LMFDB - Embedded newform 195.2.i.d.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(16,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("195.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.i (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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$0.500000 + 1.75780i$ of defining polynomial
Character	$\chi$	$=$	195.16
Dual form			195.2.i.d.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.169938 + 0.294342i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.942242 - 1.63201i) q^{4} +1.00000 q^{5} +(-0.169938 + 0.294342i) q^{6} +(-0.330062 + 0.571683i) q^{7} +1.32025 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.169938 + 0.294342i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.942242 - 1.63201i) q^{4} +1.00000 q^{5} +(-0.169938 + 0.294342i) q^{6} +(-0.330062 + 0.571683i) q^{7} +1.32025 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.169938 + 0.294342i) q^{10} +(-0.339877 - 0.588684i) q^{11} +1.88448 q^{12} +(1.93243 - 3.04397i) q^{13} -0.224361 q^{14} +(0.500000 + 0.866025i) q^{15} +(-1.66012 - 2.87542i) q^{16} +(-3.71455 + 6.43378i) q^{17} -0.339877 q^{18} +(-0.0577581 + 0.100040i) q^{19} +(0.942242 - 1.63201i) q^{20} -0.660123 q^{21} +(0.115516 - 0.200080i) q^{22} +(3.88448 + 6.72812i) q^{23} +(0.660123 + 1.14337i) q^{24} +1.00000 q^{25} +(1.22436 + 0.0515075i) q^{26} -1.00000 q^{27} +(0.621996 + 1.07733i) q^{28} +(-2.77230 - 4.80177i) q^{29} +(-0.169938 + 0.294342i) q^{30} -9.97370 q^{31} +(1.88448 - 3.26402i) q^{32} +(0.339877 - 0.588684i) q^{33} -2.52498 q^{34} +(-0.330062 + 0.571683i) q^{35} +(0.942242 + 1.63201i) q^{36} +(-4.88448 - 8.46017i) q^{37} -0.0392613 q^{38} +(3.60236 + 0.151548i) q^{39} +1.32025 q^{40} +(-2.11218 - 3.65840i) q^{41} +(-0.112180 - 0.194302i) q^{42} +(0.272303 - 0.471643i) q^{43} -1.28098 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.32025 + 2.28673i) q^{46} -5.01963 q^{47} +(1.66012 - 2.87542i) q^{48} +(3.28212 + 5.68480i) q^{49} +(0.169938 + 0.294342i) q^{50} -7.42909 q^{51} +(-3.14697 - 6.02189i) q^{52} +0.679754 q^{53} +(-0.169938 - 0.294342i) q^{54} +(-0.339877 - 0.588684i) q^{55} +(-0.435763 + 0.754763i) q^{56} -0.115516 q^{57} +(0.942242 - 1.63201i) q^{58} +(-1.11218 + 1.92635i) q^{59} +1.88448 q^{60} +(2.10236 - 3.64140i) q^{61} +(-1.69491 - 2.93568i) q^{62} +(-0.330062 - 0.571683i) q^{63} -5.35951 q^{64} +(1.93243 - 3.04397i) q^{65} +0.231033 q^{66} +(3.81691 + 6.61108i) q^{67} +(7.00000 + 12.1244i) q^{68} +(-3.88448 + 6.72812i) q^{69} -0.224361 q^{70} +(-3.65679 + 6.33374i) q^{71} +(-0.660123 + 1.14337i) q^{72} +8.01963 q^{73} +(1.66012 - 2.87542i) q^{74} +(0.500000 + 0.866025i) q^{75} +(0.108844 + 0.188524i) q^{76} +0.448721 q^{77} +(0.567573 + 1.08608i) q^{78} +9.97370 q^{79} +(-1.66012 - 2.87542i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.717881 - 1.24341i) q^{82} +1.76897 q^{83} +(-0.621996 + 1.07733i) q^{84} +(-3.71455 + 6.43378i) q^{85} +0.185099 q^{86} +(2.77230 - 4.80177i) q^{87} +(-0.448721 - 0.777208i) q^{88} +(-6.77230 - 11.7300i) q^{89} -0.339877 q^{90} +(1.10236 + 2.10943i) q^{91} +14.6405 q^{92} +(-4.98685 - 8.63748i) q^{93} +(-0.853028 - 1.47749i) q^{94} +(-0.0577581 + 0.100040i) q^{95} +3.76897 q^{96} +(-4.95206 + 8.57721i) q^{97} +(-1.11552 + 1.93213i) q^{98} +0.679754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) $ 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.169938	+	0.294342i	0.120165	+	0.208131i	0.919832	−	0.392311i	$-0.128324\pi$
$2$	0.169938	+	0.294342i	0.120165	+	0.208131i	−0.799668	+	0.600443i	$0.794991\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.942242	−	1.63201i	0.471121	−	0.816005i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.169938	+	0.294342i	−0.0693771	+	0.120165i
$7$	−0.330062	+	0.571683i	−0.124752	+	0.216076i	−0.921636	−	0.388056i	$-0.873147\pi$
$7$	−0.330062	+	0.571683i	−0.124752	+	0.216076i	0.796884	+	0.604132i	$0.206480\pi$
$8$	1.32025			0.466778
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.169938	+	0.294342i	0.0537393	+	0.0930791i
$11$	−0.339877	−	0.588684i	−0.102477	−	0.177495i	0.810228	−	0.586115i	$-0.199343\pi$
$11$	−0.339877	−	0.588684i	−0.102477	−	0.177495i	−0.912704	+	0.408620i	$0.866010\pi$
$12$	1.88448			0.544004
$13$	1.93243	−	3.04397i	0.535959	−	0.844244i
$13$	1.93243	−	3.04397i	0.535959	−	0.844244i
$14$	−0.224361			−0.0599629
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−1.66012	−	2.87542i	−0.415031	−	0.718854i
$17$	−3.71455	+	6.43378i	−0.900910	+	1.56042i	−0.0745938	+	0.997214i	$0.523766\pi$
$17$	−3.71455	+	6.43378i	−0.900910	+	1.56042i	−0.826316	+	0.563207i	$0.809567\pi$
$18$	−0.339877			−0.0801098
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	−0.872575	−	0.488481i	$-0.837551\pi$
$19$	−0.0577581	+	0.100040i	−0.0132506	+	0.0229508i	0.859324	+	0.511431i	$0.170885\pi$
$20$	0.942242	−	1.63201i	0.210692	−	0.364929i
$21$	−0.660123			−0.144051
$22$	0.115516	−	0.200080i	0.0246282	−	0.0426572i
$23$	3.88448	+	6.72812i	0.809971	+	1.40291i	0.912883	+	0.408220i	$0.133850\pi$
$23$	3.88448	+	6.72812i	0.809971	+	1.40291i	−0.102913	+	0.994690i	$0.532816\pi$
$24$	0.660123	+	1.14337i	0.134747	+	0.233389i
$25$	1.00000			0.200000
$26$	1.22436	+	0.0515075i	0.240117	+	0.0101015i
$27$	−1.00000			−0.192450
$28$	0.621996	+	1.07733i	0.117546	+	0.203596i
$29$	−2.77230	−	4.80177i	−0.514804	−	0.891666i	−0.999852	−	0.0171792i	$-0.994531\pi$
$29$	−2.77230	−	4.80177i	−0.514804	−	0.891666i	0.485049	−	0.874487i	$-0.338802\pi$
$30$	−0.169938	+	0.294342i	−0.0310264	+	0.0537393i
$31$	−9.97370			−1.79133			−0.895664	−	0.444730i	$-0.853299\pi$
$31$	−9.97370			−1.79133			−0.895664	+	0.444730i	$0.853299\pi$
$32$	1.88448	−	3.26402i	0.333133	−	0.577003i
$33$	0.339877	−	0.588684i	0.0591650	−	0.102477i
$34$	−2.52498			−0.433030
$35$	−0.330062	+	0.571683i	−0.0557906	+	0.0966321i
$36$	0.942242	+	1.63201i	0.157040	+	0.272002i
$37$	−4.88448	−	8.46017i	−0.803004	−	1.39084i	−0.917630	−	0.397435i	$-0.869900\pi$
$37$	−4.88448	−	8.46017i	−0.803004	−	1.39084i	0.114626	−	0.993409i	$-0.463433\pi$
$38$	−0.0392613			−0.00636903
$39$	3.60236	+	0.151548i	0.576840	+	0.0242670i
$40$	1.32025			0.208749
$41$	−2.11218	−	3.65840i	−0.329867	−	0.571347i	0.652618	−	0.757687i	$-0.273671\pi$
$41$	−2.11218	−	3.65840i	−0.329867	−	0.571347i	−0.982485	+	0.186340i	$0.940337\pi$
$42$	−0.112180	−	0.194302i	−0.0173098	−	0.0299814i
$43$	0.272303	−	0.471643i	0.0415259	−	0.0719249i	−0.844515	−	0.535531i	$-0.820111\pi$
$43$	0.272303	−	0.471643i	0.0415259	−	0.0719249i	0.886041	+	0.463606i	$0.153445\pi$
$44$	−1.28098			−0.193116
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−1.32025	+	2.28673i	−0.194660	+	0.337160i
$47$	−5.01963			−0.732188			−0.366094	−	0.930578i	$-0.619305\pi$
$47$	−5.01963			−0.732188			−0.366094	+	0.930578i	$0.619305\pi$
$48$	1.66012	−	2.87542i	0.239618	−	0.415031i
$49$	3.28212	+	5.68480i	0.468874	+	0.812114i
$50$	0.169938	+	0.294342i	0.0240329	+	0.0416262i
$51$	−7.42909			−1.04028
$52$	−3.14697	−	6.02189i	−0.436406	−	0.835086i
