LMFDB - Embedded newform 91.2.f.a.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	91.22
Dual form			91.2.f.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 + 0.330792i) q^{2} +(0.190983 - 0.330792i) q^{3} +(0.927051 + 1.60570i) q^{4} +0.381966 q^{5} +(0.0729490 + 0.126351i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})$	\(q+(-0.190983 + 0.330792i) q^{2} +(0.190983 - 0.330792i) q^{3} +(0.927051 + 1.60570i) q^{4} +0.381966 q^{5} +(0.0729490 + 0.126351i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +(-0.0729490 + 0.126351i) q^{10} +(2.42705 - 4.20378i) q^{11} +0.708204 q^{12} +(-2.50000 + 2.59808i) q^{13} +0.381966 q^{14} +(0.0729490 - 0.126351i) q^{15} +(-1.57295 + 2.72443i) q^{16} +(-3.73607 - 6.47106i) q^{17} -1.09017 q^{18} +(-2.42705 - 4.20378i) q^{19} +(0.354102 + 0.613323i) q^{20} -0.381966 q^{21} +(0.927051 + 1.60570i) q^{22} +(-2.23607 + 3.87298i) q^{23} +(-0.281153 + 0.486971i) q^{24} -4.85410 q^{25} +(-0.381966 - 1.32317i) q^{26} +2.23607 q^{27} +(0.927051 - 1.60570i) q^{28} +(2.04508 - 3.54219i) q^{29} +(0.0278640 + 0.0482619i) q^{30} +8.70820 q^{31} +(-2.07295 - 3.59045i) q^{32} +(-0.927051 - 1.60570i) q^{33} +2.85410 q^{34} +(-0.190983 - 0.330792i) q^{35} +(-2.64590 + 4.58283i) q^{36} +(-2.00000 + 3.46410i) q^{37} +1.85410 q^{38} +(0.381966 + 1.32317i) q^{39} -0.562306 q^{40} +(-2.61803 + 4.53457i) q^{41} +(0.0729490 - 0.126351i) q^{42} +(3.78115 + 6.54915i) q^{43} +9.00000 q^{44} +(0.545085 + 0.944115i) q^{45} +(-0.854102 - 1.47935i) q^{46} +2.23607 q^{47} +(0.600813 + 1.04064i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.927051 - 1.60570i) q^{50} -2.85410 q^{51} +(-6.48936 - 1.60570i) q^{52} +8.23607 q^{53} +(-0.427051 + 0.739674i) q^{54} +(0.927051 - 1.60570i) q^{55} +(0.736068 + 1.27491i) q^{56} -1.85410 q^{57} +(0.781153 + 1.35300i) q^{58} +(-1.11803 - 1.93649i) q^{59} +0.270510 q^{60} +(3.00000 + 5.19615i) q^{61} +(-1.66312 + 2.88061i) q^{62} +(1.42705 - 2.47172i) q^{63} -4.70820 q^{64} +(-0.954915 + 0.992377i) q^{65} +0.708204 q^{66} +(-0.354102 + 0.613323i) q^{67} +(6.92705 - 11.9980i) q^{68} +(0.854102 + 1.47935i) q^{69} +0.145898 q^{70} +(-4.09017 - 7.08438i) q^{71} +(-2.10081 - 3.63871i) q^{72} -2.00000 q^{73} +(-0.763932 - 1.32317i) q^{74} +(-0.927051 + 1.60570i) q^{75} +(4.50000 - 7.79423i) q^{76} -4.85410 q^{77} +(-0.510643 - 0.126351i) q^{78} +4.00000 q^{79} +(-0.600813 + 1.04064i) q^{80} +(-3.85410 + 6.67550i) q^{81} +(-1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(-0.354102 - 0.613323i) q^{84} +(-1.42705 - 2.47172i) q^{85} -2.88854 q^{86} +(-0.781153 - 1.35300i) q^{87} +(-3.57295 + 6.18853i) q^{88} +(-8.04508 + 13.9345i) q^{89} -0.416408 q^{90} +(3.50000 + 0.866025i) q^{91} -8.29180 q^{92} +(1.66312 - 2.88061i) q^{93} +(-0.427051 + 0.739674i) q^{94} +(-0.927051 - 1.60570i) q^{95} -1.58359 q^{96} +(-6.07295 - 10.5187i) q^{97} +(-0.190983 - 0.330792i) q^{98} +13.8541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9} - 7 q^{10} + 3 q^{11} - 24 q^{12} - 10 q^{13} + 6 q^{14} + 7 q^{15} - 13 q^{16} - 6 q^{17} + 18 q^{18} - 3 q^{19} - 12 q^{20} - 6 q^{21} - 3 q^{22} + 19 q^{24} - 6 q^{25} - 6 q^{26} - 3 q^{28} - 3 q^{29} + 18 q^{30} + 8 q^{31} - 15 q^{32} + 3 q^{33} - 2 q^{34} - 3 q^{35} - 24 q^{36} - 8 q^{37} - 6 q^{38} + 6 q^{39} + 38 q^{40} - 6 q^{41} + 7 q^{42} - 5 q^{43} + 36 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 2 q^{49} - 3 q^{50} + 2 q^{51} + 21 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} - 6 q^{56} + 6 q^{57} - 17 q^{58} - 66 q^{60} + 12 q^{61} + 9 q^{62} - q^{63} + 8 q^{64} - 15 q^{65} - 24 q^{66} + 12 q^{67} + 21 q^{68} - 10 q^{69} + 14 q^{70} + 6 q^{71} - 33 q^{72} - 8 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 6 q^{77} - 49 q^{78} + 16 q^{79} - 27 q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{84} + q^{85} + 60 q^{86} + 17 q^{87} - 21 q^{88} - 21 q^{89} + 52 q^{90} + 14 q^{91} - 60 q^{92} - 9 q^{93} + 5 q^{94} + 3 q^{95} - 60 q^{96} - 31 q^{97} - 3 q^{98} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9 - 7 * q^10 + 3 * q^11 - 24 * q^12 - 10 * q^13 + 6 * q^14 + 7 * q^15 - 13 * q^16 - 6 * q^17 + 18 * q^18 - 3 * q^19 - 12 * q^20 - 6 * q^21 - 3 * q^22 + 19 * q^24 - 6 * q^25 - 6 * q^26 - 3 * q^28 - 3 * q^29 + 18 * q^30 + 8 * q^31 - 15 * q^32 + 3 * q^33 - 2 * q^34 - 3 * q^35 - 24 * q^36 - 8 * q^37 - 6 * q^38 + 6 * q^39 + 38 * q^40 - 6 * q^41 + 7 * q^42 - 5 * q^43 + 36 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 + 21 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 - 6 * q^56 + 6 * q^57 - 17 * q^58 - 66 * q^60 + 12 * q^61 + 9 * q^62 - q^63 + 8 * q^64 - 15 * q^65 - 24 * q^66 + 12 * q^67 + 21 * q^68 - 10 * q^69 + 14 * q^70 + 6 * q^71 - 33 * q^72 - 8 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 6 * q^77 - 49 * q^78 + 16 * q^79 - 27 * q^80 - 2 * q^81 - 4 * q^82 + 12 * q^84 + q^85 + 60 * q^86 + 17 * q^87 - 21 * q^88 - 21 * q^89 + 52 * q^90 + 14 * q^91 - 60 * q^92 - 9 * q^93 + 5 * q^94 + 3 * q^95 - 60 * q^96 - 31 * q^97 - 3 * q^98 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.190983	+	0.330792i	−0.135045	+	0.233905i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−0.190983	+	0.330792i	−0.135045	+	0.233905i	0.790569	+	0.612372i	$0.209785\pi$
$3$	0.190983	−	0.330792i	0.110264	−	0.190983i	−0.805613	−	0.592443i	$-0.798164\pi$
$3$	0.190983	−	0.330792i	0.110264	−	0.190983i	0.915877	+	0.401460i	$0.131497\pi$
$4$	0.927051	+	1.60570i	0.463525	+	0.802850i
$5$	0.381966			0.170820			0.0854102	−	0.996346i	$-0.472780\pi$
$5$	0.381966			0.170820			0.0854102	+	0.996346i	$0.472780\pi$
$6$	0.0729490	+	0.126351i	0.0297813	+	0.0515827i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.47214			−0.520479
$9$	1.42705	+	2.47172i	0.475684	+	0.823908i
$10$	−0.0729490	+	0.126351i	−0.0230685	+	0.0399558i
$11$	2.42705	−	4.20378i	0.731783	−	1.26749i	−0.224337	−	0.974512i	$-0.572022\pi$
$11$	2.42705	−	4.20378i	0.731783	−	1.26749i	0.956120	−	0.292974i	$-0.0946451\pi$
$12$	0.708204			0.204441
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$	0.381966			0.102085
$15$	0.0729490	−	0.126351i	0.0188354	−	0.0326238i
$16$	−1.57295	+	2.72443i	−0.393237	+	0.681107i
$17$	−3.73607	−	6.47106i	−0.906130	−	1.56946i	−0.819394	−	0.573231i	$-0.805690\pi$
$17$	−3.73607	−	6.47106i	−0.906130	−	1.56946i	−0.0867359	−	0.996231i	$-0.527644\pi$
$18$	−1.09017			−0.256956
$19$	−2.42705	−	4.20378i	−0.556804	−	0.964412i	−0.997761	−	0.0668841i	$-0.978694\pi$
$19$	−2.42705	−	4.20378i	−0.556804	−	0.964412i	0.440957	−	0.897528i	$-0.354639\pi$
$20$	0.354102	+	0.613323i	0.0791796	+	0.137143i
$21$	−0.381966			−0.0833518
$22$	0.927051	+	1.60570i	0.197648	+	0.342336i
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	−0.999257	−	0.0385394i	$-0.987729\pi$
$23$	−2.23607	+	3.87298i	−0.466252	+	0.807573i	0.533005	+	0.846112i	$0.321063\pi$
$24$	−0.281153	+	0.486971i	−0.0573901	+	0.0994026i
$25$	−4.85410			−0.970820
$26$	−0.381966	−	1.32317i	−0.0749097	−	0.259495i
$27$	2.23607			0.430331
$28$	0.927051	−	1.60570i	0.175196	−	0.303449i
