LMFDB - Embedded newform 288.2.bf.a.11.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.27
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.256484 + 1.39076i) q^{2} +(1.72244 - 0.182220i) q^{3} +(-1.86843 + 0.713416i) q^{4} +(0.370388 + 2.81338i) q^{5} +(0.695202 + 2.34876i) q^{6} +(0.178233 + 0.665173i) q^{7} +(-1.47141 - 2.41556i) q^{8} +(2.93359 - 0.627725i) q^{9} +O(q^{10})$	\(q+(0.256484 + 1.39076i) q^{2} +(1.72244 - 0.182220i) q^{3} +(-1.86843 + 0.713416i) q^{4} +(0.370388 + 2.81338i) q^{5} +(0.695202 + 2.34876i) q^{6} +(0.178233 + 0.665173i) q^{7} +(-1.47141 - 2.41556i) q^{8} +(2.93359 - 0.627725i) q^{9} +(-3.81774 + 1.23671i) q^{10} +(-2.18098 + 1.67353i) q^{11} +(-3.08826 + 1.56928i) q^{12} +(3.45510 - 4.50278i) q^{13} +(-0.879383 + 0.418485i) q^{14} +(1.15063 + 4.77838i) q^{15} +(2.98208 - 2.66594i) q^{16} -6.90574 q^{17} +(1.62544 + 3.91892i) q^{18} +(-2.38448 + 0.987682i) q^{19} +(-2.69916 - 4.99237i) q^{20} +(0.428202 + 1.11324i) q^{21} +(-2.88686 - 2.60399i) q^{22} +(6.36737 + 1.70613i) q^{23} +(-2.97458 - 3.89254i) q^{24} +(-2.94829 + 0.789991i) q^{25} +(7.14846 + 3.65033i) q^{26} +(4.93855 - 1.61578i) q^{27} +(-0.807560 - 1.11568i) q^{28} +(9.39511 + 1.23689i) q^{29} +(-6.35047 + 2.82582i) q^{30} +(-3.44542 + 1.98921i) q^{31} +(4.47254 + 3.46358i) q^{32} +(-3.45166 + 3.27997i) q^{33} +(-1.77121 - 9.60424i) q^{34} +(-1.80537 + 0.747808i) q^{35} +(-5.03339 + 3.26573i) q^{36} +(0.725444 - 1.75138i) q^{37} +(-1.98521 - 3.06291i) q^{38} +(5.13071 - 8.38535i) q^{39} +(6.25090 - 5.03434i) q^{40} +(1.12564 - 4.20094i) q^{41} +(-1.43843 + 0.881056i) q^{42} +(-6.42742 - 8.37637i) q^{43} +(2.88110 - 4.68282i) q^{44} +(2.85260 + 8.02080i) q^{45} +(-0.739692 + 9.29308i) q^{46} +(-6.13150 - 3.54002i) q^{47} +(4.65066 - 5.13531i) q^{48} +(5.65149 - 3.26289i) q^{49} +(-1.85488 - 3.89774i) q^{50} +(-11.8947 + 1.25836i) q^{51} +(-3.24327 + 10.8781i) q^{52} +(0.365072 - 0.881362i) q^{53} +(3.51382 + 6.45392i) q^{54} +(-5.51608 - 5.51608i) q^{55} +(1.34451 - 1.40928i) q^{56} +(-3.92714 + 2.13572i) q^{57} +(0.689478 + 13.3836i) q^{58} +(-0.242656 + 0.0319462i) q^{59} +(-5.55884 - 8.10721i) q^{60} +(0.772991 - 5.87145i) q^{61} +(-3.65021 - 4.28155i) q^{62} +(0.940407 + 1.83946i) q^{63} +(-3.66988 + 7.10858i) q^{64} +(13.9477 + 8.05274i) q^{65} +(-5.44694 - 3.95917i) q^{66} +(2.17465 - 2.83406i) q^{67} +(12.9029 - 4.92667i) q^{68} +(11.2783 + 1.77845i) q^{69} +(-1.50307 - 2.31904i) q^{70} +(1.97464 + 1.97464i) q^{71} +(-5.83284 - 6.16263i) q^{72} +(0.741298 - 0.741298i) q^{73} +(2.62181 + 0.559719i) q^{74} +(-4.93429 + 1.89795i) q^{75} +(3.75060 - 3.54654i) q^{76} +(-1.50191 - 1.15245i) q^{77} +(12.9780 + 4.98488i) q^{78} +(-4.86357 + 8.42396i) q^{79} +(8.60482 + 7.40228i) q^{80} +(8.21192 - 3.68298i) q^{81} +(6.13122 + 0.488020i) q^{82} +(0.345275 + 0.0454564i) q^{83} +(-1.59427 - 1.77453i) q^{84} +(-2.55781 - 19.4285i) q^{85} +(10.0010 - 11.0874i) q^{86} +(16.4079 + 0.418491i) q^{87} +(7.25164 + 2.80585i) q^{88} +(-2.50973 + 2.50973i) q^{89} +(-10.4234 + 6.02449i) q^{90} +(3.61094 + 1.49570i) q^{91} +(-13.1142 + 1.35479i) q^{92} +(-5.57205 + 4.05412i) q^{93} +(3.35069 - 9.43540i) q^{94} +(-3.66191 - 6.34261i) q^{95} +(8.33481 + 5.15082i) q^{96} +(-2.87742 + 4.98384i) q^{97} +(5.98742 + 7.02299i) q^{98} +(-5.34760 + 6.27850i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.256484	+	1.39076i	0.181362	+	0.983416i
$2$	0.256484	+	1.39076i	0.181362	+	0.983416i
$3$	1.72244	−	0.182220i	0.994451	−	0.105205i
$3$	1.72244	−	0.182220i	0.994451	−	0.105205i
$4$	−1.86843	+	0.713416i	−0.934216	+	0.356708i
$5$	0.370388	+	2.81338i	0.165643	+	1.25818i	0.849116	+	0.528206i	$0.177135\pi$
$5$	0.370388	+	2.81338i	0.165643	+	1.25818i	−0.683473	+	0.729975i	$0.739532\pi$
$6$	0.695202	+	2.34876i	0.283815	+	0.958879i
$7$	0.178233	+	0.665173i	0.0673656	+	0.251412i	0.991394	−	0.130912i	$-0.0417906\pi$
$7$	0.178233	+	0.665173i	0.0673656	+	0.251412i	−0.924028	+	0.382324i	$0.875124\pi$
$8$	−1.47141	−	2.41556i	−0.520223	−	0.854030i
$9$	2.93359	−	0.627725i	0.977864	−	0.209242i
$10$	−3.81774	+	1.23671i	−1.20728	+	0.391082i
$11$	−2.18098	+	1.67353i	−0.657591	+	0.504587i	−0.882816	−	0.469720i	$-0.844355\pi$
$11$	−2.18098	+	1.67353i	−0.657591	+	0.504587i	0.225225	+	0.974307i	$0.427688\pi$
$12$	−3.08826	+	1.56928i	−0.891504	+	0.453012i
$13$	3.45510	−	4.50278i	0.958273	−	1.24885i	−0.0102569	−	0.999947i	$-0.503265\pi$
$13$	3.45510	−	4.50278i	0.958273	−	1.24885i	0.968530	−	0.248898i	$-0.0800684\pi$
$14$	−0.879383	+	0.418485i	−0.235025	+	0.111845i
$15$	1.15063	+	4.77838i	0.297090	+	1.23377i
$16$	2.98208	−	2.66594i	0.745519	−	0.666485i
$17$	−6.90574			−1.67489			−0.837444	−	0.546522i	$-0.815951\pi$
$17$	−6.90574			−1.67489			−0.837444	+	0.546522i	$0.815951\pi$
$18$	1.62544	+	3.91892i	0.383119	+	0.923699i
$19$	−2.38448	+	0.987682i	−0.547036	+	0.226590i	−0.639046	−	0.769168i	$-0.720671\pi$
$19$	−2.38448	+	0.987682i	−0.547036	+	0.226590i	0.0920101	+	0.995758i	$0.470671\pi$
$20$	−2.69916	−	4.99237i	−0.603549	−	1.11633i
$21$	0.428202	+	1.11324i	0.0934414	+	0.242929i
$22$	−2.88686	−	2.60399i	−0.615481	−	0.555173i
$23$	6.36737	+	1.70613i	1.32769	+	0.355753i	0.851853	−	0.523782i	$-0.175479\pi$
$23$	6.36737	+	1.70613i	1.32769	+	0.355753i	0.475835	+	0.879535i	$0.342146\pi$
$24$	−2.97458	−	3.89254i	−0.607185	−	0.794561i
$25$	−2.94829	+	0.789991i	−0.589657	+	0.157998i
$26$	7.14846	+	3.65033i	1.40193	+	0.715889i
$27$	4.93855	−	1.61578i	0.950424	−	0.310956i
$28$	−0.807560	−	1.11568i	−0.152615	−	0.210843i
$29$	9.39511	+	1.23689i	1.74463	+	0.229685i	0.934349	−	0.356360i	$-0.115982\pi$
$29$	9.39511	+	1.23689i	1.74463	+	0.229685i	0.810279	+	0.586044i	$0.199316\pi$
$30$	−6.35047	+	2.82582i	−1.15943	+	0.515922i
$31$	−3.44542	+	1.98921i	−0.618815	+	0.357273i	−0.776408	−	0.630231i	$-0.782960\pi$
$31$	−3.44542	+	1.98921i	−0.618815	+	0.357273i	0.157592	+	0.987504i	$0.449627\pi$
$32$	4.47254	+	3.46358i	0.790640	+	0.612281i
$33$	−3.45166	+	3.27997i	−0.600857	+	0.570969i
$34$	−1.77121	−	9.60424i	−0.303761	−	1.64711i
$35$	−1.80537	+	0.747808i	−0.305163	+	0.126403i
$36$	−5.03339	+	3.26573i	−0.838898	+	0.544289i
$37$	0.725444	−	1.75138i	0.119262	−	0.287925i	−0.852963	−	0.521971i	$-0.825197\pi$
$37$	0.725444	−	1.75138i	0.119262	−	0.287925i	0.972225	+	0.234047i	$0.0751968\pi$
$38$	−1.98521	−	3.06291i	−0.322044	−	0.496870i
$39$	5.13071	−	8.38535i	0.821571	−	1.34273i
$40$	6.25090	−	5.03434i	0.988354	−	0.795999i
$41$	1.12564	−	4.20094i	0.175795	−	0.656077i	−0.820620	−	0.571475i	$-0.806371\pi$
$41$	1.12564	−	4.20094i	0.175795	−	0.656077i	0.996415	−	0.0846021i	$-0.0269619\pi$
$42$	−1.43843	+	0.881056i	−0.221954	+	0.135950i
$43$	−6.42742	−	8.37637i	−0.980172	−	1.27738i	−0.960704	−	0.277574i	$-0.910470\pi$
$43$	−6.42742	−	8.37637i	−0.980172	−	1.27738i	−0.0194677	−	0.999810i	$-0.506197\pi$
$44$	2.88110	−	4.68282i	0.434342	−	0.705962i
$45$	2.85260	+	8.02080i	0.425240	+	1.19567i
$46$	−0.739692	+	9.29308i	−0.109062	+	1.37019i
$47$	−6.13150	−	3.54002i	−0.894371	−	0.516365i	−0.0190010	−	0.999819i	$-0.506049\pi$
$47$	−6.13150	−	3.54002i	−0.894371	−	0.516365i	−0.875370	+	0.483454i	$0.839382\pi$
$48$	4.65066	−	5.13531i	0.671264	−	0.741218i
$49$	5.65149	−	3.26289i	0.807356	−	0.466127i
$50$	−1.85488	−	3.89774i	−0.262319	−	0.551224i
$51$	−11.8947	+	1.25836i	−1.66559	+	0.176206i
$52$	−3.24327	+	10.8781i	−0.449761	+	1.50851i
$53$	0.365072	−	0.881362i	0.0501465	−	0.121064i	−0.896821	−	0.442393i	$-0.854130\pi$
$53$	0.365072	−	0.881362i	0.0501465	−	0.121064i	0.946968	+	0.321329i	$0.104130\pi$
$54$	3.51382	+	6.45392i	0.478170	+	0.878267i
$55$	−5.51608	−	5.51608i	−0.743788	−	0.743788i
$56$	1.34451	−	1.40928i	0.179668	−	0.188323i
$57$	−3.92714	+	2.13572i	−0.520162	+	0.282883i
$58$	0.689478	+	13.3836i	0.0905329	+	1.75735i
$59$	−0.242656	+	0.0319462i	−0.0315911	+	0.00415904i	−0.146305	−	0.989240i	$-0.546738\pi$
$59$	−0.242656	+	0.0319462i	−0.0315911	+	0.00415904i	0.114714	+	0.993399i	$0.463405\pi$
$60$	−5.55884	−	8.10721i	−0.717643	−	1.04664i
$61$	0.772991	−	5.87145i	0.0989713	−	0.751762i	−0.867944	−	0.496663i	$-0.834559\pi$
$61$	0.772991	−	5.87145i	0.0989713	−	0.751762i	0.966915	−	0.255099i	$-0.0821081\pi$
$62$	−3.65021	−	4.28155i	−0.463577	−	0.543757i
$63$	0.940407	+	1.83946i	0.118480	+	0.231751i
$64$	−3.66988	+	7.10858i	−0.458735	+	0.888573i
$65$	13.9477	+	8.05274i	1.73001	+	0.998819i
$66$	−5.44694	−	3.95917i	−0.670473	−	0.487341i
$67$	2.17465	−	2.83406i	0.265675	−	0.346235i	−0.641397	−	0.767209i	$-0.721645\pi$
$67$	2.17465	−	2.83406i	0.265675	−	0.346235i	0.907073	+	0.420974i	$0.138312\pi$
$68$	12.9029	−	4.92667i	1.56471	−	0.597446i
$69$	11.2783	+	1.77845i	1.35775	+	0.214100i
$70$	−1.50307	−	2.31904i	−0.179651	−	0.277178i
$71$	1.97464	+	1.97464i	0.234346	+	0.234346i	0.814504	−	0.580158i	$-0.197009\pi$
$71$	1.97464	+	1.97464i	0.234346	+	0.234346i	−0.580158	+	0.814504i	$0.697009\pi$
$72$	−5.83284	−	6.16263i	−0.687407	−	0.726273i
$73$	0.741298	−	0.741298i	0.0867624	−	0.0867624i	−0.662394	−	0.749156i	$-0.730459\pi$
$73$	0.741298	−	0.741298i	0.0867624	−	0.0867624i	0.749156	+	0.662394i	$0.230459\pi$
$74$	2.62181	+	0.559719i	0.304779	+	0.0650660i
$75$	−4.93429	+	1.89795i	−0.569763	+	0.219156i
$76$	3.75060	−	3.54654i	0.430224	−	0.406816i
$77$	−1.50191	−	1.15245i	−0.171158	−	0.131334i
$78$	12.9780	+	4.98488i	1.46946	+	0.564426i
