LMFDB - Embedded newform 3762.2.g.l.2089.7

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			2089.7
Root			$1.75638 + 1.75638i$ of defining polynomial
Character	$\chi$	$=$	3762.2089
Dual form			3762.2.g.l.2089.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} -1.24031 q^{5} -3.51276i q^{7} +1.00000 q^{8} -1.24031 q^{10} +(-0.393943 + 3.29315i) q^{11} -1.46033 q^{13} -3.51276i q^{14} +1.00000 q^{16} +3.83935i q^{17} +(-3.98747 + 1.76071i) q^{19} -1.24031 q^{20} +(-0.393943 + 3.29315i) q^{22} +2.48371 q^{23} -3.46162 q^{25} -1.46033 q^{26} -3.51276i q^{28} -5.89617 q^{29} +4.18521i q^{31} +1.00000 q^{32} +3.83935i q^{34} +4.35693i q^{35} +0.866253i q^{37} +(-3.98747 + 1.76071i) q^{38} -1.24031 q^{40} +11.4391 q^{41} +0.0872418i q^{43} +(-0.393943 + 3.29315i) q^{44} +2.48371 q^{46} -9.68535 q^{47} -5.33951 q^{49} -3.46162 q^{50} -1.46033 q^{52} +2.65543i q^{53} +(0.488613 - 4.08453i) q^{55} -3.51276i q^{56} -5.89617 q^{58} -0.285318i q^{59} +7.00823i q^{61} +4.18521i q^{62} +1.00000 q^{64} +1.81127 q^{65} -8.14823i q^{67} +3.83935i q^{68} +4.35693i q^{70} +15.0087i q^{71} +16.4472i q^{73} +0.866253i q^{74} +(-3.98747 + 1.76071i) q^{76} +(11.5680 + 1.38383i) q^{77} +6.48850 q^{79} -1.24031 q^{80} +11.4391 q^{82} +10.0557i q^{83} -4.76199i q^{85} +0.0872418i q^{86} +(-0.393943 + 3.29315i) q^{88} -9.47873i q^{89} +5.12980i q^{91} +2.48371 q^{92} -9.68535 q^{94} +(4.94571 - 2.18383i) q^{95} -7.60274i q^{97} -5.33951 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.24031			−0.554685			−0.277342	−	0.960771i	$-0.589454\pi$
$5$	−1.24031			−0.554685			−0.277342	+	0.960771i	$0.589454\pi$
$6$		0			0
$7$		−	3.51276i		−	1.32770i	−0.747866	−	0.663850i	$-0.768921\pi$
$7$		−	3.51276i		−	1.32770i	0.747866	−	0.663850i	$-0.231079\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.24031			−0.392221
$11$	−0.393943	+	3.29315i	−0.118778	+	0.992921i
$11$	−0.393943	+	3.29315i	−0.118778	+	0.992921i
$12$		0			0
$13$	−1.46033			−0.405023			−0.202512	−	0.979280i	$-0.564910\pi$
$13$	−1.46033			−0.405023			−0.202512	+	0.979280i	$0.564910\pi$
$14$		−	3.51276i		−	0.938826i
$15$		0			0
$16$	1.00000			0.250000
$17$			3.83935i			0.931179i	0.885001	+	0.465590i	$0.154158\pi$
$17$			3.83935i			0.931179i	−0.885001	+	0.465590i	$0.845842\pi$
$18$		0			0
$19$	−3.98747	+	1.76071i	−0.914788	+	0.403935i
$19$	−3.98747	+	1.76071i	−0.914788	+	0.403935i
$20$	−1.24031			−0.277342
$21$		0			0
$22$	−0.393943	+	3.29315i	−0.0839890	+	0.702101i
$23$	2.48371			0.517890			0.258945	−	0.965892i	$-0.416625\pi$
$23$	2.48371			0.517890			0.258945	+	0.965892i	$0.416625\pi$
$24$		0			0
$25$	−3.46162			−0.692325
$26$	−1.46033			−0.286395
$27$		0			0
$28$		−	3.51276i		−	0.663850i
$29$	−5.89617			−1.09489			−0.547446	−	0.836841i	$-0.684400\pi$
$29$	−5.89617			−1.09489			−0.547446	+	0.836841i	$0.684400\pi$
$30$		0			0
$31$			4.18521i			0.751686i	0.926683	+	0.375843i	$0.122647\pi$
$31$			4.18521i			0.751686i	−0.926683	+	0.375843i	$0.877353\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$			3.83935i			0.658443i
$35$			4.35693i			0.736455i
$36$		0			0
$37$			0.866253i			0.142411i	0.997462	+	0.0712055i	$0.0226846\pi$
$37$			0.866253i			0.142411i	−0.997462	+	0.0712055i	$0.977315\pi$
$38$	−3.98747	+	1.76071i	−0.646853	+	0.285625i
$39$		0			0
$40$	−1.24031			−0.196111
$41$	11.4391			1.78649			0.893244	−	0.449571i	$-0.148423\pi$
$41$	11.4391			1.78649			0.893244	+	0.449571i	$0.148423\pi$
$42$		0			0
$43$			0.0872418i			0.0133043i	0.999978	+	0.00665213i	$0.00211745\pi$
$43$			0.0872418i			0.0133043i	−0.999978	+	0.00665213i	$0.997883\pi$
$44$	−0.393943	+	3.29315i	−0.0593892	+	0.496460i
$45$		0			0
$46$	2.48371			0.366204
$47$	−9.68535			−1.41275			−0.706377	−	0.707836i	$-0.749671\pi$
$47$	−9.68535			−1.41275			−0.706377	+	0.707836i	$0.749671\pi$
$48$		0			0
$49$	−5.33951			−0.762788
$50$	−3.46162			−0.489548
$51$		0			0
$52$	−1.46033			−0.202512
$53$			2.65543i			0.364752i	0.983229	+	0.182376i	$0.0583787\pi$
$53$			2.65543i			0.364752i	−0.983229	+	0.182376i	$0.941621\pi$
$54$		0			0
$55$	0.488613	−	4.08453i	0.0658846	−	0.550758i
$56$		−	3.51276i		−	0.469413i
$57$		0			0
$58$	−5.89617			−0.774205
$59$		−	0.285318i		−	0.0371453i	−0.999828	−	0.0185726i	$-0.994088\pi$
$59$		−	0.285318i		−	0.0371453i	0.999828	−	0.0185726i	$-0.00591219\pi$
$60$		0			0
$61$			7.00823i			0.897312i	0.893705	+	0.448656i	$0.148097\pi$
$61$			7.00823i			0.897312i	−0.893705	+	0.448656i	$0.851903\pi$
$62$			4.18521i			0.531522i
$63$		0			0
$64$	1.00000			0.125000
$65$	1.81127			0.224660
$66$		0			0
$67$		−	8.14823i		−	0.995465i	−0.867331	−	0.497732i	$-0.834166\pi$
$67$		−	8.14823i		−	0.995465i	0.867331	−	0.497732i	$-0.165834\pi$
$68$			3.83935i			0.465590i
$69$		0			0
$70$			4.35693i			0.520752i
$71$			15.0087i			1.78120i	0.454783	+	0.890602i	$0.349717\pi$
$71$			15.0087i			1.78120i	−0.454783	+	0.890602i	$0.650283\pi$
$72$		0			0
$73$			16.4472i			1.92500i	0.271278	+	0.962501i	$0.412554\pi$
$73$			16.4472i			1.92500i	−0.271278	+	0.962501i	$0.587446\pi$
$74$			0.866253i			0.100700i
$75$		0			0
$76$	−3.98747	+	1.76071i	−0.457394	+	0.201967i
$77$	11.5680	+	1.38383i	1.31830	+	0.157702i
$78$		0			0
$79$	6.48850			0.730013			0.365007	−	0.931005i	$-0.381067\pi$
$79$	6.48850			0.730013			0.365007	+	0.931005i	$0.381067\pi$
$80$	−1.24031			−0.138671
$81$		0			0
$82$	11.4391			1.26324
$83$			10.0557i			1.10375i	0.833925	+	0.551877i	$0.186088\pi$
$83$			10.0557i			1.10375i	−0.833925	+	0.551877i	$0.813912\pi$
$84$		0			0
$85$		−	4.76199i		−	0.516511i
$86$			0.0872418i			0.00940753i
$87$		0			0
$88$	−0.393943	+	3.29315i	−0.0419945	+	0.351051i
$89$		−	9.47873i		−	1.00474i	−0.864652	−	0.502372i	$-0.832461\pi$
$89$		−	9.47873i		−	1.00474i	0.864652	−	0.502372i	$-0.167539\pi$
