LMFDB - Embedded newform 756.2.ci.a.95.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.13
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35923 - 0.390498i) q^{2} +(-1.12398 - 1.31783i) q^{3} +(1.69502 + 1.06155i) q^{4} +(-0.140742 - 0.0248166i) q^{5} +(1.01314 + 2.23015i) q^{6} +(1.14582 + 2.38476i) q^{7} +(-1.88939 - 2.10480i) q^{8} +(-0.473344 + 2.96242i) q^{9} +O(q^{10})$	\(q+(-1.35923 - 0.390498i) q^{2} +(-1.12398 - 1.31783i) q^{3} +(1.69502 + 1.06155i) q^{4} +(-0.140742 - 0.0248166i) q^{5} +(1.01314 + 2.23015i) q^{6} +(1.14582 + 2.38476i) q^{7} +(-1.88939 - 2.10480i) q^{8} +(-0.473344 + 2.96242i) q^{9} +(0.181610 + 0.0886910i) q^{10} +(-0.352547 - 1.99940i) q^{11} +(-0.506222 - 3.42691i) q^{12} +(-0.728806 + 4.13327i) q^{13} +(-0.626193 - 3.68889i) q^{14} +(0.125487 + 0.213367i) q^{15} +(1.74620 + 3.59872i) q^{16} +(2.76512 - 1.59644i) q^{17} +(1.80020 - 3.84178i) q^{18} +(-7.23499 - 4.17712i) q^{19} +(-0.212217 - 0.191470i) q^{20} +(1.85483 - 4.19042i) q^{21} +(-0.301566 + 2.85531i) q^{22} +(-3.57751 - 3.00189i) q^{23} +(-0.650130 + 4.85565i) q^{24} +(-4.67927 - 1.70312i) q^{25} +(2.60465 - 5.33347i) q^{26} +(4.43599 - 2.70591i) q^{27} +(-0.589362 + 5.25858i) q^{28} +(-4.25038 + 0.749457i) q^{29} +(-0.0872464 - 0.339018i) q^{30} +(0.406512 + 0.0716791i) q^{31} +(-0.968201 - 5.57338i) q^{32} +(-2.23860 + 2.71187i) q^{33} +(-4.38184 + 1.09016i) q^{34} +(-0.102084 - 0.364072i) q^{35} +(-3.94710 + 4.51889i) q^{36} +3.86017 q^{37} +(8.20287 + 8.50293i) q^{38} +(6.26610 - 3.68526i) q^{39} +(0.213683 + 0.343122i) q^{40} +(4.50338 + 0.794068i) q^{41} +(-4.15749 + 4.97144i) q^{42} +(-7.75389 - 9.24072i) q^{43} +(1.52489 - 3.76327i) q^{44} +(0.140137 - 0.405190i) q^{45} +(3.69043 + 5.47727i) q^{46} +(-0.0706984 - 0.400950i) q^{47} +(2.77980 - 6.34608i) q^{48} +(-4.37418 + 5.46503i) q^{49} +(5.69515 + 4.14217i) q^{50} +(-5.21177 - 1.84958i) q^{51} +(-5.62303 + 6.23231i) q^{52} +(-6.66487 - 3.84796i) q^{53} +(-7.08620 + 1.94572i) q^{54} +0.290148i q^{55} +(2.85454 - 6.91748i) q^{56} +(2.62724 + 14.2295i) q^{57} +(6.06992 + 0.641080i) q^{58} +(-12.3891 + 4.50928i) q^{59} +(-0.0137977 + 0.494874i) q^{60} +(1.95452 + 11.0846i) q^{61} +(-0.524554 - 0.256171i) q^{62} +(-7.60704 + 2.26560i) q^{63} +(-0.860385 + 7.95360i) q^{64} +(0.205147 - 0.563638i) q^{65} +(4.10176 - 2.81190i) q^{66} +(5.02569 - 5.98939i) q^{67} +(6.38165 + 0.229320i) q^{68} +(0.0650724 + 8.08860i) q^{69} +(-0.00341408 + 0.534721i) q^{70} +(-7.22701 + 12.5175i) q^{71} +(7.12965 - 4.60089i) q^{72} -8.66954 q^{73} +(-5.24686 - 1.50739i) q^{74} +(3.01499 + 8.08074i) q^{75} +(-7.82922 - 14.7607i) q^{76} +(4.36413 - 3.13169i) q^{77} +(-9.95617 + 2.56223i) q^{78} +(2.47236 + 2.94645i) q^{79} +(-0.156456 - 0.549826i) q^{80} +(-8.55189 - 2.80449i) q^{81} +(-5.81106 - 2.83789i) q^{82} +(1.33387 + 7.56476i) q^{83} +(7.59234 - 5.13385i) q^{84} +(-0.428787 + 0.156066i) q^{85} +(6.93085 + 15.5882i) q^{86} +(5.76500 + 4.75890i) q^{87} +(-3.54223 + 4.51969i) q^{88} +(-5.55676 - 3.20820i) q^{89} +(-0.348704 + 0.496025i) q^{90} +(-10.6919 + 2.99796i) q^{91} +(-2.87729 - 8.88599i) q^{92} +(-0.362450 - 0.616279i) q^{93} +(-0.0604749 + 0.572592i) q^{94} +(0.914605 + 0.767445i) q^{95} +(-6.25652 + 7.54029i) q^{96} +(2.02876 - 1.70234i) q^{97} +(8.07961 - 5.72013i) q^{98} +(6.08993 - 0.0979927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.35923	−	0.390498i	−0.961122	−	0.276124i
$2$	−1.35923	−	0.390498i	−0.961122	−	0.276124i
$3$	−1.12398	−	1.31783i	−0.648929	−	0.760849i
$3$	−1.12398	−	1.31783i	−0.648929	−	0.760849i
$4$	1.69502	+	1.06155i	0.847511	+	0.530777i
$5$	−0.140742	−	0.0248166i	−0.0629417	−	0.0110983i	0.142089	−	0.989854i	$-0.454618\pi$
$5$	−0.140742	−	0.0248166i	−0.0629417	−	0.0110983i	−0.205030	+	0.978756i	$0.565729\pi$
$6$	1.01314	+	2.23015i	0.413612	+	0.910453i
$7$	1.14582	+	2.38476i	0.433080	+	0.901355i
$7$	1.14582	+	2.38476i	0.433080	+	0.901355i
$8$	−1.88939	−	2.10480i	−0.668001	−	0.744160i
$9$	−0.473344	+	2.96242i	−0.157781	+	0.987474i
$10$	0.181610	+	0.0886910i	0.0574302	+	0.0280466i
$11$	−0.352547	−	1.99940i	−0.106297	−	0.602840i	−0.990694	−	0.136106i	$-0.956541\pi$
$11$	−0.352547	−	1.99940i	−0.106297	−	0.602840i	0.884397	−	0.466735i	$-0.154570\pi$
$12$	−0.506222	−	3.42691i	−0.146134	−	0.989265i
$13$	−0.728806	+	4.13327i	−0.202135	+	1.14636i	0.699751	+	0.714387i	$0.253294\pi$
$13$	−0.728806	+	4.13327i	−0.202135	+	1.14636i	−0.901886	+	0.431975i	$0.857817\pi$
$14$	−0.626193	−	3.68889i	−0.167357	−	0.985896i
$15$	0.125487	+	0.213367i	0.0324006	+	0.0550912i
$16$	1.74620	+	3.59872i	0.436551	+	0.899680i
$17$	2.76512	−	1.59644i	0.670640	−	0.387194i	−0.125679	−	0.992071i	$-0.540111\pi$
$17$	2.76512	−	1.59644i	0.670640	−	0.387194i	0.796319	+	0.604877i	$0.206778\pi$
$18$	1.80020	−	3.84178i	0.424312	−	0.905516i
$19$	−7.23499	−	4.17712i	−1.65982	−	0.958298i	−0.972796	−	0.231663i	$-0.925583\pi$
$19$	−7.23499	−	4.17712i	−1.65982	−	0.958298i	−0.687024	−	0.726635i	$-0.741083\pi$
$20$	−0.212217	−	0.191470i	−0.0474531	−	0.0428140i
$21$	1.85483	−	4.19042i	0.404757	−	0.914424i
$22$	−0.301566	+	2.85531i	−0.0642942	+	0.608754i
$23$	−3.57751	−	3.00189i	−0.745962	−	0.625937i	0.188469	−	0.982079i	$-0.439647\pi$
$23$	−3.57751	−	3.00189i	−0.745962	−	0.625937i	−0.934432	+	0.356142i	$0.884092\pi$
$24$	−0.650130	+	4.85565i	−0.132707	+	0.991155i
$25$	−4.67927	−	1.70312i	−0.935854	−	0.340623i
$26$	2.60465	−	5.33347i	0.510814	−	1.04598i
$27$	4.43599	−	2.70591i	0.853707	−	0.520753i
$28$	−0.589362	+	5.25858i	−0.111379	+	0.993778i
$29$	−4.25038	+	0.749457i	−0.789277	+	0.139171i	−0.553734	−	0.832693i	$-0.686798\pi$
$29$	−4.25038	+	0.749457i	−0.789277	+	0.139171i	−0.235542	+	0.971864i	$0.575687\pi$
$30$	−0.0872464	−	0.339018i	−0.0159289	−	0.0618959i
$31$	0.406512	+	0.0716791i	0.0730117	+	0.0128739i	0.210035	−	0.977694i	$-0.432642\pi$
$31$	0.406512	+	0.0716791i	0.0730117	+	0.0128739i	−0.137023	+	0.990568i	$0.543753\pi$
$32$	−0.968201	−	5.57338i	−0.171155	−	0.985244i
$33$	−2.23860	+	2.71187i	−0.389691	+	0.472077i
$34$	−4.38184	+	1.09016i	−0.751480	+	0.186961i
$35$	−0.102084	−	0.364072i	−0.0172553	−	0.0615394i
$36$	−3.94710	+	4.51889i	−0.657850	+	0.753149i
$37$	3.86017			0.634608			0.317304	−	0.948324i	$-0.397222\pi$
$37$	3.86017			0.634608			0.317304	+	0.948324i	$0.397222\pi$
$38$	8.20287	+	8.50293i	1.33068	+	1.37936i
$39$	6.26610	−	3.68526i	1.00338	−	0.590114i
$40$	0.213683	+	0.343122i	0.0337862	+	0.0542524i
$41$	4.50338	+	0.794068i	0.703310	+	0.124013i	0.513855	−	0.857877i	$-0.328217\pi$
$41$	4.50338	+	0.794068i	0.703310	+	0.124013i	0.189455	+	0.981889i	$0.439328\pi$
$42$	−4.15749	+	4.97144i	−0.641515	+	0.767110i
$43$	−7.75389	−	9.24072i	−1.18246	−	1.40920i	−0.891836	−	0.452359i	$-0.850583\pi$
$43$	−7.75389	−	9.24072i	−1.18246	−	1.40920i	−0.290621	−	0.956838i	$-0.593862\pi$
$44$	1.52489	−	3.76327i	0.229886	−	0.567334i
$45$	0.140137	−	0.405190i	0.0208903	−	0.0604022i
$46$	3.69043	+	5.47727i	0.544125	+	0.807580i
$47$	−0.0706984	−	0.400950i	−0.0103124	−	0.0584846i	0.979217	−	0.202814i	$-0.0650087\pi$
$47$	−0.0706984	−	0.400950i	−0.0103124	−	0.0584846i	−0.989530	+	0.144329i	$0.953898\pi$
$48$	2.77980	−	6.34608i	0.401229	−	0.915978i
$49$	−4.37418	+	5.46503i	−0.624883	+	0.780718i
$50$	5.69515	+	4.14217i	0.805416	+	0.585792i
$51$	−5.21177	−	1.84958i	−0.729794	−	0.258994i
$52$	−5.62303	+	6.23231i	−0.779774	+	0.864266i
$53$	−6.66487	−	3.84796i	−0.915490	−	0.528558i	−0.0332963	−	0.999446i	$-0.510600\pi$
$53$	−6.66487	−	3.84796i	−0.915490	−	0.528558i	−0.882193	+	0.470887i	$0.843934\pi$
$54$	−7.08620	+	1.94572i	−0.964309	+	0.264779i
$55$			0.290148i			0.0391235i
$56$	2.85454	−	6.91748i	0.381455	−	0.924388i
$57$	2.62724	+	14.2295i	0.347987	+	1.88474i
$58$	6.06992	+	0.641080i	0.797019	+	0.0841780i
$59$	−12.3891	+	4.50928i	−1.61293	+	0.587058i	−0.982016	−	0.188796i	$-0.939542\pi$
$59$	−12.3891	+	4.50928i	−1.61293	+	0.587058i	−0.630913	+	0.775854i	$0.717319\pi$
$60$	−0.0137977	+	0.494874i	−0.00178128	+	0.0638879i
$61$	1.95452	+	11.0846i	0.250250	+	1.41924i	0.807976	+	0.589215i	$0.200563\pi$
$61$	1.95452	+	11.0846i	0.250250	+	1.41924i	−0.557726	+	0.830025i	$0.688326\pi$
$62$	−0.524554	−	0.256171i	−0.0666184	−	0.0325337i
$63$	−7.60704	+	2.26560i	−0.958397	+	0.285438i
$64$	−0.860385	+	7.95360i	−0.107548	+	0.994200i
$65$	0.205147	−	0.563638i	0.0254454	−	0.0699107i
$66$	4.10176	−	2.81190i	0.504892	−	0.346120i
$67$	5.02569	−	5.98939i	0.613986	−	0.731720i	−0.366038	−	0.930600i	$-0.619286\pi$
$67$	5.02569	−	5.98939i	0.613986	−	0.731720i	0.980024	+	0.198880i	$0.0637303\pi$
$68$	6.38165	+	0.229320i	0.773888	+	0.0278091i
$69$	0.0650724	+	8.08860i	0.00783380	+	0.973753i
$70$	−0.00341408	+	0.534721i	−0.000408060	+	0.0639114i
$71$	−7.22701	+	12.5175i	−0.857688	+	1.48556i	0.0164408	+	0.999865i	$0.494766\pi$
$71$	−7.22701	+	12.5175i	−0.857688	+	1.48556i	−0.874129	+	0.485694i	$0.838567\pi$
$72$	7.12965	−	4.60089i	0.840237	−	0.542220i
$73$	−8.66954			−1.01469			−0.507346	−	0.861742i	$-0.669374\pi$
$73$	−8.66954			−1.01469			−0.507346	+	0.861742i	$0.669374\pi$
$74$	−5.24686	−	1.50739i	−0.609935	−	0.175230i
$75$	3.01499	+	8.08074i	0.348141	+	0.933084i
$76$	−7.82922	−	14.7607i	−0.898073	−	1.69316i
$77$	4.36413	−	3.13169i	0.497338	−	0.356889i
$78$	−9.95617	+	2.56223i	−1.12731	+	0.290115i
$79$	2.47236	+	2.94645i	0.278162	+	0.331501i	0.886979	−	0.461810i	$-0.152800\pi$
