LMFDB - Embedded newform 96.2.n.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, 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:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	96.13
Dual form			96.2.n.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29526 - 0.567706i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.35542 + 1.47066i) q^{4} +(0.825824 - 0.342068i) q^{5} +(-1.02017 + 0.979416i) q^{6} +(1.17750 - 1.17750i) q^{7} +(-0.920723 - 2.67437i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-1.29526 - 0.567706i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.35542 + 1.47066i) q^{4} +(0.825824 - 0.342068i) q^{5} +(-1.02017 + 0.979416i) q^{6} +(1.17750 - 1.17750i) q^{7} +(-0.920723 - 2.67437i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.26385 - 0.0257578i) q^{10} +(-1.46490 - 3.53657i) q^{11} +(1.87741 - 0.689447i) q^{12} +(3.01061 + 1.24703i) q^{13} +(-2.19365 + 0.856699i) q^{14} -0.893866i q^{15} +(-0.325679 + 3.98672i) q^{16} +4.58215i q^{17} +(0.514461 + 1.31732i) q^{18} +(-3.29978 - 1.36681i) q^{19} +(1.62240 + 0.750861i) q^{20} +(-0.637258 - 1.53848i) q^{21} +(-0.110307 + 5.41243i) q^{22} +(5.41196 + 5.41196i) q^{23} +(-2.82314 - 0.172801i) q^{24} +(-2.97056 + 2.97056i) q^{25} +(-3.19158 - 3.32438i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(3.32770 + 0.135696i) q^{28} +(-2.46490 + 5.95078i) q^{29} +(-0.507453 + 1.15779i) q^{30} -5.25495 q^{31} +(2.68513 - 4.97897i) q^{32} -3.82796 q^{33} +(2.60132 - 5.93510i) q^{34} +(0.569623 - 1.37519i) q^{35} +(0.0814874 - 1.99834i) q^{36} +(7.33917 - 3.03998i) q^{37} +(3.49813 + 3.64369i) q^{38} +(2.30422 - 2.30422i) q^{39} +(-1.67517 - 1.89361i) q^{40} +(-1.35921 - 1.35921i) q^{41} +(-0.0479856 + 2.35451i) q^{42} +(-2.95781 - 7.14079i) q^{43} +(3.21555 - 6.94790i) q^{44} +(-0.825824 - 0.342068i) q^{45} +(-3.93752 - 10.0823i) q^{46} +8.16360i q^{47} +(3.55862 + 1.82654i) q^{48} +4.22699i q^{49} +(5.53406 - 2.16125i) q^{50} +(4.23336 + 1.75351i) q^{51} +(2.24667 + 6.11783i) q^{52} +(-3.13863 - 7.57731i) q^{53} +(1.41392 + 0.0288161i) q^{54} +(-2.41949 - 2.41949i) q^{55} +(-4.23322 - 2.06492i) q^{56} +(-2.52554 + 2.52554i) q^{57} +(6.57099 - 6.30850i) q^{58} +(0.221996 - 0.0919539i) q^{59} +(1.31457 - 1.21156i) q^{60} +(2.66861 - 6.44260i) q^{61} +(6.80655 + 2.98327i) q^{62} -1.66523 q^{63} +(-6.30454 + 4.92471i) q^{64} +2.91280 q^{65} +(4.95822 + 2.17316i) q^{66} +(-5.52539 + 13.3395i) q^{67} +(-6.73879 + 6.21074i) q^{68} +(7.07107 - 2.92893i) q^{69} +(-1.51852 + 1.45786i) q^{70} +(1.51271 - 1.51271i) q^{71} +(-1.24002 + 2.54212i) q^{72} +(-9.62682 - 9.62682i) q^{73} +(-11.2320 - 0.228911i) q^{74} +(1.60765 + 3.88122i) q^{75} +(-2.46246 - 6.70545i) q^{76} +(-5.88923 - 2.43940i) q^{77} +(-4.29269 + 1.67645i) q^{78} +5.34497i q^{79} +(1.09477 + 3.40373i) q^{80} +1.00000i q^{81} +(0.988904 + 2.53217i) q^{82} +(5.64233 + 2.33713i) q^{83} +(1.39882 - 3.02247i) q^{84} +(1.56741 + 3.78405i) q^{85} +(-0.222724 + 10.9284i) q^{86} +(4.55453 + 4.55453i) q^{87} +(-8.10935 + 7.17388i) q^{88} +(5.09017 - 5.09017i) q^{89} +(0.875466 + 0.911893i) q^{90} +(5.01337 - 2.07660i) q^{91} +(-0.623678 + 15.2946i) q^{92} +(-2.01098 + 4.85494i) q^{93} +(4.63453 - 10.5740i) q^{94} -3.19258 q^{95} +(-3.57241 - 4.38610i) q^{96} +19.0146 q^{97} +(2.39969 - 5.47507i) q^{98} +(-1.46490 + 3.53657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	−1.29526	−	0.567706i	−0.915890	−	0.401429i
$2$	−1.29526	−	0.567706i	−0.915890	−	0.401429i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$	1.35542	+	1.47066i	0.677709	+	0.735330i
$5$	0.825824	−	0.342068i	0.369320	−	0.152977i	−0.190302	−	0.981726i	$-0.560947\pi$
$5$	0.825824	−	0.342068i	0.369320	−	0.152977i	0.559621	+	0.828748i	$0.310947\pi$
$6$	−1.02017	+	0.979416i	−0.416482	+	0.399845i
$7$	1.17750	−	1.17750i	0.445053	−	0.445053i	−0.448653	−	0.893706i	$-0.648096\pi$
$7$	1.17750	−	1.17750i	0.445053	−	0.445053i	0.893706	+	0.448653i	$0.148096\pi$
$8$	−0.920723	−	2.67437i	−0.325525	−	0.945534i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−1.26385	−	0.0257578i	−0.399666	−	0.00814532i
$11$	−1.46490	−	3.53657i	−0.441683	−	1.06632i	−0.975358	−	0.220627i	$-0.929189\pi$
$11$	−1.46490	−	3.53657i	−0.441683	−	1.06632i	0.533675	−	0.845690i	$-0.320811\pi$
$12$	1.87741	−	0.689447i	0.541961	−	0.199026i
$13$	3.01061	+	1.24703i	0.834992	+	0.345865i	0.758877	−	0.651234i	$-0.225748\pi$
$13$	3.01061	+	1.24703i	0.834992	+	0.345865i	0.0761151	+	0.997099i	$0.475748\pi$
$14$	−2.19365	+	0.856699i	−0.586276	+	0.228962i
$15$		−	0.893866i		−	0.230795i
$16$	−0.325679	+	3.98672i	−0.0814198	+	0.996680i
$17$			4.58215i			1.11134i	0.831404	+	0.555668i	$0.187537\pi$
$17$			4.58215i			1.11134i	−0.831404	+	0.555668i	$0.812463\pi$
$18$	0.514461	+	1.31732i	0.121260	+	0.310495i
$19$	−3.29978	−	1.36681i	−0.757021	−	0.313568i	−0.0294181	−	0.999567i	$-0.509365\pi$
$19$	−3.29978	−	1.36681i	−0.757021	−	0.313568i	−0.727602	+	0.685999i	$0.759365\pi$
$20$	1.62240	+	0.750861i	0.362780	+	0.167898i
$21$	−0.637258	−	1.53848i	−0.139061	−	0.335723i
$22$	−0.110307	+	5.41243i	−0.0235175	+	1.15393i
$23$	5.41196	+	5.41196i	1.12847	+	1.12847i	0.990426	+	0.138046i	$0.0440823\pi$
$23$	5.41196	+	5.41196i	1.12847	+	1.12847i	0.138046	+	0.990426i	$0.455918\pi$
$24$	−2.82314	−	0.172801i	−0.576272	−	0.0352729i
$25$	−2.97056	+	2.97056i	−0.594112	+	0.594112i
$26$	−3.19158	−	3.32438i	−0.625921	−	0.651964i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	3.32770	+	0.135696i	0.628877	+	0.0256441i
$29$	−2.46490	+	5.95078i	−0.457720	+	1.10503i	0.511599	+	0.859224i	$0.329053\pi$
$29$	−2.46490	+	5.95078i	−0.457720	+	1.10503i	−0.969318	+	0.245808i	$0.920947\pi$
$30$	−0.507453	+	1.15779i	−0.0926479	+	0.211383i
$31$	−5.25495			−0.943816			−0.471908	−	0.881648i	$-0.656435\pi$
$31$	−5.25495			−0.943816			−0.471908	+	0.881648i	$0.656435\pi$
$32$	2.68513	−	4.97897i	0.474668	−	0.880165i
$33$	−3.82796			−0.666362
$34$	2.60132	−	5.93510i	0.446122	−	1.01786i
$35$	0.569623	−	1.37519i	0.0962838	−	0.232450i
$36$	0.0814874	−	1.99834i	0.0135812	−	0.333057i
$37$	7.33917	−	3.03998i	1.20655	−	0.499770i	0.313442	−	0.949607i	$-0.398518\pi$
$37$	7.33917	−	3.03998i	1.20655	−	0.499770i	0.893111	+	0.449837i	$0.148518\pi$
$38$	3.49813	+	3.64369i	0.567472	+	0.591084i
$39$	2.30422	−	2.30422i	0.368970	−	0.368970i
$40$	−1.67517	−	1.89361i	−0.264868	−	0.299406i
$41$	−1.35921	−	1.35921i	−0.212273	−	0.212273i	0.592959	−	0.805232i	$-0.297959\pi$
$41$	−1.35921	−	1.35921i	−0.212273	−	0.212273i	−0.805232	+	0.592959i	$0.797959\pi$
$42$	−0.0479856	+	2.35451i	−0.00740435	+	0.363309i
$43$	−2.95781	−	7.14079i	−0.451062	−	1.08896i	−0.971919	−	0.235317i	$-0.924387\pi$
$43$	−2.95781	−	7.14079i	−0.451062	−	1.08896i	0.520856	−	0.853644i	$-0.325613\pi$
$44$	3.21555	−	6.94790i	0.484762	−	1.04744i
$45$	−0.825824	−	0.342068i	−0.123107	−	0.0509924i
$46$	−3.93752	−	10.0823i	−0.580555	−	1.48656i
$47$			8.16360i			1.19078i	0.803436	+	0.595391i	$0.203003\pi$
$47$			8.16360i			1.19078i	−0.803436	+	0.595391i	$0.796997\pi$
$48$	3.55862	+	1.82654i	0.513642	+	0.263638i
$49$			4.22699i			0.603856i
$50$	5.53406	−	2.16125i	0.782635	−	0.305647i
$51$	4.23336	+	1.75351i	0.592789	+	0.245541i
$52$	2.24667	+	6.11783i	0.311557	+	0.848391i
$53$	−3.13863	−	7.57731i	−0.431123	−	1.04082i	−0.978926	−	0.204216i	$-0.934535\pi$
$53$	−3.13863	−	7.57731i	−0.431123	−	1.04082i	0.547802	−	0.836608i	$-0.315465\pi$
$54$	1.41392	+	0.0288161i	0.192410	+	0.00392138i
$55$	−2.41949	−	2.41949i	−0.326244	−	0.326244i
$56$	−4.23322	−	2.06492i	−0.565688	−	0.275937i
$57$	−2.52554	+	2.52554i	−0.334516	+	0.334516i
$58$	6.57099	−	6.30850i	0.862813	−	0.828347i
$59$	0.221996	−	0.0919539i	0.0289014	−	0.0119714i	−0.368186	−	0.929752i	$-0.620021\pi$
$59$	0.221996	−	0.0919539i	0.0289014	−	0.0119714i	0.397087	+	0.917781i	$0.370021\pi$
$60$	1.31457	−	1.21156i	0.169711	−	0.156412i
$61$	2.66861	−	6.44260i	0.341681	−	0.824891i	−0.655865	−	0.754878i	$-0.727696\pi$
$61$	2.66861	−	6.44260i	0.341681	−	0.824891i	0.997546	−	0.0700128i	$-0.0223040\pi$
$62$	6.80655	+	2.98327i	0.864432	+	0.378875i
$63$	−1.66523			−0.209800
$64$	−6.30454	+	4.92471i	−0.788067	+	0.615589i
$65$	2.91280			0.361289
$66$	4.95822	+	2.17316i	0.610315	+	0.267497i
$67$	−5.52539	+	13.3395i	−0.675033	+	1.62968i	0.0979063	+	0.995196i	$0.468785\pi$
$67$	−5.52539	+	13.3395i	−0.675033	+	1.62968i	−0.772940	+	0.634479i	$0.781215\pi$
$68$	−6.73879	+	6.21074i	−0.817198	+	0.753163i
$69$	7.07107	−	2.92893i	0.851257	−	0.352602i
$70$	−1.51852	+	1.45786i	−0.181497	+	0.174247i
$71$	1.51271	−	1.51271i	0.179526	−	0.179526i	−0.611623	−	0.791149i	$-0.709483\pi$
$71$	1.51271	−	1.51271i	0.179526	−	0.179526i	0.791149	+	0.611623i	$0.209483\pi$
$72$	−1.24002	+	2.54212i	−0.146137	+	0.299591i
$73$	−9.62682	−	9.62682i	−1.12673	−	1.12673i	−0.990705	−	0.136029i	$-0.956566\pi$
$73$	−9.62682	−	9.62682i	−1.12673	−	1.12673i	−0.136029	−	0.990705i	$-0.543434\pi$
$74$	−11.2320	−	0.228911i	−1.30569	−	0.0266104i
$75$	1.60765	+	3.88122i	0.185636	+	0.448165i
$76$	−2.46246	−	6.70545i	−0.282464	−	0.769168i
