LMFDB - Embedded newform 804.2.l.a.431.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(431,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("804.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.l (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$132$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			431.4
Character	$\chi$	$=$	804.431
Dual form			804.2.l.a.707.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41305 + 0.0574626i) q^{2} +(1.12603 - 1.31608i) q^{3} +(1.99340 - 0.162395i) q^{4} +3.12863i q^{5} +(-1.51551 + 1.92438i) q^{6} +(-3.36179 + 1.94093i) q^{7} +(-2.80743 + 0.344017i) q^{8} +(-0.464114 - 2.96388i) q^{9} +O(q^{10})$	\(q+(-1.41305 + 0.0574626i) q^{2} +(1.12603 - 1.31608i) q^{3} +(1.99340 - 0.162395i) q^{4} +3.12863i q^{5} +(-1.51551 + 1.92438i) q^{6} +(-3.36179 + 1.94093i) q^{7} +(-2.80743 + 0.344017i) q^{8} +(-0.464114 - 2.96388i) q^{9} +(-0.179779 - 4.42090i) q^{10} +(1.55903 + 2.70032i) q^{11} +(2.03090 - 2.80632i) q^{12} +(1.08050 - 1.87148i) q^{13} +(4.63883 - 2.93580i) q^{14} +(4.11752 + 3.52293i) q^{15} +(3.94726 - 0.647433i) q^{16} +(0.599393 + 0.346060i) q^{17} +(0.826127 + 4.16143i) q^{18} +(-5.48529 - 3.16693i) q^{19} +(0.508073 + 6.23661i) q^{20} +(-1.23106 + 6.60992i) q^{21} +(-2.35815 - 3.72609i) q^{22} +(-2.53910 + 4.39785i) q^{23} +(-2.70850 + 4.08216i) q^{24} -4.78835 q^{25} +(-1.41925 + 2.70657i) q^{26} +(-4.42330 - 2.72661i) q^{27} +(-6.38618 + 4.41498i) q^{28} +(-0.369423 + 0.213286i) q^{29} +(-6.02068 - 4.74146i) q^{30} +(-6.48131 + 3.74199i) q^{31} +(-5.54045 + 1.14167i) q^{32} +(5.30934 + 0.988837i) q^{33} +(-0.866855 - 0.454555i) q^{34} +(-6.07246 - 10.5178i) q^{35} +(-1.40648 - 5.83282i) q^{36} +(-4.30121 + 7.44992i) q^{37} +(7.93294 + 4.15982i) q^{38} +(-1.24633 - 3.52935i) q^{39} +(-1.07630 - 8.78341i) q^{40} +(0.454630 - 0.262481i) q^{41} +(1.35972 - 9.41086i) q^{42} +2.25036i q^{43} +(3.54628 + 5.12963i) q^{44} +(9.27290 - 1.45204i) q^{45} +(3.33515 - 6.36026i) q^{46} +(0.541614 + 0.938103i) q^{47} +(3.59266 - 5.92392i) q^{48} +(4.03442 - 6.98782i) q^{49} +(6.76615 - 0.275151i) q^{50} +(1.13037 - 0.399173i) q^{51} +(1.84994 - 3.90606i) q^{52} +11.4319i q^{53} +(6.40701 + 3.59865i) q^{54} +(-8.44831 + 4.87763i) q^{55} +(8.77027 - 6.60553i) q^{56} +(-10.3445 + 3.65300i) q^{57} +(0.509755 - 0.322611i) q^{58} -12.0269 q^{59} +(8.77995 + 6.35394i) q^{60} +(3.85964 - 6.68510i) q^{61} +(8.94336 - 5.66003i) q^{62} +(7.31294 + 9.06314i) q^{63} +(7.76331 - 1.93160i) q^{64} +(5.85516 + 3.38048i) q^{65} +(-7.55916 - 1.09218i) q^{66} +(8.04128 + 1.52900i) q^{67} +(1.25103 + 0.592496i) q^{68} +(2.92880 + 8.29375i) q^{69} +(9.18504 + 14.5132i) q^{70} +(-3.94267 - 6.82891i) q^{71} +(2.32259 + 8.16122i) q^{72} +(-1.33996 + 2.32088i) q^{73} +(5.64972 - 10.7742i) q^{74} +(-5.39182 + 6.30183i) q^{75} +(-11.4486 - 5.42217i) q^{76} +(-10.4823 - 6.05194i) q^{77} +(1.96393 + 4.91552i) q^{78} +(12.7285 - 7.34878i) q^{79} +(2.02558 + 12.3495i) q^{80} +(-8.56920 + 2.75116i) q^{81} +(-0.627330 + 0.397022i) q^{82} +(-5.89765 + 10.2150i) q^{83} +(-1.38058 + 13.3761i) q^{84} +(-1.08269 + 1.87528i) q^{85} +(-0.129312 - 3.17986i) q^{86} +(-0.135280 + 0.726355i) q^{87} +(-5.30582 - 7.04462i) q^{88} +10.9007i q^{89} +(-13.0196 + 2.58465i) q^{90} +8.38868i q^{91} +(-4.34724 + 9.17898i) q^{92} +(-2.37341 + 12.7435i) q^{93} +(-0.819231 - 1.29446i) q^{94} +(9.90817 - 17.1615i) q^{95} +(-4.73618 + 8.57721i) q^{96} +(4.25136 - 7.36358i) q^{97} +(-5.29928 + 10.1059i) q^{98} +(7.27986 - 5.87404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	$ 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) $ 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.41305	+	0.0574626i	−0.999174	+	0.0406322i
$2$	−1.41305	+	0.0574626i	−0.999174	+	0.0406322i
$3$	1.12603	−	1.31608i	0.650114	−	0.759837i
$3$	1.12603	−	1.31608i	0.650114	−	0.759837i
$4$	1.99340	−	0.162395i	0.996698	−	0.0811973i
$5$			3.12863i			1.39917i	0.714551	+	0.699584i	$0.246631\pi$
$5$			3.12863i			1.39917i	−0.714551	+	0.699584i	$0.753369\pi$
$6$	−1.51551	+	1.92438i	−0.618703	+	0.785625i
$7$	−3.36179	+	1.94093i	−1.27064	+	0.733603i	−0.975108	−	0.221731i	$-0.928829\pi$
$7$	−3.36179	+	1.94093i	−1.27064	+	0.733603i	−0.295529	+	0.955334i	$0.595496\pi$
$8$	−2.80743	+	0.344017i	−0.992576	+	0.121628i
$9$	−0.464114	−	2.96388i	−0.154705	−	0.987961i
$10$	−0.179779	−	4.42090i	−0.0568512	−	1.39801i
$11$	1.55903	+	2.70032i	0.470065	+	0.814177i	0.999414	−	0.0342273i	$-0.0108970\pi$
$11$	1.55903	+	2.70032i	0.470065	+	0.814177i	−0.529349	+	0.848404i	$0.677564\pi$
$12$	2.03090	−	2.80632i	0.586270	−	0.810116i
$13$	1.08050	−	1.87148i	0.299676	−	0.519054i	−0.676386	−	0.736548i	$-0.736455\pi$
$13$	1.08050	−	1.87148i	0.299676	−	0.519054i	0.976062	+	0.217493i	$0.0697881\pi$
$14$	4.63883	−	2.93580i	1.23978	−	0.784626i
$15$	4.11752	+	3.52293i	1.06314	+	0.909618i
$16$	3.94726	−	0.647433i	0.986814	−	0.161858i
$17$	0.599393	+	0.346060i	0.145374	+	0.0839318i	0.570923	−	0.821004i	$-0.306586\pi$
$17$	0.599393	+	0.346060i	0.145374	+	0.0839318i	−0.425549	+	0.904936i	$0.639919\pi$
$18$	0.826127	+	4.16143i	0.194720	+	0.980859i
$19$	−5.48529	−	3.16693i	−1.25841	−	0.726544i	−0.285646	−	0.958335i	$-0.592208\pi$
$19$	−5.48529	−	3.16693i	−1.25841	−	0.726544i	−0.972766	+	0.231791i	$0.925541\pi$
$20$	0.508073	+	6.23661i	0.113609	+	1.39455i
$21$	−1.23106	+	6.60992i	−0.268640	+	1.44240i
$22$	−2.35815	−	3.72609i	−0.502759	−	0.794405i
$23$	−2.53910	+	4.39785i	−0.529438	+	0.917014i	0.469972	+	0.882681i	$0.344264\pi$
$23$	−2.53910	+	4.39785i	−0.529438	+	0.917014i	−0.999410	+	0.0343328i	$0.989069\pi$
$24$	−2.70850	+	4.08216i	−0.552869	+	0.833268i
$25$	−4.78835			−0.957669
$26$	−1.41925	+	2.70657i	−0.278338	+	0.530802i
$27$	−4.42330	−	2.72661i	−0.851265	−	0.524736i
$28$	−6.38618	+	4.41498i	−1.20688	+	0.834353i
$29$	−0.369423	+	0.213286i	−0.0686001	+	0.0396063i	−0.533908	−	0.845543i	$-0.679277\pi$
$29$	−0.369423	+	0.213286i	−0.0686001	+	0.0396063i	0.465308	+	0.885149i	$0.345944\pi$
$30$	−6.02068	−	4.74146i	−1.09922	−	0.865669i
$31$	−6.48131	+	3.74199i	−1.16408	+	0.672081i	−0.952278	−	0.305233i	$-0.901266\pi$
$31$	−6.48131	+	3.74199i	−1.16408	+	0.672081i	−0.211800	+	0.977313i	$0.567932\pi$
$32$	−5.54045	+	1.14167i	−0.979422	+	0.201821i
$33$	5.30934	+	0.988837i	0.924238	+	0.172134i
$34$	−0.866855	−	0.454555i	−0.148664	−	0.0779556i
$35$	−6.07246	−	10.5178i	−1.02643	−	1.77783i
$36$	−1.40648	−	5.83282i	−0.234414	−	0.972137i
$37$	−4.30121	+	7.44992i	−0.707115	+	1.22476i	0.258808	+	0.965929i	$0.416670\pi$
$37$	−4.30121	+	7.44992i	−0.707115	+	1.22476i	−0.965923	+	0.258830i	$0.916663\pi$
$38$	7.93294	+	4.15982i	1.28689	+	0.674812i
$39$	−1.24633	−	3.52935i	−0.199573	−	0.565149i
$40$	−1.07630	−	8.78341i	−0.170178	−	1.38878i
$41$	0.454630	−	0.262481i	0.0710013	−	0.0409926i	−0.464079	−	0.885794i	$-0.653615\pi$
$41$	0.454630	−	0.262481i	0.0710013	−	0.0409926i	0.535080	+	0.844801i	$0.320281\pi$
$42$	1.35972	−	9.41086i	0.209810	−	1.45213i
$43$			2.25036i			0.343177i	0.985169	+	0.171588i	$0.0548899\pi$
$43$			2.25036i			0.343177i	−0.985169	+	0.171588i	$0.945110\pi$
$44$	3.54628	+	5.12963i	0.534622	+	0.773321i
$45$	9.27290	−	1.45204i	1.38232	−	0.216458i
$46$	3.33515	−	6.36026i	0.491741	−	0.937769i
$47$	0.541614	+	0.938103i	0.0790025	+	0.136836i	0.902820	−	0.430019i	$-0.141493\pi$
$47$	0.541614	+	0.938103i	0.0790025	+	0.136836i	−0.823817	+	0.566855i	$0.808160\pi$
$48$	3.59266	−	5.92392i	0.518555	−	0.855044i
$49$	4.03442	−	6.98782i	0.576346	−	0.998261i
$50$	6.76615	−	0.275151i	0.956879	−	0.0389122i
$51$	1.13037	−	0.399173i	0.158284	−	0.0558954i
$52$	1.84994	−	3.90606i	0.256541	−	0.541673i
$53$			11.4319i			1.57030i	0.619307	+	0.785149i	$0.287414\pi$
$53$			11.4319i			1.57030i	−0.619307	+	0.785149i	$0.712586\pi$
$54$	6.40701	+	3.59865i	0.871883	+	0.489714i
$55$	−8.44831	+	4.87763i	−1.13917	+	0.657700i
$56$	8.77027	−	6.60553i	1.17198	−	0.882702i
$57$	−10.3445	+	3.65300i	−1.37017	+	0.483851i
$58$	0.509755	−	0.322611i	0.0669341	−	0.0423609i
$59$	−12.0269			−1.56577			−0.782885	−	0.622166i	$-0.786253\pi$
$59$	−12.0269			−1.56577			−0.782885	+	0.622166i	$0.786253\pi$
$60$	8.77995	+	6.35394i	1.13349	+	0.820290i
$61$	3.85964	−	6.68510i	0.494176	−	0.855939i	−0.505801	−	0.862650i	$-0.668803\pi$
$61$	3.85964	−	6.68510i	0.494176	−	0.855939i	0.999977	+	0.00671141i	$0.00213632\pi$
$62$	8.94336	−	5.66003i	1.13581	−	0.718825i
$63$	7.31294	+	9.06314i	0.921344	+	1.14185i
$64$	7.76331	−	1.93160i	0.970413	−	0.241450i
$65$	5.85516	+	3.38048i	0.726244	+	0.419297i
$66$	−7.55916	−	1.09218i	−0.930469	−	0.134438i
$67$	8.04128	+	1.52900i	0.982398	+	0.186798i
$67$	8.04128	+	1.52900i	0.982398	+	0.186798i
$68$	1.25103	+	0.592496i	0.151709	+	0.0718506i
$69$	2.92880	+	8.29375i	0.352586	+	0.998450i
$70$	9.18504	+	14.5132i	1.09782	+	1.73466i
$71$	−3.94267	−	6.82891i	−0.467909	−	0.810443i	0.531418	−	0.847110i	$-0.321659\pi$
$71$	−3.94267	−	6.82891i	−0.467909	−	0.810443i	−0.999328	+	0.0366668i	$0.988326\pi$
$72$	2.32259	+	8.16122i	0.273720	+	0.961809i
$73$	−1.33996	+	2.32088i	−0.156831	+	0.271639i	−0.933724	−	0.357993i	$-0.883461\pi$
$73$	−1.33996	+	2.32088i	−0.156831	+	0.271639i	0.776893	+	0.629632i	$0.216794\pi$
