LMFDB - Embedded newform 46.2.c.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,2,Mod(3,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("46.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	46.c (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:	$0.367311849298$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Root			$0.654861 + 0.755750i$ of defining polynomial
Character	$\chi$	$=$	46.13
Dual form			46.2.c.b.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{2} +(-0.512546 - 0.329393i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.154861 - 0.339098i) q^{5} +(-0.0867074 - 0.603063i) q^{6} +(-1.97611 - 0.580239i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.09204 - 2.39124i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{2} +(-0.512546 - 0.329393i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.154861 - 0.339098i) q^{5} +(-0.0867074 - 0.603063i) q^{6} +(-1.97611 - 0.580239i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.09204 - 2.39124i) q^{9} +(0.357685 - 0.105026i) q^{10} +(-1.61435 + 1.86306i) q^{11} +(0.398983 - 0.460451i) q^{12} +(3.58149 - 1.05162i) q^{13} +(-0.855563 - 1.87342i) q^{14} +(-0.191070 + 0.122793i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.897877 + 6.24487i) q^{17} +(1.09204 - 2.39124i) q^{18} +(0.468056 - 3.25540i) q^{19} +(0.313607 + 0.201543i) q^{20} +(0.821721 + 0.948317i) q^{21} -2.46519 q^{22} +(-1.76381 + 4.45971i) q^{23} +0.609264 q^{24} +(3.18330 + 3.67372i) q^{25} +(3.14014 + 2.01804i) q^{26} +(-0.488058 + 3.39452i) q^{27} +(0.855563 - 1.87342i) q^{28} +(-1.01510 - 7.06018i) q^{29} +(-0.217925 - 0.0639885i) q^{30} +(4.91722 - 3.16011i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(1.44111 - 0.423148i) q^{33} +(-4.13158 + 4.76809i) q^{34} +(-0.502780 + 0.580239i) q^{35} +(2.52231 - 0.740618i) q^{36} +(-1.94398 - 4.25672i) q^{37} +(2.76678 - 1.77810i) q^{38} +(-2.18207 - 0.640715i) q^{39} +(0.0530529 + 0.368991i) q^{40} +(-1.98603 + 4.34881i) q^{41} +(-0.178577 + 1.24203i) q^{42} +(-9.36979 - 6.02160i) q^{43} +(-1.61435 - 1.86306i) q^{44} -0.979978 q^{45} +(-4.52547 + 1.58749i) q^{46} +2.44502 q^{47} +(0.398983 + 0.460451i) q^{48} +(-2.32043 - 1.49125i) q^{49} +(-0.691797 + 4.81155i) q^{50} +(1.59682 - 3.49654i) q^{51} +(0.531217 + 3.69470i) q^{52} +(-5.80255 - 1.70378i) q^{53} +(-2.88502 + 1.85409i) q^{54} +(0.381761 + 0.835939i) q^{55} +(1.97611 - 0.580239i) q^{56} +(-1.31221 + 1.51437i) q^{57} +(4.67098 - 5.39060i) q^{58} +(11.3316 - 3.32727i) q^{59} +(-0.0943511 - 0.206600i) q^{60} +(1.41899 - 0.911927i) q^{61} +(5.60835 + 1.64676i) q^{62} +(0.770508 + 5.35900i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.198030 - 1.37733i) q^{65} +(1.26352 + 0.812016i) q^{66} +(9.23004 + 10.6520i) q^{67} -6.30909 q^{68} +(2.37303 - 1.70482i) q^{69} -0.767766 q^{70} +(-2.64478 - 3.05224i) q^{71} +(2.21148 + 1.42123i) q^{72} +(-1.23672 + 8.60157i) q^{73} +(1.94398 - 4.25672i) q^{74} +(-0.421487 - 2.93151i) q^{75} +(3.15565 + 0.926583i) q^{76} +(4.27116 - 2.74491i) q^{77} +(-0.944735 - 2.06868i) q^{78} +(2.28741 - 0.671644i) q^{79} +(-0.244123 + 0.281733i) q^{80} +(-3.79620 + 4.38105i) q^{81} +(-4.58718 + 1.34692i) q^{82} +(1.76013 + 3.85415i) q^{83} +(-1.05561 + 0.678398i) q^{84} +(2.25667 + 0.662618i) q^{85} +(-1.58509 - 11.0245i) q^{86} +(-1.80529 + 3.95303i) q^{87} +(0.350833 - 2.44009i) q^{88} +(-7.59749 - 4.88261i) q^{89} +(-0.641749 - 0.740618i) q^{90} -7.68762 q^{91} +(-4.16330 - 2.38054i) q^{92} -3.56122 q^{93} +(1.60115 + 1.84783i) q^{94} +(-1.03141 - 0.662850i) q^{95} +(-0.0867074 + 0.603063i) q^{96} +(-4.69697 + 10.2849i) q^{97} +(-0.392548 - 2.73023i) q^{98} +(6.21797 + 1.82576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9}+O(q^{10}) $ 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9	\( 10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9} + 4 q^{10} - 2 q^{11} - 11 q^{12} + 2 q^{13} - 15 q^{14} + 11 q^{15} - q^{16} - 9 q^{17} + 19 q^{18} + 2 q^{19} + 7 q^{20} + 33 q^{21} + 2 q^{22} + 21 q^{23} - 11 q^{25} + 9 q^{26} + 15 q^{28} - 2 q^{29} + 11 q^{31} + q^{32} - 11 q^{33} - 13 q^{34} - 17 q^{35} + 3 q^{36} - 18 q^{37} - 13 q^{38} + 4 q^{40} + 5 q^{41} - 22 q^{42} - 21 q^{43} - 2 q^{44} - 10 q^{45} - 10 q^{46} - 22 q^{47} - 11 q^{48} + 24 q^{49} - 22 q^{50} - 11 q^{51} - 20 q^{52} - 7 q^{53} + 11 q^{54} + 3 q^{55} + 7 q^{56} + 11 q^{57} + 24 q^{58} + 43 q^{59} + 11 q^{60} - 3 q^{61} + 33 q^{62} - 23 q^{63} - q^{64} + 41 q^{65} + 11 q^{66} - q^{67} + 2 q^{68} + 33 q^{69} + 6 q^{70} - 11 q^{71} + 8 q^{72} - 28 q^{73} + 18 q^{74} + 44 q^{75} + 2 q^{76} + 30 q^{77} + 34 q^{79} + 7 q^{80} + 13 q^{81} + 6 q^{82} - 3 q^{83} - 11 q^{84} + 8 q^{85} - 34 q^{86} - 33 q^{87} - 9 q^{88} - 49 q^{89} - 45 q^{90} - 52 q^{91} - q^{92} - 88 q^{93} - 11 q^{94} - 36 q^{95} + 16 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9 + 4 * q^10 - 2 * q^11 - 11 * q^12 + 2 * q^13 - 15 * q^14 + 11 * q^15 - q^16 - 9 * q^17 + 19 * q^18 + 2 * q^19 + 7 * q^20 + 33 * q^21 + 2 * q^22 + 21 * q^23 - 11 * q^25 + 9 * q^26 + 15 * q^28 - 2 * q^29 + 11 * q^31 + q^32 - 11 * q^33 - 13 * q^34 - 17 * q^35 + 3 * q^36 - 18 * q^37 - 13 * q^38 + 4 * q^40 + 5 * q^41 - 22 * q^42 - 21 * q^43 - 2 * q^44 - 10 * q^45 - 10 * q^46 - 22 * q^47 - 11 * q^48 + 24 * q^49 - 22 * q^50 - 11 * q^51 - 20 * q^52 - 7 * q^53 + 11 * q^54 + 3 * q^55 + 7 * q^56 + 11 * q^57 + 24 * q^58 + 43 * q^59 + 11 * q^60 - 3 * q^61 + 33 * q^62 - 23 * q^63 - q^64 + 41 * q^65 + 11 * q^66 - q^67 + 2 * q^68 + 33 * q^69 + 6 * q^70 - 11 * q^71 + 8 * q^72 - 28 * q^73 + 18 * q^74 + 44 * q^75 + 2 * q^76 + 30 * q^77 + 34 * q^79 + 7 * q^80 + 13 * q^81 + 6 * q^82 - 3 * q^83 - 11 * q^84 + 8 * q^85 - 34 * q^86 - 33 * q^87 - 9 * q^88 - 49 * q^89 - 45 * q^90 - 52 * q^91 - q^92 - 88 * q^93 - 11 * q^94 - 36 * q^95 + 16 * q^97 + 20 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{7}{11}\right)$

Coefficient data

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

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

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

$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$2$	0.654861	+	0.755750i	0.463056	+	0.534396i
$3$	−0.512546	−	0.329393i	−0.295919	−	0.190175i	0.384254	−	0.923227i	$-0.374459\pi$
$3$	−0.512546	−	0.329393i	−0.295919	−	0.190175i	−0.680172	+	0.733052i	$0.738095\pi$
$4$	−0.142315	+	0.989821i	−0.0711574	+	0.494911i
$5$	0.154861	−	0.339098i	0.0692558	−	0.151649i	−0.871838	−	0.489794i	$-0.837072\pi$
$5$	0.154861	−	0.339098i	0.0692558	−	0.151649i	0.941094	+	0.338145i	$0.109799\pi$
$6$	−0.0867074	−	0.603063i	−0.0353981	−	0.246199i
$7$	−1.97611	−	0.580239i	−0.746900	−	0.219310i	−0.113933	−	0.993488i	$-0.536345\pi$
$7$	−1.97611	−	0.580239i	−0.746900	−	0.219310i	−0.632967	+	0.774179i	$0.718163\pi$
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−1.09204	−	2.39124i	−0.364014	−	0.797079i
$10$	0.357685	−	0.105026i	0.113110	−	0.0332121i
$11$	−1.61435	+	1.86306i	−0.486746	+	0.561735i	−0.944993	−	0.327090i	$-0.893932\pi$
$11$	−1.61435	+	1.86306i	−0.486746	+	0.561735i	0.458247	+	0.888825i	$0.348477\pi$
$12$	0.398983	−	0.460451i	0.115177	−	0.132921i
$13$	3.58149	−	1.05162i	0.993327	−	0.291667i	0.255612	−	0.966779i	$-0.417723\pi$
$13$	3.58149	−	1.05162i	0.993327	−	0.291667i	0.737715	+	0.675112i	$0.235905\pi$
$14$	−0.855563	−	1.87342i	−0.228659	−	0.500693i
$15$	−0.191070	+	0.122793i	−0.0493340	+	0.0317050i
$16$	−0.959493	−	0.281733i	−0.239873	−	0.0704331i
$17$	0.897877	+	6.24487i	0.217767	+	1.51460i	0.746253	+	0.665662i	$0.231851\pi$
$17$	0.897877	+	6.24487i	0.217767	+	1.51460i	−0.528486	+	0.848942i	$0.677240\pi$
$18$	1.09204	−	2.39124i	0.257397	−	0.563620i
$19$	0.468056	−	3.25540i	0.107379	−	0.746840i	−0.862991	−	0.505219i	$-0.831412\pi$
$19$	0.468056	−	3.25540i	0.107379	−	0.746840i	0.970371	−	0.241621i	$-0.0776791\pi$
$20$	0.313607	+	0.201543i	0.0701247	+	0.0450664i
$21$	0.821721	+	0.948317i	0.179314	+	0.206940i
$22$	−2.46519			−0.525579
$23$	−1.76381	+	4.45971i	−0.367780	+	0.929913i
$23$	−1.76381	+	4.45971i	−0.367780	+	0.929913i
$24$	0.609264			0.124366
$25$	3.18330	+	3.67372i	0.636660	+	0.734744i
$26$	3.14014	+	2.01804i	0.615832	+	0.395771i
$27$	−0.488058	+	3.39452i	−0.0939268	+	0.653276i
$28$	0.855563	−	1.87342i	0.161686	−	0.354043i
$29$	−1.01510	−	7.06018i	−0.188499	−	1.31104i	−0.835896	−	0.548889i	$-0.815051\pi$
$29$	−1.01510	−	7.06018i	−0.188499	−	1.31104i	0.647396	−	0.762154i	$-0.275858\pi$
$30$	−0.217925	−	0.0639885i	−0.0397875	−	0.0116827i
$31$	4.91722	−	3.16011i	0.883159	−	0.567572i	−0.0185921	−	0.999827i	$-0.505918\pi$
$31$	4.91722	−	3.16011i	0.883159	−	0.567572i	0.901751	+	0.432255i	$0.142282\pi$
$32$	−0.415415	−	0.909632i	−0.0734357	−	0.160802i
$33$	1.44111	−	0.423148i	0.250865	−	0.0736607i
$34$	−4.13158	+	4.76809i	−0.708560	+	0.817721i
$35$	−0.502780	+	0.580239i	−0.0849853	+	0.0980782i
$36$	2.52231	−	0.740618i	0.420385	−	0.123436i
$37$	−1.94398	−	4.25672i	−0.319588	−	0.699801i	0.679849	−	0.733352i	$-0.262045\pi$
$37$	−1.94398	−	4.25672i	−0.319588	−	0.699801i	−0.999437	+	0.0335515i	$0.989318\pi$
$38$	2.76678	−	1.77810i	0.448831	−	0.288446i
$39$	−2.18207	−	0.640715i	−0.349412	−	0.102597i
$40$	0.0530529	+	0.368991i	0.00838840	+	0.0583426i
$41$	−1.98603	+	4.34881i	−0.310166	+	0.679169i	−0.998951	−	0.0457967i	$-0.985417\pi$
$41$	−1.98603	+	4.34881i	−0.310166	+	0.679169i	0.688784	+	0.724966i	$0.258145\pi$
$42$	−0.178577	+	1.24203i	−0.0275550	+	0.191650i
$43$	−9.36979	−	6.02160i	−1.42888	−	0.918285i	−0.999888	−	0.0149765i	$-0.995233\pi$
$43$	−9.36979	−	6.02160i	−1.42888	−	0.918285i	−0.428992	−	0.903309i	$-0.641131\pi$
$44$	−1.61435	−	1.86306i	−0.243373	−	0.280867i
$45$	−0.979978			−0.146086
$46$	−4.52547	+	1.58749i	−0.667244	+	0.234062i
$47$	2.44502			0.356643			0.178322	−	0.983972i	$-0.442933\pi$
$47$	2.44502			0.356643			0.178322	+	0.983972i	$0.442933\pi$
