LMFDB - Embedded newform 961.2.g.o.846.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			846.2
Root			$-1.29195 + 0.575212i$ of defining polynomial
Character	$\chi$	$=$	961.846
Dual form			961.2.g.o.844.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.127999 - 0.393941i) q^{2} +(-0.405162 - 0.0861198i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.378403 + 0.168476i) q^{7} +(1.28293 - 0.932102i) q^{8} +(-2.58390 - 1.15042i) q^{9} +O(q^{10})$	\(q+(0.127999 - 0.393941i) q^{2} +(-0.405162 - 0.0861198i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.378403 + 0.168476i) q^{7} +(1.28293 - 0.932102i) q^{8} +(-2.58390 - 1.15042i) q^{9} +(-0.405162 + 0.0861198i) q^{10} +(-0.338948 + 3.22488i) q^{11} +(-0.506772 - 0.562828i) q^{12} +(-2.56172 + 2.84508i) q^{13} +(0.0179342 + 0.170633i) q^{14} +(0.127999 + 0.393941i) q^{15} +(0.927051 + 2.85317i) q^{16} +(0.609237 + 5.79650i) q^{17} +(-0.783935 + 0.870648i) q^{18} +(2.95369 + 3.28040i) q^{19} +(0.191123 - 1.81841i) q^{20} +(0.167824 - 0.0356720i) q^{21} +(1.22702 + 0.546307i) q^{22} +(3.23607 - 2.35114i) q^{23} +(-0.600066 + 0.267167i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(1.95314 + 1.41904i) q^{27} +(-0.740809 - 0.157464i) q^{28} +(-2.11010 + 6.49422i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(0.415055 - 1.27741i) q^{33} +(2.36146 + 0.501943i) q^{34} +(0.335106 + 0.243469i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.67035 - 0.743688i) q^{38} +(1.28293 - 0.932102i) q^{39} +(-1.44869 - 0.644997i) q^{40} +(7.32171 - 1.55628i) q^{41} +(0.00742861 - 0.0706785i) q^{42} +(-7.29319 - 8.09990i) q^{43} +(-3.96723 + 4.40606i) q^{44} +(0.295651 + 2.81293i) q^{45} +(-0.511996 - 1.57576i) q^{46} +(2.98413 + 9.18421i) q^{47} +(-0.129891 - 1.23583i) q^{48} +(-4.56911 + 5.07451i) q^{49} +(-1.10865 - 1.23128i) q^{50} +(0.252354 - 2.40099i) q^{51} +(-6.84703 + 1.45538i) q^{52} +(5.32453 + 2.37063i) q^{53} +(0.809017 - 0.587785i) q^{54} +(2.96230 - 1.31890i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(2.28825 + 1.66251i) q^{58} +(-3.98211 - 0.846423i) q^{59} +(-0.234037 + 0.720292i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(-1.28909 + 3.96740i) q^{64} +(3.74477 + 0.795975i) q^{65} +(-0.450096 - 0.327014i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(-1.51361 + 0.673903i) q^{69} +(0.138805 - 0.100848i) q^{70} +(0.0649237 + 0.0289059i) q^{71} +(-4.38727 + 0.932542i) q^{72} +(0.191123 - 1.81841i) q^{73} +(0.277163 + 0.307821i) q^{74} +(-1.10865 + 1.23128i) q^{75} +(0.843656 + 8.02685i) q^{76} +(-0.415055 - 1.27741i) q^{77} +(-0.202979 - 0.624706i) q^{78} +(0.706336 + 6.72034i) q^{79} +(2.00739 - 2.22943i) q^{80} +(5.00863 + 5.56265i) q^{81} +(0.324091 - 3.08352i) q^{82} +(9.85099 - 2.09389i) q^{83} +(0.286587 + 0.127597i) q^{84} +(4.71530 - 3.42586i) q^{85} +(-4.12440 + 1.83630i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(-3.62867 - 2.63638i) q^{89} +(1.14597 + 0.243584i) q^{90} +(0.490035 - 1.50817i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(1.36407 - 4.19817i) q^{95} +(-1.78847 - 0.380151i) q^{96} +(-4.18389 - 3.03977i) q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21} + 14 q^{22} + 16 q^{23} + 10 q^{24} + 32 q^{25} + 24 q^{26} + 4 q^{27} + 10 q^{28} + 16 q^{29} + 48 q^{30} + 48 q^{32} - 28 q^{33} - 2 q^{34} - 4 q^{35} - 64 q^{36} - 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} + 14 q^{42} - 2 q^{43} - 26 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} + 14 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} + 40 q^{56} + 8 q^{57} - 6 q^{59} + 20 q^{60} + 64 q^{63} + 28 q^{64} - 2 q^{65} + 60 q^{66} + 8 q^{67} - 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} + 2 q^{73} - 2 q^{74} + 8 q^{75} - 2 q^{76} + 28 q^{77} - 20 q^{78} - 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} - 6 q^{83} - 22 q^{84} + 12 q^{85} - 26 q^{86} - 72 q^{88} + 16 q^{89} - 8 q^{90} - 12 q^{91} - 64 q^{92} + 64 q^{94} - 12 q^{95} - 2 q^{96} - 32 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.127999	−	0.393941i	0.0905090	−	0.278558i	−0.895548	−	0.444964i	$-0.853216\pi$
$2$	0.127999	−	0.393941i	0.0905090	−	0.278558i	0.986057	+	0.166406i	$0.0532163\pi$
$3$	−0.405162	−	0.0861198i	−0.233920	−	0.0497213i	0.0894598	−	0.995990i	$-0.471486\pi$
$3$	−0.405162	−	0.0861198i	−0.233920	−	0.0497213i	−0.323380	+	0.946269i	$0.604819\pi$
$4$	1.47923	+	1.07472i	0.739614	+	0.537361i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−0.0857864	+	0.148586i	−0.0350222	+	0.0606602i
$7$	−0.378403	+	0.168476i	−0.143023	+	0.0636779i	−0.477000	−	0.878903i	$-0.658276\pi$
$7$	−0.378403	+	0.168476i	−0.143023	+	0.0636779i	0.333977	+	0.942581i	$0.391609\pi$
$8$	1.28293	−	0.932102i	0.453584	−	0.329548i
$9$	−2.58390	−	1.15042i	−0.861299	−	0.383475i
$10$	−0.405162	+	0.0861198i	−0.128123	+	0.0272335i
$11$	−0.338948	+	3.22488i	−0.102197	+	0.972337i	0.816493	+	0.577356i	$0.195916\pi$
$11$	−0.338948	+	3.22488i	−0.102197	+	0.972337i	−0.918689	+	0.394981i	$0.870751\pi$
$12$	−0.506772	−	0.562828i	−0.146293	−	0.162474i
$13$	−2.56172	+	2.84508i	−0.710493	+	0.789082i	−0.985009	−	0.172500i	$-0.944815\pi$
$13$	−2.56172	+	2.84508i	−0.710493	+	0.789082i	0.274517	+	0.961582i	$0.411482\pi$
$14$	0.0179342	+	0.170633i	0.00479313	+	0.0456036i
$15$	0.127999	+	0.393941i	0.0330492	+	0.101715i
$16$	0.927051	+	2.85317i	0.231763	+	0.713292i
$17$	0.609237	+	5.79650i	0.147762	+	1.40586i	0.777418	+	0.628984i	$0.216529\pi$
$17$	0.609237	+	5.79650i	0.147762	+	1.40586i	−0.629657	+	0.776873i	$0.716804\pi$
$18$	−0.783935	+	0.870648i	−0.184775	+	0.205214i
$19$	2.95369	+	3.28040i	0.677622	+	0.752575i	0.979648	−	0.200724i	$-0.0643296\pi$
$19$	2.95369	+	3.28040i	0.677622	+	0.752575i	−0.302026	+	0.953300i	$0.597663\pi$
$20$	0.191123	−	1.81841i	0.0427363	−	0.406609i
$21$	0.167824	−	0.0356720i	0.0366221	−	0.00778427i
$22$	1.22702	+	0.546307i	0.261603	+	0.116473i
$23$	3.23607	−	2.35114i	0.674767	−	0.490247i	−0.196851	−	0.980433i	$-0.563071\pi$
$23$	3.23607	−	2.35114i	0.674767	−	0.490247i	0.871617	+	0.490187i	$0.163071\pi$
$24$	−0.600066	+	0.267167i	−0.122488	+	0.0545352i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	0.792893	+	1.37333i	0.155499	+	0.269332i
$27$	1.95314	+	1.41904i	0.375882	+	0.273094i
$28$	−0.740809	−	0.157464i	−0.140000	−	0.0297579i
$29$	−2.11010	+	6.49422i	−0.391836	+	1.20595i	0.539563	+	0.841945i	$0.318590\pi$
$29$	−2.11010	+	6.49422i	−0.391836	+	1.20595i	−0.931399	+	0.364001i	$0.881410\pi$
$30$	0.171573			0.0313248
$31$		0			0
$31$		0			0
$32$	4.41421			0.780330
$33$	0.415055	−	1.27741i	0.0722518	−	0.222368i
$34$	2.36146	+	0.501943i	0.404987	+	0.0860826i
$35$	0.335106	+	0.243469i	0.0566432	+	0.0411537i
$36$	−2.58579	−	4.47871i	−0.430964	−	0.746452i
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	1.67035	−	0.743688i	0.270967	−	0.120642i
$39$	1.28293	−	0.932102i	0.205433	−	0.149256i
$40$	−1.44869	−	0.644997i	−0.229058	−	0.101983i
$41$	7.32171	−	1.55628i	1.14346	−	0.243050i	0.403032	−	0.915186i	$-0.367956\pi$
$41$	7.32171	−	1.55628i	1.14346	−	0.243050i	0.740427	+	0.672136i	$0.234623\pi$
$42$	0.00742861	−	0.0706785i	0.00114626	−	0.0109059i
$43$	−7.29319	−	8.09990i	−1.11220	−	1.23522i	−0.969404	−	0.245472i	$-0.921057\pi$
$43$	−7.29319	−	8.09990i	−1.11220	−	1.23522i	−0.142797	−	0.989752i	$-0.545609\pi$
$44$	−3.96723	+	4.40606i	−0.598082	+	0.664238i
$45$	0.295651	+	2.81293i	0.0440731	+	0.419327i
$46$	−0.511996	−	1.57576i	−0.0754897	−	0.232333i
$47$	2.98413	+	9.18421i	0.435280	+	1.33966i	0.892799	+	0.450455i	$0.148738\pi$
$47$	2.98413	+	9.18421i	0.435280	+	1.33966i	−0.457519	+	0.889200i	$0.651262\pi$
$48$	−0.129891	−	1.23583i	−0.0187482	−	0.178377i
$49$	−4.56911	+	5.07451i	−0.652730	+	0.724930i
$50$	−1.10865	−	1.23128i	−0.156787	−	0.174130i
$51$	0.252354	−	2.40099i	0.0353366	−	0.336206i
$52$	−6.84703	+	1.45538i	−0.949513	+	0.201825i
$53$	5.32453	+	2.37063i	0.731381	+	0.325632i	0.738418	−	0.674343i	$-0.235573\pi$
$53$	5.32453	+	2.37063i	0.731381	+	0.325632i	−0.00703693	+	0.999975i	$0.502240\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	2.96230	−	1.31890i	0.399436	−	0.177841i
$56$	−0.328427	+	0.568852i	−0.0438879	+	0.0760161i
$57$	−0.914214	−	1.58346i	−0.121091	−	0.209735i
$58$	2.28825	+	1.66251i	0.300461	+	0.218298i
$59$	−3.98211	−	0.846423i	−0.518426	−	0.110195i	−0.0587347	−	0.998274i	$-0.518707\pi$
$59$	−3.98211	−	0.846423i	−0.518426	−	0.110195i	−0.459691	+	0.888079i	$0.652040\pi$
$60$	−0.234037	+	0.720292i	−0.0302140	+	0.0929892i
$61$	−2.82843			−0.362143			−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843			−0.362143			−0.181071	+	0.983470i	$0.557957\pi$
$62$		0			0
$63$	1.17157			0.147604
$64$	−1.28909	+	3.96740i	−0.161136	+	0.495925i
$65$	3.74477	+	0.795975i	0.464481	+	0.0987285i
$66$	−0.450096	−	0.327014i	−0.0554030	−	0.0402526i
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$67$	−1.62132	−	2.80821i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$68$	−5.32843	+	9.22911i	−0.646167	+	1.11919i
$69$	−1.51361	+	0.673903i	−0.182217	+	0.0811284i
$70$	0.138805	−	0.100848i	0.0165904	−	0.0120536i
$71$	0.0649237	+	0.0289059i	0.00770502	+	0.00343050i	0.410586	−	0.911822i	$-0.365324\pi$
$71$	0.0649237	+	0.0289059i	0.00770502	+	0.00343050i	−0.402881	+	0.915253i	$0.631991\pi$
$72$	−4.38727	+	0.932542i	−0.517044	+	0.109901i
$73$	0.191123	−	1.81841i	0.0223692	−	0.212829i	−0.977628	−	0.210343i	$-0.932542\pi$
$73$	0.191123	−	1.81841i	0.0223692	−	0.212829i	0.999997	−	0.00248608i	$-0.000791346\pi$
$74$	0.277163	+	0.307821i	0.0322195	+	0.0357834i
$75$	−1.10865	+	1.23128i	−0.128016	+	0.142176i
