LMFDB - Embedded newform 91.2.h.b.74.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(16,91)]

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, 2]))

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

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.h (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			74.3
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	91.74
Dual form			91.2.h.b.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.851125 q^{2} +(-0.330612 - 0.572636i) q^{3} -1.27559 q^{4} +(-1.72074 - 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(-2.57273 + 0.617304i) q^{7} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(1.46456 + 2.53670i) q^{10} +(0.448993 + 0.777679i) 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} +0.178289 q^{16} +1.93681 q^{17} +(-1.09063 + 1.88902i) q^{18} +(-0.519020 + 0.898968i) q^{19} +(2.19495 + 3.80177i) q^{20} +(1.20406 + 1.26915i) q^{21} +(-0.382150 - 0.661902i) q^{22} +5.65013 q^{23} +(-0.921723 - 1.59647i) q^{24} +(-3.42189 + 5.92688i) q^{25} +(2.61736 + 1.60213i) q^{26} -3.67824 q^{27} +(3.28174 - 0.787424i) q^{28} +(0.917969 - 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} +(4.56692 - 7.91014i) q^{31} -5.72761 q^{32} +(0.296885 - 0.514219i) q^{33} -1.64847 q^{34} +(6.26681 + 6.60556i) q^{35} +(-1.63452 + 2.83108i) q^{36} -10.6000 q^{37} +(0.441751 - 0.765135i) q^{38} +(-0.0612242 + 2.38329i) q^{39} +(-4.79731 - 8.30918i) q^{40} +(2.66571 - 4.61715i) q^{41} +(-1.02481 - 1.08021i) q^{42} +(1.95732 + 3.39018i) q^{43} +(-0.572729 - 0.991996i) q^{44} -8.81977 q^{45} -4.80897 q^{46} +(-3.59565 - 6.22784i) q^{47} +(-0.0589445 - 0.102095i) q^{48} +(6.23787 - 3.17631i) q^{49} +(2.91246 - 5.04452i) q^{50} +(-0.640331 - 1.10909i) q^{51} +(3.92265 + 2.40112i) q^{52} +(4.69324 - 8.12893i) q^{53} +3.13065 q^{54} +(1.54520 - 2.67637i) q^{55} +(-7.17260 + 1.72100i) q^{56} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} -0.510517 q^{59} +(1.45135 - 2.51382i) q^{60} +(-0.718095 + 1.24378i) q^{61} +(-3.88702 + 6.73252i) q^{62} +(-1.92661 + 6.50102i) q^{63} +4.51834 q^{64} +(-0.318655 + 12.4043i) q^{65} +(-0.252686 + 0.437665i) q^{66} +(4.22466 + 7.31732i) q^{67} -2.47057 q^{68} +(-1.86800 - 3.23547i) q^{69} +(-5.33385 - 5.62216i) q^{70} +(1.72419 + 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} +(-5.45026 + 9.44013i) q^{73} +9.02195 q^{74} +4.52526 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} +(-0.306789 - 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(-2.26886 + 3.92977i) q^{82} +1.51669 q^{83} +(-1.53589 - 1.61891i) q^{84} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 - 2.88547i) q^{86} -1.21396 q^{87} +(1.25176 + 2.16812i) q^{88} +13.6078 q^{89} +7.50673 q^{90} +(9.07358 + 2.94451i) q^{91} -7.20722 q^{92} -6.03951 q^{93} +(3.06035 + 5.30067i) q^{94} +3.57239 q^{95} +(1.89362 + 3.27984i) q^{96} +(-0.253120 - 0.438417i) q^{97} +(-5.30921 + 2.70344i) q^{98} +2.30134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

Character values

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

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

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 $

$2$	−0.851125			−0.601837			−0.300918	−	0.953650i	$-0.597293\pi$
$2$	−0.851125			−0.601837			−0.300918	+	0.953650i	$0.597293\pi$
$3$	−0.330612	−	0.572636i	−0.190879	−	0.330612i	0.754663	−	0.656113i	$-0.227800\pi$
$3$	−0.330612	−	0.572636i	−0.190879	−	0.330612i	−0.945542	+	0.325501i	$0.894467\pi$
$4$	−1.27559			−0.637793
$5$	−1.72074	−	2.98041i	−0.769538	−	1.33288i	−0.937814	−	0.347139i	$-0.887153\pi$
$5$	−1.72074	−	2.98041i	−0.769538	−	1.33288i	0.168276	−	0.985740i	$-0.446180\pi$
$6$	0.281392	+	0.487385i	0.114878	+	0.198974i
$7$	−2.57273	+	0.617304i	−0.972400	+	0.233319i
$7$	−2.57273	+	0.617304i	−0.972400	+	0.233319i
$8$	2.78793			0.985684
$9$	1.28139	−	2.21944i	0.427131	−	0.739812i
$10$	1.46456	+	2.53670i	0.463136	+	0.802175i
$11$	0.448993	+	0.777679i	0.135377	+	0.234479i	0.925741	−	0.378158i	$-0.123442\pi$
$11$	0.448993	+	0.777679i	0.135377	+	0.234479i	−0.790365	+	0.612637i	$0.790109\pi$
$12$	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
$16$	0.178289			0.0445723
$17$	1.93681			0.469745			0.234873	−	0.972026i	$-0.424533\pi$
$17$	1.93681			0.469745			0.234873	+	0.972026i	$0.424533\pi$
$18$	−1.09063	+	1.88902i	−0.257063	+	0.445246i
$19$	−0.519020	+	0.898968i	−0.119071	+	0.206237i	−0.919400	−	0.393324i	$-0.871325\pi$
$19$	−0.519020	+	0.898968i	−0.119071	+	0.206237i	0.800329	+	0.599562i	$0.204658\pi$
$20$	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
$23$	5.65013			1.17813			0.589067	−	0.808084i	$-0.299496\pi$
$23$	5.65013			1.17813			0.589067	+	0.808084i	$0.299496\pi$
$24$	−0.921723	−	1.59647i	−0.188146	−	0.325878i
$25$	−3.42189	+	5.92688i	−0.684378	+	1.18538i
$26$	2.61736	+	1.60213i	0.513306	+	0.314204i
$27$	−3.67824			−0.707878
$28$	3.28174	−	0.787424i	0.620190	−	0.148809i
$29$	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	$0.112140\pi$
$30$	0.968404	−	1.67733i	0.176806	−	0.306236i
$31$	4.56692	−	7.91014i	0.820244	−	1.42070i	−0.0852573	−	0.996359i	$-0.527171\pi$
$31$	4.56692	−	7.91014i	0.820244	−	1.42070i	0.905501	−	0.424345i	$-0.139495\pi$
$32$	−5.72761			−1.01251
$33$	0.296885	−	0.514219i	0.0516810	−	0.0895141i
$34$	−1.64847			−0.282710
$35$	6.26681	+	6.60556i	1.05929	+	1.11654i
$36$	−1.63452	+	2.83108i	−0.272421	+	0.471847i
$37$	−10.6000			−1.74263			−0.871316	−	0.490722i	$-0.836733\pi$
$37$	−10.6000			−1.74263			−0.871316	+	0.490722i	$0.836733\pi$
$38$	0.441751	−	0.765135i	0.0716614	−	0.124121i
$39$	−0.0612242	+	2.38329i	−0.00980372	+	0.381631i
$40$	−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	$0.0299882\pi$
$42$	−1.02481	−	1.08021i	−0.158132	−	0.166679i
$43$	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
$45$	−8.81977			−1.31477
$46$	−4.80897			−0.709044
$47$	−3.59565	−	6.22784i	−0.524479	−	0.908424i	−0.999594	−	0.0285004i	$-0.990927\pi$
$47$	−3.59565	−	6.22784i	−0.524479	−	0.908424i	0.475115	−	0.879924i	$-0.342407\pi$
$48$	−0.0589445	−	0.102095i	−0.00850791	−	0.0147361i
$49$	6.23787	−	3.17631i	0.891124	−	0.453759i
$50$	2.91246	−	5.04452i	0.411883	−	0.713403i
$51$	−0.640331	−	1.10909i	−0.0896643	−	0.155303i
$52$	3.92265	+	2.40112i	0.543973	+	0.332976i
$53$	4.69324	−	8.12893i	0.644666	−	1.11659i	−0.339712	−	0.940529i	$-0.610330\pi$
$53$	4.69324	−	8.12893i	0.644666	−	1.11659i	0.984378	−	0.176065i	$-0.0563370\pi$
$54$	3.13065			0.426027
$55$	1.54520	−	2.67637i	0.208355	−	0.360881i
$56$	−7.17260	+	1.72100i	−0.958479	+	0.229979i
$57$	0.686375			0.0909127
$58$	−0.781307	+	1.35326i	−0.102591	+	0.177692i
$59$	−0.510517			−0.0664637			−0.0332318	−	0.999448i	$-0.510580\pi$
$59$	−0.510517			−0.0664637			−0.0332318	+	0.999448i	$0.510580\pi$
$60$	1.45135	−	2.51382i	0.187369	−	0.324532i
$61$	−0.718095	+	1.24378i	−0.0919426	+	0.159249i	−0.908328	−	0.418258i	$-0.862641\pi$
$61$	−0.718095	+	1.24378i	−0.0919426	+	0.159249i	0.816386	+	0.577507i	$0.195974\pi$
$62$	−3.88702	+	6.73252i	−0.493653	+	0.855031i
$63$	−1.92661	+	6.50102i	−0.242730	+	0.819051i
$64$	4.51834			0.564792
$65$	−0.318655	+	12.4043i	−0.0395242	+	1.53857i
$66$	−0.252686	+	0.437665i	−0.0311035	+	0.0538729i
$67$	4.22466	+	7.31732i	0.516124	+	0.893953i	0.999825	+	0.0187197i	$0.00595900\pi$
$67$	4.22466	+	7.31732i	0.516124	+	0.893953i	−0.483701	+	0.875233i	$0.660708\pi$
$68$	−2.47057			−0.299600
$69$	−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	$0.767736\pi$
