LMFDB - Embedded newform 1400.2.x.b.993.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(657,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1400.657");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.x (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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			993.2
Character	$\chi$	$=$	1400.993
Dual form			1400.2.x.b.657.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16341 + 2.16341i) q^{3} +(2.61380 - 0.409966i) q^{7} -6.36066i q^{9} +O(q^{10})$	$q+(-2.16341 + 2.16341i) q^{3} +(2.61380 - 0.409966i) q^{7} -6.36066i q^{9} +0.796216 q^{11} +(-3.25130 + 3.25130i) q^{13} +(-2.52106 - 2.52106i) q^{17} +2.29803 q^{19} +(-4.76778 + 6.54163i) q^{21} +(2.08441 + 2.08441i) q^{23} +(7.27046 + 7.27046i) q^{27} +10.0797i q^{29} +3.63347i q^{31} +(-1.72254 + 1.72254i) q^{33} +(-7.30001 + 7.30001i) q^{37} -14.0678i q^{39} -2.81026i q^{41} +(-2.33689 - 2.33689i) q^{43} +(4.09923 + 4.09923i) q^{47} +(6.66386 - 2.14314i) q^{49} +10.9082 q^{51} +(-6.50379 - 6.50379i) q^{53} +(-4.97156 + 4.97156i) q^{57} -11.4005 q^{59} +3.35941i q^{61} +(-2.60765 - 16.6255i) q^{63} +(2.49153 - 2.49153i) q^{67} -9.01885 q^{69} -2.93777 q^{71} +(-4.93694 + 4.93694i) q^{73} +(2.08115 - 0.326422i) q^{77} +6.53223i q^{79} -12.3760 q^{81} +(-1.14828 + 1.14828i) q^{83} +(-21.8066 - 21.8066i) q^{87} -14.0949 q^{89} +(-7.16532 + 9.83117i) q^{91} +(-7.86067 - 7.86067i) q^{93} +(-4.30685 - 4.30685i) q^{97} -5.06446i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) $ 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−2.16341	+	2.16341i	−1.24904	+	1.24904i	−0.292900	+	0.956143i	$0.594620\pi$
$3$	−2.16341	+	2.16341i	−1.24904	+	1.24904i	−0.956143	+	0.292900i	$0.905380\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.61380	−	0.409966i	0.987922	−	0.154953i
$7$	2.61380	−	0.409966i	0.987922	−	0.154953i
$8$		0			0
$9$		−	6.36066i		−	2.12022i
$10$		0			0
$11$	0.796216			0.240068			0.120034	−	0.992770i	$-0.461700\pi$
$11$	0.796216			0.240068			0.120034	+	0.992770i	$0.461700\pi$
$12$		0			0
$13$	−3.25130	+	3.25130i	−0.901750	+	0.901750i	−0.995587	−	0.0938379i	$-0.970086\pi$
$13$	−3.25130	+	3.25130i	−0.901750	+	0.901750i	0.0938379	+	0.995587i	$0.470086\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.52106	−	2.52106i	−0.611447	−	0.611447i	0.331876	−	0.943323i	$-0.392318\pi$
$17$	−2.52106	−	2.52106i	−0.611447	−	0.611447i	−0.943323	+	0.331876i	$0.892318\pi$
$18$		0			0
$19$	2.29803			0.527203			0.263602	−	0.964632i	$-0.415090\pi$
$19$	2.29803			0.527203			0.263602	+	0.964632i	$0.415090\pi$
$20$		0			0
$21$	−4.76778	+	6.54163i	−1.04041	+	1.42750i
$22$		0			0
$23$	2.08441	+	2.08441i	0.434630	+	0.434630i	0.890200	−	0.455570i	$-0.150565\pi$
$23$	2.08441	+	2.08441i	0.434630	+	0.434630i	−0.455570	+	0.890200i	$0.650565\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	7.27046	+	7.27046i	1.39920	+	1.39920i
$28$		0			0
$29$			10.0797i			1.87176i	0.352319	+	0.935880i	$0.385393\pi$
$29$			10.0797i			1.87176i	−0.352319	+	0.935880i	$0.614607\pi$
$30$		0			0
$31$			3.63347i			0.652590i	0.945268	+	0.326295i	$0.105800\pi$
$31$			3.63347i			0.652590i	−0.945268	+	0.326295i	$0.894200\pi$
$32$		0			0
$33$	−1.72254	+	1.72254i	−0.299856	+	0.299856i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.30001	+	7.30001i	−1.20011	+	1.20011i	−0.225982	+	0.974131i	$0.572559\pi$
$37$	−7.30001	+	7.30001i	−1.20011	+	1.20011i	−0.974131	+	0.225982i	$0.927441\pi$
$38$		0			0
$39$		−	14.0678i		−	2.25265i
$40$		0			0
$41$		−	2.81026i		−	0.438889i	−0.975625	−	0.219444i	$-0.929576\pi$
$41$		−	2.81026i		−	0.438889i	0.975625	−	0.219444i	$-0.0704245\pi$
$42$		0			0
$43$	−2.33689	−	2.33689i	−0.356373	−	0.356373i	0.506101	−	0.862474i	$-0.331086\pi$
$43$	−2.33689	−	2.33689i	−0.356373	−	0.356373i	−0.862474	+	0.506101i	$0.831086\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.09923	+	4.09923i	0.597934	+	0.597934i	0.939762	−	0.341829i	$-0.111046\pi$
$47$	4.09923	+	4.09923i	0.597934	+	0.597934i	−0.341829	+	0.939762i	$0.611046\pi$
$48$		0			0
$49$	6.66386	−	2.14314i	0.951979	−	0.306162i
$50$		0			0
$51$	10.9082			1.52745
$52$		0			0
$53$	−6.50379	−	6.50379i	−0.893364	−	0.893364i	0.101474	−	0.994838i	$-0.467644\pi$
$53$	−6.50379	−	6.50379i	−0.893364	−	0.893364i	−0.994838	+	0.101474i	$0.967644\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.97156	+	4.97156i	−0.658500	+	0.658500i
$58$		0			0
$59$	−11.4005			−1.48422			−0.742112	−	0.670276i	$-0.766176\pi$
$59$	−11.4005			−1.48422			−0.742112	+	0.670276i	$0.766176\pi$
$60$		0			0
$61$			3.35941i			0.430128i	0.976600	+	0.215064i	$0.0689960\pi$
$61$			3.35941i			0.430128i	−0.976600	+	0.215064i	$0.931004\pi$
$62$		0			0
$63$	−2.60765	−	16.6255i	−0.328533	−	2.09461i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.49153	−	2.49153i	0.304389	−	0.304389i	−0.538339	−	0.842728i	$-0.680948\pi$
$67$	2.49153	−	2.49153i	0.304389	−	0.304389i	0.842728	+	0.538339i	$0.180948\pi$
$68$		0			0
$69$	−9.01885			−1.08574
$70$		0			0
$71$	−2.93777			−0.348650			−0.174325	−	0.984688i	$-0.555774\pi$
$71$	−2.93777			−0.348650			−0.174325	+	0.984688i	$0.555774\pi$
$72$		0			0
$73$	−4.93694	+	4.93694i	−0.577826	+	0.577826i	−0.934304	−	0.356478i	$-0.883977\pi$
$73$	−4.93694	+	4.93694i	−0.577826	+	0.577826i	0.356478	+	0.934304i	$0.383977\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.08115	−	0.326422i	0.237169	−	0.0371992i
$78$		0			0
$79$			6.53223i			0.734933i	0.930037	+	0.367467i	$0.119775\pi$
$79$			6.53223i			0.734933i	−0.930037	+	0.367467i	$0.880225\pi$
$80$		0			0
$81$	−12.3760			−1.37511
$82$		0			0
$83$	−1.14828	+	1.14828i	−0.126040	+	0.126040i	−0.767313	−	0.641273i	$-0.778407\pi$
