LMFDB - Embedded newform 1512.2.s.o.865.3

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			865.3
Root			$2.45973 - 2.20662i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.o.1297.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +O(q^{10})$	$q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +(1.19060 - 2.06219i) q^{11} -0.461738 q^{13} +(3.64086 - 6.30615i) q^{17} +(4.32198 + 7.48589i) q^{19} +(-1.49052 - 2.58165i) q^{23} +(-0.721387 + 1.24948i) q^{25} -3.55723 q^{29} +(4.15034 - 7.18860i) q^{31} +(2.99800 + 6.00928i) q^{35} +(1.10259 + 1.90975i) q^{37} -6.81998 q^{41} +2.38121 q^{43} +(4.21938 + 7.30819i) q^{47} +(6.94825 + 0.849602i) q^{49} +(0.181122 - 0.313712i) q^{53} +6.04413 q^{55} +(-3.73397 + 6.46743i) q^{59} +(-3.08801 - 5.34859i) q^{61} +(-0.586006 - 1.01499i) q^{65} +(-5.87173 + 10.1701i) q^{67} -9.72048 q^{71} +(-4.67912 + 8.10447i) q^{73} +(3.47593 - 5.25442i) q^{77} +(4.97903 + 8.62394i) q^{79} +3.20118 q^{83} +18.4829 q^{85} +(-3.29320 - 5.70399i) q^{89} +(-1.21938 - 0.0742739i) q^{91} +(-10.9703 + 19.0011i) q^{95} +15.6400 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.26913	+	2.19820i	0.567573	+	0.983065i	0.996805	+	0.0798707i	$0.0254507\pi$
$5$	1.26913	+	2.19820i	0.567573	+	0.983065i	−0.429233	+	0.903194i	$0.641216\pi$
$6$		0			0
$7$	2.64086	+	0.160857i	0.998150	+	0.0607983i
$7$	2.64086	+	0.160857i	0.998150	+	0.0607983i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.19060	−	2.06219i	0.358981	−	0.621773i	−0.628810	−	0.777559i	$-0.716458\pi$
$11$	1.19060	−	2.06219i	0.358981	−	0.621773i	0.987791	+	0.155786i	$0.0497911\pi$
$12$		0			0
$13$	−0.461738			−0.128063			−0.0640315	−	0.997948i	$-0.520396\pi$
$13$	−0.461738			−0.128063			−0.0640315	+	0.997948i	$0.520396\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.64086	−	6.30615i	0.883037	−	1.52947i	0.0350909	−	0.999384i	$-0.488828\pi$
$17$	3.64086	−	6.30615i	0.883037	−	1.52947i	0.847947	−	0.530082i	$-0.177839\pi$
$18$		0			0
$19$	4.32198	+	7.48589i	0.991530	+	1.71738i	0.608243	+	0.793751i	$0.291875\pi$
$19$	4.32198	+	7.48589i	0.991530	+	1.71738i	0.383287	+	0.923629i	$0.374792\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.49052	−	2.58165i	−0.310794	−	0.538312i	0.667740	−	0.744394i	$-0.267262\pi$
$23$	−1.49052	−	2.58165i	−0.310794	−	0.538312i	−0.978535	+	0.206083i	$0.933928\pi$
$24$		0			0
$25$	−0.721387	+	1.24948i	−0.144277	+	0.249896i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.55723			−0.660560			−0.330280	−	0.943883i	$-0.607143\pi$
$29$	−3.55723			−0.660560			−0.330280	+	0.943883i	$0.607143\pi$
$30$		0			0
$31$	4.15034	−	7.18860i	0.745423	−	1.29111i	−0.204574	−	0.978851i	$-0.565581\pi$
$31$	4.15034	−	7.18860i	0.745423	−	1.29111i	0.949997	−	0.312259i	$-0.101086\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.99800	+	6.00928i	0.506754	+	1.01575i
$36$		0			0
$37$	1.10259	+	1.90975i	0.181265	+	0.313961i	0.942312	−	0.334737i	$-0.108647\pi$
$37$	1.10259	+	1.90975i	0.181265	+	0.313961i	−0.761046	+	0.648698i	$0.775314\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−6.81998			−1.06510			−0.532551	−	0.846398i	$-0.678766\pi$
$41$	−6.81998			−1.06510			−0.532551	+	0.846398i	$0.678766\pi$
$42$		0			0
$43$	2.38121			0.363131			0.181565	−	0.983379i	$-0.441884\pi$
$43$	2.38121			0.363131			0.181565	+	0.983379i	$0.441884\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.21938	+	7.30819i	0.615460	+	1.06601i	0.990304	+	0.138920i	$0.0443632\pi$
$47$	4.21938	+	7.30819i	0.615460	+	1.06601i	−0.374843	+	0.927088i	$0.622303\pi$
$48$		0			0
$49$	6.94825	+	0.849602i	0.992607	+	0.121372i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.181122	−	0.313712i	0.0248790	−	0.0430917i	−0.853318	−	0.521391i	$-0.825413\pi$
$53$	0.181122	−	0.313712i	0.0248790	−	0.0430917i	0.878197	+	0.478299i	$0.158747\pi$
$54$		0			0
$55$	6.04413			0.814990
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.73397	+	6.46743i	−0.486121	+	0.841987i	−0.999873	−	0.0159521i	$-0.994922\pi$
$59$	−3.73397	+	6.46743i	−0.486121	+	0.841987i	0.513751	+	0.857939i	$0.328255\pi$
$60$		0			0
$61$	−3.08801	−	5.34859i	−0.395379	−	0.684817i	0.597770	−	0.801667i	$-0.296053\pi$
$61$	−3.08801	−	5.34859i	−0.395379	−	0.684817i	−0.993149	+	0.116851i	$0.962720\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.586006	−	1.01499i	−0.0726851	−	0.125894i
$66$		0			0
$67$	−5.87173	+	10.1701i	−0.717345	+	1.24248i	0.244702	+	0.969598i	$0.421310\pi$
$67$	−5.87173	+	10.1701i	−0.717345	+	1.24248i	−0.962048	+	0.272881i	$0.912024\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.72048			−1.15361			−0.576804	−	0.816882i	$-0.695701\pi$
$71$	−9.72048			−1.15361			−0.576804	+	0.816882i	$0.695701\pi$
$72$		0			0
$73$	−4.67912	+	8.10447i	−0.547649	+	0.948557i	0.450786	+	0.892632i	$0.351144\pi$
$73$	−4.67912	+	8.10447i	−0.547649	+	0.948557i	−0.998435	+	0.0559244i	$0.982189\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.47593	−	5.25442i	0.396119	−	0.598797i
$78$		0			0
$79$	4.97903	+	8.62394i	0.560185	+	0.970269i	0.997480	+	0.0709506i	$0.0226033\pi$
$79$	4.97903	+	8.62394i	0.560185	+	0.970269i	−0.437295	+	0.899318i	$0.644063\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.20118			0.351376			0.175688	−	0.984446i	$-0.443785\pi$
$83$	3.20118			0.351376			0.175688	+	0.984446i	$0.443785\pi$
$84$		0			0
$85$	18.4829			2.00475
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.29320	−	5.70399i	−0.349078	−	0.604621i	0.637008	−	0.770858i	$-0.280172\pi$
$89$	−3.29320	−	5.70399i	−0.349078	−	0.604621i	−0.986086	+	0.166236i	$0.946839\pi$
$90$		0			0
