LMFDB - Embedded newform 756.2.bb.a.611.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.11
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07292 - 0.921328i) q^{2} +(0.302311 + 1.97702i) q^{4} +(2.48793 - 1.43641i) q^{5} +(-2.33229 + 1.24916i) q^{7} +(1.49713 - 2.39971i) q^{8} +O(q^{10})$	\(q+(-1.07292 - 0.921328i) q^{2} +(0.302311 + 1.97702i) q^{4} +(2.48793 - 1.43641i) q^{5} +(-2.33229 + 1.24916i) q^{7} +(1.49713 - 2.39971i) q^{8} +(-3.99275 - 0.751051i) q^{10} +(-1.76883 + 3.06370i) q^{11} +(-3.15869 + 5.47102i) q^{13} +(3.65325 + 0.808558i) q^{14} +(-3.81722 + 1.19535i) q^{16} +(-3.21678 + 1.85721i) q^{17} +(-1.82312 - 1.05258i) q^{19} +(3.59194 + 4.48445i) q^{20} +(4.72047 - 1.65743i) q^{22} +(-2.74595 - 4.75613i) q^{23} +(1.62654 - 2.81725i) q^{25} +(8.42962 - 2.95977i) q^{26} +(-3.17469 - 4.23336i) q^{28} +(-2.32201 + 1.34061i) q^{29} -0.256752i q^{31} +(5.19687 + 2.23440i) q^{32} +(5.16245 + 0.971075i) q^{34} +(-4.00829 + 6.45796i) q^{35} +(-0.720918 + 1.24867i) q^{37} +(0.986290 + 2.80902i) q^{38} +(0.277792 - 8.12081i) q^{40} +(-5.24333 - 3.02724i) q^{41} +(-4.79832 + 2.77031i) q^{43} +(-6.59172 - 2.57082i) q^{44} +(-1.43577 + 7.63287i) q^{46} -2.04156 q^{47} +(3.87919 - 5.82682i) q^{49} +(-4.34076 + 1.52411i) q^{50} +(-11.7712 - 4.59085i) q^{52} +(-1.96139 + 1.13241i) q^{53} +10.1630i q^{55} +(-0.494120 + 7.46698i) q^{56} +(3.72647 + 0.700962i) q^{58} +7.10847 q^{59} +5.67070 q^{61} +(-0.236553 + 0.275474i) q^{62} +(-3.51721 - 7.18535i) q^{64} +18.1487i q^{65} +7.34613i q^{67} +(-4.64421 - 5.79819i) q^{68} +(10.2505 - 3.23592i) q^{70} +9.04391 q^{71} +(5.86192 + 10.1531i) q^{73} +(1.92392 - 0.675516i) q^{74} +(1.52982 - 3.92255i) q^{76} +(0.298371 - 9.35499i) q^{77} +12.3827i q^{79} +(-7.77997 + 8.45703i) q^{80} +(2.83659 + 8.07880i) q^{82} +(-5.49556 - 9.51858i) q^{83} +(-5.33543 + 9.24123i) q^{85} +(7.70058 + 1.44851i) q^{86} +(4.70382 + 8.83141i) q^{88} +(-7.32424 - 4.22865i) q^{89} +(0.532818 - 16.7057i) q^{91} +(8.57284 - 6.86663i) q^{92} +(2.19043 + 1.88095i) q^{94} -6.04773 q^{95} +(4.95593 + 8.58392i) q^{97} +(-9.53047 + 2.67770i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.07292	−	0.921328i	−0.758668	−	0.651477i
$2$	−1.07292	−	0.921328i	−0.758668	−	0.651477i
$3$		0			0
$3$		0			0
$4$	0.302311	+	1.97702i	0.151155	+	0.988510i
$5$	2.48793	−	1.43641i	1.11264	−	0.642382i	0.173126	−	0.984900i	$-0.444613\pi$
$5$	2.48793	−	1.43641i	1.11264	−	0.642382i	0.939511	+	0.342518i	$0.111280\pi$
$6$		0			0
$7$	−2.33229	+	1.24916i	−0.881524	+	0.472139i
$7$	−2.33229	+	1.24916i	−0.881524	+	0.472139i
$8$	1.49713	−	2.39971i	0.529315	−	0.848425i
$9$		0			0
$10$	−3.99275	−	0.751051i	−1.26262	−	0.237503i
$11$	−1.76883	+	3.06370i	−0.533321	+	0.923739i	0.465922	+	0.884826i	$0.345723\pi$
$11$	−1.76883	+	3.06370i	−0.533321	+	0.923739i	−0.999243	+	0.0389130i	$0.987610\pi$
$12$		0			0
$13$	−3.15869	+	5.47102i	−0.876064	+	1.51739i	−0.0204391	+	0.999791i	$0.506506\pi$
$13$	−3.15869	+	5.47102i	−0.876064	+	1.51739i	−0.855625	+	0.517596i	$0.826827\pi$
$14$	3.65325	+	0.808558i	0.976372	+	0.216096i
$15$		0			0
$16$	−3.81722	+	1.19535i	−0.954304	+	0.298837i
$17$	−3.21678	+	1.85721i	−0.780184	+	0.450440i	−0.836496	−	0.547974i	$-0.815399\pi$
$17$	−3.21678	+	1.85721i	−0.780184	+	0.450440i	0.0563112	+	0.998413i	$0.482066\pi$
$18$		0			0
$19$	−1.82312	−	1.05258i	−0.418252	−	0.241478i	0.276077	−	0.961136i	$-0.410966\pi$
$19$	−1.82312	−	1.05258i	−0.418252	−	0.241478i	−0.694329	+	0.719657i	$0.744299\pi$
$20$	3.59194	+	4.48445i	0.803182	+	1.00275i
$21$		0			0
$22$	4.72047	−	1.65743i	1.00641	−	0.353365i
$23$	−2.74595	−	4.75613i	−0.572571	−	0.991722i	−0.996301	−	0.0859334i	$-0.972613\pi$
$23$	−2.74595	−	4.75613i	−0.572571	−	0.991722i	0.423730	−	0.905789i	$-0.360721\pi$
$24$		0			0
$25$	1.62654	−	2.81725i	0.325308	−	0.563450i
$26$	8.42962	−	2.95977i	1.65319	−	0.580458i
$27$		0			0
$28$	−3.17469	−	4.23336i	−0.599961	−	0.800029i
$29$	−2.32201	+	1.34061i	−0.431186	+	0.248945i	−0.699852	−	0.714288i	$-0.746751\pi$
$29$	−2.32201	+	1.34061i	−0.431186	+	0.248945i	0.268666	+	0.963233i	$0.413417\pi$
$30$		0			0
$31$		−	0.256752i		−	0.0461141i	−0.999734	−	0.0230570i	$-0.992660\pi$
$31$		−	0.256752i		−	0.0461141i	0.999734	−	0.0230570i	$-0.00733993\pi$
$32$	5.19687	+	2.23440i	0.918686	+	0.394989i
$33$		0			0
$34$	5.16245	+	0.971075i	0.885352	+	0.166538i
$35$	−4.00829	+	6.45796i	−0.677524	+	1.09159i
$36$		0			0
$37$	−0.720918	+	1.24867i	−0.118518	+	0.205280i	−0.919181	−	0.393836i	$-0.871148\pi$
$37$	−0.720918	+	1.24867i	−0.118518	+	0.205280i	0.800662	+	0.599116i	$0.204481\pi$
$38$	0.986290	+	2.80902i	0.159997	+	0.455684i
$39$		0			0
$40$	0.277792	−	8.12081i	0.0439227	−	1.28401i
$41$	−5.24333	−	3.02724i	−0.818870	−	0.472775i	0.0311565	−	0.999515i	$-0.490081\pi$
$41$	−5.24333	−	3.02724i	−0.818870	−	0.472775i	−0.850027	+	0.526740i	$0.823414\pi$
$42$		0			0
$43$	−4.79832	+	2.77031i	−0.731737	+	0.422469i	−0.819057	−	0.573712i	$-0.805503\pi$
$43$	−4.79832	+	2.77031i	−0.731737	+	0.422469i	0.0873202	+	0.996180i	$0.472170\pi$
$44$	−6.59172	−	2.57082i	−0.993740	−	0.387565i
$45$		0			0
$46$	−1.43577	+	7.63287i	−0.211693	+	1.12540i
$47$	−2.04156			−0.297792			−0.148896	−	0.988853i	$-0.547572\pi$
$47$	−2.04156			−0.297792			−0.148896	+	0.988853i	$0.547572\pi$
$48$		0			0
$49$	3.87919	−	5.82682i	0.554170	−	0.832403i
$50$	−4.34076	+	1.52411i	−0.613876	+	0.215541i
$51$		0			0
$52$	−11.7712	−	4.59085i	−1.63237	−	0.636637i
$53$	−1.96139	+	1.13241i	−0.269417	+	0.155548i	−0.628623	−	0.777710i	$-0.716381\pi$
$53$	−1.96139	+	1.13241i	−0.269417	+	0.155548i	0.359206	+	0.933258i	$0.383048\pi$
$54$		0			0
$55$			10.1630i			1.37038i
$56$	−0.494120	+	7.46698i	−0.0660295	+	0.997818i
$57$		0			0
$58$	3.72647	+	0.700962i	0.489309	+	0.0920408i
$59$	7.10847			0.925444			0.462722	−	0.886503i	$-0.346873\pi$
$59$	7.10847			0.925444			0.462722	+	0.886503i	$0.346873\pi$
$60$		0			0
$61$	5.67070			0.726059			0.363029	−	0.931778i	$-0.381742\pi$
$61$	5.67070			0.726059			0.363029	+	0.931778i	$0.381742\pi$
$62$	−0.236553	+	0.275474i	−0.0300423	+	0.0349853i
$63$		0			0
$64$	−3.51721	−	7.18535i	−0.439652	−	0.898168i
$65$			18.1487i			2.25107i
$66$		0			0
$67$			7.34613i			0.897472i	0.893664	+	0.448736i	$0.148126\pi$
$67$			7.34613i			0.897472i	−0.893664	+	0.448736i	$0.851874\pi$
$68$	−4.64421	−	5.79819i	−0.563193	−	0.703134i
$69$		0			0
$70$	10.2505	−	3.23592i	1.22516	−	0.386767i
$71$	9.04391			1.07331			0.536657	−	0.843800i	$-0.319687\pi$
$71$	9.04391			1.07331			0.536657	+	0.843800i	$0.319687\pi$
$72$		0			0
$73$	5.86192	+	10.1531i	0.686085	+	1.18833i	0.973094	+	0.230407i	$0.0740057\pi$
$73$	5.86192	+	10.1531i	0.686085	+	1.18833i	−0.287009	+	0.957928i	$0.592661\pi$
$74$	1.92392	−	0.675516i	0.223651	−	0.0785272i
$75$		0			0
$76$	1.52982	−	3.92255i	0.175482	−	0.449947i
$77$	0.298371	−	9.35499i	0.0340025	−	1.06610i
$78$		0			0
$79$			12.3827i			1.39317i	0.717476	+	0.696584i	$0.245298\pi$
$79$			12.3827i			1.39317i	−0.717476	+	0.696584i	$0.754702\pi$
$80$	−7.77997	+	8.45703i	−0.869827	+	0.945525i
$81$		0			0
$82$	2.83659	+	8.07880i	0.313249	+	0.892155i
$83$	−5.49556	−	9.51858i	−0.603216	−	1.04480i	−0.992331	−	0.123611i	$-0.960553\pi$
$83$	−5.49556	−	9.51858i	−0.603216	−	1.04480i	0.389115	−	0.921189i	$-0.372781\pi$
$84$		0			0
$85$	−5.33543	+	9.24123i	−0.578708	+	1.00235i