$79$	−4.86357	+	8.42396i	−0.547195	+	0.947769i	0.451270	+	0.892387i	$0.350971\pi$
$79$	−4.86357	+	8.42396i	−0.547195	+	0.947769i	−0.998465	+	0.0553821i	$0.982362\pi$
$80$	8.60482	+	7.40228i	0.962048	+	0.827600i
$81$	8.21192	−	3.68298i	0.912436	−	0.409220i
$82$	6.13122	+	0.488020i	0.677079	+	0.0538928i
$83$	0.345275	+	0.0454564i	0.0378989	+	0.00498949i	0.149452	−	0.988769i	$-0.452249\pi$
$83$	0.345275	+	0.0454564i	0.0378989	+	0.00498949i	−0.111553	+	0.993758i	$0.535582\pi$
$84$	−1.59427	−	1.77453i	−0.173949	−	0.193617i
$85$	−2.55781	−	19.4285i	−0.277433	−	2.10731i
$86$	10.0010	−	11.0874i	1.07844	−	1.19559i
$87$	16.4079	+	0.418491i	1.75911	+	0.0448670i
$88$	7.25164	+	2.80585i	0.773027	+	0.299104i
$89$	−2.50973	+	2.50973i	−0.266031	+	0.266031i	−0.827499	−	0.561468i	$-0.810237\pi$
$89$	−2.50973	+	2.50973i	−0.266031	+	0.266031i	0.561468	+	0.827499i	$0.310237\pi$
$90$	−10.4234	+	6.02449i	−1.09872	+	0.635037i
$91$	3.61094	+	1.49570i	0.378529	+	0.156792i
$92$	−13.1142	+	1.35479i	−1.36725	+	0.141247i
$93$	−5.57205	+	4.05412i	−0.577794	+	0.420393i
$94$	3.35069	−	9.43540i	0.345597	−	0.973188i
$95$	−3.66191	−	6.34261i	−0.375704	−	0.650738i
$96$	8.33481	+	5.15082i	0.850668	+	0.525704i
$97$	−2.87742	+	4.98384i	−0.292158	+	0.506033i	−0.974320	−	0.225169i	$-0.927707\pi$
$97$	−2.87742	+	4.98384i	−0.292158	+	0.506033i	0.682162	+	0.731201i	$0.261040\pi$
$98$	5.98742	+	7.02299i	0.604820	+	0.709429i
$99$	−5.34760	+	6.27850i	−0.537454	+	0.631013i
$100$	4.94508	−	3.57940i	0.494508	−	0.357940i
$101$	−5.25575	+	4.03288i	−0.522967	+	0.401286i	−0.836229	−	0.548380i	$-0.815245\pi$
$101$	−5.25575	+	4.03288i	−0.522967	+	0.401286i	0.313263	+	0.949667i	$0.398578\pi$
$102$	−4.80089	−	16.2200i	−0.475359	−	1.60602i
$103$	−0.395385	−	0.105943i	−0.0389585	−	0.0104389i	0.239287	−	0.970949i	$-0.423086\pi$
$103$	−0.395385	−	0.105943i	−0.0389585	−	0.0104389i	−0.278246	+	0.960510i	$0.589753\pi$
$104$	−15.9606	−	1.72056i	−1.56507	−	0.168715i
$105$	−2.97337	+	1.61703i	−0.290171	+	0.157806i
$106$	1.31940	+	0.281673i	0.128151	+	0.0273585i
$107$	−15.0654	−	6.24030i	−1.45643	−	0.603272i	−0.492710	−	0.870194i	$-0.663994\pi$
$107$	−15.0654	−	6.24030i	−1.45643	−	0.603272i	−0.963718	+	0.266921i	$0.913994\pi$
$108$	−8.07462	+	6.54221i	−0.776981	+	0.629524i
$109$	−2.99282	−	7.22530i	−0.286660	−	0.692058i	0.713302	−	0.700857i	$-0.247199\pi$
$109$	−2.99282	−	7.22530i	−0.286660	−	0.692058i	−0.999961	+	0.00879943i	$0.997199\pi$
$110$	6.25676	−	9.08633i	0.596558	−	0.866347i
$111$	0.930398	−	3.14883i	0.0883094	−	0.298874i
$112$	2.30481	+	1.50844i	0.217784	+	0.142534i
$113$	8.07055	+	13.9786i	0.759213	+	1.31500i	0.943252	+	0.332077i	$0.107749\pi$
$113$	8.07055	+	13.9786i	0.759213	+	1.31500i	−0.184039	+	0.982919i	$0.558917\pi$
$114$	−3.97753	−	4.91393i	−0.372529	−	0.460232i
$115$	−2.44159	+	18.5457i	−0.227680	+	1.72940i
$116$	−18.4365	+	4.39158i	−1.71179	+	0.407748i
$117$	7.30935	−	15.3782i	0.675750	−	1.42171i
$118$	−0.106667	−	0.329282i	−0.00981948	−	0.0303129i
$119$	−1.23083	−	4.59351i	−0.112830	−	0.421087i
$120$	9.84943	−	9.81039i	0.899126	−	0.895562i
$121$	−0.891016	+	3.32532i	−0.0810015	+	0.302302i
$122$	8.36404	−	0.430887i	0.757244	−	0.0390107i
$123$	1.17335	−	7.44098i	0.105797	−	0.670931i
$124$	5.01839	−	6.17472i	0.450665	−	0.554506i
$125$	2.11506	+	5.10622i	0.189177	+	0.456714i
$126$	−2.31706	+	1.77968i	−0.206420	+	0.158546i
$127$			6.33134i			0.561815i	0.959735	+	0.280908i	$0.0906355\pi$
$127$			6.33134i			0.561815i	−0.959735	+	0.280908i	$0.909365\pi$
$128$	−10.8276	−	3.28069i	−0.957034	−	0.289975i
$129$	−12.5972	−	13.2566i	−1.10912	−	1.16718i
$130$	−7.62205	+	21.4634i	−0.668498	+	1.88246i
$131$	−9.66903	−	7.41931i	−0.844787	−	0.648228i	0.0929129	−	0.995674i	$-0.470382\pi$
$131$	−9.66903	−	7.41931i	−0.844787	−	0.648228i	−0.937700	+	0.347446i	$0.887049\pi$
$132$	4.10921	−	8.59086i	0.357661	−	0.747739i
$133$	−1.08197	−	1.41005i	−0.0938187	−	0.122267i
$134$	4.49926	+	2.29752i	0.388676	+	0.198476i
$135$	6.37498	+	13.2955i	0.548671	+	1.14430i
$136$	10.1612	+	16.6813i	0.871317	+	1.43041i
$137$	−7.82241	+	2.09601i	−0.668314	+	0.179074i	−0.576995	−	0.816748i	$-0.695775\pi$
$137$	−7.82241	+	2.09601i	−0.668314	+	0.179074i	−0.0913185	+	0.995822i	$0.529108\pi$
$138$	0.419310	+	16.1415i	0.0356940	+	1.37406i
$139$	1.60249	−	0.210972i	0.135922	−	0.0178944i	−0.0622584	−	0.998060i	$-0.519830\pi$
$139$	1.60249	−	0.210972i	0.135922	−	0.0178944i	0.198180	+	0.980166i	$0.436497\pi$
$140$	2.83971	−	2.68521i	0.239999	−	0.226941i
$141$	−11.2062	−	4.98019i	−0.943731	−	0.419408i
$142$	−2.23979	+	3.25271i	−0.187959	+	0.272962i
$143$			15.6027i			1.30476i
$144$	7.07471	−	9.69270i	0.589560	−	0.807725i
$145$			26.8901i			2.23310i
$146$	1.22110	+	0.840837i	0.101059	+	0.0695882i
$147$	9.13978	−	6.64994i	0.753837	−	0.548478i
$148$	−0.105982	+	3.78987i	−0.00871170	+	0.311526i
$149$	−2.07840	+	0.273627i	−0.170269	+	0.0224164i	−0.215179	−	0.976575i	$-0.569033\pi$
$149$	−2.07840	+	0.273627i	−0.170269	+	0.0224164i	0.0449094	+	0.998991i	$0.485700\pi$
$150$	−3.90516	−	6.37563i	−0.318855	−	0.520568i
$151$	−12.2277	+	3.27641i	−0.995077	+	0.266630i	−0.719382	−	0.694615i	$-0.755575\pi$
$151$	−12.2277	+	3.27641i	−0.995077	+	0.266630i	−0.275696	+	0.961245i	$0.588908\pi$
$152$	5.89436	+	4.30656i	0.478096	+	0.349308i
$153$	−20.2586	+	4.33491i	−1.63781	+	0.350457i
$154$	1.21757	−	2.38438i	0.0981148	−	0.192139i
$155$	−6.87255	−	8.95648i	−0.552017	−	0.719402i
$156$	−3.60414	+	19.3278i	−0.288562	+	1.54746i
$157$	4.00334	+	3.07187i	0.319501	+	0.245162i	0.756043	−	0.654522i	$-0.227130\pi$
$157$	4.00334	+	3.07187i	0.319501	+	0.245162i	−0.436542	+	0.899684i	$0.643797\pi$
$158$	−12.9631	−	4.60346i	−1.03129	−	0.366231i
$159$	0.468213	−	1.58462i	0.0371317	−	0.125668i
$160$	−8.08780	+	13.8658i	−0.639396	+	1.09619i
$161$			4.53949i			0.357762i
$162$	7.22837	+	10.4762i	0.567914	+	0.823088i
$163$	−2.58256	−	6.23486i	−0.202282	−	0.488352i	0.789887	−	0.613252i	$-0.210139\pi$
$163$	−2.58256	−	6.23486i	−0.202282	−	0.488352i	−0.992169	+	0.124900i	$0.960139\pi$
$164$	0.893840	+	8.65222i	0.0697972	+	0.675625i
$165$	−10.5062	−	8.49597i	−0.817910	−	0.661410i
$166$	0.0253387	+	0.491854i	0.00196666	+	0.0381753i
$167$	−5.66896	+	21.1569i	−0.438678	+	1.63717i	0.293432	+	0.955980i	$0.405203\pi$
$167$	−5.66896	+	21.1569i	−0.438678	+	1.63717i	−0.732109	+	0.681187i	$0.761464\pi$
$168$	2.05904	−	2.67239i	0.158859	−	0.206179i
$169$	−4.97262	−	18.5581i	−0.382509	−	1.42754i
$170$	26.3643	−	8.54039i	2.02205	−	0.655018i
$171$	−6.37508	+	4.39425i	−0.487515	+	0.336037i
$172$	17.9850	+	11.0653i	1.37135	+	0.843718i
$173$	1.26424	−	9.60287i	0.0961185	−	0.730093i	−0.873735	−	0.486403i	$-0.838309\pi$
$173$	1.26424	−	9.60287i	0.0961185	−	0.730093i	0.969853	−	0.243690i	$-0.0783579\pi$
$174$	3.62634	+	22.9268i	0.274912	+	1.73808i
$175$	−1.05096	−	1.82032i	−0.0794452	−	0.137603i
$176$	−2.04233	+	10.8049i	−0.153947	+	0.814454i
$177$	−0.412138	+	0.0992421i	−0.0309782	+	0.00745949i
$178$	−4.13414	−	2.84673i	−0.309867	−	0.213371i
$179$	−7.98790	−	19.2845i	−0.597043	−	1.44139i	−0.876580	−	0.481256i	$-0.840181\pi$
$179$	−7.98790	−	19.2845i	−0.597043	−	1.44139i	0.279537	−	0.960135i	$-0.409819\pi$
$180$	−11.0521	−	12.9512i	−0.823772	−	0.965328i
$181$	0.663688	+	0.274908i	0.0493315	+	0.0204338i	0.407213	−	0.913333i	$-0.366501\pi$
$181$	0.663688	+	0.274908i	0.0493315	+	0.0204338i	−0.357881	+	0.933767i	$0.616501\pi$
$182$	−1.15401	+	5.40557i	−0.0855410	+	0.400688i
$183$	0.261535	−	10.2541i	0.0193332	−	0.758002i
$184$	−5.24777	−	17.8912i	−0.386871	−	1.31896i
$185$	5.19598	+	1.39226i	0.382016	+	0.102361i
$186$	−7.06745	−	6.70957i	−0.518211	−	0.491969i
$187$	15.0613	−	11.5569i	1.10139	−	0.845128i
$188$	13.9818	+	2.23998i	1.01973	+	0.163367i
$189$	1.95498	+	2.99700i	0.142204	+	0.218000i
$190$	7.88183	−	6.71961i	0.571808	−	0.487492i
$191$	−2.72351	+	4.71725i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$191$	−2.72351	+	4.71725i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$192$	−5.02582	+	12.9128i	−0.362707	+	0.931903i
$193$	2.75978	+	4.78007i	0.198653	+	0.344077i	0.948092	−	0.317996i	$-0.103010\pi$
$193$	2.75978	+	4.78007i	0.198653	+	0.344077i	−0.749439	+	0.662074i	$0.769677\pi$
$194$	−7.66935	−	2.72353i	−0.550627	−	0.195538i
$195$	25.4915	+	11.3288i	1.82548	+	0.811271i
$196$	−8.23163	+	10.1283i	−0.587973	+	0.723454i
$197$	−12.2289	−	5.06537i	−0.871272	−	0.360893i	−0.0981665	−	0.995170i	$-0.531298\pi$
$197$	−12.2289	−	5.06537i	−0.871272	−	0.360893i	−0.773106	+	0.634277i	$0.781298\pi$
$198$	−10.1035	−	5.82689i	−0.718022	−	0.414099i
$199$	6.95404	−	6.95404i	0.492959	−	0.492959i	−0.416278	−	0.909237i	$-0.636666\pi$
$199$	6.95404	−	6.95404i	0.492959	−	0.492959i	0.909237	+	0.416278i	$0.136666\pi$
$200$	6.24642	+	5.95936i	0.441689	+	0.421391i
$201$	3.22928	−	5.27775i	0.227776	−	0.372264i
$202$	−6.95678	−	6.27512i	−0.489478	−	0.441516i
$203$	0.851769	+	6.46983i	0.0597825	+	0.454093i
$204$	21.3267	−	10.8371i	1.49317	−	0.758745i
$205$	12.2358	+	1.61087i	0.854583	+	0.112508i
$206$	0.0459316	−	0.577059i	0.00320021	−	0.0402056i
$207$	19.7502	+	1.00813i	1.37274	+	0.0700702i
$208$	−1.70075	−	22.6387i	−0.117926	−	1.56971i
$209$	3.54759	−	6.14460i	0.245392	−	0.425031i
$210$	−3.01152	−	3.72051i	−0.207815	−	0.256739i
$211$	21.0376	+	16.1427i	1.44829	+	1.11131i	0.972816	+	0.231580i	$0.0743896\pi$
