LMFDB - Embedded newform 48.2.k.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,2,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.383281929702$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.163368480538624.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} - 2x^{8} + 16x^{6} - 8x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 - 2x^8 + 16x^6 - 8x^4 - 32*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.5
Root			$-1.27715 + 0.607364i$ of defining polynomial
Character	$\chi$	$=$	48.11
Dual form			48.2.k.a.35.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.607364 - 1.27715i) q^{2} +(0.0835731 + 1.73003i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(0.431733 - 0.431733i) q^{5} +(2.26027 + 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 + 0.669785i) q^{8} +(-2.98603 + 0.289169i) q^{9} +O(q^{10})$	\(q+(0.607364 - 1.27715i) q^{2} +(0.0835731 + 1.73003i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(0.431733 - 0.431733i) q^{5} +(2.26027 + 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 + 0.669785i) q^{8} +(-2.98603 + 0.289169i) q^{9} +(-0.289169 - 0.813607i) q^{10} +(2.98603 + 2.98603i) q^{11} +(2.57846 - 2.31334i) q^{12} +(2.10278 - 2.10278i) q^{13} +(-1.88451 + 3.96271i) q^{14} +(0.782994 + 0.710831i) q^{15} +(-0.813607 + 3.91638i) q^{16} -2.42945i q^{17} +(-1.44430 + 3.98924i) q^{18} +(-0.710831 - 0.710831i) q^{19} +(-1.21473 - 0.124844i) q^{20} +(-0.259309 - 5.36790i) q^{21} +(5.62721 - 2.00000i) q^{22} -5.97206i q^{23} +(-1.38841 - 4.69812i) q^{24} +4.62721i q^{25} +(-1.40841 - 3.96271i) q^{26} +(-0.749823 - 5.14177i) q^{27} +(3.91638 + 4.81361i) q^{28} +(2.86119 + 2.86119i) q^{29} +(1.38340 - 0.568267i) q^{30} -0.524438i q^{31} +(4.50765 + 3.41776i) q^{32} +(-4.91638 + 5.41549i) q^{33} +(-3.10278 - 1.47556i) q^{34} +(-1.33957 + 1.33957i) q^{35} +(4.21764 + 4.26750i) q^{36} +(1.52444 + 1.52444i) q^{37} +(-1.33957 + 0.476105i) q^{38} +(3.81361 + 3.46214i) q^{39} +(-0.897225 + 1.47556i) q^{40} +1.81568 q^{41} +(-7.01311 - 2.92909i) q^{42} +(0.710831 - 0.710831i) q^{43} +(0.863466 - 8.40152i) q^{44} +(-1.16432 + 1.41401i) q^{45} +(-7.62721 - 3.62721i) q^{46} -7.53805 q^{47} +(-6.84347 - 1.08026i) q^{48} +2.62721 q^{49} +(5.90964 + 2.81040i) q^{50} +(4.20304 - 0.203037i) q^{51} +(-5.91638 - 0.608056i) q^{52} +(-8.83325 + 8.83325i) q^{53} +(-7.02222 - 2.16529i) q^{54} +2.57834 q^{55} +(8.52636 - 2.07819i) q^{56} +(1.17036 - 1.28917i) q^{57} +(5.39194 - 1.91638i) q^{58} +(-0.0804722 - 0.0804722i) q^{59} +(0.114465 - 2.11195i) q^{60} +(-5.72999 + 5.72999i) q^{61} +(-0.669785 - 0.318525i) q^{62} +(9.26498 - 0.897225i) q^{63} +(7.10278 - 3.68111i) q^{64} -1.81568i q^{65} +(3.93035 + 9.56812i) q^{66} +(-0.391944 - 0.391944i) q^{67} +(-3.76903 + 3.06650i) q^{68} +(10.3319 - 0.499104i) q^{69} +(0.897225 + 2.52444i) q^{70} +5.01985i q^{71} +(8.01187 - 2.79463i) q^{72} -13.4600i q^{73} +(2.87282 - 1.02105i) q^{74} +(-8.00523 + 0.386711i) q^{75} +(-0.205550 + 2.00000i) q^{76} +(-9.26498 - 9.26498i) q^{77} +(6.73791 - 2.76777i) q^{78} -3.47556i q^{79} +(1.33957 + 2.04209i) q^{80} +(8.83276 - 1.72693i) q^{81} +(1.10278 - 2.31889i) q^{82} +(4.55202 - 4.55202i) q^{83} +(-8.00040 + 7.17776i) q^{84} +(-1.04888 - 1.04888i) q^{85} +(-0.476105 - 1.33957i) q^{86} +(-4.71083 + 5.18907i) q^{87} +(-10.2056 - 6.20555i) q^{88} +12.5579 q^{89} +(1.09874 + 2.34584i) q^{90} +(-6.52444 + 6.52444i) q^{91} +(-9.26498 + 7.53805i) q^{92} +(0.907295 - 0.0438289i) q^{93} +(-4.57834 + 9.62721i) q^{94} -0.613779 q^{95} +(-5.53613 + 8.08401i) q^{96} -8.67609 q^{97} +(1.59567 - 3.35534i) q^{98} +(-9.77985 - 8.05292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	$ 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.607364	−	1.27715i	0.429471	−	0.903081i
$2$	0.607364	−	1.27715i	0.429471	−	0.903081i
$3$	0.0835731	+	1.73003i	0.0482510	+	0.998835i
$3$	0.0835731	+	1.73003i	0.0482510	+	0.998835i
$4$	−1.26222	−	1.55139i	−0.631109	−	0.775694i
$5$	0.431733	−	0.431733i	0.193077	−	0.193077i	−0.603947	−	0.797024i	$-0.706406\pi$
$5$	0.431733	−	0.431733i	0.193077	−	0.193077i	0.797024	+	0.603947i	$0.206406\pi$
$6$	2.26027	+	0.944024i	0.922751	+	0.385396i
$7$	−3.10278			−1.17274			−0.586369	−	0.810044i	$-0.699443\pi$
$7$	−3.10278			−1.17274			−0.586369	+	0.810044i	$0.699443\pi$
$8$	−2.74798	+	0.669785i	−0.971557	+	0.236805i
$9$	−2.98603	+	0.289169i	−0.995344	+	0.0963895i
$10$	−0.289169	−	0.813607i	−0.0914431	−	0.257285i
$11$	2.98603	+	2.98603i	0.900322	+	0.900322i	0.995464	−	0.0951415i	$-0.0303304\pi$
$11$	2.98603	+	2.98603i	0.900322	+	0.900322i	−0.0951415	+	0.995464i	$0.530330\pi$
$12$	2.57846	−	2.31334i	0.744339	−	0.667802i
$13$	2.10278	−	2.10278i	0.583205	−	0.583205i	−0.352578	−	0.935783i	$-0.614695\pi$
$13$	2.10278	−	2.10278i	0.583205	−	0.583205i	0.935783	+	0.352578i	$0.114695\pi$
$14$	−1.88451	+	3.96271i	−0.503657	+	1.05908i
$15$	0.782994	+	0.710831i	0.202168	+	0.183536i
$16$	−0.813607	+	3.91638i	−0.203402	+	0.979095i
$17$		−	2.42945i		−	0.589229i	−0.955616	−	0.294615i	$-0.904809\pi$
$17$		−	2.42945i		−	0.589229i	0.955616	−	0.294615i	$-0.0951913\pi$
$18$	−1.44430	+	3.98924i	−0.340424	+	0.940272i
$19$	−0.710831	−	0.710831i	−0.163076	−	0.163076i	0.620852	−	0.783928i	$-0.286787\pi$
$19$	−0.710831	−	0.710831i	−0.163076	−	0.163076i	−0.783928	+	0.620852i	$0.786787\pi$
$20$	−1.21473	−	0.124844i	−0.271621	−	0.0279159i
$21$	−0.259309	−	5.36790i	−0.0565858	−	1.17137i
$22$	5.62721	−	2.00000i	1.19973	−	0.426401i
$23$		−	5.97206i		−	1.24526i	−0.782516	−	0.622631i	$-0.786064\pi$
$23$		−	5.97206i		−	1.24526i	0.782516	−	0.622631i	$-0.213936\pi$
$24$	−1.38841	−	4.69812i	−0.283408	−	0.959000i
$25$			4.62721i			0.925443i
$26$	−1.40841	−	3.96271i	−0.276212	−	0.777151i
$27$	−0.749823	−	5.14177i	−0.144304	−	0.989533i
$28$	3.91638	+	4.81361i	0.740127	+	0.909686i
$29$	2.86119	+	2.86119i	0.531309	+	0.531309i	0.920962	−	0.389653i	$-0.127405\pi$
$29$	2.86119	+	2.86119i	0.531309	+	0.531309i	−0.389653	+	0.920962i	$0.627405\pi$
$30$	1.38340	−	0.568267i	0.252573	−	0.103751i
$31$		−	0.524438i		−	0.0941918i	−0.998890	−	0.0470959i	$-0.985003\pi$
$31$		−	0.524438i		−	0.0941918i	0.998890	−	0.0470959i	$-0.0149966\pi$
$32$	4.50765	+	3.41776i	0.796847	+	0.604181i
$33$	−4.91638	+	5.41549i	−0.855832	+	0.942715i
$34$	−3.10278	−	1.47556i	−0.532122	−	0.253057i
$35$	−1.33957	+	1.33957i	−0.226429	+	0.226429i
$36$	4.21764	+	4.26750i	0.702940	+	0.711250i
$37$	1.52444	+	1.52444i	0.250616	+	0.250616i	0.821223	−	0.570607i	$-0.193292\pi$
$37$	1.52444	+	1.52444i	0.250616	+	0.250616i	−0.570607	+	0.821223i	$0.693292\pi$
$38$	−1.33957	+	0.476105i	−0.217307	+	0.0772344i
$39$	3.81361	+	3.46214i	0.610666	+	0.554385i
$40$	−0.897225	+	1.47556i	−0.141864	+	0.233307i
$41$	1.81568			0.283561			0.141780	−	0.989898i	$-0.454717\pi$
$41$	1.81568			0.283561			0.141780	+	0.989898i	$0.454717\pi$
