LMFDB - Embedded newform 231.2.y.b.16.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.7
Character	$\chi$	$=$	231.16
Dual form			231.2.y.b.130.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18402 + 0.464228i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.72735 + 1.21429i) q^{4} +(0.687753 + 0.763827i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(-0.0599597 - 2.64507i) q^{7} +(1.78011 + 1.29333i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(2.18402 + 0.464228i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.72735 + 1.21429i) q^{4} +(0.687753 + 0.763827i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(-0.0599597 - 2.64507i) q^{7} +(1.78011 + 1.29333i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.14748 + 1.98749i) q^{10} +(-2.75788 - 1.84231i) q^{11} +(-1.49273 + 2.58548i) q^{12} +(1.56619 + 4.82025i) q^{13} +(1.09696 - 5.80473i) q^{14} +(-0.831533 + 0.604144i) q^{15} +(-0.707916 - 0.786220i) q^{16} +(-2.54635 + 0.541243i) q^{17} +(-2.03978 - 0.908167i) q^{18} +(-1.22983 + 0.547557i) q^{19} +(0.948233 + 2.91836i) q^{20} +(2.63685 + 0.216854i) q^{21} +(-5.16801 - 5.30393i) q^{22} +(0.946580 - 1.63952i) q^{23} +(-1.47231 + 1.63517i) q^{24} +(0.412215 - 3.92196i) q^{25} +(1.18291 + 11.2546i) q^{26} +(0.309017 - 0.951057i) q^{27} +(3.04836 - 7.28685i) q^{28} +(3.25868 - 2.36757i) q^{29} +(-2.09655 + 0.933442i) q^{30} +(2.19733 - 2.44038i) q^{31} +(-3.38146 - 5.85686i) q^{32} +(2.12050 - 2.55020i) q^{33} -5.81254 q^{34} +(1.97914 - 1.86496i) q^{35} +(-2.41528 - 1.75481i) q^{36} +(0.842673 + 8.01750i) q^{37} +(-2.94017 + 0.624953i) q^{38} +(-4.95755 + 1.05376i) q^{39} +(0.236399 + 2.24919i) q^{40} +(-0.828434 - 0.601893i) q^{41} +(5.65827 + 1.69771i) q^{42} +9.19303 q^{43} +(-5.28459 - 8.37350i) q^{44} +(-0.513916 - 0.890128i) q^{45} +(2.82846 - 3.14133i) q^{46} +(-9.03522 + 4.02274i) q^{47} +(0.855911 - 0.621855i) q^{48} +(-6.99281 + 0.317195i) q^{49} +(2.72097 - 8.37428i) q^{50} +(-0.272112 - 2.58898i) q^{51} +(-1.58164 + 15.0483i) q^{52} +(-8.15912 + 9.06162i) q^{53} +(1.11641 - 1.93367i) q^{54} +(-0.489532 - 3.37360i) q^{55} +(3.31421 - 4.78607i) q^{56} +(-0.416005 - 1.28033i) q^{57} +(8.21611 - 3.65805i) q^{58} +(5.63831 + 2.51034i) q^{59} +(-3.00149 + 0.637986i) q^{60} +(-2.33469 - 2.59294i) q^{61} +(5.93191 - 4.30978i) q^{62} +(-0.491292 + 2.59974i) q^{63} +(-4.01240 - 12.3489i) q^{64} +(-2.60468 + 4.51144i) q^{65} +(5.81508 - 4.58529i) q^{66} +(-0.556014 - 0.963044i) q^{67} +(-7.60202 - 1.61586i) q^{68} +(1.53160 + 1.11277i) q^{69} +(5.18825 - 3.15433i) q^{70} +(-2.29639 + 7.06755i) q^{71} +(-1.47231 - 1.63517i) q^{72} +(10.1096 + 4.50106i) q^{73} +(-1.88153 + 17.9016i) q^{74} +(3.85739 + 0.819913i) q^{75} -4.01908 q^{76} +(-4.70768 + 7.40525i) q^{77} -11.3166 q^{78} +(13.6777 + 2.90728i) q^{79} +(0.113665 - 1.08145i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-1.52990 - 1.69913i) q^{82} +(1.44739 - 4.45461i) q^{83} +(6.92829 + 3.79335i) q^{84} +(-2.16468 - 1.57273i) q^{85} +(20.0778 + 4.26766i) q^{86} +(2.01397 + 3.48830i) q^{87} +(-2.52662 - 6.84636i) q^{88} +(-9.17730 + 15.8955i) q^{89} +(-0.709180 - 2.18263i) q^{90} +(12.6560 - 4.43171i) q^{91} +(4.57252 - 3.32213i) q^{92} +(2.19733 + 2.44038i) q^{93} +(-21.6006 + 4.59135i) q^{94} +(-1.26406 - 0.562796i) q^{95} +(6.17823 - 2.75073i) q^{96} +(-2.19712 - 6.76203i) q^{97} +(-15.4197 - 2.55350i) q^{98} +(2.31457 + 2.37545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	2.18402	+	0.464228i	1.54434	+	0.328259i	0.899796	−	0.436311i	$-0.143715\pi$
$2$	2.18402	+	0.464228i	1.54434	+	0.328259i	0.644540	+	0.764570i	$0.277049\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	2.72735	+	1.21429i	1.36367	+	0.607147i
$5$	0.687753	+	0.763827i	0.307573	+	0.341594i	0.877038	−	0.480421i	$-0.159516\pi$
$5$	0.687753	+	0.763827i	0.307573	+	0.341594i	−0.569465	+	0.822016i	$0.692850\pi$
$6$	−0.689977	+	2.12353i	−0.281682	+	0.866928i
$7$	−0.0599597	−	2.64507i	−0.0226626	−	0.999743i
$7$	−0.0599597	−	2.64507i	−0.0226626	−	0.999743i
$8$	1.78011	+	1.29333i	0.629365	+	0.457260i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.14748	+	1.98749i	0.362864	+	0.628499i
$11$	−2.75788	−	1.84231i	−0.831532	−	0.555478i
$11$	−2.75788	−	1.84231i	−0.831532	−	0.555478i
$12$	−1.49273	+	2.58548i	−0.430913	+	0.746364i
$13$	1.56619	+	4.82025i	0.434384	+	1.33690i	0.893717	+	0.448632i	$0.148088\pi$
$13$	1.56619	+	4.82025i	0.434384	+	1.33690i	−0.459333	+	0.888264i	$0.651912\pi$
$14$	1.09696	−	5.80473i	0.293176	−	1.55138i
$15$	−0.831533	+	0.604144i	−0.214701	+	0.155989i
$16$	−0.707916	−	0.786220i	−0.176979	−	0.196555i
$17$	−2.54635	+	0.541243i	−0.617581	+	0.131271i	−0.506070	−	0.862492i	$-0.668902\pi$
$17$	−2.54635	+	0.541243i	−0.617581	+	0.131271i	−0.111511	+	0.993763i	$0.535569\pi$
$18$	−2.03978	−	0.908167i	−0.480780	−	0.214057i
$19$	−1.22983	+	0.547557i	−0.282143	+	0.125618i	−0.542929	−	0.839778i	$-0.682685\pi$
$19$	−1.22983	+	0.547557i	−0.282143	+	0.125618i	0.260786	+	0.965397i	$0.416018\pi$
$20$	0.948233	+	2.91836i	0.212031	+	0.652565i
$21$	2.63685	+	0.216854i	0.575408	+	0.0473214i
$22$	−5.16801	−	5.30393i	−1.10182	−	1.13080i
$23$	0.946580	−	1.63952i	0.197376	−	0.341864i	−0.750301	−	0.661096i	$-0.770091\pi$
$23$	0.946580	−	1.63952i	0.197376	−	0.341864i	0.947677	+	0.319232i	$0.103425\pi$
$24$	−1.47231	+	1.63517i	−0.300535	+	0.333778i
$25$	0.412215	−	3.92196i	0.0824429	−	0.784392i
$26$	1.18291	+	11.2546i	0.231987	+	2.20721i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	3.04836	−	7.28685i	0.576087	−	1.37708i
$29$	3.25868	−	2.36757i	0.605121	−	0.439646i	−0.242572	−	0.970133i	$-0.577991\pi$
$29$	3.25868	−	2.36757i	0.605121	−	0.439646i	0.847693	+	0.530487i	$0.177991\pi$
$30$	−2.09655	+	0.933442i	−0.382775	+	0.170423i
$31$	2.19733	−	2.44038i	0.394652	−	0.438305i	−0.512770	−	0.858526i	$-0.671381\pi$
$31$	2.19733	−	2.44038i	0.394652	−	0.438305i	0.907422	+	0.420221i	$0.138047\pi$
$32$	−3.38146	−	5.85686i	−0.597763	−	1.03536i
$33$	2.12050	−	2.55020i	0.369131	−	0.443932i
$34$	−5.81254			−0.996843
$35$	1.97914	−	1.86496i	0.334536	−	0.315235i
$36$	−2.41528	−	1.75481i	−0.402547	−	0.292468i
$37$	0.842673	+	8.01750i	0.138535	+	1.31807i	0.814081	+	0.580751i	$0.197241\pi$
$37$	0.842673	+	8.01750i	0.138535	+	1.31807i	−0.675547	+	0.737317i	$0.736092\pi$
$38$	−2.94017	+	0.624953i	−0.476959	+	0.101381i
$39$	−4.95755	+	1.05376i	−0.793844	+	0.168737i
$40$	0.236399	+	2.24919i	0.0373780	+	0.355628i
$41$	−0.828434	−	0.601893i	−0.129380	−	0.0939999i	0.521213	−	0.853426i	$-0.325480\pi$
$41$	−0.828434	−	0.601893i	−0.129380	−	0.0939999i	−0.650593	+	0.759427i	$0.725480\pi$
$42$	5.65827	+	1.69771i	0.873089	+	0.261963i
$43$	9.19303			1.40192			0.700962	−	0.713199i	$-0.252754\pi$
$43$	9.19303			1.40192			0.700962	+	0.713199i	$0.252754\pi$
$44$	−5.28459	−	8.37350i	−0.796682	−	1.26235i
$45$	−0.513916	−	0.890128i	−0.0766100	−	0.132692i
$46$	2.82846	−	3.14133i	0.417034	−	0.463163i
$47$	−9.03522	+	4.02274i	−1.31792	+	0.586777i	−0.940667	−	0.339332i	$-0.889799\pi$
$47$	−9.03522	+	4.02274i	−1.31792	+	0.586777i	−0.377256	+	0.926109i	$0.623132\pi$
$48$	0.855911	−	0.621855i	0.123540	−	0.0897571i
$49$	−6.99281	+	0.317195i	−0.998973	+	0.0453136i
$50$	2.72097	−	8.37428i	0.384803	−	1.18430i
$51$	−0.272112	−	2.58898i	−0.0381034	−	0.362529i
$52$	−1.58164	+	15.0483i	−0.219334	+	2.08683i
$53$	−8.15912	+	9.06162i	−1.12074	+	1.24471i	−0.154244	+	0.988033i	$0.549294\pi$
$53$	−8.15912	+	9.06162i	−1.12074	+	1.24471i	−0.966497	+	0.256677i	$0.917372\pi$
$54$	1.11641	−	1.93367i	0.151924	−	0.263140i
$55$	−0.489532	−	3.37360i	−0.0660085	−	0.454896i
$56$	3.31421	−	4.78607i	0.442880	−	0.639566i
$57$	−0.416005	−	1.28033i	−0.0551012	−	0.169584i
$58$	8.21611	−	3.65805i	1.07883	−	0.480325i
$59$	5.63831	+	2.51034i	0.734045	+	0.326818i	0.739490	−	0.673167i	$-0.235067\pi$
$59$	5.63831	+	2.51034i	0.734045	+	0.326818i	−0.00544532	+	0.999985i	$0.501733\pi$
$60$	−3.00149	+	0.637986i	−0.387491	+	0.0823637i
$61$	−2.33469	−	2.59294i	−0.298927	−	0.331992i	0.574905	−	0.818220i	$-0.305039\pi$
$61$	−2.33469	−	2.59294i	−0.298927	−	0.331992i	−0.873832	+	0.486228i	$0.838372\pi$
$62$	5.93191	−	4.30978i	0.753353	−	0.547343i
$63$	−0.491292	+	2.59974i	−0.0618970	+	0.327536i
$64$	−4.01240	−	12.3489i	−0.501550	−	1.54361i
$65$	−2.60468	+	4.51144i	−0.323071	+	0.559575i
$66$	5.81508	−	4.58529i	0.715787	−	0.564410i
$67$	−0.556014	−	0.963044i	−0.0679279	−	0.117655i	0.830061	−	0.557672i	$-0.188305\pi$
$67$	−0.556014	−	0.963044i	−0.0679279	−	0.117655i	−0.897989	+	0.440018i	$0.854972\pi$
$68$	−7.60202	−	1.61586i	−0.921880	−	0.195952i
$69$	1.53160	+	1.11277i	0.184383	+	0.133962i
$70$	5.18825	−	3.15433i	0.620115	−	0.377015i
$71$	−2.29639	+	7.06755i	−0.272531	+	0.838764i	0.717331	+	0.696732i	$0.245364\pi$
$71$	−2.29639	+	7.06755i	−0.272531	+	0.838764i	−0.989862	+	0.142032i	$0.954636\pi$
$72$	−1.47231	−	1.63517i	−0.173514	−	0.192707i
$73$	10.1096	+	4.50106i	1.18323	+	0.526809i	0.901540	−	0.432695i	$-0.142437\pi$
$73$	10.1096	+	4.50106i	1.18323	+	0.526809i	0.281693	+	0.959505i	$0.409104\pi$
$74$	−1.88153	+	17.9016i	−0.218724	+	2.08102i
$75$	3.85739	+	0.819913i	0.445413	+	0.0946754i
$76$	−4.01908			−0.461020
$77$	−4.70768	+	7.40525i	−0.536490	+	0.843907i
$78$	−11.3166			−1.28135
$79$	13.6777	+	2.90728i	1.53886	+	0.327095i	0.897803	−	0.440397i	$-0.145162\pi$
$79$	13.6777	+	2.90728i	1.53886	+	0.327095i	0.641058	+	0.767492i	$0.278496\pi$
$80$	0.113665	−	1.08145i	0.0127081	−	0.120910i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−1.52990	−	1.69913i	−0.168949	−	0.187637i