$48$	0.398983	+	0.460451i	0.0575883	+	0.0664604i
$49$	−2.32043	−	1.49125i	−0.331491	−	0.213036i
$50$	−0.691797	+	4.81155i	−0.0978348	+	0.680456i
$51$	1.59682	−	3.49654i	0.223599	−	0.489613i
$52$	0.531217	+	3.69470i	0.0736666	+	0.512362i
$53$	−5.80255	−	1.70378i	−0.797042	−	0.234033i	−0.142239	−	0.989832i	$-0.545430\pi$
$53$	−5.80255	−	1.70378i	−0.797042	−	0.234033i	−0.654803	+	0.755800i	$0.727248\pi$
$54$	−2.88502	+	1.85409i	−0.392601	+	0.252309i
$55$	0.381761	+	0.835939i	0.0514766	+	0.112718i
$56$	1.97611	−	0.580239i	0.264069	−	0.0775377i
$57$	−1.31221	+	1.51437i	−0.173806	+	0.200583i
$58$	4.67098	−	5.39060i	0.613329	−	0.707820i
$59$	11.3316	−	3.32727i	1.47526	−	0.433174i	0.557452	−	0.830209i	$-0.311779\pi$
$59$	11.3316	−	3.32727i	1.47526	−	0.433174i	0.917803	+	0.397035i	$0.129961\pi$
$60$	−0.0943511	−	0.206600i	−0.0121807	−	0.0266720i
$61$	1.41899	−	0.911927i	0.181683	−	0.116760i	−0.446638	−	0.894715i	$-0.647379\pi$
$61$	1.41899	−	0.911927i	0.181683	−	0.116760i	0.628321	+	0.777954i	$0.283743\pi$
$62$	5.60835	+	1.64676i	0.712261	+	0.209139i
$63$	0.770508	+	5.35900i	0.0970748	+	0.675170i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.198030	−	1.37733i	0.0245626	−	0.170837i
$66$	1.26352	+	0.812016i	0.155529	+	0.0999522i
$67$	9.23004	+	10.6520i	1.12763	+	1.30135i	0.948232	+	0.317577i	$0.102869\pi$
$67$	9.23004	+	10.6520i	1.12763	+	1.30135i	0.179397	+	0.983777i	$0.442585\pi$
$68$	−6.30909			−0.765090
$69$	2.37303	−	1.70482i	0.285679	−	0.205236i
$70$	−0.767766			−0.0917656
$71$	−2.64478	−	3.05224i	−0.313878	−	0.362234i	0.576787	−	0.816894i	$-0.304306\pi$
$71$	−2.64478	−	3.05224i	−0.313878	−	0.362234i	−0.890665	+	0.454660i	$0.849761\pi$
$72$	2.21148	+	1.42123i	0.260626	+	0.167494i
$73$	−1.23672	+	8.60157i	−0.144747	+	1.00674i	0.779898	+	0.625907i	$0.215271\pi$
$73$	−1.23672	+	8.60157i	−0.144747	+	1.00674i	−0.924645	+	0.380831i	$0.875638\pi$
$74$	1.94398	−	4.25672i	0.225983	−	0.494834i
$75$	−0.421487	−	2.93151i	−0.0486692	−	0.338501i
$76$	3.15565	+	0.926583i	0.361978	+	0.106286i
$77$	4.27116	−	2.74491i	0.486744	−	0.312812i
$78$	−0.944735	−	2.06868i	−0.106970	−	0.234232i
$79$	2.28741	−	0.671644i	0.257354	−	0.0755659i	−0.150511	−	0.988608i	$-0.548092\pi$
$79$	2.28741	−	0.671644i	0.257354	−	0.0755659i	0.407864	+	0.913043i	$0.366274\pi$
$80$	−0.244123	+	0.281733i	−0.0272937	+	0.0314987i
$81$	−3.79620	+	4.38105i	−0.421800	+	0.486784i
$82$	−4.58718	+	1.34692i	−0.506570	+	0.148742i
$83$	1.76013	+	3.85415i	0.193200	+	0.423048i	0.981296	−	0.192503i	$-0.0616606\pi$
$83$	1.76013	+	3.85415i	0.193200	+	0.423048i	−0.788097	+	0.615552i	$0.788933\pi$
$84$	−1.05561	+	0.678398i	−0.115176	+	0.0740193i
$85$	2.25667	+	0.662618i	0.244770	+	0.0718710i
$86$	−1.58509	−	11.0245i	−0.170924	−	1.18880i
$87$	−1.80529	+	3.95303i	−0.193547	+	0.423810i
$88$	0.350833	−	2.44009i	0.0373989	−	0.260115i
$89$	−7.59749	−	4.88261i	−0.805332	−	0.517556i	0.0720196	−	0.997403i	$-0.477056\pi$
$89$	−7.59749	−	4.88261i	−0.805332	−	0.517556i	−0.877352	+	0.479848i	$0.840692\pi$
$90$	−0.641749	−	0.740618i	−0.0676463	−	0.0780680i
$91$	−7.68762			−0.805881
$92$	−4.16330	−	2.38054i	−0.434054	−	0.248188i
$93$	−3.56122			−0.369281
$94$	1.60115	+	1.84783i	0.165146	+	0.190589i
$95$	−1.03141	−	0.662850i	−0.105821	−	0.0680070i
$96$	−0.0867074	+	0.603063i	−0.00884953	+	0.0615499i
$97$	−4.69697	+	10.2849i	−0.476905	+	1.04428i	0.506398	+	0.862300i	$0.330977\pi$
$97$	−4.69697	+	10.2849i	−0.476905	+	1.04428i	−0.983303	+	0.181976i	$0.941751\pi$
$98$	−0.392548	−	2.73023i	−0.0396533	−	0.275795i
$99$	6.21797	+	1.82576i	0.624929	+	0.183496i
$100$	−4.08936	+	2.62807i	−0.408936	+	0.262807i
$101$	−3.34482	−	7.32414i	−0.332822	−	0.728780i	0.667046	−	0.745017i	$-0.267559\pi$
$101$	−3.34482	−	7.32414i	−0.332822	−	0.728780i	−0.999868	+	0.0162372i	$0.994831\pi$
$102$	3.68820	−	1.08295i	0.365186	−	0.107228i
$103$	9.66041	−	11.1487i	0.951868	−	1.09851i	−0.0431747	−	0.999068i	$-0.513747\pi$
$103$	9.66041	−	11.1487i	0.951868	−	1.09851i	0.995043	−	0.0994469i	$-0.0317073\pi$
$104$	−2.44439	+	2.82098i	−0.239692	+	0.276620i
$105$	0.448824	−	0.131787i	0.0438008	−	0.0128611i
$106$	−2.51223	−	5.50102i	−0.244009	−	0.534306i
$107$	−5.62090	+	3.61233i	−0.543393	+	0.349217i	−0.783365	−	0.621562i	$-0.786498\pi$
$107$	−5.62090	+	3.61233i	−0.543393	+	0.349217i	0.239972	+	0.970780i	$0.422862\pi$
$108$	−3.29051	−	0.966181i	−0.316629	−	0.0929708i
$109$	0.580602	+	4.03817i	0.0556116	+	0.386787i	0.998551	+	0.0538214i	$0.0171402\pi$
$109$	0.580602	+	4.03817i	0.0556116	+	0.386787i	−0.942939	+	0.332965i	$0.891951\pi$
$110$	−0.381761	+	0.835939i	−0.0363994	+	0.0797037i
$111$	−0.405757	+	2.82210i	−0.0385127	+	0.267862i
$112$	1.73259	+	1.11347i	0.163715	+	0.105213i
$113$	−3.65755	−	4.22104i	−0.344073	−	0.397082i	0.557168	−	0.830400i	$-0.311888\pi$
$113$	−3.65755	−	4.22104i	−0.344073	−	0.397082i	−0.901241	+	0.433318i	$0.857343\pi$
$114$	−2.00379			−0.187673
$115$	1.23913	+	1.28874i	0.115550	+	0.120175i
$116$	7.13278			0.662262
$117$	−6.42581	−	7.41578i	−0.594066	−	0.685589i
$118$	9.93524	+	6.38499i	0.914613	+	0.587786i
$119$	1.84921	−	12.8616i	0.169517	−	1.17902i
$120$	0.0943511	−	0.206600i	0.00861304	−	0.0188599i
$121$	0.700596	+	4.87275i	0.0636905	+	0.442977i
$122$	1.61843	+	0.475213i	0.146525	+	0.0430238i
$123$	2.45040	−	1.57478i	0.220945	−	0.141993i
$124$	2.42815	+	5.31690i	0.218054	+	0.477472i
$125$	3.52714	−	1.03566i	0.315477	−	0.0926325i
$126$	−3.54549	+	4.09171i	−0.315857	+	0.364518i
$127$	4.94344	−	5.70503i	0.438659	−	0.506240i	−0.492771	−	0.870159i	$-0.664016\pi$
$127$	4.94344	−	5.70503i	0.438659	−	0.506240i	0.931431	+	0.363919i	$0.118562\pi$
$128$	0.959493	−	0.281733i	0.0848080	−	0.0249019i
$129$	2.81897	+	6.17269i	0.248197	+	0.543475i
$130$	1.17060	−	0.752298i	0.102668	−	0.0659809i
$131$	3.13818	+	0.921454i	0.274184	+	0.0805078i	0.415934	−	0.909395i	$-0.363455\pi$
$131$	3.13818	+	0.921454i	0.274184	+	0.0805078i	−0.141750	+	0.989903i	$0.545273\pi$
$132$	0.213750	+	1.48666i	0.0186045	+	0.129397i
$133$	−2.81384	+	6.16145i	−0.243991	+	0.534265i
$134$	−2.00588	+	13.9512i	−0.173282	+	1.20520i
$135$	1.07549	+	0.691177i	0.0925637	+	0.0594871i
$136$	−4.13158	−	4.76809i	−0.354280	−	0.408861i
$137$	15.9297			1.36096			0.680482	−	0.732765i	$-0.261771\pi$
$137$	15.9297			1.36096			0.680482	+	0.732765i	$0.261771\pi$
$138$	2.84242	+	0.677000i	0.241963	+	0.0576300i
$139$	−2.85447			−0.242113			−0.121056	−	0.992646i	$-0.538628\pi$
$139$	−2.85447			−0.242113			−0.121056	+	0.992646i	$0.538628\pi$
$140$	−0.502780	−	0.580239i	−0.0424926	−	0.0490391i
$141$	−1.25319	−	0.805375i	−0.105537	−	0.0678248i
$142$	0.574766	−	3.99758i	0.0482333	−	0.335470i
$143$	−3.82256	+	8.37023i	−0.319658	+	0.699954i
$144$	0.374117	+	2.60204i	0.0311764	+	0.216837i
$145$	−2.55129	−	0.749126i	−0.211873	−	0.0622115i
$146$	−7.31051	+	4.69818i	−0.605022	+	0.388824i
$147$	0.698121	+	1.52867i	0.0575800	+	0.126083i
$148$	4.49005	−	1.31840i	0.369080	−	0.108372i
$149$	1.91136	−	2.20583i	0.156585	−	0.180709i	−0.672037	−	0.740518i	$-0.734580\pi$
$149$	1.91136	−	2.20583i	0.156585	−	0.180709i	0.828621	+	0.559809i	$0.189126\pi$
$150$	1.93947	−	2.23827i	0.158357	−	0.182754i
$151$	−23.5672	+	6.91997i	−1.91788	+	0.563139i	−0.949353	+	0.314212i	$0.898260\pi$
$151$	−23.5672	+	6.91997i	−1.91788	+	0.563139i	−0.968522	+	0.248927i	$0.919922\pi$
$152$	1.36625	+	2.99167i	0.110817	+	0.242656i
$153$	13.9525	−	8.96670i	1.12799	−	0.724915i
$154$	4.87148	+	1.43040i	0.392555	+	0.115265i
$155$	−0.310100	−	2.15680i	−0.0249079	−	0.173238i
$156$	0.944735	−	2.06868i	0.0756393	−	0.165627i
$157$	1.86497	−	12.9711i	0.148840	−	1.03521i	−0.769282	−	0.638910i	$-0.779386\pi$
$157$	1.86497	−	12.9711i	0.148840	−	1.03521i	0.918122	−	0.396298i	$-0.129705\pi$
$158$	2.00553	+	1.28888i	0.159551	+	0.102537i
$159$	2.41286	+	2.78459i	0.191352	+	0.220832i
$160$	−0.372786			−0.0294713
$161$	6.07318	−	7.78945i	0.478634	−	0.613894i
$162$	−5.79696			−0.455452
$163$	−3.02485	−	3.49086i	−0.236924	−	0.273425i	0.624819	−	0.780770i	$-0.285173\pi$
$163$	−3.02485	−	3.49086i	−0.236924	−	0.273425i	−0.861743	+	0.507344i	$0.830627\pi$
$164$	−4.02190	−	2.58472i	−0.314058	−	0.201833i
$165$	0.0796829	−	0.554206i	0.00620330	−	0.0431449i
$166$	−1.76013	+	3.85415i	−0.136613	+	0.299140i
$167$	0.560648	+	3.89939i	0.0433843	+	0.301744i	0.999948	+	0.0102201i	$0.00325323\pi$
$167$	0.560648	+	3.89939i	0.0433843	+	0.301744i	−0.956564	+	0.291524i	$0.905838\pi$
$168$	−1.20397	−	0.353519i	−0.0928887	−	0.0272746i
$169$	0.784872	−	0.504407i	0.0603748	−	0.0388005i
$170$	0.977031	+	2.13940i	0.0749348	+	0.164084i
$171$	−8.29557	+	2.43580i	−0.634378	+	0.186270i
$172$	7.29377	−	8.41745i	0.556144	−	0.641825i
$173$	−12.4428	+	14.3598i	−0.946009	+	1.09175i	0.0496580	+	0.998766i	$0.484187\pi$
$173$	−12.4428	+	14.3598i	−0.946009	+	1.09175i	−0.995667	+	0.0929867i	$0.970359\pi$
$174$	−4.16972	+	1.22434i	−0.316105	+	0.0928169i
$175$	−4.15892	−	9.10676i	−0.314385	−	0.688406i
$176$	2.07385	−	1.33278i	0.156322	−	0.100462i
$177$	−6.90397	−	2.02719i	−0.518934	−	0.152373i
$178$	−1.28527	−	8.93923i	−0.0963348	−	0.670024i
$179$	0.996758	−	2.18260i	0.0745012	−	0.163135i	−0.868717	−	0.495309i	$-0.835055\pi$
$179$	0.996758	−	2.18260i	0.0745012	−	0.163135i	0.943218	+	0.332174i	$0.107782\pi$
$180$	0.139465	−	0.970003i	0.0103951	−	0.0722997i
$181$	21.8779	+	14.0601i	1.62617	+	1.04508i	0.951815	+	0.306673i	$0.0992158\pi$
$181$	21.8779	+	14.0601i	1.62617	+	1.04508i	0.674358	+	0.738405i	$0.264421\pi$
$182$	−5.03432	−	5.80991i	−0.373168	−	0.430659i
$183$	−1.02768			−0.0759681
$184$	−0.927287	−	4.70533i	−0.0683605	−	0.346882i
$185$	−1.74449			−0.128258
$186$	−2.33210	−	2.69139i	−0.170998	−	0.197342i
$187$	−13.0841	−	8.40863i	−0.956803	−	0.614900i
$188$	−0.347963	+	2.42014i	−0.0253778	+	0.176507i
$189$	2.93409	−	6.42476i	0.213424	−	0.467332i
$190$	−0.174484	−	1.21357i	−0.0126584	−	0.0880413i