$72$	3.57244	−	6.18764i	0.421016	−	0.729221i
$73$	−5.45026	+	9.44013i	−0.637905	+	1.10488i	0.347987	+	0.937499i	$0.386865\pi$
$73$	−5.45026	+	9.44013i	−0.637905	+	1.10488i	−0.985892	+	0.167384i	$0.946468\pi$
$74$	9.02195			1.04878
$75$	4.52526			0.522532
$76$	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	0.974915	+	0.222578i	$0.0714472\pi$
$79$	6.04589	+	10.4718i	0.680216	+	1.17817i	−0.294699	+	0.955590i	$0.595219\pi$
$80$	−0.306789	−	0.531375i	−0.0343001	−	0.0594095i
$81$	−2.62811	−	4.55201i	−0.292012	−	0.505779i
$82$	−2.26886	+	3.92977i	−0.250553	+	0.433971i
$83$	1.51669			0.166479			0.0832393	−	0.996530i	$-0.473473\pi$
$83$	1.51669			0.166479			0.0832393	+	0.996530i	$0.473473\pi$
$84$	−1.53589	−	1.61891i	−0.167579	−	0.176637i
$85$	−3.33274	−	5.77248i	−0.361487	−	0.626113i
$86$	−1.66593	−	2.88547i	−0.179642	−	0.311148i
$87$	−1.21396			−0.130151
$88$	1.25176	+	2.16812i	0.133438	+	0.231122i
$89$	13.6078			1.44243			0.721213	−	0.692714i	$-0.243585\pi$
$89$	13.6078			1.44243			0.721213	+	0.692714i	$0.243585\pi$
$90$	7.50673			0.791279
$91$	9.07358	+	2.94451i	0.951170	+	0.308668i
$92$	−7.20722			−0.751405
$93$	−6.03951			−0.626268
$94$	3.06035	+	5.30067i	0.315651	+	0.546723i
$95$	3.57239			0.366519
$96$	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	$0.841515\pi$
$98$	−5.30921	+	2.70344i	−0.536311	+	0.273089i
$99$	2.30134			0.231294
$100$	4.36491	−	7.56025i	0.436491	−	0.756025i
$101$	2.99327	+	5.18450i	0.297842	+	0.515877i	0.975642	−	0.219369i	$-0.0703999\pi$
$101$	2.99327	+	5.18450i	0.297842	+	0.515877i	−0.677800	+	0.735246i	$0.737067\pi$
$102$	0.545002	+	0.943972i	0.0539633	+	0.0934671i
$103$	2.06651	+	3.57930i	0.203619	+	0.352679i	0.949692	−	0.313186i	$-0.101396\pi$
$103$	2.06651	+	3.57930i	0.203619	+	0.352679i	−0.746073	+	0.665865i	$0.768063\pi$
$104$	−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
$107$	−14.1234			−1.36536			−0.682679	−	0.730718i	$-0.739185\pi$
$107$	−14.1234			−1.36536			−0.682679	+	0.730718i	$0.739185\pi$
$108$	4.69191			0.451479
$109$	2.10119	−	3.63936i	0.201257	−	0.348588i	−0.747677	−	0.664063i	$-0.768831\pi$
$109$	2.10119	−	3.63936i	0.201257	−	0.348588i	0.948934	+	0.315475i	$0.102164\pi$
$110$	−1.31516	+	2.27792i	−0.125396	+	0.217191i
$111$	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	$-0.390919\pi$
$114$	−0.584192			−0.0547146
$115$	−9.72240	−	16.8397i	−0.906618	−	1.57031i
$116$	−1.17095	+	2.02814i	−0.108720	+	0.188308i
$117$	−8.11830	+	4.41310i	−0.750537	+	0.407991i
$118$	0.434514			0.0400003
$119$	−4.98288	+	1.19560i	−0.456780	+	0.109601i
$120$	−3.17209	+	5.49422i	−0.289571	+	0.501552i
$121$	5.09681	−	8.82793i	0.463346	−	0.802539i
$122$	0.611189	−	1.05861i	0.0553344	−	0.0958420i
$123$	−3.52526			−0.317862
$124$	−5.82550	+	10.0901i	−0.523145	+	0.906114i
$125$	6.34531			0.567542
$126$	1.63978	−	5.53318i	0.146084	−	0.492935i
$127$	−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	$0.194169\pi$
$128$	7.60956			0.672596
$129$	1.29423	−	2.24167i	0.113950	−	0.197368i
$130$	0.271215	−	10.5576i	0.0237871	−	0.925967i
$131$	6.01770	+	10.4230i	0.525769	+	0.910659i	0.999549	+	0.0300158i	$0.00955576\pi$
$131$	6.01770	+	10.4230i	0.525769	+	0.910659i	−0.473780	+	0.880643i	$0.657111\pi$
$132$	−0.378702	+	0.655931i	−0.0329618	+	0.0570914i
$133$	0.780360	−	2.63319i	0.0676658	−	0.228327i
$134$	−3.59571	−	6.22796i	−0.310622	−	0.538014i
$135$	6.32930	+	10.9627i	0.544739	+	0.943516i
$136$	5.39970			0.463020
$137$	8.71715			0.744756			0.372378	−	0.928081i	$-0.378543\pi$
$137$	8.71715			0.744756			0.372378	+	0.928081i	$0.378543\pi$
$138$	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	$0.890506\pi$
$140$	−7.99386	−	8.42596i	−0.675604	−	0.712124i
$141$	−2.37752	+	4.11799i	−0.200224	+	0.346798i
$142$	−1.46750	−	2.54178i	−0.123150	−	0.213302i
$143$	0.0831467	−	3.23667i	0.00695307	−	0.270664i
$144$	0.228459	−	0.395702i	0.0190382	−	0.0329751i
$145$	−6.31834			−0.524710
$146$	4.63885	−	8.03473i	0.383914	−	0.664959i
$147$	−3.88118	−	2.52190i	−0.320115	−	0.208003i
$148$	13.5212			1.11144
$149$	−2.93242	+	5.07910i	−0.240233	+	0.416096i	−0.960781	−	0.277310i	$-0.910557\pi$
$149$	−2.93242	+	5.07910i	−0.240233	+	0.416096i	0.720548	+	0.693406i	$0.243891\pi$
$150$	−3.85157			−0.314479
$151$	8.42840	−	14.5984i	0.685893	−	1.18800i	−0.287262	−	0.957852i	$-0.592745\pi$
$151$	8.42840	−	14.5984i	0.685893	−	1.18800i	0.973155	−	0.230150i	$-0.0739216\pi$
$152$	−1.44699	+	2.50626i	−0.117367	+	0.203285i
$153$	2.48181	−	4.29862i	0.200643	−	0.347523i
$154$	1.39176	+	1.46699i	0.112151	+	0.118214i
$155$	−31.4339			−2.52483
$156$	0.0780967	−	3.04009i	0.00625274	−	0.243402i
$157$	0.969500	−	1.67922i	0.0773746	−	0.134017i	−0.824742	−	0.565509i	$-0.808680\pi$
$157$	0.969500	−	1.67922i	0.0773746	−	0.134017i	0.902116	+	0.431493i	$0.142013\pi$
$158$	−5.14581	−	8.91280i	−0.409379	−	0.709065i
$159$	−6.20656			−0.492212
$160$	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
$163$	5.94797	−	10.3022i	0.465881	−	0.806929i	−0.533360	−	0.845888i	$-0.679071\pi$
$163$	5.94797	−	10.3022i	0.465881	−	0.806929i	0.999241	+	0.0389590i	$0.0124042\pi$
$164$	−3.40035	+	5.88957i	−0.265522	+	0.459898i
$165$	−2.04344			−0.159082
$166$	−1.29090			−0.100193
$167$	−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
$171$	1.33013	+	2.30386i	0.101718	+	0.176181i
$172$	−2.49673	−	4.32447i	−0.190374	−	0.329738i
$173$	4.99328	−	8.64862i	0.379632	−	0.657542i	−0.611377	−	0.791340i	$-0.709384\pi$
$173$	4.99328	−	8.64862i	0.379632	−	0.657542i	0.991009	+	0.133798i	$0.0427172\pi$
$174$	1.03324			0.0783295
$175$	5.14490	−	17.3606i	0.388918	−	1.31234i
$176$	0.0800507	+	0.138652i	0.00603405	+	0.0104513i
$177$	0.168783	+	0.292341i	0.0126865	+	0.0219737i
$178$	−11.5820			−0.868105
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	0.642033	−	0.766677i	$-0.278091\pi$
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	−0.984978	+	0.172679i	$0.944758\pi$
$180$	11.2504			0.838553
$181$	6.00489			0.446340			0.223170	−	0.974780i	$-0.428360\pi$
$181$	6.00489			0.446340			0.223170	+	0.974780i	$0.428360\pi$
$182$	−7.72276	−	2.50614i	−0.572449	−	0.185768i
$183$	0.949642			0.0701995
$184$	15.7522			1.16127
$185$	18.2399	+	31.5924i	1.34102	+	2.32272i
$186$	5.14038			0.376911
$187$	0.869614	+	1.50622i	0.0635925	+	0.110145i
$188$	4.58655	+	7.94415i	0.334509	+	0.579386i
$189$	9.46312	−	2.27059i	0.688341	−	0.165161i
$190$	−3.04055			−0.220585
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	−0.888851	−	0.458197i	$-0.848496\pi$
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	0.841235	+	0.540669i	$0.181829\pi$
$192$	−1.49382	−	2.58736i	−0.107807	−	0.186727i
$193$	8.21270	+	14.2248i	0.591163	+	1.02392i	0.994076	+	0.108686i	$0.0346643\pi$
$193$	8.21270	+	14.2248i	0.591163	+	1.02392i	−0.402913	+	0.915238i	$0.632002\pi$
$194$	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	$-0.198421\pi$
$198$	−1.95873			−0.139201
$199$	−25.3788			−1.79906			−0.899528	−	0.436864i	$-0.856089\pi$
$199$	−25.3788			−1.79906			−0.899528	+	0.436864i	$0.856089\pi$
$200$	−9.54000	+	16.5238i	−0.674580	+	1.16841i
$201$	2.79344	−	4.83838i	0.197034	−	0.341273i
$202$	−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
$205$	−18.3480			−1.28148
$206$	−1.75886	−	3.04643i	−0.122546	−	0.212255i
$207$	7.24003	−	12.5401i	0.503217	−	0.871597i
$208$	−0.548271	−	0.335606i	−0.0380157	−	0.0232701i
$209$	−0.932145			−0.0644778
$210$	−1.45602	+	4.91310i	−0.100475	+	0.339036i
$211$	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	$0.103845\pi$
