LMFDB - Embedded newform 250.2.h.a.229.1

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			229.1
Character	$\chi$	$=$	250.229
Dual form			250.2.h.a.119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(-2.53185 + 0.482975i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.19016 - 0.450797i) q^{5} +(1.09745 + 2.33219i) q^{6} +(0.181387 - 0.249657i) q^{7} +(0.684547 + 0.728969i) q^{8} +(3.38765 - 1.34126i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(-2.53185 + 0.482975i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.19016 - 0.450797i) q^{5} +(1.09745 + 2.33219i) q^{6} +(0.181387 - 0.249657i) q^{7} +(0.684547 + 0.728969i) q^{8} +(3.38765 - 1.34126i) q^{9} +(0.108035 + 2.23346i) q^{10} +(5.86457 - 1.50577i) q^{11} +(1.98600 - 1.64296i) q^{12} +(2.34562 + 5.92435i) q^{13} +(-0.286923 - 0.113601i) q^{14} +(5.76286 + 0.0835580i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.399354 + 0.726422i) q^{17} +(-2.14160 - 2.94766i) q^{18} +(-0.506363 + 2.65445i) q^{19} +(2.13642 - 0.660079i) q^{20} +(-0.338665 + 0.719699i) q^{21} +(-2.91692 - 5.30586i) q^{22} +(-4.99573 - 0.314305i) q^{23} +(-2.08524 - 1.51502i) q^{24} +(4.59356 + 1.97463i) q^{25} +(5.15490 - 3.74525i) q^{26} +(-1.40044 + 0.888745i) q^{27} +(-0.0386770 + 0.306160i) q^{28} +(9.23211 + 1.16629i) q^{29} +(-1.35223 - 5.60259i) q^{30} +(-6.22060 - 3.41980i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-14.1209 + 6.64481i) q^{33} +(0.802915 + 0.206154i) q^{34} +(-0.509810 + 0.465020i) q^{35} +(-2.32246 + 2.80737i) q^{36} +(2.34879 + 1.49059i) q^{37} +(2.69698 - 0.169680i) q^{38} +(-8.80006 - 13.8667i) q^{39} +(-1.17065 - 1.90515i) q^{40} +(0.441780 + 7.02190i) q^{41} +(0.781311 + 0.149043i) q^{42} +(1.15690 - 0.375900i) q^{43} +(-4.41376 + 4.14479i) q^{44} +(-8.02412 + 1.41044i) q^{45} +(0.937957 + 4.91694i) q^{46} +(5.77426 - 6.14897i) q^{47} +(-0.948841 + 2.39650i) q^{48} +(2.13369 + 6.56683i) q^{49} +(0.770223 - 4.94032i) q^{50} +(0.660258 - 2.03207i) q^{51} +(-4.90956 - 4.06154i) q^{52} +(0.0584509 + 0.0275049i) q^{53} +(1.20910 + 1.13542i) q^{54} +(-13.5231 + 0.654129i) q^{55} +(0.306160 - 0.0386770i) q^{56} -6.96522i q^{57} +(-1.16629 - 9.23211i) q^{58} +(2.29012 + 2.76828i) q^{59} +(-5.09029 + 2.70306i) q^{60} +(-0.461945 + 7.34241i) q^{61} +(-1.76536 + 6.87564i) q^{62} +(0.279618 - 1.08904i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-2.46658 - 14.0326i) q^{65} +(9.94779 + 12.0248i) q^{66} +(1.41822 + 11.2264i) q^{67} -0.828958i q^{68} +(12.8002 - 1.61704i) q^{69} +(0.577195 + 0.378147i) q^{70} +(0.954221 + 0.896073i) q^{71} +(3.29674 + 1.55133i) q^{72} +(-2.08788 - 1.72724i) q^{73} +(0.859639 - 2.64570i) q^{74} +(-12.5839 - 2.78089i) q^{75} +(-0.835061 - 2.57005i) q^{76} +(0.687829 - 1.73726i) q^{77} +(-11.2425 + 11.9721i) q^{78} +(-0.221318 - 1.16019i) q^{79} +(-1.55416 + 1.60766i) q^{80} +(-4.85156 + 4.55592i) q^{81} +(6.69143 - 2.17418i) q^{82} +(14.8285 + 2.82869i) q^{83} +(-0.0499435 - 0.793830i) q^{84} +(1.20212 - 1.41095i) q^{85} +(-0.651800 - 1.02707i) q^{86} +(-23.9376 + 1.50602i) q^{87} +(5.11223 + 3.24432i) q^{88} +(4.13806 - 5.00206i) q^{89} +(3.36164 + 7.42126i) q^{90} +(1.90452 + 0.488998i) q^{91} +(4.52921 - 2.13128i) q^{92} +(17.4013 + 5.65402i) q^{93} +(-7.39179 - 4.06367i) q^{94} +(2.30563 - 5.58539i) q^{95} +(2.55718 + 0.323046i) q^{96} +(-0.301235 + 2.38452i) q^{97} +(5.82989 - 3.69976i) q^{98} +(17.8475 - 12.9670i) 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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	−2.53185	+	0.482975i	−1.46176	+	0.278846i	−0.856073	−	0.516855i	$-0.827102\pi$
$3$	−2.53185	+	0.482975i	−1.46176	+	0.278846i	−0.605689	+	0.795701i	$0.707102\pi$
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	−2.19016	−	0.450797i	−0.979467	−	0.201603i
$5$	−2.19016	−	0.450797i	−0.979467	−	0.201603i
$6$	1.09745	+	2.33219i	0.448031	+	0.952113i
$7$	0.181387	−	0.249657i	0.0685577	−	0.0943616i	−0.773361	−	0.633966i	$-0.781426\pi$
$7$	0.181387	−	0.249657i	0.0685577	−	0.0943616i	0.841919	+	0.539604i	$0.181426\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	3.38765	−	1.34126i	1.12922	−	0.447088i
$10$	0.108035	+	2.23346i	0.0341636	+	0.706281i
$11$	5.86457	−	1.50577i	1.76824	−	0.454006i	0.782548	−	0.622590i	$-0.213920\pi$
$11$	5.86457	−	1.50577i	1.76824	−	0.454006i	0.985687	+	0.168584i	$0.0539196\pi$
$12$	1.98600	−	1.64296i	0.573308	−	0.474282i
$13$	2.34562	+	5.92435i	0.650557	+	1.64312i	0.760622	+	0.649195i	$0.224894\pi$
$13$	2.34562	+	5.92435i	0.650557	+	1.64312i	−0.110065	+	0.993924i	$0.535106\pi$
$14$	−0.286923	−	0.113601i	−0.0766833	−	0.0303611i
$15$	5.76286	+	0.0835580i	1.48796	+	0.0215746i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−0.399354	+	0.726422i	−0.0968575	+	0.176183i	−0.920296	−	0.391222i	$-0.872053\pi$
$17$	−0.399354	+	0.726422i	−0.0968575	+	0.176183i	0.823439	+	0.567405i	$0.192053\pi$
$18$	−2.14160	−	2.94766i	−0.504780	−	0.694770i
$19$	−0.506363	+	2.65445i	−0.116168	+	0.608973i	0.875820	+	0.482638i	$0.160321\pi$
$19$	−0.506363	+	2.65445i	−0.116168	+	0.608973i	−0.991988	+	0.126335i	$0.959679\pi$
$20$	2.13642	−	0.660079i	0.477718	−	0.147598i
$21$	−0.338665	+	0.719699i	−0.0739027	+	0.157051i
$22$	−2.91692	−	5.30586i	−0.621889	−	1.13121i
$23$	−4.99573	−	0.314305i	−1.04168	−	0.0655371i	−0.467279	−	0.884110i	$-0.654766\pi$
$23$	−4.99573	−	0.314305i	−1.04168	−	0.0655371i	−0.574403	+	0.818573i	$0.694766\pi$
$24$	−2.08524	−	1.51502i	−0.425648	−	0.309251i
$25$	4.59356	+	1.97463i	0.918713	+	0.394927i
$26$	5.15490	−	3.74525i	1.01096	−	0.734504i
$27$	−1.40044	+	0.888745i	−0.269514	+	0.171039i
$28$	−0.0386770	+	0.306160i	−0.00730927	+	0.0578588i
$29$	9.23211	+	1.16629i	1.71436	+	0.216574i	0.920286	−	0.391247i	$-0.127956\pi$
$29$	9.23211	+	1.16629i	1.71436	+	0.216574i	0.794074	+	0.607821i	$0.207956\pi$
$30$	−1.35223	−	5.60259i	−0.246883	−	1.02289i
$31$	−6.22060	−	3.41980i	−1.11725	−	0.614215i	−0.187450	−	0.982274i	$-0.560022\pi$
$31$	−6.22060	−	3.41980i	−1.11725	−	0.614215i	−0.929802	+	0.368059i	$0.880022\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	−14.1209	+	6.64481i	−2.45814	+	1.15671i
$34$	0.802915	+	0.206154i	0.137699	+	0.0353550i
$35$	−0.509810	+	0.465020i	−0.0861736	+	0.0786027i
$36$	−2.32246	+	2.80737i	−0.387077	+	0.467895i
$37$	2.34879	+	1.49059i	0.386139	+	0.245051i	0.714700	−	0.699432i	$-0.246563\pi$
$37$	2.34879	+	1.49059i	0.386139	+	0.245051i	−0.328560	+	0.944483i	$0.606563\pi$
$38$	2.69698	−	0.169680i	0.437508	−	0.0275257i
$39$	−8.80006	−	13.8667i	−1.40914	−	2.22044i
$40$	−1.17065	−	1.90515i	−0.185096	−	0.301230i
$41$	0.441780	+	7.02190i	0.0689945	+	1.09664i	0.868406	+	0.495853i	$0.165145\pi$
$41$	0.441780	+	7.02190i	0.0689945	+	1.09664i	−0.799412	+	0.600783i	$0.794855\pi$
$42$	0.781311	+	0.149043i	0.120559	+	0.0229978i
$43$	1.15690	−	0.375900i	0.176426	−	0.0573242i	−0.219472	−	0.975619i	$-0.570433\pi$
$43$	1.15690	−	0.375900i	0.176426	−	0.0573242i	0.395898	+	0.918295i	$0.370433\pi$
$44$	−4.41376	+	4.14479i	−0.665399	+	0.624851i
$45$	−8.02412	+	1.41044i	−1.19616	+	0.210255i
$46$	0.937957	+	4.91694i	0.138294	+	0.724964i
$47$	5.77426	−	6.14897i	0.842263	−	0.896919i	−0.153568	−	0.988138i	$-0.549076\pi$
$47$	5.77426	−	6.14897i	0.842263	−	0.896919i	0.995831	+	0.0912191i	$0.0290763\pi$
$48$	−0.948841	+	2.39650i	−0.136953	+	0.345905i
$49$	2.13369	+	6.56683i	0.304813	+	0.938118i
$50$	0.770223	−	4.94032i	0.108926	−	0.698667i
$51$	0.660258	−	2.03207i	0.0924547	−	0.284546i
$52$	−4.90956	−	4.06154i	−0.680833	−	0.563234i
$53$	0.0584509	+	0.0275049i	0.00802885	+	0.00377809i	0.429790	−	0.902929i	$-0.358588\pi$
$53$	0.0584509	+	0.0275049i	0.00802885	+	0.00377809i	−0.421761	+	0.906707i	$0.638588\pi$
$54$	1.20910	+	1.13542i	0.164537	+	0.154511i
$55$	−13.5231	+	0.654129i	−1.82346	+	0.0882027i
$56$	0.306160	−	0.0386770i	0.0409123	−	0.00516843i
$57$		−	6.96522i		−	0.922566i
$58$	−1.16629	−	9.23211i	−0.153141	−	1.21224i
$59$	2.29012	+	2.76828i	0.298149	+	0.360400i	0.898220	−	0.439547i	$-0.144861\pi$
$59$	2.29012	+	2.76828i	0.298149	+	0.360400i	−0.600071	+	0.799947i	$0.704861\pi$
$60$	−5.09029	+	2.70306i	−0.657153	+	0.348963i
$61$	−0.461945	+	7.34241i	−0.0591461	+	0.940100i	0.850831	+	0.525440i	$0.176099\pi$
$61$	−0.461945	+	7.34241i	−0.0591461	+	0.940100i	−0.909977	+	0.414660i	$0.863901\pi$
$62$	−1.76536	+	6.87564i	−0.224201	+	0.873207i
$63$	0.279618	−	1.08904i	0.0352285	−	0.137206i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	−2.46658	−	14.0326i	−0.305942	−	1.74054i
$66$	9.94779	+	12.0248i	1.22449	+	1.48015i
$67$	1.41822	+	11.2264i	0.173263	+	1.37152i	0.803587	+	0.595187i	$0.202922\pi$
$67$	1.41822	+	11.2264i	0.173263	+	1.37152i	−0.630324	+	0.776332i	$0.717078\pi$
$68$		−	0.828958i		−	0.100526i
$69$	12.8002	−	1.61704i	1.54097	−	0.194669i
$70$	0.577195	+	0.378147i	0.0689880	+	0.0451973i
$71$	0.954221	+	0.896073i	0.113245	+	0.106344i	0.739102	−	0.673594i	$-0.235250\pi$
$71$	0.954221	+	0.896073i	0.113245	+	0.106344i	−0.625856	+	0.779938i	$0.715250\pi$
$72$	3.29674	+	1.55133i	0.388525	+	0.182826i
$73$	−2.08788	−	1.72724i	−0.244368	−	0.202159i	0.507175	−	0.861843i	$-0.330690\pi$
$73$	−2.08788	−	1.72724i	−0.244368	−	0.202159i	−0.751543	+	0.659685i	$0.770690\pi$
$74$	0.859639	−	2.64570i	0.0999310	−	0.307556i
$75$	−12.5839	−	2.78089i	−1.45306	−	0.321109i
$76$	−0.835061	−	2.57005i	−0.0957881	−	0.294805i