$53$	0.679754			0.0933714			0.0466857	−	0.998910i	$-0.485134\pi$
$53$	0.679754			0.0933714			0.0466857	+	0.998910i	$0.485134\pi$
$54$	−0.169938	−	0.294342i	−0.0231257	−	0.0400549i
$55$	−0.339877	−	0.588684i	−0.0458290	−	0.0793781i
$56$	−0.435763	+	0.754763i	−0.0582312	+	0.100859i
$57$	−0.115516			−0.0153005
$58$	0.942242	−	1.63201i	0.123722	−	0.214294i
$59$	−1.11218	+	1.92635i	−0.144794	+	0.250790i	−0.929296	−	0.369336i	$-0.879585\pi$
$59$	−1.11218	+	1.92635i	−0.144794	+	0.250790i	0.784502	+	0.620126i	$0.212918\pi$
$60$	1.88448			0.243286
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	−0.699470	−	0.714662i	$-0.746581\pi$
$61$	2.10236	−	3.64140i	0.269180	−	0.466234i	0.968650	+	0.248428i	$0.0799139\pi$
$62$	−1.69491	−	2.93568i	−0.215254	−	0.372832i
$63$	−0.330062	−	0.571683i	−0.0415838	−	0.0720253i
$64$	−5.35951			−0.669938
$65$	1.93243	−	3.04397i	0.239688	−	0.377557i
$66$	0.231033			0.0284381
$67$	3.81691	+	6.61108i	0.466310	+	0.807672i	0.999260	−	0.0384746i	$-0.0122499\pi$
$67$	3.81691	+	6.61108i	0.466310	+	0.807672i	−0.532950	+	0.846147i	$0.678917\pi$
$68$	7.00000	+	12.1244i	0.848875	+	1.47029i
$69$	−3.88448	+	6.72812i	−0.467637	+	0.809971i
$70$	−0.224361			−0.0268162
$71$	−3.65679	+	6.33374i	−0.433981	+	0.751677i	−0.997212	−	0.0746227i	$-0.976225\pi$
$71$	−3.65679	+	6.33374i	−0.433981	+	0.751677i	0.563231	+	0.826299i	$0.309558\pi$
$72$	−0.660123	+	1.14337i	−0.0777963	+	0.134747i
$73$	8.01963			0.938627			0.469313	−	0.883032i	$-0.344501\pi$
$73$	8.01963			0.938627			0.469313	+	0.883032i	$0.344501\pi$
$74$	1.66012	−	2.87542i	0.192985	−	0.334261i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	0.108844	+	0.188524i	0.0124853	+	0.0216252i
$77$	0.448721			0.0511365
$78$	0.567573	+	1.08608i	0.0642650	+	0.122974i
$79$	9.97370			1.12213			0.561064	−	0.827772i	$-0.310392\pi$
$79$	9.97370			1.12213			0.561064	+	0.827772i	$0.310392\pi$
$80$	−1.66012	−	2.87542i	−0.185607	−	0.321481i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.717881	−	1.24341i	0.0792767	−	0.137311i
$83$	1.76897			0.194169			0.0970847	−	0.995276i	$-0.469048\pi$
$83$	1.76897			0.194169			0.0970847	+	0.995276i	$0.469048\pi$
$84$	−0.621996	+	1.07733i	−0.0678653	+	0.117546i
$85$	−3.71455	+	6.43378i	−0.402899	+	0.697842i
$86$	0.185099			0.0199598
$87$	2.77230	−	4.80177i	0.297222	−	0.514804i
$88$	−0.448721	−	0.777208i	−0.0478338	−	0.0828506i
$89$	−6.77230	−	11.7300i	−0.717863	−	1.24337i	−0.961845	−	0.273595i	$-0.911787\pi$
$89$	−6.77230	−	11.7300i	−0.717863	−	1.24337i	0.243982	−	0.969780i	$-0.421546\pi$
$90$	−0.339877			−0.0358262
$91$	1.10236	+	2.10943i	0.115559	+	0.221129i
$92$	14.6405			1.52638
$93$	−4.98685	−	8.63748i	−0.517112	−	0.895664i
$94$	−0.853028	−	1.47749i	−0.0879831	−	0.152391i
$95$	−0.0577581	+	0.100040i	−0.00592586	+	0.0102639i
$96$	3.76897			0.384669
$97$	−4.95206	+	8.57721i	−0.502805	+	0.870884i	0.497190	+	0.867642i	$0.334365\pi$
$97$	−4.95206	+	8.57721i	−0.502805	+	0.870884i	−0.999995	+	0.00324223i	$0.998968\pi$
$98$	−1.11552	+	1.93213i	−0.112684	+	0.195175i
$99$	0.679754			0.0683178
$100$	0.942242	−	1.63201i	0.0942242	−	0.163201i
$101$	4.67975	+	8.10557i	0.465653	+	0.806534i	0.999231	−	0.0392165i	$-0.0124862\pi$
$101$	4.67975	+	8.10557i	0.465653	+	0.806534i	−0.533578	+	0.845751i	$0.679153\pi$
$102$	−1.26249	−	2.18669i	−0.125005	−	0.216515i
$103$	4.50535			0.443925			0.221962	−	0.975055i	$-0.428754\pi$
$103$	4.50535			0.443925			0.221962	+	0.975055i	$0.428754\pi$
$104$	2.55128	−	4.01878i	0.250173	−	0.394074i
$105$	−0.660123			−0.0644214
$106$	0.115516	+	0.200080i	0.0112199	+	0.0194335i
$107$	−0.285455	−	0.494422i	−0.0275960	−	0.0477976i	0.851898	−	0.523708i	$-0.175452\pi$
$107$	−0.285455	−	0.494422i	−0.0275960	−	0.0477976i	−0.879494	+	0.475911i	$0.842119\pi$
$108$	−0.942242	+	1.63201i	−0.0906673	+	0.157040i
$109$	15.4095			1.47596			0.737979	−	0.674823i	$-0.235780\pi$
$109$	15.4095			1.47596			0.737979	+	0.674823i	$0.235780\pi$
$110$	0.115516	−	0.200080i	0.0110140	−	0.0190769i
$111$	4.88448	−	8.46017i	0.463615	−	0.803004i
$112$	2.19177			0.207103
$113$	2.66012	−	4.60747i	0.250243	−	0.433434i	−0.713349	−	0.700809i	$-0.752823\pi$
$113$	2.66012	−	4.60747i	0.250243	−	0.433434i	0.963593	+	0.267374i	$0.0861560\pi$
$114$	−0.0196307	−	0.0340013i	−0.00183858	−	0.00318451i
$115$	3.88448	+	6.72812i	0.362230	+	0.627401i
$116$	−10.4487			−0.970139
$117$	1.66994	+	3.19551i	0.154386	+	0.295425i
$118$	−0.756009			−0.0695962
$119$	−2.45206	−	4.24709i	−0.224780	−	0.389330i
$120$	0.660123	+	1.14337i	0.0602607	+	0.104375i
$121$	5.26897	−	9.12612i	0.478997	−	0.829647i
$122$	1.42909			0.129384
$123$	2.11218	−	3.65840i	0.190449	−	0.329867i
$124$	−9.39764	+	16.2772i	−0.843933	+	1.46173i
$125$	1.00000			0.0894427
$126$	0.112180	−	0.194302i	0.00999381	−	0.0173098i
$127$	6.00982	+	10.4093i	0.533285	+	0.923676i	0.999244	+	0.0388704i	$0.0123759\pi$
$127$	6.00982	+	10.4093i	0.533285	+	0.923676i	−0.465959	+	0.884806i	$0.654291\pi$
$128$	−4.67975	−	8.10557i	−0.413636	−	0.716438i
$129$	0.544607			0.0479500
$130$	1.22436	+	0.0515075i	0.107384	+	0.00451751i
$131$	10.9041			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$131$	10.9041			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$132$	−0.640492	−	1.10937i	−0.0557477	−	0.0965579i
$133$	−0.0381275	−	0.0660387i	−0.00330607	−	0.00572629i
$134$	−1.29728	+	2.24695i	−0.112068	+	0.194107i
$135$	−1.00000			−0.0860663
$136$	−4.90411	+	8.49418i	−0.420524	+	0.728370i
$137$	−1.69491	+	2.93568i	−0.144806	+	0.250812i	−0.929301	−	0.369324i	$-0.879589\pi$
$137$	−1.69491	+	2.93568i	−0.144806	+	0.250812i	0.784494	+	0.620136i	$0.212923\pi$
$138$	−2.64049			−0.224774
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	0.359942	+	0.932975i	$0.382796\pi$
$139$	−7.40411	+	12.8243i	−0.628009	+	1.08774i	−0.987951	+	0.154768i	$0.950537\pi$
$140$	0.621996	+	1.07733i	0.0525682	+	0.0910508i
$141$	−2.50982	−	4.34713i	−0.211365	−	0.366094i
$142$	−2.48571			−0.208597
$143$	−2.44872	−	0.103015i	−0.204772	−	0.00861455i
$144$	3.32025			0.276687
$145$	−2.77230	−	4.80177i	−0.230227	−	0.398765i
$146$	1.36284	+	2.36051i	0.112790	+	0.195358i
$147$	−3.28212	+	5.68480i	−0.270705	+	0.468874i
$148$	−18.4095			−1.51325
$149$	8.54461	−	14.7997i	0.700001	−	1.21244i	−0.268464	−	0.963290i	$-0.586516\pi$
$149$	8.54461	−	14.7997i	0.700001	−	1.21244i	0.968465	−	0.249148i	$-0.0801507\pi$
$150$	−0.169938	+	0.294342i	−0.0138754	+	0.0240329i
$151$	13.0130			1.05898			0.529490	−	0.848316i	$-0.322383\pi$
$151$	13.0130			1.05898			0.529490	+	0.848316i	$0.322383\pi$
$152$	−0.0762550	+	0.132077i	−0.00618510	+	0.0107129i
$153$	−3.71455	−	6.43378i	−0.300303	−	0.520140i
$154$	0.0762550	+	0.132077i	0.00614480	+	0.0106431i
$155$	−9.97370			−0.801107
$156$	3.64163	−	5.73630i	0.291563	−	0.459272i
$157$	−0.775639			−0.0619028			−0.0309514	−	0.999521i	$-0.509854\pi$
$157$	−0.775639			−0.0619028			−0.0309514	+	0.999521i	$0.509854\pi$
$158$	1.69491	+	2.93568i	0.134840	+	0.233550i
$159$	0.339877	+	0.588684i	0.0269540	+	0.0466857i
