LMFDB - Embedded newform 750.2.o.a.469.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, degree $20$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			469.3
Character	$\chi$	$=$	750.469
Dual form			750.2.o.a.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.00451670 - 2.23606i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-1.58750 - 2.18500i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})$	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.00451670 - 2.23606i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-1.58750 - 2.18500i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(0.144911 + 2.23137i) q^{10} +(0.188269 + 2.99246i) q^{11} +(0.844328 - 0.535827i) q^{12} +(-5.06638 - 4.19128i) q^{13} +(1.72156 + 2.08101i) q^{14} +(-0.956156 - 2.02133i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.607112 - 4.80579i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-2.86198 + 6.08203i) q^{19} +(-0.284734 - 2.21787i) q^{20} +(-2.36674 - 1.30113i) q^{21} +(-0.375796 - 2.97473i) q^{22} +(0.901139 + 2.27602i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.99996 + 0.0201993i) q^{25} +(5.31956 + 3.86489i) q^{26} +(0.248690 - 0.968583i) q^{27} +(-1.84883 - 1.96881i) q^{28} +(3.85496 - 3.62005i) q^{29} +(1.08119 + 1.95730i) q^{30} +(-6.14104 - 0.775794i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(1.44448 + 2.62750i) q^{33} +(-0.304156 + 4.83443i) q^{34} +(-4.87864 + 3.55961i) q^{35} +(0.535827 - 0.844328i) q^{36} +(2.52558 + 9.83649i) q^{37} +(2.47444 - 6.24973i) q^{38} +(-6.36876 - 1.63522i) q^{39} +(0.423433 + 2.19561i) q^{40} +(-6.93002 - 2.74379i) q^{41} +(2.44377 + 1.14995i) q^{42} +(-5.20449 - 1.69104i) q^{43} +(0.561839 + 2.94526i) q^{44} +(-1.72580 - 1.42184i) q^{45} +(-1.04227 - 2.21494i) q^{46} +(10.0357 + 1.91440i) q^{47} +(0.770513 - 0.637424i) q^{48} +(-0.0909709 + 0.279980i) q^{49} +(4.98882 - 0.334109i) q^{50} +(-1.49687 - 4.60690i) q^{51} +(-5.55174 - 3.52324i) q^{52} +(2.26150 - 4.11365i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(6.69048 - 0.434499i) q^{55} +(1.96881 + 1.84883i) q^{56} +6.72176i q^{57} +(-3.62005 + 3.85496i) q^{58} +(1.22764 + 1.93445i) q^{59} +(-1.20196 - 1.88555i) q^{60} +(-1.38496 + 0.548345i) q^{61} +(6.17764 + 0.388664i) q^{62} +(-2.69548 - 0.169585i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-9.34908 + 11.3477i) q^{65} +(-1.60661 - 2.53161i) q^{66} +(7.55391 - 8.04410i) q^{67} -4.84399i q^{68} +(1.78446 + 1.67572i) q^{69} +(4.64550 - 3.85892i) q^{70} +(2.15146 - 11.2784i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-9.71642 - 6.16623i) q^{73} +(-3.13824 - 9.65850i) q^{74} +(-4.51550 + 2.14716i) q^{75} +(-2.07714 + 6.39277i) q^{76} +(6.23965 - 5.16189i) q^{77} +(6.45887 + 1.23210i) q^{78} +(-3.40890 - 7.24429i) q^{79} +(-0.560461 - 2.16469i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(7.08862 + 2.30323i) q^{82} +(-3.52164 - 1.65716i) q^{83} +(-2.51115 - 0.994235i) q^{84} +(-10.7488 - 1.33584i) q^{85} +(5.30040 + 1.36091i) q^{86} +(1.94673 - 4.91688i) q^{87} +(-0.745665 - 2.90418i) q^{88} +(0.633835 - 0.998765i) q^{89} +(1.81167 + 1.31067i) q^{90} +(-1.11508 + 17.7237i) q^{91} +(1.17929 + 2.14513i) q^{92} +(-5.88690 + 1.91277i) q^{93} +(-10.1361 - 1.28048i) q^{94} +(13.6127 + 6.37211i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-6.10799 - 6.50435i) q^{97} +(0.0732113 - 0.285139i) q^{98} +(2.42574 + 1.76240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{49}{50}\right)$	$1$

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 $

$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$2$	−0.998027	+	0.0627905i	−0.705711	+	0.0443996i
$3$	0.904827	−	0.425779i	0.522402	−	0.245824i
$3$	0.904827	−	0.425779i	0.522402	−	0.245824i
$4$	0.992115	−	0.125333i	0.496057	−	0.0626666i
$5$	−0.00451670	−	2.23606i	−0.00201993	−	0.999998i
$5$	−0.00451670	−	2.23606i	−0.00201993	−	0.999998i
$6$	−0.876307	+	0.481754i	−0.357751	+	0.196675i
$7$	−1.58750	−	2.18500i	−0.600018	−	0.825854i	0.395692	−	0.918383i	$-0.370505\pi$
$7$	−1.58750	−	2.18500i	−0.600018	−	0.825854i	−0.995710	+	0.0925296i	$0.970505\pi$
$8$	−0.982287	+	0.187381i	−0.347291	+	0.0662493i
$9$	0.637424	−	0.770513i	0.212475	−	0.256838i
$10$	0.144911	+	2.23137i	0.0458250	+	0.705620i
$11$	0.188269	+	2.99246i	0.0567654	+	0.902260i	0.918629	+	0.395120i	$0.129297\pi$
$11$	0.188269	+	2.99246i	0.0567654	+	0.902260i	−0.861864	+	0.507140i	$0.830703\pi$
$12$	0.844328	−	0.535827i	0.243736	−	0.154680i
$13$	−5.06638	−	4.19128i	−1.40516	−	1.16245i	−0.964280	−	0.264887i	$-0.914665\pi$
$13$	−5.06638	−	4.19128i	−1.40516	−	1.16245i	−0.440883	−	0.897565i	$-0.645335\pi$
$14$	1.72156	+	2.08101i	0.460107	+	0.556174i
$15$	−0.956156	−	2.02133i	−0.246879	−	0.521905i
$16$	0.968583	−	0.248690i	0.242146	−	0.0621725i
$17$	0.607112	−	4.80579i	0.147246	−	1.16558i	−0.729278	−	0.684218i	$-0.760144\pi$
$17$	0.607112	−	4.80579i	0.147246	−	1.16558i	0.876524	−	0.481358i	$-0.159856\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−2.86198	+	6.08203i	−0.656584	+	1.39531i	0.247891	+	0.968788i	$0.420262\pi$
$19$	−2.86198	+	6.08203i	−0.656584	+	1.39531i	−0.904476	+	0.426525i	$0.859738\pi$
$20$	−0.284734	−	2.21787i	−0.0636685	−	0.495930i
$21$	−2.36674	−	1.30113i	−0.516465	−	0.283929i
$22$	−0.375796	−	2.97473i	−0.0801200	−	0.634215i
$23$	0.901139	+	2.27602i	0.187900	+	0.474582i	0.992937	−	0.118643i	$-0.0378544\pi$
$23$	0.901139	+	2.27602i	0.187900	+	0.474582i	−0.805037	+	0.593225i	$0.797854\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−4.99996	+	0.0201993i	−0.999992	+	0.00403985i
$26$	5.31956	+	3.86489i	1.04325	+	0.757967i
$27$	0.248690	−	0.968583i	0.0478604	−	0.186404i
$28$	−1.84883	−	1.96881i	−0.349397	−	0.372070i
$29$	3.85496	−	3.62005i	0.715848	−	0.672226i	−0.238425	−	0.971161i	$-0.576631\pi$
$29$	3.85496	−	3.62005i	0.715848	−	0.672226i	0.954274	+	0.298935i	$0.0966313\pi$
$30$	1.08119	+	1.95730i	0.197397	+	0.357353i
$31$	−6.14104	−	0.775794i	−1.10296	−	0.139337i	−0.447296	−	0.894386i	$-0.647613\pi$
$31$	−6.14104	−	0.775794i	−1.10296	−	0.139337i	−0.655668	+	0.755049i	$0.727613\pi$
$32$	−0.951057	+	0.309017i	−0.168125	+	0.0546270i
$33$	1.44448	+	2.62750i	0.251451	+	0.457388i
$34$	−0.304156	+	4.83443i	−0.0521624	+	0.829097i
$35$	−4.87864	+	3.55961i	−0.824640	+	0.601685i
$36$	0.535827	−	0.844328i	0.0893045	−	0.140721i
$37$	2.52558	+	9.83649i	0.415203	+	1.61711i	0.740886	+	0.671631i	$0.234406\pi$
$37$	2.52558	+	9.83649i	0.415203	+	1.61711i	−0.325683	+	0.945479i	$0.605594\pi$
$38$	2.47444	−	6.24973i	0.401408	−	1.01384i
$39$	−6.36876	−	1.63522i	−1.01982	−	0.261845i
$40$	0.423433	+	2.19561i	0.0669507	+	0.347156i
$41$	−6.93002	−	2.74379i	−1.08229	−	0.428508i	−0.241792	−	0.970328i	$-0.577735\pi$
$41$	−6.93002	−	2.74379i	−1.08229	−	0.428508i	−0.840494	+	0.541820i	$0.817735\pi$
$42$	2.44377	+	1.14995i	0.377082	+	0.177441i
$43$	−5.20449	−	1.69104i	−0.793677	−	0.257881i	−0.116008	−	0.993248i	$-0.537010\pi$
$43$	−5.20449	−	1.69104i	−0.793677	−	0.257881i	−0.677669	+	0.735367i	$0.737010\pi$
$44$	0.561839	+	2.94526i	0.0847005	+	0.444015i
$45$	−1.72580	−	1.42184i	−0.257266	−	0.211955i
$46$	−1.04227	−	2.21494i	−0.153675	−	0.326576i
$47$	10.0357	+	1.91440i	1.46385	+	0.279244i	0.856895	−	0.515491i	$-0.172390\pi$
$47$	10.0357	+	1.91440i	1.46385	+	0.279244i	0.606956	+	0.794736i	$0.292390\pi$
$48$	0.770513	−	0.637424i	0.111214	−	0.0920042i
$49$	−0.0909709	+	0.279980i	−0.0129958	+	0.0399971i
$50$	4.98882	−	0.334109i	0.705526	−	0.0472502i
$51$	−1.49687	−	4.60690i	−0.209604	−	0.645096i
$52$	−5.55174	−	3.52324i	−0.769888	−	0.488586i
$53$	2.26150	−	4.11365i	0.310641	−	0.565053i	−0.674193	−	0.738555i	$-0.735508\pi$
$53$	2.26150	−	4.11365i	0.310641	−	0.565053i	0.984833	+	0.173502i	$0.0555084\pi$
$54$	−0.187381	+	0.982287i	−0.0254994	+	0.133672i
$55$	6.69048	−	0.434499i	0.902143	−	0.0585878i
$56$	1.96881	+	1.84883i	0.263093	+	0.247061i
$57$			6.72176i			0.890318i
$58$	−3.62005	+	3.85496i	−0.475336	+	0.506181i
$59$	1.22764	+	1.93445i	0.159825	+	0.251844i	0.914798	−	0.403912i	$-0.132350\pi$
$59$	1.22764	+	1.93445i	0.159825	+	0.251844i	−0.754973	+	0.655756i	$0.772350\pi$
$60$	−1.20196	−	1.88555i	−0.155172	−	0.243424i
$61$	−1.38496	+	0.548345i	−0.177326	+	0.0702083i	−0.455110	−	0.890435i	$-0.650400\pi$
$61$	−1.38496	+	0.548345i	−0.177326	+	0.0702083i	0.277784	+	0.960644i	$0.410400\pi$
$62$	6.17764	+	0.388664i	0.784561	+	0.0493604i
$63$	−2.69548	−	0.169585i	−0.339599	−	0.0213658i
$64$	0.929776	−	0.368125i	0.116222	−	0.0460156i
$65$	−9.34908	+	11.3477i	−1.15961	+	1.40751i
$66$	−1.60661	−	2.53161i	−0.197760	−	0.311620i
$67$	7.55391	−	8.04410i	0.922857	−	0.982743i	−0.0770412	−	0.997028i	$-0.524547\pi$
$67$	7.55391	−	8.04410i	0.922857	−	0.982743i	0.999898	+	0.0142852i	$0.00454729\pi$
$68$		−	4.84399i		−	0.587420i
$69$	1.78446	+	1.67572i	0.214823	+	0.201732i
$70$	4.64550	−	3.85892i	0.555243	−	0.461229i
$71$	2.15146	−	11.2784i	0.255332	−	1.33850i	−0.591358	−	0.806409i	$-0.701408\pi$
$71$	2.15146	−	11.2784i	0.255332	−	1.33850i	0.846690	−	0.532087i	$-0.178592\pi$
$72$	−0.481754	+	0.876307i	−0.0567752	+	0.103274i
$73$	−9.71642	−	6.16623i	−1.13722	−	0.721702i	−0.172508	−	0.985008i	$-0.555187\pi$
$73$	−9.71642	−	6.16623i	−1.13722	−	0.721702i	−0.964712	+	0.263306i	$0.915187\pi$
$74$	−3.13824	−	9.65850i	−0.364813	−	1.12278i