$77$	0.687829	−	1.73726i	0.0783854	−	0.197979i
$78$	−11.2425	+	11.9721i	−1.27297	+	1.35557i
$79$	−0.221318	−	1.16019i	−0.0249003	−	0.130532i	0.967666	−	0.252233i	$-0.0811650\pi$
$79$	−0.221318	−	1.16019i	−0.0249003	−	0.130532i	−0.992567	+	0.121701i	$0.961165\pi$
$80$	−1.55416	+	1.60766i	−0.173761	+	0.179742i
$81$	−4.85156	+	4.55592i	−0.539062	+	0.506213i
$82$	6.69143	−	2.17418i	0.738945	−	0.240098i
$83$	14.8285	+	2.82869i	1.62764	+	0.310489i	0.918753	−	0.394833i	$-0.129198\pi$
$83$	14.8285	+	2.82869i	1.62764	+	0.310489i	0.708887	+	0.705322i	$0.249198\pi$
$84$	−0.0499435	−	0.793830i	−0.00544929	−	0.0866139i
$85$	1.20212	−	1.41095i	0.130388	−	0.153039i
$86$	−0.651800	−	1.02707i	−0.0702854	−	0.110752i
$87$	−23.9376	+	1.50602i	−2.56638	+	0.161463i
$88$	5.11223	+	3.24432i	0.544966	+	0.345846i
$89$	4.13806	−	5.00206i	0.438634	−	0.530217i	−0.504153	−	0.863615i	$-0.668195\pi$
$89$	4.13806	−	5.00206i	0.438634	−	0.530217i	0.942786	+	0.333398i	$0.108195\pi$
$90$	3.36164	+	7.42126i	0.354348	+	0.782270i
$91$	1.90452	+	0.488998i	0.199648	+	0.0512609i
$92$	4.52921	−	2.13128i	0.472203	−	0.222202i
$93$	17.4013	+	5.65402i	1.80443	+	0.586294i
$94$	−7.39179	−	4.06367i	−0.762405	−	0.419136i
$95$	2.30563	−	5.58539i	0.236553	−	0.573049i
$96$	2.55718	+	0.323046i	0.260991	+	0.0329708i
$97$	−0.301235	+	2.38452i	−0.0305858	+	0.242112i	−0.999994	−	0.00334092i	$-0.998937\pi$
$97$	−0.301235	+	2.38452i	−0.0305858	+	0.242112i	0.969409	+	0.245453i	$0.0789366\pi$
$98$	5.82989	−	3.69976i	0.588908	−	0.373732i
$99$	17.8475	−	12.9670i	1.79374	−	1.30323i
$100$	−4.97666	+	0.482582i	−0.497666	+	0.0482582i
$101$	−12.2858	−	8.92614i	−1.22248	−	0.888184i	−0.226177	−	0.974086i	$-0.572623\pi$
$101$	−12.2858	−	8.92614i	−1.22248	−	0.888184i	−0.996304	+	0.0859022i	$0.972623\pi$
$102$	−2.13242	−	0.134161i	−0.211141	−	0.0132839i
$103$	0.260283	+	0.473453i	0.0256465	+	0.0466507i	0.888819	−	0.458258i	$-0.151526\pi$
$103$	0.260283	+	0.473453i	0.0256465	+	0.0466507i	−0.863173	+	0.504908i	$0.831526\pi$
$104$	−2.71298	+	5.76538i	−0.266030	+	0.565342i
$105$	1.06617	−	1.42358i	0.104047	−	0.138928i
$106$	0.0121046	−	0.0634548i	0.00117571	−	0.00616327i
$107$	−6.61309	−	9.10214i	−0.639311	−	0.879937i	0.359267	−	0.933235i	$-0.383027\pi$
$107$	−6.61309	−	9.10214i	−0.639311	−	0.879937i	−0.998579	+	0.0532980i	$0.983027\pi$
$108$	0.799057	−	1.45348i	0.0768893	−	0.139861i
$109$	0.0545270	−	0.0859207i	0.00522274	−	0.00822972i	−0.841707	−	0.539935i	$-0.818449\pi$
$109$	0.0545270	−	0.0859207i	0.00522274	−	0.00822972i	0.846929	+	0.531706i	$0.178449\pi$
$110$	3.99664	+	12.9356i	0.381065	+	1.23336i
$111$	−6.66670	−	2.63953i	−0.632775	−	0.250533i
$112$	−0.113601	−	0.286923i	−0.0107343	−	0.0271117i
$113$	−0.192306	+	0.159089i	−0.0180906	+	0.0149659i	−0.646425	−	0.762977i	$-0.723737\pi$
$113$	−0.192306	+	0.159089i	−0.0180906	+	0.0149659i	0.628335	+	0.777943i	$0.283737\pi$
$114$	−6.74639	+	1.73218i	−0.631858	+	0.162233i
$115$	10.7997	+	2.94044i	1.00708	+	0.274197i
$116$	−8.65202	+	3.42558i	−0.803320	+	0.318057i
$117$	15.8922	+	16.9235i	1.46924	+	1.56458i
$118$	2.11178	−	2.90662i	0.194405	−	0.267576i
$119$	0.108919	+	0.231465i	0.00998459	+	0.0212183i
$120$	3.88404	+	4.25814i	0.354563	+	0.388714i
$121$	22.4865	−	12.3621i	2.04423	−	1.12382i
$122$	7.22662	−	1.37855i	0.654267	−	0.124808i
$123$	−4.50992	−	17.5650i	−0.406646	−	1.58378i
$124$	7.09865			0.637478
$125$	−9.17046	−	6.39552i	−0.820231	−	0.572033i
$126$	−1.12436			−0.100166
$127$	−0.838830	−	3.26703i	−0.0744341	−	0.289902i	0.920459	−	0.390840i	$-0.127815\pi$
$127$	−0.838830	−	3.26703i	−0.0744341	−	0.289902i	−0.994893	+	0.100938i	$0.967815\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−2.74755	+	1.51048i	−0.241908	+	0.132990i
$130$	−12.9784	+	5.87887i	−1.13828	+	0.515611i
$131$	−3.87271	−	8.22993i	−0.338360	−	0.719052i	0.661153	−	0.750251i	$-0.270067\pi$
$131$	−3.87271	−	8.22993i	−0.338360	−	0.719052i	−0.999513	+	0.0311989i	$0.990067\pi$
$132$	9.17312	−	12.6257i	0.798417	−	1.09893i
$133$	0.570855	+	0.607899i	0.0494994	+	0.0527115i
$134$	10.5210	−	4.16555i	0.908874	−	0.359849i
$135$	3.46782	−	1.31518i	0.298463	−	0.113192i
$136$	−0.802915	+	0.206154i	−0.0688494	+	0.0176775i
$137$	3.69408	−	3.05601i	0.315606	−	0.261092i	−0.466109	−	0.884727i	$-0.654345\pi$
$137$	3.69408	−	3.05601i	0.315606	−	0.261092i	0.781716	+	0.623635i	$0.214345\pi$
$138$	−4.74953	−	11.9959i	−0.404307	−	1.02116i
$139$	0.385338	+	0.152566i	0.0326840	+	0.0129405i	0.384410	−	0.923163i	$-0.374405\pi$
$139$	0.385338	+	0.152566i	0.0326840	+	0.0129405i	−0.351726	+	0.936103i	$0.614405\pi$
$140$	0.222725	−	0.653102i	0.0188237	−	0.0551972i
$141$	−11.6497	+	18.3571i	−0.981086	+	1.54594i
$142$	0.630616	−	1.14709i	0.0529201	−	0.0962614i
$143$	22.6767	+	31.2118i	1.89632	+	2.61007i
$144$	0.682725	−	3.57897i	0.0568938	−	0.298248i
$145$	−19.6940	−	6.71616i	−1.63550	−	0.557747i
$146$	−1.15374	+	2.45183i	−0.0954846	+	0.202915i
$147$	−8.57379	−	15.5957i	−0.707155	−	1.28631i
$148$	−2.77636	−	0.174674i	−0.228215	−	0.0143581i
$149$	−11.7362	−	8.52682i	−0.961464	−	0.698544i	−0.00797340	−	0.999968i	$-0.502538\pi$
$149$	−11.7362	−	8.52682i	−0.961464	−	0.698544i	−0.953490	+	0.301424i	$0.902538\pi$
$150$	0.435967	+	12.8801i	0.0355965	+	1.05166i
$151$	−10.3332	+	7.50749i	−0.840902	+	0.610951i	−0.922622	−	0.385704i	$-0.873958\pi$
$151$	−10.3332	+	7.50749i	−0.840902	+	0.610951i	0.0817207	+	0.996655i	$0.473958\pi$
$152$	−2.28164	+	1.44797i	−0.185065	+	0.117446i
$153$	−0.378546	+	2.99650i	−0.0306036	+	0.242253i
$154$	−1.85374	−	0.234181i	−0.149378	−	0.0188709i
$155$	12.0824	+	10.2941i	0.970485	+	0.826844i
$156$	14.3919	+	7.91200i	1.15227	+	0.633467i
$157$	8.55817	+	2.78072i	0.683016	+	0.221925i	0.629915	−	0.776664i	$-0.283090\pi$
$157$	8.55817	+	2.78072i	0.683016	+	0.221925i	0.0531007	+	0.998589i	$0.483090\pi$
$158$	−1.06870	+	0.502893i	−0.0850214	+	0.0400080i
$159$	−0.161273	−	0.0414079i	−0.0127898	−	0.00328386i
$160$	1.94366	+	1.10553i	0.153660	+	0.0873997i
$161$	−0.984627	+	1.19021i	−0.0775995	+	0.0938016i
$162$	5.61932	+	3.56613i	0.441495	+	0.280181i
$163$	−9.35282	+	0.588430i	−0.732570	+	0.0460894i	−0.424694	−	0.905337i	$-0.639618\pi$
$163$	−9.35282	+	0.588430i	−0.732570	+	0.0460894i	−0.307876	+	0.951426i	$0.599618\pi$
$164$	−3.76996	−	5.94051i	−0.294385	−	0.463876i
$165$	33.9225	−	8.18749i	2.64087	−	0.637395i
$166$	−0.947879	−	15.0661i	−0.0735697	−	1.16936i
$167$	6.85388	+	1.30745i	0.530369	+	0.101173i	0.445608	−	0.895228i	$-0.352987\pi$
$167$	6.85388	+	1.30745i	0.530369	+	0.101173i	0.0847608	+	0.996401i	$0.472987\pi$
$168$	−0.756470	+	0.245792i	−0.0583629	+	0.0189633i
$169$	−20.1194	+	18.8934i	−1.54765	+	1.45334i
$170$	−1.66558	−	0.813460i	−0.127744	−	0.0623896i
$171$	1.84494	+	9.67151i	0.141086	+	0.739599i
$172$	−0.832709	+	0.886745i	−0.0634935	+	0.0676137i
$173$	−6.03997	+	15.2552i	−0.459211	+	1.15983i	0.497155	+	0.867662i	$0.334378\pi$
$173$	−6.03997	+	15.2552i	−0.459211	+	1.15983i	−0.956366	+	0.292172i	$0.905622\pi$
$174$	7.41174	+	22.8110i	0.561882	+	1.72930i
$175$	1.32619	−	0.788644i	0.100251	−	0.0596159i
$176$	1.87103	−	5.75845i	0.141035	−	0.434060i
$177$	−7.13526	−	5.90280i	−0.536319	−	0.443681i
$178$	−5.87400	−	2.76410i	−0.440275	−	0.207178i
$179$	17.6906	+	16.6126i	1.32226	+	1.24168i	0.949505	+	0.313753i	$0.101586\pi$
$179$	17.6906	+	16.6126i	1.32226	+	1.24168i	0.372754	+	0.927930i	$0.378414\pi$
$180$	6.35210	−	5.10162i	0.473458	−	0.380252i
$181$	8.14864	−	1.02941i	0.605684	−	0.0765157i	0.183490	−	0.983021i	$-0.441260\pi$
$181$	8.14864	−	1.02941i	0.605684	−	0.0765157i	0.422193	+	0.906506i	$0.361260\pi$
$182$		−	1.96630i		−	0.145752i
$183$	−2.37663	−	18.8130i	−0.175686	−	1.39069i
$184$	−3.19069	−	3.85689i	−0.235221	−	0.284333i
$185$	−4.47227	−	4.32345i	−0.328808	−	0.317867i
$186$	1.14886	−	18.2607i	0.0842388	−	1.33894i
$187$	−1.24822	+	4.86149i	−0.0912787	+	0.355507i
$188$	−2.09774	+	8.17015i	−0.152993	+	0.595870i
$189$	−0.0321391	+	0.510836i	−0.00233777	+	0.0371579i
$190$	−5.98330	−	0.844168i	−0.434074	−	0.0612423i
$191$	2.03945	+	2.46528i	0.147570	+	0.178381i	0.839119	−	0.543949i	$-0.183071\pi$
$191$	2.03945	+	2.46528i	0.147570	+	0.178381i	−0.691549	+	0.722330i	$0.743071\pi$
$192$	−0.323046	−	2.55718i	−0.0233139	−	0.184548i
$193$		−	16.6541i		−	1.19879i	−0.800454	−	0.599395i	$-0.795408\pi$
$193$		−	16.6541i		−	1.19879i	0.800454	−	0.599395i	$-0.204592\pi$
$194$	2.38452	−	0.301235i	0.171199	−	0.0216274i
$195$	13.0224	+	34.3372i	0.932556	+	2.45894i
$196$	−5.03336	−	4.72664i	−0.359526	−	0.337617i
$197$	1.62900	+	0.766551i	0.116062	+	0.0546145i	0.482934	−	0.875657i	$-0.339571\pi$
$197$	1.62900	+	0.766551i	0.116062	+	0.0546145i	−0.366872	+	0.930271i	$0.619571\pi$
$198$	−16.9981	−	14.0620i	−1.20800	−	0.999344i
$199$	0.744043	−	2.28993i	0.0527438	−	0.162329i	−0.921215	−	0.389054i	$-0.872802\pi$
$199$	0.744043	−	2.28993i	0.0527438	−	0.162329i	0.973959	+	0.226725i	$0.0728019\pi$
$200$	1.70507	+	4.70029i	0.120566	+	0.332361i
$201$	−9.01277	−	27.7385i	−0.635712	−	1.95652i
$202$	−5.59036	+	14.1196i	−0.393336	+	0.993454i
$203$	1.96575	−	2.09331i	0.137969	−	0.146922i
$204$	0.400367	+	2.09879i	0.0280313	+	0.146945i
$205$	2.19789	−	15.5782i	0.153507	−	1.08803i
$206$	0.393849	−	0.369849i	0.0274408	−	0.0257686i
$207$	−17.3453	+	5.63584i	−1.20558	+	0.391718i
$208$	6.25894	+	1.19396i	0.433979	+	0.0827860i
$209$	1.02738	+	16.3297i	0.0710651	+	1.12955i