$91$	−1.21938	−	0.0742739i	−0.127826	−	0.00778602i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.9703	+	19.0011i	−1.12553	+	1.94948i
$96$		0			0
$97$	15.6400			1.58800			0.793998	−	0.607920i	$-0.207996\pi$
$97$	15.6400			1.58800			0.793998	+	0.607920i	$0.207996\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.08911	−	15.7428i	0.904400	−	1.56647i	0.0826792	−	0.996576i	$-0.473652\pi$
$101$	9.08911	−	15.7428i	0.904400	−	1.56647i	0.821721	−	0.569890i	$-0.193014\pi$
$102$		0			0
$103$	−3.91199	−	6.77577i	−0.385460	−	0.667636i	0.606373	−	0.795180i	$-0.292624\pi$
$103$	−3.91199	−	6.77577i	−0.385460	−	0.667636i	−0.991833	+	0.127544i	$0.959291\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.27223	+	7.39972i	0.413012	+	0.715358i	0.995218	−	0.0976837i	$-0.0311433\pi$
$107$	4.27223	+	7.39972i	0.413012	+	0.715358i	−0.582205	+	0.813042i	$0.697810\pi$
$108$		0			0
$109$	3.28171	−	5.68409i	0.314331	−	0.544438i	−0.664964	−	0.746875i	$-0.731553\pi$
$109$	3.28171	−	5.68409i	0.314331	−	0.544438i	0.979295	+	0.202438i	$0.0648864\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.9770			−1.50299			−0.751496	−	0.659737i	$-0.770668\pi$
$113$	−15.9770			−1.50299			−0.751496	+	0.659737i	$0.770668\pi$
$114$		0			0
$115$	3.78333	−	6.55291i	0.352797	−	0.611062i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.6294	−	16.0680i	0.974393	−	1.47295i
$120$		0			0
$121$	2.66492	+	4.61578i	0.242266	+	0.419617i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.02917			0.807594
$126$		0			0
$127$	19.9730			1.77232			0.886160	−	0.463380i	$-0.153364\pi$
$127$	19.9730			1.77232			0.886160	+	0.463380i	$0.153364\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.73634	+	15.1318i	0.763298	+	1.32207i	0.941142	+	0.338012i	$0.109755\pi$
$131$	8.73634	+	15.1318i	0.763298	+	1.32207i	−0.177844	+	0.984059i	$0.556912\pi$
$132$		0			0
$133$	10.2096	+	20.4644i	0.885282	+	1.77449i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.74345	−	6.48385i	0.319825	−	0.553953i	−0.660627	−	0.750715i	$-0.729709\pi$
$137$	3.74345	−	6.48385i	0.319825	−	0.553953i	0.980451	+	0.196762i	$0.0630427\pi$
$138$		0			0
$139$	−13.3772			−1.13464			−0.567320	−	0.823498i	$-0.692020\pi$
$139$	−13.3772			−1.13464			−0.567320	+	0.823498i	$0.692020\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.549747	+	0.952190i	−0.0459722	+	0.0796261i
$144$		0			0
$145$	−4.51459	−	7.81949i	−0.374916	−	0.649373i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.19571	−	5.53513i	−0.261803	−	0.453455i	0.704918	−	0.709288i	$-0.250984\pi$
$149$	−3.19571	−	5.53513i	−0.261803	−	0.453455i	−0.966721	+	0.255833i	$0.917650\pi$
$150$		0			0
$151$	−2.89741	+	5.01845i	−0.235787	+	0.408396i	−0.959501	−	0.281704i	$-0.909100\pi$
$151$	−2.89741	+	5.01845i	−0.235787	+	0.408396i	0.723714	+	0.690100i	$0.242434\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	21.0693			1.69233
$156$		0			0
$157$	−1.83818	+	3.18381i	−0.146702	+	0.254096i	−0.930007	−	0.367542i	$-0.880199\pi$
$157$	−1.83818	+	3.18381i	−0.146702	+	0.254096i	0.783304	+	0.621638i	$0.213533\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.52097	−	7.05754i	−0.277491	−	0.556212i
$162$		0			0
$163$	−4.42147	−	7.65822i	−0.346316	−	0.599838i	0.639276	−	0.768978i	$-0.279234\pi$
$163$	−4.42147	−	7.65822i	−0.346316	−	0.599838i	−0.985592	+	0.169140i	$0.945901\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.91071			−0.612149			−0.306075	−	0.952008i	$-0.599016\pi$
$167$	−7.91071			−0.612149			−0.306075	+	0.952008i	$0.599016\pi$
$168$		0			0
$169$	−12.7868			−0.983600
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.52206	−	9.56450i	−0.419835	−	0.727175i	0.576088	−	0.817388i	$-0.304579\pi$
$173$	−5.52206	−	9.56450i	−0.419835	−	0.727175i	−0.995923	+	0.0902127i	$0.971245\pi$
$174$		0			0
$175$	−2.10607	+	3.18365i	−0.159204	+	0.240662i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.28809	−	2.23105i	0.0962767	−	0.166756i	−0.813864	−	0.581055i	$-0.802640\pi$
$179$	1.28809	−	2.23105i	0.0962767	−	0.166756i	0.910141	+	0.414299i	$0.135973\pi$
$180$		0			0
$181$	−20.8641			−1.55082			−0.775408	−	0.631460i	$-0.782456\pi$
$181$	−20.8641			−1.55082			−0.775408	+	0.631460i	$0.782456\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.79867	+	4.84745i	−0.205763	+	0.356391i
$186$		0			0
$187$	−8.66964	−	15.0163i	−0.633987	−	1.09810i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.19060	−	3.79424i	−0.158507	−	0.274541i	0.775824	−	0.630950i	$-0.217335\pi$
$191$	−2.19060	−	3.79424i	−0.158507	−	0.274541i	−0.934330	+	0.356408i	$0.884001\pi$
$192$		0			0
$193$	−7.40999	+	12.8345i	−0.533383	+	0.923846i	0.465857	+	0.884860i	$0.345746\pi$
$193$	−7.40999	+	12.8345i	−0.533383	+	0.923846i	−0.999240	+	0.0389858i	$0.987587\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.18623			0.440750			0.220375	−	0.975415i	$-0.429272\pi$
$197$	6.18623			0.440750			0.220375	+	0.975415i	$0.429272\pi$
$198$		0			0
$199$	2.41947	−	4.19064i	0.171512	−	0.297067i	−0.767437	−	0.641125i	$-0.778468\pi$
$199$	2.41947	−	4.19064i	0.171512	−	0.297067i	0.938949	+	0.344058i	$0.111802\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.39412	−	0.572206i	−0.659338	−	0.0401610i
$204$		0			0
$205$	−8.65544	−	14.9917i	−0.604522	−	1.04706i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	20.5831			1.42376
$210$		0			0
$211$	10.7183			0.737877			0.368939	−	0.929454i	$-0.379721\pi$
$211$	10.7183			0.737877			0.368939	+	0.929454i	$0.379721\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.02206	+	5.23437i	0.206103	+	0.356981i
$216$		0			0
$217$	12.1168	−	18.3164i	0.822541	−	1.24340i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.68112	+	2.91179i	−0.113084	+	0.195868i
