LMFDB - Embedded newform 1512.2.s.o.865.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.s (of order $3$, degree $2$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} + 28x^{5} + 14x^{4} - 52x^{3} + 306x^{2} + 1052x + 1051 $ x^8 - 3x^7 + 4x^6 + 28x^5 + 14x^4 - 52x^3 + 306x^2 + 1052*x + 1051
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.2
Root			$1.89574 + 2.48951i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.o.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0144658 + 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +O(q^{10})$	$q+(0.0144658 + 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +(1.88127 - 3.25845i) q^{11} -2.97107 q^{13} +(-0.708111 + 1.22648i) q^{17} +(-3.81196 - 6.60250i) q^{19} +(2.98512 + 5.17037i) q^{23} +(2.49958 - 4.32940i) q^{25} -9.99916 q^{29} +(4.27700 - 7.40799i) q^{31} +(-0.0753332 - 0.0135696i) q^{35} +(-0.737043 - 1.27660i) q^{37} +4.38729 q^{41} +3.76254 q^{43} +(-2.07491 - 3.59386i) q^{47} +(-1.16471 - 6.90242i) q^{49} +(-3.60385 + 6.24204i) q^{53} +0.108856 q^{55} +(6.93027 - 12.0036i) q^{59} +(-5.61831 - 9.73120i) q^{61} +(-0.0429788 - 0.0744414i) q^{65} +(-2.77742 + 4.81064i) q^{67} +11.5661 q^{71} +(2.17918 - 3.77445i) q^{73} +(3.37024 + 9.36688i) q^{77} +(-7.04556 - 12.2033i) q^{79} -6.62475 q^{83} -0.0409735 q^{85} +(-2.14423 - 3.71391i) q^{89} +(5.07491 - 6.00300i) q^{91} +(0.110286 - 0.191020i) q^{95} -6.77458 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} - 4 q^{7}+O(q^{10}) $ 8 * q + 2 * q^5 - 4 * q^7	$ 8 q + 2 q^{5} - 4 q^{7} + q^{11} - 20 q^{13} + 4 q^{17} + q^{19} - 12 q^{23} - 14 q^{25} - 12 q^{29} + 8 q^{31} - 9 q^{35} + 12 q^{41} + 2 q^{43} + 9 q^{47} + 6 q^{49} - 7 q^{53} - 36 q^{55} + 4 q^{59} - 25 q^{61} + 28 q^{65} - 30 q^{67} + 22 q^{71} + 4 q^{73} + 37 q^{77} + 7 q^{79} - 58 q^{83} + 14 q^{85} - 9 q^{89} + 15 q^{91} + 4 q^{95} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 4 * q^7 + q^11 - 20 * q^13 + 4 * q^17 + q^19 - 12 * q^23 - 14 * q^25 - 12 * q^29 + 8 * q^31 - 9 * q^35 + 12 * q^41 + 2 * q^43 + 9 * q^47 + 6 * q^49 - 7 * q^53 - 36 * q^55 + 4 * q^59 - 25 * q^61 + 28 * q^65 - 30 * q^67 + 22 * q^71 + 4 * q^73 + 37 * q^77 + 7 * q^79 - 58 * q^83 + 14 * q^85 - 9 * q^89 + 15 * q^91 + 4 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0144658	+	0.0250554i	0.00646928	+	0.0112051i	0.869242	−	0.494387i	$-0.164607\pi$
$5$	0.0144658	+	0.0250554i	0.00646928	+	0.0112051i	−0.862773	+	0.505592i	$0.831274\pi$
$6$		0			0
$7$	−1.70811	+	2.02048i	−0.645605	+	0.763671i
$7$	−1.70811	+	2.02048i	−0.645605	+	0.763671i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.88127	−	3.25845i	0.567224	−	0.982461i	−0.429615	−	0.903012i	$-0.641351\pi$
$11$	1.88127	−	3.25845i	0.567224	−	0.982461i	0.996839	−	0.0794487i	$-0.0253160\pi$
$12$		0			0
$13$	−2.97107			−0.824026			−0.412013	−	0.911178i	$-0.635174\pi$
$13$	−2.97107			−0.824026			−0.412013	+	0.911178i	$0.635174\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.708111	+	1.22648i	−0.171742	+	0.297466i	−0.939029	−	0.343838i	$-0.888273\pi$
$17$	−0.708111	+	1.22648i	−0.171742	+	0.297466i	0.767287	+	0.641304i	$0.221606\pi$
$18$		0			0
$19$	−3.81196	−	6.60250i	−0.874523	−	1.51472i	−0.857270	−	0.514867i	$-0.827841\pi$
$19$	−3.81196	−	6.60250i	−0.874523	−	1.51472i	−0.0172529	−	0.999851i	$-0.505492\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.98512	+	5.17037i	0.622440	+	1.07810i	0.989030	+	0.147715i	$0.0471917\pi$
$23$	2.98512	+	5.17037i	0.622440	+	1.07810i	−0.366590	+	0.930382i	$0.619475\pi$
$24$		0			0
$25$	2.49958	−	4.32940i	0.499916	−	0.865880i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.99916			−1.85680			−0.928399	−	0.371585i	$-0.878814\pi$
$29$	−9.99916			−1.85680			−0.928399	+	0.371585i	$0.878814\pi$
$30$		0			0
$31$	4.27700	−	7.40799i	0.768173	−	1.33051i	−0.170380	−	0.985378i	$-0.554500\pi$
$31$	4.27700	−	7.40799i	0.768173	−	1.33051i	0.938553	−	0.345136i	$-0.112167\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0753332	−	0.0135696i	−0.0127336	−	0.00229368i
$36$		0			0
$37$	−0.737043	−	1.27660i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$37$	−0.737043	−	1.27660i	−0.121169	−	0.209871i	−0.920229	+	0.391380i	$0.871998\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.38729			0.685180			0.342590	−	0.939485i	$-0.388696\pi$
$41$	4.38729			0.685180			0.342590	+	0.939485i	$0.388696\pi$
$42$		0			0
$43$	3.76254			0.573782			0.286891	−	0.957963i	$-0.407378\pi$
$43$	3.76254			0.573782			0.286891	+	0.957963i	$0.407378\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.07491	−	3.59386i	−0.302657	−	0.524218i	0.674080	−	0.738659i	$-0.264540\pi$
$47$	−2.07491	−	3.59386i	−0.302657	−	0.524218i	−0.976737	+	0.214441i	$0.931207\pi$
$48$		0			0
$49$	−1.16471	−	6.90242i	−0.166388	−	0.986060i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.60385	+	6.24204i	−0.495026	+	0.857411i	−0.999984	−	0.00573358i	$-0.998175\pi$
$53$	−3.60385	+	6.24204i	−0.495026	+	0.857411i	0.504957	+	0.863144i	$0.331508\pi$
$54$		0			0
$55$	0.108856			0.0146781
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.93027	−	12.0036i	0.902244	−	1.56273i	0.0776699	−	0.996979i	$-0.475252\pi$
$59$	6.93027	−	12.0036i	0.902244	−	1.56273i	0.824574	−	0.565754i	$-0.191415\pi$
$60$		0			0
$61$	−5.61831	−	9.73120i	−0.719351	−	1.24595i	−0.961257	−	0.275653i	$-0.911106\pi$
$61$	−5.61831	−	9.73120i	−0.719351	−	1.24595i	0.241906	−	0.970300i	$-0.422227\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0429788	−	0.0744414i	−0.00533086	−	0.00923332i
$66$		0			0
$67$	−2.77742	+	4.81064i	−0.339316	+	0.587713i	−0.984304	−	0.176480i	$-0.943529\pi$
$67$	−2.77742	+	4.81064i	−0.339316	+	0.587713i	0.644988	+	0.764193i	$0.276862\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	11.5661			1.37264			0.686319	−	0.727301i	$-0.259225\pi$
$71$	11.5661			1.37264			0.686319	+	0.727301i	$0.259225\pi$