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	−0.611265	−	0.791426i	$-0.709339\pi$
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	0.991028	+	0.133658i	$0.0426723\pi$
$30$	0.0278640	+	0.0482619i	0.00508726	+	0.00881138i
$31$	8.70820			1.56404			0.782020	−	0.623254i	$-0.214190\pi$
$31$	8.70820			1.56404			0.782020	+	0.623254i	$0.214190\pi$
$32$	−2.07295	−	3.59045i	−0.366449	−	0.634708i
$33$	−0.927051	−	1.60570i	−0.161379	−	0.279516i
$34$	2.85410			0.489474
$35$	−0.190983	−	0.330792i	−0.0322820	−	0.0559141i
$36$	−2.64590	+	4.58283i	−0.440983	+	0.763805i
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	1.85410			0.300775
$39$	0.381966	+	1.32317i	0.0611635	+	0.211877i
$40$	−0.562306			−0.0889084
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	−0.994763	−	0.102206i	$-0.967410\pi$
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	0.585895	+	0.810387i	$0.300743\pi$
$42$	0.0729490	−	0.126351i	0.0112563	−	0.0194964i
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	0.995864	+	0.0908618i	$0.0289622\pi$
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	−0.419243	+	0.907874i	$0.637704\pi$
$44$	9.00000			1.35680
$45$	0.545085	+	0.944115i	0.0812565	+	0.140740i
$46$	−0.854102	−	1.47935i	−0.125930	−	0.218118i
$47$	2.23607			0.326164			0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607			0.326164			0.163082	+	0.986613i	$0.447856\pi$
$48$	0.600813	+	1.04064i	0.0867199	+	0.150203i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.927051	−	1.60570i	0.131105	−	0.227080i
$51$	−2.85410			−0.399654
$52$	−6.48936	−	1.60570i	−0.899912	−	0.222670i
$53$	8.23607			1.13131			0.565655	−	0.824642i	$-0.308623\pi$
$53$	8.23607			1.13131			0.565655	+	0.824642i	$0.308623\pi$
$54$	−0.427051	+	0.739674i	−0.0581143	+	0.100657i
$55$	0.927051	−	1.60570i	0.125004	−	0.216512i
$56$	0.736068	+	1.27491i	0.0983612	+	0.170367i
$57$	−1.85410			−0.245582
$58$	0.781153	+	1.35300i	0.102570	+	0.177657i
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	0.784024	−	0.620730i	$-0.213164\pi$
$59$	−1.11803	−	1.93649i	−0.145556	−	0.252110i	−0.929580	+	0.368620i	$0.879830\pi$
$60$	0.270510			0.0349227
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−1.66312	+	2.88061i	−0.211216	+	0.365837i
$63$	1.42705	−	2.47172i	0.179792	−	0.311408i
$64$	−4.70820			−0.588525
$65$	−0.954915	+	0.992377i	−0.118443	+	0.123089i
$66$	0.708204			0.0871739
$67$	−0.354102	+	0.613323i	−0.0432604	+	0.0749293i	−0.886845	−	0.462067i	$-0.847108\pi$
$67$	−0.354102	+	0.613323i	−0.0432604	+	0.0749293i	0.843584	+	0.536997i	$0.180441\pi$
$68$	6.92705	−	11.9980i	0.840028	−	1.45497i
$69$	0.854102	+	1.47935i	0.102822	+	0.178093i
$70$	0.145898			0.0174382
$71$	−4.09017	−	7.08438i	−0.485414	−	0.840761i	0.514446	−	0.857523i	$-0.327998\pi$
$71$	−4.09017	−	7.08438i	−0.485414	−	0.840761i	−0.999860	+	0.0167615i	$0.994664\pi$
$72$	−2.10081	−	3.63871i	−0.247583	−	0.428827i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−0.763932	−	1.32317i	−0.0888053	−	0.153815i
$75$	−0.927051	+	1.60570i	−0.107047	+	0.185410i
$76$	4.50000	−	7.79423i	0.516185	−	0.894059i
$77$	−4.85410			−0.553176
$78$	−0.510643	−	0.126351i	−0.0578189	−	0.0143065i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−0.600813	+	1.04064i	−0.0671729	+	0.116347i
$81$	−3.85410	+	6.67550i	−0.428234	+	0.741722i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	−6.70820			−0.736321			−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820			−0.736321			−0.368161	+	0.929762i	$0.620012\pi$
$84$	−0.354102	−	0.613323i	−0.0386357	−	0.0669190i
$85$	−1.42705	−	2.47172i	−0.154785	−	0.268096i
$86$	−2.88854			−0.311480
$87$	−0.781153	−	1.35300i	−0.0837484	−	0.145056i
$88$	−3.57295	+	6.18853i	−0.380878	+	0.659699i
$89$	−8.04508	+	13.9345i	−0.852777	+	1.47705i	0.0259145	+	0.999664i	$0.491750\pi$
$89$	−8.04508	+	13.9345i	−0.852777	+	1.47705i	−0.878692	+	0.477389i	$0.841583\pi$
$90$	−0.416408			−0.0438932
$91$	3.50000	+	0.866025i	0.366900	+	0.0907841i
$92$	−8.29180			−0.864479
$93$	1.66312	−	2.88061i	0.172457	−	0.298705i
$94$	−0.427051	+	0.739674i	−0.0440469	+	0.0762915i
$95$	−0.927051	−	1.60570i	−0.0951134	−	0.164741i
$96$	−1.58359			−0.161625
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	−0.990099	−	0.140371i	$-0.955170\pi$
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	0.373484	−	0.927636i	$-0.378163\pi$
$98$	−0.190983	−	0.330792i	−0.0192922	−	0.0334151i
$99$	13.8541			1.39239
$100$	−4.50000	−	7.79423i	−0.450000	−	0.779423i
$101$	−4.28115	+	7.41517i	−0.425991	+	0.737837i	−0.996512	−	0.0834451i	$-0.973408\pi$
$101$	−4.28115	+	7.41517i	−0.425991	+	0.737837i	0.570522	+	0.821283i	$0.306741\pi$
$102$	0.545085	−	0.944115i	0.0539715	−	0.0934813i
$103$	4.70820			0.463913			0.231957	−	0.972726i	$-0.425487\pi$
$103$	4.70820			0.463913			0.231957	+	0.972726i	$0.425487\pi$
$104$	3.68034	−	3.82472i	0.360887	−	0.375045i
$105$	−0.145898			−0.0142382
$106$	−1.57295	+	2.72443i	−0.152778	+	0.264620i
$107$	2.80902	−	4.86536i	0.271558	−	0.470352i	−0.697703	−	0.716387i	$-0.745794\pi$
$107$	2.80902	−	4.86536i	0.271558	−	0.470352i	0.969261	+	0.246035i	$0.0791278\pi$
$108$	2.07295	+	3.59045i	0.199470	+	0.345492i
$109$	10.7082			1.02566			0.512830	−	0.858490i	$-0.328597\pi$
$109$	10.7082			1.02566			0.512830	+	0.858490i	$0.328597\pi$
$110$	0.354102	+	0.613323i	0.0337623	+	0.0584780i
$111$	0.763932	+	1.32317i	0.0725092	+	0.125590i
$112$	3.14590			0.297259
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	0.986505	−	0.163728i	$-0.0523521\pi$
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	−0.635046	+	0.772475i	$0.719019\pi$
$114$	0.354102	−	0.613323i	0.0331647	−	0.0574429i
$115$	−0.854102	+	1.47935i	−0.0796454	+	0.137950i
$116$	7.58359			0.704119
$117$	−9.98936	−	2.47172i	−0.923516	−	0.228511i
$118$	0.854102			0.0786265
$119$	−3.73607	+	6.47106i	−0.342485	+	0.593201i
$120$	−0.107391	+	0.186006i	−0.00980340	+	0.0169800i
$121$	−6.28115	−	10.8793i	−0.571014	−	0.989025i
$122$	−2.29180			−0.207489
$123$	1.00000	+	1.73205i	0.0901670	+	0.156174i
$124$	8.07295	+	13.9828i	0.724972	+	1.25569i
$125$	−3.76393			−0.336656
$126$	0.545085	+	0.944115i	0.0485600	+	0.0841084i
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	−0.360405	−	0.932796i	$-0.617361\pi$
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	0.988027	−	0.154278i	$-0.0493053\pi$
$128$	5.04508	−	8.73834i	0.445927	−	0.772368i
$129$	2.88854			0.254322
$130$	−0.145898	−	0.505406i	−0.0127961	−	0.0443270i
$131$	0.326238			0.0285035			0.0142518	−	0.999898i	$-0.495463\pi$
$131$	0.326238			0.0285035			0.0142518	+	0.999898i	$0.495463\pi$
$132$	1.71885	−	2.97713i	0.149606	−	0.259126i
$133$	−2.42705	+	4.20378i	−0.210452	+	0.364514i
$134$	−0.135255	−	0.234268i	−0.0116842	−	0.0202377i
$135$	0.854102			0.0735094
$136$	5.50000	+	9.52628i	0.471621	+	0.816872i
$137$	0.190983	+	0.330792i	0.0163168	+	0.0282615i	0.874069	−	0.485803i	$-0.161473\pi$
$137$	0.190983	+	0.330792i	0.0163168	+	0.0282615i	−0.857752	+	0.514064i	$0.828139\pi$
$138$	−0.652476			−0.0555424
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	0.980618	+	0.195929i	$0.0627723\pi$