$211$	21.0376	+	16.1427i	1.44829	+	1.11131i	0.475473	+	0.879731i	$0.342277\pi$
$212$	−0.0533345	+	1.90721i	−0.00366303	+	0.130988i
$213$	3.76101	+	3.04138i	0.257700	+	0.208392i
$214$	4.81472	−	22.5529i	0.329128	−	1.54169i
$215$	21.1853	−	21.1853i	1.44482	−	1.44482i
$216$	−11.1697	−	9.55189i	−0.759999	−	0.649924i
$217$	−1.93726	−	1.93726i	−0.131509	−	0.131509i
$218$	9.28105	−	6.01546i	0.628592	−	0.407419i
$219$	1.14176	−	1.41192i	0.0771531	−	0.0954087i
$220$	14.2417	+	6.37116i	0.960173	+	0.429543i
$221$	−23.8600	+	31.0950i	−1.60500	+	2.09168i
$222$	4.61790	+	0.486336i	0.309933	+	0.0326407i
$223$	8.56303	+	4.94387i	0.573423	+	0.331066i	0.758515	−	0.651655i	$-0.225925\pi$
$223$	8.56303	+	4.94387i	0.573423	+	0.331066i	−0.185092	+	0.982721i	$0.559258\pi$
$224$	−1.50673	+	3.59233i	−0.100673	+	0.240023i
$225$	−8.15317	+	4.16822i	−0.543545	+	0.277882i
$226$	−17.3709	+	14.8095i	−1.15550	+	0.985112i
$227$	0.548177	−	4.16382i	0.0363838	−	0.276362i	−0.963576	−	0.267433i	$-0.913824\pi$
$227$	0.548177	−	4.16382i	0.0363838	−	0.276362i	0.999960	−	0.00892899i	$-0.00284222\pi$
$228$	5.81393	−	6.79213i	0.385037	−	0.449820i
$229$	−10.7185	+	1.41111i	−0.708296	+	0.0932489i	−0.476063	−	0.879411i	$-0.657937\pi$
$229$	−10.7185	+	1.41111i	−0.708296	+	0.0932489i	−0.232233	+	0.972660i	$0.574603\pi$
$230$	−26.4189	+	1.36102i	−1.74201	+	0.0897427i
$231$	−2.79694	−	1.71135i	−0.184025	−	0.112599i
$232$	−10.8363	−	24.5144i	−0.711439	−	1.60945i
$233$	−10.6338	−	10.6338i	−0.696643	−	0.696643i	0.267042	−	0.963685i	$-0.413954\pi$
$233$	−10.6338	−	10.6338i	−0.696643	−	0.696643i	−0.963685	+	0.267042i	$0.913954\pi$
$234$	23.2621	+	6.22131i	1.52069	+	0.406700i
$235$	7.68839	−	18.5614i	0.501535	−	1.21081i
$236$	0.430595	−	0.232804i	0.0280293	−	0.0151542i
$237$	−6.84220	+	15.3960i	−0.444448	+	1.00008i
$238$	6.07279	−	2.88995i	0.393641	−	0.187328i
$239$	−18.4321	+	10.6418i	−1.19227	+	0.688360i	−0.958822	−	0.284008i	$-0.908336\pi$
$239$	−18.4321	+	10.6418i	−1.19227	+	0.688360i	−0.233453	+	0.972368i	$0.575002\pi$
$240$	16.1701	+	11.1820i	1.04378	+	0.721795i
$241$	−16.5010	−	9.52685i	−1.06292	−	0.613679i	−0.136683	−	0.990615i	$-0.543644\pi$
$241$	−16.5010	−	9.52685i	−1.06292	−	0.613679i	−0.926239	+	0.376936i	$0.876978\pi$
$242$	−4.85325	−	0.386300i	−0.311979	−	0.0248323i
$243$	13.4734	−	7.84008i	0.864320	−	0.502942i
$244$	2.74450	+	11.5219i	0.175699	+	0.737612i
$245$	11.2730	+	14.6912i	0.720205	+	0.938589i
$246$	10.6496	−	0.276645i	0.678992	−	0.0176382i
$247$	−3.79129	+	14.1493i	−0.241234	+	0.900298i
$248$	9.87470	+	5.39566i	0.627044	+	0.342625i
$249$	0.602999	+	0.0153798i	0.0382135	+	0.000974654i
$250$	−6.55905	+	4.25121i	−0.414831	+	0.268870i
$251$	−3.99971	+	9.65617i	−0.252460	+	0.609492i	−0.998401	−	0.0565194i	$-0.982000\pi$
$251$	−3.99971	+	9.65617i	−0.252460	+	0.609492i	0.745942	+	0.666011i	$0.232000\pi$
$252$	−3.06939	−	2.76601i	−0.193353	−	0.174242i
$253$	−16.7424	+	6.93492i	−1.05258	+	0.435994i
$254$	−8.80538	+	1.62389i	−0.552498	+	0.101892i
$255$	−7.94592	−	32.9983i	−0.497593	−	2.06643i
$256$	1.78554	−	15.9001i	0.111597	−	0.993754i
$257$	15.3667	−	8.87198i	0.958550	−	0.553419i	0.0628236	−	0.998025i	$-0.479989\pi$
$257$	15.3667	−	8.87198i	0.958550	−	0.553419i	0.895726	+	0.444606i	$0.146656\pi$
$258$	15.2058	−	20.9198i	0.946670	−	1.30241i
$259$	1.29427	+	0.170393i	0.0804218	+	0.0105877i
$260$	−31.8054	−	5.09544i	−1.97248	−	0.316006i
$261$	28.3378	−	2.26902i	1.75407	−	0.140449i
$262$	7.83853	−	15.3502i	0.484266	−	0.948341i
$263$	17.4285	−	4.66995i	1.07469	−	0.287961i	0.322269	−	0.946648i	$-0.395554\pi$
$263$	17.4285	−	4.66995i	1.07469	−	0.287961i	0.752417	+	0.658687i	$0.228888\pi$
$264$	13.0018	+	3.51151i	0.800204	+	0.216118i
$265$	2.61482	+	0.700640i	0.160627	+	0.0430400i
$266$	1.68354	−	1.86642i	0.103224	−	0.114437i
$267$	−3.86554	+	4.78018i	−0.236567	+	0.292542i
$268$	−2.04132	+	6.84667i	−0.124693	+	0.418227i
$269$	−17.7192	+	7.33955i	−1.08036	+	0.447500i	−0.850636	−	0.525755i	$-0.823783\pi$
$269$	−17.7192	+	7.33955i	−1.08036	+	0.447500i	−0.229725	+	0.973256i	$0.573783\pi$
$270$	−16.8558	+	12.2762i	−1.02581	+	0.747103i
$271$	17.7624			1.07899			0.539496	−	0.841988i	$-0.318615\pi$
$271$	17.7624			1.07899			0.539496	+	0.841988i	$0.318615\pi$
$272$	−20.5934	+	18.4103i	−1.24866	+	1.11629i
$273$	6.49216	+	1.91827i	0.392924	+	0.116099i
$274$	−4.92137	−	10.3415i	−0.297311	−	0.624753i
$275$	5.10809	−	6.65699i	0.308029	−	0.401432i
$276$	−22.3415	+	4.72321i	−1.34480	+	0.284304i
$277$	23.6800	−	18.1703i	1.42279	−	1.09175i	0.441932	−	0.897048i	$-0.354293\pi$
$277$	23.6800	−	18.1703i	1.42279	−	1.09175i	0.980863	−	0.194700i	$-0.0623735\pi$
$278$	0.704426	+	2.17457i	0.0422486	+	0.130422i
$279$	−8.85877	+	7.99831i	−0.530360	+	0.478846i
$280$	4.46282	+	3.26064i	0.266705	+	0.194861i
$281$	2.26314	+	8.44615i	0.135008	+	0.503855i	0.999998	+	0.00206658i	$0.000657813\pi$
$281$	2.26314	+	8.44615i	0.135008	+	0.503855i	−0.864990	+	0.501789i	$0.832676\pi$
$282$	4.05204	−	16.8625i	0.241296	−	1.00415i
$283$	2.28763	+	17.3762i	0.135985	+	1.03291i	0.914300	+	0.405037i	$0.132741\pi$
$283$	2.28763	+	17.3762i	0.135985	+	1.03291i	−0.778315	+	0.627874i	$0.783925\pi$
$284$	−5.09822	−	2.28074i	−0.302523	−	0.135337i
$285$	−7.46316	−	10.2575i	−0.442079	−	0.607601i
$286$	−21.6996	+	4.00184i	−1.28312	+	0.236634i
$287$	2.99498			0.176788
$288$	15.2948	+	7.35321i	0.901253	+	0.433292i
$289$	30.6893			1.80525
$290$	−37.3977	+	6.89689i	−2.19607	+	0.404999i
$291$	−4.04803	+	9.10869i	−0.237300	+	0.533961i
$292$	−0.856211	+	1.91392i	−0.0501060	+	0.112004i
$293$	−3.23844	−	24.5984i	−0.189192	−	1.43705i	−0.777738	−	0.628589i	$-0.783633\pi$
$293$	−3.23844	−	24.5984i	−0.189192	−	1.43705i	0.588546	−	0.808464i	$-0.299701\pi$
$294$	11.5927	+	11.0056i	0.676099	+	0.641862i
$295$	−0.179754	−	0.670850i	−0.0104657	−	0.0390584i
$296$	−5.29799	+	0.824646i	−0.307939	+	0.0479316i
$297$	−8.06684	+	11.7888i	−0.468086	+	0.684054i
$298$	−0.913626	−	2.82038i	−0.0529250	−	0.163380i
$299$	29.6822	−	22.7760i	1.71657	−	1.31717i
$300$	7.86536	−	7.06639i	0.454107	−	0.407978i
$301$	4.42616	−	5.76829i	0.255120	−	0.332478i
$302$	−7.69291	−	16.1655i	−0.442677	−	0.930219i
$303$	−8.31784	+	7.90409i	−0.477847	+	0.454078i
$304$	−4.47759	+	9.30221i	−0.256807	+	0.533518i
$305$	16.8049			0.962247
$306$	−11.2248	−	27.0631i	−0.641681	−	1.54709i
$307$	−19.8889	+	8.23823i	−1.13512	+	0.470181i	−0.869517	−	0.493903i	$-0.835570\pi$
$307$	−19.8889	+	8.23823i	−1.13512	+	0.470181i	−0.265600	+	0.964083i	$0.585570\pi$
$308$	3.62839	+	1.08180i	0.206747	+	0.0616411i
$309$	−0.700332	−	0.110434i	−0.0398405	−	0.00628235i
$310$	10.6936	−	11.8553i	0.607357	−	0.673334i
$311$	7.61971	+	2.04169i	0.432074	+	0.115774i	0.468300	−	0.883570i	$-0.344867\pi$
$311$	7.61971	+	2.04169i	0.432074	+	0.115774i	−0.0362256	+	0.999344i	$0.511533\pi$
$312$	−27.8047	−	0.0552243i	−1.57413	−	0.00312646i
$313$	−17.2263	+	4.61577i	−0.973687	+	0.260899i	−0.710384	−	0.703814i	$-0.751479\pi$
$313$	−17.2263	+	4.61577i	−0.973687	+	0.260899i	−0.263303	+	0.964713i	$0.584812\pi$
$314$	−3.24544	+	6.35557i	−0.183151	+	0.358666i
$315$	−4.82680	+	3.32704i	−0.271959	+	0.187457i
$316$	3.07747	−	19.2093i	0.173121	−	1.08061i
$317$	25.7295	+	3.38736i	1.44511	+	0.190253i	0.811933	−	0.583751i	$-0.198415\pi$
$317$	25.7295	+	3.38736i	1.44511	+	0.190253i	0.633181	+	0.774004i	$0.281749\pi$
$318$	2.32391	+	0.244743i	0.130318	+	0.0137245i
$319$	−22.5605	+	13.0253i	−1.26315	+	0.729279i
$320$	−21.3584	−	7.69183i	−1.19397	−	0.429986i
$321$	−27.0864	−	8.00331i	−1.51181	−	0.446701i
$322$	−6.31334	+	1.16431i	−0.351829	+	0.0648842i
$323$	16.4666	−	6.82068i	0.916225	−	0.379513i
$324$	−12.7159	+	12.7399i	−0.706440	+	0.707773i
$325$	−6.62948	+	16.0050i	−0.367737	+	0.887796i
$326$	8.00881	−	5.19087i	0.443567	−	0.287496i
$327$	−6.47153	−	11.8998i	−0.357877	−	0.658059i
$328$	−11.8039	+	3.46228i	−0.651762	+	0.191172i
$329$	1.26189	−	4.70945i	0.0695705	−	0.259640i
$330$	9.12117	−	16.7908i	0.502104	−	0.924301i
$331$	8.12742	+	10.5919i	0.446723	+	0.582181i	0.961383	−	0.275213i	$-0.0887485\pi$
$331$	8.12742	+	10.5919i	0.446723	+	0.582181i	−0.514660	+	0.857394i	$0.672082\pi$
$332$	−0.677553	+	0.161393i	−0.0371856	+	0.00885759i
$333$	1.02877	−	5.59321i	0.0563764	−	0.306506i
$334$	−30.8781	−	2.45778i	−1.68958	−	0.134483i
$335$	8.77874	+	5.06841i	0.479634	+	0.276917i
$336$	4.24477	+	2.17821i	0.231571	+	0.118831i
$337$	25.0098	−	14.4394i	1.36237	−	0.786566i	0.372433	−	0.928059i	$-0.378524\pi$
$337$	25.0098	−	14.4394i	1.36237	−	0.786566i	0.989939	+	0.141493i	$0.0451904\pi$
$338$	24.5344	−	11.6756i	1.33450	−	0.635067i
$339$	16.4482	+	22.6067i	0.893344	+	1.22783i
$340$	18.6397	+	34.4760i	1.01088	+	1.86972i
$341$	4.18539	−	10.1044i	0.226652	−	0.547186i
$342$	−7.74646	−	7.73916i	−0.418881	−	0.418486i
$343$	6.58625	+	6.58625i	0.355624	+	0.355624i
$344$	−10.7763	+	27.8509i	−0.581017	+	1.50162i
$345$	−0.826092	+	32.3888i	−0.0444753	+	1.74376i
$346$	13.6796	−	0.704725i	0.735417	−	0.0378862i
$347$	6.55856	−	0.863451i	0.352082	−	0.0463525i	0.0475888	−	0.998867i	$-0.484846\pi$
$347$	6.55856	−	0.863451i	0.352082	−	0.0463525i	0.304493	+	0.952515i	$0.401513\pi$
$348$	−30.9556	+	10.9237i	−1.65939	+	0.585573i
$349$	1.87182	−	14.2179i	0.100196	−	0.761064i	−0.865412	−	0.501061i	$-0.832943\pi$
