LMFDB - Embedded newform 72.2.n.b.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(13,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("72.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 $ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.7
Root			$-1.34532 + 0.436011i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05026 - 0.947078i) q^{2} +(-1.52768 - 0.816201i) q^{3} +(0.206086 - 1.98935i) q^{4} +(0.602794 + 0.348023i) q^{5} +(-2.37747 + 0.589613i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 - 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +(0.962695 - 0.205379i) q^{10} +(-2.37222 + 1.36960i) q^{11} +(-1.93855 + 2.87089i) q^{12} +(4.76780 + 2.75269i) q^{13} +(2.13924 + 0.693314i) q^{14} +(-0.636821 - 1.02367i) q^{15} +(-3.91506 - 0.819955i) q^{16} -5.65175 q^{17} +(4.11326 + 1.03975i) q^{18} +0.963328i q^{19} +(0.816569 - 1.12745i) q^{20} +(-0.0906219 - 2.75269i) q^{21} +(-1.19433 + 3.68512i) q^{22} +(3.28857 - 5.69597i) q^{23} +(0.682986 + 4.85114i) q^{24} +(-2.25776 - 3.91055i) q^{25} +(7.61444 - 1.62444i) q^{26} +(-0.512172 - 5.17085i) q^{27} +(2.90338 - 1.29787i) q^{28} +(-2.85076 + 1.64589i) q^{29} +(-1.63832 - 0.471999i) q^{30} +(-3.69844 + 6.40589i) q^{31} +(-4.88838 + 2.84670i) q^{32} +(4.74188 - 0.156108i) q^{33} +(-5.93580 + 5.35265i) q^{34} +1.10680i q^{35} +(5.30471 - 2.80357i) q^{36} -6.25538i q^{37} +(0.912347 + 1.01174i) q^{38} +(-5.03694 - 8.09673i) q^{39} +(-0.210173 - 1.95747i) q^{40} +(-0.931886 + 1.61407i) q^{41} +(-2.70219 - 2.80521i) q^{42} +(2.99838 - 1.73111i) q^{43} +(2.23574 + 5.00145i) q^{44} +(0.137339 + 2.08362i) q^{45} +(-1.94068 - 9.09677i) q^{46} +(3.85668 + 6.67997i) q^{47} +(5.31172 + 4.44811i) q^{48} +(2.23574 - 3.87242i) q^{49} +(-6.07483 - 1.96882i) q^{50} +(8.63408 + 4.61296i) q^{51} +(6.45866 - 8.91756i) q^{52} -2.54179i q^{53} +(-5.43511 - 4.94566i) q^{54} -1.90662 q^{55} +(1.82011 - 4.11282i) q^{56} +(0.786270 - 1.47166i) q^{57} +(-1.43525 + 4.42850i) q^{58} +(4.62019 + 2.66747i) q^{59} +(-2.16768 + 1.05590i) q^{60} +(-7.93715 + 4.58252i) q^{61} +(2.18256 + 10.2305i) q^{62} +(-2.10831 + 4.27921i) q^{63} +(-2.43802 + 7.61945i) q^{64} +(1.91600 + 3.31861i) q^{65} +(4.83235 - 4.65488i) q^{66} +(-5.95780 - 3.43974i) q^{67} +(-1.16474 + 11.2433i) q^{68} +(-9.67295 + 6.01750i) q^{69} +(1.04823 + 1.16243i) q^{70} +3.68351 q^{71} +(2.91612 - 7.96845i) q^{72} +2.83201 q^{73} +(-5.92433 - 6.56976i) q^{74} +(0.257341 + 7.81687i) q^{75} +(1.91640 + 0.198528i) q^{76} +(-3.77214 - 2.17785i) q^{77} +(-12.9583 - 3.73328i) q^{78} +(2.87870 + 4.98605i) q^{79} +(-2.07461 - 1.85680i) q^{80} +(-3.43802 + 8.31745i) q^{81} +(0.549933 + 2.57776i) q^{82} +(5.74968 - 3.31958i) q^{83} +(-5.49476 - 0.387012i) q^{84} +(-3.40684 - 1.96694i) q^{85} +(1.50957 - 4.65781i) q^{86} +(5.69844 - 0.187599i) q^{87} +(7.08487 + 3.13539i) q^{88} -2.98701 q^{89} +(2.11759 + 2.05827i) q^{90} +8.75427i q^{91} +(-10.6536 - 7.71598i) q^{92} +(10.8785 - 6.76749i) q^{93} +(10.3770 + 3.36312i) q^{94} +(-0.335261 + 0.580689i) q^{95} +(9.79138 - 0.358951i) q^{96} +(-1.24837 - 2.16224i) q^{97} +(-1.31938 - 6.18447i) q^{98} +(-7.37150 - 3.63184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) $ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.05026	−	0.947078i	0.742645	−	0.669685i
$2$	1.05026	−	0.947078i	0.742645	−	0.669685i
$3$	−1.52768	−	0.816201i	−0.882008	−	0.471234i
$3$	−1.52768	−	0.816201i	−0.882008	−	0.471234i
$4$	0.206086	−	1.98935i	0.103043	−	0.994677i
$5$	0.602794	+	0.348023i	0.269578	+	0.155641i	0.628696	−	0.777651i	$-0.283589\pi$
$5$	0.602794	+	0.348023i	0.269578	+	0.155641i	−0.359118	+	0.933292i	$0.616922\pi$
$6$	−2.37747	+	0.589613i	−0.970597	+	0.240708i
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	0.976251	−	0.216644i	$-0.0695111\pi$
$7$	0.795065	+	1.37709i	0.300506	+	0.520492i	−0.675745	+	0.737136i	$0.736178\pi$
$8$	−1.66763	−	2.28452i	−0.589596	−	0.807698i
$9$	1.66763	+	2.49379i	0.555877	+	0.831265i
$10$	0.962695	−	0.205379i	0.304431	−	0.0649464i
$11$	−2.37222	+	1.36960i	−0.715252	+	0.412951i	−0.813003	−	0.582260i	$-0.802169\pi$
$11$	−2.37222	+	1.36960i	−0.715252	+	0.412951i	0.0977506	+	0.995211i	$0.468835\pi$
$12$	−1.93855	+	2.87089i	−0.559610	+	0.828756i
$13$	4.76780	+	2.75269i	1.32235	+	0.763460i	0.984103	−	0.177597i	$-0.0568325\pi$
$13$	4.76780	+	2.75269i	1.32235	+	0.763460i	0.338248	+	0.941057i	$0.390166\pi$
$14$	2.13924	+	0.693314i	0.571735	+	0.185296i
$15$	−0.636821	−	1.02367i	−0.164427	−	0.264311i
$16$	−3.91506	−	0.819955i	−0.978764	−	0.204989i
$17$	−5.65175			−1.37075			−0.685375	−	0.728190i	$-0.740362\pi$
$17$	−5.65175			−1.37075			−0.685375	+	0.728190i	$0.740362\pi$
$18$	4.11326	+	1.03975i	0.969505	+	0.245072i
$19$			0.963328i			0.221003i	0.993876	+	0.110501i	$0.0352457\pi$
$19$			0.963328i			0.221003i	−0.993876	+	0.110501i	$0.964754\pi$
$20$	0.816569	−	1.12745i	0.182590	−	0.252105i
$21$	−0.0906219	−	2.75269i	−0.0197753	−	0.600687i
$22$	−1.19433	+	3.68512i	−0.254631	+	0.785670i
$23$	3.28857	−	5.69597i	0.685714	−	1.18769i	−0.287498	−	0.957781i	$-0.592823\pi$
$23$	3.28857	−	5.69597i	0.685714	−	1.18769i	0.973212	−	0.229910i	$-0.0738432\pi$
$24$	0.682986	+	4.85114i	0.139414	+	0.990234i
$25$	−2.25776	−	3.91055i	−0.451552	−	0.782111i
$26$	7.61444	−	1.62444i	1.49332	−	0.318580i
$27$	−0.512172	−	5.17085i	−0.0985676	−	0.995130i
$28$	2.90338	−	1.29787i	0.548686	−	0.245274i
$29$	−2.85076	+	1.64589i	−0.529373	+	0.305634i	−0.740761	−	0.671768i	$-0.765535\pi$
$29$	−2.85076	+	1.64589i	−0.529373	+	0.305634i	0.211388	+	0.977402i	$0.432202\pi$
$30$	−1.63832	−	0.471999i	−0.299115	−	0.0861749i
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	0.315226	+	0.949017i	$0.397920\pi$
$31$	−3.69844	+	6.40589i	−0.664259	+	1.15053i	−0.979486	+	0.201514i	$0.935414\pi$
$32$	−4.88838	+	2.84670i	−0.864152	+	0.503230i
$33$	4.74188	−	0.156108i	0.825455	−	0.0271749i
$34$	−5.93580	+	5.35265i	−1.01798	+	0.917971i
$35$			1.10680i			0.187084i
$36$	5.30471	−	2.80357i	0.884119	−	0.467262i
$37$		−	6.25538i		−	1.02838i	−0.857677	−	0.514189i	$-0.828093\pi$
$37$		−	6.25538i		−	1.02838i	0.857677	−	0.514189i	$-0.171907\pi$
$38$	0.912347	+	1.01174i	0.148002	+	0.164127i
$39$	−5.03694	−	8.09673i	−0.806556	−	1.29651i
$40$	−0.210173	−	1.95747i	−0.0332313	−	0.309503i
$41$	−0.931886	+	1.61407i	−0.145536	+	0.252076i	−0.929573	−	0.368639i	$-0.879824\pi$
$41$	−0.931886	+	1.61407i	−0.145536	+	0.252076i	0.784037	+	0.620714i	$0.213157\pi$
$42$	−2.70219	−	2.80521i	−0.416957	−	0.432854i
$43$	2.99838	−	1.73111i	0.457248	−	0.263992i	−0.253638	−	0.967299i	$-0.581627\pi$
$43$	2.99838	−	1.73111i	0.457248	−	0.263992i	0.710886	+	0.703307i	$0.248294\pi$
$44$	2.23574	+	5.00145i	0.337051	+	0.753996i
$45$	0.137339	+	2.08362i	0.0204733	+	0.310608i
$46$	−1.94068	−	9.09677i	−0.286138	−	1.34125i
$47$	3.85668	+	6.67997i	0.562555	+	0.974374i	0.997273	+	0.0738070i	$0.0235149\pi$
$47$	3.85668	+	6.67997i	0.562555	+	0.974374i	−0.434717	+	0.900567i	$0.643152\pi$
$48$	5.31172	+	4.44811i	0.766680	+	0.642029i
$49$	2.23574	−	3.87242i	0.319392	−	0.553203i
$50$	−6.07483	−	1.96882i	−0.859111	−	0.278433i
$51$	8.63408	+	4.61296i	1.20901	+	0.645944i
$52$	6.45866	−	8.91756i	0.895655	−	1.23664i
$53$		−	2.54179i		−	0.349141i	−0.984645	−	0.174571i	$-0.944146\pi$
$53$		−	2.54179i		−	0.349141i	0.984645	−	0.174571i	$-0.0558537\pi$
$54$	−5.43511	−	4.94566i	−0.739625	−	0.673019i
$55$	−1.90662			−0.257088
$56$	1.82011	−	4.11282i	0.243223	−	0.549598i
$57$	0.786270	−	1.47166i	0.104144	−	0.194926i
$58$	−1.43525	+	4.42850i	−0.188458	+	0.581491i
$59$	4.62019	+	2.66747i	0.601498	+	0.347275i	0.769631	−	0.638489i	$-0.220440\pi$
$59$	4.62019	+	2.66747i	0.601498	+	0.347275i	−0.168133	+	0.985764i	$0.553774\pi$
$60$	−2.16768	+	1.05590i	−0.279847	+	0.136316i
$61$	−7.93715	+	4.58252i	−1.01625	+	0.586731i	−0.913015	−	0.407926i	$-0.866252\pi$
$61$	−7.93715	+	4.58252i	−1.01625	+	0.586731i	−0.103233	+	0.994657i	$0.532919\pi$
$62$	2.18256	+	10.2305i	0.277185	+	1.29928i
$63$	−2.10831	+	4.27921i	−0.265622	+	0.539130i
$64$	−2.43802	+	7.61945i	−0.304752	+	0.952432i
$65$	1.91600	+	3.31861i	0.237651	+	0.411623i
$66$	4.83235	−	4.65488i	0.594821	−	0.572976i
$67$	−5.95780	−	3.43974i	−0.727861	−	0.420231i	0.0897783	−	0.995962i	$-0.471384\pi$
$67$	−5.95780	−	3.43974i	−0.727861	−	0.420231i	−0.817639	+	0.575731i	$0.804717\pi$
$68$	−1.16474	+	11.2433i	−0.141246	+	1.36345i
$69$	−9.67295	+	6.01750i	−1.16449	+	0.724422i
$70$	1.04823	+	1.16243i	0.125287	+	0.138937i
$71$	3.68351			0.437153			0.218576	−	0.975820i	$-0.429859\pi$
$71$	3.68351			0.437153			0.218576	+	0.975820i	$0.429859\pi$
$72$	2.91612	−	7.96845i	0.343668	−	0.939091i
$73$	2.83201			0.331461			0.165731	−	0.986171i	$-0.447002\pi$
$73$	2.83201			0.331461			0.165731	+	0.986171i	$0.447002\pi$
$74$	−5.92433	−	6.56976i	−0.688690	−	0.763719i
$75$	0.257341	+	7.81687i	0.0297151	+	0.902615i
$76$	1.91640	+	0.198528i	0.219826	+	0.0227728i
$77$	−3.77214	−	2.17785i	−0.429875	−	0.248189i
$78$	−12.9583	−	3.73328i	−1.46724	−	0.422711i
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	0.981285	−	0.192562i	$-0.0616797\pi$
