LMFDB - Embedded newform 2736.2.s.u.577.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, degree $2$, 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.2
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2736.577
Dual form			2736.2.s.u.1873.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82288 + 3.15731i) q^{5} -4.64575 q^{7} +O(q^{10})$	$q+(1.82288 + 3.15731i) q^{5} -4.64575 q^{7} +0.354249 q^{11} +(2.14575 - 3.71655i) q^{13} +(-1.64575 - 2.85052i) q^{17} +(2.64575 - 3.46410i) q^{19} +(2.82288 - 4.88936i) q^{23} +(-4.14575 + 7.18065i) q^{25} +(3.64575 - 6.31463i) q^{29} +0.645751 q^{31} +(-8.46863 - 14.6681i) q^{35} -5.00000 q^{37} +(2.00000 + 3.46410i) q^{41} +(2.67712 + 4.63692i) q^{43} +(-2.64575 + 4.58258i) q^{47} +14.5830 q^{49} +(3.46863 - 6.00784i) q^{53} +(0.645751 + 1.11847i) q^{55} +(-3.82288 - 6.62141i) q^{59} +(-2.50000 + 4.33013i) q^{61} +15.6458 q^{65} +(6.96863 - 12.0700i) q^{67} +(5.00000 + 8.66025i) q^{71} +(3.14575 + 5.44860i) q^{73} -1.64575 q^{77} +(1.67712 + 2.90486i) q^{79} +15.2915 q^{83} +(6.00000 - 10.3923i) q^{85} +(6.82288 - 11.8176i) q^{89} +(-9.96863 + 17.2662i) q^{91} +(15.7601 + 2.03884i) q^{95} +(-5.29150 - 9.16515i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 8 * q^7	$ 4 q + 2 q^{5} - 8 q^{7} + 12 q^{11} - 2 q^{13} + 4 q^{17} + 6 q^{23} - 6 q^{25} + 4 q^{29} - 8 q^{31} - 18 q^{35} - 20 q^{37} + 8 q^{41} + 16 q^{43} + 16 q^{49} - 2 q^{53} - 8 q^{55} - 10 q^{59} - 10 q^{61} + 52 q^{65} + 12 q^{67} + 20 q^{71} + 2 q^{73} + 4 q^{77} + 12 q^{79} + 40 q^{83} + 24 q^{85} + 22 q^{89} - 24 q^{91} + 26 q^{95}+O(q^{100}) $ 4 * q + 2 * q^5 - 8 * q^7 + 12 * q^11 - 2 * q^13 + 4 * q^17 + 6 * q^23 - 6 * q^25 + 4 * q^29 - 8 * q^31 - 18 * q^35 - 20 * q^37 + 8 * q^41 + 16 * q^43 + 16 * q^49 - 2 * q^53 - 8 * q^55 - 10 * q^59 - 10 * q^61 + 52 * q^65 + 12 * q^67 + 20 * q^71 + 2 * q^73 + 4 * q^77 + 12 * q^79 + 40 * q^83 + 24 * q^85 + 22 * q^89 - 24 * q^91 + 26 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	0.909174	+	0.416417i	$0.136714\pi$
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	−0.0939588	+	0.995576i	$0.529952\pi$
$6$		0			0
$7$	−4.64575			−1.75593			−0.877964	−	0.478726i	$-0.841099\pi$
$7$	−4.64575			−1.75593			−0.877964	+	0.478726i	$0.841099\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.354249			0.106810			0.0534050	−	0.998573i	$-0.482993\pi$
$11$	0.354249			0.106810			0.0534050	+	0.998573i	$0.482993\pi$
$12$		0			0
$13$	2.14575	−	3.71655i	0.595124	−	1.03079i	−0.398405	−	0.917210i	$-0.630436\pi$
$13$	2.14575	−	3.71655i	0.595124	−	1.03079i	0.993529	−	0.113576i	$-0.0362305\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.64575	−	2.85052i	−0.399153	−	0.691354i	0.594468	−	0.804119i	$-0.297363\pi$
$17$	−1.64575	−	2.85052i	−0.399153	−	0.691354i	−0.993622	+	0.112765i	$0.964029\pi$
$18$		0			0
$19$	2.64575	−	3.46410i	0.606977	−	0.794719i
$19$	2.64575	−	3.46410i	0.606977	−	0.794719i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.82288	−	4.88936i	0.588610	−	1.01950i	−0.405804	−	0.913960i	$-0.633009\pi$
$23$	2.82288	−	4.88936i	0.588610	−	1.01950i	0.994415	−	0.105543i	$-0.0336581\pi$
$24$		0			0
$25$	−4.14575	+	7.18065i	−0.829150	+	1.43613i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.64575	−	6.31463i	0.676999	−	1.17260i	−0.298881	−	0.954290i	$-0.596613\pi$
$29$	3.64575	−	6.31463i	0.676999	−	1.17260i	0.975880	−	0.218306i	$-0.0700532\pi$
$30$		0			0
$31$	0.645751			0.115980			0.0579902	−	0.998317i	$-0.481531\pi$
$31$	0.645751			0.115980			0.0579902	+	0.998317i	$0.481531\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.46863	−	14.6681i	−1.43146	−	2.47936i
$36$		0			0
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.00000	+	3.46410i	0.312348	+	0.541002i	0.978870	−	0.204483i	$-0.0655513\pi$
$41$	2.00000	+	3.46410i	0.312348	+	0.541002i	−0.666523	+	0.745485i	$0.732218\pi$
$42$		0			0
$43$	2.67712	+	4.63692i	0.408258	+	0.707123i	0.994695	−	0.102872i	$-0.0328032\pi$
$43$	2.67712	+	4.63692i	0.408258	+	0.707123i	−0.586437	+	0.809995i	$0.699470\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.64575	+	4.58258i	−0.385922	+	0.668437i	−0.991897	−	0.127047i	$-0.959450\pi$
$47$	−2.64575	+	4.58258i	−0.385922	+	0.668437i	0.605974	+	0.795484i	$0.292783\pi$
$48$		0			0
$49$	14.5830			2.08329
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.46863	−	6.00784i	0.476453	−	0.825240i	−0.523183	−	0.852220i	$-0.675256\pi$
$53$	3.46863	−	6.00784i	0.476453	−	0.825240i	0.999636	+	0.0269801i	$0.00858907\pi$
$54$		0			0
$55$	0.645751	+	1.11847i	0.0870731	+	0.150815i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.82288	−	6.62141i	−0.497696	−	0.862035i	0.502300	−	0.864693i	$-0.332487\pi$
$59$	−3.82288	−	6.62141i	−0.497696	−	0.862035i	−0.999996	+	0.00265837i	$0.999154\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	15.6458			1.94062
$66$		0			0
$67$	6.96863	−	12.0700i	0.851353	−	1.47459i	−0.0286340	−	0.999590i	$-0.509116\pi$
$67$	6.96863	−	12.0700i	0.851353	−	1.47459i	0.879987	−	0.474997i	$-0.157551\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000	+	8.66025i	0.593391	+	1.02778i	0.993772	+	0.111434i	$0.0355445\pi$
$71$	5.00000	+	8.66025i	0.593391	+	1.02778i	−0.400381	+	0.916349i	$0.631122\pi$
$72$		0			0
$73$	3.14575	+	5.44860i	0.368182	+	0.637711i	0.989281	−	0.146022i	$-0.0466469\pi$
$73$	3.14575	+	5.44860i	0.368182	+	0.637711i	−0.621099	+	0.783732i	$0.713314\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.64575			−0.187551
$78$		0			0
$79$	1.67712	+	2.90486i	0.188691	+	0.326823i	0.944814	−	0.327607i	$-0.106242\pi$