$83$	−1.14828	+	1.14828i	−0.126040	+	0.126040i	0.641273	+	0.767313i	$0.278407\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−21.8066	−	21.8066i	−2.33791	−	2.33791i
$88$		0			0
$89$	−14.0949			−1.49405			−0.747026	−	0.664795i	$-0.768519\pi$
$89$	−14.0949			−1.49405			−0.747026	+	0.664795i	$0.768519\pi$
$90$		0			0
$91$	−7.16532	+	9.83117i	−0.751130	+	1.03059i
$92$		0			0
$93$	−7.86067	−	7.86067i	−0.815114	−	0.815114i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.30685	−	4.30685i	−0.437295	−	0.437295i	0.453806	−	0.891101i	$-0.350066\pi$
$97$	−4.30685	−	4.30685i	−0.437295	−	0.437295i	−0.891101	+	0.453806i	$0.850066\pi$
$98$		0			0
$99$		−	5.06446i		−	0.508997i
$100$		0			0
$101$		−	11.6450i		−	1.15872i	−0.815072	−	0.579360i	$-0.803303\pi$
$101$		−	11.6450i		−	1.15872i	0.815072	−	0.579360i	$-0.196697\pi$
$102$		0			0
$103$	3.54280	−	3.54280i	0.349082	−	0.349082i	−0.510685	−	0.859768i	$-0.670608\pi$
$103$	3.54280	−	3.54280i	0.349082	−	0.349082i	0.859768	+	0.510685i	$0.170608\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.21284	−	9.21284i	0.890639	−	0.890639i	−0.103944	−	0.994583i	$-0.533146\pi$
$107$	9.21284	−	9.21284i	0.890639	−	0.890639i	0.994583	+	0.103944i	$0.0331462\pi$
$108$		0			0
$109$			6.01531i			0.576162i	0.957606	+	0.288081i	$0.0930173\pi$
$109$			6.01531i			0.576162i	−0.957606	+	0.288081i	$0.906983\pi$
$110$		0			0
$111$		−	31.5858i		−	2.99799i
$112$		0			0
$113$	−3.56399	−	3.56399i	−0.335272	−	0.335272i	0.519312	−	0.854585i	$-0.326188\pi$
$113$	−3.56399	−	3.56399i	−0.335272	−	0.335272i	−0.854585	+	0.519312i	$0.826188\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	20.6804	+	20.6804i	1.91191	+	1.91191i
$118$		0			0
$119$	−7.62309	−	5.55599i	−0.698807	−	0.509317i
$120$		0			0
$121$	−10.3660			−0.942367
$122$		0			0
$123$	6.07973	+	6.07973i	0.548191	+	0.548191i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−14.2615	+	14.2615i	−1.26551	+	1.26551i	−0.317123	+	0.948384i	$0.602717\pi$
$127$	−14.2615	+	14.2615i	−1.26551	+	1.26551i	−0.948384	+	0.317123i	$0.897283\pi$
$128$		0			0
$129$	10.1113			0.890250
$130$		0			0
$131$			8.24139i			0.720054i	0.932942	+	0.360027i	$0.117232\pi$
$131$			8.24139i			0.720054i	−0.932942	+	0.360027i	$0.882768\pi$
$132$		0			0
$133$	6.00657	−	0.942113i	0.520836	−	0.0816915i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.79622	+	5.79622i	−0.495204	+	0.495204i	−0.909941	−	0.414737i	$-0.863874\pi$
$137$	−5.79622	+	5.79622i	−0.495204	+	0.495204i	0.414737	+	0.909941i	$0.363874\pi$
$138$		0			0
$139$	−7.89813			−0.669911			−0.334955	−	0.942234i	$-0.608721\pi$
$139$	−7.89813			−0.669911			−0.334955	+	0.942234i	$0.608721\pi$
$140$		0			0
$141$	−17.7366			−1.49369
$142$		0			0
$143$	−2.58874	+	2.58874i	−0.216481	+	0.216481i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.78015	+	19.0531i	−0.806654	+	1.57147i
$148$		0			0
$149$		−	5.09736i		−	0.417592i	−0.977959	−	0.208796i	$-0.933045\pi$
$149$		−	5.09736i		−	0.417592i	0.977959	−	0.208796i	$-0.0669545\pi$
$150$		0			0
$151$	13.4201			1.09211			0.546057	−	0.837748i	$-0.316128\pi$
$151$	13.4201			1.09211			0.546057	+	0.837748i	$0.316128\pi$
$152$		0			0
$153$	−16.0356	+	16.0356i	−1.29640	+	1.29640i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.73434	−	2.73434i	−0.218224	−	0.218224i	0.589525	−	0.807750i	$-0.299315\pi$
$157$	−2.73434	−	2.73434i	−0.218224	−	0.218224i	−0.807750	+	0.589525i	$0.799315\pi$
$158$		0			0
$159$	28.1407			2.23170
$160$		0			0
$161$	6.30276	+	4.59368i	0.496727	+	0.362033i
$162$		0			0
$163$	15.4971	+	15.4971i	1.21383	+	1.21383i	0.969758	+	0.244068i	$0.0784820\pi$
$163$	15.4971	+	15.4971i	1.21383	+	1.21383i	0.244068	+	0.969758i	$0.421518\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.74279	+	4.74279i	0.367008	+	0.367008i	0.866385	−	0.499377i	$-0.166438\pi$
$167$	4.74279	+	4.74279i	0.367008	+	0.367008i	−0.499377	+	0.866385i	$0.666438\pi$
$168$		0			0
$169$		−	8.14196i		−	0.626305i
$170$		0			0
$171$		−	14.6169i		−	1.11779i
$172$		0			0
$173$	10.5915	−	10.5915i	0.805253	−	0.805253i	−0.178658	−	0.983911i	$-0.557176\pi$
$173$	10.5915	−	10.5915i	0.805253	−	0.805253i	0.983911	+	0.178658i	$0.0571756\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	24.6640	−	24.6640i	1.85386	−	1.85386i
$178$		0			0
$179$			18.0880i			1.35196i	0.736918	+	0.675982i	$0.236280\pi$
$179$			18.0880i			1.35196i	−0.736918	+	0.675982i	$0.763720\pi$
$180$		0			0
$181$			14.0287i			1.04274i	0.853329	+	0.521372i	$0.174580\pi$
$181$			14.0287i			1.04274i	−0.853329	+	0.521372i	$0.825420\pi$
$182$		0			0
$183$	−7.26776	−	7.26776i	−0.537248	−	0.537248i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.00731	−	2.00731i	−0.146789	−	0.146789i
$188$		0			0
$189$	21.9841	+	16.0229i	1.59911	+	1.16549i
$190$		0			0
$191$	5.39084			0.390068			0.195034	−	0.980796i	$-0.437518\pi$
$191$	5.39084			0.390068			0.195034	+	0.980796i	$0.437518\pi$
$192$		0			0
$193$	3.66005	+	3.66005i	0.263456	+	0.263456i	0.826457	−	0.563000i	$-0.190353\pi$
$193$	3.66005	+	3.66005i	0.263456	+	0.263456i	−0.563000	+	0.826457i	$0.690353\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.16340	−	9.16340i	0.652865	−	0.652865i	−0.300817	−	0.953682i	$-0.597259\pi$
$197$	9.16340	−	9.16340i	0.652865	−	0.652865i	0.953682	+	0.300817i	$0.0972593\pi$
$198$		0			0
$199$	−15.9276			−1.12908			−0.564539	−	0.825406i	$-0.690946\pi$
$199$	−15.9276			−1.12908			−0.564539	+	0.825406i	$0.690946\pi$
$200$		0			0
$201$			10.7804i			0.760391i
$202$		0			0
$203$	4.13235	+	26.3464i	0.290034	+	1.84915i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	13.2582	−	13.2582i	0.921510	−	0.921510i
$208$		0			0
$209$	1.82972			0.126565
$210$		0			0
$211$	4.20382			0.289403			0.144701	−	0.989475i	$-0.453778\pi$
$211$	4.20382			0.289403			0.144701	+	0.989475i	$0.453778\pi$
$212$		0			0
