LMFDB - Embedded newform 91.2.g.b.9.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(9,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.4
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	91.9
Dual form			91.2.g.b.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.425563 + 0.737096i) q^{2} +0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(-1.72074 + 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(1.82097 - 1.91940i) q^{7} +2.78793 q^{8} -2.56278 q^{9} +O(q^{10})$	\(q+(0.425563 + 0.737096i) q^{2} +0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(-1.72074 + 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(1.82097 - 1.91940i) q^{7} +2.78793 q^{8} -2.56278 q^{9} -2.92913 q^{10} -0.897986 q^{11} +(0.421723 - 0.730446i) q^{12} +(-3.07517 - 1.88237i) q^{13} +(2.18972 + 0.525403i) q^{14} +(-1.13779 + 1.97071i) q^{15} +(-0.0891447 - 0.154403i) q^{16} +(-0.968404 + 1.67733i) q^{17} +(-1.09063 - 1.88902i) q^{18} +1.03804 q^{19} +(2.19495 + 3.80177i) q^{20} +(1.20406 - 1.26915i) q^{21} +(-0.382150 - 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} +1.84345 q^{24} +(-3.42189 - 5.92688i) q^{25} +(0.0788077 - 3.06776i) q^{26} -3.67824 q^{27} +(-0.958938 - 3.23578i) q^{28} +(0.917969 - 1.58997i) q^{29} -1.93681 q^{30} +(4.56692 + 7.91014i) q^{31} +(2.86381 - 4.96026i) q^{32} -0.593769 q^{33} -1.64847 q^{34} +(2.58718 + 8.73000i) q^{35} +(-1.63452 + 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +(0.441751 + 0.765135i) q^{38} +(-2.03338 - 1.24467i) q^{39} +(-4.79731 + 8.30918i) q^{40} +(2.66571 - 4.61715i) q^{41} +(1.44789 + 0.347409i) q^{42} +(1.95732 + 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +(4.40988 - 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} +(-3.59565 + 6.22784i) q^{47} +(-0.0589445 - 0.102095i) q^{48} +(-0.368167 - 6.99031i) q^{49} +(2.91246 - 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(-4.04076 + 2.19655i) q^{52} +(4.69324 + 8.12893i) q^{53} +(-1.56532 - 2.71122i) q^{54} +(1.54520 - 2.67637i) q^{55} +(5.07673 - 5.35115i) q^{56} +0.686375 q^{57} +1.56261 q^{58} +(0.255259 - 0.442121i) q^{59} +(1.45135 + 2.51382i) q^{60} +1.43619 q^{61} +(-3.88702 + 6.73252i) q^{62} +(-4.66674 + 4.91900i) q^{63} +4.51834 q^{64} +(10.9018 - 5.92620i) q^{65} +(-0.252686 - 0.437665i) q^{66} -8.44932 q^{67} +(1.23528 + 2.13957i) q^{68} +(-1.86800 - 3.23547i) q^{69} +(-5.33385 + 5.62216i) q^{70} +(1.72419 + 2.98638i) q^{71} -7.14487 q^{72} +(-5.45026 - 9.44013i) q^{73} +(-4.51097 + 7.81324i) q^{74} +(-2.26263 - 3.91899i) q^{75} +(0.662054 - 1.14671i) q^{76} +(-1.63520 + 1.72359i) q^{77} +(0.0521095 - 2.02848i) q^{78} +(6.04589 - 10.4718i) q^{79} +0.613579 q^{80} +5.25621 q^{81} +4.53771 q^{82} +1.51669 q^{83} +(-0.634072 - 2.13957i) q^{84} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +(0.606982 - 1.05132i) q^{87} -2.50353 q^{88} +(-6.80391 - 11.7847i) q^{89} +7.50673 q^{90} +(-9.21280 + 2.47475i) q^{91} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} -6.12069 q^{94} +(-1.78619 + 3.09378i) q^{95} +(1.89362 - 3.27984i) q^{96} +(-0.253120 - 0.438417i) q^{97} +(4.99585 - 3.24619i) q^{98} +2.30134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.425563	+	0.737096i	0.300918	+	0.521206i	0.976344	−	0.216222i	$-0.0693735\pi$
$2$	0.425563	+	0.737096i	0.300918	+	0.521206i	−0.675426	+	0.737428i	$0.736040\pi$
$3$	0.661223			0.381757			0.190879	−	0.981614i	$-0.438866\pi$
$3$	0.661223			0.381757			0.190879	+	0.981614i	$0.438866\pi$
$4$	0.637793	−	1.10469i	0.318896	−	0.552345i
$5$	−1.72074	+	2.98041i	−0.769538	+	1.33288i	0.168276	+	0.985740i	$0.446180\pi$
$5$	−1.72074	+	2.98041i	−0.769538	+	1.33288i	−0.937814	+	0.347139i	$0.887153\pi$
$6$	0.281392	+	0.487385i	0.114878	+	0.198974i
$7$	1.82097	−	1.91940i	0.688260	−	0.725464i
$7$	1.82097	−	1.91940i	0.688260	−	0.725464i
$8$	2.78793			0.985684
$9$	−2.56278			−0.854261
$10$	−2.92913			−0.926272
$11$	−0.897986			−0.270753			−0.135377	−	0.990794i	$-0.543224\pi$
$11$	−0.897986			−0.270753			−0.135377	+	0.990794i	$0.543224\pi$
$12$	0.421723	−	0.730446i	0.121741	−	0.210862i
$13$	−3.07517	−	1.88237i	−0.852900	−	0.522075i
$13$	−3.07517	−	1.88237i	−0.852900	−	0.522075i
$14$	2.18972	+	0.525403i	0.585226	+	0.140420i
$15$	−1.13779	+	1.97071i	−0.293777	+	0.508836i
$16$	−0.0891447	−	0.154403i	−0.0222862	−	0.0386008i
$17$	−0.968404	+	1.67733i	−0.234873	+	0.406811i	−0.959236	−	0.282607i	$-0.908801\pi$
$17$	−0.968404	+	1.67733i	−0.234873	+	0.406811i	0.724363	+	0.689419i	$0.242134\pi$
$18$	−1.09063	−	1.88902i	−0.257063	−	0.445246i
$19$	1.03804			0.238142			0.119071	−	0.992886i	$-0.462008\pi$
$19$	1.03804			0.238142			0.119071	+	0.992886i	$0.462008\pi$
$20$	2.19495	+	3.80177i	0.490806	+	0.850101i
$21$	1.20406	−	1.26915i	0.262748	−	0.276951i
$22$	−0.382150	−	0.661902i	−0.0814745	−	0.141118i
$23$	−2.82506	−	4.89315i	−0.589067	−	1.02029i	−0.994355	−	0.106104i	$-0.966162\pi$
$23$	−2.82506	−	4.89315i	−0.589067	−	1.02029i	0.405288	−	0.914189i	$-0.367171\pi$
$24$	1.84345			0.376292
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$	0.0788077	−	3.06776i	0.0154555	−	0.601638i
$27$	−3.67824			−0.707878
$28$	−0.958938	−	3.23578i	−0.181222	−	0.611505i
$29$	0.917969	−	1.58997i	0.170463	−	0.295250i	−0.768119	−	0.640307i	$-0.778807\pi$
$29$	0.917969	−	1.58997i	0.170463	−	0.295250i	0.938582	+	0.345057i	$0.112140\pi$
$30$	−1.93681			−0.353611
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	0.905501	+	0.424345i	$0.139495\pi$
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	−0.0852573	+	0.996359i	$0.527171\pi$
$32$	2.86381	−	4.96026i	0.506254	−	0.876858i
$33$	−0.593769			−0.103362
$34$	−1.64847			−0.282710
$35$	2.58718	+	8.73000i	0.437313	+	1.47564i
$36$	−1.63452	+	2.83108i	−0.272421	+	0.471847i
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.860636	+	0.509221i	$0.170067\pi$
$37$	5.30001	+	9.17989i	0.871316	+	1.50916i	0.0106808	+	0.999943i	$0.496600\pi$
$38$	0.441751	+	0.765135i	0.0716614	+	0.124121i
$39$	−2.03338	−	1.24467i	−0.325601	−	0.199306i
$40$	−4.79731	+	8.30918i	−0.758521	+	1.31380i
$41$	2.66571	−	4.61715i	0.416314	−	0.721078i	−0.579251	−	0.815149i	$-0.696655\pi$
$41$	2.66571	−	4.61715i	0.416314	−	0.721078i	0.995565	+	0.0940715i	$0.0299882\pi$
$42$	1.44789	+	0.347409i	0.223414	+	0.0536064i
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	0.975790	−	0.218708i	$-0.0701841\pi$
$43$	1.95732	+	3.39018i	0.298489	+	0.516998i	−0.677302	+	0.735706i	$0.736851\pi$
$44$	−0.572729	+	0.991996i	−0.0863422	+	0.149549i
$45$	4.40988	−	7.63814i	0.657387	−	1.13863i
$46$	2.40448	−	4.16469i	0.354522	−	0.614050i
$47$	−3.59565	+	6.22784i	−0.524479	+	0.908424i	0.475115	+	0.879924i	$0.342407\pi$
$47$	−3.59565	+	6.22784i	−0.524479	+	0.908424i	−0.999594	+	0.0285004i	$0.990927\pi$
$48$	−0.0589445	−	0.102095i	−0.00850791	−	0.0147361i
$49$	−0.368167	−	6.99031i	−0.0525953	−	0.998616i
$50$	2.91246	−	5.04452i	0.411883	−	0.713403i
$51$	−0.640331	+	1.10909i	−0.0896643	+	0.155303i
$52$	−4.04076	+	2.19655i	−0.560352	+	0.304607i
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	0.984378	+	0.176065i	$0.0563370\pi$
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	−0.339712	+	0.940529i	$0.610330\pi$
$54$	−1.56532	−	2.71122i	−0.213013	−	0.368950i
$55$	1.54520	−	2.67637i	0.208355	−	0.360881i
$56$	5.07673	−	5.35115i	0.678407	−	0.715078i
$57$	0.686375			0.0909127
$58$	1.56261			0.205181
$59$	0.255259	−	0.442121i	0.0332318	−	0.0575592i	−0.848931	−	0.528503i	$-0.822753\pi$
$59$	0.255259	−	0.442121i	0.0332318	−	0.0575592i	0.882163	+	0.470944i	$0.156087\pi$
$60$	1.45135	+	2.51382i	0.187369	+	0.324532i
$61$	1.43619			0.183885			0.0919426	−	0.995764i	$-0.470692\pi$
$61$	1.43619			0.183885			0.0919426	+	0.995764i	$0.470692\pi$
$62$	−3.88702	+	6.73252i	−0.493653	+	0.855031i
$63$	−4.66674	+	4.91900i	−0.587954	+	0.619736i
$64$	4.51834			0.564792
$65$	10.9018	−	5.92620i	1.35220	−	0.735055i
$66$	−0.252686	−	0.437665i	−0.0311035	−	0.0538729i
$67$	−8.44932			−1.03225			−0.516124	−	0.856514i	$-0.672626\pi$
$67$	−8.44932			−1.03225			−0.516124	+	0.856514i	$0.672626\pi$
$68$	1.23528	+	2.13957i	0.149800	+	0.259461i
$69$	−1.86800	−	3.23547i	−0.224881	−	0.389504i
$70$	−5.33385	+	5.62216i	−0.637516	+	0.671977i
$71$	1.72419	+	2.98638i	0.204623	+	0.354418i	0.950013	−	0.312211i	$-0.101070\pi$
$71$	1.72419	+	2.98638i	0.204623	+	0.354418i	−0.745389	+	0.666629i	$0.767736\pi$
$72$	−7.14487			−0.842031
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	−0.985892	−	0.167384i	$-0.946468\pi$
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	0.347987	−	0.937499i	$-0.386865\pi$
$74$	−4.51097	+	7.81324i	−0.524390	+	0.908270i
$75$	−2.26263	−	3.91899i	−0.261266	−	0.452526i
$76$	0.662054	−	1.14671i	0.0759428	−	0.131537i
$77$	−1.63520	+	1.72359i	−0.186349	+	0.196422i
$78$	0.0521095	−	2.02848i	0.00590024	−	0.229680i
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	0.613579			0.0686002
