LMFDB - Embedded newform 230.2.g.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.1
Root			$-2.49760 + 0.733362i$ of defining polynomial
Character	$\chi$	$=$	230.121
Dual form			230.2.g.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-1.50807 - 0.442808i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(1.02927 - 1.18784i) q^{6} +(-0.440465 + 3.06350i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.445574 - 0.286353i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-1.50807 - 0.442808i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(1.02927 - 1.18784i) q^{6} +(-0.440465 + 3.06350i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.445574 - 0.286353i) q^{9} +(0.142315 + 0.989821i) q^{10} +(1.91760 + 4.19897i) q^{11} +(0.652922 + 1.42970i) q^{12} +(0.473207 + 3.29123i) q^{13} +(-2.60369 - 1.67329i) q^{14} +(-1.50807 + 0.442808i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-2.52093 + 2.90931i) q^{17} +(0.445574 - 0.286353i) q^{18} +(-0.431121 - 0.497540i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(2.02080 - 4.42493i) q^{21} -4.61612 q^{22} +(-2.16640 + 4.27863i) q^{23} -1.57173 q^{24} +(0.415415 - 0.909632i) q^{25} +(-3.19038 - 0.936781i) q^{26} +(3.63295 + 4.19265i) q^{27} +(2.60369 - 1.67329i) q^{28} +(3.43509 - 3.96430i) q^{29} +(0.223681 - 1.55574i) q^{30} +(-3.49920 + 1.02746i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-1.03254 - 7.18145i) q^{33} +(-1.59917 - 3.50169i) q^{34} +(1.28571 + 2.81532i) q^{35} +(0.0753778 + 0.524264i) q^{36} +(-1.39355 - 0.895583i) q^{37} +(0.631673 - 0.185476i) q^{38} +(0.743755 - 5.17293i) q^{39} +(0.654861 - 0.755750i) q^{40} +(7.20290 - 4.62902i) q^{41} +(3.18559 + 3.67636i) q^{42} +(-3.89465 - 1.14357i) q^{43} +(1.91760 - 4.19897i) q^{44} -0.529655 q^{45} +(-2.99203 - 3.74803i) q^{46} +12.0267 q^{47} +(0.652922 - 1.42970i) q^{48} +(-2.47460 - 0.726608i) q^{49} +(0.654861 + 0.755750i) q^{50} +(5.09000 - 3.27115i) q^{51} +(2.17746 - 2.51292i) q^{52} +(0.984705 - 6.84877i) q^{53} +(-5.32296 + 1.56296i) q^{54} +(3.88332 + 2.49566i) q^{55} +(0.440465 + 3.06350i) q^{56} +(0.429845 + 0.941228i) q^{57} +(2.17907 + 4.77149i) q^{58} +(1.38658 + 9.64389i) q^{59} +(1.32223 + 0.849743i) q^{60} +(-12.6963 + 3.72796i) q^{61} +(0.519012 - 3.60981i) q^{62} +(1.07350 - 1.23889i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.17746 + 2.51292i) q^{65} +(6.96141 + 2.04405i) q^{66} +(-2.68952 + 5.88922i) q^{67} +3.84957 q^{68} +(5.16169 - 5.49317i) q^{69} -3.09501 q^{70} +(2.54959 - 5.58283i) q^{71} +(-0.508200 - 0.149221i) q^{72} +(-6.83186 - 7.88438i) q^{73} +(1.39355 - 0.895583i) q^{74} +(-1.02927 + 1.18784i) q^{75} +(-0.0936916 + 0.651639i) q^{76} +(-13.7082 + 4.02509i) q^{77} +(4.39650 + 2.82546i) q^{78} +(-1.29275 - 8.99126i) q^{79} +(0.415415 + 0.909632i) q^{80} +(-2.96212 - 6.48613i) q^{81} +(1.21851 + 8.47495i) q^{82} +(-5.93150 - 3.81194i) q^{83} +(-4.66748 + 1.37050i) q^{84} +(-0.547851 + 3.81039i) q^{85} +(2.65813 - 3.06764i) q^{86} +(-6.93577 + 4.45735i) q^{87} +(3.02291 + 3.48863i) q^{88} +(14.2753 + 4.19161i) q^{89} +(0.220027 - 0.481791i) q^{90} -10.2911 q^{91} +(4.65227 - 1.16466i) q^{92} +5.73199 q^{93} +(-4.99605 + 10.9398i) q^{94} +(-0.631673 - 0.185476i) q^{95} +(1.02927 + 1.18784i) q^{96} +(5.29516 - 3.40299i) q^{97} +(1.68893 - 1.94913i) q^{98} +(0.347953 - 2.42006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−1.50807	−	0.442808i	−0.870683	−	0.255656i	−0.184277	−	0.982874i	$-0.558994\pi$
$3$	−1.50807	−	0.442808i	−0.870683	−	0.255656i	−0.686406	+	0.727219i	$0.740813\pi$
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	1.02927	−	1.18784i	0.420196	−	0.484932i
$7$	−0.440465	+	3.06350i	−0.166480	+	1.15790i	0.719608	+	0.694380i	$0.244321\pi$
$7$	−0.440465	+	3.06350i	−0.166480	+	1.15790i	−0.886089	+	0.463516i	$0.846588\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.445574	−	0.286353i	−0.148525	−	0.0954511i
$10$	0.142315	+	0.989821i	0.0450039	+	0.313009i
$11$	1.91760	+	4.19897i	0.578179	+	1.26604i	0.942327	+	0.334695i	$0.108633\pi$
$11$	1.91760	+	4.19897i	0.578179	+	1.26604i	−0.364147	+	0.931341i	$0.618640\pi$
$12$	0.652922	+	1.42970i	0.188482	+	0.412718i
$13$	0.473207	+	3.29123i	0.131244	+	0.912822i	0.943936	+	0.330129i	$0.107092\pi$
$13$	0.473207	+	3.29123i	0.131244	+	0.912822i	−0.812692	+	0.582694i	$0.801999\pi$
$14$	−2.60369	−	1.67329i	−0.695864	−	0.447205i
$15$	−1.50807	+	0.442808i	−0.389381	+	0.114333i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−2.52093	+	2.90931i	−0.611416	+	0.705612i	−0.974053	−	0.226319i	$-0.927331\pi$
$17$	−2.52093	+	2.90931i	−0.611416	+	0.705612i	0.362637	+	0.931930i	$0.381876\pi$
$18$	0.445574	−	0.286353i	0.105023	−	0.0674941i
$19$	−0.431121	−	0.497540i	−0.0989060	−	0.114144i	0.704139	−	0.710063i	$-0.251333\pi$
$19$	−0.431121	−	0.497540i	−0.0989060	−	0.114144i	−0.803045	+	0.595919i	$0.796788\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	2.02080	−	4.42493i	0.440974	−	0.965598i
$22$	−4.61612			−0.984159
$23$	−2.16640	+	4.27863i	−0.451725	+	0.892157i
$23$	−2.16640	+	4.27863i	−0.451725	+	0.892157i
$24$	−1.57173			−0.320829
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−3.19038	−	0.936781i	−0.625686	−	0.183718i
$27$	3.63295	+	4.19265i	0.699163	+	0.806877i
$28$	2.60369	−	1.67329i	0.492050	−	0.316222i
$29$	3.43509	−	3.96430i	0.637880	−	0.736152i	−0.341119	−	0.940020i	$-0.610806\pi$
$29$	3.43509	−	3.96430i	0.637880	−	0.736152i	0.978998	+	0.203868i	$0.0653513\pi$
$30$	0.223681	−	1.55574i	0.0408384	−	0.284037i
$31$	−3.49920	+	1.02746i	−0.628475	+	0.184537i	−0.580432	−	0.814308i	$-0.697116\pi$
$31$	−3.49920	+	1.02746i	−0.628475	+	0.184537i	−0.0480424	+	0.998845i	$0.515298\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	−1.03254	−	7.18145i	−0.179742	−	1.25013i
$34$	−1.59917	−	3.50169i	−0.274255	−	0.600535i
$35$	1.28571	+	2.81532i	0.217325	+	0.475876i
$36$	0.0753778	+	0.524264i	0.0125630	+	0.0873773i
$37$	−1.39355	−	0.895583i	−0.229099	−	0.147233i	0.421056	−	0.907035i	$-0.361660\pi$
$37$	−1.39355	−	0.895583i	−0.229099	−	0.147233i	−0.650155	+	0.759802i	$0.725296\pi$
$38$	0.631673	−	0.185476i	0.102471	−	0.0300882i
$39$	0.743755	−	5.17293i	0.119096	−	0.828332i
$40$	0.654861	−	0.755750i	0.103543	−	0.119494i
$41$	7.20290	−	4.62902i	1.12490	−	0.722931i	0.160413	−	0.987050i	$-0.448717\pi$
$41$	7.20290	−	4.62902i	1.12490	−	0.722931i	0.964490	+	0.264119i	$0.0850810\pi$
$42$	3.18559	+	3.67636i	0.491547	+	0.567275i
$43$	−3.89465	−	1.14357i	−0.593929	−	0.174393i	−0.0290652	−	0.999578i	$-0.509253\pi$
$43$	−3.89465	−	1.14357i	−0.593929	−	0.174393i	−0.564864	+	0.825184i	$0.691071\pi$
$44$	1.91760	−	4.19897i	0.289090	−	0.633018i
$45$	−0.529655			−0.0789563
$46$	−2.99203	−	3.74803i	−0.441151	−	0.552618i
$47$	12.0267			1.75427			0.877134	−	0.480246i	$-0.159453\pi$
$47$	12.0267			1.75427			0.877134	+	0.480246i	$0.159453\pi$
$48$	0.652922	−	1.42970i	0.0942411	−	0.206359i
$49$	−2.47460	−	0.726608i	−0.353514	−	0.103801i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	5.09000	−	3.27115i	0.712743	−	0.458052i
$52$	2.17746	−	2.51292i	0.301959	−	0.348480i
$53$	0.984705	−	6.84877i	0.135260	−	0.940751i	−0.803285	−	0.595594i	$-0.796917\pi$
$53$	0.984705	−	6.84877i	0.135260	−	0.940751i	0.938545	−	0.345157i	$-0.112174\pi$
$54$	−5.32296	+	1.56296i	−0.724363	+	0.212692i
$55$	3.88332	+	2.49566i	0.523627	+	0.336515i
$56$	0.440465	+	3.06350i	0.0588597	+	0.409378i
$57$	0.429845	+	0.941228i	0.0569343	+	0.124669i
$58$	2.17907	+	4.77149i	0.286126	+	0.626528i
$59$	1.38658	+	9.64389i	0.180518	+	1.25553i	0.855543	+	0.517732i	$0.173224\pi$
$59$	1.38658	+	9.64389i	0.180518	+	1.25553i	−0.675025	+	0.737795i	$0.735867\pi$
$60$	1.32223	+	0.849743i	0.170699	+	0.109701i
$61$	−12.6963	+	3.72796i	−1.62559	+	0.477316i	−0.962513	−	0.271236i	$-0.912568\pi$
$61$	−12.6963	+	3.72796i	−1.62559	+	0.477316i	−0.663076	+	0.748552i	$0.730750\pi$
$62$	0.519012	−	3.60981i	0.0659145	−	0.458446i
$63$	1.07350	−	1.23889i	0.135249	−	0.156085i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	2.17746	+	2.51292i	0.270081	+	0.311690i
$66$	6.96141	+	2.04405i	0.856890	+	0.251606i
$67$	−2.68952	+	5.88922i	−0.328577	+	0.719483i	−0.999762	−	0.0218067i	$-0.993058\pi$
$67$	−2.68952	+	5.88922i	−0.328577	+	0.719483i	0.671185	+	0.741289i	$0.265785\pi$
$68$	3.84957			0.466829
$69$	5.16169	−	5.49317i	0.621394	−	0.661300i
$70$	−3.09501			−0.369924
$71$	2.54959	−	5.58283i	0.302581	−	0.662560i	−0.695872	−	0.718166i	$-0.744982\pi$
$71$	2.54959	−	5.58283i	0.302581	−	0.662560i	0.998453	+	0.0556060i	$0.0177091\pi$
$72$	−0.508200	−	0.149221i	−0.0598920	−	0.0175859i
$73$	−6.83186	−	7.88438i	−0.799608	−	0.922797i	0.198751	−	0.980050i	$-0.436311\pi$
$73$	−6.83186	−	7.88438i	−0.799608	−	0.922797i	−0.998360	+	0.0572528i	$0.981766\pi$
$74$	1.39355	−	0.895583i	0.161997	−	0.104109i
$75$	−1.02927	+	1.18784i	−0.118849	+	0.137160i
$76$	−0.0936916	+	0.651639i	−0.0107472	+	0.0747482i
$77$	−13.7082	+	4.02509i	−1.56219	+	0.458701i
$78$	4.39650	+	2.82546i	0.497805	+	0.319920i
$79$	−1.29275	−	8.99126i	−0.145445	−	1.01160i	−0.923555	−	0.383467i	$-0.874730\pi$