$191$	10.0451	+	2.94950i	0.726836	+	0.213418i	0.624160	−	0.781297i	$-0.285441\pi$
$191$	10.0451	+	2.94950i	0.726836	+	0.213418i	0.102676	+	0.994715i	$0.467260\pi$
$192$	−0.512546	+	0.329393i	−0.0369898	+	0.0237719i
$193$	0.320385	+	0.701546i	0.0230618	+	0.0504984i	0.920812	−	0.390006i	$-0.127527\pi$
$193$	0.320385	+	0.701546i	0.0230618	+	0.0504984i	−0.897751	+	0.440504i	$0.854800\pi$
$194$	−10.8487	+	3.18546i	−0.778890	+	0.228703i
$195$	−0.555183	+	0.640715i	−0.0397575	+	0.0458826i
$196$	1.80631	−	2.08459i	0.129022	−	0.148899i
$197$	−4.99637	+	1.46707i	−0.355977	+	0.104524i	−0.454831	−	0.890578i	$-0.650300\pi$
$197$	−4.99637	+	1.46707i	−0.355977	+	0.104524i	0.0988543	+	0.995102i	$0.468482\pi$
$198$	2.69209	+	5.89485i	0.191318	+	0.418928i
$199$	−19.6372	+	12.6200i	−1.39204	+	0.894610i	−0.999682	−	0.0252020i	$-0.991977\pi$
$199$	−19.6372	+	12.6200i	−1.39204	+	0.894610i	−0.392358	+	0.919812i	$0.628341\pi$
$200$	−4.66412	−	1.36951i	−0.329803	−	0.0968390i
$201$	−1.22211	−	8.49997i	−0.0862011	−	0.599542i
$202$	3.34482	−	7.32414i	0.235341	−	0.515325i
$203$	−2.09064	+	14.5407i	−0.146734	+	1.02056i
$204$	3.23370	+	2.07817i	0.226404	+	0.145501i
$205$	1.16711	+	1.34692i	0.0815146	+	0.0940729i
$206$	14.7518			1.02781
$207$	12.5904	−	0.652494i	0.875091	−	0.0453515i
$208$	−3.73269			−0.258816
$209$	5.30941	+	6.12738i	0.367259	+	0.423840i
$210$	0.393515	+	0.252897i	0.0271551	+	0.0174515i
$211$	1.23757	−	8.60752i	0.0851981	−	0.592566i	−0.901839	−	0.432073i	$-0.857782\pi$
$211$	1.23757	−	8.60752i	0.0851981	−	0.592566i	0.987037	−	0.160493i	$-0.0513085\pi$
$212$	2.51223	−	5.50102i	0.172541	−	0.377812i
$213$	0.350184	+	2.43558i	0.0239942	+	0.166884i
$214$	−6.41093	−	1.88242i	−0.438242	−	0.128679i
$215$	−3.49292	+	2.24476i	−0.238215	+	0.153092i
$216$	−1.42464	−	3.11952i	−0.0969341	−	0.212256i
$217$	−11.5506	+	3.39156i	−0.784106	+	0.230234i
$218$	−2.67163	+	3.08323i	−0.180946	+	0.208823i
$219$	3.46717	−	4.00133i	0.234290	−	0.270385i
$220$	−0.881761	+	0.258908i	−0.0594483	+	0.0174556i
$221$	9.78298	+	21.4217i	0.658074	+	1.44098i
$222$	−2.39851	+	1.54143i	−0.160978	+	0.103454i
$223$	3.68556	+	1.08218i	0.246803	+	0.0724680i	0.402794	−	0.915290i	$-0.368039\pi$
$223$	3.68556	+	1.08218i	0.246803	+	0.0724680i	−0.155991	+	0.987758i	$0.549857\pi$
$224$	0.293103	+	2.03857i	0.0195838	+	0.136208i
$225$	5.30845	−	11.6239i	0.353897	−	0.774925i
$226$	0.794861	−	5.52838i	0.0528734	−	0.367743i
$227$	1.71113	+	1.09968i	0.113572	+	0.0729883i	0.596194	−	0.802841i	$-0.296679\pi$
$227$	1.71113	+	1.09968i	0.113572	+	0.0729883i	−0.482622	+	0.875829i	$0.660315\pi$
$228$	−1.31221	−	1.51437i	−0.0869030	−	0.100291i
$229$	27.4406			1.81333			0.906664	−	0.421853i	$-0.138620\pi$
$229$	27.4406			1.81333			0.906664	+	0.421853i	$0.138620\pi$
$230$	−0.162505	+	1.78042i	−0.0107152	+	0.117397i
$231$	−3.09332			−0.203526
$232$	4.67098	+	5.39060i	0.306665	+	0.353910i
$233$	5.92647	+	3.80871i	0.388256	+	0.249517i	0.720177	−	0.693790i	$-0.244061\pi$
$233$	5.92647	+	3.80871i	0.388256	+	0.249517i	−0.331921	+	0.943307i	$0.607697\pi$
$234$	1.39646	−	9.71261i	0.0912896	−	0.634933i
$235$	0.378638	−	0.829102i	0.0246996	−	0.0540847i
$236$	1.68074	+	11.6898i	0.109407	+	0.760943i
$237$	−1.39364	−	0.409209i	−0.0905265	−	0.0265810i
$238$	10.9311	−	7.02498i	0.708557	−	0.455362i
$239$	10.8343	+	23.7238i	0.700814	+	1.53457i	0.838982	+	0.544159i	$0.183151\pi$
$239$	10.8343	+	23.7238i	0.700814	+	1.53457i	−0.138168	+	0.990409i	$0.544121\pi$
$240$	0.217925	−	0.0639885i	0.0140670	−	0.00413044i
$241$	−0.910396	+	1.05065i	−0.0586437	+	0.0676785i	−0.784313	−	0.620365i	$-0.786985\pi$
$241$	−0.910396	+	1.05065i	−0.0586437	+	0.0676785i	0.725670	+	0.688043i	$0.241530\pi$
$242$	−3.22379	+	3.72045i	−0.207233	+	0.239159i
$243$	13.2603	−	3.89359i	0.850652	−	0.249774i
$244$	0.700702	+	1.53432i	0.0448579	+	0.0982250i
$245$	−0.865024	+	0.555917i	−0.0552644	+	0.0355163i
$246$	2.79481	+	0.820630i	0.178190	+	0.0523214i
$247$	−1.74711	−	12.1514i	−0.111166	−	0.773175i
$248$	−2.42815	+	5.31690i	−0.154188	+	0.337624i
$249$	0.367383	−	2.55521i	0.0232820	−	0.161930i
$250$	3.09249	+	1.98742i	0.195586	+	0.125696i
$251$	−17.0861	−	19.7184i	−1.07847	−	1.24462i	−0.968057	−	0.250729i	$-0.919330\pi$
$251$	−17.0861	−	19.7184i	−1.07847	−	1.24462i	−0.110408	−	0.993886i	$-0.535216\pi$
$252$	−5.41411			−0.341057
$253$	−5.46130	−	10.4856i	−0.343349	−	0.659226i
$254$	7.54884			0.473656
$255$	−0.938384	−	1.08295i	−0.0587639	−	0.0678172i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	3.98415	−	27.7104i	0.248524	−	1.72852i	−0.358229	−	0.933634i	$-0.616619\pi$
$257$	3.98415	−	27.7104i	0.248524	−	1.72852i	0.606753	−	0.794890i	$-0.292472\pi$
$258$	−2.81897	+	6.17269i	−0.175502	+	0.384295i
$259$	1.37161	+	9.53973i	0.0852275	+	0.592770i
$260$	1.33513	+	0.392029i	0.0828011	+	0.0243126i
$261$	−15.7740	+	10.1374i	−0.976388	+	0.627487i
$262$	1.35869	+	2.97511i	0.0839398	+	0.183803i
$263$	−9.05134	+	2.65771i	−0.558129	+	0.163882i	−0.548618	−	0.836073i	$-0.684846\pi$
$263$	−9.05134	+	2.65771i	−0.558129	+	0.163882i	−0.00951145	+	0.999955i	$0.503028\pi$
$264$	−0.983568	+	1.13510i	−0.0605344	+	0.0698605i
$265$	−1.47634	+	1.70378i	−0.0906907	+	0.104663i
$266$	−6.49918	+	1.90833i	−0.398490	+	0.117007i
$267$	2.28576	+	5.00512i	0.139886	+	0.306309i
$268$	−11.8572	+	7.62015i	−0.724293	+	0.465475i
$269$	−16.6675	−	4.89401i	−1.01623	−	0.298393i	−0.269132	−	0.963103i	$-0.586737\pi$
$269$	−16.6675	−	4.89401i	−1.01623	−	0.298393i	−0.747101	+	0.664710i	$0.768555\pi$
$270$	0.181941	+	1.26543i	0.0110726	+	0.0770115i
$271$	7.43784	−	16.2866i	0.451816	−	0.989340i	−0.537461	−	0.843289i	$-0.680616\pi$
$271$	7.43784	−	16.2866i	0.451816	−	0.989340i	0.989277	−	0.146051i	$-0.0466564\pi$
$272$	0.897877	−	6.24487i	0.0544418	−	0.378651i
$273$	3.94026	+	2.53225i	0.238475	+	0.153259i
$274$	10.4317	+	12.0388i	0.630203	+	0.727293i
$275$	−11.9833			−0.722623
$276$	1.34975	+	2.59150i	0.0812452	+	0.155990i
$277$	−15.2821			−0.918212			−0.459106	−	0.888382i	$-0.651830\pi$
$277$	−15.2821			−0.918212			−0.459106	+	0.888382i	$0.651830\pi$
$278$	−1.86928	−	2.15726i	−0.112112	−	0.129384i
$279$	−12.9264	−	8.30728i	−0.773882	−	0.497344i
$280$	0.109264	−	0.759951i	0.00652980	−	0.0454158i
$281$	2.46220	−	5.39146i	0.146882	−	0.321627i	−0.821863	−	0.569685i	$-0.807065\pi$
$281$	2.46220	−	5.39146i	0.146882	−	0.321627i	0.968745	+	0.248058i	$0.0797923\pi$
$282$	−0.212002	−	1.47450i	−0.0126245	−	0.0878054i
$283$	−1.50023	−	0.440506i	−0.0891791	−	0.0261854i	0.236839	−	0.971549i	$-0.423889\pi$
$283$	−1.50023	−	0.440506i	−0.0891791	−	0.0261854i	−0.326018	+	0.945364i	$0.605707\pi$
$284$	3.39756	−	2.18348i	0.201608	−	0.129566i
$285$	0.310309	+	0.679482i	0.0183811	+	0.0402490i
$286$	−8.82904	+	2.59244i	−0.522072	+	0.153294i
$287$	6.44797	−	7.44135i	0.380612	−	0.439249i
$288$	−1.72150	+	1.98671i	−0.101440	+	0.117068i
$289$	−21.8809	+	6.42481i	−1.28711	+	0.377930i
$290$	−1.10459	−	2.41871i	−0.0648636	−	0.142032i
$291$	5.79519	−	3.72435i	0.339720	−	0.218325i
$292$	−8.33802	−	2.44826i	−0.487945	−	0.143274i
$293$	−0.292908	−	2.03722i	−0.0171119	−	0.119016i	0.979475	−	0.201565i	$-0.0646028\pi$
$293$	−0.292908	−	2.03722i	−0.0171119	−	0.119016i	−0.996587	+	0.0825496i	$0.973694\pi$
$294$	−0.698121	+	1.52867i	−0.0407152	+	0.0891539i
$295$	0.626557	−	4.35780i	0.0364796	−	0.253721i
$296$	3.93674	+	2.52999i	0.228818	+	0.147053i
$297$	−5.53631	−	6.38924i	−0.321249	−	0.370741i
$298$	2.91873			0.169078
$299$	−1.62715	+	17.8273i	−0.0941007	+	1.03098i
$300$	2.96165			0.170991
$301$	15.0218	+	17.3361i	0.865841	+	0.999234i
$302$	−20.6630	−	13.2793i	−1.18902	−	0.764139i
$303$	−0.698147	+	4.85572i	−0.0401075	+	0.278954i
$304$	−1.36625	+	2.99167i	−0.0783597	+	0.171584i
$305$	−0.0894871	−	0.622397i	−0.00512402	−	0.0356383i
$306$	15.9135	+	4.67262i	0.909714	+	0.267116i
$307$	9.11420	−	5.85734i	0.520175	−	0.334296i	−0.254066	−	0.967187i	$-0.581768\pi$
$307$	9.11420	−	5.85734i	0.520175	−	0.334296i	0.774241	+	0.632891i	$0.218132\pi$
$308$	2.10912	+	4.61833i	0.120178	+	0.263154i
$309$	−8.62371	+	2.53215i	−0.490586	+	0.144049i
$310$	1.42692	−	1.64676i	0.0810439	−	0.0935296i
$311$	14.9945	−	17.3046i	0.850260	−	0.981252i	−0.149712	−	0.988730i	$-0.547835\pi$
$311$	14.9945	−	17.3046i	0.850260	−	0.981252i	0.999972	+	0.00747762i	$0.00238022\pi$
$312$	2.18207	−	0.640715i	0.123536	−	0.0362733i
$313$	−9.69914	−	21.2382i	−0.548228	−	1.20045i	−0.957604	−	0.288086i	$-0.906981\pi$
$313$	−9.69914	−	21.2382i	−0.548228	−	1.20045i	0.409376	−	0.912366i	$-0.365746\pi$
$314$	11.0242	−	7.08483i	0.622132	−	0.399820i
$315$	1.93655	+	0.568621i	0.109112	+	0.0320382i
$316$	0.339275	+	2.35971i	0.0190857	+	0.132744i
$317$	0.209132	−	0.457936i	0.0117460	−	0.0257202i	−0.903668	−	0.428234i	$-0.859136\pi$
$317$	0.209132	−	0.457936i	0.0117460	−	0.0257202i	0.915414	+	0.402513i	$0.131863\pi$
$318$	−0.524365	+	3.64704i	−0.0294049	+	0.204516i
$319$	14.7923	+	9.50643i	0.828209	+	0.532258i
$320$	−0.244123	−	0.281733i	−0.0136469	−	0.0157493i
$321$	4.07085			0.227213
$322$	9.86396	−	0.511198i	0.549697	−	0.0284880i
$323$	20.7498			1.15455
$324$	−3.79620	−	4.38105i	−0.210900	−	0.243392i
$325$	15.2643	+	9.80978i	0.846712	+	0.544149i
$326$	0.657362	−	4.57205i	0.0364079	−	0.253223i
$327$	1.03256	−	2.26100i	0.0571008	−	0.125033i
$328$	−0.680385	−	4.73218i	−0.0375680	−	0.261291i
$329$	−4.83164	−	1.41870i	−0.266377	−	0.0782153i
$330$	0.471022	−	0.302708i	0.0259289	−	0.0166635i
$331$	8.39272	+	18.3775i	0.461306	+	1.01012i	0.987188	+	0.159561i	$0.0510080\pi$
$331$	8.39272	+	18.3775i	0.461306	+	1.01012i	−0.525882	+	0.850557i	$0.676265\pi$
$332$	−4.06542	+	1.19371i	−0.223119	+	0.0655136i
$333$	−8.05593	+	9.29704i	−0.441462	+	0.509475i
$334$	−2.57982	+	2.97727i	−0.141161	+	0.162909i
$335$	5.04145	−	1.48030i	0.275444	−	0.0808777i
$336$	−0.521264	−	1.14141i	−0.0284373	−	0.0622690i
$337$	3.45398	−	2.21974i	0.188150	−	0.120917i	−0.443175	−	0.896435i	$-0.646148\pi$