$79$	2.47236	+	2.94645i	0.278162	+	0.331501i	−0.608816	+	0.793311i	$0.708355\pi$
$80$	−0.156456	−	0.549826i	−0.0174923	−	0.0614724i
$81$	−8.55189	−	2.80449i	−0.950210	−	0.311610i
$82$	−5.81106	−	2.83789i	−0.641724	−	0.313392i
$83$	1.33387	+	7.56476i	0.146411	+	0.830340i	0.966223	+	0.257707i	$0.0829670\pi$
$83$	1.33387	+	7.56476i	0.146411	+	0.830340i	−0.819812	+	0.572633i	$0.805922\pi$
$84$	7.59234	−	5.13385i	0.828392	−	0.560149i
$85$	−0.428787	+	0.156066i	−0.0465084	+	0.0169277i
$86$	6.93085	+	15.5882i	0.747372	+	1.68092i
$87$	5.76500	+	4.75890i	0.618073	+	0.510208i
$88$	−3.54223	+	4.51969i	−0.377603	+	0.481800i
$89$	−5.55676	−	3.20820i	−0.589015	−	0.340068i	0.175693	−	0.984445i	$-0.443783\pi$
$89$	−5.55676	−	3.20820i	−0.589015	−	0.340068i	−0.764708	+	0.644377i	$0.777117\pi$
$90$	−0.348704	+	0.496025i	−0.0367567	+	0.0522856i
$91$	−10.6919	+	2.99796i	−1.12082	+	0.314271i
$92$	−2.87729	−	8.88599i	−0.299978	−	0.926428i
$93$	−0.362450	−	0.616279i	−0.0375843	−	0.0639052i
$94$	−0.0604749	+	0.572592i	−0.00623751	+	0.0590584i
$95$	0.914605	+	0.767445i	0.0938365	+	0.0787381i
$96$	−6.25652	+	7.54029i	−0.638554	+	0.769577i
$97$	2.02876	−	1.70234i	0.205990	−	0.172846i	−0.533956	−	0.845512i	$-0.679295\pi$
$97$	2.02876	−	1.70234i	0.205990	−	0.172846i	0.739946	+	0.672666i	$0.234851\pi$
$98$	8.07961	−	5.72013i	0.816164	−	0.577820i
$99$	6.08993	−	0.0979927i	0.612061	−	0.00984864i
$100$	−6.12352	−	7.85412i	−0.612352	−	0.785412i
$101$	−10.7564	−	12.8190i	−1.07030	−	1.27554i	−0.959504	−	0.281694i	$-0.909104\pi$
$101$	−10.7564	−	12.8190i	−1.07030	−	1.27554i	−0.110798	−	0.993843i	$-0.535341\pi$
$102$	6.36174	+	4.54920i	0.629907	+	0.450438i
$103$	16.0802	+	2.83538i	1.58443	+	0.279378i	0.895370	−	0.445323i	$-0.146911\pi$
$103$	16.0802	+	2.83538i	1.58443	+	0.279378i	0.689063	+	0.724701i	$0.258022\pi$
$104$	10.0767	−	6.27537i	0.988103	−	0.615351i
$105$	−0.365044	+	0.543737i	−0.0356247	+	0.0530633i
$106$	7.55648	+	7.83289i	0.733950	+	0.760797i
$107$	−9.76833	−	16.9192i	−0.944340	−	1.63565i	−0.757067	−	0.653337i	$-0.773368\pi$
$107$	−9.76833	−	16.9192i	−0.944340	−	1.63565i	−0.187273	−	0.982308i	$-0.559965\pi$
$108$	10.3916	+	0.122465i	0.999931	+	0.0117842i
$109$	−3.56981	+	6.18309i	−0.341926	+	0.592233i	−0.984790	−	0.173747i	$-0.944412\pi$
$109$	−3.56981	+	6.18309i	−0.341926	+	0.592233i	0.642865	+	0.765980i	$0.277746\pi$
$110$	0.113302	−	0.394378i	0.0108029	−	0.0376025i
$111$	−4.33875	−	5.08704i	−0.411816	−	0.482840i
$112$	−6.58125	+	8.28777i	−0.621870	+	0.783121i
$113$	2.06978	−	2.46667i	0.194708	−	0.232045i	−0.659853	−	0.751395i	$-0.729381\pi$
$113$	2.06978	−	2.46667i	0.194708	−	0.232045i	0.854562	+	0.519350i	$0.173826\pi$
$114$	1.98555	−	20.3671i	0.185964	−	1.90755i
$115$	0.429009	+	0.511273i	0.0400053	+	0.0476765i
$116$	−8.00009	−	3.24167i	−0.742789	−	0.300981i
$117$	−11.8995	−	4.11549i	−1.10011	−	0.380477i
$118$	18.6006	−	1.29122i	1.71232	−	0.118866i
$119$	6.97547	+	4.76491i	0.639440	+	0.436799i
$120$	0.212001	−	0.667260i	0.0193530	−	0.0609122i
$121$	6.46333	−	2.35246i	0.587575	−	0.213860i
$122$	1.67188	−	15.8298i	0.151365	−	1.43316i
$123$	−4.01526	−	6.82720i	−0.362044	−	0.615588i
$124$	0.612956	+	0.553033i	0.0550451	+	0.0496638i
$125$	1.23514	+	0.713107i	0.110474	+	0.0637822i
$126$	11.2244	−	0.108935i	0.999953	−	0.00970472i
$127$	−7.76026	+	4.48039i	−0.688612	+	0.397570i	−0.803092	−	0.595855i	$-0.796813\pi$
$127$	−7.76026	+	4.48039i	−0.688612	+	0.397570i	0.114480	+	0.993426i	$0.463480\pi$
$128$	4.27533	−	10.4748i	0.377889	−	0.925851i
$129$	−3.46248	+	20.6047i	−0.304855	+	1.81414i
$130$	−0.498942	+	0.686005i	−0.0437601	+	0.0601666i
$131$	8.42375	+	7.06837i	0.735987	+	0.617566i	0.931757	−	0.363084i	$-0.118276\pi$
$131$	8.42375	+	7.06837i	0.735987	+	0.617566i	−0.195770	+	0.980650i	$0.562721\pi$
$132$	−6.67329	+	2.22029i	−0.580835	+	0.193251i
$133$	1.67144	−	22.0400i	0.144932	−	1.91111i
$134$	−9.16993	+	6.17844i	−0.792161	+	0.533736i
$135$	−0.691482	+	0.270749i	−0.0595133	+	0.0233024i
$136$	−8.58459	−	2.80372i	−0.736122	−	0.240417i
$137$	−0.655610	+	1.80127i	−0.0560125	+	0.153893i	−0.964543	−	0.263925i	$-0.914983\pi$
$137$	−0.655610	+	1.80127i	−0.0560125	+	0.153893i	0.908531	+	0.417818i	$0.137205\pi$
$138$	3.07013	−	11.0197i	0.261347	−	0.938059i
$139$	3.13731	+	8.61969i	0.266103	+	0.731113i	0.998725	+	0.0504770i	$0.0160742\pi$
$139$	3.13731	+	8.61969i	0.266103	+	0.731113i	−0.732622	+	0.680636i	$0.761704\pi$
$140$	0.213448	−	0.725477i	0.0180397	−	0.0613140i
$141$	−0.448920	+	0.543828i	−0.0378059	+	0.0457986i
$142$	14.7113	−	14.1921i	1.23454	−	1.19098i
$143$	8.52097			0.712559
$144$	−11.4875	+	3.46956i	−0.957290	+	0.289130i
$145$	0.616807			0.0512230
$146$	11.7839	+	3.38544i	0.975244	+	0.280181i
$147$	12.1185	−	0.378149i	0.999513	−	0.0311892i
$148$	6.54307	+	4.09778i	0.537837	+	0.336835i
$149$	−3.14923	−	8.65243i	−0.257995	−	0.708835i	−0.999291	−	0.0376564i	$-0.988011\pi$
$149$	−3.14923	−	8.65243i	−0.257995	−	0.708835i	0.741296	−	0.671178i	$-0.234211\pi$
$150$	−0.942552	−	12.1609i	−0.0769591	−	0.992937i
$151$	−6.27673	+	1.10676i	−0.510793	+	0.0900666i	−0.423104	−	0.906081i	$-0.639059\pi$
$151$	−6.27673	+	1.10676i	−0.510793	+	0.0900666i	−0.0876893	+	0.996148i	$0.527948\pi$
$152$	4.87772	+	23.1204i	0.395636	+	1.87532i
$153$	3.42048	+	8.94711i	0.276530	+	0.723331i
$154$	−7.15478	+	2.55251i	−0.576549	+	0.205687i
$155$	−0.0554345	−	0.0201765i	−0.00445261	−	0.00162062i
$156$	14.5333	+	0.405206i	1.16359	+	0.0324425i
$157$	1.63722	−	0.595901i	0.130665	−	0.0475581i	−0.275860	−	0.961198i	$-0.588963\pi$
$157$	1.63722	−	0.595901i	0.130665	−	0.0475581i	0.406525	+	0.913640i	$0.366740\pi$
$158$	−2.20993	−	4.97036i	−0.175813	−	0.395420i
$159$	2.42021	+	13.1082i	0.191935	+	1.03955i
$160$	−0.00204585	+	0.808437i	−0.000161738	+	0.0639125i
$161$	3.05960	−	11.9711i	0.241130	−	0.943458i
$162$	10.5289	+	7.15145i	0.827225	+	0.561871i
$163$	0.659004	−	0.380476i	0.0516172	−	0.0298012i	−0.473969	−	0.880541i	$-0.657179\pi$
$163$	0.659004	−	0.380476i	0.0516172	−	0.0298012i	0.525587	+	0.850740i	$0.323846\pi$
$164$	6.79039	+	6.12655i	0.530240	+	0.478403i
$165$	0.382365	−	0.326120i	0.0297671	−	0.0253884i
$166$	1.14098	−	10.8031i	0.0885575	−	0.838486i
$167$	9.53182	+	7.99815i	0.737595	+	0.618915i	0.932191	−	0.361968i	$-0.117895\pi$
$167$	9.53182	+	7.99815i	0.737595	+	0.618915i	−0.194596	+	0.980884i	$0.562339\pi$
$168$	−12.3245	+	4.01330i	−0.950856	+	0.309633i
$169$	−4.33673	−	1.57844i	−0.333594	−	0.121418i
$170$	0.643764	−	0.0446889i	0.0493744	−	0.00342748i
$171$	15.7990	−	19.4559i	1.20818	−	1.48783i
$172$	−3.33348	−	23.8944i	−0.254175	−	1.82193i
$173$	2.24119	−	6.15761i	0.170394	−	0.468154i	−0.824874	−	0.565316i	$-0.808754\pi$
$173$	2.24119	−	6.15761i	0.170394	−	0.468154i	0.995269	+	0.0971618i	$0.0309764\pi$
$174$	−5.97763	−	8.71967i	−0.453163	−	0.661037i
$175$	−1.30009	−	13.1104i	−0.0982772	−	0.991054i
$176$	6.57964	−	4.76007i	0.495959	−	0.358804i
$177$	19.8676	+	11.2584i	1.49334	+	0.846236i
$178$	6.30013	+	6.53059i	0.472215	+	0.489488i
$179$	−8.03036	−	13.9090i	−0.600217	−	1.03961i	−0.992788	−	0.119885i	$-0.961747\pi$
$179$	−8.03036	−	13.9090i	−0.600217	−	1.03961i	0.392570	−	0.919722i	$-0.371586\pi$
$180$	0.667667	−	0.538044i	0.0497649	−	0.0401035i
$181$	1.15373	+	1.99832i	0.0857562	+	0.148534i	0.905713	−	0.423891i	$-0.139336\pi$
$181$	1.15373	+	1.99832i	0.0857562	+	0.148534i	−0.819957	+	0.572425i	$0.806003\pi$
$182$	15.7035	+	0.100263i	1.16402	+	0.00743202i
$183$	12.4108	−	15.0346i	0.917432	−	1.11139i
$184$	0.440945	+	13.2017i	0.0325069	+	0.973242i
$185$	−0.543288	−	0.0957963i	−0.0399433	−	0.00704308i
$186$	0.251998	+	0.979202i	0.0184774	+	0.0717986i
$187$	−4.16675	−	4.96574i	−0.304703	−	0.363131i
$188$	0.305795	−	0.754670i	0.0223024	−	0.0550400i
$189$	11.5358	+	7.47829i	0.839107	+	0.543966i
$190$	−0.943474	−	1.40029i	−0.0684468	−	0.101587i
$191$	−12.0857	+	10.1411i	−0.874488	+	0.733783i	−0.965038	−	0.262109i	$-0.915582\pi$
$191$	−12.0857	+	10.1411i	−0.874488	+	0.733783i	0.0905500	+	0.995892i	$0.471138\pi$
$192$	11.4485	−	7.80584i	0.826227	−	0.563338i
$193$	3.84611	−	21.8124i	0.276849	−	1.57009i	−0.456178	−	0.889889i	$-0.650782\pi$
$193$	3.84611	−	21.8124i	0.276849	−	1.57009i	0.733027	−	0.680200i	$-0.238107\pi$
$194$	−3.42232	+	1.52164i	−0.245708	+	0.109247i
$195$	−0.973359	+	0.363168i	−0.0697037	+	0.0260070i
$196$	−13.2158	+	4.61991i	−0.943983	+	0.329993i
$197$	−3.56861	+	2.06034i	−0.254253	+	0.146793i	−0.621710	−	0.783247i	$-0.713562\pi$
$197$	−3.56861	+	2.06034i	−0.254253	+	0.146793i	0.367457	+	0.930041i	$0.380229\pi$
$198$	−8.31589	−	2.24491i	−0.590985	−	0.159539i
$199$	−0.935359	+	0.540030i	−0.0663059	+	0.0382817i	−0.532786	−	0.846250i	$-0.678855\pi$
$199$	−0.935359	+	0.540030i	−0.0663059	+	0.0382817i	0.466481	+	0.884531i	$0.345522\pi$
$200$	5.25626	+	13.0668i	0.371674	+	0.923962i
$201$	−13.5418	+	0.108943i	−0.955162	+	0.00768424i
$202$	9.61466	+	21.6243i	0.676485	+	1.52148i
$203$	−6.65746	−	9.27741i	−0.467262	−	0.651147i
$204$	−6.87063	−	8.66767i	−0.481040	−	0.606858i
$205$	−0.614109	−	0.223517i	−0.0428912	−	0.0156111i
$206$	−20.7496	−	10.1332i	−1.44569	−	0.706016i
$207$	10.5862	−	9.17717i	0.735795	−	0.637857i
$208$	−16.1471	+	4.59475i	−1.11960	+	0.318589i
$209$	−5.80104	+	15.9382i	−0.401267	+	1.10247i
$210$	0.708508	−	0.596516i	0.0488917	−	0.0411635i
$211$	5.36534	−	6.39416i	0.369365	−	0.440192i	−0.549063	−	0.835781i	$-0.685015\pi$
