LMFDB - Embedded newform 256.2.m.a.101.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.138337 - 1.40743i) q^{2} +(2.62742 - 0.658133i) q^{3} +(-1.96173 + 0.389399i) q^{4} +(-2.26589 - 1.07169i) q^{5} +(-1.28975 - 3.60686i) q^{6} +(-0.826757 - 2.72545i) q^{7} +(0.819432 + 2.70713i) q^{8} +(3.82441 - 2.04419i) q^{9} +O(q^{10})$	\(q+(-0.138337 - 1.40743i) q^{2} +(2.62742 - 0.658133i) q^{3} +(-1.96173 + 0.389399i) q^{4} +(-2.26589 - 1.07169i) q^{5} +(-1.28975 - 3.60686i) q^{6} +(-0.826757 - 2.72545i) q^{7} +(0.819432 + 2.70713i) q^{8} +(3.82441 - 2.04419i) q^{9} +(-1.19487 + 3.33734i) q^{10} +(-2.11868 + 0.314276i) q^{11} +(-4.89799 + 2.31419i) q^{12} +(0.782843 - 2.18790i) q^{13} +(-3.72152 + 1.54064i) q^{14} +(-6.65874 - 1.32451i) q^{15} +(3.69674 - 1.52779i) q^{16} +(4.41357 - 0.877913i) q^{17} +(-3.40611 - 5.09981i) q^{18} +(3.49386 + 3.16665i) q^{19} +(4.86237 + 1.22002i) q^{20} +(-3.96595 - 6.61678i) q^{21} +(0.735413 + 2.93841i) q^{22} +(2.93244 - 0.288820i) q^{23} +(3.93464 + 6.57345i) q^{24} +(0.813776 + 0.991589i) q^{25} +(-3.18761 - 0.799130i) q^{26} +(2.68217 - 2.43097i) q^{27} +(2.68316 + 5.02466i) q^{28} +(4.77522 + 6.43864i) q^{29} +(-0.943002 + 9.55495i) q^{30} +(2.44763 + 1.01384i) q^{31} +(-2.66165 - 4.99155i) q^{32} +(-5.35981 + 2.22010i) q^{33} +(-1.84616 - 6.09034i) q^{34} +(-1.04749 + 7.06160i) q^{35} +(-6.70643 + 5.49936i) q^{36} +(-0.110672 + 2.25277i) q^{37} +(3.97351 - 5.35543i) q^{38} +(0.616924 - 6.26373i) q^{39} +(1.04445 - 7.01222i) q^{40} +(-7.40967 + 9.02871i) q^{41} +(-8.76403 + 6.49714i) q^{42} +(2.59048 - 10.3418i) q^{43} +(4.03388 - 1.44153i) q^{44} +(-10.8564 + 0.533341i) q^{45} +(-0.812160 - 4.08726i) q^{46} +(-7.88547 - 5.26891i) q^{47} +(8.70737 - 6.44708i) q^{48} +(-0.924285 + 0.617587i) q^{49} +(1.28302 - 1.28251i) q^{50} +(11.0185 - 5.21136i) q^{51} +(-0.683757 + 4.59690i) q^{52} +(-6.89007 + 9.29019i) q^{53} +(-3.79247 - 3.43867i) q^{54} +(5.13749 + 1.55844i) q^{55} +(6.70068 - 4.47146i) q^{56} +(11.2639 + 6.02068i) q^{57} +(8.40135 - 7.61150i) q^{58} +(3.93315 + 10.9924i) q^{59} +(13.5784 + 0.00540893i) q^{60} +(1.81639 - 3.03047i) q^{61} +(1.08831 - 3.58512i) q^{62} +(-8.73320 - 8.73320i) q^{63} +(-6.65706 + 4.43661i) q^{64} +(-4.11858 + 4.11858i) q^{65} +(3.86610 + 7.23644i) q^{66} +(4.53385 + 2.71749i) q^{67} +(-8.31635 + 3.44086i) q^{68} +(7.51466 - 2.68879i) q^{69} +(10.0836 + 0.497390i) q^{70} +(4.71736 - 8.82557i) q^{71} +(8.66772 + 8.67808i) q^{72} +(1.42521 - 4.69827i) q^{73} +(3.18593 - 0.155879i) q^{74} +(2.79073 + 2.06974i) q^{75} +(-8.08709 - 4.85159i) q^{76} +(2.60818 + 5.51452i) q^{77} +(-8.90112 - 0.00177287i) q^{78} +(4.85135 + 7.26055i) q^{79} +(-10.0137 - 0.499939i) q^{80} +(-1.78035 + 2.66448i) q^{81} +(13.7323 + 9.17960i) q^{82} +(-0.750077 - 15.2682i) q^{83} +(10.3567 + 11.4360i) q^{84} +(-10.9415 - 2.74070i) q^{85} +(-14.9137 - 2.21527i) q^{86} +(16.7840 + 13.7742i) q^{87} +(-2.58689 - 5.47799i) q^{88} +(-3.99241 - 0.393218i) q^{89} +(2.25248 + 15.2059i) q^{90} +(-6.61024 - 0.324740i) q^{91} +(-5.64018 + 1.70848i) q^{92} +(7.09817 + 1.05291i) q^{93} +(-6.32477 + 11.8271i) q^{94} +(-4.52305 - 10.9196i) q^{95} +(-10.2784 - 11.3632i) q^{96} +(5.45302 - 13.1647i) q^{97} +(0.997075 + 1.21543i) q^{98} +(-7.46024 + 5.53289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	−0.138337	−	1.40743i	−0.0978189	−	0.995204i
$2$	−0.138337	−	1.40743i	−0.0978189	−	0.995204i
$3$	2.62742	−	0.658133i	1.51694	−	0.379973i	0.606995	−	0.794705i	$-0.292375\pi$
$3$	2.62742	−	0.658133i	1.51694	−	0.379973i	0.909944	+	0.414732i	$0.136125\pi$
$4$	−1.96173	+	0.389399i	−0.980863	+	0.194700i
$5$	−2.26589	−	1.07169i	−1.01334	−	0.479272i	−0.152581	−	0.988291i	$-0.548758\pi$
$5$	−2.26589	−	1.07169i	−1.01334	−	0.479272i	−0.860756	+	0.509019i	$0.830008\pi$
$6$	−1.28975	−	3.60686i	−0.526536	−	1.47250i
$7$	−0.826757	−	2.72545i	−0.312485	−	1.03012i	−0.962744	−	0.270413i	$-0.912840\pi$
$7$	−0.826757	−	2.72545i	−0.312485	−	1.03012i	0.650260	−	0.759712i	$-0.274660\pi$
$8$	0.819432	+	2.70713i	0.289713	+	0.957114i
$9$	3.82441	−	2.04419i	1.27480	−	0.681396i
$10$	−1.19487	+	3.33734i	−0.377850	+	1.05536i
$11$	−2.11868	+	0.314276i	−0.638805	+	0.0947577i	−0.458273	−	0.888811i	$-0.651532\pi$
$11$	−2.11868	+	0.314276i	−0.638805	+	0.0947577i	−0.180532	+	0.983569i	$0.557782\pi$
$12$	−4.89799	+	2.31419i	−1.41393	+	0.668049i
$13$	0.782843	−	2.18790i	0.217122	−	0.606814i	−0.782758	−	0.622326i	$-0.786188\pi$
$13$	0.782843	−	2.18790i	0.217122	−	0.606814i	0.999880	+	0.0155120i	$0.00493781\pi$
$14$	−3.72152	+	1.54064i	−0.994618	+	0.411752i
$15$	−6.65874	−	1.32451i	−1.71928	−	0.341986i
$16$	3.69674	−	1.52779i	0.924184	−	0.381947i
$17$	4.41357	−	0.877913i	1.07045	−	0.212925i	0.371743	−	0.928336i	$-0.378760\pi$
$17$	4.41357	−	0.877913i	1.07045	−	0.212925i	0.698704	+	0.715411i	$0.253760\pi$
$18$	−3.40611	−	5.09981i	−0.802828	−	1.20204i
$19$	3.49386	+	3.16665i	0.801547	+	0.726480i	0.965617	−	0.259969i	$-0.0837124\pi$
$19$	3.49386	+	3.16665i	0.801547	+	0.726480i	−0.164070	+	0.986449i	$0.552462\pi$
$20$	4.86237	+	1.22002i	1.08726	+	0.272804i
$21$	−3.96595	−	6.61678i	−0.865441	−	1.44390i
$22$	0.735413	+	2.93841i	0.156790	+	0.626472i
$23$	2.93244	−	0.288820i	0.611457	−	0.0602232i	0.212451	−	0.977172i	$-0.431855\pi$
$23$	2.93244	−	0.288820i	0.611457	−	0.0602232i	0.399006	+	0.916948i	$0.369355\pi$
$24$	3.93464	+	6.57345i	0.803154	+	1.34180i
$25$	0.813776	+	0.991589i	0.162755	+	0.198318i
$26$	−3.18761	−	0.799130i	−0.625143	−	0.156722i
$27$	2.68217	−	2.43097i	0.516183	−	0.467841i
$28$	2.68316	+	5.02466i	0.507070	+	0.949571i
$29$	4.77522	+	6.43864i	0.886736	+	1.19563i	0.979803	+	0.199965i	$0.0640830\pi$
$29$	4.77522	+	6.43864i	0.886736	+	1.19563i	−0.0930668	+	0.995660i	$0.529667\pi$
$30$	−0.943002	+	9.55495i	−0.172168	+	1.74449i
$31$	2.44763	+	1.01384i	0.439606	+	0.182091i	0.591498	−	0.806306i	$-0.298537\pi$
$31$	2.44763	+	1.01384i	0.439606	+	0.182091i	−0.151892	+	0.988397i	$0.548537\pi$
$32$	−2.66165	−	4.99155i	−0.470518	−	0.882390i
$33$	−5.35981	+	2.22010i	−0.933022	+	0.386471i
$34$	−1.84616	−	6.09034i	−0.316614	−	1.04449i
$35$	−1.04749	+	7.06160i	−0.177058	+	1.19363i
$36$	−6.70643	+	5.49936i	−1.11774	+	0.916560i
$37$	−0.110672	+	2.25277i	−0.0181943	+	0.370354i	0.972382	+	0.233394i	$0.0749831\pi$
$37$	−0.110672	+	2.25277i	−0.0181943	+	0.370354i	−0.990577	+	0.136960i	$0.956267\pi$
$38$	3.97351	−	5.35543i	0.644589	−	0.868766i
$39$	0.616924	−	6.26373i	0.0987869	−	1.00300i
$40$	1.04445	−	7.01222i	0.165142	−	1.10873i
$41$	−7.40967	+	9.02871i	−1.15720	+	1.41005i	−0.261603	+	0.965176i	$0.584251\pi$
$41$	−7.40967	+	9.02871i	−1.15720	+	1.41005i	−0.895594	+	0.444873i	$0.853249\pi$
$42$	−8.76403	+	6.49714i	−1.35232	+	1.00253i
$43$	2.59048	−	10.3418i	0.395044	−	1.57710i	−0.367409	−	0.930060i	$-0.619755\pi$
$43$	2.59048	−	10.3418i	0.395044	−	1.57710i	0.762453	−	0.647044i	$-0.223995\pi$
$44$	4.03388	−	1.44153i	0.608131	−	0.217319i
$45$	−10.8564	+	0.533341i	−1.61838	+	0.0795058i
$46$	−0.812160	−	4.08726i	−0.119746	−	0.602633i
$47$	−7.88547	−	5.26891i	−1.15021	−	0.768549i	−0.173870	−	0.984769i	$-0.555627\pi$
$47$	−7.88547	−	5.26891i	−1.15021	−	0.768549i	−0.976345	+	0.216220i	$0.930627\pi$
$48$	8.70737	−	6.44708i	1.25680	−	0.930556i
$49$	−0.924285	+	0.617587i	−0.132041	+	0.0882268i
$50$	1.28302	−	1.28251i	0.181446	−	0.181374i
$51$	11.0185	−	5.21136i	1.54290	−	0.729736i
$52$	−0.683757	+	4.59690i	−0.0948200	+	0.637475i
$53$	−6.89007	+	9.29019i	−0.946424	+	1.27611i	0.0146722	+	0.999892i	$0.495330\pi$
$53$	−6.89007	+	9.29019i	−0.946424	+	1.27611i	−0.961096	+	0.276213i	$0.910920\pi$
$54$	−3.79247	−	3.43867i	−0.516090	−	0.467944i
$55$	5.13749	+	1.55844i	0.692739	+	0.210140i
$56$	6.70068	−	4.47146i	0.895416	−	0.597524i
$57$	11.2639	+	6.02068i	1.49194	+	0.797459i
$58$	8.40135	−	7.61150i	1.10315	−	0.999438i
$59$	3.93315	+	10.9924i	0.512053	+	1.43109i	0.867990	+	0.496581i	$0.165412\pi$
$59$	3.93315	+	10.9924i	0.512053	+	1.43109i	−0.355938	+	0.934510i	$0.615838\pi$
$60$	13.5784	+	0.00540893i	1.75296	+	0.000698290i
$61$	1.81639	−	3.03047i	0.232565	−	0.388012i	−0.719217	−	0.694785i	$-0.755499\pi$
$61$	1.81639	−	3.03047i	0.232565	−	0.388012i	0.951783	+	0.306774i	$0.0992494\pi$
$62$	1.08831	−	3.58512i	0.138216	−	0.455310i
$63$	−8.73320	−	8.73320i	−1.10028	−	1.10028i
$64$	−6.65706	+	4.43661i	−0.832133	+	0.554576i
$65$	−4.11858	+	4.11858i	−0.510846	+	0.510846i
$66$	3.86610	+	7.23644i	0.475884	+	0.890744i
$67$	4.53385	+	2.71749i	0.553898	+	0.331994i	0.763515	−	0.645790i	$-0.223472\pi$
$67$	4.53385	+	2.71749i	0.553898	+	0.331994i	−0.209617	+	0.977784i	$0.567222\pi$
$68$	−8.31635	+	3.44086i	−1.00851	+	0.417266i
$69$	7.51466	−	2.68879i	0.904659	−	0.323692i
$70$	10.0836	+	0.497390i	1.20522	+	0.0594495i
$71$	4.71736	−	8.82557i	0.559848	−	1.04740i	−0.429669	−	0.902987i	$-0.641370\pi$
$71$	4.71736	−	8.82557i	0.559848	−	1.04740i	0.989517	−	0.144416i	$-0.0461303\pi$
$72$	8.66772	+	8.67808i	1.02150	+	1.02272i
$73$	1.42521	−	4.69827i	0.166808	−	0.549891i	−0.833188	−	0.552991i	$-0.813487\pi$
$73$	1.42521	−	4.69827i	0.166808	−	0.549891i	0.999995	+	0.00309940i	$0.000986572\pi$
$74$	3.18593	−	0.155879i	0.370357	−	0.0181205i
$75$	2.79073	+	2.06974i	0.322245	+	0.238993i
$76$	−8.08709	−	4.85159i	−0.927653	−	0.556516i