$75$	−4.51550	+	2.14716i	−0.521405	+	0.247932i
$76$	−2.07714	+	6.39277i	−0.238264	+	0.733301i
$77$	6.23965	−	5.16189i	0.711074	−	0.588252i
$78$	6.45887	+	1.23210i	0.731323	+	0.139507i
$79$	−3.40890	−	7.24429i	−0.383532	−	0.815046i	−0.999625	−	0.0273732i	$-0.991286\pi$
$79$	−3.40890	−	7.24429i	−0.383532	−	0.815046i	0.616094	−	0.787673i	$-0.288714\pi$
$80$	−0.560461	−	2.16469i	−0.0626615	−	0.242020i
$81$	−0.187381	−	0.982287i	−0.0208201	−	0.109143i
$82$	7.08862	+	2.30323i	0.782808	+	0.254350i
$83$	−3.52164	−	1.65716i	−0.386550	−	0.181897i	0.222677	−	0.974892i	$-0.428520\pi$
$83$	−3.52164	−	1.65716i	−0.386550	−	0.181897i	−0.609228	+	0.792995i	$0.708520\pi$
$84$	−2.51115	−	0.994235i	−0.273989	−	0.108480i
$85$	−10.7488	−	1.33584i	−1.16587	−	0.144892i
$86$	5.30040	+	1.36091i	0.571557	+	0.146751i
$87$	1.94673	−	4.91688i	0.208711	−	0.527145i
$88$	−0.745665	−	2.90418i	−0.0794882	−	0.309586i
$89$	0.633835	−	0.998765i	0.0671864	−	0.105869i	−0.809074	−	0.587707i	$-0.800031\pi$
$89$	0.633835	−	0.998765i	0.0671864	−	0.105869i	0.876260	+	0.481838i	$0.160031\pi$
$90$	1.81167	+	1.31067i	0.190967	+	0.138157i
$91$	−1.11508	+	17.7237i	−0.116892	+	1.85795i
$92$	1.17929	+	2.14513i	0.122950	+	0.223645i
$93$	−5.88690	+	1.91277i	−0.610443	+	0.198345i
$94$	−10.1361	−	1.28048i	−1.04545	−	0.132072i
$95$	13.6127	+	6.37211i	1.39664	+	0.653765i
$96$	−0.728969	+	0.684547i	−0.0744000	+	0.0698663i
$97$	−6.10799	−	6.50435i	−0.620172	−	0.660417i	0.339804	−	0.940496i	$-0.389639\pi$
$97$	−6.10799	−	6.50435i	−0.620172	−	0.660417i	−0.959977	+	0.280080i	$0.909639\pi$
$98$	0.0732113	−	0.285139i	0.00739546	−	0.0288034i
$99$	2.42574	+	1.76240i	0.243796	+	0.177128i
$100$	−4.95800	+	0.646701i	−0.495800	+	0.0646701i
$101$	−7.07217	+	5.13823i	−0.703707	+	0.511273i	−0.881137	−	0.472860i	$-0.843222\pi$
$101$	−7.07217	+	5.13823i	−0.703707	+	0.511273i	0.177430	+	0.984133i	$0.443222\pi$
$102$	1.78319	+	4.50382i	0.176562	+	0.445945i
$103$	−2.19682	−	17.3897i	−0.216460	−	1.71345i	−0.608540	−	0.793523i	$-0.708245\pi$
$103$	−2.19682	−	17.3897i	−0.216460	−	1.71345i	0.392081	−	0.919931i	$-0.371755\pi$
$104$	5.76201	+	3.16769i	0.565012	+	0.310618i
$105$	−2.89871	+	5.29806i	−0.282885	+	0.517037i
$106$	−1.99874	+	4.24753i	−0.194135	+	0.412557i
$107$	−4.79102	+	6.59427i	−0.463165	+	0.637492i	−0.975161	−	0.221495i	$-0.928906\pi$
$107$	−4.79102	+	6.59427i	−0.463165	+	0.637492i	0.511996	+	0.858988i	$0.328906\pi$
$108$	0.125333	−	0.992115i	0.0120602	−	0.0954663i
$109$	9.41248	−	2.41671i	0.901552	−	0.231479i	0.230660	−	0.973034i	$-0.425911\pi$
$109$	9.41248	−	2.41671i	0.901552	−	0.231479i	0.670892	+	0.741555i	$0.265911\pi$
$110$	−6.64999	+	0.853740i	−0.634052	+	0.0814009i
$111$	6.47339	+	7.82499i	0.614427	+	0.742715i
$112$	−2.08101	−	1.72156i	−0.196637	−	0.162672i
$113$	−4.89181	+	3.10444i	−0.460183	+	0.292041i	−0.745638	−	0.666351i	$-0.767855\pi$
$113$	−4.89181	+	3.10444i	−0.460183	+	0.292041i	0.285455	+	0.958392i	$0.407855\pi$
$114$	−0.422063	−	6.70849i	−0.0395298	−	0.628308i
$115$	5.08525	−	2.02528i	0.474202	−	0.188859i
$116$	3.37085	−	4.07466i	0.312976	−	0.378323i
$117$	−6.45887	+	1.23210i	−0.597123	+	0.113907i
$118$	−1.34668	−	1.85355i	−0.123972	−	0.170633i
$119$	−11.4645	+	6.30264i	−1.05094	+	0.577762i
$120$	1.31798	+	1.80636i	0.120314	+	0.164897i
$121$	1.99390	−	0.251889i	0.181264	−	0.0228990i
$122$	1.34780	−	0.634225i	0.122024	−	0.0574200i
$123$	−7.43871	+	0.468004i	−0.670726	+	0.0421985i
$124$	−6.18985			−0.555865
$125$	0.0677502	+	11.1801i	0.00605976	+	0.999982i
$126$	2.70081			0.240607
$127$	8.11960	−	0.510842i	0.720498	−	0.0453299i	0.301692	−	0.953405i	$-0.402449\pi$
$127$	8.11960	−	0.510842i	0.720498	−	0.0453299i	0.418806	+	0.908076i	$0.362449\pi$
$128$	−0.904827	+	0.425779i	−0.0799762	+	0.0376339i
$129$	−5.42917	+	0.685864i	−0.478012	+	0.0603869i
$130$	8.61810	−	11.9123i	0.755858	−	1.04478i
$131$	9.51457	−	5.23068i	0.831291	−	0.457006i	−0.00846856	−	0.999964i	$-0.502696\pi$
$131$	9.51457	−	5.23068i	0.831291	−	0.457006i	0.839760	+	0.542958i	$0.182696\pi$
$132$	1.76240	+	2.42574i	0.153397	+	0.211133i
$133$	17.8326	−	3.40176i	1.54629	−	0.294970i
$134$	−7.03391	+	8.50254i	−0.607637	+	0.734507i
$135$	−2.16694	−	0.551712i	−0.186500	−	0.0474838i
$136$	0.304156	+	4.83443i	0.0260812	+	0.414549i
$137$	−4.99498	+	3.16991i	−0.426750	+	0.270824i	−0.731809	−	0.681510i	$-0.761324\pi$
$137$	−4.99498	+	3.16991i	−0.426750	+	0.270824i	0.305059	+	0.952333i	$0.401324\pi$
$138$	−1.88615	−	1.56036i	−0.160560	−	0.132827i
$139$	−6.36802	−	7.69761i	−0.540128	−	0.652903i	0.427876	−	0.903838i	$-0.359262\pi$
$139$	−6.36802	−	7.69761i	−0.540128	−	0.652903i	−0.968004	+	0.250935i	$0.919262\pi$
$140$	−4.39403	+	4.14300i	−0.371363	+	0.350148i
$141$	9.89565	−	2.54077i	0.833364	−	0.213971i
$142$	−1.43904	+	11.3912i	−0.120762	+	0.955929i
$143$	11.5884	−	15.9500i	0.969069	−	1.33381i
$144$	0.425779	−	0.904827i	0.0354816	−	0.0754023i
$145$	−8.11207	−	8.60358i	−0.673671	−	0.714489i
$146$	10.0844	+	5.54396i	0.834593	+	0.458821i
$147$	0.0368966	+	0.292067i	0.00304318	+	0.0240893i
$148$	3.73851	+	9.44239i	0.307303	+	0.776160i
$149$	16.4543	−	11.9547i	1.34799	−	0.979371i	0.348879	−	0.937168i	$-0.386562\pi$
$149$	16.4543	−	11.9547i	1.34799	−	0.979371i	0.999109	−	0.0422034i	$-0.0134378\pi$
$150$	4.37177	−	2.42645i	0.356953	−	0.198119i
$151$	6.75719	+	4.90939i	0.549893	+	0.399520i	0.827746	−	0.561103i	$-0.189623\pi$
$151$	6.75719	+	4.90939i	0.549893	+	0.399520i	−0.277853	+	0.960624i	$0.589623\pi$
$152$	1.67163	−	6.51058i	0.135587	−	0.528078i
$153$	−3.31594	−	3.53111i	−0.268078	−	0.285474i
$154$	−5.90322	+	5.54349i	−0.475695	+	0.446708i
$155$	−1.70699	+	13.7353i	−0.137109	+	1.10324i
$156$	−6.52349	−	0.824108i	−0.522297	−	0.0659815i
$157$	6.01787	−	1.95533i	0.480279	−	0.156052i	−0.0588648	−	0.998266i	$-0.518748\pi$
$157$	6.01787	−	1.95533i	0.480279	−	0.156052i	0.539143	+	0.842214i	$0.318748\pi$
$158$	3.85705	+	7.01595i	0.306850	+	0.558159i
$159$	0.294758	−	4.68504i	0.0233758	−	0.371548i
$160$	0.695277	+	2.12523i	0.0549665	+	0.168014i
$161$	3.54255	−	5.58216i	0.279192	−	0.439936i
$162$	0.248690	+	0.968583i	0.0195389	+	0.0760991i
$163$	3.33669	−	8.42752i	0.261350	−	0.660095i	−0.738551	−	0.674198i	$-0.764489\pi$
$163$	3.33669	−	8.42752i	0.261350	−	0.660095i	0.999901	+	0.0141035i	$0.00448942\pi$
$164$	−7.21926	−	1.85359i	−0.563729	−	0.144741i
$165$	5.86872	−	3.24181i	0.456879	−	0.252375i
$166$	3.61875	+	1.43276i	0.280869	+	0.111204i
$167$	10.5918	+	4.98413i	0.819619	+	0.385683i	0.789415	−	0.613860i	$-0.210384\pi$
$167$	10.5918	+	4.98413i	0.819619	+	0.385683i	0.0302043	+	0.999544i	$0.490384\pi$
$168$	2.56863	+	0.834597i	0.198174	+	0.0643906i
$169$	5.66549	+	29.6995i	0.435807	+	2.28458i
$170$	10.8115	+	0.658277i	0.829201	+	0.0504876i
$171$	2.86198	+	6.08203i	0.218861	+	0.465104i
$172$	−5.37539	−	1.02541i	−0.409870	−	0.0781869i
$173$	19.2627	−	15.9355i	1.46452	−	1.21155i	0.533906	−	0.845544i	$-0.320724\pi$
$173$	19.2627	−	15.9355i	1.46452	−	1.21155i	0.930611	−	0.366010i	$-0.119276\pi$
$174$	−1.63416	+	5.02941i	−0.123885	+	0.381279i
$175$	7.98156	+	10.8929i	0.603349	+	0.823423i
$176$	0.926549	+	2.85162i	0.0698412	+	0.214949i
$177$	1.93445	+	1.22764i	0.145402	+	0.0922751i
$178$	−0.569872	+	1.03659i	−0.0427137	+	0.0776959i
$179$	−3.41928	+	17.9245i	−0.255569	+	1.33974i	0.590660	+	0.806920i	$0.298867\pi$
$179$	−3.41928	+	17.9245i	−0.255569	+	1.33974i	−0.846229	+	0.532819i	$0.821133\pi$
$180$	−1.89039	−	1.19433i	−0.140901	−	0.0890200i
$181$	5.43842	+	5.10701i	0.404234	+	0.379601i	0.859826	−	0.510588i	$-0.170572\pi$
$181$	5.43842	+	5.10701i	0.404234	+	0.379601i	−0.455591	+	0.890189i	$0.650572\pi$
$182$		−	17.7588i		−	1.31637i
$183$	−1.01968	+	1.08584i	−0.0753766	+	0.0802679i
$184$	−1.31166	−	2.06685i	−0.0966969	−	0.152370i
$185$	21.9836	−	5.69179i	1.61627	−	0.418469i
$186$	5.75518	−	2.27864i	0.421990	−	0.167078i
$187$	14.4954	+	0.911975i	1.06001	+	0.0666902i
$188$	10.1965	+	0.641507i	0.743653	+	0.0467867i
$189$	−2.51115	+	0.994235i	−0.182659	+	0.0723200i
$190$	−13.9860	−	5.50479i	−1.01465	−	0.399359i
$191$	−8.18186	−	12.8926i	−0.592019	−	0.932873i	−0.999804	−	0.0197947i	$-0.993699\pi$
$191$	−8.18186	−	12.8926i	−0.592019	−	0.932873i	0.407785	−	0.913078i	$-0.366301\pi$
$192$	0.684547	−	0.728969i	0.0494029	−	0.0526088i
$193$			14.1286i			1.01700i	0.861062	+	0.508501i	$0.169800\pi$
$193$			14.1286i			1.01700i	−0.861062	+	0.508501i	$0.830200\pi$
$194$	6.50435	+	6.10799i	0.466985	+	0.438528i
$195$	−3.62769	+	14.2483i	−0.259784	+	1.02034i
$196$	−0.0551628	+	0.289174i	−0.00394020	+	0.0206553i
$197$	8.30893	−	15.1139i	0.591987	−	1.07682i	−0.395403	−	0.918508i	$-0.629395\pi$
$197$	8.30893	−	15.1139i	0.591987	−	1.07682i	0.987389	−	0.158312i	$-0.0506051\pi$
$198$	−2.53161	−	1.60661i	−0.179914	−	0.114177i
$199$	4.60098	+	14.1604i	0.326155	+	1.00380i	0.970917	+	0.239418i	$0.0769565\pi$
$199$	4.60098	+	14.1604i	0.326155	+	1.00380i	−0.644762	+	0.764383i	$0.723044\pi$
$200$	4.90761	−	0.956740i	0.347021	−	0.0676518i
$201$	3.40997	−	10.4948i	0.240521	−	0.740247i
$202$	6.73558	−	5.57216i	0.473914	−	0.392056i
$203$	−14.0296	−	2.67628i	−0.984682	−	0.187838i
$204$	−2.06247	−	4.38297i	−0.144402	−	0.306869i
$205$	−6.10398	+	15.5083i	−0.426321	+	1.08315i
$206$	3.28440	+	17.2174i	0.228835	+	1.19959i
$207$	2.32811	+	0.756448i	0.161815	+	0.0525768i
