LMFDB - Embedded newform 670.2.k.c.531.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(81,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("670.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.k (of order $11$, degree $10$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			531.3
Character	$\chi$	$=$	670.531
Dual form			670.2.k.c.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.00970382 - 0.0212484i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0224131 - 0.00658109i) q^{6} +(-1.24834 + 1.44066i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.96422 - 2.26684i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.00970382 - 0.0212484i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0224131 - 0.00658109i) q^{6} +(-1.24834 + 1.44066i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.96422 - 2.26684i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-1.37329 + 0.403234i) q^{11} +(-0.0196511 + 0.0126290i) q^{12} +(5.04255 - 3.24065i) q^{13} +(0.271289 + 1.88686i) q^{14} +(0.0152971 + 0.0176538i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(1.09518 - 7.61716i) q^{17} +(-0.426867 - 2.96892i) q^{18} +(-3.26325 - 3.76599i) q^{19} +(0.415415 + 0.909632i) q^{20} +(0.0427253 + 0.0125453i) q^{21} +(-0.594570 + 1.30193i) q^{22} +(0.220543 + 0.482923i) q^{23} +(-0.00332438 + 0.0231216i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.853048 - 5.93308i) q^{26} +(-0.134467 - 0.0394829i) q^{27} +(1.60365 + 1.03060i) q^{28} +6.38650 q^{29} +0.0233593 q^{30} +(-4.33410 - 2.78535i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(0.0218943 + 0.0252673i) q^{33} +(-5.03948 - 5.81586i) q^{34} +(0.791889 - 1.73400i) q^{35} +(-2.52330 - 1.62163i) q^{36} -7.80267 q^{37} -4.98312 q^{38} +(-0.117791 - 0.0756994i) q^{39} +(0.959493 + 0.281733i) q^{40} +(0.924878 - 6.43267i) q^{41} +(0.0374602 - 0.0240742i) q^{42} +(-0.398910 + 2.77448i) q^{43} +(0.594570 + 1.30193i) q^{44} +(-1.24602 + 2.72840i) q^{45} +(0.509394 + 0.149572i) q^{46} +(4.37818 + 9.58687i) q^{47} +(0.0152971 + 0.0176538i) q^{48} +(0.479056 + 3.33191i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-0.172480 + 0.0506447i) q^{51} +(-3.92529 - 4.53003i) q^{52} +(1.42090 + 9.88259i) q^{53} +(-0.117896 + 0.0757672i) q^{54} +(1.20406 - 0.773801i) q^{55} +(1.82904 - 0.537056i) q^{56} +(-0.0483554 + 0.105883i) q^{57} +(4.18227 - 4.82659i) q^{58} +(5.08648 + 3.26888i) q^{59} +(0.0152971 - 0.0176538i) q^{60} +(2.57240 + 0.755324i) q^{61} +(-4.94326 + 1.45147i) q^{62} +(0.813720 + 5.65954i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-3.92529 + 4.53003i) q^{65} +0.0334335 q^{66} +(5.57911 - 5.98945i) q^{67} -7.69549 q^{68} +(0.00812122 - 0.00937239i) q^{69} +(-0.791889 - 1.73400i) q^{70} +(-2.27105 - 15.7955i) q^{71} +(-2.87796 + 0.845044i) q^{72} +(2.78050 + 0.816428i) q^{73} +(-5.10966 + 5.89687i) q^{74} +(-0.0196511 - 0.0126290i) q^{75} +(-3.26325 + 3.76599i) q^{76} +(1.13341 - 2.48181i) q^{77} +(-0.134346 + 0.0394476i) q^{78} +(-12.7910 + 8.22027i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-1.28013 - 8.90353i) q^{81} +(-4.25582 - 4.91148i) q^{82} +(12.9384 - 3.79907i) q^{83} +(0.00633714 - 0.0440758i) q^{84} +(1.09518 + 7.61716i) q^{85} +(1.83558 + 2.11838i) q^{86} +(-0.0619734 - 0.135703i) q^{87} +(1.37329 + 0.403234i) q^{88} +(-2.97108 + 6.50577i) q^{89} +(1.24602 + 2.72840i) q^{90} +(-1.62613 + 11.3100i) q^{91} +(0.446621 - 0.287026i) q^{92} +(-0.0171270 + 0.119121i) q^{93} +(10.1124 + 2.96926i) q^{94} +(4.19207 + 2.69408i) q^{95} +0.0233593 q^{96} -0.256826 q^{97} +(2.83180 + 1.81989i) q^{98} +(-1.78338 + 3.90507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

Coefficient data

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

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

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

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	−0.00970382	−	0.0212484i	−0.00560250	−	0.0122678i	0.906810	−	0.421539i	$-0.138510\pi$
$3$	−0.00970382	−	0.0212484i	−0.00560250	−	0.0122678i	−0.912413	+	0.409272i	$0.865783\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.0224131	−	0.00658109i	−0.00915012	−	0.00268672i
$7$	−1.24834	+	1.44066i	−0.471826	+	0.544517i	−0.940919	−	0.338632i	$-0.890036\pi$
$7$	−1.24834	+	1.44066i	−0.471826	+	0.544517i	0.469092	+	0.883149i	$0.344581\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	1.96422	−	2.26684i	0.654742	−	0.755612i
$10$	−0.415415	+	0.909632i	−0.131366	+	0.287651i
$11$	−1.37329	+	0.403234i	−0.414063	+	0.121580i	−0.482127	−	0.876101i	$-0.660136\pi$
$11$	−1.37329	+	0.403234i	−0.414063	+	0.121580i	0.0680647	+	0.997681i	$0.478318\pi$
$12$	−0.0196511	+	0.0126290i	−0.00567279	+	0.00364568i
$13$	5.04255	−	3.24065i	1.39855	−	0.898794i	0.398718	−	0.917074i	$-0.369455\pi$
$13$	5.04255	−	3.24065i	1.39855	−	0.898794i	0.999833	+	0.0182793i	$0.00581882\pi$
$14$	0.271289	+	1.88686i	0.0725051	+	0.504284i
$15$	0.0152971	+	0.0176538i	0.00394970	+	0.00455820i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	1.09518	−	7.61716i	0.265621	−	1.84743i	−0.222849	−	0.974853i	$-0.571536\pi$
$17$	1.09518	−	7.61716i	0.265621	−	1.84743i	0.488470	−	0.872581i	$-0.337555\pi$
$18$	−0.426867	−	2.96892i	−0.100613	−	0.699782i
$19$	−3.26325	−	3.76599i	−0.748641	−	0.863978i	0.245794	−	0.969322i	$-0.420951\pi$
$19$	−3.26325	−	3.76599i	−0.748641	−	0.863978i	−0.994436	+	0.105344i	$0.966406\pi$
$20$	0.415415	+	0.909632i	0.0928896	+	0.203400i
$21$	0.0427253	+	0.0125453i	0.00932342	+	0.00273760i
$22$	−0.594570	+	1.30193i	−0.126763	+	0.277572i
$23$	0.220543	+	0.482923i	0.0459865	+	0.100696i	0.931231	−	0.364430i	$-0.118736\pi$
$23$	0.220543	+	0.482923i	0.0459865	+	0.100696i	−0.885244	+	0.465126i	$0.846009\pi$
$24$	−0.00332438	+	0.0231216i	−0.000678586	+	0.00471967i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	0.853048	−	5.93308i	0.167296	−	1.16357i
$27$	−0.134467	−	0.0394829i	−0.0258781	−	0.00759849i
$28$	1.60365	+	1.03060i	0.303061	+	0.194766i
$29$	6.38650			1.18594			0.592971	−	0.805224i	$-0.297955\pi$
$29$	6.38650			1.18594			0.592971	+	0.805224i	$0.297955\pi$
$30$	0.0233593			0.00426481
$31$	−4.33410	−	2.78535i	−0.778427	−	0.500264i	0.0900846	−	0.995934i	$-0.471286\pi$
$31$	−4.33410	−	2.78535i	−0.778427	−	0.500264i	−0.868511	+	0.495670i	$0.834923\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	0.0218943	+	0.0252673i	0.00381130	+	0.00439848i
$34$	−5.03948	−	5.81586i	−0.864263	−	0.997413i
$35$	0.791889	−	1.73400i	0.133854	−	0.293099i
$36$	−2.52330	−	1.62163i	−0.420550	−	0.270271i
$37$	−7.80267			−1.28275			−0.641376	−	0.767227i	$-0.721636\pi$
$37$	−7.80267			−1.28275			−0.641376	+	0.767227i	$0.721636\pi$
$38$	−4.98312			−0.808370
$39$	−0.117791	−	0.0756994i	−0.0188616	−	0.0121216i
$40$	0.959493	+	0.281733i	0.151709	+	0.0445458i
$41$	0.924878	−	6.43267i	0.144442	−	1.00461i	−0.780677	−	0.624935i	$-0.785125\pi$
$41$	0.924878	−	6.43267i	0.144442	−	1.00461i	0.925118	−	0.379679i	$-0.123965\pi$
$42$	0.0374602	−	0.0240742i	0.00578023	−	0.00371473i
$43$	−0.398910	+	2.77448i	−0.0608332	+	0.423104i	0.936533	+	0.350579i	$0.114015\pi$
$43$	−0.398910	+	2.77448i	−0.0608332	+	0.423104i	−0.997367	+	0.0725258i	$0.976894\pi$
$44$	0.594570	+	1.30193i	0.0896348	+	0.196273i
$45$	−1.24602	+	2.72840i	−0.185745	+	0.406726i
$46$	0.509394	+	0.149572i	0.0751060	+	0.0220531i
$47$	4.37818	+	9.58687i	0.638623	+	1.39839i	0.901168	+	0.433469i	$0.142711\pi$
$47$	4.37818	+	9.58687i	0.638623	+	1.39839i	−0.262546	+	0.964920i	$0.584562\pi$
$48$	0.0152971	+	0.0176538i	0.00220795	+	0.00254811i
$49$	0.479056	+	3.33191i	0.0684366	+	0.475987i
$50$	0.142315	−	0.989821i	0.0201264	−	0.139982i
$51$	−0.172480	+	0.0506447i	−0.0241520	+	0.00709168i
$52$	−3.92529	−	4.53003i	−0.544340	−	0.628202i
$53$	1.42090	+	9.88259i	0.195176	+	1.35748i	0.818046	+	0.575153i	$0.195058\pi$
$53$	1.42090	+	9.88259i	0.195176	+	1.35748i	−0.622870	+	0.782326i	$0.714033\pi$
$54$	−0.117896	+	0.0757672i	−0.0160436	+	0.0103106i
$55$	1.20406	−	0.773801i	0.162355	−	0.104339i
$56$	1.82904	−	0.537056i	0.244416	−	0.0717671i
$57$	−0.0483554	+	0.105883i	−0.00640482	+	0.0140246i
$58$	4.18227	−	4.82659i	0.549158	−	0.633763i
$59$	5.08648	+	3.26888i	0.662204	+	0.425573i	0.828107	−	0.560569i	$-0.189418\pi$
$59$	5.08648	+	3.26888i	0.662204	+	0.425573i	−0.165904	+	0.986142i	$0.553054\pi$
$60$	0.0152971	−	0.0176538i	0.00197485	−	0.00227910i
$61$	2.57240	+	0.755324i	0.329362	+	0.0967094i	0.442233	−	0.896900i	$-0.354186\pi$
$61$	2.57240	+	0.755324i	0.329362	+	0.0967094i	−0.112871	+	0.993610i	$0.536005\pi$
$62$	−4.94326	+	1.45147i	−0.627795	+	0.184337i
$63$	0.813720	+	5.65954i	0.102519	+	0.713036i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−3.92529	+	4.53003i	−0.486873	+	0.561881i
$66$	0.0334335			0.00411537
$67$	5.57911	−	5.98945i	0.681596	−	0.731728i
$67$	5.57911	−	5.98945i	0.681596	−	0.731728i
$68$	−7.69549			−0.933215
$69$	0.00812122	−	0.00937239i	0.000977680	−	0.00112830i
$70$	−0.791889	−	1.73400i	−0.0946489	−	0.207252i
$71$	−2.27105	−	15.7955i	−0.269524	−	1.87458i	−0.452936	−	0.891543i	$-0.649623\pi$
$71$	−2.27105	−	15.7955i	−0.269524	−	1.87458i	0.183412	−	0.983036i	$-0.441286\pi$
$72$	−2.87796	+	0.845044i	−0.339170	+	0.0995894i
$73$	2.78050	+	0.816428i	0.325433	+	0.0955557i	0.440368	−	0.897817i	$-0.354848\pi$
$73$	2.78050	+	0.816428i	0.325433	+	0.0955557i	−0.114935	+	0.993373i	$0.536666\pi$
$74$	−5.10966	+	5.89687i	−0.593986	+	0.685497i
$75$	−0.0196511	−	0.0126290i	−0.00226912	−	0.00145827i
$76$	−3.26325	+	3.76599i	−0.374321	+	0.431989i
$77$	1.13341	−	2.48181i	0.129163	−	0.282829i
$78$	−0.134346	+	0.0394476i	−0.0152117	+	0.00446656i