$212$	−5.98663	+	10.3691i	−0.411164	+	0.712156i
$213$	1.14007	−	1.97466i	0.0781165	−	0.135302i
$214$	12.0208			0.821723
$215$	6.73608	−	11.6672i	0.459397	−	0.795699i
$216$	−10.2547			−0.697744
$217$	−6.86649	+	23.1698i	−0.466128	+	1.57287i
$218$	−1.78837	+	3.09755i	−0.121124	+	0.209793i
$219$	7.20768			0.487050
$220$	−1.97104	+	3.41393i	−0.132887	+	0.230167i
$221$	−5.95602	−	3.64579i	−0.400645	−	0.245242i
$222$	−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	$0.191825\pi$
$224$	14.7356	−	3.53568i	0.984564	−	0.236238i
$225$	8.76956	+	15.1893i	0.584637	+	1.01262i
$226$	5.85976	+	10.1494i	0.389786	+	0.675129i
$227$	26.2926			1.74510			0.872551	−	0.488523i	$-0.162464\pi$
$227$	26.2926			1.74510			0.872551	+	0.488523i	$0.162464\pi$
$228$	−0.875531			−0.0579834
$229$	−0.0342777	−	0.0593708i	−0.00226514	−	0.00392333i	0.864891	−	0.501960i	$-0.167388\pi$
$229$	−0.0342777	−	0.0593708i	−0.00226514	−	0.00392333i	−0.867156	+	0.498037i	$0.834054\pi$
$230$	8.27498	+	14.3327i	0.545636	+	0.945069i
$231$	−0.446374	+	1.50622i	−0.0293693	+	0.0991017i
$232$	2.55924	−	4.43273i	0.168022	−	0.291023i
$233$	−7.33514	−	12.7048i	−0.480541	−	0.832322i	0.519210	−	0.854647i	$-0.326226\pi$
$233$	−7.33514	−	12.7048i	−0.480541	−	0.832322i	−0.999751	+	0.0223253i	$0.992893\pi$
$234$	6.90969	−	3.75610i	0.451701	−	0.245544i
$235$	−12.3743	+	21.4330i	−0.807213	+	1.39813i
$236$	0.651208			0.0423901
$237$	3.99768	−	6.92419i	0.259677	−	0.449774i
$238$	4.24106	−	1.01761i	0.274907	−	0.0659616i
$239$	3.35434			0.216974			0.108487	−	0.994098i	$-0.465399\pi$
$239$	3.35434			0.216974			0.108487	+	0.994098i	$0.465399\pi$
$240$	−0.202856	+	0.351357i	−0.0130943	+	0.0226800i
$241$	−8.57978			−0.552672			−0.276336	−	0.961061i	$-0.589120\pi$
$241$	−8.57978			−0.552672			−0.276336	+	0.961061i	$0.589120\pi$
$242$	−4.33802	+	7.51368i	−0.278859	+	0.482998i
$243$	−7.25513	+	12.5662i	−0.465417	+	0.806125i
$244$	0.915991	−	1.58654i	0.0586403	−	0.101568i
$245$	−20.2005	−	13.1258i	−1.29056	−	0.838576i
$246$	3.00044			0.191301
$247$	3.28826	−	1.78750i	0.209227	−	0.113736i
$248$	12.7323	−	22.0530i	0.808501	−	1.40036i
$249$	−0.501436	−	0.868513i	−0.0317772	−	0.0550398i
$250$	−5.40066			−0.341568
$251$	−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
$254$	0.827704	−	1.43363i	0.0519348	−	0.0899537i
$255$	−2.20369	+	3.81690i	−0.138000	+	0.239023i
$256$	−15.5134			−0.969585
$257$	4.93792			0.308019			0.154010	−	0.988069i	$-0.450781\pi$
$257$	4.93792			0.308019			0.154010	+	0.988069i	$0.450781\pi$
$258$	−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
$262$	−5.12182	−	8.87125i	−0.316427	−	0.548068i
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	0.970406	−	0.241480i	$-0.0776327\pi$
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	−0.694330	+	0.719656i	$0.744299\pi$
$264$	0.827695	−	1.43361i	0.0509411	−	0.0882326i
$265$	−32.3034			−1.98438
$266$	−0.664184	+	2.24118i	−0.0407237	+	0.137415i
$267$	−4.49890	−	7.79233i	−0.275328	−	0.476883i
$268$	−5.38891	−	9.33387i	−0.329180	−	0.570157i
$269$	−4.82345			−0.294091			−0.147045	−	0.989130i	$-0.546976\pi$
$269$	−4.82345			−0.294091			−0.147045	+	0.989130i	$0.546976\pi$
$270$	−5.38702	−	9.33060i	−0.327844	−	0.567842i
$271$	−7.42144			−0.450820			−0.225410	−	0.974264i	$-0.572372\pi$
$271$	−7.42144			−0.450820			−0.225410	+	0.974264i	$0.572372\pi$
$272$	0.345312			0.0209376
$273$	−1.31370	−	6.16935i	−0.0795088	−	0.373386i
$274$	−7.41938			−0.448221
$275$	−6.14562			−0.370595
$276$	2.38279	+	4.12712i	0.143427	+	0.248423i
$277$	3.81631			0.229300			0.114650	−	0.993406i	$-0.463425\pi$
$277$	3.81631			0.229300			0.114650	+	0.993406i	$0.463425\pi$
$278$	1.79268	+	3.10502i	0.107518	+	0.186226i
$279$	−11.7040	−	20.2720i	−0.700702	−	1.21365i
$280$	17.4715	+	18.4159i	1.04412	+	1.10056i
$281$	8.54978			0.510037			0.255019	−	0.966936i	$-0.417918\pi$
$281$	8.54978			0.510037			0.255019	+	0.966936i	$0.417918\pi$
$282$	2.02357	−	3.50493i	0.120502	−	0.208715i
$283$	−7.63217	−	13.2193i	−0.453686	−	0.785807i	0.544926	−	0.838484i	$-0.316558\pi$
$283$	−7.63217	−	13.2193i	−0.453686	−	0.785807i	−0.998612	+	0.0526775i	$0.983224\pi$
$284$	−2.19935	−	3.80938i	−0.130507	−	0.226045i
$285$	−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
$289$	−13.2488			−0.779340
$290$	5.37770			0.315790
$291$	−0.167369	+	0.289892i	−0.00981135	+	0.0169938i
$292$	6.95227	−	12.0417i	0.406851	−	0.704687i
$293$	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
$296$	−29.5522			−1.71768
$297$	−1.65151	−	2.86049i	−0.0958301	−	0.165983i
$298$	2.49586	−	4.32295i	0.144581	−	0.250422i
$299$	−17.3751	−	10.6356i	−1.00483	−	0.615074i
$300$	−5.77236			−0.333267
$301$	−7.12843	−	7.51376i	−0.410876	−	0.433086i
$302$	−7.17362	+	12.4251i	−0.412796	+	0.714983i
$303$	1.97922	−	3.42811i	0.113703	−	0.196940i
$304$	−0.0925356	+	0.160276i	−0.00530728	+	0.00919248i
$305$	4.94262			0.283013
$306$	−2.11233	+	3.65867i	−0.120754	+	0.209152i
$307$	22.2133			1.26778			0.633891	−	0.773422i	$-0.281457\pi$
$307$	22.2133			1.26778			0.633891	+	0.773422i	$0.281457\pi$
$308$	2.08584	+	2.19859i	0.118852	+	0.125276i
$309$	1.36642	−	2.36672i	0.0777332	−	0.134638i
$310$	26.7542			1.51954
$311$	−4.92130	+	8.52394i	−0.279061	+	0.483348i	−0.971152	−	0.238463i	$-0.923357\pi$
$311$	−4.92130	+	8.52394i	−0.279061	+	0.483348i	0.692091	+	0.721811i	$0.256690\pi$
$312$	−0.170689	+	6.64445i	−0.00966337	+	0.376168i
$313$	10.4563	+	18.1108i	0.591023	+	1.02368i	0.994095	+	0.108513i	$0.0346090\pi$
$313$	10.4563	+	18.1108i	0.591023	+	1.02368i	−0.403072	+	0.915168i	$0.632058\pi$
$314$	−0.825166	+	1.42923i	−0.0465668	+	0.0806561i
$315$	22.6909	−	5.44448i	1.27849	−	0.306762i
$316$	−7.71205	−	13.3577i	−0.433837	−	0.751427i
$317$	12.6801	+	21.9626i	0.712188	+	1.23355i	0.964034	+	0.265778i	$0.0856288\pi$
$317$	12.6801	+	21.9626i	0.712188	+	1.23355i	−0.251847	+	0.967767i	$0.581038\pi$
$318$	5.28256			0.296231
$319$	1.64865			0.0923065
$320$	−7.77489	−	13.4665i	−0.434629	−	0.752800i
$321$	4.66935	+	8.08755i	0.260618	+	0.451403i
$322$	12.3722	−	2.96860i	0.689474	−	0.165433i
$323$	−1.00524	+	1.74113i	−0.0559331	+	0.0968790i
$324$	3.35237	+	5.80648i	0.186243	+	0.322582i
$325$	21.6795	−	11.7849i	1.20256	−	0.653711i
$326$	−5.06247	+	8.76845i	−0.280384	+	0.485640i
$327$	−2.77871			−0.153663
$328$	7.43183	−	12.8723i	0.410354	−	0.710755i
$329$	13.0951	+	13.8029i	0.721956	+	0.760981i
$330$	1.73923			0.0957413
$331$	−0.891417	+	1.54398i	−0.0489967	+	0.0848648i	−0.889484	−	0.456967i	$-0.848936\pi$
$331$	−0.891417	+	1.54398i	−0.0489967	+	0.0848648i	0.840487	+	0.541832i	$0.182269\pi$
$332$	−1.93467			−0.106179
$333$	−13.5828	+	23.5261i	−0.744332	+	1.28922i
$334$	7.05414	−	12.2181i	0.385985	−	0.668546i
$335$	14.5391	−	25.1824i	0.794354	−	1.37586i
$336$	0.214672	+	0.226276i	0.0117113	+	0.0123444i
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	−5.03303	−	9.85366i	−0.273761	−	0.535969i
$339$	−4.55234	+	7.88488i	−0.247249	+	0.428248i
$340$	4.25120	+	7.36329i	0.230554	+	0.399331i
$341$	8.20207			0.444167
$342$	−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
$345$	−6.42867	+	11.1348i	−0.346108	+	0.599477i
$346$	−4.24991	+	7.36106i	−0.228477	+	0.395733i
$347$	0.633389			0.0340021			0.0170010	−	0.999855i	$-0.494588\pi$
$347$	0.633389			0.0340021			0.0170010	+	0.999855i	$0.494588\pi$
$348$	1.54852			0.0830092
$349$	−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
$353$	0.550173	+	0.952928i	0.0292828	+	0.0507192i	0.880295	−	0.474426i	$-0.157344\pi$
$353$	0.550173	+	0.952928i	0.0292828	+	0.0507192i	−0.851013	+	0.525145i	$0.824011\pi$