$42$	−7.01311	−	2.92909i	−1.08215	−	0.451969i
$43$	0.710831	−	0.710831i	0.108401	−	0.108401i	−0.650826	−	0.759227i	$-0.725577\pi$
$43$	0.710831	−	0.710831i	0.108401	−	0.108401i	0.759227	+	0.650826i	$0.225577\pi$
$44$	0.863466	−	8.40152i	0.130172	−	1.26658i
$45$	−1.16432	+	1.41401i	−0.173567	+	0.210788i
$46$	−7.62721	−	3.62721i	−1.12457	−	0.534803i
$47$	−7.53805			−1.09954			−0.549769	−	0.835317i	$-0.685284\pi$
$47$	−7.53805			−1.09954			−0.549769	+	0.835317i	$0.685284\pi$
$48$	−6.84347	−	1.08026i	−0.987769	−	0.155922i
$49$	2.62721			0.375316
$50$	5.90964	+	2.81040i	0.835749	+	0.397451i
$51$	4.20304	−	0.203037i	0.588543	−	0.0284309i
$52$	−5.91638	−	0.608056i	−0.820455	−	0.0843223i
$53$	−8.83325	+	8.83325i	−1.21334	+	1.21334i	−0.243419	+	0.969921i	$0.578269\pi$
$53$	−8.83325	+	8.83325i	−1.21334	+	1.21334i	−0.969921	+	0.243419i	$0.921731\pi$
$54$	−7.02222	−	2.16529i	−0.955603	−	0.294658i
$55$	2.57834			0.347663
$56$	8.52636	−	2.07819i	1.13938	−	0.277710i
$57$	1.17036	−	1.28917i	0.155017	−	0.170755i
$58$	5.39194	−	1.91638i	0.707997	−	0.251633i
$59$	−0.0804722	−	0.0804722i	−0.0104766	−	0.0104766i	0.701849	−	0.712326i	$-0.252358\pi$
$59$	−0.0804722	−	0.0804722i	−0.0104766	−	0.0104766i	−0.712326	+	0.701849i	$0.752358\pi$
$60$	0.114465	−	2.11195i	0.0147774	−	0.272652i
$61$	−5.72999	+	5.72999i	−0.733650	+	0.733650i	−0.971341	−	0.237691i	$-0.923609\pi$
$61$	−5.72999	+	5.72999i	−0.733650	+	0.733650i	0.237691	+	0.971341i	$0.423609\pi$
$62$	−0.669785	−	0.318525i	−0.0850628	−	0.0404527i
$63$	9.26498	−	0.897225i	1.16728	−	0.113040i
$64$	7.10278	−	3.68111i	0.887847	−	0.460139i
$65$		−	1.81568i		−	0.225207i
$66$	3.93035	+	9.56812i	0.483793	+	1.17775i
$67$	−0.391944	−	0.391944i	−0.0478835	−	0.0478835i	0.682760	−	0.730643i	$-0.260780\pi$
$67$	−0.391944	−	0.391944i	−0.0478835	−	0.0478835i	−0.730643	+	0.682760i	$0.760780\pi$
$68$	−3.76903	+	3.06650i	−0.457061	+	0.371868i
$69$	10.3319	−	0.499104i	1.24381	−	0.0600850i
$70$	0.897225	+	2.52444i	0.107239	+	0.301728i
$71$			5.01985i			0.595747i	0.954605	+	0.297873i	$0.0962774\pi$
$71$			5.01985i			0.595747i	−0.954605	+	0.297873i	$0.903723\pi$
$72$	8.01187	−	2.79463i	0.944208	−	0.329350i
$73$		−	13.4600i		−	1.57537i	−0.616078	−	0.787686i	$-0.711279\pi$
$73$		−	13.4600i		−	1.57537i	0.616078	−	0.787686i	$-0.288721\pi$
$74$	2.87282	−	1.02105i	0.333959	−	0.118694i
$75$	−8.00523	+	0.386711i	−0.924365	+	0.0446535i
$76$	−0.205550	+	2.00000i	−0.0235782	+	0.229416i
$77$	−9.26498	−	9.26498i	−1.05584	−	1.05584i
$78$	6.73791	−	2.76777i	0.762918	−	0.313388i
$79$		−	3.47556i		−	0.391031i	−0.980701	−	0.195516i	$-0.937362\pi$
$79$		−	3.47556i		−	0.391031i	0.980701	−	0.195516i	$-0.0626380\pi$
$80$	1.33957	+	2.04209i	0.149769	+	0.228313i
$81$	8.83276	−	1.72693i	0.981418	−	0.191881i
$82$	1.10278	−	2.31889i	0.121781	−	0.256078i
$83$	4.55202	−	4.55202i	0.499649	−	0.499649i	−0.411680	−	0.911329i	$-0.635058\pi$
$83$	4.55202	−	4.55202i	0.499649	−	0.499649i	0.911329	+	0.411680i	$0.135058\pi$
$84$	−8.00040	+	7.17776i	−0.872915	+	0.783158i
$85$	−1.04888	−	1.04888i	−0.113767	−	0.113767i
$86$	−0.476105	−	1.33957i	−0.0513397	−	0.144450i
$87$	−4.71083	+	5.18907i	−0.505054	+	0.556326i
$88$	−10.2056	−	6.20555i	−1.08792	−	0.661514i
$89$	12.5579			1.33114			0.665568	−	0.746338i	$-0.268190\pi$
$89$	12.5579			1.33114			0.665568	+	0.746338i	$0.268190\pi$
$90$	1.09874	+	2.34584i	0.115817	+	0.247273i
$91$	−6.52444	+	6.52444i	−0.683947	+	0.683947i
$92$	−9.26498	+	7.53805i	−0.965941	+	0.785896i
$93$	0.907295	−	0.0438289i	0.0940821	−	0.00454485i
$94$	−4.57834	+	9.62721i	−0.472219	+	0.992971i
$95$	−0.613779			−0.0629724
$96$	−5.53613	+	8.08401i	−0.565029	+	0.825071i
$97$	−8.67609			−0.880923			−0.440462	−	0.897771i	$-0.645185\pi$
$97$	−8.67609			−0.880923			−0.440462	+	0.897771i	$0.645185\pi$
$98$	1.59567	−	3.35534i	0.161187	−	0.338941i
$99$	−9.77985	−	8.05292i	−0.982912	−	0.809348i
$100$	7.17860	−	5.84056i	0.717860	−	0.584056i
$101$	0.182046	−	0.182046i	0.0181142	−	0.0181142i	−0.697992	−	0.716106i	$-0.745923\pi$
$101$	0.182046	−	0.182046i	0.0181142	−	0.0181142i	0.716106	+	0.697992i	$0.245923\pi$
$102$	2.29346	−	5.49122i	0.227087	−	0.543712i
$103$	6.35720			0.626394			0.313197	−	0.949688i	$-0.398600\pi$
$103$	6.35720			0.626394			0.313197	+	0.949688i	$0.398600\pi$
$104$	−4.36997	+	7.18679i	−0.428511	+	0.704723i
$105$	−2.42945	−	2.20555i	−0.237090	−	0.215240i
$106$	5.91638	+	16.6464i	0.574650	+	1.61684i
$107$	1.64646	+	1.64646i	0.159169	+	0.159169i	0.782199	−	0.623029i	$-0.214098\pi$
$107$	1.64646	+	1.64646i	0.159169	+	0.159169i	−0.623029	+	0.782199i	$0.714098\pi$
$108$	−7.03043	+	7.65330i	−0.676504	+	0.736439i
$109$	6.57331	−	6.57331i	0.629609	−	0.629609i	−0.318360	−	0.947970i	$-0.603132\pi$
$109$	6.57331	−	6.57331i	0.629609	−	0.629609i	0.947970	+	0.318360i	$0.103132\pi$
$110$	1.56599	−	3.29292i	0.149311	−	0.313968i
$111$	−2.50993	+	2.76473i	−0.238232	+	0.262417i
$112$	2.52444	−	12.1517i	0.238537	−	1.14822i
$113$		−	8.31277i		−	0.782000i	−0.920391	−	0.391000i	$-0.872129\pi$
$113$		−	8.31277i		−	0.782000i	0.920391	−	0.391000i	$-0.127871\pi$
$114$	−0.935629	−	2.27771i	−0.0876297	−	0.213327i
$115$	−2.57834	−	2.57834i	−0.240431	−	0.240431i
$116$	0.827365	−	8.05026i	0.0768189	−	0.747447i
$117$	−5.67090	+	6.88701i	−0.524274	+	0.636704i
$118$	−0.151651	+	0.0538991i	−0.0139606	+	0.00496182i
$119$			7.53805i			0.691012i
$120$	−2.62776	−	1.42891i	−0.239880	−	0.130441i
$121$			6.83276i			0.621160i
$122$	3.83786	+	10.7982i	0.347464	+	0.977626i
$123$	0.151742	+	3.14118i	0.0136821	+	0.283231i
$124$	−0.813607	+	0.661956i	−0.0730640	+	0.0594454i
$125$	4.15639	+	4.15639i	0.371759	+	0.371759i
$126$	4.48132	−	12.3777i	0.399228	−	1.10269i
$127$			15.7789i			1.40015i	0.714070	+	0.700074i	$0.246850\pi$
$127$			15.7789i			1.40015i	−0.714070	+	0.700074i	$0.753150\pi$
$128$	−0.387362	−	11.3071i	−0.0342383	−	0.999414i
$129$	1.28917	+	1.17036i	0.113505	+	0.103044i
$130$	−2.31889	−	1.10278i	−0.203380	−	0.0967198i
$131$	0.0804722	−	0.0804722i	0.00703089	−	0.00703089i	−0.703583	−	0.710613i	$-0.748417\pi$
$131$	0.0804722	−	0.0804722i	0.00703089	−	0.00703089i	0.710613	+	0.703583i	$0.248417\pi$
$132$	14.6071	+	0.791685i	1.27138	+	0.0689073i
$133$	2.20555	+	2.20555i	0.191245	+	0.191245i
$134$	−0.738623	+	0.262518i	−0.0638073	+	0.0226781i
$135$	−2.54359	−	1.89615i	−0.218918	−	0.163194i
$136$	1.62721	+	6.67609i	0.139532	+	0.572470i
$137$	−13.2604			−1.13291			−0.566457	−	0.824091i	$-0.691686\pi$
$137$	−13.2604			−1.13291			−0.566457	+	0.824091i	$0.691686\pi$
$138$	5.63777	−	13.4985i	0.479919	−	1.14907i
$139$	8.39194	−	8.39194i	0.711795	−	0.711795i	−0.255115	−	0.966911i	$-0.582113\pi$
$139$	8.39194	−	8.39194i	0.711795	−	0.711795i	0.966911	+	0.255115i	$0.0821134\pi$
$140$	3.76903	+	0.387362i	0.318541	+	0.0327380i
$141$	−0.629978	−	13.0411i	−0.0530537	−	1.09826i
$142$	6.41110	+	3.04888i	0.538008	+	0.255856i