$72$		0			0
$73$	2.17918	−	3.77445i	0.255054	−	0.441766i	−0.709856	−	0.704346i	$-0.751240\pi$
$73$	2.17918	−	3.77445i	0.255054	−	0.441766i	0.964910	+	0.262580i	$0.0845735\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.37024	+	9.36688i	0.384074	+	1.06745i
$78$		0			0
$79$	−7.04556	−	12.2033i	−0.792688	−	1.37298i	−0.924297	−	0.381674i	$-0.875348\pi$
$79$	−7.04556	−	12.2033i	−0.792688	−	1.37298i	0.131609	−	0.991302i	$-0.457986\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.62475			−0.727161			−0.363580	−	0.931563i	$-0.618446\pi$
$83$	−6.62475			−0.727161			−0.363580	+	0.931563i	$0.618446\pi$
$84$		0			0
$85$	−0.0409735			−0.00444420
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.14423	−	3.71391i	−0.227288	−	0.393674i	0.729716	−	0.683751i	$-0.239652\pi$
$89$	−2.14423	−	3.71391i	−0.227288	−	0.393674i	−0.957003	+	0.290077i	$0.906319\pi$
$90$		0			0
$91$	5.07491	−	6.00300i	0.531996	−	0.629285i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.110286	−	0.191020i	0.0113151	−	0.0195983i
$96$		0			0
$97$	−6.77458			−0.687854			−0.343927	−	0.938996i	$-0.611757\pi$
$97$	−6.77458			−0.687854			−0.343927	+	0.938996i	$0.611757\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.37282	+	5.84190i	−0.335609	+	0.581291i	−0.983602	−	0.180355i	$-0.942275\pi$
$101$	−3.37282	+	5.84190i	−0.335609	+	0.581291i	0.647993	+	0.761646i	$0.275609\pi$
$102$		0			0
$103$	−1.38169	−	2.39315i	−0.136142	−	0.235804i	0.789891	−	0.613247i	$-0.210137\pi$
$103$	−1.38169	−	2.39315i	−0.136142	−	0.235804i	−0.926033	+	0.377442i	$0.876804\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.90134	−	15.4176i	−0.860525	−	1.49047i	−0.871423	−	0.490532i	$-0.836802\pi$
$107$	−8.90134	−	15.4176i	−0.860525	−	1.49047i	0.0108984	−	0.999941i	$-0.496531\pi$
$108$		0			0
$109$	−5.41622	+	9.38117i	−0.518780	+	0.898553i	0.480982	+	0.876731i	$0.340280\pi$
$109$	−5.41622	+	9.38117i	−0.518780	+	0.898553i	−0.999762	+	0.0218227i	$0.993053\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.879102			−0.0826990			−0.0413495	−	0.999145i	$-0.513166\pi$
$113$	−0.879102			−0.0826990			−0.0413495	+	0.999145i	$0.513166\pi$
$114$		0			0
$115$	−0.0863639	+	0.149587i	−0.00805348	+	0.0139490i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.26856	−	3.52570i	−0.116289	−	0.323200i
$120$		0			0
$121$	−1.57835	−	2.73378i	−0.143486	−	0.248526i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.289291			0.0258750
$126$		0			0
$127$	−1.27156			−0.112833			−0.0564165	−	0.998407i	$-0.517967\pi$
$127$	−1.27156			−0.112833			−0.0564165	+	0.998407i	$0.517967\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.31998	+	14.4106i	0.726920	+	1.25906i	0.958179	+	0.286171i	$0.0923824\pi$
$131$	8.31998	+	14.4106i	0.726920	+	1.25906i	−0.231258	+	0.972892i	$0.574284\pi$
$132$		0			0
$133$	19.8515	+	3.57581i	1.72134	+	0.310062i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.44515	+	4.23513i	−0.208904	+	0.361832i	−0.951369	−	0.308052i	$-0.900323\pi$
$137$	−2.44515	+	4.23513i	−0.208904	+	0.361832i	0.742466	+	0.669884i	$0.233656\pi$
$138$		0			0
$139$	−8.61187			−0.730449			−0.365225	−	0.930919i	$-0.619008\pi$
$139$	−8.61187			−0.730449			−0.365225	+	0.930919i	$0.619008\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.58938	+	9.68109i	−0.467407	+	0.809573i
$144$		0			0
$145$	−0.144645	−	0.250533i	−0.0120122	−	0.0208057i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.95920	+	8.58959i	0.406274	+	0.703686i	0.994469	−	0.105033i	$-0.0334947\pi$
$149$	4.95920	+	8.58959i	0.406274	+	0.703686i	−0.588195	+	0.808719i	$0.700161\pi$
$150$		0			0
$151$	−4.73704	+	8.20480i	−0.385495	+	0.667697i	−0.991838	−	0.127506i	$-0.959303\pi$
$151$	−4.73704	+	8.20480i	−0.385495	+	0.667697i	0.606343	+	0.795203i	$0.292636\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.247481			0.0198781
$156$		0			0
$157$	5.83745	−	10.1108i	0.465880	−	0.806927i	−0.533361	−	0.845888i	$-0.679071\pi$
$157$	5.83745	−	10.1108i	0.465880	−	0.806927i	0.999241	+	0.0389606i	$0.0124047\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−15.5456	−	2.80019i	−1.22516	−	0.220686i
$162$		0			0
$163$	−6.36680	−	11.0276i	−0.498687	−	0.863750i	0.501312	−	0.865266i	$-0.332851\pi$
$163$	−6.36680	−	11.0276i	−0.498687	−	0.863750i	−0.999999	+	0.00151597i	$0.999517\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.8597			1.53679			0.768395	−	0.639976i	$-0.221056\pi$
$167$	19.8597			1.53679			0.768395	+	0.639976i	$0.221056\pi$
$168$		0			0
$169$	−4.17275			−0.320981
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.55443	−	4.42440i	−0.194210	−	0.336381i	0.752432	−	0.658670i	$-0.228881\pi$
$173$	−2.55443	−	4.42440i	−0.194210	−	0.336381i	−0.946641	+	0.322290i	$0.895548\pi$
$174$		0			0
$175$	4.47793	+	12.4455i	0.338499	+	0.940789i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.98470	−	15.5620i	0.671548	−	1.16315i	−0.305917	−	0.952058i	$-0.598963\pi$
$179$	8.98470	−	15.5620i	0.671548	−	1.16315i	0.977465	−	0.211097i	$-0.0677035\pi$
$180$		0			0
$181$	−3.72157			−0.276622			−0.138311	−	0.990389i	$-0.544167\pi$
$181$	−3.72157			−0.276622			−0.138311	+	0.990389i	$0.544167\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0213238	−	0.0369338i	0.00156775	−	0.00271543i
$186$		0			0
$187$	2.66430	+	4.61469i	0.194833	+	0.337460i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.88127	−	4.99051i	−0.208481	−	0.361100i	0.742755	−	0.669563i	$-0.233519\pi$
$191$	−2.88127	−	4.99051i	−0.208481	−	0.361100i	−0.951236	+	0.308463i	$0.900185\pi$
$192$		0			0
$193$	−1.80635	+	3.12870i	−0.130024	+	0.225209i	−0.923686	−	0.383151i	$-0.874839\pi$
$193$	−1.80635	+	3.12870i	−0.130024	+	0.225209i	0.793661	+	0.608360i	$0.208172\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.44432			−0.459139			−0.229569	−	0.973292i	$-0.573732\pi$
$197$	−6.44432			−0.459139			−0.229569	+	0.973292i	$0.573732\pi$
$198$		0			0