$79$	−1.29275	−	8.99126i	−0.145445	−	1.01160i	0.778109	−	0.628129i	$-0.216179\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	−2.96212	−	6.48613i	−0.329124	−	0.720681i
$82$	1.21851	+	8.47495i	0.134562	+	0.935901i
$83$	−5.93150	−	3.81194i	−0.651067	−	0.418415i	0.172989	−	0.984924i	$-0.444657\pi$
$83$	−5.93150	−	3.81194i	−0.651067	−	0.418415i	−0.824056	+	0.566508i	$0.808294\pi$
$84$	−4.66748	+	1.37050i	−0.509264	+	0.149533i
$85$	−0.547851	+	3.81039i	−0.0594228	+	0.413295i
$86$	2.65813	−	3.06764i	0.286633	−	0.330792i
$87$	−6.93577	+	4.45735i	−0.743592	+	0.477878i
$88$	3.02291	+	3.48863i	0.322244	+	0.371889i
$89$	14.2753	+	4.19161i	1.51318	+	0.444309i	0.929854	−	0.367930i	$-0.119933\pi$
$89$	14.2753	+	4.19161i	1.51318	+	0.444309i	0.583325	+	0.812239i	$0.301751\pi$
$90$	0.220027	−	0.481791i	0.0231929	−	0.0507853i
$91$	−10.2911			−1.07880
$92$	4.65227	−	1.16466i	0.485032	−	0.121424i
$93$	5.73199			0.594380
$94$	−4.99605	+	10.9398i	−0.515303	+	1.12836i
$95$	−0.631673	−	0.185476i	−0.0648083	−	0.0190294i
$96$	1.02927	+	1.18784i	0.105049	+	0.121233i
$97$	5.29516	−	3.40299i	0.537642	−	0.345521i	−0.243474	−	0.969907i	$-0.578287\pi$
$97$	5.29516	−	3.40299i	0.537642	−	0.345521i	0.781116	+	0.624386i	$0.214651\pi$
$98$	1.68893	−	1.94913i	0.170608	−	0.196892i
$99$	0.347953	−	2.42006i	0.0349706	−	0.243226i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	0.408229	+	0.262353i	0.0406203	+	0.0261051i	0.560793	−	0.827956i	$-0.310496\pi$
$101$	0.408229	+	0.262353i	0.0406203	+	0.0261051i	−0.520173	+	0.854061i	$0.674133\pi$
$102$	0.861075	+	5.98891i	0.0852592	+	0.592991i
$103$	−0.523361	−	1.14600i	−0.0515683	−	0.112919i	0.882094	−	0.471073i	$-0.156133\pi$
$103$	−0.523361	−	1.14600i	−0.0515683	−	0.112919i	−0.933662	+	0.358155i	$0.883406\pi$
$104$	1.38128	+	3.02459i	0.135446	+	0.296586i
$105$	−0.692294	−	4.81501i	−0.0675610	−	0.469897i
$106$	5.82080	+	3.74080i	0.565366	+	0.363339i
$107$	−5.24545	+	1.54020i	−0.507097	+	0.148897i	−0.525267	−	0.850938i	$-0.676034\pi$
$107$	−5.24545	+	1.54020i	−0.507097	+	0.148897i	0.0181694	+	0.999835i	$0.494216\pi$
$108$	0.789517	−	5.49121i	0.0759713	−	0.528392i
$109$	−4.60586	+	5.31545i	−0.441161	+	0.509127i	−0.932167	−	0.362029i	$-0.882084\pi$
$109$	−4.60586	+	5.31545i	−0.441161	+	0.509127i	0.491005	+	0.871157i	$0.336630\pi$
$110$	−3.88332	+	2.49566i	−0.370260	+	0.237952i
$111$	1.70500	+	1.96768i	0.161832	+	0.186764i
$112$	−2.96964	−	0.871964i	−0.280604	−	0.0823929i
$113$	−1.76271	+	3.85980i	−0.165822	+	0.363100i	−0.974242	−	0.225507i	$-0.927596\pi$
$113$	−1.76271	+	3.85980i	−0.165822	+	0.363100i	0.808419	+	0.588607i	$0.200323\pi$
$114$	−1.03474			−0.0969118
$115$	0.490714	+	4.77066i	0.0457593	+	0.444866i
$116$	−5.24552			−0.487034
$117$	0.731605	−	1.60199i	0.0676369	−	0.148104i
$118$	−9.34839	−	2.74494i	−0.860589	−	0.252692i
$119$	−7.80230	−	9.00434i	−0.715236	−	0.825426i
$120$	−1.32223	+	0.849743i	−0.120702	+	0.0775706i
$121$	−6.75065	+	7.79066i	−0.613695	+	0.708242i
$122$	1.88315	−	13.0976i	0.170492	−	1.18580i
$123$	−12.9122	+	3.79137i	−1.16426	+	0.341856i
$124$	3.06799	+	1.97168i	0.275514	+	0.177062i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	0.680984	+	1.49115i	0.0606669	+	0.132842i
$127$	−4.85646	−	10.6342i	−0.430941	−	0.943630i	−0.993173	−	0.116650i	$-0.962784\pi$
$127$	−4.85646	−	10.6342i	−0.430941	−	0.943630i	0.562232	−	0.826980i	$-0.309943\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	5.36701	+	3.44917i	0.472539	+	0.303682i
$130$	−3.19038	+	0.936781i	−0.279815	+	0.0821611i
$131$	−1.99532	+	13.8778i	−0.174332	+	1.21251i	0.695268	+	0.718750i	$0.255285\pi$
$131$	−1.99532	+	13.8778i	−0.174332	+	1.21251i	−0.869600	+	0.493756i	$0.835624\pi$
$132$	−4.75121	+	5.48319i	−0.413540	+	0.477251i
$133$	1.71411	−	1.10159i	0.148632	−	0.0955202i
$134$	−4.23976	−	4.89294i	−0.366259	−	0.422686i
$135$	5.32296	+	1.56296i	0.458127	+	0.134518i
$136$	−1.59917	+	3.50169i	−0.137128	+	0.300268i
$137$	14.1520			1.20909			0.604545	−	0.796571i	$-0.293355\pi$
$137$	14.1520			1.20909			0.604545	+	0.796571i	$0.293355\pi$
$138$	2.85252	+	6.97718i	0.242822	+	0.593937i
$139$	15.1575			1.28565			0.642823	−	0.766015i	$-0.277763\pi$
$139$	15.1575			1.28565			0.642823	+	0.766015i	$0.277763\pi$
$140$	1.28571	−	2.81532i	0.108663	−	0.237938i
$141$	−18.1370	−	5.32550i	−1.52741	−	0.448488i
$142$	4.01918	+	4.63838i	0.337282	+	0.389245i
$143$	−12.9123	+	8.29825i	−1.07978	+	0.693935i
$144$	0.346850	−	0.400287i	0.0289042	−	0.0333572i
$145$	0.746516	−	5.19213i	0.0619947	−	0.431183i
$146$	10.0099	−	2.93918i	0.828429	−	0.243249i
$147$	3.41011	+	2.19155i	0.281261	+	0.180756i
$148$	0.235748	+	1.63966i	0.0193783	+	0.134779i
$149$	4.42135	+	9.68140i	0.362211	+	0.793131i	0.999742	+	0.0227068i	$0.00722841\pi$
$149$	4.42135	+	9.68140i	0.362211	+	0.793131i	−0.637531	+	0.770424i	$0.720044\pi$
$150$	−0.652922	−	1.42970i	−0.0533108	−	0.116734i
$151$	2.88013	+	20.0318i	0.234382	+	1.63016i	0.678786	+	0.734336i	$0.262506\pi$
$151$	2.88013	+	20.0318i	0.234382	+	1.63016i	−0.444404	+	0.895826i	$0.646585\pi$
$152$	−0.553831	−	0.355926i	−0.0449216	−	0.0288694i
$153$	1.95635	−	0.574437i	0.158162	−	0.0464405i
$154$	2.03324	−	14.1415i	0.163843	−	1.13955i
$155$	−2.38823	+	2.75616i	−0.191827	+	0.221380i
$156$	−4.39650	+	2.82546i	−0.352001	+	0.226218i
$157$	12.2433	+	14.1296i	0.977124	+	1.12766i	0.991804	+	0.127769i	$0.0407817\pi$
$157$	12.2433	+	14.1296i	0.977124	+	1.12766i	−0.0146796	+	0.999892i	$0.504673\pi$
$158$	8.71576	+	2.55918i	0.693389	+	0.203597i
$159$	−4.51770	+	9.89237i	−0.358277	+	0.784516i
$160$	−1.00000			−0.0790569
$161$	−12.1534	−	8.52136i	−0.957822	−	0.671577i
$162$	7.13050			0.560225
$163$	6.79272	−	14.8740i	0.532047	−	1.16502i	−0.432626	−	0.901573i	$-0.642413\pi$
$163$	6.79272	−	14.8740i	0.532047	−	1.16502i	0.964674	−	0.263448i	$-0.0848596\pi$
$164$	−8.21527	−	2.41222i	−0.641505	−	0.188363i
$165$	−4.75121	−	5.48319i	−0.369881	−	0.426866i
$166$	5.93150	−	3.81194i	0.460374	−	0.295864i
$167$	13.7666	−	15.8875i	1.06529	−	1.22942i	0.0929974	−	0.995666i	$-0.470355\pi$
$167$	13.7666	−	15.8875i	1.06529	−	1.22942i	0.972297	−	0.233749i	$-0.0750994\pi$
$168$	0.692294	−	4.81501i	0.0534116	−	0.371486i
$169$	1.86515	−	0.547659i	0.143473	−	0.0421276i
$170$	−3.23846	−	2.08123i	−0.248379	−	0.159623i
$171$	0.0496242	+	0.345144i	0.00379486	+	0.0263938i
$172$	1.68620	+	3.69226i	0.128572	+	0.281532i
$173$	9.15228	+	20.0407i	0.695835	+	1.52367i	0.844949	+	0.534846i	$0.179630\pi$
$173$	9.15228	+	20.0407i	0.695835	+	1.52367i	−0.149114	+	0.988820i	$0.547642\pi$
$174$	−1.17332	−	8.16064i	−0.0889494	−	0.618657i
$175$	2.60369	+	1.67329i	0.196820	+	0.126489i
$176$	−4.42913	+	1.30051i	−0.333858	+	0.0980296i
$177$	2.17934	−	15.1576i	0.163809	−	1.13932i
$178$	−9.74299	+	11.2440i	−0.730268	+	0.842774i
$179$	4.24907	−	2.73071i	0.317591	−	0.204103i	−0.372127	−	0.928182i	$-0.621371\pi$
$179$	4.24907	−	2.73071i	0.317591	−	0.204103i	0.689717	+	0.724079i	$0.257735\pi$
$180$	0.346850	+	0.400287i	0.0258527	+	0.0298356i
$181$	17.3987	+	5.10871i	1.29323	+	0.379728i	0.854763	−	0.519018i	$-0.173702\pi$
$181$	17.3987	+	5.10871i	1.29323	+	0.379728i	0.438470	+	0.898746i	$0.355520\pi$
$182$	4.27509	−	9.36113i	0.316891	−	0.693893i
$183$	20.7976			1.53740
$184$	−0.873214	+	4.71567i	−0.0643742	+	0.347643i
$185$	−1.65652			−0.121790
$186$	−2.38116	+	5.21400i	−0.174595	+	0.382309i
$187$	−17.0502	−	5.00640i	−1.24684	−	0.366105i
$188$	−7.87578	−	9.08914i	−0.574400	−	0.662893i
$189$	−14.4444	+	9.28285i	−1.05068	+	0.675228i
$190$	0.431121	−	0.497540i	0.0312768	−	0.0360954i
$191$	2.78038	−	19.3380i	0.201181	−	1.39925i	−0.599606	−	0.800296i	$-0.704676\pi$
$191$	2.78038	−	19.3380i	0.201181	−	1.39925i	0.800787	−	0.598950i	$-0.204415\pi$
$192$	−1.50807	+	0.442808i	−0.108835	+	0.0319569i
$193$	−3.48388	−	2.23895i	−0.250775	−	0.161163i	0.409214	−	0.912438i	$-0.365803\pi$
$193$	−3.48388	−	2.23895i	−0.250775	−	0.161163i	−0.659989	+	0.751275i	$0.729439\pi$
$194$	0.895782	+	6.23030i	0.0643134	+	0.447309i
$195$	−2.17101	−	4.75385i	−0.155469	−	0.340430i
$196$	1.07138	+	2.34600i	0.0765274	+	0.167572i
$197$	−3.61674	−	25.1550i	−0.257682	−	1.79222i	−0.549242	−	0.835664i	$-0.685083\pi$
$197$	−3.61674	−	25.1550i	−0.257682	−	1.79222i	0.291560	−	0.956553i	$-0.405826\pi$
$198$	2.05682	+	1.32184i	0.146172	+	0.0939390i
$199$	−7.06849	+	2.07550i	−0.501072	+	0.147128i	−0.522495	−	0.852642i	$-0.674999\pi$
$199$	−7.06849	+	2.07550i	−0.501072	+	0.147128i	0.0214227	+	0.999771i	$0.493180\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	6.66377	−	7.69040i	0.470026	−	0.542439i
$202$	−0.408229	+	0.262353i	−0.0287229	+	0.0184591i
$203$	10.6316	+	12.2695i	0.746193	+	0.861153i
$204$	−5.80541	−	1.70462i	−0.406460	−	0.119347i
$205$	3.55682	−	7.78836i	0.248419	−	0.543963i
$206$	1.25985			0.0877780
$207$	2.19049	−	1.28609i	0.152250	−	0.0893897i
$208$	−3.32507			−0.230552
$209$	1.26244	−	2.76435i	0.0873245	−	0.191214i
$210$	4.66748	+	1.37050i	0.322087	+	0.0945731i
$211$	5.00845	+	5.78006i	0.344796	+	0.397916i	0.901489	−	0.432803i	$-0.142475\pi$
$211$	5.00845	+	5.78006i	0.344796	+	0.397916i	−0.556693	+	0.830719i	$0.687930\pi$
