LMFDB - Embedded newform 1344.3.d.c.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,3,Mod(449,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1344.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1344.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$36.6213475300$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 8x^{2} + 9 $ x^4 + 8*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.2
Root			$-1.16372i$ of defining polynomial
Character	$\chi$	$=$	1344.449
Dual form			1344.3.d.c.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.64575 + 1.41421i) q^{3} -0.913230i q^{5} -2.64575 q^{7} +(5.00000 - 7.48331i) q^{9} +O(q^{10})$	\(q+(-2.64575 + 1.41421i) q^{3} -0.913230i q^{5} -2.64575 q^{7} +(5.00000 - 7.48331i) q^{9} -14.5544i q^{11} +0.583005 q^{13} +(1.29150 + 2.41618i) q^{15} +21.5367i q^{17} +16.0000 q^{19} +(7.00000 - 3.74166i) q^{21} -38.8308i q^{23} +24.1660 q^{25} +(-2.64575 + 26.8701i) q^{27} +35.7676i q^{29} -58.4575 q^{31} +(20.5830 + 38.5073i) q^{33} +2.41618i q^{35} -20.0000 q^{37} +(-1.54249 + 0.824494i) q^{39} +8.75149i q^{41} +11.7490 q^{43} +(-6.83399 - 4.56615i) q^{45} +8.48528i q^{47} +7.00000 q^{49} +(-30.4575 - 56.9808i) q^{51} -50.9117i q^{53} -13.2915 q^{55} +(-42.3320 + 22.6274i) q^{57} +58.2175i q^{59} -38.9150 q^{61} +(-13.2288 + 19.7990i) q^{63} -0.532418i q^{65} -70.5830 q^{67} +(54.9150 + 102.737i) q^{69} +17.0279i q^{71} +72.3320 q^{73} +(-63.9373 + 34.1759i) q^{75} +38.5073i q^{77} +20.9150 q^{79} +(-31.0000 - 74.8331i) q^{81} -145.544i q^{83} +19.6680 q^{85} +(-50.5830 - 94.6321i) q^{87} -53.6514i q^{89} -1.54249 q^{91} +(154.664 - 82.6714i) q^{93} -14.6117i q^{95} -111.166 q^{97} +(-108.915 - 72.7719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 20 q^{9}+O(q^{10}) $ 4 * q + 20 * q^9	$ 4 q + 20 q^{9} - 40 q^{13} - 16 q^{15} + 64 q^{19} + 28 q^{21} + 12 q^{25} - 128 q^{31} + 40 q^{33} - 80 q^{37} - 112 q^{39} - 80 q^{43} - 112 q^{45} + 28 q^{49} - 16 q^{51} - 32 q^{55} + 56 q^{61} - 240 q^{67} + 8 q^{69} + 120 q^{73} - 224 q^{75} - 128 q^{79} - 124 q^{81} + 248 q^{85} - 160 q^{87} - 112 q^{91} + 280 q^{93} - 360 q^{97} - 224 q^{99}+O(q^{100}) $ 4 * q + 20 * q^9 - 40 * q^13 - 16 * q^15 + 64 * q^19 + 28 * q^21 + 12 * q^25 - 128 * q^31 + 40 * q^33 - 80 * q^37 - 112 * q^39 - 80 * q^43 - 112 * q^45 + 28 * q^49 - 16 * q^51 - 32 * q^55 + 56 * q^61 - 240 * q^67 + 8 * q^69 + 120 * q^73 - 224 * q^75 - 128 * q^79 - 124 * q^81 + 248 * q^85 - 160 * q^87 - 112 * q^91 + 280 * q^93 - 360 * q^97 - 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.64575	+	1.41421i	−0.881917	+	0.471405i
$3$	−2.64575	+	1.41421i	−0.881917	+	0.471405i
$4$		0			0
$5$		−	0.913230i		−	0.182646i	−0.995821	−	0.0913230i	$-0.970890\pi$
$5$		−	0.913230i		−	0.182646i	0.995821	−	0.0913230i	$-0.0291096\pi$
$6$		0			0
$7$	−2.64575			−0.377964
$7$	−2.64575			−0.377964
$8$		0			0
$9$	5.00000	−	7.48331i	0.555556	−	0.831479i
$10$		0			0
$11$		−	14.5544i		−	1.32313i	−0.749890	−	0.661563i	$-0.769893\pi$
$11$		−	14.5544i		−	1.32313i	0.749890	−	0.661563i	$-0.230107\pi$
$12$		0			0
$13$	0.583005			0.0448466			0.0224233	−	0.999749i	$-0.492862\pi$
$13$	0.583005			0.0448466			0.0224233	+	0.999749i	$0.492862\pi$
$14$		0			0
$15$	1.29150	+	2.41618i	0.0861002	+	0.161079i
$16$		0			0
$17$			21.5367i			1.26687i	0.773798	+	0.633433i	$0.218355\pi$
$17$			21.5367i			1.26687i	−0.773798	+	0.633433i	$0.781645\pi$
$18$		0			0
$19$	16.0000			0.842105			0.421053	−	0.907036i	$-0.361661\pi$
$19$	16.0000			0.842105			0.421053	+	0.907036i	$0.361661\pi$
$20$		0			0
$21$	7.00000	−	3.74166i	0.333333	−	0.178174i
$22$		0			0
$23$		−	38.8308i		−	1.68830i	−0.536111	−	0.844148i	$-0.680107\pi$
$23$		−	38.8308i		−	1.68830i	0.536111	−	0.844148i	$-0.319893\pi$
$24$		0			0
$25$	24.1660			0.966640
$26$		0			0
$27$	−2.64575	+	26.8701i	−0.0979908	+	0.995187i
$28$		0			0
$29$			35.7676i			1.23337i	0.787212	+	0.616683i	$0.211524\pi$
$29$			35.7676i			1.23337i	−0.787212	+	0.616683i	$0.788476\pi$
$30$		0			0
$31$	−58.4575			−1.88573			−0.942863	−	0.333180i	$-0.891878\pi$
$31$	−58.4575			−1.88573			−0.942863	+	0.333180i	$0.891878\pi$
$32$		0			0
$33$	20.5830	+	38.5073i	0.623727	+	1.16689i
$34$		0			0
$35$			2.41618i			0.0690337i
$36$		0			0
$37$	−20.0000			−0.540541			−0.270270	−	0.962784i	$-0.587113\pi$
$37$	−20.0000			−0.540541			−0.270270	+	0.962784i	$0.587113\pi$
$38$		0			0
$39$	−1.54249	+	0.824494i	−0.0395509	+	0.0211409i
$40$		0			0
$41$			8.75149i			0.213451i	0.994289	+	0.106725i	$0.0340366\pi$
$41$			8.75149i			0.213451i	−0.994289	+	0.106725i	$0.965963\pi$
$42$		0			0
$43$	11.7490			0.273233			0.136616	−	0.990624i	$-0.456377\pi$
$43$	11.7490			0.273233			0.136616	+	0.990624i	$0.456377\pi$
$44$		0			0
$45$	−6.83399	−	4.56615i	−0.151866	−	0.101470i
$46$		0			0
$47$			8.48528i			0.180538i	0.995917	+	0.0902690i	$0.0287727\pi$
$47$			8.48528i			0.180538i	−0.995917	+	0.0902690i	$0.971227\pi$
$48$		0			0
$49$	7.00000			0.142857
$50$		0			0
$51$	−30.4575	−	56.9808i	−0.597206	−	1.11727i
$52$		0			0
$53$		−	50.9117i		−	0.960598i	−0.877105	−	0.480299i	$-0.840528\pi$
$53$		−	50.9117i		−	0.960598i	0.877105	−	0.480299i	$-0.159472\pi$
$54$		0			0
$55$	−13.2915			−0.241664
$56$		0			0
$57$	−42.3320	+	22.6274i	−0.742667	+	0.396972i
$58$		0			0
$59$			58.2175i			0.986738i	0.869820	+	0.493369i	$0.164235\pi$
$59$			58.2175i			0.986738i	−0.869820	+	0.493369i	$0.835765\pi$
$60$		0			0
$61$	−38.9150			−0.637951			−0.318976	−	0.947763i	$-0.603339\pi$
$61$	−38.9150			−0.637951			−0.318976	+	0.947763i	$0.603339\pi$
$62$		0			0
$63$	−13.2288	+	19.7990i	−0.209980	+	0.314270i
$64$		0			0
$65$		−	0.532418i		−	0.00819105i
$66$		0			0
$67$	−70.5830			−1.05348			−0.526739	−	0.850027i	$-0.676585\pi$
$67$	−70.5830			−1.05348			−0.526739	+	0.850027i	$0.676585\pi$
$68$		0			0
$69$	54.9150	+	102.737i	0.795870	+	1.48894i
$70$		0			0
$71$			17.0279i			0.239829i	0.992784	+	0.119915i	$0.0382621\pi$
$71$			17.0279i			0.239829i	−0.992784	+	0.119915i	$0.961738\pi$