$199$	1.29147	−	2.23689i	0.0915499	−	0.158569i	−0.816614	−	0.577185i	$-0.804151\pi$
$199$	1.29147	−	2.23689i	0.0915499	−	0.158569i	0.908163	+	0.418616i	$0.137485\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	17.0797	−	20.2032i	1.19876	−	1.41798i
$204$		0			0
$205$	0.0634655	+	0.109925i	0.00443262	+	0.00767753i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−28.6853			−1.98420
$210$		0			0
$211$	19.4162			1.33667			0.668334	−	0.743861i	$-0.267008\pi$
$211$	19.4162			1.33667			0.668334	+	0.743861i	$0.267008\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0544280	+	0.0942720i	0.00371196	+	0.00642930i
$216$		0			0
$217$	7.66213	+	21.2953i	0.520139	+	1.44562i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.10385	−	3.64397i	0.141520	−	0.245120i
$222$		0			0
$223$	11.5074			0.770589			0.385295	−	0.922794i	$-0.374100\pi$
$223$	11.5074			0.770589			0.385295	+	0.922794i	$0.374100\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.48595	+	2.57375i	−0.0986261	+	0.170826i	−0.911116	−	0.412150i	$-0.864778\pi$
$227$	−1.48595	+	2.57375i	−0.0986261	+	0.170826i	0.812490	+	0.582975i	$0.198111\pi$
$228$		0			0
$229$	−11.0775	−	19.1868i	−0.732023	−	1.26790i	−0.956017	−	0.293310i	$-0.905243\pi$
$229$	−11.0775	−	19.1868i	−0.732023	−	1.26790i	0.223995	−	0.974590i	$-0.428090\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.0056	+	17.3302i	0.655489	+	1.13534i	0.981771	+	0.190068i	$0.0608707\pi$
$233$	10.0056	+	17.3302i	0.655489	+	1.13534i	−0.326282	+	0.945272i	$0.605796\pi$
$234$		0			0
$235$	0.0600304	−	0.103976i	0.00391595	−	0.00678263i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	23.6930			1.53257			0.766286	−	0.642500i	$-0.222103\pi$
$239$	23.6930			1.53257			0.766286	+	0.642500i	$0.222103\pi$
$240$		0			0
$241$	−5.64983	+	9.78579i	−0.363938	+	0.630358i	−0.988605	−	0.150533i	$-0.951901\pi$
$241$	−5.64983	+	9.78579i	−0.363938	+	0.630358i	0.624668	+	0.780891i	$0.285234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.156095	−	0.129031i	0.00997253	−	0.00824350i
$246$		0			0
$247$	11.3256	+	19.6165i	0.720630	+	1.24817i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.76254			−0.300609			−0.150304	−	0.988640i	$-0.548025\pi$
$251$	−4.76254			−0.300609			−0.150304	+	0.988640i	$0.548025\pi$
$252$		0			0
$253$	22.4632			1.41225
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.3230	+	21.3440i	0.768687	+	1.33140i	0.938275	+	0.345890i	$0.112423\pi$
$257$	12.3230	+	21.3440i	0.768687	+	1.33140i	−0.169588	+	0.985515i	$0.554244\pi$
$258$		0			0
$259$	3.83829	+	0.691383i	0.238500	+	0.0429605i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.33787	+	9.24547i	−0.329147	+	0.570100i	−0.982343	−	0.187089i	$-0.940095\pi$
$263$	−5.33787	+	9.24547i	−0.329147	+	0.570100i	0.653196	+	0.757189i	$0.273428\pi$
$264$		0			0
$265$	−0.208530			−0.0128099
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.653264	−	1.13149i	0.0398302	−	0.0689880i	−0.845423	−	0.534097i	$-0.820652\pi$
$269$	0.653264	−	1.13149i	0.0398302	−	0.0689880i	0.885253	+	0.465109i	$0.153985\pi$
$270$		0			0
$271$	−9.83787	−	17.0397i	−0.597608	−	1.03509i	−0.993173	−	0.116650i	$-0.962785\pi$
$271$	−9.83787	−	17.0397i	−0.597608	−	1.03509i	0.395565	−	0.918438i	$-0.370549\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.40477	−	16.2895i	−0.567129	−	0.982296i
$276$		0			0
$277$	−14.3774	+	24.9024i	−0.863855	+	1.49624i	0.00432421	+	0.999991i	$0.498624\pi$
$277$	−14.3774	+	24.9024i	−0.863855	+	1.49624i	−0.868179	+	0.496250i	$0.834710\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.20853			−0.549335			−0.274667	−	0.961539i	$-0.588568\pi$
$281$	−9.20853			−0.549335			−0.274667	+	0.961539i	$0.588568\pi$
$282$		0			0
$283$	−11.2613	+	19.5051i	−0.669414	+	1.15946i	0.308654	+	0.951174i	$0.400121\pi$
$283$	−11.2613	+	19.5051i	−0.669414	+	1.15946i	−0.978068	+	0.208285i	$0.933212\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.49398	+	8.86445i	−0.442356	+	0.523252i
$288$		0			0
$289$	7.49716	+	12.9855i	0.441009	+	0.763850i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.30534			−0.193100			−0.0965501	−	0.995328i	$-0.530781\pi$
$293$	−3.30534			−0.193100			−0.0965501	+	0.995328i	$0.530781\pi$
$294$		0			0
$295$	0.401006			0.0233475
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.86898	−	15.3615i	−0.512907	−	0.888380i
$300$		0			0
$301$	−6.42683	+	7.60215i	−0.370437	+	0.438181i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.162546	−	0.281538i	0.00930737	−	0.0161208i
$306$		0			0
$307$	−14.2358			−0.812479			−0.406240	−	0.913767i	$-0.633160\pi$
$307$	−14.2358			−0.812479			−0.406240	+	0.913767i	$0.633160\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−14.9694	+	25.9278i	−0.848836	+	1.47023i	0.0334108	+	0.999442i	$0.489363\pi$
$311$	−14.9694	+	25.9278i	−0.848836	+	1.47023i	−0.882247	+	0.470786i	$0.843970\pi$
$312$		0			0
$313$	−5.47107	−	9.47617i	−0.309243	−	0.535625i	0.668954	−	0.743304i	$-0.266742\pi$
$313$	−5.47107	−	9.47617i	−0.309243	−	0.535625i	−0.978197	+	0.207679i	$0.933409\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.27700	−	9.14004i	−0.296386	−	0.513356i	0.678920	−	0.734212i	$-0.262448\pi$
$317$	−5.27700	−	9.14004i	−0.296386	−	0.513356i	−0.975306	+	0.220856i	$0.929115\pi$
$318$		0			0
$319$	−18.8111	+	32.5818i	−1.05322	+	1.82423i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	10.7972			0.600770
$324$		0			0
$325$	−7.42643	+	12.8630i	−0.411944	+	0.713508i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.8055	+	1.94638i	0.595727	+	0.107307i
$330$		0			0
$331$	15.1319	+	26.2093i	0.831727	+	1.44059i	0.896668	+	0.442704i	$0.145981\pi$
$331$	15.1319	+	26.2093i	0.831727	+	1.44059i	−0.0649412	+	0.997889i	$0.520686\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.160710			−0.00878053
$336$		0			0
$337$	26.8428			1.46222			0.731111	−	0.682259i	$-0.239002\pi$