$210$	−1.64400	−	0.678640i	−0.113447	−	0.0468306i
$211$	−3.74480	−	5.90086i	−0.257803	−	0.406232i	0.690631	−	0.723207i	$-0.257333\pi$
$211$	−3.74480	−	5.90086i	−0.257803	−	0.406232i	−0.948434	+	0.316975i	$0.897333\pi$
$212$	−0.0644716	+	0.00405621i	−0.00442792	+	0.000278581i
$213$	−2.84872	−	1.80785i	−0.195191	−	0.123872i
$214$	−7.17157	+	8.66894i	−0.490238	+	0.592596i
$215$	−2.70325	+	0.301752i	−0.184360	+	0.0205793i
$216$	−1.60653	−	0.412488i	−0.109311	−	0.0280662i
$217$	−1.98211	+	0.932711i	−0.134554	+	0.0633165i
$218$	−0.0967817	−	0.0314463i	−0.00655488	−	0.00212981i
$219$	6.12040	+	3.36472i	0.413579	+	0.227367i
$220$	11.5353	−	7.08803i	0.777708	−	0.477875i
$221$	−5.24031	−	0.662005i	−0.352501	−	0.0445313i
$222$	−0.898666	+	7.11368i	−0.0603145	+	0.477439i
$223$	8.97201	−	5.69381i	0.600811	−	0.381286i	−0.200360	−	0.979722i	$-0.564211\pi$
$223$	8.97201	−	5.69381i	0.600811	−	0.381286i	0.801170	+	0.598436i	$0.204211\pi$
$224$	−0.249657	+	0.181387i	−0.0166809	+	0.0121194i
$225$	18.2099	+	0.528176i	1.21399	+	0.0352117i
$226$	0.201916	+	0.146700i	0.0134312	+	0.00975836i
$227$	−7.93566	−	0.499270i	−0.526709	−	0.0331377i	−0.202789	−	0.979222i	$-0.565001\pi$
$227$	−7.93566	−	0.499270i	−0.526709	−	0.0331377i	−0.323919	+	0.946085i	$0.605001\pi$
$228$	3.35552	+	6.10367i	0.222225	+	0.404225i
$229$	−10.0306	+	21.3162i	−0.662843	+	1.40861i	0.236614	+	0.971604i	$0.423962\pi$
$229$	−10.0306	+	21.3162i	−0.662843	+	1.40861i	−0.899457	+	0.437009i	$0.856038\pi$
$230$	0.162273	−	11.1917i	0.0107000	−	0.737959i
$231$	−0.902425	+	4.73068i	−0.0593752	+	0.311256i
$232$	5.46963	+	7.52830i	0.359099	+	0.494257i
$233$	0.814755	−	1.48203i	0.0533764	−	0.0970913i	−0.848273	−	0.529560i	$-0.822357\pi$
$233$	0.814755	−	1.48203i	0.0533764	−	0.0970913i	0.901649	+	0.432468i	$0.142357\pi$
$234$	12.4396	−	19.6017i	0.813202	−	1.28140i
$235$	−15.4185	+	10.8642i	−1.00579	+	0.708700i
$236$	−3.34048	−	1.32259i	−0.217447	−	0.0860933i
$237$	1.12069	+	2.83054i	0.0727965	+	0.183863i
$238$	0.197106	−	0.163060i	0.0127765	−	0.0105696i
$239$	−27.9158	+	7.16755i	−1.80572	+	0.463630i	−0.992907	−	0.118894i	$-0.962065\pi$
$239$	−27.9158	+	7.16755i	−1.80572	+	0.463630i	−0.812813	+	0.582524i	$0.802065\pi$
$240$	3.15845	−	4.82097i	0.203877	−	0.311192i
$241$	−6.43087	+	2.54616i	−0.414249	+	0.164013i	−0.565999	−	0.824406i	$-0.691509\pi$
$241$	−6.43087	+	2.54616i	−0.414249	+	0.164013i	0.151750	+	0.988419i	$0.451509\pi$
$242$	−17.5659	−	18.7057i	−1.12918	−	1.20245i
$243$	13.0078	−	17.9037i	0.834449	−	1.14852i
$244$	−3.13243	−	6.65675i	−0.200533	−	0.426155i
$245$	−1.71281	−	15.3442i	−0.109427	−	0.980307i
$246$	−15.8916	+	8.73647i	−1.01321	+	0.557017i
$247$	−16.9136	+	3.22645i	−1.07619	+	0.205294i
$248$	−1.76536	−	6.87564i	−0.112101	−	0.436603i
$249$	−38.9097			−2.46580
$250$	−3.91399	+	10.4729i	−0.247543	+	0.662361i
$251$	−16.6630			−1.05176			−0.525879	−	0.850559i	$-0.676264\pi$
$251$	−16.6630			−1.05176			−0.525879	+	0.850559i	$0.676264\pi$
$252$	0.279618	+	1.08904i	0.0176142	+	0.0686030i
$253$	−29.7711	+	5.67914i	−1.87169	+	0.357044i
$254$	−2.95578	+	1.62495i	−0.185462	+	0.101959i
$255$	−2.36212	+	4.15290i	−0.147922	+	0.260065i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	5.81728	−	8.00680i	0.362872	−	0.499450i	−0.588074	−	0.808807i	$-0.700114\pi$
$257$	5.81728	−	8.00680i	0.362872	−	0.499450i	0.950946	+	0.309357i	$0.100114\pi$
$258$	2.14631	+	2.28559i	0.133623	+	0.142294i
$259$	0.798176	−	0.316020i	0.0495962	−	0.0196365i
$260$	8.92176	+	11.1086i	0.553304	+	0.688927i
$261$	32.8394	−	8.43173i	2.03271	−	0.521911i
$262$	−7.00827	+	5.79774i	−0.432972	+	0.358186i
$263$	−3.10912	−	7.85274i	−0.191717	−	0.484221i	0.801843	−	0.597535i	$-0.203853\pi$
$263$	−3.10912	−	7.85274i	−0.191717	−	0.484221i	−0.993559	+	0.113315i	$0.963853\pi$
$264$	−14.5103	−	5.74504i	−0.893048	−	0.353583i
$265$	−0.115618	−	0.0865896i	−0.00710233	−	0.00531916i
$266$	0.446835	−	0.704099i	0.0273972	−	0.0431711i
$267$	−8.06106	+	14.6630i	−0.493329	+	0.897362i
$268$	−6.65114	−	9.15451i	−0.406283	−	0.559201i
$269$	3.66587	−	19.2171i	0.223512	−	1.17169i	−0.676707	−	0.736252i	$-0.736594\pi$
$269$	3.66587	−	19.2171i	0.223512	−	1.17169i	0.900219	−	0.435438i	$-0.143406\pi$
$270$	−2.13627	−	3.03180i	−0.130009	−	0.184510i
$271$	10.8170	−	22.9872i	0.657084	−	1.39638i	−0.246997	−	0.969016i	$-0.579444\pi$
$271$	10.8170	−	22.9872i	0.657084	−	1.39638i	0.904082	−	0.427359i	$-0.140556\pi$
$272$	0.399354	+	0.726422i	0.0242144	+	0.0440458i
$273$	−5.05813	−	0.318230i	−0.306132	−	0.0192602i
$274$	−3.87868	−	2.81802i	−0.234320	−	0.170243i
$275$	29.9126	+	4.66354i	1.80380	+	0.281222i
$276$	−10.4379	+	7.58358i	−0.628288	+	0.456478i
$277$	19.1917	−	12.1794i	1.15312	−	0.731792i	0.185113	−	0.982717i	$-0.440735\pi$
$277$	19.1917	−	12.1794i	1.15312	−	0.731792i	0.968006	+	0.250925i	$0.0807349\pi$
$278$	0.0519433	−	0.411174i	0.00311535	−	0.0246606i
$279$	−25.6601	−	3.24162i	−1.53623	−	0.194071i
$280$	−0.687973	−	0.0533074i	−0.0411143	−	0.00318573i
$281$	10.6806	+	5.87169i	0.637149	+	0.350276i	0.767365	−	0.641210i	$-0.221567\pi$
$281$	10.6806	+	5.87169i	0.637149	+	0.350276i	−0.130217	+	0.991486i	$0.541567\pi$
$282$	20.6775	+	6.71853i	1.23133	+	0.400083i
$283$	19.3176	−	9.09018i	1.14831	−	0.540355i	0.245079	−	0.969503i	$-0.421186\pi$
$283$	19.3176	−	9.09018i	1.14831	−	0.540355i	0.903234	+	0.429148i	$0.141186\pi$
$284$	−1.26788	−	0.325535i	−0.0752346	−	0.0193170i
$285$	−3.13990	+	15.2549i	−0.185992	+	0.903623i
$286$	24.5918	−	29.7264i	1.45414	−	1.75776i
$287$	1.83320	+	1.16338i	0.108210	+	0.0686724i
$288$	−3.63632	+	0.228778i	−0.214272	+	0.0134809i
$289$	8.74085	+	13.7734i	0.514168	+	0.810199i
$290$	−1.60746	+	20.7455i	−0.0943933	+	1.21822i
$291$	−0.388985	−	6.18273i	−0.0228027	−	0.362438i
$292$	2.66173	+	0.507752i	0.155766	+	0.0297139i
$293$	−18.3499	+	5.96223i	−1.07201	+	0.348317i	−0.791270	−	0.611466i	$-0.790580\pi$
$293$	−18.3499	+	5.96223i	−1.07201	+	0.348317i	−0.280740	+	0.959784i	$0.590580\pi$
$294$	−12.9735	+	12.1829i	−0.756629	+	0.710522i
$295$	−3.76779	−	7.09536i	−0.219369	−	0.413108i
$296$	0.521267	+	2.73257i	0.0302980	+	0.158828i
$297$	−6.87473	+	7.32084i	−0.398912	+	0.424798i
$298$	−5.34027	+	13.4880i	−0.309353	+	0.781338i
$299$	−9.85602	−	30.3337i	−0.569988	−	1.75424i
$300$	12.3671	−	3.62543i	0.714012	−	0.209314i
$301$	0.116000	−	0.357012i	0.00668614	−	0.0205778i
$302$	9.84138	+	8.14150i	0.566308	+	0.468491i
$303$	35.4168	+	16.6659i	2.03464	+	0.957430i
$304$	1.96990	+	1.84986i	0.112982	+	0.106097i
$305$	4.32167	−	15.8728i	0.247458	−	0.908873i
$306$	2.99650	−	0.378546i	0.171299	−	0.0216400i
$307$			30.0172i			1.71317i	0.516005	+	0.856586i	$0.327419\pi$
$307$			30.0172i			1.71317i	−0.516005	+	0.856586i	$0.672581\pi$
$308$	0.234181	+	1.85374i	0.0133437	+	0.105626i
$309$	−0.887663	−	1.07300i	−0.0504974	−	0.0610408i
$310$	6.96594	−	14.2629i	0.395639	−	0.810078i
$311$	−0.616908	+	9.80547i	−0.0349816	+	0.556017i	0.941033	+	0.338314i	$0.109857\pi$
$311$	−0.616908	+	9.80547i	−0.0349816	+	0.556017i	−0.976015	+	0.217703i	$0.930143\pi$
$312$	4.08431	−	15.9074i	0.231229	−	0.900577i
$313$	5.96668	−	23.2387i	0.337257	−	1.31353i	−0.543281	−	0.839551i	$-0.682818\pi$
$313$	5.96668	−	23.2387i	0.337257	−	1.31353i	0.880537	−	0.473977i	$-0.157182\pi$
$314$	0.565026	−	8.98083i	0.0318863	−	0.506818i
$315$	−1.10334	+	2.25911i	−0.0621663	+	0.127287i
$316$	0.752869	+	0.910063i	0.0423522	+	0.0511950i
$317$	2.70475	+	21.4103i	0.151914	+	1.20252i	0.865118	+	0.501568i	$0.167243\pi$
$317$	2.70475	+	21.4103i	0.151914	+	1.20252i	−0.713204	+	0.700956i	$0.752757\pi$
$318$			0.166504i			0.00933708i
$319$	55.8985	−	7.06163i	3.12972	−	0.395375i
$320$	0.587429	−	2.15753i	0.0328383	−	0.120609i
$321$	21.1394	+	19.8512i	1.17989	+	1.10799i
$322$	1.39768	+	0.657700i	0.0778899	+	0.0366522i
$323$	−1.72603	−	1.42790i	−0.0960390	−	0.0794504i
$324$	2.05662	−	6.32964i	0.114257	−	0.351646i
$325$	−0.923678	+	31.8456i	−0.0512365	+	1.76648i
$326$	2.89590	+	8.91265i	0.160389	+	0.493626i
$327$	−0.0965563	+	0.243873i	−0.00533957	+	0.0134862i
$328$	−4.81632	+	5.12887i	−0.265937	+	0.283194i
$329$	−0.487760	−	2.55693i	−0.0268911	−	0.140968i
$330$	−16.3665	−	30.8207i	−0.900944	−	1.69662i
$331$	−4.29711	+	4.03526i	−0.236191	+	0.221798i	−0.793600	−	0.608440i	$-0.791796\pi$
$331$	−4.29711	+	4.03526i	−0.236191	+	0.221798i	0.557409	+	0.830238i	$0.311796\pi$
$332$	−14.3570	+	4.66489i	−0.787945	+	0.256019i
$333$	9.95616	+	1.89924i	0.545594	+	0.104078i
$334$	−0.438119	−	6.96370i	−0.0239728	−	0.381037i
$335$	1.95469	−	25.2268i	0.106796	−	1.37829i
$336$	0.426196	+	0.671578i	0.0232509	+	0.0366376i
$337$	5.01169	−	0.315309i	0.273004	−	0.0171760i	0.0743016	−	0.997236i	$-0.476327\pi$
$337$	5.01169	−	0.315309i	0.273004	−	0.0171760i	0.198702	+	0.980060i	$0.436327\pi$
$338$	23.3033	+	14.7887i	1.26753	+	0.804402i
$339$	0.410053	−	0.495669i	0.0222710	−	0.0269210i
$340$	−0.373692	+	1.81555i	−0.0202663	+	0.0984619i
$341$	−41.6306	−	10.6889i	−2.25442	−	0.578837i
$342$	8.90884	−	4.19218i	0.481735	−	0.226687i
$343$	4.08091	+	1.32597i	0.220348	+	0.0715955i
$344$	1.06597	+	0.586023i	0.0574734	+	0.0315963i
$345$	−28.7634	−	2.22873i	−1.54857	−	0.119991i
$346$	16.2780	+	2.05640i	0.875113	+	0.110552i
$347$	2.42226	−	19.1741i	0.130034	−	1.02932i	−0.783167	−	0.621812i	$-0.786397\pi$
$347$	2.42226	−	19.1741i	0.130034	−	1.02932i	0.913201	−	0.407511i	$-0.133603\pi$