$90$		0			0
$91$			5.12980i			0.537749i
$92$	2.48371			0.258945
$93$		0			0
$94$	−9.68535			−0.998967
$95$	4.94571	−	2.18383i	0.507419	−	0.224056i
$96$		0			0
$97$		−	7.60274i		−	0.771941i	−0.922511	−	0.385971i	$-0.873867\pi$
$97$		−	7.60274i		−	0.771941i	0.922511	−	0.385971i	$-0.126133\pi$
$98$	−5.33951			−0.539372
$99$		0			0
$100$	−3.46162			−0.346162
$101$		−	6.35126i		−	0.631974i	−0.948764	−	0.315987i	$-0.897664\pi$
$101$		−	6.35126i		−	0.631974i	0.948764	−	0.315987i	$-0.102336\pi$
$102$		0			0
$103$		−	0.950287i		−	0.0936346i	−0.998903	−	0.0468173i	$-0.985092\pi$
$103$		−	0.950287i		−	0.0936346i	0.998903	−	0.0468173i	$-0.0149079\pi$
$104$	−1.46033			−0.143197
$105$		0			0
$106$			2.65543i			0.257918i
$107$	2.41401			0.233371			0.116685	−	0.993169i	$-0.462773\pi$
$107$	2.41401			0.233371			0.116685	+	0.993169i	$0.462773\pi$
$108$		0			0
$109$	−13.0502			−1.24998			−0.624992	−	0.780631i	$-0.714898\pi$
$109$	−13.0502			−1.24998			−0.624992	+	0.780631i	$0.714898\pi$
$110$	0.488613	−	4.08453i	0.0465874	−	0.389445i
$111$		0			0
$112$		−	3.51276i		−	0.331925i
$113$			12.5345i			1.17914i	0.807716	+	0.589572i	$0.200703\pi$
$113$			12.5345i			1.17914i	−0.807716	+	0.589572i	$0.799297\pi$
$114$		0			0
$115$	−3.08058			−0.287266
$116$	−5.89617			−0.547446
$117$		0			0
$118$		−	0.285318i		−	0.0262657i
$119$	13.4867			1.23633
$120$		0			0
$121$	−10.6896	−	2.59463i	−0.971783	−	0.235875i
$122$			7.00823i			0.634495i
$123$		0			0
$124$			4.18521i			0.375843i
$125$	10.4951			0.938707
$126$		0			0
$127$	−11.9882			−1.06378			−0.531891	−	0.846813i	$-0.678519\pi$
$127$	−11.9882			−1.06378			−0.531891	+	0.846813i	$0.678519\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	1.81127			0.158859
$131$			20.6588i			1.80496i	0.430727	+	0.902482i	$0.358257\pi$
$131$			20.6588i			1.80496i	−0.430727	+	0.902482i	$0.641743\pi$
$132$		0			0
$133$	6.18496	+	14.0070i	0.536304	+	1.21456i
$134$		−	8.14823i		−	0.703900i
$135$		0			0
$136$			3.83935i			0.329221i
$137$	18.7527			1.60215			0.801076	−	0.598562i	$-0.204261\pi$
$137$	18.7527			1.60215			0.801076	+	0.598562i	$0.204261\pi$
$138$		0			0
$139$			1.91200i			0.162174i	0.996707	+	0.0810870i	$0.0258392\pi$
$139$			1.91200i			0.162174i	−0.996707	+	0.0810870i	$0.974161\pi$
$140$			4.35693i			0.368228i
$141$		0			0
$142$			15.0087i			1.25950i
$143$	0.575288	−	4.80909i	0.0481080	−	0.402156i
$144$		0			0
$145$	7.31310			0.607320
$146$			16.4472i			1.36118i
$147$		0			0
$148$			0.866253i			0.0712055i
$149$			16.0335i			1.31352i	0.754101	+	0.656759i	$0.228073\pi$
$149$			16.0335i			1.31352i	−0.754101	+	0.656759i	$0.771927\pi$
$150$		0			0
$151$	−10.6889			−0.869850			−0.434925	−	0.900467i	$-0.643225\pi$
$151$	−10.6889			−0.869850			−0.434925	+	0.900467i	$0.643225\pi$
$152$	−3.98747	+	1.76071i	−0.323426	+	0.142812i
$153$		0			0
$154$	11.5680	+	1.38383i	0.932180	+	0.111512i
$155$		−	5.19097i		−	0.416949i
$156$		0			0
$157$	−2.56348			−0.204588			−0.102294	−	0.994754i	$-0.532618\pi$
$157$	−2.56348			−0.204588			−0.102294	+	0.994754i	$0.532618\pi$
$158$	6.48850			0.516197
$159$		0			0
$160$	−1.24031			−0.0980553
$161$		−	8.72470i		−	0.687603i
$162$		0			0
$163$	23.7821			1.86275			0.931377	−	0.364055i	$-0.118608\pi$
$163$	23.7821			1.86275			0.931377	+	0.364055i	$0.118608\pi$
$164$	11.4391			0.893244
$165$		0			0
$166$			10.0557i			0.780472i
$167$	−20.9462			−1.62087			−0.810434	−	0.585830i	$-0.800769\pi$
$167$	−20.9462			−1.62087			−0.810434	+	0.585830i	$0.800769\pi$
$168$		0			0
$169$	−10.8674			−0.835956
$170$		−	4.76199i		−	0.365228i
$171$		0			0
$172$			0.0872418i			0.00665213i
$173$	−11.9048			−0.905107			−0.452554	−	0.891737i	$-0.649487\pi$
$173$	−11.9048			−0.905107			−0.452554	+	0.891737i	$0.649487\pi$
$174$		0			0
$175$			12.1599i			0.919200i
$176$	−0.393943	+	3.29315i	−0.0296946	+	0.248230i
$177$		0			0
$178$		−	9.47873i		−	0.710461i
$179$		−	13.5138i		−	1.01007i	−0.863098	−	0.505036i	$-0.831479\pi$
$179$		−	13.5138i		−	1.01007i	0.863098	−	0.505036i	$-0.168521\pi$
$180$		0			0
$181$		−	15.6841i		−	1.16579i	−0.812547	−	0.582896i	$-0.801920\pi$
$181$		−	15.6841i		−	1.16579i	0.812547	−	0.582896i	$-0.198080\pi$
$182$			5.12980i			0.380246i
$183$		0			0
$184$	2.48371			0.183102
$185$		−	1.07442i		−	0.0789933i
$186$		0			0
$187$	−12.6435	−	1.51249i	−0.924587	−	0.110604i
$188$	−9.68535			−0.706377
$189$		0			0
$190$	4.94571	−	2.18383i	0.358799	−	0.158432i
$191$	−4.63919			−0.335680			−0.167840	−	0.985814i	$-0.553679\pi$
$191$	−4.63919			−0.335680			−0.167840	+	0.985814i	$0.553679\pi$
$192$		0			0
$193$	13.7842			0.992207			0.496103	−	0.868264i	$-0.334764\pi$
$193$	13.7842			0.992207			0.496103	+	0.868264i	$0.334764\pi$
$194$		−	7.60274i		−	0.545845i
$195$		0			0
$196$	−5.33951			−0.381394
$197$			11.9744i			0.853139i	0.904455	+	0.426569i	$0.140278\pi$
$197$			11.9744i			0.853139i	−0.904455	+	0.426569i	$0.859722\pi$
$198$		0			0
$199$	7.07676			0.501658			0.250829	−	0.968031i	$-0.419297\pi$
$199$	7.07676			0.501658			0.250829	+	0.968031i	$0.419297\pi$
$200$	−3.46162			−0.244774
$201$		0			0
$202$		−	6.35126i		−	0.446873i
$203$			20.7119i			1.45369i
$204$		0			0
$205$	−14.1881			−0.990938
$206$		−	0.950287i		−	0.0662096i
$207$		0			0
$208$	−1.46033			−0.101256
$209$	−4.22744	−	13.8249i	−0.292418	−	0.956291i
$210$		0			0
$211$	−4.48799			−0.308966			−0.154483	−	0.987995i	$-0.549371\pi$
$211$	−4.48799			−0.308966			−0.154483	+	0.987995i	$0.549371\pi$
$212$			2.65543i			0.182376i
$213$		0			0
$214$	2.41401			0.165018
$215$		−	0.108207i		−	0.00737967i
$216$		0			0
$217$	14.7017			0.998013
$218$	−13.0502			−0.883873
$219$		0			0
$220$	0.488613	−	4.08453i	0.0329423	−	0.275379i
$221$		−	5.60673i		−	0.377149i
$222$		0			0