$208$	−5.94954	−	2.79964i	−0.412527	−	0.194120i
$209$	−18.7390	−	7.41931i	−1.29621	−	0.513204i
$210$	2.56032	−	5.46961i	0.176679	−	0.377439i
$211$	19.9233	+	5.11543i	1.37157	+	0.352161i	0.861407	−	0.507915i	$-0.169583\pi$
$211$	19.9233	+	5.11543i	1.37157	+	0.352161i	0.510167	+	0.860075i	$0.329583\pi$
$212$	1.72809	−	4.36465i	0.118686	−	0.299766i
$213$	−2.85539	−	11.1210i	−0.195648	−	0.762000i
$214$	4.36751	−	6.88209i	0.298557	−	0.470450i
$215$	−3.75777	+	11.6452i	−0.256278	+	0.794196i
$216$	−0.0627905	+	0.998027i	−0.00427235	+	0.0679071i
$217$	8.05378	+	14.6498i	0.546726	+	0.994491i
$218$	−9.24216	+	3.00296i	−0.625958	+	0.203386i
$219$	−11.4171	−	1.44232i	−0.771498	−	0.0974629i
$220$	6.58326	−	1.26961i	0.443843	−	0.0855972i
$221$	−23.2183	+	21.8034i	−1.56183	+	1.46666i
$222$	−6.95195	−	7.40308i	−0.466584	−	0.496862i
$223$	−6.09689	+	23.7458i	−0.408278	+	1.59014i	0.349051	+	0.937104i	$0.386504\pi$
$223$	−6.09689	+	23.7458i	−0.408278	+	1.59014i	−0.757329	+	0.653034i	$0.773496\pi$
$224$	2.18500	+	1.58750i	0.145992	+	0.106069i
$225$	−3.17153	+	3.86541i	−0.211435	+	0.257694i
$226$	4.68723	−	3.40547i	0.311790	−	0.226528i
$227$	0.715698	+	1.80765i	0.0475025	+	0.119978i	0.951591	−	0.307369i	$-0.0994485\pi$
$227$	0.715698	+	1.80765i	0.0475025	+	0.119978i	−0.904088	+	0.427346i	$0.859448\pi$
$228$	0.842460	+	6.66875i	0.0557932	+	0.441649i
$229$	−17.1523	−	9.42956i	−1.13346	−	0.623123i	−0.199283	−	0.979942i	$-0.563861\pi$
$229$	−17.1523	−	9.42956i	−1.13346	−	0.623123i	−0.934174	+	0.356819i	$0.883861\pi$
$230$	−4.94804	+	2.34059i	−0.326264	+	0.154334i
$231$	3.44798	−	7.32733i	0.226860	−	0.482103i
$232$	−3.10835	+	4.27828i	−0.204073	+	0.280883i
$233$	−1.33096	+	10.5356i	−0.0871938	+	0.690210i	0.886561	+	0.462611i	$0.153087\pi$
$233$	−1.33096	+	10.5356i	−0.0871938	+	0.690210i	−0.973755	+	0.227599i	$0.926913\pi$
$234$	6.36876	−	1.63522i	0.416339	−	0.106898i
$235$	4.23540	−	22.4490i	0.276287	−	1.46441i
$236$	1.46041	+	1.76533i	0.0950647	+	0.114913i
$237$	−6.16894	−	5.10339i	−0.400715	−	0.331501i
$238$	11.0461	−	7.01006i	0.716011	−	0.454395i
$239$	0.613810	+	9.75624i	0.0397041	+	0.631078i	0.966685	+	0.255970i	$0.0823947\pi$
$239$	0.613810	+	9.75624i	0.0397041	+	0.631078i	−0.926981	+	0.375109i	$0.877605\pi$
$240$	−1.42880	−	1.72004i	−0.0922287	−	0.111028i
$241$	0.119922	−	0.144960i	0.00772483	−	0.00933771i	−0.766637	−	0.642081i	$-0.778071\pi$
$241$	0.119922	−	0.144960i	0.00772483	−	0.00933771i	0.774362	+	0.632743i	$0.218071\pi$
$242$	−1.97415	+	0.376590i	−0.126903	+	0.0242081i
$243$	−0.587785	−	0.809017i	−0.0377064	−	0.0518985i
$244$	−1.30531	+	0.717602i	−0.0835641	+	0.0459398i
$245$	0.626463	+	0.202152i	0.0400233	+	0.0129150i
$246$	7.39465	−	0.934161i	0.471466	−	0.0595599i
$247$	39.9914	−	18.8185i	2.54459	−	1.19739i
$248$	6.17764	−	0.388664i	0.392280	−	0.0246802i
$249$	−3.89206			−0.246649
$250$	−0.769623	−	11.1538i	−0.0486752	−	0.705429i
$251$	9.52170			0.601004			0.300502	−	0.953781i	$-0.402846\pi$
$251$	9.52170			0.601004			0.300502	+	0.953781i	$0.402846\pi$
$252$	−2.69548	+	0.169585i	−0.169799	+	0.0106829i
$253$	−6.64123	+	3.12512i	−0.417530	+	0.196475i
$254$	−8.07151	+	1.01967i	−0.506451	+	0.0639797i
$255$	−10.2946	+	3.36791i	−0.644671	+	0.210907i
$256$	0.876307	−	0.481754i	0.0547692	−	0.0301096i
$257$	−4.62498	−	6.36574i	−0.288498	−	0.397084i	0.640027	−	0.768352i	$-0.278923\pi$
$257$	−4.62498	−	6.36574i	−0.288498	−	0.397084i	−0.928526	+	0.371268i	$0.878923\pi$
$258$	5.37539	−	1.02541i	0.334657	−	0.0638393i
$259$	17.4834	−	21.1338i	1.08637	−	1.31319i
$260$	−7.85312	+	12.4300i	−0.487030	+	0.770873i
$261$	−0.332051	−	5.27780i	−0.0205535	−	0.326688i
$262$	−9.16735	+	5.81778i	−0.566361	+	0.359424i
$263$	−3.40435	−	2.81633i	−0.209922	−	0.173662i	0.526521	−	0.850162i	$-0.323496\pi$
$263$	−3.40435	−	2.81633i	−0.209922	−	0.173662i	−0.736443	+	0.676500i	$0.763496\pi$
$264$	−1.91124	−	2.31029i	−0.117628	−	0.142188i
$265$	−9.20859	−	5.03827i	−0.565679	−	0.309499i
$266$	−17.5839	+	4.51477i	−1.07814	+	0.276818i
$267$	0.148258	−	1.17358i	0.00907325	−	0.0718221i
$268$	6.48615	−	8.92742i	0.396205	−	0.545329i
$269$	8.84099	−	18.7881i	0.539045	−	1.14553i	−0.430944	−	0.902379i	$-0.641819\pi$
$269$	8.84099	−	18.7881i	0.539045	−	1.14553i	0.969989	−	0.243150i	$-0.0781806\pi$
$270$	2.19730	+	0.414560i	0.133724	+	0.0252293i
$271$	0.831232	+	0.456974i	0.0504938	+	0.0277592i	0.506801	−	0.862063i	$-0.330828\pi$
$271$	0.831232	+	0.456974i	0.0504938	+	0.0277592i	−0.456307	+	0.889823i	$0.650828\pi$
$272$	−0.607112	−	4.80579i	−0.0368116	−	0.291394i
$273$	6.53743	+	16.5117i	0.395663	+	0.999332i
$274$	4.78608	−	3.47729i	0.289138	−	0.210071i
$275$	−1.00179	−	14.9584i	−0.0604099	−	0.902023i
$276$	1.98041	+	1.43885i	0.119207	+	0.0866086i
$277$	−2.31222	+	9.00550i	−0.138928	+	0.541088i	0.860568	+	0.509336i	$0.170109\pi$
$277$	−2.31222	+	9.00550i	−0.138928	+	0.541088i	−0.999496	+	0.0317523i	$0.989891\pi$
$278$	6.83879	+	7.28257i	0.410163	+	0.436780i
$279$	−4.51221	+	4.23725i	−0.270139	+	0.253677i
$280$	4.12522	−	4.41073i	0.246529	−	0.263591i
$281$	12.6887	+	1.60296i	0.756947	+	0.0956247i	0.494329	−	0.869275i	$-0.335414\pi$
$281$	12.6887	+	1.60296i	0.756947	+	0.0956247i	0.262619	+	0.964900i	$0.415414\pi$
$282$	−9.71658	+	3.15711i	−0.578614	+	0.188003i
$283$	−9.30046	−	16.9175i	−0.552855	−	1.00564i	−0.994122	−	0.108264i	$-0.965471\pi$
$283$	−9.30046	−	16.9175i	−0.552855	−	1.00564i	0.441267	−	0.897376i	$-0.354529\pi$
$284$	0.720945	−	11.4591i	0.0427802	−	0.679972i
$285$	15.0303	−	0.0303602i	0.890317	−	0.00179838i
$286$	−10.5640	+	16.6462i	−0.624662	+	0.984310i
$287$	5.00620	+	19.4979i	0.295507	+	1.15092i
$288$	−0.368125	+	0.929776i	−0.0216919	+	0.0547876i
$289$	−6.26111	−	1.60758i	−0.368301	−	0.0945636i
$290$	8.63629	+	8.07725i	0.507140	+	0.474312i
$291$	−8.29609	−	3.28466i	−0.486326	−	0.192550i
$292$	−10.4126	−	4.89981i	−0.609353	−	0.286740i
$293$	−28.1987	−	9.16231i	−1.64739	−	0.535268i	−0.669214	−	0.743070i	$-0.733369\pi$
$293$	−28.1987	−	9.16231i	−1.64739	−	0.535268i	−0.978171	+	0.207802i	$0.933369\pi$
$294$	−0.0551628	−	0.289174i	−0.00321716	−	0.0168650i
$295$	4.32001	−	2.75382i	0.251521	−	0.160334i
$296$	−4.32402	−	9.18902i	−0.251329	−	0.534101i
$297$	2.94526	+	0.561839i	0.170902	+	0.0326012i
$298$	−15.6712	+	12.9643i	−0.907807	+	0.751003i
$299$	4.97390	−	15.3081i	0.287648	−	0.885290i
$300$	−4.21078	+	2.69617i	−0.243110	+	0.155663i
$301$	4.56718	+	14.0563i	0.263248	+	0.810194i
$302$	−7.05212	−	4.47541i	−0.405804	−	0.257531i
$303$	−4.21134	+	7.66039i	−0.241935	+	0.440078i
$304$	−1.25953	+	6.60270i	−0.0722391	+	0.378691i
$305$	1.23239	+	3.09438i	0.0705664	+	0.177184i
$306$	3.53111	+	3.31594i	0.201860	+	0.189559i
$307$			4.34297i			0.247866i	0.992291	+	0.123933i	$0.0395508\pi$
$307$			4.34297i			0.247866i	−0.992291	+	0.123933i	$0.960449\pi$
$308$	5.54349	−	5.90322i	0.315870	−	0.336367i
$309$	−9.39190	−	14.7993i	−0.534287	−	0.841901i
$310$	0.841175	−	13.8153i	0.0477755	−	0.784659i
$311$	0.666236	−	0.263781i	0.0377788	−	0.0149577i	−0.349159	−	0.937063i	$-0.613533\pi$
$311$	0.666236	−	0.263781i	0.0377788	−	0.0149577i	0.386938	+	0.922106i	$0.373533\pi$
$312$	6.56236	+	0.412869i	0.371521	+	0.0233741i
$313$	−23.4783	−	1.47713i	−1.32707	−	0.0834924i	−0.616634	−	0.787250i	$-0.711504\pi$
$313$	−23.4783	−	1.47713i	−1.32707	−	0.0834924i	−0.710440	+	0.703757i	$0.751504\pi$
$314$	−5.88322	+	2.32933i	−0.332009	+	0.131452i
$315$	−0.367029	+	6.02804i	−0.0206797	+	0.339641i
$316$	−4.28997	−	6.75992i	−0.241330	−	0.380275i
$317$	−14.6121	+	15.5603i	−0.820698	+	0.873954i	−0.993827	−	0.110945i	$-0.964612\pi$
$317$	−14.6121	+	15.5603i	−0.820698	+	0.873954i	0.173129	+	0.984899i	$0.444612\pi$
$318$			4.69430i			0.263243i
$319$	11.5586	+	10.8543i	0.647158	+	0.607722i
$320$	−0.827349	−	2.07738i	−0.0462502	−	0.116129i
$321$	−1.52734	+	8.00659i	−0.0852478	+	0.446884i
$322$	−3.18505	+	5.79359i	−0.177496	+	0.322864i
$323$	27.4914	+	17.4466i	1.52966	+	0.970753i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	25.4164	+	20.8539i	1.40985	+	1.15677i
$326$	−2.80094	+	8.62041i	−0.155130	+	0.477440i
$327$	7.48768	−	6.19435i	0.414070	−	0.342548i
$328$	7.32140	+	1.39663i	0.404257	+	0.0771161i
$329$	−11.7486	−	24.9671i	−0.647721	−	1.37648i
$330$	−5.65359	+	3.60391i	−0.311220	+	0.198389i
$331$	0.418537	+	2.19405i	0.0230049	+	0.120596i	0.991937	−	0.126730i	$-0.0404482\pi$
$331$	0.418537	+	2.19405i	0.0230049	+	0.120596i	−0.968932	+	0.247326i	$0.920448\pi$
$332$	−3.70157	−	1.20271i	−0.203150	−	0.0660074i
$333$	9.18902	+	4.32402i	0.503555	+	0.236955i
$334$	−10.8839	−	4.30923i	−0.595539	−	0.235790i
$335$	−18.0212	−	16.8547i	−0.984605	−	0.920870i
$336$	−2.61596	−	0.671665i	−0.142712	−	0.0366423i
$337$	12.5614	−	31.7264i	0.684261	−	1.72825i	−0.00105239	−	0.999999i	$-0.500335\pi$
$337$	12.5614	−	31.7264i	0.684261	−	1.72825i	0.685314	−	0.728248i	$-0.259665\pi$
$338$	−7.51916	−	29.2852i	−0.408988	−	1.59290i
$339$	−3.10444	+	4.89181i	−0.168610	+	0.265687i
$340$	−10.8315	+	0.0218788i	−0.587418	+	0.00118655i
$341$	1.16536	−	18.5229i	0.0631078	−	1.00307i
$342$	−3.23823	−	5.89032i	−0.175103	−	0.318512i
$343$	−17.2242	+	5.59648i	−0.930020	+	0.302182i
$344$	5.42917	+	0.685864i	0.292721	+	0.0369793i
$345$	3.73895	−	3.99772i	0.201298	−	0.215230i
$346$	−18.2241	+	17.1136i	−0.979734	+	0.920031i
$347$	−15.2319	−	16.2204i	−0.817693	−	0.870755i	0.175826	−	0.984421i	$-0.443741\pi$