$348$	20.2511	−	12.8517i	1.08557	−	0.688926i
$349$	22.5540	−	16.3865i	1.20729	−	0.877147i	0.212307	−	0.977203i	$-0.431902\pi$
$349$	22.5540	−	16.3865i	1.20729	−	0.877147i	0.994982	+	0.100056i	$0.0319023\pi$
$350$	−1.09368	−	1.08840i	−0.0584596	−	0.0581774i
$351$	−8.55013	−	6.21203i	−0.456372	−	0.331574i
$352$	−6.04285	−	0.380184i	−0.322085	−	0.0202639i
$353$	7.35695	+	13.3822i	0.391571	+	0.712265i	0.996462	−	0.0840435i	$-0.0267835\pi$
$353$	7.35695	+	13.3822i	0.391571	+	0.712265i	−0.604891	+	0.796308i	$0.706783\pi$
$354$	−3.94288	+	8.37905i	−0.209562	+	0.445342i
$355$	−1.68595	−	2.39270i	−0.0894807	−	0.126991i
$356$	−1.21645	+	6.37686i	−0.0644718	+	0.337973i
$357$	−0.387558	−	0.533428i	−0.0205117	−	0.0282320i
$358$	11.6912	−	21.2662i	0.617899	−	1.12395i
$359$	−6.41834	+	10.1137i	−0.338747	+	0.533780i	−0.970410	−	0.241463i	$-0.922373\pi$
$359$	−6.41834	+	10.1137i	−0.338747	+	0.533780i	0.631663	+	0.775243i	$0.282373\pi$
$360$	−6.52105	−	4.88382i	−0.343689	−	0.257400i
$361$	10.8761	+	4.30613i	0.572424	+	0.226639i
$362$	−3.02356	−	7.63663i	−0.158915	−	0.401372i
$363$	−50.9618	+	42.1593i	−2.67480	+	2.21279i
$364$	−1.90452	+	0.488998i	−0.0998240	+	0.0256304i
$365$	3.79414	+	4.72414i	0.198595	+	0.247273i
$366$	−17.6309	+	6.98056i	−0.921581	+	0.364880i
$367$	7.23431	+	7.70376i	0.377628	+	0.402133i	0.889505	−	0.456926i	$-0.151050\pi$
$367$	7.23431	+	7.70376i	0.377628	+	0.402133i	−0.511877	+	0.859059i	$0.671050\pi$
$368$	−2.94222	+	4.04962i	−0.153374	+	0.211101i
$369$	10.9148	+	23.1952i	0.568203	+	1.20749i
$370$	−3.07541	+	5.40696i	−0.159883	+	0.281095i
$371$	0.0174690	−	0.00960368i	0.000906946	−	0.000498598i
$372$	−17.9727	+	3.42848i	−0.931841	+	0.177758i
$373$	7.93403	+	30.9010i	0.410808	+	1.59999i	0.751443	+	0.659797i	$0.229358\pi$
$373$	7.93403	+	30.9010i	0.410808	+	1.59999i	−0.340635	+	0.940196i	$0.610642\pi$
$374$	5.01917			0.259535
$375$	26.3071	+	11.7634i	1.35849	+	0.607457i
$376$	8.43516			0.435010
$377$	14.7455	+	57.4299i	0.759432	+	2.95779i
$378$	0.502780	−	0.0959104i	0.0258602	−	0.00493310i
$379$	5.11671	−	2.81294i	0.262828	−	0.144491i	−0.344892	−	0.938642i	$-0.612084\pi$
$379$	5.11671	−	2.81294i	0.262828	−	0.144491i	0.607720	+	0.794152i	$0.292084\pi$
$380$	0.670341	+	6.00526i	0.0343877	+	0.308063i
$381$	3.70168	+	7.86647i	0.189643	+	0.403012i
$382$	1.88063	−	2.58847i	0.0962216	−	0.132438i
$383$	−21.4901	−	22.8846i	−1.09809	−	1.16935i	−0.984420	−	0.175831i	$-0.943739\pi$
$383$	−21.4901	−	22.8846i	−1.09809	−	1.16935i	−0.113671	−	0.993518i	$-0.536261\pi$
$384$	−2.39650	+	0.948841i	−0.122296	+	0.0484203i
$385$	−2.28961	+	3.49480i	−0.116689	+	0.178111i
$386$	−16.1309	+	4.14171i	−0.821041	+	0.210808i
$387$	3.41499	−	2.82513i	0.173594	−	0.143609i
$388$	−0.884778	−	2.23469i	−0.0449178	−	0.113449i
$389$	−13.8915	−	5.50003i	−0.704327	−	0.278863i	−0.0114662	−	0.999934i	$-0.503650\pi$
$389$	−13.8915	−	5.50003i	−0.704327	−	0.278863i	−0.692861	+	0.721072i	$0.743650\pi$
$390$	30.0199	−	21.1526i	1.52012	−	1.07110i
$391$	2.22338	−	3.50349i	0.112441	−	0.177179i
$392$	−3.32640	+	6.05070i	−0.168008	+	0.305606i
$393$	13.7800	+	18.9665i	0.695107	+	0.956733i
$394$	0.337352	−	1.76846i	0.0169955	−	0.0890937i
$395$	−0.0382896	+	2.64077i	−0.00192656	+	0.132872i
$396$	−9.39299	+	19.9611i	−0.472015	+	1.00308i
$397$	−7.97449	−	14.5055i	−0.400228	−	0.728012i	0.597014	−	0.802231i	$-0.296354\pi$
$397$	−7.97449	−	14.5055i	−0.400228	−	0.728012i	−0.997242	+	0.0742188i	$0.976354\pi$
$398$	−2.40302	−	0.151185i	−0.120453	−	0.00757824i
$399$	−1.73892	−	1.26340i	−0.0870547	−	0.0632490i
$400$	4.12859	−	2.82041i	0.206430	−	0.141021i
$401$	22.3555	−	16.2423i	1.11638	−	0.811099i	0.132726	−	0.991153i	$-0.457627\pi$
$401$	22.3555	−	16.2423i	1.11638	−	0.811099i	0.983657	+	0.180053i	$0.0576271\pi$
$402$	−24.6256	+	15.6279i	−1.22821	+	0.779449i
$403$	5.66897	−	44.8746i	0.282392	−	2.23536i
$404$	15.0663	+	1.90332i	0.749577	+	0.0946936i
$405$	12.6795	−	7.79110i	0.630047	−	0.387143i
$406$	−2.51641	−	1.38341i	−0.124887	−	0.0686574i
$407$	16.0191	+	5.20494i	0.794040	+	0.257999i
$408$	1.93329	−	0.909737i	0.0957121	−	0.0450387i
$409$	12.1260	+	3.11342i	0.599591	+	0.153949i	0.536273	−	0.844044i	$-0.319832\pi$
$409$	12.1260	+	3.11342i	0.599591	+	0.153949i	0.0633183	+	0.997993i	$0.479832\pi$
$410$	−15.6354	+	1.74531i	−0.772176	+	0.0861946i
$411$	−7.87686	+	9.52149i	−0.388537	+	0.469660i
$412$	−0.456176	−	0.289498i	−0.0224742	−	0.0142625i
$413$	1.10652	−	0.0696163i	0.0544483	−	0.00342560i
$414$	9.77239	+	15.3988i	0.480287	+	0.756811i
$415$	−31.2016	−	12.8799i	−1.53162	−	0.632250i
$416$	−0.400089	−	6.35923i	−0.0196160	−	0.311787i
$417$	−1.04930	−	0.200165i	−0.0513846	−	0.00980213i
$418$	15.5612	−	5.05613i	0.761121	−	0.247303i
$419$	−17.0013	+	15.9652i	−0.830566	+	0.779953i	−0.977887	−	0.209136i	$-0.932935\pi$
$419$	−17.0013	+	15.9652i	−0.830566	+	0.779953i	0.147321	+	0.989089i	$0.452935\pi$
$420$	−0.248472	+	1.76113i	−0.0121242	+	0.0859341i
$421$	−4.70929	−	24.6870i	−0.229517	−	1.20317i	−0.891279	−	0.453455i	$-0.850191\pi$
$421$	−4.70929	−	24.6870i	−0.229517	−	1.20317i	0.661762	−	0.749714i	$-0.269809\pi$
$422$	−4.78418	+	5.09464i	−0.232890	+	0.248003i
$423$	11.3138	−	28.5754i	0.550095	−	1.38938i
$424$	0.0199622	+	0.0614373i	0.000969450	+	0.00298366i
$425$	−3.26887	+	2.54829i	−0.158564	+	0.123610i
$426$	−1.04261	+	3.20882i	−0.0505145	+	0.155468i
$427$	1.74930	+	1.44714i	0.0846544	+	0.0700322i
$428$	10.1801	+	4.79038i	0.492073	+	0.231552i
$429$	−72.4885	−	68.0713i	−3.49978	−	3.28651i
$430$	0.964542	+	2.54328i	0.0465143	+	0.122648i
$431$	−20.5070	+	2.59063i	−0.987786	+	0.124786i	−0.602592	−	0.798049i	$-0.705865\pi$
$431$	−20.5070	+	2.59063i	−0.987786	+	0.124786i	−0.385194	+	0.922836i	$0.625865\pi$
$432$			1.65864i			0.0798015i
$433$	−3.79678	−	30.0546i	−0.182462	−	1.44433i	−0.771500	−	0.636229i	$-0.780493\pi$
$433$	−3.79678	−	30.0546i	−0.182462	−	1.44433i	0.589038	−	0.808105i	$-0.299507\pi$
$434$	1.39634	+	1.68788i	0.0670264	+	0.0810210i
$435$	53.1059	+	7.49256i	2.54623	+	0.359241i
$436$	−0.00638971	+	0.101561i	−0.000306011	+	0.00486391i
$437$	3.36396	−	13.1018i	0.160920	−	0.626742i
$438$	1.73693	−	6.76489i	0.0829937	−	0.323239i
$439$	−0.421128	+	6.69364i	−0.0200993	+	0.319470i	0.975111	+	0.221716i	$0.0711658\pi$
$439$	−0.421128	+	6.69364i	−0.0200993	+	0.319470i	−0.995211	+	0.0977539i	$0.968834\pi$
$440$	−9.73405	−	9.41015i	−0.464053	−	0.448611i
$441$	16.0360	+	19.3843i	0.763621	+	0.923060i
$442$	0.662005	+	5.24031i	0.0314884	+	0.249256i
$443$			14.7027i			0.698545i	0.937021	+	0.349272i	$0.113571\pi$
$443$			14.7027i			0.698545i	−0.937021	+	0.349272i	$0.886429\pi$
$444$	7.11368	−	0.898666i	0.337600	−	0.0426488i
$445$	−11.3179	+	9.08986i	−0.536521	+	0.430901i
$446$	−7.74618	−	7.27415i	−0.366792	−	0.344441i
$447$	33.8324	+	15.9203i	1.60022	+	0.753005i
$448$	0.237775	+	0.196705i	0.0112338	+	0.00929343i
$449$	8.72202	−	26.8436i	0.411618	−	1.26683i	−0.503624	−	0.863923i	$-0.668000\pi$
$449$	8.72202	−	26.8436i	0.411618	−	1.26683i	0.915242	−	0.402906i	$-0.132000\pi$
$450$	−4.01703	−	17.7691i	−0.189365	−	0.837645i
$451$	13.1642	+	40.5152i	0.619878	+	1.90779i
$452$	0.0918771	−	0.232055i	0.00432154	−	0.0109150i
$453$	22.5361	−	23.9985i	1.05884	−	1.12755i
$454$	1.48994	+	7.81051i	0.0699261	+	0.366566i
$455$	−3.95076	−	1.92953i	−0.185214	−	0.0904580i
$456$	5.07743	−	4.76802i	0.237772	−	0.223283i
$457$	8.94388	−	2.90604i	0.418377	−	0.135939i	−0.0922607	−	0.995735i	$-0.529409\pi$
$457$	8.94388	−	2.90604i	0.418377	−	0.135939i	0.510638	+	0.859796i	$0.329409\pi$
$458$	23.1410	+	4.41438i	1.08131	+	0.206271i
$459$	−0.0863336	−	1.37223i	−0.00402971	−	0.0640503i
$460$	−10.8804	+	2.62609i	−0.507304	+	0.122442i
$461$	−17.4924	−	27.5636i	−0.814701	−	1.28376i	−0.955874	−	0.293778i	$-0.905087\pi$
$461$	−17.4924	−	27.5636i	−0.814701	−	1.28376i	0.141173	−	0.989985i	$-0.454913\pi$
$462$	4.80648	−	0.302398i	0.223618	−	0.0140688i
$463$	−24.1392	−	15.3192i	−1.12184	−	0.711944i	−0.160430	−	0.987047i	$-0.551288\pi$
$463$	−24.1392	−	15.3192i	−1.12184	−	0.711944i	−0.961415	+	0.275103i	$0.911288\pi$
$464$	5.93154	−	7.17000i	0.275365	−	0.332859i
$465$	−35.5627	−	20.2276i	−1.64918	−	0.938034i
$466$	−1.63809	−	0.420591i	−0.0758833	−	0.0194835i
$467$	−4.60810	+	2.16841i	−0.213237	+	0.100342i	−0.529432	−	0.848353i	$-0.677595\pi$
$467$	−4.60810	+	2.16841i	−0.213237	+	0.100342i	0.316194	+	0.948694i	$0.397595\pi$
$468$	−22.0795	−	7.17405i	−1.02062	−	0.331621i
$469$	3.05999	+	1.68224i	0.141297	+	0.0776788i
$470$	14.3573	+	12.2323i	0.662252	+	0.564232i
$471$	−23.0110	−	2.90696i	−1.06029	−	0.133946i
$472$	−0.450295	+	3.56445i	−0.0207265	+	0.164067i
$473$	6.21871	−	3.94652i	0.285937	−	0.181461i
$474$	2.46290	−	1.78941i	0.113125	−	0.0821901i
$475$	−7.56758	+	11.1935i	−0.347224	+	0.513593i
$476$	−0.206955	−	0.150362i	−0.00948579	−	0.00689183i
$477$	0.234903	+	0.0147788i	0.0107555	+	0.000676676i
$478$	13.8847	+	25.2562i	0.635073	+	1.15519i
$479$	−1.73336	+	3.68359i	−0.0791994	+	0.168307i	−0.940505	−	0.339780i	$-0.889647\pi$
$479$	−1.73336	+	3.68359i	−0.0791994	+	0.168307i	0.861305	+	0.508087i	$0.169647\pi$
$480$	−5.45499	−	1.86029i	−0.248985	−	0.0849102i
$481$	−3.32141	+	17.4114i	−0.151443	+	0.793893i
$482$	4.06546	+	5.59563i	0.185177	+	0.254874i
$483$	1.91808	−	3.48898i	0.0872757	−	0.158754i
$484$	−13.7496	+	21.6659i	−0.624982	+	0.984815i
$485$	1.73469	−	5.08668i	0.0787682	−	0.230974i
