LMFDB - Embedded newform 250.2.h.a.109.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(9,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.h (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:	$1.99626005053$
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			109.7
Character	$\chi$	$=$	250.109
Dual form			250.2.h.a.39.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125333 - 0.992115i) q^{2} +(-1.96590 + 1.62634i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-2.13337 - 0.669861i) q^{5} +(1.36712 + 2.15423i) q^{6} +(4.79313 - 1.55738i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(0.657659 - 3.44757i) q^{9} +O(q^{10})$	\(q+(0.125333 - 0.992115i) q^{2} +(-1.96590 + 1.62634i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-2.13337 - 0.669861i) q^{5} +(1.36712 + 2.15423i) q^{6} +(4.79313 - 1.55738i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(0.657659 - 3.44757i) q^{9} +(-0.931962 + 2.03260i) q^{10} +(0.763387 + 0.0964382i) q^{11} +(2.30859 - 1.08634i) q^{12} +(4.92050 + 0.938635i) q^{13} +(-0.944364 - 4.95053i) q^{14} +(5.28342 - 2.15270i) q^{15} +(0.876307 + 0.481754i) q^{16} +(-1.11896 - 4.35808i) q^{17} +(-3.33796 - 1.08457i) q^{18} +(1.26732 - 1.53193i) q^{19} +(1.89976 + 1.17936i) q^{20} +(-6.89000 + 10.8569i) q^{21} +(0.191355 - 0.745280i) q^{22} +(5.62772 - 5.99292i) q^{23} +(-0.788432 - 2.42654i) q^{24} +(4.10257 + 2.85813i) q^{25} +(1.54794 - 4.76406i) q^{26} +(0.626545 + 1.13968i) q^{27} +(-5.02985 + 0.316452i) q^{28} +(0.512601 + 8.14757i) q^{29} +(-1.47354 - 5.51157i) q^{30} +(-4.27081 + 1.09656i) q^{31} +(0.587785 - 0.809017i) q^{32} +(-1.65758 + 1.05193i) q^{33} +(-4.46395 + 0.563929i) q^{34} +(-11.2688 + 0.111749i) q^{35} +(-1.49437 + 3.17570i) q^{36} +(-0.861689 + 1.56741i) q^{37} +(-1.36101 - 1.44933i) q^{38} +(-11.1997 + 6.15711i) q^{39} +(1.40817 - 1.73697i) q^{40} +(-3.34548 + 3.14162i) q^{41} +(9.90775 + 8.19640i) q^{42} +(-0.855160 - 1.17703i) q^{43} +(-0.715420 - 0.283255i) q^{44} +(-3.71242 + 6.91442i) q^{45} +(-5.24032 - 6.33446i) q^{46} +(0.318467 + 0.804356i) q^{47} +(-2.50623 + 0.478088i) q^{48} +(14.8856 - 10.8150i) q^{49} +(3.34978 - 3.71200i) q^{50} +(9.28747 + 6.74774i) q^{51} +(-4.53248 - 2.13282i) q^{52} +(2.89862 + 1.83952i) q^{53} +(1.20922 - 0.478765i) q^{54} +(-1.56399 - 0.717102i) q^{55} +(-0.316452 + 5.02985i) q^{56} +5.07270i q^{57} +(8.14757 + 0.512601i) q^{58} +(-4.28658 - 9.10945i) q^{59} +(-5.65279 + 0.771136i) q^{60} +(-5.77601 - 5.42404i) q^{61} +(0.552636 + 4.37456i) q^{62} +(-2.21694 - 17.5489i) q^{63} +(-0.728969 - 0.684547i) q^{64} +(-9.86851 - 5.29851i) q^{65} +(0.835890 + 1.77636i) q^{66} +(5.84014 + 0.367430i) q^{67} +4.49943i q^{68} +(-1.31706 + 20.9340i) q^{69} +(-1.30148 + 11.1939i) q^{70} +(7.43808 - 2.94494i) q^{71} +(2.96337 + 1.88061i) q^{72} +(6.99743 + 3.29274i) q^{73} +(1.44705 + 1.05134i) q^{74} +(-12.7135 + 1.05336i) q^{75} +(-1.60848 + 1.16863i) q^{76} +(3.80920 - 0.726645i) q^{77} +(4.70486 + 11.8831i) q^{78} +(-3.15293 - 3.81124i) q^{79} +(-1.54678 - 1.61476i) q^{80} +(6.70458 + 2.65453i) q^{81} +(2.69754 + 3.71285i) q^{82} +(-3.12227 - 2.58296i) q^{83} +(9.37354 - 8.80234i) q^{84} +(-0.532136 + 10.0470i) q^{85} +(-1.27493 + 0.700896i) q^{86} +(-14.2584 - 15.1837i) q^{87} +(-0.370687 + 0.674278i) q^{88} +(-5.84572 + 12.4228i) q^{89} +(6.39460 + 4.54976i) q^{90} +(25.0464 - 3.16410i) q^{91} +(-6.94130 + 4.40508i) q^{92} +(6.61262 - 9.10149i) q^{93} +(0.837928 - 0.215143i) q^{94} +(-3.72985 + 2.41925i) q^{95} +(0.160205 + 2.54638i) q^{96} +(-10.8981 + 0.685653i) q^{97} +(-8.86405 - 16.1237i) q^{98} +(0.834525 - 2.56841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 10 q^{5}+O(q^{10}) $ 240 * q + 10 * q^5	$ 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) $ 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{27}{50}\right)$

Coefficient data

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

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

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

$2$	0.125333	−	0.992115i	0.0886240	−	0.701531i
$2$	0.125333	−	0.992115i	0.0886240	−	0.701531i
$3$	−1.96590	+	1.62634i	−1.13501	+	0.938965i	−0.998663	−	0.0516954i	$-0.983537\pi$
$3$	−1.96590	+	1.62634i	−1.13501	+	0.938965i	−0.136351	+	0.990661i	$0.543537\pi$
$4$	−0.968583	−	0.248690i	−0.484292	−	0.124345i
$5$	−2.13337	−	0.669861i	−0.954074	−	0.299571i
$5$	−2.13337	−	0.669861i	−0.954074	−	0.299571i
$6$	1.36712	+	2.15423i	0.558124	+	0.879462i
$7$	4.79313	−	1.55738i	1.81163	−	0.588635i	0.811644	−	0.584153i	$-0.198573\pi$
$7$	4.79313	−	1.55738i	1.81163	−	0.588635i	0.999990	−	0.00448271i	$-0.00142690\pi$
$8$	−0.368125	+	0.929776i	−0.130152	+	0.328726i
$9$	0.657659	−	3.44757i	0.219220	−	1.14919i
$10$	−0.931962	+	2.03260i	−0.294712	+	0.642763i
$11$	0.763387	+	0.0964382i	0.230170	+	0.0290772i	0.239572	−	0.970879i	$-0.422993\pi$
$11$	0.763387	+	0.0964382i	0.230170	+	0.0290772i	−0.00940226	+	0.999956i	$0.502993\pi$
$12$	2.30859	−	1.08634i	0.666433	−	0.313600i
$13$	4.92050	+	0.938635i	1.36470	+	0.260331i	0.817142	−	0.576437i	$-0.195557\pi$
$13$	4.92050	+	0.938635i	1.36470	+	0.260331i	0.547559	+	0.836767i	$0.315557\pi$
$14$	−0.944364	−	4.95053i	−0.252392	−	1.32308i
$15$	5.28342	−	2.15270i	1.36417	−	0.555825i
$16$	0.876307	+	0.481754i	0.219077	+	0.120438i
$17$	−1.11896	−	4.35808i	−0.271389	−	1.05699i	−0.947388	−	0.320087i	$-0.896288\pi$
$17$	−1.11896	−	4.35808i	−0.271389	−	1.05699i	0.676000	−	0.736902i	$-0.263712\pi$
$18$	−3.33796	−	1.08457i	−0.786764	−	0.255635i
$19$	1.26732	−	1.53193i	0.290743	−	0.351448i	−0.604836	−	0.796350i	$-0.706761\pi$
$19$	1.26732	−	1.53193i	0.290743	−	0.351448i	0.895579	+	0.444902i	$0.146761\pi$
$20$	1.89976	+	1.17936i	0.424800	+	0.263714i
$21$	−6.89000	+	10.8569i	−1.50352	+	2.36917i
$22$	0.191355	−	0.745280i	0.0407971	−	0.158894i
$23$	5.62772	−	5.99292i	1.17346	−	1.24961i	0.211212	−	0.977440i	$-0.432259\pi$
$23$	5.62772	−	5.99292i	1.17346	−	1.24961i	0.962249	−	0.272169i	$-0.0877410\pi$
$24$	−0.788432	−	2.42654i	−0.160938	−	0.495316i
$25$	4.10257	+	2.85813i	0.820515	+	0.571626i
$26$	1.54794	−	4.76406i	0.303575	−	0.934308i
$27$	0.626545	+	1.13968i	0.120579	+	0.219332i
$28$	−5.02985	+	0.316452i	−0.950553	+	0.0598037i
$29$	0.512601	+	8.14757i	0.0951877	+	1.51297i	0.698587	+	0.715526i	$0.253813\pi$
$29$	0.512601	+	8.14757i	0.0951877	+	1.51297i	−0.603399	+	0.797440i	$0.706187\pi$
$30$	−1.47354	−	5.51157i	−0.269030	−	1.00627i
$31$	−4.27081	+	1.09656i	−0.767059	+	0.196947i	−0.611893	−	0.790941i	$-0.709592\pi$
$31$	−4.27081	+	1.09656i	−0.767059	+	0.196947i	−0.155167	+	0.987888i	$0.549592\pi$
$32$	0.587785	−	0.809017i	0.103907	−	0.143015i
$33$	−1.65758	+	1.05193i	−0.288548	+	0.183118i
$34$	−4.46395	+	0.563929i	−0.765562	+	0.0967130i
$35$	−11.2688	+	0.111749i	−1.90477	+	0.0188890i
$36$	−1.49437	+	3.17570i	−0.249062	+	0.529284i
$37$	−0.861689	+	1.56741i	−0.141661	+	0.257680i	−0.937614	−	0.347678i	$-0.886970\pi$
$37$	−0.861689	+	1.56741i	−0.141661	+	0.257680i	0.795953	+	0.605358i	$0.206970\pi$
$38$	−1.36101	−	1.44933i	−0.220785	−	0.235112i
$39$	−11.1997	+	6.15711i	−1.79340	+	0.985927i
$40$	1.40817	−	1.73697i	0.222651	−	0.274639i
$41$	−3.34548	+	3.14162i	−0.522476	+	0.490638i	−0.900318	−	0.435232i	$-0.856666\pi$
$41$	−3.34548	+	3.14162i	−0.522476	+	0.490638i	0.377842	+	0.925870i	$0.376666\pi$
$42$	9.90775	+	8.19640i	1.52880	+	1.26473i
$43$	−0.855160	−	1.17703i	−0.130411	−	0.179495i	0.738818	−	0.673905i	$-0.235384\pi$
$43$	−0.855160	−	1.17703i	−0.130411	−	0.179495i	−0.869229	+	0.494410i	$0.835384\pi$
$44$	−0.715420	−	0.283255i	−0.107854	−	0.0427023i
$45$	−3.71242	+	6.91442i	−0.553416	+	1.03074i
$46$	−5.24032	−	6.33446i	−0.772643	−	0.933965i
$47$	0.318467	+	0.804356i	0.0464532	+	0.117327i	0.951151	−	0.308727i	$-0.0999031\pi$
$47$	0.318467	+	0.804356i	0.0464532	+	0.117327i	−0.904697	+	0.426055i	$0.859903\pi$
$48$	−2.50623	+	0.478088i	−0.361743	+	0.0690061i
$49$	14.8856	−	10.8150i	2.12651	−	1.54500i
$50$	3.34978	−	3.71200i	0.473730	−	0.524957i
$51$	9.28747	+	6.74774i	1.30051	+	0.944872i
$52$	−4.53248	−	2.13282i	−0.628542	−	0.295769i
$53$	2.89862	+	1.83952i	0.398156	+	0.252678i	0.719798	−	0.694184i	$-0.244235\pi$
$53$	2.89862	+	1.83952i	0.398156	+	0.252678i	−0.321641	+	0.946862i	$0.604235\pi$
$54$	1.20922	−	0.478765i	0.164554	−	0.0651516i
$55$	−1.56399	−	0.717102i	−0.210888	−	0.0966940i
$56$	−0.316452	+	5.02985i	−0.0422876	+	0.672142i
$57$			5.07270i			0.671896i
$58$	8.14757	+	0.512601i	1.06983	+	0.0673079i
$59$	−4.28658	−	9.10945i	−0.558065	−	1.18595i	−0.962475	−	0.271371i	$-0.912523\pi$
$59$	−4.28658	−	9.10945i	−0.558065	−	1.18595i	0.404410	−	0.914578i	$-0.367477\pi$
$60$	−5.65279	+	0.771136i	−0.729772	+	0.0995533i
$61$	−5.77601	−	5.42404i	−0.739543	−	0.694477i	0.220169	−	0.975462i	$-0.429339\pi$
$61$	−5.77601	−	5.42404i	−0.739543	−	0.694477i	−0.959712	+	0.280985i	$0.909339\pi$
$62$	0.552636	+	4.37456i	0.0701848	+	0.555570i
$63$	−2.21694	−	17.5489i	−0.279308	−	2.21095i
$64$	−0.728969	−	0.684547i	−0.0911211	−	0.0855684i
$65$	−9.86851	−	5.29851i	−1.22404	−	0.657199i
$66$	0.835890	+	1.77636i	0.102891	+	0.218654i
$67$	5.84014	+	0.367430i	0.713487	+	0.0448888i	0.415385	−	0.909645i	$-0.363647\pi$
$67$	5.84014	+	0.367430i	0.713487	+	0.0448888i	0.298101	+	0.954534i	$0.403647\pi$
$68$			4.49943i			0.545637i
$69$	−1.31706	+	20.9340i	−0.158555	+	2.52016i
$70$	−1.30148	+	11.1939i	−0.155557	+	1.33793i
$71$	7.43808	−	2.94494i	0.882737	−	0.349500i	0.117365	−	0.993089i	$-0.462555\pi$
$71$	7.43808	−	2.94494i	0.882737	−	0.349500i	0.765372	+	0.643588i	$0.222555\pi$