$349$	1.87182	−	14.2179i	0.100196	−	0.761064i	0.965608	−	0.260003i	$-0.0837236\pi$
$350$	2.26207	−	1.92852i	0.120913	−	0.103084i
$351$	9.78770	−	27.8199i	0.522429	−	1.48491i
$352$	−15.5509	−	0.0691018i	−0.828867	−	0.00368314i
$353$	−32.2434	−	18.6157i	−1.71614	−	0.990816i	−0.925681	−	0.378305i	$-0.876507\pi$
$353$	−32.2434	−	18.6157i	−1.71614	−	0.990816i	−0.790462	−	0.612511i	$-0.790160\pi$
$354$	−0.243729	−	0.547732i	−0.0129540	−	0.0291116i
$355$	−4.82402	+	6.28679i	−0.256033	+	0.333668i
$356$	2.89878	−	6.47974i	0.153635	−	0.343426i
$357$	−2.95706	−	7.68777i	−0.156504	−	0.406880i
$358$	24.7713	−	16.0554i	1.30921	−	0.848555i
$359$	10.7189	+	10.7189i	0.565724	+	0.565724i	0.930928	−	0.365204i	$-0.119001\pi$
$359$	10.7189	+	10.7189i	0.565724	+	0.565724i	−0.365204	+	0.930928i	$0.619001\pi$
$360$	15.1774	−	18.6926i	0.799919	−	0.985184i
$361$	−8.72482	+	8.72482i	−0.459201	+	0.459201i
$362$	−0.212107	+	0.993541i	−0.0111481	+	0.0522193i
$363$	−0.928782	+	5.89002i	−0.0487484	+	0.309146i
$364$	−7.81384	−	0.218511i	−0.409557	−	0.0114531i
$365$	2.36012	+	1.81098i	0.123534	+	0.0947912i
$366$	14.3280	−	2.26627i	0.748938	−	0.118460i
$367$	10.1421	−	17.5667i	0.529414	−	0.916972i	−0.469997	−	0.882668i	$-0.655745\pi$
$367$	10.1421	−	17.5667i	0.529414	−	0.916972i	0.999411	−	0.0343043i	$-0.0109215\pi$
$368$	23.5364	−	11.8872i	1.22692	−	0.619663i
$369$	0.665128	−	13.0304i	0.0346252	−	0.678338i
$370$	−0.603613	+	7.58346i	−0.0313804	+	0.394246i
$371$	0.651326	+	0.0857487i	0.0338152	+	0.00445185i
$372$	7.51871	−	11.5500i	0.389827	−	0.598841i
$373$	−0.131688	−	1.00027i	−0.00681854	−	0.0517919i	0.987697	−	0.156378i	$-0.0499817\pi$
$373$	−0.131688	−	1.00027i	−0.00681854	−	0.0517919i	−0.994516	+	0.104586i	$0.966648\pi$
$374$	19.9359	+	17.9825i	1.03086	+	0.929853i
$375$	4.57352	+	8.40974i	0.236176	+	0.434277i
$376$	0.470830	+	20.0198i	0.0242812	+	1.03244i
$377$	38.0305	−	38.0305i	1.95867	−	1.95867i
$378$	−3.66670	+	3.48760i	−0.188594	+	0.179383i
$379$	−18.0664	−	7.48335i	−0.928009	−	0.384394i	−0.133086	−	0.991104i	$-0.542489\pi$
$379$	−18.0664	−	7.48335i	−0.928009	−	0.384394i	−0.794923	+	0.606711i	$0.792489\pi$
$380$	11.3669	+	9.23827i	0.583112	+	0.473913i
$381$	1.15370	+	10.9053i	0.0591056	+	0.558698i
$382$	−7.25911	−	2.57785i	−0.371408	−	0.131894i
$383$	−6.74390	−	11.6808i	−0.344597	−	0.596860i	0.640683	−	0.767805i	$-0.278651\pi$
$383$	−6.74390	−	11.6808i	−0.344597	−	0.596860i	−0.985280	+	0.170945i	$0.945318\pi$
$384$	−19.2477	−	3.67778i	−0.982230	−	0.187681i
$385$	2.68600	−	4.65229i	0.136891	−	0.237103i
$386$	−5.94010	+	5.06420i	−0.302343	+	0.257761i
$387$	−24.1135	−	20.5382i	−1.22576	−	1.04402i
$388$	1.82072	−	11.3648i	0.0924328	−	0.576959i
$389$	−4.93028	+	3.78314i	−0.249975	+	0.191813i	−0.726147	−	0.687540i	$-0.758691\pi$
$389$	−4.93028	+	3.78314i	−0.249975	+	0.191813i	0.476172	+	0.879352i	$0.342024\pi$
$390$	−9.21747	+	38.3582i	−0.466745	+	1.94235i
$391$	−43.9714	−	11.7821i	−2.22373	−	0.595846i
$392$	−16.1974	−	8.85046i	−0.818092	−	0.447016i
$393$	−18.0063	−	11.0174i	−0.908295	−	0.555755i
$394$	3.90821	−	18.3066i	0.196893	−	0.922276i
$395$	−25.5012	−	10.5629i	−1.28310	−	0.531479i
$396$	5.51244	−	15.5460i	0.277010	−	0.781217i
$397$	4.30849	+	10.4016i	0.216237	+	0.522042i	0.994358	−	0.106072i	$-0.0338274\pi$
$397$	4.30849	+	10.4016i	0.216237	+	0.522042i	−0.778122	+	0.628113i	$0.783827\pi$
$398$	11.4550	+	7.88781i	0.574188	+	0.395380i
$399$	−2.12057	−	2.23157i	−0.106161	−	0.111718i
$400$	−6.68594	+	10.2158i	−0.334297	+	0.510788i
$401$	−5.13657	−	8.89679i	−0.256508	−	0.444285i	0.708796	−	0.705413i	$-0.249239\pi$
$401$	−5.13657	−	8.89679i	−0.256508	−	0.444285i	−0.965304	+	0.261129i	$0.915905\pi$
$402$	8.16835	+	3.13749i	0.407400	+	0.156484i
$403$	−2.94729	+	22.3869i	−0.146815	+	1.11517i
$404$	6.94289	−	11.2847i	0.345422	−	0.561434i
$405$	13.4032	+	21.7391i	0.666011	+	1.08023i
$406$	−8.77952	+	2.84401i	−0.435720	+	0.141146i
$407$	1.34880	+	5.03377i	0.0668573	+	0.249515i
$408$	20.5417	+	26.8809i	1.01697	+	1.33080i
$409$	−3.06082	+	11.4231i	−0.151348	+	0.564838i	0.848042	+	0.529928i	$0.177781\pi$
$409$	−3.06082	+	11.4231i	−0.151348	+	0.564838i	−0.999390	+	0.0349101i	$0.988886\pi$
$410$	0.897945	+	17.4302i	0.0443464	+	0.860816i
$411$	−13.0917	+	5.03564i	−0.645765	+	0.248390i
$412$	0.814332	−	0.0841266i	0.0401193	−	0.00414462i
$413$	−0.0644989	−	0.155714i	−0.00317378	−	0.00766219i
$414$	3.66355	+	27.7264i	0.180053	+	1.36268i
$415$			0.988227i			0.0485102i
$416$	31.0488	−	8.17181i	1.52229	−	0.400656i
$417$	2.72175	−	0.655393i	0.133285	−	0.0320947i
$418$	9.45557	+	3.35785i	0.462487	+	0.164238i
$419$	13.6902	+	10.5048i	0.668808	+	0.513195i	0.886444	−	0.462835i	$-0.153168\pi$
$419$	13.6902	+	10.5048i	0.668808	+	0.513195i	−0.217636	+	0.976030i	$0.569835\pi$
$420$	4.40193	−	5.14256i	0.214792	−	0.250931i
$421$	22.2624	+	29.0129i	1.08500	+	1.41400i	0.902443	+	0.430810i	$0.141772\pi$
$421$	22.2624	+	29.0129i	1.08500	+	1.41400i	0.182561	+	0.983195i	$0.441561\pi$
$422$	−17.0549	+	33.3986i	−0.830217	+	1.62582i
$423$	−20.2095	−	6.53608i	−0.982618	−	0.317795i
$424$	−2.66616	+	0.414994i	−0.129480	+	0.0201539i
$425$	20.3601	−	5.45548i	0.987610	−	0.264629i
$426$	−3.26519	+	6.01073i	−0.158199	+	0.291221i
$427$	4.04330	−	0.532311i	0.195669	−	0.0257603i
$428$	32.6006	+	0.911665i	1.57581	+	0.0440670i
$429$	2.84312	+	26.8747i	0.137267	+	1.29752i
$430$	34.8973	+	24.0300i	1.68290	+	1.15883i
$431$		−	12.9990i		−	0.626138i	−0.949730	−	0.313069i	$-0.898643\pi$
$431$		−	12.9990i		−	0.626138i	0.949730	−	0.313069i	$-0.101357\pi$
$432$	10.4196	−	17.9842i	0.501311	−	0.865267i
$433$			5.96852i			0.286829i	0.989663	+	0.143414i	$0.0458081\pi$
$433$			5.96852i			0.286829i	−0.989663	+	0.143414i	$0.954192\pi$
$434$	2.19738	−	3.19113i	0.105478	−	0.153179i
$435$	4.89992	+	46.3166i	0.234933	+	2.22071i
$436$	10.7465	+	11.3649i	0.514665	+	0.544278i
$437$	−16.8679	+	2.22071i	−0.806903	+	0.106231i
$438$	2.25649	+	1.22578i	0.107819	+	0.0585701i
$439$	11.5822	−	3.10344i	0.552789	−	0.148119i	0.0283974	−	0.999597i	$-0.490960\pi$
$439$	11.5822	−	3.10344i	0.552789	−	0.148119i	0.524391	+	0.851477i	$0.324293\pi$
$440$	−5.20799	+	21.4409i	−0.248281	+	1.02215i
$441$	14.5310	−	13.1196i	0.691951	−	0.624741i
$442$	−49.3655	−	25.2082i	−2.34808	−	1.19903i
$443$	−2.89802	−	3.77677i	−0.137689	−	0.179440i	0.719419	−	0.694576i	$-0.244408\pi$
$443$	−2.89802	−	3.77677i	−0.137689	−	0.179440i	−0.857108	+	0.515136i	$0.827741\pi$
$444$	0.508042	+	6.54714i	0.0241106	+	0.310713i
$445$	−7.99040	−	6.13125i	−0.378781	−	0.290649i
$446$	−4.67946	+	13.1772i	−0.221579	+	0.623956i
$447$	−3.53006	+	0.850032i	−0.166966	+	0.0402051i
$448$	−5.38253	−	1.17412i	−0.254301	−	0.0554722i
$449$			40.2152i			1.89787i	0.315464	+	0.948937i	$0.397840\pi$
$449$			40.2152i			1.89787i	−0.315464	+	0.948937i	$0.602160\pi$
$450$	−7.88816	−	10.2700i	−0.371852	−	0.484134i
$451$	4.57539	+	11.0460i	0.215447	+	0.520134i
$452$	−25.0518	−	20.3604i	−1.17834	−	0.957672i
$453$	−20.4645	+	7.87154i	−0.961505	+	0.369837i
$454$	5.93148	−	0.305570i	0.278378	−	0.0143411i
$455$	−2.87052	+	10.7129i	−0.134572	+	0.502230i
$456$	10.9374	+	6.34372i	0.512191	+	0.297072i
$457$	9.65641	+	36.0382i	0.451708	+	1.68580i	0.697590	+	0.716497i	$0.254256\pi$
$457$	9.65641	+	36.0382i	0.451708	+	1.68580i	−0.245883	+	0.969300i	$0.579078\pi$
$458$	−4.71164	−	14.5449i	−0.220160	−	0.679638i
$459$	−34.1044	+	11.1581i	−1.59185	+	0.520818i
$460$	−8.66888	−	36.3933i	−0.404189	−	1.69685i
$461$	−0.212665	+	1.61535i	−0.00990480	+	0.0752344i	−0.995683	−	0.0928150i	$-0.970413\pi$
$461$	−0.212665	+	1.61535i	−0.00990480	+	0.0752344i	0.985779	+	0.168049i	$0.0537468\pi$
$462$	1.66271	−	4.32881i	0.0773564	−	0.201395i
$463$	4.71907	+	8.17367i	0.219314	+	0.379863i	0.954598	−	0.297896i	$-0.0962848\pi$
$463$	4.71907	+	8.17367i	0.219314	+	0.379863i	−0.735285	+	0.677758i	$0.762951\pi$
$464$	31.3144	−	21.3583i	1.45373	−	0.991534i
$465$	−13.4696	−	14.1747i	−0.624638	−	0.657335i
$466$	12.0617	−	17.5165i	0.558746	−	0.811434i
$467$	−1.35853	−	3.27978i	−0.0628653	−	0.151770i	0.889325	−	0.457275i	$-0.151175\pi$
$467$	−1.35853	−	3.27978i	−0.0628653	−	0.151770i	−0.952190	+	0.305505i	$0.901175\pi$
$468$	−2.68600	+	33.9477i	−0.124160	+	1.56923i
$469$	2.27273	+	0.941395i	0.104945	+	0.0434696i
$470$	27.7864	+	5.93200i	1.28169	+	0.273623i
$471$	7.45526	+	4.56162i	0.343520	+	0.210188i
$472$	0.434215	+	0.539144i	0.0199864	+	0.0248161i
$473$	28.0362	+	7.51227i	1.28910	+	0.345414i
$474$	−23.1671	−	5.56703i	−1.06410	−	0.255702i
$475$	6.24986	−	4.79568i	0.286763	−	0.220041i
$476$	5.57681	+	7.70458i	0.255612	+	0.353139i
$477$	0.517719	−	2.81472i	0.0237047	−	0.128877i
$478$	−19.5277	−	22.9052i	−0.893177	−	1.04766i
$479$	−14.3663	+	24.8831i	−0.656413	+	1.13694i	0.325125	+	0.945671i	$0.394594\pi$
$479$	−14.3663	+	24.8831i	−0.656413	+	1.13694i	−0.981538	+	0.191269i	$0.938740\pi$
$480$	−11.4041	+	25.3568i	−0.520524	+	1.15737i
$481$	−5.37958	−	9.31770i	−0.245288	−	0.424851i
$482$	9.01733	−	25.3924i	0.410728	−	1.15659i
$483$	0.827185	+	7.81899i	0.0376382	+	0.355776i
$484$	−0.707532	−	6.84880i	−0.0321605	−	0.311309i
$485$	−15.0872	−	6.24933i	−0.685075	−	0.283767i
$486$	14.3594	+	16.7275i	0.651356	+	0.758773i
$487$	6.97840	−	6.97840i	0.316222	−	0.316222i	−0.531092	−	0.847314i	$-0.678218\pi$
$487$	6.97840	−	6.97840i	0.316222	−	0.316222i	0.847314	+	0.531092i	$0.178218\pi$