$81$	5.25621			0.584024
$82$	4.53771			0.501107
$83$	1.51669			0.166479			0.0832393	−	0.996530i	$-0.473473\pi$
$83$	1.51669			0.166479			0.0832393	+	0.996530i	$0.473473\pi$
$84$	−0.634072	−	2.13957i	−0.0691830	−	0.233446i
$85$	−3.33274	−	5.77248i	−0.361487	−	0.626113i
$86$	−1.66593	+	2.88547i	−0.179642	+	0.311148i
$87$	0.606982	−	1.05132i	0.0650754	−	0.112714i
$88$	−2.50353			−0.266877
$89$	−6.80391	−	11.7847i	−0.721213	−	1.24918i	−0.960514	−	0.278232i	$-0.910252\pi$
$89$	−6.80391	−	11.7847i	−0.721213	−	1.24918i	0.239301	−	0.970945i	$-0.423082\pi$
$90$	7.50673			0.791279
$91$	−9.21280	+	2.47475i	−0.965763	+	0.259424i
$92$	−7.20722			−0.751405
$93$	3.01976	+	5.23037i	0.313134	+	0.542364i
$94$	−6.12069			−0.631301
$95$	−1.78619	+	3.09378i	−0.183260	+	0.317415i
$96$	1.89362	−	3.27984i	0.193266	−	0.334747i
$97$	−0.253120	−	0.438417i	−0.0257005	−	0.0445145i	0.852889	−	0.522092i	$-0.174848\pi$
$97$	−0.253120	−	0.438417i	−0.0257005	−	0.0445145i	−0.878590	+	0.477578i	$0.841515\pi$
$98$	4.99585	−	3.24619i	0.504657	−	0.327915i
$99$	2.30134			0.231294
$100$	−8.72982			−0.872982
$101$	−5.98654			−0.595683			−0.297842	−	0.954615i	$-0.596267\pi$
$101$	−5.98654			−0.595683			−0.297842	+	0.954615i	$0.596267\pi$
$102$	−1.09000			−0.107927
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	−0.746073	−	0.665865i	$-0.768063\pi$
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	0.949692	+	0.313186i	$0.101396\pi$
$104$	−8.57338	−	5.24792i	−0.840689	−	0.514601i
$105$	1.71070	+	5.77248i	0.166947	+	0.563336i
$106$	−3.99454	+	6.91874i	−0.387984	+	0.672008i
$107$	7.06169	+	12.2312i	0.682679	+	1.18243i	0.974160	+	0.225858i	$0.0725186\pi$
$107$	7.06169	+	12.2312i	0.682679	+	1.18243i	−0.291481	+	0.956577i	$0.594148\pi$
$108$	−2.34596	+	4.06331i	−0.225740	+	0.390993i
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	0.948934	−	0.315475i	$-0.102164\pi$
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	−0.747677	+	0.664063i	$0.768831\pi$
$110$	2.63032			0.250791
$111$	3.50449	+	6.06995i	0.332631	+	0.576135i
$112$	−0.458690	−	0.110059i	−0.0433421	−	0.0103996i
$113$	−6.88472	−	11.9247i	−0.647660	−	1.12178i	−0.983680	−	0.179926i	$-0.942414\pi$
$113$	−6.88472	−	11.9247i	−0.647660	−	1.12178i	0.336020	−	0.941855i	$-0.390919\pi$
$114$	0.292096	+	0.505925i	0.0273573	+	0.0473842i
$115$	19.4448			1.81324
$116$	−1.17095	−	2.02814i	−0.108720	−	0.188308i
$117$	7.88100	+	4.82410i	0.728599	+	0.445989i
$118$	0.434514			0.0400003
$119$	1.45602	+	4.91310i	0.133473	+	0.450384i
$120$	−3.17209	+	5.49422i	−0.289571	+	0.501552i
$121$	−10.1936			−0.926693
$122$	0.611189	+	1.05861i	0.0553344	+	0.0958420i
$123$	1.76263	−	3.05297i	0.158931	−	0.275277i
$124$	11.6510			1.04629
$125$	6.34531			0.567542
$126$	−5.61177	−	1.34650i	−0.499936	−	0.119955i
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	−0.905942	−	0.423402i	$-0.860836\pi$
$127$	−0.972482	+	1.68439i	−0.0862938	+	0.149465i	0.819648	+	0.572868i	$0.194169\pi$
$128$	−3.80478	−	6.59007i	−0.336298	−	0.582485i
$129$	1.29423	+	2.24167i	0.113950	+	0.197368i
$130$	9.00758	+	5.51370i	0.790017	+	0.483584i
$131$	6.01770	−	10.4230i	0.525769	−	0.910659i	−0.473780	−	0.880643i	$-0.657111\pi$
$131$	6.01770	−	10.4230i	0.525769	−	0.910659i	0.999549	−	0.0300158i	$-0.00955576\pi$
$132$	−0.378702	+	0.655931i	−0.0329618	+	0.0570914i
$133$	1.89023	−	1.99241i	0.163904	−	0.172764i
$134$	−3.59571	−	6.22796i	−0.310622	−	0.538014i
$135$	6.32930	−	10.9627i	0.544739	−	0.943516i
$136$	−2.69985	+	4.67627i	−0.231510	+	0.400987i
$137$	−4.35857	+	7.54927i	−0.372378	+	0.644978i	−0.989931	−	0.141552i	$-0.954791\pi$
$137$	−4.35857	+	7.54927i	−0.372378	+	0.644978i	0.617553	+	0.786529i	$0.288124\pi$
$138$	1.58990	−	2.75379i	0.135341	−	0.234418i
$139$	−2.10625	−	3.64813i	−0.178650	−	0.309430i	0.762769	−	0.646672i	$-0.223840\pi$
$139$	−2.10625	−	3.64813i	−0.178650	−	0.309430i	−0.941418	+	0.337241i	$0.890506\pi$
$140$	11.2940	+	2.70990i	0.954519	+	0.229029i
$141$	−2.37752	+	4.11799i	−0.200224	+	0.346798i
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$	2.76146	+	1.69034i	0.230925	+	0.141353i
$144$	0.228459	+	0.395702i	0.0190382	+	0.0329751i
$145$	3.15917	+	5.47184i	0.262355	+	0.454412i
$146$	4.63885	−	8.03473i	0.383914	−	0.664959i
$147$	−0.243441	−	4.62216i	−0.0200786	−	0.381229i
$148$	13.5212			1.11144
$149$	5.86484			0.480466			0.240233	−	0.970715i	$-0.422776\pi$
$149$	5.86484			0.480466			0.240233	+	0.970715i	$0.422776\pi$
$150$	1.92578	−	3.33555i	0.157240	−	0.272347i
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	0.973155	+	0.230150i	$0.0739216\pi$
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	−0.287262	+	0.957852i	$0.592745\pi$
$152$	2.89398			0.234733
$153$	2.48181	−	4.29862i	0.200643	−	0.347523i
$154$	−1.96633	−	0.471805i	−0.158452	−	0.0380191i
$155$	−31.4339			−2.52483
$156$	−2.67184	+	1.45241i	−0.213919	+	0.116286i
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	0.902116	−	0.431493i	$-0.142013\pi$
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	−0.824742	+	0.565509i	$0.808680\pi$
$158$	10.2916			0.818757
$159$	3.10328	+	5.37504i	0.246106	+	0.426268i
$160$	9.85573	+	17.0706i	0.779164	+	1.34955i
$161$	−14.5362	−	3.48785i	−1.14562	−	0.274881i
$162$	2.23685	+	3.87433i	0.175743	+	0.304396i
$163$	−11.8959			−0.931762			−0.465881	−	0.884847i	$-0.654262\pi$
$163$	−11.8959			−0.931762			−0.465881	+	0.884847i	$0.654262\pi$
$164$	−3.40035	−	5.88957i	−0.265522	−	0.459898i
$165$	1.02172	−	1.76968i	0.0795410	−	0.137769i
$166$	0.645448	+	1.11795i	0.0500965	+	0.0867696i
$167$	−8.28801	+	14.3553i	−0.641346	+	1.11084i	0.343787	+	0.939048i	$0.388290\pi$
$167$	−8.28801	+	14.3553i	−0.641346	+	1.11084i	−0.985133	+	0.171796i	$0.945043\pi$
$168$	3.35685	−	3.53831i	0.258987	−	0.272986i
$169$	5.91338	+	11.5772i	0.454875	+	0.890555i
$170$	2.83658	−	4.91310i	0.217556	−	0.376818i
$171$	−2.66027			−0.203436
$172$	4.99346			0.380748
$173$	−9.98656			−0.759264			−0.379632	−	0.925138i	$-0.623949\pi$
$173$	−9.98656			−0.759264			−0.379632	+	0.925138i	$0.623949\pi$
$174$	1.03324			0.0783295
$175$	−17.6072	−	4.22469i	−1.33098	−	0.319357i
$176$	0.0800507	+	0.138652i	0.00603405	+	0.0104513i
$177$	0.168783	−	0.292341i	0.0126865	−	0.0219737i
$178$	5.79098	−	10.0303i	0.434052	−	0.751801i
$179$	9.17657			0.685889			0.342945	−	0.939356i	$-0.388576\pi$
$179$	9.17657			0.685889			0.342945	+	0.939356i	$0.388576\pi$
$180$	−5.62518	−	9.74310i	−0.419276	−	0.726208i
$181$	6.00489			0.446340			0.223170	−	0.974780i	$-0.428360\pi$
$181$	6.00489			0.446340			0.223170	+	0.974780i	$0.428360\pi$
$182$	−5.74475	−	5.73756i	−0.425829	−	0.425296i
$183$	0.949642			0.0701995
$184$	−7.87609	−	13.6418i	−0.580633	−	1.00569i
$185$	−36.4797			−2.68204
$186$	−2.57019	+	4.45170i	−0.188456	+	0.326415i
$187$	0.869614	−	1.50622i	0.0635925	−	0.110145i
$188$	4.58655	+	7.94415i	0.334509	+	0.579386i
$189$	−6.69795	+	7.06000i	−0.487204	+	0.513540i
$190$	−3.04055			−0.220585
$191$	1.31612			0.0952313			0.0476156	−	0.998866i	$-0.484838\pi$
$191$	1.31612			0.0952313			0.0476156	+	0.998866i	$0.484838\pi$
$192$	2.98763			0.215614
$193$	−16.4254			−1.18233			−0.591163	−	0.806552i	$-0.701331\pi$
$193$	−16.4254			−1.18233			−0.591163	+	0.806552i	$0.701331\pi$
$194$	0.215437	−	0.373148i	0.0154675	−	0.0267905i
$195$	7.20852	−	3.91854i	0.516213	−	0.280613i
$196$	−7.95694	−	4.05166i	−0.568353	−	0.289404i
$197$	12.7938	−	22.1594i	0.911517	−	1.57879i	0.0995951	−	0.995028i	$-0.468245\pi$
$197$	12.7938	−	22.1594i	0.911517	−	1.57879i	0.811922	−	0.583766i	$-0.198421\pi$
$198$	0.979367	+	1.69631i	0.0696006	+	0.120552i
$199$	12.6894	−	21.9787i	0.899528	−	1.55803i	0.0714284	−	0.997446i	$-0.477244\pi$
$199$	12.6894	−	21.9787i	0.899528	−	1.55803i	0.828099	−	0.560582i	$-0.189422\pi$
$200$	−9.54000	−	16.5238i	−0.674580	−	1.16841i
$201$	−5.58688			−0.394068
$202$	−2.54765	−	4.41266i	−0.179252	−	0.310473i
$203$	−1.38019	−	4.65723i	−0.0968704	−	0.326873i
$204$	0.816797	+	1.41473i	0.0571873	+	0.0990512i
$205$	9.17399	+	15.8898i	0.640740	+	1.10979i
$206$	3.51772			0.245091
$207$	7.24003	+	12.5401i	0.503217	+	0.871597i
$208$	−0.0165082	+	0.642619i	−0.00114464	+	0.0445576i
$209$	−0.932145			−0.0644778
$210$	−3.52686	+	3.71750i	−0.243377	+	0.256532i
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	−0.751173	−	0.660105i	$-0.770512\pi$
$211$	2.84824	−	4.93330i	0.196081	−	0.339622i	0.947254	+	0.320483i	$0.103845\pi$
$212$	11.9733			0.822327
$213$	1.14007	+	1.97466i	0.0781165	+	0.135302i
$214$	−6.01038	+	10.4103i	−0.410861	+	0.711633i
$215$	−13.4722			−0.918794
$216$	−10.2547			−0.697744
$217$	23.4989	+	5.63836i	1.59521	+	0.382757i
$218$	−1.78837	+	3.09755i	−0.121124	+	0.209793i
$219$	−3.60384	−	6.24203i	−0.243525	−	0.421797i
$220$	−1.97104	−	3.41393i	−0.132887	−	0.230167i
$221$	6.13536	−	3.33517i	0.412709	−	0.224348i
$222$	−2.98276	+	5.16629i	−0.200190	+	0.346739i