$79$	1.67712	+	2.90486i	0.188691	+	0.326823i	−0.756123	+	0.654430i	$0.772909\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	15.2915			1.67846			0.839230	−	0.543776i	$-0.183006\pi$
$83$	15.2915			1.67846			0.839230	+	0.543776i	$0.183006\pi$
$84$		0			0
$85$	6.00000	−	10.3923i	0.650791	−	1.12720i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.82288	−	11.8176i	0.723223	−	1.25266i	−0.236478	−	0.971637i	$-0.575993\pi$
$89$	6.82288	−	11.8176i	0.723223	−	1.25266i	0.959701	−	0.281023i	$-0.0906736\pi$
$90$		0			0
$91$	−9.96863	+	17.2662i	−1.04500	+	1.80999i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.7601	+	2.03884i	1.61696	+	0.209180i
$96$		0			0
$97$	−5.29150	−	9.16515i	−0.537271	−	0.930580i	−0.999050	−	0.0435851i	$-0.986122\pi$
$97$	−5.29150	−	9.16515i	−0.537271	−	0.930580i	0.461779	−	0.886995i	$-0.347211\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.93725	+	17.2118i	−0.988794	+	1.71264i	−0.365109	+	0.930965i	$0.618968\pi$
$101$	−9.93725	+	17.2118i	−0.988794	+	1.71264i	−0.623684	+	0.781676i	$0.714365\pi$
$102$		0			0
$103$	−7.93725			−0.782081			−0.391040	−	0.920373i	$-0.627885\pi$
$103$	−7.93725			−0.782081			−0.391040	+	0.920373i	$0.627885\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.0000			1.35343			0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000			1.35343			0.676716	+	0.736245i	$0.263403\pi$
$108$		0			0
$109$	4.35425	+	7.54178i	0.417061	+	0.722372i	0.995642	−	0.0932534i	$-0.0297267\pi$
$109$	4.35425	+	7.54178i	0.417061	+	0.722372i	−0.578581	+	0.815625i	$0.696393\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.64575			0.531108			0.265554	−	0.964096i	$-0.414445\pi$
$113$	5.64575			0.531108			0.265554	+	0.964096i	$0.414445\pi$
$114$		0			0
$115$	20.5830			1.91938
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.64575	+	13.2428i	0.700885	+	1.21397i
$120$		0			0
$121$	−10.8745			−0.988592
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−1.64575	+	2.85052i	−0.146037	+	0.252943i	−0.929759	−	0.368168i	$-0.879985\pi$
$127$	−1.64575	+	2.85052i	−0.146037	+	0.252943i	0.783722	+	0.621111i	$0.213318\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−12.2915	+	16.0934i	−1.06581	+	1.39547i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.64575	−	11.5108i	0.567785	−	0.983432i	−0.429000	−	0.903305i	$-0.641134\pi$
$137$	6.64575	−	11.5108i	0.567785	−	0.983432i	0.996785	−	0.0801276i	$-0.0255328\pi$
$138$		0			0
$139$	−2.32288	+	4.02334i	−0.197024	+	0.341255i	−0.947562	−	0.319572i	$-0.896461\pi$
$139$	−2.32288	+	4.02334i	−0.197024	+	0.341255i	0.750538	+	0.660827i	$0.229794\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.760130	−	1.31658i	0.0635652	−	0.110098i
$144$		0			0
$145$	26.5830			2.20760
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.822876	−	1.42526i	−0.0674126	−	0.116762i	0.830349	−	0.557244i	$-0.188141\pi$
$149$	−0.822876	−	1.42526i	−0.0674126	−	0.116762i	−0.897762	+	0.440482i	$0.854808\pi$
$150$		0			0
$151$	0.708497			0.0576567			0.0288283	−	0.999584i	$-0.490822\pi$
$151$	0.708497			0.0576567			0.0288283	+	0.999584i	$0.490822\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.17712	+	2.03884i	0.0945489	+	0.163764i
$156$		0			0
$157$	−5.14575	−	8.91270i	−0.410676	−	0.711311i	0.584288	−	0.811546i	$-0.301374\pi$
$157$	−5.14575	−	8.91270i	−0.410676	−	0.711311i	−0.994964	+	0.100235i	$0.968040\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−13.1144	+	22.7148i	−1.03356	+	1.79017i
$162$		0			0
$163$	−0.0627461			−0.00491465			−0.00245733	−	0.999997i	$-0.500782\pi$
$163$	−0.0627461			−0.00491465			−0.00245733	+	0.999997i	$0.500782\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.531373	+	0.920365i	−0.0411189	+	0.0712200i	−0.885852	−	0.463967i	$-0.846426\pi$
$167$	−0.531373	+	0.920365i	−0.0411189	+	0.0712200i	0.844734	+	0.535187i	$0.179759\pi$
$168$		0			0
$169$	−2.70850	−	4.69126i	−0.208346	−	0.360866i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.93725	−	8.55157i	−0.375372	−	0.650164i	0.615010	−	0.788519i	$-0.289152\pi$
$173$	−4.93725	−	8.55157i	−0.375372	−	0.650164i	−0.990383	+	0.138355i	$0.955819\pi$
$174$		0			0
$175$	19.2601	−	33.3595i	1.45593	−	2.52174i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.3542			−0.773913			−0.386956	−	0.922098i	$-0.626474\pi$
$179$	−10.3542			−0.773913			−0.386956	+	0.922098i	$0.626474\pi$
$180$		0			0
$181$	13.2915	−	23.0216i	0.987950	−	1.71118i	0.359935	−	0.932977i	$-0.382799\pi$
$181$	13.2915	−	23.0216i	0.987950	−	1.71118i	0.628015	−	0.778202i	$-0.283868\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.11438	−	15.7866i	−0.670102	−	1.16065i
$186$		0			0
$187$	−0.583005	−	1.00979i	−0.0426336	−	0.0738435i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.937254			−0.0678173			−0.0339087	−	0.999425i	$-0.510796\pi$
$191$	−0.937254			−0.0678173			−0.0339087	+	0.999425i	$0.510796\pi$
$192$		0			0
$193$	−11.0830	−	19.1963i	−0.797772	−	1.38178i	−0.921064	−	0.389411i	$-0.872678\pi$
$193$	−11.0830	−	19.1963i	−0.797772	−	1.38178i	0.123292	−	0.992370i	$-0.460655\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.6458			1.25721			0.628604	−	0.777726i	$-0.283627\pi$
$197$	17.6458			1.25721			0.628604	+	0.777726i	$0.283627\pi$
$198$		0			0
$199$	−5.96863	+	10.3380i	−0.423105	+	0.732839i	−0.996241	−	0.0866209i	$-0.972393\pi$
$199$	−5.96863	+	10.3380i	−0.423105	+	0.732839i	0.573137	+	0.819460i	$0.305726\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−16.9373	+	29.3362i	−1.18876	+	2.05900i
$204$		0			0
$205$	−7.29150	+	12.6293i	−0.509261	+	0.882065i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.937254	−	1.22715i	0.0648312	−	0.0848840i
$210$		0			0
