LMFDB - Embedded newform 670.2.k.c.241.3

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			241.3
Character	$\chi$	$=$	670.241
Dual form			670.2.k.c.531.3

$q$-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 $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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	−0.912413	−	0.409272i	$-0.865783\pi$
$3$	−0.00970382	+	0.0212484i	−0.00560250	+	0.0122678i	0.906810	+	0.421539i	$0.138510\pi$
$4$	−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	0.469092	−	0.883149i	$-0.344581\pi$
$7$	−1.24834	−	1.44066i	−0.471826	−	0.544517i	−0.940919	+	0.338632i	$0.890036\pi$
$8$	−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	0.0680647	−	0.997681i	$-0.478318\pi$
$11$	−1.37329	−	0.403234i	−0.414063	−	0.121580i	−0.482127	+	0.876101i	$0.660136\pi$
$12$	−0.0196511	−	0.0126290i	−0.00567279	−	0.00364568i
$13$	5.04255	+	3.24065i	1.39855	+	0.898794i	0.999833	−	0.0182793i	$-0.00581882\pi$
$13$	5.04255	+	3.24065i	1.39855	+	0.898794i	0.398718	+	0.917074i	$0.369455\pi$
$14$	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	0.488470	+	0.872581i	$0.337555\pi$
$17$	1.09518	+	7.61716i	0.265621	+	1.84743i	−0.222849	+	0.974853i	$0.571536\pi$
$18$	−0.426867	+	2.96892i	−0.100613	+	0.699782i
$19$	−3.26325	+	3.76599i	−0.748641	+	0.863978i	−0.994436	−	0.105344i	$-0.966406\pi$
$19$	−3.26325	+	3.76599i	−0.748641	+	0.863978i	0.245794	+	0.969322i	$0.420951\pi$
$20$	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	−0.885244	−	0.465126i	$-0.846009\pi$
$23$	0.220543	−	0.482923i	0.0459865	−	0.100696i	0.931231	+	0.364430i	$0.118736\pi$
$24$	−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	−0.868511	−	0.495670i	$-0.834923\pi$
$31$	−4.33410	+	2.78535i	−0.778427	+	0.500264i	0.0900846	+	0.995934i	$0.471286\pi$
$32$	−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	0.925118	+	0.379679i	$0.123965\pi$
$41$	0.924878	+	6.43267i	0.144442	+	1.00461i	−0.780677	+	0.624935i	$0.785125\pi$
$42$	0.0374602	+	0.0240742i	0.00578023	+	0.00371473i
$43$	−0.398910	−	2.77448i	−0.0608332	−	0.423104i	−0.997367	−	0.0725258i	$-0.976894\pi$
$43$	−0.398910	−	2.77448i	−0.0608332	−	0.423104i	0.936533	−	0.350579i	$-0.114015\pi$
$44$	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	−0.262546	−	0.964920i	$-0.584562\pi$
$47$	4.37818	−	9.58687i	0.638623	−	1.39839i	0.901168	−	0.433469i	$-0.142711\pi$
$48$	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	−0.622870	−	0.782326i	$-0.714033\pi$
$53$	1.42090	−	9.88259i	0.195176	−	1.35748i	0.818046	−	0.575153i	$-0.195058\pi$
$54$	−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	−0.165904	−	0.986142i	$-0.553054\pi$
$59$	5.08648	−	3.26888i	0.662204	−	0.425573i	0.828107	+	0.560569i	$0.189418\pi$
$60$	0.0152971	+	0.0176538i	0.00197485	+	0.00227910i
$61$	2.57240	−	0.755324i	0.329362	−	0.0967094i	−0.112871	−	0.993610i	$-0.536005\pi$
$61$	2.57240	−	0.755324i	0.329362	−	0.0967094i	0.442233	+	0.896900i	$0.354186\pi$
$62$	−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	0.183412	+	0.983036i	$0.441286\pi$
$71$	−2.27105	+	15.7955i	−0.269524	+	1.87458i	−0.452936	+	0.891543i	$0.649623\pi$
$72$	−2.87796	−	0.845044i	−0.339170	−	0.0995894i
$73$	2.78050	−	0.816428i	0.325433	−	0.0955557i	−0.114935	−	0.993373i	$-0.536666\pi$
$73$	2.78050	−	0.816428i	0.325433	−	0.0955557i	0.440368	+	0.897817i	$0.354848\pi$
$74$	−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	−0.999647	−	0.0265859i	$-0.991536\pi$
$79$	−12.7910	−	8.22027i	−1.43910	−	0.924852i	−0.439452	−	0.898266i	$-0.644827\pi$
$80$	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	0.899564	−	0.436789i	$-0.143884\pi$
