LMFDB - Embedded newform 912.2.f.i.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(113,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("912.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.20322144469993472.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 - 2x^6 + 22x^5 - 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.5
Root			$-0.171092 - 1.72358i$ of defining polynomial
Character	$\chi$	$=$	912.113
Dual form			912.2.f.i.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.171092 - 1.72358i) q^{3} -3.81594i q^{5} -2.25057 q^{7} +(-2.94146 + 0.589781i) q^{9} +O(q^{10})$	\(q+(-0.171092 - 1.72358i) q^{3} -3.81594i q^{5} -2.25057 q^{7} +(-2.94146 + 0.589781i) q^{9} +2.65557i q^{11} -2.28678i q^{13} +(-6.57708 + 0.652876i) q^{15} -2.83491i q^{17} +(-2.80672 + 3.33502i) q^{19} +(0.385054 + 3.87904i) q^{21} -4.55438i q^{23} -9.56140 q^{25} +(1.51979 + 4.96893i) q^{27} +5.88291 q^{29} -2.46613i q^{31} +(4.57708 - 0.454346i) q^{33} +8.58804i q^{35} +8.73910i q^{37} +(-3.94146 + 0.391250i) q^{39} +5.54073 q^{41} -11.2458 q^{43} +(2.25057 + 11.2244i) q^{45} +0.494972i q^{47} -1.93494 q^{49} +(-4.88619 + 0.485030i) q^{51} -7.27125 q^{53} +10.1335 q^{55} +(6.22838 + 4.26700i) q^{57} +12.5359 q^{59} +7.44911 q^{61} +(6.61995 - 1.32734i) q^{63} -8.72623 q^{65} -4.50053i q^{67} +(-7.84984 + 0.779218i) q^{69} -2.61166 q^{71} -9.17963 q^{73} +(1.63588 + 16.4798i) q^{75} -5.97653i q^{77} +5.69557i q^{79} +(8.30432 - 3.46963i) q^{81} -11.2052i q^{83} -10.8178 q^{85} +(-1.00652 - 10.1397i) q^{87} -15.6553 q^{89} +5.14657i q^{91} +(-4.25057 + 0.421935i) q^{93} +(12.7262 + 10.7103i) q^{95} -18.9286i q^{97} +(-1.56620 - 7.81123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 2 * q^7 + 3 * q^9	$ 10 q + q^{3} + 2 q^{7} + 3 q^{9} - 10 q^{15} - 2 q^{19} + 5 q^{21} - 14 q^{25} + 10 q^{27} - 6 q^{29} - 10 q^{33} - 7 q^{39} - 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} - q^{51} - 26 q^{53} + 12 q^{55} + 9 q^{57} - 2 q^{59} - 4 q^{61} + 17 q^{63} + 32 q^{65} - 27 q^{69} - 8 q^{71} - 26 q^{73} - 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} + 4 q^{89} - 18 q^{93} + 8 q^{95} - 2 q^{99}+O(q^{100}) $ 10 * q + q^3 + 2 * q^7 + 3 * q^9 - 10 * q^15 - 2 * q^19 + 5 * q^21 - 14 * q^25 + 10 * q^27 - 6 * q^29 - 10 * q^33 - 7 * q^39 - 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 - q^51 - 26 * q^53 + 12 * q^55 + 9 * q^57 - 2 * q^59 - 4 * q^61 + 17 * q^63 + 32 * q^65 - 27 * q^69 - 8 * q^71 - 26 * q^73 - 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 + 4 * q^89 - 18 * q^93 + 8 * q^95 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.171092	−	1.72358i	−0.0987799	−	0.995109i
$3$	−0.171092	−	1.72358i	−0.0987799	−	0.995109i
$4$		0			0
$5$		−	3.81594i		−	1.70654i	−0.521469	−	0.853270i	$-0.674616\pi$
$5$		−	3.81594i		−	1.70654i	0.521469	−	0.853270i	$-0.325384\pi$
$6$		0			0
$7$	−2.25057			−0.850635			−0.425318	−	0.905044i	$-0.639838\pi$
$7$	−2.25057			−0.850635			−0.425318	+	0.905044i	$0.639838\pi$
$8$		0			0
$9$	−2.94146	+	0.589781i	−0.980485	+	0.196594i
$10$		0			0
$11$			2.65557i			0.800683i	0.916366	+	0.400342i	$0.131109\pi$
$11$			2.65557i			0.800683i	−0.916366	+	0.400342i	$0.868891\pi$
$12$		0			0
$13$		−	2.28678i		−	0.634240i	−0.948385	−	0.317120i	$-0.897284\pi$
$13$		−	2.28678i		−	0.634240i	0.948385	−	0.317120i	$-0.102716\pi$
$14$		0			0
$15$	−6.57708	+	0.652876i	−1.69819	+	0.168572i
$16$		0			0
$17$		−	2.83491i		−	0.687567i	−0.939049	−	0.343783i	$-0.888291\pi$
$17$		−	2.83491i		−	0.687567i	0.939049	−	0.343783i	$-0.111709\pi$
$18$		0			0
$19$	−2.80672	+	3.33502i	−0.643905	+	0.765106i
$19$	−2.80672	+	3.33502i	−0.643905	+	0.765106i
$20$		0			0
$21$	0.385054	+	3.87904i	0.0840257	+	0.846475i
$22$		0			0
$23$		−	4.55438i		−	0.949654i	−0.880079	−	0.474827i	$-0.842511\pi$
$23$		−	4.55438i		−	0.949654i	0.880079	−	0.474827i	$-0.157489\pi$
$24$		0			0
$25$	−9.56140			−1.91228
$26$		0			0
$27$	1.51979	+	4.96893i	0.292484	+	0.956270i
$28$		0			0
$29$	5.88291			1.09243			0.546215	−	0.837645i	$-0.316068\pi$
$29$	5.88291			1.09243			0.546215	+	0.837645i	$0.316068\pi$
$30$		0			0
$31$		−	2.46613i		−	0.442930i	−0.975168	−	0.221465i	$-0.928916\pi$
$31$		−	2.46613i		−	0.442930i	0.975168	−	0.221465i	$-0.0710838\pi$
$32$		0			0
$33$	4.57708	−	0.454346i	0.796767	−	0.0790914i
$34$		0			0
$35$			8.58804i			1.45164i
$36$		0			0
$37$			8.73910i			1.43670i	0.695682	+	0.718350i	$0.255102\pi$
$37$			8.73910i			1.43670i	−0.695682	+	0.718350i	$0.744898\pi$
$38$		0			0
$39$	−3.94146	+	0.391250i	−0.631138	+	0.0626502i
$40$		0			0
$41$	5.54073			0.865316			0.432658	−	0.901558i	$-0.357576\pi$
$41$	5.54073			0.865316			0.432658	+	0.901558i	$0.357576\pi$
$42$		0			0
$43$	−11.2458			−1.71496			−0.857482	−	0.514514i	$-0.827972\pi$
$43$	−11.2458			−1.71496			−0.857482	+	0.514514i	$0.827972\pi$
$44$		0			0
$45$	2.25057	+	11.2244i	0.335495	+	1.67324i
$46$		0			0
$47$			0.494972i			0.0721991i	0.999348	+	0.0360995i	$0.0114933\pi$
$47$			0.494972i			0.0721991i	−0.999348	+	0.0360995i	$0.988507\pi$
$48$		0			0
$49$	−1.93494			−0.276420
$50$		0			0
$51$	−4.88619	+	0.485030i	−0.684204	+	0.0679178i
$52$		0			0
$53$	−7.27125			−0.998783			−0.499391	−	0.866377i	$-0.666443\pi$
$53$	−7.27125			−0.998783			−0.499391	+	0.866377i	$0.666443\pi$
$54$		0			0
$55$	10.1335			1.36640
$56$		0			0
$57$	6.22838	+	4.26700i	0.824969	+	0.565178i
$58$		0			0
$59$	12.5359			1.63204			0.816019	−	0.578024i	$-0.196176\pi$
$59$	12.5359			1.63204			0.816019	+	0.578024i	$0.196176\pi$
$60$		0			0
$61$	7.44911			0.953761			0.476881	−	0.878968i	$-0.341767\pi$
$61$	7.44911			0.953761			0.476881	+	0.878968i	$0.341767\pi$
$62$		0			0
$63$	6.61995	−	1.32734i	0.834035	−	0.167230i
$64$		0			0
$65$	−8.72623			−1.08236
$66$		0			0
$67$		−	4.50053i		−	0.549827i	−0.961469	−	0.274914i	$-0.911351\pi$