$211$	5.36534	−	6.39416i	0.369365	−	0.440192i	0.918428	+	0.395589i	$0.129460\pi$
$212$	−7.21227	−	13.5975i	−0.495341	−	0.933880i
$213$	24.6190	−	4.54550i	1.68686	−	0.311452i
$214$	6.67049	+	26.8117i	0.455986	+	1.83281i
$215$	0.861974	+	1.49298i	0.0587862	+	0.101821i
$216$	−14.0767	−	4.22435i	−0.957801	−	0.287431i
$217$	0.294853	+	1.05157i	0.0200159	+	0.0713850i
$218$	7.26668	−	7.01025i	0.492162	−	0.474794i
$219$	9.74438	+	11.4250i	0.658464	+	0.772028i
$220$	−0.308008	+	0.491807i	−0.0207659	+	0.0331576i
$221$	4.58328	+	12.5925i	0.308305	+	0.847061i
$222$	3.91088	+	8.60874i	0.262481	+	0.577781i
$223$	9.78866	−	26.8941i	0.655497	−	1.80096i	0.0591326	−	0.998250i	$-0.481167\pi$
$223$	9.78866	−	26.8941i	0.655497	−	1.80096i	0.596365	−	0.802714i	$-0.296611\pi$
$224$	12.1818	−	8.69503i	0.813931	−	0.580961i
$225$	7.26025	−	13.0558i	0.484017	−	0.870388i
$226$	−3.77654	+	2.54453i	−0.251212	+	0.169259i
$227$	0.933365	+	5.29338i	0.0619496	+	0.351334i	0.999988	+	0.00480366i	$0.00152906\pi$
$227$	0.933365	+	5.29338i	0.0619496	+	0.351334i	−0.938039	+	0.346530i	$0.887360\pi$
$228$	−10.6521	+	26.9082i	−0.705454	+	1.78204i
$229$	5.64672	−	2.05524i	0.373146	−	0.135814i	−0.148638	−	0.988892i	$-0.547489\pi$
$229$	5.64672	−	2.05524i	0.373146	−	0.135814i	0.521784	+	0.853078i	$0.325267\pi$
$230$	−0.383472	−	0.862466i	−0.0252854	−	0.0568693i
$231$	−9.03222	−	2.23121i	−0.594276	−	0.146803i
$232$	9.60811	+	7.53020i	0.630803	+	0.494382i
$233$			9.28952i			0.608577i	0.952580	+	0.304288i	$0.0984186\pi$
$233$			9.28952i			0.608577i	−0.952580	+	0.304288i	$0.901581\pi$
$234$	14.5671	+	10.2406i	0.952281	+	0.669451i
$235$			0.0581851i			0.00379557i
$236$	−25.7867	−	5.50842i	−1.67857	−	0.358568i
$237$	1.10403	−	6.56989i	0.0717144	−	0.426760i
$238$	−7.62059	−	9.20053i	−0.493969	−	0.596382i
$239$	−10.0774	+	3.66788i	−0.651854	+	0.237256i	−0.646716	−	0.762731i	$-0.723858\pi$
$239$	−10.0774	+	3.66788i	−0.651854	+	0.237256i	−0.00513880	+	0.999987i	$0.501636\pi$
$240$	−0.548723	+	0.824175i	−0.0354199	+	0.0532002i
$241$	3.40380	+	1.23888i	0.219258	+	0.0798033i	0.449313	−	0.893374i	$-0.351669\pi$
$241$	3.40380	+	1.23888i	0.219258	+	0.0798033i	−0.230056	+	0.973177i	$0.573891\pi$
$242$	−9.70379	+	0.673620i	−0.623783	+	0.0433019i
$243$	5.91631	+	14.4221i	0.379531	+	0.925179i
$244$	−8.45398	+	20.8635i	−0.541211	+	1.33565i
$245$	0.751255	−	0.660606i	0.0479959	−	0.0422046i
$246$	2.79166	+	10.8477i	0.177990	+	0.691624i
$247$	22.5381	−	26.8598i	1.43406	−	1.70905i
$248$	−0.617191	−	0.991058i	−0.0391917	−	0.0629322i
$249$	8.46981	−	10.2604i	0.536753	−	0.650229i
$250$	−1.40037	−	1.45160i	−0.0885672	−	0.0918070i
$251$	3.96451	+	6.86673i	0.250238	+	0.433424i	0.963591	−	0.267380i	$-0.0861579\pi$
$251$	3.96451	+	6.86673i	0.250238	+	0.433424i	−0.713354	+	0.700804i	$0.752825\pi$
$252$	−15.2992	−	4.23506i	−0.963757	−	0.266783i
$253$	−4.74072	+	8.21116i	−0.298046	+	0.516231i
$254$	12.2976	−	3.05952i	0.771619	−	0.191971i
$255$	0.687615	+	0.389653i	0.0430601	+	0.0244010i
$256$	−9.90155	+	12.5682i	−0.618847	+	0.785511i
$257$	−0.00211168	−	0.00580180i	−0.000131723	−	0.000361906i	0.939627	−	0.342201i	$-0.111172\pi$
$257$	−0.00211168	−	0.00580180i	−0.000131723	−	0.000361906i	−0.939758	+	0.341839i	$0.888950\pi$
$258$	12.7524	−	26.6544i	0.793930	−	1.65943i
$259$	4.42306	+	9.20558i	0.274836	+	0.572007i
$260$	0.946062	−	0.737603i	0.0586723	−	0.0457442i
$261$	−0.208316	−	12.9462i	−0.0128945	−	0.801349i
$262$	−8.68965	−	12.8970i	−0.536848	−	0.796780i
$263$	2.06189	−	1.73013i	0.127141	−	0.106684i	−0.577000	−	0.816744i	$-0.695777\pi$
$263$	2.06189	−	1.73013i	0.127141	−	0.106684i	0.704141	+	0.710060i	$0.251332\pi$
$264$	9.93756	−	0.411979i	0.611615	−	0.0253555i
$265$	0.842533	+	0.706969i	0.0517564	+	0.0434288i
$266$	−10.8784	+	29.3047i	−0.667000	+	1.79679i
$267$	2.01783	+	10.9288i	0.123489	+	0.668832i
$268$	14.8767	−	4.81710i	0.908741	−	0.294251i
$269$	−10.4123	−	6.01153i	−0.634848	−	0.366530i	0.147779	−	0.989020i	$-0.452787\pi$
$269$	−10.4123	−	6.01153i	−0.634848	−	0.366530i	−0.782627	+	0.622491i	$0.786121\pi$
$270$	1.04561	−	0.0979888i	0.0636339	−	0.00596341i
$271$	−18.1349	+	10.4702i	−1.10162	+	0.636018i	−0.936645	−	0.350280i	$-0.886086\pi$
$271$	−18.1349	+	10.4702i	−1.10162	+	0.636018i	−0.164971	+	0.986298i	$0.552753\pi$
$272$	10.5736	+	7.16317i	0.641119	+	0.434331i
$273$	15.9683	+	10.7205i	0.966446	+	0.648834i
$274$	1.59452	−	2.19233i	0.0963284	−	0.132444i
$275$	−1.75554	+	9.95614i	−0.105863	+	0.600378i
$276$	−8.47619	+	13.7794i	−0.510207	+	0.829425i
$277$	−2.04107	+	1.71266i	−0.122636	+	0.102904i	−0.702043	−	0.712134i	$-0.747729\pi$
$277$	−2.04107	+	1.71266i	−0.122636	+	0.102904i	0.579407	+	0.815038i	$0.303284\pi$
$278$	−0.898361	−	12.9413i	−0.0538801	−	0.776166i
$279$	−0.404764	+	1.17033i	−0.0242326	+	0.0700659i
$280$	−0.573423	+	0.902740i	−0.0342686	+	0.0539491i
$281$	−17.4083	−	20.7464i	−1.03849	−	1.23763i	−0.970792	−	0.239923i	$-0.922878\pi$
$281$	−17.4083	−	20.7464i	−1.03849	−	1.23763i	−0.0677016	−	0.997706i	$-0.521567\pi$
$282$	0.822551	−	0.563886i	0.0489822	−	0.0335789i
$283$	−10.2947	+	12.2687i	−0.611954	+	0.729298i	−0.979665	−	0.200642i	$-0.935697\pi$
$283$	−10.2947	+	12.2687i	−0.611954	+	0.729298i	0.367711	+	0.929940i	$0.380142\pi$
$284$	−25.5380	+	13.5457i	−1.51540	+	0.803787i
$285$	−0.0166360	−	2.06788i	−0.000985433	−	0.122491i
$286$	−11.5820	−	3.32742i	−0.684857	−	0.196755i
$287$	3.26641	+	11.6494i	0.192810	+	0.687640i
$288$	16.9690	−	0.230096i	0.999908	−	0.0135585i
$289$	−3.40275	+	5.89373i	−0.200162	+	0.346690i
$290$	−0.838383	−	0.240862i	−0.0492316	−	0.0141439i
$291$	−4.52367	−	0.760175i	−0.265182	−	0.0445622i
$292$	−14.6951	−	9.20319i	−0.859964	−	0.538576i
$293$	7.02917	+	19.3125i	0.410649	+	1.12825i	0.956847	+	0.290592i	$0.0938523\pi$
$293$	7.02917	+	19.3125i	0.410649	+	1.12825i	−0.546198	+	0.837656i	$0.683926\pi$
$294$	−16.6195	−	4.21824i	−0.969267	−	0.246013i
$295$	1.85558	−	0.327188i	0.108036	−	0.0190496i
$296$	−7.29338	−	8.12489i	−0.423919	−	0.472250i
$297$	−6.97409	−	7.91534i	−0.404678	−	0.459295i
$298$	0.901772	+	12.9904i	0.0522383	+	0.752515i
$299$	15.0149	−	12.5990i	0.868335	−	0.728619i
$300$	−3.46768	+	16.8976i	−0.200207	+	0.975584i
$301$	13.1524	−	29.0794i	0.758089	−	1.67611i
$302$	8.96372	+	0.946712i	0.515804	+	0.0544771i
$303$	−4.80325	+	28.5834i	−0.275940	+	1.64207i
$304$	2.39853	−	33.3308i	0.137565	−	1.91165i
$305$		−	1.60858i		−	0.0921068i
$306$	−1.15540	−	13.4969i	−0.0660498	−	0.771566i
$307$	−10.2999	−	5.94664i	−0.587846	−	0.339393i	0.176400	−	0.984319i	$-0.443555\pi$
$307$	−10.2999	−	5.94664i	−0.587846	−	0.339393i	−0.764245	+	0.644926i	$0.776888\pi$
$308$	10.7218	−	0.675530i	0.610929	−	0.0384919i
$309$	−14.3373	−	24.3779i	−0.815621	−	1.38681i
$310$	0.0674695	+	0.0490716i	0.00383201	+	0.00278708i
$311$	2.16394	+	1.81576i	0.122706	+	0.102962i	0.702075	−	0.712103i	$-0.252257\pi$
$311$	2.16394	+	1.81576i	0.122706	+	0.102962i	−0.579370	+	0.815065i	$0.696701\pi$
$312$	−19.5959	−	6.22599i	−1.10940	−	0.352477i
$313$	−3.93489	−	1.43218i	−0.222413	−	0.0809517i	0.228410	−	0.973565i	$-0.426647\pi$
$313$	−3.93489	−	1.43218i	−0.222413	−	0.0809517i	−0.450823	+	0.892613i	$0.648869\pi$
$314$	−2.45807	+	0.170635i	−0.138717	+	0.00962947i
$315$	1.12685	−	0.130084i	0.0634911	−	0.00732938i
$316$	1.06289	+	7.61884i	0.0597925	+	0.428593i
$317$	21.9726	−	3.87436i	1.23410	−	0.217606i	0.481717	−	0.876327i	$-0.340013\pi$
$317$	21.9726	−	3.87436i	1.23410	−	0.217606i	0.752387	+	0.658721i	$0.228902\pi$
$318$	1.82909	−	18.7621i	0.102570	−	1.05213i
$319$	2.99692	+	8.23398i	0.167795	+	0.461014i
$320$	0.318474	−	1.09805i	0.0178032	−	0.0613831i
$321$	−11.3173	+	31.8899i	−0.631668	+	1.77992i
$322$	−8.83341	+	15.0768i	−0.492267	+	0.840196i
$323$	−26.6741			−1.48419
$324$	−11.5185	−	13.8320i	−0.639918	−	0.768443i
$325$	10.4497	−	18.0994i	0.579646	−	1.00398i
$326$	−1.04431	+	0.259815i	−0.0578392	+	0.0143898i
$327$	12.1606	−	2.24527i	0.672485	−	0.124163i
$328$	−6.83731	−	10.9790i	−0.377527	−	0.606216i
$329$	0.875164	−	0.628016i	0.0482493	−	0.0346237i
$330$	−0.647072	+	0.293960i	−0.0356202	+	0.0161820i
$331$	16.9517	−	2.98905i	0.931751	−	0.164293i	0.312886	−	0.949791i	$-0.398704\pi$
$331$	16.9517	−	2.98905i	0.931751	−	0.164293i	0.618865	+	0.785498i	$0.287593\pi$
$332$	−5.76947	+	14.2384i	−0.316641	+	0.781435i
$333$	−1.82719	+	11.4354i	−0.100129	+	0.626659i
$334$	−9.83270	−	14.5935i	−0.538021	−	0.798521i
$335$	−0.855963	+	0.718238i	−0.0467662	+	0.0392415i
$336$	18.3190	−	0.642315i	0.999386	−	0.0350411i
$337$	−1.56896	+	8.89804i	−0.0854670	+	0.484707i	0.911788	+	0.410661i	$0.134702\pi$
$337$	−1.56896	+	8.89804i	−0.0854670	+	0.484707i	−0.997255	+	0.0740457i	$0.976409\pi$
$338$	5.27824	+	3.83895i	0.287098	+	0.208811i
$339$	−5.57703	+	0.0448670i	−0.302903	+	0.00243684i
$340$	−0.892475	−	0.190646i	−0.0484013	−	0.0103392i
$341$		−	0.838049i		−	0.0453829i
$342$	−29.0720	+	20.2756i	−1.57204	+	1.09638i
$343$	−18.0448	−	4.16944i	−0.974329	−	0.225129i
$344$	−4.79975	+	33.7798i	−0.258785	+	1.82128i
$345$	0.191573	−	1.14002i	0.0103140	−	0.0613767i
$346$	−5.45083	+	7.49444i	−0.293038	+	0.402904i
$347$	−2.61948	+	14.8558i	−0.140621	+	0.797503i	0.830158	+	0.557528i	$0.188250\pi$
$347$	−2.61948	+	14.8558i	−0.140621	+	0.797503i	−0.970779	+	0.239975i	$0.922861\pi$
$348$	4.71996	+	14.1863i	0.253017	+	0.760466i
$349$	1.82722	+	10.3627i	0.0978091	+	0.554703i	0.993850	+	0.110732i	$0.0353195\pi$