$72$		0			0
$73$	72.3320			0.990850			0.495425	−	0.868651i	$-0.335012\pi$
$73$	72.3320			0.990850			0.495425	+	0.868651i	$0.335012\pi$
$74$		0			0
$75$	−63.9373	+	34.1759i	−0.852497	+	0.455679i
$76$		0			0
$77$			38.5073i			0.500095i
$78$		0			0
$79$	20.9150			0.264747			0.132374	−	0.991200i	$-0.457740\pi$
$79$	20.9150			0.264747			0.132374	+	0.991200i	$0.457740\pi$
$80$		0			0
$81$	−31.0000	−	74.8331i	−0.382716	−	0.923866i
$82$		0			0
$83$		−	145.544i		−	1.75354i	−0.480910	−	0.876770i	$-0.659694\pi$
$83$		−	145.544i		−	1.75354i	0.480910	−	0.876770i	$-0.340306\pi$
$84$		0			0
$85$	19.6680			0.231388
$86$		0			0
$87$	−50.5830	−	94.6321i	−0.581414	−	1.08773i
$88$		0			0
$89$		−	53.6514i		−	0.602824i	−0.953494	−	0.301412i	$-0.902542\pi$
$89$		−	53.6514i		−	0.602824i	0.953494	−	0.301412i	$-0.0974580\pi$
$90$		0			0
$91$	−1.54249			−0.0169504
$92$		0			0
$93$	154.664	−	82.6714i	1.66305	−	0.888940i
$94$		0			0
$95$		−	14.6117i		−	0.153807i
$96$		0			0
$97$	−111.166			−1.14604			−0.573021	−	0.819541i	$-0.694229\pi$
$97$	−111.166			−1.14604			−0.573021	+	0.819541i	$0.694229\pi$
$98$		0			0
$99$	−108.915	−	72.7719i	−1.10015	−	0.735070i
$100$		0			0
$101$		−	57.8367i		−	0.572641i	−0.958134	−	0.286320i	$-0.907568\pi$
$101$		−	57.8367i		−	0.572641i	0.958134	−	0.286320i	$-0.0924322\pi$
$102$		0			0
$103$	−119.373			−1.15896			−0.579478	−	0.814988i	$-0.696744\pi$
$103$	−119.373			−1.15896			−0.579478	+	0.814988i	$0.696744\pi$
$104$		0			0
$105$	−3.41699	−	6.39261i	−0.0325428	−	0.0608820i
$106$		0			0
$107$		−	116.492i		−	1.08871i	−0.838854	−	0.544357i	$-0.816774\pi$
$107$		−	116.492i		−	1.08871i	0.838854	−	0.544357i	$-0.183226\pi$
$108$		0			0
$109$	−87.8301			−0.805780			−0.402890	−	0.915248i	$-0.631994\pi$
$109$	−87.8301			−0.805780			−0.402890	+	0.915248i	$0.631994\pi$
$110$		0			0
$111$	52.9150	−	28.2843i	0.476712	−	0.254813i
$112$		0			0
$113$		−	69.1763i		−	0.612180i	−0.952003	−	0.306090i	$-0.900979\pi$
$113$		−	69.1763i		−	0.612180i	0.952003	−	0.306090i	$-0.0990208\pi$
$114$		0			0
$115$	−35.4615			−0.308360
$116$		0			0
$117$	2.91503	−	4.36281i	0.0249148	−	0.0372890i
$118$		0			0
$119$		−	56.9808i		−	0.478830i
$120$		0			0
$121$	−90.8301			−0.750662
$122$		0			0
$123$	−12.3765	−	23.1543i	−0.100622	−	0.188246i
$124$		0			0
$125$		−	44.8999i		−	0.359199i
$126$		0			0
$127$	−27.0850			−0.213268			−0.106634	−	0.994298i	$-0.534007\pi$
$127$	−27.0850			−0.213268			−0.106634	+	0.994298i	$0.534007\pi$
$128$		0			0
$129$	−31.0850	+	16.6156i	−0.240969	+	0.128803i
$130$		0			0
$131$			145.544i			1.11102i	0.831509	+	0.555511i	$0.187477\pi$
$131$			145.544i			1.11102i	−0.831509	+	0.555511i	$0.812523\pi$
$132$		0			0
$133$	−42.3320			−0.318286
$134$		0			0
$135$	24.5385	+	2.41618i	0.181767	+	0.0178976i
$136$		0			0
$137$		−	24.8088i		−	0.181086i	−0.995893	−	0.0905431i	$-0.971140\pi$
$137$		−	24.8088i		−	0.181086i	0.995893	−	0.0905431i	$-0.0288603\pi$
$138$		0			0
$139$	−146.458			−1.05365			−0.526826	−	0.849973i	$-0.676618\pi$
$139$	−146.458			−1.05365			−0.526826	+	0.849973i	$0.676618\pi$
$140$		0			0
$141$	−12.0000	−	22.4499i	−0.0851064	−	0.159219i
$142$		0			0
$143$		−	8.48528i		−	0.0593376i
$144$		0			0
$145$	32.6640			0.225269
$146$		0			0
$147$	−18.5203	+	9.89949i	−0.125988	+	0.0673435i
$148$		0			0
$149$			219.552i			1.47351i	0.676162	+	0.736753i	$0.263642\pi$
$149$			219.552i			1.47351i	−0.676162	+	0.736753i	$0.736358\pi$
$150$		0			0
$151$	−211.660			−1.40172			−0.700861	−	0.713298i	$-0.747201\pi$
$151$	−211.660			−1.40172			−0.700861	+	0.713298i	$0.747201\pi$
$152$		0			0
$153$	161.166	+	107.684i	1.05337	+	0.703814i
$154$		0			0
$155$			53.3852i			0.344420i
$156$		0			0
$157$	−208.745			−1.32959			−0.664793	−	0.747027i	$-0.731480\pi$
$157$	−208.745			−1.32959			−0.664793	+	0.747027i	$0.731480\pi$
$158$		0			0
$159$	72.0000	+	134.700i	0.452830	+	0.847168i
$160$		0			0
$161$			102.737i			0.638116i
$162$		0			0
$163$	−266.996			−1.63801			−0.819006	−	0.573784i	$-0.805475\pi$
$163$	−266.996			−1.63801			−0.819006	+	0.573784i	$0.805475\pi$
$164$		0			0
$165$	35.1660	−	18.7970i	0.213127	−	0.113921i
$166$		0			0
$167$			7.19124i			0.0430613i	0.999768	+	0.0215307i	$0.00685395\pi$
$167$			7.19124i			0.0430613i	−0.999768	+	0.0215307i	$0.993146\pi$
$168$		0			0
$169$	−168.660			−0.997989
$170$		0			0
$171$	80.0000	−	119.733i	0.467836	−	0.700193i
$172$		0			0
$173$		−	192.536i		−	1.11293i	−0.830872	−	0.556464i	$-0.812158\pi$
$173$		−	192.536i		−	1.11293i	0.830872	−	0.556464i	$-0.187842\pi$
$174$		0			0
$175$	−63.9373			−0.365356
$176$		0			0
$177$	−82.3320	−	154.029i	−0.465153	−	0.870221i
$178$		0			0
$179$		−	43.6631i		−	0.243928i	−0.992535	−	0.121964i	$-0.961081\pi$
$179$		−	43.6631i		−	0.243928i	0.992535	−	0.121964i	$-0.0389193\pi$
$180$		0			0
$181$	81.0850			0.447983			0.223992	−	0.974591i	$-0.428091\pi$
$181$	81.0850			0.447983			0.223992	+	0.974591i	$0.428091\pi$
$182$		0			0
$183$	102.959	−	55.0342i	0.562620	−	0.300733i
$184$		0			0
$185$			18.2646i			0.0987276i
$186$		0			0
$187$	313.454			1.67622
$188$		0			0
$189$	7.00000	−	71.0915i	0.0370370	−	0.376145i
$190$		0			0
$191$		−	53.5571i		−	0.280404i	−0.990123	−	0.140202i	$-0.955225\pi$
$191$		−	53.5571i		−	0.280404i	0.990123	−	0.140202i	$-0.0447751\pi$
$192$		0			0
$193$	−110.494			−0.572508			−0.286254	−	0.958154i	$-0.592410\pi$
$193$	−110.494			−0.572508			−0.286254	+	0.958154i	$0.592410\pi$
$194$		0			0
$195$	0.752953	+	1.40865i	0.00386130	+	0.00722382i
$196$		0			0
$197$		−	86.1469i		−	0.437294i	−0.975804	−	0.218647i	$-0.929836\pi$
$197$		−	86.1469i		−	0.437294i	0.975804	−	0.218647i	$-0.0701643\pi$
$198$		0			0
$199$	−88.0000			−0.442211			−0.221106	−	0.975250i	$-0.570967\pi$
$199$	−88.0000			−0.442211			−0.221106	+	0.975250i	$0.570967\pi$
$200$		0			0
$201$	186.745	−	99.8194i	0.929080	−	0.496614i
$202$		0			0
$203$		−	94.6321i		−	0.466168i
$204$		0			0
$205$	7.99213			0.0389860
$206$		0			0