$79$	2.87870	+	4.98605i	0.323879	+	0.560975i	−0.657406	+	0.753537i	$0.728346\pi$
$80$	−2.07461	−	1.85680i	−0.231948	−	0.207596i
$81$	−3.43802	+	8.31745i	−0.382002	+	0.924162i
$82$	0.549933	+	2.57776i	0.0607299	+	0.284666i
$83$	5.74968	−	3.31958i	0.631110	−	0.364371i	−0.150072	−	0.988675i	$-0.547951\pi$
$83$	5.74968	−	3.31958i	0.631110	−	0.364371i	0.781182	+	0.624304i	$0.214617\pi$
$84$	−5.49476	−	0.387012i	−0.599527	−	0.0422264i
$85$	−3.40684	−	1.96694i	−0.369524	−	0.213345i
$86$	1.50957	−	4.65781i	0.162781	−	0.502265i
$87$	5.69844	−	0.187599i	0.610937	−	0.0201128i
$88$	7.08487	+	3.13539i	0.755250	+	0.334233i
$89$	−2.98701			−0.316622			−0.158311	−	0.987389i	$-0.550605\pi$
$89$	−2.98701			−0.316622			−0.158311	+	0.987389i	$0.550605\pi$
$90$	2.11759	+	2.05827i	0.223214	+	0.216960i
$91$			8.75427i			0.917697i
$92$	−10.6536	−	7.71598i	−1.11071	−	0.804447i
$93$	10.8785	−	6.76749i	1.12805	−	0.701756i
$94$	10.3770	+	3.36312i	1.07030	+	0.346879i
$95$	−0.335261	+	0.580689i	−0.0343970	+	0.0595774i
$96$	9.79138	−	0.358951i	0.999329	−	0.0366353i
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	0.795664	−	0.605738i	$-0.207122\pi$
$97$	−1.24837	−	2.16224i	−0.126753	−	0.219543i	−0.922417	+	0.386196i	$0.873789\pi$
$98$	−1.31938	−	6.18447i	−0.133277	−	0.624726i
$99$	−7.37150	−	3.63184i	−0.740864	−	0.365014i
$100$	−8.24477	+	3.68557i	−0.824477	+	0.368557i
$101$	8.22136	−	4.74661i	0.818056	−	0.472305i	−0.0316896	−	0.999498i	$-0.510089\pi$
$101$	8.22136	−	4.74661i	0.818056	−	0.472305i	0.849746	+	0.527193i	$0.176755\pi$
$102$	13.4369	−	3.33234i	1.33045	−	0.329951i
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	−0.231989	−	0.972719i	$-0.574523\pi$
$103$	7.37220	−	12.7690i	0.726405	−	1.25817i	0.958393	−	0.285451i	$-0.0921435\pi$
$104$	−1.66237	−	15.4826i	−0.163008	−	1.51819i
$105$	0.903375	−	1.69085i	0.0881604	−	0.165010i
$106$	−2.40727	−	2.66953i	−0.233815	−	0.259288i
$107$		−	7.83384i		−	0.757325i	−0.925535	−	0.378663i	$-0.876384\pi$
$107$		−	7.83384i		−	0.757325i	0.925535	−	0.378663i	$-0.123616\pi$
$108$	−10.3922	−	0.0467464i	−0.999990	−	0.00449818i
$109$			0.242400i			0.0232177i	0.999933	+	0.0116089i	$0.00369529\pi$
$109$			0.242400i			0.0232177i	−0.999933	+	0.0116089i	$0.996305\pi$
$110$	−2.00244	+	1.80571i	−0.190925	+	0.172168i
$111$	−5.10565	+	9.55623i	−0.484607	+	0.907038i
$112$	−1.98357	−	6.04331i	−0.187430	−	0.571039i
$113$	4.34789	−	7.53076i	0.409015	−	0.708435i	−0.585765	−	0.810481i	$-0.699206\pi$
$113$	4.34789	−	7.53076i	0.409015	−	0.708435i	0.994780	+	0.102046i	$0.0325391\pi$
$114$	−0.567991	−	2.29028i	−0.0531972	−	0.214505i
$115$	3.96466	−	2.28900i	0.369706	−	0.213450i
$116$	2.68675	+	6.01037i	0.249459	+	0.558049i
$117$	1.08629	+	16.4804i	0.100427	+	1.52361i
$118$	7.37870	−	1.57415i	0.679264	−	0.144912i
$119$	−4.49350	−	7.78298i	−0.411919	−	0.713464i
$120$	−1.27661	+	3.16193i	−0.116538	+	0.288644i
$121$	−1.74837	+	3.02827i	−0.158943	+	0.275297i
$122$	−3.99606	+	12.3299i	−0.361786	+	1.11630i
$123$	2.74103	−	1.70519i	0.247151	−	0.153751i
$124$	11.9814	+	8.67767i	1.07596	+	0.779277i
$125$		−	6.62325i		−	0.592401i
$126$	1.83847	+	6.49101i	0.163784	+	0.578265i
$127$	−1.72754			−0.153295			−0.0766473	−	0.997058i	$-0.524422\pi$
$127$	−1.72754			−0.153295			−0.0766473	+	0.997058i	$0.524422\pi$
$128$	4.65567	+	10.3114i	0.411507	+	0.911407i
$129$	−5.99350	+	0.197313i	−0.527699	+	0.0173725i
$130$	5.15529	+	1.67080i	0.452148	+	0.146539i
$131$	−5.74968	−	3.31958i	−0.502352	−	0.290033i	0.227332	−	0.973817i	$-0.427000\pi$
$131$	−5.74968	−	3.31958i	−0.502352	−	0.290033i	−0.729684	+	0.683784i	$0.760333\pi$
$132$	0.666679	−	9.46544i	0.0580269	−	0.823861i
$133$	−1.32659	+	0.765908i	−0.115030	+	0.0664127i
$134$	−9.51493	+	2.02989i	−0.821964	+	0.175356i
$135$	1.49084	−	3.29521i	0.128311	−	0.283606i
$136$	9.42503	+	12.9115i	0.808189	+	1.10715i
$137$	1.81325	+	3.14063i	0.154916	+	0.268322i	0.933028	−	0.359803i	$-0.117156\pi$
$137$	1.81325	+	3.14063i	0.154916	+	0.268322i	−0.778112	+	0.628125i	$0.783823\pi$
$138$	−4.46005	+	15.4810i	−0.379665	+	1.31783i
$139$	−14.9919	−	8.65556i	−1.27159	−	0.734155i	−0.296307	−	0.955093i	$-0.595755\pi$
$139$	−14.9919	−	8.65556i	−1.27159	−	0.734155i	−0.975288	+	0.220937i	$0.929088\pi$
$140$	2.20182	+	0.228097i	0.186088	+	0.0192777i
$141$	−0.439587	−	13.3527i	−0.0370199	−	1.12450i
$142$	3.86864	−	3.48858i	0.324649	−	0.292755i
$143$	−15.0804			−1.26109
$144$	−4.48407	−	11.1307i	−0.373673	−	0.927561i
$145$	−2.29123			−0.190276
$146$	2.97434	−	2.68213i	0.246158	−	0.221975i
$147$	−6.57619	+	4.09102i	−0.542395	+	0.337421i
$148$	−12.4442	−	1.28914i	−1.02290	−	0.105967i
$149$	18.7251	+	10.8109i	1.53402	+	0.885665i	0.999171	+	0.0407158i	$0.0129638\pi$
$149$	18.7251	+	10.8109i	1.53402	+	0.885665i	0.534846	+	0.844949i	$0.320369\pi$
$150$	7.67346	+	7.96602i	0.626536	+	0.650422i
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	−0.999810	−	0.0194749i	$-0.993801\pi$
$151$	−6.35019	−	10.9988i	−0.516771	−	0.895073i	0.483039	−	0.875599i	$-0.339533\pi$
$152$	2.20074	−	1.60648i	0.178503	−	0.130302i
$153$	−9.42503	−	14.0943i	−0.761968	−	1.13946i
$154$	−6.02431	+	1.28521i	−0.485453	+	0.103565i
$155$	−4.45880	+	2.57429i	−0.358139	+	0.206772i
$156$	−17.1453	+	8.35164i	−1.37272	+	0.668666i
$157$	15.1285	+	8.73443i	1.20738	+	0.697083i	0.962187	−	0.272390i	$-0.0878140\pi$
$157$	15.1285	+	8.73443i	1.20738	+	0.697083i	0.245197	+	0.969473i	$0.421147\pi$
$158$	7.74556	+	2.51029i	0.616203	+	0.199708i
$159$	−2.07461	+	3.88304i	−0.164527	+	0.307945i
$160$	−3.93741	+	0.0147030i	−0.311279	+	0.00116238i
$161$	10.4585			0.824245
$162$	4.26647	+	11.9915i	0.335206	+	0.942145i
$163$			8.56748i			0.671057i	0.942030	+	0.335528i	$0.108915\pi$
$163$			8.56748i			0.671057i	−0.942030	+	0.335528i	$0.891085\pi$
$164$	3.01891	+	2.18649i	0.235738	+	0.170736i
$165$	2.91270	+	1.55618i	0.226754	+	0.121149i
$166$	2.89475	−	8.93182i	0.224676	−	0.693244i
$167$	−5.97532	+	10.3496i	−0.462384	+	0.800873i	−0.999079	−	0.0429032i	$-0.986339\pi$
$167$	−5.97532	+	10.3496i	−0.462384	+	0.800873i	0.536695	+	0.843776i	$0.319673\pi$
$168$	−6.13744	+	4.79750i	−0.473514	+	0.370135i
$169$	8.65464	+	14.9903i	0.665741	+	1.15310i
$170$	−5.44091	+	1.16075i	−0.417299	+	0.0890254i
$171$	−2.40234	+	1.60648i	−0.183712	+	0.122850i
$172$	−2.82587	−	6.32159i	−0.215471	−	0.482017i
$173$	−11.2973	+	6.52248i	−0.858916	+	0.495895i	−0.863649	−	0.504094i	$-0.831827\pi$
$173$	−11.2973	+	6.52248i	−0.858916	+	0.495895i	0.00473326	+	0.999989i	$0.498493\pi$
$174$	5.80716	−	5.59390i	0.440240	−	0.424072i
$175$	3.59013	−	6.21829i	0.271388	−	0.470058i
$176$	10.4104	−	3.41696i	0.784714	−	0.257563i
$177$	−4.88100	−	7.84605i	−0.366878	−	0.589746i
$178$	−3.13713	+	2.82893i	−0.235138	+	0.212037i
$179$			3.31875i			0.248055i	0.992279	+	0.124028i	$0.0395811\pi$
$179$			3.31875i			0.248055i	−0.992279	+	0.124028i	$0.960419\pi$
$180$	4.17336	+	0.156188i	0.311064	+	0.0116415i
$181$		−	14.9128i		−	1.10846i	−0.832363	−	0.554231i	$-0.813013\pi$
$181$		−	14.9128i		−	1.10846i	0.832363	−	0.554231i	$-0.186987\pi$
$182$	8.29098	+	9.19425i	0.614569	+	0.681523i
$183$	15.8657	−	0.522318i	1.17283	−	0.0386108i
$184$	−18.4966	+	1.98598i	−1.36359	+	0.146409i
$185$	2.17702	−	3.77070i	0.160058	−	0.277228i
$186$	5.01593	−	17.4104i	0.367786	−	1.27660i
$187$	13.4072	−	7.74065i	0.980432	−	0.566053i
$188$	14.0836	−	6.29566i	1.02715	−	0.459158i
$189$	6.71353	−	4.81647i	0.488337	−	0.350346i
$190$	0.197847	+	0.927391i	0.0143533	+	0.0672800i
$191$	3.65884	+	6.33729i	0.264744	+	0.458550i	0.967497	−	0.252884i	$-0.0813792\pi$
$191$	3.65884	+	6.33729i	0.264744	+	0.458550i	−0.702752	+	0.711434i	$0.748046\pi$
$192$	9.94353	−	9.65020i	0.717612	−	0.696443i
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	0.217189	+	0.976130i	$0.430311\pi$
$193$	−10.2354	+	17.7282i	−0.736759	+	1.27610i	−0.953947	+	0.299974i	$0.903022\pi$
$194$	−3.35893	−	1.08861i	−0.241157	−	0.0781576i
$195$	−0.218387	−	6.63364i	−0.0156390	−	0.475044i
$196$	−7.24287	−	5.24574i	−0.517348	−	0.374696i
$197$			20.5437i			1.46368i	0.681479	+	0.731838i	$0.261337\pi$
$197$			20.5437i			1.46368i	−0.681479	+	0.731838i	$0.738663\pi$
$198$	−11.1816	+	3.16701i	−0.794643	+	0.225070i
$199$	1.95597			0.138655			0.0693275	−	0.997594i	$-0.477915\pi$
$199$	1.95597			0.138655			0.0693275	+	0.997594i	$0.477915\pi$
$200$	−5.16861	+	11.6792i	−0.365476	+	0.825847i
$201$	6.29411	+	10.1176i	0.443952	+	0.713640i
$202$	4.13915	−	12.7714i	0.291229	−	0.898595i
$203$	−4.53308	−	2.61718i	−0.318160	−	0.183690i
$204$	10.9562	−	16.2256i	0.767086	−	1.13602i
$205$	−1.12347	+	0.648636i	−0.0784666	+	0.0453027i
$206$	−4.35055	−	20.3928i	−0.303117	−	1.42084i
$207$	19.6887	−	1.29776i	1.36846	−	0.0902003i
$208$	−16.4091	−	14.6863i	−1.13777	−	1.01831i
$209$	−1.31938	−	2.28523i	−0.0912633	−	0.158073i
$210$	−0.652586	−	2.63139i	−0.0450327	−	0.181583i
$211$	9.10981	+	5.25955i	0.627145	+	0.362082i	0.779646	−	0.626221i	$-0.215399\pi$
$211$	9.10981	+	5.25955i	0.627145	+	0.362082i	−0.152501	+	0.988303i	$0.548733\pi$
$212$	−5.05651	−	0.523826i	−0.347283	−	0.0359765i
$213$	−5.62724	−	3.00649i	−0.385572	−	0.206001i
