LMFDB - Embedded newform 2400.2.w.d.2143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2400,2,Mod(607,2400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("2400.607");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2400 = 2^{5} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2400.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1640964851$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 480)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2143.2
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2400.2143
Dual form			2400.2.w.d.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})$	$q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{9} -5.41421i q^{11} +(-3.41421 - 3.41421i) q^{13} +(-5.41421 + 5.41421i) q^{17} -4.82843 q^{19} +1.41421 q^{21} +(-4.24264 + 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{27} -0.242641i q^{29} +1.65685i q^{31} +(-3.82843 - 3.82843i) q^{33} +(0.585786 - 0.585786i) q^{37} -4.82843 q^{39} -6.48528 q^{41} +(-4.82843 + 4.82843i) q^{43} +(6.24264 + 6.24264i) q^{47} -5.00000i q^{49} +7.65685i q^{51} +(2.82843 + 2.82843i) q^{53} +(-3.41421 + 3.41421i) q^{57} +1.41421 q^{59} -3.17157 q^{61} +(1.00000 - 1.00000i) q^{63} +(3.65685 + 3.65685i) q^{67} +6.00000i q^{69} +2.34315i q^{71} +(-7.48528 - 7.48528i) q^{73} +(5.41421 - 5.41421i) q^{77} +2.34315 q^{79} -1.00000 q^{81} +(-3.07107 + 3.07107i) q^{83} +(-0.171573 - 0.171573i) q^{87} -3.65685i q^{89} -6.82843i q^{91} +(1.17157 + 1.17157i) q^{93} +(-0.656854 + 0.656854i) q^{97} -5.41421 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{7}+O(q^{10}) $ 4 * q + 4 * q^7	$ 4 q + 4 q^{7} - 8 q^{13} - 16 q^{17} - 8 q^{19} - 4 q^{33} + 8 q^{37} - 8 q^{39} + 8 q^{41} - 8 q^{43} + 8 q^{47} - 8 q^{57} - 24 q^{61} + 4 q^{63} - 8 q^{67} + 4 q^{73} + 16 q^{77} + 32 q^{79} - 4 q^{81} + 16 q^{83} - 12 q^{87} + 16 q^{93} + 20 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^7 - 8 * q^13 - 16 * q^17 - 8 * q^19 - 4 * q^33 + 8 * q^37 - 8 * q^39 + 8 * q^41 - 8 * q^43 + 8 * q^47 - 8 * q^57 - 24 * q^61 + 4 * q^63 - 8 * q^67 + 4 * q^73 + 16 * q^77 + 32 * q^79 - 4 * q^81 + 16 * q^83 - 12 * q^87 + 16 * q^93 + 20 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1601$	$1951$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$-1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	5.41421i		−	1.63245i	−0.577736	−	0.816223i	$-0.696064\pi$
$11$		−	5.41421i		−	1.63245i	0.577736	−	0.816223i	$-0.303936\pi$
$12$		0			0
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	0.0517287	−	0.998661i	$-0.483527\pi$
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	−0.998661	+	0.0517287i	$0.983527\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.394051	+	0.919089i	$0.628927\pi$
$17$	−5.41421	+	5.41421i	−1.31314	+	1.31314i	−0.919089	+	0.394051i	$0.871073\pi$
$18$		0			0
$19$	−4.82843			−1.10772			−0.553859	−	0.832611i	$-0.686845\pi$
$19$	−4.82843			−1.10772			−0.553859	+	0.832611i	$0.686845\pi$
$20$		0			0
$21$	1.41421			0.308607
$22$		0			0
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	−0.994003	−	0.109351i	$-0.965123\pi$
$23$	−4.24264	+	4.24264i	−0.884652	+	0.884652i	0.109351	+	0.994003i	$0.465123\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	0.242641i		−	0.0450572i	−0.999746	−	0.0225286i	$-0.992828\pi$
$29$		−	0.242641i		−	0.0450572i	0.999746	−	0.0225286i	$-0.00717169\pi$
$30$		0			0
$31$			1.65685i			0.297580i	0.988869	+	0.148790i	$0.0475378\pi$
$31$			1.65685i			0.297580i	−0.988869	+	0.148790i	$0.952462\pi$
$32$		0			0
$33$	−3.82843	−	3.82843i	−0.666444	−	0.666444i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.585786	−	0.585786i	0.0963027	−	0.0963027i	−0.657314	−	0.753617i	$-0.728307\pi$
$37$	0.585786	−	0.585786i	0.0963027	−	0.0963027i	0.753617	+	0.657314i	$0.228307\pi$
$38$		0			0
$39$	−4.82843			−0.773167
$40$		0			0
$41$	−6.48528			−1.01283			−0.506415	−	0.862290i	$-0.669030\pi$
$41$	−6.48528			−1.01283			−0.506415	+	0.862290i	$0.669030\pi$
$42$		0			0
$43$	−4.82843	+	4.82843i	−0.736328	+	0.736328i	−0.971865	−	0.235537i	$-0.924315\pi$
$43$	−4.82843	+	4.82843i	−0.736328	+	0.736328i	0.235537	+	0.971865i	$0.424315\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.24264	+	6.24264i	0.910583	+	0.910583i	0.996318	−	0.0857352i	$-0.0273239\pi$
$47$	6.24264	+	6.24264i	0.910583	+	0.910583i	−0.0857352	+	0.996318i	$0.527324\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$			7.65685i			1.07217i
$52$		0			0
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	0.874157	−	0.485643i	$-0.161414\pi$
$53$	2.82843	+	2.82843i	0.388514	+	0.388514i	−0.485643	+	0.874157i	$0.661414\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.41421	+	3.41421i	−0.452224	+	0.452224i
$58$		0			0
$59$	1.41421			0.184115			0.0920575	−	0.995754i	$-0.470656\pi$
$59$	1.41421			0.184115			0.0920575	+	0.995754i	$0.470656\pi$
$60$		0			0
$61$	−3.17157			−0.406078			−0.203039	−	0.979171i	$-0.565082\pi$
$61$	−3.17157			−0.406078			−0.203039	+	0.979171i	$0.565082\pi$
$62$		0			0
$63$	1.00000	−	1.00000i	0.125988	−	0.125988i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.65685	+	3.65685i	0.446756	+	0.446756i	0.894275	−	0.447519i	$-0.147692\pi$
$67$	3.65685	+	3.65685i	0.446756	+	0.446756i	−0.447519	+	0.894275i	$0.647692\pi$
$68$		0			0
$69$			6.00000i			0.722315i
$70$		0			0
$71$			2.34315i			0.278080i	0.990287	+	0.139040i	$0.0444017\pi$
$71$			2.34315i			0.278080i	−0.990287	+	0.139040i	$0.955598\pi$
$72$		0			0
$73$	−7.48528	−	7.48528i	−0.876086	−	0.876086i	0.117041	−	0.993127i	$-0.462659\pi$
$73$	−7.48528	−	7.48528i	−0.876086	−	0.876086i	−0.993127	+	0.117041i	$0.962659\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.41421	−	5.41421i	0.617007	−	0.617007i
$78$		0			0
$79$	2.34315			0.263624			0.131812	−	0.991275i	$-0.457920\pi$
