LMFDB - Embedded newform 1728.3.q.f.1601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,3,Mod(449,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1728.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1728.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$47.0845896815$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1728.1601
Dual form			1728.3.q.f.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +O(q^{10})$	$q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +(-5.29796 - 3.05878i) q^{11} +(8.39898 + 14.5475i) q^{13} -25.1701i q^{17} -17.5959 q^{19} +(12.3990 - 7.15855i) q^{23} +(14.7980 - 25.6308i) q^{25} +(16.1969 + 9.35131i) q^{29} +(-23.3990 - 40.5282i) q^{31} +50.2295i q^{35} +49.5959 q^{37} +(34.5000 - 19.9186i) q^{41} +(22.0959 - 38.2713i) q^{43} +(28.8031 + 16.6295i) q^{47} +(1.39388 + 2.41427i) q^{49} +10.1708i q^{53} -45.2020 q^{55} +(14.2980 - 8.25493i) q^{59} +(10.6010 - 18.3615i) q^{61} +(107.490 + 62.0593i) q^{65} +(43.4898 + 75.3265i) q^{67} -30.2555i q^{71} -48.7878 q^{73} +(36.0153 - 20.7934i) q^{77} +(55.7929 - 96.6361i) q^{79} +(85.0857 + 49.1243i) q^{83} +(-92.9898 - 161.063i) q^{85} -75.5103i q^{89} -114.192 q^{91} +(-112.596 + 65.0073i) q^{95} +(70.2980 - 121.760i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{5} + 6 q^{7}+O(q^{10}) $ 4 * q + 6 * q^5 + 6 * q^7	$ 4 q + 6 q^{5} + 6 q^{7} + 18 q^{11} + 14 q^{13} + 8 q^{19} + 30 q^{23} + 20 q^{25} + 6 q^{29} - 74 q^{31} + 120 q^{37} + 138 q^{41} + 10 q^{43} + 174 q^{47} - 112 q^{49} - 220 q^{55} + 18 q^{59} + 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} + 438 q^{77} + 86 q^{79} + 66 q^{83} - 176 q^{85} - 300 q^{91} - 372 q^{95} + 242 q^{97}+O(q^{100}) $ 4 * q + 6 * q^5 + 6 * q^7 + 18 * q^11 + 14 * q^13 + 8 * q^19 + 30 * q^23 + 20 * q^25 + 6 * q^29 - 74 * q^31 + 120 * q^37 + 138 * q^41 + 10 * q^43 + 174 * q^47 - 112 * q^49 - 220 * q^55 + 18 * q^59 + 62 * q^61 + 234 * q^65 - 22 * q^67 + 40 * q^73 + 438 * q^77 + 86 * q^79 + 66 * q^83 - 176 * q^85 - 300 * q^91 - 372 * q^95 + 242 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	6.39898	−	3.69445i	1.27980	−	0.738891i	0.302985	−	0.952995i	$-0.402017\pi$
$5$	6.39898	−	3.69445i	1.27980	−	0.738891i	0.976811	+	0.214105i	$0.0686834\pi$
$6$		0			0
$7$	−3.39898	+	5.88721i	−0.485568	+	0.841029i	−0.999862	−	0.0165847i	$-0.994721\pi$
$7$	−3.39898	+	5.88721i	−0.485568	+	0.841029i	0.514294	+	0.857614i	$0.328054\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.29796	−	3.05878i	−0.481633	−	0.278071i	0.239464	−	0.970905i	$-0.423028\pi$
$11$	−5.29796	−	3.05878i	−0.481633	−	0.278071i	−0.721097	+	0.692835i	$0.756362\pi$
$12$		0			0
$13$	8.39898	+	14.5475i	0.646075	+	1.11904i	0.984052	+	0.177881i	$0.0569242\pi$
$13$	8.39898	+	14.5475i	0.646075	+	1.11904i	−0.337977	+	0.941154i	$0.609743\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	25.1701i		−	1.48059i	−0.672279	−	0.740297i	$-0.734685\pi$
$17$		−	25.1701i		−	1.48059i	0.672279	−	0.740297i	$-0.265315\pi$
$18$		0			0
$19$	−17.5959			−0.926101			−0.463050	−	0.886332i	$-0.653245\pi$
$19$	−17.5959			−0.926101			−0.463050	+	0.886332i	$0.653245\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	12.3990	−	7.15855i	0.539086	−	0.311241i	−0.205622	−	0.978631i	$-0.565922\pi$
$23$	12.3990	−	7.15855i	0.539086	−	0.311241i	0.744708	+	0.667390i	$0.232589\pi$
$24$		0			0
$25$	14.7980	−	25.6308i	0.591918	−	1.02523i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	16.1969	+	9.35131i	0.558515	+	0.322459i	0.752549	−	0.658536i	$-0.228824\pi$
$29$	16.1969	+	9.35131i	0.558515	+	0.322459i	−0.194034	+	0.980995i	$0.562157\pi$
$30$		0			0
$31$	−23.3990	−	40.5282i	−0.754806	−	1.30736i	−0.945471	−	0.325707i	$-0.894398\pi$
$31$	−23.3990	−	40.5282i	−0.754806	−	1.30736i	0.190665	−	0.981655i	$-0.438936\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			50.2295i			1.43513i
$36$		0			0
$37$	49.5959			1.34043			0.670215	−	0.742167i	$-0.266202\pi$
$37$	49.5959			1.34043			0.670215	+	0.742167i	$0.266202\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	34.5000	−	19.9186i	0.841463	−	0.485819i	−0.0162980	−	0.999867i	$-0.505188\pi$
$41$	34.5000	−	19.9186i	0.841463	−	0.485819i	0.857761	+	0.514048i	$0.171855\pi$
$42$		0			0
$43$	22.0959	−	38.2713i	0.513859	−	0.890029i	−0.486012	−	0.873952i	$-0.661549\pi$
$43$	22.0959	−	38.2713i	0.513859	−	0.890029i	0.999871	−	0.0160771i	$-0.00511772\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	28.8031	+	16.6295i	0.612831	+	0.353818i	0.774073	−	0.633097i	$-0.218216\pi$
$47$	28.8031	+	16.6295i	0.612831	+	0.353818i	−0.161242	+	0.986915i	$0.551550\pi$
$48$		0			0
$49$	1.39388	+	2.41427i	0.0284465	+	0.0492707i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.1708i			0.191902i	0.995386	+	0.0959509i	$0.0305892\pi$
$53$			10.1708i			0.191902i	−0.995386	+	0.0959509i	$0.969411\pi$
$54$		0			0
$55$	−45.2020			−0.821855
$56$		0			0
$57$		0			0
$58$		0			0
$59$	14.2980	−	8.25493i	0.242338	−	0.139914i	−0.373913	−	0.927464i	$-0.621984\pi$
$59$	14.2980	−	8.25493i	0.242338	−	0.139914i	0.616251	+	0.787550i	$0.288651\pi$
$60$		0			0
$61$	10.6010	−	18.3615i	0.173787	−	0.301008i	−0.765954	−	0.642896i	$-0.777733\pi$
$61$	10.6010	−	18.3615i	0.173787	−	0.301008i	0.939741	+	0.341887i	$0.111066\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	107.490	+	62.0593i	1.65369	+	0.954758i
$66$		0			0
$67$	43.4898	+	75.3265i	0.649101	+	1.12428i	0.983338	+	0.181787i	$0.0581883\pi$
$67$	43.4898	+	75.3265i	0.649101	+	1.12428i	−0.334236	+	0.942489i	$0.608478\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	30.2555i		−	0.426134i	−0.977038	−	0.213067i	$-0.931655\pi$
$71$		−	30.2555i		−	0.426134i	0.977038	−	0.213067i	$-0.0683453\pi$
$72$		0			0
$73$	−48.7878			−0.668325			−0.334163	−	0.942515i	$-0.608454\pi$
$73$	−48.7878			−0.668325			−0.334163	+	0.942515i	$0.608454\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	36.0153	−	20.7934i	0.467731	−	0.270045i