$337$	3.45398	−	2.21974i	0.188150	−	0.120917i	0.631325	+	0.775518i	$0.282511\pi$
$338$	0.895187	+	0.262851i	0.0486918	+	0.0142972i
$339$	0.484281	+	3.36825i	0.0263025	+	0.182938i
$340$	−0.977031	+	2.13940i	−0.0529869	+	0.116025i
$341$	−2.05066	+	14.2626i	−0.111049	+	0.772365i
$342$	−7.27330	−	4.67426i	−0.393295	−	0.252755i
$343$	13.1611	+	15.1887i	0.710634	+	0.820115i
$344$	11.1379			0.600515
$345$	−0.210610	−	1.06870i	−0.0113389	−	0.0575368i
$346$	−19.0007			−1.02148
$347$	−15.9888	−	18.4520i	−0.858322	−	0.990557i	−1.00000		0.000643827i	$-0.999795\pi$
$347$	−15.9888	−	18.4520i	−0.858322	−	0.990557i	0.141678	−	0.989913i	$-0.454750\pi$
$348$	−3.65588	−	2.34949i	−0.195976	−	0.125946i
$349$	−2.46135	+	17.1191i	−0.131753	+	0.916362i	0.811516	+	0.584331i	$0.198643\pi$
$349$	−2.46135	+	17.1191i	−0.131753	+	0.916362i	−0.943268	+	0.332031i	$0.892266\pi$
$350$	4.15892	−	9.10676i	0.222303	−	0.486777i
$351$	1.82177	+	12.6707i	0.0972389	+	0.676311i
$352$	2.36533	+	0.694523i	0.126072	+	0.0370182i
$353$	−8.05818	+	5.17868i	−0.428894	+	0.275633i	−0.737227	−	0.675645i	$-0.763865\pi$
$353$	−8.05818	+	5.17868i	−0.428894	+	0.275633i	0.308333	+	0.951278i	$0.400229\pi$
$354$	−2.98909	−	6.54520i	−0.158868	−	0.347873i
$355$	−1.44458	+	0.424167i	−0.0766703	+	0.0225124i
$356$	5.91415	−	6.82529i	0.313449	−	0.361740i
$357$	−5.18431	+	5.98302i	−0.274383	+	0.316655i
$358$	2.30223	−	0.675997i	0.121677	−	0.0357275i
$359$	0.0520416	+	0.113955i	0.00274665	+	0.00601433i	0.911000	−	0.412406i	$-0.135311\pi$
$359$	0.0520416	+	0.113955i	0.00274665	+	0.00601433i	−0.908254	+	0.418420i	$0.862584\pi$
$360$	0.824410	−	0.529816i	0.0434502	−	0.0279237i
$361$	7.85182	+	2.30550i	0.413254	+	0.121342i
$362$	3.70109	+	25.7416i	0.194525	+	1.35295i
$363$	1.24596	−	2.72828i	0.0653961	−	0.143198i
$364$	1.09406	−	7.60937i	0.0573444	−	0.398839i
$365$	2.72525	+	1.75141i	0.142646	+	0.0916732i
$366$	−0.672986	−	0.776667i	−0.0351775	−	0.0405970i
$367$	−4.23470			−0.221050			−0.110525	−	0.993873i	$-0.535253\pi$
$367$	−4.23470			−0.221050			−0.110525	+	0.993873i	$0.535253\pi$
$368$	2.94881	−	3.78213i	0.153717	−	0.197157i
$369$	12.5679			0.654257
$370$	−1.14240	−	1.31840i	−0.0593905	−	0.0685403i
$371$	10.4779	+	6.73373i	0.543985	+	0.349598i
$372$	0.506814	−	3.52497i	0.0262771	−	0.182761i
$373$	−0.260238	+	0.569842i	−0.0134746	+	0.0295053i	−0.916250	−	0.400608i	$-0.868799\pi$
$373$	−0.260238	+	0.569842i	−0.0134746	+	0.0295053i	0.902775	+	0.430113i	$0.141526\pi$
$374$	−2.21344	−	15.3948i	−0.114454	−	0.796045i
$375$	−2.14896	−	0.630993i	−0.110972	−	0.0325843i
$376$	−2.05689	+	1.32188i	−0.106076	+	0.0681708i
$377$	−11.0602	−	24.2185i	−0.569629	−	1.24731i
$378$	6.77693	−	1.98989i	0.348568	−	0.102349i
$379$	6.88978	−	7.95124i	0.353904	−	0.408428i	−0.550684	−	0.834714i	$-0.685633\pi$
$379$	6.88978	−	7.95124i	0.353904	−	0.408428i	0.904588	+	0.426286i	$0.140178\pi$
$380$	0.802889	−	0.926583i	0.0411873	−	0.0475327i
$381$	−4.41294	+	1.29576i	−0.226082	+	0.0663836i
$382$	4.34904	+	9.52307i	0.222516	+	0.487243i
$383$	−12.9300	+	8.30958i	−0.660690	+	0.424600i	−0.827559	−	0.561379i	$-0.810271\pi$
$383$	−12.9300	+	8.30958i	−0.660690	+	0.424600i	0.166868	+	0.985979i	$0.446635\pi$
$384$	−0.584585	−	0.171650i	−0.0298320	−	0.00875946i
$385$	−0.269357	−	1.87342i	−0.0137277	−	0.0954784i
$386$	−0.320385	+	0.701546i	−0.0163072	+	0.0357078i
$387$	−4.16687	+	28.9812i	−0.211814	+	1.47320i
$388$	−9.51179	−	6.11286i	−0.482888	−	0.310333i
$389$	−14.2332	−	16.4260i	−0.721653	−	0.832832i	0.269851	−	0.962902i	$-0.413025\pi$
$389$	−14.2332	−	16.4260i	−0.721653	−	0.832832i	−0.991505	+	0.130069i	$0.958480\pi$
$390$	−0.847787			−0.0429294
$391$	−29.4340	−	7.01051i	−1.48854	−	0.354537i
$392$	2.75831			0.139315
$393$	−1.30494	−	1.50598i	−0.0658256	−	0.0759668i
$394$	−4.38067	−	2.81528i	−0.220695	−	0.141832i
$395$	0.126477	−	0.879667i	0.00636375	−	0.0442608i
$396$	−2.69209	+	5.89485i	−0.135282	+	0.296227i
$397$	−1.44578	−	10.0556i	−0.0725615	−	0.504676i	−0.993397	−	0.114726i	$-0.963401\pi$
$397$	−1.44578	−	10.0556i	−0.0725615	−	0.504676i	0.920836	−	0.389951i	$-0.127508\pi$
$398$	−22.3972	−	6.57641i	−1.12267	−	0.329645i
$399$	3.47176	−	2.23116i	0.173805	−	0.111698i
$400$	−2.01935	−	4.42175i	−0.100967	−	0.221087i
$401$	30.6059	−	8.98672i	1.52839	−	0.448775i	0.593831	−	0.804590i	$-0.297615\pi$
$401$	30.6059	−	8.98672i	1.52839	−	0.448775i	0.934557	+	0.355814i	$0.115796\pi$
$402$	5.62354	−	6.48991i	0.280477	−	0.323687i
$403$	14.2878	−	16.4889i	0.711724	−	0.821373i
$404$	7.72561	−	2.26844i	0.384364	−	0.112859i
$405$	0.897722	+	1.96574i	0.0446082	+	0.0976782i
$406$	−12.3582	+	7.94214i	−0.613327	+	0.394162i
$407$	11.0688	+	3.25010i	0.548661	+	0.161101i
$408$	0.547045	+	3.80478i	0.0270828	+	0.188365i
$409$	−5.48958	+	12.0205i	−0.271442	+	0.594375i	−0.995436	−	0.0954310i	$-0.969577\pi$
$409$	−5.48958	+	12.0205i	−0.271442	+	0.594375i	0.723994	+	0.689806i	$0.242304\pi$
$410$	−0.253638	+	1.76409i	−0.0125263	+	0.0871221i
$411$	−8.16469	−	5.24712i	−0.402734	−	0.258822i
$412$	9.66041	+	11.1487i	0.475934	+	0.549257i
$413$	−24.3232			−1.19687
$414$	8.73806	+	9.08787i	0.429452	+	0.446645i
$415$	1.57951			0.0775351
$416$	−2.44439	−	2.82098i	−0.119846	−	0.138310i
$417$	1.46305	+	0.940242i	0.0716457	+	0.0460439i
$418$	−1.15384	+	8.02516i	−0.0564364	+	0.392524i
$419$	1.74597	−	3.82315i	0.0852964	−	0.186773i	−0.862177	−	0.506606i	$-0.830900\pi$
$419$	1.74597	−	3.82315i	0.0852964	−	0.186773i	0.947474	+	0.319834i	$0.103627\pi$
$420$	0.0665710	+	0.463011i	0.00324833	+	0.0225926i
$421$	−6.75035	−	1.98208i	−0.328992	−	0.0966007i	0.113066	−	0.993588i	$-0.463933\pi$
$421$	−6.75035	−	1.98208i	−0.328992	−	0.0966007i	−0.442057	+	0.896987i	$0.645751\pi$
$422$	7.31557	−	4.70143i	0.356116	−	0.228862i
$423$	−2.67007	−	5.84663i	−0.129823	−	0.284273i
$424$	5.80255	−	1.70378i	0.281797	−	0.0827430i
$425$	−20.0837	+	23.1778i	−0.974204	+	1.12429i
$426$	−1.61137	+	1.85962i	−0.0780711	+	0.0900989i
$427$	−3.33321	+	0.978719i	−0.161305	+	0.0473635i
$428$	−2.77563	−	6.07778i	−0.134165	−	0.293780i
$429$	4.71633	−	3.03100i	0.227707	−	0.146338i
$430$	−3.98386	−	1.16977i	−0.192119	−	0.0564111i
$431$	−5.23996	−	36.4447i	−0.252400	−	1.75548i	−0.583714	−	0.811959i	$-0.698401\pi$
$431$	−5.23996	−	36.4447i	−0.252400	−	1.75548i	0.331315	−	0.943520i	$-0.392508\pi$
$432$	1.42464	−	3.11952i	0.0685428	−	0.150088i
$433$	3.87488	−	26.9504i	0.186215	−	1.29515i	−0.655486	−	0.755207i	$-0.727536\pi$
$433$	3.87488	−	26.9504i	0.186215	−	1.29515i	0.841701	−	0.539944i	$-0.181555\pi$
$434$	−10.1272	−	6.50836i	−0.486121	−	0.312411i
$435$	1.06090	+	1.22434i	0.0508661	+	0.0587026i
$436$	−4.07970			−0.195382
$437$	13.6926	+	7.82930i	0.655004	+	0.374526i
$438$	5.29452			0.252982
$439$	15.8395	+	18.2798i	0.755980	+	0.872448i	0.995134	−	0.0985339i	$-0.0314153\pi$
$439$	15.8395	+	18.2798i	0.755980	+	0.872448i	−0.239153	+	0.970982i	$0.576870\pi$
$440$	−0.773100	−	0.496841i	−0.0368561	−	0.0236860i
$441$	−1.03193	+	7.17722i	−0.0491394	+	0.341772i
$442$	−9.78298	+	21.4217i	−0.465329	+	1.01893i
$443$	−2.19556	−	15.2705i	−0.104314	−	0.725522i	−0.973108	−	0.230348i	$-0.926014\pi$
$443$	−2.19556	−	15.2705i	−0.104314	−	0.725522i	0.868794	−	0.495174i	$-0.164896\pi$
$444$	−2.73563	−	0.803253i	−0.129827	−	0.0381207i
$445$	−2.83223	+	1.82017i	−0.134261	+	0.0862842i
$446$	1.59567	+	3.49404i	0.0755573	+	0.165447i
$447$	−1.70625	+	0.500999i	−0.0807027	+	0.0236964i
$448$	−1.34871	+	1.55649i	−0.0637206	+	0.0735375i
$449$	−11.3449	+	13.0927i	−0.535397	+	0.617881i	−0.957418	−	0.288705i	$-0.906775\pi$
$449$	−11.3449	+	13.0927i	−0.535397	+	0.617881i	0.422021	+	0.906586i	$0.361321\pi$
$450$	12.2610	−	3.60017i	0.577991	−	0.169713i
$451$	−4.89594	−	10.7206i	−0.230541	−	0.504814i
$452$	4.69860	−	3.01960i	0.221003	−	0.142030i
$453$	14.3587	+	4.21609i	0.674630	+	0.198089i
$454$	0.289473	+	2.01333i	0.0135856	+	0.0944901i
$455$	−1.19051	+	2.60685i	−0.0558120	+	0.122211i
$456$	0.285170	−	1.98340i	0.0133543	−	0.0928812i
$457$	−5.77854	−	3.71364i	−0.270309	−	0.173717i	0.398464	−	0.917184i	$-0.369544\pi$
$457$	−5.77854	−	3.71364i	−0.270309	−	0.173717i	−0.668772	+	0.743467i	$0.733180\pi$
$458$	17.9698	+	20.7383i	0.839674	+	0.969035i
$459$	−21.6366			−1.00991
$460$	−1.45197	+	1.04311i	−0.0676983	+	0.0486353i
$461$	−0.341091			−0.0158862			−0.00794309	−	0.999968i	$-0.502528\pi$
$461$	−0.341091			−0.0158862			−0.00794309	+	0.999968i	$0.502528\pi$
$462$	−2.02570	−	2.33778i	−0.0942439	−	0.108763i
$463$	13.7279	+	8.82237i	0.637988	+	0.410010i	0.819259	−	0.573423i	$-0.194385\pi$
$463$	13.7279	+	8.82237i	0.637988	+	0.410010i	−0.181271	+	0.983433i	$0.558021\pi$
$464$	−1.01510	+	7.06018i	−0.0471249	+	0.327761i
$465$	−0.551493	+	1.20760i	−0.0255749	+	0.0560012i
$466$	1.00258	+	6.97310i	0.0464436	+	0.323022i
$467$	34.7667	+	10.2084i	1.60881	+	0.472389i	0.957980	−	0.286834i	$-0.0926028\pi$
$467$	34.7667	+	10.2084i	1.60881	+	0.472389i	0.650830	+	0.759223i	$0.274421\pi$
$468$	8.25479	−	5.30503i	0.381578	−	0.245225i
$469$	−12.0589	−	26.4052i	−0.556827	−	1.21928i
$470$	0.874549	−	0.256791i	0.0403399	−	0.0118449i
$471$	−5.22848	+	6.03399i	−0.240916	+	0.278031i
$472$	−7.73393	+	8.92543i	−0.355983	+	0.410826i
$473$	26.3448	−	7.73552i	1.21133	−	0.355680i
$474$	−0.603379	−	1.32122i	−0.0277141	−	0.0606854i
$475$	13.4494	−	8.64340i	0.617100	−	0.396586i
$476$	12.4675	+	3.66078i	0.571446	+	0.167792i
$477$	2.26248	+	15.7359i	0.103592	+	0.720497i
$478$	−10.8343	+	23.7238i	−0.495550	+	1.08510i
$479$	1.81532	−	12.6259i	0.0829443	−	0.576890i	−0.905389	−	0.424583i	$-0.860421\pi$
$479$	1.81532	−	12.6259i	0.0829443	−	0.576890i	0.988333	−	0.152307i	$-0.0486703\pi$
$480$	0.191070	+	0.122793i	0.00872110	+	0.00560471i
$481$	−11.4388	−	13.2011i	−0.521565	−	0.601918i
$482$	−1.39021			−0.0633224
$483$	−5.67857	+	1.99198i	−0.258384	+	0.0906384i
$484$	−4.92286			−0.223766
$485$	2.76022	+	3.18546i	0.125335	+	0.144644i