$74$	5.64972	−	10.7742i	0.656766	−	1.25248i
$75$	−5.39182	+	6.30183i	−0.622594	+	0.727673i
$76$	−11.4486	−	5.42217i	−1.31325	−	0.621966i
$77$	−10.4823	−	6.05194i	−1.19456	−	0.689682i
$78$	1.96393	+	4.91552i	0.222372	+	0.556573i
$79$	12.7285	−	7.34878i	1.43206	−	0.826802i	0.434785	−	0.900534i	$-0.356824\pi$
$79$	12.7285	−	7.34878i	1.43206	−	0.826802i	0.997278	+	0.0737321i	$0.0234910\pi$
$80$	2.02558	+	12.3495i	0.226467	+	1.38072i
$81$	−8.56920	+	2.75116i	−0.952133	+	0.305685i
$82$	−0.627330	+	0.397022i	−0.0692770	+	0.0438437i
$83$	−5.89765	+	10.2150i	−0.647351	+	1.12125i	0.336402	+	0.941719i	$0.390790\pi$
$83$	−5.89765	+	10.2150i	−0.647351	+	1.12125i	−0.983753	+	0.179527i	$0.942543\pi$
$84$	−1.38058	+	13.3761i	−0.150634	+	1.45945i
$85$	−1.08269	+	1.87528i	−0.117435	+	0.203403i
$86$	−0.129312	−	3.17986i	−0.0139440	−	0.342894i
$87$	−0.135280	+	0.726355i	−0.0145035	+	0.0778734i
$88$	−5.30582	−	7.04462i	−0.565602	−	0.750959i
$89$			10.9007i			1.15547i	0.816224	+	0.577736i	$0.196064\pi$
$89$			10.9007i			1.15547i	−0.816224	+	0.577736i	$0.803936\pi$
$90$	−13.0196	+	2.58465i	−1.37239	+	0.272446i
$91$			8.38868i			0.879373i
$92$	−4.34724	+	9.17898i	−0.453231	+	0.956975i
$93$	−2.37341	+	12.7435i	−0.246111	+	1.32144i
$94$	−0.819231	−	1.29446i	−0.0844972	−	0.133513i
$95$	9.90817	−	17.1615i	1.01656	−	1.76073i
$96$	−4.73618	+	8.57721i	−0.483385	+	0.875408i
$97$	4.25136	−	7.36358i	0.431661	−	0.747658i	−0.565356	−	0.824847i	$-0.691261\pi$
$97$	4.25136	−	7.36358i	0.431661	−	0.747658i	0.997016	+	0.0771889i	$0.0245945\pi$
$98$	−5.29928	+	10.1059i	−0.535309	+	1.02085i
$99$	7.27986	−	5.87404i	0.731654	−	0.590363i
$100$	−9.54507	+	0.777601i	−0.954507	+	0.0777601i
$101$	−8.46176	+	4.88540i	−0.841976	+	0.486115i	−0.857935	−	0.513758i	$-0.828253\pi$
$101$	−8.46176	+	4.88540i	−0.841976	+	0.486115i	0.0159593	+	0.999873i	$0.494920\pi$
$102$	−1.57433	+	0.629004i	−0.155882	+	0.0622807i
$103$	4.47251	−	2.58220i	0.440689	−	0.254432i	−0.263201	−	0.964741i	$-0.584778\pi$
$103$	4.47251	−	2.58220i	0.440689	−	0.254432i	0.703890	+	0.710309i	$0.251445\pi$
$104$	−2.38960	+	5.62574i	−0.234320	+	0.551650i
$105$	−20.6800	−	3.85154i	−2.01816	−	0.375872i
$106$	−0.656909	−	16.1539i	−0.0638047	−	1.56900i
$107$	−3.16938			−0.306395			−0.153198	−	0.988196i	$-0.548957\pi$
$107$	−3.16938			−0.306395			−0.153198	+	0.988196i	$0.548957\pi$
$108$	−9.26018	−	4.71689i	−0.891061	−	0.453883i
$109$	7.19838			0.689480			0.344740	−	0.938698i	$-0.387967\pi$
$109$	7.19838			0.689480			0.344740	+	0.938698i	$0.387967\pi$
$110$	11.6576	−	7.37778i	1.11151	−	0.703444i
$111$	4.96137	+	14.0496i	0.470912	+	1.33352i
$112$	−12.0132	+	9.83788i	−1.13514	+	0.929593i
$113$	15.6907	−	9.05906i	1.47606	−	0.852205i	0.476426	−	0.879214i	$-0.341932\pi$
$113$	15.6907	−	9.05906i	1.47606	−	0.852205i	0.999635	+	0.0270099i	$0.00859855\pi$
$114$	14.4074	−	5.75628i	1.34937	−	0.539125i
$115$	−13.7592	−	7.94390i	−1.28306	−	0.740773i
$116$	−0.701769	+	0.485156i	−0.0651576	+	0.0450456i
$117$	−6.04831	−	2.33389i	−0.559166	−	0.215768i
$118$	16.9946	−	0.691097i	1.56448	−	0.0636207i
$119$	−2.68671			−0.246290
$120$	−12.7716	−	8.47389i	−1.16588	−	0.773557i
$121$	0.638850	−	1.10652i	0.0580772	−	0.100593i
$122$	−5.06971	+	9.66813i	−0.458990	+	0.875311i
$123$	0.166482	−	0.893889i	0.0150112	−	0.0805993i
$124$	−12.3121	+	8.51179i	−1.10566	+	0.764381i
$125$			0.662184i			0.0592276i
$126$	−10.8543	−	12.3864i	−0.966979	−	1.10347i
$127$	−15.7761	+	9.10831i	−1.39990	+	0.808232i	−0.994382	−	0.105855i	$-0.966242\pi$
$127$	−15.7761	+	9.10831i	−1.39990	+	0.808232i	−0.405518	+	0.914087i	$0.632909\pi$
$128$	−10.8589	+	3.17554i	−0.959801	+	0.280681i
$129$	2.96165	+	2.53397i	0.260759	+	0.223104i
$130$	−8.46786	−	4.44032i	−0.742681	−	0.389442i
$131$	6.59829			0.576495			0.288248	−	0.957556i	$-0.406927\pi$
$131$	6.59829			0.576495			0.288248	+	0.957556i	$0.406927\pi$
$132$	10.7442	+	1.10894i	0.935163	+	0.0965205i
$133$	24.5872			2.13198
$134$	−11.4506	−	1.69848i	−0.989177	−	0.146726i
$135$	8.53056	−	13.8389i	0.734194	−	1.19106i
$136$	−1.80180	−	0.765336i	−0.154503	−	0.0656270i
$137$			4.26431i			0.364324i	0.983268	+	0.182162i	$0.0583096\pi$
$137$			4.26431i			0.364324i	−0.983268	+	0.182162i	$0.941690\pi$
$138$	−4.61511	−	11.5512i	−0.392864	−	0.983299i
$139$		−	17.5185i		−	1.48590i	−0.669346	−	0.742951i	$-0.733426\pi$
$139$		−	17.5185i		−	1.48590i	0.669346	−	0.742951i	$-0.266574\pi$
$140$	−13.8129	−	19.9800i	−1.16740	−	1.68862i
$141$	1.84449	+	0.343526i	0.155334	+	0.0289301i
$142$	5.96359	+	9.42301i	0.500453	+	0.790761i
$143$	6.73811			0.563469
$144$	−3.75089	−	11.3987i	−0.312574	−	0.949893i
$145$	−0.667295	−	1.15579i	−0.0554158	−	0.0959830i
$146$	1.76006	−	3.35651i	0.145664	−	0.277787i
$147$	−4.65363	−	13.1781i	−0.383825	−	1.08691i
$148$	−7.36419	+	15.5491i	−0.605333	+	1.27813i
$149$		−	12.6760i		−	1.03846i	−0.854634	−	0.519230i	$-0.826219\pi$
$149$		−	12.6760i		−	1.03846i	0.854634	−	0.519230i	$-0.173781\pi$
$150$	7.25677	−	9.21460i	0.592513	−	0.752369i
$151$	15.1657	+	8.75591i	1.23417	+	0.712546i	0.967896	−	0.251352i	$-0.0808753\pi$
$151$	15.1657	+	8.75591i	1.23417	+	0.712546i	0.266270	+	0.963898i	$0.414209\pi$
$152$	16.4890	+	7.00391i	1.33744	+	0.568092i
$153$	0.747493	−	1.93714i	0.0604312	−	0.156609i
$154$	15.1597	+	7.94933i	1.22160	+	0.640575i
$155$	−11.7073	−	20.2776i	−0.940353	−	1.62874i
$156$	−3.05758	−	6.83300i	−0.244803	−	0.547078i
$157$	−8.31353	+	14.3995i	−0.663492	+	1.14920i	0.316200	+	0.948693i	$0.397593\pi$
$157$	−8.31353	+	14.3995i	−0.663492	+	1.14920i	−0.979692	+	0.200509i	$0.935740\pi$
$158$	−17.5636	+	11.1156i	−1.39729	+	0.884307i
$159$	15.0453	+	12.8727i	1.19317	+	1.02087i
$160$	−3.57187	−	17.3340i	−0.282381	−	1.37038i
$161$		−	19.7128i		−	1.55359i
$162$	11.9506	−	4.37992i	0.938926	−	0.344119i
$163$	−9.04496	+	5.22211i	−0.708456	+	0.409027i	−0.810489	−	0.585754i	$-0.800799\pi$
$163$	−9.04496	+	5.22211i	−0.708456	+	0.409027i	0.102033	+	0.994781i	$0.467465\pi$
$164$	0.863632	−	0.597058i	0.0674384	−	0.0466224i
$165$	−3.09371	+	16.6110i	−0.240845	+	1.29316i
$166$	7.74667	−	14.7732i	0.601258	−	1.14662i
$167$	1.48946	+	2.57983i	0.115258	+	0.199633i	0.917883	−	0.396851i	$-0.129897\pi$
$167$	1.48946	+	2.57983i	0.115258	+	0.199633i	−0.802625	+	0.596484i	$0.796564\pi$
$168$	1.18220	−	18.9804i	0.0912086	−	1.46437i
$169$	4.16505	+	7.21408i	0.320389	+	0.554929i
$170$	1.42214	−	2.71207i	0.109073	−	0.208006i
$171$	−6.84061	+	17.7276i	−0.523115	+	1.35566i
$172$	0.365446	+	4.48586i	0.0278650	+	0.342044i
$173$	2.86458	+	1.65386i	0.217790	+	0.125741i	0.604926	−	0.796281i	$-0.293203\pi$
$173$	2.86458	+	1.65386i	0.217790	+	0.125741i	−0.387137	+	0.922022i	$0.626536\pi$
$174$	0.149418	−	1.03415i	0.0113274	−	0.0783984i
$175$	16.0974	−	9.29385i	1.21685	−	0.702549i
$176$	7.90217	+	9.64948i	0.595648	+	0.727357i
$177$	−13.5427	+	15.8283i	−1.01793	+	1.18973i
$178$	−0.626382	−	15.4032i	−0.0469493	−	1.15452i
$179$	12.0592			0.901347			0.450673	−	0.892689i	$-0.351184\pi$
$179$	12.0592			0.901347			0.450673	+	0.892689i	$0.351184\pi$
$180$	18.2488	−	4.40037i	1.36018	−	0.327984i
$181$	3.17676	+	5.50231i	0.236127	+	0.408983i	0.959600	−	0.281369i	$-0.0907886\pi$
$181$	3.17676	+	5.50231i	0.236127	+	0.408983i	−0.723473	+	0.690353i	$0.757455\pi$
$182$	−0.482035	−	11.8536i	−0.0357308	−	0.878646i
$183$	−4.45203	−	12.6072i	−0.329103	−	0.931951i
$184$	5.61540	−	13.2201i	0.413973	−	0.974601i
$185$	−23.3081	−	13.4569i	−1.71364	−	0.989372i
$186$	2.62146	−	18.1435i	0.192215	−	1.33035i
$187$			2.15807i			0.157814i
$188$	1.23199	+	1.78206i	0.0898524	+	0.129970i
$189$	20.1624	+	0.580967i	1.46660	+	0.0422591i
$190$	−13.0146	+	24.8193i	−0.944175	+	1.80058i
$191$	−3.45902	+	5.99121i	−0.250286	+	0.433508i	−0.963605	−	0.267332i	$-0.913858\pi$
$191$	−3.45902	+	5.99121i	−0.250286	+	0.433508i	0.713318	+	0.700840i	$0.247191\pi$
$192$	6.19957	−	12.3921i	0.447416	−	0.894326i
$193$	6.94511			0.499920			0.249960	−	0.968256i	$-0.419582\pi$
$193$	6.94511			0.499920			0.249960	+	0.968256i	$0.419582\pi$
$194$	−5.58424	+	10.6494i	−0.400925	+	0.764580i
$195$	11.0421	−	3.89932i	0.790738	−	0.279236i
$196$	6.90742	−	14.5847i	0.493387	−	1.04176i
$197$	23.2985	−	13.4514i	1.65995	−	0.958372i	0.687214	−	0.726455i	$-0.258833\pi$
$197$	23.2985	−	13.4514i	1.65995	−	0.958372i	0.972735	−	0.231918i	$-0.0745000\pi$
$198$	−9.94924	+	8.71860i	−0.707062	+	0.619604i
$199$	10.4850	+	6.05355i	0.743265	+	0.429124i	0.823255	−	0.567671i	$-0.192155\pi$
$199$	10.4850	+	6.05355i	0.743265	+	0.429124i	−0.0799900	+	0.996796i	$0.525489\pi$
$200$	13.4429	−	1.64727i	0.950559	−	0.116480i
$201$	11.0670	−	8.86123i	0.780606	−	0.625023i
$202$	11.6761	−	7.38952i	0.821529	−	0.519925i
$203$	0.827948	−	1.43405i	0.0581105	−	0.100650i
$204$	2.18846	−	0.979277i	0.153223	−	0.0685631i
$205$	0.821206	+	1.42237i	0.0573555	+	0.0993427i
$206$	−6.17147	+	3.90577i	−0.429987	+	0.272128i
$207$	14.2131	+	5.48448i	0.987881	+	0.381198i
$208$	3.05334	−	8.08675i	0.211711	−	0.560715i
$209$		−	19.7494i		−	1.36609i
$210$	29.4431	+	4.25408i	2.03177	+	0.293559i
$211$	12.7723	+	7.37411i	0.879284	+	0.507655i	0.870422	−	0.492306i	$-0.163846\pi$
$211$	12.7723	+	7.37411i	0.879284	+	0.507655i	0.00886188	+	0.999961i	$0.497179\pi$