$223$		−	21.1024i		−	1.41312i	−0.707653	−	0.706561i	$-0.750246\pi$
$223$		−	21.1024i		−	1.41312i	0.707653	−	0.706561i	$-0.249754\pi$
$224$		−	3.51276i		−	0.234706i
$225$		0			0
$226$			12.5345i			0.833780i
$227$	−22.0436			−1.46308			−0.731542	−	0.681796i	$-0.761199\pi$
$227$	−22.0436			−1.46308			−0.731542	+	0.681796i	$0.761199\pi$
$228$		0			0
$229$	−21.3204			−1.40889			−0.704445	−	0.709759i	$-0.748804\pi$
$229$	−21.3204			−1.40889			−0.704445	+	0.709759i	$0.748804\pi$
$230$	−3.08058			−0.203128
$231$		0			0
$232$	−5.89617			−0.387102
$233$			15.5808i			1.02073i	0.859957	+	0.510367i	$0.170490\pi$
$233$			15.5808i			1.02073i	−0.859957	+	0.510367i	$0.829510\pi$
$234$		0			0
$235$	12.0129			0.783633
$236$		−	0.285318i		−	0.0185726i
$237$		0			0
$238$	13.4867			0.874215
$239$		−	13.0572i		−	0.844602i	−0.906456	−	0.422301i	$-0.861223\pi$
$239$		−	13.0572i		−	0.844602i	0.906456	−	0.422301i	$-0.138777\pi$
$240$		0			0
$241$	22.5139			1.45025			0.725124	−	0.688618i	$-0.241782\pi$
$241$	22.5139			1.45025			0.725124	+	0.688618i	$0.241782\pi$
$242$	−10.6896	−	2.59463i	−0.687155	−	0.166789i
$243$		0			0
$244$			7.00823i			0.448656i
$245$	6.62267			0.423107
$246$		0			0
$247$	5.82303	−	2.57122i	0.370510	−	0.163603i
$248$			4.18521i			0.265761i
$249$		0			0
$250$	10.4951			0.663766
$251$	−11.1642			−0.704679			−0.352339	−	0.935872i	$-0.614614\pi$
$251$	−11.1642			−0.704679			−0.352339	+	0.935872i	$0.614614\pi$
$252$		0			0
$253$	−0.978443	+	8.17923i	−0.0615142	+	0.514224i
$254$	−11.9882			−0.752208
$255$		0			0
$256$	1.00000			0.0625000
$257$			14.7993i			0.923153i	0.887100	+	0.461576i	$0.152716\pi$
$257$			14.7993i			0.923153i	−0.887100	+	0.461576i	$0.847284\pi$
$258$		0			0
$259$	3.04294			0.189079
$260$	1.81127			0.112330
$261$		0			0
$262$			20.6588i			1.27630i
$263$		−	21.0066i		−	1.29532i	−0.761929	−	0.647661i	$-0.775747\pi$
$263$		−	21.0066i		−	1.29532i	0.761929	−	0.647661i	$-0.224253\pi$
$264$		0			0
$265$		−	3.29357i		−	0.202322i
$266$	6.18496	+	14.0070i	0.379224	+	0.858826i
$267$		0			0
$268$		−	8.14823i		−	0.497732i
$269$			10.6393i			0.648691i	0.945939	+	0.324346i	$0.105144\pi$
$269$			10.6393i			0.648691i	−0.945939	+	0.324346i	$0.894856\pi$
$270$		0			0
$271$			3.47948i			0.211363i	0.994400	+	0.105682i	$0.0337024\pi$
$271$			3.47948i			0.211363i	−0.994400	+	0.105682i	$0.966298\pi$
$272$			3.83935i			0.232795i
$273$		0			0
$274$	18.7527			1.13289
$275$	1.36368	−	11.3996i	0.0822332	−	0.687424i
$276$		0			0
$277$		−	12.0892i		−	0.726369i	−0.931717	−	0.363184i	$-0.881690\pi$
$277$		−	12.0892i		−	0.726369i	0.931717	−	0.363184i	$-0.118310\pi$
$278$			1.91200i			0.114674i
$279$		0			0
$280$			4.35693i			0.260376i
$281$	−24.0267			−1.43331			−0.716656	−	0.697427i	$-0.754328\pi$
$281$	−24.0267			−1.43331			−0.716656	+	0.697427i	$0.754328\pi$
$282$		0			0
$283$			14.5867i			0.867091i	0.901132	+	0.433546i	$0.142738\pi$
$283$			14.5867i			0.867091i	−0.901132	+	0.433546i	$0.857262\pi$
$284$			15.0087i			0.890602i
$285$		0			0
$286$	0.575288	−	4.80909i	0.0340175	−	0.284367i
$287$		−	40.1829i		−	2.37192i
$288$		0			0
$289$	2.25940			0.132906
$290$	7.31310			0.429440
$291$		0			0
$292$			16.4472i			0.962501i
$293$	−6.21249			−0.362938			−0.181469	−	0.983397i	$-0.558085\pi$
$293$	−6.21249			−0.362938			−0.181469	+	0.983397i	$0.558085\pi$
$294$		0			0
$295$			0.353884i			0.0206039i
$296$			0.866253i			0.0503499i
$297$		0			0
$298$			16.0335i			0.928797i
$299$	−3.62705			−0.209758
$300$		0			0
$301$	0.306460			0.0176641
$302$	−10.6889			−0.615077
$303$		0			0
$304$	−3.98747	+	1.76071i	−0.228697	+	0.100984i
$305$		−	8.69240i		−	0.497725i
$306$		0			0
$307$	−19.4830			−1.11195			−0.555976	−	0.831198i	$-0.687655\pi$
$307$	−19.4830			−1.11195			−0.555976	+	0.831198i	$0.687655\pi$
$308$	11.5680	+	1.38383i	0.659151	+	0.0788511i
$309$		0			0
$310$		−	5.19097i		−	0.294827i
$311$	−32.6639			−1.85220			−0.926100	−	0.377278i	$-0.876860\pi$
$311$	−32.6639			−1.85220			−0.926100	+	0.377278i	$0.876860\pi$
$312$		0			0
$313$	23.9814			1.35551			0.677755	−	0.735288i	$-0.262953\pi$
$313$	23.9814			1.35551			0.677755	+	0.735288i	$0.262953\pi$
$314$	−2.56348			−0.144666
$315$		0			0
$316$	6.48850			0.365007
$317$		−	8.59009i		−	0.482467i	−0.970467	−	0.241234i	$-0.922448\pi$
$317$		−	8.59009i		−	0.482467i	0.970467	−	0.241234i	$-0.0775520\pi$
$318$		0			0
$319$	2.32276	−	19.4169i	0.130049	−	1.08714i
$320$	−1.24031			−0.0693356
$321$		0			0
$322$		−	8.72470i		−	0.486209i
$323$	−6.75998	−	15.3093i	−0.376136	−	0.851831i
$324$		0			0
$325$	5.05512			0.280408
$326$	23.7821			1.31717
$327$		0			0
$328$	11.4391			0.631619
$329$			34.0223i			1.87571i
$330$		0			0
$331$		−	2.34762i		−	0.129037i	−0.997917	−	0.0645183i	$-0.979449\pi$
$331$		−	2.34762i		−	0.129037i	0.997917	−	0.0645183i	$-0.0205511\pi$
$332$			10.0557i			0.551877i
$333$		0			0
$334$	−20.9462			−1.14613
$335$			10.1064i			0.552169i
$336$		0			0
$337$	−3.48485			−0.189832			−0.0949159	−	0.995485i	$-0.530258\pi$
$337$	−3.48485			−0.189832			−0.0949159	+	0.995485i	$0.530258\pi$
$338$	−10.8674			−0.591110
$339$		0			0
$340$		−	4.76199i		−	0.258255i
$341$	−13.7825	−	1.64874i	−0.746364	−	0.0892841i
$342$		0			0
$343$		−	5.83290i		−	0.314947i
$344$			0.0872418i			0.00470376i
$345$		0			0
$346$	−11.9048			−0.640007
$347$			10.4391i			0.560400i	0.959942	+	0.280200i	$0.0904008\pi$
$347$			10.4391i			0.560400i	−0.959942	+	0.280200i	$0.909599\pi$
$348$		0			0
$349$			9.20478i			0.492720i	0.969178	+	0.246360i	$0.0792346\pi$
$349$			9.20478i			0.492720i	−0.969178	+	0.246360i	$0.920765\pi$
$350$			12.1599i			0.649972i
$351$		0			0
$352$	−0.393943	+	3.29315i	−0.0209973	+	0.175525i
$353$	11.1530			0.593615			0.296808	−	0.954937i	$-0.404078\pi$