$83$	1.44739	−	4.45461i	0.158872	−	0.488957i	−0.839661	−	0.543111i	$-0.817246\pi$
$83$	1.44739	−	4.45461i	0.158872	−	0.488957i	0.998533	+	0.0541542i	$0.0172463\pi$
$84$	6.92829	+	3.79335i	0.755938	+	0.413888i
$85$	−2.16468	−	1.57273i	−0.234792	−	0.170587i
$86$	20.0778	+	4.26766i	2.16504	+	0.460194i
$87$	2.01397	+	3.48830i	0.215921	+	0.373985i
$88$	−2.52662	−	6.84636i	−0.269339	−	0.729824i
$89$	−9.17730	+	15.8955i	−0.972792	+	1.68492i	−0.285754	+	0.958303i	$0.592244\pi$
$89$	−9.17730	+	15.8955i	−0.972792	+	1.68492i	−0.687038	+	0.726621i	$0.741089\pi$
$90$	−0.709180	−	2.18263i	−0.0747542	−	0.230070i
$91$	12.6560	−	4.43171i	1.32671	−	0.464570i
$92$	4.57252	−	3.32213i	0.476718	−	0.346356i
$93$	2.19733	+	2.44038i	0.227852	+	0.253056i
$94$	−21.6006	+	4.59135i	−2.22793	+	0.473561i
$95$	−1.26406	−	0.562796i	−0.129690	−	0.0577416i
$96$	6.17823	−	2.75073i	0.630563	−	0.280745i
$97$	−2.19712	−	6.76203i	−0.223083	−	0.686580i	−0.998481	−	0.0551061i	$-0.982450\pi$
$97$	−2.19712	−	6.76203i	−0.223083	−	0.686580i	0.775397	−	0.631474i	$-0.217550\pi$
$98$	−15.4197	−	2.55350i	−1.55762	−	0.257942i
$99$	2.31457	+	2.37545i	0.232623	+	0.238741i
$100$	5.88667	−	10.1960i	0.588667	−	1.01960i
$101$	4.18856	−	4.65187i	0.416778	−	0.462878i	−0.497798	−	0.867293i	$-0.665858\pi$
$101$	4.18856	−	4.65187i	0.416778	−	0.462878i	0.914576	+	0.404414i	$0.132525\pi$
$102$	0.607576	−	5.78070i	0.0601590	−	0.572375i
$103$	−1.10285	−	10.4930i	−0.108667	−	1.03390i	−0.903943	−	0.427653i	$-0.859340\pi$
$103$	−1.10285	−	10.4930i	−0.108667	−	1.03390i	0.795276	−	0.606248i	$-0.207326\pi$
$104$	−3.44616	+	10.6062i	−0.337923	+	1.04002i
$105$	1.64786	+	2.16324i	0.160815	+	0.211111i
$106$	−22.0264	+	16.0031i	−2.13939	+	1.55436i
$107$	−5.85260	+	2.60575i	−0.565792	+	0.251907i	−0.669639	−	0.742686i	$-0.733551\pi$
$107$	−5.85260	+	2.60575i	−0.565792	+	0.251907i	0.103847	+	0.994593i	$0.466885\pi$
$108$	1.99766	−	2.21863i	0.192225	−	0.213487i
$109$	0.0464491	+	0.0804522i	0.00444901	+	0.00770592i	0.868241	−	0.496142i	$-0.165250\pi$
$109$	0.0464491	+	0.0804522i	0.00444901	+	0.00770592i	−0.863792	+	0.503848i	$0.831917\pi$
$110$	0.496970	−	7.59526i	0.0473842	−	0.724180i
$111$	−8.06166			−0.765179
$112$	−2.03716	+	1.91963i	−0.192494	+	0.181388i
$113$	−9.18338	−	6.67212i	−0.863900	−	0.627660i	0.0650432	−	0.997882i	$-0.479281\pi$
$113$	−9.18338	−	6.67212i	−0.863900	−	0.627660i	−0.928943	+	0.370222i	$0.879281\pi$
$114$	−0.314198	−	2.98939i	−0.0294273	−	0.279982i
$115$	1.90333	−	0.404565i	0.177486	−	0.0377259i
$116$	11.7625	−	2.50019i	1.09212	−	0.232137i
$117$	−0.529782	−	5.04054i	−0.0489784	−	0.465998i
$118$	11.1488	+	8.10009i	1.02633	+	0.745673i
$119$	1.58431	+	6.70283i	0.145233	+	0.614447i
$120$	−2.26158			−0.206453
$121$	4.21178	+	10.1617i	0.382889	+	0.923794i
$122$	−3.89531	−	6.74687i	−0.352664	−	0.610833i
$123$	0.685191	−	0.760981i	0.0617815	−	0.0686154i
$124$	8.95623	−	3.98757i	0.804293	−	0.358094i
$125$	7.43687	−	5.40320i	0.665174	−	0.483277i
$126$	−2.27986	+	5.44981i	−0.203106	+	0.485508i
$127$	3.42572	−	10.5433i	0.303984	−	0.935566i	−0.676071	−	0.736837i	$-0.736319\pi$
$127$	3.42572	−	10.5433i	0.303984	−	0.935566i	0.980054	−	0.198729i	$-0.0636814\pi$
$128$	−1.61663	−	15.3812i	−0.142891	−	1.35952i
$129$	−0.960933	+	9.14267i	−0.0846054	+	0.804967i
$130$	−7.78302	+	8.64392i	−0.682616	+	0.758122i
$131$	2.66318	−	4.61277i	0.232683	−	0.403019i	−0.725914	−	0.687786i	$-0.758583\pi$
$131$	2.66318	−	4.61277i	0.232683	−	0.403019i	0.958597	+	0.284767i	$0.0919161\pi$
$132$	8.88002	−	4.38037i	0.772907	−	0.381262i
$133$	1.52207	+	3.22016i	0.131980	+	0.279224i
$134$	−0.767274	−	2.36143i	−0.0662824	−	0.203996i
$135$	0.938971	−	0.418057i	0.0808137	−	0.0359806i
$136$	−5.23279	−	2.32979i	−0.448708	−	0.199778i
$137$	3.99047	−	0.848200i	0.340929	−	0.0724666i	−0.0342658	−	0.999413i	$-0.510909\pi$
$137$	3.99047	−	0.848200i	0.340929	−	0.0724666i	0.375194	+	0.926946i	$0.377576\pi$
$138$	2.82846	+	3.14133i	0.240775	+	0.267408i
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.353799	+	0.935321i	$0.615110\pi$
$139$	−15.9478	+	11.5867i	−1.35267	+	0.982774i	−0.998873	+	0.0474531i	$0.984890\pi$
$140$	7.66242	−	2.68313i	0.647592	−	0.226766i
$141$	−3.05627	−	9.40622i	−0.257384	−	0.792146i
$142$	−8.29631	+	14.3696i	−0.696211	+	1.20587i
$143$	4.56102	−	16.1791i	0.381412	−	1.35296i
$144$	0.528982	+	0.916223i	0.0440818	+	0.0763520i
$145$	4.04958	+	0.860765i	0.336299	+	0.0714826i
$146$	19.9900	+	14.5236i	1.65438	+	1.20198i
$147$	0.415490	−	6.98766i	0.0342690	−	0.576332i
$148$	−7.43734	+	22.8898i	−0.611345	+	1.88153i
$149$	3.20177	+	3.55593i	0.262300	+	0.291313i	0.859880	−	0.510495i	$-0.170538\pi$
$149$	3.20177	+	3.55593i	0.262300	+	0.291313i	−0.597581	+	0.801809i	$0.703871\pi$
$150$	8.04399	+	3.58141i	0.656789	+	0.292421i
$151$	0.574488	−	5.46589i	0.0467512	−	0.444808i	−0.945959	−	0.324285i	$-0.894876\pi$
$151$	0.574488	−	5.46589i	0.0467512	−	0.444808i	0.992711	−	0.120523i	$-0.0384570\pi$
$152$	−2.89741	−	0.615863i	−0.235011	−	0.0499531i
$153$	2.60324			0.210459
$154$	−13.7194	+	13.9878i	−1.10554	+	1.12717i
$155$	3.37525			0.271107
$156$	−14.8006	−	3.14596i	−1.18499	−	0.251878i
$157$	−2.17333	+	20.6778i	−0.173450	+	1.65027i	0.468456	+	0.883487i	$0.344810\pi$
$157$	−2.17333	+	20.6778i	−0.173450	+	1.65027i	−0.641906	+	0.766783i	$0.721856\pi$
$158$	28.5227	+	12.6991i	2.26915	+	1.01029i
$159$	−8.15912	−	9.06162i	−0.647060	−	0.718633i
$160$	2.14802	−	6.61092i	0.169816	−	0.522639i
$161$	−4.39342	−	2.40547i	−0.346250	−	0.189577i
$162$	1.80638	+	1.31241i	0.141923	+	0.103113i
$163$	7.15721	+	1.52131i	0.560596	+	0.119158i	0.479491	−	0.877547i	$-0.340821\pi$
$163$	7.15721	+	1.52131i	0.560596	+	0.119158i	0.0811058	+	0.996705i	$0.474155\pi$
$164$	−1.52856	−	2.64754i	−0.119360	−	0.206738i
$165$	3.40629	−	0.134214i	0.265179	−	0.0104485i
$166$	5.22908	−	9.05704i	0.405856	−	0.702963i
$167$	1.84641	+	5.68265i	0.142879	+	0.439737i	0.996732	−	0.0807774i	$-0.0257403\pi$
$167$	1.84641	+	5.68265i	0.142879	+	0.439737i	−0.853853	+	0.520514i	$0.825740\pi$
$168$	4.41342	+	3.79633i	0.340503	+	0.292894i
$169$	−10.2646	+	7.45766i	−0.789584	+	0.573666i
$170$	−3.99760	−	4.43978i	−0.306602	−	0.340516i
$171$	1.31680	−	0.279895i	0.100698	−	0.0214041i
$172$	25.0726	+	11.1630i	1.91177	+	0.851174i
$173$	1.35215	−	0.602016i	0.102802	−	0.0457704i	−0.354691	−	0.934983i	$-0.615414\pi$
$173$	1.35215	−	0.602016i	0.102802	−	0.0457704i	0.457493	+	0.889213i	$0.348747\pi$
$174$	2.77919	+	8.55347i	0.210690	+	0.648437i
$175$	−10.3986	−	0.855178i	−0.786059	−	0.0646454i
$176$	0.503884	+	3.47250i	0.0379817	+	0.261750i
$177$	−3.08595	+	5.34502i	−0.231954	+	0.401756i
$178$	−27.4226	+	30.4559i	−2.05541	+	2.28276i
$179$	0.564712	−	5.37288i	0.0422086	−	0.401588i	−0.952937	−	0.303170i	$-0.901955\pi$
$179$	0.564712	−	5.37288i	0.0422086	−	0.401588i	0.995145	−	0.0984181i	$-0.0313782\pi$
$180$	−0.320750	−	3.05174i	−0.0239073	−	0.227463i
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	−0.0695958	−	0.997575i	$-0.522171\pi$
$181$	7.70985	−	23.7285i	0.573068	−	1.76372i	0.642664	−	0.766148i	$-0.277829\pi$
$182$	29.6983	−	3.80369i	2.20138	−	0.281948i
$183$	2.82278	−	2.05087i	0.208666	−	0.151605i
$184$	3.80546	−	1.69430i	0.280542	−	0.124905i
$185$	−5.54443	+	6.15772i	−0.407635	+	0.452724i
$186$	3.66612	+	6.34991i	0.268813	+	0.465598i
$187$	8.01966	+	3.19848i	0.586456	+	0.233896i
$188$	−29.5270			−2.15348
$189$	−2.53414	−	0.760347i	−0.184332	−	0.0553071i
$190$	−2.49947	−	1.81597i	−0.181330	−	0.131744i
$191$	−2.38876	−	22.7275i	−0.172844	−	1.64451i	−0.645863	−	0.763453i	$-0.723502\pi$
$191$	−2.38876	−	22.7275i	−0.172844	−	1.64451i	0.473019	−	0.881052i	$-0.343164\pi$
$192$	12.7007	−	2.69961i	0.916591	−	0.194827i
$193$	7.17998	−	1.52615i	0.516826	−	0.109855i	0.0578881	−	0.998323i	$-0.481563\pi$
$193$	7.17998	−	1.52615i	0.516826	−	0.109855i	0.458938	+	0.888468i	$0.348230\pi$
$194$	−1.65943	−	15.7884i	−0.119140	−	1.13354i
$195$	−4.21446	−	3.06199i	−0.301804	−	0.219273i
$196$	−19.4570	−	7.62623i	−1.38979	−	0.544730i
$197$	26.2782			1.87224			0.936121	−	0.351679i	$-0.114389\pi$
$197$	26.2782			1.87224			0.936121	+	0.351679i	$0.114389\pi$
$198$	3.95233	+	6.26252i	0.280880	+	0.445058i
$199$	−6.06430	−	10.5037i	−0.429887	−	0.744586i	0.566976	−	0.823734i	$-0.308113\pi$
$199$	−6.06430	−	10.5037i	−0.429887	−	0.744586i	−0.996863	+	0.0791483i	$0.974780\pi$
$200$	5.80617	−	6.44840i	0.410558	−	0.455971i
$201$	1.01589	−	0.452302i	0.0716552	−	0.0319029i
$202$	11.3074	−	8.21534i	0.795589	−	0.578029i
$203$	−6.45778	−	8.47748i	−0.453247	−	0.595002i
$204$	2.40163	−	7.39147i	0.168148	−	0.517506i
$205$	−0.110016	−	1.04673i	−0.00768387	−	0.0731071i
$206$	2.46247	−	23.4288i	0.171568	−	1.63236i
$207$	−1.26677	+	1.40689i	−0.0880467	+	0.0977857i
$208$	2.68104	−	4.64370i	0.185897	−	0.321983i
$209$	4.40050	+	0.755639i	0.304389	+	0.0522686i
$210$	2.59473	+	5.48955i	0.179053	+	0.378815i
$211$	5.52303	+	16.9981i	0.380221	+	1.17020i	0.939888	+	0.341483i	$0.110929\pi$
$211$	5.52303	+	16.9981i	0.380221	+	1.17020i	−0.559667	+	0.828718i	$0.689071\pi$
$212$	−33.2563	+	14.8066i	−2.28405	+	1.01692i
$213$	−6.78880	−	3.02257i	−0.465161	−	0.207103i
$214$	−13.9919	+	2.97406i	−0.956464	+	0.203303i
$215$	6.32253	+	7.02189i	0.431193	+	0.478889i
$216$	1.78011	−	1.29333i	0.121121	−	0.0879998i
$217$	−6.58673	−	5.66577i	−0.447137	−	0.384617i
$218$	0.0640976	+	0.197272i	0.00434124	+	0.0133610i
$219$	−5.53314	+	9.58368i	−0.373895	+	0.647605i
$220$	2.76142	−	9.79542i	0.186175	−	0.660407i
$221$	−6.59700	−	11.4263i	−0.443762	−	0.768619i