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	−0.320629	+	0.947205i	$0.603894\pi$
$140$	0.354102	−	0.613323i	0.0299271	−	0.0518352i
$141$	0.427051	−	0.739674i	0.0359642	−	0.0622918i
$142$	3.12461			0.262212
$143$	4.85410	+	16.8151i	0.405920	+	1.40615i
$144$	−8.97871			−0.748226
$145$	0.781153	−	1.35300i	0.0648712	−	0.112360i
$146$	0.381966	−	0.661585i	0.0316117	−	0.0547531i
$147$	0.190983	+	0.330792i	0.0157520	+	0.0272833i
$148$	−7.41641			−0.609625
$149$	2.42705	+	4.20378i	0.198832	+	0.344387i	0.948150	−	0.317823i	$-0.102952\pi$
$149$	2.42705	+	4.20378i	0.198832	+	0.344387i	−0.749318	+	0.662210i	$0.769619\pi$
$150$	−0.354102	−	0.613323i	−0.0289123	−	0.0500776i
$151$	−14.7082			−1.19694			−0.598468	−	0.801146i	$-0.704224\pi$
$151$	−14.7082			−1.19694			−0.598468	+	0.801146i	$0.704224\pi$
$152$	3.57295	+	6.18853i	0.289804	+	0.501956i
$153$	10.6631	−	18.4691i	0.862062	−	1.49314i
$154$	0.927051	−	1.60570i	0.0747039	−	0.129391i
$155$	3.32624			0.267170
$156$	−1.77051	+	1.83997i	−0.141754	+	0.147315i
$157$	8.14590			0.650113			0.325057	−	0.945695i	$-0.394617\pi$
$157$	8.14590			0.650113			0.325057	+	0.945695i	$0.394617\pi$
$158$	−0.763932	+	1.32317i	−0.0607752	+	0.105266i
$159$	1.57295	−	2.72443i	0.124743	−	0.216061i
$160$	−0.791796	−	1.37143i	−0.0625970	−	0.108421i
$161$	4.47214			0.352454
$162$	−1.47214	−	2.54981i	−0.115662	−	0.200332i
$163$	−4.85410	−	8.40755i	−0.380203	−	0.658530i	0.610888	−	0.791717i	$-0.290812\pi$
$163$	−4.85410	−	8.40755i	−0.380203	−	0.658530i	−0.991091	+	0.133186i	$0.957479\pi$
$164$	−9.70820			−0.758083
$165$	−0.354102	−	0.613323i	−0.0275668	−	0.0477471i
$166$	1.28115	−	2.21902i	0.0994368	−	0.172230i
$167$	−4.88197	+	8.45581i	−0.377778	+	0.654330i	−0.990739	−	0.135783i	$-0.956645\pi$
$167$	−4.88197	+	8.45581i	−0.377778	+	0.654330i	0.612961	+	0.790113i	$0.289978\pi$
$168$	0.562306			0.0433828
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	1.09017			0.0836122
$171$	6.92705	−	11.9980i	0.529725	−	0.917510i
$172$	−7.01064	+	12.1428i	−0.534557	+	0.925879i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$	0.596748			0.0452393
$175$	2.42705	+	4.20378i	0.183468	+	0.317776i
$176$	7.63525	+	13.2246i	0.575529	+	0.996845i
$177$	−0.854102			−0.0641982
$178$	−3.07295	−	5.32250i	−0.230327	−	0.398939i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$	−1.01064	+	1.75049i	−0.0753289	+	0.130473i
$181$	−3.70820			−0.275629			−0.137814	−	0.990458i	$-0.544008\pi$
$181$	−3.70820			−0.275629			−0.137814	+	0.990458i	$0.544008\pi$
$182$	−0.954915	+	0.992377i	−0.0707830	+	0.0735599i
$183$	2.29180			0.169414
$184$	3.29180	−	5.70156i	0.242674	−	0.420324i
$185$	−0.763932	+	1.32317i	−0.0561654	+	0.0972813i
$186$	0.635255	+	1.10029i	0.0465792	+	0.0806775i
$187$	−36.2705			−2.65236
$188$	2.07295	+	3.59045i	0.151185	+	0.261861i
$189$	−1.11803	−	1.93649i	−0.0813250	−	0.140859i
$190$	0.708204			0.0513785
$191$	−11.8090	−	20.4538i	−0.854470	−	1.47999i	−0.877135	−	0.480243i	$-0.840548\pi$
$191$	−11.8090	−	20.4538i	−0.854470	−	1.47999i	0.0226649	−	0.999743i	$-0.492785\pi$
$192$	−0.899187	+	1.55744i	−0.0648932	+	0.112398i
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	4.63932			0.333084
$195$	0.145898	+	0.505406i	0.0104480	+	0.0361928i
$196$	−1.85410			−0.132436
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	−0.970839	−	0.239732i	$-0.922940\pi$
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	0.693034	+	0.720905i	$0.256274\pi$
$198$	−2.64590	+	4.58283i	−0.188036	+	0.325688i
$199$	−1.20820	−	2.09267i	−0.0856473	−	0.148345i	0.820020	−	0.572336i	$-0.193962\pi$
$199$	−1.20820	−	2.09267i	−0.0856473	−	0.148345i	−0.905667	+	0.423990i	$0.860629\pi$
$200$	7.14590			0.505291
$201$	0.135255	+	0.234268i	0.00954015	+	0.0165240i
$202$	−1.63525	−	2.83234i	−0.115056	−	0.199283i
$203$	−4.09017			−0.287074
$204$	−2.64590	−	4.58283i	−0.185250	−	0.320862i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	−0.899187	+	1.55744i	−0.0626493	+	0.108512i
$207$	−12.7639			−0.887155
$208$	−3.14590	−	10.8977i	−0.218129	−	0.755620i
$209$	−23.5623			−1.62984
$210$	0.0278640	−	0.0482619i	0.00192280	−	0.00333039i
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	−0.676330	−	0.736599i	$-0.736430\pi$
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	0.976078	+	0.217419i	$0.0697638\pi$
$212$	7.63525	+	13.2246i	0.524391	+	0.908273i
$213$	−3.12461			−0.214095
$214$	1.07295	+	1.85840i	0.0733453	+	0.127038i
$215$	1.44427	+	2.50155i	0.0984985	+	0.170604i
$216$	−3.29180			−0.223978
$217$	−4.35410	−	7.54153i	−0.295576	−	0.511952i
$218$	−2.04508	+	3.54219i	−0.138511	+	0.239907i
$219$	−0.381966	+	0.661585i	−0.0258109	+	0.0447057i
$220$	3.43769			0.231769
$221$	26.1525	+	6.47106i	1.75921	+	0.435291i
$222$	−0.583592			−0.0391681
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	−0.553676	−	0.832732i	$-0.686775\pi$
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	0.998005	+	0.0631310i	$0.0201086\pi$
$224$	−2.07295	+	3.59045i	−0.138505	+	0.239897i
$225$	−6.92705	−	11.9980i	−0.461803	−	0.799867i
$226$	−2.85410			−0.189852
$227$	3.73607	+	6.47106i	0.247972	+	0.429499i	0.962963	−	0.269634i	$-0.0869027\pi$
$227$	3.73607	+	6.47106i	0.247972	+	0.429499i	−0.714991	+	0.699133i	$0.753569\pi$
$228$	−1.71885	−	2.97713i	−0.113833	−	0.197165i
$229$	27.1246			1.79244			0.896222	−	0.443605i	$-0.146301\pi$
$229$	27.1246			1.79244			0.896222	+	0.443605i	$0.146301\pi$
$230$	−0.326238	−	0.565061i	−0.0215115	−	0.0372590i
$231$	−0.927051	+	1.60570i	−0.0609955	+	0.105647i
$232$	−3.01064	+	5.21459i	−0.197658	+	0.342354i
$233$	0.381966			0.0250234			0.0125117	−	0.999922i	$-0.496017\pi$
$233$	0.381966			0.0250234			0.0125117	+	0.999922i	$0.496017\pi$
$234$	2.72542	−	2.83234i	0.178167	−	0.185156i
$235$	0.854102			0.0557155
$236$	2.07295	−	3.59045i	0.134937	−	0.233719i
$237$	0.763932	−	1.32317i	0.0496227	−	0.0859491i
$238$	−1.42705	−	2.47172i	−0.0925020	−	0.160218i
$239$	−11.2918			−0.730406			−0.365203	−	0.930928i	$-0.619000\pi$
$239$	−11.2918			−0.730406			−0.365203	+	0.930928i	$0.619000\pi$
$240$	0.229490	+	0.397489i	0.0148135	+	0.0256578i
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	0.785670	−	0.618646i	$-0.212319\pi$
$241$	−2.21885	−	3.84316i	−0.142929	−	0.247559i	−0.928598	+	0.371087i	$0.878985\pi$
$242$	4.79837			0.308451
$243$	4.82624	+	8.35929i	0.309603	+	0.536249i
$244$	−5.56231	+	9.63420i	−0.356090	+	0.616766i
$245$	−0.190983	+	0.330792i	−0.0122015	+	0.0211335i
$246$	−0.763932			−0.0487065
$247$	16.9894	+	4.20378i	1.08101	+	0.267480i
$248$	−12.8197			−0.814049
$249$	−1.28115	+	2.21902i	−0.0811898	+	0.140625i
$250$	0.718847	−	1.24508i	0.0454639	−	0.0787457i
$251$	−2.61803	−	4.53457i	−0.165249	−	0.286219i	0.771495	−	0.636236i	$-0.219509\pi$
$251$	−2.61803	−	4.53457i	−0.165249	−	0.286219i	−0.936744	+	0.350016i	$0.886176\pi$
$252$	5.29180			0.333352
$253$	10.8541	+	18.7999i	0.682392	+	1.18194i
$254$	2.70163	+	4.67935i	0.169515	+	0.293609i
$255$	−1.09017			−0.0682691
$256$	−2.78115	−	4.81710i	−0.173822	−	0.301069i
$257$	12.8713	−	22.2938i	0.802891	−	1.39065i	−0.114815	−	0.993387i	$-0.536627\pi$