$337$	26.8428			1.46222			0.731111	+	0.682259i	$0.239002\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−16.0924	−	27.8728i	−0.871452	−	1.50940i
$342$		0			0
$343$	15.9357	+	9.43682i	0.860447	+	0.509540i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.08938	+	15.7433i	−0.487944	+	0.845143i	−0.999904	−	0.0138661i	$-0.995586\pi$
$347$	−9.08938	+	15.7433i	−0.487944	+	0.845143i	0.511960	+	0.859009i	$0.328919\pi$
$348$		0			0
$349$	5.15586			0.275987			0.137993	−	0.990433i	$-0.455935\pi$
$349$	5.15586			0.275987			0.137993	+	0.990433i	$0.455935\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.1838	−	24.5670i	0.754926	−	1.30757i	−0.190485	−	0.981690i	$-0.561006\pi$
$353$	14.1838	−	24.5670i	0.754926	−	1.30757i	0.945411	−	0.325880i	$-0.105661\pi$
$354$		0			0
$355$	0.167312	+	0.289792i	0.00887998	+	0.0153806i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.9793	+	22.4808i	0.685020	+	1.18649i	0.973431	+	0.228982i	$0.0735397\pi$
$359$	12.9793	+	22.4808i	0.685020	+	1.18649i	−0.288411	+	0.957507i	$0.593127\pi$
$360$		0			0
$361$	−19.5620	+	33.8824i	−1.02958	+	1.78329i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.126094			0.00660006
$366$		0			0
$367$	9.91062	−	17.1657i	0.517330	−	0.896042i	−0.482467	−	0.875914i	$-0.660259\pi$
$367$	9.91062	−	17.1657i	0.517330	−	0.896042i	0.999797	−	0.0201281i	$-0.00640740\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.45618	−	17.9436i	−0.335188	−	0.931586i
$372$		0			0
$373$	−4.58294	−	7.93789i	−0.237296	−	0.411008i	0.722642	−	0.691223i	$-0.242928\pi$
$373$	−4.58294	−	7.93789i	−0.237296	−	0.411008i	−0.959937	+	0.280215i	$0.909594\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	29.7082			1.53005
$378$		0			0
$379$	6.12575			0.314658			0.157329	−	0.987546i	$-0.449712\pi$
$379$	6.12575			0.314658			0.157329	+	0.987546i	$0.449712\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.25795	+	7.37498i	0.217571	+	0.376844i	0.954065	−	0.299600i	$-0.0968533\pi$
$383$	4.25795	+	7.37498i	0.217571	+	0.376844i	−0.736494	+	0.676444i	$0.763520\pi$
$384$		0			0
$385$	−0.185938	+	0.219942i	−0.00947628	+	0.0112093i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.16773	+	5.48667i	−0.160610	+	0.278185i	−0.935088	−	0.354416i	$-0.884680\pi$
$389$	−3.16773	+	5.48667i	−0.160610	+	0.278185i	0.774477	+	0.632602i	$0.218013\pi$
$390$		0			0
$391$	−8.45517			−0.427596
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.203839	−	0.353059i	0.0102562	−	0.0177643i
$396$		0			0
$397$	15.6401	+	27.0895i	0.784956	+	1.35958i	0.929026	+	0.370015i	$0.120648\pi$
$397$	15.6401	+	27.0895i	0.784956	+	1.35958i	−0.144070	+	0.989567i	$0.546019\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.31454	−	2.27686i	−0.0656452	−	0.113701i	0.831335	−	0.555772i	$-0.187577\pi$
$401$	−1.31454	−	2.27686i	−0.0656452	−	0.113701i	−0.896980	+	0.442071i	$0.854244\pi$
$402$		0			0
$403$	−12.7073	+	22.0096i	−0.632994	+	1.09638i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.54630			−0.274920
$408$		0			0
$409$	6.89574	−	11.9438i	0.340972	−	0.590581i	−0.643641	−	0.765327i	$-0.722577\pi$
$409$	6.89574	−	11.9438i	0.340972	−	0.590581i	0.984614	+	0.174746i	$0.0559105\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.4154	+	34.5059i	0.610921	+	1.69793i
$414$		0			0
$415$	−0.0958321	−	0.165986i	−0.00470421	−	0.00814793i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.84532			−0.139003			−0.0695016	−	0.997582i	$-0.522141\pi$
$419$	−2.84532			−0.139003			−0.0695016	+	0.997582i	$0.522141\pi$
$420$		0			0
$421$	29.4374			1.43469			0.717347	−	0.696716i	$-0.245356\pi$
$421$	29.4374			1.43469			0.717347	+	0.696716i	$0.245356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.53996	+	6.13139i	0.171713	+	0.297416i
$426$		0			0
$427$	29.2584	+	5.27026i	1.41592	+	0.255046i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.36096	+	4.08930i	−0.113723	+	0.196975i	−0.917269	−	0.398269i	$-0.869611\pi$
$431$	−2.36096	+	4.08930i	−0.113723	+	0.196975i	0.803545	+	0.595243i	$0.202944\pi$
$432$		0			0
$433$	−3.83813			−0.184449			−0.0922243	−	0.995738i	$-0.529398\pi$
$433$	−3.83813			−0.184449			−0.0922243	+	0.995738i	$0.529398\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	22.7583	−	39.4185i	1.08868	−	1.88564i
$438$		0			0
$439$	−9.23018	−	15.9871i	−0.440533	−	0.763025i	0.557196	−	0.830381i	$-0.311877\pi$
$439$	−9.23018	−	15.9871i	−0.440533	−	0.763025i	−0.997729	+	0.0673558i	$0.978544\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−11.3001	−	19.5723i	−0.536883	−	0.929908i	−0.999070	−	0.0431258i	$-0.986268\pi$
$443$	−11.3001	−	19.5723i	−0.536883	−	0.929908i	0.462187	−	0.886783i	$-0.347065\pi$
$444$		0			0
$445$	0.0620357	−	0.107449i	0.00294078	−	0.00509357i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.0043			−0.944063			−0.472031	−	0.881582i	$-0.656479\pi$
$449$	−20.0043			−0.944063			−0.472031	+	0.881582i	$0.656479\pi$
$450$		0			0
$451$	8.25368	−	14.2958i	0.388650	−	0.673162i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.223820	+	0.0403163i	0.0104929	+	0.00189006i
$456$		0			0
$457$	−13.5196	−	23.4167i	−0.632423	−	1.09539i	−0.987055	−	0.160382i	$-0.948727\pi$
$457$	−13.5196	−	23.4167i	−0.632423	−	1.09539i	0.354632	−	0.935006i	$-0.384606\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	30.9557			1.44175			0.720875	−	0.693065i	$-0.243740\pi$
$461$	30.9557			1.44175			0.720875	+	0.693065i	$0.243740\pi$
$462$		0			0
$463$	3.96105			0.184086			0.0920428	−	0.995755i	$-0.470660\pi$
$463$	3.96105			0.184086			0.0920428	+	0.995755i	$0.470660\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5834	−	23.5271i	−0.628563	−	1.08870i	−0.987840	−	0.155472i	$-0.950310\pi$
$467$	−13.5834	−	23.5271i	−0.628563	−	1.08870i	0.359277	−	0.933231i	$-0.383023\pi$
$468$		0			0
$469$	−4.97567	−	13.8288i	−0.229755	−	0.638557i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.07835	−	12.2601i	0.325463	−	0.563718i
$474$		0			0
$475$	−38.1132			−1.74875