$214$	−7.41926	−	8.22755i	−0.507170	−	0.562424i
$215$	2.40987			0.164352
$216$	−10.9588	+	9.79313i	−0.745650	+	0.666338i
$217$	−11.7620			−0.798456
$218$	0.229572	+	0.254583i	0.0155486	+	0.0172425i
$219$	−4.32641	−	2.31149i	−0.292351	−	0.156196i
$220$	−0.392926	+	3.79293i	−0.0264911	+	0.255720i
$221$	−26.9464	−	15.5575i	−1.81261	−	1.04651i
$222$	3.68825	+	14.8720i	0.247539	+	0.998141i
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	0.923417	−	0.383799i	$-0.125384\pi$
$223$	1.93129	+	3.34510i	0.129329	+	0.224004i	−0.794088	+	0.607803i	$0.792051\pi$
$224$	−7.80675	−	4.46844i	−0.521610	−	0.298560i
$225$	5.98701	−	12.1517i	0.399134	−	0.810116i
$226$	−2.56582	−	12.0270i	−0.170676	−	0.800027i
$227$	−13.9183	+	8.03574i	−0.923790	+	0.533351i	−0.884842	−	0.465891i	$-0.845734\pi$
$227$	−13.9183	+	8.03574i	−0.923790	+	0.533351i	−0.0389481	+	0.999241i	$0.512401\pi$
$228$	−2.76561	−	1.86746i	−0.183157	−	0.123675i
$229$	−7.46319	−	4.30888i	−0.493182	−	0.284739i	0.232712	−	0.972546i	$-0.425240\pi$
$229$	−7.46319	−	4.30888i	−0.493182	−	0.284739i	−0.725893	+	0.687807i	$0.758573\pi$
$230$	1.99606	−	6.15888i	0.131616	−	0.406105i
$231$	3.98507	+	6.40589i	0.262199	+	0.421476i
$232$	8.51408	+	3.76788i	0.558977	+	0.247373i
$233$	24.1535			1.58235			0.791176	−	0.611589i	$-0.209469\pi$
$233$	24.1535			1.58235			0.791176	+	0.611589i	$0.209469\pi$
$234$	16.7491	+	16.2799i	1.09492	+	1.06425i
$235$			5.36886i			0.350226i
$236$	6.25870	−	8.64147i	0.407406	−	0.562512i
$237$	−0.328116	−	9.96670i	−0.0213134	−	0.647407i
$238$	−12.0904	−	3.91844i	−0.783706	−	0.253995i
$239$	−2.01493	+	3.48996i	−0.130335	+	0.225746i	−0.923806	−	0.382862i	$-0.874939\pi$
$239$	−2.01493	+	3.48996i	−0.130335	+	0.225746i	0.793471	+	0.608608i	$0.208272\pi$
$240$	1.65383	+	4.52989i	0.106754	+	0.292403i
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	0.942366	−	0.334583i	$-0.108595\pi$
$241$	2.81649	+	4.87830i	0.181426	+	0.314239i	−0.760940	+	0.648822i	$0.775262\pi$
$242$	1.03177	+	4.83631i	0.0663244	+	0.310890i
$243$	12.0409	−	9.90032i	0.772425	−	0.635106i
$244$	7.48051	+	16.7342i	0.478891	+	1.07130i
$245$	2.69539	−	1.55618i	0.172202	−	0.0994209i
$246$	1.26385	−	4.38686i	0.0805802	−	0.279696i
$247$	−2.65175	+	4.59296i	−0.168727	+	0.292243i
$248$	20.8020	−	2.23351i	1.32093	−	0.141828i
$249$	−11.4931	+	0.378368i	−0.728348	+	0.0239781i
$250$	−6.27273	−	6.95612i	−0.396722	−	0.439944i
$251$			13.8828i			0.876276i	0.898908	+	0.438138i	$0.144362\pi$
$251$			13.8828i			0.876276i	−0.898908	+	0.438138i	$0.855638\pi$
$252$	8.07837	+	5.07606i	0.508889	+	0.319762i
$253$			18.0161i			1.13267i
$254$	−1.81437	+	1.63612i	−0.113843	+	0.102659i
$255$	3.59915	+	5.78553i	0.225388	+	0.362304i
$256$	14.6553	+	6.42034i	0.915959	+	0.401271i
$257$	−5.42539	+	9.39705i	−0.338427	+	0.586172i	−0.984137	−	0.177410i	$-0.943228\pi$
$257$	−5.42539	+	9.39705i	−0.338427	+	0.586172i	0.645710	+	0.763582i	$0.276561\pi$
$258$	−6.10786	+	5.88355i	−0.380259	+	0.366294i
$259$	8.61423	−	4.97343i	0.535262	−	0.309034i
$260$	6.99676	−	3.12769i	0.433921	−	0.193971i
$261$	−8.85853	−	4.36448i	−0.548329	−	0.270155i
$262$	−9.18256	+	1.95898i	−0.567300	+	0.121026i
$263$	−11.6051	−	20.1005i	−0.715598	−	1.23945i	−0.962728	−	0.270470i	$-0.912821\pi$
$263$	−11.6051	−	20.1005i	−0.715598	−	1.23945i	0.247130	−	0.968982i	$-0.420513\pi$
$264$	−8.26433	−	10.5726i	−0.508634	−	0.650696i
$265$	0.884601	−	1.53217i	0.0543406	−	0.0941207i
$266$	−0.667890	+	2.06079i	−0.0409509	+	0.126355i
$267$	4.56320	+	2.43800i	0.279263	+	0.149203i
$268$	−8.07067	+	11.1433i	−0.492995	+	0.680685i
$269$			4.01966i			0.245083i	0.992463	+	0.122541i	$0.0391044\pi$
$269$			4.01966i			0.245083i	−0.992463	+	0.122541i	$0.960896\pi$
$270$	−1.55505	−	4.87276i	−0.0946372	−	0.296547i
$271$	−6.75621			−0.410411			−0.205205	−	0.978719i	$-0.565786\pi$
$271$	−6.75621			−0.410411			−0.205205	+	0.978719i	$0.565786\pi$
$272$	22.1269	+	4.63418i	1.34164	+	0.280988i
$273$	7.14525	−	13.3738i	0.432450	−	0.809417i
$274$	4.87880	+	1.58119i	0.294739	+	0.0955233i
$275$	10.7118	+	6.18447i	0.645947	+	0.372938i
$276$	9.97748	+	20.4830i	0.600574	+	1.23293i
$277$	−1.83595	+	1.05999i	−0.110312	+	0.0636885i	−0.554141	−	0.832423i	$-0.686953\pi$
$277$	−1.83595	+	1.05999i	−0.110312	+	0.0636885i	0.443829	+	0.896111i	$0.353620\pi$
$278$	−23.9428	+	5.10790i	−1.43600	+	0.306352i
$279$	−22.1426	+	1.45950i	−1.32564	+	0.0873781i
$280$	2.52851	−	1.84574i	0.151107	−	0.110304i
$281$	−13.0580	−	22.6171i	−0.778976	−	1.34923i	−0.932533	−	0.361086i	$-0.882406\pi$
$281$	−13.0580	−	22.6171i	−0.778976	−	1.34923i	0.153557	−	0.988140i	$-0.450927\pi$
$282$	−13.1077	−	13.6075i	−0.780554	−	0.810313i
$283$	16.5376	+	9.54799i	0.983058	+	0.567569i	0.903192	−	0.429237i	$-0.141217\pi$
$283$	16.5376	+	9.54799i	0.983058	+	0.567569i	0.0798661	+	0.996806i	$0.474551\pi$
$284$	0.759119	−	7.32781i	0.0450455	−	0.434826i
$285$	0.986131	−	0.613468i	0.0584134	−	0.0363387i
$286$	−15.8383	+	14.2823i	−0.936539	+	0.844531i
$287$	−2.96364			−0.174938
$288$	−15.2511	−	7.44338i	−0.898680	−	0.438605i
$289$	14.9423			0.878956
$290$	−2.40638	+	2.16998i	−0.141308	+	0.127425i
$291$	0.142290	+	4.32215i	0.00834120	+	0.253369i
$292$	0.583636	−	5.63386i	0.0341547	−	0.329697i
$293$	5.07116	+	2.92784i	0.296261	+	0.171046i	0.640762	−	0.767740i	$-0.278619\pi$
$293$	5.07116	+	2.92784i	0.296261	+	0.171046i	−0.344501	+	0.938786i	$0.611952\pi$
$294$	−3.03218	+	10.5248i	−0.176840	+	0.613818i
$295$	1.85668	+	3.21587i	0.108100	+	0.187235i
$296$	−14.2905	+	10.4317i	−0.830619	+	0.606328i
$297$	8.29700	+	11.5649i	0.481441	+	0.671065i
$298$	29.9049	−	6.37984i	1.73235	−	0.369574i
$299$	31.3585	−	18.1048i	1.81351	−	1.04703i
$300$	15.6036	+	1.09900i	0.900872	+	0.0634510i
$301$	4.76780	+	2.75269i	0.274812	+	0.158663i
$302$	−17.0861	−	5.53751i	−0.983195	−	0.318648i
$303$	−16.4338	+	0.541021i	−0.944098	+	0.0310808i
$304$	0.789886	−	3.77149i	0.0453031	−	0.216310i
$305$	−6.37929			−0.365277
$306$	−23.2471	−	5.87642i	−1.32895	−	0.335932i
$307$		−	13.7071i		−	0.782305i	−0.920326	−	0.391152i	$-0.872077\pi$
$307$		−	13.7071i		−	0.782305i	0.920326	−	0.391152i	$-0.127923\pi$
$308$	−5.10989	+	7.05530i	−0.291163	+	0.402013i
$309$	−21.6845	+	13.4898i	−1.23359	+	0.767409i
$310$	−2.24484	+	6.92649i	−0.127498	+	0.393398i
$311$	−9.57980	+	16.5927i	−0.543221	+	0.940886i	0.455496	+	0.890238i	$0.349462\pi$
$311$	−9.57980	+	16.5927i	−0.543221	+	0.940886i	−0.998717	+	0.0506479i	$0.983871\pi$
$312$	−10.0973	+	25.0093i	−0.571650	+	1.41587i
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	−0.963812	−	0.266582i	$-0.914106\pi$
$313$	−12.6102	−	21.8416i	−0.712773	−	1.23456i	0.251039	−	0.967977i	$-0.419228\pi$
$314$	24.1610	−	5.15444i	1.36348	−	0.290882i
$315$	−2.76014	+	1.84574i	−0.155516	+	0.103996i
$316$	10.5123	−	4.69919i	0.591362	−	0.264350i
$317$	−2.13931	+	1.23513i	−0.120156	+	0.0693719i	−0.558873	−	0.829253i	$-0.688766\pi$
$317$	−2.13931	+	1.23513i	−0.120156	+	0.0693719i	0.438718	+	0.898625i	$0.355433\pi$
$318$	1.49867	+	6.04302i	0.0840412	+	0.338876i
$319$	4.50843	−	7.80883i	0.252424	−	0.437211i
$320$	−4.12137	+	3.74447i	−0.230392	+	0.209322i
$321$	−6.39399	+	11.9676i	−0.356878	+	0.667967i
$322$	10.9841	−	9.90502i	0.612121	−	0.551985i
$323$		−	5.44449i		−	0.302939i
$324$	15.8378	+	8.55354i	0.879880	+	0.475197i
$325$		−	24.8597i		−	1.37897i
$326$	8.11408	+	8.99807i	0.449397	+	0.498357i
$327$	0.197847	−	0.370310i	0.0109410	−	0.0204782i
$328$	5.24142	−	0.562771i	0.289409	−	0.0310738i
$329$	−6.13262	+	10.6220i	−0.338103	+	0.585611i
$330$	4.53292	−	1.12417i	0.249529	−	0.0618833i
$331$	−24.4404	+	14.1107i	−1.34336	+	0.775592i	−0.987300	−	0.158869i	$-0.949215\pi$
$331$	−24.4404	+	14.1107i	−1.34336	+	0.775592i	−0.356065	+	0.934461i	$0.615882\pi$
$332$	−5.41889	−	12.1223i	−0.297400	−	0.665296i
$333$	15.5996	−	10.4317i	0.854854	−	0.571651i
$334$	3.52621	+	16.5288i	0.192946	+	0.904416i
$335$	−2.39422	−	4.14691i	−0.130810	−	0.226570i
$336$	−1.90229	+	10.8513i	−0.103779	+	0.591985i
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	−0.671982	−	0.740567i	$-0.734557\pi$
$337$	5.60565	−	9.70927i	0.305359	−	0.528897i	0.977341	+	0.211670i	$0.0678902\pi$
$338$	23.2866	+	7.54704i	1.26662	+	0.410505i
$339$	−12.7888	+	7.95587i	−0.694593	+	0.432103i
$340$	−4.61504	+	6.37205i	−0.250286	+	0.345573i
$341$		−	20.2616i		−	1.09723i
$342$	−1.00162	+	3.96242i	−0.0541615	+	0.214263i
$343$	18.2411			0.984929
$344$	−8.95494	−	3.96298i	−0.482818	−	0.213669i
$345$	−7.92503	+	0.260901i	−0.426669	+	0.0140465i
$346$	−5.68775	+	17.5497i	−0.305776	+	0.943477i
$347$	−17.8303	−	10.2943i	−0.957180	−	0.552628i	−0.0618763	−	0.998084i	$-0.519708\pi$
$347$	−17.8303	−	10.2943i	−0.957180	−	0.552628i	−0.895304	+	0.445455i	$0.853042\pi$
$348$	0.801166	−	11.3749i	0.0429470	−	0.609757i
$349$	−2.93968	+	1.69723i	−0.157358	+	0.0908505i	−0.576611	−	0.817019i	$-0.695625\pi$
$349$	−2.93968	+	1.69723i	−0.157358	+	0.0908505i	0.419253	+	0.907869i	$0.362292\pi$
$350$	−2.11864	−	9.93094i	−0.113246	−	0.530831i
$351$	11.7918	−	26.0634i	0.629401	−	1.39116i
$352$	7.69748	−	13.4482i	0.410277	−	0.716789i
$353$	−0.503241	−	0.871639i	−0.0267848	−	0.0463926i	0.852322	−	0.523017i	$-0.175194\pi$