$349$	1.82722	+	10.3627i	0.0978091	+	0.554703i	−0.896041	+	0.443971i	$0.853569\pi$
$350$	−3.35247	+	18.3278i	−0.179197	+	0.979661i
$351$	7.95128	+	20.3072i	0.424408	+	1.08392i
$352$	−10.8021	+	3.90070i	−0.575752	+	0.207908i
$353$	−8.65235	+	23.7721i	−0.460518	+	1.26526i	0.464579	+	0.885532i	$0.346206\pi$
$353$	−8.65235	+	23.7721i	−0.460518	+	1.26526i	−0.925097	+	0.379731i	$0.876016\pi$
$354$	−22.6083	−	23.0611i	−1.20162	−	1.22568i
$355$	1.32779	−	1.58239i	0.0704716	−	0.0839848i
$356$	−6.01315	−	11.3368i	−0.318697	−	0.600847i
$357$	−1.56094	−	14.5481i	−0.0826137	−	0.769969i
$358$	5.48369	+	22.0414i	0.289822	+	1.16492i
$359$	−6.71720	+	11.6345i	−0.354520	+	0.614048i	−0.987036	−	0.160500i	$-0.948689\pi$
$359$	−6.71720	+	11.6345i	−0.354520	+	0.614048i	0.632515	+	0.774548i	$0.282023\pi$
$360$	−1.11762	+	0.470604i	−0.0589037	+	0.0248030i
$361$	25.3967	+	43.9884i	1.33667	+	2.31518i
$362$	−0.787848	−	3.16671i	−0.0414084	−	0.166439i
$363$	−10.3648	−	5.87344i	−0.544010	−	0.308276i
$364$	−21.3056	−	6.26848i	−1.11672	−	0.328557i
$365$	1.22017	+	0.215149i	0.0638665	+	0.0112614i
$366$	−22.7401	+	15.5891i	−1.18865	+	0.814856i
$367$	−19.4173	+	3.42380i	−1.01358	+	0.178721i	−0.655679	−	0.755040i	$-0.727617\pi$
$367$	−19.4173	+	3.42380i	−1.01358	+	0.178721i	−0.357897	+	0.933761i	$0.616506\pi$
$368$	4.55589	−	18.1164i	0.237492	−	0.944380i
$369$	−4.48401	+	12.9651i	−0.233428	+	0.674934i
$370$	0.701046	+	0.342362i	0.0364456	+	0.0177986i
$371$	1.53973	−	20.3032i	0.0799386	−	1.05409i
$372$	0.0398526	−	1.42937i	0.00206626	−	0.0741093i
$373$	3.75328	−	21.2859i	0.194338	−	1.10214i	−0.719021	−	0.694988i	$-0.755410\pi$
$373$	3.75328	−	21.2859i	0.194338	−	1.10214i	0.913359	−	0.407155i	$-0.133479\pi$
$374$	3.72447	+	8.37670i	0.192588	+	0.433149i
$375$	−0.448515	−	2.42921i	−0.0231612	−	0.125444i
$376$	−0.710344	+	0.906359i	−0.0366332	+	0.0467419i
$377$		−	18.1142i		−	0.932928i
$378$	−12.7596	−	14.6695i	−0.656283	−	0.754515i
$379$		−	19.1810i		−	0.985262i	−0.870238	−	0.492631i	$-0.836035\pi$
$379$		−	19.1810i		−	0.985262i	0.870238	−	0.492631i	$-0.163965\pi$
$380$	0.735591	+	2.27174i	0.0377350	+	0.116538i
$381$	14.6268	+	5.19083i	0.749351	+	0.265934i
$382$	20.3873	−	9.06465i	1.04310	−	0.463788i
$383$	−3.12931	+	17.7472i	−0.159900	+	0.906841i	0.794267	+	0.607568i	$0.207855\pi$
$383$	−3.12931	+	17.7472i	−0.159900	+	0.906841i	−0.954168	+	0.299272i	$0.903256\pi$
$384$	−18.6094	+	6.13931i	−0.949656	+	0.313295i
$385$	−0.691934	+	0.332458i	−0.0352642	+	0.0169436i
$386$	−13.7454	+	28.1462i	−0.699625	+	1.43260i
$387$	31.0452	−	18.5963i	1.57812	−	0.945301i
$388$	5.24592	−	0.731852i	0.266321	−	0.0371542i
$389$	14.1112	−	2.48819i	0.715468	−	0.126156i	0.195948	−	0.980614i	$-0.437222\pi$
$389$	14.1112	−	2.48819i	0.715468	−	0.126156i	0.519520	+	0.854458i	$0.326111\pi$
$390$	1.46484	−	0.113534i	0.0741749	−	0.00574903i
$391$	−14.6846	−	2.58929i	−0.742631	−	0.130946i
$392$	19.7674	−	1.11879i	0.998402	−	0.0565076i
$393$	−0.153222	−	19.0458i	−0.00772904	−	0.960731i
$394$	5.65513	−	1.40694i	0.284902	−	0.0708808i
$395$	−0.274844	−	0.476044i	−0.0138289	−	0.0239524i
$396$	10.4266	+	6.29869i	0.523956	+	0.316521i
$397$	4.22322	−	7.31483i	0.211957	−	0.367121i	−0.740370	−	0.672200i	$-0.765350\pi$
$397$	4.22322	−	7.31483i	0.211957	−	0.367121i	0.952327	+	0.305079i	$0.0986829\pi$
$398$	1.48225	−	0.368770i	0.0742985	−	0.0184848i
$399$	−30.9236	+	22.5698i	−1.54811	+	1.12990i
$400$	−2.04192	−	19.8134i	−0.102096	−	0.990668i
$401$	8.42098	−	10.0357i	0.420524	−	0.501161i	−0.513640	−	0.858006i	$-0.671703\pi$
$401$	8.42098	−	10.0357i	0.420524	−	0.501161i	0.934164	+	0.356845i	$0.116148\pi$
$402$	18.4489	+	5.13995i	0.920149	+	0.256358i
$403$	−0.592537	+	1.62798i	−0.0295164	+	0.0810956i
$404$	−4.62429	−	33.1470i	−0.230067	−	1.64912i
$405$	1.13401	+	0.606938i	0.0563495	+	0.0301590i
$406$	5.42622	+	15.2099i	0.269299	+	0.754854i
$407$	−1.36089	−	7.71800i	−0.0674569	−	0.382567i
$408$	5.95407	+	14.4643i	0.294771	+	0.716091i
$409$	4.84383	−	27.4707i	0.239512	−	1.35834i	−0.593388	−	0.804917i	$-0.702210\pi$
$409$	4.84383	−	27.4707i	0.239512	−	1.35834i	0.832900	−	0.553423i	$-0.186679\pi$
$410$	0.747434	+	0.543621i	0.0369131	+	0.0268475i
$411$	3.11066	−	1.16061i	0.153438	−	0.0572487i
$412$	24.2465	+	21.8761i	1.19454	+	1.07776i
$413$	−24.9493	−	24.3783i	−1.22768	−	1.19958i
$414$	−17.9728	+	8.33999i	−0.883317	+	0.409888i
$415$		−	1.09778i		−	0.0538880i
$416$	23.7419	+	0.0600817i	1.16404	+	0.00294575i
$417$	7.83301	−	13.8228i	0.383584	−	0.676905i
$418$	14.1088	−	19.3985i	0.690085	−	0.948810i
$419$	−6.52500	+	37.0051i	−0.318767	+	1.80782i	0.231506	+	0.972833i	$0.425635\pi$
$419$	−6.52500	+	37.0051i	−0.318767	+	1.80782i	−0.550273	+	0.834985i	$0.685476\pi$
$420$	−1.19597	+	0.534133i	−0.0583571	+	0.0260630i
$421$	16.1268	−	13.5320i	0.785972	−	0.659509i	−0.158773	−	0.987315i	$-0.550754\pi$
$421$	16.1268	−	13.5320i	0.785972	−	0.659509i	0.944745	+	0.327806i	$0.106309\pi$
$422$	−9.78964	+	6.59599i	−0.476552	+	0.321088i
$423$	1.22125	−	0.0196511i	0.0593792	−	0.000955467i
$424$	4.49335	+	21.2985i	0.218217	+	1.03435i
$425$	−15.6577	+	2.76087i	−0.759508	+	0.133922i
$426$	−35.2379	−	3.43528i	−1.70728	−	0.166440i
$427$	−24.1947	+	17.3621i	−1.17086	+	0.840209i
$428$	1.40317	−	39.0481i	0.0678246	−	1.88746i
$429$	−9.57739	−	11.2292i	−0.462401	−	0.542150i
$430$	−0.588616	−	2.36591i	−0.0283856	−	0.114094i
$431$	14.5780	−	25.2498i	0.702196	−	1.21624i	−0.265498	−	0.964111i	$-0.585536\pi$
$431$	14.5780	−	25.2498i	0.702196	−	1.21624i	0.967694	−	0.252127i	$-0.0811302\pi$
$432$	17.4840	+	11.2388i	0.841198	+	0.540728i
$433$	−3.07200			−0.147631			−0.0738155	−	0.997272i	$-0.523518\pi$
$433$	−3.07200			−0.147631			−0.0738155	+	0.997272i	$0.523518\pi$
$434$	0.00986104	−	1.54446i	0.000473345	−	0.0741366i
$435$	−0.693278	−	0.812845i	−0.0332401	−	0.0389730i
$436$	−12.6146	+	6.69093i	−0.604130	+	0.320437i
$437$	13.3440	+	36.6623i	0.638330	+	1.75380i
$438$	−8.78344	−	19.3343i	−0.419689	−	0.923830i
$439$	7.78002	−	1.37183i	0.371320	−	0.0654738i	0.0151256	−	0.999886i	$-0.495185\pi$
$439$	7.78002	−	1.37183i	0.371320	−	0.0654738i	0.356194	+	0.934412i	$0.384074\pi$
$440$	0.610704	−	0.548204i	0.0291142	−	0.0261346i
$441$	−14.1192	−	15.5450i	−0.672344	−	0.740239i
$442$	−1.31241	−	18.9058i	−0.0624250	−	0.899259i
$443$	−12.4124	−	4.51776i	−0.589733	−	0.214645i	0.0298792	−	0.999554i	$-0.490488\pi$
$443$	−12.4124	−	4.51776i	−0.589733	−	0.214645i	−0.619612	+	0.784908i	$0.712710\pi$
$444$	−1.95410	−	13.2285i	−0.0927376	−	0.627795i
$445$	0.702453	+	0.589428i	0.0332995	+	0.0279416i
$446$	−23.8072	+	32.7329i	−1.12730	+	1.54995i
$447$	−7.86275	+	13.8753i	−0.371896	+	0.656279i
$448$	−19.9533	+	7.06160i	−0.942704	+	0.333629i
$449$	32.9158	+	19.0039i	1.55339	+	0.896852i	0.997862	+	0.0653557i	$0.0208182\pi$
$449$	32.9158	+	19.0039i	1.55339	+	0.896852i	0.555531	+	0.831496i	$0.312515\pi$
$450$	−14.9666	+	14.9108i	−0.705534	+	0.702900i
$451$		−	9.28399i		−	0.437166i
$452$	6.12683	−	1.98387i	0.288182	−	0.0933135i
$453$	8.51342	+	7.02768i	0.399996	+	0.330189i
$454$	0.798394	−	7.55941i	0.0374705	−	0.354780i
$455$	1.57920	−	0.156601i	0.0740342	−	0.00734156i
$456$	24.9863	−	32.4149i	1.17009	−	1.51797i
$457$	0.671673	−	0.563601i	0.0314195	−	0.0263641i	−0.626943	−	0.779065i	$-0.715694\pi$
$457$	0.671673	−	0.563601i	0.0314195	−	0.0263641i	0.658362	+	0.752701i	$0.271250\pi$
$458$	−8.47777	+	0.588512i	−0.396140	+	0.0274993i
$459$	7.94621	−	14.5640i	0.370897	−	0.679788i
$460$	0.184436	+	1.32204i	0.00859936	+	0.0616403i
$461$	−15.5113	+	2.73507i	−0.722435	+	0.127385i	−0.522763	−	0.852478i	$-0.675099\pi$
$461$	−15.5113	+	2.73507i	−0.722435	+	0.127385i	−0.199672	+	0.979863i	$0.563988\pi$
$462$	11.4056	+	6.55980i	0.530636	+	0.305190i
$463$	−0.727097	−	1.99768i	−0.0337910	−	0.0928401i	0.921650	−	0.388023i	$-0.126842\pi$
$463$	−0.727097	−	1.99768i	−0.0337910	−	0.0928401i	−0.955441	+	0.295183i	$0.904620\pi$
$464$	−10.1191	−	13.9872i	−0.469768	−	0.649341i
$465$	0.0357180	+	0.0957311i	0.00165638	+	0.00443943i
$466$	3.62754	−	12.6266i	0.168043	−	0.584917i
$467$	10.6520	−	18.4498i	0.492914	−	0.853753i	−0.507052	−	0.861915i	$-0.669265\pi$
$467$	10.6520	−	18.4498i	0.492914	−	0.853753i	0.999967	+	0.00816242i	$0.00259821\pi$
$468$	−15.8011	−	19.6078i	−0.730407	−	0.906372i
$469$	20.0418	+	5.12231i	0.925445	+	0.236526i
$470$	0.0227212	−	0.0790870i	0.00104805	−	0.00364801i
$471$	−2.62550	−	1.48780i	−0.120977	−	0.0685542i
$472$	32.8991	+	17.5569i	1.51430	+	0.808121i
$473$	−15.7422	+	18.7609i	−0.723829	+	0.862626i
$474$	−4.06616	+	8.49888i	−0.186765	+	0.390367i
$475$	26.7403	+	31.8679i	1.22693	+	1.46220i
$476$	6.76536	+	15.4815i	0.310090	+	0.709592i
$477$	14.5541	−	17.9227i	0.666385	−	0.820626i
$478$	15.1299	−	1.05029i	0.692024	−	0.0480391i
$479$	−1.03268	+	0.866517i	−0.0471841	+	0.0395922i	−0.666075	−	0.745885i	$-0.732027\pi$
$479$	−1.03268	+	0.866517i	−0.0471841	+	0.0395922i	0.618891	+	0.785477i	$0.287582\pi$
$480$	1.06768	−	0.905969i	0.0487327	−	0.0413517i
$481$	−2.81331	+	15.9551i	−0.128276	+	0.727490i
$482$	−4.14277	−	3.01310i	−0.188698	−	0.137243i
$483$	−19.2148	+	9.42328i	−0.874305	+	0.428774i
$484$	13.4527	+	2.87371i	0.611489	+	0.130623i
$485$	−0.327779	+	0.189243i	−0.0148837	+	0.00859308i
$486$	−2.40983	−	21.9133i	−0.109312	−	0.994007i
$487$	7.88799	+	4.55413i	0.357439	+	0.206367i	0.667957	−	0.744200i	$-0.267169\pi$
