LMFDB - Embedded newform 504.2.cs.b.85.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.19
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.106383 + 1.41021i) q^{2} +(-1.33989 - 1.09759i) q^{3} +(-1.97737 + 0.300044i) q^{4} +(0.882573 + 0.509554i) q^{5} +(1.40529 - 2.00628i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-0.633481 - 2.75657i) q^{8} +(0.590596 + 2.94129i) q^{9} +O(q^{10})$	\(q+(0.106383 + 1.41021i) q^{2} +(-1.33989 - 1.09759i) q^{3} +(-1.97737 + 0.300044i) q^{4} +(0.882573 + 0.509554i) q^{5} +(1.40529 - 2.00628i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-0.633481 - 2.75657i) q^{8} +(0.590596 + 2.94129i) q^{9} +(-0.624686 + 1.29882i) q^{10} +(-0.460041 + 0.265605i) q^{11} +(2.97877 + 1.76831i) q^{12} +(-2.87597 - 1.66044i) q^{13} +(1.16808 - 0.797234i) q^{14} +(-0.623268 - 1.65145i) q^{15} +(3.81995 - 1.18659i) q^{16} -1.57677 q^{17} +(-4.08500 + 1.14577i) q^{18} -6.67660i q^{19} +(-1.89806 - 0.742764i) q^{20} +(-0.280596 + 1.70917i) q^{21} +(-0.423498 - 0.620497i) q^{22} +(4.54128 - 7.86573i) q^{23} +(-2.17679 + 4.38880i) q^{24} +(-1.98071 - 3.43069i) q^{25} +(2.03561 - 4.23235i) q^{26} +(2.43700 - 4.58923i) q^{27} +(1.24853 + 1.56243i) q^{28} +(0.922434 - 0.532567i) q^{29} +(2.26258 - 1.05462i) q^{30} +(0.293798 - 0.508873i) q^{31} +(2.07972 + 5.26068i) q^{32} +(0.907927 + 0.149055i) q^{33} +(-0.167742 - 2.22358i) q^{34} -1.01911i q^{35} +(-2.05034 - 5.63880i) q^{36} +10.6869i q^{37} +(9.41539 - 0.710276i) q^{38} +(2.03099 + 5.38143i) q^{39} +(0.845530 - 2.75567i) q^{40} +(4.53928 - 7.86226i) q^{41} +(-2.44013 - 0.213872i) q^{42} +(-4.73102 + 2.73146i) q^{43} +(0.829976 - 0.663230i) q^{44} +(-0.977502 + 2.89685i) q^{45} +(11.5754 + 5.56737i) q^{46} +(-4.54937 - 7.87973i) q^{47} +(-6.42069 - 2.60283i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(4.62727 - 3.15818i) q^{50} +(2.11270 + 1.73065i) q^{51} +(6.18504 + 2.42038i) q^{52} -1.22534i q^{53} +(6.73102 + 2.94845i) q^{54} -0.541359 q^{55} +(-2.07052 + 1.92690i) q^{56} +(-7.32817 + 8.94589i) q^{57} +(0.849161 + 1.24417i) q^{58} +(-0.630723 - 0.364148i) q^{59} +(1.72793 + 3.07851i) q^{60} +(5.94302 - 3.43120i) q^{61} +(0.748871 + 0.360181i) q^{62} +(2.25194 - 1.98212i) q^{63} +(-7.19740 + 3.49248i) q^{64} +(-1.69217 - 2.93092i) q^{65} +(-0.113611 + 1.29622i) q^{66} +(-12.3090 - 7.10662i) q^{67} +(3.11786 - 0.473101i) q^{68} +(-14.7182 + 5.55473i) q^{69} +(1.43715 - 0.108416i) q^{70} +5.22734 q^{71} +(7.73376 - 3.49127i) q^{72} -8.49965 q^{73} +(-15.0707 + 1.13690i) q^{74} +(-1.11156 + 6.77074i) q^{75} +(2.00327 + 13.2021i) q^{76} +(0.460041 + 0.265605i) q^{77} +(-7.37287 + 3.43661i) q^{78} +(5.26132 + 9.11287i) q^{79} +(3.97602 + 0.899215i) q^{80} +(-8.30239 + 3.47423i) q^{81} +(11.5703 + 5.56491i) q^{82} +(-3.39540 + 1.96033i) q^{83} +(0.0420159 - 3.46385i) q^{84} +(-1.39162 - 0.803452i) q^{85} +(-4.35522 - 6.38114i) q^{86} +(-1.82050 - 0.298873i) q^{87} +(1.02359 + 1.09988i) q^{88} -8.88356 q^{89} +(-4.18914 - 1.07031i) q^{90} +3.32088i q^{91} +(-6.61971 + 16.9160i) q^{92} +(-0.952190 + 0.359363i) q^{93} +(10.6281 - 7.25382i) q^{94} +(3.40209 - 5.89259i) q^{95} +(2.98748 - 9.33140i) q^{96} +(8.24618 + 14.2828i) q^{97} +(-1.27447 - 0.612973i) q^{98} +(-1.05292 - 1.19625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.106383	+	1.41021i	0.0752240	+	0.997167i
$2$	0.106383	+	1.41021i	0.0752240	+	0.997167i
$3$	−1.33989	−	1.09759i	−0.773584	−	0.633693i
$3$	−1.33989	−	1.09759i	−0.773584	−	0.633693i
$4$	−1.97737	+	0.300044i	−0.988683	+	0.150022i
$5$	0.882573	+	0.509554i	0.394699	+	0.227879i	0.684194	−	0.729300i	$-0.260154\pi$
$5$	0.882573	+	0.509554i	0.394699	+	0.227879i	−0.289495	+	0.957179i	$0.593487\pi$
$6$	1.40529	−	2.00628i	0.573706	−	0.819061i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−0.633481	−	2.75657i	−0.223969	−	0.974596i
$9$	0.590596	+	2.94129i	0.196865	+	0.980431i
$10$	−0.624686	+	1.29882i	−0.197543	+	0.410722i
$11$	−0.460041	+	0.265605i	−0.138707	+	0.0800828i	−0.567748	−	0.823203i	$-0.692185\pi$
$11$	−0.460041	+	0.265605i	−0.138707	+	0.0800828i	0.429040	+	0.903285i	$0.358852\pi$
$12$	2.97877	+	1.76831i	0.859897	+	0.510467i
$13$	−2.87597	−	1.66044i	−0.797649	−	0.460523i	0.0449993	−	0.998987i	$-0.485671\pi$
$13$	−2.87597	−	1.66044i	−0.797649	−	0.460523i	−0.842649	+	0.538464i	$0.819005\pi$
$14$	1.16808	−	0.797234i	0.312183	−	0.213070i
$15$	−0.623268	−	1.65145i	−0.160927	−	0.426402i
$16$	3.81995	−	1.18659i	0.954987	−	0.296648i
$17$	−1.57677			−0.382424			−0.191212	−	0.981549i	$-0.561242\pi$
$17$	−1.57677			−0.382424			−0.191212	+	0.981549i	$0.561242\pi$
$18$	−4.08500	+	1.14577i	−0.962844	+	0.270059i
$19$		−	6.67660i		−	1.53172i	−0.643009	−	0.765859i	$-0.722314\pi$
$19$		−	6.67660i		−	1.53172i	0.643009	−	0.765859i	$-0.277686\pi$
$20$	−1.89806	−	0.742764i	−0.424419	−	0.166087i
$21$	−0.280596	+	1.70917i	−0.0612312	+	0.372972i
$22$	−0.423498	−	0.620497i	−0.0902900	−	0.132290i
$23$	4.54128	−	7.86573i	0.946923	−	1.64012i	0.195069	−	0.980789i	$-0.437507\pi$
$23$	4.54128	−	7.86573i	0.946923	−	1.64012i	0.751854	−	0.659330i	$-0.229160\pi$
$24$	−2.17679	+	4.38880i	−0.444336	+	0.895860i
$25$	−1.98071	−	3.43069i	−0.396142	−	0.686138i
$26$	2.03561	−	4.23235i	0.399216	−	0.830032i
$27$	2.43700	−	4.58923i	0.469000	−	0.883198i
$28$	1.24853	+	1.56243i	0.235950	+	0.295271i
$29$	0.922434	−	0.532567i	0.171292	−	0.0988953i	−0.411903	−	0.911228i	$-0.635136\pi$
$29$	0.922434	−	0.532567i	0.171292	−	0.0988953i	0.583195	+	0.812332i	$0.301802\pi$
$30$	2.26258	−	1.05462i	0.413088	−	0.192547i
$31$	0.293798	−	0.508873i	0.0527677	−	0.0913963i	−0.838435	−	0.545002i	$-0.816529\pi$
$31$	0.293798	−	0.508873i	0.0527677	−	0.0913963i	0.891203	+	0.453605i	$0.149862\pi$
$32$	2.07972	+	5.26068i	0.367645	+	0.929966i
$33$	0.907927	+	0.149055i	0.158050	+	0.0259472i
$34$	−0.167742	−	2.22358i	−0.0287675	−	0.381340i
$35$		−	1.01911i		−	0.172261i
$36$	−2.05034	−	5.63880i	−0.341723	−	0.939801i
$37$			10.6869i			1.75691i	0.477821	+	0.878457i	$0.341427\pi$
$37$			10.6869i			1.75691i	−0.477821	+	0.878457i	$0.658573\pi$
$38$	9.41539	−	0.710276i	1.52738	−	0.115222i
$39$	2.03099	+	5.38143i	0.325219	+	0.861718i
$40$	0.845530	−	2.75567i	0.133690	−	0.435710i
$41$	4.53928	−	7.86226i	0.708916	−	1.22788i	−0.256344	−	0.966586i	$-0.582518\pi$
$41$	4.53928	−	7.86226i	0.708916	−	1.22788i	0.965260	−	0.261293i	$-0.0841488\pi$
$42$	−2.44013	−	0.213872i	−0.376521	−	0.0330012i
$43$	−4.73102	+	2.73146i	−0.721474	+	0.416543i	−0.815295	−	0.579046i	$-0.803425\pi$
$43$	−4.73102	+	2.73146i	−0.721474	+	0.416543i	0.0938206	+	0.995589i	$0.470092\pi$
$44$	0.829976	−	0.663230i	0.125124	−	0.0999856i
$45$	−0.977502	+	2.89685i	−0.145717	+	0.431836i
$46$	11.5754	+	5.56737i	1.70670	+	0.820864i
$47$	−4.54937	−	7.87973i	−0.663593	−	1.14938i	−0.979665	−	0.200642i	$-0.935697\pi$
$47$	−4.54937	−	7.87973i	−0.663593	−	1.14938i	0.316071	−	0.948735i	$-0.397636\pi$
$48$	−6.42069	−	2.60283i	−0.926747	−	0.375687i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	4.62727	−	3.15818i	0.654394	−	0.446634i
$51$	2.11270	+	1.73065i	0.295837	+	0.242340i
$52$	6.18504	+	2.42038i	0.857710	+	0.335646i
$53$		−	1.22534i		−	0.168313i	−0.996453	−	0.0841566i	$-0.973180\pi$
$53$		−	1.22534i		−	0.168313i	0.996453	−	0.0841566i	$-0.0268196\pi$
$54$	6.73102	+	2.94845i	0.915976	+	0.401234i
$55$	−0.541359			−0.0729969
$56$	−2.07052	+	1.92690i	−0.276685	+	0.257493i
$57$	−7.32817	+	8.94589i	−0.970639	+	1.18491i
$58$	0.849161	+	1.24417i	0.111500	+	0.163367i
$59$	−0.630723	−	0.364148i	−0.0821132	−	0.0474081i	0.458381	−	0.888756i	$-0.348429\pi$
$59$	−0.630723	−	0.364148i	−0.0821132	−	0.0474081i	−0.540494	+	0.841348i	$0.681763\pi$
$60$	1.72793	+	3.07851i	0.223075	+	0.397434i
$61$	5.94302	−	3.43120i	0.760925	−	0.439320i	−0.0687027	−	0.997637i	$-0.521886\pi$
$61$	5.94302	−	3.43120i	0.760925	−	0.439320i	0.829628	+	0.558317i	$0.188553\pi$
$62$	0.748871	+	0.360181i	0.0951068	+	0.0457430i
$63$	2.25194	−	1.98212i	0.283717	−	0.249723i
$64$	−7.19740	+	3.49248i	−0.899675	+	0.436559i
$65$	−1.69217	−	2.93092i	−0.209887	−	0.363536i
$66$	−0.113611	+	1.29622i	−0.0139846	+	0.159554i
$67$	−12.3090	−	7.10662i	−1.50379	−	0.868212i	−0.999990	−	0.00439022i	$-0.998603\pi$
$67$	−12.3090	−	7.10662i	−1.50379	−	0.868212i	−0.503797	−	0.863822i	$-0.668064\pi$
$68$	3.11786	−	0.473101i	0.378096	−	0.0573719i
$69$	−14.7182	+	5.55473i	−1.77186	+	0.668711i
$70$	1.43715	−	0.108416i	0.171773	−	0.0129581i
$71$	5.22734			0.620371			0.310186	−	0.950676i	$-0.399609\pi$
$71$	5.22734			0.620371			0.310186	+	0.950676i	$0.399609\pi$
$72$	7.73376	−	3.49127i	0.911432	−	0.411451i
$73$	−8.49965			−0.994809			−0.497404	−	0.867519i	$-0.665713\pi$
$73$	−8.49965			−0.994809			−0.497404	+	0.867519i	$0.665713\pi$
$74$	−15.0707	+	1.13690i	−1.75194	+	0.132162i
$75$	−1.11156	+	6.77074i	−0.128352	+	0.781818i
$76$	2.00327	+	13.2021i	0.229791	+	1.51438i
$77$	0.460041	+	0.265605i	0.0524265	+	0.0302685i
$78$	−7.37287	+	3.43661i	−0.834813	+	0.389119i
