LMFDB - Embedded newform 946.2.q.c.49.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(49,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("946.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.q (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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.19
Character	$\chi$	$=$	946.49
Dual form			946.2.q.c.251.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(2.10987 - 0.939377i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.33563 - 2.59398i) q^{5} +(1.54539 + 1.71633i) q^{6} +(3.92251 + 1.74641i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.56175 - 1.73450i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(2.10987 - 0.939377i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.33563 - 2.59398i) q^{5} +(1.54539 + 1.71633i) q^{6} +(3.92251 + 1.74641i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.56175 - 1.73450i) q^{9} +(1.74527 - 3.02290i) q^{10} +(0.181517 - 3.31165i) q^{11} +(-1.15477 + 2.00012i) q^{12} +(-3.26413 + 3.62518i) q^{13} +(-0.448816 + 4.27020i) q^{14} +(-7.36461 - 3.27894i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.16943 - 0.673682i) q^{17} +(2.13221 + 0.949322i) q^{18} +(7.32525 - 3.26141i) q^{19} +(3.41427 + 0.725725i) q^{20} +9.91654 q^{21} +(3.20566 - 0.850724i) q^{22} +(3.71914 - 6.44174i) q^{23} +(-2.25908 - 0.480181i) q^{24} +(-0.750923 + 7.14456i) q^{25} +(-4.45643 - 1.98413i) q^{26} +(-0.475318 + 1.46288i) q^{27} +(-4.19989 + 0.892714i) q^{28} +(3.37762 + 1.50382i) q^{29} +(0.842664 - 8.01741i) q^{30} +(-4.86370 - 1.03381i) q^{31} +1.00000 q^{32} +(-2.72791 - 7.15769i) q^{33} +(1.62012 + 2.80612i) q^{34} +(-4.63137 - 14.2539i) q^{35} +(-0.243969 + 2.32121i) q^{36} +(-0.916927 - 8.72398i) q^{37} +(5.36541 + 5.95890i) q^{38} +(-3.48149 + 10.7149i) q^{39} +(0.364861 + 3.47142i) q^{40} +(0.499213 + 0.362700i) q^{41} +(3.06438 + 9.43119i) q^{42} +(-6.53020 - 0.597047i) q^{43} +(1.79969 + 2.78588i) q^{44} -8.14693 q^{45} +(7.27574 + 1.54651i) q^{46} +(-1.01605 - 0.738201i) q^{47} +(-0.241413 - 2.29689i) q^{48} +(7.65219 + 8.49862i) q^{49} +(-7.02692 + 1.49362i) q^{50} +(6.05425 - 4.39867i) q^{51} +(0.509907 - 4.85144i) q^{52} +(-2.10732 - 0.447925i) q^{53} -1.53816 q^{54} +(-9.01433 + 7.26395i) q^{55} +(-2.14686 - 3.71847i) q^{56} +(12.3917 - 13.7623i) q^{57} +(-0.386470 + 3.67702i) q^{58} +(2.28316 - 1.65881i) q^{59} +(7.88541 - 1.67610i) q^{60} +(0.370379 - 0.0787264i) q^{61} +(-0.519753 - 4.94512i) q^{62} +(9.15512 - 4.07612i) q^{63} +(0.309017 + 0.951057i) q^{64} +17.0275 q^{65} +(5.96439 - 4.80624i) q^{66} +(-5.62642 + 9.74524i) q^{67} +(-2.16814 + 2.40796i) q^{68} +(1.79570 - 17.0849i) q^{69} +(12.1251 - 8.80939i) q^{70} +(-7.48264 + 1.59048i) q^{71} +(-2.28299 + 0.485265i) q^{72} +(10.4166 + 4.63779i) q^{73} +(8.01365 - 3.56791i) q^{74} +(5.12708 + 15.7795i) q^{75} +(-4.00924 + 6.94421i) q^{76} +(6.49552 - 12.6730i) q^{77} -11.2663 q^{78} +(0.384353 - 0.426867i) q^{79} +(-3.18877 + 1.41973i) q^{80} +(1.10324 + 10.4966i) q^{81} +(-0.190683 + 0.586861i) q^{82} +(6.80268 + 7.55514i) q^{83} +(-8.02265 + 5.82879i) q^{84} +(-9.15013 - 6.64796i) q^{85} +(-1.45012 - 6.39509i) q^{86} +8.53901 q^{87} +(-2.09339 + 2.57249i) q^{88} +(-1.75426 + 3.03846i) q^{89} +(-2.51754 - 7.74819i) q^{90} +(-19.1346 + 8.51929i) q^{91} +(0.777512 + 7.39754i) q^{92} +(-11.2329 + 2.38763i) q^{93} +(0.388095 - 1.19443i) q^{94} +(-25.5691 - 11.3841i) q^{95} +(2.10987 - 0.939377i) q^{96} +(5.71814 + 17.5986i) q^{97} +(-5.71801 + 9.90388i) q^{98} +(-5.46057 - 5.48681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 44 q^{2} + 7 q^{3} - 44 q^{4} + 9 q^{5} - 8 q^{6} + 8 q^{7} - 44 q^{8} + 33 q^{9}+O(q^{10}) $ 176 * q - 44 * q^2 + 7 * q^3 - 44 * q^4 + 9 * q^5 - 8 * q^6 + 8 * q^7 - 44 * q^8 + 33 * q^9	\( 176 q - 44 q^{2} + 7 q^{3} - 44 q^{4} + 9 q^{5} - 8 q^{6} + 8 q^{7} - 44 q^{8} + 33 q^{9} - 6 q^{10} + 16 q^{11} + 2 q^{12} + 16 q^{13} + 8 q^{14} + 4 q^{15} - 44 q^{16} + 5 q^{17} + 18 q^{18} + 10 q^{19} + 9 q^{20} - 36 q^{21} + 26 q^{22} - 40 q^{23} - 8 q^{24} + 45 q^{25} - 9 q^{26} - 32 q^{27} - 7 q^{28} + 2 q^{29} + 4 q^{30} + 18 q^{31} + 176 q^{32} - 36 q^{33} - 86 q^{35} + 18 q^{36} - 5 q^{37} - 5 q^{38} - 36 q^{39} - 6 q^{40} + 22 q^{41} + 4 q^{42} - 36 q^{43} - 34 q^{44} - 32 q^{45} + 5 q^{46} - 32 q^{47} + 7 q^{48} + 62 q^{49} + 10 q^{50} - 54 q^{51} - 9 q^{52} + 23 q^{53} - 52 q^{54} - 70 q^{55} - 2 q^{56} + 10 q^{57} + 2 q^{58} - 76 q^{59} + 9 q^{60} - 12 q^{61} - 2 q^{62} - 46 q^{63} - 44 q^{64} - 20 q^{65} - 6 q^{66} - 22 q^{67} + 5 q^{68} - 101 q^{69} + 84 q^{70} - 8 q^{71} + 33 q^{72} + 53 q^{73} - 5 q^{74} + 76 q^{75} - 10 q^{76} + 28 q^{77} + 64 q^{78} + 17 q^{79} - 6 q^{80} + 73 q^{81} - 38 q^{82} + 10 q^{83} + 14 q^{84} - 24 q^{85} + 9 q^{86} - 12 q^{87} + 6 q^{88} - 64 q^{89} - 12 q^{90} - 23 q^{91} + 15 q^{92} + 100 q^{93} - 2 q^{94} + 27 q^{95} + 7 q^{96} + 60 q^{97} - 118 q^{98} - 25 q^{99}+O(q^{100}) \) 176 * q - 44 * q^2 + 7 * q^3 - 44 * q^4 + 9 * q^5 - 8 * q^6 + 8 * q^7 - 44 * q^8 + 33 * q^9 - 6 * q^10 + 16 * q^11 + 2 * q^12 + 16 * q^13 + 8 * q^14 + 4 * q^15 - 44 * q^16 + 5 * q^17 + 18 * q^18 + 10 * q^19 + 9 * q^20 - 36 * q^21 + 26 * q^22 - 40 * q^23 - 8 * q^24 + 45 * q^25 - 9 * q^26 - 32 * q^27 - 7 * q^28 + 2 * q^29 + 4 * q^30 + 18 * q^31 + 176 * q^32 - 36 * q^33 - 86 * q^35 + 18 * q^36 - 5 * q^37 - 5 * q^38 - 36 * q^39 - 6 * q^40 + 22 * q^41 + 4 * q^42 - 36 * q^43 - 34 * q^44 - 32 * q^45 + 5 * q^46 - 32 * q^47 + 7 * q^48 + 62 * q^49 + 10 * q^50 - 54 * q^51 - 9 * q^52 + 23 * q^53 - 52 * q^54 - 70 * q^55 - 2 * q^56 + 10 * q^57 + 2 * q^58 - 76 * q^59 + 9 * q^60 - 12 * q^61 - 2 * q^62 - 46 * q^63 - 44 * q^64 - 20 * q^65 - 6 * q^66 - 22 * q^67 + 5 * q^68 - 101 * q^69 + 84 * q^70 - 8 * q^71 + 33 * q^72 + 53 * q^73 - 5 * q^74 + 76 * q^75 - 10 * q^76 + 28 * q^77 + 64 * q^78 + 17 * q^79 - 6 * q^80 + 73 * q^81 - 38 * q^82 + 10 * q^83 + 14 * q^84 - 24 * q^85 + 9 * q^86 - 12 * q^87 + 6 * q^88 - 64 * q^89 - 12 * q^90 - 23 * q^91 + 15 * q^92 + 100 * q^93 - 2 * q^94 + 27 * q^95 + 7 * q^96 + 60 * q^97 - 118 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	2.10987	−	0.939377i	1.21814	−	0.542349i	0.305920	−	0.952057i	$-0.401036\pi$
$3$	2.10987	−	0.939377i	1.21814	−	0.542349i	0.912217	+	0.409708i	$0.134369\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−2.33563	−	2.59398i	−1.04453	−	1.16006i	−0.986835	−	0.161729i	$-0.948293\pi$
$5$	−2.33563	−	2.59398i	−1.04453	−	1.16006i	−0.0576908	−	0.998334i	$-0.518374\pi$
$6$	1.54539	+	1.71633i	0.630902	+	0.700687i
$7$	3.92251	+	1.74641i	1.48257	+	0.660082i	0.978998	−	0.203872i	$-0.0653526\pi$
$7$	3.92251	+	1.74641i	1.48257	+	0.660082i	0.503571	+	0.863954i	$0.332019\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	1.56175	−	1.73450i	0.520583	−	0.578166i
$10$	1.74527	−	3.02290i	0.551904	−	0.955925i
$11$	0.181517	−	3.31165i	0.0547295	−	0.998501i
$11$	0.181517	−	3.31165i	0.0547295	−	0.998501i
$12$	−1.15477	+	2.00012i	−0.333354	+	0.577386i
$13$	−3.26413	+	3.62518i	−0.905307	+	1.00544i	0.0946441	+	0.995511i	$0.469829\pi$
$13$	−3.26413	+	3.62518i	−0.905307	+	1.00544i	−0.999951	+	0.00993365i	$0.996838\pi$
$14$	−0.448816	+	4.27020i	−0.119951	+	1.14126i
$15$	−7.36461	−	3.27894i	−1.90153	−	0.846618i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.16943	−	0.673682i	0.768699	−	0.163392i	0.193161	−	0.981167i	$-0.438126\pi$
$17$	3.16943	−	0.673682i	0.768699	−	0.163392i	0.575538	+	0.817775i	$0.304793\pi$
$18$	2.13221	+	0.949322i	0.502567	+	0.223757i
$19$	7.32525	−	3.26141i	1.68053	−	0.748219i	0.680650	−	0.732609i	$-0.261698\pi$
$19$	7.32525	−	3.26141i	1.68053	−	0.748219i	0.999878	−	0.0156104i	$-0.00496913\pi$
$20$	3.41427	+	0.725725i	0.763454	+	0.162277i
$21$	9.91654			2.16397
$22$	3.20566	−	0.850724i	0.683449	−	0.181375i
$23$	3.71914	−	6.44174i	0.775495	−	1.34320i	−0.159021	−	0.987275i	$-0.550834\pi$
$23$	3.71914	−	6.44174i	0.775495	−	1.34320i	0.934516	−	0.355921i	$-0.115833\pi$
$24$	−2.25908	−	0.480181i	−0.461132	−	0.0980166i
$25$	−0.750923	+	7.14456i	−0.150185	+	1.42891i
$26$	−4.45643	−	1.98413i	−0.873977	−	0.389120i
$27$	−0.475318	+	1.46288i	−0.0914751	+	0.281531i
$28$	−4.19989	+	0.892714i	−0.793705	+	0.168707i
$29$	3.37762	+	1.50382i	0.627209	+	0.279251i	0.695625	−	0.718405i	$-0.255128\pi$
$29$	3.37762	+	1.50382i	0.627209	+	0.279251i	−0.0684155	+	0.997657i	$0.521794\pi$
$30$	0.842664	−	8.01741i	0.153849	−	1.46377i
$31$	−4.86370	−	1.03381i	−0.873547	−	0.185678i	−0.250741	−	0.968054i	$-0.580674\pi$
$31$	−4.86370	−	1.03381i	−0.873547	−	0.185678i	−0.622806	+	0.782376i	$0.714007\pi$
$32$	1.00000			0.176777
$33$	−2.72791	−	7.15769i	−0.474868	−	1.24599i
$34$	1.62012	+	2.80612i	0.277848	+	0.481246i
$35$	−4.63137	−	14.2539i	−0.782844	−	2.40935i
$36$	−0.243969	+	2.32121i	−0.0406615	+	0.386869i
$37$	−0.916927	−	8.72398i	−0.150742	−	1.43421i	−0.764452	−	0.644681i	$-0.776990\pi$
$37$	−0.916927	−	8.72398i	−0.150742	−	1.43421i	0.613710	−	0.789532i	$-0.289676\pi$
$38$	5.36541	+	5.95890i	0.870385	+	0.966661i
$39$	−3.48149	+	10.7149i	−0.557485	+	1.71576i
$40$	0.364861	+	3.47142i	0.0576897	+	0.548880i
$41$	0.499213	+	0.362700i	0.0779640	+	0.0566442i	0.626085	−	0.779755i	$-0.284656\pi$
$41$	0.499213	+	0.362700i	0.0779640	+	0.0566442i	−0.548120	+	0.836399i	$0.684656\pi$
$42$	3.06438	+	9.43119i	0.472844	+	1.45526i
$43$	−6.53020	−	0.597047i	−0.995846	−	0.0910488i
$43$	−6.53020	−	0.597047i	−0.995846	−	0.0910488i
$44$	1.79969	+	2.78588i	0.271314	+	0.419987i
$45$	−8.14693			−1.21447
$46$	7.27574	+	1.54651i	1.07275	+	0.228020i
$47$	−1.01605	−	0.738201i	−0.148206	−	0.107678i	0.511212	−	0.859455i	$-0.329197\pi$
$47$	−1.01605	−	0.738201i	−0.148206	−	0.107678i	−0.659417	+	0.751777i	$0.729197\pi$
$48$	−0.241413	−	2.29689i	−0.0348450	−	0.331528i
$49$	7.65219	+	8.49862i	1.09317	+	1.21409i