$212$	−5.82080	+	3.74080i	−0.399774	+	0.256919i
$213$	−6.31708	+	7.29030i	−0.432839	+	0.499523i
$214$	0.778021	−	5.41126i	0.0531844	−	0.369906i
$215$	−3.89465	+	1.14357i	−0.265613	+	0.0779910i
$216$	4.66700	+	2.99930i	0.317549	+	0.204077i
$217$	−1.60634	−	11.1724i	−0.109046	−	0.758430i
$218$	−2.92176	−	6.39775i	−0.197886	−	0.433311i
$219$	6.81162	+	14.9154i	0.460287	+	1.00789i
$220$	−0.656942	−	4.56913i	−0.0442910	−	0.308051i
$221$	−10.7681	−	6.92026i	−0.724343	−	0.465507i
$222$	−2.49814	+	0.733521i	−0.167664	+	0.0492307i
$223$	1.32012	−	9.18165i	0.0884019	−	0.614849i	−0.896669	−	0.442701i	$-0.854020\pi$
$223$	1.32012	−	9.18165i	0.0884019	−	0.614849i	0.985071	−	0.172148i	$-0.0550706\pi$
$224$	2.02680	−	2.33905i	0.135421	−	0.156284i
$225$	−0.445574	+	0.286353i	−0.0297050	+	0.0190902i
$226$	−2.77874	−	3.20684i	−0.184839	−	0.213316i
$227$	−17.8454	−	5.23989i	−1.18444	−	0.347784i	−0.370558	−	0.928809i	$-0.620833\pi$
$227$	−17.8454	−	5.23989i	−1.18444	−	0.347784i	−0.813885	+	0.581026i	$0.802652\pi$
$228$	0.429845	−	0.941228i	0.0284672	−	0.0623344i
$229$	12.9449			0.855424			0.427712	−	0.903915i	$-0.359320\pi$
$229$	12.9449			0.855424			0.427712	+	0.903915i	$0.359320\pi$
$230$	−4.54340	−	1.53543i	−0.299583	−	0.101244i
$231$	22.4552			1.47744
$232$	2.17907	−	4.77149i	0.143063	−	0.313264i
$233$	13.3345	+	3.91537i	0.873573	+	0.256504i	0.687635	−	0.726057i	$-0.258649\pi$
$233$	13.3345	+	3.91537i	0.873573	+	0.256504i	0.185939	+	0.982561i	$0.440467\pi$
$234$	1.15330	+	1.33098i	0.0753937	+	0.0870090i
$235$	10.1175	−	6.50210i	0.659991	−	0.424150i
$236$	6.38035	−	7.36331i	0.415325	−	0.479311i
$237$	−2.03185	+	14.1319i	−0.131983	+	0.917963i
$238$	11.4318	−	3.35669i	0.741015	−	0.217582i
$239$	−20.7486	−	13.3343i	−1.34211	−	0.862523i	−0.345010	−	0.938599i	$-0.612125\pi$
$239$	−20.7486	−	13.3343i	−1.34211	−	0.862523i	−0.997102	+	0.0760758i	$0.975761\pi$
$240$	−0.223681	−	1.55574i	−0.0144385	−	0.100422i
$241$	1.02706	+	2.24894i	0.0661586	+	0.144867i	0.939823	−	0.341662i	$-0.110990\pi$
$241$	1.02706	+	2.24894i	0.0661586	+	0.144867i	−0.873664	+	0.486529i	$0.838263\pi$
$242$	−4.28232	−	9.37696i	−0.275278	−	0.602774i
$243$	−0.773593	−	5.38046i	−0.0496260	−	0.345156i
$244$	11.1317	+	7.15390i	0.712633	+	0.457981i
$245$	−2.47460	+	0.726608i	−0.158096	+	0.0464213i
$246$	1.91518	−	13.3204i	0.122107	−	0.849275i
$247$	1.43351	−	1.65436i	0.0912120	−	0.105264i
$248$	−3.06799	+	1.97168i	−0.194818	+	0.125202i
$249$	7.25714	+	8.37519i	0.459903	+	0.530756i
$250$	0.959493	+	0.281733i	0.0606837	+	0.0178183i
$251$	−5.44152	+	11.9153i	−0.343466	+	0.752086i	−0.999998	−	0.00221295i	$-0.999296\pi$
$251$	−5.44152	+	11.9153i	−0.343466	+	0.752086i	0.656532	+	0.754299i	$0.272023\pi$
$252$	−1.63929			−0.103265
$253$	−22.1201	−	0.891909i	−1.39068	−	0.0560738i
$254$	11.6906			0.733535
$255$	2.51347	−	5.50373i	0.157399	−	0.344657i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	4.85069	+	5.59799i	0.302577	+	0.349193i	0.886594	−	0.462549i	$-0.153065\pi$
$257$	4.85069	+	5.59799i	0.302577	+	0.349193i	−0.584016	+	0.811742i	$0.698520\pi$
$258$	−5.36701	+	3.44917i	−0.334136	+	0.214736i
$259$	3.35743	−	3.87469i	0.208621	−	0.240761i
$260$	0.473207	−	3.29123i	0.0293471	−	0.204113i
$261$	−2.66578	+	0.782743i	−0.165007	+	0.0484505i
$262$	−11.7948	−	7.58004i	−0.728684	−	0.468297i
$263$	2.39439	+	16.6534i	0.147645	+	1.02689i	0.920061	+	0.391775i	$0.128139\pi$
$263$	2.39439	+	16.6534i	0.147645	+	1.02689i	−0.772417	+	0.635116i	$0.780952\pi$
$264$	−3.01396	−	6.59965i	−0.185496	−	0.406181i
$265$	−2.87434	−	6.29393i	−0.176569	−	0.386633i
$266$	0.289976	+	2.01683i	0.0177796	+	0.123660i
$267$	−19.6720	−	12.6424i	−1.20391	−	0.773705i
$268$	6.21203	−	1.82402i	0.379460	−	0.111420i
$269$	−0.964015	+	6.70487i	−0.0587770	+	0.408803i	0.939098	+	0.343649i	$0.111663\pi$
$269$	−0.964015	+	6.70487i	−0.0587770	+	0.408803i	−0.997875	+	0.0651542i	$0.979246\pi$
$270$	−3.63295	+	4.19265i	−0.221095	+	0.255157i
$271$	−9.50059	+	6.10566i	−0.577119	+	0.370892i	−0.796400	−	0.604770i	$-0.793265\pi$
$271$	−9.50059	+	6.10566i	−0.577119	+	0.370892i	0.219281	+	0.975662i	$0.429629\pi$
$272$	−2.52093	−	2.90931i	−0.152854	−	0.176403i
$273$	15.5197	+	4.55700i	0.939295	+	0.275802i
$274$	−5.87897	+	12.8731i	−0.355161	+	0.777695i
$275$	4.61612			0.278362
$276$	−7.53165	−	0.303685i	−0.453352	−	0.0182797i
$277$	−21.1774			−1.27243			−0.636213	−	0.771514i	$-0.719500\pi$
$277$	−21.1774			−1.27243			−0.636213	+	0.771514i	$0.719500\pi$
$278$	−6.29667	+	13.7878i	−0.377649	+	0.826936i
$279$	1.85337	+	0.544198i	0.110958	+	0.0325803i
$280$	2.02680	+	2.33905i	0.121124	+	0.139785i
$281$	23.2729	−	14.9566i	1.38834	−	0.892233i	0.388766	−	0.921337i	$-0.372901\pi$
$281$	23.2729	−	14.9566i	1.38834	−	0.892233i	0.999576	+	0.0291031i	$0.00926513\pi$
$282$	12.3786	−	14.2857i	0.737137	−	0.850701i
$283$	3.53492	−	24.5859i	0.210129	−	1.46148i	−0.562592	−	0.826735i	$-0.690196\pi$
$283$	3.53492	−	24.5859i	0.210129	−	1.46148i	0.772721	−	0.634746i	$-0.218895\pi$
$284$	−5.88885	+	1.72912i	−0.349439	+	0.102605i
$285$	0.870475	+	0.559420i	0.0515625	+	0.0331372i
$286$	−2.18438	−	15.1927i	−0.129165	−	0.898362i
$287$	11.0084	+	24.1050i	0.649805	+	1.42287i
$288$	0.220027	+	0.481791i	0.0129652	+	0.0283898i
$289$	0.310362	+	2.15861i	0.0182566	+	0.126977i
$290$	4.41281	+	2.83594i	0.259129	+	0.166532i
$291$	−9.49233	+	2.78720i	−0.556450	+	0.163388i
$292$	−1.48470	+	10.3263i	−0.0868857	+	0.604304i
$293$	−17.1115	+	19.7477i	−0.999663	+	1.15367i	−0.0115512	+	0.999933i	$0.503677\pi$
$293$	−17.1115	+	19.7477i	−0.999663	+	1.15367i	−0.988112	+	0.153739i	$0.950869\pi$
$294$	−3.41011	+	2.19155i	−0.198882	+	0.127814i
$295$	6.38035	+	7.36331i	0.371478	+	0.428709i
$296$	−1.58942	−	0.466696i	−0.0923832	−	0.0271261i
$297$	−10.6382	+	23.2945i	−0.617294	+	1.35168i
$298$	−10.6432			−0.616544
$299$	−15.1071	−	5.10543i	−0.873667	−	0.295255i
$300$	1.57173			0.0907441
$301$	5.21880	−	11.4276i	0.300807	−	0.658675i
$302$	−19.4180	−	5.70164i	−1.11738	−	0.328092i
$303$	−0.499465	−	0.576413i	−0.0286935	−	0.0331141i
$304$	0.553831	−	0.355926i	0.0317644	−	0.0204137i
$305$	−8.66529	+	10.0003i	−0.496173	+	0.572614i
$306$	−0.290172	+	2.01819i	−0.0165880	+	0.115372i
$307$	10.2382	−	3.00620i	0.584323	−	0.171573i	0.0238075	−	0.999717i	$-0.492421\pi$
$307$	10.2382	−	3.00620i	0.584323	−	0.171573i	0.560516	+	0.828144i	$0.310603\pi$
$308$	12.0189	+	7.72409i	0.684841	+	0.440121i
$309$	0.281805	+	1.95999i	0.0160313	+	0.111500i
$310$	−1.51499	−	3.31736i	−0.0860455	−	0.188413i
$311$	7.65049	+	16.7522i	0.433820	+	0.949933i	0.992692	+	0.120679i	$0.0385071\pi$
$311$	7.65049	+	16.7522i	0.433820	+	0.949933i	−0.558872	+	0.829254i	$0.688766\pi$
$312$	−0.743755	−	5.17293i	−0.0421069	−	0.292860i
$313$	5.69917	+	3.66263i	0.322136	+	0.207024i	0.691707	−	0.722178i	$-0.256859\pi$
$313$	5.69917	+	3.66263i	0.322136	+	0.207024i	−0.369571	+	0.929202i	$0.620495\pi$
$314$	−17.9388	+	5.26730i	−1.01234	+	0.297251i
$315$	0.233295	−	1.62260i	0.0131447	−	0.0914232i
$316$	−5.94857	+	6.86502i	−0.334633	+	0.386187i
$317$	−1.83441	+	1.17890i	−0.103031	+	0.0662137i	−0.591141	−	0.806568i	$-0.701323\pi$
$317$	−1.83441	+	1.17890i	−0.103031	+	0.0662137i	0.488111	+	0.872782i	$0.337686\pi$
$318$	−7.12170	−	8.21888i	−0.399365	−	0.460892i
$319$	23.2331	+	6.82185i	1.30080	+	0.381951i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	8.59251			0.479587
$322$	12.8000	−	7.51521i	0.713316	−	0.418806i
$323$	2.53433			0.141014
$324$	−2.96212	+	6.48613i	−0.164562	+	0.360341i
$325$	3.19038	+	0.936781i	0.176971	+	0.0519633i
$326$	10.7081	+	12.3578i	0.593065	+	0.684433i
$327$	9.29967	−	5.97654i	0.514273	−	0.330503i
$328$	5.60698	−	6.47080i	0.309594	−	0.357290i
$329$	−5.29732	+	36.8437i	−0.292051	+	2.03126i
$330$	6.96141	−	2.04405i	0.383213	−	0.112522i
$331$	4.03736	+	2.59466i	0.221913	+	0.142615i	0.646874	−	0.762597i	$-0.276076\pi$
$331$	4.03736	+	2.59466i	0.221913	+	0.142615i	−0.424961	+	0.905212i	$0.639712\pi$
$332$	1.00343	+	6.97902i	0.0550705	+	0.383024i
$333$	0.364479	+	0.798097i	0.0199733	+	0.0437355i
$334$	8.73295	+	19.1225i	0.477846	+	1.04634i
$335$	0.921387	+	6.40839i	0.0503408	+	0.350128i
$336$	4.09230	+	2.62996i	0.223253	+	0.143476i
$337$	12.3539	−	3.62743i	0.672959	−	0.197599i	0.0726389	−	0.997358i	$-0.476858\pi$
$337$	12.3539	−	3.62743i	0.672959	−	0.197599i	0.600320	+	0.799760i	$0.295040\pi$
$338$	−0.276645	+	1.92411i	−0.0150475	+	0.104658i
$339$	4.36744	−	5.04030i	0.237207	−	0.273751i
$340$	3.23846	−	2.08123i	0.175630	−	0.112871i
$341$	−11.0243	−	12.7228i	−0.597001	−	0.688976i
$342$	−0.334569	−	0.0982383i	−0.0180914	−	0.00531212i
$343$	−5.68405	+	12.4463i	−0.306910	+	0.672038i
$344$	−4.05907			−0.218851
$345$	1.37246	−	7.41177i	0.0738907	−	0.399036i
$346$	−22.0317			−1.18443
$347$	12.4746	−	27.3155i	0.669670	−	1.46637i	−0.203559	−	0.979063i	$-0.565251\pi$
$347$	12.4746	−	27.3155i	0.669670	−	1.46637i	0.873229	−	0.487310i	$-0.162022\pi$
$348$	7.91060	+	2.32276i	0.424053	+	0.124513i
$349$	−10.4632	−	12.0751i	−0.560080	−	0.646366i	0.403122	−	0.915146i	$-0.367925\pi$