$160$	1.88448	−	3.26402i	0.148982	−	0.258044i
$161$	−5.12847			−0.404180
$162$	0.169938	−	0.294342i	0.0133516	−	0.0231257i
$163$	−6.09903	+	10.5638i	−0.477713	+	0.827423i	−0.999674	−	0.0255466i	$-0.991867\pi$
$163$	−6.09903	+	10.5638i	−0.477713	+	0.827423i	0.521961	+	0.852969i	$0.325201\pi$
$164$	−7.96074			−0.621629
$165$	0.339877	−	0.588684i	0.0264594	−	0.0458290i
$166$	0.300616	+	0.520681i	0.0233323	+	0.0404127i
$167$	0.795270	+	1.37745i	0.0615398	+	0.106590i	0.895154	−	0.445757i	$-0.147066\pi$
$167$	0.795270	+	1.37745i	0.0615398	+	0.106590i	−0.833614	+	0.552347i	$0.813732\pi$
$168$	−0.871525			−0.0672396
$169$	−5.53146	−	11.7645i	−0.425497	−	0.904960i
$170$	−2.52498			−0.193657
$171$	−0.0577581	−	0.100040i	−0.00441688	−	0.00765025i
$172$	−0.513151	−	0.888804i	−0.0391274	−	0.0677707i
$173$	−6.37467	+	11.0412i	−0.484657	+	0.839451i	−0.999845	−	0.0176268i	$-0.994389\pi$
$173$	−6.37467	+	11.0412i	−0.484657	+	0.839451i	0.515188	+	0.857077i	$0.327722\pi$
$174$	1.88448			0.142862
$175$	−0.330062	+	0.571683i	−0.0249503	+	0.0432152i
$176$	−1.12847	+	1.95458i	−0.0850620	+	0.147332i
$177$	−2.22436			−0.167193
$178$	2.30175	−	3.98675i	0.172523	−	0.298819i
$179$	−8.88115	−	15.3826i	−0.663808	−	1.14975i	−0.979607	−	0.200923i	$-0.935606\pi$
$179$	−8.88115	−	15.3826i	−0.663808	−	1.14975i	0.315799	−	0.948826i	$-0.397728\pi$
$180$	0.942242	+	1.63201i	0.0702306	+	0.121643i
$181$	7.02630			0.522261			0.261130	−	0.965304i	$-0.415905\pi$
$181$	7.02630			0.522261			0.261130	+	0.965304i	$0.415905\pi$
$182$	−0.433560	+	0.682946i	−0.0321376	+	0.0506233i
$183$	4.20473			0.310823
$184$	5.12847	+	8.88278i	0.378076	+	0.654847i
$185$	−4.88448	−	8.46017i	−0.359114	−	0.622004i
$186$	1.69491	−	2.93568i	0.124277	−	0.215254i
$187$	5.04995			0.369289
$188$	−4.72971	+	8.19209i	−0.344949	+	0.597470i
$189$	0.330062	−	0.571683i	0.0240084	−	0.0415838i
$190$	−0.0392613			−0.00284832
$191$	6.97703	−	12.0846i	0.504840	−	0.874409i	−0.495144	−	0.868811i	$-0.664885\pi$
$191$	6.97703	−	12.0846i	0.504840	−	0.874409i	0.999984	−	0.00559828i	$-0.00178200\pi$
$192$	−2.67975	−	4.64147i	−0.193395	−	0.334969i
$193$	−11.8747	−	20.5675i	−0.854757	−	1.48048i	−0.876870	−	0.480728i	$-0.840373\pi$
$193$	−11.8747	−	20.5675i	−0.854757	−	1.48048i	0.0221126	−	0.999755i	$-0.492961\pi$
$194$	−3.36618			−0.241678
$195$	3.60236	+	0.151548i	0.257971	+	0.0108525i
$196$	12.3702			0.883586
$197$	−7.90411	−	13.6903i	−0.563145	−	0.975395i	−0.997220	−	0.0745186i	$-0.976258\pi$
$197$	−7.90411	−	13.6903i	−0.563145	−	0.975395i	0.434075	−	0.900877i	$-0.357075\pi$
$198$	0.115516	+	0.200080i	0.00820939	+	0.0142191i
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	−0.978537	−	0.206069i	$-0.933933\pi$
$199$	−4.38448	+	7.59415i	−0.310808	+	0.538335i	0.667730	+	0.744404i	$0.267266\pi$
$200$	1.32025			0.0933555
$201$	−3.81691	+	6.61108i	−0.269224	+	0.466310i
$202$	−1.59054	+	2.75490i	−0.111910	+	0.193834i
$203$	3.66012			0.256890
$204$	−7.00000	+	12.1244i	−0.490098	+	0.848875i
$205$	−2.11218	−	3.65840i	−0.147521	−	0.255514i
$206$	0.765631	+	1.32611i	0.0533441	+	0.0923946i
$207$	−7.76897			−0.539981
$208$	−11.9607	−	0.503175i	−0.829328	−	0.0348889i
$209$	0.0785226			0.00543152
$210$	−0.112180	−	0.194302i	−0.00774118	−	0.0134081i
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	0.673665	−	0.739037i	$-0.264719\pi$
$211$	−4.40411	−	7.62815i	−0.303192	−	0.525143i	−0.976857	+	0.213893i	$0.931386\pi$
$212$	0.640492	−	1.10937i	0.0439892	−	0.0761915i
$213$	−7.31357			−0.501118
$214$	0.0970195	−	0.168043i	0.00663211	−	0.0114872i
$215$	0.272303	−	0.471643i	0.0185709	−	0.0321658i
$216$	−1.32025			−0.0898314
$217$	3.29193	−	5.70180i	0.223471	−	0.387063i
$218$	2.61866	+	4.53565i	0.177358	+	0.307193i
$219$	4.00982	+	6.94520i	0.270958	+	0.469313i
$220$	−1.28098			−0.0863640
$221$	12.4061	+	23.7398i	0.834526	+	1.59691i
$222$	3.32025			0.222840
$223$	−5.01963	−	8.69426i	−0.336139	−	0.582210i	0.647564	−	0.762011i	$-0.275788\pi$
$223$	−5.01963	−	8.69426i	−0.336139	−	0.582210i	−0.983703	+	0.179801i	$0.942455\pi$
$224$	1.24399	+	2.15466i	0.0831177	+	0.143964i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	1.80823			0.120282
$227$	−0.605701	+	1.04910i	−0.0402018	+	0.0696315i	−0.885426	−	0.464780i	$-0.846133\pi$
$227$	−0.605701	+	1.04910i	−0.0402018	+	0.0696315i	0.845224	+	0.534412i	$0.179467\pi$
$228$	−0.108844	+	0.188524i	−0.00720839	+	0.0124853i
$229$	19.2440			1.27168			0.635839	−	0.771821i	$-0.280654\pi$
$229$	19.2440			1.27168			0.635839	+	0.771821i	$0.280654\pi$
$230$	−1.32025	+	2.28673i	−0.0870545	+	0.150783i
$231$	0.224361	+	0.388604i	0.0147618	+	0.0255683i
$232$	−3.66012	−	6.33952i	−0.240299	−	0.416210i
$233$	−23.9081			−1.56627			−0.783137	−	0.621849i	$-0.786382\pi$
$233$	−23.9081			−1.56627			−0.783137	+	0.621849i	$0.786382\pi$
$234$	−0.656787	+	1.03457i	−0.0429355	+	0.0676322i
$235$	−5.01963			−0.327445
$236$	2.09589	+	3.63018i	0.136431	+	0.236305i
$237$	4.98685	+	8.63748i	0.323931	+	0.561064i
$238$	0.833398	−	1.44349i	0.0540211	−	0.0935674i
$239$	18.6798			1.20829			0.604146	−	0.796873i	$-0.293514\pi$
$239$	18.6798			1.20829			0.604146	+	0.796873i	$0.293514\pi$
$240$	1.66012	−	2.87542i	0.107160	−	0.185607i
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	−0.947544	−	0.319626i	$-0.896443\pi$
$241$	−3.05776	+	5.29619i	−0.196968	+	0.341158i	0.750576	+	0.660784i	$0.229776\pi$
$242$	3.58160			0.230234
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−3.96187	−	6.86216i	−0.253633	−	0.439305i
$245$	3.28212	+	5.68480i	0.209687	+	0.363188i
$246$	1.43576			0.0915409
$247$	0.192905	+	0.369134i	0.0122743	+	0.0234874i
$248$	−13.1677			−0.836152
$249$	0.884484	+	1.53197i	0.0560519	+	0.0970847i
$250$	0.169938	+	0.294342i	0.0107479	+	0.0186158i
$251$	−1.67975	+	2.90942i	−0.106025	+	0.183641i	−0.914157	−	0.405361i	$-0.867146\pi$
$251$	−1.67975	+	2.90942i	−0.106025	+	0.183641i	0.808131	+	0.589002i	$0.200479\pi$
$252$	−1.24399			−0.0783641
$253$	2.64049	−	4.57347i	0.166006	−	0.287531i
$254$	−2.04260	+	3.53788i	−0.128164	+	0.221986i
$255$	−7.42909			−0.465228
$256$	−3.76897	+	6.52804i	−0.235560	+	0.408003i
$257$	5.05442	+	8.75452i	0.315286	+	0.546092i	0.979498	−	0.201452i	$-0.0645662\pi$
$257$	5.05442	+	8.75452i	0.315286	+	0.546092i	−0.664212	+	0.747544i	$0.731233\pi$
$258$	0.0925496	+	0.160301i	0.00576189	+	0.00997988i
$259$	6.44872			0.400704
$260$	−3.14697	−	6.02189i	−0.195167	−	0.373462i
$261$	5.54461			0.343203
$262$	1.85303	+	3.20954i	0.114480	+	0.198286i
$263$	11.2592	+	19.5014i	0.694269	+	1.20251i	0.970426	+	0.241397i	$0.0776056\pi$
$263$	11.2592	+	19.5014i	0.694269	+	1.20251i	−0.276157	+	0.961112i	$0.589061\pi$
$264$	0.448721	−	0.777208i	0.0276169	−	0.0478338i
$265$	0.679754			0.0417569
$266$	0.0129587	−	0.0224450i	0.000794546	−	0.00137619i
$267$	6.77230	−	11.7300i	0.414458	−	0.717863i
$268$	14.3858			0.878753
$269$	−4.24733	+	7.35659i	−0.258964	+	0.448539i	−0.965965	−	0.258674i	$-0.916714\pi$
$269$	−4.24733	+	7.35659i	−0.258964	+	0.448539i	0.707001	+	0.707213i	$0.250048\pi$