$50$	−7.02692	+	1.49362i	−0.993757	+	0.211230i
$51$	6.05425	−	4.39867i	0.847764	−	0.615937i
$52$	0.509907	−	4.85144i	0.0707114	−	0.672774i
$53$	−2.10732	−	0.447925i	−0.289463	−	0.0615272i	0.0608918	−	0.998144i	$-0.480606\pi$
$53$	−2.10732	−	0.447925i	−0.289463	−	0.0615272i	−0.350354	+	0.936617i	$0.613939\pi$
$54$	−1.53816			−0.209317
$55$	−9.01433	+	7.26395i	−1.21549	+	0.979471i
$56$	−2.14686	−	3.71847i	−0.286886	−	0.496901i
$57$	12.3917	−	13.7623i	1.64132	−	1.82287i
$58$	−0.386470	+	3.67702i	−0.0507460	+	0.482816i
$59$	2.28316	−	1.65881i	0.297242	−	0.215959i	−0.429161	−	0.903228i	$-0.641191\pi$
$59$	2.28316	−	1.65881i	0.297242	−	0.215959i	0.726403	+	0.687269i	$0.241191\pi$
$60$	7.88541	−	1.67610i	1.01800	−	0.216383i
$61$	0.370379	−	0.0787264i	0.0474221	−	0.0100799i	−0.184140	−	0.982900i	$-0.558950\pi$
$61$	0.370379	−	0.0787264i	0.0474221	−	0.0100799i	0.231562	+	0.972820i	$0.425616\pi$
$62$	−0.519753	−	4.94512i	−0.0660087	−	0.628031i
$63$	9.15512	−	4.07612i	1.15344	−	0.513543i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	17.0275			2.11200
$66$	5.96439	−	4.80624i	0.734166	−	0.591608i
$67$	−5.62642	+	9.74524i	−0.687376	+	1.19057i	0.285308	+	0.958436i	$0.407904\pi$
$67$	−5.62642	+	9.74524i	−0.687376	+	1.19057i	−0.972684	+	0.232134i	$0.925429\pi$
$68$	−2.16814	+	2.40796i	−0.262925	+	0.292008i
$69$	1.79570	−	17.0849i	0.216177	−	2.05679i
$70$	12.1251	−	8.80939i	1.44922	−	1.05292i
$71$	−7.48264	+	1.59048i	−0.888026	+	0.188756i	−0.629270	−	0.777187i	$-0.716646\pi$
$71$	−7.48264	+	1.59048i	−0.888026	+	0.188756i	−0.258756	+	0.965943i	$0.583313\pi$
$72$	−2.28299	+	0.485265i	−0.269053	+	0.0571891i
$73$	10.4166	+	4.63779i	1.21918	+	0.542812i	0.912529	−	0.409011i	$-0.134126\pi$
$73$	10.4166	+	4.63779i	1.21918	+	0.542812i	0.306647	+	0.951823i	$0.400793\pi$
$74$	8.01365	−	3.56791i	0.931568	−	0.414761i
$75$	5.12708	+	15.7795i	0.592024	+	1.82206i
$76$	−4.00924	+	6.94421i	−0.459892	+	0.796556i
$77$	6.49552	−	12.6730i	0.740233	−	1.44422i
$78$	−11.2663			−1.27566
$79$	0.384353	−	0.426867i	0.0432430	−	0.0480263i	−0.721135	−	0.692794i	$-0.756379\pi$
$79$	0.384353	−	0.426867i	0.0432430	−	0.0480263i	0.764378	+	0.644768i	$0.223046\pi$
$80$	−3.18877	+	1.41973i	−0.356516	+	0.158731i
$81$	1.10324	+	10.4966i	0.122582	+	1.16629i
$82$	−0.190683	+	0.586861i	−0.0210574	+	0.0648079i
$83$	6.80268	+	7.55514i	0.746691	+	0.829284i	0.990059	−	0.140650i	$-0.0449192\pi$
$83$	6.80268	+	7.55514i	0.746691	+	0.829284i	−0.243369	+	0.969934i	$0.578253\pi$
$84$	−8.02265	+	5.82879i	−0.875342	+	0.635974i
$85$	−9.15013	−	6.64796i	−0.992471	−	0.721072i
$86$	−1.45012	−	6.39509i	−0.156370	−	0.689600i
$87$	8.53901			0.915478
$88$	−2.09339	+	2.57249i	−0.223156	+	0.274228i
$89$	−1.75426	+	3.03846i	−0.185951	+	0.322076i	−0.943896	−	0.330241i	$-0.892870\pi$
$89$	−1.75426	+	3.03846i	−0.185951	+	0.322076i	0.757946	+	0.652318i	$0.226203\pi$
$90$	−2.51754	−	7.74819i	−0.265372	−	0.816731i
$91$	−19.1346	+	8.51929i	−2.00585	+	0.893064i
$92$	0.777512	+	7.39754i	0.0810613	+	0.771246i
$93$	−11.2329	+	2.38763i	−1.16480	+	0.247586i
$94$	0.388095	−	1.19443i	0.0400290	−	0.123197i
$95$	−25.5691	−	11.3841i	−2.62334	−	1.16798i
$96$	2.10987	−	0.939377i	0.215338	−	0.0958747i
$97$	5.71814	+	17.5986i	0.580589	+	1.78687i	0.616305	+	0.787508i	$0.288629\pi$
$97$	5.71814	+	17.5986i	0.580589	+	1.78687i	−0.0357156	+	0.999362i	$0.511371\pi$
$98$	−5.71801	+	9.90388i	−0.577606	+	1.00044i
$99$	−5.46057	−	5.48681i	−0.548808	−	0.551446i
$100$	−3.59196	−	6.22145i	−0.359196	−	0.622145i
$101$	−8.87226	+	9.85365i	−0.882823	+	0.980474i	−0.999920	−	0.0126461i	$-0.995975\pi$
$101$	−8.87226	+	9.85365i	−0.882823	+	0.980474i	0.117097	+	0.993120i	$0.462641\pi$
$102$	6.05425	+	4.39867i	0.599460	+	0.435533i
$103$	−1.86112	−	0.828622i	−0.183381	−	0.0816466i	0.312992	−	0.949756i	$-0.398669\pi$
$103$	−1.86112	−	0.828622i	−0.183381	−	0.0816466i	−0.496373	+	0.868109i	$0.665335\pi$
$104$	4.77157	−	1.01423i	0.467890	−	0.0994532i
$105$	−23.1614	−	25.7233i	−2.26032	−	2.51034i
$106$	−0.225196	−	2.14260i	−0.0218730	−	0.208107i
$107$	−5.36563	−	3.89836i	−0.518715	−	0.376868i	0.297405	−	0.954751i	$-0.403879\pi$
$107$	−5.36563	−	3.89836i	−0.518715	−	0.376868i	−0.816119	+	0.577883i	$0.803879\pi$
$108$	−0.475318	−	1.46288i	−0.0457375	−	0.140766i
$109$	−5.78405	+	10.0183i	−0.554011	+	0.959576i	0.443968	+	0.896042i	$0.353570\pi$
$109$	−5.78405	+	10.0183i	−0.554011	+	0.959576i	−0.997980	+	0.0635333i	$0.979763\pi$
$110$	−9.69401	−	6.32845i	−0.924287	−	0.603394i
$111$	−10.1297	−	17.5452i	−0.961468	−	1.66531i
$112$	2.87306	−	3.19085i	0.271479	−	0.301507i
$113$	4.32298	+	3.14083i	0.406672	+	0.295464i	0.772253	−	0.635315i	$-0.219130\pi$
$113$	4.32298	+	3.14083i	0.406672	+	0.295464i	−0.365581	+	0.930779i	$0.619130\pi$
$114$	16.9180	+	7.53238i	1.58452	+	0.705472i
$115$	−25.3963	+	5.39815i	−2.36822	+	0.503380i
$116$	−3.61648	+	0.768706i	−0.335781	+	0.0713725i
$117$	1.19012	+	11.3233i	0.110027	+	1.04684i
$118$	2.28316	+	1.65881i	0.210182	+	0.152706i
$119$	13.6086	+	2.89260i	1.24750	+	0.265164i
$120$	4.03079	+	6.98153i	0.367959	+	0.637323i
$121$	−10.9341	−	1.20225i	−0.994009	−	0.109295i
$122$	0.189327	+	0.327923i	0.0171408	+	0.0296888i
$123$	1.39399	+	0.296302i	0.125692	+	0.0267166i
$124$	4.54248	−	2.02244i	0.407926	−	0.181621i
$125$	6.16717	−	4.48071i	0.551608	−	0.400767i
$126$	6.70571	+	7.44745i	0.597392	+	0.663471i
$127$	−1.11041	+	3.41749i	−0.0985329	+	0.303253i	−0.988158	−	0.153438i	$-0.950965\pi$
$127$	−1.11041	+	3.41749i	−0.0985329	+	0.303253i	0.889625	+	0.456691i	$0.150965\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−14.3388	+	4.87462i	−1.26246	+	0.429187i
$130$	5.26177	+	16.1941i	0.461488	+	1.42031i
$131$	−0.354041			−0.0309327			−0.0154663	−	0.999880i	$-0.504923\pi$
$131$	−0.354041			−0.0309327			−0.0154663	+	0.999880i	$0.504923\pi$
$132$	6.41411	+	4.18726i	0.558277	+	0.364455i
$133$	34.4291			2.98538
$134$	−11.0069	−	2.33960i	−0.950854	−	0.202110i
$135$	4.90485	−	2.18378i	0.422142	−	0.187950i
$136$	−2.96010	−	1.31792i	−0.253826	−	0.113011i
$137$	−2.18056	+	6.71106i	−0.186298	+	0.573365i	−0.999968	−	0.00796114i	$-0.997466\pi$
$137$	−2.18056	+	6.71106i	−0.186298	+	0.573365i	0.813671	+	0.581326i	$0.197466\pi$
$138$	16.8036	−	3.57173i	1.43042	−	0.304045i
$139$	1.05372	+	10.0255i	0.0893755	+	0.850351i	0.943743	+	0.330681i	$0.107278\pi$
$139$	1.05372	+	10.0255i	0.0893755	+	0.850351i	−0.854367	+	0.519670i	$0.826055\pi$
$140$	12.1251	+	8.80939i	1.02476	+	0.744529i
$141$	−2.83718	−	0.603061i	−0.238934	−	0.0507869i
$142$	−3.82490	−	6.62493i	−0.320979	−	0.555952i
$143$	11.4129	+	11.4677i	0.954391	+	0.958977i
$144$	−1.16700	−	2.02130i	−0.0972499	−	0.168442i
$145$	−3.98802	−	12.2739i	−0.331187	−	1.01929i
$146$	−1.19188	+	11.3400i	−0.0986407	+	0.938503i
$147$	24.1286	+	10.7427i	1.99009	+	0.886045i
$148$	5.86963	+	6.51889i	0.482481	+	0.535849i
$149$	6.26225	+	6.95494i	0.513024	+	0.569771i	0.942882	−	0.333126i	$-0.108103\pi$
$149$	6.26225	+	6.95494i	0.513024	+	0.569771i	−0.429859	+	0.902896i	$0.641437\pi$
$150$	−13.4229	+	9.75228i	−1.09597	+	0.796270i
$151$	5.91869	+	4.30018i	0.481656	+	0.349944i	0.801966	−	0.597369i	$-0.203787\pi$
$151$	5.91869	+	4.30018i	0.481656	+	0.349944i	−0.320311	+	0.947313i	$0.603787\pi$
$152$	−7.84326	−	1.66714i	−0.636173	−	0.135223i
$153$	3.78135	−	6.54949i	0.305704	−	0.529495i
$154$	14.0599	+	2.26144i	1.13298	+	0.182232i
$155$	8.67813	+	15.0310i	0.697044	+	1.20732i
$156$	−3.48149	−	10.7149i	−0.278742	−	0.857881i
$157$	0.755866	−	7.19158i	0.0603246	−	0.573951i	−0.922056	−	0.387057i	$-0.873492\pi$
$157$	0.755866	−	7.19158i	0.0603246	−	0.573951i	0.982380	−	0.186893i	$-0.0598418\pi$
$158$	0.524746	+	0.233632i	0.0417465	+	0.0185868i
$159$	−4.86695	+	1.03450i	−0.385974	+	0.0820413i
$160$	−2.33563	−	2.59398i	−0.184648	−	0.205072i
$161$	25.8383	−	18.7726i	2.03634	−	1.47949i
$162$	−9.64197	+	4.29288i	−0.757545	+	0.337281i
$163$	12.3702	−	13.7385i	0.968912	−	1.07609i	−0.0281592	−	0.999603i	$-0.508965\pi$
$163$	12.3702	−	13.7385i	0.968912	−	1.07609i	0.997071	−	0.0764821i	$-0.0243688\pi$
$164$	−0.617062			−0.0481844
$165$	−12.1955	+	23.7939i	−0.949419	+	1.85235i
$166$	−5.08322	+	8.80439i	−0.394534	+	0.683354i
$167$	−16.7806	−	3.56682i	−1.29852	−	0.276009i	−0.493754	−	0.869602i	$-0.664376\pi$
$167$	−16.7806	−	3.56682i	−1.29852	−	0.276009i	−0.804765	+	0.593593i	$0.797709\pi$
$168$	−8.02265	−	5.82879i	−0.618961	−	0.449701i
$169$	−1.12854	−	10.7373i	−0.0868108	−	0.825950i
$170$	3.49504	−	10.7566i	0.268057	−	0.824995i
$171$	5.78329	−	17.7991i	0.442259	−	1.36113i
$172$	5.63398	−	3.35534i	0.429587	−	0.255842i
$173$	−18.0997	−	13.1502i	−1.37609	−	0.999790i	−0.997233	−	0.0743358i	$-0.976316\pi$
$173$	−18.0997	−	13.1502i	−1.37609	−	0.999790i	−0.378860	−	0.925454i	$-0.623684\pi$
$174$	2.63870	+	8.12108i	0.200039	+	0.615658i
$175$	−15.4228	+	26.7132i	−1.16586	+	2.01932i
$176$	−3.09348	−	1.19599i	−0.233180	−	0.0901512i
$177$	3.25892	−	5.64462i	0.244956	−	0.424276i
$178$	−3.43184	−	0.729461i	−0.257227	−	0.0546754i
$179$	2.60562	−	24.7909i	0.194753	−	1.85296i	−0.264165	−	0.964477i	$-0.585096\pi$
$179$	2.60562	−	24.7909i	0.194753	−	1.85296i	0.458919	−	0.888478i	$-0.348237\pi$
$180$	6.59100	−	4.78864i	0.491264	−	0.356924i
$181$	−6.60396	+	1.40371i	−0.490868	+	0.104337i	−0.446694	−	0.894687i	$-0.647399\pi$
$181$	−6.60396	+	1.40371i	−0.490868	+	0.104337i	−0.0441738	+	0.999024i	$0.514066\pi$
$182$	−14.0153	−	15.5655i	−1.03888	−	1.15379i
$183$	0.707498	−	0.514028i	0.0522998	−	0.0379980i
$184$	−6.79521	+	3.02542i	−0.500950	+	0.223037i
$185$	−20.4882	+	22.7545i	−1.50632	+	1.67294i
$186$	−5.74194	−	9.94534i	−0.421020	−	0.729228i
$187$	−1.65570	−	10.6183i	−0.121077	−	0.776489i
$188$	1.25590			0.0915962
$189$	−4.41923	+	4.90805i	−0.321452	+	0.357008i
$190$	2.92564	−	27.8356i	0.212248	−	2.01940i
$191$	1.18567	+	11.2809i	0.0857918	+	0.816254i	0.949817	+	0.312806i	$0.101269\pi$