$86$	7.70058	+	1.44851i	0.830375	+	0.156196i
$87$		0			0
$88$	4.70382	+	8.83141i	0.501429	+	0.941432i
$89$	−7.32424	−	4.22865i	−0.776368	−	0.448236i	0.0587737	−	0.998271i	$-0.481281\pi$
$89$	−7.32424	−	4.22865i	−0.776368	−	0.448236i	−0.835142	+	0.550035i	$0.814614\pi$
$90$		0			0
$91$	0.532818	−	16.7057i	0.0558545	−	1.75124i
$92$	8.57284	−	6.86663i	0.893780	−	0.715896i
$93$		0			0
$94$	2.19043	+	1.88095i	0.225925	+	0.194005i
$95$	−6.04773			−0.620484
$96$		0			0
$97$	4.95593	+	8.58392i	0.503198	+	0.871565i	0.999993	+	0.00369720i	$0.00117686\pi$
$97$	4.95593	+	8.58392i	0.503198	+	0.871565i	−0.496795	+	0.867868i	$0.665490\pi$
$98$	−9.53047	+	2.67770i	−0.962723	+	0.270489i
$99$		0			0
$100$	6.06149	+	2.36402i	0.606149	+	0.236402i
$101$	13.0619	+	7.54132i	1.29971	+	0.750389i	0.980354	−	0.197245i	$-0.0631995\pi$
$101$	13.0619	+	7.54132i	1.29971	+	0.750389i	0.319358	+	0.947634i	$0.396533\pi$
$102$		0			0
$103$	−1.24890	+	0.721050i	−0.123057	+	0.0710472i	−0.560265	−	0.828313i	$-0.689301\pi$
$103$	−1.24890	+	0.721050i	−0.123057	+	0.0710472i	0.437208	+	0.899361i	$0.355967\pi$
$104$	8.39988	+	15.7708i	0.823676	+	1.54645i
$105$		0			0
$106$	3.14773	+	0.592099i	0.305734	+	0.0575097i
$107$	−1.82752	+	3.16536i	−0.176673	+	0.306007i	−0.940739	−	0.339131i	$-0.889867\pi$
$107$	−1.82752	+	3.16536i	−0.176673	+	0.306007i	0.764066	+	0.645138i	$0.223200\pi$
$108$		0			0
$109$	−7.28399	−	12.6162i	−0.697680	−	1.20842i	−0.969269	−	0.246003i	$-0.920883\pi$
$109$	−7.28399	−	12.6162i	−0.697680	−	1.20842i	0.271589	−	0.962413i	$-0.412451\pi$
$110$	9.36348	−	10.9041i	0.892773	−	1.03967i
$111$		0			0
$112$	7.40969	−	7.55622i	0.700150	−	0.713996i
$113$	12.2439	+	7.06904i	1.15181	+	0.664999i	0.949328	−	0.314286i	$-0.101765\pi$
$113$	12.2439	+	7.06904i	1.15181	+	0.664999i	0.202484	+	0.979286i	$0.435099\pi$
$114$		0			0
$115$	−13.6635	−	7.88863i	−1.27413	−	0.735618i
$116$	−3.35238	−	4.18537i	−0.311261	−	0.388602i
$117$		0			0
$118$	−7.62681	−	6.54923i	−0.702105	−	0.602906i
$119$	5.18253	−	8.34984i	0.475082	−	0.765429i
$120$		0			0
$121$	−0.757488	−	1.31201i	−0.0688625	−	0.119273i
$122$	−6.08420	−	5.22457i	−0.550838	−	0.473011i
$123$		0			0
$124$	0.507605	−	0.0776189i	0.0455842	−	0.00697039i
$125$			5.01857i			0.448875i
$126$		0			0
$127$		−	16.9477i		−	1.50386i	−0.659242	−	0.751931i	$-0.729123\pi$
$127$		−	16.9477i		−	1.50386i	0.659242	−	0.751931i	$-0.270877\pi$
$128$	−2.84638	+	10.9498i	−0.251586	+	0.967835i
$129$		0			0
$130$	16.7209	−	19.4721i	1.46652	−	1.70782i
$131$	2.60082	+	4.50475i	0.227235	+	0.393582i	0.956988	−	0.290129i	$-0.0936982\pi$
$131$	2.60082	+	4.50475i	0.227235	+	0.393582i	−0.729753	+	0.683711i	$0.760365\pi$
$132$		0			0
$133$	5.56689	+	0.177552i	0.482711	+	0.0153957i
$134$	6.76819	−	7.88180i	0.584683	−	0.680884i
$135$		0			0
$136$	−0.359172	+	10.4998i	−0.0307987	+	0.900353i
$137$	−11.3449	−	6.54999i	−0.969262	−	0.559604i	−0.0702508	−	0.997529i	$-0.522380\pi$
$137$	−11.3449	−	6.54999i	−0.969262	−	0.559604i	−0.899011	+	0.437926i	$0.855713\pi$
$138$		0			0
$139$	−3.88147	−	2.24097i	−0.329222	−	0.190076i	0.326274	−	0.945275i	$-0.394207\pi$
$139$	−3.88147	−	2.24097i	−0.329222	−	0.190076i	−0.655496	+	0.755199i	$0.727540\pi$
$140$	−13.9793	−	5.97215i	−1.18146	−	0.504739i
$141$		0			0
$142$	−9.70338	−	8.33240i	−0.814290	−	0.699240i
$143$	−11.1744	−	19.3546i	−0.934447	−	1.61851i
$144$		0			0
$145$	−3.85133	+	6.67070i	−0.319836	+	0.553972i
$146$	3.06500	−	16.2942i	0.253662	−	1.34852i
$147$		0			0
$148$	−2.68658	−	1.04778i	−0.220836	−	0.0861273i
$149$	−7.31351	+	4.22246i	−0.599146	+	0.345917i	−0.768706	−	0.639603i	$-0.779099\pi$
$149$	−7.31351	+	4.22246i	−0.599146	+	0.345917i	0.169559	+	0.985520i	$0.445766\pi$
$150$		0			0
$151$	5.44907	+	3.14602i	0.443439	+	0.256020i	0.705055	−	0.709152i	$-0.250922\pi$
$151$	5.44907	+	3.14602i	0.443439	+	0.256020i	−0.261616	+	0.965172i	$0.584256\pi$
$152$	−5.25533	+	2.79911i	−0.426263	+	0.227038i
$153$		0			0
$154$	−8.93914	+	9.76225i	−0.720336	+	0.786664i
$155$	−0.368801	−	0.638783i	−0.0296228	−	0.0513083i
$156$		0			0
$157$	−9.99614			−0.797779			−0.398889	−	0.916999i	$-0.630604\pi$
$157$	−9.99614			−0.797779			−0.398889	+	0.916999i	$0.630604\pi$
$158$	11.4086	−	13.2857i	0.907617	−	1.05695i
$159$		0			0
$160$	16.1390	−	1.90581i	1.27590	−	0.150667i
$161$	12.3455	+	7.66256i	0.972965	+	0.603894i
$162$		0			0
$163$	10.9225	+	6.30608i	0.855513	+	0.493930i	0.862507	−	0.506045i	$-0.168893\pi$
$163$	10.9225	+	6.30608i	0.855513	+	0.493930i	−0.00699437	+	0.999976i	$0.502226\pi$
$164$	4.39979	−	11.2813i	0.343566	−	0.880924i
$165$		0			0
$166$	−2.87345	+	15.2759i	−0.223023	+	1.18564i
$167$	−4.48097	+	7.76126i	−0.346748	+	0.600585i	−0.985670	−	0.168687i	$-0.946047\pi$
$167$	−4.48097	+	7.76126i	−0.346748	+	0.600585i	0.638922	+	0.769272i	$0.279381\pi$
$168$		0			0
$169$	−13.4547	−	23.3042i	−1.03498	−	1.79263i
$170$	14.2387	−	4.99942i	1.09206	−	0.383438i
$171$		0			0
$172$	−6.92755	−	8.64888i	−0.528220	−	0.659471i
$173$		−	6.30433i		−	0.479309i	−0.970858	−	0.239655i	$-0.922966\pi$
$173$		−	6.30433i		−	0.479309i	0.970858	−	0.239655i	$-0.0770342\pi$
$174$		0			0
$175$	−0.274370	+	8.60247i	−0.0207404	+	0.650286i
$176$	3.08981	−	13.8092i	0.232903	−	1.04090i
$177$		0			0
$178$	3.96234	+	11.2850i	0.296990	+	0.845848i
$179$	−7.19492	−	12.4620i	−0.537773	−	0.931451i	−0.999024	−	0.0441806i	$-0.985932\pi$
$179$	−7.19492	−	12.4620i	−0.537773	−	0.931451i	0.461250	−	0.887270i	$-0.347401\pi$
$180$		0			0
$181$	23.8306			1.77132			0.885658	−	0.464338i	$-0.153708\pi$
$181$	23.8306			1.77132			0.885658	+	0.464338i	$0.153708\pi$
$182$	−15.9631	+	17.4330i	−1.18327	+	1.29222i
$183$		0			0
$184$	−15.5244	−	0.531049i	−1.14447	−	0.0391494i
$185$			4.14213i			0.304536i
$186$		0			0
$187$		−	13.1403i		−	0.960916i
$188$	−0.617185	−	4.03620i	−0.0450128	−	0.294370i
$189$		0			0
$190$	6.48873	+	5.57194i	0.470742	+	0.404231i
$191$	−5.49898			−0.397892			−0.198946	−	0.980010i	$-0.563752\pi$
$191$	−5.49898			−0.397892			−0.198946	+	0.980010i	$0.563752\pi$
$192$		0			0
$193$	−12.0441			−0.866957			−0.433478	−	0.901164i	$-0.642714\pi$
$193$	−12.0441			−0.866957			−0.433478	+	0.901164i	$0.642714\pi$
$194$	2.59129	−	13.7759i	0.186044	−	0.989051i
$195$		0			0
$196$	12.6925	+	5.90773i	0.906605	+	0.421981i
$197$		−	11.2108i		−	0.798738i	−0.916790	−	0.399369i	$-0.869229\pi$
$197$		−	11.2108i		−	0.798738i	0.916790	−	0.399369i	$-0.130771\pi$
$198$		0			0
$199$	15.7110	−	9.07074i	1.11372	−	0.643008i	0.173931	−	0.984758i	$-0.444353\pi$
$199$	15.7110	−	9.07074i	1.11372	−	0.643008i	0.939791	+	0.341750i	$0.111020\pi$
$200$	−4.32545	−	8.12102i	−0.305855	−	0.574243i
$201$		0			0
$202$	−7.06638	−	20.1256i	−0.497189	−	1.41603i
$203$	3.74096	−	6.02726i	0.262564	−	0.423031i
$204$		0			0
$205$	−17.3934			−1.21481
$206$	2.00429	+	0.377013i	0.139645	+	0.0262678i
$207$		0			0
$208$	5.51765	−	24.6598i	0.382580	−	1.70985i
$209$	6.44956	−	3.72366i	0.446125	−	0.257571i
$210$		0			0
$211$	1.59074	+	0.918416i	0.109511	+	0.0632264i	0.553755	−	0.832679i	$-0.313194\pi$
$211$	1.59074	+	0.918416i	0.109511	+	0.0632264i	−0.444244	+	0.895906i	$0.646528\pi$
$212$	−2.83174	−	3.53536i	−0.194485	−	0.242810i
$213$		0			0
$214$	4.87712	−	1.71243i	0.333393	−	0.117059i
$215$	−7.95860	+	13.7847i	−0.542772	+	0.940109i
$216$		0			0
$217$	0.320725	+	0.598822i	0.0217722	+	0.0406507i
$218$	−3.80856	+	20.2471i	−0.257948	+	1.37131i