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.83788	+	15.3077i	−0.403813	+	0.699425i	−0.994183	−	0.107708i	$-0.965649\pi$
$479$	−8.83788	+	15.3077i	−0.403813	+	0.699425i	0.590369	+	0.807133i	$0.298982\pi$
$480$		0			0
$481$	2.18980	+	3.79285i	0.0998465	+	0.172939i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.0979995	−	0.169740i	−0.00444993	−	0.00770750i
$486$		0			0
$487$	6.79665	−	11.7722i	0.307986	−	0.533447i	−0.669936	−	0.742419i	$-0.733678\pi$
$487$	6.79665	−	11.7722i	0.307986	−	0.533447i	0.977922	+	0.208972i	$0.0670117\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−21.8256			−0.984974			−0.492487	−	0.870320i	$-0.663912\pi$
$491$	−21.8256			−0.984974			−0.492487	+	0.870320i	$0.663912\pi$
$492$		0			0
$493$	7.08052	−	12.2638i	0.318890	−	0.552334i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.7561	+	23.3690i	−0.886182	+	1.04824i
$498$		0			0
$499$	−10.6374	−	18.4245i	−0.476194	−	0.824792i	0.523434	−	0.852066i	$-0.324651\pi$
$499$	−10.6374	−	18.4245i	−0.476194	−	0.824792i	−0.999628	+	0.0272740i	$0.991317\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.2281			−1.21404			−0.607020	−	0.794687i	$-0.707635\pi$
$503$	−27.2281			−1.21404			−0.607020	+	0.794687i	$0.707635\pi$
$504$		0			0
$505$	−0.195162			−0.00868459
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.23879	+	16.0021i	0.409502	+	0.709279i	0.994834	−	0.101515i	$-0.0323691\pi$
$509$	9.23879	+	16.0021i	0.409502	+	0.709279i	−0.585332	+	0.810794i	$0.699036\pi$
$510$		0			0
$511$	3.90394	+	10.8502i	0.172700	+	0.479984i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0399743	−	0.0692376i	0.00176148	−	0.00305097i
$516$		0			0
$517$	−15.6139			−0.686698
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.93913	+	5.09073i	−0.128766	+	0.223029i	−0.923199	−	0.384323i	$-0.874435\pi$
$521$	−2.93913	+	5.09073i	−0.128766	+	0.223029i	0.794433	+	0.607352i	$0.207768\pi$
$522$		0			0
$523$	−6.22258	−	10.7778i	−0.272094	−	0.471281i	0.697304	−	0.716776i	$-0.254383\pi$
$523$	−6.22258	−	10.7778i	−0.272094	−	0.471281i	−0.969398	+	0.245495i	$0.921050\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.05719	+	10.4914i	0.263855	+	0.457011i
$528$		0			0
$529$	−6.32183	+	10.9497i	−0.274862	+	0.476075i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.0349			−0.564606
$534$		0			0
$535$	0.257529	−	0.446054i	0.0111340	−	0.0192846i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.6824	−	9.19015i	−1.06314	−	0.395848i
$540$		0			0
$541$	10.7362	+	18.5957i	0.461586	+	0.799490i	0.999040	−	0.0438031i	$-0.0139474\pi$
$541$	10.7362	+	18.5957i	0.461586	+	0.799490i	−0.537455	+	0.843293i	$0.680614\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.313399			−0.0134245
$546$		0			0
$547$	30.6741			1.31153			0.655764	−	0.754966i	$-0.272347\pi$
$547$	30.6741			1.31153			0.655764	+	0.754966i	$0.272347\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	38.1164	+	66.0195i	1.62381	+	2.81253i
$552$		0			0
$553$	36.6911	+	6.60910i	1.56027	+	0.281047i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.5857	−	35.6555i	0.872244	−	1.51077i	0.0125744	−	0.999921i	$-0.495997\pi$
$557$	20.5857	−	35.6555i	0.872244	−	1.51077i	0.859670	−	0.510850i	$-0.170669\pi$
$558$		0			0
$559$	−11.1788			−0.472811
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.56848	−	7.91283i	0.192538	−	0.333486i	−0.753552	−	0.657388i	$-0.771661\pi$
$563$	4.56848	−	7.91283i	0.192538	−	0.333486i	0.946091	+	0.323902i	$0.104995\pi$
$564$		0			0
$565$	−0.0127169	−	0.0220263i	−0.000535003	−	0.000926653i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.7123	+	20.2863i	0.491004	+	0.850445i	0.999946	−	0.0103562i	$-0.00329653\pi$
$569$	11.7123	+	20.2863i	0.491004	+	0.850445i	−0.508942	+	0.860801i	$0.669963\pi$
$570$		0			0
$571$	−9.91580	+	17.1747i	−0.414963	+	0.718738i	−0.995425	−	0.0955501i	$-0.969539\pi$
$571$	−9.91580	+	17.1747i	−0.414963	+	0.718738i	0.580461	+	0.814288i	$0.302872\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	29.8462			1.24467
$576$		0			0
$577$	15.2800	−	26.4658i	0.636116	−	1.10178i	−0.350162	−	0.936689i	$-0.613873\pi$
$577$	15.2800	−	26.4658i	0.636116	−	1.10178i	0.986278	−	0.165095i	$-0.0527932\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.3158	−	13.3852i	0.469459	−	0.555312i
$582$		0			0
$583$	13.5596	+	23.4859i	0.561582	+	0.972688i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.37643			−0.180635			−0.0903174	−	0.995913i	$-0.528788\pi$
$587$	−4.37643			−0.180635			−0.0903174	+	0.995913i	$0.528788\pi$
$588$		0			0
$589$	−65.2150			−2.68714
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−22.2762	−	38.5835i	−0.914773	−	1.58443i	−0.807234	−	0.590232i	$-0.799036\pi$
$593$	−22.2762	−	38.5835i	−0.914773	−	1.58443i	−0.107539	−	0.994201i	$-0.534297\pi$
$594$		0			0
$595$	0.0699872	−	0.0827862i	0.00286920	−	0.00339390i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.85577	+	11.8745i	−0.280119	+	0.485181i	−0.971414	−	0.237392i	$-0.923707\pi$
$599$	−6.85577	+	11.8745i	−0.280119	+	0.485181i	0.691295	+	0.722573i	$0.257041\pi$
$600$		0			0
$601$	−2.21373			−0.0902997			−0.0451499	−	0.998980i	$-0.514377\pi$
$601$	−2.21373			−0.0902997			−0.0451499	+	0.998980i	$0.514377\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.0456641	−	0.0790925i	0.00185651	−	0.00321557i
$606$		0			0
$607$	1.58980	+	2.75361i	0.0645280	+	0.111766i	0.896484	−	0.443075i	$-0.146113\pi$
$607$	1.58980	+	2.75361i	0.0645280	+	0.111766i	−0.831957	+	0.554841i	$0.812779\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.16471	+	10.6776i	0.249398	+	0.431969i
$612$		0			0
$613$	−6.15827	+	10.6664i	−0.248730	+	0.430814i	−0.963174	−	0.268880i	$-0.913347\pi$
$613$	−6.15827	+	10.6664i	−0.248730	+	0.430814i	0.714443	+	0.699693i	$0.246680\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−45.9405			−1.84949			−0.924747	−	0.380583i	$-0.875723\pi$