$191$	1.18567	+	11.2809i	0.0857918	+	0.816254i	−0.864025	+	0.503448i	$0.832064\pi$
$192$	1.54539	+	1.71633i	0.111529	+	0.123865i
$193$	−4.93604	+	15.1916i	−0.355304	+	1.09351i	0.600529	+	0.799603i	$0.294957\pi$
$193$	−4.93604	+	15.1916i	−0.355304	+	1.09351i	−0.955833	+	0.293910i	$0.905043\pi$
$194$	−14.9703	+	10.8765i	−1.07480	+	0.780891i
$195$	35.9258	−	15.9952i	2.57270	−	1.14544i
$196$	−11.1861	−	2.37768i	−0.799008	−	0.169834i
$197$	9.63058	+	16.6807i	0.686151	+	1.18845i	0.973074	+	0.230494i	$0.0740343\pi$
$197$	9.63058	+	16.6807i	0.686151	+	1.18845i	−0.286923	+	0.957954i	$0.592632\pi$
$198$	3.53086	−	6.88883i	0.250927	−	0.489568i
$199$	−2.75825			−0.195527			−0.0977636	−	0.995210i	$-0.531169\pi$
$199$	−2.75825			−0.195527			−0.0977636	+	0.995210i	$0.531169\pi$
$200$	4.80697	−	5.33869i	0.339904	−	0.377502i
$201$	−2.71658	+	25.8466i	−0.191613	+	1.82308i
$202$	−12.1131	−	5.39308i	−0.852271	−	0.379456i
$203$	10.6225	+	11.7975i	0.745551	+	0.828019i
$204$	−2.31252	+	7.11720i	−0.161909	+	0.498303i
$205$	−0.225142	−	2.14208i	−0.0157246	−	0.149610i
$206$	0.212950	−	2.02608i	0.0148369	−	0.141164i
$207$	−5.36482	−	16.5112i	−0.372881	−	1.14761i
$208$	2.43908	+	4.22461i	0.169120	+	0.292924i
$209$	−9.47101	−	24.8507i	−0.655123	−	1.71896i
$210$	17.3071	−	29.9767i	1.19430	−	2.06859i
$211$	−6.97820	−	21.4767i	−0.480399	−	1.47852i	−0.838536	−	0.544847i	$-0.816588\pi$
$211$	−6.97820	−	21.4767i	−0.480399	−	1.47852i	0.358137	−	0.933669i	$-0.383412\pi$
$212$	1.96814	−	0.876273i	0.135172	−	0.0601827i
$213$	−14.2934	+	10.3847i	−0.979366	+	0.711551i
$214$	2.04949	−	6.30767i	0.140100	−	0.431184i
$215$	13.7034	+	18.3337i	0.934565	+	1.25035i
$216$	1.24440	−	0.904109i	0.0846707	−	0.0615168i
$217$	−17.2724	−	12.5492i	−1.17253	−	0.851893i
$218$	−11.3153	−	2.40514i	−0.766369	−	0.162897i
$219$	26.3344			1.77952
$220$	3.02310	−	11.1751i	0.203817	−	0.753428i
$221$	−7.90319	+	13.6887i	−0.531626	+	0.920804i
$222$	13.5562	−	15.0557i	0.909831	−	1.01047i
$223$	5.21833	+	3.79134i	0.349445	+	0.253887i	0.748636	−	0.662981i	$-0.230709\pi$
$223$	5.21833	+	3.79134i	0.349445	+	0.253887i	−0.399191	+	0.916868i	$0.630709\pi$
$224$	3.92251	+	1.74641i	0.262084	+	0.116687i
$225$	11.2195	+	12.4605i	0.747964	+	0.830699i
$226$	−1.65123	+	5.08197i	−0.109838	+	0.338048i
$227$	−1.84602	−	17.5637i	−0.122524	−	1.16574i	−0.867076	−	0.498177i	$-0.834003\pi$
$227$	−1.84602	−	17.5637i	−0.122524	−	1.16574i	0.744551	−	0.667565i	$-0.232664\pi$
$228$	−1.93577	+	18.4176i	−0.128199	+	1.21974i
$229$	2.01031	−	2.23267i	0.132845	−	0.147539i	−0.673052	−	0.739595i	$-0.735017\pi$
$229$	2.01031	−	2.23267i	0.132845	−	0.147539i	0.805897	+	0.592056i	$0.201684\pi$
$230$	−12.9818	−	22.4852i	−0.855997	−	1.48263i
$231$	1.80002	−	32.8401i	0.118433	−	2.16072i
$232$	−1.84864	−	3.20193i	−0.121369	−	0.210217i
$233$	−12.0412	+	13.3731i	−0.788848	+	0.876104i	−0.994736	−	0.102471i	$-0.967325\pi$
$233$	−12.0412	+	13.3731i	−0.788848	+	0.876104i	0.205888	+	0.978575i	$0.433992\pi$
$234$	−10.4013	+	4.63095i	−0.679953	+	0.302735i
$235$	0.458231	+	4.35977i	0.0298917	+	0.284400i
$236$	−0.872088	+	2.68401i	−0.0567681	+	0.174714i
$237$	0.409947	−	1.26169i	0.0266289	−	0.0819554i
$238$	1.45427	+	13.8364i	0.0942662	+	0.896883i
$239$	10.3330	−	4.60053i	0.668384	−	0.297584i	−0.0443520	−	0.999016i	$-0.514122\pi$
$239$	10.3330	−	4.60053i	0.668384	−	0.297584i	0.712736	+	0.701432i	$0.247456\pi$
$240$	−5.39424	+	5.99092i	−0.348197	+	0.386712i
$241$	−5.83049	−	10.0987i	−0.375575	−	0.650514i	0.614838	−	0.788653i	$-0.289221\pi$
$241$	−5.83049	−	10.0987i	−0.375575	−	0.650514i	−0.990413	+	0.138139i	$0.955888\pi$
$242$	−2.23542	−	10.7705i	−0.143698	−	0.692352i
$243$	9.88074	+	17.1139i	0.633850	+	1.09786i
$244$	−0.253368	+	0.281394i	−0.0162202	+	0.0180144i
$245$	4.17256	−	39.6993i	0.266575	−	2.53629i
$246$	0.148967	+	1.41732i	0.00949778	+	0.0903653i
$247$	−12.0874	+	37.2010i	−0.769100	+	2.36705i
$248$	3.32716	+	3.69518i	0.211275	+	0.234644i
$249$	21.4499	+	9.55011i	1.35933	+	0.605214i
$250$	6.16717	+	4.48071i	0.390046	+	0.283385i
$251$	13.6717	−	15.1840i	0.862950	−	0.958403i	−0.136531	−	0.990636i	$-0.543595\pi$
$251$	13.6717	−	15.1840i	0.862950	−	0.958403i	0.999480	+	0.0322331i	$0.0102619\pi$
$252$	−5.01076	+	8.67890i	−0.315648	+	0.546719i
$253$	−20.6577	−	13.4858i	−1.29874	−	0.847845i
$254$	−3.59336			−0.225467
$255$	−25.5506	−	5.43094i	−1.60004	−	0.340099i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	13.1013	−	9.51864i	0.817235	−	0.593756i	−0.0986839	−	0.995119i	$-0.531463\pi$
$257$	13.1013	−	9.51864i	0.817235	−	0.593756i	0.915919	+	0.401363i	$0.131463\pi$
$258$	−9.06696	−	12.1306i	−0.564484	−	0.755220i
$259$	11.6390	−	35.8212i	0.723213	−	2.22582i
$260$	−13.7755	+	10.0085i	−0.854320	+	0.620700i
$261$	7.88337	−	3.50990i	0.487968	−	0.217257i
$262$	−0.109405	−	0.336713i	−0.00675904	−	0.0208022i
$263$	−1.75865	+	3.04607i	−0.108443	+	0.187829i	−0.915140	−	0.403137i	$-0.867920\pi$
$263$	−1.75865	+	3.04607i	−0.108443	+	0.187829i	0.806697	+	0.590966i	$0.201253\pi$
$264$	−2.00026	+	7.39412i	−0.123107	+	0.455076i
$265$	3.76001	+	6.51253i	0.230976	+	0.400062i
$266$	10.6392	+	32.7440i	0.652330	+	2.00767i
$267$	−0.847001	+	8.05868i	−0.0518356	+	0.493183i
$268$	−1.17624	−	11.1912i	−0.0718504	−	0.683611i
$269$	−0.841452	+	2.58972i	−0.0513042	+	0.157898i	−0.973426	−	0.229001i	$-0.926454\pi$
$269$	−0.841452	+	2.58972i	−0.0513042	+	0.157898i	0.922122	+	0.386900i	$0.126454\pi$
$270$	3.59258	+	3.98996i	0.218637	+	0.242822i
$271$	−25.6755	−	11.4314i	−1.55967	−	0.694411i	−0.567980	−	0.823042i	$-0.692275\pi$
$271$	−25.6755	−	11.4314i	−1.55967	−	0.694411i	−0.991692	+	0.128631i	$0.958942\pi$
$272$	0.338697	−	3.22248i	0.0205365	−	0.195392i
$273$	−32.3689	+	35.9493i	−1.95905	+	2.17575i
$274$	−7.05643			−0.426294
$275$	23.5240	+	3.78366i	1.41855	+	0.228163i
$276$	8.58953	+	14.8775i	0.517029	+	0.895520i
$277$	16.0994	+	3.42202i	0.967317	+	0.205610i	0.664375	−	0.747400i	$-0.268698\pi$
$277$	16.0994	+	3.42202i	0.967317	+	0.205610i	0.302942	+	0.953009i	$0.402031\pi$
$278$	−9.20919	+	4.10020i	−0.552331	+	0.245914i
$279$	−9.38903	+	6.82153i	−0.562106	+	0.408394i
$280$	−4.63137	+	14.2539i	−0.276777	+	0.851833i
$281$	10.2747	+	11.4113i	0.612940	+	0.680739i	0.967086	−	0.254451i	$-0.0818949\pi$
$281$	10.2747	+	11.4113i	0.612940	+	0.680739i	−0.354146	+	0.935190i	$0.615228\pi$
$282$	−0.303192	−	2.88468i	−0.0180548	−	0.171780i
$283$	0.977382	−	9.29917i	0.0580993	−	0.552778i	−0.926295	−	0.376800i	$-0.877024\pi$
$283$	0.977382	−	9.29917i	0.0580993	−	0.552778i	0.984394	−	0.175978i	$-0.0563089\pi$
$284$	5.11872	−	5.68492i	0.303740	−	0.337338i
$285$	−64.6416			−3.82904
$286$	−7.37966	+	14.3980i	−0.436369	+	0.851371i
$287$	1.32474	+	2.29453i	0.0781972	+	0.135442i
$288$	1.56175	−	1.73450i	0.0920270	−	0.102206i
$289$	−5.93886	+	2.64415i	−0.349345	+	0.155538i
$290$	10.4408	−	7.58566i	0.613103	−	0.445445i
$291$	28.5963	+	31.7594i	1.67634	+	1.86177i
$292$	−11.1533	+	2.37070i	−0.652696	+	0.138735i
$293$	3.64968	−	2.65165i	0.213217	−	0.154911i	−0.476051	−	0.879418i	$-0.657932\pi$
$293$	3.64968	−	2.65165i	0.213217	−	0.154911i	0.689268	+	0.724507i	$0.257932\pi$
$294$	−2.76081	+	26.2673i	−0.161013	+	1.53194i
$295$	−9.63553	−	2.04810i	−0.561002	−	0.119245i
$296$	−4.38601	+	7.59680i	−0.254932	+	0.441555i
$297$	4.75827	+	1.83963i	0.276103	+	0.106746i
$298$	−4.67939	+	8.10495i	−0.271070	+	0.469507i
$299$	11.2127	+	34.5093i	0.648449	+	1.99572i
$300$	−13.4229	−	9.75228i	−0.774969	−	0.563048i
$301$	−24.5721	−	13.7463i	−1.41631	−	0.792326i
$302$	−2.26074	+	6.95783i	−0.130091	+	0.400378i
$303$	−9.46307	+	29.1243i	−0.543639	+	1.67315i
$304$	−0.838160	−	7.97456i	−0.0480718	−	0.457372i
$305$	−1.06928	−	0.776879i	−0.0612269	−	0.0444840i
$306$	7.39743	+	1.57237i	0.422883	+	0.0898866i
$307$	2.55694	−	4.42874i	0.145932	−	0.252762i	−0.783788	−	0.621028i	$-0.786715\pi$
$307$	2.55694	−	4.42874i	0.145932	−	0.252762i	0.929720	+	0.368266i	$0.120049\pi$
$308$	2.19401	+	14.0706i	0.125015	+	0.801748i
$309$	−4.70511			−0.267664
$310$	−11.6136	+	12.8982i	−0.659608	+	0.732569i
$311$	−10.3703	+	4.61717i	−0.588047	+	0.261816i	−0.679118	−	0.734029i	$-0.737638\pi$
$311$	−10.3703	+	4.61717i	−0.588047	+	0.261816i	0.0910709	+	0.995844i	$0.470971\pi$
$312$	9.11466	−	6.62219i	0.516016	−	0.374908i
$313$	0.381554	+	0.423759i	0.0215667	+	0.0239523i	0.753832	−	0.657068i	$-0.228203\pi$
$313$	0.381554	+	0.423759i	0.0215667	+	0.0239523i	−0.732265	+	0.681020i	$0.761537\pi$
$314$	7.07318	−	1.50345i	0.399162	−	0.0848446i
$315$	−31.9564	−	14.2279i	−1.80054	−	0.801651i
$316$	−0.0600418	+	0.571259i	−0.00337761	+	0.0321358i
$317$	−2.54908	−	7.84528i	−0.143171	−	0.440635i	0.853600	−	0.520928i	$-0.174414\pi$
$317$	−2.54908	−	7.84528i	−0.143171	−	0.440635i	−0.996771	+	0.0802938i	$0.974414\pi$
$318$	−2.48784	−	4.30907i	−0.139511	−	0.241640i
$319$	5.59321	−	10.9126i	0.313160	−	0.610986i
$320$	1.74527	−	3.02290i	0.0975637	−	0.168985i
$321$	−14.9828	−	3.18470i	−0.836260	−	0.177752i
$322$	25.8383	+	18.7726i	1.43991	+	1.04616i
$323$	21.0197	−	15.2717i	1.16957	−	0.849740i
$324$	−7.06230	−	7.84348i	−0.392350	−	0.435749i
$325$	−23.4492	−	26.0430i	−1.30073	−	1.44461i
$326$	16.8887	+	7.51935i	0.935381	+	0.416458i
$327$	−2.79269	+	26.5707i	−0.154436	+	1.46936i
$328$	−0.190683	−	0.586861i	−0.0105287	−	0.0324040i
$329$	−2.69625	−	4.67004i	−0.148649	−	0.257467i
$330$	−26.3979	−	4.24591i	−1.45316	−	0.233730i
$331$	−15.3664	−	26.6153i	−0.844612	−	1.46291i	−0.885958	−	0.463766i	$-0.846498\pi$
$331$	−15.3664	−	26.6153i	−0.844612	−	1.46291i	0.0413460	−	0.999145i	$-0.486835\pi$
$332$	−9.94428	−	2.11372i	−0.545763	−	0.116006i
$333$	−16.5637	−	12.0343i	−0.907687	−	0.659473i
$334$	−1.79323	−	17.0615i	−0.0981214	−	0.933562i
$335$	38.4202	−	8.16646i	2.09912	−	0.446182i
$336$	3.06438	−	9.43119i	0.167176	−	0.514513i