$79$	−12.7910	+	8.22027i	−1.43910	+	0.924852i	−0.439452	+	0.898266i	$0.644827\pi$
$79$	−12.7910	+	8.22027i	−1.43910	+	0.924852i	−0.999647	+	0.0265859i	$0.991536\pi$
$80$	0.841254	−	0.540641i	0.0940550	−	0.0604455i
$81$	−1.28013	−	8.90353i	−0.142237	−	0.989281i
$82$	−4.25582	−	4.91148i	−0.469977	−	0.542382i
$83$	12.9384	−	3.79907i	1.42018	−	0.417002i	0.520615	−	0.853791i	$-0.325703\pi$
$83$	12.9384	−	3.79907i	1.42018	−	0.417002i	0.899564	+	0.436789i	$0.143884\pi$
$84$	0.00633714	−	0.0440758i	0.000691438	−	0.00480906i
$85$	1.09518	+	7.61716i	0.118789	+	0.826197i
$86$	1.83558	+	2.11838i	0.197936	+	0.228430i
$87$	−0.0619734	−	0.135703i	−0.00664425	−	0.0145489i
$88$	1.37329	+	0.403234i	0.146393	+	0.0429849i
$89$	−2.97108	+	6.50577i	−0.314934	+	0.689610i	−0.999215	−	0.0396085i	$-0.987389\pi$
$89$	−2.97108	+	6.50577i	−0.314934	+	0.689610i	0.684281	+	0.729218i	$0.260116\pi$
$90$	1.24602	+	2.72840i	0.131342	+	0.287599i
$91$	−1.62613	+	11.3100i	−0.170465	+	1.18561i
$92$	0.446621	−	0.287026i	0.0465634	−	0.0299245i
$93$	−0.0171270	+	0.119121i	−0.00177599	+	0.0123523i
$94$	10.1124	+	2.96926i	1.04301	+	0.306256i
$95$	4.19207	+	2.69408i	0.430097	+	0.276407i
$96$	0.0233593			0.00238410
$97$	−0.256826			−0.0260767			−0.0130383	−	0.999915i	$-0.504150\pi$
$97$	−0.256826			−0.0260767			−0.0130383	+	0.999915i	$0.504150\pi$
$98$	2.83180	+	1.81989i	0.286055	+	0.183837i
$99$	−1.78338	+	3.90507i	−0.179237	+	0.392474i
$100$	−0.654861	−	0.755750i	−0.0654861	−	0.0755750i
$101$	−7.06864	−	8.15765i	−0.703356	−	0.811716i	0.285846	−	0.958276i	$-0.407725\pi$
$101$	−7.06864	−	8.15765i	−0.703356	−	0.811716i	−0.989202	+	0.146560i	$0.953180\pi$
$102$	−0.0746757	+	0.163517i	−0.00739399	+	0.0161906i
$103$	11.0971	+	7.13168i	1.09343	+	0.702705i	0.957621	−	0.288030i	$-0.0930002\pi$
$103$	11.0971	+	7.13168i	1.09343	+	0.702705i	0.135809	+	0.990735i	$0.456637\pi$
$104$	−5.99409			−0.587769
$105$	−0.0445290			−0.00434559
$106$	8.39926	+	5.39788i	0.815808	+	0.524288i
$107$	2.22301	+	0.652735i	0.214906	+	0.0631022i	0.387414	−	0.921906i	$-0.373369\pi$
$107$	2.22301	+	0.652735i	0.214906	+	0.0631022i	−0.172507	+	0.985008i	$0.555187\pi$
$108$	−0.0199445	+	0.138717i	−0.00191916	+	0.0133480i
$109$	−2.18808	+	1.40619i	−0.209580	+	0.134689i	−0.641220	−	0.767357i	$-0.721571\pi$
$109$	−2.18808	+	1.40619i	−0.209580	+	0.134689i	0.431640	+	0.902046i	$0.357935\pi$
$110$	0.203691	−	1.41670i	0.0194211	−	0.135077i
$111$	0.0757157	+	0.165794i	0.00718662	+	0.0157365i
$112$	0.791889	−	1.73400i	0.0748265	−	0.163847i
$113$	−0.649424	−	0.190688i	−0.0610927	−	0.0179384i	0.251043	−	0.967976i	$-0.419226\pi$
$113$	−0.649424	−	0.190688i	−0.0610927	−	0.0179384i	−0.312136	+	0.950037i	$0.601044\pi$
$114$	0.0483554	+	0.105883i	0.00452889	+	0.00991689i
$115$	−0.347665	−	0.401227i	−0.0324199	−	0.0374146i
$116$	−0.908893	−	6.32149i	−0.0843886	−	0.586936i
$117$	2.55868	−	17.7960i	0.236550	−	1.64524i
$118$	5.80140	−	1.70344i	0.534062	−	0.156815i
$119$	9.60655	+	11.0866i	0.880631	+	1.01630i
$120$	−0.00332438	−	0.0231216i	−0.000303473	−	0.00211070i
$121$	−7.53046	+	4.83953i	−0.684587	+	0.439958i
$122$	2.25540	−	1.44946i	0.204194	−	0.131228i
$123$	−0.145659	+	0.0427693i	−0.0131336	+	0.00385637i
$124$	−2.14020	+	4.68638i	−0.192195	+	0.420849i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	4.81007	+	3.09124i	0.428515	+	0.275390i
$127$	5.86705	−	6.77093i	0.520616	−	0.600823i	−0.433169	−	0.901313i	$-0.642605\pi$
$127$	5.86705	−	6.77093i	0.520616	−	0.600823i	0.953785	+	0.300490i	$0.0971501\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	0.0628243	−	0.0184469i	0.00553137	−	0.00162416i
$130$	0.853048	+	5.93308i	0.0748172	+	0.520365i
$131$	0.469108	+	1.02720i	0.0409861	+	0.0897471i	0.929018	−	0.370036i	$-0.120655\pi$
$131$	0.469108	+	1.02720i	0.0409861	+	0.0897471i	−0.888031	+	0.459783i	$0.847927\pi$
$132$	0.0218943	−	0.0252673i	0.00190565	−	0.00219924i
$133$	9.49914			0.823679
$134$	−0.872990	−	8.13867i	−0.0754149	−	0.703074i
$135$	0.140143			0.0120616
$136$	−5.03948	+	5.81586i	−0.432131	+	0.498706i
$137$	7.11730	+	15.5847i	0.608072	+	1.33149i	0.923885	+	0.382671i	$0.124996\pi$
$137$	7.11730	+	15.5847i	0.608072	+	1.33149i	−0.315812	+	0.948822i	$0.602277\pi$
$138$	−0.00176491	−	0.0122752i	−0.000150239	−	0.00104494i
$139$	−10.5847	+	3.10796i	−0.897786	+	0.263614i	−0.697891	−	0.716204i	$-0.745878\pi$
$139$	−10.5847	+	3.10796i	−0.897786	+	0.263614i	−0.199895	+	0.979817i	$0.564060\pi$
$140$	−1.82904	−	0.537056i	−0.154582	−	0.0453895i
$141$	0.161221	−	0.186059i	0.0135772	−	0.0156690i
$142$	−13.4247	−	8.62750i	−1.12657	−	0.724004i
$143$	−5.61814	+	6.48368i	−0.469813	+	0.542193i
$144$	−1.24602	+	2.72840i	−0.103835	+	0.227367i
$145$	−6.12780	+	1.79928i	−0.508886	+	0.149422i
$146$	2.43786	−	1.56671i	0.201758	−	0.129662i
$147$	0.0661490	−	0.0425114i	0.00545588	−	0.00350628i
$148$	1.11044	+	7.72325i	0.0912773	+	0.634847i
$149$	−1.36211	−	1.57196i	−0.111588	−	0.128780i	0.697207	−	0.716869i	$-0.254426\pi$
$149$	−1.36211	−	1.57196i	−0.111588	−	0.128780i	−0.808796	+	0.588090i	$0.799880\pi$
$150$	−0.0224131	+	0.00658109i	−0.00183002	+	0.000537344i
$151$	0.214538	−	1.49214i	0.0174588	−	0.121429i	−0.979228	−	0.202761i	$-0.935008\pi$
$151$	0.214538	−	1.49214i	0.0174588	−	0.121429i	0.996687	+	0.0813325i	$0.0259176\pi$
$152$	0.709173	+	4.93240i	0.0575215	+	0.400071i
$153$	−15.1157	−	17.4444i	−1.22203	−	1.41030i
$154$	−1.13341	−	2.48181i	−0.0913324	−	0.199990i
$155$	4.94326	+	1.45147i	0.397052	+	0.116585i
$156$	−0.0581656	+	0.127365i	−0.00465697	+	0.0101973i
$157$	6.98641	+	15.2981i	0.557576	+	1.22092i	0.953153	+	0.302488i	$0.0978173\pi$
$157$	6.98641	+	15.2981i	0.557576	+	1.22092i	−0.395577	+	0.918433i	$0.629455\pi$
$158$	−2.16385	+	15.0499i	−0.172147	+	1.19731i
$159$	0.196201	−	0.126091i	0.0155598	−	0.00999966i
$160$	0.142315	−	0.989821i	0.0112510	−	0.0782523i
$161$	−0.971038	−	0.285122i	−0.0765285	−	0.0224708i
$162$	−7.56715	−	4.86311i	−0.594532	−	0.382082i
$163$	−9.80318			−0.767844			−0.383922	−	0.923365i	$-0.625427\pi$
$163$	−9.80318			−0.767844			−0.383922	+	0.923365i	$0.625427\pi$
$164$	−6.49881			−0.507472
$165$	−0.0281260	−	0.0180755i	−0.00218961	−	0.00140718i
$166$	5.60174	−	12.2661i	0.434779	−	0.952033i
$167$	0.395506	+	0.456438i	0.0306052	+	0.0353202i	0.770846	−	0.637022i	$-0.219834\pi$
$167$	0.395506	+	0.456438i	0.0306052	+	0.0353202i	−0.740241	+	0.672342i	$0.765288\pi$
$168$	−0.0291603	−	0.0336528i	−0.00224977	−	0.00259637i
$169$	9.52509	−	20.8570i	0.732699	−	1.60439i
$170$	6.47386	+	4.16050i	0.496522	+	0.319096i
$171$	−14.9467			−1.14300
$172$	2.80301			0.213728
$173$	19.6361	+	12.6194i	1.49291	+	0.959433i	0.995782	+	0.0917543i	$0.0292474\pi$
$173$	19.6361	+	12.6194i	1.49291	+	0.959433i	0.497125	+	0.867679i	$0.334389\pi$
$174$	−0.143141	−	0.0420301i	−0.0108515	−	0.00318629i
$175$	−0.271289	+	1.88686i	−0.0205075	+	0.142633i
$176$	1.20406	−	0.773801i	0.0907593	−	0.0583275i
$177$	0.0201003	−	0.139800i	0.00151083	−	0.0105080i
$178$	2.97108	+	6.50577i	0.222692	+	0.487628i
$179$	3.36960	−	7.37839i	0.251856	−	0.551487i	−0.740903	−	0.671612i	$-0.765602\pi$
$179$	3.36960	−	7.37839i	0.251856	−	0.551487i	0.992759	+	0.120125i	$0.0383296\pi$
$180$	2.87796	+	0.845044i	0.214510	+	0.0629859i
$181$	4.75940	+	10.4216i	0.353763	+	0.774634i	0.999935	+	0.0114413i	$0.00364194\pi$
$181$	4.75940	+	10.4216i	0.353763	+	0.774634i	−0.646171	+	0.763193i	$0.723631\pi$
$182$	7.48263	+	8.63542i	0.554650	+	0.640100i
$183$	−0.00891266	−	0.0619889i	−0.000658843	−	0.00458235i
$184$	0.0755548	−	0.525495i	0.00556997	−	0.0387400i
$185$	7.48661	−	2.19827i	0.550426	−	0.161620i
$186$	0.0788100	+	0.0909516i	0.00577863	+	0.00666889i
$187$	1.56750	+	10.9022i	0.114627	+	0.797247i
$188$	8.86621	−	5.69797i	0.646635	−	0.415567i
$189$	0.224741	−	0.144432i	0.0163475	−	0.0105059i
$190$	4.78127	−	1.40391i	0.346870	−	0.101850i
$191$	−6.27179	+	13.7333i	−0.453811	+	0.993707i	0.535044	+	0.844824i	$0.320295\pi$
$191$	−6.27179	+	13.7333i	−0.453811	+	0.993707i	−0.988855	+	0.148883i	$0.952432\pi$
$192$	0.0152971	−	0.0176538i	0.00110397	−	0.00127405i
$193$	−8.51583	−	5.47279i	−0.612983	−	0.393940i	0.196992	−	0.980405i	$-0.436883\pi$
$193$	−8.51583	−	5.47279i	−0.612983	−	0.393940i	−0.809974	+	0.586465i	$0.800519\pi$
$194$	−0.168185	+	0.194096i	−0.0120750	+	0.0139353i
$195$	0.134346	+	0.0394476i	0.00962073	+	0.00282490i
$196$	3.22982	−	0.948360i	0.230701	−	0.0677400i
$197$	−1.69958	−	11.8208i	−0.121090	−	0.842198i	−0.956325	−	0.292305i	$-0.905578\pi$
$197$	−1.69958	−	11.8208i	−0.121090	−	0.842198i	0.835235	−	0.549893i	$-0.185331\pi$
$198$	1.78338	+	3.90507i	0.126740	+	0.277521i
$199$	4.73283	−	5.46197i	0.335501	−	0.387189i	−0.562783	−	0.826605i	$-0.690269\pi$
$199$	4.73283	−	5.46197i	0.335501	−	0.387189i	0.898284	+	0.439416i	$0.144815\pi$
$200$	−1.00000			−0.0707107
$201$	−0.181405	−	0.0604265i	−0.0127953	−	0.00426216i
$202$	−10.7941			−0.759471
$203$	−7.97249	+	9.20074i	−0.559559	+	0.645766i
$204$	0.0746757	+	0.163517i	0.00522834	+	0.0114485i
$205$	0.924878	+	6.43267i	0.0645963	+	0.449277i
$206$	12.6568	−	3.71638i	0.881843	−	0.258932i
$207$	1.52790	+	0.448633i	0.106197	+	0.0311821i
$208$	−3.92529	+	4.53003i	−0.272170	+	0.314101i
$209$	5.99997	+	3.85595i	0.415027	+	0.266722i
$210$	−0.0291603	+	0.0336528i	−0.00201225	+	0.00232226i
$211$	4.83259	−	10.5819i	0.332689	−	0.728488i	−0.667176	−	0.744900i	$-0.732497\pi$
$211$	4.83259	−	10.5819i	0.332689	−	0.728488i	0.999865	+	0.0164123i	$0.00522442\pi$
$212$	9.57979	−	2.81288i	0.657943	−	0.193189i
$213$	−0.313591	+	0.201533i	−0.0214869	+	0.0138088i
$214$	1.94907	−	1.25259i	0.133235	−	0.0856252i
$215$	−0.398910	−	2.77448i	−0.0272055	−	0.189218i