$487$	7.88799	+	4.55413i	0.357439	+	0.206367i	−0.310518	+	0.950568i	$0.600502\pi$
$488$	19.6381	−	25.0571i	0.888974	−	1.13428i
$489$	−1.24211	−	0.440807i	−0.0561701	−	0.0199340i
$490$	−1.27910	+	0.604554i	−0.0577836	+	0.0273109i
$491$	−4.49199	−	3.76922i	−0.202721	−	0.170103i	0.535776	−	0.844360i	$-0.320019\pi$
$491$	−4.49199	−	3.76922i	−0.202721	−	0.170103i	−0.738496	+	0.674258i	$0.764464\pi$
$492$	0.441491	−	15.8347i	0.0199040	−	0.713883i
$493$	−10.5563	+	8.85783i	−0.475434	+	0.398937i
$494$	−41.1232	+	27.7076i	−1.85022	+	1.24663i
$495$	−0.859541	−	0.137340i	−0.0386335	−	0.00617296i
$496$	0.451900	+	1.58809i	0.0202909	+	0.0713073i
$497$	−38.1322	−	2.89182i	−1.71046	−	0.129716i
$498$	−15.5191	+	10.6389i	−0.695429	+	0.476739i
$499$	2.91903	+	8.01996i	0.130674	+	0.359023i	0.987724	−	0.156210i	$-0.0499277\pi$
$499$	2.91903	+	8.01996i	0.130674	+	0.359023i	−0.857050	+	0.515233i	$0.827705\pi$
$500$	1.33658	+	2.51990i	0.0597738	+	0.112693i
$501$	−0.173377	−	21.5511i	−0.00774593	−	0.962830i
$502$	−2.70724	−	10.8816i	−0.120830	−	0.485670i
$503$	7.32289	−	12.6836i	0.326512	−	0.565535i	−0.655306	−	0.755364i	$-0.727460\pi$
$503$	7.32289	−	12.6836i	0.326512	−	0.565535i	0.981817	+	0.189829i	$0.0607935\pi$
$504$	19.1413	+	11.7307i	0.852622	+	0.522528i
$505$	1.19575	+	2.07111i	0.0532104	+	0.0921631i
$506$	9.65018	−	9.30963i	0.429003	−	0.413864i
$507$	2.79428	+	7.48919i	0.124098	+	0.332607i
$508$	−17.9100	−	0.643583i	−0.794628	−	0.0285544i
$509$	20.4605	−	24.3839i	0.906895	−	1.08080i	−0.0895022	−	0.995987i	$-0.528528\pi$
$509$	20.4605	−	24.3839i	0.906895	−	1.08080i	0.996397	−	0.0848088i	$-0.0270280\pi$
$510$	−0.782469	−	0.798141i	−0.0346483	−	0.0353423i
$511$	−9.93375	−	20.6748i	−0.439443	−	0.914599i
$512$	18.3664	−	13.2165i	0.811686	−	0.584094i
$513$	−43.3973	+	1.04757i	−1.91604	+	0.0462513i
$514$	0.000604674		0.00871059i	2.66710e−5		0.000384208i
$515$	−2.19280	−	0.798114i	−0.0966263	−	0.0351691i
$516$	−27.7420	+	31.2498i	−1.22127	+	1.37569i
$517$	−0.776734	+	0.282708i	−0.0341607	+	0.0124335i
$518$	−2.41721	−	14.2397i	−0.106206	−	0.625657i
$519$	−10.6337	+	3.96752i	−0.466768	+	0.174155i
$520$	−1.57395	+	0.633139i	−0.0690223	+	0.0277650i
$521$			5.77721i			0.253104i	0.991960	+	0.126552i	$0.0403911\pi$
$521$			5.77721i			0.253104i	−0.991960	+	0.126552i	$0.959609\pi$
$522$	−4.77231	+	17.6782i	−0.208878	+	0.773754i
$523$			17.8743i			0.781590i	0.920478	+	0.390795i	$0.127800\pi$
$523$			17.8743i			0.781590i	−0.920478	+	0.390795i	$0.872200\pi$
$524$	6.77499	+	20.9233i	0.295967	+	0.914039i
$525$	−15.8160	+	16.4491i	−0.690267	+	0.717898i
$526$	−3.47819	+	1.54648i	−0.151656	+	0.0674298i
$527$	1.23849	−	0.450772i	0.0539493	−	0.0196359i
$528$	−13.6683	−	3.32062i	−0.594838	−	0.144512i
$529$	−0.206658	−	1.17202i	−0.00898514	−	0.0509573i
$530$	−0.869128	−	1.28994i	−0.0377525	−	0.0560315i
$531$	−7.49407	−	38.8363i	−0.325215	−	1.68535i
$532$	26.2298	−	35.5839i	1.13720	−	1.54276i
$533$	−6.56419	+	18.0350i	−0.284327	+	0.781181i
$534$	1.52498	−	15.6427i	0.0659924	−	0.676927i
$535$	0.954936	+	2.62367i	0.0412855	+	0.113431i
$536$	−22.1020	+	0.738220i	−0.954661	+	0.0318863i
$537$	−9.30371	+	26.2161i	−0.401485	+	1.13131i
$538$	11.8052	+	12.2370i	0.508959	+	0.527576i
$539$	12.4689	+	6.81904i	0.537072	+	0.293717i
$540$	−1.45949	−	0.275120i	−0.0628066	−	0.0118393i
$541$	9.09244	+	15.7486i	0.390915	+	0.677084i	0.992570	−	0.121671i	$-0.0388254\pi$
$541$	9.09244	+	15.7486i	0.390915	+	0.677084i	−0.601656	+	0.798755i	$0.705492\pi$
$542$	28.7381	−	7.14977i	1.23441	−	0.307109i
$543$	1.33668	−	3.76649i	0.0573623	−	0.161636i
$544$	−11.5748	−	13.8654i	−0.496264	−	0.594473i
$545$	0.655865	−	0.781630i	0.0280942	−	0.0334814i
$546$	−17.5183	−	20.8072i	−0.749714	−	0.890468i
$547$	−4.39628	+	12.0787i	−0.187971	+	0.516447i	−0.997503	−	0.0706297i	$-0.977499\pi$
$547$	−4.39628	+	12.0787i	−0.187971	+	0.516447i	0.809531	+	0.587077i	$0.199721\pi$
$548$	−3.02342	+	2.35723i	−0.129154	+	0.100696i
$549$	−33.7625	+	0.543270i	−1.44095	+	0.0231862i
$550$	6.27403	−	12.8472i	0.267526	−	0.547805i
$551$	33.8821	+	12.3321i	1.44342	+	0.525363i
$552$	16.9020	−	15.4195i	0.719395	−	0.656298i
$553$	−4.19369	+	9.27210i	−0.178334	+	0.394290i
$554$	3.44309	−	1.53087i	0.146283	−	0.0650405i
$555$	0.484401	+	0.823633i	0.0205617	+	0.0349613i
$556$	−3.83246	+	17.9410i	−0.162533	+	0.760868i
$557$	31.8547	−	18.3913i	1.34972	−	0.779264i	0.361515	−	0.932366i	$-0.382260\pi$
$557$	31.8547	−	18.3913i	1.34972	−	0.779264i	0.988210	+	0.153102i	$0.0489264\pi$
$558$	1.00718	−	1.43269i	0.0426373	−	0.0606507i
$559$	43.8455	−	25.3142i	1.85447	−	1.07068i
$560$	1.13193	−	1.00311i	0.0478329	−	0.0423893i
$561$	−1.86066	+	11.0725i	−0.0785569	+	0.467479i
$562$	15.5605	+	34.9971i	0.656380	+	1.47626i
$563$	−6.71957	+	38.1086i	−0.283196	+	1.60609i	0.428462	+	0.903560i	$0.359055\pi$
$563$	−6.71957	+	38.1086i	−0.283196	+	1.60609i	−0.711659	+	0.702525i	$0.752056\pi$
$564$	−1.33823	+	0.445247i	−0.0563498	+	0.0187483i
$565$	−0.352519	+	0.295799i	−0.0148306	+	0.0124443i
$566$	18.7837	−	12.6560i	0.789539	−	0.531969i
$567$	−3.11091	−	23.6077i	−0.130646	−	0.991429i
$568$	40.0016	−	8.43914i	1.67843	−	0.354099i
$569$	17.3067	+	20.6253i	0.725534	+	0.864658i	0.995156	−	0.0983085i	$-0.0313432\pi$
$569$	17.3067	+	20.6253i	0.725534	+	0.864658i	−0.269622	+	0.962966i	$0.586899\pi$
$570$	−0.784892	+	2.81723i	−0.0328755	+	0.118001i
$571$	10.0363	+	1.76967i	0.420005	+	0.0740583i	0.379657	−	0.925127i	$-0.376042\pi$
$571$	10.0363	+	1.76967i	0.420005	+	0.0740583i	0.0403486	+	0.999186i	$0.487153\pi$
$572$	14.4432	+	9.04548i	0.603902	+	0.378210i
$573$	26.9482	+	4.52848i	1.12578	+	0.189180i
$574$	0.109242	−	17.1097i	0.00455966	−	0.714145i
$575$	11.6276	+	20.1396i	0.484903	+	0.839877i
$576$	−23.1547	−	6.31361i	−0.964778	−	0.263067i
$577$	−6.69819	−	11.6016i	−0.278850	−	0.482982i	0.692250	−	0.721658i	$-0.256620\pi$
$577$	−6.69819	−	11.6016i	−0.278850	−	0.482982i	−0.971099	+	0.238677i	$0.923286\pi$
$578$	6.92662	−	6.68218i	0.288109	−	0.277942i
$579$	−33.0679	+	19.4481i	−1.37426	+	0.808237i
$580$	1.04550	+	0.654774i	0.0434121	+	0.0271880i
$581$	−16.5118	+	11.8488i	−0.685024	+	0.491572i
$582$	5.85188	+	2.79974i	0.242568	+	0.116053i
$583$	−5.34392	+	14.6823i	−0.221322	+	0.608078i
$584$	16.3802	+	18.2477i	0.677816	+	0.755094i
$585$	1.57263	+	0.874527i	0.0650202	+	0.0361573i
$586$	−2.01278	−	28.9950i	−0.0831473	−	1.19777i
$587$	14.5314	+	5.28901i	0.599777	+	0.218301i	0.624024	−	0.781405i	$-0.285497\pi$
$587$	14.5314	+	5.28901i	0.599777	+	0.218301i	−0.0242474	+	0.999706i	$0.507719\pi$
$588$	20.9425	+	12.2234i	0.863653	+	0.504086i
$589$	−2.64170	−	2.21665i	−0.108849	−	0.0913354i
$590$	−2.64993	−	0.279875i	−0.109096	−	0.0115223i
$591$	6.72622	+	2.38704i	0.276680	+	0.0981898i
$592$	6.74064	+	13.8917i	0.277038	+	0.570944i
$593$	1.73456	−	1.00145i	0.0712297	−	0.0411245i	−0.463962	−	0.885855i	$-0.653573\pi$
$593$	1.73456	−	1.00145i	0.0712297	−	0.0411245i	0.535192	+	0.844731i	$0.320239\pi$
$594$	6.38848	+	13.4822i	0.262122	+	0.553179i
$595$	−0.863492	−	0.843731i	−0.0353997	−	0.0345896i
$596$	3.84702	−	18.0091i	0.157580	−	0.737683i
$597$	1.76299	+	0.625661i	0.0721544	+	0.0256066i
$598$	−25.3286	+	11.2617i	−1.03576	+	0.460524i
$599$	−19.2792	+	7.01707i	−0.787729	+	0.286710i	−0.704392	−	0.709812i	$-0.748780\pi$
$599$	−19.2792	+	7.01707i	−0.787729	+	0.286710i	−0.0833371	+	0.996521i	$0.526558\pi$
$600$	11.3119	−	21.6137i	0.461805	−	0.882374i
$601$	−21.7235	−	7.90669i	−0.886118	−	0.322521i	−0.141442	−	0.989947i	$-0.545174\pi$
$601$	−21.7235	−	7.90669i	−0.886118	−	0.322521i	−0.744676	+	0.667426i	$0.767396\pi$
$602$	−29.2326	+	34.3897i	−1.19143	+	1.40162i
$603$	15.3642	+	17.7233i	0.625679	+	0.721747i
$604$	−11.8141	−	4.78711i	−0.480708	−	0.194785i
$605$	−0.968042	+	0.170692i	−0.0393565	+	0.00693961i
$606$	17.6905	−	36.9758i	0.718627	−	1.50204i
$607$	−1.04929	−	2.88290i	−0.0425894	−	0.117013i	0.916575	−	0.399863i	$-0.130942\pi$
$607$	−1.04929	−	2.88290i	−0.0425894	−	0.117013i	−0.959164	+	0.282850i	$0.908720\pi$
$608$	−16.2758	+	44.3676i	−0.660070	+	1.79935i
$609$	−4.74319	+	19.2010i	−0.192204	+	0.778064i
$610$	−0.628146	+	2.18643i	−0.0254329	+	0.0885259i
$611$	1.70876			0.0691290
$612$	−3.70006	+	18.7966i	−0.149566	+	0.759807i
$613$	3.22185			0.130129			0.0650647	−	0.997881i	$-0.479275\pi$
$613$	3.22185			0.130129			0.0650647	+	0.997881i	$0.479275\pi$
$614$	11.6778	+	12.1050i	0.471277	+	0.488516i
$615$	0.395688	+	1.06052i	0.0159557	+	0.0427643i
$616$	−14.8371	−	3.26862i	−0.597806	−	0.131697i
$617$	10.1428	+	27.8672i	0.408335	+	1.12189i	0.958066	+	0.286549i	$0.0925081\pi$
$617$	10.1428	+	27.8672i	0.408335	+	1.12189i	−0.549731	+	0.835342i	$0.685270\pi$
$618$	9.96819	+	38.7339i	0.400980	+	1.55811i
$619$	11.0286	−	30.3009i	0.443277	−	1.21789i	−0.494046	−	0.869436i	$-0.664483\pi$
$619$	11.0286	−	30.3009i	0.443277	−	1.21789i	0.937324	−	0.348459i	$-0.113295\pi$
$620$	−0.0725443	−	0.0930464i	−0.00291345	−	0.00373683i
$621$	−23.9927	−	3.63592i	−0.962792	−	0.145904i
$622$	−2.23224	−	3.31305i	−0.0895047	−	0.132841i
$623$	1.28373	−	16.9276i	0.0514315	−	0.678189i
$624$	24.2041	+	16.1147i	0.968939	+	0.645105i
$625$	18.9167	+	15.8730i	0.756670	+	0.634921i
$626$	4.78916	+	3.48323i	0.191413	+	0.139218i
$627$	27.5241	−	10.2695i	1.09921	−	0.410123i
$628$	3.40771	+	0.727938i	0.135983	+	0.0290479i
$629$	10.6738	−	6.16253i	0.425593	−	0.245716i