$488$	−15.3202	+	6.77212i	−0.693514	+	0.306560i
$489$	−5.58442	−	10.2686i	−0.252536	−	0.464361i
$490$	−17.5407	+	19.4461i	−0.792407	+	0.878486i
$491$	2.58835	+	19.6605i	0.116811	+	0.887266i	0.945058	+	0.326903i	$0.106005\pi$
$491$	2.58835	+	19.6605i	0.116811	+	0.887266i	−0.828247	+	0.560363i	$0.810662\pi$
$492$	3.11619	+	14.7401i	0.140489	+	0.664533i
$493$	−64.8802	−	8.54164i	−2.92206	−	0.384696i
$494$	−20.6507	−	1.64371i	−0.929119	−	0.0739541i
$495$	−19.6445	−	12.7193i	−0.882954	−	0.571692i
$496$	−4.97137	+	15.1172i	−0.223221	+	0.678784i
$497$	−0.961531	+	1.66542i	−0.0431306	+	0.0747043i
$498$	0.133270	+	0.842572i	0.00597197	+	0.0377566i
$499$	−13.1879	−	10.1195i	−0.590373	−	0.453009i	0.269867	−	0.962898i	$-0.413020\pi$
$499$	−13.1879	−	10.1195i	−0.590373	−	0.453009i	−0.860241	+	0.509888i	$0.829687\pi$
$500$	−7.59471	−	8.03170i	−0.339646	−	0.359188i
$501$	−5.90924	+	37.4744i	−0.264006	+	1.67423i
$502$	−14.4553	−	3.08599i	−0.645171	−	0.137735i
$503$	22.3214	−	22.3214i	0.995261	−	0.995261i	−0.00472801	−	0.999989i	$-0.501505\pi$
$503$	22.3214	−	22.3214i	0.995261	−	0.995261i	0.999989	+	0.00472801i	$0.00150498\pi$
$504$	3.05961	−	4.97823i	0.136286	−	0.221748i
$505$	−13.2927	−	13.2927i	−0.591517	−	0.591517i
$506$	−13.9390	−	21.5059i	−0.619662	−	0.956056i
$507$	−11.9467	−	31.0590i	−0.530571	−	1.37938i
$508$	−4.51688	−	11.8297i	−0.200404	−	0.524857i
$509$	−9.15955	+	11.9370i	−0.405990	+	0.529097i	−0.950941	−	0.309371i	$-0.899881\pi$
$509$	−9.15955	+	11.9370i	−0.405990	+	0.529097i	0.544951	+	0.838468i	$0.316548\pi$
$510$	43.8547	−	19.5144i	1.94192	−	0.864113i
$511$	0.625215	+	0.360968i	0.0276579	+	0.0159683i
$512$	22.5711	−	1.59485i	0.997513	−	0.0704829i
$513$	−10.1800	+	8.73050i	−0.449457	+	0.385461i
$514$	16.2801	+	19.0959i	0.718086	+	0.842285i
$515$	0.151612	−	1.15161i	0.00668083	−	0.0507459i
$516$	32.9944	+	15.7820i	1.45250	+	0.694764i
$517$	19.2970	−	2.54050i	0.848681	−	0.111731i
$518$	0.0949822	+	1.84372i	0.00417328	+	0.0810083i
$519$	0.427745	−	16.7707i	0.0187759	−	0.736153i
$520$	−1.07103	−	45.5406i	−0.0469677	−	1.99709i
$521$	1.96702	+	1.96702i	0.0861766	+	0.0861766i	0.748881	−	0.662704i	$-0.230591\pi$
$521$	1.96702	+	1.96702i	0.0861766	+	0.0861766i	−0.662704	+	0.748881i	$0.730591\pi$
$522$	10.4239	+	38.8292i	0.456240	+	1.69951i
$523$	11.8341	−	28.5699i	0.517467	−	1.24928i	−0.421987	−	0.906602i	$-0.638667\pi$
$523$	11.8341	−	28.5699i	0.517467	−	1.24928i	0.939454	−	0.342674i	$-0.111333\pi$
$524$	23.3590	+	6.96443i	1.02044	+	0.304242i
$525$	−2.14191	−	2.94388i	−0.0934808	−	0.128481i
$526$	10.9649	+	23.0411i	0.478093	+	1.00464i
$527$	23.7932	−	13.7370i	1.03645	−	0.598393i
$528$	−1.54892	+	18.9830i	−0.0674081	+	0.826130i
$529$	17.7139	+	10.2271i	0.770169	+	0.444657i
$530$	−0.303762	+	3.81630i	−0.0131946	+	0.165769i
$531$	−0.691799	+	0.246038i	−0.0300215	+	0.0106772i
$532$	3.02754	+	1.86269i	0.131261	+	0.0807578i
$533$	−15.0267	−	19.5832i	−0.650879	−	0.848242i
$534$	−7.63954	−	4.15000i	−0.330595	−	0.179588i
$535$	11.9763	−	44.6961i	0.517779	−	1.93238i
$536$	−10.0456	−	1.08293i	−0.433906	−	0.0467753i
$537$	−17.2727	−	31.7608i	−0.745371	−	1.37058i
$538$	−14.7523	−	22.7607i	−0.636015	−	0.981285i
$539$	−6.86527	+	16.5742i	−0.295708	+	0.713902i
$540$	−21.3965	−	20.2938i	−0.920757	−	0.873307i
$541$	33.8580	−	14.0244i	1.45567	−	0.602958i	0.492129	−	0.870522i	$-0.336219\pi$
$541$	33.8580	−	14.0244i	1.45567	−	0.602958i	0.963540	+	0.267564i	$0.0862187\pi$
$542$	4.55578	+	24.7033i	0.195688	+	1.06110i
$543$	1.19326	+	0.352576i	0.0512075	+	0.0151305i
$544$	−30.8862	−	23.9186i	−1.32423	−	1.02550i
$545$	19.2190	−	11.0961i	0.823251	−	0.475304i
$546$	−1.00271	+	9.52105i	−0.0429121	+	0.407463i
$547$	29.7132	+	3.91181i	1.27044	+	0.167257i	0.735439	−	0.677591i	$-0.236976\pi$
$547$	29.7132	+	3.91181i	1.27044	+	0.167257i	0.535005	+	0.844849i	$0.320310\pi$
$548$	13.1203	−	9.49688i	0.560472	−	0.405687i
$549$	−1.41802	−	17.7097i	−0.0605195	−	0.755830i
$550$	10.5684	+	5.39672i	0.450639	+	0.230117i
$551$	−23.6241	+	6.33005i	−1.00642	+	0.269669i
$552$	−12.2991	−	29.8602i	−0.523484	−	1.27094i
$553$	−6.47024	−	1.73369i	−0.275142	−	0.0737242i
$554$	31.3441	+	28.2729i	1.33168	+	1.20120i
$555$	9.20346	+	1.45127i	0.390665	+	0.0616030i
$556$	−2.84364	+	1.53743i	−0.120597	+	0.0652016i
$557$	16.4791	−	6.82585i	0.698240	−	0.289220i	−0.00518860	−	0.999987i	$-0.501652\pi$
$557$	16.4791	−	6.82585i	0.698240	−	0.289220i	0.703428	+	0.710766i	$0.251652\pi$
$558$	−13.3959	−	10.2690i	−0.567092	−	0.434721i
$559$	−59.9243			−2.53453
$560$	−3.39013	+	7.04302i	−0.143259	+	0.297622i
$561$	23.8363	−	22.6506i	1.00637	−	0.956309i
$562$	−11.1661	+	5.31379i	−0.471014	+	0.224149i
$563$	3.48199	−	4.53782i	0.146748	−	0.191246i	−0.714195	−	0.699946i	$-0.753207\pi$
$563$	3.48199	−	4.53782i	0.146748	−	0.191246i	0.860944	+	0.508700i	$0.169874\pi$
$564$	24.4909	+	1.31047i	1.03125	+	0.0551807i
$565$	−36.3379	+	27.8830i	−1.52874	+	1.17305i
$566$	−23.5795	+	7.63827i	−0.991119	+	0.321060i
$567$	3.91345	+	4.80592i	0.164349	+	0.201830i
$568$	1.86435	−	7.67537i	0.0782264	−	0.322051i
$569$	−10.9310	−	40.7951i	−0.458252	−	1.71022i	−0.678347	−	0.734742i	$-0.737303\pi$
$569$	−10.9310	−	40.7951i	−0.458252	−	1.71022i	0.220095	−	0.975479i	$-0.429363\pi$
$570$	12.3515	−	13.0104i	0.517348	−	0.544944i
$571$	0.0296664	+	0.225339i	0.00124150	+	0.00943014i	0.992054	−	0.125810i	$-0.0401529\pi$
$571$	0.0296664	+	0.225339i	0.00124150	+	0.00943014i	−0.990813	+	0.135240i	$0.956820\pi$
$572$	−11.1312	−	29.1525i	−0.465419	−	1.21893i
$573$	−3.83150	+	8.62146i	−0.160063	+	0.360167i
$574$	0.768164	+	4.16530i	0.0320626	+	0.173856i
$575$	−20.1206			−0.839089
$576$	−6.30369	+	23.1574i	−0.262654	+	0.964890i
$577$	9.78981			0.407555			0.203778	−	0.979017i	$-0.434678\pi$
$577$	9.78981			0.407555			0.203778	+	0.979017i	$0.434678\pi$
$578$	7.87132	+	42.6815i	0.327404	+	1.77532i
$579$	5.62457	+	7.73050i	0.233749	+	0.321268i
$580$	−19.1839	−	50.2424i	−0.796566	−	2.08620i
$581$	0.0313030	+	0.237770i	0.00129867	+	0.00986435i
$582$	−13.7063	−	3.29361i	−0.568143	−	0.136524i
$583$	0.678767	+	2.53319i	0.0281117	+	0.104914i
$584$	−2.88141	−	0.699895i	−0.119234	−	0.0289619i
$585$	45.9719	+	14.8681i	1.90070	+	0.614720i
$586$	33.3799	−	10.8130i	1.37891	−	0.446680i
$587$	18.1865	−	13.9550i	0.750638	−	0.575985i	−0.161012	−	0.986952i	$-0.551476\pi$
$587$	18.1865	−	13.9550i	0.750638	−	0.575985i	0.911650	+	0.410967i	$0.134809\pi$
$588$	−12.3329	+	18.9454i	−0.508600	+	0.781296i
$589$	6.25080	−	8.14620i	0.257560	−	0.335658i
$590$	0.886888	−	0.422057i	0.0365126	−	0.0173758i
$591$	−21.9865	−	6.49645i	−0.904405	−	0.267228i
$592$	−2.50573	−	7.15673i	−0.102985	−	0.294140i
$593$	−18.4963			−0.759552			−0.379776	−	0.925078i	$-0.623999\pi$
$593$	−18.4963			−0.759552			−0.379776	+	0.925078i	$0.623999\pi$
$594$	−18.4644	−	8.19542i	−0.757603	−	0.336262i
$595$	12.4674	−	5.16417i	0.511114	−	0.211710i
$596$	3.68814	−	1.99402i	0.151072	−	0.0816782i
$597$	10.7107	−	13.2451i	0.438362	−	0.542085i
$598$	39.2889	+	35.4392i	1.60664	+	1.44922i
$599$	−24.8364	−	6.65490i	−1.01479	−	0.271912i	−0.287160	−	0.957883i	$-0.592711\pi$
$599$	−24.8364	−	6.65490i	−1.01479	−	0.271912i	−0.727629	+	0.685971i	$0.759378\pi$
$600$	11.8450	+	9.12642i	0.483570	+	0.372585i
$601$	−17.3271	+	4.64278i	−0.706787	+	0.189383i	−0.594269	−	0.804267i	$-0.702558\pi$
$601$	−17.3271	+	4.64278i	−0.706787	+	0.189383i	−0.112519	+	0.993650i	$0.535892\pi$
$602$	9.15755	+	4.67626i	0.373234	+	0.190590i
$603$	4.60052	−	9.67904i	0.187348	−	0.394161i
$604$	20.5092	−	14.8452i	0.834508	−	0.604042i
$605$	−9.68540	−	1.27511i	−0.393768	−	0.0518405i
$606$	−13.1261	−	9.54085i	−0.533211	−	0.387570i
$607$	−31.3908	+	18.1235i	−1.27411	+	0.735609i	−0.975759	−	0.218847i	$-0.929770\pi$
$607$	−31.3908	+	18.1235i	−1.27411	+	0.735609i	−0.298353	+	0.954456i	$0.596437\pi$
$608$	−14.0856	−	3.84138i	−0.571246	−	0.155789i
$609$	2.64605	+	10.9887i	0.107223	+	0.445283i
$610$	4.31019	+	23.3716i	0.174515	+	0.946289i
$611$	−37.1249	+	15.3776i	−1.50191	+	0.622112i
$612$	34.7593	−	22.5523i	1.40506	−	0.911623i
$613$	−9.80226	+	23.6648i	−0.395910	+	0.955811i	0.592716	+	0.805412i	$0.298056\pi$
$613$	−9.80226	+	23.6648i	−0.395910	+	0.955811i	−0.988625	+	0.150399i	$0.951944\pi$
$614$	−16.5586	−	25.5477i	−0.668250	−	1.03102i
$615$	21.3689	+	0.545024i	0.861677	+	0.0219775i
$616$	−0.573896	+	5.32369i	−0.0231229	+	0.214497i
$617$	3.16019	−	11.7940i	0.127224	−	0.474807i	−0.872685	−	0.488284i	$-0.837623\pi$
$617$	3.16019	−	11.7940i	0.127224	−	0.474807i	0.999909	+	0.0134763i	$0.00428977\pi$
$618$	−0.0260373	−	1.00232i	−0.00104737	−	0.0403192i
$619$	24.7334	+	32.2332i	0.994119	+	1.29556i	0.955088	+	0.296323i	$0.0957604\pi$
$619$	24.7334	+	32.2332i	0.994119	+	1.29556i	0.0390309	+	0.999238i	$0.487573\pi$
$620$	19.2306	+	11.8316i	0.772319	+	0.475168i
$621$	34.2023	−	1.86244i	1.37249	−	0.0747370i
$622$	−0.885175	+	11.1209i	−0.0354923	+	0.445906i
$623$	−2.11672	−	1.22209i	−0.0848046	−	0.0489620i
$624$	−7.05466	−	38.6839i	−0.282413	−	1.54859i
$625$	−26.7991	+	15.4725i	−1.07197	+	0.618900i
$626$	−10.8377	−	22.7738i	−0.433162	−	0.910223i
$627$	4.99083	−	11.2301i	0.199315	−	0.448489i
$628$	−9.67148	−	2.88353i	−0.385934	−	0.115065i
$629$	−5.00973	+	12.0946i	−0.199751	+	0.482242i
$630$	−5.86511	−	5.85959i	−0.233672	−	0.233452i