$223$	−1.17906	+	2.04219i	−0.0789558	+	0.136755i	−0.902800	−	0.430061i	$-0.858492\pi$
$223$	−1.17906	+	2.04219i	−0.0789558	+	0.136755i	0.823844	+	0.566817i	$0.191825\pi$
$224$	−4.30581	−	14.5292i	−0.287694	−	0.970776i
$225$	8.76956	+	15.1893i	0.584637	+	1.01262i
$226$	5.85976	−	10.1494i	0.389786	−	0.675129i
$227$	−13.1463	+	22.7701i	−0.872551	+	1.51130i	−0.0132022	+	0.999913i	$0.504203\pi$
$227$	−13.1463	+	22.7701i	−0.872551	+	1.51130i	−0.859349	+	0.511390i	$0.829131\pi$
$228$	0.437765	−	0.758232i	0.0289917	−	0.0502151i
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	−0.867156	−	0.498037i	$-0.834054\pi$
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	0.864891	+	0.501960i	$0.167388\pi$
$230$	8.27498	+	14.3327i	0.545636	+	0.945069i
$231$	−1.08123	+	1.13968i	−0.0711400	+	0.0749854i
$232$	2.55924	−	4.43273i	0.168022	−	0.291023i
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	−0.999751	−	0.0223253i	$-0.992893\pi$
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	0.519210	+	0.854647i	$0.326226\pi$
$234$	−0.201967	+	7.86202i	−0.0132030	+	0.513956i
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	−0.325604	−	0.563963i	−0.0211950	−	0.0367109i
$237$	3.99768	−	6.92419i	0.259677	−	0.449774i
$238$	−3.00180	+	3.16406i	−0.194578	+	0.205096i
$239$	3.35434			0.216974			0.108487	−	0.994098i	$-0.465399\pi$
$239$	3.35434			0.216974			0.108487	+	0.994098i	$0.465399\pi$
$240$	0.405713			0.0261886
$241$	4.28989	−	7.43031i	0.276336	−	0.478628i	−0.694135	−	0.719845i	$-0.744213\pi$
$241$	4.28989	−	7.43031i	0.276336	−	0.478628i	0.970471	+	0.241216i	$0.0775464\pi$
$242$	−4.33802	−	7.51368i	−0.278859	−	0.482998i
$243$	14.5103			0.930833
$244$	0.915991	−	1.58654i	0.0586403	−	0.101568i
$245$	21.4675	+	10.9312i	1.37151	+	0.698370i
$246$	3.00044			0.191301
$247$	−3.19215	−	1.95397i	−0.203112	−	0.124328i
$248$	12.7323	+	22.0530i	0.808501	+	1.40036i
$249$	1.00287			0.0635544
$250$	2.70033	+	4.67711i	0.170784	+	0.295806i
$251$	−10.7575	−	18.6326i	−0.679010	−	1.17608i	−0.975280	−	0.220975i	$-0.929076\pi$
$251$	−10.7575	−	18.6326i	−0.679010	−	1.17608i	0.296270	−	0.955104i	$-0.404257\pi$
$252$	2.45755	+	8.29260i	0.154811	+	0.522385i
$253$	2.53687	+	4.39399i	0.159492	+	0.276248i
$254$	−1.65541			−0.103870
$255$	−2.20369	−	3.81690i	−0.138000	−	0.239023i
$256$	7.75668	−	13.4350i	0.484793	−	0.839686i
$257$	−2.46896	−	4.27636i	−0.154010	−	0.266752i	0.778688	−	0.627411i	$-0.215885\pi$
$257$	−2.46896	−	4.27636i	−0.154010	−	0.266752i	−0.932698	+	0.360659i	$0.882552\pi$
$258$	−1.10155	+	1.90794i	−0.0685795	+	0.118783i
$259$	27.2710	+	6.54344i	1.69454	+	0.406590i
$260$	0.406471	−	15.8228i	0.0252083	−	0.981288i
$261$	−2.35256	+	4.07475i	−0.145620	+	0.252221i
$262$	10.2436			0.632854
$263$	−8.95439			−0.552151			−0.276076	−	0.961136i	$-0.589034\pi$
$263$	−8.95439			−0.552151			−0.276076	+	0.961136i	$0.589034\pi$
$264$	−1.65539			−0.101882
$265$	−32.3034			−1.98438
$266$	2.27301	+	0.545389i	0.139367	+	0.0334400i
$267$	−4.49890	−	7.79233i	−0.275328	−	0.476883i
$268$	−5.38891	+	9.33387i	−0.329180	+	0.570157i
$269$	2.41172	−	4.17723i	0.147045	−	0.254690i	−0.783089	−	0.621910i	$-0.786357\pi$
$269$	2.41172	−	4.17723i	0.147045	−	0.254690i	0.930134	+	0.367220i	$0.119690\pi$
$270$	10.7740			0.655688
$271$	3.71072	+	6.42715i	0.225410	+	0.390422i	0.956442	−	0.291921i	$-0.0942945\pi$
$271$	3.71072	+	6.42715i	0.225410	+	0.390422i	−0.731032	+	0.682343i	$0.760961\pi$
$272$	0.345312			0.0209376
$273$	−6.09171	+	1.63636i	−0.368687	+	0.0990371i
$274$	−7.41938			−0.448221
$275$	3.07281	+	5.32226i	0.185297	+	0.320944i
$276$	−4.76558			−0.286854
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	−0.917640	−	0.397413i	$-0.869908\pi$
$277$	−1.90816	+	3.30503i	−0.114650	+	0.198580i	0.802990	+	0.595993i	$0.203241\pi$
$278$	1.79268	−	3.10502i	0.107518	−	0.186226i
$279$	−11.7040	−	20.2720i	−0.700702	−	1.21365i
$280$	7.21288	+	24.3387i	0.431052	+	1.45451i
$281$	8.54978			0.510037			0.255019	−	0.966936i	$-0.417918\pi$
$281$	8.54978			0.510037			0.255019	+	0.966936i	$0.417918\pi$
$282$	−4.04714			−0.241004
$283$	15.2643			0.907371			0.453686	−	0.891162i	$-0.350109\pi$
$283$	15.2643			0.907371			0.453686	+	0.891162i	$0.350109\pi$
$284$	4.39870			0.261015
$285$	−1.18107	+	2.04568i	−0.0699607	+	0.121176i
$286$	−0.0707683	+	2.75481i	−0.00418461	+	0.162895i
$287$	−4.00797	−	13.5242i	−0.236583	−	0.798310i
$288$	−7.33932	+	12.7121i	−0.432474	+	0.749066i
$289$	6.62439	+	11.4738i	0.389670	+	0.674928i
$290$	−2.68885	+	4.65723i	−0.157895	+	0.273482i
$291$	−0.167369	−	0.289892i	−0.00981135	−	0.0169938i
$292$	−13.9045			−0.813702
$293$	2.96982	+	5.14388i	0.173499	+	0.300509i	0.939641	−	0.342163i	$-0.111159\pi$
$293$	2.96982	+	5.14388i	0.173499	+	0.300509i	−0.766142	+	0.642671i	$0.777826\pi$
$294$	3.30337	−	2.14646i	0.192657	−	0.125184i
$295$	0.878467	+	1.52155i	0.0511463	+	0.0885881i
$296$	14.7761	+	25.5929i	0.858842	+	1.48756i
$297$	3.30301			0.191660
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$	−0.523159	+	20.3651i	−0.0302551	+	1.17774i
$300$	−5.77236			−0.333267
$301$	10.0713	+	2.41653i	0.580501	+	0.139286i
$302$	−7.17362	+	12.4251i	−0.412796	+	0.714983i
$303$	−3.95844			−0.227406
$304$	−0.0925356	−	0.160276i	−0.00530728	−	0.00919248i
$305$	−2.47131	+	4.28043i	−0.141507	+	0.245097i
$306$	4.22467			0.241508
$307$	22.2133			1.26778			0.633891	−	0.773422i	$-0.281457\pi$
$307$	22.2133			1.26778			0.633891	+	0.773422i	$0.281457\pi$
$308$	0.861114	+	2.90569i	0.0490665	+	0.165567i
$309$	1.36642	−	2.36672i	0.0777332	−	0.134638i
$310$	−13.3771	−	23.1698i	−0.759769	−	1.31596i
$311$	−4.92130	−	8.52394i	−0.279061	−	0.483348i	0.692091	−	0.721811i	$-0.256690\pi$
$311$	−4.92130	−	8.52394i	−0.279061	−	0.483348i	−0.971152	+	0.238463i	$0.923357\pi$
$312$	−5.66892	−	3.47005i	−0.320939	−	0.196453i
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	−0.403072	−	0.915168i	$-0.632058\pi$
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	0.994095	−	0.108513i	$-0.0346090\pi$
$314$	−0.825166	+	1.42923i	−0.0465668	+	0.0806561i
$315$	−6.63038	−	22.3731i	−0.373579	−	1.26058i
$316$	−7.71205	−	13.3577i	−0.433837	−	0.751427i
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	−0.251847	−	0.967767i	$-0.581038\pi$
$317$	12.6801	−	21.9626i	0.712188	−	1.23355i	0.964034	−	0.265778i	$-0.0856288\pi$
$318$	−2.64128	+	4.57483i	−0.148116	+	0.256544i
$319$	−0.824324	+	1.42777i	−0.0461533	+	0.0799398i
$320$	−7.77489	+	13.4665i	−0.434629	+	0.752800i
$321$	4.66935	+	8.08755i	0.260618	+	0.451403i
$322$	−3.61521	−	12.1989i	−0.201468	−	0.679819i
$323$	−1.00524	+	1.74113i	−0.0559331	+	0.0968790i
$324$	3.35237	−	5.80648i	0.186243	−	0.322582i
$325$	−0.633681	+	24.6674i	−0.0351503	+	1.36830i
$326$	−5.06247	−	8.76845i	−0.280384	−	0.485640i
$327$	1.38935	+	2.40643i	0.0768314	+	0.133076i
$328$	7.43183	−	12.8723i	0.410354	−	0.710755i
$329$	5.40615	+	18.2422i	0.298051	+	1.00572i
$330$	1.73923			0.0957413
$331$	1.78283			0.0979935			0.0489967	−	0.998799i	$-0.484398\pi$
$331$	1.78283			0.0979935			0.0489967	+	0.998799i	$0.484398\pi$
$332$	0.967335	−	1.67547i	0.0530894	−	0.0919536i
$333$	−13.5828	−	23.5261i	−0.744332	−	1.28922i
$334$	−14.1083			−0.771971
$335$	14.5391	−	25.1824i	0.794354	−	1.37586i
$336$	−0.303297	−	0.0727734i	−0.0165462	−	0.00397012i
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	−6.01701	+	9.28556i	−0.327282	+	0.505068i
$339$	−4.55234	−	7.88488i	−0.247249	−	0.428248i
$340$	−8.50240			−0.461107
$341$	−4.10103	−	7.10320i	−0.222083	−	0.384660i
$342$	−1.13211	−	1.96087i	−0.0612176	−	0.106032i
$343$	−14.0876	−	12.0225i	−0.760659	−	0.649152i
$344$	5.45689	+	9.45160i	0.294216	+	0.509596i
$345$	12.8573			0.692216
$346$	−4.24991	−	7.36106i	−0.228477	−	0.395733i
$347$	−0.316694	+	0.548531i	−0.0170010	+	0.0294467i	−0.874401	−	0.485204i	$-0.838745\pi$
$347$	−0.316694	+	0.548531i	−0.0170010	+	0.0294467i	0.857400	+	0.514651i	$0.172079\pi$
$348$	−0.774258	−	1.34105i	−0.0415046	−	0.0718881i
$349$	−15.2994	+	26.4994i	−0.818960	+	1.41848i	0.0874885	+	0.996166i	$0.472116\pi$
$349$	−15.2994	+	26.4994i	−0.818960	+	1.41848i	−0.906449	+	0.422315i	$0.861217\pi$
$350$	−4.37895	−	14.7761i	−0.234065	−	0.789813i
$351$	11.3112	+	6.92381i	0.603749	+	0.369565i
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	−1.10035			−0.0585655			−0.0292828	−	0.999571i	$-0.509322\pi$
$353$	−1.10035			−0.0585655			−0.0292828	+	0.999571i	$0.509322\pi$
$354$	0.287311			0.0152704
$355$	−11.8675			−0.629862
$356$	−17.3579			−0.919969
$357$	0.962755	+	3.24866i	0.0509544	+	0.171937i
$358$	3.90521	+	6.76402i	0.206397	+	0.357489i
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	−0.707763	−	0.706450i	$-0.750295\pi$
$359$	4.88693	−	8.46441i	0.257922	−	0.446734i	0.965685	+	0.259716i	$0.0836288\pi$
$360$	12.2945	−	21.2946i	0.647975	−	1.12233i
$361$	−17.9225			−0.943288
$362$	2.55546	+	4.42618i	0.134312	+	0.232635i