$79$	2.34315			0.263624			0.131812	+	0.991275i	$0.457920\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−3.07107	+	3.07107i	−0.337093	+	0.337093i	−0.855272	−	0.518179i	$-0.826610\pi$
$83$	−3.07107	+	3.07107i	−0.337093	+	0.337093i	0.518179	+	0.855272i	$0.326610\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.171573	−	0.171573i	−0.0183945	−	0.0183945i
$88$		0			0
$89$		−	3.65685i		−	0.387626i	−0.981039	−	0.193813i	$-0.937915\pi$
$89$		−	3.65685i		−	0.387626i	0.981039	−	0.193813i	$-0.0620855\pi$
$90$		0			0
$91$		−	6.82843i		−	0.715814i
$92$		0			0
$93$	1.17157	+	1.17157i	0.121486	+	0.121486i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.656854	+	0.656854i	−0.0666934	+	0.0666934i	−0.739667	−	0.672973i	$-0.765017\pi$
$97$	−0.656854	+	0.656854i	−0.0666934	+	0.0666934i	0.672973	+	0.739667i	$0.265017\pi$
$98$		0			0
$99$	−5.41421			−0.544149
$100$		0			0
$101$	−5.41421			−0.538734			−0.269367	−	0.963038i	$-0.586815\pi$
$101$	−5.41421			−0.538734			−0.269367	+	0.963038i	$0.586815\pi$
$102$		0			0
$103$	11.8284	−	11.8284i	1.16549	−	1.16549i	0.182234	−	0.983255i	$-0.441667\pi$
$103$	11.8284	−	11.8284i	1.16549	−	1.16549i	0.983255	−	0.182234i	$-0.0583330\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.58579	−	6.58579i	−0.636672	−	0.636672i	0.313061	−	0.949733i	$-0.398646\pi$
$107$	−6.58579	−	6.58579i	−0.636672	−	0.636672i	−0.949733	+	0.313061i	$0.898646\pi$
$108$		0			0
$109$		−	20.1421i		−	1.92927i	−0.263595	−	0.964633i	$-0.584908\pi$
$109$		−	20.1421i		−	1.92927i	0.263595	−	0.964633i	$-0.415092\pi$
$110$		0			0
$111$		−	0.828427i		−	0.0786308i
$112$		0			0
$113$	−5.07107	−	5.07107i	−0.477046	−	0.477046i	0.427140	−	0.904186i	$-0.359521\pi$
$113$	−5.07107	−	5.07107i	−0.477046	−	0.477046i	−0.904186	+	0.427140i	$0.859521\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.41421	+	3.41421i	−0.315644	+	0.315644i
$118$		0			0
$119$	−10.8284			−0.992640
$120$		0			0
$121$	−18.3137			−1.66488
$122$		0			0
$123$	−4.58579	+	4.58579i	−0.413486	+	0.413486i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.48528	−	7.48528i	−0.664211	−	0.664211i	0.292159	−	0.956370i	$-0.405626\pi$
$127$	−7.48528	−	7.48528i	−0.664211	−	0.664211i	−0.956370	+	0.292159i	$0.905626\pi$
$128$		0			0
$129$			6.82843i			0.601209i
$130$		0			0
$131$			21.8995i			1.91337i	0.291129	+	0.956684i	$0.405969\pi$
$131$			21.8995i			1.91337i	−0.291129	+	0.956684i	$0.594031\pi$
$132$		0			0
$133$	−4.82843	−	4.82843i	−0.418678	−	0.418678i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.75736	−	1.75736i	0.150141	−	0.150141i	−0.628040	−	0.778181i	$-0.716143\pi$
$137$	1.75736	−	1.75736i	0.150141	−	0.150141i	0.778181	+	0.628040i	$0.216143\pi$
$138$		0			0
$139$	8.34315			0.707656			0.353828	−	0.935310i	$-0.384880\pi$
$139$	8.34315			0.707656			0.353828	+	0.935310i	$0.384880\pi$
$140$		0			0
$141$	8.82843			0.743488
$142$		0			0
$143$	−18.4853	+	18.4853i	−1.54582	+	1.54582i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.53553	−	3.53553i	−0.291606	−	0.291606i
$148$		0			0
$149$		−	20.7279i		−	1.69810i	−0.528314	−	0.849049i	$-0.677176\pi$
$149$		−	20.7279i		−	1.69810i	0.528314	−	0.849049i	$-0.322824\pi$
$150$		0			0
$151$			17.3137i			1.40897i	0.709719	+	0.704485i	$0.248822\pi$
$151$			17.3137i			1.40897i	−0.709719	+	0.704485i	$0.751178\pi$
$152$		0			0
$153$	5.41421	+	5.41421i	0.437713	+	0.437713i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.41421	−	1.41421i	0.112867	−	0.112867i	−0.648418	−	0.761285i	$-0.724569\pi$
$157$	1.41421	−	1.41421i	0.112867	−	0.112867i	0.761285	+	0.648418i	$0.224569\pi$
$158$		0			0
$159$	4.00000			0.317221
$160$		0			0
$161$	−8.48528			−0.668734
$162$		0			0
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	−0.860598	−	0.509284i	$-0.829910\pi$
$163$	−4.48528	+	4.48528i	−0.351314	+	0.351314i	0.509284	+	0.860598i	$0.329910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.24264	+	4.24264i	0.328305	+	0.328305i	0.851942	−	0.523636i	$-0.175425\pi$
$167$	4.24264	+	4.24264i	0.328305	+	0.328305i	−0.523636	+	0.851942i	$0.675425\pi$
$168$		0			0
$169$			10.3137i			0.793362i
$170$		0			0
$171$			4.82843i			0.369239i
$172$		0			0
$173$	2.58579	+	2.58579i	0.196594	+	0.196594i	0.798538	−	0.601944i	$-0.205607\pi$
$173$	2.58579	+	2.58579i	0.196594	+	0.196594i	−0.601944	+	0.798538i	$0.705607\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.00000	−	1.00000i	0.0751646	−	0.0751646i
$178$		0			0
$179$	−16.7279			−1.25030			−0.625152	−	0.780503i	$-0.714963\pi$
$179$	−16.7279			−1.25030			−0.625152	+	0.780503i	$0.714963\pi$
$180$		0			0
$181$	20.1421			1.49715			0.748577	−	0.663048i	$-0.230738\pi$
$181$	20.1421			1.49715			0.748577	+	0.663048i	$0.230738\pi$
$182$		0			0
$183$	−2.24264	+	2.24264i	−0.165781	+	0.165781i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	29.3137	+	29.3137i	2.14363	+	2.14363i
$188$		0			0
$189$		−	1.41421i		−	0.102869i
$190$		0			0
$191$		−	1.17157i		−	0.0847720i	−0.999101	−	0.0423860i	$-0.986504\pi$
$191$		−	1.17157i		−	0.0847720i	0.999101	−	0.0423860i	$-0.0134959\pi$
$192$		0			0
$193$	−9.82843	−	9.82843i	−0.707466	−	0.707466i	0.258536	−	0.966002i	$-0.416760\pi$
$193$	−9.82843	−	9.82843i	−0.707466	−	0.707466i	−0.966002	+	0.258536i	$0.916760\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.8284	+	14.8284i	−1.05648	+	1.05648i	−0.0581753	+	0.998306i	$0.518528\pi$
$197$	−14.8284	+	14.8284i	−1.05648	+	1.05648i	−0.998306	+	0.0581753i	$0.981472\pi$
$198$		0			0
$199$	21.3137			1.51089			0.755444	−	0.655213i	$-0.227421\pi$
$199$	21.3137			1.51089			0.755444	+	0.655213i	$0.227421\pi$
$200$		0			0
$201$	5.17157			0.364775
$202$		0			0
$203$	0.242641	−	0.242641i	0.0170300	−	0.0170300i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.24264	+	4.24264i	0.294884	+	0.294884i
$208$		0			0
$209$			26.1421i			1.80829i