$631$	−7.40747	−	7.40747i	−0.294887	−	0.294887i	0.544120	−	0.839007i	$-0.316863\pi$
$631$	−7.40747	−	7.40747i	−0.294887	−	0.294887i	−0.839007	+	0.544120i	$0.816863\pi$
$632$	27.5049	−	0.646865i	1.09409	−	0.0257309i
$633$	39.1775	+	23.9714i	1.55717	+	0.952777i
$634$	1.88821	+	36.6524i	0.0749904	+	1.45565i
$635$	−17.8125	+	2.34505i	−0.706866	+	0.0930606i
$636$	0.255667	+	3.29478i	0.0101378	+	0.130646i
$637$	4.83441	−	36.7210i	0.191546	−	1.45494i
$638$	−23.9015	−	28.0355i	−0.946271	−	1.10994i
$639$	7.03231	+	4.55325i	0.278194	+	0.180124i
$640$	5.21940	−	31.6773i	0.206315	−	1.25216i
$641$	−15.8499	−	9.15095i	−0.626034	−	0.361441i	0.153180	−	0.988198i	$-0.451048\pi$
$641$	−15.8499	−	9.15095i	−0.626034	−	0.361441i	−0.779215	+	0.626757i	$0.784382\pi$
$642$	4.18348	−	39.7234i	0.165109	−	1.56776i
$643$	24.4185	−	31.8229i	0.962973	−	1.25497i	−0.00397349	−	0.999992i	$-0.501265\pi$
$643$	24.4185	−	31.8229i	0.962973	−	1.25497i	0.966947	−	0.254979i	$-0.0820685\pi$
$644$	−3.23854	−	8.48172i	−0.127616	−	0.334227i
$645$	32.6300	−	40.3507i	1.28480	−	1.58881i
$646$	13.7093	+	21.1517i	0.539387	+	0.832202i
$647$	−4.46265	−	4.46265i	−0.175445	−	0.175445i	0.613922	−	0.789367i	$-0.289591\pi$
$647$	−4.46265	−	4.46265i	−0.175445	−	0.175445i	−0.789367	+	0.613922i	$0.789591\pi$
$648$	−20.9796	−	14.4172i	−0.824157	−	0.566362i
$649$	0.475765	−	0.475765i	0.0186754	−	0.0186754i
$650$	−23.9594	−	5.11500i	−0.939767	−	0.200627i
$651$	−3.68981	−	2.98380i	−0.144615	−	0.116944i
$652$	9.27339	+	9.80697i	0.363174	+	0.384071i
$653$	13.1616	+	10.0992i	0.515053	+	0.395214i	0.833323	−	0.552786i	$-0.186435\pi$
$653$	13.1616	+	10.0992i	0.515053	+	0.395214i	−0.318270	+	0.948000i	$0.603102\pi$
$654$	14.8899	−	12.0525i	0.582241	−	0.471289i
$655$	17.2920	−	29.9507i	0.675655	−	1.17027i
$656$	−7.84271	−	15.5284i	−0.306207	−	0.606283i
$657$	1.70933	−	2.64000i	0.0666875	−	0.102996i
$658$	6.87338	+	0.547093i	0.267952	+	0.0213279i
$659$	−18.2601	−	2.40399i	−0.711312	−	0.0936460i	−0.233817	−	0.972281i	$-0.575122\pi$
$659$	−18.2601	−	2.40399i	−0.711312	−	0.0936460i	−0.477495	+	0.878635i	$0.658455\pi$
$660$	25.6914	+	8.37881i	1.00003	+	0.326145i
$661$	1.21184	+	9.20480i	0.0471349	+	0.358025i	0.998717	+	0.0506318i	$0.0161235\pi$
$661$	1.21184	+	9.20480i	0.0471349	+	0.358025i	−0.951582	+	0.307394i	$0.900543\pi$
$662$	−12.6462	+	14.0199i	−0.491508	+	0.544900i
$663$	−35.4313	+	57.9070i	−1.37604	+	2.24892i
$664$	−0.398241	−	0.900920i	−0.0154547	−	0.0349625i
$665$	3.56626	−	3.56626i	0.138294	−	0.138294i
$666$	8.04268	−	0.00379022i	0.311647	−	0.000146868i
$667$	57.7118	+	23.9050i	2.23461	+	0.925606i
$668$	−4.50157	−	43.5745i	−0.174171	−	1.68595i
$669$	15.6502	+	6.95516i	0.605071	+	0.268902i
$670$	−4.79733	+	13.5091i	−0.185337	+	0.521902i
$671$	8.14014	+	14.0991i	0.314247	+	0.544291i
$672$	−1.94066	+	6.46213i	−0.0748624	+	0.249282i
$673$	15.0839	−	26.1260i	0.581440	−	1.00708i	−0.413869	−	0.910336i	$-0.635823\pi$
$673$	15.0839	−	26.1260i	0.581440	−	1.00708i	0.995309	−	0.0967468i	$-0.0308437\pi$
$674$	26.4964	+	31.0792i	1.02060	+	1.19713i
$675$	−13.2838	+	8.66518i	−0.511294	+	0.333523i
$676$	22.5306	+	31.1269i	0.866562	+	1.19719i
$677$	−0.337483	+	0.258960i	−0.0129705	+	0.00995262i	−0.615226	−	0.788351i	$-0.710935\pi$
$677$	−0.337483	+	0.258960i	−0.0129705	+	0.00995262i	0.602256	+	0.798303i	$0.294269\pi$
$678$	−27.2218	+	28.6738i	−1.04545	+	1.10121i
$679$	−3.82797	−	1.02570i	−0.146904	−	0.0393628i
$680$	−43.1671	+	34.7659i	−1.65538	+	1.33321i
$681$	0.185471	−	7.27182i	0.00710727	−	0.278657i
$682$	15.1263	+	3.22926i	0.579217	+	0.123655i
$683$	30.9070	+	12.8021i	1.18262	+	0.489858i	0.885346	−	0.464933i	$-0.153922\pi$
$683$	30.9070	+	12.8021i	1.18262	+	0.489858i	0.297276	+	0.954791i	$0.403922\pi$
$684$	8.77648	−	12.7584i	0.335577	−	0.487831i
$685$	−8.79420	−	21.2311i	−0.336009	−	0.811197i
$686$	−7.47063	+	10.8492i	−0.285230	+	0.414223i
$687$	−18.2048	+	4.38367i	−0.694555	+	0.167248i
$688$	−41.4979	−	7.84387i	−1.58209	−	0.299045i
$689$	−2.70721	−	4.68903i	−0.103137	−	0.178638i
$690$	−45.2570	+	7.15832i	−1.72290	+	0.272513i
$691$	4.77363	−	36.2593i	0.181597	−	1.37937i	−0.621450	−	0.783454i	$-0.713456\pi$
$691$	4.77363	−	36.2593i	0.181597	−	1.37937i	0.803047	−	0.595916i	$-0.203211\pi$
$692$	4.48869	+	18.8442i	0.170634	+	0.716350i
$693$	−5.12941	−	2.43804i	−0.194850	−	0.0926136i
$694$	2.88302	+	8.89993i	0.109438	+	0.337837i
$695$	1.18709	+	4.43028i	0.0450289	+	0.168050i
$696$	−23.1319	−	40.2500i	−0.876813	−	1.52567i
$697$	−7.77338	+	29.0106i	−0.294438	+	1.09886i
$698$	20.2537	−	1.04340i	0.766615	−	0.0394934i
$699$	−20.2537	−	16.3784i	−0.766067	−	0.619487i
$700$	3.26229	+	2.65137i	0.123303	+	0.100212i
$701$	10.6564	+	25.7268i	0.402487	+	0.971689i	0.987061	+	0.160348i	$0.0512617\pi$
$701$	10.6564	+	25.7268i	0.402487	+	0.971689i	−0.584574	+	0.811340i	$0.698738\pi$
$702$	41.2012	+	6.47701i	1.55504	+	0.244459i
$703$			4.89262i			0.184529i
$704$	−3.89246	−	21.6453i	−0.146703	−	0.815790i
$705$	9.86052	−	33.3719i	0.371369	−	1.25686i
$706$	17.6201	−	49.6175i	0.663142	−	1.86738i
$707$	−3.61931	−	2.77719i	−0.136118	−	0.104447i
$708$	0.699251	−	0.479453i	0.0262795	−	0.0180190i
$709$	−1.01870	−	1.32759i	−0.0382580	−	0.0498587i	0.773833	−	0.633390i	$-0.218337\pi$
$709$	−1.01870	−	1.32759i	−0.0382580	−	0.0498587i	−0.812091	+	0.583531i	$0.801670\pi$
$710$	−9.98071	−	5.09660i	−0.374569	−	0.191272i
$711$	−8.97981	+	27.7654i	−0.336769	+	1.04129i
$712$	9.75527	+	2.36956i	0.365594	+	0.0888029i
$713$	−25.3321	+	6.78771i	−0.948694	+	0.254202i
$714$	9.93341	−	6.08435i	0.371748	−	0.227701i
$715$	−43.8963	+	5.77905i	−1.64163	+	0.216124i
$716$	28.6827	+	30.3331i	1.07192	+	1.13360i
$717$	−29.8091	+	21.6885i	−1.11324	+	0.809973i
$718$	−12.1582	+	17.6567i	−0.453742	+	0.658943i
$719$			36.1234i			1.34718i	0.739107	+	0.673588i	$0.235248\pi$
$719$			36.1234i			1.34718i	−0.739107	+	0.673588i	$0.764752\pi$
$720$	29.8896	+	16.3138i	1.11392	+	0.607979i
$721$		−	0.281882i		−	0.0104978i
$722$	−14.3719	−	9.89636i	−0.534867	−	0.368304i
$723$	−30.1579	−	13.4026i	−1.12159	−	0.498449i
$724$	−1.43618	−	0.0401622i	−0.0533752	−	0.00149262i
$725$	−28.6766	+	3.77535i	−1.06502	+	0.140213i
$726$	−8.42982	+	0.218982i	−0.312860	+	0.00812719i
$727$	−34.3861	+	9.21373i	−1.27531	+	0.341718i	−0.832063	−	0.554681i	$-0.812840\pi$
$727$	−34.3861	+	9.21373i	−1.27531	+	0.341718i	−0.443247	+	0.896399i	$0.646174\pi$
$728$	−1.70023	−	10.9232i	−0.0630147	−	0.404842i
$729$	21.7785	−	15.9592i	0.806612	−	0.591081i
$730$	−1.91331	+	3.74685i	−0.0708149	+	0.138677i
$731$	44.3861	+	57.8451i	1.64168	+	2.13948i
$732$	6.82675	+	19.3456i	0.252324	+	0.715034i
$733$	32.0239	+	24.5728i	1.18283	+	0.907616i	0.997183	−	0.0750011i	$-0.0238960\pi$
$733$	32.0239	+	24.5728i	1.18283	+	0.907616i	0.185645	+	0.982617i	$0.440563\pi$
$734$	27.0323	+	9.59969i	0.997781	+	0.354331i
$735$	22.0941	+	23.2506i	0.814952	+	0.857612i
$736$	22.5690	+	29.6846i	0.831903	+	1.09419i
$737$			9.82036i			0.361737i
$738$	18.2928	−	2.41707i	0.673368	−	0.0889735i
$739$	−15.5905	−	37.6388i	−0.573506	−	1.38457i	−0.898552	−	0.438868i	$-0.855380\pi$
$739$	−15.5905	−	37.6388i	−0.573506	−	1.38457i	0.325046	−	0.945698i	$-0.394620\pi$
$740$	−10.7016	+	1.10556i	−0.393399	+	0.0406410i
$741$	−3.95199	+	25.0622i	−0.145180	+	0.920681i
$742$	0.0477988	+	0.927832i	0.00175475	+	0.0340618i
$743$	9.81938	−	36.6464i	0.360238	−	1.34443i	−0.513524	−	0.858075i	$-0.671660\pi$
$743$	9.81938	−	36.6464i	0.360238	−	1.34443i	0.873763	−	0.486353i	$-0.161673\pi$
$744$	17.9918	+	7.49433i	0.659610	+	0.274756i
$745$	−1.53963	−	5.74598i	−0.0564077	−	0.210517i
$746$	1.35736	−	0.439699i	0.0496964	−	0.0160985i
$747$	1.04143	−	0.0833877i	0.0381040	−	0.00305100i
$748$	−19.8961	+	32.3383i	−0.727474	+	1.18241i
$749$	1.46573	−	11.1333i	0.0535566	−	0.406803i
$750$	−10.5229	+	8.51764i	−0.384242	+	0.311020i
$751$	8.29232	+	14.3627i	0.302591	+	0.524103i	0.976722	−	0.214509i	$-0.0688150\pi$
$751$	8.29232	+	14.3627i	0.302591	+	0.524103i	−0.674131	+	0.738612i	$0.735482\pi$
$752$	−27.7221	+	5.78958i	−1.01092	+	0.211124i
$753$	−5.12972	+	17.3610i	−0.186937	+	0.632669i
$754$	62.6455	+	43.1371i	2.28142	+	1.57096i
$755$	−13.7468	−	33.1877i	−0.500297	−	1.20782i
$756$	−5.79086	−	4.20498i	−0.210612	−	0.152934i
$757$	−12.3850	−	5.13003i	−0.450140	−	0.186454i	0.146084	−	0.989272i	$-0.453333\pi$
$757$	−12.3850	−	5.13003i	−0.450140	−	0.186454i	−0.596224	+	0.802818i	$0.703333\pi$
$758$	5.77381	−	27.0454i	0.209714	−	0.982333i
$759$	−27.5740	+	14.9958i	−1.00087	+	0.544312i
$760$	−9.93278	+	18.1782i	−0.360300	+	0.659391i
$761$	13.0952	+	3.50886i	0.474702	+	0.127196i	0.488235	−	0.872712i	$-0.337641\pi$
$761$	13.0952	+	3.50886i	0.474702	+	0.127196i	−0.0135326	+	0.999908i	$0.504308\pi$
$762$	−14.8708	+	4.40156i	−0.538713	+	0.159452i
$763$	4.27265	−	3.27852i	0.154680	−	0.118690i
$764$	1.72332	−	10.7569i	0.0623477	−	0.389170i
$765$	−19.6993	−	55.3896i	−0.712230	−	2.00262i
$766$	14.5155	−	12.3751i	0.524465	−	0.447130i
$767$	−0.694553	+	1.20300i	−0.0250789	+	0.0434379i
$768$	0.178184	−	27.7122i	0.00642965	−	0.999979i
$769$	8.64344	+	14.9709i	0.311690	+	0.539863i	0.978728	−	0.205160i	$-0.0657715\pi$
$769$	8.64344	+	14.9709i	0.311690	+	0.539863i	−0.667038	+	0.745024i	$0.732438\pi$
$770$	7.15914	+	2.54235i	0.257997	+	0.0916198i
$771$	24.8516	−	18.0816i	0.895008	−	0.651192i