$77$	2.60818	+	5.51452i	0.297229	+	0.628438i
$78$	−8.90112	−	0.00177287i	−1.00785	−	0.000200738i
$79$	4.85135	+	7.26055i	0.545819	+	0.816876i	0.997147	−	0.0754822i	$-0.0240496\pi$
$79$	4.85135	+	7.26055i	0.545819	+	0.816876i	−0.451328	+	0.892358i	$0.649050\pi$
$80$	−10.0137	−	0.499939i	−1.11957	−	0.0558949i
$81$	−1.78035	+	2.66448i	−0.197817	+	0.296054i
$82$	13.7323	+	9.17960i	1.51648	+	1.01372i
$83$	−0.750077	−	15.2682i	−0.0823316	−	1.67590i	−0.584703	−	0.811247i	$-0.698789\pi$
$83$	−0.750077	−	15.2682i	−0.0823316	−	1.67590i	0.502372	−	0.864652i	$-0.332461\pi$
$84$	10.3567	+	11.4360i	1.13001	+	1.24777i
$85$	−10.9415	−	2.74070i	−1.18677	−	0.297271i
$86$	−14.9137	−	2.21527i	−1.60818	−	0.238879i
$87$	16.7840	+	13.7742i	1.79943	+	1.47675i
$88$	−2.58689	−	5.47799i	−0.275764	−	0.583956i
$89$	−3.99241	−	0.393218i	−0.423195	−	0.0416811i	−0.115822	−	0.993270i	$-0.536950\pi$
$89$	−3.99241	−	0.393218i	−0.423195	−	0.0416811i	−0.307373	+	0.951589i	$0.599450\pi$
$90$	2.25248	+	15.2059i	0.237433	+	1.60284i
$91$	−6.61024	−	0.324740i	−0.692941	−	0.0340420i
$92$	−5.64018	+	1.70848i	−0.588030	+	0.178121i
$93$	7.09817	+	1.05291i	0.736046	+	0.109182i
$94$	−6.32477	+	11.8271i	−0.652350	+	1.21988i
$95$	−4.52305	−	10.9196i	−0.464055	−	1.12033i
$96$	−10.2784	−	11.3632i	−1.04903	−	1.15975i
$97$	5.45302	−	13.1647i	0.553670	−	1.33668i	−0.361034	−	0.932553i	$-0.617576\pi$
$97$	5.45302	−	13.1647i	0.553670	−	1.33668i	0.914704	−	0.404125i	$-0.132424\pi$
$98$	0.997075	+	1.21543i	0.100720	+	0.122777i
$99$	−7.46024	+	5.53289i	−0.749782	+	0.556077i
$100$	−1.98253	−	1.62834i	−0.198253	−	0.162834i
$101$	2.65564	+	2.93005i	0.264246	+	0.291550i	0.858593	−	0.512659i	$-0.171339\pi$
$101$	2.65564	+	2.93005i	0.264246	+	0.291550i	−0.594347	+	0.804209i	$0.702589\pi$
$102$	−8.85889	−	14.7868i	−0.877161	−	1.46412i
$103$	6.94510	−	5.69969i	0.684321	−	0.561608i	−0.226702	−	0.973964i	$-0.572794\pi$
$103$	6.94510	−	5.69969i	0.684321	−	0.561608i	0.911022	+	0.412357i	$0.135294\pi$
$104$	6.56441	+	0.326421i	0.643693	+	0.0320082i
$105$	1.89528	+	19.2431i	0.184961	+	1.87794i
$106$	14.0285	+	8.41213i	1.36256	+	0.817058i
$107$	−10.3192	+	6.18508i	−0.997593	+	0.597934i	−0.917031	−	0.398815i	$-0.869421\pi$
$107$	−10.3192	+	6.18508i	−0.997593	+	0.597934i	−0.0805618	+	0.996750i	$0.525671\pi$
$108$	−4.31505	+	5.81334i	−0.415216	+	0.559388i
$109$	−12.6725	+	13.9819i	−1.21380	+	1.33923i	−0.289683	+	0.957123i	$0.593550\pi$
$109$	−12.6725	+	13.9819i	−1.21380	+	1.33923i	−0.924120	+	0.382103i	$0.875200\pi$
$110$	1.48269	−	7.44625i	0.141369	−	0.709972i
$111$	1.19184	+	5.99181i	0.113125	+	0.568717i
$112$	−7.22022	−	8.81217i	−0.682247	−	0.832672i
$113$	1.45939	−	7.33683i	0.137288	−	0.690191i	−0.849424	−	0.527711i	$-0.823051\pi$
$113$	1.45939	−	7.33683i	0.137288	−	0.690191i	0.986712	−	0.162480i	$-0.0519494\pi$
$114$	6.91548	−	16.6861i	0.647694	−	1.56279i
$115$	−6.95412	−	2.48822i	−0.648475	−	0.232028i
$116$	−11.8749	−	10.7714i	−1.10255	−	1.00010i
$117$	−1.47857	−	9.96770i	−0.136694	−	0.921514i
$118$	14.9270	−	7.05630i	1.37414	−	0.649585i
$119$	−6.04166	−	11.3031i	−0.553838	−	1.03616i
$120$	−1.87078	−	19.1114i	−0.170778	−	1.74462i
$121$	−6.13633	+	1.86143i	−0.557848	+	0.169221i
$122$	−4.51645	−	2.13722i	−0.408900	−	0.193495i
$123$	−13.5262	+	28.5987i	−1.21962	+	2.57866i
$124$	−5.19636	−	1.03577i	−0.466647	−	0.0930151i
$125$	2.26395	+	9.03819i	0.202494	+	0.808400i
$126$	−11.0833	+	13.4995i	−0.987375	+	1.20263i
$127$		−	5.17031i		−	0.458791i	−0.973333	−	0.229396i	$-0.926325\pi$
$127$		−	5.17031i		−	0.458791i	0.973333	−	0.229396i	$-0.0736749\pi$
$128$	7.16514	+	8.75561i	0.633315	+	0.773894i
$129$		−	28.8770i		−	2.54248i
$130$	6.36636	+	5.22686i	0.558367	+	0.458426i
$131$	−0.111394	−	0.444709i	−0.00973251	−	0.0388544i	0.964970	−	0.262359i	$-0.0845003\pi$
$131$	−0.111394	−	0.444709i	−0.00973251	−	0.0388544i	−0.974703	+	0.223504i	$0.928250\pi$
$132$	9.64996	−	6.44234i	0.839921	−	0.560734i
$133$	5.74199	−	12.1404i	0.497893	−	1.05271i
$134$	3.19748	−	6.75701i	0.276220	−	0.583717i
$135$	−8.68273	+	2.63388i	−0.747290	+	0.226688i
$136$	5.99324	+	11.2287i	0.513916	+	0.962852i
$137$	3.27847	+	6.13360i	0.280099	+	0.524028i	0.982150	−	0.188098i	$-0.0602323\pi$
$137$	3.27847	+	6.13360i	0.280099	+	0.524028i	−0.702051	+	0.712126i	$0.747732\pi$
$138$	−4.82384	−	10.2044i	−0.410633	−	0.868657i
$139$	0.925145	+	6.23682i	0.0784698	+	0.529000i	0.992393	+	0.123113i	$0.0392876\pi$
$139$	0.925145	+	6.23682i	0.0784698	+	0.529000i	−0.913923	+	0.405888i	$0.866962\pi$
$140$	−0.694895	−	14.2608i	−0.0587293	−	1.20526i
$141$	−24.1861	−	8.65391i	−2.03683	−	0.728791i
$142$	−13.0740	−	5.41847i	−1.09714	−	0.454708i
$143$	−0.970986	+	4.88148i	−0.0811979	+	0.408210i
$144$	11.0147	−	13.3997i	0.917895	−	1.11664i
$145$	−3.91992	−	19.7068i	−0.325532	−	1.63656i
$146$	−6.80965	−	1.35593i	−0.563571	−	0.112218i
$147$	−2.02203	+	2.23096i	−0.166774	+	0.184007i
$148$	−0.660121	−	4.46242i	−0.0542616	−	0.366809i
$149$	−16.2207	+	9.72230i	−1.32885	+	0.796482i	−0.989549	−	0.144196i	$-0.953940\pi$
$149$	−16.2207	+	9.72230i	−1.32885	+	0.796482i	−0.339301	+	0.940678i	$0.610190\pi$
$150$	2.52696	−	4.21408i	0.206326	−	0.344078i
$151$	0.772735	+	7.84571i	0.0628843	+	0.638475i	0.974034	+	0.226400i	$0.0726958\pi$
$151$	0.772735	+	7.84571i	0.0628843	+	0.638475i	−0.911150	+	0.412075i	$0.864804\pi$
$152$	−5.70954	+	12.0532i	−0.463105	+	0.977642i
$153$	15.0847	−	12.3797i	1.21952	−	1.00084i
$154$	7.40051	−	4.43369i	0.596350	−	0.357277i
$155$	−4.45953	−	4.92033i	−0.358198	−	0.395211i
$156$	1.22886	+	12.5280i	0.0983874	+	1.00304i
$157$	−13.4812	+	9.99832i	−1.07592	+	0.797953i	−0.980310	−	0.197466i	$-0.936729\pi$
$157$	−13.4812	+	9.99832i	−1.07592	+	0.797953i	−0.0956055	+	0.995419i	$0.530479\pi$
$158$	9.54761	−	7.83234i	0.759567	−	0.623107i
$159$	−11.9889	+	28.9438i	−0.950782	+	2.29539i
$160$	0.681634	+	14.1628i	0.0538879	+	1.11966i
$161$	−3.21159	−	7.75345i	−0.253108	−	0.611058i
$162$	3.99637	+	2.13713i	0.313984	+	0.167908i
$163$	−15.0404	−	2.23103i	−1.17806	−	0.174748i	−0.471148	−	0.882054i	$-0.656160\pi$
$163$	−15.0404	−	2.23103i	−1.17806	−	0.174748i	−0.706907	+	0.707306i	$0.749910\pi$
$164$	11.0200	−	20.5972i	0.860516	−	1.60837i
$165$	14.5240	+	0.713517i	1.13069	+	0.0555472i
$166$	−21.3851	+	3.16783i	−1.65981	+	0.245871i
$167$	0.547162	+	0.0538908i	0.0423407	+	0.00417019i	0.119165	−	0.992874i	$-0.461978\pi$
$167$	0.547162	+	0.0538908i	0.0423407	+	0.00417019i	−0.0768246	+	0.997045i	$0.524478\pi$
$168$	14.6626	−	16.1583i	1.13125	−	1.24664i
$169$	5.87508	+	4.82155i	0.451929	+	0.370888i
$170$	−2.34374	+	15.7785i	−0.179756	+	1.21016i
$171$	19.8352	+	4.96845i	1.51683	+	0.379947i
$172$	−1.05473	+	21.2964i	−0.0804224	+	1.62384i
$173$	0.445878	+	9.07605i	0.0338995	+	0.690039i	0.954262	+	0.298973i	$0.0966439\pi$
$173$	0.445878	+	9.07605i	0.0338995	+	0.690039i	−0.920362	+	0.391067i	$0.872106\pi$
$174$	17.0645	−	25.5278i	1.29365	−	1.93526i
$175$	2.02974	−	3.03771i	0.153434	−	0.229630i
$176$	−7.35204	+	4.39868i	−0.554181	+	0.331563i
$177$	17.5685	+	26.2931i	1.32053	+	1.97631i
$178$	−0.00113000	+	5.67344i	−8.46974e−5	+	0.425243i
$179$	−1.53312	−	3.24150i	−0.114591	−	0.242281i	0.838540	−	0.544839i	$-0.183409\pi$
$179$	−1.53312	−	3.24150i	−0.114591	−	0.242281i	−0.953131	+	0.302558i	$0.902159\pi$
$180$	21.0896	−	5.27375i	1.57193	−	0.393082i
$181$	12.4773	+	9.25377i	0.927428	+	0.687828i	0.950110	−	0.311915i	$-0.100970\pi$
$181$	12.4773	+	9.25377i	0.927428	+	0.687828i	−0.0226818	+	0.999743i	$0.507220\pi$
$182$	0.457390	+	9.34838i	0.0339040	+	0.692948i
$183$	2.77797	−	9.15773i	0.205353	−	0.676959i
$184$	3.18481	+	7.70182i	0.234787	+	0.567786i
$185$	2.66503	−	4.98593i	0.195937	−	0.366573i
$186$	0.499966	−	10.1358i	0.0366593	−	0.743196i
$187$	−9.07501	+	3.24709i	−0.663630	+	0.237451i
$188$	17.5208	+	7.26555i	1.27784	+	0.529895i
$189$	−8.84301	−	5.30029i	−0.643234	−	0.385540i
$190$	−14.7429	+	7.87646i	−1.06956	+	0.571418i
$191$	10.5245	−	10.5245i	0.761529	−	0.761529i	−0.215070	−	0.976599i	$-0.568998\pi$
$191$	10.5245	−	10.5245i	0.761529	−	0.761529i	0.976599	+	0.215070i	$0.0689979\pi$
$192$	−14.5710	+	16.0381i	−1.05157	+	1.15745i
$193$	4.96614	+	4.96614i	0.357471	+	0.357471i	0.862880	−	0.505409i	$-0.168658\pi$
$193$	4.96614	+	4.96614i	0.357471	+	0.357471i	−0.505409	+	0.862880i	$0.668658\pi$
$194$	−19.2828	−	5.85358i	−1.38443	−	0.420262i
$195$	−8.11064	+	13.5318i	−0.580815	+	0.969031i
$196$	1.57271	−	1.57145i	0.112336	−	0.112247i
$197$	1.99896	+	5.58672i	0.142420	+	0.398037i	0.991480	−	0.130259i	$-0.0415810\pi$
$197$	1.99896	+	5.58672i	0.142420	+	0.398037i	−0.849060	+	0.528296i	$0.822831\pi$
$198$	8.81919	+	9.73437i	0.626753	+	0.691792i
$199$	−17.4707	−	9.33828i	−1.23846	−	0.661973i	−0.283579	−	0.958949i	$-0.591522\pi$
$199$	−17.4707	−	9.33828i	−1.23846	−	0.661973i	−0.954885	+	0.296976i	$0.904022\pi$
$200$	−2.01752	+	3.01553i	−0.142660	+	0.213231i
$201$	13.7008	+	4.15609i	0.966378	+	0.293148i
$202$	3.75646	−	4.14296i	0.264304	−	0.291498i
$203$	13.6003	−	18.3378i	0.954552	−	1.28706i
$204$	−19.5860	+	14.5138i	−1.37129	+	1.01617i
$205$	26.4654	−	12.5172i	1.84843	−	0.874241i
$206$	−8.98269	−	8.98627i	−0.625854	−	0.626103i
$207$	10.6245	−	7.09903i	0.738451	−	0.493417i
$208$	−0.448685	−	9.28411i	−0.0311107	−	0.643737i
$209$	−8.39756	−	5.61107i	−0.580871	−	0.388126i