$353$	11.1530			0.593615			0.296808	+	0.954937i	$0.404078\pi$
$354$		0			0
$355$		−	18.6155i		−	0.988007i
$356$		−	9.47873i		−	0.502372i
$357$		0			0
$358$		−	13.5138i		−	0.714229i
$359$		−	7.51000i		−	0.396363i	−0.980165	−	0.198181i	$-0.936496\pi$
$359$		−	7.51000i		−	0.396363i	0.980165	−	0.198181i	$-0.0635035\pi$
$360$		0			0
$361$	12.7998	−	14.0416i	0.673673	−	0.739029i
$362$		−	15.6841i		−	0.824339i
$363$		0			0
$364$			5.12980i			0.268875i
$365$		−	20.3997i		−	1.06777i
$366$		0			0
$367$	22.6374			1.18166			0.590831	−	0.806796i	$-0.298800\pi$
$367$	22.6374			1.18166			0.590831	+	0.806796i	$0.298800\pi$
$368$	2.48371			0.129473
$369$		0			0
$370$		−	1.07442i		−	0.0558567i
$371$	9.32791			0.484281
$372$		0			0
$373$	7.75500			0.401539			0.200769	−	0.979639i	$-0.435656\pi$
$373$	7.75500			0.401539			0.200769	+	0.979639i	$0.435656\pi$
$374$	−12.6435	−	1.51249i	−0.653782	−	0.0782088i
$375$		0			0
$376$	−9.68535			−0.499484
$377$	8.61037			0.443456
$378$		0			0
$379$		−	8.63502i		−	0.443551i	−0.975098	−	0.221776i	$-0.928815\pi$
$379$		−	8.63502i		−	0.443551i	0.975098	−	0.221776i	$-0.0711852\pi$
$380$	4.94571	−	2.18383i	0.253709	−	0.112028i
$381$		0			0
$382$	−4.63919			−0.237362
$383$		−	9.49540i		−	0.485192i	−0.970127	−	0.242596i	$-0.922001\pi$
$383$		−	9.49540i		−	0.485192i	0.970127	−	0.242596i	$-0.0779990\pi$
$384$		0			0
$385$	−14.3480	−	1.71638i	−0.731242	−	0.0874750i
$386$	13.7842			0.701596
$387$		0			0
$388$		−	7.60274i		−	0.385971i
$389$	−13.9837			−0.709003			−0.354502	−	0.935055i	$-0.615349\pi$
$389$	−13.9837			−0.709003			−0.354502	+	0.935055i	$0.615349\pi$
$390$		0			0
$391$			9.53585i			0.482248i
$392$	−5.33951			−0.269686
$393$		0			0
$394$			11.9744i			0.603260i
$395$	−8.04777			−0.404927
$396$		0			0
$397$	−5.11408			−0.256668			−0.128334	−	0.991731i	$-0.540963\pi$
$397$	−5.11408			−0.256668			−0.128334	+	0.991731i	$0.540963\pi$
$398$	7.07676			0.354726
$399$		0			0
$400$	−3.46162			−0.173081
$401$		−	19.3832i		−	0.967948i	−0.875082	−	0.483974i	$-0.839193\pi$
$401$		−	19.3832i		−	0.967948i	0.875082	−	0.483974i	$-0.160807\pi$
$402$		0			0
$403$		−	6.11180i		−	0.304450i
$404$		−	6.35126i		−	0.315987i
$405$		0			0
$406$			20.7119i			1.02791i
$407$	−2.85270	−	0.341255i	−0.141403	−	0.0169154i
$408$		0			0
$409$	−3.13095			−0.154815			−0.0774077	−	0.997000i	$-0.524664\pi$
$409$	−3.13095			−0.154815			−0.0774077	+	0.997000i	$0.524664\pi$
$410$	−14.1881			−0.700699
$411$		0			0
$412$		−	0.950287i		−	0.0468173i
$413$	−1.00226			−0.0493178
$414$		0			0
$415$		−	12.4722i		−	0.612236i
$416$	−1.46033			−0.0715987
$417$		0			0
$418$	−4.22744	−	13.8249i	−0.206771	−	0.676200i
$419$	13.3636			0.652854			0.326427	−	0.945222i	$-0.394155\pi$
$419$	13.3636			0.652854			0.326427	+	0.945222i	$0.394155\pi$
$420$		0			0
$421$		−	9.51090i		−	0.463533i	−0.972771	−	0.231767i	$-0.925549\pi$
$421$		−	9.51090i		−	0.463533i	0.972771	−	0.231767i	$-0.0744505\pi$
$422$	−4.48799			−0.218472
$423$		0			0
$424$			2.65543i			0.128959i
$425$		−	13.2904i		−	0.644678i
$426$		0			0
$427$	24.6183			1.19136
$428$	2.41401			0.116685
$429$		0			0
$430$		−	0.108207i		−	0.00521821i
$431$	35.6693			1.71813			0.859064	−	0.511868i	$-0.171046\pi$
$431$	35.6693			1.71813			0.859064	+	0.511868i	$0.171046\pi$
$432$		0			0
$433$			8.16673i			0.392468i	0.980557	+	0.196234i	$0.0628712\pi$
$433$			8.16673i			0.392468i	−0.980557	+	0.196234i	$0.937129\pi$
$434$	14.7017			0.705702
$435$		0			0
$436$	−13.0502			−0.624992
$437$	−9.90373	+	4.37310i	−0.473760	+	0.209194i
$438$		0			0
$439$	−4.92870			−0.235234			−0.117617	−	0.993059i	$-0.537526\pi$
$439$	−4.92870			−0.235234			−0.117617	+	0.993059i	$0.537526\pi$
$440$	0.488613	−	4.08453i	0.0232937	−	0.194722i
$441$		0			0
$442$		−	5.60673i		−	0.266685i
$443$	−29.5995			−1.40631			−0.703156	−	0.711035i	$-0.748227\pi$
$443$	−29.5995			−1.40631			−0.703156	+	0.711035i	$0.748227\pi$
$444$		0			0
$445$			11.7566i			0.557316i
$446$		−	21.1024i		−	0.999227i
$447$		0			0
$448$		−	3.51276i		−	0.165963i
$449$		−	3.96730i		−	0.187228i	−0.995609	−	0.0936142i	$-0.970158\pi$
$449$		−	3.96730i		−	0.187228i	0.995609	−	0.0936142i	$-0.0298420\pi$
$450$		0			0
$451$	−4.50636	+	37.6707i	−0.212196	+	1.77384i
$452$			12.5345i			0.589572i
$453$		0			0
$454$	−22.0436			−1.03456
$455$		−	6.36256i		−	0.298281i
$456$		0			0
$457$		−	0.864501i		−	0.0404397i	−0.999796	−	0.0202198i	$-0.993563\pi$
$457$		−	0.864501i		−	0.0404397i	0.999796	−	0.0202198i	$-0.00643661\pi$
$458$	−21.3204			−0.996236
$459$		0			0
$460$	−3.08058			−0.143633
$461$		−	21.5097i		−	1.00181i	−0.865503	−	0.500904i	$-0.833001\pi$
$461$		−	21.5097i		−	1.00181i	0.865503	−	0.500904i	$-0.166999\pi$
$462$		0			0
$463$	13.6859			0.636039			0.318019	−	0.948084i	$-0.396982\pi$
$463$	13.6859			0.636039			0.318019	+	0.948084i	$0.396982\pi$
$464$	−5.89617			−0.273723
$465$		0			0
$466$			15.5808i			0.721768i
$467$	23.7719			1.10003			0.550017	−	0.835154i	$-0.314621\pi$
$467$	23.7719			1.10003			0.550017	+	0.835154i	$0.314621\pi$
$468$		0			0
$469$	−28.6228			−1.32168
$470$	12.0129			0.554112
$471$		0			0
$472$		−	0.285318i		−	0.0131328i
$473$	−0.287300	−	0.0343683i	−0.0132101	−	0.00158026i
$474$		0			0
$475$	13.8031	−	6.09492i	0.633330	−	0.279654i
$476$	13.4867			0.618163
$477$		0			0
$478$		−	13.0572i		−	0.597224i
$479$			24.9680i			1.14082i	0.821361	+	0.570408i	$0.193215\pi$
$479$			24.9680i			1.14082i	−0.821361	+	0.570408i	$0.806785\pi$
$480$		0			0
$481$		−	1.26502i		−	0.0576798i
$482$	22.5139			1.02548
$483$		0			0
$484$	−10.6896	−	2.59463i	−0.485892	−	0.117938i
$485$			9.42978i			0.428184i
$486$		0			0
$487$		−	38.9273i		−	1.76397i	−0.471281	−	0.881983i	$-0.656208\pi$
$487$		−	38.9273i		−	1.76397i	0.471281	−	0.881983i	$-0.343792\pi$