$78$		0			0
$79$	55.7929	−	96.6361i	0.706239	−	1.22324i	−0.260004	−	0.965608i	$-0.583724\pi$
$79$	55.7929	−	96.6361i	0.706239	−	1.22324i	0.966243	−	0.257634i	$-0.0829428\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	85.0857	+	49.1243i	1.02513	+	0.591859i	0.915585	−	0.402123i	$-0.131728\pi$
$83$	85.0857	+	49.1243i	1.02513	+	0.591859i	0.109544	+	0.993982i	$0.465061\pi$
$84$		0			0
$85$	−92.9898	−	161.063i	−1.09400	−	1.89486i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	75.5103i		−	0.848431i	−0.905561	−	0.424215i	$-0.860550\pi$
$89$		−	75.5103i		−	0.848431i	0.905561	−	0.424215i	$-0.139450\pi$
$90$		0			0
$91$	−114.192			−1.25486
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−112.596	+	65.0073i	−1.18522	+	0.684287i
$96$		0			0
$97$	70.2980	−	121.760i	0.724721	−	1.25525i	−0.234367	−	0.972148i	$-0.575302\pi$
$97$	70.2980	−	121.760i	0.724721	−	1.25525i	0.959089	−	0.283106i	$-0.0913648\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	28.1969	+	16.2795i	0.279178	+	0.161183i	0.633051	−	0.774110i	$-0.281802\pi$
$101$	28.1969	+	16.2795i	0.279178	+	0.161183i	−0.353873	+	0.935293i	$0.615136\pi$
$102$		0			0
$103$	67.7929	+	117.421i	0.658183	+	1.14001i	0.981086	+	0.193574i	$0.0620081\pi$
$103$	67.7929	+	117.421i	0.658183	+	1.14001i	−0.322903	+	0.946432i	$0.604659\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	35.3409i		−	0.330289i	−0.986269	−	0.165144i	$-0.947191\pi$
$107$		−	35.3409i		−	0.330289i	0.986269	−	0.165144i	$-0.0528090\pi$
$108$		0			0
$109$	−53.5959			−0.491706			−0.245853	−	0.969307i	$-0.579068\pi$
$109$	−53.5959			−0.491706			−0.245853	+	0.969307i	$0.579068\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−143.076	+	82.6047i	−1.26615	+	0.731015i	−0.974258	−	0.225435i	$-0.927620\pi$
$113$	−143.076	+	82.6047i	−1.26615	+	0.731015i	−0.291897	+	0.956450i	$0.594286\pi$
$114$		0			0
$115$	52.8939	−	91.6149i	0.459947	−	0.796651i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	148.182	+	85.5527i	1.24522	+	0.718930i
$120$		0			0
$121$	−41.7878	−	72.3785i	−0.345353	−	0.598170i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	33.9588i		−	0.271670i
$126$		0			0
$127$	−11.9796			−0.0943275			−0.0471637	−	0.998887i	$-0.515018\pi$
$127$	−11.9796			−0.0943275			−0.0471637	+	0.998887i	$0.515018\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.3082	−	7.68347i	0.101589	−	0.0586525i	−0.448345	−	0.893861i	$-0.647986\pi$
$131$	13.3082	−	7.68347i	0.101589	−	0.0586525i	0.549934	+	0.835208i	$0.314653\pi$
$132$		0			0
$133$	59.8082	−	103.591i	0.449685	−	0.778878i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	47.7122	+	27.5467i	0.348265	+	0.201071i	0.663921	−	0.747803i	$-0.268891\pi$
$137$	47.7122	+	27.5467i	0.348265	+	0.201071i	−0.315656	+	0.948874i	$0.602225\pi$
$138$		0			0
$139$	−50.4898	−	87.4509i	−0.363236	−	0.629143i	0.625255	−	0.780420i	$-0.284995\pi$
$139$	−50.4898	−	87.4509i	−0.363236	−	0.629143i	−0.988491	+	0.151277i	$0.951661\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	102.762i		−	0.718619i
$144$		0			0
$145$	138.192			0.953047
$146$		0			0
$147$		0			0
$148$		0			0
$149$	187.389	−	108.189i	1.25764	−	0.726100i	0.285027	−	0.958519i	$-0.407997\pi$
$149$	187.389	−	108.189i	1.25764	−	0.726100i	0.972616	+	0.232419i	$0.0746641\pi$
$150$		0			0
$151$	−76.7929	+	133.009i	−0.508562	+	0.880855i	0.491389	+	0.870940i	$0.336489\pi$
$151$	−76.7929	+	133.009i	−0.508562	+	0.880855i	−0.999951	+	0.00991488i	$0.996844\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−299.459	−	172.893i	−1.93199	−	1.11544i
$156$		0			0
$157$	40.9847	+	70.9876i	0.261049	+	0.452150i	0.966521	−	0.256588i	$-0.0825983\pi$
$157$	40.9847	+	70.9876i	0.261049	+	0.452150i	−0.705472	+	0.708738i	$0.749265\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			97.3271i			0.604516i
$162$		0			0
$163$	55.2122			0.338725			0.169363	−	0.985554i	$-0.445829\pi$
$163$	55.2122			0.338725			0.169363	+	0.985554i	$0.445829\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−133.803	+	77.2512i	−0.801216	+	0.462582i	−0.843896	−	0.536507i	$-0.819744\pi$
$167$	−133.803	+	77.2512i	−0.801216	+	0.462582i	0.0426802	+	0.999089i	$0.486410\pi$
$168$		0			0
$169$	−56.5857	+	98.0093i	−0.334827	+	0.579937i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	22.8031	+	13.1654i	0.131810	+	0.0761003i	0.564455	−	0.825464i	$-0.309086\pi$
$173$	22.8031	+	13.1654i	0.131810	+	0.0761003i	−0.432645	+	0.901564i	$0.642420\pi$
$174$		0			0
$175$	100.596	+	174.237i	0.574834	+	0.995641i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	266.700i		−	1.48995i	−0.667094	−	0.744973i	$-0.732462\pi$
$179$		−	266.700i		−	1.48995i	0.667094	−	0.744973i	$-0.267538\pi$
$180$		0			0
$181$	58.4041			0.322674			0.161337	−	0.986899i	$-0.448419\pi$
$181$	58.4041			0.322674			0.161337	+	0.986899i	$0.448419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	317.363	−	183.230i	1.71548	−	0.990431i
$186$		0			0
$187$	−76.9898	+	133.350i	−0.411710	+	0.713103i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−99.5602	−	57.4811i	−0.521258	−	0.300948i	0.216191	−	0.976351i	$-0.430636\pi$
$191$	−99.5602	−	57.4811i	−0.521258	−	0.300948i	−0.737449	+	0.675403i	$0.763970\pi$
$192$		0			0
$193$	−108.490	−	187.910i	−0.562123	−	0.973626i	−0.997311	−	0.0732863i	$-0.976651\pi$
$193$	−108.490	−	187.910i	−0.562123	−	0.973626i	0.435188	−	0.900340i	$-0.356682\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			171.105i			0.868555i	0.900779	+	0.434278i	$0.142996\pi$
$197$			171.105i			0.868555i	−0.900779	+	0.434278i	$0.857004\pi$
$198$		0			0
$199$	62.0000			0.311558			0.155779	−	0.987792i	$-0.450211\pi$
$199$	62.0000			0.311558			0.155779	+	0.987792i	$0.450211\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−110.106	+	63.5698i	−0.542395	+	0.313152i
$204$		0			0
$205$	147.177	−	254.917i	0.717934	−	1.24350i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	93.2225	+	53.8220i	0.446040	+	0.257522i
