83304			−0.235203
$845$	5.51840			0.189839
$846$		0			0
$847$	1.94217	−	3.85277i	0.0667336	−	0.132383i
$848$			4.43450i			0.152281i
$849$		0			0
$850$		−	24.5841i		−	0.843229i
$851$		−	69.2601i		−	2.37421i
$852$		0			0
$853$			39.8016i			1.36278i	0.731920	+	0.681390i	$0.238624\pi$
$853$			39.8016i			1.36278i	−0.731920	+	0.681390i	$0.761376\pi$
$854$	−1.91177			−0.0654196
$855$		0			0
$856$	2.31418			0.0790970
$857$	−20.5092			−0.700582			−0.350291	−	0.936641i	$-0.613917\pi$
$857$	−20.5092			−0.700582			−0.350291	+	0.936641i	$0.613917\pi$
$858$		0			0
$859$	36.9792			1.26171			0.630856	−	0.775900i	$-0.282704\pi$
$859$	36.9792			1.26171			0.630856	+	0.775900i	$0.282704\pi$
$860$		−	7.14006i		−	0.243474i
$861$		0			0
$862$	9.17278			0.312426
$863$			11.0139i			0.374917i	0.982273	+	0.187458i	$0.0600250\pi$
$863$			11.0139i			0.374917i	−0.982273	+	0.187458i	$0.939975\pi$
$864$		0			0
$865$	−10.1936			−0.346591
$866$			38.9700i			1.32426i
$867$		0			0
$868$	1.05325			0.0357498
$869$	−49.8852	−	11.8625i	−1.69224	−	0.402407i
$870$		0			0
$871$		−	60.7894i		−	2.05977i
$872$	14.1894			0.480513
$873$		0			0
$874$	−24.1186	−	22.8506i	−0.815824	−	0.772934i
$875$			4.19997i			0.141985i
$876$		0			0
$877$	1.15451			0.0389850			0.0194925	−	0.999810i	$-0.493795\pi$
$877$	1.15451			0.0389850			0.0194925	+	0.999810i	$0.493795\pi$
$878$	−14.9980			−0.506160
$879$		0			0
$880$	−4.13322	−	0.982862i	−0.139331	−	0.0331323i
$881$	33.2868			1.12146			0.560731	−	0.827998i	$-0.310520\pi$
$881$	33.2868			1.12146			0.560731	+	0.827998i	$0.310520\pi$
$882$		0			0
$883$	3.06728			0.103222			0.0516112	−	0.998667i	$-0.483564\pi$
$883$	3.06728			0.103222			0.0516112	+	0.998667i	$0.483564\pi$
$884$		−	30.4475i		−	1.02406i
$885$		0			0
$886$	21.6446			0.727164
$887$	19.7574			0.663388			0.331694	−	0.943387i	$-0.392380\pi$
$887$	19.7574			0.663388			0.331694	+	0.943387i	$0.392380\pi$
$888$		0			0
$889$			4.63310i			0.155389i
$890$			5.57820i			0.186982i
$891$		0			0
$892$		−	29.3935i		−	0.984168i
$893$	−30.5556	−	28.9492i	−1.02250	−	0.968748i
$894$		0			0
$895$			3.38354i			0.113099i
$896$		−	0.392237i		−	0.0131037i
$897$		0			0
$898$		−	28.0549i		−	0.936203i
$899$		−	8.06735i		−	0.269061i
$900$		0			0
$901$	−32.4543			−1.08121
$902$	−2.66414	−	0.633522i	−0.0887063	−	0.0210940i
$903$		0			0
$904$			8.73342i			0.290469i
$905$		−	10.0715i		−	0.334790i
$906$		0			0
$907$			33.1350i			1.10023i	0.835089	+	0.550115i	$0.185416\pi$
$907$			33.1350i			1.10023i	−0.835089	+	0.550115i	$0.814584\pi$
$908$	24.3018			0.806485
$909$		0			0
$910$			2.09030i			0.0692928i
$911$		−	14.9875i		−	0.496557i	−0.968689	−	0.248279i	$-0.920135\pi$
$911$		−	14.9875i		−	0.496557i	0.968689	−	0.248279i	$-0.0798649\pi$
$912$		0			0
$913$	−4.83265	+	20.3227i	−0.159937	+	0.672583i
$914$		−	13.6597i		−	0.451823i
$915$		0			0
$916$	−19.5240			−0.645090
$917$	−2.51188			−0.0829497
$918$		0			0
$919$		−	20.4574i		−	0.674828i	−0.941356	−	0.337414i	$-0.890448\pi$