$210$		0			0
$211$		−	17.3137i		−	1.19192i	−0.803012	−	0.595962i	$-0.796771\pi$
$211$		−	17.3137i		−	1.19192i	0.803012	−	0.595962i	$-0.203229\pi$
$212$		0			0
$213$	1.65685	+	1.65685i	0.113526	+	0.113526i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.65685	+	1.65685i	−0.112475	+	0.112475i
$218$		0			0
$219$	−10.5858			−0.715321
$220$		0			0
$221$	36.9706			2.48691
$222$		0			0
$223$	−12.6569	+	12.6569i	−0.847566	+	0.847566i	−0.989829	−	0.142263i	$-0.954562\pi$
$223$	−12.6569	+	12.6569i	−0.847566	+	0.847566i	0.142263	+	0.989829i	$0.454562\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.65685	−	9.65685i	−0.640948	−	0.640948i	0.309841	−	0.950789i	$-0.399724\pi$
$227$	−9.65685	−	9.65685i	−0.640948	−	0.640948i	−0.950789	+	0.309841i	$0.899724\pi$
$228$		0			0
$229$		−	12.3431i		−	0.815658i	−0.913058	−	0.407829i	$-0.866286\pi$
$229$		−	12.3431i		−	0.815658i	0.913058	−	0.407829i	$-0.133714\pi$
$230$		0			0
$231$		−	7.65685i		−	0.503784i
$232$		0			0
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	0.436475	−	0.899716i	$-0.356227\pi$
$233$	−7.07107	−	7.07107i	−0.463241	−	0.463241i	−0.899716	+	0.436475i	$0.856227\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.65685	−	1.65685i	0.107624	−	0.107624i
$238$		0			0
$239$	−23.3137			−1.50804			−0.754019	−	0.656852i	$-0.771887\pi$
$239$	−23.3137			−1.50804			−0.754019	+	0.656852i	$0.771887\pi$
$240$		0			0
$241$	−24.9706			−1.60850			−0.804248	−	0.594294i	$-0.797431\pi$
$241$	−24.9706			−1.60850			−0.804248	+	0.594294i	$0.797431\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	16.4853	+	16.4853i	1.04893	+	1.04893i
$248$		0			0
$249$			4.34315i			0.275236i
$250$		0			0
$251$		−	11.7574i		−	0.742118i	−0.928609	−	0.371059i	$-0.878995\pi$
$251$		−	11.7574i		−	0.742118i	0.928609	−	0.371059i	$-0.121005\pi$
$252$		0			0
$253$	22.9706	+	22.9706i	1.44415	+	1.44415i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.41421	+	7.41421i	−0.462486	+	0.462486i	−0.899469	−	0.436984i	$-0.856047\pi$
$257$	−7.41421	+	7.41421i	−0.462486	+	0.462486i	0.436984	+	0.899469i	$0.356047\pi$
$258$		0			0
$259$	1.17157			0.0727980
$260$		0			0
$261$	−0.242641			−0.0150191
$262$		0			0
$263$	11.5563	−	11.5563i	0.712595	−	0.712595i	−0.254482	−	0.967077i	$-0.581905\pi$
$263$	11.5563	−	11.5563i	0.712595	−	0.712595i	0.967077	+	0.254482i	$0.0819051\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.58579	−	2.58579i	−0.158248	−	0.158248i
$268$		0			0
$269$			13.8995i			0.847467i	0.905787	+	0.423734i	$0.139281\pi$
$269$			13.8995i			0.847467i	−0.905787	+	0.423734i	$0.860719\pi$
$270$		0			0
$271$		−	16.3431i		−	0.992775i	−0.868101	−	0.496388i	$-0.834659\pi$
$271$		−	16.3431i		−	0.992775i	0.868101	−	0.496388i	$-0.165341\pi$
$272$		0			0
$273$	−4.82843	−	4.82843i	−0.292230	−	0.292230i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	11.8995	−	11.8995i	0.714971	−	0.714971i	−0.252600	−	0.967571i	$-0.581286\pi$
$277$	11.8995	−	11.8995i	0.714971	−	0.714971i	0.967571	+	0.252600i	$0.0812855\pi$
$278$		0			0
$279$	1.65685			0.0991933
$280$		0			0
$281$	12.8284			0.765280			0.382640	−	0.923898i	$-0.375015\pi$
$281$	12.8284			0.765280			0.382640	+	0.923898i	$0.375015\pi$
$282$		0			0
$283$	0.828427	−	0.828427i	0.0492449	−	0.0492449i	−0.682056	−	0.731300i	$-0.738914\pi$
$283$	0.828427	−	0.828427i	0.0492449	−	0.0492449i	0.731300	+	0.682056i	$0.238914\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.48528	−	6.48528i	−0.382814	−	0.382814i
$288$		0			0
$289$		−	41.6274i		−	2.44867i
$290$		0			0
$291$			0.928932i			0.0544550i
$292$		0			0
$293$	−4.00000	−	4.00000i	−0.233682	−	0.233682i	0.580545	−	0.814228i	$-0.302839\pi$
$293$	−4.00000	−	4.00000i	−0.233682	−	0.233682i	−0.814228	+	0.580545i	$0.802839\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.82843	+	3.82843i	−0.222148	+	0.222148i
$298$		0			0
$299$	28.9706			1.67541
$300$		0			0
$301$	−9.65685			−0.556612
$302$		0			0
$303$	−3.82843	+	3.82843i	−0.219937	+	0.219937i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−10.9706	−	10.9706i	−0.626123	−	0.626123i	0.320967	−	0.947090i	$-0.395992\pi$
$307$	−10.9706	−	10.9706i	−0.626123	−	0.626123i	−0.947090	+	0.320967i	$0.895992\pi$
$308$		0			0
$309$		−	16.7279i		−	0.951618i
$310$		0			0
$311$			8.00000i			0.453638i	0.973937	+	0.226819i	$0.0728326\pi$
$311$			8.00000i			0.453638i	−0.973937	+	0.226819i	$0.927167\pi$
$312$		0			0
$313$	−7.82843	−	7.82843i	−0.442489	−	0.442489i	0.450359	−	0.892848i	$-0.351296\pi$
$313$	−7.82843	−	7.82843i	−0.442489	−	0.442489i	−0.892848	+	0.450359i	$0.851296\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.75736	+	3.75736i	−0.211034	+	0.211034i	−0.804707	−	0.593672i	$-0.797677\pi$
$317$	−3.75736	+	3.75736i	−0.211034	+	0.211034i	0.593672	+	0.804707i	$0.297677\pi$
$318$		0			0
$319$	−1.31371			−0.0735536
$320$		0			0
$321$	−9.31371			−0.519841
$322$		0			0
$323$	26.1421	−	26.1421i	1.45459	−	1.45459i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−14.2426	−	14.2426i	−0.787620	−	0.787620i
$328$		0			0
$329$			12.4853i			0.688336i
$330$		0			0
$331$		−	2.48528i		−	0.136603i	−0.997665	−	0.0683017i	$-0.978242\pi$
$331$		−	2.48528i		−	0.136603i	0.997665	−	0.0683017i	$-0.0217580\pi$
$332$		0			0
$333$	−0.585786	−	0.585786i	−0.0321009	−	0.0321009i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	11.4853	−	11.4853i	0.625643	−	0.625643i	−0.321326	−	0.946969i	$-0.604128\pi$
$337$	11.4853	−	11.4853i	0.625643	−	0.625643i	0.946969	+	0.321326i	$0.104128\pi$
$338$		0			0
$339$	−7.17157			−0.389506
$340$		0			0
$341$	8.97056			0.485783
$342$		0			0
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.82843	+	6.82843i	0.366569	+	0.366569i	0.866224	−	0.499655i	$-0.166540\pi$
$347$	6.82843	+	6.82843i	0.366569	+	0.366569i	−0.499655	+	0.866224i	$0.666540\pi$
$348$		0			0