$83$	12.9384	+	3.79907i	1.42018	+	0.417002i	0.520615	+	0.853791i	$0.325703\pi$
$84$	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	0.684281	−	0.729218i	$-0.260116\pi$
$89$	−2.97108	−	6.50577i	−0.314934	−	0.689610i	−0.999215	+	0.0396085i	$0.987389\pi$
$90$	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	−0.989202	−	0.146560i	$-0.953180\pi$
$101$	−7.06864	+	8.15765i	−0.703356	+	0.811716i	0.285846	+	0.958276i	$0.407725\pi$
$102$	−0.0746757	−	0.163517i	−0.00739399	−	0.0161906i
$103$	11.0971	−	7.13168i	1.09343	−	0.702705i	0.135809	−	0.990735i	$-0.456637\pi$
$103$	11.0971	−	7.13168i	1.09343	−	0.702705i	0.957621	+	0.288030i	$0.0930002\pi$
$104$	−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	−0.172507	−	0.985008i	$-0.555187\pi$
$107$	2.22301	−	0.652735i	0.214906	−	0.0631022i	0.387414	+	0.921906i	$0.373369\pi$
$108$	−0.0199445	−	0.138717i	−0.00191916	−	0.0133480i
$109$	−2.18808	−	1.40619i	−0.209580	−	0.134689i	0.431640	−	0.902046i	$-0.357935\pi$
$109$	−2.18808	−	1.40619i	−0.209580	−	0.134689i	−0.641220	+	0.767357i	$0.721571\pi$
$110$	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	−0.312136	−	0.950037i	$-0.601044\pi$
$113$	−0.649424	+	0.190688i	−0.0610927	+	0.0179384i	0.251043	+	0.967976i	$0.419226\pi$
$114$	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	0.953785	−	0.300490i	$-0.0971501\pi$
$127$	5.86705	+	6.77093i	0.520616	+	0.600823i	−0.433169	+	0.901313i	$0.642605\pi$
$128$	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	−0.888031	−	0.459783i	$-0.847927\pi$
$131$	0.469108	−	1.02720i	0.0409861	−	0.0897471i	0.929018	+	0.370036i	$0.120655\pi$
$132$	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	−0.315812	−	0.948822i	$-0.602277\pi$
$137$	7.11730	−	15.5847i	0.608072	−	1.33149i	0.923885	−	0.382671i	$-0.124996\pi$
$138$	−0.00176491	+	0.0122752i	−0.000150239	+	0.00104494i
$139$	−10.5847	−	3.10796i	−0.897786	−	0.263614i	−0.199895	−	0.979817i	$-0.564060\pi$
$139$	−10.5847	−	3.10796i	−0.897786	−	0.263614i	−0.697891	+	0.716204i	$0.745878\pi$
$140$	−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	−0.808796	−	0.588090i	$-0.799880\pi$
$149$	−1.36211	+	1.57196i	−0.111588	+	0.128780i	0.697207	+	0.716869i	$0.254426\pi$
$150$	−0.0224131	−	0.00658109i	−0.00183002	−	0.000537344i
$151$	0.214538	+	1.49214i	0.0174588	+	0.121429i	0.996687	−	0.0813325i	$-0.0259176\pi$
$151$	0.214538	+	1.49214i	0.0174588	+	0.121429i	−0.979228	+	0.202761i	$0.935008\pi$
$152$	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	−0.395577	−	0.918433i	$-0.629455\pi$
$157$	6.98641	−	15.2981i	0.557576	−	1.22092i	0.953153	−	0.302488i	$-0.0978173\pi$
$158$	−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	−0.740241	−	0.672342i	$-0.765288\pi$
$167$	0.395506	−	0.456438i	0.0306052	−	0.0353202i	0.770846	+	0.637022i	$0.219834\pi$
$168$	−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	0.497125	−	0.867679i	$-0.334389\pi$
$173$	19.6361	−	12.6194i	1.49291	−	0.959433i	0.995782	−	0.0917543i	$-0.0292474\pi$
$174$	−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	0.992759	−	0.120125i	$-0.0383296\pi$
$179$	3.36960	+	7.37839i	0.251856	+	0.551487i	−0.740903	+	0.671612i	$0.765602\pi$
$180$	2.87796	−	0.845044i	0.214510	−	0.0629859i
$181$	4.75940	−	10.4216i	0.353763	−	0.774634i	−0.646171	−	0.763193i	$-0.723631\pi$
$181$	4.75940	−	10.4216i	0.353763	−	0.774634i	0.999935	−	0.0114413i	$-0.00364194\pi$
$182$	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	−0.988855	−	0.148883i	$-0.952432\pi$
$191$	−6.27179	−	13.7333i	−0.453811	−	0.993707i	0.535044	−	0.844824i	$-0.320295\pi$
$192$	0.0152971	+	0.0176538i	0.00110397	+	0.00127405i
$193$	−8.51583	+	5.47279i	−0.612983	+	0.393940i	−0.809974	−	0.586465i	$-0.800519\pi$