$76$	0.843656	+	8.02685i	0.0967740	+	0.920743i
$77$	−0.415055	−	1.27741i	−0.0472999	−	0.145574i
$78$	−0.202979	−	0.624706i	−0.0229829	−	0.0707340i
$79$	0.706336	+	6.72034i	0.0794691	+	0.756098i	0.959600	+	0.281367i	$0.0907878\pi$
$79$	0.706336	+	6.72034i	0.0794691	+	0.756098i	−0.880131	+	0.474731i	$0.842546\pi$
$80$	2.00739	−	2.22943i	0.224433	−	0.249258i
$81$	5.00863	+	5.56265i	0.556515	+	0.618072i
$82$	0.324091	−	3.08352i	0.0357899	−	0.340518i
$83$	9.85099	−	2.09389i	1.08129	−	0.229835i	0.367377	−	0.930072i	$-0.380256\pi$
$83$	9.85099	−	2.09389i	1.08129	−	0.229835i	0.713910	+	0.700238i	$0.246923\pi$
$84$	0.286587	+	0.127597i	0.0312692	+	0.0139219i
$85$	4.71530	−	3.42586i	0.511446	−	0.371587i
$86$	−4.12440	+	1.83630i	−0.444746	+	0.198013i
$87$	1.41421	−	2.44949i	0.151620	−	0.262613i
$88$	2.57107	+	4.45322i	0.274077	+	0.474715i
$89$	−3.62867	−	2.63638i	−0.384638	−	0.279456i	0.378617	−	0.925554i	$-0.376400\pi$
$89$	−3.62867	−	2.63638i	−0.384638	−	0.279456i	−0.763255	+	0.646098i	$0.776400\pi$
$90$	1.14597	+	0.243584i	0.120796	+	0.0256760i
$91$	0.490035	−	1.50817i	0.0513696	−	0.158099i
$92$	7.31371			0.762507
$93$		0			0
$94$	4.00000			0.412568
$95$	1.36407	−	4.19817i	0.139950	−	0.430723i
$96$	−1.78847	−	0.380151i	−0.182535	−	0.0387990i
$97$	−4.18389	−	3.03977i	−0.424810	−	0.308642i	0.354760	−	0.934957i	$-0.384562\pi$
$97$	−4.18389	−	3.03977i	−0.424810	−	0.308642i	−0.779570	+	0.626315i	$0.784562\pi$
$98$	1.41421	+	2.44949i	0.142857	+	0.247436i
$99$	4.58579	−	7.94282i	0.460889	−	0.798283i
$100$	6.68141	−	2.97475i	0.668141	−	0.297475i
$101$	6.86474	−	4.98752i	0.683067	−	0.496277i	−0.191307	−	0.981530i	$-0.561273\pi$
$101$	6.86474	−	4.98752i	0.683067	−	0.496277i	0.874374	+	0.485253i	$0.161273\pi$
$102$	−0.913545	−	0.406737i	−0.0904545	−	0.0402729i
$103$	−2.02581	+	0.430599i	−0.199609	+	0.0424282i	−0.306631	−	0.951828i	$-0.599202\pi$
$103$	−2.02581	+	0.430599i	−0.199609	+	0.0424282i	0.107022	+	0.994257i	$0.465868\pi$
$104$	−0.634599	+	6.03781i	−0.0622276	+	0.592056i
$105$	−0.114805	−	0.127503i	−0.0112038	−	0.0124431i
$106$	1.61542	−	1.79411i	0.156904	−	0.174259i
$107$	−1.29764	−	12.3462i	−0.125447	−	1.19355i	−0.858294	−	0.513159i	$-0.828475\pi$
$107$	−1.29764	−	12.3462i	−0.125447	−	1.19355i	0.732846	−	0.680394i	$-0.238191\pi$
$108$	1.36407	+	4.19817i	0.131257	+	0.403969i
$109$	−3.34617	−	10.2984i	−0.320505	−	0.986412i	−0.973429	−	0.228989i	$-0.926458\pi$
$109$	−3.34617	−	10.2984i	−0.320505	−	0.986412i	0.652924	−	0.757423i	$-0.273542\pi$
$110$	−0.140397	−	1.33579i	−0.0133863	−	0.127362i
$111$	0.277163	−	0.307821i	0.0263071	−	0.0292170i
$112$	−0.831489	−	0.923462i	−0.0785683	−	0.0872590i
$113$	−1.74112	+	16.5656i	−0.163790	+	1.55836i	0.536127	+	0.844137i	$0.319887\pi$
$113$	−1.74112	+	16.5656i	−0.163790	+	1.55836i	−0.699917	+	0.714224i	$0.746780\pi$
$114$	−0.740809	+	0.157464i	−0.0693831	+	0.0147478i
$115$	−3.65418	−	1.62695i	−0.340754	−	0.151714i
$116$	−10.1008	+	7.33866i	−0.937836	+	0.681378i
$117$	9.89226	−	4.40432i	0.914540	−	0.407179i
$118$	−0.843146	+	1.46037i	−0.0776179	+	0.134438i
$119$	−1.20711	−	2.09077i	−0.110655	−	0.191661i
$120$	0.531406	+	0.386089i	0.0485105	+	0.0352450i
$121$	0.474677	+	0.100896i	0.0431524	+	0.00917233i
$122$	−0.362036	+	1.11423i	−0.0327772	+	0.100878i
$123$	−3.10051			−0.279563
$124$		0			0
$125$	−9.00000			−0.804984
$126$	0.149960	−	0.461530i	0.0133595	−	0.0411164i
$127$	−8.70502	−	1.85031i	−0.772446	−	0.164188i	−0.195205	−	0.980762i	$-0.562537\pi$
$127$	−8.70502	−	1.85031i	−0.772446	−	0.164188i	−0.577241	+	0.816574i	$0.695871\pi$
$128$	8.54027	+	6.20487i	0.754860	+	0.548438i
$129$	2.25736	+	3.90986i	0.198749	+	0.344244i
$130$	0.792893	−	1.37333i	0.0695413	−	0.120449i
$131$	−12.0978	+	5.38627i	−1.05699	+	0.470600i	−0.860259	−	0.509858i	$-0.829698\pi$
$131$	−12.0978	+	5.38627i	−1.05699	+	0.470600i	−0.196727	+	0.980458i	$0.563031\pi$
$132$	1.98682	−	1.44351i	0.172930	−	0.125641i
$133$	−1.67035	−	0.743688i	−0.144838	−	0.0644860i
$134$	−1.31379	+	0.279256i	−0.113495	+	0.0241240i
$135$	0.252354	−	2.40099i	0.0217192	−	0.206644i
$136$	6.18453	+	6.86862i	0.530319	+	0.588979i
$137$	6.34689	−	7.04894i	0.542252	−	0.602231i	−0.408281	−	0.912856i	$-0.633872\pi$
$137$	6.34689	−	7.04894i	0.542252	−	0.602231i	0.950533	+	0.310625i	$0.100538\pi$
$138$	0.0717370	+	0.682532i	0.00610666	+	0.0581010i
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$	0.234037	+	0.720292i	0.0197797	+	0.0608757i
$141$	−0.418114	−	3.97809i	−0.0352115	−	0.335015i
$142$	0.0196974	−	0.0218761i	0.00165297	−	0.00183580i
$143$	−8.30673	−	9.22556i	−0.694644	−	0.771480i
$144$	0.886953	−	8.43880i	0.0739128	−	0.703233i
$145$	6.67921	−	1.41971i	0.554678	−	0.117900i
$146$	−0.691882	−	0.308046i	−0.0572606	−	0.0254941i
$147$	2.28825	−	1.66251i	0.188731	−	0.137121i
$148$	−1.67035	+	0.743688i	−0.137302	+	0.0611308i
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$	0.343146	+	0.594346i	0.0280177	+	0.0485281i
$151$	−4.29888	−	3.12332i	−0.349838	−	0.254172i	0.398963	−	0.916967i	$-0.369370\pi$
$151$	−4.29888	−	3.12332i	−0.349838	−	0.254172i	−0.748801	+	0.662795i	$0.769370\pi$
$152$	6.84703	+	1.45538i	0.555368	+	0.118047i
$153$	5.09423	−	15.6784i	0.411844	−	1.26753i
$154$	−0.556349			−0.0448319
$155$		0			0
$156$	2.89949			0.232145
$157$	2.83417	−	8.72268i	0.226192	−	0.696146i	−0.771977	−	0.635651i	$-0.780732\pi$
$157$	2.83417	−	8.72268i	0.226192	−	0.696146i	0.998168	−	0.0604954i	$-0.0192681\pi$
$158$	2.73783	+	0.581943i	0.217810	+	0.0462969i
$159$	−1.95314	−	1.41904i	−0.154894	−	0.112537i
$160$	−2.20711	−	3.82282i	−0.174487	−	0.302221i
$161$	−0.828427	+	1.43488i	−0.0652892	+	0.113084i
$162$	2.83245	−	1.26109i	0.222538	−	0.0990805i
$163$	−16.9655	+	12.3262i	−1.32884	+	0.965462i	−0.329068	+	0.944306i	$0.606734\pi$
$163$	−16.9655	+	12.3262i	−1.32884	+	0.965462i	−0.999776	+	0.0211551i	$0.993266\pi$
$164$	12.5030	+	5.56672i	0.976324	+	0.434688i
$165$	−1.31379	+	0.279256i	−0.102279	+	0.0217400i
$166$	0.436048	−	4.14872i	0.0338439	−	0.322003i
$167$	15.0931	+	16.7626i	1.16794	+	1.29713i	0.946775	+	0.321896i	$0.104320\pi$
$167$	15.0931	+	16.7626i	1.16794	+	1.29713i	0.221167	+	0.975236i	$0.429013\pi$
$168$	0.182056	−	0.202193i	0.0140459	−	0.0155996i
$169$	−0.173188	−	1.64778i	−0.0133222	−	0.126752i
$170$	−0.746033	−	2.29605i	−0.0572181	−	0.176099i
$171$	−3.85816	−	11.8742i	−0.295041	−	0.908043i
$172$	−2.08314	−	19.8198i	−0.158838	−	1.51124i
$173$	5.56296	−	6.17829i	0.422944	−	0.469727i	−0.493584	−	0.869698i	$-0.664313\pi$
$173$	5.56296	−	6.17829i	0.422944	−	0.469727i	0.916528	+	0.399972i	$0.130980\pi$
$174$	−0.783935	−	0.870648i	−0.0594300	−	0.0660037i
$175$	−0.173188	+	1.64778i	−0.0130918	+	0.124560i
$176$	−9.51534	+	2.02255i	−0.717246	+	0.152455i
$177$	1.54050	+	0.685877i	0.115791	+	0.0515536i
$178$	−1.50304	+	1.09203i	−0.112658	+	0.0818508i
$179$	−13.9248	+	6.19974i	−1.04079	+	0.463390i	−0.854689	−	0.519140i	$-0.826252\pi$
$179$	−13.9248	+	6.19974i	−1.04079	+	0.463390i	−0.186103	+	0.982530i	$0.559586\pi$
$180$	−2.58579	+	4.47871i	−0.192733	+	0.333824i
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	0.541200	−	0.840894i	$-0.317970\pi$
$181$	−6.15685	−	10.6640i	−0.457635	−	0.792648i	−0.998835	+	0.0482461i	$0.984637\pi$
$182$	−0.531406	−	0.386089i	−0.0393905	−	0.0286188i
$183$	1.14597	+	0.243584i	0.0847126	+	0.0180062i
$184$	1.96014	−	6.03269i	0.144503	−	0.444736i
$185$	1.00000			0.0735215
$186$		0			0
$187$	−18.8995			−1.38207
$188$	−5.45627	+	16.7927i	−0.397939	+	1.22473i
$189$	−0.978148	−	0.207912i	−0.0711498	−	0.0151234i
$190$	−1.47923	−	1.07472i	−0.107315	−	0.0779686i
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	0.944817	+	0.327599i	$0.106239\pi$
$191$	10.4497	+	18.0995i	0.756117	+	1.30963i	−0.188700	+	0.982035i	$0.560427\pi$
$192$	0.863961	−	1.49642i	0.0623510	−	0.107995i
$193$	6.52467	−	2.90497i	0.469656	−	0.209104i	−0.158242	−	0.987400i	$-0.550582\pi$
$193$	6.52467	−	2.90497i	0.469656	−	0.209104i	0.627897	+	0.778296i	$0.283916\pi$
$194$	−1.73302	+	1.25912i	−0.124424	+	0.0903992i
$195$	−1.44869	−	0.644997i	−0.103743	−	0.0461892i
$196$	−12.2124	+	2.59584i	−0.872318	+	0.185417i
$197$	1.40960	−	13.4114i	0.100430	−	0.955523i	−0.822034	−	0.569439i	$-0.807161\pi$
$197$	1.40960	−	13.4114i	0.100430	−	0.955523i	0.922463	−	0.386085i	$-0.126173\pi$
$198$	−2.54202	−	2.82320i	−0.180654	−	0.200636i
$199$	12.3215	−	13.6844i	0.873449	−	0.970063i	−0.126311	−	0.991991i	$-0.540314\pi$
$199$	12.3215	−	13.6844i	0.873449	−	0.970063i	0.999760	+	0.0219274i	$0.00698027\pi$
$200$	−0.663039	−	6.30840i	−0.0468840	−	0.446071i
$201$	0.415055	+	1.27741i	0.0292757	+	0.0901014i
$202$	−1.08611	−	3.34270i	−0.0764183	−	0.235191i
$203$	−0.295651	−	2.81293i	−0.0207506	−	0.197429i
$204$	2.95369	−	3.28040i	0.206799	−	0.229674i
$205$	−5.00863	−	5.56265i	−0.349818	−	0.388512i
$206$	−0.0896712	+	0.853165i	−0.00624769	+	0.0594428i
$207$	−11.0665	+	2.35225i	−0.769173	+	0.163493i
$208$	−10.4923	−	4.67148i	−0.727512	−	0.323909i
$209$	−11.5800	+	8.41339i	−0.801008	+	0.581966i
$210$	−0.0649237	+	0.0289059i	−0.00448016	+	0.00199470i
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	−0.987706	−	0.156324i	$-0.950035\pi$
$211$	−5.20711	+	9.01897i	−0.358472	+	0.620892i	0.629234	+	0.777216i	$0.283369\pi$
$212$	5.32843	+	9.22911i	0.365958	+	0.633858i
$213$	−0.0238152	−	0.0173028i	−0.00163179	−	0.00118557i
$214$	−5.02977	−	1.06911i	−0.343828	−	0.0730829i
$215$	−3.36813	+	10.3660i	−0.229705	+	0.706958i
$216$	3.82843			0.260491
$217$		0			0
$218$	−4.48528			−0.303782
$219$	−0.234037	+	0.720292i	−0.0158147	+	0.0486728i
$220$	5.79937	+	1.23269i	0.390993	+	0.0831082i