$212$	1.85649	+	22.7884i	0.127504	+	1.56511i
$213$	−13.4269	−	2.50070i	−0.919999	−	0.171345i
$214$	4.47848	−	0.182121i	0.306142	−	0.0124495i
$215$	−7.04056			−0.480162
$216$	13.3561	+	6.13307i	0.908768	+	0.417303i
$217$	14.5259	−	25.1595i	0.986080	−	1.70794i
$218$	−10.1716	+	0.413637i	−0.688910	+	0.0280151i
$219$	1.54562	+	4.37687i	0.104443	+	0.295762i
$220$	−16.0487	+	11.0950i	−1.08200	+	0.748026i
$221$	1.29528	−	0.747833i	0.0871303	−	0.0503047i
$222$	−7.81797	−	19.5676i	−0.524707	−	1.31329i
$223$		−	9.96923i		−	0.667589i	−0.942646	−	0.333794i	$-0.891671\pi$
$223$		−	9.96923i		−	0.667589i	0.942646	−	0.333794i	$-0.108329\pi$
$224$	16.4099	−	14.5917i	1.09643	−	0.974948i
$225$	2.22234	+	14.1921i	0.148156	+	0.946140i
$226$	−21.6512	+	13.7025i	−1.44022	+	0.911476i
$227$	1.03687	+	1.79591i	0.0688194	+	0.119199i	0.898382	−	0.439215i	$-0.144743\pi$
$227$	1.03687	+	1.79591i	0.0688194	+	0.119199i	−0.829562	+	0.558414i	$0.811410\pi$
$228$	−20.0275	+	8.96177i	−1.32635	+	0.593507i
$229$	6.22625	−	10.7842i	0.411442	−	0.712638i	−0.583606	−	0.812037i	$-0.698359\pi$
$229$	6.22625	−	10.7842i	0.411442	−	0.712638i	0.995048	+	0.0993988i	$0.0316920\pi$
$230$	19.8989	+	10.4345i	1.31210	+	0.688028i
$231$	−19.7682	+	6.98080i	−1.30065	+	0.459303i
$232$	0.963754	−	0.725873i	0.0632735	−	0.0476559i
$233$	−14.0961	+	8.13841i	−0.923469	+	0.533165i	−0.884740	−	0.466085i	$-0.845664\pi$
$233$	−14.0961	+	8.13841i	−0.923469	+	0.533165i	−0.0387288	+	0.999250i	$0.512331\pi$
$234$	8.68065	+	2.95034i	0.567472	+	0.192870i
$235$	−2.93498	+	1.69451i	−0.191457	+	0.110538i
$236$	−23.9744	+	1.95310i	−1.56060	+	0.127136i
$237$	4.66107	−	25.0266i	0.302769	−	1.62565i
$238$	3.79644	−	0.154385i	0.246087	−	0.0100073i
$239$	−7.67616	−	13.2955i	−0.496530	−	0.860015i	0.503462	−	0.864017i	$-0.332059\pi$
$239$	−7.67616	−	13.2955i	−0.496530	−	0.860015i	−0.999992	+	0.00400264i	$0.998726\pi$
$240$	18.5338	+	11.2401i	1.19635	+	0.725546i
$241$	−25.6934			−1.65505			−0.827527	−	0.561426i	$-0.810253\pi$
$241$	−25.6934			−1.65505			−0.827527	+	0.561426i	$0.810253\pi$
$242$	−0.839140	+	1.60027i	−0.0539420	+	0.102869i
$243$	−6.02843	+	14.3756i	−0.386724	+	0.922195i
$244$	6.60817	−	13.9528i	0.423045	−	0.893238i
$245$	21.8623	+	12.6222i	1.39673	+	0.806405i
$246$	−0.183882	+	1.27267i	−0.0117239	+	0.0811426i
$247$	−11.8537	+	6.84372i	−0.754231	+	0.435456i
$248$	16.9085	−	12.7350i	1.07369	−	0.808676i
$249$	6.80283	+	19.2642i	0.431112	+	1.22082i
$250$	−0.0380508	−	0.935697i	−0.00240655	−	0.0591787i
$251$	9.37795	−	16.2431i	0.591931	−	1.02525i	−0.402041	−	0.915621i	$-0.631699\pi$
$251$	9.37795	−	16.2431i	0.591931	−	1.02525i	0.993972	−	0.109633i	$-0.0349674\pi$
$252$	16.0494	+	16.8788i	1.01102	+	1.06327i
$253$	−15.8341			−0.995482
$254$	21.7689	−	13.7770i	1.36590	−	0.864446i
$255$	1.24887	+	3.53653i	0.0782071	+	0.221466i
$256$	15.1617	−	5.11117i	0.947604	−	0.319448i
$257$	−3.25613	+	1.87993i	−0.203112	+	0.117267i	−0.598106	−	0.801417i	$-0.704080\pi$
$257$	−3.25613	+	1.87993i	−0.203112	+	0.117267i	0.394994	+	0.918684i	$0.370747\pi$
$258$	−4.33055	−	3.41044i	−0.269608	−	0.212325i
$259$		−	33.3934i		−	2.07497i
$260$	12.2206	+	5.78779i	0.757891	+	0.358943i
$261$	0.803610	+	0.995936i	0.0497422	+	0.0616469i
$262$	−9.32368	+	0.379155i	−0.576019	+	0.0234243i
$263$	2.39264			0.147537			0.0737683	−	0.997275i	$-0.476497\pi$
$263$	2.39264			0.147537			0.0737683	+	0.997275i	$0.476497\pi$
$264$	−15.2458	−	0.949587i	−0.938312	−	0.0584431i
$265$	−35.7664			−2.19711
$266$	−34.7428	+	1.41284i	−2.13022	+	0.0866270i
$267$	14.3462	+	12.2745i	0.877970	+	0.751188i
$268$	16.2778	+	1.74205i	0.994322	+	0.106413i
$269$			11.6122i			0.708007i	0.935244	+	0.354003i	$0.115180\pi$
$269$			11.6122i			0.708007i	−0.935244	+	0.354003i	$0.884820\pi$
$270$	−11.2589	+	20.0452i	−0.685192	+	1.21991i
$271$			27.2998i			1.65835i	0.558992	+	0.829173i	$0.311188\pi$
$271$			27.2998i			1.65835i	−0.558992	+	0.829173i	$0.688812\pi$
$272$	2.59001	+	0.977919i	0.157042	+	0.0592950i
$273$	11.0401	+	9.44590i	0.668180	+	0.571692i
$274$	−0.245038	−	6.02566i	−0.0148033	−	0.364023i
$275$	−7.46518	−	12.9301i	−0.450167	−	0.779712i
$276$	7.18512	+	16.0571i	0.432493	+	0.966524i
$277$	−21.4347			−1.28789			−0.643945	−	0.765072i	$-0.722703\pi$
$277$	−21.4347			−1.28789			−0.643945	+	0.765072i	$0.722703\pi$
$278$	1.00666	+	24.7545i	0.0603754	+	1.48467i
$279$	14.0989	+	17.4731i	0.844078	+	1.04609i
$280$	20.6663	+	27.4390i	1.23505	+	1.63979i
$281$	−18.1809	−	10.4968i	−1.08458	−	0.626184i	−0.152453	−	0.988311i	$-0.548717\pi$
$281$	−18.1809	−	10.4968i	−1.08458	−	0.626184i	−0.932129	+	0.362127i	$0.882051\pi$
$282$	−2.62609	−	0.379429i	−0.156381	−	0.0225947i
$283$		−	17.0226i		−	1.01189i	−0.862565	−	0.505945i	$-0.831144\pi$
$283$		−	17.0226i		−	1.01189i	0.862565	−	0.505945i	$-0.168856\pi$
$284$	−8.96829	−	12.9725i	−0.532170	−	0.769774i
$285$	−11.4289	−	32.3642i	−0.676989	−	1.91709i
$286$	−9.52126	+	0.387189i	−0.563004	+	0.0228950i
$287$	−1.01891	+	1.76481i	−0.0601446	+	0.104173i
$288$	5.95518	+	15.8914i	0.350913	+	0.936408i
$289$	−8.26049	−	14.3076i	−0.485911	−	0.841622i
$290$	1.00933	+	1.59484i	0.0592700	+	0.0936521i
$291$	−4.90387	−	13.8867i	−0.287470	−	0.814055i
$292$	−2.29418	+	4.84404i	−0.134256	+	0.283476i
$293$		−	31.3841i		−	1.83348i	−0.399487	−	0.916739i	$-0.630812\pi$
$293$		−	31.3841i		−	1.83348i	0.399487	−	0.916739i	$-0.369188\pi$
$294$	7.33304	+	18.3539i	0.427672	+	1.07042i
$295$		−	37.6278i		−	2.19077i
$296$	9.51245	−	22.3948i	0.552900	−	1.30167i
$297$	0.466655	−	16.1952i	0.0270781	−	0.939741i
$298$	0.728397	+	17.9118i	0.0421949	+	1.03760i
$299$	5.48698	+	9.50372i	0.317320	+	0.549614i
$300$	−9.72465	+	13.4376i	−0.561453	+	0.775823i
$301$	−4.36780	−	7.56524i	−0.251756	−	0.436053i
$302$	−21.9329	−	11.5010i	−1.26210	−	0.661811i
$303$	−3.09863	+	16.6374i	−0.178012	+	0.955795i
$304$	−23.7022	−	8.94934i	−1.35942	−	0.513280i
$305$	20.9152	+	12.0754i	1.19760	+	0.691436i
$306$	−0.944928	+	2.78022i	−0.0540180	+	0.158935i
$307$	20.1002	+	11.6049i	1.14718	+	0.662325i	0.948199	−	0.317678i	$-0.102903\pi$
$307$	20.1002	+	11.6049i	1.14718	+	0.662325i	0.198982	+	0.980003i	$0.436237\pi$
$308$	−21.8781	−	10.3616i	−1.24662	−	0.590410i
$309$	1.63780	−	8.79380i	0.0931711	−	0.500262i
$310$	17.7082	+	27.9805i	1.00576	+	1.58919i
$311$	−11.2737			−0.639275			−0.319637	−	0.947540i	$-0.603561\pi$
$311$	−11.2737			−0.639275			−0.319637	+	0.947540i	$0.603561\pi$
$312$	4.71315	+	9.47965i	0.266830	+	0.536680i
$313$	−0.457922			−0.0258833			−0.0129416	−	0.999916i	$-0.504120\pi$
$313$	−0.457922			−0.0258833			−0.0129416	+	0.999916i	$0.504120\pi$
$314$	10.9200	−	20.8248i	0.616249	−	1.17521i
$315$	−28.3552	+	22.8795i	−1.59764	+	1.28912i
$316$	24.1795	−	16.7161i	1.36020	−	0.940352i
$317$	19.0349	+	10.9898i	1.06910	+	0.617248i	0.927937	−	0.372738i	$-0.121581\pi$
$317$	19.0349	+	10.9898i	1.06910	+	0.617248i	0.141168	+	0.989986i	$0.454914\pi$
$318$	−21.9994	−	17.3252i	−1.23367	−	0.971548i
$319$	−1.15188	−	0.665040i	−0.0644930	−	0.0372351i
$320$	6.04328	+	24.2885i	0.337830	+	1.35777i
$321$	−3.56881	+	4.17114i	−0.199192	+	0.232811i
$322$	1.13275	+	27.8551i	0.0631257	+	1.55231i
$323$	−2.19189	−	3.79647i	−0.121960	−	0.211241i
$324$	−16.6350	+	6.87574i	−0.924168	+	0.381986i
$325$	−5.17380	+	8.96128i	−0.286991	+	0.497082i
$326$	12.4809	−	7.89883i	0.691251	−	0.437476i
$327$	8.10559	−	9.47362i	0.448240	−	0.523892i
$328$	−1.18604	+	0.893296i	−0.0654883	+	0.0493240i
$329$	−3.64158	−	2.10247i	−0.200767	−	0.115913i
$330$	3.41704	−	23.6498i	0.188102	−	1.30188i
$331$	−2.10330	+	1.21434i	−0.115608	+	0.0667462i	−0.556689	−	0.830721i	$-0.687928\pi$
$331$	−2.10330	+	1.21434i	−0.115608	+	0.0667462i	0.441081	+	0.897467i	$0.354595\pi$
$332$	−10.0975	+	21.3203i	−0.554172	+	1.17011i
$333$	24.0769	+	9.29067i	1.31941	+	0.509126i
$334$	−2.25292	−	3.55982i	−0.123274	−	0.194785i
$335$	−4.78369	+	25.1582i	−0.261361	+	1.37454i
$336$	−0.579839	+	26.8881i	−0.0316328	+	1.46686i
$337$	9.53217	−	16.5102i	0.519250	−	0.899368i	−0.480499	−	0.876995i	$-0.659545\pi$
$337$	9.53217	−	16.5102i	0.519250	−	0.899368i	0.999750	−	0.0223731i	$-0.00712216\pi$
$338$	−6.29995	−	9.95449i	−0.342672	−	0.541453i
$339$	5.74584	−	30.8510i	0.312071	−	1.67560i
$340$	−1.85370	+	3.91400i	−0.100531	+	0.212266i
$341$	−20.2091	−	11.6677i	−1.09438	−	0.631843i
$342$	8.64743	−	25.4429i	0.467599	−	1.37580i
$343$			4.14910i			0.224030i
$344$	−0.774162	−	6.31773i	−0.0417400	−	0.340629i
$345$	−25.9481	+	9.16315i	−1.39700	+	0.493327i
$346$	−4.14281	−	2.17238i	−0.222719	−	0.116788i
$347$	15.2394	+	26.3954i	0.818093	+	1.41698i	0.907086	+	0.420946i	$0.138302\pi$
$347$	15.2394	+	26.3954i	0.818093	+	1.41698i	−0.0889925	+	0.996032i	$0.528365\pi$
$348$	−0.151710	+	1.46988i	−0.00813252	+	0.0787940i
$349$	−2.36348			−0.126514			−0.0632570	−	0.997997i	$-0.520149\pi$
$349$	−2.36348			−0.126514			−0.0632570	+	0.997997i	$0.520149\pi$
$350$	−22.2123	+	14.0576i	−1.18730	+	0.751412i
$351$	−9.88215	+	5.33201i	−0.527470	+	0.284602i
$352$	−11.7206	−	13.1811i	−0.624711	−	0.702554i
$353$	2.25672	+	1.30292i	0.120113	+	0.0693474i	0.558853	−	0.829267i	$-0.311242\pi$
$353$	2.25672	+	1.30292i	0.120113	+	0.0693474i	−0.438740	+	0.898614i	$0.644575\pi$