$349$		−	2.48528i		−	0.133034i	−0.997785	−	0.0665170i	$-0.978811\pi$
$349$		−	2.48528i		−	0.133034i	0.997785	−	0.0665170i	$-0.0211887\pi$
$350$		0			0
$351$			4.82843i			0.257722i
$352$		0			0
$353$	−7.07107	−	7.07107i	−0.376355	−	0.376355i	0.493430	−	0.869785i	$-0.335743\pi$
$353$	−7.07107	−	7.07107i	−0.376355	−	0.376355i	−0.869785	+	0.493430i	$0.835743\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.65685	+	7.65685i	−0.405244	+	0.405244i
$358$		0			0
$359$	3.79899			0.200503			0.100252	−	0.994962i	$-0.468035\pi$
$359$	3.79899			0.200503			0.100252	+	0.994962i	$0.468035\pi$
$360$		0			0
$361$	4.31371			0.227037
$362$		0			0
$363$	−12.9497	+	12.9497i	−0.679685	+	0.679685i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.82843	−	9.82843i	−0.513040	−	0.513040i	0.402417	−	0.915457i	$-0.368170\pi$
$367$	−9.82843	−	9.82843i	−0.513040	−	0.513040i	−0.915457	+	0.402417i	$0.868170\pi$
$368$		0			0
$369$			6.48528i			0.337610i
$370$		0			0
$371$			5.65685i			0.293689i
$372$		0			0
$373$	−2.58579	−	2.58579i	−0.133887	−	0.133887i	0.636987	−	0.770874i	$-0.280180\pi$
$373$	−2.58579	−	2.58579i	−0.133887	−	0.133887i	−0.770874	+	0.636987i	$0.780180\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.828427	+	0.828427i	−0.0426662	+	0.0426662i
$378$		0			0
$379$	22.2843			1.14467			0.572333	−	0.820021i	$-0.306038\pi$
$379$	22.2843			1.14467			0.572333	+	0.820021i	$0.306038\pi$
$380$		0			0
$381$	−10.5858			−0.542326
$382$		0			0
$383$	3.89949	−	3.89949i	0.199255	−	0.199255i	−0.600426	−	0.799681i	$-0.705002\pi$
$383$	3.89949	−	3.89949i	0.199255	−	0.199255i	0.799681	+	0.600426i	$0.205002\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.82843	+	4.82843i	0.245443	+	0.245443i
$388$		0			0
$389$			19.7574i			1.00174i	0.865523	+	0.500869i	$0.166986\pi$
$389$			19.7574i			1.00174i	−0.865523	+	0.500869i	$0.833014\pi$
$390$		0			0
$391$		−	45.9411i		−	2.32334i
$392$		0			0
$393$	15.4853	+	15.4853i	0.781129	+	0.781129i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	6.10051	−	6.10051i	0.306176	−	0.306176i	−0.537248	−	0.843424i	$-0.680536\pi$
$397$	6.10051	−	6.10051i	0.306176	−	0.306176i	0.843424	+	0.537248i	$0.180536\pi$
$398$		0			0
$399$	−6.82843			−0.341849
$400$		0			0
$401$	−0.343146			−0.0171359			−0.00856794	−	0.999963i	$-0.502727\pi$
$401$	−0.343146			−0.0171359			−0.00856794	+	0.999963i	$0.502727\pi$
$402$		0			0
$403$	5.65685	−	5.65685i	0.281788	−	0.281788i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.17157	−	3.17157i	−0.157209	−	0.157209i
$408$		0			0
$409$			29.9411i			1.48049i	0.672335	+	0.740247i	$0.265291\pi$
$409$			29.9411i			1.48049i	−0.672335	+	0.740247i	$0.734709\pi$
$410$		0			0
$411$		−	2.48528i		−	0.122590i
$412$		0			0
$413$	1.41421	+	1.41421i	0.0695889	+	0.0695889i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.89949	−	5.89949i	0.288900	−	0.288900i
$418$		0			0
$419$	19.7574			0.965210			0.482605	−	0.875838i	$-0.339691\pi$
$419$	19.7574			0.965210			0.482605	+	0.875838i	$0.339691\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$		0			0
$423$	6.24264	−	6.24264i	0.303528	−	0.303528i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.17157	−	3.17157i	−0.153483	−	0.153483i
$428$		0			0
$429$			26.1421i			1.26215i
$430$		0			0
$431$			26.1421i			1.25922i	0.776910	+	0.629611i	$0.216786\pi$
$431$			26.1421i			1.25922i	−0.776910	+	0.629611i	$0.783214\pi$
$432$		0			0
$433$	14.7990	+	14.7990i	0.711194	+	0.711194i	0.966785	−	0.255591i	$-0.0822700\pi$
$433$	14.7990	+	14.7990i	0.711194	+	0.711194i	−0.255591	+	0.966785i	$0.582270\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	20.4853	−	20.4853i	0.979944	−	0.979944i
$438$		0			0
$439$	25.3137			1.20816			0.604079	−	0.796925i	$-0.293541\pi$
$439$	25.3137			1.20816			0.604079	+	0.796925i	$0.293541\pi$
$440$		0			0
$441$	−5.00000			−0.238095
$442$		0			0
$443$	24.0000	−	24.0000i	1.14027	−	1.14027i	0.151875	−	0.988400i	$-0.451469\pi$
$443$	24.0000	−	24.0000i	1.14027	−	1.14027i	0.988400	−	0.151875i	$-0.0485310\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−14.6569	−	14.6569i	−0.693245	−	0.693245i
$448$		0			0
$449$			12.1421i			0.573023i	0.958077	+	0.286511i	$0.0924956\pi$
$449$			12.1421i			0.573023i	−0.958077	+	0.286511i	$0.907504\pi$
$450$		0			0
$451$			35.1127i			1.65339i
$452$		0			0
$453$	12.2426	+	12.2426i	0.575209	+	0.575209i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.31371	−	8.31371i	0.388899	−	0.388899i	−0.485396	−	0.874295i	$-0.661324\pi$
$457$	8.31371	−	8.31371i	0.388899	−	0.388899i	0.874295	+	0.485396i	$0.161324\pi$
$458$		0			0
$459$	7.65685			0.357391
$460$		0			0
$461$	−0.928932			−0.0432647			−0.0216323	−	0.999766i	$-0.506886\pi$
$461$	−0.928932			−0.0432647			−0.0216323	+	0.999766i	$0.506886\pi$
$462$		0			0
$463$	19.8284	−	19.8284i	0.921505	−	0.921505i	−0.0756307	−	0.997136i	$-0.524097\pi$
$463$	19.8284	−	19.8284i	0.921505	−	0.921505i	0.997136	+	0.0756307i	$0.0240970\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.41421	−	9.41421i	−0.435638	−	0.435638i	0.454903	−	0.890541i	$-0.349674\pi$
$467$	−9.41421	−	9.41421i	−0.435638	−	0.435638i	−0.890541	+	0.454903i	$0.849674\pi$
$468$		0			0
$469$			7.31371i			0.337716i
$470$		0			0
$471$		−	2.00000i		−	0.0921551i
$472$		0			0
$473$	26.1421	+	26.1421i	1.20202	+	1.20202i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.82843	−	2.82843i	0.129505	−	0.129505i
$478$		0			0
$479$	−38.6274			−1.76493			−0.882466	−	0.470376i	$-0.844118\pi$
$479$	−38.6274			−1.76493			−0.882466	+	0.470376i	$0.844118\pi$
$480$		0			0
$481$	−4.00000			−0.182384
$482$		0			0
$483$	−6.00000	+	6.00000i	−0.273009	+	0.273009i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−9.82843	−	9.82843i	−0.445369	−	0.445369i	0.448443	−	0.893811i	$-0.351979\pi$
$487$	−9.82843	−	9.82843i	−0.445369	−	0.445369i	−0.893811	+	0.448443i	$0.851979\pi$