$257$	12.8713	−	22.2938i	0.802891	−	1.39065i	0.917706	−	0.397261i	$-0.130039\pi$
$258$	−0.551663	+	0.955508i	−0.0343450	+	0.0594873i
$259$	4.00000			0.248548
$260$	−2.47871	−	0.613323i	−0.153723	−	0.0380367i
$261$	11.6738			0.722588
$262$	−0.0623059	+	0.107917i	−0.00384927	+	0.00666713i
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$	1.36475	+	2.36381i	0.0839943	+	0.145482i
$265$	3.14590			0.193251
$266$	−0.927051	−	1.60570i	−0.0568411	−	0.0984517i
$267$	3.07295	+	5.32250i	0.188061	+	0.325732i
$268$	−1.31308			−0.0802093
$269$	−6.87132	−	11.9015i	−0.418952	−	0.725646i	0.576882	−	0.816827i	$-0.304269\pi$
$269$	−6.87132	−	11.9015i	−0.418952	−	0.725646i	−0.995834	+	0.0911812i	$0.970936\pi$
$270$	−0.163119	+	0.282530i	−0.00992710	+	0.0171942i
$271$	−9.20820	+	15.9491i	−0.559359	+	0.968837i	0.438192	+	0.898882i	$0.355619\pi$
$271$	−9.20820	+	15.9491i	−0.559359	+	0.968837i	−0.997550	+	0.0699558i	$0.977714\pi$
$272$	23.5066			1.42530
$273$	0.954915	−	0.992377i	0.0577941	−	0.0600614i
$274$	−0.145898			−0.00881402
$275$	−11.7812	+	20.4056i	−0.710430	+	1.23050i
$276$	−1.58359	+	2.74286i	−0.0953210	+	0.165101i
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−5.94427			−0.356514
$279$	12.4271	+	21.5243i	0.743988	+	1.28863i
$280$	0.281153	+	0.486971i	0.0168021	+	0.0291021i
$281$	−2.18034			−0.130068			−0.0650341	−	0.997883i	$-0.520716\pi$
$281$	−2.18034			−0.130068			−0.0650341	+	0.997883i	$0.520716\pi$
$282$	0.163119	+	0.282530i	0.00971359	+	0.0168244i
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	−0.594812	−	0.803865i	$-0.702774\pi$
$283$	6.70820	−	11.6190i	0.398761	−	0.690675i	0.993573	+	0.113190i	$0.0361069\pi$
$284$	7.58359	−	13.1352i	0.450003	−	0.779429i
$285$	−0.708204			−0.0419504
$286$	−6.48936	−	1.60570i	−0.383724	−	0.0949470i
$287$	5.23607			0.309075
$288$	5.91641	−	10.2475i	0.348628	−	0.603841i
$289$	−19.4164	+	33.6302i	−1.14214	+	1.97825i
$290$	0.298374	+	0.516799i	0.0175211	+	0.0303475i
$291$	−4.63932			−0.271962
$292$	−1.85410	−	3.21140i	−0.108503	−	0.187933i
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	0.982157	−	0.188065i	$-0.0602216\pi$
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	−0.653947	+	0.756540i	$0.726888\pi$
$294$	−0.145898			−0.00850895
$295$	−0.427051	−	0.739674i	−0.0248639	−	0.0430655i
$296$	2.94427	−	5.09963i	0.171132	−	0.296410i
$297$	5.42705	−	9.39993i	0.314909	−	0.545439i
$298$	−1.85410			−0.107405
$299$	−4.47214	−	15.4919i	−0.258630	−	0.895922i
$300$	−3.43769			−0.198475
$301$	3.78115	−	6.54915i	0.217942	−	0.377487i
$302$	2.80902	−	4.86536i	0.161641	−	0.279970i
$303$	1.63525	+	2.83234i	0.0939429	+	0.162714i
$304$	15.2705			0.875824
$305$	1.14590	+	1.98475i	0.0656139	+	0.113647i
$306$	4.07295	+	7.05455i	0.232835	+	0.403282i
$307$	1.85410			0.105819			0.0529096	−	0.998599i	$-0.483150\pi$
$307$	1.85410			0.105819			0.0529096	+	0.998599i	$0.483150\pi$
$308$	−4.50000	−	7.79423i	−0.256411	−	0.444117i
$309$	0.899187	−	1.55744i	0.0511530	−	0.0885995i
$310$	−0.635255	+	1.10029i	−0.0360801	+	0.0624925i
$311$	−12.3262			−0.698957			−0.349478	−	0.936944i	$-0.613641\pi$
$311$	−12.3262			−0.698957			−0.349478	+	0.936944i	$0.613641\pi$
$312$	−0.562306	−	1.94788i	−0.0318343	−	0.110277i
$313$	−15.1246			−0.854894			−0.427447	−	0.904041i	$-0.640587\pi$
$313$	−15.1246			−0.854894			−0.427447	+	0.904041i	$0.640587\pi$
$314$	−1.55573	+	2.69460i	−0.0877948	+	0.152065i
$315$	0.545085	−	0.944115i	0.0307121	−	0.0531948i
$316$	3.70820	+	6.42280i	0.208603	+	0.361311i
$317$	21.7639			1.22238			0.611192	−	0.791482i	$-0.290690\pi$
$317$	21.7639			1.22238			0.611192	+	0.791482i	$0.290690\pi$
$318$	0.600813	+	1.04064i	0.0336919	+	0.0583561i
$319$	−9.92705	−	17.1942i	−0.555808	−	0.962688i
$320$	−1.79837			−0.100532
$321$	−1.07295	−	1.85840i	−0.0598862	−	0.103726i
$322$	−0.854102	+	1.47935i	−0.0475972	+	0.0824408i
$323$	−18.1353	+	31.4112i	−1.00907	+	1.74776i
$324$	−14.2918			−0.793989
$325$	12.1353	−	12.6113i	0.673143	−	0.699551i
$326$	3.70820			0.205378
$327$	2.04508	−	3.54219i	0.113093	−	0.195884i
$328$	3.85410	−	6.67550i	0.212807	−	0.368593i
$329$	−1.11803	−	1.93649i	−0.0616392	−	0.106762i
$330$	0.270510			0.0148911
$331$	8.42705	+	14.5961i	0.463193	+	0.802273i	0.999118	−	0.0419923i	$-0.0133705\pi$
$331$	8.42705	+	14.5961i	0.463193	+	0.802273i	−0.535925	+	0.844265i	$0.680037\pi$
$332$	−6.21885	−	10.7714i	−0.341304	−	0.591155i
$333$	−11.4164			−0.625615
$334$	−1.86475	−	3.22983i	−0.102034	−	0.176729i
$335$	−0.135255	+	0.234268i	−0.00738977	+	0.0127994i
$336$	0.600813	−	1.04064i	0.0327770	−	0.0567715i
$337$	8.56231			0.466419			0.233209	−	0.972427i	$-0.425077\pi$
$337$	8.56231			0.466419			0.233209	+	0.972427i	$0.425077\pi$
$338$	4.39261	+	2.31555i	0.238926	+	0.125949i
$339$	2.85410			0.155014
$340$	2.64590	−	4.58283i	0.143494	−	0.248539i
$341$	21.1353	−	36.6073i	1.14454	−	1.98240i
$342$	2.64590	+	4.58283i	0.143074	+	0.247811i
$343$	1.00000			0.0539949
$344$	−5.56637	−	9.64124i	−0.300119	−	0.519821i
$345$	0.326238	+	0.565061i	0.0175641	+	0.0304218i
$346$	−3.43769			−0.184812
$347$	−17.6180	−	30.5153i	−0.945786	−	1.63815i	−0.754171	−	0.656679i	$-0.771961\pi$
$347$	−17.6180	−	30.5153i	−0.945786	−	1.63815i	−0.191615	−	0.981470i	$-0.561373\pi$
$348$	1.44834	−	2.50859i	0.0776390	−	0.134475i
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	−0.946953	−	0.321372i	$-0.895856\pi$
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	0.751793	+	0.659400i	$0.229189\pi$
$350$	−1.85410			−0.0991059
$351$	−5.59017	+	5.80948i	−0.298381	+	0.310087i
$352$	−20.1246			−1.07265
$353$	−14.4271	+	24.9884i	−0.767874	+	1.33000i	0.170839	+	0.985299i	$0.445352\pi$
$353$	−14.4271	+	24.9884i	−0.767874	+	1.33000i	−0.938713	+	0.344699i	$0.887981\pi$
$354$	0.163119	−	0.282530i	0.00866967	−	0.0150163i
$355$	−1.56231	−	2.70599i	−0.0829186	−	0.143619i
$356$	−29.8328			−1.58114
$357$	1.42705	+	2.47172i	0.0755275	+	0.130818i
$358$	1.71885	+	2.97713i	0.0908439	+	0.157346i
$359$	−10.9098			−0.575799			−0.287899	−	0.957661i	$-0.592957\pi$
$359$	−10.9098			−0.575799			−0.287899	+	0.957661i	$0.592957\pi$
$360$	−0.802439	−	1.38987i	−0.0422923	−	0.0732523i
$361$	−2.28115	+	3.95107i	−0.120061	+	0.207951i
$362$	0.708204	−	1.22665i	0.0372224	−	0.0644710i
$363$	−4.79837			−0.251849
$364$	1.85410	+	6.42280i	0.0971813	+	0.336646i
$365$	−0.763932			−0.0399860
$366$	−0.437694	+	0.758108i	−0.0228786	+	0.0396270i
$367$	−12.7082	+	22.0113i	−0.663363	+	1.14898i	0.316364	+	0.948638i	$0.397538\pi$
$367$	−12.7082	+	22.0113i	−0.663363	+	1.14898i	−0.979726	+	0.200340i	$0.935795\pi$
$368$	−7.03444	−	12.1840i	−0.366696	−	0.635135i
$369$	−14.9443			−0.777968
$370$	−0.291796	−	0.505406i	−0.0151698	−	0.0262748i
$371$	−4.11803	−	7.13264i	−0.213798	−	0.370308i
$372$	6.16718			0.319754
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	0.871636	−	0.490155i	$-0.163060\pi$
$373$	0.218847	+	0.379054i	0.0113315	+	0.0196267i	−0.860304	+	0.509781i	$0.829726\pi$
$374$	6.92705	−	11.9980i	0.358189	−	0.620402i
$375$	−0.718847	+	1.24508i	−0.0371211	+	0.0642956i
$376$	−3.29180			−0.169761