$347$	−15.2319	−	16.2204i	−0.817693	−	0.870755i	−0.993519	+	0.113666i	$0.963741\pi$
$348$	1.31513	−	5.12210i	0.0704984	−	0.274573i
$349$	5.49107	+	3.98949i	0.293930	+	0.213553i	0.724970	−	0.688780i	$-0.241853\pi$
$349$	5.49107	+	3.98949i	0.293930	+	0.213553i	−0.431040	+	0.902333i	$0.641853\pi$
$350$	−8.64978	−	10.3702i	−0.462350	−	0.554310i
$351$	−5.31956	+	3.86489i	−0.283937	+	0.206292i
$352$	−1.10378	−	2.78782i	−0.0588314	−	0.148591i
$353$	1.74056	+	13.7779i	0.0926404	+	0.733325i	0.968193	+	0.250203i	$0.0804972\pi$
$353$	1.74056	+	13.7779i	0.0926404	+	0.733325i	−0.875553	+	0.483122i	$0.839503\pi$
$354$	−2.00772	−	1.10375i	−0.106709	−	0.0586638i
$355$	−25.2289	−	4.75987i	−1.33901	−	0.252628i
$356$	0.503659	−	1.07033i	0.0266939	−	0.0567274i
$357$	−7.68982	+	10.5841i	−0.406988	+	0.560171i
$358$	2.28704	−	18.1038i	0.120874	−	0.956817i
$359$	5.12746	−	1.31651i	0.270617	−	0.0694826i	−0.110943	−	0.993827i	$-0.535387\pi$
$359$	5.12746	−	1.31651i	0.270617	−	0.0694826i	0.381560	+	0.924344i	$0.375387\pi$
$360$	1.96165	+	1.07327i	0.103388	+	0.0565665i
$361$	−16.6890	−	20.1736i	−0.878371	−	1.06177i
$362$	−5.74836	−	4.75545i	−0.302127	−	0.249941i
$363$	1.69689	−	1.07688i	0.0890636	−	0.0565214i
$364$	1.11508	+	17.7237i	0.0584461	+	0.928975i
$365$	−13.7442	+	21.7544i	−0.719404	+	1.13868i
$366$	0.949483	−	1.14773i	0.0496303	−	0.0599927i
$367$	18.2663	−	3.48449i	0.953495	−	0.181889i	0.312916	−	0.949781i	$-0.398694\pi$
$367$	18.2663	−	3.48449i	0.953495	−	0.181889i	0.640579	+	0.767892i	$0.278694\pi$
$368$	1.43885	+	1.98041i	0.0750053	+	0.103236i
$369$	−6.53148	+	3.59071i	−0.340015	+	0.186925i
$370$	−21.5828	+	7.06092i	−1.12204	+	0.367080i
$371$	−12.5785	+	1.58903i	−0.653041	+	0.0824983i
$372$	−5.60075	+	2.63551i	−0.290385	+	0.136645i
$373$	−19.4648	+	1.22462i	−1.00785	+	0.0634086i	−0.558124	−	0.829757i	$-0.688479\pi$
$373$	−19.4648	+	1.22462i	−1.00785	+	0.0634086i	−0.449727	+	0.893166i	$0.648479\pi$
$374$	−14.5241			−0.751022
$375$	4.82157	+	10.0872i	0.248985	+	0.520903i
$376$	−10.2166			−0.526882
$377$	−34.7033	+	2.18335i	−1.78731	+	0.112448i
$378$	2.44377	−	1.14995i	0.125694	−	0.0591470i
$379$	14.0713	−	1.77762i	0.722793	−	0.0913100i	0.244675	−	0.969605i	$-0.421319\pi$
$379$	14.0713	−	1.77762i	0.722793	−	0.0913100i	0.478119	+	0.878295i	$0.341319\pi$
$380$	14.3040	+	4.61574i	0.733781	+	0.236782i
$381$	7.12933	−	3.91938i	0.365247	−	0.200796i
$382$	8.97525	+	12.3534i	0.459214	+	0.632053i
$383$	17.7919	−	3.39399i	0.909124	−	0.173425i	0.288452	−	0.957494i	$-0.406860\pi$
$383$	17.7919	−	3.39399i	0.909124	−	0.173425i	0.620673	+	0.784070i	$0.286860\pi$
$384$	−0.637424	+	0.770513i	−0.0325284	+	0.0393201i
$385$	−11.5705	−	13.9289i	−0.589687	−	0.709885i
$386$	−0.887144	−	14.1008i	−0.0451545	−	0.717710i
$387$	−4.62043	+	2.93222i	−0.234870	+	0.149053i
$388$	−6.87504	−	5.68753i	−0.349027	−	0.288740i
$389$	6.61141	+	7.99182i	0.335212	+	0.405201i	0.911006	−	0.412393i	$-0.135307\pi$
$389$	6.61141	+	7.99182i	0.335212	+	0.405201i	−0.575794	+	0.817595i	$0.695307\pi$
$390$	2.72587	−	14.4480i	0.138030	−	0.731603i
$391$	11.4852	−	2.94889i	0.580829	−	0.149132i
$392$	0.0368966	−	0.292067i	0.00186356	−	0.0147516i
$393$	6.38192	−	8.78396i	0.321925	−	0.443092i
$394$	−7.34352	+	15.6058i	−0.369961	+	0.786208i
$395$	−16.1833	+	7.65524i	−0.814270	+	0.385177i
$396$	2.62750	+	1.44448i	0.132037	+	0.0725877i
$397$	−3.49327	−	27.6521i	−0.175322	−	1.38782i	−0.796733	−	0.604332i	$-0.793440\pi$
$397$	−3.49327	−	27.6521i	−0.175322	−	1.38782i	0.621411	−	0.783485i	$-0.286560\pi$
$398$	−5.48104	−	13.8435i	−0.274739	−	0.693913i
$399$	14.6871	−	10.6708i	0.735273	−	0.534207i
$400$	−4.83785	+	1.26300i	−0.241893	+	0.0631502i
$401$	27.9026	+	20.2724i	1.39339	+	1.01236i	0.995484	+	0.0949285i	$0.0302622\pi$
$401$	27.9026	+	20.2724i	1.39339	+	1.01236i	0.397904	+	0.917427i	$0.369738\pi$
$402$	−2.74427	+	10.6882i	−0.136872	+	0.533080i
$403$	27.8613	+	29.6693i	1.38787	+	1.47793i
$404$	−6.37241	+	5.98409i	−0.317039	+	0.297720i
$405$	−2.19561	+	0.423433i	−0.109101	+	0.0210406i
$406$	14.1699	+	1.79008i	0.703241	+	0.0888400i
$407$	−28.9598	+	9.40961i	−1.43548	+	0.466417i
$408$	2.33361	+	4.24482i	0.115531	+	0.210150i
$409$	−0.565174	+	8.98318i	−0.0279461	+	0.444190i	0.959028	+	0.283311i	$0.0914329\pi$
$409$	−0.565174	+	8.98318i	−0.0279461	+	0.444190i	−0.986974	+	0.160879i	$0.948567\pi$
$410$	5.11816	−	15.8610i	0.252768	−	0.783320i
$411$	−3.16991	+	4.99498i	−0.156360	+	0.246384i
$412$	−4.35900	−	16.9772i	−0.214753	−	0.836407i
$413$	2.27791	−	5.75333i	0.112088	−	0.283103i
$414$	−2.37101	−	0.608773i	−0.116529	−	0.0299195i
$415$	−3.68961	+	7.88210i	−0.181116	+	0.386917i
$416$	6.11359	+	2.42054i	0.299744	+	0.118677i
$417$	−9.03944	−	4.25364i	−0.442663	−	0.208302i
$418$	19.1679	+	6.22803i	0.937534	+	0.304623i
$419$	−3.99171	−	20.9253i	−0.195008	−	1.02227i	−0.936331	−	0.351118i	$-0.885802\pi$
$419$	−3.99171	−	20.9253i	−0.195008	−	1.02227i	0.741323	−	0.671148i	$-0.234198\pi$
$420$	−2.21183	+	5.61959i	−0.107926	+	0.274208i
$421$	−0.366331	−	0.778493i	−0.0178539	−	0.0379414i	0.895701	−	0.444656i	$-0.146674\pi$
$421$	−0.366331	−	0.778493i	−0.0178539	−	0.0379414i	−0.913555	+	0.406715i	$0.866674\pi$
$422$	−20.2052	−	3.85434i	−0.983572	−	0.187626i
$423$	7.87204	−	6.51232i	0.382752	−	0.316640i
$424$	−1.45062	+	4.46455i	−0.0704483	+	0.216818i
$425$	−2.93846	+	24.0410i	−0.142536	+	1.16616i
$426$	3.54805	+	10.9198i	0.171904	+	0.529065i
$427$	3.39676	+	2.15565i	0.164381	+	0.104319i
$428$	−3.92676	+	7.14275i	−0.189807	+	0.345258i
$429$	3.69428	−	19.3661i	0.178362	−	0.935005i
$430$	3.01914	−	11.8582i	0.145596	−	0.571852i
$431$	−12.8667	−	12.0827i	−0.619768	−	0.582001i	0.309732	−	0.950824i	$-0.399761\pi$
$431$	−12.8667	−	12.0827i	−0.619768	−	0.582001i	−0.929500	+	0.368823i	$0.879761\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−10.1639	+	10.8234i	−0.488445	+	0.520141i	−0.925221	−	0.379430i	$-0.876120\pi$
$433$	−10.1639	+	10.8234i	−0.488445	+	0.520141i	0.436776	+	0.899570i	$0.356120\pi$
$434$	−8.95775	−	14.1152i	−0.429986	−	0.677549i
$435$	−11.0032	−	4.33080i	−0.527565	−	0.207646i
$436$	9.03537	−	3.57735i	0.432716	−	0.171324i
$437$	−16.4218	−	1.03317i	−0.785563	−	0.0494235i
$438$	11.4852	+	0.722585i	0.548782	+	0.0345265i
$439$	−27.7507	+	10.9873i	−1.32447	+	0.524394i	−0.920630	−	0.390437i	$-0.872324\pi$
$439$	−27.7507	+	10.9873i	−1.32447	+	0.524394i	−0.403837	+	0.914831i	$0.632324\pi$
$440$	−6.49055	+	1.68047i	−0.309425	+	0.0801134i
$441$	0.157741	+	0.248560i	0.00751148	+	0.0118362i
$442$	21.8034	−	23.2183i	1.03708	−	1.10438i
$443$		−	11.7699i		−	0.559206i	−0.960116	−	0.279603i	$-0.909797\pi$
$443$		−	11.7699i		−	0.559206i	0.960116	−	0.279603i	$-0.0902029\pi$
$444$	7.40308	+	6.95195i	0.351335	+	0.329925i
$445$	−2.23616	−	1.41278i	−0.106004	−	0.0669724i
$446$	4.59385	−	24.0818i	0.217525	−	1.14031i
$447$	9.79821	−	17.8229i	0.463439	−	0.842993i
$448$	−2.28037	−	1.44717i	−0.107737	−	0.0683722i
$449$	6.20199	+	19.0878i	0.292690	+	0.900808i	0.983988	+	0.178237i	$0.0570394\pi$
$449$	6.20199	+	19.0878i	0.292690	+	0.900808i	−0.691297	+	0.722570i	$0.742961\pi$
$450$	2.92256	−	4.05692i	0.137771	−	0.191245i
$451$	6.90596	−	21.2543i	0.325189	−	1.00083i
$452$	−4.46415	+	3.69306i	−0.209976	+	0.173707i
$453$	8.20441	+	1.56507i	0.385477	+	0.0735336i
$454$	−0.827789	−	1.75914i	−0.0388501	−	0.0825606i
$455$	39.6364	+	2.41334i	1.85818	+	0.113139i
$456$	−1.25953	−	6.60270i	−0.0589830	−	0.309200i
$457$	−8.86005	−	2.87880i	−0.414456	−	0.134665i	0.0943644	−	0.995538i	$-0.469918\pi$
$457$	−8.86005	−	2.87880i	−0.414456	−	0.134665i	−0.508820	+	0.860873i	$0.669918\pi$
$458$	17.7106	+	8.33395i	0.827560	+	0.389420i
$459$	−4.50382	−	1.78319i	−0.210221	−	0.0832322i
$460$	4.79131	−	2.64666i	0.223396	−	0.123401i
$461$	−16.8409	−	4.32400i	−0.784358	−	0.201389i	−0.164786	−	0.986329i	$-0.552693\pi$
$461$	−16.8409	−	4.32400i	−0.784358	−	0.201389i	−0.619571	+	0.784940i	$0.712693\pi$
$462$	−2.98109	+	7.52937i	−0.138693	+	0.350298i
$463$	−4.54636	−	17.7069i	−0.211287	−	0.822909i	−0.982489	−	0.186319i	$-0.940344\pi$
$463$	−4.54636	−	17.7069i	−0.211287	−	0.822909i	0.771202	−	0.636590i	$-0.219656\pi$
$464$	2.83358	−	4.46501i	0.131546	−	0.207283i
$465$	4.30366	+	13.1548i	0.199578	+	0.610041i
$466$	0.666794	−	10.5984i	0.0308886	−	0.490960i
$467$	12.2890	+	22.3537i	0.568669	+	1.03441i	0.991735	+	0.128306i	$0.0409540\pi$
$467$	12.2890	+	22.3537i	0.568669	+	1.03441i	−0.423065	+	0.906099i	$0.639046\pi$
$468$	−6.25352	+	2.03189i	−0.289069	+	0.0939242i
$469$	−29.5682	−	3.73533i	−1.36533	−	0.172482i
$470$	−2.81746	+	22.6707i	−0.129960	+	1.04572i
$471$	4.61260	−	4.33152i	0.212537	−	0.199586i
$472$	−1.56838	−	1.67015i	−0.0721903	−	0.0768749i
$473$	4.08052	−	15.8926i	0.187623	−	0.730742i
$474$	6.47721	+	4.70597i	0.297508	+	0.216152i
$475$	14.1870	−	30.4677i	0.650942	−	1.39795i
$476$	−10.5841	+	7.68982i	−0.485123	+	0.352462i
$477$	−1.72809	−	4.36465i	−0.0791237	−	0.199844i
$478$	−1.22520	−	9.69844i	−0.0560393	−	0.443596i
$479$	22.9620	+	12.6235i	1.04916	+	0.576780i	0.910478	−	0.413557i	$-0.135714\pi$
$479$	22.9620	+	12.6235i	1.04916	+	0.576780i	0.138681	+	0.990337i	$0.455714\pi$
$480$	1.53398	+	1.62693i	0.0700164	+	0.0742588i
$481$	28.4319	−	60.4209i	1.29638	−	2.75496i
$482$	−0.110583	+	0.152204i	−0.00503691	+	0.00693271i