$222$	−17.6068	−	3.74245i	−1.18169	−	0.251177i
$223$	1.70719	+	1.24034i	0.114322	+	0.0830596i	0.643477	−	0.765465i	$-0.277491\pi$
$223$	1.70719	+	1.24034i	0.114322	+	0.0830596i	−0.529155	+	0.848525i	$0.677491\pi$
$224$	−15.2891	+	9.29537i	−1.02154	+	0.621073i
$225$	−1.21863	+	3.75055i	−0.0812419	+	0.250037i
$226$	−16.9593	−	18.8352i	−1.12812	−	1.25290i
$227$	−10.3161	−	4.59301i	−0.684702	−	0.304849i	0.0347454	−	0.999396i	$-0.488938\pi$
$227$	−10.3161	−	4.59301i	−0.684702	−	0.304849i	−0.719447	+	0.694547i	$0.755605\pi$
$228$	0.420108	−	3.99706i	0.0278223	−	0.264712i
$229$	−27.2660	−	5.79557i	−1.80179	−	0.382982i	−0.819910	−	0.572492i	$-0.805977\pi$
$229$	−27.2660	−	5.79557i	−1.80179	−	0.382982i	−0.981879	+	0.189510i	$0.939310\pi$
$230$	4.34472			0.286482
$231$	−6.87260	−	5.45595i	−0.452184	−	0.358975i
$232$	8.86285			0.581875
$233$	6.72177	+	1.42876i	0.440358	+	0.0936009i	0.422755	−	0.906244i	$-0.361063\pi$
$233$	6.72177	+	1.42876i	0.440358	+	0.0936009i	0.0176030	+	0.999845i	$0.494397\pi$
$234$	1.18291	−	11.2546i	0.0773289	−	0.735736i
$235$	−9.28668	−	4.13470i	−0.605796	−	0.269718i
$236$	12.3293	+	13.6931i	0.802572	+	0.891347i
$237$	−4.32107	+	13.2989i	−0.280683	+	0.863855i
$238$	0.348518	+	15.3746i	0.0225911	+	0.996587i
$239$	−9.02995	−	6.56065i	−0.584099	−	0.424373i	0.256100	−	0.966650i	$-0.417562\pi$
$239$	−9.02995	−	6.56065i	−0.584099	−	0.424373i	−0.840200	+	0.542277i	$0.817562\pi$
$240$	1.06365	+	0.226085i	0.0686580	+	0.0145937i
$241$	−8.25275	−	14.2942i	−0.531606	−	0.920769i	−0.999319	−	0.0368888i	$-0.988255\pi$
$241$	−8.25275	−	14.2942i	−0.531606	−	0.920769i	0.467713	−	0.883880i	$-0.345078\pi$
$242$	4.48126	+	24.1487i	0.288066	+	1.55234i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.21893	−	9.90686i	−0.206071	−	0.634222i
$245$	−5.05161	−	5.12315i	−0.322736	−	0.327306i
$246$	1.84974	−	1.34391i	0.117935	−	0.0856848i
$247$	−4.56551	−	5.07052i	−0.290497	−	0.322629i
$248$	7.06770	−	1.50229i	0.448800	−	0.0953953i
$249$	4.27891	+	1.90509i	0.271165	+	0.120730i
$250$	18.7506	−	8.34830i	1.18589	−	0.527993i
$251$	−7.05468	−	21.7121i	−0.445288	−	1.37045i	−0.882168	−	0.470935i	$-0.843917\pi$
$251$	−7.05468	−	21.7121i	−0.445288	−	1.37045i	0.436880	−	0.899520i	$-0.356083\pi$
$252$	−4.49677	+	6.49382i	−0.283270	+	0.409072i
$253$	−5.63107	+	2.77771i	−0.354022	+	0.174633i
$254$	12.3763	−	21.4365i	0.776561	−	1.34504i
$255$	1.79039	−	1.98842i	0.112118	−	0.124520i
$256$	0.895151	−	8.51679i	0.0559469	−	0.532299i
$257$	−0.780433	−	7.42532i	−0.0486821	−	0.463179i	−0.991523	−	0.129935i	$-0.958523\pi$
$257$	−0.780433	−	7.42532i	−0.0486821	−	0.463179i	0.942841	−	0.333244i	$-0.108143\pi$
$258$	−6.34298	+	19.5217i	−0.394897	+	1.21537i
$259$	21.1563	−	2.70966i	1.31459	−	0.168370i
$260$	−12.5821	+	9.14143i	−0.780309	+	0.566927i
$261$	−3.67971	+	1.63831i	−0.227768	+	0.101409i
$262$	7.95782	−	8.83806i	0.491636	−	0.546017i
$263$	−11.1744	−	19.3547i	−0.689045	−	1.19346i	−0.972147	−	0.234371i	$-0.924697\pi$
$263$	−11.1744	−	19.3547i	−0.689045	−	1.19346i	0.283102	−	0.959090i	$-0.408636\pi$
$264$	7.07296	−	1.79714i	0.435310	−	0.110606i
$265$	−12.5330			−0.769895
$266$	1.82934	+	7.73949i	0.112164	+	0.474539i
$267$	−14.8492	−	10.7886i	−0.908755	−	0.660249i
$268$	−0.347025	−	3.30172i	−0.0211979	−	0.201685i
$269$	1.12709	−	0.239571i	0.0687199	−	0.0146069i	−0.173423	−	0.984847i	$-0.555483\pi$
$269$	1.12709	−	0.239571i	0.0687199	−	0.0146069i	0.242143	+	0.970240i	$0.422150\pi$
$270$	2.24481	−	0.477148i	0.136614	−	0.0290383i
$271$	0.748840	+	7.12474i	0.0454888	+	0.432797i	0.993438	+	0.114375i	$0.0364864\pi$
$271$	0.748840	+	7.12474i	0.0454888	+	0.432797i	−0.947949	+	0.318422i	$0.896847\pi$
$272$	2.22814	+	1.61884i	0.135101	+	0.0981564i
$273$	3.08452	+	13.0499i	0.186684	+	0.789816i
$274$	9.10902			0.550296
$275$	−8.36231	+	10.0569i	−0.504266	+	0.606451i
$276$	2.82597	+	4.89473i	0.170104	+	0.294628i
$277$	6.76523	−	7.51355i	0.406483	−	0.451445i	−0.504793	−	0.863240i	$-0.668431\pi$
$277$	6.76523	−	7.51355i	0.406483	−	0.451445i	0.911277	+	0.411795i	$0.135098\pi$
$278$	−40.2092	+	17.9023i	−2.41159	+	1.07371i
$279$	−2.65670	+	1.93020i	−0.159052	+	0.115558i
$280$	5.93509	−	0.760154i	0.354690	−	0.0454279i
$281$	−6.23152	+	19.1787i	−0.371742	+	1.14410i	0.573909	+	0.818919i	$0.305426\pi$
$281$	−6.23152	+	19.1787i	−0.371742	+	1.14410i	−0.945651	+	0.325184i	$0.894574\pi$
$282$	−2.30832	−	21.9622i	−0.137458	−	1.30783i
$283$	0.205094	−	1.95134i	0.0121916	−	0.115995i	−0.986734	−	0.162348i	$-0.948093\pi$
$283$	0.205094	−	1.95134i	0.0121916	−	0.115995i	0.998925	+	0.0463529i	$0.0147599\pi$
$284$	−14.8451	+	16.4872i	−0.880897	+	0.978335i
$285$	0.691843	−	1.19831i	0.0409812	−	0.0709816i
$286$	17.4721	−	33.2181i	1.03315	−	1.96423i
$287$	−1.54238	+	2.22736i	−0.0910436	+	0.131477i
$288$	2.08986	+	6.43191i	0.123146	+	0.379004i
$289$	−9.33932	+	4.15813i	−0.549372	+	0.244596i
$290$	8.44478	+	3.75986i	0.495894	+	0.220786i
$291$	6.95465	−	1.47826i	0.407689	−	0.0866569i
$292$	22.1067	+	24.5519i	1.29369	+	1.43679i
$293$	22.6634	−	16.4659i	1.32401	−	0.961949i	0.324136	−	0.946011i	$-0.394927\pi$
$293$	22.6634	−	16.4659i	1.32401	−	0.961949i	0.999873	−	0.0159379i	$-0.00507341\pi$
$294$	4.15131	−	15.0683i	0.242109	−	0.878802i
$295$	1.96030	+	6.03318i	0.114133	+	0.351266i
$296$	−8.86920	+	15.3619i	−0.515512	+	0.892892i
$297$	−2.60437	+	2.05359i	−0.151121	+	0.119162i
$298$	5.34198	+	9.25258i	0.309453	+	0.535988i
$299$	9.38544	+	1.99494i	0.542774	+	0.115370i
$300$	9.52483	+	6.92019i	0.549916	+	0.399537i
$301$	−0.551211	−	24.3162i	−0.0317713	−	1.40156i
$302$	3.79211	−	11.6709i	0.218211	−	0.671586i
$303$	4.18856	+	4.65187i	0.240627	+	0.267243i
$304$	1.30112	+	0.579295i	0.0746242	+	0.0332249i
$305$	0.374866	−	3.56661i	0.0214647	−	0.204223i
$306$	5.68553	+	1.20850i	0.325020	+	0.0690851i
$307$	17.2450			0.984223			0.492111	−	0.870532i	$-0.336225\pi$
$307$	17.2450			0.984223			0.492111	+	0.870532i	$0.336225\pi$
$308$	−21.8317	+	14.4802i	−1.24397	+	0.825086i
$309$	10.5508			0.600211
$310$	7.37162	+	1.56689i	0.418680	+	0.0889931i
$311$	−3.13802	+	29.8563i	−0.177941	+	1.69299i	0.433060	+	0.901365i	$0.357434\pi$
$311$	−3.13802	+	29.8563i	−0.177941	+	1.69299i	−0.611001	+	0.791630i	$0.709233\pi$
$312$	−10.1879	−	4.53593i	−0.576774	−	0.256796i
$313$	18.3059	+	20.3308i	1.03471	+	1.14916i	0.988652	+	0.150225i	$0.0479997\pi$
$313$	18.3059	+	20.3308i	1.03471	+	1.14916i	0.0460593	+	0.998939i	$0.485334\pi$
$314$	−14.3458	+	44.1519i	−0.809581	+	2.49163i
$315$	−2.32364	+	1.41272i	−0.130922	+	0.0795975i
$316$	33.7736	+	24.5379i	1.89991	+	1.38037i
$317$	25.0514	+	5.32483i	1.40702	+	0.299072i	0.847963	−	0.530055i	$-0.177829\pi$
$317$	25.0514	+	5.32483i	1.40702	+	0.299072i	0.559061	+	0.829127i	$0.311162\pi$
$318$	−13.6130	−	23.5785i	−0.763381	−	1.32221i
$319$	−13.3488	+	0.525967i	−0.747391	+	0.0294485i
$320$	6.67289	−	11.5578i	0.373026	−	0.646099i
$321$	−1.97971	−	6.09291i	−0.110497	−	0.340073i
$322$	−8.47863	−	7.29314i	−0.472496	−	0.406431i
$323$	2.83522	−	2.05991i	0.157756	−	0.114616i
$324$	1.99766	+	2.21863i	0.110981	+	0.123257i
$325$	19.5504	−	4.15557i	1.08446	−	0.230510i
$326$	14.9253	+	6.64516i	0.826634	+	0.368041i
$327$	−0.0848667	+	0.0377851i	−0.00469314	+	0.00208952i
$328$	−0.696262	−	2.14287i	−0.0384446	−	0.118320i
$329$	11.1822	+	23.6576i	0.616494	+	1.30429i
$330$	7.50171	+	1.28817i	0.412956	+	0.0709114i
$331$	6.59787	−	11.4279i	0.362652	−	0.628132i	−0.625744	−	0.780028i	$-0.715205\pi$
$331$	6.59787	−	11.4279i	0.362652	−	0.628132i	0.988396	+	0.151897i	$0.0485381\pi$
$332$	9.35674	−	10.3917i	0.513518	−	0.570320i
$333$	0.842673	−	8.01750i	0.0461782	−	0.439356i
$334$	1.39454	+	13.2682i	0.0763060	+	0.726003i
$335$	0.353199	−	1.08704i	0.0192973	−	0.0593911i
$336$	−1.69617	−	2.22666i	−0.0925338	−	0.121474i
$337$	17.5919	−	12.7813i	0.958292	−	0.696240i	0.00553877	−	0.999985i	$-0.498237\pi$
$337$	17.5919	−	12.7813i	0.958292	−	0.696240i	0.952754	+	0.303745i	$0.0982369\pi$
$338$	−25.8801	+	11.5226i	−1.40769	+	0.626746i
$339$	7.59549	−	8.43565i	0.412531	−	0.458162i
$340$	−3.99408	−	6.91794i	−0.216609	−	0.375178i
$341$	−10.5559	+	2.68211i	−0.571634	+	0.145244i
$342$	3.00586			0.162538
$343$	1.25829	+	18.4775i	0.0679413	+	0.997689i
$344$	16.3646	+	11.8896i	0.882321	+	0.641044i
$345$	0.203397	+	1.93519i	0.0109505	+	0.104187i
$346$	3.23260	−	0.687110i	0.173786	−	0.0369393i
$347$	−13.4293	+	2.85449i	−0.720923	+	0.153237i	−0.553741	−	0.832689i	$-0.686800\pi$
$347$	−13.4293	+	2.85449i	−0.720923	+	0.153237i	−0.167182	+	0.985926i	$0.553467\pi$
$348$	1.25698	+	11.9594i	0.0673813	+	0.641090i
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.0363964	−	0.999337i	$-0.511588\pi$
$349$	−18.6455	−	13.5467i	−0.998070	−	0.725140i	−0.961673	+	0.274197i	$0.911588\pi$
$350$	−22.3137	−	6.69504i	−1.19272	−	0.357865i
$351$	5.06831			0.270526
$352$	−1.46450	+	22.3822i	−0.0780582	+	1.19297i
$353$	2.13324	+	3.69489i	0.113541	+	0.196659i	0.917196	−	0.398437i	$-0.130447\pi$
$353$	2.13324	+	3.69489i	0.113541	+	0.196659i	−0.803655	+	0.595096i	$0.797114\pi$
$354$	−9.22108	+	10.2410i	−0.490095	+	0.544306i
$355$	−6.97774	+	3.10669i	−0.370340	+	0.164886i
$356$	−44.3316	+	32.2088i	−2.34957	+	1.70706i
$357$	−6.83171	+	0.874991i	−0.361573	+	0.0463094i
$358$	3.72758	−	11.4723i	0.197009	−	0.606331i
$359$	−1.63997	−	15.6033i	−0.0865545	−	0.823511i	−0.948557	−	0.316607i	$-0.897456\pi$
$359$	−1.63997	−	15.6033i	−0.0865545	−	0.823511i	0.862002	−	0.506904i	$-0.169210\pi$
$360$	0.236399	−	2.24919i	0.0124593	−	0.118543i
$361$	−11.5008	+	12.7729i	−0.605306	+	0.672260i