$77$	−5.88923	−	2.43940i	−0.671140	−	0.277995i
$78$	−4.29269	+	1.67645i	−0.486052	+	0.189821i
$79$			5.34497i			0.601356i	0.953726	+	0.300678i	$0.0972129\pi$
$79$			5.34497i			0.601356i	−0.953726	+	0.300678i	$0.902787\pi$
$80$	1.09477	+	3.40373i	0.122399	+	0.380549i
$81$			1.00000i			0.111111i
$82$	0.988904	+	2.53217i	0.109206	+	0.279631i
$83$	5.64233	+	2.33713i	0.619327	+	0.256533i	0.670210	−	0.742171i	$-0.266204\pi$
$83$	5.64233	+	2.33713i	0.619327	+	0.256533i	−0.0508839	+	0.998705i	$0.516204\pi$
$84$	1.39882	−	3.02247i	0.152624	−	0.329778i
$85$	1.56741	+	3.78405i	0.170009	+	0.410438i
$86$	−0.222724	+	10.9284i	−0.0240169	+	1.17844i
$87$	4.55453	+	4.55453i	0.488297	+	0.488297i
$88$	−8.10935	+	7.17388i	−0.864460	+	0.764739i
$89$	5.09017	−	5.09017i	0.539557	−	0.539557i	−0.383842	−	0.923399i	$-0.625399\pi$
$89$	5.09017	−	5.09017i	0.539557	−	0.539557i	0.923399	+	0.383842i	$0.125399\pi$
$90$	0.875466	+	0.911893i	0.0922823	+	0.0961220i
$91$	5.01337	−	2.07660i	0.525544	−	0.217687i
$92$	−0.623678	+	15.2946i	−0.0650229	+	1.59458i
$93$	−2.01098	+	4.85494i	−0.208529	+	0.503434i
$94$	4.63453	−	10.5740i	0.478015	−	1.09063i
$95$	−3.19258			−0.327551
$96$	−3.57241	−	4.38610i	−0.364608	−	0.447655i
$97$	19.0146			1.93064			0.965319	−	0.261072i	$-0.0840761\pi$
$97$	19.0146			1.93064			0.965319	+	0.261072i	$0.0840761\pi$
$98$	2.39969	−	5.47507i	0.242405	−	0.553066i
$99$	−1.46490	+	3.53657i	−0.147228	+	0.355439i
$100$	−8.39503	−	0.342329i	−0.839503	−	0.0342329i
$101$	−3.55331	+	1.47183i	−0.353567	+	0.146452i	−0.552396	−	0.833582i	$-0.686286\pi$
$101$	−3.55331	+	1.47183i	−0.353567	+	0.146452i	0.198828	+	0.980034i	$0.436286\pi$
$102$	−4.48784	−	4.67457i	−0.444362	−	0.462851i
$103$	3.30552	−	3.30552i	0.325703	−	0.325703i	−0.525247	−	0.850950i	$-0.676027\pi$
$103$	3.30552	−	3.30552i	0.325703	−	0.325703i	0.850950	+	0.525247i	$0.176027\pi$
$104$	0.563100	−	9.19966i	0.0552165	−	0.902101i
$105$	−1.05253	−	1.05253i	−0.102716	−	0.102716i
$106$	−0.236339	+	11.5964i	−0.0229553	+	1.12635i
$107$	−4.98987	−	12.0466i	−0.482389	−	1.16459i	−0.958471	−	0.285190i	$-0.907943\pi$
$107$	−4.98987	−	12.0466i	−0.482389	−	1.16459i	0.476082	−	0.879401i	$-0.342057\pi$
$108$	−1.81504	−	0.840016i	−0.174652	−	0.0808306i
$109$	−4.16532	−	1.72533i	−0.398966	−	0.165257i	0.174174	−	0.984715i	$-0.444275\pi$
$109$	−4.16532	−	1.72533i	−0.398966	−	0.165257i	−0.573139	+	0.819458i	$0.694275\pi$
$110$	1.76032	+	4.50745i	0.167840	+	0.429768i
$111$		−	7.94386i		−	0.753998i
$112$	4.31087	+	5.07784i	0.407339	+	0.479811i
$113$		−	15.7676i		−	1.48329i	−0.670792	−	0.741645i	$-0.734046\pi$
$113$		−	15.7676i		−	1.48329i	0.670792	−	0.741645i	$-0.265954\pi$
$114$	4.70501	−	1.83748i	0.440664	−	0.172095i
$115$	6.32059	+	2.61807i	0.589398	+	0.244137i
$116$	−12.0925	+	4.44078i	−1.12276	+	0.412316i
$117$	−1.24703	−	3.01061i	−0.115288	−	0.278331i
$118$	−0.339747	−	0.00692414i	−0.0312762	−	0.000637419i
$119$	5.39548	+	5.39548i	0.494603	+	0.494603i
$120$	−2.39053	+	0.823002i	−0.218225	+	0.0751295i
$121$	−2.58325	+	2.58325i	−0.234841	+	0.234841i
$122$	−7.11407	+	6.82989i	−0.644077	+	0.618349i
$123$	−1.77589	+	0.735600i	−0.160127	+	0.0663268i
$124$	−7.12265	−	7.72824i	−0.639633	−	0.694016i
$125$	−3.14736	+	7.59841i	−0.281509	+	0.679623i
$126$	2.15692	+	0.945364i	0.192154	+	0.0842198i
$127$	5.62550			0.499182			0.249591	−	0.968351i	$-0.419704\pi$
$127$	5.62550			0.499182			0.249591	+	0.968351i	$0.419704\pi$
$128$	10.9618	−	2.79968i	0.968898	−	0.247459i
$129$	−7.72914			−0.680513
$130$	−3.77285	−	1.65362i	−0.330901	−	0.145032i
$131$	2.77061	−	6.68884i	0.242069	−	0.584407i	−0.755419	−	0.655242i	$-0.772567\pi$
$131$	2.77061	−	6.68884i	0.242069	−	0.584407i	0.997488	+	0.0708355i	$0.0225665\pi$
$132$	−5.18849	−	5.62963i	−0.451600	−	0.489996i
$133$	−5.49490	+	2.27606i	−0.476468	+	0.197360i
$134$	14.7297	−	14.1413i	1.27246	−	1.22163i
$135$	−0.632058	+	0.632058i	−0.0543989	+	0.0543989i
$136$	12.2544	−	4.21889i	1.05081	−	0.361767i
$137$	3.13785	+	3.13785i	0.268085	+	0.268085i	0.828328	−	0.560243i	$-0.189292\pi$
$137$	3.13785	+	3.13785i	0.268085	+	0.268085i	−0.560243	+	0.828328i	$0.689292\pi$
$138$	−10.8217	−	0.220549i	−0.921202	−	0.0187744i
$139$	3.60636	+	8.70653i	0.305888	+	0.738478i	0.999830	+	0.0184473i	$0.00587229\pi$
$139$	3.60636	+	8.70653i	0.305888	+	0.738478i	−0.693942	+	0.720031i	$0.744128\pi$
$140$	2.79452	−	1.02624i	0.236180	−	0.0867330i
$141$	7.54218	+	3.12407i	0.635166	+	0.263094i
$142$	−2.81814	+	1.10059i	−0.236493	+	0.0923591i
$143$		−	12.4740i		−	1.04313i
$144$	3.04933	−	2.58875i	0.254111	−	0.215729i
$145$			5.75746i			0.478131i
$146$	7.00407	+	17.9345i	0.579661	+	1.48427i
$147$	3.90523	+	1.61760i	0.322098	+	0.133417i
$148$	14.4184	+	6.67297i	1.18519	+	0.548515i
$149$	−1.00661	−	2.43018i	−0.0824648	−	0.199088i	0.877269	−	0.479999i	$-0.159363\pi$
$149$	−1.00661	−	2.43018i	−0.0824648	−	0.199088i	−0.959734	+	0.280912i	$0.909363\pi$
$150$	0.121057	−	5.93988i	0.00988424	−	0.484989i
$151$	−14.3784	−	14.3784i	−1.17010	−	1.17010i	−0.982186	−	0.187914i	$-0.939827\pi$
$151$	−14.3784	−	14.3784i	−1.17010	−	1.17010i	−0.187914	−	0.982186i	$-0.560173\pi$
$152$	−0.617186	+	10.0833i	−0.0500604	+	0.817863i
$153$	3.24007	−	3.24007i	0.261944	−	0.261944i
$154$	6.24324	+	6.50301i	0.503095	+	0.524028i
$155$	−4.33966	+	1.79755i	−0.348570	+	0.144382i
$156$	6.51190	+	0.265540i	0.521370	+	0.0212602i
$157$	−2.10034	+	5.07067i	−0.167625	+	0.404684i	−0.985262	−	0.171051i	$-0.945284\pi$
$157$	−2.10034	+	5.07067i	−0.167625	+	0.404684i	0.817637	+	0.575734i	$0.195284\pi$
$158$	3.03437	−	6.92315i	0.241402	−	0.550776i
$159$	−8.20163			−0.650431
$160$	0.514300	−	5.03024i	0.0406590	−	0.397676i
$161$	12.7452			1.00446
$162$	0.567706	−	1.29526i	0.0446032	−	0.101766i
$163$	−4.14645	+	10.0104i	−0.324775	+	0.784076i	0.674189	+	0.738559i	$0.264493\pi$
$163$	−4.14645	+	10.0104i	−0.324775	+	0.784076i	−0.998964	+	0.0455168i	$0.985507\pi$
$164$	0.156636	−	3.84124i	0.0122312	−	0.299950i
$165$	−3.16122	+	1.30942i	−0.246101	+	0.101938i
$166$	−5.98151	−	6.23039i	−0.464255	−	0.483572i
$167$	−5.38194	+	5.38194i	−0.416467	+	0.416467i	−0.883984	−	0.467517i	$-0.845149\pi$
$167$	−5.38194	+	5.38194i	−0.416467	+	0.416467i	0.467517	+	0.883984i	$0.345149\pi$
$168$	−3.52772	+	3.12078i	−0.272170	+	0.240773i
$169$	−1.68373	−	1.68373i	−0.129518	−	0.129518i
$170$	0.118026	−	5.79117i	0.00905218	−	0.444163i
$171$	1.36681	+	3.29978i	0.104523	+	0.252340i
$172$	6.49260	−	14.0287i	0.495056	−	1.06968i
$173$	−9.62485	−	3.98675i	−0.731764	−	0.303107i	−0.0144874	−	0.999895i	$-0.504612\pi$
$173$	−9.62485	−	3.98675i	−0.731764	−	0.303107i	−0.717277	+	0.696788i	$0.754612\pi$
$174$	−3.31369	−	8.48496i	−0.251210	−	0.643243i
$175$			6.99566i			0.528822i
$176$	14.5764	−	4.68834i	1.09874	−	0.353397i
$177$		−	0.240287i		−	0.0180611i
$178$	−9.48283	+	3.70339i	−0.710768	+	0.277581i
$179$	−12.7809	−	5.29402i	−0.955288	−	0.395693i	−0.150072	−	0.988675i	$-0.547951\pi$
$179$	−12.7809	−	5.29402i	−0.955288	−	0.395693i	−0.805216	+	0.592982i	$0.797951\pi$
$180$	−0.616273	−	1.67815i	−0.0459343	−	0.125082i
$181$	8.21217	+	19.8259i	0.610406	+	1.47365i	0.862556	+	0.505962i	$0.168862\pi$
$181$	8.21217	+	19.8259i	0.610406	+	1.47365i	−0.252150	+	0.967688i	$0.581138\pi$
$182$	−7.67254	−	0.156369i	−0.568726	−	0.0115908i
$183$	−4.93096	−	4.93096i	−0.364507	−	0.364507i
$184$	9.49069	−	19.4565i	0.699663	−	1.43435i
$185$	5.02098	−	5.02098i	0.369150	−	0.369150i
$186$	5.36093	−	5.14678i	0.393083	−	0.377380i
$187$	16.2051	−	6.71238i	1.18504	−	0.490858i
$188$	−12.0059	+	11.0651i	−0.875618	+	0.807005i
$189$	−0.637258	+	1.53848i	−0.0463537	+	0.111908i
$190$	4.13523	+	1.81245i	0.300001	+	0.131489i
$191$	−10.3772			−0.750866			−0.375433	−	0.926850i	$-0.622506\pi$
$191$	−10.3772			−0.750866			−0.375433	+	0.926850i	$0.622506\pi$
$192$	2.13720	+	7.70924i	0.154239	+	0.556366i
$193$	−8.76090			−0.630623			−0.315312	−	0.948988i	$-0.602109\pi$
$193$	−8.76090			−0.630623			−0.315312	+	0.948988i	$0.602109\pi$
$194$	−24.6289	−	10.7947i	−1.76825	−	0.775014i
$195$	1.11468	−	2.69108i	0.0798240	−	0.192712i
$196$	−6.21647	+	5.72935i	−0.444033	+	0.409239i
$197$	−4.35045	+	1.80201i	−0.309956	+	0.128388i	−0.532239	−	0.846594i	$-0.678649\pi$
$197$	−4.35045	+	1.80201i	−0.309956	+	0.128388i	0.222283	+	0.974982i	$0.428649\pi$
$198$	3.90516	−	3.74917i	0.277528	−	0.266442i
$199$	3.47990	−	3.47990i	0.246684	−	0.246684i	−0.572925	−	0.819608i	$-0.694191\pi$
$199$	3.47990	−	3.47990i	0.246684	−	0.246684i	0.819608	+	0.572925i	$0.194191\pi$
$200$	10.6794	+	5.20932i	0.755151	+	0.368355i
$201$	10.2096	+	10.2096i	0.720129	+	0.720129i
$202$	5.43804	+	0.110829i	0.382619	+	0.00779790i
$203$	4.10463	+	9.90945i	0.288088	+	0.695507i
$204$	3.15915	+	8.60258i	0.221185	+	0.602301i
$205$	−1.58741	−	0.657527i	−0.110870	−	0.0459237i
$206$	−6.15809	+	2.40496i	−0.429054	+	0.167561i
$207$		−	7.65367i		−	0.531967i
$208$	−5.95207	+	11.5963i	−0.412702	+	0.804060i
$209$			13.6721i			0.945722i
$210$	0.765773	+	1.96082i	0.0528434	+	0.135310i
$211$	−4.76129	−	1.97219i	−0.327781	−	0.135771i	0.212724	−	0.977112i	$-0.431767\pi$