$210$		0			0
$211$	64.7020	+	112.067i	0.306645	+	0.531124i	0.977626	−	0.210350i	$-0.0674603\pi$
$211$	64.7020	+	112.067i	0.306645	+	0.531124i	−0.670981	+	0.741474i	$0.734127\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	326.529i		−	1.51874i
$216$		0			0
$217$	318.131			1.46604
$218$		0			0
$219$		0			0
$220$		0			0
$221$	366.161	−	211.403i	1.65684	−	0.956576i
$222$		0			0
$223$	49.1867	−	85.1939i	0.220568	−	0.382036i	−0.734412	−	0.678704i	$-0.762542\pi$
$223$	49.1867	−	85.1939i	0.220568	−	0.382036i	0.954981	+	0.296668i	$0.0958755\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	383.651	+	221.501i	1.69009	+	0.975775i	0.954434	+	0.298423i	$0.0964607\pi$
$227$	383.651	+	221.501i	1.69009	+	0.975775i	0.735659	+	0.677352i	$0.236873\pi$
$228$		0			0
$229$	−56.0051	−	97.0037i	−0.244564	−	0.423597i	0.717445	−	0.696615i	$-0.245311\pi$
$229$	−56.0051	−	97.0037i	−0.244564	−	0.423597i	−0.962009	+	0.273018i	$0.911978\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	80.8526i		−	0.347007i	−0.984833	−	0.173503i	$-0.944491\pi$
$233$		−	80.8526i		−	0.347007i	0.984833	−	0.173503i	$-0.0555088\pi$
$234$		0			0
$235$	245.747			1.04573
$236$		0			0
$237$		0			0
$238$		0			0
$239$	37.3888	−	21.5864i	0.156438	−	0.0903197i	−0.419737	−	0.907646i	$-0.637878\pi$
$239$	37.3888	−	21.5864i	0.156438	−	0.0903197i	0.576176	+	0.817326i	$0.304544\pi$
$240$		0			0
$241$	140.904	−	244.053i	0.584664	−	1.01267i	−0.410253	−	0.911972i	$-0.634560\pi$
$241$	140.904	−	244.053i	0.584664	−	1.01267i	0.994917	−	0.100696i	$-0.0321071\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	17.8388	+	10.2992i	0.0728113	+	0.0420376i
$246$		0			0
$247$	−147.788	−	255.976i	−0.598331	−	1.03634i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	15.5131i		−	0.0618050i	−0.999522	−	0.0309025i	$-0.990162\pi$
$251$		−	15.5131i		−	0.0618050i	0.999522	−	0.0309025i	$-0.00983814\pi$
$252$		0			0
$253$	−87.5857			−0.346189
$254$		0			0
$255$		0			0
$256$		0			0
$257$	312.035	−	180.153i	1.21414	−	0.700986i	0.250484	−	0.968121i	$-0.419410\pi$
$257$	312.035	−	180.153i	1.21414	−	0.700986i	0.963659	+	0.267135i	$0.0860770\pi$
$258$		0			0
$259$	−168.576	+	291.981i	−0.650871	+	1.12734i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−42.4296	−	24.4967i	−0.161329	−	0.0931435i	0.417162	−	0.908832i	$-0.363025\pi$
$263$	−42.4296	−	24.4967i	−0.161329	−	0.0931435i	−0.578491	+	0.815689i	$0.696358\pi$
$264$		0			0
$265$	37.5755	+	65.0827i	0.141794	+	0.245595i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	281.700i		−	1.04721i	−0.851961	−	0.523606i	$-0.824587\pi$
$269$		−	281.700i		−	1.04721i	0.851961	−	0.523606i	$-0.175413\pi$
$270$		0			0
$271$	89.5959			0.330612			0.165306	−	0.986242i	$-0.447139\pi$
$271$	89.5959			0.330612			0.165306	+	0.986242i	$0.447139\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−156.798	+	90.5273i	−0.570174	+	0.329190i
$276$		0			0
$277$	42.1969	−	73.0872i	0.152336	−	0.263853i	−0.779750	−	0.626091i	$-0.784654\pi$
$277$	42.1969	−	73.0872i	0.152336	−	0.263853i	0.932086	+	0.362238i	$0.117987\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	23.2673	+	13.4334i	0.0828019	+	0.0478057i	0.540829	−	0.841132i	$-0.318110\pi$
$281$	23.2673	+	13.4334i	0.0828019	+	0.0478057i	−0.458027	+	0.888938i	$0.651444\pi$
$282$		0			0
$283$	−90.4898	−	156.733i	−0.319752	−	0.553827i	0.660684	−	0.750664i	$-0.270266\pi$
$283$	−90.4898	−	156.733i	−0.319752	−	0.553827i	−0.980436	+	0.196837i	$0.936933\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			270.811i			0.943594i
$288$		0			0
$289$	−344.535			−1.19216
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−407.985	+	235.550i	−1.39244	+	0.803925i	−0.993585	−	0.113089i	$-0.963925\pi$
$293$	−407.985	+	235.550i	−1.39244	+	0.803925i	−0.398854	+	0.917014i	$0.630592\pi$
$294$		0			0
$295$	60.9949	−	105.646i	0.206762	−	0.358123i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	208.278	+	120.249i	0.696580	+	0.402171i
$300$		0			0
$301$	150.207	+	260.166i	0.499027	+	0.864340i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	156.660i		−	0.513639i
$306$		0			0
$307$	464.747			1.51383			0.756917	−	0.653511i	$-0.226705\pi$
$307$	464.747			1.51383			0.756917	+	0.653511i	$0.226705\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−218.348	+	126.063i	−0.702083	+	0.405348i	−0.808123	−	0.589014i	$-0.799516\pi$
$311$	−218.348	+	126.063i	−0.702083	+	0.405348i	0.106039	+	0.994362i	$0.466183\pi$
$312$		0			0
$313$	−98.1061	+	169.925i	−0.313438	+	0.542891i	−0.979104	−	0.203359i	$-0.934814\pi$
$313$	−98.1061	+	169.925i	−0.313438	+	0.542891i	0.665666	+	0.746250i	$0.268147\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	98.9847	+	57.1488i	0.312255	+	0.180280i	0.647935	−	0.761696i	$-0.275633\pi$
$317$	98.9847	+	57.1488i	0.312255	+	0.180280i	−0.335680	+	0.941976i	$0.608966\pi$
$318$		0			0
$319$	−57.2071	−	99.0857i	−0.179333	−	0.310613i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			442.891i			1.37118i
$324$		0			0
$325$	497.151			1.52970
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−195.802	+	113.046i	−0.595143	+	0.343606i
$330$		0			0
$331$	−27.2980	+	47.2815i	−0.0824712	+	0.142844i	−0.904311	−	0.426875i	$-0.859615\pi$
$331$	−27.2980	+	47.2815i	−0.0824712	+	0.142844i	0.821840	+	0.569719i	$0.192948\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	556.581	+	321.342i	1.66143	+	0.959230i
$336$		0			0
$337$	118.884	+	205.913i	0.352771	+	0.611016i	0.986734	−	0.162347i	$-0.0519063\pi$
$337$	118.884	+	205.913i	0.352771	+	0.611016i	−0.633963	+	0.773363i	$0.718573\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			286.289i			0.839558i
$342$		0			0
$343$	−352.051			−1.02639
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−108.349	+	62.5553i	−0.312245	+	0.180275i	−0.647931	−	0.761699i	$-0.724365\pi$
$347$	−108.349	+	62.5553i	−0.312245	+	0.180275i	0.335686	+	0.941974i	$0.391032\pi$
$348$		0			0