$617$	−45.9405			−1.84949			−0.924747	+	0.380583i	$0.875723\pi$
$618$		0			0
$619$	6.79648	−	11.7718i	0.273174	−	0.473151i	−0.696499	−	0.717558i	$-0.745260\pi$
$619$	6.79648	−	11.7718i	0.273174	−	0.473151i	0.969673	+	0.244407i	$0.0785933\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.1665	+	2.01139i	0.447375	+	0.0805848i
$624$		0			0
$625$	−12.4937	−	21.6398i	−0.499749	−	0.865590i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.08763			0.0832393
$630$		0			0
$631$	0.682615			0.0271745			0.0135872	−	0.999908i	$-0.495675\pi$
$631$	0.682615			0.0271745			0.0135872	+	0.999908i	$0.495675\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.0183941	−	0.0318596i	−0.000729949	−	0.00126431i
$636$		0			0
$637$	3.46044	+	20.5076i	0.137108	+	0.812540i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	23.7325	−	41.1059i	0.937378	−	1.62359i	0.167042	−	0.985950i	$-0.446579\pi$
$641$	23.7325	−	41.1059i	0.937378	−	1.62359i	0.770337	−	0.637637i	$-0.220088\pi$
$642$		0			0
$643$	34.4928			1.36026			0.680132	−	0.733090i	$-0.261923\pi$
$643$	34.4928			1.36026			0.680132	+	0.733090i	$0.261923\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.6587	+	21.9255i	−0.497665	+	0.861980i	−0.999996	−	0.00269463i	$-0.999142\pi$
$647$	−12.6587	+	21.9255i	−0.497665	+	0.861980i	0.502332	+	0.864675i	$0.332476\pi$
$648$		0			0
$649$	−26.0754	−	45.1639i	−1.02355	−	1.77284i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.19122	−	7.25941i	−0.164015	−	0.284083i	0.772290	−	0.635270i	$-0.219111\pi$
$653$	−4.19122	−	7.25941i	−0.164015	−	0.284083i	−0.936305	+	0.351188i	$0.885778\pi$
$654$		0			0
$655$	−0.240710	+	0.416922i	−0.00940531	+	0.0162905i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.4114			0.756160			0.378080	−	0.925773i	$-0.376584\pi$
$659$	19.4114			0.756160			0.378080	+	0.925773i	$0.376584\pi$
$660$		0			0
$661$	5.39833	−	9.35019i	0.209971	−	0.363680i	−0.741734	−	0.670694i	$-0.765996\pi$
$661$	5.39833	−	9.35019i	0.209971	−	0.363680i	0.951705	+	0.307014i	$0.0993298\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.197574	+	0.549115i	0.00766158	+	0.0212938i
$666$		0			0
$667$	−29.8487	−	51.6994i	−1.15574	−	2.00181i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−42.2782			−1.63213
$672$		0			0
$673$	−5.07074			−0.195463			−0.0977314	−	0.995213i	$-0.531159\pi$
$673$	−5.07074			−0.195463			−0.0977314	+	0.995213i	$0.531159\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.2737	−	31.6511i	−0.702317	−	1.21645i	−0.967651	−	0.252292i	$-0.918816\pi$
$677$	−18.2737	−	31.6511i	−0.702317	−	1.21645i	0.265334	−	0.964157i	$-0.414518\pi$
$678$		0			0
$679$	11.5717	−	13.6879i	0.444082	−	0.525295i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−5.34590	+	9.25937i	−0.204555	+	0.354300i	−0.949991	−	0.312278i	$-0.898908\pi$
$683$	−5.34590	+	9.25937i	−0.204555	+	0.354300i	0.745436	+	0.666577i	$0.232241\pi$
$684$		0			0
$685$	−0.141484			−0.00540583
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.7073	−	18.5455i	0.407915	−	0.706529i
$690$		0			0
$691$	−11.4686	−	19.8643i	−0.436288	−	0.755673i	0.561112	−	0.827740i	$-0.310374\pi$
$691$	−11.4686	−	19.8643i	−0.436288	−	0.755673i	−0.997400	+	0.0720673i	$0.977040\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.124577	−	0.215774i	−0.00472549	−	0.00818478i
$696$		0			0
$697$	−3.10669	+	5.38094i	−0.117674	+	0.203818i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	47.9789			1.81214			0.906069	−	0.423129i	$-0.139068\pi$
$701$	47.9789			1.81214			0.906069	+	0.423129i	$0.139068\pi$
$702$		0			0
$703$	−5.61915	+	9.73265i	−0.211930	+	0.367074i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.04232	−	16.7934i	−0.227245	−	0.631579i
$708$		0			0
$709$	−10.3095	−	17.8566i	−0.387183	−	0.670620i	0.604887	−	0.796312i	$-0.293218\pi$
$709$	−10.3095	−	17.8566i	−0.387183	−	0.670620i	−0.992069	+	0.125692i	$0.959885\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	51.0694			1.91256
$714$		0			0
$715$	−0.323419			−0.0120952
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.59498	+	4.49464i	0.0967765	+	0.167622i	0.910349	−	0.413842i	$-0.135813\pi$
$719$	2.59498	+	4.49464i	0.0967765	+	0.167622i	−0.813572	+	0.581464i	$0.802480\pi$
$720$		0			0
$721$	7.19541	+	1.29609i	0.267971	+	0.0482690i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−24.9937	+	43.2904i	−0.928244	+	1.60776i
$726$		0			0
$727$	−39.9339			−1.48107			−0.740534	−	0.672019i	$-0.765427\pi$
$727$	−39.9339			−1.48107			−0.740534	+	0.672019i	$0.765427\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.66430	+	4.61469i	−0.0985425	+	0.170681i
$732$		0			0
$733$	−24.6661	−	42.7229i	−0.911062	−	1.57800i	−0.812567	−	0.582867i	$-0.801931\pi$
$733$	−24.6661	−	42.7229i	−0.911062	−	1.57800i	−0.0984942	−	0.995138i	$-0.531403\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.4502	+	18.1002i	0.384937	+	0.666730i
$738$		0			0
$739$	−16.5576	+	28.6786i	−0.609081	+	1.05496i	0.382311	+	0.924034i	$0.375128\pi$
$739$	−16.5576	+	28.6786i	−0.609081	+	1.05496i	−0.991392	+	0.130926i	$0.958205\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.4157			−0.859040			−0.429520	−	0.903057i	$-0.641317\pi$
$743$	−23.4157			−0.859040			−0.429520	+	0.903057i	$0.641317\pi$
$744$		0			0
$745$	−0.143477	+	0.248510i	−0.00525660	+	0.00910470i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	46.3554	+	8.34991i	1.69379	+	0.305099i
$750$		0			0
$751$	−9.41364	−	16.3049i	−0.343508	−	0.594974i	0.641573	−	0.767062i	$-0.278282\pi$
$751$	−9.41364	−	16.3049i	−0.343508	−	0.594974i	−0.985082	+	0.172088i	$0.944949\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.274100			−0.00997551
$756$		0			0
$757$	27.0156			0.981897			0.490949	−	0.871188i	$-0.336650\pi$
$757$	27.0156			0.981897			0.490949	+	0.871188i	$0.336650\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.64356	−	16.7031i	−0.349579	−	0.605488i	0.636596	−	0.771198i	$-0.280342\pi$