$67$		−	4.50053i		−	0.549827i	0.961469	−	0.274914i	$-0.0886493\pi$
$68$		0			0
$69$	−7.84984	+	0.779218i	−0.945010	+	0.0938068i
$70$		0			0
$71$	−2.61166			−0.309947			−0.154974	−	0.987919i	$-0.549529\pi$
$71$	−2.61166			−0.309947			−0.154974	+	0.987919i	$0.549529\pi$
$72$		0			0
$73$	−9.17963			−1.07439			−0.537197	−	0.843457i	$-0.680517\pi$
$73$	−9.17963			−1.07439			−0.537197	+	0.843457i	$0.680517\pi$
$74$		0			0
$75$	1.63588	+	16.4798i	0.188895	+	1.90293i
$76$		0			0
$77$		−	5.97653i		−	0.681089i
$78$		0			0
$79$			5.69557i			0.640802i	0.947282	+	0.320401i	$0.103818\pi$
$79$			5.69557i			0.640802i	−0.947282	+	0.320401i	$0.896182\pi$
$80$		0			0
$81$	8.30432	−	3.46963i	0.922702	−	0.385514i
$82$		0			0
$83$		−	11.2052i		−	1.22993i	−0.788553	−	0.614967i	$-0.789169\pi$
$83$		−	11.2052i		−	1.22993i	0.788553	−	0.614967i	$-0.210831\pi$
$84$		0			0
$85$	−10.8178			−1.17336
$86$		0			0
$87$	−1.00652	−	10.1397i	−0.107910	−	1.08709i
$88$		0			0
$89$	−15.6553			−1.65946			−0.829729	−	0.558166i	$-0.811505\pi$
$89$	−15.6553			−1.65946			−0.829729	+	0.558166i	$0.811505\pi$
$90$		0			0
$91$			5.14657i			0.539507i
$92$		0			0
$93$	−4.25057	+	0.421935i	−0.440764	+	0.0437526i
$94$		0			0
$95$	12.7262	+	10.7103i	1.30568	+	1.09885i
$96$		0			0
$97$		−	18.9286i		−	1.92191i	−0.276701	−	0.960956i	$-0.589241\pi$
$97$		−	18.9286i		−	1.92191i	0.276701	−	0.960956i	$-0.410759\pi$
$98$		0			0
$99$	−1.56620	−	7.81123i	−0.157409	−	0.785058i
$100$		0			0
$101$		−	6.35529i		−	0.632375i	−0.948697	−	0.316187i	$-0.897597\pi$
$101$		−	6.35529i		−	0.632375i	0.948697	−	0.316187i	$-0.102403\pi$
$102$		0			0
$103$		−	9.42351i		−	0.928526i	−0.885697	−	0.464263i	$-0.846319\pi$
$103$		−	9.42351i		−	0.928526i	0.885697	−	0.464263i	$-0.153681\pi$
$104$		0			0
$105$	14.8022	−	1.46934i	1.44454	−	0.143393i
$106$		0			0
$107$	−15.6997			−1.51775			−0.758873	−	0.651239i	$-0.774250\pi$
$107$	−15.6997			−1.51775			−0.758873	+	0.651239i	$0.774250\pi$
$108$		0			0
$109$			7.91372i			0.757997i	0.925397	+	0.378999i	$0.123731\pi$
$109$			7.91372i			0.757997i	−0.925397	+	0.378999i	$0.876269\pi$
$110$		0			0
$111$	15.0625	−	1.49519i	1.42967	−	0.141917i
$112$		0			0
$113$	−14.3770			−1.35247			−0.676236	−	0.736685i	$-0.736390\pi$
$113$	−14.3770			−1.35247			−0.676236	+	0.736685i	$0.736390\pi$
$114$		0			0
$115$	−17.3793			−1.62062
$116$		0			0
$117$	1.34870	+	6.72647i	0.124688	+	0.621863i
$118$		0			0
$119$			6.38016i			0.584868i
$120$		0			0
$121$	3.94797			0.358907
$122$		0			0
$123$	−0.947973	−	9.54988i	−0.0854759	−	0.861084i
$124$		0			0
$125$			17.4060i			1.55684i
$126$		0			0
$127$		−	19.0356i		−	1.68914i	−0.535445	−	0.844570i	$-0.679856\pi$
$127$		−	19.0356i		−	1.68914i	0.535445	−	0.844570i	$-0.320144\pi$
$128$		0			0
$129$	1.92406	+	19.3830i	0.169404	+	1.70658i
$130$		0			0
$131$		−	4.97632i		−	0.434783i	−0.976085	−	0.217391i	$-0.930245\pi$
$131$		−	4.97632i		−	0.434783i	0.976085	−	0.217391i	$-0.0697548\pi$
$132$		0			0
$133$	6.31671	−	7.50569i	0.547728	−	0.650826i
$134$		0			0
$135$	18.9611	−	5.79944i	1.63191	−	0.499137i
$136$		0			0
$137$			18.9827i			1.62180i	0.585185	+	0.810900i	$0.301022\pi$
$137$			18.9827i			1.62180i	−0.585185	+	0.810900i	$0.698978\pi$
$138$		0			0
$139$	−3.00108			−0.254548			−0.127274	−	0.991868i	$-0.540623\pi$
$139$	−3.00108			−0.254548			−0.127274	+	0.991868i	$0.540623\pi$
$140$		0			0
$141$	0.853124	−	0.0846857i	0.0718460	−	0.00713182i
$142$		0			0
$143$	6.07270			0.507825
$144$		0			0
$145$		−	22.4488i		−	1.86427i
$146$		0			0
$147$	0.331052	+	3.33502i	0.0273047	+	0.275068i
$148$		0			0
$149$		−	7.61357i		−	0.623728i	−0.950127	−	0.311864i	$-0.899047\pi$
$149$		−	7.61357i		−	0.623728i	0.950127	−	0.311864i	$-0.100953\pi$
$150$		0			0
$151$		−	3.94125i		−	0.320735i	−0.987057	−	0.160367i	$-0.948732\pi$
$151$		−	3.94125i		−	0.320735i	0.987057	−	0.160367i	$-0.0512679\pi$
$152$		0			0
$153$	1.67198	+	8.33876i	0.135171	+	0.674149i
$154$		0			0
$155$	−9.41060			−0.755878
$156$		0			0
$157$	3.86987			0.308850			0.154425	−	0.988005i	$-0.450648\pi$
$157$	3.86987			0.308850			0.154425	+	0.988005i	$0.450648\pi$
$158$		0			0
$159$	1.24405	+	12.5326i	0.0986597	+	0.993898i
$160$		0			0
$161$			10.2500i			0.807809i
$162$		0			0
$163$	0.867596			0.0679554			0.0339777	−	0.999423i	$-0.489182\pi$
$163$	0.867596			0.0679554			0.0339777	+	0.999423i	$0.489182\pi$
$164$		0			0
$165$	−1.73376	−	17.4659i	−0.134973	−	1.35972i
$166$		0			0
$167$	−9.30604			−0.720123			−0.360061	−	0.932929i	$-0.617244\pi$
$167$	−9.30604			−0.720123			−0.360061	+	0.932929i	$0.617244\pi$
$168$		0			0
$169$	7.77062			0.597740
$170$		0			0
$171$	6.28890	−	11.4652i	0.480924	−	0.876762i
$172$		0			0
$173$	21.0436			1.59992			0.799959	−	0.600055i	$-0.204855\pi$
$173$	21.0436			1.59992			0.799959	+	0.600055i	$0.204855\pi$
$174$		0			0
$175$	21.5186			1.62665
$176$		0			0
$177$	−2.14480	−	21.6067i	−0.161213	−	1.62406i
$178$		0			0
$179$	16.5117			1.23414			0.617070	−	0.786909i	$-0.288320\pi$
$179$	16.5117			1.23414			0.617070	+	0.786909i	$0.288320\pi$
$180$		0			0
$181$			3.25684i			0.242079i	0.992648	+	0.121040i	$0.0386228\pi$
$181$			3.25684i			0.242079i	−0.992648	+	0.121040i	$0.961377\pi$
$182$		0			0
$183$	−1.27448	−	12.8391i	−0.0942125	−	0.949097i
$184$		0			0
$185$	33.3479			2.45179
$186$		0			0
$187$	7.52829			0.550523
$188$		0			0
$189$	−3.42040	−	11.1829i	−0.248798	−	0.813437i
$190$		0			0
$191$		−	11.3069i		−	0.818135i	−0.912504	−	0.409068i	$-0.865854\pi$
$191$		−	11.3069i		−	0.818135i	0.912504	−	0.409068i	$-0.134146\pi$
$192$		0			0
$193$			3.09844i			0.223031i	0.993763	+	0.111515i	$0.0355705\pi$
$193$			3.09844i			0.223031i	−0.993763	+	0.111515i	$0.964430\pi$
$194$		0			0
$195$	1.49299	+	15.0404i	0.106915	+	1.07706i
$196$		0			0
$197$		−	16.0935i		−	1.14662i	−0.819339	−	0.573309i	$-0.805659\pi$
$197$		−	16.0935i		−	1.14662i	0.819339	−	0.573309i	$-0.194341\pi$