$363$	−6.74026			−0.353772
$364$	−3.14203	+	11.7557i	−0.164687	+	0.616164i
$365$	37.5139			1.96357
$366$	0.404132	+	0.699977i	0.0211243	+	0.0365884i
$367$	−11.1473			−0.581882			−0.290941	−	0.956741i	$-0.593968\pi$
$367$	−11.1473			−0.581882			−0.290941	+	0.956741i	$0.593968\pi$
$368$	−0.503679	+	0.872397i	−0.0262561	+	0.0454769i
$369$	−6.83165	+	11.8328i	−0.355641	+	0.615989i
$370$	−15.5244	−	26.8891i	−0.807076	−	1.39790i
$371$	24.1489	+	5.79432i	1.25375	+	0.300826i
$372$	7.70391			0.399429
$373$	−30.7301			−1.59115			−0.795573	−	0.605858i	$-0.792830\pi$
$373$	−30.7301			−1.59115			−0.795573	+	0.605858i	$0.792830\pi$
$374$	1.48030			0.0765445
$375$	4.19567			0.216663
$376$	−10.0244	+	17.3628i	−0.516970	+	0.895419i
$377$	−5.81582	+	3.16147i	−0.299530	+	0.162824i
$378$	−8.05430	−	1.93256i	−0.414269	−	0.0994002i
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	0.413341	+	0.910576i	$0.364362\pi$
$379$	−11.3286	+	19.6217i	−0.581912	+	1.00790i	−0.995253	+	0.0973246i	$0.968972\pi$
$380$	2.27844	+	3.94638i	0.116882	+	0.202445i
$381$	−0.643028	+	1.11376i	−0.0329433	+	0.0570595i
$382$	0.560093	+	0.970109i	0.0286568	+	0.0496351i
$383$	−0.589263			−0.0301099			−0.0150550	−	0.999887i	$-0.504792\pi$
$383$	−0.589263			−0.0301099			−0.0150550	+	0.999887i	$0.504792\pi$
$384$	−2.51581	−	4.35751i	−0.128384	−	0.222368i
$385$	−2.32325	−	7.83942i	−0.118404	−	0.399534i
$386$	−6.99004	−	12.1071i	−0.355783	−	0.616235i
$387$	−5.01619	−	8.68830i	−0.254988	−	0.441651i
$388$	−0.645753			−0.0327832
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	0.784695	−	0.619883i	$-0.212820\pi$
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	−0.929181	+	0.369624i	$0.879486\pi$
$390$	5.95602	+	3.64579i	0.301595	+	0.184612i
$391$	10.9432			0.553422
$392$	−1.02643	−	19.4885i	−0.0518423	−	0.984319i
$393$	3.97904	−	6.89191i	0.200716	−	0.347651i
$394$	21.7782			1.09717
$395$	20.8068	+	36.0384i	1.04690	+	1.81329i
$396$	1.46778	−	2.54227i	0.0737588	−	0.127754i
$397$	−25.5283			−1.28123			−0.640614	−	0.767863i	$-0.721320\pi$
$397$	−25.5283			−1.28123			−0.640614	+	0.767863i	$0.721320\pi$
$398$	21.6005			1.08274
$399$	1.24987	−	1.31743i	0.0625716	−	0.0659538i
$400$	−0.610086	+	1.05670i	−0.0305043	+	0.0528350i
$401$	−12.7506	−	22.0846i	−0.636733	−	1.10285i	−0.986145	−	0.165884i	$-0.946952\pi$
$401$	−12.7506	−	22.0846i	−0.636733	−	1.10285i	0.349413	−	0.936969i	$-0.386381\pi$
$402$	−2.37757	−	4.11807i	−0.118582	−	0.205391i
$403$	0.845724	−	32.9217i	0.0421285	−	1.63995i
$404$	−3.81817	+	6.61327i	−0.189961	+	0.329022i
$405$	−9.04457	+	15.6657i	−0.449428	+	0.778433i
$406$	2.84547	−	2.99928i	0.141218	−	0.148852i
$407$	−4.75934	−	8.24341i	−0.235912	−	0.408611i
$408$	−1.78520	+	3.09206i	−0.0883807	+	0.153080i
$409$	−0.0734938	+	0.127295i	−0.00363403	+	0.00629433i	−0.867837	−	0.496850i	$-0.834490\pi$
$409$	−0.0734938	+	0.127295i	−0.00363403	+	0.00629433i	0.864203	+	0.503144i	$0.167823\pi$
$410$	−7.80822	+	13.5242i	−0.385621	+	0.667914i
$411$	−2.88199	+	4.99175i	−0.142158	+	0.246225i
$412$	−2.63601	−	4.56570i	−0.129867	−	0.224936i
$413$	−0.383788	−	1.29503i	−0.0188850	−	0.0637242i
$414$	−6.16217	+	10.6732i	−0.302854	+	0.524559i
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$	−18.1437	+	9.86292i	−0.889570	+	0.483569i
$417$	−1.39270	−	2.41223i	−0.0682008	−	0.118127i
$418$	−0.396686	−	0.687080i	−0.0194026	−	0.0336062i
$419$	−6.84795	+	11.8610i	−0.334544	+	0.579447i	−0.983397	−	0.181466i	$-0.941916\pi$
$419$	−6.84795	+	11.8610i	−0.334544	+	0.579447i	0.648853	+	0.760914i	$0.275249\pi$
$420$	7.46787	+	1.79185i	0.364395	+	0.0874334i
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	4.84842			0.236017
$423$	9.21486	−	15.9606i	0.448042	−	0.776032i
$424$	13.0844	+	22.6629i	0.635437	+	1.10061i
$425$	13.2551			0.642966
$426$	−0.970345	+	1.68069i	−0.0470134	+	0.0814295i
$427$	2.61525	−	2.75662i	0.126561	−	0.133402i
$428$	18.0156			0.870816
$429$	1.82594	+	1.11769i	0.0881574	+	0.0539627i
$430$	−5.73325	−	9.93028i	−0.276482	−	0.478881i
$431$	22.2910			1.07372			0.536861	−	0.843671i	$-0.319610\pi$
$431$	22.2910			1.07372			0.536861	+	0.843671i	$0.319610\pi$
$432$	0.327896	+	0.567932i	0.0157759	+	0.0273246i
$433$	12.9481	+	22.4268i	0.622247	+	1.07776i	0.989066	+	0.147472i	$0.0471136\pi$
$433$	12.9481	+	22.4268i	0.622247	+	1.07776i	−0.366819	+	0.930292i	$0.619553\pi$
$434$	5.84424	+	19.7204i	0.280533	+	0.946611i
$435$	2.08892	+	3.61811i	0.100156	+	0.173475i
$436$	5.36049			0.256721
$437$	−2.93253	−	5.07929i	−0.140282	−	0.242975i
$438$	3.06732	−	5.31275i	0.146562	−	0.253853i
$439$	13.9919	+	24.2347i	0.667798	+	1.15666i	0.978519	+	0.206159i	$0.0660963\pi$
$439$	13.9919	+	24.2347i	0.667798	+	1.15666i	−0.310721	+	0.950501i	$0.600570\pi$
$440$	4.30792	−	7.46153i	0.205372	−	0.355715i
$441$	0.943533	+	17.9147i	0.0449301	+	0.853079i
$442$	5.06932	+	3.10302i	0.241123	+	0.147596i
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	0.137741	+	0.990468i	$0.456016\pi$
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	−0.926641	+	0.375947i	$0.877317\pi$
$444$	8.94055			0.424300
$445$	46.8310			2.22000
$446$	−2.00706			−0.0950370
$447$	3.87796			0.183421
$448$	8.22774	−	8.67249i	0.388724	−	0.409736i
$449$	−9.84320	−	17.0489i	−0.464529	−	0.804589i	0.534651	−	0.845073i	$-0.320443\pi$
$449$	−9.84320	−	17.0489i	−0.464529	−	0.804589i	−0.999180	+	0.0404845i	$0.987110\pi$
$450$	−7.46399	+	12.9280i	−0.351856	+	0.609433i
$451$	−2.39377	+	4.14614i	−0.112718	+	0.195234i
$452$	−17.5641			−0.826146
$453$	5.57305	+	9.65281i	0.261845	+	0.453528i
$454$	−22.3783			−1.05027
$455$	8.47706	−	31.7163i	0.397411	−	1.48688i
$456$	1.91357			0.0896111
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	0.874628	−	0.484794i	$-0.161105\pi$
$457$	0.373471	+	0.646871i	0.0174702	+	0.0302593i	−0.857158	+	0.515053i	$0.827772\pi$
$458$	−0.0583493			−0.00272648
$459$	3.56203	−	6.16961i	0.166261	−	0.287973i
$460$	12.4017	−	21.4805i	0.578235	−	1.00153i
$461$	16.5855	+	28.7269i	0.772464	+	1.33795i	0.936209	+	0.351445i	$0.114309\pi$
$461$	16.5855	+	28.7269i	0.772464	+	1.33795i	−0.163744	+	0.986503i	$0.552357\pi$
$462$	−1.30019	−	0.311968i	−0.0604901	−	0.0145141i
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	−0.327328			−0.0151958
$465$	−20.7848			−0.963874
$466$	−12.4863			−0.578414
$467$	14.8033	−	25.6400i	0.685013	−	1.18648i	−0.288420	−	0.957504i	$-0.593130\pi$
$467$	14.8033	−	25.6400i	0.685013	−	1.18648i	0.973433	−	0.228973i	$-0.0735367\pi$
$468$	10.3556	−	5.62928i	0.478687	−	0.260214i
$469$	−15.3859	+	16.2176i	−0.710456	+	0.748859i
$470$	10.5321	−	18.2422i	0.485810	−	0.841448i
$471$	0.641056	+	1.11034i	0.0295383	+	0.0511618i
$472$	0.711644	−	1.23260i	0.0327561	−	0.0567352i
$473$	−1.75765	−	3.04434i	−0.0808168	−	0.139979i
$474$	6.80506			0.312567
$475$	−3.55205	−	6.15234i	−0.162979	−	0.282289i
$476$	6.35609	+	1.52509i	0.291331	+	0.0699024i
$477$	−12.0278	−	20.8327i	−0.550714	−	0.953864i
$478$	1.42748	+	2.47247i	0.0652915	+	0.113088i
$479$	14.0905			0.643813			0.321907	−	0.946771i	$-0.395676\pi$
$479$	14.0905			0.643813			0.321907	+	0.946771i	$0.395676\pi$
$480$	6.51684	+	11.2875i	0.297452	+	0.515201i
$481$	0.981481	−	38.2063i	0.0447517	−	1.74206i
$482$	7.30247			0.332618
$483$	−9.61171	−	2.30625i	−0.437348	−	0.104938i
$484$	−6.50142	+	11.2608i	−0.295519	+	0.511854i
$485$	1.74222			0.0791100
$486$	6.17502	+	10.6955i	0.280105	+	0.485156i
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	−0.610602	−	0.791938i	$-0.709072\pi$
$487$	8.39773	−	14.5453i	0.380537	−	0.659110i	0.991139	+	0.132828i	$0.0424057\pi$
$488$	4.00400			0.181253
$489$	−7.86587			−0.355707
$490$	1.07841	+	20.4755i	0.0487176	+	0.924990i
$491$	−10.8345	+	18.7659i	−0.488954	+	0.846893i	−0.999919	−	0.0127081i	$-0.995955\pi$
$491$	−10.8345	+	18.7659i	−0.488954	+	0.846893i	0.510965	+	0.859601i	$0.329288\pi$
$492$	−2.24839	−	3.89432i	−0.101365	−	0.175570i
$493$	1.77793	+	3.07947i	0.0800740	+	0.138692i
$494$	0.0818055	−	3.18446i	0.00368060	−	0.143276i
$495$	−3.96001	+	6.85895i	−0.177989	+	0.308287i
$496$	0.814234	−	1.41029i	0.0365602	−	0.0633241i
$497$	8.87173	+	2.12870i	0.397952	+	0.0954851i
$498$	0.426785	+	0.739213i	0.0191247	+	0.0331249i
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	−0.478051	−	0.878332i	$-0.658656\pi$
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	0.999683	−	0.0251622i	$-0.00801023\pi$
$500$	4.04699	−	7.00960i	0.180987	−	0.313479i
$501$	−5.48023	+	9.49203i	−0.244838	+	0.424073i
$502$	9.15601	−	15.8587i	0.408653	−	0.707807i
$503$	21.9415	+	38.0037i	0.978322	+	1.69450i	0.668506	+	0.743707i	$0.266934\pi$
$503$	21.9415	+	38.0037i	0.978322	+	1.69450i	0.309816	+	0.950796i	$0.399732\pi$
$504$	−13.0106	+	13.7138i	−0.579537	+	0.610863i
$505$	10.3013	−	17.8423i	0.458401	−	0.793974i
$506$	−2.15919	+	3.73983i	−0.0959879	+	0.166256i
$507$	3.91006	+	7.65512i	0.173652	+	0.339976i