$761$	−9.64356	−	16.7031i	−0.349579	−	0.605488i	−0.986175	+	0.165709i	$0.947009\pi$
$762$		0			0
$763$	−9.70300	−	26.9675i	−0.351272	−	0.976288i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−20.5903	+	35.6635i	−0.743473	+	1.28773i
$768$		0			0
$769$	−3.26639			−0.117789			−0.0588946	−	0.998264i	$-0.518758\pi$
$769$	−3.26639			−0.117789			−0.0588946	+	0.998264i	$0.518758\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.9963	+	19.0462i	−0.395510	+	0.685044i	−0.993166	−	0.116709i	$-0.962766\pi$
$773$	−10.9963	+	19.0462i	−0.395510	+	0.685044i	0.597656	+	0.801753i	$0.296099\pi$
$774$		0			0
$775$	−21.3814	−	37.0337i	−0.768044	−	1.33029i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.7242	−	28.9671i	−0.599205	−	1.03785i
$780$		0			0
$781$	21.7589	−	37.6875i	0.778593	−	1.34856i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.337773			0.0120556
$786$		0			0
$787$	−4.64724	+	8.04926i	−0.165656	+	0.286925i	−0.936888	−	0.349629i	$-0.886308\pi$
$787$	−4.64724	+	8.04926i	−0.165656	+	0.286925i	0.771232	+	0.636554i	$0.219641\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.50160	−	1.77621i	0.0533909	−	0.0631548i
$792$		0			0
$793$	16.6924	+	28.9121i	0.592764	+	1.02670i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.4137			−1.00647			−0.503233	−	0.864151i	$-0.667856\pi$
$797$	−28.4137			−1.00647			−0.503233	+	0.864151i	$0.667856\pi$
$798$		0			0
$799$	5.87708			0.207916
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.19925	−	14.2015i	−0.289345	−	0.501161i
$804$		0			0
$805$	−0.154718	−	0.430008i	−0.00545311	−	0.0151558i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.2425	−	24.6687i	0.500739	−	0.867305i	−0.499261	−	0.866452i	$-0.666395\pi$
$809$	14.2425	−	24.6687i	0.500739	−	0.867305i	1.00000		0.000853079i	$-0.000271543\pi$
$810$		0			0
$811$	48.5507			1.70484			0.852422	−	0.522854i	$-0.175133\pi$
$811$	48.5507			1.70484			0.852422	+	0.522854i	$0.175133\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.184201	−	0.319046i	0.00645229	−	0.0111757i
$816$		0			0
$817$	−14.3426	−	24.8422i	−0.501785	−	0.869118i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.56647	+	9.64141i	0.194271	+	0.336487i	0.946661	−	0.322230i	$-0.104433\pi$
$821$	5.56647	+	9.64141i	0.194271	+	0.336487i	−0.752390	+	0.658718i	$0.771099\pi$
$822$		0			0
$823$	19.5218	−	33.8128i	0.680488	−	1.17864i	−0.294344	−	0.955699i	$-0.595101\pi$
$823$	19.5218	−	33.8128i	0.680488	−	1.17864i	0.974832	−	0.222940i	$-0.0715654\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	48.0851			1.67208			0.836042	−	0.548666i	$-0.184864\pi$
$827$	48.0851			1.67208			0.836042	+	0.548666i	$0.184864\pi$
$828$		0			0
$829$	−1.64180	+	2.84369i	−0.0570222	+	0.0987653i	−0.893127	−	0.449804i	$-0.851494\pi$
$829$	−1.64180	+	2.84369i	−0.0570222	+	0.0987653i	0.836105	+	0.548569i	$0.184827\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.29046	+	3.45918i	0.321895	+	0.119853i
$834$		0			0
$835$	0.287286	+	0.497593i	0.00994193	+	0.0172199i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−14.1274			−0.487733			−0.243866	−	0.969809i	$-0.578416\pi$
$839$	−14.1274			−0.487733			−0.243866	+	0.969809i	$0.578416\pi$
$840$		0			0
$841$	70.9833			2.44770
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.0603620	−	0.104550i	−0.00207652	−	0.00359663i
$846$		0			0
$847$	8.21956	+	1.48057i	0.282427	+	0.0508731i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.40031	−	7.62157i	0.150841	−	0.261264i
$852$		0			0
$853$	18.5850			0.636337			0.318169	−	0.948034i	$-0.396932\pi$
$853$	18.5850			0.636337			0.318169	+	0.948034i	$0.396932\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.4244	−	26.7159i	0.526888	−	0.912597i	−0.472621	−	0.881266i	$-0.656692\pi$
$857$	15.4244	−	26.7159i	0.526888	−	0.912597i	0.999509	−	0.0313313i	$-0.00997470\pi$
$858$		0			0
$859$	−18.1410	−	31.4211i	−0.618962	−	1.07207i	−0.989675	−	0.143327i	$-0.954220\pi$
$859$	−18.1410	−	31.4211i	−0.618962	−	1.07207i	0.370713	−	0.928747i	$-0.379113\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−21.2584	−	36.8207i	−0.723646	−	1.25339i	−0.959529	−	0.281610i	$-0.909132\pi$
$863$	−21.2584	−	36.8207i	−0.723646	−	1.25339i	0.235883	−	0.971781i	$-0.424202\pi$
$864$		0			0
$865$	0.0739035	−	0.128005i	0.00251279	−	0.00435229i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−53.0184			−1.79853
$870$		0			0
$871$	8.25191	−	14.2927i	0.279605	−	0.484291i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.494141	+	0.584508i	−0.0167050	+	0.0197600i
$876$		0			0
$877$	−9.35752	−	16.2077i	−0.315981	−	0.547295i	0.663664	−	0.748030i	$-0.269000\pi$
$877$	−9.35752	−	16.2077i	−0.315981	−	0.547295i	−0.979646	+	0.200735i	$0.935667\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.832933			0.0280622			0.0140311	−	0.999902i	$-0.495534\pi$
$881$	0.832933			0.0280622			0.0140311	+	0.999902i	$0.495534\pi$
$882$		0			0
$883$	−1.67225			−0.0562756			−0.0281378	−	0.999604i	$-0.508958\pi$
$883$	−1.67225			−0.0562756			−0.0281378	+	0.999604i	$0.508958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.0691	+	46.8850i	0.908890	+	1.57424i	0.815608	+	0.578605i	$0.196403\pi$
$887$	27.0691	+	46.8850i	0.908890	+	1.57424i	0.0932821	+	0.995640i	$0.470264\pi$
$888$		0			0
$889$	2.17197	−	2.56918i	0.0728456	−	0.0861674i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−15.8190	+	27.3993i	−0.529362	+	0.916881i
$894$		0			0
$895$	0.519882			0.0173777
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−42.7665	+	74.0737i	−1.42634	+	2.47050i
$900$		0			0
$901$	−5.10385	−	8.84012i	−0.170034	−	0.294507i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.0538353	−	0.0932454i	−0.00178955	−	0.00309958i
$906$		0			0
$907$	8.74481	−	15.1465i	0.290367	−	0.502930i	−0.683530	−	0.729923i	$-0.739556\pi$
$907$	8.74481	−	15.1465i	0.290367	−	0.502930i	0.973896	+	0.226993i	$0.0728894\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	31.7838			1.05304			0.526522	−	0.850162i	$-0.323496\pi$