$337$	−13.0851	−	5.82587i	−0.712792	−	0.317355i	0.0181118	−	0.999836i	$-0.494235\pi$
$337$	−13.0851	−	5.82587i	−0.712792	−	0.317355i	−0.730904	+	0.682481i	$0.760901\pi$
$338$	9.86309	−	4.39133i	0.536481	−	0.238857i
$339$	12.0714	+	2.56585i	0.655627	+	0.139358i
$340$	11.3102			0.613381
$341$	−4.30647	+	15.9192i	−0.233209	+	0.862075i
$342$	18.7151			1.01200
$343$	5.88585	+	18.1148i	0.317806	+	0.978107i
$344$	4.93211	+	4.32138i	0.265921	+	0.232993i
$345$	−48.5121	+	35.2461i	−2.61180	+	1.89759i
$346$	6.91346	−	21.2774i	0.371670	−	1.14388i
$347$	1.63645	+	1.81747i	0.0878495	+	0.0975667i	0.785467	−	0.618904i	$-0.212423\pi$
$347$	1.63645	+	1.81747i	0.0878495	+	0.0975667i	−0.697617	+	0.716471i	$0.745756\pi$
$348$	−6.90821	+	5.01910i	−0.370319	+	0.269052i
$349$	20.6235	−	9.18219i	1.10395	−	0.491512i	0.227880	−	0.973689i	$-0.426821\pi$
$349$	20.6235	−	9.18219i	1.10395	−	0.491512i	0.876073	+	0.482178i	$0.160154\pi$
$350$	−30.1716	−	6.41318i	−1.61274	−	0.342799i
$351$	−3.75171	−	6.49814i	−0.200251	−	0.346845i
$352$	0.181517	−	3.31165i	0.00967491	−	0.176512i
$353$	0.280986	+	0.486681i	0.0149554	+	0.0259034i	0.873406	−	0.486992i	$-0.161906\pi$
$353$	0.280986	+	0.486681i	0.0149554	+	0.0259034i	−0.858451	+	0.512896i	$0.828573\pi$
$354$	6.37542	+	1.35514i	0.338850	+	0.0720247i
$355$	21.6024	+	15.6950i	1.14654	+	0.833007i
$356$	−0.366739	−	3.48929i	−0.0194371	−	0.184932i
$357$	31.4297	−	6.68059i	1.66344	−	0.353575i
$358$	24.3827	−	5.18270i	1.28867	−	0.273914i
$359$	−9.28523	−	4.13405i	−0.490056	−	0.218187i	0.146805	−	0.989165i	$-0.453101\pi$
$359$	−9.28523	−	4.13405i	−0.490056	−	0.218187i	−0.636861	+	0.770979i	$0.719768\pi$
$360$	6.59100	+	4.78864i	0.347376	+	0.252384i
$361$	30.3090	−	33.6616i	1.59521	−	1.77166i
$362$	−3.37575	−	5.84696i	−0.177425	−	0.307310i
$363$	−24.1989	+	7.73465i	−1.27012	+	0.405964i
$364$	10.4727	−	18.1393i	0.548920	−	0.950758i
$365$	−12.2991	−	37.8528i	−0.643765	−	1.98130i
$366$	0.707498	+	0.514028i	0.0369815	+	0.0268687i
$367$	0.513270	+	4.88343i	0.0267925	+	0.254913i	0.999717	+	0.0237901i	$0.00757334\pi$
$367$	0.513270	+	4.88343i	0.0267925	+	0.254913i	−0.972925	+	0.231123i	$0.925760\pi$
$368$	−4.97718	−	5.52772i	−0.259454	−	0.288152i
$369$	1.40875	−	0.299439i	0.0733365	−	0.0155882i
$370$	−27.9720	−	12.4539i	−1.45420	−	0.647449i
$371$	−7.48372	−	5.43724i	−0.388535	−	0.282287i
$372$	7.68422	−	8.53419i	0.398408	−	0.442477i
$373$	13.7233	+	23.7694i	0.710564	+	1.23073i	0.964646	+	0.263550i	$0.0848934\pi$
$373$	13.7233	+	23.7694i	0.710564	+	1.23073i	−0.254082	+	0.967183i	$0.581773\pi$
$374$	9.58699	−	4.85590i	0.495731	−	0.251093i
$375$	8.80288	−	15.2470i	0.454579	−	0.787353i
$376$	0.388095	+	1.19443i	0.0200145	+	0.0615983i
$377$	−16.4766	+	7.33586i	−0.848588	+	0.377816i
$378$	−6.03345	−	2.68627i	−0.310327	−	0.138167i
$379$	−0.00187041	+	0.00575653i	−9.60766e−5	+	0.000295693i	−0.951105	−	0.308869i	$-0.900049\pi$
$379$	−0.00187041	+	0.00575653i	−9.60766e−5	+	0.000295693i	0.951008	+	0.309165i	$0.100049\pi$
$380$	27.3773	−	5.81922i	1.40442	−	0.298520i
$381$	0.867484	+	8.25356i	0.0444426	+	0.422843i
$382$	−10.3623	+	4.61361i	−0.530184	+	0.236053i
$383$	3.54751	+	10.9181i	0.181270	+	0.557890i	0.999864	−	0.0164814i	$-0.00524644\pi$
$383$	3.54751	+	10.9181i	0.181270	+	0.557890i	−0.818595	+	0.574372i	$0.805246\pi$
$384$	−1.15477	+	2.00012i	−0.0589292	+	0.102068i
$385$	−48.0446	+	12.7502i	−2.44858	+	0.649808i
$386$	−15.9734			−0.813023
$387$	−11.2341	+	10.3942i	−0.571062	+	0.528366i
$388$	−14.9703	−	10.8765i	−0.760001	−	0.552173i
$389$	−19.1304	+	13.8991i	−0.969952	+	0.704711i	−0.955441	−	0.295183i	$-0.904619\pi$
$389$	−19.1304	+	13.8991i	−0.969952	+	0.704711i	−0.0145114	+	0.999895i	$0.504619\pi$
$390$	26.3140	+	29.2247i	1.33246	+	1.47985i
$391$	7.44786	−	22.9221i	0.376654	−	1.15922i
$392$	−1.19539	−	11.3734i	−0.0603763	−	0.574442i
$393$	−0.746981	+	0.332578i	−0.0376802	+	0.0167763i
$394$	−12.8882	+	14.3138i	−0.649300	+	0.721121i
$395$	−2.00499			−0.100882
$396$	7.64276	+	1.22928i	0.384063	+	0.0617737i
$397$	3.87416	−	6.71023i	0.194438	−	0.336777i	−0.752278	−	0.658846i	$-0.771045\pi$
$397$	3.87416	−	6.71023i	0.194438	−	0.336777i	0.946716	+	0.322069i	$0.104378\pi$
$398$	−0.852346	−	2.62325i	−0.0427243	−	0.131492i
$399$	72.6411	−	32.3419i	3.63660	−	1.61912i
$400$	6.56283	+	2.92196i	0.328141	+	0.146098i
$401$	9.67052	−	2.05553i	0.482923	−	0.102648i	0.0399841	−	0.999200i	$-0.487269\pi$
$401$	9.67052	−	2.05553i	0.482923	−	0.102648i	0.442939	+	0.896552i	$0.353936\pi$
$402$	−25.4210	+	5.40340i	−1.26788	+	0.269497i
$403$	19.6235	−	14.2573i	0.977517	−	0.710207i
$404$	1.38598	−	13.1868i	0.0689553	−	0.656065i
$405$	24.6513	−	27.3780i	1.22493	−	1.36043i
$406$	−7.93752	+	13.7482i	−0.393932	+	0.682311i
$407$	−29.0572	+	1.45299i	−1.44031	+	0.0720221i
$408$	−7.48346			−0.370487
$409$	3.28628	+	10.1141i	0.162496	+	0.500111i	0.998843	−	0.0480893i	$-0.0153132\pi$
$409$	3.28628	+	10.1141i	0.162496	+	0.500111i	−0.836347	+	0.548200i	$0.815313\pi$
$410$	1.96767	−	0.876063i	0.0971763	−	0.0432657i
$411$	1.70351	+	16.2079i	0.0840282	+	0.799475i
$412$	1.99273	−	0.423567i	0.0981746	−	0.0208676i
$413$	11.8527	−	2.51936i	0.583231	−	0.123970i
$414$	14.0453	−	10.2045i	0.690288	−	0.501524i
$415$	3.70934	−	35.2920i	0.182084	−	1.73242i
$416$	−3.26413	+	3.62518i	−0.160037	+	0.177739i
$417$	11.6409	+	20.1627i	0.570059	+	0.987371i
$418$	20.7077	−	16.6868i	1.01285	−	0.816176i
$419$	37.8736			1.85025			0.925123	−	0.379669i	$-0.123962\pi$
$419$	37.8736			1.85025			0.925123	+	0.379669i	$0.123962\pi$
$420$	33.8577	+	7.19668i	1.65209	+	0.351162i
$421$	−1.29795	+	12.3492i	−0.0632581	+	0.601861i	0.916271	+	0.400559i	$0.131184\pi$
$421$	−1.29795	+	12.3492i	−0.0632581	+	0.601861i	−0.979529	+	0.201302i	$0.935483\pi$
$422$	18.2692	−	13.2733i	0.889329	−	0.646135i
$423$	−2.86722	+	0.609446i	−0.139409	+	0.0296323i
$424$	1.44157	+	1.60103i	0.0700090	+	0.0777529i
$425$	2.43317	+	23.1500i	0.118026	+	1.12294i
$426$	−14.2934	−	10.3847i	−0.692516	−	0.503142i
$427$	1.59030	+	0.338029i	0.0769601	+	0.0163584i
$428$	6.63228			0.320583
$429$	34.8522	+	13.4744i	1.68268	+	0.650552i
$430$	−13.2018	+	18.6981i	−0.636647	+	0.901705i
$431$	4.30425	+	13.2471i	0.207328	+	0.638091i	0.999610	+	0.0279351i	$0.00889319\pi$
$431$	4.30425	+	13.2471i	0.207328	+	0.638091i	−0.792281	+	0.610156i	$0.791107\pi$
$432$	1.24440	+	0.904109i	0.0598712	+	0.0434990i
$433$	−1.46625	−	13.9504i	−0.0704635	−	0.670415i	−0.971560	−	0.236796i	$-0.923903\pi$
$433$	−1.46625	−	13.9504i	−0.0704635	−	0.670415i	0.901096	−	0.433620i	$-0.142764\pi$
$434$	6.59749	−	20.3050i	0.316690	−	0.974670i
$435$	−19.9440	−	22.1500i	−0.956241	−	1.06201i
$436$	−1.20920	−	11.5047i	−0.0579099	−	0.550976i
$437$	6.23447	−	59.3170i	0.298235	−	2.83752i
$438$	8.13779	+	25.0455i	0.388839	+	1.19672i
$439$	5.83759	+	10.1110i	0.278613	+	0.482571i	0.971040	−	0.238916i	$-0.0767921\pi$
$439$	5.83759	+	10.1110i	0.278613	+	0.482571i	−0.692427	+	0.721487i	$0.743459\pi$
$440$	11.5624	−	0.578171i	0.551215	−	0.0275632i
$441$	26.6916			1.27103
$442$	−15.4610	−	3.28633i	−0.735404	−	0.156315i
$443$	−2.40518	+	22.8838i	−0.114274	+	1.08724i	0.775660	+	0.631151i	$0.217417\pi$
$443$	−2.40518	+	22.8838i	−0.114274	+	1.08724i	−0.889933	+	0.456090i	$0.849249\pi$
$444$	18.5079	+	8.24024i	0.878345	+	0.391064i
$445$	11.9790	−	2.54622i	0.567859	−	0.120702i
$446$	−1.99322	+	6.13451i	−0.0943819	+	0.290478i
$447$	19.7459	+	8.79143i	0.933948	+	0.415820i
$448$	−0.448816	+	4.27020i	−0.0212046	+	0.201748i
$449$	−11.3986	−	2.42285i	−0.537933	−	0.114341i	−0.0690696	−	0.997612i	$-0.522003\pi$
$449$	−11.3986	−	2.42285i	−0.537933	−	0.114341i	−0.468863	+	0.883271i	$0.655336\pi$
$450$	−8.38361	+	14.5208i	−0.395207	+	0.684519i
$451$	1.29175	−	1.58739i	0.0608262	−	0.0747471i
$452$	−5.34350			−0.251337
$453$	16.5272	+	3.51296i	0.776514	+	0.165053i
$454$	16.1336	−	7.18314i	0.757187	−	0.337122i
$455$	66.7903	+	29.7370i	3.13118	+	1.39409i
$456$	−18.1144	+	3.85033i	−0.848283	+	0.180308i
$457$	−5.02537	+	15.4665i	−0.235077	+	0.723492i	0.762034	+	0.647537i	$0.224201\pi$
$457$	−5.02537	+	15.4665i	−0.235077	+	0.723492i	−0.997111	+	0.0759557i	$0.975799\pi$
$458$	2.74462	+	1.22198i	0.128248	+	0.0570995i
$459$	−0.520970	+	4.95670i	−0.0243168	+	0.231359i
$460$	17.3731	−	19.2948i	0.810024	−	0.899623i
$461$	−10.8431	+	18.7807i	−0.505012	+	0.874706i	0.494972	+	0.868909i	$0.335178\pi$
$461$	−10.8431	+	18.7807i	−0.505012	+	0.874706i	−0.999983	+	0.00579662i	$0.998155\pi$
$462$	31.7891	−	8.43624i	1.47896	−	0.392489i
$463$	−21.3753	+	37.0231i	−0.993394	+	1.72061i	−0.397318	+	0.917681i	$0.630059\pi$
$463$	−21.3753	+	37.0231i	−0.993394	+	1.72061i	−0.596076	+	0.802928i	$0.703274\pi$
$464$	2.47396	−	2.74761i	0.114851	−	0.127554i
$465$	32.4295	+	23.5614i	1.50388	+	1.09263i
$466$	−16.4396	−	7.31937i	−0.761548	−	0.339063i
$467$	−7.20372	−	8.00054i	−0.333348	−	0.370221i	0.553047	−	0.833150i	$-0.313465\pi$
$467$	−7.20372	−	8.00054i	−0.333348	−	0.370221i	−0.886395	+	0.462929i	$0.846798\pi$
$468$	−7.61847	−	8.46117i	−0.352164	−	0.391118i
$469$	−39.0889	+	28.3997i	−1.80496	+	1.31138i
$470$	−4.00479	+	1.78305i	−0.184727	+	0.0822458i
$471$	−5.16082	−	15.8834i	−0.237798	−	0.731867i
$472$	−2.82214			−0.129899
$473$	−3.16256	+	21.5174i	−0.145415	+	0.989371i
$474$	1.32662			0.0609335
$475$	17.8006	+	54.7847i	0.816749	+	2.51370i
$476$	−12.7098	+	5.65878i	−0.582554	+	0.259370i
$477$	−4.06803	+	2.95560i	−0.186262	+	0.135327i
$478$	7.56843	+	8.40559i	0.346172	+	0.384463i
$479$	−22.1885	−	24.6428i	−1.01382	−	1.12596i	−0.992005	−	0.126195i	$-0.959724\pi$
$479$	−22.1885	−	24.6428i	−1.01382	−	1.12596i	−0.0218107	−	0.999762i	$-0.506943\pi$
$480$	−7.36461	−	3.27894i	−0.336147	−	0.149662i
$481$	34.6190	+	25.1522i	1.57849	+	1.14684i
$482$	7.80271	−	8.66579i	0.355404	−	0.394716i
$483$	36.8810	−	63.8798i	1.67814	−	2.90663i
$484$	9.55254	−	5.45427i	0.434206	−	0.247921i