$377$	4.09017	+	14.1688i	0.210654	+	0.729728i
$378$	0.854102			0.0439303
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	−0.652403	−	0.757872i	$-0.726239\pi$
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	0.982538	+	0.186061i	$0.0595722\pi$
$380$	1.71885	−	2.97713i	0.0881750	−	0.152724i
$381$	−2.70163	−	4.67935i	−0.138408	−	0.239731i
$382$	9.02129			0.461569
$383$	−12.4894	−	21.6322i	−0.638176	−	1.10535i	−0.985833	−	0.167732i	$-0.946356\pi$
$383$	−12.4894	−	21.6322i	−0.638176	−	1.10535i	0.347656	−	0.937622i	$-0.386978\pi$
$384$	−1.92705	−	3.33775i	−0.0983394	−	0.170329i
$385$	−1.85410			−0.0944938
$386$	1.14590	+	1.98475i	0.0583247	+	0.101021i
$387$	−10.7918	+	18.6919i	−0.548578	+	0.950165i
$388$	11.2599	−	19.5027i	0.571633	−	0.990098i
$389$	23.8885			1.21120			0.605599	−	0.795770i	$-0.292934\pi$
$389$	23.8885			1.21120			0.605599	+	0.795770i	$0.292934\pi$
$390$	−0.195048	−	0.0482619i	−0.00987666	−	0.00244384i
$391$	33.4164			1.68994
$392$	0.736068	−	1.27491i	0.0371770	−	0.0643925i
$393$	0.0623059	−	0.107917i	0.00314292	−	0.00544369i
$394$	−1.48936	−	2.57964i	−0.0750327	−	0.129960i
$395$	1.52786			0.0768752
$396$	12.8435	+	22.2455i	0.645408	+	1.11788i
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	0.985913	+	0.167258i	$0.0534914\pi$
$397$	12.7082	+	22.0113i	0.637806	+	1.10471i	−0.348107	+	0.937455i	$0.613175\pi$
$398$	0.922986			0.0462651
$399$	0.927051	+	1.60570i	0.0464106	+	0.0803855i
$400$	7.63525	−	13.2246i	0.381763	−	0.661232i
$401$	10.2254	−	17.7110i	0.510633	−	0.884443i	−0.489291	−	0.872121i	$-0.662744\pi$
$401$	10.2254	−	17.7110i	0.510633	−	0.884443i	0.999924	−	0.0123222i	$-0.00392237\pi$
$402$	−0.103326			−0.00515341
$403$	−21.7705	+	22.6246i	−1.08447	+	1.12701i
$404$	−15.8754			−0.789830
$405$	−1.47214	+	2.54981i	−0.0731510	+	0.126701i
$406$	0.781153	−	1.35300i	0.0387680	−	0.0671481i
$407$	9.70820	+	16.8151i	0.481218	+	0.833494i
$408$	4.20163			0.208011
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	−0.877110	−	0.480290i	$-0.840532\pi$
$409$	−17.2812	−	29.9318i	−0.854498	−	1.48003i	0.0226119	−	0.999744i	$-0.492802\pi$
$410$	−0.381966	−	0.661585i	−0.0188640	−	0.0326733i
$411$	0.145898			0.00719662
$412$	4.36475	+	7.55996i	0.215036	+	0.372453i
$413$	−1.11803	+	1.93649i	−0.0550149	+	0.0952885i
$414$	2.43769	−	4.22221i	0.119806	−	0.207510i
$415$	−2.56231			−0.125779
$416$	14.5106	+	3.59045i	0.711443	+	0.176036i
$417$	5.94427			0.291092
$418$	4.50000	−	7.79423i	0.220102	−	0.381228i
$419$	−2.97214	+	5.14789i	−0.145198	+	0.251491i	−0.929447	−	0.368956i	$-0.879715\pi$
$419$	−2.97214	+	5.14789i	−0.145198	+	0.251491i	0.784249	+	0.620447i	$0.213049\pi$
$420$	−0.135255	−	0.234268i	−0.00659976	−	0.0114311i
$421$	−25.4164			−1.23872			−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164			−1.23872			−0.619360	+	0.785107i	$0.712608\pi$
$422$	1.66312	+	2.88061i	0.0809594	+	0.140226i
$423$	3.19098	+	5.52694i	0.155151	+	0.268729i
$424$	−12.1246			−0.588823
$425$	18.1353	+	31.4112i	0.879689	+	1.52367i
$426$	0.596748	−	1.03360i	0.0289125	−	0.0500780i
$427$	3.00000	−	5.19615i	0.145180	−	0.251459i
$428$	10.4164			0.503496
$429$	6.48936	+	1.60570i	0.313309	+	0.0775239i
$430$	−1.10333			−0.0532071
$431$	8.39919	−	14.5478i	0.404575	−	0.700744i	−0.589697	−	0.807624i	$-0.700753\pi$
$431$	8.39919	−	14.5478i	0.404575	−	0.700744i	0.994272	+	0.106881i	$0.0340863\pi$
$432$	−3.51722	+	6.09201i	−0.169222	+	0.293102i
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$	3.32624			0.159665
$435$	−0.298374	−	0.516799i	−0.0143059	−	0.0247786i
$436$	9.92705	+	17.1942i	0.475420	+	0.823451i
$437$	21.7082			1.03844
$438$	−0.145898	−	0.252703i	−0.00697128	−	0.0120746i
$439$	−4.07295	+	7.05455i	−0.194391	+	0.336696i	−0.946701	−	0.322114i	$-0.895606\pi$
$439$	−4.07295	+	7.05455i	−0.194391	+	0.336696i	0.752310	+	0.658810i	$0.228940\pi$
$440$	−1.36475	+	2.36381i	−0.0650617	+	0.112690i
$441$	−2.85410			−0.135910
$442$	−7.13525	+	7.41517i	−0.339389	+	0.352704i
$443$	−0.763932			−0.0362955			−0.0181478	−	0.999835i	$-0.505777\pi$
$443$	−0.763932			−0.0362955			−0.0181478	+	0.999835i	$0.505777\pi$
$444$	−1.41641	+	2.45329i	−0.0672197	+	0.116428i
$445$	−3.07295	+	5.32250i	−0.145672	+	0.252311i
$446$	2.53444	+	4.38978i	0.120009	+	0.207862i
$447$	1.85410			0.0876960
$448$	2.35410	+	4.07742i	0.111221	+	0.192640i
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	−0.977381	−	0.211484i	$-0.932170\pi$
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	0.305540	−	0.952179i	$-0.401163\pi$
$450$	5.29180			0.249458
$451$	12.7082	+	22.0113i	0.598406	+	1.03647i
$452$	−6.92705	+	11.9980i	−0.325821	+	0.564339i
$453$	−2.80902	+	4.86536i	−0.131979	+	0.228595i
$454$	−2.85410			−0.133950
$455$	1.33688	+	0.330792i	0.0626739	+	0.0155078i
$456$	2.72949			0.127820
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	−0.701072	−	0.713091i	$-0.747295\pi$
$457$	5.70820	−	9.88690i	0.267019	−	0.462490i	0.968090	+	0.250601i	$0.0806282\pi$
$458$	−5.18034	+	8.97261i	−0.242061	+	0.419263i
$459$	−8.35410	−	14.4697i	−0.389936	−	0.675389i
$460$	−3.16718			−0.147671
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.809505	−	0.587113i	$-0.800264\pi$
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.103702	−	0.994608i	$-0.533069\pi$
$462$	−0.354102	−	0.613323i	−0.0164743	−	0.0285343i
$463$	−6.70820			−0.311757			−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820			−0.311757			−0.155878	+	0.987776i	$0.549821\pi$
$464$	6.43363	+	11.1434i	0.298674	+	0.517318i
$465$	0.635255	−	1.10029i	0.0294592	−	0.0510249i
$466$	−0.0729490	+	0.126351i	−0.00337930	+	0.00585312i
$467$	33.6525			1.55725			0.778625	−	0.627489i	$-0.215917\pi$
$467$	33.6525			1.55725			0.778625	+	0.627489i	$0.215917\pi$
$468$	−5.29180	−	18.3313i	−0.244613	−	0.847366i
$469$	0.708204			0.0327018
$470$	−0.163119	+	0.282530i	−0.00752412	+	0.0130322i
$471$	1.55573	−	2.69460i	0.0716842	−	0.124161i
$472$	1.64590	+	2.85078i	0.0757586	+	0.131218i
$473$	36.7082			1.68785
$474$	0.291796	+	0.505406i	0.0134026	+	0.0232140i
$475$	11.7812	+	20.4056i	0.540556	+	0.936271i
$476$	−13.8541			−0.635002
$477$	11.7533	+	20.3573i	0.538146	+	0.932096i
$478$	2.15654	−	3.73524i	0.0986379	−	0.170846i
$479$	10.9894	−	19.0341i	0.502117	−	0.869691i	−0.497880	−	0.867246i	$-0.665888\pi$
$479$	10.9894	−	19.0341i	0.502117	−	0.869691i	0.999997	−	0.00244569i	$-0.000778487\pi$
$480$	−0.604878			−0.0276088
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	1.69505			0.0772073
$483$	0.854102	−	1.47935i	0.0388630	−	0.0673127i
$484$	11.6459	−	20.1713i	0.529359	−	0.916877i
$485$	−2.31966	−	4.01777i	−0.105330	−	0.182438i
$486$	−3.68692			−0.167242
$487$	8.48936	+	14.7040i	0.384689	+	0.666302i	0.991726	−	0.128372i	$-0.0409752\pi$
$487$	8.48936	+	14.7040i	0.384689	+	0.666302i	−0.607037	+	0.794674i	$0.707642\pi$
$488$	−4.41641	−	7.64944i	−0.199921	−	0.346274i
$489$	−3.70820			−0.167691
$490$	−0.0729490	−	0.126351i	−0.00329550	−	0.00570797i
$491$	−7.30902	+	12.6596i	−0.329851	+	0.571319i	−0.982482	−	0.186357i	$-0.940332\pi$
$491$	−7.30902	+	12.6596i	−0.329851	+	0.571319i	0.652631	+	0.757676i	$0.273665\pi$