$193$	−8.51583	+	5.47279i	−0.612983	+	0.393940i	0.196992	+	0.980405i	$0.436883\pi$
$194$	−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	0.835235	+	0.549893i	$0.185331\pi$
$197$	−1.69958	+	11.8208i	−0.121090	+	0.842198i	−0.956325	+	0.292305i	$0.905578\pi$
$198$	1.78338	−	3.90507i	0.126740	−	0.277521i
$199$	4.73283	+	5.46197i	0.335501	+	0.387189i	0.898284	−	0.439416i	$-0.144815\pi$
$199$	4.73283	+	5.46197i	0.335501	+	0.387189i	−0.562783	+	0.826605i	$0.690269\pi$
$200$	−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	0.999865	−	0.0164123i	$-0.00522442\pi$
$211$	4.83259	+	10.5819i	0.332689	+	0.728488i	−0.667176	+	0.744900i	$0.732497\pi$
$212$	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	−0.832022	−	0.554743i	$-0.812817\pi$
$223$	−10.5489	−	23.0990i	−0.706410	−	1.54682i	0.125612	−	0.992079i	$-0.459911\pi$
$224$	−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	−0.968212	−	0.250131i	$-0.919526\pi$
$227$	−1.65264	−	11.4944i	−0.109689	−	0.762907i	0.858523	−	0.512776i	$-0.171383\pi$
$228$	0.111687	−	0.0327944i	0.00739668	−	0.00217186i
$229$	20.1432	−	12.9452i	1.33110	−	0.855445i	0.334874	−	0.942263i	$-0.391306\pi$
$229$	20.1432	−	12.9452i	1.33110	−	0.855445i	0.996224	+	0.0868180i	$0.0276699\pi$
$230$	−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	0.822661	−	0.568532i	$-0.192489\pi$
$233$	−2.22456	−	4.87110i	−0.145736	−	0.319116i	−0.968396	+	0.249416i	$0.919761\pi$
$234$	−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	−0.926457	−	0.376400i	$-0.877162\pi$
$241$	−23.3227	+	6.84816i	−1.50235	+	0.441128i	−0.575888	+	0.817528i	$0.695344\pi$
$242$	−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	−0.813660	−	0.581342i	$-0.802528\pi$
$251$	−3.11698	−	21.6790i	−0.196742	−	1.36837i	0.616918	−	0.787028i	$-0.288381\pi$
$252$	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	0.448721	−	0.893672i	$-0.351880\pi$
$257$	5.49958	+	1.61482i	0.343054	+	0.100730i	−0.105667	+	0.994402i	$0.533698\pi$
$258$	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	0.988470	−	0.151414i	$-0.0483826\pi$
$263$	28.1883	+	8.27683i	1.73816	+	0.510371i	0.749694	+	0.661785i	$0.230201\pi$
$264$	−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	−0.982665	−	0.185391i	$-0.940645\pi$
$271$	−3.27673	+	7.17503i	−0.199047	+	0.435852i	0.783618	+	0.621243i	$0.213372\pi$
$272$	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	0.772493	−	0.635023i	$-0.219009\pi$
$277$	0.565819	+	0.652990i	0.0339968	+	0.0392343i	−0.738497	+	0.674257i	$0.764464\pi$
$278$	−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	0.185620	−	0.982622i	$-0.440571\pi$
$281$	−10.5791	−	6.79877i	−0.631095	−	0.405580i	−0.816715	+	0.577041i	$0.804207\pi$
$282$	−0.0350366	+	0.243685i	−0.00208640	+	0.0145112i
$283$	11.2958	−	13.0360i	0.671463	−	0.774910i	−0.313141	−	0.949707i	$-0.601381\pi$
$283$	11.2958	−	13.0360i	0.671463	−	0.774910i	0.984605	+	0.174797i	$0.0559268\pi$
$284$	−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	0.970893	+	0.239513i	$0.0769877\pi$
$293$	27.2521	+	17.5139i	1.59209	+	1.02317i	0.621192	+	0.783658i	$0.286649\pi$
$294$	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	−0.967984	−	0.251011i	$-0.919237\pi$
$307$	−20.0055	+	12.8567i	−1.14177	+	0.733772i	−0.173788	+	0.984783i	$0.555601\pi$
$308$	−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	−0.820432	−	0.571745i	$-0.806267\pi$
$311$	−3.42674	−	23.8335i	−0.194312	−	1.35147i	0.626119	−	0.779727i	$-0.284642\pi$
$312$	0.0581656	−	0.127365i	0.00329298	−	0.00721061i
$313$	2.52327	+	5.52519i	0.142624	+	0.312302i	0.967441	−	0.253097i	$-0.0814493\pi$