$211$	5.32288	+	9.21949i	0.366442	+	0.634696i	0.989006	−	0.147873i	$-0.0472425\pi$
$211$	5.32288	+	9.21949i	0.366442	+	0.634696i	−0.622565	+	0.782568i	$0.713909\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−9.76013	+	16.9050i	−0.665635	+	1.15291i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−14.1255			−0.950183
$222$		0			0
$223$	−2.67712	−	4.63692i	−0.179274	−	0.310511i	0.762358	−	0.647155i	$-0.224041\pi$
$223$	−2.67712	−	4.63692i	−0.179274	−	0.310511i	−0.941632	+	0.336644i	$0.890708\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.5203			1.03012			0.515058	−	0.857155i	$-0.327770\pi$
$227$	15.5203			1.03012			0.515058	+	0.857155i	$0.327770\pi$
$228$		0			0
$229$	−9.70850			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$229$	−9.70850			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.93725	−	3.35542i	−0.126914	−	0.219821i	0.795566	−	0.605867i	$-0.207174\pi$
$233$	−1.93725	−	3.35542i	−0.126914	−	0.219821i	−0.922479	+	0.386046i	$0.873840\pi$
$234$		0			0
$235$	−19.2915			−1.25844
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.93725			0.319364			0.159682	−	0.987168i	$-0.448953\pi$
$239$	4.93725			0.319364			0.159682	+	0.987168i	$0.448953\pi$
$240$		0			0
$241$	−5.43725	+	9.41760i	−0.350244	+	0.606641i	−0.986292	−	0.165009i	$-0.947235\pi$
$241$	−5.43725	+	9.41760i	−0.350244	+	0.606641i	0.636048	+	0.771650i	$0.280568\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	26.5830	+	46.0431i	1.69833	+	2.94159i
$246$		0			0
$247$	−7.19738	−	17.2662i	−0.457959	−	1.09862i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.64575	−	11.5108i	0.419476	−	0.726554i	−0.576411	−	0.817160i	$-0.695547\pi$
$251$	6.64575	−	11.5108i	0.419476	−	0.726554i	0.995887	+	0.0906062i	$0.0288805\pi$
$252$		0			0
$253$	1.00000	−	1.73205i	0.0628695	−	0.108893i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.82288	−	13.5496i	0.487978	−	0.845202i	−0.511927	−	0.859029i	$-0.671068\pi$
$257$	7.82288	−	13.5496i	0.487978	−	0.845202i	0.999904	+	0.0138271i	$0.00440144\pi$
$258$		0			0
$259$	23.2288			1.44336
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$	25.2915			1.55364
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.82288	−	11.8176i	−0.415998	−	0.720530i	0.579535	−	0.814948i	$-0.303234\pi$
$269$	−6.82288	−	11.8176i	−0.415998	−	0.720530i	−0.995533	+	0.0944179i	$0.969901\pi$
$270$		0			0
$271$	5.29150	+	9.16515i	0.321436	+	0.556743i	0.980785	−	0.195094i	$-0.0625012\pi$
$271$	5.29150	+	9.16515i	0.321436	+	0.556743i	−0.659349	+	0.751837i	$0.729168\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.46863	+	2.54374i	−0.0885615	+	0.153393i
$276$		0			0
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.46863	+	6.00784i	−0.206921	+	0.358398i	−0.950743	−	0.309980i	$-0.899678\pi$
$281$	−3.46863	+	6.00784i	−0.206921	+	0.358398i	0.743822	+	0.668378i	$0.233011\pi$
$282$		0			0
$283$	−2.70850	−	4.69126i	−0.161003	−	0.278866i	0.774225	−	0.632910i	$-0.218140\pi$
$283$	−2.70850	−	4.69126i	−0.161003	−	0.278866i	−0.935229	+	0.354044i	$0.884806\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.29150	−	16.0934i	−0.548460	−	0.949961i
$288$		0			0
$289$	3.08301	−	5.33992i	0.181353	−	0.314113i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	24.5830			1.43615			0.718077	−	0.695963i	$-0.245022\pi$
$293$	24.5830			1.43615			0.718077	+	0.695963i	$0.245022\pi$
$294$		0			0
$295$	13.9373	−	24.1400i	0.811458	−	1.40549i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−12.1144	−	20.9827i	−0.700593	−	1.21346i
$300$		0			0
$301$	−12.4373	−	21.5420i	−0.716871	−	1.24166i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−18.2288			−1.04378
$306$		0			0
$307$	−13.9373	−	24.1400i	−0.795441	−	1.37774i	−0.922559	−	0.385857i	$-0.873906\pi$
$307$	−13.9373	−	24.1400i	−0.795441	−	1.37774i	0.127118	−	0.991888i	$-0.459427\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	17.0627			0.967540			0.483770	−	0.875195i	$-0.339267\pi$
$311$	17.0627			0.967540			0.483770	+	0.875195i	$0.339267\pi$
$312$		0			0
$313$	9.64575	−	16.7069i	0.545210	−	0.944332i	−0.453384	−	0.891316i	$-0.649783\pi$
$313$	9.64575	−	16.7069i	0.545210	−	0.944332i	0.998594	−	0.0530161i	$-0.0168835\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.46863	+	9.47194i	−0.307149	+	0.531997i	−0.977737	−	0.209832i	$-0.932708\pi$
$317$	−5.46863	+	9.47194i	−0.307149	+	0.531997i	0.670589	+	0.741829i	$0.266042\pi$
$318$		0			0
$319$	1.29150	−	2.23695i	0.0723103	−	0.125245i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−14.2288	−	1.84073i	−0.791709	−	0.102421i
$324$		0			0
$325$	17.7915	+	30.8158i	0.986895	+	1.70935i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.2915	−	21.2895i	0.677652	−	1.17373i
$330$		0			0
$331$	21.2288			1.16684			0.583419	−	0.812171i	$-0.301715\pi$
$331$	21.2288			1.16684			0.583419	+	0.812171i	$0.301715\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	50.8118			2.77614
$336$		0			0
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	0.998080	+	0.0619313i	$0.0197260\pi$
$337$	10.1458	+	17.5730i	0.552674	+	0.957260i	−0.445406	+	0.895329i	$0.646941\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.228757			0.0123879
$342$		0			0
$343$	−35.2288			−1.90217
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.40588	−	16.2915i	−0.504934	−	0.874572i	−0.999984	−	0.00570686i	$-0.998183\pi$
$347$	−9.40588	−	16.2915i	−0.504934	−	0.874572i	0.495050	−	0.868865i	$-0.335150\pi$
$348$		0			0
$349$	10.8745			0.582099			0.291050	−	0.956708i	$-0.405996\pi$
$349$	10.8745			0.582099			0.291050	+	0.956708i	$0.405996\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	10.9373			0.582131			0.291066	−	0.956703i	$-0.405990\pi$