$492$	−1.85410	+	3.21140i	−0.0835894	+	0.144781i
$493$	−30.5623			−1.37646
$494$	−4.63525	+	4.81710i	−0.208550	+	0.216731i
$495$	5.29180			0.237849
$496$	−13.6976	+	23.7249i	−0.615039	+	1.06528i
$497$	−4.09017	+	7.08438i	−0.183469	+	0.317778i
$498$	−0.489357	−	0.847591i	−0.0219286	−	0.0379815i
$499$	8.14590			0.364660			0.182330	−	0.983237i	$-0.441636\pi$
$499$	8.14590			0.364660			0.182330	+	0.983237i	$0.441636\pi$
$500$	−3.48936	−	6.04374i	−0.156049	−	0.270284i
$501$	1.86475	+	3.22983i	0.0833107	+	0.144298i
$502$	2.00000			0.0892644
$503$	−12.1910	−	21.1154i	−0.543569	−	0.941489i	−0.998695	−	0.0510624i	$-0.983739\pi$
$503$	−12.1910	−	21.1154i	−0.543569	−	0.941489i	0.455126	−	0.890427i	$-0.349594\pi$
$504$	−2.10081	+	3.63871i	−0.0935777	+	0.162081i
$505$	−1.63525	+	2.83234i	−0.0727679	+	0.126038i
$506$	−8.29180			−0.368615
$507$	−4.39261	−	2.31555i	−0.195083	−	0.102837i
$508$	26.2279			1.16368
$509$	−15.2984	+	26.4976i	−0.678089	+	1.17448i	0.297467	+	0.954732i	$0.403858\pi$
$509$	−15.2984	+	26.4976i	−0.678089	+	1.17448i	−0.975556	+	0.219752i	$0.929475\pi$
$510$	0.208204	−	0.360620i	0.00921943	−	0.0159685i
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	22.3050			0.985749
$513$	−5.42705	−	9.39993i	−0.239610	−	0.415017i
$514$	4.91641	+	8.51547i	0.216853	+	0.375601i
$515$	1.79837			0.0792458
$516$	2.67783	+	4.63813i	0.117885	+	0.204182i
$517$	5.42705	−	9.39993i	0.238681	−	0.413408i
$518$	−0.763932	+	1.32317i	−0.0335652	+	0.0581367i
$519$	3.43769			0.150898
$520$	1.40576	−	1.46091i	0.0616469	−	0.0640653i
$521$	−12.6525			−0.554315			−0.277158	−	0.960824i	$-0.589392\pi$
$521$	−12.6525			−0.554315			−0.277158	+	0.960824i	$0.589392\pi$
$522$	−2.22949	+	3.86159i	−0.0975821	+	0.169017i
$523$	19.5623	−	33.8829i	0.855400	−	1.48160i	−0.0208736	−	0.999782i	$-0.506645\pi$
$523$	19.5623	−	33.8829i	0.855400	−	1.48160i	0.876274	−	0.481814i	$-0.160022\pi$
$524$	0.302439	+	0.523840i	0.0132121	+	0.0228841i
$525$	1.85410			0.0809196
$526$	−1.71885	−	2.97713i	−0.0749453	−	0.129809i
$527$	−32.5344	−	56.3513i	−1.41722	−	2.45470i
$528$	5.83282			0.253841
$529$	1.50000	+	2.59808i	0.0652174	+	0.112960i
$530$	−0.600813	+	1.04064i	−0.0260977	+	0.0452025i
$531$	3.19098	−	5.52694i	0.138477	−	0.239849i
$532$	−9.00000			−0.390199
$533$	−5.23607	−	18.1383i	−0.226799	−	0.785656i
$534$	−2.34752			−0.101587
$535$	1.07295	−	1.85840i	0.0463876	−	0.0803457i
$536$	0.521286	−	0.902894i	0.0225161	−	0.0389991i
$537$	−1.71885	−	2.97713i	−0.0741737	−	0.128473i
$538$	5.24922			0.226310
$539$	2.42705	+	4.20378i	0.104540	+	0.181069i
$540$	0.791796	+	1.37143i	0.0340735	+	0.0590170i
$541$	1.72949			0.0743566			0.0371783	−	0.999309i	$-0.488163\pi$
$541$	1.72949			0.0743566			0.0371783	+	0.999309i	$0.488163\pi$
$542$	−3.51722	−	6.09201i	−0.151078	−	0.261674i
$543$	−0.708204	+	1.22665i	−0.0303919	+	0.0526404i
$544$	−15.4894	+	26.8284i	−0.664101	+	1.15026i
$545$	4.09017			0.175204
$546$	0.145898	+	0.505406i	0.00624386	+	0.0216294i
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	−0.354102	+	0.613323i	−0.0151265	+	0.0261998i
$549$	−8.56231	+	14.8303i	−0.365430	+	0.632944i
$550$	−4.50000	−	7.79423i	−0.191881	−	0.332347i
$551$	−19.8541			−0.845813
$552$	−1.25735	−	2.17780i	−0.0535165	−	0.0926934i
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	−1.90983			−0.0811409
$555$	0.291796	+	0.505406i	0.0123861	+	0.0214533i
$556$	−14.4271	+	24.9884i	−0.611843	+	1.05974i
$557$	−9.48936	+	16.4360i	−0.402077	+	0.696418i	−0.993976	−	0.109594i	$-0.965045\pi$
$557$	−9.48936	+	16.4360i	−0.402077	+	0.696418i	0.591899	+	0.806012i	$0.298378\pi$
$558$	−9.49342			−0.401889
$559$	−26.4681	−	6.54915i	−1.11948	−	0.276999i
$560$	1.20163			0.0507780
$561$	−6.92705	+	11.9980i	−0.292460	+	0.506556i
$562$	0.416408	−	0.721240i	0.0175651	−	0.0304237i
$563$	19.4721	+	33.7267i	0.820653	+	1.42141i	0.905197	+	0.424992i	$0.139723\pi$
$563$	19.4721	+	33.7267i	0.820653	+	1.42141i	−0.0845442	+	0.996420i	$0.526943\pi$
$564$	1.58359			0.0666813
$565$	1.42705	+	2.47172i	0.0600365	+	0.103986i
$566$	2.56231	+	4.43804i	0.107702	+	0.186545i
$567$	7.70820			0.323714
$568$	6.02129	+	10.4292i	0.252648	+	0.437598i
$569$	1.47214	−	2.54981i	0.0617151	−	0.106894i	−0.833517	−	0.552494i	$-0.813676\pi$
$569$	1.47214	−	2.54981i	0.0617151	−	0.106894i	0.895232	+	0.445600i	$0.147010\pi$
$570$	0.135255	−	0.234268i	0.00566521	−	0.00981242i
$571$	−35.6869			−1.49345			−0.746726	−	0.665132i	$-0.768375\pi$
$571$	−35.6869			−1.49345			−0.746726	+	0.665132i	$0.768375\pi$
$572$	−22.5000	+	23.3827i	−0.940772	+	0.977679i
$573$	−9.02129			−0.376870
$574$	−1.00000	+	1.73205i	−0.0417392	+	0.0722944i
$575$	10.8541	−	18.7999i	0.452647	−	0.784008i
$576$	−6.71885	−	11.6374i	−0.279952	−	0.484891i
$577$	9.83282			0.409345			0.204673	−	0.978830i	$-0.434387\pi$
$577$	9.83282			0.409345			0.204673	+	0.978830i	$0.434387\pi$
$578$	−7.41641	−	12.8456i	−0.308482	−	0.534306i
$579$	−1.14590	−	1.98475i	−0.0476219	−	0.0824835i
$580$	2.89667			0.120278
$581$	3.35410	+	5.80948i	0.139152	+	0.241018i
$582$	0.886031	−	1.53465i	0.0367272	−	0.0636133i
$583$	19.9894	−	34.6226i	0.827875	−	1.43392i
$584$	2.94427			0.121835
$585$	−3.81559	−	0.944115i	−0.157755	−	0.0390343i
$586$	−4.29180			−0.177292
$587$	15.5451	−	26.9249i	0.641614	−	1.11131i	−0.343458	−	0.939168i	$-0.611598\pi$
$587$	15.5451	−	26.9249i	0.641614	−	1.11131i	0.985072	−	0.172141i	$-0.0550683\pi$
$588$	−0.354102	+	0.613323i	−0.0146029	+	0.0252930i
$589$	−21.1353	−	36.6073i	−0.870863	−	1.50838i
$590$	0.326238			0.0134310
$591$	1.48936	+	2.57964i	0.0612640	+	0.106112i
$592$	−6.29180	−	10.8977i	−0.258591	−	0.447893i
$593$	19.2016			0.788516			0.394258	−	0.919000i	$-0.371002\pi$
$593$	19.2016			0.788516			0.394258	+	0.919000i	$0.371002\pi$
$594$	2.07295	+	3.59045i	0.0850541	+	0.147318i
$595$	−1.42705	+	2.47172i	−0.0585034	+	0.101331i
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$	−0.922986			−0.0377753
$598$	5.97871	+	1.47935i	0.244488	+	0.0604950i
$599$	−8.50658			−0.347569			−0.173785	−	0.984784i	$-0.555600\pi$
$599$	−8.50658			−0.347569			−0.173785	+	0.984784i	$0.555600\pi$
$600$	1.36475	−	2.36381i	0.0557155	−	0.0965021i
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	−0.293535	−	0.955948i	$-0.594832\pi$
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	0.974643	−	0.223765i	$-0.0718348\pi$
$602$	1.44427	+	2.50155i	0.0588641	+	0.101956i
$603$	−2.02129			−0.0823131
$604$	−13.6353	−	23.6170i	−0.554811	−	0.960960i
$605$	−2.39919	−	4.15551i	−0.0975408	−	0.168946i
$606$	−1.24922			−0.0507462
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$	−10.0623	+	17.4284i	−0.408080	+	0.706816i
$609$	−0.781153	+	1.35300i	−0.0316539	+	0.0548262i
$610$	−0.875388			−0.0354434
$611$	−5.59017	+	5.80948i	−0.226154	+	0.235026i
$612$	39.5410			1.59835
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	−0.974180	−	0.225771i	$-0.927510\pi$
$613$	−7.21885	+	12.5034i	−0.291566	+	0.505008i	0.682614	+	0.730779i	$0.260843\pi$
$614$	−0.354102	+	0.613323i	−0.0142904	+	0.0247517i
$615$	0.381966	+	0.661585i	0.0154024	+	0.0266777i