$486$	−20.5761	−	8.14665i	−0.933351	−	0.369540i
$487$	−3.22572	−	8.14725i	−0.146171	−	0.369187i	0.838182	−	0.545390i	$-0.183618\pi$
$487$	−3.22572	−	8.14725i	−0.146171	−	0.369187i	−0.984354	+	0.176203i	$0.943618\pi$
$488$	−5.66861	+	4.68948i	−0.256606	+	0.212283i
$489$	23.3957	−	6.00700i	1.05799	−	0.271646i
$490$	−14.4362	+	5.47495i	−0.652161	+	0.247333i
$491$	35.0274	−	13.8683i	1.58077	−	0.625870i	0.596509	−	0.802607i	$-0.296554\pi$
$491$	35.0274	−	13.8683i	1.58077	−	0.625870i	0.984258	+	0.176737i	$0.0565542\pi$
$492$	12.4141	+	13.2197i	0.559670	+	0.595988i
$493$	−4.53409	+	6.24064i	−0.204205	+	0.281064i
$494$	7.33133	+	15.5799i	0.329852	+	0.700972i
$495$	−44.9342	+	20.3540i	−2.01964	+	0.914846i
$496$	−6.22060	+	3.41980i	−0.279313	+	0.153554i
$497$	0.396794	−	0.0756925i	0.0177986	−	0.00339527i
$498$	9.67644	+	37.6873i	0.433612	+	1.68881i
$499$	7.65035			0.342477			0.171238	−	0.985230i	$-0.445223\pi$
$499$	7.65035			0.342477			0.171238	+	0.985230i	$0.445223\pi$
$500$	11.1172	+	1.18653i	0.497176	+	0.0530634i
$501$	−17.9844			−0.803485
$502$	4.14392	+	16.1395i	0.184952	+	0.720341i
$503$	−33.0108	+	6.29714i	−1.47188	+	0.280775i	−0.860047	−	0.510214i	$-0.829566\pi$
$503$	−33.0108	+	6.29714i	−1.47188	+	0.280775i	−0.611829	+	0.790990i	$0.709566\pi$
$504$	0.985286	−	0.541666i	0.0438881	−	0.0241277i
$505$	22.8839	+	25.0880i	1.01832	+	1.11640i
$506$	12.9045	+	27.4234i	0.573674	+	1.21912i
$507$	41.8142	−	57.5524i	1.85704	−	2.55599i
$508$	2.30897	+	2.45881i	0.102444	+	0.109092i
$509$	−15.4703	+	6.12511i	−0.685707	+	0.271491i	−0.685036	−	0.728509i	$-0.740214\pi$
$509$	−15.4703	+	6.12511i	−0.685707	+	0.271491i	−0.000671050		1.00000i	$0.500214\pi$
$510$	4.60986	+	1.25512i	0.204128	+	0.0555778i
$511$	−0.809932	+	0.207955i	−0.0358293	+	0.00919940i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	−1.65000	−	4.16742i	−0.0728492	−	0.183996i
$514$	−9.20195	−	3.64331i	−0.405881	−	0.160700i
$515$	−0.356629	−	1.15427i	−0.0157150	−	0.0508633i
$516$	1.68001	−	2.64728i	0.0739585	−	0.116540i
$517$	24.6047	−	44.7558i	1.08211	−	1.96836i
$518$	−0.504590	−	0.694509i	−0.0221704	−	0.0305150i
$519$	7.92438	−	41.5411i	0.347842	−	1.82345i
$520$	8.54087	−	11.4041i	0.374542	−	0.500102i
$521$	10.8698	−	23.0994i	0.476212	−	1.01200i	−0.512010	−	0.858979i	$-0.671099\pi$
$521$	10.8698	−	23.0994i	0.476212	−	1.01200i	0.988223	−	0.153024i	$-0.0489010\pi$
$522$	−16.3337	−	29.7108i	−0.714905	−	1.30041i
$523$	−4.06989	−	0.256056i	−0.177964	−	0.0111965i	−0.0264414	−	0.999650i	$-0.508418\pi$
$523$	−4.06989	−	0.256056i	−0.177964	−	0.0111965i	−0.151522	+	0.988454i	$0.548418\pi$
$524$	7.35848	+	5.34625i	0.321457	+	0.233552i
$525$	−2.97682	+	2.63724i	−0.129919	+	0.115099i
$526$	−6.83282	+	4.96434i	−0.297925	+	0.216455i
$527$	4.96844	−	3.15307i	0.216429	−	0.137350i
$528$	−1.95598	+	15.4832i	−0.0851231	+	0.673819i
$529$	2.03989	+	0.257698i	0.0886908	+	0.0112043i
$530$	−0.0551163	+	0.133519i	−0.00239410	+	0.00579970i
$531$	11.4711	+	6.30631i	0.497805	+	0.273671i
$532$	−0.793102	−	0.257694i	−0.0343853	−	0.0111725i
$533$	−40.5640	+	19.0879i	−1.75702	+	0.826791i
$534$	16.2071	+	4.16127i	0.701348	+	0.180076i
$535$	10.3805	+	22.9163i	0.448787	+	0.990756i
$536$	−7.21283	+	8.71882i	−0.311547	+	0.376596i
$537$	−52.8134	−	33.5164i	−2.27907	−	1.44634i
$538$	−19.5251	+	1.22841i	−0.841785	+	0.0529607i
$539$	22.4013	+	35.2988i	0.964892	+	1.52043i
$540$	−2.40528	+	2.82313i	−0.103507	+	0.121488i
$541$	−1.16487	−	18.5151i	−0.0500819	−	0.796028i	−0.940269	−	0.340433i	$-0.889426\pi$
$541$	−1.16487	−	18.5151i	−0.0500819	−	0.796028i	0.890187	−	0.455595i	$-0.150574\pi$
$542$	−24.9551	−	4.76045i	−1.07191	−	0.204479i
$543$	−20.1339	+	6.54191i	−0.864029	+	0.280740i
$544$	0.604285	−	0.567461i	0.0259085	−	0.0243297i
$545$	−0.158155	+	0.163599i	−0.00677463	+	0.00700782i
$546$	0.949672	+	4.97836i	0.0406422	+	0.213054i
$547$	7.65113	−	8.14763i	0.327139	−	0.348367i	−0.544283	−	0.838901i	$-0.683198\pi$
$547$	7.65113	−	8.14763i	0.327139	−	0.348367i	0.871422	+	0.490534i	$0.163198\pi$
$548$	−1.76490	+	4.45764i	−0.0753929	+	0.190421i
$549$	8.28321	+	25.4931i	0.353519	+	1.08802i
$550$	−2.92194	−	30.1326i	−0.124592	−	1.28486i
$551$	−7.77065	+	23.9156i	−0.331041	+	1.01884i
$552$	9.94113	+	8.22402i	0.423122	+	0.350037i
$553$	−0.329794	−	0.155189i	−0.0140243	−	0.00659933i
$554$	−16.5696	−	15.5599i	−0.703975	−	0.661076i
$555$	13.4112	+	8.78632i	0.569274	+	0.372958i
$556$	−0.411174	+	0.0519433i	−0.0174377	+	0.00220289i
$557$		−	26.5523i		−	1.12506i	−0.826778	−	0.562528i	$-0.809829\pi$
$557$		−	26.5523i		−	1.12506i	0.826778	−	0.562528i	$-0.190171\pi$
$558$	3.24162	+	25.6601i	0.137229	+	1.08628i
$559$	4.94061	+	5.97217i	0.208966	+	0.252596i
$560$	0.119459	+	0.679617i	0.00504808	+	0.0287190i
$561$	0.812316	−	12.9114i	0.0342960	−	0.545120i
$562$	3.03107	−	11.8052i	0.127858	−	0.497974i
$563$	0.602825	−	2.34785i	0.0254060	−	0.0989499i	−0.954616	−	0.297840i	$-0.903734\pi$
$563$	0.602825	−	2.34785i	0.0254060	−	0.0989499i	0.980022	+	0.198890i	$0.0637337\pi$
$564$	1.36517	−	21.6987i	0.0574840	−	0.913681i
$565$	0.492897	−	0.261739i	0.0207363	−	0.0110115i
$566$	−13.6087	−	16.4501i	−0.572016	−	0.691448i
$567$	0.257410	+	2.03761i	0.0108102	+	0.0855715i
$568$			1.30900i			0.0549245i
$569$	−22.2363	+	2.80909i	−0.932193	+	0.117763i	−0.576737	−	0.816930i	$-0.695674\pi$
$569$	−22.2363	+	2.80909i	−0.932193	+	0.117763i	−0.355456	+	0.934693i	$0.615674\pi$
$570$	15.5565	−	0.752486i	0.651591	−	0.0315182i
$571$	2.03394	+	1.90999i	0.0851176	+	0.0799307i	0.725938	−	0.687760i	$-0.241406\pi$
$571$	2.03394	+	1.90999i	0.0851176	+	0.0799307i	−0.640821	+	0.767691i	$0.721406\pi$
$572$	−34.9082	−	16.4265i	−1.45958	−	0.686828i
$573$	−6.35425	−	5.25669i	−0.265453	−	0.219602i
$574$	0.670936	−	2.06493i	0.0280043	−	0.0861885i
$575$	−22.3276	−	11.3085i	−0.931124	−	0.471597i
$576$	1.12591	+	3.46518i	0.0469127	+	0.144383i
$577$	−6.13850	+	15.5041i	−0.255549	+	0.645443i	−0.999746	−	0.0225164i	$-0.992832\pi$
$577$	−6.13850	+	15.5041i	−0.255549	+	0.645443i	0.744197	+	0.667960i	$0.232832\pi$
$578$	11.1669	−	11.8915i	0.464482	−	0.494623i
$579$	8.04353	+	42.1657i	0.334278	+	1.75234i
$580$	20.4935	−	3.60224i	0.850947	−	0.149575i
$581$	3.39589	−	3.18896i	0.140885	−	0.132300i
$582$	−5.89176	+	1.91435i	−0.244221	+	0.0793522i
$583$	0.384206	+	0.0732912i	0.0159122	+	0.00303541i
$584$	−0.170145	−	2.70438i	−0.00704065	−	0.111908i
$585$	−27.1774	−	44.2293i	−1.12365	−	1.82866i
$586$	10.3383	+	16.2906i	0.427073	+	0.672959i
$587$	−27.6838	+	1.74172i	−1.14263	+	0.0718885i	−0.622802	−	0.782380i	$-0.714006\pi$
$587$	−27.6838	+	1.74172i	−1.14263	+	0.0718885i	−0.519833	+	0.854268i	$0.674006\pi$
$588$	15.0265	+	9.53614i	0.619684	+	0.393264i
$589$	12.2276	−	14.7806i	0.503829	−	0.609024i
$590$	−5.93543	+	5.41396i	−0.244358	+	0.222889i
$591$	−4.49461	−	1.15402i	−0.184884	−	0.0474700i
$592$	2.51709	−	1.18445i	0.103452	−	0.0486807i
$593$	−0.0971166	−	0.0315551i	−0.00398810	−	0.00129581i	0.307022	−	0.951702i	$-0.400667\pi$
$593$	−0.0971166	−	0.0315551i	−0.00398810	−	0.00129581i	−0.311010	+	0.950407i	$0.600667\pi$
$594$	8.80052	+	4.83813i	0.361090	+	0.198511i
$595$	−0.134206	−	0.556044i	−0.00550191	−	0.0227956i
$596$	14.3923	+	1.81817i	0.589532	+	0.0744752i
$597$	−0.777823	+	6.15710i	−0.0318342	+	0.251993i
$598$	−26.9296	+	17.0901i	−1.10123	+	0.698864i
$599$	8.37580	−	6.08538i	0.342226	−	0.248642i	−0.403374	−	0.915035i	$-0.632163\pi$
$599$	8.37580	−	6.08538i	0.342226	−	0.248642i	0.745600	+	0.666393i	$0.232163\pi$
$600$	−6.58709	−	11.0769i	−0.268917	−	0.452213i
$601$	−0.421086	−	0.305937i	−0.0171764	−	0.0124794i	0.579164	−	0.815211i	$-0.303379\pi$
$601$	−0.421086	−	0.305937i	−0.0171764	−	0.0124794i	−0.596340	+	0.802732i	$0.703379\pi$
$602$	−0.374644	−	0.0235706i	−0.0152693	−	0.000960666i
$603$	19.8620	+	36.1288i	0.808842	+	1.47128i
$604$	5.43827	−	11.5569i	0.221280	−	0.470244i
$605$	−54.8217	+	16.9380i	−2.22882	+	0.688627i
$606$	7.33449	−	38.4487i	0.297943	−	1.56187i
$607$	−1.12192	−	1.54419i	−0.0455374	−	0.0626769i	0.785641	−	0.618683i	$-0.212333\pi$
$607$	−1.12192	−	1.54419i	−0.0455374	−	0.0626769i	−0.831179	+	0.556006i	$0.812333\pi$
$608$	1.30185	−	2.36806i	0.0527970	−	0.0960374i
$609$	−3.96596	+	6.24936i	−0.160709	+	0.253237i
$610$	−16.4489	−	0.238499i	−0.665995	−	0.00965653i
$611$	49.9729	+	19.7857i	2.02169	+	0.800442i
$612$	−1.11185	−	2.80822i	−0.0449440	−	0.113516i
$613$	−27.2770	+	22.5655i	−1.10171	+	0.911411i	−0.996546	−	0.0830443i	$-0.973536\pi$
$613$	−27.2770	+	22.5655i	−1.10171	+	0.911411i	−0.105161	+	0.994455i	$0.533536\pi$
$614$	29.0741	−	7.46497i	1.17334	−	0.301262i
$615$	1.95918	+	40.5031i	0.0790019	+	1.63324i
$616$	1.73726	−	0.687829i	0.0699962	−	0.0277134i
$617$	−16.0459	−	17.0872i	−0.645984	−	0.687903i	0.319731	−	0.947508i	$-0.396408\pi$
$617$	−16.0459	−	17.0872i	−0.645984	−	0.687903i	−0.965715	+	0.259605i	$0.916408\pi$
$618$	−0.818537	+	1.12662i	−0.0329264	+	0.0453193i
$619$	14.4932	+	30.7997i	0.582532	+	1.23794i	0.951255	+	0.308404i	$0.0997949\pi$
$619$	14.4932	+	30.7997i	0.582532	+	1.23794i	−0.368724	+	0.929539i	$0.620205\pi$
$620$	−15.5472	−	3.20005i	−0.624389	−	0.128517i
$621$	7.27555	−	3.99977i	0.291958	−	0.160505i
$622$	9.65083	−	1.84100i	0.386963	−	0.0738172i
$623$	−0.498211	−	1.94040i	−0.0199604	−	0.0777406i
$624$	−16.4233			−0.657459
$625$	17.2017	+	18.1412i	0.688066	+	0.725648i
$626$	−23.9924			−0.958931