$313$	2.52327	+	5.52519i	0.142624	+	0.312302i	−0.824817	+	0.565399i	$0.808722\pi$
$314$	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	0.398259	+	0.917273i	$0.369614\pi$
$317$	−4.31391	+	30.0039i	−0.242293	+	1.68519i	−0.640553	+	0.767914i	$0.721295\pi$
$318$	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	0.812113	+	0.583501i	$0.198317\pi$
$331$	−2.39234	+	16.6391i	−0.131495	+	0.914567i	−0.943607	+	0.331066i	$0.892592\pi$
$332$	−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	0.557922	−	0.829894i	$-0.311599\pi$
$337$	−6.29528	−	7.26514i	−0.342926	−	0.395757i	−0.900847	+	0.434137i	$0.857054\pi$
$338$	−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	0.646315	−	0.763071i	$-0.276309\pi$
$347$	4.11100	+	2.64198i	0.220690	+	0.141829i	−0.425625	+	0.904900i	$0.639946\pi$
$348$	−0.125502	−	0.0806552i	−0.00672761	−	0.00432357i
$349$	2.01499	−	14.0146i	0.107860	−	0.750184i	−0.862068	−	0.506793i	$-0.830831\pi$
$349$	2.01499	−	14.0146i	0.107860	−	0.750184i	0.969928	−	0.243391i	$-0.0782599\pi$
$350$	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	0.797385	+	0.603471i	$0.206216\pi$
$353$	−2.58748	+	17.9963i	−0.137718	+	0.957847i	−0.935103	+	0.354376i	$0.884693\pi$
$354$	−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	0.633146	+	0.774032i	$0.281763\pi$
$359$	4.61778	+	32.1173i	0.243717	+	1.69509i	−0.389430	+	0.921056i	$0.627328\pi$
$360$	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	0.931366	+	0.364084i	$0.118618\pi$
$367$	11.4294	+	25.0268i	0.596607	+	1.30639i	−0.334759	+	0.942304i	$0.608655\pi$
$368$	−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	−0.988267	−	0.152734i	$-0.951192\pi$
$379$	−4.39315	+	9.61966i	−0.225661	+	0.494129i	0.762606	+	0.646863i	$0.223919\pi$
$380$	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	−0.660522	−	0.750807i	$-0.729665\pi$
$383$	3.45702	−	3.98961i	0.176645	−	0.203860i	0.837167	+	0.546947i	$0.184210\pi$
$384$	−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	0.825978	−	0.563703i	$-0.190624\pi$
$389$	12.9450	+	8.31926i	0.656339	+	0.421803i	−0.169639	+	0.985506i	$0.554260\pi$
$390$	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	−0.461567	−	0.887105i	$-0.652713\pi$
$397$	−26.4894	−	7.77800i	−1.32947	−	0.390367i	−0.867900	+	0.496739i	$0.834531\pi$
$398$	−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	0.563970	−	0.825795i	$-0.309273\pi$
$409$	−6.74828	−	7.78793i	−0.333681	−	0.385088i	−0.897651	+	0.440707i	$0.854728\pi$
$410$	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	0.824858	+	0.565340i	$0.191255\pi$
$419$	3.94421	+	27.4326i	0.192687	+	1.34017i	−0.632171	+	0.774829i	$0.717836\pi$
$420$	0.00633714	−	0.0440758i	0.000309221	−	0.00215068i
$421$	5.14397	−	5.93645i	0.250702	−	0.289325i	−0.616424	−	0.787414i	$-0.711419\pi$
$421$	5.14397	−	5.93645i	0.250702	−	0.289325i	0.867126	+	0.498089i	$0.165965\pi$
$422$	−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	−0.455129	−	0.890425i	$-0.650407\pi$
$433$	3.44930	−	2.21673i	0.165763	−	0.106529i	0.620892	+	0.783896i	$0.286771\pi$
$434$	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	−0.726100	−	0.687589i	$-0.758669\pi$
$443$	−4.69631	−	32.6635i	−0.223128	−	1.55189i	0.502972	−	0.864303i	$-0.332240\pi$
$444$	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	−0.712041	−	0.702138i	$-0.752229\pi$
$449$	6.03666	−	13.2184i	0.284888	−	0.623817i	0.996928	+	0.0783215i	$0.0249561\pi$
$450$	−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	0.144487	−	0.989507i	$-0.453847\pi$
$457$	−14.8698	−	9.55621i	−0.695578	−	0.447021i	−0.840065	+	0.542486i	$0.817483\pi$
$458$	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	−0.575777	−	0.817607i	$-0.695300\pi$