$354$	18.2269	−	23.1444i	0.968746	−	1.23011i
$355$	21.3652	−	12.3352i	1.13395	−	0.654684i
$356$	1.77021	+	21.7294i	0.0938211	+	1.15166i
$357$	−3.02531	+	3.53592i	−0.160117	+	0.187140i
$358$	−17.0402	+	0.692953i	−0.900602	+	0.0366237i
$359$	−6.06613			−0.320158			−0.160079	−	0.987104i	$-0.551175\pi$
$359$	−6.06613			−0.320158			−0.160079	+	0.987104i	$0.551175\pi$
$360$	−25.5335	+	7.26654i	−1.34573	+	0.382980i
$361$	10.5589	+	18.2886i	0.555733	+	0.962557i
$362$	−4.80508	−	7.59247i	−0.252550	−	0.399051i
$363$	−0.736901	−	2.08675i	−0.0386773	−	0.109526i
$364$	1.36228	+	16.7220i	0.0714027	+	0.876469i
$365$	−7.26119	−	4.19225i	−0.380068	−	0.219432i
$366$	7.01536	+	17.5587i	0.366699	+	0.917809i
$367$	−26.8948	+	15.5277i	−1.40390	+	0.810541i	−0.994790	−	0.101946i	$-0.967493\pi$
$367$	−26.8948	+	15.5277i	−1.40390	+	0.810541i	−0.409107	+	0.912486i	$0.634160\pi$
$368$	−7.17516	+	19.0033i	−0.374031	+	0.990616i
$369$	−0.988962	−	1.22565i	−0.0514833	−	0.0638047i
$370$	33.7086	+	17.6759i	1.75243	+	0.918926i
$371$	−22.1886	−	38.4318i	−1.15198	−	1.99528i
$372$	−2.66167	+	25.7882i	−0.138001	+	1.33706i
$373$	8.51305	+	14.7450i	0.440789	+	0.763469i	0.997748	−	0.0670709i	$-0.0213654\pi$
$373$	8.51305	+	14.7450i	0.440789	+	0.763469i	−0.556959	+	0.830540i	$0.688032\pi$
$374$	−0.124008	−	3.04945i	−0.00641231	−	0.157683i
$375$	0.871485	+	0.745639i	0.0450033	+	0.0385046i
$376$	−1.84326	−	2.44733i	−0.0950591	−	0.126211i
$377$			0.921821i			0.0474762i
$378$	−28.5237	+	0.337650i	−1.46710	+	0.0173668i
$379$	2.67149	+	1.54238i	0.137225	+	0.0792269i	0.567041	−	0.823690i	$-0.308088\pi$
$379$	2.67149	+	1.54238i	0.137225	+	0.0792269i	−0.429816	+	0.902917i	$0.641422\pi$
$380$	16.9640	−	35.8186i	0.870234	−	1.83746i
$381$	−5.77708	+	31.0187i	−0.295969	+	1.58914i
$382$	4.54349	−	8.66461i	0.232465	−	0.443320i
$383$	−4.05625	+	7.02563i	−0.207265	+	0.358993i	−0.950852	−	0.309646i	$-0.899789\pi$
$383$	−4.05625	+	7.02563i	−0.207265	+	0.358993i	0.743587	+	0.668639i	$0.233123\pi$
$384$	−8.04820	+	17.8669i	−0.410708	+	0.911767i
$385$	18.9343	−	32.7952i	0.964981	−	1.67140i
$386$	−9.81376	+	0.399084i	−0.499507	+	0.0203129i
$387$	6.66981	−	1.04443i	0.339045	−	0.0530911i
$388$	7.27885	−	15.3689i	0.369528	−	0.780239i
$389$	10.6702	+	6.16044i	0.541001	+	0.312347i	0.745484	−	0.666523i	$-0.232218\pi$
$389$	10.6702	+	6.16044i	0.541001	+	0.312347i	−0.204484	+	0.978870i	$0.565552\pi$
$390$	−15.3789	+	6.14442i	−0.778739	+	0.311135i
$391$	−3.04383	+	1.75736i	−0.153933	+	0.0888734i
$392$	−8.92242	+	21.0057i	−0.450650	+	1.06095i
$393$	7.42987	−	8.68385i	0.374787	−	0.438042i
$394$	−32.1489	+	20.3462i	−1.61964	+	1.02503i
$395$	22.9916	+	39.8227i	1.15683	+	2.00370i
$396$	13.5577	−	12.8915i	0.681302	−	0.647822i
$397$	16.0319			0.804616			0.402308	−	0.915504i	$-0.368208\pi$
$397$	16.0319			0.804616			0.402308	+	0.915504i	$0.368208\pi$
$398$	−15.1637	−	7.95144i	−0.760088	−	0.398570i
$399$	27.6859	−	32.3586i	1.38603	−	1.61996i
$400$	−18.9008	+	3.10013i	−0.945042	+	0.155007i
$401$			28.5086i			1.42365i	0.702357	+	0.711825i	$0.252131\pi$
$401$			28.5086i			1.42365i	−0.702357	+	0.711825i	$0.747869\pi$
$402$	−15.1290	+	13.1573i	−0.754566	+	0.656225i
$403$			16.1728i			0.805626i
$404$	−16.0743	+	11.1127i	−0.799725	+	0.552876i
$405$	−8.60737	−	26.8099i	−0.427704	−	1.33219i
$406$	−1.08752	+	2.07395i	−0.0539729	+	0.102928i
$407$	−26.8229			−1.32956
$408$	−3.03612	+	1.50952i	−0.150311	+	0.0747323i
$409$	13.8958	+	24.0683i	0.687106	+	1.19010i	0.972770	+	0.231772i	$0.0744523\pi$
$409$	13.8958	+	24.0683i	0.687106	+	1.19010i	−0.285665	+	0.958330i	$0.592214\pi$
$410$	−1.24213	−	1.96269i	−0.0613447	−	0.0969302i
$411$	5.61215	+	4.80174i	0.276827	+	0.236852i
$412$	8.49614	−	5.87366i	0.418575	−	0.289375i
$413$	40.4319	−	23.3434i	1.98953	−	1.14865i
$414$	−20.3989	−	6.93310i	−1.00255	−	0.340743i
$415$	−31.9591	−	18.4516i	−1.56881	−	0.905753i
$416$	−3.84983	+	11.6024i	−0.188753	+	0.568854i
$417$	−23.0557	−	19.7264i	−1.12904	−	0.966004i
$418$	1.13485	+	27.9068i	0.0555073	+	1.36496i
$419$	−7.89132	+	13.6682i	−0.385516	+	0.667734i	−0.991841	−	0.127483i	$-0.959310\pi$
$419$	−7.89132	+	13.6682i	−0.385516	+	0.667734i	0.606324	+	0.795218i	$0.292643\pi$
$420$	−41.8489	−	4.31933i	−2.04202	−	0.210762i
$421$	−4.46753	+	7.73800i	−0.217734	+	0.377127i	−0.954115	−	0.299441i	$-0.903200\pi$
$421$	−4.46753	+	7.73800i	−0.217734	+	0.377127i	0.736381	+	0.676567i	$0.236533\pi$
$422$	−18.4716	−	9.68603i	−0.899185	−	0.471509i
$423$	2.52906	−	2.04067i	0.122967	−	0.0992206i
$424$	−3.93278	−	32.0944i	−0.190993	−	1.55864i
$425$	−2.87010	−	1.65705i	−0.139220	−	0.0803789i
$426$	19.1166	+	2.76205i	0.926201	+	0.133822i
$427$			29.9652i			1.45012i
$428$	−6.31783	+	0.514690i	−0.305384	+	0.0248785i
$429$	7.58731	−	8.86787i	0.366319	−	0.428145i
$430$	9.94863	−	0.404569i	0.479765	−	0.0195100i
$431$	0.542380	+	0.939429i	0.0261255	+	0.0452507i	0.878793	−	0.477204i	$-0.158350\pi$
$431$	0.542380	+	0.939429i	0.0261255	+	0.0452507i	−0.852667	+	0.522455i	$0.825016\pi$
$432$	−19.2252	−	7.89883i	−0.924973	−	0.380033i
$433$	5.54118	+	9.59761i	0.266292	+	0.461232i	0.967901	−	0.251330i	$-0.0808680\pi$
$433$	5.54118	+	9.59761i	0.266292	+	0.461232i	−0.701609	+	0.712562i	$0.747535\pi$
$434$	−19.0800	+	36.3863i	−0.915869	+	1.74660i
$435$	−2.27250	−	0.423241i	−0.108958	−	0.0202929i
$436$	14.3492	−	1.16898i	0.687203	−	0.0559838i
$437$	27.8554	−	16.0823i	1.33250	−	0.769321i
$438$	−2.43554	−	6.09591i	−0.116375	−	0.291274i
$439$	7.19094	+	4.15169i	0.343205	+	0.198150i	0.661688	−	0.749779i	$-0.269840\pi$
$439$	7.19094	+	4.15169i	0.343205	+	0.198150i	−0.318483	+	0.947928i	$0.603173\pi$
$440$	22.0400	−	16.6000i	1.05072	−	0.791372i
$441$	−22.5835	−	8.71440i	−1.07541	−	0.414972i
$442$	−1.78732	+	1.13115i	−0.0850143	+	0.0538034i
$443$	8.71175	+	15.0892i	0.413908	+	0.716909i	0.995313	−	0.0967049i	$-0.0308303\pi$
$443$	8.71175	+	15.0892i	0.413908	+	0.716909i	−0.581405	+	0.813614i	$0.697497\pi$
$444$	12.1715	+	27.2006i	0.577636	+	1.29088i
$445$	−34.1043			−1.61670
$446$	0.572858	+	14.0870i	0.0271256	+	0.667038i
$447$	−16.6826	−	14.2736i	−0.789061	−	0.675117i
$448$	−22.3495	+	21.5617i	−1.05591	+	1.01869i
$449$	2.93596	−	1.69508i	0.138557	−	0.0799957i	−0.429119	−	0.903248i	$-0.641176\pi$
$449$	2.93596	−	1.69508i	0.138557	−	0.0799957i	0.567676	+	0.823252i	$0.307843\pi$
$450$	−3.95578	−	19.9264i	−0.186477	−	0.939339i
$451$	1.41756	+	0.818431i	0.0667505	+	0.0385384i
$452$	29.8067	−	20.6064i	1.40199	−	0.969243i
$453$	28.6005	−	10.0998i	1.34377	−	0.474529i
$454$	−1.56834	−	2.47812i	−0.0736059	−	0.116304i
$455$	−26.2451			−1.23039
$456$	27.7848	−	13.8142i	1.30114	−	0.646910i
$457$	−2.42171	−	4.19452i	−0.113283	−	0.196211i	0.803809	−	0.594887i	$-0.202803\pi$
$457$	−2.42171	−	4.19452i	−0.113283	−	0.196211i	−0.917092	+	0.398676i	$0.869470\pi$
$458$	−8.17828	+	15.5963i	−0.382146	+	0.728768i
$459$	−1.70773	−	3.16504i	−0.0797098	−	0.147731i
$460$	−28.7177	−	13.6009i	−1.33897	−	0.634146i
$461$		−	31.3995i		−	1.46242i	−0.682153	−	0.731210i	$-0.738956\pi$
$461$		−	31.3995i		−	1.46242i	0.682153	−	0.731210i	$-0.261044\pi$
$462$	27.5322	−	11.0001i	1.28091	−	0.511772i
$463$	−3.41494	−	1.97161i	−0.158706	−	0.0916287i	0.418544	−	0.908197i	$-0.362541\pi$
$463$	−3.41494	−	1.97161i	−0.158706	−	0.0916287i	−0.577249	+	0.816568i	$0.695874\pi$
$464$	−1.32012	+	1.08107i	−0.0612849	+	0.0501875i
$465$	−39.8697	−	7.42552i	−1.84891	−	0.344350i
$466$	19.4508	−	12.3099i	0.901043	−	0.570247i
$467$	−4.18750	+	7.25297i	−0.193774	+	0.335627i	−0.946498	−	0.322709i	$-0.895406\pi$
$467$	−4.18750	+	7.25297i	−0.193774	+	0.335627i	0.752724	+	0.658337i	$0.228740\pi$
$468$	−12.4357	−	3.67015i	−0.574840	−	0.169653i
$469$	−30.0008	+	10.4674i	−1.38531	+	0.483338i
$470$	4.04989	−	2.56307i	0.186807	−	0.118226i
$471$	9.58950	+	27.1555i	0.441861	+	1.25126i
$472$	33.7647	−	4.13746i	1.55415	−	0.190442i
$473$	−6.07670	+	3.50838i	−0.279407	+	0.161316i
$474$	−5.14821	+	35.6315i	−0.236465	+	1.63661i
$475$	26.2655	+	15.1644i	1.20514	+	0.695789i
$476$	−5.35568	+	0.436307i	−0.245477	+	0.0199981i
$477$	33.8829	−	5.30573i	1.55139	−	0.242933i
$478$	11.6108	+	18.3461i	0.531064	+	0.839129i
$479$	20.1456	−	34.8933i	0.920478	−	1.59431i	0.121802	−	0.992554i	$-0.461133\pi$
$479$	20.1456	−	34.8933i	0.920478	−	1.59431i	0.798677	−	0.601761i	$-0.205534\pi$
$480$	−26.8350	−	14.8178i	−1.22484	−	0.676336i
$481$	9.29490	+	16.0992i	0.423811	+	0.734062i
$482$	36.3059	−	1.47641i	1.65369	−	0.0672485i
$483$	−25.9436	−	22.1972i	−1.18048	−	1.01001i
$484$	1.09379	−	2.30948i	0.0497176	−	0.104976i
$485$	23.0379	+	13.3010i	1.04610	+	0.603966i
$486$	7.69239	−	20.6598i	0.348934	−	0.937147i
$487$	2.16926	+	1.25242i	0.0982986	+	0.0567527i	0.548343	−	0.836253i	$-0.315259\pi$
$487$	2.16926	+	1.25242i	0.0982986	+	0.0567527i	−0.450045	+	0.893006i	$0.648592\pi$
$488$	−8.53588	+	20.0957i	−0.386401	+	0.909690i
$489$	−3.31220	+	17.7841i	−0.149783	+	0.804226i
$490$	−31.6178	−	16.5795i	−1.42835	−	0.748986i
$491$	0.0937207			0.00422956			0.00211478	−	0.999998i	$-0.499327\pi$
$491$	0.0937207			0.00422956			0.00211478	+	0.999998i	$0.499327\pi$
$492$	0.186702	−	1.80891i	0.00841718	−	0.0815520i
$493$	−0.295239			−0.0132969