$353$	−0.503241	−	0.871639i	−0.0267848	−	0.0463926i	−0.879107	+	0.476624i	$0.841860\pi$
$354$	−12.5571	−	3.61770i	−0.667404	−	0.192279i
$355$	2.22040	+	1.28195i	0.117847	+	0.0680388i
$356$	−0.615580	+	5.94222i	−0.0326257	+	0.314937i
$357$	0.512172	+	15.5575i	0.0271070	+	0.823392i
$358$	3.14312	+	3.48555i	0.166119	+	0.184217i
$359$	31.4772			1.66131			0.830653	−	0.556791i	$-0.187968\pi$
$359$	31.4772			1.66131			0.830653	+	0.556791i	$0.187968\pi$
$360$	4.53103	−	3.78846i	0.238806	−	0.199669i
$361$	18.0720			0.951158
$362$	−14.1236	−	15.6623i	−0.742320	−	0.823193i
$363$	5.14264	−	3.19921i	0.269918	−	0.167915i
$364$	17.4154	+	1.80413i	0.912812	+	0.0945622i
$365$	1.70712	+	0.985604i	0.0893546	+	0.0515889i
$366$	16.1684	−	15.5746i	0.845137	−	0.814099i
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	0.546138	−	0.837695i	$-0.316098\pi$
$367$	−8.66667	−	15.0111i	−0.452397	−	0.783574i	−0.998534	+	0.0541214i	$0.982764\pi$
$368$	−17.5454	+	19.6036i	−0.914616	+	1.02191i
$369$	−5.57921	+	0.367747i	−0.290442	+	0.0191441i
$370$	−1.28472	−	6.02202i	−0.0667895	−	0.313070i
$371$	3.50027	−	2.02088i	0.181725	−	0.104919i
$372$	−11.2210	−	23.0359i	−0.581783	−	1.19436i
$373$	−11.2742	−	6.50917i	−0.583757	−	0.337032i	0.178868	−	0.983873i	$-0.442756\pi$
$373$	−11.2742	−	6.50917i	−0.583757	−	0.337032i	−0.762625	+	0.646841i	$0.776090\pi$
$374$	6.75003	−	20.8274i	0.349036	−	1.07696i
$375$	−5.40590	+	10.1182i	−0.279160	+	0.522503i
$376$	8.82897	−	19.9504i	0.455319	−	1.02886i
$377$	−18.1225			−0.933357
$378$	2.48937	−	11.4168i	0.128039	−	0.587215i
$379$		−	22.8643i		−	1.17446i	−0.809421	−	0.587229i	$-0.800219\pi$
$379$		−	22.8643i		−	1.17446i	0.809421	−	0.587229i	$-0.199781\pi$
$380$	1.08610	+	0.786624i	0.0557159	+	0.0403530i
$381$	2.63914	+	1.41002i	0.135207	+	0.0722377i
$382$	9.84463	+	3.19059i	0.503695	+	0.163245i
$383$	15.0117	−	26.0010i	0.767061	−	1.32859i	−0.172089	−	0.985081i	$-0.555052\pi$
$383$	15.0117	−	26.0010i	0.767061	−	1.32859i	0.939150	−	0.343508i	$-0.111615\pi$
$384$	1.30378	−	19.5525i	0.0665334	−	0.997784i
$385$	−1.51588	−	2.62559i	−0.0772565	−	0.133812i
$386$	6.04020	+	28.3129i	0.307438	+	1.44109i
$387$	9.31722	+	4.59047i	0.473621	+	0.233347i
$388$	−4.55874	+	2.03785i	−0.231435	+	0.103456i
$389$	32.9474	−	19.0222i	1.67050	−	0.964463i	0.703140	−	0.711051i	$-0.251780\pi$
$389$	32.9474	−	19.0222i	1.67050	−	0.964463i	0.967358	−	0.253412i	$-0.0815528\pi$
$390$	−6.51193	−	6.76020i	−0.329745	−	0.342316i
$391$	−18.5862	+	32.1922i	−0.939943	+	1.62803i
$392$	−12.5750	+	1.35018i	−0.635134	+	0.0681943i
$393$	6.07425	+	9.76417i	0.306405	+	0.492537i
$394$	19.4565	+	21.5762i	0.980203	+	1.08699i
$395$			4.00742i			0.201635i
$396$	−8.74418	+	13.9161i	−0.439412	+	0.699308i
$397$			37.4510i			1.87961i	0.341709	+	0.939806i	$0.388994\pi$
$397$			37.4510i			1.87961i	−0.341709	+	0.939806i	$0.611006\pi$
$398$	2.05427	−	1.85246i	0.102971	−	0.0928553i
$399$	2.65175	−	0.0872987i	0.132753	−	0.00437040i
$400$	5.63278	+	17.1613i	0.281639	+	0.858065i
$401$	−2.35402	+	4.07728i	−0.117554	+	0.203610i	−0.918798	−	0.394728i	$-0.870839\pi$
$401$	−2.35402	+	4.07728i	−0.117554	+	0.203610i	0.801244	+	0.598338i	$0.204172\pi$
$402$	16.1926	+	4.66507i	0.807613	+	0.232673i
$403$	−35.2669	+	20.3613i	−1.75677	+	1.01427i
$404$	−7.74837	−	17.3334i	−0.385496	−	0.862369i
$405$	−4.96708	+	3.81720i	−0.246816	+	0.189678i
$406$	−7.23958	+	1.54447i	−0.359294	+	0.0766508i
$407$	8.56739	+	14.8391i	0.424670	+	0.735549i
$408$	−3.86006	−	27.4174i	−0.191102	−	1.35736i
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	−0.702400	−	0.711782i	$-0.747888\pi$
$409$	5.36377	−	9.29032i	0.265221	−	0.459377i	0.967622	+	0.252405i	$0.0812216\pi$
$410$	−0.565625	+	1.74525i	−0.0279342	+	0.0861917i
$411$	−0.206675	−	6.27787i	−0.0101945	−	0.309664i
$412$	−23.8828	−	17.2974i	−1.17662	−	0.852183i
$413$			8.48324i			0.417433i
$414$	19.4491	−	20.0097i	0.955873	−	0.983423i
$415$	4.62117			0.226844
$416$	−31.1430	+	0.116294i	−1.52691	+	0.00570177i
$417$	15.8382	+	25.4594i	0.775598	+	1.24675i
$418$	−3.54998	−	1.15053i	−0.173635	−	0.0562742i
$419$	3.57600	+	2.06460i	0.174699	+	0.100863i	0.584800	−	0.811178i	$-0.301173\pi$
$419$	3.57600	+	2.06460i	0.174699	+	0.100863i	−0.410101	+	0.912040i	$0.634506\pi$
$420$	−3.17752	−	2.14559i	−0.155047	−	0.104694i
$421$	13.7321	−	7.92824i	0.669262	−	0.386399i	−0.126535	−	0.991962i	$-0.540386\pi$
$421$	13.7321	−	7.92824i	0.669262	−	0.386399i	0.795797	+	0.605563i	$0.207052\pi$
$422$	14.5489	−	3.10381i	0.708227	−	0.151091i
$423$	−10.2270	+	20.7575i	−0.497251	+	1.00926i
$424$	−5.80675	+	4.23876i	−0.282001	+	0.205852i
$425$	12.7603	+	22.1015i	0.618965	+	1.07208i
$426$	−8.75744	+	2.17185i	−0.424299	+	0.105226i
$427$	−12.6211	−	7.28679i	−0.610778	−	0.352633i
$428$	−15.5843	−	1.61444i	−0.753294	−	0.0780370i
$429$	23.0381	+	12.3086i	1.11229	+	0.594267i
$430$	2.53099	−	2.28234i	0.122055	−	0.110064i
$431$	16.1853			0.779619			0.389810	−	0.920895i	$-0.372541\pi$
$431$	16.1853			0.779619			0.389810	+	0.920895i	$0.372541\pi$
$432$	−2.23468	+	20.6641i	−0.107516	+	0.994203i
$433$	−32.8306			−1.57774			−0.788868	−	0.614563i	$-0.789332\pi$
$433$	−32.8306			−1.57774			−0.788868	+	0.614563i	$0.789332\pi$
$434$	−12.3531	+	11.1395i	−0.592969	+	0.534714i
$435$	3.50027	+	1.87011i	0.167825	+	0.0896647i
$436$	0.482219	+	0.0499552i	0.0230941	+	0.00239242i
$437$	5.48709	+	3.16797i	0.262483	+	0.151545i
$438$	−6.73300	+	1.66979i	−0.321715	+	0.0797855i
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	0.999686	+	0.0250450i	$0.00797290\pi$
$439$	10.9273	+	18.9267i	0.521533	+	0.903321i	−0.478154	+	0.878276i	$0.658694\pi$
$440$	3.17953	+	4.35569i	0.151578	+	0.207650i
$441$	13.3854	−	0.882284i	0.637401	−	0.0420135i
$442$	−43.0349	+	9.18095i	−2.04696	+	0.436693i
$443$	−30.4500	+	17.5803i	−1.44672	+	0.835265i	−0.998284	−	0.0585501i	$-0.981352\pi$
$443$	−30.4500	+	17.5803i	−1.44672	+	0.835265i	−0.448436	+	0.893815i	$0.648019\pi$
$444$	17.9585	+	12.1263i	0.852274	+	0.575491i
$445$	−1.80055	−	1.03955i	−0.0853543	−	0.0492793i
$446$	5.19643	+	1.68413i	0.246058	+	0.0797459i
$447$	−19.7821	−	31.7991i	−0.935660	−	1.50405i
$448$	−12.4311	+	2.70058i	−0.587313	+	0.127591i
$449$	3.21851			0.151891			0.0759453	−	0.997112i	$-0.475803\pi$
$449$	3.21851			0.151891			0.0759453	+	0.997112i	$0.475803\pi$
$450$	−5.22075	−	18.4326i	−0.246108	−	0.868923i
$451$		−	5.10526i		−	0.240397i
$452$	−14.0853	−	10.2015i	−0.662518	−	0.479837i
$453$	0.723798	+	21.9858i	0.0340070	+	1.03298i
$454$	−7.00735	+	21.6213i	−0.328871	+	1.01474i
$455$	−3.04669	+	5.27703i	−0.142831	+	0.247391i
$456$	−4.67324	+	0.657940i	−0.218844	+	0.0308109i
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	0.945147	−	0.326645i	$-0.105918\pi$
$457$	4.05512	+	7.02368i	0.189691	+	0.328554i	−0.755456	+	0.655199i	$0.772585\pi$
$458$	−11.9191	+	2.54279i	−0.556944	+	0.118817i
$459$	2.89467	+	29.2243i	0.135112	+	1.36408i
$460$	−3.73657	−	8.35884i	−0.174218	−	0.389733i
$461$	−18.1813	+	10.4970i	−0.846789	+	0.488894i	−0.859566	−	0.511024i	$-0.829266\pi$
$461$	−18.1813	+	10.4970i	−0.846789	+	0.488894i	0.0127771	+	0.999918i	$0.495933\pi$
$462$	10.2522	+	2.95366i	0.476977	+	0.137417i
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	−0.950708	−	0.310086i	$-0.899642\pi$
$463$	−4.45005	+	7.70772i	−0.206812	+	0.358208i	0.743897	+	0.668294i	$0.232975\pi$
$464$	12.5105	−	4.10625i	0.580783	−	0.190628i
$465$	8.91276	−	0.293419i	0.413319	−	0.0136070i
$466$	25.3675	−	22.8753i	1.17513	−	1.05968i
$467$		−	26.0527i		−	1.20557i	−0.797902	−	0.602787i	$-0.794057\pi$
$467$		−	26.0527i		−	1.20557i	0.797902	−	0.602787i	$-0.205943\pi$
$468$	33.0092	+	1.23537i	1.52585	+	0.0571049i
$469$		−	10.9392i		−	0.505128i
$470$	5.08473	+	5.63869i	0.234541	+	0.260094i
$471$	−15.9825	−	25.6913i	−0.736433	−	1.18379i
$472$	−1.61090	−	15.0033i	−0.0741477	−	0.690581i
$473$	−4.74188	+	8.21317i	−0.218032	+	0.377642i
$474$	−9.78385	−	10.1569i	−0.449387	−	0.466520i
$475$	3.76715	−	2.17496i	0.172849	−	0.0997942i
$476$	−16.4091	+	7.33521i	−0.752112	+	0.336209i
$477$	6.33869	−	4.23876i	0.290229	−	0.194080i
$478$	1.18907	+	5.57365i	0.0543866	+	0.254933i
$479$	8.71143	+	15.0886i	0.398035	+	0.689418i	0.993483	−	0.113976i	$-0.0363588\pi$
$479$	8.71143	+	15.0886i	0.398035	+	0.689418i	−0.595448	+	0.803394i	$0.703025\pi$
$480$	6.02711	+	3.19126i	0.275099	+	0.145660i
$481$	17.2191	−	29.8244i	0.785125	−	1.35988i
$482$	7.57817	+	2.45604i	0.345176	+	0.111870i
$483$	−15.9773	−	8.53624i	−0.726991	−	0.388412i
$484$	5.66399	+	4.10221i	0.257454	+	0.186464i
$485$		−	1.73785i		−	0.0789118i
$486$	3.26970	−	21.8016i	0.148317	−	0.988940i
$487$	−29.7367			−1.34750			−0.673750	−	0.738959i	$-0.735318\pi$
$487$	−29.7367			−1.34750			−0.673750	+	0.738959i	$0.735318\pi$
$488$	23.7051	+	10.4906i	1.07308	+	0.474887i
$489$	6.99279	−	13.0884i	0.316225	−	0.591878i
$490$	1.35703	−	4.18714i	0.0613042	−	0.189156i
$491$	20.6346	+	11.9134i	0.931229	+	0.537645i	0.887200	−	0.461385i	$-0.152647\pi$
$491$	20.6346	+	11.9134i	0.931229	+	0.537645i	0.0440286	+	0.999030i	$0.485981\pi$
$492$	−2.82733	−	5.80430i	−0.127466	−	0.261678i