$486$	11.6263	+	7.47174i	0.527378	+	0.338925i
$487$	−4.77328	+	33.1989i	−0.216298	+	1.50438i	0.535243	+	0.844698i	$0.320220\pi$
$487$	−4.77328	+	33.1989i	−0.216298	+	1.50438i	−0.751541	+	0.659686i	$0.770689\pi$
$488$	−0.700702	+	1.53432i	−0.0317193	+	0.0694556i
$489$	0.400507	+	2.78559i	0.0181116	+	0.125969i
$490$	−0.986605	−	0.289693i	−0.0445703	−	0.0130870i
$491$	−31.0235	+	19.9376i	−1.40007	+	0.899770i	−0.999861	−	0.0166550i	$-0.994698\pi$
$491$	−31.0235	+	19.9376i	−1.40007	+	0.899770i	−0.400207	+	0.916425i	$0.631062\pi$
$492$	1.21002	+	2.64957i	0.0545519	+	0.119452i
$493$	43.1785	−	12.6783i	1.94466	−	0.571004i
$494$	8.03930	−	9.27785i	0.361705	−	0.417430i
$495$	1.58203	−	1.82576i	0.0711070	−	0.0820618i
$496$	−5.60835	+	1.64676i	−0.251822	+	0.0739417i
$497$	3.45535	+	7.56617i	0.154994	+	0.339389i
$498$	2.17168	−	1.39566i	0.0973154	−	0.0625408i
$499$	−1.74302	−	0.511796i	−0.0780281	−	0.0229111i	0.242485	−	0.970155i	$-0.422037\pi$
$499$	−1.74302	−	0.511796i	−0.0780281	−	0.0229111i	−0.320514	+	0.947244i	$0.603856\pi$
$500$	0.523157	+	3.63863i	0.0233963	+	0.162725i
$501$	0.997076	−	2.18329i	0.0445461	−	0.0975423i
$502$	3.71317	−	25.8256i	0.165727	−	1.15265i
$503$	−36.3640	−	23.3697i	−1.62139	−	1.04200i	−0.955087	−	0.296324i	$-0.904239\pi$
$503$	−36.3640	−	23.3697i	−1.62139	−	1.04200i	−0.666304	−	0.745681i	$-0.732124\pi$
$504$	−3.54549	−	4.09171i	−0.157928	−	0.182259i
$505$	−3.00158			−0.133569
$506$	4.34812	−	10.9940i	0.193298	−	0.488743i
$507$	−0.568431			−0.0252449
$508$	4.94344	+	5.70503i	0.219330	+	0.253120i
$509$	19.8613	+	12.7641i	0.880335	+	0.565757i	0.900898	−	0.434032i	$-0.142909\pi$
$509$	19.8613	+	12.7641i	0.880335	+	0.565757i	−0.0205626	+	0.999789i	$0.506546\pi$
$510$	0.203930	−	1.41837i	0.00903019	−	0.0628064i
$511$	7.43486	−	16.2801i	0.328899	−	0.720188i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	10.8221	+	3.17765i	0.477806	+	0.140297i
$514$	23.5511	−	15.1354i	1.03880	−	0.667594i
$515$	−2.28448	−	5.00232i	−0.100666	−	0.220428i
$516$	−6.51104	+	1.91181i	−0.286633	+	0.0841629i
$517$	−3.94713	+	4.55524i	−0.173595	+	0.200339i
$518$	−6.31144	+	7.28379i	−0.277309	+	0.320031i
$519$	11.1075	−	3.26146i	0.487566	−	0.143162i
$520$	0.578047	+	1.26575i	0.0253490	+	0.0555067i
$521$	11.1492	−	7.16515i	0.488455	−	0.313911i	−0.273129	−	0.961977i	$-0.588059\pi$
$521$	11.1492	−	7.16515i	0.488455	−	0.313911i	0.761584	+	0.648067i	$0.224422\pi$
$522$	−17.9911	−	5.28266i	−0.787449	−	0.231216i
$523$	2.34845	+	16.3338i	0.102690	+	0.714227i	0.974501	+	0.224384i	$0.0720369\pi$
$523$	2.34845	+	16.3338i	0.102690	+	0.714227i	−0.871810	+	0.489843i	$0.837054\pi$
$524$	−1.35869	+	2.97511i	−0.0593544	+	0.129968i
$525$	−0.868069	+	6.03755i	−0.0378856	+	0.263500i
$526$	−7.93593	−	5.10011i	−0.346023	−	0.222375i
$527$	24.1495	+	27.8700i	1.05197	+	1.21404i
$528$	−1.50195			−0.0653640
$529$	−16.7779	−	15.7321i	−0.729476	−	0.684007i
$530$	−2.25443			−0.0979261
$531$	−20.3309	−	23.4631i	−0.882287	−	1.01821i
$532$	−5.69828	−	3.66206i	−0.247052	−	0.158771i
$533$	−2.53967	+	17.6638i	−0.110005	+	0.765102i
$534$	−2.28576	+	5.00512i	−0.0989147	+	0.216593i
$535$	0.354477	+	2.46544i	0.0153254	+	0.106590i
$536$	−13.5237	−	3.97093i	−0.584136	−	0.171518i
$537$	−1.22982	+	0.790355i	−0.0530705	+	0.0341063i
$538$	−7.21622	−	15.8013i	−0.311113	−	0.681243i
$539$	6.52430	−	1.91571i	0.281021	−	0.0825154i
$540$	−0.837201	+	0.966181i	−0.0360274	+	0.0415778i
$541$	11.5093	−	13.2824i	0.494823	−	0.571056i	−0.452325	−	0.891853i	$-0.649405\pi$
$541$	11.5093	−	13.2824i	0.494823	−	0.571056i	0.947148	+	0.320797i	$0.103951\pi$
$542$	17.1793	−	5.04431i	0.737915	−	0.216672i
$543$	−6.58214	−	14.4129i	−0.282467	−	0.618516i
$544$	5.30755	−	3.41095i	0.227559	−	0.146243i
$545$	1.45925	+	0.428474i	0.0625073	+	0.0183538i
$546$	0.666573	+	4.63612i	0.0285267	+	0.198408i
$547$	−6.97178	+	15.2661i	−0.298092	+	0.652730i	−0.998114	−	0.0613912i	$-0.980446\pi$
$547$	−6.97178	+	15.2661i	−0.298092	+	0.652730i	0.700022	+	0.714121i	$0.253174\pi$
$548$	−2.26703	+	15.7675i	−0.0968426	+	0.673555i
$549$	−3.73023	−	2.39727i	−0.159202	−	0.102313i
$550$	−7.84742	−	9.05641i	−0.334615	−	0.386167i
$551$	−23.4588			−0.999379
$552$	−1.07463	+	2.71714i	−0.0457392	+	0.115649i
$553$	−4.90989			−0.208790
$554$	−10.0076	−	11.5494i	−0.425184	−	0.490688i
$555$	0.894132	+	0.574624i	0.0379538	+	0.0243914i
$556$	0.406233	−	2.82541i	0.0172281	−	0.119824i
$557$	−2.94060	+	6.43902i	−0.124597	+	0.272830i	−0.961644	−	0.274302i	$-0.911553\pi$
$557$	−2.94060	+	6.43902i	−0.124597	+	0.272830i	0.837046	+	0.547132i	$0.184280\pi$
$558$	−2.18676	−	15.2092i	−0.0925727	−	0.643857i
$559$	−39.8902	−	11.7128i	−1.68718	−	0.495400i
$560$	0.645886	−	0.415086i	0.0272937	−	0.0175406i
$561$	3.93645	+	8.61962i	0.166197	+	0.363921i
$562$	5.68699	−	1.66985i	0.239891	−	0.0704384i
$563$	−13.8766	+	16.0145i	−0.584830	+	0.674930i	−0.968636	−	0.248484i	$-0.920068\pi$
$563$	−13.8766	+	16.0145i	−0.584830	+	0.674930i	0.383806	+	0.923414i	$0.374613\pi$
$564$	0.975524	−	1.12581i	0.0410770	−	0.0474054i
$565$	−1.99775	+	0.586594i	−0.0840462	+	0.0246782i
$566$	−0.649526	−	1.42226i	−0.0273016	−	0.0597822i
$567$	10.0438	−	6.45474i	0.421799	−	0.271074i
$568$	3.87510	+	1.13783i	0.162595	+	0.0477423i
$569$	1.88114	+	13.0836i	0.0788615	+	0.548494i	0.990501	+	0.137504i	$0.0439079\pi$
$569$	1.88114	+	13.0836i	0.0788615	+	0.548494i	−0.911640	+	0.410990i	$0.865183\pi$
$570$	−0.310309	+	0.679482i	−0.0129974	+	0.0284604i
$571$	−3.20729	+	22.3072i	−0.134221	+	0.933527i	0.805746	+	0.592261i	$0.201765\pi$
$571$	−3.20729	+	22.3072i	−0.134221	+	0.933527i	−0.939967	+	0.341266i	$0.889144\pi$
$572$	−7.74103	−	4.97486i	−0.323669	−	0.208009i
$573$	−4.17701	−	4.82053i	−0.174497	−	0.201381i
$574$	9.84632			0.410978
$575$	−21.9985	+	7.71682i	−0.917399	+	0.321814i
$576$	−2.62880			−0.109533
$577$	9.68345	+	11.1753i	0.403127	+	0.465233i	0.920623	−	0.390452i	$-0.127681\pi$
$577$	9.68345	+	11.1753i	0.403127	+	0.465233i	−0.517496	+	0.855686i	$0.673136\pi$
$578$	−19.1845	−	12.3291i	−0.797969	−	0.512824i
$579$	0.0668723	−	0.465107i	0.00277912	−	0.0193292i
$580$	1.10459	−	2.41871i	0.0458655	−	0.100431i
$581$	−1.24189	−	8.63754i	−0.0515223	−	0.358345i
$582$	6.60972	+	1.94079i	0.273982	+	0.0804483i
$583$	12.5416	−	8.06002i	0.519421	−	0.333812i
$584$	−3.60997	−	7.90472i	−0.149381	−	0.327100i
$585$	−3.50978	+	1.03056i	−0.145112	+	0.0426086i
$586$	1.34781	−	1.55546i	0.0556776	−	0.0642554i
$587$	−9.99065	+	11.5298i	−0.412358	+	0.475887i	−0.923494	−	0.383613i	$-0.874680\pi$
$587$	−9.99065	+	11.5298i	−0.412358	+	0.475887i	0.511136	+	0.859500i	$0.329225\pi$
$588$	−1.61246	+	0.473462i	−0.0664969	+	0.0195252i
$589$	−7.98587	−	17.4866i	−0.329052	−	0.720524i
$590$	3.70371	−	2.38023i	0.152479	−	0.0979926i
$591$	3.04411	+	0.893832i	0.125218	+	0.0367674i
$592$	0.665978	+	4.63198i	0.0273715	+	0.190373i
$593$	−1.54253	+	3.37768i	−0.0633443	+	0.138705i	−0.938657	−	0.344854i	$-0.887929\pi$
$593$	−1.54253	+	3.37768i	−0.0633443	+	0.138705i	0.875312	+	0.483558i	$0.160656\pi$
$594$	1.20315	−	8.36812i	0.0493660	−	0.343348i
$595$	−4.07495	−	2.61881i	−0.167057	−	0.107361i
$596$	1.91136	+	2.20583i	0.0782924	+	0.0903543i
$597$	14.2219			0.582063
$598$	−14.5385	+	10.4446i	−0.594523	+	0.427113i
$599$	−8.17752			−0.334124			−0.167062	−	0.985946i	$-0.553428\pi$
$599$	−8.17752			−0.334124			−0.167062	+	0.985946i	$0.553428\pi$
$600$	1.93947	+	2.23827i	0.0791786	+	0.0913769i
$601$	28.9896	+	18.6305i	1.18251	+	0.759952i	0.975846	−	0.218460i	$-0.0701033\pi$
$601$	28.9896	+	18.6305i	1.18251	+	0.759952i	0.206663	+	0.978412i	$0.433740\pi$
$602$	−3.26455	+	22.7054i	−0.133053	+	0.925404i
$603$	15.3920	−	33.7037i	0.626809	−	1.37252i
$604$	−3.49556	−	24.3122i	−0.142232	−	0.989248i
$605$	1.76083	+	0.517027i	0.0715880	+	0.0210201i
$606$	−4.12690	+	2.65220i	−0.167644	+	0.107738i
$607$	7.92178	+	17.3463i	0.321535	+	0.704063i	0.999519	−	0.0310132i	$-0.00987340\pi$
$607$	7.92178	+	17.3463i	0.321535	+	0.704063i	−0.677984	+	0.735077i	$0.737146\pi$
$608$	−3.15565	+	0.926583i	−0.127979	+	0.0375779i
$609$	5.86116	−	6.76414i	0.237506	−	0.274097i
$610$	0.411774	−	0.475213i	0.0166723	−	0.0192408i
$611$	8.75683	−	2.57124i	0.354263	−	0.104021i
$612$	6.88979	+	15.0865i	0.278503	+	0.609837i
$613$	9.99590	−	6.42398i	0.403731	−	0.259462i	−0.322980	−	0.946406i	$-0.604685\pi$
$613$	9.99590	−	6.42398i	0.403731	−	0.259462i	0.726710	+	0.686944i	$0.241048\pi$
$614$	10.3952	+	3.05231i	0.419517	+	0.123181i
$615$	−0.154532	−	1.07480i	−0.00623135	−	0.0433400i
$616$	−2.10912	+	4.61833i	−0.0849789	+	0.186078i
$617$	1.52507	−	10.6071i	0.0613972	−	0.427027i	−0.935820	−	0.352478i	$-0.885339\pi$
$617$	1.52507	−	10.6071i	0.0613972	−	0.427027i	0.997217	−	0.0745490i	$-0.0237517\pi$
$618$	−7.56100	−	4.85916i	−0.304148	−	0.195464i
$619$	3.76265	+	4.34233i	0.151234	+	0.174533i	0.826311	−	0.563214i	$-0.190435\pi$
$619$	3.76265	+	4.34233i	0.151234	+	0.174533i	−0.675077	+	0.737747i	$0.735890\pi$
$620$	2.17897			0.0875097
$621$	−14.2777	−	8.16388i	−0.572945	−	0.327605i
$622$	22.8972			0.918095
$623$	12.1804	+	14.0569i	0.487998	+	0.563179i
$624$	1.91318	+	1.22952i	0.0765883	+	0.0492203i
$625$	−3.26396	+	22.7013i	−0.130558	+	0.908053i
$626$	9.69914	−	21.2382i	0.387656	−	0.848848i
$627$	−0.702996	−	4.88945i	−0.0280750	−	0.195266i
$628$	12.5737	+	3.69197i	0.501744	+	0.147325i
$629$	24.8372	−	15.9619i	0.990326	−	0.636444i
$630$	0.838432	+	1.83591i	0.0334039	+	0.0731444i
$631$	13.1735	−	3.86808i	0.524428	−	0.153986i	−0.00879404	−	0.999961i	$-0.502799\pi$
$631$	13.1735	−	3.86808i	0.524428	−	0.153986i	0.533222	+	0.845975i	$0.320981\pi$
$632$	−1.56117	+	1.80169i	−0.0621001	+	0.0716674i
$633$	−3.46957	+	4.00410i	−0.137903	+	0.159149i
$634$	0.483037	−	0.141833i	0.0191839	−	0.00563289i
$635$	−1.16902	−	2.55980i	−0.0463911	−	0.101582i
$636$	−3.09963	+	1.99201i	−0.122908	+	0.0789884i
$637$	−9.87884	−	2.90069i	−0.391414	−	0.114930i