$362$	27.8539	−	48.2444i	1.46397	−	2.53567i
$363$	−10.5463	+	3.12652i	−0.553538	+	0.164100i
$364$	39.8987	+	3.28126i	2.09126	+	0.171985i
$365$	3.51484	+	10.8176i	0.183975	+	0.566218i
$366$	7.11708	−	3.16873i	0.372016	−	0.165632i
$367$	−12.2359	−	5.44776i	−0.638708	−	0.284371i	0.0617209	−	0.998093i	$-0.480341\pi$
$367$	−12.2359	−	5.44776i	−0.638708	−	0.284371i	−0.700429	+	0.713722i	$0.747008\pi$
$368$	−1.95913	+	0.416425i	−0.102127	+	0.0217077i
$369$	0.685191	+	0.760981i	0.0356696	+	0.0396151i
$370$	−14.9677	+	10.8747i	−0.778136	+	0.565349i
$371$	24.4579	+	21.0381i	1.26979	+	1.09225i
$372$	3.02954	+	9.32398i	0.157075	+	0.483426i
$373$	−12.3967	+	21.4717i	−0.641877	+	1.11176i	0.343137	+	0.939286i	$0.388511\pi$
$373$	−12.3967	+	21.4717i	−0.641877	+	1.11176i	−0.985013	+	0.172478i	$0.944823\pi$
$374$	16.0303	+	10.7085i	0.828906	+	0.553724i
$375$	4.59624	+	7.96092i	0.237349	+	0.411100i
$376$	−21.2864	−	4.52457i	−1.09776	−	0.233337i
$377$	16.5160	+	11.9996i	0.850616	+	0.618009i
$378$	−5.18164	−	2.83703i	−0.266515	−	0.145921i
$379$	3.42758	−	10.5490i	0.176063	−	0.541865i	−0.823618	−	0.567145i	$-0.808048\pi$
$379$	3.42758	−	10.5490i	0.176063	−	0.541865i	0.999680	+	0.0252801i	$0.00804775\pi$
$380$	−2.76413	−	3.06988i	−0.141797	−	0.157482i
$381$	10.1274	+	4.50903i	0.518845	+	0.231005i
$382$	5.33365	−	50.7463i	0.272893	−	2.59641i
$383$	2.66420	+	0.566293i	0.136134	+	0.0289362i	0.275475	−	0.961308i	$-0.411165\pi$
$383$	2.66420	+	0.566293i	0.136134	+	0.0289362i	−0.139341	+	0.990245i	$0.544498\pi$
$384$	15.4659			0.789242
$385$	−8.89406	+	1.49713i	−0.453283	+	0.0763007i
$386$	16.3897			0.834214
$387$	−8.99214	−	1.91134i	−0.457096	−	0.0971587i
$388$	2.21879	−	21.1104i	0.112642	−	1.07172i
$389$	−20.0317	−	8.91868i	−1.01565	−	0.452195i	−0.169719	−	0.985492i	$-0.554286\pi$
$389$	−20.0317	−	8.91868i	−1.01565	−	0.452195i	−0.845928	+	0.533297i	$0.820953\pi$
$390$	−7.78302	−	8.64392i	−0.394108	−	0.437702i
$391$	−1.52294	+	4.68713i	−0.0770185	+	0.237039i
$392$	−12.8582	−	8.47935i	−0.649438	−	0.428272i
$393$	4.30912	+	3.13076i	0.217366	+	0.157926i
$394$	57.3921	+	12.1991i	2.89137	+	0.614580i
$395$	7.18622	+	12.4469i	0.361578	+	0.626271i
$396$	3.42816	+	9.28925i	0.172272	+	0.466802i
$397$	−6.46252	+	11.1934i	−0.324344	+	0.561781i	−0.981379	−	0.192079i	$-0.938477\pi$
$397$	−6.46252	+	11.1934i	−0.324344	+	0.561781i	0.657035	+	0.753860i	$0.271810\pi$
$398$	−8.36846	−	25.7555i	−0.419473	−	1.29101i
$399$	−3.36162	+	1.17713i	−0.168292	+	0.0589302i
$400$	−3.37534	+	2.45233i	−0.168767	+	0.122616i
$401$	7.36558	+	8.18030i	0.367819	+	0.408505i	0.898434	−	0.439108i	$-0.144706\pi$
$401$	7.36558	+	8.18030i	0.367819	+	0.408505i	−0.530615	+	0.847613i	$0.678039\pi$
$402$	2.42869	−	0.516234i	0.121132	−	0.0257474i
$403$	15.2047	+	6.76956i	0.757399	+	0.337216i
$404$	17.0724	−	7.60113i	0.849385	−	0.378170i
$405$	0.317617	+	0.977526i	0.0157825	+	0.0485736i
$406$	−10.1684	−	21.5129i	−0.504651	−	1.06767i
$407$	12.4467	−	23.6637i	0.616962	−	1.17297i
$408$	2.86400	−	4.96060i	0.141789	−	0.245586i
$409$	7.43127	−	8.25326i	0.367453	−	0.408098i	−0.530856	−	0.847462i	$-0.678130\pi$
$409$	7.43127	−	8.25326i	0.367453	−	0.408098i	0.898309	+	0.439364i	$0.144796\pi$
$410$	0.245646	−	2.33716i	0.0121316	−	0.115424i
$411$	0.426436	+	4.05727i	0.0210345	+	0.200130i
$412$	9.73367	−	29.9571i	0.479543	−	1.47588i
$413$	6.30195	−	15.0642i	0.310098	−	0.741263i
$414$	−3.41977	+	2.48461i	−0.168073	+	0.122112i
$415$	4.39800	−	1.95812i	0.215889	−	0.0961201i
$416$	22.9355	−	25.4724i	1.12450	−	1.24889i
$417$	−9.85627	−	17.0716i	−0.482664	−	0.835998i
$418$	9.25999	+	3.69317i	0.452921	+	0.180639i
$419$	−35.9681			−1.75716			−0.878578	−	0.477599i	$-0.841507\pi$
$419$	−35.9681			−1.75716			−0.878578	+	0.477599i	$0.841507\pi$
$420$	1.86749	+	7.90090i	0.0911241	+	0.385525i
$421$	16.1469	+	11.7314i	0.786953	+	0.571755i	0.907058	−	0.421006i	$-0.138323\pi$
$421$	16.1469	+	11.7314i	0.786953	+	0.571755i	−0.120105	+	0.992761i	$0.538323\pi$
$422$	4.17140	+	39.6882i	0.203061	+	1.93199i
$423$	9.67416	−	2.05631i	0.470374	−	0.0999810i
$424$	−26.2438	+	5.57829i	−1.27451	+	0.270906i
$425$	1.07309	+	10.2098i	0.0520526	+	0.495248i
$426$	−13.4237	−	9.75290i	−0.650381	−	0.472530i
$427$	−6.71853	+	6.33091i	−0.325132	+	0.306374i
$428$	−19.1262			−0.924501
$429$	15.6137	+	6.22721i	0.753836	+	0.300652i
$430$	10.5488	+	18.2710i	0.508708	+	0.881108i
$431$	9.68790	−	10.7595i	0.466650	−	0.518267i	−0.463176	−	0.886266i	$-0.653290\pi$
$431$	9.68790	−	10.7595i	0.466650	−	0.518267i	0.929826	+	0.367999i	$0.119957\pi$
$432$	−0.966498	+	0.430313i	−0.0465007	+	0.0207034i
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.986718	−	0.162443i	$-0.948063\pi$
$433$	−23.6623	+	17.1917i	−1.13714	+	0.826179i	−0.150420	+	0.988622i	$0.548063\pi$
$434$	−11.7554	−	15.4319i	−0.564275	−	0.740755i
$435$	−1.27935	+	3.93742i	−0.0613399	+	0.188785i
$436$	0.0289903	+	0.275824i	0.00138838	+	0.0132096i
$437$	−0.266402	+	2.53465i	−0.0127437	+	0.121249i
$438$	−16.5335	+	18.3623i	−0.790002	+	0.877386i
$439$	−9.92126	+	17.1841i	−0.473516	+	0.820154i	−0.999540	−	0.0303159i	$-0.990349\pi$
$439$	−9.92126	+	17.1841i	−0.473516	+	0.820154i	0.526025	+	0.850469i	$0.323682\pi$
$440$	3.49174	−	6.63851i	0.166462	−	0.316479i
$441$	6.90595	+	1.14362i	0.328855	+	0.0544582i
$442$	−9.10356	−	28.0179i	−0.433012	−	1.33268i
$443$	−7.79296	+	3.46965i	−0.370255	+	0.164848i	−0.583425	−	0.812167i	$-0.698288\pi$
$443$	−7.79296	+	3.46965i	−0.370255	+	0.164848i	0.213170	+	0.977015i	$0.431621\pi$
$444$	−21.9870	−	9.78923i	−1.04346	−	0.464576i
$445$	−18.4532	+	3.92234i	−0.874764	+	0.185937i
$446$	3.15273	+	3.50146i	0.149286	+	0.165799i
$447$	−3.87113	+	2.81254i	−0.183098	+	0.133029i
$448$	−32.4231	+	11.3535i	−1.53185	+	0.536404i
$449$	−3.28407	−	10.1073i	−0.154985	−	0.476994i	0.843175	−	0.537640i	$-0.180684\pi$
$449$	−3.28407	−	10.1073i	−0.154985	−	0.476994i	−0.998159	+	0.0606458i	$0.980684\pi$
$450$	−4.40262	+	7.62556i	−0.207542	+	0.359472i
$451$	1.17585	+	3.18618i	0.0553685	+	0.150031i
$452$	−16.9444	−	29.3485i	−0.796997	−	1.38044i
$453$	5.37589	+	1.14268i	0.252581	+	0.0536879i
$454$	−20.3983	−	14.8202i	−0.957340	−	0.695548i
$455$	12.0893	+	6.61907i	0.566753	+	0.310307i
$456$	0.915351	−	2.81716i	0.0428653	−	0.131926i
$457$	3.36927	+	3.74196i	0.157608	+	0.175041i	0.816777	−	0.576953i	$-0.195759\pi$
$457$	3.36927	+	3.74196i	0.157608	+	0.175041i	−0.659169	+	0.751995i	$0.729092\pi$
$458$	−56.8591	−	25.3153i	−2.65685	−	1.18291i
$459$	−0.272112	+	2.58898i	−0.0127011	+	0.120843i
$460$	5.68230	+	1.20781i	0.264939	+	0.0563144i
$461$	15.3843			0.716519			0.358260	−	0.933622i	$-0.383370\pi$
$461$	15.3843			0.716519			0.358260	+	0.933622i	$0.383370\pi$
$462$	−12.4771	−	15.1064i	−0.580487	−	0.702812i
$463$	31.6955			1.47302			0.736508	−	0.676429i	$-0.236473\pi$
$463$	31.6955			1.47302			0.736508	+	0.676429i	$0.236473\pi$
$464$	−4.16830	−	0.885999i	−0.193508	−	0.0411315i
$465$	−0.352810	+	3.35676i	−0.0163612	+	0.155666i
$466$	14.0172	+	6.24087i	0.649335	+	0.289103i
$467$	12.0800	+	13.4162i	0.558995	+	0.620827i	0.954707	−	0.297548i	$-0.0961688\pi$
$467$	12.0800	+	13.4162i	0.558995	+	0.620827i	−0.395712	+	0.918375i	$0.629502\pi$
$468$	4.67580	−	14.3906i	0.216139	−	0.665207i
$469$	−2.51398	+	1.52844i	−0.116085	+	0.0705768i
$470$	−18.3629	−	13.3414i	−0.847016	−	0.615393i
$471$	−20.3374	−	4.32284i	−0.937097	−	0.199186i
$472$	6.79013	+	11.7609i	0.312541	+	0.541337i
$473$	−25.3532	−	16.9364i	−1.16574	−	0.778737i
$474$	−15.6110	+	27.0391i	−0.717037	+	1.24195i
$475$	1.64054	+	5.04906i	0.0752731	+	0.231667i
$476$	−3.81825	+	20.2048i	−0.175009	+	0.926084i
$477$	9.86484	−	7.16723i	0.451680	−	0.328165i
$478$	−16.6760	−	18.5205i	−0.762741	−	0.847110i
$479$	−6.31935	+	1.34322i	−0.288738	+	0.0613733i	−0.350004	−	0.936748i	$-0.613820\pi$
$479$	−6.31935	+	1.34322i	−0.288738	+	0.0613733i	0.0612654	+	0.998122i	$0.480486\pi$
$480$	6.35018	+	2.82728i	0.289845	+	0.129047i
$481$	−37.3265	+	16.6188i	−1.70194	+	0.757754i
$482$	−11.3884	−	35.0500i	−0.518728	−	1.59648i
$483$	2.85153	−	4.11791i	0.129749	−	0.187371i
$484$	−0.852333	+	32.8290i	−0.0387424	+	1.49223i
$485$	3.65395	−	6.32883i	0.165917	−	0.287377i
$486$	−1.49404	+	1.65930i	−0.0677712	+	0.0752675i
$487$	−0.457903	+	4.35666i	−0.0207496	+	0.197419i	−0.999986	−	0.00530285i	$-0.998312\pi$
$487$	−0.457903	+	4.35666i	−0.0207496	+	0.197419i	0.979236	+	0.202722i	$0.0649787\pi$
$488$	−0.802497	−	7.63525i	−0.0363273	−	0.345632i
$489$	−2.26111	+	6.95899i	−0.102251	+	0.314696i
$490$	−8.65452	−	13.5342i	−0.390971	−	0.611411i
$491$	−33.0596	+	24.0192i	−1.49196	+	1.08397i	−0.518510	+	0.855071i	$0.673513\pi$
$491$	−33.0596	+	24.0192i	−1.49196	+	1.08397i	−0.973450	+	0.228901i	$0.926487\pi$
$492$	2.79281	−	1.24344i	0.125910	−	0.0560586i
$493$	−7.01630	+	7.79239i	−0.315998	+	0.350952i
$494$	−7.61730	−	13.1936i	−0.342719	−	0.593606i
$495$	−0.222576	+	3.40166i	−0.0100040	+	0.152893i
$496$	−3.47420			−0.155996
$497$	18.8319	+	5.65034i	0.844725	+	0.253452i
$498$	8.46084	+	6.14716i	0.379139	+	0.275461i
$499$	−3.46970	−	33.0120i	−0.155325	−	1.47782i	−0.743310	−	0.668947i	$-0.766745\pi$
$499$	−3.46970	−	33.0120i	−0.155325	−	1.47782i	0.587985	−	0.808872i	$-0.299921\pi$
$500$	26.8440	−	5.70587i	1.20050	−	0.255174i
$501$	−5.84452	+	1.24229i	−0.261114	+	0.0555015i
$502$	−5.32822	−	50.6946i	−0.237810	−	2.26261i
$503$	17.0117	+	12.3597i	0.758516	+	0.551094i	0.898455	−	0.439066i	$-0.144691\pi$
$503$	17.0117	+	12.3597i	0.758516	+	0.551094i	−0.139939	+	0.990160i	$0.544691\pi$
$504$	−4.23687	+	3.99242i	−0.188725	+	0.177837i