$349$	−10.4632	−	12.0751i	−0.560080	−	0.646366i	−0.963202	+	0.268780i	$0.913380\pi$
$350$	−2.60369	+	1.67329i	−0.139173	+	0.0894410i
$351$	−12.0798	+	13.9409i	−0.644774	+	0.744109i
$352$	0.656942	−	4.56913i	0.0350151	−	0.243535i
$353$	10.1746	−	2.98753i	0.541539	−	0.159010i	0.000488027	−	1.00000i	$-0.499845\pi$
$353$	10.1746	−	2.98753i	0.541539	−	0.159010i	0.541051	+	0.840990i	$0.318026\pi$
$354$	12.8825	+	8.27909i	0.684698	+	0.440029i
$355$	−0.873452	−	6.07499i	−0.0463580	−	0.322427i
$356$	−6.18053	−	13.5335i	−0.327567	−	0.717272i
$357$	7.77920	+	17.0341i	0.411719	+	0.901539i
$358$	0.718815	+	4.99947i	0.0379906	+	0.264230i
$359$	−12.8838	−	8.27991i	−0.679980	−	0.436997i	0.154531	−	0.987988i	$-0.450613\pi$
$359$	−12.8838	−	8.27991i	−0.679980	−	0.436997i	−0.834511	+	0.550991i	$0.814250\pi$
$360$	−0.508200	+	0.149221i	−0.0267845	+	0.00786464i
$361$	2.64230	−	18.3776i	0.139068	−	0.967242i
$362$	−11.8747	+	13.7042i	−0.624121	+	0.720275i
$363$	13.6302	−	8.75960i	0.715400	−	0.459760i
$364$	6.73925	+	7.77751i	0.353233	+	0.407652i
$365$	−10.0099	−	2.93918i	−0.523944	−	0.153844i
$366$	−8.63963	+	18.9181i	−0.451601	+	0.988867i
$367$	−17.7427			−0.926163			−0.463082	−	0.886316i	$-0.653256\pi$
$367$	−17.7427			−0.926163			−0.463082	+	0.886316i	$0.653256\pi$
$368$	−3.92677	−	2.75326i	−0.204697	−	0.143524i
$369$	−4.53496			−0.236081
$370$	0.688144	−	1.50682i	0.0357749	−	0.0783361i
$371$	20.5475	+	6.03330i	1.06677	+	0.313233i
$372$	−3.75366	−	4.33195i	−0.194618	−	0.224601i
$373$	−19.6654	+	12.6382i	−1.01824	+	0.654381i	−0.939512	−	0.342515i	$-0.888721\pi$
$373$	−19.6654	+	12.6382i	−1.01824	+	0.654381i	−0.0787250	+	0.996896i	$0.525085\pi$
$374$	11.6369	−	13.4297i	0.601731	−	0.694434i
$375$	−0.223681	+	1.55574i	−0.0115508	+	0.0803378i
$376$	11.5395	−	3.38830i	0.595104	−	0.174738i
$377$	14.6729	+	9.42972i	0.755694	+	0.485655i
$378$	−2.44356	−	16.9953i	−0.125683	−	0.874145i
$379$	6.10345	+	13.3647i	0.313513	+	0.686498i	0.999140	−	0.0414549i	$-0.0131993\pi$
$379$	6.10345	+	13.3647i	0.313513	+	0.686498i	−0.685627	+	0.727953i	$0.740472\pi$
$380$	0.273484	+	0.598847i	0.0140295	+	0.0307202i
$381$	2.61497	+	18.1875i	0.133969	+	0.931775i
$382$	16.4354	+	10.5624i	0.840909	+	0.540419i
$383$	−18.1356	+	5.32511i	−0.926688	+	0.272100i	−0.710050	−	0.704152i	$-0.751327\pi$
$383$	−18.1356	+	5.32511i	−0.926688	+	0.272100i	−0.216639	+	0.976252i	$0.569509\pi$
$384$	0.223681	−	1.55574i	0.0114147	−	0.0793908i
$385$	−9.35594	+	10.7973i	−0.476823	+	0.550283i
$386$	3.48388	−	2.23895i	0.177325	−	0.113960i
$387$	1.40789	+	1.62479i	0.0715671	+	0.0825929i
$388$	−6.03940	−	1.77333i	−0.306604	−	0.0900271i
$389$	1.88681	−	4.13154i	0.0956652	−	0.209478i	−0.855749	−	0.517391i	$-0.826903\pi$
$389$	1.88681	−	4.13154i	0.0956652	−	0.209478i	0.951414	+	0.307913i	$0.0996307\pi$
$390$	5.22613			0.264635
$391$	−6.98654	−	17.0889i	−0.353324	−	0.864222i
$392$	−2.57907			−0.130263
$393$	9.15427	−	20.0451i	0.461772	−	1.01114i
$394$	24.3842	+	7.15985i	1.22846	+	0.360708i
$395$	−5.94857	−	6.86502i	−0.299305	−	0.345416i
$396$	−2.05682	+	1.32184i	−0.103359	+	0.0664249i
$397$	−3.50565	+	4.04574i	−0.175944	+	0.203050i	−0.836871	−	0.547400i	$-0.815618\pi$
$397$	−3.50565	+	4.04574i	−0.175944	+	0.203050i	0.660927	+	0.750450i	$0.270163\pi$
$398$	1.04842	−	7.29192i	0.0525525	−	0.365511i
$399$	−3.07279	+	0.902252i	−0.153832	+	0.0451691i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−3.18523	−	22.1538i	−0.159063	−	1.10631i	−0.900365	−	0.435135i	$-0.856701\pi$
$401$	−3.18523	−	22.1538i	−0.159063	−	1.10631i	0.741303	−	0.671171i	$-0.234208\pi$
$402$	4.22720	+	9.25628i	0.210834	+	0.461661i
$403$	−5.03744	−	11.0305i	−0.250933	−	0.549466i
$404$	−0.0690601	−	0.480324i	−0.00343587	−	0.0238970i
$405$	−5.99856	−	3.85504i	−0.298071	−	0.191558i
$406$	−15.5773	+	4.57391i	−0.773088	+	0.226999i
$407$	1.08824	−	7.56886i	0.0539419	−	0.375174i
$408$	3.96223	−	4.57266i	0.196160	−	0.226380i
$409$	−1.78223	+	1.14537i	−0.0881257	+	0.0566349i	−0.583962	−	0.811781i	$-0.698498\pi$
$409$	−1.78223	+	1.14537i	−0.0881257	+	0.0566349i	0.495836	+	0.868416i	$0.334862\pi$
$410$	5.60698	+	6.47080i	0.276909	+	0.319570i
$411$	−21.3422	−	6.26664i	−1.05273	−	0.309110i
$412$	−0.523361	+	1.14600i	−0.0257841	+	0.0564594i
$413$	−30.1548			−1.48382
$414$	0.259909	+	2.52680i	0.0127738	+	0.124186i
$415$	−7.05079			−0.346110
$416$	1.38128	−	3.02459i	0.0677231	−	0.148293i
$417$	−22.8586	−	6.71189i	−1.11939	−	0.328683i
$418$	1.99011	+	2.29670i	0.0973392	+	0.112335i
$419$	−13.3123	+	8.55528i	−0.650347	+	0.417953i	−0.823793	−	0.566891i	$-0.808146\pi$
$419$	−13.3123	+	8.55528i	−0.650347	+	0.417953i	0.173446	+	0.984843i	$0.444510\pi$
$420$	−3.18559	+	3.67636i	−0.155441	+	0.179388i
$421$	−4.84558	+	33.7017i	−0.236159	+	1.64252i	0.434440	+	0.900701i	$0.356946\pi$
$421$	−4.84558	+	33.7017i	−0.236159	+	1.64252i	−0.670599	+	0.741820i	$0.733963\pi$
$422$	−7.33832	+	2.15472i	−0.357224	+	0.104890i
$423$	−5.35877	−	3.44387i	−0.260552	−	0.167447i
$424$	−0.984705	−	6.84877i	−0.0478215	−	0.332606i
$425$	1.59917	+	3.50169i	0.0775711	+	0.169857i
$426$	−4.00728	−	8.77472i	−0.194153	−	0.425137i
$427$	−5.82835	−	40.5371i	−0.282054	−	1.96173i
$428$	4.59905	+	2.95563i	0.222303	+	0.142866i
$429$	23.1472	−	6.79663i	1.11756	−	0.328144i
$430$	0.577666	−	4.01776i	0.0278575	−	0.193753i
$431$	8.93468	−	10.3112i	0.430369	−	0.496672i	−0.498599	−	0.866833i	$-0.666152\pi$
$431$	8.93468	−	10.3112i	0.430369	−	0.496672i	0.928968	+	0.370161i	$0.120697\pi$
$432$	−4.66700	+	2.99930i	−0.224541	+	0.144304i
$433$	7.25765	+	8.37578i	0.348781	+	0.402514i	0.902850	−	0.429957i	$-0.141471\pi$
$433$	7.25765	+	8.37578i	0.348781	+	0.402514i	−0.554069	+	0.832471i	$0.686926\pi$
$434$	10.8300	+	3.17999i	0.519859	+	0.152644i
$435$	−3.42491	+	7.49952i	−0.164212	+	0.359574i
$436$	7.03334			0.336836
$437$	3.06277	−	0.766739i	0.146512	−	0.0366781i
$438$	−16.3972			−0.783486
$439$	−4.62006	+	10.1165i	−0.220504	+	0.482835i	−0.987263	−	0.159100i	$-0.949141\pi$
$439$	−4.62006	+	10.1165i	−0.220504	+	0.482835i	0.766759	+	0.641935i	$0.221868\pi$
$440$	4.42913	+	1.30051i	0.211151	+	0.0619994i
$441$	0.894551	+	1.03237i	0.0425977	+	0.0491603i
$442$	10.7681	−	6.92026i	0.512188	−	0.329163i
$443$	7.77041	−	8.96754i	0.369183	−	0.426060i	−0.540512	−	0.841336i	$-0.681769\pi$
$443$	7.77041	−	8.96754i	0.369183	−	0.426060i	0.909696	+	0.415276i	$0.136315\pi$
$444$	0.370532	−	2.57711i	0.0175847	−	0.122304i
$445$	14.2753	−	4.19161i	0.676714	−	0.198701i
$446$	7.80352	+	5.01502i	0.369507	+	0.237468i
$447$	−2.38068	−	16.5580i	−0.112602	−	0.783167i
$448$	1.28571	+	2.81532i	0.0607442	+	0.133011i
$449$	−3.84991	−	8.43013i	−0.181689	−	0.397842i	0.796771	−	0.604281i	$-0.206540\pi$
$449$	−3.84991	−	8.43013i	−0.181689	−	0.397842i	−0.978459	+	0.206439i	$0.933812\pi$
$450$	−0.0753778	−	0.524264i	−0.00355334	−	0.0247140i
$451$	33.2494	+	21.3681i	1.56565	+	1.00618i
$452$	4.07138	−	1.19546i	0.191501	−	0.0562299i
$453$	4.52680	−	31.4846i	0.212688	−	1.47928i
$454$	12.1796	−	14.0560i	0.571619	−	0.659683i
$455$	−8.65744	+	5.56380i	−0.405867	+	0.260835i
$456$	0.677607	+	0.782001i	0.0317319	+	0.0366205i
$457$	13.0182	+	3.82250i	0.608967	+	0.178809i	0.571654	−	0.820495i	$-0.306302\pi$
$457$	13.0182	+	3.82250i	0.608967	+	0.178809i	0.0373130	+	0.999304i	$0.488120\pi$
$458$	−5.37751	+	11.7751i	−0.251275	+	0.550215i
$459$	−21.3562			−0.996821
$460$	3.28408	−	3.49498i	0.153121	−	0.162954i
$461$	23.6869			1.10321			0.551605	−	0.834106i	$-0.314016\pi$
$461$	23.6869			1.10321			0.551605	+	0.834106i	$0.314016\pi$
$462$	−9.32823	+	20.4260i	−0.433989	+	0.950303i
$463$	−1.55201	−	0.455711i	−0.0721280	−	0.0211787i	0.245469	−	0.969404i	$-0.421058\pi$
$463$	−1.55201	−	0.455711i	−0.0721280	−	0.0211787i	−0.317597	+	0.948226i	$0.602876\pi$
$464$	3.43509	+	3.96430i	0.159470	+	0.184038i
$465$	4.82206	−	3.09895i	0.223618	−	0.143710i
$466$	−9.10090	+	10.5030i	−0.421591	+	0.486542i
$467$	−2.68477	+	18.6730i	−0.124236	+	0.864083i	0.828436	+	0.560084i	$0.189231\pi$
$467$	−2.68477	+	18.6730i	−0.124236	+	0.864083i	−0.952672	+	0.303999i	$0.901678\pi$
$468$	−1.68980	+	0.496171i	−0.0781112	+	0.0229355i
$469$	−16.8570	−	10.8333i	−0.778385	−	0.500237i
$470$	1.71157	+	11.9042i	0.0789489	+	0.549102i
$471$	−12.2071	−	26.7298i	−0.562472	−	1.23164i
$472$	4.04741	+	8.86260i	0.186297	+	0.407934i
$473$	−2.66657	−	18.5464i	−0.122609	−	0.852766i
$474$	−12.0107	−	7.71883i	−0.551671	−	0.354537i
$475$	−0.631673	+	0.185476i	−0.0289831	+	0.00851022i
$476$	−1.69560	+	11.7932i	−0.0777178	+	0.540539i
$477$	−2.39993	+	2.76966i	−0.109885	+	0.126814i
$478$	20.7486	−	13.3343i	0.949017	−	0.609896i
$479$	−8.77261	−	10.1241i	−0.400831	−	0.462583i	0.519072	−	0.854731i	$-0.326278\pi$
$479$	−8.77261	−	10.1241i	−0.400831	−	0.462583i	−0.919902	+	0.392147i	$0.871732\pi$
$480$	1.50807	+	0.442808i	0.0688335	+	0.0202113i
$481$	2.28813	−	5.01030i	0.104330	−	0.228450i
$482$	−2.47237			−0.112613
$483$	14.5548	+	18.2324i	0.662266	+	0.829603i
$484$	10.3085			0.468569
$485$	2.61477	−	5.72556i	0.118731	−	0.259984i
$486$	5.21560	+	1.53144i	0.236584	+	0.0694674i
$487$	4.54326	+	5.24320i	0.205875	+	0.237592i	0.849292	−	0.527924i	$-0.177029\pi$