$207$	−290.583	−	194.154i	−1.40378	−	0.937942i
$208$		0			0
$209$		−	232.870i		−	1.11421i
$210$		0			0
$211$	61.2549			0.290308			0.145154	−	0.989409i	$-0.453632\pi$
$211$	61.2549			0.290308			0.145154	+	0.989409i	$0.453632\pi$
$212$		0			0
$213$	−24.0810	−	45.0515i	−0.113057	−	0.211509i
$214$		0			0
$215$		−	10.7296i		−	0.0499049i
$216$		0			0
$217$	154.664			0.712738
$218$		0			0
$219$	−191.373	+	102.293i	−0.873847	+	0.467091i
$220$		0			0
$221$			12.5560i			0.0568146i
$222$		0			0
$223$	150.494			0.674861			0.337431	−	0.941350i	$-0.390442\pi$
$223$	150.494			0.674861			0.337431	+	0.941350i	$0.390442\pi$
$224$		0			0
$225$	120.830	−	180.842i	0.537022	−	0.803742i
$226$		0			0
$227$		−	190.558i		−	0.839464i	−0.907648	−	0.419732i	$-0.862124\pi$
$227$		−	190.558i		−	0.839464i	0.907648	−	0.419732i	$-0.137876\pi$
$228$		0			0
$229$	142.915			0.624083			0.312042	−	0.950068i	$-0.398987\pi$
$229$	142.915			0.624083			0.312042	+	0.950068i	$0.398987\pi$
$230$		0			0
$231$	−54.4575	−	101.881i	−0.235747	−	0.441042i
$232$		0			0
$233$			7.83826i			0.0336406i	0.999859	+	0.0168203i	$0.00535432\pi$
$233$			7.83826i			0.0336406i	−0.999859	+	0.0168203i	$0.994646\pi$
$234$		0			0
$235$	7.74902			0.0329745
$236$		0			0
$237$	−55.3360	+	29.5783i	−0.233485	+	0.124803i
$238$		0			0
$239$			213.369i			0.892756i	0.894844	+	0.446378i	$0.147286\pi$
$239$			213.369i			0.892756i	−0.894844	+	0.446378i	$0.852714\pi$
$240$		0			0
$241$	−130.000			−0.539419			−0.269710	−	0.962942i	$-0.586928\pi$
$241$	−130.000			−0.539419			−0.269710	+	0.962942i	$0.586928\pi$
$242$		0			0
$243$	187.848	+	154.149i	0.773038	+	0.634359i
$244$		0			0
$245$		−	6.39261i		−	0.0260923i
$246$		0			0
$247$	9.32808			0.0377655
$248$		0			0
$249$	205.830	+	385.073i	0.826627	+	1.54648i
$250$		0			0
$251$			389.258i			1.55083i	0.631453	+	0.775415i	$0.282459\pi$
$251$			389.258i			1.55083i	−0.631453	+	0.775415i	$0.717541\pi$
$252$		0			0
$253$	−565.158			−2.23383
$254$		0			0
$255$	−52.0366	+	27.8147i	−0.204065	+	0.109077i
$256$		0			0
$257$			336.139i			1.30793i	0.756523	+	0.653967i	$0.226897\pi$
$257$			336.139i			1.30793i	−0.756523	+	0.653967i	$0.773103\pi$
$258$		0			0
$259$	52.9150			0.204305
$260$		0			0
$261$	267.660	+	178.838i	1.02552	+	0.685203i
$262$		0			0
$263$		−	438.933i		−	1.66895i	−0.551048	−	0.834473i	$-0.685772\pi$
$263$		−	438.933i		−	1.66895i	0.551048	−	0.834473i	$-0.314228\pi$
$264$		0			0
$265$	−46.4941			−0.175449
$266$		0			0
$267$	75.8745	+	141.948i	0.284174	+	0.531641i
$268$		0			0
$269$			14.4601i			0.0537549i	0.999639	+	0.0268775i	$0.00855639\pi$
$269$			14.4601i			0.0537549i	−0.999639	+	0.0268775i	$0.991444\pi$
$270$		0			0
$271$	61.5425			0.227094			0.113547	−	0.993533i	$-0.463779\pi$
$271$	61.5425			0.227094			0.113547	+	0.993533i	$0.463779\pi$
$272$		0			0
$273$	4.08104	−	2.18141i	0.0149489	−	0.00799050i
$274$		0			0
$275$		−	351.721i		−	1.27899i
$276$		0			0
$277$	−150.494			−0.543300			−0.271650	−	0.962396i	$-0.587569\pi$
$277$	−150.494			−0.543300			−0.271650	+	0.962396i	$0.587569\pi$
$278$		0			0
$279$	−292.288	+	437.456i	−1.04763	+	1.56794i
$280$		0			0
$281$			300.220i			1.06840i	0.845359	+	0.534199i	$0.179387\pi$
$281$			300.220i			1.06840i	−0.845359	+	0.534199i	$0.820613\pi$
$282$		0			0
$283$	−98.8340			−0.349237			−0.174618	−	0.984636i	$-0.555869\pi$
$283$	−98.8340			−0.349237			−0.174618	+	0.984636i	$0.555869\pi$
$284$		0			0
$285$	20.6640	+	38.6589i	0.0725054	+	0.135645i
$286$		0			0
$287$		−	23.1543i		−	0.0806769i
$288$		0			0
$289$	−174.830			−0.604948
$290$		0			0
$291$	294.118	−	157.212i	1.01071	−	0.540249i
$292$		0			0
$293$		−	7.15424i		−	0.0244172i	−0.999925	−	0.0122086i	$-0.996114\pi$
$293$		−	7.15424i		−	0.0244172i	0.999925	−	0.0122086i	$-0.00388621\pi$
$294$		0			0
$295$	53.1660			0.180224
$296$		0			0
$297$	391.077	+	38.5073i	1.31676	+	0.129654i
$298$		0			0
$299$		−	22.6386i		−	0.0757142i
$300$		0			0
$301$	−31.0850			−0.103272
$302$		0			0
$303$	81.7935	+	153.022i	0.269945	+	0.505022i
$304$		0			0
$305$			35.5384i			0.116519i
$306$		0			0
$307$	−105.830			−0.344723			−0.172362	−	0.985034i	$-0.555140\pi$
$307$	−105.830			−0.344723			−0.172362	+	0.985034i	$0.555140\pi$
$308$		0			0
$309$	315.830	−	168.818i	1.02210	−	0.546337i
$310$		0			0
$311$		−	265.403i		−	0.853385i	−0.904397	−	0.426692i	$-0.859679\pi$
$311$		−	265.403i		−	0.853385i	0.904397	−	0.426692i	$-0.140321\pi$
$312$		0			0
$313$	259.328			0.828524			0.414262	−	0.910158i	$-0.364040\pi$
$313$	259.328			0.828524			0.414262	+	0.910158i	$0.364040\pi$
$314$		0			0
$315$	18.0810	+	12.0809i	0.0574001	+	0.0383521i
$316$		0			0
$317$		−	37.8233i		−	0.119316i	−0.998219	−	0.0596581i	$-0.980999\pi$
$317$		−	37.8233i		−	0.119316i	0.998219	−	0.0596581i	$-0.0190011\pi$
$318$		0			0
$319$	520.575			1.63190
$320$		0			0
$321$	164.745	+	308.210i	0.513225	+	0.960155i
$322$		0			0
$323$			344.587i			1.06683i
$324$		0			0
$325$	14.0889			0.0433505
$326$		0			0
$327$	232.376	−	124.210i	0.710631	−	0.379848i
$328$		0			0
$329$		−	22.4499i		−	0.0682369i
$330$		0			0
$331$	−145.490			−0.439547			−0.219774	−	0.975551i	$-0.570532\pi$
$331$	−145.490			−0.439547			−0.219774	+	0.975551i	$0.570532\pi$
$332$		0			0
$333$	−100.000	+	149.666i	−0.300300	+	0.449448i
$334$		0			0
$335$			64.4585i			0.192414i
$336$		0			0
$337$	−600.316			−1.78135			−0.890677	−	0.454637i	$-0.849769\pi$
$337$	−600.316			−1.78135			−0.890677	+	0.454637i	$0.849769\pi$
$338$		0			0
$339$	97.8301	+	183.023i	0.288584	+	0.539892i
$340$		0			0
$341$			850.813i			2.49505i
$342$		0			0
$343$	−18.5203			−0.0539949
$344$		0			0
$345$	93.8222	−	50.1501i	0.271948	−	0.145363i
$346$		0			0
$347$		−	31.6395i		−	0.0911803i	−0.998960	−	0.0455901i	$-0.985483\pi$
$347$		−	31.6395i		−	0.0911803i	0.998960	−	0.0455901i	$-0.0145168\pi$
$348$		0			0
$349$	592.405			1.69744			0.848718	−	0.528846i	$-0.177375\pi$
$349$	592.405			1.69744			0.848718	+	0.528846i	$0.177375\pi$
$350$		0			0
$351$	−1.54249	+	15.6654i	−0.00439455	+	0.0446307i