$216$	0.0917744	+	0.105913i	0.00624445	+	0.00720648i
$217$	9.42314	−	2.76688i	0.639684	−	0.187828i
$218$	−0.370157	+	2.57450i	−0.0250702	+	0.174367i
$219$	−0.00963367	−	0.0670037i	−0.000650983	−	0.00452769i
$220$	−0.937280	−	1.08168i	−0.0631914	−	0.0729268i
$221$	−19.1620	−	41.9590i	−1.28898	−	2.82247i
$222$	0.174882	+	0.0513501i	0.0117373	+	0.00344639i
$223$	−10.5489	+	23.0990i	−0.706410	+	1.54682i	0.125612	+	0.992079i	$0.459911\pi$
$223$	−10.5489	+	23.0990i	−0.706410	+	1.54682i	−0.832022	+	0.554743i	$0.812817\pi$
$224$	−0.791889	−	1.73400i	−0.0529103	−	0.115857i
$225$	0.426867	−	2.96892i	0.0284578	−	0.197928i
$226$	−0.569395	+	0.365928i	−0.0378756	+	0.0243412i
$227$	−1.65264	+	11.4944i	−0.109689	+	0.762907i	0.858523	+	0.512776i	$0.171383\pi$
$227$	−1.65264	+	11.4944i	−0.109689	+	0.762907i	−0.968212	+	0.250131i	$0.919526\pi$
$228$	0.111687	+	0.0327944i	0.00739668	+	0.00217186i
$229$	20.1432	+	12.9452i	1.33110	+	0.855445i	0.996224	−	0.0868180i	$-0.0276699\pi$
$229$	20.1432	+	12.9452i	1.33110	+	0.855445i	0.334874	+	0.942263i	$0.391306\pi$
$230$	−0.530899			−0.0350064
$231$	−0.0637329			−0.00419332
$232$	−5.37266	−	3.45280i	−0.352733	−	0.226687i
$233$	−2.22456	+	4.87110i	−0.145736	+	0.319116i	−0.968396	−	0.249416i	$-0.919761\pi$
$233$	−2.22456	+	4.87110i	−0.145736	+	0.319116i	0.822661	+	0.568532i	$0.192489\pi$
$234$	−11.7737	−	13.5876i	−0.769673	−	0.888250i
$235$	−6.90176	−	7.96506i	−0.450221	−	0.519583i
$236$	2.51173	−	5.49992i	0.163500	−	0.358014i
$237$	0.298789	+	0.192020i	0.0194084	+	0.0124730i
$238$	14.6696			0.950890
$239$	−0.440210			−0.0284748			−0.0142374	−	0.999899i	$-0.504532\pi$
$239$	−0.440210			−0.0284748			−0.0142374	+	0.999899i	$0.504532\pi$
$240$	−0.0196511	−	0.0126290i	−0.00126848	−	0.000815199i
$241$	−23.3227	−	6.84816i	−1.50235	−	0.441128i	−0.575888	−	0.817528i	$-0.695344\pi$
$241$	−23.3227	−	6.84816i	−1.50235	−	0.441128i	−0.926457	+	0.376400i	$0.877162\pi$
$242$	−1.27393	+	8.86036i	−0.0818912	+	0.569566i
$243$	−0.530452	+	0.340901i	−0.0340285	+	0.0218688i
$244$	0.381546	−	2.65371i	0.0244260	−	0.169886i
$245$	−1.39836	−	3.06198i	−0.0893378	−	0.195622i
$246$	−0.0630633	+	0.138089i	−0.00402077	+	0.00880426i
$247$	−28.6594	−	8.41515i	−1.82355	−	0.535443i
$248$	2.14020	+	4.68638i	0.135903	+	0.297585i
$249$	−0.206277	−	0.238056i	−0.0130723	−	0.0150862i
$250$	0.142315	+	0.989821i	0.00900078	+	0.0626018i
$251$	−3.11698	+	21.6790i	−0.196742	+	1.36837i	0.616918	+	0.787028i	$0.288381\pi$
$251$	−3.11698	+	21.6790i	−0.196742	+	1.36837i	−0.813660	+	0.581342i	$0.802528\pi$
$252$	5.48613	−	1.61087i	0.345594	−	0.101476i
$253$	−0.497601	−	0.574262i	−0.0312839	−	0.0361036i
$254$	−1.27503	−	8.86804i	−0.0800026	−	0.556430i
$255$	0.151225	−	0.0971865i	0.00947008	−	0.00608605i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	5.49958	−	1.61482i	0.343054	−	0.100730i	−0.105667	−	0.994402i	$-0.533698\pi$
$257$	5.49958	−	1.61482i	0.343054	−	0.100730i	0.448721	+	0.893672i	$0.351880\pi$
$258$	0.0271999	−	0.0595595i	0.00169339	−	0.00370802i
$259$	9.74035	−	11.2410i	0.605236	−	0.698480i
$260$	5.04255	+	3.24065i	0.312726	+	0.200976i
$261$	12.5445	−	14.4771i	0.776486	−	0.896113i
$262$	1.08351	+	0.318147i	0.0669394	+	0.0196552i
$263$	28.1883	−	8.27683i	1.73816	−	0.510371i	0.749694	−	0.661785i	$-0.230201\pi$
$263$	28.1883	−	8.27683i	1.73816	−	0.510371i	0.988470	+	0.151414i	$0.0483826\pi$
$264$	−0.00475808	−	0.0330932i	−0.000292839	−	0.00203674i
$265$	−4.14759	−	9.08197i	−0.254785	−	0.557901i
$266$	6.22061	−	7.17897i	0.381410	−	0.440171i
$267$	0.167068			0.0102244
$268$	−6.72248	−	4.66993i	−0.410641	−	0.285261i
$269$	22.0239			1.34282			0.671409	−	0.741087i	$-0.265689\pi$
$269$	22.0239			1.34282			0.671409	+	0.741087i	$0.265689\pi$
$270$	0.0917744	−	0.105913i	0.00558521	−	0.00644568i
$271$	−3.27673	−	7.17503i	−0.199047	−	0.435852i	0.783618	−	0.621243i	$-0.213372\pi$
$271$	−3.27673	−	7.17503i	−0.199047	−	0.435852i	−0.982665	+	0.185391i	$0.940645\pi$
$272$	1.09518	+	7.61716i	0.0664052	+	0.461858i
$273$	0.256099	−	0.0751974i	0.0154998	−	0.00455116i
$274$	16.4390	+	4.82692i	0.993116	+	0.291605i
$275$	−0.937280	+	1.08168i	−0.0565201	+	0.0652277i
$276$	−0.0104328	−	0.00670473i	−0.000627979	−	0.000403577i
$277$	0.565819	−	0.652990i	0.0339968	−	0.0392343i	−0.738497	−	0.674257i	$-0.764464\pi$
$277$	0.565819	−	0.652990i	0.0339968	−	0.0392343i	0.772493	+	0.635023i	$0.219009\pi$
$278$	−4.58269	+	10.0347i	−0.274852	+	0.601841i
$279$	−14.8271	+	4.35362i	−0.887674	+	0.260645i
$280$	−1.60365	+	1.03060i	−0.0958363	+	0.0615903i
$281$	−10.5791	+	6.79877i	−0.631095	+	0.405580i	−0.816715	−	0.577041i	$-0.804207\pi$
$281$	−10.5791	+	6.79877i	−0.631095	+	0.405580i	0.185620	+	0.982622i	$0.440571\pi$
$282$	−0.0350366	−	0.243685i	−0.00208640	−	0.0145112i
$283$	11.2958	+	13.0360i	0.671463	+	0.774910i	0.984605	−	0.174797i	$-0.0559268\pi$
$283$	11.2958	+	13.0360i	0.671463	+	0.774910i	−0.313141	+	0.949707i	$0.601381\pi$
$284$	−15.3115	+	4.49586i	−0.908571	+	0.266780i
$285$	0.0165658	−	0.115218i	0.000981274	−	0.00682491i
$286$	1.22094	+	8.49182i	0.0721956	+	0.502132i
$287$	8.11270	+	9.36255i	0.478878	+	0.552654i
$288$	1.24602	+	2.72840i	0.0734223	+	0.160772i
$289$	−40.5104	−	11.8949i	−2.38296	−	0.699701i
$290$	−2.65305	+	5.80936i	−0.155792	+	0.341137i
$291$	0.00249219	+	0.00545714i	0.000146095	+	0.000319903i
$292$	0.412412	−	2.86839i	0.0241346	−	0.167860i
$293$	27.2521	−	17.5139i	1.59209	−	1.02317i	0.621192	−	0.783658i	$-0.286649\pi$
$293$	27.2521	−	17.5139i	1.59209	−	1.02317i	0.970893	−	0.239513i	$-0.0769877\pi$
$294$	0.0111904	−	0.0778312i	0.000652639	−	0.00453921i
$295$	−5.80140	−	1.70344i	−0.337770	−	0.0991783i
$296$	6.56403	+	4.21844i	0.381526	+	0.245192i
$297$	0.200582			0.0116390
$298$	−2.08000			−0.120491
$299$	2.67708	+	1.72046i	0.154820	+	0.0994966i
$300$	−0.00970382	+	0.0212484i	−0.000560250	+	0.00122678i
$301$	−3.49910	−	4.03818i	−0.201685	−	0.232757i
$302$	−0.987193	−	1.13928i	−0.0568066	−	0.0655583i
$303$	−0.104744	+	0.229358i	−0.00601739	+	0.0131763i
$304$	4.19207	+	2.69408i	0.240432	+	0.154516i
$305$	−2.68100			−0.153513
$306$	−23.0823			−1.31953
$307$	−20.0055	−	12.8567i	−1.14177	−	0.733772i	−0.173788	−	0.984783i	$-0.555601\pi$
$307$	−20.0055	−	12.8567i	−1.14177	−	0.733772i	−0.967984	+	0.251011i	$0.919237\pi$
$308$	−2.61785	−	0.768670i	−0.149166	−	0.0437990i
$309$	0.0438524	−	0.305000i	0.00249468	−	0.0173509i
$310$	4.33410	−	2.78535i	0.246160	−	0.158197i
$311$	−3.42674	+	23.8335i	−0.194312	+	1.35147i	0.626119	+	0.779727i	$0.284642\pi$
$311$	−3.42674	+	23.8335i	−0.194312	+	1.35147i	−0.820432	+	0.571745i	$0.806267\pi$
$312$	0.0581656	+	0.127365i	0.00329298	+	0.00721061i
$313$	2.52327	−	5.52519i	0.142624	−	0.312302i	−0.824817	−	0.565399i	$-0.808722\pi$
$313$	2.52327	−	5.52519i	0.142624	−	0.312302i	0.967441	+	0.253097i	$0.0814493\pi$
$314$	16.1367	+	4.73815i	0.910644	+	0.267389i
$315$	−2.37524	−	5.20104i	−0.133829	−	0.293045i
$316$	9.95694	+	11.4909i	0.560122	+	0.646415i
$317$	−4.31391	−	30.0039i	−0.242293	−	1.68519i	−0.640553	−	0.767914i	$-0.721295\pi$
$317$	−4.31391	−	30.0039i	−0.242293	−	1.68519i	0.398259	−	0.917273i	$-0.369614\pi$
$318$	0.0331914	−	0.230851i	0.00186128	−	0.0129455i
$319$	−8.77051	+	2.57526i	−0.491055	+	0.144187i
$320$	−0.654861	−	0.755750i	−0.0366078	−	0.0422477i
$321$	−0.00770212	−	0.0535694i	−0.000429891	−	0.00298995i
$322$	−0.851375	+	0.547146i	−0.0474453	+	0.0304912i
$323$	−32.2601	+	20.7323i	−1.79500	+	1.15357i
$324$	−8.63073	+	2.53421i	−0.479485	+	0.140789i
$325$	2.49003	−	5.45241i	0.138122	−	0.302446i
$326$	−6.41972	+	7.40875i	−0.355555	+	0.410333i
$327$	0.0511120	+	0.0328477i	0.00282650	+	0.00181648i
$328$	−4.25582	+	4.91148i	−0.234988	+	0.271191i
$329$	−19.2768	−	5.66018i	−1.06277	−	0.312056i
$330$	−0.0320792	+	0.00941929i	−0.00176590	+	0.000518515i
$331$	−2.39234	−	16.6391i	−0.131495	−	0.914567i	−0.943607	−	0.331066i	$-0.892592\pi$
$331$	−2.39234	−	16.6391i	−0.131495	−	0.914567i	0.812113	−	0.583501i	$-0.198317\pi$
$332$	−5.60174	−	12.2661i	−0.307435	−	0.673189i
$333$	−15.3262	+	17.6874i	−0.839871	+	0.969262i
$334$	0.603954			0.0330469
$335$	−3.66569	+	7.31866i	−0.200278	+	0.399861i
$336$	−0.0445290			−0.00242926
$337$	−6.29528	+	7.26514i	−0.342926	+	0.395757i	−0.900847	−	0.434137i	$-0.857054\pi$
$337$	−6.29528	+	7.26514i	−0.342926	+	0.395757i	0.557922	+	0.829894i	$0.311599\pi$
$338$	−9.52509	−	20.8570i	−0.518096	−	1.13447i
$339$	0.00225008	+	0.0156496i	0.000122207	+	0.000849971i
$340$	7.38377	−	2.16807i	0.400441	−	0.117580i
$341$	7.07512	+	2.07744i	0.383139	+	0.112500i
$342$	−9.78798	+	11.2959i	−0.529273	+	0.610814i
$343$	−16.6237	−	10.6834i	−0.897595	−	0.576849i
$344$	1.83558	−	2.11838i	0.0989680	−	0.114215i
$345$	−0.00515175	+	0.0112808i	−0.000277361	+	0.000607336i
$346$	22.3960	−	6.57606i	1.20402	−	0.353531i
$347$	4.11100	−	2.64198i	0.220690	−	0.141829i	−0.425625	−	0.904900i	$-0.639946\pi$
$347$	4.11100	−	2.64198i	0.220690	−	0.141829i	0.646315	+	0.763071i	$0.276309\pi$
$348$	−0.125502	+	0.0806552i	−0.00672761	+	0.00432357i
$349$	2.01499	+	14.0146i	0.107860	+	0.750184i	0.969928	+	0.243391i	$0.0782599\pi$
$349$	2.01499	+	14.0146i	0.107860	+	0.750184i	−0.862068	+	0.506793i	$0.830831\pi$
$350$	1.24834	+	1.44066i	0.0667263	+	0.0770063i
$351$	−0.806004	+	0.236664i	−0.0430213	+	0.0126322i
$352$	0.203691	−	1.41670i	0.0108567	−	0.0755103i
$353$	−2.58748	−	17.9963i	−0.137718	−	0.957847i	−0.935103	−	0.354376i	$-0.884693\pi$
$353$	−2.58748	−	17.9963i	−0.137718	−	0.957847i	0.797385	−	0.603471i	$-0.206216\pi$
$354$	−0.0924912	−	0.106741i	−0.00491585	−	0.00567319i
$355$	6.62916	+	14.5158i	0.351839	+	0.770420i
$356$	6.86238	+	2.01498i	0.363705	+	0.106794i