$487$	4.54326	+	5.24320i	0.205875	+	0.237592i	−0.643417	+	0.765516i	$0.722484\pi$
$488$	−11.1317	+	7.15390i	−0.503908	+	0.323842i
$489$	−16.8302	+	19.4231i	−0.761088	+	0.878343i
$490$	0.367040	−	2.55282i	0.0165812	−	0.115325i
$491$	−1.75393	+	0.515002i	−0.0791540	+	0.0232417i	−0.321070	−	0.947056i	$-0.604042\pi$
$491$	−1.75393	+	0.515002i	−0.0791540	+	0.0232417i	0.241916	+	0.970297i	$0.422224\pi$
$492$	11.3210	+	7.27558i	0.510391	+	0.328009i
$493$	2.87376	+	19.9875i	0.129428	+	0.900190i
$494$	0.909356	+	1.99121i	0.0409138	+	0.0895888i
$495$	−1.01567	−	2.22400i	−0.0456509	−	0.0999616i
$496$	−0.519012	−	3.60981i	−0.0233043	−	0.162085i
$497$	15.9800	+	10.2697i	0.716802	+	0.460661i
$498$	−10.6331	+	3.12215i	−0.476479	+	0.139907i
$499$	5.40506	−	37.5930i	0.241964	−	1.68290i	−0.400278	−	0.916394i	$-0.631086\pi$
$499$	5.40506	−	37.5930i	0.241964	−	1.68290i	0.642242	−	0.766502i	$-0.278004\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	−27.7961	+	17.8635i	−1.24184	+	0.798082i
$502$	−8.57803	−	9.89957i	−0.382856	−	0.441839i
$503$	−5.26992	−	1.54739i	−0.234974	−	0.0689946i	0.162125	−	0.986770i	$-0.448165\pi$
$503$	−5.26992	−	1.54739i	−0.234974	−	0.0689946i	−0.397100	+	0.917776i	$0.629983\pi$
$504$	0.680984	−	1.49115i	0.0303334	−	0.0664210i
$505$	0.485263			0.0215939
$506$	10.0003	−	19.7507i	0.444570	−	0.878025i
$507$	−3.05528			−0.135690
$508$	−4.85646	+	10.6342i	−0.215471	+	0.471815i
$509$	−27.0117	−	7.93136i	−1.19727	−	0.351551i	−0.378464	−	0.925616i	$-0.623548\pi$
$509$	−27.0117	−	7.93136i	−1.19727	−	0.351551i	−0.818810	+	0.574064i	$0.805366\pi$
$510$	3.96223	+	4.57266i	0.175451	+	0.202481i
$511$	27.1630	−	17.4566i	1.20162	−	0.772236i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.519771	−	3.61508i	0.0229484	−	0.159610i
$514$	−7.10716	+	2.08685i	−0.313483	+	0.0920470i
$515$	−1.05985	−	0.681127i	−0.0467028	−	0.0300140i
$516$	−0.907937	−	6.31484i	−0.0399697	−	0.277995i
$517$	23.0624	+	50.4995i	1.01428	+	2.22097i
$518$	2.12981	+	4.66363i	0.0935785	+	0.204908i
$519$	−4.92806	−	34.2754i	−0.216318	−	1.50452i
$520$	2.79723	+	1.79767i	0.122667	+	0.0788330i
$521$	−18.3567	+	5.39001i	−0.804221	+	0.236141i	−0.657909	−	0.753098i	$-0.728559\pi$
$521$	−18.3567	+	5.39001i	−0.804221	+	0.236141i	−0.146313	+	0.989238i	$0.546741\pi$
$522$	0.395396	−	2.75004i	0.0173060	−	0.120366i
$523$	22.1124	−	25.5191i	0.966907	−	1.11587i	−0.0263165	−	0.999654i	$-0.508378\pi$
$523$	22.1124	−	25.5191i	0.966907	−	1.11587i	0.993224	−	0.116217i	$-0.0370768\pi$
$524$	11.7948	−	7.58004i	0.515257	−	0.331136i
$525$	−3.18559	−	3.67636i	−0.139030	−	0.160450i
$526$	−16.1431	−	4.74004i	−0.703873	−	0.206676i
$527$	5.83205	−	12.7704i	0.254048	−	0.556288i
$528$	7.25530			0.315746
$529$	−13.6134	−	18.5385i	−0.591888	−	0.806020i
$530$	6.91920			0.300551
$531$	2.14373	−	4.69412i	0.0930301	−	0.203707i
$532$	−1.95503	−	0.574049i	−0.0847614	−	0.0248882i
$533$	18.6436	+	21.5159i	0.807545	+	0.931956i
$534$	19.6720	−	12.6424i	0.851292	−	0.547092i
$535$	−3.58006	+	4.13161i	−0.154779	+	0.178625i
$536$	−0.921387	+	6.40839i	−0.0397979	+	0.276800i
$537$	−7.61707	+	2.23657i	−0.328701	+	0.0965152i
$538$	−5.69850	−	3.66220i	−0.245680	−	0.157889i
$539$	−1.69430	−	11.7841i	−0.0729786	−	0.507577i
$540$	−2.30459	−	5.04634i	−0.0991737	−	0.217160i
$541$	−11.3756	−	24.9091i	−0.489076	−	1.07093i	−0.979867	−	0.199650i	$-0.936020\pi$
$541$	−11.3756	−	24.9091i	−0.489076	−	1.07093i	0.490791	−	0.871277i	$-0.336708\pi$
$542$	−1.60721	−	11.1784i	−0.0690357	−	0.480154i
$543$	−23.9762	−	15.4086i	−1.02892	−	0.661245i
$544$	3.69364	−	1.08455i	0.158363	−	0.0464997i
$545$	−1.00095	+	6.96175i	−0.0428760	+	0.298209i
$546$	−10.5923	+	12.2242i	−0.453309	+	0.523146i
$547$	5.11845	−	3.28943i	0.218849	−	0.140646i	−0.426623	−	0.904429i	$-0.640297\pi$
$547$	5.11845	−	3.28943i	0.218849	−	0.140646i	0.645472	+	0.763784i	$0.276661\pi$
$548$	−9.26761	−	10.6954i	−0.395893	−	0.456885i
$549$	6.72464	+	1.97453i	0.287001	+	0.0842710i
$550$	−1.91760	+	4.19897i	−0.0817669	+	0.179045i
$551$	−3.45334			−0.147117
$552$	3.40500	−	6.72487i	0.144926	−	0.286230i
$553$	28.1142			1.19554
$554$	8.79740	−	19.2636i	0.373766	−	0.818433i
$555$	2.49814	+	0.733521i	0.106040	+	0.0311362i
$556$	−9.92608	−	11.4553i	−0.420960	−	0.485813i
$557$	−5.92104	+	3.80522i	−0.250882	+	0.161232i	−0.660038	−	0.751232i	$-0.729460\pi$
$557$	−5.92104	+	3.80522i	−0.250882	+	0.161232i	0.409155	+	0.912465i	$0.365823\pi$
$558$	−1.26494	+	1.45982i	−0.0535491	+	0.0617989i
$559$	1.92078	−	13.3593i	0.0812404	−	0.565040i
$560$	−2.96964	+	0.871964i	−0.125490	+	0.0368472i
$561$	23.4960	+	15.1000i	0.992003	+	0.637522i
$562$	3.93707	+	27.3829i	0.166075	+	1.15508i
$563$	2.26169	+	4.95242i	0.0953191	+	0.208720i	0.951285	−	0.308312i	$-0.0997641\pi$
$563$	2.26169	+	4.95242i	0.0953191	+	0.208720i	−0.855966	+	0.517032i	$0.827037\pi$
$564$	7.85246	+	17.1945i	0.330648	+	0.724019i
$565$	0.603879	+	4.20007i	0.0254054	+	0.176698i
$566$	20.8957	+	13.4288i	0.878310	+	0.564456i
$567$	21.1750	−	6.21754i	0.889266	−	0.261112i
$568$	0.873452	−	6.07499i	0.0366492	−	0.254901i
$569$	25.4406	−	29.3601i	1.06653	−	1.23084i	0.0946096	−	0.995514i	$-0.469840\pi$
$569$	25.4406	−	29.3601i	1.06653	−	1.23084i	0.971917	−	0.235323i	$-0.0756148\pi$
$570$	−0.870475	+	0.559420i	−0.0364602	+	0.0234315i
$571$	−2.34967	−	2.71166i	−0.0983306	−	0.113480i	0.704451	−	0.709752i	$-0.251193\pi$
$571$	−2.34967	−	2.71166i	−0.0983306	−	0.113480i	−0.802782	+	0.596273i	$0.796648\pi$
$572$	14.7272	+	4.32429i	0.615774	+	0.180808i
$573$	−12.7560	+	27.9318i	−0.532890	+	1.16687i
$574$	−26.4998			−1.10608
$575$	2.99203	+	3.74803i	0.124776	+	0.156304i
$576$	−0.529655			−0.0220690
$577$	−0.951604	+	2.08372i	−0.0396158	+	0.0867465i	−0.928405	−	0.371569i	$-0.878820\pi$
$577$	−0.951604	+	2.08372i	−0.0396158	+	0.0867465i	0.888789	+	0.458316i	$0.151547\pi$
$578$	−2.09247	−	0.614405i	−0.0870353	−	0.0255559i
$579$	4.26250	+	4.91919i	0.177143	+	0.204434i
$580$	−4.41281	+	2.83594i	−0.183232	+	0.117756i
$581$	14.2905	−	16.4922i	0.592871	−	0.684210i
$582$	1.40793	−	9.79237i	0.0583606	−	0.405907i
$583$	30.6460	−	8.99849i	1.26923	−	0.372679i
$584$	−8.77640	−	5.64025i	−0.363170	−	0.233395i
$585$	−0.250637	−	1.74322i	−0.0103625	−	0.0720731i
$586$	−10.8548	−	23.7686i	−0.448406	−	0.981873i
$587$	17.7891	+	38.9528i	0.734237	+	1.60775i	0.792808	+	0.609471i	$0.208618\pi$
$587$	17.7891	+	38.9528i	0.734237	+	1.60775i	−0.0585718	+	0.998283i	$0.518655\pi$
$588$	−0.576889	−	4.01235i	−0.0237905	−	0.165466i
$589$	2.01978	+	1.29803i	0.0832236	+	0.0534846i
$590$	−9.34839	+	2.74494i	−0.384867	+	0.113007i
$591$	−5.68454	+	39.5369i	−0.233831	+	1.62633i
$592$	1.08479	−	1.25192i	0.0445846	−	0.0514534i
$593$	19.5324	−	12.5527i	0.802100	−	0.515478i	−0.0742005	−	0.997243i	$-0.523640\pi$
$593$	19.5324	−	12.5527i	0.802100	−	0.515478i	0.876300	+	0.481765i	$0.160004\pi$
$594$	−16.7701	−	19.3538i	−0.688087	−	0.794095i
$595$	−11.4318	−	3.35669i	−0.468659	−	0.137611i
$596$	4.42135	−	9.68140i	0.181105	−	0.396566i
$597$	11.5788			0.473889
$598$	10.9198	−	11.6210i	0.446543	−	0.475220i
$599$	23.8660			0.975139			0.487569	−	0.873084i	$-0.337884\pi$
$599$	23.8660			0.975139			0.487569	+	0.873084i	$0.337884\pi$
$600$	−0.652922	+	1.42970i	−0.0266554	+	0.0583672i
$601$	−5.69305	−	1.67163i	−0.232224	−	0.0681872i	0.163550	−	0.986535i	$-0.447706\pi$
$601$	−5.69305	−	1.67163i	−0.232224	−	0.0681872i	−0.395774	+	0.918348i	$0.629524\pi$
$602$	8.22692	+	9.49438i	0.335304	+	0.386962i
$603$	2.88478	−	1.85393i	0.117477	−	0.0754980i
$604$	13.2529	−	15.2947i	0.539253	−	0.622332i
$605$	−1.46706	+	10.2036i	−0.0596443	+	0.414835i
$606$	0.731809	−	0.214879i	0.0297277	−	0.00872884i
$607$	−38.9094	−	25.0056i	−1.57929	−	1.01495i	−0.976094	−	0.217349i	$-0.930259\pi$
$607$	−38.9094	−	25.0056i	−1.57929	−	1.01495i	−0.603191	−	0.797596i	$-0.706105\pi$
$608$	0.0936916	+	0.651639i	0.00379970	+	0.0264275i
$609$	−10.6001	−	23.2111i	−0.429539	−	0.940559i
$610$	−5.49688	−	12.0365i	−0.222562	−	0.487343i
$611$	5.69110	+	39.5825i	0.230237	+	1.60133i
$612$	−1.71527	−	1.10234i	−0.0693357	−	0.0445593i
$613$	40.3622	−	11.8514i	1.63022	−	0.478674i	0.666478	−	0.745525i	$-0.267801\pi$
$613$	40.3622	−	11.8514i	1.63022	−	0.478674i	0.963738	+	0.266851i	$0.0859830\pi$
$614$	−1.51856	+	10.5618i	−0.0612839	+	0.426239i
$615$	−8.81268	+	10.1704i	−0.355362	+	0.410109i
$616$	−12.0189	+	7.72409i	−0.484256	+	0.311212i
$617$	16.0546	+	18.5280i	0.646335	+	0.745910i	0.980482	−	0.196611i	$-0.0629936\pi$
$617$	16.0546	+	18.5280i	0.646335	+	0.745910i	−0.334147	+	0.942521i	$0.608448\pi$
$618$	−1.89994	−	0.557873i	−0.0764268	−	0.0224409i
$619$	12.0248	−	26.3307i	0.483318	−	1.05832i	−0.498220	−	0.867051i	$-0.666013\pi$
$619$	12.0248	−	26.3307i	0.483318	−	1.05832i	0.981538	−	0.191268i	$-0.0612600\pi$
$620$	3.64693			0.146464
$621$	−25.8093	+	6.46113i	−1.03569	+	0.259276i
$622$	−18.4165			−0.738435
$623$	−19.1288	+	41.8862i	−0.766378	+	1.67813i
$624$	5.01443	+	1.47237i	0.200738	+	0.0589420i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	−5.69917	+	3.66263i	−0.227785	+	0.146388i
$627$	−3.12791	+	3.60981i	−0.124917	+	0.144162i