$198$		0			0
$199$	−16.6477			−1.18012			−0.590060	−	0.807359i	$-0.700896\pi$
$199$	−16.6477			−1.18012			−0.590060	+	0.807359i	$0.700896\pi$
$200$		0			0
$201$	−7.75702	+	0.770004i	−0.547138	+	0.0543119i
$202$		0			0
$203$	−13.2399			−0.929259
$204$		0			0
$205$		−	21.1431i		−	1.47670i
$206$		0			0
$207$	2.68609	+	13.3965i	0.186696	+	0.931122i
$208$		0			0
$209$	−8.85636	−	7.45342i	−0.612607	−	0.515564i
$210$		0			0
$211$		−	1.08804i		−	0.0749035i	−0.999298	−	0.0374517i	$-0.988076\pi$
$211$		−	1.08804i		−	0.0749035i	0.999298	−	0.0374517i	$-0.0119240\pi$
$212$		0			0
$213$	0.446834	+	4.50141i	0.0306166	+	0.308432i
$214$		0			0
$215$			42.9132i			2.92666i
$216$		0			0
$217$			5.55019i			0.376772i
$218$		0			0
$219$	1.57056	+	15.8218i	0.106129	+	1.06914i
$220$		0			0
$221$	−6.48283			−0.436082
$222$		0			0
$223$		−	1.72681i		−	0.115636i	−0.998327	−	0.0578178i	$-0.981586\pi$
$223$		−	1.72681i		−	0.115636i	0.998327	−	0.0578178i	$-0.0184143\pi$
$224$		0			0
$225$	28.1244	−	5.63913i	1.87496	−	0.375942i
$226$		0			0
$227$	−3.56905			−0.236886			−0.118443	−	0.992961i	$-0.537790\pi$
$227$	−3.56905			−0.236886			−0.118443	+	0.992961i	$0.537790\pi$
$228$		0			0
$229$	−14.7138			−0.972315			−0.486157	−	0.873871i	$-0.661602\pi$
$229$	−14.7138			−0.972315			−0.486157	+	0.873871i	$0.661602\pi$
$230$		0			0
$231$	−10.3010	+	1.02254i	−0.677758	+	0.0672780i
$232$		0			0
$233$		−	10.1712i		−	0.666339i	−0.942867	−	0.333170i	$-0.891882\pi$
$233$		−	10.1712i		−	0.666339i	0.942867	−	0.333170i	$-0.108118\pi$
$234$		0			0
$235$	1.88878			0.123211
$236$		0			0
$237$	9.81677	−	0.974466i	0.637668	−	0.0632984i
$238$		0			0
$239$		−	29.2902i		−	1.89462i	−0.320311	−	0.947312i	$-0.603788\pi$
$239$		−	29.2902i		−	1.89462i	0.320311	−	0.947312i	$-0.396212\pi$
$240$		0			0
$241$			2.87075i			0.184922i	0.995716	+	0.0924608i	$0.0294733\pi$
$241$			2.87075i			0.184922i	−0.995716	+	0.0924608i	$0.970527\pi$
$242$		0			0
$243$	−7.40098	−	13.7195i	−0.474773	−	0.880108i
$244$		0			0
$245$			7.38361i			0.471721i
$246$		0			0
$247$	7.62647	+	6.41835i	0.485260	+	0.408390i
$248$		0			0
$249$	−19.3131	+	1.91712i	−1.22392	+	0.121493i
$250$		0			0
$251$			2.16863i			0.136883i	0.997655	+	0.0684413i	$0.0218026\pi$
$251$			2.16863i			0.136883i	−0.997655	+	0.0684413i	$0.978197\pi$
$252$		0			0
$253$	12.0945			0.760372
$254$		0			0
$255$	1.85085	+	18.6454i	0.115904	+	1.16762i
$256$		0			0
$257$	26.8626			1.67564			0.837820	−	0.545946i	$-0.183830\pi$
$257$	26.8626			1.67564			0.837820	+	0.545946i	$0.183830\pi$
$258$		0			0
$259$		−	19.6680i		−	1.22211i
$260$		0			0
$261$	−17.3043	+	3.46963i	−1.07111	+	0.214765i
$262$		0			0
$263$		−	6.20316i		−	0.382503i	−0.981541	−	0.191252i	$-0.938745\pi$
$263$		−	6.20316i		−	0.382503i	0.981541	−	0.191252i	$-0.0612547\pi$
$264$		0			0
$265$			27.7466i			1.70446i
$266$		0			0
$267$	2.67849	+	26.9832i	0.163921	+	1.65134i
$268$		0			0
$269$	−12.0218			−0.732979			−0.366490	−	0.930422i	$-0.619440\pi$
$269$	−12.0218			−0.732979			−0.366490	+	0.930422i	$0.619440\pi$
$270$		0			0
$271$	24.1381			1.46629			0.733143	−	0.680074i	$-0.238052\pi$
$271$	24.1381			1.46629			0.733143	+	0.680074i	$0.238052\pi$
$272$		0			0
$273$	8.87052	−	0.880536i	0.536868	−	0.0532924i
$274$		0			0
$275$		−	25.3909i		−	1.53113i
$276$		0			0
$277$	−1.68544			−0.101268			−0.0506342	−	0.998717i	$-0.516124\pi$
$277$	−1.68544			−0.101268			−0.0506342	+	0.998717i	$0.516124\pi$
$278$		0			0
$279$	1.45448	+	7.25401i	0.0870772	+	0.434286i
$280$		0			0
$281$	−5.07094			−0.302507			−0.151253	−	0.988495i	$-0.548331\pi$
$281$	−5.07094			−0.302507			−0.151253	+	0.988495i	$0.548331\pi$
$282$		0			0
$283$	−1.63234			−0.0970326			−0.0485163	−	0.998822i	$-0.515449\pi$
$283$	−1.63234			−0.0970326			−0.0485163	+	0.998822i	$0.515449\pi$
$284$		0			0
$285$	16.2826	−	23.7671i	0.964500	−	1.40784i
$286$		0			0
$287$	−12.4698			−0.736068
$288$		0			0
$289$	8.96329			0.527252
$290$		0			0
$291$	−32.6250	+	3.23854i	−1.91251	+	0.189846i
$292$		0			0
$293$	23.0567			1.34699			0.673493	−	0.739194i	$-0.264793\pi$
$293$	23.0567			1.34699			0.673493	+	0.739194i	$0.264793\pi$
$294$		0			0
$295$		−	47.8364i		−	2.78514i
$296$		0			0
$297$	−13.1953	+	4.03591i	−0.765669	+	0.234187i
$298$		0			0
$299$	−10.4149			−0.602309
$300$		0			0
$301$	25.3094			1.45881
$302$		0			0
$303$	−10.9538	+	1.08734i	−0.629282	+	0.0624659i
$304$		0			0
$305$		−	28.4254i		−	1.62763i
$306$		0			0
$307$			24.7799i			1.41426i	0.707083	+	0.707131i	$0.250011\pi$
$307$			24.7799i			1.41426i	−0.707083	+	0.707131i	$0.749989\pi$
$308$		0			0
$309$	−16.2422	+	1.61229i	−0.923985	+	0.0917198i
$310$		0			0
$311$		−	15.9484i		−	0.904348i	−0.891930	−	0.452174i	$-0.850649\pi$
$311$		−	15.9484i		−	0.904348i	0.891930	−	0.452174i	$-0.149351\pi$
$312$		0			0
$313$	−12.3639			−0.698851			−0.349426	−	0.936964i	$-0.613623\pi$
$313$	−12.3639			−0.698851			−0.349426	+	0.936964i	$0.613623\pi$
$314$		0			0
$315$	−5.06506	−	25.2613i	−0.285384	−	1.42331i
$316$		0			0
$317$	5.32435			0.299045			0.149523	−	0.988758i	$-0.452226\pi$
$317$	5.32435			0.299045			0.149523	+	0.988758i	$0.452226\pi$
$318$		0			0
$319$			15.6225i			0.874689i
$320$		0			0
$321$	2.68609	+	27.0597i	0.149923	+	1.51032i
$322$		0			0
$323$	9.45448	+	7.95678i	0.526061	+	0.442727i
$324$		0			0
$325$			21.8649i			1.21284i
$326$		0			0
$327$	13.6399	−	1.35397i	0.754290	−	0.0748749i
$328$		0			0
$329$		−	1.11397i		−	0.0614151i
$330$		0			0
$331$			28.7284i			1.57905i	0.613716	+	0.789527i	$0.289674\pi$
$331$			28.7284i			1.57905i	−0.613716	+	0.789527i	$0.710326\pi$
$332$		0			0
$333$	−5.15416	−	25.7057i	−0.282446	−	1.40866i
$334$		0			0
$335$	−17.1738			−0.938303
$336$		0			0
$337$		−	13.6377i		−	0.742893i	−0.928454	−	0.371446i	$-0.878862\pi$
$337$		−	13.6377i		−	0.742893i	0.928454	−	0.371446i	$-0.121138\pi$
$338$		0			0