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	−9.96210	−	17.2549i	−0.441563	−	0.764809i	0.556243	−	0.831020i	$-0.312242\pi$
$509$	−9.96210	−	17.2549i	−0.441563	−	0.764809i	−0.997806	+	0.0662109i	$0.978909\pi$
$510$	1.87561	−	3.24866i	0.0830536	−	0.143853i
$511$	−28.0441	−	6.72894i	−1.24060	−	0.297671i
$512$	−2.01529			−0.0890641
$513$	−3.81816			−0.168576
$514$	2.10139	−	3.63972i	0.0926886	−	0.160541i
$515$	7.11185	+	12.3181i	0.313386	+	0.542800i
$516$	3.30179			0.145353
$517$	3.22884	−	5.59252i	0.142004	−	0.245959i
$518$	6.78237	+	22.8860i	0.298000	+	1.00555i
$519$	−6.60335			−0.289855
$520$	30.3935	−	16.5219i	1.33284	−	0.724532i
$521$	8.26204	+	14.3103i	0.361967	+	0.626944i	0.988284	−	0.152623i	$-0.0487721\pi$
$521$	8.26204	+	14.3103i	0.361967	+	0.626944i	−0.626318	+	0.779568i	$0.715439\pi$
$522$	−4.00464			−0.175278
$523$	5.99809	+	10.3890i	0.262278	+	0.454279i	0.966847	−	0.255357i	$-0.0821929\pi$
$523$	5.99809	+	10.3890i	0.262278	+	0.454279i	−0.704569	+	0.709636i	$0.748860\pi$
$524$	−7.67609	−	13.2954i	−0.335332	−	0.580812i
$525$	−11.6423	−	2.79346i	−0.508111	−	0.121917i
$526$	−3.81065	−	6.60024i	−0.166152	−	0.287784i
$527$	−17.6905			−0.770611
$528$	0.0529314	+	0.0916798i	0.00230354	+	0.00398985i
$529$	−4.46197	+	7.72837i	−0.193999	+	0.336016i
$530$	−13.7471	−	23.8107i	−0.597137	−	1.03427i
$531$	−0.654173	+	1.13306i	−0.0283887	+	0.0491706i
$532$	−0.995416	−	3.35886i	−0.0431567	−	0.145625i
$533$	−16.8887	+	9.18068i	−0.731531	+	0.397660i
$534$	3.82913	−	6.63225i	0.165703	−	0.287005i
$535$	−48.6053			−2.10139
$536$	−23.5561			−1.01747
$537$	6.06776			0.261843
$538$	4.10536			0.176995
$539$	0.330609	+	6.27720i	0.0142403	+	0.270378i
$540$	−8.07356	−	13.9838i	−0.347431	−	0.601767i
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	0.153739	+	0.988112i	$0.450869\pi$
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	−3.15829	+	5.47031i	−0.135660	+	0.234970i
$543$	3.97057			0.170394
$544$	5.54665	+	9.60707i	0.237811	+	0.411900i
$545$	−14.4624			−0.619500
$546$	−3.79856	−	3.79381i	−0.162563	−	0.162360i
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	5.55973	+	9.62974i	0.237500	+	0.411362i
$549$	−3.68064			−0.157086
$550$	−2.61535	+	4.52991i	−0.111519	+	0.193156i
$551$	0.952888	−	1.65045i	0.0405944	−	0.0703115i
$552$	−5.20786	−	9.02027i	−0.221661	−	0.383928i
$553$	−9.09016	−	30.6732i	−0.386553	−	1.30436i
$554$	−3.24816			−0.138001
$555$	−24.1213			−1.02389
$556$	−5.37340			−0.227883
$557$	10.8280			0.458796			0.229398	−	0.973333i	$-0.426324\pi$
$557$	10.8280			0.458796			0.229398	+	0.973333i	$0.426324\pi$
$558$	9.96160	−	17.2540i	0.421708	−	0.730420i
$559$	0.362466	−	14.1098i	0.0153307	−	0.596781i
$560$	1.11731	−	1.17770i	0.0472148	−	0.0497670i
$561$	0.575009	−	0.995945i	0.0242769	−	0.0420488i
$562$	3.63847	+	6.30201i	0.153480	+	0.265834i
$563$	6.92997	−	12.0031i	0.292064	−	0.505869i	−0.682234	−	0.731134i	$-0.738991\pi$
$563$	6.92997	−	12.0031i	0.292064	−	0.505869i	0.974298	+	0.225265i	$0.0723248\pi$
$564$	3.03274	+	5.25285i	0.127701	+	0.221185i
$565$	47.3873			1.99360
$566$	6.49594	+	11.2513i	0.273045	+	0.472927i
$567$	9.57138	−	10.0888i	0.401960	−	0.423688i
$568$	4.80692	+	8.32583i	0.201694	+	0.349344i
$569$	−13.7060	−	23.7395i	−0.574586	−	0.995212i	−0.996086	−	0.0883842i	$-0.971830\pi$
$569$	−13.7060	−	23.7395i	−0.574586	−	0.995212i	0.421500	−	0.906828i	$-0.361504\pi$
$570$	−2.01048			−0.0842099
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$	3.62854	−	1.97247i	0.151717	−	0.0824732i
$573$	0.870251			0.0363552
$574$	8.26302	−	8.70967i	0.344892	−	0.363535i
$575$	−19.3341	+	33.4876i	−0.806288	+	1.39653i
$576$	−11.5795			−0.482480
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$578$	−5.63818	+	9.76562i	−0.234518	+	0.406196i
$579$	−10.8609			−0.451362
$580$	8.05959			0.334656
$581$	2.76184	−	2.91113i	0.114581	−	0.120774i
$582$	0.142452	−	0.246734i	0.00590483	−	0.0102275i
$583$	−4.21447	−	7.29967i	−0.174545	−	0.302321i
$584$	−15.1950	−	26.3185i	−0.628772	−	1.08907i
$585$	−27.9389	+	15.1876i	−1.15513	+	0.627929i
$586$	−2.52769	+	4.37809i	−0.104418	+	0.180857i
$587$	7.54051	−	13.0606i	0.311230	−	0.539067i	−0.667399	−	0.744701i	$-0.732592\pi$
$587$	7.54051	−	13.0606i	0.311230	−	0.539067i	0.978629	+	0.205634i	$0.0659256\pi$
$588$	−5.26131	−	2.67905i	−0.216973	−	0.110482i
$589$	4.74064	+	8.21104i	0.195335	+	0.338330i
$590$	−0.747686	+	1.29503i	−0.0307817	+	0.0533155i
$591$	8.45953	−	14.6523i	0.347978	−	0.602716i
$592$	0.944935	−	1.63668i	0.0388366	−	0.0672670i
$593$	−12.9245	+	22.3859i	−0.530747	+	0.919281i	0.468609	+	0.883405i	$0.344755\pi$
$593$	−12.9245	+	22.3859i	−0.530747	+	0.919281i	−0.999356	+	0.0358751i	$0.988578\pi$
$594$	1.40564	+	2.43464i	0.0576740	+	0.0998944i
$595$	−17.1485	−	4.11463i	−0.703020	−	0.168684i
$596$	3.74055	−	6.47882i	0.153219	−	0.265383i
$597$	8.39052	−	14.5328i	0.343401	−	0.594788i
$598$	−15.2337	+	8.28101i	−0.622952	+	0.338636i
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	0.958477	+	0.285170i	$0.0920501\pi$
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	−0.232274	+	0.972650i	$0.574617\pi$
$600$	−6.30807	−	10.9259i	−0.257526	−	0.446048i
$601$	13.6474	−	23.6379i	0.556688	−	0.964212i	−0.441082	−	0.897467i	$-0.645405\pi$
$601$	13.6474	−	23.6379i	0.556688	−	0.964212i	0.997770	−	0.0667449i	$-0.0212614\pi$
$602$	2.50477	+	8.45192i	0.102087	+	0.344474i
$603$	21.6538			0.881810
$604$	21.5023			0.874915
$605$	17.5406	−	30.3811i	0.713125	−	1.23517i
$606$	−1.68456	−	2.91775i	−0.0684308	−	0.118526i
$607$	−38.9258			−1.57995			−0.789976	−	0.613138i	$-0.789907\pi$
$607$	−38.9258			−1.57995			−0.789976	+	0.613138i	$0.789907\pi$
$608$	2.97274	−	5.14894i	0.120561	−	0.208817i
$609$	−0.912614	−	3.07947i	−0.0369810	−	0.124786i
$610$	−4.20679			−0.170328
$611$	22.7803	−	12.3834i	0.921593	−	0.500977i
$612$	−3.16576	−	5.48326i	−0.127968	−	0.221648i
$613$	0.886645			0.0358113			0.0179056	−	0.999840i	$-0.494300\pi$
$613$	0.886645			0.0358113			0.0179056	+	0.999840i	$0.494300\pi$
$614$	9.45317	+	16.3734i	0.381499	+	0.660775i
$615$	6.06606	+	10.5067i	0.244607	+	0.423672i
$616$	−4.55884	+	4.80526i	−0.183681	+	0.193609i
$617$	−17.3944	−	30.1280i	−0.700272	−	1.21291i	−0.968371	−	0.249515i	$-0.919729\pi$
$617$	−17.3944	−	30.1280i	−0.700272	−	1.21291i	0.268099	−	0.963391i	$-0.413605\pi$
$618$	2.32600			0.0935653
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	0.844631	−	0.535350i	$-0.179820\pi$
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	−0.885942	+	0.463797i	$0.846487\pi$
$620$	−20.0483	+	34.7247i	−0.805161	+	1.39458i
$621$	10.3913	+	17.9982i	0.416987	+	0.722243i
$622$	4.18864	−	7.25494i	0.167949	−	0.290897i
$623$	−35.0092	−	8.40016i	−1.40262	−	0.336545i
$624$	−0.0109156	+	0.424915i	−0.000436975	+	0.0170102i
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	17.7992			0.711398
$627$	−0.616356			−0.0246149
$628$	2.47336			0.0986979
$629$	−20.5302			−0.818593
$630$	13.6695	−	14.4084i	0.544606	−	0.574044i
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.827023	+	0.562168i	$0.190033\pi$
$631$	22.6169	+	39.1736i	0.900363	+	1.55947i	0.0733401	+	0.997307i	$0.476634\pi$
$632$	16.8555	−	29.1946i	0.670477	−	1.16130i
$633$	1.88332	−	3.26201i	0.0748554	−	0.129653i
$634$	21.5848			0.857241
$635$	−3.34678	−	5.79679i	−0.132813	−	0.230038i
$636$	7.91700			0.313929
$637$	−12.0262	+	22.1894i	−0.476494	+	0.879178i
$638$	−1.40321			−0.0555534
$639$	−4.41872	−	7.65345i	−0.174802	−	0.302766i
$640$	26.1881			1.03518
$641$	9.53097	−	16.5081i	0.376451	−	0.652032i	−0.614092	−	0.789234i	$-0.710478\pi$
$641$	9.53097	−	16.5081i	0.376451	−	0.652032i	0.990543	+	0.137202i	$0.0438111\pi$
$642$	−3.97420	+	6.88352i	−0.156849	+	0.271671i
$643$	5.26755	+	9.12367i	0.207732	+	0.359802i	0.951000	−	0.309192i	$-0.100058\pi$
$643$	5.26755	+	9.12367i	0.207732	+	0.359802i	−0.743268	+	0.668994i	$0.766725\pi$
$644$	−13.1241	+	13.8335i	−0.517162	+	0.545117i
$645$	−8.90811			−0.350756
$646$	−1.71117			−0.0673252
$647$	−24.1608			−0.949860			−0.474930	−	0.880024i	$-0.657527\pi$
$647$	−24.1608			−0.949860			−0.474930	+	0.880024i	$0.657527\pi$
$648$	14.6540			0.575663
$649$	−0.229219	+	0.397019i	−0.00899762	+	0.0155843i
$650$	−18.4520	+	10.0305i	−0.723745	+	0.393427i
$651$	15.5380	+	3.72822i	0.608983	+	0.146120i
$652$	−7.58714	+	13.1413i	−0.297135	+	0.514654i
$653$	16.8445	+	29.1755i	0.659176	+	1.14173i	0.980829	+	0.194869i	$0.0624282\pi$
$653$	16.8445	+	29.1755i	0.659176	+	1.14173i	−0.321653	+	0.946858i	$0.604238\pi$
$654$	−1.18251	+	2.04817i	−0.0462400	+	0.0800900i
$655$	20.7098	+	35.8704i	0.809199	+	1.40157i
$656$	−0.950537			−0.0371122
$657$	13.9678	+	24.1930i	0.544937	+	0.943859i
$658$	−11.1456	+	11.7480i	−0.434500	+	0.457986i
$659$	2.10030	+	3.63782i	0.0818159	+	0.141709i	0.904030	−	0.427469i	$-0.140595\pi$
$659$	2.10030	+	3.63782i	0.0818159	+	0.141709i	−0.822214	+	0.569178i	$0.807261\pi$
$660$	−1.30329	−	2.25737i	−0.0507307	−	0.0878681i