$143$	12.5579			1.05014
$144$	1.29696	−	11.9297i	0.108080	−	0.994142i
$145$	2.47054			0.205167
$146$	−17.1904	−	8.17510i	−1.42269	−	0.676576i
$147$	0.219564	+	4.54517i	0.0181094	+	0.374879i
$148$	0.440820	−	4.28917i	0.0362351	−	0.352567i
$149$	5.79002	−	5.79002i	0.474337	−	0.474337i	−0.428978	−	0.903315i	$-0.641126\pi$
$149$	5.79002	−	5.79002i	0.474337	−	0.474337i	0.903315	+	0.428978i	$0.141126\pi$
$150$	−4.36820	+	10.4587i	−0.356662	+	0.853953i
$151$	9.94610			0.809402			0.404701	−	0.914449i	$-0.367376\pi$
$151$	9.94610			0.809402			0.404701	+	0.914449i	$0.367376\pi$
$152$	2.42945	+	1.47725i	0.197055	+	0.119820i
$153$	0.702522	+	7.25443i	0.0567955	+	0.586486i
$154$	−17.4600	+	6.20555i	−1.40696	+	0.500057i
$155$	−0.226417	−	0.226417i	−0.0181863	−	0.0181863i
$156$	0.557507	−	10.2864i	0.0446363	−	0.823568i
$157$	−9.15165	+	9.15165i	−0.730381	+	0.730381i	−0.970695	−	0.240314i	$-0.922750\pi$
$157$	−9.15165	+	9.15165i	−0.730381	+	0.730381i	0.240314	+	0.970695i	$0.422750\pi$
$158$	−4.43881	−	2.11093i	−0.353133	−	0.167937i
$159$	−16.0200	−	14.5436i	−1.27047	−	1.15338i
$160$	3.42166	−	0.470539i	0.270506	−	0.0371994i
$161$			18.5300i			1.46037i
$162$	3.15915	−	12.3296i	0.248206	−	0.968707i
$163$	15.7003	+	15.7003i	1.22974	+	1.22974i	0.964062	+	0.265678i	$0.0855959\pi$
$163$	15.7003	+	15.7003i	1.22974	+	1.22974i	0.265678	+	0.964062i	$0.414404\pi$
$164$	−2.29178	−	2.81682i	−0.178958	−	0.219956i
$165$	0.215480	+	4.46061i	0.0167751	+	0.347258i
$166$	−3.04888	−	8.57834i	−0.236639	−	0.665808i
$167$		−	19.1437i		−	1.48139i	−0.671843	−	0.740694i	$-0.734497\pi$
$167$		−	19.1437i		−	1.48139i	0.671843	−	0.740694i	$-0.265503\pi$
$168$	4.30792	+	14.5772i	0.332363	+	1.12466i
$169$			4.15667i			0.319744i
$170$	−1.97662	+	0.702522i	−0.151600	+	0.0538810i
$171$	2.32811	+	1.91701i	0.178035	+	0.146598i
$172$	−2.00000	−	0.205550i	−0.152499	−	0.0156730i
$173$	13.3281	+	13.3281i	1.01331	+	1.01331i	0.999910	+	0.0134040i	$0.00426674\pi$
$173$	13.3281	+	13.3281i	1.01331	+	1.01331i	0.0134040	+	0.999910i	$0.495733\pi$
$174$	3.76603	+	9.16808i	0.285502	+	0.695031i
$175$		−	14.3572i		−	1.08530i
$176$	−14.1239	+	9.26498i	−1.06463	+	0.698374i
$177$	0.132494	−	0.145945i	0.00995889	−	0.0109699i
$178$	7.62721	−	16.0383i	0.571684	−	1.20212i
$179$	−9.18451	+	9.18451i	−0.686483	+	0.686483i	−0.961453	−	0.274970i	$-0.911332\pi$
$179$	−9.18451	+	9.18451i	−0.686483	+	0.686483i	0.274970	+	0.961453i	$0.411332\pi$
$180$	3.66331	+	0.0215261i	0.273047	+	0.00160446i
$181$	−16.5139	−	16.5139i	−1.22747	−	1.22747i	−0.964919	−	0.262548i	$-0.915437\pi$
$181$	−16.5139	−	16.5139i	−1.22747	−	1.22747i	−0.262548	−	0.964919i	$-0.584563\pi$
$182$	4.36997	+	12.2954i	0.323924	+	0.911395i
$183$	−10.3919	−	9.43420i	−0.768195	−	0.697396i
$184$	4.00000	+	16.4111i	0.294884	+	1.20984i
$185$	1.31630			0.0967764
$186$	0.495082	−	1.18537i	0.0363012	−	0.0869156i
$187$	7.25443	−	7.25443i	0.530496	−	0.530496i
$188$	9.51467	+	11.6944i	0.693929	+	0.852904i
$189$	2.32653	+	15.9537i	0.169230	+	1.16046i
$190$	−0.372787	+	0.783887i	−0.0270448	+	0.0568692i
$191$	−3.17852			−0.229989			−0.114995	−	0.993366i	$-0.536685\pi$
$191$	−3.17852			−0.229989			−0.114995	+	0.993366i	$0.536685\pi$
$192$	6.96205	+	11.9804i	0.502443	+	0.864611i
$193$	−11.4600			−0.824907			−0.412454	−	0.910979i	$-0.635328\pi$
$193$	−11.4600			−0.824907			−0.412454	+	0.910979i	$0.635328\pi$
$194$	−5.26954	+	11.0807i	−0.378331	+	0.795545i
$195$	3.14118	−	0.151742i	0.224944	−	0.0108664i
$196$	−3.31612	−	4.07583i	−0.236866	−	0.291130i
$197$	14.8053	−	14.8053i	1.05483	−	1.05483i	0.0564281	−	0.998407i	$-0.482029\pi$
$197$	14.8053	−	14.8053i	1.05483	−	1.05483i	0.998407	−	0.0564281i	$-0.0179712\pi$
$198$	−16.2247	+	7.59928i	−1.15304	+	0.540057i
$199$	−24.4550			−1.73357			−0.866783	−	0.498686i	$-0.833816\pi$
$199$	−24.4550			−1.73357			−0.866783	+	0.498686i	$0.833816\pi$
$200$	−3.09924	−	12.7155i	−0.219149	−	0.899120i
$201$	0.645320	−	0.710831i	0.0455173	−	0.0501382i
$202$	−0.121932	−	0.343068i	−0.00857908	−	0.0241382i
$203$	−8.87762	−	8.87762i	−0.623087	−	0.623087i
$204$	−5.62014	−	6.26426i	−0.393489	−	0.438586i
$205$	0.783887	−	0.783887i	0.0547491	−	0.0547491i
$206$	3.86113	−	8.11909i	0.269018	−	0.565684i
$207$	1.72693	+	17.8328i	0.120030	+	1.23946i
$208$	6.52444	+	9.94610i	0.452388	+	0.689638i
$209$		−	4.24513i		−	0.293642i
$210$	−4.29238	+	1.76320i	−0.296202	+	0.121673i
$211$	−6.18639	−	6.18639i	−0.425889	−	0.425889i	0.461336	−	0.887225i	$-0.347370\pi$
$211$	−6.18639	−	6.18639i	−0.425889	−	0.425889i	−0.887225	+	0.461336i	$0.847370\pi$
$212$	24.8533	+	2.55430i	1.70693	+	0.175430i
$213$	−8.68451	+	0.419525i	−0.595053	+	0.0287454i
$214$	3.10278	−	1.10278i	0.212101	−	0.0753842i
$215$		−	0.613779i		−	0.0418594i
$216$	5.50438	+	13.6272i	0.374526	+	0.927217i
$217$			1.62721i			0.110462i
$218$	−4.40271	−	12.3875i	−0.298189	−	0.838987i
$219$	23.2862	−	1.12489i	1.57354	−	0.0760132i
$220$	−3.25443	−	4.00000i	−0.219413	−	0.269680i
$221$	−5.10860	−	5.10860i	−0.343641	−	0.343641i
$222$	2.00653	+	4.88475i	0.134670	+	0.327843i
$223$		−	8.18996i		−	0.548441i	−0.961667	−	0.274220i	$-0.911580\pi$
$223$		−	8.18996i		−	0.548441i	0.961667	−	0.274220i	$-0.0884197\pi$
$224$	−13.9862	−	10.6046i	−0.934493	−	0.708547i
$225$	−1.33804	−	13.8170i	−0.0892030	−	0.921133i
$226$	−10.6167	−	5.04888i	−0.706209	−	0.335846i
$227$	9.91030	−	9.91030i	0.657770	−	0.657770i	−0.297082	−	0.954852i	$-0.596014\pi$
$227$	9.91030	−	9.91030i	0.657770	−	0.657770i	0.954852	+	0.297082i	$0.0960135\pi$
$228$	−3.47725	−	0.188462i	−0.230286	−	0.0124812i
$229$	7.15165	+	7.15165i	0.472594	+	0.472594i	0.902753	−	0.430159i	$-0.141542\pi$
$229$	7.15165	+	7.15165i	0.472594	+	0.472594i	−0.430159	+	0.902753i	$0.641542\pi$
$230$	−4.85891	+	1.72693i	−0.320387	+	0.113871i
$231$	15.2544	−	16.8030i	1.00367	−	1.10556i
$232$	−9.77886	−	5.94610i	−0.642014	−	0.390381i
$233$	−19.6431			−1.28686			−0.643432	−	0.765503i	$-0.722490\pi$
$233$	−19.6431			−1.28686			−0.643432	+	0.765503i	$0.722490\pi$
$234$	5.35144	+	11.4255i	0.349835	+	0.746908i
$235$	−3.25443	+	3.25443i	−0.212295	+	0.212295i
$236$	−0.0232700	+	0.226417i	−0.00151475	+	0.0147385i
$237$	6.01284	−	0.290464i	0.390576	−	0.0188676i
$238$	9.62721	+	4.57834i	0.624040	+	0.296770i
$239$	9.44247			0.610782			0.305391	−	0.952227i	$-0.401213\pi$
$239$	9.44247			0.610782			0.305391	+	0.952227i	$0.401213\pi$
$240$	−3.42094	+	2.48817i	−0.220820	+	0.160610i
$241$	16.6167			1.07037			0.535186	−	0.844734i	$-0.320241\pi$
$241$	16.6167			1.07037			0.535186	+	0.844734i	$0.320241\pi$
$242$	8.72646	+	4.14997i	0.560958	+	0.266770i
$243$	3.72583	+	15.1366i	0.239012	+	0.971017i
$244$	16.1219	+	1.65693i	1.03210	+	0.106074i
$245$	1.13425	−	1.13425i	0.0724649	−	0.0724649i
$246$	4.10392	+	1.71404i	0.261656	+	0.109283i
$247$	−2.98944			−0.190213
$248$	0.351261	+	1.44114i	0.0223051	+	0.0915128i
$249$	8.25557	+	7.49472i	0.523176	+	0.474958i