$483$	0.828624	−	6.55924i	0.0377037	−	0.298456i
$484$	1.94661	−	0.499805i	0.0884823	−	0.0227184i
$485$	−14.5165	+	13.6872i	−0.659163	+	0.621505i
$486$	0.637424	+	0.770513i	0.0289141	+	0.0349512i
$487$	5.34918	+	4.42523i	0.242395	+	0.200526i	0.750687	−	0.660659i	$-0.229723\pi$
$487$	5.34918	+	4.42523i	0.242395	+	0.200526i	−0.508292	+	0.861185i	$0.669723\pi$
$488$	1.25768	−	0.798148i	0.0569325	−	0.0361304i
$489$	−0.569135	−	9.04615i	−0.0257372	−	0.409081i
$490$	−0.637920	−	0.162417i	−0.0288183	−	0.00733727i
$491$	3.05871	−	3.69735i	0.138038	−	0.166859i	−0.696964	−	0.717106i	$-0.745466\pi$
$491$	3.05871	−	3.69735i	0.138038	−	0.166859i	0.835002	+	0.550247i	$0.185466\pi$
$492$	−7.32140	+	1.39663i	−0.330074	+	0.0629650i
$493$	−15.0568	−	20.7239i	−0.678124	−	0.933358i
$494$	−38.7308	+	21.2925i	−1.74258	+	0.957993i
$495$	3.92988	−	5.43206i	0.176635	−	0.244153i
$496$	−6.14104	+	0.775794i	−0.275741	+	0.0348342i
$497$	−28.0587	+	13.2034i	−1.25861	+	0.592255i
$498$	3.88438	−	0.244384i	0.174063	−	0.0109511i
$499$	20.2126			0.904842			0.452421	−	0.891804i	$-0.350560\pi$
$499$	20.2126			0.904842			0.452421	+	0.891804i	$0.350560\pi$
$500$	1.46846	+	11.0835i	0.0656715	+	0.495668i
$501$	11.7059			0.522981
$502$	−9.50291	+	0.597872i	−0.424135	+	0.0266843i
$503$	−10.6939	+	5.03215i	−0.476816	+	0.224373i	−0.649142	−	0.760667i	$-0.724872\pi$
$503$	−10.6939	+	5.03215i	−0.476816	+	0.224373i	0.172326	+	0.985040i	$0.444872\pi$
$504$	2.67952	−	0.338502i	0.119355	−	0.0150781i
$505$	11.5214	+	15.7906i	0.512694	+	0.702673i
$506$	6.43189	−	3.53596i	0.285933	−	0.157193i
$507$	17.7717	+	24.4607i	0.789270	+	1.08634i
$508$	7.99155	−	1.52447i	0.354568	−	0.0676374i
$509$	6.72048	−	8.12367i	0.297880	−	0.360075i	−0.600244	−	0.799817i	$-0.704930\pi$
$509$	6.72048	−	8.12367i	0.297880	−	0.360075i	0.898124	+	0.439742i	$0.144930\pi$
$510$	10.0628	−	4.00767i	0.445587	−	0.177463i
$511$	1.95157	+	31.0193i	0.0863323	+	1.37221i
$512$	−0.844328	+	0.535827i	−0.0373144	+	0.0236804i
$513$	5.17920	+	4.28461i	0.228667	+	0.189170i
$514$	5.01556	+	6.06277i	0.221227	+	0.267418i
$515$	−38.8745	+	4.99078i	−1.71301	+	0.219920i
$516$	−5.30040	+	1.36091i	−0.233337	+	0.0599108i
$517$	−3.83936	+	30.3917i	−0.168855	+	1.33663i
$518$	−16.1219	+	22.1899i	−0.708356	+	0.974969i
$519$	10.6444	−	22.6205i	0.467238	−	0.992931i
$520$	7.05714	−	12.8985i	0.309476	−	0.565638i
$521$	−30.6835	−	16.8684i	−1.34427	−	0.739018i	−0.363023	−	0.931780i	$-0.618255\pi$
$521$	−30.6835	−	16.8684i	−1.34427	−	0.739018i	−0.981245	+	0.192762i	$0.938255\pi$
$522$	0.662792	+	5.24654i	0.0290096	+	0.229635i
$523$	−4.77443	−	12.0588i	−0.208771	−	0.527296i	0.787228	−	0.616663i	$-0.211516\pi$
$523$	−4.77443	−	12.0588i	−0.208771	−	0.527296i	−0.995999	+	0.0893667i	$0.971516\pi$
$524$	8.78396	−	6.38192i	0.383729	−	0.278796i
$525$	11.8599	+	6.45777i	0.517608	+	0.281840i
$526$	3.57448	+	2.59701i	0.155855	+	0.113235i
$527$	−7.45661	+	29.0416i	−0.324815	+	1.26507i
$528$	2.05253	+	2.18572i	0.0893248	+	0.0951213i
$529$	12.3981	−	11.6426i	0.539047	−	0.506199i
$530$	9.50678	+	4.45012i	0.412948	+	0.193301i
$531$	2.27305	+	0.287153i	0.0986419	+	0.0124614i
$532$	17.2657	−	5.60996i	0.748562	−	0.243223i
$533$	23.6101	+	42.9467i	1.02267	+	1.86023i
$534$	−0.0742756	+	1.18058i	−0.00321422	+	0.0510885i
$535$	14.7668	+	10.6832i	0.638427	+	0.461877i
$536$	−5.91279	+	9.31707i	−0.255394	+	0.402436i
$537$	4.53802	+	17.6744i	0.195830	+	0.762708i
$538$	−7.64383	+	19.3061i	−0.329549	+	0.832346i
$539$	−0.854955	−	0.219515i	−0.0368255	−	0.00945518i
$540$	−2.21900	−	0.275772i	−0.0954904	−	0.0118673i
$541$	−40.5974	−	16.0736i	−1.74542	−	0.691060i	−0.999692	−	0.0248056i	$-0.992103\pi$
$541$	−40.5974	−	16.0736i	−1.74542	−	0.691060i	−0.745725	−	0.666254i	$-0.767897\pi$
$542$	−0.858286	−	0.403879i	−0.0368665	−	0.0173481i
$543$	7.09528	+	2.30540i	0.304488	+	0.0989341i
$544$	0.907672	+	4.75819i	0.0389161	+	0.204006i
$545$	−5.44644	−	21.0360i	−0.233300	−	0.901083i
$546$	−7.56131	−	16.0686i	−0.323594	−	0.687673i
$547$	29.2905	+	5.58746i	1.25237	+	0.238903i	0.770557	−	0.637371i	$-0.219978\pi$
$547$	29.2905	+	5.58746i	1.25237	+	0.238903i	0.481814	+	0.876273i	$0.339978\pi$
$548$	−4.55830	+	3.77095i	−0.194721	+	0.161087i
$549$	−0.460300	+	1.41666i	−0.0196451	+	0.0604615i
$550$	1.93905	+	14.8659i	0.0826815	+	0.633886i
$551$	10.9844	+	33.8065i	0.467951	+	1.44021i
$552$	−2.06685	−	1.31166i	−0.0879708	−	0.0558280i
$553$	−10.4172	+	18.9488i	−0.442983	+	0.805783i
$554$	1.74220	−	9.13291i	0.0740188	−	0.388020i
$555$	17.4679	−	14.5103i	0.741472	−	0.615926i
$556$	−7.28257	−	6.83879i	−0.308850	−	0.290029i
$557$		−	36.5203i		−	1.54741i	−0.633544	−	0.773707i	$-0.718400\pi$
$557$		−	36.5203i		−	1.54741i	0.633544	−	0.773707i	$-0.281600\pi$
$558$	4.23725	−	4.51221i	0.179377	−	0.191017i
$559$	19.2803	+	30.3809i	0.815471	+	1.28498i
$560$	−3.84012	+	4.66105i	−0.162275	+	0.196965i
$561$	13.5042	−	5.34667i	0.570146	−	0.225737i
$562$	−12.7644	−	0.803066i	−0.538432	−	0.0338753i
$563$	2.77585	+	0.174641i	0.116988	+	0.00736026i	0.121177	−	0.992631i	$-0.461333\pi$
$563$	2.77585	+	0.174641i	0.116988	+	0.00736026i	−0.00418860	+	0.999991i	$0.501333\pi$
$564$	9.49917	−	3.76099i	0.399987	−	0.158366i
$565$	6.96381	+	10.9244i	0.292970	+	0.459592i
$566$	10.3444	+	16.3001i	0.434806	+	0.685145i
$567$	−1.84883	+	1.96881i	−0.0776437	+	0.0826821i
$568$			11.4817i			0.481763i
$569$	0.446135	+	0.418949i	0.0187029	+	0.0175632i	0.693842	−	0.720127i	$-0.255916\pi$
$569$	0.446135	+	0.418949i	0.0187029	+	0.0175632i	−0.675139	+	0.737690i	$0.735916\pi$
$570$	−14.9987	+	0.974059i	−0.628227	+	0.0407988i
$571$	−3.59200	+	18.8299i	−0.150320	+	0.788007i	0.824645	+	0.565651i	$0.191375\pi$
$571$	−3.59200	+	18.8299i	−0.150320	+	0.788007i	−0.974965	+	0.222357i	$0.928625\pi$
$572$	9.49793	−	17.2767i	0.397128	−	0.722374i
$573$	−12.8926	−	8.18186i	−0.538594	−	0.341802i
$574$	−6.22060	−	19.1450i	−0.259643	−	0.799099i
$575$	−4.55163	−	11.3618i	−0.189816	−	0.473819i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−31.0563	+	25.6920i	−1.29289	+	1.06957i	−0.299585	+	0.954070i	$0.596848\pi$
$577$	−31.0563	+	25.6920i	−1.29289	+	1.06957i	−0.993307	+	0.115504i	$0.963152\pi$
$578$	6.34970	+	1.21127i	0.264113	+	0.0503822i
$579$	6.01568	+	12.7840i	0.250003	+	0.531284i
$580$	−9.12642	−	7.51903i	−0.378954	−	0.312211i
$581$	1.96970	+	10.3255i	0.0817170	+	0.428375i
$582$	8.48597	+	2.75726i	0.351755	+	0.114292i
$583$	12.7357	+	5.99296i	0.527458	+	0.248203i
$584$	10.6998	+	4.23633i	0.442759	+	0.175301i
$585$	2.78422	+	14.4369i	0.115113	+	0.596891i
$586$	28.7184	+	7.37362i	1.18634	+	0.304601i
$587$	−0.439955	+	1.11120i	−0.0181589	+	0.0458641i	−0.938573	−	0.345081i	$-0.887852\pi$
$587$	−0.439955	+	1.11120i	−0.0181589	+	0.0458641i	0.920414	+	0.390945i	$0.127852\pi$
$588$	0.0732113	+	0.285139i	0.00301918	+	0.0117589i
$589$	22.2940	−	35.1297i	0.918607	−	1.44749i
$590$	−4.13857	+	3.01964i	−0.170382	+	0.124317i
$591$	1.08296	−	17.2132i	0.0445472	−	0.708057i
$592$	4.89247	+	8.89938i	0.201079	+	0.365762i
$593$	−4.32609	+	1.40563i	−0.177651	+	0.0577224i	−0.396492	−	0.918038i	$-0.629773\pi$
$593$	−4.32609	+	1.40563i	−0.177651	+	0.0577224i	0.218841	+	0.975761i	$0.429773\pi$
$594$	−2.97473	−	0.375796i	−0.122055	−	0.0154191i
$595$	14.1449	+	25.6068i	0.579883	+	1.04978i
$596$	14.8262	−	13.9228i	0.607306	−	0.570298i
$597$	10.1923	+	10.8537i	0.417142	+	0.444211i
$598$	−4.00289	+	15.5902i	−0.163690	+	0.637531i
$599$	11.0791	+	8.04945i	0.452681	+	0.328892i	0.790653	−	0.612264i	$-0.209741\pi$
$599$	11.0791	+	8.04945i	0.452681	+	0.328892i	−0.337973	+	0.941156i	$0.609741\pi$
$600$	4.03318	−	2.95524i	0.164654	−	0.120647i
$601$	−20.8975	+	15.1829i	−0.852426	+	0.619324i	−0.925814	−	0.377980i	$-0.876619\pi$
$601$	−20.8975	+	15.1829i	−0.852426	+	0.619324i	0.0733878	+	0.997303i	$0.476619\pi$
$602$	−5.44078	−	13.7418i	−0.221749	−	0.560075i
$603$	−1.38304	−	10.9479i	−0.0563217	−	0.445832i
$604$	7.31922	+	4.02378i	0.297815	+	0.163725i
$605$	−0.572245	−	4.45736i	−0.0232651	−	0.181217i
$606$	3.72203	−	7.90971i	0.151197	−	0.321310i
$607$	0.992264	−	1.36573i	0.0402747	−	0.0554334i	−0.788405	−	0.615157i	$-0.789093\pi$
$607$	0.992264	−	1.36573i	0.0402747	−	0.0554334i	0.828679	+	0.559723i	$0.189093\pi$
$608$	0.842460	−	6.66875i	0.0341662	−	0.270454i
$609$	−13.8338	+	3.55192i	−0.560575	+	0.143931i
$610$	−1.42425	−	3.01089i	−0.0576664	−	0.121908i
$611$	−42.8207	−	51.7613i	−1.73234	−	2.09404i
$612$	−3.73236	−	3.08767i	−0.150872	−	0.124812i
$613$	11.7372	−	7.44864i	0.474060	−	0.300848i	−0.277249	−	0.960798i	$-0.589423\pi$
$613$	11.7372	−	7.44864i	0.474060	−	0.300848i	0.751309	+	0.659950i	$0.229423\pi$
$614$	−0.272697	−	4.33440i	−0.0110052	−	0.174922i
$615$	1.08009	+	16.6313i	0.0435532	+	0.670640i
$616$	−5.16189	+	6.23965i	−0.207978	+	0.251403i
$617$	20.7785	−	3.96371i	0.836511	−	0.159573i	0.248709	−	0.968578i	$-0.419994\pi$
$617$	20.7785	−	3.96371i	0.836511	−	0.159573i	0.587802	+	0.809005i	$0.299994\pi$
$618$	10.3026	+	14.1803i	0.414432	+	0.570417i
$619$	18.7524	−	10.3092i	0.753722	−	0.414362i	−0.0580676	−	0.998313i	$-0.518494\pi$
$619$	18.7524	−	10.3092i	0.753722	−	0.414362i	0.811789	+	0.583951i	$0.198494\pi$
$620$	0.0279577	+	13.8409i	0.00112281	+	0.555864i
$621$	2.42862	−	0.306806i	0.0974570	−	0.0123117i
$622$	−0.648358	+	0.305094i	−0.0259968	+	0.0122332i