$485$	32.2950	−	55.9366i	1.46644	−	2.53995i
$486$	−13.2230	+	14.6856i	−0.599808	+	0.666154i
$487$	−0.555367	+	5.28396i	−0.0251661	+	0.239439i	0.974707	+	0.223488i	$0.0717443\pi$
$487$	−0.555367	+	5.28396i	−0.0251661	+	0.239439i	−0.999873	+	0.0159513i	$0.994922\pi$
$488$	−0.345917	−	0.154012i	−0.0156589	−	0.00697180i
$489$	13.1940	−	40.6069i	0.596652	−	1.83631i
$490$	39.0456	−	8.29941i	1.76390	−	0.374929i
$491$	−5.04226	−	2.24496i	−0.227554	−	0.101314i	0.289793	−	0.957089i	$-0.406414\pi$
$491$	−5.04226	−	2.24496i	−0.227554	−	0.101314i	−0.517347	+	0.855776i	$0.673080\pi$
$492$	−1.30192	+	0.579653i	−0.0586952	+	0.0261328i
$493$	11.7182	+	2.49079i	0.527762	+	0.112179i
$494$	−39.1155			−1.75989
$495$	−1.47881	+	26.9798i	−0.0664675	+	1.21265i
$496$	−2.48618	+	4.30619i	−0.111633	+	0.193354i
$497$	−32.1284	−	6.82909i	−1.44115	−	0.306327i
$498$	−2.45431	+	23.3512i	−0.109980	+	1.04639i
$499$	−19.1129	−	8.50959i	−0.855609	−	0.380942i	−0.0684224	−	0.997656i	$-0.521797\pi$
$499$	−19.1129	−	8.50959i	−0.855609	−	0.380942i	−0.787187	+	0.616715i	$0.788463\pi$
$500$	−2.35565	+	7.24994i	−0.105348	+	0.324227i
$501$	−38.7555	+	8.23773i	−1.73147	+	0.368035i
$502$	18.6656	+	8.31045i	0.833086	+	0.370914i
$503$	−3.59820	+	34.2346i	−0.160436	+	1.52645i	0.557406	+	0.830240i	$0.311797\pi$
$503$	−3.59820	+	34.2346i	−0.160436	+	1.52645i	−0.717842	+	0.696206i	$0.754870\pi$
$504$	−9.80253	−	2.08359i	−0.436640	−	0.0928106i
$505$	46.2825			2.05954
$506$	6.44217	−	23.8140i	0.286389	−	1.05866i
$507$	−12.4675	−	21.5943i	−0.553701	−	0.959038i
$508$	−1.11041	−	3.41749i	−0.0492664	−	0.151627i
$509$	3.67901	−	35.0034i	0.163069	−	1.55150i	−0.540789	−	0.841158i	$-0.681874\pi$
$509$	3.67901	−	35.0034i	0.163069	−	1.55150i	0.703858	−	0.710340i	$-0.251459\pi$
$510$	−2.73043	−	25.9783i	−0.120905	−	1.15034i
$511$	32.7599	+	36.3835i	1.44921	+	1.60951i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	1.28923	+	12.2662i	0.0569207	+	0.541565i
$514$	13.1013	+	9.51864i	0.577873	+	0.419849i
$515$	2.19745	+	6.76305i	0.0968312	+	0.298016i
$516$	8.73507	−	12.3718i	0.384540	−	0.544637i
$517$	−2.62910	+	3.23080i	−0.115628	+	0.142090i
$518$	37.6646			1.65489
$519$	−50.5410	−	10.7428i	−2.21850	−	0.471558i
$520$	−13.7755	−	10.0085i	−0.604096	−	0.438901i
$521$	0.447833	+	4.26085i	0.0196199	+	0.186671i	0.999942	−	0.0107315i	$-0.00341601\pi$
$521$	0.447833	+	4.26085i	0.0196199	+	0.186671i	−0.980322	+	0.197403i	$0.936749\pi$
$522$	5.77421	+	6.41291i	0.252730	+	0.280685i
$523$	10.1003	−	2.14689i	0.441656	−	0.0938769i	0.0182840	−	0.999833i	$-0.494180\pi$
$523$	10.1003	−	2.14689i	0.441656	−	0.0938769i	0.423372	+	0.905956i	$0.360846\pi$
$524$	0.286425	−	0.208100i	0.0125125	−	0.00909089i
$525$	−7.44656	+	70.8492i	−0.324994	+	3.09211i
$526$	−3.44044	−	0.731287i	−0.150010	−	0.0318856i
$527$	−16.1116			−0.701832
$528$	−7.65034	+	0.382551i	−0.332938	+	0.0166484i
$529$	−16.1640	−	27.9969i	−0.702784	−	1.21726i
$530$	−5.03188	+	5.58847i	−0.218571	+	0.242748i
$531$	0.688514	−	6.55077i	0.0298790	−	0.284279i
$532$	−27.8537	+	20.2369i	−1.20761	+	0.877382i
$533$	−2.94435	+	0.625841i	−0.127534	+	0.0271082i
$534$	−7.92599	+	1.68472i	−0.342991	+	0.0729051i
$535$	2.41986	+	23.0235i	0.104620	+	0.995391i
$536$	10.2800	−	4.57694i	0.444027	−	0.197694i
$537$	−17.7904	−	54.7533i	−0.767713	−	2.36278i
$538$	−2.72299			−0.117397
$539$	29.5335	−	23.7988i	1.27210	−	1.02509i
$540$	−2.68451	+	4.64971i	−0.115523	+	0.200092i
$541$	−2.11434	+	2.34821i	−0.0909026	+	0.100958i	−0.786880	−	0.617106i	$-0.788305\pi$
$541$	−2.11434	+	2.34821i	−0.0909026	+	0.100958i	0.695977	+	0.718064i	$0.254971\pi$
$542$	2.93780	−	27.9513i	0.126189	−	1.20061i
$543$	−12.6149	+	9.16526i	−0.541357	+	0.393319i
$544$	3.16943	−	0.673682i	0.135888	−	0.0288839i
$545$	39.4966	−	8.39526i	1.69185	−	0.359613i
$546$	−44.1923	−	19.6757i	−1.89126	−	0.842041i
$547$	16.6306	−	7.40443i	0.711074	−	0.316591i	−0.0191325	−	0.999817i	$-0.506090\pi$
$547$	16.6306	−	7.40443i	0.711074	−	0.316591i	0.730207	+	0.683226i	$0.239424\pi$
$548$	−2.18056	−	6.71106i	−0.0931488	−	0.286682i
$549$	0.441888	−	0.765372i	0.0188593	−	0.0326653i
$550$	3.67084	+	23.5419i	0.156525	+	1.00383i
$551$	29.6465			1.26298
$552$	−11.4950	+	12.7665i	−0.489261	+	0.543379i
$553$	2.25311	−	1.00315i	0.0958120	−	0.0426583i
$554$	1.72044	+	16.3689i	0.0730944	+	0.695446i
$555$	−21.8526	+	67.2552i	−0.927589	+	2.85483i
$556$	−6.74532	−	7.49143i	−0.286065	−	0.317708i
$557$	20.1208	−	14.6186i	0.852547	−	0.619412i	−0.0732999	−	0.997310i	$-0.523353\pi$
$557$	20.1208	−	14.6186i	0.852547	−	0.619412i	0.925847	+	0.377898i	$0.123353\pi$
$558$	−9.38903	−	6.82153i	−0.397469	−	0.288778i
$559$	23.4798	−	21.7243i	0.993091	−	0.918842i
$560$	−14.9874			−0.633334
$561$	−13.4679	−	20.8480i	−0.568616	−	0.880204i
$562$	−7.67768	+	13.2981i	−0.323864	+	0.560948i
$563$	−3.38842	−	10.4285i	−0.142805	−	0.439508i	0.853917	−	0.520409i	$-0.174220\pi$
$563$	−3.38842	−	10.4285i	−0.142805	−	0.439508i	−0.996722	+	0.0809005i	$0.974220\pi$
$564$	2.64980	−	1.17977i	0.111577	−	0.0496771i
$565$	−1.94964	−	18.5496i	−0.0820218	−	0.780386i
$566$	9.14607	−	1.94406i	0.384438	−	0.0817148i
$567$	−14.0040	+	43.0998i	−0.588112	+	1.81002i
$568$	6.98845	+	3.11146i	0.293229	+	0.130554i
$569$	4.72763	−	2.10488i	0.198193	−	0.0882410i	−0.305240	−	0.952275i	$-0.598737\pi$
$569$	4.72763	−	2.10488i	0.198193	−	0.0882410i	0.503433	+	0.864034i	$0.332070\pi$
$570$	−19.9754	−	61.4778i	−0.836676	−	2.57502i
$571$	−6.12036	+	10.6008i	−0.256129	+	0.443628i	−0.965202	−	0.261507i	$-0.915781\pi$
$571$	−6.12036	+	10.6008i	−0.256129	+	0.443628i	0.709073	+	0.705135i	$0.249114\pi$
$572$	−15.9737	−	2.56926i	−0.667896	−	0.107426i
$573$	13.0986	+	22.6874i	0.547201	+	0.947780i
$574$	−1.77285	+	1.96895i	−0.0739975	+	0.0821826i
$575$	43.2306	+	31.4089i	1.80284	+	1.30984i
$576$	2.13221	+	0.949322i	0.0888422	+	0.0395551i
$577$	32.5316	−	6.91480i	1.35431	−	0.287867i	0.527119	−	0.849792i	$-0.323272\pi$
$577$	32.5316	−	6.91480i	1.35431	−	0.287867i	0.827188	+	0.561925i	$0.189939\pi$
$578$	−4.34995	−	4.83111i	−0.180934	−	0.200947i
$579$	3.85618	+	36.6891i	0.160257	+	1.52475i
$580$	10.4408	+	7.58566i	0.433529	+	0.314977i
$581$	13.4892	+	41.5154i	0.559625	+	1.72235i
$582$	−21.3682	+	37.0109i	−0.885742	+	1.53415i
$583$	−1.86589	+	6.89741i	−0.0772771	+	0.285661i
$584$	−5.70122	−	9.87480i	−0.235918	−	0.408622i
$585$	26.5926	−	29.5341i	1.09947	−	1.22108i
$586$	3.64968	+	2.65165i	0.150767	+	0.109539i
$587$	5.12307	+	2.28094i	0.211452	+	0.0941444i	0.509729	−	0.860335i	$-0.329745\pi$
$587$	5.12307	+	2.28094i	0.211452	+	0.0941444i	−0.298278	+	0.954479i	$0.596412\pi$
$588$	−25.8348	+	5.49136i	−1.06541	+	0.226460i
$589$	−38.9995	+	8.28961i	−1.60695	+	0.341567i
$590$	−1.02969	−	9.79683i	−0.0423916	−	0.403329i
$591$	35.9887	+	26.1474i	1.48038	+	1.07556i
$592$	−8.58034	−	1.82381i	−0.352650	−	0.0749580i
$593$	−15.1857	−	26.3024i	−0.623602	−	1.08011i	−0.988809	−	0.149185i	$-0.952335\pi$
$593$	−15.1857	−	26.3024i	−0.623602	−	1.08011i	0.365207	−	0.930926i	$-0.380998\pi$
$594$	−0.279203	+	5.09386i	−0.0114558	+	0.209004i
$595$	−24.2814	−	42.0566i	−0.995439	−	1.72415i
$596$	−9.15428	−	1.94580i	−0.374974	−	0.0797031i
$597$	−5.81956	+	2.59104i	−0.238179	+	0.106044i
$598$	−29.3553	+	21.3279i	−1.20043	+	0.872162i
$599$	−12.9495	−	14.3818i	−0.529101	−	0.587626i	0.418046	−	0.908426i	$-0.362715\pi$
$599$	−12.9495	−	14.3818i	−0.529101	−	0.587626i	−0.947147	+	0.320800i	$0.896048\pi$
$600$	5.12708	−	15.7795i	0.209312	−	0.644196i
$601$	−30.3179	+	22.0272i	−1.23669	+	0.898510i	−0.997373	−	0.0724313i	$-0.976924\pi$
$601$	−30.3179	+	22.0272i	−1.23669	+	0.898510i	−0.239319	+	0.970941i	$0.576924\pi$
$602$	5.48037	−	27.6173i	0.223363	−	1.12560i
$603$	8.11605	+	24.9786i	0.330511	+	1.01721i
$604$	−7.31590			−0.297680
$605$	22.4194	+	31.1709i	0.911479	+	1.26728i
$606$	−30.6232			−1.24398
$607$	35.7687	+	7.60288i	1.45181	+	0.308591i	0.865260	−	0.501323i	$-0.167153\pi$
$607$	35.7687	+	7.60288i	1.45181	+	0.308591i	0.586548	+	0.809915i	$0.300487\pi$
$608$	7.32525	−	3.26141i	0.297078	−	0.132268i
$609$	33.4943	+	14.9126i	1.35726	+	0.604291i
$610$	0.408430	−	1.25702i	0.0165368	−	0.0508951i
$611$	5.99262	−	1.27377i	0.242436	−	0.0515313i
$612$	0.790517	+	7.52127i	0.0319547	+	0.304029i
$613$	2.91971	+	2.12130i	0.117926	+	0.0856784i	0.645185	−	0.764026i	$-0.276780\pi$
$613$	2.91971	+	2.12130i	0.117926	+	0.0856784i	−0.527259	+	0.849705i	$0.676780\pi$
$614$	5.00212	+	1.06323i	0.201869	+	0.0429086i
$615$	−2.48724	−	4.30803i	−0.100295	−	0.173717i
$616$	−12.7040	+	6.43469i	−0.511858	+	0.259261i
$617$	11.9213	+	20.6483i	0.479933	+	0.831268i	0.999735	−	0.0230186i	$-0.00732770\pi$
$617$	11.9213	+	20.6483i	0.479933	+	0.831268i	−0.519802	+	0.854287i	$0.673994\pi$
$618$	−1.45396	−	4.47482i	−0.0584868	−	0.180004i
$619$	−3.58936	+	34.1505i	−0.144269	+	1.37262i	0.647622	+	0.761961i	$0.275763\pi$
$619$	−3.58936	+	34.1505i	−0.144269	+	1.37262i	−0.791891	+	0.610663i	$0.790903\pi$
$620$	−15.8557	−	7.05942i	−0.636781	−	0.283513i
$621$	7.65572	+	8.50254i	0.307213	+	0.341195i
$622$	−7.59580	−	8.43599i	−0.304564	−	0.338252i
$623$	−12.1875	+	8.85473i	−0.488281	+	0.354757i
$624$	9.11466	+	6.62219i	0.364878	+	0.265100i
$625$	9.10751	+	1.93586i	0.364301	+	0.0774345i
$626$	−0.285112	+	0.493828i	−0.0113954	+	0.0197374i
$627$	−43.3268	−	43.5350i	−1.73031	−	1.73862i
$628$	3.61560	+	6.26240i	0.144278	+	0.249897i
$629$	−8.78332	−	27.0323i	−0.350214	−	1.07785i
$630$	3.65647	−	34.7890i	0.145677	−	1.38603i
$631$	28.8270	+	12.8346i	1.14758	+	0.510938i	0.890289	−	0.455395i	$-0.150502\pi$
$631$	28.8270	+	12.8346i	1.14758	+	0.510938i	0.257295	+	0.966333i	$0.417169\pi$
$632$	−0.561854	+	0.119426i	−0.0223493	+	0.00475050i
$633$	−34.8978	−	38.7579i	−1.38706	−	1.54049i
$634$	6.67359	−	4.84865i	0.265042	−	0.192564i
$635$	11.4584	−	5.10161i	0.454713	−	0.202451i