$72$	2.96337	+	1.88061i	0.349236	+	0.221632i
$73$	6.99743	+	3.29274i	0.818987	+	0.385386i	0.789174	−	0.614169i	$-0.210509\pi$
$73$	6.99743	+	3.29274i	0.818987	+	0.385386i	0.0298130	+	0.999555i	$0.490509\pi$
$74$	1.44705	+	1.05134i	0.168216	+	0.122216i
$75$	−12.7135	+	1.05336i	−1.46803	+	0.121631i
$76$	−1.60848	+	1.16863i	−0.184505	+	0.134051i
$77$	3.80920	−	0.726645i	0.434099	−	0.0828088i
$78$	4.70486	+	11.8831i	0.532721	+	1.34550i
$79$	−3.15293	−	3.81124i	−0.354733	−	0.428798i	0.562717	−	0.826650i	$-0.309756\pi$
$79$	−3.15293	−	3.81124i	−0.354733	−	0.428798i	−0.917450	+	0.397851i	$0.869756\pi$
$80$	−1.54678	−	1.61476i	−0.172936	−	0.180536i
$81$	6.70458	+	2.65453i	0.744953	+	0.294948i
$82$	2.69754	+	3.71285i	0.297894	+	0.410016i
$83$	−3.12227	−	2.58296i	−0.342713	−	0.283517i	0.450104	−	0.892976i	$-0.351387\pi$
$83$	−3.12227	−	2.58296i	−0.342713	−	0.283517i	−0.792818	+	0.609459i	$0.791387\pi$
$84$	9.37354	−	8.80234i	1.02274	−	0.960414i
$85$	−0.532136	+	10.0470i	−0.0577183	+	1.08975i
$86$	−1.27493	+	0.700896i	−0.137479	+	0.0755796i
$87$	−14.2584	−	15.1837i	−1.52866	−	1.62786i
$88$	−0.370687	+	0.674278i	−0.0395154	+	0.0718783i
$89$	−5.84572	+	12.4228i	−0.619645	+	1.31681i	0.310832	+	0.950465i	$0.399392\pi$
$89$	−5.84572	+	12.4228i	−0.619645	+	1.31681i	−0.930478	+	0.366348i	$0.880608\pi$
$90$	6.39460	+	4.54976i	0.674050	+	0.479587i
$91$	25.0464	−	3.16410i	2.62558	−	0.331687i
$92$	−6.94130	+	4.40508i	−0.723680	+	0.459261i
$93$	6.61262	−	9.10149i	0.685696	−	0.943780i
$94$	0.837928	−	0.215143i	0.0864257	−	0.0221903i
$95$	−3.72985	+	2.41925i	−0.382674	+	0.248209i
$96$	0.160205	+	2.54638i	0.0163508	+	0.259889i
$97$	−10.8981	+	0.685653i	−1.10654	+	0.0696175i	−0.605528	−	0.795824i	$-0.707038\pi$
$97$	−10.8981	+	0.685653i	−1.10654	+	0.0696175i	−0.501010	+	0.865441i	$0.667038\pi$
$98$	−8.86405	−	16.1237i	−0.895405	−	1.62874i
$99$	0.834525	−	2.56841i	0.0838730	−	0.258134i
$100$	−3.26290	−	3.78860i	−0.326290	−	0.378860i
$101$	2.80751	+	8.64063i	0.279358	+	0.859774i	0.988033	+	0.154240i	$0.0492929\pi$
$101$	2.80751	+	8.64063i	0.279358	+	0.859774i	−0.708676	+	0.705534i	$0.750707\pi$
$102$	7.85856	−	8.36852i	0.778113	−	0.828607i
$103$	−0.198350	+	0.772523i	−0.0195440	+	0.0761189i	−0.977607	−	0.210438i	$-0.932511\pi$
$103$	−0.198350	+	0.772523i	−0.0195440	+	0.0761189i	0.958063	+	0.286557i	$0.0925109\pi$
$104$	−2.68408	+	4.22943i	−0.263195	+	0.414730i
$105$	21.9716	−	18.5465i	2.14421	−	1.80995i
$106$	2.18831	−	2.64521i	0.212547	−	0.256926i
$107$	9.68659	+	3.14736i	0.936438	+	0.304267i	0.737193	−	0.675682i	$-0.236151\pi$
$107$	9.68659	+	3.14736i	0.936438	+	0.304267i	0.199245	+	0.979950i	$0.436151\pi$
$108$	−0.323434	−	1.25969i	−0.0311224	−	0.121214i
$109$	−6.10178	−	3.35448i	−0.584445	−	0.321301i	0.161956	−	0.986798i	$-0.448220\pi$
$109$	−6.10178	−	3.35448i	−0.584445	−	0.321301i	−0.746401	+	0.665497i	$0.768220\pi$
$110$	−0.907467	+	1.46178i	−0.0865236	+	0.139375i
$111$	−0.855132	−	4.48276i	−0.0811656	−	0.425485i
$112$	4.95053	+	0.944364i	0.467781	+	0.0892340i
$113$	3.40084	−	1.60032i	0.319924	−	0.150545i	−0.259111	−	0.965848i	$-0.583429\pi$
$113$	3.40084	−	1.60032i	0.319924	−	0.150545i	0.579035	+	0.815303i	$0.303429\pi$
$114$	5.03271	+	0.635779i	0.471356	+	0.0595461i
$115$	−16.0205	+	9.01534i	−1.49392	+	0.840685i
$116$	1.52972	−	8.01907i	0.142031	−	0.744552i
$117$	6.47202	−	16.3465i	0.598338	−	1.51123i
$118$	−9.57487	+	3.11106i	−0.881438	+	0.286397i
$119$	−12.1505	−	19.1462i	−1.11384	−	1.75513i
$120$	0.0565734	+	5.70486i	0.00516442	+	0.520781i
$121$	−10.0810	−	2.58835i	−0.916451	−	0.235305i
$122$	−6.10519	+	5.05066i	−0.552738	+	0.457265i
$123$	1.46757	−	11.6170i	0.132326	−	1.04747i
$124$	4.40933			0.395970
$125$	−6.83777	−	8.84561i	−0.611589	−	0.791176i
$126$	−17.6884			−1.57580
$127$	−0.745286	+	5.89955i	−0.0661335	+	0.523500i	0.923896	+	0.382643i	$0.124986\pi$
$127$	−0.745286	+	5.89955i	−0.0661335	+	0.523500i	−0.990030	+	0.140858i	$0.955014\pi$
$128$	−0.770513	+	0.637424i	−0.0681044	+	0.0563409i
$129$	3.59540	+	0.923142i	0.316557	+	0.0812781i
$130$	−6.49358	+	9.12661i	−0.569525	+	0.800457i
$131$	2.39595	+	3.77541i	0.209335	+	0.329859i	0.932730	−	0.360575i	$-0.117420\pi$
$131$	2.39595	+	3.77541i	0.209335	+	0.329859i	−0.723395	+	0.690434i	$0.757420\pi$
$132$	1.86711	−	0.606662i	0.162511	−	0.0528031i
$133$	3.68864	−	9.31643i	0.319845	−	0.807837i
$134$	1.09650	−	5.74804i	0.0947229	−	0.496555i
$135$	−0.573227	−	2.85106i	−0.0493355	−	0.245381i
$136$	4.46395	+	0.563929i	0.382781	+	0.0483565i
$137$	−11.1352	+	5.23981i	−0.951342	+	0.447668i	−0.837868	−	0.545873i	$-0.816198\pi$
$137$	−11.1352	+	5.23981i	−0.951342	+	0.447668i	−0.113474	+	0.993541i	$0.536198\pi$
$138$	20.6039	+	3.93041i	1.75392	+	0.334578i
$139$	0.675223	+	3.53964i	0.0572716	+	0.300228i	0.999385	−	0.0350661i	$-0.0111642\pi$
$139$	0.675223	+	3.53964i	0.0572716	+	0.300228i	−0.942113	+	0.335295i	$0.891164\pi$
$140$	10.9425	+	2.69419i	0.924813	+	0.227701i
$141$	−1.93423	−	1.06335i	−0.162891	−	0.0895503i
$142$	−1.98948	−	7.74852i	−0.166954	−	0.650242i
$143$	3.66572	+	1.19107i	0.306543	+	0.0996019i
$144$	2.23719	−	2.70430i	0.186433	−	0.225358i
$145$	4.36417	−	17.7252i	0.362424	−	1.47200i
$146$	4.14379	−	6.52956i	0.342942	−	0.540391i
$147$	−11.6747	+	45.4701i	−0.962916	+	3.75031i
$148$	1.22442	−	1.30387i	0.100646	−	0.107177i
$149$	0.585808	+	1.80293i	0.0479913	+	0.147702i	0.972180	−	0.234233i	$-0.0752579\pi$
$149$	0.585808	+	1.80293i	0.0479913	+	0.147702i	−0.924189	+	0.381935i	$0.875258\pi$
$150$	−0.548375	+	12.7453i	−0.0447746	+	1.04065i
$151$	−3.93876	+	12.1222i	−0.320531	+	0.986494i	0.652886	+	0.757456i	$0.273558\pi$
$151$	−3.93876	+	12.1222i	−0.320531	+	0.986494i	−0.973417	+	0.229038i	$0.926442\pi$
$152$	0.957818	+	1.74226i	0.0776893	+	0.141316i
$153$	−15.7607	+	0.991577i	−1.27417	+	0.0801643i
$154$	−0.243495	−	3.87024i	−0.0196214	−	0.311873i
$155$	9.84577	+	0.521480i	0.790831	+	0.0418863i
$156$	12.3791	−	3.17841i	0.991121	−	0.254477i
$157$	−3.55777	+	4.89685i	−0.283941	+	0.390811i	−0.927034	−	0.374977i	$-0.877651\pi$
$157$	−3.55777	+	4.89685i	−0.283941	+	0.390811i	0.643094	+	0.765788i	$0.277651\pi$
$158$	−4.17636	+	2.65040i	−0.332253	+	0.210854i
$159$	−8.69009	+	1.09781i	−0.689169	+	0.0870622i
$160$	−1.79589	+	1.33220i	−0.141978	+	0.105320i
$161$	17.6412	−	37.4894i	1.39032	−	2.95458i
$162$	3.47391	−	6.31901i	0.272936	−	0.496468i
$163$	2.20654	+	2.34972i	0.172829	+	0.184045i	0.809552	−	0.587049i	$-0.199710\pi$
$163$	2.20654	+	2.34972i	0.172829	+	0.184045i	−0.636722	+	0.771093i	$0.719710\pi$
$164$	4.02166	−	2.21093i	0.314039	−	0.172645i
$165$	4.24090	−	1.13382i	0.330153	−	0.0882678i
$166$	−2.95392	+	2.77392i	−0.229269	+	0.215298i
$167$	−3.65737	−	3.02564i	−0.283016	−	0.234131i	0.485074	−	0.874473i	$-0.338793\pi$
$167$	−3.65737	−	3.02564i	−0.283016	−	0.234131i	−0.768090	+	0.640342i	$0.778793\pi$
$168$	−7.55811	−	10.4029i	−0.583121	−	0.802597i
$169$	11.2432	+	4.45148i	0.864858	+	0.342422i
$170$	9.90104	+	1.78716i	0.759375	+	0.137069i
$171$	−4.44796	−	5.37666i	−0.340144	−	0.411163i
$172$	0.535579	+	1.35272i	0.0408375	+	0.103144i
$173$	−18.0066	+	3.43495i	−1.36902	+	0.261154i	−0.818902	−	0.573934i	$-0.805417\pi$
$173$	−18.0066	+	3.43495i	−1.36902	+	0.261154i	−0.550116	+	0.835088i	$0.685417\pi$
$174$	−16.8510	+	12.2430i	−1.27747	+	0.928136i
$175$	24.1154	+	7.31011i	1.82295	+	0.552592i
$176$	0.622501	+	0.452274i	0.0469228	+	0.0340914i
$177$	23.2420	+	10.9369i	1.74698	+	0.822065i
$178$	11.5922	+	7.35661i	0.868870	+	0.551402i
$179$	0.773784	−	0.306363i	0.0578353	−	0.0228986i	−0.339029	−	0.940776i	$-0.610098\pi$
$179$	0.773784	−	0.306363i	0.0578353	−	0.0228986i	0.396864	+	0.917877i	$0.370098\pi$
$180$	5.31534	−	5.77394i	0.396182	−	0.430364i
$181$	−0.906962	+	14.4157i	−0.0674139	+	1.07151i	0.808327	+	0.588733i	$0.200373\pi$
$181$	−0.906962	+	14.4157i	−0.0674139	+	1.07151i	−0.875741	+	0.482781i	$0.839627\pi$
$182$		−	25.2455i		−	1.87132i
$183$	20.1764	+	1.26939i	1.49148	+	0.0938360i
$184$	3.50037	+	7.43866i	0.258051	+	0.548386i
$185$	2.88825	−	2.76665i	0.212348	−	0.203408i
$186$	−8.20094	−	7.70119i	−0.601322	−	0.564679i
$187$	−0.433917	−	3.43481i	−0.0317312	−	0.251178i
$188$	−0.108427	−	0.858285i	−0.00790783	−	0.0625969i
$189$	4.77803	+	4.48687i	0.347551	+	0.326372i
$190$	1.93269	+	4.00365i	0.140212	+	0.290455i
$191$	−5.15943	−	10.9643i	−0.373323	−	0.793352i	−0.999902	−	0.0139942i	$-0.995545\pi$
$191$	−5.15943	−	10.9643i	−0.373323	−	0.793352i	0.626579	−	0.779358i	$-0.284455\pi$
$192$	2.54638	+	0.160205i	0.183769	+	0.0115618i
$193$			7.50128i			0.539954i	0.962867	+	0.269977i	$0.0870161\pi$
$193$			7.50128i			0.539954i	−0.962867	+	0.269977i	$0.912984\pi$
$194$	−0.685653	+	10.8981i	−0.0492270	+	0.782441i
$195$	28.0177	−	5.63315i	2.00639	−	0.403399i
$196$	−17.1075	+	6.77333i	−1.22196	+	0.483809i
$197$	−3.09682	−	1.96530i	−0.220640	−	0.140022i	0.420913	−	0.907101i	$-0.361710\pi$
$197$	−3.09682	−	1.96530i	−0.220640	−	0.140022i	−0.641553	+	0.767079i	$0.721710\pi$
$198$	−2.44356	−	1.14985i	−0.173656	−	0.0817164i
$199$	0.0810004	+	0.0588503i	0.00574197	+	0.00417179i	0.590653	−	0.806926i	$-0.298870\pi$
$199$	0.0810004	+	0.0588503i	0.00574197	+	0.00417179i	−0.584911	+	0.811098i	$0.698870\pi$
$200$	−4.16768	+	2.76233i	−0.294699	+	0.195326i
$201$	−12.0787	+	8.77569i	−0.851966	+	0.618990i
$202$	8.92437	−	1.70241i	0.627916	−	0.119781i
$203$	15.1458	+	38.2540i	1.06303	+	2.68491i
$204$	−7.31759	−	8.84545i	−0.512334	−	0.619305i
$205$	9.24161	−	4.46124i	0.645462	−	0.311586i
$206$	0.741571	+	0.293609i	0.0516677	+	0.0204567i