$79$	5.26132	+	9.11287i	0.591945	+	1.02528i	0.993970	+	0.109650i	$0.0349729\pi$
$79$	5.26132	+	9.11287i	0.591945	+	1.02528i	−0.402026	+	0.915628i	$0.631694\pi$
$80$	3.97602	+	0.899215i	0.444532	+	0.100535i
$81$	−8.30239	+	3.47423i	−0.922488	+	0.386026i
$82$	11.5703	+	5.56491i	1.27773	+	0.614541i
$83$	−3.39540	+	1.96033i	−0.372693	+	0.215174i	−0.674634	−	0.738152i	$-0.735699\pi$
$83$	−3.39540	+	1.96033i	−0.372693	+	0.215174i	0.301941	+	0.953327i	$0.402365\pi$
$84$	0.0420159	−	3.46385i	0.00458431	−	0.377937i
$85$	−1.39162	−	0.803452i	−0.150942	−	0.0871466i
$86$	−4.35522	−	6.38114i	−0.469636	−	0.688096i
$87$	−1.82050	−	0.298873i	−0.195178	−	0.0320425i
$88$	1.02359	+	1.09988i	0.109115	+	0.117248i
$89$	−8.88356			−0.941655			−0.470827	−	0.882225i	$-0.656045\pi$
$89$	−8.88356			−0.941655			−0.470827	+	0.882225i	$0.656045\pi$
$90$	−4.18914	−	1.07031i	−0.441574	−	0.112820i
$91$			3.32088i			0.348123i
$92$	−6.61971	+	16.9160i	−0.690153	+	1.76362i
$93$	−0.952190	+	0.359363i	−0.0987375	+	0.0372642i
$94$	10.6281	−	7.25382i	1.09620	−	0.748174i
$95$	3.40209	−	5.89259i	0.349047	−	0.604567i
$96$	2.98748	−	9.33140i	0.304909	−	0.952382i
$97$	8.24618	+	14.2828i	0.837272	+	1.45020i	0.892167	+	0.451706i	$0.149184\pi$
$97$	8.24618	+	14.2828i	0.837272	+	1.45020i	−0.0548945	+	0.998492i	$0.517482\pi$
$98$	−1.27447	−	0.612973i	−0.128741	−	0.0619196i
$99$	−1.05292	−	1.19625i	−0.105822	−	0.120228i
$100$	4.94594	+	6.18943i	0.494594	+	0.618943i
$101$	9.23496	−	5.33181i	0.918913	−	0.530535i	0.0356250	−	0.999365i	$-0.488658\pi$
$101$	9.23496	−	5.33181i	0.918913	−	0.530535i	0.883288	+	0.468830i	$0.155324\pi$
$102$	−2.21582	+	3.16346i	−0.219399	+	0.313229i
$103$	−1.68846	+	2.92450i	−0.166369	+	0.288160i	−0.937141	−	0.348952i	$-0.886538\pi$
$103$	−1.68846	+	2.92450i	−0.166369	+	0.288160i	0.770772	+	0.637112i	$0.219871\pi$
$104$	−2.75525	+	8.97967i	−0.270175	+	0.880529i
$105$	−1.11856	+	1.36549i	−0.109160	+	0.133258i
$106$	1.72798	−	0.130355i	0.167836	−	0.0126612i
$107$			11.0062i			1.06401i	0.846741	+	0.532006i	$0.178562\pi$
$107$			11.0062i			1.06401i	−0.846741	+	0.532006i	$0.821438\pi$
$108$	−3.44187	+	9.80579i	−0.331194	+	0.943563i
$109$		−	1.33859i		−	0.128213i	−0.997943	−	0.0641066i	$-0.979580\pi$
$109$		−	1.33859i		−	0.128213i	0.997943	−	0.0641066i	$-0.0204198\pi$
$110$	−0.0575914	−	0.763429i	−0.00549112	−	0.0727901i
$111$	11.7298	−	14.3192i	1.11335	−	1.35912i
$112$	−2.93759	−	2.71488i	−0.277576	−	0.256532i
$113$	0.490602	−	0.849748i	0.0461520	−	0.0799375i	−0.842027	−	0.539436i	$-0.818637\pi$
$113$	0.490602	−	0.849748i	0.0461520	−	0.0799375i	0.888179	+	0.459498i	$0.151971\pi$
$114$	−13.3951	−	9.38254i	−1.25457	−	0.878755i
$115$	8.01603	−	4.62806i	0.747499	−	0.431569i
$116$	−1.66420	+	1.32985i	−0.154517	+	0.123474i
$117$	3.18530	−	9.43970i	0.294481	−	0.872701i
$118$	0.446426	−	0.928189i	0.0410968	−	0.0854467i
$119$	0.788387	+	1.36553i	0.0722713	+	0.125178i
$120$	−4.15751	+	2.76425i	−0.379527	+	0.252340i
$121$	−5.35891	+	9.28190i	−0.487173	+	0.843809i
$122$	5.47094	+	8.01586i	0.495315	+	0.725722i
$123$	−14.7116	+	5.55228i	−1.32650	+	0.500632i
$124$	−0.428262	+	1.09438i	−0.0384591	+	0.0982783i
$125$		−	9.13265i		−	0.816849i
$126$	3.03476	+	2.96483i	0.270358	+	0.264128i
$127$	−7.33825			−0.651164			−0.325582	−	0.945514i	$-0.605560\pi$
$127$	−7.33825			−0.651164			−0.325582	+	0.945514i	$0.605560\pi$
$128$	−5.69079	−	9.77829i	−0.503000	−	0.864287i
$129$	9.33706	+	1.53288i	0.822082	+	0.134962i
$130$	3.95318	−	2.69810i	0.346717	−	0.236639i
$131$	2.00773	+	1.15916i	0.175416	+	0.101277i	0.585137	−	0.810934i	$-0.301041\pi$
$131$	2.00773	+	1.15916i	0.175416	+	0.101277i	−0.409721	+	0.912211i	$0.634374\pi$
$132$	−1.84003	−	0.0223192i	−0.160154	−	0.00194264i
$133$	−5.78211	+	3.33830i	−0.501372	+	0.289467i
$134$	8.71234	−	18.1143i	0.752631	−	1.56484i
$135$	4.48929	−	2.80855i	0.386377	−	0.241722i
$136$	0.998857	+	4.34650i	0.0856513	+	0.372709i
$137$	−7.08353	−	12.2690i	−0.605187	−	1.04821i	−0.992022	−	0.126065i	$-0.959765\pi$
$137$	−7.08353	−	12.2690i	−0.605187	−	1.04821i	0.386835	−	0.922149i	$-0.373568\pi$
$138$	−9.39908	−	20.1647i	−0.800103	−	1.71653i
$139$	−5.26163	−	3.03781i	−0.446286	−	0.257663i	0.259974	−	0.965616i	$-0.416286\pi$
$139$	−5.26163	−	3.03781i	−0.446286	−	0.257663i	−0.706260	+	0.707952i	$0.749619\pi$
$140$	0.305777	+	2.01515i	0.0258429	+	0.170311i
$141$	−2.55307	+	15.5513i	−0.215007	+	1.30965i
$142$	0.556099	+	7.37163i	0.0466668	+	0.618613i
$143$	1.76408			0.147520
$144$	5.74616	+	10.5348i	0.478846	+	0.877899i
$145$	1.08549			0.0901448
$146$	−0.904217	−	11.9863i	−0.0748335	−	0.991990i
$147$	1.62048	−	0.611582i	0.133655	−	0.0504424i
$148$	−3.20653	−	21.1319i	−0.263575	−	1.73703i
$149$	14.2667	+	8.23687i	1.16877	+	0.674791i	0.953390	−	0.301739i	$-0.0975673\pi$
$149$	14.2667	+	8.23687i	1.16877	+	0.674791i	0.215381	+	0.976530i	$0.430901\pi$
$150$	−9.66640	−	0.847239i	−0.789258	−	0.0691767i
$151$	−5.44569	−	9.43221i	−0.443164	−	0.767582i	0.554759	−	0.832011i	$-0.312811\pi$
$151$	−5.44569	−	9.43221i	−0.443164	−	0.767582i	−0.997922	+	0.0644293i	$0.979477\pi$
$152$	−18.4045	+	4.22950i	−1.49281	+	0.343058i
$153$	−0.931237	−	4.63775i	−0.0752860	−	0.374940i
$154$	−0.325617	+	0.677008i	−0.0262390	+	0.0545549i
$155$	0.518597	−	0.299412i	0.0416547	−	0.0240493i
$156$	−5.63067	−	10.0317i	−0.450814	−	0.803176i
$157$	5.10653	+	2.94826i	0.407545	+	0.235296i	0.689735	−	0.724062i	$-0.257727\pi$
$157$	5.10653	+	2.94826i	0.407545	+	0.235296i	−0.282189	+	0.959359i	$0.591061\pi$
$158$	−12.2913	+	8.38900i	−0.977845	+	0.667393i
$159$	−1.34492	+	1.64182i	−0.106659	+	0.130204i
$160$	−0.845100	+	5.70267i	−0.0668110	+	0.450835i
$161$	−9.08257			−0.715807
$162$	−5.78261	−	11.3385i	−0.454325	−	0.890836i
$163$		−	8.70153i		−	0.681557i	−0.940144	−	0.340778i	$-0.889309\pi$
$163$		−	8.70153i		−	0.681557i	0.940144	−	0.340778i	$-0.110691\pi$
$164$	−6.61679	+	16.9085i	−0.516684	+	1.32033i
$165$	0.725361	+	0.594190i	0.0564692	+	0.0462576i
$166$	−3.12569	−	4.57966i	−0.242600	−	0.355451i
$167$	2.22448	−	3.85292i	0.172136	−	0.298148i	−0.767031	−	0.641610i	$-0.778267\pi$
$167$	2.22448	−	3.85292i	0.172136	−	0.298148i	0.939166	+	0.343463i	$0.111600\pi$
$168$	4.88921	−	0.309243i	0.377211	−	0.0238586i
$169$	−0.985883	−	1.70760i	−0.0758371	−	0.131354i
$170$	0.984988	−	2.04794i	0.0755452	−	0.157070i
$171$	19.6378	−	3.94317i	1.50174	−	0.301542i
$172$	8.53541	−	6.82060i	0.650819	−	0.520066i
$173$	12.4842	−	7.20774i	0.949154	−	0.547994i	0.0563360	−	0.998412i	$-0.482058\pi$
$173$	12.4842	−	7.20774i	0.949154	−	0.547994i	0.892818	+	0.450418i	$0.148725\pi$
$174$	0.227803	−	2.59907i	0.0172697	−	0.197035i
$175$	−1.98071	+	3.43069i	−0.149728	+	0.259336i
$176$	−1.44217	+	1.56048i	−0.108707	+	0.117625i
$177$	0.445413	+	1.18019i	0.0334793	+	0.0887087i
$178$	−0.945058	−	12.5276i	−0.0708351	−	0.938987i
$179$			15.2951i			1.14321i	0.820528	+	0.571606i	$0.193679\pi$
$179$			15.2951i			1.14321i	−0.820528	+	0.571606i	$0.806321\pi$
$180$	1.06370	−	6.02142i	0.0792835	−	0.448810i
$181$			4.73091i			0.351646i	0.984422	+	0.175823i	$0.0562586\pi$
$181$			4.73091i			0.351646i	−0.984422	+	0.175823i	$0.943741\pi$
$182$	−4.68312	+	0.353284i	−0.347136	+	0.0261872i
$183$	−11.7290	−	1.92557i	−0.867034	−	0.142342i
$184$	−24.5593	−	7.53559i	−1.81054	−	0.555531i
$185$	−5.44555	+	9.43197i	−0.400365	+	0.693452i
$186$	−0.608073	−	1.30455i	−0.0445861	−	0.0956546i
$187$	0.725380	−	0.418799i	0.0530451	−	0.0306256i
$188$	11.3600	+	14.2161i	0.828515	+	1.03682i
$189$	−5.19289	+	0.184114i	−0.377727	+	0.0133923i
$190$	8.67169	+	4.17078i	0.629111	+	0.302580i
$191$	9.54918	+	16.5397i	0.690955	+	1.19677i	0.971525	+	0.236935i	$0.0761429\pi$
$191$	9.54918	+	16.5397i	0.690955	+	1.19677i	−0.280571	+	0.959833i	$0.590524\pi$
$192$	13.4770	+	3.22027i	0.972620	+	0.232403i
$193$	7.46102	−	12.9229i	0.537056	−	0.930209i	−0.462005	−	0.886878i	$-0.652870\pi$
$193$	7.46102	−	12.9229i	0.537056	−	0.930209i	0.999061	−	0.0433311i	$-0.0137970\pi$
$194$	−19.2644	+	13.1483i	−1.38311	+	0.943990i
$195$	−0.949632	+	5.78440i	−0.0680046	+	0.414230i
$196$	0.728837	−	1.86247i	0.0520598	−	0.133034i
$197$		−	5.90926i		−	0.421018i	−0.977592	−	0.210509i	$-0.932488\pi$
$197$		−	5.90926i		−	0.421018i	0.977592	−	0.210509i	$-0.0675121\pi$
$198$	1.57495	−	1.61209i	0.111926	−	0.114566i
$199$	17.8052			1.26218			0.631088	−	0.775711i	$-0.282609\pi$
$199$	17.8052			1.26218			0.631088	+	0.775711i	$0.282609\pi$
$200$	−8.20221	+	7.63325i	−0.579984	+	0.539752i
$201$	8.69256	+	23.0323i	0.613126	+	1.62458i
$202$	8.50139	+	12.4560i	0.598156	+	0.876401i
$203$	−0.922434	−	0.532567i	−0.0647422	−	0.0373789i
$204$	−4.69685	−	2.78823i	−0.328845	−	0.195215i
$205$	8.01249	−	4.62601i	0.559616	−	0.323095i
$206$	−4.30378	−	2.06996i	−0.299858	−	0.144221i
$207$	25.8175	+	8.71177i	1.79444	+	0.605510i
$208$	−12.9563	−	2.93020i	−0.898358	−	0.203172i
$209$	1.77334	+	3.07151i	0.122664	+	0.212461i
$210$	−2.04462	−	1.43214i	−0.141092	−	0.0988269i
$211$	−4.80318	−	2.77312i	−0.330665	−	0.190909i	0.325471	−	0.945552i	$-0.394477\pi$