$636$	3.32938	−	3.69765i	0.132018	−	0.146621i
$637$	−55.7868			−2.21035
$638$	12.1069	+	1.94730i	0.479315	+	0.0770942i
$639$	−8.92732	+	15.4626i	−0.353159	+	0.611690i
$640$	3.41427	+	0.725725i	0.134961	+	0.0286868i
$641$	15.5457	+	11.2946i	0.614019	+	0.446111i	0.850827	−	0.525445i	$-0.176101\pi$
$641$	15.5457	+	11.2946i	0.614019	+	0.446111i	−0.236808	+	0.971556i	$0.576101\pi$
$642$	−1.60112	−	15.2336i	−0.0631911	−	0.601224i
$643$	−2.55872	+	7.87494i	−0.100906	+	0.310557i	−0.988748	−	0.149592i	$-0.952204\pi$
$643$	−2.55872	+	7.87494i	−0.100906	+	0.310557i	0.887842	+	0.460149i	$0.152204\pi$
$644$	−9.86935	+	30.3747i	−0.388907	+	1.19693i
$645$	46.1347	+	25.8091i	1.81655	+	1.01623i
$646$	21.0197	+	15.2717i	0.827008	+	0.600857i
$647$	−14.0843	−	43.3471i	−0.553712	−	1.70415i	−0.699320	−	0.714809i	$-0.746514\pi$
$647$	−14.0843	−	43.3471i	−0.553712	−	1.70415i	0.145607	−	0.989342i	$-0.453486\pi$
$648$	5.27722	−	9.14042i	0.207309	−	0.359070i
$649$	−5.07897	−	7.86212i	−0.199367	−	0.308615i
$650$	17.5221	−	30.3493i	0.687275	−	1.19040i
$651$	−48.2311	−	10.2518i	−1.89033	−	0.401801i
$652$	−1.93242	+	18.3858i	−0.0756794	+	0.720042i
$653$	0.768115	−	0.558068i	0.0300587	−	0.0218389i	−0.572654	−	0.819797i	$-0.694086\pi$
$653$	0.768115	−	0.558068i	0.0300587	−	0.0218389i	0.602713	+	0.797958i	$0.294086\pi$
$654$	−26.1332	+	5.55478i	−1.02189	+	0.217209i
$655$	0.826908	+	0.918375i	0.0323100	+	0.0358839i
$656$	0.499213	−	0.362700i	0.0194910	−	0.0141610i
$657$	24.3124	−	10.8246i	0.948518	−	0.422308i
$658$	3.60828	−	4.00740i	0.140666	−	0.156225i
$659$	0.563019	+	0.975178i	0.0219321	+	0.0379875i	0.876783	−	0.480886i	$-0.159685\pi$
$659$	0.563019	+	0.975178i	0.0219321	+	0.0379875i	−0.854851	+	0.518874i	$0.826352\pi$
$660$	−4.11931	−	26.4180i	−0.160344	−	1.02832i
$661$	−32.9680			−1.28231			−0.641153	−	0.767413i	$-0.721543\pi$
$661$	−32.9680			−1.28231			−0.641153	+	0.767413i	$0.721543\pi$
$662$	20.5642	−	22.8389i	0.799251	−	0.887658i
$663$	−3.81587	+	36.3056i	−0.148196	+	1.40999i
$664$	−1.06268	−	10.1107i	−0.0412401	−	0.392373i
$665$	−80.4137	−	89.3085i	−3.11831	−	3.46323i
$666$	6.32678	−	19.4718i	0.245158	−	0.754518i
$667$	22.2491	−	16.1649i	0.861487	−	0.625907i
$668$	15.6723	−	6.97775i	0.606379	−	0.269977i
$669$	14.5715	+	3.09727i	0.563367	+	0.119747i
$670$	19.6393	+	34.0162i	0.758731	+	1.31416i
$671$	−0.193484	−	1.24086i	−0.00746938	−	0.0479027i
$672$	9.91654			0.382539
$673$	−2.55502	+	2.83764i	−0.0984888	+	0.109383i	−0.790374	−	0.612625i	$-0.790114\pi$
$673$	−2.55502	+	2.83764i	−0.0984888	+	0.109383i	0.691885	+	0.722008i	$0.256780\pi$
$674$	1.49721	−	14.2450i	0.0576703	−	0.548696i
$675$	−10.0947	−	4.49445i	−0.388545	−	0.172991i
$676$	7.22426	+	8.02336i	0.277856	+	0.308591i
$677$	11.6106	−	35.7338i	0.446232	−	1.37336i	−0.434895	−	0.900481i	$-0.643215\pi$
$677$	11.6106	−	35.7338i	0.446232	−	1.37336i	0.881127	−	0.472879i	$-0.156785\pi$
$678$	1.28999	+	12.2734i	0.0495418	+	0.471359i
$679$	−8.30502	+	79.0170i	−0.318717	+	3.03239i
$680$	3.49504	+	10.7566i	0.134029	+	0.412498i
$681$	−20.3938	−	35.3230i	−0.781491	−	1.35358i
$682$	−16.4709	+	0.823617i	−0.630702	+	0.0315379i
$683$	−20.1953	+	34.9793i	−0.772753	+	1.33845i	0.163296	+	0.986577i	$0.447787\pi$
$683$	−20.1953	+	34.9793i	−0.772753	+	1.33845i	−0.936049	+	0.351870i	$0.885546\pi$
$684$	5.78329	+	17.7991i	0.221130	+	0.680567i
$685$	22.5013	−	10.0182i	0.859732	−	0.382777i
$686$	−15.4094	+	11.1956i	−0.588332	+	0.427448i
$687$	2.14418	−	6.59909i	0.0818054	−	0.251771i
$688$	−2.58577	+	6.02609i	−0.0985815	+	0.229743i
$689$	8.50237	−	6.17734i	0.323915	−	0.235338i
$690$	−48.5121	−	35.2461i	−1.84682	−	1.34180i
$691$	12.6212	+	2.68272i	0.480133	+	0.102055i	0.441619	−	0.897203i	$-0.354404\pi$
$691$	12.6212	+	2.68272i	0.480133	+	0.102055i	0.0385140	+	0.999258i	$0.487738\pi$
$692$	22.3724			0.850472
$693$	−11.8369	−	31.0585i	−0.449646	−	1.17981i
$694$	−1.22282	+	2.11799i	−0.0464177	+	0.0803977i
$695$	23.5448	−	26.1492i	0.893107	−	0.991895i
$696$	−6.90821	−	5.01910i	−0.261855	−	0.190249i
$697$	1.82656	+	0.813239i	0.0691861	+	0.0308036i
$698$	15.1058	+	16.7767i	0.571763	+	0.635008i
$699$	−12.8431	+	39.5269i	−0.485770	+	1.49505i
$700$	−3.22425	−	30.6767i	−0.121865	−	1.15947i
$701$	2.85268	−	27.1414i	0.107744	−	1.02512i	−0.798394	−	0.602136i	$-0.794317\pi$
$701$	2.85268	−	27.1414i	0.107744	−	1.02512i	0.906138	−	0.422982i	$-0.139017\pi$
$702$	5.02076	−	5.57612i	0.189496	−	0.210457i
$703$	−35.1692	−	60.9148i	−1.32643	−	2.29745i
$704$	3.20566	−	0.850724i	0.120818	−	0.0320629i
$705$	5.06228	+	8.76812i	0.190656	+	0.330227i
$706$	−0.376032	+	0.417626i	−0.0141522	+	0.0157176i
$707$	−52.0100	+	23.1564i	−1.95604	+	0.870885i
$708$	0.681301	+	6.48214i	0.0256049	+	0.243614i
$709$	−13.1533	+	40.4816i	−0.493982	+	1.52032i	0.324556	+	0.945866i	$0.394785\pi$
$709$	−13.1533	+	40.4816i	−0.493982	+	1.52032i	−0.818538	+	0.574453i	$0.805215\pi$
$710$	−8.25137	+	25.3951i	−0.309669	+	0.953062i
$711$	−0.140137	−	1.33332i	−0.00525556	−	0.0500033i
$712$	3.20518	−	1.42704i	0.120119	−	0.0534806i
$713$	−24.7484	+	27.4858i	−0.926833	+	1.02935i
$714$	16.0659	+	27.8270i	0.601253	+	1.04140i
$715$	3.09078	−	56.3890i	0.115589	−	2.10883i
$716$	12.4637	+	21.5878i	0.465791	+	0.806773i
$717$	17.4796	−	19.4131i	0.652789	−	0.724995i
$718$	1.06242	−	10.1083i	0.0396492	−	0.377237i
$719$	1.16089	+	11.0451i	0.0432939	+	0.411914i	0.994609	+	0.103694i	$0.0330664\pi$
$719$	1.16089	+	11.0451i	0.0432939	+	0.411914i	−0.951315	+	0.308219i	$0.900267\pi$
$720$	−2.51754	+	7.74819i	−0.0938231	+	0.288758i
$721$	−5.85312	−	6.50055i	−0.217982	−	0.242093i
$722$	41.3801	+	18.4236i	1.54001	+	0.685655i
$723$	−21.7881	−	15.8300i	−0.810307	−	0.588723i
$724$	4.51763	−	5.01734i	0.167896	−	0.186468i
$725$	−13.2804	+	23.0024i	−0.493223	+	0.854287i
$726$	−14.8340	−	20.6244i	−0.550541	−	0.765444i
$727$	24.9877			0.926742			0.463371	−	0.886164i	$-0.346640\pi$
$727$	24.9877			0.926742			0.463371	+	0.886164i	$0.346640\pi$
$728$	20.4878	+	4.35481i	0.759327	+	0.161400i
$729$	11.3074	+	8.21529i	0.418792	+	0.304270i
$730$	32.1995	−	23.3943i	1.19176	−	0.865861i
$731$	−21.0992	+	2.50698i	−0.780382	+	0.0927242i
$732$	−0.270240	+	0.831714i	−0.00998837	+	0.0307410i
$733$	26.8177	−	19.4842i	0.990535	−	0.719666i	0.0304967	−	0.999535i	$-0.490291\pi$
$733$	26.8177	−	19.4842i	0.990535	−	0.719666i	0.960038	+	0.279869i	$0.0902911\pi$
$734$	−4.48581	+	1.99721i	−0.165574	+	0.0737185i
$735$	−28.4890	−	87.6801i	−1.05083	−	3.23413i
$736$	3.71914	−	6.44174i	0.137089	−	0.237446i
$737$	31.2516	+	20.4017i	1.15117	+	0.751505i
$738$	0.720110	+	1.24727i	0.0265076	+	0.0459126i
$739$	1.22817	+	3.77992i	0.0451789	+	0.139046i	0.971101	−	0.238667i	$-0.0767104\pi$
$739$	1.22817	+	3.77992i	0.0451789	+	0.139046i	−0.925923	+	0.377713i	$0.876710\pi$
$740$	3.20058	−	30.4514i	0.117655	−	1.11942i
$741$	9.44300	+	89.8441i	0.346897	+	3.30051i
$742$	2.85852	−	8.79763i	0.104940	−	0.322971i
$743$	−7.02830	−	7.80572i	−0.257843	−	0.286364i	0.600299	−	0.799775i	$-0.295048\pi$
$743$	−7.02830	−	7.80572i	−0.257843	−	0.286364i	−0.858143	+	0.513411i	$0.828381\pi$
$744$	10.4911	+	4.67092i	0.384621	+	0.171244i
$745$	3.41466	−	32.4883i	0.125104	−	1.19028i
$746$	−18.3653	+	20.3967i	−0.672402	+	0.746778i
$747$	23.7284			0.868178
$748$	7.58078	+	7.61721i	0.277181	+	0.278513i
$749$	−14.2386	−	24.6619i	−0.520266	−	0.901127i
$750$	17.2210	+	3.66044i	0.628823	+	0.133660i
$751$	38.9237	−	17.3300i	1.42035	−	0.632379i	0.454324	−	0.890836i	$-0.349881\pi$
$751$	38.9237	−	17.3300i	1.42035	−	0.632379i	0.966023	+	0.258457i	$0.0832140\pi$
$752$	−1.01605	+	0.738201i	−0.0370514	+	0.0269194i
$753$	14.5821	−	44.8791i	0.531401	−	1.63549i
$754$	−12.0684	−	13.4033i	−0.439504	−	0.488119i
$755$	−2.66929	−	25.3966i	−0.0971454	−	0.924277i
$756$	0.690352	−	6.56826i	0.0251078	−	0.238885i
$757$	−9.54005	+	10.5953i	−0.346739	+	0.385093i	−0.891137	−	0.453734i	$-0.850091\pi$
$757$	−9.54005	+	10.5953i	−0.346739	+	0.385093i	0.544398	+	0.838827i	$0.316758\pi$
$758$	−0.00605278			−0.000219847
$759$	−56.2535	−	9.04795i	−2.04187	−	0.328420i
$760$	13.9944	+	24.2391i	0.507632	+	0.879244i
$761$	21.7662	−	24.1738i	0.789023	−	0.876299i	−0.205729	−	0.978609i	$-0.565957\pi$
$761$	21.7662	−	24.1738i	0.789023	−	0.876299i	0.994753	+	0.102310i	$0.0326234\pi$
$762$	−7.58154	+	3.37552i	−0.274650	+	0.122282i
$763$	−40.1840	+	29.1954i	−1.45476	+	1.05694i
$764$	−7.58995	−	8.42949i	−0.274595	−	0.304968i
$765$	−25.8211	+	5.48844i	−0.933563	+	0.198435i
$766$	−9.28751	+	6.74777i	−0.335572	+	0.243807i
$767$	−1.43903	+	13.6914i	−0.0519603	+	0.494369i
$768$	−2.25908	−	0.480181i	−0.0815174	−	0.0173271i
$769$	−8.90659	+	15.4267i	−0.321180	+	0.556300i	−0.980732	−	0.195359i	$-0.937413\pi$
$769$	−8.90659	+	15.4267i	−0.321180	+	0.556300i	0.659552	+	0.751659i	$0.270746\pi$
$770$	−26.9727	−	41.7531i	−0.972029	−	1.50468i
$771$	18.7005	−	32.3902i	0.673481	−	1.16650i
$772$	−4.93604	−	15.1916i	−0.177652	−	0.546757i
$773$	−9.88431	−	7.18137i	−0.355514	−	0.258296i	0.395665	−	0.918395i	$-0.370514\pi$
$773$	−9.88431	−	7.18137i	−0.355514	−	0.258296i	−0.751179	+	0.660099i	$0.770514\pi$
$774$	−13.3570	−	7.47230i	−0.480107	−	0.268586i
$775$	11.0384	−	33.9727i	0.396511	−	1.22033i
$776$	5.71814	−	17.5986i	0.205269	−	0.631754i
$777$	−9.09274	−	86.5116i	−0.326200	−	3.10359i
$778$	−19.1304	−	13.8991i	−0.685860	−	0.498306i
$779$	4.83978	+	1.02873i	0.173403	+	0.0368580i
$780$	−19.6628	+	34.0570i	−0.704043	+	1.21944i
$781$	3.90891	+	25.0686i	0.139872	+	0.897026i
$782$	24.1018			0.861878
$783$	−3.80535	+	4.22627i	−0.135992	+	0.151034i
$784$	10.4473	−	4.65145i	0.373119	−	0.166123i
$785$	−20.4202	+	14.8362i	−0.728830	+	0.529526i
$786$	−0.547130	−	0.607649i	−0.0195155	−	0.0216741i
$787$	41.6439	−	8.85169i	1.48445	−	0.315529i	0.606806	−	0.794850i	$-0.292450\pi$
$787$	41.6439	−	8.85169i	1.48445	−	0.315529i	0.877640	+	0.479321i	$0.159117\pi$