$210$	26.8212	−	5.32952i	1.85084	−	0.367772i
$211$	11.0758	−	0.544119i	0.762489	−	0.0374587i	0.335892	−	0.941900i	$-0.390962\pi$
$211$	11.0758	−	0.544119i	0.762489	−	0.0374587i	0.426597	+	0.904442i	$0.359712\pi$
$212$	9.89884	−	20.9078i	0.679855	−	1.43595i
$213$	6.58608	−	26.2931i	0.451271	−	1.80157i
$214$	10.1326	+	13.6679i	0.692650	+	0.934320i
$215$	−16.9528	+	20.6571i	−1.15617	+	1.40880i
$216$	8.77880	+	5.26894i	0.597322	+	0.358506i
$217$	0.739581	−	7.50909i	0.0502060	−	0.509750i
$218$	21.4317	+	15.9014i	1.45154	+	1.07698i
$219$	0.652517	−	13.2823i	0.0440930	−	0.897534i
$220$	−10.6852	−	1.05670i	−0.720396	−	0.0712426i
$221$	1.53434	−	10.3437i	0.103211	−	0.695793i
$222$	8.26818	−	2.50633i	0.554924	−	0.168214i
$223$	4.29180	−	1.77772i	0.287400	−	0.119045i	−0.234326	−	0.972158i	$-0.575288\pi$
$223$	4.29180	−	1.77772i	0.287400	−	0.119045i	0.521726	+	0.853113i	$0.325288\pi$
$224$	−11.4037	+	11.3810i	−0.761942	+	0.760426i
$225$	5.13921	+	2.12873i	0.342614	+	0.141915i
$226$	−10.5280	−	1.03903i	−0.700310	−	0.0691154i
$227$	−11.2611	−	15.1839i	−0.747427	−	1.00779i	−0.999200	−	0.0400022i	$-0.987263\pi$
$227$	−11.2611	−	15.1839i	−0.747427	−	1.00779i	0.251773	−	0.967786i	$-0.418987\pi$
$228$	−24.4411	−	7.42477i	−1.61865	−	0.491717i
$229$	4.80485	−	4.35486i	0.317513	−	0.287777i	−0.497206	−	0.867632i	$-0.665641\pi$
$229$	4.80485	−	4.35486i	0.317513	−	0.287777i	0.814720	+	0.579855i	$0.196891\pi$
$230$	−2.53999	+	10.1317i	−0.167482	+	0.668061i
$231$	10.4821	+	12.7724i	0.689668	+	0.840363i
$232$	−13.5172	+	18.2031i	−0.887450	+	1.19510i
$233$	−9.07982	+	0.894284i	−0.594839	+	0.0585865i	−0.390957	−	0.920409i	$-0.627856\pi$
$233$	−9.07982	+	0.894284i	−0.594839	+	0.0585865i	−0.203882	+	0.978995i	$0.565356\pi$
$234$	−13.8243	+	3.45988i	−0.903723	+	0.226180i
$235$	12.2210	+	20.3895i	0.797210	+	1.33006i
$236$	−11.9962	−	20.0325i	−0.780886	−	1.30401i
$237$	17.5249	+	15.8837i	1.13837	+	1.03175i
$238$	−15.0726	+	10.0669i	−0.977013	+	0.652538i
$239$	−9.42572	+	1.87489i	−0.609699	+	0.121277i	−0.490277	−	0.871567i	$-0.663104\pi$
$239$	−9.42572	+	1.87489i	−0.609699	+	0.121277i	−0.119422	+	0.992844i	$0.538104\pi$
$240$	−26.6392	+	5.27680i	−1.71955	+	0.340616i
$241$	−9.40889	−	1.87154i	−0.606080	−	0.120557i	−0.117495	−	0.993073i	$-0.537487\pi$
$241$	−9.40889	−	1.87154i	−0.606080	−	0.120557i	−0.488584	+	0.872517i	$0.662487\pi$
$242$	3.46872	+	8.37895i	0.222978	+	0.538619i
$243$	−6.58265	+	18.3973i	−0.422277	+	1.18019i
$244$	−2.38320	+	6.65225i	−0.152569	+	0.425867i
$245$	2.75619	−	0.408842i	0.176086	−	0.0261199i
$246$	42.1219	+	15.0809i	2.68560	+	0.961525i
$247$	9.66346	−	5.16523i	0.614871	−	0.328655i
$248$	−0.738930	+	7.45680i	−0.0469221	+	0.473507i
$249$	−12.0193	−	39.6222i	−0.761689	−	2.51095i
$250$	12.4074	−	4.43667i	0.784715	−	0.280599i
$251$	13.9615	+	6.60330i	0.881242	+	0.416796i	0.813949	−	0.580937i	$-0.197314\pi$
$251$	13.9615	+	6.60330i	0.881242	+	0.416796i	0.0672932	+	0.997733i	$0.478564\pi$
$252$	20.5328	+	13.7314i	1.29345	+	0.865000i
$253$	−6.12213	+	1.53351i	−0.384895	+	0.0964111i
$254$	−7.27686	+	0.715245i	−0.456591	+	0.0448784i
$255$	−30.5516			−1.91322
$256$	11.3317	−	11.2957i	0.708233	−	0.705979i
$257$	9.82757			0.613027			0.306514	−	0.951866i	$-0.400838\pi$
$257$	9.82757			0.613027			0.306514	+	0.951866i	$0.400838\pi$
$258$	−40.6424	+	3.99475i	−2.53028	+	0.248702i
$259$	6.23133	−	1.56087i	0.387196	−	0.0969875i
$260$	6.47575	−	9.68329i	0.401609	−	0.600532i
$261$	31.4242	+	14.8625i	1.94511	+	0.919968i
$262$	−0.610487	+	0.218299i	−0.0377160	+	0.0134865i
$263$	−1.86730	−	6.15568i	−0.115143	−	0.379575i	0.880360	−	0.474306i	$-0.157301\pi$
$263$	−1.86730	−	6.15568i	−0.115143	−	0.379575i	−0.995503	+	0.0947308i	$0.969801\pi$
$264$	−10.4021	−	12.6904i	−0.640205	−	0.781043i
$265$	25.5683	−	13.6665i	1.57065	−	0.839529i
$266$	−17.8811	−	6.40199i	−1.09636	−	0.392531i
$267$	−10.7485	+	1.59439i	−0.657799	+	0.0975752i
$268$	−9.95236	−	3.56548i	−0.607937	−	0.217797i
$269$	5.77346	−	16.1357i	0.352014	−	0.983813i	−0.626821	−	0.779163i	$-0.715644\pi$
$269$	5.77346	−	16.1357i	0.352014	−	0.983813i	0.978835	−	0.204650i	$-0.0656057\pi$
$270$	4.90814	+	11.8560i	0.298700	+	0.721532i
$271$	−2.65347	−	0.527808i	−0.161187	−	0.0320621i	0.113837	−	0.993499i	$-0.463686\pi$
$271$	−2.65347	−	0.527808i	−0.161187	−	0.0320621i	−0.275024	+	0.961437i	$0.588686\pi$
$272$	14.9745	−	9.98841i	0.907964	−	0.605636i
$273$	−17.5816	+	3.49719i	−1.06408	+	0.211660i
$274$	8.17908	−	5.46273i	0.494116	−	0.330016i
$275$	−2.03576	−	1.84511i	−0.122761	−	0.111264i
$276$	−13.6947	+	8.20087i	−0.824324	+	0.493635i
$277$	5.88070	+	9.81136i	0.353337	+	0.589507i	0.982161	−	0.188040i	$-0.0602135\pi$
$277$	5.88070	+	9.81136i	0.353337	+	0.589507i	−0.628824	+	0.777547i	$0.716464\pi$
$278$	8.64992	−	2.16486i	0.518788	−	0.129840i
$279$	11.4332	−	1.12607i	0.684488	−	0.0674162i
$280$	−19.9750	+	2.95081i	−1.19373	+	0.176345i
$281$	−3.66022	−	4.45999i	−0.218350	−	0.266061i	0.652302	−	0.757959i	$-0.273803\pi$
$281$	−3.66022	−	4.45999i	−0.218350	−	0.266061i	−0.870653	+	0.491898i	$0.836303\pi$
$282$	−8.83396	+	35.2374i	−0.526055	+	2.09835i
$283$	−4.29699	+	3.89457i	−0.255430	+	0.231508i	−0.789223	−	0.614107i	$-0.789516\pi$
$283$	−4.29699	+	3.89457i	−0.255430	+	0.231508i	0.533793	+	0.845615i	$0.320766\pi$
$284$	−5.81751	+	19.1503i	−0.345206	+	1.13636i
$285$	−19.0705	−	25.7136i	−1.12964	−	1.52314i
$286$	7.00467	+	0.691308i	0.414195	+	0.0408779i
$287$	30.7334	+	12.7302i	1.81413	+	0.751438i
$288$	−20.3829	−	13.6488i	−1.20108	−	0.804264i
$289$	3.00288	−	1.24383i	0.176640	−	0.0731667i
$290$	−27.1937	+	8.24319i	−1.59687	+	0.484057i
$291$	5.66318	−	38.1781i	0.331982	−	2.23804i
$292$	−0.966358	+	9.77169i	−0.0565518	+	0.571845i
$293$	−0.718315	+	14.6216i	−0.0419644	+	0.854205i	0.881889	+	0.471458i	$0.156272\pi$
$293$	−0.718315	+	14.6216i	−0.0419644	+	0.854205i	−0.923853	+	0.382747i	$0.874978\pi$
$294$	3.41965	+	2.53724i	0.199438	+	0.147975i
$295$	2.86834	−	29.1227i	0.167001	−	1.69559i
$296$	−6.18923	+	1.54639i	−0.359742	+	0.0898822i
$297$	−4.91864	+	5.99338i	−0.285409	+	0.347771i
$298$	15.9274	+	21.4845i	0.922649	+	1.24457i
$299$	1.66373	−	6.64199i	0.0962161	−	0.384116i
$300$	−6.28060	−	2.97356i	−0.362610	−	0.171679i
$301$	−30.3277	+	1.48990i	−1.74806	+	0.0858766i
$302$	10.9354	−	2.17292i	0.629262	−	0.125038i
$303$	8.90583	+	5.95068i	0.511626	+	0.341858i
$304$	17.7539	+	6.36839i	1.01825	+	0.365252i
$305$	−7.36345	+	4.92010i	−0.421630	+	0.281724i
$306$	−19.5103	−	19.5181i	−1.11533	−	1.11577i
$307$	7.90231	−	3.73751i	0.451008	−	0.213311i	−0.188534	−	0.982067i	$-0.560374\pi$
$307$	7.90231	−	3.73751i	0.451008	−	0.213311i	0.639543	+	0.768755i	$0.279124\pi$
$308$	−7.26388	−	9.80236i	−0.413898	−	0.558541i
$309$	14.4965	−	19.5463i	0.824677	−	1.11195i
$310$	−6.30811	+	6.95715i	−0.358277	+	0.395139i
$311$	28.1117	+	8.52759i	1.59407	+	0.483555i	0.957685	−	0.287818i	$-0.0929297\pi$
$311$	28.1117	+	8.52759i	1.59407	+	0.483555i	0.636383	+	0.771373i	$0.280430\pi$
$312$	17.4622	−	3.46261i	0.988605	−	0.196032i
$313$	12.9695	+	6.93235i	0.733080	+	0.391839i	0.795294	−	0.606223i	$-0.207316\pi$
$313$	12.9695	+	6.93235i	0.733080	+	0.391839i	−0.0622143	+	0.998063i	$0.519816\pi$
$314$	15.9369	+	17.5907i	0.899371	+	0.992700i
$315$	10.4292	+	29.1477i	0.587620	+	1.64229i
$316$	−12.3443	−	12.3541i	−0.694419	−	0.694973i
$317$	2.55886	−	4.26920i	0.143720	−	0.239782i	−0.777448	−	0.628947i	$-0.783486\pi$
$317$	2.55886	−	4.26920i	0.143720	−	0.239782i	0.921168	+	0.389165i	$0.127236\pi$
$318$	42.3949	+	12.8696i	2.37739	+	0.721689i
$319$	−12.1407	−	12.1407i	−0.679746	−	0.679746i
$320$	19.8388	−	2.91858i	1.10902	−	0.163154i
$321$	−23.0422	+	23.0422i	−1.28609	+	1.28609i
$322$	−10.4682	+	5.59268i	−0.583369	+	0.311668i
$323$	18.2004	+	10.9089i	1.01270	+	0.606988i
$324$	2.45501	−	5.92025i	0.136390	−	0.328903i
$325$	2.80656	−	1.00420i	0.155680	−	0.0557031i
$326$	−1.05938	+	21.4770i	−0.0586738	+	1.18950i
$327$	−24.0939	+	45.0765i	−1.33240	+	2.49274i
$328$	−30.5136	−	12.6605i	−1.68483	−	0.699060i
$329$	−7.84079	+	25.8476i	−0.432277	+	1.42502i
$330$	−1.00497	−	20.5402i	−0.0553220	−	1.13070i
$331$	9.49285	+	7.04038i	0.521774	+	0.386974i	0.824288	−	0.566171i	$-0.191576\pi$
$331$	9.49285	+	7.04038i	0.521774	+	0.386974i	−0.302513	+	0.953145i	$0.597826\pi$
$332$	7.41686	+	29.6599i	0.407053	+	1.62780i
$333$	4.18184	+	8.84176i	0.229163	+	0.484525i
$334$	0.000154868	−	0.777548i	8.47398e−6	−	0.0425455i
$335$	−7.36091	−	11.0164i	−0.402170	−	0.601889i
$336$	−24.7701	−	18.4014i	−1.35132	−	1.00388i
$337$	2.17383	−	3.25337i	0.118416	−	0.177222i	−0.767526	−	0.641017i	$-0.778513\pi$
$337$	2.17383	−	3.25337i	0.118416	−	0.177222i	0.885942	+	0.463795i	$0.153513\pi$
$338$	5.97326	−	8.93576i	0.324903	−	0.486041i
$339$	−0.994198	−	20.2374i	−0.0539974	−	1.09914i
$340$	22.5314	+	1.11590i	1.22194	+	0.0605180i
$341$	−5.50435	−	1.37877i	−0.298077	−	0.0746645i
$342$	4.24882	−	28.6040i	0.229750	−	1.54673i
$343$	−12.9639	−	10.6392i	−0.699983	−	0.574461i
$344$	30.1192	−	1.46162i	1.62392	−	0.0788053i
$345$	−19.9089	−	1.96086i	−1.07186	−	0.105569i
$346$	12.7122	−	1.88309i	0.683414	−	0.101236i
$347$	−19.8630	−	0.975808i	−1.06630	−	0.0523841i	−0.491659	−	0.870788i	$-0.663609\pi$
$347$	−19.8630	−	0.975808i	−1.06630	−	0.0523841i	−0.574644	+	0.818404i	$0.694859\pi$