$616$	7.14590			0.287916
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	0.626955	−	0.779056i	$-0.284301\pi$
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	−0.988159	+	0.153431i	$0.950968\pi$
$618$	0.343459	+	0.594888i	0.0138159	+	0.0239299i
$619$	−17.4164			−0.700025			−0.350012	−	0.936745i	$-0.613823\pi$
$619$	−17.4164			−0.700025			−0.350012	+	0.936745i	$0.613823\pi$
$620$	3.08359	+	5.34094i	0.123840	+	0.214497i
$621$	−5.00000	+	8.66025i	−0.200643	+	0.347524i
$622$	2.35410	−	4.07742i	0.0943909	−	0.163490i
$623$	16.0902			0.644639
$624$	−4.20569	−	1.04064i	−0.168362	−	0.0416589i
$625$	22.8328			0.913313
$626$	2.88854	−	5.00310i	0.115449	−	0.199964i
$627$	−4.50000	+	7.79423i	−0.179713	+	0.311272i
$628$	7.55166	+	13.0799i	0.301344	+	0.521943i
$629$	29.8885			1.19173
$630$	0.208204	+	0.360620i	0.00829504	+	0.0143674i
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	0.929507	+	0.368804i	$0.120233\pi$
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	−0.145360	+	0.989379i	$0.546434\pi$
$632$	−5.88854			−0.234234
$633$	−1.66312	−	2.88061i	−0.0661030	−	0.114494i
$634$	−4.15654	+	7.19934i	−0.165077	+	0.285922i
$635$	2.70163	−	4.67935i	0.107211	−	0.185694i
$636$	5.83282			0.231286
$637$	−1.00000	−	3.46410i	−0.0396214	−	0.137253i
$638$	7.58359			0.300237
$639$	11.6738	−	20.2195i	0.461807	−	0.799873i
$640$	1.92705	−	3.33775i	0.0761734	−	0.131936i
$641$	4.74671	+	8.22154i	0.187484	+	0.324731i	0.944411	−	0.328768i	$-0.106633\pi$
$641$	4.74671	+	8.22154i	0.187484	+	0.324731i	−0.756927	+	0.653500i	$0.773300\pi$
$642$	0.819660			0.0323494
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	4.14590	+	7.18091i	0.163371	+	0.282967i
$645$	1.10333			0.0434434
$646$	−6.92705	−	11.9980i	−0.272541	−	0.472055i
$647$	−14.6180	+	25.3192i	−0.574694	+	0.995400i	0.421381	+	0.906884i	$0.361546\pi$
$647$	−14.6180	+	25.3192i	−0.574694	+	0.995400i	−0.996075	+	0.0885157i	$0.971788\pi$
$648$	5.67376	−	9.82724i	0.222886	−	0.386051i
$649$	−10.8541			−0.426061
$650$	1.85410	+	6.42280i	0.0727239	+	0.251923i
$651$	−3.32624			−0.130366
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	1.30902	−	2.26728i	0.0512258	−	0.0887257i	−0.839275	−	0.543706i	$-0.817021\pi$
$653$	1.30902	−	2.26728i	0.0512258	−	0.0887257i	0.890501	+	0.454981i	$0.150354\pi$
$654$	0.781153	+	1.35300i	0.0305455	+	0.0529064i
$655$	0.124612			0.00486899
$656$	−8.23607	−	14.2653i	−0.321564	−	0.556966i
$657$	−2.85410	−	4.94345i	−0.111349	−	0.192862i
$658$	0.854102			0.0332964
$659$	−5.94427	−	10.2958i	−0.231556	−	0.401067i	0.726710	−	0.686944i	$-0.241048\pi$
$659$	−5.94427	−	10.2958i	−0.231556	−	0.401067i	−0.958266	+	0.285877i	$0.907715\pi$
$660$	0.656541	−	1.13716i	0.0255558	−	0.0442640i
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	−0.988057	−	0.154092i	$-0.950755\pi$
$661$	−9.27051	+	16.0570i	−0.360581	+	0.624545i	0.627476	+	0.778636i	$0.284088\pi$
$662$	−6.43769			−0.250208
$663$	7.13525	−	7.41517i	0.277110	−	0.287982i
$664$	9.87539			0.383239
$665$	−0.927051	+	1.60570i	−0.0359495	+	0.0622664i
$666$	2.18034	−	3.77646i	0.0844865	−	0.146335i
$667$	9.14590	+	15.8412i	0.354131	+	0.613372i
$668$	−18.1033			−0.700439
$669$	−2.53444	−	4.38978i	−0.0979872	−	0.169719i
$670$	−0.0516628	−	0.0894826i	−0.00199591	−	0.00345701i
$671$	29.1246			1.12434
$672$	0.791796	+	1.37143i	0.0305442	+	0.0529041i
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	0.127806	+	0.991799i	$0.459207\pi$
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	−0.922826	+	0.385216i	$0.874127\pi$
$674$	−1.63525	+	2.83234i	−0.0629877	+	0.109098i
$675$	−10.8541			−0.417775
$676$	20.3951	−	12.8456i	0.784428	−	0.494061i
$677$	1.25735			0.0483240			0.0241620	−	0.999708i	$-0.492308\pi$
$677$	1.25735			0.0483240			0.0241620	+	0.999708i	$0.492308\pi$
$678$	−0.545085	+	0.944115i	−0.0209339	+	0.0362585i
$679$	−6.07295	+	10.5187i	−0.233058	+	0.403669i
$680$	2.10081	+	3.63871i	0.0805625	+	0.139538i
$681$	2.85410			0.109369
$682$	8.07295	+	13.9828i	0.309129	+	0.535427i
$683$	3.73607	+	6.47106i	0.142957	+	0.247608i	0.928609	−	0.371060i	$-0.121006\pi$
$683$	3.73607	+	6.47106i	0.142957	+	0.247608i	−0.785652	+	0.618669i	$0.787672\pi$
$684$	25.6869			0.982164
$685$	0.0729490	+	0.126351i	0.00278724	+	0.00482764i
$686$	−0.190983	+	0.330792i	−0.00729177	+	0.0126297i
$687$	5.18034	−	8.97261i	0.197642	−	0.342326i
$688$	−23.7902			−0.906995
$689$	−20.5902	+	21.3979i	−0.784423	+	0.815196i
$690$	−0.249224			−0.00948778
$691$	−0.427051	+	0.739674i	−0.0162458	+	0.0281385i	−0.874034	−	0.485865i	$-0.838505\pi$
$691$	−0.427051	+	0.739674i	−0.0162458	+	0.0281385i	0.857788	+	0.514003i	$0.171838\pi$
$692$	−8.34346	+	14.4513i	−0.317171	+	0.549356i
$693$	−6.92705	−	11.9980i	−0.263137	−	0.455766i
$694$	13.4590			0.510896
$695$	2.97214	+	5.14789i	0.112740	+	0.195271i
$696$	1.14996	+	1.99179i	0.0435892	+	0.0754988i
$697$	39.1246			1.48195
$698$	−1.39261	−	2.41207i	−0.0527110	−	0.0912982i
$699$	0.0729490	−	0.126351i	0.00275919	−	0.00477905i
$700$	−4.50000	+	7.79423i	−0.170084	+	0.294594i
$701$	6.76393			0.255470			0.127735	−	0.991808i	$-0.459229\pi$
$701$	6.76393			0.255470			0.127735	+	0.991808i	$0.459229\pi$
$702$	−0.854102	−	2.95870i	−0.0322360	−	0.111669i
$703$	19.4164			0.732304
$704$	−11.4271	+	19.7922i	−0.430673	+	0.745948i
$705$	0.163119	−	0.282530i	0.00614342	−	0.0106407i
$706$	−5.51064	−	9.54471i	−0.207396	−	0.359220i
$707$	8.56231			0.322019
$708$	−0.791796	−	1.37143i	−0.0297575	−	0.0515415i
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	0.831943	−	0.554861i	$-0.187229\pi$
$709$	−1.71885	−	2.97713i	−0.0645527	−	0.111808i	−0.896495	+	0.443053i	$0.853895\pi$
$710$	1.19350			0.0447911
$711$	5.70820	+	9.88690i	0.214074	+	0.370788i
$712$	11.8435	−	20.5135i	0.443852	−	0.768775i
$713$	−19.4721	+	33.7267i	−0.729237	+	1.26308i
$714$	−1.09017			−0.0407986
$715$	1.85410	+	6.42280i	0.0693395	+	0.240199i
$716$	16.6869			0.623619
$717$	−2.15654	+	3.73524i	−0.0805375	+	0.139495i
$718$	2.08359	−	3.60889i	0.0777590	−	0.134682i
$719$	16.0623	+	27.8207i	0.599023	+	1.03754i	0.992966	+	0.118403i	$0.0377775\pi$
$719$	16.0623	+	27.8207i	0.599023	+	1.03754i	−0.393943	+	0.919135i	$0.628889\pi$
$720$	−3.42956			−0.127812
$721$	−2.35410	−	4.07742i	−0.0876713	−	0.151851i
$722$	−0.871323	−	1.50918i	−0.0324273	−	0.0561657i
$723$	−1.69505			−0.0630395
$724$	−3.43769	−	5.95426i	−0.127761	−	0.221288i
$725$	−9.92705	+	17.1942i	−0.368681	+	0.638575i
$726$	0.916408	−	1.58726i	0.0340111	−	0.0589089i
$727$	−17.2918			−0.641317			−0.320659	−	0.947195i	$-0.603904\pi$
$727$	−17.2918			−0.641317			−0.320659	+	0.947195i	$0.603904\pi$
$728$	−5.15248	−	1.27491i	−0.190963	−	0.0472512i
$729$	−19.4377			−0.719915
$730$	0.145898	−	0.252703i	0.00539993	−	0.00935295i
$731$	28.2533	−	48.9361i	1.04499	−	1.80997i
$732$	2.12461	+	3.67994i	0.0785279	+	0.136014i
$733$	1.27051			0.0469274			0.0234637	−	0.999725i	$-0.492531\pi$
$733$	1.27051			0.0469274			0.0234637	+	0.999725i	$0.492531\pi$
$734$	−4.85410	−	8.40755i	−0.179168	−	0.310328i
$735$	0.0729490	+	0.126351i	0.00269077	+	0.00466054i