$494$	16.3565	−	10.3516i	0.735915	−	0.465742i
$495$	18.3777	+	22.7760i	0.826017	+	1.02371i
$496$	−23.1607	+	18.9668i	−1.03995	+	0.851634i
$497$	26.5089	+	15.3049i	1.18909	+	0.686519i
$498$	−10.7197	−	26.8303i	−0.480360	−	1.20229i
$499$	7.14838	+	4.12712i	0.320006	+	0.184755i	0.651395	−	0.758739i	$-0.274184\pi$
$499$	7.14838	+	4.12712i	0.320006	+	0.184755i	−0.331389	+	0.943494i	$0.607517\pi$
$500$	0.107535	+	1.32000i	0.00480912	+	0.0590320i
$501$	5.07243	+	0.944713i	0.226619	+	0.0422067i
$502$	−12.3181	+	23.4911i	−0.549784	+	1.04846i
$503$	10.2356	+	17.7285i	0.456381	+	0.790474i	0.998766	−	0.0496551i	$-0.0158122\pi$
$503$	10.2356	+	17.7285i	0.456381	+	0.790474i	−0.542386	+	0.840130i	$0.682479\pi$
$504$	−23.6484	−	22.9283i	−1.05338	−	1.02131i
$505$	−15.2846	−	26.4737i	−0.680156	−	1.17807i
$506$	22.3743	−	0.909869i	0.994660	−	0.0404486i
$507$	14.1843	+	2.64174i	0.629945	+	0.117324i
$508$	−29.9688	+	20.7184i	−1.32965	+	0.919231i
$509$		−	13.5810i		−	0.601967i	−0.953629	−	0.300983i	$-0.902685\pi$
$509$		−	13.5810i		−	0.601967i	0.953629	−	0.300983i	$-0.0973149\pi$
$510$	−1.96792	−	4.92551i	−0.0871411	−	0.218105i
$511$		−	10.4031i		−	0.460205i
$512$	−21.1304	+	8.09354i	−0.933841	+	0.357687i
$513$	15.6281	+	28.9645i	0.689997	+	1.27882i
$514$	4.49304	−	2.84353i	0.198179	−	0.125423i
$515$	8.07876	+	13.9928i	0.355993	+	0.616598i
$516$	6.31524	+	4.57026i	0.278013	+	0.201194i
$517$	−1.68878	+	2.92506i	−0.0742727	+	0.128644i
$518$	1.91887	+	47.1864i	0.0843104	+	2.07325i
$519$	5.40221	−	1.90770i	0.237131	−	0.0837388i
$520$	−17.6009	−	7.47618i	−0.771850	−	0.327852i
$521$			30.1476i			1.32079i	0.750918	+	0.660396i	$0.229611\pi$
$521$			30.1476i			1.32079i	−0.750918	+	0.660396i	$0.770389\pi$
$522$	−1.19277	−	1.36113i	−0.0522060	−	0.0595749i
$523$	−13.5204	−	7.80601i	−0.591206	−	0.341333i	0.174368	−	0.984681i	$-0.444212\pi$
$523$	−13.5204	−	7.80601i	−0.591206	−	0.341333i	−0.765574	+	0.643348i	$0.777545\pi$
$524$	13.1530	−	1.07153i	0.574592	−	0.0468098i
$525$	5.89476	−	31.6506i	0.257268	−	1.38134i
$526$	−3.38091	+	0.137487i	−0.147415	+	0.00599473i
$527$	−5.17980			−0.225636
$528$	21.5975	+	0.465749i	0.939912	+	0.0202691i
$529$	−1.39403	−	2.41453i	−0.0606099	−	0.104979i
$530$	50.5395	−	2.05523i	2.19530	−	0.0892734i
$531$	5.58186	+	35.6463i	0.242232	+	1.54692i
$532$	49.0120	−	3.99282i	2.12494	−	0.173111i
$533$		−	1.13444i		−	0.0491380i
$534$	−20.9771	−	16.5201i	−0.907768	−	0.714894i
$535$		−	9.91582i		−	0.428698i
$536$	−23.1013	−	1.52624i	−0.997825	−	0.0659233i
$537$	13.5790	−	15.8708i	0.585978	−	0.684877i
$538$	−0.667266	−	16.4085i	−0.0287679	−	0.707422i
$539$	25.1591			1.08368
$540$	14.7574	−	28.9717i	0.635059	−	1.24674i
$541$	15.1697			0.652197			0.326098	−	0.945336i	$-0.394266\pi$
$541$	15.1697			0.652197			0.326098	+	0.945336i	$0.394266\pi$
$542$	−1.56872	−	38.5759i	−0.0673822	−	1.65698i
$543$	10.8186	+	2.01491i	0.464270	+	0.0864679i
$544$	−3.71599	−	1.23302i	−0.159322	−	0.0528651i
$545$			22.5211i			0.964697i
$546$	−16.1430	−	12.7131i	−0.690857	−	0.544070i
$547$	−5.45750	+	3.15089i	−0.233346	+	0.134722i	−0.612115	−	0.790769i	$-0.709681\pi$
$547$	−5.45750	+	3.15089i	−0.233346	+	0.134722i	0.378769	+	0.925491i	$0.376348\pi$
$548$	0.692500	+	8.50045i	0.0295821	+	0.363121i
$549$	−21.6052	−	8.33687i	−0.922085	−	0.355809i
$550$	11.2916	+	17.8418i	0.481477	+	0.760777i
$551$	2.70185			0.115103
$552$	−11.0756	−	22.2766i	−0.471408	−	0.948153i
$553$	−28.5269	+	49.4101i	−1.21309	+	2.10113i
$554$	30.2883	−	1.23170i	1.28683	−	0.0523297i
$555$	−43.9559	+	15.5223i	−1.86582	+	0.658885i
$556$	−2.84491	−	34.9213i	−0.120651	−	1.48099i
$557$	−23.0824	+	13.3266i	−0.978031	+	0.564666i	−0.901675	−	0.432414i	$-0.857662\pi$
$557$	−23.0824	+	13.3266i	−0.978031	+	0.564666i	−0.0763557	+	0.997081i	$0.524328\pi$
$558$	−20.9264	−	23.8802i	−0.885885	−	1.01093i
$559$	4.21150	+	2.43151i	0.178127	+	0.102842i
$560$	−30.7791	−	37.5850i	−1.30066	−	1.58825i
$561$	2.84018	+	2.43005i	0.119913	+	0.102597i
$562$	26.2936	+	13.7877i	1.10913	+	0.581598i
$563$	26.4147			1.11325			0.556623	−	0.830765i	$-0.312097\pi$
$563$	26.4147			1.11325			0.556623	+	0.830765i	$0.312097\pi$
$564$	3.73258	+	0.385249i	0.157170	+	0.0162219i
$565$	28.3425	+	49.0906i	1.19238	+	2.06526i
$566$	0.978165	+	24.0538i	0.0411153	+	1.01106i
$567$	23.4680	−	25.8810i	0.985564	−	1.08690i
$568$	13.4180	+	17.8153i	0.563008	+	0.747515i
$569$	−37.3448	+	21.5610i	−1.56558	+	0.903885i	−0.568900	+	0.822406i	$0.692631\pi$
$569$	−37.3448	+	21.5610i	−1.56558	+	0.903885i	−0.996675	+	0.0814790i	$0.974036\pi$
$570$	18.0093	+	45.0754i	0.754326	+	1.88800i
$571$	31.9529	−	18.4480i	1.33719	−	0.772026i	0.350799	−	0.936451i	$-0.385910\pi$
$571$	31.9529	−	18.4480i	1.33719	−	0.772026i	0.986390	+	0.164425i	$0.0525768\pi$
$572$	13.4317	−	1.09423i	0.561609	−	0.0457522i
$573$	3.98992	+	11.2986i	0.166681	+	0.472006i
$574$	1.33836	−	2.55231i	0.0558621	−	0.106531i
$575$	12.1581	−	21.0584i	0.507027	−	0.878196i
$576$	−9.32811	−	22.1130i	−0.388671	−	0.921377i
$577$	−0.639070	−	1.10690i	−0.0266048	−	0.0460809i	0.852416	−	0.522863i	$-0.175136\pi$
$577$	−0.639070	−	1.10690i	−0.0266048	−	0.0460809i	−0.879021	+	0.476783i	$0.841803\pi$
$578$	12.4946	+	19.7426i	0.519707	+	0.821184i
$579$	7.82041	−	9.14030i	0.325005	−	0.379858i
$580$	−1.51788	−	2.19558i	−0.0630264	−	0.0911664i
$581$		−	45.7877i		−	1.89959i
$582$	7.72736	+	19.3408i	0.320309	+	0.801702i
$583$	−30.8699	+	17.8227i	−1.27850	+	0.738143i
$584$	2.96342	−	6.97668i	0.122627	−	0.288697i
$585$	7.30188	−	18.9229i	0.301896	−	0.782367i
$586$	1.80341	+	44.3471i	0.0744982	+	1.83196i
$587$	2.50375	−	4.33662i	0.103341	−	0.178991i	−0.809718	−	0.586819i	$-0.800380\pi$
$587$	2.50375	−	4.33662i	0.103341	−	0.178991i	0.913059	+	0.407827i	$0.133713\pi$
$588$	−11.4166	−	25.5135i	−0.470812	−	1.05216i
$589$	47.4025			1.95318
$590$	2.16219	+	53.1698i	0.0890160	+	2.18897i
$591$	8.53174	−	45.8093i	0.350949	−	1.88434i
$592$	−12.1547	+	32.1915i	−0.499554	+	1.32306i
$593$	−11.9436	−	6.89562i	−0.490463	−	0.283169i	0.234303	−	0.972164i	$-0.424719\pi$
$593$	−11.9436	−	6.89562i	−0.490463	−	0.283169i	−0.724767	+	0.688994i	$0.758052\pi$
$594$	0.271213	+	22.9114i	0.0111280	+	0.940065i
$595$		−	8.40573i		−	0.344601i
$596$	−2.05852	−	25.2683i	−0.0843202	−	1.03503i
$597$	19.7734	−	6.98265i	0.809272	−	0.285781i
$598$	−8.29945	−	13.1139i	−0.339390	−	0.536267i
$599$	−4.07814	−	7.06354i	−0.166628	−	0.288608i	0.770604	−	0.637314i	$-0.219955\pi$
$599$	−4.07814	−	7.06354i	−0.166628	−	0.288608i	−0.937232	+	0.348706i	$0.886621\pi$
$600$	12.9692	−	19.5468i	0.529466	−	0.797995i
$601$	5.19782	−	9.00289i	0.212024	−	0.367236i	−0.740324	−	0.672250i	$-0.765328\pi$
$601$	5.19782	−	9.00289i	0.212024	−	0.367236i	0.952348	+	0.305014i	$0.0986613\pi$
$602$	6.60661	+	10.4391i	0.269265	+	0.425464i
$603$	0.799714	−	24.5430i	0.0325669	−	0.999470i
$604$	31.6531	+	14.9912i	1.28795	+	0.609982i
$605$	3.46190	+	1.99873i	0.140746	+	0.0812598i
$606$	3.42248	−	23.6875i	0.139029	−	0.962238i
$607$	−38.6396	+	22.3086i	−1.56833	+	0.905479i	−0.571971	+	0.820273i	$0.693821\pi$
$607$	−38.6396	+	22.3086i	−1.56833	+	0.905479i	−0.996363	+	0.0852051i	$0.972845\pi$
$608$	34.0066	+	11.2838i	1.37915	+	0.457620i
$609$	−0.955022	−	2.70442i	−0.0386995	−	0.109589i
$610$	−30.2480	−	15.8613i	−1.22471	−	0.642203i
$611$	2.34085			0.0947006
$612$	1.17547	−	3.98288i	0.0475155	−	0.160998i
$613$	−9.56292	+	16.5635i	−0.386243	+	0.668992i	−0.991941	−	0.126703i	$-0.959561\pi$
$613$	−9.56292	+	16.5635i	−0.386243	+	0.668992i	0.605698	+	0.795695i	$0.292894\pi$
$614$	−29.0694	−	15.2432i	−1.17314	−	0.615165i
$615$	2.79665	+	0.520862i	0.112772	+	0.0210032i
$616$	31.5102	+	13.3843i	1.26958	+	0.539269i
$617$		−	41.1558i		−	1.65687i	−0.560085	−	0.828435i	$-0.689232\pi$
$617$		−	41.1558i		−	1.65687i	0.560085	−	0.828435i	$-0.310768\pi$
$618$	−1.80897	+	12.5201i	−0.0727674	+	0.503634i
$619$	−19.6667	−	11.3546i	−0.790471	−	0.456379i	0.0496572	−	0.998766i	$-0.484187\pi$
$619$	−19.6667	−	11.3546i	−0.790471	−	0.456379i	−0.840128	+	0.542388i	$0.817520\pi$
$620$	−26.6303	−	38.5202i	−1.06950	−	1.54701i
$621$	23.2224	−	12.5299i	0.931883	−	0.502806i
$622$	15.9303	−	0.647818i	0.638747	−	0.0259751i
$623$	−21.1575	−	36.6459i	−0.847657	−	1.46819i
$624$	−7.20462	−	13.1243i	−0.288416	−	0.525394i
$625$	−26.0135			−1.04054
$626$	0.647064	−	0.0263134i	0.0258619	−	0.00105169i
$627$	−25.9917	−	22.2384i	−1.03801	−	0.888115i
$628$	−14.2338	+	30.0539i	−0.567989	+	1.19928i
$629$	−5.15623	+	2.97695i	−0.205592	+	0.118699i
$630$	38.7525	−	33.9592i	1.54394	−	1.35297i
$631$	0.137790	+	0.0795528i	0.00548532	+	0.00316695i	0.502740	−	0.864438i	$-0.332325\pi$
$631$	0.137790	+	0.0795528i	0.00548532	+	0.00316695i	−0.497255	+	0.867605i	$0.665659\pi$
$632$	−33.2061	+	25.0100i	−1.32087	+	0.994843i
$633$	24.0869	−	8.50591i	0.957370	−	0.338079i
$634$	−27.5286	−	14.4353i	−1.09330	−	0.573298i
$635$	−28.4966	−	49.3575i	−1.13085	−	1.95869i
$636$	32.0817	+	23.2171i	1.27212	+	0.920619i
$637$	−8.71836	−	15.1007i	−0.345434	−	0.598310i
$638$	1.66588	+	0.873541i	0.0659527	+	0.0345838i
$639$	−18.4102	+	14.8550i	−0.728298	+	0.587656i
$640$	−9.93511	−	33.9735i	−0.392720	−	1.34292i