$505$	6.43392			0.286306
$506$	−13.5879	+	3.45249i	−0.604054	+	0.153482i
$507$	−6.34387	−	10.9879i	−0.281741	−	0.487990i
$508$	22.1458	−	24.5954i	0.982561	−	1.09124i
$509$	28.3988	−	12.6440i	1.25876	−	0.560434i	0.334567	−	0.942372i	$-0.391410\pi$
$509$	28.3988	−	12.6440i	1.25876	−	0.560434i	0.924188	+	0.381938i	$0.124743\pi$
$510$	4.83332	−	3.51161i	0.214023	−	0.155497i
$511$	11.2995	−	27.0104i	0.499859	−	1.19487i
$512$	−3.64970	+	11.2326i	−0.161296	+	0.496417i
$513$	0.140718	+	1.33884i	0.00621286	+	0.0591114i
$514$	1.74256	−	16.5794i	0.0768611	−	0.731284i
$515$	7.25631	−	8.05895i	0.319751	−	0.355120i
$516$	−13.7227	+	23.7684i	−0.604108	+	1.04635i
$517$	32.3292	+	5.55146i	1.42184	+	0.244153i
$518$	47.4638	+	3.90341i	2.08544	+	0.171506i
$519$	0.457380	+	1.40767i	0.0200768	+	0.0617899i
$520$	−10.4714	+	4.66217i	−0.459201	+	0.204450i
$521$	26.7411	+	11.9059i	1.17155	+	0.521607i	0.897890	−	0.440220i	$-0.145099\pi$
$521$	26.7411	+	11.9059i	1.17155	+	0.521607i	0.273659	+	0.961827i	$0.411766\pi$
$522$	−8.79712	+	1.86989i	−0.385039	+	0.0818427i
$523$	−6.27297	−	6.96684i	−0.274298	−	0.304639i	0.590218	−	0.807244i	$-0.299042\pi$
$523$	−6.27297	−	6.96684i	−0.274298	−	0.304639i	−0.864516	+	0.502605i	$0.832375\pi$
$524$	12.8647	−	9.34674i	0.561996	−	0.408314i
$525$	1.93744	−	10.2522i	0.0845568	−	0.447444i
$526$	−15.4202	−	47.4585i	−0.672353	−	2.06929i
$527$	−4.27433	+	7.40335i	−0.186193	+	0.322495i
$528$	−3.50615	+	0.138148i	−0.152586	+	0.00601213i
$529$	9.70797	+	16.8147i	0.422086	+	0.731074i
$530$	−27.3723	−	5.81816i	−1.18898	−	0.252725i
$531$	−4.99317	−	3.62775i	−0.216685	−	0.157431i
$532$	0.240983	+	10.6307i	0.0104479	+	0.460901i
$533$	1.60378	−	4.93594i	0.0694676	−	0.213799i
$534$	−27.4226	−	30.4559i	−1.18669	−	1.31795i
$535$	−6.01549	−	2.67827i	−0.260072	−	0.115792i
$536$	0.255764	−	2.43343i	0.0110473	−	0.105108i
$537$	5.28442	+	1.12324i	0.228039	+	0.0484713i
$538$	2.57281			0.110922
$539$	19.8697	+	12.0081i	0.855848	+	0.517227i
$540$	3.06855			0.132049
$541$	−38.3716	−	8.15613i	−1.64972	−	0.350659i	−0.713117	−	0.701045i	$-0.752717\pi$
$541$	−38.3716	−	8.15613i	−1.64972	−	0.350659i	−0.936605	+	0.350386i	$0.886050\pi$
$542$	−1.67202	+	15.9082i	−0.0718194	+	0.683316i
$543$	22.7926	+	10.1479i	0.978123	+	0.435489i
$544$	11.7804	+	13.0834i	0.505079	+	0.560947i
$545$	−0.0295061	+	0.0908103i	−0.00126390	+	0.00388989i
$546$	0.678539	+	29.9332i	0.0290388	+	1.28102i
$547$	4.06399	+	2.95266i	0.173764	+	0.126247i	0.671268	−	0.741215i	$-0.265750\pi$
$547$	4.06399	+	2.95266i	0.173764	+	0.126247i	−0.497504	+	0.867462i	$0.665750\pi$
$548$	11.9134	+	2.53226i	0.508914	+	0.108173i
$549$	1.74457	+	3.02169i	0.0744566	+	0.128963i
$550$	−22.9321	+	18.0824i	−0.977829	+	0.771035i
$551$	−2.71125	+	4.69602i	−0.115503	+	0.200057i
$552$	1.28724	+	3.96172i	0.0547886	+	0.168622i
$553$	6.86986	−	36.3528i	0.292136	−	1.54588i
$554$	18.2634	−	13.2691i	0.775938	−	0.563752i
$555$	−5.54443	−	6.15772i	−0.235348	−	0.261381i
$556$	−57.5649	+	12.2358i	−2.44129	+	0.518913i
$557$	−8.73306	−	3.88821i	−0.370032	−	0.164749i	0.213292	−	0.976989i	$-0.431581\pi$
$557$	−8.73306	−	3.88821i	−0.370032	−	0.164749i	−0.583324	+	0.812240i	$0.698248\pi$
$558$	−6.69833	+	2.98229i	−0.283563	+	0.126250i
$559$	14.3981	+	44.3126i	0.608973	+	1.87423i
$560$	−2.86733	−	0.235809i	−0.121167	−	0.00996474i
$561$	−4.01925	+	7.64140i	−0.169693	+	0.322620i
$562$	−22.5130	+	38.9937i	−0.949656	+	1.64485i
$563$	16.9546	−	18.8300i	0.714550	−	0.793588i	−0.271071	−	0.962559i	$-0.587378\pi$
$563$	16.9546	−	18.8300i	0.714550	−	0.793588i	0.985621	+	0.168971i	$0.0540446\pi$
$564$	3.08641	−	29.3653i	0.129961	−	1.23650i
$565$	−1.21956	−	11.6033i	−0.0513071	−	0.488154i
$566$	1.35380	−	4.16656i	0.0569044	−	0.175134i
$567$	1.02107	−	2.44078i	0.0428810	−	0.102503i
$568$	−13.2285	+	9.61106i	−0.555055	+	0.403271i
$569$	−31.1862	+	13.8850i	−1.30739	+	0.582089i	−0.937823	−	0.347114i	$-0.887162\pi$
$569$	−31.1862	+	13.8850i	−1.30739	+	0.582089i	−0.369570	+	0.929203i	$0.620495\pi$
$570$	2.06729	−	2.29596i	0.0865891	−	0.0961670i
$571$	22.6152	+	39.1707i	0.946416	+	1.63924i	0.752891	+	0.658145i	$0.228659\pi$
$571$	22.6152	+	39.1707i	0.946416	+	1.63924i	0.193525	+	0.981095i	$0.438008\pi$
$572$	32.0857	−	38.5876i	1.34157	−	1.61343i
$573$	22.8527			0.954686
$574$	−4.40259	+	4.14858i	−0.183760	+	0.173158i
$575$	−6.03995	−	4.38828i	−0.251884	−	0.183004i
$576$	1.35724	+	12.9133i	0.0565516	+	0.538053i
$577$	0.896469	−	0.190550i	0.0373205	−	0.00793272i	−0.189214	−	0.981936i	$-0.560594\pi$
$577$	0.896469	−	0.190550i	0.0373205	−	0.00793272i	0.226534	+	0.974003i	$0.427261\pi$
$578$	−22.3276	+	4.74588i	−0.928705	+	0.197402i
$579$	0.767279	+	7.30017i	0.0318870	+	0.303385i
$580$	9.99940	+	7.26499i	0.415202	+	0.301662i
$581$	−11.8695	−	3.56135i	−0.492432	−	0.147750i
$582$	15.8753			0.658054
$583$	39.1962	−	9.95921i	1.62334	−	0.412468i
$584$	12.1748	+	21.0874i	0.503796	+	0.872601i
$585$	3.48575	−	3.87131i	0.144118	−	0.160059i
$586$	57.1412	−	25.4409i	2.36048	−	1.05095i
$587$	0.0318255	−	0.0231226i	0.00131358	−	0.000954370i	−0.587128	−	0.809494i	$-0.699742\pi$
$587$	0.0318255	−	0.0231226i	0.00131358	−	0.000954370i	0.588442	+	0.808540i	$0.299742\pi$
$588$	9.61826	−	18.5533i	0.396650	−	0.765124i
$589$	−1.36610	+	4.20442i	−0.0562891	+	0.173240i
$590$	1.48056	+	14.0866i	0.0609539	+	0.579937i
$591$	−2.74682	+	26.1342i	−0.112989	+	1.07502i
$592$	5.70698	−	6.33824i	0.234555	−	0.260500i
$593$	−4.44625	+	7.70113i	−0.182586	+	0.316248i	−0.942760	−	0.333471i	$-0.891780\pi$
$593$	−4.44625	+	7.70113i	−0.182586	+	0.316248i	0.760175	+	0.649719i	$0.225113\pi$
$594$	−6.64134	+	3.27607i	−0.272497	+	0.134419i
$595$	−4.03019	+	5.82003i	−0.165222	+	0.238598i
$596$	4.41441	+	13.5862i	0.180821	+	0.556511i
$597$	11.0800	−	4.93315i	0.453476	−	0.201900i
$598$	19.5719	+	8.71397i	0.800354	+	0.356341i
$599$	24.4142	−	5.18941i	0.997539	−	0.212033i	0.319918	−	0.947445i	$-0.396345\pi$
$599$	24.4142	−	5.18941i	0.997539	−	0.212033i	0.677621	+	0.735412i	$0.263011\pi$
$600$	5.80617	+	6.44840i	0.237036	+	0.263255i
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	−0.943741	−	0.330685i	$-0.892720\pi$
$601$	−22.5755	+	16.4021i	−0.920874	+	0.669054i	0.0228677	+	0.999738i	$0.492720\pi$
$602$	10.0844	−	53.3630i	0.411010	−	2.17491i
$603$	0.343635	+	1.05760i	0.0139939	+	0.0430688i
$604$	8.20402	−	14.2098i	0.333817	−	0.578188i
$605$	−4.86515	+	10.2058i	−0.197796	+	0.414927i
$606$	6.98838	+	12.1042i	0.283884	+	0.491701i
$607$	−8.19793	−	1.74252i	−0.332744	−	0.0707268i	0.0385103	−	0.999258i	$-0.487739\pi$
$607$	−8.19793	−	1.74252i	−0.332744	−	0.0707268i	−0.371254	+	0.928531i	$0.621072\pi$
$608$	7.36559	+	5.35141i	0.298714	+	0.217028i
$609$	9.10606	−	5.53626i	0.368996	−	0.224341i
$610$	2.47443	−	7.61552i	0.100187	−	0.308343i
$611$	−33.5415	−	37.2516i	−1.35694	−	1.50704i
$612$	7.09994	+	3.16110i	0.286998	+	0.127780i
$613$	2.10155	−	19.9949i	0.0848807	−	0.807586i	−0.866419	−	0.499318i	$-0.833584\pi$
$613$	2.10155	−	19.9949i	0.0848807	−	0.807586i	0.951300	−	0.308268i	$-0.0997493\pi$
$614$	37.6634	+	8.00560i	1.51997	+	0.323080i
$615$	1.05250			0.0424409
$616$	−17.9576	+	7.09360i	−0.723533	+	0.285809i
$617$	−22.3648			−0.900374			−0.450187	−	0.892934i	$-0.648643\pi$
$617$	−22.3648			−0.900374			−0.450187	+	0.892934i	$0.648643\pi$
$618$	23.0431	+	4.89795i	0.926928	+	0.197025i
$619$	−1.80571	+	17.1802i	−0.0725775	+	0.690529i	0.896377	+	0.443292i	$0.146189\pi$
$619$	−1.80571	+	17.1802i	−0.0725775	+	0.690529i	−0.968955	+	0.247237i	$0.920477\pi$
$620$	9.20549	+	4.09855i	0.369701	+	0.164602i
$621$	−1.26677	−	1.40689i	−0.0508338	−	0.0564566i
$622$	−20.7136	+	63.7500i	−0.830541	+	2.55614i
$623$	42.5951	+	23.3215i	1.70654	+	0.934357i
$624$	4.33802	+	3.15175i	0.173660	+	0.126171i
$625$	−10.0451	−	2.13515i	−0.401804	−	0.0854060i
$626$	30.5424	+	52.9010i	1.22072	+	2.11435i
$627$	−1.21148	+	4.29740i	−0.0483817	+	0.171622i
$628$	−31.0364	+	53.7566i	−1.23849	+	2.14512i
$629$	−6.48516	−	19.9593i	−0.258580	−	0.795828i
$630$	−5.73070	+	2.00670i	−0.228316	+	0.0799489i
$631$	−31.1456	+	22.6286i	−1.23989	+	0.900830i	−0.997591	−	0.0693729i	$-0.977900\pi$
$631$	−31.1456	+	22.6286i	−1.23989	+	0.900830i	−0.242295	+	0.970203i	$0.577900\pi$
$632$	20.5878	+	22.8650i	0.818937	+	0.909522i
$633$	−17.4823	+	3.71599i	−0.694860	+	0.147697i
$634$	52.2407	+	23.2591i	2.07475	+	0.923736i
$635$	10.4093	−	4.63452i	0.413081	−	0.183915i
$636$	−11.2493	−	34.6218i	−0.446064	−	1.37284i
$637$	−12.4810	−	33.2103i	−0.494517	−	1.31584i
$638$	−29.3983	−	5.04818i	−1.16389	−	0.199859i
$639$	3.71563	−	6.43566i	0.146988	−	0.254591i
$640$	10.6367	−	11.8133i	0.420454	−	0.466961i
$641$	1.94310	−	18.4873i	0.0767478	−	0.730206i	−0.886706	−	0.462333i	$-0.847012\pi$
$641$	1.94310	−	18.4873i	0.0767478	−	0.730206i	0.963454	−	0.267873i	$-0.0863209\pi$
$642$	−1.49522	−	14.2261i	−0.0590117	−	0.561459i
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	−0.992539	−	0.121931i	$-0.961091\pi$
$643$	−2.98936	+	9.20029i	−0.117889	+	0.362824i	0.874650	+	0.484755i	$0.161091\pi$
$644$	−9.06144	−	11.8955i	−0.357071	−	0.468746i
$645$	−7.64430	+	5.55391i	−0.300994	+	0.218685i
$646$	7.14845	−	3.18270i	0.281252	−	0.125222i
$647$	−14.2954	+	15.8767i	−0.562010	+	0.624176i	−0.955442	−	0.295178i	$-0.904621\pi$
$647$	−14.2954	+	15.8767i	−0.562010	+	0.624176i	0.393432	+	0.919354i	$0.371288\pi$
$648$	1.10017	+	1.90555i	0.0432188	+	0.0748571i
$649$	−10.9249	−	17.3107i	−0.428841	−	0.679505i
$650$	44.6277			1.75044
$651$	6.32323	−	5.95842i	0.247827	−	0.233529i
$652$	17.6729	+	12.8401i	0.692124	+	0.502858i