$339$	2.45978	+	24.7799i	0.133597	+	1.34586i
$340$		0			0
$341$	6.54897			0.354646
$342$		0			0
$343$	20.1087			1.08577
$344$		0			0
$345$	2.97345	+	29.9545i	0.160085	+	1.61270i
$346$		0			0
$347$			12.6100i			0.676938i	0.940978	+	0.338469i	$0.109909\pi$
$347$			12.6100i			0.676938i	−0.940978	+	0.338469i	$0.890091\pi$
$348$		0			0
$349$	−21.8201			−1.16800			−0.584002	−	0.811752i	$-0.698514\pi$
$349$	−21.8201			−1.16800			−0.584002	+	0.811752i	$0.698514\pi$
$350$		0			0
$351$	11.3629	−	3.47544i	0.606505	−	0.185505i
$352$		0			0
$353$			35.9018i			1.91086i	0.295219	+	0.955430i	$0.404607\pi$
$353$			35.9018i			1.91086i	−0.295219	+	0.955430i	$0.595393\pi$
$354$		0			0
$355$			9.96595i			0.528938i
$356$		0			0
$357$	10.9967	−	1.09159i	0.582008	−	0.0577733i
$358$		0			0
$359$		−	14.5408i		−	0.767434i	−0.923451	−	0.383717i	$-0.874644\pi$
$359$		−	14.5408i		−	0.767434i	0.923451	−	0.383717i	$-0.125356\pi$
$360$		0			0
$361$	−3.24470	−	18.7209i	−0.170773	−	0.985310i
$362$		0			0
$363$	−0.675466	−	6.80465i	−0.0354528	−	0.357151i
$364$		0			0
$365$			35.0289i			1.83350i
$366$		0			0
$367$	−23.8603			−1.24550			−0.622748	−	0.782422i	$-0.713984\pi$
$367$	−23.8603			−1.24550			−0.622748	+	0.782422i	$0.713984\pi$
$368$		0			0
$369$	−16.2978	+	3.26782i	−0.848430	+	0.170116i
$370$		0			0
$371$	16.3644			0.849600
$372$		0			0
$373$		−	15.5769i		−	0.806543i	−0.915080	−	0.403271i	$-0.867873\pi$
$373$		−	15.5769i		−	0.806543i	0.915080	−	0.403271i	$-0.132127\pi$
$374$		0			0
$375$	30.0007	−	2.97803i	1.54923	−	0.153785i
$376$		0			0
$377$		−	13.4529i		−	0.692862i
$378$		0			0
$379$			5.11160i			0.262565i	0.991345	+	0.131283i	$0.0419095\pi$
$379$			5.11160i			0.262565i	−0.991345	+	0.131283i	$0.958090\pi$
$380$		0			0
$381$	−32.8095	+	3.25684i	−1.68088	+	0.166853i
$382$		0			0
$383$	9.56084			0.488536			0.244268	−	0.969708i	$-0.421452\pi$
$383$	9.56084			0.488536			0.244268	+	0.969708i	$0.421452\pi$
$384$		0			0
$385$	−22.8061			−1.16231
$386$		0			0
$387$	33.0789	−	6.63254i	1.68150	−	0.337151i
$388$		0			0
$389$			28.6239i			1.45129i	0.688070	+	0.725645i	$0.258458\pi$
$389$			28.6239i			1.45129i	−0.688070	+	0.725645i	$0.741542\pi$
$390$		0			0
$391$	−12.9113			−0.652951
$392$		0			0
$393$	−8.57708	+	0.851407i	−0.432656	+	0.0429478i
$394$		0			0
$395$	21.7340			1.09355
$396$		0			0
$397$	31.1771			1.56473			0.782367	−	0.622817i	$-0.214012\pi$
$397$	31.1771			1.56473			0.782367	+	0.622817i	$0.214012\pi$
$398$		0			0
$399$	−14.0174	−	9.60319i	−0.701747	−	0.480761i
$400$		0			0
$401$	−23.8686			−1.19194			−0.595972	−	0.803006i	$-0.703233\pi$
$401$	−23.8686			−1.19194			−0.595972	+	0.803006i	$0.703233\pi$
$402$		0			0
$403$	−5.63950			−0.280924
$404$		0			0
$405$	−13.2399	−	31.6888i	−0.657896	−	1.57463i
$406$		0			0
$407$	−23.2073			−1.15034
$408$		0			0
$409$		−	15.6493i		−	0.773806i	−0.922120	−	0.386903i	$-0.873545\pi$
$409$		−	15.6493i		−	0.773806i	0.922120	−	0.386903i	$-0.126455\pi$
$410$		0			0
$411$	32.7182	−	3.24778i	1.61387	−	0.160201i
$412$		0			0
$413$	−28.2130			−1.38827
$414$		0			0
$415$	−42.7585			−2.09893
$416$		0			0
$417$	0.513460	+	5.17259i	0.0251442	+	0.253303i
$418$		0			0
$419$		−	15.8833i		−	0.775952i	−0.921669	−	0.387976i	$-0.873174\pi$
$419$		−	15.8833i		−	0.775952i	0.921669	−	0.387976i	$-0.126826\pi$
$420$		0			0
$421$			11.2495i			0.548266i	0.961692	+	0.274133i	$0.0883908\pi$
$421$			11.2495i			0.548266i	−0.961692	+	0.274133i	$0.911609\pi$
$422$		0			0
$423$	−0.291925	−	1.45594i	−0.0141939	−	0.0707901i
$424$		0			0
$425$			27.1057i			1.31482i
$426$		0			0
$427$	−16.7647			−0.811303
$428$		0			0
$429$	−1.03899	−	10.4668i	−0.0501629	−	0.505341i
$430$		0			0
$431$	17.0654			0.822011			0.411005	−	0.911633i	$-0.365178\pi$
$431$	17.0654			0.822011			0.411005	+	0.911633i	$0.365178\pi$
$432$		0			0
$433$			3.09844i			0.148902i	0.997225	+	0.0744509i	$0.0237204\pi$
$433$			3.09844i			0.148902i	−0.997225	+	0.0744509i	$0.976280\pi$
$434$		0			0
$435$	−38.6924	+	3.84081i	−1.85516	+	0.184153i
$436$		0			0
$437$	15.1889	+	12.7829i	0.726586	+	0.611487i
$438$		0			0
$439$			25.0460i			1.19538i	0.801728	+	0.597689i	$0.203914\pi$
$439$			25.0460i			1.19538i	−0.801728	+	0.597689i	$0.796086\pi$
$440$		0			0
$441$	5.69153	−	1.14119i	0.271025	−	0.0543423i
$442$		0			0
$443$			14.1750i			0.673473i	0.941599	+	0.336736i	$0.109323\pi$
$443$			14.1750i			0.673473i	−0.941599	+	0.336736i	$0.890677\pi$
$444$		0			0
$445$			59.7397i			2.83193i
$446$		0			0
$447$	−13.1226	+	1.30262i	−0.620678	+	0.0616118i
$448$		0			0
$449$	29.2647			1.38109			0.690543	−	0.723291i	$-0.257372\pi$
$449$	29.2647			1.38109			0.690543	+	0.723291i	$0.257372\pi$
$450$		0			0
$451$			14.7138i			0.692844i
$452$		0			0
$453$	−6.79306	+	0.674316i	−0.319166	+	0.0316821i
$454$		0			0
$455$	19.6390			0.920690
$456$		0			0
$457$	−23.0600			−1.07870			−0.539351	−	0.842081i	$-0.681330\pi$
$457$	−23.0600			−1.07870			−0.539351	+	0.842081i	$0.681330\pi$
$458$		0			0
$459$	14.0865	−	4.30848i	0.657499	−	0.201103i
$460$		0			0
$461$		−	33.5397i		−	1.56210i	−0.624468	−	0.781050i	$-0.714684\pi$
$461$		−	33.5397i		−	1.56210i	0.624468	−	0.781050i	$-0.285316\pi$
$462$		0			0
$463$	0.0911044			0.00423398			0.00211699	−	0.999998i	$-0.499326\pi$
$463$	0.0911044			0.00423398			0.00211699	+	0.999998i	$0.499326\pi$
$464$		0			0
$465$	1.61008	+	16.2199i	0.0746655	+	0.752181i
$466$		0			0
$467$			15.5968i			0.721735i	0.932617	+	0.360867i	$0.117519\pi$
$467$			15.5968i			0.721735i	−0.932617	+	0.360867i	$0.882481\pi$
$468$		0			0
$469$			10.1288i			0.467703i
$470$		0			0
$471$	−0.662104	−	6.67004i	−0.0305081	−	0.307339i
$472$		0			0
$473$		−	29.8639i		−	1.37314i
$474$		0			0
$475$	26.8361	−	31.8875i	1.23133	−	1.46310i
$476$		0			0
$477$	21.3880	−	4.28844i	0.979291	−	0.196354i
$478$		0			0
$479$		−	24.6287i		−	1.12531i	−0.826690	−	0.562657i	$-0.809779\pi$