$638$	2.50241	+	17.4047i	0.0990714	+	0.689057i
$639$	−4.41042	+	9.65747i	−0.174473	+	0.382044i
$640$	0.0530529	−	0.368991i	0.00209710	−	0.0145857i
$641$	30.5273	+	19.6187i	1.20576	+	0.774892i	0.979943	−	0.199279i	$-0.0638599\pi$
$641$	30.5273	+	19.6187i	1.20576	+	0.774892i	0.225813	+	0.974171i	$0.427496\pi$
$642$	2.66584	+	3.07654i	0.105212	+	0.121421i
$643$	−14.8477			−0.585535			−0.292768	−	0.956184i	$-0.594576\pi$
$643$	−14.8477			−0.585535			−0.292768	+	0.956184i	$0.594576\pi$
$644$	6.84586	+	7.11992i	0.269765	+	0.280564i
$645$	2.52969			0.0996066
$646$	13.5882	+	15.6817i	0.534622	+	0.616987i
$647$	1.61467	+	1.03768i	0.0634792	+	0.0407956i	0.571995	−	0.820257i	$-0.306169\pi$
$647$	1.61467	+	1.03768i	0.0634792	+	0.0407956i	−0.508516	+	0.861052i	$0.669806\pi$
$648$	0.824994	−	5.73796i	0.0324088	−	0.225408i
$649$	−12.0944	+	26.4830i	−0.474746	+	1.03955i
$650$	2.58226	+	17.9600i	0.101285	+	0.704451i
$651$	7.03737	+	2.06636i	0.275816	+	0.0809870i
$652$	3.88581	−	2.49726i	0.152180	−	0.0978001i
$653$	−9.92317	−	21.7287i	−0.388324	−	0.850310i	−0.998322	−	0.0579075i	$-0.981557\pi$
$653$	−9.92317	−	21.7287i	−0.388324	−	0.850310i	0.609998	−	0.792403i	$-0.291170\pi$
$654$	2.38493	−	0.700279i	0.0932582	−	0.0273831i
$655$	0.798444	−	0.921454i	0.0311978	−	0.0360042i
$656$	3.13079	−	3.61312i	0.122237	−	0.141069i
$657$	21.9190	−	6.43598i	0.855140	−	0.251092i
$658$	−2.09187	−	4.58056i	−0.0815497	−	0.178569i
$659$	−1.46729	+	0.942968i	−0.0571574	+	0.0367328i	−0.568907	−	0.822402i	$-0.692634\pi$
$659$	−1.46729	+	0.942968i	−0.0571574	+	0.0367328i	0.511750	+	0.859134i	$0.328997\pi$
$660$	0.537225	+	0.157744i	0.0209115	+	0.00614016i
$661$	−4.36964	−	30.3915i	−0.169959	−	1.18209i	−0.878964	−	0.476888i	$-0.841765\pi$
$661$	−4.36964	−	30.3915i	−0.169959	−	1.18209i	0.709005	−	0.705204i	$-0.249144\pi$
$662$	−8.39272	+	18.3775i	−0.326192	+	0.714262i
$663$	2.04195	−	14.2021i	0.0793027	−	0.551563i
$664$	−3.56443	−	2.29072i	−0.138327	−	0.0888972i
$665$	1.65358	+	1.90833i	0.0641231	+	0.0740020i
$666$	−12.3017			−0.476683
$667$	33.2768	+	7.92577i	1.28848	+	0.306887i
$668$	−3.93949			−0.152424
$669$	−1.53256	−	1.76866i	−0.0592521	−	0.0683805i
$670$	4.42019	+	2.84068i	0.170767	+	0.109745i
$671$	−0.591768	+	4.11583i	−0.0228449	+	0.158890i
$672$	0.521264	−	1.14141i	0.0201082	−	0.0440308i
$673$	−1.67682	−	11.6625i	−0.0646367	−	0.449558i	−0.996279	−	0.0861824i	$-0.972533\pi$
$673$	−1.67682	−	11.6625i	−0.0646367	−	0.449558i	0.931643	−	0.363376i	$-0.118376\pi$
$674$	3.93944	+	1.15672i	0.151742	+	0.0445554i
$675$	−14.0242	+	9.01278i	−0.539790	+	0.346902i
$676$	0.387574	+	0.848668i	0.0149067	+	0.0326411i
$677$	−27.3889	+	8.04212i	−1.05264	+	0.309084i	−0.761885	−	0.647713i	$-0.775726\pi$
$677$	−27.3889	+	8.04212i	−1.05264	+	0.309084i	−0.290758	+	0.956797i	$0.593908\pi$
$678$	−2.22841	+	2.57173i	−0.0855818	+	0.0987666i
$679$	15.2494	−	17.5988i	0.585220	−	0.675380i
$680$	−2.25667	+	0.662618i	−0.0865393	+	0.0254102i
$681$	−0.514808	−	1.12727i	−0.0197275	−	0.0431972i
$682$	−12.1219	+	7.79025i	−0.464170	+	0.298304i
$683$	−14.4113	−	4.23154i	−0.551433	−	0.161915i	−0.00586616	−	0.999983i	$-0.501867\pi$
$683$	−14.4113	−	4.23154i	−0.551433	−	0.161915i	−0.545566	+	0.838068i	$0.683685\pi$
$684$	−1.23042	−	8.55778i	−0.0470464	−	0.327215i
$685$	2.46688	−	5.40171i	0.0942546	−	0.206389i
$686$	−2.86019	+	19.8930i	−0.109202	+	0.759519i
$687$	−14.0646	−	9.03876i	−0.536598	−	0.344850i
$688$	7.29377	+	8.41745i	0.278072	+	0.320912i
$689$	−22.5735			−0.859983
$690$	0.669748	−	0.859017i	0.0254969	−	0.0327022i
$691$	20.7588			0.789701			0.394851	−	0.918745i	$-0.370796\pi$
$691$	20.7588			0.789701			0.394851	+	0.918745i	$0.370796\pi$
$692$	−12.4428	−	14.3598i	−0.473005	−	0.545877i
$693$	−11.2280	−	7.21581i	−0.426517	−	0.274106i
$694$	3.47469	−	24.1670i	0.131898	−	0.917367i
$695$	−0.442045	+	0.967943i	−0.0167677	+	0.0367162i
$696$	−0.618465	−	4.30152i	−0.0234428	−	0.163049i
$697$	−28.9410	−	8.49783i	−1.09622	−	0.321878i
$698$	−14.5496	+	9.35043i	−0.550709	+	0.353919i
$699$	−1.78302	−	3.90428i	−0.0674401	−	0.147673i
$700$	9.60594	−	2.82056i	0.363070	−	0.106607i
$701$	−15.6028	+	18.0066i	−0.589311	+	0.680101i	−0.969580	−	0.244775i	$-0.921286\pi$
$701$	−15.6028	+	18.0066i	−0.589311	+	0.680101i	0.380269	+	0.924876i	$0.375831\pi$
$702$	−8.38286	+	9.67434i	−0.316391	+	0.365134i
$703$	−14.7672	+	4.33605i	−0.556956	+	0.163537i
$704$	1.02408	+	2.24241i	0.0385963	+	0.0845141i
$705$	−0.467170	+	0.300232i	−0.0175946	+	0.0113074i
$706$	−9.19077	−	2.69865i	−0.345899	−	0.101565i
$707$	2.35999	+	16.4141i	0.0887567	+	0.617317i
$708$	2.98909	−	6.54520i	0.112337	−	0.245984i
$709$	2.59095	−	18.0204i	0.0973050	−	0.676771i	−0.881531	−	0.472126i	$-0.843487\pi$
$709$	2.59095	−	18.0204i	0.0973050	−	0.676771i	0.978836	−	0.204645i	$-0.0656041\pi$
$710$	−1.26656	−	0.813970i	−0.0475332	−	0.0305478i
$711$	−4.10401	−	4.73628i	−0.153912	−	0.177624i
$712$	9.03115			0.338457
$713$	5.42010	+	27.5032i	0.202984	+	1.03000i
$714$	−7.91667			−0.296274
$715$	2.24636	+	2.59244i	0.0840092	+	0.0969518i
$716$	2.01853	+	1.29723i	0.0754359	+	0.0484797i
$717$	2.26139	−	15.7283i	0.0844531	−	0.587385i
$718$	−0.0520416	+	0.113955i	−0.00194218	+	0.00425277i
$719$	1.78226	+	12.3959i	0.0664671	+	0.462289i	0.995688	+	0.0927643i	$0.0295703\pi$
$719$	1.78226	+	12.3959i	0.0664671	+	0.462289i	−0.929221	+	0.369524i	$0.879521\pi$
$720$	0.940282	+	0.276092i	0.0350422	+	0.0102893i
$721$	−25.5590	+	16.4257i	−0.951865	+	0.611727i
$722$	3.39947	+	7.44380i	0.126515	+	0.277029i
$723$	0.812697	−	0.238629i	0.0302245	−	0.00887473i
$724$	−17.0305	+	19.6543i	−0.632934	+	0.730445i
$725$	22.7058	−	26.2039i	0.843271	−	0.973187i
$726$	2.87783	−	0.845007i	0.106806	−	0.0313611i
$727$	−5.15039	−	11.2778i	−0.191017	−	0.418270i	0.789756	−	0.613422i	$-0.210207\pi$
$727$	−5.15039	−	11.2778i	−0.191017	−	0.418270i	−0.980773	+	0.195152i	$0.937480\pi$
$728$	6.46723	−	4.15624i	0.239692	−	0.154040i
$729$	8.60738	+	2.52735i	0.318792	+	0.0936057i
$730$	0.461031	+	3.20654i	0.0170635	+	0.118679i
$731$	29.1912	−	63.9198i	1.07968	−	2.36416i
$732$	0.146254	−	1.01722i	0.00540570	−	0.0375974i
$733$	−13.8021	−	8.87008i	−0.509793	−	0.327624i	0.260330	−	0.965520i	$-0.416169\pi$
$733$	−13.8021	−	8.87008i	−0.509793	−	0.327624i	−0.770123	+	0.637896i	$0.779805\pi$
$734$	−2.77314	−	3.20037i	−0.102358	−	0.118128i
$735$	0.626480			0.0231081
$736$	4.78940	−	0.248210i	0.176540	−	0.00914915i
$737$	−34.7460			−1.27988
$738$	8.23020	+	9.49816i	0.302958	+	0.349632i
$739$	−35.5232	−	22.8294i	−1.30674	−	0.839792i	−0.312813	−	0.949815i	$-0.601271\pi$
$739$	−35.5232	−	22.8294i	−1.30674	−	0.839792i	−0.993929	+	0.110023i	$0.964908\pi$
$740$	0.248267	−	1.72673i	0.00912648	−	0.0634760i
$741$	−3.10712	+	6.80363i	−0.114143	+	0.249938i
$742$	1.77255	+	12.3283i	0.0650722	+	0.452587i
$743$	13.8891	+	4.07820i	0.509541	+	0.149615i	0.526390	−	0.850243i	$-0.323545\pi$
$743$	13.8891	+	4.07820i	0.509541	+	0.149615i	−0.0168491	+	0.999858i	$0.505363\pi$
$744$	2.99589	−	1.92534i	0.109835	−	0.0705864i
$745$	−0.451997	−	0.989735i	−0.0165599	−	0.0362611i
$746$	−0.601077	+	0.176492i	−0.0220070	+	0.00646184i
$747$	7.29406	−	8.41779i	0.266876	−	0.307991i
$748$	10.1851	−	11.7542i	0.372404	−	0.429778i
$749$	13.2035	−	3.87691i	0.482447	−	0.141659i
$750$	−0.930400	−	2.03729i	−0.0339734	−	0.0743913i
$751$	−24.5633	+	15.7859i	−0.896327	+	0.576034i	−0.905699	−	0.423922i	$-0.860653\pi$
$751$	−24.5633	+	15.7859i	−0.896327	+	0.576034i	0.00937174	+	0.999956i	$0.497017\pi$
$752$	−2.34598	−	0.688843i	−0.0855492	−	0.0251195i
$753$	2.26230	+	15.7346i	0.0824428	+	0.573402i
$754$	11.0602	−	24.2185i	0.402789	−	0.881984i
$755$	−1.30310	+	9.06323i	−0.0474245	+	0.329845i
$756$	5.94180	+	3.81856i	0.216101	+	0.138880i
$757$	10.7066	+	12.3561i	0.389140	+	0.449091i	0.916191	−	0.400743i	$-0.131248\pi$
$757$	10.7066	+	12.3561i	0.389140	+	0.449091i	−0.527051	+	0.849834i	$0.676702\pi$
$758$	10.5210			0.382140
$759$	−0.654729	+	7.17328i	−0.0237652	+	0.260374i
$760$	1.22605			0.0444733
$761$	3.34567	+	3.86111i	0.121281	+	0.139965i	0.813143	−	0.582064i	$-0.197755\pi$
$761$	3.34567	+	3.86111i	0.121281	+	0.139965i	−0.691862	+	0.722030i	$0.743209\pi$
$762$	−3.86913	−	2.48654i	−0.140164	−	0.0900778i
$763$	1.19577	−	8.31677i	0.0432898	−	0.301087i
$764$	−4.34904	+	9.52307i	−0.157343	+	0.344532i
$765$	−0.879900	−	6.11984i	−0.0318128	−	0.221263i
$766$	−14.7473	−	4.33020i	−0.532841	−	0.156456i
$767$	37.0852	−	23.8332i	1.33907	−	0.860567i
$768$	−0.253098	−	0.554206i	−0.00913287	−	0.0199982i
$769$	−27.4772	+	8.06804i	−0.990854	+	0.290941i	−0.736698	−	0.676222i	$-0.763616\pi$
$769$	−27.4772	+	8.06804i	−0.990854	+	0.290941i	−0.254156	+	0.967163i	$0.581798\pi$
$770$	1.23945	−	1.43040i	0.0446665	−	0.0515479i
$771$	−11.1697	+	12.8905i	−0.402265	+	0.464239i
$772$	−0.740001	+	0.217284i	−0.0266332	+	0.00782022i
$773$	10.3555	+	22.6753i	0.372460	+	0.815575i	0.999335	+	0.0364547i	$0.0116065\pi$
$773$	10.3555	+	22.6753i	0.372460	+	0.815575i	−0.626875	+	0.779120i	$0.715666\pi$
$774$	−24.6313	+	15.8296i	−0.885353	+	0.568982i
$775$	27.2623	+	8.00495i	0.979292	+	0.287546i
$776$	−1.60911	−	11.1916i	−0.0577636	−	0.401755i
$777$	2.43931	−	5.34135i	0.0875098	−	0.191620i
$778$	3.09318	−	21.5135i	0.110896	−	0.771297i
$779$	13.2275	+	8.50081i	0.473925	+	0.304573i
$780$	−0.555183	−	0.640715i	−0.0198787	−	0.0229413i
$781$	9.95612			0.356258
$782$	−13.9770	−	26.8356i	−0.499816	−	0.959640i
$783$	24.4613			0.874177
$784$	1.80631	+	2.08459i	0.0645109	+	0.0744496i
$785$	−4.10967	−	2.64112i	−0.146680	−	0.0942657i
$786$	0.283591	−	1.97242i	0.0101154	−	0.0703539i
$787$	−2.13186	+	4.66813i	−0.0759927	+	0.166401i	−0.943815	−	0.330473i	$-0.892792\pi$
$787$	−2.13186	+	4.66813i	−0.0759927	+	0.166401i	0.867823	+	0.496874i	$0.165519\pi$
$788$	−0.741077	−	5.15430i	−0.0263998	−	0.183614i
$789$	5.51466	+	1.61925i	0.196327	+	0.0576468i