$221$	−18.0522	−	13.1157i	−1.21432	−	0.882255i
$222$	−0.0857864	−	0.148586i	−0.00575761	−	0.00997247i
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	−0.128706	−	0.991683i	$-0.541082\pi$
$223$	11.8640	−	20.5490i	0.794470	−	1.37606i	0.923175	−	0.384379i	$-0.125584\pi$
$224$	−1.67035	+	0.743688i	−0.111605	+	0.0496898i
$225$	−9.15298	+	6.65003i	−0.610199	+	0.443335i
$226$	6.30300	+	2.80628i	0.419269	+	0.186671i
$227$	18.0118	−	3.82853i	1.19549	−	0.254108i	0.433170	−	0.901312i	$-0.357395\pi$
$227$	18.0118	−	3.82853i	1.19549	−	0.254108i	0.762317	+	0.647204i	$0.224062\pi$
$228$	0.349454	−	3.32483i	0.0231431	−	0.220192i
$229$	−3.67037	−	4.07636i	−0.242545	−	0.269373i	0.609565	−	0.792736i	$-0.291344\pi$
$229$	−3.67037	−	4.07636i	−0.242545	−	0.269373i	−0.852110	+	0.523363i	$0.824677\pi$
$230$	−1.10865	+	1.23128i	−0.0731023	+	0.0811884i
$231$	0.0581543	+	0.553301i	0.00382627	+	0.0364046i
$232$	3.34617	+	10.2984i	0.219687	+	0.676126i
$233$	−2.83417	−	8.72268i	−0.185673	−	0.571442i	0.814287	−	0.580463i	$-0.197128\pi$
$233$	−2.83417	−	8.72268i	−0.185673	−	0.571442i	−0.999959	+	0.00902109i	$0.997128\pi$
$234$	−0.468840	−	4.46071i	−0.0306490	−	0.291606i
$235$	6.46170	−	7.17644i	0.421515	−	0.468139i
$236$	−4.98077	−	5.53171i	−0.324221	−	0.360084i
$237$	0.292574	−	2.78366i	0.0190047	−	0.180818i
$238$	−0.978148	+	0.207912i	−0.0634039	+	0.0134769i
$239$	−19.4061	−	8.64016i	−1.25528	−	0.558886i	−0.332094	−	0.943246i	$-0.607755\pi$
$239$	−19.4061	−	8.64016i	−1.25528	−	0.558886i	−0.923183	+	0.384361i	$0.874422\pi$
$240$	−1.00532	+	0.730406i	−0.0648930	+	0.0471475i
$241$	12.1896	−	5.42715i	0.785199	−	0.349593i	0.0253383	−	0.999679i	$-0.491934\pi$
$241$	12.1896	−	5.42715i	0.785199	−	0.349593i	0.759861	+	0.650086i	$0.225267\pi$
$242$	0.100505	−	0.174080i	0.00646071	−	0.0111903i
$243$	−5.17157	−	8.95743i	−0.331757	−	0.574619i
$244$	−4.18389	−	3.03977i	−0.267846	−	0.194602i
$245$	6.67921	+	1.41971i	0.426719	+	0.0907019i
$246$	−0.396862	+	1.22141i	−0.0253030	+	0.0778745i
$247$	−16.8995			−1.07529
$248$		0			0
$249$	−4.17157			−0.264363
$250$	−1.15199	+	3.54546i	−0.0728583	+	0.224235i
$251$	−6.27405	−	1.33359i	−0.396014	−	0.0841755i	0.00560002	−	0.999984i	$-0.498217\pi$
$251$	−6.27405	−	1.33359i	−0.396014	−	0.0841755i	−0.401614	+	0.915809i	$0.631551\pi$
$252$	1.73302	+	1.25912i	0.109170	+	0.0793168i
$253$	6.48528	+	11.2328i	0.407726	+	0.706202i
$254$	−1.84315	+	3.19242i	−0.115649	+	0.200310i
$255$	−2.20549	+	0.981949i	−0.138113	+	0.0614920i
$256$	−3.21225	+	2.33384i	−0.200766	+	0.145865i
$257$	20.3846	+	9.07580i	1.27156	+	0.566133i	0.927853	−	0.372946i	$-0.121652\pi$
$257$	20.3846	+	9.07580i	1.27156	+	0.566133i	0.343702	+	0.939079i	$0.388319\pi$
$258$	1.82919	−	0.388807i	0.113881	−	0.0242061i
$259$	0.0432971	−	0.411944i	0.00269035	−	0.0255970i
$260$	4.68391	+	5.20201i	0.290484	+	0.322615i
$261$	12.9234	−	14.3529i	0.799938	−	0.888421i
$262$	0.573368	+	5.45523i	0.0354228	+	0.337025i
$263$	−7.20433	−	22.1727i	−0.444238	−	1.36722i	−0.883317	−	0.468776i	$-0.844695\pi$
$263$	−7.20433	−	22.1727i	−0.444238	−	1.36722i	0.439079	−	0.898448i	$-0.355305\pi$
$264$	−0.658188	−	2.02570i	−0.0405087	−	0.124673i
$265$	−0.609237	−	5.79650i	−0.0374251	−	0.356076i
$266$	−0.506772	+	0.562828i	−0.0310722	+	0.0345092i
$267$	1.24315	+	1.38066i	0.0760798	+	0.0844952i
$268$	0.619742	−	5.89645i	0.0378568	−	0.360183i
$269$	25.5997	−	5.44138i	1.56084	−	0.331767i	0.655080	−	0.755560i	$-0.272635\pi$
$269$	25.5997	−	5.44138i	1.56084	−	0.331767i	0.905759	+	0.423793i	$0.139302\pi$
$270$	−0.913545	−	0.406737i	−0.0555966	−	0.0247532i
$271$	0.555221	−	0.403392i	0.0337273	−	0.0245043i	−0.570794	−	0.821093i	$-0.693364\pi$
$271$	0.555221	−	0.403392i	0.0337273	−	0.0245043i	0.604521	+	0.796589i	$0.293364\pi$
$272$	−15.9736	+	7.11190i	−0.968542	+	0.431223i
$273$	−0.328427	+	0.568852i	−0.0198773	+	0.0344285i
$274$	−1.96447	−	3.40256i	−0.118678	−	0.205556i
$275$	10.4934	+	7.62391i	0.632776	+	0.459739i
$276$	−2.96324	−	0.629855i	−0.178366	−	0.0379128i
$277$	4.37016	−	13.4500i	0.262577	−	0.808130i	−0.729664	−	0.683806i	$-0.760324\pi$
$277$	4.37016	−	13.4500i	0.262577	−	0.808130i	0.992242	−	0.124325i	$-0.0396764\pi$
$278$		0			0
$279$		0			0
$280$	0.656854			0.0392545
$281$	0.618034	−	1.90211i	0.0368688	−	0.113471i	−0.930928	−	0.365202i	$-0.881000\pi$
$281$	0.618034	−	1.90211i	0.0368688	−	0.113471i	0.967797	+	0.251731i	$0.0809999\pi$
$282$	−1.62065	−	0.344479i	−0.0965082	−	0.0205134i
$283$	11.0486	+	8.02730i	0.656773	+	0.477173i	0.865572	−	0.500785i	$-0.166955\pi$
$283$	11.0486	+	8.02730i	0.656773	+	0.477173i	−0.208799	+	0.977959i	$0.566955\pi$
$284$	0.0649712	+	0.112533i	0.00385533	+	0.00667763i
$285$	−0.914214	+	1.58346i	−0.0541533	+	0.0937963i
$286$	−4.69757	+	2.09149i	−0.277773	+	0.123673i
$287$	−2.50836	+	1.82243i	−0.148064	+	0.107575i
$288$	−11.4059	−	5.07822i	−0.672097	−	0.299237i
$289$	−16.5997	+	3.52838i	−0.976454	+	0.207552i
$290$	0.295651	−	2.81293i	0.0173612	−	0.165181i
$291$	1.43337	+	1.59192i	0.0840256	+	0.0933198i
$292$	2.23700	−	2.48444i	0.130911	−	0.145391i
$293$	−1.54692	−	14.7179i	−0.0903718	−	0.859830i	−0.941984	−	0.335658i	$-0.891041\pi$
$293$	−1.54692	−	14.7179i	−0.0903718	−	0.859830i	0.851612	−	0.524172i	$-0.175625\pi$
$294$	−0.362036	−	1.11423i	−0.0211144	−	0.0649833i
$295$	1.25803	+	3.87182i	0.0732453	+	0.225426i
$296$	0.165760	+	1.57710i	0.00963459	+	0.0916670i
$297$	−5.23824	+	5.81766i	−0.303954	+	0.337575i
$298$	0.277163	+	0.307821i	0.0160556	+	0.0178316i
$299$	−1.60072	+	15.2298i	−0.0925719	+	0.880763i
$300$	−2.96324	+	0.629855i	−0.171083	+	0.0363647i
$301$	4.12440	+	1.83630i	0.237727	+	0.105843i
$302$	−1.78065	+	1.29372i	−0.102465	+	0.0744453i
$303$	−3.21086	+	1.42956i	−0.184459	+	0.0821264i
$304$	−6.62132	+	11.4685i	−0.379759	+	0.657761i
$305$	1.41421	+	2.44949i	0.0809776	+	0.140257i
$306$	−5.52431	−	4.01365i	−0.315804	−	0.229445i
$307$	10.9970	+	2.33748i	0.627630	+	0.133407i	0.510736	−	0.859738i	$-0.329373\pi$
$307$	10.9970	+	2.33748i	0.627630	+	0.133407i	0.116894	+	0.993144i	$0.462706\pi$
$308$	0.758898	−	2.33565i	0.0432422	−	0.133086i
$309$	0.857864			0.0488022
$310$		0			0
$311$	11.3137			0.641542			0.320771	−	0.947157i	$-0.396058\pi$
$311$	11.3137			0.641542			0.320771	+	0.947157i	$0.396058\pi$
$312$	0.777091	−	2.39164i	0.0439941	−	0.135400i
$313$	1.78847	+	0.380151i	0.101090	+	0.0214874i	0.258179	−	0.966097i	$-0.416878\pi$
$313$	1.78847	+	0.380151i	0.101090	+	0.0214874i	−0.157089	+	0.987584i	$0.550211\pi$
$314$	−3.07345	−	2.23299i	−0.173445	−	0.126015i
$315$	−0.585786	−	1.01461i	−0.0330053	−	0.0571669i
$316$	−6.17767	+	10.7000i	−0.347521	+	0.601924i
$317$	−7.15162	+	3.18411i	−0.401675	+	0.178837i	−0.597623	−	0.801777i	$-0.703888\pi$
$317$	−7.15162	+	3.18411i	−0.401675	+	0.178837i	0.195948	+	0.980614i	$0.437222\pi$
$318$	−0.809017	+	0.587785i	−0.0453674	+	0.0329614i
$319$	−20.2278	−	9.00602i	−1.13254	−	0.504240i
$320$	4.08041	−	0.867319i	0.228102	−	0.0484846i
$321$	−0.537500	+	5.11397i	−0.0300003	+	0.285434i
$322$	0.459219	+	0.510014i	0.0255913	+	0.0284220i
$323$	−17.2153	+	19.1196i	−0.957887	+	1.06384i
$324$	1.43061	+	13.6113i	0.0794782	+	0.756184i
$325$	4.73220	+	14.5642i	0.262495	+	0.807877i
$326$	2.68421	+	8.26115i	0.148665	+	0.457543i
$327$	0.468840	+	4.46071i	0.0259269	+	0.246678i
$328$	7.94262	−	8.82117i	0.438558	−	0.487068i
$329$	−2.67652	−	2.97258i	−0.147561	−	0.163884i
$330$	−0.0581543	+	0.553301i	−0.00320129	+	0.0304582i
$331$	−9.04067	+	1.92165i	−0.496920	+	0.105624i	−0.449552	−	0.893254i	$-0.648417\pi$
$331$	−9.04067	+	1.92165i	−0.496920	+	0.105624i	−0.0473675	+	0.998878i	$0.515083\pi$
$332$	16.8222	+	7.48974i	0.923239	+	0.411053i
$333$	2.28825	−	1.66251i	0.125395	−	0.0911049i
$334$	8.53539	−	3.80020i	0.467036	−	0.207938i
$335$	−1.62132	+	2.80821i	−0.0885822	+	0.153429i
$336$	0.257359	+	0.445759i	0.0140401	+	0.0243182i
$337$	−7.53495	−	5.47446i	−0.410455	−	0.298213i	0.363331	−	0.931660i	$-0.381639\pi$
$337$	−7.53495	−	5.47446i	−0.410455	−	0.298213i	−0.773786	+	0.633447i	$0.781639\pi$
$338$	−0.671294	−	0.142688i	−0.0365136	−	0.00776121i
$339$	2.13206	−	6.56181i	0.115798	−	0.356389i
$340$	10.6569			0.577949
$341$		0			0
$342$	−5.17157			−0.279647
$343$	1.77003	−	5.44758i	0.0955724	−	0.294142i
$344$	−16.9066	−	3.59360i	−0.911541	−	0.193754i
$345$	1.34042	+	0.973874i	0.0721660	+	0.0524316i
$346$	−1.72183	−	2.98229i	−0.0925659	−	0.160329i
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	−0.728044	−	0.685530i	$-0.759570\pi$
$347$	4.27817	−	7.41002i	0.229664	−	0.397790i	0.957709	+	0.287740i	$0.0929038\pi$
$348$	4.72447	−	2.10347i	0.253258	−	0.112758i
$349$	21.9346	−	15.9364i	1.17413	−	0.853058i	0.182636	−	0.983181i	$-0.441537\pi$
$349$	21.9346	−	15.9364i	1.17413	−	0.853058i	0.991498	+	0.130122i	$0.0415370\pi$
$350$	0.626958	+	0.279140i	0.0335123	+	0.0149207i
$351$	−9.04067	+	1.92165i	−0.482555	+	0.102570i
$352$	−1.49619	+	14.2353i	−0.0797472	+	0.758744i
$353$	2.00739	+	2.22943i	0.106843	+	0.118661i	0.794194	−	0.607664i	$-0.207893\pi$
$353$	2.00739	+	2.22943i	0.106843	+	0.118661i	−0.687351	+	0.726325i	$0.741227\pi$
$354$	0.467378	−	0.519075i	0.0248408	−	0.0275885i
$355$	−0.00742861	−	0.0706785i	−0.000394270	−	0.00375123i
$356$	−2.53425	−	7.79962i	−0.134315	−	0.413379i
$357$	0.309017	+	0.951057i	0.0163549	+	0.0503352i
$358$	0.659962	+	6.27912i	0.0348801	+	0.331862i
$359$	4.75117	−	5.27670i	0.250757	−	0.278494i	−0.604604	−	0.796526i	$-0.706669\pi$
$359$	4.75117	−	5.27670i	0.250757	−	0.278494i	0.855361	+	0.518032i	$0.173335\pi$
$360$	3.00124	+	3.33321i	0.158179	+	0.175676i
$361$	−0.0507257	+	0.482623i	−0.00266977	+	0.0254012i