$461$	−1.52962	+	0.983028i	−0.0712416	+	0.0457842i	0.504535	+	0.863391i	$0.331664\pi$
$462$	−0.0417362	−	0.0481661i	−0.00194174	−	0.00224089i
$463$	−18.9287	+	5.55797i	−0.879692	+	0.258301i	−0.690233	−	0.723588i	$-0.742492\pi$
$463$	−18.9287	+	5.55797i	−0.879692	+	0.258301i	−0.189460	+	0.981889i	$0.560674\pi$
$464$	−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	0.244086	−	0.969754i	$-0.421512\pi$
$467$	−16.2192	−	18.7179i	−0.750534	−	0.866162i	−0.994620	+	0.103591i	$0.966967\pi$
$468$	−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	0.998992	−	0.0448973i	$-0.0142961\pi$
$479$	6.80351	+	14.8976i	0.310860	+	0.680689i	−0.688132	+	0.725586i	$0.741569\pi$
$480$	−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	−0.867779	−	0.496951i	$-0.834453\pi$
$487$	2.31397	−	16.0940i	0.104856	−	0.729290i	0.972635	−	0.232339i	$-0.0746379\pi$
$488$	−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	0.997418	+	0.0718081i	$0.0228769\pi$
$491$	8.83055	+	19.3362i	0.398517	+	0.872631i	−0.598901	+	0.800823i	$0.704396\pi$
$492$	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	−0.393996	−	0.919112i	$-0.628908\pi$
$503$	12.8249	−	14.8007i	0.571832	−	0.659929i	0.965828	+	0.259183i	$0.0834532\pi$
$504$	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	−0.0561303	−	0.998423i	$-0.517876\pi$
$509$	9.84650	−	2.89119i	0.436438	−	0.128150i	0.492569	+	0.870274i	$0.336058\pi$
$510$	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	−0.754397	−	0.656419i	$-0.772070\pi$
$521$	0.0616937	−	0.0711983i	0.00270285	−	0.00311925i	0.757099	+	0.653300i	$0.226616\pi$
$522$	−2.72618	+	18.9610i	−0.119322	+	0.829901i
$523$	28.7408	+	18.4706i	1.25675	+	0.807662i	0.987835	−	0.155503i	$-0.0497000\pi$
$523$	28.7408	+	18.4706i	1.25675	+	0.807662i	0.268911	+	0.963165i	$0.413336\pi$
$524$	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	0.812763	−	0.582594i	$-0.197962\pi$
$541$	27.4817	+	8.06935i	1.18153	+	0.346928i	0.368766	+	0.929522i	$0.379780\pi$
$542$	−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	0.516223	−	0.856454i	$-0.327338\pi$
$547$	11.4008	+	3.34757i	0.487463	+	0.143132i	−0.0287601	+	0.999586i	$0.509156\pi$
$548$	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	0.0561389	−	0.998423i	$-0.482121\pi$
$557$	15.1790	−	4.45695i	0.643154	−	0.188847i	0.587015	+	0.809576i	$0.300303\pi$
$558$	−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	0.253411	−	0.967359i	$-0.418447\pi$
$563$	23.4806	−	6.89452i	0.989588	−	0.290569i	0.736177	+	0.676789i	$0.236629\pi$
$564$	−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	−0.990789	−	0.135415i	$-0.956763\pi$
$569$	−17.0733	+	19.7036i	−0.715748	+	0.826018i	0.275041	+	0.961433i	$0.411309\pi$
$570$	−0.0762274	+	0.0879712i	−0.00319282	+	0.00368471i
$571$	−16.4722	−	36.0690i	−0.689338	−	1.50944i	−0.852437	−	0.522831i	$-0.824876\pi$
$571$	−16.4722	−	36.0690i	−0.689338	−	1.50944i	0.163098	−	0.986610i	$-0.447851\pi$
$572$	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	−0.952830	−	0.303504i	$-0.901843\pi$
$577$	−2.98106	−	20.7338i	−0.124103	−	0.863158i	0.828727	−	0.559653i	$-0.189066\pi$
$578$	−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	0.810589	−	0.585616i	$-0.199147\pi$
$587$	28.4896	+	8.36530i	1.17589	+	0.345273i	0.365303	+	0.930889i	$0.380966\pi$
$588$	−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	0.910557	−	0.413385i	$-0.135653\pi$
$593$	0.0451383	+	0.0988391i	0.00185361	+	0.00405884i	−0.908703	+	0.417443i	$0.862926\pi$
$594$	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	−0.716035	−	0.698064i	$-0.754045\pi$