$348$	−38.2892	−	20.4856i	−2.05252	−	1.09815i
$349$	2.55306	+	0.378710i	0.136662	+	0.0202719i	0.214711	−	0.976678i	$-0.431119\pi$
$349$	2.55306	+	0.378710i	0.136662	+	0.0202719i	−0.0780489	+	0.996950i	$0.524869\pi$
$350$	−4.55616	−	2.43649i	−0.243537	−	0.130236i
$351$	−3.21901	−	7.77138i	−0.171818	−	0.414805i
$352$	7.20790	+	9.73899i	0.384183	+	0.519090i
$353$	−12.3008	+	29.6968i	−0.654707	+	1.58060i	0.151161	+	0.988509i	$0.451699\pi$
$353$	−12.3008	+	29.6968i	−0.654707	+	1.58060i	−0.805869	+	0.592094i	$0.798301\pi$
$354$	34.5754	−	28.3638i	1.83766	−	1.50752i
$355$	−20.1473	+	14.9422i	−1.06931	+	0.793051i
$356$	7.98514	−	0.783256i	0.423212	−	0.0415125i
$357$	−23.3129	−	25.7219i	−1.23385	−	1.36134i
$358$	−4.35011	+	2.60618i	−0.229910	+	0.137741i
$359$	0.129379	−	0.106179i	0.00682838	−	0.00560391i	−0.630973	−	0.775805i	$-0.717344\pi$
$359$	0.129379	−	0.106179i	0.00682838	−	0.00560391i	0.637801	+	0.770201i	$0.279844\pi$
$360$	−10.3399	−	28.9526i	−0.544961	−	1.52594i
$361$	0.317060	+	3.21916i	0.0166874	+	0.169430i
$362$	11.2980	−	18.8410i	0.593809	−	0.990263i
$363$	−14.8976	+	8.92928i	−0.781922	+	0.468666i
$364$	13.0939	−	1.93697i	0.686309	−	0.101525i
$365$	−8.26443	+	9.11839i	−0.432580	+	0.477278i
$366$	−13.2732	−	2.64295i	−0.693800	−	0.138149i
$367$	0.858837	+	4.31767i	0.0448309	+	0.225380i	0.996705	−	0.0811081i	$-0.0258459\pi$
$367$	0.858837	+	4.31767i	0.0448309	+	0.225380i	−0.951874	+	0.306488i	$0.900846\pi$
$368$	10.3992	−	5.54785i	0.542096	−	0.289202i
$369$	−9.88122	+	49.6763i	−0.514396	+	2.58604i
$370$	−7.38602	−	3.06112i	−0.383981	−	0.159140i
$371$	31.0164	+	11.0978i	1.61029	+	0.576171i
$372$	−14.3347	+	0.698493i	−0.743218	+	0.0362152i
$373$	−1.52397	−	10.2738i	−0.0789081	−	0.531955i	−0.992201	−	0.124651i	$-0.960219\pi$
$373$	−1.52397	−	10.2738i	−0.0789081	−	0.531955i	0.913293	−	0.407304i	$-0.133531\pi$
$374$	5.82546	+	12.3233i	0.301228	+	0.637220i
$375$	11.8967	+	22.2571i	0.614341	+	1.14935i
$376$	7.80198	−	25.6645i	0.402357	−	1.32354i
$377$	17.8253	−	5.40726i	0.918052	−	0.278488i
$378$	−6.23649	+	13.1791i	−0.320770	+	0.677862i
$379$	15.8822	−	33.5801i	0.815813	−	1.72489i	0.137012	−	0.990569i	$-0.456250\pi$
$379$	15.8822	−	33.5801i	0.815813	−	1.72489i	0.678801	−	0.734322i	$-0.262500\pi$
$380$	13.1251	+	19.6600i	0.673301	+	1.00854i
$381$	−3.40275	−	13.5846i	−0.174328	−	0.695958i
$382$	−16.2685	−	13.3566i	−0.832369	−	0.683385i
$383$			12.3768i			0.632424i	0.948689	+	0.316212i	$0.102411\pi$
$383$			12.3768i			0.632424i	−0.948689	+	0.316212i	$0.897589\pi$
$384$	24.5882	+	18.2890i	1.25476	+	0.933307i
$385$		−	15.2904i		−	0.779273i
$386$	6.30251	−	7.67651i	0.320789	−	0.390724i
$387$	−11.2335	−	44.8465i	−0.571029	−	2.27968i
$388$	−5.57098	+	27.9490i	−0.282824	+	1.41890i
$389$	13.2825	−	28.0834i	0.673447	−	1.42388i	−0.220354	−	0.975420i	$-0.570721\pi$
$389$	13.2825	−	28.0834i	0.673447	−	1.42388i	0.893801	−	0.448464i	$-0.148029\pi$
$390$	20.1670	+	9.54322i	1.02120	+	0.483240i
$391$	12.6890	−	3.84916i	0.641709	−	0.194660i
$392$	−2.42928	−	1.99609i	−0.122697	−	0.100818i
$393$	−0.585355	−	1.09512i	−0.0295273	−	0.0552416i
$394$	7.58639	−	3.58625i	0.382197	−	0.180672i
$395$	−3.21158	−	21.6507i	−0.161592	−	1.08937i
$396$	12.4804	−	13.7590i	0.627166	−	0.691417i
$397$	−20.2662	−	7.25135i	−1.01713	−	0.363935i	−0.225046	−	0.974348i	$-0.572253\pi$
$397$	−20.2662	−	7.25135i	−1.01713	−	0.363935i	−0.792083	+	0.610413i	$0.791003\pi$
$398$	−10.7261	+	25.8806i	−0.537653	+	1.29728i
$399$	7.09657	−	35.6769i	0.355273	−	1.78608i
$400$	4.52326	+	2.42237i	0.226163	+	0.121118i
$401$	−5.34823	−	26.8873i	−0.267078	−	1.34269i	−0.848546	−	0.529121i	$-0.822522\pi$
$401$	−5.34823	−	26.8873i	−0.267078	−	1.34269i	0.581469	−	0.813569i	$-0.302478\pi$
$402$	3.95408	−	19.8578i	0.197212	−	0.990419i
$403$	4.13428	−	4.56148i	0.205943	−	0.227224i
$404$	−6.35059	−	4.71384i	−0.315954	−	0.234522i
$405$	6.88957	−	4.12945i	0.342345	−	0.205194i
$406$	−27.6907	−	16.6046i	−1.37426	−	0.824075i
$407$	−0.473515	−	4.80768i	−0.0234713	−	0.238308i
$408$	23.1367	+	25.5581i	1.14544	+	1.26531i
$409$	−22.7448	+	18.6662i	−1.12466	+	0.922983i	−0.997623	−	0.0689152i	$-0.978046\pi$
$409$	−22.7448	+	18.6662i	−1.12466	+	0.922983i	−0.127035	+	0.991898i	$0.540546\pi$
$410$	−21.2783	−	35.5167i	−1.05086	−	1.75404i
$411$	12.6506	+	13.9578i	0.624010	+	0.688489i
$412$	−11.4049	+	13.8857i	−0.561880	+	0.684097i
$413$	26.7076	−	19.8077i	1.31419	−	0.974672i
$414$	−11.4612	−	13.9711i	−0.563285	−	0.686644i
$415$	−14.6631	+	35.3998i	−0.719783	+	1.73771i
$416$	−13.0047	+	1.91583i	−0.637606	+	0.0939311i
$417$	6.53540	+	15.7779i	0.320040	+	0.772645i
$418$	−6.73550	+	12.5952i	−0.329444	+	0.616052i
$419$	0.922756	+	0.136878i	0.0450796	+	0.00668692i	0.169232	−	0.985576i	$-0.445871\pi$
$419$	0.922756	+	0.136878i	0.0450796	+	0.00668692i	−0.124153	+	0.992263i	$0.539621\pi$
$420$	−11.2113	−	37.0118i	−0.547055	−	1.80599i
$421$	3.86154	+	0.189705i	0.188200	+	0.00924568i	0.142949	−	0.989730i	$-0.454341\pi$
$421$	3.86154	+	0.189705i	0.188200	+	0.00924568i	0.0452506	+	0.998976i	$0.485591\pi$
$422$	−2.29800	−	15.5131i	−0.111865	−	0.755168i
$423$	−40.9279	−	4.03105i	−1.98998	−	0.195996i
$424$	−30.7957	−	11.0396i	−1.49557	−	0.536131i
$425$	4.46218	+	3.66202i	0.216448	+	0.177634i
$426$	−37.9168	−	5.63215i	−1.83708	−	0.272878i
$427$	−9.76112	−	2.44503i	−0.472374	−	0.118323i
$428$	17.8349	−	16.1517i	0.862084	−	0.780723i
$429$	0.661479	+	13.4647i	0.0319365	+	0.650082i
$430$	31.4187	+	21.0023i	1.51514	+	1.01282i
$431$	13.9879	−	20.9343i	0.673771	−	1.00837i	−0.324280	−	0.945961i	$-0.605122\pi$
$431$	13.9879	−	20.9343i	0.673771	−	1.00837i	0.998051	−	0.0624084i	$-0.0198781\pi$
$432$	6.20124	−	13.0844i	0.298358	−	0.629526i
$433$	−9.07983	−	13.5889i	−0.436349	−	0.653042i	0.546499	−	0.837460i	$-0.315960\pi$
$433$	−9.07983	−	13.5889i	−0.436349	−	0.653042i	−0.982848	+	0.184418i	$0.940960\pi$
$434$	−10.6708	−	0.00212536i	−0.512217	−	0.000102020i
$435$	−23.2689	−	49.1981i	−1.11566	−	2.35887i
$436$	19.4154	−	32.3634i	0.929828	−	1.54992i
$437$	11.1601	+	8.27693i	0.533862	+	0.395939i
$438$	−18.7842	+	0.919057i	−0.897542	+	0.0439142i
$439$	−4.33853	+	14.3022i	−0.207067	+	0.682607i	0.790473	+	0.612497i	$0.209835\pi$
$439$	−4.33853	+	14.3022i	−0.207067	+	0.682607i	−0.997539	+	0.0701097i	$0.977665\pi$
$440$	−0.00907330	+	15.1849i	−0.000432553	+	0.723910i
$441$	−2.27238	+	4.25132i	−0.108208	+	0.202444i
$442$	−14.7703	−	0.728568i	−0.702552	−	0.0346544i
$443$	−26.0634	+	9.32565i	−1.23831	+	0.443075i	−0.872959	−	0.487794i	$-0.837802\pi$
$443$	−26.0634	+	9.32565i	−1.23831	+	0.443075i	−0.365353	+	0.930869i	$0.619052\pi$
$444$	−4.67128	−	11.2902i	−0.221689	−	0.535808i
$445$	8.62496	+	5.16960i	0.408862	+	0.245063i
$446$	−3.09574	−	5.79449i	−0.146587	−	0.274377i
$447$	−36.2199	+	36.2199i	−1.71314	+	1.71314i
$448$	17.5956	+	14.4755i	0.831312	+	0.683904i
$449$	16.6650	+	16.6650i	0.786471	+	0.786471i	0.980914	−	0.194443i	$-0.0622899\pi$
$449$	16.6650	+	16.6650i	0.786471	+	0.786471i	−0.194443	+	0.980914i	$0.562290\pi$
$450$	2.28510	−	7.52756i	0.107721	−	0.354853i
$451$	12.8612	−	21.4576i	0.605610	−	1.01040i
$452$	−0.00595975	+	14.9611i	−0.000280323	+	0.703713i
$453$	7.19382	+	20.1054i	0.337995	+	0.944634i
$454$	−19.8124	+	17.9497i	−0.929843	+	0.842423i
$455$	14.6301	+	7.81992i	0.685867	+	0.366604i
$456$	−7.06875	+	35.4263i	−0.331024	+	1.65899i
$457$	1.84559	+	0.559853i	0.0863330	+	0.0261888i	0.333156	−	0.942872i	$-0.391887\pi$
$457$	1.84559	+	0.559853i	0.0863330	+	0.0261888i	−0.246823	+	0.969061i	$0.579387\pi$
$458$	−6.79386	−	6.16006i	−0.317456	−	0.287841i
$459$	9.70373	−	13.0840i	0.452931	−	0.610707i
$460$	14.6110	+	2.17328i	0.681240	+	0.101330i
$461$	−9.13912	+	4.32248i	−0.425651	+	0.201318i	−0.628363	−	0.777920i	$-0.716275\pi$
$461$	−9.13912	+	4.32248i	−0.425651	+	0.201318i	0.202711	+	0.979239i	$0.435025\pi$
$462$	16.5262	−	16.5197i	0.768871	−	0.768564i
$463$	10.1199	−	6.76191i	0.470312	−	0.314253i	−0.297732	−	0.954650i	$-0.596230\pi$
$463$	10.1199	−	6.76191i	0.470312	−	0.314253i	0.768044	+	0.640397i	$0.221230\pi$
$464$	27.4896	+	16.5064i	1.27617	+	0.766291i
$465$	−14.9553	−	9.99279i	−0.693534	−	0.463405i
$466$	2.51472	+	12.6555i	0.116492	+	0.586255i
$467$	23.9262	−	1.17542i	1.10717	−	0.0543919i	0.512745	−	0.858541i	$-0.328629\pi$
$467$	23.9262	−	1.17542i	1.10717	−	0.0543919i	0.594428	+	0.804149i	$0.297379\pi$
$468$	6.78196	+	18.9781i	0.313496	+	0.877265i
$469$	3.65799	−	14.6035i	0.168910	−	0.674327i
$470$	27.0062	−	20.0208i	1.24570	−	0.923492i
$471$	−28.8404	+	35.1422i	−1.32890	+	1.61927i
$472$	−26.5349	+	19.6551i	−1.22137	+	0.904698i
$473$	−2.23821	+	22.7250i	−0.102913	+	1.04489i
$474$	19.9308	−	26.8624i	0.915452	−	1.23383i
$475$	−0.296796	+	6.04142i	−0.0136179	+	0.277199i
$476$	16.2535	+	19.8211i	0.744979	+	0.908497i
$477$	−7.35955	+	49.6141i	−0.336971	+	2.27167i
$478$	3.94271	+	13.0067i	0.180335	+	0.594912i
$479$	6.28447	−	2.60311i	0.287145	−	0.118939i	−0.234462	−	0.972125i	$-0.575333\pi$
$479$	6.28447	−	2.60311i	0.287145	−	0.118939i	0.521607	+	0.853186i	$0.325333\pi$
$480$	11.1119	+	36.7628i	0.507187	+	1.67799i
$481$	4.84220	+	2.00571i	0.220785	+	0.0914523i
$482$	−1.33247	+	13.5013i	−0.0606925	+	0.614966i
$483$	−13.5410	−	18.2579i	−0.616136	−	0.830763i
$484$	11.3129	−	6.04110i	0.514225	−	0.274596i