$623$	−3.18852	+	0.200604i	−0.127745	+	0.00803705i
$624$	−6.57534			−0.263224
$625$	24.9992	−	0.201991i	0.999967	−	0.00807964i
$626$	23.5248			0.940239
$627$	−20.1146	+	1.26550i	−0.803299	+	0.0505393i
$628$	5.72535	−	2.69415i	0.228466	−	0.107508i
$629$	48.8054	−	6.16556i	1.94600	−	0.245837i
$630$	−0.0121988	−	6.03919i	−0.000486010	−	0.240607i
$631$	−36.3423	+	19.9794i	−1.44677	+	0.795366i	−0.995292	−	0.0969188i	$-0.969101\pi$
$631$	−36.3423	+	19.9794i	−1.44677	+	0.795366i	−0.451473	+	0.892285i	$0.649101\pi$
$632$	4.70597	+	6.47721i	0.187193	+	0.257649i
$633$	20.2052	−	3.85434i	0.803083	−	0.153196i
$634$	13.6062	−	16.4471i	0.540372	−	0.653198i
$635$	−1.17895	−	18.1536i	−0.0467852	−	0.720405i
$636$	−0.294758	−	4.68504i	−0.0116879	−	0.185774i
$637$	1.63437	−	1.03720i	0.0647560	−	0.0410954i
$638$	−12.2174	−	10.1071i	−0.483690	−	0.400143i
$639$	−7.31874	−	8.84684i	−0.289525	−	0.349975i
$640$	0.956156	+	2.02133i	0.0377954	+	0.0799000i
$641$	17.1089	−	4.39282i	0.675760	−	0.173506i	0.104812	−	0.994492i	$-0.466576\pi$
$641$	17.1089	−	4.39282i	0.675760	−	0.173506i	0.570948	+	0.820986i	$0.306576\pi$
$642$	1.02159	−	8.08670i	0.0403188	−	0.319156i
$643$	−11.9023	+	16.3821i	−0.469379	+	0.646045i	−0.976421	−	0.215877i	$-0.930739\pi$
$643$	−11.9023	+	16.3821i	−0.469379	+	0.646045i	0.507041	+	0.861922i	$0.330739\pi$
$644$	2.81498	−	5.98215i	0.110926	−	0.235730i
$645$	1.55816	+	12.1369i	0.0613524	+	0.477889i
$646$	−28.5326	−	15.6859i	−1.12260	−	0.617155i
$647$	−2.99407	−	23.7005i	−0.117709	−	0.931762i	−0.934780	−	0.355226i	$-0.884404\pi$
$647$	−2.99407	−	23.7005i	−0.117709	−	0.931762i	0.817072	−	0.576536i	$-0.195596\pi$
$648$	0.368125	+	0.929776i	0.0144613	+	0.0365251i
$649$	−5.55764	+	4.03786i	−0.218156	+	0.158500i
$650$	−26.6757	−	19.2168i	−1.04631	−	0.753746i
$651$	13.5248	+	9.82638i	0.530081	+	0.385126i
$652$	2.25413	−	8.77927i	0.0882787	−	0.343823i
$653$	24.5624	+	26.1563i	0.961199	+	1.02357i	0.999704	+	0.0243149i	$0.00774045\pi$
$653$	24.5624	+	26.1563i	0.961199	+	1.02357i	−0.0385050	+	0.999258i	$0.512260\pi$
$654$	−7.08396	+	6.65228i	−0.277005	+	0.260125i
$655$	−11.7391	−	21.2515i	−0.458685	−	0.830367i
$656$	−7.39465	−	0.934161i	−0.288713	−	0.0364729i
$657$	−10.9446	+	3.55613i	−0.426991	+	0.138738i
$658$	13.2931	+	24.1801i	0.518220	+	0.942638i
$659$	1.81292	−	28.8156i	0.0706215	−	1.12250i	−0.789952	−	0.613169i	$-0.789894\pi$
$659$	1.81292	−	28.8156i	0.0706215	−	1.12250i	0.860573	−	0.509327i	$-0.170106\pi$
$660$	5.41614	−	3.95180i	0.210823	−	0.153823i
$661$	16.0901	−	25.3539i	0.625832	−	0.986153i	−0.372478	−	0.928041i	$-0.621492\pi$
$661$	16.0901	−	25.3539i	0.625832	−	0.986153i	0.998310	−	0.0581123i	$-0.0185081\pi$
$662$	−0.555477	−	2.16344i	−0.0215892	−	0.0840845i
$663$	−11.7251	+	29.6142i	−0.455364	+	1.15012i
$664$	3.76978	+	0.967916i	0.146296	+	0.0375624i
$665$	−7.68709	−	39.8596i	−0.298093	−	1.54569i
$666$	−9.44239	−	3.73851i	−0.365885	−	0.144864i
$667$	11.7131	+	5.51179i	0.453535	+	0.213417i
$668$	11.1330	+	3.61732i	0.430748	+	0.139958i
$669$	4.59385	+	24.0818i	0.177608	+	0.931056i
$670$	19.0440	+	15.6899i	0.735733	+	0.606152i
$671$	−1.90164	−	4.04120i	−0.0734121	−	0.156009i
$672$	2.65297	+	0.506082i	0.102341	+	0.0195225i
$673$	15.6480	−	12.9452i	0.603187	−	0.499000i	−0.284972	−	0.958536i	$-0.591984\pi$
$673$	15.6480	−	12.9452i	0.603187	−	0.499000i	0.888159	+	0.459536i	$0.151984\pi$
$674$	−10.5445	+	32.4525i	−0.406158	+	1.25002i
$675$	−1.22387	+	4.84790i	−0.0471070	+	0.186596i
$676$	9.34315	+	28.7553i	0.359352	+	1.10597i
$677$	31.5555	+	20.0257i	1.21278	+	0.769651i	0.979241	−	0.202698i	$-0.0649709\pi$
$677$	31.5555	+	20.0257i	1.21278	+	0.769651i	0.233534	+	0.972349i	$0.424971\pi$
$678$	2.79115	−	5.07708i	0.107193	−	0.194984i
$679$	−4.51560	+	23.6716i	−0.173293	+	0.908433i
$680$	10.8087	−	0.701949i	0.414495	−	0.0269185i
$681$	1.41724	+	1.33088i	0.0543088	+	0.0509994i
$682$			18.5595i			0.710680i
$683$	−16.5124	+	17.5840i	−0.631831	+	0.672831i	−0.962614	−	0.270875i	$-0.912687\pi$
$683$	−16.5124	+	17.5840i	−0.631831	+	0.672831i	0.330784	+	0.943707i	$0.392687\pi$
$684$	3.60170	+	5.67537i	0.137714	+	0.217003i
$685$	7.11068	+	11.1548i	0.271685	+	0.426202i
$686$	16.8388	−	6.66696i	0.642909	−	0.254546i
$687$	−19.5348	−	1.22902i	−0.745299	−	0.0468902i
$688$	−5.46152	−	0.343610i	−0.208219	−	0.0131000i
$689$	−28.6991	+	11.3628i	−1.09335	+	0.432887i
$690$	−3.48055	+	4.22461i	−0.132502	+	0.160828i
$691$	16.7703	+	26.4258i	0.637974	+	1.00529i	0.997397	+	0.0721110i	$0.0229736\pi$
$691$	16.7703	+	26.4258i	0.637974	+	1.00529i	−0.359423	+	0.933175i	$0.617026\pi$
$692$	17.1136	−	18.2241i	0.650560	−	0.692776i
$693$		−	8.09805i		−	0.307619i
$694$	16.2204	+	15.2319i	0.615717	+	0.578197i
$695$	−17.1836	+	14.2741i	−0.651811	+	0.541446i
$696$	−0.990917	+	5.19457i	−0.0375606	+	0.196900i
$697$	−17.3934	+	31.6384i	−0.658821	+	1.19839i
$698$	−5.73073	−	3.63683i	−0.216911	−	0.137656i
$699$	3.28155	+	10.0996i	0.124120	+	0.382001i
$700$	9.28386	+	9.80661i	0.350897	+	0.370655i
$701$	7.60419	−	23.4033i	0.287206	−	0.883930i	−0.698522	−	0.715588i	$-0.746159\pi$
$701$	7.60419	−	23.4033i	0.287206	−	0.883930i	0.985729	−	0.168342i	$-0.0538413\pi$
$702$	5.06638	−	4.19128i	0.191218	−	0.158190i
$703$	−67.0540	−	12.7912i	−2.52899	−	0.482431i
$704$	1.27665	+	2.71301i	0.0481154	+	0.102250i
$705$	−5.72602	−	22.1158i	−0.215654	−	0.832930i
$706$	−2.60224	−	13.6414i	−0.0979367	−	0.513402i
$707$	22.4541	+	7.29578i	0.844474	+	0.274386i
$708$	2.07306	+	0.975509i	0.0779104	+	0.0366619i
$709$	10.5296	+	4.16898i	0.395449	+	0.156569i	0.557429	−	0.830225i	$-0.311788\pi$
$709$	10.5296	+	4.16898i	0.395449	+	0.156569i	−0.161980	+	0.986794i	$0.551788\pi$
$710$	25.4780	+	3.16634i	0.956171	+	0.118831i
$711$	−7.75474	−	1.99108i	−0.290825	−	0.0746713i
$712$	−0.435459	+	1.09984i	−0.0163195	+	0.0412183i
$713$	−3.76821	−	14.6762i	−0.141121	−	0.549629i
$714$	7.01006	−	11.0461i	0.262345	−	0.413389i
$715$	−35.7176	−	25.8403i	−1.33576	−	0.966373i
$716$	−1.14578	+	18.2117i	−0.0428199	+	0.680603i
$717$	4.70940	+	8.56636i	0.175876	+	0.319916i
$718$	−5.03468	+	1.63587i	−0.187893	+	0.0610500i
$719$	−22.1110	−	2.79327i	−0.824603	−	0.104172i	−0.298304	−	0.954471i	$-0.596421\pi$
$719$	−22.1110	−	2.79327i	−0.824603	−	0.104172i	−0.526299	+	0.850300i	$0.676421\pi$
$720$	−2.02517	−	0.947983i	−0.0754738	−	0.0353292i
$721$	−34.5090	+	32.4061i	−1.28518	+	1.20687i
$722$	17.9228	+	19.0859i	0.667018	+	0.710302i
$723$	0.0467872	−	0.182224i	0.00174004	−	0.00677699i
$724$	6.03561	+	4.38513i	0.224312	+	0.162972i
$725$	−19.2015	+	18.1780i	−0.713127	+	0.675113i
$726$	−1.62592	+	1.18130i	−0.0603436	+	0.0438422i
$727$	−18.3862	−	46.4382i	−0.681906	−	1.72230i	−0.691534	−	0.722344i	$-0.743065\pi$
$727$	−18.3862	−	46.4382i	−0.681906	−	1.72230i	0.00962821	−	0.999954i	$-0.496935\pi$
$728$	−2.22576	−	17.6187i	−0.0824922	−	0.652993i
$729$	−0.876307	−	0.481754i	−0.0324558	−	0.0178427i
$730$	12.3511	−	22.5745i	0.457135	−	0.835518i
$731$	−11.2865	+	23.9850i	−0.417446	+	0.887118i
$732$	−0.875543	+	1.20508i	−0.0323610	+	0.0445411i
$733$	4.36353	−	34.5409i	0.161171	−	1.27580i	−0.679268	−	0.733890i	$-0.737703\pi$
$733$	4.36353	−	34.5409i	0.161171	−	1.27580i	0.840439	−	0.541907i	$-0.182297\pi$
$734$	−18.0115	+	4.62457i	−0.664816	+	0.170696i
$735$	0.652913	−	0.0838223i	0.0240831	−	0.00309183i
$736$	−1.56036	−	1.88615i	−0.0575157	−	0.0695245i
$737$	25.4938	+	21.0903i	0.939076	+	0.776871i
$738$	6.29313	−	3.99374i	0.231653	−	0.147012i
$739$	1.13158	+	17.9859i	0.0416257	+	0.661622i	0.962419	+	0.271570i	$0.0875429\pi$
$739$	1.13158	+	17.9859i	0.0416257	+	0.661622i	−0.920793	+	0.390052i	$0.872457\pi$
$740$	21.0969	−	8.40219i	0.775538	−	0.308871i
$741$	28.1728	−	34.0550i	1.03495	−	1.25104i
$742$	12.4539	−	2.37570i	0.457196	−	0.0872147i
$743$	14.3735	+	19.7834i	0.527312	+	0.725783i	0.986718	−	0.162443i	$-0.0519375\pi$
$743$	14.3735	+	19.7834i	0.527312	+	0.725783i	−0.459405	+	0.888227i	$0.651937\pi$
$744$	5.42421	−	2.98198i	0.198861	−	0.109325i
$745$	−26.8059	−	36.7389i	−0.982092	−	1.34601i
$746$	19.3495	−	2.44441i	0.708437	−	0.0894964i
$747$	−3.52164	+	1.65716i	−0.128850	+	0.0606323i
$748$	14.4954	−	0.911975i	0.530005	−	0.0333451i
$749$	22.0142			0.804383
$750$	−5.44544	−	9.76459i	−0.198839	−	0.356552i
$751$	−33.1496			−1.20965			−0.604824	−	0.796359i	$-0.706756\pi$
$751$	−33.1496			−1.20965			−0.604824	+	0.796359i	$0.706756\pi$
$752$	10.1965	−	0.641507i	0.371827	−	0.0233933i
$753$	8.61549	−	4.05414i	0.313966	−	0.147741i
$754$	34.4978	−	4.35808i	1.25633	−	0.158712i
$755$	10.9472	−	15.1317i	0.398409	−	0.550699i
$756$	−2.36674	+	1.30113i	−0.0860775	+	0.0473215i
$757$	8.77685	+	12.0803i	0.319000	+	0.439066i	0.938162	−	0.346198i	$-0.112527\pi$
$757$	8.77685	+	12.0803i	0.319000	+	0.439066i	−0.619162	+	0.785264i	$0.712527\pi$
$758$	−13.9319	+	2.65765i	−0.506029	+	0.0965303i
$759$	−4.67855	+	5.65539i	−0.169821	+	0.205278i
$760$	−14.5656	−	3.70847i	−0.528351	−	0.134520i
$761$	−1.79089	−	28.4653i	−0.0649196	−	1.03187i	−0.886784	−	0.462184i	$-0.847066\pi$
$761$	−1.79089	−	28.4653i	−0.0649196	−	1.03187i	0.821864	−	0.569683i	$-0.192934\pi$
$762$	−6.86916	+	4.35930i	−0.248844	+	0.157921i
$763$	−20.2228	−	16.7298i	−0.732115	−	0.605658i
$764$	−9.73321	−	11.7654i	−0.352135	−	0.425658i
$765$	−7.88082	+	7.43059i	−0.284932	+	0.268654i
$766$	−17.5437	+	4.50446i	−0.633880	+	0.162753i