$270$	−0.169938	−	0.294342i	−0.0103421	−	0.0179131i
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	0.687912	−	0.725794i	$-0.258527\pi$
$271$	−4.68510	−	8.11483i	−0.284600	−	0.492941i	−0.972512	+	0.232853i	$0.925194\pi$
$272$	24.6664			1.49562
$273$	−1.27564	+	2.00939i	−0.0772052	+	0.121614i
$274$	−1.15212			−0.0696024
$275$	−0.339877	−	0.588684i	−0.0204953	−	0.0354990i
$276$	7.32025	+	12.6790i	0.440627	+	0.763188i
$277$	−0.359508	+	0.622685i	−0.0216007	+	0.0374135i	−0.876624	−	0.481177i	$-0.840210\pi$
$277$	−0.359508	+	0.622685i	−0.0216007	+	0.0374135i	0.855023	+	0.518590i	$0.173543\pi$
$278$	−5.03297			−0.301858
$279$	4.98685	−	8.63748i	0.298555	−	0.517112i
$280$	−0.435763	+	0.754763i	−0.0260418	+	0.0451057i
$281$	1.54461			0.0921435			0.0460718	−	0.998938i	$-0.485330\pi$
$281$	1.54461			0.0921435			0.0460718	+	0.998938i	$0.485330\pi$
$282$	0.853028	−	1.47749i	0.0507971	−	0.0879831i
$283$	9.05977	+	15.6920i	0.538547	+	0.932791i	0.998983	+	0.0450980i	$0.0143600\pi$
$283$	9.05977	+	15.6920i	0.538547	+	0.932791i	−0.460435	+	0.887693i	$0.652307\pi$
$284$	6.89116	+	11.9358i	0.408915	+	0.708261i
$285$	−0.115516			−0.00684259
$286$	−0.385810	−	0.738268i	−0.0228134	−	0.0436547i
$287$	2.78860			0.164606
$288$	1.88448	+	3.26402i	0.111044	+	0.192334i
$289$	−19.0957	−	33.0747i	−1.12328	−	1.94557i
$290$	0.942242	−	1.63201i	0.0553303	−	0.0958350i
$291$	−9.90411			−0.580589
$292$	7.55643	−	13.0881i	0.442207	−	0.765924i
$293$	15.2525	−	26.4181i	0.891059	−	1.54336i	0.0524523	−	0.998623i	$-0.483296\pi$
$293$	15.2525	−	26.4181i	0.891059	−	1.54336i	0.838607	−	0.544737i	$-0.183370\pi$
$294$	−2.23103			−0.130116
$295$	−1.11218	+	1.92635i	−0.0647536	+	0.112157i
$296$	−6.44872	−	11.1695i	−0.374824	−	0.649215i
$297$	0.339877	+	0.588684i	0.0197217	+	0.0341589i
$298$	5.80823			0.336462
$299$	27.9867	+	1.17737i	1.61851	+	0.0680890i
$300$	1.88448			0.108801
$301$	0.179754	+	0.311343i	0.0103608	+	0.0179455i
$302$	2.21140	+	3.83026i	0.127252	+	0.220407i
$303$	−4.67975	+	8.10557i	−0.268845	+	0.465653i
$304$	0.383543			0.0219977
$305$	2.10236	−	3.64140i	0.120381	−	0.208506i
$306$	1.26249	−	2.18669i	0.0721716	−	0.125005i
$307$	−4.77564			−0.272560			−0.136280	−	0.990670i	$-0.543515\pi$
$307$	−4.77564			−0.272560			−0.136280	+	0.990670i	$0.543515\pi$
$308$	0.422804	−	0.732318i	0.0240915	−	0.0417277i
$309$	2.25267	+	3.90174i	0.128150	+	0.221962i
$310$	−1.69491	−	2.93568i	−0.0962647	−	0.166735i
$311$	30.5812			1.73410			0.867051	−	0.498220i	$-0.166013\pi$
$311$	30.5812			1.73410			0.867051	+	0.498220i	$0.166013\pi$
$312$	4.75601	+	0.200080i	0.269256	+	0.0113273i
$313$	−26.7230			−1.51048			−0.755238	−	0.655451i	$-0.772479\pi$
$313$	−26.7230			−1.51048			−0.755238	+	0.655451i	$0.772479\pi$
$314$	−0.131811	−	0.228303i	−0.00743852	−	0.0128839i
$315$	−0.330062	−	0.571683i	−0.0185969	−	0.0322107i
$316$	9.39764	−	16.2772i	0.528658	−	0.915663i
$317$	−20.6271			−1.15854			−0.579268	−	0.815137i	$-0.696662\pi$
$317$	−20.6271			−1.15854			−0.579268	+	0.815137i	$0.696662\pi$
$318$	−0.115516	+	0.200080i	−0.00647783	+	0.0112199i
$319$	−1.88448	+	3.26402i	−0.105511	+	0.182750i
$320$	−5.35951			−0.299606
$321$	0.285455	−	0.494422i	0.0159325	−	0.0275960i
$322$	−0.871525	−	1.50953i	−0.0485682	−	0.0841226i
$323$	−0.429091	−	0.743207i	−0.0238752	−	0.0413531i
$324$	−1.88448			−0.104694
$325$	1.93243	−	3.04397i	0.107192	−	0.168849i
$326$	−4.14584			−0.229617
$327$	7.70473	+	13.3450i	0.426073	+	0.737979i
$328$	−2.78860	−	4.82999i	−0.153975	−	0.266692i
$329$	1.65679	−	2.86964i	0.0913416	−	0.158208i
$330$	0.231033			0.0127179
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	−0.930335	−	0.366711i	$-0.880484\pi$
$331$	−2.68510	+	4.65073i	−0.147586	+	0.255627i	0.782749	+	0.622338i	$0.213817\pi$
$332$	1.66680	−	2.88697i	0.0914773	−	0.158443i
$333$	9.76897			0.535336
$334$	−0.270294	+	0.468163i	−0.0147898	+	0.0256167i
$335$	3.81691	+	6.61108i	0.208540	+	0.361202i
$336$	1.09589	+	1.89813i	0.0597855	+	0.103551i
$337$	28.7623			1.56678			0.783391	−	0.621529i	$-0.213488\pi$
$337$	28.7623			1.56678			0.783391	+	0.621529i	$0.213488\pi$
$338$	2.52277	−	3.62738i	0.137221	−	0.197303i
$339$	5.32025			0.288956
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	3.38983	+	5.87136i	0.183570	+	0.317952i
$342$	0.0196307	−	0.0340013i	0.00106150	−	0.00183858i
$343$	−8.95407			−0.483474
$344$	0.359508	−	0.622685i	0.0193833	−	0.0335729i
$345$	−3.88448	+	6.72812i	−0.209134	+	0.362230i
$346$	−4.33320			−0.232955
$347$	−11.1981	+	19.3956i	−0.601143	+	1.04121i	0.391505	+	0.920176i	$0.371955\pi$
$347$	−11.1981	+	19.3956i	−0.601143	+	1.04121i	−0.992648	+	0.121035i	$0.961379\pi$
$348$	−5.22436	−	9.04886i	−0.280055	−	0.485070i
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	0.980585	−	0.196096i	$-0.0628263\pi$
$349$	5.98685	+	10.3695i	0.320469	+	0.555068i	−0.660116	+	0.751164i	$0.729493\pi$
$350$	−0.224361			−0.0119926
$351$	−1.93243	+	3.04397i	−0.103145	+	0.162475i
$352$	−2.56197			−0.136553
$353$	8.51830	+	14.7541i	0.453384	+	0.785283i	0.998594	−	0.0530161i	$-0.0168834\pi$
$353$	8.51830	+	14.7541i	0.453384	+	0.785283i	−0.545210	+	0.838299i	$0.683550\pi$
$354$	−0.378004	−	0.654723i	−0.0200907	−	0.0347981i
$355$	−3.65679	+	6.33374i	−0.194082	+	0.336160i
$356$	−25.5246			−1.35280
$357$	2.45206	−	4.24709i	0.129777	−	0.224780i
$358$	3.01850	−	5.22819i	0.159533	−	0.276318i
$359$	−35.0825			−1.85159			−0.925793	−	0.378031i	$-0.876601\pi$
$359$	−35.0825			−1.85159			−0.925793	+	0.378031i	$0.876601\pi$
$360$	−0.660123	+	1.14337i	−0.0347915	+	0.0602607i
$361$	9.49333	+	16.4429i	0.499649	+	0.865417i
$362$	1.19404	+	2.06814i	0.0627573	+	0.108699i
$363$	10.5379			0.553098
$364$	4.48131	+	0.188524i	0.234884	+	0.00988133i
$365$	8.01963			0.419767
$366$	0.714545	+	1.23763i	0.0373499	+	0.0646919i
$367$	−10.0413	−	17.3920i	−0.524150	−	0.907855i	−0.999605	−	0.0281143i	$-0.991050\pi$
$367$	−10.0413	−	17.3920i	−0.524150	−	0.907855i	0.475455	−	0.879740i	$-0.342284\pi$
$368$	12.8974	−	22.3390i	0.672326	−	1.16450i
$369$	4.22436			0.219911
$370$	1.66012	−	2.87542i	0.0863057	−	0.149486i
$371$	−0.224361	+	0.388604i	−0.0116482	+	0.0201753i
$372$	−18.7953			−0.974489
$373$	11.7395	−	20.3334i	0.607849	−	1.05283i	−0.383745	−	0.923439i	$-0.625366\pi$
$373$	11.7395	−	20.3334i	0.607849	−	1.05283i	0.991594	−	0.129387i	$-0.0413009\pi$
$374$	0.858181	+	1.48641i	0.0443755	+	0.0768606i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−6.62715			−0.341769
$377$	−19.9737	−	0.840272i	−1.02870	−	0.0432762i
$378$	0.224361			0.0115399
$379$	−10.5707	−	18.3090i	−0.542981	−	0.940471i	−0.998731	−	0.0503631i	$-0.983962\pi$
$379$	−10.5707	−	18.3090i	−0.542981	−	0.940471i	0.455750	−	0.890108i	$-0.349371\pi$
$380$	0.108844	+	0.188524i	0.00558359	+	0.00967107i
$381$	−6.00982	+	10.4093i	−0.307892	+	0.533285i
$382$	4.74266			0.242656
$383$	−0.869323	+	1.50571i	−0.0444203	+	0.0769383i	−0.887381	−	0.461037i	$-0.847477\pi$
$383$	−0.869323	+	1.50571i	−0.0444203	+	0.0769383i	0.842960	+	0.537976i	$0.180811\pi$
$384$	4.67975	−	8.10557i	0.238813	−	0.413636i