$788$	−17.5960	−	7.83422i	−0.626830	−	0.279083i
$789$	−0.849122	+	8.07885i	−0.0302295	+	0.287615i
$790$	−0.619576	−	1.90686i	−0.0220435	−	0.0678430i
$791$	11.4717	+	19.8696i	0.407888	+	0.706483i
$792$	1.19263	+	7.64857i	0.0423782	+	0.271780i
$793$	−0.923566	+	1.59966i	−0.0327968	+	0.0568057i
$794$	7.57899	+	1.61096i	0.268968	+	0.0571710i
$795$	14.0509	+	10.2086i	0.498333	+	0.362060i
$796$	2.23147	−	1.62126i	0.0790924	−	0.0574640i
$797$	−21.8416	−	24.2575i	−0.773668	−	0.859246i	0.219539	−	0.975604i	$-0.429545\pi$
$797$	−21.8416	−	24.2575i	−0.773668	−	0.859246i	−0.993207	+	0.116358i	$0.962878\pi$
$798$	53.2063	+	59.0916i	1.88348	+	2.09182i
$799$	−3.71760	−	1.65518i	−0.131519	−	0.0585561i
$800$	−0.750923	+	7.14456i	−0.0265491	+	0.252598i
$801$	2.53050	+	7.78807i	0.0894107	+	0.275178i
$802$	4.94328	+	8.56202i	0.174553	+	0.302335i
$803$	17.2496	−	33.6545i	0.608724	−	1.18764i
$804$	−12.9945	−	22.5071i	−0.458279	−	0.793763i
$805$	−109.045	−	23.1781i	−3.84332	−	0.816922i
$806$	19.6235	+	14.2573i	0.691209	+	0.502193i
$807$	0.657367	+	6.25443i	0.0231404	+	0.220166i
$808$	12.9696	−	2.75678i	0.456270	−	0.0969832i
$809$	−0.142901	+	0.439805i	−0.00502414	+	0.0154627i	−0.953537	−	0.301275i	$-0.902588\pi$
$809$	−0.142901	+	0.439805i	−0.00502414	+	0.0154627i	0.948513	+	0.316738i	$0.102588\pi$
$810$	33.6557	+	14.9845i	1.18254	+	0.526502i
$811$	17.5240	−	7.80217i	0.615350	−	0.273971i	−0.0752998	−	0.997161i	$-0.523991\pi$
$811$	17.5240	−	7.80217i	0.615350	−	0.273971i	0.690650	+	0.723190i	$0.257325\pi$
$812$	−15.5281	−	3.30061i	−0.544931	−	0.115829i
$813$	−64.9104			−2.27651
$814$	−10.3611	−	27.1861i	−0.363155	−	0.952871i
$815$	−64.5298			−2.26038
$816$	−2.31252	−	7.11720i	−0.0809543	−	0.249152i
$817$	−49.7826	+	16.9242i	−1.74167	+	0.592101i
$818$	−8.60358	+	6.25087i	−0.300817	+	0.218556i
$819$	−15.1068	+	46.4940i	−0.527875	+	1.62463i
$820$	1.44123	+	1.60065i	0.0503299	+	0.0558970i
$821$	−2.61520	+	1.90005i	−0.0912710	+	0.0663123i	−0.632485	−	0.774573i	$-0.717965\pi$
$821$	−2.61520	+	1.90005i	−0.0912710	+	0.0663123i	0.541214	+	0.840885i	$0.317965\pi$
$822$	−14.8882	+	6.62864i	−0.519285	+	0.231200i
$823$	3.64009	+	0.773726i	0.126886	+	0.0269704i	0.270917	−	0.962603i	$-0.412673\pi$
$823$	3.64009	+	0.773726i	0.126886	+	0.0269704i	−0.144031	+	0.989573i	$0.546007\pi$
$824$	1.01862	+	1.76431i	0.0354854	+	0.0614625i
$825$	53.1869	−	14.1148i	1.85173	−	0.491416i
$826$	6.05873	+	10.4940i	0.210810	+	0.365134i
$827$	−47.9165	−	10.1850i	−1.66622	−	0.354166i	−0.724165	−	0.689627i	$-0.757774\pi$
$827$	−47.9165	−	10.1850i	−1.66622	−	0.354166i	−0.942054	+	0.335461i	$0.891108\pi$
$828$	14.0453	+	10.2045i	0.488108	+	0.354631i
$829$	0.233276	+	2.21948i	0.00810203	+	0.0770856i	0.997826	−	0.0659071i	$-0.0209941\pi$
$829$	0.233276	+	2.21948i	0.00810203	+	0.0770856i	−0.989724	+	0.142993i	$0.954327\pi$
$830$	34.7110	−	7.37804i	1.20484	−	0.256096i
$831$	37.1822	−	7.90332i	1.28984	−	0.274163i
$832$	−4.45643	−	1.98413i	−0.154499	−	0.0687873i
$833$	29.9784	+	21.7806i	1.03869	+	0.754653i
$834$	−15.5786	+	17.3018i	−0.539443	+	0.599112i
$835$	29.9410	+	51.8592i	1.03615	+	1.79466i
$836$	22.2691	+	14.5377i	0.770192	+	0.502798i
$837$	3.82415	−	6.62362i	0.132182	−	0.228946i
$838$	11.7036	+	36.0199i	0.404293	+	1.24429i
$839$	−13.2498	−	9.62655i	−0.457434	−	0.332345i	0.335090	−	0.942186i	$-0.391233\pi$
$839$	−13.2498	−	9.62655i	−0.457434	−	0.332345i	−0.792524	+	0.609841i	$0.791233\pi$
$840$	3.61816	+	34.4245i	0.124838	+	1.18776i
$841$	−10.2579	−	11.3926i	−0.353721	−	0.392847i
$842$	−12.1458	+	2.58168i	−0.418573	+	0.0889704i
$843$	32.3979	+	14.4245i	1.11584	+	0.496805i
$844$	18.2692	+	13.2733i	0.628850	+	0.456887i
$845$	−25.2166	+	28.0059i	−0.867478	+	0.963432i
$846$	−1.46564	−	2.53856i	−0.0503897	−	0.0872774i
$847$	−40.7895	−	23.8113i	−1.40154	−	0.818165i
$848$	−1.07720	+	1.86576i	−0.0369912	+	0.0640706i
$849$	−6.67327	−	20.5382i	−0.229026	−	0.704870i
$850$	−21.2651	+	9.46783i	−0.729387	+	0.324744i
$851$	−59.6078	−	26.5391i	−2.04333	−	0.909749i
$852$	5.45958	−	16.8029i	0.187042	−	0.575657i
$853$	−6.23836	+	1.32600i	−0.213597	+	0.0454015i	−0.313467	−	0.949599i	$-0.601491\pi$
$853$	−6.23836	+	1.32600i	−0.213597	+	0.0454015i	0.0998701	+	0.995000i	$0.468157\pi$
$854$	0.169945	+	1.61692i	0.00581541	+	0.0553300i
$855$	−59.6783	+	26.5705i	−2.04095	+	0.908691i
$856$	2.04949	+	6.30767i	0.0700500	+	0.215592i
$857$	5.41352	−	9.37650i	0.184922	−	0.320295i	−0.758628	−	0.651524i	$-0.774130\pi$
$857$	5.41352	−	9.37650i	0.184922	−	0.320295i	0.943550	+	0.331229i	$0.107463\pi$
$858$	−2.04504	+	37.3102i	−0.0698164	+	1.27375i
$859$	21.7871			0.743367			0.371683	−	0.928360i	$-0.378781\pi$
$859$	21.7871			0.743367			0.371683	+	0.928360i	$0.378781\pi$
$860$	−21.8626	−	6.77761i	−0.745508	−	0.231115i
$861$	4.95047	+	3.59673i	0.168712	+	0.122576i
$862$	−11.2687	+	8.18717i	−0.383812	+	0.278856i
$863$	−22.2150	−	24.6723i	−0.756208	−	0.839854i	0.235023	−	0.971990i	$-0.424483\pi$
$863$	−22.2150	−	24.6723i	−0.756208	−	0.839854i	−0.991232	+	0.132135i	$0.957817\pi$
$864$	−0.475318	+	1.46288i	−0.0161707	+	0.0497682i
$865$	8.16284	+	77.6642i	0.277545	+	2.64066i
$866$	12.8146	−	5.70541i	0.435456	−	0.193878i
$867$	−10.0464	+	11.1577i	−0.341194	+	0.378934i
$868$	21.3499			0.724663
$869$	−1.34387	−	1.35033i	−0.0455876	−	0.0458067i
$870$	14.9029	−	25.8126i	0.505256	−	0.875129i
$871$	−16.9629	−	52.2065i	−0.574767	−	1.76895i
$872$	10.5680	−	4.70517i	0.357877	−	0.159337i
$873$	39.4551	+	17.5665i	1.33535	+	0.594537i
$874$	58.3404	−	12.4006i	1.97339	−	0.419458i
$875$	32.0159	−	6.80520i	1.08234	−	0.230058i
$876$	−21.3050	+	15.4790i	−0.719830	+	0.522987i
$877$	−2.31903	+	22.0641i	−0.0783080	+	0.745051i	0.882962	+	0.469444i	$0.155546\pi$
$877$	−2.31903	+	22.0641i	−0.0783080	+	0.745051i	−0.961270	+	0.275607i	$0.911121\pi$
$878$	−7.81221	+	8.67634i	−0.263649	+	0.292812i
$879$	5.20947	−	9.02307i	0.175711	−	0.304341i
$880$	4.12285	+	10.8178i	0.138981	+	0.364669i
$881$	−3.90457			−0.131548			−0.0657742	−	0.997835i	$-0.520952\pi$
$881$	−3.90457			−0.131548			−0.0657742	+	0.997835i	$0.520952\pi$
$882$	8.24817	+	25.3853i	0.277730	+	0.854766i
$883$	1.15667	−	0.514981i	0.0389249	−	0.0173305i	−0.387182	−	0.922003i	$-0.626551\pi$
$883$	1.15667	−	0.514981i	0.0389249	−	0.0173305i	0.426107	+	0.904673i	$0.359885\pi$
$884$	−1.65222	−	15.7198i	−0.0555701	−	0.528714i
$885$	−22.2537	+	4.73017i	−0.748050	+	0.159003i
$886$	−22.5070	+	4.78402i	−0.756138	+	0.160722i
$887$	39.6536	−	28.8100i	1.33144	−	0.967346i	0.331724	−	0.943376i	$-0.392370\pi$
$887$	39.6536	−	28.8100i	1.33144	−	0.967346i	0.999713	−	0.0239692i	$-0.00763037\pi$
$888$	−2.11768	+	20.1484i	−0.0710648	+	0.676136i
$889$	−10.3239	+	11.4659i	−0.346254	+	0.384554i
$890$	6.12331	+	10.6059i	0.205254	+	0.355510i
$891$	34.9615	−	1.74823i	1.17125	−	0.0585679i
$892$	−6.45021			−0.215969
$893$	−9.85038	−	2.09376i	−0.329630	−	0.0700651i
$894$	−2.25934	+	21.4961i	−0.0755635	+	0.718938i
$895$	−70.3928	+	51.1434i	−2.35297	+	1.70953i
$896$	−4.19989	+	0.892714i	−0.140308	+	0.0298235i
$897$	56.0746	+	62.2772i	1.87228	+	2.07938i
$898$	−1.21810	−	11.5894i	−0.0406484	−	0.386744i
$899$	−14.8731	−	10.8059i	−0.496046	−	0.360398i
$900$	−16.4008	−	3.48610i	−0.546694	−	0.116203i
$901$	−6.98075			−0.232563
$902$	1.90887	+	0.738000i	0.0635583	+	0.0245727i
$903$	−64.7570	−	5.92064i	−2.15498	−	0.197026i
$904$	−1.65123	−	5.08197i	−0.0549192	−	0.169024i
$905$	19.0656	+	13.8520i	0.633762	+	0.460455i
$906$	1.76615	+	16.8038i	0.0586766	+	0.558270i
$907$	−3.94319	+	12.1359i	−0.130932	+	0.402966i	−0.994935	−	0.100520i	$-0.967949\pi$
$907$	−3.94319	+	12.1359i	−0.130932	+	0.402966i	0.864004	+	0.503486i	$0.167949\pi$
$908$	11.8171	+	13.1243i	0.392165	+	0.435544i
$909$	3.23488	+	30.7778i	0.107294	+	1.02084i
$910$	−7.64219	+	72.7106i	−0.253336	+	2.41033i
$911$	11.7264	+	36.0901i	0.388512	+	1.19572i	0.933900	+	0.357534i	$0.116382\pi$
$911$	11.7264	+	36.0901i	0.388512	+	1.19572i	−0.545388	+	0.838184i	$0.683618\pi$
$912$	−9.25953	−	16.0380i	−0.306614	−	0.531070i
$913$	26.2548	−	21.1567i	0.868907	−	0.700185i
$914$	−16.2624			−0.537914
$915$	−2.98583	−	0.634658i	−0.0987086	−	0.0209812i
$916$	−0.314041	+	2.98790i	−0.0103762	+	0.0987229i
$917$	−1.38873	−	0.618301i	−0.0458598	−	0.0204181i
$918$	−4.87509	+	1.03623i	−0.160902	+	0.0342008i
$919$	6.40222	−	19.7040i	0.211190	−	0.649975i	−0.788213	−	0.615403i	$-0.788993\pi$
$919$	6.40222	−	19.7040i	0.211190	−	0.649975i	0.999402	−	0.0345718i	$-0.0110067\pi$
$920$	23.7190	+	10.5604i	0.781992	+	0.348165i
$921$	1.23456	−	11.7460i	0.0406800	−	0.387044i
$922$	−21.2122	−	4.50880i	−0.698587	−	0.148489i
$923$	18.6585	−	32.3175i	0.614152	−	1.06374i
$924$	17.8467	+	27.6263i	0.587113	+	0.908837i
$925$	63.0175			2.07200
$926$	−41.8164	−	8.88835i	−1.37417	−	0.292089i
$927$	−4.34384	+	1.93400i	−0.142670	+	0.0635210i
$928$	3.37762	+	1.50382i	0.110876	+	0.0493652i
$929$	−51.0307	+	10.8469i	−1.67426	+	0.355876i	−0.944674	−	0.328010i	$-0.893622\pi$
$929$	−51.0307	+	10.8469i	−1.67426	+	0.355876i	−0.729589	+	0.683886i	$0.760289\pi$
$930$	−12.3870	+	38.1231i	−0.406184	+	1.25011i
$931$	83.7717	+	37.2976i	2.74551	+	1.22238i
$932$	1.88103	−	17.8968i	0.0616150	−	0.586228i
$933$	−17.5428	+	19.4833i	−0.574327	+	0.637854i
$934$	5.38289	−	9.32345i	0.176134	−	0.305072i
$935$	−23.6766	+	29.0953i	−0.774309	+	0.951519i
$936$	5.69281	−	9.86024i	0.186075	−	0.322292i
$937$	7.75724	−	8.61529i	0.253418	−	0.281449i	−0.602990	−	0.797749i	$-0.706024\pi$
$937$	7.75724	−	8.61529i	0.253418	−	0.281449i	0.856408	+	0.516299i	$0.172691\pi$
$938$	−39.0889	−	28.3997i	−1.27630	−	0.927284i
$939$	1.20310	+	0.535655i	0.0392617	+	0.0174804i
$940$	−2.93333	−	3.25779i	−0.0956746	−	0.106257i
$941$	−17.7529	−	19.7166i	−0.578730	−	0.642744i	0.380698	−	0.924699i	$-0.375684\pi$
$941$	−17.7529	−	19.7166i	−0.578730	−	0.642744i	−0.959428	+	0.281955i	$0.909017\pi$