$349$	−269.985	+	467.627i	−0.773595	+	1.33991i	0.161986	+	0.986793i	$0.448210\pi$
$349$	−269.985	+	467.627i	−0.773595	+	1.33991i	−0.935581	+	0.353113i	$0.885123\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−254.490	−	146.930i	−0.720934	−	0.416232i	0.0941622	−	0.995557i	$-0.469983\pi$
$353$	−254.490	−	146.930i	−0.720934	−	0.416232i	−0.815096	+	0.579325i	$0.803316\pi$
$354$		0			0
$355$	−111.778	−	193.604i	−0.314866	−	0.545364i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	422.550i		−	1.17702i	−0.808490	−	0.588509i	$-0.799715\pi$
$359$		−	422.550i		−	1.17702i	0.808490	−	0.588509i	$-0.200285\pi$
$360$		0			0
$361$	−51.3837			−0.142337
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−312.192	+	180.244i	−0.855320	+	0.493819i
$366$		0			0
$367$	−131.358	+	227.519i	−0.357924	+	0.619943i	−0.987614	−	0.156904i	$-0.949849\pi$
$367$	−131.358	+	227.519i	−0.357924	+	0.619943i	0.629690	+	0.776847i	$0.283182\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−59.8775	−	34.5703i	−0.161395	−	0.0931814i
$372$		0			0
$373$	60.9847	+	105.629i	0.163498	+	0.283187i	0.936121	−	0.351679i	$-0.114389\pi$
$373$	60.9847	+	105.629i	0.163498	+	0.283187i	−0.772623	+	0.634865i	$0.781056\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			314.166i			0.833331i
$378$		0			0
$379$	−641.151			−1.69169			−0.845846	−	0.533428i	$-0.820904\pi$
$379$	−641.151			−1.69169			−0.845846	+	0.533428i	$0.820904\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	640.681	−	369.897i	1.67280	−	0.965789i	0.706733	−	0.707481i	$-0.250168\pi$
$383$	640.681	−	369.897i	1.67280	−	0.965789i	0.966063	−	0.258308i	$-0.0831650\pi$
$384$		0			0
$385$	153.641	−	266.114i	0.399067	−	0.691204i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	75.7520	+	43.7355i	0.194735	+	0.112430i	0.594197	−	0.804319i	$-0.297470\pi$
$389$	75.7520	+	43.7355i	0.194735	+	0.112430i	−0.399462	+	0.916750i	$0.630803\pi$
$390$		0			0
$391$	−180.182	−	312.084i	−0.460823	−	0.798168i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	824.496i		−	2.08733i
$396$		0			0
$397$	−483.090			−1.21685			−0.608425	−	0.793611i	$-0.708199\pi$
$397$	−483.090			−1.21685			−0.608425	+	0.793611i	$0.708199\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−317.682	+	183.414i	−0.792224	+	0.457390i	−0.840745	−	0.541432i	$-0.817882\pi$
$401$	−317.682	+	183.414i	−0.792224	+	0.457390i	0.0485212	+	0.998822i	$0.484549\pi$
$402$		0			0
$403$	393.055	−	680.791i	0.975323	−	1.68931i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−262.757	−	151.703i	−0.645595	−	0.372734i
$408$		0			0
$409$	−267.641	−	463.567i	−0.654379	−	1.13342i	−0.982049	−	0.188625i	$-0.939597\pi$
$409$	−267.641	−	463.567i	−0.654379	−	1.13342i	0.327671	−	0.944792i	$-0.393736\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			112.233i			0.271751i
$414$		0			0
$415$	725.949			1.74927
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−605.620	+	349.655i	−1.44539	+	0.834499i	−0.998202	−	0.0599386i	$-0.980910\pi$
$419$	−605.620	+	349.655i	−1.44539	+	0.834499i	−0.447193	+	0.894438i	$0.647576\pi$
$420$		0			0
$421$	−180.772	+	313.107i	−0.429388	+	0.743722i	−0.996819	−	0.0796989i	$-0.974604\pi$
$421$	−180.772	+	313.107i	−0.429388	+	0.743722i	0.567431	+	0.823421i	$0.307937\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−645.131	−	372.466i	−1.51795	−	0.876391i
$426$		0			0
$427$	72.0653	+	124.821i	0.168771	+	0.292320i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			463.747i			1.07598i	0.842952	+	0.537989i	$0.180816\pi$
$431$			463.747i			1.07598i	−0.842952	+	0.537989i	$0.819184\pi$
$432$		0			0
$433$	−689.514			−1.59241			−0.796206	−	0.605026i	$-0.793163\pi$
$433$	−689.514			−1.59241			−0.796206	+	0.605026i	$0.793163\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−218.171	+	125.961i	−0.499248	+	0.288241i
$438$		0			0
$439$	−310.772	+	538.274i	−0.707910	+	1.22614i	0.257721	+	0.966219i	$0.417028\pi$
$439$	−310.772	+	538.274i	−0.707910	+	1.22614i	−0.965631	+	0.259917i	$0.916305\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	698.843	+	403.477i	1.57752	+	0.910784i	0.995204	+	0.0978236i	$0.0311881\pi$
$443$	698.843	+	403.477i	1.57752	+	0.910784i	0.582320	+	0.812960i	$0.302145\pi$
$444$		0			0
$445$	−278.969	−	483.189i	−0.626897	−	1.08582i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			317.554i			0.707248i	0.935388	+	0.353624i	$0.115051\pi$
$449$			317.554i			0.707248i	−0.935388	+	0.353624i	$0.884949\pi$
$450$		0			0
$451$	−243.706			−0.540368
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−730.711	+	421.876i	−1.60596	+	0.927201i
$456$		0			0
$457$	−285.843	+	495.094i	−0.625477	+	1.08336i	0.362972	+	0.931800i	$0.381762\pi$
$457$	−285.843	+	495.094i	−0.625477	+	1.08336i	−0.988448	+	0.151557i	$0.951571\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−478.550	−	276.291i	−1.03807	−	0.599330i	−0.118784	−	0.992920i	$-0.537899\pi$
$461$	−478.550	−	276.291i	−1.03807	−	0.599330i	−0.919286	+	0.393591i	$0.871233\pi$
$462$		0			0
$463$	−60.1663	−	104.211i	−0.129949	−	0.225078i	0.793708	−	0.608299i	$-0.208148\pi$
$463$	−60.1663	−	104.211i	−0.129949	−	0.225078i	−0.923657	+	0.383221i	$0.874815\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	880.440i		−	1.88531i	−0.333767	−	0.942656i	$-0.608320\pi$
$467$		−	880.440i		−	1.88531i	0.333767	−	0.942656i	$-0.391680\pi$
$468$		0			0
$469$	−591.284			−1.26073
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−234.127	+	135.173i	−0.494982	+	0.285778i
$474$		0			0
$475$	−260.384	+	450.998i	−0.548176	+	0.949469i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	593.793	+	342.826i	1.23965	+	0.715713i	0.969023	−	0.246971i	$-0.0794353\pi$
$479$	593.793	+	342.826i	1.23965	+	0.715713i	0.270628	+	0.962684i	$0.412769\pi$
$480$		0			0
$481$	416.555	+	721.495i	0.866019	+	1.49999i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1038.85i		−	2.14196i
$486$		0			0
$487$	−391.131			−0.803143			−0.401571	−	0.915828i	$-0.631536\pi$