$653$	−3.34516	−	31.8270i	−0.130906	−	1.24549i	−0.840865	−	0.541245i	$-0.817953\pi$
$653$	−3.34516	−	31.8270i	−0.130906	−	1.24549i	0.709959	−	0.704243i	$-0.248713\pi$
$654$	−0.202892	+	0.0431259i	−0.00793369	+	0.00168636i
$655$	5.35497	−	1.13823i	0.209236	−	0.0444745i
$656$	0.113242	+	1.07742i	0.00442134	+	0.0420662i
$657$	−8.95281	−	6.50460i	−0.349282	−	0.253769i
$658$	13.4396	+	56.8598i	0.523930	+	2.21663i
$659$	−33.3651			−1.29972			−0.649860	−	0.760054i	$-0.725173\pi$
$659$	−33.3651			−1.29972			−0.649860	+	0.760054i	$0.725173\pi$
$660$	9.45311	+	3.77019i	0.367962	+	0.146754i
$661$	−13.3562	−	23.1336i	−0.519495	−	0.899792i	−0.999743	−	0.0226592i	$-0.992787\pi$
$661$	−13.3562	−	23.1336i	−0.519495	−	0.899792i	0.480248	−	0.877133i	$-0.340547\pi$
$662$	19.7150	−	21.8958i	0.766246	−	0.851003i
$663$	12.0533	−	5.36649i	0.468112	−	0.208417i
$664$	8.33778	−	6.05775i	0.323569	−	0.235086i
$665$	−1.41284	+	3.37727i	−0.0547877	+	0.130965i
$666$	5.56236	−	17.1192i	0.215537	−	0.663355i
$667$	−0.797087	−	7.58377i	−0.0308633	−	0.293645i
$668$	−1.86462	+	17.7407i	−0.0721443	+	0.686407i
$669$	−1.41200	+	1.56818i	−0.0545910	+	0.0606295i
$670$	1.27603	−	2.21014i	0.0492972	−	0.0853853i
$671$	1.66180	+	11.4522i	0.0641531	+	0.442109i
$672$	−7.64631	−	16.1769i	−0.294963	−	0.624039i
$673$	0.507396	+	1.56161i	0.0195587	+	0.0601954i	0.960359	−	0.278764i	$-0.0899249\pi$
$673$	0.507396	+	1.56161i	0.0195587	+	0.0601954i	−0.940801	+	0.338960i	$0.889925\pi$
$674$	44.3545	−	19.7479i	1.70847	−	0.760661i
$675$	−3.60262	−	1.60399i	−0.138665	−	0.0617377i
$676$	−37.0509	+	7.87542i	−1.42504	+	0.302901i
$677$	0.330469	+	0.367023i	0.0127010	+	0.0141058i	0.749462	−	0.662048i	$-0.230312\pi$
$677$	0.330469	+	0.367023i	0.0127010	+	0.0141058i	−0.736761	+	0.676153i	$0.763646\pi$
$678$	20.5048	−	14.8976i	0.787481	−	0.572139i
$679$	−17.7543	+	6.21698i	−0.681348	+	0.238586i
$680$	−1.81931	−	5.59927i	−0.0697675	−	0.214722i
$681$	5.64617	−	9.77946i	0.216362	−	0.374750i
$682$	−24.2994	+	0.957440i	−0.930473	+	0.0366623i
$683$	12.6490	+	21.9087i	0.484000	+	0.838312i	0.999831	−	0.0183779i	$-0.00585018\pi$
$683$	12.6490	+	21.9087i	0.484000	+	0.838312i	−0.515831	+	0.856690i	$0.672517\pi$
$684$	3.93125	+	0.835613i	0.150315	+	0.0319505i
$685$	3.39234	+	2.46468i	0.129614	+	0.0941704i
$686$	−5.82962	+	40.9393i	−0.222576	+	1.56307i
$687$	8.61390	−	26.5108i	0.328641	−	1.01145i
$688$	−6.50789	−	7.22774i	−0.248111	−	0.275555i
$689$	−56.4580	−	25.1367i	−2.15088	−	0.957633i
$690$	−0.454147	+	4.32092i	−0.0172891	+	0.164494i
$691$	1.50675	+	0.320269i	0.0573194	+	0.0121836i	0.236482	−	0.971636i	$-0.424006\pi$
$691$	1.50675	+	0.320269i	0.0573194	+	0.0121836i	−0.179163	+	0.983819i	$0.557339\pi$
$692$	4.41881			0.167978
$693$	6.14445	−	6.26465i	0.233408	−	0.237974i
$694$	−30.6550			−1.16365
$695$	−19.8184	−	4.21253i	−0.751755	−	0.159790i
$696$	−0.926420	+	8.81430i	−0.0351159	+	0.334105i
$697$	2.43525	+	1.08425i	0.0922418	+	0.0410687i
$698$	−34.4334	−	38.2421i	−1.30332	−	1.44749i
$699$	−2.12355	+	6.53560i	−0.0803199	+	0.247199i
$700$	−27.3221	−	14.9593i	−1.03268	−	0.565409i
$701$	6.24771	+	4.53922i	0.235973	+	0.171444i	0.699487	−	0.714645i	$-0.253412\pi$
$701$	6.24771	+	4.53922i	0.235973	+	0.171444i	−0.463515	+	0.886089i	$0.653412\pi$
$702$	11.0693	+	2.35285i	0.417783	+	0.0888026i
$703$	−5.42638	−	9.39877i	−0.204660	−	0.354481i
$704$	−11.6848	+	41.4488i	−0.440387	+	1.56216i
$705$	5.08277	−	8.80362i	0.191428	−	0.331563i
$706$	2.94378	+	9.06002i	0.110791	+	0.340979i
$707$	−12.5557	−	10.8001i	−0.472205	−	0.406181i
$708$	−14.9069	+	10.8305i	−0.560235	+	0.407034i
$709$	13.4603	+	14.9492i	0.505512	+	0.561428i	0.940843	−	0.338843i	$-0.110035\pi$
$709$	13.4603	+	14.9492i	0.505512	+	0.561428i	−0.435331	+	0.900270i	$0.643369\pi$
$710$	−16.6817	+	3.54581i	−0.626055	+	0.133072i
$711$	−12.7743	−	5.68751i	−0.479075	−	0.213298i
$712$	−36.8948	+	16.4266i	−1.38269	+	0.615613i
$713$	−1.92112	−	5.91259i	−0.0719464	−	0.221428i
$714$	−15.3268	−	1.26047i	−0.573591	−	0.0471720i
$715$	15.4949	−	7.64337i	0.579475	−	0.285846i
$716$	8.06442	−	13.9680i	0.301382	−	0.522008i
$717$	7.46859	−	8.29471i	0.278920	−	0.309772i
$718$	3.66176	−	34.8393i	0.136656	−	1.30019i
$719$	2.18055	+	20.7466i	0.0813209	+	0.773716i	0.956856	+	0.290562i	$0.0938423\pi$
$719$	2.18055	+	20.7466i	0.0813209	+	0.773716i	−0.875535	+	0.483154i	$0.839491\pi$
$720$	−0.336028	+	1.03419i	−0.0125230	+	0.0385419i
$721$	−27.6885	+	3.54628i	−1.03117	+	0.132070i
$722$	−31.0476	+	22.5574i	−1.15547	+	0.839499i
$723$	15.0785	−	6.71339i	0.560776	−	0.249674i
$724$	49.8408	−	55.3538i	1.85232	−	2.05721i
$725$	−7.94223	−	13.7563i	−0.294967	−	0.510898i
$726$	−24.4848	+	1.93249i	−0.908716	+	0.0717214i
$727$	−41.6247			−1.54378			−0.771888	−	0.635758i	$-0.780687\pi$
$727$	−41.6247			−1.54378			−0.771888	+	0.635758i	$0.780687\pi$
$728$	28.2607	+	8.47939i	1.04741	+	0.314267i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	2.65467	+	25.2575i	0.0982537	+	0.934822i
$731$	−23.4087	+	4.97566i	−0.865801	+	0.184032i
$732$	10.1891	−	2.16575i	0.376599	−	0.0800485i
$733$	−5.22719	−	49.7334i	−0.193071	−	1.83694i	−0.477958	−	0.878383i	$-0.658623\pi$
$733$	−5.22719	−	49.7334i	−0.193071	−	1.83694i	0.284888	−	0.958561i	$-0.408044\pi$
$734$	−24.1944	−	17.5783i	−0.893032	−	0.648826i
$735$	5.62312	−	4.48842i	0.207412	−	0.165558i
$736$	−12.8033			−0.471935
$737$	−0.240808	+	3.68031i	−0.00887028	+	0.135566i
$738$	1.14320	+	1.98008i	0.0420818	+	0.0728879i
$739$	2.59014	−	2.87664i	0.0952797	−	0.105819i	−0.693619	−	0.720342i	$-0.743985\pi$
$739$	2.59014	−	2.87664i	0.0952797	−	0.105819i	0.788899	+	0.614523i	$0.210652\pi$
$740$	−22.5989	+	10.0617i	−0.830752	+	0.369875i
$741$	5.51996	−	4.01049i	0.202781	−	0.147329i
$742$	43.6500	+	57.3017i	1.60244	+	2.10361i
$743$	−2.87081	+	8.83546i	−0.105320	+	0.324141i	−0.989805	−	0.142426i	$-0.954510\pi$
$743$	−2.87081	+	8.83546i	−0.105320	+	0.324141i	0.884485	+	0.466568i	$0.154510\pi$
$744$	0.755281	+	7.18602i	0.0276899	+	0.263452i
$745$	−0.514086	+	4.89121i	−0.0188347	+	0.179200i
$746$	−37.0424	+	41.1398i	−1.35622	+	1.50623i
$747$	−2.34193	+	4.05634i	−0.0856866	+	0.148414i
$748$	17.9885	+	18.4616i	0.657726	+	0.675024i
$749$	7.24330	+	15.3243i	0.264665	+	0.559938i
$750$	6.34260	+	19.5205i	0.231599	+	0.712788i
$751$	−19.7733	+	8.80364i	−0.721538	+	0.321249i	−0.734446	−	0.678667i	$-0.762558\pi$
$751$	−19.7733	+	8.80364i	−0.721538	+	0.321249i	0.0129078	+	0.999917i	$0.495891\pi$
$752$	9.55894	+	4.25591i	0.348579	+	0.155197i
$753$	22.3306	−	4.74651i	0.813771	−	0.172972i
$754$	30.5007	+	33.8745i	1.11077	+	1.23364i
$755$	4.57010	−	3.32037i	0.166323	−	0.120841i
$756$	−5.98820	−	5.15093i	−0.217789	−	0.187337i
$757$	3.03614	+	9.34428i	0.110350	+	0.339624i	0.990949	−	0.134239i	$-0.0428591\pi$
$757$	3.03614	+	9.34428i	0.110350	+	0.339624i	−0.880599	+	0.473863i	$0.842859\pi$
$758$	12.3830	−	21.4480i	0.449772	−	0.779028i
$759$	−2.17389	−	5.89057i	−0.0789073	−	0.213814i
$760$	−1.52229	−	2.63668i	−0.0552193	−	0.0956426i
$761$	32.5181	+	6.91194i	1.17878	+	0.250557i	0.755319	−	0.655357i	$-0.227482\pi$
$761$	32.5181	+	6.91194i	1.17878	+	0.250557i	0.423461	+	0.905914i	$0.360815\pi$
$762$	20.0253	+	14.5493i	0.725442	+	0.527064i
$763$	0.210017	−	0.127685i	0.00760311	−	0.00462251i
$764$	21.0829	−	64.8866i	0.762753	−	2.34751i
$765$	1.79039	+	1.98842i	0.0647315	+	0.0718916i
$766$	5.55578	+	2.47359i	0.200738	+	0.0893745i
$767$	−3.26976	+	31.1097i	−0.118064	+	1.12331i
$768$	8.37657	+	1.78049i	0.302263	+	0.0642480i
$769$	2.47573			0.0892770			0.0446385	−	0.999003i	$-0.485786\pi$
$769$	2.47573			0.0892770			0.0446385	+	0.999003i	$0.485786\pi$
$770$	−20.1198	−	0.859111i	−0.725068	−	0.0309602i
$771$	7.46622			0.268889
$772$	21.4355	+	4.55626i	0.771481	+	0.163983i
$773$	3.08232	−	29.3263i	0.110863	−	1.05479i	−0.787733	−	0.616017i	$-0.788745\pi$
$773$	3.08232	−	29.3263i	0.110863	−	1.05479i	0.898596	−	0.438777i	$-0.144588\pi$
$774$	−18.7517	−	8.34880i	−0.674017	−	0.300092i
$775$	−8.66530	−	9.62380i	−0.311267	−	0.345697i
$776$	4.83440	−	14.8788i	0.173545	−	0.534116i
$777$	0.483375	+	21.3237i	0.0173410	+	0.764982i
$778$	−39.6093	−	28.7779i	−1.42006	−	1.03174i
$779$	1.34841	+	0.286612i	0.0483116	+	0.0102690i
$780$	−7.77616	−	13.4687i	−0.278431	−	0.482257i
$781$	19.3538	−	15.2608i	0.692533	−	0.546074i
$782$	−5.50204	+	9.52981i	−0.196752	+	0.340785i
$783$	−1.24470	−	3.83080i	−0.0444821	−	0.136902i
$784$	5.19971	+	5.27334i	0.185704	+	0.188334i
$785$	−17.2890	+	12.5612i	−0.617071	+	0.448328i
$786$	7.95782	+	8.83806i	0.283846	+	0.315243i
$787$	24.0002	−	5.10140i	0.855515	−	0.181845i	0.240780	−	0.970580i	$-0.422597\pi$
$787$	24.0002	−	5.10140i	0.855515	−	0.181845i	0.614734	+	0.788734i	$0.289263\pi$
$788$	71.6697	+	31.9094i	2.55313	+	1.13673i
$789$	20.4167	−	9.09010i	0.726854	−	0.323616i
$790$	9.91665	+	30.5203i	0.352819	+	1.08586i
$791$	−17.0976	+	24.6908i	−0.607921	+	0.877903i
$792$	1.04797	+	7.22206i	0.0372380	+	0.256625i
$793$	8.84203	−	15.3148i	0.313990	−	0.543846i
$794$	−19.3106	+	21.4466i	−0.685306	+	0.761110i
$795$	1.31005	−	12.4643i	0.0464628	−	0.442064i
$796$	−3.78491	−	36.0111i	−0.134153	−	1.27638i
$797$	−5.49479	+	16.9112i	−0.194635	+	0.599026i	0.805345	+	0.592806i	$0.201980\pi$
$797$	−5.49479	+	16.9112i	−0.194635	+	0.599026i	−0.999981	+	0.00622010i	$0.998020\pi$
$798$	−7.88831	+	1.01032i	−0.279243	+	0.0357649i
$799$	20.8296	−	15.1336i	0.736897	−	0.535387i
$800$	−24.3642	+	10.8477i	−0.861406	+	0.383523i
$801$	12.2816	−	13.6401i	0.433950	−	0.481950i
$802$	12.2891	+	21.2853i	0.433942	+	0.751609i