$479$		−	24.6287i		−	1.12531i	0.826690	−	0.562657i	$-0.190221\pi$
$480$		0			0
$481$	19.9844			0.911212
$482$		0			0
$483$	17.6666	−	1.75368i	0.803859	−	0.0797954i
$484$		0			0
$485$	−72.2306			−3.27982
$486$		0			0
$487$		−	2.30362i		−	0.104387i	−0.998637	−	0.0521936i	$-0.983379\pi$
$487$		−	2.30362i		−	0.104387i	0.998637	−	0.0521936i	$-0.0166213\pi$
$488$		0			0
$489$	−0.148439	−	1.49537i	−0.00671263	−	0.0676230i
$490$		0			0
$491$			12.9715i			0.585394i	0.956205	+	0.292697i	$0.0945528\pi$
$491$			12.9715i			0.585394i	−0.956205	+	0.292697i	$0.905447\pi$
$492$		0			0
$493$		−	16.6775i		−	0.751118i
$494$		0			0
$495$	−29.8072	+	5.97653i	−1.33973	+	0.268625i
$496$		0			0
$497$	5.87773			0.263652
$498$		0			0
$499$	−12.6523			−0.566396			−0.283198	−	0.959061i	$-0.591395\pi$
$499$	−12.6523			−0.566396			−0.283198	+	0.959061i	$0.591395\pi$
$500$		0			0
$501$	1.59219	+	16.0397i	0.0711337	+	0.716601i
$502$		0			0
$503$		−	22.6642i		−	1.01055i	−0.862959	−	0.505274i	$-0.831392\pi$
$503$		−	22.6642i		−	1.01055i	0.862959	−	0.505274i	$-0.168608\pi$
$504$		0			0
$505$	−24.2514			−1.07917
$506$		0			0
$507$	−1.32949	−	13.3933i	−0.0590447	−	0.594816i
$508$		0			0
$509$	−25.4307			−1.12720			−0.563598	−	0.826049i	$-0.690583\pi$
$509$	−25.4307			−1.12720			−0.563598	+	0.826049i	$0.690583\pi$
$510$		0			0
$511$	20.6594			0.913918
$512$		0			0
$513$	−20.8371	−	8.87782i	−0.919980	−	0.391965i
$514$		0			0
$515$	−35.9596			−1.58457
$516$		0			0
$517$	−1.31443			−0.0578086
$518$		0			0
$519$	−3.60039	−	36.2704i	−0.158040	−	1.59209i
$520$		0			0
$521$	−0.871132			−0.0381650			−0.0190825	−	0.999818i	$-0.506075\pi$
$521$	−0.871132			−0.0381650			−0.0190825	+	0.999818i	$0.506075\pi$
$522$		0			0
$523$			8.22847i			0.359806i	0.983684	+	0.179903i	$0.0575784\pi$
$523$			8.22847i			0.359806i	−0.983684	+	0.179903i	$0.942422\pi$
$524$		0			0
$525$	−3.68166	−	37.0890i	−0.160681	−	1.61870i
$526$		0			0
$527$	−6.99125			−0.304544
$528$		0			0
$529$	2.25761			0.0981568
$530$		0			0
$531$	−36.8739	+	7.39345i	−1.60019	+	0.320849i
$532$		0			0
$533$		−	12.6704i		−	0.548818i
$534$		0			0
$535$			59.9091i			2.59009i
$536$		0			0
$537$	−2.82501	−	28.4592i	−0.121908	−	1.22810i
$538$		0			0
$539$		−	5.13835i		−	0.221324i
$540$		0			0
$541$	−14.0921			−0.605868			−0.302934	−	0.953012i	$-0.597966\pi$
$541$	−14.0921			−0.605868			−0.302934	+	0.953012i	$0.597966\pi$
$542$		0			0
$543$	5.61343	−	0.557220i	0.240895	−	0.0239126i
$544$		0			0
$545$	30.1983			1.29355
$546$		0			0
$547$		−	16.2685i		−	0.695590i	−0.937571	−	0.347795i	$-0.886930\pi$
$547$		−	16.2685i		−	0.695590i	0.937571	−	0.347795i	$-0.113070\pi$
$548$		0			0
$549$	−21.9112	+	4.39335i	−0.935148	+	0.187503i
$550$		0			0
$551$	−16.5117	+	19.6196i	−0.703420	+	0.835824i
$552$		0			0
$553$		−	12.8183i		−	0.545089i
$554$		0			0
$555$	−5.70556	−	57.4778i	−0.242187	−	2.43980i
$556$		0			0
$557$		−	0.902307i		−	0.0382320i	−0.999817	−	0.0191160i	$-0.993915\pi$
$557$		−	0.902307i		−	0.0382320i	0.999817	−	0.0191160i	$-0.00608518\pi$
$558$		0			0
$559$			25.7167i			1.08770i
$560$		0			0
$561$	−1.28803	−	12.9756i	−0.0543806	−	0.547830i
$562$		0			0
$563$	12.2095			0.514571			0.257285	−	0.966335i	$-0.417172\pi$
$563$	12.2095			0.514571			0.257285	+	0.966335i	$0.417172\pi$
$564$		0			0
$565$			54.8617i			2.30805i
$566$		0			0
$567$	−18.6894	+	7.80864i	−0.784883	+	0.327932i
$568$		0			0
$569$	−24.4024			−1.02300			−0.511500	−	0.859283i	$-0.670910\pi$
$569$	−24.4024			−1.02300			−0.511500	+	0.859283i	$0.670910\pi$
$570$		0			0
$571$	5.61343			0.234915			0.117457	−	0.993078i	$-0.462526\pi$
$571$	5.61343			0.234915			0.117457	+	0.993078i	$0.462526\pi$
$572$		0			0
$573$	−19.4883	+	1.93451i	−0.814134	+	0.0808153i
$574$		0			0
$575$			43.5463i			1.81601i
$576$		0			0
$577$	−8.55433			−0.356121			−0.178061	−	0.984020i	$-0.556982\pi$
$577$	−8.55433			−0.356121			−0.178061	+	0.984020i	$0.556982\pi$
$578$		0			0
$579$	5.34042	−	0.530119i	0.221940	−	0.0220310i
$580$		0			0
$581$			25.2182i			1.04623i
$582$		0			0
$583$		−	19.3093i		−	0.799708i
$584$		0			0
$585$	25.6678	−	5.14657i	1.06123	−	0.212784i
$586$		0			0
$587$		−	20.8038i		−	0.858663i	−0.903147	−	0.429332i	$-0.858749\pi$
$587$		−	20.8038i		−	0.858663i	0.903147	−	0.429332i	$-0.141251\pi$
$588$		0			0
$589$	8.22458	+	6.92172i	0.338888	+	0.285205i
$590$		0			0
$591$	−27.7385	+	2.75348i	−1.14101	+	0.113263i
$592$		0			0
$593$		−	4.86257i		−	0.199682i	−0.995003	−	0.0998408i	$-0.968167\pi$
$593$		−	4.86257i		−	0.199682i	0.995003	−	0.0998408i	$-0.0318334\pi$
$594$		0			0
$595$	24.3463			0.998102
$596$		0			0
$597$	2.84828	+	28.6936i	0.116572	+	1.17435i
$598$		0			0
$599$	−0.185633			−0.00758475			−0.00379238	−	0.999993i	$-0.501207\pi$
$599$	−0.185633			−0.00758475			−0.00379238	+	0.999993i	$0.501207\pi$
$600$		0			0
$601$			16.6772i			0.680278i	0.940375	+	0.340139i	$0.110474\pi$
$601$			16.6772i			0.680278i	−0.940375	+	0.340139i	$0.889526\pi$
$602$		0			0
$603$	2.65433	+	13.2381i	0.108093	+	0.539098i
$604$		0			0
$605$		−	15.0652i		−	0.612489i
$606$		0			0
$607$			6.42863i			0.260930i	0.991453	+	0.130465i	$0.0416470\pi$
$607$			6.42863i			0.260930i	−0.991453	+	0.130465i	$0.958353\pi$
$608$		0			0
$609$	2.26524	+	22.8200i	0.0917921	+	0.924714i
$610$		0			0
$611$	1.13189			0.0457915
$612$		0			0
$613$	17.4017			0.702848			0.351424	−	0.936216i	$-0.385698\pi$
$613$	17.4017			0.702848			0.351424	+	0.936216i	$0.385698\pi$
$614$		0			0
$615$	−36.4418	+	3.61741i	−1.46947	+	0.145868i
$616$		0			0
$617$		−	25.5793i		−	1.02978i	−0.857255	−	0.514892i	$-0.827832\pi$
$617$		−	25.5793i		−	1.02978i	0.857255	−	0.514892i	$-0.172168\pi$
$618$		0			0
$619$	24.0223			0.965536			0.482768	−	0.875748i	$-0.339631\pi$
$619$	24.0223			0.965536			0.482768	+	0.875748i	$0.339631\pi$
$620$		0			0
$621$	22.6304	−	6.92172i	0.908126	−	0.277759i