$772$	−8.56663	−	6.96237i	−0.308320	−	0.250581i
$773$	16.9010	+	7.00063i	0.607887	+	0.251795i	0.665325	−	0.746554i	$-0.268293\pi$
$773$	16.9010	+	7.00063i	0.607887	+	0.251795i	−0.0574376	+	0.998349i	$0.518293\pi$
$774$	22.3790	−	38.8038i	0.804397	−	1.39477i
$775$	8.58661	−	8.58661i	0.308440	−	0.308440i
$776$	16.2727	−	0.382703i	0.584155	−	0.0137382i
$777$	2.26034	+	0.0576512i	0.0810894	+	0.00206822i
$778$	−6.52598	−	5.88653i	−0.233968	−	0.211042i
$779$	1.46514	+	11.1288i	0.0524940	+	0.398731i
$780$	−55.7113	−	2.98102i	−1.99478	−	0.106737i
$781$	−7.61126	−	1.00204i	−0.272352	−	0.0358559i
$782$	5.10812	−	64.1756i	0.182666	−	2.29492i
$783$	48.3967	−	9.07196i	1.72956	−	0.324206i
$784$	8.15451	−	24.7967i	0.291232	−	0.885597i
$785$	−7.15954	+	12.4007i	−0.255535	+	0.442600i
$786$	10.7043	−	27.8682i	0.381809	−	0.994025i
$787$	−19.2584	−	14.7775i	−0.686486	−	0.526759i	0.205594	−	0.978637i	$-0.434088\pi$
$787$	−19.2584	−	14.7775i	−0.686486	−	0.526759i	−0.892080	+	0.451878i	$0.850754\pi$
$788$	26.4626	+	0.740016i	0.942690	+	0.0263620i
$789$	29.1686	−	11.2195i	1.03843	−	0.399426i
$790$	8.14988	−	38.1753i	0.289960	−	1.35822i
$791$	−7.85975	+	7.85975i	−0.279461	+	0.279461i
$792$	23.0346	+	3.67918i	0.818500	+	0.130734i
$793$	−23.7671	−	23.7671i	−0.843993	−	0.843993i
$794$	−13.3611	+	8.65992i	−0.474167	+	0.307329i
$795$	4.63155	+	0.730337i	0.164264	+	0.0259024i
$796$	−8.03203	+	17.9543i	−0.284688	+	0.636372i
$797$	3.06282	−	3.99155i	0.108491	−	0.141388i	−0.735952	−	0.677034i	$-0.763265\pi$
$797$	3.06282	−	3.99155i	0.108491	−	0.141388i	0.844443	+	0.535646i	$0.179932\pi$
$798$	2.55969	−	3.52156i	0.0906120	−	0.124662i
$799$	42.3425	+	24.4465i	1.49797	+	0.864854i
$800$	−15.9225	−	6.67837i	−0.562946	−	0.236116i
$801$	−5.78711	+	8.93795i	−0.204477	+	0.315807i
$802$	11.0559	−	9.42562i	0.390396	−	0.332830i
$803$	−0.376176	+	2.85734i	−0.0132750	+	0.100833i
$804$	−2.26845	+	12.1649i	−0.0800020	+	0.429024i
$805$	−12.7713	+	1.68137i	−0.450129	+	0.0592606i
$806$	−31.8907	+	1.64290i	−1.12330	+	0.0578688i
$807$	−29.1829	+	15.8707i	−1.02729	+	0.558676i
$808$	17.4750	+	6.76155i	0.614770	+	0.237871i
$809$	0.504387	+	0.504387i	0.0177333	+	0.0177333i	0.715918	−	0.698185i	$-0.246008\pi$
$809$	0.504387	+	0.504387i	0.0177333	+	0.0177333i	−0.698185	+	0.715918i	$0.746008\pi$
$810$	−26.7962	+	24.2164i	−0.941523	+	0.850878i
$811$	13.1867	−	31.8355i	0.463047	−	1.11789i	−0.504093	−	0.863649i	$-0.668173\pi$
$811$	13.1867	−	31.8355i	0.463047	−	1.11789i	0.967140	−	0.254245i	$-0.0818269\pi$
$812$	−6.20715	−	11.4808i	−0.217828	−	0.402896i
$813$	30.5947	−	3.23667i	1.07300	−	0.113515i
$814$	−6.65483	+	3.16693i	−0.233252	+	0.111001i
$815$	16.5845	−	9.57505i	0.580929	−	0.335399i
$816$	−32.1162	+	35.4631i	−1.12429	+	1.24146i
$817$	23.5992	+	13.6250i	0.825632	+	0.476679i
$818$	−16.6719	−	1.32702i	−0.582920	−	0.0463981i
$819$	11.5319	+	2.12109i	0.402957	+	0.0741170i
$820$	−24.0109	+	5.71939i	−0.838498	+	0.199730i
$821$	12.4191	+	16.1849i	0.433431	+	0.564859i	0.958095	−	0.286451i	$-0.0924756\pi$
$821$	12.4191	+	16.1849i	0.433431	+	0.564859i	−0.524664	+	0.851310i	$0.675809\pi$
$822$	−10.3612	−	16.9158i	−0.361388	−	0.590008i
$823$	−6.93293	+	25.8740i	−0.241667	+	0.901912i	0.733363	+	0.679837i	$0.237950\pi$
$823$	−6.93293	+	25.8740i	−0.241667	+	0.901912i	−0.975030	+	0.222075i	$0.928717\pi$
$824$	0.325863	+	1.11096i	0.0113520	+	0.0387023i
$825$	7.58534	−	12.3971i	0.264088	−	0.431610i
$826$	0.200018	−	0.129641i	0.00695952	−	0.00451078i
$827$	−14.6945	+	35.4756i	−0.510977	+	1.23361i	0.432339	+	0.901711i	$0.357688\pi$
$827$	−14.6945	+	35.4756i	−0.510977	+	1.23361i	−0.943316	+	0.331896i	$0.892312\pi$
$828$	−37.6212	+	12.2065i	−1.30743	+	0.424205i
$829$	3.50068	−	1.45003i	0.121584	−	0.0503616i	−0.321062	−	0.947058i	$-0.604040\pi$
$829$	3.50068	−	1.45003i	0.121584	−	0.0503616i	0.442646	+	0.896696i	$0.354040\pi$
$830$	−1.37439	+	0.253465i	−0.0477057	+	0.00879788i
$831$	37.4764	−	35.6122i	1.30004	−	1.23538i
$832$	19.3286	+	41.0855i	0.670097	+	1.42438i
$833$	−39.0277	+	22.5327i	−1.35223	+	0.780711i
$834$	1.60958	+	3.61721i	0.0557352	+	0.125254i
$835$	−61.6220	−	8.11269i	−2.13252	−	0.280751i
$836$	−2.24477	+	14.0117i	−0.0776369	+	0.484604i
$837$	−13.8012	+	15.3908i	−0.477040	+	0.531985i
$838$	−11.0984	+	21.7341i	−0.383388	+	0.750791i
$839$	−6.71785	+	1.80004i	−0.231926	+	0.0621444i	−0.372910	−	0.927867i	$-0.621640\pi$
$839$	−6.71785	+	1.80004i	−0.231926	+	0.0621444i	0.140984	+	0.990012i	$0.454973\pi$
$840$	8.28109	+	4.80305i	0.285725	+	0.165721i
$841$	58.7263	+	15.7357i	2.02505	+	0.542609i
$842$	−34.6401	+	38.4031i	−1.19378	+	1.32346i
$843$	5.43718	+	14.1356i	0.187266	+	0.486856i
$844$	−50.8238	−	15.1530i	−1.74943	−	0.521588i
$845$	50.3691	−	20.8636i	1.73275	−	0.717728i
$846$	3.90672	−	29.7829i	0.134316	−	1.02396i
$847$	−2.37072			−0.0814589
$848$	−1.26098	−	3.60155i	−0.0433024	−	0.123678i
$849$	7.10659	+	29.5127i	0.243898	+	1.01287i
$850$	12.8093	+	26.9168i	0.439356	+	0.923239i
$851$	7.60725	−	9.91396i	0.260773	−	0.339846i
$852$	−9.19696	−	2.99944i	−0.315083	−	0.102759i
$853$	−25.3122	+	19.4228i	−0.866674	+	0.665023i	−0.943265	−	0.332040i	$-0.892263\pi$
$853$	−25.3122	+	19.4228i	−0.866674	+	0.665023i	0.0765910	+	0.997063i	$0.475596\pi$
$854$	1.77736	+	5.48673i	0.0608200	+	0.187752i
$855$	−14.7240	−	16.3080i	−0.503549	−	0.557720i
$856$	7.09363	+	45.5735i	0.242455	+	1.55767i
$857$	3.70167	+	13.8148i	0.126447	+	0.471905i	0.999887	−	0.0150259i	$-0.00478307\pi$
$857$	3.70167	+	13.8148i	0.126447	+	0.471905i	−0.873441	+	0.486931i	$0.838116\pi$
$858$	−36.6470	+	10.8470i	−1.25111	+	0.370311i
$859$	−3.15827	−	23.9894i	−0.107759	−	0.818508i	−0.956915	−	0.290367i	$-0.906223\pi$
$859$	−3.15827	−	23.9894i	−0.107759	−	0.818508i	0.849157	−	0.528141i	$-0.177111\pi$
$860$	−24.4693	+	54.6971i	−0.834397	+	1.86516i
$861$	5.15867	−	0.545745i	0.175807	−	0.0185989i
$862$	18.0785	−	3.33403i	0.615755	−	0.113557i
$863$	−4.17868			−0.142244			−0.0711219	−	0.997468i	$-0.522658\pi$
$863$	−4.17868			−0.142244			−0.0711219	+	0.997468i	$0.522658\pi$
$864$	27.6842	+	9.87845i	0.941836	+	0.336072i
$865$	27.4848			0.934510
$866$	−8.30078	+	1.53083i	−0.282072	+	0.0520197i
$867$	52.8604	−	5.59220i	1.79523	−	0.189921i
$868$	5.00170	+	2.23756i	0.169769	+	0.0759478i
$869$	−3.49035	−	26.5118i	−0.118402	−	0.899352i
$870$	−63.1586	+	18.6941i	−2.14128	+	0.633789i
$871$	−5.24749	−	19.5839i	−0.177804	−	0.663575i
$872$	−13.0495	+	17.8607i	−0.441911	+	0.604841i
$873$	−5.31270	+	16.4268i	−0.179808	+	0.555963i
$874$	−7.41483	−	22.8897i	−0.250810	−	0.774256i
$875$	−3.01954	+	2.31698i	−0.102079	+	0.0783281i
$876$	−1.12602	+	3.45263i	−0.0380446	+	0.116653i
$877$	−7.85094	+	10.2315i	−0.265107	+	0.345495i	−0.906871	−	0.421408i	$-0.861536\pi$
$877$	−7.85094	+	10.2315i	−0.265107	+	0.345495i	0.641764	+	0.766902i	$0.278203\pi$
$878$	7.28680	+	15.3121i	0.245918	+	0.516758i
$879$	−10.0603	−	41.7791i	−0.339326	−	1.40917i
$880$	−31.1549	−	1.74383i	−1.05023	−	0.0587846i
$881$	−42.3840			−1.42795			−0.713977	−	0.700169i	$-0.753108\pi$
$881$	−42.3840			−1.42795			−0.713977	+	0.700169i	$0.753108\pi$
$882$	21.9731	+	16.8441i	0.739874	+	0.567172i
$883$	−16.3800	+	6.78482i	−0.551231	+	0.228327i	−0.640873	−	0.767647i	$-0.721428\pi$
$883$	−16.3800	+	6.78482i	−0.551231	+	0.228327i	0.0896423	+	0.995974i	$0.471428\pi$
$884$	22.3972	−	75.1211i	0.753299	−	2.52659i
$885$	−0.431857	−	1.12274i	−0.0145167	−	0.0377406i
$886$	4.50929	−	4.99913i	0.151493	−	0.167949i
$887$	−20.1062	−	5.38743i	−0.675099	−	0.180892i	−0.0950485	−	0.995473i	$-0.530301\pi$
$887$	−20.1062	−	5.38743i	−0.675099	−	0.180892i	−0.580051	+	0.814580i	$0.696967\pi$
$888$	−8.97520	+	2.38580i	−0.301188	+	0.0800622i
$889$	−4.21143	+	1.12845i	−0.141247	+	0.0378470i
$890$	6.47769	−	12.6853i	0.217133	−	0.425212i
$891$	−11.7465	+	21.7754i	−0.393522	+	0.729503i
$892$	−19.5265	−	3.12828i	−0.653795	−	0.104742i
$893$	18.1168	+	2.38512i	0.606256	+	0.0798151i
$894$	−2.08759	−	4.69145i	−0.0698196	−	0.156906i
$895$	51.2960	−	29.6157i	1.71463	−	0.989945i
$896$	0.252393	−	7.78696i	0.00843185	−	0.260144i
$897$	46.9756	−	44.6389i	1.56847	−	1.49045i
$898$	−55.9298	+	10.3146i	−1.86640	+	0.344202i
$899$	−34.8305	+	14.4273i	−1.16166	+	0.481176i
$900$	12.2600	−	13.6046i	0.408666	−	0.453488i
$901$	−2.52109	+	6.08646i	−0.0839898	+	0.202769i
$902$	−14.1888	+	9.19639i	−0.472435	+	0.306206i
$903$	6.57270	−	10.7421i	0.218726	−	0.357473i
$904$	21.8910	−	40.0632i	0.728085	−	1.33248i
$905$	−0.527600	+	1.96903i	−0.0175380	+	0.0654527i
$906$	−16.1962	−	26.4423i	−0.538084	−	0.878485i
$907$	21.5141	+	28.0377i	0.714363	+	0.930975i	0.999622	−	0.0274748i	$-0.00874660\pi$
$907$	21.5141	+	28.0377i	0.714363	+	0.930975i	−0.285260	+	0.958450i	$0.592080\pi$
$908$	1.94630	+	8.17089i	0.0645904	+	0.271161i
$909$	−12.8867	+	15.1300i	−0.427424	+	0.501830i
$910$	−15.6354	−	1.24451i	−0.518307	−	0.0412552i
$911$	−15.2050	−	8.77860i	−0.503764	−	0.290848i	0.226503	−	0.974011i	$-0.427271\pi$
$911$	−15.2050	−	8.77860i	−0.503764	−	0.290848i	−0.730266	+	0.683162i	$0.760604\pi$
$912$	−6.01732	+	16.8384i	−0.199253	+	0.557575i
$913$	−0.829112	+	0.478688i	−0.0274396	+	0.0158423i
$914$	−47.6438	+	22.6730i	−1.57592	+	0.749956i
$915$	28.9454	−	3.06219i	0.956907	−	0.101233i
$916$	19.0200	−	10.2833i	0.628439	−	0.339770i
$917$	3.21179	−	7.75394i	0.106063	−	0.256058i