$487$	−391.131			−0.803143			−0.401571	+	0.915828i	$0.631536\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−166.469	+	96.1111i	−0.339042	+	0.195746i	−0.659848	−	0.751399i	$-0.729379\pi$
$491$	−166.469	+	96.1111i	−0.339042	+	0.195746i	0.320807	+	0.947145i	$0.396046\pi$
$492$		0			0
$493$	235.373	−	407.679i	0.477431	−	0.826935i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	178.120	+	102.838i	0.358391	+	0.206917i
$498$		0			0
$499$	−304.692	−	527.742i	−0.610605	−	1.05760i	−0.991139	−	0.132832i	$-0.957593\pi$
$499$	−304.692	−	527.742i	−0.610605	−	1.05760i	0.380534	−	0.924767i	$-0.375740\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	232.130i		−	0.461491i	−0.973014	−	0.230746i	$-0.925883\pi$
$503$		−	232.130i		−	0.461491i	0.973014	−	0.230746i	$-0.0741165\pi$
$504$		0			0
$505$	240.576			0.476387
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−223.136	+	128.827i	−0.438381	+	0.253099i	−0.702910	−	0.711278i	$-0.748117\pi$
$509$	−223.136	+	128.827i	−0.438381	+	0.253099i	0.264530	+	0.964377i	$0.414783\pi$
$510$		0			0
$511$	165.829	−	287.224i	0.324518	−	0.562081i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	867.610	+	500.915i	1.68468	+	0.972650i
$516$		0			0
$517$	−101.732	−	176.204i	−0.196773	−	0.340821i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			484.088i			0.929152i	0.885533	+	0.464576i	$0.153793\pi$
$521$			484.088i			0.929152i	−0.885533	+	0.464576i	$0.846207\pi$
$522$		0			0
$523$	−644.384			−1.23209			−0.616046	−	0.787711i	$-0.711266\pi$
$523$	−644.384			−1.23209			−0.616046	+	0.787711i	$0.711266\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1020.10	+	588.955i	−1.93567	+	1.11756i
$528$		0			0
$529$	−162.010	+	280.610i	−0.306257	+	0.530454i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	579.530	+	334.592i	1.08730	+	0.627752i
$534$		0			0
$535$	−130.565	−	226.146i	−0.244047	−	0.422702i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	17.0542i		−	0.0316405i
$540$		0			0
$541$	332.302			0.614237			0.307118	−	0.951671i	$-0.400635\pi$
$541$	332.302			0.614237			0.307118	+	0.951671i	$0.400635\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−342.959	+	198.008i	−0.629283	+	0.363317i
$546$		0			0
$547$	157.329	−	272.501i	0.287621	−	0.498174i	−0.685621	−	0.727959i	$-0.740469\pi$
$547$	157.329	−	272.501i	0.287621	−	0.498174i	0.973241	+	0.229785i	$0.0738024\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−285.000	−	164.545i	−0.517241	−	0.298629i
$552$		0			0
$553$	379.278	+	656.928i	0.685855	+	1.18793i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			664.080i			1.19224i	0.802894	+	0.596122i	$0.203293\pi$
$557$			664.080i			1.19224i	−0.802894	+	0.596122i	$0.796707\pi$
$558$		0			0
$559$	742.333			1.32797
$560$		0			0
$561$		0			0
$562$		0			0
$563$	211.024	−	121.835i	0.374821	−	0.216403i	−0.300741	−	0.953706i	$-0.597234\pi$
$563$	211.024	−	121.835i	0.374821	−	0.216403i	0.675563	+	0.737302i	$0.263901\pi$
$564$		0			0
$565$	−610.358	+	1057.17i	−1.08028	+	1.87110i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	502.155	+	289.919i	0.882522	+	0.509524i	0.871489	−	0.490415i	$-0.163155\pi$
$569$	502.155	+	289.919i	0.882522	+	0.509524i	0.0110330	+	0.999939i	$0.496488\pi$
$570$		0			0
$571$	356.843	+	618.070i	0.624944	+	1.08243i	0.988552	+	0.150882i	$0.0482114\pi$
$571$	356.843	+	618.070i	0.624944	+	1.08243i	−0.363608	+	0.931552i	$0.618455\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	423.728i		−	0.736918i
$576$		0			0
$577$	829.433			1.43749			0.718746	−	0.695273i	$-0.244717\pi$
$577$	829.433			1.43749			0.718746	+	0.695273i	$0.244717\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−578.409	+	333.945i	−0.995541	+	0.574776i
$582$		0			0
$583$	31.1102	−	53.8844i	0.0533623	−	0.0924261i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−777.480	−	448.878i	−1.32450	−	0.764699i	−0.340054	−	0.940406i	$-0.610445\pi$
$587$	−777.480	−	448.878i	−1.32450	−	0.764699i	−0.984442	+	0.175707i	$0.943779\pi$
$588$		0			0
$589$	411.727	+	713.131i	0.699026	+	1.21075i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	378.065i		−	0.637547i	−0.947831	−	0.318774i	$-0.896729\pi$
$593$		−	378.065i		−	0.637547i	0.947831	−	0.318774i	$-0.103271\pi$
$594$		0			0
$595$	1264.28			2.12484
$596$		0			0
$597$		0			0
$598$		0			0
$599$	822.438	−	474.835i	1.37302	−	0.792712i	0.381711	−	0.924282i	$-0.375335\pi$
$599$	822.438	−	474.835i	1.37302	−	0.792712i	0.991307	+	0.131569i	$0.0420016\pi$
$600$		0			0
$601$	−252.308	+	437.011i	−0.419814	+	0.727139i	−0.995920	−	0.0902356i	$-0.971238\pi$
$601$	−252.308	+	437.011i	−0.419814	+	0.727139i	0.576107	+	0.817375i	$0.304571\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−534.798	−	308.766i	−0.883964	−	0.510357i
$606$		0			0
$607$	429.954	+	744.702i	0.708326	+	1.22686i	0.965478	+	0.260486i	$0.0838828\pi$
$607$	429.954	+	744.702i	0.708326	+	1.22686i	−0.257151	+	0.966371i	$0.582784\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			558.682i			0.914373i
$612$		0			0
$613$	655.253			1.06893			0.534464	−	0.845191i	$-0.320513\pi$
$613$	655.253			1.06893			0.534464	+	0.845191i	$0.320513\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	147.227	−	85.0013i	0.238617	−	0.137765i	−0.375924	−	0.926650i	$-0.622675\pi$
$617$	147.227	−	85.0013i	0.238617	−	0.137765i	0.614541	+	0.788885i	$0.289341\pi$
$618$		0			0
$619$	−270.531	+	468.573i	−0.437045	+	0.756983i	−0.997460	−	0.0712282i	$-0.977308\pi$
$619$	−270.531	+	468.573i	−0.437045	+	0.756983i	0.560415	+	0.828212i	$0.310641\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	444.545	+	256.658i	0.713555	+	0.411971i
$624$		0			0
$625$	244.490	+	423.469i	0.391184	+	0.677550i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	1248.33i		−	1.98463i
$630$		0			0
$631$	−260.788			−0.413293			−0.206646	−	0.978416i	$-0.566255\pi$
$631$	−260.788			−0.413293			−0.206646	+	0.978416i	$0.566255\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−76.6571	+	44.2580i	−0.120720	+	0.0696977i