$362$	−4.98905	+	1.06045i	−0.262218	+	0.0557363i
$363$	−0.183632	−	0.0817582i	−0.00963817	−	0.00429119i
$364$	2.34574	−	1.70428i	0.122950	−	0.0893286i
$365$	−1.67035	+	0.743688i	−0.0874302	+	0.0389264i
$366$	0.242641	−	0.420266i	0.0126830	−	0.0219677i
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	0.987151	+	0.159792i	$0.0510824\pi$
$367$	12.1066	+	20.9692i	0.631959	+	1.09459i	−0.355191	+	0.934794i	$0.615584\pi$
$368$	9.70820	+	7.05342i	0.506075	+	0.367685i
$369$	−20.7089	−	4.40182i	−1.07806	−	0.229149i
$370$	0.127999	−	0.393941i	0.00665435	−	0.0204800i
$371$	−2.41421			−0.125340
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−2.41912	+	7.44528i	−0.125090	+	0.384986i
$375$	3.64646	+	0.775079i	0.188302	+	0.0400249i
$376$	12.3891	+	9.00117i	0.638916	+	0.464200i
$377$	−13.0711	−	22.6398i	−0.673194	−	1.16601i
$378$	−0.207107	+	0.358719i	−0.0106524	+	0.0184505i
$379$	6.74633	−	3.00366i	0.346536	−	0.154288i	−0.226086	−	0.974107i	$-0.572593\pi$
$379$	6.74633	−	3.00366i	0.346536	−	0.154288i	0.572622	+	0.819820i	$0.305926\pi$
$380$	6.52963	−	4.74405i	0.334963	−	0.243365i
$381$	3.36759	+	1.49935i	0.172527	+	0.0768140i
$382$	8.46768	−	1.79986i	0.433244	−	0.0920889i
$383$	−0.533148	+	5.07256i	−0.0272426	+	0.259196i	0.972420	+	0.233235i	$0.0749312\pi$
$383$	−0.533148	+	5.07256i	−0.0272426	+	0.259196i	−0.999663	+	0.0259608i	$0.991735\pi$
$384$	−2.92583	−	3.24946i	−0.149308	−	0.165823i
$385$	−0.898740	+	0.998152i	−0.0458040	+	0.0508705i
$386$	−0.309234	−	2.94216i	−0.0157396	−	0.149752i
$387$	9.52651	+	29.3196i	0.484260	+	1.49040i
$388$	−2.92202	−	8.99304i	−0.148343	−	0.456553i
$389$	1.16467	+	11.0811i	0.0590511	+	0.561834i	0.983548	+	0.180645i	$0.0578186\pi$
$389$	1.16467	+	11.0811i	0.0590511	+	0.561834i	−0.924497	+	0.381189i	$0.875515\pi$
$390$	−0.439521	+	0.488138i	−0.0222560	+	0.0247178i
$391$	15.5999	+	17.3255i	0.788922	+	0.876186i
$392$	−1.13188	+	10.7691i	−0.0571685	+	0.543922i
$393$	5.36541	−	1.14045i	0.270649	−	0.0575283i
$394$	−5.10287	−	2.27194i	−0.257079	−	0.114459i
$395$	5.46682	−	3.97188i	0.275065	−	0.199847i
$396$	15.3197	−	6.82079i	0.769846	−	0.342758i
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	−0.0493613	−	0.998781i	$-0.515719\pi$
$397$	16.7426	−	28.9991i	0.840289	−	1.45542i	0.889650	−	0.456642i	$-0.150948\pi$
$398$	−3.81371	−	6.60554i	−0.191164	−	0.331106i
$399$	0.612717	+	0.445165i	0.0306742	+	0.0222861i
$400$	11.7378	+	2.49494i	0.586889	+	0.124747i
$401$	−8.29044	+	25.5154i	−0.414005	+	1.27418i	0.499133	+	0.866525i	$0.333652\pi$
$401$	−8.29044	+	25.5154i	−0.414005	+	1.27418i	−0.913138	+	0.407651i	$0.866348\pi$
$402$	0.556349			0.0277482
$403$		0			0
$404$	15.5147			0.771886
$405$	2.31308	−	7.11893i	0.114938	−	0.353742i
$406$	−1.14597	−	0.243584i	−0.0568736	−	0.0120889i
$407$	−2.62335	−	1.90598i	−0.130035	−	0.0944757i
$408$	−1.91421	−	3.31552i	−0.0947677	−	0.164142i
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	0.489215	+	0.872163i	$0.337283\pi$
$409$	−10.3284	+	17.8894i	−0.510708	+	0.884572i	−0.999923	+	0.0124088i	$0.996050\pi$
$410$	−2.83245	+	1.26109i	−0.139885	+	0.0622807i
$411$	−3.17857	+	2.30937i	−0.156787	+	0.113913i
$412$	−3.45941	−	1.54023i	−0.170433	−	0.0758816i
$413$	1.64944	−	0.350600i	0.0811637	−	0.0172519i
$414$	−0.489851	+	4.66062i	−0.0240749	+	0.229057i
$415$	−6.73886	−	7.48426i	−0.330798	−	0.367388i
$416$	−11.3080	+	12.5588i	−0.554419	+	0.615744i
$417$		0			0
$418$	1.83214	+	5.63875i	0.0896129	+	0.275800i
$419$	8.65248	+	26.6296i	0.422701	+	1.30094i	0.905178	+	0.425032i	$0.139737\pi$
$419$	8.65248	+	26.6296i	0.422701	+	1.30094i	−0.482477	+	0.875908i	$0.660263\pi$
$420$	−0.0327915	−	0.311990i	−0.00160006	−	0.0152236i
$421$	−20.8382	+	23.1431i	−1.01559	+	1.12793i	−0.0238426	+	0.999716i	$0.507590\pi$
$421$	−20.8382	+	23.1431i	−1.01559	+	1.12793i	−0.991747	+	0.128211i	$0.959077\pi$
$422$	2.88643	+	3.20571i	0.140509	+	0.156052i
$423$	2.85506	−	27.1641i	0.138818	−	1.32076i
$424$	9.04067	−	1.92165i	0.439054	−	0.0933237i
$425$	21.2981	+	9.48254i	1.03311	+	0.459971i
$426$	−0.00986459	+	0.00716705i	−0.000477941	+	0.000347245i
$427$	1.07029	−	0.476522i	0.0517947	−	0.0230605i
$428$	11.3492	−	19.6575i	0.548586	−	0.950179i
$429$	2.57107	+	4.45322i	0.124132	+	0.215003i
$430$	3.65248	+	2.65369i	0.176138	+	0.127972i
$431$	16.3912	+	3.48405i	0.789535	+	0.167821i	0.584994	−	0.811037i	$-0.301097\pi$
$431$	16.3912	+	3.48405i	0.789535	+	0.167821i	0.204540	+	0.978858i	$0.434430\pi$
$432$	−2.23810	+	6.88816i	−0.107681	+	0.331407i
$433$	27.1127			1.30295			0.651477	−	0.758669i	$-0.274150\pi$
$433$	27.1127			1.30295			0.651477	+	0.758669i	$0.274150\pi$
$434$		0			0
$435$	−2.82843			−0.135613
$436$	6.11822	−	18.8300i	0.293010	−	0.901791i
$437$	17.2710	+	3.67107i	0.826184	+	0.175611i
$438$	0.253796	+	0.184393i	0.0121268	+	0.00881065i
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	0.840255	−	0.542191i	$-0.182405\pi$
$439$	−1.03553	−	1.79360i	−0.0494233	−	0.0856037i	−0.889679	+	0.456587i	$0.849072\pi$
$440$	2.57107	−	4.45322i	0.122571	−	0.212299i
$441$	17.6440	−	7.85559i	0.840188	−	0.374076i
$442$	−7.47745	+	5.43269i	−0.355666	+	0.258407i
$443$	−4.34606	−	1.93499i	−0.206488	−	0.0919343i	0.300887	−	0.953660i	$-0.402717\pi$
$443$	−4.34606	−	1.93499i	−0.206488	−	0.0919343i	−0.507375	+	0.861726i	$0.669384\pi$
$444$	0.740809	−	0.157464i	0.0351572	−	0.00747290i
$445$	−0.468840	+	4.46071i	−0.0222251	+	0.211458i
$446$	−6.57650	−	7.30394i	−0.311406	−	0.345852i
$447$	0.277163	−	0.307821i	0.0131094	−	0.0145594i
$448$	−0.180617	−	1.71846i	−0.00853335	−	0.0811894i
$449$	−12.5546	−	38.6390i	−0.592486	−	1.82349i	−0.566860	−	0.823814i	$-0.691842\pi$
$449$	−12.5546	−	38.6390i	−0.592486	−	1.82349i	−0.0256264	−	0.999672i	$-0.508158\pi$
$450$	1.44814	+	4.45693i	0.0682661	+	0.210102i
$451$	2.53712	+	24.1391i	0.119468	+	1.13667i
$452$	−20.3789	+	22.6331i	−0.958545	+	1.06457i
$453$	1.47276	+	1.63567i	0.0691965	+	0.0768504i
$454$	0.797282	−	7.58563i	0.0374183	−	0.356011i
$455$	−1.55113	+	0.329704i	−0.0727182	+	0.0154567i
$456$	−2.64882	−	1.17933i	−0.124042	−	0.0552272i
$457$	25.1707	−	18.2876i	1.17744	−	0.855457i	0.185556	−	0.982634i	$-0.440591\pi$
$457$	25.1707	−	18.2876i	1.17744	−	0.855457i	0.991880	+	0.127177i	$0.0405915\pi$
$458$	−2.07565	+	0.924137i	−0.0969886	+	0.0431821i
$459$	−7.03553	+	12.1859i	−0.328391	+	0.568789i
$460$	−3.65685	−	6.33386i	−0.170502	−	0.295318i
$461$	1.73302	+	1.25912i	0.0807150	+	0.0586429i	0.627411	−	0.778688i	$-0.284115\pi$
$461$	1.73302	+	1.25912i	0.0807150	+	0.0586429i	−0.546696	+	0.837331i	$0.684115\pi$
$462$	0.225412	+	0.0479127i	0.0104871	+	0.00222910i
$463$	−2.77206	+	8.53151i	−0.128828	+	0.396493i	−0.994579	−	0.103982i	$-0.966841\pi$
$463$	−2.77206	+	8.53151i	−0.128828	+	0.396493i	0.865751	+	0.500475i	$0.166841\pi$
$464$	−20.4853			−0.951005
$465$		0			0
$466$	−3.79899			−0.175985
$467$	−2.47214	+	7.60845i	−0.114397	+	0.352077i	−0.991821	−	0.127639i	$-0.959260\pi$
$467$	−2.47214	+	7.60845i	−0.114397	+	0.352077i	0.877424	+	0.479716i	$0.159260\pi$
$468$	19.3663	+	4.11644i	0.895209	+	0.190283i
$469$	1.08663	+	0.789481i	0.0501758	+	0.0364549i
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	−1.89949	+	3.29002i	−0.0875241	+	0.151596i
$472$	−5.89771	+	2.62583i	−0.271464	+	0.120864i
$473$	28.5932	−	20.7742i	1.31472	−	0.955198i
$474$	−1.05915	−	0.471562i	−0.0486482	−	0.0216596i
$475$	17.2710	−	3.67107i	0.792448	−	0.168440i
$476$	0.461411	−	4.39003i	0.0211487	−	0.201217i
$477$	−11.0308	−	12.2510i	−0.505066	−	0.560933i
$478$	−5.88767	+	6.53892i	−0.269296	+	0.299083i
$479$	1.64402	+	15.6418i	0.0751170	+	0.714690i	0.965663	+	0.259797i	$0.0836558\pi$
$479$	1.64402	+	15.6418i	0.0751170	+	0.714690i	−0.890546	+	0.454893i	$0.849678\pi$
$480$	0.565015	+	1.73894i	0.0257893	+	0.0793713i
$481$	−1.18305	−	3.64105i	−0.0539424	−	0.166018i
$482$	−0.577720	−	5.49663i	−0.0263144	−	0.250365i
$483$	0.459219	−	0.510014i	0.0208952	−	0.0232064i
$484$	0.593721	+	0.659394i	0.0269873	+	0.0299724i
$485$	−0.540577	+	5.14324i	−0.0245463	+	0.233543i
$486$	−4.19065	+	0.890750i	−0.190092	+	0.0404052i
$487$	17.7089	+	7.88450i	0.802466	+	0.357281i	0.766640	−	0.642077i	$-0.221927\pi$
$487$	17.7089	+	7.88450i	0.802466	+	0.357281i	0.0358258	+	0.999358i	$0.488594\pi$
$488$	−3.62867	+	2.63638i	−0.164262	+	0.119343i
$489$	7.93532	−	3.53303i	0.358848	−	0.159769i
$490$	1.41421	−	2.44949i	0.0638877	−	0.110657i
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	0.847579	−	0.530669i	$-0.178059\pi$
$491$	−0.792893	−	1.37333i	−0.0357828	−	0.0619776i	−0.883362	+	0.468691i	$0.844726\pi$
$492$	−4.58636	−	3.33218i	−0.206769	−	0.150226i
$493$	−38.9293	−	8.27468i	−1.75329	−	0.372673i
$494$	−2.16312	+	6.65740i	−0.0973233	+	0.299530i
$495$	−9.17157			−0.412232
$496$		0			0
$497$	−0.0294373			−0.00132044
$498$	−0.533957	+	1.64335i	−0.0239272	+	0.0736403i
$499$	2.16484	+	0.460151i	0.0969115	+	0.0205992i	0.256112	−	0.966647i	$-0.417558\pi$
$499$	2.16484	+	0.460151i	0.0969115	+	0.0205992i	−0.159201	+	0.987246i	$0.550892\pi$
$500$	−13.3131	−	9.67250i	−0.595378	−	0.432567i
$501$	−4.67157	−	8.09140i	−0.208710	−	0.361497i
$502$	−1.32843	+	2.30090i	−0.0592906	+	0.102694i
$503$	−12.2276	+	5.44408i	−0.545202	+	0.242739i	−0.660807	−	0.750556i	$-0.729786\pi$
$503$	−12.2276	+	5.44408i	−0.545202	+	0.242739i	0.115605	+	0.993295i	$0.463119\pi$
$504$	1.50304	−	1.09203i	0.0669509	−	0.0486427i
$505$	−7.75169	−	3.45127i	−0.344946	−	0.153580i
$506$	5.25518	−	1.11702i	0.233621	−	0.0496577i
$507$	−0.0717370	+	0.682532i	−0.00318595	+	0.0303123i
$508$	−10.8881	−	12.0925i	−0.483083	−	0.536518i