$353$	10.9373			0.582131			0.291066	+	0.956703i	$0.405990\pi$
$354$		0			0
$355$	−18.2288	+	31.5731i	−0.967482	+	1.67573i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	−5.00000	−	18.3303i	−0.263158	−	0.964753i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−11.4686	+	19.8642i	−0.600295	+	1.03974i
$366$		0			0
$367$	−6.61438	+	11.4564i	−0.345268	+	0.598021i	−0.985402	−	0.170241i	$-0.945545\pi$
$367$	−6.61438	+	11.4564i	−0.345268	+	0.598021i	0.640135	+	0.768263i	$0.278879\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.1144	+	27.9109i	−0.836617	+	1.44906i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.6458	−	27.0992i	−0.805797	−	1.39568i
$378$		0			0
$379$	8.52026			0.437656			0.218828	−	0.975763i	$-0.429777\pi$
$379$	8.52026			0.437656			0.218828	+	0.975763i	$0.429777\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.82288	−	10.0855i	−0.297535	−	0.515346i	0.678036	−	0.735028i	$-0.262831\pi$
$383$	−5.82288	−	10.0855i	−0.297535	−	0.515346i	−0.975571	+	0.219683i	$0.929498\pi$
$384$		0			0
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.88562	+	8.46215i	−0.247711	+	0.429048i	−0.962890	−	0.269893i	$-0.913012\pi$
$389$	−4.88562	+	8.46215i	−0.247711	+	0.429048i	0.715179	+	0.698941i	$0.246345\pi$
$390$		0			0
$391$	−18.5830			−0.939783
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.11438	+	10.5904i	−0.307648	+	0.532862i
$396$		0			0
$397$	11.1458	+	19.3050i	0.559389	+	0.968891i	0.997548	+	0.0699927i	$0.0222976\pi$
$397$	11.1458	+	19.3050i	0.559389	+	0.968891i	−0.438158	+	0.898898i	$0.644369\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.17712	+	12.4311i	0.358408	+	0.620782i	0.987695	−	0.156392i	$-0.0499862\pi$
$401$	7.17712	+	12.4311i	0.358408	+	0.620782i	−0.629287	+	0.777173i	$0.716653\pi$
$402$		0			0
$403$	1.38562	−	2.39997i	0.0690227	−	0.119551i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.77124			−0.0877973
$408$		0			0
$409$	2.35425	−	4.07768i	0.116410	−	0.201628i	−0.801932	−	0.597415i	$-0.796195\pi$
$409$	2.35425	−	4.07768i	0.116410	−	0.201628i	0.918343	+	0.395787i	$0.129528\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	17.7601	+	30.7614i	0.873919	+	1.51367i
$414$		0			0
$415$	27.8745	+	48.2801i	1.36831	+	2.36998i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	22.9373			1.12056			0.560279	−	0.828304i	$-0.310694\pi$
$419$	22.9373			1.12056			0.560279	+	0.828304i	$0.310694\pi$
$420$		0			0
$421$	10.2288	+	17.7167i	0.498519	+	0.863460i	0.999999	−	0.00170916i	$-0.000544044\pi$
$421$	10.2288	+	17.7167i	0.498519	+	0.863460i	−0.501479	+	0.865170i	$0.667211\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	27.2915			1.32383
$426$		0			0
$427$	11.6144	−	20.1167i	0.562059	−	0.973515i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.2288	−	29.8411i	0.829880	−	1.43739i	−0.0682519	−	0.997668i	$-0.521742\pi$
$431$	17.2288	−	29.8411i	0.829880	−	1.43739i	0.898132	−	0.439726i	$-0.144925\pi$
$432$		0			0
$433$	5.14575	−	8.91270i	0.247289	−	0.428317i	−0.715484	−	0.698629i	$-0.753794\pi$
$433$	5.14575	−	8.91270i	0.247289	−	0.428317i	0.962773	+	0.270312i	$0.0871270\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.46863	−	22.7148i	−0.452946	−	1.08659i
$438$		0			0
$439$	−9.26013	−	16.0390i	−0.441962	−	0.765500i	0.555873	−	0.831267i	$-0.312384\pi$
$439$	−9.26013	−	16.0390i	−0.441962	−	0.765500i	−0.997835	+	0.0657667i	$0.979051\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.64575	+	16.7069i	−0.458283	+	0.793770i	−0.998870	−	0.0475179i	$-0.984869\pi$
$443$	−9.64575	+	16.7069i	−0.458283	+	0.793770i	0.540587	+	0.841288i	$0.318202\pi$
$444$		0			0
$445$	49.7490			2.35833
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.29150			−0.344107			−0.172054	−	0.985088i	$-0.555040\pi$
$449$	−7.29150			−0.344107			−0.172054	+	0.985088i	$0.555040\pi$
$450$		0			0
$451$	0.708497	+	1.22715i	0.0333618	+	0.0577844i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−72.6863			−3.40758
$456$		0			0
$457$	−34.8745			−1.63136			−0.815680	−	0.578503i	$-0.803637\pi$
$457$	−34.8745			−1.63136			−0.815680	+	0.578503i	$0.803637\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.23987	−	3.87957i	−0.104321	−	0.180690i	0.809139	−	0.587617i	$-0.199934\pi$
$461$	−2.23987	−	3.87957i	−0.104321	−	0.180690i	−0.913461	+	0.406927i	$0.866600\pi$
$462$		0			0
$463$	−33.2288			−1.54427			−0.772136	−	0.635458i	$-0.780811\pi$
$463$	−33.2288			−1.54427			−0.772136	+	0.635458i	$0.780811\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.16601			−0.424152			−0.212076	−	0.977253i	$-0.568023\pi$
$467$	−9.16601			−0.424152			−0.212076	+	0.977253i	$0.568023\pi$
$468$		0			0
$469$	−32.3745	+	56.0743i	−1.49492	+	2.58927i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.948368	+	1.64262i	0.0436060	+	0.0755278i
$474$		0			0
$475$	13.9059	+	33.3595i	0.638046	+	1.53064i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.416995	−	0.722256i	0.0190530	−	0.0330007i	−0.856342	−	0.516410i	$-0.827268\pi$
$479$	0.416995	−	0.722256i	0.0190530	−	0.0330007i	0.875395	+	0.483409i	$0.160602\pi$
$480$		0			0
$481$	−10.7288	+	18.5828i	−0.489189	+	0.847301i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	19.2915	−	33.4139i	0.875982	−	1.51725i
$486$		0			0
$487$	−0.708497			−0.0321051			−0.0160525	−	0.999871i	$-0.505110\pi$
$487$	−0.708497			−0.0321051			−0.0160525	+	0.999871i	$0.505110\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	11.5830	+	20.0624i	0.522734	+	0.905401i	0.999650	+	0.0264527i	$0.00842113\pi$