$790$	0.747632	−	0.480474i	0.0265996	−	0.0170945i
$791$	4.77852	+	10.4635i	0.169904	+	0.372039i
$792$	−6.21797	+	1.82576i	−0.220946	+	0.0648756i
$793$	4.12308	−	4.75829i	0.146415	−	0.168972i
$794$	6.65273	−	7.67767i	0.236097	−	0.272470i
$795$	1.31791	−	0.386972i	0.0467413	−	0.0137245i
$796$	−9.69692	−	21.2333i	−0.343698	−	0.752594i
$797$	−8.01241	+	5.14926i	−0.283814	+	0.182396i	−0.674800	−	0.738000i	$-0.735770\pi$
$797$	−8.01241	+	5.14926i	−0.283814	+	0.182396i	0.390986	+	0.920396i	$0.372134\pi$
$798$	3.95972	+	1.16268i	0.140173	+	0.0411584i
$799$	2.19533	+	15.2689i	0.0776653	+	0.540174i
$800$	2.01935	−	4.42175i	0.0713946	−	0.156332i
$801$	−3.37871	+	23.4994i	−0.119381	+	0.830311i
$802$	26.8343	+	17.2454i	0.947553	+	0.608956i
$803$	−14.0288	−	16.1901i	−0.495065	−	0.571335i
$804$	8.58738			0.302854
$805$	−1.70089	−	3.26568i	−0.0599483	−	0.115100i
$806$	21.8180			0.768506
$807$	6.93078	+	7.99855i	0.243975	+	0.281562i
$808$	6.77358	+	4.35311i	0.238294	+	0.153142i
$809$	1.51002	−	10.5024i	0.0530894	−	0.369245i	−0.945906	−	0.324440i	$-0.894824\pi$
$809$	1.51002	−	10.5024i	0.0530894	−	0.369245i	0.998996	−	0.0448052i	$-0.0142667\pi$
$810$	−0.897722	+	1.96574i	−0.0315427	+	0.0690690i
$811$	4.38612	+	30.5061i	0.154018	+	1.07122i	0.909397	+	0.415928i	$0.136543\pi$
$811$	4.38612	+	30.5061i	0.154018	+	1.07122i	−0.755380	+	0.655287i	$0.772548\pi$
$812$	−14.0952	−	4.13872i	−0.494643	−	0.145240i
$813$	−9.17692	+	5.89765i	−0.321849	+	0.206840i
$814$	4.79227	+	10.4936i	0.167969	+	0.367801i
$815$	−1.65217	+	0.485122i	−0.0578731	+	0.0169931i
$816$	−2.51722	+	2.90503i	−0.0881204	+	0.101696i
$817$	−23.9883	+	27.6840i	−0.839244	+	0.968539i
$818$	−12.6794	+	3.72301i	−0.443325	+	0.130172i
$819$	8.39520	+	18.3829i	0.293352	+	0.642351i
$820$	−1.49931	+	0.963546i	−0.0523580	+	0.0336485i
$821$	−40.3116	−	11.8365i	−1.40688	−	0.413098i	−0.511842	−	0.859080i	$-0.671037\pi$
$821$	−40.3116	−	11.8365i	−1.40688	−	0.413098i	−0.895042	+	0.445982i	$0.852855\pi$
$822$	−1.38122	−	9.60659i	−0.0481756	−	0.335068i
$823$	−11.6572	+	25.5257i	−0.406344	+	0.889770i	0.590243	+	0.807226i	$0.299032\pi$
$823$	−11.6572	+	25.5257i	−0.406344	+	0.889770i	−0.996587	+	0.0825444i	$0.973695\pi$
$824$	−2.09941	+	14.6017i	−0.0731363	+	0.508674i
$825$	6.14202	+	3.94723i	0.213838	+	0.137425i
$826$	−15.9283	−	18.3823i	−0.554217	−	0.639601i
$827$	36.3429			1.26377			0.631883	−	0.775064i	$-0.282282\pi$
$827$	36.3429			1.26377			0.631883	+	0.775064i	$0.282282\pi$
$828$	−1.14594	+	12.5551i	−0.0398243	+	0.436319i
$829$	30.0375			1.04325			0.521623	−	0.853176i	$-0.325327\pi$
$829$	30.0375			1.04325			0.521623	+	0.853176i	$0.325327\pi$
$830$	1.03436	+	1.19371i	0.0359031	+	0.0414344i
$831$	7.83277	+	5.03382i	0.271716	+	0.174621i
$832$	0.531217	−	3.69470i	0.0184166	−	0.128091i
$833$	7.22922	−	15.8298i	0.250478	−	0.548469i
$834$	0.247503	+	1.72142i	0.00857034	+	0.0596080i
$835$	1.40910	+	0.413748i	0.0487638	+	0.0143184i
$836$	−6.82062	+	4.38335i	−0.235896	+	0.151601i
$837$	8.32715	+	18.2339i	0.287829	+	0.630257i
$838$	4.03271	−	1.18411i	0.139308	−	0.0409044i
$839$	21.8884	−	25.2606i	0.755671	−	0.872091i	−0.239434	−	0.970913i	$-0.576962\pi$
$839$	21.8884	−	25.2606i	0.755671	−	0.872091i	0.995105	+	0.0988214i	$0.0315073\pi$
$840$	−0.306326	+	0.353519i	−0.0105692	+	0.0121976i
$841$	−20.9904	+	6.16334i	−0.723807	+	0.212529i
$842$	−2.92258	−	6.39956i	−0.100719	−	0.220543i
$843$	−3.03790	+	1.95234i	−0.104631	+	0.0672421i
$844$	8.34378	+	2.44995i	0.287205	+	0.0843309i
$845$	−0.0494973	−	0.344261i	−0.00170276	−	0.0118429i
$846$	2.67007	−	5.84663i	0.0917988	−	0.201011i
$847$	1.44290	−	10.0356i	0.0495787	−	0.344828i
$848$	5.08750	+	3.26954i	0.174705	+	0.112276i
$849$	0.623835	+	0.719944i	0.0214099	+	0.0247084i
$850$	−30.6687			−1.05193
$851$	22.4125	−	1.16153i	0.768292	−	0.0398166i
$852$	−2.46063			−0.0842998
$853$	−3.84662	−	4.43924i	−0.131706	−	0.151997i	0.686066	−	0.727540i	$-0.259336\pi$
$853$	−3.84662	−	4.43924i	−0.131706	−	0.151997i	−0.817772	+	0.575543i	$0.804791\pi$
$854$	−2.92245	−	1.87815i	−0.100004	−	0.0642689i
$855$	−0.458684	+	3.19022i	−0.0156867	+	0.109103i
$856$	2.77563	−	6.07778i	0.0948690	−	0.207734i
$857$	−2.11934	−	14.7404i	−0.0723954	−	0.503521i	−0.993466	−	0.114126i	$-0.963593\pi$
$857$	−2.11934	−	14.7404i	−0.0723954	−	0.503521i	0.921071	−	0.389395i	$-0.127316\pi$
$858$	5.37922	+	1.57948i	0.183644	+	0.0539226i
$859$	−6.65486	+	4.27682i	−0.227061	+	0.145923i	−0.649225	−	0.760596i	$-0.724907\pi$
$859$	−6.65486	+	4.27682i	−0.227061	+	0.145923i	0.422165	+	0.906519i	$0.361270\pi$
$860$	−1.72482	−	3.77683i	−0.0588159	−	0.128789i
$861$	−5.75601	+	1.69012i	−0.196164	+	0.0575991i
$862$	24.1116	−	27.8263i	0.821245	−	0.947767i
$863$	2.64187	−	3.04888i	0.0899302	−	0.103785i	−0.709001	−	0.705208i	$-0.750854\pi$
$863$	2.64187	−	3.04888i	0.0899302	−	0.103785i	0.798931	+	0.601423i	$0.205399\pi$
$864$	3.29051	−	0.966181i	0.111945	−	0.0328701i
$865$	2.94246	+	6.44309i	0.100047	+	0.219072i
$866$	22.9052	−	14.7203i	0.778351	−	0.500216i
$867$	13.3313	+	3.91441i	0.452753	+	0.132940i
$868$	−1.71322	−	11.9157i	−0.0581504	−	0.404445i
$869$	−2.44137	+	5.34586i	−0.0828179	+	0.181346i
$870$	−0.230555	+	1.60354i	−0.00781654	+	0.0543652i
$871$	44.2592	+	28.4437i	1.49967	+	0.963777i
$872$	−2.67163	−	3.08323i	−0.0904730	−	0.104411i
$873$	29.7230			1.00597
$874$	3.04973	+	15.4752i	0.103159	+	0.523458i
$875$	−7.57096			−0.255945
$876$	3.46717	+	4.00133i	0.117145	+	0.135193i
$877$	−43.6317	−	28.0404i	−1.47334	−	0.946857i	−0.997740	−	0.0671940i	$-0.978595\pi$
$877$	−43.6317	−	28.0404i	−1.47334	−	0.946857i	−0.475598	−	0.879663i	$-0.657768\pi$
$878$	−3.44226	+	23.9415i	−0.116171	+	0.807985i
$879$	−0.520917	+	1.14065i	−0.0175701	+	0.0384732i
$880$	−0.130785	−	0.909632i	−0.00440877	−	0.0306637i
$881$	31.1274	+	9.13983i	1.04871	+	0.307929i	0.760295	−	0.649578i	$-0.225054\pi$
$881$	31.1274	+	9.13983i	1.04871	+	0.307929i	0.288413	+	0.957506i	$0.406872\pi$
$882$	−6.09995	+	3.92020i	−0.205396	+	0.132000i
$883$	−2.76535	−	6.05528i	−0.0930615	−	0.203776i	0.857377	−	0.514689i	$-0.172093\pi$
$883$	−2.76535	−	6.05528i	−0.0930615	−	0.203776i	−0.950438	+	0.310913i	$0.899365\pi$
$884$	−22.5960	+	6.63477i	−0.759984	+	0.223151i
$885$	−1.75657	+	2.02719i	−0.0590464	+	0.0681432i
$886$	10.1029	−	11.6593i	0.339412	−	0.391703i
$887$	−40.8783	+	12.0029i	−1.37256	+	0.403019i	−0.883172	−	0.469048i	$-0.844597\pi$
$887$	−40.8783	+	12.0029i	−1.37256	+	0.403019i	−0.489385	+	0.872068i	$0.662779\pi$
$888$	−1.18440	−	2.59347i	−0.0397458	−	0.0870312i
$889$	−13.0791	+	8.40541i	−0.438658	+	0.281908i
$890$	−3.23031	−	0.948504i	−0.108280	−	0.0317939i
$891$	−2.03376	−	14.1451i	−0.0681336	−	0.473880i
$892$	−1.59567	+	3.49404i	−0.0534271	+	0.116989i
$893$	1.14441	−	7.95953i	0.0382961	−	0.266355i
$894$	−1.49598	−	0.961410i	−0.0500332	−	0.0321544i
$895$	−0.585754	−	0.675997i	−0.0195796	−	0.0225961i
$896$	−2.05954			−0.0688043
$897$	6.70617	−	8.60131i	0.223912	−	0.287189i
$898$	−17.3241			−0.578112
$899$	−27.3024	−	31.5086i	−0.910586	−	1.05087i
$900$	10.7501	+	6.90867i	0.358336	+	0.230289i
$901$	5.42993	−	37.7660i	0.180897	−	1.25817i
$902$	4.89594	−	10.7206i	0.163017	−	0.356958i
$903$	−1.98897	−	13.8336i	−0.0661888	−	0.460353i
$904$	5.35899	+	1.57354i	0.178237	+	0.0523352i
$905$	8.15577	−	5.24140i	0.271107	−	0.174230i
$906$	6.21663	+	13.6125i	0.206534	+	0.452246i
$907$	−32.8643	+	9.64984i	−1.09124	+	0.320418i	−0.777367	−	0.629047i	$-0.783445\pi$
$907$	−32.8643	+	9.64984i	−1.09124	+	0.320418i	−0.313875	+	0.949464i	$0.601627\pi$
$908$	−1.33201	+	1.53722i	−0.0442042	+	0.0510143i
$909$	−13.8611	+	15.9965i	−0.459743	+	0.530572i
$910$	−2.74975	+	0.807398i	−0.0911532	+	0.0267650i
$911$	−14.6448	−	32.0677i	−0.485205	−	1.06245i	−0.980999	−	0.194011i	$-0.937850\pi$
$911$	−14.6448	−	32.0677i	−0.485205	−	1.06245i	0.495794	−	0.868440i	$-0.334877\pi$
$912$	1.68570	−	1.08333i	0.0558191	−	0.0358727i
$913$	−10.0220	−	2.94273i	−0.331680	−	0.0973901i
$914$	−0.977556	−	6.79905i	−0.0323347	−	0.224893i
$915$	−0.159147	+	0.348483i	−0.00526124	+	0.0115205i
$916$	−3.90521	+	27.1613i	−0.129032	+	0.897436i
$917$	−5.66674	−	3.64179i	−0.187132	−	0.120263i
$918$	−14.1689	−	16.3518i	−0.467645	−	0.539691i
$919$	34.5723			1.14043			0.570217	−	0.821494i	$-0.306859\pi$
$919$	34.5723			1.14043			0.570217	+	0.821494i	$0.306859\pi$
$920$	−1.73917	−	0.414230i	−0.0573386	−	0.0136568i
$921$	−6.60081			−0.217504
$922$	−0.223367	−	0.257779i	−0.00735620	−	0.00848951i
$923$	−12.6821	−	8.15026i	−0.417435	−	0.268269i
$924$	0.440226	−	3.06184i	0.0144824	−	0.100727i
$925$	9.44975	−	20.6921i	0.310706	−	0.680351i
$926$	2.32234	+	16.1523i	0.0763169	+	0.530796i
$927$	−37.2088	−	10.9255i	−1.22210	−	0.358840i
$928$	−6.00048	+	3.85627i	−0.196975	+	0.126588i
$929$	12.8087	+	28.0472i	0.420241	+	0.920200i	0.994811	+	0.101744i	$0.0324423\pi$
$929$	12.8087	+	28.0472i	0.420241	+	0.920200i	−0.574569	+	0.818456i	$0.694830\pi$
$930$	−1.27380	+	0.374020i	−0.0417694	+	0.0122646i
$931$	−5.94071	+	6.85595i	−0.194699	+	0.224695i
$932$	−4.61337	+	5.32411i	−0.151116	+	0.174397i
$933$	−13.3854	+	3.93030i	−0.438217	+	0.128672i
$934$	15.0523	+	32.9600i	0.492527	+	1.07848i
$935$	−4.87756	+	3.13462i	−0.159513	+	0.102513i
$936$	9.41501	+	2.76450i	0.307739	+	0.0903604i
$937$	0.649995	+	4.52082i	0.0212344	+	0.147689i	0.997680	−	0.0680739i	$-0.0216854\pi$
$937$	0.649995	+	4.52082i	0.0212344	+	0.147689i	−0.976446	+	0.215763i	$0.930776\pi$
$938$	12.0589	−	26.4052i	0.393736	−	0.862162i
$939$	−2.02445	+	14.0804i	−0.0660655	+	0.459495i
$940$	0.766777	+	0.492778i	0.0250095	+	0.0160726i
$941$	−7.54865	−	8.71161i	−0.246079	−	0.283990i	0.619251	−	0.785193i	$-0.287436\pi$
$941$	−7.54865	−	8.71161i	−0.246079	−	0.283990i	−0.865330	+	0.501203i	$0.832891\pi$
$942$	−7.98411			−0.260136
$943$	−15.8914	−	16.5276i	−0.517495	−	0.538212i
$944$	−11.8100			−0.384384
$945$	−1.72425	−	1.98989i	−0.0560897	−	0.0647310i