$641$	−22.2717	+	12.8586i	−0.879681	+	0.507884i	−0.870553	−	0.492074i	$-0.836239\pi$
$641$	−22.2717	+	12.8586i	−0.879681	+	0.507884i	−0.00912793	+	0.999958i	$0.502906\pi$
$642$	4.80321	−	6.09909i	0.189568	−	0.240712i
$643$		−	28.6540i		−	1.13000i	−0.825090	−	0.565001i	$-0.808876\pi$
$643$		−	28.6540i		−	1.13000i	0.825090	−	0.565001i	$-0.191124\pi$
$644$	−3.20126	−	39.2955i	−0.126147	−	1.54846i
$645$	−7.92788	+	9.26591i	−0.312160	+	0.364845i
$646$	3.31540	+	5.23864i	0.130443	+	0.206111i
$647$	6.31604	−	10.9397i	0.248309	−	0.430084i	−0.714748	−	0.699382i	$-0.753458\pi$
$647$	6.31604	−	10.9397i	0.248309	−	0.430084i	0.963057	+	0.269298i	$0.0867918\pi$
$648$	23.1110	−	10.6716i	0.907884	−	0.419221i
$649$	−18.7503	−	32.4765i	−0.736014	−	1.27481i
$650$	6.79587	−	12.9600i	0.266556	−	0.508333i
$651$	−16.7553	−	47.4475i	−0.656693	−	1.85962i
$652$	−17.1822	+	11.8786i	−0.672905	+	0.465201i
$653$	−14.6952	−	8.48427i	−0.575067	−	0.332015i	0.184104	−	0.982907i	$-0.441062\pi$
$653$	−14.6952	−	8.48427i	−0.575067	−	0.332015i	−0.759170	+	0.650892i	$0.774395\pi$
$654$	−10.9092	+	13.8524i	−0.426583	+	0.541672i
$655$			20.6436i			0.806613i
$656$	1.62460	−	1.33042i	0.0634301	−	0.0519442i
$657$	7.50071	+	2.89433i	0.292631	+	0.112919i
$658$	5.26654	+	2.76163i	0.205311	+	0.107660i
$659$	13.0433	+	22.5916i	0.508094	+	0.880045i	0.999956	+	0.00937191i	$0.00298321\pi$
$659$	13.0433	+	22.5916i	0.508094	+	0.880045i	−0.491862	+	0.870673i	$0.663683\pi$
$660$	−3.46945	+	33.6147i	−0.135048	+	1.30845i
$661$	46.5683			1.81130			0.905649	−	0.424028i	$-0.139384\pi$
$661$	46.5683			1.81130			0.905649	+	0.424028i	$0.139384\pi$
$662$	2.90228	−	1.83678i	0.112800	−	0.0713884i
$663$	0.474324	−	2.54678i	0.0184212	−	0.0989085i
$664$	13.0431	−	30.7069i	0.506170	−	1.19166i
$665$			76.9243i			2.98300i
$666$	−34.5557	−	11.7446i	−1.33901	−	0.455095i
$667$		−	2.16622i		−	0.0838763i
$668$	3.38804	+	4.90073i	0.131087	+	0.189615i
$669$	−13.1203	−	11.2256i	−0.507259	−	0.434009i
$670$	5.31392	−	35.8246i	0.205295	−	1.38402i
$671$	24.0692			0.929181
$672$	−0.725719	−	38.0274i	−0.0279952	−	1.46694i
$673$	−4.96752			−0.191484			−0.0957419	−	0.995406i	$-0.530522\pi$
$673$	−4.96752			−0.191484			−0.0957419	+	0.995406i	$0.530522\pi$
$674$	−12.5207	+	23.8774i	−0.482278	+	0.919724i
$675$	21.1803	+	13.0560i	0.815230	+	0.502524i
$676$	9.47412	+	13.7041i	0.364389	+	0.527082i
$677$	−27.8327	+	16.0692i	−1.06970	+	0.617590i	−0.928099	−	0.372334i	$-0.878558\pi$
$677$	−27.8327	+	16.0692i	−1.06970	+	0.617590i	−0.141599	+	0.989924i	$0.545224\pi$
$678$	−6.34635	+	43.9240i	−0.243730	+	1.68689i
$679$			33.0064i			1.26667i
$680$	2.39446	−	5.63718i	0.0918232	−	0.216176i
$681$	3.53110	+	0.657649i	0.135312	+	0.0252012i
$682$	29.2269	+	15.3258i	1.11915	+	0.586854i
$683$	−22.3249	+	38.6679i	−0.854239	+	1.47959i	0.0231105	+	0.999733i	$0.492643\pi$
$683$	−22.3249	+	38.6679i	−0.854239	+	1.47959i	−0.877349	+	0.479852i	$0.840690\pi$
$684$	−10.7572	+	36.4489i	−0.411312	+	1.39366i
$685$	−13.3415			−0.509751
$686$	−0.238418	−	5.86287i	−0.00910285	−	0.223845i
$687$	−7.18186	−	20.3375i	−0.274005	−	0.775925i
$688$	1.45696	+	8.88275i	0.0555460	+	0.338652i
$689$	21.3946	+	12.3522i	0.815070	+	0.470581i
$690$	36.1393	−	14.4390i	1.37580	−	0.549683i
$691$	21.6967	−	12.5266i	0.825383	−	0.476535i	−0.0268863	−	0.999638i	$-0.508559\pi$
$691$	21.6967	−	12.5266i	0.825383	−	0.476535i	0.852269	+	0.523103i	$0.175226\pi$
$692$	5.97881	+	2.83161i	0.227280	+	0.107642i
$693$	−13.0723	+	33.8770i	−0.496574	+	1.28688i
$694$	−23.0507	−	36.4222i	−0.874992	−	1.38257i
$695$	54.8090			2.07902
$696$	0.129910	−	2.08573i	0.00492423	−	0.0790593i
$697$	0.363336			0.0137623
$698$	3.33970	−	0.135812i	0.126410	−	0.00514054i
$699$	−5.16190	+	27.7157i	−0.195241	+	1.04830i
$700$	30.5793	−	21.1405i	1.15579	−	0.799034i
$701$	−30.2156	+	17.4450i	−1.14123	+	0.658889i	−0.946735	−	0.322015i	$-0.895640\pi$
$701$	−30.2156	+	17.4450i	−1.14123	+	0.658889i	−0.194495	+	0.980904i	$0.562307\pi$
$702$	13.6575	−	8.10223i	0.515471	−	0.305799i
$703$	47.1868	−	27.2433i	1.77968	−	1.02750i
$704$	17.3192	+	17.9520i	0.652741	+	0.676591i
$705$	−1.07477	+	5.77073i	−0.0404781	+	0.217338i
$706$	−3.26372	−	1.71141i	−0.122832	−	0.0644097i
$707$	18.9644	−	32.8474i	0.713231	−	1.23535i
$708$	−24.4254	+	33.7514i	−0.917964	+	1.26845i
$709$	−3.97696	+	6.88829i	−0.149358	+	0.258695i	−0.930990	−	0.365044i	$-0.881054\pi$
$709$	−3.97696	+	6.88829i	−0.149358	+	0.258695i	0.781632	+	0.623739i	$0.214387\pi$
$710$	−29.4811	+	18.6579i	−1.10641	+	0.700218i
$711$	−27.6884	−	34.3150i	−1.03840	−	1.28691i
$712$	−3.75002	−	30.6029i	−0.140538	−	1.14689i
$713$		−	38.0051i		−	1.42330i
$714$	4.07173	−	5.17025i	0.152380	−	0.193492i
$715$			21.0811i			0.788388i
$716$	24.0388	−	1.95835i	0.898370	−	0.0731869i
$717$	−26.1415	−	4.86871i	−0.976272	−	0.181825i
$718$	8.57172	−	0.348576i	0.319894	−	0.0130087i
$719$	8.25627	−	14.3003i	0.307907	−	0.533310i	−0.669997	−	0.742363i	$-0.733705\pi$
$719$	8.25627	−	14.3003i	0.307907	−	0.533310i	0.977904	+	0.209053i	$0.0670382\pi$
$720$	35.6624	−	11.7352i	1.32906	−	0.437344i
$721$	−10.0238	+	17.3616i	−0.373304	+	0.646581i
$722$	−15.9711	−	25.2359i	−0.594385	−	0.939182i
$723$	−28.9315	+	33.8144i	−1.07597	+	1.25757i
$724$	7.22609	+	10.4524i	0.268555	+	0.388460i
$725$	1.76892	−	1.02129i	0.0656962	−	0.0379297i
$726$	1.16119	+	2.90633i	0.0430956	+	0.107864i
$727$	20.9256	+	12.0814i	0.776086	+	0.448074i	0.835042	−	0.550187i	$-0.185444\pi$
$727$	20.9256	+	12.0814i	0.776086	+	0.448074i	−0.0589551	+	0.998261i	$0.518777\pi$
$728$	−2.88585	−	23.5506i	−0.106957	−	0.872844i
$729$	12.1312	+	24.1212i	0.449304	+	0.893379i
$730$	10.5013	+	5.50659i	0.388670	+	0.203808i
$731$	−0.778759	+	1.34885i	−0.0288034	+	0.0498890i
$732$	−10.9220	−	24.4082i	−0.403688	−	0.902151i
$733$	−21.6975	−	37.5812i	−0.801417	−	1.38809i	−0.918684	−	0.394994i	$-0.870747\pi$
$733$	−21.6975	−	37.5812i	−0.801417	−	1.38809i	0.117267	−	0.993100i	$-0.462587\pi$
$734$	37.1113	−	23.4868i	1.36980	−	0.866915i
$735$	41.2295	−	14.5595i	1.52077	−	0.537035i
$736$	9.04684	−	27.2649i	0.333471	−	1.00500i
$737$	8.40780	+	24.0978i	0.309705	+	0.887653i
$738$	1.46788	+	1.67507i	0.0540333	+	0.0616602i
$739$	−7.83774	−	4.52512i	−0.288316	−	0.166459i	0.348866	−	0.937173i	$-0.386567\pi$
$739$	−7.83774	−	4.52512i	−0.288316	−	0.166459i	−0.637182	+	0.770713i	$0.719900\pi$
$740$	−48.6475	−	23.0399i	−1.78832	−	0.846962i
$741$	−4.34073	+	23.3066i	−0.159461	+	0.856189i
$742$	33.5619	+	53.0309i	1.23210	+	1.94682i
$743$	10.0449	−	17.3983i	0.368513	−	0.638282i	−0.620821	−	0.783953i	$-0.713201\pi$
$743$	10.0449	−	17.3983i	0.368513	−	0.638282i	0.989333	+	0.145670i	$0.0465338\pi$
$744$	2.27920	−	36.5929i	0.0835596	−	1.34156i
$745$	39.6586			1.45298
$746$	−12.8766	−	20.3462i	−0.471446	−	0.744928i
$747$	33.0133	+	12.7390i	1.20789	+	0.466096i
$748$	0.350459	+	4.30189i	0.0128140	+	0.157293i
$749$	10.6548	−	6.15154i	0.389317	−	0.224772i
$750$	−1.27429	−	1.00354i	−0.0465307	−	0.0366443i
$751$		−	35.8366i		−	1.30770i	−0.756626	−	0.653848i	$-0.773153\pi$
$751$		−	35.8366i		−	1.30770i	0.756626	−	0.653848i	$-0.226847\pi$
$752$	2.74525	+	3.35227i	0.100109	+	0.122245i
$753$	−10.8173	−	30.6323i	−0.394204	−	1.11630i
$754$	−0.0529702	−	1.30258i	−0.00192906	−	0.0474370i
$755$	−27.3940	+	47.4479i	−0.996971	+	1.72680i
$756$	40.2859	−	2.11616i	1.46519	−	0.0769641i
$757$	−1.91138	−	3.31061i	−0.0694704	−	0.120326i	0.829198	−	0.558955i	$-0.188798\pi$
$757$	−1.91138	−	3.31061i	−0.0694704	−	0.120326i	−0.898668	+	0.438629i	$0.855464\pi$
$758$	−3.86356	−	2.02595i	−0.140331	−	0.0735857i
$759$	−17.8297	+	20.8389i	−0.647177	+	0.756404i
$760$	−21.9127	+	51.5881i	−0.794855	+	1.87130i
$761$			41.9504i			1.52070i	0.649514	+	0.760350i	$0.274972\pi$
$761$			41.9504i			1.52070i	−0.649514	+	0.760350i	$0.725028\pi$
$762$	6.38086	−	44.1629i	0.231154	−	1.59985i
$763$	−24.1994	+	13.9716i	−0.876078	+	0.505804i
$764$	−5.92227	+	12.5046i	−0.214260	+	0.452400i
$765$	6.06060	+	2.33863i	0.219122	+	0.0845534i
$766$	5.32796	−	10.1606i	0.192507	−	0.367118i
$767$	−12.9950	+	22.5081i	−0.469224	+	0.812720i
$768$	10.3458	−	25.7092i	0.373322	−	0.927702i
$769$	8.49270	+	14.7098i	0.306255	+	0.530449i	0.977540	−	0.210750i	$-0.0675908\pi$
$769$	8.49270	+	14.7098i	0.306255	+	0.530449i	−0.671285	+	0.741199i	$0.734257\pi$
$770$	−24.8705	+	47.4291i	−0.896272	+	1.70923i
$771$	−1.19237	+	6.40217i	−0.0429422	+	0.230569i
$772$	13.8444	−	1.12785i	0.498270	−	0.0405922i
$773$	−16.3350	+	9.43101i	−0.587529	+	0.339210i	−0.764120	−	0.645074i	$-0.776826\pi$
$773$	−16.3350	+	9.43101i	−0.587529	+	0.339210i	0.176591	+	0.984284i	$0.443493\pi$
$774$	−9.36473	+	1.85908i	−0.336608	+	0.0668234i
$775$	31.0348	−	17.9179i	1.11480	−	0.643631i
$776$	−9.40221	+	22.1353i	−0.337520	+	0.794610i
$777$	−43.9483	−	37.6020i	−1.57664	−	1.34896i
$778$	−15.4315	−	8.09185i	−0.553245	−	0.290107i
$779$	−3.32504			−0.119132
$780$	21.3780	−	9.56606i	0.765454	−	0.342520i
$781$	12.2935	−	21.2930i	0.439896	−	0.761922i
$782$	4.20009	−	2.65813i	0.150195	−	0.0950546i
$783$	2.21562	+	0.0638417i	0.0791797	+	0.00228152i
$784$	11.4007	−	30.1947i	0.407170	−	1.07838i
$785$	−45.0506	−	26.0100i	−1.60793	−	0.928336i
$786$	−9.99975	+	12.6976i	−0.356679	+	0.452909i