$491$	11.5830	+	20.0624i	0.522734	+	0.905401i	−0.476916	+	0.878949i	$0.658246\pi$
$492$		0			0
$493$	−24.0000			−1.08091
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.2288	−	40.2334i	−1.04195	−	1.80471i
$498$		0			0
$499$	−11.5516	−	20.0080i	−0.517122	−	0.895682i	−0.999802	−	0.0198850i	$-0.993670\pi$
$499$	−11.5516	−	20.0080i	−0.517122	−	0.895682i	0.482680	−	0.875797i	$-0.339663\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.3542	+	17.9341i	−0.461673	+	0.799641i	−0.999045	−	0.0437044i	$-0.986084\pi$
$503$	−10.3542	+	17.9341i	−0.461673	+	0.799641i	0.537371	+	0.843346i	$0.319417\pi$
$504$		0			0
$505$	−72.4575			−3.22432
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−22.1660	+	38.3927i	−0.982491	+	1.70172i	−0.329897	+	0.944017i	$0.607014\pi$
$509$	−22.1660	+	38.3927i	−0.982491	+	1.70172i	−0.652594	+	0.757708i	$0.726319\pi$
$510$		0			0
$511$	−14.6144	−	25.3128i	−0.646502	−	1.11977i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.4686	−	25.0604i	−0.637564	−	1.10429i
$516$		0			0
$517$	−0.937254	+	1.62337i	−0.0412204	+	0.0713958i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.6458			0.773074			0.386537	−	0.922274i	$-0.373671\pi$
$521$	17.6458			0.773074			0.386537	+	0.922274i	$0.373671\pi$
$522$		0			0
$523$	−17.1974	+	29.7867i	−0.751989	+	1.30248i	0.194868	+	0.980829i	$0.437572\pi$
$523$	−17.1974	+	29.7867i	−0.751989	+	1.30248i	−0.946857	+	0.321654i	$0.895761\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.06275	−	1.84073i	−0.0462939	−	0.0801835i
$528$		0			0
$529$	−4.43725	−	7.68555i	−0.192924	−	0.334154i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	17.1660			0.743542
$534$		0			0
$535$	25.5203	+	44.2024i	1.10334	+	1.91104i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.16601			0.222516
$540$		0			0
$541$	−13.4373	+	23.2740i	−0.577713	+	1.00063i	0.418028	+	0.908434i	$0.362721\pi$
$541$	−13.4373	+	23.2740i	−0.577713	+	1.00063i	−0.995741	+	0.0921937i	$0.970612\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−15.8745	+	27.4955i	−0.679989	+	1.17778i
$546$		0			0
$547$	−0.614378	+	1.06413i	−0.0262689	+	0.0454991i	−0.878861	−	0.477078i	$-0.841696\pi$
$547$	−0.614378	+	1.06413i	−0.0262689	+	0.0454991i	0.852592	+	0.522577i	$0.175029\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.2288	−	29.3362i	−0.520963	−	1.24976i
$552$		0			0
$553$	−7.79150	−	13.4953i	−0.331328	−	0.573878i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.9373	+	31.0682i	−0.760026	+	1.31640i	0.182811	+	0.983148i	$0.441480\pi$
$557$	−17.9373	+	31.0682i	−0.760026	+	1.31640i	−0.942837	+	0.333255i	$0.891853\pi$
$558$		0			0
$559$	22.9778			0.971856
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$		0			0
$565$	10.2915	+	17.8254i	0.432967	+	0.749920i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−41.1660			−1.72577			−0.862884	−	0.505401i	$-0.831344\pi$
$569$	−41.1660			−1.72577			−0.862884	+	0.505401i	$0.831344\pi$
$570$		0			0
$571$	−3.93725			−0.164769			−0.0823845	−	0.996601i	$-0.526254\pi$
$571$	−3.93725			−0.164769			−0.0823845	+	0.996601i	$0.526254\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.4059	+	40.5402i	0.976093	+	1.69064i
$576$		0			0
$577$	−0.708497			−0.0294951			−0.0147476	−	0.999891i	$-0.504694\pi$
$577$	−0.708497			−0.0294951			−0.0147476	+	0.999891i	$0.504694\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−71.0405			−2.94726
$582$		0			0
$583$	1.22876	−	2.12827i	0.0508899	−	0.0881439i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.1144	+	22.7148i	0.541288	+	0.937539i	0.998830	+	0.0483509i	$0.0153966\pi$
$587$	13.1144	+	22.7148i	0.541288	+	0.937539i	−0.457542	+	0.889188i	$0.651270\pi$
$588$		0			0
$589$	1.70850	−	2.23695i	0.0703974	−	0.0921718i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.46863	−	7.73989i	0.183505	−	0.317839i	−0.759567	−	0.650429i	$-0.774589\pi$
$593$	4.46863	−	7.73989i	0.183505	−	0.317839i	0.943072	+	0.332590i	$0.107922\pi$
$594$		0			0
$595$	−27.8745	+	48.2801i	−1.14274	+	1.97929i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.82288	−	6.62141i	0.156198	−	0.270544i	−0.777296	−	0.629135i	$-0.783409\pi$
$599$	3.82288	−	6.62141i	0.156198	−	0.270544i	0.933495	+	0.358591i	$0.116743\pi$
$600$		0			0
$601$	−19.7085			−0.803926			−0.401963	−	0.915656i	$-0.631672\pi$
$601$	−19.7085			−0.803926			−0.401963	+	0.915656i	$0.631672\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.8229	−	34.3342i	−0.805914	−	1.39588i
$606$		0			0
$607$	35.9373			1.45865			0.729324	−	0.684168i	$-0.239835\pi$
$607$	35.9373			1.45865			0.729324	+	0.684168i	$0.239835\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.3542	+	19.6661i	0.459344	+	0.795607i
$612$		0			0
$613$	4.58301	+	7.93800i	0.185106	+	0.320613i	0.943612	−	0.331053i	$-0.107404\pi$
$613$	4.58301	+	7.93800i	0.185106	+	0.320613i	−0.758506	+	0.651666i	$0.774071\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.53137	−	16.5088i	0.383719	−	0.664620i	−0.607872	−	0.794035i	$-0.707977\pi$
$617$	9.53137	−	16.5088i	0.383719	−	0.664620i	0.991591	+	0.129415i	$0.0413099\pi$
$618$		0			0
$619$	−23.9373			−0.962119			−0.481060	−	0.876688i	$-0.659748\pi$
$619$	−23.9373			−0.962119			−0.481060	+	0.876688i	$0.659748\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−31.6974	+	54.9015i	−1.26993	+	2.19958i
$624$		0			0
$625$	−1.14575	−	1.98450i	−0.0458301	−	0.0793800i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.22876	+	14.2526i	0.328102	+	0.568289i
$630$		0			0
$631$	−8.96863	+	15.5341i	−0.357035	+	0.618403i	−0.987464	−	0.157844i	$-0.949546\pi$
$631$	−8.96863	+	15.5341i	−0.357035	+	0.618403i	0.630429	+	0.776247i	$0.282879\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.0000			−0.476205