$485$	−26.4644	+	23.9859i	−1.20169	+	1.08915i
$486$	26.8035	+	6.71961i	1.21583	+	0.304808i
$487$	−5.83853	−	7.11427i	−0.264569	−	0.322378i	0.623733	−	0.781637i	$-0.285615\pi$
$487$	−5.83853	−	7.11427i	−0.264569	−	0.322378i	−0.888303	+	0.459259i	$0.848115\pi$
$488$	9.69227	+	2.43394i	0.438748	+	0.110179i
$489$	−40.9857	+	4.03674i	−1.85344	+	0.182548i
$490$	−0.956699	−	3.82259i	−0.0432192	−	0.172687i
$491$	−11.6546	−	19.4446i	−0.525966	−	0.877521i	0.474029	−	0.880509i	$-0.342799\pi$
$491$	−11.6546	−	19.4446i	−0.525966	−	0.877521i	−0.999996	+	0.00298756i	$0.999049\pi$
$492$	15.3984	−	61.3700i	0.694212	−	2.76677i
$493$	26.7283	+	24.2251i	1.20378	+	1.09104i
$494$	−8.60651	−	12.8861i	−0.387225	−	0.579774i
$495$	22.8336	−	4.54189i	1.02629	−	0.204143i
$496$	10.5972	+	0.00844273i	0.475826	+	0.000379090i
$497$	−27.9538	−	5.56036i	−1.25390	−	0.249416i
$498$	−54.1028	+	22.3975i	−2.42440	+	1.00365i
$499$	−9.19383	+	25.6950i	−0.411572	+	1.15027i	0.539684	+	0.841867i	$0.318544\pi$
$499$	−9.19383	+	25.6950i	−0.411572	+	1.15027i	−0.951257	+	0.308400i	$0.900206\pi$
$500$	−7.96071	−	16.8489i	−0.356014	−	0.753504i
$501$	1.47309	−	0.218512i	0.0658128	−	0.00976240i
$502$	7.36230	−	20.5633i	0.328595	−	0.917786i
$503$	15.7192	−	8.40210i	0.700885	−	0.374631i	−0.0821400	−	0.996621i	$-0.526175\pi$
$503$	15.7192	−	8.40210i	0.700885	−	0.374631i	0.783025	+	0.621990i	$0.213675\pi$
$504$	16.4856	−	30.7981i	0.734328	−	1.37186i
$505$	−2.87729	−	9.48517i	−0.128038	−	0.422084i
$506$	3.00523	+	8.40433i	0.133599	+	0.373618i
$507$	18.6095	+	8.80163i	0.826476	+	0.390894i
$508$	2.01332	+	10.1427i	0.0893264	+	0.450011i
$509$	24.2589	−	6.07655i	1.07526	−	0.269338i	0.335383	−	0.942082i	$-0.391134\pi$
$509$	24.2589	−	6.07655i	1.07526	−	0.269338i	0.739876	+	0.672744i	$0.234884\pi$
$510$	4.22641	+	42.9993i	0.187149	+	1.90404i
$511$	−13.9832			−0.618581
$512$	−17.4655	−	14.3860i	−0.771872	−	0.635778i
$513$	17.0692			0.753622
$514$	−1.35952	−	13.8316i	−0.0599657	−	0.610087i
$515$	−21.8451	+	5.47191i	−0.962610	+	0.241121i
$516$	11.2447	+	56.6487i	0.495019	+	2.49382i
$517$	18.3627	+	8.68489i	0.807589	+	0.381961i
$518$	−3.05883	−	8.55424i	−0.134397	−	0.375852i
$519$	7.14476	+	23.5531i	0.313620	+	1.03387i
$520$	−14.5244	−	7.77461i	−0.636937	−	0.340939i
$521$	0.458114	−	0.244867i	0.0200703	−	0.0107278i	−0.461331	−	0.887228i	$-0.652628\pi$
$521$	0.458114	−	0.244867i	0.0200703	−	0.0107278i	0.481401	+	0.876500i	$0.340128\pi$
$522$	16.5709	−	46.2834i	0.725287	−	2.02577i
$523$	−23.1667	+	3.43646i	−1.01301	+	0.150266i	−0.632540	−	0.774528i	$-0.717988\pi$
$523$	−23.1667	+	3.43646i	−1.01301	+	0.150266i	−0.380469	+	0.924793i	$0.624238\pi$
$524$	0.391693	+	0.829020i	0.0171112	+	0.0362159i
$525$	3.33374	−	9.31717i	0.145496	−	0.406635i
$526$	−8.40537	+	3.47966i	−0.366492	+	0.151720i
$527$	11.6928	+	2.32585i	0.509347	+	0.101315i
$528$	−16.4219	+	16.3958i	−0.714673	+	0.713535i
$529$	−14.0423	+	2.79318i	−0.610533	+	0.121443i
$530$	−22.7718	−	34.0950i	−0.989142	−	1.48099i
$531$	37.5126	+	33.9994i	1.62791	+	1.47545i
$532$	−6.53674	+	26.0521i	−0.283403	+	1.12950i
$533$	13.9533	+	23.2797i	0.604385	+	1.00836i
$534$	3.73091	+	14.9072i	0.161452	+	0.645099i
$535$	30.0106	−	2.95578i	1.29747	−	0.127790i
$536$	−3.64140	+	14.5005i	−0.157284	+	0.626326i
$537$	−6.16148	−	7.50778i	−0.265887	−	0.323985i
$538$	−23.5086	−	5.89358i	−1.01353	−	0.254090i
$539$	1.76417	−	1.59895i	0.0759881	−	0.0688716i
$540$	16.0075	−	8.54799i	0.688853	−	0.367847i
$541$	1.57426	+	2.12264i	0.0676826	+	0.0912595i	0.835752	−	0.549108i	$-0.185032\pi$
$541$	1.57426	+	2.12264i	0.0676826	+	0.0912595i	−0.768069	+	0.640367i	$0.778782\pi$
$542$	−0.375781	+	3.80759i	−0.0161412	+	0.163550i
$543$	38.8732	+	16.1018i	1.66821	+	0.690994i
$544$	−16.1295	−	19.6938i	−0.691548	−	0.844367i
$545$	43.6987	−	18.1006i	1.87184	−	0.775343i
$546$	7.35424	+	24.2611i	0.314732	+	1.03828i
$547$	−5.04873	+	34.0358i	−0.215868	+	1.45527i	0.562156	+	0.827031i	$0.309972\pi$
$547$	−5.04873	+	34.0358i	−0.215868	+	1.45527i	−0.778024	+	0.628234i	$0.783778\pi$
$548$	−8.81989	−	10.7558i	−0.376767	−	0.459465i
$549$	0.751778	−	15.3028i	0.0320851	−	0.653107i
$550$	−2.31524	+	3.12044i	−0.0987221	+	0.133056i
$551$	−3.70497	+	37.6172i	−0.157837	+	1.60255i
$552$	13.4366	+	18.1399i	0.571902	+	0.772084i
$553$	15.7774	−	19.2248i	0.670924	−	0.817523i
$554$	12.9953	−	9.63396i	0.552117	−	0.409308i
$555$	3.72075	−	14.8541i	0.157937	−	0.630519i
$556$	−4.24350	−	11.8747i	−0.179964	−	0.503599i
$557$	9.72519	−	0.477768i	0.412069	−	0.0202437i	0.158022	−	0.987436i	$-0.449488\pi$
$557$	9.72519	−	0.477768i	0.412069	−	0.0202437i	0.254047	+	0.967192i	$0.418238\pi$
$558$	−3.16650	−	15.9357i	−0.134049	−	0.674610i
$559$	−20.5988	−	13.7637i	−0.871236	−	0.582141i
$560$	6.91634	+	27.7052i	0.292269	+	1.17076i
$561$	−21.7068	+	14.5040i	−0.916462	+	0.612360i
$562$	−5.77078	+	5.76849i	−0.243426	+	0.243329i
$563$	−3.64943	+	1.72605i	−0.153805	+	0.0727445i	−0.502908	−	0.864340i	$-0.667736\pi$
$563$	−3.64943	+	1.72605i	−0.153805	+	0.0727445i	0.349103	+	0.937085i	$0.386486\pi$
$564$	50.8162	+	7.55857i	2.13975	+	0.318273i
$565$	−11.1696	+	15.0604i	−0.469908	+	0.633597i
$566$	6.07577	+	5.50896i	0.255384	+	0.231559i
$567$	8.73385	+	2.64938i	0.366787	+	0.111264i
$568$	27.7575	+	5.53855i	1.16468	+	0.232392i
$569$	−6.04268	−	3.22988i	−0.253322	−	0.135404i	0.339849	−	0.940480i	$-0.389624\pi$
$569$	−6.04268	−	3.22988i	−0.253322	−	0.135404i	−0.593171	+	0.805077i	$0.702124\pi$
$570$	−33.5519	+	30.3975i	−1.40534	+	1.27321i
$571$	−9.41869	−	26.3235i	−0.394160	−	1.10160i	−0.960705	−	0.277572i	$-0.910470\pi$
$571$	−9.41869	−	26.3235i	−0.394160	−	1.10160i	0.566545	−	0.824031i	$-0.308280\pi$
$572$	0.00396525	−	9.95422i	0.000165795	−	0.416207i
$573$	20.7258	−	34.5789i	0.865832	−	1.44455i
$574$	13.6653	−	45.0161i	0.570378	−	1.87894i
$575$	2.67274	+	2.67274i	0.111461	+	0.111461i
$576$	−16.3901	+	30.5757i	−0.682919	+	1.27399i
$577$	3.60587	−	3.60587i	0.150114	−	0.150114i	−0.628055	−	0.778169i	$-0.716149\pi$
$577$	3.60587	−	3.60587i	0.150114	−	0.150114i	0.778169	+	0.628055i	$0.216149\pi$
$578$	−2.16602	−	4.05428i	−0.0900945	−	0.168636i
$579$	16.3165	+	9.77974i	0.678091	+	0.406432i
$580$	15.3636	+	37.1329i	0.637939	+	1.54186i
$581$	−40.9926	+	14.6674i	−1.70066	+	0.608505i
$582$	−54.5164	−	2.68911i	−2.25978	−	0.111467i
$583$	11.6781	−	21.8483i	0.483659	−	0.904863i
$584$	13.8867	+	0.00829760i	0.574635	+	0.000343357i
$585$	−7.33197	+	24.1703i	−0.303140	+	0.999317i
$586$	20.6783	−	1.01173i	0.854214	−	0.0417943i
$587$	−22.6655	−	16.8098i	−0.935503	−	0.693817i	0.0165131	−	0.999864i	$-0.494743\pi$
$587$	−22.6655	−	16.8098i	−0.935503	−	0.693817i	−0.952016	+	0.306047i	$0.900993\pi$
$588$	3.09793	−	5.16391i	0.127756	−	0.212956i
$589$	5.34119	+	11.2930i	0.220080	+	0.465320i
$590$	−41.3850	−	0.00824283i	−1.70379	−	0.000339352i
$591$	8.92890	+	13.3630i	0.367286	+	0.549682i
$592$	3.03264	+	8.49699i	0.124641	+	0.349224i
$593$	−18.5631	+	27.7817i	−0.762296	+	1.14086i	0.223793	+	0.974637i	$0.428156\pi$
$593$	−18.5631	+	27.7817i	−0.762296	+	1.14086i	−0.986089	+	0.166220i	$0.946844\pi$
$594$	9.11570	+	6.09355i	0.374022	+	0.250021i
$595$	1.57631	+	32.0864i	0.0646222	+	1.31542i
$596$	28.0347	−	25.3888i	1.14834	−	1.03997i
$597$	−52.0486	−	13.0375i	−2.13021	−	0.533589i
$598$	−9.57830	−	1.42276i	−0.391686	−	0.0581808i
$599$	−32.0675	−	26.3171i	−1.31024	−	1.07529i	−0.991861	−	0.127328i	$-0.959360\pi$
$599$	−32.0675	−	26.3171i	−1.31024	−	1.07529i	−0.318383	−	0.947962i	$-0.603140\pi$
$600$	−3.31625	+	9.25086i	−0.135385	+	0.377665i
$601$	14.5939	+	1.43737i	0.595298	+	0.0586317i	0.391179	−	0.920314i	$-0.372067\pi$
$601$	14.5939	+	1.43737i	0.595298	+	0.0586317i	0.204119	+	0.978946i	$0.434567\pi$
$602$	6.29237	+	42.4780i	0.256458	+	1.73128i
$603$	22.8944	+	1.12473i	0.932330	+	0.0458024i
$604$	−4.57101	−	15.0902i	−0.185992	−	0.614013i
$605$	15.8991	+	2.35841i	0.646391	+	0.0958830i
$606$	7.14317	−	13.3575i	0.290172	−	0.542613i
$607$	4.70402	+	11.3565i	0.190930	+	0.460947i	0.990136	−	0.140111i	$-0.0447461\pi$
$607$	4.70402	+	11.3565i	0.190930	+	0.460947i	−0.799205	+	0.601058i	$0.794746\pi$
$608$	6.50706	−	25.8683i	0.263896	−	1.04910i
$609$	23.6648	−	57.1319i	0.958946	−	2.31510i
$610$	7.94334	+	9.68292i	0.321617	+	0.392050i
$611$	−17.7009	+	13.1279i	−0.716103	+	0.531098i
$612$	−24.7713	+	30.1594i	−1.00132	+	1.21912i
$613$	−30.7481	−	33.9253i	−1.24190	−	1.37023i	−0.903134	−	0.429360i	$-0.858739\pi$
$613$	−30.7481	−	33.9253i	−1.24190	−	1.37023i	−0.338770	−	0.940869i	$-0.610011\pi$
$614$	−6.35347	−	10.6049i	−0.256405	−	0.427980i
$615$	61.2977	−	50.3057i	2.47176	−	2.02852i
$616$	−12.7913	+	11.5794i	−0.515376	+	0.466549i
$617$	−1.68816	−	17.1402i	−0.0679629	−	0.690039i	−0.967445	−	0.253081i	$-0.918556\pi$
$617$	−1.68816	−	17.1402i	−0.0679629	−	0.690039i	0.899482	−	0.436958i	$-0.143944\pi$
$618$	−29.5154	−	17.6989i	−1.18728	−	0.711952i
$619$	3.63304	−	2.17756i	0.146024	−	0.0875236i	−0.439225	−	0.898377i	$-0.644747\pi$
$619$	3.63304	−	2.17756i	0.146024	−	0.0875236i	0.585249	+	0.810854i	$0.300997\pi$
$620$	10.6643	+	7.91581i	0.428291	+	0.317906i
$621$	7.16318	−	7.90335i	0.287449	−	0.317151i
$622$	8.11312	−	40.7450i	0.325306	−	1.63372i
$623$	2.22906	+	11.2062i	0.0893054	+	0.448968i
$624$	−7.28906	−	24.0979i	−0.291796	−	0.964688i