$622$		0			0
$623$	35.2333			1.41159
$624$		0			0
$625$	18.6134			0.744537
$626$		0			0
$627$	−11.3313	+	16.5399i	−0.452529	+	0.660538i
$628$		0			0
$629$	24.7746			0.987827
$630$		0			0
$631$	16.6250			0.661832			0.330916	−	0.943660i	$-0.392642\pi$
$631$	16.6250			0.661832			0.330916	+	0.943660i	$0.392642\pi$
$632$		0			0
$633$	−1.87532	+	0.186154i	−0.0745371	+	0.00739896i
$634$		0			0
$635$	−72.6389			−2.88259
$636$		0			0
$637$			4.42478i			0.175316i
$638$		0			0
$639$	7.68209	−	1.54031i	0.303899	−	0.0609337i
$640$		0			0
$641$	17.3470			0.685165			0.342582	−	0.939488i	$-0.388698\pi$
$641$	17.3470			0.685165			0.342582	+	0.939488i	$0.388698\pi$
$642$		0			0
$643$	33.7478			1.33088			0.665442	−	0.746449i	$-0.268243\pi$
$643$	33.7478			1.33088			0.665442	+	0.746449i	$0.268243\pi$
$644$		0			0
$645$	73.9643	−	7.34210i	2.91234	−	0.289095i
$646$		0			0
$647$			24.6469i			0.968971i	0.874799	+	0.484485i	$0.160993\pi$
$647$			24.6469i			0.968971i	−0.874799	+	0.484485i	$0.839007\pi$
$648$		0			0
$649$			33.2900i			1.30675i
$650$		0			0
$651$	9.56620	−	0.949593i	0.374929	−	0.0372175i
$652$		0			0
$653$			16.5941i			0.649377i	0.945821	+	0.324688i	$0.105259\pi$
$653$			16.5941i			0.649377i	−0.945821	+	0.324688i	$0.894741\pi$
$654$		0			0
$655$	−18.9893			−0.741974
$656$		0			0
$657$	27.0015	−	5.41397i	1.05343	−	0.211219i
$658$		0			0
$659$	22.1807			0.864038			0.432019	−	0.901865i	$-0.357801\pi$
$659$	22.1807			0.864038			0.432019	+	0.901865i	$0.357801\pi$
$660$		0			0
$661$			9.15429i			0.356061i	0.984025	+	0.178030i	$0.0569725\pi$
$661$			9.15429i			0.356061i	−0.984025	+	0.178030i	$0.943027\pi$
$662$		0			0
$663$	1.10916	+	11.1737i	0.0430762	+	0.433949i
$664$		0			0
$665$	−28.6413	−	24.1042i	−1.11066	−	0.934720i
$666$		0			0
$667$		−	26.7930i		−	1.03743i
$668$		0			0
$669$	−2.97629	+	0.295443i	−0.115070	+	0.0114225i
$670$		0			0
$671$			19.7816i			0.763660i
$672$		0			0
$673$		−	28.9193i		−	1.11476i	−0.830259	−	0.557378i	$-0.811807\pi$
$673$		−	28.9193i		−	1.11476i	0.830259	−	0.557378i	$-0.188193\pi$
$674$		0			0
$675$	−14.5314	−	47.5099i	−0.559312	−	1.82866i
$676$		0			0
$677$	44.2974			1.70249			0.851244	−	0.524770i	$-0.175849\pi$
$677$	44.2974			1.70249			0.851244	+	0.524770i	$0.175849\pi$
$678$		0			0
$679$			42.6002i			1.63485i
$680$		0			0
$681$	0.610635	+	6.15154i	0.0233996	+	0.235727i
$682$		0			0
$683$	40.8231			1.56205			0.781026	−	0.624498i	$-0.214697\pi$
$683$	40.8231			1.56205			0.781026	+	0.624498i	$0.214697\pi$
$684$		0			0
$685$	72.4368			2.76767
$686$		0			0
$687$	2.51741	+	25.3604i	0.0960452	+	0.967560i
$688$		0			0
$689$			16.6278i			0.633468i
$690$		0			0
$691$	2.00931			0.0764379			0.0382190	−	0.999269i	$-0.487832\pi$
$691$	2.00931			0.0764379			0.0382190	+	0.999269i	$0.487832\pi$
$692$		0			0
$693$	3.52485	+	17.5797i	0.133898	+	0.667798i
$694$		0			0
$695$			11.4519i			0.434396i
$696$		0			0
$697$		−	15.7075i		−	0.594962i
$698$		0			0
$699$	−17.5309	+	1.74021i	−0.663081	+	0.0658210i
$700$		0			0
$701$		−	42.7737i		−	1.61554i	−0.589498	−	0.807770i	$-0.700674\pi$
$701$		−	42.7737i		−	1.61554i	0.589498	−	0.807770i	$-0.299326\pi$
$702$		0			0
$703$	−29.1451	−	24.5282i	−1.09923	−	0.925098i
$704$		0			0
$705$	−0.323156	−	3.25547i	−0.0121707	−	0.122608i
$706$		0			0
$707$			14.3030i			0.537920i
$708$		0			0
$709$	−7.35699			−0.276297			−0.138149	−	0.990411i	$-0.544115\pi$
$709$	−7.35699			−0.276297			−0.138149	+	0.990411i	$0.544115\pi$
$710$		0			0
$711$	−3.35914	−	16.7533i	−0.125978	−	0.628297i
$712$		0			0
$713$	−11.2317			−0.420630
$714$		0			0
$715$		−	23.1731i		−	0.866624i
$716$		0			0
$717$	−50.4840	+	5.01131i	−1.88536	+	0.187151i
$718$		0			0
$719$			28.5523i			1.06482i	0.846487	+	0.532410i	$0.178713\pi$
$719$			28.5523i			1.06482i	−0.846487	+	0.532410i	$0.821287\pi$
$720$		0			0
$721$			21.2083i			0.789837i
$722$		0			0
$723$	4.94797	−	0.491163i	0.184017	−	0.0182665i
$724$		0			0
$725$	−56.2489			−2.08903
$726$		0			0
$727$	−17.2105			−0.638301			−0.319151	−	0.947704i	$-0.603398\pi$
$727$	−17.2105			−0.638301			−0.319151	+	0.947704i	$0.603398\pi$
$728$		0			0
$729$	−22.3805	+	15.1035i	−0.828906	+	0.559388i
$730$		0			0
$731$			31.8807i			1.17915i
$732$		0			0
$733$	46.4961			1.71737			0.858686	−	0.512502i	$-0.171281\pi$
$733$	46.4961			1.71737			0.858686	+	0.512502i	$0.171281\pi$
$734$		0			0
$735$	12.7262	−	1.26327i	0.469414	−	0.0465966i
$736$		0			0
$737$	11.9515			0.440237
$738$		0			0
$739$	31.9538			1.17544			0.587720	−	0.809065i	$-0.300026\pi$
$739$	31.9538			1.17544			0.587720	+	0.809065i	$0.300026\pi$
$740$		0			0
$741$	9.75772	−	14.2430i	0.358459	−	0.523228i
$742$		0			0
$743$	−5.76126			−0.211360			−0.105680	−	0.994400i	$-0.533702\pi$
$743$	−5.76126			−0.211360			−0.105680	+	0.994400i	$0.533702\pi$
$744$		0			0
$745$	−29.0529			−1.06442
$746$		0			0
$747$	6.60863	+	32.9597i	0.241797	+	1.20593i
$748$		0			0
$749$	35.3332			1.29105
$750$		0			0
$751$			24.9383i			0.910010i	0.890489	+	0.455005i	$0.150363\pi$
$751$			24.9383i			0.910010i	−0.890489	+	0.455005i	$0.849637\pi$
$752$		0			0
$753$	3.73780	−	0.371034i	0.136213	−	0.0135212i
$754$		0			0
$755$	−15.0396			−0.547347
$756$		0			0
$757$	−46.0990			−1.67550			−0.837748	−	0.546056i	$-0.816128\pi$
$757$	−46.0990			−1.67550			−0.837748	+	0.546056i	$0.816128\pi$
$758$		0			0
$759$	−2.06926	−	20.8458i	−0.0751095	−	0.756653i
$760$		0			0
$761$		−	13.9040i		−	0.504019i	−0.967725	−	0.252009i	$-0.918909\pi$
$761$		−	13.9040i		−	0.504019i	0.967725	−	0.252009i	$-0.0810914\pi$
$762$		0			0
$763$		−	17.8104i		−	0.644779i
$764$		0			0
$765$	31.8202	−	6.38016i	1.15046	−	0.230675i
$766$		0			0
$767$		−	28.6670i		−	1.03510i
$768$		0			0
$769$	−10.8204			−0.390192			−0.195096	−	0.980784i	$-0.562502\pi$
$769$	−10.8204			−0.390192			−0.195096	+	0.980784i	$0.562502\pi$
$770$		0			0
$771$	−4.59597	−	46.2998i	−0.165520	−	1.66745i