$352$		0			0
$353$		−	621.977i		−	1.76197i	−0.473141	−	0.880987i	$-0.656880\pi$
$353$		−	621.977i		−	1.76197i	0.473141	−	0.880987i	$-0.343120\pi$
$354$		0			0
$355$	15.5504			0.0438038
$356$		0			0
$357$	80.5830	+	150.757i	0.225723	+	0.422289i
$358$		0			0
$359$			499.509i			1.39139i	0.718337	+	0.695696i	$0.244904\pi$
$359$			499.509i			1.39139i	−0.718337	+	0.695696i	$0.755096\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$		0			0
$363$	240.314	−	128.453i	0.662021	−	0.353865i
$364$		0			0
$365$		−	66.0558i		−	0.180975i
$366$		0			0
$367$	73.0039			0.198921			0.0994604	−	0.995042i	$-0.468288\pi$
$367$	73.0039			0.198921			0.0994604	+	0.995042i	$0.468288\pi$
$368$		0			0
$369$	65.4902	+	43.7575i	0.177480	+	0.118584i
$370$		0			0
$371$			134.700i			0.363072i
$372$		0			0
$373$	474.664			1.27256			0.636279	−	0.771459i	$-0.280473\pi$
$373$	474.664			1.27256			0.636279	+	0.771459i	$0.280473\pi$
$374$		0			0
$375$	63.4980	+	118.794i	0.169328	+	0.316784i
$376$		0			0
$377$			20.8527i			0.0553122i
$378$		0			0
$379$	223.660			0.590132			0.295066	−	0.955477i	$-0.404658\pi$
$379$	223.660			0.590132			0.295066	+	0.955477i	$0.404658\pi$
$380$		0			0
$381$	71.6601	−	38.3039i	0.188084	−	0.100535i
$382$		0			0
$383$			518.175i			1.35294i	0.736471	+	0.676469i	$0.236491\pi$
$383$			518.175i			1.35294i	−0.736471	+	0.676469i	$0.763509\pi$
$384$		0			0
$385$	35.1660			0.0913403
$386$		0			0
$387$	58.7451	−	87.9216i	0.151796	−	0.227188i
$388$		0			0
$389$		−	44.1383i		−	0.113466i	−0.998389	−	0.0567330i	$-0.981932\pi$
$389$		−	44.1383i		−	0.113466i	0.998389	−	0.0567330i	$-0.0180684\pi$
$390$		0			0
$391$	836.288			2.13884
$392$		0			0
$393$	−205.830	−	385.073i	−0.523741	−	0.979829i
$394$		0			0
$395$		−	19.1002i		−	0.0483550i
$396$		0			0
$397$	−299.417			−0.754199			−0.377099	−	0.926173i	$-0.623079\pi$
$397$	−299.417			−0.754199			−0.377099	+	0.926173i	$0.623079\pi$
$398$		0			0
$399$	112.000	−	59.8665i	0.280702	−	0.150041i
$400$		0			0
$401$			277.008i			0.690794i	0.938457	+	0.345397i	$0.112256\pi$
$401$			277.008i			0.690794i	−0.938457	+	0.345397i	$0.887744\pi$
$402$		0			0
$403$	−34.0810			−0.0845683
$404$		0			0
$405$	−68.3399	+	28.3101i	−0.168740	+	0.0699016i
$406$		0			0
$407$			291.088i			0.715203i
$408$		0			0
$409$	−740.980			−1.81169			−0.905844	−	0.423612i	$-0.860762\pi$
$409$	−740.980			−1.81169			−0.905844	+	0.423612i	$0.860762\pi$
$410$		0			0
$411$	35.0850	+	65.6380i	0.0853649	+	0.159703i
$412$		0			0
$413$		−	154.029i		−	0.372952i
$414$		0			0
$415$	−132.915			−0.320277
$416$		0			0
$417$	387.490	−	207.122i	0.929233	−	0.496696i
$418$		0			0
$419$		−	89.7998i		−	0.214319i	−0.994242	−	0.107160i	$-0.965824\pi$
$419$		−	89.7998i		−	0.214319i	0.994242	−	0.107160i	$-0.0341756\pi$
$420$		0			0
$421$	−281.150			−0.667815			−0.333908	−	0.942606i	$-0.608367\pi$
$421$	−281.150			−0.667815			−0.333908	+	0.942606i	$0.608367\pi$
$422$		0			0
$423$	63.4980	+	42.4264i	0.150114	+	0.100299i
$424$		0			0
$425$			520.456i			1.22460i
$426$		0			0
$427$	102.959			0.241123
$428$		0			0
$429$	12.0000	+	22.4499i	0.0279720	+	0.0523309i
$430$		0			0
$431$			560.200i			1.29977i	0.760033	+	0.649885i	$0.225183\pi$
$431$			560.200i			1.29977i	−0.760033	+	0.649885i	$0.774817\pi$
$432$		0			0
$433$	−543.004			−1.25405			−0.627025	−	0.778999i	$-0.715728\pi$
$433$	−543.004			−1.25405			−0.627025	+	0.778999i	$0.715728\pi$
$434$		0			0
$435$	−86.4209	+	46.1939i	−0.198669	+	0.106193i
$436$		0			0
$437$		−	621.293i		−	1.42172i
$438$		0			0
$439$	342.170			0.779430			0.389715	−	0.920935i	$-0.372573\pi$
$439$	342.170			0.779430			0.389715	+	0.920935i	$0.372573\pi$
$440$		0			0
$441$	35.0000	−	52.3832i	0.0793651	−	0.118783i
$442$		0			0
$443$			399.816i			0.902519i	0.892393	+	0.451259i	$0.149025\pi$
$443$			399.816i			0.902519i	−0.892393	+	0.451259i	$0.850975\pi$
$444$		0			0
$445$	−48.9961			−0.110104
$446$		0			0
$447$	−310.494	−	580.881i	−0.694618	−	1.29951i
$448$		0			0
$449$		−	737.040i		−	1.64151i	−0.571277	−	0.820757i	$-0.693552\pi$
$449$		−	737.040i		−	1.64151i	0.571277	−	0.820757i	$-0.306448\pi$
$450$		0			0
$451$	127.373			0.282422
$452$		0			0
$453$	560.000	−	299.333i	1.23620	−	0.660778i
$454$		0			0
$455$			1.40865i			0.00309592i
$456$		0			0
$457$	665.336			1.45588			0.727939	−	0.685642i	$-0.240479\pi$
$457$	665.336			1.45588			0.727939	+	0.685642i	$0.240479\pi$
$458$		0			0
$459$	−578.693	−	56.9808i	−1.26077	−	0.124141i
$460$		0			0
$461$			318.865i			0.691682i	0.938293	+	0.345841i	$0.112406\pi$
$461$			318.865i			0.691682i	−0.938293	+	0.345841i	$0.887594\pi$
$462$		0			0
$463$	402.332			0.868968			0.434484	−	0.900680i	$-0.356931\pi$
$463$	402.332			0.868968			0.434484	+	0.900680i	$0.356931\pi$
$464$		0			0
$465$	−75.4980	−	141.244i	−0.162361	−	0.303750i
$466$		0			0
$467$			697.087i			1.49269i	0.665558	+	0.746346i	$0.268194\pi$
$467$			697.087i			1.49269i	−0.665558	+	0.746346i	$0.731806\pi$
$468$		0			0
$469$	186.745			0.398177
$470$		0			0
$471$	552.288	−	295.210i	1.17259	−	0.626773i
$472$		0			0
$473$		−	171.000i		−	0.361522i
$474$		0			0
$475$	386.656			0.814013
$476$		0			0
$477$	−380.988	−	254.558i	−0.798717	−	0.533665i
$478$		0			0
$479$		−	163.808i		−	0.341980i	−0.985273	−	0.170990i	$-0.945303\pi$
$479$		−	163.808i		−	0.341980i	0.985273	−	0.170990i	$-0.0546966\pi$
$480$		0			0
$481$	−11.6601			−0.0242414
$482$		0			0
$483$	−145.292	−	271.816i	−0.300811	−	0.562765i
$484$		0			0
$485$			101.520i			0.209320i
$486$		0			0
$487$	−103.498			−0.212522			−0.106261	−	0.994338i	$-0.533888\pi$
$487$	−103.498			−0.212522			−0.106261	+	0.994338i	$0.533888\pi$
$488$		0			0
$489$	706.405	−	377.589i	1.44459	−	0.772167i
$490$		0			0
$491$		−	570.094i		−	1.16109i	−0.814229	−	0.580544i	$-0.802840\pi$
$491$		−	570.094i		−	1.16109i	0.814229	−	0.580544i	$-0.197160\pi$
$492$		0			0
$493$	−770.316			−1.56251
$494$		0			0
$495$	−66.4575	+	99.4645i	−0.134258	+	0.200938i
$496$		0			0