$222$		0			0
$223$	−21.2398			−1.42232			−0.711160	−	0.703030i	$-0.751830\pi$
$223$	−21.2398			−1.42232			−0.711160	+	0.703030i	$0.751830\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.45226	+	5.97948i	−0.229134	+	0.396872i	−0.957552	−	0.288261i	$-0.906923\pi$
$227$	−3.45226	+	5.97948i	−0.229134	+	0.396872i	0.728418	+	0.685134i	$0.240256\pi$
$228$		0			0
$229$	−0.392301	−	0.679486i	−0.0259240	−	0.0449017i	0.852772	−	0.522283i	$-0.174919\pi$
$229$	−0.392301	−	0.679486i	−0.0259240	−	0.0449017i	−0.878696	+	0.477381i	$0.841586\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.73197	−	6.46396i	−0.244489	−	0.423468i	0.717499	−	0.696560i	$-0.245287\pi$
$233$	−3.73197	−	6.46396i	−0.244489	−	0.423468i	−0.961988	+	0.273092i	$0.911954\pi$
$234$		0			0
$235$	−10.7099	+	18.5501i	−0.698637	+	1.21007i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−15.0314			−0.972298			−0.486149	−	0.873876i	$-0.661599\pi$
$239$	−15.0314			−0.972298			−0.486149	+	0.873876i	$0.661599\pi$
$240$		0			0
$241$	6.93877	−	12.0183i	0.446965	−	0.774167i	−0.551221	−	0.834359i	$-0.685838\pi$
$241$	6.93877	−	12.0183i	0.446965	−	0.774167i	0.998187	+	0.0601923i	$0.0191714\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.95064	+	16.3519i	0.444060	+	1.04468i
$246$		0			0
$247$	−1.99562	−	3.45652i	−0.126978	−	0.219933i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.38121			−0.213420			−0.106710	−	0.994290i	$-0.534032\pi$
$251$	−3.38121			−0.213420			−0.106710	+	0.994290i	$0.534032\pi$
$252$		0			0
$253$	−7.09847			−0.446277
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.39269	+	5.87632i	0.211630	+	0.366555i	0.952225	−	0.305398i	$-0.0987894\pi$
$257$	3.39269	+	5.87632i	0.211630	+	0.366555i	−0.740595	+	0.671952i	$0.765456\pi$
$258$		0			0
$259$	2.60460	+	5.22074i	0.161842	+	0.324401i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.883211	+	1.52977i	−0.0544611	+	0.0943294i	−0.891971	−	0.452093i	$-0.850677\pi$
$263$	−0.883211	+	1.52977i	−0.0544611	+	0.0943294i	0.837510	+	0.546423i	$0.184011\pi$
$264$		0			0
$265$	0.919470			0.0564826
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.88431	+	17.1201i	−0.602657	+	1.04383i	0.389760	+	0.920916i	$0.372558\pi$
$269$	−9.88431	+	17.1201i	−0.602657	+	1.04383i	−0.992417	+	0.122916i	$0.960775\pi$
$270$		0			0
$271$	−5.38321	−	9.32399i	−0.327007	−	0.566392i	0.654910	−	0.755707i	$-0.272707\pi$
$271$	−5.38321	−	9.32399i	−0.327007	−	0.566392i	−0.981916	+	0.189315i	$0.939373\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.71777	+	2.97527i	0.103586	+	0.179415i
$276$		0			0
$277$	−8.41476	+	14.5748i	−0.505594	+	0.875714i	0.494385	+	0.869243i	$0.335393\pi$
$277$	−8.41476	+	14.5748i	−0.505594	+	0.875714i	−0.999979	+	0.00647123i	$0.997940\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.08053			−0.482044			−0.241022	−	0.970520i	$-0.577483\pi$
$281$	−8.08053			−0.482044			−0.241022	+	0.970520i	$0.577483\pi$
$282$		0			0
$283$	−0.217047	+	0.375936i	−0.0129021	+	0.0223471i	−0.872404	−	0.488785i	$-0.837440\pi$
$283$	−0.217047	+	0.375936i	−0.0129021	+	0.0223471i	0.859502	+	0.511132i	$0.170774\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−18.0106	−	1.09704i	−1.06313	−	0.0647564i
$288$		0			0
$289$	−18.0117	−	31.1971i	−1.05951	−	1.83513i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−29.1458			−1.70272			−0.851358	−	0.524584i	$-0.824221\pi$
$293$	−29.1458			−1.70272			−0.851358	+	0.524584i	$0.824221\pi$
$294$		0			0
$295$	−18.9556			−1.10364
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.688229	+	1.19205i	0.0398013	+	0.0689379i
$300$		0			0
$301$	6.28843	+	0.383035i	0.362459	+	0.0220777i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.83818	−	13.5761i	0.448813	−	0.777366i
$306$		0			0
$307$	−2.73324			−0.155994			−0.0779972	−	0.996954i	$-0.524853\pi$
$307$	−2.73324			−0.155994			−0.0779972	+	0.996954i	$0.524853\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.423810	−	0.734061i	0.0240321	−	0.0416248i	−0.853759	−	0.520668i	$-0.825683\pi$
$311$	0.423810	−	0.734061i	0.0240321	−	0.0416248i	0.877791	+	0.479043i	$0.159016\pi$
$312$		0			0
$313$	−2.96174	−	5.12988i	−0.167407	−	0.289958i	0.770100	−	0.637923i	$-0.220206\pi$
$313$	−2.96174	−	5.12988i	−0.167407	−	0.289958i	−0.937508	+	0.347965i	$0.886873\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.15034	−	8.92065i	−0.289272	−	0.501034i	0.684364	−	0.729140i	$-0.260080\pi$
$317$	−5.15034	−	8.92065i	−0.289272	−	0.501034i	−0.973636	+	0.228107i	$0.926746\pi$
$318$		0			0
$319$	−4.23525	+	7.33566i	−0.237128	+	0.410718i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	62.9428			3.50223
$324$		0			0
$325$	0.333092	−	0.576932i	0.0184766	−	0.0320024i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.96721	+	19.9786i	0.549510	+	1.10146i
$330$		0			0
$331$	7.41437	+	12.8421i	0.407530	+	0.705863i	0.994612	−	0.103664i	$-0.0330567\pi$
$331$	7.41437	+	12.8421i	0.407530	+	0.705863i	−0.587082	+	0.809528i	$0.699723\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−29.8080			−1.62858
$336$		0			0
$337$	−24.4701			−1.33297			−0.666487	−	0.745517i	$-0.732203\pi$
$337$	−24.4701			−1.33297			−0.666487	+	0.745517i	$0.732203\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.88282	−	17.1175i	−0.535185	−	0.926967i
$342$		0			0
$343$	18.2127	+	3.36135i	0.983392	+	0.181496i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.04975	+	7.01437i	−0.217402	+	0.376551i	−0.954013	−	0.299766i	$-0.903092\pi$
$347$	−4.04975	+	7.01437i	−0.217402	+	0.376551i	0.736611	+	0.676317i	$0.236425\pi$
$348$		0			0