$207$	−16.9599	−	23.3433i	−1.17879	−	1.62247i
$208$	3.85967	+	3.19300i	0.267620	+	0.221395i
$209$	1.11519	−	1.04723i	0.0771394	−	0.0724387i
$210$	−15.6465	−	24.1228i	−1.07971	−	1.66463i
$211$	−21.8478	+	12.0109i	−1.50406	+	0.826866i	−0.999337	−	0.0364140i	$-0.988407\pi$
$211$	−21.8478	+	12.0109i	−1.50406	+	0.826866i	−0.504726	+	0.863280i	$0.668407\pi$
$212$	−2.35009	−	2.50259i	−0.161405	−	0.171878i
$213$	−9.83306	+	17.8863i	−0.673750	+	1.22555i
$214$	4.33660	−	9.21574i	0.296444	−	0.629975i
$215$	1.03593	+	3.08388i	0.0706500	+	0.210319i
$216$	−1.29030	+	0.163002i	−0.0877935	+	0.0110909i
$217$	−18.7628	+	11.9072i	−1.27370	+	0.808315i
$218$	−4.09279	+	5.63324i	−0.277199	+	0.381531i
$219$	−19.1114	+	4.90696i	−1.29143	+	0.331582i
$220$	1.33652	+	1.08352i	0.0901080	+	0.0730510i
$221$	−1.41521	−	22.4942i	−0.0951977	−	1.51312i
$222$	−4.55459	+	0.286550i	−0.305684	+	0.0192320i
$223$	7.62134	+	13.8632i	0.510363	+	0.928347i	0.998456	+	0.0555549i	$0.0176928\pi$
$223$	7.62134	+	13.8632i	0.510363	+	0.928347i	−0.488093	+	0.872792i	$0.662307\pi$
$224$	1.55738	−	4.79313i	0.104057	−	0.320255i
$225$	12.5517	−	12.2642i	0.836779	−	0.817615i
$226$	−1.16146	−	3.57460i	−0.0772590	−	0.237779i
$227$	1.38052	−	1.47011i	0.0916286	−	0.0975745i	−0.681520	−	0.731800i	$-0.738681\pi$
$227$	1.38052	−	1.47011i	0.0916286	−	0.0975745i	0.773149	+	0.634225i	$0.218681\pi$
$228$	1.26153	−	4.91334i	0.0835469	−	0.325394i
$229$	8.81004	−	13.8824i	0.582184	−	0.917375i	−0.417777	−	0.908549i	$-0.637191\pi$
$229$	8.81004	−	13.8824i	0.582184	−	0.917375i	0.999961	−	0.00882532i	$-0.00280922\pi$
$230$	6.93636	+	17.0241i	0.457370	+	1.12253i
$231$	−6.30675	+	7.62356i	−0.414954	+	0.501593i
$232$	−7.76412	−	2.52271i	−0.509739	−	0.165624i
$233$	−0.101571	−	0.395593i	−0.00665414	−	0.0259162i	0.965169	−	0.261626i	$-0.0842586\pi$
$233$	−0.101571	−	0.395593i	−0.00665414	−	0.0259162i	−0.971824	+	0.235710i	$0.924259\pi$
$234$	−15.4064	−	8.46974i	−1.00715	−	0.553684i
$235$	−0.140603	−	1.92932i	−0.00917192	−	0.125855i
$236$	1.88648	+	9.88929i	0.122800	+	0.643738i
$237$	12.3967	+	2.36480i	0.805253	+	0.153610i
$238$	−20.5181	+	9.65507i	−1.32999	+	0.625845i
$239$	0.206496	+	0.0260865i	0.0133571	+	0.00168740i	0.132009	−	0.991249i	$-0.457857\pi$
$239$	0.206496	+	0.0260865i	0.0133571	+	0.00168740i	−0.118652	+	0.992936i	$0.537857\pi$
$240$	5.66697	+	0.658882i	0.365801	+	0.0425306i
$241$	−5.08545	+	26.6589i	−0.327583	+	1.71725i	0.313338	+	0.949642i	$0.398553\pi$
$241$	−5.08545	+	26.6589i	−0.327583	+	1.71725i	−0.640921	+	0.767607i	$0.721447\pi$
$242$	−3.83142	+	9.67706i	−0.246293	+	0.622065i
$243$	−21.2084	+	6.89103i	−1.36052	+	0.442060i
$244$	4.24565	+	6.69007i	0.271800	+	0.428288i
$245$	−39.0010	+	13.1012i	−2.49168	+	0.837003i
$246$	−11.3414	−	2.91199i	−0.723104	−	0.185662i
$247$	7.67376	−	6.34829i	0.488270	−	0.403932i
$248$	0.552636	−	4.37456i	0.0350924	−	0.277785i
$249$	10.3388			0.655197
$250$	−9.63286	+	5.67521i	−0.609236	+	0.358932i
$251$	−17.2831			−1.09090			−0.545451	−	0.838143i	$-0.683642\pi$
$251$	−17.2831			−1.09090			−0.545451	+	0.838143i	$0.683642\pi$
$252$	−2.21694	+	17.5489i	−0.139654	+	1.10548i
$253$	4.87407	−	4.03219i	0.306430	−	0.253501i
$254$	5.75962	+	1.47882i	0.361391	+	0.0927894i
$255$	−15.2936	−	20.6168i	−0.957722	−	1.29107i
$256$	0.535827	+	0.844328i	0.0334892	+	0.0527705i
$257$	−0.180358	+	0.0586020i	−0.0112505	+	0.00365549i	−0.314637	−	0.949212i	$-0.601883\pi$
$257$	−0.180358	+	0.0586020i	−0.0112505	+	0.00365549i	0.303386	+	0.952868i	$0.401883\pi$
$258$	1.36649	−	3.45135i	0.0850737	−	0.214872i
$259$	−1.68914	+	8.85476i	−0.104958	+	0.550208i
$260$	8.24078	+	7.58624i	0.511072	+	0.470479i
$261$	28.4264	+	3.59109i	1.75955	+	0.222283i
$262$	4.04593	−	1.90387i	0.249958	−	0.117621i
$263$	−0.711781	−	0.135779i	−0.0438903	−	0.00837252i	0.165389	−	0.986228i	$-0.447112\pi$
$263$	−0.711781	−	0.135779i	−0.0438903	−	0.00837252i	−0.209280	+	0.977856i	$0.567112\pi$
$264$	−0.367867	−	1.92843i	−0.0226406	−	0.118686i
$265$	−4.95162	−	5.86606i	−0.304176	−	0.360349i
$266$	−8.78066	−	4.82721i	−0.538377	−	0.295975i
$267$	−8.71151	−	33.9291i	−0.533136	−	2.07643i
$268$	−5.56528	−	1.80827i	−0.339954	−	0.110458i
$269$	−1.10896	+	1.34050i	−0.0676143	+	0.0817317i	−0.803236	−	0.595661i	$-0.796890\pi$
$269$	−1.10896	+	1.34050i	−0.0676143	+	0.0817317i	0.735622	+	0.677393i	$0.236890\pi$
$270$	−2.90043	+	0.211374i	−0.176514	+	0.0128638i
$271$	14.9785	−	23.6024i	0.909881	−	1.43374i	0.00886336	−	0.999961i	$-0.497179\pi$
$271$	14.9785	−	23.6024i	0.909881	−	1.43374i	0.901018	−	0.433782i	$-0.142821\pi$
$272$	1.11896	−	4.35808i	0.0678471	−	0.264247i
$273$	−44.0929	+	46.9542i	−2.66862	+	2.84180i
$274$	3.80289	+	11.7041i	0.229741	+	0.707070i
$275$	2.85622	+	2.57750i	0.172236	+	0.155429i
$276$	6.48177	−	19.9488i	0.390157	−	1.20078i
$277$	−11.0785	−	20.1517i	−0.665642	−	1.21080i	−0.966387	−	0.257094i	$-0.917235\pi$
$277$	−11.0785	−	20.1517i	−0.665642	−	1.21080i	0.300744	−	0.953705i	$-0.402765\pi$
$278$	3.59636	−	0.226264i	0.215695	−	0.0135704i
$279$	0.971721	+	15.4451i	0.0581754	+	0.924672i
$280$	4.04441	−	10.5186i	0.241700	−	0.628605i
$281$	23.5457	−	6.04551i	1.40462	−	0.360645i	0.531049	−	0.847341i	$-0.321798\pi$
$281$	23.5457	−	6.04551i	1.40462	−	0.360645i	0.873571	+	0.486696i	$0.161798\pi$
$282$	−1.29739	+	1.78570i	−0.0772584	+	0.106337i
$283$	11.9433	−	7.57944i	0.709955	−	0.450551i	−0.131193	−	0.991357i	$-0.541881\pi$
$283$	11.9433	−	7.57944i	0.709955	−	0.450551i	0.841147	+	0.540806i	$0.181881\pi$
$284$	−7.93677	+	1.00265i	−0.470961	+	0.0594962i
$285$	3.39801	−	10.8220i	0.201281	−	0.641039i
$286$	1.64111	−	3.48754i	0.0970409	−	0.206222i
$287$	−11.1426	+	20.2684i	−0.657729	+	1.19640i
$288$	−2.40258	−	2.55849i	−0.141573	−	0.150760i
$289$	−2.84353	+	1.56325i	−0.167267	+	0.0919556i
$290$	−17.0384	−	6.55131i	−1.00053	−	0.384706i
$291$	20.3096	−	19.0719i	1.19057	−	1.11802i
$292$	−5.95872	−	4.92948i	−0.348708	−	0.288476i
$293$	5.08846	+	7.00366i	0.297271	+	0.409158i	0.931359	−	0.364103i	$-0.118624\pi$
$293$	5.08846	+	7.00366i	0.297271	+	0.409158i	−0.634088	+	0.773261i	$0.718624\pi$
$294$	43.6483	+	17.2816i	2.54562	+	1.00788i
$295$	3.04282	+	22.3053i	0.177160	+	1.29866i
$296$	−1.14013	−	1.37818i	−0.0662686	−	0.0801050i
$297$	0.368387	+	0.930440i	0.0213760	+	0.0539896i
$298$	1.86214	−	0.355221i	0.107871	−	0.0205774i
$299$	33.3164	−	24.2057i	1.92673	−	1.39985i
$300$	12.5761	+	2.14146i	0.726080	+	0.123637i
$301$	−5.93198	−	4.30983i	−0.341913	−	0.248415i
$302$	11.5330	+	5.42702i	0.663650	+	0.312290i
$303$	−19.5718	−	12.4207i	−1.12437	−	0.713549i
$304$	1.84857	−	0.731902i	0.106023	−	0.0419774i
$305$	8.68905	+	15.4406i	0.497533	+	0.884128i
$306$	−0.991577	+	15.7607i	−0.0566847	+	0.900977i
$307$		−	24.4812i		−	1.39722i	−0.715505	−	0.698608i	$-0.753803\pi$
$307$		−	24.4812i		−	1.39722i	0.715505	−	0.698608i	$-0.246197\pi$
$308$	−3.87024	−	0.243495i	−0.220527	−	0.0138744i
$309$	−0.866444	−	1.84129i	−0.0492903	−	0.104747i
$310$	1.75137	−	9.70277i	0.0994712	−	0.551080i
$311$	16.8209	+	15.7959i	0.953825	+	0.895701i	0.994633	−	0.103466i	$-0.0329932\pi$
$311$	16.8209	+	15.7959i	0.953825	+	0.895701i	−0.0408079	+	0.999167i	$0.512993\pi$
$312$	−1.60184	−	12.6798i	−0.0906862	−	0.717855i
$313$	−3.63731	−	28.7923i	−0.205593	−	1.62744i	−0.670382	−	0.742016i	$-0.733870\pi$
$313$	−3.63731	−	28.7923i	−0.205593	−	1.62744i	0.464789	−	0.885421i	$-0.346130\pi$
$314$	4.41233	+	4.14345i	0.249002	+	0.233828i
$315$	−7.02575	+	38.9234i	−0.395856	+	2.19308i
$316$	2.10606	+	4.47561i	0.118475	+	0.251773i
$317$	−12.8021	−	0.805440i	−0.719037	−	0.0452380i	−0.300944	−	0.953642i	$-0.597302\pi$
$317$	−12.8021	−	0.805440i	−0.719037	−	0.0452380i	−0.418094	+	0.908404i	$0.637302\pi$
$318$			8.75915i			0.491189i
$319$	−0.394423	+	6.26918i	−0.0220835	+	0.351007i
$320$	1.09661	+	1.94870i	0.0613025	+	0.108936i
$321$	−24.1616	+	9.56624i	−1.34857	+	0.533935i
$322$	−34.9827	−	22.2007i	−1.94951	−	1.23720i
$323$	−8.09434	−	3.80891i	−0.450381	−	0.211933i
$324$	−5.83379	−	4.23850i	−0.324099	−	0.235472i
$325$	17.5040	+	17.9142i	0.970945	+	0.993703i
$326$	2.60775	−	1.89464i	0.144430	−	0.104934i
$327$	17.4510	−	3.32896i	0.965043	−	0.184092i
$328$	−1.68945	−	4.26706i	−0.0932841	−	0.235609i
$329$	2.77915	+	3.35941i	0.153219	+	0.185210i
$330$	−0.593354	−	4.34956i	−0.0326631	−	0.239436i
$331$	−8.45617	−	3.34803i	−0.464793	−	0.184025i	0.124043	−	0.992277i	$-0.460414\pi$
$331$	−8.45617	−	3.34803i	−0.464793	−	0.184025i	−0.588836	+	0.808252i	$0.700414\pi$
$332$	2.38182	+	3.27829i	0.130719	+	0.179920i
$333$	4.83704	+	4.00155i	0.265068	+	0.219284i
$334$	−3.46017	+	3.24931i	−0.189332	+	0.177795i
$335$	−12.2131	−	4.69595i	−0.667272	−	0.256567i
$336$	−11.2681	+	6.19469i	−0.614726	+	0.337948i
$337$	−17.5321	−	18.6698i	−0.955034	−	1.01701i	−0.999838	−	0.0180125i	$-0.994266\pi$
$337$	−17.5321	−	18.6698i	−0.955034	−	1.01701i	0.0448034	−	0.998996i	$-0.485734\pi$
$338$	5.82552	−	10.5966i	0.316867	−	0.576378i
$339$	−4.08307	+	8.67697i	−0.221762	+	0.471268i
$340$	3.01400	−	9.59898i	0.163457	−	0.520578i
$341$	−3.36603	+	0.425228i	−0.182281	+	0.0230274i
$342$	−5.89174	+	3.73901i	−0.318589	+	0.202183i
$343$	33.7691	−	46.4792i	1.82336	−	2.50964i
$344$	1.40918	−	0.361815i	0.0759777	−	0.0195078i
$345$	16.8327	−	43.7779i	0.906241	−	2.35692i
$346$	1.15103	+	18.2951i	0.0618799	+	0.983553i
$347$	34.8067	−	2.18985i	1.86852	−	0.117557i	0.912175	−	0.409800i	$-0.134402\pi$
$347$	34.8067	−	2.18985i	1.86852	−	0.117557i	0.956344	+	0.292243i	$0.0944015\pi$
$348$	10.0344	+	18.2526i	0.537902	+	0.978439i
$349$	−7.20723	+	22.1816i	−0.385794	+	1.18735i	0.550108	+	0.835093i	$0.314586\pi$