$509$	−21.9468	+	24.3744i	−0.972775	+	1.08038i	0.0239662	+	0.999713i	$0.492371\pi$
$509$	−21.9468	+	24.3744i	−0.972775	+	1.08038i	−0.996741	+	0.0806635i	$0.974296\pi$
$510$	0.104528	+	0.994522i	0.00462860	+	0.0440382i
$511$	0.234037	+	0.720292i	0.0103532	+	0.0318638i
$512$	7.03241	+	21.6435i	0.310792	+	0.956518i
$513$	1.11394	+	10.5985i	0.0491819	+	0.467934i
$514$	6.18453	−	6.86862i	0.272788	−	0.302962i
$515$	1.38581	+	1.53910i	0.0610663	+	0.0678210i
$516$	−0.862865	+	8.20961i	−0.0379855	+	0.361408i
$517$	−30.6294	+	6.51049i	−1.34708	+	0.286331i
$518$	−0.156740	−	0.0697850i	−0.00688674	−	0.00306618i
$519$	−2.78597	+	2.02413i	−0.122291	+	0.0888493i
$520$	5.54620	−	2.46933i	0.243217	−	0.108287i
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	−0.550169	−	0.835054i	$-0.685437\pi$
$521$	10.2279	−	17.7153i	0.448093	−	0.776121i	0.998262	+	0.0589331i	$0.0187699\pi$
$522$	−4.00000	−	6.92820i	−0.175075	−	0.303239i
$523$	6.47214	+	4.70228i	0.283007	+	0.205616i	0.720228	−	0.693738i	$-0.244037\pi$
$523$	6.47214	+	4.70228i	0.283007	+	0.205616i	−0.437221	+	0.899354i	$0.644037\pi$
$524$	−23.6841	−	5.03421i	−1.03464	−	0.219920i
$525$	0.212076	−	0.652702i	0.00925574	−	0.0284863i
$526$	−9.65685			−0.421059
$527$		0			0
$528$	4.02944			0.175359
$529$	−2.16312	+	6.65740i	−0.0940487	+	0.289452i
$530$	−2.36146	−	0.501943i	−0.102575	−	0.0218030i
$531$	9.31560	+	6.76818i	0.404263	+	0.293714i
$532$	−1.67157	−	2.89525i	−0.0724719	−	0.125525i
$533$	−14.3284	+	24.8176i	−0.620633	+	1.07497i
$534$	0.703021	−	0.313005i	0.0304227	−	0.0135451i
$535$	−10.0433	+	7.29689i	−0.434210	+	0.315472i
$536$	−4.69757	−	2.09149i	−0.202904	−	0.0903388i
$537$	6.17574	−	1.31269i	0.266503	−	0.0566469i
$538$	1.13315	−	10.7812i	0.0488537	−	0.464812i
$539$	−14.8160	−	16.4548i	−0.638169	−	0.708759i
$540$	2.95369	−	3.28040i	0.127106	−	0.141166i
$541$	3.27010	+	31.1129i	0.140592	+	1.33765i	0.806332	+	0.591463i	$0.201450\pi$
$541$	3.27010	+	31.1129i	0.140592	+	1.33765i	−0.665739	+	0.746184i	$0.731884\pi$
$542$	−0.0878446	−	0.270358i	−0.00377325	−	0.0116129i
$543$	1.57614	+	4.85087i	0.0676388	+	0.208171i
$544$	2.68930	+	25.5870i	0.115303	+	1.09703i
$545$	−7.24563	+	8.04709i	−0.310369	+	0.344699i
$546$	0.182056	+	0.202193i	0.00779126	+	0.00865307i
$547$	2.06213	−	19.6199i	0.0881703	−	0.838884i	−0.857659	−	0.514219i	$-0.828082\pi$
$547$	2.06213	−	19.6199i	0.0881703	−	0.838884i	0.945829	−	0.324665i	$-0.105252\pi$
$548$	16.9642	−	3.60584i	0.724673	−	0.154034i
$549$	7.30836	+	3.25389i	0.311913	+	0.138873i
$550$	4.34651	−	3.15793i	0.185336	−	0.134654i
$551$	−27.5362	+	12.2599i	−1.17308	+	0.522290i
$552$	−1.31371	+	2.27541i	−0.0559151	+	0.0968479i
$553$	−1.39949	−	2.42400i	−0.0595126	−	0.103079i
$554$	−4.73911	−	3.44317i	−0.201346	−	0.146286i
$555$	−0.405162	−	0.0861198i	−0.0171982	−	0.00365558i
$556$		0			0
$557$	27.5147			1.16584			0.582918	−	0.812531i	$-0.301911\pi$
$557$	27.5147			1.16584			0.582918	+	0.812531i	$0.301911\pi$
$558$		0			0
$559$	41.7279			1.76490
$560$	−0.383997	+	1.18182i	−0.0162268	+	0.0499411i
$561$	7.65736	+	1.62762i	0.323294	+	0.0687182i
$562$	−0.670212	−	0.486937i	−0.0282712	−	0.0205402i
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	0.692095	−	0.721807i	$-0.256688\pi$
$563$	−6.62132	−	11.4685i	−0.279055	−	0.483338i	−0.971150	+	0.238468i	$0.923355\pi$
$564$	3.65685	−	6.33386i	0.153981	−	0.266704i
$565$	15.2168	−	6.77495i	0.640175	−	0.285024i
$566$	4.57649	−	3.32502i	0.192364	−	0.139761i
$567$	−2.83245	−	1.26109i	−0.118952	−	0.0529608i
$568$	0.110236	−	0.0234313i	0.00462538	−	0.000983156i
$569$	1.37373	−	13.0701i	0.0575896	−	0.547929i	−0.927248	−	0.374449i	$-0.877832\pi$
$569$	1.37373	−	13.0701i	0.0575896	−	0.547929i	0.984837	−	0.173480i	$-0.0555013\pi$
$570$	0.506772	+	0.562828i	0.0212264	+	0.0235743i
$571$	−14.1190	+	15.6807i	−0.590861	+	0.656218i	−0.962221	−	0.272271i	$-0.912225\pi$
$571$	−14.1190	+	15.6807i	−0.590861	+	0.656218i	0.371359	+	0.928489i	$0.378892\pi$
$572$	−2.37264	−	22.5741i	−0.0992050	−	0.943872i
$573$	−2.67512	−	8.23316i	−0.111755	−	0.343945i
$574$	0.396862	+	1.22141i	0.0165647	+	0.0509809i
$575$	−1.67246	−	15.9124i	−0.0697462	−	0.663591i
$576$	7.89507	−	8.76836i	0.328961	−	0.365348i
$577$	−0.0196974	−	0.0218761i	−0.000820012	−	0.000910716i	0.742735	−	0.669586i	$-0.233528\pi$
$577$	−0.0196974	−	0.0218761i	−0.000820012	−	0.000910716i	−0.743555	+	0.668675i	$0.766862\pi$
$578$	−0.734776	+	6.99093i	−0.0305627	+	0.290784i
$579$	−2.89372	+	0.615080i	−0.120259	+	0.0255618i
$580$	11.4059	+	5.07822i	0.473603	+	0.210862i
$581$	−3.37487	+	2.45199i	−0.140013	+	0.101726i
$582$	0.810590	−	0.360898i	0.0336001	−	0.0149597i
$583$	−9.44975	+	16.3674i	−0.391369	+	0.677870i
$584$	−1.44975	−	2.51104i	−0.0599910	−	0.103907i
$585$	−8.76038	−	6.36479i	−0.362197	−	0.263152i
$586$	−5.99599	−	1.27449i	−0.247692	−	0.0526486i
$587$	−9.78251	+	30.1075i	−0.403767	+	1.24267i	0.518153	+	0.855288i	$0.326620\pi$
$587$	−9.78251	+	30.1075i	−0.403767	+	1.24267i	−0.921920	+	0.387380i	$0.873380\pi$
$588$	5.17157			0.213272
$589$		0			0
$590$	1.68629			0.0694235
$591$	−1.72610	+	5.31240i	−0.0710024	+	0.218523i
$592$	−2.93444	−	0.623735i	−0.120605	−	0.0256354i
$593$	1.06281	+	0.772178i	0.0436445	+	0.0317096i	0.609394	−	0.792868i	$-0.291413\pi$
$593$	1.06281	+	0.772178i	0.0436445	+	0.0317096i	−0.565749	+	0.824577i	$0.691413\pi$
$594$	1.62132	+	2.80821i	0.0665236	+	0.115222i
$595$	−1.20711	+	2.09077i	−0.0494866	+	0.0857132i
$596$	−1.67035	+	0.743688i	−0.0684203	+	0.0304627i
$597$	−6.17071	+	4.48328i	−0.252550	+	0.183489i
$598$	5.79475	+	2.57999i	0.236965	+	0.105504i
$599$	−14.7705	+	3.13957i	−0.603507	+	0.128279i	−0.499525	−	0.866300i	$-0.666492\pi$
$599$	−14.7705	+	3.13957i	−0.603507	+	0.128279i	−0.103983	+	0.994579i	$0.533159\pi$
$600$	−0.274640	+	2.61302i	−0.0112121	+	0.106676i
$601$	−4.35920	−	4.84138i	−0.177815	−	0.197484i	0.647648	−	0.761940i	$-0.275753\pi$
$601$	−4.35920	−	4.84138i	−0.177815	−	0.197484i	−0.825463	+	0.564456i	$0.809086\pi$
$602$	1.25131	−	1.38972i	0.0509997	−	0.0566409i
$603$	0.958690	+	9.12133i	0.0390409	+	0.371449i
$604$	−3.00233	−	9.24021i	−0.122163	−	0.375979i
$605$	−0.149960	−	0.461530i	−0.00609675	−	0.0187639i
$606$	0.152177	+	1.44787i	0.00618177	+	0.0588157i
$607$	−1.06110	+	1.17847i	−0.0430686	+	0.0478326i	−0.764294	−	0.644868i	$-0.776912\pi$
$607$	−1.06110	+	1.17847i	−0.0430686	+	0.0478326i	0.721226	+	0.692700i	$0.243579\pi$
$608$	13.0382	+	14.4804i	0.528769	+	0.587257i
$609$	−0.122463	+	1.16515i	−0.00496244	+	0.0472145i
$610$	1.14597	−	0.243584i	0.0463990	−	0.00986242i
$611$	−33.7743	−	15.0373i	−1.36636	−	0.608343i
$612$	24.3855	−	17.7171i	0.985725	−	0.716171i
$613$	11.2491	−	5.00844i	0.454348	−	0.202289i	−0.166786	−	0.985993i	$-0.553339\pi$
$613$	11.2491	−	5.00844i	0.454348	−	0.202289i	0.621134	+	0.783704i	$0.286672\pi$
$614$	2.32843	−	4.03295i	0.0939677	−	0.162757i
$615$	1.55025	+	2.68512i	0.0625122	+	0.108274i
$616$	−1.72316	−	1.25195i	−0.0694281	−	0.0504424i
$617$	32.5569	+	6.92019i	1.31069	+	0.278596i	0.809694	−	0.586852i	$-0.199633\pi$
$617$	32.5569	+	6.92019i	1.31069	+	0.278596i	0.500998	+	0.865448i	$0.332966\pi$
$618$	0.109806	−	0.337948i	0.00441704	−	0.0135942i
$619$	−20.3431			−0.817660			−0.408830	−	0.912611i	$-0.634063\pi$
$619$	−20.3431			−0.817660			−0.408830	+	0.912611i	$0.634063\pi$
$620$		0			0
$621$	9.65685			0.387516
$622$	1.44814	−	4.45693i	0.0580653	−	0.178707i
$623$	1.81727	+	0.386272i	0.0728072	+	0.0154756i
$624$	3.84878	+	2.79631i	0.154075	+	0.111942i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.378680	−	0.655892i	0.0151351	−	0.0262147i
$627$	5.41635	−	2.41151i	0.216308	−	0.0963066i
$628$	13.5669	−	9.85690i	0.541376	−	0.393333i
$629$	−5.32453	−	2.37063i	−0.212303	−	0.0945234i
$630$	−0.474677	+	0.100896i	−0.0189116	+	0.00401978i
$631$	−5.22770	+	49.7382i	−0.208111	+	1.98005i	−0.00957315	+	0.999954i	$0.503047\pi$
$631$	−5.22770	+	49.7382i	−0.208111	+	1.98005i	−0.198538	+	0.980093i	$0.563619\pi$
$632$	7.17022	+	7.96334i	0.285216	+	0.316765i
$633$	2.88643	−	3.20571i	0.114725	−	0.127416i
$634$	0.338948	+	3.22488i	0.0134614	+	0.128076i
$635$	2.75010	+	8.46392i	0.109134	+	0.335881i
$636$	−1.36407	−	4.19817i	−0.0540888	−	0.166468i
$637$	−2.73260	−	25.9989i	−0.108269	−	1.03011i
$638$	−6.13698	+	6.81581i	−0.242965	+	0.269840i
$639$	−0.134502	−	0.149380i	−0.00532082	−	0.00590937i
$640$	1.10344	−	10.4985i	0.0436173	−	0.414990i
$641$	13.6653	−	2.90464i	0.539746	−	0.114727i	0.0700311	−	0.997545i	$-0.477690\pi$
$641$	13.6653	−	2.90464i	0.539746	−	0.114727i	0.469715	+	0.882818i	$0.344357\pi$
$642$	1.94580	+	0.866326i	0.0767946	+	0.0341911i
$643$	−28.5694	+	20.7569i	−1.12667	+	0.818571i	−0.985206	−	0.171373i	$-0.945180\pi$
$643$	−28.5694	+	20.7569i	−1.12667	+	0.818571i	−0.141460	+	0.989944i	$0.545180\pi$
$644$	−2.76753	+	1.23218i	−0.109056	+	0.0485548i
$645$	2.25736	−	3.90986i	0.0888834	−	0.153951i
$646$	5.32843	+	9.22911i	0.209644	+	0.363114i
$647$	36.6596	+	26.6347i	1.44124	+	1.04712i	0.987782	+	0.155839i	$0.0498082\pi$
$647$	36.6596	+	26.6347i	1.44124	+	1.04712i	0.453454	+	0.891280i	$0.350192\pi$
$648$	11.6107	+	2.46792i	0.456110	+	0.0969492i
$649$	4.07934	−	12.5549i	0.160128	−	0.492823i
$650$	6.34315			0.248799
$651$		0			0
$652$	−38.3431			−1.50163
$653$	−1.89802	+	5.84152i	−0.0742754	+	0.228596i	−0.981301	−	0.192479i	$-0.938347\pi$
$653$	−1.89802	+	5.84152i	−0.0742754	+	0.228596i	0.907026	+	0.421075i	$0.138347\pi$
$654$	1.81727	+	0.386272i	0.0710607	+	0.0151044i
$655$	10.7135	+	7.78383i	0.418612	+	0.304139i
$656$	11.2279	+	19.4473i	0.438377	+	0.759291i
$657$	−2.58579	+	4.47871i	−0.100881	+	0.174731i