$636$		0			0
$637$	31.2915	−	54.1985i	1.23981	−	2.14742i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.291503	+	0.504897i	0.0115137	+	0.0199422i	0.871725	−	0.489996i	$-0.163002\pi$
$641$	0.291503	+	0.504897i	0.0115137	+	0.0199422i	−0.860211	+	0.509938i	$0.829668\pi$
$642$		0			0
$643$	−22.9686	−	39.7828i	−0.905794	−	1.56888i	−0.819848	−	0.572582i	$-0.805942\pi$
$643$	−22.9686	−	39.7828i	−0.905794	−	1.56888i	−0.0859467	−	0.996300i	$-0.527391\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.7085			0.656879			0.328439	−	0.944525i	$-0.393477\pi$
$647$	16.7085			0.656879			0.328439	+	0.944525i	$0.393477\pi$
$648$		0			0
$649$	−1.35425	−	2.34563i	−0.0531589	−	0.0920739i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	39.8745			1.56041			0.780205	−	0.625524i	$-0.215115\pi$
$653$	39.8745			1.56041			0.780205	+	0.625524i	$0.215115\pi$
$654$		0			0
$655$	10.9373	−	18.9439i	0.427354	−	0.740199i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.1144	+	29.6430i	−0.666682	+	1.15473i	0.312145	+	0.950034i	$0.398953\pi$
$659$	−17.1144	+	29.6430i	−0.666682	+	1.15473i	−0.978826	+	0.204692i	$0.934381\pi$
$660$		0			0
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	−0.845922	−	0.533306i	$-0.820949\pi$
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	0.884818	+	0.465937i	$0.154283\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−73.2176	−	9.47194i	−2.83926	−	0.367306i
$666$		0			0
$667$	−20.5830	−	35.6508i	−0.796977	−	1.38040i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.885622	+	1.53394i	−0.0341890	+	0.0592172i
$672$		0			0
$673$	7.12549			0.274668			0.137334	−	0.990525i	$-0.456147\pi$
$673$	7.12549			0.274668			0.137334	+	0.990525i	$0.456147\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−23.1660			−0.890342			−0.445171	−	0.895446i	$-0.646857\pi$
$677$	−23.1660			−0.890342			−0.445171	+	0.895446i	$0.646857\pi$
$678$		0			0
$679$	24.5830	+	42.5790i	0.943409	+	1.63403i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.228757			0.00875313			0.00437656	−	0.999990i	$-0.498607\pi$
$683$	0.228757			0.00875313			0.00437656	+	0.999990i	$0.498607\pi$
$684$		0			0
$685$	48.4575			1.85147
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.8856	−	25.7827i	−0.567097	−	0.982241i
$690$		0			0
$691$	13.1660			0.500859			0.250429	−	0.968135i	$-0.419428\pi$
$691$	13.1660			0.500859			0.250429	+	0.968135i	$0.419428\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.9373			−0.642467
$696$		0			0
$697$	6.58301	−	11.4021i	0.249349	−	0.431885i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	22.0516	+	38.1945i	0.832879	+	1.44259i	0.895746	+	0.444566i	$0.146642\pi$
$701$	22.0516	+	38.1945i	0.832879	+	1.44259i	−0.0628673	+	0.998022i	$0.520024\pi$
$702$		0			0
$703$	−13.2288	+	17.3205i	−0.498932	+	0.653255i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	46.1660	−	79.9619i	1.73625	−	3.00728i
$708$		0			0
$709$	1.79150	−	3.10297i	0.0672813	−	0.116535i	−0.830422	−	0.557134i	$-0.811901\pi$
$709$	1.79150	−	3.10297i	0.0672813	−	0.116535i	0.897704	+	0.440600i	$0.145234\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.82288	−	3.15731i	0.0682672	−	0.118242i
$714$		0			0
$715$	5.54249			0.207277
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.468627	+	0.811686i	0.0174768	+	0.0302708i	0.874632	−	0.484788i	$-0.161103\pi$
$719$	0.468627	+	0.811686i	0.0174768	+	0.0302708i	−0.857155	+	0.515059i	$0.827770\pi$
$720$		0			0
$721$	36.8745			1.37328
$722$		0			0
$723$		0			0
$724$		0			0
$725$	30.2288	+	52.3577i	1.12267	+	1.94452i
$726$		0			0
$727$	12.2601	+	21.2352i	0.454703	+	0.787569i	0.998671	−	0.0515372i	$-0.0164121\pi$
$727$	12.2601	+	21.2352i	0.454703	+	0.787569i	−0.543968	+	0.839106i	$0.683079\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.81176	−	15.2624i	0.325915	−	0.564501i
$732$		0			0
$733$	−13.1660			−0.486298			−0.243149	−	0.969989i	$-0.578180\pi$
$733$	−13.1660			−0.486298			−0.243149	+	0.969989i	$0.578180\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.46863	−	4.27579i	0.0909330	−	0.157501i
$738$		0			0
$739$	−16.3229	−	28.2720i	−0.600447	−	1.04000i	−0.992753	−	0.120170i	$-0.961656\pi$
$739$	−16.3229	−	28.2720i	−0.600447	−	1.04000i	0.392307	−	0.919834i	$-0.371677\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.11438	+	5.39426i	0.114255	+	0.197896i	0.917482	−	0.397778i	$-0.130218\pi$
$743$	3.11438	+	5.39426i	0.114255	+	0.197896i	−0.803226	+	0.595674i	$0.796885\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−65.0405			−2.37653
$750$		0			0
$751$	−1.32288	+	2.29129i	−0.0482724	+	0.0836103i	−0.889152	−	0.457612i	$-0.848705\pi$
$751$	−1.32288	+	2.29129i	−0.0482724	+	0.0836103i	0.840880	+	0.541222i	$0.182038\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.29150	+	2.23695i	0.0470026	+	0.0814109i
$756$		0			0
$757$	−6.79150	−	11.7632i	−0.246841	−	0.427542i	0.715806	−	0.698299i	$-0.246059\pi$
$757$	−6.79150	−	11.7632i	−0.246841	−	0.427542i	−0.962648	+	0.270757i	$0.912726\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	35.5203			1.28761			0.643804	−	0.765190i	$-0.277355\pi$
$761$	35.5203			1.28761			0.643804	+	0.765190i	$0.277355\pi$
$762$		0			0
$763$	−20.2288	−	35.0372i	−0.732330	−	1.26843i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−32.8118			−1.18476
$768$		0			0
$769$	5.79150	−	10.0312i	0.208847	−	0.361733i	−0.742505	−	0.669841i	$-0.766362\pi$
$769$	5.79150	−	10.0312i	0.208847	−	0.361733i	0.951352	+	0.308107i	$0.0996956\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	18.8745	−	32.6916i	0.678869	−	1.17584i	−0.296453	−	0.955047i	$-0.595804\pi$