$250$	7.83276	−	2.78389i	0.495387	−	0.176068i
$251$	2.03382	+	2.03382i	0.128374	+	0.128374i	0.768374	−	0.640001i	$-0.221066\pi$
$251$	2.03382	+	2.03382i	0.128374	+	0.128374i	−0.640001	+	0.768374i	$0.721066\pi$
$252$	−13.0864	−	13.2411i	−0.824364	−	0.834110i
$253$	17.8328	−	17.8328i	1.12114	−	1.12114i
$254$	20.1520	+	9.58351i	1.26445	+	0.601323i
$255$	1.72693	−	1.90225i	0.108145	−	0.119123i
$256$	−14.6761	−	6.37279i	−0.917256	−	0.398299i
$257$			15.0761i			0.940421i	0.882554	+	0.470211i	$0.155822\pi$
$257$			15.0761i			0.940421i	−0.882554	+	0.470211i	$0.844178\pi$
$258$	2.27771	−	0.935629i	0.141804	−	0.0582497i
$259$	−4.72999	−	4.72999i	−0.293907	−	0.293907i
$260$	−2.81682	+	2.29178i	−0.174692	+	0.142130i
$261$	−9.37096	−	7.71623i	−0.580048	−	0.477623i
$262$	−0.0538991	−	0.151651i	−0.00332990	−	0.00936903i
$263$			29.8138i			1.83840i	0.393796	+	0.919198i	$0.371162\pi$
$263$			29.8138i			1.83840i	−0.393796	+	0.919198i	$0.628838\pi$
$264$	9.88290	−	18.1746i	0.608250	−	1.11857i
$265$			7.62721i			0.468536i
$266$	4.15639	−	1.47725i	0.254844	−	0.0905757i
$267$	1.04950	+	21.7256i	0.0642285	+	1.32958i
$268$	−0.113338	+	1.10278i	−0.00692321	+	0.0673627i
$269$	−16.3713	−	16.3713i	−0.998176	−	0.998176i	0.00182258	−	0.999998i	$-0.499420\pi$
$269$	−16.3713	−	16.3713i	−0.998176	−	0.998176i	−0.999998	+	0.00182258i	$0.999420\pi$
$270$	−3.96655	+	2.09690i	−0.241397	+	0.127613i
$271$			13.3466i			0.810751i	0.914150	+	0.405375i	$0.132859\pi$
$271$			13.3466i			0.810751i	−0.914150	+	0.405375i	$0.867141\pi$
$272$	9.51467	+	1.97662i	0.576912	+	0.119850i
$273$	−11.8328	−	10.7422i	−0.716151	−	0.650149i
$274$	−8.05390	+	16.9355i	−0.486554	+	1.02311i
$275$	−13.8170	+	13.8170i	−0.833197	+	0.833197i
$276$	−13.8154	−	15.3988i	−0.831588	−	0.926896i
$277$	10.6811	+	10.6811i	0.641766	+	0.641766i	0.950989	−	0.309224i	$-0.100069\pi$
$277$	10.6811	+	10.6811i	0.641766	+	0.641766i	−0.309224	+	0.950989i	$0.600069\pi$
$278$	−5.62080	−	15.8147i	−0.337113	−	0.948504i
$279$	0.151651	+	1.56599i	0.00907911	+	0.0937533i
$280$	2.78389	−	4.57834i	0.166369	−	0.273608i
$281$	−17.5943			−1.04959			−0.524794	−	0.851229i	$-0.675858\pi$
$281$	−17.5943			−1.04959			−0.524794	+	0.851229i	$0.675858\pi$
$282$	−17.0380	−	7.11610i	−1.01460	−	0.423758i
$283$	−17.1758	+	17.1758i	−1.02100	+	1.02100i	−0.0212224	+	0.999775i	$0.506756\pi$
$283$	−17.1758	+	17.1758i	−1.02100	+	1.02100i	−0.999775	+	0.0212224i	$0.993244\pi$
$284$	7.78774	−	6.33615i	0.462117	−	0.375982i
$285$	−0.0512954	−	1.06186i	−0.00303848	−	0.0628990i
$286$	7.62721	−	16.0383i	0.451007	−	0.948365i
$287$	−5.63363			−0.332543
$288$	−14.4483	−	8.90208i	−0.851373	−	0.524560i
$289$	11.0978			0.652809
$290$	1.50052	−	3.15525i	0.0881133	−	0.185282i
$291$	−0.725088	−	15.0099i	−0.0425054	−	0.879897i
$292$	−20.8816	+	16.9894i	−1.22201	+	0.994232i
$293$	−3.72465	+	3.72465i	−0.217597	+	0.217597i	−0.807485	−	0.589888i	$-0.799172\pi$
$293$	−3.72465	+	3.72465i	−0.217597	+	0.217597i	0.589888	+	0.807485i	$0.299172\pi$
$294$	5.93821	+	2.48015i	0.346323	+	0.144645i
$295$	−0.0694851			−0.00404558
$296$	−5.21017	−	3.16808i	−0.302835	−	0.184141i
$297$	13.1145	−	17.5925i	0.760979	−	1.02082i
$298$	−3.87807	−	10.9114i	−0.224650	−	0.632078i
$299$	−12.5579	−	12.5579i	−0.726242	−	0.726242i
$300$	10.7043	+	11.9311i	0.618013	+	0.688843i
$301$	−2.20555	+	2.20555i	−0.127126	+	0.127126i
$302$	6.04090	−	12.7027i	0.347615	−	0.730956i
$303$	0.330160	+	0.299731i	0.0189672	+	0.0172191i
$304$	3.36222	−	2.20555i	0.192837	−	0.126497i
$305$			4.94765i			0.283302i
$306$	9.69167	+	3.50885i	0.554036	+	0.200588i
$307$	−13.4408	−	13.4408i	−0.767108	−	0.767108i	0.210488	−	0.977596i	$-0.432495\pi$
$307$	−13.4408	−	13.4408i	−0.767108	−	0.767108i	−0.977596	+	0.210488i	$0.932495\pi$
$308$	−2.67914	+	26.0680i	−0.152658	+	1.48536i
$309$	0.531291	+	10.9982i	0.0302241	+	0.625664i
$310$	−0.426686	+	0.151651i	−0.0242341	+	0.00861320i
$311$			13.8320i			0.784341i	0.919893	+	0.392170i	$0.128276\pi$
$311$			13.8320i			0.784341i	−0.919893	+	0.392170i	$0.871724\pi$
$312$	−12.7986	−	6.95958i	−0.724578	−	0.394008i
$313$		−	3.94056i		−	0.222734i	−0.993779	−	0.111367i	$-0.964477\pi$
$313$		−	3.94056i		−	0.222734i	0.993779	−	0.111367i	$-0.0355229\pi$
$314$	6.12964	+	17.2464i	0.345916	+	0.973271i
$315$	3.61264	−	4.38736i	0.203549	−	0.247200i
$316$	−5.39194	+	4.38692i	−0.303321	+	0.246784i
$317$	8.92199	+	8.92199i	0.501109	+	0.501109i	0.911782	−	0.410673i	$-0.134706\pi$
$317$	8.92199	+	8.92199i	0.501109	+	0.501109i	−0.410673	+	0.911782i	$0.634706\pi$
$318$	−28.3043	+	11.6267i	−1.58723	+	0.651994i
$319$			17.0872i			0.956699i
$320$	1.47725	−	4.65576i	0.0825805	−	0.260265i
$321$	−2.71083	+	2.98603i	−0.151304	+	0.166664i
$322$	23.6655	+	11.2544i	1.31883	+	0.627185i
$323$	−1.72693	+	1.72693i	−0.0960891	+	0.0960891i
$324$	−13.8280	−	11.5233i	−0.768223	−	0.640182i
$325$	9.72999	+	9.72999i	0.539723	+	0.539723i
$326$	29.5874	−	10.5158i	1.63869	−	0.582417i
$327$	11.9214	+	10.8227i	0.659255	+	0.598497i
$328$	−4.98944	+	1.21611i	−0.275496	+	0.0671486i
$329$	23.3889			1.28947
$330$	5.82774	+	2.43401i	0.320806	+	0.133988i
$331$	9.44082	−	9.44082i	0.518914	−	0.518914i	−0.398328	−	0.917243i	$-0.630410\pi$
$331$	9.44082	−	9.44082i	0.518914	−	0.518914i	0.917243	+	0.398328i	$0.130410\pi$
$332$	−12.8076	−	1.31630i	−0.702908	−	0.0722414i
$333$	−4.99284	−	4.11120i	−0.273606	−	0.225292i
$334$	−24.4494	−	11.6272i	−1.33781	−	0.636213i
$335$	−0.338430			−0.0184904
$336$	21.2337	+	3.35181i	1.15840	+	0.182856i
$337$	5.94056			0.323603			0.161801	−	0.986823i	$-0.448270\pi$
$337$	5.94056			0.323603			0.161801	+	0.986823i	$0.448270\pi$
$338$	5.30869	+	2.52461i	0.288755	+	0.137321i
$339$	14.3814	−	0.694724i	0.781089	−	0.0377322i
$340$	−0.303302	+	2.95112i	−0.0164489	+	0.160047i
$341$	1.56599	−	1.56599i	0.0848030	−	0.0848030i
$342$	3.86233	−	1.80902i	0.208851	−	0.0978208i
$343$	13.5678			0.732591
$344$	−1.47725	+	2.42945i	−0.0796477	+	0.130987i
$345$	4.24513	−	4.67609i	0.228550	−	0.251752i
$346$	25.1169	−	8.92694i	1.35029	−	0.479915i
$347$	−4.09918	−	4.09918i	−0.220056	−	0.220056i	0.588466	−	0.808522i	$-0.299732\pi$
$347$	−4.09918	−	4.09918i	−0.220056	−	0.220056i	−0.808522	+	0.588466i	$0.799732\pi$
$348$	13.9964	+	0.758585i	0.750283	+	0.0406644i
$349$	−8.10278	+	8.10278i	−0.433732	+	0.433732i	−0.889896	−	0.456164i	$-0.849223\pi$
$349$	−8.10278	+	8.10278i	−0.433732	+	0.433732i	0.456164	+	0.889896i	$0.349223\pi$
$350$	−18.3363	−	8.72004i	−0.980116	−	0.466106i
$351$	−12.3887	−	9.23527i	−0.661259	−	0.492942i
$352$	3.25443	+	23.6655i	0.173461	+	1.26138i
$353$		−	29.2465i		−	1.55664i	−0.627870	−	0.778318i	$-0.716073\pi$
$353$		−	29.2465i		−	1.55664i	0.627870	−	0.778318i	$-0.283927\pi$
$354$	−0.105921	−	0.257857i	−0.00562965	−	0.0137049i
$355$	2.16724	+	2.16724i	0.115025	+	0.115025i
$356$	−15.8508	−	19.4822i	−0.840092	−	1.03255i