$354$	−0.143655	−	0.248819i	−0.00763520	−	0.0132246i
$355$	5.93375	−	10.2776i	0.314931	−	0.545476i
$356$	−17.3579			−0.919969
$357$	2.33204	+	2.45810i	0.123425	+	0.130096i
$358$	3.90521	+	6.76402i	0.206397	+	0.357489i
$359$	4.88693	+	8.46441i	0.257922	+	0.446734i	0.965685	−	0.259716i	$-0.0836288\pi$
$359$	4.88693	+	8.46441i	0.257922	+	0.446734i	−0.707763	+	0.706450i	$0.750295\pi$
$360$	−24.5889			−1.29595
$361$	8.96124	+	15.5213i	0.471644	+	0.816912i
$362$	−5.11091			−0.268624
$363$	−6.74026			−0.353772
$364$	−11.5741	−	3.75597i	−0.606649	−	0.196866i
$365$	37.5139			1.96357
$366$	−0.808264			−0.0422487
$367$	5.57363	+	9.65381i	0.290941	+	0.503925i	0.974033	−	0.226408i	$-0.0726983\pi$
$367$	5.57363	+	9.65381i	0.290941	+	0.503925i	−0.683092	+	0.730333i	$0.739365\pi$
$368$	1.00736			0.0525121
$369$	−6.83165	−	11.8328i	−0.355641	−	0.615989i
$370$	−15.5244	−	26.8891i	−0.807076	−	1.39790i
$371$	−7.05641	+	23.8107i	−0.366351	+	1.23619i
$372$	7.70391			0.399429
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	−0.126902	−	0.991915i	$-0.540504\pi$
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	0.922475	−	0.386057i	$-0.126163\pi$
$374$	−0.740150	−	1.28198i	−0.0382723	−	0.0662895i
$375$	−2.09783	−	3.63355i	−0.108332	−	0.187636i
$376$	−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	$0.968972\pi$
$380$	−4.55689			−0.233763
$381$	1.28606			0.0658866
$382$	0.560093	−	0.970109i	0.0286568	−	0.0496351i
$383$	0.294631	−	0.510317i	0.0150550	−	0.0260760i	−0.858400	−	0.512981i	$-0.828541\pi$
$383$	0.294631	−	0.510317i	0.0150550	−	0.0260760i	0.873455	+	0.486905i	$0.161874\pi$
$384$	−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
$387$	10.0324			0.509975
$388$	0.322877	+	0.559239i	0.0163916	+	0.0283910i
$389$	−2.84973	+	4.93587i	−0.144487	+	0.250259i	−0.929181	−	0.369624i	$-0.879486\pi$
$389$	−2.84973	+	4.93587i	−0.144487	+	0.250259i	0.784695	+	0.619883i	$0.212820\pi$
$390$	−6.13536	+	3.33517i	−0.310676	+	0.168883i
$391$	10.9432			0.553422
$392$	17.3908	−	8.85535i	0.878367	−	0.447263i
$393$	3.97904	−	6.89191i	0.200716	−	0.347651i
$394$	−10.8891	+	18.8605i	−0.548584	+	0.950176i
$395$	20.8068	−	36.0384i	1.04690	−	1.81329i
$396$	−2.93556			−0.147518
$397$	12.7641	−	22.1082i	0.640614	−	1.10958i	−0.344682	−	0.938720i	$-0.612013\pi$
$397$	12.7641	−	22.1082i	0.640614	−	1.10958i	0.985296	−	0.170857i	$-0.0546535\pi$
$398$	21.6005			1.08274
$399$	−1.76586	+	0.423703i	−0.0884035	+	0.0212117i
$400$	−0.610086	+	1.05670i	−0.0305043	+	0.0528350i
$401$	25.5011			1.27347			0.636733	−	0.771085i	$-0.280286\pi$
$401$	25.5011			1.27347			0.636733	+	0.771085i	$0.280286\pi$
$402$	−2.37757	+	4.11807i	−0.118582	+	0.205391i
$403$	−28.9339	+	15.7284i	−1.44130	+	0.783489i
$404$	−3.81817	−	6.61327i	−0.189961	−	0.329022i
$405$	−9.04457	+	15.6657i	−0.449428	+	0.778433i
$406$	1.17472	−	3.96388i	0.0583002	−	0.196724i
$407$	−4.75934	−	8.24341i	−0.235912	−	0.408611i
$408$	−1.78520	−	3.09206i	−0.0883807	−	0.153080i
$409$	0.146988			0.00726807			0.00363403	−	0.999993i	$-0.498843\pi$
$409$	0.146988			0.00726807			0.00363403	+	0.999993i	$0.498843\pi$
$410$	15.6164			0.771241
$411$	−2.88199	−	4.99175i	−0.142158	−	0.246225i
$412$	−2.63601	−	4.56570i	−0.129867	−	0.224936i
$413$	1.31342	−	0.315145i	0.0646293	−	0.0155072i
$414$	−6.16217	+	10.6732i	−0.302854	+	0.524559i
$415$	−2.60983	−	4.52036i	−0.128112	−	0.221896i
$416$	17.6134	+	10.7815i	0.863568	+	0.528606i
$417$	−1.39270	+	2.41223i	−0.0682008	+	0.118127i
$418$	0.793372			0.0388051
$419$	−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	$0.275249\pi$
$420$	−2.18215	+	7.36329i	−0.106478	+	0.359292i
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	−2.42421	+	4.19885i	−0.118009	+	0.204397i
$423$	−18.4297			−0.896084
$424$	13.0844	−	22.6629i	0.635437	−	1.10061i
$425$	−6.62754	+	11.4792i	−0.321483	+	0.556825i
$426$	−0.970345	+	1.68069i	−0.0470134	+	0.0814295i
$427$	1.07967	−	3.64318i	0.0522491	−	0.176306i
$428$	18.0156			0.870816
$429$	−1.88092	+	1.02247i	−0.0908118	+	0.0493652i
$430$	−5.73325	+	9.93028i	−0.276482	+	0.478881i
$431$	−11.1455	−	19.3046i	−0.536861	−	0.929870i	−0.999071	−	0.0430997i	$-0.986277\pi$
$431$	−11.1455	−	19.3046i	−0.536861	−	0.929870i	0.462210	−	0.886771i	$-0.347057\pi$
$432$	−0.655791			−0.0315518
$433$	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
$436$	−2.68024	+	4.64232i	−0.128360	+	0.222327i
$437$	−2.93253	+	5.07929i	−0.140282	+	0.242975i
$438$	−6.13464			−0.293124
$439$	−27.9838			−1.33560			−0.667798	−	0.744343i	$-0.732763\pi$
$439$	−27.9838			−1.33560			−0.667798	+	0.744343i	$0.732763\pi$
$440$	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	−0.926641	−	0.375947i	$-0.877317\pi$
$443$	−16.6044	−	28.7597i	−0.788900	−	1.36642i	0.137741	−	0.990468i	$-0.456016\pi$
$444$	−4.47028	−	7.74275i	−0.212150	−	0.367454i
$445$	−23.4155	−	40.5568i	−1.11000	−	1.92258i
$446$	1.00353	−	1.73816i	0.0475185	−	0.0823044i
$447$	3.87796			0.183421
$448$	−11.6245	+	2.78919i	−0.549204	+	0.131777i
$449$	−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
$451$	4.78755			0.225437
$452$	8.78205	+	15.2110i	0.413073	+	0.715464i
$453$	−11.1461			−0.523690
$454$	−22.3783			−1.05027
$455$	−6.83744	−	32.1097i	−0.320544	−	1.50533i
$456$	1.91357			0.0896111
$457$	−0.746942			−0.0349405			−0.0174702	−	0.999847i	$-0.505561\pi$
$457$	−0.746942			−0.0349405			−0.0174702	+	0.999847i	$0.505561\pi$
$458$	0.0291746	+	0.0505320i	0.00136324	+	0.00236120i
$459$	−7.12405			−0.332522
$460$	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	$0.552357\pi$
$462$	0.379920	−	1.28198i	0.0176755	−	0.0596430i
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	0.163664	−	0.283475i	0.00759792	−	0.0131600i
$465$	10.3924	+	18.0002i	0.481937	+	0.834740i
$466$	6.24313	+	10.8134i	0.289207	+	0.500922i
$467$	14.8033	+	25.6400i	0.685013	+	1.18648i	0.973433	+	0.228973i	$0.0735367\pi$
$467$	14.8033	+	25.6400i	0.685013	+	1.18648i	−0.288420	+	0.957504i	$0.593130\pi$
$468$	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
$471$	−1.28211			−0.0590766
$472$	−1.42329			−0.0655122
$473$	−1.75765	+	3.04434i	−0.0808168	+	0.139979i
$474$	−3.40253	+	5.89335i	−0.156283	+	0.270691i
$475$	−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
$478$	−2.85496			−0.130583
$479$	−7.04527	−	12.2028i	−0.321907	−	0.557559i	0.658975	−	0.752165i	$-0.270990\pi$
$479$	−7.04527	−	12.2028i	−0.321907	−	0.557559i	−0.980881	+	0.194606i	$0.937657\pi$
$480$	6.51684	−	11.2875i	0.297452	−	0.515201i
$481$	32.5969	+	19.9531i	1.48629	+	0.909785i
$482$	7.30247			0.332618
$483$	6.80312	+	7.17086i	0.309553	+	0.326285i
$484$	−6.50142	+	11.2608i	−0.295519	+	0.511854i
$485$	−0.871108	+	1.50880i	−0.0395550	+	0.0685112i
$486$	6.17502	−	10.6955i	0.280105	−	0.485156i
$487$	−16.7955			−0.761075			−0.380537	−	0.924766i	$-0.624261\pi$
$487$	−16.7955			−0.761075			−0.380537	+	0.924766i	$0.624261\pi$
$488$	−2.00200	+	3.46757i	−0.0906263	+	0.156969i
$489$	−7.86587			−0.355707
$490$	17.1931	+	11.1717i	0.776706	+	0.504686i
$491$	−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	$0.329288\pi$
$492$	4.49677			0.202730
$493$	1.77793	−	3.07947i	0.0800740	−	0.138692i
$494$	−2.79873	+	1.52138i	−0.125921	+	0.0684503i
$495$	−3.96001	−	6.85895i	−0.177989	−	0.308287i
$496$	0.814234	−	1.41029i	0.0365602	−	0.0633241i
$497$	−6.27937	−	6.61880i	−0.281668	−	0.296894i
$498$	0.426785	+	0.739213i	0.0191247	+	0.0331249i
$499$	11.6524	+	20.1825i	0.521633	+	0.903495i	0.999683	+	0.0251622i	$0.00801023\pi$