$385$	0.448721			0.0228689
$386$	4.03593	−	6.99043i	0.205423	−	0.355803i
$387$	0.272303	+	0.471643i	0.0138420	+	0.0239750i
$388$	9.33207	+	16.1636i	0.473764	+	0.820584i
$389$	−26.6664			−1.35204			−0.676020	−	0.736883i	$-0.736297\pi$
$389$	−26.6664			−1.35204			−0.676020	+	0.736883i	$0.736297\pi$
$390$	0.567573	+	1.08608i	0.0287402	+	0.0549959i
$391$	−57.7164			−2.91884
$392$	4.33320	+	7.50533i	0.218860	+	0.379076i
$393$	5.45206	+	9.44324i	0.275020	+	0.476348i
$394$	2.68643	−	4.65303i	0.135340	−	0.234416i
$395$	9.97370			0.501831
$396$	0.640492	−	1.10937i	0.0321860	−	0.0557477i
$397$	−7.27230	+	12.5960i	−0.364986	+	0.632175i	−0.988774	−	0.149419i	$-0.952260\pi$
$397$	−7.27230	+	12.5960i	−0.364986	+	0.632175i	0.623788	+	0.781594i	$0.285593\pi$
$398$	−2.98037			−0.149392
$399$	0.0381275	−	0.0660387i	0.00190876	−	0.00330607i
$400$	−1.66012	−	2.87542i	−0.0830062	−	0.143771i
$401$	4.18510	+	7.24880i	0.208994	+	0.361988i	0.951398	−	0.307964i	$-0.0996478\pi$
$401$	4.18510	+	7.24880i	0.208994	+	0.361988i	−0.742404	+	0.669952i	$0.766314\pi$
$402$	−2.59456			−0.129405
$403$	−19.2734	+	30.3596i	−0.960078	+	1.51232i
$404$	17.6378			0.877515
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	0.621996	+	1.07733i	0.0308691	+	0.0534669i
$407$	−3.32025	+	5.75084i	−0.164578	+	0.285058i
$408$	−9.80823			−0.485580
$409$	−8.62734	+	14.9430i	−0.426595	+	0.738883i	−0.996568	−	0.0827798i	$-0.973620\pi$
$409$	−8.62734	+	14.9430i	−0.426595	+	0.738883i	0.569973	+	0.821663i	$0.306954\pi$
$410$	0.717881	−	1.24341i	0.0354536	−	0.0614075i
$411$	−3.38983			−0.167208
$412$	4.24513	−	7.35277i	0.209142	−	0.362245i
$413$	−0.734176	−	1.27163i	−0.0361264	−	0.0625728i
$414$	−1.32025	−	2.28673i	−0.0648866	−	0.112387i
$415$	1.76897			0.0868352
$416$	−6.29394	−	12.0438i	−0.308586	−	0.590495i
$417$	−14.8082			−0.725162
$418$	0.0133440	+	0.0231125i	0.000652677	+	0.00113047i
$419$	−6.43243	−	11.1413i	−0.314245	−	0.544288i	0.665032	−	0.746815i	$-0.268418\pi$
$419$	−6.43243	−	11.1413i	−0.314245	−	0.544288i	−0.979277	+	0.202527i	$0.935085\pi$
$420$	−0.621996	+	1.07733i	−0.0303503	+	0.0525682i
$421$	24.5616			1.19706			0.598529	−	0.801101i	$-0.295752\pi$
$421$	24.5616			1.19706			0.598529	+	0.801101i	$0.295752\pi$
$422$	1.49686	−	2.59263i	0.0728658	−	0.126207i
$423$	2.50982	−	4.34713i	0.122031	−	0.211365i
$424$	0.897442			0.0435837
$425$	−3.71455	+	6.43378i	−0.180182	+	0.312084i
$426$	−1.24286	−	2.15269i	−0.0602166	−	0.104298i
$427$	1.38782	+	2.40377i	0.0671613	+	0.116327i
$428$	−1.07587			−0.0520041
$429$	−1.13515	−	2.17216i	−0.0548054	−	0.104873i
$430$	0.185099			0.00892628
$431$	−12.3898	−	21.4598i	−0.596797	−	1.03368i	−0.993291	−	0.115645i	$-0.963106\pi$
$431$	−12.3898	−	21.4598i	−0.596797	−	1.03368i	0.396493	−	0.918038i	$-0.370227\pi$
$432$	1.66012	+	2.87542i	0.0798727	+	0.138344i
$433$	7.02945	−	12.1754i	0.337814	−	0.585110i	−0.646208	−	0.763162i	$-0.723646\pi$
$433$	7.02945	−	12.1754i	0.337814	−	0.585110i	0.984021	+	0.178051i	$0.0569793\pi$
$434$	2.23770			0.107413
$435$	2.77230	−	4.80177i	0.132922	−	0.230227i
$436$	14.5194	−	25.1484i	0.695355	−	1.20439i
$437$	−0.897442			−0.0429305
$438$	−1.36284	+	2.36051i	−0.0651192	+	0.112790i
$439$	−10.4226	−	18.0525i	−0.497444	−	0.861598i	0.502552	−	0.864547i	$-0.332395\pi$
$439$	−10.4226	−	18.0525i	−0.497444	−	0.861598i	−0.999996	+	0.00294880i	$0.999061\pi$
$440$	−0.448721	−	0.777208i	−0.0213919	−	0.0370519i
$441$	−6.56424			−0.312583
$442$	−4.87933	+	7.68594i	−0.232086	+	0.365583i
$443$	−11.4291			−0.543012			−0.271506	−	0.962437i	$-0.587522\pi$
$443$	−11.4291			−0.543012			−0.271506	+	0.962437i	$0.587522\pi$
$444$	−9.20473	−	15.9431i	−0.436837	−	0.756624i
$445$	−6.77230	−	11.7300i	−0.321038	−	0.556054i
$446$	1.70606	−	2.95498i	0.0807841	−	0.139922i
$447$	17.0892			0.808292
$448$	1.76897	−	3.06394i	0.0835759	−	0.144758i
$449$	−12.9541	+	22.4371i	−0.611340	+	1.05887i	0.379675	+	0.925120i	$0.376036\pi$
$449$	−12.9541	+	22.4371i	−0.611340	+	1.05887i	−0.991015	+	0.133752i	$0.957297\pi$
$450$	−0.339877			−0.0160220
$451$	−1.43576	+	2.48681i	−0.0676074	+	0.117099i
$452$	−5.01296	−	8.68270i	−0.235790	−	0.408400i
$453$	6.50648	+	11.2696i	0.305701	+	0.529490i
$454$	−0.411728			−0.0193233
$455$	1.10236	+	2.10943i	0.0516797	+	0.0988917i
$456$	−0.152510			−0.00714193
$457$	−2.95206	−	5.11311i	−0.138091	−	0.239181i	0.788683	−	0.614800i	$-0.210763\pi$
$457$	−2.95206	−	5.11311i	−0.138091	−	0.239181i	−0.926774	+	0.375619i	$0.877430\pi$
$458$	3.27029	+	5.66432i	0.152811	+	0.264676i
$459$	3.71455	−	6.43378i	0.173380	−	0.300303i
$460$	14.6405			0.682616
$461$	7.74600	−	13.4165i	0.360767	−	0.624867i	−0.627320	−	0.778762i	$-0.715848\pi$
$461$	7.74600	−	13.4165i	0.360767	−	0.624867i	0.988087	+	0.153894i	$0.0491815\pi$
$462$	−0.0762550	+	0.132077i	−0.00354770	+	0.00614480i
$463$	17.4420			0.810601			0.405300	−	0.914184i	$-0.367167\pi$
$463$	17.4420			0.810601			0.405300	+	0.914184i	$0.367167\pi$
$464$	−9.20473	+	15.9431i	−0.427319	+	0.740138i
$465$	−4.98685	−	8.63748i	−0.231260	−	0.400553i
$466$	−4.06291	−	7.03717i	−0.188211	−	0.325991i
$467$	−20.4790			−0.947657			−0.473829	−	0.880617i	$-0.657128\pi$
$467$	−20.4790			−0.947657			−0.473829	+	0.880617i	$0.657128\pi$
$468$	6.78860	+	0.285589i	0.313803	+	0.0132014i
$469$	−5.03926			−0.232691
$470$	−0.853028	−	1.47749i	−0.0393473	−	0.0681514i
$471$	−0.387820	−	0.671723i	−0.0178698	−	0.0309514i
$472$	−1.46835	+	2.54326i	−0.0675864	+	0.117063i
$473$	−0.370199			−0.0170217
$474$	−1.69491	+	2.93568i	−0.0778500	+	0.134840i
$475$	−0.0577581	+	0.100040i	−0.00265013	+	0.00459015i
$476$	−9.24172			−0.423594
$477$	−0.339877	+	0.588684i	−0.0155619	+	0.0269540i
$478$	3.17441	+	5.49824i	0.145194	+	0.251483i
$479$	20.4953	+	35.4990i	0.936456	+	1.62199i	0.772017	+	0.635602i	$0.219248\pi$
$479$	20.4953	+	35.4990i	0.936456	+	1.62199i	0.164439	+	0.986387i	$0.447419\pi$
$480$	3.76897			0.172029
$481$	−35.1914	−	1.48046i	−1.60459	−	0.0675033i
$482$	−2.07852			−0.0946741
$483$	−2.56424	−	4.44139i	−0.116677	−	0.202090i
$484$	−9.92928	−	17.1980i	−0.451331	−	0.781728i
$485$	−4.95206	+	8.57721i	−0.224861	+	0.389471i
$486$	0.339877			0.0154171
$487$	−12.0315	+	20.8391i	−0.545197	+	0.944309i	0.453397	+	0.891309i	$0.350212\pi$
$487$	−12.0315	+	20.8391i	−0.545197	+	0.944309i	−0.998594	+	0.0530008i	$0.983121\pi$
$488$	2.77564	−	4.80755i	0.125647	−	0.217627i
$489$	−12.1981			−0.551615
$490$	−1.11552	+	1.93213i	−0.0503939	+	0.0872848i
$491$	−18.3865	−	31.8463i	−0.829771	−	1.43721i	−0.898218	−	0.439550i	$-0.855138\pi$
$491$	−18.3865	−	31.8463i	−0.829771	−	1.43721i	0.0684471	−	0.997655i	$-0.478196\pi$
$492$	−3.98037	−	6.89420i	−0.179449	−	0.310815i
$493$	41.1914			1.85517
$494$	−0.0758696	+	0.119510i	−0.00341354	+	0.00537701i
$495$	0.679754			0.0305527
$496$	16.5576	+	28.6785i	0.743457	+	1.28770i
$497$	−2.41393	−	4.18105i	−0.108280	−	0.187546i
$498$	−0.300616	+	0.520681i	−0.0134709	+	0.0233323i
$499$	34.8212			1.55881			0.779405	−	0.626520i	$-0.215521\pi$
$499$	34.8212			1.55881			0.779405	+	0.626520i	$0.215521\pi$