$942$	13.5112	−	9.81646i	0.440219	−	0.319838i
$943$	4.19307	−	1.86687i	0.136545	−	0.0607937i
$944$	−0.872088	−	2.68401i	−0.0283840	−	0.0873571i
$945$	23.0531			0.749917
$946$	−21.4415	+	3.64147i	−0.697125	+	0.118394i
$947$	−1.37482			−0.0446757			−0.0223378	−	0.999750i	$-0.507111\pi$
$947$	−1.37482			−0.0446757			−0.0223378	+	0.999750i	$0.507111\pi$
$948$	0.409947	+	1.26169i	0.0133145	+	0.0409777i
$949$	−50.8141	+	22.6239i	−1.64950	+	0.734403i
$950$	−46.6027	+	33.8588i	−1.51199	+	1.09853i
$951$	−12.7479	−	14.1580i	−0.413380	−	0.459104i
$952$	−9.30938	−	10.3391i	−0.301719	−	0.335093i
$953$	29.7510	+	13.2460i	0.963729	+	0.429080i	0.827418	−	0.561586i	$-0.189809\pi$
$953$	29.7510	+	13.2460i	0.963729	+	0.429080i	0.136311	+	0.990666i	$0.456475\pi$
$954$	−4.06803	−	2.95560i	−0.131707	−	0.0956910i
$955$	26.4931	−	29.4235i	0.857295	−	0.952123i
$956$	−5.65542	+	9.79548i	−0.182909	+	0.316808i
$957$	1.54998	−	28.2782i	0.0501037	−	0.914106i
$958$	16.5801	−	28.7175i	0.535677	−	0.927820i
$959$	−20.2735	+	22.5160i	−0.654667	+	0.727081i
$960$	0.842664	−	8.01741i	0.0271969	−	0.258761i
$961$	−5.73308	−	2.55253i	−0.184938	−	0.0823397i
$962$	−13.2233	+	40.6970i	−0.426335	+	1.31213i
$963$	−15.1415	+	3.21842i	−0.487927	+	0.103712i
$964$	10.6528	+	4.74294i	0.343104	+	0.152760i
$965$	50.9354	−	22.6779i	1.63967	−	0.730028i
$966$	72.1501	+	15.3360i	2.32139	+	0.493427i
$967$	59.2896			1.90663			0.953313	−	0.301984i	$-0.0976491\pi$
$967$	59.2896			1.90663			0.953313	+	0.301984i	$0.0976491\pi$
$968$	8.13921	+	7.39954i	0.261604	+	0.237830i
$969$	30.0030	−	51.9668i	0.963836	−	1.66941i
$970$	63.1786	+	13.4290i	2.02854	+	0.431180i
$971$	−0.191059	+	1.81781i	−0.00613138	+	0.0583362i	−0.997160	−	0.0753154i	$-0.976004\pi$
$971$	−0.191059	+	1.81781i	−0.00613138	+	0.0583362i	0.991028	+	0.133652i	$0.0426703\pi$
$972$	−18.0530	−	8.03772i	−0.579051	−	0.257810i
$973$	−13.3754	+	41.1653i	−0.428796	+	1.31970i
$974$	−5.19696	+	1.10465i	−0.166521	+	0.0353952i
$975$	−73.9391	−	32.9198i	−2.36795	−	1.05428i
$976$	0.0395800	−	0.376579i	0.00126693	−	0.0120540i
$977$	44.8567	+	9.53459i	1.43509	+	0.305038i	0.858845	−	0.512236i	$-0.171183\pi$
$977$	44.8567	+	9.53459i	1.43509	+	0.305038i	0.576248	+	0.817275i	$0.304516\pi$
$978$	42.6966			1.36529
$979$	9.74390	+	6.36102i	0.311416	+	0.203299i
$980$	19.9590	+	34.5700i	0.637566	+	1.10430i
$981$	8.34343	+	25.6784i	0.266385	+	0.819849i
$982$	0.576939	−	5.48920i	0.0184109	−	0.175168i
$983$	−1.30880	−	12.4524i	−0.0417442	−	0.397170i	−0.995366	−	0.0961614i	$-0.969344\pi$
$983$	−1.30880	−	12.4524i	−0.0417442	−	0.397170i	0.953622	−	0.301008i	$-0.0973232\pi$
$984$	−0.953599	−	1.05908i	−0.0303996	−	0.0337622i
$985$	20.7758	−	63.9414i	0.661973	−	2.03734i
$986$	1.25225	+	11.9144i	0.0398798	+	0.379431i
$987$	−10.0757	−	7.32040i	−0.320712	−	0.233011i
$988$	−12.0874	−	37.2010i	−0.384550	−	1.18352i
$989$	−28.1328	+	39.8454i	−0.894570	+	1.26701i
$990$	−26.1163	+	6.93079i	−0.830030	+	0.220275i
$991$	−14.1658			−0.449991			−0.224995	−	0.974360i	$-0.572237\pi$
$991$	−14.1658			−0.449991			−0.224995	+	0.974360i	$0.572237\pi$
$992$	−4.86370	−	1.03381i	−0.154423	−	0.0328236i
$993$	−57.4229	−	41.7202i	−1.82226	−	1.32395i
$994$	−3.43336	−	32.6662i	−0.108899	−	1.03611i
$995$	6.44225	+	7.15485i	0.204233	+	0.226824i
$996$	−22.9668	+	4.88173i	−0.727730	+	0.154684i
$997$	28.2265	−	20.5078i	0.893943	−	0.649488i	−0.0429601	−	0.999077i	$-0.513679\pi$
$997$	28.2265	−	20.5078i	0.893943	−	0.649488i	0.936903	+	0.349589i	$0.113679\pi$
$998$	2.18691	−	20.8070i	0.0692253	−	0.658635i
$999$	13.1980	+	2.80531i	0.417565	+	0.0887562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.q.c.49.19	✓	176
11.9	even	5	inner	946.2.q.c.823.4	yes	176
43.36	even	3	inner	946.2.q.c.423.4	yes	176
473.251	even	15	inner	946.2.q.c.251.19	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.q.c.49.19	✓	176	1.1	even	1	trivial
946.2.q.c.251.19	yes	176	473.251	even	15	inner
946.2.q.c.423.4	yes	176	43.36	even	3	inner
946.2.q.c.823.4	yes	176	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.10987 - 0.939377i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.33563 - 2.59398i) q^{5} +(1.54539 + 1.71633i) q^{6} +(3.92251 + 1.74641i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.56175 - 1.73450i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(2.10987 - 0.939377i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-2.33563 - 2.59398i) q^{5} +(1.54539 + 1.71633i) q^{6} +(3.92251 + 1.74641i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(1.56175 - 1.73450i) q^{9} +(1.74527 - 3.02290i) q^{10} +(0.181517 - 3.31165i) q^{11} +(-1.15477 + 2.00012i) q^{12} +(-3.26413 + 3.62518i) q^{13} +(-0.448816 + 4.27020i) q^{14} +(-7.36461 - 3.27894i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.16943 - 0.673682i) q^{17} +(2.13221 + 0.949322i) q^{18} +(7.32525 - 3.26141i) q^{19} +(3.41427 + 0.725725i) q^{20} +9.91654 q^{21} +(3.20566 - 0.850724i) q^{22} +(3.71914 - 6.44174i) q^{23} +(-2.25908 - 0.480181i) q^{24} +(-0.750923 + 7.14456i) q^{25} +(-4.45643 - 1.98413i) q^{26} +(-0.475318 + 1.46288i) q^{27} +(-4.19989 + 0.892714i) q^{28} +(3.37762 + 1.50382i) q^{29} +(0.842664 - 8.01741i) q^{30} +(-4.86370 - 1.03381i) q^{31} +1.00000 q^{32} +(-2.72791 - 7.15769i) q^{33} +(1.62012 + 2.80612i) q^{34} +(-4.63137 - 14.2539i) q^{35} +(-0.243969 + 2.32121i) q^{36} +(-0.916927 - 8.72398i) q^{37} +(5.36541 + 5.95890i) q^{38} +(-3.48149 + 10.7149i) q^{39} +(0.364861 + 3.47142i) q^{40} +(0.499213 + 0.362700i) q^{41} +(3.06438 + 9.43119i) q^{42} +(-6.53020 - 0.597047i) q^{43} +(1.79969 + 2.78588i) q^{44} -8.14693 q^{45} +(7.27574 + 1.54651i) q^{46} +(-1.01605 - 0.738201i) q^{47} +(-0.241413 - 2.29689i) q^{48} +(7.65219 + 8.49862i) q^{49} +(-7.02692 + 1.49362i) q^{50} +(6.05425 - 4.39867i) q^{51} +(0.509907 - 4.85144i) q^{52} +(-2.10732 - 0.447925i) q^{53} -1.53816 q^{54} +(-9.01433 + 7.26395i) q^{55} +(-2.14686 - 3.71847i) q^{56} +(12.3917 - 13.7623i) q^{57} +(-0.386470 + 3.67702i) q^{58} +(2.28316 - 1.65881i) q^{59} +(7.88541 - 1.67610i) q^{60} +(0.370379 - 0.0787264i) q^{61} +(-0.519753 - 4.94512i) q^{62} +(9.15512 - 4.07612i) q^{63} +(0.309017 + 0.951057i) q^{64} +17.0275 q^{65} +(5.96439 - 4.80624i) q^{66} +(-5.62642 + 9.74524i) q^{67} +(-2.16814 + 2.40796i) q^{68} +(1.79570 - 17.0849i) q^{69} +(12.1251 - 8.80939i) q^{70} +(-7.48264 + 1.59048i) q^{71} +(-2.28299 + 0.485265i) q^{72} +(10.4166 + 4.63779i) q^{73} +(8.01365 - 3.56791i) q^{74} +(5.12708 + 15.7795i) q^{75} +(-4.00924 + 6.94421i) q^{76} +(6.49552 - 12.6730i) q^{77} -11.2663 q^{78} +(0.384353 - 0.426867i) q^{79} +(-3.18877 + 1.41973i) q^{80} +(1.10324 + 10.4966i) q^{81} +(-0.190683 + 0.586861i) q^{82} +(6.80268 + 7.55514i) q^{83} +(-8.02265 + 5.82879i) q^{84} +(-9.15013 - 6.64796i) q^{85} +(-1.45012 - 6.39509i) q^{86} +8.53901 q^{87} +(-2.09339 + 2.57249i) q^{88} +(-1.75426 + 3.03846i) q^{89} +(-2.51754 - 7.74819i) q^{90} +(-19.1346 + 8.51929i) q^{91} +(0.777512 + 7.39754i) q^{92} +(-11.2329 + 2.38763i) q^{93} +(0.388095 - 1.19443i) q^{94} +(-25.5691 - 11.3841i) q^{95} +(2.10987 - 0.939377i) q^{96} +(5.71814 + 17.5986i) q^{97} +(-5.71801 + 9.90388i) q^{98} +(-5.46057 - 5.48681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 44 q^{2} + 7 q^{3} - 44 q^{4} + 9 q^{5} - 8 q^{6} + 8 q^{7} - 44 q^{8} + 33 q^{9}+O(q^{10}) \) 176 * q - 44 * q^2 + 7 * q^3 - 44 * q^4 + 9 * q^5 - 8 * q^6 + 8 * q^7 - 44 * q^8 + 33 * q^9	\( 176 q - 44 q^{2} + 7 q^{3} - 44 q^{4} + 9 q^{5} - 8 q^{6} + 8 q^{7} - 44 q^{8} + 33 q^{9} - 6 q^{10} + 16 q^{11} + 2 q^{12} + 16 q^{13} + 8 q^{14} + 4 q^{15} - 44 q^{16} + 5 q^{17} + 18 q^{18} + 10 q^{19} + 9 q^{20} - 36 q^{21} + 26 q^{22} - 40 q^{23} - 8 q^{24} + 45 q^{25} - 9 q^{26} - 32 q^{27} - 7 q^{28} + 2 q^{29} + 4 q^{30} + 18 q^{31} + 176 q^{32} - 36 q^{33} - 86 q^{35} + 18 q^{36} - 5 q^{37} - 5 q^{38} - 36 q^{39} - 6 q^{40} + 22 q^{41} + 4 q^{42} - 36 q^{43} - 34 q^{44} - 32 q^{45} + 5 q^{46} - 32 q^{47} + 7 q^{48} + 62 q^{49} + 10 q^{50} - 54 q^{51} - 9 q^{52} + 23 q^{53} - 52 q^{54} - 70 q^{55} - 2 q^{56} + 10 q^{57} + 2 q^{58} - 76 q^{59} + 9 q^{60} - 12 q^{61} - 2 q^{62} - 46 q^{63} - 44 q^{64} - 20 q^{65} - 6 q^{66} - 22 q^{67} + 5 q^{68} - 101 q^{69} + 84 q^{70} - 8 q^{71} + 33 q^{72} + 53 q^{73} - 5 q^{74} + 76 q^{75} - 10 q^{76} + 28 q^{77} + 64 q^{78} + 17 q^{79} - 6 q^{80} + 73 q^{81} - 38 q^{82} + 10 q^{83} + 14 q^{84} - 24 q^{85} + 9 q^{86} - 12 q^{87} + 6 q^{88} - 64 q^{89} - 12 q^{90} - 23 q^{91} + 15 q^{92} + 100 q^{93} - 2 q^{94} + 27 q^{95} + 7 q^{96} + 60 q^{97} - 118 q^{98} - 25 q^{99}+O(q^{100}) \) 176 * q - 44 * q^2 + 7 * q^3 - 44 * q^4 + 9 * q^5 - 8 * q^6 + 8 * q^7 - 44 * q^8 + 33 * q^9 - 6 * q^10 + 16 * q^11 + 2 * q^12 + 16 * q^13 + 8 * q^14 + 4 * q^15 - 44 * q^16 + 5 * q^17 + 18 * q^18 + 10 * q^19 + 9 * q^20 - 36 * q^21 + 26 * q^22 - 40 * q^23 - 8 * q^24 + 45 * q^25 - 9 * q^26 - 32 * q^27 - 7 * q^28 + 2 * q^29 + 4 * q^30 + 18 * q^31 + 176 * q^32 - 36 * q^33 - 86 * q^35 + 18 * q^36 - 5 * q^37 - 5 * q^38 - 36 * q^39 - 6 * q^40 + 22 * q^41 + 4 * q^42 - 36 * q^43 - 34 * q^44 - 32 * q^45 + 5 * q^46 - 32 * q^47 + 7 * q^48 + 62 * q^49 + 10 * q^50 - 54 * q^51 - 9 * q^52 + 23 * q^53 - 52 * q^54 - 70 * q^55 - 2 * q^56 + 10 * q^57 + 2 * q^58 - 76 * q^59 + 9 * q^60 - 12 * q^61 - 2 * q^62 - 46 * q^63 - 44 * q^64 - 20 * q^65 - 6 * q^66 - 22 * q^67 + 5 * q^68 - 101 * q^69 + 84 * q^70 - 8 * q^71 + 33 * q^72 + 53 * q^73 - 5 * q^74 + 76 * q^75 - 10 * q^76 + 28 * q^77 + 64 * q^78 + 17 * q^79 - 6 * q^80 + 73 * q^81 - 38 * q^82 + 10 * q^83 + 14 * q^84 - 24 * q^85 + 9 * q^86 - 12 * q^87 + 6 * q^88 - 64 * q^89 - 12 * q^90 - 23 * q^91 + 15 * q^92 + 100 * q^93 - 2 * q^94 + 27 * q^95 + 7 * q^96 + 60 * q^97 - 118 * q^98 - 25 * q^99

Introduction

L-functions

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