$357$	0.142351	−	0.311706i	0.00753403	−	0.0164972i
$358$	−3.36960	−	7.37839i	−0.178089	−	0.389960i
$359$	4.61778	−	32.1173i	0.243717	−	1.69509i	−0.389430	−	0.921056i	$-0.627328\pi$
$359$	4.61778	−	32.1173i	0.243717	−	1.69509i	0.633146	−	0.774032i	$-0.281763\pi$
$360$	2.52330	−	1.62163i	0.132990	−	0.0854673i
$361$	−0.829913	+	5.77217i	−0.0436796	+	0.303799i
$362$	10.9929	+	3.22780i	0.577773	+	0.169650i
$363$	0.175907	+	0.113048i	0.00923270	+	0.00593350i
$364$	11.4263			0.598901
$365$	−2.89788			−0.151682
$366$	−0.0526846	−	0.0338584i	−0.00275387	−	0.00176980i
$367$	11.4294	−	25.0268i	0.596607	−	1.30639i	−0.334759	−	0.942304i	$-0.608655\pi$
$367$	11.4294	−	25.0268i	0.596607	−	1.30639i	0.931366	−	0.364084i	$-0.118618\pi$
$368$	−0.347665	−	0.401227i	−0.0181233	−	0.0209154i
$369$	−12.7651	−	14.7317i	−0.664526	−	0.766904i
$370$	3.24135	−	7.09756i	0.168510	−	0.368985i
$371$	−16.0112	−	10.2898i	−0.831259	−	0.534218i
$372$	0.120346			0.00623966
$373$	8.11941			0.420407			0.210204	−	0.977658i	$-0.432587\pi$
$373$	8.11941			0.420407			0.210204	+	0.977658i	$0.432587\pi$
$374$	9.26582	+	5.95478i	0.479124	+	0.307914i
$375$	0.0224131	+	0.00658109i	0.00115741	+	0.000339846i
$376$	1.49990	−	10.4320i	0.0773513	−	0.537990i
$377$	32.2042	−	20.6964i	1.65860	−	1.06592i
$378$	0.0380194	−	0.264431i	0.00195551	−	0.0136008i
$379$	−4.39315	−	9.61966i	−0.225661	−	0.494129i	0.762606	−	0.646863i	$-0.223919\pi$
$379$	−4.39315	−	9.61966i	−0.225661	−	0.494129i	−0.988267	+	0.152734i	$0.951192\pi$
$380$	2.07006	−	4.53281i	0.106192	−	0.232528i
$381$	−0.200804	−	0.0589615i	−0.0102875	−	0.00302069i
$382$	6.27179	+	13.7333i	0.320893	+	0.702657i
$383$	3.45702	+	3.98961i	0.176645	+	0.203860i	0.837167	−	0.546947i	$-0.184210\pi$
$383$	3.45702	+	3.98961i	0.176645	+	0.203860i	−0.660522	+	0.750807i	$0.729665\pi$
$384$	−0.00332438	−	0.0231216i	−0.000169647	−	0.00117992i
$385$	−0.388287	+	2.70060i	−0.0197890	+	0.137635i
$386$	−9.71274	+	2.85192i	−0.494365	+	0.145159i
$387$	5.50575	+	6.35397i	0.279873	+	0.322990i
$388$	0.0365501	+	0.254212i	0.00185555	+	0.0129056i
$389$	12.9450	−	8.31926i	0.656339	−	0.421803i	−0.169639	−	0.985506i	$-0.554260\pi$
$389$	12.9450	−	8.31926i	0.656339	−	0.421803i	0.825978	+	0.563703i	$0.190624\pi$
$390$	0.117791	−	0.0756994i	0.00596456	−	0.00383319i
$391$	3.92004	−	1.15103i	0.198245	−	0.0582099i
$392$	1.39836	−	3.06198i	0.0706277	−	0.154653i
$393$	0.0172743	−	0.0199356i	0.000871372	−	0.00100562i
$394$	−10.0466	−	6.45653i	−0.506138	−	0.325275i
$395$	9.95694	−	11.4909i	0.500988	−	0.578171i
$396$	4.11912	+	1.20948i	0.206994	+	0.0607788i
$397$	−26.4894	+	7.77800i	−1.32947	+	0.390367i	−0.867900	−	0.496739i	$-0.834531\pi$
$397$	−26.4894	+	7.77800i	−1.32947	+	0.390367i	−0.461567	+	0.887105i	$0.652713\pi$
$398$	−1.02854	−	7.15366i	−0.0515561	−	0.358581i
$399$	−0.0921779	−	0.201841i	−0.00461467	−	0.0101047i
$400$	−0.654861	+	0.755750i	−0.0327430	+	0.0377875i
$401$	0.147474			0.00736448			0.00368224	−	0.999993i	$-0.498828\pi$
$401$	0.147474			0.00736448			0.00368224	+	0.999993i	$0.498828\pi$
$402$	−0.164462	+	0.0975258i	−0.00820264	+	0.00486415i
$403$	−30.8812			−1.53830
$404$	−7.06864	+	8.15765i	−0.351678	+	0.405858i
$405$	3.73670	+	8.18222i	0.185678	+	0.406578i
$406$	1.73259	+	12.0504i	0.0859869	+	0.598052i
$407$	10.7153	−	3.14631i	0.531139	−	0.155957i
$408$	0.172480	+	0.0506447i	0.00853903	+	0.00250729i
$409$	−6.74828	+	7.78793i	−0.333681	+	0.385088i	−0.897651	−	0.440707i	$-0.854728\pi$
$409$	−6.74828	+	7.78793i	−0.333681	+	0.385088i	0.563970	+	0.825795i	$0.309273\pi$
$410$	5.46715	+	3.51352i	0.270003	+	0.173521i
$411$	0.262085	−	0.302463i	0.0129277	−	0.0149194i
$412$	5.47981	−	11.9991i	0.269971	−	0.591153i
$413$	−11.0590	+	3.24721i	−0.544177	+	0.159785i
$414$	1.33962	−	0.860920i	0.0658386	−	0.0423119i
$415$	−11.3440	+	7.29036i	−0.556856	+	0.357870i
$416$	0.853048	+	5.93308i	0.0418241	+	0.290893i
$417$	0.168752	+	0.194750i	0.00826381	+	0.00953694i
$418$	6.84328	−	2.00937i	0.334716	−	0.0982814i
$419$	3.94421	−	27.4326i	0.192687	−	1.34017i	−0.632171	−	0.774829i	$-0.717836\pi$
$419$	3.94421	−	27.4326i	0.192687	−	1.34017i	0.824858	−	0.565340i	$-0.191255\pi$
$420$	0.00633714	+	0.0440758i	0.000309221	+	0.00215068i
$421$	5.14397	+	5.93645i	0.250702	+	0.289325i	0.867126	−	0.498089i	$-0.165965\pi$
$421$	5.14397	+	5.93645i	0.250702	+	0.289325i	−0.616424	+	0.787414i	$0.711419\pi$
$422$	−4.83259	−	10.5819i	−0.235247	−	0.515119i
$423$	30.3316	+	8.90616i	1.47477	+	0.433032i
$424$	4.14759	−	9.08197i	0.201425	−	0.441059i
$425$	−3.19682	−	7.00007i	−0.155069	−	0.339553i
$426$	−0.0530502	+	0.368972i	−0.00257029	+	0.0178768i
$427$	−4.29938	+	2.76304i	−0.208061	+	0.133713i
$428$	0.329723	−	2.29328i	0.0159378	−	0.110850i
$429$	0.192285	+	0.0564601i	0.00928362	+	0.00272592i
$430$	−2.35804	−	1.51542i	−0.113715	−	0.0730802i
$431$	5.40578			0.260387			0.130194	−	0.991489i	$-0.458440\pi$
$431$	5.40578			0.260387			0.130194	+	0.991489i	$0.458440\pi$
$432$	0.140143			0.00674265
$433$	3.44930	+	2.21673i	0.165763	+	0.106529i	0.620892	−	0.783896i	$-0.286771\pi$
$433$	3.44930	+	2.21673i	0.165763	+	0.106529i	−0.455129	+	0.890425i	$0.650407\pi$
$434$	4.07977	−	8.93346i	0.195835	−	0.428820i
$435$	0.0976950	+	0.112746i	0.00468412	+	0.00540576i
$436$	1.70327	+	1.96568i	0.0815721	+	0.0941392i
$437$	1.09900	−	2.40646i	0.0525721	−	0.115117i
$438$	−0.0569467	−	0.0365974i	−0.00272102	−	0.00174869i
$439$	16.8876			0.806002			0.403001	−	0.915200i	$-0.367967\pi$
$439$	16.8876			0.806002			0.403001	+	0.915200i	$0.367967\pi$
$440$	−1.43127			−0.0682330
$441$	8.49386	+	5.45867i	0.404470	+	0.259937i
$442$	−44.2590	−	12.9956i	−2.10518	−	0.618138i
$443$	−4.69631	+	32.6635i	−0.223128	+	1.55189i	0.502972	+	0.864303i	$0.332240\pi$
$443$	−4.69631	+	32.6635i	−0.223128	+	1.55189i	−0.726100	+	0.687589i	$0.758669\pi$
$444$	0.153331	−	0.0985401i	0.00727678	−	0.00467650i
$445$	1.01785	−	7.07929i	0.0482506	−	0.335590i
$446$	10.5489	+	23.0990i	0.499507	+	1.09377i
$447$	−0.0201839	+	0.0441967i	−0.000954667	+	0.00209043i
$448$	−1.82904	−	0.537056i	−0.0864142	−	0.0253735i
$449$	6.03666	+	13.2184i	0.284888	+	0.623817i	0.996928	−	0.0783215i	$-0.0249561\pi$
$449$	6.03666	+	13.2184i	0.284888	+	0.623817i	−0.712041	+	0.702138i	$0.752229\pi$
$450$	−1.96422	−	2.26684i	−0.0925944	−	0.106860i
$451$	1.32375	+	9.20686i	0.0623328	+	0.433534i
$452$	−0.0963245	+	0.669952i	−0.00453072	+	0.0315119i
$453$	−0.0337875	+	0.00992090i	−0.00158747	+	0.000466124i
$454$	7.60460	+	8.77618i	0.356902	+	0.411887i
$455$	−1.62613	−	11.3100i	−0.0762342	−	0.530221i
$456$	0.0979240	−	0.0629320i	0.00458571	−	0.00294706i
$457$	−14.8698	+	9.55621i	−0.695578	+	0.447021i	−0.840065	−	0.542486i	$-0.817483\pi$
$457$	−14.8698	+	9.55621i	−0.695578	+	0.447021i	0.144487	+	0.989507i	$0.453847\pi$
$458$	22.9743	−	6.74587i	1.07352	−	0.315214i
$459$	−0.448013	+	0.981012i	−0.0209115	+	0.0457897i
$460$	−0.347665	+	0.401227i	−0.0162100	+	0.0187073i
$461$	−1.52962	−	0.983028i	−0.0712416	−	0.0457842i	0.504535	−	0.863391i	$-0.331664\pi$
$461$	−1.52962	−	0.983028i	−0.0712416	−	0.0457842i	−0.575777	+	0.817607i	$0.695300\pi$
$462$	−0.0417362	+	0.0481661i	−0.00194174	+	0.00224089i
$463$	−18.9287	−	5.55797i	−0.879692	−	0.258301i	−0.189460	−	0.981889i	$-0.560674\pi$
$463$	−18.9287	−	5.55797i	−0.879692	−	0.258301i	−0.690233	+	0.723588i	$0.742492\pi$
$464$	−6.12780	+	1.79928i	−0.284476	+	0.0835297i
$465$	−0.0171270	−	0.119121i	−0.000794248	−	0.00552411i
$466$	2.22456	+	4.87110i	0.103051	+	0.225649i
$467$	−16.2192	+	18.7179i	−0.750534	+	0.866162i	−0.994620	−	0.103591i	$-0.966967\pi$
$467$	−16.2192	+	18.7179i	−0.750534	+	0.866162i	0.244086	+	0.969754i	$0.421512\pi$
$468$	−17.9790			−0.831079
$469$	1.66415	+	15.5144i	0.0768432	+	0.716389i
$470$	−10.5393			−0.486141
$471$	0.257265	−	0.296900i	0.0118542	−	0.0136804i
$472$	−2.51173	−	5.49992i	−0.115612	−	0.253154i
$473$	−0.570947	−	3.97102i	−0.0262522	−	0.182588i
$474$	0.340784	−	0.100063i	0.0156527	−	0.00459606i
$475$	−4.78127	−	1.40391i	−0.219380	−	0.0644157i
$476$	9.60655	−	11.0866i	0.440316	−	0.508151i
$477$	25.1932	+	16.1907i	1.15352	+	0.741321i
$478$	−0.288276	+	0.332688i	−0.0131854	+	0.0152168i
$479$	6.80351	−	14.8976i	0.310860	−	0.680689i	−0.688132	−	0.725586i	$-0.741569\pi$
$479$	6.80351	−	14.8976i	0.310860	−	0.680689i	0.998992	+	0.0448973i	$0.0142961\pi$
$480$	−0.0224131	+	0.00658109i	−0.00102301	+	0.000300384i
$481$	−39.3453	+	25.2857i	−1.79399	+	1.15293i
$482$	−20.4486	+	13.1415i	−0.931408	+	0.598580i
$483$	0.00336438	+	0.0233998i	0.000153085	+	0.00106473i
$484$	5.86197	+	6.76507i	0.266453	+	0.307503i
$485$	0.246422	−	0.0723562i	0.0111895	−	0.00328552i
$486$	−0.0897365	+	0.624131i	−0.00407053	+	0.0283112i
$487$	2.31397	+	16.0940i	0.104856	+	0.729290i	0.972635	+	0.232339i	$0.0746379\pi$
$487$	2.31397	+	16.0940i	0.104856	+	0.729290i	−0.867779	+	0.496951i	$0.834453\pi$
$488$	−1.75568	−	2.02616i	−0.0794759	−	0.0917201i
$489$	0.0951283	+	0.208302i	0.00430185	+	0.00941974i
$490$	−3.22982	−	0.948360i	−0.145908	−	0.0428425i
$491$	8.83055	−	19.3362i	0.398517	−	0.872631i	−0.598901	−	0.800823i	$-0.704396\pi$
$491$	8.83055	−	19.3362i	0.398517	−	0.872631i	0.997418	−	0.0718081i	$-0.0228769\pi$
$492$	0.0630633	+	0.138089i	0.00284311	+	0.00622555i
$493$	6.99438	−	48.6470i	0.315011	−	2.19095i
$494$	−25.1276	+	16.1486i	−1.13055	+	0.726558i
$495$	0.610960	−	4.24932i	0.0274606	−	0.190993i
$496$	4.94326	+	1.45147i	0.221959	+	0.0651730i
$497$	25.5909	+	16.4463i	1.14791	+	0.737716i
$498$	−0.314993			−0.0141152
$499$	38.8495			1.73914			0.869571	−	0.493808i	$-0.164395\pi$
$499$	38.8495			1.73914			0.869571	+	0.493808i	$0.164395\pi$