$349$	−7.20723	+	22.1816i	−0.385794	+	1.18735i	−0.935903	+	0.352259i	$0.885414\pi$
$350$	10.2749	−	23.0090i	0.549218	−	1.22988i
$351$	2.01317	+	6.19590i	0.107455	+	0.330712i
$352$	0.526728	−	0.560908i	0.0280747	−	0.0298965i
$353$	−5.24145	+	20.4141i	−0.278974	+	1.08653i	0.662395	+	0.749155i	$0.269540\pi$
$353$	−5.24145	+	20.4141i	−0.278974	+	1.08653i	−0.941369	+	0.337379i	$0.890460\pi$
$354$	13.7636	−	21.6880i	0.731528	−	1.15270i
$355$	−17.8409	+	1.30019i	−0.946897	+	0.0690068i
$356$	8.75149	−	10.5787i	0.463828	−	0.560672i
$357$	55.0249	+	17.8787i	2.91222	+	0.946239i
$358$	−0.206966	−	0.806080i	−0.0109385	−	0.0426026i
$359$	26.1833	+	14.3944i	1.38190	+	0.759706i	0.987258	−	0.159130i	$-0.0508688\pi$
$359$	26.1833	+	14.3944i	1.38190	+	0.759706i	0.394642	+	0.918835i	$0.370869\pi$
$360$	−5.06223	−	5.99709i	−0.266803	−	0.316074i
$361$	2.81955	+	14.7806i	0.148397	+	0.777925i
$362$	14.1884	+	2.70658i	0.745726	+	0.142255i
$363$	24.0277	−	11.3066i	1.26113	−	0.593441i
$364$	−25.0464	−	3.16410i	−1.31279	−	0.165844i
$365$	−12.7225	−	11.7120i	−0.665924	−	0.613032i
$366$	3.78815	−	19.8582i	0.198010	−	1.03800i
$367$	−9.97664	+	25.1981i	−0.520777	+	1.31533i	0.396848	+	0.917884i	$0.370104\pi$
$367$	−9.97664	+	25.1981i	−0.520777	+	1.31533i	−0.917625	+	0.397447i	$0.869896\pi$
$368$	7.81872	−	2.54046i	0.407579	−	0.132430i
$369$	8.63075	+	13.5999i	0.449299	+	0.707982i
$370$	−2.38284	−	3.21223i	−0.123878	−	0.166996i
$371$	16.7583	+	4.30281i	0.870049	+	0.223391i
$372$	−8.66832	+	7.17105i	−0.449431	+	0.371802i
$373$	1.50656	−	11.9256i	0.0780067	−	0.617486i	−0.903848	−	0.427853i	$-0.859270\pi$
$373$	1.50656	−	11.9256i	0.0780067	−	0.617486i	0.981855	−	0.189633i	$-0.0607299\pi$
$374$	−3.46211			−0.179021
$375$	27.8283	+	6.26909i	1.43705	+	0.323734i
$376$	−0.865107			−0.0446145
$377$	−5.12534	+	40.5712i	−0.263968	+	2.08952i
$378$	5.05034	−	4.17800i	0.259761	−	0.214893i
$379$	6.49703	+	1.66815i	0.333730	+	0.0856873i	0.411837	−	0.911258i	$-0.364887\pi$
$379$	6.49703	+	1.66815i	0.333730	+	0.0856873i	−0.0781067	+	0.996945i	$0.524887\pi$
$380$	4.21431	−	1.41567i	0.216189	−	0.0726221i
$381$	−8.12948	−	12.8100i	−0.416486	−	0.656277i
$382$	−11.5245	+	3.74455i	−0.589647	+	0.191588i
$383$	−3.86408	+	9.75956i	−0.197445	+	0.498690i	−0.994441	−	0.105295i	$-0.966421\pi$
$383$	−3.86408	+	9.75956i	−0.197445	+	0.498690i	0.796996	+	0.603985i	$0.206421\pi$
$384$	0.478088	−	2.50623i	0.0243973	−	0.127895i
$385$	−8.61321	−	1.00143i	−0.438970	−	0.0510377i
$386$	7.44213	+	0.940159i	0.378794	+	0.0478529i
$387$	−4.62028	+	2.17414i	−0.234862	+	0.110518i
$388$	10.7263	+	2.04614i	0.544544	+	0.103877i
$389$	1.87080	+	9.80709i	0.0948535	+	0.497239i	0.997730	+	0.0673397i	$0.0214511\pi$
$389$	1.87080	+	9.80709i	0.0948535	+	0.497239i	−0.902877	+	0.429900i	$0.858549\pi$
$390$	−2.07719	−	28.5028i	−0.105183	−	1.44329i
$391$	−32.4148	−	17.8202i	−1.63929	−	0.901206i
$392$	4.57578	+	17.8215i	0.231112	+	0.900122i
$393$	−10.8503	−	3.52547i	−0.547324	−	0.177836i
$394$	−2.33794	+	2.82609i	−0.117784	+	0.142376i
$395$	4.17339	+	10.2428i	0.209986	+	0.515373i
$396$	−1.44704	+	2.28018i	−0.0727167	+	0.114583i
$397$	3.98185	−	15.5083i	0.199843	−	0.778338i	−0.787040	−	0.616902i	$-0.788388\pi$
$397$	3.98185	−	15.5083i	0.199843	−	0.778338i	0.986883	−	0.161436i	$-0.0516125\pi$
$398$	0.0685383	−	0.0729858i	0.00343551	−	0.00365845i
$399$	7.90014	+	24.3141i	0.395502	+	1.21723i
$400$	2.21820	+	4.48103i	0.110910	+	0.224051i
$401$	−5.72451	+	17.6182i	−0.285868	+	0.879813i	0.700269	+	0.713880i	$0.253064\pi$
$401$	−5.72451	+	17.6182i	−0.285868	+	0.879813i	−0.986137	+	0.165933i	$0.946936\pi$
$402$	7.19263	+	13.0833i	0.358736	+	0.652538i
$403$	−22.0438	+	1.38688i	−1.09808	+	0.0690852i
$404$	−0.570470	−	9.06736i	−0.0283820	−	0.451118i
$405$	−12.5252	−	10.1542i	−0.622383	−	0.504569i
$406$	39.8507	−	10.2319i	1.97776	−	0.507801i
$407$	−0.808959	+	1.11344i	−0.0400986	+	0.0551910i
$408$	−9.69283	+	6.15126i	−0.479867	+	0.304533i
$409$	29.0674	−	3.67206i	1.43729	−	0.181572i	0.632236	−	0.774776i	$-0.282137\pi$
$409$	29.0674	−	3.67206i	1.43729	−	0.181572i	0.805052	+	0.593204i	$0.202137\pi$
$410$	−3.26778	−	9.72788i	−0.161384	−	0.480426i
$411$	13.3690	−	28.4105i	0.659442	−	1.40139i
$412$	0.384237	−	0.698925i	0.0189300	−	0.0344335i
$413$	−34.7330	−	36.9869i	−1.70910	−	1.82001i
$414$	−25.2848	+	13.9005i	−1.24268	+	0.683170i
$415$	4.93074	+	7.60191i	0.242040	+	0.373163i
$416$	3.65157	−	3.42905i	0.179033	−	0.168123i
$417$	−7.08406	−	5.86045i	−0.346908	−	0.286987i
$418$	−0.899206	−	1.23765i	−0.0439816	−	0.0605355i
$419$	−23.4185	−	9.27204i	−1.14407	−	0.452969i	−0.281826	−	0.959465i	$-0.590940\pi$
$419$	−23.4185	−	9.27204i	−1.14407	−	0.452969i	−0.862242	+	0.506497i	$0.830940\pi$
$420$	−25.8936	+	12.4997i	−1.26348	+	0.609924i
$421$	−2.14012	−	2.58696i	−0.104303	−	0.126081i	0.715778	−	0.698327i	$-0.246072\pi$
$421$	−2.14012	−	2.58696i	−0.104303	−	0.126081i	−0.820082	+	0.572247i	$0.806072\pi$
$422$	9.17795	+	23.1809i	0.446776	+	1.12843i
$423$	2.98252	−	0.568945i	0.145015	−	0.0276631i
$424$	−2.77740	+	2.01790i	−0.134882	+	0.0979978i
$425$	7.86531	−	21.0775i	0.381524	−	1.02241i
$426$	16.5128	+	11.9973i	0.800049	+	0.581270i
$427$	−36.1325	−	17.0027i	−1.74857	−	0.822817i
$428$	−8.59955	−	5.45744i	−0.415675	−	0.263795i
$429$	−9.14352	+	3.62018i	−0.441453	+	0.174784i
$430$	3.18940	−	0.641251i	0.153806	−	0.0309239i
$431$	0.749419	−	11.9117i	0.0360983	−	0.573765i	−0.937857	−	0.347023i	$-0.887193\pi$
$431$	0.749419	−	11.9117i	0.0360983	−	0.573765i	0.973955	−	0.226742i	$-0.0728075\pi$
$432$			1.30055i			0.0625728i
$433$	22.2517	+	1.39996i	1.06935	+	0.0672776i	0.587693	−	0.809084i	$-0.300036\pi$
$433$	22.2517	+	1.39996i	1.06935	+	0.0672776i	0.481653	+	0.876362i	$0.340036\pi$
$434$	9.46173	+	20.1072i	0.454178	+	0.965176i
$435$	20.2476	+	41.9436i	0.970797	+	2.01104i
$436$	5.07586	+	4.76655i	0.243089	+	0.228276i
$437$	−2.04858	−	16.2162i	−0.0979970	−	0.775726i
$438$	2.47298	+	19.5757i	0.118164	+	0.935362i
$439$	−25.5523	−	23.9952i	−1.21954	−	1.14523i	−0.984896	−	0.173147i	$-0.944606\pi$
$439$	−25.5523	−	23.9952i	−1.21954	−	1.14523i	−0.234648	−	0.972080i	$-0.575394\pi$
$440$	1.24249	−	1.19018i	0.0592333	−	0.0567395i
$441$	−27.4958	−	58.4316i	−1.30932	−	2.78246i
$442$	−22.4942	−	1.41521i	−1.06994	−	0.0673149i
$443$		−	8.78257i		−	0.417273i	−0.977993	−	0.208636i	$-0.933098\pi$
$443$		−	8.78257i		−	0.417273i	0.977993	−	0.208636i	$-0.0669025\pi$
$444$	−0.286550	+	4.55459i	−0.0135991	+	0.216151i
$445$	20.7927	−	22.5866i	0.985666	−	1.07071i
$446$	14.7091	−	5.82373i	0.696494	−	0.275762i
$447$	−4.08381	−	2.59167i	−0.193158	−	0.122582i
$448$	−4.56015	−	2.14584i	−0.215447	−	0.101381i
$449$	−10.9406	−	7.94879i	−0.516318	−	0.375127i	0.298897	−	0.954285i	$-0.403381\pi$
$449$	−10.9406	−	7.94879i	−0.516318	−	0.375127i	−0.815215	+	0.579159i	$0.803381\pi$
$450$	−10.5944	−	13.9898i	−0.499424	−	0.659487i
$451$	−2.85687	+	2.07564i	−0.134525	+	0.0977379i
$452$	−3.69198	+	0.704283i	−0.173656	+	0.0331267i
$453$	−11.9716	−	30.2369i	−0.562476	−	1.42065i
$454$	−1.28549	−	1.55389i	−0.0603311	−	0.0729277i
$455$	−55.5529	−	10.0274i	−2.60436	−	0.470092i
$456$	−4.71648	−	1.86739i	−0.220869	−	0.0874484i
$457$	18.1564	+	24.9902i	0.849322	+	1.16899i	0.984012	+	0.178104i	$0.0569964\pi$
$457$	18.1564	+	24.9902i	0.849322	+	1.16899i	−0.134689	+	0.990888i	$0.543004\pi$
$458$	−12.6687	−	10.4805i	−0.591971	−	0.489721i
$459$	4.26574	−	4.00579i	0.199108	−	0.186974i
$460$	17.7592	−	4.74798i	0.828026	−	0.221376i
$461$	−17.5163	+	9.62965i	−0.815814	+	0.448498i	−0.834286	−	0.551332i	$-0.814120\pi$
$461$	−17.5163	+	9.62965i	−0.815814	+	0.448498i	0.0184719	+	0.999829i	$0.494120\pi$
$462$	6.77300	+	7.21251i	0.315108	+	0.335556i
$463$	−7.56734	+	13.7649i	−0.351684	+	0.639711i	−0.991689	−	0.128660i	$-0.958932\pi$
$463$	−7.56734	+	13.7649i	−0.351684	+	0.639711i	0.640005	+	0.768371i	$0.278932\pi$
$464$	−3.47592	+	7.38671i	−0.161366	+	0.342920i
$465$	−20.2039	+	14.9873i	−0.936934	+	0.695021i
$466$	−0.405204	+	0.0511892i	−0.0187707	+	0.00237129i
$467$	−15.4492	+	9.80434i	−0.714902	+	0.453691i	−0.842891	−	0.538085i	$-0.819148\pi$
$467$	−15.4492	+	9.80434i	−0.714902	+	0.453691i	0.127989	+	0.991776i	$0.459148\pi$
$468$	−10.3339	+	14.2234i	−0.477684	+	0.657476i
$469$	28.5648	−	7.33419i	1.31900	−	0.338662i
$470$	−1.93173	−	0.102314i	−0.0891041	−	0.00471939i
$471$	−0.969694	−	15.4128i	−0.0446811	−	0.710186i
$472$	10.0477	−	0.632151i	0.462485	−	0.0290971i
$473$	−0.539307	−	0.980996i	−0.0247974	−	0.0451063i
$474$	3.89987	−	12.0026i	0.179127	−	0.551297i
$475$	9.57772	−	2.66268i	0.439456	−	0.122172i
$476$	7.00734	+	21.5664i	0.321181	+	0.988494i
$477$	8.24818	−	8.78342i	0.377658	−	0.402165i
$478$	0.0517616	−	0.201598i	0.00236752	−	0.00922089i
$479$	10.4284	−	16.4325i	0.476484	−	0.750819i	−0.518036	−	0.855359i	$-0.673337\pi$
$479$	10.4284	−	16.4325i	0.476484	−	0.750819i	0.994521	+	0.104539i	$0.0333369\pi$
$480$	1.36395	−	5.53971i	0.0622553	−	0.252852i
$481$	−5.71116	+	6.90360i	−0.260406	+	0.314777i
$482$	25.8113	+	8.38659i	1.17567	+	0.381999i
$483$	26.2895	+	102.391i	1.19621	+	4.65894i
$484$	9.12055	+	5.01406i	0.414570	+	0.227912i
$485$	23.7091	+	5.83748i	1.07657	+	0.265066i
$486$	4.17857	+	21.9048i	0.189544	+	0.993624i
$487$	−14.6296	−	2.79075i	−0.662931	−	0.126461i	−0.155075	−	0.987903i	$-0.549562\pi$
$487$	−14.6296	−	2.79075i	−0.662931	−	0.126461i	−0.507856	+	0.861442i	$0.669562\pi$
$488$	7.16944	−	3.37368i	0.324545	−	0.152719i
$489$	−8.15928	−	1.03076i	−0.368975	−	0.0466124i
$490$	8.10974	+	40.3355i	0.366361	+	1.82217i