$211$	−4.76129	−	1.97219i	−0.327781	−	0.135771i	−0.540505	+	0.841341i	$0.681767\pi$
$212$	6.88950	−	14.8863i	0.473173	−	1.02239i
$213$	−0.818674	−	1.97645i	−0.0560946	−	0.135424i
$214$	−0.375739	+	18.4363i	−0.0256850	+	1.26028i
$215$	−4.88527	−	4.88527i	−0.333173	−	0.333173i
$216$	1.87408	+	2.11845i	0.127515	+	0.144142i
$217$	−6.18769	+	6.18769i	−0.420048	+	0.420048i
$218$	4.41571	+	4.59944i	0.299070	+	0.311514i
$219$	−12.5780	+	5.21000i	−0.849946	+	0.352059i
$220$	0.278824	−	6.83768i	0.0187983	−	0.460996i
$221$	−5.71410	+	13.7951i	−0.384372	+	0.927956i
$222$	−4.50978	+	10.2894i	−0.302677	+	0.690579i
$223$	12.6045			0.844059			0.422029	−	0.906582i	$-0.361318\pi$
$223$	12.6045			0.844059			0.422029	+	0.906582i	$0.361318\pi$
$224$	−2.70099	−	9.02446i	−0.180468	−	0.602972i
$225$	4.20100			0.280067
$226$	−8.95136	+	20.4232i	−0.595436	+	1.35853i
$227$	1.84453	−	4.45310i	0.122426	−	0.295563i	−0.850771	−	0.525537i	$-0.823864\pi$
$227$	1.84453	−	4.45310i	0.122426	−	0.295563i	0.973197	+	0.229975i	$0.0738644\pi$
$228$	−7.13737	−	0.291045i	−0.472684	−	0.0192749i
$229$	−19.3957	+	8.03395i	−1.28170	+	0.530898i	−0.916502	−	0.400031i	$-0.868999\pi$
$229$	−19.3957	+	8.03395i	−1.28170	+	0.530898i	−0.365200	+	0.930929i	$0.618999\pi$
$230$	−6.70053	−	6.97933i	−0.441820	−	0.460204i
$231$	−4.50742	+	4.50742i	−0.296566	+	0.296566i
$232$	18.1841	+	1.11303i	1.19384	+	0.0730737i
$233$	13.4162	+	13.4162i	0.878921	+	0.878921i	0.993423	−	0.114502i	$-0.0365271\pi$
$233$	13.4162	+	13.4162i	0.878921	+	0.878921i	−0.114502	+	0.993423i	$0.536527\pi$
$234$	−0.0939019	+	4.60748i	−0.00613856	+	0.301200i
$235$	2.79250	+	6.74169i	0.182163	+	0.439780i
$236$	0.436131	+	0.201845i	0.0283897	+	0.0131390i
$237$	4.93811	+	2.04543i	0.320765	+	0.132865i
$238$	−3.92552	−	10.0516i	−0.254454	−	0.651550i
$239$		−	4.57889i		−	0.296184i	−0.988974	−	0.148092i	$-0.952687\pi$
$239$		−	4.57889i		−	0.296184i	0.988974	−	0.148092i	$-0.0473131\pi$
$240$	3.56359	+	0.291113i	0.230029	+	0.0187913i
$241$		−	14.5911i		−	0.939895i	−0.882694	−	0.469948i	$-0.844273\pi$
$241$		−	14.5911i		−	0.939895i	0.882694	−	0.469948i	$-0.155727\pi$
$242$	4.81253	−	1.87947i	0.309361	−	0.120817i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	13.0920	−	4.80780i	0.838127	−	0.307788i
$245$	1.44592	+	3.49075i	0.0923763	+	0.223016i
$246$	2.71786	+	0.0553908i	0.173284	+	0.00353159i
$247$	−8.22987	−	8.22987i	−0.523654	−	0.523654i
$248$	4.83835	+	14.0537i	0.307236	+	0.892410i
$249$	4.31845	−	4.31845i	0.273671	−	0.273671i
$250$	8.39034	−	8.05517i	0.530651	−	0.509454i
$251$	−1.91315	+	0.792453i	−0.120757	+	0.0500192i	−0.442244	−	0.896895i	$-0.645817\pi$
$251$	−1.91315	+	0.792453i	−0.120757	+	0.0500192i	0.321487	+	0.946914i	$0.395817\pi$
$252$	−2.25709	−	2.44899i	−0.142183	−	0.154272i
$253$	11.2118	−	27.0678i	0.704882	−	1.70174i
$254$	−7.28650	−	3.19363i	−0.457196	−	0.200386i
$255$	4.09583			0.256491
$256$	−15.7879	−	2.59678i	−0.986742	−	0.162299i
$257$	−21.4012			−1.33497			−0.667485	−	0.744624i	$-0.732629\pi$
$257$	−21.4012			−1.33497			−0.667485	+	0.744624i	$0.732629\pi$
$258$	10.0113	+	4.38788i	0.623275	+	0.273178i
$259$	5.06229	−	12.2214i	0.314555	−	0.759403i
$260$	3.94807	+	4.28374i	0.244849	+	0.265666i
$261$	5.95078	−	2.46490i	0.368344	−	0.152573i
$262$	−7.38597	+	7.09093i	−0.456307	+	0.438079i
$263$	4.14877	−	4.14877i	0.255824	−	0.255824i	−0.567529	−	0.823353i	$-0.692101\pi$
$263$	4.14877	−	4.14877i	0.255824	−	0.255824i	0.823353	+	0.567529i	$0.192101\pi$
$264$	3.52449	+	10.2374i	0.216917	+	0.630068i
$265$	−5.18391	−	5.18391i	−0.318445	−	0.318445i
$266$	8.40949	+	0.171388i	0.515619	+	0.0105085i
$267$	−2.75478	−	6.65062i	−0.168590	−	0.407011i
$268$	−27.1070	+	9.95460i	−1.65583	+	0.608074i
$269$	28.0039	+	11.5996i	1.70743	+	0.707241i	1.00000		0.000457143i	$0.000145513\pi$
$269$	28.0039	+	11.5996i	1.70743	+	0.707241i	0.707430	+	0.706783i	$0.249854\pi$
$270$	1.17751	−	0.459859i	0.0716607	−	0.0279861i
$271$		−	10.3370i		−	0.627930i	−0.949435	−	0.313965i	$-0.898343\pi$
$271$		−	10.3370i		−	0.627930i	0.949435	−	0.313965i	$-0.101657\pi$
$272$	−18.2678	−	1.49231i	−1.10765	−	0.0904847i
$273$		−	5.42643i		−	0.328422i
$274$	−2.28297	−	5.84572i	−0.137919	−	0.353153i
$275$	14.8572	+	6.15404i	0.895920	+	0.371102i
$276$	13.8917	+	6.42921i	0.836184	+	0.386993i
$277$	−6.39508	−	15.4391i	−0.384243	−	0.927645i	−0.991135	−	0.132860i	$-0.957584\pi$
$277$	−6.39508	−	15.4391i	−0.384243	−	0.927645i	0.606892	−	0.794785i	$-0.292416\pi$
$278$	0.271560	−	13.3246i	0.0162871	−	0.799157i
$279$	3.71581	+	3.71581i	0.222460	+	0.222460i
$280$	−4.20224	−	0.257214i	−0.251132	−	0.0153715i
$281$	7.85631	−	7.85631i	0.468668	−	0.468668i	−0.432815	−	0.901483i	$-0.642480\pi$
$281$	7.85631	−	7.85631i	0.468668	−	0.468668i	0.901483	+	0.432815i	$0.142480\pi$
$282$	−7.99556	−	8.32824i	−0.476129	−	0.495940i
$283$	6.76840	−	2.80356i	0.402340	−	0.166655i	−0.172331	−	0.985039i	$-0.555130\pi$
$283$	6.76840	−	2.80356i	0.402340	−	0.166655i	0.574671	+	0.818385i	$0.305130\pi$
$284$	4.27504	+	0.174326i	0.253677	+	0.0103443i
$285$	−1.22175	+	2.94956i	−0.0723700	+	0.174717i
$286$	−7.08157	+	16.1571i	−0.418742	+	0.955392i
$287$	−3.20094			−0.188945
$288$	−5.41933	+	1.62199i	−0.319337	+	0.0955766i
$289$	−3.99613			−0.235067
$290$	3.26855	−	7.45743i	0.191936	−	0.437916i
$291$	7.27657	−	17.5672i	0.426560	−	1.02981i
$292$	1.10940	−	27.2061i	0.0649228	−	1.59212i
$293$	12.3397	−	5.11128i	0.720895	−	0.298604i	0.00809031	−	0.999967i	$-0.497425\pi$
$293$	12.3397	−	5.11128i	0.720895	−	0.298604i	0.712804	+	0.701363i	$0.247425\pi$
$294$	−4.13999	−	4.31224i	−0.241449	−	0.251495i
$295$	0.151875	−	0.151875i	0.00884253	−	0.00884253i
$296$	−14.8874	−	16.8287i	−0.865312	−	0.978148i
$297$	2.70678	+	2.70678i	0.157063	+	0.157063i
$298$	−0.0757981	+	3.71918i	−0.00439086	+	0.215446i
$299$	9.54439	+	23.0422i	0.551966	+	1.33256i
$300$	−3.52891	+	7.62499i	−0.203742	+	0.440229i
$301$	−11.8911	−	4.92545i	−0.685392	−	0.283898i
$302$	10.4611	+	26.7866i	0.601971	+	1.54139i
$303$			3.84607i			0.220951i
$304$	6.52376	−	12.7101i	0.374164	−	0.728977i
$305$		−	6.23330i		−	0.356918i
$306$	−6.03616	+	2.35734i	−0.345064	+	0.134760i
$307$	−7.47343	−	3.09560i	−0.426531	−	0.176675i	0.159082	−	0.987265i	$-0.449146\pi$
$307$	−7.47343	−	3.09560i	−0.426531	−	0.176675i	−0.585614	+	0.810590i	$0.699146\pi$
$308$	−4.39484	−	11.9675i	−0.250420	−	0.681909i
$309$	−1.78894	−	4.31887i	−0.101769	−	0.245692i
$310$	6.64149	+	0.135356i	0.377211	+	0.00768768i
$311$	12.5179	+	12.5179i	0.709823	+	0.709823i	0.966498	−	0.256675i	$-0.0826271\pi$
$311$	12.5179	+	12.5179i	0.709823	+	0.709823i	−0.256675	+	0.966498i	$0.582627\pi$
$312$	−8.28389	−	4.04079i	−0.468983	−	0.228765i
$313$	2.11020	−	2.11020i	0.119276	−	0.119276i	−0.644950	−	0.764225i	$-0.723122\pi$
$313$	2.11020	−	2.11020i	0.119276	−	0.119276i	0.764225	+	0.644950i	$0.223122\pi$
$314$	5.59915	−	5.37548i	0.315978	−	0.303356i
$315$	−1.37519	+	0.569623i	−0.0774832	+	0.0320946i
$316$	−7.86063	+	7.24467i	−0.442195	+	0.407545i
$317$	13.3122	−	32.1384i	0.747686	−	1.80507i	0.176408	−	0.984317i	$-0.443552\pi$
$317$	13.3122	−	32.1384i	0.747686	−	1.80507i	0.571278	−	0.820756i	$-0.306448\pi$
$318$	10.6233	+	4.65612i	0.595724	+	0.261102i
$319$	24.6562			1.38048
$320$	−3.52186	+	6.22352i	−0.196878	+	0.347906i
$321$	−13.0392			−0.727776
$322$	−16.5083	−	7.23551i	−0.919974	−	0.403219i
$323$	6.26294	−	15.1201i	0.348479	−	0.841304i
$324$	−1.47066	+	1.35542i	−0.0817033	+	0.0753011i
$325$	−12.6476	+	5.23880i	−0.701561	+	0.290596i
$326$	11.0537	−	10.6122i	0.612209	−	0.587753i
$327$	−3.18800	+	3.18800i	−0.176297	+	0.176297i
$328$	−2.38358	+	4.88649i	−0.131611	+	0.269811i
$329$	9.61262	+	9.61262i	0.529961	+	0.529961i
$330$	4.83798	+	0.0985996i	0.266322	+	0.00542773i
$331$	−1.26744	−	3.05988i	−0.0696650	−	0.168186i	0.885212	−	0.465188i	$-0.154013\pi$
$331$	−1.26744	−	3.05988i	−0.0696650	−	0.168186i	−0.954877	+	0.297002i	$0.904013\pi$
$332$	4.21060	+	11.4657i	0.231087	+	0.629264i
$333$	−7.33917	−	3.03998i	−0.402184	−	0.166590i
$334$	10.0264	−	3.91567i	0.548620	−	0.214256i
$335$			12.9061i			0.705136i
$336$	6.34102	−	2.03952i	0.345931	−	0.111265i
$337$			10.1534i			0.553088i	0.961001	+	0.276544i	$0.0891892\pi$
$337$			10.1534i			0.553088i	−0.961001	+	0.276544i	$0.910811\pi$
$338$	1.22501	+	3.13674i	0.0666317	+	0.170616i
$339$	−14.5674	−	6.03400i	−0.791190	−	0.327722i
$340$	−3.44056	+	7.43410i	−0.186591	+	0.403171i
$341$	7.69795	+	18.5845i	0.416868	+	1.00641i
$342$	0.102921	−	5.05003i	0.00556534	−	0.273074i
$343$	13.2198	+	13.2198i	0.713801	+	0.713801i
$344$	−16.3738	+	14.4850i	−0.882817	+	0.780978i
$345$	4.83757	−	4.83757i	0.260446	−	0.260446i
$346$	10.2034	+	10.6280i	0.548540	+	0.571364i
$347$	−25.9794	+	10.7610i	−1.39465	+	0.577681i	−0.948356	−	0.317208i	$-0.897255\pi$
$347$	−25.9794	+	10.7610i	−1.39465	+	0.577681i	−0.446289	+	0.894889i	$0.647255\pi$
$348$	−0.524867	+	12.8715i	−0.0281358	+	0.689983i
$349$	5.71239	−	13.7909i	0.305777	−	0.738212i	−0.694055	−	0.719922i	$-0.744178\pi$