$219$		0			0
$220$	−20.0925	+	3.07239i	−1.35464	+	0.207141i
$221$		−	23.4654i		−	1.57846i
$222$		0			0
$223$	−4.03987	+	2.33242i	−0.270530	+	0.156190i	−0.629128	−	0.777301i	$-0.716588\pi$
$223$	−4.03987	+	2.33242i	−0.270530	+	0.156190i	0.358599	+	0.933492i	$0.383255\pi$
$224$	−14.9118	+	1.28046i	−0.996333	+	0.0855546i
$225$		0			0
$226$	−6.62385	−	18.8652i	−0.440612	−	1.25489i
$227$	−6.60761	+	11.4447i	−0.438563	+	0.759613i	−0.997579	−	0.0695441i	$-0.977846\pi$
$227$	−6.60761	+	11.4447i	−0.438563	+	0.759613i	0.559016	+	0.829157i	$0.311179\pi$
$228$		0			0
$229$	7.59786	+	13.1599i	0.502081	+	0.869630i	0.999997	+	0.00240457i	$0.000765399\pi$
$229$	7.59786	+	13.1599i	0.502081	+	0.869630i	−0.497916	+	0.867225i	$0.665901\pi$
$230$	7.39182	+	21.0524i	0.487402	+	1.38816i
$231$		0			0
$232$	−0.259265	+	7.57921i	−0.0170216	+	0.497599i
$233$	−5.56063	−	3.21043i	−0.364289	−	0.210322i	0.306671	−	0.951815i	$-0.400785\pi$
$233$	−5.56063	−	3.21043i	−0.364289	−	0.210322i	−0.670961	+	0.741493i	$0.734118\pi$
$234$		0			0
$235$	−5.07926	+	2.93251i	−0.331335	+	0.191296i
$236$	2.14897	+	14.0536i	0.139886	+	0.914811i
$237$		0			0
$238$	−13.2534	+	4.18390i	−0.859089	+	0.271202i
$239$	5.51439	−	9.55121i	0.356696	−	0.617816i	−0.630710	−	0.776018i	$-0.717236\pi$
$239$	5.51439	−	9.55121i	0.356696	−	0.617816i	0.987407	+	0.158202i	$0.0505697\pi$
$240$		0			0
$241$	2.06017	−	3.56832i	0.132707	−	0.229855i	−0.792012	−	0.610505i	$-0.790966\pi$
$241$	2.06017	−	3.56832i	0.132707	−	0.229855i	0.924719	+	0.380650i	$0.124300\pi$
$242$	−0.396066	+	2.10557i	−0.0254601	+	0.135351i
$243$		0			0
$244$	1.71431	+	11.2111i	0.109748	+	0.717716i
$245$	1.28147	−	20.0689i	0.0818700	−	1.28215i
$246$		0			0
$247$	11.5174	−	6.64955i	0.732832	−	0.423101i
$248$	−0.616131	−	0.384391i	−0.0391244	−	0.0244089i
$249$		0			0
$250$	4.62375	−	5.38452i	0.292432	−	0.340547i
$251$	12.6369			0.797636			0.398818	−	0.917030i	$-0.369421\pi$
$251$	12.6369			0.797636			0.398818	+	0.917030i	$0.369421\pi$
$252$		0			0
$253$	19.4285			1.22146
$254$	−15.6143	+	18.1835i	−0.979731	+	1.14093i
$255$		0			0
$256$	13.1423	−	9.12581i	0.821393	−	0.570363i
$257$	−14.1631	+	8.17705i	−0.883468	+	0.510070i	−0.871800	−	0.489862i	$-0.837047\pi$
$257$	−14.1631	+	8.17705i	−0.883468	+	0.510070i	−0.0116674	+	0.999932i	$0.503714\pi$
$258$		0			0
$259$	0.121607	−	3.81280i	0.00755627	−	0.236916i
$260$	−35.8804	+	5.48655i	−2.22521	+	0.340261i
$261$		0			0
$262$	1.35988	−	7.22945i	0.0840139	−	0.446637i
$263$	−8.92864	+	15.4649i	−0.550564	+	0.953604i	0.447670	+	0.894199i	$0.352254\pi$
$263$	−8.92864	+	15.4649i	−0.550564	+	0.953604i	−0.998234	+	0.0594057i	$0.981079\pi$
$264$		0			0
$265$	−3.25320	+	5.63471i	−0.199842	+	0.346137i
$266$	−5.80924	−	5.31943i	−0.356187	−	0.326155i
$267$		0			0
$268$	−14.5234	+	2.22081i	−0.887161	+	0.135658i
$269$	−8.25228	+	4.76446i	−0.503150	+	0.290494i	−0.730014	−	0.683433i	$-0.760486\pi$
$269$	−8.25228	+	4.76446i	−0.503150	+	0.290494i	0.226863	+	0.973927i	$0.427153\pi$
$270$		0			0
$271$	1.00748	+	0.581671i	0.0612002	+	0.0353340i	0.530288	−	0.847818i	$-0.322084\pi$
$271$	1.00748	+	0.581671i	0.0612002	+	0.0353340i	−0.469088	+	0.883152i	$0.655417\pi$
$272$	10.0591	−	10.9345i	0.609925	−	0.663004i
$273$		0			0
$274$	6.13749	+	17.4800i	0.370779	+	1.05601i
$275$	5.75414	+	9.96646i	0.346987	+	0.601000i
$276$		0			0
$277$	11.8702	−	20.5598i	0.713212	−	1.23532i	−0.250434	−	0.968134i	$-0.580573\pi$
$277$	11.8702	−	20.5598i	0.713212	−	1.23532i	0.963645	−	0.267185i	$-0.0860935\pi$
$278$	2.09984	+	5.98048i	0.125940	+	0.358685i
$279$		0			0
$280$	9.49631	+	19.2871i	0.567513	+	1.15263i
$281$	−6.09203	+	3.51723i	−0.363420	+	0.209821i	−0.670580	−	0.741837i	$-0.733955\pi$
$281$	−6.09203	+	3.51723i	−0.363420	+	0.209821i	0.307160	+	0.951658i	$0.400621\pi$
$282$		0			0
$283$			19.0379i			1.13168i	0.824514	+	0.565842i	$0.191449\pi$
$283$			19.0379i			1.13168i	−0.824514	+	0.565842i	$0.808551\pi$
$284$	2.73407	+	17.8800i	0.162237	+	1.06098i
$285$		0			0
$286$	−5.84271	+	31.0611i	−0.345486	+	1.83668i
$287$	16.0105	+	0.510644i	0.945069	+	0.0301424i
$288$		0			0
$289$	−1.60154	+	2.77395i	−0.0942082	+	0.163173i
$290$	10.2781	−	3.60879i	0.603549	−	0.211915i
$291$		0			0
$292$	−18.3008	+	14.6585i	−1.07098	+	0.857825i
$293$	13.1105	+	7.56934i	0.765923	+	0.442206i	0.831418	−	0.555647i	$-0.187529\pi$
$293$	13.1105	+	7.56934i	0.765923	+	0.442206i	−0.0654953	+	0.997853i	$0.520863\pi$
$294$		0			0
$295$	17.6854	−	10.2107i	1.02968	−	0.594488i
$296$	1.91713	+	3.59941i	0.111431	+	0.209211i
$297$		0			0
$298$	11.7371	+	2.20779i	0.679910	+	0.127894i
$299$	34.6945			2.00644
$300$		0			0
$301$	7.73053	−	12.4551i	0.445580	−	0.717898i
$302$	−2.94789	−	8.39580i	−0.169632	−	0.483124i
$303$		0			0
$304$	8.21744	+	1.83866i	0.471303	+	0.105454i
$305$	14.1083	−	8.14544i	0.807840	−	0.466407i
$306$		0			0
$307$			14.8488i			0.847463i	0.905788	+	0.423732i	$0.139280\pi$
$307$			14.8488i			0.847463i	−0.905788	+	0.423732i	$0.860720\pi$
$308$	18.5852	−	2.23823i	1.05899	−	0.127535i
$309$		0			0
$310$	−0.192834	+	1.02515i	−0.0109522	+	0.0582246i
$311$	6.46138			0.366391			0.183195	−	0.983077i	$-0.441356\pi$
$311$	6.46138			0.366391			0.183195	+	0.983077i	$0.441356\pi$
$312$		0			0
$313$	−12.2306			−0.691312			−0.345656	−	0.938361i	$-0.612344\pi$
$313$	−12.2306			−0.691312			−0.345656	+	0.938361i	$0.612344\pi$
$314$	10.7250	+	9.20972i	0.605250	+	0.519735i
$315$		0			0
$316$	−24.4809	+	3.74343i	−1.37716	+	0.210585i
$317$		−	20.0298i		−	1.12498i	−0.826803	−	0.562492i	$-0.809843\pi$
$317$		−	20.0298i		−	1.12498i	0.826803	−	0.562492i	$-0.190157\pi$
$318$		0			0
$319$		−	9.48523i		−	0.531071i
$320$	−19.0717	−	12.8245i	−1.06614	−	0.716912i
$321$		0			0
$322$	−6.18605	−	19.5956i	−0.344735	−	1.09202i
$323$	7.81944			0.435085
$324$		0			0
$325$	10.2755	+	17.7977i	0.569982	+	0.987237i
$326$	−5.90894	−	16.8291i	−0.327266	−	0.932076i
$327$		0			0
$328$	−15.1144	+	8.05030i	−0.834555	+	0.444504i
$329$	4.76152	−	2.55024i	0.262511	−	0.140599i
$330$		0			0
$331$		−	27.5156i		−	1.51240i	−0.654343	−	0.756198i	$-0.727055\pi$
$331$		−	27.5156i		−	1.51240i	0.654343	−	0.756198i	$-0.272945\pi$
$332$	17.1571	−	13.7424i	0.941616	−	0.754212i
$333$		0			0
$334$	11.9584	−	4.19877i	0.654334	−	0.229746i
$335$	10.5520	+	18.2767i	0.576520	+	0.998562i
$336$		0			0
$337$	7.03073	−	12.1776i	0.382988	−	0.663355i	−0.608500	−	0.793554i	$-0.708228\pi$
$337$	7.03073	−	12.1776i	0.382988	−	0.663355i	0.991488	+	0.130199i	$0.0415616\pi$
$338$	−7.03502	+	37.3997i	−0.382655	+	2.03428i
$339$		0			0
$340$	−19.8831	−	7.75453i	−1.07831	−	0.420548i
$341$	0.786611	+	0.454150i	0.0425974	+	0.0245936i
$342$		0			0
$343$	−1.76877	+	18.4356i	−0.0955048	+	0.995429i
$344$	−0.535760	+	15.6621i	−0.0288862	+	0.844443i
$345$		0			0
$346$	−5.80835	+	6.76404i	−0.312259	+	0.363637i
$347$	−16.8286			−0.903404			−0.451702	−	0.892169i	$-0.649183\pi$
$347$	−16.8286			−0.903404			−0.451702	+	0.892169i	$0.649183\pi$
$348$		0			0
$349$	0.669636	+	1.15984i	0.0358448	+	0.0620850i	0.883391	−	0.468636i	$-0.155254\pi$
$349$	0.669636	+	1.15984i	0.0358448	+	0.0620850i	−0.847546	+	0.530721i	$0.821921\pi$
$350$	8.22007	−	8.97697i	0.439381	−	0.479839i
$351$		0			0
$352$	−16.0379	+	11.9694i	−0.854821	+	0.637970i
$353$	−1.26103	−	0.728056i	−0.0671179	−	0.0387505i	0.466066	−	0.884750i	$-0.345671\pi$