$491$	−5.30311	+	27.7999i	−0.239326	+	1.25459i	0.636240	+	0.771491i	$0.280489\pi$
$491$	−5.30311	+	27.7999i	−0.239326	+	1.25459i	−0.875566	+	0.483099i	$0.839511\pi$
$492$	−4.31049	+	10.8870i	−0.194332	+	0.490826i
$493$	34.9341	−	11.3508i	1.57335	−	0.511214i
$494$	−5.33645	−	8.40891i	−0.240098	−	0.378335i
$495$	−3.50083	+	4.92035i	−0.157351	+	0.221153i
$496$	−4.27081	−	1.09656i	−0.191765	−	0.0492368i
$497$	31.0653	−	25.6994i	1.39347	−	1.15278i
$498$	1.29580	−	10.2573i	0.0580662	−	0.459641i
$499$	−14.1252			−0.632331			−0.316166	−	0.948704i	$-0.602395\pi$
$499$	−14.1252			−0.632331			−0.316166	+	0.948704i	$0.602395\pi$
$500$	4.42314	+	10.2682i	0.197809	+	0.459208i
$501$	12.1107			0.541067
$502$	−2.16615	+	17.1469i	−0.0966801	+	0.765302i
$503$	17.2726	−	14.2892i	0.770148	−	0.637122i	−0.167038	−	0.985950i	$-0.553420\pi$
$503$	17.2726	−	14.2892i	0.770148	−	0.637122i	0.937187	+	0.348828i	$0.113420\pi$
$504$	17.1326	+	4.39892i	0.763149	+	0.195943i
$505$	−0.201451	−	20.3143i	−0.00896445	−	0.903976i
$506$	−3.38951	−	5.34101i	−0.150682	−	0.237437i
$507$	−29.3426	+	9.53397i	−1.30315	+	0.423419i
$508$	2.18903	−	5.52886i	0.0971225	−	0.245303i
$509$	4.74854	−	24.8927i	0.210475	−	1.10335i	−0.707500	−	0.706714i	$-0.750177\pi$
$509$	4.74854	−	24.8927i	0.210475	−	1.10335i	0.917975	−	0.396638i	$-0.129823\pi$
$510$	−22.3710	+	12.5890i	−0.990604	+	0.557452i
$511$	38.6677	+	4.88486i	1.71056	+	0.216094i
$512$	0.904827	−	0.425779i	0.0399881	−	0.0188170i
$513$	2.53994	+	0.484520i	0.112141	+	0.0213921i
$514$	0.0355350	+	0.186281i	0.00156738	+	0.00821651i
$515$	0.940638	−	1.51521i	0.0414494	−	0.0667683i
$516$	−3.25287	−	1.78828i	−0.143200	−	0.0787246i
$517$	0.165543	+	0.644747i	0.00728057	+	0.0283559i
$518$	8.57324	+	2.78561i	0.376686	+	0.122393i
$519$	29.8129	−	36.0376i	1.30864	−	1.58187i
$520$	8.55927	−	7.22499i	0.375349	−	0.316837i
$521$	−9.57829	+	15.0930i	−0.419633	+	0.661235i	−0.986721	−	0.162421i	$-0.948070\pi$
$521$	−9.57829	+	15.0930i	−0.419633	+	0.661235i	0.567089	+	0.823657i	$0.308070\pi$
$522$	7.12555	−	27.7522i	0.311877	−	1.21468i
$523$	−3.92390	+	4.17853i	−0.171580	+	0.182714i	−0.809011	−	0.587793i	$-0.799997\pi$
$523$	−3.92390	+	4.17853i	−0.171580	+	0.182714i	0.637431	+	0.770507i	$0.279997\pi$
$524$	−1.38177	−	4.25264i	−0.0603628	−	0.185778i
$525$	−59.2971	+	24.8487i	−2.58794	+	1.08449i
$526$	−0.223918	+	0.689150i	−0.00976331	+	0.0300484i
$527$	9.55775	+	17.3855i	0.416342	+	0.757324i
$528$	−1.95933	+	0.123270i	−0.0852687	+	0.00536465i
$529$	−2.79960	−	44.4983i	−0.121722	−	1.93471i
$530$	−6.44041	+	4.17737i	−0.279754	+	0.181453i
$531$	−34.2246	+	8.78737i	−1.48522	+	0.381340i
$532$	−5.88965	+	8.10641i	−0.255349	+	0.351457i
$533$	−19.4103	+	12.3181i	−0.840752	+	0.533557i
$534$	−34.7534	+	4.39037i	−1.50393	+	0.189990i
$535$	−18.5568	−	13.2032i	−0.802282	−	0.570823i
$536$	−2.49153	+	5.29476i	−0.107618	+	0.228699i
$537$	−1.02293	+	1.86071i	−0.0441429	+	0.0802956i
$538$	1.19094	+	1.26822i	0.0513451	+	0.0546769i
$539$	12.4064	−	6.82048i	0.534382	−	0.293779i
$540$	−0.153813	+	2.90405i	−0.00661905	+	0.124970i
$541$	−27.8925	+	26.1928i	−1.19919	+	1.12612i	−0.210275	+	0.977642i	$0.567436\pi$
$541$	−27.8925	+	26.1928i	−1.19919	+	1.12612i	−0.988916	+	0.148473i	$0.952564\pi$
$542$	−21.5390	−	17.8186i	−0.925178	−	0.765374i
$543$	−21.6618	−	29.8150i	−0.929598	−	1.27948i
$544$	−4.18347	−	1.65635i	−0.179365	−	0.0710155i
$545$	10.7703	+	11.2437i	0.461351	+	0.481628i
$546$	41.0576	+	49.6301i	1.75710	+	2.12397i
$547$	4.02401	+	10.1635i	0.172054	+	0.434560i	0.990059	−	0.140652i	$-0.0449198\pi$
$547$	4.02401	+	10.1635i	0.172054	+	0.434560i	−0.818005	+	0.575211i	$0.804920\pi$
$548$	12.0884	−	2.30599i	0.516392	−	0.0985071i
$549$	−22.4984	+	16.3460i	−0.960208	+	0.697632i
$550$	2.91516	−	2.51065i	0.124303	−	0.107054i
$551$	13.1311	+	9.54031i	0.559404	+	0.406431i
$552$	−18.9791	−	8.93091i	−0.807806	−	0.380125i
$553$	−21.0480	−	13.3575i	−0.895052	−	0.568017i
$554$	−21.3813	+	8.46546i	−0.908404	+	0.359663i
$555$	−1.17851	+	10.1362i	−0.0500249	+	0.430259i
$556$	0.226264	−	3.59636i	0.00959572	−	0.152520i
$557$		−	23.8420i		−	1.01022i	−0.863056	−	0.505108i	$-0.831453\pi$
$557$		−	23.8420i		−	1.01022i	0.863056	−	0.505108i	$-0.168547\pi$
$558$	15.4451	+	0.971721i	0.653841	+	0.0411362i
$559$	−3.10301	−	6.59424i	−0.131243	−	0.278907i
$560$	−9.92874	−	5.33085i	−0.419566	−	0.225269i
$561$	6.43919	+	6.04680i	0.271863	+	0.255296i
$562$	−3.04678	−	24.1178i	−0.128521	−	1.01735i
$563$	−0.610506	−	4.83265i	−0.0257298	−	0.203672i	0.974009	−	0.226507i	$-0.0727307\pi$
$563$	−0.610506	−	4.83265i	−0.0257298	−	0.203672i	−0.999739	+	0.0228352i	$0.992731\pi$
$564$	1.60902	+	1.51097i	0.0677518	+	0.0636232i
$565$	−8.32726	+	1.13598i	−0.350330	+	0.0477910i
$566$	−6.02278	−	12.7991i	−0.253156	−	0.537985i
$567$	36.2701	+	2.28192i	1.52320	+	0.0958316i
$568$			7.99985i			0.335666i
$569$	−1.69945	+	27.0120i	−0.0712446	+	1.13240i	0.786250	+	0.617908i	$0.212020\pi$
$569$	−1.69945	+	27.0120i	−0.0712446	+	1.13240i	−0.857495	+	0.514492i	$0.827980\pi$
$570$	−10.3108	−	4.72757i	−0.431870	−	0.198016i
$571$	−25.0946	+	9.93566i	−1.05018	+	0.415795i	−0.828888	−	0.559414i	$-0.811026\pi$
$571$	−25.0946	+	9.93566i	−1.05018	+	0.415795i	−0.221289	+	0.975208i	$0.571026\pi$
$572$	−3.25435	−	2.06527i	−0.136071	−	0.0863534i
$573$	27.9746	+	13.1639i	1.16866	+	0.549928i
$574$	18.7120	+	13.5951i	0.781024	+	0.567447i
$575$	40.2167	−	8.50162i	1.67715	−	0.354542i
$576$	−2.83944	+	2.06297i	−0.118310	+	0.0859571i
$577$	3.10628	−	0.592555i	0.129316	−	0.0246684i	−0.122317	−	0.992491i	$-0.539032\pi$
$577$	3.10628	−	0.592555i	0.129316	−	0.0246684i	0.251633	+	0.967823i	$0.419032\pi$
$578$	1.19453	+	3.01704i	0.0496859	+	0.125492i
$579$	−12.1996	−	14.7468i	−0.506998	−	0.612855i
$580$	−8.63513	+	16.0830i	−0.358554	+	0.667810i
$581$	−18.9881	−	7.51792i	−0.787759	−	0.311896i
$582$	−16.3761	−	22.5398i	−0.678811	−	0.934303i
$583$	2.03537	+	1.68380i	0.0842964	+	0.0697360i
$584$	−5.63744	+	5.29391i	−0.233279	+	0.219063i
$585$	−24.7571	+	30.5377i	−1.02358	+	1.26258i
$586$	7.58619	−	4.17054i	0.313382	−	0.172283i
$587$	14.5357	+	15.4790i	0.599954	+	0.638886i	0.955226	−	0.295877i	$-0.0956117\pi$
$587$	14.5357	+	15.4790i	0.599954	+	0.638886i	−0.355272	+	0.934763i	$0.615612\pi$
$588$	22.6159	−	41.1382i	0.932665	−	1.69651i
$589$	−3.73263	+	7.93225i	−0.153800	+	0.326843i
$590$	22.5108	−	0.223232i	0.926753	−	0.00919033i
$591$	9.28430	−	1.17288i	0.381905	−	0.0482458i
$592$	−1.51021	+	0.958407i	−0.0620691	+	0.0393903i
$593$	−20.5672	+	28.3084i	−0.844595	+	1.16249i	0.140433	+	0.990090i	$0.455151\pi$
$593$	−20.5672	+	28.3084i	−0.844595	+	1.16249i	−0.985028	+	0.172395i	$0.944849\pi$
$594$	0.969275	−	0.248867i	0.0397698	−	0.0102112i
$595$	13.0964	+	48.9851i	0.536898	+	2.00819i
$596$	−0.119033	−	1.89197i	−0.00487578	−	0.0774982i
$597$	−0.254949	+	0.0160400i	−0.0104344	+	0.000656475i
$598$	−19.8392	−	36.0874i	−0.811287	−	1.47572i
$599$	4.22797	−	13.0124i	0.172750	−	0.531671i	−0.826773	−	0.562535i	$-0.809826\pi$
$599$	4.22797	−	13.0124i	0.172750	−	0.531671i	0.999524	+	0.0308646i	$0.00982608\pi$
$600$	3.70077	−	12.2085i	0.151083	−	0.498410i
$601$	0.311592	+	0.958982i	0.0127101	+	0.0391177i	0.957210	−	0.289393i	$-0.0934534\pi$
$601$	0.311592	+	0.958982i	0.0127101	+	0.0391177i	−0.944500	+	0.328510i	$0.893453\pi$
$602$	−5.01932	+	5.34503i	−0.204572	+	0.217847i
$603$	5.10756	−	19.8926i	0.207996	−	0.810091i
$604$	6.82969	−	10.7619i	0.277896	−	0.437894i
$605$	19.7726	+	12.2748i	0.803871	+	0.499040i
$606$	−14.7757	+	17.8608i	−0.600223	+	0.725545i
$607$	−40.9437	−	13.3034i	−1.66185	−	0.539969i	−0.680594	−	0.732661i	$-0.738278\pi$
$607$	−40.9437	−	13.3034i	−1.66185	−	0.539969i	−0.981259	+	0.192692i	$0.938278\pi$
$608$	−0.494443	−	1.92573i	−0.0200523	−	0.0780986i
$609$	−91.9892	−	50.5715i	−3.72759	−	2.04926i
$610$	16.4079	−	6.68531i	0.664337	−	0.270680i
$611$	0.812020	+	4.25676i	0.0328508	+	0.172210i
$612$	15.5121	+	2.95909i	0.627040	+	0.119614i
$613$	1.25444	−	0.590297i	0.0506665	−	0.0238419i	−0.400279	−	0.916393i	$-0.631087\pi$
$613$	1.25444	−	0.590297i	0.0506665	−	0.0238419i	0.450946	+	0.892551i	$0.351087\pi$
$614$	−24.2882	−	3.06831i	−0.980190	−	0.123827i
$615$	−10.9126	+	23.8003i	−0.440040	+	0.959721i
$616$	−0.726645	+	3.80920i	−0.0292773	+	0.153477i
$617$	2.13666	−	5.39659i	0.0860187	−	0.217258i	−0.880400	−	0.474233i	$-0.842726\pi$
$617$	2.13666	−	5.39659i	0.0860187	−	0.217258i	0.966418	+	0.256974i	$0.0827256\pi$
$618$	−1.93536	+	0.628837i	−0.0778517	+	0.0252955i
$619$	23.0918	+	36.3869i	0.928138	+	1.46251i	0.886152	+	0.463394i	$0.153369\pi$
$619$	23.0918	+	36.3869i	0.928138	+	1.46251i	0.0419861	+	0.999118i	$0.486631\pi$
$620$	−9.40676	−	2.95364i	−0.377785	−	0.118621i
$621$	10.3560	+	2.65898i	0.415573	+	0.106701i
$622$	17.7795	−	14.7085i	0.712894	−	0.589757i
$623$	−8.67227	+	68.6481i	−0.347447	+	2.75033i
$624$	−12.7806			−0.511635
$625$	8.66220	+	23.4514i	0.346488	+	0.938054i
$626$	−29.0211			−1.15992
$627$	−0.489202	+	3.87244i	−0.0195369	+	0.154650i
$628$	4.66379	−	3.85822i	0.186105	−	0.153960i
$629$	7.79507	+	2.00143i	0.310810	+	0.0798024i
$630$	37.7359	+	11.8487i	1.50343	+	0.472065i
$631$	−14.0516	−	22.1418i	−0.559386	−	0.881451i	0.440481	−	0.897762i	$-0.354808\pi$
$631$	−14.0516	−	22.1418i	−0.559386	−	0.881451i	−0.999867	+	0.0163111i	$0.994808\pi$
$632$	4.70428	−	1.52851i	0.187126	−	0.0608009i
$633$	23.4168	−	59.1441i	0.930734	−	2.35077i
$634$	−2.40362	+	12.6002i	−0.0954598	+	0.500418i
$635$	5.54185	−	12.0867i	0.219922	−	0.479646i
$636$	8.69009	+	1.09781i	0.344584	+	0.0435311i