$628$	2.66073	−	18.5058i	0.106175	−	0.738461i
$629$	6.11858	−	1.79658i	0.243964	−	0.0716343i
$630$	1.37906	+	0.886265i	0.0549429	+	0.0353096i
$631$	4.28089	+	29.7743i	0.170420	+	1.18529i	0.877999	+	0.478662i	$0.158878\pi$
$631$	4.28089	+	29.7743i	0.170420	+	1.18529i	−0.707580	+	0.706633i	$0.750213\pi$
$632$	−3.77351	−	8.26284i	−0.150102	−	0.328678i
$633$	−4.99362	−	10.9345i	−0.198479	−	0.434608i
$634$	−0.310327	−	2.15837i	−0.0123246	−	0.0857198i
$635$	−9.83478	−	6.32043i	−0.390281	−	0.250819i
$636$	10.4346	−	3.06388i	0.413760	−	0.121491i
$637$	1.22043	−	8.48830i	0.0483554	−	0.336319i
$638$	−15.8568	+	18.2997i	−0.627775	+	0.724491i
$639$	−2.73469	+	1.75748i	−0.108183	+	0.0695249i
$640$	0.654861	+	0.755750i	0.0258856	+	0.0298736i
$641$	−44.4028	−	13.0378i	−1.75380	−	0.514963i	−0.762549	−	0.646930i	$-0.776052\pi$
$641$	−44.4028	−	13.0378i	−1.75380	−	0.514963i	−0.991254	+	0.131967i	$0.957871\pi$
$642$	−3.56946	+	7.81602i	−0.140875	+	0.308474i
$643$	2.13128			0.0840494			0.0420247	−	0.999117i	$-0.486619\pi$
$643$	2.13128			0.0840494			0.0420247	+	0.999117i	$0.486619\pi$
$644$	1.51876	+	14.7652i	0.0598477	+	0.581831i
$645$	6.37978			0.251204
$646$	−1.05280	+	2.30531i	−0.0414218	+	0.0907010i
$647$	−8.75876	−	2.57180i	−0.344342	−	0.101108i	0.104989	−	0.994473i	$-0.466519\pi$
$647$	−8.75876	−	2.57180i	−0.344342	−	0.101108i	−0.449331	+	0.893365i	$0.648338\pi$
$648$	−4.66948	−	5.38887i	−0.183435	−	0.211695i
$649$	−37.8354	+	24.3154i	−1.48517	+	0.954461i
$650$	−2.17746	+	2.51292i	−0.0854070	+	0.0985649i
$651$	−2.52475	+	17.5600i	−0.0989526	+	0.688230i
$652$	−15.6893	+	4.60679i	−0.614440	+	0.180416i
$653$	−11.4285	−	7.34466i	−0.447232	−	0.287419i	0.297575	−	0.954698i	$-0.403822\pi$
$653$	−11.4285	−	7.34466i	−0.447232	−	0.287419i	−0.744807	+	0.667280i	$0.767459\pi$
$654$	1.57322	+	10.9420i	0.0615180	+	0.427867i
$655$	5.82432	+	12.7535i	0.227575	+	0.498319i
$656$	3.55682	+	7.78836i	0.138871	+	0.304084i
$657$	0.786381	+	5.46940i	0.0306797	+	0.213382i
$658$	−31.3136	−	20.1240i	−1.22073	−	0.784517i
$659$	25.3382	−	7.43996i	0.987035	−	0.289820i	0.251909	−	0.967751i	$-0.418942\pi$
$659$	25.3382	−	7.43996i	0.987035	−	0.289820i	0.735125	+	0.677931i	$0.237123\pi$
$660$	−1.03254	+	7.18145i	−0.0401915	+	0.279538i
$661$	−19.9562	+	23.0306i	−0.776204	+	0.895788i	−0.996829	−	0.0795711i	$-0.974645\pi$
$661$	−19.9562	+	23.0306i	−0.776204	+	0.895788i	0.220625	+	0.975359i	$0.429190\pi$
$662$	−4.03736	+	2.59466i	−0.156917	+	0.100844i
$663$	13.1747	+	15.2044i	0.511663	+	0.590491i
$664$	−6.76518	−	1.98644i	−0.262540	−	0.0770887i
$665$	0.846436	−	1.85344i	0.0328234	−	0.0718732i
$666$	−0.877385			−0.0339980
$667$	9.52003	+	23.2857i	0.368617	+	0.901627i
$668$	−21.0222			−0.813375
$669$	−6.05654	+	13.2620i	−0.234159	+	0.512738i
$670$	−6.21203	−	1.82402i	−0.239992	−	0.0704680i
$671$	−40.0000	−	46.1624i	−1.54418	−	1.78208i
$672$	−4.09230	+	2.62996i	−0.157864	+	0.101453i
$673$	−26.3249	+	30.3805i	−1.01475	+	1.17108i	−0.0295693	+	0.999563i	$0.509414\pi$
$673$	−26.3249	+	30.3805i	−1.01475	+	1.17108i	−0.985180	+	0.171521i	$0.945132\pi$
$674$	−1.83237	+	12.7444i	−0.0705801	+	0.490895i
$675$	5.32296	−	1.56296i	0.204881	−	0.0601584i
$676$	−1.63531	−	1.05095i	−0.0628965	−	0.0404211i
$677$	5.50463	+	38.2856i	0.211560	+	1.47143i	0.767949	+	0.640511i	$0.221278\pi$
$677$	5.50463	+	38.2856i	0.211560	+	1.47143i	−0.556388	+	0.830922i	$0.687813\pi$
$678$	2.77052	+	6.06658i	0.106401	+	0.232986i
$679$	8.09275	+	17.7206i	0.310571	+	0.680056i
$680$	0.547851	+	3.81039i	0.0210091	+	0.146122i
$681$	24.5918	+	15.8042i	0.942361	+	0.605619i
$682$	16.1527	−	4.74286i	0.618519	−	0.181614i
$683$	−7.22696	+	50.2646i	−0.276532	+	1.92332i	0.0961594	+	0.995366i	$0.469344\pi$
$683$	−7.22696	+	50.2646i	−0.276532	+	1.92332i	−0.372691	+	0.927955i	$0.621565\pi$
$684$	0.228346	−	0.263525i	0.00873101	−	0.0100761i
$685$	11.9054	−	7.65117i	0.454884	−	0.292336i
$686$	−8.96034	−	10.3408i	−0.342107	−	0.394813i
$687$	−19.5218	−	5.73212i	−0.744803	−	0.218694i
$688$	1.68620	−	3.69226i	0.0642858	−	0.140766i
$689$	23.0068			0.876491
$690$	6.17184	+	4.32739i	0.234958	+	0.164741i
$691$	36.5261			1.38952			0.694760	−	0.719242i	$-0.255511\pi$
$691$	36.5261			1.38952			0.694760	+	0.719242i	$0.255511\pi$
$692$	9.15228	−	20.0407i	0.347918	−	0.761833i
$693$	7.26061	+	2.13191i	0.275808	+	0.0809845i
$694$	19.6649	+	22.6945i	0.746470	+	0.861472i
$695$	12.7513	−	8.19479i	0.483686	−	0.310846i
$696$	−5.39904	+	6.23082i	−0.204650	+	0.236179i
$697$	−4.69075	+	32.6249i	−0.177675	+	1.23576i
$698$	15.3305	−	4.50143i	0.580267	−	0.170382i
$699$	−18.3756	−	11.8093i	−0.695029	−	0.446668i
$700$	−0.440465	−	3.06350i	−0.0166480	−	0.115790i
$701$	−16.0489	−	35.1421i	−0.606157	−	1.32730i	−0.925171	−	0.379550i	$-0.876079\pi$
$701$	−16.0489	−	35.1421i	−0.606157	−	1.32730i	0.319014	−	0.947750i	$-0.396648\pi$
$702$	−7.66292	−	16.7795i	−0.289218	−	0.633300i
$703$	0.155202	+	1.07945i	0.00585356	+	0.0407124i
$704$	3.88332	+	2.49566i	0.146358	+	0.0940587i
$705$	−18.1370	+	5.32550i	−0.683079	+	0.200570i
$706$	−1.50913	+	10.4962i	−0.0567967	+	0.395030i
$707$	−0.983531	+	1.13505i	−0.0369895	+	0.0426881i
$708$	−12.8825	+	8.27909i	−0.484155	+	0.311147i
$709$	−13.8835	−	16.0224i	−0.521405	−	0.601734i	0.432577	−	0.901597i	$-0.357604\pi$
$709$	−13.8835	−	16.0224i	−0.521405	−	0.601734i	−0.953982	+	0.299863i	$0.903059\pi$
$710$	5.88885	+	1.72912i	0.221005	+	0.0648928i
$711$	−1.99866	+	4.37646i	−0.0749556	+	0.164130i
$712$	14.8780			0.557575
$713$	3.18454	−	17.1977i	0.119262	−	0.644058i
$714$	−18.7263			−0.700815
$715$	−6.37617	+	13.9619i	−0.238455	+	0.522144i
$716$	−4.84629	−	1.42300i	−0.181114	−	0.0531799i
$717$	25.3857	+	29.2966i	0.948045	+	1.09410i
$718$	12.8838	−	8.27991i	0.480819	−	0.309003i
$719$	−21.2014	+	24.4677i	−0.790678	+	0.912491i	−0.997832	−	0.0658171i	$-0.979035\pi$
$719$	−21.2014	+	24.4677i	−0.790678	+	0.912491i	0.207153	+	0.978308i	$0.433580\pi$
$720$	0.0753778	−	0.524264i	0.00280916	−	0.0195382i
$721$	3.74130	−	1.09855i	0.139333	−	0.0409120i
$722$	15.6192	+	10.0379i	0.581287	+	0.373570i
$723$	−0.553021	−	3.84635i	−0.0205671	−	0.143047i
$724$	−7.53280	−	16.4945i	−0.279954	−	0.613015i
$725$	−2.17907	−	4.77149i	−0.0809286	−	0.177209i
$726$	2.30582	+	16.0373i	0.0855770	+	0.595201i
$727$	−7.49250	−	4.81514i	−0.277882	−	0.178584i	0.394275	−	0.918992i	$-0.370996\pi$
$727$	−7.49250	−	4.81514i	−0.277882	−	0.178584i	−0.672157	+	0.740409i	$0.734632\pi$
$728$	−9.87426	+	2.89934i	−0.365964	+	0.107457i
$729$	−4.26021	+	29.6304i	−0.157786	+	1.09742i
$730$	6.83186	−	7.88438i	0.252858	−	0.291814i
$731$	13.1452	−	8.44788i	0.486191	−	0.312456i
$732$	−13.6195	−	15.7178i	−0.503392	−	0.580945i
$733$	6.42865	+	1.88762i	0.237448	+	0.0697210i	0.398291	−	0.917259i	$-0.369603\pi$
$733$	6.42865	+	1.88762i	0.237448	+	0.0697210i	−0.160844	+	0.986980i	$0.551421\pi$
$734$	7.37060	−	16.1394i	0.272054	−	0.595715i
$735$	4.05361			0.149520
$736$	4.13570	−	2.42817i	0.152444	−	0.0895037i
$737$	−29.8861			−1.10087
$738$	1.88389	−	4.12514i	0.0693470	−	0.151849i
$739$	−31.7456	−	9.32136i	−1.16778	−	0.342892i	−0.360330	−	0.932825i	$-0.617336\pi$
$739$	−31.7456	−	9.32136i	−1.16778	−	0.342892i	−0.807452	+	0.589933i	$0.799154\pi$
$740$	1.08479	+	1.25192i	0.0398777	+	0.0460213i
$741$	−2.89439	+	1.86011i	−0.106328	+	0.0683329i
$742$	−14.0238	+	16.1844i	−0.514831	+	0.594147i
$743$	0.891036	−	6.19729i	0.0326889	−	0.227356i	−0.966927	−	0.255051i	$-0.917908\pi$
$743$	0.891036	−	6.19729i	0.0326889	−	0.227356i	0.999616	+	0.0276949i	$0.00881670\pi$
$744$	5.49981	−	1.61489i	0.201633	−	0.0592047i
$745$	8.95363	+	5.75415i	0.328036	+	0.210816i
$746$	−3.32680	−	23.1384i	−0.121803	−	0.847157i
$747$	1.55136	+	3.39701i	0.0567614	+	0.124290i
$748$	7.38195	+	16.1642i	0.269911	+	0.591022i
$749$	−2.40798	−	16.7479i	−0.0879857	−	0.611954i
$750$	−1.32223	−	0.849743i	−0.0482809	−	0.0310282i
$751$	26.1656	−	7.68291i	0.954796	−	0.280353i	0.233014	−	0.972473i	$-0.425141\pi$
$751$	26.1656	−	7.68291i	0.954796	−	0.280353i	0.721782	+	0.692120i	$0.243323\pi$
$752$	−1.71157	+	11.9042i	−0.0624146	+	0.434103i
$753$	13.4824	−	15.5595i	0.491325	−	0.567019i
$754$	−14.6729	+	9.42972i	−0.534356	+	0.343410i
$755$	13.2529	+	15.2947i	0.482323	+	0.556630i
$756$	16.4746	+	4.83738i	0.599175	+	0.175934i
$757$	14.6884	−	32.1632i	0.533860	−	1.16899i	−0.430060	−	0.902800i	$-0.641508\pi$
$757$	14.6884	−	32.1632i	0.533860	−	1.16899i	0.963920	−	0.266191i	$-0.0857652\pi$
$758$	−14.6924			−0.533652
$759$	32.9637	+	11.1400i	1.19651	+	0.404358i
$760$	−0.658340			−0.0238805
$761$	13.0661	−	28.6109i	0.473647	−	1.03714i	−0.510514	−	0.859869i	$-0.670545\pi$
$761$	13.0661	−	28.6109i	0.473647	−	1.03714i	0.984162	−	0.177274i	$-0.0567278\pi$
$762$	−17.6303	−	5.17671i	−0.638677	−	0.187532i
$763$	−14.2552	−	16.4513i	−0.516072	−	0.595579i
$764$	−16.4354	+	10.5624i	−0.594612	+	0.382134i
$765$	1.33522	−	1.54093i	0.0482752	−	0.0557125i
$766$	2.68993	−	18.7089i	0.0971912	−	0.675980i
$767$	−31.0841	+	9.12711i	−1.12238	+	0.329561i
$768$	1.32223	+	0.849743i	0.0477117	+	0.0306625i
$769$	3.39576	+	23.6180i	0.122454	+	0.851688i	0.954761	+	0.297373i	$0.0961106\pi$