$488$		0			0
$489$			6.34315i			0.286847i
$490$		0			0
$491$		−	5.21320i		−	0.235269i	−0.993057	−	0.117634i	$-0.962469\pi$
$491$		−	5.21320i		−	0.235269i	0.993057	−	0.117634i	$-0.0375311\pi$
$492$		0			0
$493$	1.31371	+	1.31371i	0.0591665	+	0.0591665i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.34315	+	2.34315i	−0.105104	+	0.105104i
$498$		0			0
$499$	−25.7990			−1.15492			−0.577461	−	0.816418i	$-0.695956\pi$
$499$	−25.7990			−1.15492			−0.577461	+	0.816418i	$0.695956\pi$
$500$		0			0
$501$	6.00000			0.268060
$502$		0			0
$503$	−30.2426	+	30.2426i	−1.34845	+	1.34845i	−0.461109	+	0.887343i	$0.652548\pi$
$503$	−30.2426	+	30.2426i	−1.34845	+	1.34845i	−0.887343	+	0.461109i	$0.847452\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.29289	+	7.29289i	0.323889	+	0.323889i
$508$		0			0
$509$			22.3848i			0.992188i	0.868269	+	0.496094i	$0.165233\pi$
$509$			22.3848i			0.992188i	−0.868269	+	0.496094i	$0.834767\pi$
$510$		0			0
$511$		−	14.9706i		−	0.662259i
$512$		0			0
$513$	3.41421	+	3.41421i	0.150741	+	0.150741i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	33.7990	−	33.7990i	1.48648	−	1.48648i
$518$		0			0
$519$	3.65685			0.160518
$520$		0			0
$521$	−4.82843			−0.211537			−0.105769	−	0.994391i	$-0.533730\pi$
$521$	−4.82843			−0.211537			−0.105769	+	0.994391i	$0.533730\pi$
$522$		0			0
$523$	14.9706	−	14.9706i	0.654617	−	0.654617i	−0.299484	−	0.954101i	$-0.596815\pi$
$523$	14.9706	−	14.9706i	0.654617	−	0.654617i	0.954101	+	0.299484i	$0.0968146\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.97056	−	8.97056i	−0.390764	−	0.390764i
$528$		0			0
$529$		−	13.0000i		−	0.565217i
$530$		0			0
$531$		−	1.41421i		−	0.0613716i
$532$		0			0
$533$	22.1421	+	22.1421i	0.959082	+	0.959082i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.8284	+	11.8284i	−0.510434	+	0.510434i
$538$		0			0
$539$	−27.0711			−1.16603
$540$		0			0
$541$	4.14214			0.178084			0.0890422	−	0.996028i	$-0.471619\pi$
$541$	4.14214			0.178084			0.0890422	+	0.996028i	$0.471619\pi$
$542$		0			0
$543$	14.2426	−	14.2426i	0.611210	−	0.611210i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−14.9706	−	14.9706i	−0.640095	−	0.640095i	0.310484	−	0.950579i	$-0.399509\pi$
$547$	−14.9706	−	14.9706i	−0.640095	−	0.640095i	−0.950579	+	0.310484i	$0.899509\pi$
$548$		0			0
$549$			3.17157i			0.135359i
$550$		0			0
$551$			1.17157i			0.0499107i
$552$		0			0
$553$	2.34315	+	2.34315i	0.0996407	+	0.0996407i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.8284	−	14.8284i	0.628301	−	0.628301i	−0.319340	−	0.947640i	$-0.603461\pi$
$557$	14.8284	−	14.8284i	0.628301	−	0.628301i	0.947640	+	0.319340i	$0.103461\pi$
$558$		0			0
$559$	32.9706			1.39451
$560$		0			0
$561$	41.4558			1.75027
$562$		0			0
$563$	−2.82843	+	2.82843i	−0.119204	+	0.119204i	−0.764192	−	0.644988i	$-0.776862\pi$
$563$	−2.82843	+	2.82843i	−0.119204	+	0.119204i	0.644988	+	0.764192i	$0.276862\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.00000	−	1.00000i	−0.0419961	−	0.0419961i
$568$		0			0
$569$		−	29.3137i		−	1.22889i	−0.788958	−	0.614447i	$-0.789379\pi$
$569$		−	29.3137i		−	1.22889i	0.788958	−	0.614447i	$-0.210621\pi$
$570$		0			0
$571$		−	3.17157i		−	0.132726i	−0.997796	−	0.0663631i	$-0.978860\pi$
$571$		−	3.17157i		−	0.132726i	0.997796	−	0.0663631i	$-0.0211396\pi$
$572$		0			0
$573$	−0.828427	−	0.828427i	−0.0346080	−	0.0346080i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−29.2843	+	29.2843i	−1.21912	+	1.21912i	−0.251180	+	0.967940i	$0.580819\pi$
$577$	−29.2843	+	29.2843i	−1.21912	+	1.21912i	−0.967940	+	0.251180i	$0.919181\pi$
$578$		0			0
$579$	−13.8995			−0.577643
$580$		0			0
$581$	−6.14214			−0.254819
$582$		0			0
$583$	15.3137	−	15.3137i	0.634229	−	0.634229i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−29.4142	−	29.4142i	−1.21405	−	1.21405i	−0.969681	−	0.244373i	$-0.921418\pi$
$587$	−29.4142	−	29.4142i	−1.21405	−	1.21405i	−0.244373	−	0.969681i	$-0.578582\pi$
$588$		0			0
$589$		−	8.00000i		−	0.329634i
$590$		0			0
$591$			20.9706i			0.862614i
$592$		0			0
$593$	6.72792	+	6.72792i	0.276283	+	0.276283i	0.831623	−	0.555340i	$-0.187412\pi$
$593$	6.72792	+	6.72792i	0.276283	+	0.276283i	−0.555340	+	0.831623i	$0.687412\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.0711	−	15.0711i	0.616818	−	0.616818i
$598$		0			0
$599$	32.7696			1.33893			0.669464	−	0.742845i	$-0.266524\pi$
$599$	32.7696			1.33893			0.669464	+	0.742845i	$0.266524\pi$
$600$		0			0
$601$	19.6569			0.801820			0.400910	−	0.916117i	$-0.368694\pi$
$601$	19.6569			0.801820			0.400910	+	0.916117i	$0.368694\pi$
$602$		0			0
$603$	3.65685	−	3.65685i	0.148919	−	0.148919i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	20.3137	+	20.3137i	0.824508	+	0.824508i	0.986751	−	0.162243i	$-0.0518728\pi$
$607$	20.3137	+	20.3137i	0.824508	+	0.824508i	−0.162243	+	0.986751i	$0.551873\pi$
$608$		0			0
$609$		−	0.343146i		−	0.0139050i
$610$		0			0
$611$		−	42.6274i		−	1.72452i
$612$		0			0
$613$	−28.7279	−	28.7279i	−1.16031	−	1.16031i	−0.984408	−	0.175902i	$-0.943716\pi$
$613$	−28.7279	−	28.7279i	−1.16031	−	1.16031i	−0.175902	−	0.984408i	$-0.556284\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.75736	+	3.75736i	−0.151266	+	0.151266i	−0.778683	−	0.627417i	$-0.784112\pi$
$617$	−3.75736	+	3.75736i	−0.151266	+	0.151266i	0.627417	+	0.778683i	$0.284112\pi$
$618$		0			0
$619$	46.2843			1.86032			0.930161	−	0.367152i	$-0.119667\pi$
$619$	46.2843			1.86032			0.930161	+	0.367152i	$0.119667\pi$
$620$		0			0
$621$	6.00000			0.240772
$622$		0			0
$623$	3.65685	−	3.65685i	0.146509	−	0.146509i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	18.4853	+	18.4853i	0.738231	+	0.738231i
$628$		0			0
$629$			6.34315i			0.252918i
$630$		0			0
$631$		−	24.0000i		−	0.955425i	−0.878516	−	0.477712i	$-0.841466\pi$