$919$		−	20.4574i		−	0.674828i	0.941356	−	0.337414i	$-0.109552\pi$
$920$	−9.76374			−0.321901
$921$		0			0
$922$			29.8154i			0.981918i
$923$			36.4289i			1.19907i
$924$		0			0
$925$		−	30.5233i		−	1.00360i
$926$	10.2461			0.336709
$927$		0			0
$928$	−3.00432			−0.0986216
$929$	45.9441			1.50738			0.753689	−	0.657231i	$-0.228272\pi$
$929$	45.9441			1.50738			0.753689	+	0.657231i	$0.228272\pi$
$930$		0			0
$931$	21.6630	+	20.5241i	0.709977	+	0.672651i
$932$			9.93903i			0.325564i
$933$		0			0
$934$	27.9949			0.916021
$935$	7.19317	−	30.2494i	0.235242	−	0.989260i
$936$		0			0
$937$			59.0141i			1.92791i	0.266070	+	0.963954i	$0.414275\pi$
$937$			59.0141i			1.92791i	−0.266070	+	0.963954i	$0.585725\pi$
$938$	5.73129			0.187133
$939$		0			0
$940$	−12.3696			−0.403451
$941$	−40.6727			−1.32589			−0.662946	−	0.748667i	$-0.730694\pi$
$941$	−40.6727			−1.32589			−0.662946	+	0.748667i	$0.730694\pi$
$942$		0			0
$943$	−6.29340			−0.204941
$944$			6.49403i			0.211363i
$945$		0			0
$946$	−4.27682	+	17.9853i	−0.139051	+	0.584752i
$947$	−7.56822			−0.245934			−0.122967	−	0.992411i	$-0.539241\pi$
$947$	−7.56822			−0.245934			−0.122967	+	0.992411i	$0.539241\pi$
$948$		0			0
$949$		−	42.8818i		−	1.39200i
$950$	−10.6292	−	10.0704i	−0.344856	−	0.326726i
$951$		0			0
$952$	2.87062			0.0930374
$953$	31.4260			1.01799			0.508994	−	0.860770i	$-0.330018\pi$
$953$	31.4260			1.01799			0.508994	+	0.860770i	$0.330018\pi$
$954$		0			0
$955$	−6.17482			−0.199813
$956$			4.70511i			0.152174i
$957$		0			0
$958$			34.9593i			1.12948i
$959$			4.12464i			0.133192i
$960$		0			0
$961$	23.7894			0.767401
$962$		−	37.8031i		−	1.21882i
$963$		0			0
$964$	−18.6944			−0.602107
$965$	−1.28223			−0.0412764
$966$		0			0
$967$			13.4842i			0.433624i	0.976213	+	0.216812i	$0.0695659\pi$
$967$			13.4842i			0.433624i	−0.976213	+	0.216812i	$0.930434\pi$
$968$	9.82255	+	4.95151i	0.315709	+	0.159148i
$969$		0			0
$970$		−	7.91834i		−	0.254243i
$971$			49.1332i			1.57676i	0.615190	+	0.788379i	$0.289079\pi$
$971$			49.1332i			1.57676i	−0.615190	+	0.788379i	$0.710921\pi$
$972$		0			0
$973$	3.77651			0.121069
$974$		−	5.81207i		−	0.186231i
$975$		0			0
$976$		−	4.87403i		−	0.156014i
$977$			41.7887i			1.33694i	0.743740	+	0.668469i	$0.233050\pi$
$977$			41.7887i			1.33694i	−0.743740	+	0.668469i	$0.766950\pi$
$978$		0			0
$979$	3.34128	−	14.0511i	0.106788	−	0.449074i
$980$	8.76967			0.280137
$981$		0			0
$982$		−	14.0518i		−	0.448412i
$983$		−	32.0576i		−	1.02248i	−0.859438	−	0.511240i	$-0.829186\pi$
$983$		−	32.0576i		−	1.02248i	0.859438	−	0.511240i	$-0.170814\pi$
$984$		0			0
$985$		−	18.4408i		−	0.587574i
$986$		−	21.9874i		−	0.700221i
$987$		0			0
$988$	−13.1642	−	12.4722i	−0.418810	−	0.396792i
$989$			42.4859i			1.35097i
$990$		0			0
$991$			41.3431i			1.31331i	0.754192	+	0.656654i	$0.228029\pi$
$991$			41.3431i			1.31331i	−0.754192	+	0.656654i	$0.771971\pi$
$992$			2.68525i			0.0852567i
$993$		0			0
$994$	−3.43456			−0.108938
$995$	12.2778			0.389232
$996$		0			0