$499$	11.6524	+	20.1825i	0.521633	+	0.903495i	−0.478051	+	0.878332i	$0.658656\pi$
$500$	−8.09399			−0.361974
$501$	10.9605			0.489677
$502$	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	$0.399732\pi$
$504$	−5.37125	+	18.1244i	−0.239255	+	0.807325i
$505$	10.3013	−	17.8423i	0.458401	−	0.793974i
$506$	−2.15919	−	3.73983i	−0.0959879	−	0.166256i
$507$	4.67450	−	7.21378i	0.207602	−	0.320375i
$508$	1.24048	−	2.14858i	0.0550376	−	0.0953279i
$509$	19.9242			0.883125			0.441563	−	0.897230i	$-0.354424\pi$
$509$	19.9242			0.883125			0.441563	+	0.897230i	$0.354424\pi$
$510$	1.87561	−	3.24866i	0.0830536	−	0.143853i
$511$	8.19461	−	27.6514i	0.362508	−	1.22322i
$512$	−2.01529			−0.0890641
$513$	1.90908	−	3.30662i	0.0842879	−	0.145991i
$514$	−4.20279			−0.185377
$515$	7.11185	−	12.3181i	0.313386	−	0.542800i
$516$	−1.65090	+	2.85944i	−0.0726767	+	0.125880i
$517$	3.22884	−	5.59252i	0.142004	−	0.245959i
$518$	−23.2110	+	5.56929i	−1.01983	+	0.244700i
$519$	−6.60335			−0.289855
$520$	−0.888388	+	34.5825i	−0.0389584	+	1.51654i
$521$	8.26204	−	14.3103i	0.361967	−	0.626944i	−0.626318	−	0.779568i	$-0.715439\pi$
$521$	8.26204	−	14.3103i	0.361967	−	0.626944i	0.988284	+	0.152623i	$0.0487721\pi$
$522$	2.00232	+	3.46812i	0.0876392	+	0.151796i
$523$	−11.9962			−0.524556			−0.262278	−	0.964992i	$-0.584474\pi$
$523$	−11.9962			−0.524556			−0.262278	+	0.964992i	$0.584474\pi$
$524$	−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
$527$	8.84526	−	15.3204i	0.385305	−	0.667369i
$528$	0.0529314	−	0.0916798i	0.00230354	−	0.00398985i
$529$	8.92395			0.387998
$530$	27.4942			1.19427
$531$	−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
$535$	24.3026	+	42.0934i	1.05070	+	1.81986i
$536$	11.7781	+	20.4002i	0.508735	+	0.881155i
$537$	−3.03388	+	5.25484i	−0.130922	+	0.226763i
$538$	4.10536			0.176995
$539$	5.27091	+	3.42492i	0.227034	+	0.147522i
$540$	−8.07356	−	13.9838i	−0.347431	−	0.601767i
$541$	−18.1158	−	31.3775i	−0.778860	−	1.34903i	−0.932599	−	0.360914i	$-0.882465\pi$
$541$	−18.1158	−	31.3775i	−0.778860	−	1.34903i	0.153739	−	0.988112i	$-0.450869\pi$
$542$	6.31658			0.271320
$543$	−1.98529	−	3.43862i	−0.0851968	−	0.147565i
$544$	−11.0933			−0.475621
$545$	−14.4624			−0.619500
$546$	1.11812	+	5.25089i	0.0478513	+	0.224717i
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	−11.1195			−0.475000
$549$	1.84032	+	3.18753i	0.0785430	+	0.136040i
$550$	5.23069			0.223037
$551$	0.952888	+	1.65045i	0.0405944	+	0.0703115i
$552$	−5.20786	−	9.02027i	−0.221661	−	0.383928i
$553$	−22.0187	−	23.2089i	−0.936331	−	0.986944i
$554$	−3.24816			−0.138001
$555$	12.0606	−	20.8896i	0.511945	−	0.886715i
$556$	2.68670	+	4.65350i	0.113941	+	0.197352i
$557$	−5.41399	−	9.37731i	−0.229398	−	0.397329i	0.728232	−	0.685331i	$-0.240342\pi$
$557$	−5.41399	−	9.37731i	−0.229398	−	0.397329i	−0.957630	+	0.288002i	$0.907009\pi$
$558$	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
$562$	−7.27694			−0.306959
$563$	−13.8599			−0.584127			−0.292064	−	0.956399i	$-0.594342\pi$
$563$	−13.8599			−0.584127			−0.292064	+	0.956399i	$0.594342\pi$
$564$	3.03274	−	5.25285i	0.127701	−	0.221185i
$565$	−23.6936	+	41.0386i	−0.996798	+	1.72651i
$566$	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
$569$	27.4120			1.14917			0.574586	−	0.818444i	$-0.305163\pi$
$569$	27.4120			1.14917			0.574586	+	0.818444i	$0.305163\pi$
$570$	1.00524	+	1.74113i	0.0421049	+	0.0729279i
$571$	0.103879	−	0.179923i	0.00434719	−	0.00752956i	−0.863844	−	0.503760i	$-0.831950\pi$
$571$	0.103879	−	0.179923i	0.00434719	−	0.00752956i	0.868191	+	0.496230i	$0.165283\pi$
$572$	−0.106061	+	4.12865i	−0.00443462	+	0.172627i
$573$	0.870251			0.0363552
$574$	3.41129	−	11.5108i	0.142384	−	0.480452i
$575$	−19.3341	+	33.4876i	−0.806288	+	1.39653i
$576$	5.78976	−	10.0282i	0.241240	−	0.417840i
$577$	1.66328	−	2.88089i	0.0692434	−	0.119933i	−0.829325	−	0.558766i	$-0.811275\pi$
$577$	1.66328	−	2.88089i	0.0692434	−	0.119933i	0.898568	+	0.438833i	$0.144608\pi$
$578$	11.2764			0.469035
$579$	5.43043	−	9.40577i	0.225681	−	0.390891i
$580$	8.05959			0.334656
$581$	−3.90204	+	0.936261i	−0.161884	+	0.0388426i
$582$	0.142452	−	0.246734i	0.00590483	−	0.0102275i
$583$	8.42893			0.349091
$584$	−15.1950	+	26.3185i	−0.628772	+	1.08907i
$585$	27.1223	+	16.6020i	1.12137	+	0.686410i
$586$	−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	$0.0659256\pi$
$588$	4.95078	+	3.21690i	0.204167	+	0.132663i
$589$	4.74064	+	8.21104i	0.195335	+	0.338330i
$590$	−0.747686	−	1.29503i	−0.0307817	−	0.0533155i
$591$	−16.9191			−0.695957
$592$	−1.88987			−0.0776732
$593$	−12.9245	−	22.3859i	−0.530747	−	0.919281i	−0.999356	−	0.0358751i	$-0.988578\pi$
$593$	−12.9245	−	22.3859i	−0.530747	−	0.919281i	0.468609	−	0.883405i	$-0.344755\pi$
$594$	1.40564	+	2.43464i	0.0576740	+	0.0998944i
$595$	12.1376	+	12.7937i	0.497594	+	0.524491i
$596$	3.74055	−	6.47882i	0.153219	−	0.265383i
$597$	8.39052	+	14.5328i	0.343401	+	0.594788i
$598$	14.7884	+	9.05225i	0.604743	+	0.370174i
$599$	17.7734	−	30.7845i	0.726203	−	1.25782i	−0.232274	−	0.972650i	$-0.574617\pi$
$599$	17.7734	−	30.7845i	0.726203	−	1.25782i	0.958477	−	0.285170i	$-0.0920501\pi$
$600$	12.6161			0.515052
$601$	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	$-0.0212614\pi$
$602$	6.06719	+	6.39515i	0.247280	+	0.260647i
$603$	21.6538			0.881810
$604$	−10.7511	+	18.6215i	−0.437458	+	0.757699i
$605$	−35.0811			−1.42625
$606$	−1.68456	+	2.91775i	−0.0684308	+	0.118526i
$607$	19.4629	−	33.7108i	0.789976	−	1.36828i	−0.136006	−	0.990708i	$-0.543426\pi$
$607$	19.4629	−	33.7108i	0.789976	−	1.36828i	0.925981	−	0.377570i	$-0.123240\pi$
$608$	2.97274	−	5.14894i	0.120561	−	0.208817i
$609$	3.12320	−	0.749386i	0.126559	−	0.0303666i
$610$	−4.20679			−0.170328
$611$	−0.665859	+	25.9200i	−0.0269378	+	1.04861i
$612$	−3.16576	+	5.48326i	−0.127968	+	0.221648i
$613$	−0.443322	−	0.767857i	−0.0179056	−	0.0310135i	0.856934	−	0.515427i	$-0.172367\pi$
$613$	−0.443322	−	0.767857i	−0.0179056	−	0.0310135i	−0.874839	+	0.484413i	$0.839033\pi$
$614$	−18.9063			−0.762997
$615$	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	$-0.413605\pi$
$618$	−1.16300	+	2.01437i	−0.0467827	+	0.0810300i
$619$	−1.02781	+	1.78021i	−0.0413111	+	0.0715529i	−0.885942	−	0.463797i	$-0.846487\pi$
$619$	−1.02781	+	1.78021i	−0.0413111	+	0.0715529i	0.844631	+	0.535350i	$0.179820\pi$
$620$	40.0967			1.61032
$621$	−20.7825			−0.833975
$622$	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
$626$	−8.89959	−	15.4145i	−0.355699	−	0.616089i
$627$	0.308178	+	0.533780i	0.0123074	+	0.0213171i
$628$	−1.23668	+	2.14199i	−0.0493489	+	0.0854749i
$629$	−20.5302			−0.818593
$630$	−19.3128	+	4.63393i	−0.769439	+	0.184620i
$631$	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
$633$	−3.76665			−0.149711
$634$	−10.7924	−	18.6930i	−0.428621	−	0.742393i
$635$	6.69355			0.265625
$636$	7.91700			0.313929
$637$	−25.1615	−	1.97426i	−0.996936	−	0.0782229i
$638$	−1.40321			−0.0555534
$639$	8.83744			0.349604
$640$	−13.0941	−	22.6796i	−0.517588	−	0.896489i
$641$	−19.0619			−0.752902			−0.376451	−	0.926437i	$-0.622856\pi$
$641$	−19.0619			−0.752902			−0.376451	+	0.926437i	$0.622856\pi$
$642$	−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	$0.766725\pi$
$644$	18.5422	−	4.44905i	0.730666	−	0.175317i
$645$	−8.90811			−0.350756
$646$	0.855587	−	1.48192i	0.0336626	−	0.0583053i
$647$	12.0804	+	20.9239i	0.474930	+	0.822603i	0.999588	−	0.0287105i	$-0.00914011\pi$
$647$	12.0804	+	20.9239i	0.474930	+	0.822603i	−0.524658	+	0.851313i	$0.675807\pi$
$648$	−7.32699	−	12.6907i	−0.287831	−	0.498538i