$488$			7.00823i			0.317248i
$489$		0			0
$490$	6.62267			0.299182
$491$			6.50352i			0.293500i	0.989174	+	0.146750i	$0.0468812\pi$
$491$			6.50352i			0.293500i	−0.989174	+	0.146750i	$0.953119\pi$
$492$		0			0
$493$		−	22.6375i		−	1.01954i
$494$	5.82303	−	2.57122i	0.261990	−	0.115685i
$495$		0			0
$496$			4.18521i			0.187921i
$497$	52.7220			2.36491
$498$		0			0
$499$	0.684772			0.0306546			0.0153273	−	0.999883i	$-0.495121\pi$
$499$	0.684772			0.0306546			0.0153273	+	0.999883i	$0.495121\pi$
$500$	10.4951			0.469353
$501$		0			0
$502$	−11.1642			−0.498283
$503$			25.8805i			1.15396i	0.816760	+	0.576978i	$0.195768\pi$
$503$			25.8805i			1.15396i	−0.816760	+	0.576978i	$0.804232\pi$
$504$		0			0
$505$			7.87755i			0.350546i
$506$	−0.978443	+	8.17923i	−0.0434971	+	0.363611i
$507$		0			0
$508$	−11.9882			−0.531891
$509$			29.7825i			1.32008i	0.751228	+	0.660042i	$0.229462\pi$
$509$			29.7825i			1.32008i	−0.751228	+	0.660042i	$0.770538\pi$
$510$		0			0
$511$	57.7752			2.55583
$512$	1.00000			0.0441942
$513$		0			0
$514$			14.7993i			0.652768i
$515$			1.17865i			0.0519377i
$516$		0			0
$517$	3.81548	−	31.8953i	0.167805	−	1.40275i
$518$	3.04294			0.133699
$519$		0			0
$520$	1.81127			0.0794294
$521$		−	13.0835i		−	0.573198i	−0.958051	−	0.286599i	$-0.907475\pi$
$521$		−	13.0835i		−	0.573198i	0.958051	−	0.286599i	$-0.0925247\pi$
$522$		0			0
$523$	15.4307			0.674736			0.337368	−	0.941373i	$-0.390463\pi$
$523$	15.4307			0.674736			0.337368	+	0.941373i	$0.390463\pi$
$524$			20.6588i			0.902482i
$525$		0			0
$526$		−	21.0066i		−	0.915931i
$527$	−16.0685			−0.699954
$528$		0			0
$529$	−16.8312			−0.731790
$530$		−	3.29357i		−	0.143063i
$531$		0			0
$532$	6.18496	+	14.0070i	0.268152	+	0.607282i
$533$	−16.7049			−0.723570
$534$		0			0
$535$	−2.99412			−0.129447
$536$		−	8.14823i		−	0.351950i
$537$		0			0
$538$			10.6393i			0.458694i
$539$	2.10347	−	17.5838i	0.0906027	−	0.757388i
$540$		0			0
$541$			4.87397i			0.209548i	0.994496	+	0.104774i	$0.0334120\pi$
$541$			4.87397i			0.209548i	−0.994496	+	0.104774i	$0.966588\pi$
$542$			3.47948i			0.149456i
$543$		0			0
$544$			3.83935i			0.164611i
$545$	16.1864			0.693348
$546$		0			0
$547$	38.3889			1.64139			0.820694	−	0.571367i	$-0.193587\pi$
$547$	38.3889			1.64139			0.820694	+	0.571367i	$0.193587\pi$
$548$	18.7527			0.801076
$549$		0			0
$550$	1.36368	−	11.3996i	0.0581477	−	0.486082i
$551$	23.5108	−	10.3814i	1.00159	−	0.442265i
$552$		0			0
$553$		−	22.7926i		−	0.969239i
$554$		−	12.0892i		−	0.513620i
$555$		0			0
$556$			1.91200i			0.0810870i
$557$		−	23.8274i		−	1.00960i	−0.863236	−	0.504800i	$-0.831566\pi$
$557$		−	23.8274i		−	1.00960i	0.863236	−	0.504800i	$-0.168434\pi$
$558$		0			0
$559$		−	0.127402i		−	0.00538853i
$560$			4.35693i			0.184114i
$561$		0			0
$562$	−24.0267			−1.01350
$563$	9.81809			0.413783			0.206892	−	0.978364i	$-0.433665\pi$
$563$	9.81809			0.413783			0.206892	+	0.978364i	$0.433665\pi$
$564$		0			0
$565$		−	15.5467i		−	0.654053i
$566$			14.5867i			0.613126i
$567$		0			0
$568$			15.0087i			0.629751i
$569$	31.9095			1.33772			0.668859	−	0.743389i	$-0.266783\pi$
$569$	31.9095			1.33772			0.668859	+	0.743389i	$0.266783\pi$
$570$		0			0
$571$		−	34.9981i		−	1.46463i	−0.680968	−	0.732313i	$-0.738441\pi$
$571$		−	34.9981i		−	1.46463i	0.680968	−	0.732313i	$-0.261559\pi$
$572$	0.575288	−	4.80909i	0.0240540	−	0.201078i
$573$		0			0
$574$		−	40.1829i		−	1.67720i
$575$	−8.59768			−0.358548
$576$		0			0
$577$	43.8833			1.82689			0.913443	−	0.406966i	$-0.133413\pi$
$577$	43.8833			1.82689			0.913443	+	0.406966i	$0.133413\pi$
$578$	2.25940			0.0939785
$579$		0			0
$580$	7.31310			0.303660
$581$	35.3232			1.46545
$582$		0			0
$583$	−8.74472	−	1.04609i	−0.362169	−	0.0433246i
$584$			16.4472i			0.680591i
$585$		0			0
$586$	−6.21249			−0.256636
$587$	33.2220			1.37122			0.685609	−	0.727970i	$-0.259536\pi$
$587$	33.2220			1.37122			0.685609	+	0.727970i	$0.259536\pi$
$588$		0			0
$589$	−7.36894	−	16.6884i	−0.303632	−	0.687633i
$590$			0.353884i			0.0145692i
$591$		0			0
$592$			0.866253i			0.0356028i
$593$			12.4613i			0.511725i	0.966713	+	0.255863i	$0.0823595\pi$
$593$			12.4613i			0.511725i	−0.966713	+	0.255863i	$0.917641\pi$
$594$		0			0
$595$	−16.7278			−0.685772
$596$			16.0335i			0.656759i
$597$		0			0
$598$	−3.62705			−0.148321
$599$			7.41888i			0.303127i	0.988448	+	0.151564i	$0.0484308\pi$
$599$			7.41888i			0.303127i	−0.988448	+	0.151564i	$0.951569\pi$
$600$		0			0
$601$	−8.62434			−0.351794			−0.175897	−	0.984409i	$-0.556283\pi$
$601$	−8.62434			−0.351794			−0.175897	+	0.984409i	$0.556283\pi$
$602$	0.306460			0.0124904
$603$		0			0
$604$	−10.6889			−0.434925
$605$	13.2585	+	3.21815i	0.539033	+	0.130836i
$606$		0			0
$607$	1.64452			0.0667489			0.0333744	−	0.999443i	$-0.489375\pi$
$607$	1.64452			0.0667489			0.0333744	+	0.999443i	$0.489375\pi$
$608$	−3.98747	+	1.76071i	−0.161713	+	0.0714062i
$609$		0			0
$610$		−	8.69240i		−	0.351945i
$611$	14.1438			0.572198
$612$		0			0
$613$			45.0831i			1.82089i	0.413629	+	0.910445i	$0.364261\pi$
$613$			45.0831i			1.82089i	−0.413629	+	0.910445i	$0.635739\pi$
$614$	−19.4830			−0.786269
$615$		0			0
$616$	11.5680	+	1.38383i	0.466090	+	0.0557561i
$617$	−7.39187			−0.297586			−0.148793	−	0.988868i	$-0.547539\pi$
$617$	−7.39187			−0.297586			−0.148793	+	0.988868i	$0.547539\pi$
$618$		0			0
$619$	−17.9405			−0.721091			−0.360545	−	0.932742i	$-0.617409\pi$
$619$	−17.9405			−0.721091			−0.360545	+	0.932742i	$0.617409\pi$
$620$		−	5.19097i		−	0.208474i
$621$		0			0
$622$	−32.6639			−1.30970
$623$	−33.2966			−1.33400
$624$		0			0
$625$	4.29096			0.171638
$626$	23.9814			0.958490
$627$		0			0
$628$	−2.56348			−0.102294
$629$	−3.32585			−0.132610
$630$		0			0