$213$	6.35560	−	6.35560i	0.435479	−	0.435479i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.48960	+	9.49715i	0.101121	+	0.644708i
$218$		0			0
$219$		−	21.3612i		−	1.44346i
$220$		0			0
$221$	16.3935			1.10274
$222$		0			0
$223$	8.79408	−	8.79408i	0.588895	−	0.588895i	−0.348437	−	0.937332i	$-0.613288\pi$
$223$	8.79408	−	8.79408i	0.588895	−	0.588895i	0.937332	+	0.348437i	$0.113288\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.9267	−	12.9267i	−0.857973	−	0.857973i	0.133126	−	0.991099i	$-0.457498\pi$
$227$	−12.9267	−	12.9267i	−0.857973	−	0.857973i	−0.991099	+	0.133126i	$0.957498\pi$
$228$		0			0
$229$	15.2917			1.01050			0.505252	−	0.862972i	$-0.331400\pi$
$229$	15.2917			1.01050			0.505252	+	0.862972i	$0.331400\pi$
$230$		0			0
$231$	−3.79618	+	5.20855i	−0.249770	+	0.342697i
$232$		0			0
$233$	6.89086	+	6.89086i	0.451435	+	0.451435i	0.895831	−	0.444395i	$-0.146581\pi$
$233$	6.89086	+	6.89086i	0.451435	+	0.451435i	−0.444395	+	0.895831i	$0.646581\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−14.1319	−	14.1319i	−0.917963	−	0.917963i
$238$		0			0
$239$		−	4.40870i		−	0.285175i	−0.989782	−	0.142588i	$-0.954458\pi$
$239$		−	4.40870i		−	0.285175i	0.989782	−	0.142588i	$-0.0455423\pi$
$240$		0			0
$241$			9.82692i			0.633008i	0.948591	+	0.316504i	$0.102509\pi$
$241$			9.82692i			0.633008i	−0.948591	+	0.316504i	$0.897491\pi$
$242$		0			0
$243$	4.96286	−	4.96286i	0.318368	−	0.318368i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.47158	+	7.47158i	−0.475405	+	0.475405i
$248$		0			0
$249$		−	4.96840i		−	0.314860i
$250$		0			0
$251$		−	0.723170i		−	0.0456461i	−0.999740	−	0.0228230i	$-0.992735\pi$
$251$		−	0.723170i		−	0.0456461i	0.999740	−	0.0228230i	$-0.00726543\pi$
$252$		0			0
$253$	1.65964	+	1.65964i	0.104341	+	0.104341i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.32060	+	6.32060i	0.394268	+	0.394268i	0.876206	−	0.481938i	$-0.160067\pi$
$257$	6.32060	+	6.32060i	0.394268	+	0.394268i	−0.481938	+	0.876206i	$0.660067\pi$
$258$		0			0
$259$	−16.0880	+	22.0735i	−0.999658	+	1.37158i
$260$		0			0
$261$	64.1137			3.96854
$262$		0			0
$263$	−6.22755	−	6.22755i	−0.384007	−	0.384007i	0.488537	−	0.872543i	$-0.337531\pi$
$263$	−6.22755	−	6.22755i	−0.384007	−	0.384007i	−0.872543	+	0.488537i	$0.837531\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	30.4929	−	30.4929i	1.86613	−	1.86613i
$268$		0			0
$269$	−3.12088			−0.190283			−0.0951417	−	0.995464i	$-0.530330\pi$
$269$	−3.12088			−0.190283			−0.0951417	+	0.995464i	$0.530330\pi$
$270$		0			0
$271$			5.17480i			0.314347i	0.987571	+	0.157173i	$0.0502382\pi$
$271$			5.17480i			0.314347i	−0.987571	+	0.157173i	$0.949762\pi$
$272$		0			0
$273$	−5.76732	−	36.7703i	−0.349054	−	2.22544i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−18.9267	+	18.9267i	−1.13719	+	1.13719i	−0.148242	+	0.988951i	$0.547362\pi$
$277$	−18.9267	+	18.9267i	−1.13719	+	1.13719i	−0.988951	+	0.148242i	$0.952638\pi$
$278$		0			0
$279$	23.1112			1.38363
$280$		0			0
$281$	−10.2646			−0.612333			−0.306166	−	0.951978i	$-0.599046\pi$
$281$	−10.2646			−0.612333			−0.306166	+	0.951978i	$0.599046\pi$
$282$		0			0
$283$	−23.3112	+	23.3112i	−1.38571	+	1.38571i	−0.551598	+	0.834110i	$0.685982\pi$
$283$	−23.3112	+	23.3112i	−1.38571	+	1.38571i	−0.834110	+	0.551598i	$0.814018\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.15211	−	7.34545i	−0.0680070	−	0.433588i
$288$		0			0
$289$		−	4.28850i		−	0.252265i
$290$		0			0
$291$	18.6349			1.09240
$292$		0			0
$293$	7.53673	−	7.53673i	0.440301	−	0.440301i	−0.451812	−	0.892113i	$-0.649222\pi$
$293$	7.53673	−	7.53673i	0.440301	−	0.440301i	0.892113	+	0.451812i	$0.149222\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	5.78886	+	5.78886i	0.335904	+	0.335904i
$298$		0			0
$299$	−13.5541			−0.783854
$300$		0			0
$301$	−7.06621	−	5.15011i	−0.407289	−	0.296848i
$302$		0			0
$303$	25.1929	+	25.1929i	1.44729	+	1.44729i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	5.09625	+	5.09625i	0.290858	+	0.290858i	0.837419	−	0.546561i	$-0.184063\pi$
$307$	5.09625	+	5.09625i	0.290858	+	0.290858i	−0.546561	+	0.837419i	$0.684063\pi$
$308$		0			0
$309$			15.3290i			0.872038i
$310$		0			0
$311$			8.88013i			0.503546i	0.967786	+	0.251773i	$0.0810136\pi$
$311$			8.88013i			0.503546i	−0.967786	+	0.251773i	$0.918986\pi$
$312$		0			0
$313$	6.50060	−	6.50060i	0.367436	−	0.367436i	−0.499105	−	0.866541i	$-0.666338\pi$
$313$	6.50060	−	6.50060i	0.367436	−	0.367436i	0.866541	+	0.499105i	$0.166338\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.87753	+	3.87753i	−0.217784	+	0.217784i	−0.807564	−	0.589780i	$-0.799214\pi$
$317$	−3.87753	+	3.87753i	−0.217784	+	0.217784i	0.589780	+	0.807564i	$0.299214\pi$
$318$		0			0
$319$			8.02565i			0.449350i
$320$		0			0
$321$			39.8623i			2.22489i
$322$		0			0
$323$	−5.79346	−	5.79346i	−0.322357	−	0.322357i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.0136	−	13.0136i	−0.719652	−	0.719652i
$328$		0			0
$329$	12.3951	+	9.03400i	0.683363	+	0.498060i
$330$		0			0
$331$	6.56299			0.360735			0.180367	−	0.983599i	$-0.442271\pi$
$331$	6.56299			0.360735			0.180367	+	0.983599i	$0.442271\pi$
$332$		0			0
$333$	46.4328	+	46.4328i	2.54450	+	2.54450i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.62582	+	3.62582i	−0.197511	+	0.197511i	−0.798932	−	0.601421i	$-0.794601\pi$
$337$	−3.62582	+	3.62582i	−0.197511	+	0.197511i	0.601421	+	0.798932i	$0.294601\pi$
$338$		0			0
$339$	15.4207			0.837540
$340$		0			0
$341$			2.89303i			0.156666i
$342$		0			0
$343$	16.5393	−	8.33367i	0.893041	−	0.449976i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.698071	−	0.698071i	0.0374744	−	0.0374744i	−0.688121	−	0.725596i	$-0.741564\pi$
$347$	0.698071	−	0.698071i	0.0374744	−	0.0374744i	0.725596	+	0.688121i	$0.241564\pi$
$348$		0			0
$349$	1.36446			0.0730378			0.0365189	−	0.999333i	$-0.488373\pi$