$500$	0.841254	+	0.540641i	0.0376220	+	0.0241782i
$501$	0.00586066	−	0.0128331i	0.000261835	−	0.000573339i
$502$	14.3427	+	16.5524i	0.640148	+	0.738770i
$503$	12.8249	+	14.8007i	0.571832	+	0.659929i	0.965828	−	0.259183i	$-0.0834532\pi$
$503$	12.8249	+	14.8007i	0.571832	+	0.659929i	−0.393996	+	0.919112i	$0.628908\pi$
$504$	2.37524	−	5.20104i	0.105801	−	0.231673i
$505$	9.08058	+	5.83574i	0.404081	+	0.259687i
$506$	−0.759858			−0.0337798
$507$	−0.535608			−0.0237872
$508$	−7.53698	−	4.84372i	−0.334400	−	0.214906i
$509$	9.84650	+	2.89119i	0.436438	+	0.128150i	0.492569	−	0.870274i	$-0.336058\pi$
$509$	9.84650	+	2.89119i	0.436438	+	0.128150i	−0.0561303	+	0.998423i	$0.517876\pi$
$510$	0.0255827	−	0.177932i	0.00113282	−	0.00787896i
$511$	−4.64719	+	2.98657i	−0.205580	+	0.132118i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	0.290106	+	0.635243i	0.0128085	+	0.0280467i
$514$	2.38106	−	5.21379i	0.105024	−	0.229970i
$515$	−12.6568	−	3.71638i	−0.557726	−	0.163763i
$516$	−0.0271999	−	0.0595595i	−0.00119741	−	0.00262196i
$517$	−9.87827	−	11.4001i	−0.434446	−	0.501377i
$518$	−2.11678	−	14.7225i	−0.0930060	−	0.646871i
$519$	0.0775961	−	0.539693i	0.00340609	−	0.0236899i
$520$	5.75129	−	1.68873i	0.252211	−	0.0740557i
$521$	0.0616937	+	0.0711983i	0.00270285	+	0.00311925i	0.757099	−	0.653300i	$-0.226616\pi$
$521$	0.0616937	+	0.0711983i	0.00270285	+	0.00311925i	−0.754397	+	0.656419i	$0.772070\pi$
$522$	−2.72618	−	18.9610i	−0.119322	−	0.829901i
$523$	28.7408	−	18.4706i	1.25675	−	0.807662i	0.268911	−	0.963165i	$-0.413336\pi$
$523$	28.7408	−	18.4706i	1.25675	−	0.807662i	0.987835	+	0.155503i	$0.0497000\pi$
$524$	0.949986	−	0.610519i	0.0415003	−	0.0266706i
$525$	0.0427253	−	0.0125453i	0.00186468	−	0.000547520i
$526$	12.2042	−	26.7235i	0.532128	−	1.16520i
$527$	−25.9631	+	29.9630i	−1.13097	+	1.30521i
$528$	−0.0281260	−	0.0180755i	−0.00122403	−	0.000786635i
$529$	14.8772	−	17.1692i	0.646836	−	0.746488i
$530$	−9.57979	−	2.81288i	−0.416119	−	0.122184i
$531$	17.4010	−	5.10940i	0.755140	−	0.221729i
$532$	−1.35187	−	9.40245i	−0.0586109	−	0.407648i
$533$	−16.1823	−	35.4342i	−0.700932	−	1.53483i
$534$	0.109406	−	0.126262i	0.00473447	−	0.00546387i
$535$	−2.31686			−0.100167
$536$	−7.93159	+	2.02236i	−0.342592	+	0.0873525i
$537$	−0.189477			−0.00817654
$538$	14.4226	−	16.6445i	0.621801	−	0.717596i
$539$	−2.00142	−	4.38250i	−0.0862074	−	0.188768i
$540$	−0.0199445	−	0.138717i	−0.000858273	−	0.00596942i
$541$	27.4817	−	8.06935i	1.18153	−	0.346928i	0.368766	−	0.929522i	$-0.379780\pi$
$541$	27.4817	−	8.06935i	1.18153	−	0.346928i	0.812763	+	0.582594i	$0.197962\pi$
$542$	−7.56832	−	2.22226i	−0.325087	−	0.0954542i
$543$	0.175259	−	0.202259i	0.00752107	−	0.00867978i
$544$	6.47386	+	4.16050i	0.277564	+	0.178380i
$545$	1.70327	−	1.96568i	0.0729603	−	0.0842006i
$546$	0.110879	−	0.242791i	0.00474517	−	0.0103905i
$547$	11.4008	−	3.34757i	0.487463	−	0.143132i	−0.0287601	−	0.999586i	$-0.509156\pi$
$547$	11.4008	−	3.34757i	0.487463	−	0.143132i	0.516223	+	0.856454i	$0.327338\pi$
$548$	14.4132	−	9.26280i	0.615701	−	0.395687i
$549$	6.76496	−	4.34758i	0.288722	−	0.185550i
$550$	0.203691	+	1.41670i	0.00868539	+	0.0604082i
$551$	−20.8408	−	24.0515i	−0.887846	−	1.02463i
$552$	−0.0118991	+	0.00349389i	−0.000506460	+	0.000148710i
$553$	4.12486	−	28.6891i	0.175407	−	1.21998i
$554$	−0.122964	−	0.855235i	−0.00522425	−	0.0363354i
$555$	−0.119358	−	0.137747i	−0.00506648	−	0.00584703i
$556$	4.58269	+	10.0347i	0.194349	+	0.425566i
$557$	15.1790	+	4.45695i	0.643154	+	0.188847i	0.587015	−	0.809576i	$-0.300303\pi$
$557$	15.1790	+	4.45695i	0.643154	+	0.188847i	0.0561389	+	0.998423i	$0.482121\pi$
$558$	−6.41942	+	14.0566i	−0.271756	+	0.595062i
$559$	6.97960	+	15.2832i	0.295205	+	0.646410i
$560$	−0.271289	+	1.88686i	−0.0114641	+	0.0797343i
$561$	0.216444	−	0.139100i	0.00913825	−	0.00587280i
$562$	−1.78966	+	12.4474i	−0.0754924	+	0.525061i
$563$	23.4806	+	6.89452i	0.989588	+	0.290569i	0.736177	−	0.676789i	$-0.236629\pi$
$563$	23.4806	+	6.89452i	0.989588	+	0.290569i	0.253411	+	0.967359i	$0.418447\pi$
$564$	−0.207109	−	0.133101i	−0.00872086	−	0.00560455i
$565$	0.676841			0.0284749
$566$	17.2491			0.725034
$567$	14.4250	+	9.27036i	0.605792	+	0.389319i
$568$	−6.62916	+	14.5158i	−0.278153	+	0.609071i
$569$	−17.0733	−	19.7036i	−0.715748	−	0.826018i	0.275041	−	0.961433i	$-0.411309\pi$
$569$	−17.0733	−	19.7036i	−0.715748	−	0.826018i	−0.990789	+	0.135415i	$0.956763\pi$
$570$	−0.0762274	−	0.0879712i	−0.00319282	−	0.00368471i
$571$	−16.4722	+	36.0690i	−0.689338	+	1.50944i	0.163098	+	0.986610i	$0.447851\pi$
$571$	−16.4722	+	36.0690i	−0.689338	+	1.50944i	−0.852437	+	0.522831i	$0.824876\pi$
$572$	7.21723	+	4.63823i	0.301768	+	0.193934i
$573$	0.352671			0.0147331
$574$	12.3884			0.517083
$575$	0.446621	+	0.287026i	0.0186254	+	0.0119698i
$576$	2.87796	+	0.845044i	0.119915	+	0.0352102i
$577$	−2.98106	+	20.7338i	−0.124103	+	0.863158i	0.828727	+	0.559653i	$0.189066\pi$
$577$	−2.98106	+	20.7338i	−0.124103	+	0.863158i	−0.952830	+	0.303504i	$0.901843\pi$
$578$	−35.5182	+	22.8262i	−1.47736	+	0.949444i
$579$	−0.0336520	+	0.234055i	−0.00139853	+	0.00972698i
$580$	2.65305	+	5.80936i	0.110162	+	0.241221i
$581$	−10.6784	+	23.3824i	−0.443013	+	0.970064i
$582$	0.00575627	+	0.00169019i	0.000238605	+	7.00607e-5i
$583$	−5.93631	−	12.9987i	−0.245857	−	0.538352i
$584$	−1.89771	−	2.19007i	−0.0785278	−	0.0906259i
$585$	2.55868	+	17.7960i	0.105788	+	0.735774i
$586$	4.61024	−	32.0649i	0.190447	−	1.32459i
$587$	28.4896	−	8.36530i	1.17589	−	0.345273i	0.365303	−	0.930889i	$-0.380966\pi$
$587$	28.4896	−	8.36530i	1.17589	−	0.345273i	0.810589	+	0.585616i	$0.199147\pi$
$588$	−0.0514927	−	0.0594257i	−0.00212352	−	0.00245068i
$589$	3.65362	+	25.4115i	0.150545	+	1.04706i
$590$	−5.08648	+	3.26888i	−0.209407	+	0.134578i
$591$	−0.234681	+	0.150820i	−0.00965349	+	0.00620392i
$592$	7.48661	−	2.19827i	0.307698	−	0.0903482i
$593$	0.0451383	−	0.0988391i	0.00185361	−	0.00405884i	−0.908703	−	0.417443i	$-0.862926\pi$
$593$	0.0451383	−	0.0988391i	0.00185361	−	0.00405884i	0.910557	+	0.413385i	$0.135653\pi$
$594$	0.131354	−	0.151590i	0.00538950	−	0.00621982i
$595$	−12.3409	−	7.93099i	−0.505926	−	0.325139i
$596$	−1.36211	+	1.57196i	−0.0557942	+	0.0643899i
$597$	−0.161985	−	0.0475630i	−0.00662959	−	0.00194662i
$598$	3.05335	−	0.896545i	0.124861	−	0.0366624i
$599$	4.10346	+	28.5402i	0.167663	+	1.16612i	0.883698	+	0.468057i	$0.155046\pi$
$599$	4.10346	+	28.5402i	0.167663	+	1.16612i	−0.716035	+	0.698064i	$0.754045\pi$
$600$	0.00970382	+	0.0212484i	0.000396157	+	0.000867463i
$601$	3.39815	−	3.92167i	0.138613	−	0.159968i	−0.682199	−	0.731167i	$-0.738976\pi$
$601$	3.39815	−	3.92167i	0.138613	−	0.159968i	0.820812	+	0.571199i	$0.193521\pi$
$602$	−5.34327			−0.217776
$603$	−2.61849	−	24.4116i	−0.106633	−	0.994115i
$604$	−1.50749			−0.0613387
$605$	5.86197	−	6.76507i	0.238323	−	0.275039i
$606$	0.104744	+	0.229358i	0.00425494	+	0.00931702i
$607$	−2.11847	−	14.7343i	−0.0859860	−	0.598046i	−0.986567	−	0.163357i	$-0.947768\pi$
$607$	−2.11847	−	14.7343i	−0.0859860	−	0.598046i	0.900581	−	0.434688i	$-0.143141\pi$
$608$	4.78127	−	1.40391i	0.193906	−	0.0569360i
$609$	0.272865	+	0.0801203i	0.0110570	+	0.00324664i
$610$	−1.75568	+	2.02616i	−0.0710854	+	0.0820369i
$611$	53.1448	+	34.1541i	2.15001	+	1.38173i
$612$	−15.1157	+	17.4444i	−0.611015	+	0.705149i
$613$	−17.2149	+	37.6953i	−0.695302	+	1.52250i	0.150274	+	0.988644i	$0.451984\pi$
$613$	−17.2149	+	37.6953i	−0.695302	+	1.52250i	−0.845576	+	0.533855i	$0.820743\pi$
$614$	−22.8173	+	6.69975i	−0.920830	+	0.270380i
$615$	0.127709	−	0.0820736i	0.00514973	−	0.00330953i
$616$	−2.29525	+	1.47507i	−0.0924782	+	0.0594321i
$617$	2.95767	+	20.5711i	0.119071	+	0.828159i	0.958582	+	0.284816i	$0.0919326\pi$
$617$	2.95767	+	20.5711i	0.119071	+	0.828159i	−0.839511	+	0.543343i	$0.817158\pi$
$618$	−0.201787	−	0.232874i	−0.00811705	−	0.00936758i
$619$	−27.1439	+	7.97018i	−1.09101	+	0.320349i	−0.777274	−	0.629163i	$-0.783398\pi$
$619$	−27.1439	+	7.97018i	−1.09101	+	0.320349i	−0.313733	+	0.949511i	$0.601580\pi$
$620$	0.733199	−	5.09951i	0.0294460	−	0.204801i
$621$	−0.0105885	−	0.0736446i	−0.000424902	−	0.00295526i
$622$	15.7681	+	18.1974i	0.632243	+	0.729648i
$623$	−5.66366	−	12.4017i	−0.226910	−	0.496863i
$624$	0.134346	+	0.0394476i	0.00537815	+	0.00157917i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−2.52327	−	5.52519i	−0.100850	−	0.220831i
$627$	0.0237101	−	0.164907i	0.000946890	−	0.00658576i
$628$	14.1481	−	9.09244i	0.564571	−	0.362828i
$629$	−8.54535	+	59.4342i	−0.340725	+	2.36980i
$630$	−5.48613	−	1.61087i	−0.218573	−	0.0641788i
$631$	−27.0909	−	17.4103i	−1.07847	−	0.693091i	−0.124267	−	0.992249i	$-0.539658\pi$
$631$	−27.0909	−	17.4103i	−1.07847	−	0.693091i	−0.954204	+	0.299158i	$0.903294\pi$
$632$	15.2047			0.604809
$633$	−0.271743			−0.0108008
$634$	−25.5004	−	16.3881i	−1.01275	−	0.650856i
$635$	−3.72180	+	8.14960i	−0.147695	+	0.323407i
$636$	−0.152730	−	0.176260i	−0.00605613	−	0.00698915i
$637$	13.2132	+	15.2488i	0.523526	+	0.604181i
$638$	−3.79722	+	8.31475i	−0.150333	+	0.329184i
$639$	−40.2666	−	25.8778i	−1.59292	−	1.02371i
$640$	−1.00000			−0.0395285
$641$	15.8179			0.624770			0.312385	−	0.949956i	$-0.398872\pi$
$641$	15.8179			0.624770			0.312385	+	0.949956i	$0.398872\pi$
$642$	−0.0455289	−	0.0292596i	−0.00179688	−	0.00115479i
$643$	1.91021	+	0.560889i	0.0753315	+	0.0221193i	0.319181	−	0.947694i	$-0.396592\pi$
$643$	1.91021	+	0.560889i	0.0753315	+	0.0221193i	−0.243850	+	0.969813i	$0.578410\pi$
$644$	−0.144027	+	1.00173i	−0.00567547	+	0.0394737i
$645$	−0.0550824	+	0.0353993i	−0.00216887	+	0.00139385i
$646$	−5.45743	+	37.9573i	−0.214720	+	1.49341i