$357$	−13.0411	+	0.629978i	−0.690207	+	0.0333420i
$358$	6.15165	+	17.3083i	0.325125	+	0.914773i
$359$		−	21.3235i		−	1.12541i	−0.826657	−	0.562706i	$-0.809760\pi$
$359$		−	21.3235i		−	1.12541i	0.826657	−	0.562706i	$-0.190240\pi$
$360$	2.25246	−	4.66552i	0.118715	−	0.245895i
$361$		−	17.9894i		−	0.946812i
$362$	−31.1206	+	11.0608i	−1.63566	+	0.581340i
$363$	−11.8209	+	0.571035i	−0.620437	+	0.0299716i
$364$	18.3572	+	1.88666i	0.962179	+	0.0988880i
$365$	−5.81112	−	5.81112i	−0.304168	−	0.304168i
$366$	−18.3606	+	7.54207i	−0.959722	+	0.394230i
$367$		−	32.8277i		−	1.71359i	−0.515654	−	0.856797i	$-0.672451\pi$
$367$		−	32.8277i		−	1.71359i	0.515654	−	0.856797i	$-0.327549\pi$
$368$	23.3889	+	4.85891i	1.21923	+	0.253288i
$369$	−5.42166	+	0.525036i	−0.282240	+	0.0273323i
$370$	0.799473	−	1.68111i	0.0415626	−	0.0873969i
$371$	27.4076	−	27.4076i	1.42293	−	1.42293i
$372$	−1.21320	−	1.35224i	−0.0629015	−	0.0701106i
$373$	1.35720	+	1.35720i	0.0702732	+	0.0702732i	0.741370	−	0.671097i	$-0.234176\pi$
$373$	1.35720	+	1.35720i	0.0702732	+	0.0702732i	−0.671097	+	0.741370i	$0.734176\pi$
$374$	−4.85891	−	13.6711i	−0.251248	−	0.706914i
$375$	−6.84333	+	7.53805i	−0.353388	+	0.389263i
$376$	20.7144	−	5.04888i	1.06826	−	0.260376i
$377$	12.0329			0.619724
$378$	21.7884	+	6.71840i	1.12067	+	0.345557i
$379$	−17.3869	+	17.3869i	−0.893106	+	0.893106i	−0.994814	−	0.101708i	$-0.967569\pi$
$379$	−17.3869	+	17.3869i	−0.893106	+	0.893106i	0.101708	+	0.994814i	$0.467569\pi$
$380$	0.774723	+	0.952209i	0.0397425	+	0.0488473i
$381$	−27.2980	+	1.31869i	−1.39852	+	0.0675585i
$382$	−1.93051	+	4.05944i	−0.0987737	+	0.207699i
$383$	32.9757			1.68498			0.842491	−	0.538711i	$-0.181088\pi$
$383$	32.9757			1.68498			0.842491	+	0.538711i	$0.181088\pi$
$384$	19.5292	−	1.61512i	0.996598	−	0.0824211i
$385$	−8.00000			−0.407718
$386$	−6.96037	+	14.6361i	−0.354274	+	0.744958i
$387$	−1.91701	+	2.32811i	−0.0974473	+	0.118345i
$388$	10.9511	+	13.4600i	0.555959	+	0.683327i
$389$	−3.97434	+	3.97434i	−0.201507	+	0.201507i	−0.800645	−	0.599138i	$-0.795510\pi$
$389$	−3.97434	+	3.97434i	−0.201507	+	0.201507i	0.599138	+	0.800645i	$0.295510\pi$
$390$	1.71404	−	4.10392i	0.0867938	−	0.207810i
$391$	−14.5089			−0.733744
$392$	−7.21953	+	1.75967i	−0.364641	+	0.0888767i
$393$	0.145945	+	0.132494i	0.00736195	+	0.00668346i
$394$	−9.91638	−	27.9008i	−0.499580	−	1.40562i
$395$	−1.50052	−	1.50052i	−0.0754991	−	0.0754991i
$396$	−0.148883	+	25.3369i	−0.00748164	+	1.27323i
$397$	−15.9355	+	15.9355i	−0.799782	+	0.799782i	−0.983061	−	0.183279i	$-0.941329\pi$
$397$	−15.9355	+	15.9355i	−0.799782	+	0.799782i	0.183279	+	0.983061i	$0.441329\pi$
$398$	−14.8530	+	31.2326i	−0.744516	+	1.56555i
$399$	−3.63135	+	4.00000i	−0.181795	+	0.200250i
$400$	−18.1219	−	3.76473i	−0.906097	−	0.188237i
$401$			29.7716i			1.48672i	0.668891	+	0.743361i	$0.266769\pi$
$401$			29.7716i			1.48672i	−0.668891	+	0.743361i	$0.733231\pi$
$402$	−0.515894	−	1.25590i	−0.0257305	−	0.0626387i
$403$	−1.10278	−	1.10278i	−0.0549331	−	0.0549331i
$404$	−0.512205	−	0.0526419i	−0.0254832	−	0.00261903i
$405$	3.06782	−	4.55897i	0.152441	−	0.226537i
$406$	−16.7300	+	5.94610i	−0.830295	+	0.295100i
$407$			9.10404i			0.451270i
$408$	−11.4139	+	3.37307i	−0.565071	+	0.166992i
$409$		−	15.6655i		−	0.774610i	−0.921952	−	0.387305i	$-0.873406\pi$
$409$		−	15.6655i		−	0.774610i	0.921952	−	0.387305i	$-0.126594\pi$
$410$	−0.525036	−	1.47725i	−0.0259297	−	0.0729559i
$411$	−1.10821	−	22.9410i	−0.0546642	−	1.13159i
$412$	−8.02418	−	9.86248i	−0.395323	−	0.485890i
$413$	0.249687	+	0.249687i	0.0122863	+	0.0122863i
$414$	23.8240	+	8.62542i	1.17088	+	0.423916i
$415$		−	3.93051i		−	0.192941i
$416$	16.6654	−	2.29178i	0.817086	−	0.112364i
$417$	15.2197	+	13.8170i	0.745311	+	0.676621i
$418$	−5.42166	−	2.57834i	−0.265182	−	0.126111i
$419$	−14.1554	+	14.1554i	−0.691538	+	0.691538i	−0.962570	−	0.271032i	$-0.912635\pi$
$419$	−14.1554	+	14.1554i	−0.691538	+	0.691538i	0.271032	+	0.962570i	$0.412635\pi$
$420$	−0.355160	+	6.55291i	−0.0173300	+	0.319749i
$421$	−7.35720	−	7.35720i	−0.358568	−	0.358568i	0.504717	−	0.863285i	$-0.331597\pi$
$421$	−7.35720	−	7.35720i	−0.358568	−	0.358568i	−0.863285	+	0.504717i	$0.831597\pi$
$422$	−11.6583	+	4.14356i	−0.567519	+	0.201705i
$423$	22.5089	−	2.17977i	1.09442	−	0.105984i
$424$	18.3572	−	30.1900i	0.891504	−	1.46615i
$425$	11.2416			0.545298
$426$	−4.73886	+	11.3462i	−0.229599	+	0.549726i
$427$	17.7789	−	17.7789i	0.860380	−	0.860380i
$428$	0.476105	−	4.63249i	0.0230134	−	0.223920i
$429$	1.04950	+	21.7256i	0.0506705	+	1.04892i
$430$	−0.783887	−	0.372787i	−0.0378024	−	0.0179774i
$431$	−20.7097			−0.997553			−0.498776	−	0.866731i	$-0.666217\pi$
$431$	−20.7097			−0.997553			−0.498776	+	0.866731i	$0.666217\pi$
$432$	20.7472	+	1.24678i	0.998199	+	0.0599858i
$433$	−23.4005			−1.12456			−0.562279	−	0.826948i	$-0.690075\pi$
$433$	−23.4005			−1.12456			−0.562279	+	0.826948i	$0.690075\pi$
$434$	2.07819	+	0.988310i	0.0997565	+	0.0474404i
$435$	0.206471	+	4.27411i	0.00989951	+	0.204928i
$436$	−18.4947	−	1.90080i	−0.885736	−	0.0910316i
$437$	−4.24513	+	4.24513i	−0.203072	+	0.203072i
$438$	12.7065	−	30.4232i	0.607142	−	1.45368i
$439$	20.2594			0.966931			0.483465	−	0.875363i	$-0.339378\pi$
$439$	20.2594			0.966931			0.483465	+	0.875363i	$0.339378\pi$
$440$	−7.08522	+	1.72693i	−0.337774	+	0.0823283i
$441$	−7.84494	+	0.759707i	−0.373569	+	0.0361765i
$442$	−9.62721	+	3.42166i	−0.457920	+	0.162752i
$443$	−4.05264	−	4.05264i	−0.192547	−	0.192547i	0.604249	−	0.796796i	$-0.293473\pi$
$443$	−4.05264	−	4.05264i	−0.192547	−	0.192547i	−0.796796	+	0.604249i	$0.793473\pi$
$444$	7.45725	+	0.404173i	0.353905	+	0.0191812i
$445$	5.42166	−	5.42166i	0.257011	−	0.257011i
$446$	−10.4598	−	4.97429i	−0.495286	−	0.235539i
$447$	10.5008	+	9.53303i	0.496671	+	0.450897i
$448$	−22.0383	+	11.4217i	−1.04121	+	0.539623i
$449$		−	5.38394i		−	0.254084i	−0.991897	−	0.127042i	$-0.959452\pi$
$449$		−	5.38394i		−	0.254084i	0.991897	−	0.127042i	$-0.0405483\pi$
$450$	−18.4590	−	6.68306i	−0.870168	−	0.315043i
$451$	5.42166	+	5.42166i	0.255296	+	0.255296i
$452$	−12.8963	+	10.4925i	−0.606592	+	0.493528i
$453$	0.831227	+	17.2071i	0.0390544	+	0.808459i
$454$	−6.63778	−	18.6761i	−0.311526	−	0.876512i
$455$			5.63363i			0.264109i
$456$	−2.35265	+	4.32650i	−0.110173	+	0.202607i
$457$			28.0766i			1.31337i	0.754165	+	0.656685i	$0.228042\pi$
$457$			28.0766i			1.31337i	−0.754165	+	0.656685i	$0.771958\pi$
$458$	13.4774	−	4.79007i	0.629756	−	0.223825i
$459$	−12.4917	+	1.82166i	−0.583062	+	0.0850279i
$460$	−0.745574	+	7.25443i	−0.0347626	+	0.338239i
$461$	22.7962	+	22.7962i	1.06172	+	1.06172i	0.997965	+	0.0637594i	$0.0203090\pi$
$461$	22.7962	+	22.7962i	1.06172	+	1.06172i	0.0637594	+	0.997965i	$0.479691\pi$
$462$	−12.1950	−	29.6877i	−0.567362	−	1.38120i
$463$		−	0.740035i		−	0.0343923i	−0.999852	−	0.0171962i	$-0.994526\pi$