$349$	1.36446			0.0730378			0.0365189	+	0.999333i	$0.488373\pi$
$350$		0			0
$351$	−47.2770			−2.52346
$352$		0			0
$353$	−8.57760	+	8.57760i	−0.456539	+	0.456539i	−0.897518	−	0.440978i	$-0.854632\pi$
$353$	−8.57760	+	8.57760i	−0.456539	+	0.456539i	0.440978	+	0.897518i	$0.354632\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	28.5117	−	4.47198i	1.50900	−	0.236682i
$358$		0			0
$359$		−	20.0825i		−	1.05992i	−0.848024	−	0.529958i	$-0.822208\pi$
$359$		−	20.0825i		−	1.05992i	0.848024	−	0.529958i	$-0.177792\pi$
$360$		0			0
$361$	−13.7191			−0.722057
$362$		0			0
$363$	22.4260	−	22.4260i	1.17706	−	1.17706i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.7210	+	18.7210i	0.977228	+	0.977228i	0.999746	−	0.0225182i	$-0.00716838\pi$
$367$	18.7210	+	18.7210i	0.977228	+	0.977228i	−0.0225182	+	0.999746i	$0.507168\pi$
$368$		0			0
$369$	−17.8751			−0.930540
$370$		0			0
$371$	−19.6659	−	14.3332i	−1.02100	−	0.744145i
$372$		0			0
$373$	14.2070	+	14.2070i	0.735612	+	0.735612i	0.971726	−	0.236113i	$-0.0758736\pi$
$373$	14.2070	+	14.2070i	0.735612	+	0.735612i	−0.236113	+	0.971726i	$0.575874\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−32.7723	−	32.7723i	−1.68786	−	1.68786i
$378$		0			0
$379$			32.8094i			1.68530i	0.538459	+	0.842652i	$0.319007\pi$
$379$			32.8094i			1.68530i	−0.538459	+	0.842652i	$0.680993\pi$
$380$		0			0
$381$		−	61.7070i		−	3.16135i
$382$		0			0
$383$	−4.07047	+	4.07047i	−0.207991	+	0.207991i	−0.803413	−	0.595422i	$-0.796985\pi$
$383$	−4.07047	+	4.07047i	−0.207991	+	0.207991i	0.595422	+	0.803413i	$0.296985\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−14.8642	+	14.8642i	−0.755588	+	0.755588i
$388$		0			0
$389$			7.60774i			0.385728i	0.981226	+	0.192864i	$0.0617776\pi$
$389$			7.60774i			0.385728i	−0.981226	+	0.192864i	$0.938222\pi$
$390$		0			0
$391$		−	10.5099i		−	0.531506i
$392$		0			0
$393$	−17.8295	−	17.8295i	−0.899378	−	0.899378i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−18.7106	−	18.7106i	−0.939059	−	0.939059i	0.0591880	−	0.998247i	$-0.481149\pi$
$397$	−18.7106	−	18.7106i	−0.939059	−	0.939059i	−0.998247	+	0.0591880i	$0.981149\pi$
$398$		0			0
$399$	−10.9565	+	15.0328i	−0.548510	+	0.752582i
$400$		0			0
$401$	4.07435			0.203463			0.101732	−	0.994812i	$-0.467562\pi$
$401$	4.07435			0.203463			0.101732	+	0.994812i	$0.467562\pi$
$402$		0			0
$403$	−11.8135	−	11.8135i	−0.588473	−	0.588473i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.81238	+	5.81238i	−0.288109	+	0.288109i
$408$		0			0
$409$	−7.30032			−0.360978			−0.180489	−	0.983577i	$-0.557768\pi$
$409$	−7.30032			−0.360978			−0.180489	+	0.983577i	$0.557768\pi$
$410$		0			0
$411$		−	25.0791i		−	1.23706i
$412$		0			0
$413$	−29.7987	+	4.67383i	−1.46630	+	0.229984i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	17.0869	−	17.0869i	0.836748	−	0.836748i
$418$		0			0
$419$	38.4444			1.87813			0.939066	−	0.343737i	$-0.111693\pi$
$419$	38.4444			1.87813			0.939066	+	0.343737i	$0.111693\pi$
$420$		0			0
$421$	−18.4603			−0.899698			−0.449849	−	0.893105i	$-0.648522\pi$
$421$	−18.4603			−0.899698			−0.449849	+	0.893105i	$0.648522\pi$
$422$		0			0
$423$	26.0738	−	26.0738i	1.26775	−	1.26775i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.37724	+	8.78080i	0.0666495	+	0.424933i
$428$		0			0
$429$		−	11.2010i		−	0.540789i
$430$		0			0
$431$	18.3985			0.886227			0.443113	−	0.896466i	$-0.353874\pi$
$431$	18.3985			0.886227			0.443113	+	0.896466i	$0.353874\pi$
$432$		0			0
$433$	13.6373	−	13.6373i	0.655368	−	0.655368i	−0.298913	−	0.954280i	$-0.596624\pi$
$433$	13.6373	−	13.6373i	0.655368	−	0.655368i	0.954280	+	0.298913i	$0.0966240\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.79003	+	4.79003i	0.229138	+	0.229138i
$438$		0			0
$439$	13.8974			0.663285			0.331642	−	0.943405i	$-0.392397\pi$
$439$	13.8974			0.663285			0.331642	+	0.943405i	$0.392397\pi$
$440$		0			0
$441$	−13.6317	−	42.3865i	−0.649131	−	2.01840i
$442$		0			0
$443$	−18.8725	−	18.8725i	−0.896659	−	0.896659i	0.0984802	−	0.995139i	$-0.468602\pi$
$443$	−18.8725	−	18.8725i	−0.896659	−	0.896659i	−0.995139	+	0.0984802i	$0.968602\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	11.0277	+	11.0277i	0.521591	+	0.521591i
$448$		0			0
$449$			5.54414i			0.261644i	0.991406	+	0.130822i	$0.0417617\pi$
$449$			5.54414i			0.261644i	−0.991406	+	0.130822i	$0.958238\pi$
$450$		0			0
$451$		−	2.23757i		−	0.105363i
$452$		0			0
$453$	−29.0332	+	29.0332i	−1.36410	+	1.36410i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	20.7321	−	20.7321i	0.969806	−	0.969806i	−0.0297514	−	0.999557i	$-0.509472\pi$
$457$	20.7321	−	20.7321i	0.969806	−	0.969806i	0.999557	+	0.0297514i	$0.00947155\pi$
$458$		0			0
$459$		−	36.6586i		−	1.71108i
$460$		0			0
$461$		−	19.0221i		−	0.885950i	−0.896534	−	0.442975i	$-0.853923\pi$
$461$		−	19.0221i		−	0.885950i	0.896534	−	0.442975i	$-0.146077\pi$
$462$		0			0
$463$	14.5483	+	14.5483i	0.676115	+	0.676115i	0.959119	−	0.283004i	$-0.0913309\pi$
$463$	14.5483	+	14.5483i	0.676115	+	0.676115i	−0.283004	+	0.959119i	$0.591331\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−6.09112	−	6.09112i	−0.281863	−	0.281863i	0.551989	−	0.833852i	$-0.313869\pi$
$467$	−6.09112	−	6.09112i	−0.281863	−	0.281863i	−0.833852	+	0.551989i	$0.813869\pi$
$468$		0			0
$469$	5.49092	−	7.53381i	0.253547	−	0.347879i
$470$		0			0
$471$	11.8310			0.545143
$472$		0			0
$473$	−1.86067	−	1.86067i	−0.0855538	−	0.0855538i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−41.3684	+	41.3684i	−1.89413	+	1.89413i
$478$		0			0
$479$	−17.2499			−0.788169			−0.394085	−	0.919074i	$-0.628938\pi$
$479$	−17.2499			−0.788169			−0.394085	+	0.919074i	$0.628938\pi$
$480$		0			0
$481$		−	47.4691i		−	2.16440i
$482$		0			0