$767$	1.88813	−	14.9461i	0.0681763	−	0.539671i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	−6.79093	+	14.4315i	−0.244887	+	0.520412i	−0.989049	−	0.147588i	$-0.952849\pi$
$769$	−6.79093	+	14.4315i	−0.244887	+	0.520412i	0.744162	+	0.667999i	$0.232849\pi$
$770$	12.4223	+	13.1749i	0.447667	+	0.474792i
$771$	−6.89521	−	3.79067i	−0.248325	−	0.136518i
$772$	1.77079	+	14.0172i	0.0637320	+	0.504491i
$773$	18.4068	+	46.4904i	0.662048	+	1.67214i	0.737803	+	0.675016i	$0.235863\pi$
$773$	18.4068	+	46.4904i	0.662048	+	1.67214i	−0.0757547	+	0.997126i	$0.524137\pi$
$774$	4.42720	−	3.21655i	0.159132	−	0.115617i
$775$	30.7206	+	3.75489i	1.10352	+	0.134880i
$776$	7.21859	+	5.24462i	0.259132	+	0.188271i
$777$	6.82113	−	26.5665i	0.244706	−	0.953069i
$778$	−7.10017	−	7.56092i	−0.254553	−	0.271072i
$779$	36.5214	−	34.2959i	1.30851	−	1.22878i
$780$	−1.81329	+	14.5907i	−0.0649263	+	0.522429i
$781$	34.1551	+	4.31479i	1.22217	+	0.154395i
$782$	−11.2773	+	3.66423i	−0.403276	+	0.131032i
$783$	−2.54763	−	4.63412i	−0.0910448	−	0.165610i
$784$	−0.0184848	+	0.293807i	−0.000660171	+	0.0104931i
$785$	−4.39941	−	13.4475i	−0.157022	−	0.479962i
$786$	−5.81778	+	9.16735i	−0.207513	+	0.326989i
$787$	12.8353	+	49.9902i	0.457530	+	1.78196i	0.608644	+	0.793444i	$0.291714\pi$
$787$	12.8353	+	49.9902i	0.457530	+	1.78196i	−0.151114	+	0.988516i	$0.548286\pi$
$788$	6.34914	−	16.0361i	0.226179	−	0.571262i
$789$	−4.27949	−	1.09879i	−0.152354	−	0.0391178i
$790$	15.6707	−	8.65630i	0.557538	−	0.307977i
$791$	14.5489	+	5.76033i	0.517301	+	0.204814i
$792$	−2.71301	−	1.27665i	−0.0964026	−	0.0453636i
$793$	9.31501	+	3.02663i	0.330786	+	0.107479i
$794$	5.22266	+	27.3781i	0.185345	+	0.971614i
$795$	−10.4774	−	0.637936i	−0.371594	−	0.0226253i
$796$	6.33946	+	13.4720i	0.224696	+	0.477504i
$797$	−21.7668	−	4.15224i	−0.771020	−	0.147080i	−0.213163	−	0.977017i	$-0.568376\pi$
$797$	−21.7668	−	4.15224i	−0.771020	−	0.147080i	−0.557857	+	0.829937i	$0.688376\pi$
$798$	−13.9881	+	11.5719i	−0.495172	+	0.409642i
$799$	15.2930	−	47.0670i	0.541027	−	1.66511i
$800$	4.74900	−	1.56428i	0.167903	−	0.0553058i
$801$	−0.365540	−	1.12502i	−0.0129157	−	0.0397505i
$802$	−29.1204	−	18.4804i	−1.02828	−	0.652565i
$803$	16.6229	−	30.2369i	0.586608	−	1.06704i
$804$	2.06773	−	10.8394i	0.0729234	−	0.382278i
$805$	−12.4981	−	7.89615i	−0.440499	−	0.278303i
$806$	−29.6693	−	27.8613i	−1.04506	−	0.981373i
$807$		−	20.7643i		−	0.730936i
$808$	5.98409	−	6.37241i	0.210520	−	0.224181i
$809$	−16.2404	−	25.5907i	−0.570981	−	0.899723i	0.429012	−	0.903299i	$-0.358862\pi$
$809$	−16.2404	−	25.5907i	−0.570981	−	0.899723i	−0.999994	+	0.00357596i	$0.998862\pi$
$810$	2.16469	−	0.560461i	0.0760595	−	0.0196926i
$811$	3.92262	−	1.55307i	0.137742	−	0.0545358i	−0.298242	−	0.954490i	$-0.596400\pi$
$811$	3.92262	−	1.55307i	0.137742	−	0.0545358i	0.435984	+	0.899954i	$0.356400\pi$
$812$	−14.2544	−	0.896808i	−0.500230	−	0.0314718i
$813$	0.946691	+	0.0595608i	0.0332019	+	0.00208889i
$814$	28.3118	−	11.2094i	0.992329	−	0.392891i
$815$	−18.8595	−	7.42299i	−0.660621	−	0.260016i
$816$	−2.59554	−	4.08991i	−0.0908620	−	0.143176i
$817$	25.1801	−	26.8141i	0.880941	−	0.938107i
$818$		−	9.00095i		−	0.314711i
$819$	12.9456	+	12.1567i	0.452355	+	0.424790i
$820$	−4.11214	+	16.1511i	−0.143602	+	0.564021i
$821$	3.77619	−	19.7955i	0.131790	−	0.690867i	−0.853651	−	0.520846i	$-0.825617\pi$
$821$	3.77619	−	19.7955i	0.131790	−	0.690867i	0.985440	−	0.170021i	$-0.0543835\pi$
$822$	2.85002	−	5.18416i	0.0994058	−	0.180819i
$823$	−22.7481	−	14.4364i	−0.792948	−	0.503220i	0.0766042	−	0.997062i	$-0.475592\pi$
$823$	−22.7481	−	14.4364i	−0.792948	−	0.503220i	−0.869552	+	0.493842i	$0.835592\pi$
$824$	5.41641	+	16.6700i	0.188690	+	0.580727i
$825$	−7.27540	−	13.1082i	−0.253297	−	0.456369i
$826$	−1.91216	+	5.88501i	−0.0665324	+	0.204766i
$827$	−35.8749	+	29.6783i	−1.24749	+	1.03202i	−0.249521	+	0.968370i	$0.580273\pi$
$827$	−35.8749	+	29.6783i	−1.24749	+	1.03202i	−0.997973	+	0.0636465i	$0.979727\pi$
$828$	2.40456	+	0.458694i	0.0835642	+	0.0159407i
$829$	5.53789	+	11.7686i	0.192339	+	0.408741i	0.977614	−	0.210406i	$-0.0674786\pi$
$829$	5.53789	+	11.7686i	0.192339	+	0.408741i	−0.785275	+	0.619147i	$0.787479\pi$
$830$	3.18740	−	8.09822i	0.110636	−	0.281093i
$831$	1.74220	+	9.13291i	0.0604361	+	0.316817i
$832$	−6.25352	−	2.03189i	−0.216802	−	0.0704431i
$833$	1.29029	+	0.607166i	0.0447060	+	0.0210371i
$834$	9.28869	+	3.67765i	0.321641	+	0.127347i
$835$	11.0970	−	23.7065i	0.384027	−	0.820396i
$836$	−19.5212	−	5.01218i	−0.675153	−	0.173350i
$837$	−2.27864	+	5.75518i	−0.0787612	+	0.198928i
$838$	5.29774	+	20.6333i	0.183007	+	0.712767i
$839$	−12.2447	+	19.2946i	−0.422735	+	0.666124i	−0.987228	−	0.159314i	$-0.949072\pi$
$839$	−12.2447	+	19.2946i	−0.422735	+	0.666124i	0.564493	+	0.825438i	$0.309072\pi$
$840$	1.85461	−	5.74738i	0.0639901	−	0.198303i
$841$	−0.0649587	+	1.03249i	−0.00223995	+	0.0356030i
$842$	0.414490	+	0.753955i	0.0142843	+	0.0259830i
$843$	12.1636	−	3.95220i	0.418938	−	0.136121i
$844$	20.4073	+	2.57804i	0.702448	+	0.0887399i
$845$	66.3844	−	12.8025i	2.28369	−	0.440420i
$846$	−7.44760	+	6.99376i	−0.256054	+	0.240450i
$847$	−3.71569	−	3.95681i	−0.127673	−	0.135958i
$848$	1.16743	−	4.54682i	0.0400896	−	0.156139i
$849$	−15.6184	−	11.3474i	−0.536023	−	0.389443i
$850$	1.42312	−	24.1781i	0.0488125	−	0.829301i
$851$	−20.1121	+	14.6123i	−0.689435	+	0.500904i
$852$	−4.22671	−	10.6755i	−0.144805	−	0.365735i
$853$	5.78353	+	45.7814i	0.198024	+	1.56752i	0.707296	+	0.706918i	$0.249915\pi$
$853$	5.78353	+	45.7814i	0.198024	+	1.56752i	−0.509271	+	0.860606i	$0.670085\pi$
$854$	−3.52541	−	1.93811i	−0.120637	−	0.0663207i
$855$	13.5869	−	6.42705i	0.464661	−	0.219800i
$856$	3.47051	−	7.37522i	0.118620	−	0.252080i
$857$	−17.4584	+	24.0294i	−0.596367	+	0.820829i	−0.995370	−	0.0961209i	$-0.969356\pi$
$857$	−17.4584	+	24.0294i	−0.596367	+	0.820829i	0.399003	+	0.916950i	$0.369356\pi$
$858$	−2.47099	+	19.5599i	−0.0843581	+	0.667763i
$859$	38.7259	−	9.94312i	1.32131	−	0.339255i	0.478795	−	0.877927i	$-0.341074\pi$
$859$	38.7259	−	9.94312i	1.32131	−	0.339255i	0.842516	+	0.538672i	$0.181074\pi$
$860$	−2.26860	+	12.0243i	−0.0773588	+	0.410027i
$861$	12.8315	+	15.5107i	0.437297	+	0.528602i
$862$	13.6000	+	11.2509i	0.463218	+	0.383207i
$863$	−11.8667	+	7.53086i	−0.403948	+	0.256353i	−0.722244	−	0.691638i	$-0.756889\pi$
$863$	−11.8667	+	7.53086i	−0.403948	+	0.256353i	0.318296	+	0.947991i	$0.396889\pi$
$864$	0.0627905	+	0.998027i	0.00213618	+	0.0339536i
$865$	−35.7198	−	43.0007i	−1.21451	−	1.46207i
$866$	9.46421	−	11.4403i	0.321607	−	0.388756i
$867$	−6.34970	+	1.21127i	−0.215647	+	0.0411369i
$868$	9.82638	+	13.5248i	0.333529	+	0.459063i
$869$	21.0364	−	11.5649i	0.713612	−	0.392312i
$870$	11.2535	+	3.63136i	0.381528	+	0.123115i
$871$	−71.9860	+	9.09395i	−2.43915	+	0.308137i
$872$	−8.79291	+	4.13763i	−0.297766	+	0.140118i
$873$	−8.90507	+	0.560259i	−0.301391	+	0.0189619i
$874$	16.4543			0.556575
$875$	24.3211	−	17.8965i	0.822202	−	0.605011i
$876$	−11.5079			−0.388815
$877$	−0.335604	+	0.0211144i	−0.0113325	+	0.000712982i	−0.0684558	−	0.997654i	$-0.521807\pi$
$877$	−0.335604	+	0.0211144i	−0.0113325	+	0.000712982i	0.0571232	+	0.998367i	$0.481807\pi$
$878$	27.0060	−	12.7081i	0.911409	−	0.428876i
$879$	−29.4161	+	3.71611i	−0.992179	+	0.125341i
$880$	6.37223	−	2.08470i	0.214808	−	0.0702753i
$881$	6.24704	−	3.43434i	0.210468	−	0.115706i	−0.373033	−	0.927818i	$-0.621682\pi$
$881$	6.24704	−	3.43434i	0.210468	−	0.115706i	0.583501	+	0.812112i	$0.301682\pi$
$882$	−0.173037	−	0.238165i	−0.00582646	−	0.00801943i
$883$	−8.60872	+	1.64220i	−0.289706	+	0.0552645i	−0.330186	−	0.943916i	$-0.607111\pi$
$883$	−8.60872	+	1.64220i	−0.289706	+	0.0552645i	0.0404795	+	0.999180i	$0.487111\pi$
$884$	−20.3025	+	24.5415i	−0.682847	+	0.825420i
$885$	2.73634	−	4.33110i	0.0919812	−	0.145588i
$886$	0.739040	+	11.7467i	0.0248285	+	0.394638i
$887$	−1.45164	+	0.921239i	−0.0487413	+	0.0309322i	−0.559974	−	0.828510i	$-0.689189\pi$
$887$	−1.45164	+	0.921239i	−0.0487413	+	0.0309322i	0.511233	+	0.859442i	$0.329189\pi$
$888$	−7.82499	−	6.47339i	−0.262589	−	0.217233i
$889$	−14.0060	−	16.9304i	−0.469748	−	0.567827i
$890$	2.32046	+	1.26959i	0.0777820	+	0.0425567i
$891$	2.90418	−	0.745665i	0.0972935	−	0.0249807i
$892$	−3.07267	+	24.3227i	−0.102881	+	0.814385i
$893$	−40.3654	+	55.5581i	−1.35077	+	1.85918i
$894$	−8.65977	+	18.4029i	−0.289626	+	0.615486i
$895$	40.0957	+	7.56477i	1.34025	+	0.252862i
$896$	2.36674	+	1.30113i	0.0790672	+	0.0434676i
$897$	−2.01735	−	15.9690i	−0.0673574	−	0.533188i
$898$	−7.38828	−	18.6607i	−0.246550	−	0.622715i
$899$	−26.4819	+	19.2402i	−0.883221	+	0.641697i
$900$	−2.66206	+	4.23243i	−0.0887352	+	0.141081i
$901$	−18.3963	−	13.3657i	−0.612871	−	0.445277i
$902$	−5.55776	+	21.6460i	−0.185053	+	0.720734i
$903$	10.1174	+	10.7739i	0.336686	+	0.358535i
$904$	4.22345	−	3.96608i	0.140470	−	0.131910i
$905$	11.3950	−	12.1837i	0.378784	−	0.405000i
$906$	−8.28649	−	1.04683i	−0.275300	−	0.0347785i
$907$	−48.9594	+	15.9079i	−1.62567	+	0.528212i	−0.973270	−	0.229664i	$-0.926237\pi$
$907$	−48.9594	+	15.9079i	−1.62567	+	0.528212i	−0.652399	+	0.757876i	$0.726237\pi$
$908$	0.936613	+	1.70369i	0.0310826	+	0.0565390i
$909$	−0.548895	+	8.72443i	−0.0182057	+	0.289371i
$910$	−39.7097	+	0.0802110i	−1.31636	+	0.00265897i