$500$	0.942242	−	1.63201i	0.0421383	−	0.0729857i
$501$	−0.795270	+	1.37745i	−0.0355300	+	0.0615398i
$502$	−1.14182			−0.0509619
$503$	16.0130	−	27.7353i	0.713983	−	1.23665i	−0.249368	−	0.968409i	$-0.580223\pi$
$503$	16.0130	−	27.7353i	0.713983	−	1.23665i	0.963351	−	0.268245i	$-0.0864438\pi$
$504$	−0.435763	−	0.754763i	−0.0194104	−	0.0336198i
$505$	4.67975	+	8.10557i	0.208246	+	0.360693i
$506$	1.79488			0.0797924
$507$	7.42261	−	10.6726i	0.329650	−	0.473988i
$508$	22.6508			1.00497
$509$	20.6731	+	35.8068i	0.916318	+	1.58711i	0.804960	+	0.593329i	$0.202187\pi$
$509$	20.6731	+	35.8068i	0.916318	+	1.58711i	0.111359	+	0.993780i	$0.464480\pi$
$510$	−1.26249	−	2.18669i	−0.0559039	−	0.0968284i
$511$	−2.64697	+	4.58469i	−0.117095	+	0.202815i
$512$	−21.2810			−0.940496
$513$	0.0577581	−	0.100040i	0.00255008	−	0.00441688i
$514$	−1.71788	+	2.97546i	−0.0757725	+	0.131242i
$515$	4.50535			0.198529
$516$	0.513151	−	0.888804i	0.0225902	−	0.0391274i
$517$	1.70606	+	2.95498i	0.0750323	+	0.129960i
$518$	1.09589	+	1.89813i	0.0481505	+	0.0833990i
$519$	−12.7493			−0.559634
$520$	2.55128	−	4.01878i	0.111881	−	0.176235i
$521$	4.40279			0.192890			0.0964448	−	0.995338i	$-0.469253\pi$
$521$	4.40279			0.192890			0.0964448	+	0.995338i	$0.469253\pi$
$522$	0.942242	+	1.63201i	0.0412408	+	0.0714312i
$523$	16.2244	+	28.1014i	0.709442	+	1.22879i	0.965064	+	0.262013i	$0.0843862\pi$
$523$	16.2244	+	28.1014i	0.709442	+	1.22879i	−0.255623	+	0.966777i	$0.582280\pi$
$524$	10.2743	−	17.7956i	0.448835	−	0.777406i
$525$	−0.660123			−0.0288101
$526$	−3.82673	+	6.62808i	−0.166853	+	0.288998i
$527$	37.0478	−	64.1686i	1.61383	−	2.79523i
$528$	−2.25695			−0.0982211
$529$	−18.6784	+	32.3520i	−0.812106	+	1.40661i
$530$	0.115516	+	0.200080i	0.00501771	+	0.00869092i
$531$	−1.11218	−	1.92635i	−0.0482645	−	0.0835966i
$532$	−0.143701			−0.00623024
$533$	−15.2177	−	0.640192i	−0.659151	−	0.0277298i
$534$	4.60350			0.199213
$535$	−0.285455	−	0.494422i	−0.0123413	−	0.0213757i
$536$	5.03926	+	8.72826i	0.217663	+	0.377003i
$537$	8.88115	−	15.3826i	0.383250	−	0.663808i
$538$	−2.88714			−0.124473
$539$	2.23103	−	3.86426i	0.0960974	−	0.166446i
$540$	−0.942242	+	1.63201i	−0.0405476	+	0.0702306i
$541$	−8.57720			−0.368762			−0.184381	−	0.982855i	$-0.559028\pi$
$541$	−8.57720			−0.368762			−0.184381	+	0.982855i	$0.559028\pi$
$542$	1.59236	−	2.75804i	0.0683976	−	0.118468i
$543$	3.51315	+	6.08496i	0.150764	+	0.261130i
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	15.4095			0.660069
$546$	−0.808229	−	0.0340013i	−0.0345890	−	0.00145512i
$547$	−32.4920			−1.38926			−0.694629	−	0.719368i	$-0.744431\pi$
$547$	−32.4920			−1.38926			−0.694629	+	0.719368i	$0.744431\pi$
$548$	3.19404	+	5.53224i	0.136443	+	0.236325i
$549$	2.10236	+	3.64140i	0.0897268	+	0.155411i
$550$	0.115516	−	0.200080i	0.00492563	−	0.00853144i
$551$	0.640492			0.0272859
$552$	−5.12847	+	8.88278i	−0.218282	+	0.378076i
$553$	−3.29193	+	5.70180i	−0.139987	+	0.242465i
$554$	−0.244377			−0.0103826
$555$	4.88448	−	8.46017i	0.207335	−	0.359114i
$556$	13.9529	+	24.1672i	0.591736	+	1.02492i
$557$	20.6075	+	35.6933i	0.873169	+	1.51237i	0.858701	+	0.512477i	$0.171272\pi$
$557$	20.6075	+	35.6933i	0.873169	+	1.51237i	0.0144676	+	0.999895i	$0.495395\pi$
$558$	3.38983			0.143503
$559$	−0.909460	−	1.74030i	−0.0384661	−	0.0736068i
$560$	2.19177			0.0926192
$561$	2.52498	+	4.37339i	0.106605	+	0.184645i
$562$	0.262488	+	0.454643i	0.0110724	+	0.0191779i
$563$	6.08921	−	10.5468i	0.256630	−	0.444496i	−0.708707	−	0.705503i	$-0.750721\pi$
$563$	6.08921	−	10.5468i	0.256630	−	0.444496i	0.965337	+	0.261007i	$0.0840546\pi$
$564$	−9.45941			−0.398313
$565$	2.66012	−	4.60747i	0.111912	−	0.193838i
$566$	−3.07921	+	5.33334i	−0.129429	+	0.224177i
$567$	0.660123			0.0277226
$568$	−4.82786	+	8.36210i	−0.202572	+	0.350866i
$569$	−3.47169	−	6.01314i	−0.145541	−	0.252084i	0.784034	−	0.620718i	$-0.213159\pi$
$569$	−3.47169	−	6.01314i	−0.145541	−	0.252084i	−0.929575	+	0.368634i	$0.879826\pi$
$570$	−0.0196307	−	0.0340013i	−0.000822238	−	0.00142416i
$571$	3.51429			0.147068			0.0735341	−	0.997293i	$-0.476572\pi$
$571$	3.51429			0.147068			0.0735341	+	0.997293i	$0.476572\pi$
$572$	−2.47541	+	3.89927i	−0.103502	+	0.163037i
$573$	13.9541			0.582939
$574$	0.473890	+	0.820802i	0.0197798	+	0.0342596i
$575$	3.88448	+	6.72812i	0.161994	+	0.280582i
$576$	2.67975	−	4.64147i	0.111656	−	0.193395i
$577$	3.14182			0.130796			0.0653978	−	0.997859i	$-0.479168\pi$
$577$	3.14182			0.130796			0.0653978	+	0.997859i	$0.479168\pi$
$578$	6.49018	−	11.2413i	0.269956	−	0.467578i
$579$	11.8747	−	20.5675i	0.493494	−	0.854757i
$580$	−10.4487			−0.433860
$581$	−0.583868	+	1.01129i	−0.0242229	+	0.0419553i
$582$	−1.68309	−	2.91520i	−0.0697663	−	0.120839i
$583$	−0.231033	−	0.400160i	−0.00956839	−	0.0165729i
$584$	10.5879			0.438130
$585$	1.66994	+	3.19551i	0.0690435	+	0.132118i
$586$	10.3679			0.428295
$587$	−18.9889	−	32.8897i	−0.783754	−	1.35750i	−0.929741	−	0.368215i	$-0.879969\pi$
$587$	−18.9889	−	32.8897i	−0.783754	−	1.35750i	0.145987	−	0.989287i	$-0.453364\pi$
$588$	6.18510	+	10.7129i	0.255069	+	0.441793i
$589$	0.576062	−	0.997769i	0.0237362	−	0.0411124i
$590$	−0.756009			−0.0311244
$591$	7.90411	−	13.6903i	0.325132	−	0.563145i
$592$	−16.2177	+	28.0899i	−0.666543	+	1.15449i
$593$	10.4487			0.429078			0.214539	−	0.976715i	$-0.431175\pi$
$593$	10.4487			0.429078			0.214539	+	0.976715i	$0.431175\pi$
$594$	−0.115516	+	0.200080i	−0.00473969	+	0.00820939i
$595$	−2.45206	−	4.24709i	−0.100525	−	0.174114i
$596$	−16.1022	−	27.8898i	−0.659571	−	1.14241i
$597$	−8.76897			−0.358890
$598$	4.40946	+	8.43773i	0.180316	+	0.345044i
$599$	−45.5705			−1.86196			−0.930981	−	0.365069i	$-0.881045\pi$
$599$	−45.5705			−1.86196			−0.930981	+	0.365069i	$0.881045\pi$
$600$	0.660123	+	1.14337i	0.0269494	+	0.0466778i
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	0.976472	−	0.215643i	$-0.0691848\pi$
$601$	7.39096	+	12.8015i	0.301484	+	0.522185i	−0.674989	+	0.737828i	$0.735851\pi$
$602$	−0.0610942	+	0.105818i	−0.00249001	+	0.00431283i
$603$	−7.63382			−0.310873
$604$	12.2614	−	21.2373i	0.498907	−	0.864133i
$605$	5.26897	−	9.12612i	0.214214	−	0.371030i
$606$	−3.18108			−0.129223
$607$	9.46722	−	16.3977i	0.384263	−	0.665562i	−0.607404	−	0.794393i	$-0.707789\pi$
$607$	9.46722	−	16.3977i	0.384263	−	0.665562i	0.991667	+	0.128831i	$0.0411224\pi$
$608$	0.217689	+	0.377048i	0.00882844	+	0.0152913i
$609$	1.83006	+	3.16976i	0.0741578	+	0.128445i
$610$	1.42909			0.0578622
$611$	−9.70007	+	15.2796i	−0.392423	+	0.618146i
$612$	−14.0000			−0.565916
$613$	1.29193	+	2.23770i	0.0521807	+	0.0903797i	0.890936	−	0.454129i	$-0.150049\pi$
$613$	1.29193	+	2.23770i	0.0521807	+	0.0903797i	−0.838755	+	0.544509i	$0.816716\pi$
$614$	−0.811565	−	1.40567i	−0.0327521	−	0.0567283i
$615$	2.11218	−	3.65840i	0.0851713	−	0.147521i
$616$	0.592422			0.0238694
$617$	−7.01963	+	12.1584i	−0.282600	+	0.489477i	−0.972024	−	0.234880i	$-0.924530\pi$
$617$	−7.01963	+	12.1584i	−0.282600	+	0.489477i	0.689425	+	0.724357i	$0.257863\pi$