$787$	41.1472	+	23.7563i	1.46674	+	0.846822i	0.999308	−	0.0372074i	$-0.0118462\pi$
$787$	41.1472	+	23.7563i	1.46674	+	0.846822i	0.467431	+	0.884029i	$0.345180\pi$
$788$	44.2587	−	30.5975i	1.57665	−	1.08999i
$789$	2.69418	−	3.14890i	0.0959155	−	0.112104i
$790$	−34.7765	−	54.9501i	−1.23729	−	1.95504i
$791$	−35.1660	+	60.9093i	−1.25036	+	2.16569i
$792$	−18.4169	+	18.9953i	−0.654417	+	0.674970i
$793$	−8.34067	−	14.4465i	−0.296186	−	0.513009i
$794$	−22.6538	+	0.921233i	−0.803952	+	0.0326933i
$795$	−40.2740	+	47.0713i	−1.42837	+	1.66945i
$796$	21.8839	+	10.3644i	0.775655	+	0.367356i
$797$	−2.65101	+	1.53056i	−0.0939036	+	0.0542152i	−0.546216	−	0.837644i	$-0.683932\pi$
$797$	−2.65101	+	1.53056i	−0.0939036	+	0.0542152i	0.452313	+	0.891859i	$0.350599\pi$
$798$	−37.2620	+	47.3151i	−1.31906	+	1.67494i
$799$			0.749722i			0.0265233i
$800$	26.5296	−	5.46672i	0.937963	−	0.193278i
$801$	32.3084	−	5.05917i	1.14156	−	0.178757i
$802$	−1.63818	−	40.2839i	−0.0578460	−	1.42247i
$803$	−8.35616			−0.294883
$804$	20.6219	−	19.4612i	0.727279	−	0.686342i
$805$	61.6743			2.17373
$806$	−0.929332	−	22.8529i	−0.0327343	−	0.804960i
$807$	15.2825	+	13.0757i	0.537970	+	0.460285i
$808$	22.0751	−	16.6264i	0.776600	−	0.584914i
$809$		−	15.1517i		−	0.532706i	−0.963876	−	0.266353i	$-0.914181\pi$
$809$		−	15.1517i		−	0.532706i	0.963876	−	0.266353i	$-0.0858186\pi$
$810$	13.7032	+	37.3890i	0.481481	+	1.31371i
$811$	−31.2231	+	18.0266i	−1.09639	+	0.633001i	−0.935271	−	0.353934i	$-0.884844\pi$
$811$	−31.2231	+	18.0266i	−1.09639	+	0.633001i	−0.161120	+	0.986935i	$0.551511\pi$
$812$	1.41755	−	2.99308i	0.0497461	−	0.105036i
$813$	35.9287	+	30.7404i	1.26007	+	1.07811i
$814$	37.9020	−	1.54131i	1.32846	−	0.0540230i
$815$	−16.3381	−	28.2984i	−0.572298	−	0.991249i
$816$	4.20344	−	2.30748i	0.147150	−	0.0807780i
$817$	7.12674	−	12.3439i	0.249333	−	0.431858i
$818$	−21.0185	−	33.2111i	−0.734895	−	1.16120i
$819$	24.8631	−	3.89331i	0.868786	−	0.136043i
$820$	1.86797	+	2.70199i	0.0652325	+	0.0943575i
$821$	−4.44935	−	2.56884i	−0.155284	−	0.0896530i	0.420345	−	0.907364i	$-0.361909\pi$
$821$	−4.44935	−	2.56884i	−0.155284	−	0.0896530i	−0.575628	+	0.817711i	$0.695242\pi$
$822$	−8.20615	−	6.46258i	−0.286222	−	0.225408i
$823$	1.69647	+	0.979459i	0.0591353	+	0.0341418i	0.529276	−	0.848450i	$-0.322464\pi$
$823$	1.69647	+	0.979459i	0.0591353	+	0.0341418i	−0.470141	+	0.882591i	$0.655797\pi$
$824$	−11.6679	+	8.78796i	−0.406471	+	0.306143i
$825$	−25.4230	−	4.73489i	−0.885114	−	0.164848i
$826$	−55.7908	+	35.3086i	−1.94121	+	1.22854i
$827$	8.45757	−	14.6489i	0.294098	−	0.509393i	−0.680676	−	0.732584i	$-0.738314\pi$
$827$	8.45757	−	14.6489i	0.294098	−	0.509393i	0.974775	+	0.223191i	$0.0716473\pi$
$828$	29.2230	+	8.62461i	1.01557	+	0.299726i
$829$	−44.3022			−1.53868			−0.769339	−	0.638841i	$-0.779414\pi$
$829$	−44.3022			−1.53868			−0.769339	+	0.638841i	$0.779414\pi$
$830$	46.2199	+	24.2365i	1.60432	+	0.841261i
$831$	−24.1362	+	28.2098i	−0.837274	+	0.978586i
$832$	4.77328	−	16.6159i	0.165484	−	0.576054i
$833$	4.83641	−	2.79230i	0.167572	−	0.0967475i
$834$	33.7123	+	26.5494i	1.16736	+	0.919331i
$835$	−8.07133	+	4.65998i	−0.279320	+	0.161265i
$836$	−3.20719	−	39.3683i	−0.110923	−	1.36158i
$837$	38.8717	+	1.12007i	1.34360	+	0.0387151i
$838$	10.3654	−	19.7672i	0.358067	−	0.682847i
$839$	12.9474	+	22.4255i	0.446993	+	0.774215i	0.998189	−	0.0601612i	$-0.0191615\pi$
$839$	12.9474	+	22.4255i	0.446993	+	0.774215i	−0.551196	+	0.834376i	$0.685828\pi$
$840$	59.3826	+	3.69867i	2.04890	+	0.127616i
$841$	−14.4090	+	24.9572i	−0.496863	+	0.860591i
$842$	5.86818	−	11.1909i	0.202231	−	0.385662i
$843$	−34.2868	+	12.1078i	−1.18090	+	0.417015i
$844$	26.6579	+	12.6254i	0.917601	+	0.434583i
$845$	−22.5702	+	13.0309i	−0.776439	+	0.448277i
$846$	−3.45641	+	3.02888i	−0.118834	+	0.104135i
$847$			4.95985i			0.170423i
$848$	7.40142	+	45.1248i	0.254166	+	1.54959i
$849$	−22.4031	−	19.1680i	−0.768872	−	0.657844i
$850$	4.15080	+	2.17657i	0.142371	+	0.0746557i
$851$	−21.8424	−	37.8321i	−0.748748	−	1.29687i
$852$	−27.1713	−	2.80442i	−0.930874	−	0.0960778i
$853$	−16.3007	+	28.2337i	−0.558127	+	0.966704i	0.439526	+	0.898230i	$0.355146\pi$
$853$	−16.3007	+	28.2337i	−0.558127	+	0.966704i	−0.997653	+	0.0684740i	$0.978187\pi$
$854$	−1.72188	−	42.3422i	−0.0589214	−	1.44892i
$855$	−55.4631	−	21.4018i	−1.89680	−	0.731925i
$856$	8.89780	−	1.09032i	0.304121	−	0.0372663i
$857$		−	31.1096i		−	1.06268i	−0.847158	−	0.531342i	$-0.821688\pi$
$857$		−	31.1096i		−	1.06268i	0.847158	−	0.531342i	$-0.178312\pi$
$858$	−10.2117	+	12.9667i	−0.348620	+	0.442676i
$859$	49.9893	−	28.8613i	1.70561	−	0.984736i	0.765779	−	0.643104i	$-0.222354\pi$
$859$	49.9893	−	28.8613i	1.70561	−	0.984736i	0.939834	−	0.341632i	$-0.110980\pi$
$860$	−14.0346	+	1.14335i	−0.478577	+	0.0389878i
$861$	1.17530	+	3.32820i	0.0400541	+	0.113425i
$862$	−0.820389	−	1.29629i	−0.0279426	−	0.0441518i
$863$	−50.0737			−1.70453			−0.852264	−	0.523112i	$-0.824771\pi$
$863$	−50.0737			−1.70453			−0.852264	+	0.523112i	$0.824771\pi$
$864$	27.6200	+	10.0567i	0.939651	+	0.342135i
$865$	−5.17433	+	8.96221i	−0.175933	+	0.304724i
$866$	−8.38145	−	13.2435i	−0.284813	−	0.450031i
$867$	−28.1314	−	5.23933i	−0.955393	−	0.177937i
$868$	24.8700	−	52.5119i	0.844144	−	1.78237i
$869$	39.6881	+	22.9139i	1.34633	+	0.777302i
$870$	3.23547	+	0.467475i	0.109693	+	0.0158489i
$871$	11.5501	−	13.3970i	0.391359	−	0.453939i
$872$	−20.2089	+	2.47636i	−0.684361	+	0.0838602i
$873$	−23.7979	−	9.18300i	−0.805437	−	0.310797i
$874$	−38.4368	+	24.3257i	−1.30014	+	0.822828i
$875$	−1.28525	−	2.22612i	−0.0434495	−	0.0752568i
$876$	3.79181	+	8.47384i	0.128114	+	0.286305i
$877$	−18.7411	+	32.4605i	−0.632842	+	1.09611i	0.354126	+	0.935198i	$0.384778\pi$
$877$	−18.7411	+	32.4605i	−0.632842	+	1.09611i	−0.986968	+	0.160917i	$0.948555\pi$
$878$	−10.3997	−	5.45332i	−0.350973	−	0.184041i
$879$	−41.3038	−	35.3394i	−1.39314	−	1.19197i
$880$	−30.1897	+	24.7230i	−1.01769	+	0.833412i
$881$	−24.6895	−	14.2545i	−0.831811	−	0.480246i	0.0226612	−	0.999743i	$-0.492786\pi$
$881$	−24.6895	−	14.2545i	−0.831811	−	0.480246i	−0.854472	+	0.519497i	$0.826119\pi$
$882$	32.4123	+	11.0161i	1.09138	+	0.370933i
$883$	−1.38212	+	0.797968i	−0.0465121	+	0.0268538i	−0.523076	−	0.852286i	$-0.675216\pi$
$883$	−1.38212	+	0.797968i	−0.0465121	+	0.0268538i	0.476564	+	0.879140i	$0.341882\pi$
$884$	2.46057	−	1.70107i	0.0827580	−	0.0572133i
$885$	−49.5211	−	42.3700i	−1.66463	−	1.42425i
$886$	−13.1772	−	20.8211i	−0.442695	−	0.699499i
$887$	−13.0545	+	22.6110i	−0.438326	+	0.759203i	−0.997561	−	0.0698063i	$-0.977762\pi$
$887$	−13.0545	+	22.6110i	−0.438326	+	0.759203i	0.559234	+	0.829010i	$0.311095\pi$
$888$	−18.7620	−	37.7363i	−0.629610	−	1.26635i
$889$	35.3572	−	61.2405i	1.18584	−	2.05394i
$890$	48.1909	−	1.95972i	1.61536	−	0.0656900i
$891$	−20.7886	−	18.8504i	−0.696446	−	0.631513i
$892$	−1.61895	−	19.8726i	−0.0542064	−	0.665385i
$893$		−	6.86102i		−	0.229595i
$894$	24.3935	+	19.2106i	0.815841	+	0.642499i
$895$			37.7288i			1.26113i
$896$	30.3419	−	31.7519i	1.01365	−	1.06076i
$897$	18.6861	+	3.48019i	0.623911	+	0.116200i
$898$	−4.05124	+	2.56393i	−0.135192	+	0.0855594i
$899$	1.59623	−	2.76475i	0.0532372	−	0.0922095i
$900$	6.73472	+	27.9296i	0.224491	+	0.930986i
$901$	−3.95613	+	6.85222i	−0.131798	+	0.228281i
$902$	−2.05011	−	1.07502i	−0.0682613	−	0.0357944i
$903$	−14.8747	−	2.77034i	−0.494999	−	0.0921910i
$904$	−40.9342	+	30.8305i	−1.36145	+	1.02541i
$905$	−17.2147	+	9.93892i	−0.572236	+	0.330381i
$906$	−39.8334	+	15.9149i	−1.32338	+	0.528738i
$907$	−9.53834	+	5.50697i	−0.316716	+	0.182856i	−0.649928	−	0.759996i	$-0.725201\pi$
$907$	−9.53834	+	5.50697i	−0.316716	+	0.182856i	0.333212	+	0.942852i	$0.391867\pi$
$908$	2.35854	+	3.41158i	0.0782708	+	0.113217i
$909$	18.4070	+	22.8123i	0.610520	+	0.756635i
$910$	37.0855	−	1.50811i	1.22937	−	0.0499934i
$911$	38.6175			1.27945			0.639727	−	0.768602i	$-0.279047\pi$
$911$	38.6175			1.27945			0.639727	+	0.768602i	$0.279047\pi$
$912$	−38.4674	+	21.1167i	−1.27378	+	0.699244i
$913$	−36.7785			−1.21719
$914$	3.66301	+	5.78789i	0.121162	+	0.191446i
$915$	39.4433	−	13.9288i	1.30396	−	0.460470i
$916$	10.6601	−	22.5082i	0.352219	−	0.743693i
$917$	−22.1821	+	12.8068i	−0.732516	+	0.422918i
$918$	2.59497	+	4.37421i	0.0856466	+	0.144370i
$919$	10.7071	+	6.18172i	0.353193	+	0.203916i	0.666091	−	0.745871i	$-0.267966\pi$
$919$	10.7071	+	6.18172i	0.353193	+	0.203916i	−0.312898	+	0.949787i	$0.601300\pi$
$920$	41.3609	+	17.5685i	1.36363	+	0.579217i
$921$	37.9063	−	13.3860i	1.24906	−	0.441084i
$922$	1.80430	+	44.3689i	0.0594213	+	1.46121i
$923$	−17.0402			−0.560885
$924$	−38.2721	+	17.1257i	−1.25906	+	0.563395i
$925$	20.5957	−	35.6728i	0.677182	−	1.17291i
$926$	4.93875	+	2.58975i	0.162298	+	0.0851045i
$927$	−9.72910	−	12.0575i	−0.319545	−	0.396022i
$928$	1.80326	−	1.60346i	0.0591951	−	0.0526362i
$929$			8.67323i			0.284559i	0.989827	+	0.142280i	$0.0454432\pi$
$929$			8.67323i			0.284559i	−0.989827	+	0.142280i	$0.954557\pi$
$930$	56.7644	+	8.20159i	1.86138	+	0.268941i
$931$	−44.2599	+	25.5535i	−1.45056	+	0.837482i
$932$	−26.7776	+	18.5122i	−0.877128	+	0.606388i
$933$	−12.6946	+	14.8371i	−0.415601	+	0.485745i