$803$	−19.5886	−	31.0383i	−0.691265	−	1.09532i
$804$	3.31991			0.117084
$805$	−1.18423	−	5.01018i	−0.0417385	−	0.176586i
$806$	30.0647	+	21.8433i	1.05898	+	0.769397i
$807$	0.120445	+	1.14596i	0.00423987	+	0.0403396i
$808$	13.4725	−	2.86367i	0.473961	−	0.100744i
$809$	12.1736	−	2.58759i	0.428003	−	0.0909748i	0.0111266	−	0.999938i	$-0.496458\pi$
$809$	12.1736	−	2.58759i	0.428003	−	0.0909748i	0.416876	+	0.908963i	$0.363125\pi$
$810$	0.239888	+	2.28238i	0.00842881	+	0.0801948i
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	0.907426	−	0.420212i	$-0.138044\pi$
$811$	22.4462	+	16.3081i	0.788191	+	0.572654i	−0.119235	+	0.992866i	$0.538044\pi$
$812$	−7.31846	−	30.9627i	−0.256828	−	1.08658i
$813$	−7.16398			−0.251252
$814$	38.1693	−	45.9040i	1.33783	−	1.60893i
$815$	3.76038	+	6.51317i	0.131720	+	0.228146i
$816$	−1.84287	+	2.04672i	−0.0645135	+	0.0716495i
$817$	−11.3059	+	5.03370i	−0.395543	+	0.176107i
$818$	20.0614	−	14.5755i	0.701432	−	0.509620i
$819$	−13.3008	+	1.70354i	−0.464769	+	0.0595266i
$820$	0.970991	−	2.98840i	0.0339085	−	0.104360i
$821$	3.42925	+	32.6271i	0.119682	+	1.13870i	0.875265	+	0.483643i	$0.160687\pi$
$821$	3.42925	+	32.6271i	0.119682	+	1.13870i	−0.755584	+	0.655052i	$0.772647\pi$
$822$	−0.952152	+	9.05912i	−0.0332101	+	0.315973i
$823$	−0.439254	+	0.487840i	−0.0153114	+	0.0170050i	−0.750752	−	0.660584i	$-0.770309\pi$
$823$	−0.439254	+	0.487840i	−0.0153114	+	0.0170050i	0.735440	+	0.677589i	$0.236975\pi$
$824$	11.6076	−	20.1050i	0.404371	−	0.700390i
$825$	−9.12767	−	9.36772i	−0.317785	−	0.326142i
$826$	20.7568	−	29.9751i	0.722222	−	1.04297i
$827$	6.33848	+	19.5078i	0.220411	+	0.678354i	0.998725	+	0.0504794i	$0.0160749\pi$
$827$	6.33848	+	19.5078i	0.220411	+	0.678354i	−0.778315	+	0.627875i	$0.783925\pi$
$828$	−5.16331	+	2.29885i	−0.179437	+	0.0798907i
$829$	−7.69066	−	3.42410i	−0.267108	−	0.118924i	0.268813	−	0.963192i	$-0.413369\pi$
$829$	−7.69066	−	3.42410i	−0.267108	−	0.118924i	−0.535921	+	0.844268i	$0.680035\pi$
$830$	10.5143	−	2.23489i	0.364958	−	0.0775742i
$831$	6.76523	+	7.51355i	0.234683	+	0.260642i
$832$	53.2405	−	38.6815i	1.84578	−	1.34104i
$833$	17.6345	−	4.59250i	0.610998	−	0.159121i
$834$	−13.6012	−	41.8602i	−0.470971	−	1.44950i
$835$	−3.07069	+	5.31860i	−0.106266	+	0.184058i
$836$	11.0841	+	7.40439i	0.383353	+	0.256086i
$837$	−1.64193	−	2.84390i	−0.0567533	−	0.0982997i
$838$	−78.5550	−	16.6974i	−2.71364	−	0.576802i
$839$	−31.8742	−	23.1580i	−1.10042	−	0.799503i	−0.119293	−	0.992859i	$-0.538063\pi$
$839$	−31.8742	−	23.1580i	−1.10042	−	0.799503i	−0.981129	+	0.193356i	$0.938063\pi$
$840$	0.135604	+	5.98204i	0.00467877	+	0.206400i
$841$	−3.94789	+	12.1504i	−0.136134	+	0.418978i
$842$	29.8192	+	33.1176i	1.02764	+	1.14131i
$843$	−18.4222	−	8.20210i	−0.634495	−	0.282495i
$844$	−5.57751	+	53.0665i	−0.191986	+	1.82662i
$845$	−12.7559	−	2.71135i	−0.438816	−	0.0932731i
$846$	22.0832			0.759235
$847$	26.6260	−	11.7498i	0.914880	−	0.403727i
$848$	12.9004			0.443002
$849$	1.91921	+	0.407942i	0.0658673	+	0.0140005i
$850$	−2.39602	+	22.7966i	−0.0821826	+	0.781916i
$851$	13.9425	+	6.20762i	0.477944	+	0.212794i
$852$	−14.8451	−	16.4872i	−0.508586	−	0.564842i
$853$	8.34555	−	25.6850i	0.285746	−	0.879436i	−0.700428	−	0.713723i	$-0.747007\pi$
$853$	8.34555	−	25.6850i	0.285746	−	0.879436i	0.986174	−	0.165713i	$-0.0529925\pi$
$854$	−17.6124	+	10.7079i	−0.602684	+	0.366417i
$855$	1.11943	+	0.813310i	0.0382835	+	0.0278146i
$856$	−13.7884	−	2.93081i	−0.471277	−	0.100173i
$857$	7.07983	+	12.2626i	0.241842	+	0.418883i	0.961239	−	0.275716i	$-0.0889150\pi$
$857$	7.07983	+	12.2626i	0.241842	+	0.418883i	−0.719397	+	0.694599i	$0.755582\pi$
$858$	31.2098	+	20.8487i	1.06548	+	0.711762i
$859$	−8.62094	+	14.9319i	−0.294143	+	0.509470i	−0.974785	−	0.223146i	$-0.928367\pi$
$859$	−8.62094	+	14.9319i	−0.294143	+	0.509470i	0.680642	+	0.732616i	$0.261701\pi$
$860$	8.71713	+	26.8286i	0.297252	+	0.914846i
$861$	−2.05393	−	1.76675i	−0.0699979	−	0.0602107i
$862$	26.1534	−	19.0016i	0.890790	−	0.647197i
$863$	14.3180	+	15.9018i	0.487392	+	0.541303i	0.935803	−	0.352524i	$-0.114677\pi$
$863$	14.3180	+	15.9018i	0.487392	+	0.541303i	−0.448411	+	0.893828i	$0.648010\pi$
$864$	−6.61513	+	1.40609i	−0.225051	+	0.0478361i
$865$	1.38978	+	0.618771i	0.0472540	+	0.0210388i
$866$	−59.6598	+	26.5623i	−2.02732	+	0.902623i
$867$	−3.15913	−	9.72280i	−0.107290	−	0.330204i
$868$	−11.0844	−	23.4508i	−0.376230	−	0.795971i
$869$	−32.3653	−	33.2165i	−1.09792	−	1.12679i
$870$	−4.62198	+	8.00550i	−0.156700	+	0.271412i
$871$	3.77128	−	4.18844i	0.127785	−	0.141920i
$872$	−0.0213664	+	0.203288i	−0.000723558	+	0.00688419i
$873$	0.743199	+	7.07107i	0.0251535	+	0.239319i
$874$	−1.75848	+	5.41205i	−0.0594815	+	0.183065i
$875$	−14.7378	−	19.3471i	−0.498227	−	0.654050i
$876$	−26.7282	+	19.4192i	−0.903063	+	0.656114i
$877$	14.8886	−	6.62884i	0.502753	−	0.223840i	−0.139659	−	0.990200i	$-0.544601\pi$
$877$	14.8886	−	6.62884i	0.502753	−	0.223840i	0.642412	+	0.766360i	$0.277934\pi$
$878$	−29.6456	+	32.9248i	−1.00049	+	1.11116i
$879$	14.0067	+	24.2604i	0.472436	+	0.818282i
$880$	−2.30584	+	2.77310i	−0.0777300	+	0.0934813i
$881$	36.6728			1.23554			0.617769	−	0.786359i	$-0.288036\pi$
$881$	36.6728			1.23554			0.617769	+	0.786359i	$0.288036\pi$
$882$	14.5518	+	5.70363i	0.489986	+	0.192051i
$883$	6.10529	+	4.43575i	0.205459	+	0.149275i	0.685757	−	0.727831i	$-0.259471\pi$
$883$	6.10529	+	4.43575i	0.205459	+	0.149275i	−0.480298	+	0.877106i	$0.659471\pi$
$884$	−4.11739	−	39.1743i	−0.138483	−	1.31758i
$885$	−6.20504	+	1.31892i	−0.208580	+	0.0443351i
$886$	−18.6307	+	3.96008i	−0.625911	+	0.133041i
$887$	−1.28747	−	12.2494i	−0.0432289	−	0.411296i	−0.994642	−	0.103378i	$-0.967035\pi$
$887$	−1.28747	−	12.2494i	−0.0432289	−	0.411296i	0.951413	−	0.307917i	$-0.0996320\pi$
$888$	−14.3507	−	10.4264i	−0.481577	−	0.349886i
$889$	−28.0932	−	8.42911i	−0.942215	−	0.282703i
$890$	−42.1230			−1.41197
$891$	−1.77011	−	2.80476i	−0.0593010	−	0.0939631i
$892$	3.14995	+	5.45588i	0.105468	+	0.182676i
$893$	8.90913	−	9.89459i	0.298133	−	0.331110i
$894$	−9.76028	+	4.34556i	−0.326433	+	0.145337i
$895$	4.49234	−	3.26387i	0.150162	−	0.109099i
$896$	−40.5874	+	5.19835i	−1.35593	+	0.173665i
$897$	−2.96505	+	9.12550i	−0.0990003	+	0.304691i
$898$	−2.48037	−	23.5992i	−0.0827711	−	0.787514i
$899$	1.38262	−	13.1547i	0.0461129	−	0.438735i
$900$	−7.87790	+	8.74929i	−0.262597	+	0.291643i
$901$	15.8714	−	27.4901i	0.528754	−	0.915829i
$902$	1.08896	+	7.50455i	0.0362585	+	0.249874i
$903$	24.2406	+	1.99354i	0.806677	+	0.0663410i
$904$	−7.71822	−	23.7542i	−0.256704	−	0.790054i
$905$	23.4269	−	10.4303i	0.778737	−	0.346716i
$906$	11.2106	+	4.99128i	0.372447	+	0.165824i
$907$	−1.48512	+	0.315671i	−0.0493125	+	0.0104817i	−0.232502	−	0.972596i	$-0.574691\pi$
$907$	−1.48512	+	0.315671i	−0.0493125	+	0.0104817i	0.183189	+	0.983078i	$0.441358\pi$
$908$	−22.5583	−	25.0535i	−0.748622	−	0.831429i
$909$	−5.06421	+	3.67936i	−0.167969	+	0.122037i
$910$	23.3305	+	20.0684i	0.773397	+	0.665260i
$911$	−4.72572	−	14.5443i	−0.156570	−	0.481873i	0.841747	−	0.539873i	$-0.181528\pi$
$911$	−4.72572	−	14.5443i	−0.156570	−	0.481873i	−0.998317	+	0.0579998i	$0.981528\pi$
$912$	−0.712125	+	1.23344i	−0.0235808	+	0.0408432i
$913$	−12.1985	+	9.61872i	−0.403711	+	0.318333i
$914$	5.62144	+	9.73662i	0.185941	+	0.322059i
$915$	3.50788	+	0.745624i	0.115967	+	0.0246496i
$916$	−67.3264	−	48.9155i	−2.22453	−	1.61621i
$917$	−12.3608	−	6.76773i	−0.408189	−	0.223490i
$918$	−1.79617	+	5.52806i	−0.0592826	+	0.182453i
$919$	−12.5558	−	13.9447i	−0.414179	−	0.459992i	0.499569	−	0.866274i	$-0.333492\pi$
$919$	−12.5558	−	13.9447i	−0.414179	−	0.459992i	−0.913748	+	0.406282i	$0.866825\pi$
$920$	3.91137	+	1.74145i	0.128954	+	0.0574141i
$921$	−1.80259	+	17.1505i	−0.0593974	+	0.565128i
$922$	33.5997	+	7.14183i	1.10655	+	0.235204i
$923$	−37.6639			−1.23972
$924$	−12.1188	−	23.2256i	−0.398681	−	0.764068i
$925$	31.7917			1.04530
$926$	69.2237	+	14.7139i	2.27483	+	0.483530i
$927$	−1.10285	+	10.4930i	−0.0362225	+	0.344634i
$928$	−24.8856	−	11.0798i	−0.816909	−	0.363711i
$929$	23.2698	+	25.8437i	0.763457	+	0.847905i	0.992080	−	0.125610i	$-0.0400888\pi$
$929$	23.2698	+	25.8437i	0.763457	+	0.847905i	−0.228623	+	0.973515i	$0.573422\pi$
$930$	−2.32885	+	7.16745i	−0.0763659	+	0.235030i
$931$	8.42630	−	4.21906i	0.276161	−	0.138274i
$932$	16.5977	+	12.0589i	0.543675	+	0.395003i
$933$	−29.3647	−	6.24166i	−0.961358	−	0.204343i
$934$	20.1548	+	34.9091i	0.659484	+	1.14226i
$935$	3.07246	+	8.32541i	0.100480	+	0.272270i
$936$	5.57600	−	9.65791i	0.182257	−	0.315679i
$937$	−2.05971	−	6.33914i	−0.0672878	−	0.207091i	0.911759	−	0.410725i	$-0.134725\pi$
$937$	−2.05971	−	6.33914i	−0.0672878	−	0.207091i	−0.979047	+	0.203635i	$0.934725\pi$
$938$	−6.20014	+	2.17108i	−0.202442	+	0.0708884i
$939$	−22.1329	+	16.0805i	−0.722279	+	0.524767i
$940$	−20.3073	−	22.5535i	−0.662351	−	0.735615i
$941$	46.3509	−	9.85219i	1.51100	−	0.321172i	0.623440	−	0.781871i	$-0.285735\pi$
$941$	46.3509	−	9.85219i	1.51100	−	0.321172i	0.887556	+	0.460699i	$0.152401\pi$
$942$	−42.4105	−	18.8824i	−1.38181	−	0.615220i
$943$	−1.77100	+	0.788499i	−0.0576716	+	0.0256771i
$944$	−2.01777	−	6.21006i	−0.0656728	−	0.202120i
$945$	−1.16209	−	2.45858i	−0.0378028	−	0.0799775i
$946$	−47.5097	−	48.7592i	−1.54467	−	1.58530i
$947$	9.06351	−	15.6985i	0.294524	−	0.510131i	−0.680350	−	0.732888i	$-0.738172\pi$
$947$	9.06351	−	15.6985i	0.294524	−	0.510131i	0.974874	+	0.222756i	$0.0715054\pi$
$948$	−27.9338	+	31.0236i	−0.907248	+	1.00760i
$949$	−5.86272	+	55.7801i	−0.190312	+	1.81070i