$211$	−4.80318	−	2.77312i	−0.330665	−	0.190909i	−0.656136	+	0.754642i	$0.727810\pi$
$212$	0.367655	+	2.42294i	0.0252506	+	0.166408i
$213$	−7.00405	−	5.73747i	−0.479909	−	0.393125i
$214$	−15.5211	+	1.17087i	−1.06100	+	0.0800393i
$215$	−5.56730			−0.379687
$216$	−14.1943	−	3.81057i	−0.965803	−	0.259277i
$217$	−0.587596			−0.0398886
$218$	1.88768	−	0.142403i	0.127850	−	0.00964472i
$219$	11.3886	+	9.32913i	0.769569	+	0.630404i
$220$	1.07047	−	0.162431i	0.0721708	−	0.0109511i
$221$	4.53475	+	2.61814i	0.305040	+	0.176115i
$222$	21.4409	+	15.0182i	1.43902	+	1.00795i
$223$	0.266176	+	0.461030i	0.0178245	+	0.0308729i	0.874800	−	0.484484i	$-0.160993\pi$
$223$	0.266176	+	0.461030i	0.0178245	+	0.0308729i	−0.856976	+	0.515357i	$0.827659\pi$
$224$	3.51603	−	4.43143i	0.234924	−	0.296087i
$225$	8.92086	−	7.85200i	0.594724	−	0.523466i
$226$	1.25051	+	0.601452i	0.0831828	+	0.0400080i
$227$	20.3653	−	11.7579i	1.35169	−	0.780400i	0.363206	−	0.931709i	$-0.381682\pi$
$227$	20.3653	−	11.7579i	1.35169	−	0.780400i	0.988487	+	0.151309i	$0.0483487\pi$
$228$	11.8063	−	19.8881i	0.781891	−	1.31712i
$229$	7.61907	+	4.39887i	0.503482	+	0.290686i	0.730150	−	0.683286i	$-0.239450\pi$
$229$	7.61907	+	4.39887i	0.503482	+	0.290686i	−0.226668	+	0.973972i	$0.572783\pi$
$230$	7.37929	+	10.8119i	0.486576	+	0.712917i
$231$	−0.324878	−	0.860816i	−0.0213754	−	0.0566375i
$232$	−2.05241	−	2.20539i	−0.134747	−	0.144791i
$233$	−7.22567			−0.473370			−0.236685	−	0.971586i	$-0.576061\pi$
$233$	−7.22567			−0.473370			−0.236685	+	0.971586i	$0.576061\pi$
$234$	13.6508	+	3.48771i	0.892380	+	0.227999i
$235$		−	9.27259i		−	0.604877i
$236$	1.35643	+	0.530810i	0.0882961	+	0.0345528i
$237$	2.95261	−	17.9850i	0.191793	−	1.16825i
$238$	−1.84180	+	1.25706i	−0.119386	+	0.0814829i
$239$	2.89727	−	5.01821i	0.187409	−	0.324601i	−0.756977	−	0.653442i	$-0.773324\pi$
$239$	2.89727	−	5.01821i	0.187409	−	0.324601i	0.944386	+	0.328840i	$0.106658\pi$
$240$	−4.34044	−	5.56888i	−0.280174	−	0.359470i
$241$	−0.819304	−	1.41908i	−0.0527760	−	0.0914107i	0.838430	−	0.545009i	$-0.183474\pi$
$241$	−0.819304	−	1.41908i	−0.0527760	−	0.0914107i	−0.891206	+	0.453598i	$0.850140\pi$
$242$	−13.6595	−	6.56973i	−0.878066	−	0.422318i
$243$	14.9375	+	4.45754i	0.958244	+	0.285951i
$244$	−10.7220	+	8.56790i	−0.686406	+	0.548504i
$245$	−0.882573	+	0.509554i	−0.0563855	+	0.0325542i
$246$	−9.39493	−	20.1558i	−0.598999	−	1.28509i
$247$	−11.0861	+	19.2017i	−0.705391	+	1.22177i
$248$	−1.58886	−	0.487515i	−0.100893	−	0.0309572i
$249$	6.70109	+	1.10012i	0.424664	+	0.0697176i
$250$	12.8789	−	0.971557i	0.814535	−	0.0614467i
$251$		−	4.27441i		−	0.269798i	−0.990859	−	0.134899i	$-0.956929\pi$
$251$		−	4.27441i		−	0.269798i	0.990859	−	0.134899i	$-0.0430710\pi$
$252$	−3.85818	+	4.59505i	−0.243042	+	0.289461i
$253$			4.82474i			0.303329i
$254$	−0.780664	−	10.3484i	−0.0489832	−	0.649319i
$255$	0.982753	+	2.60396i	0.0615424	+	0.163066i
$256$	13.1840	−	9.06544i	0.824000	−	0.566590i
$257$	6.70479	−	11.6130i	0.418233	−	0.724401i	−0.577529	−	0.816370i	$-0.695983\pi$
$257$	6.70479	−	11.6130i	0.418233	−	0.724401i	0.995762	+	0.0919692i	$0.0293161\pi$
$258$	−1.16837	+	13.3303i	−0.0727394	+	0.829905i
$259$	9.25512	−	5.34345i	0.575085	−	0.332026i
$260$	4.22544	+	5.28777i	0.262050	+	0.327934i
$261$	2.11122	+	2.39861i	0.130681	+	0.148470i
$262$	−1.42107	+	2.95463i	−0.0877942	+	0.182538i
$263$	9.07571	+	15.7196i	0.559633	+	0.969312i	0.997527	+	0.0702856i	$0.0223910\pi$
$263$	9.07571	+	15.7196i	0.559633	+	0.969312i	−0.437894	+	0.899026i	$0.644276\pi$
$264$	−0.164273	−	2.59719i	−0.0101103	−	0.159846i
$265$	0.624376	−	1.08145i	0.0383551	−	0.0664330i
$266$	−5.32281	−	7.79883i	−0.326362	−	0.478177i
$267$	11.9030	+	9.75049i	0.728449	+	0.596721i
$268$	26.4718	+	10.3591i	1.61702	+	0.632785i
$269$		−	0.743967i		−	0.0453605i	−0.999743	−	0.0226802i	$-0.992780\pi$
$269$		−	0.743967i		−	0.0453605i	0.999743	−	0.0226802i	$-0.00721996\pi$
$270$	4.43822	+	6.03204i	0.270101	+	0.367099i
$271$	−28.7540			−1.74668			−0.873341	−	0.487109i	$-0.838052\pi$
$271$	−28.7540			−1.74668			−0.873341	+	0.487109i	$0.838052\pi$
$272$	−6.02320	+	1.87099i	−0.365210	+	0.113445i
$273$	3.64496	−	4.44960i	0.220603	−	0.269302i
$274$	16.5483	−	11.2945i	0.999720	−	0.682323i
$275$	1.82241	+	1.05217i	0.109896	+	0.0634483i
$276$	27.4365	−	15.3998i	1.65148	−	0.926961i
$277$	18.6613	−	10.7741i	1.12125	−	0.647352i	0.179528	−	0.983753i	$-0.442543\pi$
$277$	18.6613	−	10.7741i	1.12125	−	0.647352i	0.941719	+	0.336401i	$0.109210\pi$
$278$	3.72419	−	7.74316i	0.223362	−	0.464404i
$279$	1.67026	+	0.563607i	0.0999959	+	0.0337423i
$280$	−2.80925	+	0.645586i	−0.167885	+	0.0385811i
$281$	13.0958	+	22.6826i	0.781231	+	1.35313i	0.931225	+	0.364445i	$0.118741\pi$
$281$	13.0958	+	22.6826i	0.781231	+	1.35313i	−0.149993	+	0.988687i	$0.547925\pi$
$282$	−22.2021	−	1.94597i	−1.32212	−	0.115881i
$283$	−14.5054	−	8.37467i	−0.862254	−	0.497823i	0.00251233	−	0.999997i	$-0.499200\pi$
$283$	−14.5054	−	8.37467i	−0.862254	−	0.497823i	−0.864767	+	0.502174i	$0.832534\pi$
$284$	−10.3364	+	1.56843i	−0.613350	+	0.0930692i
$285$	−11.0261	+	4.16131i	−0.653127	+	0.246495i
$286$	0.187668	+	2.48772i	0.0110970	+	0.147102i
$287$	−9.07855			−0.535890
$288$	−14.2449	+	9.22399i	−0.839391	+	0.543529i
$289$	−14.5138			−0.853752
$290$	0.115477	+	1.53076i	0.00678105	+	0.0898894i
$291$	4.62770	−	28.1882i	0.271280	−	1.65242i
$292$	16.8069	−	2.55027i	0.983550	−	0.149243i
$293$	−13.7719	−	7.95124i	−0.804566	−	0.464516i	0.0404996	−	0.999180i	$-0.487105\pi$
$293$	−13.7719	−	7.95124i	−0.804566	−	0.464516i	−0.845065	+	0.534663i	$0.820438\pi$
$294$	1.03485	+	2.22016i	0.0603536	+	0.129482i
$295$	−0.371106	−	0.642775i	−0.0216066	−	0.0374238i
$296$	29.4592	−	6.76995i	1.71228	−	0.393495i
$297$	0.0978029	+	2.75851i	0.00567510	+	0.160065i
$298$	−10.0980	+	20.9952i	−0.584959	+	1.21622i
$299$	−26.1212	+	15.0811i	−1.51063	+	0.872160i
$300$	0.166443	−	13.7217i	0.00960957	−	0.792226i
$301$	4.73102	+	2.73146i	0.272692	+	0.157439i
$302$	12.7220	−	8.68297i	0.732071	−	0.499649i
$303$	−18.2259	−	2.99217i	−1.04705	−	0.171896i
$304$	−7.92240	−	25.5043i	−0.454381	−	1.46277i
$305$	6.99353			0.400448
$306$	6.44112	−	1.80661i	0.368214	−	0.103277i
$307$		−	28.9966i		−	1.65493i	−0.561520	−	0.827463i	$-0.689783\pi$
$307$		−	28.9966i		−	1.65493i	0.561520	−	0.827463i	$-0.310217\pi$
$308$	−0.989361	−	0.387165i	−0.0563741	−	0.0220608i
$309$	5.47225	−	2.06527i	0.311305	−	0.117489i
$310$	0.477402	+	0.699476i	0.0271146	+	0.0397276i
$311$	−5.69923	+	9.87136i	−0.323174	+	0.559754i	−0.981141	−	0.193293i	$-0.938083\pi$
$311$	−5.69923	+	9.87136i	−0.323174	+	0.559754i	0.657967	+	0.753047i	$0.271417\pi$
$312$	13.5477	−	9.00761i	0.766988	−	0.509955i
$313$	9.21156	+	15.9549i	0.520668	+	0.901824i	0.999711	+	0.0240324i	$0.00765050\pi$
$313$	9.21156	+	15.9549i	0.520668	+	0.901824i	−0.479043	+	0.877791i	$0.659016\pi$
$314$	−3.61440	+	7.51490i	−0.203973	+	0.424091i
$315$	2.99749	−	0.601881i	0.168890	−	0.0339122i
$316$	−13.1378	−	16.4409i	−0.739059	−	0.924870i
$317$	10.5200	−	6.07372i	0.590862	−	0.341134i	−0.174577	−	0.984644i	$-0.555856\pi$
$317$	10.5200	−	6.07372i	0.590862	−	0.341134i	0.765438	+	0.643510i	$0.222522\pi$
$318$	−2.45838	−	1.72195i	−0.137859	−	0.0965623i
$319$	−0.282905	+	0.490005i	−0.0158396	+	0.0274350i
$320$	−8.13184	−	0.585099i	−0.454584	−	0.0327080i
$321$	12.0803	−	14.7471i	0.674257	−	0.823103i
$322$	−0.966229	−	12.8083i	−0.0538459	−	0.713779i
$323$			10.5275i			0.585765i
$324$	15.3744	−	9.36090i	0.854136	−	0.520050i
$325$			13.1554i			0.729730i
$326$	12.2710	−	0.925694i	0.679626	−	0.0512694i
$327$	−1.46922	+	1.79355i	−0.0812479	+	0.0991838i
$328$	−24.5484	−	7.53226i	−1.35546	−	0.415900i
$329$	−4.54937	+	7.87973i	−0.250815	+	0.434424i
$330$	−0.760765	+	1.08612i	−0.0418787	+	0.0597889i
$331$	6.00568	−	3.46738i	0.330102	−	0.190584i	−0.325784	−	0.945444i	$-0.605628\pi$
$331$	6.00568	−	3.46738i	0.330102	−	0.190584i	0.655886	+	0.754860i	$0.272295\pi$
$332$	6.12575	−	4.89506i	0.336194	−	0.268651i
$333$	−31.4333	+	6.31164i	−1.72253	+	0.345876i
$334$	5.67006	+	2.72710i	0.310252	+	0.149220i
$335$	−7.24241	−	12.5442i	−0.395695	−	0.685365i
$336$	0.956224	+	6.86190i	0.0521663	+	0.374347i
$337$	7.11627	−	12.3257i	0.387648	−	0.671426i	−0.604485	−	0.796617i	$-0.706621\pi$
$337$	7.11627	−	12.3257i	0.387648	−	0.671426i	0.992133	+	0.125191i	$0.0399543\pi$
$338$	2.30319	−	1.57196i	0.125277	−	0.0855032i
$339$	−1.59003	+	0.600087i	−0.0863583	+	0.0325922i
$340$	2.99281	+	1.17117i	0.162308	+	0.0635157i
$341$			0.312136i			0.0169031i
$342$	7.64982	+	27.2739i	0.413655	+	1.47480i
$343$	1.00000			0.0539949
$344$	10.5265	+	11.3111i	0.567550	+	0.609853i
$345$	−15.8203	−	2.59723i	−0.851736	−	0.139830i
$346$	11.4925	+	16.8385i	0.617841	+	0.905242i
$347$	−16.1154	−	9.30425i	−0.865122	−	0.499478i	0.000602118	−	1.00000i	$-0.499808\pi$
$347$	−16.1154	−	9.30425i	−0.865122	−	0.499478i	−0.865724	+	0.500521i	$0.833142\pi$
$348$	3.68946	+	0.0447526i	0.197776	+	0.00239899i