$349$	−9.77262			−0.523117			−0.261558	−	0.965188i	$-0.584236\pi$
$349$	−9.77262			−0.523117			−0.261558	+	0.965188i	$0.584236\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.8247	−	23.9452i	0.735817	−	1.27447i	−0.218547	−	0.975826i	$-0.570132\pi$
$353$	13.8247	−	23.9452i	0.735817	−	1.27447i	0.954364	−	0.298646i	$-0.0965350\pi$
$354$		0			0
$355$	−12.3366	−	21.3676i	−0.654757	−	1.13407i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.65854	−	13.2650i	−0.404202	−	0.700099i	0.590026	−	0.807384i	$-0.299118\pi$
$359$	−7.65854	−	13.2650i	−0.404202	−	0.700099i	−0.994228	+	0.107285i	$0.965784\pi$
$360$		0			0
$361$	−27.8590	+	48.2532i	−1.46626	+	2.53964i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−23.7537			−1.24332
$366$		0			0
$367$	14.9503	−	25.8946i	0.780397	−	1.35169i	−0.151314	−	0.988486i	$-0.548350\pi$
$367$	14.9503	−	25.8946i	0.780397	−	1.35169i	0.931711	−	0.363201i	$-0.118316\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.528780	−	0.799335i	0.0274529	−	0.0414994i
$372$		0			0
$373$	−6.83894	−	11.8454i	−0.354107	−	0.613331i	0.632858	−	0.774268i	$-0.281882\pi$
$373$	−6.83894	−	11.8454i	−0.354107	−	0.613331i	−0.986965	+	0.160937i	$0.948548\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.64251			0.0845934
$378$		0			0
$379$	35.6036			1.82883			0.914416	−	0.404776i	$-0.132651\pi$
$379$	35.6036			1.82883			0.914416	+	0.404776i	$0.132651\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.62266	−	6.27463i	−0.185109	−	0.320618i	0.758504	−	0.651668i	$-0.225931\pi$
$383$	−3.62266	−	6.27463i	−0.185109	−	0.320618i	−0.943613	+	0.331050i	$0.892597\pi$
$384$		0			0
$385$	15.9617	+	0.972242i	0.813483	+	0.0495501i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.11518	−	10.5918i	0.310052	−	0.537025i	−0.668321	−	0.743873i	$-0.732987\pi$
$389$	6.11518	−	10.5918i	0.310052	−	0.537025i	0.978373	+	0.206847i	$0.0663203\pi$
$390$		0			0
$391$	−21.7071			−1.09777
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−12.6381	+	21.8898i	−0.635891	+	1.10140i
$396$		0			0
$397$	−18.3826	−	31.8397i	−0.922598	−	1.59799i	−0.795379	−	0.606112i	$-0.792728\pi$
$397$	−18.3826	−	31.8397i	−0.922598	−	1.59799i	−0.127219	−	0.991875i	$-0.540605\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.3870	+	33.5793i	0.968141	+	1.67687i	0.700927	+	0.713233i	$0.252770\pi$
$401$	19.3870	+	33.5793i	0.968141	+	1.67687i	0.267215	+	0.963637i	$0.413897\pi$
$402$		0			0
$403$	−1.91637	+	3.31925i	−0.0954611	+	0.165344i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.25101			0.260283
$408$		0			0
$409$	7.45973	−	12.9206i	0.368860	−	0.638885i	−0.620527	−	0.784185i	$-0.713081\pi$
$409$	7.45973	−	12.9206i	0.368860	−	0.638885i	0.989388	+	0.145300i	$0.0464148\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.9012	+	16.4789i	−0.536414	+	0.810874i
$414$		0			0
$415$	4.06272	+	7.03684i	0.199431	+	0.345425i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	29.1418			1.42367			0.711835	−	0.702346i	$-0.247864\pi$
$419$	29.1418			1.42367			0.711835	+	0.702346i	$0.247864\pi$
$420$		0			0
$421$	12.7049			0.619197			0.309598	−	0.950867i	$-0.399805\pi$
$421$	12.7049			0.619197			0.309598	+	0.950867i	$0.399805\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.25293	+	9.09835i	0.254805	+	0.441335i
$426$		0			0
$427$	−7.29463	−	14.6216i	−0.353012	−	0.707588i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.7466	−	27.2738i	0.758485	−	1.31373i	−0.185138	−	0.982712i	$-0.559273\pi$
$431$	15.7466	−	27.2738i	0.758485	−	1.31373i	0.943623	−	0.331022i	$-0.107393\pi$
$432$		0			0
$433$	−37.4599			−1.80021			−0.900105	−	0.435674i	$-0.856510\pi$
$433$	−37.4599			−1.80021			−0.900105	+	0.435674i	$0.856510\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.8840	−	22.3157i	0.616324	−	1.06750i
$438$		0			0
$439$	−11.4652	−	19.8583i	−0.547205	−	0.947786i	−0.998465	−	0.0553937i	$-0.982359\pi$
$439$	−11.4652	−	19.8583i	−0.547205	−	0.947786i	0.451260	−	0.892393i	$-0.350975\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.6561	+	18.4570i	0.506289	+	0.876918i	0.999974	+	0.00727709i	$0.00231639\pi$
$443$	10.6561	+	18.4570i	0.506289	+	0.876918i	−0.493685	+	0.869641i	$0.664350\pi$
$444$		0			0
$445$	8.35900	−	14.4782i	0.396255	−	0.686333i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.5729			0.546157			0.273078	−	0.961992i	$-0.411958\pi$
$449$	11.5729			0.546157			0.273078	+	0.961992i	$0.411958\pi$
$450$		0			0
$451$	−8.11989	+	14.0641i	−0.382351	+	0.662251i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.38429	−	2.77471i	−0.0648965	−	0.130081i
$456$		0			0
$457$	2.18422	+	3.78318i	0.102174	+	0.176970i	0.912580	−	0.408898i	$-0.134087\pi$
$457$	2.18422	+	3.78318i	0.102174	+	0.176970i	−0.810406	+	0.585868i	$0.800754\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	23.7118			1.10437			0.552184	−	0.833722i	$-0.313794\pi$
$461$	23.7118			1.10437			0.552184	+	0.833722i	$0.313794\pi$
$462$		0			0
$463$	−17.9888			−0.836009			−0.418004	−	0.908445i	$-0.637270\pi$
$463$	−17.9888			−0.836009			−0.418004	+	0.908445i	$0.637270\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.0603	−	33.0135i	−0.882007	−	1.52768i	−0.849106	−	0.528222i	$-0.822859\pi$
$467$	−19.0603	−	33.0135i	−0.882007	−	1.52768i	−0.0329003	−	0.999459i	$-0.510474\pi$
$468$		0			0
$469$	−17.1423	+	25.9133i	−0.791559	+	1.19657i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.83508	−	4.91049i	0.130357	−	0.225785i
$474$		0			0
$475$	−12.4713			−0.572221
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.5599	+	21.7544i	−0.573878	+	0.993986i	0.422284	+	0.906463i	$0.361228\pi$