$630$	−1.58245	−	0.263221i	−0.0630465	−	0.0104870i
$631$	−29.8847	−	17.2539i	−1.18969	−	0.686868i	−0.231455	−	0.972846i	$-0.574348\pi$
$631$	−29.8847	−	17.2539i	−1.18969	−	0.686868i	−0.958236	+	0.285977i	$0.907682\pi$
$632$	1.53042	−	10.7708i	0.0608769	−	0.428441i
$633$	−14.4569	+	0.116305i	−0.574611	+	0.00462272i
$634$	−31.3788	−	3.31410i	−1.24621	−	0.131620i
$635$	1.20338	−	0.437996i	0.0477548	−	0.0173813i
$636$	−9.81273	+	24.7878i	−0.389100	+	0.982902i
$637$	−19.4005	−	22.0626i	−0.768675	−	0.874153i
$638$	−0.858161	−	12.3622i	−0.0339749	−	0.489423i
$639$	−33.6614	−	27.3345i	−1.33162	−	1.08134i
$640$	−0.861667	+	1.36815i	−0.0340604	+	0.0540807i
$641$	6.94759	+	8.27982i	0.274413	+	0.327033i	0.885596	−	0.464457i	$-0.153750\pi$
$641$	6.94759	+	8.27982i	0.274413	+	0.327033i	−0.611183	+	0.791490i	$0.709306\pi$
$642$	27.8357	−	38.9263i	1.09859	−	1.53630i
$643$	10.1850	−	12.1381i	0.401659	−	0.478679i	−0.526866	−	0.849948i	$-0.676633\pi$
$643$	10.1850	−	12.1381i	0.401659	−	0.478679i	0.928525	+	0.371270i	$0.121077\pi$
$644$	17.8941	−	17.0434i	0.705127	−	0.671605i
$645$	0.998655	−	2.81402i	0.0393220	−	0.110802i
$646$	36.2563	+	10.4162i	1.42649	+	0.409820i
$647$	12.6178	−	21.8546i	0.496055	−	0.859193i	−0.503934	−	0.863742i	$-0.668115\pi$
$647$	12.6178	−	21.8546i	0.496055	−	0.859193i	0.999990	+	0.00454903i	$0.00144801\pi$
$648$	10.2550	+	23.2988i	0.402854	+	0.915264i
$649$	13.3836	+	23.1811i	0.525352	+	0.909936i
$650$	−21.2714	+	20.5207i	−0.834332	+	0.804889i
$651$	1.05438	−	1.57050i	0.0413242	−	0.0615529i
$652$	1.52092	+	0.0546533i	0.0595639	+	0.00214039i
$653$	−29.6130	−	5.22157i	−1.15885	−	0.204336i	−0.439012	−	0.898481i	$-0.644671\pi$
$653$	−29.6130	−	5.22157i	−1.15885	−	0.204336i	−0.719835	+	0.694145i	$0.755783\pi$
$654$	−17.4059	−	1.69687i	−0.680625	−	0.0663529i
$655$	−1.01016	−	1.20387i	−0.0394703	−	0.0470389i
$656$	5.00619	+	17.5930i	0.195459	+	0.686892i
$657$	4.10367	−	25.6828i	0.160100	−	1.00198i
$658$	−1.43479	+	0.511870i	−0.0559339	+	0.0199548i
$659$	2.53823	−	2.12983i	0.0988755	−	0.0829664i	−0.592010	−	0.805931i	$-0.701665\pi$
$659$	2.53823	−	2.12983i	0.0988755	−	0.0829664i	0.690885	+	0.722964i	$0.257221\pi$
$660$	0.994312	−	0.146879i	0.0387035	−	0.00571727i
$661$	24.0855	+	20.2101i	0.936818	+	0.786084i	0.977029	−	0.213108i	$-0.0683585\pi$
$661$	24.0855	+	20.2101i	0.936818	+	0.786084i	−0.0402108	+	0.999191i	$0.512803\pi$
$662$	−24.2085	−	2.55681i	−0.940891	−	0.0993732i
$663$	11.4432	−	20.1936i	0.444417	−	0.784256i
$664$	13.4021	−	17.1003i	0.520103	−	0.663622i
$665$	−0.782199	+	3.06047i	−0.0303324	+	0.118680i
$666$	6.94909	−	14.8299i	0.269272	−	0.574647i
$667$	17.4556	+	10.0780i	0.675883	+	0.390221i
$668$	7.66618	+	23.6756i	0.296613	+	0.916036i
$669$	−46.4441	+	17.3286i	−1.79563	+	0.669964i
$670$	1.44392	−	0.642000i	0.0557836	−	0.0248026i
$671$	21.4735	−	7.81570i	0.828974	−	0.301722i
$672$	−25.1507	−	6.28050i	−0.970208	−	0.242275i
$673$	−3.58827	−	20.3501i	−0.138318	−	0.784439i	−0.972492	−	0.232937i	$-0.925166\pi$
$673$	−3.58827	−	20.3501i	−0.138318	−	0.784439i	0.834174	−	0.551501i	$-0.185945\pi$
$674$	5.60725	−	11.4818i	0.215983	−	0.442263i
$675$	−25.3657	+	5.10670i	−0.976326	+	0.196557i
$676$	−5.67525	−	7.27916i	−0.218279	−	0.279968i
$677$	−23.1044	−	27.5347i	−0.887974	−	1.05825i	−0.997930	−	0.0643098i	$-0.979515\pi$
$677$	−23.1044	−	27.5347i	−0.887974	−	1.05825i	0.109956	−	0.993936i	$-0.464929\pi$
$678$	7.59800	+	2.11684i	0.291799	+	0.0812966i
$679$	6.38427	+	2.88755i	0.245006	+	0.110814i
$680$	1.13863	+	0.607642i	0.0436646	+	0.0233020i
$681$	5.92668	−	7.17966i	0.227111	−	0.275125i
$682$	−0.327256	+	1.13910i	−0.0125313	+	0.0436185i
$683$	22.5797			0.863989			0.431995	−	0.901876i	$-0.357810\pi$
$683$	22.5797			0.863989			0.431995	+	0.901876i	$0.357810\pi$
$684$	47.4332	−	16.2066i	1.81365	−	0.619675i
$685$	0.136973	−	0.237245i	0.00523348	−	0.00906466i
$686$	22.8989	+	12.7137i	0.874286	+	0.485412i
$687$	−9.05524	−	5.13136i	−0.345479	−	0.195774i
$688$	19.7149	−	44.0402i	0.751624	−	1.67902i
$689$	20.7620	−	24.7432i	0.790971	−	0.942642i
$690$	−0.705568	+	1.47474i	−0.0268605	+	0.0561425i
$691$	−13.4128	+	36.8515i	−0.510248	+	1.40190i	0.370731	+	0.928740i	$0.379107\pi$
$691$	−13.4128	+	36.8515i	−0.510248	+	1.40190i	−0.880979	+	0.473155i	$0.843115\pi$
$692$	10.3355	−	8.05814i	0.392897	−	0.306325i
$693$	7.21166	+	14.4108i	0.273948	+	0.547419i
$694$	9.36166	−	19.1696i	0.355364	−	0.727669i
$695$	−0.227640	−	1.29101i	−0.00863488	−	0.0489708i
$696$	−0.875799	−	21.1256i	−0.0331971	−	0.800765i
$697$	13.7201	−	4.99370i	0.519685	−	0.189150i
$698$	1.56299	−	14.7988i	0.0591602	−	0.560144i
$699$	12.2420	−	10.4412i	0.463035	−	0.394923i
$700$	11.7138	−	23.6026i	0.442738	−	0.892093i
$701$		−	42.3618i		−	1.59998i	−0.600012	−	0.799991i	$-0.704837\pi$
$701$		−	42.3618i		−	1.59998i	0.600012	−	0.799991i	$-0.295163\pi$
$702$	−2.87770	−	30.7072i	−0.108612	−	1.15897i
$703$	−27.9283	−	16.1244i	−1.05333	−	0.608143i
$704$	16.2057	−	1.08377i	0.610776	−	0.0408462i
$705$	0.0766779	−	0.0653988i	0.00288786	−	0.00246306i
$706$	21.0435	−	28.9331i	0.791984	−	1.08891i
$707$	18.2453	−	40.3398i	0.686186	−	1.51713i
$708$	21.7246	+	40.1738i	0.816459	+	1.50982i
$709$	−5.59386	−	31.7244i	−0.210082	−	1.19143i	−0.889240	−	0.457441i	$-0.848766\pi$
$709$	−5.59386	−	31.7244i	−0.210082	−	1.19143i	0.679158	−	0.733992i	$-0.262345\pi$
$710$	−2.42269	+	1.63234i	−0.0909220	+	0.0612607i
$711$	−9.89889	+	5.92950i	−0.371238	+	0.222374i
$712$	3.74629	+	17.7574i	0.140398	+	0.665488i
$713$	−1.23913	−	1.47674i	−0.0464057	−	0.0553042i
$714$	−3.55934	+	20.3838i	−0.133205	+	0.762845i
$715$	−1.19926	−	0.211462i	−0.0448497	−	0.00790822i
$716$	1.15352	−	32.1007i	0.0431089	−	1.19966i
$717$	16.1605	+	9.15770i	0.603523	+	0.342000i
$718$	13.6735	−	13.1910i	0.510291	−	0.492283i
$719$	11.2790			0.420634			0.210317	−	0.977633i	$-0.432550\pi$
$719$	11.2790			0.420634			0.210317	+	0.977633i	$0.432550\pi$
$720$	1.70287	−	0.203232i	0.0634624	−	0.00757402i
$721$	11.6634	+	41.5964i	0.434367	+	1.54913i
$722$	−17.3426	−	69.7078i	−0.645426	−	2.59425i
$723$	−2.19316	−	5.87809i	−0.0815646	−	0.218609i
$724$	−0.165727	+	4.61195i	−0.00615920	+	0.171402i
$725$	21.1651	+	3.73198i	0.786053	+	0.138602i
$726$	11.7946	+	12.0308i	0.437738	+	0.446505i
$727$	29.1133	−	5.13347i	1.07975	−	0.190390i	0.394648	−	0.918833i	$-0.370867\pi$
$727$	29.1133	−	5.13347i	1.07975	−	0.190390i	0.685107	+	0.728443i	$0.259756\pi$
$728$	26.5114	+	16.8401i	0.982577	+	0.624136i
$729$	12.3561	−	24.0068i	0.457632	−	0.889142i
$730$	−1.57448	−	0.768910i	−0.0582740	−	0.0284586i
$731$	−36.1927	−	13.1731i	−1.33864	−	0.487223i
$732$	36.9966	−	12.3092i	1.36743	−	0.454963i
$733$	1.66572	+	1.39771i	0.0615248	+	0.0516255i	0.673032	−	0.739614i	$-0.264992\pi$
$733$	1.66572	+	1.39771i	0.0615248	+	0.0516255i	−0.611507	+	0.791239i	$0.709436\pi$
$734$	27.7296	+	2.92869i	1.02352	+	0.108100i
$735$	−1.71496	−	0.247518i	−0.0632573	−	0.00912983i
$736$	−13.2669	+	22.8453i	−0.489025	+	0.842087i
$737$	−13.7470	−	7.93681i	−0.506375	−	0.292356i
$738$	11.1576	−	15.8715i	0.410719	−	0.584239i
$739$	−9.29505	+	5.36650i	−0.341924	+	0.197410i	−0.661123	−	0.750278i	$-0.729920\pi$
$739$	−9.29505	+	5.36650i	−0.341924	+	0.197410i	0.319198	+	0.947688i	$0.396586\pi$
$740$	−0.819192	−	0.739107i	−0.0301141	−	0.0271701i
$741$	−60.7289	+	0.488562i	−2.23093	+	0.0179478i
$742$	−10.0212	+	26.9955i	−0.367890	+	0.991036i
$743$	1.32772	−	7.52987i	0.0487093	−	0.276244i	−0.950719	−	0.310054i	$-0.899653\pi$
$743$	1.32772	−	7.52987i	0.0487093	−	0.276244i	0.999428	+	0.0338097i	$0.0107640\pi$
$744$	−0.612334	+	1.92728i	−0.0224493	+	0.0706575i
$745$	0.228505	+	1.29591i	0.00837176	+	0.0474786i
$746$	−13.4137	+	27.4669i	−0.491110	+	1.00563i
$747$	−23.0414	+	0.370758i	−0.843040	+	0.0135653i
$748$	−1.79133	−	12.8403i	−0.0654976	−	0.469487i
$749$	29.1556	−	42.6816i	1.06532	−	1.55955i
$750$	−0.338967	+	3.47701i	−0.0123773	+	0.126962i
$751$	−20.7774	−	3.66361i	−0.758176	−	0.133687i	−0.218821	−	0.975765i	$-0.570221\pi$
$751$	−20.7774	−	3.66361i	−0.758176	−	0.133687i	−0.539356	+	0.842078i	$0.681332\pi$
$752$	1.31945	−	0.954564i	0.0481155	−	0.0348094i
$753$	4.59315	−	12.9426i	0.167384	−	0.471655i
$754$	−7.07355	+	24.6214i	−0.257604	+	0.896657i
$755$	0.910865			0.0331498
$756$	11.6149	+	24.9218i	0.422428	+	0.906396i
$757$	−42.3227			−1.53824			−0.769122	−	0.639102i	$-0.779306\pi$
$757$	−42.3227			−1.53824			−0.769122	+	0.639102i	$0.779306\pi$
$758$	−7.49015	+	26.0714i	−0.272054	+	0.946957i
$759$	16.1494	−	2.98172i	0.586185	−	0.108230i
$760$	−0.112729	−	3.37507i	−0.00408912	−	0.122427i
$761$	6.10214	+	1.07597i	0.221202	+	0.0390039i	0.283151	−	0.959075i	$-0.408620\pi$
$761$	6.10214	+	1.07597i	0.221202	+	0.0390039i	−0.0619484	+	0.998079i	$0.519731\pi$
$762$	−17.8541	−	12.7673i	−0.646787	−	0.462509i
$763$	−18.8356	−	1.42843i	−0.681893	−	0.0517125i
$764$	−31.2508	+	4.35976i	−1.13061	+	0.157731i
$765$	−0.259369	−	1.34412i	−0.00937749	−	0.0485967i
$766$	11.1837	−	22.9006i	0.404084	−	0.827432i
$767$	−9.60876	−	54.4940i	−0.346952	−	1.96766i
$768$	27.6918	−	1.07782i	0.999243	−	0.0388926i
$769$	3.66507	−	20.7857i	0.132166	−	0.749550i	−0.844625	−	0.535358i	$-0.820177\pi$
$769$	3.66507	−	20.7857i	0.132166	−	0.749550i	0.976791	−	0.214193i	$-0.0687120\pi$
$770$	1.07032	−	0.181688i	0.0385718	−	0.00654760i
$771$	−0.00527229	+	0.00930393i	−0.000189877	+	0.000335073i
$772$	29.6743	−	32.8896i	1.06800	−	1.18372i