$625$	5.80751	−	29.1963i	0.232301	−	1.16785i
$626$	7.96264	−	19.2127i	0.318251	−	0.767894i
$627$	−25.7567	−	9.21590i	−1.02862	−	0.368048i
$628$	22.5530	−	24.8635i	0.899964	−	0.992163i
$629$	1.48928	+	10.0399i	0.0593816	+	0.400318i
$630$	39.5807	−	18.7106i	1.57693	−	0.745449i
$631$	−10.4766	−	19.6003i	−0.417066	−	0.780276i	0.582402	−	0.812901i	$-0.302113\pi$
$631$	−10.4766	−	19.6003i	−0.417066	−	0.780276i	−0.999468	+	0.0326255i	$0.989613\pi$
$632$	−15.6799	+	19.0827i	−0.623712	+	0.759070i
$633$	28.7426	−	8.71898i	1.14242	−	0.346548i
$634$	−6.36259	−	3.01083i	−0.252691	−	0.119575i
$635$	−5.54095	+	11.7154i	−0.219886	+	0.464910i
$636$	12.2483	−	61.4482i	0.485675	−	2.43658i
$637$	0.627649	+	2.50572i	0.0248684	+	0.0992801i
$638$	−15.4076	+	18.7666i	−0.609994	+	0.742978i
$639$		−	43.3958i		−	1.71671i
$640$	−6.85215	−	27.5180i	−0.270855	−	1.08775i
$641$			13.8184i			0.545795i	0.962043	+	0.272898i	$0.0879820\pi$
$641$			13.8184i			0.545795i	−0.962043	+	0.272898i	$0.912018\pi$
$642$	35.6179	+	29.2427i	1.40572	+	1.15412i
$643$	−2.41840	−	9.65480i	−0.0953725	−	0.380748i	0.903481	−	0.428629i	$-0.141003\pi$
$643$	−2.41840	−	9.65480i	−0.0953725	−	0.380748i	−0.998853	+	0.0478808i	$0.984753\pi$
$644$	9.31944	+	13.9596i	0.367237	+	0.550084i
$645$	−30.9470	+	65.4320i	−1.21854	+	2.57638i
$646$	12.8358	−	27.1250i	0.505016	−	1.06722i
$647$	−1.52846	+	0.463654i	−0.0600900	+	0.0182281i	−0.320187	−	0.947355i	$-0.603746\pi$
$647$	−1.52846	+	0.463654i	−0.0600900	+	0.0182281i	0.260097	+	0.965583i	$0.416246\pi$
$648$	−8.67197	−	2.63627i	−0.340667	−	0.103563i
$649$	−11.7877	−	22.0533i	−0.462709	−	0.865667i
$650$	−1.80160	−	3.81112i	−0.0706644	−	0.149484i
$651$	−2.99880	−	20.2162i	−0.117532	−	0.792337i
$652$	30.3739	−	1.48005i	1.18953	−	0.0579631i
$653$	36.5518	+	13.0784i	1.43038	+	0.511799i	0.934304	−	0.356478i	$-0.116023\pi$
$653$	36.5518	+	13.0784i	1.43038	+	0.511799i	0.496079	+	0.868277i	$0.334773\pi$
$654$	66.7752	+	27.6748i	2.61112	+	1.08217i
$655$	−0.224182	+	1.12704i	−0.00875952	+	0.0440371i
$656$	−13.5976	+	44.6972i	−0.530899	+	1.74513i
$657$	−4.15359	−	20.8815i	−0.162047	−	0.814665i
$658$	37.4634	+	7.45969i	1.46048	+	0.290809i
$659$	−17.6492	+	19.4729i	−0.687517	+	0.758558i	−0.980277	−	0.197628i	$-0.936676\pi$
$659$	−17.6492	+	19.4729i	−0.687517	+	0.758558i	0.292760	+	0.956186i	$0.405426\pi$
$660$	−28.7699	+	4.25590i	−1.11987	+	0.165661i
$661$	−10.6301	+	6.37145i	−0.413464	+	0.247821i	−0.705679	−	0.708532i	$-0.749358\pi$
$661$	−10.6301	+	6.37145i	−0.413464	+	0.247821i	0.292215	+	0.956353i	$0.405608\pi$
$662$	8.59564	−	14.3345i	0.334079	−	0.557126i
$663$	−2.77618	−	28.1870i	−0.107818	−	1.09469i
$664$	40.7182	−	14.5418i	1.58017	−	0.564330i
$665$	−26.0214	+	21.3552i	−1.00907	+	0.828120i
$666$	11.8657	−	7.10879i	0.459785	−	0.275460i
$667$	15.8627	+	17.5018i	0.614205	+	0.677671i
$668$	−1.09437	+	0.107346i	−0.0423423	+	0.00415333i
$669$	10.1064	−	7.49540i	0.390735	−	0.289789i
$670$	−14.4865	+	11.8840i	−0.559663	+	0.459117i
$671$	−2.89594	+	6.99143i	−0.111797	+	0.269901i
$672$	−22.4721	+	37.4078i	−0.866878	+	1.44304i
$673$	−10.0763	−	24.3264i	−0.388413	−	0.937713i	−0.990276	−	0.139114i	$-0.955575\pi$
$673$	−10.0763	−	24.3264i	−0.388413	−	0.937713i	0.601863	−	0.798599i	$-0.294425\pi$
$674$	−4.87961	−	2.60946i	−0.187956	−	0.100513i
$675$	4.59321	+	0.681338i	0.176793	+	0.0262247i
$676$	−13.4028	−	7.17081i	−0.515492	−	0.275800i
$677$	7.73210	+	0.379854i	0.297169	+	0.0145990i	0.197106	−	0.980382i	$-0.436846\pi$
$677$	7.73210	+	0.379854i	0.297169	+	0.0145990i	0.100063	+	0.994981i	$0.468096\pi$
$678$	−28.3452	+	4.19884i	−1.08859	+	0.161255i
$679$	−40.3882	−	3.97789i	−1.54996	−	0.152658i
$680$	−1.54638	−	31.8658i	−0.0593010	−	1.22200i
$681$	−39.5807	−	32.4830i	−1.51673	−	1.24475i
$682$	−1.17907	+	7.93773i	−0.0451488	+	0.303951i
$683$	22.5912	+	5.65879i	0.864427	+	0.216528i	0.649741	−	0.760155i	$-0.274877\pi$
$683$	22.5912	+	5.65879i	0.864427	+	0.216528i	0.214686	+	0.976683i	$0.431127\pi$
$684$	−40.8459	−	2.02294i	−1.56178	−	0.0773491i
$685$	−0.855374	−	17.4115i	−0.0326822	−	0.665261i
$686$	−13.1805	+	19.7175i	−0.503235	+	0.752819i
$687$	9.75826	−	14.6043i	0.372301	−	0.557187i
$688$	−6.22372	−	42.1885i	−0.237277	−	1.60842i
$689$	14.9321	+	22.3475i	0.568870	+	0.851374i
$690$	−0.00563498	+	28.2917i	−0.000214520	+	1.07705i
$691$	13.1169	+	27.7334i	0.498991	+	1.05503i	0.983611	+	0.180302i	$0.0577076\pi$
$691$	13.1169	+	27.7334i	0.498991	+	1.05503i	−0.484621	+	0.874724i	$0.661042\pi$
$692$	−4.40890	−	17.6311i	−0.167601	−	0.670234i
$693$	21.2475	+	15.7582i	0.807124	+	0.598604i
$694$	1.37441	+	28.0908i	0.0521717	+	1.06631i
$695$	4.58764	−	15.1234i	0.174019	−	0.573664i
$696$	−23.5353	+	56.7234i	−0.892104	+	2.15009i
$697$	−24.7767	+	46.3539i	−0.938483	+	1.75578i
$698$	0.179827	−	3.64564i	0.00680655	−	0.137990i
$699$	−23.2679	+	8.32539i	−0.880073	+	0.314895i
$700$	−2.79890	+	6.74954i	−0.105789	+	0.255109i
$701$	−19.7010	−	11.8083i	−0.744097	−	0.445994i	0.0911728	−	0.995835i	$-0.470938\pi$
$701$	−19.7010	−	11.8083i	−0.744097	−	0.445994i	−0.835270	+	0.549841i	$0.814688\pi$
$702$	−10.4924	+	5.60560i	−0.396009	+	0.211570i
$703$	−7.52042	+	7.52042i	−0.283638	+	0.283638i
$704$	12.7098	−	11.4919i	0.479020	−	0.433117i
$705$	45.5287	+	45.5287i	1.71471	+	1.71471i
$706$	43.4979	+	13.2044i	1.63707	+	0.496955i
$707$	5.79014	−	9.66026i	0.217760	−	0.363311i
$708$	−44.7031	−	44.7387i	−1.68005	−	1.68138i
$709$	3.01010	+	8.41265i	0.113047	+	0.315944i	0.984720	−	0.174142i	$-0.0557153\pi$
$709$	3.01010	+	8.41265i	0.113047	+	0.315944i	−0.871674	+	0.490086i	$0.836965\pi$
$710$	23.8173	+	26.2888i	0.893846	+	0.986602i
$711$	33.3955	+	17.8502i	1.25243	+	0.669437i
$712$	−2.20702	−	11.1302i	−0.0827115	−	0.417121i
$713$	7.47034	+	2.26610i	0.279766	+	0.0848662i
$714$	−32.9767	+	36.3696i	−1.23412	+	1.36110i
$715$	7.43156	−	10.0203i	0.277924	−	0.374738i
$716$	4.26979	+	5.76195i	0.159570	+	0.215334i
$717$	−23.5314	+	11.1295i	−0.878795	+	0.415639i
$718$	−0.167337	−	0.167404i	−0.00624498	−	0.00624747i
$719$	−14.8424	+	9.91736i	−0.553528	+	0.369855i	−0.800653	−	0.599128i	$-0.795514\pi$
$719$	−14.8424	+	9.91736i	−0.553528	+	0.369855i	0.247126	+	0.968983i	$0.420514\pi$
$720$	−39.3185	+	18.5579i	−1.46531	+	0.691613i
$721$	−21.2762	−	14.2163i	−0.792366	−	0.529442i
$722$	4.48689	−	0.891569i	0.166985	−	0.0331808i
$723$	−25.9528	+	1.27498i	−0.965195	+	0.0474170i
$724$	−28.0804	−	13.2947i	−1.04360	−	0.494095i
$725$	−2.49852	+	9.97467i	−0.0927929	+	0.370450i
$726$	14.6282	+	19.7321i	0.542905	+	0.732327i
$727$	−1.69210	+	2.06183i	−0.0627564	+	0.0764689i	−0.803443	−	0.595382i	$-0.797001\pi$
$727$	−1.69210	+	2.06183i	−0.0627564	+	0.0764689i	0.740686	+	0.671851i	$0.234501\pi$
$728$	−4.53753	−	18.1609i	−0.168172	−	0.673086i
$729$	−4.24520	+	43.1022i	−0.157230	+	1.59638i
$730$	13.9768	+	10.3702i	0.517304	+	0.383818i
$731$	2.35407	−	47.9183i	0.0870685	−	1.77232i
$732$	−1.88360	+	19.0467i	−0.0696197	+	0.703986i
$733$	2.23543	−	15.0701i	0.0825677	−	0.556626i	−0.907933	−	0.419116i	$-0.862340\pi$
$733$	2.23543	−	15.0701i	0.0825677	−	0.556626i	0.990500	−	0.137510i	$-0.0439099\pi$
$734$	5.95801	−	1.80605i	0.219914	−	0.0666624i
$735$	6.97258	−	2.88814i	0.257187	−	0.106530i
$736$	−9.24681	−	13.8687i	−0.340842	−	0.511207i
$737$	−10.4598	−	4.33259i	−0.385292	−	0.159593i
$738$	71.2829	+	7.03509i	2.62396	+	0.258965i
$739$	0.0261608	+	0.0352737i	0.000962340	+	0.00129757i	0.803688	−	0.595050i	$-0.202868\pi$
$739$	0.0261608	+	0.0352737i	0.000962340	+	0.00129757i	−0.802726	+	0.596348i	$0.796618\pi$
$740$	−3.28655	+	10.8188i	−0.120816	+	0.397707i
$741$	21.9905	−	19.9310i	0.807841	−	0.732185i
$742$	11.3287	−	45.1887i	0.415891	−	1.65893i
$743$	−5.46973	−	6.66489i	−0.200665	−	0.244511i	0.662949	−	0.748665i	$-0.269305\pi$
$743$	−5.46973	−	6.66489i	−0.200665	−	0.244511i	−0.863614	+	0.504153i	$0.831805\pi$
$744$	2.96609	+	20.0784i	0.108742	+	0.736111i
$745$	47.1735	−	4.64619i	1.72830	−	0.170223i
$746$	−14.2488	+	3.56612i	−0.521685	+	0.130565i
$747$	−34.0796	−	56.8584i	−1.24691	−	2.08034i
$748$	16.5383	−	9.90370i	0.604699	−	0.362115i
$749$	25.3886	+	23.0109i	0.927680	+	0.840800i
$750$	29.6796	−	19.8227i	1.08375	−	0.723823i
$751$	−3.40080	+	0.676461i	−0.124097	+	0.0246844i	−0.256748	−	0.966478i	$-0.582651\pi$
$751$	−3.40080	+	0.676461i	−0.124097	+	0.0246844i	0.132651	+	0.991163i	$0.457651\pi$
$752$	−37.2003	−	7.43041i	−1.35656	−	0.270959i
$753$	41.0285	+	8.16107i	1.49516	+	0.297406i
$754$	−10.0762	−	24.3399i	−0.366955	−	0.886408i
$755$	6.65721	−	18.6056i	0.242281	−	0.677129i
$756$	19.4115	+	6.95426i	0.705989	+	0.252924i
$757$	−17.4923	+	2.59473i	−0.635767	+	0.0943071i	−0.456831	−	0.889554i	$-0.651016\pi$
$757$	−17.4923	+	2.59473i	−0.635767	+	0.0943071i	−0.178936	+	0.983861i	$0.557266\pi$
$758$	−49.4587	−	17.7077i	−1.79642	−	0.643173i
$759$	−15.0761	+	8.05835i	−0.547228	+	0.292500i
$760$	25.8544	−	21.1923i	0.937838	−	0.768726i
$761$	−13.6362	−	44.9526i	−0.494313	−	1.62953i	−0.749044	−	0.662520i	$-0.769487\pi$
$761$	−13.6362	−	44.9526i	−0.494313	−	1.62953i	0.254731	−	0.967012i	$-0.418013\pi$
$762$	−18.6486	+	6.66839i	−0.675568	+	0.241570i
$763$	48.5842	+	22.9786i	1.75886	+	0.831881i
$764$	−16.5480	+	24.7445i	−0.598686	+	0.895225i
$765$	−47.4473	+	11.8849i	−1.71546	+	0.429700i
$766$	17.4195	−	1.71216i	0.629391	−	0.0618630i