$772$		0			0
$773$	27.2320			0.979469			0.489734	−	0.871872i	$-0.337094\pi$
$773$	27.2320			0.979469			0.489734	+	0.871872i	$0.337094\pi$
$774$		0			0
$775$			23.5797i			0.847006i
$776$		0			0
$777$	−33.8993	+	3.36503i	−1.21613	+	0.120720i
$778$		0			0
$779$	−15.5512	+	18.4784i	−0.557181	+	0.662058i
$780$		0			0
$781$		−	6.93544i		−	0.248170i
$782$		0			0
$783$	8.94081	+	29.2317i	0.319518	+	1.04466i
$784$		0			0
$785$		−	14.7672i		−	0.527064i
$786$		0			0
$787$			17.8222i			0.635292i	0.948209	+	0.317646i	$0.102892\pi$
$787$			17.8222i			0.635292i	−0.948209	+	0.317646i	$0.897108\pi$
$788$		0			0
$789$	−10.6916	+	1.06131i	−0.380633	+	0.0377837i
$790$		0			0
$791$	32.3564			1.15046
$792$		0			0
$793$		−	17.0345i		−	0.604913i
$794$		0			0
$795$	47.8236	−	4.74723i	1.69613	−	0.168367i
$796$		0			0
$797$	9.42768			0.333946			0.166973	−	0.985961i	$-0.446601\pi$
$797$	9.42768			0.333946			0.166973	+	0.985961i	$0.446601\pi$
$798$		0			0
$799$	1.40320			0.0496417
$800$		0			0
$801$	46.0494	−	9.23320i	1.62707	−	0.326239i
$802$		0			0
$803$		−	24.3771i		−	0.860250i
$804$		0			0
$805$	39.1132			1.37856
$806$		0			0
$807$	2.05682	+	20.7205i	0.0724036	+	0.729394i
$808$		0			0
$809$			17.3813i			0.611094i	0.952177	+	0.305547i	$0.0988393\pi$
$809$			17.3813i			0.611094i	−0.952177	+	0.305547i	$0.901161\pi$
$810$		0			0
$811$		−	16.7489i		−	0.588132i	−0.955785	−	0.294066i	$-0.904991\pi$
$811$		−	16.7489i		−	0.588132i	0.955785	−	0.294066i	$-0.0950086\pi$
$812$		0			0
$813$	−4.12984	−	41.6040i	−0.144840	−	1.45912i
$814$		0			0
$815$		−	3.31070i		−	0.115969i
$816$		0			0
$817$	31.5637	−	37.5049i	1.10427	−	1.31213i
$818$		0			0
$819$	−3.03535	−	15.1384i	−0.106064	−	0.528978i
$820$		0			0
$821$		−	0.825562i		−	0.0288123i	−0.999896	−	0.0144061i	$-0.995414\pi$
$821$		−	0.825562i		−	0.0288123i	0.999896	−	0.0144061i	$-0.00458578\pi$
$822$		0			0
$823$	41.5102			1.44696			0.723478	−	0.690348i	$-0.242543\pi$
$823$	41.5102			1.44696			0.723478	+	0.690348i	$0.242543\pi$
$824$		0			0
$825$	−43.7633	+	4.34418i	−1.52364	+	0.151245i
$826$		0			0
$827$	14.7955			0.514490			0.257245	−	0.966346i	$-0.417185\pi$
$827$	14.7955			0.514490			0.257245	+	0.966346i	$0.417185\pi$
$828$		0			0
$829$		−	24.0746i		−	0.836146i	−0.908413	−	0.418073i	$-0.862706\pi$
$829$		−	24.0746i		−	0.836146i	0.908413	−	0.418073i	$-0.137294\pi$
$830$		0			0
$831$	0.288366	+	2.90500i	0.0100033	+	0.100773i
$832$		0			0
$833$			5.48537i			0.190057i
$834$		0			0
$835$			35.5113i			1.22892i
$836$		0			0
$837$	12.2540	−	3.74801i	0.423561	−	0.129550i
$838$		0			0
$839$	29.4785			1.01771			0.508856	−	0.860852i	$-0.330069\pi$
$839$	29.4785			1.01771			0.508856	+	0.860852i	$0.330069\pi$
$840$		0			0
$841$	5.60863			0.193401
$842$		0			0
$843$	0.867596	+	8.74016i	0.0298816	+	0.301027i
$844$		0			0
$845$		−	29.6522i		−	1.02007i
$846$		0			0
$847$	−8.88519			−0.305299
$848$		0			0
$849$	0.279280	+	2.81347i	0.00958487	+	0.0965580i
$850$		0			0
$851$	39.8012			1.36437
$852$		0			0
$853$	−25.1274			−0.860345			−0.430172	−	0.902747i	$-0.641547\pi$
$853$	−25.1274			−0.860345			−0.430172	+	0.902747i	$0.641547\pi$
$854$		0			0
$855$	−43.7504	−	23.9981i	−1.49623	−	0.820716i
$856$		0			0
$857$	−14.6045			−0.498879			−0.249440	−	0.968390i	$-0.580246\pi$
$857$	−14.6045			−0.498879			−0.249440	+	0.968390i	$0.580246\pi$
$858$		0			0
$859$	−43.8175			−1.49503			−0.747517	−	0.664243i	$-0.768754\pi$
$859$	−43.8175			−1.49503			−0.747517	+	0.664243i	$0.768754\pi$
$860$		0			0
$861$	2.13348	+	21.4927i	0.0727088	+	0.732469i
$862$		0			0
$863$	5.32564			0.181287			0.0906434	−	0.995883i	$-0.471108\pi$
$863$	5.32564			0.181287			0.0906434	+	0.995883i	$0.471108\pi$
$864$		0			0
$865$		−	80.3013i		−	2.73032i
$866$		0			0
$867$	−1.53355	−	15.4489i	−0.0520819	−	0.524674i
$868$		0			0
$869$	−15.1250			−0.513079
$870$		0			0
$871$	−10.2917			−0.348722
$872$		0			0
$873$	11.1638	+	55.6777i	0.377836	+	1.88441i
$874$		0			0
$875$		−	39.1735i		−	1.32431i
$876$		0			0
$877$			28.4136i			0.959460i	0.877416	+	0.479730i	$0.159265\pi$
$877$			28.4136i			0.959460i	−0.877416	+	0.479730i	$0.840735\pi$
$878$		0			0
$879$	−3.94481	−	39.7400i	−0.133055	−	1.34040i
$880$		0			0
$881$		−	41.8937i		−	1.41143i	−0.708494	−	0.705717i	$-0.750625\pi$
$881$		−	41.8937i		−	1.41143i	0.708494	−	0.705717i	$-0.249375\pi$
$882$		0			0
$883$	34.5054			1.16120			0.580600	−	0.814189i	$-0.302818\pi$
$883$	34.5054			1.16120			0.580600	+	0.814189i	$0.302818\pi$
$884$		0			0
$885$	−82.4498	+	8.18441i	−2.77152	+	0.275116i
$886$		0			0
$887$	−31.4766			−1.05688			−0.528441	−	0.848970i	$-0.677223\pi$
$887$	−31.4766			−1.05688			−0.528441	+	0.848970i	$0.677223\pi$
$888$		0			0
$889$			42.8410i			1.43684i
$890$		0			0
$891$	9.21383	+	22.0527i	0.308675	+	0.738792i
$892$		0			0
$893$	−1.65074	−	1.38925i	−0.0552399	−	0.0464893i
$894$		0			0
$895$		−	63.0075i		−	2.10611i
$896$		0			0
$897$	1.78190	+	17.9509i	0.0594960	+	0.599363i
$898$		0			0
$899$		−	14.5080i		−	0.483869i
$900$		0			0
$901$			20.6133i			0.686730i
$902$		0			0
$903$	−4.33023	−	43.6228i	−0.144101	−	1.45167i
$904$		0			0
$905$	12.4279			0.413118
$906$		0			0
$907$		−	27.2812i		−	0.905859i	−0.891546	−	0.452929i	$-0.850379\pi$
$907$		−	27.2812i		−	0.905859i	0.891546	−	0.452929i	$-0.149621\pi$
$908$		0			0
$909$	3.74823	+	18.6938i	0.124321	+	0.620034i
$910$		0			0
$911$	9.78855			0.324309			0.162155	−	0.986765i	$-0.448156\pi$
$911$	9.78855			0.324309			0.162155	+	0.986765i	$0.448156\pi$
$912$		0			0
$913$	29.7562			0.984787
$914$		0			0
$915$	−48.9934	+	4.86335i	−1.61967	+	0.160777i
$916$		0			0
$917$			11.1995i			0.369842i
$918$		0			0
$919$	−22.0317			−0.726758			−0.363379	−	0.931641i	$-0.618377\pi$
$919$	−22.0317			−0.726758			−0.363379	+	0.931641i	$0.618377\pi$
$920$		0			0
$921$	42.7101	−	4.23963i	1.40734	−	0.139701i