$493$	16.1118	−	9.30215i	0.725639	−	0.418948i
$494$	1.56487	+	7.33521i	0.0704070	+	0.330027i
$495$	−3.17953	−	4.75471i	−0.142909	−	0.213708i
$496$	19.7321	−	22.0469i	0.885999	−	0.989933i
$497$	2.92863	+	5.07254i	0.131367	+	0.227534i
$498$	−11.7124	+	11.2823i	−0.524846	+	0.505571i
$499$	−16.8622	−	9.73540i	−0.754856	−	0.435816i	0.0725899	−	0.997362i	$-0.476874\pi$
$499$	−16.8622	−	9.73540i	−0.754856	−	0.435816i	−0.827446	+	0.561546i	$0.810207\pi$
$500$	−13.1760	−	1.36496i	−0.589248	−	0.0610427i
$501$	17.5757	−	10.9338i	0.785226	−	0.488485i
$502$	13.1481	+	14.5806i	0.586830	+	0.650762i
$503$	1.23494			0.0550631			0.0275316	−	0.999621i	$-0.491235\pi$
$503$	1.23494			0.0550631			0.0275316	+	0.999621i	$0.491235\pi$
$504$	13.2918	−	2.31967i	0.592064	−	0.103326i
$505$	6.60772			0.294040
$506$	17.0627	+	18.9216i	0.758529	+	0.841168i
$507$	−0.986461	−	29.9643i	−0.0438103	−	1.33076i
$508$	−0.356022	+	3.43669i	−0.0157959	+	0.152479i
$509$	0.392870	+	0.226823i	0.0174136	+	0.0100538i	0.508682	−	0.860955i	$-0.330133\pi$
$509$	0.392870	+	0.226823i	0.0174136	+	0.0100538i	−0.491268	+	0.871009i	$0.663466\pi$
$510$	9.25939	+	2.66762i	0.410013	+	0.118124i
$511$	2.25163	+	3.89993i	0.0996061	+	0.172523i
$512$	21.4725	−	7.13674i	0.948958	−	0.315403i
$513$	4.98123	−	0.493390i	0.219927	−	0.0217837i
$514$	3.20168	+	15.0076i	0.141220	+	0.661957i
$515$	8.88784	−	5.13140i	0.391645	−	0.226116i
$516$	−0.842650	+	11.9639i	−0.0370956	+	0.526680i
$517$	−18.2978	−	10.5643i	−0.804737	−	0.464615i
$518$	4.33694	−	13.3817i	0.190554	−	0.587960i
$519$	22.5823	−	0.743436i	0.991254	−	0.0326332i
$520$	4.38624	−	9.91136i	0.192349	−	0.434642i
$521$	−29.0873			−1.27434			−0.637170	−	0.770724i	$-0.719895\pi$
$521$	−29.0873			−1.27434			−0.637170	+	0.770724i	$0.719895\pi$
$522$	−13.4373	+	3.80588i	−0.588132	+	0.166579i
$523$		−	2.95874i		−	0.129377i	−0.997906	−	0.0646883i	$-0.979395\pi$
$523$		−	2.95874i		−	0.129377i	0.997906	−	0.0646883i	$-0.0206053\pi$
$524$	−7.78875	+	10.7540i	−0.340253	+	0.469792i
$525$	−10.5600	+	6.56930i	−0.460874	+	0.286708i
$526$	−31.2251	−	10.1199i	−1.36148	−	0.441247i
$527$	20.9026	−	36.2044i	0.910534	−	1.57709i
$528$	−18.6927	−	3.27695i	−0.813496	−	0.142611i
$529$	−10.1294	−	17.5446i	−0.440407	−	0.762808i
$530$	−0.522029	−	2.44697i	−0.0226755	−	0.106289i
$531$	1.05265	+	15.9702i	0.0456813	+	0.693046i
$532$	1.25027	+	2.79690i	0.0542061	+	0.121261i
$533$	−8.88610	+	5.13039i	−0.384900	+	0.222222i
$534$	7.10152	−	1.76118i	0.307313	−	0.0762136i
$535$	2.72636	−	4.72219i	0.117871	−	0.204158i
$536$	2.07728	+	19.3469i	0.0897246	+	0.835658i
$537$	2.70877	−	5.07000i	0.116892	−	0.218787i
$538$	3.80693	+	4.22168i	0.164128	+	0.182010i
$539$			12.2483i			0.527573i
$540$	−6.24809	−	3.64491i	−0.268875	−	0.156852i
$541$			14.9753i			0.643838i	0.946767	+	0.321919i	$0.104328\pi$
$541$			14.9753i			0.643838i	−0.946767	+	0.321919i	$0.895672\pi$
$542$	−7.09577	+	6.39866i	−0.304789	+	0.274846i
$543$	−12.1719	+	22.7821i	−0.522345	+	0.977672i
$544$	27.6279	−	16.0888i	1.18454	−	0.689803i
$545$	−0.0843608	+	0.146117i	−0.00361362	+	0.00625897i
$546$	−5.16163	−	20.8130i	−0.220897	−	0.890715i
$547$	15.7731	−	9.10661i	0.674409	−	0.389370i	−0.123336	−	0.992365i	$-0.539359\pi$
$547$	15.7731	−	9.10661i	0.674409	−	0.389370i	0.797745	+	0.602995i	$0.206026\pi$
$548$	6.62152	−	2.95995i	0.282857	−	0.126443i
$549$	−24.6641	−	12.1517i	−1.05264	−	0.518621i
$550$	17.1074	−	3.64964i	0.729460	−	0.155621i
$551$	−1.58553	−	2.74622i	−0.0675459	−	0.116993i
$552$	29.8780	+	12.0630i	1.27169	+	0.513437i
$553$	−4.57750	+	7.92846i	−0.194655	+	0.337153i
$554$	−0.924333	+	2.85205i	−0.0392711	+	0.121172i
$555$	−6.40345	+	3.98356i	−0.271811	+	0.169093i
$556$	−20.3086	+	28.0404i	−0.861276	+	1.18918i
$557$		−	35.7359i		−	1.51418i	−0.653310	−	0.757090i	$-0.726620\pi$
$557$		−	35.7359i		−	1.51418i	0.653310	−	0.757090i	$-0.273380\pi$
$558$	−21.8732	+	22.5036i	−0.925966	+	0.952654i
$559$	19.0609			0.806190
$560$	0.907529	−	4.33320i	0.0383501	−	0.183111i
$561$	−26.7999	+	0.882284i	−1.13149	+	0.0372501i
$562$	−35.1345	−	11.3869i	−1.48206	−	0.480327i
$563$	−8.04256	−	4.64337i	−0.338953	−	0.195695i	0.320856	−	0.947128i	$-0.396030\pi$
$563$	−8.04256	−	4.64337i	−0.338953	−	0.195695i	−0.659809	+	0.751433i	$0.729363\pi$
$564$	−26.6539	−	1.87731i	−1.12233	−	0.0790489i
$565$	5.24176	−	3.02633i	0.220523	−	0.127319i
$566$	26.4114	−	5.63454i	1.11016	−	0.236838i
$567$	−14.1873	+	1.87845i	−0.595813	+	0.0788873i
$568$	−6.14274	−	8.41504i	−0.257744	−	0.353087i
$569$	−5.66727	−	9.81599i	−0.237584	−	0.411508i	0.722436	−	0.691437i	$-0.243022\pi$
$569$	−5.66727	−	9.81599i	−0.237584	−	0.411508i	−0.960021	+	0.279930i	$0.909689\pi$
$570$	0.454691	−	1.57824i	0.0190449	−	0.0661053i
$571$	37.7843	+	21.8148i	1.58122	+	0.912920i	0.994681	+	0.103002i	$0.0328448\pi$
$571$	37.7843	+	21.8148i	1.58122	+	0.912920i	0.586543	+	0.809918i	$0.300489\pi$
$572$	−3.10785	+	30.0002i	−0.129946	+	1.25437i
$573$	−0.417036	−	12.6677i	−0.0174219	−	0.529201i
$574$	−3.11258	+	2.80680i	−0.129917	+	0.117153i
$575$	−29.6992			−1.23854
$576$	−23.0671	+	6.62652i	−0.961128	+	0.276105i
$577$	6.98123			0.290632			0.145316	−	0.989385i	$-0.453580\pi$
$577$	6.98123			0.290632			0.145316	+	0.989385i	$0.453580\pi$
$578$	15.6932	−	14.1515i	0.652752	−	0.588624i
$579$	30.1062	−	18.7289i	1.25117	−	0.778348i
$580$	−0.472190	+	4.55807i	−0.0196066	+	0.189264i
$581$	9.14274	+	5.27856i	0.379305	+	0.218992i
$582$	4.24285	+	4.40461i	0.175872	+	0.182577i
$583$	3.48124	+	6.02968i	0.144178	+	0.249724i
$584$	−4.72274	−	6.46976i	−0.195428	−	0.267721i
$585$	−5.08076	+	10.3123i	−0.210063	+	0.426363i
$586$	8.09892	−	1.72780i	0.334563	−	0.0713749i
$587$	7.34574	−	4.24107i	0.303191	−	0.175048i	−0.340684	−	0.940178i	$-0.610659\pi$
$587$	7.34574	−	4.24107i	0.303191	−	0.175048i	0.643876	+	0.765130i	$0.277325\pi$
$588$	6.78322	+	13.9255i	0.279735	+	0.574276i
$589$	−6.17097	−	3.56281i	−0.254270	−	0.146803i
$590$	4.99568	+	1.61907i	0.205669	+	0.0666561i
$591$	16.7678	−	31.3842i	0.689734	−	1.29097i
$592$	−5.12913	+	24.4902i	−0.210806	+	1.00654i
$593$	−9.40869			−0.386368			−0.193184	−	0.981163i	$-0.561881\pi$
$593$	−9.40869			−0.386368			−0.193184	+	0.981163i	$0.561881\pi$
$594$	19.6669	+	4.28826i	0.806942	+	0.175950i
$595$		−	6.25538i		−	0.256445i
$596$	25.3657	−	35.0228i	1.03902	−	1.43459i
$597$	−2.98810	−	1.59647i	−0.122295	−	0.0653390i
$598$	15.7878	−	48.7137i	0.645613	−	1.99205i
$599$	−14.9623	+	25.9155i	−0.611344	+	1.05888i	0.379670	+	0.925122i	$0.376038\pi$
$599$	−14.9623	+	25.9155i	−0.611344	+	1.05888i	−0.991014	+	0.133757i	$0.957296\pi$
$600$	17.4286	−	13.6236i	0.711520	−	0.556179i
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	0.900750	−	0.434337i	$-0.143017\pi$
$601$	1.81973	+	3.15186i	0.0742282	+	0.128567i	−0.826522	+	0.562904i	$0.809684\pi$
$602$	7.61444	−	1.62444i	0.310342	−	0.0662074i
$603$	−1.35741	−	20.5937i	−0.0552781	−	0.838641i
$604$	−23.1893	+	10.3661i	−0.943558	+	0.421789i
$605$	−2.10782	+	1.21695i	−0.0856950	+	0.0494760i
$606$	−16.7474	+	16.1323i	−0.680315	+	0.655331i
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	−0.782814	−	0.622256i	$-0.786216\pi$
$607$	3.63358	−	6.29355i	0.147482	−	0.255447i	0.930296	+	0.366809i	$0.119550\pi$
$608$	−2.74231	−	4.70912i	−0.111215	−	0.190980i
$609$	4.78897	+	7.69812i	0.194059	+	0.311944i
$610$	−6.69990	+	6.04169i	−0.271271	+	0.244621i
$611$			42.4651i			1.71795i
$612$	−29.9809	+	15.8451i	−1.21191	+	0.640499i
$613$			32.6469i			1.31859i	0.751882	+	0.659297i	$0.229146\pi$
$613$			32.6469i			1.31859i	−0.751882	+	0.659297i	$0.770854\pi$
$614$	−12.9817	−	14.3960i	−0.523898	−	0.580975i
$615$	2.24572	−	0.0739319i	0.0905563	−	0.00298122i
$616$	1.31521	+	12.2494i	0.0529915	+	0.493541i
$617$	15.6751	−	27.1501i	0.631056	−	1.09302i	−0.356280	−	0.934379i	$-0.615955\pi$
$617$	15.6751	−	27.1501i	0.631056	−	1.09302i	0.987336	−	0.158642i	$-0.0507115\pi$
$618$	−9.99840	+	34.7047i	−0.402194	+	1.39603i
$619$	1.72589	−	0.996445i	0.0693695	−	0.0400505i	−0.464914	−	0.885356i	$-0.653915\pi$
$619$	1.72589	−	0.996445i	0.0693695	−	0.0400505i	0.534284	+	0.845305i	$0.320581\pi$
$620$	4.20227	+	9.40065i	0.168767	+	0.377539i
$621$	−31.1373	−	14.0874i	−1.24950	−	0.565307i
$622$	5.65332	+	26.4994i	0.226677	+	1.06253i
$623$	−2.37486	−	4.11339i	−0.0951469	−	0.164799i
$624$	13.0810	+	35.8292i	0.523658	+	1.43432i
$625$	−8.98375	+	15.5603i	−0.359350	+	0.622413i
$626$	−33.9297	−	10.9964i	−1.35610	−	0.439505i
$627$	0.150383	+	4.56798i	0.00600574	+	0.182428i
$628$	20.4936	−	28.2959i	0.817785	−	1.12913i
$629$			35.3538i			1.40965i
$630$	−1.15080	+	4.55257i	−0.0458490	+	0.181379i
$631$	−15.4643			−0.615623			−0.307812	−	0.951447i	$-0.599597\pi$
$631$	−15.4643			−0.615623			−0.307812	+	0.951447i	$0.599597\pi$
$632$	6.59010	−	14.8913i	0.262140	−	0.592345i
$633$	−9.62404	−	15.4704i	−0.382521	−	0.614892i
$634$	−1.07706	+	3.32330i	−0.0427756	+	0.131985i
$635$	−1.04135	−	0.601225i	−0.0413248	−	0.0238589i
$636$	7.29720	+	4.92737i	0.289353	+	0.195383i
$637$	21.3192	−	12.3086i	0.844697	−	0.487686i
$638$	−2.66056	−	12.4711i	−0.105332	−	0.493737i