$349$	−20.2304	+	11.6800i	−1.08291	+	0.625216i	−0.931679	−	0.363283i	$-0.881656\pi$
$349$	−20.2304	+	11.6800i	−1.08291	+	0.625216i	−0.151227	+	0.988499i	$0.548323\pi$
$350$	−5.04869	−	2.42824i	−0.269864	−	0.129795i
$351$	−14.6289	+	9.15198i	−0.780831	+	0.488497i
$352$	−2.35402	−	1.86775i	−0.125469	−	0.0995512i
$353$	−4.79707	−	8.30877i	−0.255322	−	0.442231i	0.709661	−	0.704544i	$-0.248848\pi$
$353$	−4.79707	−	8.30877i	−0.255322	−	0.442231i	−0.964983	+	0.262312i	$0.915515\pi$
$354$	−1.61693	+	0.753676i	−0.0859389	+	0.0400574i
$355$	4.61351	+	2.66361i	0.244860	+	0.141370i
$356$	17.5660	−	2.66545i	0.930998	−	0.141269i
$357$	0.442437	−	2.69498i	0.0234163	−	0.142633i
$358$	−21.5693	+	1.62714i	−1.13997	+	0.0859970i
$359$	9.36646			0.494343			0.247171	−	0.968972i	$-0.420499\pi$
$359$	9.36646			0.494343			0.247171	+	0.968972i	$0.420499\pi$
$360$	8.60460	+	0.859461i	0.453502	+	0.0452976i
$361$	−25.5770			−1.34616
$362$	−6.67157	+	0.503288i	−0.350650	+	0.0264522i
$363$	17.3680	−	6.55482i	0.911586	−	0.344039i
$364$	−0.996408	−	6.56659i	−0.0522260	−	0.344183i
$365$	−7.50157	−	4.33103i	−0.392650	−	0.226697i
$366$	1.46768	−	16.7452i	0.0767168	−	0.875285i
$367$	−16.5527	−	28.6701i	−0.864042	−	1.49656i	−0.867995	−	0.496573i	$-0.834592\pi$
$367$	−16.5527	−	28.6701i	−0.864042	−	1.49656i	0.00395310	−	0.999992i	$-0.498742\pi$
$368$	8.01405	−	35.4353i	0.417761	−	1.84720i
$369$	25.8061	+	8.70792i	1.34341	+	0.453316i
$370$	−13.8803	−	6.67595i	−0.721604	−	0.347066i
$371$	−1.06117	+	0.612669i	−0.0550934	+	0.0318082i
$372$	1.77500	−	0.996291i	0.0920296	−	0.0516553i
$373$	−11.1264	−	6.42386i	−0.576106	−	0.332615i	0.183479	−	0.983024i	$-0.441264\pi$
$373$	−11.1264	−	6.42386i	−0.576106	−	0.332615i	−0.759584	+	0.650409i	$0.774598\pi$
$374$	0.667761	+	0.978383i	0.0345291	+	0.0505910i
$375$	−10.0239	+	12.2367i	−0.517632	+	0.631902i
$376$	−18.8391	+	17.5323i	−0.971554	+	0.904161i
$377$	−3.53718			−0.182174
$378$	−0.812073	−	7.30346i	−0.0417685	−	0.375649i
$379$			26.7604i			1.37459i	0.726379	+	0.687294i	$0.241202\pi$
$379$			26.7604i			1.37459i	−0.726379	+	0.687294i	$0.758798\pi$
$380$	−4.95914	+	12.6726i	−0.254398	+	0.650089i
$381$	9.83242	+	8.05438i	0.503730	+	0.412638i
$382$	−22.3085	+	15.2259i	−1.14140	+	0.779023i
$383$	−15.8893	+	27.5211i	−0.811905	+	1.40626i	0.0996247	+	0.995025i	$0.468236\pi$
$383$	−15.8893	+	27.5211i	−0.811905	+	1.40626i	−0.911529	+	0.411235i	$0.865098\pi$
$384$	−3.10752	+	19.3480i	−0.158580	+	0.987346i
$385$	0.270680	+	0.468831i	0.0137951	+	0.0238938i
$386$	19.0176	+	9.14681i	0.967973	+	0.465561i
$387$	−10.8281	−	12.3021i	−0.550425	−	0.625353i
$388$	−20.5912	−	25.7681i	−1.04536	−	1.30818i
$389$	17.8191	−	10.2878i	0.903462	−	0.521614i	0.0251400	−	0.999684i	$-0.491997\pi$
$389$	17.8191	−	10.2878i	0.903462	−	0.521614i	0.878322	+	0.478070i	$0.158663\pi$
$390$	−8.25823	−	0.723816i	−0.418172	−	0.0366518i
$391$	−7.16058	+	12.4025i	−0.362126	+	0.627221i
$392$	2.70400	+	0.829676i	0.136573	+	0.0419050i
$393$	−1.41785	−	3.75681i	−0.0715210	−	0.189506i
$394$	8.33328	−	0.628644i	0.419825	−	0.0316706i
$395$			10.7237i			0.539568i
$396$	2.44093	+	2.04950i	0.122661	+	0.102991i
$397$			4.65516i			0.233636i	0.993153	+	0.116818i	$0.0372694\pi$
$397$			4.65516i			0.233636i	−0.993153	+	0.116818i	$0.962731\pi$
$398$	1.89417	+	25.1090i	0.0949460	+	1.25860i
$399$	11.4115	+	1.87343i	0.571287	+	0.0937888i
$400$	−11.6370	−	10.7548i	−0.581852	−	0.537738i
$401$	18.0905	−	31.3337i	0.903397	−	1.56473i	0.0803434	−	0.996767i	$-0.474398\pi$
$401$	18.0905	−	31.3337i	0.903397	−	1.56473i	0.823054	−	0.567963i	$-0.192268\pi$
$402$	−31.5556	+	14.7086i	−1.57385	+	0.733596i
$403$	−1.68991	+	0.975668i	−0.0841802	+	0.0486015i
$404$	−16.6611	+	13.3138i	−0.828922	+	0.662388i
$405$	−9.09778	−	1.16425i	−0.452072	−	0.0578522i
$406$	0.652899	−	1.35748i	0.0324028	−	0.0673705i
$407$	−2.83849	−	4.91641i	−0.140699	−	0.243697i
$408$	3.43231	−	6.92015i	0.169925	−	0.342598i
$409$	15.0738	−	26.1087i	0.745353	−	1.29099i	−0.204676	−	0.978830i	$-0.565614\pi$
$409$	15.0738	−	26.1087i	0.745353	−	1.29099i	0.950030	−	0.312160i	$-0.101052\pi$
$410$	7.37602	+	10.8071i	0.364276	+	0.533726i
$411$	−3.97523	+	24.2139i	−0.196083	+	1.19438i
$412$	2.46123	−	6.28942i	0.121256	−	0.309858i
$413$			0.728296i			0.0358371i
$414$	−9.53886	+	37.3348i	−0.468809	+	1.83490i
$415$	−3.99558			−0.196135
$416$	2.75385	−	18.5828i	0.135019	−	0.911096i
$417$	3.71573	+	9.84543i	0.181960	+	0.482133i
$418$	−4.14281	+	2.82753i	−0.202631	+	0.138299i
$419$	−21.5686	−	12.4527i	−1.05370	−	0.608352i	−0.130015	−	0.991512i	$-0.541503\pi$
$419$	−21.5686	−	12.4527i	−1.05370	−	0.608352i	−0.923682	+	0.383160i	$0.874836\pi$
$420$	1.80210	−	3.03569i	0.0879334	−	0.148126i
$421$	16.2644	−	9.39026i	0.792679	−	0.457654i	−0.0482257	−	0.998836i	$-0.515357\pi$
$421$	16.2644	−	9.39026i	0.792679	−	0.457654i	0.840905	+	0.541183i	$0.182023\pi$
$422$	3.39970	−	7.06849i	0.165495	−	0.344089i
$423$	20.4898	−	18.0348i	0.996246	−	0.876880i
$424$	−3.37774	+	0.776229i	−0.164037	+	0.0376970i
$425$	3.12313	+	5.40942i	0.151494	+	0.262396i
$426$	7.34591	−	10.4875i	0.355910	−	0.508122i
$427$	−5.94302	−	3.43120i	−0.287603	−	0.166047i
$428$	−3.30235	−	21.7633i	−0.159625	−	1.05197i
$429$	−2.36367	−	1.93624i	−0.114119	−	0.0934824i
$430$	−0.592265	−	7.85104i	−0.0285616	−	0.378611i
$431$	25.5152			1.22902			0.614512	−	0.788907i	$-0.289353\pi$
$431$	25.5152			1.22902			0.614512	+	0.788907i	$0.289353\pi$
$432$	3.86366	−	20.4223i	0.185890	−	0.982570i
$433$	28.3473			1.36228			0.681141	−	0.732152i	$-0.261484\pi$
$433$	28.3473			1.36228			0.681141	+	0.732152i	$0.261484\pi$
$434$	−0.0625101	−	0.828632i	−0.00300058	−	0.0397756i
$435$	−1.45443	−	1.19142i	−0.0697346	−	0.0571242i
$436$	0.401634	+	2.64687i	0.0192348	+	0.126762i
$437$	−52.5164	−	30.3203i	−2.51220	−	1.45042i
$438$	−11.9444	+	17.0527i	−0.570728	+	0.814810i
$439$	−13.4116	−	23.2295i	−0.640099	−	1.10868i	−0.985410	−	0.170196i	$-0.945560\pi$
$439$	−13.4116	−	23.2295i	−0.640099	−	1.10868i	0.345311	−	0.938488i	$-0.387773\pi$
$440$	0.342941	+	1.49230i	0.0163491	+	0.0711425i
$441$	−2.84253	−	0.959175i	−0.135359	−	0.0456750i
$442$	−3.20970	+	6.67346i	−0.152670	+	0.317424i
$443$	16.7988	−	9.69878i	0.798134	−	0.460803i	−0.0446844	−	0.999001i	$-0.514228\pi$
$443$	16.7988	−	9.69878i	0.798134	−	0.460803i	0.842818	+	0.538198i	$0.180895\pi$
$444$	−18.8977	+	31.8338i	−0.896847	+	1.51077i
$445$	−7.84039	−	4.52665i	−0.371670	−	0.214584i
$446$	−0.621831	+	0.424409i	−0.0294446	+	0.0200963i
$447$	−10.0750	−	26.6954i	−0.476533	−	1.26265i
$448$	6.62327	+	4.48690i	0.312920	+	0.211986i
$449$	0.267790			0.0126378			0.00631890	−	0.999980i	$-0.497989\pi$
$449$	0.267790			0.0126378			0.00631890	+	0.999980i	$0.497989\pi$
$450$	12.0220	+	11.7449i	0.566721	+	0.553662i
$451$			4.82261i			0.227088i
$452$	−0.715138	+	1.82746i	−0.0336373	+	0.0859567i
$453$	−3.05608	+	18.6152i	−0.143587	+	0.874619i
$454$	18.7476	+	27.4684i	0.879869	+	1.28916i
$455$	−1.69217	+	2.93092i	−0.0793300	+	0.137404i
$456$	29.3023	+	14.5336i	1.37220	+	0.680597i
$457$	7.19146	+	12.4560i	0.336403	+	0.582666i	0.983753	−	0.179526i	$-0.0574564\pi$
$457$	7.19146	+	12.4560i	0.336403	+	0.582666i	−0.647351	+	0.762192i	$0.724123\pi$
$458$	−5.39278	+	11.2124i	−0.251988	+	0.523922i
$459$	−3.84260	+	7.23618i	−0.179357	+	0.337756i
$460$	−14.4620	+	11.5565i	−0.674294	+	0.538826i
$461$	9.94724	−	5.74304i	0.463289	−	0.267480i	−0.250137	−	0.968210i	$-0.580476\pi$
$461$	9.94724	−	5.74304i	0.463289	−	0.267480i	0.713426	+	0.700730i	$0.247142\pi$
$462$	1.17937	−	0.549721i	0.0548691	−	0.0255753i
$463$	−10.0951	+	17.4853i	−0.469161	+	0.812611i	−0.999379	−	0.0352506i	$-0.988777\pi$
$463$	−10.0951	+	17.4853i	−0.469161	+	0.812611i	0.530217	+	0.847862i	$0.322110\pi$
$464$	2.89171	−	3.12893i	0.134244	−	0.145257i
$465$	−1.02349	−	0.168028i	−0.0474633	−	0.00779210i
$466$	−0.768688	−	10.1897i	−0.0356088	−	0.472028i
$467$			36.8773i			1.70648i	0.521520	+	0.853239i	$0.325365\pi$
$467$			36.8773i			1.70648i	−0.521520	+	0.853239i	$0.674635\pi$
$468$	−3.46619	+	19.6215i	−0.160224	+	0.907003i
$469$			14.2132i			0.656307i
$470$	13.0763	−	0.986444i	0.603163	−	0.0455013i
$471$	−3.60620	−	9.55520i	−0.166165	−	0.440280i
$472$	−0.604250	+	1.96932i	−0.0278129	+	0.0906451i
$473$	1.45098	−	2.51316i	0.0667159	−	0.115555i
$474$	25.6767	+	2.25050i	1.17937	+	0.103369i
$475$	−22.9053	+	13.2244i	−1.05097	+	0.606777i
$476$	−1.96865	−	2.46359i	−0.0902328	−	0.112919i
$477$	3.60408	−	0.723680i	0.165019	−	0.0331350i
$478$	7.38494	+	3.55189i	0.337779	+	0.162460i
$479$	20.3145	+	35.1857i	0.928192	+	1.60768i	0.786345	+	0.617788i	$0.211971\pi$
$479$	20.3145	+	35.1857i	0.928192	+	1.60768i	0.141848	+	0.989888i	$0.454696\pi$
$480$	7.39152	−	6.71336i	0.337375	−	0.306421i
$481$	17.7449	−	30.7351i	0.809100	−	1.40140i
$482$	1.91403	−	1.30635i	0.0871817	−	0.0595027i
$483$	12.1696	+	9.96893i	0.553737	+	0.453602i
$484$	7.81155	−	19.9616i	0.355070	−	0.907346i
$485$			16.8075i			0.763189i
$486$	−4.69695	+	21.5392i	−0.213058	+	0.977040i