$483$	−23.5734	+	3.69742i	−1.07263	+	0.168239i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.7915	−	19.7915i	0.896839	−	0.896839i	−0.0983164	−	0.995155i	$-0.531346\pi$
$487$	19.7915	−	19.7915i	0.896839	−	0.896839i	0.995155	+	0.0983164i	$0.0313457\pi$
$488$		0			0
$489$	−67.0530			−3.03224
$490$		0			0
$491$	38.8114			1.75153			0.875767	−	0.482735i	$-0.160357\pi$
$491$	38.8114			1.75153			0.875767	+	0.482735i	$0.160357\pi$
$492$		0			0
$493$	25.4116	−	25.4116i	1.14448	−	1.14448i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.67874	+	1.20439i	−0.344439	+	0.0540242i
$498$		0			0
$499$			8.21748i			0.367865i	0.982939	+	0.183932i	$0.0588828\pi$
$499$			8.21748i			0.367865i	−0.982939	+	0.183932i	$0.941117\pi$
$500$		0			0
$501$	−20.5212			−0.916818
$502$		0			0
$503$	−13.7880	+	13.7880i	−0.614775	+	0.614775i	−0.944187	−	0.329411i	$-0.893150\pi$
$503$	−13.7880	+	13.7880i	−0.614775	+	0.614775i	0.329411	+	0.944187i	$0.393150\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	17.6144	+	17.6144i	0.782282	+	0.782282i
$508$		0			0
$509$	−3.30389			−0.146442			−0.0732212	−	0.997316i	$-0.523328\pi$
$509$	−3.30389			−0.146442			−0.0732212	+	0.997316i	$0.523328\pi$
$510$		0			0
$511$	−10.8802	+	14.9281i	−0.481311	+	0.660382i
$512$		0			0
$513$	16.7077	+	16.7077i	0.737663	+	0.737663i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.26387	+	3.26387i	0.143545	+	0.143545i
$518$		0			0
$519$			45.8272i			2.01159i
$520$		0			0
$521$			17.8887i			0.783717i	0.920025	+	0.391859i	$0.128168\pi$
$521$			17.8887i			0.783717i	−0.920025	+	0.391859i	$0.871832\pi$
$522$		0			0
$523$	8.57838	−	8.57838i	0.375106	−	0.375106i	−0.494227	−	0.869333i	$-0.664549\pi$
$523$	8.57838	−	8.57838i	0.375106	−	0.375106i	0.869333	+	0.494227i	$0.164549\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.16020	−	9.16020i	0.399025	−	0.399025i
$528$		0			0
$529$		−	14.3105i		−	0.622194i
$530$		0			0
$531$			72.5149i			3.14688i
$532$		0			0
$533$	9.13701	+	9.13701i	0.395768	+	0.395768i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−39.1318	−	39.1318i	−1.68866	−	1.68866i
$538$		0			0
$539$	5.30587	−	1.70640i	0.228540	−	0.0734998i
$540$		0			0
$541$	9.47422			0.407328			0.203664	−	0.979041i	$-0.434715\pi$
$541$	9.47422			0.407328			0.203664	+	0.979041i	$0.434715\pi$
$542$		0			0
$543$	−30.3498	−	30.3498i	−1.30243	−	1.30243i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.34561	+	7.34561i	−0.314076	+	0.314076i	−0.846486	−	0.532411i	$-0.821286\pi$
$547$	−7.34561	+	7.34561i	−0.314076	+	0.314076i	0.532411	+	0.846486i	$0.321286\pi$
$548$		0			0
$549$	21.3680			0.911965
$550$		0			0
$551$			23.1635i			0.986798i
$552$		0			0
$553$	2.67799	+	17.0739i	0.113880	+	0.726056i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.79776	+	8.79776i	−0.372773	+	0.372773i	−0.868486	−	0.495713i	$-0.834907\pi$
$557$	−8.79776	+	8.79776i	−0.372773	+	0.372773i	0.495713	+	0.868486i	$0.334907\pi$
$558$		0			0
$559$	15.1959			0.642718
$560$		0			0
$561$	8.68525			0.366692
$562$		0			0
$563$	2.78671	−	2.78671i	0.117446	−	0.117446i	−0.645941	−	0.763387i	$-0.723535\pi$
$563$	2.78671	−	2.78671i	0.117446	−	0.117446i	0.763387	+	0.645941i	$0.223535\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−32.3483	+	5.07373i	−1.35850	+	0.213077i
$568$		0			0
$569$			0.247978i			0.0103958i	0.999986	+	0.00519788i	$0.00165455\pi$
$569$			0.247978i			0.0103958i	−0.999986	+	0.00519788i	$0.998345\pi$
$570$		0			0
$571$	−39.7125			−1.66192			−0.830959	−	0.556334i	$-0.812208\pi$
$571$	−39.7125			−1.66192			−0.830959	+	0.556334i	$0.812208\pi$
$572$		0			0
$573$	−11.6626	+	11.6626i	−0.487212	+	0.487212i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	28.2036	+	28.2036i	1.17413	+	1.17413i	0.981215	+	0.192916i	$0.0617945\pi$
$577$	28.2036	+	28.2036i	1.17413	+	1.17413i	0.192916	+	0.981215i	$0.438205\pi$
$578$		0			0
$579$	−15.8364			−0.658136
$580$		0			0
$581$	−2.53062	+	3.47213i	−0.104988	+	0.144048i
$582$		0			0
$583$	−5.17842	−	5.17842i	−0.214468	−	0.214468i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−24.6383	−	24.6383i	−1.01693	−	1.01693i	−0.999854	−	0.0170778i	$-0.994564\pi$
$587$	−24.6383	−	24.6383i	−1.01693	−	1.01693i	−0.0170778	−	0.999854i	$-0.505436\pi$
$588$		0			0
$589$			8.34981i			0.344048i
$590$		0			0
$591$			39.6483i			1.63091i
$592$		0			0
$593$	29.6964	−	29.6964i	1.21948	−	1.21948i	0.251670	−	0.967813i	$-0.419020\pi$
$593$	29.6964	−	29.6964i	1.21948	−	1.21948i	0.967813	−	0.251670i	$-0.0809798\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	34.4579	−	34.4579i	1.41027	−	1.41027i
$598$		0			0
$599$		−	28.4830i		−	1.16378i	−0.813267	−	0.581891i	$-0.802313\pi$
$599$		−	28.4830i		−	1.16378i	0.813267	−	0.581891i	$-0.197687\pi$
$600$		0			0
$601$			11.7809i			0.480555i	0.970704	+	0.240277i	$0.0772384\pi$
$601$			11.7809i			0.480555i	−0.970704	+	0.240277i	$0.922762\pi$
$602$		0			0
$603$	−15.8478	−	15.8478i	−0.645372	−	0.645372i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	28.0405	+	28.0405i	1.13813	+	1.13813i	0.988785	+	0.149344i	$0.0477161\pi$
$607$	28.0405	+	28.0405i	1.13813	+	1.13813i	0.149344	+	0.988785i	$0.452284\pi$
$608$		0			0
$609$	−65.9379	−	48.0579i	−2.67194	−	1.94741i
$610$		0			0
$611$	−26.6557			−1.07837
$612$		0			0
$613$	−28.8251	−	28.8251i	−1.16423	−	1.16423i	−0.983539	−	0.180695i	$-0.942165\pi$
$613$	−28.8251	−	28.8251i	−1.16423	−	1.16423i	−0.180695	−	0.983539i	$-0.557835\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.96881	+	6.96881i	−0.280554	+	0.280554i	−0.833330	−	0.552776i	$-0.813568\pi$
$617$	−6.96881	+	6.96881i	−0.280554	+	0.280554i	0.552776	+	0.833330i	$0.313568\pi$
$618$		0			0
$619$	20.2636			0.814464			0.407232	−	0.913325i	$-0.366494\pi$
$619$	20.2636			0.814464			0.407232	+	0.913325i	$0.366494\pi$
$620$		0			0