$639$	6.14274	+	9.18592i	0.243003	+	0.363390i
$640$	−0.782194	+	7.83593i	−0.0309189	+	0.309742i
$641$	−12.3638	−	21.4147i	−0.488340	−	0.845829i	0.511570	−	0.859241i	$-0.329064\pi$
$641$	−12.3638	−	21.4147i	−0.488340	−	0.845829i	−0.999910	+	0.0134123i	$0.995731\pi$
$642$	4.61893	+	18.6247i	0.182295	+	0.735058i
$643$	40.0176	+	23.1042i	1.57814	+	0.911141i	0.995119	+	0.0986850i	$0.0314636\pi$
$643$	40.0176	+	23.1042i	1.57814	+	0.911141i	0.583023	+	0.812456i	$0.301870\pi$
$644$	2.15535	−	20.8057i	0.0849326	−	0.819858i
$645$	−3.68152	−	1.96694i	−0.144960	−	0.0774482i
$646$	−5.15636	−	5.71812i	−0.202874	−	0.224976i
$647$	−6.36971			−0.250419			−0.125210	−	0.992130i	$-0.539960\pi$
$647$	−6.36971			−0.250419			−0.125210	+	0.992130i	$0.539960\pi$
$648$	24.7347	−	6.01624i	0.971670	−	0.236340i
$649$	−14.6135			−0.573630
$650$	−23.5441	−	26.1091i	−0.923474	−	1.02408i
$651$	17.9686	+	9.60016i	0.704245	+	0.376260i
$652$	17.0438	+	1.76564i	0.667485	+	0.0691476i
$653$	−31.8848	−	18.4087i	−1.24775	−	0.720389i	−0.277090	−	0.960844i	$-0.589370\pi$
$653$	−31.8848	−	18.4087i	−1.24775	−	0.720389i	−0.970660	+	0.240455i	$0.922703\pi$
$654$	−0.142922	−	0.576298i	−0.00558870	−	0.0225350i
$655$	−2.31058	−	4.00205i	−0.0902820	−	0.156373i
$656$	4.97185	−	5.55509i	0.194118	−	0.216890i
$657$	4.72274	+	7.06244i	0.184252	+	0.275532i
$658$	3.61904	+	16.9639i	0.141085	+	0.661323i
$659$	−6.46565	+	3.73294i	−0.251866	+	0.145415i	−0.620618	−	0.784113i	$-0.713118\pi$
$659$	−6.46565	+	3.73294i	−0.251866	+	0.145415i	0.368752	+	0.929528i	$0.379785\pi$
$660$	3.69606	−	5.47369i	0.143869	−	0.213063i
$661$	−2.51984	−	1.45483i	−0.0980102	−	0.0565862i	0.450194	−	0.892931i	$-0.351355\pi$
$661$	−2.51984	−	1.45483i	−0.0980102	−	0.0565862i	−0.548204	+	0.836345i	$0.684688\pi$
$662$	−12.3048	+	37.9668i	−0.478240	+	1.47562i
$663$	28.4675	+	45.7607i	1.10559	+	1.77720i
$664$	−17.1720	−	7.59940i	−0.666402	−	0.294914i
$665$	−1.06622			−0.0413461
$666$	6.50404	−	25.7300i	0.252026	−	0.997017i
$667$			21.6505i			0.838310i
$668$	19.3575	+	14.0199i	0.748965	+	0.542447i
$669$	−0.220130	−	6.68657i	−0.00851071	−	0.258518i
$670$	−6.44199	−	2.08781i	−0.248876	−	0.0806592i
$671$	12.5525	−	21.7415i	0.484582	−	0.839321i
$672$	8.27909	+	13.1982i	0.319373	+	0.509133i
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	0.911799	+	0.410637i	$0.134694\pi$
$673$	21.0527	+	36.4643i	0.811522	+	1.40560i	−0.100277	+	0.994960i	$0.531973\pi$
$674$	−3.30806	−	15.5062i	−0.127422	−	0.597278i
$675$	−19.0645	+	13.6774i	−0.733794	+	0.526444i
$676$	31.6046	−	14.1279i	1.21556	−	0.543379i
$677$	−32.9941	+	19.0492i	−1.26807	+	0.732119i	−0.974622	−	0.223858i	$-0.928135\pi$
$677$	−32.9941	+	19.0492i	−1.26807	+	0.732119i	−0.293445	+	0.955976i	$0.594802\pi$
$678$	−5.89673	+	20.4677i	−0.226463	+	0.786058i
$679$	1.98507	−	3.43825i	0.0761801	−	0.131948i
$680$	1.18785	+	11.0631i	0.0455518	+	0.424251i
$681$	27.8215	−	0.915918i	1.06612	−	0.0350981i
$682$	−19.1893	−	21.2799i	−0.734796	−	0.814849i
$683$		−	47.0728i		−	1.80119i	−0.434659	−	0.900595i	$-0.643131\pi$
$683$		−	47.0728i		−	1.80119i	0.434659	−	0.900595i	$-0.356869\pi$
$684$	2.70076	+	5.11018i	0.103266	+	0.195393i
$685$			2.52421i			0.0964450i
$686$	19.1579	−	17.2758i	0.731453	−	0.659593i
$687$	7.88448	+	12.6741i	0.300812	+	0.483546i
$688$	−13.1582	+	4.31887i	−0.501653	+	0.164656i
$689$	6.99676	−	12.1187i	0.266555	−	0.461687i
$690$	−8.07623	+	7.77963i	−0.307457	+	0.296166i
$691$	−3.38522	+	1.95446i	−0.128780	+	0.0743512i	−0.563006	−	0.826453i	$-0.690355\pi$
$691$	−3.38522	+	1.95446i	−0.128780	+	0.0743512i	0.434226	+	0.900804i	$0.357022\pi$
$692$	10.6473	+	23.8185i	0.404750	+	0.905442i
$693$	−0.859436	−	13.0388i	−0.0326473	−	0.495302i
$694$	−28.4760	+	6.07498i	−1.08093	+	0.230603i
$695$	−6.02468	−	10.4350i	−0.228529	−	0.395824i
$696$	−9.93146	−	12.7053i	−0.376451	−	0.481594i
$697$	5.26678	−	9.12234i	0.199494	−	0.345533i
$698$	−1.48002	+	4.56664i	−0.0560196	+	0.172850i
$699$	−36.8990	−	19.7142i	−1.39565	−	0.745658i
$700$	−11.6305	−	8.42354i	−0.439591	−	0.318380i
$701$			16.4480i			0.621231i	0.950536	+	0.310615i	$0.100535\pi$
$701$			16.4480i			0.621231i	−0.950536	+	0.310615i	$0.899465\pi$
$702$	−12.2997	−	38.5411i	−0.464221	−	1.45464i
$703$	6.02598			0.227274
$704$	−4.65211	−	21.4142i	−0.175333	−	0.807076i
$705$	4.38207	−	8.20192i	0.165038	−	0.308902i
$706$	−1.35404	−	0.438838i	−0.0509601	−	0.0165159i
$707$	13.0730	+	7.54772i	0.491662	+	0.283861i
$708$	−16.6145	+	8.09307i	−0.624410	+	0.304156i
$709$	6.84805	−	3.95372i	0.257184	−	0.148485i	−0.365865	−	0.930668i	$-0.619227\pi$
$709$	6.84805	−	3.95372i	0.257184	−	0.148485i	0.623049	+	0.782183i	$0.285894\pi$
$710$	3.54610	−	0.756515i	0.133083	−	0.0283915i
$711$	−7.63358	+	15.4938i	−0.286282	+	0.581062i
$712$	4.98123	+	6.82387i	0.186679	+	0.255735i
$713$	24.3251	+	42.1324i	0.910984	+	1.57787i
$714$	15.2721	+	15.8544i	0.571544	+	0.593334i
$715$	−9.09037	−	5.24833i	−0.339961	−	0.196276i
$716$	6.60217	+	0.683947i	0.246735	+	0.0255603i
$717$	5.92668	−	3.68696i	0.221336	−	0.137692i
$718$	33.0592	−	29.8114i	1.23376	−	1.11255i
$719$	−37.0556			−1.38194			−0.690970	−	0.722884i	$-0.742816\pi$
$719$	−37.0556			−1.38194			−0.690970	+	0.722884i	$0.742816\pi$
$720$	1.17078	−	8.27010i	0.0436325	−	0.308208i
$721$	23.4455			0.873156
$722$	18.9803	−	17.1156i	0.706372	−	0.636977i
$723$	−0.321025	−	9.75131i	−0.0119390	−	0.362655i
$724$	−29.6669	−	3.07332i	−1.10256	−	0.114219i
$725$	12.8727	+	7.43204i	0.478079	+	0.276019i
$726$	2.37119	−	8.23048i	0.0880033	−	0.305462i
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	0.913792	−	0.406182i	$-0.133140\pi$
$727$	2.83467	+	4.90979i	0.105132	+	0.182094i	−0.808660	+	0.588276i	$0.799807\pi$
$728$	19.9993	−	14.5989i	0.741222	−	0.541071i
$729$	−26.4754	+	5.29673i	−0.980569	+	0.196175i
$730$	2.72636	−	0.581634i	0.100907	−	0.0215272i
$731$	−16.9461	+	9.78381i	−0.626773	+	0.361867i
$732$	2.23062	−	31.6701i	0.0824461	−	1.17056i
$733$	−10.8544	−	6.26677i	−0.400915	−	0.231469i	0.285964	−	0.958240i	$-0.407686\pi$
$733$	−10.8544	−	6.26677i	−0.400915	−	0.231469i	−0.686879	+	0.726772i	$0.741020\pi$
$734$	−23.3190	−	7.55754i	−0.860718	−	0.278954i
$735$	−5.38786	+	0.177375i	−0.198734	+	0.00654256i
$736$	0.138933	+	37.2056i	0.00512114	+	1.37142i
$737$	18.8443			0.694139
$738$	−5.51132	+	5.67018i	−0.202875	+	0.208722i
$739$			1.83358i			0.0674492i	0.999431	+	0.0337246i	$0.0107369\pi$
$739$			1.83358i			0.0674492i	−0.999431	+	0.0337246i	$0.989263\pi$
$740$	−7.05261	−	5.10795i	−0.259259	−	0.187772i
$741$	7.79981	−	4.85223i	0.286533	−	0.178251i
$742$	1.76226	−	5.43749i	0.0646945	−	0.199616i
$743$	−15.6588	+	27.1219i	−0.574467	+	0.995006i	0.421632	+	0.906767i	$0.361457\pi$
$743$	−15.6588	+	27.1219i	−0.574467	+	0.995006i	−0.996099	+	0.0882391i	$0.971876\pi$
$744$	−33.6018	−	13.5665i	−1.23190	−	0.497372i
$745$	7.52491	+	13.0335i	0.275691	+	0.477511i
$746$	−18.0055	+	3.84125i	−0.659230	+	0.140638i
$747$	17.8667	+	8.80269i	0.653708	+	0.322074i
$748$	−12.6359	−	28.2669i	−0.462013	−	1.03354i
$749$	10.7879	−	6.22841i	0.394182	−	0.227581i
$750$	3.90515	+	15.7466i	0.142596	+	0.574983i
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	−0.791834	−	0.610736i	$-0.790874\pi$
$751$	3.64466	−	6.31274i	0.132996	−	0.230355i	0.924830	+	0.380381i	$0.124207\pi$
$752$	−9.62186	−	29.3148i	−0.350873	−	1.06900i
$753$	11.3312	−	21.2086i	0.412931	−	0.772883i
$754$	−19.0333	+	17.1634i	−0.693153	+	0.625055i
$755$		−	8.84005i		−	0.321722i
$756$	−8.19810	−	14.3482i	−0.298162	−	0.521838i
$757$			12.8156i			0.465792i	0.972502	+	0.232896i	$0.0748202\pi$
$757$			12.8156i			0.465792i	−0.972502	+	0.232896i	$0.925180\pi$
$758$	−21.6542	−	24.0134i	−0.786518	−	0.872206i
$759$	14.7048	−	27.5230i	0.533750	−	0.999020i
$760$	1.88568	−	0.202466i	0.0684009	−	0.00734421i
$761$	12.5800	−	21.7892i	0.456025	−	0.789859i	−0.542721	−	0.839913i	$-0.682606\pi$
$761$	12.5800	−	21.7892i	0.456025	−	0.789859i	0.998747	+	0.0500541i	$0.0159394\pi$
$762$	4.10718	−	1.01858i	0.148787	−	0.0368993i
$763$	−0.333807	+	0.192724i	−0.0120846	+	0.00697706i
$764$	13.3611	−	5.97269i	0.483389	−	0.216084i
$765$	−0.776207	−	11.7761i	−0.0280638	−	0.425765i
$766$	−8.85883	−	41.5250i	−0.320083	−	1.50036i
$767$	14.6854	+	25.4359i	0.530261	+	0.918439i
$768$	−17.1484	−	21.7700i	−0.618791	−	0.785556i
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	−0.992044	−	0.125890i	$-0.959821\pi$
$769$	−10.7318	+	18.5880i	−0.386998	+	0.670300i	0.605046	+	0.796190i	$0.293155\pi$
$770$	−4.07870	−	1.32188i	−0.146986	−	0.0476374i
$771$	15.9582	−	9.92750i	0.574719	−	0.357530i
$772$	33.1583	+	24.0153i	1.19339	+	0.864330i
$773$		−	20.2122i		−	0.726981i	−0.931598	−	0.363491i	$-0.881585\pi$
$773$		−	20.2122i		−	0.726981i	0.931598	−	0.363491i	$-0.118415\pi$
$774$	14.1330	−	4.00295i	0.508001	−	0.143883i
$775$	33.4007			1.19979
$776$	−2.85786	+	6.45775i	−0.102591	+	0.231820i
$777$	−17.2191	+	0.566874i	−0.617733	+	0.0203365i
$778$	16.5878	−	51.1820i	0.594701	−	1.83496i
$779$	−1.55488	−	0.897712i	−0.0557095	−	0.0321639i
$780$	−13.2417	−	0.932648i	−0.474127	−	0.0333942i
$781$	−8.73811	+	5.04495i	−0.312674	+	0.180523i