$658$	−1.51361	+	0.673903i	−0.0590067	+	0.0262715i
$659$	1.34042	−	0.973874i	0.0522155	−	0.0379368i	−0.561371	−	0.827564i	$-0.689726\pi$
$659$	1.34042	−	0.973874i	0.0522155	−	0.0379368i	0.613587	+	0.789627i	$0.289726\pi$
$660$	−2.24353	−	0.998882i	−0.0873291	−	0.0388814i
$661$	−4.75171	+	1.01001i	−0.184820	+	0.0392847i	−0.299392	−	0.954130i	$-0.596784\pi$
$661$	−4.75171	+	1.01001i	−0.184820	+	0.0392847i	0.114572	+	0.993415i	$0.463450\pi$
$662$	−0.400180	+	3.80745i	−0.0155534	+	0.147981i
$663$	6.18453	+	6.86862i	0.240187	+	0.266755i
$664$	10.6864	−	11.8684i	0.414712	−	0.460585i
$665$	0.191123	+	1.81841i	0.00741142	+	0.0705149i
$666$	−0.362036	−	1.11423i	−0.0140286	−	0.0431756i
$667$	8.44040	+	25.9769i	0.326814	+	1.00583i
$668$	4.31103	+	41.0167i	0.166799	+	1.58698i
$669$	−6.57650	+	7.30394i	−0.254262	+	0.282387i
$670$	0.898740	+	0.998152i	0.0347214	+	0.0385620i
$671$	0.958690	−	9.12133i	0.0370098	−	0.352125i
$672$	0.740809	−	0.157464i	0.0285773	−	0.00607430i
$673$	8.53539	+	3.80020i	0.329015	+	0.146487i	0.564595	−	0.825368i	$-0.309032\pi$
$673$	8.53539	+	3.80020i	0.329015	+	0.146487i	−0.235580	+	0.971855i	$0.575699\pi$
$674$	−3.12108	+	2.26760i	−0.120219	+	0.0873445i
$675$	8.82198	−	3.92780i	0.339558	−	0.151181i
$676$	1.51472	−	2.62357i	0.0582584	−	0.100907i
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	0.951711	+	0.306994i	$0.0993232\pi$
$677$	19.2990	+	33.4268i	0.741720	+	1.28470i	−0.209991	+	0.977703i	$0.567343\pi$
$678$	−2.31206	−	1.67981i	−0.0887942	−	0.0645127i
$679$	2.09532	+	0.445375i	0.0804112	+	0.0170919i
$680$	2.85613	−	8.79027i	0.109528	−	0.337092i
$681$	−7.62742			−0.292283
$682$		0			0
$683$	−1.37258			−0.0525204			−0.0262602	−	0.999655i	$-0.508360\pi$
$683$	−1.37258			−0.0525204			−0.0262602	+	0.999655i	$0.508360\pi$
$684$	7.05437	−	21.7111i	0.269731	−	0.830146i
$685$	−9.27801	−	1.97210i	−0.354494	−	0.0753501i
$686$	−1.91946	−	1.39457i	−0.0732853	−	0.0532449i
$687$	1.13604	+	1.96768i	0.0433426	+	0.0750716i
$688$	16.3492	−	28.3177i	0.623309	−	1.07960i
$689$	−20.3846	+	9.07580i	−0.776591	+	0.345761i
$690$	0.555221	−	0.403392i	0.0211369	−	0.0153569i
$691$	−0.0649237	−	0.0289059i	−0.00246981	−	0.00109963i	0.405501	−	0.914094i	$-0.367097\pi$
$691$	−0.0649237	−	0.0289059i	−0.00246981	−	0.00109963i	−0.407971	+	0.912995i	$0.633764\pi$
$692$	14.8688	−	3.16047i	0.565228	−	0.120143i
$693$	−0.397103	+	3.77818i	−0.0150847	+	0.143521i
$694$	−2.37150	−	2.63382i	−0.0900210	−	0.0999785i
$695$		0			0
$696$	−0.468840	−	4.46071i	−0.0177713	−	0.169083i
$697$	13.4816	+	41.4921i	0.510653	+	1.57163i
$698$	−3.47040	−	10.6808i	−0.131357	−	0.404274i
$699$	0.397103	+	3.77818i	0.0150198	+	0.142904i
$700$	−2.02709	+	2.25131i	−0.0766168	+	0.0850915i
$701$	−9.02341	−	10.0215i	−0.340810	−	0.378507i	0.548238	−	0.836322i	$-0.315299\pi$
$701$	−9.02341	−	10.0215i	−0.340810	−	0.378507i	−0.889047	+	0.457815i	$0.848632\pi$
$702$	−0.400180	+	3.80745i	−0.0151038	+	0.143703i
$703$	−4.31775	+	0.917767i	−0.162847	+	0.0346142i
$704$	−12.3574	−	5.50189i	−0.465739	−	0.207360i
$705$	−3.23607	+	2.35114i	−0.121877	+	0.0885491i
$706$	1.13521	−	0.505428i	0.0427241	−	0.0190220i
$707$	−1.75736	+	3.04384i	−0.0660923	+	0.114475i
$708$	1.54163	+	2.67018i	0.0579380	+	0.100352i
$709$	−14.0071	−	10.1767i	−0.526047	−	0.382196i	0.292830	−	0.956165i	$-0.405403\pi$
$709$	−14.0071	−	10.1767i	−0.526047	−	0.382196i	−0.818877	+	0.573969i	$0.805403\pi$
$710$	−0.0287940	−	0.00612035i	−0.00108062	−	0.000229693i
$711$	5.90615	−	18.1773i	0.221498	−	0.681700i
$712$	−7.11270			−0.266560
$713$		0			0
$714$	0.414214			0.0155016
$715$	−3.83620	+	11.8066i	−0.143466	+	0.441543i
$716$	−27.2610	−	5.79451i	−1.01879	−	0.216551i
$717$	7.11853	+	5.17192i	0.265846	+	0.193149i
$718$	−1.47056	−	2.54709i	−0.0548809	−	0.0950565i
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	−0.780911	−	0.624642i	$-0.785245\pi$
$719$	4.03553	−	6.98975i	0.150500	−	0.260674i	0.931411	+	0.363968i	$0.118578\pi$
$720$	−7.75169	+	3.45127i	−0.288888	+	0.128621i
$721$	0.694027	−	0.504240i	0.0258469	−	0.0187789i
$722$	0.183632	+	0.0817582i	0.00683407	+	0.00304272i
$723$	−5.40614	+	1.14911i	−0.201056	+	0.0427358i
$724$	2.35343	−	22.3914i	0.0874645	−	0.832169i
$725$	18.2764	+	20.2980i	0.678770	+	0.753850i
$726$	−0.0557126	+	0.0618751i	−0.00206769	+	0.00229640i
$727$	−4.26901	−	40.6169i	−0.158329	−	1.50640i	−0.728599	−	0.684940i	$-0.759828\pi$
$727$	−4.26901	−	40.6169i	−0.158329	−	1.50640i	0.570271	−	0.821457i	$-0.306838\pi$
$728$	−0.777091	−	2.39164i	−0.0288009	−	0.0886401i
$729$	−5.61532	−	17.2822i	−0.207975	−	0.640081i
$730$	0.0791656	+	0.753210i	0.00293005	+	0.0278776i
$731$	42.5078	−	47.2097i	1.57221	−	1.74611i
$732$	1.43337	+	1.59192i	0.0529788	+	0.0588389i
$733$	−1.63351	+	15.5418i	−0.0603351	+	0.574050i	0.922035	+	0.387105i	$0.126525\pi$
$733$	−1.63351	+	15.5418i	−0.0603351	+	0.574050i	−0.982371	+	0.186944i	$0.940142\pi$
$734$	9.81027	−	2.08524i	0.362104	−	0.0769675i
$735$	−2.58390	−	1.15042i	−0.0953085	−	0.0424341i
$736$	14.2847	−	10.3784i	0.526541	−	0.382554i
$737$	9.60567	−	4.27672i	0.353830	−	0.157535i
$738$	−4.38478	+	7.59466i	−0.161406	+	0.279563i
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	−0.886764	−	0.462223i	$-0.847052\pi$
$739$	−22.9350	−	39.7246i	−0.843679	−	1.46129i	0.0430851	−	0.999071i	$-0.486281\pi$
$740$	1.47923	+	1.07472i	0.0543775	+	0.0395076i
$741$	6.84703	+	1.45538i	0.251532	+	0.0534648i
$742$	−0.309017	+	0.951057i	−0.0113444	+	0.0349144i
$743$	5.65685			0.207530			0.103765	−	0.994602i	$-0.466911\pi$
$743$	5.65685			0.207530			0.103765	+	0.994602i	$0.466911\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	1.27999	−	3.93941i	0.0468638	−	0.144232i
$747$	−27.8628	−	5.92242i	−1.01945	−	0.216690i
$748$	−27.9567	−	20.3117i	−1.02220	−	0.742670i
$749$	2.57107	+	4.45322i	0.0939448	+	0.162717i
$750$	0.772078	−	1.33728i	0.0281923	−	0.0488305i
$751$	6.61648	−	2.94585i	0.241439	−	0.107495i	−0.282450	−	0.959282i	$-0.591147\pi$
$751$	6.61648	−	2.94585i	0.241439	−	0.107495i	0.523889	+	0.851786i	$0.324481\pi$
$752$	−23.4377	+	17.0285i	−0.854684	+	0.620964i
$753$	2.42716	+	1.08064i	0.0884505	+	0.0393807i
$754$	−10.5918	+	2.25136i	−0.385731	+	0.0819896i
$755$	−0.555434	+	5.28460i	−0.0202143	+	0.192326i
$756$	−1.22346	−	1.35879i	−0.0444967	−	0.0494186i
$757$	15.6196	−	17.3473i	0.567705	−	0.630500i	−0.389113	−	0.921190i	$-0.627218\pi$
$757$	15.6196	−	17.3473i	0.567705	−	0.630500i	0.956817	+	0.290690i	$0.0938850\pi$
$758$	−0.319739	−	3.04212i	−0.0116135	−	0.110495i
$759$	−1.66022	−	5.10963i	−0.0602621	−	0.185468i
$760$	−2.16312	−	6.65740i	−0.0784646	−	0.241489i
$761$	−3.18350	−	30.2890i	−0.115402	−	1.09798i	−0.886969	−	0.461828i	$-0.847194\pi$
$761$	−3.18350	−	30.2890i	−0.115402	−	1.09798i	0.771568	−	0.636147i	$-0.219473\pi$
$762$	1.02170	−	1.13472i	0.0370124	−	0.0411064i
$763$	3.00124	+	3.33321i	0.108652	+	0.120670i
$764$	−3.99437	+	38.0039i	−0.144511	+	1.37493i
$765$	−16.1250	+	3.42748i	−0.583002	+	0.123921i
$766$	1.93005	+	0.859312i	0.0697354	+	0.0310482i
$767$	12.6092	−	9.16110i	0.455291	−	0.330788i
$768$	1.50247	−	0.668944i	0.0542158	−	0.0241384i
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	0.331721	+	0.943378i	$0.392371\pi$
$769$	−18.0563	+	31.2745i	−0.651129	+	1.12779i	−0.982849	+	0.184410i	$0.940963\pi$
$770$	0.278175	+	0.481813i	0.0100247	+	0.0173633i
$771$	−7.47745	−	5.43269i	−0.269294	−	0.195653i
$772$	12.7735	+	2.71509i	0.459729	+	0.0977183i
$773$	5.56231	−	17.1190i	0.200062	−	0.615728i	−0.799818	−	0.600243i	$-0.795071\pi$
$773$	5.56231	−	17.1190i	0.200062	−	0.615728i	0.999880	−	0.0154855i	$-0.00492938\pi$
$774$	12.7696			0.458992
$775$		0			0
$776$	−8.20101			−0.294399
$777$	−0.0530189	+	0.163176i	−0.00190204	+	0.00585389i
$778$	4.51437	+	0.959559i	0.161848	+	0.0344019i
$779$	26.7312	+	19.4214i	0.957746	+	0.695843i
$780$	−1.44975	−	2.51104i	−0.0519093	−	0.0899095i
$781$	−0.115224	+	0.199573i	−0.00412303	+	0.00714129i
$782$	8.82198	−	3.92780i	0.315473	−	0.140458i
$783$	−13.3369	+	9.68981i	−0.476621	+	0.346285i
$784$	−18.7142	−	8.33211i	−0.668366	−	0.297576i
$785$	−8.97115	+	1.90688i	−0.320194	+	0.0680594i
$786$	0.237497	−	2.25963i	0.00847123	−	0.0805984i
$787$	28.3806	+	31.5199i	1.01166	+	1.12356i	0.992313	+	0.123750i	$0.0394922\pi$
$787$	28.3806	+	31.5199i	1.01166	+	1.12356i	0.0193475	+	0.999813i	$0.493841\pi$
$788$	16.4987	−	18.3236i	0.587740	−	0.652752i
$789$	1.00942	+	9.60395i	0.0359362	+	0.341910i
$790$	−0.864935	−	2.66200i	−0.0307730	−	0.0947096i
$791$	−2.13206	−	6.56181i	−0.0758074	−	0.233311i
$792$	−1.52028	−	14.4645i	−0.0540207	−	0.513973i
$793$	7.24563	−	8.04709i	0.257300	−	0.285761i
$794$	−9.28088	−	10.3075i	−0.329366	−	0.365798i
$795$	−0.252354	+	2.40099i	−0.00895008	+	0.0851543i
$796$	32.9333	−	7.00019i	1.16729	−	0.248115i
$797$	25.9957	+	11.5740i	0.920815	+	0.409973i	0.811713	−	0.584057i	$-0.198536\pi$
$797$	25.9957	+	11.5740i	0.920815	+	0.409973i	0.109103	+	0.994030i	$0.465202\pi$
$798$	0.253796	−	0.184393i	0.00898426	−	0.00652745i
$799$	−51.4182	+	22.8929i	−1.81905	+	0.809892i
$800$	8.82843	−	15.2913i	0.312132	−	0.540629i
$801$	6.34315	+	10.9867i	0.224124	+	0.388194i
$802$	8.99036	+	6.53188i	0.317461	+	0.230649i
$803$	5.79937	+	1.23269i	0.204655	+	0.0435008i
$804$	−0.758898	+	2.33565i	−0.0267643	+	0.0823719i
$805$	1.65685			0.0583964
$806$		0			0
$807$	−10.8406			−0.381608
$808$	4.15808	−	12.7973i	0.146281	−	0.450206i
$809$	11.7666	+	2.50106i	0.413690	+	0.0879326i	0.410055	−	0.912061i	$-0.365509\pi$
$809$	11.7666	+	2.50106i	0.413690	+	0.0879326i	0.00363537	+	0.999993i	$0.498843\pi$
$810$	−2.50836	−	1.82243i	−0.0881348	−	0.0640337i