$661$	17.6726			0.687385			0.343693	−	0.939082i	$-0.388322\pi$
$661$	17.6726			0.687385			0.343693	+	0.939082i	$0.388322\pi$
$662$	0.758708	+	1.31412i	0.0294880	+	0.0510748i
$663$	4.05684	−	2.20529i	0.157555	−	0.0856465i
$664$	4.22844			0.164095
$665$	2.68559	+	9.06208i	0.104143	+	0.351413i
$666$	11.5607	−	20.0236i	0.447966	−	0.775900i
$667$	−10.3733			−0.401655
$668$	10.5721	+	18.3114i	0.409046	+	0.708488i
$669$	−0.779623	+	1.35035i	−0.0301420	+	0.0522074i
$670$	24.7491			0.956143
$671$	−1.28968			−0.0497875
$672$	−2.84710	−	9.60707i	−0.109829	−	0.370601i
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	−0.596149	−	0.802874i	$-0.703303\pi$
$673$	10.3052	−	17.8491i	0.397235	−	0.688031i	0.993384	+	0.114843i	$0.0366366\pi$
$674$	4.06901	+	7.04774i	0.156733	+	0.271469i
$675$	12.5865	+	21.8005i	0.484456	+	0.839102i
$676$	16.5607	+	0.851419i	0.636952	+	0.0327469i
$677$	10.6537	−	18.4527i	0.409455	−	0.709196i	−0.585374	−	0.810763i	$-0.699052\pi$
$677$	10.6537	−	18.4527i	0.409455	−	0.709196i	0.994829	+	0.101567i	$0.0323857\pi$
$678$	3.87461	−	6.71102i	0.148804	−	0.257735i
$679$	−1.30242	−	0.312505i	−0.0499823	−	0.0119928i
$680$	−9.29147	−	16.0933i	−0.356312	−	0.617150i
$681$	−8.69264	+	15.0561i	−0.333103	+	0.576951i
$682$	3.49049	−	6.04571i	0.133658	−	0.231502i
$683$	3.34878	−	5.80026i	0.128138	−	0.221941i	−0.794817	−	0.606849i	$-0.792433\pi$
$683$	3.34878	−	5.80026i	0.128138	−	0.221941i	0.922955	+	0.384908i	$0.125767\pi$
$684$	−1.69670	+	2.93877i	−0.0648750	+	0.112367i
$685$	−14.9999	−	25.9806i	−0.573118	−	0.992670i
$686$	2.86655	−	15.5002i	0.109445	−	0.591801i
$687$	−0.0226652	+	0.0392573i	−0.000864732	+	0.00149776i
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$	0.869117	−	33.8323i	0.0331107	−	1.28891i
$690$	5.47161	+	9.47710i	0.208301	+	0.360787i
$691$	12.4632	+	21.5868i	0.474121	+	0.821202i	0.999561	−	0.0296291i	$-0.00943262\pi$
$691$	12.4632	+	21.5868i	0.474121	+	0.821202i	−0.525440	+	0.850831i	$0.676099\pi$
$692$	−6.36936	+	11.0321i	−0.242127	+	0.419376i
$693$	4.19067	−	4.41719i	0.159190	−	0.167795i
$694$	−0.539093			−0.0204637
$695$	14.4972			0.549911
$696$	1.69223	−	2.93102i	0.0641437	−	0.111100i
$697$	5.16298	+	8.94254i	0.195562	+	0.338723i
$698$	−26.0435			−0.985761
$699$	−4.85017	+	8.40073i	−0.183450	+	0.317745i
$700$	−15.8967	+	16.7560i	−0.600839	+	0.633317i
$701$	−4.94583			−0.186801			−0.0934007	−	0.995629i	$-0.529774\pi$
$701$	−4.94583			−0.186801			−0.0934007	+	0.995629i	$0.529774\pi$
$702$	−0.289874	+	11.2840i	−0.0109406	+	0.425886i
$703$	5.50162	+	9.52908i	0.207497	+	0.359396i
$704$	−4.05741			−0.152919
$705$	−8.18220	−	14.1720i	−0.308160	−	0.533748i
$706$	−0.468266	−	0.811061i	−0.0176234	−	0.0305247i
$707$	−10.9013	+	11.4905i	−0.409985	+	0.432147i
$708$	−0.215297	−	0.372905i	−0.00809136	−	0.0140146i
$709$	−4.64497			−0.174446			−0.0872228	−	0.996189i	$-0.527799\pi$
$709$	−4.64497			−0.174446			−0.0872228	+	0.996189i	$0.527799\pi$
$710$	−5.05037	−	8.74749i	−0.189537	−	0.328288i
$711$	−15.4943	+	26.8369i	−0.581082	+	1.00646i
$712$	−18.9688	−	32.8550i	−0.710888	−	1.23129i
$713$	25.8037	−	44.6933i	0.966356	−	1.67378i
$714$	−1.98486	+	2.09215i	−0.0742816	+	0.0782968i
$715$	−9.78966	+	5.32165i	−0.366113	+	0.199018i
$716$	5.85275	−	10.1373i	0.218728	−	0.378847i
$717$	2.21797			0.0828315
$718$	8.31878			0.310454
$719$	31.7413			1.18375			0.591875	−	0.806030i	$-0.298388\pi$
$719$	31.7413			1.18375			0.591875	+	0.806030i	$0.298388\pi$
$720$	−1.57247			−0.0586025
$721$	−3.10705	−	10.4842i	−0.115713	−	0.390453i
$722$	−7.62714	−	13.2106i	−0.283853	−	0.491647i
$723$	2.83658	−	4.91309i	0.105493	−	0.182720i
$724$	3.82987	−	6.63354i	0.142336	−	0.246533i
$725$	−12.5647			−0.466643
$726$	−2.86840	−	4.96822i	−0.106456	−	0.184388i
$727$	47.8755			1.77560			0.887801	−	0.460227i	$-0.152232\pi$
$727$	47.8755			1.77560			0.887801	+	0.460227i	$0.152232\pi$
$728$	−25.6847	+	6.89944i	−0.951937	+	0.255710i
$729$	−6.17412			−0.228671
$730$	15.9645	+	27.6514i	0.590873	+	1.02342i
$731$	−7.58192			−0.280427
$732$	0.605675	−	1.04906i	0.0223864	−	0.0387743i
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	−0.787251	−	0.616633i	$-0.788496\pi$
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	0.927645	+	0.373463i	$0.121830\pi$
$734$	−4.74386	−	8.21660i	−0.175099	−	0.303280i
$735$	14.1948	+	7.22797i	0.523583	+	0.266608i
$736$	−32.3618			−1.19287
$737$	7.58737			0.279484
$738$	−11.6292			−0.428076
$739$	−33.4236			−1.22951			−0.614754	−	0.788719i	$-0.710745\pi$
$739$	−33.4236			−1.22951			−0.614754	+	0.788719i	$0.710745\pi$
$740$	−23.2665	+	40.2988i	−0.855294	+	1.48141i
$741$	−2.11072	−	1.29201i	−0.0775394	−	0.0474632i
$742$	6.00589	+	20.2659i	0.220483	+	0.743984i
$743$	1.46912	−	2.54458i	0.0538966	−	0.0933517i	−0.837818	−	0.545949i	$-0.816169\pi$
$743$	1.46912	−	2.54458i	0.0538966	−	0.0933517i	0.891715	+	0.452597i	$0.149503\pi$
$744$	8.41888	+	14.5819i	0.308651	+	0.534599i
$745$	−10.0919	+	17.4796i	−0.369737	+	0.640403i
$746$	−13.0776	−	22.6511i	−0.478805	−	0.829314i
$747$	−3.88695			−0.142216
$748$	−1.10927	−	1.92131i	−0.0405588	−	0.0702499i
$749$	36.3356	+	8.71842i	1.32767	+	0.318564i
$750$	1.78552	+	3.09261i	0.0651980	+	0.112926i
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	0.854901	−	0.518791i	$-0.173618\pi$
$751$	−0.598389	−	1.03644i	−0.0218355	−	0.0378202i	−0.876737	+	0.480971i	$0.840284\pi$
$752$	1.28213			0.0467545
$753$	−7.11313	−	12.3203i	−0.259217	−	0.448977i
$754$	−4.80531	−	2.94141i	−0.174999	−	0.107120i
$755$	−58.0123			−2.11128
$756$	3.52721	+	11.9020i	0.128283	+	0.432871i
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	−0.951661	−	0.307150i	$-0.900625\pi$
$757$	−5.77321	+	9.99950i	−0.209831	+	0.363438i	0.741830	+	0.670588i	$0.233958\pi$
$758$	−19.2841			−0.700432
$759$	1.67744	+	2.90541i	0.0608871	+	0.105460i
$760$	−4.97979	+	8.62525i	−0.180636	+	0.312871i
$761$	34.6497			1.25605			0.628026	−	0.778192i	$-0.283863\pi$
$761$	34.6497			1.25605			0.628026	+	0.778192i	$0.283863\pi$
$762$	−1.09459			−0.0396530
$763$	10.8116	+	2.59414i	0.391405	+	0.0939143i
$764$	0.839413	−	1.45391i	0.0303689	−	0.0526005i
$765$	8.54110	+	14.7936i	0.308804	+	0.534864i
$766$	−0.250768	−	0.434344i	−0.00906063	−	0.0156935i
$767$	−1.61720	+	0.879108i	−0.0583937	+	0.0317427i
$768$	5.12890	−	8.88351i	0.185073	−	0.320556i
$769$	3.27437	−	5.67138i	0.118077	−	0.204515i	−0.800929	−	0.598760i	$-0.795660\pi$
$769$	3.27437	−	5.67138i	0.118077	−	0.204515i	0.919006	+	0.394245i	$0.128994\pi$
$770$	4.78972	−	5.04862i	0.172610	−	0.181940i
$771$	−1.63253	−	2.82763i	−0.0587943	−	0.101835i
$772$	−10.4760	+	18.1450i	−0.377039	+	0.653051i
$773$	−16.9637	+	29.3821i	−0.610143	+	1.05680i	0.381073	+	0.924545i	$0.375555\pi$
$773$	−16.9637	+	29.3821i	−0.610143	+	1.05680i	−0.991216	+	0.132254i	$0.957779\pi$
$774$	4.26941	−	7.39484i	0.153461	−	0.265802i
$775$	31.2550	−	54.1352i	1.12271	−	1.94459i
$776$	−0.705683	−	1.22228i	−0.0253325	−	0.0438772i
$777$	18.0322	+	4.32667i	0.646902	+	0.155219i
$778$	2.42547	−	4.20104i	0.0869575	−	0.150615i
$779$	2.76711	−	4.79278i	0.0991422	−	0.171719i
$780$	0.268768	−	10.4624i	0.00962345	−	0.374614i
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	4.65703	+	8.06620i	0.166535	+	0.288447i
$783$	−3.37651	+	5.84829i	−0.120667	+	0.209001i
$784$	−1.04651	+	0.679995i	−0.0373752	+	0.0242855i
$785$	−6.67303			−0.238171
$786$	6.77333			0.241597
$787$	−6.48717	+	11.2361i	−0.231243	+	0.400524i	−0.958174	−	0.286186i	$-0.907612\pi$
$787$	−6.48717	+	11.2361i	−0.231243	+	0.400524i	0.726932	+	0.686710i	$0.240946\pi$
$788$	−16.3195	−	28.2662i	−0.581359	−	1.00694i
$789$	−5.92085			−0.210788
$790$	−17.7092	+	30.6732i	−0.630065	+	1.09130i
$791$	−35.4251	−	8.49994i	−1.25957	−	0.302223i
$792$	6.41600			0.227983
$793$	−4.41653	−	2.70344i	−0.156836	−	0.0960019i
$794$	−10.8639	−	18.8168i	−0.385545	−	0.667784i
$795$	−21.3597			−0.757552
$796$	−16.1864	−	28.0357i	−0.573712	−	0.993699i
$797$	−2.20956	−	3.82707i	−0.0782667	−	0.135562i	0.824235	−	0.566247i	$-0.191605\pi$
$797$	−2.20956	−	3.82707i	−0.0782667	−	0.135562i	−0.902502	+	0.430685i	$0.858272\pi$
$798$	1.50297	+	0.360624i	0.0532044	+	0.0127660i
$799$	−6.96408	−	12.0621i	−0.246371	−	0.426728i
$800$	−39.1985			−1.38588
$801$	17.4369	+	30.2017i	0.616104	+	1.06712i
$802$	10.8523	−	18.7968i	0.383209	−	0.663737i
$803$	4.89426	+	8.47711i	0.172715	+	0.299151i
$804$	−3.56327	+	6.17177i	−0.125667	+	0.217662i
$805$	35.4083	−	37.3223i	1.24798	−	1.31544i
$806$	24.6264	−	13.3869i	0.867427	−	0.471532i
$807$	1.59469	−	2.76208i	0.0561356	−	0.0972298i
$808$	−16.6901			−0.587155
$809$	11.4716			0.403320			0.201660	−	0.979456i	$-0.435366\pi$
$809$	11.4716			0.403320			0.201660	+	0.979456i	$0.435366\pi$
$810$	−15.3961			−0.540965
$811$	23.8664			0.838063			0.419032	−	0.907972i	$-0.362370\pi$
$811$	23.8664			0.838063			0.419032	+	0.907972i	$0.362370\pi$