$637$	83.3957	−	39.2430i	3.30426	−	1.55486i
$638$	6.17031	+	1.17705i	0.244285	+	0.0465998i
$639$	−5.26118	−	27.5801i	−0.208129	−	1.09105i
$640$	2.07078	−	0.843727i	0.0818547	−	0.0333512i
$641$	39.9046	+	21.9377i	1.57614	+	0.866489i	0.998748	+	0.0500201i	$0.0159286\pi$
$641$	39.9046	+	21.9377i	1.57614	+	0.866489i	0.577389	+	0.816469i	$0.304071\pi$
$642$	6.46256	+	25.1700i	0.255057	+	0.993381i
$643$	−8.75318	−	2.84408i	−0.345192	−	0.112160i	0.131290	−	0.991344i	$-0.458088\pi$
$643$	−8.75318	−	2.84408i	−0.345192	−	0.112160i	−0.476482	+	0.879184i	$0.658088\pi$
$644$	−26.4101	+	31.9244i	−1.04071	+	1.25800i
$645$	−7.05196	−	4.37783i	−0.277671	−	0.172377i
$646$	−4.79336	+	7.55313i	−0.188592	+	0.297174i
$647$	−5.82830	+	22.6997i	−0.229134	+	0.892418i	0.745114	+	0.666938i	$0.232395\pi$
$647$	−5.82830	+	22.6997i	−0.229134	+	0.892418i	−0.974248	+	0.225481i	$0.927605\pi$
$648$	−4.93624	+	5.25656i	−0.193914	+	0.206497i
$649$	−2.39382	−	7.36742i	−0.0939657	−	0.289197i
$650$	19.9668	−	15.1207i	0.783162	−	0.593082i
$651$	17.5206	−	53.9230i	0.686688	−	2.11341i
$652$	−1.55286	−	2.82465i	−0.0608148	−	0.110622i
$653$	37.1936	−	2.34002i	1.45550	−	0.0915722i	0.684781	−	0.728749i	$-0.259898\pi$
$653$	37.1936	−	2.34002i	1.45550	−	0.0915722i	0.770718	+	0.637177i	$0.219898\pi$
$654$	−1.11552	−	17.7306i	−0.0436202	−	0.693323i
$655$	−2.58245	−	9.65931i	−0.100905	−	0.377420i
$656$	−4.44515	+	1.14132i	−0.173554	+	0.0445611i
$657$	15.9539	−	21.9586i	0.622420	−	0.856688i
$658$	3.68124	−	2.33619i	0.143510	−	0.0910740i
$659$	−11.2351	+	1.41932i	−0.437656	+	0.0552889i	−0.341075	−	0.940036i	$-0.610791\pi$
$659$	−11.2351	+	1.41932i	−0.437656	+	0.0552889i	−0.0965818	+	0.995325i	$0.530791\pi$
$660$	−4.38963	+	0.0435306i	−0.170866	+	0.00169443i
$661$	−7.03966	+	14.9600i	−0.273811	+	0.581878i	−0.993682	−	0.112229i	$-0.964201\pi$
$661$	−7.03966	+	14.9600i	−0.273811	+	0.581878i	0.719871	+	0.694108i	$0.244201\pi$
$662$	−4.38147	+	7.96987i	−0.170291	+	0.309758i
$663$	39.3653	+	41.9198i	1.52882	+	1.62803i
$664$	3.55096	−	1.95216i	0.137804	−	0.0757584i
$665$	−14.1100	+	17.4046i	−0.547161	+	0.674920i
$666$	4.57624	−	4.29737i	0.177326	−	0.166520i
$667$	51.7125	+	42.7803i	2.00231	+	1.65646i
$668$	2.79002	+	3.84013i	0.107949	+	0.148579i
$669$	−37.5290	−	14.8588i	−1.45095	−	0.574473i
$670$	−6.18962	+	11.5282i	−0.239126	+	0.445374i
$671$	−3.88625	−	4.69767i	−0.150027	−	0.181351i
$672$	4.73358	+	11.9557i	0.182602	+	0.461199i
$673$	−21.1802	+	4.04034i	−0.816436	+	0.155744i	−0.578652	−	0.815574i	$-0.696421\pi$
$673$	−21.1802	+	4.04034i	−0.816436	+	0.155744i	−0.237784	+	0.971318i	$0.576421\pi$
$674$	−20.7199	+	15.0539i	−0.798102	+	0.579855i
$675$	−0.686909	+	6.46637i	−0.0264391	+	0.248891i
$676$	−9.78290	−	7.10769i	−0.376265	−	0.273373i
$677$	−36.9824	−	17.4026i	−1.42135	−	0.668835i	−0.447135	−	0.894467i	$-0.647556\pi$
$677$	−36.9824	−	17.4026i	−1.42135	−	0.668835i	−0.974213	+	0.225631i	$0.927556\pi$
$678$	8.09681	+	5.13839i	0.310956	+	0.197339i
$679$	−51.1684	+	20.2590i	−1.96366	+	0.777469i
$680$	−9.14553	−	4.19330i	−0.350715	−	0.160806i
$681$	−0.323085	+	5.13528i	−0.0123806	+	0.196785i
$682$			3.39278i			0.129916i
$683$	7.11432	+	0.447595i	0.272222	+	0.0171267i	0.198315	−	0.980138i	$-0.436453\pi$
$683$	7.11432	+	0.447595i	0.272222	+	0.0171267i	0.0739071	+	0.997265i	$0.476453\pi$
$684$	2.97110	+	6.31390i	0.113603	+	0.241418i
$685$	27.2654	−	3.71947i	1.04176	−	0.142114i
$686$	−41.8803	−	39.3282i	−1.59900	−	1.50156i
$687$	5.25777	+	41.6195i	0.200596	+	1.58788i
$688$	−0.182345	−	1.44341i	−0.00695185	−	0.0550296i
$689$	12.5360	+	11.7721i	0.477584	+	0.448482i
$690$	−41.3230	−	22.1868i	−1.57314	−	0.844636i
$691$	−2.44156	−	5.18859i	−0.0928815	−	0.197383i	0.852988	−	0.521931i	$-0.174788\pi$
$691$	−2.44156	−	5.18859i	−0.0928815	−	0.197383i	−0.945869	+	0.324547i	$0.894788\pi$
$692$	18.2951	+	1.15103i	0.695477	+	0.0437557i
$693$		−	13.6104i		−	0.517016i
$694$	2.18985	−	34.8067i	0.0831256	−	1.32124i
$695$	0.930565	−	8.00368i	0.0352983	−	0.303597i
$696$	19.3663	−	7.66765i	0.734077	−	0.290641i
$697$	17.4349	+	11.0645i	0.660393	+	0.419098i
$698$	21.1034	+	9.93049i	0.798774	+	0.375874i
$699$	0.843046	+	0.612509i	0.0318869	+	0.0231672i
$700$	−21.5398	−	13.0777i	−0.814128	−	0.494291i
$701$	−18.6511	+	13.5508i	−0.704442	+	0.511807i	−0.881376	−	0.472416i	$-0.843382\pi$
$701$	−18.6511	+	13.5508i	−0.704442	+	0.511807i	0.176934	+	0.984223i	$0.443382\pi$
$702$	6.39936	−	1.22074i	0.241528	−	0.0460740i
$703$	1.30912	+	3.30645i	0.0493742	+	0.124705i
$704$	−0.490469	−	0.592875i	−0.0184852	−	0.0223448i
$705$	3.41413	+	3.56419i	0.128584	+	0.134235i
$706$	19.5962	+	7.75869i	0.737513	+	0.292002i
$707$	26.9135	+	37.0433i	1.01219	+	1.39316i
$708$	−19.7919	−	16.3733i	−0.743827	−	0.615347i
$709$	−2.90593	+	2.72885i	−0.109135	+	0.102484i	−0.737194	−	0.675681i	$-0.763850\pi$
$709$	−2.90593	+	2.72885i	−0.109135	+	0.102484i	0.628059	+	0.778165i	$0.283850\pi$
$710$	−0.946122	+	17.8632i	−0.0355073	+	0.670393i
$711$	−15.2131	+	8.36346i	−0.570535	+	0.313654i
$712$	−9.39846	−	10.0083i	−0.352222	−	0.375079i
$713$	−17.4633	+	31.7657i	−0.654007	+	1.18963i
$714$	24.6341	−	52.3502i	0.921909	−	1.95916i
$715$	−7.02251	−	4.99651i	−0.262627	−	0.186859i
$716$	−0.825663	+	0.104306i	−0.0308565	+	0.00389808i
$717$	−0.448376	+	0.284548i	−0.0167449	+	0.0106267i
$718$	17.5625	−	24.1727i	0.655426	−	0.902117i
$719$	−46.3858	+	11.9098i	−1.72990	+	0.444162i	−0.976871	−	0.213829i	$-0.931407\pi$
$719$	−46.3858	+	11.9098i	−1.72990	+	0.444162i	−0.753026	+	0.657991i	$0.771407\pi$
$720$	−6.58427	+	4.27067i	−0.245381	+	0.159159i
$721$	0.252395	+	4.01171i	0.00939970	+	0.149404i
$722$	15.0174	−	0.944815i	0.558890	−	0.0351624i
$723$	−33.3588	−	60.6794i	−1.24063	−	2.25669i
$724$	4.46352	−	13.7373i	0.165885	−	0.510543i
$725$	−21.1838	+	34.8911i	−0.786747	+	1.29582i
$726$	−8.20595	−	25.2553i	−0.304551	−	0.937313i
$727$	8.29029	−	8.82826i	0.307470	−	0.327422i	−0.556613	−	0.830772i	$-0.687899\pi$
$727$	8.29029	−	8.82826i	0.307470	−	0.327422i	0.864083	+	0.503350i	$0.167899\pi$
$728$	−6.27829	+	24.4523i	−0.232689	+	0.906264i
$729$	18.8950	−	29.7738i	0.699816	−	1.10273i
$730$	−13.2141	+	11.1542i	−0.489078	+	0.412837i
$731$	−4.17268	+	5.04390i	−0.154332	+	0.186555i
$732$	−19.2268	−	6.24717i	−0.710644	−	0.230902i
$733$	−2.43970	−	9.50201i	−0.0901124	−	0.350965i	0.907498	−	0.420057i	$-0.137990\pi$
$733$	−2.43970	−	9.50201i	−0.0901124	−	0.350965i	−0.997610	+	0.0690919i	$0.977990\pi$
$734$	23.7490	+	13.0561i	0.876593	+	0.481911i
$735$	55.3652	−	89.1843i	2.04218	−	3.28961i
$736$	−1.54048	−	8.07547i	−0.0567828	−	0.297666i
$737$	4.42285	+	0.843704i	0.162918	+	0.0310782i
$738$	14.5744	−	6.85818i	0.536490	−	0.252453i
$739$	41.3234	+	5.22036i	1.52011	+	0.192034i	0.840609	−	0.541643i	$-0.182198\pi$
$739$	41.3234	+	5.22036i	1.52011	+	0.192034i	0.679498	+	0.733677i	$0.262198\pi$
$740$	−3.48555	+	1.96145i	−0.128131	+	0.0721045i
$741$	−4.76142	+	24.9602i	−0.174915	+	0.916937i
$742$	6.36925	−	16.0869i	0.233823	−	0.590568i
$743$	34.6461	−	11.2572i	1.27104	−	0.412987i	0.405626	−	0.914039i	$-0.367054\pi$
$743$	34.6461	−	11.2572i	1.27104	−	0.412987i	0.865417	+	0.501052i	$0.167054\pi$
$744$	6.02808	+	9.49873i	0.221000	+	0.348241i
$745$	−0.0420342	−	4.23874i	−0.00154002	−	0.155295i
$746$	−11.6428	−	2.98936i	−0.426273	−	0.109448i
$747$	−10.9583	+	9.06552i	−0.400944	+	0.331690i
$748$	−0.433917	+	3.43481i	−0.0158656	+	0.125589i
$749$	51.3308			1.87559
$750$	9.70747	−	26.8232i	0.354467	−	0.979443i
$751$	−10.4947			−0.382958			−0.191479	−	0.981497i	$-0.561328\pi$
$751$	−10.4947			−0.382958			−0.191479	+	0.981497i	$0.561328\pi$
$752$	−0.108427	+	0.858285i	−0.00395391	+	0.0312984i
$753$	33.9770	−	28.1082i	1.23819	−	1.02432i
$754$	39.6089	+	10.1698i	1.44247	+	0.370364i
$755$	16.5231	−	23.2229i	0.601336	−	0.845167i
$756$	−3.51208	−	5.53416i	−0.127733	−	0.201275i
$757$	46.4003	−	15.0764i	1.68645	−	0.547960i	0.700303	−	0.713846i	$-0.253048\pi$
$757$	46.4003	−	15.0764i	1.68645	−	0.547960i	0.986145	+	0.165886i	$0.0530484\pi$
$758$	2.46929	−	6.23672i	0.0896887	−	0.226528i
$759$	−3.02427	+	15.8538i	−0.109774	+	0.575455i
$760$	−0.876309	−	4.35851i	−0.0317871	−	0.158100i
$761$	47.6077	+	6.01425i	1.72578	+	0.218016i	0.924740	−	0.380599i	$-0.124282\pi$
$761$	47.6077	+	6.01425i	1.72578	+	0.218016i	0.801037	+	0.598615i	$0.204282\pi$
$762$	−13.7279	+	6.45986i	−0.497309	+	0.234016i
$763$	−34.4709	−	6.57567i	−1.24793	−	0.238055i
$764$	2.27061	+	11.9030i	0.0821480	+	0.430635i
$765$	34.2876	+	8.44205i	1.23967	+	0.305223i
$766$	9.19830	+	5.05681i	0.332348	+	0.182710i
$767$	−12.5417	−	48.8465i	−0.452853	−	1.76375i
$768$	−2.42654	−	0.788432i	−0.0875603	−	0.0284501i
$769$	−9.73037	+	11.7620i	−0.350886	+	0.424148i	−0.916196	−	0.400730i	$-0.868757\pi$
$769$	−9.73037	+	11.7620i	−0.350886	+	0.424148i	0.565310	+	0.824878i	$0.308757\pi$
$770$	−2.07306	+	8.41978i	−0.0747078	+	0.303428i
$771$	0.259261	−	0.408529i	0.00933704	−	0.0147128i
$772$	1.86549	−	7.26561i	0.0671405	−	0.261495i
$773$	34.3847	−	36.6160i	1.23673	−	1.31699i	0.305665	−	0.952139i	$-0.401121\pi$
$773$	34.3847	−	36.6160i	1.23673	−	1.31699i	0.931068	−	0.364847i	$-0.118879\pi$
$774$	1.57792	+	4.85634i	0.0567172	+	0.174558i
$775$	−20.6554	−	7.70781i	−0.741964	−	0.276873i
$776$	3.37437	−	10.3852i	0.121133	−	0.372808i
$777$	−11.0801	−	20.1547i	−0.397498	−	0.723046i
$778$	9.96424	−	0.626897i	0.357235	−	0.0224753i
$779$	0.572930	+	9.10646i	0.0205274	+	0.326273i
$780$	−28.5383	−	1.51153i	−1.02184	−	0.0541215i
$781$	5.96213	−	1.53082i	0.213342	−	0.0547769i
$782$	−21.7423	+	29.9257i	−0.777504	+	1.07014i