$621$			30.3093i			1.21627i
$622$		0			0
$623$	−36.8411	+	5.77841i	−1.47601	+	0.231507i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.95844	+	3.95844i	−0.158085	+	0.158085i
$628$		0			0
$629$	36.8075			1.46761
$630$		0			0
$631$	2.95896			0.117794			0.0588972	−	0.998264i	$-0.481242\pi$
$631$	2.95896			0.117794			0.0588972	+	0.998264i	$0.481242\pi$
$632$		0			0
$633$	−9.09457	+	9.09457i	−0.361477	+	0.361477i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−14.6982	+	28.6342i	−0.582365	+	1.13453i
$638$		0			0
$639$			18.6862i			0.739213i
$640$		0			0
$641$	23.8186			0.940776			0.470388	−	0.882460i	$-0.344114\pi$
$641$	23.8186			0.940776			0.470388	+	0.882460i	$0.344114\pi$
$642$		0			0
$643$	25.3400	−	25.3400i	0.999312	−	0.999312i	−0.000687568	−	1.00000i	$-0.500219\pi$
$643$	25.3400	−	25.3400i	0.999312	−	0.999312i	1.00000		0.000687568i	$0.000218860\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.4265	+	16.4265i	0.645792	+	0.645792i	0.951973	−	0.306181i	$-0.0990513\pi$
$647$	16.4265	+	16.4265i	0.645792	+	0.645792i	−0.306181	+	0.951973i	$0.599051\pi$
$648$		0			0
$649$	−9.07729			−0.356315
$650$		0			0
$651$	−23.7688	−	17.3236i	−0.931573	−	0.678965i
$652$		0			0
$653$	22.4103	+	22.4103i	0.876984	+	0.876984i	0.993221	−	0.116237i	$-0.0370833\pi$
$653$	22.4103	+	22.4103i	0.876984	+	0.876984i	−0.116237	+	0.993221i	$0.537083\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	31.4022	+	31.4022i	1.22512	+	1.22512i
$658$		0			0
$659$		−	45.0537i		−	1.75504i	−0.479537	−	0.877521i	$-0.659195\pi$
$659$		−	45.0537i		−	1.75504i	0.479537	−	0.877521i	$-0.340805\pi$
$660$		0			0
$661$			28.5466i			1.11033i	0.831739	+	0.555167i	$0.187345\pi$
$661$			28.5466i			1.11033i	−0.831739	+	0.555167i	$0.812655\pi$
$662$		0			0
$663$	−35.4658	+	35.4658i	−1.37738	+	1.37738i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.0103	+	21.0103i	−0.813522	+	0.813522i
$668$		0			0
$669$			38.0503i			1.47111i
$670$		0			0
$671$			2.67481i			0.103260i
$672$		0			0
$673$	−1.86064	−	1.86064i	−0.0717223	−	0.0717223i	0.670336	−	0.742058i	$-0.266150\pi$
$673$	−1.86064	−	1.86064i	−0.0717223	−	0.0717223i	−0.742058	+	0.670336i	$0.766150\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.24734	+	2.24734i	0.0863723	+	0.0863723i	0.748973	−	0.662601i	$-0.230547\pi$
$677$	2.24734	+	2.24734i	0.0863723	+	0.0863723i	−0.662601	+	0.748973i	$0.730547\pi$
$678$		0			0
$679$	−13.0229	−	9.49157i	−0.499773	−	0.364253i
$680$		0			0
$681$	55.9313			2.14329
$682$		0			0
$683$	23.1882	+	23.1882i	0.887271	+	0.887271i	0.994260	−	0.106989i	$-0.0341210\pi$
$683$	23.1882	+	23.1882i	0.887271	+	0.887271i	−0.106989	+	0.994260i	$0.534121\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−33.0821	+	33.0821i	−1.26216	+	1.26216i
$688$		0			0
$689$	42.2916			1.61118
$690$		0			0
$691$			26.5659i			1.01061i	0.862940	+	0.505307i	$0.168621\pi$
$691$			26.5659i			1.01061i	−0.862940	+	0.505307i	$0.831379\pi$
$692$		0			0
$693$	−2.07626	−	13.2375i	−0.0788704	−	0.502849i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−7.08484	+	7.08484i	−0.268357	+	0.268357i
$698$		0			0
$699$	−29.8155			−1.12772
$700$		0			0
$701$	24.7343			0.934201			0.467100	−	0.884204i	$-0.345299\pi$
$701$	24.7343			0.934201			0.467100	+	0.884204i	$0.345299\pi$
$702$		0			0
$703$	−16.7756	+	16.7756i	−0.632704	+	0.632704i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.77405	−	30.4376i	−0.179547	−	1.14473i
$708$		0			0
$709$			2.16805i			0.0814230i	0.999171	+	0.0407115i	$0.0129625\pi$
$709$			2.16805i			0.0814230i	−0.999171	+	0.0407115i	$0.987038\pi$
$710$		0			0
$711$	41.5492			1.55822
$712$		0			0
$713$	−7.57364	+	7.57364i	−0.283635	+	0.283635i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.53781	+	9.53781i	0.356196	+	0.356196i
$718$		0			0
$719$	−39.9675			−1.49054			−0.745269	−	0.666764i	$-0.767679\pi$
$719$	−39.9675			−1.49054			−0.745269	+	0.666764i	$0.767679\pi$
$720$		0			0
$721$	7.80772	−	10.7126i	0.290775	−	0.398957i
$722$		0			0
$723$	−21.2596	−	21.2596i	−0.790654	−	0.790654i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	10.2654	+	10.2654i	0.380722	+	0.380722i	0.871362	−	0.490641i	$-0.163237\pi$
$727$	10.2654	+	10.2654i	0.380722	+	0.380722i	−0.490641	+	0.871362i	$0.663237\pi$
$728$		0			0
$729$		−	15.6545i		−	0.579798i
$730$		0			0
$731$			11.7829i			0.435806i
$732$		0			0
$733$	−34.1656	+	34.1656i	−1.26194	+	1.26194i	−0.311781	+	0.950154i	$0.600926\pi$
$733$	−34.1656	+	34.1656i	−1.26194	+	1.26194i	−0.950154	+	0.311781i	$0.899074\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.98380	−	1.98380i	0.0730742	−	0.0730742i
$738$		0			0
$739$		−	27.7193i		−	1.01967i	−0.860272	−	0.509835i	$-0.829707\pi$
$739$		−	27.7193i		−	1.01967i	0.860272	−	0.509835i	$-0.170293\pi$
$740$		0			0
$741$		−	32.3281i		−	1.18760i
$742$		0			0
$743$	−18.8434	−	18.8434i	−0.691299	−	0.691299i	0.271219	−	0.962518i	$-0.412573\pi$
$743$	−18.8434	−	18.8434i	−0.691299	−	0.691299i	−0.962518	+	0.271219i	$0.912573\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.30382	+	7.30382i	0.267233	+	0.267233i
$748$		0			0
$749$	20.3035	−	27.8574i	0.741875	−	1.01789i
$750$		0			0
$751$	−3.96211			−0.144580			−0.0722898	−	0.997384i	$-0.523031\pi$
$751$	−3.96211			−0.144580			−0.0722898	+	0.997384i	$0.523031\pi$
$752$		0			0
$753$	1.56451	+	1.56451i	0.0570139	+	0.0570139i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	12.4177	−	12.4177i	0.451328	−	0.451328i	−0.444467	−	0.895795i	$-0.646607\pi$
$757$	12.4177	−	12.4177i	0.451328	−	0.451328i	0.895795	+	0.444467i	$0.146607\pi$
$758$		0			0
$759$	−7.18096			−0.260652
$760$		0			0
$761$		−	18.1007i		−	0.656148i	−0.944652	−	0.328074i	$-0.893600\pi$
$761$		−	18.1007i		−	0.656148i	0.944652	−	0.328074i	$-0.106400\pi$
$762$		0			0