$463$		−	0.740035i		−	0.0343923i	0.999852	−	0.0171962i	$-0.00547398\pi$
$464$	−13.5334	+	8.87762i	−0.628272	+	0.412133i
$465$	0.372787	−	0.410632i	0.0172876	−	0.0190426i
$466$	−11.9305	+	25.0872i	−0.552670	+	1.16214i
$467$	9.73282	−	9.73282i	0.450381	−	0.450381i	−0.445100	−	0.895481i	$-0.646832\pi$
$467$	9.73282	−	9.73282i	0.450381	−	0.450381i	0.895481	+	0.445100i	$0.146832\pi$
$468$	17.8423	+	0.104844i	0.824762	+	0.00484641i
$469$	1.21611	+	1.21611i	0.0561549	+	0.0561549i
$470$	2.17977	+	6.13301i	0.100545	+	0.282895i
$471$	−16.5975	−	15.0678i	−0.764772	−	0.694289i
$472$	0.275035	+	0.167237i	0.0126595	+	0.00769770i
$473$	4.24513			0.195191
$474$	3.28101	−	7.85571i	0.150702	−	0.360825i
$475$	3.28917	−	3.28917i	0.150917	−	0.150917i
$476$	11.6944	−	9.51467i	0.536014	−	0.436104i
$477$	23.8221	−	28.9307i	1.09074	−	1.32464i
$478$	5.73501	−	12.0594i	0.262313	−	0.551586i
$479$	−28.2478			−1.29067			−0.645337	−	0.763898i	$-0.723283\pi$
$479$	−28.2478			−1.29067			−0.645337	+	0.763898i	$0.723283\pi$
$480$	1.10001	+	5.88027i	0.0502082	+	0.268396i
$481$	6.41110			0.292321
$482$	10.0923	−	21.2219i	0.459694	−	0.966633i
$483$	−32.0575	+	1.54861i	−1.45866	+	0.0704641i
$484$	10.6003	−	8.62444i	0.481830	−	0.392020i
$485$	−3.74576	+	3.74576i	−0.170086	+	0.170086i
$486$	21.5947	+	4.43501i	0.979555	+	0.201176i
$487$	19.7094			0.893117			0.446559	−	0.894754i	$-0.352649\pi$
$487$	19.7094			0.893117			0.446559	+	0.894754i	$0.352649\pi$
$488$	11.9080	−	19.5837i	0.539051	−	0.886515i
$489$	−25.8499	+	28.4741i	−1.16897	+	1.28764i
$490$	−0.759707	−	2.13752i	−0.0343201	−	0.0965632i
$491$	29.4414	+	29.4414i	1.32867	+	1.32867i	0.906529	+	0.422143i	$0.138722\pi$
$491$	29.4414	+	29.4414i	1.32867	+	1.32867i	0.422143	+	0.906529i	$0.361278\pi$
$492$	4.68165	−	4.20027i	0.211065	−	0.189363i
$493$	6.95112	−	6.95112i	0.313063	−	0.313063i
$494$	−1.81568	+	3.81796i	−0.0816911	+	0.171778i
$495$	−7.69899	+	0.745574i	−0.346044	+	0.0335111i
$496$	2.05390	+	0.426686i	0.0922228	+	0.0191588i
$497$		−	15.5755i		−	0.698656i
$498$	14.5860	−	5.99158i	0.653615	−	0.268489i
$499$	4.43026	+	4.43026i	0.198326	+	0.198326i	0.799282	−	0.600956i	$-0.205213\pi$
$499$	4.43026	+	4.43026i	0.198326	+	0.198326i	−0.600956	+	0.799282i	$0.705213\pi$
$500$	1.20190	−	11.6944i	0.0537504	−	0.522991i
$501$	33.1193	−	1.59990i	1.47966	−	0.0714784i
$502$	3.83276	−	1.36222i	0.171065	−	0.0607990i
$503$		−	27.6805i		−	1.23421i	−0.786879	−	0.617107i	$-0.788304\pi$
$503$		−	27.6805i		−	1.23421i	0.786879	−	0.617107i	$-0.211696\pi$
$504$	−24.8590	+	8.67111i	−1.10731	+	0.386242i
$505$		−	0.157190i		−	0.00699488i
$506$	−11.9441	−	33.6061i	−0.530981	−	1.49397i
$507$	−7.19119	+	0.347386i	−0.319372	+	0.0154280i
$508$	24.4791	−	19.9164i	1.08609	−	0.883647i
$509$	−17.3235	−	17.3235i	−0.767851	−	0.767851i	0.209877	−	0.977728i	$-0.432694\pi$
$509$	−17.3235	−	17.3235i	−0.767851	−	0.767851i	−0.977728	+	0.209877i	$0.932694\pi$
$510$	−1.38058	−	3.36091i	−0.0611330	−	0.148823i
$511$			41.7633i			1.84750i
$512$	−17.0527	+	14.8730i	−0.753631	+	0.657298i
$513$	−3.12193	+	4.18793i	−0.137837	+	0.184902i
$514$	19.2544	+	9.15667i	0.849276	+	0.403884i
$515$	2.74461	−	2.74461i	0.120942	−	0.120942i
$516$	0.188462	−	3.47725i	0.00829659	−	0.153077i
$517$	−22.5089	−	22.5089i	−0.989938	−	0.989938i
$518$	−8.91372	+	3.16808i	−0.391646	+	0.139197i
$519$	−21.9441	+	24.1719i	−0.963240	+	1.06103i
$520$	1.21611	+	4.98944i	0.0533301	+	0.218801i
$521$	10.1284			0.443735			0.221868	−	0.975077i	$-0.428785\pi$
$521$	10.1284			0.443735			0.221868	+	0.975077i	$0.428785\pi$
$522$	−15.5464	+	7.28156i	−0.680445	+	0.318705i
$523$	1.45641	−	1.45641i	0.0636842	−	0.0636842i	−0.674547	−	0.738232i	$-0.735661\pi$
$523$	1.45641	−	1.45641i	0.0636842	−	0.0636842i	0.738232	+	0.674547i	$0.235661\pi$
$524$	−0.226417	−	0.0232700i	−0.00989108	−	0.00101656i
$525$	24.8384	−	1.19988i	1.08404	−	0.0523669i
$526$	38.0766	+	18.1078i	1.66022	+	0.789538i
$527$	−1.27410			−0.0555006
$528$	−17.2091	−	23.6605i	−0.748930	−	1.02969i
$529$	−12.6655			−0.550675
$530$	9.74109	+	4.63249i	0.423126	+	0.201223i
$531$	0.263563	+	0.217023i	0.0114376	+	0.00941798i
$532$	0.637776	−	6.20555i	0.0276511	−	0.269045i
$533$	3.81796	−	3.81796i	0.165374	−	0.165374i
$534$	28.3842	+	11.8550i	1.22831	+	0.513014i
$535$	1.42166			0.0614638
$536$	1.33957	+	0.814535i	0.0578606	+	0.0351825i
$537$	−16.6571	−	15.1219i	−0.718806	−	0.652560i
$538$	−30.8519	+	10.9653i	−1.33012	+	0.472746i
$539$	7.84494	+	7.84494i	0.337905	+	0.337905i
$540$	0.268914	+	6.33945i	0.0115722	+	0.272807i
$541$	5.18996	−	5.18996i	0.223134	−	0.223134i	−0.586683	−	0.809817i	$-0.699566\pi$
$541$	5.18996	−	5.18996i	0.223134	−	0.223134i	0.809817	+	0.586683i	$0.199566\pi$
$542$	17.0456	+	8.10626i	0.732173	+	0.348194i
$543$	27.1894	−	29.9497i	1.16681	−	1.28526i
$544$	8.30330	−	10.9511i	0.356001	−	0.469526i
$545$		−	5.67583i		−	0.243126i
$546$	−20.9062	+	8.58776i	−0.894703	+	0.367522i
$547$	12.6413	+	12.6413i	0.540505	+	0.540505i	0.923677	−	0.383172i	$-0.125168\pi$
$547$	12.6413	+	12.6413i	0.540505	+	0.540505i	−0.383172	+	0.923677i	$0.625168\pi$
$548$	16.7376	+	20.5721i	0.714993	+	0.878795i
$549$	15.4530	−	18.7669i	0.659518	−	0.800950i
$550$	9.25443	+	26.0383i	0.394610	+	1.11028i
$551$		−	4.06764i		−	0.173287i
$552$	−28.0575	+	8.29166i	−1.19420	+	0.352916i
$553$			10.7839i			0.458578i
$554$	20.1287	−	7.15405i	0.855186	−	0.303947i
$555$	0.110007	+	2.27724i	0.00466955	+	0.0966636i
$556$	−23.6116	−	2.42669i	−1.00136	−	0.102914i
$557$	−6.90317	−	6.90317i	−0.292497	−	0.292497i	0.545569	−	0.838066i	$-0.316314\pi$
$557$	−6.90317	−	6.90317i	−0.292497	−	0.292497i	−0.838066	+	0.545569i	$0.816314\pi$
$558$	2.09211	+	0.757443i	0.0885660	+	0.0320651i
$559$		−	2.98944i		−	0.126440i
$560$	−4.15639	−	6.33615i	−0.175639	−	0.267751i
$561$	13.1567	+	11.9441i	0.555475	+	0.504281i
$562$	−10.6861	+	22.4705i	−0.450767	+	0.947862i
$563$	−18.3840	+	18.3840i	−0.774794	+	0.774794i	−0.978940	−	0.204146i	$-0.934558\pi$
$563$	−18.3840	+	18.3840i	−0.774794	+	0.774794i	0.204146	+	0.978940i	$0.434558\pi$
$564$	−19.4366	+	17.4380i	−0.818428	+	0.734274i
$565$	−3.58890	−	3.58890i	−0.150986	−	0.150986i
$566$	11.5041	+	32.3681i	0.483554	+	1.36053i
$567$	−27.4061	+	5.35828i	−1.15095	+	0.225027i
$568$	−3.36222	−	13.7944i	−0.141076	−	0.578802i
$569$	−43.5570			−1.82601			−0.913003	−	0.407953i	$-0.866243\pi$
$569$	−43.5570			−1.82601			−0.913003	+	0.407953i	$0.866243\pi$
$570$	−1.38731	−	0.579422i	−0.0581079	−	0.0242693i
$571$	7.00859	−	7.00859i	0.293301	−	0.293301i	−0.545082	−	0.838383i	$-0.683502\pi$
$571$	7.00859	−	7.00859i	0.293301	−	0.293301i	0.838383	+	0.545082i	$0.183502\pi$
$572$	−15.8508	−	19.4822i	−0.662756	−	0.814591i
$573$	−0.265638	−	5.49894i	−0.0110972	−	0.229721i
$574$	−3.42166	+	7.19499i	−0.142817	+	0.300313i
$575$	27.6340			1.15242
$576$	−20.1446	+	13.0458i	−0.839360	+	0.543576i
$577$	28.4494			1.18436			0.592182	−	0.805804i	$-0.298267\pi$