$773$	−39.3083	+	22.6947i	−1.41382	+	0.816271i	−0.995746	−	0.0921409i	$-0.970629\pi$
$773$	−39.3083	+	22.6947i	−1.41382	+	0.816271i	−0.418077	+	0.908412i	$0.637296\pi$
$774$	−49.4594	+	13.1535i	−1.77778	+	0.472794i
$775$	−1.78010	−	1.02774i	−0.0639432	−	0.0369176i
$776$	−7.41621	−	1.05377i	−0.266227	−	0.0378280i
$777$	7.15995	−	16.1757i	0.256862	−	0.580301i
$778$	−20.1521	−	2.12838i	−0.722487	−	0.0763061i
$779$	−29.2650	−	24.5563i	−1.04853	−	0.879819i
$780$	−2.03539	−	0.417697i	−0.0728786	−	0.0149559i
$781$	27.5754	+	10.0366i	0.986725	+	0.359138i
$782$	18.9486	+	9.25374i	0.677602	+	0.330913i
$783$	−16.8267	+	14.8258i	−0.601337	+	0.529829i
$784$	−27.3053	−	6.19842i	−0.975189	−	0.221372i
$785$	−0.245214	+	0.0432379i	−0.00875208	+	0.00154323i
$786$	−7.22907	+	25.9474i	−0.257852	+	0.925514i
$787$	52.3693	+	9.23412i	1.86676	+	0.329161i	0.988762	−	0.149498i	$-0.0477657\pi$
$787$	52.3693	+	9.23412i	1.86676	+	0.329161i	0.878001	+	0.478659i	$0.158877\pi$
$788$	−8.23605	−	0.295956i	−0.293397	−	0.0105430i
$789$	−4.59753	−	0.772585i	−0.163676	−	0.0275048i
$790$	0.187683	+	0.754381i	0.00667745	+	0.0268397i
$791$	8.25401	+	2.10957i	0.293479	+	0.0750077i
$792$	−11.7125	−	12.6329i	−0.416187	−	0.448892i
$793$	−47.2401			−1.67755
$794$	−8.59676	+	8.29339i	−0.305088	+	0.294321i
$795$	−0.0153251	−	1.90493i	−0.000543525	−	0.0675610i
$796$	−2.15873	−	0.0775723i	−0.0765140	−	0.00274948i
$797$	31.5719	+	5.56698i	1.11833	+	0.197193i	0.702110	−	0.712069i	$-0.252242\pi$
$797$	31.5719	+	5.56698i	1.11833	+	0.197193i	0.416225	+	0.909261i	$0.363353\pi$
$798$	50.8457	−	18.6020i	1.79992	−	0.658503i
$799$	−0.835583	−	0.995809i	−0.0295608	−	0.0352292i
$800$	−4.96163	+	27.7283i	−0.175420	+	0.980344i
$801$	12.1343	−	14.9429i	0.428744	−	0.527981i
$802$	−15.3650	+	10.3525i	−0.542557	+	0.365560i
$803$	3.05642	+	17.3338i	0.107859	+	0.611698i
$804$	−23.0692	−	14.1907i	−0.813589	−	0.500466i
$805$	−0.727697	+	1.60891i	−0.0256480	+	0.0567067i
$806$	1.44112	−	1.98142i	0.0507613	−	0.0697926i
$807$	3.78101	+	20.4784i	0.133098	+	0.720875i
$808$	−6.65835	+	46.8602i	−0.234240	+	1.64854i
$809$	9.75653	+	5.63293i	0.343021	+	0.198043i	0.661607	−	0.749851i	$-0.269875\pi$
$809$	9.75653	+	5.63293i	0.343021	+	0.198043i	−0.318586	+	0.947894i	$0.603208\pi$
$810$	−1.30438	−	1.26780i	−0.0458312	−	0.0445459i
$811$			19.4379i			0.682557i	0.939962	+	0.341279i	$0.110860\pi$
$811$			19.4379i			0.682557i	−0.939962	+	0.341279i	$0.889140\pi$
$812$	−1.43607	−	22.7927i	−0.0503960	−	0.799866i
$813$	34.1811	+	12.1304i	1.19878	+	0.425432i
$814$	−1.16410	+	11.0220i	−0.0408016	+	0.386320i
$815$	−0.102192	+	0.0371947i	−0.00357962	+	0.00130287i
$816$	−2.44467	−	21.9854i	−0.0855806	−	0.769644i
$817$	17.4997	+	99.2455i	0.612235	+	3.47216i
$818$	−17.3112	+	35.4476i	−0.605270	+	1.23940i
$819$	−3.82025	−	33.0931i	−0.133490	−	1.15637i
$820$	−0.803653	−	1.03078i	−0.0280648	−	0.0359963i
$821$	−17.7849	+	48.8637i	−0.620698	+	1.70535i	0.0845747	+	0.996417i	$0.473047\pi$
$821$	−17.7849	+	48.8637i	−0.620698	+	1.70535i	−0.705273	+	0.708936i	$0.749175\pi$
$822$	−4.68132	+	0.362833i	−0.163280	+	0.0126553i
$823$	−4.12030	+	4.91038i	−0.143625	+	0.171165i	−0.833061	−	0.553181i	$-0.813414\pi$
$823$	−4.12030	+	4.91038i	−0.143625	+	0.171165i	0.689436	+	0.724346i	$0.257858\pi$
$824$	−24.4140	−	39.2029i	−0.850501	−	1.36570i
$825$	15.0937	−	8.87699i	0.525494	−	0.309057i
$826$	24.3922	+	42.8785i	0.848713	+	1.49193i
$827$	12.6851	−	21.9712i	0.441102	−	0.764012i	−0.556669	−	0.830734i	$-0.687921\pi$
$827$	12.6851	−	21.9712i	0.441102	−	0.764012i	0.997772	+	0.0667225i	$0.0212542\pi$
$828$	27.6860	−	4.31763i	0.962155	−	0.150048i
$829$	39.9321			1.38690			0.693450	−	0.720505i	$-0.256090\pi$
$829$	39.9321			1.38690			0.693450	+	0.720505i	$0.256090\pi$
$830$	−0.428682	+	1.49214i	−0.0148798	+	0.0517929i
$831$	4.55112	+	0.764787i	0.157877	+	0.0265302i
$832$	−32.2473	−	9.35283i	−1.11797	−	0.324251i
$833$	−3.37054	+	22.0946i	−0.116782	+	0.765532i
$834$	−16.0446	+	15.7296i	−0.555581	+	0.544672i
$835$	−1.14304	−	1.36222i	−0.0395566	−	0.0471417i
$836$	−26.7522	+	20.8575i	−0.925244	+	0.721373i
$837$	1.99724	−	0.782019i	0.0690348	−	0.0270305i
$838$	23.3194	−	47.7505i	0.805556	−	1.64951i
$839$	−3.11104	−	17.6436i	−0.107405	−	0.609125i	−0.990232	−	0.139427i	$-0.955474\pi$
$839$	−3.11104	−	17.6436i	−0.107405	−	0.609125i	0.882827	−	0.469698i	$-0.155637\pi$
$840$	1.83417	−	0.258988i	0.0632850	−	0.00893593i
$841$	−9.74700	+	3.54762i	−0.336104	+	0.122332i
$842$	−27.2043	+	12.0956i	−0.937521	+	0.416843i
$843$	−7.77365	+	46.2597i	−0.267739	+	1.59327i
$844$	15.8821	−	5.14264i	0.546685	−	0.177017i
$845$	0.571188	+	0.329776i	0.0196495	+	0.0113446i
$846$	−1.66763	−	0.450185i	−0.0573344	−	0.0154777i
$847$	13.0159	+	12.7180i	0.447231	+	0.436996i
$848$	2.20953	−	30.7043i	0.0758755	−	1.05439i
$849$	27.7390	−	0.223159i	0.952000	−	0.00765880i
$850$	22.3605	+	2.36163i	0.766959	+	0.0810031i
$851$	−13.8098	−	11.5878i	−0.473393	−	0.397224i
$852$	46.5550	+	18.4297i	1.59495	+	0.631390i
$853$	−18.2971	+	15.3531i	−0.626481	+	0.525680i	−0.899833	−	0.436234i	$-0.856312\pi$
$853$	−18.2971	+	15.3531i	−0.626481	+	0.525680i	0.273352	+	0.961914i	$0.411867\pi$
$854$	39.6660	−	14.1511i	1.35734	−	0.484241i
$855$	−2.70642	+	2.34618i	−0.0925575	+	0.0802377i
$856$	−17.1554	+	52.5275i	−0.586361	+	1.79535i
$857$	−4.85869	−	5.79036i	−0.165970	−	0.197795i	0.676649	−	0.736306i	$-0.263432\pi$
$857$	−4.85869	−	5.79036i	−0.165970	−	0.197795i	−0.842619	+	0.538511i	$0.818987\pi$
$858$	8.63292	+	19.0030i	0.294723	+	0.648752i
$859$	−27.8797	−	4.91594i	−0.951242	−	0.167730i	−0.323567	−	0.946205i	$-0.604882\pi$
$859$	−27.8797	−	4.91594i	−0.951242	−	0.167730i	−0.627675	+	0.778476i	$0.715993\pi$
$860$	−0.123818	+	3.44567i	−0.00422215	+	0.117496i
$861$	11.6805	−	17.3982i	0.398070	−	0.592929i
$862$	−29.6748	+	28.6276i	−1.01073	+	0.975061i
$863$	22.2189	+	38.4843i	0.756340	+	1.31002i	0.944705	+	0.327920i	$0.106348\pi$
$863$	22.2189	+	38.4843i	0.756340	+	1.31002i	−0.188366	+	0.982099i	$0.560319\pi$
$864$	−19.3760	−	22.1036i	−0.659186	−	0.751980i
$865$	−0.468240	+	0.811016i	−0.0159206	+	0.0275754i
$866$	4.17556	+	1.19961i	0.141891	+	0.0407644i
$867$	11.5915	−	2.14019i	0.393670	−	0.0726847i
$868$	−0.616513	+	2.09543i	−0.0209258	+	0.0711236i
$869$	5.01949	−	5.98199i	0.170274	−	0.202925i
$870$	0.624910	+	1.37557i	0.0211864	+	0.0466362i
$871$	21.0930	+	25.1376i	0.714708	+	0.851756i
$872$	19.7590	−	4.16855i	0.669123	−	0.141165i
$873$	4.08273	+	6.81585i	0.138180	+	0.230681i
$874$	−3.82101	−	55.0434i	−0.129248	−	1.86187i
$875$	−0.285343	+	3.76260i	−0.00964635	+	0.127199i
$876$	4.38871	+	29.7098i	0.148281	+	1.00380i
$877$	−42.5553	+	15.4889i	−1.43699	+	0.523022i	−0.938926	−	0.344119i	$-0.888178\pi$
$877$	−42.5553	+	15.4889i	−1.43699	+	0.523022i	−0.498064	+	0.867140i	$0.665956\pi$
$878$	−11.1105	−	1.17345i	−0.374963	−	0.0396021i
$879$	17.5499	−	30.9701i	0.591944	−	1.04459i
$880$	−1.04416	+	0.506657i	−0.0351987	+	0.0170794i
$881$	31.2033	+	18.0152i	1.05126	+	0.606948i	0.923003	−	0.384793i	$-0.125727\pi$
$881$	31.2033	+	18.0152i	1.05126	+	0.606948i	0.128261	+	0.991740i	$0.459060\pi$
$882$	13.1210	+	26.6428i	0.441807	+	0.897110i
$883$	−33.7825	+	19.5044i	−1.13687	+	0.656374i	−0.945654	−	0.325173i	$-0.894577\pi$
$883$	−33.7825	+	19.5044i	−1.13687	+	0.656374i	−0.191219	+	0.981547i	$0.561244\pi$
$884$	−5.59883	+	26.2099i	−0.188309	+	0.881535i
$885$	−2.51681	−	2.07758i	−0.0846016	−	0.0698371i
$886$	15.1072	+	10.9877i	0.507536	+	0.369139i
$887$	8.98004	+	7.53515i	0.301520	+	0.253006i	0.780977	−	0.624560i	$-0.214722\pi$
$887$	8.98004	+	7.53515i	0.301520	+	0.253006i	−0.479456	+	0.877566i	$0.659166\pi$
$888$	−2.50961	+	18.7436i	−0.0842171	+	0.628995i
$889$	−19.5765	−	13.3727i	−0.656576	−	0.448504i
$890$	−0.724626	−	1.07548i	−0.0242895	−	0.0360500i
$891$	−2.59233	+	18.0873i	−0.0868465	+	0.605948i
$892$	45.1416	−	35.1949i	1.51145	−	1.17841i
$893$	−1.16332	+	3.19619i	−0.0389289	+	0.106956i
$894$	16.1056	−	15.7893i	0.538651	−	0.528075i
$895$	0.785035	+	2.15687i	0.0262408	+	0.0720961i
$896$	29.8787	−	1.80662i	0.998177	−	0.0603550i
$897$	−33.4798	−	5.62606i	−1.11786	−	0.187849i
$898$	−37.3192	−	38.6843i	−1.24536	−	1.29091i
$899$	−1.78155			−0.0594181
$900$	26.1658	−	14.4227i	0.872192	−	0.480758i
$901$	−24.5722			−0.818618
$902$	−3.62538	+	12.6191i	−0.120712	+	0.420170i
$903$	−53.1046	+	15.3521i	−1.76721	+	0.510885i
$904$	−9.10247	+	0.304028i	−0.302744	+	0.0101118i
$905$	−0.112787	−	0.309880i	−0.00374917	−	0.0103007i
$906$	−8.82742	−	12.8767i	−0.293271	−	0.427800i
$907$	−5.64803	+	0.995899i	−0.187540	+	0.0330683i	−0.266629	−	0.963799i	$-0.585910\pi$
$907$	−5.64803	+	0.995899i	−0.187540	+	0.0330683i	0.0790894	+	0.996868i	$0.474799\pi$
$908$	−4.03714	+	9.96321i	−0.133977	+	0.330641i
$909$	43.0667	−	25.7972i	1.42843	−	0.855640i
$910$	−2.20766	−	0.403820i	−0.0731831	−	0.0133865i
$911$	−39.2905	−	14.3006i	−1.30175	−	0.473799i	−0.404186	−	0.914677i	$-0.632445\pi$
$911$	−39.2905	−	14.3006i	−1.30175	−	0.473799i	−0.897567	+	0.440878i	$0.854667\pi$
$912$	−46.6202	+	34.3022i	−1.54375	+	1.13586i
$913$	14.6547	−	5.33387i	0.485000	−	0.176525i
$914$	−1.13304	+	0.503777i	−0.0374778	+	0.0166635i
$915$	−2.11983	+	1.80801i	−0.0700793	+	0.0597708i
$916$	11.7531	+	2.51063i	0.388332	+	0.0829535i
$917$	−7.20426	+	28.1877i	−0.237906	+	0.930841i
$918$	−16.4879	+	16.6928i	−0.544183	+	0.550946i