$479$	−12.5599	+	21.7544i	−0.573878	+	0.993986i	−0.996163	+	0.0875226i	$0.972105\pi$
$480$		0			0
$481$	−0.509110	−	0.881804i	−0.0232134	−	0.0402068i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	19.8491	+	34.3797i	0.901303	+	1.56110i
$486$		0			0
$487$	−9.03388	+	15.6471i	−0.409364	+	0.709040i	−0.994819	−	0.101666i	$-0.967583\pi$
$487$	−9.03388	+	15.6471i	−0.409364	+	0.709040i	0.585454	+	0.810705i	$0.300916\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.327654			−0.0147868			−0.00739341	−	0.999973i	$-0.502353\pi$
$491$	−0.327654			−0.0147868			−0.00739341	+	0.999973i	$0.502353\pi$
$492$		0			0
$493$	−12.9514	+	22.4324i	−0.583299	+	1.01030i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−25.6704	−	1.56361i	−1.15147	−	0.0701375i
$498$		0			0
$499$	−15.8610	−	27.4721i	−0.710036	−	1.22982i	−0.964843	−	0.262827i	$-0.915345\pi$
$499$	−15.8610	−	27.4721i	−0.710036	−	1.22982i	0.254807	−	0.966992i	$-0.417988\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.18155			−0.231034			−0.115517	−	0.993306i	$-0.536852\pi$
$503$	−5.18155			−0.231034			−0.115517	+	0.993306i	$0.536852\pi$
$504$		0			0
$505$	46.1411			2.05325
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.6104	−	20.1098i	−0.514622	−	0.891352i	−0.999856	−	0.0169675i	$-0.994599\pi$
$509$	−11.6104	−	20.1098i	−0.514622	−	0.891352i	0.485234	−	0.874384i	$-0.338735\pi$
$510$		0			0
$511$	−13.6605	+	20.6501i	−0.604307	+	0.913506i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.92966	−	17.1987i	0.437553	−	0.757864i
$516$		0			0
$517$	20.0945			0.883753
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.26713	+	12.5870i	−0.318379	+	0.551448i	−0.980150	−	0.198258i	$-0.936472\pi$
$521$	−7.26713	+	12.5870i	−0.318379	+	0.551448i	0.661771	+	0.749706i	$0.269805\pi$
$522$		0			0
$523$	−3.12827	−	5.41833i	−0.136790	−	0.236927i	0.789490	−	0.613764i	$-0.210345\pi$
$523$	−3.12827	−	5.41833i	−0.136790	−	0.236927i	−0.926280	+	0.376837i	$0.877012\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.2216	−	52.3453i	−1.31647	−	2.28020i
$528$		0			0
$529$	7.05671	−	12.2226i	0.306814	−	0.531417i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	3.14904			0.136400
$534$		0			0
$535$	−10.8440	+	18.7824i	−0.468829	+	0.812035i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.0247	−	13.3170i	0.431792	−	0.573606i
$540$		0			0
$541$	2.45463	+	4.25155i	0.105533	+	0.182788i	0.913956	−	0.405814i	$-0.133012\pi$
$541$	2.45463	+	4.25155i	0.105533	+	0.182788i	−0.808423	+	0.588602i	$0.799679\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.6597			0.713623
$546$		0			0
$547$	8.88087			0.379719			0.189859	−	0.981811i	$-0.439197\pi$
$547$	8.88087			0.379719			0.189859	+	0.981811i	$0.439197\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−15.3743	−	26.6290i	−0.654965	−	1.13443i
$552$		0			0
$553$	11.7617	+	23.5755i	0.500158	+	1.00253i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.4047	+	28.4138i	−0.695090	+	1.20393i	0.275061	+	0.961427i	$0.411302\pi$
$557$	−16.4047	+	28.4138i	−0.695090	+	1.20393i	−0.970150	+	0.242504i	$0.922031\pi$
$558$		0			0
$559$	−1.09949			−0.0465036
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.56981	−	9.64719i	0.234739	−	0.406581i	−0.724457	−	0.689319i	$-0.757910\pi$
$563$	5.56981	−	9.64719i	0.234739	−	0.406581i	0.959197	+	0.282739i	$0.0912430\pi$
$564$		0			0
$565$	−20.2769	−	35.1207i	−0.853057	−	1.47754i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.6416	+	18.4318i	0.446120	+	0.772702i	0.998129	−	0.0611354i	$-0.0194721\pi$
$569$	10.6416	+	18.4318i	0.446120	+	0.772702i	−0.552010	+	0.833838i	$0.686139\pi$
$570$		0			0
$571$	2.00310	−	3.46947i	0.0838272	−	0.145193i	−0.821064	−	0.570837i	$-0.806619\pi$
$571$	2.00310	−	3.46947i	0.0838272	−	0.145193i	0.904891	+	0.425644i	$0.139952\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.30096			0.179362
$576$		0			0
$577$	13.9834	−	24.2200i	0.582137	−	1.00829i	−0.413089	−	0.910691i	$-0.635550\pi$
$577$	13.9834	−	24.2200i	0.582137	−	1.00829i	0.995226	−	0.0976001i	$-0.0311166\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.45387	+	0.514934i	0.350726	+	0.0213630i
$582$		0			0
$583$	−0.431289	−	0.747014i	−0.0178622	−	0.0309382i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	32.7133			1.35022			0.675110	−	0.737717i	$-0.264096\pi$
$587$	32.7133			1.35022			0.675110	+	0.737717i	$0.264096\pi$
$588$		0			0
$589$	71.7507			2.95644
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−15.7076	−	27.2063i	−0.645032	−	1.11723i	−0.984294	−	0.176537i	$-0.943511\pi$
$593$	−15.7076	−	27.2063i	−0.645032	−	1.11723i	0.339262	−	0.940692i	$-0.389823\pi$
$594$		0			0
$595$	48.8107	+	2.97311i	2.00104	+	0.121886i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−5.70680	+	9.88447i	−0.233174	+	0.403868i	−0.958740	−	0.284283i	$-0.908244\pi$
$599$	−5.70680	+	9.88447i	−0.233174	+	0.403868i	0.725567	+	0.688152i	$0.241578\pi$
$600$		0			0
$601$	7.69610			0.313930			0.156965	−	0.987604i	$-0.449829\pi$
$601$	7.69610			0.313930			0.156965	+	0.987604i	$0.449829\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.76428	+	11.7161i	−0.275007	+	0.476326i
$606$		0			0
$607$	−0.228866	−	0.396407i	−0.00928938	−	0.0160897i	0.861343	−	0.508023i	$-0.169624\pi$
$607$	−0.228866	−	0.396407i	−0.00928938	−	0.0160897i	−0.870633	+	0.491934i	$0.836290\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.94825	−	3.37447i	−0.0788178	−	0.136516i
$612$		0			0
$613$	−5.34094	+	9.25078i	−0.215719	+	0.373636i	−0.953495	−	0.301410i	$-0.902543\pi$
$613$	−5.34094	+	9.25078i	−0.215719	+	0.373636i	0.737776	+	0.675046i	$0.235876\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−28.0379			−1.12876			−0.564382	−	0.825514i	$-0.690886\pi$