$631$	−5.87651			−0.233940			−0.116970	−	0.993135i	$-0.537318\pi$
$631$	−5.87651			−0.233940			−0.116970	+	0.993135i	$0.537318\pi$
$632$	6.48850			0.258099
$633$		0			0
$634$		−	8.59009i		−	0.341156i
$635$	14.8691			0.590064
$636$		0			0
$637$	7.79746			0.308947
$638$	2.32276	−	19.4169i	0.0919588	−	0.768724i
$639$		0			0
$640$	−1.24031			−0.0490277
$641$		−	0.654202i		−	0.0258394i	−0.999917	−	0.0129197i	$-0.995887\pi$
$641$		−	0.654202i		−	0.0258394i	0.999917	−	0.0129197i	$-0.00411259\pi$
$642$		0			0
$643$	−21.0249			−0.829142			−0.414571	−	0.910017i	$-0.636068\pi$
$643$	−21.0249			−0.829142			−0.414571	+	0.910017i	$0.636068\pi$
$644$		−	8.72470i		−	0.343801i
$645$		0			0
$646$	−6.75998	−	15.3093i	−0.265968	−	0.602336i
$647$	12.6223			0.496235			0.248117	−	0.968730i	$-0.420188\pi$
$647$	12.6223			0.496235			0.248117	+	0.968730i	$0.420188\pi$
$648$		0			0
$649$	0.939594	+	0.112399i	0.0368823	+	0.00441205i
$650$	5.05512			0.198278
$651$		0			0
$652$	23.7821			0.931377
$653$	−31.4754			−1.23173			−0.615865	−	0.787852i	$-0.711193\pi$
$653$	−31.4754			−1.23173			−0.615865	+	0.787852i	$0.711193\pi$
$654$		0			0
$655$		−	25.6233i		−	1.00119i
$656$	11.4391			0.446622
$657$		0			0
$658$			34.0223i			1.32633i
$659$	4.52269			0.176179			0.0880894	−	0.996113i	$-0.471924\pi$
$659$	4.52269			0.176179			0.0880894	+	0.996113i	$0.471924\pi$
$660$		0			0
$661$			49.6747i			1.93212i	0.258312	+	0.966061i	$0.416834\pi$
$661$			49.6747i			1.93212i	−0.258312	+	0.966061i	$0.583166\pi$
$662$		−	2.34762i		−	0.0912427i
$663$		0			0
$664$			10.0557i			0.390236i
$665$	−7.67129	−	17.3731i	−0.297480	−	0.673700i
$666$		0			0
$667$	−14.6444			−0.567033
$668$	−20.9462			−0.810434
$669$		0			0
$670$			10.1064i			0.390443i
$671$	−23.0791	−	2.76085i	−0.890959	−	0.106581i
$672$		0			0
$673$	22.3215			0.860429			0.430215	−	0.902727i	$-0.358438\pi$
$673$	22.3215			0.860429			0.430215	+	0.902727i	$0.358438\pi$
$674$	−3.48485			−0.134231
$675$		0			0
$676$	−10.8674			−0.417978
$677$	−14.3875			−0.552956			−0.276478	−	0.961020i	$-0.589167\pi$
$677$	−14.3875			−0.552956			−0.276478	+	0.961020i	$0.589167\pi$
$678$		0			0
$679$	−26.7066			−1.02491
$680$		−	4.76199i		−	0.182614i
$681$		0			0
$682$	−13.7825	−	1.64874i	−0.527759	−	0.0631334i
$683$		−	49.0000i		−	1.87493i	−0.348077	−	0.937466i	$-0.613165\pi$
$683$		−	49.0000i		−	1.87493i	0.348077	−	0.937466i	$-0.386835\pi$
$684$		0			0
$685$	−23.2592			−0.888690
$686$		−	5.83290i		−	0.222701i
$687$		0			0
$688$			0.0872418i			0.00332606i
$689$		−	3.87781i		−	0.147733i
$690$		0			0
$691$	32.3554			1.23086			0.615429	−	0.788193i	$-0.288983\pi$
$691$	32.3554			1.23086			0.615429	+	0.788193i	$0.288983\pi$
$692$	−11.9048			−0.452554
$693$		0			0
$694$			10.4391i			0.396263i
$695$		−	2.37148i		−	0.0899554i
$696$		0			0
$697$			43.9187i			1.66354i
$698$			9.20478i			0.348406i
$699$		0			0
$700$			12.1599i			0.459600i
$701$		−	13.6693i		−	0.516284i	−0.966107	−	0.258142i	$-0.916890\pi$
$701$		−	13.6693i		−	0.516284i	0.966107	−	0.258142i	$-0.0831102\pi$
$702$		0			0
$703$	−1.52522	−	3.45416i	−0.0575248	−	0.130276i
$704$	−0.393943	+	3.29315i	−0.0148473	+	0.124115i
$705$		0			0
$706$	11.1530			0.419750
$707$	−22.3105			−0.839072
$708$		0			0
$709$	−37.1934			−1.39683			−0.698413	−	0.715695i	$-0.746110\pi$
$709$	−37.1934			−1.39683			−0.698413	+	0.715695i	$0.746110\pi$
$710$		−	18.6155i		−	0.698626i
$711$		0			0
$712$		−	9.47873i		−	0.355231i
$713$			10.3949i			0.389291i
$714$		0			0
$715$	−0.713537	+	5.96477i	−0.0266848	+	0.223070i
$716$		−	13.5138i		−	0.505036i
$717$		0			0
$718$		−	7.51000i		−	0.280271i
$719$	8.36848			0.312092			0.156046	−	0.987750i	$-0.450125\pi$
$719$	8.36848			0.312092			0.156046	+	0.987750i	$0.450125\pi$
$720$		0			0
$721$	−3.33813			−0.124319
$722$	12.7998	−	14.0416i	0.476359	−	0.522573i
$723$		0			0
$724$		−	15.6841i		−	0.582896i
$725$	20.4103			0.758020
$726$		0			0
$727$	−41.2999			−1.53173			−0.765864	−	0.643003i	$-0.777688\pi$
$727$	−41.2999			−1.53173			−0.765864	+	0.643003i	$0.777688\pi$
$728$			5.12980i			0.190123i
$729$		0			0
$730$		−	20.3997i		−	0.755027i
$731$	−0.334952			−0.0123886
$732$		0			0
$733$			26.2954i			0.971244i	0.874169	+	0.485622i	$0.161407\pi$
$733$			26.2954i			0.971244i	−0.874169	+	0.485622i	$0.838593\pi$
$734$	22.6374			0.835561
$735$		0			0
$736$	2.48371			0.0915509
$737$	26.8333	+	3.20994i	0.988418	+	0.118240i
$738$		0			0
$739$			19.6684i			0.723512i	0.932273	+	0.361756i	$0.117823\pi$
$739$			19.6684i			0.723512i	−0.932273	+	0.361756i	$0.882177\pi$
$740$		−	1.07442i		−	0.0394966i
$741$		0			0
$742$	9.32791			0.342438
$743$	−22.1725			−0.813429			−0.406715	−	0.913555i	$-0.633326\pi$
$743$	−22.1725			−0.813429			−0.406715	+	0.913555i	$0.633326\pi$
$744$		0			0
$745$		−	19.8866i		−	0.728588i
$746$	7.75500			0.283931
$747$		0			0
$748$	−12.6435	−	1.51249i	−0.462293	−	0.0553020i
$749$		−	8.47983i		−	0.309846i
$750$		0			0
$751$		−	25.8074i		−	0.941725i	−0.882207	−	0.470862i	$-0.843943\pi$
$751$		−	25.8074i		−	0.941725i	0.882207	−	0.470862i	$-0.156057\pi$
$752$	−9.68535			−0.353188
$753$		0			0
$754$	8.61037			0.313571
$755$	13.2576			0.482492
$756$		0			0
$757$	−35.4702			−1.28919			−0.644593	−	0.764526i	$-0.722973\pi$
$757$	−35.4702			−1.28919			−0.644593	+	0.764526i	$0.722973\pi$
$758$		−	8.63502i		−	0.313638i
$759$		0			0
$760$	4.94571	−	2.18383i	0.179400	−	0.0792159i
$761$			6.33445i			0.229623i	0.993387	+	0.114812i	$0.0366265\pi$
$761$			6.33445i			0.229623i	−0.993387	+	0.114812i	$0.963374\pi$
$762$		0			0
$763$			45.8424i			1.65961i
$764$	−4.63919			−0.167840
$765$		0			0
$766$		−	9.49540i		−	0.343083i
$767$			0.416659i			0.0150447i
$768$		0			0
$769$		−	30.6965i		−	1.10694i	−0.832868	−	0.553472i	$-0.813302\pi$