$767$	27.1293			0.979584
$768$	22.3391	−	37.1362i	0.806092	−	1.34004i
$769$	−35.8887			−1.29418			−0.647089	−	0.762414i	$-0.724014\pi$
$769$	−35.8887			−1.29418			−0.647089	+	0.762414i	$0.724014\pi$
$770$	−21.5202	+	2.11523i	−0.775536	+	0.0762277i
$771$	25.8211	−	6.46785i	0.929925	−	0.232934i
$772$	−11.6760	−	7.80840i	−0.420229	−	0.281030i
$773$	14.0529	+	6.64654i	0.505449	+	0.239059i	0.663231	−	0.748414i	$-0.269185\pi$
$773$	14.0529	+	6.64654i	0.505449	+	0.239059i	−0.157783	+	0.987474i	$0.550435\pi$
$774$	−61.5644	+	22.0143i	−2.21289	+	0.791287i
$775$	0.986507	+	3.25208i	0.0354364	+	0.116818i
$776$	40.1070	+	3.97439i	1.43976	+	0.142672i
$777$	15.3450	−	8.20209i	0.550500	−	0.294248i
$778$	−41.3629	−	14.8092i	−1.48293	−	0.530934i
$779$	−54.4792	+	8.08122i	−1.95192	+	0.289540i
$780$	10.6416	−	29.7039i	0.381030	−	1.06357i
$781$	−7.22090	+	20.1811i	−0.258384	+	0.722136i
$782$	−7.17278	−	17.3264i	−0.256498	−	0.619590i
$783$	28.4601	+	5.66106i	1.01708	+	0.202310i
$784$	−2.47329	+	3.69517i	−0.0883320	+	0.131970i
$785$	41.2619	−	8.20751i	1.47270	−	0.292938i
$786$	−1.46033	+	0.975343i	−0.0520884	+	0.0347893i
$787$	34.3095	+	31.0963i	1.22300	+	1.10846i	0.990735	+	0.135812i	$0.0433644\pi$
$787$	34.3095	+	31.0963i	1.22300	+	1.10846i	0.232267	+	0.972652i	$0.425386\pi$
$788$	−6.09687	−	10.1812i	−0.217192	−	0.362691i
$789$	−8.95744	−	14.9446i	−0.318893	−	0.532041i
$790$	−30.0276	+	7.51517i	−1.06833	+	0.267378i
$791$	−21.2028	+	2.08829i	−0.753883	+	0.0742510i
$792$	−21.0914	−	15.6620i	−0.749450	−	0.556525i
$793$	−5.20841	−	6.34646i	−0.184956	−	0.225370i
$794$	−7.40222	+	29.5263i	−0.262695	+	1.04785i
$795$	58.1841	−	52.7350i	2.06358	−	1.87032i
$796$	37.9090	+	11.5161i	1.34365	+	0.408176i
$797$	−21.5731	−	29.0880i	−0.764158	−	1.03035i	−0.998308	−	0.0581476i	$-0.981481\pi$
$797$	−21.5731	−	29.0880i	−0.764158	−	1.03035i	0.234150	−	0.972201i	$-0.424769\pi$
$798$	−51.1945	−	5.05251i	−1.81227	−	0.178857i
$799$	−39.4287	−	16.3319i	−1.39489	−	0.577781i
$800$	2.78358	−	6.70127i	0.0984144	−	0.236926i
$801$	−16.0724	+	6.65742i	−0.567891	+	0.235228i
$802$	−37.1022	+	11.2468i	−1.31013	+	0.397137i
$803$	−1.54299	+	10.4020i	−0.0544511	+	0.367079i
$804$	−28.4955	−	2.81803i	−1.00496	−	0.0993842i
$805$	−1.03217	+	21.0103i	−0.0363792	+	0.740515i
$806$	−6.99189	−	5.18770i	−0.246279	−	0.182729i
$807$	4.54981	−	46.1950i	0.160161	−	1.62614i
$808$	−5.75589	+	9.59012i	−0.202491	+	0.337379i
$809$	−17.2165	+	20.9784i	−0.605301	+	0.737561i	−0.982022	−	0.188766i	$-0.939551\pi$
$809$	−17.2165	+	20.9784i	−0.605301	+	0.737561i	0.376722	+	0.926327i	$0.377051\pi$
$810$	−6.76499	−	9.12534i	−0.237698	−	0.320632i
$811$	−8.18198	+	32.6643i	−0.287308	+	1.14700i	0.638688	+	0.769466i	$0.279478\pi$
$811$	−8.18198	+	32.6643i	−0.287308	+	1.14700i	−0.925996	+	0.377533i	$0.876772\pi$
$812$	−19.5393	+	41.2697i	−0.685693	+	1.44828i
$813$	−7.31914	+	0.359566i	−0.256693	+	0.0126105i
$814$	−6.70097	+	1.33152i	−0.234869	+	0.0466697i
$815$	31.6889	+	21.1739i	1.11001	+	0.741688i
$816$	32.7706	−	36.0989i	1.14720	−	1.26372i
$817$	41.7995	−	27.9295i	1.46238	−	0.977131i
$818$	29.4178	+	29.4295i	1.02857	+	1.02898i
$819$	−25.9441	+	12.2706i	−0.906560	+	0.428771i
$820$	−47.0437	+	34.8610i	−1.64284	+	1.21740i
$821$	23.6446	−	31.8810i	0.825201	−	1.11266i	−0.166745	−	0.986000i	$-0.553326\pi$
$821$	23.6446	−	31.8810i	0.825201	−	1.11266i	0.991947	−	0.126655i	$-0.0404242\pi$
$822$	17.8946	−	19.7358i	0.624147	−	0.688365i
$823$	8.43389	+	2.55839i	0.293987	+	0.0891800i	0.433833	−	0.900993i	$-0.357161\pi$
$823$	8.43389	+	2.55839i	0.293987	+	0.0891800i	−0.139846	+	0.990173i	$0.544661\pi$
$824$	21.1208	+	14.1307i	0.735779	+	0.492268i
$825$	−6.56311	−	3.50806i	−0.228498	−	0.122135i
$826$	−31.5726	−	34.8489i	−1.09855	−	1.21255i
$827$	−12.7109	−	35.5246i	−0.442002	−	1.23531i	−0.931639	−	0.363386i	$-0.881621\pi$
$827$	−12.7109	−	35.5246i	−0.442002	−	1.23531i	0.489637	−	0.871926i	$-0.337129\pi$
$828$	−18.0779	+	18.0635i	−0.628251	+	0.627751i
$829$	−2.42745	+	4.04996i	−0.0843088	+	0.140661i	−0.896995	−	0.442041i	$-0.854254\pi$
$829$	−2.42745	+	4.04996i	−0.0843088	+	0.140661i	0.812686	+	0.582702i	$0.198004\pi$
$830$	51.8513	+	15.7402i	1.79978	+	0.546350i
$831$	21.9082	+	21.9082i	0.759988	+	0.759988i
$832$	4.49542	+	18.0382i	0.155851	+	0.625360i
$833$	−3.53720	+	3.53720i	−0.122557	+	0.122557i
$834$	21.3022	−	11.3808i	0.737633	−	0.394084i
$835$	−1.18205	−	0.708496i	−0.0409067	−	0.0245185i
$836$	18.6587	+	7.73738i	0.645323	+	0.267603i
$837$	9.02955	−	3.23083i	0.312107	−	0.111674i
$838$	0.0649951	−	1.31765i	0.00224522	−	0.0455175i
$839$	14.9669	−	28.0011i	0.516714	−	0.966704i	−0.479312	−	0.877644i	$-0.659114\pi$
$839$	14.9669	−	28.0011i	0.516714	−	0.966704i	0.996026	−	0.0890595i	$-0.0283861\pi$
$840$	−50.5406	+	20.8992i	−1.74382	+	0.721091i
$841$	−10.2351	+	33.7406i	−0.352934	+	1.16347i
$842$	−0.267196	−	5.46110i	−0.00920819	−	0.188202i
$843$	−12.5522	−	9.30933i	−0.432320	−	0.320630i
$844$	−21.5158	+	5.38032i	−0.740604	+	0.185198i
$845$	−8.14508	−	17.2213i	−0.280199	−	0.592432i
$846$	−0.0115841	+	58.1609i	−0.000398271	+	1.99961i
$847$	10.1465	+	15.1853i	0.348638	+	0.521774i
$848$	−11.2773	+	44.8700i	−0.387265	+	1.54084i
$849$	−8.72684	+	13.0606i	−0.299504	+	0.448240i
$850$	4.53676	−	6.78681i	0.155609	−	0.232786i
$851$	0.326109	+	6.63809i	0.0111789	+	0.227551i
$852$	−2.68157	+	54.1444i	−0.0918690	+	1.85496i
$853$	−19.3298	−	4.84185i	−0.661838	−	0.165782i	−0.102515	−	0.994731i	$-0.532689\pi$
$853$	−19.3298	−	4.84185i	−0.661838	−	0.165782i	−0.559323	+	0.828950i	$0.688939\pi$
$854$	−2.09089	+	14.0763i	−0.0715489	+	0.481682i
$855$	−39.6197	−	32.5150i	−1.35497	−	1.11199i
$856$	−25.1997	−	22.8671i	−0.861307	−	0.781581i
$857$	−18.4341	−	1.81560i	−0.629698	−	0.0620198i	−0.221866	−	0.975077i	$-0.571215\pi$
$857$	−18.4341	−	1.81560i	−0.629698	−	0.0620198i	−0.407831	+	0.913057i	$0.633715\pi$
$858$	18.8591	−	2.79365i	0.643841	−	0.0953737i
$859$	−4.27600	−	0.210067i	−0.145895	−	0.00716738i	−0.0240111	−	0.999712i	$-0.507644\pi$
$859$	−4.27600	−	0.210067i	−0.145895	−	0.00716738i	−0.121884	+	0.992544i	$0.538894\pi$
$860$	25.2130	−	47.1250i	0.859755	−	1.60695i
$861$	89.1274	+	13.2208i	3.03745	+	0.450564i
$862$	−31.3986	−	16.7910i	−1.06944	−	0.571902i
$863$	−6.30574	−	15.2234i	−0.214650	−	0.518210i	0.779477	−	0.626431i	$-0.215485\pi$
$863$	−6.30574	−	15.2234i	−0.214650	−	0.518210i	−0.994127	+	0.108220i	$0.965485\pi$
$864$	−19.2733	−	6.91776i	−0.655692	−	0.235347i
$865$	8.71636	−	21.0432i	0.296365	−	0.715489i
$866$	−17.8694	+	14.6591i	−0.607227	+	0.498136i
$867$	7.07120	−	5.24436i	0.240151	−	0.178108i
$868$	1.47318	+	15.0188i	0.0500030	+	0.509770i
$869$	−12.5602	−	13.8581i	−0.426077	−	0.470104i
$870$	−66.0239	+	39.5554i	−2.23842	+	1.34105i
$871$	9.49488	−	7.79225i	0.321722	−	0.264030i
$872$	−48.2351	−	22.8488i	−1.63345	−	0.773757i
$873$	−6.05667	−	61.4944i	−0.204987	−	2.08127i
$874$	10.1053	−	16.8521i	0.341818	−	0.570032i
$875$	22.7614	−	13.6427i	0.769477	−	0.461207i
$876$	3.89205	+	26.3103i	0.131500	+	0.888942i
$877$	−4.98753	+	5.50289i	−0.168417	+	0.185819i	−0.819311	−	0.573349i	$-0.805644\pi$
$877$	−4.98753	+	5.50289i	−0.168417	+	0.185819i	0.650894	+	0.759168i	$0.274394\pi$
$878$	20.7295	+	4.12766i	0.699588	+	0.139302i
$879$	7.73568	+	38.8899i	0.260918	+	1.31172i
$880$	21.3729	−	2.08786i	0.720481	−	0.0703816i
$881$	6.19251	−	31.1319i	0.208631	−	1.04886i	−0.724487	−	0.689288i	$-0.757923\pi$
$881$	6.19251	−	31.1319i	0.208631	−	1.04886i	0.933118	−	0.359570i	$-0.117077\pi$
$882$	6.29779	+	2.61010i	0.212058	+	0.0878867i
$883$	7.60644	+	2.72163i	0.255977	+	0.0915901i	0.461751	−	0.887009i	$-0.347221\pi$
$883$	7.60644	+	2.72163i	0.255977	+	0.0915901i	−0.205774	+	0.978600i	$0.565971\pi$
$884$	1.01787	+	20.8890i	0.0342346	+	0.702573i
$885$	−11.6303	−	78.4052i	−0.390949	−	2.63556i
$886$	16.7307	+	35.3924i	0.562080	+	1.18903i
$887$	26.3981	+	49.3874i	0.886362	+	1.65827i	0.743719	+	0.668492i	$0.233060\pi$
$887$	26.3981	+	49.3874i	0.886362	+	1.65827i	0.142643	+	0.989774i	$0.454440\pi$
$888$	−15.2439	+	8.13635i	−0.511553	+	0.273038i
$889$	−14.0914	+	4.27459i	−0.472612	+	0.143365i
$890$	6.08271	−	12.8542i	0.203893	−	0.430873i
$891$	2.93460	−	6.20470i	0.0983129	−	0.207865i
$892$	−7.72710	+	5.15863i	−0.258722	+	0.172724i
$893$	−10.8660	−	43.3794i	−0.363616	−	1.45164i
$894$	55.9876	+	45.9665i	1.87250	+	1.53735i
$895$			8.98791i			0.300433i
$896$	17.9392	−	26.7670i	0.599306	−	0.894224i
$897$		−	18.5462i		−	0.619240i
$898$	21.1495	−	25.7603i	0.705767	−	0.859631i
$899$	5.16020	+	20.6007i	0.172102	+	0.687071i
$900$	−10.9106	−	2.17478i	−0.363688	−	0.0724927i
$901$	−22.2538	+	47.0517i	−0.741382	+	1.56752i
$902$	−31.9793	−	15.1329i	−1.06479	−	0.503869i
$903$	−78.7029	+	23.8743i	−2.61907	+	0.794486i
$904$	21.0576	−	2.06129i	0.700365	−	0.0685574i
$905$	−18.3550	−	34.3397i	−0.610140	−	1.14149i
$906$	27.3018	−	12.9061i	0.907041	−	0.428777i
$907$	1.69747	+	11.4434i	0.0563635	+	0.379972i	0.998942	+	0.0459874i	$0.0146434\pi$
$907$	1.69747	+	11.4434i	0.0563635	+	0.379972i	−0.942578	+	0.333985i	$0.891607\pi$
$908$	28.0038	+	25.4015i	0.929339	+	0.842979i
$909$	16.1458	+	5.77706i	0.535523	+	0.191613i
$910$	8.98213	−	21.6726i	0.297755	−	0.718439i
$911$	3.19663	−	16.0706i	0.105909	−	0.532441i	−0.891009	−	0.453987i	$-0.850001\pi$