$618$	−0.765631	+	1.32611i	−0.0307982	+	0.0533441i
$619$	−17.8582			−0.717781			−0.358890	−	0.933380i	$-0.616845\pi$
$619$	−17.8582			−0.717781			−0.358890	+	0.933380i	$0.616845\pi$
$620$	−9.39764	+	16.2772i	−0.377418	+	0.653707i
$621$	−3.88448	−	6.72812i	−0.155879	−	0.269990i
$622$	5.19692	+	9.00134i	0.208378	+	0.360921i
$623$	8.94111			0.358218
$624$	−5.54461	−	10.6099i	−0.221962	−	0.424736i
$625$	1.00000			0.0400000
$626$	−4.54127	−	7.86571i	−0.181506	−	0.314377i
$627$	0.0392613	+	0.0680026i	0.00156795	+	0.00271576i
$628$	−0.730840	+	1.26585i	−0.0291637	+	0.0505130i
$629$	72.5745			2.89374
$630$	0.112180	−	0.194302i	0.00446937	−	0.00774118i
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	−0.503113	−	0.864221i	$-0.667812\pi$
$631$	12.4815	−	21.6186i	0.496881	−	0.860623i	0.999994	+	0.00359801i	$0.00114528\pi$
$632$	13.1677			0.523784
$633$	4.40411	−	7.62815i	0.175048	−	0.303192i
$634$	−3.50535	−	6.07144i	−0.139215	−	0.241128i
$635$	6.00982	+	10.4093i	0.238492	+	0.413081i
$636$	1.28098			0.0507944
$637$	23.6468	+	0.994794i	0.936920	+	0.0394152i
$638$	−1.28098			−0.0507147
$639$	−3.65679	−	6.33374i	−0.144660	−	0.250559i
$640$	−4.67975	−	8.10557i	−0.184984	−	0.320401i
$641$	−11.6535	+	20.1844i	−0.460284	+	0.797235i	−0.998975	−	0.0452686i	$-0.985586\pi$
$641$	−11.6535	+	20.1844i	−0.460284	+	0.797235i	0.538691	+	0.842503i	$0.318919\pi$
$642$	0.194039			0.00765811
$643$	−22.7395	+	39.3860i	−0.896759	+	1.55323i	−0.0651470	+	0.997876i	$0.520752\pi$
$643$	−22.7395	+	39.3860i	−0.896759	+	1.55323i	−0.831612	+	0.555357i	$0.812582\pi$
$644$	−4.83226	+	8.36973i	−0.190418	+	0.329813i
$645$	0.544607			0.0214439
$646$	0.145838	−	0.252599i	0.00573792	−	0.00993836i
$647$	−3.20473	−	5.55076i	−0.125991	−	0.218223i	0.796129	−	0.605127i	$-0.206878\pi$
$647$	−3.20473	−	5.55076i	−0.125991	−	0.218223i	−0.922120	+	0.386904i	$0.873544\pi$
$648$	−0.660123	−	1.14337i	−0.0259321	−	0.0449157i
$649$	1.51202			0.0593519
$650$	1.22436	+	0.0515075i	0.0480234	+	0.00202029i
$651$	6.58387			0.258042
$652$	11.4935	+	19.9074i	0.450121	+	0.779632i
$653$	−0.740848	−	1.28319i	−0.0289916	−	0.0502150i	0.851166	−	0.524897i	$-0.175896\pi$
$653$	−0.740848	−	1.28319i	−0.0289916	−	0.0502150i	−0.880157	+	0.474682i	$0.842563\pi$
$654$	−2.61866	+	4.53565i	−0.102398	+	0.177358i
$655$	10.9041			0.426059
$656$	−7.01296	+	12.1468i	−0.273810	+	0.474253i
$657$	−4.00982	+	6.94520i	−0.156438	+	0.270958i
$658$	1.12621			0.0439041
$659$	3.54461	−	6.13944i	0.138078	−	0.239159i	−0.788691	−	0.614790i	$-0.789241\pi$
$659$	3.54461	−	6.13944i	0.138078	−	0.239159i	0.926769	+	0.375631i	$0.122574\pi$
$660$	−0.640492	−	1.10937i	−0.0249311	−	0.0431820i
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	0.854339	−	0.519716i	$-0.173962\pi$
$661$	−0.589214	−	1.02055i	−0.0229178	−	0.0396947i	−0.877257	+	0.480021i	$0.840629\pi$
$662$	−1.82521			−0.0709387
$663$	−14.3562	+	22.6139i	−0.557548	+	0.878251i
$664$	2.33547			0.0906339
$665$	−0.0381275	−	0.0660387i	−0.00147852	−	0.00256087i
$666$	1.66012	+	2.87542i	0.0643285	+	0.111420i
$667$	21.5379	−	37.3048i	0.833952	−	1.44445i
$668$	2.99735			0.115971
$669$	5.01963	−	8.69426i	0.194070	−	0.336139i
$670$	−1.29728	+	2.24695i	−0.0501183	+	0.0868074i
$671$	−2.85818			−0.110339
$672$	−1.24399	+	2.15466i	−0.0479880	+	0.0831177i
$673$	−6.77878	−	11.7412i	−0.261303	−	0.452590i	0.705286	−	0.708923i	$-0.250819\pi$
$673$	−6.77878	−	11.7412i	−0.261303	−	0.452590i	−0.966588	+	0.256334i	$0.917485\pi$
$674$	4.88782	+	8.46595i	0.188272	+	0.326096i
$675$	−1.00000			−0.0384900
$676$	−24.4117	−	2.05759i	−0.938913	−	0.0791381i
$677$	9.53793			0.366573			0.183286	−	0.983060i	$-0.441326\pi$
$677$	9.53793			0.366573			0.183286	+	0.983060i	$0.441326\pi$
$678$	0.904114	+	1.56597i	0.0347223	+	0.0601408i
$679$	−3.26897	−	5.66202i	−0.125451	−	0.217288i
$680$	−4.90411	+	8.49418i	−0.188064	+	0.325737i
$681$	−1.21140			−0.0464210
$682$	−1.15212	+	1.99554i	−0.0441171	+	0.0764131i
$683$	22.2592	−	38.5540i	0.851723	−	1.47523i	−0.0279296	−	0.999610i	$-0.508891\pi$
$683$	22.2592	−	38.5540i	0.851723	−	1.47523i	0.879652	−	0.475617i	$-0.157775\pi$
$684$	−0.217689			−0.00832353
$685$	−1.69491	+	2.93568i	−0.0647594	+	0.112166i
$686$	−1.52164	−	2.63556i	−0.0580965	−	0.100626i
$687$	9.62200	+	16.6658i	0.367102	+	0.635839i
$688$	−1.80823			−0.0689381
$689$	1.31357	−	2.06915i	0.0500432	−	0.0788282i
$690$	−2.64049			−0.100522
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	0.911867	−	0.410486i	$-0.134641\pi$
$691$	2.64030	+	4.57313i	0.100442	+	0.173970i	−0.811425	+	0.584457i	$0.801308\pi$
$692$	12.0130	+	20.8071i	0.456664	+	0.790966i
$693$	−0.224361	+	0.388604i	−0.00852275	+	0.0147618i
$694$	−7.61192			−0.288945
$695$	−7.40411	+	12.8243i	−0.280854	+	0.486454i
$696$	3.66012	−	6.33952i	0.138737	−	0.240299i
$697$	31.3832			1.18872
$698$	−2.03479	+	3.52436i	−0.0770180	+	0.133399i
$699$	−11.9541	−	20.7051i	−0.452144	−	0.783137i
$700$	0.621996	+	1.07733i	0.0235092	+	0.0407192i
$701$	20.1392			0.760646			0.380323	−	0.924854i	$-0.375813\pi$
$701$	20.1392			0.760646			0.380323	+	0.924854i	$0.375813\pi$
$702$	−1.22436	−	0.0515075i	−0.0462105	−	0.00194403i
$703$	1.12847			0.0425612
$704$	1.82157	+	3.15506i	0.0686531	+	0.118911i
$705$	−2.50982	−	4.34713i	−0.0945251	−	0.163722i
$706$	−2.89517	+	5.01459i	−0.108961	+	0.188727i
$707$	−6.17843			−0.232364
$708$	−2.09589	+	3.63018i	−0.0787682	+	0.136431i
$709$	−0.770294	+	1.33419i	−0.0289290	+	0.0501065i	−0.880127	−	0.474737i	$-0.842543\pi$
$709$	−0.770294	+	1.33419i	−0.0289290	+	0.0501065i	0.851198	+	0.524844i	$0.175876\pi$
$710$	−2.48571			−0.0932872
$711$	−4.98685	+	8.63748i	−0.187021	+	0.323931i
$712$	−8.94111	−	15.4865i	−0.335082	−	0.580379i
$713$	−38.7427	−	67.1043i	−1.45092	−	2.51307i
$714$	1.66680			0.0623782
$715$	−2.44872	−	0.103015i	−0.0915770	−	0.00385254i
$716$	−33.4728			−1.25094
$717$	9.33988	+	16.1771i	0.348804	+	0.604146i
$718$	−5.96187	−	10.3263i	−0.222495	−	0.385373i
$719$	−18.5020	+	32.0464i	−0.690009	+	1.19513i	0.281826	+	0.959466i	$0.409060\pi$
$719$	−18.5020	+	32.0464i	−0.690009	+	1.19513i	−0.971835	+	0.235664i	$0.924273\pi$
$720$	3.32025			0.123738
$721$	−1.48704	+	2.57563i	−0.0553803	+	0.0959215i
$722$	−3.22656	+	5.58857i	−0.120080	+	0.207985i
$723$	−6.11552			−0.227438
$724$	6.62048	−	11.4670i	0.246048	−	0.426168i
$725$	−2.77230	−	4.80177i	−0.102961	−	0.178333i
$726$	1.79080	+	3.10176i	0.0664628	+	0.115117i
$727$	−44.9015			−1.66530			−0.832652	−	0.553797i	$-0.813178\pi$
$727$	−44.9015			−1.66530			−0.832652	+	0.553797i	$0.813178\pi$
$728$	1.45539	+	2.78497i	0.0539405	+	0.103218i
$729$	1.00000			0.0370370
$730$	1.36284	+	2.36051i	0.0504411	+	0.0873666i
$731$	2.02297	+	3.50388i	0.0748221	+	0.129596i
$732$	3.96187	−	6.86216i	0.146435	−	0.253633i
$733$	−4.94072			−0.182490			−0.0912449	−	0.995828i	$-0.529085\pi$
$733$	−4.94072			−0.182490			−0.0912449	+	0.995828i	$0.529085\pi$
$734$	3.41280	−	5.91114i	0.125969	−	0.218184i
$735$	−3.28212	+	5.68480i	−0.121063	+	0.209687i
$736$	29.2810			1.07931