$353$	−1.26103	−	0.728056i	−0.0671179	−	0.0387505i	−0.533183	+	0.846000i	$0.679004\pi$
$354$		0			0
$355$	22.5006	−	12.9908i	1.19421	−	0.689478i
$356$	6.14593	−	15.7585i	0.325734	−	0.835201i
$357$		0			0
$358$	−3.76199	+	19.9996i	−0.198827	+	1.05701i
$359$	−0.574142	+	0.994443i	−0.0303021	+	0.0524847i	−0.880779	−	0.473528i	$-0.842980\pi$
$359$	−0.574142	+	0.994443i	−0.0303021	+	0.0524847i	0.850477	+	0.526013i	$0.176314\pi$
$360$		0			0
$361$	−7.28416	−	12.6165i	−0.383377	−	0.664028i
$362$	−25.5683	−	21.9558i	−1.34384	−	1.15397i
$363$		0			0
$364$	33.1887	−	3.99693i	1.73956	−	0.209496i
$365$	29.1681	+	16.8402i	1.52673	+	0.881457i
$366$		0			0
$367$	−2.17914	−	1.25813i	−0.113750	−	0.0656738i	0.442045	−	0.896993i	$-0.354253\pi$
$367$	−2.17914	−	1.25813i	−0.113750	−	0.0656738i	−0.555796	+	0.831319i	$0.687586\pi$
$368$	16.1671	+	14.8728i	0.842770	+	0.775299i
$369$		0			0
$370$	3.81626	−	4.44417i	0.198398	−	0.231042i
$371$	3.15997	−	5.09119i	0.164058	−	0.264322i
$372$		0			0
$373$	1.97879	+	3.42737i	0.102458	+	0.177462i	0.912697	−	0.408637i	$-0.133996\pi$
$373$	1.97879	+	3.42737i	0.102458	+	0.177462i	−0.810239	+	0.586100i	$0.800663\pi$
$374$	−12.1065	+	14.0985i	−0.626015	+	0.729016i
$375$		0			0
$376$	−3.05648	+	4.89915i	−0.157626	+	0.252654i
$377$		−	16.9383i		−	0.872368i
$378$		0			0
$379$			5.59867i			0.287584i	0.989608	+	0.143792i	$0.0459297\pi$
$379$			5.59867i			0.287584i	−0.989608	+	0.143792i	$0.954070\pi$
$380$	−1.82829	−	11.9565i	−0.0937895	−	0.613355i
$381$		0			0
$382$	5.89996	+	5.06636i	0.301868	+	0.259218i
$383$	13.0440	+	22.5928i	0.666516	+	1.15444i	0.978872	+	0.204474i	$0.0655483\pi$
$383$	13.0440	+	22.5928i	0.666516	+	1.15444i	−0.312357	+	0.949965i	$0.601118\pi$
$384$		0			0
$385$	−12.6953	−	23.7032i	−0.647010	−	1.20803i
$386$	12.9224	+	11.0966i	0.657733	+	0.564802i
$387$		0			0
$388$	−15.4724	+	12.3930i	−0.785490	+	0.629158i
$389$	5.54894	+	3.20368i	0.281342	+	0.162433i	0.634031	−	0.773308i	$-0.281399\pi$
$389$	5.54894	+	3.20368i	0.281342	+	0.162433i	−0.352689	+	0.935741i	$0.614732\pi$
$390$		0			0
$391$	17.6663	+	10.1996i	0.893422	+	0.515817i
$392$	−8.17504	−	18.0324i	−0.412902	−	0.910776i
$393$		0			0
$394$	−10.3288	+	12.0283i	−0.520359	+	0.605977i
$395$	17.7867	+	30.8074i	0.894945	+	1.55009i
$396$		0			0
$397$	−11.5465	+	19.9991i	−0.579500	+	1.00372i	0.416036	+	0.909348i	$0.363419\pi$
$397$	−11.5465	+	19.9991i	−0.579500	+	1.00372i	−0.995537	+	0.0943761i	$0.969914\pi$
$398$	−25.2137	−	4.74280i	−1.26385	−	0.237735i
$399$		0			0
$400$	−2.84126	+	12.6983i	−0.142063	+	0.634917i
$401$	−28.4389	+	16.4192i	−1.42017	+	0.819936i	−0.996313	−	0.0857921i	$-0.972658\pi$
$401$	−28.4389	+	16.4192i	−1.42017	+	0.819936i	−0.423858	+	0.905728i	$0.639325\pi$
$402$		0			0
$403$	1.40470	+	0.811002i	0.0699729	+	0.0403989i
$404$	−10.9606	+	28.1035i	−0.545309	+	1.39820i
$405$		0			0
$406$	−9.56683	+	3.02011i	−0.474794	+	0.149886i
$407$	−2.55036	−	4.41735i	−0.126416	−	0.218960i
$408$		0			0
$409$	−7.30793			−0.361354			−0.180677	−	0.983543i	$-0.557829\pi$
$409$	−7.30793			−0.361354			−0.180677	+	0.983543i	$0.557829\pi$
$410$	18.6617	+	16.0250i	0.921636	+	0.791419i
$411$		0			0
$412$	−1.80308	−	2.25111i	−0.0888316	−	0.110904i
$413$	−16.5790	+	8.87963i	−0.815801	+	0.436938i
$414$		0			0
$415$	−27.3452	−	15.7877i	−1.34232	−	0.774989i
$416$	−28.6397	+	21.3744i	−1.40418	+	1.04797i
$417$		0			0
$418$	−10.3506	−	1.94698i	−0.506263	−	0.0952298i
$419$	−4.39689	+	7.61563i	−0.214802	+	0.372048i	−0.953211	−	0.302305i	$-0.902244\pi$
$419$	−4.39689	+	7.61563i	−0.214802	+	0.372048i	0.738409	+	0.674353i	$0.235577\pi$
$420$		0			0
$421$	18.6580	+	32.3165i	0.909334	+	1.57501i	0.814992	+	0.579472i	$0.196741\pi$
$421$	18.6580	+	32.3165i	0.909334	+	1.57501i	0.0943413	+	0.995540i	$0.469926\pi$
$422$	−0.860576	−	2.45098i	−0.0418922	−	0.119312i
$423$		0			0
$424$	−0.219000	+	6.40212i	−0.0106356	+	0.310914i
$425$			12.0833i			0.586127i
$426$		0			0
$427$	−13.2257	+	7.08362i	−0.640038	+	0.342800i
$428$	−6.81046	−	2.65613i	−0.329196	−	0.128389i
$429$		0			0
$430$	21.2392	−	7.45739i	1.02424	−	0.359627i
$431$	−11.2054	−	19.4082i	−0.539743	−	0.934862i	−0.998918	−	0.0465160i	$-0.985188\pi$
$431$	−11.2054	−	19.4082i	−0.539743	−	0.934862i	0.459175	−	0.888346i	$-0.348145\pi$
$432$		0			0
$433$	−41.0490			−1.97269			−0.986343	−	0.164702i	$-0.947334\pi$
$433$	−41.0490			−1.97269			−0.986343	+	0.164702i	$0.947334\pi$
$434$	0.207599	−	0.937980i	0.00996508	−	0.0450245i
$435$		0			0
$436$	22.7405	−	18.2146i	1.08907	−	0.872322i
$437$			11.5613i			0.553053i
$438$		0			0
$439$			39.0269i			1.86265i	0.364186	+	0.931326i	$0.381347\pi$
$439$			39.0269i			1.86265i	−0.364186	+	0.931326i	$0.618653\pi$
$440$	24.3883	+	15.2154i	1.16267	+	0.725364i
$441$		0			0
$442$	−21.6194	+	25.1765i	−1.02833	+	1.19752i
$443$	14.6222			0.694721			0.347360	−	0.937732i	$-0.387078\pi$
$443$	14.6222			0.694721			0.347360	+	0.937732i	$0.387078\pi$
$444$		0			0
$445$	−24.2963			−1.15175
$446$	6.48338	+	1.21955i	0.306997	+	0.0577472i
$447$		0			0
$448$	17.1788	+	12.3648i	0.811624	+	0.584181i
$449$		−	4.89587i		−	0.231051i	−0.993305	−	0.115525i	$-0.963145\pi$
$449$		−	4.89587i		−	0.231051i	0.993305	−	0.115525i	$-0.0368551\pi$
$450$		0			0
$451$	18.5491	−	10.7093i	0.873441	−	0.504282i
$452$	−10.2742	+	26.3435i	−0.483256	+	1.23910i
$453$		0			0
$454$	17.6338	−	6.19148i	0.827594	−	0.290581i
$455$	−22.6707	−	42.3281i	−1.06282	−	1.98437i
$456$		0			0
$457$	−29.0153			−1.35728			−0.678639	−	0.734472i	$-0.737430\pi$
$457$	−29.0153			−1.35728			−0.678639	+	0.734472i	$0.737430\pi$
$458$	3.97267	−	21.1196i	0.185631	−	0.986855i
$459$		0			0
$460$	11.4654	−	29.3978i	0.534575	−	1.37068i
$461$	6.60037	−	3.81073i	0.307410	−	0.177483i	−0.338357	−	0.941018i	$-0.609871\pi$
$461$	6.60037	−	3.81073i	0.307410	−	0.177483i	0.645767	+	0.763535i	$0.276538\pi$
$462$		0			0
$463$	−11.4432	−	6.60672i	−0.531810	−	0.307040i	0.209943	−	0.977714i	$-0.432672\pi$
$463$	−11.4432	−	6.60672i	−0.531810	−	0.307040i	−0.741753	+	0.670673i	$0.766005\pi$
$464$	7.26111	−	7.89301i	0.337088	−	0.366424i
$465$		0			0
$466$	3.00825	+	8.56770i	0.139354	+	0.396891i
$467$	4.71551	−	8.16751i	0.218208	−	0.377947i	−0.736052	−	0.676925i	$-0.763312\pi$
$467$	4.71551	−	8.16751i	0.218208	−	0.377947i	0.954260	+	0.298977i	$0.0966455\pi$
$468$		0			0
$469$	−9.17650	−	17.1333i	−0.423731	−	0.791144i
$470$	8.15144	+	1.53332i	0.375998	+	0.0707266i
$471$		0			0
$472$	10.6423	−	17.0583i	0.489851	−	0.785170i
$473$		−	19.6008i		−	0.901246i
$474$		0			0
$475$	−5.93076	+	3.42413i	−0.272122	+	0.157110i
$476$	18.0745	+	7.72172i	0.828445	+	0.353924i
$477$		0			0
$478$	−14.7163	+	5.16711i	−0.673107	+	0.236338i
$479$	−1.97012	+	3.41235i	−0.0900170	+	0.155914i	−0.907518	−	0.420013i	$-0.862025\pi$
$479$	−1.97012	+	3.41235i	−0.0900170	+	0.155914i	0.817501	+	0.575927i	$0.195359\pi$
$480$		0			0
$481$	−4.55432	−	7.88831i	−0.207659	−	0.359676i
$482$	−5.49798	+	1.93042i	−0.250426	+	0.0879284i
$483$		0			0
$484$	2.36487	−	1.89420i	0.107494	−	0.0861001i
$485$	24.6600	+	14.2375i	1.11976	+	0.646491i
$486$		0			0
$487$	−29.7489	+	17.1756i	−1.34805	+	0.778299i	−0.987974	−	0.154623i	$-0.950584\pi$
$487$	−29.7489	+	17.1756i	−1.34805	+	0.778299i	−0.360079	+	0.932922i	$0.617250\pi$
$488$	8.48977	−	13.6080i	0.384314	−	0.616007i
$489$		0			0
$490$	−19.8649	+	20.3516i	−0.897405	+	0.919392i