$649$	−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
$653$	−33.6890			−1.31835			−0.659176	−	0.751988i	$-0.729095\pi$
$653$	−33.6890			−1.31835			−0.659176	+	0.751988i	$0.729095\pi$
$654$	2.36503			0.0924799
$655$	20.7098	−	35.8704i	0.809199	−	1.40157i
$656$	0.475268	−	0.823189i	0.0185561	−	0.0321401i
$657$	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	$0.807261\pi$
$660$	2.60659			0.101461
$661$	−8.83631	−	15.3049i	−0.343693	−	0.595293i	0.641423	−	0.767188i	$-0.278345\pi$
$661$	−8.83631	−	15.3049i	−0.343693	−	0.595293i	−0.985115	+	0.171894i	$0.945011\pi$
$662$	0.758708	−	1.31412i	0.0294880	−	0.0510748i
$663$	−0.118580	+	4.61597i	−0.00460525	+	0.179270i
$664$	4.22844			0.164095
$665$	−9.19079	+	2.20525i	−0.356404	+	0.0855160i
$666$	11.5607	−	20.0236i	0.447966	−	0.775900i
$667$	5.18664	−	8.98353i	0.200828	−	0.347844i
$668$	10.5721	−	18.3114i	0.409046	−	0.708488i
$669$	1.55925			0.0602839
$670$	−12.3746	+	21.4334i	−0.478071	+	0.828044i
$671$	−1.28968			−0.0497875
$672$	−6.89642	−	7.26920i	−0.266035	−	0.280415i
$673$	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	$0.0366366\pi$
$674$	−8.13803			−0.313465
$675$	12.5865	−	21.8005i	0.484456	−	0.839102i
$676$	−7.54302	−	14.7677i	−0.290116	−	0.567990i
$677$	10.6537	+	18.4527i	0.409455	+	0.709196i	0.994829	−	0.101567i	$-0.0323857\pi$
$677$	10.6537	+	18.4527i	0.409455	+	0.709196i	−0.585374	+	0.810763i	$0.699052\pi$
$678$	3.87461	−	6.71102i	0.148804	−	0.257735i
$679$	0.921847	+	0.971677i	0.0353772	+	0.0372895i
$680$	−9.29147	−	16.0933i	−0.356312	−	0.617150i
$681$	−8.69264	−	15.0561i	−0.333103	−	0.576951i
$682$	−6.98099			−0.267316
$683$	−6.69757			−0.256275			−0.128138	−	0.991756i	$-0.540900\pi$
$683$	−6.69757			−0.256275			−0.128138	+	0.991756i	$0.540900\pi$
$684$	−1.69670	−	2.93877i	−0.0648750	−	0.112367i
$685$	−14.9999	−	25.9806i	−0.573118	−	0.992670i
$686$	11.9903	−	10.2326i	0.457792	−	0.390683i
$687$	−0.0226652	+	0.0392573i	−0.000864732	+	0.00149776i
$688$	0.348970	+	0.604433i	0.0133043	+	0.0230438i
$689$	−29.7342	+	16.1635i	−1.13278	+	0.615779i
$690$	5.47161	−	9.47710i	0.208301	−	0.360787i
$691$	−24.9263			−0.948242			−0.474121	−	0.880460i	$-0.657234\pi$
$691$	−24.9263			−0.948242			−0.474121	+	0.880460i	$0.657234\pi$
$692$	−6.36936	+	11.0321i	−0.242127	+	0.419376i
$693$	−5.92074	+	1.42063i	−0.224910	+	0.0539653i
$694$	−0.539093			−0.0204637
$695$	−7.24861	+	12.5550i	−0.274955	+	0.476237i
$696$	−3.38445			−0.128287
$697$	5.16298	−	8.94254i	0.195562	−	0.338723i
$698$	13.0217	−	22.5543i	0.492880	−	0.853694i
$699$	−4.85017	+	8.40073i	−0.183450	+	0.317745i
$700$	−6.56276	+	22.1449i	−0.248049	+	0.837000i
$701$	−4.94583			−0.186801			−0.0934007	−	0.995629i	$-0.529774\pi$
$701$	−4.94583			−0.186801			−0.0934007	+	0.995629i	$0.529774\pi$
$702$	−9.62728	−	5.89303i	−0.363358	−	0.222418i
$703$	5.50162	−	9.52908i	0.207497	−	0.359396i
$704$	2.02870	+	3.51382i	0.0764597	+	0.132432i
$705$	16.3644			0.616319
$706$	−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
$709$	2.32249	−	4.02267i	0.0872228	−	0.151074i	−0.819113	−	0.573632i	$-0.805534\pi$
$709$	2.32249	−	4.02267i	0.0872228	−	0.151074i	0.906336	+	0.422557i	$0.138867\pi$
$710$	−5.05037	+	8.74749i	−0.189537	+	0.328288i
$711$	30.9886			1.16216
$712$	37.9377			1.42178
$713$	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
$717$	−1.10898	−	1.92082i	−0.0414157	−	0.0717342i
$718$	−4.15939	−	7.20427i	−0.155227	−	0.268861i
$719$	−15.8706	+	27.4887i	−0.591875	+	1.02516i	0.402105	+	0.915594i	$0.368279\pi$
$719$	−15.8706	+	27.4887i	−0.591875	+	1.02516i	−0.993980	+	0.109564i	$0.965055\pi$
$720$	−1.57247			−0.0586025
$721$	−7.52609	−	7.93291i	−0.280286	−	0.295437i
$722$	−7.62714	−	13.2106i	−0.283853	−	0.491647i
$723$	2.83658	+	4.91309i	0.105493	+	0.182720i
$724$	−7.65975			−0.284672
$725$	6.28237	+	10.8814i	0.233322	+	0.404125i
$726$	5.73681			0.212913
$727$	47.8755			1.77560			0.887801	−	0.460227i	$-0.152232\pi$
$727$	47.8755			1.77560			0.887801	+	0.460227i	$0.152232\pi$
$728$	25.2965	+	8.20909i	0.937552	+	0.304249i
$729$	−6.17412			−0.228671
$730$	−31.9290			−1.18175
$731$	3.79096	+	6.56613i	0.140214	+	0.242857i
$732$	−1.21135			−0.0447728
$733$	3.80104	+	6.58359i	0.140395	+	0.243171i	0.927645	−	0.373463i	$-0.121830\pi$
$733$	3.80104	+	6.58359i	0.140395	+	0.243171i	−0.787251	+	0.616633i	$0.788496\pi$
$734$	−4.74386	−	8.21660i	−0.175099	−	0.303280i
$735$	−0.837796	+	15.9071i	−0.0309026	+	0.586740i
$736$	−32.3618			−1.19287
$737$	−3.79368	+	6.57086i	−0.139742	+	0.242041i
$738$	5.81459	+	10.0712i	0.214038	+	0.370725i
$739$	16.7118	+	28.9457i	0.614754	+	1.06479i	0.990428	+	0.138033i	$0.0440781\pi$
$739$	16.7118	+	28.9457i	0.614754	+	1.06479i	−0.375673	+	0.926752i	$0.622589\pi$
$740$	−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	$0.149503\pi$
$744$	−16.8378			−0.617302
$745$	20.1837			0.739474
$746$	−13.0776	+	22.6511i	−0.478805	+	0.829314i
$747$	1.94348	−	3.36620i	0.0711081	−	0.123163i
$748$	−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
$751$	1.19678			0.0436711			0.0218355	−	0.999762i	$-0.493049\pi$
$751$	1.19678			0.0436711			0.0218355	+	0.999762i	$0.493049\pi$
$752$	−0.641065	−	1.11036i	−0.0233773	−	0.0404906i
$753$	−7.11313	+	12.3203i	−0.259217	+	0.448977i
$754$	4.94999	−	2.69081i	0.180268	−	0.0979936i
$755$	−58.0123			−2.11128
$756$	−12.0710	+	2.89634i	−0.439019	+	0.105339i
$757$	−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	$0.233958\pi$
$758$	9.64207	−	16.7006i	0.350216	−	0.606592i
$759$	1.67744	−	2.90541i	0.0608871	−	0.105460i
$760$	9.95959			0.361272
$761$	−17.3249	+	30.0075i	−0.628026	+	1.08777i	0.359921	+	0.932983i	$0.382803\pi$
$761$	−17.3249	+	30.0075i	−0.628026	+	1.08777i	−0.987947	+	0.154790i	$0.950530\pi$
$762$	−1.09459			−0.0396530
$763$	−3.15919	+	10.6602i	−0.114370	+	0.385924i
$764$	0.839413	−	1.45391i	0.0303689	−	0.0526005i
$765$	−17.0822			−0.617608
$766$	−0.250768	+	0.434344i	−0.00906063	+	0.0156935i
$767$	1.56993	+	0.960982i	0.0566869	+	0.0346990i
$768$	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	$0.128994\pi$
$770$	1.97738	−	6.67233i	0.0712597	−	0.240454i
$771$	−1.63253	−	2.82763i	−0.0587943	−	0.101835i
$772$	−10.4760	−	18.1450i	−0.377039	−	0.653051i
$773$	33.9275			1.22029			0.610143	−	0.792291i	$-0.291112\pi$
$773$	33.9275			1.22029			0.610143	+	0.792291i	$0.291112\pi$
$774$	−8.53882			−0.306922
$775$	31.2550	+	54.1352i	1.12271	+	1.94459i
$776$	−0.705683	−	1.22228i	−0.0253325	−	0.0438772i
$777$	−12.7631	−	13.4530i	−0.457874	−	0.482624i
$778$	2.42547	−	4.20104i	0.0869575	−	0.150615i
$779$	2.76711	+	4.79278i	0.0991422	+	0.171719i
$780$	−9.19508	+	4.99844i	−0.329237	+	0.178973i
$781$	−1.54830	+	2.68173i	−0.0554024	+	0.0959598i
$782$	−9.31405			−0.333070
$783$	−3.37651	+	5.84829i	−0.120667	+	0.209001i
$784$	1.11215	−	0.566303i	0.0397195	−	0.0202251i
$785$	−6.67303			−0.238171
$786$	−3.38667	+	5.86588i	−0.120798	+	0.209229i
$787$	12.9743			0.462485			0.231243	−	0.972896i	$-0.425721\pi$
$787$	12.9743			0.462485			0.231243	+	0.972896i	$0.425721\pi$
$788$	−16.3195	+	28.2662i	−0.581359	+	1.00694i
$789$	2.96042	−	5.12760i	0.105394	−	0.182548i
$790$	−17.7092	+	30.6732i	−0.630065	+	1.09130i
$791$	25.0737	+	26.4290i	0.891518	+	0.939708i
$792$	6.41600			0.227983
$793$	4.54951	−	2.47311i	0.161558	−	0.0878227i
$794$	−10.8639	+	18.8168i	−0.385545	+	0.667784i
$795$	10.6799	+	18.4981i	0.378776	+	0.656059i
$796$	32.3728			1.14742
$797$	−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
$800$	19.5993	−	33.9469i	0.692938	−	1.20020i