$599$	4.10346	−	28.5402i	0.167663	−	1.16612i	0.883698	−	0.468057i	$-0.155046\pi$
$600$	0.00970382	−	0.0212484i	0.000396157	−	0.000867463i
$601$	3.39815	+	3.92167i	0.138613	+	0.159968i	0.820812	−	0.571199i	$-0.193521\pi$
$601$	3.39815	+	3.92167i	0.138613	+	0.159968i	−0.682199	+	0.731167i	$0.738976\pi$
$602$	−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	0.900581	+	0.434688i	$0.143141\pi$
$607$	−2.11847	+	14.7343i	−0.0859860	+	0.598046i	−0.986567	+	0.163357i	$0.947768\pi$
$608$	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	−0.845576	−	0.533855i	$-0.820743\pi$
$613$	−17.2149	−	37.6953i	−0.695302	−	1.52250i	0.150274	−	0.988644i	$-0.451984\pi$
$614$	−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	−0.839511	−	0.543343i	$-0.817158\pi$
$617$	2.95767	−	20.5711i	0.119071	−	0.828159i	0.958582	−	0.284816i	$-0.0919326\pi$
$618$	−0.201787	+	0.232874i	−0.00811705	+	0.00936758i
$619$	−27.1439	−	7.97018i	−1.09101	−	0.320349i	−0.313733	−	0.949511i	$-0.601580\pi$
$619$	−27.1439	−	7.97018i	−1.09101	−	0.320349i	−0.777274	+	0.629163i	$0.783398\pi$
$620$	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	−0.954204	−	0.299158i	$-0.903294\pi$
$631$	−27.0909	+	17.4103i	−1.07847	+	0.693091i	−0.124267	+	0.992249i	$0.539658\pi$
$632$	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	−0.243850	−	0.969813i	$-0.578410\pi$
$643$	1.91021	−	0.560889i	0.0753315	−	0.0221193i	0.319181	+	0.947694i	$0.396592\pi$
$644$	−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	−0.210692	−	0.977553i	$-0.567572\pi$
$647$	16.9422	−	37.0983i	0.666067	−	1.45848i	0.876759	−	0.480930i	$-0.159701\pi$
$648$	−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	−0.879874	−	0.475208i	$-0.842373\pi$
$653$	−4.33196	−	30.1294i	−0.169523	−	1.17906i	0.710351	−	0.703848i	$-0.248536\pi$
$654$	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	0.596630	−	0.802516i	$-0.296506\pi$
$659$	17.0629	+	5.01011i	0.664675	+	0.195166i	0.0680444	+	0.997682i	$0.478324\pi$
$660$	−0.0138888	−	0.0304121i	−0.000540619	−	0.00118379i
$661$	14.1796	+	16.3641i	0.551523	+	0.636492i	0.961237	−	0.275722i	$-0.0889170\pi$
$661$	14.1796	+	16.3641i	0.551523	+	0.636492i	−0.409714	+	0.912214i	$0.634372\pi$
$662$	−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	0.600622	+	0.799533i	$0.294920\pi$
$673$	−10.2977	+	22.5489i	−0.396949	+	0.869196i	−0.997571	+	0.0696631i	$0.977808\pi$
$674$	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	0.294974	−	0.955505i	$-0.404689\pi$
$677$	−18.0257	−	20.8028i	−0.692784	−	0.799516i	−0.987759	+	0.155989i	$0.950143\pi$
$678$	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	0.113483	−	0.993540i	$-0.463799\pi$
$683$	−19.4212	−	12.4812i	−0.743130	−	0.477581i	−0.856613	+	0.515959i	$0.827436\pi$
$684$	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	0.152710	−	0.988271i	$-0.451200\pi$
$691$	21.4363	−	6.29428i	0.815477	−	0.239446i	0.662767	+	0.748826i	$0.269382\pi$
$692$	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	0.00501725	−	0.999987i	$-0.498403\pi$
$701$	24.2715	−	15.5983i	0.916722	−	0.589141i	0.911705	+	0.410846i	$0.134767\pi$
$702$	−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	0.120277	−	0.992740i	$-0.461622\pi$
$709$	28.5780	−	18.3660i	1.07327	−	0.689749i	0.952993	+	0.302992i	$0.0979855\pi$
$710$	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	−0.993096	−	0.117301i	$-0.962576\pi$
$719$	−0.192524	+	1.33904i	−0.00717995	+	0.0499376i	0.985916	+	0.167238i	$0.0534849\pi$
$720$	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	0.976967	+	0.213389i	$0.0684502\pi$
$727$	13.4399	+	29.4293i	0.498458	+	1.09147i	−0.478509	+	0.878083i	$0.658823\pi$