$647$	16.9422	+	37.0983i	0.666067	+	1.45848i	0.876759	+	0.480930i	$0.159701\pi$
$647$	16.9422	+	37.0983i	0.666067	+	1.45848i	−0.210692	+	0.977553i	$0.567572\pi$
$648$	−3.73670	+	8.18222i	−0.146791	+	0.321428i
$649$	−8.30335	−	2.43808i	−0.325935	−	0.0957031i
$650$	−2.49003	−	5.45241i	−0.0976672	−	0.213861i
$651$	−0.150232	−	0.173377i	−0.00588807	−	0.00679520i
$652$	1.39514	+	9.70340i	0.0546378	+	0.380014i
$653$	−4.33196	+	30.1294i	−0.169523	+	1.17906i	0.710351	+	0.703848i	$0.248536\pi$
$653$	−4.33196	+	30.1294i	−0.169523	+	1.17906i	−0.879874	+	0.475208i	$0.842373\pi$
$654$	0.0582959	−	0.0171172i	0.00227955	−	0.000669336i
$655$	−0.739502	−	0.853431i	−0.0288947	−	0.0333463i
$656$	0.924878	+	6.43267i	0.0361104	+	0.251153i
$657$	7.31224	−	4.69929i	0.285277	−	0.183337i
$658$	−16.9013	+	10.8618i	−0.658882	+	0.423438i
$659$	17.0629	−	5.01011i	0.664675	−	0.195166i	0.0680444	−	0.997682i	$-0.478324\pi$
$659$	17.0629	−	5.01011i	0.664675	−	0.195166i	0.596630	+	0.802516i	$0.296506\pi$
$660$	−0.0138888	+	0.0304121i	−0.000540619	+	0.00118379i
$661$	14.1796	−	16.3641i	0.551523	−	0.636492i	−0.409714	−	0.912214i	$-0.634372\pi$
$661$	14.1796	−	16.3641i	0.551523	−	0.636492i	0.961237	+	0.275722i	$0.0889170\pi$
$662$	−14.1416	−	9.08828i	−0.549630	−	0.353226i
$663$	−0.705617	+	0.814326i	−0.0274039	+	0.0316258i
$664$	−12.9384	−	3.79907i	−0.502109	−	0.147433i
$665$	−9.11435	+	2.67622i	−0.353439	+	0.103779i
$666$	3.33070	+	23.1655i	0.129062	+	0.897647i
$667$	1.40850	+	3.08418i	0.0545373	+	0.119420i
$668$	0.395506	−	0.456438i	0.0153026	−	0.0176601i
$669$	0.593182			0.0229337
$670$	3.13056	+	7.56304i	0.120944	+	0.292186i
$671$	−3.83722			−0.148134
$672$	−0.0291603	+	0.0336528i	−0.00112488	+	0.00129818i
$673$	−10.2977	−	22.5489i	−0.396949	−	0.869196i	−0.997571	−	0.0696631i	$-0.977808\pi$
$673$	−10.2977	−	22.5489i	−0.396949	−	0.869196i	0.600622	−	0.799533i	$-0.294920\pi$
$674$	1.36809	+	9.51530i	0.0526970	+	0.366516i
$675$	−0.134467	+	0.0394829i	−0.00517562	+	0.00151970i
$676$	−22.0003	−	6.45987i	−0.846165	−	0.248457i
$677$	−18.0257	+	20.8028i	−0.692784	+	0.799516i	−0.987759	−	0.155989i	$-0.950143\pi$
$677$	−18.0257	+	20.8028i	−0.692784	+	0.799516i	0.294974	+	0.955505i	$0.404689\pi$
$678$	0.0133007	+	0.00854784i	0.000510810	+	0.000328278i
$679$	0.320605	−	0.369997i	0.0123037	−	0.0141992i
$680$	3.19682	−	7.00007i	0.122593	−	0.268440i
$681$	0.260274	−	0.0764232i	0.00997370	−	0.00292854i
$682$	6.20325	−	3.98658i	0.237535	−	0.152654i
$683$	−19.4212	+	12.4812i	−0.743130	+	0.477581i	−0.856613	−	0.515959i	$-0.827436\pi$
$683$	−19.4212	+	12.4812i	−0.743130	+	0.477581i	0.113483	+	0.993540i	$0.463799\pi$
$684$	2.12713	+	14.7945i	0.0813329	+	0.565683i
$685$	−11.2197	−	12.9483i	−0.428684	−	0.494727i
$686$	−18.9602	+	5.56721i	−0.723903	+	0.212557i
$687$	0.0795998	−	0.553628i	0.00303692	−	0.0211222i
$688$	−0.398910	−	2.77448i	−0.0152083	−	0.105776i
$689$	39.1910	+	45.2288i	1.49306	+	1.72308i
$690$	0.00515175	+	0.0112808i	0.000196124	+	0.000429451i
$691$	21.4363	+	6.29428i	0.815477	+	0.239446i	0.662767	−	0.748826i	$-0.269382\pi$
$691$	21.4363	+	6.29428i	0.815477	+	0.239446i	0.152710	+	0.988271i	$0.451200\pi$
$692$	9.69641	−	21.2322i	0.368602	−	0.807126i
$693$	−3.39960	−	7.44408i	−0.129140	−	0.282777i
$694$	0.695457	−	4.83701i	0.0263992	−	0.183610i
$695$	9.28037	−	5.96413i	0.352025	−	0.226232i
$696$	−0.0212311	+	0.147666i	−0.000804765	+	0.00559726i
$697$	−47.9858	−	14.0899i	−1.81759	−	0.533693i
$698$	11.9111	+	7.65478i	0.450840	+	0.289738i
$699$	0.125090			0.00473133
$700$	1.90626			0.0720499
$701$	24.2715	+	15.5983i	0.916722	+	0.589141i	0.911705	−	0.410846i	$-0.134767\pi$
$701$	24.2715	+	15.5983i	0.916722	+	0.589141i	0.00501725	+	0.999987i	$0.498403\pi$
$702$	−0.348962	+	0.764119i	−0.0131707	+	0.0288398i
$703$	25.4621	+	29.3848i	0.960321	+	1.10827i
$704$	−0.937280	−	1.08168i	−0.0353251	−	0.0407673i
$705$	−0.102271	+	0.223943i	−0.00385176	+	0.00843418i
$706$	−15.2951	−	9.82959i	−0.575640	−	0.369942i
$707$	20.5764			0.773855
$708$	−0.141238			−0.00530805
$709$	28.5780	+	18.3660i	1.07327	+	0.689749i	0.952993	−	0.302992i	$-0.0979855\pi$
$709$	28.5780	+	18.3660i	1.07327	+	0.689749i	0.120277	+	0.992740i	$0.461622\pi$
$710$	15.3115	+	4.49586i	0.574631	+	0.168727i
$711$	−6.49037	+	45.1415i	−0.243408	+	1.69294i
$712$	6.01672	−	3.86671i	0.225486	−	0.144911i
$713$	0.389255	−	2.70732i	0.0145777	−	0.101390i
$714$	−0.142351	−	0.311706i	−0.00532736	−	0.0116653i
$715$	3.56390	−	7.80386i	0.133282	−	0.291848i
$716$	−7.78283	−	2.28525i	−0.290858	−	0.0854037i
$717$	0.00427172	+	0.00935376i	0.000159530	+	0.000349322i
$718$	−21.2487	−	24.5223i	−0.792993	−	0.915163i
$719$	−0.192524	−	1.33904i	−0.00717995	−	0.0499376i	0.985916	−	0.167238i	$-0.0534849\pi$
$719$	−0.192524	−	1.33904i	−0.00717995	−	0.0499376i	−0.993096	+	0.117301i	$0.962576\pi$
$720$	0.426867	−	2.96892i	0.0159084	−	0.110645i
$721$	−24.1272	+	7.08439i	−0.898544	+	0.263836i
$722$	3.81884	+	4.40718i	0.142123	+	0.164018i
$723$	0.0808067	+	0.562023i	0.00300523	+	0.0209019i
$724$	9.63822	−	6.19411i	0.358202	−	0.230202i
$725$	5.37266	−	3.45280i	0.199536	−	0.128234i
$726$	0.200631	−	0.0589104i	0.00744610	−	0.00218637i
$727$	13.4399	−	29.4293i	0.498458	−	1.09147i	−0.478509	−	0.878083i	$-0.658823\pi$
$727$	13.4399	−	29.4293i	0.498458	−	1.09147i	0.976967	−	0.213389i	$-0.0684502\pi$
$728$	7.48263	−	8.63542i	0.277325	−	0.320050i
$729$	−22.6891	−	14.5814i	−0.840336	−	0.540051i
$730$	−1.89771	+	2.19007i	−0.0702374	+	0.0810583i
$731$	20.6968	+	6.07713i	0.765499	+	0.224771i
$732$	−0.0600895	+	0.0176439i	−0.00222097	+	0.000652136i
$733$	1.26760	+	8.81636i	0.0468199	+	0.325640i	0.999748	+	0.0224436i	$0.00714461\pi$
$733$	1.26760	+	8.81636i	0.0468199	+	0.325640i	−0.952928	+	0.303196i	$0.901946\pi$
$734$	−11.4294	−	25.0268i	−0.421865	−	0.923756i
$735$	−0.0514927	+	0.0594257i	−0.00189934	+	0.00219195i
$736$	−0.530899			−0.0195692
$737$	−5.24658	+	10.4749i	−0.193260	+	0.385850i
$738$	−19.4929			−0.717543
$739$	0.553358	−	0.638609i	0.0203556	−	0.0234916i	−0.745480	−	0.666527i	$-0.767780\pi$
$739$	0.553358	−	0.638609i	0.0203556	−	0.0234916i	0.765836	+	0.643036i	$0.222325\pi$
$740$	−3.24135	−	7.09756i	−0.119154	−	0.260912i
$741$	0.0992969	+	0.690625i	0.00364776	+	0.0253707i
$742$	−18.2616	+	5.36208i	−0.670404	+	0.196848i
$743$	−40.1027	−	11.7752i	−1.47123	−	0.431991i	−0.554728	−	0.832032i	$-0.687178\pi$
$743$	−40.1027	−	11.7752i	−1.47123	−	0.431991i	−0.916497	+	0.400041i	$0.868996\pi$
$744$	0.0788100	−	0.0909516i	0.00288931	−	0.00333445i
$745$	1.74981	+	1.12453i	0.0641079	+	0.0411997i
$746$	5.31708	−	6.13624i	0.194672	−	0.224664i
$747$	16.8022	−	36.7916i	0.614759	−	1.34613i
$748$	10.5681	−	3.10309i	0.386410	−	0.113460i
$749$	−3.71543	+	2.38776i	−0.135759	+	0.0872469i
$750$	0.0196511	−	0.0126290i	0.000717558	−	0.000461146i
$751$	5.57375	+	38.7663i	0.203389	+	1.41460i	0.794134	+	0.607743i	$0.207925\pi$
$751$	5.57375	+	38.7663i	0.203389	+	1.41460i	−0.590745	+	0.806858i	$0.701166\pi$
$752$	−6.90176	−	7.96506i	−0.251681	−	0.290456i
$753$	0.490892	−	0.144139i	0.0178891	−	0.00525271i
$754$	5.44799	−	37.8916i	0.198404	−	1.37993i
$755$	0.214538	+	1.49214i	0.00780782	+	0.0543046i
$756$	−0.174946	−	0.201898i	−0.00636272	−	0.00734297i
$757$	−12.1136	−	26.5250i	−0.440275	−	0.964069i	−0.991548	−	0.129743i	$-0.958585\pi$
$757$	−12.1136	−	26.5250i	−0.440275	−	0.964069i	0.551272	−	0.834325i	$-0.314143\pi$
$758$	−10.1470	−	2.97942i	−0.368554	−	0.108217i
$759$	−0.00737353	+	0.0161458i	−0.000267642	+	0.000586054i
$760$	−2.07006	−	4.53281i	−0.0750891	−	0.164422i
$761$	−2.12240	+	14.7616i	−0.0769368	+	0.535107i	0.914507	+	0.404571i	$0.132579\pi$
$761$	−2.12240	+	14.7616i	−0.0769368	+	0.535107i	−0.991443	+	0.130537i	$0.958330\pi$
$762$	−0.176059	+	0.113146i	−0.00637794	+	0.00409886i
$763$	0.705616	−	4.90766i	0.0255450	−	0.177669i
$764$	14.4861	+	4.25350i	0.524088	+	0.153886i
$765$	19.4180	+	12.4792i	0.702061	+	0.451187i
$766$	5.27901			0.190738
$767$	36.2421			1.30863
$768$	−0.0196511	−	0.0126290i	−0.000709099	−	0.000455710i
$769$	−16.2454	+	35.5725i	−0.585825	+	1.28278i	0.352107	+	0.935960i	$0.385465\pi$
$769$	−16.2454	+	35.5725i	−0.585825	+	1.28278i	−0.937932	+	0.346819i	$0.887262\pi$
$770$	1.78670	+	2.06196i	0.0643882	+	0.0743080i
$771$	−0.0876793	−	0.101187i	−0.00315769	−	0.00364417i
$772$	−4.20516	+	9.20801i	−0.151347	+	0.331403i
$773$	−27.3612	−	17.5840i	−0.984113	−	0.632451i	−0.0535431	−	0.998566i	$-0.517051\pi$
$773$	−27.3612	−	17.5840i	−0.984113	−	0.632451i	−0.930570	+	0.366115i	$0.880688\pi$
$774$	8.40751			0.302202
$775$	−5.15195			−0.185063
$776$	0.216056	+	0.138850i	0.00775594	+	0.00498444i
$777$	−0.333371	−	0.0978866i	−0.0119596	−	0.00351166i
$778$	2.18991	−	15.2312i	0.0785120	−	0.546063i
$779$	−27.2435	+	17.5083i	−0.976099	+	0.627301i
$780$	0.0199266	−	0.138593i	0.000713488	−	0.00496242i
$781$	9.48809	+	20.7760i	0.339511	+	0.743425i
$782$	1.69719	−	3.71633i	0.0606914	−	0.132896i
$783$	−0.858770	−	0.252158i	−0.0306899	−	0.00901138i
$784$	−1.39836	−	3.06198i	−0.0499413	−	0.109356i
$785$	−11.0134	−	12.7101i	−0.393084	−	0.453644i
$786$	−0.00375406	−	0.0261101i	−0.000133903	−	0.000931315i
$787$	1.60267	−	11.1468i	0.0571291	−	0.397342i	−0.941114	−	0.338090i	$-0.890219\pi$
$787$	1.60267	−	11.1468i	0.0571291	−	0.397342i	0.998243	−	0.0592522i	$-0.0188716\pi$
$788$	−11.4586	+	3.36455i	−0.408196	+	0.119857i
$789$	−0.449404	−	0.518639i	−0.0159992	−	0.0184640i
$790$	−2.16385	−	15.0499i	−0.0769863	−	0.535452i
$791$	1.08542	−	0.697554i	0.0385929	−	0.0248022i
$792$	3.61152	−	2.32098i	0.128330	−	0.0824725i
$793$	15.4192	−	4.52748i	0.547551	−	0.160776i
$794$	−11.4687	+	25.1129i	−0.407008	+	0.891223i