$773$	18.8745	−	32.6916i	0.678869	−	1.17584i	0.975322	−	0.220788i	$-0.0708629\pi$
$774$		0			0
$775$	−2.67712	+	4.63692i	−0.0961651	+	0.166563i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.2915	+	2.23695i	0.619532	+	0.0801470i
$780$		0			0
$781$	1.77124	+	3.06788i	0.0633801	+	0.109778i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	18.7601	−	32.4935i	0.669578	−	1.15974i
$786$		0			0
$787$	19.8118			0.706213			0.353107	−	0.935583i	$-0.385125\pi$
$787$	19.8118			0.706213			0.353107	+	0.935583i	$0.385125\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.2288			−0.932587
$792$		0			0
$793$	10.7288	+	18.5828i	0.380989	+	0.659893i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−45.2915			−1.60431			−0.802154	−	0.597118i	$-0.796313\pi$
$797$	−45.2915			−1.60431			−0.802154	+	0.597118i	$0.796313\pi$
$798$		0			0
$799$	17.4170			0.616169
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.11438	+	1.93016i	0.0393256	+	0.0681139i
$804$		0			0
$805$	−95.6235			−3.37029
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.9373			0.384533			0.192267	−	0.981343i	$-0.438416\pi$
$809$	10.9373			0.384533			0.192267	+	0.981343i	$0.438416\pi$
$810$		0			0
$811$	2.22876	−	3.86032i	0.0782622	−	0.135554i	−0.824238	−	0.566243i	$-0.808396\pi$
$811$	2.22876	−	3.86032i	0.0782622	−	0.135554i	0.902500	+	0.430689i	$0.141730\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.114378	−	0.198109i	−0.00400650	−	0.00693946i
$816$		0			0
$817$	23.1458	+	2.99429i	0.809767	+	0.104757i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.06275	+	12.2330i	−0.246492	+	0.426936i	−0.962550	−	0.271105i	$-0.912611\pi$
$821$	−7.06275	+	12.2330i	−0.246492	+	0.426936i	0.716058	+	0.698040i	$0.245944\pi$
$822$		0			0
$823$	17.6458	−	30.5633i	0.615092	−	1.06537i	−0.375276	−	0.926913i	$-0.622452\pi$
$823$	17.6458	−	30.5633i	0.615092	−	1.06537i	0.990368	−	0.138458i	$-0.0442146\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.35425	+	14.4700i	−0.290506	+	0.503171i	−0.973929	−	0.226851i	$-0.927157\pi$
$827$	−8.35425	+	14.4700i	−0.290506	+	0.503171i	0.683424	+	0.730022i	$0.260490\pi$
$828$		0			0
$829$	−51.5830			−1.79155			−0.895776	−	0.444506i	$-0.853379\pi$
$829$	−51.5830			−1.79155			−0.895776	+	0.444506i	$0.853379\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−24.0000	−	41.5692i	−0.831551	−	1.44029i
$834$		0			0
$835$	−3.87451			−0.134083
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.82288	−	8.35347i	−0.166504	−	0.288394i	0.770684	−	0.637217i	$-0.219915\pi$
$839$	−4.82288	−	8.35347i	−0.166504	−	0.288394i	−0.937188	+	0.348824i	$0.886581\pi$
$840$		0			0
$841$	−12.0830	−	20.9284i	−0.416655	−	0.721668i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	9.87451	−	17.1031i	0.339693	−	0.588366i
$846$		0			0
$847$	50.5203			1.73590
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.1144	+	24.4468i	−0.483835	+	0.838026i
$852$		0			0
$853$	−17.3745	−	30.0935i	−0.594892	−	1.03038i	−0.993562	−	0.113289i	$-0.963862\pi$
$853$	−17.3745	−	30.0935i	−0.594892	−	1.03038i	0.398670	−	0.917094i	$-0.369472\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−3.03137	+	5.25049i	−0.103429	+	0.179144i	−0.913095	−	0.407746i	$-0.866315\pi$
$859$	−3.03137	+	5.25049i	−0.103429	+	0.179144i	0.809666	+	0.586891i	$0.199648\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.7085			−0.909168			−0.454584	−	0.890704i	$-0.650212\pi$
$863$	−26.7085			−0.909168			−0.454584	+	0.890704i	$0.650212\pi$
$864$		0			0
$865$	18.0000	−	31.1769i	0.612018	−	1.06005i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.594119	+	1.02904i	0.0201541	+	0.0349079i
$870$		0			0
$871$	−29.9059	−	51.7985i	−1.01332	−	1.75513i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	55.7490			1.88466
$876$		0			0
$877$	9.08301	+	15.7322i	0.306711	+	0.531240i	0.977641	−	0.210282i	$-0.0674381\pi$
$877$	9.08301	+	15.7322i	0.306711	+	0.531240i	−0.670930	+	0.741521i	$0.734105\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−30.6863			−1.03385			−0.516923	−	0.856032i	$-0.672923\pi$
$881$	−30.6863			−1.03385			−0.516923	+	0.856032i	$0.672923\pi$
$882$		0			0
$883$	8.67712	−	15.0292i	0.292008	−	0.505774i	−0.682276	−	0.731095i	$-0.739010\pi$
$883$	8.67712	−	15.0292i	0.292008	−	0.505774i	0.974285	+	0.225321i	$0.0723431\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.05163	+	13.9458i	−0.270347	+	0.468255i	−0.968951	−	0.247254i	$-0.920472\pi$
$887$	−8.05163	+	13.9458i	−0.270347	+	0.468255i	0.698603	+	0.715509i	$0.253805\pi$
$888$		0			0
$889$	7.64575	−	13.2428i	0.256430	−	0.444150i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.87451	+	21.2895i	0.296974	+	0.712426i
$894$		0			0
$895$	−18.8745	−	32.6916i	−0.630905	−	1.09276i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.35425	−	4.07768i	0.0785186	−	0.135998i
$900$		0			0
$901$	−22.8340			−0.760710
$902$		0			0
$903$		0			0
$904$		0			0
$905$	96.9150			3.22156
$906$		0			0
$907$	−1.41699	−	2.45431i	−0.0470505	−	0.0814939i	0.841541	−	0.540193i	$-0.181649\pi$
$907$	−1.41699	−	2.45431i	−0.0470505	−	0.0814939i	−0.888592	+	0.458699i	$0.848316\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	43.7490			1.44947			0.724735	−	0.689028i	$-0.241962\pi$
$911$	43.7490			1.44947			0.724735	+	0.689028i	$0.241962\pi$
$912$		0			0
$913$	5.41699			0.179276
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.9373	+	24.1400i	0.460249	+	0.797174i
$918$		0			0
$919$	−1.22876			−0.0405329			−0.0202665	−	0.999795i	$-0.506451\pi$
$919$	−1.22876			−0.0405329			−0.0202665	+	0.999795i	$0.506451\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	42.9150			1.41257