$911$	−6.56615	+	10.3466i	−0.217546	+	0.342798i	−0.935521	−	0.353271i	$-0.885069\pi$
$911$	−6.56615	+	10.3466i	−0.217546	+	0.342798i	0.717975	+	0.696069i	$0.245069\pi$
$912$	1.67163	+	6.51058i	0.0553533	+	0.215587i
$913$	4.29596	−	10.8504i	0.142176	−	0.359094i
$914$	9.02333	+	2.31680i	0.298465	+	0.0766328i
$915$	2.43262	+	2.27516i	0.0804200	+	0.0752143i
$916$	−18.1989	−	7.20545i	−0.601309	−	0.238075i
$917$	−26.5334	−	12.4857i	−0.876210	−	0.412313i
$918$	4.60690	+	1.49687i	0.152050	+	0.0494042i
$919$	5.60563	+	29.3858i	0.184913	+	0.969347i	0.946845	+	0.321690i	$0.104251\pi$
$919$	5.60563	+	29.3858i	0.184913	+	0.969347i	−0.761932	+	0.647657i	$0.775749\pi$
$920$	−4.61567	+	2.94229i	−0.152174	+	0.0970045i
$921$	1.84915	+	3.92964i	0.0609314	+	0.129486i
$922$	17.0791	+	3.25802i	0.562472	+	0.107297i
$923$	−58.1709	+	48.1232i	−1.91472	+	1.58399i
$924$	2.50243	−	7.70170i	0.0823240	−	0.253367i
$925$	−12.8265	−	49.1311i	−0.421733	−	1.61542i
$926$	5.64921	+	17.3865i	0.185645	+	0.571355i
$927$	−14.7993	−	9.39190i	−0.486072	−	0.308471i
$928$	−2.54763	+	4.63412i	−0.0836300	+	0.152122i
$929$	−3.85705	+	20.2194i	−0.126546	+	0.663376i	0.861320	+	0.508063i	$0.169638\pi$
$929$	−3.85705	+	20.2194i	−0.126546	+	0.663376i	−0.987865	+	0.155312i	$0.950362\pi$
$930$	−5.12117	−	12.8587i	−0.167930	−	0.421652i
$931$	−1.44249	−	1.35459i	−0.0472756	−	0.0443947i
$932$			10.6193i			0.347848i
$933$	0.490515	−	0.522346i	0.0160588	−	0.0171008i
$934$	−13.6684	−	21.5379i	−0.447244	−	0.704743i
$935$	1.97376	−	32.4168i	0.0645489	−	1.06014i
$936$	6.11359	−	2.42054i	0.199829	−	0.0791179i
$937$	−15.5887	−	0.980756i	−0.509260	−	0.0320399i	−0.193917	−	0.981018i	$-0.562119\pi$
$937$	−15.5887	−	0.980756i	−0.509260	−	0.0320399i	−0.315342	+	0.948978i	$0.602119\pi$
$938$	29.7444	+	1.87136i	0.971189	+	0.0611020i
$939$	−21.8728	+	8.66004i	−0.713791	+	0.282610i
$940$	1.38840	−	22.8028i	0.0452845	−	0.743746i
$941$	−9.13254	−	14.3906i	−0.297712	−	0.469120i	0.662237	−	0.749295i	$-0.269607\pi$
$941$	−9.13254	−	14.3906i	−0.297712	−	0.469120i	−0.959949	+	0.280175i	$0.909607\pi$
$942$	−4.33152	+	4.61260i	−0.141128	+	0.150287i
$943$		−	18.2454i		−	0.594151i
$944$	1.67015	+	1.56838i	0.0543588	+	0.0510463i
$945$	2.23452	+	5.61060i	0.0726888	+	0.182513i
$946$	−3.07457	+	16.1174i	−0.0999628	+	0.524023i
$947$	17.6540	−	32.1125i	0.573678	−	1.04352i	−0.417207	−	0.908811i	$-0.636991\pi$
$947$	17.6540	−	32.1125i	0.573678	−	1.04352i	0.990886	−	0.134706i	$-0.0430089\pi$
$948$	−6.75992	−	4.28997i	−0.219552	−	0.139332i
$949$	23.3827	+	71.9647i	0.759036	+	2.33607i
$950$	−12.2459	+	31.2984i	−0.397309	+	1.01545i
$951$	−6.59617	+	20.3009i	−0.213895	+	0.658302i
$952$	10.0804	−	8.33923i	0.326707	−	0.270276i
$953$	−4.71091	−	0.898655i	−0.152601	−	0.0291103i	0.110514	−	0.993875i	$-0.464750\pi$
$953$	−4.71091	−	0.898655i	−0.152601	−	0.0291103i	−0.263116	+	0.964764i	$0.584750\pi$
$954$	1.99874	+	4.24753i	0.0647115	+	0.137519i
$955$	−28.7916	+	18.3534i	−0.931675	+	0.593902i
$956$	1.83175	+	9.60237i	0.0592431	+	0.310563i
$957$	15.0801	+	4.89981i	0.487469	+	0.158388i
$958$	−23.7093	−	11.1567i	−0.766013	−	0.360458i
$959$	14.8558	+	5.88182i	0.479718	+	0.189934i
$960$	−1.63311	−	1.52740i	−0.0527085	−	0.0492966i
$961$	7.08448	+	1.81899i	0.228532	+	0.0586770i
$962$	−24.5819	+	62.0869i	−0.792554	+	2.00176i
$963$	2.02706	+	7.89489i	0.0653212	+	0.254409i
$964$	0.100808	−	0.158847i	0.00324680	−	0.00511613i
$965$	31.5925	−	0.0638148i	1.01700	−	0.00205427i
$966$	−0.415131	+	6.59832i	−0.0133566	+	0.212298i
$967$	−4.24550	−	7.72254i	−0.136526	−	0.248340i	0.799202	−	0.601063i	$-0.205256\pi$
$967$	−4.24550	−	7.72254i	−0.136526	−	0.248340i	−0.935728	+	0.352723i	$0.885256\pi$
$968$	−1.91139	+	0.621047i	−0.0614343	+	0.0199612i
$969$	32.3033	+	4.08086i	1.03773	+	0.131096i
$970$	13.6285	−	14.5717i	0.437584	−	0.467870i
$971$	13.7292	−	12.8926i	0.440590	−	0.413742i	−0.432245	−	0.901756i	$-0.642279\pi$
$971$	13.7292	−	12.8926i	0.440590	−	0.413742i	0.872836	+	0.488014i	$0.162279\pi$
$972$	−0.684547	−	0.728969i	−0.0219569	−	0.0233817i
$973$	−6.71009	+	26.1341i	−0.215116	+	0.837820i
$974$	−5.61649	−	4.08062i	−0.179964	−	0.130751i
$975$	31.8766	+	8.04739i	1.02087	+	0.257723i
$976$	−1.20508	+	0.875543i	−0.0385737	+	0.0280254i
$977$	4.07812	+	10.3002i	0.130471	+	0.329531i	0.980296	−	0.197533i	$-0.0632929\pi$
$977$	4.07812	+	10.3002i	0.130471	+	0.329531i	−0.849826	+	0.527064i	$0.823293\pi$
$978$	1.13602	+	8.99256i	0.0363261	+	0.287550i
$979$	3.10809	+	1.70869i	0.0993351	+	0.0546099i
$980$	0.646860	+	0.122041i	0.0206632	+	0.00389847i
$981$	4.13763	−	8.79291i	0.132104	−	0.280736i
$982$	−2.82052	+	3.88211i	−0.0900064	+	0.123883i
$983$	5.86593	−	46.4336i	0.187094	−	1.48100i	−0.566718	−	0.823912i	$-0.691787\pi$
$983$	5.86593	−	46.4336i	0.187094	−	1.48100i	0.753812	−	0.657090i	$-0.228213\pi$
$984$	7.21926	−	1.85359i	0.230142	−	0.0590903i
$985$	−33.8331	−	18.5110i	−1.07801	−	0.589810i
$986$	16.3284	+	19.7376i	0.520001	+	0.628573i
$987$	−21.2609	−	17.5886i	−0.676742	−	0.559850i
$988$	37.3175	−	23.6824i	1.18723	−	0.753437i
$989$	−0.841129	−	13.3694i	−0.0267464	−	0.425121i
$990$	−3.58105	+	5.66810i	−0.113813	+	0.180144i
$991$	20.4126	−	24.6746i	0.648428	−	0.783815i	−0.339186	−	0.940719i	$-0.610152\pi$
$991$	20.4126	−	24.6746i	0.648428	−	0.783815i	0.987614	+	0.156905i	$0.0501516\pi$
$992$	6.08021	−	1.15986i	0.193047	−	0.0368257i
$993$	1.31289	+	1.80703i	0.0416632	+	0.0573444i
$994$	27.1743	−	14.9392i	0.861917	−	0.473843i
$995$	31.6427	−	10.3520i	1.00314	−	0.328182i
$996$	−3.86137	+	0.487804i	−0.122352	+	0.0154567i
$997$	5.54677	−	2.61011i	0.175668	−	0.0826631i	−0.335934	−	0.941885i	$-0.609052\pi$
$997$	5.54677	−	2.61011i	0.175668	−	0.0826631i	0.511602	+	0.859222i	$0.329052\pi$
$998$	−20.1728	+	1.26916i	−0.638557	+	0.0401746i
$999$	10.1556			0.321307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.469.3	yes	240
125.4	even	50	inner	750.2.o.a.379.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.379.3	✓	240	125.4	even	50	inner
750.2.o.a.469.3	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.00451670 - 2.23606i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-1.58750 - 2.18500i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +O(q^{10})\)	\(q+(-0.998027 + 0.0627905i) q^{2} +(0.904827 - 0.425779i) q^{3} +(0.992115 - 0.125333i) q^{4} +(-0.00451670 - 2.23606i) q^{5} +(-0.876307 + 0.481754i) q^{6} +(-1.58750 - 2.18500i) q^{7} +(-0.982287 + 0.187381i) q^{8} +(0.637424 - 0.770513i) q^{9} +(0.144911 + 2.23137i) q^{10} +(0.188269 + 2.99246i) q^{11} +(0.844328 - 0.535827i) q^{12} +(-5.06638 - 4.19128i) q^{13} +(1.72156 + 2.08101i) q^{14} +(-0.956156 - 2.02133i) q^{15} +(0.968583 - 0.248690i) q^{16} +(0.607112 - 4.80579i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-2.86198 + 6.08203i) q^{19} +(-0.284734 - 2.21787i) q^{20} +(-2.36674 - 1.30113i) q^{21} +(-0.375796 - 2.97473i) q^{22} +(0.901139 + 2.27602i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.99996 + 0.0201993i) q^{25} +(5.31956 + 3.86489i) q^{26} +(0.248690 - 0.968583i) q^{27} +(-1.84883 - 1.96881i) q^{28} +(3.85496 - 3.62005i) q^{29} +(1.08119 + 1.95730i) q^{30} +(-6.14104 - 0.775794i) q^{31} +(-0.951057 + 0.309017i) q^{32} +(1.44448 + 2.62750i) q^{33} +(-0.304156 + 4.83443i) q^{34} +(-4.87864 + 3.55961i) q^{35} +(0.535827 - 0.844328i) q^{36} +(2.52558 + 9.83649i) q^{37} +(2.47444 - 6.24973i) q^{38} +(-6.36876 - 1.63522i) q^{39} +(0.423433 + 2.19561i) q^{40} +(-6.93002 - 2.74379i) q^{41} +(2.44377 + 1.14995i) q^{42} +(-5.20449 - 1.69104i) q^{43} +(0.561839 + 2.94526i) q^{44} +(-1.72580 - 1.42184i) q^{45} +(-1.04227 - 2.21494i) q^{46} +(10.0357 + 1.91440i) q^{47} +(0.770513 - 0.637424i) q^{48} +(-0.0909709 + 0.279980i) q^{49} +(4.98882 - 0.334109i) q^{50} +(-1.49687 - 4.60690i) q^{51} +(-5.55174 - 3.52324i) q^{52} +(2.26150 - 4.11365i) q^{53} +(-0.187381 + 0.982287i) q^{54} +(6.69048 - 0.434499i) q^{55} +(1.96881 + 1.84883i) q^{56} +6.72176i q^{57} +(-3.62005 + 3.85496i) q^{58} +(1.22764 + 1.93445i) q^{59} +(-1.20196 - 1.88555i) q^{60} +(-1.38496 + 0.548345i) q^{61} +(6.17764 + 0.388664i) q^{62} +(-2.69548 - 0.169585i) q^{63} +(0.929776 - 0.368125i) q^{64} +(-9.34908 + 11.3477i) q^{65} +(-1.60661 - 2.53161i) q^{66} +(7.55391 - 8.04410i) q^{67} -4.84399i q^{68} +(1.78446 + 1.67572i) q^{69} +(4.64550 - 3.85892i) q^{70} +(2.15146 - 11.2784i) q^{71} +(-0.481754 + 0.876307i) q^{72} +(-9.71642 - 6.16623i) q^{73} +(-3.13824 - 9.65850i) q^{74} +(-4.51550 + 2.14716i) q^{75} +(-2.07714 + 6.39277i) q^{76} +(6.23965 - 5.16189i) q^{77} +(6.45887 + 1.23210i) q^{78} +(-3.40890 - 7.24429i) q^{79} +(-0.560461 - 2.16469i) q^{80} +(-0.187381 - 0.982287i) q^{81} +(7.08862 + 2.30323i) q^{82} +(-3.52164 - 1.65716i) q^{83} +(-2.51115 - 0.994235i) q^{84} +(-10.7488 - 1.33584i) q^{85} +(5.30040 + 1.36091i) q^{86} +(1.94673 - 4.91688i) q^{87} +(-0.745665 - 2.90418i) q^{88} +(0.633835 - 0.998765i) q^{89} +(1.81167 + 1.31067i) q^{90} +(-1.11508 + 17.7237i) q^{91} +(1.17929 + 2.14513i) q^{92} +(-5.88690 + 1.91277i) q^{93} +(-10.1361 - 1.28048i) q^{94} +(13.6127 + 6.37211i) q^{95} +(-0.728969 + 0.684547i) q^{96} +(-6.10799 - 6.50435i) q^{97} +(0.0732113 - 0.285139i) q^{98} +(2.42574 + 1.76240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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