$812$	−6.02506	−	1.44566i	−0.211438	−	0.0507328i
$813$	2.45361	+	4.24978i	0.0860520	+	0.149046i
$814$	4.05079	−	7.01618i	0.141980	−	0.245917i
$815$	20.4698	−	35.4548i	0.717026	−	1.24193i
$816$	0.228329			0.00799310
$817$	2.03178	+	3.51914i	0.0710829	+	0.123119i
$818$	−0.125105			−0.00437419
$819$	23.6104	−	6.34225i	0.825014	−	0.221616i
$820$	23.4044			0.817318
$821$	−15.4847	−	26.8203i	−0.540420	−	0.936035i	−0.998880	−	0.0473197i	$-0.984932\pi$
$821$	−15.4847	−	26.8203i	−0.540420	−	0.936035i	0.458460	−	0.888715i	$-0.348401\pi$
$822$	−4.90587			−0.171112
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	−0.781148	−	0.624346i	$-0.785366\pi$
$823$	4.30678	−	7.45957i	0.150125	−	0.260024i	0.931273	+	0.364321i	$0.118699\pi$
$824$	5.76129	−	9.97885i	0.200704	−	0.347630i
$825$	2.03181	+	3.51920i	0.0707386	+	0.122523i
$826$	0.791236	−	0.834005i	0.0275306	−	0.0290188i
$827$	22.9128			0.796756			0.398378	−	0.917221i	$-0.369573\pi$
$827$	22.9128			0.796756			0.398378	+	0.917221i	$0.369573\pi$
$828$	18.4706			0.641896
$829$	−42.5611			−1.47821			−0.739104	−	0.673591i	$-0.764751\pi$
$829$	−42.5611			−1.47821			−0.739104	+	0.673591i	$0.764751\pi$
$830$	−4.44259			−0.154204
$831$	−1.26172	+	2.18536i	−0.0437685	+	0.0758093i
$832$	−13.8947	−	8.50518i	−0.481711	−	0.294864i
$833$	12.0816	+	6.15191i	0.418601	+	0.213151i
$834$	1.18536	−	2.05311i	0.0410458	−	0.0710933i
$835$	−28.5230	−	49.4033i	−0.987080	−	1.70967i
$836$	−0.594515	+	1.02973i	−0.0205617	+	0.0356140i
$837$	−16.7982	−	29.0954i	−0.580632	−	1.00568i
$838$	−11.6569			−0.402682
$839$	−0.920524	−	1.59439i	−0.0317800	−	0.0550446i	0.849698	−	0.527270i	$-0.176784\pi$
$839$	−0.920524	−	1.59439i	−0.0317800	−	0.0550446i	−0.881478	+	0.472225i	$0.843451\pi$
$840$	4.76932	+	16.0933i	0.164557	+	0.555271i
$841$	12.8147	+	22.1957i	0.441885	+	0.765367i
$842$	1.46465	+	2.53686i	0.0504753	+	0.0874258i
$843$	5.65332			0.194711
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$	−44.6802	−	2.29709i	−1.53705	−	0.0790224i
$846$	15.6860			0.539296
$847$	−18.5622	+	19.5656i	−0.637806	+	0.672282i
$848$	0.836755	−	1.44930i	0.0287343	−	0.0497692i
$849$	10.0931			0.346396
$850$	5.64087	+	9.77027i	0.193480	+	0.335118i
$851$	29.9457	−	51.8675i	1.02653	−	1.77800i
$852$	2.90852			0.0996442
$853$	−27.0293			−0.925466			−0.462733	−	0.886498i	$-0.653131\pi$
$853$	−27.0293			−0.925466			−0.462733	+	0.886498i	$0.653131\pi$
$854$	3.14485	+	0.754579i	0.107614	+	0.0258212i
$855$	4.57763	−	7.92869i	0.156552	−	0.271155i
$856$	19.6875	+	34.0998i	0.672906	+	1.16551i
$857$	−8.39268	−	14.5365i	−0.286688	−	0.496559i	0.686329	−	0.727291i	$-0.259221\pi$
$857$	−8.39268	−	14.5365i	−0.286688	−	0.496559i	−0.973017	+	0.230732i	$0.925888\pi$
$858$	−0.0467936	+	1.82154i	−0.00159751	+	0.0621865i
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.0296769	+	0.999560i	$0.509448\pi$
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.850806	+	0.525481i	$0.823886\pi$
$860$	−8.59245	+	14.8826i	−0.293000	+	0.507491i
$861$	−2.65016	−	8.94254i	−0.0903173	−	0.304761i
$862$	9.48624	+	16.4306i	0.323102	+	0.559630i
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	−0.990145	−	0.140049i	$-0.955274\pi$
$863$	−10.9807	+	19.0191i	−0.373787	+	0.647417i	0.616358	+	0.787466i	$0.288607\pi$
$864$	−10.5338	+	18.2450i	−0.358366	+	0.620709i
$865$	17.1843	−	29.7640i	0.584283	−	1.01201i
$866$	−11.0205	+	19.0880i	−0.374491	+	0.648638i
$867$	4.38020	+	7.58673i	0.148759	+	0.257659i
$868$	21.2161	−	22.3629i	0.720120	−	0.759046i
$869$	−5.42913	+	9.40352i	−0.184170	+	0.318993i
$870$	−1.77793	+	3.07947i	−0.0602775	+	0.104404i
$871$	25.9831	+	15.9047i	0.880404	+	0.538911i
$872$	5.85797	+	10.1463i	0.198376	+	0.343597i
$873$	0.648693	+	1.12357i	0.0219549	+	0.0380270i
$874$	2.49595	−	4.32311i	0.0844267	−	0.146231i
$875$	11.5546	−	12.1792i	0.390617	−	0.411731i
$876$	−9.19401			−0.310637
$877$	−9.61745			−0.324758			−0.162379	−	0.986728i	$-0.551917\pi$
$877$	−9.61745			−0.324758			−0.162379	+	0.986728i	$0.551917\pi$
$878$	−11.9089	+	20.6268i	−0.401905	+	0.696120i
$879$	1.96371	+	3.40125i	0.0662344	+	0.114721i
$880$	−0.550986			−0.0185737
$881$	−14.4863	+	25.0910i	−0.488055	+	0.845336i	−0.999906	−	0.0137383i	$-0.995627\pi$
$881$	−14.4863	+	25.0910i	−0.488055	+	0.845336i	0.511851	+	0.859075i	$0.328960\pi$
$882$	−12.8033	+	8.31928i	−0.431109	+	0.280125i
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	0.228755	−	8.90481i	0.00769388	−	0.299501i
$885$	0.580863	+	1.00608i	0.0195255	+	0.0338191i
$886$	−28.2649			−0.949578
$887$	15.7072	+	27.2057i	0.527397	+	0.913478i	0.999490	+	0.0319293i	$0.0101651\pi$
$887$	15.7072	+	27.2057i	0.527397	+	0.913478i	−0.472094	+	0.881548i	$0.656502\pi$
$888$	9.77029	+	16.9226i	0.327869	+	0.567886i
$889$	1.46215	+	4.93379i	0.0490390	+	0.165474i
$890$	19.9295	+	34.5190i	0.668039	+	1.15708i
$891$	−4.72001			−0.158126
$892$	1.50399	+	2.60499i	0.0503574	+	0.0872216i
$893$	−3.73242	+	6.46474i	−0.124901	+	0.216334i
$894$	1.65032	+	2.85843i	0.0551949	+	0.0956003i
$895$	−15.7905	+	27.3499i	−0.527818	+	0.914208i
$896$	−19.5773	−	4.69741i	−0.654033	−	0.156930i
$897$	−0.345925	+	13.4659i	−0.0115501	+	0.449613i
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	16.7692			0.559283
$900$	22.3726			0.745755
$901$	−18.1798			−0.605658
$902$	−4.07480			−0.135676
$903$	6.65939	+	1.59786i	0.221611	+	0.0531736i
$904$	−19.1942	−	33.2453i	−0.638388	−	1.10572i
$905$	−10.3328	+	17.8970i	−0.343475	+	0.594917i
$906$	−4.74337	+	8.21575i	−0.157588	+	0.272950i
$907$	9.73642			0.323292			0.161646	−	0.986849i	$-0.448320\pi$
$907$	9.73642			0.323292			0.161646	+	0.986849i	$0.448320\pi$
$908$	16.7692	+	29.0452i	0.556507	+	0.963898i
$909$	15.3422			0.508869
$910$	26.9855	−	7.24886i	0.894560	−	0.240297i
$911$	−38.4372			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$911$	−38.4372			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$912$	−0.0611867	−	0.105979i	−0.00202609	−	0.00350930i
$913$	−1.36197			−0.0450746
$914$	−0.317871	+	0.550568i	−0.0105142	+	0.0182112i
$915$	−1.63409	+	2.83032i	−0.0540212	+	0.0935675i
$916$	0.0437242	+	0.0757325i	0.00144469	+	0.00250227i
$917$	−9.04778	−	30.5302i	−0.298784	−	1.00820i
$918$	6.06346			0.200124
$919$	54.2804			1.79055			0.895273	−	0.445519i	$-0.146981\pi$
$919$	54.2804			1.79055			0.895273	+	0.445519i	$0.146981\pi$
$920$	54.2108			1.78728
$921$	14.6880			0.483985
$922$	−14.1164	+	24.4502i	−0.464897	+	0.805226i
$923$	0.319293	−	12.4292i	0.0105097	−	0.409112i
$924$	0.569388	+	1.92131i	0.0187315	+	0.0632063i
$925$	36.2721	−	62.8251i	1.19262	−	2.06568i
$926$	−13.0869	−	22.6673i	−0.430064	−	0.744892i
$927$	−5.29602	+	9.17297i	−0.173944	+	0.301280i
$928$	−5.25777	−	9.10673i	−0.172595	−	0.298943i
$929$	−38.1920			−1.25304			−0.626519	−	0.779406i	$-0.715521\pi$
$929$	−38.1920			−1.25304			−0.626519	+	0.779406i	$0.715521\pi$
$930$	−8.84526	−	15.3204i	−0.290047	−	0.502377i
$931$	−0.382172	−	7.25622i	−0.0125252	−	0.237813i
$932$	9.35660	+	16.2061i	0.306486	+	0.530849i
$933$	−3.25408	−	5.63622i	−0.106534	−	0.184522i
$934$	25.1988			0.824531
$935$	2.99276	+	5.18361i	0.0978736	+	0.169522i
$936$	21.9717	+	13.4493i	0.718168	+	0.439604i
$937$	−19.0376			−0.621931			−0.310966	−	0.950421i	$-0.600652\pi$
$937$	−19.0376			−0.621931			−0.310966	+	0.950421i	$0.600652\pi$
$938$	−18.5016	−	4.43930i	−0.604098	−	0.144948i
$939$	6.91392	−	11.9753i	0.225627	−	0.390798i
$940$	−31.5691			−1.02967
$941$	−23.0811	−	39.9776i	−0.752422	−	1.30323i	−0.946646	−	0.322275i	$-0.895552\pi$
$941$	−23.0811	−	39.9776i	−0.752422	−	1.30323i	0.194224	−	0.980957i	$-0.437781\pi$
$942$	−0.545619	+	0.945040i	−0.0177772	+	0.0307911i
$943$	−30.1232			−0.980948
$944$	−0.0910198			−0.00296244
$945$	−9.51626	−	32.1111i	−0.309564	−	1.04457i
$946$	1.49598	−	2.59111i	0.0486385	−	0.0842443i
$947$	4.59687	+	7.96201i	0.149378	+	0.258730i	0.930998	−	0.365025i	$-0.118940\pi$
$947$	4.59687	+	7.96201i	0.149378	+	0.258730i	−0.781620	+	0.623755i	$0.785606\pi$
$948$	−5.09938	−	8.83239i	−0.165620	−	0.286863i
$949$	−1.00930	+	39.2894i	−0.0327634	+	1.27539i
$950$	3.02324	−	5.23641i	0.0980869	−	0.169892i
$951$	8.38440	−	14.5222i	0.271883	−	0.470915i
$952$	4.05929	+	13.6974i	0.131562	+	0.443936i
$953$	22.3232	+	38.6648i	0.723118	+	1.25248i	0.959744	+	0.280876i	$0.0906250\pi$
$953$	22.3232	+	38.6648i	0.723118	+	1.25248i	−0.236626	+	0.971601i	$0.576042\pi$
$954$	10.2371	−	17.7312i	0.331440	−	0.574070i
$955$	−2.26470	+	3.92258i	−0.0732841	+	0.126932i
$956$	2.13937	−	3.70550i	0.0691923	−	0.119844i
$957$	−0.545062	+	0.944075i	−0.0176194	+	0.0305176i
$958$	5.99641	+	10.3861i	0.193735	+	0.335559i
$959$	6.55323	+	22.1128i	0.211615	+	0.714059i
$960$	−5.14093	+	8.90436i	−0.165923	+	0.287387i
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$	28.5794	−	15.5357i	0.921437	−	0.500892i
$963$	−18.0976	−	31.3459i	−0.583186	−	1.01011i
$964$	−5.47212	−	9.47799i	−0.176245	−	0.305266i