$349$	5.71239	−	13.7909i	0.305777	−	0.738212i	0.999833	−	0.0182903i	$-0.00582231\pi$
$350$	3.97148	−	9.06123i	0.212285	−	0.484343i
$351$	−3.25866			−0.173934
$352$	−21.5419	−	2.20248i	−1.14819	−	0.117392i
$353$	−18.8434			−1.00293			−0.501467	−	0.865177i	$-0.667206\pi$
$353$	−18.8434			−1.00293			−0.501467	+	0.865177i	$0.667206\pi$
$354$	−0.136412	+	0.311235i	−0.00725024	+	0.0165420i
$355$	0.731784	−	1.76668i	0.0388391	−	0.0937658i
$356$	14.3852	+	0.586594i	0.762415	+	0.0310894i
$357$	7.04954	−	2.92001i	0.373101	−	0.154543i
$358$	13.5492	+	14.1129i	0.716096	+	0.745892i
$359$	−18.8776	+	18.8776i	−0.996324	+	0.996324i	−0.999993	−	0.00366976i	$-0.998832\pi$
$359$	−18.8776	+	18.8776i	−0.996324	+	0.996324i	0.00366976	+	0.999993i	$0.498832\pi$
$360$	−0.154461	+	2.52351i	−0.00814081	+	0.133001i
$361$	−4.41468	−	4.41468i	−0.232352	−	0.232352i
$362$	0.618378	−	30.3419i	0.0325012	−	1.59474i
$363$	1.39805	+	3.37519i	0.0733785	+	0.177151i
$364$	9.84919	+	4.55829i	0.516238	+	0.238919i
$365$	−11.2431	−	4.65704i	−0.588490	−	0.243760i
$366$	3.58756	+	9.18623i	0.187525	+	0.480172i
$367$			25.6668i			1.33980i	0.742453	+	0.669898i	$0.233662\pi$
$367$			25.6668i			1.33980i	−0.742453	+	0.669898i	$0.766338\pi$
$368$	−23.3385	+	19.8134i	−1.21661	+	1.03285i
$369$			1.92221i			0.100066i
$370$	−9.35395	+	3.65306i	−0.486288	+	0.189913i
$371$	−12.6180	−	5.22655i	−0.655094	−	0.271349i
$372$	−9.86568	+	3.62301i	−0.511512	+	0.187844i
$373$	3.11418	+	7.51829i	0.161246	+	0.389282i	0.983767	−	0.179453i	$-0.0574328\pi$
$373$	3.11418	+	7.51829i	0.161246	+	0.389282i	−0.822521	+	0.568735i	$0.807433\pi$
$374$	−24.8006	−	0.505444i	−1.28241	−	0.0261359i
$375$	5.81557	+	5.81557i	0.300315	+	0.300315i
$376$	21.8325	−	7.51641i	1.12593	−	0.387629i
$377$	−14.8417	+	14.8417i	−0.764384	+	0.764384i
$378$	1.69882	−	1.63096i	0.0873779	−	0.0838874i
$379$	−5.17051	+	2.14170i	−0.265591	+	0.110012i	−0.511505	−	0.859280i	$-0.670912\pi$
$379$	−5.17051	+	2.14170i	−0.265591	+	0.110012i	0.245914	+	0.969292i	$0.420912\pi$
$380$	−4.32728	−	4.69519i	−0.221985	−	0.240858i
$381$	2.15278	−	5.19728i	0.110290	−	0.266265i
$382$	13.4412	+	5.89119i	0.687711	+	0.301419i
$383$	33.8865			1.73152			0.865758	−	0.500462i	$-0.166837\pi$
$383$	33.8865			1.73152			0.865758	+	0.500462i	$0.166837\pi$
$384$	1.60835	−	11.1988i	0.0820757	−	0.571487i
$385$	−5.69790			−0.290392
$386$	11.3477	+	4.97362i	0.577582	+	0.253150i
$387$	−2.95781	+	7.14079i	−0.150354	+	0.362987i
$388$	25.7727	+	27.9640i	1.30841	+	1.41966i
$389$	−3.06573	+	1.26987i	−0.155439	+	0.0643847i	−0.459046	−	0.888412i	$-0.651809\pi$
$389$	−3.06573	+	1.26987i	−0.155439	+	0.0643847i	0.303608	+	0.952797i	$0.401809\pi$
$390$	−2.97155	+	2.85285i	−0.150470	+	0.144459i
$391$	−24.7984	+	24.7984i	−1.25411	+	1.25411i
$392$	11.3046	−	3.89189i	0.570966	−	0.196570i
$393$	−5.11942	−	5.11942i	−0.258240	−	0.258240i
$394$	6.65799	+	0.135692i	0.335425	+	0.00683606i
$395$	1.82834	+	4.41400i	0.0919938	+	0.222093i
$396$	−7.18664	+	2.63917i	−0.361142	+	0.132623i
$397$	21.9201	+	9.07961i	1.10014	+	0.455693i	0.857531	−	0.514432i	$-0.171997\pi$
$397$	21.9201	+	9.07961i	1.10014	+	0.455693i	0.242608	+	0.970124i	$0.421997\pi$
$398$	−6.48295	+	2.53183i	−0.324961	+	0.126909i
$399$			5.94764i			0.297754i
$400$	−10.8753	−	12.8102i	−0.543767	−	0.640512i
$401$		−	7.03254i		−	0.351188i	−0.984463	−	0.175594i	$-0.943815\pi$
$401$		−	7.03254i		−	0.351188i	0.984463	−	0.175594i	$-0.0561846\pi$
$402$	−7.42806	−	19.0202i	−0.370478	−	0.948639i
$403$	−15.8206	−	6.55310i	−0.788079	−	0.326433i
$404$	−6.98078	−	3.23076i	−0.347307	−	0.160736i
$405$	0.342068	+	0.825824i	0.0169975	+	0.0410355i
$406$	0.309079	−	15.1656i	0.0153394	−	0.752655i
$407$	−21.5023	−	21.5023i	−1.06583	−	1.06583i
$408$	0.791801	−	12.9361i	0.0392000	−	0.640431i
$409$	−5.52966	+	5.52966i	−0.273424	+	0.273424i	−0.830477	−	0.557053i	$-0.811932\pi$
$409$	−5.52966	+	5.52966i	−0.273424	+	0.273424i	0.557053	+	0.830477i	$0.311932\pi$
$410$	1.68283	+	1.75285i	0.0831093	+	0.0865673i
$411$	4.09980	−	1.69819i	0.202228	−	0.0837657i
$412$	9.34166	+	0.380930i	0.460231	+	0.0187671i
$413$	0.153125	−	0.369676i	0.00753478	−	0.0181906i
$414$	−4.34504	+	9.91353i	−0.213547	+	0.487223i
$415$	5.45903			0.267973
$416$	14.2928	−	11.6413i	0.700762	−	0.570760i
$417$	9.42388			0.461489
$418$	7.76176	−	17.7090i	0.379640	−	0.866177i
$419$	−7.37792	+	17.8119i	−0.360435	+	0.870167i	0.634801	+	0.772675i	$0.281082\pi$
$419$	−7.37792	+	17.8119i	−0.360435	+	0.870167i	−0.995236	+	0.0974917i	$0.968918\pi$
$420$	0.121294	−	2.97452i	0.00591853	−	0.145142i
$421$	−5.73622	+	2.37602i	−0.279566	+	0.115800i	−0.518061	−	0.855344i	$-0.673346\pi$
$421$	−5.73622	+	2.37602i	−0.279566	+	0.115800i	0.238495	+	0.971144i	$0.423346\pi$
$422$	5.04751	+	5.25753i	0.245709	+	0.255932i
$423$	5.77253	−	5.77253i	0.280670	−	0.280670i
$424$	−17.3748	+	15.3705i	−0.843793	+	0.746456i
$425$	−13.6116	−	13.6116i	−0.660257	−	0.660257i
$426$	−0.0616463	+	3.02480i	−0.00298677	+	0.146552i
$427$	−4.44387	−	10.7284i	−0.215054	−	0.519186i
$428$	10.9531	−	23.6666i	0.529439	−	1.14397i
$429$	−11.5245	−	4.77360i	−0.556407	−	0.230471i
$430$	3.55432	+	9.10111i	0.171404	+	0.438895i
$431$		−	16.9436i		−	0.816146i	−0.912949	−	0.408073i	$-0.866201\pi$
$431$		−	16.9436i		−	0.816146i	0.912949	−	0.408073i	$-0.133799\pi$
$432$	−1.22476	−	3.80788i	−0.0589265	−	0.183207i
$433$		−	26.4587i		−	1.27152i	−0.771886	−	0.635761i	$-0.780686\pi$
$433$		−	26.4587i		−	1.27152i	0.771886	−	0.635761i	$-0.219314\pi$
$434$	11.5275	−	4.50191i	0.553337	−	0.216098i
$435$	5.31920	+	2.20328i	0.255036	+	0.105639i
$436$	−3.10838	−	8.46432i	−0.148864	−	0.405367i
$437$	−10.4611	−	25.2554i	−0.500424	−	1.20813i
$438$	19.2496	+	0.392314i	0.919783	+	0.0187455i
$439$	9.68299	+	9.68299i	0.462144	+	0.462144i	0.899358	−	0.437214i	$-0.144035\pi$
$439$	9.68299	+	9.68299i	0.462144	+	0.462144i	−0.437214	+	0.899358i	$0.644035\pi$
$440$	−4.24295	+	8.69831i	−0.202274	+	0.414676i
$441$	2.98894	−	2.98894i	0.142330	−	0.142330i
$442$	15.2328	−	14.6243i	0.724551	−	0.695608i
$443$	10.4314	−	4.32084i	0.495612	−	0.205289i	−0.120855	−	0.992670i	$-0.538563\pi$
$443$	10.4314	−	4.32084i	0.495612	−	0.205289i	0.616467	+	0.787381i	$0.288563\pi$
$444$	11.6827	−	10.7673i	0.554437	−	0.510992i
$445$	2.46240	−	5.94476i	0.116729	−	0.281809i
$446$	−16.3261	−	7.15565i	−0.773065	−	0.338830i
$447$	−2.63040			−0.124414
$448$	−1.62474	+	13.2224i	−0.0767620	+	0.624701i
$449$	−23.6353			−1.11542			−0.557708	−	0.830037i	$-0.688319\pi$
$449$	−23.6353			−1.11542			−0.557708	+	0.830037i	$0.688319\pi$
$450$	−5.44141	−	2.38494i	−0.256511	−	0.112427i
$451$	−2.81585	+	6.79805i	−0.132593	+	0.320108i
$452$	23.1888	−	21.3717i	1.09071	−	1.00524i
$453$	−18.7863	+	7.78155i	−0.882658	+	0.365609i
$454$	−4.91721	+	4.72079i	−0.230776	+	0.221557i
$455$	3.42982	−	3.42982i	0.160792	−	0.160792i
$456$	9.07956	+	4.42891i	0.425189	+	0.207403i
$457$	23.4812	+	23.4812i	1.09840	+	1.09840i	0.994597	+	0.103807i	$0.0331025\pi$
$457$	23.4812	+	23.4812i	1.09840	+	1.09840i	0.103807	+	0.994597i	$0.466898\pi$
$458$	29.6834	+	0.604958i	1.38702	+	0.0282678i
$459$	−1.75351	−	4.23336i	−0.0818470	−	0.197596i
$460$	4.71675	+	12.8440i	0.219920	+	0.598855i
$461$	25.8692	+	10.7154i	1.20485	+	0.499064i	0.892562	−	0.450924i	$-0.148905\pi$
$461$	25.8692	+	10.7154i	1.20485	+	0.499064i	0.312286	+	0.949988i	$0.398905\pi$
$462$	8.39719	−	3.27941i	0.390673	−	0.152572i
$463$			19.5222i			0.907272i	0.891187	+	0.453636i	$0.149873\pi$
$463$			19.5222i			0.907272i	−0.891187	+	0.453636i	$0.850127\pi$
$464$	−22.9213	−	11.7649i	−1.06410	−	0.546171i
$465$			4.69722i			0.217828i
$466$	−9.76103	−	24.9939i	−0.452171	−	1.15782i
$467$	−5.42932	−	2.24890i	−0.251239	−	0.104067i	0.253510	−	0.967333i	$-0.418415\pi$
$467$	−5.42932	−	2.24890i	−0.251239	−	0.104067i	−0.504749	+	0.863266i	$0.668415\pi$
$468$	2.73732	−	5.91460i	0.126533	−	0.273402i
$469$	9.20107	+	22.2133i	0.424866	+	1.02572i
$470$	0.210276	−	10.3176i	0.00969930	−	0.475915i
$471$	3.88092	+	3.88092i	0.178824	+	0.178824i
$472$	−0.450316	−	0.509037i	−0.0207275	−	0.0234303i
$473$	−20.9211	+	20.9211i	−0.961951	+	0.961951i
$474$	−5.23495	−	5.45277i	−0.240449	−	0.250454i
$475$	13.8624	−	5.74198i	0.636049	−	0.263460i
$476$	−0.621779	+	15.2481i	−0.0284992	+	0.698893i
$477$	−3.13863	+	7.57731i	−0.143708	+	0.346941i
$478$	−2.59946	+	5.93087i	−0.118897	+	0.271272i
$479$	14.2300			0.650187			0.325094	−	0.945682i	$-0.394604\pi$
$479$	14.2300			0.650187			0.325094	+	0.945682i	$0.394604\pi$
$480$	−4.45053	−	2.40014i	−0.203138	−	0.109551i
$481$	25.8863			1.18031
$482$	−8.28346	+	18.8993i	−0.377301	+	0.860841i
$483$	4.87736	−	11.7750i	0.221928	−	0.535781i
$484$	−7.30048	−	0.297696i	−0.331840	−	0.0135316i
$485$	15.7027	−	6.50427i	0.713023	−	0.295344i
$486$	−0.979416	−	1.02017i	−0.0444272	−	0.0462758i
$487$	17.2727	−	17.2727i	0.782700	−	0.782700i	−0.197586	−	0.980286i	$-0.563310\pi$
$487$	17.2727	−	17.2727i	0.782700	−	0.782700i	0.980286	+	0.197586i	$0.0633102\pi$
$488$	−19.6870	−	1.20502i	−0.891188	−	0.0545485i
$489$	7.66164	+	7.66164i	0.346471	+	0.346471i