$631$		−	24.0000i		−	0.955425i	0.878516	−	0.477712i	$-0.158534\pi$
$632$		0			0
$633$	−12.2426	−	12.2426i	−0.486601	−	0.486601i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−17.0711	+	17.0711i	−0.676380	+	0.676380i
$638$		0			0
$639$	2.34315			0.0926934
$640$		0			0
$641$	−0.343146			−0.0135534			−0.00677672	−	0.999977i	$-0.502157\pi$
$641$	−0.343146			−0.0135534			−0.00677672	+	0.999977i	$0.502157\pi$
$642$		0			0
$643$	−14.3431	+	14.3431i	−0.565638	+	0.565638i	−0.930904	−	0.365265i	$-0.880978\pi$
$643$	−14.3431	+	14.3431i	−0.565638	+	0.565638i	0.365265	+	0.930904i	$0.380978\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	20.5858	+	20.5858i	0.809311	+	0.809311i	0.984530	−	0.175219i	$-0.0560633\pi$
$647$	20.5858	+	20.5858i	0.809311	+	0.809311i	−0.175219	+	0.984530i	$0.556063\pi$
$648$		0			0
$649$		−	7.65685i		−	0.300558i
$650$		0			0
$651$			2.34315i			0.0918351i
$652$		0			0
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	0.785231	−	0.619203i	$-0.212544\pi$
$653$	4.24264	+	4.24264i	0.166027	+	0.166027i	−0.619203	+	0.785231i	$0.712544\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−7.48528	+	7.48528i	−0.292029	+	0.292029i
$658$		0			0
$659$	10.3848			0.404533			0.202267	−	0.979330i	$-0.435169\pi$
$659$	10.3848			0.404533			0.202267	+	0.979330i	$0.435169\pi$
$660$		0			0
$661$	20.8284			0.810132			0.405066	−	0.914287i	$-0.367249\pi$
$661$	20.8284			0.810132			0.405066	+	0.914287i	$0.367249\pi$
$662$		0			0
$663$	26.1421	−	26.1421i	1.01528	−	1.01528i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.02944	+	1.02944i	0.0398600	+	0.0398600i
$668$		0			0
$669$			17.8995i			0.692034i
$670$		0			0
$671$			17.1716i			0.662901i
$672$		0			0
$673$	7.82843	+	7.82843i	0.301764	+	0.301764i	0.841704	−	0.539940i	$-0.181553\pi$
$673$	7.82843	+	7.82843i	0.301764	+	0.301764i	−0.539940	+	0.841704i	$0.681553\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.2426	+	28.2426i	−1.08545	+	1.08545i	−0.0894627	+	0.995990i	$0.528515\pi$
$677$	−28.2426	+	28.2426i	−1.08545	+	1.08545i	−0.995990	+	0.0894627i	$0.971485\pi$
$678$		0			0
$679$	−1.31371			−0.0504155
$680$		0			0
$681$	−13.6569			−0.523332
$682$		0			0
$683$	12.2426	−	12.2426i	0.468452	−	0.468452i	−0.432961	−	0.901413i	$-0.642531\pi$
$683$	12.2426	−	12.2426i	0.468452	−	0.468452i	0.901413	+	0.432961i	$0.142531\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.72792	−	8.72792i	−0.332991	−	0.332991i
$688$		0			0
$689$		−	19.3137i		−	0.735794i
$690$		0			0
$691$		−	7.85786i		−	0.298927i	−0.988767	−	0.149464i	$-0.952245\pi$
$691$		−	7.85786i		−	0.298927i	0.988767	−	0.149464i	$-0.0477547\pi$
$692$		0			0
$693$	−5.41421	−	5.41421i	−0.205669	−	0.205669i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	35.1127	−	35.1127i	1.32999	−	1.32999i
$698$		0			0
$699$	−10.0000			−0.378235
$700$		0			0
$701$	−31.3553			−1.18427			−0.592137	−	0.805837i	$-0.701716\pi$
$701$	−31.3553			−1.18427			−0.592137	+	0.805837i	$0.701716\pi$
$702$		0			0
$703$	−2.82843	+	2.82843i	−0.106676	+	0.106676i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.41421	−	5.41421i	−0.203622	−	0.203622i
$708$		0			0
$709$			14.2843i			0.536457i	0.963355	+	0.268229i	$0.0864382\pi$
$709$			14.2843i			0.536457i	−0.963355	+	0.268229i	$0.913562\pi$
$710$		0			0
$711$		−	2.34315i		−	0.0878748i
$712$		0			0
$713$	−7.02944	−	7.02944i	−0.263254	−	0.263254i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−16.4853	+	16.4853i	−0.615654	+	0.615654i
$718$		0			0
$719$	16.2843			0.607301			0.303650	−	0.952784i	$-0.401795\pi$
$719$	16.2843			0.607301			0.303650	+	0.952784i	$0.401795\pi$
$720$		0			0
$721$	23.6569			0.881027
$722$		0			0
$723$	−17.6569	+	17.6569i	−0.656665	+	0.656665i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	15.1421	+	15.1421i	0.561591	+	0.561591i	0.929759	−	0.368168i	$-0.120015\pi$
$727$	15.1421	+	15.1421i	0.561591	+	0.561591i	−0.368168	+	0.929759i	$0.620015\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	52.2843i		−	1.93380i
$732$		0			0
$733$	9.75736	+	9.75736i	0.360396	+	0.360396i	0.863959	−	0.503563i	$-0.167978\pi$
$733$	9.75736	+	9.75736i	0.360396	+	0.360396i	−0.503563	+	0.863959i	$0.667978\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.7990	−	19.7990i	0.729305	−	0.729305i
$738$		0			0
$739$	1.51472			0.0557198			0.0278599	−	0.999612i	$-0.491131\pi$
$739$	1.51472			0.0557198			0.0278599	+	0.999612i	$0.491131\pi$
$740$		0			0
$741$	23.3137			0.856450
$742$		0			0
$743$	−27.4142	+	27.4142i	−1.00573	+	1.00573i	−0.00574646	+	0.999983i	$0.501829\pi$
$743$	−27.4142	+	27.4142i	−1.00573	+	1.00573i	−0.999983	+	0.00574646i	$0.998171\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.07107	+	3.07107i	0.112364	+	0.112364i
$748$		0			0
$749$		−	13.1716i		−	0.481279i
$750$		0			0
$751$			33.6569i			1.22816i	0.789245	+	0.614078i	$0.210472\pi$
$751$			33.6569i			1.22816i	−0.789245	+	0.614078i	$0.789528\pi$
$752$		0			0
$753$	−8.31371	−	8.31371i	−0.302968	−	0.302968i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−33.5563	+	33.5563i	−1.21963	+	1.21963i	−0.251863	+	0.967763i	$0.581043\pi$
$757$	−33.5563	+	33.5563i	−1.21963	+	1.21963i	−0.967763	+	0.251863i	$0.918957\pi$
$758$		0			0
$759$	32.4853			1.17914
$760$		0			0
$761$	34.4853			1.25009			0.625045	−	0.780589i	$-0.285081\pi$
$761$	34.4853			1.25009			0.625045	+	0.780589i	$0.285081\pi$
$762$		0			0
$763$	20.1421	−	20.1421i	0.729194	−	0.729194i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.82843	−	4.82843i	−0.174344	−	0.174344i
$768$		0			0
$769$			39.6569i			1.43006i	0.699092	+	0.715031i	$0.253588\pi$
$769$			39.6569i			1.43006i	−0.699092	+	0.715031i	$0.746412\pi$
$770$		0			0
$771$			10.4853i			0.377618i
$772$		0			0
$773$	15.0711	+	15.0711i	0.542069	+	0.542069i	0.924135	−	0.382066i	$-0.124787\pi$