$728$	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	−0.952928	−	0.303196i	$-0.901946\pi$
$733$	1.26760	−	8.81636i	0.0468199	−	0.325640i	0.999748	−	0.0224436i	$-0.00714461\pi$
$734$	−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	0.765836	−	0.643036i	$-0.222325\pi$
$739$	0.553358	+	0.638609i	0.0203556	+	0.0234916i	−0.745480	+	0.666527i	$0.767780\pi$
$740$	−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	−0.916497	−	0.400041i	$-0.868996\pi$
$743$	−40.1027	+	11.7752i	−1.47123	+	0.431991i	−0.554728	+	0.832032i	$0.687178\pi$
$744$	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	−0.590745	−	0.806858i	$-0.701166\pi$
$751$	5.57375	−	38.7663i	0.203389	−	1.41460i	0.794134	−	0.607743i	$-0.207925\pi$
$752$	−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	0.551272	+	0.834325i	$0.314143\pi$
$757$	−12.1136	+	26.5250i	−0.440275	+	0.964069i	−0.991548	+	0.129743i	$0.958585\pi$
$758$	−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	−0.991443	−	0.130537i	$-0.958330\pi$
$761$	−2.12240	−	14.7616i	−0.0769368	−	0.535107i	0.914507	−	0.404571i	$-0.132579\pi$
$762$	−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	−0.937932	−	0.346819i	$-0.887262\pi$
$769$	−16.2454	−	35.5725i	−0.585825	−	1.28278i	0.352107	−	0.935960i	$-0.385465\pi$
$770$	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	−0.930570	−	0.366115i	$-0.880688\pi$
$773$	−27.3612	+	17.5840i	−0.984113	+	0.632451i	−0.0535431	+	0.998566i	$0.517051\pi$
$774$	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	0.998243	+	0.0592522i	$0.0188716\pi$
$787$	1.60267	+	11.1468i	0.0571291	+	0.397342i	−0.941114	+	0.338090i	$0.890219\pi$
$788$	−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	0.503661	−	0.863902i	$-0.331986\pi$
$797$	−11.9453	−	13.7857i	−0.423126	−	0.488313i	−0.926787	+	0.375588i	$0.877441\pi$
$798$	−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	−0.440159	−	0.897920i	$-0.645078\pi$
$809$	−36.8591	−	10.8228i	−1.29590	−	0.380509i	−0.855737	+	0.517411i	$0.826896\pi$
$810$	8.63073	−	2.53421i	0.303253	−	0.0890430i
$811$	−23.9155	−	27.6000i	−0.839788	−	0.969167i	0.160051	−	0.987109i	$-0.448834\pi$
$811$	−23.9155	−	27.6000i	−0.839788	−	0.969167i	−0.999839	+	0.0179418i	$0.994289\pi$
$812$	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	0.966737	+	0.255773i	$0.0823300\pi$
$821$	3.18678	+	22.1645i	0.111219	+	0.773547i	−0.855518	+	0.517774i	$0.826761\pi$
$822$	−0.0569566	+	0.396142i	−0.00198659	+	0.0138170i
$823$	−27.4190	+	31.6432i	−0.955767	+	1.10301i	0.0388349	+	0.999246i	$0.487635\pi$
$823$	−27.4190	+	31.6432i	−0.955767	+	1.10301i	−0.994602	+	0.103768i	$0.966910\pi$
$824$	−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	−0.642314	−	0.766442i	$-0.722025\pi$
$827$	10.2823	−	22.5151i	0.357550	−	0.782926i	0.999864	−	0.0164842i	$-0.00524733\pi$
$828$	0.226623	+	1.57620i	0.00787570	+	0.0547767i
$829$	3.36819	+	2.16460i	0.116982	+	0.0751798i	0.597824	−	0.801628i	$-0.296032\pi$
$829$	3.36819	+	2.16460i	0.116982	+	0.0751798i	−0.480841	+	0.876808i	$0.659669\pi$
$830$	−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	0.935200	−	0.354119i	$-0.115219\pi$
$839$	1.59742	+	3.49786i	0.0551490	+	0.120760i	−0.880051	+	0.474879i	$0.842492\pi$
$840$	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	0.913915	+	0.405906i	$0.133044\pi$
$853$	−2.25872	+	15.7097i	−0.0773370	+	0.537890i	−0.991252	+	0.131984i	$0.957865\pi$
$854$	−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	0.752944	+	0.658084i	$0.228633\pi$
$857$	−4.53475	+	31.5399i	−0.154904	+	1.07738i	−0.907848	+	0.419298i	$0.862276\pi$
$858$	0.168590	+	0.108346i	0.00575556	+	0.00369887i
$859$	2.12209	+	1.36379i	0.0724048	+	0.0465318i	0.576342	−	0.817208i	$-0.304479\pi$