$636$		0			0
$637$	−23.4143	+	40.5547i	−0.0367571	+	0.0636652i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−585.418	−	337.991i	−0.913289	−	0.527288i	−0.0318012	−	0.999494i	$-0.510124\pi$
$641$	−585.418	−	337.991i	−0.913289	−	0.527288i	−0.881488	+	0.472206i	$0.843458\pi$
$642$		0			0
$643$	378.318	+	655.267i	0.588364	+	1.01908i	0.994447	+	0.105241i	$0.0335613\pi$
$643$	378.318	+	655.267i	0.588364	+	1.01908i	−0.406082	+	0.913837i	$0.633105\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	554.770i		−	0.857450i	−0.903435	−	0.428725i	$-0.858963\pi$
$647$		−	554.770i		−	0.857450i	0.903435	−	0.428725i	$-0.141037\pi$
$648$		0			0
$649$	−101.000			−0.155624
$650$		0			0
$651$		0			0
$652$		0			0
$653$	174.499	−	100.747i	0.267227	−	0.154283i	−0.360400	−	0.932798i	$-0.617360\pi$
$653$	174.499	−	100.747i	0.267227	−	0.154283i	0.627627	+	0.778514i	$0.284026\pi$
$654$		0			0
$655$	56.7724	−	98.3328i	0.0866755	−	0.150126i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	89.7122	+	51.7954i	0.136134	+	0.0785969i	0.566520	−	0.824048i	$-0.308289\pi$
$659$	89.7122	+	51.7954i	0.136134	+	0.0785969i	−0.430386	+	0.902645i	$0.641623\pi$
$660$		0			0
$661$	109.207	+	189.152i	0.165215	+	0.286161i	0.936732	−	0.350048i	$-0.113835\pi$
$661$	109.207	+	189.152i	0.165215	+	0.286161i	−0.771517	+	0.636209i	$0.780502\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	883.834i		−	1.32907i
$666$		0			0
$667$	267.767			0.401450
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−112.328	+	64.8523i	−0.167403	+	0.0966503i
$672$		0			0
$673$	−394.429	+	683.170i	−0.586075	+	1.01511i	0.408665	+	0.912684i	$0.365994\pi$
$673$	−394.429	+	683.170i	−0.586075	+	1.01511i	−0.994740	+	0.102428i	$0.967339\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−634.550	−	366.358i	−0.937297	−	0.541149i	−0.0481850	−	0.998838i	$-0.515344\pi$
$677$	−634.550	−	366.358i	−0.937297	−	0.541149i	−0.889112	+	0.457690i	$0.848677\pi$
$678$		0			0
$679$	477.883	+	827.717i	0.703804	+	1.21902i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	1353.33i		−	1.98145i	−0.135883	−	0.990725i	$-0.543387\pi$
$683$		−	1353.33i		−	1.98145i	0.135883	−	0.990725i	$-0.456613\pi$
$684$		0			0
$685$	407.080			0.594277
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−147.959	+	85.4243i	−0.214745	+	0.123983i
$690$		0			0
$691$	368.257	−	637.840i	0.532934	−	0.923068i	−0.466327	−	0.884613i	$-0.654423\pi$
$691$	368.257	−	637.840i	0.532934	−	0.923068i	0.999260	−	0.0384555i	$-0.0122438\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−646.166	−	373.064i	−0.929736	−	0.536783i
$696$		0			0
$697$	−501.353	−	868.369i	−0.719301	−	1.24587i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			1068.34i			1.52403i	0.647561	+	0.762014i	$0.275789\pi$
$701$			1068.34i			1.52403i	−0.647561	+	0.762014i	$0.724211\pi$
$702$		0			0
$703$	−872.686			−1.24137
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−191.682	+	110.667i	−0.271120	+	0.156531i
$708$		0			0
$709$	136.944	−	237.194i	0.193151	−	0.334547i	−0.753142	−	0.657858i	$-0.771463\pi$
$709$	136.944	−	237.194i	0.193151	−	0.334547i	0.946293	+	0.323311i	$0.104796\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−580.247	−	335.006i	−0.813811	−	0.469854i
$714$		0			0
$715$	−379.651	−	657.575i	−0.530980	−	0.919685i
$716$		0			0
$717$		0			0
$718$		0			0
$719$			654.423i			0.910185i	0.890444	+	0.455092i	$0.150394\pi$
$719$			654.423i			0.910185i	−0.890444	+	0.455092i	$0.849606\pi$
$720$		0			0
$721$	−921.706			−1.27837
$722$		0			0
$723$		0			0
$724$		0			0
$725$	479.363	−	276.761i	0.661191	−	0.381739i
$726$		0			0
$727$	583.166	−	1010.07i	0.802155	−	1.38937i	−0.116041	−	0.993244i	$-0.537020\pi$
$727$	583.166	−	1010.07i	0.802155	−	1.38937i	0.918195	−	0.396128i	$-0.129646\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−963.292	−	556.157i	−1.31777	−	0.760816i
$732$		0			0
$733$	439.146	+	760.623i	0.599108	+	1.03768i	0.992953	+	0.118508i	$0.0378112\pi$
$733$	439.146	+	760.623i	0.599108	+	1.03768i	−0.393845	+	0.919177i	$0.628855\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	532.103i		−	0.721984i
$738$		0			0
$739$	−593.151			−0.802640			−0.401320	−	0.915938i	$-0.631448\pi$
$739$	−593.151			−0.802640			−0.401320	+	0.915938i	$0.631448\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−47.0561	+	27.1679i	−0.0633326	+	0.0365651i	−0.531332	−	0.847164i	$-0.678308\pi$
$743$	−47.0561	+	27.1679i	−0.0633326	+	0.0365651i	0.467999	+	0.883729i	$0.344975\pi$
$744$		0			0
$745$	799.398	−	1384.60i	1.07302	−	1.85852i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	208.059	+	120.123i	0.277783	+	0.160378i
$750$		0			0
$751$	455.570	+	789.071i	0.606618	+	1.05069i	0.991793	+	0.127850i	$0.0408077\pi$
$751$	455.570	+	789.071i	0.606618	+	1.05069i	−0.385175	+	0.922844i	$0.625859\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1134.83i			1.50309i
$756$		0			0
$757$	−1272.22			−1.68061			−0.840304	−	0.542115i	$-0.817624\pi$
$757$	−1272.22			−1.68061			−0.840304	+	0.542115i	$0.817624\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−399.480	+	230.640i	−0.524940	+	0.303074i	−0.738954	−	0.673756i	$-0.764680\pi$
$761$	−399.480	+	230.640i	−0.524940	+	0.303074i	0.214013	+	0.976831i	$0.431346\pi$
$762$		0			0
$763$	182.171	−	315.530i	0.238757	−	0.413539i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	240.177	+	138.666i	0.313138	+	0.180790i
$768$		0			0
$769$	−269.439	−	466.682i	−0.350376	−	0.606868i	0.635940	−	0.771739i	$-0.280613\pi$
$769$	−269.439	−	466.682i	−0.350376	−	0.606868i	−0.986315	+	0.164871i	$0.947279\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1036.29i			1.34061i	0.742087	+	0.670304i	$0.233836\pi$
$773$			1036.29i			1.34061i	−0.742087	+	0.670304i	$0.766164\pi$
$774$		0			0
$775$	−1385.03			−1.78713
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−607.059	+	350.486i	−0.779280	+	0.449918i