$491$	−15.4355	+	26.7350i	−0.696592	+	1.20653i	0.273049	+	0.962000i	$0.411968\pi$
$491$	−15.4355	+	26.7350i	−0.696592	+	1.20653i	−0.969641	+	0.244533i	$0.921365\pi$
$492$		0			0
$493$	4.97959	−	8.62491i	0.224270	−	0.388446i
$494$	−18.4836	−	3.47683i	−0.831616	−	0.156430i
$495$		0			0
$496$	0.306908	+	0.980079i	0.0137806	+	0.0440069i
$497$	−21.0931	+	11.2973i	−0.946153	+	0.506753i
$498$		0			0
$499$	−4.44052	+	2.56373i	−0.198785	+	0.114768i	−0.596089	−	0.802919i	$-0.703279\pi$
$499$	−4.44052	+	2.56373i	−0.198785	+	0.114768i	0.397304	+	0.917687i	$0.369946\pi$
$500$	−9.92182	+	1.51717i	−0.443717	+	0.0678498i
$501$		0			0
$502$	−13.5584	−	11.6428i	−0.605141	−	0.519642i
$503$	−6.16708			−0.274976			−0.137488	−	0.990503i	$-0.543903\pi$
$503$	−6.16708			−0.274976			−0.137488	+	0.990503i	$0.543903\pi$
$504$		0			0
$505$	43.3297			1.92814
$506$	−20.8452	−	17.9000i	−0.926680	−	0.795751i
$507$		0			0
$508$	33.5059	−	5.12346i	1.48658	−	0.227317i
$509$	8.65668	−	4.99794i	0.383701	−	0.221530i	−0.295726	−	0.955273i	$-0.595562\pi$
$509$	8.65668	−	4.99794i	0.383701	−	0.221530i	0.679427	+	0.733743i	$0.262228\pi$
$510$		0			0
$511$	−26.3546	−	16.3576i	−1.16586	−	0.723619i
$512$	−22.5085	−	2.31710i	−0.994743	−	0.102402i
$513$		0			0
$514$	22.7296	+	4.27551i	1.00256	+	0.188585i
$515$	−2.07145	+	3.58785i	−0.0912788	+	0.158099i
$516$		0			0
$517$	3.61116	−	6.25472i	0.158819	−	0.275082i
$518$	−3.64331	+	3.97879i	−0.160078	+	0.174818i
$519$		0			0
$520$	43.5516	+	27.1709i	1.90986	+	1.19152i
$521$	−10.2779	+	5.93396i	−0.450284	+	0.259971i	−0.707950	−	0.706263i	$-0.750380\pi$
$521$	−10.2779	+	5.93396i	−0.450284	+	0.259971i	0.257666	+	0.966234i	$0.417046\pi$
$522$		0			0
$523$	13.5741	+	7.83700i	0.593553	+	0.342688i	0.766501	−	0.642243i	$-0.221996\pi$
$523$	13.5741	+	7.83700i	0.593553	+	0.342688i	−0.172948	+	0.984931i	$0.555329\pi$
$524$	−8.11973	+	6.50371i	−0.354712	+	0.284116i
$525$		0			0
$526$	23.8279	−	8.36634i	1.03895	−	0.364790i
$527$	0.476843	+	0.825917i	0.0207716	+	0.0359775i
$528$		0			0
$529$	−3.58052	+	6.20165i	−0.155675	+	0.269637i
$530$	8.68183	−	3.04832i	0.377115	−	0.132411i
$531$		0			0
$532$	1.33191	+	11.0595i	0.0577454	+	0.479492i
$533$	33.1241	−	19.1242i	1.43477	−	0.828362i
$534$		0			0
$535$			10.5003i			0.453967i
$536$	17.6286	+	10.9981i	0.761439	+	0.475046i
$537$		0			0
$538$	13.2437	+	2.49118i	0.570974	+	0.107402i
$539$	10.9900	+	22.1913i	0.473373	+	0.955847i
$540$		0			0
$541$	16.2898	−	28.2148i	0.700354	−	1.21305i	−0.267988	−	0.963422i	$-0.586359\pi$
$541$	16.2898	−	28.2148i	0.700354	−	1.21305i	0.968342	−	0.249627i	$-0.0803079\pi$
$542$	−0.545039	−	1.55231i	−0.0234114	−	0.0666773i
$543$		0			0
$544$	−20.8670	+	2.46412i	−0.894663	+	0.105648i
$545$	−36.2442	−	20.9256i	−1.55253	−	0.896353i
$546$		0			0
$547$	−14.3949	+	8.31091i	−0.615482	+	0.355349i	−0.775108	−	0.631829i	$-0.782305\pi$
$547$	−14.3949	+	8.31091i	−0.615482	+	0.355349i	0.159626	+	0.987178i	$0.448971\pi$
$548$	9.51978	−	24.4093i	0.406665	−	1.04271i
$549$		0			0
$550$	3.00865	−	15.9946i	0.128289	−	0.682014i
$551$	5.64440			0.240459
$552$		0			0
$553$	−15.4680	−	28.8802i	−0.657768	−	1.22811i
$554$	−31.6781	+	11.1227i	−1.34587	+	0.472556i
$555$		0			0
$556$	3.25703	−	8.35121i	0.138129	−	0.354170i
$557$	9.30728	−	5.37356i	0.394362	−	0.227685i	−0.289686	−	0.957122i	$-0.593551\pi$
$557$	9.30728	−	5.37356i	0.394362	−	0.227685i	0.684049	+	0.729436i	$0.260218\pi$
$558$		0			0
$559$		−	35.0023i		−	1.48044i
$560$	7.58099	−	29.4427i	0.320355	−	1.24418i
$561$		0			0
$562$	9.77678	+	1.83905i	0.412408	+	0.0775755i
$563$	0.697444			0.0293937			0.0146969	−	0.999892i	$-0.495322\pi$
$563$	0.697444			0.0293937			0.0146969	+	0.999892i	$0.495322\pi$
$564$		0			0
$565$	40.6161			1.70873
$566$	17.5401	−	20.4261i	0.737266	−	0.858573i
$567$		0			0
$568$	13.5399	−	21.7028i	0.568121	−	0.910627i
$569$			5.87563i			0.246319i	0.992387	+	0.123160i	$0.0393027\pi$
$569$			5.87563i			0.246319i	−0.992387	+	0.123160i	$0.960697\pi$
$570$		0			0
$571$			35.9571i			1.50476i	0.658732	+	0.752378i	$0.271093\pi$
$571$			35.9571i			1.50476i	−0.658732	+	0.752378i	$0.728907\pi$
$572$	34.8862	−	27.9430i	1.45867	−	1.16836i
$573$		0			0
$574$	−16.7075	−	15.2988i	−0.697357	−	0.638559i
$575$	−17.8656			−0.745048
$576$		0			0
$577$	−15.0558	−	26.0774i	−0.626782	−	1.08562i	−0.988193	−	0.153212i	$-0.951038\pi$
$577$	−15.0558	−	26.0774i	−0.626782	−	1.08562i	0.361411	−	0.932406i	$-0.382295\pi$
$578$	4.27404	−	1.50068i	0.177776	−	0.0624200i
$579$		0			0
$580$	−14.3524	−	5.59754i	−0.595951	−	0.232425i
$581$	24.7075	+	15.3353i	1.02504	+	0.636215i
$582$		0			0
$583$		−	8.01212i		−	0.331828i
$584$	33.1406	+	1.13365i	1.37137	+	0.0469110i
$585$		0			0
$586$	−7.09265	−	20.2004i	−0.292995	−	0.834469i
$587$	−16.3434	−	28.3076i	−0.674563	−	1.16838i	−0.976596	−	0.215080i	$-0.930999\pi$
$587$	−16.3434	−	28.3076i	−0.674563	−	1.16838i	0.302033	−	0.953297i	$-0.402335\pi$
$588$		0			0
$589$	−0.270252	+	0.468090i	−0.0111355	+	0.0192873i
$590$	−28.3824	−	5.33883i	−1.16848	−	0.219796i
$591$		0			0
$592$	1.25931	−	5.62818i	0.0517573	−	0.231317i
$593$	23.5045	+	13.5704i	0.965216	+	0.557268i	0.897774	−	0.440455i	$-0.145183\pi$
$593$	23.5045	+	13.5704i	0.965216	+	0.557268i	0.0674416	+	0.997723i	$0.478516\pi$
$594$		0			0
$595$	0.899997	−	28.2181i	0.0368963	−	1.15683i
$596$	−10.5588	−	13.1825i	−0.432507	−	0.539975i
$597$		0			0
$598$	−37.2244	−	31.9650i	−1.52222	−	1.30715i
$599$	47.0612			1.92287			0.961433	−	0.275038i	$-0.0886904\pi$
$599$	47.0612			1.92287			0.961433	+	0.275038i	$0.0886904\pi$
$600$		0			0
$601$	6.84978	+	11.8642i	0.279408	+	0.483950i	0.971238	−	0.238111i	$-0.0765283\pi$
$601$	6.84978	+	11.8642i	0.279408	+	0.483950i	−0.691829	+	0.722061i	$0.743195\pi$
$602$	−19.7694	+	6.24092i	−0.805742	+	0.254361i
$603$		0			0
$604$	−4.57244	+	11.7240i	−0.186050	+	0.477043i
$605$	−3.76916	−	2.17612i	−0.153238	−	0.0884720i
$606$		0			0
$607$	38.2780	−	22.0998i	1.55366	−	0.897005i	0.555818	−	0.831304i	$-0.312405\pi$
$607$	38.2780	−	22.0998i	1.55366	−	0.897005i	0.997839	−	0.0657010i	$-0.0209283\pi$
$608$	−7.12264	−	9.54369i	−0.288861	−	0.387048i
$609$		0			0
$610$	−22.6417	−	4.25899i	−0.916736	−	0.172441i
$611$	6.44866	−	11.1694i	0.260885	−	0.451866i
$612$		0			0
$613$	15.3894	+	26.6553i	0.621573	+	1.07660i	0.989193	+	0.146620i	$0.0468394\pi$
$613$	15.3894	+	26.6553i	0.621573	+	1.07660i	−0.367620	+	0.929976i	$0.619827\pi$
$614$	13.6806	−	15.9315i	0.552103	−	0.642943i
$615$		0			0
$616$	−22.0026	−	14.7216i	−0.886508	−	0.593151i
$617$	−6.67742	−	3.85521i	−0.268823	−	0.155205i	0.359530	−	0.933134i	$-0.382937\pi$
$617$	−6.67742	−	3.85521i	−0.268823	−	0.155205i	−0.628353	+	0.777929i	$0.716270\pi$
$618$		0			0
$619$	11.8501	+	6.84165i	0.476295	+	0.274989i	0.718871	−	0.695143i	$-0.244659\pi$
$619$	11.8501	+	6.84165i	0.476295	+	0.274989i	−0.242576	+	0.970132i	$0.577992\pi$
$620$	1.15139	−	0.922239i	0.0462411	−	0.0370380i
$621$		0			0
$622$	−6.93253	−	5.95304i	−0.277969	−	0.238695i
$623$	22.3645	+	0.713302i	0.896017	+	0.0285779i
$624$		0			0
$625$	15.3414	+	26.5721i	0.613657	+	1.06289i
$626$	13.1224	+	11.2684i	0.524477	+	0.450374i
$627$		0			0
$628$	−3.02194	−	19.7626i	−0.120588	−	0.788612i
$629$		−	5.35559i		−	0.213541i
$630$		0			0
$631$			7.14717i			0.284524i	0.989829	+	0.142262i	$0.0454376\pi$
$631$			7.14717i			0.284524i	−0.989829	+	0.142262i	$0.954562\pi$