$490$	0.108878	−	5.34230i	0.00491860	−	0.241341i
$491$	−2.16195	−	5.21940i	−0.0975673	−	0.235548i	0.867558	−	0.497335i	$-0.165688\pi$
$491$	−2.16195	−	5.21940i	−0.0975673	−	0.235548i	−0.965126	+	0.261787i	$0.915688\pi$
$492$	−3.48890	−	1.61469i	−0.157292	−	0.0727959i
$493$	−27.2674	−	11.2945i	−1.22806	−	0.508680i
$494$	5.98771	+	15.3320i	0.269400	+	0.689819i
$495$			3.42168i			0.153793i
$496$	1.71143	−	20.9500i	0.0768453	−	0.940683i
$497$		−	3.56243i		−	0.159797i
$498$	−8.04515	+	3.14193i	−0.360512	+	0.140793i
$499$	−14.2581	−	5.90591i	−0.638281	−	0.264385i	0.0399860	−	0.999200i	$-0.487269\pi$
$499$	−14.2581	−	5.90591i	−0.638281	−	0.264385i	−0.678267	+	0.734816i	$0.737269\pi$
$500$	−15.4407	+	5.67033i	−0.690528	+	0.253585i
$501$	2.91268	+	7.03184i	0.130129	+	0.314159i
$502$	2.92792	+	0.0596719i	0.130679	+	0.00266329i
$503$	−9.06568	−	9.06568i	−0.404219	−	0.404219i	0.475498	−	0.879717i	$-0.342268\pi$
$503$	−9.06568	−	9.06568i	−0.404219	−	0.404219i	−0.879717	+	0.475498i	$0.842268\pi$
$504$	1.53322	+	4.45346i	0.0682950	+	0.198373i
$505$	−2.43094	+	2.43094i	−0.108176	+	0.108176i
$506$	−29.8888	+	28.6949i	−1.32872	+	1.27564i
$507$	−2.19990	+	0.911227i	−0.0977008	+	0.0404690i
$508$	7.62490	+	8.27319i	0.338300	+	0.367063i
$509$	8.46300	−	20.4315i	0.375116	−	0.905610i	−0.617750	−	0.786375i	$-0.711956\pi$
$509$	8.46300	−	20.4315i	0.375116	−	0.905610i	0.992866	−	0.119236i	$-0.0380444\pi$
$510$	−5.30518	−	2.32523i	−0.234917	−	0.102963i
$511$	−22.6711			−1.00291
$512$	18.9752	+	12.3264i	0.838595	+	0.544755i
$513$	3.57165			0.157692
$514$	27.7202	+	12.1496i	1.22269	+	0.535895i
$515$	1.59907	−	3.86049i	0.0704633	−	0.170114i
$516$	−10.4762	−	11.3669i	−0.461190	−	0.500401i
$517$	28.8712	−	11.9588i	1.26975	−	0.525949i
$518$	−13.4952	+	12.9561i	−0.592945	+	0.569259i
$519$	−7.36654	+	7.36654i	−0.323355	+	0.323355i
$520$	−2.68188	−	7.78992i	−0.117608	−	0.341610i
$521$	−6.25345	−	6.25345i	−0.273969	−	0.273969i	0.556727	−	0.830696i	$-0.312057\pi$
$521$	−6.25345	−	6.25345i	−0.273969	−	0.273969i	−0.830696	+	0.556727i	$0.812057\pi$
$522$	−9.10717	−	0.185607i	−0.398610	−	0.00812380i
$523$	0.570636	+	1.37764i	0.0249522	+	0.0602399i	0.935865	−	0.352360i	$-0.114621\pi$
$523$	0.570636	+	1.37764i	0.0249522	+	0.0602399i	−0.910912	+	0.412600i	$0.864621\pi$
$524$	13.5923	−	4.99156i	0.593784	−	0.218057i
$525$	6.46315	+	2.67712i	0.282075	+	0.116839i
$526$	−7.72904	+	3.01847i	−0.337002	+	0.131612i
$527$		−	24.0790i		−	1.04890i
$528$	1.24669	−	15.2610i	0.0542551	−	0.664150i
$529$			35.5787i			1.54690i
$530$	3.77159	+	9.65747i	0.163827	+	0.419493i
$531$	−0.221996	−	0.0919539i	−0.00963382	−	0.00399046i
$532$	−10.7952	−	4.99611i	−0.468032	−	0.216609i
$533$	−2.39707	−	5.78703i	−0.103829	−	0.250664i
$534$	−0.207435	+	10.1782i	−0.00897661	+	0.440455i
$535$	−8.24152	−	8.24152i	−0.356312	−	0.356312i
$536$	40.7621	+	2.49499i	1.76065	+	0.107767i
$537$	−9.78207	+	9.78207i	−0.422127	+	0.422127i
$538$	−29.6873	−	30.9226i	−1.27991	−	1.33317i
$539$	14.9491	−	6.19211i	0.643902	−	0.266713i
$540$	−1.78625	−	0.0728388i	−0.0768678	−	0.00313448i
$541$	−12.3150	+	29.7310i	−0.529463	+	1.27824i	0.402413	+	0.915458i	$0.368172\pi$
$541$	−12.3150	+	29.7310i	−0.529463	+	1.27824i	−0.931876	+	0.362778i	$0.881828\pi$
$542$	−5.86840	+	13.3892i	−0.252069	+	0.575115i
$543$	21.4594			0.920912
$544$	22.8144	+	12.3037i	0.978159	+	0.527515i
$545$	−4.03000			−0.172626
$546$	−3.08062	+	7.02866i	−0.131838	+	0.300799i
$547$	12.9326	−	31.2221i	0.552959	−	1.33496i	−0.362287	−	0.932067i	$-0.618004\pi$
$547$	12.9326	−	31.2221i	0.552959	−	1.33496i	0.915246	−	0.402895i	$-0.131996\pi$
$548$	−0.361608	+	8.86781i	−0.0154471	+	0.378814i
$549$	−6.44260	+	2.66861i	−0.274964	+	0.113894i
$550$	−15.7503	−	16.4056i	−0.671593	−	0.699538i
$551$	16.2672	−	16.2672i	0.693006	−	0.693006i
$552$	−14.3436	−	16.2139i	−0.610502	−	0.690111i
$553$	6.29369	+	6.29369i	0.267635	+	0.267635i
$554$	−0.481551	+	23.6282i	−0.0204591	+	1.00387i
$555$	−2.71734	−	6.56023i	−0.115345	−	0.278466i
$556$	−7.91621	+	17.1047i	−0.335722	+	0.725402i
$557$	−2.78310	−	1.15280i	−0.117924	−	0.0488456i	0.322941	−	0.946419i	$-0.395328\pi$
$557$	−2.78310	−	1.15280i	−0.117924	−	0.0488456i	−0.440865	+	0.897573i	$0.645328\pi$
$558$	−2.70347	−	6.92244i	−0.114447	−	0.293050i
$559$		−	25.1866i		−	1.06528i
$560$	5.29699	+	2.71880i	0.223839	+	0.114890i
$561$		−	17.5403i		−	0.740552i
$562$	−14.6361	+	5.71592i	−0.617386	+	0.241112i
$563$	35.0055	+	14.4998i	1.47531	+	0.611092i	0.968062	−	0.250709i	$-0.0806638\pi$
$563$	35.0055	+	14.4998i	1.47531	+	0.611092i	0.507245	+	0.861802i	$0.330664\pi$
$564$	5.62836	+	15.3264i	0.236997	+	0.645358i
$565$	−5.39358	−	13.0213i	−0.226910	−	0.547808i
$566$	−10.3585	−	0.211109i	−0.435399	−	0.00887357i
$567$	1.17750	+	1.17750i	0.0494503	+	0.0494503i
$568$	−5.43834	−	2.65277i	−0.228188	−	0.111308i
$569$	11.2443	−	11.2443i	0.471387	−	0.471387i	−0.430976	−	0.902363i	$-0.641831\pi$
$569$	11.2443	−	11.2443i	0.471387	−	0.471387i	0.902363	+	0.430976i	$0.141831\pi$
$570$	3.25697	−	3.12686i	0.136419	−	0.130970i
$571$	−17.4655	+	7.23445i	−0.730909	+	0.302752i	−0.716925	−	0.697150i	$-0.754451\pi$
$571$	−17.4655	+	7.23445i	−0.730909	+	0.302752i	−0.0139834	+	0.999902i	$0.504451\pi$
$572$	18.3450	−	16.9075i	0.767044	−	0.706938i
$573$	−3.97117	+	9.58726i	−0.165898	+	0.400514i
$574$	4.14606	+	1.81719i	0.173053	+	0.0758482i
$575$	−32.1531			−1.34088
$576$	7.94028	+	0.975685i	0.330845	+	0.0406535i
$577$	−1.06924			−0.0445129			−0.0222564	−	0.999752i	$-0.507085\pi$
$577$	−1.06924			−0.0445129			−0.0222564	+	0.999752i	$0.507085\pi$
$578$	5.17605	+	2.26863i	0.215295	+	0.0943626i
$579$	−3.35265	+	8.09401i	−0.139331	+	0.336376i
$580$	−8.46726	+	7.80377i	−0.351584	+	0.324034i
$581$	9.39581	−	3.89187i	0.389804	−	0.161462i
$582$	−19.3981	+	18.6232i	−0.804076	+	0.771956i
$583$	−22.2000	+	22.2000i	−0.919429	+	0.919429i
$584$	−16.8821	+	34.6093i	−0.698585	+	1.43214i
$585$	−2.05966	−	2.05966i	−0.0851565	−	0.0851565i
$586$	−18.8849	−	0.384881i	−0.780129	−	0.0158993i
$587$	−5.82611	−	14.0655i	−0.240469	−	0.580544i	0.756860	−	0.653577i	$-0.226732\pi$
$587$	−5.82611	−	14.0655i	−0.240469	−	0.580544i	−0.997330	+	0.0730327i	$0.976732\pi$
$588$	2.91429	+	7.93579i	0.120183	+	0.327267i
$589$	17.3402	+	7.18253i	0.714488	+	0.295951i
$590$	−0.282939	+	0.110498i	−0.0116484	+	0.00454914i
$591$			4.70889i			0.193698i
$592$	9.72935	+	30.2493i	0.399874	+	1.24324i
$593$			41.5874i			1.70779i	0.520447	+	0.853894i	$0.325765\pi$
$593$			41.5874i			1.70779i	−0.520447	+	0.853894i	$0.674235\pi$
$594$	−1.96934	−	5.04264i	−0.0808028	−	0.206902i
$595$	6.30134	+	2.61010i	0.258330	+	0.107004i
$596$	2.20958	−	4.77429i	0.0905079	−	0.195562i
$597$	−1.88331	−	4.54671i	−0.0770787	−	0.186084i
$598$	0.718695	−	35.2641i	0.0293896	−	1.44206i
$599$	2.97009	+	2.97009i	0.121354	+	0.121354i	0.765176	−	0.643821i	$-0.222652\pi$
$599$	2.97009	+	2.97009i	0.121354	+	0.121354i	−0.643821	+	0.765176i	$0.722652\pi$
$600$	8.89963	−	7.87300i	0.363326	−	0.321414i
$601$	24.7211	−	24.7211i	1.00840	−	1.00840i	0.00843176	−	0.999964i	$-0.497316\pi$
$601$	24.7211	−	24.7211i	1.00840	−	1.00840i	0.999964	−	0.00843176i	$-0.00268394\pi$
$602$	12.6059	+	13.1304i	0.513778	+	0.535156i
$603$	13.3395	−	5.52539i	0.543225	−	0.225011i
$604$	1.65698	−	40.6345i	0.0674215	−	1.65340i
$605$	−1.24967	+	3.01696i	−0.0508062	+	0.122657i
$606$	2.18344	−	4.98168i	0.0886962	−	0.202367i
$607$	−6.96020			−0.282506			−0.141253	−	0.989974i	$-0.545113\pi$
$607$	−6.96020			−0.282506			−0.141253	+	0.989974i	$0.545113\pi$
$608$	−15.6656	+	12.7594i	−0.635325	+	0.517462i
$609$	10.7259			0.434636
$610$	−3.53869	+	8.07378i	−0.143277	+	0.326898i
$611$	−10.1803	+	24.5774i	−0.411850	+	0.994294i
$612$	9.15670	+	0.373388i	0.370138	+	0.0150933i
$613$	7.35571	−	3.04684i	0.297094	−	0.123061i	−0.229157	−	0.973389i	$-0.573597\pi$
$613$	7.35571	−	3.04684i	0.297094	−	0.123061i	0.526252	+	0.850329i	$0.323597\pi$
$614$	7.92268	+	8.25233i	0.319733	+	0.333037i
$615$	−1.21495	+	1.21495i	−0.0489916	+	0.0489916i
$616$	−1.10151	+	17.9960i	−0.0443812	+	0.725079i
$617$	−9.81719	−	9.81719i	−0.395225	−	0.395225i	0.481320	−	0.876545i	$-0.340158\pi$
$617$	−9.81719	−	9.81719i	−0.395225	−	0.395225i	−0.876545	+	0.481320i	$0.840158\pi$
$618$	−0.134707	+	6.60967i	−0.00541872	+	0.265880i
$619$	−4.68397	−	11.3081i	−0.188265	−	0.454511i	0.801361	−	0.598181i	$-0.204110\pi$
$619$	−4.68397	−	11.3081i	−0.188265	−	0.454511i	−0.989626	+	0.143670i	$0.954110\pi$
$620$	−8.52564	−	3.94574i	−0.342398	−	0.158465i
$621$	−7.07107	−	2.92893i	−0.283752	−	0.117534i
$622$	−9.10747	−	23.3204i	−0.365176	−	0.935063i
$623$		−	11.9873i		−	0.480262i
$624$	8.43584	+	9.93671i	0.337704	+	0.397787i
$625$		−	13.6535i		−	0.546138i
$626$	−3.93124	+	1.53529i	−0.157124	+	0.0613626i
$627$	12.6314	+	5.23210i	0.504450	+	0.208950i
$628$	−10.3041	+	3.78400i	−0.411177	+	0.150998i
$629$	13.9297	+	33.6292i	0.555412	+	1.34088i
$630$	2.10461	+	0.0428927i	0.0838498	+	0.00170889i
$631$	−29.7384	−	29.7384i	−1.18387	−	1.18387i	−0.978735	−	0.205130i	$-0.934238\pi$