$780$		0			0
$781$	−92.5449	+	160.292i	−0.118495	+	0.205240i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	524.520	+	302.832i	0.668179	+	0.385773i
$786$		0			0
$787$	706.096	+	1222.99i	0.897199	+	1.55399i	0.831059	+	0.556185i	$0.187735\pi$
$787$	706.096	+	1222.99i	0.897199	+	1.55399i	0.0661406	+	0.997810i	$0.478931\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	1123.09i		−	1.41983i
$792$		0			0
$793$	356.151			0.449119
$794$		0			0
$795$		0			0
$796$		0			0
$797$	60.4602	−	34.9067i	0.0758597	−	0.0437976i	−0.461590	−	0.887093i	$-0.652721\pi$
$797$	60.4602	−	34.9067i	0.0758597	−	0.0437976i	0.537450	+	0.843296i	$0.319388\pi$
$798$		0			0
$799$	418.565	−	724.976i	0.523861	−	0.907355i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	258.476	+	149.231i	0.321887	+	0.185842i
$804$		0			0
$805$	359.570	+	622.794i	0.446671	+	0.773657i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1263.33i			1.56160i	0.624781	+	0.780800i	$0.285188\pi$
$809$			1263.33i			1.56160i	−0.624781	+	0.780800i	$0.714812\pi$
$810$		0			0
$811$	−442.241			−0.545303			−0.272652	−	0.962113i	$-0.587901\pi$
$811$	−442.241			−0.545303			−0.272652	+	0.962113i	$0.587901\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	353.302	−	203.979i	0.433499	−	0.250281i
$816$		0			0
$817$	−388.798	+	673.418i	−0.475885	+	0.824257i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	498.077	+	287.565i	0.606671	+	0.350261i	0.771661	−	0.636034i	$-0.219426\pi$
$821$	498.077	+	287.565i	0.606671	+	0.350261i	−0.164991	+	0.986295i	$0.552759\pi$
$822$		0			0
$823$	−11.6214	−	20.1289i	−0.0141208	−	0.0244580i	0.858879	−	0.512179i	$-0.171162\pi$
$823$	−11.6214	−	20.1289i	−0.0141208	−	0.0244580i	−0.872999	+	0.487721i	$0.837828\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			790.958i			0.956418i	0.878246	+	0.478209i	$0.158714\pi$
$827$			790.958i			0.956418i	−0.878246	+	0.478209i	$0.841286\pi$
$828$		0			0
$829$	−1159.78			−1.39901			−0.699503	−	0.714630i	$-0.746595\pi$
$829$	−1159.78			−1.39901			−0.699503	+	0.714630i	$0.746595\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	60.7673	−	35.0840i	0.0729500	−	0.0421177i
$834$		0			0
$835$	−570.802	+	988.658i	−0.683595	+	1.18402i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	473.470	+	273.358i	0.564327	+	0.325814i	0.754880	−	0.655862i	$-0.227695\pi$
$839$	473.470	+	273.358i	0.564327	+	0.325814i	−0.190553	+	0.981677i	$0.561028\pi$
$840$		0			0
$841$	−245.606	−	425.402i	−0.292041	−	0.505829i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			836.213i			0.989601i
$846$		0			0
$847$	568.143			0.670771
$848$		0			0
$849$		0			0
$850$		0			0
$851$	614.939	−	355.035i	0.722607	−	0.417197i
$852$		0			0
$853$	108.317	−	187.611i	0.126984	−	0.219943i	−0.795523	−	0.605924i	$-0.792804\pi$
$853$	108.317	−	187.611i	0.126984	−	0.219943i	0.922507	+	0.385981i	$0.126137\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−489.741	−	282.752i	−0.571460	−	0.329932i	0.186273	−	0.982498i	$-0.440359\pi$
$857$	−489.741	−	282.752i	−0.571460	−	0.329932i	−0.757732	+	0.652566i	$0.773693\pi$
$858$		0			0
$859$	−187.884	−	325.424i	−0.218724	−	0.378841i	0.735694	−	0.677314i	$-0.236856\pi$
$859$	−187.884	−	325.424i	−0.218724	−	0.378841i	−0.954418	+	0.298473i	$0.903523\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1429.35i		−	1.65626i	−0.560534	−	0.828131i	$-0.689404\pi$
$863$		−	1429.35i		−	1.65626i	0.560534	−	0.828131i	$-0.310596\pi$
$864$		0			0
$865$	194.555			0.224919
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−591.177	+	341.316i	−0.680295	+	0.392769i
$870$		0			0
$871$	−730.540	+	1265.33i	−0.838737	+	1.45273i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	199.922	+	115.425i	0.228483	+	0.131915i
$876$		0			0
$877$	−420.813	−	728.870i	−0.479833	−	0.831095i	0.519900	−	0.854227i	$-0.325969\pi$
$877$	−420.813	−	728.870i	−0.479833	−	0.831095i	−0.999732	+	0.0231327i	$0.992636\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	449.261i		−	0.509944i	−0.966948	−	0.254972i	$-0.917934\pi$
$881$		−	449.261i		−	0.509944i	0.966948	−	0.254972i	$-0.0820663\pi$
$882$		0			0
$883$	122.445			0.138669			0.0693346	−	0.997593i	$-0.477912\pi$
$883$	122.445			0.138669			0.0693346	+	0.997593i	$0.477912\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1361.09	+	785.828i	−1.53449	+	0.885940i	−0.535346	+	0.844633i	$0.679819\pi$
$887$	−1361.09	+	785.828i	−1.53449	+	0.885940i	−0.999147	+	0.0413069i	$0.986848\pi$
$888$		0			0
$889$	40.7184	−	70.5263i	0.0458025	−	0.0793322i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−506.816	−	292.611i	−0.567543	−	0.327671i
$894$		0			0
$895$	−985.312	−	1706.61i	−1.10091	−	1.90683i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	875.244i		−	0.973575i
$900$		0			0
$901$	256.000			0.284129
$902$		0			0
$903$		0			0
$904$		0			0
$905$	373.727	−	215.771i	0.412957	−	0.238421i
$906$		0			0
$907$	349.288	−	604.984i	0.385102	−	0.667017i	−0.606681	−	0.794945i	$-0.707500\pi$
$907$	349.288	−	604.984i	0.385102	−	0.667017i	0.991783	+	0.127929i	$0.0408328\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−70.4888	−	40.6967i	−0.0773752	−	0.0446726i	0.460813	−	0.887497i	$-0.347558\pi$
$911$	−70.4888	−	40.6967i	−0.0773752	−	0.0446726i	−0.538188	+	0.842825i	$0.680891\pi$
$912$		0			0
$913$	−300.520	−	520.517i	−0.329157	−	0.570117i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			104.464i			0.113919i
$918$		0			0
$919$	348.665			0.379396			0.189698	−	0.981842i	$-0.439249\pi$
$919$	348.665			0.379396			0.189698	+	0.981842i	$0.439249\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	440.141	−	254.115i	0.476859	−	0.275315i
$924$		0			0
$925$	733.918	−	1271.18i	0.793425	−	1.37425i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	932.298	+	538.262i	1.00355	+	0.579400i	0.909297	−	0.416148i	$-0.136620\pi$
$929$	932.298	+	538.262i	1.00355	+	0.579400i	0.0942533	+	0.995548i	$0.469954\pi$
$930$		0			0