$632$	29.7150	+	18.5386i	1.18200	+	0.737424i
$633$		0			0
$634$	−18.4540	+	21.4903i	−0.732901	+	0.853489i
$635$	−24.3438	−	42.1646i	−0.966053	−	1.67325i
$636$		0			0
$637$	19.6255	+	39.6283i	0.777590	+	1.57013i
$638$	−8.73901	+	10.1769i	−0.345981	+	0.402907i
$639$		0			0
$640$	8.64680	+	31.3309i	0.341795	+	1.23846i
$641$	−39.6338	−	22.8826i	−1.56544	−	0.903809i	−0.996690	−	0.0813000i	$-0.974093\pi$
$641$	−39.6338	−	22.8826i	−1.56544	−	0.903809i	−0.568753	−	0.822509i	$-0.692574\pi$
$642$		0			0
$643$	7.64287	+	4.41261i	0.301405	+	0.174016i	0.643074	−	0.765804i	$-0.277659\pi$
$643$	7.64287	+	4.41261i	0.301405	+	0.174016i	−0.341669	+	0.939820i	$0.610992\pi$
$644$	−11.4168	+	26.7239i	−0.449887	+	1.05307i
$645$		0			0
$646$	−8.38963	−	7.20427i	−0.330085	−	0.283448i
$647$	−9.24938	−	16.0204i	−0.363630	−	0.629826i	0.624925	−	0.780685i	$-0.285130\pi$
$647$	−9.24938	−	16.0204i	−0.363630	−	0.629826i	−0.988555	+	0.150858i	$0.951796\pi$
$648$		0			0
$649$	−12.5736	+	21.7782i	−0.493559	+	0.854869i
$650$	5.37272	−	28.5626i	0.210735	−	1.12032i
$651$		0			0
$652$	−9.16528	+	23.5003i	−0.358940	+	0.920343i
$653$	−13.4600	+	7.77115i	−0.526732	+	0.304109i	−0.739685	−	0.672954i	$-0.765025\pi$
$653$	−13.4600	+	7.77115i	−0.526732	+	0.304109i	0.212953	+	0.977062i	$0.431692\pi$
$654$		0			0
$655$	12.9413	+	7.47169i	0.505660	+	0.291943i
$656$	23.6335	+	5.28802i	0.922734	+	0.206462i
$657$		0			0
$658$	−7.45833	−	1.65072i	−0.290756	−	0.0643517i
$659$	−24.9174	−	43.1582i	−0.970644	−	1.68120i	−0.693619	−	0.720342i	$-0.743985\pi$
$659$	−24.9174	−	43.1582i	−0.970644	−	1.68120i	−0.277025	−	0.960863i	$-0.589348\pi$
$660$		0			0
$661$	34.9248			1.35842			0.679209	−	0.733945i	$-0.262323\pi$
$661$	34.9248			1.35842			0.679209	+	0.733945i	$0.262323\pi$
$662$	−25.3509	+	29.5220i	−0.985291	+	1.14741i
$663$		0			0
$664$	−31.0694	−	1.06280i	−1.20573	−	0.0412448i
$665$	14.1051	−	7.55460i	0.546972	−	0.292955i
$666$		0			0
$667$	12.7522	+	7.36251i	0.493769	+	0.285078i
$668$	−16.6988	−	6.51265i	−0.646097	−	0.251982i
$669$		0			0
$670$	5.51732	−	29.3313i	0.213153	−	1.13317i
$671$	−10.0305	+	17.3733i	−0.387222	+	0.670689i
$672$		0			0
$673$	−17.4451	−	30.2158i	−0.672459	−	1.16473i	−0.977205	−	0.212300i	$-0.931905\pi$
$673$	−17.4451	−	30.2158i	−0.672459	−	1.16473i	0.304745	−	0.952434i	$-0.401429\pi$
$674$	−18.7629	+	6.58795i	−0.722722	+	0.253758i
$675$		0			0
$676$	42.0054	−	33.6453i	1.61559	−	1.29405i
$677$			25.5382i			0.981513i	0.871297	+	0.490757i	$0.163280\pi$
$677$			25.5382i			0.981513i	−0.871297	+	0.490757i	$0.836720\pi$
$678$		0			0
$679$	−22.2814	−	13.8295i	−0.855081	−	0.530727i
$680$	14.1885	+	26.6388i	0.544102	+	1.02155i
$681$		0			0
$682$	−0.425549	−	1.21199i	−0.0162951	−	0.0464096i
$683$	0.707620	+	1.22563i	0.0270763	+	0.0468976i	0.879246	−	0.476368i	$-0.158047\pi$
$683$	0.707620	+	1.22563i	0.0270763	+	0.0468976i	−0.852170	+	0.523265i	$0.824714\pi$
$684$		0			0
$685$	−37.6339			−1.43792
$686$	18.8830	−	18.1503i	0.720956	−	0.692981i
$687$		0			0
$688$	15.0047	−	16.3105i	0.572051	−	0.621834i
$689$		−	14.3077i		−	0.545080i
$690$		0			0
$691$			29.7159i			1.13045i	0.824938	+	0.565223i	$0.191210\pi$
$691$			29.7159i			1.13045i	−0.824938	+	0.565223i	$0.808790\pi$
$692$	12.4638	−	1.90587i	0.473802	−	0.0724501i
$693$		0			0
$694$	18.0557	+	15.5046i	0.685384	+	0.588547i
$695$	−12.8758			−0.488406
$696$		0			0
$697$	22.4889			0.851826
$698$	0.350131	−	1.86137i	0.0132526	−	0.0704540i
$699$		0			0
$700$	−17.0902	+	2.05818i	−0.645949	+	0.0777920i
$701$			37.7345i			1.42521i	0.701565	+	0.712605i	$0.252485\pi$
$701$			37.7345i			1.42521i	−0.701565	+	0.712605i	$0.747515\pi$
$702$		0			0
$703$	2.62864	−	1.51765i	0.0991410	−	0.0572391i
$704$	28.2351	+	1.93396i	1.06415	+	0.0728888i
$705$		0			0
$706$	0.682205	+	1.94297i	0.0256751	+	0.0731245i
$707$	−39.8846	−	1.27209i	−1.50002	−	0.0478420i
$708$		0			0
$709$	4.38026			0.164504			0.0822521	−	0.996612i	$-0.473789\pi$
$709$	4.38026			0.164504			0.0822521	+	0.996612i	$0.473789\pi$
$710$	−36.1101	−	6.79244i	−1.35519	−	0.254916i
$711$		0			0
$712$	−21.1129	+	11.2452i	−0.791238	+	0.421432i
$713$	−1.22115	+	0.705030i	−0.0457324	+	0.0264036i
$714$		0			0
$715$	−55.6021	−	32.1019i	−2.07940	−	1.20054i
$716$	22.4624	−	17.9919i	0.839461	−	0.672388i
$717$		0			0
$718$	1.53222	−	0.537984i	0.0571818	−	0.0200774i
$719$	−21.7265	+	37.6314i	−0.810261	+	1.40341i	0.102421	+	0.994741i	$0.467341\pi$
$719$	−21.7265	+	37.6314i	−0.810261	+	1.40341i	−0.912681	+	0.408672i	$0.865992\pi$
$720$		0			0
$721$	2.01208	−	3.24177i	0.0749339	−	0.120730i
$722$	−3.80865	+	20.2476i	−0.141743	+	0.753538i
$723$		0			0
$724$	7.20425	+	47.1136i	0.267744	+	1.75096i
$725$			8.72224i			0.323936i
$726$		0			0
$727$	21.6003	−	12.4710i	0.801112	−	0.462522i	−0.0427480	−	0.999086i	$-0.513611\pi$
$727$	21.6003	−	12.4710i	0.801112	−	0.462522i	0.843860	+	0.536564i	$0.180278\pi$
$728$	−39.2912	−	26.2893i	−1.45623	−	0.974345i
$729$		0			0
$730$	−15.7797	−	44.9416i	−0.584032	−	1.66336i
$731$	10.2901	−	17.8230i	0.380593	−	0.659207i
$732$		0			0
$733$	7.50044	+	12.9912i	0.277035	+	0.479839i	0.970647	−	0.240510i	$-0.0773148\pi$
$733$	7.50044	+	12.9912i	0.277035	+	0.479839i	−0.693611	+	0.720349i	$0.743981\pi$
$734$	1.17890	+	3.35758i	0.0435139	+	0.123930i
$735$		0			0
$736$	−3.64329	−	30.8526i	−0.134293	−	1.13724i
$737$	−22.5063	−	12.9940i	−0.829030	−	0.478641i
$738$		0			0
$739$	−3.08238	+	1.77962i	−0.113387	+	0.0654642i	−0.555621	−	0.831436i	$-0.687519\pi$
$739$	−3.08238	+	1.77962i	−0.113387	+	0.0654642i	0.442234	+	0.896900i	$0.354186\pi$
$740$	−8.18908	+	1.25221i	−0.301036	+	0.0460322i
$741$		0			0
$742$	−8.08105	+	2.55107i	−0.296665	+	0.0936527i
$743$	24.3308	−	42.1422i	0.892610	−	1.54605i	0.0558753	−	0.998438i	$-0.482205\pi$
$743$	24.3308	−	42.1422i	0.892610	−	1.54605i	0.836735	−	0.547608i	$-0.184462\pi$
$744$		0			0
$745$	−12.1304	+	21.0104i	−0.444422	+	0.769761i
$746$	1.03465	−	5.50040i	0.0378811	−	0.201384i
$747$		0			0
$748$	25.9787	−	3.97246i	0.949875	−	0.145247i
$749$	0.308272	−	9.66542i	0.0112640	−	0.353167i
$750$		0			0
$751$	−18.5968	+	10.7369i	−0.678607	+	0.391794i	−0.799330	−	0.600892i	$-0.794812\pi$
$751$	−18.5968	+	10.7369i	−0.678607	+	0.391794i	0.120723	+	0.992686i	$0.461479\pi$
$752$	7.79307	−	2.44037i	0.284184	−	0.0889913i
$753$		0			0
$754$	−15.6057	+	18.1734i	−0.568328	+	0.661838i
$755$	18.0759			0.657849
$756$		0			0
$757$	2.47427			0.0899289			0.0449645	−	0.998989i	$-0.485683\pi$
$757$	2.47427			0.0899289			0.0449645	+	0.998989i	$0.485683\pi$
$758$	5.15821	−	6.00692i	0.187354	−	0.218181i
$759$		0			0
$760$	−9.05423	+	14.5128i	−0.328432	+	0.526435i
$761$	−38.9915	+	22.5118i	−1.41344	+	0.816051i	−0.995711	−	0.0925199i	$-0.970508\pi$
$761$	−38.9915	+	22.5118i	−1.41344	+	0.816051i	−0.417731	+	0.908571i	$0.637174\pi$
$762$		0			0
$763$	32.7481	+	20.3259i	1.18556	+	0.735847i
$764$	−1.66240	−	10.8716i	−0.0601435	−	0.393320i
$765$		0			0
$766$	6.82026	−	36.2580i	0.246426	−	1.31006i
$767$	−22.4535	+	38.8906i	−0.810748	+	1.40426i
$768$		0			0
$769$	−7.14970	+	12.3836i	−0.257825	+	0.446566i	−0.965659	−	0.259813i	$-0.916339\pi$
$769$	−7.14970	+	12.3836i	−0.257825	+	0.446566i	0.707834	+	0.706379i	$0.249672\pi$
$770$	−8.21740	+	37.1281i	−0.296134	+	1.33800i
$771$		0			0
$772$	−3.64107	−	23.8115i	−0.131045	−	0.856995i