$795$	−0.152730	+	0.176260i	−0.00541677	+	0.00625128i
$796$	−6.07993	−	3.90733i	−0.215497	−	0.138492i
$797$	−11.9453	+	13.7857i	−0.423126	+	0.488313i	−0.926787	−	0.375588i	$-0.877441\pi$
$797$	−11.9453	+	13.7857i	−0.423126	+	0.488313i	0.503661	+	0.863902i	$0.331986\pi$
$798$	−0.212905	−	0.0625146i	−0.00753677	−	0.00221299i
$799$	77.8197	−	22.8499i	2.75306	−	0.808372i
$800$	0.142315	+	0.989821i	0.00503159	+	0.0349955i
$801$	8.91163	+	19.5138i	0.314877	+	0.689485i
$802$	0.0965746	−	0.111453i	0.00341017	−	0.00393555i
$803$	−4.14765			−0.146367
$804$	−0.0339948	+	0.188158i	−0.00119891	+	0.00663583i
$805$	1.01203			0.0356694
$806$	−20.2229	+	23.3385i	−0.712322	+	0.822063i
$807$	−0.213716	−	0.467972i	−0.00752315	−	0.0164734i
$808$	1.53616	+	10.6842i	0.0540420	+	0.375870i
$809$	−36.8591	+	10.8228i	−1.29590	+	0.380509i	−0.855737	−	0.517411i	$-0.826896\pi$
$809$	−36.8591	+	10.8228i	−1.29590	+	0.380509i	−0.440159	+	0.897920i	$0.645078\pi$
$810$	8.63073	+	2.53421i	0.303253	+	0.0890430i
$811$	−23.9155	+	27.6000i	−0.839788	+	0.969167i	−0.999839	−	0.0179418i	$-0.994289\pi$
$811$	−23.9155	+	27.6000i	−0.839788	+	0.969167i	0.160051	+	0.987109i	$0.448834\pi$
$812$	10.2417	+	6.58194i	0.359413	+	0.230981i
$813$	−0.120661	+	0.139250i	−0.00423177	+	0.00488372i
$814$	4.63923	−	10.1585i	0.162605	−	0.356055i
$815$	9.40608	−	2.76188i	0.329481	−	0.0967443i
$816$	0.151225	−	0.0971865i	0.00529394	−	0.00340221i
$817$	11.7504	−	7.55154i	0.411095	−	0.264195i
$818$	1.46654	+	10.2000i	0.0512764	+	0.356635i
$819$	22.4438	+	25.9015i	0.784250	+	0.905073i
$820$	6.23557	−	1.83093i	0.217755	−	0.0639388i
$821$	3.18678	−	22.1645i	0.111219	−	0.773547i	−0.855518	−	0.517774i	$-0.826761\pi$
$821$	3.18678	−	22.1645i	0.111219	−	0.773547i	0.966737	−	0.255773i	$-0.0823300\pi$
$822$	−0.0569566	−	0.396142i	−0.00198659	−	0.0138170i
$823$	−27.4190	−	31.6432i	−0.955767	−	1.10301i	−0.994602	−	0.103768i	$-0.966910\pi$
$823$	−27.4190	−	31.6432i	−0.955767	−	1.10301i	0.0388349	−	0.999246i	$-0.487635\pi$
$824$	−5.47981	−	11.9991i	−0.190898	−	0.418008i
$825$	0.0320792	+	0.00941929i	0.00111685	+	0.000327938i
$826$	−4.78801	+	10.4843i	−0.166596	+	0.364795i
$827$	10.2823	+	22.5151i	0.357550	+	0.782926i	0.999864	+	0.0164842i	$0.00524733\pi$
$827$	10.2823	+	22.5151i	0.357550	+	0.782926i	−0.642314	+	0.766442i	$0.722025\pi$
$828$	0.226623	−	1.57620i	0.00787570	−	0.0547767i
$829$	3.36819	−	2.16460i	0.116982	−	0.0751798i	−0.480841	−	0.876808i	$-0.659669\pi$
$829$	3.36819	−	2.16460i	0.116982	−	0.0751798i	0.597824	+	0.801628i	$0.296032\pi$
$830$	−1.91907	+	13.3474i	−0.0666119	+	0.463296i
$831$	−0.0193656	−	0.00568625i	−0.000671785	−	0.000197254i
$832$	5.04255	+	3.24065i	0.174819	+	0.112349i
$833$	25.9043			0.897532
$834$	0.257691			0.00892311
$835$	−0.508079	−	0.326522i	−0.0175828	−	0.0112998i
$836$	2.96282	−	6.48766i	0.102471	−	0.224380i
$837$	0.472817	+	0.545660i	0.0163429	+	0.0188608i
$838$	−18.1492	−	20.9453i	−0.626955	−	0.723545i
$839$	1.59742	−	3.49786i	0.0551490	−	0.120760i	−0.880051	−	0.474879i	$-0.842492\pi$
$839$	1.59742	−	3.49786i	0.0551490	−	0.120760i	0.935200	+	0.354119i	$0.115219\pi$
$840$	0.0374602	+	0.0240742i	0.00129250	+	0.000830639i
$841$	11.7873			0.406460
$842$	7.85505			0.270703
$843$	0.247121	+	0.158815i	0.00851128	+	0.00546987i
$844$	−11.1619	−	3.27744i	−0.384210	−	0.112814i
$845$	−3.26315	+	22.6957i	−0.112256	+	0.780756i
$846$	26.5938	−	17.0908i	0.914313	−	0.587594i
$847$	2.42844	−	16.8902i	0.0834421	−	0.580353i
$848$	−4.14759	−	9.08197i	−0.142429	−	0.311876i
$849$	0.167382	−	0.366516i	0.00574454	−	0.0125788i
$850$	−7.38377	−	2.16807i	−0.253261	−	0.0743642i
$851$	−1.72083	−	3.76809i	−0.0589892	−	0.129168i
$852$	0.244110	+	0.281718i	0.00836307	+	0.00965150i
$853$	−2.25872	−	15.7097i	−0.0773370	−	0.537890i	−0.991252	−	0.131984i	$-0.957865\pi$
$853$	−2.25872	−	15.7097i	−0.0773370	−	0.537890i	0.913915	−	0.405906i	$-0.133044\pi$
$854$	−0.727326	+	5.05866i	−0.0248886	+	0.173104i
$855$	14.3412	−	4.21096i	0.490459	−	0.144012i
$856$	−1.51722	−	1.75096i	−0.0518575	−	0.0598468i
$857$	−4.53475	−	31.5399i	−0.154904	−	1.07738i	−0.907848	−	0.419298i	$-0.862276\pi$
$857$	−4.53475	−	31.5399i	−0.154904	−	1.07738i	0.752944	−	0.658084i	$-0.228633\pi$
$858$	0.168590	−	0.108346i	0.00575556	−	0.00369887i
$859$	2.12209	−	1.36379i	0.0724048	−	0.0465318i	−0.503938	−	0.863740i	$-0.668116\pi$
$859$	2.12209	−	1.36379i	0.0724048	−	0.0465318i	0.576342	+	0.817208i	$0.304479\pi$
$860$	−2.68947	+	0.789700i	−0.0917102	+	0.0269285i
$861$	0.120215	−	0.263235i	0.00409692	−	0.00897101i
$862$	3.54004	−	4.08542i	0.120574	−	0.139150i
$863$	21.5595	+	13.8555i	0.733894	+	0.471645i	0.853445	−	0.521183i	$-0.174509\pi$
$863$	21.5595	+	13.8555i	0.733894	+	0.471645i	−0.119551	+	0.992828i	$0.538145\pi$
$864$	0.0917744	−	0.105913i	0.00312223	−	0.00360324i
$865$	−22.3960	−	6.57606i	−0.761487	−	0.223593i
$866$	3.93410	−	1.15516i	0.133686	−	0.0392538i
$867$	0.140357	+	0.976207i	0.00476679	+	0.0331537i
$868$	−4.07977	−	8.93346i	−0.138477	−	0.303221i
$869$	14.2510	−	16.4466i	0.483433	−	0.557912i
$870$	0.149184			0.00505782
$871$	8.72319	−	48.2820i	0.295574	−	1.63597i
$872$	2.60097			0.0880800
$873$	−0.504463	+	0.582182i	−0.0170735	+	0.0197039i
$874$	−1.09900	−	2.40646i	−0.0371741	−	0.0813999i
$875$	−0.271289	−	1.88686i	−0.00917125	−	0.0637874i
$876$	−0.0649506	+	0.0190712i	−0.00219448	+	0.000644357i
$877$	−21.8779	−	6.42394i	−0.738765	−	0.216921i	−0.109364	−	0.994002i	$-0.534881\pi$
$877$	−21.8779	−	6.42394i	−0.738765	−	0.216921i	−0.629401	+	0.777081i	$0.716700\pi$
$878$	11.0590	−	12.7628i	0.373224	−	0.430724i
$879$	−0.636591	−	0.409112i	−0.0214717	−	0.0137990i
$880$	−0.937280	+	1.08168i	−0.0315957	+	0.0364634i
$881$	21.4099	−	46.8810i	0.721316	−	1.57946i	−0.0907338	−	0.995875i	$-0.528921\pi$
$881$	21.4099	−	46.8810i	0.721316	−	1.57946i	0.812050	−	0.583587i	$-0.198351\pi$
$882$	9.68769	−	2.84456i	0.326201	−	0.0957814i
$883$	17.6809	−	11.3628i	0.595010	−	0.382390i	−0.208200	−	0.978086i	$-0.566760\pi$
$883$	17.6809	−	11.3628i	0.595010	−	0.382390i	0.803209	+	0.595697i	$0.203124\pi$
$884$	−38.8049	+	24.9384i	−1.30515	+	0.838769i
$885$	0.0201003	+	0.139800i	0.000675663	+	0.00469934i
$886$	21.6100	+	24.9393i	0.726003	+	0.837852i
$887$	−36.6234	+	10.7536i	−1.22969	+	0.361070i	−0.831134	−	0.556073i	$-0.812308\pi$
$887$	−36.6234	+	10.7536i	−1.22969	+	0.361070i	−0.398558	+	0.917143i	$0.630489\pi$
$888$	0.0259391	−	0.180410i	0.000870458	−	0.00605417i
$889$	2.43054	+	16.9048i	0.0815178	+	0.566968i
$890$	−4.68362	−	5.40519i	−0.156995	−	0.181182i
$891$	5.34821	+	11.7109i	0.179172	+	0.392331i
$892$	24.3651	+	7.15425i	0.815805	+	0.239542i
$893$	21.8170	−	47.7726i	0.730078	−	1.59865i
$894$	0.0201839	+	0.0441967i	0.000675052	+	0.00147816i
$895$	−1.15437	+	8.02884i	−0.0385864	+	0.268375i
$896$	−1.60365	+	1.03060i	−0.0535741	+	0.0344300i
$897$	0.0105790	−	0.0735788i	0.000353224	−	0.00245672i
$898$	13.9430	+	4.09404i	0.465284	+	0.136620i
$899$	−27.6797	−	17.7887i	−0.923169	−	0.593285i
$900$	−2.99945			−0.0999818
$901$	76.8335			2.55969
$902$	7.82495	+	5.02879i	0.260542	+	0.167440i
$903$	−0.0518502	+	0.113536i	−0.00172547	+	0.00377824i
$904$	0.443237	+	0.511522i	0.0147418	+	0.0170130i
$905$	−7.50272	−	8.65860i	−0.249399	−	0.287822i
$906$	−0.0146284	+	0.0320317i	−0.000485995	+	0.00106418i
$907$	−24.8885	−	15.9949i	−0.826410	−	0.531102i	0.0577250	−	0.998333i	$-0.481615\pi$
$907$	−24.8885	−	15.9949i	−0.826410	−	0.531102i	−0.884135	+	0.467231i	$0.845252\pi$
$908$	11.6126			0.385376
$909$	−32.3764			−1.07386
$910$	−9.61241	−	6.17752i	−0.318648	−	0.204783i
$911$	−49.0986	−	14.4167i	−1.62671	−	0.477645i	−0.663899	−	0.747822i	$-0.731100\pi$
$911$	−49.0986	−	14.4167i	−1.62671	−	0.477645i	−0.962811	+	0.270177i	$0.912918\pi$
$912$	0.0165658	−	0.115218i	0.000548549	−	0.00381524i
$913$	−16.2363	+	10.4345i	−0.537344	+	0.345330i
$914$	−2.51552	+	17.4958i	−0.0832059	+	0.578709i
$915$	0.0260159	+	0.0569669i	0.000860060	+	0.00188327i
$916$	9.94679	−	21.7804i	0.328651	−	0.719646i
$917$	−2.06545	−	0.606471i	−0.0682071	−	0.0200274i
$918$	0.448013	+	0.981012i	0.0147866	+	0.0323782i
$919$	−10.5205	−	12.1413i	−0.347039	−	0.400504i	0.555217	−	0.831706i	$-0.312635\pi$
$919$	−10.5205	−	12.1413i	−0.347039	−	0.400504i	−0.902256	+	0.431202i	$0.858090\pi$
$920$	0.0755548	+	0.525495i	0.00249097	+	0.0173251i
$921$	−0.0790556	+	0.549844i	−0.00260497	+	0.0181180i
$922$	−1.74461	+	0.512264i	−0.0574557	+	0.0168705i
$923$	−62.6395	−	72.2898i	−2.06180	−	2.37945i
$924$	0.00907014	+	0.0630842i	0.000298386	+	0.00207532i
$925$	−6.56403	+	4.21844i	−0.215824	+	0.138702i
$926$	−16.5961	+	10.6657i	−0.545382	+	0.350496i
$927$	37.9636	−	11.1471i	1.24689	−	0.366119i
$928$	−2.65305	+	5.80936i	−0.0870905	+	0.190702i
$929$	−19.3377	+	22.3169i	−0.634449	+	0.732193i	−0.978383	−	0.206801i	$-0.933695\pi$
$929$	−19.3377	+	22.3169i	−0.634449	+	0.732193i	0.343934	+	0.938994i	$0.388240\pi$
$930$	−0.101242	−	0.0650640i	−0.00331984	−	0.00213353i
$931$	10.9847	−	12.6770i	0.360008	−	0.415471i
$932$	5.13811	+	1.50868i	0.168304	+	0.0494186i
$933$	0.539676	−	0.158463i	0.0176682	−	0.00518785i
$934$	3.52476	+	24.5153i	0.115334	+	0.802164i
$935$	−4.57551	−	10.0190i	−0.149635	−	0.327655i
$936$	−11.7737	+	13.5876i	−0.384837	+	0.444125i
$937$	28.5568			0.932910			0.466455	−	0.884545i	$-0.345531\pi$
$937$	28.5568			0.932910			0.466455	+	0.884545i	$0.345531\pi$
$938$	12.8148	+	8.90211i	0.418418	+	0.290664i
$939$	−0.141887			−0.00463030
$940$	−6.90176	+	7.96506i	−0.225111	+	0.259792i
$941$	−1.77775	−	3.89274i	−0.0579531	−	0.126900i	0.878440	−	0.477853i	$-0.158585\pi$
$941$	−1.77775	−	3.89274i	−0.0579531	−	0.126900i	−0.936393	+	0.350953i	$0.885858\pi$