$782$	10.9682	+	51.4127i	0.392223	+	1.83851i
$783$	9.97073	+	13.8979i	0.356325	+	0.496670i
$784$	−11.9283	+	13.3276i	−0.426010	+	0.475984i
$785$	6.07957	+	10.5301i	0.216989	+	0.375836i
$786$	15.6270	+	4.50211i	0.557395	+	0.160585i
$787$	−17.5726	−	10.1455i	−0.626395	−	0.361649i	0.152960	−	0.988232i	$-0.451120\pi$
$787$	−17.5726	−	10.1455i	−0.626395	−	0.361649i	−0.779355	+	0.626583i	$0.784453\pi$
$788$	40.8686	+	4.23376i	1.45588	+	0.150821i
$789$	1.32275	+	40.1793i	0.0470912	+	1.43042i
$790$	3.79534	+	4.20882i	0.135032	+	0.149743i
$791$	13.8274			0.491646
$792$	3.99594	+	22.8969i	0.141989	+	0.813605i
$793$	−50.4570			−1.79178
$794$	35.4690	+	39.3332i	1.25875	+	1.39588i
$795$	−2.60195	+	1.61866i	−0.0922818	+	0.0574081i
$796$	0.403098	−	3.89112i	0.0142874	−	0.137917i
$797$	28.8758	+	16.6715i	1.02283	+	0.590533i	0.914924	−	0.403627i	$-0.132251\pi$
$797$	28.8758	+	16.6715i	1.02283	+	0.590533i	0.107910	+	0.994161i	$0.465584\pi$
$798$	2.70234	−	2.60310i	0.0956619	−	0.0921487i
$799$	−21.7970	−	37.7535i	−0.771122	−	1.33562i
$800$	22.1690	+	12.6891i	0.783792	+	0.448628i
$801$	−4.98123	−	7.44898i	−0.176003	−	0.263197i
$802$	1.38918	+	6.51164i	0.0490535	+	0.229934i
$803$	−6.71815	+	3.87873i	−0.237078	+	0.136877i
$804$	21.4246	−	10.4361i	0.755587	−	0.368053i
$805$	6.30432	+	3.63980i	0.222198	+	0.128286i
$806$	−17.7556	+	54.7852i	−0.625413	+	1.92972i
$807$	3.28085	−	6.14076i	0.115491	−	0.216165i
$808$	−24.5539	−	10.8662i	−0.863803	−	0.382273i
$809$	30.6920			1.07907			0.539536	−	0.841962i	$-0.318600\pi$
$809$	30.6920			1.07907			0.539536	+	0.841962i	$0.318600\pi$
$810$	−1.60153	+	8.71327i	−0.0562722	+	0.306153i
$811$		−	49.5457i		−	1.73978i	−0.493241	−	0.869892i	$-0.664188\pi$
$811$		−	49.5457i		−	1.73978i	0.493241	−	0.869892i	$-0.335812\pi$
$812$	−6.14069	+	8.47854i	−0.215496	+	0.297538i
$813$	10.3213	+	5.51443i	0.361985	+	0.193399i
$814$	23.0518	+	7.47096i	0.807965	+	0.261857i
$815$	−2.98168	+	5.16443i	−0.104444	+	0.180902i
$816$	−30.0205	−	25.1396i	−1.05093	−	0.880061i
$817$	1.66763	+	2.88842i	0.0583430	+	0.101053i
$818$	−3.16532	−	14.8372i	−0.110673	−	0.518769i
$819$	−21.8314	+	14.5989i	−0.762849	+	0.510127i
$820$	1.05884	+	2.36865i	0.0369761	+	0.0827170i
$821$	32.9739	−	19.0375i	1.15080	−	0.664414i	0.201716	−	0.979444i	$-0.435348\pi$
$821$	32.9739	−	19.0375i	1.15080	−	0.664414i	0.949082	+	0.315030i	$0.102015\pi$
$822$	−6.16269	−	6.39765i	−0.214949	−	0.223144i
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	−0.600201	−	0.799849i	$-0.704913\pi$
$823$	11.2626	−	19.5074i	0.392589	−	0.679984i	0.992790	+	0.119865i	$0.0382461\pi$
$824$	−41.4651	+	4.45211i	−1.44451	+	0.155097i
$825$	−11.3165	−	18.1909i	−0.393990	−	0.633326i
$826$	8.03429	+	8.90960i	0.279549	+	0.310004i
$827$			33.5317i			1.16601i	0.812468	+	0.583006i	$0.198124\pi$
$827$			33.5317i			1.16601i	−0.812468	+	0.583006i	$0.801876\pi$
$828$	1.47586	−	39.4352i	0.0512897	−	1.37047i
$829$		−	37.7559i		−	1.31132i	−0.755058	−	0.655658i	$-0.772391\pi$
$829$		−	37.7559i		−	1.31132i	0.755058	−	0.655658i	$-0.227609\pi$
$830$	4.85342	−	4.37661i	0.168465	−	0.151914i
$831$	3.66991	−	0.120818i	0.127308	−	0.00419113i
$832$	−32.5980	+	29.6169i	−1.13013	+	1.02678i
$833$	−12.6359	+	21.8860i	−0.437807	+	0.758304i
$834$	40.7462	+	11.7389i	1.41092	+	0.406486i
$835$	−7.20378	+	4.15910i	−0.249297	+	0.143932i
$836$	−4.81804	+	2.15376i	−0.166635	+	0.0744892i
$837$	35.0181	+	15.8432i	1.21040	+	0.547620i
$838$	5.71107	−	1.21838i	0.197286	−	0.0420884i
$839$	−9.90604	−	17.1578i	−0.341994	−	0.592352i	0.642809	−	0.766027i	$-0.277769\pi$
$839$	−9.90604	−	17.1578i	−0.341994	−	0.592352i	−0.984803	+	0.173675i	$0.944436\pi$
$840$	−5.36926	+	0.755932i	−0.185257	+	0.0260821i
$841$	−9.08210	+	15.7307i	−0.313176	+	0.542436i
$842$	6.91361	−	21.3321i	0.238259	−	0.735152i
$843$	1.48836	+	45.2098i	0.0512618	+	1.55711i
$844$	12.3405	−	17.0387i	0.424778	−	0.586497i
$845$			12.0481i			0.414466i
$846$	8.91803	+	31.4865i	0.306608	+	1.08253i
$847$	−5.56028			−0.191053
$848$	−2.08415	+	9.95124i	−0.0715700	+	0.341727i
$849$	−17.4711	−	28.0843i	−0.599607	−	0.963851i
$850$	34.3334	+	11.1273i	1.17763	+	0.381662i
$851$	−35.6304	−	20.5712i	−1.22140	−	0.705173i
$852$	−7.14066	+	10.5750i	−0.244635	+	0.362293i
$853$	5.95424	−	3.43768i	0.203869	−	0.117704i	−0.394590	−	0.918857i	$-0.629113\pi$
$853$	5.95424	−	3.43768i	0.203869	−	0.117704i	0.598459	+	0.801153i	$0.295780\pi$
$854$	−20.1566	+	4.30015i	−0.689744	+	0.147148i
$855$	−2.00721	+	0.132303i	−0.0686451	+	0.00452466i
$856$	−17.8965	+	13.0639i	−0.611690	+	0.446516i
$857$	−3.87316	−	6.70851i	−0.132305	−	0.229158i	0.792260	−	0.610184i	$-0.208904\pi$
$857$	−3.87316	−	6.70851i	−0.132305	−	0.229158i	−0.924565	+	0.381025i	$0.875571\pi$
$858$	35.8532	−	8.89159i	1.22401	−	0.303554i
$859$	−0.594592	−	0.343288i	−0.0202872	−	0.0117128i	0.489822	−	0.871822i	$-0.337062\pi$
$859$	−0.594592	−	0.343288i	−0.0202872	−	0.0117128i	−0.510109	+	0.860110i	$0.670395\pi$
$860$	0.496640	−	4.79409i	0.0169353	−	0.163477i
$861$	4.52750	+	2.41892i	0.154297	+	0.0824367i
$862$	16.9988	−	15.3288i	0.578980	−	0.522100i
$863$	−42.9194			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$863$	−42.9194			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$864$	17.2236	+	23.8191i	0.585957	+	0.810342i
$865$	−9.07991			−0.308726
$866$	−34.4806	+	31.0931i	−1.17170	+	1.05659i
$867$	−22.8270	−	12.1959i	−0.775246	−	0.414194i
$868$	−2.42398	+	23.3988i	−0.0822752	+	0.794206i
$869$	−13.6578	−	7.88535i	−0.463310	−	0.267492i
$870$	5.44733	−	1.35094i	0.184682	−	0.0458011i
$871$	−18.9371	−	32.8000i	−0.641658	−	1.11138i
$872$	0.553766	−	0.404233i	0.0187529	−	0.0136891i
$873$	3.31037	−	6.71901i	0.112039	−	0.227404i
$874$	8.76318	−	1.86951i	0.296419	−	0.0632372i
$875$	9.12082	−	5.26591i	0.308340	−	0.178020i
$876$	−5.48998	+	8.13039i	−0.185489	+	0.274700i
$877$	−14.7508	−	8.51640i	−0.498100	−	0.287578i	0.229828	−	0.973231i	$-0.426183\pi$
$877$	−14.7508	−	8.51640i	−0.498100	−	0.287578i	−0.727929	+	0.685653i	$0.759517\pi$
$878$	29.4016	+	9.52888i	0.992255	+	0.321584i
$879$	−5.35742	−	8.61190i	−0.180701	−	0.290472i
$880$	7.46451	+	1.56334i	0.251629	+	0.0527001i
$881$	−7.90546			−0.266342			−0.133171	−	0.991093i	$-0.542516\pi$
$881$	−7.90546			−0.266342			−0.133171	+	0.991093i	$0.542516\pi$
$882$	13.2226	−	13.6037i	0.445227	−	0.458059i
$883$		−	7.53298i		−	0.253505i	−0.991934	−	0.126752i	$-0.959545\pi$
$883$		−	7.53298i		−	0.253505i	0.991934	−	0.126752i	$-0.0404554\pi$
$884$	−36.5027	+	50.3998i	−1.22772	+	1.69513i
$885$	−0.211626	−	6.42826i	−0.00711372	−	0.216083i
$886$	−15.3304	+	47.3023i	−0.515035	+	1.58915i
$887$	7.02719	−	12.1715i	0.235950	−	0.408677i	−0.723598	−	0.690221i	$-0.757513\pi$
$887$	7.02719	−	12.1715i	0.235950	−	0.408677i	0.959548	+	0.281544i	$0.0908465\pi$
$888$	30.3457	−	4.27234i	1.01833	−	0.143370i
$889$	−1.37351	−	2.37899i	−0.0460660	−	0.0797886i
$890$	−2.87558	+	0.613468i	−0.0963896	+	0.0205635i
$891$	−3.23587	−	24.4396i	−0.108406	−	0.818757i
$892$	7.05260	−	3.15265i	0.236138	−	0.105558i
$893$	−6.43501	+	3.71525i	−0.215339	+	0.124326i
$894$	−50.8925	−	14.6621i	−1.70210	−	0.490374i
$895$	−1.15500	+	2.00052i	−0.0386075	+	0.0668701i
$896$	−10.4982	+	14.6095i	−0.350719	+	0.488069i
$897$	−62.6831	+	2.06360i	−2.09293	+	0.0689016i
$898$	3.38026	−	3.04818i	0.112801	−	0.101719i
$899$		−	24.3489i		−	0.812081i
$900$	−22.9403	−	14.4146i	−0.764676	−	0.480486i
$901$			14.3655i			0.478585i
$902$	−4.83508	−	5.36184i	−0.160990	−	0.178530i
$903$	−5.03694	−	8.09673i	−0.167619	−	0.269442i
$904$	−24.4548	+	2.62571i	−0.813355	+	0.0873300i
$905$	5.19001	−	8.98936i	0.172522	−	0.298816i
$906$	21.5824	+	22.4053i	0.717028	+	0.744365i
$907$	−39.7958	+	22.9761i	−1.32140	+	0.762910i	−0.983952	−	0.178435i	$-0.942897\pi$
$907$	−39.7958	+	22.9761i	−1.32140	+	0.762910i	−0.337447	+	0.941345i	$0.609563\pi$
$908$	13.1176	+	29.3445i	0.435322	+	0.973831i
$909$	25.5472	+	12.5868i	0.847349	+	0.417478i
$910$	1.79794	+	8.42770i	0.0596012	+	0.279375i
$911$	25.7911	+	44.6715i	0.854497	+	1.48003i	0.877111	+	0.480288i	$0.159468\pi$
$911$	25.7911	+	44.6715i	0.854497	+	1.48003i	−0.0226136	+	0.999744i	$0.507199\pi$
$912$	−4.28499	+	5.11693i	−0.141890	+	0.169438i
$913$	−9.09302	+	15.7496i	−0.300935	+	0.521235i
$914$	10.9109	+	3.53616i	0.360900	+	0.116966i
$915$	9.74553	+	5.20679i	0.322177	+	0.172131i
$916$	−10.1099	+	13.9589i	−0.334042	+	0.461216i
$917$		−	10.5571i		−	0.348627i
$918$	30.7179	+	27.9516i	1.01384	+	0.922541i
$919$	−21.2048			−0.699481			−0.349741	−	0.936847i	$-0.613730\pi$
$919$	−21.2048			−0.699481			−0.349741	+	0.936847i	$0.613730\pi$
$920$	−11.8408	−	5.24012i	−0.390381	−	0.172762i
$921$	−11.1877	+	20.9401i	−0.368649	+	0.689999i
$922$	−9.15362	+	28.2437i	−0.301458	+	0.930157i
$923$	17.5623	+	10.1396i	0.578069	+	0.333748i
$924$	13.5648	−	6.60756i	0.446250	−	0.217373i
$925$	−24.4620	+	14.1231i	−0.804305	+	0.464366i
$926$	2.62611	+	12.3096i	0.0862992	+	0.404520i
$927$	44.1374	−	2.90927i	1.44966	−	0.0955528i
$928$	9.25027	−	16.1610i	0.303655	−	0.530511i
$929$	1.70516	+	2.95343i	0.0559446	+	0.0968989i	0.892641	−	0.450767i	$-0.148850\pi$