$577$	28.4494			1.18436			0.592182	+	0.805804i	$0.298267\pi$
$578$	6.74037	−	14.1735i	0.280362	−	0.589539i
$579$	−0.957746	−	19.8261i	−0.0398026	−	0.823946i
$580$	−3.11836	−	3.83276i	−0.129483	−	0.159147i
$581$	−14.1239	+	14.1239i	−0.585958	+	0.585958i
$582$	−19.6103	−	8.19044i	−0.812873	−	0.339504i
$583$	−52.7527			−2.18479
$584$	9.01530	+	36.9877i	0.373056	+	1.53056i
$585$	0.525036	+	5.42166i	0.0217076	+	0.224158i
$586$	2.49472	+	7.01916i	0.103056	+	0.289959i
$587$	19.9011	+	19.9011i	0.821405	+	0.821405i	0.986310	−	0.164904i	$-0.0527315\pi$
$587$	19.9011	+	19.9011i	0.821405	+	0.821405i	−0.164904	+	0.986310i	$0.552732\pi$
$588$	6.77418	−	6.07762i	0.279362	−	0.250637i
$589$	−0.372787	+	0.372787i	−0.0153604	+	0.0153604i
$590$	−0.0422027	+	0.0887428i	−0.00173746	+	0.00365348i
$591$	26.8510	+	24.3764i	1.10450	+	1.00271i
$592$	−7.21057	+	4.72999i	−0.296353	+	0.194401i
$593$		−	20.4344i		−	0.839140i	−0.907723	−	0.419570i	$-0.862181\pi$
$593$		−	20.4344i		−	0.839140i	0.907723	−	0.419570i	$-0.137819\pi$
$594$	−14.5029	−	27.4342i	−0.595063	−	1.12564i
$595$	3.25443	+	3.25443i	0.133418	+	0.133418i
$596$	−16.2908	−	1.67429i	−0.667298	−	0.0685816i
$597$	−2.04378	−	42.3079i	−0.0836462	−	1.73155i
$598$	−23.6655	+	8.41110i	−0.967755	+	0.343955i
$599$		−	32.6704i		−	1.33488i	−0.744665	−	0.667438i	$-0.767391\pi$
$599$		−	32.6704i		−	1.33488i	0.744665	−	0.667438i	$-0.232609\pi$
$600$	21.7392	−	6.42446i	0.887499	−	0.262278i
$601$		−	6.73553i		−	0.274748i	−0.990519	−	0.137374i	$-0.956134\pi$
$601$		−	6.73553i		−	0.274748i	0.990519	−	0.137374i	$-0.0438662\pi$
$602$	1.47725	+	4.15639i	0.0602080	+	0.169402i
$603$	1.28369	+	1.05702i	0.0522760	+	0.0430451i
$604$	−12.5542	−	15.4303i	−0.510821	−	0.627848i
$605$	2.94993	+	2.94993i	0.119932	+	0.119932i
$606$	0.583328	−	0.239617i	0.0236961	−	0.00973378i
$607$		−	21.2388i		−	0.862058i	−0.902338	−	0.431029i	$-0.858151\pi$
$607$		−	21.2388i		−	0.862058i	0.902338	−	0.431029i	$-0.141849\pi$
$608$	−0.774723	−	5.63363i	−0.0314192	−	0.228474i
$609$	14.6167	−	16.1005i	0.592297	−	0.652426i
$610$	6.31889	+	3.00502i	0.255844	+	0.121670i
$611$	−15.8508	+	15.8508i	−0.641256	+	0.641256i
$612$	10.3677	−	10.2466i	0.419089	−	0.414193i
$613$	−9.62219	−	9.62219i	−0.388637	−	0.388637i	0.485564	−	0.874201i	$-0.338614\pi$
$613$	−9.62219	−	9.62219i	−0.388637	−	0.388637i	−0.874201	+	0.485564i	$0.838614\pi$
$614$	−25.3294	+	9.00246i	−1.02221	+	0.363310i
$615$	1.42166	+	1.29064i	0.0573270	+	0.0520436i
$616$	31.6655	+	19.2544i	1.27584	+	0.775783i
$617$	3.74576			0.150798			0.0753992	−	0.997153i	$-0.475977\pi$
$617$	3.74576			0.150798			0.0753992	+	0.997153i	$0.475977\pi$
$618$	14.3690	+	6.00135i	0.578005	+	0.241410i
$619$	−13.0680	+	13.0680i	−0.525249	+	0.525249i	−0.919152	−	0.393903i	$-0.871124\pi$
$619$	−13.0680	+	13.0680i	−0.525249	+	0.525249i	0.393903	+	0.919152i	$0.371124\pi$
$620$	−0.0654727	+	0.637049i	−0.00262945	+	0.0255845i
$621$	−30.7070	+	4.47799i	−1.23223	+	0.179696i
$622$	17.6655	+	8.40105i	0.708323	+	0.336852i
$623$	−38.9643			−1.56107
$624$	−16.6618	+	12.1187i	−0.667007	+	0.485137i
$625$	−19.5472			−0.781887
$626$	−5.03268	−	2.39335i	−0.201147	−	0.0956576i
$627$	7.34422	−	0.354779i	0.293300	−	0.0141685i
$628$	25.7491	+	2.64637i	1.02750	+	0.105602i
$629$	3.70355	−	3.70355i	0.147670	−	0.147670i
$630$	−3.40913	−	7.27860i	−0.135823	−	0.289986i
$631$	−7.51388			−0.299123			−0.149561	−	0.988752i	$-0.547786\pi$
$631$	−7.51388			−0.299123			−0.149561	+	0.988752i	$0.547786\pi$
$632$	2.32788	+	9.55077i	0.0925981	+	0.379909i
$633$	10.1857	−	11.2197i	0.404843	−	0.445942i
$634$	16.8136	−	5.97582i	0.667754	−	0.237330i
$635$	6.81226	+	6.81226i	0.270336	+	0.270336i
$636$	−2.34195	+	43.2105i	−0.0928645	+	1.71341i
$637$	5.52444	−	5.52444i	0.218886	−	0.218886i
$638$	21.8229	+	10.3781i	0.863976	+	0.410874i
$639$	−1.45158	−	14.9894i	−0.0574238	−	0.592973i
$640$	−5.04888	−	4.71440i	−0.199574	−	0.186353i
$641$		−	27.7227i		−	1.09498i	−0.836811	−	0.547491i	$-0.815583\pi$
$641$		−	27.7227i		−	1.09498i	0.836811	−	0.547491i	$-0.184417\pi$
$642$	2.16715	+	5.27574i	0.0855304	+	0.208217i
$643$	19.7003	+	19.7003i	0.776903	+	0.776903i	0.979303	−	0.202400i	$-0.0648742\pi$
$643$	19.7003	+	19.7003i	0.776903	+	0.776903i	−0.202400	+	0.979303i	$0.564874\pi$
$644$	28.7472	−	23.3889i	1.13280	−	0.921651i
$645$	1.06186	−	0.0512954i	0.0418106	−	0.00201976i
$646$	1.15667	+	3.25443i	0.0455087	+	0.128044i
$647$			5.29520i			0.208176i	0.994568	+	0.104088i	$0.0331923\pi$
$647$			5.29520i			0.208176i	−0.994568	+	0.104088i	$0.966808\pi$
$648$	−23.1156	+	10.6616i	−0.908065	+	0.418828i
$649$		−	0.480585i		−	0.0188646i
$650$	18.3363	−	6.51700i	0.719208	−	0.255618i
$651$	−2.81513	+	0.135991i	−0.110334	+	0.00532992i
$652$	4.54002	−	44.1744i	0.177801	−	1.73000i
$653$	29.7039	+	29.7039i	1.16240	+	1.16240i	0.983948	+	0.178457i	$0.0571104\pi$
$653$	29.7039	+	29.7039i	1.16240	+	1.16240i	0.178457	+	0.983948i	$0.442890\pi$
$654$	21.0628	−	8.65210i	0.823622	−	0.338324i
$655$		−	0.0694851i		−	0.00271501i
$656$	−1.47725	+	7.11088i	−0.0576767	+	0.277633i
$657$	3.89220	+	40.1919i	0.151849	+	1.56804i
$658$	14.2056	−	29.8711i	0.553790	−	1.16450i
$659$	1.03268	−	1.03268i	0.0402276	−	0.0402276i	−0.686707	−	0.726934i	$-0.740944\pi$
$659$	1.03268	−	1.03268i	0.0402276	−	0.0402276i	0.726934	+	0.686707i	$0.240944\pi$
$660$	6.64815	−	5.96456i	0.258779	−	0.232170i
$661$	29.8277	+	29.8277i	1.16016	+	1.16016i	0.984439	+	0.175725i	$0.0562271\pi$
$661$	29.8277	+	29.8277i	1.16016	+	1.16016i	0.175725	+	0.984439i	$0.443773\pi$
$662$	−6.32332	−	17.7913i	−0.245763	−	0.691480i
$663$	8.41110	−	9.26498i	0.326660	−	0.359822i
$664$	−9.45998	+	15.5577i	−0.367118	+	0.603757i
$665$	1.90442			0.0738502
$666$	−8.28308	+	3.87961i	−0.320963	+	0.150332i
$667$	17.0872	−	17.0872i	0.661619	−	0.661619i
$668$	−29.6994	+	24.1636i	−1.14910	+	0.934918i
$669$	14.1689	−	0.684461i	0.547802	−	0.0264628i
$670$	−0.205550	+	0.432226i	−0.00794109	+	0.0166983i
$671$	−34.2198			−1.32104
$672$	17.1774	−	25.0829i	0.662631	−	0.967593i
$673$	−0.891685			−0.0343719			−0.0171860	−	0.999852i	$-0.505471\pi$
$673$	−0.891685			−0.0343719			−0.0171860	+	0.999852i	$0.505471\pi$
$674$	3.60808	−	7.58698i	0.138978	−	0.292240i
$675$	23.7920	−	3.46959i	0.915756	−	0.133545i
$676$	6.44861	−	5.24663i	0.248024	−	0.201794i
$677$	−8.13073	+	8.13073i	−0.312489	+	0.312489i	−0.845873	−	0.533384i	$-0.820920\pi$
$677$	−8.13073	+	8.13073i	−0.312489	+	0.312489i	0.533384	+	0.845873i	$0.320920\pi$
$678$	7.84746	−	18.7891i	0.301380	−	0.721591i
$679$	26.9200			1.03309
$680$	3.58481	+	2.17977i	0.137471	+	0.0835902i
$681$	17.9734	+	16.3169i	0.688742	+	0.625266i
$682$	−1.04888	−	2.95112i	−0.0401635	−	0.113004i
$683$	−14.5917	−	14.5917i	−0.558337	−	0.558337i	0.370497	−	0.928834i	$-0.379187\pi$
$683$	−14.5917	−	14.5917i	−0.558337	−	0.558337i	−0.928834	+	0.370497i	$0.879187\pi$