$631$	−29.7384	−	29.7384i	−1.18387	−	1.18387i	−0.205130	−	0.978735i	$-0.565762\pi$
$632$	14.2944	−	4.92123i	0.568602	−	0.195756i
$633$	−3.64414	+	3.64414i	−0.144841	+	0.144841i
$634$	−35.4880	+	34.0703i	−1.40941	+	1.35311i
$635$	4.64567	−	1.92430i	0.184358	−	0.0763635i
$636$	−11.1166	−	12.0618i	−0.440803	−	0.478281i
$637$	−5.27121	+	12.7258i	−0.208853	+	0.504215i
$638$	−31.9363	−	13.9975i	−1.26437	−	0.554166i
$639$	−2.13930			−0.0846293
$640$	8.09487	−	6.06173i	0.319978	−	0.239611i
$641$	10.7253			0.423623			0.211811	−	0.977311i	$-0.432064\pi$
$641$	10.7253			0.423623			0.211811	+	0.977311i	$0.432064\pi$
$642$	16.8892	+	7.40242i	0.666562	+	0.292150i
$643$	−6.96903	+	16.8247i	−0.274832	+	0.663502i	−0.999677	−	0.0254092i	$-0.991911\pi$
$643$	−6.96903	+	16.8247i	−0.274832	+	0.663502i	0.724846	+	0.688911i	$0.241911\pi$
$644$	17.2750	+	18.7438i	0.680732	+	0.738609i
$645$	−6.38291	+	2.64389i	−0.251327	+	0.104103i
$646$	−16.6959	+	16.0290i	−0.656893	+	0.630652i
$647$	33.4123	−	33.4123i	1.31357	−	1.31357i	0.394808	−	0.918764i	$-0.370811\pi$
$647$	33.4123	−	33.4123i	1.31357	−	1.31357i	0.918764	−	0.394808i	$-0.129189\pi$
$648$	2.67437	−	0.920723i	0.105059	−	0.0361694i
$649$	−0.650403	−	0.650403i	−0.0255306	−	0.0255306i
$650$	19.3560	+	0.394482i	0.759207	+	0.0154729i
$651$	3.34876	+	8.08461i	0.131248	+	0.316861i
$652$	−20.3421	+	7.47029i	−0.796657	+	0.292559i
$653$	−10.9408	−	4.53181i	−0.428145	−	0.177343i	0.158196	−	0.987408i	$-0.449432\pi$
$653$	−10.9408	−	4.53181i	−0.428145	−	0.177343i	−0.586341	+	0.810064i	$0.699432\pi$
$654$	5.93915	−	2.31945i	0.232239	−	0.0906979i
$655$		−	6.47154i		−	0.252864i
$656$	5.86146	−	4.97613i	0.228852	−	0.194285i
$657$			13.6144i			0.531148i
$658$	−6.99374	−	17.9080i	−0.272644	−	0.698128i
$659$	−0.739338	−	0.306244i	−0.0288005	−	0.0119296i	0.368237	−	0.929732i	$-0.379962\pi$
$659$	−0.739338	−	0.306244i	−0.0288005	−	0.0119296i	−0.397037	+	0.917803i	$0.629962\pi$
$660$	−6.21049	−	2.87427i	−0.241743	−	0.111881i
$661$	3.14127	+	7.58370i	0.122181	+	0.294972i	0.973122	−	0.230290i	$-0.0739674\pi$
$661$	3.14127	+	7.58370i	0.122181	+	0.294972i	−0.850941	+	0.525262i	$0.823967\pi$
$662$	−0.0954387	+	4.68289i	−0.00370933	+	0.182006i
$663$	10.5583	+	10.5583i	0.410050	+	0.410050i
$664$	1.05533	−	17.2416i	0.0409549	−	0.669102i
$665$	−3.75926	+	3.75926i	−0.145778	+	0.145778i
$666$	7.78035	+	8.10408i	0.301482	+	0.314027i
$667$	−45.5453	+	18.8655i	−1.76352	+	0.730475i
$668$	−15.2098	−	0.620218i	−0.588484	−	0.0239969i
$669$	4.82353	−	11.6450i	0.186488	−	0.450223i
$670$	7.32688	−	16.7168i	0.283062	−	0.645827i
$671$	−26.6940			−1.03051
$672$	−9.37114	−	0.958120i	−0.361500	−	0.0369603i
$673$	32.0221			1.23436			0.617180	−	0.786822i	$-0.288275\pi$
$673$	32.0221			1.23436			0.617180	+	0.786822i	$0.288275\pi$
$674$	5.76412	−	13.1513i	0.222026	−	0.506568i
$675$	1.60765	−	3.88122i	0.0618787	−	0.149388i
$676$	0.194034	−	4.75835i	0.00746284	−	0.183013i
$677$	−22.8528	+	9.46594i	−0.878304	+	0.363805i	−0.775839	−	0.630931i	$-0.782673\pi$
$677$	−22.8528	+	9.46594i	−0.878304	+	0.363805i	−0.102465	+	0.994737i	$0.532673\pi$
$678$	15.4430	+	16.0856i	0.593086	+	0.617764i
$679$	22.3897	−	22.3897i	0.859236	−	0.859236i
$680$	8.67682	−	7.67589i	0.332741	−	0.294357i
$681$	−3.40825	−	3.40825i	−0.130605	−	0.130605i
$682$	0.579658	−	28.4420i	0.0221962	−	1.08910i
$683$	6.46834	+	15.6160i	0.247504	+	0.597528i	0.997991	−	0.0633577i	$-0.0201809\pi$
$683$	6.46834	+	15.6160i	0.247504	+	0.597528i	−0.750487	+	0.660885i	$0.770181\pi$
$684$	−3.00024	+	6.48269i	−0.114717	+	0.247872i
$685$	3.66467	+	1.51796i	0.140020	+	0.0579981i
$686$	−9.61815	−	24.6280i	−0.367223	−	0.940303i
$687$			20.9937i			0.800960i
$688$	29.4316	−	9.46637i	1.12207	−	0.360902i
$689$		−	26.7263i		−	1.01819i
$690$	−9.01225	+	3.51961i	−0.343090	+	0.133989i
$691$	23.6307	+	9.78817i	0.898955	+	0.372359i	0.783818	−	0.620990i	$-0.213269\pi$
$691$	23.6307	+	9.78817i	0.898955	+	0.372359i	0.115137	+	0.993350i	$0.463269\pi$
$692$	−7.18256	−	19.5586i	−0.273040	−	0.743506i
$693$	2.43940	+	5.88923i	0.0926650	+	0.223713i
$694$	39.7592	+	0.810306i	1.50924	+	0.0307588i
$695$	5.95644	+	5.95644i	0.225941	+	0.225941i
$696$	7.98705	−	16.3740i	0.302749	−	0.620654i
$697$	6.22811	−	6.22811i	0.235907	−	0.235907i
$698$	−15.2283	+	14.6199i	−0.576398	+	0.553373i
$699$	17.5290	−	7.26077i	0.663009	−	0.274628i
$700$	−10.2882	+	9.48205i	−0.388859	+	0.358388i
$701$	−9.69117	+	23.3965i	−0.366030	+	0.883675i	0.628362	+	0.777921i	$0.283726\pi$
$701$	−9.69117	+	23.3965i	−0.366030	+	0.883675i	−0.994392	+	0.105754i	$0.966274\pi$
$702$	4.22082	+	1.84996i	0.159305	+	0.0698223i
$703$	−28.3727			−1.07010
$704$	26.6521	+	15.0823i	1.00449	+	0.568434i
$705$	7.29716			0.274827
$706$	24.4072	+	10.6975i	0.918577	+	0.402606i
$707$	−2.45094	+	5.91709i	−0.0921771	+	0.222535i
$708$	0.353380	−	0.325690i	0.0132808	−	0.0122402i
$709$	−11.9720	+	4.95898i	−0.449619	+	0.186238i	−0.595991	−	0.802991i	$-0.703240\pi$
$709$	−11.9720	+	4.95898i	−0.449619	+	0.186238i	0.146372	+	0.989230i	$0.453240\pi$
$710$	−1.95081	+	1.87288i	−0.0732126	+	0.0702881i
$711$	3.77946	−	3.77946i	0.141741	−	0.141741i
$712$	−18.2996	−	8.92637i	−0.685808	−	0.334530i
$713$	−28.4396	−	28.4396i	−1.06507	−	1.06507i
$714$	−10.7887	−	0.219878i	−0.403758	−	0.00822871i
$715$	−4.26695	−	10.3013i	−0.159575	−	0.385248i
$716$	−9.53776	−	25.9719i	−0.356443	−	0.970617i
$717$	−4.23034	−	1.75226i	−0.157985	−	0.0654395i
$718$	35.1685	−	13.7346i	1.31248	−	0.512570i
$719$			18.7152i			0.697960i	0.937130	+	0.348980i	$0.113472\pi$
$719$			18.7152i			0.697960i	−0.937130	+	0.348980i	$0.886528\pi$
$720$	1.63268	−	3.18092i	0.0608464	−	0.118546i
$721$		−	7.78449i		−	0.289910i
$722$	3.21194	+	8.22442i	0.119536	+	0.306081i
$723$	−13.4804	−	5.58377i	−0.501342	−	0.207663i
$724$	−18.0263	+	38.9497i	−0.669941	+	1.44756i
$725$	−10.3550	−	24.9993i	−0.384576	−	0.928449i
$726$	0.105273	−	5.16544i	0.00390706	−	0.191707i
$727$	37.4952	+	37.4952i	1.39062	+	1.39062i	0.823931	+	0.566690i	$0.191776\pi$
$727$	37.4952	+	37.4952i	1.39062	+	1.39062i	0.566690	+	0.823931i	$0.308224\pi$
$728$	−10.1695	−	11.4956i	−0.376908	−	0.426057i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	11.9189	+	12.4149i	0.441139	+	0.459495i
$731$	32.7202	−	13.5532i	1.21020	−	0.501282i
$732$	0.568246	−	13.9353i	0.0210030	−	0.515062i
$733$	−11.1057	+	26.8115i	−0.410198	+	0.990305i	0.574887	+	0.818233i	$0.305046\pi$
$733$	−11.1057	+	26.8115i	−0.410198	+	0.990305i	−0.985084	+	0.172072i	$0.944954\pi$
$734$	14.5712	−	33.2453i	0.537833	−	1.22711i
$735$	3.77836			0.139367
$736$	41.4778	−	12.4142i	1.52889	−	0.457592i
$737$	55.2701			2.03590
$738$	1.09125	−	2.48978i	0.0401696	−	0.0916499i
$739$	0.383327	−	0.925433i	0.0141009	−	0.0340426i	−0.916672	−	0.399640i	$-0.869135\pi$
$739$	0.383327	−	0.925433i	0.0141009	−	0.0340426i	0.930773	+	0.365597i	$0.119135\pi$
$740$	14.1897	+	0.578621i	0.521624	+	0.0212705i
$741$	−10.7528	+	4.45397i	−0.395015	+	0.163621i
$742$	13.3765	+	13.9331i	0.491067	+	0.511500i
$743$	−34.4148	+	34.4148i	−1.26256	+	1.26256i	−0.312708	+	0.949849i	$0.601236\pi$
$743$	−34.4148	+	34.4148i	−1.26256	+	1.26256i	−0.949849	+	0.312708i	$0.898764\pi$
$744$	14.8355	+	0.908061i	0.543895	+	0.0332911i
$745$	−1.66257	−	1.66257i	−0.0609118	−	0.0609118i
$746$	0.234498	−	11.5061i	0.00858559	−	0.421269i
$747$	−2.33713	−	5.64233i	−0.0855111	−	0.206442i
$748$	31.8364	+	14.7341i	1.16405	+	0.538733i
$749$	−20.0605	−	8.30931i	−0.732993	−	0.303616i
$750$	−4.23117	−	10.8342i	−0.154500	−	0.395611i
$751$		−	20.2742i		−	0.739816i	−0.929068	−	0.369908i	$-0.879389\pi$
$751$		−	20.2742i		−	0.739816i	0.929068	−	0.369908i	$-0.120611\pi$
$752$	−32.5460	−	2.65871i	−1.18683	−	0.0969533i
$753$			2.07078i			0.0754634i
$754$	27.6496	−	10.7982i	1.00694	−	0.393246i
$755$	−16.7924	−	6.95566i	−0.611139	−	0.253142i
$756$	−3.12633	+	1.14809i	−0.113703	+	0.0417557i
$757$	−18.5068	−	44.6794i	−0.672641	−	1.62390i	−0.777106	−	0.629370i	$-0.783313\pi$
$757$	−18.5068	−	44.6794i	−0.672641	−	1.62390i	0.104465	−	0.994529i	$-0.466687\pi$
$758$	7.91303	+	0.161270i	0.287414	+	0.00585760i
$759$	−20.7168	−	20.7168i	−0.751971	−	0.751971i
$760$	2.93948	+	8.53814i	0.106626	+	0.309711i
$761$	13.1682	−	13.1682i	0.477345	−	0.477345i	−0.426936	−	0.904282i	$-0.640407\pi$
$761$	13.1682	−	13.1682i	0.477345	−	0.477345i	0.904282	+	0.426936i	$0.140407\pi$
$762$	−5.73895	+	5.50970i	−0.207900	+	0.199595i
$763$	−6.93624	+	2.87308i	−0.251109	+	0.104013i
$764$	−14.0654	−	15.2613i	−0.508869	−	0.552134i
$765$	1.56741	−	3.78405i	0.0566697	−	0.136813i
$766$	−43.8919	−	19.2376i	−1.58588	−	0.695081i
$767$	0.783013			0.0282730
$768$	−8.44087	+	13.5923i	−0.304584	+	0.490471i
$769$	−40.4343			−1.45810			−0.729049	−	0.684461i	$-0.760037\pi$
$769$	−40.4343			−1.45810			−0.729049	+	0.684461i	$0.760037\pi$
$770$	7.38029	+	3.23474i	0.265967	+	0.116572i
$771$	−8.18988	+	19.7721i	−0.294951	+	0.712075i
$772$	−11.8747	−	12.8843i	−0.427379	−	0.463716i
$773$	2.36151	−	0.978168i	0.0849375	−	0.0351823i	−0.339810	−	0.940494i	$-0.610363\pi$
$773$	2.36151	−	0.978168i	0.0849375	−	0.0351823i	0.424748	+	0.905312i	$0.360363\pi$