$627$	−10.4880	−	40.8480i	−0.418850	−	1.63131i
$628$	−8.83920	+	1.68617i	−0.352722	+	0.0672854i
$629$	−2.02080	+	1.11094i	−0.0805744	+	0.0442962i
$630$	2.46253	+	0.506860i	0.0981095	+	0.0201938i
$631$	8.62068	+	18.3199i	0.343184	+	0.729303i	0.999687	−	0.0250205i	$-0.00796511\pi$
$631$	8.62068	+	18.3199i	0.343184	+	0.729303i	−0.656503	+	0.754323i	$0.727965\pi$
$632$	0.694240	−	0.955540i	0.0276154	−	0.0380093i
$633$	12.3312	+	13.1314i	0.490122	+	0.521927i
$634$	20.0650	−	7.94431i	0.796885	−	0.315509i
$635$	0.364401	+	7.53344i	0.0144608	+	0.298955i
$636$	0.161273	−	0.0414079i	0.00639489	−	0.00164193i
$637$	−33.8994	+	28.0440i	−1.34314	+	1.11114i
$638$	−20.7412	−	52.3862i	−0.821151	−	2.07399i
$639$	4.43444	+	1.75572i	0.175424	+	0.0694551i
$640$	−2.23583	−	0.0324182i	−0.0883791	−	0.00128144i
$641$	−2.52240	+	3.97467i	−0.0996290	+	0.156990i	−0.890486	−	0.455011i	$-0.849635\pi$
$641$	−2.52240	+	3.97467i	−0.0996290	+	0.156990i	0.790857	+	0.612001i	$0.209635\pi$
$642$	13.9704	−	25.4121i	0.551368	−	1.00294i
$643$	−7.30462	−	10.0539i	−0.288066	−	0.396489i	0.640319	−	0.768109i	$-0.278802\pi$
$643$	−7.30462	−	10.0539i	−0.288066	−	0.396489i	−0.928385	+	0.371620i	$0.878802\pi$
$644$	0.289447	−	1.51734i	0.0114058	−	0.0597914i
$645$	6.69847	−	2.06959i	0.263752	−	0.0814901i
$646$	−0.953791	+	2.02691i	−0.0375264	+	0.0797477i
$647$	−2.44244	−	4.44278i	−0.0960222	−	0.174664i	0.823933	−	0.566687i	$-0.191775\pi$
$647$	−2.44244	−	4.44278i	−0.0960222	−	0.174664i	−0.919955	+	0.392023i	$0.871775\pi$
$648$	−6.64224	−	0.417894i	−0.260932	−	0.0164164i
$649$	17.5990	+	12.7864i	0.690821	+	0.501911i
$650$	31.0748	−	7.02502i	1.21886	−	0.275544i
$651$	4.56792	−	3.31879i	0.179031	−	0.130074i
$652$	7.91246	−	5.02140i	0.309876	−	0.196653i
$653$	2.77046	−	21.9304i	0.108416	−	0.858204i	−0.840310	−	0.542106i	$-0.817627\pi$
$653$	2.77046	−	21.9304i	0.108416	−	0.858204i	0.948726	−	0.316098i	$-0.102373\pi$
$654$	0.260224	+	0.0328739i	0.0101756	+	0.00128547i
$655$	4.77181	+	19.7706i	0.186450	+	0.772503i
$656$	6.16550	+	3.38951i	0.240722	+	0.132338i
$657$	−9.38969	−	3.05090i	−0.366327	−	0.119027i
$658$	−2.35530	+	1.10832i	−0.0918190	+	0.0432067i
$659$	0.507741	+	0.130366i	0.0197788	+	0.00507833i	0.258566	−	0.965994i	$-0.416750\pi$
$659$	0.507741	+	0.130366i	0.0197788	+	0.00507833i	−0.238788	+	0.971072i	$0.576750\pi$
$660$	−25.7822	+	23.5171i	−1.00357	+	0.915400i
$661$	−3.75714	+	4.54161i	−0.146136	+	0.176648i	−0.838502	−	0.544898i	$-0.816568\pi$
$661$	−3.75714	+	4.54161i	−0.146136	+	0.176648i	0.692366	+	0.721546i	$0.256568\pi$
$662$	4.97713	+	3.15858i	0.193442	+	0.122762i
$663$	13.5874	−	0.854846i	0.527690	−	0.0331995i
$664$	8.08878	+	12.7459i	0.313906	+	0.494636i
$665$	−0.976222	−	1.58873i	−0.0378563	−	0.0616084i
$666$	−0.636425	−	10.1157i	−0.0246610	−	0.391975i
$667$	−45.7545	−	8.72815i	−1.77162	−	0.337955i
$668$	−6.63597	+	2.15616i	−0.256753	+	0.0834242i
$669$	−19.9658	+	18.7491i	−0.771922	+	0.724883i
$670$	−24.9204	+	4.38037i	−0.962759	+	0.169229i
$671$	8.34685	+	43.7557i	0.322226	+	1.68917i
$672$	0.544488	−	0.579821i	0.0210041	−	0.0223671i
$673$	3.01886	−	7.62477i	0.116369	−	0.293913i	−0.859905	−	0.510454i	$-0.829477\pi$
$673$	3.01886	−	7.62477i	0.116369	−	0.293913i	0.976274	+	0.216541i	$0.0694774\pi$
$674$	−1.55176	−	4.77582i	−0.0597715	−	0.183958i
$675$	−8.18795	+	1.31716i	−0.315154	+	0.0506974i
$676$	8.52883	−	26.2490i	0.328032	−	1.00958i
$677$	5.91717	+	4.89511i	0.227415	+	0.188134i	0.744153	−	0.668010i	$-0.232854\pi$
$677$	5.91717	+	4.89511i	0.227415	+	0.188134i	−0.516737	+	0.856144i	$0.672854\pi$
$678$	−0.582072	−	0.273902i	−0.0223543	−	0.0105192i
$679$	0.540673	+	0.507726i	0.0207491	+	0.0194847i
$680$	1.85144	−	0.0895564i	0.0709996	−	0.00343433i
$681$	20.3330	−	2.56866i	0.779163	−	0.0984311i
$682$			42.9809i			1.64582i
$683$	3.21353	+	25.4377i	0.122962	+	0.973346i	0.926028	+	0.377455i	$0.123201\pi$
$683$	3.21353	+	25.4377i	0.122962	+	0.973346i	−0.803066	+	0.595891i	$0.796799\pi$
$684$	−6.27602	−	7.58640i	−0.239970	−	0.290073i
$685$	−9.46825	+	5.02785i	−0.361763	+	0.192104i
$686$	0.269429	−	4.28245i	0.0102868	−	0.163505i
$687$	15.1008	−	58.8138i	0.576132	−	2.24389i
$688$	0.302516	−	1.17822i	0.0115333	−	0.0449193i
$689$	−0.0258453	+	0.410800i	−0.000984629	+	0.0156502i
$690$	4.99447	+	28.4140i	0.190136	+	1.08170i
$691$	−5.39881	−	6.52604i	−0.205381	−	0.248262i	0.657758	−	0.753229i	$-0.271505\pi$
$691$	−5.39881	−	6.52604i	−0.205381	−	0.248262i	−0.863139	+	0.504967i	$0.831505\pi$
$692$	−2.05640	−	16.2780i	−0.0781724	−	0.618798i
$693$		−	6.80778i		−	0.258606i
$694$	−19.1741	+	2.42226i	−0.727841	+	0.0919477i
$695$	−0.775174	−	0.507853i	−0.0294040	−	0.0192640i
$696$	−17.4842	−	16.4188i	−0.662738	−	0.622353i
$697$	−5.27729	−	2.48330i	−0.199892	−	0.0940618i
$698$	−21.4806	−	17.7703i	−0.813053	−	0.672616i
$699$	−1.34705	+	4.14579i	−0.0509500	+	0.156808i
$700$	−0.782219	+	1.32999i	−0.0295651	+	0.0502690i
$701$	5.35652	+	16.4857i	0.202313	+	0.622656i	0.999813	+	0.0193367i	$0.00615545\pi$
$701$	5.35652	+	16.4857i	0.202313	+	0.622656i	−0.797500	+	0.603319i	$0.793845\pi$
$702$	−3.89054	+	9.82638i	−0.146839	+	0.370873i
$703$	−5.14604	+	5.47997i	−0.194086	+	0.206681i
$704$	1.13456	+	5.94755i	0.0427602	+	0.224157i
$705$	33.7901	−	34.9532i	1.27261	−	1.31641i
$706$	11.1322	−	10.4538i	0.418966	−	0.393436i
$707$	−4.45695	+	1.44815i	−0.167621	+	0.0544633i
$708$	9.09637	+	1.73522i	0.341862	+	0.0652137i
$709$	0.456213	+	7.25130i	0.0171334	+	0.272328i	0.997261	+	0.0739607i	$0.0235639\pi$
$709$	0.456213	+	7.25130i	0.0171334	+	0.272328i	−0.980128	+	0.198367i	$0.936436\pi$
$710$	−1.89825	+	2.22802i	−0.0712401	+	0.0836160i
$711$	−2.30587	−	3.63347i	−0.0864770	−	0.136266i
$712$	6.47904	−	0.407627i	0.242812	−	0.0152765i
$713$	30.0016	+	19.0396i	1.12357	+	0.713038i
$714$	−0.420287	+	0.508040i	−0.0157289	+	0.0190129i
$715$	−35.5954	−	78.5814i	−1.33119	−	2.93878i
$716$	−23.5056	−	6.03521i	−0.878445	−	0.225546i
$717$	67.2166	−	31.6298i	2.51025	−	1.18123i
$718$	11.3921	+	3.70152i	0.425150	+	0.138140i
$719$	4.51535	+	2.48234i	0.168394	+	0.0925755i	0.563722	−	0.825965i	$-0.309369\pi$
$719$	4.51535	+	2.48234i	0.168394	+	0.0925755i	−0.395328	+	0.918540i	$0.629369\pi$
$720$	−3.10867	+	7.53073i	−0.115853	+	0.280654i
$721$	0.165413	+	0.0208965i	0.00616030	+	0.000778227i
$722$	1.46608	−	11.6053i	0.0545620	−	0.431903i
$723$	15.0522	−	9.55244i	0.559799	−	0.355259i
$724$	−6.64479	+	4.82772i	−0.246952	+	0.179421i
$725$	40.1053	+	23.5874i	1.48947	+	0.876015i
$726$	53.5084	+	38.8762i	1.98588	+	1.44283i
$727$	−42.2598	−	2.65876i	−1.56733	−	0.0986081i	−0.744784	−	0.667306i	$-0.767447\pi$
$727$	−42.2598	−	2.65876i	−1.56733	−	0.0986081i	−0.822547	+	0.568698i	$0.807447\pi$
$728$	0.947270	+	1.72308i	0.0351082	+	0.0638615i
$729$	−15.7855	+	33.5459i	−0.584648	+	1.24244i
$730$	3.63216	−	4.84979i	0.134432	−	0.179499i
$731$	−0.188951	+	0.990515i	−0.00698860	+	0.0366355i
$732$	11.1459	+	15.3410i	0.411963	+	0.567019i
$733$	3.95842	−	7.20034i	0.146208	−	0.265951i	−0.793055	−	0.609150i	$-0.791511\pi$
$733$	3.95842	−	7.20034i	0.146208	−	0.265951i	0.939263	+	0.343199i	$0.111511\pi$
$734$	5.66263	−	8.92288i	0.209012	−	0.329349i
$735$	11.7475	+	38.0220i	0.433311	+	1.40246i
$736$	4.65410	+	1.84269i	0.171552	+	0.0679223i
$737$	25.2215	+	63.7024i	0.929048	+	2.34651i
$738$	19.7521	−	16.3403i	0.727083	−	0.601496i
$739$	−29.2057	+	7.49875i	−1.07435	+	0.275846i	−0.744114	−	0.668053i	$-0.767128\pi$
$739$	−29.2057	+	7.49875i	−1.07435	+	0.275846i	−0.330235	+	0.943899i	$0.607128\pi$
$740$	6.00192	+	1.63414i	0.220635	+	0.0600721i
$741$	41.2644	−	16.3377i	1.51589	−	0.600182i
$742$	−0.0136463	−	0.0145319i	−0.000500972	−	0.000533481i
$743$	9.82140	−	13.5180i	0.360312	−	0.495927i	−0.589924	−	0.807459i	$-0.700842\pi$
$743$	9.82140	−	13.5180i	0.360312	−	0.495927i	0.950236	+	0.311532i	$0.100842\pi$
$744$	7.79039	+	16.5554i	0.285610	+	0.606951i
$745$	21.8601	+	23.9657i	0.800894	+	0.878035i
$746$	27.9571	−	15.3695i	1.02358	−	0.562719i
$747$	54.0278	−	10.3064i	1.97677	−	0.377090i
$748$	−1.24822	−	4.86149i	−0.0456394	−	0.177754i
$749$	−3.47194			−0.126862
$750$	4.85149	−	28.4060i	0.177151	−	1.03724i
$751$	36.8126			1.34331			0.671656	−	0.740863i	$-0.265583\pi$
$751$	36.8126			1.34331			0.671656	+	0.740863i	$0.265583\pi$
$752$	−2.09774	−	8.17015i	−0.0764967	−	0.297935i
$753$	42.1881	−	8.04781i	1.53742	−	0.293279i
$754$	51.9586	−	28.5645i	1.89222	−	1.04026i
$755$	26.0156	−	11.7844i	0.946805	−	0.428878i
$756$	−0.217933	−	0.463132i	−0.00792616	−	0.0168440i
$757$	−6.20234	+	8.53679i	−0.225428	+	0.310275i	−0.906717	−	0.421740i	$-0.861420\pi$
$757$	−6.20234	+	8.53679i	−0.225428	+	0.310275i	0.681289	+	0.732014i	$0.261420\pi$
$758$	−3.99704	−	4.25641i	−0.145179	−	0.154600i
$759$	72.6329	−	28.7574i	2.63641	−	1.04383i
$760$	5.64989	−	2.14273i	0.204943	−	0.0777249i
$761$	−45.7150	+	11.7376i	−1.65717	+	0.425488i	−0.957373	−	0.288855i	$-0.906725\pi$
$761$	−45.7150	+	11.7376i	−1.65717	+	0.425488i	−0.699795	+	0.714344i	$0.746725\pi$
$762$	6.69876	−	5.54170i	0.242671	−	0.200755i
$763$	−0.0115603	−	0.0291979i	−0.000418510	−	0.00105704i
$764$	−2.97484	−	1.17782i	−0.107626	−	0.0426122i
$765$	2.17989	−	6.39216i	0.0788141	−	0.231109i
$766$	−16.8213	+	26.5061i	−0.607778	+	0.957704i
$767$	−11.0285	+	20.0608i	−0.398217	+	0.724355i
$768$	1.51502	+	2.08524i	0.0546685	+	0.0752447i
$769$	8.05766	−	42.2397i	0.290567	−	1.52320i	−0.475081	−	0.879942i	$-0.657581\pi$