$737$	2.59456	−	4.49391i	0.0955718	−	0.165535i
$738$	0.717881	+	1.24341i	0.0264256	+	0.0457704i
$739$	−3.01963	−	5.23015i	−0.111079	−	0.192394i	0.805127	−	0.593103i	$-0.202097\pi$
$739$	−3.01963	−	5.23015i	−0.111079	−	0.192394i	−0.916206	+	0.400709i	$0.868764\pi$
$740$	−18.4095			−0.676745
$741$	−0.223227	+	0.351628i	−0.00820044	+	0.0129174i
$742$	−0.152510			−0.00559882
$743$	6.52945	+	11.3093i	0.239542	+	0.414899i	0.960583	−	0.277993i	$-0.0896693\pi$
$743$	6.52945	+	11.3093i	0.239542	+	0.414899i	−0.721041	+	0.692893i	$0.756336\pi$
$744$	−6.58387	−	11.4036i	−0.241376	−	0.418076i
$745$	8.54461	−	14.7997i	0.313050	−	0.542219i
$746$	7.97998			0.292168
$747$	−0.884484	+	1.53197i	−0.0323616	+	0.0560519i
$748$	4.75828	−	8.24158i	0.173980	−	0.301342i
$749$	0.376871			0.0137706
$750$	−0.169938	+	0.294342i	−0.00620527	+	0.0107479i
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.855475	−	0.517845i	$-0.826735\pi$
$751$	−24.0118	−	41.5897i	−0.876204	−	1.51763i	−0.0207292	−	0.999785i	$-0.506599\pi$
$752$	8.33320	+	14.4335i	0.303881	+	0.526337i
$753$	−3.35951			−0.122427
$754$	−3.14697	−	6.02189i	−0.114606	−	0.219304i
$755$	13.0130			0.473590
$756$	−0.621996	−	1.07733i	−0.0226218	−	0.0391820i
$757$	2.28212	+	3.95275i	0.0829450	+	0.143665i	0.904514	−	0.426445i	$-0.140234\pi$
$757$	2.28212	+	3.95275i	0.0829450	+	0.143665i	−0.821569	+	0.570110i	$0.806901\pi$
$758$	3.59274	−	6.22281i	0.130494	−	0.226023i
$759$	5.28098			0.191688
$760$	−0.0762550	+	0.132077i	−0.00276606	+	0.00479095i
$761$	−10.5446	+	18.2638i	−0.382242	+	0.662062i	−0.991382	−	0.131000i	$-0.958181\pi$
$761$	−10.5446	+	18.2638i	−0.382242	+	0.662062i	0.609141	+	0.793062i	$0.291514\pi$
$762$	−4.08519			−0.147991
$763$	−5.08607	+	8.80933i	−0.184128	+	0.318919i
$764$	−13.1481	−	22.7732i	−0.475682	−	0.823905i
$765$	−3.71455	−	6.43378i	−0.134300	−	0.232614i
$766$	−0.590926			−0.0213510
$767$	3.71455	+	7.10797i	0.134124	+	0.256654i
$768$	−7.53793			−0.272002
$769$	−21.1666	−	36.6616i	−0.763287	−	1.32205i	−0.941147	−	0.337996i	$-0.890251\pi$
$769$	−21.1666	−	36.6616i	−0.763287	−	1.32205i	0.177860	−	0.984056i	$-0.443083\pi$
$770$	0.0762550	+	0.132077i	0.00274804	+

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.169938 + 0.294342i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.942242 - 1.63201i) q^{4} +1.00000 q^{5} +(-0.169938 + 0.294342i) q^{6} +(-0.330062 + 0.571683i) q^{7} +1.32025 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.169938 + 0.294342i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.942242 - 1.63201i) q^{4} +1.00000 q^{5} +(-0.169938 + 0.294342i) q^{6} +(-0.330062 + 0.571683i) q^{7} +1.32025 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.169938 + 0.294342i) q^{10} +(-0.339877 - 0.588684i) q^{11} +1.88448 q^{12} +(1.93243 - 3.04397i) q^{13} -0.224361 q^{14} +(0.500000 + 0.866025i) q^{15} +(-1.66012 - 2.87542i) q^{16} +(-3.71455 + 6.43378i) q^{17} -0.339877 q^{18} +(-0.0577581 + 0.100040i) q^{19} +(0.942242 - 1.63201i) q^{20} -0.660123 q^{21} +(0.115516 - 0.200080i) q^{22} +(3.88448 + 6.72812i) q^{23} +(0.660123 + 1.14337i) q^{24} +1.00000 q^{25} +(1.22436 + 0.0515075i) q^{26} -1.00000 q^{27} +(0.621996 + 1.07733i) q^{28} +(-2.77230 - 4.80177i) q^{29} +(-0.169938 + 0.294342i) q^{30} -9.97370 q^{31} +(1.88448 - 3.26402i) q^{32} +(0.339877 - 0.588684i) q^{33} -2.52498 q^{34} +(-0.330062 + 0.571683i) q^{35} +(0.942242 + 1.63201i) q^{36} +(-4.88448 - 8.46017i) q^{37} -0.0392613 q^{38} +(3.60236 + 0.151548i) q^{39} +1.32025 q^{40} +(-2.11218 - 3.65840i) q^{41} +(-0.112180 - 0.194302i) q^{42} +(0.272303 - 0.471643i) q^{43} -1.28098 q^{44} +(-0.500000 + 0.866025i) q^{45} +(-1.32025 + 2.28673i) q^{46} -5.01963 q^{47} +(1.66012 - 2.87542i) q^{48} +(3.28212 + 5.68480i) q^{49} +(0.169938 + 0.294342i) q^{50} -7.42909 q^{51} +(-3.14697 - 6.02189i) q^{52} +0.679754 q^{53} +(-0.169938 - 0.294342i) q^{54} +(-0.339877 - 0.588684i) q^{55} +(-0.435763 + 0.754763i) q^{56} -0.115516 q^{57} +(0.942242 - 1.63201i) q^{58} +(-1.11218 + 1.92635i) q^{59} +1.88448 q^{60} +(2.10236 - 3.64140i) q^{61} +(-1.69491 - 2.93568i) q^{62} +(-0.330062 - 0.571683i) q^{63} -5.35951 q^{64} +(1.93243 - 3.04397i) q^{65} +0.231033 q^{66} +(3.81691 + 6.61108i) q^{67} +(7.00000 + 12.1244i) q^{68} +(-3.88448 + 6.72812i) q^{69} -0.224361 q^{70} +(-3.65679 + 6.33374i) q^{71} +(-0.660123 + 1.14337i) q^{72} +8.01963 q^{73} +(1.66012 - 2.87542i) q^{74} +(0.500000 + 0.866025i) q^{75} +(0.108844 + 0.188524i) q^{76} +0.448721 q^{77} +(0.567573 + 1.08608i) q^{78} +9.97370 q^{79} +(-1.66012 - 2.87542i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.717881 - 1.24341i) q^{82} +1.76897 q^{83} +(-0.621996 + 1.07733i) q^{84} +(-3.71455 + 6.43378i) q^{85} +0.185099 q^{86} +(2.77230 - 4.80177i) q^{87} +(-0.448721 - 0.777208i) q^{88} +(-6.77230 - 11.7300i) q^{89} -0.339877 q^{90} +(1.10236 + 2.10943i) q^{91} +14.6405 q^{92} +(-4.98685 - 8.63748i) q^{93} +(-0.853028 - 1.47749i) q^{94} +(-0.0577581 + 0.100040i) q^{95} +3.76897 q^{96} +(-4.95206 + 8.57721i) q^{97} +(-1.11552 + 1.93213i) q^{98} +0.679754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} - 6 q^{4} + 6 q^{5} - 3 q^{7} + 12 q^{8} - 3 q^{9} - 12 q^{12} + 3 q^{13} + 24 q^{14} + 3 q^{15} - 12 q^{16} - 12 q^{19} - 6 q^{20} - 6 q^{21} + 24 q^{22} + 6 q^{24} + 6 q^{25} - 18 q^{26} - 6 q^{27} - 12 q^{28} - 6 q^{29} + 6 q^{31} - 12 q^{32} - 3 q^{35} - 6 q^{36} - 6 q^{37} + 12 q^{38} + 12 q^{39} + 12 q^{40} + 12 q^{42} - 9 q^{43} - 24 q^{44} - 3 q^{45} - 12 q^{46} - 24 q^{47} + 12 q^{48} + 6 q^{49} + 12 q^{52} - 30 q^{56} - 24 q^{57} - 6 q^{58} + 6 q^{59} - 12 q^{60} + 3 q^{61} + 6 q^{62} - 3 q^{63} - 24 q^{64} + 3 q^{65} + 48 q^{66} - 9 q^{67} + 42 q^{68} + 24 q^{70} + 12 q^{71} - 6 q^{72} + 42 q^{73} + 12 q^{74} + 3 q^{75} - 48 q^{76} - 48 q^{77} + 12 q^{78} - 6 q^{79} - 12 q^{80} - 3 q^{81} + 18 q^{82} - 36 q^{83} + 12 q^{84} - 12 q^{86} + 6 q^{87} + 48 q^{88} - 30 q^{89} - 3 q^{91} + 96 q^{92} + 3 q^{93} - 36 q^{94} - 12 q^{95} - 24 q^{96} - 15 q^{97} - 30 q^{98}+O(q^{100}) \) 6 * q + 3 * q^3 - 6 * q^4 + 6 * q^5 - 3 * q^7 + 12 * q^8 - 3 * q^9 - 12 * q^12 + 3 * q^13 + 24 * q^14 + 3 * q^15 - 12 * q^16 - 12 * q^19 - 6 * q^20 - 6 * q^21 + 24 * q^22 + 6 * q^24 + 6 * q^25 - 18 * q^26 - 6 * q^27 - 12 * q^28 - 6 * q^29 + 6 * q^31 - 12 * q^32 - 3 * q^35 - 6 * q^36 - 6 * q^37 + 12 * q^38 + 12 * q^39 + 12 * q^40 + 12 * q^42 - 9 * q^43 - 24 * q^44 - 3 * q^45 - 12 * q^46 - 24 * q^47 + 12 * q^48 + 6 * q^49 + 12 * q^52 - 30 * q^56 - 24 * q^57 - 6 * q^58 + 6 * q^59 - 12 * q^60 + 3 * q^61 + 6 * q^62 - 3 * q^63 - 24 * q^64 + 3 * q^65 + 48 * q^66 - 9 * q^67 + 42 * q^68 + 24 * q^70 + 12 * q^71 - 6 * q^72 + 42 * q^73 + 12 * q^74 + 3 * q^75 - 48 * q^76 - 48 * q^77 + 12 * q^78 - 6 * q^79 - 12 * q^80 - 3 * q^81 + 18 * q^82 - 36 * q^83 + 12 * q^84 - 12 * q^86 + 6 * q^87 + 48 * q^88 - 30 * q^89 - 3 * q^91 + 96 * q^92 + 3 * q^93 - 36 * q^94 - 12 * q^95 - 24 * q^96 - 15 * q^97 - 30 * q^98

Introduction

L-functions

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