$774$	7.88503	−	7.57005i	0.283421	−	0.272100i
$775$	15.6101	−	15.6101i	0.560732	−	0.560732i
$776$	−17.5072	−	50.8521i	−0.628470	−	1.82548i
$777$	−9.35389	−	9.35389i	−0.335569	−	0.335569i
$778$	4.69184	+	0.0956211i	0.168211	+	0.00342818i
$779$	2.62731	+	6.34288i	0.0941330	+	0.227257i
$780$	5.46852	−	2.00822i	0.195804	−	0.0719059i
$781$	−7.56578	−	3.13385i	−0.270725	−	0.112138i
$782$	46.1988	−	18.0423i	1.65206	−	0.645191i
$783$		−	6.44108i		−	0.230185i
$784$	−16.8518	−	1.37664i	−0.601851	−	0.0491658i
$785$			4.90594i			0.175101i
$786$	3.72467	+	9.53733i	0.132855	+	0.340185i
$787$	27.5997	+	11.4322i	0.983825	+	0.407514i	0.815841	−	0.578276i	$-0.196274\pi$
$787$	27.5997	+	11.4322i	0.983825	+	0.407514i	0.167984	+	0.985790i	$0.446274\pi$
$788$	−8.54682	−	3.95554i	−0.304468	−	0.140910i
$789$	−2.24530	−	5.42063i	−0.0799348	−	0.192980i
$790$	0.137674	−	6.75526i	0.00489824	−	0.240341i
$791$	−18.5663	−	18.5663i	−0.660142	−	0.660142i
$792$	10.8069	+	0.661476i	0.384006	+	0.0235045i
$793$	16.0683	−	16.0683i	0.570602	−	0.570602i
$794$	−23.2378	−	24.2047i	−0.824679	−	0.858993i
$795$	−6.77310	+	2.80551i	−0.240217	+	0.0995012i
$796$	9.83447	+	0.401026i	0.348574	+	0.0142140i
$797$	−21.0345	+	50.7818i	−0.745080	+	1.79878i	−0.161238	+	0.986916i	$0.551549\pi$
$797$	−21.0345	+	50.7818i	−0.745080	+	1.79878i	−0.583842	+	0.811867i	$0.698451\pi$
$798$	3.37651	−	7.70376i	0.119527	−	0.272710i
$799$	−37.4069			−1.32336
$800$	6.81398	+	22.7666i	0.240911	+	0.804922i
$801$	−7.19858			−0.254349
$802$	−3.99242	+	9.10900i	−0.140977	+	0.321650i
$803$	−19.9437	+	48.1483i	−0.703796	+	1.69911i
$804$	−1.17656	+	28.8531i	−0.0414940	+	1.01757i
$805$	10.5253	−	4.35971i	0.370967	−	0.153659i
$806$	16.7716	+	17.4694i	0.590754	+	0.615335i
$807$	21.4333	−	21.4333i	0.754487	−	0.754487i
$808$	7.20783	+	8.14773i	0.253571	+	0.286636i
$809$	10.8210	+	10.8210i	0.380446	+	0.380446i	0.871263	−	0.490817i	$-0.163302\pi$
$809$	10.8210	+	10.8210i	0.380446	+	0.380446i	−0.490817	+	0.871263i	$0.663302\pi$
$810$	0.0257578	−	1.26385i	0.000905035	−	0.0444073i
$811$	9.28572	+	22.4177i	0.326066	+	0.787192i	0.998877	+	0.0473779i	$0.0150865\pi$
$811$	9.28572	+	22.4177i	0.326066	+	0.787192i	−0.672811	+	0.739814i	$0.734913\pi$
$812$	−9.00994	+	19.4680i	−0.316187	+	0.683192i
$813$	−9.55017	−	3.95581i	−0.334939	−	0.138736i
$814$	15.6441	+	40.0581i	0.548327	+	1.40403i
$815$			9.68520i			0.339258i
$816$	−8.36949	+	16.3061i	−0.292991	+	0.570829i
$817$			27.6058i			0.965805i
$818$	10.3016	−	4.02315i	0.360187	−	0.140666i
$819$	−5.01337	−	2.07660i	−0.175181	−	0.0725624i
$820$	−1.18461	−	3.22577i	−0.0413683	−	0.112649i
$821$	2.83930	+	6.85468i	0.0990924	+	0.239230i	0.965650	−	0.259847i	$-0.0836723\pi$
$821$	2.83930	+	6.85468i	0.0990924	+	0.239230i	−0.866557	+	0.499078i	$0.833672\pi$
$822$	−6.27440	−	0.127874i	−0.218845	−	0.00446013i
$823$	25.2545	+	25.2545i	0.880317	+	0.880317i	0.993567	−	0.113250i	$-0.0361260\pi$
$823$	25.2545	+	25.2545i	0.880317	+	0.880317i	−0.113250	+	0.993567i	$0.536126\pi$
$824$	−11.8837	−	5.79673i	−0.413987	−	0.201939i
$825$	11.3712	−	11.3712i	0.395894	−	0.395894i
$826$	−0.408204	+	0.391898i	−0.0142032	+	0.0136359i
$827$	−30.9624	+	12.8251i	−1.07667	+	0.445971i	−0.849339	−	0.527847i	$-0.822999\pi$
$827$	−30.9624	+	12.8251i	−1.07667	+	0.445971i	−0.227330	+	0.973818i	$0.572999\pi$
$828$	11.2559	−	10.3739i	0.391171	−	0.360519i
$829$	−9.26963	+	22.3789i	−0.321948	+	0.777251i	0.677193	+	0.735805i	$0.263196\pi$
$829$	−9.26963	+	22.3789i	−0.321948	+	0.777251i	−0.999141	+	0.0414451i	$0.986804\pi$
$830$	−7.07089	−	3.09913i	−0.245434	−	0.107572i
$831$	−16.7112			−0.579703
$832$	−25.1218	+	6.96440i	−0.870941	+	0.241447i
$833$	−19.3687			−0.671087
$834$	−12.2064	−	5.34999i	−0.422673	−	0.185255i
$835$	−2.60355	+	6.28552i	−0.0900994	+	0.217519i
$836$	−20.1071	+	18.5315i	−0.695417	+	0.640925i
$837$	4.85494	−	2.01098i	0.167811	−	0.0695097i
$838$	19.6683	−	18.8826i	0.679429	−	0.652288i
$839$	23.7415	−	23.7415i	0.819648	−	0.819648i	−0.166409	−	0.986057i	$-0.553217\pi$
$839$	23.7415	−	23.7415i	0.819648	−	0.819648i	0.986057	+	0.166409i	$0.0532171\pi$
$840$	−1.84576	+	3.78393i	−0.0636848	+	0.130558i
$841$	−8.83001	−	8.83001i	−0.304483	−	0.304483i
$842$	8.77880	+	0.178915i	0.302538	+	0.00616581i
$843$	−4.25181	−	10.2648i	−0.146440	−	0.353537i
$844$	−3.55312	−	9.67539i	−0.122304	−	0.333041i
$845$	−1.96641	−	0.814514i	−0.0676466	−	0.0280201i
$846$	−10.7541	+	4.19985i	−0.369732	+	0.144394i
$847$			6.08356i			0.209034i
$848$	31.2308	−	10.0451i	1.07247	−	0.344948i
$849$		−	7.32606i		−	0.251430i
$850$	9.90320	+	25.3579i	0.339677	+	0.869770i
$851$	56.1716	+	23.2670i	1.92554	+	0.797584i
$852$	1.79704	−	3.88291i	0.0615657	−	0.133026i
$853$	−7.82863	−	18.9000i	−0.268047	−	0.647123i	0.731344	−	0.682009i	$-0.238893\pi$
$853$	−7.82863	−	18.9000i	−0.268047	−	0.647123i	−0.999391	+	0.0348853i	$0.988893\pi$
$854$	−0.334624	+	16.4190i	−0.0114506	+	0.561846i
$855$	2.25749	+	2.25749i	0.0772046	+	0.0772046i
$856$	−27.6229	+	24.4364i	−0.944130	+	0.835218i
$857$	−19.1000	+	19.1000i	−0.652445	+	0.652445i	−0.953581	−	0.301136i	$-0.902634\pi$
$857$	−19.1000	+	19.1000i	−0.652445	+	0.652445i	0.301136	+	0.953581i	$0.402634\pi$
$858$	12.2172	+	12.7256i	0.417090	+	0.434445i
$859$	23.7460	−	9.83590i	0.810202	−	0.335597i	0.0611672	−	0.998128i	$-0.480518\pi$
$859$	23.7460	−	9.83590i	0.810202	−	0.335597i	0.749035	+	0.662531i	$0.230518\pi$
$860$	0.562981	−	13.8062i	0.0191975	−	0.470786i
$861$	−1.22495	+	2.95728i	−0.0417460	+	0.100784i
$862$	−9.61901	+	21.9465i	−0.327625	+	0.747500i
$863$	7.14216			0.243122			0.121561	−	0.992584i	$-0.461210\pi$
$863$	7.14216			0.243122			0.121561	+	0.992584i	$0.461210\pi$
$864$	−0.575366	+	5.62752i	−0.0195743	+	0.191452i
$865$	−9.31217			−0.316623
$866$	−15.0207	+	34.2709i	−0.510426	+	1.16457i
$867$	−1.52925	+	3.69195i	−0.0519362	+	0.125385i
$868$	−17.4869	−	0.713074i	−0.593544	−	0.0242033i
$869$	18.9029	−	7.82983i	0.641236	−	0.265609i
$870$	−5.63895	−	5.87358i	−0.191178	−	0.199133i
$871$	−33.2695	+	33.2695i	−1.12730	+	1.12730i
$872$	−0.779076	+	12.7282i	−0.0263828	+	0.431031i
$873$	−13.4453	−	13.4453i	−0.455056	−	0.455056i
$874$	−0.787725	+	38.6513i	−0.0266452	+	1.30740i
$875$	5.24110	+	12.6531i	0.177182	+	0.427754i
$876$	−24.7107	−	11.4363i	−0.834896	−	0.386397i
$877$	13.2121	+	5.47264i	0.446141	+	0.184798i	0.594432	−	0.804146i	$-0.297377\pi$
$877$	13.2121	+	5.47264i	0.446141	+	0.184798i	−0.148290	+	0.988944i	$0.547377\pi$
$878$	−7.04493	−	18.0391i	−0.237755	−	0.608791i
$879$		−	13.3564i		−	0.450501i
$880$	10.4338	−	8.85787i	0.351724	−	0.298599i
$881$		−	8.29862i		−	0.279588i	−0.990181	−	0.139794i	$-0.955356\pi$
$881$		−	8.29862i		−	0.279588i	0.990181	−	0.139794i	$-0.0446440\pi$
$882$	−5.56830	+	2.17462i	−0.187494	+	0.0732234i
$883$	23.1211	+	9.57707i	0.778087	+	0.322294i	0.736143	−	0.676826i	$-0.236645\pi$
$883$	23.1211	+	9.57707i	0.778087	+	0.322294i	0.0419435	+	0.999120i	$0.486645\pi$
$884$	−28.0328	+	10.2946i	−0.942847	+	0.346245i
$885$	−0.0821944	−	0.198435i	−0.00276293	−	0.00667031i
$886$	−15.9644	−	0.325360i	−0.536336	−	0.0109307i
$887$	27.8541	+	27.8541i	0.935249	+	0.935249i	0.998027	−	0.0627784i	$-0.0199961\pi$
$887$	27.8541	+	27.8541i	0.935249	+	0.935249i	−0.0627784	+	0.998027i	$0.519996\pi$
$888$	−21.2448	+	7.31409i	−0.712930	+	0.245445i
$889$	6.62401	−	6.62401i	0.222162	−	0.222162i
$890$	−6.56434	+	6.30212i	−0.220037	+	0.211247i
$891$	3.53657	−	1.46490i	0.118480	−	0.0490759i
$892$	17.0844	+	18.5369i	0.572026	+	0.620661i
$893$	11.1581	−	26.9380i	0.373392	−	0.901447i
$894$	3.40707	+	1.49330i	0.113949	+	0.0499433i
$895$	−12.3657			−0.413339
$896$	9.61093	−	16.2042i	0.321079	−	0.541343i
$897$	24.9407			0.832745
$898$	30.6139	+	13.4179i	1.02160	+	0.447761i
$899$	12.9529	−	31.2711i	0.432003	−	1.04295i
$900$	5.69412	+	6.17825i	0.189804	+	0.205942i
$901$	34.7204	−	14.3817i	1.15670	−	0.479123i
$902$	7.50656	−	7.20670i	0.249941	−	0.239957i
$903$	−9.10105	+	9.10105i	−0.302864	+	0.302864i
$904$	−42.1684	+	14.5176i	−1.40250	+	0.482848i
$905$	13.5636	+	13.5636i	0.450870	+	0.450870i
$906$	28.7509	+	0.585952i	0.955184	+	0.0194670i
$907$	−5.14391	−	12.4185i	−0.170801	−	0.412349i	0.815180	−	0.579207i	$-0.196638\pi$
$907$	−5.14391	−	12.4185i	−0.170801	−	0.412349i	−0.985981	+	0.166858i	$0.946638\pi$
$908$	9.04911	−	3.32313i	0.300305	−	0.110282i
$909$	3.55331	+	1.47183i	0.117856	+	0.0488175i
$910$	−6.38966	+	2.49539i	−0.211815	+	0.0827215i
$911$			43.4302i			1.43891i	0.694541	+	0.719454i	$0.255608\pi$
$911$			43.4302i			1.43891i	−0.694541	+	0.719454i	$0.744392\pi$
$912$	−9.24610	−	10.8911i	−0.306169	−	0.360641i
$913$		−	23.3782i		−	0.773705i
$914$	−17.0839	−	43.7448i	−0.565086	−	1.44695i
$915$	−5.75882	−	2.38538i	−0.190381	−	0.0788583i
$916$	−38.1044	−	17.6351i	−1.25901	−	0.582679i
$917$	−4.61371	−	11.1385i	−0.152358	−	0.367825i
$918$	−0.132040	+	6.47880i	−0.00435797	+	0.213832i
$919$	13.6438	+	13.6438i	0.450068	+	0.450068i	0.895377	−	0.445309i	$-0.146906\pi$
$919$	13.6438	+	13.6438i	0.450068	+	0.450068i	−0.445309	+	0.895377i	$0.646906\pi$