$769$	8.05766	−	42.2397i	0.290567	−	1.52320i	0.765647	−	0.643261i	$-0.222419\pi$
$770$	3.95440	+	1.34855i	0.142507	+	0.0485985i
$771$	−10.8614	+	23.0816i	−0.391163	+	0.831263i
$772$	8.02318	+	14.5941i	0.288761	+	0.525254i
$773$	26.0412	+	1.63837i	0.936636	+	0.0589281i	0.523766	−	0.851862i	$-0.324527\pi$
$773$	26.0412	+	1.63837i	0.936636	+	0.0589281i	0.412869	+	0.910790i	$0.364527\pi$
$774$	−3.58565	−	2.60512i	−0.128883	−	0.0936393i
$775$	−21.8219	−	27.9925i	−0.783864	−	1.00552i
$776$	−1.94445	+	1.41273i	−0.0698018	+	0.0507140i
$777$	−1.86823	+	1.18561i	−0.0670223	+	0.0425337i
$778$	−1.87256	+	14.8229i	−0.0671347	+	0.531426i
$779$	−18.8630	−	2.38295i	−0.675836	−	0.0853780i
$780$	−27.9537	−	23.8163i	−1.00090	−	0.852761i
$781$	6.94538	+	3.81825i	0.248525	+	0.136628i
$782$	−3.94635	−	1.28225i	−0.141121	−	0.0458531i
$783$	−13.9655	+	6.57168i	−0.499087	+	0.234853i
$784$	6.68784	+	1.71715i	0.238852	+	0.0613267i
$785$	−17.4902	−	9.94820i	−0.624251	−	0.355067i
$786$	14.9437	−	18.0638i	0.533024	−	0.644315i
$787$	24.3382	+	15.4455i	0.867562	+	0.550572i	0.893485	−	0.449092i	$-0.148253\pi$
$787$	24.3382	+	15.4455i	0.867562	+	0.550572i	−0.0259233	+	0.999664i	$0.508253\pi$
$788$	−1.79680	+	0.113045i	−0.0640082	+	0.00402705i
$789$	11.6645	+	18.3803i	0.415267	+	0.654356i
$790$	2.56733	−	0.619646i	0.0913414	−	0.0220460i
$791$	0.00483608	+	0.0768672i	0.000171951	+	0.00273308i
$792$	21.6699	+	4.13376i	0.770008	+	0.146887i
$793$	−44.5826	+	14.4858i	−1.58317	+	0.514404i
$794$	−12.0666	+	11.3313i	−0.428229	+	0.402134i
$795$	0.334546	+	0.163391i	0.0118651	+	0.00579488i
$796$	0.451172	+	2.36513i	0.0159914	+	0.0838297i
$797$	8.15005	−	8.67892i	0.288689	−	0.307423i	−0.568234	−	0.822867i	$-0.692373\pi$
$797$	8.15005	−	8.67892i	0.288689	−	0.307423i	0.856923	+	0.515444i	$0.172373\pi$
$798$	−0.791254	+	1.99848i	−0.0280101	+	0.0707454i
$799$	2.16077	+	6.65017i	0.0764425	+	0.235266i
$800$	−3.75854	−	3.29748i	−0.132885	−	0.116583i
$801$	7.30921	−	22.4954i	0.258258	−	0.794838i
$802$	−21.2916	−	17.6139i	−0.751831	−	0.621969i
$803$	−14.8453	−	6.98569i	−0.523881	−	0.246520i
$804$	21.2611	+	19.9655i	0.749820	+	0.704128i
$805$	2.69303	−	2.16288i	0.0949168	−	0.0762314i
$806$	−44.8746	+	5.66897i	−1.58064	+	0.199681i
$807$			50.4254i			1.77506i
$808$	−1.90332	−	15.0663i	−0.0669585	−	0.530031i
$809$	−28.3587	−	34.2798i	−0.997041	−	1.20521i	−0.978682	−	0.205384i	$-0.934156\pi$
$809$	−28.3587	−	34.2798i	−0.997041	−	1.20521i	−0.0183590	−	0.999831i	$-0.505844\pi$
$810$	−10.6996	−	10.3435i	−0.375945	−	0.363435i
$811$	0.483529	−	7.68548i	0.0169790	−	0.269874i	−0.980373	−	0.197151i	$-0.936831\pi$
$811$	0.483529	−	7.68548i	0.0169790	−	0.269874i	0.997352	−	0.0727229i	$-0.0231689\pi$
$812$	−0.714140	+	2.78139i	−0.0250614	+	0.0976078i
$813$	−16.2846	+	63.4245i	−0.571127	+	2.22439i
$814$	1.05761	−	16.8103i	0.0370693	−	0.589200i
$815$	20.7494	+	2.92748i	0.726820	+	0.102545i
$816$	−1.36195	−	1.64631i	−0.0476776	−	0.0576324i
$817$	0.411995	+	3.26128i	0.0144139	+	0.114098i
$818$		−	12.5193i		−	0.437727i
$819$	7.10772	−	0.897914i	0.248364	−	0.0313757i
$820$	5.57884	+	14.7101i	0.194821	+	0.513700i
$821$	32.0908	+	30.1352i	1.11998	+	1.05173i	0.998248	+	0.0591632i	$0.0188432\pi$
$821$	32.0908	+	30.1352i	1.11998	+	1.05173i	0.121727	+	0.992564i	$0.461157\pi$
$822$	11.1813	+	5.26150i	0.389991	+	0.183516i
$823$	−33.3469	−	27.5870i	−1.16240	−	0.961621i	−0.162714	−	0.986673i	$-0.552025\pi$
$823$	−33.3469	−	27.5870i	−1.16240	−	0.961621i	−0.999686	+	0.0250526i	$0.992025\pi$
$824$	−0.166956	+	0.513839i	−0.00581620	+	0.0179004i
$825$	−77.9865	+	2.63969i	−2.71514	+	0.0919022i
$826$	−0.342610	−	1.05444i	−0.0119209	−	0.0366888i
$827$	19.1065	−	48.2574i	0.664397	−	1.67807i	−0.0684266	−	0.997656i	$-0.521798\pi$
$827$	19.1065	−	48.2574i	0.664397	−	1.67807i	0.732823	−	0.680419i	$-0.238202\pi$
$828$	12.4847	−	13.2949i	0.433875	−	0.462030i
$829$	−6.58041	−	34.4957i	−0.228547	−	1.19809i	−0.892757	−	0.450539i	$-0.851232\pi$
$829$	−6.58041	−	34.4957i	−0.228547	−	1.19809i	0.664210	−	0.747546i	$-0.268768\pi$
$830$	−4.71576	+	33.4244i	−0.163686	+	1.16018i
$831$	−42.7081	+	40.1056i	−1.48153	+	1.39125i
$832$	−6.05994	+	1.96900i	−0.210091	+	0.0682626i
$833$	−5.62238	−	1.07253i	−0.194804	−	0.0371609i
$834$	0.0670743	+	1.06612i	0.00232259	+	0.0369166i
$835$	−14.4217	−	5.95322i	−0.499082	−	0.206020i
$836$	−8.76718	−	13.8149i	−0.303219	−	0.477797i
$837$	11.7509	−	0.739304i	0.406170	−	0.0255541i
$838$	19.6917	+	12.4967i	0.680239	+	0.431693i
$839$	24.1716	−	29.2184i	0.834495	−	1.00873i	−0.165252	−	0.986251i	$-0.552844\pi$
$839$	24.1716	−	29.2184i	0.834495	−	1.00873i	0.999747	−	0.0224797i	$-0.00715611\pi$
$840$	1.76759	−	0.197308i	0.0609876	−	0.00680777i
$841$	55.7827	+	14.3226i	1.92354	+	0.493881i
$842$	−22.7402	+	10.7007i	−0.783680	+	0.368772i
$843$	−29.8774	−	9.70776i	−1.02903	−	0.334353i
$844$	6.12436	+	3.36689i	0.210809	+	0.115893i
$845$	52.5818	−	32.3097i	1.80887	−	1.11149i
$846$	−30.4912	−	3.85194i	−1.04831	−	0.132432i
$847$	0.992473	−	7.85623i	0.0341018	−	0.269943i
$848$	0.0545428	−	0.0346139i	0.00187301	−	0.00118865i
$849$	−44.5189	+	32.3449i	−1.52788	+	1.11007i
$850$	3.28116	+	2.53244i	0.112543	+	0.0868620i
$851$	−11.2654	−	8.18482i	−0.386174	−	0.280572i
$852$	3.36729	+	0.211852i	0.115362	+	0.00725794i
$853$	−9.87268	−	17.9583i	−0.338034	−	0.614882i	0.651588	−	0.758573i	$-0.274103\pi$
$853$	−9.87268	−	17.9583i	−0.338034	−	0.614882i	−0.989623	+	0.143691i	$0.954103\pi$
$854$	0.966646	−	2.05423i	0.0330780	−	0.0702942i
$855$	0.319187	−	22.0138i	0.0109160	−	0.752856i
$856$	2.10820	−	11.0516i	0.0720568	−	0.377735i
$857$	−31.0909	−	42.7930i	−1.06205	−	1.46178i	−0.877877	−	0.478886i	$-0.841041\pi$
$857$	−31.0909	−	42.7930i	−1.06205	−	1.46178i	−0.184168	−	0.982895i	$-0.558959\pi$
$858$	−47.9055	+	87.1398i	−1.63547	+	2.97490i
$859$	−5.68156	+	8.95271i	−0.193852	+	0.305463i	−0.927325	−	0.374256i	$-0.877898\pi$
$859$	−5.68156	+	8.95271i	−0.193852	+	0.305463i	0.733473	+	0.679719i	$0.237898\pi$
$860$	2.22350	−	1.56673i	0.0758209	−	0.0534249i
$861$	−5.20327	−	2.06012i	−0.177327	−	0.0702087i
$862$	7.60912	+	19.2184i	0.259168	+	0.654583i
$863$	2.31013	−	1.91111i	0.0786378	−	0.0650548i	−0.597275	−	0.802037i	$-0.703750\pi$
$863$	2.31013	−	1.91111i	0.0786378	−	0.0650548i	0.675912	+	0.736982i	$0.263750\pi$
$864$	1.60653	−	0.412488i	0.0546554	−	0.0140331i
$865$	20.1055	−	30.6885i	0.683608	−	1.04344i
$866$	−28.1662	+	11.1518i	−0.957126	+	0.378953i
$867$	−28.7827	−	30.6504i	−0.977511	−	1.04094i
$868$	1.28760	−	1.77223i	0.0437040	−	0.0601534i
$869$	−3.04492	−	6.47078i	−0.103292	−	0.219506i
$870$	−5.94973	−	53.3008i	−0.201715	−	1.80707i
$871$	−63.1824	+	34.7348i	−2.14085	+	1.17694i
$872$	0.0999598	−	0.0190684i	0.00338507	−	0.000645736i
$873$	2.17780	+	8.48196i	0.0737073	+	0.287071i
$874$	−13.5267			−0.457548
$875$	−3.26009	+	1.12941i	−0.110211	+	0.0381810i
$876$	−6.98432			−0.235978
$877$	6.76432	+	26.3453i	0.228415	+	0.889617i	0.974614	+	0.223893i	$0.0718768\pi$
$877$	6.76432	+	26.3453i	0.228415	+	0.889617i	−0.746199	+	0.665723i	$0.768123\pi$
$878$	6.58808	−	1.25674i	0.222337	−	0.0424130i
$879$	43.5794	−	23.9580i	1.46990	−	0.808083i
$880$	−6.69375	+	11.7685i	−0.225646	+	0.396714i
$881$	4.52658	+	9.61946i	0.152504	+	0.324088i	0.966451	−	0.256852i	$-0.0826852\pi$
$881$	4.52658	+	9.61946i	0.152504	+	0.324088i	−0.813947	+	0.580940i	$0.802685\pi$
$882$	14.7873	−	20.3529i	0.497913	−	0.685318i
$883$	20.1817	+	21.4913i	0.679167	+	0.723239i	0.972534	−	0.232761i	$-0.0747759\pi$
$883$	20.1817	+	21.4913i	0.679167	+	0.723239i	−0.293367	+	0.956000i	$0.594776\pi$
$884$	4.91104	−	1.94442i	0.165176	−	0.0653979i
$885$	12.9664	+	16.1446i	0.435859	+	0.542695i
$886$	14.2408	−	3.65640i	0.478427	−	0.122839i
$887$	11.5905	−	9.58851i	0.389171	−	0.321951i	−0.422177	−	0.906513i	$-0.638734\pi$
$887$	11.5905	−	9.58851i	0.389171	−	0.321951i	0.811348	+	0.584563i	$0.198734\pi$
$888$	−2.63953	−	6.66670i	−0.0885769	−	0.223720i
$889$	−0.967790	−	0.383175i	−0.0324586	−	0.0128513i
$890$	11.6189	+	8.70178i	0.389468	+	0.291684i
$891$	−21.5922	+	34.0238i	−0.723365	+	1.13984i
$892$	−5.11922	+	9.31183i	−0.171404	+	0.311783i
$893$	13.3982	+	18.4411i	0.448355	+	0.617108i
$894$	7.00637	−	36.7287i	0.234328	−	1.22839i
$895$	−31.2563	−	44.3590i	−1.04478	−	1.48276i
$896$	0.131393	−	0.279224i	0.00438952	−	0.00932821i
$897$	39.6043	+	72.0400i	1.32235	+	2.40535i
$898$	−28.1694	−	1.77227i	−0.940023	−	0.0591413i
$899$	−53.4408	−	38.8270i	−1.78235	−	1.29495i
$900$	−16.2119	+	8.30983i	−0.540396	+	0.276994i
$901$	−0.0433228	+	0.0314758i	−0.00144329	+	0.00104861i
$902$	35.9686	−	22.8263i	1.19762	−	0.760034i
$903$	−0.121267	+	0.959925i	−0.00403550	+	0.0319443i
$904$	−0.247614	−	0.0312809i	−0.00823550	−	0.00104039i
$905$	−18.3108	−	1.41881i	−0.608673	−	0.0471629i
$906$	−28.8490	−	15.8599i	−0.958444	−	0.526909i
$907$	11.9040	+	3.86785i	0.395266	+	0.128430i	0.499904	−	0.866081i	$-0.333368\pi$
$907$	11.9040	+	3.86785i	0.395266	+	0.128430i	−0.104638	+	0.994510i	$0.533368\pi$
$908$	7.19460	−	3.38552i	0.238761	−	0.112352i
$909$	−53.5922	−	13.7601i	−1.77754	−	0.456395i
$910$	−0.886401	+	4.30649i	−0.0293839	+	0.142759i
$911$	−31.1202	+	37.6179i	−1.03106	+	1.24634i	−0.0623725	+	0.998053i	$0.519867\pi$
$911$	−31.1202	+	37.6179i	−1.03106	+	1.24634i	−0.968687	+	0.248284i	$0.920133\pi$