$617$	−28.0379			−1.12876			−0.564382	+	0.825514i	$0.690886\pi$
$618$		0			0
$619$	17.6447	−	30.5616i	0.709201	−	1.22837i	−0.255953	−	0.966689i	$-0.582389\pi$
$619$	17.6447	−	30.5616i	0.709201	−	1.22837i	0.965154	−	0.261683i	$-0.0842776\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.77934	−	15.5931i	−0.311673	−	0.624726i
$624$		0			0
$625$	15.0661	+	26.0953i	0.602645	+	1.04381i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.0576			0.640257
$630$		0			0
$631$	−4.12466			−0.164200			−0.0821001	−	0.996624i	$-0.526163\pi$
$631$	−4.12466			−0.164200			−0.0821001	+	0.996624i	$0.526163\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	25.3484	+	43.9047i	1.00592	+	1.74230i
$636$		0			0
$637$	−3.20827	−	0.392294i	−0.127116	−	0.0155432i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.4998	+	28.5785i	−0.651704	+	1.12878i	0.331006	+	0.943629i	$0.392612\pi$
$641$	−16.4998	+	28.5785i	−0.651704	+	1.12878i	−0.982709	+	0.185155i	$0.940721\pi$
$642$		0			0
$643$	3.45306			0.136175			0.0680876	−	0.997679i	$-0.478310\pi$
$643$	3.45306			0.136175			0.0680876	+	0.997679i	$0.478310\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.0623	+	26.0887i	−0.592161	+	1.02565i	0.401779	+	0.915736i	$0.368392\pi$
$647$	−15.0623	+	26.0887i	−0.592161	+	1.02565i	−0.993941	+	0.109917i	$0.964941\pi$
$648$		0			0
$649$	8.89136	+	15.4003i	0.349016	+	0.604514i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	23.7003	+	41.0501i	0.927464	+	1.60641i	0.787550	+	0.616250i	$0.211349\pi$
$653$	23.7003	+	41.0501i	0.927464	+	1.60641i	0.139913	+	0.990164i	$0.455318\pi$
$654$		0			0
$655$	−22.1751	+	38.4085i	−0.866454	+	1.50074i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−33.8623			−1.31909			−0.659544	−	0.751666i	$-0.729251\pi$
$659$	−33.8623			−1.31909			−0.659544	+	0.751666i	$0.729251\pi$
$660$		0			0
$661$	1.57142	−	2.72178i	0.0611212	−	0.105865i	−0.833846	−	0.551998i	$-0.813866\pi$
$661$	1.57142	−	2.72178i	0.0611212	−	0.105865i	0.894967	+	0.446133i	$0.147199\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−32.0275	+	48.4146i	−1.24197	+	1.87744i
$666$		0			0
$667$	5.30211	+	9.18352i	0.205298	+	0.355587i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.7064			−0.567734
$672$		0			0
$673$	4.50186			0.173534			0.0867670	−	0.996229i	$-0.472346\pi$
$673$	4.50186			0.173534			0.0867670	+	0.996229i	$0.472346\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.5827	+	18.3298i	0.406727	+	0.704472i	0.994521	−	0.104539i	$-0.0333366\pi$
$677$	10.5827	+	18.3298i	0.406727	+	0.704472i	−0.587794	+	0.809011i	$0.700003\pi$
$678$		0			0
$679$	41.3029	+	2.51580i	1.58506	+	0.0965475i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.44153	+	16.3532i	−0.361270	+	0.625738i	−0.988170	−	0.153361i	$-0.950990\pi$
$683$	−9.44153	+	16.3532i	−0.361270	+	0.625738i	0.626900	+	0.779100i	$0.284323\pi$
$684$		0			0
$685$	19.0037			0.726095
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0836309	+	0.144853i	−0.00318608	+	0.00551846i
$690$		0			0
$691$	13.3286	+	23.0857i	0.507042	+	0.878223i	0.999967	+	0.00815061i	$0.00259445\pi$
$691$	13.3286	+	23.0857i	0.507042	+	0.878223i	−0.492925	+	0.870072i	$0.664072\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.9774	−	29.4058i	−0.643990	−	1.11542i
$696$		0			0
$697$	−24.8306	+	43.0078i	−0.940524	+	1.62904i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−7.77329			−0.293593			−0.146797	−	0.989167i	$-0.546896\pi$
$701$	−7.77329			−0.293593			−0.146797	+	0.989167i	$0.546896\pi$
$702$		0			0
$703$	−9.53078	+	16.5078i	−0.359460	+	0.622603i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	26.5354	−	40.1124i	0.997965	−	1.50858i
$708$		0			0
$709$	20.1123	+	34.8355i	0.755332	+	1.30827i	0.945209	+	0.326466i	$0.105858\pi$
$709$	20.1123	+	34.8355i	0.755332	+	1.30827i	−0.189877	+	0.981808i	$0.560809\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.7446			−0.926693
$714$		0			0
$715$	−2.79080			−0.104370
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−16.1822	−	28.0284i	−0.603495	−	1.04528i	−0.992287	−	0.123959i	$-0.960441\pi$
$719$	−16.1822	−	28.0284i	−0.603495	−	1.04528i	0.388792	−	0.921325i	$-0.372892\pi$
$720$		0			0
$721$	−9.24108	−	18.5231i	−0.344156	−	0.689836i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.56614	−	4.44468i	0.0953039	−	0.165071i
$726$		0			0
$727$	35.4282			1.31396			0.656980	−	0.753908i	$-0.271834\pi$
$727$	35.4282			1.31396			0.656980	+	0.753908i	$0.271834\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.66964	−	15.0163i	0.320658	−	0.555396i
$732$		0			0
$733$	−2.49927	−	4.32887i	−0.0923128	−	0.159890i	0.816171	−	0.577810i	$-0.196093\pi$
$733$	−2.49927	−	4.32887i	−0.0923128	−	0.159890i	−0.908484	+	0.417920i	$0.862759\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.9818	+	24.2172i	0.515026	+	0.892052i
$738$		0			0
$739$	16.5002	−	28.5792i	0.606969	−	1.05130i	−0.384768	−	0.923014i	$-0.625718\pi$
$739$	16.5002	−	28.5792i	0.606969	−	1.05130i	0.991737	−	0.128288i	$-0.0409483\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	45.0817			1.65389			0.826944	−	0.562285i	$-0.190078\pi$
$743$	45.0817			1.65389			0.826944	+	0.562285i	$0.190078\pi$
$744$		0			0
$745$	8.11154	−	14.0496i	0.297184	−	0.514738i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.0921	+	20.2288i	0.368756	+	0.739145i
$750$		0			0
$751$	−13.2833	−	23.0074i	−0.484715	−	0.839552i	0.515130	−	0.857112i	$-0.327743\pi$
$751$	−13.2833	−	23.0074i	−0.484715	−	0.839552i	−0.999846	+	0.0175601i	$0.994410\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−14.7087			−0.535306