$924$		0			0
$925$	20.7288	−	35.9033i	0.681557	−	1.18049i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	18.7601	+	32.4935i	0.615500	+	1.06608i	0.990297	+	0.138970i	$0.0443792\pi$
$929$	18.7601	+	32.4935i	0.615500	+	1.06608i	−0.374797	+	0.927107i	$0.622287\pi$
$930$		0			0
$931$	38.5830	−	50.5170i	1.26451	−	1.65563i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.12549	−	3.68146i	0.0695110	−	0.120397i
$936$		0			0
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	−0.803176	−	0.595742i	$-0.796858\pi$
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	0.917516	+	0.397699i	$0.130191\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−19.8745	+	34.4237i	−0.647890	+	1.12218i	0.335735	+	0.941956i	$0.391015\pi$
$941$	−19.8745	+	34.4237i	−0.647890	+	1.12218i	−0.983626	+	0.180223i	$0.942318\pi$
$942$		0			0
$943$	22.5830			0.735404
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.1660	−	48.7850i	−0.915272	−	1.58530i	−0.806502	−	0.591231i	$-0.798642\pi$
$947$	−28.1660	−	48.7850i	−0.915272	−	1.58530i	−0.108770	−	0.994067i	$-0.534691\pi$
$948$		0			0
$949$	27.0000			0.876457
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.7601	+	37.6897i	0.704880	+	1.22089i	0.966735	+	0.255780i	$0.0823324\pi$
$953$	21.7601	+	37.6897i	0.704880	+	1.22089i	−0.261855	+	0.965107i	$0.584334\pi$
$954$		0			0
$955$	−1.70850	−	2.95920i	−0.0552857	−	0.0957576i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−30.8745	+	53.4762i	−0.996990	+	1.72684i
$960$		0			0
$961$	−30.5830			−0.986549
$962$		0			0
$963$		0			0
$964$		0			0
$965$	40.4059	−	69.9850i	1.30071	−	2.25290i
$966$		0			0
$967$	−6.96863	−	12.0700i	−0.224096	−	0.388146i	0.731952	−	0.681356i	$-0.238610\pi$
$967$	−6.96863	−	12.0700i	−0.224096	−	0.388146i	−0.956048	+	0.293211i	$0.905276\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.5203	+	39.0062i	0.722710	+	1.25177i	0.959910	+	0.280309i	$0.0904369\pi$
$971$	22.5203	+	39.0062i	0.722710	+	1.25177i	−0.237200	+	0.971461i	$0.576230\pi$
$972$		0			0
$973$	10.7915	−	18.6914i	0.345960	−	0.599220i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	54.9150			1.75689			0.878444	−	0.477846i	$-0.158582\pi$
$977$	54.9150			1.75689			0.878444	+	0.477846i	$0.158582\pi$
$978$		0			0
$979$	2.41699	−	4.18636i	0.0772475	−	0.133797i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−29.4686	−	51.0412i	−0.939903	−	1.62796i	−0.765648	−	0.643260i	$-0.777582\pi$
$983$	−29.4686	−	51.0412i	−0.939903	−	1.62796i	−0.174255	−	0.984701i	$-0.555752\pi$
$984$		0			0
$985$	32.1660	+	55.7132i	1.02489	+	1.77517i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	30.2288			0.961219
$990$		0			0
$991$	5.96863	+	10.3380i	0.189600	+	0.328396i	0.945117	−	0.326733i	$-0.105948\pi$
$991$	5.96863	+	10.3380i	0.189600	+	0.328396i	−0.755517	+	0.655129i	$0.772614\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−43.5203			−1.37968
$996$		0			0
$997$	14.0203	−	24.2838i	0.444026	−	0.769076i	−0.553958	−	0.832545i	$-0.686883\pi$
$997$	14.0203	−	24.2838i	0.444026	−	0.769076i	0.997984	+	0.0634691i	$0.0202164\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.u.577.2		4
3.2	odd	2		912.2.q.g.577.1		4
4.3	odd	2		684.2.k.g.577.2		4
12.11	even	2		228.2.i.b.121.1	yes	4
19.11	even	3	inner	2736.2.s.u.1873.2		4
57.11	odd	6		912.2.q.g.49.1		4
76.11	odd	6		684.2.k.g.505.2		4
228.11	even	6		228.2.i.b.49.1	✓	4
228.83	even	6		4332.2.a.h.1.2		2
228.107	odd	6		4332.2.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.i.b.49.1	✓	4	228.11	even	6
228.2.i.b.121.1	yes	4	12.11	even	2
684.2.k.g.505.2		4	76.11	odd	6
684.2.k.g.577.2		4	4.3	odd	2
912.2.q.g.49.1		4	57.11	odd	6
912.2.q.g.577.1		4	3.2	odd	2
2736.2.s.u.577.2		4	1.1	even	1	trivial
2736.2.s.u.1873.2		4	19.11	even	3	inner
4332.2.a.h.1.2		2	228.83	even	6
4332.2.a.m.1.2		2	228.107	odd	6

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82288 + 3.15731i) q^{5} -4.64575 q^{7} +O(q^{10})\)	\(q+(1.82288 + 3.15731i) q^{5} -4.64575 q^{7} +0.354249 q^{11} +(2.14575 - 3.71655i) q^{13} +(-1.64575 - 2.85052i) q^{17} +(2.64575 - 3.46410i) q^{19} +(2.82288 - 4.88936i) q^{23} +(-4.14575 + 7.18065i) q^{25} +(3.64575 - 6.31463i) q^{29} +0.645751 q^{31} +(-8.46863 - 14.6681i) q^{35} -5.00000 q^{37} +(2.00000 + 3.46410i) q^{41} +(2.67712 + 4.63692i) q^{43} +(-2.64575 + 4.58258i) q^{47} +14.5830 q^{49} +(3.46863 - 6.00784i) q^{53} +(0.645751 + 1.11847i) q^{55} +(-3.82288 - 6.62141i) q^{59} +(-2.50000 + 4.33013i) q^{61} +15.6458 q^{65} +(6.96863 - 12.0700i) q^{67} +(5.00000 + 8.66025i) q^{71} +(3.14575 + 5.44860i) q^{73} -1.64575 q^{77} +(1.67712 + 2.90486i) q^{79} +15.2915 q^{83} +(6.00000 - 10.3923i) q^{85} +(6.82288 - 11.8176i) q^{89} +(-9.96863 + 17.2662i) q^{91} +(15.7601 + 2.03884i) q^{95} +(-5.29150 - 9.16515i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 8 * q^7	\( 4 q + 2 q^{5} - 8 q^{7} + 12 q^{11} - 2 q^{13} + 4 q^{17} + 6 q^{23} - 6 q^{25} + 4 q^{29} - 8 q^{31} - 18 q^{35} - 20 q^{37} + 8 q^{41} + 16 q^{43} + 16 q^{49} - 2 q^{53} - 8 q^{55} - 10 q^{59} - 10 q^{61} + 52 q^{65} + 12 q^{67} + 20 q^{71} + 2 q^{73} + 4 q^{77} + 12 q^{79} + 40 q^{83} + 24 q^{85} + 22 q^{89} - 24 q^{91} + 26 q^{95}+O(q^{100}) \) 4 * q + 2 * q^5 - 8 * q^7 + 12 * q^11 - 2 * q^13 + 4 * q^17 + 6 * q^23 - 6 * q^25 + 4 * q^29 - 8 * q^31 - 18 * q^35 - 20 * q^37 + 8 * q^41 + 16 * q^43 + 16 * q^49 - 2 * q^53 - 8 * q^55 - 10 * q^59 - 10 * q^61 + 52 * q^65 + 12 * q^67 + 20 * q^71 + 2 * q^73 + 4 * q^77 + 12 * q^79 + 40 * q^83 + 24 * q^85 + 22 * q^89 - 24 * q^91 + 26 * q^95

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