$950$	1.23906	+	11.7888i	0.0402003	+	0.382481i
$951$	−7.91424	+	24.3575i	−0.256637	+	0.789847i
$952$	−5.84871	+	13.9808i	−0.189558	+	0.453121i
$953$	35.0699	−	25.4797i	1.13602	−	0.825370i	0.149464	−	0.988767i	$-0.452245\pi$
$953$	35.0699	−	25.4797i	1.13602	−	0.825370i	0.986560	+	0.163398i	$0.0522453\pi$
$954$	24.8722	−	11.0738i	0.805269	−	0.358529i
$955$	15.7170	−	17.4555i	0.508591	−	0.564848i
$956$	−16.6613	−	28.8582i	−0.538865	−	0.933341i
$957$	0.872247	−	13.3307i	0.0281957	−	0.430920i
$958$	−14.4252			−0.466056
$959$	−2.48282	−	10.5042i	−0.0801743	−	0.339199i
$960$	10.7970	+	7.84445i	0.348470	+	0.253178i
$961$	2.11318	+	20.1055i	0.0681670	+	0.648566i
$962$	−89.2368	+	18.9679i	−2.87711	+	0.611549i
$963$	6.26647	−	1.33198i	0.201934	−	0.0429224i
$964$	−5.15079	−	49.0065i	−0.165896	−	1.57839i
$965$	6.10377	+	4.43465i	0.196487	+	0.142756i
$966$	8.13944	−	7.66984i	0.261882	−	0.246773i
$967$	−48.3991			−1.55641			−0.778205	−	0.628011i	$-0.783869\pi$
$967$	−48.3991			−1.55641			−0.778205	+	0.628011i	$0.783869\pi$
$968$	−5.64500	+	23.5362i	−0.181437	+	0.756484i
$969$	1.75226	+	3.03501i	0.0562908	+	0.0974986i
$970$	10.9183	−	12.1260i	0.350566	−	0.389343i
$971$	−50.5867	+	22.5226i	−1.62340	+	0.722786i	−0.998329	−	0.0577799i	$-0.981598\pi$
$971$	−50.5867	+	22.5226i	−1.62340	+	0.722786i	−0.625074	+	0.780566i	$0.714931\pi$
$972$	−2.41528	+	1.75481i	−0.0774703	+	0.0562855i
$973$	31.6040	+	41.4883i	1.01318	+	1.33005i
$974$	−3.02255	+	9.30246i	−0.0968488	+	0.298070i
$975$	2.08923	+	19.8777i	0.0669089	+	0.636596i
$976$	−0.385855	+	3.67117i	−0.0123509	+	0.117511i
$977$	−9.32677	+	10.3584i	−0.298390	+	0.331395i	−0.873632	−	0.486588i	$-0.838241\pi$
$977$	−9.32677	+	10.3584i	−0.298390	+	0.331395i	0.575242	+	0.817983i	$0.304908\pi$
$978$	−8.16887	+	14.1489i	−0.261212	+	0.452432i
$979$	54.5944	−	26.9305i	1.74484	−	0.860704i
$980$	−7.55650	−	20.1068i	−0.241384	−	0.642287i
$981$	−0.0287071	−	0.0883514i	−0.000916547	−	0.00282084i
$982$	−83.3533	+	37.1113i	−2.65991	+	1.18427i
$983$	−8.47090	−	3.77149i	−0.270180	−	0.120292i	0.267175	−	0.963648i	$-0.413910\pi$
$983$	−8.47090	−	3.77149i	−0.270180	−	0.120292i	−0.537355	+	0.843356i	$0.680576\pi$
$984$	2.20391	−	0.468456i	0.0702582	−	0.0149338i
$985$	18.0729	+	20.0720i	0.575850	+	0.639547i
$986$	−18.9412	+	13.7616i	−0.603211	+	0.438258i
$987$	−24.6969	+	8.64803i	−0.786110	+	0.275270i
$988$	−6.29465	−	19.3729i	−0.200260	−	0.616336i
$989$	8.70193	−	15.0722i	0.276705	−	0.479268i
$990$	−2.06525	+	7.32596i	−0.0656381	+	0.232834i
$991$	−10.8473	−	18.7881i	−0.344576	−	0.596823i	0.640701	−	0.767791i	$-0.278644\pi$
$991$	−10.8473	−	18.7881i	−0.344576	−	0.596823i	−0.985277	+	0.170968i	$0.945311\pi$
$992$	−21.7231	−	4.61740i	−0.689710	−	0.146602i
$993$	10.6756	+	7.75627i	0.338779	+	0.246138i
$994$	38.5062	+	21.0827i	1.22134	+	0.668704i
$995$	3.85226	−	11.8560i	0.122125	−	0.375861i
$996$	9.35674	+	10.3917i	0.296480	+	0.329274i
$997$	−8.93098	−	3.97633i	−0.282847	−	0.125932i	0.260410	−	0.965498i	$-0.416142\pi$
$997$	−8.93098	−	3.97633i	−0.282847	−	0.125932i	−0.543257	+	0.839567i	$0.682809\pi$
$998$	7.74719	−	73.7096i	0.245233	−	2.33324i
$999$	7.88549	+	1.67611i	0.249486	+	0.0530299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.b.16.7	✓	64
3.2	odd	2		693.2.by.c.478.2		64
7.4	even	3	inner	231.2.y.b.214.2	yes	64
11.9	even	5	inner	231.2.y.b.163.2	yes	64
21.11	odd	6		693.2.by.c.676.7		64
33.20	odd	10		693.2.by.c.163.7		64
77.53	even	15	inner	231.2.y.b.130.7	yes	64
231.53	odd	30		693.2.by.c.361.2		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.b.16.7	✓	64	1.1	even	1	trivial
231.2.y.b.130.7	yes	64	77.53	even	15	inner
231.2.y.b.163.2	yes	64	11.9	even	5	inner
231.2.y.b.214.2	yes	64	7.4	even	3	inner
693.2.by.c.163.7		64	33.20	odd	10
693.2.by.c.361.2		64	231.53	odd	30
693.2.by.c.478.2		64	3.2	odd	2
693.2.by.c.676.7		64	21.11	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18402 + 0.464228i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.72735 + 1.21429i) q^{4} +(0.687753 + 0.763827i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(-0.0599597 - 2.64507i) q^{7} +(1.78011 + 1.29333i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(2.18402 + 0.464228i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(2.72735 + 1.21429i) q^{4} +(0.687753 + 0.763827i) q^{5} +(-0.689977 + 2.12353i) q^{6} +(-0.0599597 - 2.64507i) q^{7} +(1.78011 + 1.29333i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.14748 + 1.98749i) q^{10} +(-2.75788 - 1.84231i) q^{11} +(-1.49273 + 2.58548i) q^{12} +(1.56619 + 4.82025i) q^{13} +(1.09696 - 5.80473i) q^{14} +(-0.831533 + 0.604144i) q^{15} +(-0.707916 - 0.786220i) q^{16} +(-2.54635 + 0.541243i) q^{17} +(-2.03978 - 0.908167i) q^{18} +(-1.22983 + 0.547557i) q^{19} +(0.948233 + 2.91836i) q^{20} +(2.63685 + 0.216854i) q^{21} +(-5.16801 - 5.30393i) q^{22} +(0.946580 - 1.63952i) q^{23} +(-1.47231 + 1.63517i) q^{24} +(0.412215 - 3.92196i) q^{25} +(1.18291 + 11.2546i) q^{26} +(0.309017 - 0.951057i) q^{27} +(3.04836 - 7.28685i) q^{28} +(3.25868 - 2.36757i) q^{29} +(-2.09655 + 0.933442i) q^{30} +(2.19733 - 2.44038i) q^{31} +(-3.38146 - 5.85686i) q^{32} +(2.12050 - 2.55020i) q^{33} -5.81254 q^{34} +(1.97914 - 1.86496i) q^{35} +(-2.41528 - 1.75481i) q^{36} +(0.842673 + 8.01750i) q^{37} +(-2.94017 + 0.624953i) q^{38} +(-4.95755 + 1.05376i) q^{39} +(0.236399 + 2.24919i) q^{40} +(-0.828434 - 0.601893i) q^{41} +(5.65827 + 1.69771i) q^{42} +9.19303 q^{43} +(-5.28459 - 8.37350i) q^{44} +(-0.513916 - 0.890128i) q^{45} +(2.82846 - 3.14133i) q^{46} +(-9.03522 + 4.02274i) q^{47} +(0.855911 - 0.621855i) q^{48} +(-6.99281 + 0.317195i) q^{49} +(2.72097 - 8.37428i) q^{50} +(-0.272112 - 2.58898i) q^{51} +(-1.58164 + 15.0483i) q^{52} +(-8.15912 + 9.06162i) q^{53} +(1.11641 - 1.93367i) q^{54} +(-0.489532 - 3.37360i) q^{55} +(3.31421 - 4.78607i) q^{56} +(-0.416005 - 1.28033i) q^{57} +(8.21611 - 3.65805i) q^{58} +(5.63831 + 2.51034i) q^{59} +(-3.00149 + 0.637986i) q^{60} +(-2.33469 - 2.59294i) q^{61} +(5.93191 - 4.30978i) q^{62} +(-0.491292 + 2.59974i) q^{63} +(-4.01240 - 12.3489i) q^{64} +(-2.60468 + 4.51144i) q^{65} +(5.81508 - 4.58529i) q^{66} +(-0.556014 - 0.963044i) q^{67} +(-7.60202 - 1.61586i) q^{68} +(1.53160 + 1.11277i) q^{69} +(5.18825 - 3.15433i) q^{70} +(-2.29639 + 7.06755i) q^{71} +(-1.47231 - 1.63517i) q^{72} +(10.1096 + 4.50106i) q^{73} +(-1.88153 + 17.9016i) q^{74} +(3.85739 + 0.819913i) q^{75} -4.01908 q^{76} +(-4.70768 + 7.40525i) q^{77} -11.3166 q^{78} +(13.6777 + 2.90728i) q^{79} +(0.113665 - 1.08145i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-1.52990 - 1.69913i) q^{82} +(1.44739 - 4.45461i) q^{83} +(6.92829 + 3.79335i) q^{84} +(-2.16468 - 1.57273i) q^{85} +(20.0778 + 4.26766i) q^{86} +(2.01397 + 3.48830i) q^{87} +(-2.52662 - 6.84636i) q^{88} +(-9.17730 + 15.8955i) q^{89} +(-0.709180 - 2.18263i) q^{90} +(12.6560 - 4.43171i) q^{91} +(4.57252 - 3.32213i) q^{92} +(2.19733 + 2.44038i) q^{93} +(-21.6006 + 4.59135i) q^{94} +(-1.26406 - 0.562796i) q^{95} +(6.17823 - 2.75073i) q^{96} +(-2.19712 - 6.76203i) q^{97} +(-15.4197 - 2.55350i) q^{98} +(2.31457 + 2.37545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q + 4 q^{2} + 8 q^{3} + 10 q^{4} - 4 q^{5} - 8 q^{6} - q^{7} + 8 q^{8} + 8 q^{9} - 14 q^{10} + 11 q^{11} - 30 q^{12} - 8 q^{13} + 6 q^{14} - 12 q^{15} - 4 q^{17} - q^{18} - 2 q^{19} + 24 q^{20} - 2 q^{21} - 14 q^{22} + 16 q^{24} - 10 q^{25} + 4 q^{26} - 16 q^{27} + 29 q^{28} - 58 q^{29} + 11 q^{30} - 19 q^{31} - 64 q^{32} + 6 q^{33} - 88 q^{34} + 17 q^{35} - 20 q^{36} - 20 q^{37} + 29 q^{38} + 4 q^{39} + 51 q^{40} - 68 q^{41} - 11 q^{42} + 92 q^{43} - 21 q^{44} - 4 q^{45} - 5 q^{46} - 26 q^{47} - 10 q^{48} + 37 q^{49} - 10 q^{50} + 6 q^{51} - 14 q^{52} - 3 q^{53} - 6 q^{54} - 32 q^{55} + 24 q^{56} - 36 q^{57} + 52 q^{58} + 7 q^{59} - 12 q^{60} - 21 q^{61} + 92 q^{62} - 7 q^{63} - 72 q^{64} - 66 q^{65} - 23 q^{66} - 4 q^{67} - 17 q^{68} + 40 q^{69} - q^{70} + 58 q^{71} + 16 q^{72} - 3 q^{73} - 28 q^{74} + 20 q^{75} + 168 q^{76} - 34 q^{77} + 132 q^{78} + 9 q^{79} - 5 q^{80} + 8 q^{81} - 42 q^{82} + 60 q^{83} - 39 q^{84} + 110 q^{85} + 13 q^{86} - 46 q^{87} + 92 q^{88} - 10 q^{89} + 8 q^{90} + 10 q^{91} + 110 q^{92} - 19 q^{93} - 46 q^{94} + 43 q^{95} - 4 q^{96} + 64 q^{97} - 88 q^{98} + 28 q^{99}+O(q^{100}) \) 64 * q + 4 * q^2 + 8 * q^3 + 10 * q^4 - 4 * q^5 - 8 * q^6 - q^7 + 8 * q^8 + 8 * q^9 - 14 * q^10 + 11 * q^11 - 30 * q^12 - 8 * q^13 + 6 * q^14 - 12 * q^15 - 4 * q^17 - q^18 - 2 * q^19 + 24 * q^20 - 2 * q^21 - 14 * q^22 + 16 * q^24 - 10 * q^25 + 4 * q^26 - 16 * q^27 + 29 * q^28 - 58 * q^29 + 11 * q^30 - 19 * q^31 - 64 * q^32 + 6 * q^33 - 88 * q^34 + 17 * q^35 - 20 * q^36 - 20 * q^37 + 29 * q^38 + 4 * q^39 + 51 * q^40 - 68 * q^41 - 11 * q^42 + 92 * q^43 - 21 * q^44 - 4 * q^45 - 5 * q^46 - 26 * q^47 - 10 * q^48 + 37 * q^49 - 10 * q^50 + 6 * q^51 - 14 * q^52 - 3 * q^53 - 6 * q^54 - 32 * q^55 + 24 * q^56 - 36 * q^57 + 52 * q^58 + 7 * q^59 - 12 * q^60 - 21 * q^61 + 92 * q^62 - 7 * q^63 - 72 * q^64 - 66 * q^65 - 23 * q^66 - 4 * q^67 - 17 * q^68 + 40 * q^69 - q^70 + 58 * q^71 + 16 * q^72 - 3 * q^73 - 28 * q^74 + 20 * q^75 + 168 * q^76 - 34 * q^77 + 132 * q^78 + 9 * q^79 - 5 * q^80 + 8 * q^81 - 42 * q^82 + 60 * q^83 - 39 * q^84 + 110 * q^85 + 13 * q^86 - 46 * q^87 + 92 * q^88 - 10 * q^89 + 8 * q^90 + 10 * q^91 + 110 * q^92 - 19 * q^93 - 46 * q^94 + 43 * q^95 - 4 * q^96 + 64 * q^97 - 88 * q^98 + 28 * q^99

Introduction

L-functions

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