$756$		0			0
$757$	−15.6833			−0.570021			−0.285010	−	0.958524i	$-0.591997\pi$
$757$	−15.6833			−0.570021			−0.285010	+	0.958524i	$0.591997\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.3282	+	38.6735i	0.809396	+	1.40191i	0.913283	+	0.407326i	$0.133539\pi$
$761$	22.3282	+	38.6735i	0.809396	+	1.40191i	−0.103887	+	0.994589i	$0.533128\pi$
$762$		0			0
$763$	9.58086	−	14.4830i	0.346851	−	0.524320i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.72412	−	2.98626i	0.0622542	−	0.107827i
$768$		0			0
$769$	−7.15705			−0.258090			−0.129045	−	0.991639i	$-0.541191\pi$
$769$	−7.15705			−0.258090			−0.129045	+	0.991639i	$0.541191\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.9545	−	36.2942i	0.753679	−	1.30541i	−0.192349	−	0.981327i	$-0.561611\pi$
$773$	20.9545	−	36.2942i	0.753679	−	1.30541i	0.946028	−	0.324084i	$-0.105056\pi$
$774$		0			0
$775$	5.98800	+	10.3715i	0.215095	+	0.372556i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−29.4758	−	51.0536i	−1.05608	−	1.82918i
$780$		0			0
$781$	−11.5732	+	20.0454i	−0.414123	+	0.717282i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.33155			−0.333057
$786$		0			0
$787$	−4.62627	+	8.01294i	−0.164909	+	0.285630i	−0.936623	−	0.350339i	$-0.886066\pi$
$787$	−4.62627	+	8.01294i	−0.164909	+	0.285630i	0.771714	+	0.635970i	$0.219400\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−42.1930	−	2.57002i	−1.50021	−	0.0913794i
$792$		0			0
$793$	1.42585	+	2.46965i	0.0506335	+	0.0876997i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.389964			−0.0138132			−0.00690662	−	0.999976i	$-0.502198\pi$
$797$	−0.389964			−0.0138132			−0.00690662	+	0.999976i	$0.502198\pi$
$798$		0			0
$799$	61.4487			2.17390
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.1420	+	19.2984i	0.393191	+	0.681027i
$804$		0			0
$805$	11.0453	−	16.6967i	0.389296	−	0.588482i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25.3440	−	43.8972i	0.891049	−	1.54334i	0.0524297	−	0.998625i	$-0.483303\pi$
$809$	25.3440	−	43.8972i	0.891049	−	1.54334i	0.838619	−	0.544718i	$-0.183363\pi$
$810$		0			0
$811$	22.5296			0.791121			0.395560	−	0.918440i	$-0.370550\pi$
$811$	22.5296			0.791121			0.395560	+	0.918440i	$0.370550\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.2229	−	19.4386i	0.393120	−	0.680903i
$816$		0			0
$817$	10.2915	+	17.8255i	0.360055	+	0.623634i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.4991	−	21.6491i	−0.436221	−	0.755558i	0.561173	−	0.827699i	$-0.310350\pi$
$821$	−12.4991	−	21.6491i	−0.436221	−	0.755558i	−0.997394	+	0.0721409i	$0.977017\pi$
$822$		0			0
$823$	−11.9706	+	20.7338i	−0.417271	+	0.722734i	−0.995664	−	0.0930242i	$-0.970347\pi$
$823$	−11.9706	+	20.7338i	−0.417271	+	0.722734i	0.578393	+	0.815758i	$0.303680\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	42.7292			1.48584			0.742921	−	0.669380i	$-0.233440\pi$
$827$	42.7292			1.48584			0.742921	+	0.669380i	$0.233440\pi$
$828$		0			0
$829$	19.4971	−	33.7700i	0.677162	−	1.17288i	−0.298670	−	0.954356i	$-0.596543\pi$
$829$	19.4971	−	33.7700i	0.677162	−	1.17288i	0.975832	−	0.218522i	$-0.0701237\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	30.6553	−	40.7234i	1.06214	−	1.41098i
$834$		0			0
$835$	−10.0397	−	17.3893i	−0.347439	−	0.601782i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−56.4891			−1.95022			−0.975110	−	0.221721i	$-0.928833\pi$
$839$	−56.4891			−1.95022			−0.975110	+	0.221721i	$0.928833\pi$
$840$		0			0
$841$	−16.3461			−0.563660
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.2281	−	28.1079i	−0.558264	−	0.966942i
$846$		0			0
$847$	6.29520	+	12.6183i	0.216306	+	0.433570i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.28687	−	5.69303i	0.112673	−	0.195155i
$852$		0			0
$853$	−19.6327			−0.672212			−0.336106	−	0.941824i	$-0.609110\pi$
$853$	−19.6327			−0.672212			−0.336106	+	0.941824i	$0.609110\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.4020	+	19.7488i	−0.389485	+	0.674607i	−0.992380	−	0.123213i	$-0.960680\pi$
$857$	−11.4020	+	19.7488i	−0.389485	+	0.674607i	0.602896	+	0.797820i	$0.294014\pi$
$858$		0			0
$859$	1.26314	+	2.18782i	0.0430978	+	0.0746476i	0.886770	−	0.462212i	$-0.152944\pi$
$859$	1.26314	+	2.18782i	0.0430978	+	0.0746476i	−0.843672	+	0.536859i	$0.819611\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.2946	+	26.4911i	0.520635	+	0.901767i	0.999712	+	0.0239938i	$0.00763819\pi$
$863$	15.2946	+	26.4911i	0.520635	+	0.901767i	−0.479077	+	0.877773i	$0.659028\pi$
$864$		0			0
$865$	14.0164	−	24.2772i	0.476573	−	0.825450i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	23.7122			0.804382
$870$		0			0
$871$	2.71120	−	4.69593i	0.0918655	−	0.159116i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	23.8447	+	1.45241i	0.806100	+	0.0491004i
$876$		0			0
$877$	10.8010	+	18.7079i	0.364724	+	0.631721i	0.988732	−	0.149697i	$-0.0478299\pi$
$877$	10.8010	+	18.7079i	0.364724	+	0.631721i	−0.624008	+	0.781418i	$0.714497\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	43.2366			1.45668			0.728338	−	0.685218i	$-0.240293\pi$
$881$	43.2366			1.45668			0.728338	+	0.685218i	$0.240293\pi$
$882$		0			0
$883$	−30.7820			−1.03590			−0.517949	−	0.855411i	$-0.673304\pi$
$883$	−30.7820			−1.03590			−0.517949	+	0.855411i	$0.673304\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4.61259	+	7.98924i	0.154876	+	0.268252i	0.933014	−	0.359841i	$-0.117169\pi$
$887$	4.61259	+	7.98924i	0.154876	+	0.268252i	−0.778138	+	0.628093i	$0.783836\pi$
$888$		0			0
$889$	52.7459	+	3.21281i	1.76904	+	0.107754i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−36.4722	+	63.1717i	−1.22049	+	2.11396i