$801$	17.4369	−	30.2017i	0.616104	−	1.06712i
$802$	−21.7047			−0.766418
$803$	−9.78852			−0.345429
$804$	−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
$808$	8.34504	+	14.4540i	0.293578	+	0.508491i
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	0.747403	−	0.664371i	$-0.231300\pi$
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	−0.949063	+	0.315085i	$0.897967\pi$
$810$	7.69807	−	13.3334i	0.270482	−	0.468489i
$811$	23.8664			0.838063			0.419032	−	0.907972i	$-0.362370\pi$
$811$	23.8664			0.838063			0.419032	+	0.907972i	$0.362370\pi$
$812$	1.76055	−	5.94069i	0.0617833	−	0.208477i
$813$	2.45361	+	4.24978i	0.0860520	+	0.149046i
$814$	4.05079	+	7.01618i	0.141980	+	0.245917i
$815$	−40.9396			−1.43405
$816$	−0.114164	−	0.197738i	−0.00399655	−	0.00692223i
$817$	−4.06355			−0.142166
$818$	−0.125105			−0.00437419
$819$	18.1620	−	16.3652i	0.634630	−	0.571845i
$820$	23.4044			0.817318
$821$	30.9694			1.08084			0.540420	−	0.841395i	$-0.318265\pi$
$821$	30.9694			1.08084			0.540420	+	0.841395i	$0.318265\pi$
$822$	2.45293	+	4.24861i	0.0855559	+	0.148187i
$823$	−8.61357			−0.300250			−0.150125	−	0.988667i	$-0.547968\pi$
$823$	−8.61357			−0.300250			−0.150125	+	0.988667i	$0.547968\pi$
$824$	5.76129	+	9.97885i	0.200704	+	0.347630i
$825$	2.03181	+	3.51920i	0.0707386	+	0.122523i
$826$	−1.11789	+	0.268228i	−0.0388963	+	0.00933283i
$827$	22.9128			0.796756			0.398378	−	0.917221i	$-0.369573\pi$
$827$	22.9128			0.796756			0.398378	+	0.917221i	$0.369573\pi$
$828$	−9.23528	+	15.9960i	−0.320948	+	0.555898i
$829$	21.2806	+	36.8590i	0.739104	+	1.28017i	0.952899	+	0.303287i	$0.0980842\pi$
$829$	21.2806	+	36.8590i	0.739104	+	1.28017i	−0.213795	+	0.976879i	$0.568582\pi$
$830$	2.22129	+	3.84739i	0.0771022	+	0.133545i
$831$	−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
$835$	57.0460			1.97416
$836$	1.18903			0.0411235
$837$	−16.7982	+	29.0954i	−0.580632	+	1.00568i
$838$	5.82846	−	10.0952i	0.201341	−	0.348733i
$839$	−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
$842$	−2.92931			−0.100951
$843$	−2.82666	−	4.89591i	−0.0973553	−	0.168624i
$844$	−3.63317	+	6.29284i	−0.125059	+	0.216609i
$845$	24.3294	−	37.5457i	0.836958	−	1.29161i
$846$	15.6860			0.539296
$847$	−7.66319	+	25.8582i	−0.263310	+	0.888497i
$848$	0.836755	−	1.44930i	0.0287343	−	0.0497692i
$849$	−5.04657	+	8.74092i	−0.173198	+	0.299988i
$850$	5.64087	−	9.77027i	0.193480	−	0.335118i
$851$	−59.8915			−2.05305
$852$	−1.45426	+	2.51885i	−0.0498221	+	0.0862944i
$853$	−27.0293			−0.925466			−0.462733	−	0.886498i	$-0.653131\pi$
$853$	−27.0293			−0.925466			−0.462733	+	0.886498i	$0.653131\pi$
$854$	−0.918939	+	3.10081i	−0.0314454	+	0.106107i
$855$	4.57763	−	7.92869i	0.156552	−	0.271155i
$856$	−39.3750			−1.34581
$857$	−8.39268	+	14.5365i	−0.286688	+	0.496559i	−0.973017	−	0.230732i	$-0.925888\pi$
$857$	−8.39268	+	14.5365i	−0.286688	+	0.496559i	0.686329	+	0.727291i	$0.259221\pi$
$858$	1.60090	−	0.870248i	0.0546538	−	0.0297098i
$859$	−25.8058	−	44.6969i	−0.880482	−	1.52504i	−0.850806	−	0.525481i	$-0.823886\pi$
$859$	−25.8058	−	44.6969i	−0.880482	−	1.52504i	−0.0296769	−	0.999560i	$-0.509448\pi$
$860$	−8.59245	+	14.8826i	−0.293000	+	0.507491i
$861$	9.06955	−	2.17616i	0.309089	−	0.0741633i
$862$	9.48624	+	16.4306i	0.323102	+	0.559630i
$863$	−10.9807	−	19.0191i	−0.373787	−	0.647417i	0.616358	−	0.787466i	$-0.288607\pi$
$863$	−10.9807	−	19.0191i	−0.373787	−	0.647417i	−0.990145	+	0.140049i	$0.955274\pi$
$864$	21.0676			0.716733
$865$	−34.3685			−1.16857
$866$	−11.0205	−	19.0880i	−0.374491	−	0.648638i
$867$	4.38020	+	7.58673i	0.148759	+	0.257659i
$868$	8.75880	−	29.5551i	0.297293	−	1.00317i
$869$	−5.42913	+	9.40352i	−0.184170	+	0.318993i
$870$	−1.77793	−	3.07947i	−0.0602775	−	0.104404i
$871$	0.782342	−	30.4544i	0.0265086	−	1.03191i
$872$	5.85797	−	10.1463i	0.198376	−	0.343597i
$873$	−1.29739			−0.0439098
$874$	2.49595	−	4.32311i	0.0844267	−	0.146231i
$875$	−16.3248	+	3.91699i	−0.551878	+	0.132418i
$876$	−9.19401			−0.310637
$877$	4.80873	−	8.32896i	0.162379	−	0.281249i	−0.773342	−	0.633989i	$-0.781417\pi$
$877$	4.80873	−	8.32896i	0.162379	−	0.281249i	0.935721	+	0.352740i	$0.114750\pi$
$878$	23.8178			0.803811
$879$	1.96371	−	3.40125i	0.0662344	−	0.114721i
$880$	0.275493	−	0.477167i	0.00928686	−	0.0160853i
$881$	−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	$0.328960\pi$
$882$	−0.803065	+	15.2476i	−0.0270406	+	0.513414i
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	7.59742	+	4.65051i	0.255529	+	0.156414i
$885$	0.580863	−	1.00608i	0.0195255	−	0.0338191i
$886$	14.1325	+	24.4781i	0.474789	+	0.822359i
$887$	−31.4144			−1.05479			−0.527397	−	0.849619i	$-0.676832\pi$
$887$	−31.4144			−1.05479			−0.527397	+	0.849619i	$0.676832\pi$
$888$	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
$891$	2.36000	−	4.08765i	0.0790631	−	0.136941i
$892$	1.50399	−	2.60499i	0.0503574	−	0.0872216i
$893$	7.46484			0.249801
$894$	−3.30063			−0.110390
$895$	−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
$899$	−8.38459	−	14.5225i	−0.279642	−	0.484354i
$900$	−11.1863	−	19.3753i	−0.372877	−	0.645843i
$901$	9.08991	−	15.7442i	0.302829	−	0.524515i
$902$	−4.07480			−0.135676
$903$	−1.94591	+	6.56613i	−0.0647557	+	0.218507i
$904$	−19.1942	−	33.2453i	−0.638388	−	1.10572i
$905$	−10.3328	−	17.8970i	−0.343475	−	0.594917i
$906$	9.48673			0.315176
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	0.773813	−	0.633414i	$-0.218347\pi$
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	−0.935459	+	0.353435i	$0.885014\pi$
$908$	−33.5385			−1.11301
$909$	15.3422			0.508869
$910$	5.81952	+	27.3294i	0.192915	+	0.905960i
$911$	−38.4372			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$911$	−38.4372			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$912$	0.122373			0.00405219
$913$	0.680984	+	1.17950i	0.0225373	+	0.0390357i
$914$	0.635741			0.0210285
$915$	−1.63409	−	2.83032i	−0.0540212	−	0.0935675i
$916$	0.0437242	+	0.0757325i	0.00144469	+	0.00250227i
$917$	−21.9161	−	23.1007i	−0.723732	−	0.762853i
$918$	6.06346			0.200124
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.0618056	+	0.998088i	$0.519686\pi$
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.833467	+	0.552569i	$0.813647\pi$
$920$	−27.1054	−	46.9479i	−0.893639	−	1.54783i
$921$	−7.34398	−	12.7202i	−0.241993	−	0.419143i
$922$	−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
$926$	26.1739			0.860128
$927$	10.5920			0.347888
$928$	−5.25777	+	9.10673i	−0.172595	+	0.298943i
$929$	19.0960	−	33.0752i	0.626519	−	1.08516i	−0.361726	−	0.932284i	$-0.617812\pi$
$929$	19.0960	−	33.0752i	0.626519	−	1.08516i	0.988245	−	0.152878i	$-0.0488542\pi$
$930$	−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
$933$	6.50815			0.213067
$934$	−12.5994	−	21.8228i	−0.412266	−	0.714065i
$935$	2.99276	−	5.18361i	0.0978736	−	0.169522i
$936$	−22.6333	+	12.3034i	−0.739792	+	0.402150i
$937$	−19.0376			−0.621931			−0.310966	−	0.950421i	$-0.600652\pi$
$937$	−19.0376			−0.621931			−0.310966	+	0.950421i	$0.600652\pi$
$938$	13.0953	+	13.8032i	0.427578	+	0.450691i
$939$	6.91392	−	11.9753i	0.225627	−	0.390798i
$940$	15.7845	−	27.3396i	0.514835	−	0.891720i
$941$	−23.0811	+	39.9776i	−0.752422	+	1.30323i	0.194224	+	0.980957i	$0.437781\pi$
$941$	−23.0811	+	39.9776i	−0.752422	+	1.30323i	−0.946646	+	0.322275i	$0.895552\pi$
$942$	1.09124			0.0355545
$943$	15.0616	−	26.0875i	0.490474	−	0.849526i
$944$	−0.0910198			−0.00296244
$945$	−23.0509	−	24.2969i	−0.749845	−	0.790377i
$946$	1.49598	−	2.59111i	0.0486385	−	0.0842443i