$773$	15.0711	+	15.0711i	0.542069	+	0.542069i	−0.382066	+	0.924135i	$0.624787\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.828427	−	0.828427i	0.0297197	−	0.0297197i
$778$		0			0
$779$	31.3137			1.12193
$780$		0			0
$781$	12.6863			0.453951
$782$		0			0
$783$	−0.171573	+	0.171573i	−0.00613151	+	0.00613151i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	20.8284	+	20.8284i	0.742453	+	0.742453i	0.973050	−	0.230596i	$-0.0740677\pi$
$787$	20.8284	+	20.8284i	0.742453	+	0.742453i	−0.230596	+	0.973050i	$0.574068\pi$
$788$		0			0
$789$		−	16.3431i		−	0.581831i
$790$		0			0
$791$		−	10.1421i		−	0.360613i
$792$		0			0
$793$	10.8284	+	10.8284i	0.384529	+	0.384529i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.75736	−	3.75736i	0.133092	−	0.133092i	−0.637422	−	0.770515i	$-0.719999\pi$
$797$	3.75736	−	3.75736i	0.133092	−	0.133092i	0.770515	+	0.637422i	$0.219999\pi$
$798$		0			0
$799$	−67.5980			−2.39144
$800$		0			0
$801$	−3.65685			−0.129209
$802$		0			0
$803$	−40.5269	+	40.5269i	−1.43016	+	1.43016i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.82843	+	9.82843i	0.345977	+	0.345977i
$808$		0			0
$809$		−	10.9706i		−	0.385704i	−0.981228	−	0.192852i	$-0.938226\pi$
$809$		−	10.9706i		−	0.385704i	0.981228	−	0.192852i	$-0.0617738\pi$
$810$		0			0
$811$			30.0000i			1.05344i	0.850038	+	0.526721i	$0.176579\pi$
$811$			30.0000i			1.05344i	−0.850038	+	0.526721i	$0.823421\pi$
$812$		0			0
$813$	−11.5563	−	11.5563i	−0.405299	−	0.405299i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	23.3137	−	23.3137i	0.815643	−	0.815643i
$818$		0			0
$819$	−6.82843			−0.238605
$820$		0			0
$821$	−25.2132			−0.879947			−0.439973	−	0.898011i	$-0.645012\pi$
$821$	−25.2132			−0.879947			−0.439973	+	0.898011i	$0.645012\pi$
$822$		0			0
$823$	−28.6569	+	28.6569i	−0.998915	+	0.998915i	−0.999999	−	0.00108427i	$-0.999655\pi$
$823$	−28.6569	+	28.6569i	−0.998915	+	0.998915i	0.00108427	+	0.999999i	$0.499655\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	37.4558	+	37.4558i	1.30247	+	1.30247i	0.926724	+	0.375744i	$0.122613\pi$
$827$	37.4558	+	37.4558i	1.30247	+	1.30247i	0.375744	+	0.926724i	$0.377387\pi$
$828$		0			0
$829$		−	25.7990i		−	0.896036i	−0.894025	−	0.448018i	$-0.852130\pi$
$829$		−	25.7990i		−	0.896036i	0.894025	−	0.448018i	$-0.147870\pi$
$830$		0			0
$831$		−	16.8284i		−	0.583772i
$832$		0			0
$833$	27.0711	+	27.0711i	0.937957	+	0.937957i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.17157	−	1.17157i	0.0404955	−	0.0404955i
$838$		0			0
$839$	−23.1127			−0.797939			−0.398969	−	0.916964i	$-0.630632\pi$
$839$	−23.1127			−0.797939			−0.398969	+	0.916964i	$0.630632\pi$
$840$		0			0
$841$	28.9411			0.997970
$842$		0			0
$843$	9.07107	−	9.07107i	0.312424	−	0.312424i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−18.3137	−	18.3137i	−0.629266	−	0.629266i
$848$		0			0
$849$		−	1.17157i		−	0.0402083i
$850$		0			0
$851$			4.97056i			0.170389i
$852$		0			0
$853$	−19.5563	−	19.5563i	−0.669597	−	0.669597i	0.288026	−	0.957623i	$-0.407001\pi$
$853$	−19.5563	−	19.5563i	−0.669597	−	0.669597i	−0.957623	+	0.288026i	$0.907001\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	31.0711	−	31.0711i	1.06137	−	1.06137i	0.0633779	−	0.997990i	$-0.479813\pi$
$857$	31.0711	−	31.0711i	1.06137	−	1.06137i	0.997990	−	0.0633779i	$-0.0201873\pi$
$858$		0			0
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$		0			0
$861$	−9.17157			−0.312566
$862$		0			0
$863$	1.61522	−	1.61522i	0.0549829	−	0.0549829i	−0.679081	−	0.734064i	$-0.737621\pi$
$863$	1.61522	−	1.61522i	0.0549829	−	0.0549829i	0.734064	+	0.679081i	$0.237621\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−29.4350	−	29.4350i	−0.999666	−	0.999666i
$868$		0			0
$869$		−	12.6863i		−	0.430353i
$870$		0			0
$871$		−	24.9706i		−	0.846095i
$872$		0			0
$873$	0.656854	+	0.656854i	0.0222311	+	0.0222311i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−4.92893	+	4.92893i	−0.166438	+	0.166438i	−0.785412	−	0.618974i	$-0.787549\pi$
$877$	−4.92893	+	4.92893i	−0.166438	+	0.166438i	0.618974	+	0.785412i	$0.287549\pi$
$878$		0			0
$879$	−5.65685			−0.190801
$880$		0			0
$881$	1.31371			0.0442600			0.0221300	−	0.999755i	$-0.492955\pi$
$881$	1.31371			0.0442600			0.0221300	+	0.999755i	$0.492955\pi$
$882$		0			0
$883$	−16.4853	+	16.4853i	−0.554774	+	0.554774i	−0.927815	−	0.373041i	$-0.878315\pi$
$883$	−16.4853	+	16.4853i	−0.554774	+	0.554774i	0.373041	+	0.927815i	$0.378315\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	32.7279	+	32.7279i	1.09890	+	1.09890i	0.994540	+	0.104356i	$0.0332782\pi$
$887$	32.7279	+	32.7279i	1.09890	+	1.09890i	0.104356	+	0.994540i	$0.466722\pi$
$888$		0			0
$889$		−	14.9706i		−	0.502097i
$890$		0			0
$891$			5.41421i			0.181383i
$892$		0			0
$893$	−30.1421	−	30.1421i	−1.00867	−	1.00867i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	20.4853	−	20.4853i	0.683984	−	0.683984i
$898$		0			0
$899$	0.402020			0.0134081
$900$		0			0
$901$	−30.6274			−1.02035
$902$		0			0
$903$	−6.82843	+	6.82843i	−0.227236	+	0.227236i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−23.5147	−	23.5147i	−0.780793	−	0.780793i	0.199171	−	0.979965i	$-0.436175\pi$
$907$	−23.5147	−	23.5147i	−0.780793	−	0.780793i	−0.979965	+	0.199171i	$0.936175\pi$
$908$		0			0
$909$			5.41421i			0.179578i
$910$		0			0
$911$			4.48528i			0.148604i	0.997236	+	0.0743020i	$0.0236729\pi$
$911$			4.48528i			0.148604i	−0.997236	+	0.0743020i	$0.976327\pi$
$912$		0			0
$913$	16.6274	+	16.6274i	0.550287	+	0.550287i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.8995	+	21.8995i	−0.723185	+	0.723185i
$918$		0			0
$919$	21.9411			0.723771			0.361885	−	0.932223i	$-0.382133\pi$
$919$	21.9411			0.723771			0.361885	+	0.932223i	$0.382133\pi$
$920$		0			0
$921$	−15.5147			−0.511227
$922$		0			0