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	0.961007	−	0.276524i	$-0.0891827\pi$
$811$	6.86396	+	11.8887i	0.241026	+	0.417470i	−0.719981	+	0.693994i	$0.755849\pi$
$812$	2.58579	−	4.47871i	0.0907433	−	0.157172i
$813$	−0.259695	+	0.115624i	−0.00910789	+	0.00405509i
$814$	−1.08663	+	0.789481i	−0.0380863	+	0.0276713i
$815$	19.1576	+	8.52950i	0.671060	+	0.298775i
$816$	7.08437	−	1.50583i	0.248003	−	0.0527146i
$817$	5.02915	−	47.8491i	0.175948	−	1.67403i
$818$	5.72532	+	6.35861i	0.200181	+	0.222323i
$819$	−3.00124	+	3.33321i	−0.104872	+	0.116472i
$820$	−1.43061	−	13.6113i	−0.0499590	−	0.475328i
$821$	2.62210	+	8.06998i	0.0915118	+	0.281644i	0.986329	−	0.164789i	$-0.0526942\pi$
$821$	2.62210	+	8.06998i	0.0915118	+	0.281644i	−0.894817	+	0.446433i	$0.852694\pi$
$822$	0.502900	+	1.54777i	0.0175406	+	0.0539845i
$823$	−3.78531	−	36.0148i	−0.131948	−	1.25540i	−0.837380	−	0.546621i	$-0.815914\pi$
$823$	−3.78531	−	36.0148i	−0.131948	−	1.25540i	0.705433	−	0.708777i	$-0.250753\pi$
$824$	−2.19761	+	2.44069i	−0.0765572	+	0.0850254i
$825$	−3.59496	−	3.99261i	−0.125160	−	0.139005i
$826$	0.0730115	−	0.694658i	0.00254040	−	0.0241703i
$827$	−36.0932	+	7.67184i	−1.25508	+	0.266776i	−0.787024	−	0.616922i	$-0.788379\pi$
$827$	−36.0932	+	7.67184i	−1.25508	+	0.266776i	−0.468058	+	0.883698i	$0.655046\pi$
$828$	−18.8979	−	8.41387i	−0.656746	−	0.292402i
$829$	−31.0876	+	22.5865i	−1.07972	+	0.784461i	−0.977634	−	0.210315i	$-0.932551\pi$
$829$	−31.0876	+	22.5865i	−1.07972	+	0.784461i	−0.102084	+	0.994776i	$0.532551\pi$
$830$	−3.81092	+	1.69673i	−0.132279	+	0.0588944i
$831$	−2.92893	+	5.07306i	−0.101604	+	0.175982i
$832$	−7.98528	−	13.8309i	−0.276840	−	0.479501i
$833$	−32.1981	−	23.3933i	−1.11560	−	0.810528i
$834$		0			0
$835$	6.97030	−	21.4524i	0.241217	−	0.742390i
$836$	−26.1716			−0.905163
$837$		0			0
$838$	11.5980			0.400646
$839$	−4.52012	+	13.9115i	−0.156052	+	0.480278i	−0.998266	−	0.0588649i	$-0.981252\pi$
$839$	−4.52012	+	13.9115i	−0.156052	+	0.480278i	0.842214	+	0.539143i	$0.181252\pi$
$840$	−0.266132	−	0.0565682i	−0.00918244	−	0.00195179i
$841$	−14.2609	−	10.3611i	−0.491754	−	0.357281i
$842$	6.44975	+	11.1713i	0.222273	+	0.384988i
$843$	−0.414214	+	0.717439i	−0.0142663	+	0.0247099i
$844$	−17.3954	+	7.74493i	−0.598774	+	0.266591i
$845$	−1.34042	+	0.973874i	−0.0461120	+	0.0335023i
$846$	−10.3356	−	4.60170i	−0.355345	−	0.158210i
$847$	−0.196618	+	0.0417924i	−0.00675586	+	0.00143600i
$848$	−1.82771	+	17.3895i	−0.0627638	+	0.597158i
$849$	−3.78517	−	4.20386i	−0.129907	−	0.144276i
$850$	6.46170	−	7.17644i	0.221634	−	0.246150i
$851$	0.418114	+	3.97809i	0.0143328	+	0.136367i
$852$	−0.0166325	−	0.0511895i	−0.000569820	−	0.00175372i
$853$	−4.79431	−	14.7554i	−0.164154	−	0.505214i	0.834819	−	0.550525i	$-0.185572\pi$
$853$	−4.79431	−	14.7554i	−0.164154	−	0.505214i	−0.998973	+	0.0453103i	$0.985572\pi$
$854$	−0.0507257	−	0.482623i	−0.00173580	−	0.0165150i
$855$	−8.35428	+	9.27837i	−0.285710	+	0.317314i
$856$	−13.1727	−	14.6298i	−0.450234	−	0.500035i
$857$	2.03677	−	19.3785i	0.0695746	−	0.661958i	−0.903043	−	0.429549i	$-0.858672\pi$
$857$	2.03677	−	19.3785i	0.0695746	−	0.661958i	0.972618	−	0.232409i	$-0.0746608\pi$
$858$	2.08340	−	0.442840i	0.0711260	−	0.0151183i
$859$	−45.1152	−	20.0866i	−1.53931	−	0.685346i	−0.550544	−	0.834806i	$-0.685580\pi$
$859$	−45.1152	−	20.0866i	−1.53931	−	0.685346i	−0.988768	+	0.149460i	$0.952246\pi$
$860$	−16.1228	+	11.7139i	−0.549784	+	0.399442i
$861$	1.17324	−	0.522360i	0.0399839	−	0.0178020i
$862$	3.47056	−	6.01119i	0.118208	−	0.204742i
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	0.887423	−	0.460956i	$-0.152493\pi$
$863$	1.30761	+	2.26485i	0.0445116	+	0.0770964i	−0.842911	+	0.538053i	$0.819160\pi$
$864$	8.62158	+	6.26394i	0.293312	+	0.213104i
$865$	−8.13203	−	1.72852i	−0.276497	−	0.0587713i
$866$	3.47040	−	10.6808i	0.117929	−	0.362948i
$867$	7.02944			0.238732
$868$		0			0
$869$	−21.9117			−0.743303
$870$	−0.362036	+	1.11423i	−0.0122742	+	0.0377760i
$871$	12.1429	+	2.58106i	0.411448	+	0.0874559i
$872$	−13.8921	−	10.0932i	−0.470446	−	0.341799i
$873$	7.31371	+	12.6677i	0.247532	+	0.428737i
$874$	3.65685	−	6.33386i	0.123695	−	0.214246i
$875$	3.40563	−	1.51628i	0.115131	−	0.0512597i
$876$	−1.12031	+	0.813951i	−0.0378517	+	0.0275009i
$877$	49.1747	+	21.8940i	1.66051	+	0.739308i	0.999934	−	0.0114501i	$-0.00364474\pi$
$877$	49.1747	+	21.8940i	1.66051	+	0.739308i	0.660578	+	0.750758i	$0.270311\pi$
$878$	−0.839118	+	0.178360i	−0.0283189	+	0.00601936i
$879$	−0.640753	+	6.09636i	−0.0216121	+	0.205625i
$880$	6.50925	+	7.22925i	0.219427	+	0.243698i
$881$	7.81966	−	8.68461i	0.263451	−	0.292592i	−0.596877	−	0.802333i	$-0.703592\pi$
$881$	7.81966	−	8.68461i	0.263451	−	0.292592i	0.860328	+	0.509741i	$0.170259\pi$
$882$	−0.836228	−	7.95618i	−0.0281573	−	0.267898i
$883$	−9.35835	−	28.8021i	−0.314934	−	0.969266i	−0.975782	−	0.218747i	$-0.929803\pi$
$883$	−9.35835	−	28.8021i	−0.314934	−	0.969266i	0.660848	−	0.750520i	$-0.270197\pi$
$884$	−12.6076	−	38.8021i	−0.424039	−	1.30506i
$885$	−0.176265	−	1.67705i	−0.00592510	−	0.0563735i
$886$	−1.31856	+	1.46441i	−0.0442980	+	0.0491979i
$887$	−34.3437	−	38.1426i	−1.15315	−	1.28070i	−0.953688	−	0.300797i	$-0.902747\pi$
$887$	−34.3437	−	38.1426i	−1.15315	−	1.28070i	−0.199461	−	0.979906i	$-0.563919\pi$
$888$	0.0686600	−	0.653256i	0.00230408	−	0.0219218i
$889$	3.60574	−	0.766423i	0.120933	−	0.0257050i
$890$	1.69724	+	0.755662i	0.0568917	+	0.0253298i
$891$	−19.6365	+	14.2668i	−0.657848	+	0.477955i
$892$	39.6340	−	17.6462i	1.32704	−	0.590838i
$893$	−21.3137	+	36.9164i	−0.713236	+	1.23536i
$894$	−0.0857864	−	0.148586i	−0.00286913	−	0.00496947i
$895$	12.3316	+	8.95940i	0.412198	+	0.299480i
$896$	−4.27703	−	0.909111i	−0.142886	−	0.0303713i
$897$	1.96014	−	6.03269i	0.0654472	−	0.201426i
$898$	−16.8284			−0.561572
$899$		0			0
$900$	−20.6863			−0.689543
$901$	−10.4975	+	32.3079i	−0.349722	+	1.07633i
$902$	9.83412	+	2.09031i	0.327441	+	0.0695996i
$903$	−1.51291	−	1.09919i	−0.0503464	−	0.0365788i
$904$	13.2071	+	22.8754i	0.439262	+	0.760824i
$905$	−6.15685	+	10.6640i	−0.204661	+	0.354483i
$906$	0.832869	−	0.370817i	0.0276702	−	0.0123196i
$907$	−26.4438	+	19.2125i	−0.878051	+	0.637941i	−0.932735	−	0.360562i	$-0.882585\pi$
$907$	−26.4438	+	19.2125i	−0.878051	+	0.637941i	0.0546843	+	0.998504i	$0.482585\pi$
$908$	30.7582	+	13.6944i	1.02075	+	0.454466i
$909$	−23.4755	+	4.98988i	−0.778635	+	0.165504i
$910$	−0.0686600	+	0.653256i	−0.00227606	+	0.0216552i
$911$	0.641274	+	0.712207i	0.0212464	+	0.0235965i	0.753674	−	0.657248i	$-0.228280\pi$
$911$	0.641274	+	0.712207i	0.0212464	+	0.0235965i	−0.732428	+	0.680845i	$0.761613\pi$
$912$	3.67037	−	4.07636i	0.121538	−	0.134982i
$913$	3.41357	+	32.4780i	0.112973	+	1.07486i
$914$	−3.98240	−	12.2566i	−0.131726	−	0.405411i
$915$	−0.362036	−	1.11423i	−0.0119685	−	0.0368354i
$916$	−1.04836	−	9.97449i	−0.0346388	−	0.329567i
$917$	3.67037	−	4.07636i	0.121206	−	0.134613i
$918$	3.89998	+	4.33137i	0.128718	+	0.142956i
$919$	3.64799	−	34.7083i	0.120336	−	1.14492i	−0.753074	−	0.657936i	$-0.771430\pi$
$919$	3.64799	−	34.7083i	0.120336	−	1.14492i	0.873410	−	0.486986i	$-0.161904\pi$
$920$	−6.20453	+	1.31881i	−0.204557	+	0.0434800i
$921$	−4.25425	−	1.89411i	−0.140182	−	0.0624132i
$922$	0.717842	−	0.521543i	0.0236409	−	0.0171761i
$923$	−0.248556	+	0.110664i	−0.00818131	+	0.00364255i
$924$	−0.508622	+	0.880959i	−0.0167324	+	0.0289814i
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	3.00609	+	2.18405i	0.0987862	+	0.0717724i
$927$	5.72986	+	1.21792i	0.188193	+	0.0400017i
$928$	−9.31443	+	28.6669i	−0.305761	+	0.941036i
$929$	7.51472			0.246550			0.123275	−	0.992373i	$-0.460660\pi$
$929$	7.51472			0.246550			0.123275	+	0.992373i	$0.460660\pi$
$930$		0			0
$931$	−30.1421			−0.987869
$932$	5.18208	−	15.9488i	0.169745	−	0.522420i
$933$	−4.58388	−	0.974335i	−0.150070	−	0.0318983i
$934$	2.68085	+	1.94775i	0.0877200	+	0.0637323i
$935$	9.44975	+	16.3674i	0.309040	+	0.535273i
$936$	8.58579	−	14.8710i	0.280635	−	0.486074i
$937$	14.3301	−	6.38019i	0.468145	−	0.208432i	−0.159086	−	0.987265i	$-0.550855\pi$
$937$	14.3301	−	6.38019i	0.468145	−	0.208432i	0.627231	+	0.778833i	$0.284188\pi$
$938$	0.450096	−	0.327014i	0.0146962	−	0.0106774i
$939$	−0.691882	−	0.308046i	−0.0225787	−	0.0100527i
$940$	17.2710	−	3.67107i	0.563318	−	0.119737i
$941$	3.65850	−	34.8083i	0.119264	−	1.13472i	−0.757178	−	0.653209i	$-0.773422\pi$
$941$	3.65850	−	34.8083i	0.119264	−	1.13472i	0.876441	−	0.481508i	$-0.159911\pi$
$942$	1.05294	+	1.16941i	0.0343066	+	0.0381014i
$943$	20.0345	−	22.2506i	0.652414	−	0.724579i
$944$	−1.27663	−	12.1463i	−0.0415507	−	0.395328i
$945$	0.309017	+	0.951057i	0.0100523	+	0.0309379i
$946$	−4.52389	−	13.9231i	−0.147084	−	0.452679i
$947$	−1.99655	−	18.9959i	−0.0648790	−	0.617283i	−0.977857	−	0.209274i	$-0.932890\pi$
$947$	−1.99655	−	18.9959i	−0.0648790	−	0.617283i	0.912978	−	0.408009i	$-0.133777\pi$
$948$	3.42444	−	3.80323i	0.111221	−	0.123523i
$949$	4.68391	+	5.20201i	0.152046	+	0.168865i
$950$	0.764491	−	7.27364i	0.0248034	−	0.235988i
$951$	3.17178	−	0.674183i	0.102852	−	0.0218619i
$952$	−3.49744	−	1.55716i	−0.113353	−	0.0504679i
$953$	−2.84347	+	2.06590i	−0.0921089	+	0.0669211i	−0.632887	−	0.774245i	$-0.718130\pi$
$953$	−2.84347	+	2.06590i	−0.0921089	+	0.0669211i	0.540778	+	0.841166i	$0.318130\pi$
$954$	−6.23808	+	2.77737i	−0.201965	+	0.0899207i
$955$	10.4497	−	18.0995i	0.338146	−	0.585686i
$956$	−19.4203	−	33.6370i	−0.628098	−	1.08790i
$957$	7.41996	+	5.39092i	0.239853	+	0.174264i
$958$	6.37236	+	1.35449i	0.205881	+	0.0437615i
$959$	−1.21411	+	3.73664i	−0.0392056	+	0.120662i