$487$	3.40398			0.154249			0.0771246	−	0.997021i	$-0.475426\pi$
$487$	3.40398			0.154249			0.0771246	+	0.997021i	$0.475426\pi$
$488$	−13.2232	−	14.2088i	−0.598584	−	0.643200i
$489$	−9.55071	+	11.6591i	−0.431898	+	0.527242i
$490$	−0.812467	−	1.19040i	−0.0367035	−	0.0537769i
$491$	27.8392	+	16.0729i	1.25636	+	0.725362i	0.972366	−	0.233463i	$-0.0750057\pi$
$491$	27.8392	+	16.0729i	1.25636	+	0.725362i	0.283998	+	0.958825i	$0.408339\pi$
$492$	27.4244	−	15.3930i	1.23639	−	0.693971i
$493$	−1.45447	+	0.839739i	−0.0655060	+	0.0378199i
$494$	−28.2577	−	13.5910i	−1.27137	−	0.611486i
$495$	−0.319725	−	1.59230i	−0.0143706	−	0.0715684i
$496$	0.518469	−	2.29249i	0.0232799	−	0.102936i
$497$	−2.61367	−	4.52701i	−0.117239	−	0.203064i
$498$	−0.838522	+	9.56695i	−0.0375751	+	0.428705i
$499$	−3.28590	−	1.89712i	−0.147097	−	0.0849266i	0.424645	−	0.905360i	$-0.360399\pi$
$499$	−3.28590	−	1.89712i	−0.147097	−	0.0849266i	−0.571742	+	0.820433i	$0.693732\pi$
$500$	2.74019	+	18.0586i	0.122545	+	0.807605i
$501$	−7.20948	+	2.72091i	−0.322096	+	0.121561i
$502$	6.02780	−	0.454724i	0.269034	−	0.0202953i
$503$	−4.40691			−0.196495			−0.0982473	−	0.995162i	$-0.531324\pi$
$503$	−4.40691			−0.196495			−0.0982473	+	0.995162i	$0.531324\pi$
$504$	−6.89041	−	4.95199i	−0.306923	−	0.220579i
$505$	10.8674			0.483592
$506$	−6.80389	+	0.513270i	−0.302470	+	0.0228176i
$507$	−0.553270	+	3.37008i	−0.0245716	+	0.149671i
$508$	14.5104	−	2.20179i	0.643795	−	0.0976888i
$509$	9.49367	+	5.48118i	0.420800	+	0.242949i	0.695419	−	0.718604i	$-0.255219\pi$
$509$	9.49367	+	5.48118i	0.420800	+	0.242949i	−0.274620	+	0.961553i	$0.588552\pi$
$510$	−3.56757	+	1.66290i	−0.157975	+	0.0736345i
$511$	4.24983	+	7.36091i	0.188001	+	0.325628i
$512$	14.1867	+	17.6278i	0.626969	+	0.779044i
$513$	−30.6405	−	16.2709i	−1.35281	−	0.718376i
$514$	17.0901	+	8.21971i	0.753810	+	0.362556i
$515$	−2.98038	+	1.72072i	−0.131331	+	0.0758242i
$516$	−18.9227	−	0.229530i	−0.833026	−	0.0101045i
$517$	4.18579	+	2.41667i	0.184091	+	0.106285i
$518$	8.51995	+	12.4832i	0.374345	+	0.548480i
$519$	−24.6385	−	4.04493i	−1.08151	−	0.177553i
$520$	−7.00734	+	6.52126i	−0.307292	+	0.285976i
$521$	−23.7430			−1.04020			−0.520101	−	0.854105i	$-0.674106\pi$
$521$	−23.7430			−1.04020			−0.520101	+	0.854105i	$0.674106\pi$
$522$	−3.15794	+	3.23243i	−0.138219	+	0.141480i
$523$			1.88064i			0.0822349i	0.999154	+	0.0411174i	$0.0130918\pi$
$523$			1.88064i			0.0822349i	−0.999154	+	0.0411174i	$0.986908\pi$
$524$	−4.31782	−	1.68968i	−0.188625	−	0.0738142i
$525$	6.41942	−	2.42273i	0.280166	−	0.105737i
$526$	−21.2024	+	14.4709i	−0.924468	+	0.630962i
$527$	−0.463253	+	0.802378i	−0.0201796	+	0.0349521i
$528$	3.64510	−	0.507955i	0.158633	−	0.0221059i
$529$	−29.7465	−	51.5225i	−1.29333	−	2.24011i
$530$	1.59149	+	0.765451i	0.0691300	+	0.0332491i
$531$	0.698563	−	2.07021i	0.0303151	−	0.0898392i
$532$	10.4317	−	8.33592i	0.452272	−	0.361408i
$533$	−26.1096	+	15.0744i	−1.13093	+	0.652944i
$534$	−12.4839	+	17.8229i	−0.540233	+	0.771273i
$535$	−5.60826	+	9.71380i	−0.242466	+	0.419964i
$536$	−11.7924	+	38.4327i	−0.509354	+	1.66004i
$537$	16.7878	−	20.4937i	0.724446	−	0.884370i
$538$	1.04915	−	0.0791453i	0.0452320	−	0.00341220i
$539$		−	0.531209i		−	0.0228808i
$540$	−8.03428	+	6.90051i	−0.345740	+	0.296951i
$541$			40.4904i			1.74082i	0.492330	+	0.870409i	$0.336145\pi$
$541$			40.4904i			1.74082i	−0.492330	+	0.870409i	$0.663855\pi$
$542$	−3.05894	−	40.5491i	−0.131393	−	1.74173i
$543$	5.19260	−	6.33889i	0.222836	−	0.272028i
$544$	−3.27924	−	8.29491i	−0.140596	−	0.355641i
$545$	0.682082	−	1.18140i	0.0292172	−	0.0506056i
$546$	6.66262	+	4.66679i	0.285134	+	0.199720i
$547$	−4.60768	+	2.66024i	−0.197010	+	0.113744i	−0.595260	−	0.803533i	$-0.702951\pi$
$547$	−4.60768	+	2.66024i	−0.197010	+	0.113744i	0.398250	+	0.917277i	$0.369618\pi$
$548$	17.6880	+	22.1350i	0.755593	+	0.945560i
$549$	13.6021	+	15.4537i	0.580523	+	0.659547i
$550$	−1.28991	+	2.68191i	−0.0550017	+	0.114357i
$551$	−3.55574	−	6.15872i	−0.151480	−	0.262370i
$552$	24.6357	+	37.0529i	1.04857	+	1.57707i
$553$	5.26132	−	9.11287i	0.223734	−	0.387519i
$554$	17.1789	+	25.1701i	0.729863	+	1.06937i
$555$	17.6488	−	6.66080i	0.749152	−	0.282735i
$556$	11.3156	+	4.42813i	0.479890	+	0.187795i
$557$			16.4627i			0.697548i	0.937207	+	0.348774i	$0.113402\pi$
$557$			16.4627i			0.697548i	−0.937207	+	0.348774i	$0.886598\pi$
$558$	−0.617116	+	2.41537i	−0.0261246	+	0.102251i
$559$	18.1417			0.767311
$560$	−1.20926	−	3.89294i	−0.0511008	−	0.164507i
$561$	−1.43160	−	0.235027i	−0.0604421	−	0.00992284i
$562$	−30.5940	+	20.8809i	−1.29053	+	0.880806i
$563$	−23.8259	−	13.7559i	−1.00414	−	0.579742i	−0.0946717	−	0.995509i	$-0.530180\pi$
$563$	−23.8259	−	13.7559i	−1.00414	−	0.579742i	−0.909472	+	0.415766i	$0.863513\pi$
$564$	0.382292	−	31.5166i	0.0160974	−	1.32709i
$565$	0.865985	−	0.499976i	0.0364322	−	0.0210342i
$566$	10.2669	−	21.3465i	0.431550	−	0.897259i
$567$	7.15997	+	5.45297i	0.300690	+	0.229003i
$568$	−3.31142	−	14.4095i	−0.138944	−	0.604611i
$569$	−4.48171	−	7.76254i	−0.187883	−	0.325423i	0.756661	−	0.653807i	$-0.226829\pi$
$569$	−4.48171	−	7.76254i	−0.187883	−	0.325423i	−0.944544	+	0.328384i	$0.893496\pi$
$570$	−7.04129	−	15.1063i	−0.294927	−	0.632734i
$571$	34.1415	+	19.7116i	1.42878	+	0.824905i	0.997024	−	0.0770870i	$-0.0245619\pi$
$571$	34.1415	+	19.7116i	1.42878	+	0.824905i	0.431753	+	0.901992i	$0.357895\pi$
$572$	−3.48823	+	0.529301i	−0.145850	+	0.0221312i
$573$	5.35893	−	32.6424i	0.223873	−	1.36365i
$574$	−0.965802	−	12.8026i	−0.0403118	−	0.534372i
$575$	−35.9799			−1.50046
$576$	−14.5231	−	19.1070i	−0.605131	−	0.796126i
$577$	10.2990			0.428754			0.214377	−	0.976751i	$-0.431228\pi$
$577$	10.2990			0.428754			0.214377	+	0.976751i	$0.431228\pi$
$578$	−1.54402	−	20.4674i	−0.0642227	−	0.851333i
$579$	−24.1809	+	9.12605i	−1.00493	+	0.379266i
$580$	−2.14640	+	0.325693i	−0.0891246	+	0.0135237i
$581$	3.39540	+	1.96033i	0.140865	+	0.0813283i
$582$	40.2436	+	3.52726i	1.66815	+	0.146210i
$583$	0.325456	+	0.563706i	0.0134790	+	0.0233463i
$584$	5.38437	+	23.4299i	0.222807	+	0.969537i
$585$	7.62130	−	6.70814i	0.315102	−	0.277348i
$586$	9.74779	−	20.2672i	0.402677	−	0.837229i
$587$	−23.0981	+	13.3357i	−0.953359	+	0.550422i	−0.894123	−	0.447822i	$-0.852200\pi$
$587$	−23.0981	+	13.3357i	−0.953359	+	0.550422i	−0.0592365	+	0.998244i	$0.518867\pi$
$588$	−3.02079	+	1.69554i	−0.124575	+	0.0699227i
$589$	−3.39754	−	1.96157i	−0.139993	−	0.0808252i
$590$	0.866966	−	0.591717i	0.0356924	−	0.0243606i
$591$	−6.48594	+	7.91775i	−0.266796	+	0.325693i
$592$	12.6810	+	40.8234i	0.521185	+	1.67783i
$593$	38.8521			1.59546			0.797732	−	0.603012i	$-0.206033\pi$
$593$	38.8521			1.59546			0.797732	+	0.603012i	$0.206033\pi$
$594$	−3.87967	+	0.431380i	−0.159185	+	0.0176998i
$595$			1.60690i			0.0658766i
$596$	−30.6819	−	12.0067i	−1.25678	−	0.491813i
$597$	−23.8569	−	19.5428i	−0.976400	−	0.799833i
$598$	−24.0462	−	35.2319i	−0.983324	−	1.44074i
$599$	17.8141	−	30.8550i	0.727866	−	1.26070i	−0.229918	−	0.973210i	$-0.573846\pi$
$599$	17.8141	−	30.8550i	0.727866	−	1.26070i	0.957783	−	0.287491i	$-0.0928210\pi$
$600$	19.3682	−	1.22504i	0.790704	−	0.0500121i
$601$	9.94699	+	17.2287i	0.405746	+	0.702773i	0.994408	−	0.105607i	$-0.0336784\pi$
$601$	9.94699	+	17.2287i	0.405746	+	0.702773i	−0.588662	+	0.808379i	$0.700345\pi$
$602$	−3.34862	+	6.96230i	−0.136480	+	0.283762i
$603$	13.6330	−	40.4016i	0.555178	−	1.64528i
$604$	13.5982	+	17.0170i	0.553302	+	0.692411i
$605$	−9.45926	+	5.46131i	−0.384574	+	0.222034i
$606$	2.28065	−	26.0207i	0.0926452	−	1.05702i
$607$	4.08912	−	7.08256i	0.165972	−	0.287472i	−0.771028	−	0.636801i	$-0.780257\pi$
$607$	4.08912	−	7.08256i	0.165972	−	0.287472i	0.937000	+	0.349329i	$0.113591\pi$
$608$	35.1235	−	13.8854i	1.42445	−	0.563129i
$609$	0.651417	+	1.72603i	0.0263968	+	0.0699424i
$610$	0.743991	+	9.86232i	0.0301233	+	0.399314i
$611$			30.2158i			1.22240i
$612$	3.23292	+	8.89112i	0.130683	+	0.359402i
$613$		−	0.00502522i		−	0.000202967i	−1.00000		0.000101483i	$-0.999968\pi$
$613$		−	0.00502522i		−	0.000202967i	1.00000		0.000101483i	$-3.23031e-5\pi$
$614$	40.8913	−	3.08475i	1.65024	−	0.124490i
$615$	−15.8133	−	2.59609i	−0.637653	−	0.104684i
$616$	0.440732	−	1.43639i	0.0177576	−	0.0578739i
$617$	−14.1735	+	24.5491i	−0.570602	+	0.988311i	0.425903	+	0.904769i	$0.359957\pi$
$617$	−14.1735	+	24.5491i	−0.570602	+	0.988311i	−0.996504	+	0.0835420i	$0.973377\pi$
$618$	3.49460	+	7.49730i	0.140574	+	0.301585i
$619$	−34.5886	+	19.9697i	−1.39023	+	0.802652i	−0.993341	−	0.115213i	$-0.963245\pi$
$619$	−34.5886	+	19.9697i	−1.39023	+	0.802652i	−0.396893	+	0.917865i	$0.629912\pi$
$620$	−0.935618	+	0.747648i	−0.0375753	+	0.0300263i
$621$	−25.0306	−	40.0098i	−1.00444	−	1.60554i
$622$	−14.5270	−	6.98695i	−0.582478	−	0.280151i
$623$	4.44178	+	7.69338i	0.177956	+	0.308229i
$624$	14.1438	+	18.1468i	0.566206	+	0.726454i
$625$	−5.24997	+	9.09321i	−0.209999	+	0.363729i
$626$	−21.5197	+	14.6875i	−0.860102	+	0.587032i