$736$	18.5410			0.683431
$737$	1.71885	+	2.97713i	0.0633145	+	0.109664i
$738$	2.85410	−	4.94345i	0.105061	−	0.181971i
$739$	23.5623	−	40.8111i	0.866753	−	1.50126i	0.00145790	−	0.999999i	$-0.499536\pi$
$739$	23.5623	−	40.8111i	0.866753	−	1.50126i	0.865296	−	0.501262i	$-0.167131\pi$
$740$	−2.83282			−0.104136
$741$	4.63525	−	4.81710i	0.170280	−	0.176961i
$742$	3.14590			0.115490
$743$	−11.8369	+	20.5021i	−0.434253	+	0.752148i	−0.997234	−	0.0743213i	$-0.976321\pi$
$743$	−11.8369	+	20.5021i	−0.434253	+	0.752148i	0.562981	+	0.826470i	$0.309654\pi$
$744$	−2.44834	+	4.24064i	−0.0897604	+	0.155470i
$745$	0.927051	+	1.60570i	0.0339645	+	0.0588283i
$746$	−0.167184			−0.00612105
$747$	−9.57295	−	16.5808i	−0.350256	−	0.606661i
$748$	−33.6246	−	58.2395i	−1.22944	−	2.12945i
$749$	−5.61803			−0.205278
$750$	−0.274575	−	0.475578i	−0.0100261	−	0.0173657i
$751$	−4.64590	+	8.04693i	−0.169531	+	0.293637i	−0.938255	−	0.345944i	$-0.887559\pi$
$751$	−4.64590	+	8.04693i	−0.169531	+	0.293637i	0.768724	+	0.639581i	$0.220892\pi$
$752$	−3.51722	+	6.09201i	−0.128260	+	0.222153i
$753$	−2.00000			−0.0728841
$754$	−5.46807	−	1.35300i	−0.199135	−	0.0492732i
$755$	−5.61803			−0.204461
$756$	2.07295	−	3.59045i	0.0753924	−	0.130584i
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	2.45492	+	4.25204i	0.0891665	+	0.154441i
$759$	8.29180			0.300973
$760$	1.36475	+	2.36381i	0.0495045	+	0.0857443i
$761$	11.0729	+	19.1789i	0.401394	+	0.695235i	0.993894	−	0.110335i	$-0.0351925\pi$
$761$	11.0729	+	19.1789i	0.401394	+	0.695235i	−0.592500	+	0.805570i	$0.701859\pi$
$762$	2.06386			0.0747657
$763$	−5.35410	−	9.27358i	−0.193832	−	0.335726i
$764$	21.8951	−	37.9235i	0.792138	−	1.37202i
$765$	4.07295	−	7.05455i	0.147258	−	0.255058i
$766$	9.54102			0.344731
$767$	7.82624	+	1.93649i	0.282589	+	0.0699227i
$768$	−2.12461			−0.0766653
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	−0.931872	−	0.362788i	$-0.881825\pi$
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	0.780120	+

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.330792i) q^{2} +(0.190983 - 0.330792i) q^{3} +(0.927051 + 1.60570i) q^{4} +0.381966 q^{5} +(0.0729490 + 0.126351i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})\)	\(q+(-0.190983 + 0.330792i) q^{2} +(0.190983 - 0.330792i) q^{3} +(0.927051 + 1.60570i) q^{4} +0.381966 q^{5} +(0.0729490 + 0.126351i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +(-0.0729490 + 0.126351i) q^{10} +(2.42705 - 4.20378i) q^{11} +0.708204 q^{12} +(-2.50000 + 2.59808i) q^{13} +0.381966 q^{14} +(0.0729490 - 0.126351i) q^{15} +(-1.57295 + 2.72443i) q^{16} +(-3.73607 - 6.47106i) q^{17} -1.09017 q^{18} +(-2.42705 - 4.20378i) q^{19} +(0.354102 + 0.613323i) q^{20} -0.381966 q^{21} +(0.927051 + 1.60570i) q^{22} +(-2.23607 + 3.87298i) q^{23} +(-0.281153 + 0.486971i) q^{24} -4.85410 q^{25} +(-0.381966 - 1.32317i) q^{26} +2.23607 q^{27} +(0.927051 - 1.60570i) q^{28} +(2.04508 - 3.54219i) q^{29} +(0.0278640 + 0.0482619i) q^{30} +8.70820 q^{31} +(-2.07295 - 3.59045i) q^{32} +(-0.927051 - 1.60570i) q^{33} +2.85410 q^{34} +(-0.190983 - 0.330792i) q^{35} +(-2.64590 + 4.58283i) q^{36} +(-2.00000 + 3.46410i) q^{37} +1.85410 q^{38} +(0.381966 + 1.32317i) q^{39} -0.562306 q^{40} +(-2.61803 + 4.53457i) q^{41} +(0.0729490 - 0.126351i) q^{42} +(3.78115 + 6.54915i) q^{43} +9.00000 q^{44} +(0.545085 + 0.944115i) q^{45} +(-0.854102 - 1.47935i) q^{46} +2.23607 q^{47} +(0.600813 + 1.04064i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.927051 - 1.60570i) q^{50} -2.85410 q^{51} +(-6.48936 - 1.60570i) q^{52} +8.23607 q^{53} +(-0.427051 + 0.739674i) q^{54} +(0.927051 - 1.60570i) q^{55} +(0.736068 + 1.27491i) q^{56} -1.85410 q^{57} +(0.781153 + 1.35300i) q^{58} +(-1.11803 - 1.93649i) q^{59} +0.270510 q^{60} +(3.00000 + 5.19615i) q^{61} +(-1.66312 + 2.88061i) q^{62} +(1.42705 - 2.47172i) q^{63} -4.70820 q^{64} +(-0.954915 + 0.992377i) q^{65} +0.708204 q^{66} +(-0.354102 + 0.613323i) q^{67} +(6.92705 - 11.9980i) q^{68} +(0.854102 + 1.47935i) q^{69} +0.145898 q^{70} +(-4.09017 - 7.08438i) q^{71} +(-2.10081 - 3.63871i) q^{72} -2.00000 q^{73} +(-0.763932 - 1.32317i) q^{74} +(-0.927051 + 1.60570i) q^{75} +(4.50000 - 7.79423i) q^{76} -4.85410 q^{77} +(-0.510643 - 0.126351i) q^{78} +4.00000 q^{79} +(-0.600813 + 1.04064i) q^{80} +(-3.85410 + 6.67550i) q^{81} +(-1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(-0.354102 - 0.613323i) q^{84} +(-1.42705 - 2.47172i) q^{85} -2.88854 q^{86} +(-0.781153 - 1.35300i) q^{87} +(-3.57295 + 6.18853i) q^{88} +(-8.04508 + 13.9345i) q^{89} -0.416408 q^{90} +(3.50000 + 0.866025i) q^{91} -8.29180 q^{92} +(1.66312 - 2.88061i) q^{93} +(-0.427051 + 0.739674i) q^{94} +(-0.927051 - 1.60570i) q^{95} -1.58359 q^{96} +(-6.07295 - 10.5187i) q^{97} +(-0.190983 - 0.330792i) q^{98} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 6 q^{5} + 7 q^{6} - 2 q^{7} + 12 q^{8} - q^{9} - 7 q^{10} + 3 q^{11} - 24 q^{12} - 10 q^{13} + 6 q^{14} + 7 q^{15} - 13 q^{16} - 6 q^{17} + 18 q^{18} - 3 q^{19} - 12 q^{20} - 6 q^{21} - 3 q^{22} + 19 q^{24} - 6 q^{25} - 6 q^{26} - 3 q^{28} - 3 q^{29} + 18 q^{30} + 8 q^{31} - 15 q^{32} + 3 q^{33} - 2 q^{34} - 3 q^{35} - 24 q^{36} - 8 q^{37} - 6 q^{38} + 6 q^{39} + 38 q^{40} - 6 q^{41} + 7 q^{42} - 5 q^{43} + 36 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 2 q^{49} - 3 q^{50} + 2 q^{51} + 21 q^{52} + 24 q^{53} + 5 q^{54} - 3 q^{55} - 6 q^{56} + 6 q^{57} - 17 q^{58} - 66 q^{60} + 12 q^{61} + 9 q^{62} - q^{63} + 8 q^{64} - 15 q^{65} - 24 q^{66} + 12 q^{67} + 21 q^{68} - 10 q^{69} + 14 q^{70} + 6 q^{71} - 33 q^{72} - 8 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 6 q^{77} - 49 q^{78} + 16 q^{79} - 27 q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{84} + q^{85} + 60 q^{86} + 17 q^{87} - 21 q^{88} - 21 q^{89} + 52 q^{90} + 14 q^{91} - 60 q^{92} - 9 q^{93} + 5 q^{94} + 3 q^{95} - 60 q^{96} - 31 q^{97} - 3 q^{98} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 6 * q^5 + 7 * q^6 - 2 * q^7 + 12 * q^8 - q^9 - 7 * q^10 + 3 * q^11 - 24 * q^12 - 10 * q^13 + 6 * q^14 + 7 * q^15 - 13 * q^16 - 6 * q^17 + 18 * q^18 - 3 * q^19 - 12 * q^20 - 6 * q^21 - 3 * q^22 + 19 * q^24 - 6 * q^25 - 6 * q^26 - 3 * q^28 - 3 * q^29 + 18 * q^30 + 8 * q^31 - 15 * q^32 + 3 * q^33 - 2 * q^34 - 3 * q^35 - 24 * q^36 - 8 * q^37 - 6 * q^38 + 6 * q^39 + 38 * q^40 - 6 * q^41 + 7 * q^42 - 5 * q^43 + 36 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 2 * q^49 - 3 * q^50 + 2 * q^51 + 21 * q^52 + 24 * q^53 + 5 * q^54 - 3 * q^55 - 6 * q^56 + 6 * q^57 - 17 * q^58 - 66 * q^60 + 12 * q^61 + 9 * q^62 - q^63 + 8 * q^64 - 15 * q^65 - 24 * q^66 + 12 * q^67 + 21 * q^68 - 10 * q^69 + 14 * q^70 + 6 * q^71 - 33 * q^72 - 8 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 6 * q^77 - 49 * q^78 + 16 * q^79 - 27 * q^80 - 2 * q^81 - 4 * q^82 + 12 * q^84 + q^85 + 60 * q^86 + 17 * q^87 - 21 * q^88 - 21 * q^89 + 52 * q^90 + 14 * q^91 - 60 * q^92 - 9 * q^93 + 5 * q^94 + 3 * q^95 - 60 * q^96 - 31 * q^97 - 3 * q^98 + 42 * q^99

Introduction

L-functions

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