$783$	−8.96446	+	5.68902i	−0.320364	+	0.203309i
$784$	18.2545	−	2.30608i	0.651945	−	0.0823599i
$785$	10.8703	−	8.06360i	0.387976	−	0.287802i
$786$	−4.85757	+	10.3229i	−0.173264	+	0.368204i
$787$	−9.22957	+	16.7885i	−0.328999	+	0.598446i	−0.988137	−	0.153575i	$-0.950921\pi$
$787$	−9.22957	+	16.7885i	−0.328999	+	0.598446i	0.659138	+	0.752022i	$0.270921\pi$
$788$	2.51078	+	2.67371i	0.0894428	+	0.0952470i
$789$	1.62011	−	0.890665i	0.0576776	−	0.0317085i
$790$	10.6851	−	2.85671i	0.380160	−	0.101637i
$791$	13.8084	−	12.9669i	0.490970	−	0.461051i
$792$	2.08083	+	1.72142i	0.0739392	+	0.0611678i
$793$	−23.3297	−	32.1105i	−0.828461	−	1.14028i
$794$	−14.8869	−	5.89415i	−0.528317	−	0.209176i
$795$	19.2746	+	3.47910i	0.683599	+	0.123391i
$796$	−0.0638202	−	0.0771454i	−0.00226205	−	0.00273435i
$797$	−7.03693	−	17.7733i	−0.249261	−	0.629561i	0.750239	−	0.661166i	$-0.229938\pi$
$797$	−7.03693	−	17.7733i	−0.249261	−	0.629561i	−0.999500	+	0.0316048i	$0.989938\pi$
$798$	25.1126	−	4.79048i	0.888975	−	0.169581i
$799$	3.14909	−	2.28795i	0.111407	−	0.0809418i
$800$	4.72371	−	1.63909i	0.167008	−	0.0579504i
$801$	38.9839	+	28.3235i	1.37743	+	1.00076i
$802$	16.7618	+	7.88752i	0.591881	+	0.278518i
$803$	5.02420	+	3.18845i	0.177300	+	0.112518i
$804$	13.8817	−	5.49614i	0.489568	−	0.193834i
$805$	−62.7478	+	68.1617i	−2.21157	+	2.40238i
$806$	−1.38688	+	22.0438i	−0.0488506	+	0.776458i
$807$		−	4.43883i		−	0.156254i
$808$	−9.06736	−	0.570470i	−0.318989	−	0.0200691i
$809$	−6.81846	−	14.4900i	−0.239724	−	0.509440i	0.748372	−	0.663280i	$-0.230836\pi$
$809$	−6.81846	−	14.4900i	−0.239724	−	0.509440i	−0.988096	+	0.153840i	$0.950836\pi$
$810$	−11.6440	+	11.1538i	−0.409129	+	0.391904i
$811$	−30.7614	−	28.8869i	−1.08018	−	1.01435i	−0.999845	−	0.0175867i	$-0.994402\pi$
$811$	−30.7614	−	28.8869i	−1.08018	−	1.01435i	−0.0803328	−	0.996768i	$-0.525598\pi$
$812$	−5.15662	−	40.8188i	−0.180962	−	1.43246i
$813$	8.93908	+	70.7601i	0.313507	+	2.48166i
$814$	1.00327	+	0.942131i	0.0351645	+	0.0330217i
$815$	−3.13338	−	6.49092i	−0.109758	−	0.227367i
$816$	4.88792	+	10.3874i	0.171111	+	0.363630i
$817$	−2.88688	−	0.181627i	−0.100999	−	0.00635433i
$818$		−	29.2984i		−	1.02439i
$819$	5.56355	−	88.4301i	0.194406	−	3.09000i
$820$	−10.0607	+	2.02278i	−0.351336	+	0.0706386i
$821$	1.55140	−	0.614241i	0.0541441	−	0.0214372i	−0.340896	−	0.940101i	$-0.610731\pi$
$821$	1.55140	−	0.614241i	0.0541441	−	0.0214372i	0.395041	+	0.918664i	$0.370731\pi$
$822$	−26.5109	−	16.8243i	−0.924673	−	0.586815i
$823$	−18.2280	−	8.57745i	−0.635388	−	0.298991i	0.0809776	−	0.996716i	$-0.474196\pi$
$823$	−18.2280	−	8.57745i	−0.635388	−	0.298991i	−0.716366	+	0.697725i	$0.754196\pi$
$824$	−0.645256	−	0.468806i	−0.0224785	−	0.0163316i
$825$	−9.80692	−	0.421949i	−0.341433	−	0.0146904i
$826$	−41.0485	+	29.8235i	−1.42826	+	1.03769i
$827$	5.98121	−	1.14098i	0.207987	−	0.0396757i	−0.0823347	−	0.996605i	$-0.526238\pi$
$827$	5.98121	−	1.14098i	0.207987	−	0.0396757i	0.290322	+	0.956929i	$0.406238\pi$
$828$	10.6218	+	26.8276i	0.369133	+	0.932325i
$829$	12.0677	+	14.5873i	0.419127	+	0.506638i	0.937245	−	0.348671i	$-0.113367\pi$
$829$	12.0677	+	14.5873i	0.419127	+	0.506638i	−0.518118	+	0.855309i	$0.673367\pi$
$830$	8.15995	−	3.93908i	0.283236	−	0.136728i
$831$	54.5526	+	21.5989i	1.89241	+	0.749258i
$832$	−2.94435	−	4.05255i	−0.102077	−	0.140497i
$833$	−63.7889	−	52.7708i	−2.21016	−	1.82840i
$834$	−6.70210	+	6.29370i	−0.232075	+	0.217933i
$835$	5.77578	+	8.90474i	0.199879	+	0.308161i
$836$	−1.34059	+	0.736997i	−0.0463654	+	0.0254896i
$837$	−3.92558	−	4.18032i	−0.135688	−	0.144493i
$838$	−12.1340	+	22.0717i	−0.419163	+	0.762455i
$839$	10.2981	−	21.8846i	0.355530	−	0.755540i	−0.644428	−	0.764665i	$-0.722905\pi$
$839$	10.2981	−	21.8846i	0.355530	−	0.755540i	0.999958	+	0.00912503i	$0.00290463\pi$
$840$	9.15582	+	27.2561i	0.315906	+	0.940424i
$841$	−37.3487	+	4.71824i	−1.28789	+	0.162698i
$842$	−2.83479	+	1.79901i	−0.0976935	+	0.0619982i
$843$	−36.4565	+	50.1781i	−1.25563	+	1.72823i
$844$	24.1484	−	6.20025i	0.831222	−	0.213421i
$845$	−21.0040	−	17.0280i	−0.722559	−	0.585782i
$846$	−0.190651	−	3.03031i	−0.00655471	−	0.104184i
$847$	−52.3504	+	3.29361i	−1.79878	+	0.113170i
$848$	1.65389	+	3.00841i	0.0567947	+	0.103309i
$849$	−11.1526	+	34.3242i	−0.382757	+	1.17800i
$850$	−19.9255	−	10.4450i	−0.683438	−	0.358260i
$851$	4.54399	+	13.9850i	0.155766	+	0.479398i
$852$	13.9723	−	14.8790i	0.478682	−	0.509745i
$853$	3.10731	−	12.1022i	0.106392	−	0.414370i	−0.892969	−	0.450119i	$-0.851382\pi$
$853$	3.10731	−	12.1022i	0.106392	−	0.414370i	0.999361	+	0.0357487i	$0.0113816\pi$
$854$	−21.3972	+	33.7166i	−0.732197	+	1.15376i
$855$	5.88755	+	14.4499i	0.201350	+	0.494178i
$856$	−6.49222	+	7.84774i	−0.221899	+	0.268230i
$857$	16.4719	+	5.35203i	0.562668	+	0.182822i	0.576521	−	0.817082i	$-0.304410\pi$
$857$	16.4719	+	5.35203i	0.562668	+	0.182822i	−0.0138531	+	0.999904i	$0.504410\pi$
$858$	2.44564	+	9.52515i	0.0834929	+	0.325183i
$859$	46.2586	+	25.4309i	1.57832	+	0.867690i	0.998601	+	0.0528752i	$0.0168386\pi$
$859$	46.2586	+	25.4309i	1.57832	+	0.867690i	0.579721	+	0.814815i	$0.303161\pi$
$860$	−0.236457	−	3.24462i	−0.00806313	−	0.110641i
$861$	−11.0579	−	57.9673i	−0.376851	−	1.97552i
$862$	−11.7238	−	2.23644i	−0.399315	−	0.0761734i
$863$	−7.02435	+	3.30541i	−0.239112	+	0.112517i	−0.541602	−	0.840635i	$-0.682182\pi$
$863$	−7.02435	+	3.30541i	−0.239112	+	0.112517i	0.302490	+	0.953152i	$0.402182\pi$
$864$	1.29030	+	0.163002i	0.0438967	+	0.00554545i
$865$	40.7158	+	4.73390i	1.38438	+	0.160958i
$866$	4.17779	−	21.9007i	0.141967	−	0.744217i
$867$	3.04775	−	7.69773i	0.103507	−	0.261428i
$868$	21.1345	−	6.86702i	0.717352	−	0.233082i
$869$	−2.03936	−	3.21352i	−0.0691805	−	0.109011i
$870$	44.1505	−	14.8310i	1.49684	−	0.502818i
$871$	28.3915	+	7.28970i	0.962010	+	0.247002i
$872$	5.36513	−	4.43843i	0.181686	−	0.150304i
$873$	−4.80342	+	38.0230i	−0.162571	+	1.28688i
$874$	−16.3451			−0.552881
$875$	−46.5504	−	31.7492i	−1.57369	−	1.07332i
$876$	19.7313			0.666657
$877$	−4.49074	+	35.5479i	−0.151642	+	1.20037i	0.714161	+	0.699982i	$0.246808\pi$
$877$	−4.49074	+	35.5479i	−0.151642	+	1.20037i	−0.865803	+	0.500386i	$0.833192\pi$
$878$	−27.0085	+	22.3434i	−0.911494	+	0.754053i
$879$	−21.3937	−	5.49297i	−0.721592	−	0.185273i
$880$	−1.02507	−	1.38186i	−0.0345550	−	0.0465824i
$881$	22.8784	+	36.0506i	0.770793	+	1.21458i	0.971989	+	0.235025i	$0.0755172\pi$
$881$	22.8784	+	36.0506i	0.770793	+	1.21458i	−0.201196	+	0.979551i	$0.564483\pi$
$882$	−61.4169	+	19.9556i	−2.06802	+	0.671939i
$883$	1.69961	−	4.29272i	0.0571964	−	0.144462i	−0.898368	−	0.439243i	$-0.855247\pi$
$883$	1.69961	−	4.29272i	0.0571964	−	0.144462i	0.955565	+	0.294781i	$0.0952468\pi$
$884$	−4.22333	+	22.1395i	−0.142046	+	0.744630i
$885$	−42.2577	−	38.9013i	−1.42048	−	1.30765i
$886$	−8.71332	−	1.10075i	−0.292730	−	0.0369804i
$887$	−24.7468	+	11.6450i	−0.830917	+	0.391000i	−0.793702	−	0.608307i	$-0.791849\pi$
$887$	−24.7468	+	11.6450i	−0.830917	+	0.391000i	−0.0372155	+	0.999307i	$0.511849\pi$
$888$	4.48276	+	0.855132i	0.150432	+	0.0286964i
$889$	5.61560	+	29.4380i	0.188341	+	0.987319i
$890$	−19.8025	−	23.4596i	−0.663782	−	0.786366i
$891$	4.86219	+	2.67301i	0.162889	+	0.0895493i
$892$	−3.93427	−	15.3230i	−0.131729	−	0.513052i
$893$	1.63581	+	0.531508i	0.0547404	+	0.0177862i
$894$	−3.08307	+	3.72679i	−0.103113	+	0.124642i
$895$	−1.85599	+	0.135259i	−0.0620389	+	0.00452120i
$896$	−2.70046	+	4.25524i	−0.0902160	+	0.142158i
$897$	−26.1300	+	101.770i	−0.872456	+	3.39799i
$898$	−9.25733	+	9.85805i	−0.308921	+	0.328968i
$899$	−11.1235	−	34.2346i	−0.370989	−	1.14179i
$900$	−15.2073	+	8.75745i	−0.506911	+	0.291915i
$901$	4.77332	−	14.6908i	0.159022	−	0.489421i
$902$	1.70121	+	3.09449i	0.0566440	+	0.103035i
$903$	18.6709	−	1.17467i	0.621329	−	0.0390907i
$904$	0.236002	+	3.75114i	0.00784930	+	0.124761i
$905$	11.5914	−	30.1466i	0.385312	−	1.00211i
$906$	−31.4989	+	8.08754i	−1.04648	+	0.268691i
$907$	16.1184	−	22.1851i	0.535204	−	0.736645i	−0.452709	−	0.891658i	$-0.649542\pi$
$907$	16.1184	−	22.1851i	0.535204	−	0.736645i	0.987912	+	0.155014i	$0.0495422\pi$
$908$	−1.70275	+	1.08060i	−0.0565079	+	0.0358610i
$909$	31.6355	−	3.99650i	1.04928	−	0.132555i
$910$	−16.9110	+	53.8580i	−0.560593	+	1.78538i
$911$	−18.2905	+	38.8693i	−0.605992	+	1.28780i	0.332698	+	0.943034i	$0.392041\pi$
$911$	−18.2905	+	38.8693i	−0.605992	+	1.28780i	−0.938689	+	0.344764i	$0.887959\pi$
$912$	−2.44379	+	4.44525i	−0.0809221	+	0.147197i
$913$	−2.13440	−	2.27291i	−0.0706384	−	0.0752222i
$914$	27.0687	−	14.8812i	0.895354	−	0.492225i
$915$	−42.1935	−	16.2235i	−1.39487	−	0.536331i
$916$	−11.9857	+	11.2553i	−0.396018	+	0.371885i
$917$	17.3638	+	14.3646i	0.573405	+	0.474362i
$918$	−3.43957	−	4.73416i	−0.113523	−	0.156251i
$919$	−34.2516	−	13.5612i	−1.12986	−	0.447342i	−0.272547	−	0.962143i	$-0.587866\pi$
$919$	−34.2516	−	13.5612i	−1.12986	−	0.447342i	−0.857310	+	0.514801i	$0.827866\pi$
$920$	−2.48473	−	18.2142i	−0.0819191	−	0.600505i
$921$	39.8146	+	48.1276i	1.31194	+	1.58586i
$922$	7.35835	+	18.5851i	0.242334	+	0.612067i
$923$	39.3633	−	7.50894i	1.29566	−	0.247160i
$924$	8.00452	−	5.81562i	0.263329	−	0.191320i
$925$	−8.01499	+	3.96758i	−0.263531	+	0.130453i
$926$	12.7080	+	9.23287i	0.417609	+	0.303411i
$927$	2.53288	+	1.19188i	0.0831906	+	0.0391465i
$928$	6.89282	+	4.37432i	0.226268	+	0.143594i
$929$	−8.18187	+	3.23943i	−0.268439	+	0.106282i	−0.498488	−	0.866897i	$-0.666111\pi$
$929$	−8.18187	+	3.23943i	−0.268439	+	0.106282i	0.230049	+	0.973179i	$0.426111\pi$
$930$	12.3369	+	21.9230i	0.404544	+	0.718884i