$929$	1.70516	+	2.95343i	0.0559446	+	0.0968989i	−0.836697	+	0.547666i	$0.815516\pi$
$930$	9.08281	−	8.74925i	0.297837	−	0.286899i
$931$	3.73042	+	2.15376i	0.122259	+	0.0705865i
$932$	4.97770	−	48.0500i	0.163050	−	1.57393i
$933$	28.1779	−	17.5293i	0.922502	−	0.573885i
$934$	−24.6739	−	27.3621i	−0.807356	−	0.895314i
$935$	10.7757			0.352403
$936$	35.8382	−	29.9648i	1.17141	−	0.979432i
$937$	29.4448			0.961919			0.480959	−	0.876743i	$-0.340288\pi$
$937$	29.4448			0.961919			0.480959	+	0.876743i	$0.340288\pi$
$938$	−10.3603	−	11.4890i	−0.338277	−	0.375130i
$939$	1.43732	+	43.6595i	0.0469053	+	1.42477i
$940$	10.6806	+	1.10645i	0.348362	+	0.0360883i
$941$	40.5880	+	23.4335i	1.32313	+	0.763910i	0.984227	−	0.176911i	$-0.0566106\pi$
$941$	40.5880	+	23.4335i	1.32313	+	0.763910i	0.338904	+	0.940821i	$0.389944\pi$
$942$	−41.1174	−	11.8459i	−1.33968	−	0.385960i
$943$	6.12914	+	10.6160i	0.199592	+	0.345704i
$944$	−15.9011	−	14.2316i	−0.517537	−	0.463201i
$945$	5.72312	−	0.566874i	0.186173	−	0.0184404i
$946$	2.79832	+	13.1169i	0.0909812	+	0.426467i
$947$	31.5821	−	18.2340i	1.02628	−	0.592524i	0.110365	−	0.993891i	$-0.464798\pi$
$947$	31.5821	−	18.2340i	1.02628	−	0.592524i	0.915917	+	0.401367i	$0.131465\pi$
$948$	−19.8949	−	1.40126i	−0.646157	−	0.0455107i
$949$	13.5024	+	7.79564i	0.438308	+	0.253057i
$950$	1.89662	−	5.85206i	0.0615344	−	0.189866i
$951$	4.27630	−	0.140781i	0.138669	−	0.00456514i
$952$	−10.2868	+	23.2446i	−0.333398	+	0.753362i
$953$	38.0590			1.23285			0.616426	−	0.787413i	$-0.288580\pi$
$953$	38.0590			1.23285			0.616426	+	0.787413i	$0.288580\pi$
$954$	2.64283	−	10.4550i	0.0855647	−	0.338494i
$955$			5.09344i			0.164820i
$956$	6.52751	+	4.72763i	0.211115	+	0.152903i
$957$	−13.2610	+	8.24963i	−0.428668	+	0.266673i
$958$	23.4394	+	7.59657i	0.757292	+	0.245434i
$959$	−2.88330	+	4.99401i	−0.0931065	+	0.161265i
$960$	9.35239	−	2.35650i	0.301847	−	0.0760558i
$961$	−11.8569	−	20.5368i	−0.382481	−	0.662477i
$962$	−10.1615	−	47.6312i	−0.327620	−	1.53569i
$963$	19.5360	−	13.0639i	0.629538	−	0.420980i
$964$	10.2851	−	4.59764i	0.331261	−	0.148080i
$965$	−12.3397	+	7.12430i	−0.397228	+	0.229339i
$966$	−24.8647	+	6.16646i	−0.800010	+	0.198403i
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	−0.620090	−	0.784531i	$-0.712904\pi$
$967$	11.4864	−	19.8951i	0.369378	−	0.639782i	0.989468	+	0.144749i	$0.0462374\pi$
$968$	9.83377	−	1.05585i	0.316069	−	0.0339364i
$969$	−4.44380	+	8.31745i	−0.142755	+	0.267195i
$970$	−1.64588	−	1.82519i	−0.0528461	−	0.0586034i
$971$		−	53.8829i		−	1.72919i	−0.502474	−	0.864593i	$-0.667577\pi$
$971$		−	53.8829i		−	1.72919i	0.502474	−	0.864593i	$-0.332423\pi$
$972$	−17.2138	−	25.9940i	−0.552132	−	0.833757i
$973$		−	27.5269i		−	0.882473i
$974$	−31.2313	+	28.1630i	−1.00071	+	0.902401i
$975$	−20.2905	+	37.9777i	−0.649816	+	1.21626i
$976$	34.8319	−	11.4327i	1.11494	−	0.365952i
$977$	19.1024	−	33.0863i	0.611140	−	1.05853i	−0.379909	−	0.925024i	$-0.624045\pi$
$977$	19.1024	−	33.0863i	0.611140	−	1.05853i	0.991049	−	0.133501i	$-0.0426220\pi$
$978$	−5.05150	−	20.3689i	−0.161529	−	0.651326i
$979$	7.08585	−	4.09102i	0.226465	−	0.130749i
$980$	−2.54032	−	5.68279i	−0.0811475	−	0.181530i
$981$	−0.604495	+	0.404233i	−0.0193001	+	0.0129062i
$982$	32.9547	−	7.03045i	1.05163	−	0.224351i
$983$	−24.3307	−	42.1420i	−0.776028	−	1.34412i	−0.934215	−	0.356711i	$-0.883898\pi$
$983$	−24.3307	−	42.1420i	−0.776028	−	1.34412i	0.158186	−	0.987409i	$-0.449435\pi$
$984$	−8.46656	−	3.41832i	−0.269904	−	0.108972i
$985$	−7.14968	+	12.3836i	−0.227808	+	0.394574i
$986$	8.11169	−	25.0288i	0.258329	−	0.797079i
$987$	18.0384	−	11.2216i	0.574169	−	0.357188i
$988$	8.59054	+	6.22181i	0.273301	+	0.197942i
$989$		−	22.7715i		−	0.724093i
$990$	−7.84241	−	1.98241i	−0.249248	−	0.0630051i
$991$	−12.7822			−0.406040			−0.203020	−	0.979175i	$-0.565076\pi$
$991$	−12.7822			−0.406040			−0.203020	+	0.979175i	$0.565076\pi$
$992$	−0.156249	−	41.8428i	−0.00496091	−	1.32851i
$993$	48.8543	−	1.60834i	1.55034	−	0.0510392i
$994$	7.87991	+	2.55383i	0.249936	+	0.0810027i
$995$	1.17905	+	0.680723i	0.0373783	+	0.0215804i
$996$	−1.61586	+	22.9419i	−0.0512006	+	0.726942i
$997$	−21.1161	+	12.1914i	−0.668752	+	0.386104i	−0.795604	−	0.605817i	$-0.792846\pi$
$997$	−21.1161	+	12.1914i	−0.668752	+	0.386104i	0.126851	+	0.991922i	$0.459513\pi$
$998$	−26.9299	+	5.74514i	−0.852450	+	0.181859i
$999$	−32.3456	+	3.20383i	−1.02337	+	0.101365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.b.13.7	yes	16
3.2	odd	2		216.2.n.b.37.2		16
4.3	odd	2		288.2.r.b.49.7		16
8.3	odd	2		288.2.r.b.49.2		16
8.5	even	2	inner	72.2.n.b.13.1	✓	16
9.2	odd	6		216.2.n.b.181.8		16
9.4	even	3		648.2.d.j.325.6		8
9.5	odd	6		648.2.d.k.325.3		8
9.7	even	3	inner	72.2.n.b.61.1	yes	16
12.11	even	2		864.2.r.b.145.4		16
24.5	odd	2		216.2.n.b.37.8		16
24.11	even	2		864.2.r.b.145.5		16
36.7	odd	6		288.2.r.b.241.2		16
36.11	even	6		864.2.r.b.721.5		16
36.23	even	6		2592.2.d.k.1297.5		8
36.31	odd	6		2592.2.d.j.1297.4		8
72.5	odd	6		648.2.d.k.325.4		8
72.11	even	6		864.2.r.b.721.4		16
72.13	even	6		648.2.d.j.325.5		8
72.29	odd	6		216.2.n.b.181.2		16
72.43	odd	6		288.2.r.b.241.7		16
72.59	even	6		2592.2.d.k.1297.4		8
72.61	even	6	inner	72.2.n.b.61.7	yes	16
72.67	odd	6		2592.2.d.j.1297.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.1	✓	16	8.5	even	2	inner
72.2.n.b.13.7	yes	16	1.1	even	1	trivial
72.2.n.b.61.1	yes	16	9.7	even	3	inner
72.2.n.b.61.7	yes	16	72.61	even	6	inner
216.2.n.b.37.2		16	3.2	odd	2
216.2.n.b.37.8		16	24.5	odd	2
216.2.n.b.181.2		16	72.29	odd	6
216.2.n.b.181.8		16	9.2	odd	6
288.2.r.b.49.2		16	8.3	odd	2
288.2.r.b.49.7		16	4.3	odd	2
288.2.r.b.241.2		16	36.7	odd	6
288.2.r.b.241.7		16	72.43	odd	6
648.2.d.j.325.5		8	72.13	even	6
648.2.d.j.325.6		8	9.4	even	3
648.2.d.k.325.3		8	9.5	odd	6
648.2.d.k.325.4		8	72.5	odd	6
864.2.r.b.145.4		16	12.11	even	2
864.2.r.b.145.5		16	24.11	even	2
864.2.r.b.721.4		16	72.11	even	6
864.2.r.b.721.5		16	36.11	even	6
2592.2.d.j.1297.4		8	36.31	odd	6
2592.2.d.j.1297.5		8	72.67	odd	6
2592.2.d.k.1297.4		8	72.59	even	6
2592.2.d.k.1297.5		8	36.23	even	6

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05026 - 0.947078i) q^{2} +(-1.52768 - 0.816201i) q^{3} +(0.206086 - 1.98935i) q^{4} +(0.602794 + 0.348023i) q^{5} +(-2.37747 + 0.589613i) q^{6} +(0.795065 + 1.37709i) q^{7} +(-1.66763 - 2.28452i) q^{8} +(1.66763 + 2.49379i) q^{9} +(0.962695 - 0.205379i) q^{10} +(-2.37222 + 1.36960i) q^{11} +(-1.93855 + 2.87089i) q^{12} +(4.76780 + 2.75269i) q^{13} +(2.13924 + 0.693314i) q^{14} +(-0.636821 - 1.02367i) q^{15} +(-3.91506 - 0.819955i) q^{16} -5.65175 q^{17} +(4.11326 + 1.03975i) q^{18} +0.963328i q^{19} +(0.816569 - 1.12745i) q^{20} +(-0.0906219 - 2.75269i) q^{21} +(-1.19433 + 3.68512i) q^{22} +(3.28857 - 5.69597i) q^{23} +(0.682986 + 4.85114i) q^{24} +(-2.25776 - 3.91055i) q^{25} +(7.61444 - 1.62444i) q^{26} +(-0.512172 - 5.17085i) q^{27} +(2.90338 - 1.29787i) q^{28} +(-2.85076 + 1.64589i) q^{29} +(-1.63832 - 0.471999i) q^{30} +(-3.69844 + 6.40589i) q^{31} +(-4.88838 + 2.84670i) q^{32} +(4.74188 - 0.156108i) q^{33} +(-5.93580 + 5.35265i) q^{34} +1.10680i q^{35} +(5.30471 - 2.80357i) q^{36} -6.25538i q^{37} +(0.912347 + 1.01174i) q^{38} +(-5.03694 - 8.09673i) q^{39} +(-0.210173 - 1.95747i) q^{40} +(-0.931886 + 1.61407i) q^{41} +(-2.70219 - 2.80521i) q^{42} +(2.99838 - 1.73111i) q^{43} +(2.23574 + 5.00145i) q^{44} +(0.137339 + 2.08362i) q^{45} +(-1.94068 - 9.09677i) q^{46} +(3.85668 + 6.67997i) q^{47} +(5.31172 + 4.44811i) q^{48} +(2.23574 - 3.87242i) q^{49} +(-6.07483 - 1.96882i) q^{50} +(8.63408 + 4.61296i) q^{51} +(6.45866 - 8.91756i) q^{52} -2.54179i q^{53} +(-5.43511 - 4.94566i) q^{54} -1.90662 q^{55} +(1.82011 - 4.11282i) q^{56} +(0.786270 - 1.47166i) q^{57} +(-1.43525 + 4.42850i) q^{58} +(4.62019 + 2.66747i) q^{59} +(-2.16768 + 1.05590i) q^{60} +(-7.93715 + 4.58252i) q^{61} +(2.18256 + 10.2305i) q^{62} +(-2.10831 + 4.27921i) q^{63} +(-2.43802 + 7.61945i) q^{64} +(1.91600 + 3.31861i) q^{65} +(4.83235 - 4.65488i) q^{66} +(-5.95780 - 3.43974i) q^{67} +(-1.16474 + 11.2433i) q^{68} +(-9.67295 + 6.01750i) q^{69} +(1.04823 + 1.16243i) q^{70} +3.68351 q^{71} +(2.91612 - 7.96845i) q^{72} +2.83201 q^{73} +(-5.92433 - 6.56976i) q^{74} +(0.257341 + 7.81687i) q^{75} +(1.91640 + 0.198528i) q^{76} +(-3.77214 - 2.17785i) q^{77} +(-12.9583 - 3.73328i) q^{78} +(2.87870 + 4.98605i) q^{79} +(-2.07461 - 1.85680i) q^{80} +(-3.43802 + 8.31745i) q^{81} +(0.549933 + 2.57776i) q^{82} +(5.74968 - 3.31958i) q^{83} +(-5.49476 - 0.387012i) q^{84} +(-3.40684 - 1.96694i) q^{85} +(1.50957 - 4.65781i) q^{86} +(5.69844 - 0.187599i) q^{87} +(7.08487 + 3.13539i) q^{88} -2.98701 q^{89} +(2.11759 + 2.05827i) q^{90} +8.75427i q^{91} +(-10.6536 - 7.71598i) q^{92} +(10.8785 - 6.76749i) q^{93} +(10.3770 + 3.36312i) q^{94} +(-0.335261 + 0.580689i) q^{95} +(9.79138 - 0.358951i) q^{96} +(-1.24837 - 2.16224i) q^{97} +(-1.31938 - 6.18447i) q^{98} +(-7.37150 - 3.63184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100}) \) 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Introduction

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