$912$	−5.88093	−	3.73215i	−0.194737	−	0.123584i
$913$	91.2222	−	5.73921i	3.01901	−	0.189940i
$914$	−5.03900	−	7.94019i	−0.166675	−	0.262638i
$915$	−3.27564	+	42.2747i	−0.108289	+	1.39756i
$916$	−1.47924	−	23.5118i	−0.0488754	−	0.776852i
$917$	−2.75712	−	0.525949i	−0.0910481	−	0.0173684i
$918$	−1.30765	+	0.424882i	−0.0431589	+	0.0140232i
$919$	1.01447	−	0.952655i	0.0334644	−	0.0314252i	−0.667635	−	0.744489i	$-0.732693\pi$
$919$	1.01447	−	0.952655i	0.0334644	−	0.0314252i	0.701099	+	0.713064i	$0.252693\pi$
$920$	5.24944	+	9.88554i	0.173069	+	0.325917i
$921$	−14.4976	−	75.9989i	−0.477711	−	2.50425i
$922$	−22.3474	+	23.7976i	−0.735973	+	0.783732i
$923$	−3.07042	+	7.75498i	−0.101064	+	0.255258i
$924$	−1.48822	−	4.58027i	−0.0489588	−	0.150680i
$925$	7.84596	+	11.4851i	0.257974	+	0.377628i
$926$	−8.83475	+	27.1906i	−0.290328	+	0.893538i
$927$	1.51677	+	1.25478i	0.0498174	+	0.0412125i
$928$	−8.41985	−	3.96208i	−0.276395	−	0.130062i
$929$	5.93169	+	5.57022i	0.194612	+	0.182753i	0.775727	−	0.631068i	$-0.217383\pi$
$929$	5.93169	+	5.57022i	0.194612	+	0.182753i	−0.581115	+	0.813822i	$0.697383\pi$
$930$	−10.7481	+	39.4758i	−0.352443	+	1.29446i
$931$	−18.5117	+	2.33858i	−0.606698	+	0.0766437i
$932$			1.69123i			0.0553980i
$933$	−3.17389	−	25.1239i	−0.103908	−	0.822519i
$934$	3.24627	+	3.92406i	0.106221	+	0.128399i
$935$	4.92534	−	10.0847i	0.161076	−	0.329806i
$936$	−1.45773	+	23.1699i	−0.0476473	+	0.757332i
$937$	−14.9471	+	58.2150i	−0.488300	+	1.90180i	−0.0599196	+	0.998203i	$0.519084\pi$
$937$	−14.9471	+	58.2150i	−0.488300	+	1.90180i	−0.428380	+	0.903599i	$0.640916\pi$
$938$	0.868404	−	3.38221i	0.0283544	−	0.110433i
$939$	−3.88300	+	61.7185i	−0.126717	+	2.01411i
$940$	8.27746	−	16.9483i	0.269981	−	0.552791i
$941$	−8.08045	−	9.76758i	−0.263415	−	0.318414i	0.622178	−	0.782876i	$-0.286248\pi$
$941$	−8.08045	−	9.76758i	−0.263415	−	0.318414i	−0.885593	+	0.464462i	$0.846248\pi$
$942$	2.90696	+	23.0110i	0.0947140	+	0.749738i
$943$		−	35.2184i		−	1.14687i
$944$	3.56445	−	0.450295i	0.116013	−	0.0146558i
$945$	0.300673	−	1.10432i	0.00978090	−	0.0359236i
$946$	−5.36906	−	5.04188i	−0.174563	−	0.163926i
$947$	9.75691	+	4.59125i	0.317057	+	0.149196i	0.577722	−	0.816234i	$-0.303942\pi$
$947$	9.75691	+	4.59125i	0.317057	+	0.149196i	−0.260665	+	0.965429i	$0.583942\pi$
$948$	−2.34569	−	1.94052i	−0.0761844	−	0.0630252i
$949$	5.33543	−	16.4208i	0.173196	−	0.533041i
$950$	12.7238	+	4.54612i	0.412815	+	0.147495i
$951$	−17.1887	−	52.9013i	−0.557381	−	1.71544i
$952$	−0.0941703	+	0.237847i	−0.00305208	+	0.00770867i
$953$	−26.6562	+	28.3859i	−0.863478	+	0.919510i	−0.997442	−	0.0714759i	$-0.977229\pi$
$953$	−26.6562	+	28.3859i	−0.863478	+	0.919510i	0.133965	+	0.990986i	$0.457229\pi$
$954$	−0.0441034	−	0.231198i	−0.00142790	−	0.00748531i
$955$	−3.35538	−	6.31872i	−0.108578	−	0.204469i
$956$	21.0098	−	19.7295i	0.679505	−	0.638097i
$957$	−138.116	+	44.8766i	−4.46465	+	1.45065i
$958$	3.99893	+	0.762837i	0.129200	+	0.0246461i
$959$	−0.0928981	−	1.47657i	−0.00299983	−	0.0476810i
$960$	−0.445246	+	5.74624i	−0.0143703	+	0.185459i
$961$	10.3902	+	16.3723i	0.335166	+	0.528138i
$962$	17.6904	−	1.11299i	0.570362	−	0.0358841i
$963$	−34.6112	−	21.9649i	−1.11533	−	0.707810i
$964$	4.40879	−	5.32931i	0.141998	−	0.171646i
$965$	−7.50763	+	36.4751i	−0.241679	+	1.17418i
$966$	−3.85637	−	0.990148i	−0.124077	−	0.0318575i
$967$	−43.7778	+	20.6003i	−1.40780	+	0.662459i	−0.971434	−	0.237311i	$-0.923734\pi$
$967$	−43.7778	+	20.6003i	−1.40780	+	0.662459i	−0.436364	+	0.899770i	$0.643734\pi$
$968$	24.4046	+	7.92955i	0.784395	+	0.254865i
$969$	5.05969	+	2.78159i	0.162541	+	0.0893574i
$970$	−5.35827	−	0.415184i	−0.172044	−	0.0133308i
$971$	57.9877	+	7.32555i	1.86091	+	0.235088i	0.973952	−	0.226755i	$-0.0728117\pi$
$971$	57.9877	+	7.32555i	1.86091	+	0.235088i	0.886962	+	0.461843i	$0.152812\pi$
$972$	−2.77364	+	21.9557i	−0.0889647	+	0.704228i
$973$	0.107984	−	0.0685290i	0.00346182	−	0.00219694i
$974$	−7.08908	+	5.15052i	−0.227149	+	0.165033i
$975$	−13.0420	−	81.0743i	−0.417680	−	2.59646i
$976$	5.95188	+	4.32429i	0.190515	+	0.138417i
$977$	50.9450	+	3.20518i	1.62987	+	0.102543i	0.851184	−	0.524867i	$-0.175885\pi$
$977$	50.9450	+	3.20518i	1.62987	+	0.102543i	0.778689	+	0.627410i	$0.215885\pi$
$978$	−11.6366	−	21.1668i	−0.372096	−	0.676840i
$979$	16.7360	−	35.5659i	0.534886	−	1.13669i
$980$	8.89309	+	12.6211i	0.284079	+	0.403166i
$981$	0.0694757	−	0.364204i	0.00221819	−	0.0116282i
$982$	−22.1436	−	30.4781i	−0.706631	−	0.972595i
$983$	11.6821	−	21.2497i	0.372602	−	0.677760i	−0.621829	−	0.783153i	$-0.713610\pi$
$983$	11.6821	−	21.2497i	0.372602	−	0.677760i	0.994431	+	0.105393i	$0.0336101\pi$
$984$	9.71708	−	15.3117i	0.309769	−	0.488118i
$985$	−3.22221	−	2.41322i	−0.102668	−	0.0768914i
$986$	7.17217	+	2.83966i	0.228408	+	0.0904332i
$987$	2.46987	+	6.23817i	0.0786167	+	0.198563i
$988$	13.2672	−	10.9756i	0.422085	−	0.349179i
$989$	−5.89771	+	1.51428i	−0.187536	+	0.0481512i
$990$	30.8893	+	38.4607i	0.981726	+	1.22236i
$991$	46.9513	−	18.5893i	1.49146	−	0.590509i	0.525864	−	0.850569i	$-0.323742\pi$
$991$	46.9513	−	18.5893i	1.49146	−	0.590509i	0.965593	+	0.260060i	$0.0837422\pi$
$992$	4.85936	+	5.17470i	0.154285	+	0.164297i
$993$	8.93070	−	12.2920i	0.283407	−	0.390076i
$994$	−0.171993	−	0.365504i	−0.00545529	−	0.0115931i
$995$	−2.66186	+	4.67989i	−0.0843868	+	0.148362i
$996$	34.0968	−	18.7449i	1.08040	−	0.593954i
$997$	51.2702	−	9.78031i	1.62374	−	0.309746i	0.706391	−	0.707822i	$-0.250322\pi$
$997$	51.2702	−	9.78031i	1.62374	−	0.309746i	0.917352	+	0.398077i	$0.130322\pi$
$998$	−1.90257	−	7.41000i	−0.0602247	−	0.234560i
$999$	−4.61409			−0.145983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.h.a.229.1	yes	240
125.119	even	50	inner	250.2.h.a.119.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
250.2.h.a.119.1	✓	240	125.119	even	50	inner
250.2.h.a.229.1	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)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-2.53185 + 0.482975i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.19016 - 0.450797i) q^{5} +(1.09745 + 2.33219i) q^{6} +(0.181387 - 0.249657i) q^{7} +(0.684547 + 0.728969i) q^{8} +(3.38765 - 1.34126i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-2.53185 + 0.482975i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(-2.19016 - 0.450797i) q^{5} +(1.09745 + 2.33219i) q^{6} +(0.181387 - 0.249657i) q^{7} +(0.684547 + 0.728969i) q^{8} +(3.38765 - 1.34126i) q^{9} +(0.108035 + 2.23346i) q^{10} +(5.86457 - 1.50577i) q^{11} +(1.98600 - 1.64296i) q^{12} +(2.34562 + 5.92435i) q^{13} +(-0.286923 - 0.113601i) q^{14} +(5.76286 + 0.0835580i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.399354 + 0.726422i) q^{17} +(-2.14160 - 2.94766i) q^{18} +(-0.506363 + 2.65445i) q^{19} +(2.13642 - 0.660079i) q^{20} +(-0.338665 + 0.719699i) q^{21} +(-2.91692 - 5.30586i) q^{22} +(-4.99573 - 0.314305i) q^{23} +(-2.08524 - 1.51502i) q^{24} +(4.59356 + 1.97463i) q^{25} +(5.15490 - 3.74525i) q^{26} +(-1.40044 + 0.888745i) q^{27} +(-0.0386770 + 0.306160i) q^{28} +(9.23211 + 1.16629i) q^{29} +(-1.35223 - 5.60259i) q^{30} +(-6.22060 - 3.41980i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-14.1209 + 6.64481i) q^{33} +(0.802915 + 0.206154i) q^{34} +(-0.509810 + 0.465020i) q^{35} +(-2.32246 + 2.80737i) q^{36} +(2.34879 + 1.49059i) q^{37} +(2.69698 - 0.169680i) q^{38} +(-8.80006 - 13.8667i) q^{39} +(-1.17065 - 1.90515i) q^{40} +(0.441780 + 7.02190i) q^{41} +(0.781311 + 0.149043i) q^{42} +(1.15690 - 0.375900i) q^{43} +(-4.41376 + 4.14479i) q^{44} +(-8.02412 + 1.41044i) q^{45} +(0.937957 + 4.91694i) q^{46} +(5.77426 - 6.14897i) q^{47} +(-0.948841 + 2.39650i) q^{48} +(2.13369 + 6.56683i) q^{49} +(0.770223 - 4.94032i) q^{50} +(0.660258 - 2.03207i) q^{51} +(-4.90956 - 4.06154i) q^{52} +(0.0584509 + 0.0275049i) q^{53} +(1.20910 + 1.13542i) q^{54} +(-13.5231 + 0.654129i) q^{55} +(0.306160 - 0.0386770i) q^{56} -6.96522i q^{57} +(-1.16629 - 9.23211i) q^{58} +(2.29012 + 2.76828i) q^{59} +(-5.09029 + 2.70306i) q^{60} +(-0.461945 + 7.34241i) q^{61} +(-1.76536 + 6.87564i) q^{62} +(0.279618 - 1.08904i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(-2.46658 - 14.0326i) q^{65} +(9.94779 + 12.0248i) q^{66} +(1.41822 + 11.2264i) q^{67} -0.828958i q^{68} +(12.8002 - 1.61704i) q^{69} +(0.577195 + 0.378147i) q^{70} +(0.954221 + 0.896073i) q^{71} +(3.29674 + 1.55133i) q^{72} +(-2.08788 - 1.72724i) q^{73} +(0.859639 - 2.64570i) q^{74} +(-12.5839 - 2.78089i) q^{75} +(-0.835061 - 2.57005i) q^{76} +(0.687829 - 1.73726i) q^{77} +(-11.2425 + 11.9721i) q^{78} +(-0.221318 - 1.16019i) q^{79} +(-1.55416 + 1.60766i) q^{80} +(-4.85156 + 4.55592i) q^{81} +(6.69143 - 2.17418i) q^{82} +(14.8285 + 2.82869i) q^{83} +(-0.0499435 - 0.793830i) q^{84} +(1.20212 - 1.41095i) q^{85} +(-0.651800 - 1.02707i) q^{86} +(-23.9376 + 1.50602i) q^{87} +(5.11223 + 3.24432i) q^{88} +(4.13806 - 5.00206i) q^{89} +(3.36164 + 7.42126i) q^{90} +(1.90452 + 0.488998i) q^{91} +(4.52921 - 2.13128i) q^{92} +(17.4013 + 5.65402i) q^{93} +(-7.39179 - 4.06367i) q^{94} +(2.30563 - 5.58539i) q^{95} +(2.55718 + 0.323046i) q^{96} +(-0.301235 + 2.38452i) q^{97} +(5.82989 - 3.69976i) q^{98} +(17.8475 - 12.9670i) 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

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Groups

Database

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