$931$	2.29699	−	36.5096i	0.0752809	−	1.19655i
$932$			0.408425i			0.0133784i
$933$	−58.7576	−	3.69671i	−1.92364	−	0.121025i
$934$	7.79073	+	16.5562i	0.254921	+	0.541734i
$935$	−1.37514	+	7.61840i	−0.0449718	+	0.249148i
$936$	12.8160	+	12.0351i	0.418905	+	0.393378i
$937$	−1.32886	−	10.5190i	−0.0434120	−	0.343642i	−0.998829	−	0.0483815i	$-0.984594\pi$
$937$	−1.32886	−	10.5190i	−0.0434120	−	0.343642i	0.955417	−	0.295260i	$-0.0954063\pi$
$938$	−3.69624	−	29.2588i	−0.120687	−	0.955333i
$939$	53.9765	+	50.6873i	1.76146	+	1.65412i
$940$	−0.343617	+	1.90367i	−0.0112076	+	0.0620910i
$941$	−6.71541	−	14.2710i	−0.218916	−	0.465221i	0.764958	−	0.644080i	$-0.222759\pi$
$941$	−6.71541	−	14.2710i	−0.218916	−	0.465221i	−0.983875	+	0.178859i	$0.942759\pi$
$942$	−15.4128	−	0.969694i	−0.502177	−	0.0315943i
$943$			37.7293i			1.22864i
$944$	0.632151	−	10.0477i	0.0205747	−	0.327026i
$945$	−7.18775	−	12.7728i	−0.233818	−	0.415499i
$946$	−1.04085	+	0.412103i	−0.0338411	+	0.0133986i
$947$	13.7491	+	8.72545i	0.446786	+	0.283539i	0.740125	−	0.672469i	$-0.234766\pi$
$947$	13.7491	+	8.72545i	0.446786	+	0.283539i	−0.293339	+	0.956009i	$0.594766\pi$
$948$	−11.4191	−	5.37344i	−0.370877	−	0.174521i
$949$	31.3402	+	22.7700i	1.01734	+	0.739144i
$950$	−1.44128	−	9.83591i	−0.0467611	−	0.319119i
$951$	26.4776	−	19.2371i	0.858594	−	0.623805i
$952$	22.2746	−	4.24910i	0.721923	−	0.137714i
$953$	−10.4294	−	26.3418i	−0.337843	−	0.853294i	−0.995031	−	0.0995671i	$-0.968254\pi$
$953$	−10.4294	−	26.3418i	−0.337843	−	0.853294i	0.657188	−	0.753727i	$-0.271746\pi$
$954$	−7.68039	−	9.28400i	−0.248662	−	0.300581i
$955$	3.66241	+	26.8472i	0.118513	+	0.868754i
$956$	−0.193521	−	0.0766204i	−0.00625892	−	0.00247808i
$957$	−9.42039	−	12.9661i	−0.304518	−	0.419133i
$958$	−14.9959	−	12.4057i	−0.484495	−	0.400809i
$959$	−45.2120	+	42.4568i	−1.45997	+	1.37100i
$960$	−5.32508	−	2.04750i	−0.171866	−	0.0660828i
$961$	−10.1282	+	5.56800i	−0.326715	+	0.179613i
$962$	6.13337	+	6.53138i	0.197748	+	0.210580i
$963$	17.2212	−	31.3253i	0.554946	−	1.00944i
$964$	11.5555	−	24.5566i	0.372177	−	0.790916i
$965$	5.02481	−	16.0030i	0.161754	−	0.515156i
$966$	104.878	−	13.2492i	3.37441	−	0.426287i
$967$	−20.7323	+	13.1571i	−0.666705	+	0.423104i	−0.825649	−	0.564183i	$-0.809191\pi$
$967$	−20.7323	+	13.1571i	−0.666705	+	0.423104i	0.158944	+	0.987288i	$0.449191\pi$
$968$	6.11763	−	8.42020i	0.196628	−	0.270635i
$969$	22.1072	−	5.67617i	0.710187	−	0.182345i
$970$	8.76299	−	22.7905i	0.281363	−	0.731759i
$971$	−3.60168	−	57.2470i	−0.115583	−	1.83714i	−0.448026	−	0.894021i	$-0.647873\pi$
$971$	−3.60168	−	57.2470i	−0.115583	−	1.83714i	0.332443	−	0.943124i	$-0.392127\pi$
$972$	22.2558	−	1.40022i	0.713856	−	0.0449120i
$973$	8.74901	+	15.9144i	0.280480	+	0.510192i
$974$	−4.60232	+	14.1645i	−0.147468	+	0.453859i
$975$	−63.5456	−	6.75031i	−2.03509	−	0.216183i
$976$	−2.44851	−	7.53574i	−0.0783749	−	0.241213i
$977$	23.2052	−	24.7110i	0.742399	−	0.790575i	−0.241290	−	0.970453i	$-0.577570\pi$
$977$	23.2052	−	24.7110i	0.742399	−	0.790575i	0.983689	+	0.179878i	$0.0575704\pi$
$978$	−2.04526	+	7.96575i	−0.0654001	+	0.254717i
$979$	−5.66058	+	8.91964i	−0.180913	+	0.285073i
$980$	41.0338	−	2.99042i	1.31078	−	0.0955253i
$981$	−15.5777	+	18.8302i	−0.497358	+	0.601202i
$982$	26.9160	+	8.74554i	0.858924	+	0.279081i
$983$	5.79351	+	22.5642i	0.184784	+	0.719688i	0.991651	+	0.128954i	$0.0411618\pi$
$983$	5.79351	+	22.5642i	0.184784	+	0.719688i	−0.806866	+	0.590734i	$0.798838\pi$
$984$	10.2610	+	5.64101i	0.327107	+	0.179829i
$985$	5.29020	+	6.26717i	0.168560	+	0.199689i
$986$	−6.88288	−	36.0813i	−0.219195	−	1.14906i
$987$	−10.9271	−	2.08445i	−0.347812	−	0.0663487i
$988$	−9.01143	+	4.24046i	−0.286692	+	0.134907i
$989$	−11.8664	−	1.49908i	−0.377330	−	0.0476679i
$990$	4.44279	+	4.08991i	0.141201	+	0.129986i
$991$	−5.32895	+	27.9354i	−0.169280	+	0.887396i	0.791728	+	0.610874i	$0.209182\pi$
$991$	−5.32895	+	27.9354i	−0.169280	+	0.887396i	−0.961008	+	0.276522i	$0.910818\pi$
$992$	−1.62318	+	4.09969i	−0.0515361	+	0.130165i
$993$	22.0690	−	7.17066i	0.700339	−	0.227554i
$994$	−21.6033	−	34.0413i	−0.685214	−	1.07972i
$995$	−0.133383	−	0.179809i	−0.00422852	−	0.00570032i
$996$	−10.0140	−	2.57116i	−0.317306	−	0.0814704i
$997$	−5.03906	+	4.16867i	−0.159589	+	0.132023i	−0.713791	−	0.700359i	$-0.753023\pi$
$997$	−5.03906	+	4.16867i	−0.159589	+	0.132023i	0.554202	+	0.832382i	$0.313023\pi$
$998$	−1.77036	+	14.0138i	−0.0560397	+	0.443600i
$999$	−2.32623			−0.0735987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.109.7	yes	240
125.39	even	50	inner	250.2.h.a.39.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.39.7	✓	240	125.39	even	50	inner
250.2.h.a.109.7	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.125333 - 0.992115i) q^{2} +(-1.96590 + 1.62634i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-2.13337 - 0.669861i) q^{5} +(1.36712 + 2.15423i) q^{6} +(4.79313 - 1.55738i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(0.657659 - 3.44757i) q^{9} +O(q^{10})\)	\(q+(0.125333 - 0.992115i) q^{2} +(-1.96590 + 1.62634i) q^{3} +(-0.968583 - 0.248690i) q^{4} +(-2.13337 - 0.669861i) q^{5} +(1.36712 + 2.15423i) q^{6} +(4.79313 - 1.55738i) q^{7} +(-0.368125 + 0.929776i) q^{8} +(0.657659 - 3.44757i) q^{9} +(-0.931962 + 2.03260i) q^{10} +(0.763387 + 0.0964382i) q^{11} +(2.30859 - 1.08634i) q^{12} +(4.92050 + 0.938635i) q^{13} +(-0.944364 - 4.95053i) q^{14} +(5.28342 - 2.15270i) q^{15} +(0.876307 + 0.481754i) q^{16} +(-1.11896 - 4.35808i) q^{17} +(-3.33796 - 1.08457i) q^{18} +(1.26732 - 1.53193i) q^{19} +(1.89976 + 1.17936i) q^{20} +(-6.89000 + 10.8569i) q^{21} +(0.191355 - 0.745280i) q^{22} +(5.62772 - 5.99292i) q^{23} +(-0.788432 - 2.42654i) q^{24} +(4.10257 + 2.85813i) q^{25} +(1.54794 - 4.76406i) q^{26} +(0.626545 + 1.13968i) q^{27} +(-5.02985 + 0.316452i) q^{28} +(0.512601 + 8.14757i) q^{29} +(-1.47354 - 5.51157i) q^{30} +(-4.27081 + 1.09656i) q^{31} +(0.587785 - 0.809017i) q^{32} +(-1.65758 + 1.05193i) q^{33} +(-4.46395 + 0.563929i) q^{34} +(-11.2688 + 0.111749i) q^{35} +(-1.49437 + 3.17570i) q^{36} +(-0.861689 + 1.56741i) q^{37} +(-1.36101 - 1.44933i) q^{38} +(-11.1997 + 6.15711i) q^{39} +(1.40817 - 1.73697i) q^{40} +(-3.34548 + 3.14162i) q^{41} +(9.90775 + 8.19640i) q^{42} +(-0.855160 - 1.17703i) q^{43} +(-0.715420 - 0.283255i) q^{44} +(-3.71242 + 6.91442i) q^{45} +(-5.24032 - 6.33446i) q^{46} +(0.318467 + 0.804356i) q^{47} +(-2.50623 + 0.478088i) q^{48} +(14.8856 - 10.8150i) q^{49} +(3.34978 - 3.71200i) q^{50} +(9.28747 + 6.74774i) q^{51} +(-4.53248 - 2.13282i) q^{52} +(2.89862 + 1.83952i) q^{53} +(1.20922 - 0.478765i) q^{54} +(-1.56399 - 0.717102i) q^{55} +(-0.316452 + 5.02985i) q^{56} +5.07270i q^{57} +(8.14757 + 0.512601i) q^{58} +(-4.28658 - 9.10945i) q^{59} +(-5.65279 + 0.771136i) q^{60} +(-5.77601 - 5.42404i) q^{61} +(0.552636 + 4.37456i) q^{62} +(-2.21694 - 17.5489i) q^{63} +(-0.728969 - 0.684547i) q^{64} +(-9.86851 - 5.29851i) q^{65} +(0.835890 + 1.77636i) q^{66} +(5.84014 + 0.367430i) q^{67} +4.49943i q^{68} +(-1.31706 + 20.9340i) q^{69} +(-1.30148 + 11.1939i) q^{70} +(7.43808 - 2.94494i) q^{71} +(2.96337 + 1.88061i) q^{72} +(6.99743 + 3.29274i) q^{73} +(1.44705 + 1.05134i) q^{74} +(-12.7135 + 1.05336i) q^{75} +(-1.60848 + 1.16863i) q^{76} +(3.80920 - 0.726645i) q^{77} +(4.70486 + 11.8831i) q^{78} +(-3.15293 - 3.81124i) q^{79} +(-1.54678 - 1.61476i) q^{80} +(6.70458 + 2.65453i) q^{81} +(2.69754 + 3.71285i) q^{82} +(-3.12227 - 2.58296i) q^{83} +(9.37354 - 8.80234i) q^{84} +(-0.532136 + 10.0470i) q^{85} +(-1.27493 + 0.700896i) q^{86} +(-14.2584 - 15.1837i) q^{87} +(-0.370687 + 0.674278i) q^{88} +(-5.84572 + 12.4228i) q^{89} +(6.39460 + 4.54976i) q^{90} +(25.0464 - 3.16410i) q^{91} +(-6.94130 + 4.40508i) q^{92} +(6.61262 - 9.10149i) q^{93} +(0.837928 - 0.215143i) q^{94} +(-3.72985 + 2.41925i) q^{95} +(0.160205 + 2.54638i) q^{96} +(-10.8981 + 0.685653i) q^{97} +(-8.86405 - 16.1237i) q^{98} +(0.834525 - 2.56841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 10 q^{5}+O(q^{10}) \) 240 * q + 10 * q^5	\( 240 q + 10 q^{5} + 10 q^{11} - 40 q^{12} + 20 q^{15} - 10 q^{17} - 20 q^{19} - 20 q^{22} - 60 q^{23} - 10 q^{24} - 110 q^{25} + 30 q^{26} - 10 q^{28} - 20 q^{29} - 20 q^{30} + 10 q^{31} + 30 q^{33} - 10 q^{35} + 10 q^{37} - 20 q^{39} + 30 q^{41} + 10 q^{42} - 160 q^{45} + 20 q^{46} - 220 q^{47} + 10 q^{48} + 40 q^{49} + 20 q^{51} + 10 q^{55} - 30 q^{59} - 50 q^{60} + 40 q^{61} - 20 q^{63} - 50 q^{65} - 10 q^{67} - 20 q^{69} - 50 q^{71} - 50 q^{74} - 10 q^{75} + 10 q^{76} - 40 q^{77} - 170 q^{78} - 40 q^{79} + 50 q^{81} - 200 q^{82} - 50 q^{83} - 30 q^{84} + 20 q^{85} - 20 q^{87} + 10 q^{88} - 40 q^{89} + 30 q^{90} - 240 q^{91} + 10 q^{92} - 100 q^{93} - 100 q^{95} + 20 q^{97} + 40 q^{98} - 30 q^{99}+O(q^{100}) \) 240 * q + 10 * q^5 + 10 * q^11 - 40 * q^12 + 20 * q^15 - 10 * q^17 - 20 * q^19 - 20 * q^22 - 60 * q^23 - 10 * q^24 - 110 * q^25 + 30 * q^26 - 10 * q^28 - 20 * q^29 - 20 * q^30 + 10 * q^31 + 30 * q^33 - 10 * q^35 + 10 * q^37 - 20 * q^39 + 30 * q^41 + 10 * q^42 - 160 * q^45 + 20 * q^46 - 220 * q^47 + 10 * q^48 + 40 * q^49 + 20 * q^51 + 10 * q^55 - 30 * q^59 - 50 * q^60 + 40 * q^61 - 20 * q^63 - 50 * q^65 - 10 * q^67 - 20 * q^69 - 50 * q^71 - 50 * q^74 - 10 * q^75 + 10 * q^76 - 40 * q^77 - 170 * q^78 - 40 * q^79 + 50 * q^81 - 200 * q^82 - 50 * q^83 - 30 * q^84 + 20 * q^85 - 20 * q^87 + 10 * q^88 - 40 * q^89 + 30 * q^90 - 240 * q^91 + 10 * q^92 - 100 * q^93 - 100 * q^95 + 20 * q^97 + 40 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more