$960$	−1.72792			−0.0557684
$961$		0			0
$962$	−1.58579			−0.0511278
$963$	−10.8504	+	33.3942i	−0.349650	+	1.07611i
$964$	23.8638	+	5.07242i	0.768602	+	0.163371i
$965$	−5.77811	−	4.19804i	−0.186004	−	0.135140i
$966$	−0.142136	−	0.246186i	−0.00457314	−	0.00792091i
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	−0.714742	−	0.699388i	$-0.753456\pi$
$967$	7.72183	−	13.3746i	0.248317	−	0.430098i	0.963059	+	0.269290i	$0.0867892\pi$
$968$	0.703021	−	0.313005i	0.0225960	−	0.0100604i
$969$	8.62158	−	6.26394i	0.276965	−	0.201227i
$970$	1.95694	+	0.871285i	0.0628335	+	0.0279753i
$971$	0.683221	−	0.145223i	0.0219256	−	0.00466043i	−0.196936	−	0.980416i	$-0.563099\pi$
$971$	0.683221	−	0.145223i	0.0219256	−	0.00466043i	0.218861	+	0.975756i	$0.429766\pi$
$972$	1.97681	−	18.8081i	0.0634062	−	0.603270i
$973$		0			0
$974$	5.37274	−	5.96703i	0.172154	−	0.191196i
$975$	−0.663039	−	6.30840i	−0.0212343	−	0.202030i
$976$	−2.62210	−	8.06998i	−0.0839313	−	0.258314i
$977$	−0.149960	−	0.461530i	−0.00479765	−	0.0147657i	0.948629	−	0.316391i	$-0.102471\pi$
$977$	−0.149960	−	0.461530i	−0.00479765	−	0.0147657i	−0.953427	+	0.301625i	$0.902471\pi$
$978$	−0.376091	−	3.57827i	−0.0120261	−	0.114420i
$979$	9.73194	−	10.8084i	0.311034	−	0.345438i
$980$	8.35428	+	9.27837i	0.266868	+	0.296387i
$981$	−3.20144	+	30.4596i	−0.102214	+	0.972501i
$982$	−0.642500	+	0.136568i	−0.0205030	+	0.00435805i
$983$	−35.4827	−	15.7979i	−1.13172	−	0.503875i	−0.246545	−	0.969131i	$-0.579295\pi$
$983$	−35.4827	−	15.7979i	−1.13172	−	0.503875i	−0.885176	+	0.465256i	$0.845962\pi$
$984$	−3.97773	+	2.88999i	−0.126805	+	0.0921294i
$985$	−12.3194	+	5.48496i	−0.392529	+	0.174765i
$986$	−8.24264	+	14.2767i	−0.262499	+	0.454662i
$987$	0.828427	+	1.43488i	0.0263691	+	0.0456727i
$988$	−24.9982	−	18.1623i	−0.795299	−	0.577819i
$989$	−42.6453	−	9.06453i	−1.35604	−	0.288235i
$990$	−1.17395	+	3.61305i	−0.0373107	+	0.114830i
$991$	47.9411			1.52290			0.761450	−	0.648224i	$-0.224488\pi$
$991$	47.9411			1.52290			0.761450	+	0.648224i	$0.224488\pi$
$992$		0			0
$993$	3.82843			0.121491
$994$	−0.00376794	+	0.0115965i	−0.000119512	+	0.000367819i
$995$	−18.0118	−	3.82853i	−0.571013	−	0.121373i
$996$	−6.17071	−	4.48328i	−0.195526	−	0.142058i
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	−0.999823	−	0.0188015i	$-0.994015\pi$
$997$	−16.2990	−	28.2307i	−0.516194	−	0.894075i	0.483629	−	0.875273i	$-0.339318\pi$
$998$	0.458369	−	0.793919i	0.0145094	−	0.0251311i
$999$	−2.20549	+	0.981949i	−0.0697787	+	0.0310675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.o.846.2		16
31.2	even	5		31.2.c.a.5.2	✓	4
31.3	odd	30		961.2.g.r.732.1		16
31.4	even	5	inner	961.2.g.o.547.2		16
31.5	even	3		961.2.d.l.628.2		8
31.6	odd	6		961.2.g.r.448.2		16
31.7	even	15	inner	961.2.g.o.844.2		16
31.8	even	5	inner	961.2.g.o.235.1		16
31.9	even	15		961.2.d.l.388.1		8
31.10	even	15		961.2.a.a.1.2		2
31.11	odd	30		961.2.d.i.531.2		8
31.12	odd	30		961.2.c.a.521.2		4
31.13	odd	30		961.2.d.i.374.1		8
31.14	even	15	inner	961.2.g.o.338.1		16
31.15	odd	10		961.2.g.r.816.1		16
31.16	even	5	inner	961.2.g.o.816.1		16
31.17	odd	30		961.2.g.r.338.1		16
31.18	even	15		961.2.d.l.374.1		8
31.19	even	15		31.2.c.a.25.2	yes	4
31.20	even	15		961.2.d.l.531.2		8
31.21	odd	30		961.2.a.c.1.2		2
31.22	odd	30		961.2.d.i.388.1		8
31.23	odd	10		961.2.g.r.235.1		16
31.24	odd	30		961.2.g.r.844.2		16
31.25	even	3	inner	961.2.g.o.448.2		16
31.26	odd	6		961.2.d.i.628.2		8
31.27	odd	10		961.2.g.r.547.2		16
31.28	even	15	inner	961.2.g.o.732.1		16
31.29	odd	10		961.2.c.a.439.2		4
31.30	odd	2		961.2.g.r.846.2		16
93.2	odd	10		279.2.h.c.253.1		4
93.41	odd	30		8649.2.a.l.1.1		2
93.50	odd	30		279.2.h.c.118.1		4
93.83	even	30		8649.2.a.k.1.1		2
124.19	odd	30		496.2.i.h.273.2		4
124.95	odd	10		496.2.i.h.129.2		4
155.2	odd	20		775.2.o.d.749.3		8
155.19	even	30		775.2.e.e.676.1		4
155.33	odd	20		775.2.o.d.749.2		8
155.64	even	10		775.2.e.e.501.1		4
155.112	odd	60		775.2.o.d.149.3		8
155.143	odd	60		775.2.o.d.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.2	✓	4	31.2	even	5
31.2.c.a.25.2	yes	4	31.19	even	15
279.2.h.c.118.1		4	93.50	odd	30
279.2.h.c.253.1		4	93.2	odd	10
496.2.i.h.129.2		4	124.95	odd	10
496.2.i.h.273.2		4	124.19	odd	30
775.2.e.e.501.1		4	155.64	even	10
775.2.e.e.676.1		4	155.19	even	30
775.2.o.d.149.2		8	155.143	odd	60
775.2.o.d.149.3		8	155.112	odd	60
775.2.o.d.749.2		8	155.33	odd	20
775.2.o.d.749.3		8	155.2	odd	20
961.2.a.a.1.2		2	31.10	even	15
961.2.a.c.1.2		2	31.21	odd	30
961.2.c.a.439.2		4	31.29	odd	10
961.2.c.a.521.2		4	31.12	odd	30
961.2.d.i.374.1		8	31.13	odd	30
961.2.d.i.388.1		8	31.22	odd	30
961.2.d.i.531.2		8	31.11	odd	30
961.2.d.i.628.2		8	31.26	odd	6
961.2.d.l.374.1		8	31.18	even	15
961.2.d.l.388.1		8	31.9	even	15
961.2.d.l.531.2		8	31.20	even	15
961.2.d.l.628.2		8	31.5	even	3
961.2.g.o.235.1		16	31.8	even	5	inner
961.2.g.o.338.1		16	31.14	even	15	inner
961.2.g.o.448.2		16	31.25	even	3	inner
961.2.g.o.547.2		16	31.4	even	5	inner
961.2.g.o.732.1		16	31.28	even	15	inner
961.2.g.o.816.1		16	31.16	even	5	inner
961.2.g.o.844.2		16	31.7	even	15	inner
961.2.g.o.846.2		16	1.1	even	1	trivial
961.2.g.r.235.1		16	31.23	odd	10
961.2.g.r.338.1		16	31.17	odd	30
961.2.g.r.448.2		16	31.6	odd	6
961.2.g.r.547.2		16	31.27	odd	10
961.2.g.r.732.1		16	31.3	odd	30
961.2.g.r.816.1		16	31.15	odd	10
961.2.g.r.844.2		16	31.24	odd	30
961.2.g.r.846.2		16	31.30	odd	2
8649.2.a.k.1.1		2	93.83	even	30
8649.2.a.l.1.1		2	93.41	odd	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.127999 - 0.393941i) q^{2} +(-0.405162 - 0.0861198i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.378403 + 0.168476i) q^{7} +(1.28293 - 0.932102i) q^{8} +(-2.58390 - 1.15042i) q^{9} +O(q^{10})\)	\(q+(0.127999 - 0.393941i) q^{2} +(-0.405162 - 0.0861198i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.0857864 + 0.148586i) q^{6} +(-0.378403 + 0.168476i) q^{7} +(1.28293 - 0.932102i) q^{8} +(-2.58390 - 1.15042i) q^{9} +(-0.405162 + 0.0861198i) q^{10} +(-0.338948 + 3.22488i) q^{11} +(-0.506772 - 0.562828i) q^{12} +(-2.56172 + 2.84508i) q^{13} +(0.0179342 + 0.170633i) q^{14} +(0.127999 + 0.393941i) q^{15} +(0.927051 + 2.85317i) q^{16} +(0.609237 + 5.79650i) q^{17} +(-0.783935 + 0.870648i) q^{18} +(2.95369 + 3.28040i) q^{19} +(0.191123 - 1.81841i) q^{20} +(0.167824 - 0.0356720i) q^{21} +(1.22702 + 0.546307i) q^{22} +(3.23607 - 2.35114i) q^{23} +(-0.600066 + 0.267167i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.792893 + 1.37333i) q^{26} +(1.95314 + 1.41904i) q^{27} +(-0.740809 - 0.157464i) q^{28} +(-2.11010 + 6.49422i) q^{29} +0.171573 q^{30} +4.41421 q^{32} +(0.415055 - 1.27741i) q^{33} +(2.36146 + 0.501943i) q^{34} +(0.335106 + 0.243469i) q^{35} +(-2.58579 - 4.47871i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(1.67035 - 0.743688i) q^{38} +(1.28293 - 0.932102i) q^{39} +(-1.44869 - 0.644997i) q^{40} +(7.32171 - 1.55628i) q^{41} +(0.00742861 - 0.0706785i) q^{42} +(-7.29319 - 8.09990i) q^{43} +(-3.96723 + 4.40606i) q^{44} +(0.295651 + 2.81293i) q^{45} +(-0.511996 - 1.57576i) q^{46} +(2.98413 + 9.18421i) q^{47} +(-0.129891 - 1.23583i) q^{48} +(-4.56911 + 5.07451i) q^{49} +(-1.10865 - 1.23128i) q^{50} +(0.252354 - 2.40099i) q^{51} +(-6.84703 + 1.45538i) q^{52} +(5.32453 + 2.37063i) q^{53} +(0.809017 - 0.587785i) q^{54} +(2.96230 - 1.31890i) q^{55} +(-0.328427 + 0.568852i) q^{56} +(-0.914214 - 1.58346i) q^{57} +(2.28825 + 1.66251i) q^{58} +(-3.98211 - 0.846423i) q^{59} +(-0.234037 + 0.720292i) q^{60} -2.82843 q^{61} +1.17157 q^{63} +(-1.28909 + 3.96740i) q^{64} +(3.74477 + 0.795975i) q^{65} +(-0.450096 - 0.327014i) q^{66} +(-1.62132 - 2.80821i) q^{67} +(-5.32843 + 9.22911i) q^{68} +(-1.51361 + 0.673903i) q^{69} +(0.138805 - 0.100848i) q^{70} +(0.0649237 + 0.0289059i) q^{71} +(-4.38727 + 0.932542i) q^{72} +(0.191123 - 1.81841i) q^{73} +(0.277163 + 0.307821i) q^{74} +(-1.10865 + 1.23128i) q^{75} +(0.843656 + 8.02685i) q^{76} +(-0.415055 - 1.27741i) q^{77} +(-0.202979 - 0.624706i) q^{78} +(0.706336 + 6.72034i) q^{79} +(2.00739 - 2.22943i) q^{80} +(5.00863 + 5.56265i) q^{81} +(0.324091 - 3.08352i) q^{82} +(9.85099 - 2.09389i) q^{83} +(0.286587 + 0.127597i) q^{84} +(4.71530 - 3.42586i) q^{85} +(-4.12440 + 1.83630i) q^{86} +(1.41421 - 2.44949i) q^{87} +(2.57107 + 4.45322i) q^{88} +(-3.62867 - 2.63638i) q^{89} +(1.14597 + 0.243584i) q^{90} +(0.490035 - 1.50817i) q^{91} +7.31371 q^{92} +4.00000 q^{94} +(1.36407 - 4.19817i) q^{95} +(-1.78847 - 0.380151i) q^{96} +(-4.18389 - 3.03977i) q^{97} +(1.41421 + 2.44949i) q^{98} +(4.58579 - 7.94282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21} + 14 q^{22} + 16 q^{23} + 10 q^{24} + 32 q^{25} + 24 q^{26} + 4 q^{27} + 10 q^{28} + 16 q^{29} + 48 q^{30} + 48 q^{32} - 28 q^{33} - 2 q^{34} - 4 q^{35} - 64 q^{36} - 8 q^{37} - 2 q^{38} + 12 q^{39} - 6 q^{40} + 2 q^{41} + 14 q^{42} - 2 q^{43} - 26 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 8 q^{49} + 8 q^{50} - 2 q^{51} + 14 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} + 40 q^{56} + 8 q^{57} - 6 q^{59} + 20 q^{60} + 64 q^{63} + 28 q^{64} - 2 q^{65} + 60 q^{66} + 8 q^{67} - 40 q^{68} + 8 q^{69} + 12 q^{70} - 14 q^{71} - 8 q^{72} + 2 q^{73} - 2 q^{74} + 8 q^{75} - 2 q^{76} + 28 q^{77} - 20 q^{78} - 22 q^{79} + 6 q^{80} - 2 q^{81} - 26 q^{82} - 6 q^{83} - 22 q^{84} + 12 q^{85} - 26 q^{86} - 72 q^{88} + 16 q^{89} - 8 q^{90} - 12 q^{91} - 64 q^{92} + 64 q^{94} - 12 q^{95} - 2 q^{96} - 32 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Introduction

L-functions

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