$942$	−0.0559091	−	0.388856i	−0.00182162	−	0.0126696i
$943$	3.31046	−	0.972038i	0.107803	−	0.0316539i
$944$	−5.80140	−	1.70344i	−0.188819	−	0.0554424i
$945$	−0.174946	+	0.201898i	−0.00569099	+	0.00656775i
$946$	−3.37499	−	2.16897i	−0.109730	−	0.0705194i
$947$	−13.4411	+	15.5118i	−0.436776	+	0.504066i	−0.930874	−	0.365340i	$-0.880953\pi$
$947$	−13.4411	+	15.5118i	−0.436776	+	0.504066i	0.494098	+	0.869406i	$0.335498\pi$
$948$	0.147543	−	0.323075i	0.00479199	−	0.0104930i
$949$	16.6666	−	4.89374i	0.541019	−	0.158858i
$950$	−4.19207	+	2.69408i	−0.136009	+	0.0874075i
$951$	−0.595674	+	0.382816i	−0.0193160	+	0.0124137i
$952$	−2.08770	−	14.5203i	−0.0676629	−	0.470606i
$953$	13.2955	+	15.3439i	0.430684	+	0.497036i	0.929062	−	0.369924i	$-0.120616\pi$
$953$	13.2955	+	15.3439i	0.430684	+	0.497036i	−0.498378	+	0.866960i	$0.666071\pi$
$954$	28.7341	−	8.43710i	0.930302	−	0.273161i
$955$	2.14862	−	14.9440i	0.0695277	−	0.483576i
$956$	0.0626484	+	0.435729i	0.00202619	+	0.0140925i
$957$	0.139828	+	0.161370i	0.00451998	+	0.00521634i
$958$	−6.80351	−	14.8976i	−0.219811	−	0.481320i
$959$	−31.3370	−	9.20137i	−1.01192	−	0.297128i
$960$	−0.00970382	+	0.0212484i	−0.000313190	+	0.000685789i
$961$	−1.85168	−	4.05461i	−0.0597316	−	0.130794i
$962$	−6.65605	+	46.2939i	−0.214600	+	1.49257i
$963$	5.84613	−	3.75708i	0.188389	−	0.121070i
$964$	−3.45929	+	24.0599i	−0.111416	+	0.774917i
$965$	9.71274	+	2.85192i	0.312664	+	0.0918065i
$966$	0.0198876	+	0.0127810i	0.000639872	+	0.000411221i
$967$	−39.0952			−1.25722			−0.628608	−	0.777722i	$-0.716375\pi$
$967$	−39.0952			−1.25722			−0.628608	+	0.777722i	$0.716375\pi$
$968$	8.95148			0.287711
$969$	0.753574	+	0.484292i	0.0242083	+	0.0155577i
$970$	0.106689	−	0.233617i	0.00342559	−	0.00750099i
$971$	−18.8949	−	21.8058i	−0.606365	−	0.699782i	0.366693	−	0.930342i	$-0.380490\pi$
$971$	−18.8949	−	21.8058i	−0.606365	−	0.699782i	−0.973058	+	0.230559i	$0.925944\pi$
$972$	0.412922	+	0.476537i	0.0132445	+	0.0152849i
$973$	8.73581	−	19.1287i	0.280057	−	0.613240i
$974$	13.6784	+	8.79056i	0.438284	+	0.281668i
$975$	−0.140018			−0.00448416
$976$	−2.68100			−0.0858166
$977$	−14.5651	−	9.36043i	−0.465979	−	0.299467i	0.286503	−	0.958079i	$-0.407507\pi$
$977$	−14.5651	−	9.36043i	−0.465979	−	0.299467i	−0.752482	+	0.658613i	$0.771144\pi$
$978$	0.219720	+	0.0645156i	0.00702587	+	0.00206298i
$979$	1.45681	−	10.1324i	0.0465599	−	0.323831i
$980$	−2.83180	+	1.81989i	−0.0904586	+	0.0581342i
$981$	−1.11027	+	7.72209i	−0.0354482	+	0.246547i
$982$	−8.83055	−	19.3362i	−0.281794	−	0.617043i
$983$	0.924928	−	2.02531i	0.0295006	−	0.0645974i	−0.894308	−	0.447452i	$-0.852332\pi$
$983$	0.924928	−	2.02531i	0.0295006	−	0.0645974i	0.923809	+	0.382854i	$0.125059\pi$
$984$	0.145659	+	0.0427693i	0.00464343	+	0.00136343i
$985$	4.96104	+	10.8632i	0.158072	+	0.346129i
$986$	−32.1846	−	37.1430i	−1.02497	−	1.18287i
$987$	0.0667889	+	0.464527i	0.00212591	+	0.0147861i
$988$	−4.25084	+	29.5653i	−0.135237	+	0.940596i
$989$	−1.42784	+	0.419251i	−0.0454026	+	0.0133314i
$990$	−2.81133	−	3.24445i	−0.0893499	−	0.103115i
$991$	2.92199	+	20.3229i	0.0928201	+	0.645578i	0.982120	+	0.188254i	$0.0602829\pi$
$991$	2.92199	+	20.3229i	0.0928201	+	0.645578i	−0.889300	+	0.457324i	$0.848808\pi$
$992$	4.33410	−	2.78535i	0.137608	−	0.0884351i
$993$	−0.330339	+	0.212296i	−0.0104830	+	0.00673702i
$994$	29.1877	−	8.57029i	0.925778	−	0.271833i
$995$	−3.00230	+	6.57411i	−0.0951792	+	0.208413i
$996$	−0.206277	+	0.238056i	−0.00653613	+	0.00754309i
$997$	4.69528	+	3.01747i	0.148701	+	0.0955643i	0.612876	−	0.790179i	$-0.290013\pi$
$997$	4.69528	+	3.01747i	0.148701	+	0.0955643i	−0.464175	+	0.885744i	$0.653649\pi$
$998$	25.4410	−	29.3605i	0.805321	−	0.929390i
$999$	1.04920	+	0.308072i	0.0331952	+	0.00974698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.k.c.531.3	yes	50
67.40	even	11	inner	670.2.k.c.241.3	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.241.3	✓	50	67.40	even	11	inner
670.2.k.c.531.3	yes	50	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.00970382 - 0.0212484i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0224131 - 0.00658109i) q^{6} +(-1.24834 + 1.44066i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.96422 - 2.26684i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.00970382 - 0.0212484i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.0224131 - 0.00658109i) q^{6} +(-1.24834 + 1.44066i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(1.96422 - 2.26684i) q^{9} +(-0.415415 + 0.909632i) q^{10} +(-1.37329 + 0.403234i) q^{11} +(-0.0196511 + 0.0126290i) q^{12} +(5.04255 - 3.24065i) q^{13} +(0.271289 + 1.88686i) q^{14} +(0.0152971 + 0.0176538i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(1.09518 - 7.61716i) q^{17} +(-0.426867 - 2.96892i) q^{18} +(-3.26325 - 3.76599i) q^{19} +(0.415415 + 0.909632i) q^{20} +(0.0427253 + 0.0125453i) q^{21} +(-0.594570 + 1.30193i) q^{22} +(0.220543 + 0.482923i) q^{23} +(-0.00332438 + 0.0231216i) q^{24} +(0.841254 - 0.540641i) q^{25} +(0.853048 - 5.93308i) q^{26} +(-0.134467 - 0.0394829i) q^{27} +(1.60365 + 1.03060i) q^{28} +6.38650 q^{29} +0.0233593 q^{30} +(-4.33410 - 2.78535i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(0.0218943 + 0.0252673i) q^{33} +(-5.03948 - 5.81586i) q^{34} +(0.791889 - 1.73400i) q^{35} +(-2.52330 - 1.62163i) q^{36} -7.80267 q^{37} -4.98312 q^{38} +(-0.117791 - 0.0756994i) q^{39} +(0.959493 + 0.281733i) q^{40} +(0.924878 - 6.43267i) q^{41} +(0.0374602 - 0.0240742i) q^{42} +(-0.398910 + 2.77448i) q^{43} +(0.594570 + 1.30193i) q^{44} +(-1.24602 + 2.72840i) q^{45} +(0.509394 + 0.149572i) q^{46} +(4.37818 + 9.58687i) q^{47} +(0.0152971 + 0.0176538i) q^{48} +(0.479056 + 3.33191i) q^{49} +(0.142315 - 0.989821i) q^{50} +(-0.172480 + 0.0506447i) q^{51} +(-3.92529 - 4.53003i) q^{52} +(1.42090 + 9.88259i) q^{53} +(-0.117896 + 0.0757672i) q^{54} +(1.20406 - 0.773801i) q^{55} +(1.82904 - 0.537056i) q^{56} +(-0.0483554 + 0.105883i) q^{57} +(4.18227 - 4.82659i) q^{58} +(5.08648 + 3.26888i) q^{59} +(0.0152971 - 0.0176538i) q^{60} +(2.57240 + 0.755324i) q^{61} +(-4.94326 + 1.45147i) q^{62} +(0.813720 + 5.65954i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-3.92529 + 4.53003i) q^{65} +0.0334335 q^{66} +(5.57911 - 5.98945i) q^{67} -7.69549 q^{68} +(0.00812122 - 0.00937239i) q^{69} +(-0.791889 - 1.73400i) q^{70} +(-2.27105 - 15.7955i) q^{71} +(-2.87796 + 0.845044i) q^{72} +(2.78050 + 0.816428i) q^{73} +(-5.10966 + 5.89687i) q^{74} +(-0.0196511 - 0.0126290i) q^{75} +(-3.26325 + 3.76599i) q^{76} +(1.13341 - 2.48181i) q^{77} +(-0.134346 + 0.0394476i) q^{78} +(-12.7910 + 8.22027i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-1.28013 - 8.90353i) q^{81} +(-4.25582 - 4.91148i) q^{82} +(12.9384 - 3.79907i) q^{83} +(0.00633714 - 0.0440758i) q^{84} +(1.09518 + 7.61716i) q^{85} +(1.83558 + 2.11838i) q^{86} +(-0.0619734 - 0.135703i) q^{87} +(1.37329 + 0.403234i) q^{88} +(-2.97108 + 6.50577i) q^{89} +(1.24602 + 2.72840i) q^{90} +(-1.62613 + 11.3100i) q^{91} +(0.446621 - 0.287026i) q^{92} +(-0.0171270 + 0.119121i) q^{93} +(10.1124 + 2.96926i) q^{94} +(4.19207 + 2.69408i) q^{95} +0.0233593 q^{96} -0.256826 q^{97} +(2.83180 + 1.81989i) q^{98} +(-1.78338 + 3.90507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9	\( 50 q + 5 q^{2} - 2 q^{3} - 5 q^{4} - 5 q^{5} + 2 q^{6} - q^{7} + 5 q^{8} - q^{9} + 5 q^{10} - 12 q^{11} - 2 q^{12} + 24 q^{13} + 23 q^{14} - 2 q^{15} - 5 q^{16} + 31 q^{17} + q^{18} + 4 q^{19} - 5 q^{20} + 12 q^{21} + q^{22} + 27 q^{23} - 9 q^{24} - 5 q^{25} - 2 q^{26} - 14 q^{27} + 10 q^{28} - 36 q^{29} + 2 q^{30} - 13 q^{31} + 5 q^{32} - 42 q^{33} + 2 q^{34} + 21 q^{35} - q^{36} - 50 q^{37} - 26 q^{38} - 31 q^{39} + 5 q^{40} - 10 q^{41} + 21 q^{42} + 16 q^{43} - q^{44} - q^{45} + 17 q^{46} - 13 q^{47} - 2 q^{48} - 40 q^{49} + 5 q^{50} - 19 q^{51} - 20 q^{52} - 5 q^{53} + 47 q^{54} + 10 q^{55} + 12 q^{56} - 90 q^{57} - 8 q^{58} - 20 q^{59} - 2 q^{60} + 12 q^{61} + 13 q^{62} - 15 q^{63} - 5 q^{64} - 20 q^{65} + 20 q^{66} - 21 q^{67} - 24 q^{68} + 77 q^{69} - 21 q^{70} + 24 q^{71} + 12 q^{72} - 68 q^{73} - 16 q^{74} - 2 q^{75} + 4 q^{76} + 7 q^{77} + 53 q^{78} - 26 q^{79} - 5 q^{80} - 21 q^{81} + 21 q^{82} - 10 q^{83} + 12 q^{84} + 31 q^{85} - 27 q^{86} + 61 q^{87} + 12 q^{88} + 51 q^{89} + q^{90} - 10 q^{91} - 6 q^{92} - 38 q^{93} - 9 q^{94} + 15 q^{95} + 2 q^{96} + 72 q^{97} - 37 q^{98} - 32 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 2 * q^3 - 5 * q^4 - 5 * q^5 + 2 * q^6 - q^7 + 5 * q^8 - q^9 + 5 * q^10 - 12 * q^11 - 2 * q^12 + 24 * q^13 + 23 * q^14 - 2 * q^15 - 5 * q^16 + 31 * q^17 + q^18 + 4 * q^19 - 5 * q^20 + 12 * q^21 + q^22 + 27 * q^23 - 9 * q^24 - 5 * q^25 - 2 * q^26 - 14 * q^27 + 10 * q^28 - 36 * q^29 + 2 * q^30 - 13 * q^31 + 5 * q^32 - 42 * q^33 + 2 * q^34 + 21 * q^35 - q^36 - 50 * q^37 - 26 * q^38 - 31 * q^39 + 5 * q^40 - 10 * q^41 + 21 * q^42 + 16 * q^43 - q^44 - q^45 + 17 * q^46 - 13 * q^47 - 2 * q^48 - 40 * q^49 + 5 * q^50 - 19 * q^51 - 20 * q^52 - 5 * q^53 + 47 * q^54 + 10 * q^55 + 12 * q^56 - 90 * q^57 - 8 * q^58 - 20 * q^59 - 2 * q^60 + 12 * q^61 + 13 * q^62 - 15 * q^63 - 5 * q^64 - 20 * q^65 + 20 * q^66 - 21 * q^67 - 24 * q^68 + 77 * q^69 - 21 * q^70 + 24 * q^71 + 12 * q^72 - 68 * q^73 - 16 * q^74 - 2 * q^75 + 4 * q^76 + 7 * q^77 + 53 * q^78 - 26 * q^79 - 5 * q^80 - 21 * q^81 + 21 * q^82 - 10 * q^83 + 12 * q^84 + 31 * q^85 - 27 * q^86 + 61 * q^87 + 12 * q^88 + 51 * q^89 + q^90 - 10 * q^91 - 6 * q^92 - 38 * q^93 - 9 * q^94 + 15 * q^95 + 2 * q^96 + 72 * q^97 - 37 * q^98 - 32 * q^99

Introduction

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