$911$	31.7838			1.05304			0.526522	+	0.850162i	$0.323496\pi$
$912$		0			0
$913$	−12.4629	+	21.5865i	−0.412463	+	0.714407i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−43.3279	−	7.80457i	−1.43081	−	0.257729i
$918$		0			0
$919$	−18.2038	−	31.5300i	−0.600489	−	1.04008i	−0.992747	−	0.120223i	$-0.961639\pi$
$919$	−18.2038	−	31.5300i	−0.600489	−	1.04008i	0.392258	−	0.919855i	$-0.371694\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−34.3635			−1.13109
$924$		0			0
$925$	−7.36919			−0.242298
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.9728	+	38.0581i	0.720905	+	1.24864i	0.960637	+	0.277805i	$0.0896070\pi$
$929$	21.9728	+	38.0581i	0.720905	+	1.24864i	−0.239732	+	0.970839i	$0.577060\pi$
$930$		0			0
$931$	−41.1334	+	34.0018i	−1.34809	+	1.11436i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.0770821	+	0.133510i	−0.00252085	+	0.00436625i
$936$		0			0
$937$	−51.0774			−1.66863			−0.834313	−	0.551291i	$-0.814135\pi$
$937$	−51.0774			−1.66863			−0.834313	+	0.551291i	$0.814135\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	22.0898	−	38.2607i	0.720107	−	1.24726i	−0.240850	−	0.970562i	$-0.577426\pi$
$941$	22.0898	−	38.2607i	0.720107	−	1.24726i	0.960957	−	0.276699i	$-0.0892406\pi$
$942$		0			0
$943$	13.0966	+	22.6839i	0.426483	+	0.738690i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.16730	−	10.6821i	−0.200410	−	0.347121i	0.748250	−	0.663416i	$-0.230894\pi$
$947$	−6.16730	−	10.6821i	−0.200410	−	0.347121i	−0.948661	+	0.316296i	$0.897561\pi$
$948$		0			0
$949$	−6.47449	+	11.2141i	−0.210171	+	0.364027i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	40.4140			1.30914			0.654570	−	0.756002i	$-0.272850\pi$
$953$	40.4140			1.30914			0.654570	+	0.756002i	$0.272850\pi$
$954$		0			0
$955$	0.0833595	−	0.144383i	0.00269745	−	0.00467212i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.38042	−	12.1745i	−0.141451	−	0.393134i
$960$		0			0
$961$	−21.0855	−	36.5212i	−0.680179	−	1.17810i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.104521			−0.00336466
$966$		0			0
$967$	−5.69549			−0.183155			−0.0915774	−	0.995798i	$-0.529191\pi$
$967$	−5.69549			−0.183155			−0.0915774	+	0.995798i	$0.529191\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.52609	−	13.0356i	−0.241524	−	0.418331i	0.719625	−	0.694363i	$-0.244314\pi$
$971$	−7.52609	−	13.0356i	−0.241524	−	0.418331i	−0.961149	+	0.276032i	$0.910980\pi$
$972$		0			0
$973$	14.7100	−	17.4002i	0.471582	−	0.557823i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.01262	−	15.6103i	0.288339	−	0.499418i	−0.685074	−	0.728473i	$-0.740230\pi$
$977$	9.01262	−	15.6103i	0.288339	−	0.499418i	0.973413	+	0.229055i	$0.0735636\pi$
$978$		0			0
$979$	−16.1355			−0.515692
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.99700	+	3.45890i	−0.0636943	+	0.110322i	−0.896114	−	0.443824i	$-0.853622\pi$
$983$	−1.99700	+	3.45890i	−0.0636943	+	0.110322i	0.832420	+	0.554146i	$0.186955\pi$
$984$		0			0
$985$	−0.0932219	−	0.161465i	−0.00297030	−	0.00514471i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	11.2316	+	19.4537i	0.357145	+	0.618593i
$990$		0			0
$991$	4.18202	−	7.24347i	0.132846	−	0.230097i	−0.791926	−	0.610617i	$-0.790922\pi$
$991$	4.18202	−	7.24347i	0.132846	−	0.230097i	0.924773	+	0.380520i	$0.124255\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.0747284			0.00236905
$996$		0			0
$997$	0.0375384	−	0.0650184i	0.00118885	−	0.00205915i	−0.865430	−	0.501029i	$-0.832955\pi$
$997$	0.0375384	−	0.0650184i	0.00118885	−	0.00205915i	0.866619	+	0.498970i	$0.166288\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.o.865.2	yes	8
3.2	odd	2		1512.2.s.n.865.3	✓	8
7.2	even	3	inner	1512.2.s.o.1297.2	yes	8
21.2	odd	6		1512.2.s.n.1297.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.n.865.3	✓	8	3.2	odd	2
1512.2.s.n.1297.3	yes	8	21.2	odd	6
1512.2.s.o.865.2	yes	8	1.1	even	1	trivial
1512.2.s.o.1297.2	yes	8	7.2	even	3	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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0144658 + 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +O(q^{10})\)	\(q+(0.0144658 + 0.0250554i) q^{5} +(-1.70811 + 2.02048i) q^{7} +(1.88127 - 3.25845i) q^{11} -2.97107 q^{13} +(-0.708111 + 1.22648i) q^{17} +(-3.81196 - 6.60250i) q^{19} +(2.98512 + 5.17037i) q^{23} +(2.49958 - 4.32940i) q^{25} -9.99916 q^{29} +(4.27700 - 7.40799i) q^{31} +(-0.0753332 - 0.0135696i) q^{35} +(-0.737043 - 1.27660i) q^{37} +4.38729 q^{41} +3.76254 q^{43} +(-2.07491 - 3.59386i) q^{47} +(-1.16471 - 6.90242i) q^{49} +(-3.60385 + 6.24204i) q^{53} +0.108856 q^{55} +(6.93027 - 12.0036i) q^{59} +(-5.61831 - 9.73120i) q^{61} +(-0.0429788 - 0.0744414i) q^{65} +(-2.77742 + 4.81064i) q^{67} +11.5661 q^{71} +(2.17918 - 3.77445i) q^{73} +(3.37024 + 9.36688i) q^{77} +(-7.04556 - 12.2033i) q^{79} -6.62475 q^{83} -0.0409735 q^{85} +(-2.14423 - 3.71391i) q^{89} +(5.07491 - 6.00300i) q^{91} +(0.110286 - 0.191020i) q^{95} -6.77458 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 8 * q + 2 * q^5 - 4 * q^7	\( 8 q + 2 q^{5} - 4 q^{7} + q^{11} - 20 q^{13} + 4 q^{17} + q^{19} - 12 q^{23} - 14 q^{25} - 12 q^{29} + 8 q^{31} - 9 q^{35} + 12 q^{41} + 2 q^{43} + 9 q^{47} + 6 q^{49} - 7 q^{53} - 36 q^{55} + 4 q^{59} - 25 q^{61} + 28 q^{65} - 30 q^{67} + 22 q^{71} + 4 q^{73} + 37 q^{77} + 7 q^{79} - 58 q^{83} + 14 q^{85} - 9 q^{89} + 15 q^{91} + 4 q^{95} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 4 * q^7 + q^11 - 20 * q^13 + 4 * q^17 + q^19 - 12 * q^23 - 14 * q^25 - 12 * q^29 + 8 * q^31 - 9 * q^35 + 12 * q^41 + 2 * q^43 + 9 * q^47 + 6 * q^49 - 7 * q^53 - 36 * q^55 + 4 * q^59 - 25 * q^61 + 28 * q^65 - 30 * q^67 + 22 * q^71 + 4 * q^73 + 37 * q^77 + 7 * q^79 - 58 * q^83 + 14 * q^85 - 9 * q^89 + 15 * q^91 + 4 * q^95 - 8 * q^97

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