$769$		−	30.6965i		−	1.10694i	0.832868	−	0.553472i	$-0.186698\pi$
$770$	−14.3480	−	1.71638i	−0.517066	−	0.0618541i
$771$		0			0
$772$	13.7842			0.496103
$773$			9.20215i			0.330978i	0.986212	+	0.165489i	$0.0529203\pi$
$773$			9.20215i			0.330978i	−0.986212	+	0.165489i	$0.947080\pi$
$774$		0			0
$775$		−	14.4876i		−	0.520411i
$776$		−	7.60274i		−	0.272923i
$777$		0			0
$778$	−13.9837			−0.501341
$779$	−45.6131	+	20.1410i	−1.63426	+	0.721625i
$780$		0			0
$781$	−49.4258	−	5.91258i	−1.76859	−	0.211569i
$782$			9.53585i			0.341001i
$783$		0			0
$784$	−5.33951			−0.190697
$785$	3.17952			0.113482
$786$		0			0
$787$	15.7616			0.561839			0.280919	−	0.959731i	$-0.409361\pi$
$787$	15.7616			0.561839			0.280919	+	0.959731i	$0.409361\pi$
$788$			11.9744i			0.426569i
$789$		0			0
$790$	−8.04777			−0.286327
$791$	44.0306			1.56555
$792$		0			0
$793$		−	10.2343i		−	0.363432i
$794$	−5.11408			−0.181492
$795$		0			0
$796$	7.07676			0.250829
$797$			34.8417i			1.23416i	0.786902	+	0.617078i	$0.211684\pi$
$797$			34.8417i			1.23416i	−0.786902	+	0.617078i	$0.788316\pi$
$798$		0			0
$799$		−	37.1854i		−	1.31553i
$800$	−3.46162			−0.122387
$801$		0			0
$802$		−	19.3832i		−	0.684443i
$803$	−54.1631	−	6.47928i	−1.91137	−	0.228649i
$804$		0			0
$805$			10.8214i			0.381403i
$806$		−	6.11180i		−	0.215279i
$807$		0			0
$808$		−	6.35126i		−	0.223437i
$809$		−	18.3477i		−	0.645069i	−0.946558	−	0.322535i	$-0.895465\pi$
$809$		−	18.3477i		−	0.645069i	0.946558	−	0.322535i	$-0.104535\pi$
$810$		0			0
$811$	−38.1546			−1.33979			−0.669895	−	0.742456i	$-0.733661\pi$
$811$	−38.1546			−1.33979			−0.669895	+	0.742456i	$0.733661\pi$
$812$			20.7119i			0.726844i
$813$		0			0
$814$	−2.85270	−	0.341255i	−0.0999870	−	0.0119610i
$815$	−29.4972			−1.03324
$816$		0			0
$817$	−0.153608	−	0.347874i	−0.00537405	−	0.0121706i
$818$	−3.13095			−0.109471
$819$		0			0
$820$	−14.1881			−0.495469
$821$		−	1.50930i		−	0.0526749i	−0.999653	−	0.0263375i	$-0.991616\pi$
$821$		−	1.50930i		−	0.0526749i	0.999653	−	0.0263375i	$-0.00838445\pi$
$822$		0			0
$823$	43.1342			1.50357			0.751783	−	0.659411i	$-0.229194\pi$
$823$	43.1342			1.50357			0.751783	+	0.659411i	$0.229194\pi$
$824$		−	0.950287i		−	0.0331048i
$825$		0			0
$826$	−1.00226			−0.0348729
$827$	6.47290			0.225085			0.112542	−	0.993647i	$-0.464101\pi$
$827$	6.47290			0.225085			0.112542	+	0.993647i	$0.464101\pi$
$828$		0			0
$829$		−	0.483782i		−	0.0168024i	−0.999965	−	0.00840122i	$-0.997326\pi$
$829$		−	0.483782i		−	0.0168024i	0.999965	−	0.00840122i	$-0.00267422\pi$
$830$		−	12.4722i		−	0.432916i
$831$		0			0
$832$	−1.46033			−0.0506279
$833$		−	20.5003i		−	0.710292i
$834$		0			0
$835$	25.9799			0.899071
$836$	−4.22744	−	13.8249i	−0.146209	−	0.478145i
$837$		0			0
$838$	13.3636			0.461638
$839$			10.4365i			0.360306i	0.983639	+	0.180153i	$0.0576593\pi$
$839$			10.4365i			0.360306i	−0.983639	+	0.180153i	$0.942341\pi$
$840$		0			0
$841$	5.76482			0.198787
$842$		−	9.51090i		−	0.327767i
$843$		0			0
$844$	−4.48799			−0.154483
$845$	13.4790			0.463692
$846$		0			0
$847$	−9.11431	+	37.5501i	−0.313171	+	1.29024i
$848$			2.65543i			0.0911879i
$849$		0			0
$850$		−	13.2904i		−	0.455856i
$851$			2.15152i			0.0737533i
$852$		0			0
$853$		−	31.0469i		−	1.06302i	−0.847051	−	0.531512i	$-0.821624\pi$
$853$		−	31.0469i		−	1.06302i	0.847051	−	0.531512i	$-0.178376\pi$
$854$	24.6183			0.842419
$855$		0			0
$856$	2.41401			0.0825090
$857$	31.0251			1.05980			0.529898	−	0.848062i	$-0.322230\pi$
$857$	31.0251			1.05980			0.529898	+	0.848062i	$0.322230\pi$
$858$		0			0
$859$	0.450113			0.0153576			0.00767882	−	0.999971i	$-0.497556\pi$
$859$	0.450113			0.0153576			0.00767882	+	0.999971i	$0.497556\pi$
$860$		−	0.108207i		−	0.00368983i
$861$		0			0
$862$	35.6693			1.21490
$863$		−	11.8108i		−	0.402044i	−0.979587	−	0.201022i	$-0.935574\pi$
$863$		−	11.8108i		−	0.402044i	0.979587	−	0.201022i	$-0.0644263\pi$
$864$		0			0
$865$	14.7657			0.502049
$866$			8.16673i			0.277517i
$867$		0			0
$868$	14.7017			0.499007
$869$	−2.55610	+	21.3676i	−0.0867098	+	0.724846i
$870$		0			0
$871$			11.8991i			0.403186i
$872$	−13.0502			−0.441936
$873$		0			0
$874$	−9.90373	+	4.37310i	−0.334999	+	0.147922i
$875$		−	36.8667i		−	1.24632i
$876$		0			0
$877$	−26.0537			−0.879772			−0.439886	−	0.898054i	$-0.644981\pi$
$877$	−26.0537			−0.879772			−0.439886	+	0.898054i	$0.644981\pi$
$878$	−4.92870			−0.166336
$879$		0			0
$880$	0.488613	−	4.08453i	0.0164711	−	0.137690i
$881$	−44.2433			−1.49059			−0.745297	−	0.666732i	$-0.767692\pi$
$881$	−44.2433			−1.49059			−0.745297	+	0.666732i	$0.767692\pi$
$882$		0			0
$883$	8.43478			0.283853			0.141926	−	0.989877i	$-0.454670\pi$
$883$	8.43478			0.283853			0.141926	+	0.989877i	$0.454670\pi$
$884$		−	5.60673i		−	0.188575i
$885$		0			0
$886$	−29.5995			−0.994413
$887$	−8.25836			−0.277288			−0.138644	−	0.990342i	$-0.544274\pi$
$887$	−8.25836			−0.277288			−0.138644	+	0.990342i	$0.544274\pi$
$888$		0			0
$889$			42.1118i			1.41238i
$890$			11.7566i			0.394082i
$891$		0			0
$892$		−	21.1024i		−	0.706561i
$893$	38.6200	−	17.0531i	1.29237	−	0.570660i
$894$		0			0
$895$			16.7614i			0.560272i
$896$		−	3.51276i		−	0.117353i
$897$		0			0
$898$		−	3.96730i		−	0.132390i
$899$		−	24.6767i		−	0.823014i
$900$		0			0
$901$	−10.1951			−0.339649
$902$	−4.50636	+	37.6707i	−0.150045	+	1.25430i
$903$		0			0
$904$			12.5345i			0.416890i
$905$			19.4532i			0.646647i
$906$		0			0
$907$			25.1764i			0.835969i	0.908454	+	0.417984i	$0.137263\pi$
$907$			25.1764i			0.835969i	−0.908454	+	0.417984i	$0.862737\pi$
$908$	−22.0436			−0.731542
$909$		0			0
$910$		−	6.36256i		−	0.210917i
$911$		−	38.9230i		−	1.28958i	−0.764361	−	0.644789i	$-0.776945\pi$
$911$		−	38.9230i		−	1.28958i	0.764361	−	0.644789i	$-0.223055\pi$
$912$		0			0