$965$	28.2638	−	48.9544i	0.909845	−	1.57590i
$966$	−2.39046	−	8.06620i	−0.0769117	−	0.259526i
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	−28.4191			−0.913426
$969$	−0.664689	+	1.15128i	−0.0213529	+	0.0369843i
$970$	0.741422	+	1.28418i	0.0238056	+	0.0412326i
$971$	7.26873			0.233265			0.116632	−	0.993175i	$-0.462790\pi$
$971$	7.26873			0.233265			0.116632	+	0.993175i	$0.462790\pi$
$972$	9.25454	−	16.0293i	0.296839	−	0.514141i
$973$	−10.8376	−	2.60039i	−0.347438	−	0.0833648i
$974$	14.2950			0.458043
$975$	−0.419005	+	16.3107i	−0.0134189	+	0.522360i
$976$	−0.128029	−	0.221752i	−0.00409810	−	0.00709811i
$977$	42.8101			1.36962			0.684808	−	0.728723i	$-0.259886\pi$
$977$	42.8101			1.36962			0.684808	+	0.728723i	$0.259886\pi$
$978$	−3.34742	−	5.79790i	−0.107039	−	0.185397i
$979$	6.10982	+	10.5825i	0.195271	+	0.338219i
$980$	25.7674	−	16.7431i	0.823110	−	0.534838i
$981$	−5.38489	−	9.32690i	−0.171926	−	0.297785i
$982$	−18.4430			−0.588541
$983$	23.1544	+	40.1046i	0.738511	+	1.27914i	0.953166	+	0.302448i	$0.0978040\pi$
$983$	23.1544	+	40.1046i	0.738511	+	1.27914i	−0.214655	+	0.976690i	$0.568863\pi$
$984$	4.91410	−	8.51147i	0.156656	−	0.271336i
$985$	44.0294	+	76.2612i	1.40289	+	2.42988i
$986$	−1.51324	+	2.62101i	−0.0481914	+	0.0834700i
$987$	3.57467	+	12.0621i	0.113783	+	0.383942i
$988$	−4.19446	+	2.28010i	−0.133444	+	0.0725398i
$989$	11.0591	−	19.1550i	0.351660	−	0.609092i
$990$	−6.74094			−0.214241
$991$	−58.2324			−1.84981			−0.924907	−	0.380194i	$-0.875857\pi$
$991$	−58.2324			−1.84981			−0.924907	+	0.380194i	$0.875857\pi$
$992$	52.3151			1.66101
$993$	1.17885			0.0374097
$994$	2.20642	+	7.44521i	0.0699835	+	0.236148i
$995$	43.6703	+	75.6392i	1.38444	+	2.39792i
$996$	0.639625	−	1.10786i	0.0202673	−	0.0351040i
$997$	2.24739	−	3.89260i	0.0711757	−	0.123280i	−0.828241	−	0.560372i	$-0.810658\pi$
$997$	2.24739	−	3.89260i	0.0711757	−	0.123280i	0.899417	+	0.437092i	$0.143992\pi$
$998$	19.8353			0.627875
$999$	−19.4947	−	33.7658i	−0.616786	−	1.06830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.g.b.9.4	✓	12
3.2	odd	2		819.2.n.d.100.3		12
7.2	even	3		637.2.f.k.295.4		12
7.3	odd	6		637.2.h.l.165.3		12
7.4	even	3		91.2.h.b.74.3	yes	12
7.5	odd	6		637.2.f.j.295.4		12
7.6	odd	2		637.2.g.l.373.4		12
13.3	even	3		91.2.h.b.16.3	yes	12
13.4	even	6		1183.2.e.g.170.3		12
13.9	even	3		1183.2.e.h.170.4		12
21.11	odd	6		819.2.s.d.802.4		12
39.29	odd	6		819.2.s.d.289.4		12
91.3	odd	6		637.2.g.l.263.4		12
91.4	even	6		1183.2.e.g.508.3		12
91.9	even	3		8281.2.a.bz.1.3		6
91.16	even	3		637.2.f.k.393.4		12
91.30	even	6		8281.2.a.ce.1.4		6
91.55	odd	6		637.2.h.l.471.3		12
91.61	odd	6		8281.2.a.ca.1.3		6
91.68	odd	6		637.2.f.j.393.4		12
91.74	even	3		1183.2.e.h.508.4		12
91.81	even	3	inner	91.2.g.b.81.4	yes	12
91.82	odd	6		8281.2.a.cf.1.4		6
273.263	odd	6		819.2.n.d.172.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	1.1	even	1	trivial
91.2.g.b.81.4	yes	12	91.81	even	3	inner
91.2.h.b.16.3	yes	12	13.3	even	3
91.2.h.b.74.3	yes	12	7.4	even	3
637.2.f.j.295.4		12	7.5	odd	6
637.2.f.j.393.4		12	91.68	odd	6
637.2.f.k.295.4		12	7.2	even	3
637.2.f.k.393.4		12	91.16	even	3
637.2.g.l.263.4		12	91.3	odd	6
637.2.g.l.373.4		12	7.6	odd	2
637.2.h.l.165.3		12	7.3	odd	6
637.2.h.l.471.3		12	91.55	odd	6
819.2.n.d.100.3		12	3.2	odd	2
819.2.n.d.172.3		12	273.263	odd	6
819.2.s.d.289.4		12	39.29	odd	6
819.2.s.d.802.4		12	21.11	odd	6
1183.2.e.g.170.3		12	13.4	even	6
1183.2.e.g.508.3		12	91.4	even	6
1183.2.e.h.170.4		12	13.9	even	3
1183.2.e.h.508.4		12	91.74	even	3
8281.2.a.bz.1.3		6	91.9	even	3
8281.2.a.ca.1.3		6	91.61	odd	6
8281.2.a.ce.1.4		6	91.30	even	6
8281.2.a.cf.1.4		6	91.82	odd	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.425563 + 0.737096i) q^{2} +0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(-1.72074 + 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(1.82097 - 1.91940i) q^{7} +2.78793 q^{8} -2.56278 q^{9} +O(q^{10})\)	\(q+(0.425563 + 0.737096i) q^{2} +0.661223 q^{3} +(0.637793 - 1.10469i) q^{4} +(-1.72074 + 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(1.82097 - 1.91940i) q^{7} +2.78793 q^{8} -2.56278 q^{9} -2.92913 q^{10} -0.897986 q^{11} +(0.421723 - 0.730446i) q^{12} +(-3.07517 - 1.88237i) q^{13} +(2.18972 + 0.525403i) q^{14} +(-1.13779 + 1.97071i) q^{15} +(-0.0891447 - 0.154403i) q^{16} +(-0.968404 + 1.67733i) q^{17} +(-1.09063 - 1.88902i) q^{18} +1.03804 q^{19} +(2.19495 + 3.80177i) q^{20} +(1.20406 - 1.26915i) q^{21} +(-0.382150 - 0.661902i) q^{22} +(-2.82506 - 4.89315i) q^{23} +1.84345 q^{24} +(-3.42189 - 5.92688i) q^{25} +(0.0788077 - 3.06776i) q^{26} -3.67824 q^{27} +(-0.958938 - 3.23578i) q^{28} +(0.917969 - 1.58997i) q^{29} -1.93681 q^{30} +(4.56692 + 7.91014i) q^{31} +(2.86381 - 4.96026i) q^{32} -0.593769 q^{33} -1.64847 q^{34} +(2.58718 + 8.73000i) q^{35} +(-1.63452 + 2.83108i) q^{36} +(5.30001 + 9.17989i) q^{37} +(0.441751 + 0.765135i) q^{38} +(-2.03338 - 1.24467i) q^{39} +(-4.79731 + 8.30918i) q^{40} +(2.66571 - 4.61715i) q^{41} +(1.44789 + 0.347409i) q^{42} +(1.95732 + 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +(4.40988 - 7.63814i) q^{45} +(2.40448 - 4.16469i) q^{46} +(-3.59565 + 6.22784i) q^{47} +(-0.0589445 - 0.102095i) q^{48} +(-0.368167 - 6.99031i) q^{49} +(2.91246 - 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(-4.04076 + 2.19655i) q^{52} +(4.69324 + 8.12893i) q^{53} +(-1.56532 - 2.71122i) q^{54} +(1.54520 - 2.67637i) q^{55} +(5.07673 - 5.35115i) q^{56} +0.686375 q^{57} +1.56261 q^{58} +(0.255259 - 0.442121i) q^{59} +(1.45135 + 2.51382i) q^{60} +1.43619 q^{61} +(-3.88702 + 6.73252i) q^{62} +(-4.66674 + 4.91900i) q^{63} +4.51834 q^{64} +(10.9018 - 5.92620i) q^{65} +(-0.252686 - 0.437665i) q^{66} -8.44932 q^{67} +(1.23528 + 2.13957i) q^{68} +(-1.86800 - 3.23547i) q^{69} +(-5.33385 + 5.62216i) q^{70} +(1.72419 + 2.98638i) q^{71} -7.14487 q^{72} +(-5.45026 - 9.44013i) q^{73} +(-4.51097 + 7.81324i) q^{74} +(-2.26263 - 3.91899i) q^{75} +(0.662054 - 1.14671i) q^{76} +(-1.63520 + 1.72359i) q^{77} +(0.0521095 - 2.02848i) q^{78} +(6.04589 - 10.4718i) q^{79} +0.613579 q^{80} +5.25621 q^{81} +4.53771 q^{82} +1.51669 q^{83} +(-0.634072 - 2.13957i) q^{84} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +(0.606982 - 1.05132i) q^{87} -2.50353 q^{88} +(-6.80391 - 11.7847i) q^{89} +7.50673 q^{90} +(-9.21280 + 2.47475i) q^{91} -7.20722 q^{92} +(3.01976 + 5.23037i) q^{93} -6.12069 q^{94} +(-1.78619 + 3.09378i) q^{95} +(1.89362 - 3.27984i) q^{96} +(-0.253120 - 0.438417i) q^{97} +(4.99585 - 3.24619i) q^{98} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + q^{5} - 9 q^{6} + 9 q^{7} - 6 q^{8} - 6 q^{9} - 8 q^{10} - 8 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} + 8 q^{16} + 5 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} - 9 q^{21} - 5 q^{22} - q^{23} + 22 q^{24} + 7 q^{25} + 5 q^{26} - 8 q^{27} - 7 q^{28} + 3 q^{29} + 10 q^{30} + 16 q^{31} + 8 q^{32} - 32 q^{33} + 32 q^{34} + 8 q^{35} - 21 q^{36} - 13 q^{37} - 17 q^{38} - 23 q^{39} - 5 q^{40} - 8 q^{41} + 2 q^{42} - 11 q^{43} + 21 q^{44} - 7 q^{45} + 16 q^{46} - q^{47} + 21 q^{48} - 3 q^{49} + 6 q^{50} - 20 q^{51} - 25 q^{52} - 2 q^{53} - 18 q^{54} + 9 q^{55} - 18 q^{56} + 42 q^{57} + 16 q^{58} + 13 q^{59} + 20 q^{60} + 10 q^{61} + 5 q^{62} + 32 q^{63} - 30 q^{64} + 19 q^{65} + 18 q^{66} + 22 q^{67} + 29 q^{68} + 23 q^{69} - 39 q^{70} + 6 q^{71} - 50 q^{72} - 30 q^{73} - 3 q^{74} - 3 q^{75} - 9 q^{76} + 11 q^{77} + 16 q^{78} + 7 q^{79} + 14 q^{80} + 12 q^{81} - 2 q^{82} - 54 q^{83} + 5 q^{84} - q^{85} - 7 q^{86} + 16 q^{87} + 4 q^{89} - 16 q^{90} - 20 q^{91} + 54 q^{92} - 7 q^{93} - 90 q^{94} - 6 q^{95} + 19 q^{96} - 35 q^{97} + 62 q^{98} - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + q^5 - 9 * q^6 + 9 * q^7 - 6 * q^8 - 6 * q^9 - 8 * q^10 - 8 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 + 8 * q^16 + 5 * q^17 + 3 * q^18 + 2 * q^19 - q^20 - 9 * q^21 - 5 * q^22 - q^23 + 22 * q^24 + 7 * q^25 + 5 * q^26 - 8 * q^27 - 7 * q^28 + 3 * q^29 + 10 * q^30 + 16 * q^31 + 8 * q^32 - 32 * q^33 + 32 * q^34 + 8 * q^35 - 21 * q^36 - 13 * q^37 - 17 * q^38 - 23 * q^39 - 5 * q^40 - 8 * q^41 + 2 * q^42 - 11 * q^43 + 21 * q^44 - 7 * q^45 + 16 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 - 25 * q^52 - 2 * q^53 - 18 * q^54 + 9 * q^55 - 18 * q^56 + 42 * q^57 + 16 * q^58 + 13 * q^59 + 20 * q^60 + 10 * q^61 + 5 * q^62 + 32 * q^63 - 30 * q^64 + 19 * q^65 + 18 * q^66 + 22 * q^67 + 29 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 - 50 * q^72 - 30 * q^73 - 3 * q^74 - 3 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 + 14 * q^80 + 12 * q^81 - 2 * q^82 - 54 * q^83 + 5 * q^84 - q^85 - 7 * q^86 + 16 * q^87 + 4 * q^89 - 16 * q^90 - 20 * q^91 + 54 * q^92 - 7 * q^93 - 90 * q^94 - 6 * q^95 + 19 * q^96 - 35 * q^97 + 62 * q^98 - 20 * q^99

Introduction

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