$497$		−	45.0515i		−	0.0906469i
$498$		0			0
$499$	487.660			0.977275			0.488637	−	0.872487i	$-0.337494\pi$
$499$	487.660			0.977275			0.488637	+	0.872487i	$0.337494\pi$
$500$		0			0
$501$	−10.1699	−	19.0262i	−0.0202993	−	0.0379765i
$502$		0			0
$503$			97.9412i			0.194714i	0.995250	+	0.0973571i	$0.0310389\pi$
$503$			97.9412i			0.194714i	−0.995250	+	0.0973571i	$0.968961\pi$
$504$		0			0
$505$	−52.8182			−0.104591
$506$		0			0
$507$	446.233	−	238.521i	0.880143	−	0.470456i
$508$		0			0
$509$		−	318.104i		−	0.624958i	−0.949925	−	0.312479i	$-0.898841\pi$
$509$		−	318.104i		−	0.624958i	0.949925	−	0.312479i	$-0.101159\pi$
$510$		0			0
$511$	−191.373			−0.374506
$512$		0			0
$513$	−42.3320	+	429.921i	−0.0825186	+	0.838052i
$514$		0			0
$515$			109.015i			0.211679i
$516$		0			0
$517$	123.498			0.238874
$518$		0			0
$519$	272.288	+	509.403i	0.524639	+	0.981509i
$520$		0			0
$521$			727.150i			1.39568i	0.716253	+	0.697840i	$0.245856\pi$
$521$			727.150i			1.39568i	−0.716253	+	0.697840i	$0.754144\pi$
$522$		0			0
$523$	207.624			0.396986			0.198493	−	0.980102i	$-0.436395\pi$
$523$	207.624			0.396986			0.198493	+	0.980102i	$0.436395\pi$
$524$		0			0
$525$	169.162	−	90.4209i	0.322213	−	0.172230i
$526$		0			0
$527$		−	1258.98i		−	2.38896i
$528$		0			0
$529$	−978.830			−1.85034
$530$		0			0
$531$	435.660	+	291.088i	0.820452	+	0.548188i
$532$		0			0
$533$			5.10216i			0.00957254i
$534$		0			0
$535$	−106.384			−0.198849
$536$		0			0
$537$	61.7490	+	115.522i	0.114989	+	0.215124i
$538$		0			0
$539$		−	101.881i		−	0.189018i
$540$		0			0
$541$	−1025.15			−1.89492			−0.947459	−	0.319878i	$-0.896358\pi$
$541$	−1025.15			−1.89492			−0.947459	+	0.319878i	$0.896358\pi$
$542$		0			0
$543$	−214.531	+	114.671i	−0.395084	+	0.211181i
$544$		0			0
$545$			80.2091i			0.147173i
$546$		0			0
$547$	560.089			1.02393			0.511964	−	0.859007i	$-0.328918\pi$
$547$	560.089			1.02393			0.511964	+	0.859007i	$0.328918\pi$
$548$		0			0
$549$	−194.575	+	291.213i	−0.354417	+	0.530443i
$550$		0			0
$551$			572.281i			1.03862i
$552$		0			0
$553$	−55.3360			−0.100065
$554$		0			0
$555$	−25.8301	−	48.3236i	−0.0465406	−	0.0870696i
$556$		0			0
$557$		−	575.705i		−	1.03358i	−0.856112	−	0.516791i	$-0.827126\pi$
$557$		−	575.705i		−	1.03358i	0.856112	−	0.516791i	$-0.172874\pi$
$558$		0			0
$559$	6.84974			0.0122536
$560$		0			0
$561$	−829.320	+	443.290i	−1.47829	+	0.790179i
$562$		0			0
$563$			468.558i			0.832251i	0.909307	+	0.416126i	$0.136612\pi$
$563$			468.558i			0.832251i	−0.909307	+	0.416126i	$0.863388\pi$
$564$		0			0
$565$	−63.1739			−0.111812
$566$		0			0
$567$	82.0183	+	197.990i	0.144653	+	0.349189i
$568$		0			0
$569$		−	506.455i		−	0.890079i	−0.895511	−	0.445039i	$-0.853190\pi$
$569$		−	506.455i		−	0.890079i	0.895511	−	0.445039i	$-0.146810\pi$
$570$		0			0
$571$	−32.9150			−0.0576445			−0.0288223	−	0.999585i	$-0.509176\pi$
$571$	−32.9150			−0.0576445			−0.0288223	+	0.999585i	$0.509176\pi$
$572$		0			0
$573$	75.7411	+	141.699i	0.132183	+	0.247293i
$574$		0			0
$575$		−	938.385i		−	1.63197i
$576$		0			0
$577$	−252.154			−0.437009			−0.218505	−	0.975836i	$-0.570118\pi$
$577$	−252.154			−0.437009			−0.218505	+	0.975836i	$0.570118\pi$
$578$		0			0
$579$	292.340	−	156.262i	0.504905	−	0.269883i
$580$		0			0
$581$			385.073i			0.662776i
$582$		0			0
$583$	−740.988			−1.27099
$584$		0			0
$585$	−3.98425	−	2.66209i	−0.00681069	−	0.00455058i
$586$		0			0
$587$		−	366.882i		−	0.625012i	−0.949916	−	0.312506i	$-0.898832\pi$
$587$		−	366.882i		−	0.625012i	0.949916	−	0.312506i	$-0.101168\pi$
$588$		0			0
$589$	−935.320			−1.58798
$590$		0			0
$591$	121.830	+	227.923i	0.206142	+	0.385657i
$592$		0			0
$593$		−	620.757i		−	1.04681i	−0.852085	−	0.523404i	$-0.824662\pi$
$593$		−	620.757i		−	1.04681i	0.852085	−	0.523404i	$-0.175338\pi$
$594$		0			0
$595$	−52.0366			−0.0874564
$596$		0			0
$597$	232.826	−	124.451i	0.389993	−	0.208460i
$598$		0			0
$599$		−	26.3488i		−	0.0439879i	−0.999758	−	0.0219940i	$-0.992999\pi$
$599$		−	26.3488i		−	0.0439879i	0.999758	−	0.0219940i	$-0.00700146\pi$
$600$		0			0
$601$	930.470			1.54820			0.774102	−	0.633061i	$-0.218202\pi$
$601$	930.470			1.54820			0.774102	+	0.633061i	$0.218202\pi$
$602$		0			0
$603$	−352.915	+	528.195i	−0.585265	+	0.875945i
$604$		0			0
$605$			82.9488i			0.137105i
$606$		0			0
$607$	216.146			0.356089			0.178045	−	0.984022i	$-0.443023\pi$
$607$	216.146			0.356089			0.178045	+	0.984022i	$0.443023\pi$
$608$		0			0
$609$	133.830	+	250.373i	0.219754	+	0.411122i
$610$		0			0
$611$			4.94696i			0.00809650i
$612$		0			0
$613$	268.834			0.438555			0.219277	−	0.975663i	$-0.429630\pi$
$613$	268.834			0.438555			0.219277	+	0.975663i	$0.429630\pi$
$614$		0			0
$615$	−21.1452	+	11.3026i	−0.0343824	+	0.0183782i
$616$		0			0
$617$		−	531.338i		−	0.861163i	−0.902552	−	0.430582i	$-0.858308\pi$
$617$		−	531.338i		−	0.861163i	0.902552	−	0.430582i	$-0.141692\pi$
$618$		0			0
$619$	−425.203			−0.686919			−0.343459	−	0.939168i	$-0.611599\pi$
$619$	−425.203			−0.686919			−0.343459	+	0.939168i	$0.611599\pi$
$620$		0			0
$621$	1043.39	+	102.737i	1.68017	+	0.165437i
$622$		0			0
$623$			141.948i			0.227846i
$624$		0			0
$625$	563.146			0.901034
$626$		0			0
$627$	329.328	+	616.116i	0.525244	+	0.982642i
$628$		0			0
$629$		−	430.734i		−	0.684792i
$630$		0			0
$631$	−453.490			−0.718685			−0.359342	−	0.933206i	$-0.616999\pi$
$631$	−453.490			−0.718685			−0.359342	+	0.933206i	$0.616999\pi$
$632$		0			0
$633$	−162.065	+	86.6275i	−0.256027	+	0.136852i
$634$		0			0
$635$			24.7348i			0.0389525i
$636$		0			0
$637$	4.08104			0.00640665
$638$		0			0
$639$	127.425	+	85.1393i	0.199413	+	0.133238i
$640$		0			0
$641$		−	463.455i		−	0.723019i	−0.932368	−	0.361510i	$-0.882261\pi$
$641$		−	463.455i		−	0.723019i	0.932368	−	0.361510i	$-0.117739\pi$
$642$		0			0
$643$	−820.988			−1.27681			−0.638405	−	0.769701i	$-0.720405\pi$
$643$	−820.988			−1.27681			−0.638405	+	0.769701i	$0.720405\pi$
$644$		0			0
$645$	15.1739	+	28.3877i	0.0235254	+	0.0440120i