$773$	42.1150	−	24.3151i	1.51477	−	0.874553i	0.514920	−	0.857238i	$-0.327822\pi$
$773$	42.1150	−	24.3151i	1.51477	−	0.874553i	0.999850	−	0.0173147i	$-0.00551170\pi$
$774$		0			0
$775$	−0.723336	−	0.417618i	−0.0259830	−	0.0150013i
$776$	28.0186	+	0.958443i	1.00581	+	0.0344061i
$777$		0			0
$778$	−3.00192	−	8.54968i	−0.107624	−	0.306521i
$779$	6.37281	+	11.0380i	0.228330	+	0.395478i
$780$		0			0
$781$	−15.9971	+	27.7078i	−0.572421	+	0.991463i
$782$	−9.55728	−	27.2198i	−0.341768	−	0.973378i
$783$		0			0
$784$	−7.84263	+	26.8792i	−0.280094	+	0.959973i
$785$	−24.8697	+	14.3585i	−0.887639	+	0.512478i
$786$		0			0
$787$		−	38.9653i		−	1.38896i	−0.719510	−	0.694482i	$-0.755634\pi$
$787$		−	38.9653i		−	1.38896i	0.719510	−	0.694482i	$-0.244366\pi$
$788$	22.1640	−	3.38915i	0.789560	−	0.120733i
$789$		0			0
$790$	9.30008	−	49.4413i	0.330882	−	1.75904i
$791$	−37.3868	−	1.19243i	−1.32932	−	0.0423978i
$792$		0			0
$793$	−17.9120	+	31.0245i	−0.636074	+	1.10171i
$794$	30.8141	−	10.8193i	1.09355	−	0.383963i
$795$		0			0
$796$	22.6826	+	28.3188i	0.803965	+	1.00373i
$797$	26.8665	+	15.5114i	0.951662	+	0.549442i	0.893597	−	0.448871i	$-0.148174\pi$
$797$	26.8665	+	15.5114i	0.951662	+	0.549442i	0.0580649	+	0.998313i	$0.481507\pi$
$798$		0			0
$799$	6.56725	−	3.79161i	0.232333	−	0.134137i
$800$	14.7478	−	11.0066i	0.521413	−	0.389141i
$801$		0			0
$802$	45.6401	+	8.58507i	1.61161	+	0.303149i
$803$	−41.4748			−1.46361
$804$		0			0
$805$	41.7215	+	1.33068i	1.47049	+	0.0469002i
$806$	−0.759927	−	2.16433i	−0.0267673	−	0.0762351i
$807$		0			0
$808$	37.6524	−	20.0545i	1.32461	−	0.705517i
$809$	5.35787	−	3.09337i	0.188373	−	0.108757i	−0.402848	−	0.915267i	$-0.631980\pi$
$809$	5.35787	−	3.09337i	0.188373	−	0.108757i	0.591221	+	0.806510i	$0.298646\pi$
$810$		0			0
$811$		−	6.48257i		−	0.227634i	−0.993502	−	0.113817i	$-0.963692\pi$
$811$		−	6.48257i		−	0.227634i	0.993502	−	0.113817i	$-0.0363077\pi$
$812$	13.0469	+	5.57385i	0.457858	+	0.195604i
$813$		0			0
$814$	−1.33350	+	7.08917i	−0.0467391	+	0.248475i
$815$	36.2325			1.26917
$816$		0			0
$817$	11.6639			0.408068
$818$	7.84081	+	6.73299i	0.274148	+	0.235414i
$819$		0			0
$820$	−5.25821	−	34.3871i	−0.183625	−	1.20085i
$821$		−	26.5139i		−	0.925341i	−0.886530	−	0.462670i	$-0.846891\pi$
$821$		−	26.5139i		−	0.925341i	0.886530	−	0.462670i	$-0.153109\pi$
$822$		0			0
$823$		−	25.8006i		−	0.899353i	−0.893192	−	0.449676i	$-0.851539\pi$
$823$		−	25.8006i		−	0.899353i	0.893192	−	0.449676i	$-0.148461\pi$
$824$	−0.139446	+	4.07649i	−0.00485784	+	0.142011i
$825$		0			0
$826$	25.9690	+	5.74761i	0.903578	+	0.199985i
$827$	−40.3698			−1.40379			−0.701897	−	0.712278i	$-0.747663\pi$
$827$	−40.3698			−1.40379			−0.701897	+	0.712278i	$0.747663\pi$
$828$		0			0
$829$	−13.9633	−	24.1851i	−0.484965	−	0.839984i	0.514886	−	0.857259i	$-0.327834\pi$
$829$	−13.9633	−	24.1851i	−0.484965	−	0.839984i	−0.999851	+	0.0172749i	$0.994501\pi$
$830$	14.7935	+	42.1328i	0.513489	+	1.46245i
$831$		0			0
$832$	50.4210	+	3.45358i	1.74803	+	0.119731i
$833$	−1.65688	+	25.9481i	−0.0574075	+	0.899048i
$834$		0			0
$835$			25.7460i			0.890977i
$836$	9.31151	+	11.6252i	0.322045	+	0.402066i
$837$		0			0
$838$	11.7340	−	4.11998i	0.405344	−	0.142322i
$839$	−6.10301	−	10.5707i	−0.210699	−	0.364942i	0.741234	−	0.671246i	$-0.234241\pi$
$839$	−6.10301	−	10.5707i	−0.210699	−	0.364942i	−0.951934	+	0.306305i	$0.900907\pi$
$840$		0			0
$841$	−10.9055	+	18.8889i	−0.376053	+	0.651342i
$842$	9.75564	−	51.8631i	0.336202	−	1.78732i
$843$		0			0
$844$	−1.33483	+	3.42258i	−0.0459467	+	0.117810i
$845$	−66.9488	−	38.6529i	−2.30311	−	1.32970i
$846$		0			0
$847$	3.40559	+	2.11376i	0.117018	+	0.0726297i
$848$	6.13342	−	6.66718i	0.210622	−	0.228952i
$849$		0			0
$850$	11.1327	−	12.9644i	0.381848	−	0.444676i
$851$	7.91843			0.271440
$852$		0			0
$853$	−4.47707	−	7.75452i	−0.153292	−	0.265510i	0.779144	−	0.626845i	$-0.215654\pi$
$853$	−4.47707	−	7.75452i	−0.153292	−	0.265510i	−0.932436	+	0.361336i	$0.882321\pi$
$854$	20.7165	+	4.58509i	0.708904	+	0.156899i
$855$		0			0
$856$	4.85991	+	9.12448i	0.166108	+	0.311868i
$857$	14.0612	+	8.11822i	0.480320	+	0.277313i	0.720550	−	0.693403i	$-0.243889\pi$
$857$	14.0612	+	8.11822i	0.480320	+	0.277313i	−0.240230	+	0.970716i	$0.577223\pi$
$858$		0			0
$859$	29.2919	−	16.9117i	0.999426	−	0.577019i	0.0913477	−	0.995819i	$-0.470883\pi$
$859$	29.2919	−	16.9117i	0.999426	−	0.577019i	0.908078	+	0.418800i	$0.137549\pi$
$860$	−29.6586	−	11.5671i	−1.01135	−	0.394433i
$861$		0			0
$862$	−5.85891	+	31.1473i	−0.199555	+	1.06088i
$863$	10.1074	−	17.5066i	0.344062	−	0.595932i	−0.641121	−	0.767440i	$-0.721530\pi$
$863$	10.1074	−	17.5066i	0.344062	−	0.595932i	0.985183	+	0.171507i	$0.0548638\pi$
$864$		0			0
$865$	−9.05560	−	15.6848i	−0.307900	−	0.533298i
$866$	44.0422	+	37.8195i	1.49662	+	1.28516i
$867$		0			0
$868$	−1.08692	+	0.815110i	−0.0368926	+	0.0276666i
$869$	−37.9370	−	21.9029i	−1.28692	−	0.743005i
$870$		0			0
$871$	−40.1908	−	23.2042i	−1.36181	−	0.786243i
$872$	−41.1804	−	1.40867i	−1.39454	−	0.0477037i
$873$		0			0
$874$	10.6518	−	12.4044i	0.360302	−	0.419584i
$875$	−6.26901	−	11.7048i	−0.211931	−	0.395694i
$876$		0			0
$877$	11.1716	+	19.3497i	0.377237	+	0.653394i	0.990659	−	0.136361i	$-0.0435408\pi$
$877$	11.1716	+	19.3497i	0.377237	+	0.653394i	−0.613422	+	0.789755i	$0.710207\pi$
$878$	35.9566	−	41.8727i	1.21348	−	1.41314i
$879$		0			0
$880$	−12.1484	−	38.7945i	−0.409521	−	1.30776i
$881$			50.5729i			1.70384i	0.523669	+	0.851922i	$0.324563\pi$
$881$			50.5729i			1.70384i	−0.523669	+	0.851922i	$0.675437\pi$
$882$		0			0
$883$			48.7254i			1.63974i	0.572549	+	0.819870i	$0.305954\pi$
$883$			48.7254i			1.63974i	−0.572549	+	0.819870i	$0.694046\pi$
$884$	46.3916	−	7.09385i	1.56032	−	0.238592i
$885$		0			0
$886$	−15.6884	−	13.4718i	−0.527063	−	0.452595i
$887$	14.2298	+	24.6468i	0.477791	+	0.827558i	0.999676	−	0.0254580i	$-0.00810442\pi$
$887$	14.2298	+	24.6468i	0.477791	+	0.827558i	−0.521885	+	0.853016i	$0.674771\pi$
$888$		0			0
$889$	21.1704	+	39.5269i	0.710031	+	1.32569i
$890$	26.0680	+	22.3848i	0.873800	+	0.750342i
$891$		0			0
$892$	−5.83254	−	7.28179i	−0.195288	−	0.243812i
$893$	3.72201	+	2.14890i	0.124552	+	0.0719103i
$894$		0			0
$895$	−35.8009	−	20.6697i	−1.19669	−	0.690911i
$896$	−7.03948	−	29.0937i	−0.235173	−	0.971954i
$897$		0			0
$898$	−4.51070	+	5.25288i	−0.150524	+	0.175291i
$899$	0.344205	+	0.596181i	0.0114799	+	0.0198837i
$900$		0			0
$901$	4.20624	−	7.28541i	0.140130	−	0.242712i
$902$	−29.7684	−	5.59955i	−0.991180	−	0.186445i
$903$		0			0
$904$	35.2944	−	18.7986i	1.17387	−	0.625233i
$905$	59.2890	−	34.2305i	1.97083	−	1.13786i
$906$		0			0
$907$	−14.4058	−	8.31721i	−0.478338	−	0.276168i	0.241386	−	0.970429i	$-0.422398\pi$
$907$	−14.4058	−	8.31721i	−0.478338	−	0.276168i	−0.719723	+	0.694261i	$0.755731\pi$
$908$	−24.6240	−	9.60352i	−0.817176	−	0.318704i
$909$		0			0
$910$	−14.6743	+	66.3017i	−0.486448	+	2.19788i
$911$	20.7017	+	35.8564i	0.685877	+	1.18797i	0.973160	+	0.230129i	$0.0739147\pi$
$911$	20.7017	+	35.8564i	0.685877	+	1.18797i	−0.287283	+	0.957846i	$0.592752\pi$
$912$		0			0
$913$	38.8827			1.28683
$914$	31.1311	+	26.7326i	1.02972	+	0.884236i
$915$		0			0
$916$	−23.7204	+	18.9995i	−0.783746	+	0.627761i
$917$	−11.6930	−	7.25757i	−0.386138	−	0.239666i
$918$		0			0
$919$	32.1594	+	18.5672i	1.06084	+	0.612476i	0.925664	−	0.378346i	$-0.123507\pi$