$946$	23.0983	+	14.8444i	0.750990	+	0.482632i
$947$	8.54365	−	59.4224i	0.277631	−	1.93097i	−0.0793268	−	0.996849i	$-0.525277\pi$
$947$	8.54365	−	59.4224i	0.277631	−	1.93097i	0.356958	−	0.934120i	$-0.383814\pi$
$948$	0.603379	−	1.32122i	0.0195968	−	0.0429111i
$949$	4.61629	+	32.1070i	0.149851	+	1.04224i
$950$	15.3397	+	4.50415i	0.497686	+	0.146134i
$951$	−0.258031	+	0.165826i	−0.00836722	+	0.00537729i
$952$	5.39782	+	11.8196i	0.174944	+	0.383075i
$953$	9.06804	−	2.66262i	0.293743	−	0.0862506i	−0.131541	−	0.991311i	$-0.541993\pi$
$953$	9.06804	−	2.66262i	0.293743	−	0.0862506i	0.425284	+	0.905060i	$0.360174\pi$
$954$	−10.4108	+	12.0147i	−0.337062	+	0.388990i
$955$	2.55575	−	2.94950i	0.0827023	−	0.0954435i
$956$	−25.0243	+	7.34778i	−0.809342	+	0.237644i
$957$	−4.45038	−	9.74496i	−0.143860	−	0.315010i
$958$	10.7308	−	6.89625i	0.346696	−	0.222808i
$959$	−31.4788	−	9.24301i	−1.01650	−	0.298472i
$960$	0.0323233	+	0.224813i	0.00104323	+	0.00725582i
$961$	1.31494	−	2.87931i	0.0424173	−	0.0928809i
$962$	2.48589	−	17.2897i	0.0801483	−	0.557444i
$963$	14.7762	+	9.49609i	0.476156	+	0.306007i
$964$	−0.910396	−	1.05065i	−0.0293219	−	0.0338392i
$965$	0.287508			0.00925520
$966$	−5.22412	−	2.98711i	−0.168083	−	0.0961086i
$967$	−39.0760			−1.25660			−0.628300	−	0.777971i	$-0.716249\pi$
$967$	−39.0760			−1.25660			−0.628300	+	0.777971i	$0.716249\pi$
$968$	−3.22379	−	3.72045i	−0.103616	−	0.119580i
$969$	−10.6352	−	6.83485i	−0.341653	−	0.219567i
$970$	−0.599853	+	4.17207i	−0.0192601	+	0.133957i
$971$	−17.2322	+	37.7334i	−0.553009	+	1.21092i	0.402353	+	0.915484i	$0.368192\pi$
$971$	−17.2322	+	37.7334i	−0.553009	+	1.21092i	−0.955362	+	0.295437i	$0.904535\pi$
$972$	1.96681	+	13.6795i	0.0630856	+	0.438770i
$973$	5.64075	+	1.65627i	0.180834	+	0.0530977i
$974$	−28.2159	+	18.1332i	−0.904094	+	0.581026i
$975$	−4.59239	−	10.0559i	−0.147074	−	0.322047i
$976$	−1.61843	+	0.475213i	−0.0518046	+	0.0152112i
$977$	13.5638	−	15.6535i	0.433944	−	0.500798i	−0.496090	−	0.868271i	$-0.665231\pi$
$977$	13.5638	−	15.6535i	0.433944	−	0.500798i	0.930034	+	0.367473i	$0.119777\pi$
$978$	−1.84293	+	2.12686i	−0.0589305	+	0.0680094i
$979$	21.3616	−	6.27235i	0.682721	−	0.200465i
$980$	−0.427153	−	0.935335i	−0.0136449	−	0.0298782i
$981$	9.02219	−	5.79821i	0.288056	−	0.185123i
$982$	−35.3838	−	10.3896i	−1.12914	−	0.331547i
$983$	3.53975	+	24.6195i	0.112901	+	0.785240i	0.965073	+	0.261980i	$0.0843754\pi$
$983$	3.53975	+	24.6195i	0.112901	+	0.785240i	−0.852173	+	0.523260i	$0.824715\pi$
$984$	−1.21002	+	2.64957i	−0.0385740	+	0.0844653i
$985$	−0.276263	+	1.92145i	−0.00880247	+	0.0612225i
$986$	37.8576	+	24.3296i	1.20563	+	0.774811i
$987$	2.00913	+	2.31866i	0.0639513	+	0.0738037i
$988$	12.2764			0.390563
$989$	43.3811	−	31.1655i	1.37944	−	0.991007i
$990$	2.41583			0.0767800
$991$	6.02871	+	6.95750i	0.191508	+	0.221012i	0.843381	−	0.537316i	$-0.180562\pi$
$991$	6.02871	+	6.95750i	0.191508	+	0.221012i	−0.651873	+	0.758328i	$0.726016\pi$
$992$	−4.91722	−	3.16011i	−0.156122	−	0.100334i
$993$	1.75177	−	12.1838i	0.0555907	−	0.386642i
$994$	−3.45535	+	7.56617i	−0.109597	+	0.239984i
$995$	1.23840	+	8.61326i	0.0392599	+	0.273059i
$996$	2.47691	+	0.727288i	0.0784840	+	0.0230450i
$997$	35.9389	−	23.0965i	1.13820	−	0.731474i	0.170940	−	0.985281i	$-0.445319\pi$
$997$	35.9389	−	23.0965i	1.13820	−	0.731474i	0.967255	+	0.253808i	$0.0816831\pi$
$998$	−0.754644	−	1.65244i	−0.0238878	−	0.0523070i
$999$	15.3983	−	4.52135i	0.487181	−	0.143049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.2.c.b.13.1	✓	10
3.2	odd	2		414.2.i.c.289.1		10
4.3	odd	2		368.2.m.a.289.1		10
23.4	even	11		1058.2.a.j.1.3		5
23.16	even	11	inner	46.2.c.b.39.1	yes	10
23.19	odd	22		1058.2.a.k.1.3		5
69.50	odd	22		9522.2.a.bz.1.3		5
69.62	odd	22		414.2.i.c.361.1		10
69.65	even	22		9522.2.a.bw.1.3		5
92.19	even	22		8464.2.a.bv.1.3		5
92.27	odd	22		8464.2.a.bu.1.3		5
92.39	odd	22		368.2.m.a.177.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.b.13.1	✓	10	1.1	even	1	trivial
46.2.c.b.39.1	yes	10	23.16	even	11	inner
368.2.m.a.177.1		10	92.39	odd	22
368.2.m.a.289.1		10	4.3	odd	2
414.2.i.c.289.1		10	3.2	odd	2
414.2.i.c.361.1		10	69.62	odd	22
1058.2.a.j.1.3		5	23.4	even	11
1058.2.a.k.1.3		5	23.19	odd	22
8464.2.a.bu.1.3		5	92.27	odd	22
8464.2.a.bv.1.3		5	92.19	even	22
9522.2.a.bw.1.3		5	69.65	even	22
9522.2.a.bz.1.3		5	69.50	odd	22

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.512546 - 0.329393i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.154861 - 0.339098i) q^{5} +(-0.0867074 - 0.603063i) q^{6} +(-1.97611 - 0.580239i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.09204 - 2.39124i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{2} +(-0.512546 - 0.329393i) q^{3} +(-0.142315 + 0.989821i) q^{4} +(0.154861 - 0.339098i) q^{5} +(-0.0867074 - 0.603063i) q^{6} +(-1.97611 - 0.580239i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-1.09204 - 2.39124i) q^{9} +(0.357685 - 0.105026i) q^{10} +(-1.61435 + 1.86306i) q^{11} +(0.398983 - 0.460451i) q^{12} +(3.58149 - 1.05162i) q^{13} +(-0.855563 - 1.87342i) q^{14} +(-0.191070 + 0.122793i) q^{15} +(-0.959493 - 0.281733i) q^{16} +(0.897877 + 6.24487i) q^{17} +(1.09204 - 2.39124i) q^{18} +(0.468056 - 3.25540i) q^{19} +(0.313607 + 0.201543i) q^{20} +(0.821721 + 0.948317i) q^{21} -2.46519 q^{22} +(-1.76381 + 4.45971i) q^{23} +0.609264 q^{24} +(3.18330 + 3.67372i) q^{25} +(3.14014 + 2.01804i) q^{26} +(-0.488058 + 3.39452i) q^{27} +(0.855563 - 1.87342i) q^{28} +(-1.01510 - 7.06018i) q^{29} +(-0.217925 - 0.0639885i) q^{30} +(4.91722 - 3.16011i) q^{31} +(-0.415415 - 0.909632i) q^{32} +(1.44111 - 0.423148i) q^{33} +(-4.13158 + 4.76809i) q^{34} +(-0.502780 + 0.580239i) q^{35} +(2.52231 - 0.740618i) q^{36} +(-1.94398 - 4.25672i) q^{37} +(2.76678 - 1.77810i) q^{38} +(-2.18207 - 0.640715i) q^{39} +(0.0530529 + 0.368991i) q^{40} +(-1.98603 + 4.34881i) q^{41} +(-0.178577 + 1.24203i) q^{42} +(-9.36979 - 6.02160i) q^{43} +(-1.61435 - 1.86306i) q^{44} -0.979978 q^{45} +(-4.52547 + 1.58749i) q^{46} +2.44502 q^{47} +(0.398983 + 0.460451i) q^{48} +(-2.32043 - 1.49125i) q^{49} +(-0.691797 + 4.81155i) q^{50} +(1.59682 - 3.49654i) q^{51} +(0.531217 + 3.69470i) q^{52} +(-5.80255 - 1.70378i) q^{53} +(-2.88502 + 1.85409i) q^{54} +(0.381761 + 0.835939i) q^{55} +(1.97611 - 0.580239i) q^{56} +(-1.31221 + 1.51437i) q^{57} +(4.67098 - 5.39060i) q^{58} +(11.3316 - 3.32727i) q^{59} +(-0.0943511 - 0.206600i) q^{60} +(1.41899 - 0.911927i) q^{61} +(5.60835 + 1.64676i) q^{62} +(0.770508 + 5.35900i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.198030 - 1.37733i) q^{65} +(1.26352 + 0.812016i) q^{66} +(9.23004 + 10.6520i) q^{67} -6.30909 q^{68} +(2.37303 - 1.70482i) q^{69} -0.767766 q^{70} +(-2.64478 - 3.05224i) q^{71} +(2.21148 + 1.42123i) q^{72} +(-1.23672 + 8.60157i) q^{73} +(1.94398 - 4.25672i) q^{74} +(-0.421487 - 2.93151i) q^{75} +(3.15565 + 0.926583i) q^{76} +(4.27116 - 2.74491i) q^{77} +(-0.944735 - 2.06868i) q^{78} +(2.28741 - 0.671644i) q^{79} +(-0.244123 + 0.281733i) q^{80} +(-3.79620 + 4.38105i) q^{81} +(-4.58718 + 1.34692i) q^{82} +(1.76013 + 3.85415i) q^{83} +(-1.05561 + 0.678398i) q^{84} +(2.25667 + 0.662618i) q^{85} +(-1.58509 - 11.0245i) q^{86} +(-1.80529 + 3.95303i) q^{87} +(0.350833 - 2.44009i) q^{88} +(-7.59749 - 4.88261i) q^{89} +(-0.641749 - 0.740618i) q^{90} -7.68762 q^{91} +(-4.16330 - 2.38054i) q^{92} -3.56122 q^{93} +(1.60115 + 1.84783i) q^{94} +(-1.03141 - 0.662850i) q^{95} +(-0.0867074 + 0.603063i) q^{96} +(-4.69697 + 10.2849i) q^{97} +(-0.392548 - 2.73023i) q^{98} +(6.21797 + 1.82576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9}+O(q^{10}) \) 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9	\( 10 q + q^{2} - q^{4} - 4 q^{5} - 7 q^{7} + q^{8} - 19 q^{9} + 4 q^{10} - 2 q^{11} - 11 q^{12} + 2 q^{13} - 15 q^{14} + 11 q^{15} - q^{16} - 9 q^{17} + 19 q^{18} + 2 q^{19} + 7 q^{20} + 33 q^{21} + 2 q^{22} + 21 q^{23} - 11 q^{25} + 9 q^{26} + 15 q^{28} - 2 q^{29} + 11 q^{31} + q^{32} - 11 q^{33} - 13 q^{34} - 17 q^{35} + 3 q^{36} - 18 q^{37} - 13 q^{38} + 4 q^{40} + 5 q^{41} - 22 q^{42} - 21 q^{43} - 2 q^{44} - 10 q^{45} - 10 q^{46} - 22 q^{47} - 11 q^{48} + 24 q^{49} - 22 q^{50} - 11 q^{51} - 20 q^{52} - 7 q^{53} + 11 q^{54} + 3 q^{55} + 7 q^{56} + 11 q^{57} + 24 q^{58} + 43 q^{59} + 11 q^{60} - 3 q^{61} + 33 q^{62} - 23 q^{63} - q^{64} + 41 q^{65} + 11 q^{66} - q^{67} + 2 q^{68} + 33 q^{69} + 6 q^{70} - 11 q^{71} + 8 q^{72} - 28 q^{73} + 18 q^{74} + 44 q^{75} + 2 q^{76} + 30 q^{77} + 34 q^{79} + 7 q^{80} + 13 q^{81} + 6 q^{82} - 3 q^{83} - 11 q^{84} + 8 q^{85} - 34 q^{86} - 33 q^{87} - 9 q^{88} - 49 q^{89} - 45 q^{90} - 52 q^{91} - q^{92} - 88 q^{93} - 11 q^{94} - 36 q^{95} + 16 q^{97} + 20 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 - q^4 - 4 * q^5 - 7 * q^7 + q^8 - 19 * q^9 + 4 * q^10 - 2 * q^11 - 11 * q^12 + 2 * q^13 - 15 * q^14 + 11 * q^15 - q^16 - 9 * q^17 + 19 * q^18 + 2 * q^19 + 7 * q^20 + 33 * q^21 + 2 * q^22 + 21 * q^23 - 11 * q^25 + 9 * q^26 + 15 * q^28 - 2 * q^29 + 11 * q^31 + q^32 - 11 * q^33 - 13 * q^34 - 17 * q^35 + 3 * q^36 - 18 * q^37 - 13 * q^38 + 4 * q^40 + 5 * q^41 - 22 * q^42 - 21 * q^43 - 2 * q^44 - 10 * q^45 - 10 * q^46 - 22 * q^47 - 11 * q^48 + 24 * q^49 - 22 * q^50 - 11 * q^51 - 20 * q^52 - 7 * q^53 + 11 * q^54 + 3 * q^55 + 7 * q^56 + 11 * q^57 + 24 * q^58 + 43 * q^59 + 11 * q^60 - 3 * q^61 + 33 * q^62 - 23 * q^63 - q^64 + 41 * q^65 + 11 * q^66 - q^67 + 2 * q^68 + 33 * q^69 + 6 * q^70 - 11 * q^71 + 8 * q^72 - 28 * q^73 + 18 * q^74 + 44 * q^75 + 2 * q^76 + 30 * q^77 + 34 * q^79 + 7 * q^80 + 13 * q^81 + 6 * q^82 - 3 * q^83 - 11 * q^84 + 8 * q^85 - 34 * q^86 - 33 * q^87 - 9 * q^88 - 49 * q^89 - 45 * q^90 - 52 * q^91 - q^92 - 88 * q^93 - 11 * q^94 - 36 * q^95 + 16 * q^97 + 20 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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