$918$	−24.2655	−	44.5691i	−0.800882	−	1.47100i
$919$	−21.4242	−	21.4242i	−0.706718	−	0.706718i	0.259126	−	0.965844i	$-0.416566\pi$
$919$	−21.4242	−	21.4242i	−0.706718	−	0.706718i	−0.965844	+	0.259126i	$0.916566\pi$
$920$	48.3910	−	21.3907i	1.59540	−	0.705229i
$921$	−32.7562	+	17.8140i	−1.07935	+	0.586991i
$922$	−2.30111	+	0.118546i	−0.0757831	+	0.00390409i
$923$	15.7139	−	2.06878i	0.517230	−	0.0680947i
$924$	6.44680	+	1.20216i	0.212084	+	0.0395483i
$925$	−0.755245	+	5.73666i	−0.0248323	+	0.188620i
$926$	−10.1573	+	8.65951i	−0.333788	+	0.284569i
$927$	−1.22640	−	0.0626007i	−0.0402803	−	0.00205608i
$928$	37.7359	+	38.0728i	1.23874	+	1.24980i
$929$	−6.13817	−	3.54387i	−0.201387	−	0.116271i	0.395915	−	0.918287i	$-0.370427\pi$
$929$	−6.13817	−	3.54387i	−0.201387	−	0.116271i	−0.597302	+	0.802016i	$0.703761\pi$
$930$	16.2589	−	22.3686i	0.533149	−	0.733494i
$931$	−10.2531	+	13.3622i	−0.336033	+	0.437927i
$932$	27.4548	+	12.2822i	0.899313	+	0.402317i
$933$	13.4965	+	2.12823i	0.441856	+	0.0696752i
$934$	4.21295	−	2.73060i	0.137852	−	0.0893480i
$935$	38.0926	+	38.0926i	1.24576	+	1.24576i
$936$	−47.9020	+	4.97145i	−1.56573	+	0.162497i
$937$	−6.65530	+	6.65530i	−0.217419	+	0.217419i	−0.807410	−	0.589991i	$-0.799131\pi$
$937$	−6.65530	+	6.65530i	−0.217419	+	0.217419i	0.589991	+	0.807410i	$0.299131\pi$
$938$	−0.726337	+	3.40228i	−0.0237157	+	0.111088i
$939$	−28.8301	+	11.0894i	−0.940836	+	0.361887i
$940$	−1.12322	+	40.1657i	−0.0366354	+	1.31006i
$941$	−18.5433	−	14.2288i	−0.604493	−	0.463844i	0.260605	−	0.965445i	$-0.416078\pi$
$941$	−18.5433	−	14.2288i	−0.604493	−	0.463844i	−0.865099	+	0.501601i	$0.832744\pi$
$942$	−4.43197	+	11.5385i	−0.144401	+	0.375944i
$943$	14.3347	−	24.8285i	0.466803	−	0.808526i
$944$	−0.638451	+	0.742171i	−0.0207798	+	0.0241556i
$945$	−7.70761	+	6.61016i	−0.250729	+	0.215029i
$946$	−3.25694	+	40.9184i	−0.105892	+	1.33037i
$947$	20.5726	+	2.70843i	0.668520	+	0.0880123i	0.457144	−	0.889393i	$-0.348872\pi$
$947$	20.5726	+	2.70843i	0.668520	+	0.0880123i	0.211376	+	0.977405i	$0.432206\pi$
$948$	1.80043	−	33.6477i	0.0584753	−	1.09283i
$949$	−0.776639	−	5.89916i	−0.0252108	−	0.191495i
$950$	8.27264	+	7.46204i	0.268400	+	0.242101i
$951$	44.9348	+	1.14608i	1.45711	+	0.0371643i
$952$	−9.28486	+	9.73210i	−0.300924	+	0.315419i
$953$	−19.2927	+	19.2927i	−0.624952	+	0.624952i	−0.946794	−	0.321841i	$-0.895698\pi$
$953$	−19.2927	+	19.2927i	−0.624952	+	0.624952i	0.321841	+	0.946794i	$0.395698\pi$
$954$	4.04739	−	0.00190739i	0.131039	−	6.17539e-5i
$955$	−14.2802	−	5.91504i	−0.462096	−	0.191406i
$956$	26.8471	−	33.0332i	0.868298	−	1.06837i
$957$	−36.4857	+	26.5463i	−1.17941	+	0.858121i
$958$	−38.2912	−	13.5979i	−1.23713	−	0.439330i
$959$	−2.78842	−	4.82968i	−0.0900426	−	0.155958i
$960$	−38.1902	−	9.35678i	−1.23258	−	0.301989i
$961$	−7.58607	+	13.1395i	−0.244712	+	0.423854i
$962$	11.5789	−	9.87155i	0.373319	−	0.318271i
$963$	−48.1130	−	8.84955i	−1.55042	−	0.285173i
$964$	37.6276	+	6.02820i	1.21190	+	0.194155i
$965$	−12.4260	+	9.53478i	−0.400006	+	0.306935i
$966$	−10.6622	+	3.15586i	−0.343050	+	0.101538i
$967$	47.8320	+	12.8166i	1.53817	+	0.412152i	0.925675	−	0.378319i	$-0.123498\pi$
$967$	47.8320	+	12.8166i	1.53817	+	0.412152i	0.612499	+	0.790472i	$0.290164\pi$
$968$	9.34357	−	2.74061i	0.300314	−	0.0880867i
$969$	27.1198	−	14.7487i	0.871214	−	0.473798i
$970$	4.82169	−	22.5855i	0.154815	−	0.725178i
$971$	47.4354	+	19.6484i	1.52228	+	0.630547i	0.978046	−	0.208390i	$-0.0668222\pi$
$971$	47.4354	+	19.6484i	1.52228	+	0.630547i	0.544229	+	0.838937i	$0.316822\pi$
$972$	−19.5809	+	24.2608i	−0.628059	+	0.778166i
$973$	0.425949	+	1.02833i	0.0136553	+	0.0329668i
$974$	11.4951	+	7.91544i	0.368328	+	0.253627i
$975$	−8.50244	+	28.7756i	−0.272296	+	0.921557i
$976$	−13.3478	−	19.5698i	−0.427253	−	0.626415i
$977$	−3.79556	−	6.57411i	−0.121431	−	0.210324i	0.798901	−	0.601462i	$-0.205415\pi$
$977$	−3.79556	−	6.57411i	−0.121431	−	0.210324i	−0.920332	+	0.391138i	$0.872082\pi$
$978$	12.8488	−	10.4003i	0.410860	−	0.332566i
$979$	1.27358	−	9.67378i	0.0407037	−	0.309175i
$980$	−31.5438	−	19.4073i	−1.00763	−	0.619942i
$981$	−13.3152	−	19.3174i	−0.425122	−	0.616757i
$982$	−26.6792	+	8.64238i	−0.851367	+	0.275790i
$983$	6.90394	+	25.7659i	0.220201	+	0.821803i	0.984270	+	0.176668i	$0.0565320\pi$
$983$	6.90394	+	25.7659i	0.220201	+	0.821803i	−0.764069	+	0.645135i	$0.776801\pi$
$984$	−19.7006	+	8.11447i	−0.628033	+	0.258680i
$985$	9.72137	−	36.2807i	0.309749	−	1.15600i
$986$	−4.76136	−	92.4237i	−0.151633	−	2.94337i
$987$	1.31538	−	8.34169i	0.0418690	−	0.265519i
$988$	−3.01056	−	29.1418i	−0.0957788	−	0.927123i
$989$	−26.6345	−	64.3014i	−0.846929	−	2.04467i
$990$	12.6511	−	30.5831i	0.402077	−	0.971995i
$991$			25.3003i			0.803691i	0.915707	+	0.401846i	$0.131631\pi$
$991$			25.3003i			0.803691i	−0.915707	+	0.401846i	$0.868369\pi$
$992$	−22.2996	−	3.03666i	−0.708012	−	0.0964140i
$993$	15.9290	+	16.7628i	0.505492	+	0.531953i
$994$	−2.56282	−	0.910106i	−0.0812877	−	0.0288668i
$995$	22.1401	+	16.9887i	0.701887	+	0.538577i
$996$	−1.13763	+	0.401453i	−0.0360473	+	0.0127205i
$997$	3.05393	+	3.97996i	0.0967191	+	0.126047i	0.839206	−	0.543814i	$-0.183020\pi$
$997$	3.05393	+	3.97996i	0.0967191	+	0.126047i	−0.742487	+	0.669861i	$0.766354\pi$
$998$	10.6913	−	20.9368i	0.338426	−	0.662741i
$999$	0.752806	−	9.82142i	0.0238177	−	0.310736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.27	✓	368
3.2	odd	2		864.2.bn.a.683.20		368
9.4	even	3		864.2.bn.a.395.5		368
9.5	odd	6	inner	288.2.bf.a.203.42	yes	368
32.3	odd	8	inner	288.2.bf.a.227.42	yes	368
96.35	even	8		864.2.bn.a.35.5		368
288.67	odd	24		864.2.bn.a.611.20		368
288.131	even	24	inner	288.2.bf.a.131.27	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.27	✓	368	1.1	even	1	trivial
288.2.bf.a.131.27	yes	368	288.131	even	24	inner
288.2.bf.a.203.42	yes	368	9.5	odd	6	inner
288.2.bf.a.227.42	yes	368	32.3	odd	8	inner
864.2.bn.a.35.5		368	96.35	even	8
864.2.bn.a.395.5		368	9.4	even	3
864.2.bn.a.611.20		368	288.67	odd	24
864.2.bn.a.683.20		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.256484 + 1.39076i) q^{2} +(1.72244 - 0.182220i) q^{3} +(-1.86843 + 0.713416i) q^{4} +(0.370388 + 2.81338i) q^{5} +(0.695202 + 2.34876i) q^{6} +(0.178233 + 0.665173i) q^{7} +(-1.47141 - 2.41556i) q^{8} +(2.93359 - 0.627725i) q^{9} +O(q^{10})\)	\(q+(0.256484 + 1.39076i) q^{2} +(1.72244 - 0.182220i) q^{3} +(-1.86843 + 0.713416i) q^{4} +(0.370388 + 2.81338i) q^{5} +(0.695202 + 2.34876i) q^{6} +(0.178233 + 0.665173i) q^{7} +(-1.47141 - 2.41556i) q^{8} +(2.93359 - 0.627725i) q^{9} +(-3.81774 + 1.23671i) q^{10} +(-2.18098 + 1.67353i) q^{11} +(-3.08826 + 1.56928i) q^{12} +(3.45510 - 4.50278i) q^{13} +(-0.879383 + 0.418485i) q^{14} +(1.15063 + 4.77838i) q^{15} +(2.98208 - 2.66594i) q^{16} -6.90574 q^{17} +(1.62544 + 3.91892i) q^{18} +(-2.38448 + 0.987682i) q^{19} +(-2.69916 - 4.99237i) q^{20} +(0.428202 + 1.11324i) q^{21} +(-2.88686 - 2.60399i) q^{22} +(6.36737 + 1.70613i) q^{23} +(-2.97458 - 3.89254i) q^{24} +(-2.94829 + 0.789991i) q^{25} +(7.14846 + 3.65033i) q^{26} +(4.93855 - 1.61578i) q^{27} +(-0.807560 - 1.11568i) q^{28} +(9.39511 + 1.23689i) q^{29} +(-6.35047 + 2.82582i) q^{30} +(-3.44542 + 1.98921i) q^{31} +(4.47254 + 3.46358i) q^{32} +(-3.45166 + 3.27997i) q^{33} +(-1.77121 - 9.60424i) q^{34} +(-1.80537 + 0.747808i) q^{35} +(-5.03339 + 3.26573i) q^{36} +(0.725444 - 1.75138i) q^{37} +(-1.98521 - 3.06291i) q^{38} +(5.13071 - 8.38535i) q^{39} +(6.25090 - 5.03434i) q^{40} +(1.12564 - 4.20094i) q^{41} +(-1.43843 + 0.881056i) q^{42} +(-6.42742 - 8.37637i) q^{43} +(2.88110 - 4.68282i) q^{44} +(2.85260 + 8.02080i) q^{45} +(-0.739692 + 9.29308i) q^{46} +(-6.13150 - 3.54002i) q^{47} +(4.65066 - 5.13531i) q^{48} +(5.65149 - 3.26289i) q^{49} +(-1.85488 - 3.89774i) q^{50} +(-11.8947 + 1.25836i) q^{51} +(-3.24327 + 10.8781i) q^{52} +(0.365072 - 0.881362i) q^{53} +(3.51382 + 6.45392i) q^{54} +(-5.51608 - 5.51608i) q^{55} +(1.34451 - 1.40928i) q^{56} +(-3.92714 + 2.13572i) q^{57} +(0.689478 + 13.3836i) q^{58} +(-0.242656 + 0.0319462i) q^{59} +(-5.55884 - 8.10721i) q^{60} +(0.772991 - 5.87145i) q^{61} +(-3.65021 - 4.28155i) q^{62} +(0.940407 + 1.83946i) q^{63} +(-3.66988 + 7.10858i) q^{64} +(13.9477 + 8.05274i) q^{65} +(-5.44694 - 3.95917i) q^{66} +(2.17465 - 2.83406i) q^{67} +(12.9029 - 4.92667i) q^{68} +(11.2783 + 1.77845i) q^{69} +(-1.50307 - 2.31904i) q^{70} +(1.97464 + 1.97464i) q^{71} +(-5.83284 - 6.16263i) q^{72} +(0.741298 - 0.741298i) q^{73} +(2.62181 + 0.559719i) q^{74} +(-4.93429 + 1.89795i) q^{75} +(3.75060 - 3.54654i) q^{76} +(-1.50191 - 1.15245i) q^{77} +(12.9780 + 4.98488i) q^{78} +(-4.86357 + 8.42396i) q^{79} +(8.60482 + 7.40228i) q^{80} +(8.21192 - 3.68298i) q^{81} +(6.13122 + 0.488020i) q^{82} +(0.345275 + 0.0454564i) q^{83} +(-1.59427 - 1.77453i) q^{84} +(-2.55781 - 19.4285i) q^{85} +(10.0010 - 11.0874i) q^{86} +(16.4079 + 0.418491i) q^{87} +(7.25164 + 2.80585i) q^{88} +(-2.50973 + 2.50973i) q^{89} +(-10.4234 + 6.02449i) q^{90} +(3.61094 + 1.49570i) q^{91} +(-13.1142 + 1.35479i) q^{92} +(-5.57205 + 4.05412i) q^{93} +(3.35069 - 9.43540i) q^{94} +(-3.66191 - 6.34261i) q^{95} +(8.33481 + 5.15082i) q^{96} +(-2.87742 + 4.98384i) q^{97} +(5.98742 + 7.02299i) q^{98} +(-5.34760 + 6.27850i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more