$919$	32.1594	+	18.5672i	1.06084	+	0.612476i	0.135175	+	0.990822i	$0.456840\pi$
$920$	−39.3864	+	20.9781i	−1.29853	+	0.691629i
$921$		0			0
$922$	−10.5926	−	1.99250i	−0.348848	−	0.0656196i
$923$	−28.5669	+	49.4794i	−0.940292	+	1.62863i
$924$		0			0
$925$	2.34521	+	4.06202i	0.0771099	+	0.133558i
$926$	6.19065	+	17.6314i	0.203437	+	0.579404i
$927$		0			0
$928$	−15.0626	+	1.77870i	−0.494455	+	0.0583888i
$929$			33.5384i			1.10036i	0.835046	+	0.550180i	$0.185441\pi$
$929$			33.5384i			1.10036i	−0.835046	+	0.550180i	$0.814559\pi$
$930$		0			0
$931$	−13.2054	+	6.53984i	−0.432790	+	0.214335i
$932$	4.66605	−	11.9640i	0.152842	−	0.391895i
$933$		0			0
$934$	−12.5843	+	4.41854i	−0.411772	+	0.144579i
$935$	−18.8749	−	32.6923i	−0.617275	−	1.06915i
$936$		0			0
$937$	20.2579			0.661796			0.330898	−	0.943666i	$-0.392648\pi$
$937$	20.2579			0.661796			0.330898	+	0.943666i	$0.392648\pi$
$938$	−5.93977	+	26.8372i	−0.193940	+	0.876267i
$939$		0			0
$940$	−7.33315	−	9.15528i	−0.239181	−	0.298612i
$941$			7.87319i			0.256659i	0.991732	+	0.128329i	$0.0409615\pi$
$941$			7.87319i			0.256659i	−0.991732	+	0.128329i	$0.959039\pi$
$942$		0			0
$943$			33.2506i			1.08279i
$944$	−27.1346	+	8.49710i	−0.883155	+	0.276557i
$945$		0			0
$946$	−18.0588	+	21.0301i	−0.587141	+	0.683747i
$947$	−35.4032			−1.15045			−0.575225	−	0.817995i	$-0.695086\pi$
$947$	−35.4032			−1.15045			−0.575225	+	0.817995i	$0.695086\pi$
$948$		0			0
$949$	−74.0640			−2.40422
$950$	9.51797	+	1.79036i	0.308804	+	0.0580871i
$951$		0			0
$952$	−12.2783	−	24.9373i	−0.397941	−	0.808224i
$953$			23.9458i			0.775681i	0.921727	+	0.387840i	$0.126779\pi$
$953$			23.9458i			0.775681i	−0.921727	+	0.387840i	$0.873221\pi$
$954$		0			0
$955$	−13.6811	+	7.89878i	−0.442710	+	0.255599i
$956$	20.5500	+	8.01463i	0.664634	+	0.259212i
$957$		0			0
$958$	5.25767	−	1.84605i	0.169867	−	0.0596430i
$959$	34.6417	+	1.10487i	1.11864	+	0.0356782i
$960$		0			0
$961$	30.9341			0.997873
$962$	−2.38130	+	12.6595i	−0.0767763	+	0.408160i
$963$		0			0
$964$	7.67744	+	2.99425i	0.247274	+	0.0964384i
$965$	−29.9650	+	17.3003i	−0.964609	+	0.556917i
$966$		0			0
$967$	−2.20834	−	1.27499i	−0.0710154	−	0.0410008i	0.464072	−	0.885798i	$-0.346388\pi$
$967$	−2.20834	−	1.27499i	−0.0710154	−	0.0410008i	−0.535087	+	0.844797i	$0.679721\pi$
$968$	−4.28249	−	0.146493i	−0.137645	−	0.00470846i
$969$		0			0
$970$	−13.3408	−	37.9957i	−0.428349	−	1.21997i
$971$	18.4002	−	31.8700i	0.590489	−	1.02276i	−0.403677	−	0.914901i	$-0.632268\pi$
$971$	18.4002	−	31.8700i	0.590489	−	1.02276i	0.994167	−	0.107856i	$-0.0343985\pi$
$972$		0			0
$973$	11.8521	+	0.378013i	0.379959	+	0.0121185i
$974$	47.7425	+	8.98054i	1.52977	+	0.287755i
$975$		0			0
$976$	−21.6463	+	6.77846i	−0.692881	+	0.216973i
$977$			15.3282i			0.490391i	0.969474	+	0.245196i	$0.0788522\pi$
$977$			15.3282i			0.490391i	−0.969474	+	0.245196i	$0.921148\pi$
$978$		0			0
$979$	25.9106	−	14.9595i	0.828107	−	0.478108i
$980$	40.0639	−	3.53354i	1.27980	−	0.112875i
$981$		0			0
$982$	41.1927	−	14.4634i	1.31451	−	0.461545i
$983$	−4.36785	+	7.56535i	−0.139313	+	0.241297i	−0.927237	−	0.374476i	$-0.877823\pi$
$983$	−4.36785	+	7.56535i	−0.139313	+	0.241297i	0.787924	+	0.615773i	$0.211156\pi$
$984$		0			0
$985$	−16.1033	−	27.8918i	−0.513095	−	0.888706i
$986$	−13.2891	+	4.66599i	−0.423210	+	0.148595i
$987$		0			0
$988$	16.6281	+	20.7598i	0.529011	+	0.660458i
$989$	26.3519	+	15.2143i	0.837943	+	0.483787i
$990$		0			0
$991$	−14.8582	+	8.57839i	−0.471986	+	0.272501i	−0.717071	−	0.697000i	$-0.754518\pi$
$991$	−14.8582	+	8.57839i	−0.471986	+	0.272501i	0.245084	+	0.969502i	$0.421184\pi$
$992$	0.573686	−	1.33431i	0.0182146	−	0.0423644i
$993$		0			0
$994$	33.0397	+	7.31253i	1.04795	+	0.231939i
$995$	26.0586	−	45.1348i	0.826113	−	1.43087i
$996$		0			0
$997$	−8.43829	+	14.6155i	−0.267243	+	0.462879i	−0.968149	−	0.250375i	$-0.919446\pi$
$997$	−8.43829	+	14.6155i	−0.267243	+	0.462879i	0.700906	+	0.713254i	$0.252779\pi$
$998$	7.12635	+	1.34049i	0.225581	+	0.0424325i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.11		88
3.2	odd	2		252.2.bb.a.23.34	yes	88
4.3	odd	2	inner	756.2.bb.a.611.34		88
7.4	even	3		756.2.o.a.179.41		88
9.2	odd	6		756.2.o.a.359.26		88
9.7	even	3		252.2.o.a.191.19	yes	88
12.11	even	2		252.2.bb.a.23.11	yes	88
21.11	odd	6		252.2.o.a.95.4	✓	88
28.11	odd	6		756.2.o.a.179.26		88
36.7	odd	6		252.2.o.a.191.4	yes	88
36.11	even	6		756.2.o.a.359.41		88
63.11	odd	6	inner	756.2.bb.a.683.34		88
63.25	even	3		252.2.bb.a.11.11	yes	88
84.11	even	6		252.2.o.a.95.19	yes	88
252.11	even	6	inner	756.2.bb.a.683.11		88
252.151	odd	6		252.2.bb.a.11.34	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.4	✓	88	21.11	odd	6
252.2.o.a.95.19	yes	88	84.11	even	6
252.2.o.a.191.4	yes	88	36.7	odd	6
252.2.o.a.191.19	yes	88	9.7	even	3
252.2.bb.a.11.11	yes	88	63.25	even	3
252.2.bb.a.11.34	yes	88	252.151	odd	6
252.2.bb.a.23.11	yes	88	12.11	even	2
252.2.bb.a.23.34	yes	88	3.2	odd	2
756.2.o.a.179.26		88	28.11	odd	6
756.2.o.a.179.41		88	7.4	even	3
756.2.o.a.359.26		88	9.2	odd	6
756.2.o.a.359.41		88	36.11	even	6
756.2.bb.a.611.11		88	1.1	even	1	trivial
756.2.bb.a.611.34		88	4.3	odd	2	inner
756.2.bb.a.683.11		88	252.11	even	6	inner
756.2.bb.a.683.34		88	63.11	odd	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07292 - 0.921328i) q^{2} +(0.302311 + 1.97702i) q^{4} +(2.48793 - 1.43641i) q^{5} +(-2.33229 + 1.24916i) q^{7} +(1.49713 - 2.39971i) q^{8} +O(q^{10})\)	\(q+(-1.07292 - 0.921328i) q^{2} +(0.302311 + 1.97702i) q^{4} +(2.48793 - 1.43641i) q^{5} +(-2.33229 + 1.24916i) q^{7} +(1.49713 - 2.39971i) q^{8} +(-3.99275 - 0.751051i) q^{10} +(-1.76883 + 3.06370i) q^{11} +(-3.15869 + 5.47102i) q^{13} +(3.65325 + 0.808558i) q^{14} +(-3.81722 + 1.19535i) q^{16} +(-3.21678 + 1.85721i) q^{17} +(-1.82312 - 1.05258i) q^{19} +(3.59194 + 4.48445i) q^{20} +(4.72047 - 1.65743i) q^{22} +(-2.74595 - 4.75613i) q^{23} +(1.62654 - 2.81725i) q^{25} +(8.42962 - 2.95977i) q^{26} +(-3.17469 - 4.23336i) q^{28} +(-2.32201 + 1.34061i) q^{29} -0.256752i q^{31} +(5.19687 + 2.23440i) q^{32} +(5.16245 + 0.971075i) q^{34} +(-4.00829 + 6.45796i) q^{35} +(-0.720918 + 1.24867i) q^{37} +(0.986290 + 2.80902i) q^{38} +(0.277792 - 8.12081i) q^{40} +(-5.24333 - 3.02724i) q^{41} +(-4.79832 + 2.77031i) q^{43} +(-6.59172 - 2.57082i) q^{44} +(-1.43577 + 7.63287i) q^{46} -2.04156 q^{47} +(3.87919 - 5.82682i) q^{49} +(-4.34076 + 1.52411i) q^{50} +(-11.7712 - 4.59085i) q^{52} +(-1.96139 + 1.13241i) q^{53} +10.1630i q^{55} +(-0.494120 + 7.46698i) q^{56} +(3.72647 + 0.700962i) q^{58} +7.10847 q^{59} +5.67070 q^{61} +(-0.236553 + 0.275474i) q^{62} +(-3.51721 - 7.18535i) q^{64} +18.1487i q^{65} +7.34613i q^{67} +(-4.64421 - 5.79819i) q^{68} +(10.2505 - 3.23592i) q^{70} +9.04391 q^{71} +(5.86192 + 10.1531i) q^{73} +(1.92392 - 0.675516i) q^{74} +(1.52982 - 3.92255i) q^{76} +(0.298371 - 9.35499i) q^{77} +12.3827i q^{79} +(-7.77997 + 8.45703i) q^{80} +(2.83659 + 8.07880i) q^{82} +(-5.49556 - 9.51858i) q^{83} +(-5.33543 + 9.24123i) q^{85} +(7.70058 + 1.44851i) q^{86} +(4.70382 + 8.83141i) q^{88} +(-7.32424 - 4.22865i) q^{89} +(0.532818 - 16.7057i) q^{91} +(8.57284 - 6.86663i) q^{92} +(2.19043 + 1.88095i) q^{94} -6.04773 q^{95} +(4.95593 + 8.58392i) q^{97} +(-9.53047 + 2.67770i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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