$627$	0.995184	−	6.06187i	0.0397438	−	0.242088i
$628$	−10.9821	−	4.29760i	−0.438233	−	0.171493i
$629$		−	16.8508i		−	0.671886i
$630$	1.16766	+	4.16305i	0.0465206	+	0.165860i
$631$	22.3402			0.889350			0.444675	−	0.895692i	$-0.353319\pi$
$631$	22.3402			0.889350			0.444675	+	0.895692i	$0.353319\pi$
$632$	21.7874	−	20.2760i	0.866655	−	0.806538i
$633$	3.39198	+	8.98759i	0.134819	+	0.357225i
$634$	9.68435	+	14.1892i	0.384615	+	0.563526i
$635$	−6.47654	−	3.73923i	−0.257014	−	0.148387i
$636$	2.16678	−	3.65000i	0.0859184	−	0.144732i
$637$	2.87597	−	1.66044i	0.113950	−	0.0657890i
$638$	−0.721105	−	0.346826i	−0.0285488	−	0.0137310i
$639$	3.08725	+	15.3751i	0.122130	+	0.608231i
$640$	−0.0399774	−	11.5298i	−0.00158025	−	0.455756i
$641$	16.5505	+	28.6663i	0.653706	+	1.13225i	0.982216	+	0.187752i	$0.0601201\pi$
$641$	16.5505	+	28.6663i	0.653706	+	1.13225i	−0.328510	+	0.944500i	$0.606547\pi$
$642$	22.0816	+	15.4669i	0.871491	+	0.610430i
$643$	27.5783	+	15.9223i	1.08758	+	0.627915i	0.932931	−	0.360055i	$-0.117242\pi$
$643$	27.5783	+	15.9223i	1.08758	+	0.627915i	0.154649	+	0.987969i	$0.450575\pi$
$644$	17.9596	−	2.72517i	0.707706	−	0.107387i
$645$	7.45956	+	6.11061i	0.293720	+	0.240605i
$646$	−14.8459	+	1.11994i	−0.584106	+	0.0440636i
$647$	−43.9490			−1.72781			−0.863906	−	0.503653i	$-0.831989\pi$
$647$	−43.9490			−1.72781			−0.863906	+	0.503653i	$0.831989\pi$
$648$	14.8364	+	20.6853i	0.582828	+	0.812595i
$649$	0.386878			0.0151863
$650$	−18.5518	+	1.39951i	−0.727662	+	0.0548932i
$651$	0.787313	+	0.644939i	0.0308572	+	0.0252772i
$652$	2.61084	+	17.2061i	0.102248	+	0.673843i
$653$	−25.2475	−	14.5766i	−0.988010	−	0.570428i	−0.0833311	−	0.996522i	$-0.526556\pi$
$653$	−25.2475	−	14.5766i	−0.988010	−	0.570428i	−0.904679	+	0.426094i	$0.859889\pi$
$654$	−2.68558	−	1.88110i	−0.105015	−	0.0735567i
$655$	1.18131	+	2.04609i	0.0461577	+	0.0799475i
$656$	8.01051	−	35.4197i	0.312758	−	1.38291i
$657$	−5.01986	−	25.0000i	−0.195843	−	0.975341i
$658$	−11.5960	−	5.57728i	−0.452060	−	0.217425i
$659$	6.76166	−	3.90384i	0.263397	−	0.152072i	−0.362486	−	0.931989i	$-0.618072\pi$
$659$	6.76166	−	3.90384i	0.263397	−	0.152072i	0.625883	+	0.779917i	$0.284739\pi$
$660$	−1.61259	−	0.957291i	−0.0627698	−	0.0372625i
$661$	−4.42808	−	2.55655i	−0.172232	−	0.0994383i	0.411406	−	0.911452i	$-0.365038\pi$
$661$	−4.42808	−	2.55655i	−0.172232	−	0.0994383i	−0.583638	+	0.812014i	$0.698371\pi$
$662$	5.52862	+	8.10038i	0.214876	+	0.314830i
$663$	−3.20241	−	8.48530i	−0.124371	−	0.329542i
$664$	7.55472	+	8.11783i	0.293180	+	0.315033i
$665$	−6.80418			−0.263855
$666$	−12.2447	−	43.6560i	−0.474472	−	1.69163i
$667$		−	9.67416i		−	0.374585i
$668$	−3.24257	+	8.28607i	−0.125459	+	0.320598i
$669$	0.149376	−	0.909881i	0.00577521	−	0.0351780i
$670$	16.9195	−	11.5478i	0.653657	−	0.446130i
$671$	−1.82269	+	3.15698i	−0.0703640	+	0.121874i
$672$	−9.57497	+	2.07846i	−0.369362	+	0.0801784i
$673$	13.0481	+	22.6000i	0.502969	+	0.871167i	0.999994	+	0.00343118i	$0.00109218\pi$
$673$	13.0481	+	22.6000i	0.502969	+	0.871167i	−0.497026	+	0.867736i	$0.665574\pi$
$674$	18.1389	+	8.72417i	0.698684	+	0.336042i
$675$	−20.5712	+	0.729351i	−0.791786	+	0.0280727i
$676$	2.46180	+	3.08074i	0.0946848	+	0.118490i
$677$	30.0217	−	17.3330i	1.15383	−	0.666163i	0.204011	−	0.978969i	$-0.434602\pi$
$677$	30.0217	−	17.3330i	1.15383	−	0.666163i	0.949817	+	0.312806i	$0.101269\pi$
$678$	−1.01540	−	2.17843i	−0.0389961	−	0.0836619i
$679$	8.24618	−	14.2828i	0.316459	−	0.548123i
$680$	−1.33321	+	4.34507i	−0.0511263	+	0.166626i
$681$	−40.1926	−	6.59846i	−1.54018	−	0.252853i
$682$	−0.440177	+	0.0332060i	−0.0168552	+	0.00127152i
$683$		−	22.9461i		−	0.878009i	−0.898485	−	0.439004i	$-0.855331\pi$
$683$		−	22.9461i		−	0.878009i	0.898485	−	0.439004i	$-0.144669\pi$
$684$	−37.6480	+	13.6893i	−1.43951	+	0.523423i
$685$		−	14.4378i		−	0.551638i
$686$	0.106383	+	1.41021i	0.00406172	+	0.0538419i
$687$	−5.38054	−	14.2566i	−0.205280	−	0.543923i
$688$	−14.8311	+	16.0478i	−0.565432	+	0.611817i
$689$	−2.03460	+	3.52403i	−0.0775121	+	0.134255i
$690$	1.97963	−	22.5862i	0.0753632	−	0.859841i
$691$	11.4669	−	6.62042i	0.436221	−	0.251853i	−0.265772	−	0.964036i	$-0.585627\pi$
$691$	11.4669	−	6.62042i	0.436221	−	0.251853i	0.701994	+	0.712183i	$0.252294\pi$
$692$	−22.5231	+	17.9981i	−0.856201	+	0.684186i
$693$	−0.509522	+	1.50998i	−0.0193552	+	0.0573593i
$694$	11.4065	−	23.7159i	0.432985	−	0.900244i
$695$	−3.09585	−	5.36217i	−0.117432	−	0.203399i
$696$	0.329385	+	5.20767i	0.0124853	+	0.197396i
$697$	−7.15742	+	12.3970i	−0.271106	+	0.469570i
$698$	−18.6234	−	27.2864i	−0.704905	−	1.03281i
$699$	9.68159	+	7.93082i	0.366191	+	0.299971i
$700$	2.88723	−	7.37803i	0.109127	−	0.278863i
$701$		−	31.2014i		−	1.17846i	−0.807965	−	0.589231i	$-0.799431\pi$
$701$		−	31.2014i		−	1.17846i	0.807965	−	0.589231i	$-0.200569\pi$
$702$	−14.4624	−	19.6561i	−0.545850	−	0.741872i
$703$	71.3521			2.69110
$704$	2.38348	−	3.51834i	0.0898308	−	0.132603i
$705$	−10.1775	+	12.4242i	−0.383307	+	0.467923i
$706$	11.2068	−	7.64877i	0.421772	−	0.287865i
$707$	−9.23496	−	5.33181i	−0.347317	−	0.200523i
$708$	−1.23485	−	2.20003i	−0.0464086	−	0.0826821i
$709$	16.9769	−	9.80164i	0.637582	−	0.368108i	−0.146100	−	0.989270i	$-0.546672\pi$
$709$	16.9769	−	9.80164i	0.637582	−	0.368108i	0.783683	+	0.621162i	$0.213339\pi$
$710$	−3.26544	+	6.78936i	−0.122550	+	0.254800i
$711$	−23.6963	+	20.8571i	−0.888681	+	0.782202i
$712$	5.62756	+	24.4882i	0.210902	+	0.917733i
$713$	−2.66844	−	4.62188i	−0.0999339	−	0.173091i
$714$	3.84754	+	0.337229i	0.143991	+	0.0126205i
$715$	1.55693	+	0.898894i	0.0582259	+	0.0336167i
$716$	−4.58920	−	30.2441i	−0.171507	−	1.13027i
$717$	−9.38995	+	3.54383i	−0.350674	+	0.132347i
$718$	0.996431	+	13.2086i	0.0371865	+	0.492942i
$719$	−12.6761			−0.472740			−0.236370	−	0.971663i	$-0.575958\pi$
$719$	−12.6761			−0.472740			−0.236370	+	0.971663i	$0.575958\pi$
$720$	−0.296635	+	12.2257i	−0.0110549	+	0.455625i
$721$	3.37692			0.125763
$722$	−2.72095	−	36.0689i	−0.101263	−	1.34234i
$723$	−0.459787	+	2.80066i	−0.0170997	+	0.104158i
$724$	−1.41948	−	9.35474i	−0.0527546	−	0.347666i
$725$	−3.65415	−	2.10972i	−0.135712	−	0.0783531i
$726$	11.0913	+	23.7952i	0.411637	+	0.883123i
$727$	5.17924	+	8.97070i	0.192087	+	0.332705i	0.945942	−	0.324337i	$-0.105141\pi$
$727$	5.17924	+	8.97070i	0.192087	+	0.332705i	−0.753855	+	0.657041i	$0.771808\pi$
$728$	9.15425	−	2.10371i	0.339279	−	0.0779688i
$729$	−15.1221	−	22.3679i	−0.560077	−	0.828440i
$730$	5.30961	−	11.0395i	0.196517	−	0.408590i
$731$	7.45976	−	4.30689i	0.275909	−	0.159296i
$732$	23.7703	+	0.288330i	0.878576	+	0.0106570i
$733$	1.74065	+	1.00497i	0.0642925	+	0.0371193i	0.531802	−	0.846869i	$-0.321515\pi$
$733$	1.74065	+	1.00497i	0.0642925	+	0.0371193i	−0.467509	+	0.883988i	$0.654849\pi$
$734$	38.6698	−	26.3927i	1.42733	−	0.974172i
$735$	1.74183	+	0.285958i	0.0642484	+	0.0105477i
$736$	50.8237	+	7.53176i	1.87339	+	0.277624i
$737$	7.55021			0.278115
$738$	−9.53464	+	37.3183i	−0.350975	+	1.37370i
$739$		−	46.7137i		−	1.71839i	−0.511648	−	0.859195i	$-0.670965\pi$
$739$		−	46.7137i		−	1.71839i	0.511648	−	0.859195i	$-0.329035\pi$
$740$	7.93784	−	20.2843i	0.291801	−	0.745668i
$741$	35.9297	−	13.5601i	1.31991	−	0.498143i
$742$	−0.976881	−	1.43130i	−0.0358624	−	0.0525446i
$743$	1.91611	−	3.31880i	0.0702952	−	0.121755i	−0.828735	−	0.559641i	$-0.810939\pi$
$743$	1.91611	−	3.31880i	0.0702952	−	0.121755i	0.899031	+	0.437886i	$0.144273\pi$
$744$	1.59381	+	2.39713i	0.0584317	+	0.0878831i
$745$	8.39426	+	14.5393i	0.307542	+	0.532678i
$746$	7.87530	−	16.3740i	0.288335	−	0.599494i
$747$	−7.77122	−	8.82908i	−0.284334	−	0.323039i
$748$	−1.30868	+	1.04576i	−0.0478502	+	0.0382369i
$749$	9.53167	−	5.50311i	0.348280	−	0.201079i
$750$	−18.3227	−	12.8340i	−0.669050	−	0.468631i
$751$	0.458053	−	0.793372i	0.0167146	−	0.0289505i	−0.857547	−	0.514405i	$-0.828013\pi$
$751$	0.458053	−	0.793372i	0.0167146	−	0.0289505i	0.874262	+	0.485455i	$0.161346\pi$
$752$	−26.7284	−	24.7019i	−0.974683	−	0.900787i
$753$	−4.69154	+	5.72722i	−0.170969	+	0.208712i
$754$	−0.376296	−	4.98816i	−0.0137039	−	0.181658i
$755$		−	11.0995i		−	0.403952i
$756$	10.2130	−	1.92215i	0.371443	−	0.0699080i
$757$		−	17.7660i		−	0.645716i	−0.946447	−	0.322858i	$-0.895356\pi$
$757$		−	17.7660i		−	0.645716i	0.946447	−	0.322858i	$-0.104644\pi$
$758$	−37.7377	+	2.84684i	−1.37069	+	0.103402i
$759$	5.29559	−	6.46461i	0.192218	−	0.234651i
$760$	−18.3985	−	5.64526i	−0.667384	−	0.204775i
$761$	−10.1666	+	17.6091i	−0.368540	+	0.638331i	−0.989338	−	0.145641i	$-0.953476\pi$
$761$	−10.1666	+	17.6091i	−0.368540	+	0.638331i	0.620797	+	0.783971i	$0.286809\pi$
$762$	−10.3123	+	14.7226i	−0.373577	+	0.533343i
$763$	−1.15925	+	0.669293i	−0.0419676	+	0.0242300i
$764$	−23.8448	−	29.8398i	−0.862676	−	1.07957i
$765$	1.54130	−	4.56767i	0.0557258	−	0.165145i
$766$	−40.5007	−	19.4794i	−1.46335	−	0.703820i
$767$	1.20929	+	2.09455i	0.0436650	+	0.0756300i
$768$	−27.6152	−	2.32396i	−0.996478	−	0.0838585i