$894$		0			0
$895$	6.53905			0.218576
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−14.7637	+	25.5715i	−0.492397	+	0.852856i
$900$		0			0
$901$	−1.31888	−	2.28436i	−0.0439382	−	0.0761032i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−26.4793	−	45.8635i	−0.880201	−	1.52455i
$906$		0			0
$907$	−22.6210	+	39.1807i	−0.751118	+	1.30097i	0.196164	+	0.980571i	$0.437152\pi$
$907$	−22.6210	+	39.1807i	−0.751118	+	1.30097i	−0.947281	+	0.320403i	$0.896182\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.3678			0.741078			0.370539	−	0.928817i	$-0.379173\pi$
$911$	22.3678			0.741078			0.370539	+	0.928817i	$0.379173\pi$
$912$		0			0
$913$	3.81134	−	6.60144i	0.126137	−	0.218476i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.6374	+	41.3662i	0.681506	+	1.36603i
$918$		0			0
$919$	−5.36191	−	9.28710i	−0.176873	−	0.306353i	0.763935	−	0.645293i	$-0.223265\pi$
$919$	−5.36191	−	9.28710i	−0.176873	−	0.306353i	−0.940808	+	0.338940i	$0.889932\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.48832			0.147735
$924$		0			0
$925$	−3.18159			−0.104610
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.63065	+	14.9487i	0.283162	+	0.490452i	0.972162	−	0.234310i	$-0.0752831\pi$
$929$	8.63065	+	14.9487i	0.283162	+	0.490452i	−0.688999	+	0.724762i	$0.741950\pi$
$930$		0			0
$931$	23.6702	+	55.6858i	0.775758	+	1.82503i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	22.0058	−	38.1152i	0.719667	−	1.24650i
$936$		0			0
$937$	−35.1775			−1.14920			−0.574600	−	0.818434i	$-0.694842\pi$
$937$	−35.1775			−1.14920			−0.574600	+	0.818434i	$0.694842\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.2711	−	35.1106i	0.660820	−	1.14457i	−0.319580	−	0.947559i	$-0.603542\pi$
$941$	20.2711	−	35.1106i	0.660820	−	1.14457i	0.980401	−	0.197015i	$-0.0631247\pi$
$942$		0			0
$943$	10.1653	+	17.6068i	0.331028	+	0.573357i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.5133	+	25.1378i	0.471619	+	0.816867i	0.999473	−	0.0324677i	$-0.0103366\pi$
$947$	14.5133	+	25.1378i	0.471619	+	0.816867i	−0.527854	+	0.849335i	$0.677003\pi$
$948$		0			0
$949$	2.16053	−	3.74214i	0.0701337	−	0.121475i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−57.3207			−1.85680			−0.928400	−	0.371583i	$-0.878815\pi$
$953$	−57.3207			−1.85680			−0.928400	+	0.371583i	$0.878815\pi$
$954$		0			0
$955$	5.56033	−	9.63077i	0.179928	−	0.311644i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	10.9289	−	16.5208i	0.352912	−	0.533483i
$960$		0			0
$961$	−18.9506	−	32.8234i	−0.611310	−	1.05882i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−37.6170			−1.21093
$966$		0			0
$967$	13.7030			0.440660			0.220330	−	0.975425i	$-0.429287\pi$
$967$	13.7030			0.440660			0.220330	+	0.975425i	$0.429287\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.4734	+	26.8007i	0.496566	+	0.860077i	0.999992	−	0.00396126i	$-0.00126091\pi$
$971$	15.4734	+	26.8007i	0.496566	+	0.860077i	−0.503427	+	0.864038i	$0.667928\pi$
$972$		0			0
$973$	−35.3273	−	2.15182i	−1.13254	−	0.0689842i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.0622	−	41.6769i	0.769818	−	1.33336i	−0.167844	−	0.985814i	$-0.553680\pi$
$977$	24.0622	−	41.6769i	0.769818	−	1.33336i	0.937662	−	0.347550i	$-0.112986\pi$
$978$		0			0
$979$	−15.6836			−0.501249
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.3437	+	19.6478i	−0.361806	+	0.626667i	−0.988258	−	0.152793i	$-0.951173\pi$
$983$	−11.3437	+	19.6478i	−0.361806	+	0.626667i	0.626452	+	0.779460i	$0.284506\pi$
$984$		0			0
$985$	7.85113	+	13.5986i	0.250158	+	0.433286i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.54923	−	6.14745i	−0.112859	−	0.195478i
$990$		0			0
$991$	22.8326	−	39.5472i	0.725300	−	1.25626i	−0.233550	−	0.972345i	$-0.575034\pi$
$991$	22.8326	−	39.5472i	0.725300	−	1.25626i	0.958850	−	0.283912i	$-0.0916323\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.2825			0.389381
$996$		0			0
$997$	−20.5374	+	35.5717i	−0.650425	+	1.12657i	0.332595	+	0.943070i	$0.392076\pi$
$997$	−20.5374	+	35.5717i	−0.650425	+	1.12657i	−0.983020	+	0.183499i	$0.941258\pi$
$998$		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.865.3	yes	8
3.2	odd	2		1512.2.s.n.865.2	✓	8
7.2	even	3	inner	1512.2.s.o.1297.3	yes	8
21.2	odd	6		1512.2.s.n.1297.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.n.865.2	✓	8	3.2	odd	2
1512.2.s.n.1297.2	yes	8	21.2	odd	6
1512.2.s.o.865.3	yes	8	1.1	even	1	trivial
1512.2.s.o.1297.3	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)

\(f(q)\)	\(=\)	\(q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +O(q^{10})\)	\(q+(1.26913 + 2.19820i) q^{5} +(2.64086 + 0.160857i) q^{7} +(1.19060 - 2.06219i) q^{11} -0.461738 q^{13} +(3.64086 - 6.30615i) q^{17} +(4.32198 + 7.48589i) q^{19} +(-1.49052 - 2.58165i) q^{23} +(-0.721387 + 1.24948i) q^{25} -3.55723 q^{29} +(4.15034 - 7.18860i) q^{31} +(2.99800 + 6.00928i) q^{35} +(1.10259 + 1.90975i) q^{37} -6.81998 q^{41} +2.38121 q^{43} +(4.21938 + 7.30819i) q^{47} +(6.94825 + 0.849602i) q^{49} +(0.181122 - 0.313712i) q^{53} +6.04413 q^{55} +(-3.73397 + 6.46743i) q^{59} +(-3.08801 - 5.34859i) q^{61} +(-0.586006 - 1.01499i) q^{65} +(-5.87173 + 10.1701i) q^{67} -9.72048 q^{71} +(-4.67912 + 8.10447i) q^{73} +(3.47593 - 5.25442i) q^{77} +(4.97903 + 8.62394i) q^{79} +3.20118 q^{83} +18.4829 q^{85} +(-3.29320 - 5.70399i) q^{89} +(-1.21938 - 0.0742739i) q^{91} +(-10.9703 + 19.0011i) q^{95} +15.6400 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 4 q^{7}+O(q^{10}) \) 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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