$769$	3.39576	+	23.6180i	0.122454	+	0.851688i	−0.832307	+	0.554315i	$0.812980\pi$
$770$	−5.93500	−	12.9958i	−0.213882	−	0.468337i
$771$	−4.83632	−	10.5901i	−0.174176	−	0.381392i
$772$	0.589368	+	4.09915i	0.0212118	+	0.147531i
$773$	−18.6134	−	11.9621i	−0.669478	−	0.430247i	0.161259	−	0.986912i	$-0.448444\pi$
$773$	−18.6134	−	11.9621i	−0.669478	−	0.430247i	−0.830737	+	0.556665i	$0.812081\pi$
$774$	−2.06282	+	0.605699i	−0.0741466	+	0.0217714i
$775$	−0.519012	+	3.60981i	−0.0186434	+	0.129668i
$776$	4.12193	−	4.75697i	0.147969	−	0.170765i
$777$	−6.77898	+	4.35659i	−0.243195	+	0.156292i
$778$	2.97437	+	3.43261i	0.106636	+	0.123065i
$779$	−5.40845	−	1.58806i	−0.193778	−	0.0568983i
$780$	−2.17101	+	4.75385i	−0.0777347	+	0.170215i
$781$	28.3312			1.01377
$782$	18.4469	+	0.743800i	0.659660	+	0.0265982i
$783$	29.1005			1.03997
$784$	1.07138	−	2.34600i	0.0382637	−	0.0837859i
$785$	17.9388	+	5.26730i	0.640262	+	0.187998i
$786$	14.4308	+	16.6540i	0.514730	+	0.594030i
$787$	−2.71056	+	1.74197i	−0.0966210	+	0.0620945i	−0.588059	−	0.808818i	$-0.700108\pi$
$787$	−2.71056	+	1.74197i	−0.0966210	+	0.0620945i	0.491438	+	0.870912i	$0.336471\pi$
$788$	−16.6424	+	19.2063i	−0.592860	+	0.684197i
$789$	3.76335	−	26.1746i	0.133979	−	0.931842i
$790$	8.71576	−	2.55918i	0.310093	−	0.0910515i
$791$	−11.0481	−	7.10019i	−0.392826	−	0.252454i
$792$	−0.347953	−	2.42006i	−0.0123640	−	0.0859932i
$793$	−18.2775	−	40.0222i	−0.649054	−	1.42123i
$794$	−2.22383	−	4.86952i	−0.0789209	−	0.172813i
$795$	1.54769	+	10.7644i	0.0548910	+	0.381776i
$796$	6.19743	+	3.98285i	0.219662	+	0.141168i
$797$	35.2856	−	10.3608i	1.24988	−	0.366998i	0.411161	−	0.911563i	$-0.365123\pi$
$797$	35.2856	−	10.3608i	1.24988	−	0.366998i	0.838719	+	0.544565i	$0.183305\pi$
$798$	0.455765	−	3.16992i	0.0161339	−	0.112214i
$799$	−30.3184	+	34.9893i	−1.07259	+	1.23783i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	−5.16043	−	5.95545i	−0.182335	−	0.210425i
$802$	21.4750	+	6.30561i	0.758307	+	0.222659i
$803$	20.0055	−	43.8059i	0.705977	−	1.54587i
$804$	−10.1759			−0.358875
$805$	−14.8311	−	0.598006i	−0.522727	−	0.0210769i
$806$	12.1263			0.427130
$807$	4.42277	−	9.68452i	0.155689	−	0.340911i
$808$	0.465607	+	0.136714i	0.0163800	+	0.00480960i
$809$	−20.8187	−	24.0260i	−0.731945	−	0.844710i	0.260744	−	0.965408i	$-0.416032\pi$
$809$	−20.8187	−	24.0260i	−0.731945	−	0.844710i	−0.992689	+	0.120698i	$0.961487\pi$
$810$	5.99856	−	3.85504i	0.210768	−	0.135452i
$811$	−19.5129	+	22.5191i	−0.685192	+	0.790754i	−0.986673	−	0.162719i	$-0.947974\pi$
$811$	−19.5129	+	22.5191i	−0.685192	+	0.790754i	0.301480	+	0.953472i	$0.402519\pi$
$812$	2.31047	−	16.0697i	0.0810816	−	0.563935i
$813$	17.0312	−	5.00080i	0.597309	−	0.175386i
$814$	6.43281	+	4.13411i	0.225470	+	0.144901i
$815$	−2.32708	−	16.1852i	−0.0815142	−	0.566944i
$816$	2.51347	+	5.50373i	0.0879890	+	0.192669i
$817$	1.11009	+	2.43077i	0.0388372	+	0.0850417i
$818$	−0.301500	−	2.09698i	−0.0105417	−	0.0733191i
$819$	4.58546	+	2.94690i	0.160229	+	0.102973i
$820$	−8.21527	+	2.41222i	−0.286890	+	0.0842384i
$821$	−4.87783	+	33.9261i	−0.170238	+	1.18403i	0.708144	+	0.706068i	$0.249533\pi$
$821$	−4.87783	+	33.9261i	−0.170238	+	1.18403i	−0.878382	+	0.477960i	$0.841376\pi$
$822$	14.5662	−	16.8103i	0.508055	−	0.586327i
$823$	−7.72991	+	4.96771i	−0.269448	+	0.173163i	−0.668387	−	0.743814i	$-0.733015\pi$
$823$	−7.72991	+	4.96771i	−0.269448	+	0.173163i	0.398939	+	0.916977i	$0.369378\pi$
$824$	−0.825027	−	0.952132i	−0.0287412	−	0.0331691i
$825$	−6.96141	−	2.04405i	−0.242365	−	0.0711649i
$826$	12.5268	−	27.4298i	0.435862	−	0.954405i
$827$	−28.0261			−0.974563			−0.487282	−	0.873245i	$-0.662011\pi$
$827$	−28.0261			−0.974563			−0.487282	+	0.873245i	$0.662011\pi$
$828$	−2.40643	−	0.813251i	−0.0836293	−	0.0282624i
$829$	−12.8397			−0.445940			−0.222970	−	0.974825i	$-0.571575\pi$
$829$	−12.8397			−0.445940			−0.222970	+	0.974825i	$0.571575\pi$
$830$	2.92900	−	6.41362i	0.101667	−	0.222620i
$831$	31.9369	+	9.37752i	1.10788	+	0.325303i
$832$	2.17746	+	2.51292i	0.0754898	+	0.0871199i
$833$	8.35222	−	5.36765i	0.289387	−	0.185978i
$834$	15.6011	−	18.0047i	0.540224	−	0.623451i
$835$	2.99178	−	20.8083i	0.103535	−	0.720100i
$836$	−2.91588	+	0.856178i	−0.100848	+	0.0296115i
$837$	−17.0202	−	10.9382i	−0.588304	−	0.378080i
$838$	−2.25204	−	15.6633i	−0.0777953	−	0.541078i
$839$	22.1117	+	48.4179i	0.763382	+	1.67157i	0.740705	+	0.671830i	$0.234492\pi$
$839$	22.1117	+	48.4179i	0.763382	+	1.67157i	0.0226769	+	0.999743i	$0.492781\pi$
$840$	−2.02080	−	4.42493i	−0.0697241	−	0.152675i
$841$	0.211266	+	1.46939i	0.00728505	+	0.0506686i
$842$	−28.6432	−	18.4079i	−0.987111	−	0.634378i
$843$	−41.7199	+	12.2501i	−1.43691	+	0.421915i
$844$	1.08844	−	7.57027i	0.0374657	−	0.260579i
$845$	1.27298	−	1.46910i	0.0437919	−	0.0505385i
$846$	5.35877	−	3.44387i	0.184238	−	0.118403i
$847$	−20.8933	−	24.1122i	−0.717902	−	0.828504i
$848$	6.63893	+	1.94936i	0.227982	+	0.0669414i
$849$	−16.2177	+	35.5119i	−0.556591	+	1.21877i
$850$	−3.84957			−0.132039
$851$	6.85087	−	4.02232i	0.234845	−	0.137883i
$852$	9.64645			0.330482
$853$	−5.23398	+	11.4608i	−0.179208	+	0.392411i	−0.977823	−	0.209431i	$-0.932839\pi$
$853$	−5.23398	+	11.4608i	−0.179208	+	0.392411i	0.798616	+	0.601842i	$0.205566\pi$
$854$	39.2950	+	11.5381i	1.34465	+	0.394824i
$855$	0.228346	+	0.263525i	0.00780925	+	0.00901236i
$856$	−4.59905	+	2.95563i	−0.157192	+	0.101021i
$857$	33.9244	−	39.1509i	1.15884	−	1.33737i	0.227254	−	0.973835i	$-0.427025\pi$
$857$	33.9244	−	39.1509i	1.15884	−	1.33737i	0.931581	−	0.363533i	$-0.118429\pi$
$858$	−3.43326	+	23.8789i	−0.117210	+	0.815211i
$859$	−11.9794	+	3.51746i	−0.408731	+	0.120014i	−0.479633	−	0.877469i	$-0.659230\pi$
$859$	−11.9794	+	3.51746i	−0.408731	+	0.120014i	0.0709026	+	0.997483i	$0.477412\pi$
$860$	3.41471	+	2.19450i	0.116441	+	0.0748318i
$861$	−5.92749	−	41.2266i	−0.202008	−	1.40500i
$862$	5.66777	+	12.4107i	0.193045	+	0.422710i
$863$	−11.8241	−	25.8911i	−0.402496	−	0.881343i	−0.997011	−	0.0772587i	$-0.975383\pi$
$863$	−11.8241	−	25.8911i	−0.402496	−	0.881343i	0.594515	−	0.804084i	$-0.297344\pi$
$864$	−0.789517	−	5.49121i	−0.0268599	−	0.186815i
$865$	18.5342	+	11.9112i	0.630182	+	0.404993i
$866$	−10.6338	+	3.12237i	−0.361352	+	0.106102i
$867$	0.487806	−	3.39276i	0.0165667	−	0.115224i
$868$	−7.39158	+	8.53034i	−0.250887	+	0.289539i
$869$	35.2750	−	22.6699i	1.19662	−	0.769023i
$870$	−5.39904	−	6.23082i	−0.183045	−	0.211245i
$871$	−20.6555	−	6.06499i	−0.699884	−	0.205504i
$872$	−2.92176	+	6.39775i	−0.0989432	+	0.216655i
$873$	−3.33384			−0.112834
$874$	−0.574872	+	3.10451i	−0.0194453	+	0.105012i
$875$	3.09501			0.104630
$876$	6.81162	−	14.9154i	0.230143	−	0.503944i
$877$	11.3444	+	3.33101i	0.383072	+	0.112480i	0.467598	−	0.883941i	$-0.345119\pi$
$877$	11.3444	+	3.33101i	0.383072	+	0.112480i	−0.0845260	+	0.996421i	$0.526938\pi$
$878$	−7.28307	−	8.40511i	−0.245792	−	0.283659i
$879$	34.5497	−	22.2037i	1.16533	−	0.748913i
$880$	−3.02291	+	3.48863i	−0.101902	+	0.117602i
$881$	7.21559	−	50.1855i	0.243099	−	1.69079i	−0.393282	−	0.919418i	$-0.628660\pi$
$881$	7.21559	−	50.1855i	0.243099	−	1.69079i	0.636381	−	0.771375i	$-0.280430\pi$
$882$	−1.31068	+	0.384852i	−0.0441330	+	0.0129586i
$883$	−3.89349	−	2.50219i	−0.131026	−	0.0842054i	0.473486	−	0.880801i	$-0.342996\pi$
$883$	−3.89349	−	2.50219i	−0.131026	−	0.0842054i	−0.604512	+	0.796596i	$0.706632\pi$
$884$	1.82164	+	12.6698i	0.0612685	+	0.426132i
$885$	−6.36145	−	13.9296i	−0.213838	−	0.468240i
$886$	4.92921	+	10.7935i	0.165600	+	0.362614i
$887$	3.95174	+	27.4850i	0.132687	+	0.922855i	0.942032	+	0.335522i	$0.108913\pi$
$887$	3.95174	+	27.4850i	0.132687	+	0.922855i	−0.809346	+	0.587333i	$0.800178\pi$
$888$	2.19030	+	1.40762i	0.0735015	+	0.0472365i
$889$	34.7169	−	10.1938i	1.16437	−	0.341889i
$890$	−2.11735	+	14.7265i	−0.0709739	+	0.493634i
$891$	21.5549	−	24.8757i	0.722116	−	0.833366i
$892$	−7.80352	+	5.01502i	−0.261281	+	0.167915i
$893$	−5.18494	−	5.98375i	−0.173508	−	0.200238i
$894$	16.0507	+	4.71290i	0.536815	+	0.157623i
$895$	2.09821	−	4.59444i	0.0701355	−	0.153575i
$896$	−3.09501			−0.103397
$897$	20.5218	+	14.3889i	0.685203	+	0.480431i
$898$	9.26763			0.309265
$899$	−7.94690	+	17.4013i	−0.265044	+	0.580365i
$900$	0.508200	+	0.149221i	0.0169400	+	0.00497404i
$901$	17.4428	+	20.1301i	0.581105	+	0.670631i
$902$	−33.2494	+	21.3681i	−1.10708	+	0.711480i
$903$	−12.9305	+	14.9226i	−0.430301	+	0.496594i
$904$	−0.603879	+	4.20007i	−0.0200847	+	0.139692i
$905$	17.3987	−	5.10871i	0.578352	−	0.169819i
$906$	26.7589	+	17.1969i	0.889005	+	0.571329i
$907$	5.33349	+	37.0952i	0.177096	+	1.23173i	0.863440	+	0.504451i	$0.168305\pi$
$907$	5.33349	+	37.0952i	0.177096	+	1.23173i	−0.686345	+	0.727276i	$0.740786\pi$
$908$	7.72623	+	16.9181i	0.256404	+	0.561446i
$909$	−0.106771	−	0.233796i	−0.00354137	−	0.00775451i
$910$	−1.46458	−	10.1864i	−0.0485503	−	0.337675i
$911$	48.5025	+	31.1707i	1.60696	+	1.03273i	0.963665	+	0.267113i	$0.0860698\pi$
$911$	48.5025	+	31.1707i	1.60696	+	1.03273i	0.643296	+	0.765618i	$0.277567\pi$