$646$		0			0
$647$			996.660i			1.54043i	0.637783	+	0.770216i	$0.279852\pi$
$647$			996.660i			1.54043i	−0.637783	+	0.770216i	$0.720148\pi$
$648$		0			0
$649$	847.320			1.30558
$650$		0			0
$651$	−409.203	+	218.728i	−0.628575	+	0.335988i
$652$		0			0
$653$		−	357.602i		−	0.547629i	−0.961782	−	0.273815i	$-0.911715\pi$
$653$		−	357.602i		−	0.547629i	0.961782	−	0.273815i	$-0.0882855\pi$
$654$		0			0
$655$	132.915			0.202924
$656$		0			0
$657$	361.660	−	541.283i	0.550472	−	0.823871i
$658$		0			0
$659$		−	131.562i		−	0.199640i	−0.995006	−	0.0998198i	$-0.968173\pi$
$659$		−	131.562i		−	0.199640i	0.995006	−	0.0998198i	$-0.0318266\pi$
$660$		0			0
$661$	250.915			0.379599			0.189800	−	0.981823i	$-0.439216\pi$
$661$	250.915			0.379599			0.189800	+	0.981823i	$0.439216\pi$
$662$		0			0
$663$	−17.7569	−	33.2201i	−0.0267826	−	0.0501057i
$664$		0			0
$665$			38.6589i			0.0581337i
$666$		0			0
$667$	1388.88			2.08228
$668$		0			0
$669$	−398.170	+	212.831i	−0.595172	+	0.318133i
$670$		0			0
$671$			566.384i			0.844090i
$672$		0			0
$673$	196.502			0.291979			0.145990	−	0.989286i	$-0.453363\pi$
$673$	196.502			0.291979			0.145990	+	0.989286i	$0.453363\pi$
$674$		0			0
$675$	−63.9373	+	649.342i	−0.0947219	+	0.961988i
$676$		0			0
$677$			54.1838i			0.0800352i	0.999199	+	0.0400176i	$0.0127414\pi$
$677$			54.1838i			0.0800352i	−0.999199	+	0.0400176i	$0.987259\pi$
$678$		0			0
$679$	294.118			0.433163
$680$		0			0
$681$	269.490	+	504.170i	0.395727	+	0.740338i
$682$		0			0
$683$		−	749.006i		−	1.09664i	−0.836268	−	0.548321i	$-0.815267\pi$
$683$		−	749.006i		−	1.09664i	0.836268	−	0.548321i	$-0.184733\pi$
$684$		0			0
$685$	−22.6562			−0.0330747
$686$		0			0
$687$	−378.118	+	202.112i	−0.550390	+	0.294196i
$688$		0			0
$689$		−	29.6818i		−	0.0430795i
$690$		0			0
$691$	−475.137			−0.687608			−0.343804	−	0.939041i	$-0.611716\pi$
$691$	−475.137			−0.687608			−0.343804	+	0.939041i	$0.611716\pi$
$692$		0			0
$693$	288.162	+	192.536i	0.415818	+	0.277830i
$694$		0			0
$695$			133.749i			0.192445i
$696$		0			0
$697$	−188.478			−0.270414
$698$		0			0
$699$	−11.0850	−	20.7381i	−0.0158583	−	0.0296682i
$700$		0			0
$701$		−	1251.49i		−	1.78529i	−0.450760	−	0.892645i	$-0.648847\pi$
$701$		−	1251.49i		−	1.78529i	0.450760	−	0.892645i	$-0.351153\pi$
$702$		0			0
$703$	−320.000			−0.455192
$704$		0			0
$705$	−20.5020	+	10.9588i	−0.0290808	+	0.0155443i
$706$		0			0
$707$			153.022i			0.216438i
$708$		0			0
$709$	16.5098			0.0232861			0.0116430	−	0.999932i	$-0.496294\pi$
$709$	16.5098			0.0232861			0.0116430	+	0.999932i	$0.496294\pi$
$710$		0			0
$711$	104.575	−	156.514i	0.147082	−	0.220132i
$712$		0			0
$713$			2269.95i			3.18366i
$714$		0			0
$715$	−7.74902			−0.0108378
$716$		0			0
$717$	−301.749	−	564.521i	−0.420849	−	0.787337i
$718$		0			0
$719$		−	1327.59i		−	1.84643i	−0.384279	−	0.923217i	$-0.625550\pi$
$719$		−	1327.59i		−	1.84643i	0.384279	−	0.923217i	$-0.374450\pi$
$720$		0			0
$721$	315.830			0.438044
$722$		0			0
$723$	343.948	−	183.848i	0.475723	−	0.254285i
$724$		0			0
$725$			864.360i			1.19222i
$726$		0			0
$727$	−202.782			−0.278929			−0.139465	−	0.990227i	$-0.544538\pi$
$727$	−202.782			−0.278929			−0.139465	+	0.990227i	$0.544538\pi$
$728$		0			0
$729$	−715.000	−	142.183i	−0.980796	−	0.195038i
$730$		0			0
$731$			253.035i			0.346149i
$732$		0			0
$733$	582.559			0.794760			0.397380	−	0.917654i	$-0.369919\pi$
$733$	582.559			0.794760			0.397380	+	0.917654i	$0.369919\pi$
$734$		0			0
$735$	9.04052	+	16.9133i	0.0123000	+	0.0230112i
$736$		0			0
$737$			1027.29i			1.39388i
$738$		0			0
$739$	256.810			0.347511			0.173755	−	0.984789i	$-0.444410\pi$
$739$	256.810			0.347511			0.173755	+	0.984789i	$0.444410\pi$
$740$		0			0
$741$	−24.6798	+	13.1919i	−0.0333061	+	0.0178028i
$742$		0			0
$743$		−	573.256i		−	0.771542i	−0.922595	−	0.385771i	$-0.873936\pi$
$743$		−	573.256i		−	0.771542i	0.922595	−	0.385771i	$-0.126064\pi$
$744$		0			0
$745$	200.502			0.269130
$746$		0			0
$747$	−1089.15	−	727.719i	−1.45803	−	0.974189i
$748$		0			0
$749$			308.210i			0.411495i
$750$		0			0
$751$	−579.085			−0.771085			−0.385543	−	0.922690i	$-0.625986\pi$
$751$	−579.085			−0.771085			−0.385543	+	0.922690i	$0.625986\pi$
$752$		0			0
$753$	−550.494	−	1029.88i	−0.731068	−	1.36770i
$754$		0			0
$755$			193.294i			0.256019i
$756$		0			0
$757$	−1167.13			−1.54179			−0.770895	−	0.636963i	$-0.780191\pi$
$757$	−1167.13			−1.54179			−0.770895	+	0.636963i	$0.780191\pi$
$758$		0			0
$759$	1495.27	−	799.254i	1.97005	−	1.05304i
$760$		0			0
$761$		−	800.970i		−	1.05252i	−0.850323	−	0.526261i	$-0.823593\pi$
$761$		−	800.970i		−	1.05252i	0.850323	−	0.526261i	$-0.176407\pi$
$762$		0			0
$763$	232.376			0.304556
$764$		0			0
$765$	98.3399	−	147.182i	0.128549	−	0.192394i
$766$		0			0
$767$			33.9411i			0.0442518i
$768$		0			0
$769$	−242.680			−0.315578			−0.157789	−	0.987473i	$-0.550437\pi$
$769$	−242.680			−0.315578			−0.157789	+	0.987473i	$0.550437\pi$
$770$		0			0
$771$	−475.373	−	889.341i	−0.616566	−	1.15349i
$772$		0			0
$773$			1262.83i			1.63367i	0.576870	+	0.816836i	$0.304274\pi$
$773$			1262.83i			1.63367i	−0.576870	+	0.816836i	$0.695726\pi$
$774$		0			0
$775$	−1412.68			−1.82282
$776$		0			0
$777$	−140.000	+	74.8331i	−0.180180	+	0.0963104i
$778$		0			0
$779$			140.024i			0.179748i
$780$		0			0
$781$	247.830			0.317324
$782$		0			0
$783$	−961.077	−	94.6321i	−1.22743	−	0.120858i
$784$		0			0
$785$			190.632i			0.242844i
$786$		0			0
$787$	−1347.00			−1.71156			−0.855782	−	0.517336i	$-0.826924\pi$
$787$	−1347.00			−1.71156			−0.855782	+	0.517336i	$0.826924\pi$
$788$		0			0
$789$	620.745	+	1161.31i	0.786749	+	1.47187i
$790$		0			0
$791$			183.023i			0.231382i
$792$		0			0
$793$	−22.6877			−0.0286099
$794$		0			0
$795$	123.012	−	65.7526i	0.154732	−	0.0827076i
$796$		0			0
$797$			1210.62i			1.51897i	0.650523	+	0.759487i	$0.274550\pi$
$797$			1210.62i			1.51897i	−0.650523	+	0.759487i	$0.725450\pi$
$798$		0			0