$923$	8.00000	−	8.00000i	0.263323	−	0.263323i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−11.8284	−	11.8284i	−0.388497	−	0.388497i
$928$		0			0
$929$			10.2010i			0.334684i	0.985899	+	0.167342i	$0.0535185\pi$
$929$			10.2010i			0.334684i	−0.985899	+	0.167342i	$0.946482\pi$
$930$		0			0
$931$			24.1421i			0.791227i
$932$		0			0
$933$	5.65685	+	5.65685i	0.185197	+	0.185197i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.31371	+	4.31371i	−0.140923	+	0.140923i	−0.774049	−	0.633126i	$-0.781771\pi$
$937$	−4.31371	+	4.31371i	−0.140923	+	0.140923i	0.633126	+	0.774049i	$0.281771\pi$
$938$		0			0
$939$	−11.0711			−0.361291
$940$		0			0
$941$	24.9289			0.812660			0.406330	−	0.913726i	$-0.366808\pi$
$941$	24.9289			0.812660			0.406330	+	0.913726i	$0.366808\pi$
$942$		0			0
$943$	27.5147	−	27.5147i	0.896003	−	0.896003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.9706	−	16.9706i	−0.551469	−	0.551469i	0.375396	−	0.926865i	$-0.377507\pi$
$947$	−16.9706	−	16.9706i	−0.551469	−	0.551469i	−0.926865	+	0.375396i	$0.877507\pi$
$948$		0			0
$949$			51.1127i			1.65919i
$950$		0			0
$951$			5.31371i			0.172309i
$952$		0			0
$953$	−17.0711	−	17.0711i	−0.552986	−	0.552986i	0.374315	−	0.927301i	$-0.377878\pi$
$953$	−17.0711	−	17.0711i	−0.552986	−	0.552986i	−0.927301	+	0.374315i	$0.877878\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.928932	+	0.928932i	−0.0300281	+	0.0300281i
$958$		0			0
$959$	3.51472			0.113496
$960$		0			0
$961$	28.2548			0.911446
$962$		0			0
$963$	−6.58579	+	6.58579i	−0.212224	+	0.212224i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.34315	−	1.34315i	−0.0431927	−	0.0431927i	0.685181	−	0.728373i	$-0.259723\pi$
$967$	−1.34315	−	1.34315i	−0.0431927	−	0.0431927i	−0.728373	+	0.685181i	$0.759723\pi$
$968$		0			0
$969$		−	36.9706i		−	1.18767i
$970$		0			0
$971$			56.0416i			1.79846i	0.437475	+	0.899231i	$0.355873\pi$
$971$			56.0416i			1.79846i	−0.437475	+	0.899231i	$0.644127\pi$
$972$		0			0
$973$	8.34315	+	8.34315i	0.267469	+	0.267469i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.0416	+	20.0416i	−0.641189	+	0.641189i	−0.950848	−	0.309659i	$-0.899785\pi$
$977$	−20.0416	+	20.0416i	−0.641189	+	0.641189i	0.309659	+	0.950848i	$0.399785\pi$
$978$		0			0
$979$	−19.7990			−0.632778
$980$		0			0
$981$	−20.1421			−0.643089
$982$		0			0
$983$	31.8995	−	31.8995i	1.01744	−	1.01744i	0.0175906	−	0.999845i	$-0.494400\pi$
$983$	31.8995	−	31.8995i	1.01744	−	1.01744i	0.999845	−	0.0175906i	$-0.00559955\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	8.82843	+	8.82843i	0.281012	+	0.281012i
$988$		0			0
$989$		−	40.9706i		−	1.30279i
$990$		0			0
$991$			46.9706i			1.49207i	0.665907	+	0.746035i	$0.268045\pi$
$991$			46.9706i			1.49207i	−0.665907	+	0.746035i	$0.731955\pi$
$992$		0			0
$993$	−1.75736	−	1.75736i	−0.0557681	−	0.0557681i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.55635	+	5.55635i	−0.175971	+	0.175971i	−0.789597	−	0.613626i	$-0.789710\pi$
$997$	−5.55635	+	5.55635i	−0.175971	+	0.175971i	0.613626	+	0.789597i	$0.289710\pi$
$998$		0			0
$999$	−0.828427			−0.0262103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2400.2.w.d.2143.2		4
4.3	odd	2		2400.2.w.c.2143.1		4
5.2	odd	4		2400.2.w.c.607.1		4
5.3	odd	4		480.2.w.b.127.2	yes	4
5.4	even	2		480.2.w.a.223.1	yes	4
15.8	even	4		1440.2.x.n.127.2		4
15.14	odd	2		1440.2.x.m.703.2		4
20.3	even	4		480.2.w.a.127.1	✓	4
20.7	even	4	inner	2400.2.w.d.607.2		4
20.19	odd	2		480.2.w.b.223.2	yes	4
40.3	even	4		960.2.w.a.127.2		4
40.13	odd	4		960.2.w.b.127.1		4
40.19	odd	2		960.2.w.b.703.1		4
40.29	even	2		960.2.w.a.703.2		4
60.23	odd	4		1440.2.x.m.127.2		4
60.59	even	2		1440.2.x.n.703.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
480.2.w.a.127.1	✓	4	20.3	even	4
480.2.w.a.223.1	yes	4	5.4	even	2
480.2.w.b.127.2	yes	4	5.3	odd	4
480.2.w.b.223.2	yes	4	20.19	odd	2
960.2.w.a.127.2		4	40.3	even	4
960.2.w.a.703.2		4	40.29	even	2
960.2.w.b.127.1		4	40.13	odd	4
960.2.w.b.703.1		4	40.19	odd	2
1440.2.x.m.127.2		4	60.23	odd	4
1440.2.x.m.703.2		4	15.14	odd	2
1440.2.x.n.127.2		4	15.8	even	4
1440.2.x.n.703.2		4	60.59	even	2
2400.2.w.c.607.1		4	5.2	odd	4
2400.2.w.c.2143.1		4	4.3	odd	2
2400.2.w.d.607.2		4	20.7	even	4	inner
2400.2.w.d.2143.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.00000 + 1.00000i) q^{7} -1.00000i q^{9} -5.41421i q^{11} +(-3.41421 - 3.41421i) q^{13} +(-5.41421 + 5.41421i) q^{17} -4.82843 q^{19} +1.41421 q^{21} +(-4.24264 + 4.24264i) q^{23} +(-0.707107 - 0.707107i) q^{27} -0.242641i q^{29} +1.65685i q^{31} +(-3.82843 - 3.82843i) q^{33} +(0.585786 - 0.585786i) q^{37} -4.82843 q^{39} -6.48528 q^{41} +(-4.82843 + 4.82843i) q^{43} +(6.24264 + 6.24264i) q^{47} -5.00000i q^{49} +7.65685i q^{51} +(2.82843 + 2.82843i) q^{53} +(-3.41421 + 3.41421i) q^{57} +1.41421 q^{59} -3.17157 q^{61} +(1.00000 - 1.00000i) q^{63} +(3.65685 + 3.65685i) q^{67} +6.00000i q^{69} +2.34315i q^{71} +(-7.48528 - 7.48528i) q^{73} +(5.41421 - 5.41421i) q^{77} +2.34315 q^{79} -1.00000 q^{81} +(-3.07107 + 3.07107i) q^{83} +(-0.171573 - 0.171573i) q^{87} -3.65685i q^{89} -6.82843i q^{91} +(1.17157 + 1.17157i) q^{93} +(-0.656854 + 0.656854i) q^{97} -5.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{7}+O(q^{10}) \) 4 * q + 4 * q^7	\( 4 q + 4 q^{7} - 8 q^{13} - 16 q^{17} - 8 q^{19} - 4 q^{33} + 8 q^{37} - 8 q^{39} + 8 q^{41} - 8 q^{43} + 8 q^{47} - 8 q^{57} - 24 q^{61} + 4 q^{63} - 8 q^{67} + 4 q^{73} + 16 q^{77} + 32 q^{79} - 4 q^{81} + 16 q^{83} - 12 q^{87} + 16 q^{93} + 20 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^7 - 8 * q^13 - 16 * q^17 - 8 * q^19 - 4 * q^33 + 8 * q^37 - 8 * q^39 + 8 * q^41 - 8 * q^43 + 8 * q^47 - 8 * q^57 - 24 * q^61 + 4 * q^63 - 8 * q^67 + 4 * q^73 + 16 * q^77 + 32 * q^79 - 4 * q^81 + 16 * q^83 - 12 * q^87 + 16 * q^93 + 20 * q^97 - 16 * q^99

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