$919$	16.9746	−	9.80027i	0.559939	−	0.323281i	−0.193182	−	0.981163i	$-0.561881\pi$
$919$	16.9746	−	9.80027i	0.559939	−	0.323281i	0.753121	+	0.657882i	$0.228547\pi$
$920$	0.265562	−	1.86898i	0.00875532	−	0.0616183i
$921$	3.74020	+	20.2574i	0.123244	+	0.667503i
$922$	22.1515	+	2.33956i	0.729522	+	0.0770492i
$923$	−46.4712	−	38.9940i	−1.52962	−	1.28350i
$924$	−12.9413	−	13.3702i	−0.425736	−	0.439846i
$925$	−18.0628	−	6.57431i	−0.593900	−	0.216162i
$926$	0.208202	+	2.99924i	0.00684194	+	0.0985612i
$927$	−16.0111	+	46.2943i	−0.525873	+	1.52051i
$928$	8.29224	+	22.9634i	0.272206	+	0.753810i
$929$	−10.0252	+	27.5440i	−0.328916	+	0.903689i	0.659471	+	0.751730i	$0.270780\pi$
$929$	−10.0252	+	27.5440i	−0.328916	+	0.903689i	−0.988387	+	0.151959i	$0.951442\pi$
$930$	−0.0111663	−	0.144069i	−0.000366156	−	0.00472420i
$931$	54.4753	−	21.2679i	1.78535	−	0.697027i
$932$	−9.86134	+	15.7459i	−0.323019	+	0.515776i
$933$	−0.0393605	−	4.89257i	−0.00128860	−	0.160176i
$934$	−21.6831	+	20.9179i	−0.709493	+	0.684455i
$935$	0.463204	+	0.802293i	0.0151484	+	0.0262378i
$936$	13.8206	+	32.8219i	0.451739	+	1.07282i
$937$	−22.3299	−	38.6765i	−0.729485	−	1.26351i	−0.957101	−	0.289754i	$-0.906426\pi$
$937$	−22.3299	−	38.6765i	−0.729485	−	1.26351i	0.227616	−	0.973751i	$-0.426907\pi$
$938$	−25.2412	−	14.7887i	−0.824155	−	0.482868i
$939$	2.53536	+	6.79525i	0.0827383	+	0.221754i
$940$	−0.0617666	+	0.0986250i	−0.00201461	+	0.00321679i
$941$	−28.8077	−	5.07958i	−0.939105	−	0.165590i	−0.316914	−	0.948454i	$-0.602646\pi$
$941$	−28.8077	−	5.07958i	−0.939105	−	0.165590i	−0.622192	+	0.782865i	$0.713758\pi$
$942$	2.98768	+	3.04752i	0.0973439	+	0.0992935i
$943$	−13.7272	−	16.3594i	−0.447019	−	0.532737i
$944$	−37.8616	−	36.7109i	−1.23229	−	1.19484i
$945$	−1.43799	−	1.33879i	−0.0467778	−	0.0435508i
$946$	28.7235	−	19.3531i	0.933880	−	0.629223i
$947$	28.0667	−	23.5508i	0.912046	−	0.765297i	−0.0604615	−	0.998171i	$-0.519257\pi$
$947$	28.0667	−	23.5508i	0.912046	−	0.765297i	0.972507	+	0.232873i	$0.0748128\pi$
$948$	8.84565	−	9.96413i	0.287293	−	0.323620i
$949$	6.31841	−	35.8335i	0.205104	−	1.16320i
$950$	−23.9020	−	53.7579i	−0.775483	−	1.74414i
$951$	−29.8025	−	24.6014i	−0.966412	−	0.797756i
$952$	−3.15020	−	23.6848i	−0.102099	−	0.767628i
$953$	−30.5908	+	17.6616i	−0.990932	+	0.572115i	−0.905553	−	0.424234i	$-0.860543\pi$
$953$	−30.5908	+	17.6616i	−0.990932	+	0.572115i	−0.0853790	+	0.996349i	$0.527210\pi$
$954$	−26.7811	+	18.6778i	−0.867071	+	0.604717i
$955$	1.95263	−	1.12735i	0.0631856	−	0.0364802i
$956$	−20.9751	−	4.48060i	−0.678384	−	0.144913i
$957$	7.48249	−	13.2042i	0.241875	−	0.426833i
$958$	1.74202	−	0.774540i	0.0562821	−	0.0250243i
$959$	−5.04682	+	0.500464i	−0.162970	+	0.0161608i
$960$	−1.80500	+	0.814495i	−0.0582563	+	0.0262877i
$961$	−28.9704	−	10.5443i	−0.934528	−	0.340140i
$962$	10.0544	−	20.5881i	0.324166	−	0.663787i
$963$	54.7457	−	20.9293i	1.76416	−	0.674437i
$964$	4.45437	+	5.71325i	0.143466	+	0.184011i
$965$	−1.08262	+	2.97447i	−0.0348507	+	0.0957516i
$966$	29.7972	−	5.30507i	0.958709	−	0.170688i
$967$	1.93205	−	2.30253i	0.0621306	−	0.0740444i	−0.734084	−	0.679059i	$-0.762388\pi$
$967$	1.93205	−	2.30253i	0.0621306	−	0.0740444i	0.796215	+	0.605014i	$0.206833\pi$
$968$	−17.1632	−	9.15931i	−0.551647	−	0.294391i
$969$	29.9812	+	35.1519i	0.963133	+	1.12924i
$970$	0.519426	−	0.129228i	0.0166778	−	0.00414927i
$971$	−0.469556	−	0.813294i	−0.0150688	−	0.0260999i	0.858393	−	0.512993i	$-0.171463\pi$
$971$	−0.469556	−	0.813294i	−0.0150688	−	0.0260999i	−0.873461	+	0.486893i	$0.838130\pi$
$972$	−5.28158	+	30.7263i	−0.169407	+	0.985546i
$973$	−16.9611	+	17.3584i	−0.543749	+	0.556484i
$974$	−8.94323	−	9.27037i	−0.286559	−	0.297042i
$975$	−35.5972	+	6.57245i	−1.14002	+	0.210487i
$976$	−36.4774	+	26.3897i	−1.16761	+	0.844715i
$977$	3.91393	+	10.7534i	0.125218	+	0.344033i	0.986423	−	0.164224i	$-0.0525121\pi$
$977$	3.91393	+	10.7534i	0.125218	+	0.344033i	−0.861205	+	0.508257i	$0.830290\pi$
$978$	1.51618	+	1.08420i	0.0484821	+	0.0346689i
$979$	−4.45543	+	12.2412i	−0.142396	+	0.391230i
$980$	1.97466	−	0.322244i	0.0630783	−	0.0102937i
$981$	−16.6272	−	13.5020i	−0.530865	−	0.431086i
$982$	4.63378	+	6.87736i	0.147870	+	0.219465i
$983$	−4.30949	−	24.4404i	−0.137452	−	0.779526i	−0.973121	−	0.230294i	$-0.926031\pi$
$983$	−4.30949	−	24.4404i	−0.137452	−	0.779526i	0.835670	−	0.549232i	$-0.185080\pi$
$984$	−6.78350	+	21.3506i	−0.216250	+	0.680632i
$985$	0.553385	−	0.201416i	0.0176323	−	0.00641763i
$986$	17.8075	−	7.91761i	0.567106	−	0.252148i
$987$	−1.81128	−	0.447438i	−0.0576538	−	0.0142421i
$988$	66.7157	−	21.6026i	2.12251	−	0.687270i
$989$			56.3351i			1.79135i
$990$	1.11468	+	0.522326i	0.0354270	+	0.0166006i
$991$			22.6581i			0.719758i	0.932999	+	0.359879i	$0.117182\pi$
$991$			22.6581i			0.719758i	−0.932999	+	0.359879i	$0.882818\pi$
$992$	0.00590912	−	2.33505i	0.000187615	−	0.0741378i
$993$	−22.9924	−	18.9798i	−0.729643	−	0.602307i
$994$	50.7013	+	18.8212i	1.60815	+	0.596973i
$995$	0.145046	−	0.0527925i	0.00459827	−	0.00167363i
$996$	25.2485	−	8.40051i	0.800031	−	0.266180i
$997$	−57.2962	−	20.8541i	−1.81459	−	0.660456i	−0.996329	−	0.0856058i	$-0.972717\pi$
$997$	−57.2962	−	20.8541i	−1.81459	−	0.660456i	−0.818259	−	0.574850i	$-0.805060\pi$
$998$	−0.835855	−	12.0409i	−0.0264585	−	0.381147i
$999$	17.1237	−	10.4453i	0.541769	−	0.330474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.13	yes	840
4.3	odd	2	inner	756.2.ci.a.95.67	yes	840
7.2	even	3		756.2.bs.a.527.80	yes	840
27.2	odd	18		756.2.bs.a.515.29	✓	840
28.23	odd	6		756.2.bs.a.527.29	yes	840
108.83	even	18		756.2.bs.a.515.80	yes	840
189.2	odd	18	inner	756.2.ci.a.191.67	yes	840
756.191	even	18	inner	756.2.ci.a.191.13	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.29	✓	840	27.2	odd	18
756.2.bs.a.515.80	yes	840	108.83	even	18
756.2.bs.a.527.29	yes	840	28.23	odd	6
756.2.bs.a.527.80	yes	840	7.2	even	3
756.2.ci.a.95.13	yes	840	1.1	even	1	trivial
756.2.ci.a.95.67	yes	840	4.3	odd	2	inner
756.2.ci.a.191.13	yes	840	756.191	even	18	inner
756.2.ci.a.191.67	yes	840	189.2	odd	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35923 - 0.390498i) q^{2} +(-1.12398 - 1.31783i) q^{3} +(1.69502 + 1.06155i) q^{4} +(-0.140742 - 0.0248166i) q^{5} +(1.01314 + 2.23015i) q^{6} +(1.14582 + 2.38476i) q^{7} +(-1.88939 - 2.10480i) q^{8} +(-0.473344 + 2.96242i) q^{9} +O(q^{10})\)	\(q+(-1.35923 - 0.390498i) q^{2} +(-1.12398 - 1.31783i) q^{3} +(1.69502 + 1.06155i) q^{4} +(-0.140742 - 0.0248166i) q^{5} +(1.01314 + 2.23015i) q^{6} +(1.14582 + 2.38476i) q^{7} +(-1.88939 - 2.10480i) q^{8} +(-0.473344 + 2.96242i) q^{9} +(0.181610 + 0.0886910i) q^{10} +(-0.352547 - 1.99940i) q^{11} +(-0.506222 - 3.42691i) q^{12} +(-0.728806 + 4.13327i) q^{13} +(-0.626193 - 3.68889i) q^{14} +(0.125487 + 0.213367i) q^{15} +(1.74620 + 3.59872i) q^{16} +(2.76512 - 1.59644i) q^{17} +(1.80020 - 3.84178i) q^{18} +(-7.23499 - 4.17712i) q^{19} +(-0.212217 - 0.191470i) q^{20} +(1.85483 - 4.19042i) q^{21} +(-0.301566 + 2.85531i) q^{22} +(-3.57751 - 3.00189i) q^{23} +(-0.650130 + 4.85565i) q^{24} +(-4.67927 - 1.70312i) q^{25} +(2.60465 - 5.33347i) q^{26} +(4.43599 - 2.70591i) q^{27} +(-0.589362 + 5.25858i) q^{28} +(-4.25038 + 0.749457i) q^{29} +(-0.0872464 - 0.339018i) q^{30} +(0.406512 + 0.0716791i) q^{31} +(-0.968201 - 5.57338i) q^{32} +(-2.23860 + 2.71187i) q^{33} +(-4.38184 + 1.09016i) q^{34} +(-0.102084 - 0.364072i) q^{35} +(-3.94710 + 4.51889i) q^{36} +3.86017 q^{37} +(8.20287 + 8.50293i) q^{38} +(6.26610 - 3.68526i) q^{39} +(0.213683 + 0.343122i) q^{40} +(4.50338 + 0.794068i) q^{41} +(-4.15749 + 4.97144i) q^{42} +(-7.75389 - 9.24072i) q^{43} +(1.52489 - 3.76327i) q^{44} +(0.140137 - 0.405190i) q^{45} +(3.69043 + 5.47727i) q^{46} +(-0.0706984 - 0.400950i) q^{47} +(2.77980 - 6.34608i) q^{48} +(-4.37418 + 5.46503i) q^{49} +(5.69515 + 4.14217i) q^{50} +(-5.21177 - 1.84958i) q^{51} +(-5.62303 + 6.23231i) q^{52} +(-6.66487 - 3.84796i) q^{53} +(-7.08620 + 1.94572i) q^{54} +0.290148i q^{55} +(2.85454 - 6.91748i) q^{56} +(2.62724 + 14.2295i) q^{57} +(6.06992 + 0.641080i) q^{58} +(-12.3891 + 4.50928i) q^{59} +(-0.0137977 + 0.494874i) q^{60} +(1.95452 + 11.0846i) q^{61} +(-0.524554 - 0.256171i) q^{62} +(-7.60704 + 2.26560i) q^{63} +(-0.860385 + 7.95360i) q^{64} +(0.205147 - 0.563638i) q^{65} +(4.10176 - 2.81190i) q^{66} +(5.02569 - 5.98939i) q^{67} +(6.38165 + 0.229320i) q^{68} +(0.0650724 + 8.08860i) q^{69} +(-0.00341408 + 0.534721i) q^{70} +(-7.22701 + 12.5175i) q^{71} +(7.12965 - 4.60089i) q^{72} -8.66954 q^{73} +(-5.24686 - 1.50739i) q^{74} +(3.01499 + 8.08074i) q^{75} +(-7.82922 - 14.7607i) q^{76} +(4.36413 - 3.13169i) q^{77} +(-9.95617 + 2.56223i) q^{78} +(2.47236 + 2.94645i) q^{79} +(-0.156456 - 0.549826i) q^{80} +(-8.55189 - 2.80449i) q^{81} +(-5.81106 - 2.83789i) q^{82} +(1.33387 + 7.56476i) q^{83} +(7.59234 - 5.13385i) q^{84} +(-0.428787 + 0.156066i) q^{85} +(6.93085 + 15.5882i) q^{86} +(5.76500 + 4.75890i) q^{87} +(-3.54223 + 4.51969i) q^{88} +(-5.55676 - 3.20820i) q^{89} +(-0.348704 + 0.496025i) q^{90} +(-10.6919 + 2.99796i) q^{91} +(-2.87729 - 8.88599i) q^{92} +(-0.362450 - 0.616279i) q^{93} +(-0.0604749 + 0.572592i) q^{94} +(0.914605 + 0.767445i) q^{95} +(-6.25652 + 7.54029i) q^{96} +(2.02876 - 1.70234i) q^{97} +(8.07961 - 5.72013i) q^{98} +(6.08993 - 0.0979927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more