$931$	−24.5265	−	42.4812i	−0.0263443	−	0.0456297i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1137.74i			1.21683i
$936$		0			0
$937$	−1437.39			−1.53404			−0.767018	−	0.641626i	$-0.778260\pi$
$937$	−1437.39			−1.53404			−0.767018	+	0.641626i	$0.778260\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−186.591	+	107.728i	−0.198290	+	0.114483i	−0.595858	−	0.803090i	$-0.703188\pi$
$941$	−186.591	+	107.728i	−0.198290	+	0.114483i	0.397568	+	0.917573i	$0.369854\pi$
$942$		0			0
$943$	285.177	−	493.940i	0.302414	−	0.523797i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	407.651	+	235.357i	0.430466	+	0.248529i	0.699545	−	0.714589i	$-0.253386\pi$
$947$	407.651	+	235.357i	0.430466	+	0.248529i	−0.269079	+	0.963118i	$0.586719\pi$
$948$		0			0
$949$	−409.767	−	709.738i	−0.431789	−	0.747880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1192.14i			1.25093i	0.780251	+	0.625466i	$0.215091\pi$
$953$			1192.14i			1.25093i	−0.780251	+	0.625466i	$0.784909\pi$
$954$		0			0
$955$	−849.445			−0.889471
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−324.346	+	187.261i	−0.338213	+	0.195267i
$960$		0			0
$961$	−614.524	+	1064.39i	−0.639464	+	1.10758i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1388.45	−	801.621i	−1.43881	−	0.830695i
$966$		0			0
$967$	−96.3888	−	166.950i	−0.0996782	−	0.172648i	0.811873	−	0.583834i	$-0.198448\pi$
$967$	−96.3888	−	166.950i	−0.0996782	−	0.172648i	−0.911551	+	0.411186i	$0.865115\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$			202.388i			0.208433i	0.994555	+	0.104216i	$0.0332335\pi$
$971$			202.388i			0.208433i	−0.994555	+	0.104216i	$0.966767\pi$
$972$		0			0
$973$	686.455			0.705504
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−35.1980	+	20.3216i	−0.0360266	+	0.0208000i	−0.517905	−	0.855438i	$-0.673288\pi$
$977$	−35.1980	+	20.3216i	−0.0360266	+	0.0208000i	0.481879	+	0.876238i	$0.339955\pi$
$978$		0			0
$979$	−230.969	+	400.051i	−0.235924	+	0.408632i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	631.105	+	364.369i	0.642019	+	0.370670i	0.785392	−	0.618999i	$-0.212461\pi$
$983$	631.105	+	364.369i	0.642019	+	0.370670i	−0.143373	+	0.989669i	$0.545795\pi$
$984$		0			0
$985$	632.141	+	1094.90i	0.641767	+	1.11157i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	632.699i		−	0.639736i
$990$		0			0
$991$	−746.527			−0.753306			−0.376653	−	0.926354i	$-0.622925\pi$
$991$	−746.527			−0.753306			−0.376653	+	0.926354i	$0.622925\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	396.737	−	229.056i	0.398730	−	0.230207i
$996$		0			0
$997$	119.046	−	206.194i	0.119404	−	0.206814i	−0.800128	−	0.599830i	$-0.795235\pi$
$997$	119.046	−	206.194i	0.119404	−	0.206814i	0.919532	+	0.393016i	$0.128568\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.3.q.f.1601.2		4
3.2	odd	2		576.3.q.c.65.1		4
4.3	odd	2		1728.3.q.e.1601.2		4
8.3	odd	2		216.3.m.a.89.1		4
8.5	even	2		432.3.q.c.305.1		4
9.4	even	3		576.3.q.c.257.1		4
9.5	odd	6	inner	1728.3.q.f.449.2		4
12.11	even	2		576.3.q.h.65.1		4
24.5	odd	2		144.3.q.d.65.2		4
24.11	even	2		72.3.m.a.65.2	yes	4
36.23	even	6		1728.3.q.e.449.2		4
36.31	odd	6		576.3.q.h.257.1		4
72.5	odd	6		432.3.q.c.17.1		4
72.11	even	6		648.3.e.b.161.4		4
72.13	even	6		144.3.q.d.113.2		4
72.29	odd	6		1296.3.e.c.161.4		4
72.43	odd	6		648.3.e.b.161.1		4
72.59	even	6		216.3.m.a.17.1		4
72.61	even	6		1296.3.e.c.161.1		4
72.67	odd	6		72.3.m.a.41.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.m.a.41.2	✓	4	72.67	odd	6
72.3.m.a.65.2	yes	4	24.11	even	2
144.3.q.d.65.2		4	24.5	odd	2
144.3.q.d.113.2		4	72.13	even	6
216.3.m.a.17.1		4	72.59	even	6
216.3.m.a.89.1		4	8.3	odd	2
432.3.q.c.17.1		4	72.5	odd	6
432.3.q.c.305.1		4	8.5	even	2
576.3.q.c.65.1		4	3.2	odd	2
576.3.q.c.257.1		4	9.4	even	3
576.3.q.h.65.1		4	12.11	even	2
576.3.q.h.257.1		4	36.31	odd	6
648.3.e.b.161.1		4	72.43	odd	6
648.3.e.b.161.4		4	72.11	even	6
1296.3.e.c.161.1		4	72.61	even	6
1296.3.e.c.161.4		4	72.29	odd	6
1728.3.q.e.449.2		4	36.23	even	6
1728.3.q.e.1601.2		4	4.3	odd	2
1728.3.q.f.449.2		4	9.5	odd	6	inner
1728.3.q.f.1601.2		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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1728.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +O(q^{10})\)	\(q+(6.39898 - 3.69445i) q^{5} +(-3.39898 + 5.88721i) q^{7} +(-5.29796 - 3.05878i) q^{11} +(8.39898 + 14.5475i) q^{13} -25.1701i q^{17} -17.5959 q^{19} +(12.3990 - 7.15855i) q^{23} +(14.7980 - 25.6308i) q^{25} +(16.1969 + 9.35131i) q^{29} +(-23.3990 - 40.5282i) q^{31} +50.2295i q^{35} +49.5959 q^{37} +(34.5000 - 19.9186i) q^{41} +(22.0959 - 38.2713i) q^{43} +(28.8031 + 16.6295i) q^{47} +(1.39388 + 2.41427i) q^{49} +10.1708i q^{53} -45.2020 q^{55} +(14.2980 - 8.25493i) q^{59} +(10.6010 - 18.3615i) q^{61} +(107.490 + 62.0593i) q^{65} +(43.4898 + 75.3265i) q^{67} -30.2555i q^{71} -48.7878 q^{73} +(36.0153 - 20.7934i) q^{77} +(55.7929 - 96.6361i) q^{79} +(85.0857 + 49.1243i) q^{83} +(-92.9898 - 161.063i) q^{85} -75.5103i q^{89} -114.192 q^{91} +(-112.596 + 65.0073i) q^{95} +(70.2980 - 121.760i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{5} + 6 q^{7}+O(q^{10}) \) 4 * q + 6 * q^5 + 6 * q^7	\( 4 q + 6 q^{5} + 6 q^{7} + 18 q^{11} + 14 q^{13} + 8 q^{19} + 30 q^{23} + 20 q^{25} + 6 q^{29} - 74 q^{31} + 120 q^{37} + 138 q^{41} + 10 q^{43} + 174 q^{47} - 112 q^{49} - 220 q^{55} + 18 q^{59} + 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} + 438 q^{77} + 86 q^{79} + 66 q^{83} - 176 q^{85} - 300 q^{91} - 372 q^{95} + 242 q^{97}+O(q^{100}) \) 4 * q + 6 * q^5 + 6 * q^7 + 18 * q^11 + 14 * q^13 + 8 * q^19 + 30 * q^23 + 20 * q^25 + 6 * q^29 - 74 * q^31 + 120 * q^37 + 138 * q^41 + 10 * q^43 + 174 * q^47 - 112 * q^49 - 220 * q^55 + 18 * q^59 + 62 * q^61 + 234 * q^65 - 22 * q^67 + 40 * q^73 + 438 * q^77 + 86 * q^79 + 66 * q^83 - 176 * q^85 - 300 * q^91 - 372 * q^95 + 242 * q^97

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