$769$	19.9093	−	34.4840i	0.717949	−	1.24352i	−0.243862	−	0.969810i	$-0.578414\pi$
$769$	19.9093	−	34.4840i	0.717949	−	1.24352i	0.961811	−	0.273715i	$-0.0882524\pi$
$770$	−0.632353	+	0.431590i	−0.0227884	+	0.0155534i
$771$	−21.7300	+	8.20106i	−0.782587	+	0.295354i
$772$	−10.8757	+	27.7919i	−0.391427	+	1.00025i
$773$			42.4752i			1.52773i	0.645378	+	0.763864i	$0.276700\pi$
$773$			42.4752i			1.52773i	−0.645378	+	0.763864i	$0.723300\pi$
$774$	16.1966	−	16.5787i	0.582176	−	0.595907i
$775$	−2.32771			−0.0836140
$776$	34.1478	−	31.7791i	1.22583	−	1.14080i
$777$	−18.2657	−	2.99870i	−0.655280	−	0.107578i
$778$	16.4036	+	24.0341i	0.588098	+	0.861664i
$779$	−52.4932	−	30.3069i	−1.88076	−	1.08586i
$780$	0.142196	−	11.7228i	0.00509143	−	0.419744i
$781$	−2.40479	+	1.38841i	−0.0860501	+	0.0496811i
$782$	−18.2518	−	8.77849i	−0.652684	−	0.313918i
$783$	−0.196106	−	5.53113i	−0.00700825	−	0.197666i
$784$	−0.882355	+	3.90147i	−0.0315127	+	0.139338i
$785$	3.00459	+	5.20410i	0.107238	+	0.185742i
$786$	5.14705	−	2.39912i	0.183589	−	0.0855737i
$787$	21.2496	+	12.2685i	0.757467	+	0.437324i	0.828386	−	0.560158i	$-0.189260\pi$
$787$	21.2496	+	12.2685i	0.757467	+	0.437324i	−0.0709183	+	0.997482i	$0.522593\pi$
$788$	1.77304	+	11.6848i	0.0631618	+	0.416253i
$789$	5.09323	−	31.0239i	0.181324	−	1.10448i
$790$	−15.1226	+	1.14082i	−0.538039	+	0.0405885i
$791$	−0.981204			−0.0348876
$792$	−2.63054	+	3.66025i	−0.0934723	+	0.130061i
$793$	−22.7892			−0.809268
$794$	−6.56474	+	0.495229i	−0.232974	+	0.0175750i
$795$	−2.02358	+	0.763714i	−0.0717691	+	0.0270862i
$796$	−35.2074	+	5.34233i	−1.24789	+	0.189354i
$797$	32.2181	+	18.6011i	1.14122	+	0.658886i	0.946733	−	0.322019i	$-0.104361\pi$
$797$	32.2181	+	18.6011i	1.14122	+	0.658886i	0.194490	+	0.980904i	$0.437695\pi$
$798$	−1.42794	+	16.2918i	−0.0505486	+	0.576724i
$799$	7.17333	+	12.4246i	0.253774	+	0.439549i
$800$	13.9285	−	17.5547i	0.492445	−	0.620654i
$801$	−5.24659	−	26.1291i	−0.185379	−	0.923227i
$802$	46.1115	+	22.1780i	1.62825	+	0.783133i
$803$	3.91019	−	2.25755i	0.137987	−	0.0796671i
$804$	−24.0991	−	42.9352i	−0.849909	−	1.51421i
$805$	−8.01603	−	4.62806i	−0.282528	−	0.163118i
$806$	−1.55567	−	2.27932i	−0.0547961	−	0.0802857i
$807$	−0.816570	+	0.996832i	−0.0287446	+	0.0350902i
$808$	−20.5477	−	22.0793i	−0.722866	−	0.776746i
$809$	−17.7904			−0.625476			−0.312738	−	0.949839i	$-0.601246\pi$
$809$	−17.7904			−0.625476			−0.312738	+	0.949839i	$0.601246\pi$
$810$	0.673991	−	12.9536i	0.0236816	−	0.455143i
$811$			2.10159i			0.0737968i	0.999319	+	0.0368984i	$0.0117478\pi$
$811$			2.10159i			0.0737968i	−0.999319	+	0.0368984i	$0.988252\pi$
$812$	1.98378	+	0.776310i	0.0696171	+	0.0272431i
$813$	38.5272	+	31.5601i	1.35121	+	1.10686i
$814$	6.63118	−	4.52588i	0.232423	−	0.158632i
$815$	4.43390	−	7.67974i	0.155313	−	0.269010i
$816$	10.1240	+	4.10408i	0.354410	+	0.143672i
$817$	18.2369	+	31.5872i	0.638027	+	1.10509i
$818$	38.4222	+	18.4797i	1.34340	+	0.646128i
$819$	−9.76767	+	1.96130i	−0.341310	+	0.0685333i
$820$	−14.4556	+	11.5514i	−0.504812	+	0.403393i
$821$	5.99935	−	3.46373i	0.209379	−	0.120885i	−0.391644	−	0.920117i	$-0.628093\pi$
$821$	5.99935	−	3.46373i	0.209379	−	0.120885i	0.601023	+	0.799232i	$0.294760\pi$
$822$	−34.5695	−	3.02994i	−1.20575	−	0.105681i
$823$	−2.11593	+	3.66490i	−0.0737568	+	0.127750i	−0.900545	−	0.434763i	$-0.856832\pi$
$823$	−2.11593	+	3.66490i	−0.0737568	+	0.127750i	0.826788	+	0.562513i	$0.190166\pi$
$824$	9.13122	+	2.80175i	0.318101	+	0.0976037i
$825$	−1.28698	−	3.41005i	−0.0448068	−	0.118723i
$826$	−1.02705	+	0.0774782i	−0.0357356	+	0.00269581i
$827$		−	29.9978i		−	1.04313i	−0.853213	−	0.521563i	$-0.825349\pi$
$827$		−	29.9978i		−	1.04313i	0.853213	−	0.521563i	$-0.174651\pi$
$828$	−53.6645	−	9.47998i	−1.86497	−	0.329452i
$829$		−	16.3881i		−	0.569182i	−0.958649	−	0.284591i	$-0.908142\pi$
$829$		−	16.3881i		−	0.569182i	0.958649	−	0.284591i	$-0.0918578\pi$
$830$	−0.425061	−	5.63459i	−0.0147541	−	0.195580i
$831$	−36.8295	−	6.04634i	−1.27760	−	0.209745i
$832$	26.4985	+	1.90661i	0.918671	+	0.0660999i
$833$	0.788387	−	1.36553i	0.0273160	−	0.0473127i
$834$	−13.4888	+	6.28734i	−0.467079	+	0.217713i
$835$	3.92654	−	2.26699i	0.135883	−	0.0784524i
$836$	−4.42812	−	5.54142i	−0.153150	−	0.191654i
$837$	−1.61935	−	2.58843i	−0.0559730	−	0.0894692i
$838$	15.2663	−	31.7410i	0.527365	−	1.09647i
$839$	22.4352	+	38.8589i	0.774550	+	1.34156i	0.935047	+	0.354523i	$0.115357\pi$
$839$	22.4352	+	38.8589i	0.774550	+	1.34156i	−0.160498	+	0.987036i	$0.551310\pi$
$840$	4.47266	+	2.21839i	0.154321	+	0.0765416i
$841$	−13.9327	+	24.1322i	−0.480439	+	0.832146i
$842$	14.9725	+	21.9372i	0.515985	+	0.756007i
$843$	7.34928	−	44.7660i	0.253123	−	1.54182i
$844$	10.3297	+	4.04231i	0.355563	+	0.139142i
$845$		−	2.00944i		−	0.0691269i
$846$	27.6125	+	26.9762i	0.949337	+	0.927461i
$847$	10.7178			0.368269
$848$	−1.45398	−	4.68073i	−0.0499298	−	0.160737i
$849$	10.2436	+	27.1420i	0.351559	+	0.931513i
$850$	−7.29616	+	4.97973i	−0.250256	+	0.170803i
$851$	84.0603	+	48.5322i	2.88155	+	1.66366i
$852$	15.5710	+	9.24356i	0.533455	+	0.316679i
$853$	−44.2375	+	25.5405i	−1.51466	+	0.874492i	−0.514812	+	0.857303i	$0.672138\pi$
$853$	−44.2375	+	25.5405i	−1.51466	+	0.874492i	−0.999852	+	0.0171883i	$0.994529\pi$
$854$	4.20647	−	8.74590i	0.143942	−	0.299279i
$855$	19.3411	+	6.52639i	0.661451	+	0.223198i
$856$	30.3395	−	6.97224i	1.03698	−	0.238306i
$857$	−2.54846	−	4.41407i	−0.0870539	−	0.150782i	0.819211	−	0.573493i	$-0.194412\pi$
$857$	−2.54846	−	4.41407i	−0.0870539	−	0.150782i	−0.906265	+	0.422711i	$0.861079\pi$
$858$	2.47904	−	3.53925i	0.0846330	−	0.120828i
$859$	10.7160	+	6.18687i	0.365624	+	0.211093i	0.671545	−	0.740964i	$-0.265631\pi$
$859$	10.7160	+	6.18687i	0.365624	+	0.211093i	−0.305921	+	0.952057i	$0.598964\pi$
$860$	11.0086	−	1.67043i	0.375390	−	0.0569613i
$861$	12.1642	+	9.96452i	0.414556	+	0.339590i
$862$	2.71438	+	35.9817i	0.0924522	+	1.22554i
$863$	55.3473			1.88405			0.942023	−	0.335549i	$-0.108922\pi$
$863$	55.3473			1.88405			0.942023	+	0.335549i	$0.108922\pi$
$864$	29.2108	+	3.27597i	0.993770	+	0.111451i
$865$	14.6909			0.499507
$866$	3.01566	+	39.9755i	0.102476	+	1.35842i
$867$	19.4468	+	15.9302i	0.660449	+	0.541017i
$868$	1.16189	−	0.176304i	0.0394372	−	0.00598416i
$869$	−4.84084	−	2.79486i	−0.164214	−	0.0948092i
$870$	1.52542	−	2.17779i	0.0517166	−	0.0738341i
$871$	23.6002	+	40.8768i	0.799663	+	1.38506i
$872$	−3.68991	+	0.847969i	−0.124956	+	0.0287158i
$873$	−37.1397	+	32.6898i	−1.25699	+	1.10638i
$874$	37.1711	−	77.2845i	1.25733	−	2.61419i
$875$	−7.90911	+	4.56633i	−0.267377	+	0.154370i
$876$	−25.3185	−	15.0300i	−0.855433	−	0.507817i
$877$	−13.1943	−	7.61773i	−0.445540	−	0.257233i	0.260405	−	0.965500i	$-0.416144\pi$
$877$	−13.1943	−	7.61773i	−0.445540	−	0.257233i	−0.705945	+	0.708267i	$0.749477\pi$
$878$	31.3317	−	21.3843i	1.05739	−	0.721685i
$879$	9.72566	+	25.7697i	0.328038	+	0.869190i
$880$	−2.06796	+	0.642373i	−0.0697111	+	0.0216544i
$881$	−8.71803			−0.293718			−0.146859	−	0.989157i	$-0.546916\pi$
$881$	−8.71803			−0.293718			−0.146859	+	0.989157i	$0.546916\pi$
$882$	1.05024	−	4.11060i	0.0353633	−	0.138411i
$883$			51.8630i			1.74533i	0.488319	+	0.872665i	$0.337610\pi$
$883$			51.8630i			1.74533i	−0.488319	+	0.872665i	$0.662390\pi$
$884$	−9.75241	−	3.81639i	−0.328009	−	0.128359i
$885$	−0.208262	+	1.26857i	−0.00700066	+	0.0426424i
$886$	15.4644	+	22.6580i	0.519536	+	0.761209i
$887$	3.53612	−	6.12474i	0.118731	−	0.205648i	−0.800534	−	0.599287i	$-0.795451\pi$
$887$	3.53612	−	6.12474i	0.118731	−	0.205648i	0.919265	+	0.393639i	$0.128784\pi$
$888$	−46.9027	−	23.2632i	−1.57395	−	0.780660i
$889$	3.66912	+	6.35511i	0.123058	+	0.213143i
$890$	5.54943	−	11.5381i	0.186017	−	0.386759i
$891$	2.89667	−	3.80344i	0.0970420	−	0.127420i
$892$	−0.664656	−	0.831761i	−0.0222543	−	0.0278494i
$893$	−52.6098	+	30.3743i	−1.76052	+	1.01644i
$894$	36.5743	−	17.0478i	1.22323	−	0.570164i
$895$	−7.79369	+	13.4991i	−0.260514	+	0.451224i
$896$	−5.62285	+	9.81751i	−0.187846	+	0.327980i
$897$	51.5522	+	8.46338i	1.72128	+	0.282584i
$898$	0.0284883	+	0.377639i	0.000950666	+	0.0126020i
$899$		−	0.625869i		−	0.0208739i
$900$	−15.2839	+	18.2029i	−0.509462	+	0.606764i
$901$			1.93208i			0.0643670i
$902$	−6.80088	+	0.513043i	−0.226444	+	0.0170825i
$903$	−3.34102	−	8.85257i	−0.111182	−	0.294595i
$904$	−2.65318	−	0.814082i	−0.0882435	−	0.0270760i
$905$	−2.41066	+	4.17538i	−0.0801329	+	0.138794i
$906$	−26.5764	−	2.32937i	−0.882942	−	0.0773880i
$907$	16.9317	−	9.77555i	0.562209	−	0.324592i	−0.191822	−	0.981430i	$-0.561440\pi$
$907$	16.9317	−	9.77555i	0.562209	−	0.324592i	0.754032	+	0.656838i	$0.228106\pi$
$908$	−36.7418	+	29.3602i	−1.21932	+	0.974352i
$909$	21.1365	+	24.0138i	0.701055	+	0.796487i
$910$	−4.31322	−	2.07451i	−0.142982	−	0.0687692i
$911$	−16.8404	−	29.1684i	−0.557946	−	0.966391i	−0.997668	−	0.0682571i	$-0.978256\pi$
$911$	−16.8404	−	29.1684i	−0.557946	−	0.966391i	0.439722	−	0.898134i	$-0.355077\pi$
$912$	−17.3781	+	42.8684i	−0.575446	+	1.41951i