$997$			10.1676i			0.322011i	0.986954	+	0.161006i	$0.0514737\pi$
$997$			10.1676i			0.322011i	−0.986954	+	0.161006i	$0.948526\pi$
$998$	7.99077			0.252943
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3762.2.g.l.2089.13		20
3.2	odd	2		1254.2.g.a.835.14	yes	20
11.10	odd	2		3762.2.g.k.2089.14		20
19.18	odd	2		3762.2.g.k.2089.13		20
33.32	even	2		1254.2.g.b.835.14	yes	20
57.56	even	2		1254.2.g.b.835.4	yes	20
209.208	even	2	inner	3762.2.g.l.2089.14		20
627.626	odd	2		1254.2.g.a.835.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1254.2.g.a.835.4	✓	20	627.626	odd	2
1254.2.g.a.835.14	yes	20	3.2	odd	2
1254.2.g.b.835.4	yes	20	57.56	even	2
1254.2.g.b.835.14	yes	20	33.32	even	2
3762.2.g.k.2089.13		20	19.18	odd	2
3762.2.g.k.2089.14		20	11.10	odd	2
3762.2.g.l.2089.13		20	1.1	even	1	trivial
3762.2.g.l.2089.14		20	209.208	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:	\( N \)	\(=\)	\( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3762.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +1.28096 q^{5} -0.392237i q^{7} +1.00000 q^{8} +1.28096 q^{10} +(-3.22665 - 0.767284i) q^{11} -4.16029 q^{13} -0.392237i q^{14} +1.00000 q^{16} +7.31859i q^{17} +(3.16426 + 2.99791i) q^{19} +1.28096 q^{20} +(-3.22665 - 0.767284i) q^{22} -7.62219 q^{23} -3.35913 q^{25} -4.16029 q^{26} -0.392237i q^{28} -3.00432 q^{29} +2.68525i q^{31} +1.00000 q^{32} +7.31859i q^{34} -0.502441i q^{35} +9.08665i q^{37} +(3.16426 + 2.99791i) q^{38} +1.28096 q^{40} +0.825668 q^{41} -5.57398i q^{43} +(-3.22665 - 0.767284i) q^{44} -7.62219 q^{46} -9.65646 q^{47} +6.84615 q^{49} -3.35913 q^{50} -4.16029 q^{52} +4.43450i q^{53} +(-4.13322 - 0.982862i) q^{55} -0.392237i q^{56} -3.00432 q^{58} +6.49403i q^{59} -4.87403i q^{61} +2.68525i q^{62} +1.00000 q^{64} -5.32918 q^{65} +14.6118i q^{67} +7.31859i q^{68} -0.502441i q^{70} -8.75634i q^{71} +10.3074i q^{73} +9.08665i q^{74} +(3.16426 + 2.99791i) q^{76} +(-0.300957 + 1.26561i) q^{77} +15.4604 q^{79} +1.28096 q^{80} +0.825668 q^{82} -6.29838i q^{83} +9.37485i q^{85} -5.57398i q^{86} +(-3.22665 - 0.767284i) q^{88} +4.35469i q^{89} +1.63182i q^{91} -7.62219 q^{92} -9.65646 q^{94} +(4.05330 + 3.84021i) q^{95} -6.18155i q^{97} +6.84615 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 20 q^{4} - 4 q^{5} + 20 q^{8} - 4 q^{10} - 6 q^{11} + 4 q^{13} + 20 q^{16} + 2 q^{19} - 4 q^{20} - 6 q^{22} + 8 q^{23} + 32 q^{25} + 4 q^{26} - 4 q^{29} + 20 q^{32} + 2 q^{38} - 4 q^{40}+ \cdots - 36 q^{98}+O(q^{100}) \) 20 * q + 20 * q^2 + 20 * q^4 - 4 * q^5 + 20 * q^8 - 4 * q^10 - 6 * q^11 + 4 * q^13 + 20 * q^16 + 2 * q^19 - 4 * q^20 - 6 * q^22 + 8 * q^23 + 32 * q^25 + 4 * q^26 - 4 * q^29 + 20 * q^32 + 2 * q^38 - 4 * q^40 + 24 * q^41 - 6 * q^44 + 8 * q^46 - 8 * q^47 - 36 * q^49 + 32 * q^50 + 4 * q^52 + 8 * q^55 - 4 * q^58 + 20 * q^64 + 24 * q^65 + 2 * q^76 - 28 * q^77 + 24 * q^79 - 4 * q^80 + 24 * q^82 - 6 * q^88 + 8 * q^92 - 8 * q^94 - 32 * q^95 - 36 * q^98

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