$799$	−182.745			−0.228717
$800$		0			0
$801$	−401.490	−	268.257i	−0.501236	−	0.334902i
$802$		0			0
$803$		−	1052.75i		−	1.31102i
$804$		0			0
$805$	93.8222			0.116549
$806$		0			0
$807$	−20.4496	−	38.2578i	−0.0253403	−	0.0474074i
$808$		0			0
$809$			310.876i			0.384271i	0.981368	+	0.192136i	$0.0615414\pi$
$809$			310.876i			0.384271i	−0.981368	+	0.192136i	$0.938459\pi$
$810$		0			0
$811$	65.7777			0.0811069			0.0405535	−	0.999177i	$-0.487088\pi$
$811$	65.7777			0.0811069			0.0405535	+	0.999177i	$0.487088\pi$
$812$		0			0
$813$	−162.826	+	87.0342i	−0.200278	+	0.107053i
$814$		0			0
$815$			243.829i			0.299177i
$816$		0			0
$817$	187.984			0.230091
$818$		0			0
$819$	−7.71243	+	11.5429i	−0.00941689	+	0.0140939i
$820$		0			0
$821$			370.994i			0.451880i	0.974141	+	0.225940i	$0.0725453\pi$
$821$			370.994i			0.451880i	−0.974141	+	0.225940i	$0.927455\pi$
$822$		0			0
$823$	441.077			0.535938			0.267969	−	0.963428i	$-0.413647\pi$
$823$	441.077			0.535938			0.267969	+	0.963428i	$0.413647\pi$
$824$		0			0
$825$	497.409	+	930.567i	0.602920	+	1.12796i
$826$		0			0
$827$			116.492i			0.140861i	0.997517	+	0.0704307i	$0.0224374\pi$
$827$			116.492i			0.140861i	−0.997517	+	0.0704307i	$0.977563\pi$
$828$		0			0
$829$	881.425			1.06324			0.531619	−	0.846983i	$-0.321584\pi$
$829$	881.425			1.06324			0.531619	+	0.846983i	$0.321584\pi$
$830$		0			0
$831$	398.170	−	212.831i	0.479146	−	0.256114i
$832$		0			0
$833$			150.757i			0.180981i
$834$		0			0
$835$	6.56726			0.00786498
$836$		0			0
$837$	154.664	−	1570.76i	0.184784	−	1.87665i
$838$		0			0
$839$		−	1346.42i		−	1.60480i	−0.596789	−	0.802398i	$-0.703557\pi$
$839$		−	1346.42i		−	1.60480i	0.596789	−	0.802398i	$-0.296443\pi$
$840$		0			0
$841$	−438.320			−0.521189
$842$		0			0
$843$	−424.575	−	794.307i	−0.503648	−	0.942239i
$844$		0			0
$845$			154.026i			0.182279i
$846$		0			0
$847$	240.314			0.283723
$848$		0			0
$849$	261.490	−	139.772i	0.307998	−	0.164632i
$850$		0			0
$851$			776.616i			0.912592i
$852$		0			0
$853$	966.235			1.13275			0.566375	−	0.824148i	$-0.308346\pi$
$853$	966.235			1.13275			0.566375	+	0.824148i	$0.308346\pi$
$854$		0			0
$855$	−109.344	−	73.0584i	−0.127888	−	0.0854484i
$856$		0			0
$857$		−	982.241i		−	1.14614i	−0.819507	−	0.573069i	$-0.805753\pi$
$857$		−	982.241i		−	1.14614i	0.819507	−	0.573069i	$-0.194247\pi$
$858$		0			0
$859$	−1309.49			−1.52444			−0.762218	−	0.647321i	$-0.775889\pi$
$859$	−1309.49			−1.52444			−0.762218	+	0.647321i	$0.775889\pi$
$860$		0			0
$861$	32.7451	+	61.2604i	0.0380315	+	0.0711503i
$862$		0			0
$863$			1001.55i			1.16054i	0.814423	+	0.580272i	$0.197054\pi$
$863$			1001.55i			1.16054i	−0.814423	+	0.580272i	$0.802946\pi$
$864$		0			0
$865$	−175.830			−0.203272
$866$		0			0
$867$	462.557	−	247.247i	0.533514	−	0.285175i
$868$		0			0
$869$		−	304.405i		−	0.350294i
$870$		0			0
$871$	−41.1503			−0.0472448
$872$		0			0
$873$	−555.830	+	831.890i	−0.636690	+	0.952910i
$874$		0			0
$875$			118.794i			0.135765i
$876$		0			0
$877$	33.1424			0.0377906			0.0188953	−	0.999821i	$-0.493985\pi$
$877$	33.1424			0.0377906			0.0188953	+	0.999821i	$0.493985\pi$
$878$		0			0
$879$	10.1176	+	18.9283i	0.0115104	+	0.0215339i
$880$		0			0
$881$		−	944.040i		−	1.07156i	−0.844359	−	0.535778i	$-0.820019\pi$
$881$		−	944.040i		−	1.07156i	0.844359	−	0.535778i	$-0.179981\pi$
$882$		0			0
$883$	−55.5138			−0.0628695			−0.0314348	−	0.999506i	$-0.510008\pi$
$883$	−55.5138			−0.0628695			−0.0314348	+	0.999506i	$0.510008\pi$
$884$		0			0
$885$	−140.664	+	75.1881i	−0.158942	+	0.0849583i
$886$		0			0
$887$		−	20.1317i		−	0.0226964i	−0.999936	−	0.0113482i	$-0.996388\pi$
$887$		−	20.1317i		−	0.0226964i	0.999936	−	0.0113482i	$-0.00361231\pi$
$888$		0			0
$889$	71.6601			0.0806075
$890$		0			0
$891$	−1089.15	+	451.186i	−1.22239	+	0.506381i
$892$		0			0
$893$			135.765i			0.152032i
$894$		0			0
$895$	−39.8745			−0.0445525
$896$		0			0
$897$	32.0157	+	59.8960i	0.0356920	+	0.0667737i
$898$		0			0
$899$		−	2090.88i		−	2.32579i
$900$		0			0
$901$	1096.47			1.21695
$902$		0			0
$903$	82.2431	−	43.9608i	0.0910776	−	0.0486830i
$904$		0			0
$905$		−	74.0493i		−	0.0818224i
$906$		0			0
$907$	−219.644			−0.242166			−0.121083	−	0.992642i	$-0.538637\pi$
$907$	−219.644			−0.242166			−0.121083	+	0.992642i	$0.538637\pi$
$908$		0			0
$909$	−432.810	−	289.184i	−0.476139	−	0.318134i
$910$		0			0
$911$			827.126i			0.907932i	0.891019	+	0.453966i	$0.149991\pi$
$911$			827.126i			0.907932i	−0.891019	+	0.453966i	$0.850009\pi$
$912$		0			0
$913$	−2118.30			−2.32015
$914$		0			0
$915$	−50.2589	−	94.0257i	−0.0549277	−	0.102760i
$916$		0			0
$917$		−	385.073i		−	0.419927i
$918$		0			0
$919$	−1029.39			−1.12011			−0.560057	−	0.828454i	$-0.689221\pi$
$919$	−1029.39			−1.12011			−0.560057	+	0.828454i	$0.689221\pi$
$920$		0			0
$921$	280.000	−	149.666i	0.304017	−	0.162504i
$922$		0			0
$923$			9.92733i			0.0107555i
$924$		0			0
$925$	−483.320			−0.522508
$926$		0			0
$927$	−596.863	+	893.302i	−0.643865	+	0.963649i
$928$		0			0
$929$			1440.98i			1.55111i	0.631282	+	0.775553i	$0.282529\pi$
$929$			1440.98i			1.55111i	−0.631282	+	0.775553i	$0.717471\pi$
$930$		0			0
$931$	112.000			0.120301
$932$		0			0
$933$	375.336	+	702.189i	0.402289	+	0.752614i
$934$		0			0
$935$		−	286.255i		−	0.306155i
$936$		0			0
$937$	1010.00			1.07791			0.538954	−	0.842335i	$-0.318820\pi$
$937$	1010.00			1.07791			0.538954	+	0.842335i	$0.318820\pi$
$938$		0			0
$939$	−686.118	+	366.745i	−0.730690	+	0.390570i
$940$		0			0
$941$			191.775i			0.203799i	0.994795	+	0.101899i	$0.0324920\pi$
$941$			191.775i			0.203799i	−0.994795	+	0.101899i	$0.967508\pi$
$942$		0			0
$943$	339.827			0.360368
$944$		0			0
$945$	−64.9229	−	6.39261i	−0.0687015	−	0.00676467i
$946$		0			0
$947$			893.108i			0.943092i	0.881841	+	0.471546i	$0.156304\pi$
$947$			893.108i			0.943092i	−0.881841	+	0.471546i	$0.843696\pi$
$948$		0			0
$949$	42.1699			0.0444362
$950$		0			0
$951$	53.4902	+	100.071i	0.0562462	+	0.105227i