$763$	2.46607	+	15.7228i	0.0892779	+	0.569204i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.0666	−	37.0666i	1.33840	−	1.33840i
$768$		0			0
$769$	21.5274			0.776299			0.388149	−	0.921596i	$-0.373114\pi$
$769$	21.5274			0.776299			0.388149	+	0.921596i	$0.373114\pi$
$770$		0			0
$771$	−27.3480			−0.984915
$772$		0			0
$773$	12.4318	−	12.4318i	0.447143	−	0.447143i	−0.447261	−	0.894403i	$-0.647600\pi$
$773$	12.4318	−	12.4318i	0.447143	−	0.447143i	0.894403	+	0.447261i	$0.147600\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−12.9491	−	82.5587i	−0.464546	−	2.96178i
$778$		0			0
$779$		−	6.45805i		−	0.231384i
$780$		0			0
$781$	−2.33910			−0.0836997
$782$		0			0
$783$	−73.2843	+	73.2843i	−2.61897	+	2.61897i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	23.9985	+	23.9985i	0.855455	+	0.855455i	0.990799	−	0.135343i	$-0.0432138\pi$
$787$	23.9985	+	23.9985i	0.855455	+	0.855455i	−0.135343	+	0.990799i	$0.543214\pi$
$788$		0			0
$789$	26.9454			0.959283
$790$		0			0
$791$	−10.7767	−	7.85444i	−0.383174	−	0.279272i
$792$		0			0
$793$	−10.9225	−	10.9225i	−0.387868	−	0.387868i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	14.6111	+	14.6111i	0.517552	+	0.517552i	0.916830	−	0.399278i	$-0.130739\pi$
$797$	14.6111	+	14.6111i	0.517552	+	0.517552i	−0.399278	+	0.916830i	$0.630739\pi$
$798$		0			0
$799$		−	20.6688i		−	0.731210i
$800$		0			0
$801$			89.6525i			3.16772i
$802$		0			0
$803$	−3.93087	+	3.93087i	−0.138718	+	0.138718i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.75173	−	6.75173i	0.237672	−	0.237672i
$808$		0			0
$809$		−	10.5234i		−	0.369983i	−0.982740	−	0.184991i	$-0.940774\pi$
$809$		−	10.5234i		−	0.369983i	0.982740	−	0.184991i	$-0.0592258\pi$
$810$		0			0
$811$		−	30.8109i		−	1.08192i	−0.841050	−	0.540958i	$-0.818062\pi$
$811$		−	30.8109i		−	1.08192i	0.841050	−	0.540958i	$-0.181938\pi$
$812$		0			0
$813$	−11.1952	−	11.1952i	−0.392633	−	0.392633i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.37024	−	5.37024i	−0.187881	−	0.187881i
$818$		0			0
$819$	62.5327	+	45.5761i	2.18507	+	1.59256i
$820$		0			0
$821$	5.63075			0.196515			0.0982573	−	0.995161i	$-0.468673\pi$
$821$	5.63075			0.196515			0.0982573	+	0.995161i	$0.468673\pi$
$822$		0			0
$823$	32.8777	+	32.8777i	1.14604	+	1.14604i	0.987324	+	0.158720i	$0.0507368\pi$
$823$	32.8777	+	32.8777i	1.14604	+	1.14604i	0.158720	+	0.987324i	$0.449263\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.06998	−	4.06998i	0.141527	−	0.141527i	−0.632794	−	0.774321i	$-0.718092\pi$
$827$	4.06998	−	4.06998i	0.141527	−	0.141527i	0.774321	+	0.632794i	$0.218092\pi$
$828$		0			0
$829$	−25.8830			−0.898955			−0.449478	−	0.893292i	$-0.648390\pi$
$829$	−25.8830			−0.898955			−0.449478	+	0.893292i	$0.648390\pi$
$830$		0			0
$831$		−	81.8922i		−	2.84081i
$832$		0			0
$833$	−22.2030	−	11.3970i	−0.769287	−	0.394883i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−26.4170	+	26.4170i	−0.913105	+	0.913105i
$838$		0			0
$839$	17.6763			0.610253			0.305126	−	0.952312i	$-0.401301\pi$
$839$	17.6763			0.610253			0.305126	+	0.952312i	$0.401301\pi$
$840$		0			0
$841$	−72.6011			−2.50348
$842$		0			0
$843$	22.2064	−	22.2064i	0.764830	−	0.764830i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−27.0947	+	4.24973i	−0.930985	+	0.146022i
$848$		0			0
$849$		−	100.863i		−	3.46162i
$850$		0			0
$851$	−30.4324			−1.04321
$852$		0			0
$853$	40.0308	−	40.0308i	1.37063	−	1.37063i	0.511117	−	0.859511i	$-0.329232\pi$
$853$	40.0308	−	40.0308i	1.37063	−	1.37063i	0.859511	−	0.511117i	$-0.170768\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.8266	+	30.8266i	1.05302	+	1.05302i	0.998514	+	0.0545034i	$0.0173576\pi$
$857$	30.8266	+	30.8266i	1.05302	+	1.05302i	0.0545034	+	0.998514i	$0.482642\pi$
$858$		0			0
$859$	46.9929			1.60338			0.801689	−	0.597741i	$-0.203935\pi$
$859$	46.9929			1.60338			0.801689	+	0.597741i	$0.203935\pi$
$860$		0			0
$861$	18.3837	+	13.3987i	0.626514	+	0.456626i
$862$		0			0
$863$	22.4965	+	22.4965i	0.765789	+	0.765789i	0.977362	−	0.211573i	$-0.0678586\pi$
$863$	22.4965	+	22.4965i	0.765789	+	0.765789i	−0.211573	+	0.977362i	$0.567859\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.27776	+	9.27776i	0.315089	+	0.315089i
$868$		0			0
$869$			5.20106i			0.176434i
$870$		0			0
$871$			16.2015i			0.548966i
$872$		0			0
$873$	−27.3944	+	27.3944i	−0.927160	+	0.927160i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−19.0005	+	19.0005i	−0.641602	+	0.641602i	−0.950949	−	0.309347i	$-0.899890\pi$
$877$	−19.0005	+	19.0005i	−0.641602	+	0.641602i	0.309347	+	0.950949i	$0.399890\pi$
$878$		0			0
$879$			32.6100i			1.09991i
$880$		0			0
$881$		−	18.8855i		−	0.636268i	−0.948046	−	0.318134i	$-0.896944\pi$
$881$		−	18.8855i		−	0.636268i	0.948046	−	0.318134i	$-0.103056\pi$
$882$		0			0
$883$	−2.94189	−	2.94189i	−0.0990023	−	0.0990023i	0.655871	−	0.754873i	$-0.272302\pi$
$883$	−2.94189	−	2.94189i	−0.0990023	−	0.0990023i	−0.754873	+	0.655871i	$0.772302\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.662275	+	0.662275i	0.0222370	+	0.0222370i	0.718138	−	0.695901i	$-0.244995\pi$
$887$	0.662275	+	0.662275i	0.0222370	+	0.0222370i	−0.695901	+	0.718138i	$0.744995\pi$
$888$		0			0
$889$	−31.4300	+	43.1235i	−1.05413	+	1.44632i
$890$		0			0
$891$	−9.85394			−0.330120
$892$		0			0
$893$	9.42013	+	9.42013i	0.315233	+	0.315233i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	29.3230	−	29.3230i	0.979068	−	0.979068i
$898$		0			0
$899$	−36.6244			−1.22149
$900$		0			0
$901$			32.7929i			1.09249i
$902$		0			0
$903$	26.4289	−	4.14529i	0.879498	−	0.137947i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−32.0100	+	32.0100i	−1.06288	+	1.06288i	−0.0649902	+	0.997886i	$0.520702\pi$
$907$	−32.0100	+	32.0100i	−1.06288	+	1.06288i	−0.997886	+	0.0649902i	$0.979298\pi$
$908$		0			0