$911$	3.19663	−	16.0706i	0.105909	−	0.532441i	0.996918	−	0.0784547i	$-0.0249986\pi$
$912$	50.8380	+	5.04801i	1.68341	+	0.167156i
$913$	6.38759	+	32.1126i	0.211398	+	1.06277i
$914$	0.532642	−	2.67499i	0.0176182	−	0.0884807i
$915$	−16.1088	+	17.7733i	−0.532539	+	0.587567i
$916$	−7.73002	+	10.4140i	−0.255407	+	0.344090i
$917$	−1.11994	+	0.671265i	−0.0369836	+	0.0221671i
$918$	−19.7572	−	11.8473i	−0.652084	−	0.391020i
$919$	1.89722	+	19.2628i	0.0625834	+	0.635420i	0.974400	+	0.224822i	$0.0721801\pi$
$919$	1.89722	+	19.2628i	0.0625834	+	0.635420i	−0.911816	+	0.410598i	$0.865320\pi$
$920$	1.03751	−	20.8646i	0.0342057	−	0.687885i
$921$	18.3029	−	15.0208i	0.603100	−	0.494951i
$922$	7.34788	+	12.2647i	0.241989	+	0.403917i
$923$	−15.6165	−	17.2302i	−0.514023	−	0.567137i
$924$	−25.5365	−	20.9743i	−0.840089	−	0.690003i
$925$	−2.32389	+	1.72351i	−0.0764090	+	0.0566687i
$926$	−10.9169	−	13.3077i	−0.358751	−	0.437317i
$927$	14.9096	−	35.9950i	0.489697	−	1.18223i
$928$	19.4288	−	40.9732i	0.637783	−	1.34501i
$929$	11.4952	+	27.7519i	0.377145	+	0.910509i	0.992498	+	0.122258i	$0.0390135\pi$
$929$	11.4952	+	27.7519i	0.377145	+	0.910509i	−0.615353	+	0.788252i	$0.710987\pi$
$930$	−11.9953	+	22.4309i	−0.393342	+	0.735538i
$931$	−5.18501	−	0.769123i	−0.169932	−	0.0252070i
$932$	17.4639	−	5.29002i	0.572049	−	0.173280i
$933$	79.4734	+	3.90428i	2.60184	+	0.127820i
$934$	−4.96420	−	33.5119i	−0.162434	−	1.09654i
$935$	24.0428	+	2.36801i	0.786284	+	0.0774422i
$936$	25.7722	−	12.1705i	0.842392	−	0.397806i
$937$	29.5155	+	24.2228i	0.964230	+	0.791323i	0.978005	−	0.208582i	$-0.0668847\pi$
$937$	29.5155	+	24.2228i	0.964230	+	0.791323i	−0.0137746	+	0.999905i	$0.504385\pi$
$938$	−21.0595	−	3.12816i	−0.687616	−	0.102138i
$939$	38.6387	+	9.67849i	1.26093	+	0.315846i
$940$	−31.9139	−	35.2398i	−1.04092	−	1.14939i
$941$	−1.35013	−	27.4825i	−0.0440129	−	0.895904i	−0.914717	−	0.404096i	$-0.867586\pi$
$941$	−1.35013	−	27.4825i	−0.0440129	−	0.895904i	0.870704	−	0.491808i	$-0.163664\pi$
$942$	53.4499	+	35.7295i	1.74149	+	1.16413i
$943$	−19.1208	+	28.6163i	−0.622658	+	0.931874i
$944$	31.3339	+	34.6271i	1.01983	+	1.12701i
$945$	14.3570	+	21.4868i	0.467034	+	0.698966i
$946$	32.2934	+	0.00643202i	1.04995	+	0.000209123i
$947$	−16.4374	−	34.7539i	−0.534142	−	1.12935i	−0.973003	−	0.230794i	$-0.925868\pi$
$947$	−16.4374	−	34.7539i	−0.534142	−	1.12935i	0.438860	−	0.898555i	$-0.355382\pi$
$948$	−40.5642	−	24.3352i	−1.31746	−	0.790370i
$949$	−9.16363	−	6.79621i	−0.297464	−	0.220614i
$950$	8.54394	−	0.418031i	0.277202	−	0.0135627i
$951$	3.91349	−	12.9010i	0.126904	−	0.418345i
$952$	25.6483	−	25.6177i	0.831267	−	0.830274i
$953$	3.37899	−	6.32164i	0.109456	−	0.204778i	−0.821229	−	0.570598i	$-0.806711\pi$
$953$	3.37899	−	6.32164i	0.109456	−	0.204778i	0.930686	+	0.365820i	$0.119211\pi$
$954$	70.8465	+	3.49461i	2.29374	+	0.113142i
$955$	−35.1264	+	12.5684i	−1.13666	+	0.406705i
$956$	17.7606	−	7.34839i	0.574419	−	0.237664i
$957$	−39.8887	−	23.9084i	−1.28942	−	0.772848i
$958$	−4.53308	−	8.48485i	−0.146457	−	0.274133i
$959$	14.0063	−	14.0063i	0.452288	−	0.452288i
$960$	50.2040	−	20.7249i	1.62033	−	0.668894i
$961$	−16.9573	−	16.9573i	−0.547010	−	0.547010i
$962$	2.15304	−	7.09253i	0.0694167	−	0.228672i
$963$	−26.8213	+	44.7486i	−0.864304	+	1.44200i
$964$	19.1864	+	0.00764289i	0.617954	+	0.000246161i
$965$	−5.93059	−	16.5749i	−0.190912	−	0.533564i
$966$	−23.8235	+	21.5837i	−0.766509	+	0.694445i
$967$	3.81215	+	2.03763i	0.122590	+	0.0655259i	0.531552	−	0.847026i	$-0.321609\pi$
$967$	3.81215	+	2.03763i	0.122590	+	0.0655259i	−0.408962	+	0.912552i	$0.634109\pi$
$968$	−10.0674	−	15.0865i	−0.323580	−	0.484898i
$969$	54.9996	+	16.6839i	1.76684	+	0.535966i
$970$	37.4196	+	33.9287i	1.20147	+	1.08938i
$971$	15.7913	−	21.2921i	0.506768	−	0.683297i	−0.473540	−	0.880772i	$-0.657024\pi$
$971$	15.7913	−	21.2921i	0.506768	−	0.683297i	0.980308	+	0.197475i	$0.0632741\pi$
$972$	5.74947	−	38.6537i	0.184414	−	1.23982i
$973$	16.2333	−	7.67778i	0.520416	−	0.246138i
$974$	−9.20516	+	9.20150i	−0.294952	+	0.294835i
$975$	6.71309	−	4.48554i	0.214991	−	0.143652i
$976$	2.08481	−	13.9779i	0.0667331	−	0.447422i
$977$	45.0775	+	30.1198i	1.44216	+	0.963617i	0.997698	+	0.0678177i	$0.0216036\pi$
$977$	45.0775	+	30.1198i	1.44216	+	0.963617i	0.444458	+	0.895800i	$0.353396\pi$
$978$	11.3513	+	57.1261i	0.362973	+	1.82669i
$979$	8.58221	−	0.421617i	0.274289	−	0.0134749i
$980$	−5.24768	+	1.87529i	−0.167631	+	0.0599040i
$981$	−19.8830	+	79.3775i	−0.634816	+	2.53433i
$982$	−25.7546	+	19.0930i	−0.821864	+	0.609282i
$983$	−13.9096	+	16.9489i	−0.443648	+	0.540587i	−0.946039	−	0.324054i	$-0.894954\pi$
$983$	−13.9096	+	16.9489i	−0.443648	+	0.540587i	0.502391	+	0.864641i	$0.332454\pi$
$984$	−88.5042	−	13.1824i	−2.82141	−	0.420240i
$985$	1.45778	−	14.8011i	0.0464489	−	0.471603i
$986$	30.3977	−	40.9695i	0.968060	−	1.30473i
$987$	−3.58983	+	73.0727i	−0.114266	+	2.32593i
$988$	−16.9457	+	13.8957i	−0.539115	+	0.442081i
$989$	4.60951	−	31.0748i	0.146574	−	0.988121i
$990$	−9.55112	−	31.5084i	−0.303555	−	1.00140i
$991$	−45.8965	+	19.0110i	−1.45795	+	0.603903i	−0.964075	−	0.265630i	$-0.914420\pi$
$991$	−45.8965	+	19.0110i	−1.45795	+	0.603903i	−0.493876	+	0.869533i	$0.664420\pi$
$992$	−1.45410	−	14.9159i	−0.0461676	−	0.473582i
$993$	29.5752	+	12.2504i	0.938540	+	0.388756i
$994$	−3.95878	+	40.1123i	−0.125565	+	1.27228i
$995$	29.5789	+	39.8826i	0.937716	+	1.26436i
$996$	39.0073	+	73.0475i	1.23599	+	2.31460i
$997$	9.77341	−	8.85811i	0.309527	−	0.280539i	−0.501983	−	0.864878i	$-0.667396\pi$
$997$	9.77341	−	8.85811i	0.309527	−	0.280539i	0.811510	+	0.584339i	$0.198646\pi$
$998$	37.4358	+	9.38511i	1.18501	+	0.297081i
$999$	5.17959	+	6.31135i	0.163875	+	0.199682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.17	✓	992
256.109	even	64	inner	256.2.m.a.109.17	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.17	✓	992	1.1	even	1	trivial
256.2.m.a.109.17	yes	992	256.109	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.138337 - 1.40743i) q^{2} +(2.62742 - 0.658133i) q^{3} +(-1.96173 + 0.389399i) q^{4} +(-2.26589 - 1.07169i) q^{5} +(-1.28975 - 3.60686i) q^{6} +(-0.826757 - 2.72545i) q^{7} +(0.819432 + 2.70713i) q^{8} +(3.82441 - 2.04419i) q^{9} +O(q^{10})\)	\(q+(-0.138337 - 1.40743i) q^{2} +(2.62742 - 0.658133i) q^{3} +(-1.96173 + 0.389399i) q^{4} +(-2.26589 - 1.07169i) q^{5} +(-1.28975 - 3.60686i) q^{6} +(-0.826757 - 2.72545i) q^{7} +(0.819432 + 2.70713i) q^{8} +(3.82441 - 2.04419i) q^{9} +(-1.19487 + 3.33734i) q^{10} +(-2.11868 + 0.314276i) q^{11} +(-4.89799 + 2.31419i) q^{12} +(0.782843 - 2.18790i) q^{13} +(-3.72152 + 1.54064i) q^{14} +(-6.65874 - 1.32451i) q^{15} +(3.69674 - 1.52779i) q^{16} +(4.41357 - 0.877913i) q^{17} +(-3.40611 - 5.09981i) q^{18} +(3.49386 + 3.16665i) q^{19} +(4.86237 + 1.22002i) q^{20} +(-3.96595 - 6.61678i) q^{21} +(0.735413 + 2.93841i) q^{22} +(2.93244 - 0.288820i) q^{23} +(3.93464 + 6.57345i) q^{24} +(0.813776 + 0.991589i) q^{25} +(-3.18761 - 0.799130i) q^{26} +(2.68217 - 2.43097i) q^{27} +(2.68316 + 5.02466i) q^{28} +(4.77522 + 6.43864i) q^{29} +(-0.943002 + 9.55495i) q^{30} +(2.44763 + 1.01384i) q^{31} +(-2.66165 - 4.99155i) q^{32} +(-5.35981 + 2.22010i) q^{33} +(-1.84616 - 6.09034i) q^{34} +(-1.04749 + 7.06160i) q^{35} +(-6.70643 + 5.49936i) q^{36} +(-0.110672 + 2.25277i) q^{37} +(3.97351 - 5.35543i) q^{38} +(0.616924 - 6.26373i) q^{39} +(1.04445 - 7.01222i) q^{40} +(-7.40967 + 9.02871i) q^{41} +(-8.76403 + 6.49714i) q^{42} +(2.59048 - 10.3418i) q^{43} +(4.03388 - 1.44153i) q^{44} +(-10.8564 + 0.533341i) q^{45} +(-0.812160 - 4.08726i) q^{46} +(-7.88547 - 5.26891i) q^{47} +(8.70737 - 6.44708i) q^{48} +(-0.924285 + 0.617587i) q^{49} +(1.28302 - 1.28251i) q^{50} +(11.0185 - 5.21136i) q^{51} +(-0.683757 + 4.59690i) q^{52} +(-6.89007 + 9.29019i) q^{53} +(-3.79247 - 3.43867i) q^{54} +(5.13749 + 1.55844i) q^{55} +(6.70068 - 4.47146i) q^{56} +(11.2639 + 6.02068i) q^{57} +(8.40135 - 7.61150i) q^{58} +(3.93315 + 10.9924i) q^{59} +(13.5784 + 0.00540893i) q^{60} +(1.81639 - 3.03047i) q^{61} +(1.08831 - 3.58512i) q^{62} +(-8.73320 - 8.73320i) q^{63} +(-6.65706 + 4.43661i) q^{64} +(-4.11858 + 4.11858i) q^{65} +(3.86610 + 7.23644i) q^{66} +(4.53385 + 2.71749i) q^{67} +(-8.31635 + 3.44086i) q^{68} +(7.51466 - 2.68879i) q^{69} +(10.0836 + 0.497390i) q^{70} +(4.71736 - 8.82557i) q^{71} +(8.66772 + 8.67808i) q^{72} +(1.42521 - 4.69827i) q^{73} +(3.18593 - 0.155879i) q^{74} +(2.79073 + 2.06974i) q^{75} +(-8.08709 - 4.85159i) q^{76} +(2.60818 + 5.51452i) q^{77} +(-8.90112 - 0.00177287i) q^{78} +(4.85135 + 7.26055i) q^{79} +(-10.0137 - 0.499939i) q^{80} +(-1.78035 + 2.66448i) q^{81} +(13.7323 + 9.17960i) q^{82} +(-0.750077 - 15.2682i) q^{83} +(10.3567 + 11.4360i) q^{84} +(-10.9415 - 2.74070i) q^{85} +(-14.9137 - 2.21527i) q^{86} +(16.7840 + 13.7742i) q^{87} +(-2.58689 - 5.47799i) q^{88} +(-3.99241 - 0.393218i) q^{89} +(2.25248 + 15.2059i) q^{90} +(-6.61024 - 0.324740i) q^{91} +(-5.64018 + 1.70848i) q^{92} +(7.09817 + 1.05291i) q^{93} +(-6.32477 + 11.8271i) q^{94} +(-4.52305 - 10.9196i) q^{95} +(-10.2784 - 11.3632i) q^{96} +(5.45302 - 13.1647i) q^{97} +(0.997075 + 1.21543i) q^{98} +(-7.46024 + 5.53289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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