$952$		0			0
$953$		−	1300.12i		−	1.36423i	−0.731243	−	0.682117i	$-0.761059\pi$
$953$		−	1300.12i		−	1.36423i	0.731243	−	0.682117i	$-0.238941\pi$
$954$		0			0
$955$	−48.9099			−0.0512146
$956$		0			0
$957$	−1377.31	+	736.204i	−1.43920	+	0.769284i
$958$		0			0
$959$			65.6380i			0.0684442i
$960$		0			0
$961$	2456.28			2.55596
$962$		0			0
$963$	−871.749	−	582.462i	−0.905243	−	0.604841i
$964$		0			0
$965$			100.907i			0.104566i
$966$		0			0
$967$	−375.247			−0.388053			−0.194026	−	0.980996i	$-0.562155\pi$
$967$	−375.247			−0.388053			−0.194026	+	0.980996i	$0.562155\pi$
$968$		0			0
$969$	−487.320	−	911.693i	−0.502910	−	0.940859i
$970$		0			0
$971$		−	1045.06i		−	1.07628i	−0.842856	−	0.538138i	$-0.819128\pi$
$971$		−	1045.06i		−	1.07628i	0.842856	−	0.538138i	$-0.180872\pi$
$972$		0			0
$973$	387.490			0.398243
$974$		0			0
$975$	−37.2758	+	19.9247i	−0.0382315	+	0.0204356i
$976$		0			0
$977$			459.425i			0.470241i	0.971966	+	0.235120i	$0.0755484\pi$
$977$			459.425i			0.470241i	−0.971966	+	0.235120i	$0.924452\pi$
$978$		0			0
$979$	−780.863			−0.797613
$980$		0			0
$981$	−439.150	+	657.260i	−0.447656	+	0.669990i
$982$		0			0
$983$		−	103.265i		−	0.105051i	−0.998620	−	0.0525257i	$-0.983273\pi$
$983$		−	103.265i		−	0.105051i	0.998620	−	0.0525257i	$-0.0167271\pi$
$984$		0			0
$985$	−78.6719			−0.0798700
$986$		0			0
$987$	31.7490	+	59.3970i	0.0321672	+	0.0601793i
$988$		0			0
$989$		−	456.224i		−	0.461298i
$990$		0			0
$991$	1329.73			1.34180			0.670901	−	0.741547i	$-0.265908\pi$
$991$	1329.73			1.34180			0.670901	+	0.741547i	$0.265908\pi$
$992$		0			0
$993$	384.931	−	205.754i	0.387644	−	0.207205i
$994$		0			0
$995$			80.3643i			0.0807681i
$996$		0			0
$997$	−664.259			−0.666258			−0.333129	−	0.942881i	$-0.608104\pi$
$997$	−664.259			−0.666258			−0.333129	+	0.942881i	$0.608104\pi$
$998$		0			0
$999$	52.9150	−	537.401i	0.0529680	−	0.537939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.3.d.c.449.2		4
3.2	odd	2	inner	1344.3.d.c.449.1		4
4.3	odd	2		1344.3.d.e.449.3		4
8.3	odd	2		336.3.d.b.113.2		4
8.5	even	2		42.3.b.a.29.2	✓	4
12.11	even	2		1344.3.d.e.449.4		4
24.5	odd	2		42.3.b.a.29.4	yes	4
24.11	even	2		336.3.d.b.113.1		4
40.13	odd	4		1050.3.c.a.449.4		8
40.29	even	2		1050.3.e.a.701.3		4
40.37	odd	4		1050.3.c.a.449.6		8
56.5	odd	6		294.3.h.g.263.2		8
56.13	odd	2		294.3.b.h.197.1		4
56.37	even	6		294.3.h.d.263.1		8
56.45	odd	6		294.3.h.g.275.4		8
56.53	even	6		294.3.h.d.275.3		8
72.5	odd	6		1134.3.q.a.1079.1		8
72.13	even	6		1134.3.q.a.1079.4		8
72.29	odd	6		1134.3.q.a.701.4		8
72.61	even	6		1134.3.q.a.701.1		8
120.29	odd	2		1050.3.e.a.701.1		4
120.53	even	4		1050.3.c.a.449.7		8
120.77	even	4		1050.3.c.a.449.1		8
168.5	even	6		294.3.h.g.263.4		8
168.53	odd	6		294.3.h.d.275.1		8
168.101	even	6		294.3.h.g.275.2		8
168.125	even	2		294.3.b.h.197.3		4
168.149	odd	6		294.3.h.d.263.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.b.a.29.2	✓	4	8.5	even	2
42.3.b.a.29.4	yes	4	24.5	odd	2
294.3.b.h.197.1		4	56.13	odd	2
294.3.b.h.197.3		4	168.125	even	2
294.3.h.d.263.1		8	56.37	even	6
294.3.h.d.263.3		8	168.149	odd	6
294.3.h.d.275.1		8	168.53	odd	6
294.3.h.d.275.3		8	56.53	even	6
294.3.h.g.263.2		8	56.5	odd	6
294.3.h.g.263.4		8	168.5	even	6
294.3.h.g.275.2		8	168.101	even	6
294.3.h.g.275.4		8	56.45	odd	6
336.3.d.b.113.1		4	24.11	even	2
336.3.d.b.113.2		4	8.3	odd	2
1050.3.c.a.449.1		8	120.77	even	4
1050.3.c.a.449.4		8	40.13	odd	4
1050.3.c.a.449.6		8	40.37	odd	4
1050.3.c.a.449.7		8	120.53	even	4
1050.3.e.a.701.1		4	120.29	odd	2
1050.3.e.a.701.3		4	40.29	even	2
1134.3.q.a.701.1		8	72.61	even	6
1134.3.q.a.701.4		8	72.29	odd	6
1134.3.q.a.1079.1		8	72.5	odd	6
1134.3.q.a.1079.4		8	72.13	even	6
1344.3.d.c.449.1		4	3.2	odd	2	inner
1344.3.d.c.449.2		4	1.1	even	1	trivial
1344.3.d.e.449.3		4	4.3	odd	2
1344.3.d.e.449.4		4	12.11	even	2

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1344.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.64575 + 1.41421i) q^{3} -0.913230i q^{5} -2.64575 q^{7} +(5.00000 - 7.48331i) q^{9} +O(q^{10})\)	\(q+(-2.64575 + 1.41421i) q^{3} -0.913230i q^{5} -2.64575 q^{7} +(5.00000 - 7.48331i) q^{9} -14.5544i q^{11} +0.583005 q^{13} +(1.29150 + 2.41618i) q^{15} +21.5367i q^{17} +16.0000 q^{19} +(7.00000 - 3.74166i) q^{21} -38.8308i q^{23} +24.1660 q^{25} +(-2.64575 + 26.8701i) q^{27} +35.7676i q^{29} -58.4575 q^{31} +(20.5830 + 38.5073i) q^{33} +2.41618i q^{35} -20.0000 q^{37} +(-1.54249 + 0.824494i) q^{39} +8.75149i q^{41} +11.7490 q^{43} +(-6.83399 - 4.56615i) q^{45} +8.48528i q^{47} +7.00000 q^{49} +(-30.4575 - 56.9808i) q^{51} -50.9117i q^{53} -13.2915 q^{55} +(-42.3320 + 22.6274i) q^{57} +58.2175i q^{59} -38.9150 q^{61} +(-13.2288 + 19.7990i) q^{63} -0.532418i q^{65} -70.5830 q^{67} +(54.9150 + 102.737i) q^{69} +17.0279i q^{71} +72.3320 q^{73} +(-63.9373 + 34.1759i) q^{75} +38.5073i q^{77} +20.9150 q^{79} +(-31.0000 - 74.8331i) q^{81} -145.544i q^{83} +19.6680 q^{85} +(-50.5830 - 94.6321i) q^{87} -53.6514i q^{89} -1.54249 q^{91} +(154.664 - 82.6714i) q^{93} -14.6117i q^{95} -111.166 q^{97} +(-108.915 - 72.7719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 20 q^{9}+O(q^{10}) \) 4 * q + 20 * q^9	\( 4 q + 20 q^{9} - 40 q^{13} - 16 q^{15} + 64 q^{19} + 28 q^{21} + 12 q^{25} - 128 q^{31} + 40 q^{33} - 80 q^{37} - 112 q^{39} - 80 q^{43} - 112 q^{45} + 28 q^{49} - 16 q^{51} - 32 q^{55} + 56 q^{61} - 240 q^{67} + 8 q^{69} + 120 q^{73} - 224 q^{75} - 128 q^{79} - 124 q^{81} + 248 q^{85} - 160 q^{87} - 112 q^{91} + 280 q^{93} - 360 q^{97} - 224 q^{99}+O(q^{100}) \) 4 * q + 20 * q^9 - 40 * q^13 - 16 * q^15 + 64 * q^19 + 28 * q^21 + 12 * q^25 - 128 * q^31 + 40 * q^33 - 80 * q^37 - 112 * q^39 - 80 * q^43 - 112 * q^45 + 28 * q^49 - 16 * q^51 - 32 * q^55 + 56 * q^61 - 240 * q^67 + 8 * q^69 + 120 * q^73 - 224 * q^75 - 128 * q^79 - 124 * q^81 + 248 * q^85 - 160 * q^87 - 112 * q^91 + 280 * q^93 - 360 * q^97 - 224 * q^99

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