$859$	2.12209	+	1.36379i	0.0724048	+	0.0465318i	−0.503938	+	0.863740i	$0.668116\pi$
$860$	−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	−0.119551	−	0.992828i	$-0.538145\pi$
$863$	21.5595	−	13.8555i	0.733894	−	0.471645i	0.853445	+	0.521183i	$0.174509\pi$
$864$	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	−0.629401	−	0.777081i	$-0.716700\pi$
$877$	−21.8779	+	6.42394i	−0.738765	+	0.216921i	−0.109364	+	0.994002i	$0.534881\pi$
$878$	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	0.812050	+	0.583587i	$0.198351\pi$
$881$	21.4099	+	46.8810i	0.721316	+	1.57946i	−0.0907338	+	0.995875i	$0.528921\pi$
$882$	9.68769	+	2.84456i	0.326201	+	0.0957814i
$883$	17.6809	+	11.3628i	0.595010	+	0.382390i	0.803209	−	0.595697i	$-0.203124\pi$
$883$	17.6809	+	11.3628i	0.595010	+	0.382390i	−0.208200	+	0.978086i	$0.566760\pi$
$884$	−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	−0.398558	−	0.917143i	$-0.630489\pi$
$887$	−36.6234	−	10.7536i	−1.22969	−	0.361070i	−0.831134	+	0.556073i	$0.812308\pi$
$888$	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	−0.884135	−	0.467231i	$-0.845252\pi$
$907$	−24.8885	+	15.9949i	−0.826410	+	0.531102i	0.0577250	+	0.998333i	$0.481615\pi$
$908$	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	−0.962811	−	0.270177i	$-0.912918\pi$
$911$	−49.0986	+	14.4167i	−1.62671	+	0.477645i	−0.663899	+	0.747822i	$0.731100\pi$
$912$	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	−0.902256	−	0.431202i	$-0.858090\pi$
$919$	−10.5205	+	12.1413i	−0.347039	+	0.400504i	0.555217	+	0.831706i	$0.312635\pi$
$920$	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	0.343934	−	0.938994i	$-0.388240\pi$
$929$	−19.3377	−	22.3169i	−0.634449	−	0.732193i	−0.978383	+	0.206801i	$0.933695\pi$
$930$	−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	−0.936393	−	0.350953i	$-0.885858\pi$
$941$	−1.77775	+	3.89274i	−0.0579531	+	0.126900i	0.878440	+	0.477853i	$0.158585\pi$
$942$	−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	0.494098	−	0.869406i	$-0.335498\pi$
$947$	−13.4411	−	15.5118i	−0.436776	−	0.504066i	−0.930874	+	0.365340i	$0.880953\pi$
$948$	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	−0.498378	−	0.866960i	$-0.666071\pi$
$953$	13.2955	−	15.3439i	0.430684	−	0.497036i	0.929062	+	0.369924i	$0.120616\pi$
$954$	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	−0.973058	−	0.230559i	$-0.925944\pi$
$971$	−18.8949	+	21.8058i	−0.606365	+	0.699782i	0.366693	+	0.930342i	$0.380490\pi$
$972$	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	−0.752482	−	0.658613i	$-0.771144\pi$
$977$	−14.5651	+	9.36043i	−0.465979	+	0.299467i	0.286503	+	0.958079i	$0.407507\pi$
$978$	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	0.923809	−	0.382854i	$-0.125059\pi$
$983$	0.924928	+	2.02531i	0.0295006	+	0.0645974i	−0.894308	+	0.447452i	$0.852332\pi$
$984$	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	−0.889300	−	0.457324i	$-0.848808\pi$
$991$	2.92199	−	20.3229i	0.0928201	−	0.645578i	0.982120	−	0.188254i	$-0.0602829\pi$
$992$	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	−0.464175	−	0.885744i	$-0.653649\pi$
$997$	4.69528	−	3.01747i	0.148701	−	0.0955643i	0.612876	+	0.790179i	$0.290013\pi$
$998$	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.241.3	✓	50
67.62	even	11	inner	670.2.k.c.531.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.k.c.241.3	✓	50	1.1	even	1	trivial
670.2.k.c.531.3	yes	50	67.62	even	11	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
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

L-functions

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