$947$	−9.19374			−0.298756			−0.149378	−	0.988780i	$-0.547727\pi$
$947$	−9.19374			−0.298756			−0.149378	+	0.988780i	$0.547727\pi$
$948$	−5.09938	+	8.83239i	−0.165620	+	0.286863i
$949$	34.5303	−	18.7706i	1.12090	−	0.609320i
$950$	3.02324	+	5.23641i	0.0980869	+	0.169892i
$951$	8.38440	−	14.5222i	0.271883	−	0.470915i
$952$	−13.8920	+	3.33325i	−0.450241	+	0.108031i
$953$	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
$955$	4.52941			0.146568
$956$	−4.27874			−0.138385
$957$	−0.545062	−	0.944075i	−0.0176194	−	0.0305176i
$958$	5.99641	+	10.3861i	0.193735	+	0.335559i
$959$	−22.4269	+	5.38113i	−0.724201	+	0.173766i
$960$	−5.14093	+	8.90436i	−0.165923	+	0.287387i
$961$	−26.2136	−	45.4032i	−0.845599	−	1.46462i
$962$	−27.7441	−	16.9826i	−0.894504	−	0.547542i
$963$	−18.0976	+	31.3459i	−0.583186	+	1.01011i
$964$	10.9442			0.352490
$965$	28.2638	−	48.9544i	0.909845	−	1.57590i
$966$	−5.79031	−	6.10330i	−0.186300	−	0.196370i
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	14.2096	−	24.6117i	0.456713	−	0.791050i
$969$	1.32938			0.0427058
$970$	0.741422	−	1.28418i	0.0238056	−	0.0412326i
$971$	−3.63437	+	6.29491i	−0.116632	+	0.202013i	−0.918431	−	0.395581i	$-0.870543\pi$
$971$	−3.63437	+	6.29491i	−0.116632	+	0.202013i	0.801799	+	0.597594i	$0.203877\pi$
$972$	9.25454	−	16.0293i	0.296839	−	0.514141i
$973$	7.67081	+	8.08545i	0.245915	+	0.259208i
$974$	14.2950			0.458043
$975$	−13.9160	−	8.51821i	−0.445668	−	0.272801i
$976$	−0.128029	+	0.221752i	−0.00409810	+	0.00709811i
$977$	−21.4050	−	37.0746i	−0.684808	−	1.18612i	−0.973497	−	0.228699i	$-0.926553\pi$
$977$	−21.4050	−	37.0746i	−0.684808	−	1.18612i	0.288689	−	0.957423i	$-0.406781\pi$
$978$	6.69484			0.214077
$979$	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
$982$	9.22152	−	15.9721i	0.294270	−	0.509691i
$983$	23.1544	−	40.1046i	0.738511	−	1.27914i	−0.214655	−	0.976690i	$-0.568863\pi$
$983$	23.1544	−	40.1046i	0.738511	−	1.27914i	0.953166	−	0.302448i	$-0.0978040\pi$
$984$	−9.82820			−0.313312
$985$	−88.0588			−2.80579
$986$	−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
$990$	3.37047	+	5.83782i	0.107121	+	0.185538i
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.791711	+	0.610896i	$0.209190\pi$
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.133195	+	0.991090i	$0.457476\pi$
$992$	−26.1576	+	45.3062i	−0.830504	+	1.43847i
$993$	1.17885			0.0374097
$994$	5.34453	+	5.63343i	0.169518	+	0.178681i
$995$	43.6703	+	75.6392i	1.38444	+	2.39792i
$996$	0.639625	+	1.10786i	0.0202673	+	0.0351040i
$997$	−4.49479			−0.142351			−0.0711757	−	0.997464i	$-0.522675\pi$
$997$	−4.49479			−0.142351			−0.0711757	+	0.997464i	$0.522675\pi$
$998$	−9.91765	−	17.1779i	−0.313938	−	0.543756i
$999$	38.9894			1.23357

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	7.2	even	3
91.2.g.b.81.4	yes	12	13.3	even	3
91.2.h.b.16.3	yes	12	91.16	even	3	inner
91.2.h.b.74.3	yes	12	1.1	even	1	trivial
637.2.f.j.295.4		12	7.3	odd	6
637.2.f.j.393.4		12	91.3	odd	6
637.2.f.k.295.4		12	7.4	even	3
637.2.f.k.393.4		12	91.81	even	3
637.2.g.l.263.4		12	91.55	odd	6
637.2.g.l.373.4		12	7.5	odd	6
637.2.h.l.165.3		12	7.6	odd	2
637.2.h.l.471.3		12	91.68	odd	6
819.2.n.d.100.3		12	21.2	odd	6
819.2.n.d.172.3		12	39.29	odd	6
819.2.s.d.289.4		12	273.107	odd	6
819.2.s.d.802.4		12	3.2	odd	2
1183.2.e.g.170.3		12	91.30	even	6
1183.2.e.g.508.3		12	13.4	even	6
1183.2.e.h.170.4		12	91.9	even	3
1183.2.e.h.508.4		12	13.9	even	3
8281.2.a.bz.1.3		6	91.74	even	3
8281.2.a.ca.1.3		6	91.87	odd	6
8281.2.a.ce.1.4		6	91.4	even	6
8281.2.a.cf.1.4		6	91.17	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.851125 q^{2} +(-0.330612 - 0.572636i) q^{3} -1.27559 q^{4} +(-1.72074 - 2.98041i) q^{5} +(0.281392 + 0.487385i) q^{6} +(-2.57273 + 0.617304i) q^{7} +2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(1.46456 + 2.53670i) q^{10} +(0.448993 + 0.777679i) 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} +0.178289 q^{16} +1.93681 q^{17} +(-1.09063 + 1.88902i) q^{18} +(-0.519020 + 0.898968i) q^{19} +(2.19495 + 3.80177i) q^{20} +(1.20406 + 1.26915i) q^{21} +(-0.382150 - 0.661902i) q^{22} +5.65013 q^{23} +(-0.921723 - 1.59647i) q^{24} +(-3.42189 + 5.92688i) q^{25} +(2.61736 + 1.60213i) q^{26} -3.67824 q^{27} +(3.28174 - 0.787424i) q^{28} +(0.917969 - 1.58997i) q^{29} +(0.968404 - 1.67733i) q^{30} +(4.56692 - 7.91014i) q^{31} -5.72761 q^{32} +(0.296885 - 0.514219i) q^{33} -1.64847 q^{34} +(6.26681 + 6.60556i) q^{35} +(-1.63452 + 2.83108i) q^{36} -10.6000 q^{37} +(0.441751 - 0.765135i) q^{38} +(-0.0612242 + 2.38329i) q^{39} +(-4.79731 - 8.30918i) q^{40} +(2.66571 - 4.61715i) q^{41} +(-1.02481 - 1.08021i) q^{42} +(1.95732 + 3.39018i) q^{43} +(-0.572729 - 0.991996i) q^{44} -8.81977 q^{45} -4.80897 q^{46} +(-3.59565 - 6.22784i) q^{47} +(-0.0589445 - 0.102095i) q^{48} +(6.23787 - 3.17631i) q^{49} +(2.91246 - 5.04452i) q^{50} +(-0.640331 - 1.10909i) q^{51} +(3.92265 + 2.40112i) q^{52} +(4.69324 - 8.12893i) q^{53} +3.13065 q^{54} +(1.54520 - 2.67637i) q^{55} +(-7.17260 + 1.72100i) q^{56} +0.686375 q^{57} +(-0.781307 + 1.35326i) q^{58} -0.510517 q^{59} +(1.45135 - 2.51382i) q^{60} +(-0.718095 + 1.24378i) q^{61} +(-3.88702 + 6.73252i) q^{62} +(-1.92661 + 6.50102i) q^{63} +4.51834 q^{64} +(-0.318655 + 12.4043i) q^{65} +(-0.252686 + 0.437665i) q^{66} +(4.22466 + 7.31732i) q^{67} -2.47057 q^{68} +(-1.86800 - 3.23547i) q^{69} +(-5.33385 - 5.62216i) q^{70} +(1.72419 + 2.98638i) q^{71} +(3.57244 - 6.18764i) q^{72} +(-5.45026 + 9.44013i) q^{73} +9.02195 q^{74} +4.52526 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} +(-0.306789 - 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(-2.26886 + 3.92977i) q^{82} +1.51669 q^{83} +(-1.53589 - 1.61891i) q^{84} +(-3.33274 - 5.77248i) q^{85} +(-1.66593 - 2.88547i) q^{86} -1.21396 q^{87} +(1.25176 + 2.16812i) q^{88} +13.6078 q^{89} +7.50673 q^{90} +(9.07358 + 2.94451i) q^{91} -7.20722 q^{92} -6.03951 q^{93} +(3.06035 + 5.30067i) q^{94} +3.57239 q^{95} +(1.89362 + 3.27984i) q^{96} +(-0.253120 - 0.438417i) q^{97} +(-5.30921 + 2.70344i) q^{98} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + q^{3} + 8 q^{4} + q^{5} - 9 q^{6} - 3 q^{7} - 6 q^{8} + 3 q^{9} + 4 q^{10} + 4 q^{11} + 5 q^{12} - 2 q^{13} - 2 q^{14} - 2 q^{15} - 16 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - q^{20}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 + q^3 + 8 * q^4 + q^5 - 9 * q^6 - 3 * q^7 - 6 * q^8 + 3 * q^9 + 4 * q^10 + 4 * q^11 + 5 * q^12 - 2 * q^13 - 2 * q^14 - 2 * q^15 - 16 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - q^20 - 9 * q^21 - 5 * q^22 + 2 * q^23 - 11 * q^24 + 7 * q^25 - 16 * q^26 - 8 * q^27 - q^28 + 3 * q^29 - 5 * q^30 + 16 * q^31 - 16 * q^32 + 16 * q^33 + 32 * q^34 + 20 * q^35 - 21 * q^36 + 26 * q^37 - 17 * q^38 - 20 * q^39 - 5 * q^40 - 8 * q^41 + 50 * q^42 - 11 * q^43 + 21 * q^44 + 14 * q^45 - 32 * q^46 - q^47 + 21 * q^48 - 3 * q^49 + 6 * q^50 - 20 * q^51 + 41 * q^52 - 2 * q^53 + 36 * q^54 + 9 * q^55 + 9 * q^56 + 42 * q^57 - 8 * q^58 - 26 * q^59 + 20 * q^60 - 5 * q^61 + 5 * q^62 - 40 * q^63 - 30 * q^64 - 5 * q^65 + 18 * q^66 - 11 * q^67 - 58 * q^68 + 23 * q^69 - 39 * q^70 + 6 * q^71 + 25 * q^72 - 30 * q^73 + 6 * q^74 + 6 * q^75 - 9 * q^76 + 11 * q^77 + 16 * q^78 + 7 * q^79 - 7 * q^80 - 6 * q^81 + q^82 - 54 * q^83 - 46 * q^84 - q^85 - 7 * q^86 - 32 * q^87 - 8 * q^89 - 16 * q^90 - 23 * q^91 + 54 * q^92 + 14 * q^93 + 45 * q^94 + 12 * q^95 + 19 * q^96 - 35 * q^97 + 20 * q^98 - 20 * q^99

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