$909$	−74.0698			−2.45674
$910$		0			0
$911$	−42.6612			−1.41343			−0.706714	−	0.707499i	$-0.749823\pi$
$911$	−42.6612			−1.41343			−0.706714	+	0.707499i	$0.749823\pi$
$912$		0			0
$913$	−0.914280	+	0.914280i	−0.0302583	+	0.0302583i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.37869	+	21.5413i	0.111574	+	0.711357i
$918$		0			0
$919$			30.3500i			1.00115i	0.865692	+	0.500577i	$0.166879\pi$
$919$			30.3500i			1.00115i	−0.865692	+	0.500577i	$0.833121\pi$
$920$		0			0
$921$	−22.0505			−0.726589
$922$		0			0
$923$	9.55160	−	9.55160i	0.314395	−	0.314395i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−22.5345	−	22.5345i	−0.740130	−	0.740130i
$928$		0			0
$929$	−16.7434			−0.549334			−0.274667	−	0.961539i	$-0.588568\pi$
$929$	−16.7434			−0.549334			−0.274667	+	0.961539i	$0.588568\pi$
$930$		0			0
$931$	15.3137	−	4.92498i	0.501887	−	0.161410i
$932$		0			0
$933$	−19.2113	−	19.2113i	−0.628951	−	0.628951i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	31.0760	+	31.0760i	1.01521	+	1.01521i	0.999883	+	0.0153259i	$0.00487859\pi$
$937$	31.0760	+	31.0760i	1.01521	+	1.01521i	0.0153259	+	0.999883i	$0.495121\pi$
$938$		0			0
$939$			28.1269i			0.917886i
$940$		0			0
$941$		−	45.0141i		−	1.46742i	−0.679464	−	0.733709i	$-0.737788\pi$
$941$		−	45.0141i		−	1.46742i	0.679464	−	0.733709i	$-0.262212\pi$
$942$		0			0
$943$	5.85773	−	5.85773i	0.190754	−	0.190754i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.7267	+	18.7267i	−0.608535	+	0.608535i	−0.942563	−	0.334028i	$-0.891592\pi$
$947$	−18.7267	+	18.7267i	−0.608535	+	0.608535i	0.334028	+	0.942563i	$0.391592\pi$
$948$		0			0
$949$		−	32.1030i		−	1.04211i
$950$		0			0
$951$		−	16.7773i		−	0.544042i
$952$		0			0
$953$	3.06721	+	3.06721i	0.0993566	+	0.0993566i	0.755038	−	0.655681i	$-0.227618\pi$
$953$	3.06721	+	3.06721i	0.0993566	+	0.0993566i	−0.655681	+	0.755038i	$0.727618\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−17.3627	−	17.3627i	−0.561258	−	0.561258i
$958$		0			0
$959$	−12.7739	+	17.5264i	−0.412490	+	0.565956i
$960$		0			0
$961$	17.7979			0.574126
$962$		0			0
$963$	−58.5997	−	58.5997i	−1.88835	−	1.88835i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	20.0904	−	20.0904i	0.646063	−	0.646063i	−0.305976	−	0.952039i	$-0.598983\pi$
$967$	20.0904	−	20.0904i	0.646063	−	0.646063i	0.952039	+	0.305976i	$0.0989828\pi$
$968$		0			0
$969$	25.0672			0.805276
$970$		0			0
$971$		−	43.8425i		−	1.40697i	−0.710708	−	0.703487i	$-0.751625\pi$
$971$		−	43.8425i		−	1.40697i	0.710708	−	0.703487i	$-0.248375\pi$
$972$		0			0
$973$	−20.6441	+	3.23797i	−0.661820	+	0.103804i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.5360	+	25.5360i	−0.816968	+	0.816968i	−0.985667	−	0.168700i	$-0.946043\pi$
$977$	−25.5360	+	25.5360i	−0.816968	+	0.816968i	0.168700	+	0.985667i	$0.446043\pi$
$978$		0			0
$979$	−11.2225			−0.358674
$980$		0			0
$981$	38.2613			1.22159
$982$		0			0
$983$	13.5331	−	13.5331i	0.431639	−	0.431639i	−0.457547	−	0.889186i	$-0.651272\pi$
$983$	13.5331	−	13.5331i	0.431639	−	0.431639i	0.889186	+	0.457547i	$0.151272\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−46.3598	+	7.27140i	−1.47565	+	0.231451i
$988$		0			0
$989$		−	9.74209i		−	0.309780i
$990$		0			0
$991$	−16.6536			−0.529019			−0.264510	−	0.964383i	$-0.585210\pi$
$991$	−16.6536			−0.529019			−0.264510	+	0.964383i	$0.585210\pi$
$992$		0			0
$993$	−14.1984	+	14.1984i	−0.450573	+	0.450573i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−31.7663	−	31.7663i	−1.00605	−	1.00605i	−0.999982	−	0.00606773i	$-0.998069\pi$
$997$	−31.7663	−	31.7663i	−1.00605	−	1.00605i	−0.00606773	−	0.999982i	$-0.501931\pi$
$998$		0			0
$999$	−106.149			−3.35840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.993.2		24
5.2	odd	4	inner	1400.2.x.b.657.11		24
5.3	odd	4		280.2.x.a.97.2	✓	24
5.4	even	2		280.2.x.a.153.11	yes	24
7.6	odd	2	inner	1400.2.x.b.993.11		24
20.3	even	4		560.2.bj.d.97.11		24
20.19	odd	2		560.2.bj.d.433.2		24
35.13	even	4		280.2.x.a.97.11	yes	24
35.27	even	4	inner	1400.2.x.b.657.2		24
35.34	odd	2		280.2.x.a.153.2	yes	24
140.83	odd	4		560.2.bj.d.97.2		24
140.139	even	2		560.2.bj.d.433.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.2	✓	24	5.3	odd	4
280.2.x.a.97.11	yes	24	35.13	even	4
280.2.x.a.153.2	yes	24	35.34	odd	2
280.2.x.a.153.11	yes	24	5.4	even	2
560.2.bj.d.97.2		24	140.83	odd	4
560.2.bj.d.97.11		24	20.3	even	4
560.2.bj.d.433.2		24	20.19	odd	2
560.2.bj.d.433.11		24	140.139	even	2
1400.2.x.b.657.2		24	35.27	even	4	inner
1400.2.x.b.657.11		24	5.2	odd	4	inner
1400.2.x.b.993.2		24	1.1	even	1	trivial
1400.2.x.b.993.11		24	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16341 + 2.16341i) q^{3} +(2.61380 - 0.409966i) q^{7} -6.36066i q^{9} +O(q^{10})\)	\(q+(-2.16341 + 2.16341i) q^{3} +(2.61380 - 0.409966i) q^{7} -6.36066i q^{9} +0.796216 q^{11} +(-3.25130 + 3.25130i) q^{13} +(-2.52106 - 2.52106i) q^{17} +2.29803 q^{19} +(-4.76778 + 6.54163i) q^{21} +(2.08441 + 2.08441i) q^{23} +(7.27046 + 7.27046i) q^{27} +10.0797i q^{29} +3.63347i q^{31} +(-1.72254 + 1.72254i) q^{33} +(-7.30001 + 7.30001i) q^{37} -14.0678i q^{39} -2.81026i q^{41} +(-2.33689 - 2.33689i) q^{43} +(4.09923 + 4.09923i) q^{47} +(6.66386 - 2.14314i) q^{49} +10.9082 q^{51} +(-6.50379 - 6.50379i) q^{53} +(-4.97156 + 4.97156i) q^{57} -11.4005 q^{59} +3.35941i q^{61} +(-2.60765 - 16.6255i) q^{63} +(2.49153 - 2.49153i) q^{67} -9.01885 q^{69} -2.93777 q^{71} +(-4.93694 + 4.93694i) q^{73} +(2.08115 - 0.326422i) q^{77} +6.53223i q^{79} -12.3760 q^{81} +(-1.14828 + 1.14828i) q^{83} +(-21.8066 - 21.8066i) q^{87} -14.0949 q^{89} +(-7.16532 + 9.83117i) q^{91} +(-7.86067 - 7.86067i) q^{93} +(-4.30685 - 4.30685i) q^{97} -5.06446i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

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