$922$		0			0
$923$			5.97231i			0.196581i
$924$		0			0
$925$		−	83.5581i		−	2.74737i
$926$		0			0
$927$	5.55781	+	27.7188i	0.182542	+	0.910406i
$928$		0			0
$929$			33.7271i			1.10655i	0.832999	+	0.553275i	$0.186622\pi$
$929$			33.7271i			1.10655i	−0.832999	+	0.553275i	$0.813378\pi$
$930$		0			0
$931$	5.43082	−	6.45305i	0.177988	−	0.211490i
$932$		0			0
$933$	−27.4883	+	2.72863i	−0.899925	+	0.0893315i
$934$		0			0
$935$		−	28.7275i		−	0.939490i
$936$		0			0
$937$	−3.78483			−0.123645			−0.0618224	−	0.998087i	$-0.519691\pi$
$937$	−3.78483			−0.123645			−0.0618224	+	0.998087i	$0.519691\pi$
$938$		0			0
$939$	2.11537	+	21.3102i	0.0690325	+	0.695433i
$940$		0			0
$941$	−45.8637			−1.49511			−0.747557	−	0.664197i	$-0.768773\pi$
$941$	−45.8637			−1.49511			−0.747557	+	0.664197i	$0.768773\pi$
$942$		0			0
$943$		−	25.2346i		−	0.821751i
$944$		0			0
$945$	−42.6733	+	13.0520i	−1.38816	+	0.424583i
$946$		0			0
$947$		−	59.6666i		−	1.93890i	−0.245282	−	0.969452i	$-0.578881\pi$
$947$		−	59.6666i		−	1.93890i	0.245282	−	0.969452i	$-0.421119\pi$
$948$		0			0
$949$			20.9918i			0.681424i
$950$		0			0
$951$	−0.910953	−	9.17694i	−0.0295397	−	0.297583i
$952$		0			0
$953$	15.1016			0.489188			0.244594	−	0.969626i	$-0.421345\pi$
$953$	15.1016			0.489188			0.244594	+	0.969626i	$0.421345\pi$
$954$		0			0
$955$	−43.1463			−1.39618
$956$		0			0
$957$	26.9265	−	2.67287i	0.870412	−	0.0864018i
$958$		0			0
$959$		−	42.7218i		−	1.37956i
$960$		0			0
$961$	24.9182			0.803813
$962$		0			0
$963$	46.1799	−	9.25937i	1.48813	−	0.298379i
$964$		0			0
$965$	11.8235			0.380611
$966$		0			0
$967$	37.4893			1.20557			0.602787	−	0.797902i	$-0.294057\pi$
$967$	37.4893			1.20557			0.602787	+	0.797902i	$0.294057\pi$
$968$		0			0
$969$	12.0966	−	17.6569i	0.388598	−	0.567221i
$970$		0			0
$971$	18.2468			0.585569			0.292785	−	0.956178i	$-0.405418\pi$
$971$	18.2468			0.585569			0.292785	+	0.956178i	$0.405418\pi$
$972$		0			0
$973$	6.75413			0.216527
$974$		0			0
$975$	37.6858	−	3.74090i	1.20691	−	0.119805i
$976$		0			0
$977$	−8.75446			−0.280080			−0.140040	−	0.990146i	$-0.544723\pi$
$977$	−8.75446			−0.280080			−0.140040	+	0.990146i	$0.544723\pi$
$978$		0			0
$979$		−	41.5737i		−	1.32870i
$980$		0			0
$981$	−4.66736	−	23.2779i	−0.149017	−	0.743205i
$982$		0			0
$983$	−50.3083			−1.60459			−0.802293	−	0.596930i	$-0.796387\pi$
$983$	−50.3083			−1.60459			−0.802293	+	0.596930i	$0.796387\pi$
$984$		0			0
$985$	−61.4120			−1.95675
$986$		0			0
$987$	−1.92001	+	0.190591i	−0.0611147	+	0.00606658i
$988$		0			0
$989$			51.2175i			1.62862i
$990$		0			0
$991$		−	41.2656i		−	1.31085i	−0.755262	−	0.655423i	$-0.772491\pi$
$991$		−	41.2656i		−	1.31085i	0.755262	−	0.655423i	$-0.227509\pi$
$992$		0			0
$993$	49.5157	−	4.91519i	1.57133	−	0.155979i
$994$		0			0
$995$			63.5265i			2.01392i
$996$		0			0
$997$	−0.380791			−0.0120598			−0.00602988	−	0.999982i	$-0.501919\pi$
$997$	−0.380791			−0.0120598			−0.00602988	+	0.999982i	$0.501919\pi$
$998$		0			0
$999$	−43.4240	+	13.2816i	−1.37387	+	0.420212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.f.i.113.5		10
3.2	odd	2		912.2.f.h.113.5		10
4.3	odd	2		456.2.f.a.113.6	yes	10
12.11	even	2		456.2.f.b.113.6	yes	10
19.18	odd	2		912.2.f.h.113.6		10
57.56	even	2	inner	912.2.f.i.113.6		10
76.75	even	2		456.2.f.b.113.5	yes	10
228.227	odd	2		456.2.f.a.113.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.f.a.113.5	✓	10	228.227	odd	2
456.2.f.a.113.6	yes	10	4.3	odd	2
456.2.f.b.113.5	yes	10	76.75	even	2
456.2.f.b.113.6	yes	10	12.11	even	2
912.2.f.h.113.5		10	3.2	odd	2
912.2.f.h.113.6		10	19.18	odd	2
912.2.f.i.113.5		10	1.1	even	1	trivial
912.2.f.i.113.6		10	57.56	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.171092 - 1.72358i) q^{3} -3.81594i q^{5} -2.25057 q^{7} +(-2.94146 + 0.589781i) q^{9} +O(q^{10})\)	\(q+(-0.171092 - 1.72358i) q^{3} -3.81594i q^{5} -2.25057 q^{7} +(-2.94146 + 0.589781i) q^{9} +2.65557i q^{11} -2.28678i q^{13} +(-6.57708 + 0.652876i) q^{15} -2.83491i q^{17} +(-2.80672 + 3.33502i) q^{19} +(0.385054 + 3.87904i) q^{21} -4.55438i q^{23} -9.56140 q^{25} +(1.51979 + 4.96893i) q^{27} +5.88291 q^{29} -2.46613i q^{31} +(4.57708 - 0.454346i) q^{33} +8.58804i q^{35} +8.73910i q^{37} +(-3.94146 + 0.391250i) q^{39} +5.54073 q^{41} -11.2458 q^{43} +(2.25057 + 11.2244i) q^{45} +0.494972i q^{47} -1.93494 q^{49} +(-4.88619 + 0.485030i) q^{51} -7.27125 q^{53} +10.1335 q^{55} +(6.22838 + 4.26700i) q^{57} +12.5359 q^{59} +7.44911 q^{61} +(6.61995 - 1.32734i) q^{63} -8.72623 q^{65} -4.50053i q^{67} +(-7.84984 + 0.779218i) q^{69} -2.61166 q^{71} -9.17963 q^{73} +(1.63588 + 16.4798i) q^{75} -5.97653i q^{77} +5.69557i q^{79} +(8.30432 - 3.46963i) q^{81} -11.2052i q^{83} -10.8178 q^{85} +(-1.00652 - 10.1397i) q^{87} -15.6553 q^{89} +5.14657i q^{91} +(-4.25057 + 0.421935i) q^{93} +(12.7262 + 10.7103i) q^{95} -18.9286i q^{97} +(-1.56620 - 7.81123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 2 * q^7 + 3 * q^9	\( 10 q + q^{3} + 2 q^{7} + 3 q^{9} - 10 q^{15} - 2 q^{19} + 5 q^{21} - 14 q^{25} + 10 q^{27} - 6 q^{29} - 10 q^{33} - 7 q^{39} - 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} - q^{51} - 26 q^{53} + 12 q^{55} + 9 q^{57} - 2 q^{59} - 4 q^{61} + 17 q^{63} + 32 q^{65} - 27 q^{69} - 8 q^{71} - 26 q^{73} - 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} + 4 q^{89} - 18 q^{93} + 8 q^{95} - 2 q^{99}+O(q^{100}) \) 10 * q + q^3 + 2 * q^7 + 3 * q^9 - 10 * q^15 - 2 * q^19 + 5 * q^21 - 14 * q^25 + 10 * q^27 - 6 * q^29 - 10 * q^33 - 7 * q^39 - 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 - q^51 - 26 * q^53 + 12 * q^55 + 9 * q^57 - 2 * q^59 - 4 * q^61 + 17 * q^63 + 32 * q^65 - 27 * q^69 - 8 * q^71 - 26 * q^73 - 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 + 4 * q^89 - 18 * q^93 + 8 * q^95 - 2 * q^99

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