$913$	1.04135	−	1.80367i	0.0344635	−	0.0596926i
$914$	−16.8005	+	11.4666i	−0.555710	+	0.379280i
$915$	−9.37054	−	7.67602i	−0.309781	−	0.253761i
$916$	−16.3855	−	6.41212i	−0.541393	−	0.211862i
$917$		−	2.31833i		−	0.0765580i
$918$	−10.6133	−	4.64905i	−0.350291	−	0.153441i
$919$	28.7464			0.948256			0.474128	−	0.880456i	$-0.342763\pi$
$919$	28.7464			0.948256			0.474128	+	0.880456i	$0.342763\pi$
$920$	−17.8356	−	19.1650i	−0.588022	−	0.631851i
$921$	−31.8264	+	38.8522i	−1.04872	+	1.28022i
$922$	9.15709	+	13.4167i	0.301573	+	0.441856i
$923$	−15.0336	−	8.67968i	−0.494838	−	0.285695i
$924$	0.900685	+	1.60467i	0.0296303	+	0.0527898i
$925$	36.6634	−	21.1676i	1.20549	−	0.695988i
$926$	−25.7318	−	12.3761i	−0.845601	−	0.406704i
$927$	−9.59901	−	3.23906i	−0.315273	−	0.106385i
$928$	4.72007	+	3.74504i	0.154944	+	0.122937i
$929$	−0.995543	−	1.72433i	−0.0326627	−	0.0565735i	0.849232	−	0.528020i	$-0.177065\pi$
$929$	−0.995543	−	1.72433i	−0.0326627	−	0.0565735i	−0.881895	+	0.471446i	$0.843732\pi$
$930$	0.128072	−	1.46121i	0.00419964	−	0.0479150i
$931$	5.78211	+	3.33830i	0.189501	+	0.109408i
$932$	14.2878	−	2.16802i	0.468012	−	0.0710157i
$933$	18.4710	−	6.97110i	0.604714	−	0.228223i
$934$	−52.0046	+	3.92311i	−1.70164	+	0.128368i
$935$	0.853602			0.0279158
$936$	−28.0391	−	2.80065i	−0.916486	−	0.0915421i
$937$	5.66538			0.185080			0.0925400	−	0.995709i	$-0.470501\pi$
$937$	5.66538			0.185080			0.0925400	+	0.995709i	$0.470501\pi$
$938$	−20.0436	+	1.51205i	−0.654447	+	0.0493700i
$939$	5.16946	−	31.4883i	0.168699	−	1.02758i
$940$	2.78218	+	18.3353i	0.0907447	+	0.598032i
$941$	0.452187	+	0.261070i	0.0147409	+	0.00851065i	0.507352	−	0.861739i	$-0.330624\pi$
$941$	0.452187	+	0.261070i	0.0147409	+	0.00851065i	−0.492611	+	0.870249i	$0.663958\pi$
$942$	13.0912	−	6.10200i	0.426533	−	0.198814i
$943$	−41.2283	−	71.4095i	−1.34258	−	2.32541i
$944$	−2.84142	−	0.642616i	−0.0924805	−	0.0209154i
$945$	−4.67692	−	2.48356i	−0.152140	−	0.0807903i
$946$	3.69844	+	1.77882i	0.120247	+	0.0578344i
$947$	−3.20937	+	1.85293i	−0.104290	+	0.0602121i	−0.551238	−	0.834348i	$-0.685844\pi$
$947$	−3.20937	+	1.85293i	−0.104290	+	0.0602121i	0.446948	+	0.894560i	$0.352511\pi$
$948$	−0.442118	+	36.4488i	−0.0143593	+	1.18380i
$949$	24.4447	+	14.1132i	0.793509	+	0.458132i
$950$	−21.0859	−	30.8944i	−0.684116	−	1.00235i
$951$	−20.7621	−	3.40853i	−0.673256	−	0.110529i
$952$	3.26475	−	3.03828i	0.105811	−	0.0984713i
$953$	8.98029			0.290900			0.145450	−	0.989366i	$-0.453537\pi$
$953$	8.98029			0.290900			0.145450	+	0.989366i	$0.453537\pi$
$954$	1.40395	+	5.00551i	0.0454546	+	0.162059i
$955$			19.4633i			0.629817i
$956$	−4.22327	+	10.7921i	−0.136590	+	0.349043i
$957$	0.916885	−	0.346039i	0.0296387	−	0.0111858i
$958$	−47.4580	+	32.3908i	−1.53330	+	1.04650i
$959$	−7.08353	+	12.2690i	−0.228739	+	0.396188i
$960$	10.2536	+	9.70939i	0.330932	+	0.313369i
$961$	15.3274	+	26.5478i	0.494431	+	0.856380i
$962$	45.2307	+	21.7543i	1.45829	+	0.701388i
$963$	−32.3725	+	6.50023i	−1.04319	+	0.209467i
$964$	2.04585	+	2.56020i	0.0658923	+	0.0824586i
$965$	13.1698	−	7.60359i	0.423951	−	0.244768i
$966$	−12.7636	+	18.2222i	−0.410662	+	0.586290i
$967$	11.6303	−	20.1443i	0.374006	−	0.647797i	−0.616172	−	0.787612i	$-0.711317\pi$
$967$	11.6303	−	20.1443i	0.374006	−	0.647797i	0.990178	+	0.139815i	$0.0446506\pi$
$968$	28.9810	+	8.89232i	0.931485	+	0.285810i
$969$	11.5549	−	14.1057i	0.371196	−	0.453139i
$970$	−23.7020	+	1.78803i	−0.761026	+	0.0574101i
$971$		−	61.2560i		−	1.96580i	−0.184144	−	0.982899i	$-0.558951\pi$
$971$		−	61.2560i		−	1.96580i	0.184144	−	0.982899i	$-0.441049\pi$
$972$	−30.8744	−	4.33227i	−0.990298	−	0.138958i
$973$			6.07561i			0.194775i
$974$	0.362125	+	4.80032i	0.0116032	+	0.153812i
$975$	14.4392	−	17.6267i	0.462425	−	0.564508i
$976$	18.6306	−	20.1589i	0.596350	−	0.645272i
$977$	21.0695	−	36.4934i	0.674072	−	1.16753i	−0.302668	−	0.953096i	$-0.597877\pi$
$977$	21.0695	−	36.4934i	0.674072	−	1.16753i	0.976739	−	0.214430i	$-0.0687895\pi$
$978$	−17.4577	−	12.2281i	−0.558237	−	0.391013i
$979$	4.08680	−	2.35951i	0.130615	−	0.0754104i
$980$	1.59228	−	1.27238i	0.0508636	−	0.0406448i
$981$	3.93717	−	0.790563i	0.125704	−	0.0252407i
$982$	−19.7046	+	40.9689i	−0.628798	+	1.30737i
$983$	−25.5381	−	44.2333i	−0.814538	−	1.41082i	−0.909659	−	0.415356i	$-0.863657\pi$
$983$	−25.5381	−	44.2333i	−0.814538	−	1.41082i	0.0951203	−	0.995466i	$-0.469676\pi$
$984$	24.6248	+	37.0365i	0.785011	+	1.18068i
$985$	3.01109	−	5.21536i	0.0959412	−	0.166175i
$986$	−1.33894	−	1.96177i	−0.0426404	−	0.0624755i
$987$	14.7443	−	5.56462i	0.469318	−	0.177124i
$988$	16.1599	−	41.2950i	0.514115	−	1.31377i
$989$			49.6173i			1.57774i
$990$	2.21145	−	0.620271i	0.0702846	−	0.0197135i
$991$	−5.48195			−0.174140			−0.0870699	−	0.996202i	$-0.527750\pi$
$991$	−5.48195			−0.174140			−0.0870699	+	0.996202i	$0.527750\pi$
$992$	3.28804	+	0.487267i	0.104395	+	0.0154707i
$993$	−11.8527	−	1.94587i	−0.376134	−	0.0617503i
$994$	6.10597	−	4.16741i	0.193670	−	0.132182i
$995$	15.7144	+	9.07270i	0.498179	+	0.287624i
$996$	−13.5806	−	0.164730i	−0.430317	−	0.00521968i
$997$	−4.32336	+	2.49609i	−0.136922	+	0.0790520i	−0.566896	−	0.823789i	$-0.691856\pi$
$997$	−4.32336	+	2.49609i	−0.136922	+	0.0790520i	0.429974	+	0.902841i	$0.358523\pi$
$998$	2.32576	−	4.83562i	0.0736208	−	0.153069i
$999$	49.0446	+	26.0439i	1.55170	+	0.823994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.19	✓	72
8.5	even	2	inner	504.2.cs.b.85.30	yes	72
9.7	even	3	inner	504.2.cs.b.421.30	yes	72
72.61	even	6	inner	504.2.cs.b.421.19	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.19	✓	72	1.1	even	1	trivial
504.2.cs.b.85.30	yes	72	8.5	even	2	inner
504.2.cs.b.421.19	yes	72	72.61	even	6	inner
504.2.cs.b.421.30	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.106383 + 1.41021i) q^{2} +(-1.33989 - 1.09759i) q^{3} +(-1.97737 + 0.300044i) q^{4} +(0.882573 + 0.509554i) q^{5} +(1.40529 - 2.00628i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-0.633481 - 2.75657i) q^{8} +(0.590596 + 2.94129i) q^{9} +O(q^{10})\)	\(q+(0.106383 + 1.41021i) q^{2} +(-1.33989 - 1.09759i) q^{3} +(-1.97737 + 0.300044i) q^{4} +(0.882573 + 0.509554i) q^{5} +(1.40529 - 2.00628i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(-0.633481 - 2.75657i) q^{8} +(0.590596 + 2.94129i) q^{9} +(-0.624686 + 1.29882i) q^{10} +(-0.460041 + 0.265605i) q^{11} +(2.97877 + 1.76831i) q^{12} +(-2.87597 - 1.66044i) q^{13} +(1.16808 - 0.797234i) q^{14} +(-0.623268 - 1.65145i) q^{15} +(3.81995 - 1.18659i) q^{16} -1.57677 q^{17} +(-4.08500 + 1.14577i) q^{18} -6.67660i q^{19} +(-1.89806 - 0.742764i) q^{20} +(-0.280596 + 1.70917i) q^{21} +(-0.423498 - 0.620497i) q^{22} +(4.54128 - 7.86573i) q^{23} +(-2.17679 + 4.38880i) q^{24} +(-1.98071 - 3.43069i) q^{25} +(2.03561 - 4.23235i) q^{26} +(2.43700 - 4.58923i) q^{27} +(1.24853 + 1.56243i) q^{28} +(0.922434 - 0.532567i) q^{29} +(2.26258 - 1.05462i) q^{30} +(0.293798 - 0.508873i) q^{31} +(2.07972 + 5.26068i) q^{32} +(0.907927 + 0.149055i) q^{33} +(-0.167742 - 2.22358i) q^{34} -1.01911i q^{35} +(-2.05034 - 5.63880i) q^{36} +10.6869i q^{37} +(9.41539 - 0.710276i) q^{38} +(2.03099 + 5.38143i) q^{39} +(0.845530 - 2.75567i) q^{40} +(4.53928 - 7.86226i) q^{41} +(-2.44013 - 0.213872i) q^{42} +(-4.73102 + 2.73146i) q^{43} +(0.829976 - 0.663230i) q^{44} +(-0.977502 + 2.89685i) q^{45} +(11.5754 + 5.56737i) q^{46} +(-4.54937 - 7.87973i) q^{47} +(-6.42069 - 2.60283i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(4.62727 - 3.15818i) q^{50} +(2.11270 + 1.73065i) q^{51} +(6.18504 + 2.42038i) q^{52} -1.22534i q^{53} +(6.73102 + 2.94845i) q^{54} -0.541359 q^{55} +(-2.07052 + 1.92690i) q^{56} +(-7.32817 + 8.94589i) q^{57} +(0.849161 + 1.24417i) q^{58} +(-0.630723 - 0.364148i) q^{59} +(1.72793 + 3.07851i) q^{60} +(5.94302 - 3.43120i) q^{61} +(0.748871 + 0.360181i) q^{62} +(2.25194 - 1.98212i) q^{63} +(-7.19740 + 3.49248i) q^{64} +(-1.69217 - 2.93092i) q^{65} +(-0.113611 + 1.29622i) q^{66} +(-12.3090 - 7.10662i) q^{67} +(3.11786 - 0.473101i) q^{68} +(-14.7182 + 5.55473i) q^{69} +(1.43715 - 0.108416i) q^{70} +5.22734 q^{71} +(7.73376 - 3.49127i) q^{72} -8.49965 q^{73} +(-15.0707 + 1.13690i) q^{74} +(-1.11156 + 6.77074i) q^{75} +(2.00327 + 13.2021i) q^{76} +(0.460041 + 0.265605i) q^{77} +(-7.37287 + 3.43661i) q^{78} +(5.26132 + 9.11287i) q^{79} +(3.97602 + 0.899215i) q^{80} +(-8.30239 + 3.47423i) q^{81} +(11.5703 + 5.56491i) q^{82} +(-3.39540 + 1.96033i) q^{83} +(0.0420159 - 3.46385i) q^{84} +(-1.39162 - 0.803452i) q^{85} +(-4.35522 - 6.38114i) q^{86} +(-1.82050 - 0.298873i) q^{87} +(1.02359 + 1.09988i) q^{88} -8.88356 q^{89} +(-4.18914 - 1.07031i) q^{90} +3.32088i q^{91} +(-6.61971 + 16.9160i) q^{92} +(-0.952190 + 0.359363i) q^{93} +(10.6281 - 7.25382i) q^{94} +(3.40209 - 5.89259i) q^{95} +(2.98748 - 9.33140i) q^{96} +(8.24618 + 14.2828i) q^{97} +(-1.27447 - 0.612973i) q^{98} +(-1.05292 - 1.19625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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