$912$	−0.992821	+	0.291519i	−0.0328756	+	0.00965315i
$913$	4.63196	−	32.2160i	0.153295	−	1.06619i
$914$	−8.88503	+	10.2539i	−0.293891	+	0.339168i
$915$	17.4960	−	11.2440i	0.578401	−	0.371716i
$916$	−8.47712	−	9.78312i	−0.280092	−	0.323243i
$917$	−41.6357	−	12.2254i	−1.37493	−	0.403717i
$918$	8.87167	−	19.4263i	0.292809	−	0.641162i
$919$	21.9974			0.725627			0.362813	−	0.931862i	$-0.381816\pi$
$919$	21.9974			0.725627			0.362813	+	0.931862i	$0.381816\pi$
$920$	1.81489	+	4.43916i	0.0598351	+	0.146355i
$921$	−16.7710			−0.552624
$922$	−9.83990	+	21.5464i	−0.324060	+	0.709592i
$923$	19.5809	+	5.74946i	0.644512	+	0.189246i
$924$	−14.7050	−	16.9705i	−0.483760	−	0.558289i
$925$	−1.39355	+	0.895583i	−0.0458198	+	0.0294466i
$926$	1.05926	−	1.22245i	0.0348094	−	0.0401721i
$927$	−0.0949648	+	0.660495i	−0.00311905	+	0.0216935i
$928$	−5.03304	+	1.47783i	−0.165218	+	0.0485123i
$929$	45.0266	+	28.9369i	1.47728	+	0.949387i	0.997401	+	0.0720505i	$0.0229543\pi$
$929$	45.0266	+	28.9369i	1.47728	+	0.949387i	0.479875	+	0.877337i	$0.340682\pi$
$930$	0.815748	+	5.67365i	0.0267494	+	0.186046i
$931$	0.705335	+	1.54447i	0.0231164	+	0.0506179i
$932$	−5.77322	−	12.6416i	−0.189108	−	0.414089i
$933$	−4.11942	−	28.6512i	−0.134864	−	0.937998i
$934$	−15.8703	−	10.1992i	−0.519291	−	0.333728i
$935$	−17.0502	+	5.00640i	−0.557603	+	0.163727i
$936$	0.250637	−	1.74322i	0.00819231	−	0.0569788i
$937$	20.9264	−	24.1504i	0.683637	−	0.788959i	−0.302808	−	0.953052i	$-0.597924\pi$
$937$	20.9264	−	24.1504i	0.683637	−	0.788959i	0.986445	+	0.164092i	$0.0524695\pi$
$938$	16.8570	−	10.8333i	0.550401	−	0.353721i
$939$	−6.97288	−	8.04713i	−0.227551	−	0.262608i
$940$	−11.5395	−	3.38830i	−0.376377	−	0.110514i
$941$	5.29906	−	11.6033i	0.172744	−	0.378257i	−0.803381	−	0.595465i	$-0.796968\pi$
$941$	5.29906	−	11.6033i	0.172744	−	0.378257i	0.976125	+	0.217208i	$0.0696950\pi$
$942$	29.3853			0.957423
$943$	4.20154	+	40.8469i	0.136821	+	1.33016i
$944$	−9.74306			−0.317109
$945$	−7.13272	+	15.6185i	−0.232027	+	0.508069i
$946$	17.9782	+	5.27887i	0.584521	+	0.171631i
$947$	−27.2435	−	31.4407i	−0.885294	−	1.02168i	−0.999601	−	0.0282385i	$-0.991010\pi$
$947$	−27.2435	−	31.4407i	−0.885294	−	1.02168i	0.114307	−	0.993445i	$-0.463535\pi$
$948$	12.0107	−	7.71883i	0.390090	−	0.250696i
$949$	22.7164	−	26.2161i	0.737406	−	0.851012i
$950$	0.0936916	−	0.651639i	0.00303976	−	0.0211420i
$951$	3.28844	−	0.965572i	0.106635	−	0.0313108i
$952$	−10.0231	−	6.44144i	−0.324850	−	0.208768i
$953$	5.12782	+	35.6648i	0.166106	+	1.15529i	0.886838	+	0.462081i	$0.152897\pi$
$953$	5.12782	+	35.6648i	0.166106	+	1.15529i	−0.720732	+	0.693214i	$0.756194\pi$
$954$	−1.52241	−	3.33361i	−0.0492898	−	0.107930i
$955$	−8.11588	−	17.7713i	−0.262624	−	0.575066i
$956$	3.51003	+	24.4128i	0.113523	+	0.789567i
$957$	−32.0163	−	20.5756i	−1.03494	−	0.665115i
$958$	12.8535	−	3.77413i	0.415278	−	0.121937i
$959$	−6.23348	+	43.3548i	−0.201290	+	1.40000i
$960$	−1.02927	+	1.18784i	−0.0332194	+	0.0383373i
$961$	−14.8901	+	9.56931i	−0.480327	+	0.308687i
$962$	3.60701	+	4.16271i	0.116295	+	0.134211i
$963$	2.77828	+	0.815777i	0.0895289	+	0.0262880i
$964$	1.02706	−	2.24894i	0.0330793	−	0.0724336i
$965$	−4.14130			−0.133313
$966$	−22.6311	+	5.66549i	−0.728143	+	0.182284i
$967$	−23.6047			−0.759075			−0.379537	−	0.925176i	$-0.623917\pi$
$967$	−23.6047			−0.759075			−0.379537	+	0.925176i	$0.623917\pi$
$968$	−4.28232	+	9.37696i	−0.137639	+	0.301387i
$969$	−3.82193	−	1.12222i	−0.122778	−	0.0360509i
$970$	4.12193	+	4.75697i	0.132347	+	0.152737i
$971$	−9.35840	+	6.01428i	−0.300325	+	0.193007i	−0.682121	−	0.731239i	$-0.738942\pi$
$971$	−9.35840	+	6.01428i	−0.300325	+	0.193007i	0.381795	+	0.924247i	$0.375306\pi$
$972$	−3.55968	+	4.10809i	−0.114177	+	0.131767i
$973$	−6.67637	+	46.4352i	−0.214035	+	1.48864i
$974$	−6.65672	+	1.95459i	−0.213295	+	0.0626290i
$975$	−4.39650	−	2.82546i	−0.140801	−	0.0904870i
$976$	−1.88315	−	13.0976i	−0.0602781	−	0.419243i
$977$	−18.5553	−	40.6305i	−0.593638	−	1.29989i	−0.933219	−	0.359309i	$-0.883012\pi$
$977$	−18.5553	−	40.6305i	−0.593638	−	1.29989i	0.339581	−	0.940577i	$-0.389715\pi$
$978$	−10.6763	−	23.3779i	−0.341392	−	0.747544i
$979$	9.77395	+	67.9793i	0.312377	+	2.17263i
$980$	2.16965	+	1.39435i	0.0693070	+	0.0445409i
$981$	3.57435	−	1.04952i	0.114120	−	0.0335087i
$982$	0.260149	−	1.80937i	0.00830168	−	0.0577395i
$983$	12.5137	−	14.4416i	0.399126	−	0.460616i	−0.520239	−	0.854020i	$-0.674157\pi$
$983$	12.5137	−	14.4416i	0.399126	−	0.460616i	0.919366	+	0.393404i	$0.128703\pi$
$984$	−11.3210	+	7.27558i	−0.360901	+	0.231937i
$985$	−16.6424	−	19.2063i	−0.530271	−	0.611965i
$986$	−19.3750	−	5.68903i	−0.617027	−	0.181176i
$987$	24.3034	−	53.2171i	0.773586	−	1.69392i
$988$	−2.18903			−0.0696423
$989$	13.3303	−	14.1864i	0.423879	−	0.451100i
$990$	2.44495			0.0777056
$991$	−2.90441	+	6.35977i	−0.0922616	+	0.202025i	−0.950137	−	0.311833i	$-0.899057\pi$
$991$	−2.90441	+	6.35977i	−0.0922616	+	0.202025i	0.857875	+	0.513858i	$0.171784\pi$
$992$	3.49920	+	1.02746i	0.111100	+	0.0326218i
$993$	−4.93968	−	5.70069i	−0.156756	−	0.180906i
$994$	−15.9800	+	10.2697i	−0.506855	+	0.325736i
$995$	−4.82430	+	5.56753i	−0.152940	+	0.176503i
$996$	1.57713	−	10.9692i	0.0499732	−	0.347571i
$997$	−40.2289	+	11.8123i	−1.27406	+	0.374098i	−0.847710	−	0.530460i	$-0.822019\pi$
$997$	−40.2289	+	11.8123i	−1.27406	+	0.374098i	−0.426351	+	0.904558i	$0.640201\pi$
$998$	31.9505	+	20.5333i	1.01138	+	0.649971i
$999$	−1.30785	−	9.09630i	−0.0413786	−	0.287794i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.121.1	✓	20
23.2	even	11		5290.2.a.bj.1.7		10
23.4	even	11	inner	230.2.g.b.211.1	yes	20
23.21	odd	22		5290.2.a.bi.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.121.1	✓	20	1.1	even	1	trivial
230.2.g.b.211.1	yes	20	23.4	even	11	inner
5290.2.a.bi.1.7		10	23.21	odd	22
5290.2.a.bj.1.7		10	23.2	even	11

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-1.50807 - 0.442808i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(1.02927 - 1.18784i) q^{6} +(-0.440465 + 3.06350i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.445574 - 0.286353i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-1.50807 - 0.442808i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(1.02927 - 1.18784i) q^{6} +(-0.440465 + 3.06350i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.445574 - 0.286353i) q^{9} +(0.142315 + 0.989821i) q^{10} +(1.91760 + 4.19897i) q^{11} +(0.652922 + 1.42970i) q^{12} +(0.473207 + 3.29123i) q^{13} +(-2.60369 - 1.67329i) q^{14} +(-1.50807 + 0.442808i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-2.52093 + 2.90931i) q^{17} +(0.445574 - 0.286353i) q^{18} +(-0.431121 - 0.497540i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(2.02080 - 4.42493i) q^{21} -4.61612 q^{22} +(-2.16640 + 4.27863i) q^{23} -1.57173 q^{24} +(0.415415 - 0.909632i) q^{25} +(-3.19038 - 0.936781i) q^{26} +(3.63295 + 4.19265i) q^{27} +(2.60369 - 1.67329i) q^{28} +(3.43509 - 3.96430i) q^{29} +(0.223681 - 1.55574i) q^{30} +(-3.49920 + 1.02746i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(-1.03254 - 7.18145i) q^{33} +(-1.59917 - 3.50169i) q^{34} +(1.28571 + 2.81532i) q^{35} +(0.0753778 + 0.524264i) q^{36} +(-1.39355 - 0.895583i) q^{37} +(0.631673 - 0.185476i) q^{38} +(0.743755 - 5.17293i) q^{39} +(0.654861 - 0.755750i) q^{40} +(7.20290 - 4.62902i) q^{41} +(3.18559 + 3.67636i) q^{42} +(-3.89465 - 1.14357i) q^{43} +(1.91760 - 4.19897i) q^{44} -0.529655 q^{45} +(-2.99203 - 3.74803i) q^{46} +12.0267 q^{47} +(0.652922 - 1.42970i) q^{48} +(-2.47460 - 0.726608i) q^{49} +(0.654861 + 0.755750i) q^{50} +(5.09000 - 3.27115i) q^{51} +(2.17746 - 2.51292i) q^{52} +(0.984705 - 6.84877i) q^{53} +(-5.32296 + 1.56296i) q^{54} +(3.88332 + 2.49566i) q^{55} +(0.440465 + 3.06350i) q^{56} +(0.429845 + 0.941228i) q^{57} +(2.17907 + 4.77149i) q^{58} +(1.38658 + 9.64389i) q^{59} +(1.32223 + 0.849743i) q^{60} +(-12.6963 + 3.72796i) q^{61} +(0.519012 - 3.60981i) q^{62} +(1.07350 - 1.23889i) q^{63} +(0.841254 - 0.540641i) q^{64} +(2.17746 + 2.51292i) q^{65} +(6.96141 + 2.04405i) q^{66} +(-2.68952 + 5.88922i) q^{67} +3.84957 q^{68} +(5.16169 - 5.49317i) q^{69} -3.09501 q^{70} +(2.54959 - 5.58283i) q^{71} +(-0.508200 - 0.149221i) q^{72} +(-6.83186 - 7.88438i) q^{73} +(1.39355 - 0.895583i) q^{74} +(-1.02927 + 1.18784i) q^{75} +(-0.0936916 + 0.651639i) q^{76} +(-13.7082 + 4.02509i) q^{77} +(4.39650 + 2.82546i) q^{78} +(-1.29275 - 8.99126i) q^{79} +(0.415415 + 0.909632i) q^{80} +(-2.96212 - 6.48613i) q^{81} +(1.21851 + 8.47495i) q^{82} +(-5.93150 - 3.81194i) q^{83} +(-4.66748 + 1.37050i) q^{84} +(-0.547851 + 3.81039i) q^{85} +(2.65813 - 3.06764i) q^{86} +(-6.93577 + 4.45735i) q^{87} +(3.02291 + 3.48863i) q^{88} +(14.2753 + 4.19161i) q^{89} +(0.220027 - 0.481791i) q^{90} -10.2911 q^{91} +(4.65227 - 1.16466i) q^{92} +5.73199 q^{93} +(-4.99605 + 10.9398i) q^{94} +(-0.631673 - 0.185476i) q^{95} +(1.02927 + 1.18784i) q^{96} +(5.29516 - 3.40299i) q^{97} +(1.68893 - 1.94913i) q^{98} +(0.347953 - 2.42006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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