$934$	5.50036	−	10.4894i	0.179977	−	0.343224i
$935$	−6.75181			−0.220808
$936$	17.7831	+	4.47150i	0.581259	+	0.146156i
$937$	−6.74398			−0.220316			−0.110158	−	0.993914i	$-0.535136\pi$
$937$	−6.74398			−0.220316			−0.110158	+	0.993914i	$0.535136\pi$
$938$	41.7910	−	16.5148i	1.36452	−	0.539227i
$939$	−0.515633	+	0.602660i	−0.0168271	+	0.0196671i
$940$	−5.57540	+	3.85446i	−0.181849	+	0.125719i
$941$			7.88174i			0.256938i	0.991714	+	0.128469i	$0.0410062\pi$
$941$			7.88174i			0.256938i	−0.991714	+	0.128469i	$0.958994\pi$
$942$	−15.1108	−	37.8209i	−0.492337	−	1.23227i
$943$			2.66586i			0.0868122i
$944$	−47.4733	+	7.78662i	−1.54512	+	0.253433i
$945$	−1.81763	+	63.0807i	−0.0591276	+	2.05201i
$946$	8.38505	−	5.30669i	0.272621	−	0.172535i
$947$	46.3054			1.50472			0.752362	−	0.658750i	$-0.228915\pi$
$947$	46.3054			1.50472			0.752362	+	0.658750i	$0.228915\pi$
$948$	5.22717	−	50.6448i	0.169771	−	1.64487i
$949$	2.89565	+	5.01541i	0.0939968	+	0.162807i
$950$	−37.9857	−	19.9187i	−1.23242	−	0.646247i
$951$	35.8972	−	12.6765i	1.16405	−	0.411064i
$952$	7.54274	−	0.924273i	0.244462	−	0.0299558i
$953$		−	10.2149i		−	0.330894i	−0.986219	−	0.165447i	$-0.947093\pi$
$953$		−	10.2149i		−	0.330894i	0.986219	−	0.165447i	$-0.0529067\pi$
$954$	−47.5733	+	9.44424i	−1.54024	+	0.305769i
$955$	−18.7443	−	10.8220i	−0.606551	−	0.350192i
$956$	−17.4607	−	25.2566i	−0.564721	−	0.816858i
$957$	−2.17230	+	0.767111i	−0.0702204	+	0.0247972i
$958$	−26.4617	+	50.4634i	−0.854938	+	1.63040i
$959$	−8.27672	−	14.3357i	−0.267269	−	0.462924i
$960$	38.7705	+	19.3962i	1.25131	+	0.626009i
$961$	12.5049	−	21.6592i	0.403384	−	0.698682i
$962$	−14.0592	−	22.2148i	−0.453287	−	0.716235i
$963$	1.47095	+	9.39366i	0.0474008	+	0.302707i
$964$	−51.2170	+	4.17246i	−1.64959	+	0.134386i
$965$			21.7287i			0.699472i
$966$	37.9350	+	29.8749i	1.22054	+	0.961210i
$967$	−10.5754	+	6.10572i	−0.340083	+	0.196347i	−0.660309	−	0.750994i	$-0.729575\pi$
$967$	−10.5754	+	6.10572i	−0.340083	+	0.196347i	0.320226	+	0.947341i	$0.396241\pi$
$968$	−1.41286	+	3.32625i	−0.0454112	+	0.106910i
$969$	−7.46459	−	1.39024i	−0.239797	−	0.0446609i
$970$	−33.3180	−	17.4710i	−1.06978	−	0.560961i
$971$	16.1242	+	27.9279i	0.517449	+	0.896248i	0.999795	+	0.0202671i	$0.00645168\pi$
$971$	16.1242	+	27.9279i	0.517449	+	0.896248i	−0.482345	+	0.875981i	$0.660215\pi$
$972$	−9.68253	+	29.6353i	−0.310567	+	0.950551i
$973$	34.0022	+	58.8936i	1.09006	+	1.88804i
$974$	−3.13723	−	1.64508i	−0.100523	−	0.0527118i
$975$	5.96788	+	16.8998i	0.191125	+	0.541226i
$976$	10.9068	−	28.8866i	0.349119	−	0.924639i
$977$	36.5451	+	21.0993i	1.16918	+	0.675028i	0.953487	−	0.301433i	$-0.0974649\pi$
$977$	36.5451	+	21.0993i	1.16918	+	0.675028i	0.215695	+	0.976461i	$0.430798\pi$
$978$	3.65837	−	25.3201i	0.116982	−	0.809647i
$979$	−29.4354	+	16.9945i	−0.940759	+	0.543147i
$980$	45.6301	+	21.6108i	1.45760	+	0.690331i
$981$	−3.34087	−	21.3351i	−0.106666	−	0.681179i
$982$	−0.132432	+	0.00538544i	−0.00422606	+	0.000171856i
$983$	−5.37065			−0.171297			−0.0856486	−	0.996325i	$-0.527296\pi$
$983$	−5.37065			−0.171297			−0.0856486	+	0.996325i	$0.527296\pi$
$984$	−0.159874	+	2.56680i	−0.00509660	+	0.0818266i
$985$	42.0845	+	72.8925i	1.34092	+	2.32255i
$986$	0.417186	−	0.0169652i	0.0132859	−	0.000540282i
$987$	−6.86754	+	2.42516i	−0.218596	+	0.0771937i
$988$	−22.5177	+	15.5672i	−0.716383	+	0.495259i
$989$	−9.89674	−	5.71389i	−0.314698	−	0.181691i
$990$	−27.2773	−	31.1275i	−0.866930	−	0.989297i
$991$			51.0522i			1.62173i	0.585236	+	0.810863i	$0.301002\pi$
$991$			51.0522i			1.62173i	−0.585236	+	0.810863i	$0.698998\pi$
$992$	31.6373	−	28.1318i	1.00448	−	0.893186i
$993$	−0.770212	+	4.13548i	−0.0244420	+	0.131236i
$994$	−38.3377	−	20.1033i	−1.21600	−	0.637637i
$995$	−18.9393	+	32.8039i	−0.600417	+	1.03995i
$996$	16.6891	+	37.2964i	0.528815	+	1.18178i
$997$	−30.6414			−0.970424			−0.485212	−	0.874396i	$-0.661258\pi$
$997$	−30.6414			−0.970424			−0.485212	+	0.874396i	$0.661258\pi$
$998$	−10.3381	−	5.42105i	−0.327248	−	0.171600i
$999$	39.3386	−	21.2255i	1.24462	−	0.671546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.l.a.431.4	✓	264
3.2	odd	2	inner	804.2.l.a.431.129	yes	264
4.3	odd	2	inner	804.2.l.a.431.46	yes	264
12.11	even	2	inner	804.2.l.a.431.87	yes	264
67.37	even	3	inner	804.2.l.a.707.87	yes	264
201.104	odd	6	inner	804.2.l.a.707.46	yes	264
268.171	odd	6	inner	804.2.l.a.707.129	yes	264
804.707	even	6	inner	804.2.l.a.707.4	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.l.a.431.4	✓	264	1.1	even	1	trivial
804.2.l.a.431.46	yes	264	4.3	odd	2	inner
804.2.l.a.431.87	yes	264	12.11	even	2	inner
804.2.l.a.431.129	yes	264	3.2	odd	2	inner
804.2.l.a.707.4	yes	264	804.707	even	6	inner
804.2.l.a.707.46	yes	264	201.104	odd	6	inner
804.2.l.a.707.87	yes	264	67.37	even	3	inner
804.2.l.a.707.129	yes	264	268.171	odd	6	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41305 + 0.0574626i) q^{2} +(1.12603 - 1.31608i) q^{3} +(1.99340 - 0.162395i) q^{4} +3.12863i q^{5} +(-1.51551 + 1.92438i) q^{6} +(-3.36179 + 1.94093i) q^{7} +(-2.80743 + 0.344017i) q^{8} +(-0.464114 - 2.96388i) q^{9} +O(q^{10})\)	\(q+(-1.41305 + 0.0574626i) q^{2} +(1.12603 - 1.31608i) q^{3} +(1.99340 - 0.162395i) q^{4} +3.12863i q^{5} +(-1.51551 + 1.92438i) q^{6} +(-3.36179 + 1.94093i) q^{7} +(-2.80743 + 0.344017i) q^{8} +(-0.464114 - 2.96388i) q^{9} +(-0.179779 - 4.42090i) q^{10} +(1.55903 + 2.70032i) q^{11} +(2.03090 - 2.80632i) q^{12} +(1.08050 - 1.87148i) q^{13} +(4.63883 - 2.93580i) q^{14} +(4.11752 + 3.52293i) q^{15} +(3.94726 - 0.647433i) q^{16} +(0.599393 + 0.346060i) q^{17} +(0.826127 + 4.16143i) q^{18} +(-5.48529 - 3.16693i) q^{19} +(0.508073 + 6.23661i) q^{20} +(-1.23106 + 6.60992i) q^{21} +(-2.35815 - 3.72609i) q^{22} +(-2.53910 + 4.39785i) q^{23} +(-2.70850 + 4.08216i) q^{24} -4.78835 q^{25} +(-1.41925 + 2.70657i) q^{26} +(-4.42330 - 2.72661i) q^{27} +(-6.38618 + 4.41498i) q^{28} +(-0.369423 + 0.213286i) q^{29} +(-6.02068 - 4.74146i) q^{30} +(-6.48131 + 3.74199i) q^{31} +(-5.54045 + 1.14167i) q^{32} +(5.30934 + 0.988837i) q^{33} +(-0.866855 - 0.454555i) q^{34} +(-6.07246 - 10.5178i) q^{35} +(-1.40648 - 5.83282i) q^{36} +(-4.30121 + 7.44992i) q^{37} +(7.93294 + 4.15982i) q^{38} +(-1.24633 - 3.52935i) q^{39} +(-1.07630 - 8.78341i) q^{40} +(0.454630 - 0.262481i) q^{41} +(1.35972 - 9.41086i) q^{42} +2.25036i q^{43} +(3.54628 + 5.12963i) q^{44} +(9.27290 - 1.45204i) q^{45} +(3.33515 - 6.36026i) q^{46} +(0.541614 + 0.938103i) q^{47} +(3.59266 - 5.92392i) q^{48} +(4.03442 - 6.98782i) q^{49} +(6.76615 - 0.275151i) q^{50} +(1.13037 - 0.399173i) q^{51} +(1.84994 - 3.90606i) q^{52} +11.4319i q^{53} +(6.40701 + 3.59865i) q^{54} +(-8.44831 + 4.87763i) q^{55} +(8.77027 - 6.60553i) q^{56} +(-10.3445 + 3.65300i) q^{57} +(0.509755 - 0.322611i) q^{58} -12.0269 q^{59} +(8.77995 + 6.35394i) q^{60} +(3.85964 - 6.68510i) q^{61} +(8.94336 - 5.66003i) q^{62} +(7.31294 + 9.06314i) q^{63} +(7.76331 - 1.93160i) q^{64} +(5.85516 + 3.38048i) q^{65} +(-7.55916 - 1.09218i) q^{66} +(8.04128 + 1.52900i) q^{67} +(1.25103 + 0.592496i) q^{68} +(2.92880 + 8.29375i) q^{69} +(9.18504 + 14.5132i) q^{70} +(-3.94267 - 6.82891i) q^{71} +(2.32259 + 8.16122i) q^{72} +(-1.33996 + 2.32088i) q^{73} +(5.64972 - 10.7742i) q^{74} +(-5.39182 + 6.30183i) q^{75} +(-11.4486 - 5.42217i) q^{76} +(-10.4823 - 6.05194i) q^{77} +(1.96393 + 4.91552i) q^{78} +(12.7285 - 7.34878i) q^{79} +(2.02558 + 12.3495i) q^{80} +(-8.56920 + 2.75116i) q^{81} +(-0.627330 + 0.397022i) q^{82} +(-5.89765 + 10.2150i) q^{83} +(-1.38058 + 13.3761i) q^{84} +(-1.08269 + 1.87528i) q^{85} +(-0.129312 - 3.17986i) q^{86} +(-0.135280 + 0.726355i) q^{87} +(-5.30582 - 7.04462i) q^{88} +10.9007i q^{89} +(-13.0196 + 2.58465i) q^{90} +8.38868i q^{91} +(-4.34724 + 9.17898i) q^{92} +(-2.37341 + 12.7435i) q^{93} +(-0.819231 - 1.29446i) q^{94} +(9.90817 - 17.1615i) q^{95} +(-4.73618 + 8.57721i) q^{96} +(4.25136 - 7.36358i) q^{97} +(-5.29928 + 10.1059i) q^{98} +(7.27986 - 5.87404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9}+O(q^{10}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9	\( 264 q - 2 q^{4} - 3 q^{6} - 12 q^{9} + 2 q^{10} + 2 q^{12} - 18 q^{16} + q^{18} - 4 q^{22} - 248 q^{25} + 7 q^{30} - 38 q^{34} + 13 q^{36} + 4 q^{37} + 48 q^{40} - 12 q^{42} + 48 q^{45} - 2 q^{46} - 11 q^{48} + 128 q^{49} + 32 q^{52} - 8 q^{54} - 2 q^{57} - 32 q^{58} + 68 q^{60} - 8 q^{61} + 4 q^{64} + 30 q^{66} - 40 q^{69} - 140 q^{70} + 108 q^{72} - 4 q^{73} - 120 q^{76} + 44 q^{78} - 28 q^{81} - 64 q^{82} + 33 q^{84} + 16 q^{85} - 14 q^{88} + 42 q^{90} + 16 q^{93} - 12 q^{94} - 4 q^{96} + 20 q^{97}+O(q^{100}) \) 264 * q - 2 * q^4 - 3 * q^6 - 12 * q^9 + 2 * q^10 + 2 * q^12 - 18 * q^16 + q^18 - 4 * q^22 - 248 * q^25 + 7 * q^30 - 38 * q^34 + 13 * q^36 + 4 * q^37 + 48 * q^40 - 12 * q^42 + 48 * q^45 - 2 * q^46 - 11 * q^48 + 128 * q^49 + 32 * q^52 - 8 * q^54 - 2 * q^57 - 32 * q^58 + 68 * q^60 - 8 * q^61 + 4 * q^64 + 30 * q^66 - 40 * q^69 - 140 * q^70 + 108 * q^72 - 4 * q^73 - 120 * q^76 + 44 * q^78 - 28 * q^81 - 64 * q^82 + 33 * q^84 + 16 * q^85 - 14 * q^88 + 42 * q^90 + 16 * q^93 - 12 * q^94 - 4 * q^96 + 20 * q^97

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