$913$	−33.1148	−	3.96137i	−1.09594	−	0.131102i
$914$		−	0.864501i		−	0.0285952i
$915$		0			0
$916$	−21.3204			−0.704445
$917$	72.5694			2.39645
$918$		0			0
$919$		−	16.0625i		−	0.529854i	−0.964268	−	0.264927i	$-0.914652\pi$
$919$		−	16.0625i		−	0.529854i	0.964268	−	0.264927i	$-0.0853478\pi$
$920$	−3.08058			−0.101564
$921$		0			0
$922$		−	21.5097i		−	0.708385i
$923$		−	21.9177i		−	0.721429i
$924$		0			0
$925$		−	2.99864i		−	0.0985947i
$926$	13.6859			0.449747
$927$		0			0
$928$	−5.89617			−0.193551
$929$	−48.5133			−1.59167			−0.795835	−	0.605513i	$-0.792968\pi$
$929$	−48.5133			−1.59167			−0.795835	+	0.605513i	$0.792968\pi$
$930$		0			0
$931$	21.2911	−	9.40134i	0.697789	−	0.308116i
$932$			15.5808i			0.510367i
$933$		0			0
$934$	23.7719			0.777841
$935$	15.6819	+	1.87596i	0.512854	+	0.0613503i
$936$		0			0
$937$			54.1045i			1.76752i	0.467944	+	0.883758i	$0.344995\pi$
$937$			54.1045i			1.76752i	−0.467944	+	0.883758i	$0.655005\pi$
$938$	−28.6228			−0.934568
$939$		0			0
$940$	12.0129			0.391816
$941$	15.7291			0.512755			0.256377	−	0.966577i	$-0.417471\pi$
$941$	15.7291			0.512755			0.256377	+	0.966577i	$0.417471\pi$
$942$		0			0
$943$	28.4115			0.925205
$944$		−	0.285318i		−	0.00928631i
$945$		0			0
$946$	−0.287300	−	0.0343683i	−0.00934093	−	0.00111741i
$947$	17.4786			0.567979			0.283989	−	0.958827i	$-0.408342\pi$
$947$	17.4786			0.567979			0.283989	+	0.958827i	$0.408342\pi$
$948$		0			0
$949$		−	24.0184i		−	0.779671i
$950$	13.8031	−	6.09492i	0.447832	−	0.197745i
$951$		0			0
$952$	13.4867			0.437107
$953$	−23.2275			−0.752412			−0.376206	−	0.926536i	$-0.622771\pi$
$953$	−23.2275			−0.752412			−0.376206	+	0.926536i	$0.622771\pi$
$954$		0			0
$955$	5.75405			0.186197
$956$		−	13.0572i		−	0.422301i
$957$		0			0
$958$			24.9680i			0.806679i
$959$		−	65.8739i		−	2.12718i
$960$		0			0
$961$	13.4840			0.434968
$962$		−	1.26502i		−	0.0407858i
$963$		0			0
$964$	22.5139			0.725124
$965$	−17.0967			−0.550362
$966$		0			0
$967$			9.79540i			0.314999i	0.987519	+	0.157499i	$0.0503432\pi$
$967$			9.79540i			0.314999i	−0.987519	+	0.157499i	$0.949657\pi$
$968$	−10.6896	−	2.59463i	−0.343577	−	0.0833944i
$969$		0			0
$970$			9.42978i			0.302772i
$971$		−	42.9936i		−	1.37973i	−0.723938	−	0.689865i	$-0.757670\pi$
$971$		−	42.9936i		−	1.37973i	0.723938	−	0.689865i	$-0.242330\pi$
$972$		0			0
$973$	6.71642			0.215318
$974$		−	38.9273i		−	1.24731i
$975$		0			0
$976$			7.00823i			0.224328i
$977$			25.7784i			0.824723i	0.911020	+	0.412361i	$0.135296\pi$
$977$			25.7784i			0.824723i	−0.911020	+	0.412361i	$0.864704\pi$
$978$		0			0
$979$	31.2149	+	3.73409i	0.997631	+	0.119342i
$980$	6.62267			0.211553
$981$		0			0
$982$			6.50352i			0.207536i
$983$		−	1.72387i		−	0.0549829i	−0.999622	−	0.0274914i	$-0.991248\pi$
$983$		−	1.72387i		−	0.0549829i	0.999622	−	0.0274914i	$-0.00875190\pi$
$984$		0			0
$985$		−	14.8520i		−	0.473223i
$986$		−	22.6375i		−	0.720923i
$987$		0			0
$988$	5.82303	−	2.57122i	0.185255	−	0.0818015i
$989$			0.216684i			0.00689014i
$990$		0			0
$991$		−	18.7121i		−	0.594409i	−0.954814	−	0.297204i	$-0.903946\pi$
$991$		−	18.7121i		−	0.594409i	0.954814	−	0.297204i	$-0.0960543\pi$
$992$			4.18521i			0.132881i
$993$		0			0
$994$	52.7220			1.67224
$995$	−8.77739			−0.278262
$996$		0			0
$997$		−	56.9988i		−	1.80517i	−0.430512	−	0.902585i	$-0.641667\pi$
$997$		−	56.9988i		−	1.80517i	0.430512	−	0.902585i	$-0.358333\pi$
$998$	0.684772			0.0216761
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3762.2.g.l.2089.7		20
3.2	odd	2		1254.2.g.a.835.7	✓	20
11.10	odd	2		3762.2.g.k.2089.8		20
19.18	odd	2		3762.2.g.k.2089.7		20
33.32	even	2		1254.2.g.b.835.7	yes	20
57.56	even	2		1254.2.g.b.835.17	yes	20
209.208	even	2	inner	3762.2.g.l.2089.8		20
627.626	odd	2		1254.2.g.a.835.17	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1254.2.g.a.835.7	✓	20	3.2	odd	2
1254.2.g.a.835.17	yes	20	627.626	odd	2
1254.2.g.b.835.7	yes	20	33.32	even	2
1254.2.g.b.835.17	yes	20	57.56	even	2
3762.2.g.k.2089.7		20	19.18	odd	2
3762.2.g.k.2089.8		20	11.10	odd	2
3762.2.g.l.2089.7		20	1.1	even	1	trivial
3762.2.g.l.2089.8		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} -1.24031 q^{5} -3.51276i q^{7} +1.00000 q^{8} -1.24031 q^{10} +(-0.393943 + 3.29315i) q^{11} -1.46033 q^{13} -3.51276i q^{14} +1.00000 q^{16} +3.83935i q^{17} +(-3.98747 + 1.76071i) q^{19} -1.24031 q^{20} +(-0.393943 + 3.29315i) q^{22} +2.48371 q^{23} -3.46162 q^{25} -1.46033 q^{26} -3.51276i q^{28} -5.89617 q^{29} +4.18521i q^{31} +1.00000 q^{32} +3.83935i q^{34} +4.35693i q^{35} +0.866253i q^{37} +(-3.98747 + 1.76071i) q^{38} -1.24031 q^{40} +11.4391 q^{41} +0.0872418i q^{43} +(-0.393943 + 3.29315i) q^{44} +2.48371 q^{46} -9.68535 q^{47} -5.33951 q^{49} -3.46162 q^{50} -1.46033 q^{52} +2.65543i q^{53} +(0.488613 - 4.08453i) q^{55} -3.51276i q^{56} -5.89617 q^{58} -0.285318i q^{59} +7.00823i q^{61} +4.18521i q^{62} +1.00000 q^{64} +1.81127 q^{65} -8.14823i q^{67} +3.83935i q^{68} +4.35693i q^{70} +15.0087i q^{71} +16.4472i q^{73} +0.866253i q^{74} +(-3.98747 + 1.76071i) q^{76} +(11.5680 + 1.38383i) q^{77} +6.48850 q^{79} -1.24031 q^{80} +11.4391 q^{82} +10.0557i q^{83} -4.76199i q^{85} +0.0872418i q^{86} +(-0.393943 + 3.29315i) q^{88} -9.47873i q^{89} +5.12980i q^{91} +2.48371 q^{92} -9.68535 q^{94} +(4.94571 - 2.18383i) q^{95} -7.60274i q^{97} -5.33951 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} + 20 q^{4} - 4 q^{5} + 20 q^{8} - 4 q^{10} - 6 q^{11} + 4 q^{13} + 20 q^{16} + 2 q^{19} - 4 q^{20} - 6 q^{22} + 8 q^{23} + 32 q^{25} + 4 q^{26} - 4 q^{29} + 20 q^{32} + 2 q^{38} - 4 q^{40}+ \cdots - 36 q^{98}+O(q^{100}) \) 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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