$920$	1.18219	−	19.3141i	0.0389758	−	0.636768i
$921$	−5.71992	+	5.71992i	−0.188478	+	0.188478i
$922$	−27.4242	−	28.5653i	−0.903170	−	0.940749i
$923$	6.44058	−	2.66778i	0.211994	−	0.0878110i
$924$	−12.7383	−	0.519438i	−0.419060	−	0.0170882i
$925$	−12.7710	+	30.8319i	−0.419907	+	1.01375i
$926$	11.0829	−	25.2864i	0.364205	−	0.830961i
$927$	−4.67471			−0.153538
$928$	23.0102	+	28.2512i	0.755346	+	0.927392i
$929$	52.3939			1.71899			0.859494	−	0.511146i	$-0.170779\pi$
$929$	52.3939			1.71899			0.859494	+	0.511146i	$0.170779\pi$
$930$	2.66664	−	6.08414i	0.0874426	−	0.199507i
$931$	5.77751	−	13.9481i	0.189350	−	0.457132i
$932$	−1.54609	+	37.9151i	−0.0506437	+	1.24195i
$933$	16.3554	−	6.77462i	0.535451	−	0.221791i
$934$	5.75569	+	5.99518i	0.188332	+	0.196168i
$935$	11.0865	−	11.0865i	0.362567	−	0.362567i
$936$	−6.90331	+	6.10697i	−0.225642	+	0.199613i
$937$	−18.9484	−	18.9484i	−0.619017	−	0.619017i	0.326262	−	0.945279i	$-0.394211\pi$
$937$	−18.9484	−	18.9484i	−0.619017	−	0.619017i	−0.945279	+	0.326262i	$0.894211\pi$
$938$	0.692842	−	33.9957i	0.0226221	−	1.11000i
$939$	−1.14203	−	2.75711i	−0.0372688	−	0.0899748i
$940$	−6.12973	+	13.2446i	−0.199930	+	0.431992i
$941$	−3.46272	−	1.43430i	−0.112881	−	0.0467570i	0.325528	−	0.945532i	$-0.394458\pi$
$941$	−3.46272	−	1.43430i	−0.112881	−	0.0467570i	−0.438409	+	0.898775i	$0.644458\pi$
$942$	−2.82360	−	7.23005i	−0.0919978	−	0.235568i
$943$		−	14.7120i		−	0.479088i
$944$	0.294295	+	0.914984i	0.00957848	+	0.0297802i
$945$			1.48850i			0.0484208i
$946$	38.9753	−	15.2213i	1.26720	−	0.494886i
$947$	−52.3991	−	21.7044i	−1.70274	−	0.705298i	−0.702760	−	0.711427i	$-0.748049\pi$
$947$	−52.3991	−	21.7044i	−1.70274	−	0.705298i	−0.999981	+	0.00612896i	$0.998049\pi$
$948$	3.68507	+	10.0347i	0.119686	+	0.325912i
$949$	−16.9776	−	40.9875i	−0.551116	−	1.33051i
$950$	−21.2152	−	0.432373i	−0.688312	−	0.0140280i
$951$	−24.5977	−	24.5977i	−0.797635	−	0.797635i
$952$	9.46178	−	19.3973i	0.306658	−	0.628669i
$953$	−10.0461	+	10.0461i	−0.325424	+	0.325424i	−0.850843	−	0.525419i	$-0.823908\pi$
$953$	−10.0461	+	10.0461i	−0.325424	+	0.325424i	0.525419	+	0.850843i	$0.323908\pi$
$954$	8.36704	−	8.03281i	0.270893	−	0.260072i
$955$	−8.56972	+	3.54970i	−0.277310	+	0.114865i
$956$	6.73398	−	6.20631i	0.217793	−	0.200726i
$957$	9.43552	−	22.7794i	0.305007	−	0.736352i
$958$	−18.4317	−	8.07848i	−0.595500	−	0.261004i
$959$	7.38963			0.238624
$960$	4.40203	+	5.63541i	0.142075	+	0.181882i
$961$	−3.38553			−0.109211
$962$	−33.5296	−	14.6958i	−1.08104	−	0.473813i
$963$	−4.98987	+	12.0466i	−0.160796	+	0.388197i
$964$	21.4585	−	19.7771i	0.691133	−	0.636976i
$965$	−7.23496	+	2.99682i	−0.232902	+	0.0964710i
$966$	−13.0022	+	12.4828i	−0.418339	+	0.401628i
$967$	34.5937	−	34.5937i	1.11246	−	1.11246i	0.119640	−	0.992817i	$-0.461826\pi$
$967$	34.5937	−	34.5937i	1.11246	−	1.11246i	0.992817	−	0.119640i	$-0.0381741\pi$
$968$	9.28705	+	4.53012i	0.298497	+	0.145604i
$969$	−11.5724	−	11.5724i	−0.371759	−	0.371759i
$970$	−24.0317	−	0.489773i	−0.771610	−	0.0157257i
$971$	−11.4425	−	27.6245i	−0.367206	−	0.886513i	−0.994206	−	0.107494i	$-0.965717\pi$
$971$	−11.4425	−	27.6245i	−0.367206	−	0.886513i	0.627000	−	0.779019i	$-0.284283\pi$
$972$	0.689447	+	1.87741i	0.0221140	+	0.0602179i
$973$	14.4984	+	6.00544i	0.464798	+	0.192526i
$974$	−32.1785	+	12.5669i	−1.03107	+	0.402668i
$975$			13.6896i			0.438419i
$976$	24.8157	+	12.7372i	0.794333	+	0.407709i
$977$		−	7.83370i		−	0.250622i	−0.992117	−	0.125311i	$-0.960007\pi$
$977$		−	7.83370i		−	0.250622i	0.992117	−	0.125311i	$-0.0399929\pi$
$978$	−5.57428	−	14.2734i	−0.178246	−	0.456413i
$979$	−25.4583	−	10.5452i	−0.813651	−	0.337025i
$980$	−3.17389	+	6.85788i	−0.101386	+	0.219067i
$981$	1.72533	+	4.16532i	0.0550857	+	0.132989i
$982$	−0.162795	+	7.98785i	−0.00519500	+	0.254903i
$983$	−13.3719	−	13.3719i	−0.426497	−	0.426497i	0.460937	−	0.887433i	$-0.347514\pi$
$983$	−13.3719	−	13.3719i	−0.426497	−	0.426497i	−0.887433	+	0.460937i	$0.847514\pi$
$984$	3.60237	+	4.07212i	0.114839	+	0.129814i
$985$	−2.97629	+	2.97629i	−0.0948326	+	0.0948326i
$986$	28.9065	+	30.1093i	0.920571	+	0.958875i
$987$	12.5595	−	5.20232i	0.399773	−	0.165592i
$988$	0.948415	−	23.2583i	0.0301731	−	0.739944i
$989$	22.6381	−	54.6533i	0.719851	−	1.73787i
$990$	1.94251	−	4.43198i	0.0617370	−	0.140858i
$991$	42.1375			1.33854			0.669270	−	0.743019i	$-0.266607\pi$
$991$	42.1375			1.33854			0.669270	+	0.743019i	$0.266607\pi$
$992$	−14.1102	+	26.1642i	−0.447999	+	0.830714i
$993$	−3.31199			−0.105103
$994$	−2.02242	+	4.61429i	−0.0641471	+	0.146356i
$995$	1.68342	−	4.06415i	0.0533681	−	0.128842i
$996$	12.2043	+	0.497661i	0.386708	+	0.0157690i
$997$	6.17091	−	2.55607i	0.195435	−	0.0809517i	−0.282820	−	0.959173i	$-0.591270\pi$
$997$	6.17091	−	2.55607i	0.195435	−	0.0809517i	0.478254	+	0.878221i	$0.341270\pi$
$998$	15.1152	+	15.7441i	0.478464	+	0.498372i
$999$	−5.61716	+	5.61716i	−0.177719	+	0.177719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.13.1	✓	32
3.2	odd	2		288.2.v.d.109.8		32
4.3	odd	2		384.2.n.a.145.3		32
8.3	odd	2		768.2.n.b.289.6		32
8.5	even	2		768.2.n.a.289.2		32
12.11	even	2		1152.2.v.c.145.4		32
32.5	even	8	inner	96.2.n.a.37.1	yes	32
32.11	odd	8		768.2.n.b.481.6		32
32.21	even	8		768.2.n.a.481.2		32
32.27	odd	8		384.2.n.a.241.3		32
96.5	odd	8		288.2.v.d.37.8		32
96.59	even	8		1152.2.v.c.1009.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.1	✓	32	1.1	even	1	trivial
96.2.n.a.37.1	yes	32	32.5	even	8	inner
288.2.v.d.37.8		32	96.5	odd	8
288.2.v.d.109.8		32	3.2	odd	2
384.2.n.a.145.3		32	4.3	odd	2
384.2.n.a.241.3		32	32.27	odd	8
768.2.n.a.289.2		32	8.5	even	2
768.2.n.a.481.2		32	32.21	even	8
768.2.n.b.289.6		32	8.3	odd	2
768.2.n.b.481.6		32	32.11	odd	8
1152.2.v.c.145.4		32	12.11	even	2
1152.2.v.c.1009.4		32	96.59	even	8

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29526 - 0.567706i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.35542 + 1.47066i) q^{4} +(0.825824 - 0.342068i) q^{5} +(-1.02017 + 0.979416i) q^{6} +(1.17750 - 1.17750i) q^{7} +(-0.920723 - 2.67437i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-1.29526 - 0.567706i) q^{2} +(0.382683 - 0.923880i) q^{3} +(1.35542 + 1.47066i) q^{4} +(0.825824 - 0.342068i) q^{5} +(-1.02017 + 0.979416i) q^{6} +(1.17750 - 1.17750i) q^{7} +(-0.920723 - 2.67437i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-1.26385 - 0.0257578i) q^{10} +(-1.46490 - 3.53657i) q^{11} +(1.87741 - 0.689447i) q^{12} +(3.01061 + 1.24703i) q^{13} +(-2.19365 + 0.856699i) q^{14} -0.893866i q^{15} +(-0.325679 + 3.98672i) q^{16} +4.58215i q^{17} +(0.514461 + 1.31732i) q^{18} +(-3.29978 - 1.36681i) q^{19} +(1.62240 + 0.750861i) q^{20} +(-0.637258 - 1.53848i) q^{21} +(-0.110307 + 5.41243i) q^{22} +(5.41196 + 5.41196i) q^{23} +(-2.82314 - 0.172801i) q^{24} +(-2.97056 + 2.97056i) q^{25} +(-3.19158 - 3.32438i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(3.32770 + 0.135696i) q^{28} +(-2.46490 + 5.95078i) q^{29} +(-0.507453 + 1.15779i) q^{30} -5.25495 q^{31} +(2.68513 - 4.97897i) q^{32} -3.82796 q^{33} +(2.60132 - 5.93510i) q^{34} +(0.569623 - 1.37519i) q^{35} +(0.0814874 - 1.99834i) q^{36} +(7.33917 - 3.03998i) q^{37} +(3.49813 + 3.64369i) q^{38} +(2.30422 - 2.30422i) q^{39} +(-1.67517 - 1.89361i) q^{40} +(-1.35921 - 1.35921i) q^{41} +(-0.0479856 + 2.35451i) q^{42} +(-2.95781 - 7.14079i) q^{43} +(3.21555 - 6.94790i) q^{44} +(-0.825824 - 0.342068i) q^{45} +(-3.93752 - 10.0823i) q^{46} +8.16360i q^{47} +(3.55862 + 1.82654i) q^{48} +4.22699i q^{49} +(5.53406 - 2.16125i) q^{50} +(4.23336 + 1.75351i) q^{51} +(2.24667 + 6.11783i) q^{52} +(-3.13863 - 7.57731i) q^{53} +(1.41392 + 0.0288161i) q^{54} +(-2.41949 - 2.41949i) q^{55} +(-4.23322 - 2.06492i) q^{56} +(-2.52554 + 2.52554i) q^{57} +(6.57099 - 6.30850i) q^{58} +(0.221996 - 0.0919539i) q^{59} +(1.31457 - 1.21156i) q^{60} +(2.66861 - 6.44260i) q^{61} +(6.80655 + 2.98327i) q^{62} -1.66523 q^{63} +(-6.30454 + 4.92471i) q^{64} +2.91280 q^{65} +(4.95822 + 2.17316i) q^{66} +(-5.52539 + 13.3395i) q^{67} +(-6.73879 + 6.21074i) q^{68} +(7.07107 - 2.92893i) q^{69} +(-1.51852 + 1.45786i) q^{70} +(1.51271 - 1.51271i) q^{71} +(-1.24002 + 2.54212i) q^{72} +(-9.62682 - 9.62682i) q^{73} +(-11.2320 - 0.228911i) q^{74} +(1.60765 + 3.88122i) q^{75} +(-2.46246 - 6.70545i) q^{76} +(-5.88923 - 2.43940i) q^{77} +(-4.29269 + 1.67645i) q^{78} +5.34497i q^{79} +(1.09477 + 3.40373i) q^{80} +1.00000i q^{81} +(0.988904 + 2.53217i) q^{82} +(5.64233 + 2.33713i) q^{83} +(1.39882 - 3.02247i) q^{84} +(1.56741 + 3.78405i) q^{85} +(-0.222724 + 10.9284i) q^{86} +(4.55453 + 4.55453i) q^{87} +(-8.10935 + 7.17388i) q^{88} +(5.09017 - 5.09017i) q^{89} +(0.875466 + 0.911893i) q^{90} +(5.01337 - 2.07660i) q^{91} +(-0.623678 + 15.2946i) q^{92} +(-2.01098 + 4.85494i) q^{93} +(4.63453 - 10.5740i) q^{94} -3.19258 q^{95} +(-3.57241 - 4.38610i) q^{96} +19.0146 q^{97} +(2.39969 - 5.47507i) q^{98} +(-1.46490 + 3.53657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

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