$684$	0.0354419	−	6.03150i	0.00135515	−	0.230620i
$685$	−5.72496	+	5.72496i	−0.218740	+	0.218740i
$686$	8.24057	−	17.3281i	0.314626	−	0.661589i
$687$	−11.7749	+	12.9703i	−0.449241	+	0.494847i
$688$	2.20555	+	3.36222i	0.0840858	+	0.128184i
$689$			37.1487i			1.41525i
$690$	−3.39373	−	8.26175i	−0.129197	−	0.314519i
$691$	−11.2197	−	11.2197i	−0.426817	−	0.426817i	0.460726	−	0.887543i	$-0.347589\pi$
$691$	−11.2197	−	11.2197i	−0.426817	−	0.426817i	−0.887543	+	0.460726i	$0.847589\pi$
$692$	3.85406	−	37.4999i	0.146509	−	1.42553i
$693$	30.3447	+	24.9864i	1.15270	+	0.949154i
$694$	−7.72496	+	2.74557i	−0.293236	+	0.104221i
$695$		−	7.24616i		−	0.274863i
$696$	9.46970	−	17.4147i	0.358948	−	0.660102i
$697$		−	4.41110i		−	0.167082i
$698$	5.42712	+	15.2698i	0.205420	+	0.577970i
$699$	−1.64164	−	33.9833i	−0.0620924	−	1.28536i
$700$	−22.2736	+	18.1219i	−0.841862	+	0.684945i
$701$	−14.7166	−	14.7166i	−0.555837	−	0.555837i	0.372282	−	0.928120i	$-0.378575\pi$
$701$	−14.7166	−	14.7166i	−0.555837	−	0.555837i	−0.928120	+	0.372282i	$0.878575\pi$
$702$	−19.3193	+	10.2130i	−0.729158	+	0.385466i
$703$		−	2.16724i		−	0.0817389i
$704$	32.2010	+	10.2172i	1.21362	+	0.385075i
$705$	−5.90225	−	5.35828i	−0.222292	−	0.201805i
$706$	−37.3522	−	17.7633i	−1.40577	−	0.668530i
$707$	−0.564847	+	0.564847i	−0.0212433	+	0.0212433i
$708$	−0.393654	−	0.0213356i	−0.0147944	−	0.000801839i
$709$	−23.2978	−	23.2978i	−0.874966	−	0.874966i	0.118043	−	0.993009i	$-0.462338\pi$
$709$	−23.2978	−	23.2978i	−0.874966	−	0.874966i	−0.993009	+	0.118043i	$0.962338\pi$
$710$	4.08419	−	1.45158i	0.153277	−	0.0544770i
$711$	1.00502	+	10.3781i	0.0376913	+	0.389211i
$712$	−34.5089	+	8.41110i	−1.29327	+	0.315219i
$713$	−3.13198			−0.117293
$714$	−7.11610	+	17.0380i	−0.266313	+	0.637632i
$715$	5.42166	−	5.42166i	0.202759	−	0.202759i
$716$	25.8416	+	2.65587i	0.965746	+	0.0992546i
$717$	0.789136	+	16.3358i	0.0294708	+	0.610071i
$718$	−27.2333	−	12.9511i	−1.01634	−	0.483332i
$719$	27.3421			1.01969			0.509844	−	0.860267i	$-0.329703\pi$
$719$	27.3421			1.01969			0.509844	+	0.860267i	$0.329703\pi$
$720$	−4.59051	−	5.71039i	−0.171078	−	0.212814i
$721$	−19.7250			−0.734596
$722$	−22.9752	−	10.9261i	−0.855048	−	0.406628i
$723$	1.38871	+	28.7474i	0.0516465	+	1.06913i
$724$	−4.77529	+	46.4635i	−0.177472	+	1.72680i
$725$	−13.2393	+	13.2393i	−0.491696	+	0.491696i
$726$	−6.45029	+	15.4439i	−0.239393	+	0.573176i
$727$	24.1517			0.895735			0.447868	−	0.894100i	$-0.352184\pi$
$727$	24.1517			0.895735			0.447868	+	0.894100i	$0.352184\pi$
$728$	13.5590	−	22.2990i	0.502532	−	0.826456i
$729$	−25.8755	+	7.71083i	−0.958353	+	0.285586i
$730$	−10.9511	+	3.89220i	−0.405319	+	0.144057i
$731$	−1.72693	−	1.72693i	−0.0638729	−	0.0638729i
$732$	−1.51919	+	28.0300i	−0.0561508	+	1.03602i
$733$	−6.00502	+	6.00502i	−0.221801	+	0.221801i	−0.809256	−	0.587456i	$-0.800130\pi$
$733$	−6.00502	+	6.00502i	−0.221801	+	0.221801i	0.587456	+	0.809256i	$0.300130\pi$
$734$	−41.9259	−	19.9384i	−1.54751	−	0.735939i
$735$	2.05709	+	1.86751i	0.0758770	+	0.0688840i
$736$	20.4111	−	26.9200i	0.752363	−	0.992283i
$737$		−	2.34071i		−	0.0862212i
$738$	−2.62237	+	7.24316i	−0.0965308	+	0.266624i
$739$	−10.9008	−	10.9008i	−0.400992	−	0.400992i	0.477590	−	0.878583i	$-0.341510\pi$
$739$	−10.9008	−	10.9008i	−0.400992	−	0.400992i	−0.878583	+	0.477590i	$0.841510\pi$
$740$	−1.66146	−	2.04209i	−0.0610765	−	0.0750688i
$741$	−0.249837	−	5.17183i	−0.00917798	−	0.189992i
$742$	−18.3572	−	51.6499i	−0.673914	−	1.89613i
$743$			1.29064i			0.0473490i	0.999720	+	0.0236745i	$0.00753652\pi$
$743$			1.29064i			0.0473490i	−0.999720	+	0.0236745i	$0.992463\pi$
$744$	−2.46387	+	0.728134i	−0.0903299	+	0.0266947i
$745$		−	4.99948i		−	0.183167i
$746$	2.55766	−	0.909033i	0.0936427	−	0.0332821i
$747$	−12.2762	+	14.9088i	−0.449162	+	0.545483i
$748$	−20.4111	−	2.09775i	−0.746304	−	0.0767014i
$749$	−5.10860	−	5.10860i	−0.186664	−	0.186664i
$750$	5.47083	+	13.3183i	0.199766	+	0.486315i
$751$		−	1.46552i		−	0.0534774i	−0.999642	−	0.0267387i	$-0.991488\pi$
$751$		−	1.46552i		−	0.0534774i	0.999642	−	0.0267387i	$-0.00851221\pi$
$752$	6.13301	−	29.5219i	0.223648	−	1.07655i
$753$	−3.34861	+	3.68855i	−0.122030	+	0.134418i
$754$	7.30833	−	15.3678i	0.266154	−	0.559661i
$755$	4.29406	−	4.29406i	0.156277	−	0.156277i
$756$	21.8138	−	23.7465i	0.793362	−	0.863651i
$757$	4.71943	+	4.71943i	0.171530	+	0.171530i	0.787651	−	0.616121i	$-0.211297\pi$
$757$	4.71943	+	4.71943i	0.171530	+	0.171530i	−0.616121	+	0.787651i	$0.711297\pi$
$758$	11.6455	+	32.7659i	0.422984	+	1.19011i
$759$	32.3416	+	29.3609i	1.17393	+	1.06573i
$760$	1.68665	−	0.411100i	0.0611813	−	0.0149122i
$761$	29.1578			1.05697			0.528485	−	0.848943i	$-0.322760\pi$
$761$	29.1578			1.05697			0.528485	+	0.848943i	$0.322760\pi$
$762$	−14.8956	+	35.6645i	−0.539612	+	1.29199i
$763$	−20.3955	+	20.3955i	−0.738367	+	0.738367i
$764$	4.01198	+	4.93111i	0.145148	+	0.178401i
$765$	3.43528	+	2.82867i	0.124203	+	0.102271i
$766$	20.0283	−	42.1149i	0.723651	−	1.52167i
$767$	−0.338430			−0.0122200
$768$	9.79861	−	25.9227i	0.353577	−	0.935405i
$769$	20.8122			0.750505			0.375253	−	0.926923i	$-0.377556\pi$
$769$	20.8122			0.750505			0.375253	+	0.926923i	$0.377556\pi$
$770$	−4.85891	+	10.2172i	−0.175103	+	0.368202i
$771$	−26.0822	+	1.25996i	−0.939326	+	0.0453762i
$772$	14.4650	+	17.7789i	0.520607	+	0.639875i
$773$	−26.6607	+	26.6607i	−0.958918	+	0.958918i	−0.999189	−	0.0402703i	$-0.987178\pi$
$773$	−26.6607	+	26.6607i	−0.958918	+	0.958918i	0.0402703	+	0.999189i	$0.487178\pi$
$774$	1.80902	+	3.86233i	0.0650240	+	0.138828i
$775$	2.42669			0.0871691
$776$	23.8417	−	5.81112i	0.855867	−	0.208607i
$777$	7.78774	−	8.57834i	0.279384	−	0.307746i
$778$	2.66196	+	7.48970i	0.0954357	+	0.268519i
$779$	−1.29064	−	1.29064i	−0.0462419	−	0.0462419i
$780$	−4.20027	−	4.68165i	−0.150394	−	0.167630i
$781$	−14.9894	+	14.9894i	−0.536364	+	0.536364i
$782$	−8.81215	+	18.5300i	−0.315122	+	0.662630i
$783$	12.5662	−	16.8569i	0.449078	−	0.602418i
$784$	−2.13752	+	10.2892i	−0.0763399	+	0.367470i
$785$			7.90214i			0.282040i
$786$	0.257857	−	0.105921i	0.00919744	−	0.00377809i
$787$	−32.7875	−	32.7875i	−1.16875	−	1.16875i	−0.982504	−	0.186243i	$-0.940369\pi$
$787$	−32.7875	−	32.7875i	−1.16875	−	1.16875i	−0.186243	−	0.982504i	$-0.559631\pi$
$788$	−41.6563	−	4.28123i	−1.48395	−	0.152513i
$789$	−51.5788	+	2.49163i	−1.83625	+	0.0887044i
$790$	−2.82774	+	1.00502i	−0.100606	+	0.0357571i
$791$			25.7927i			0.917082i
$792$	32.2685	+	15.5788i	1.14661	+	0.553570i
$793$			24.0978i			0.855736i
$794$	10.6734	+	30.0307i	0.378784	+	1.06575i
$795$	−13.1953	+	0.637430i	−0.467990	+	0.0226073i
$796$	30.8675	+	37.9391i	1.09407	+	1.34472i
$797$	−11.2627	−	11.2627i	−0.398945	−	0.398945i	0.478916	−	0.877861i	$-0.341030\pi$
$797$	−11.2627	−	11.2627i	−0.398945	−	0.398945i	−0.877861	+	0.478916i	$0.841030\pi$
$798$	2.90305	+	7.06723i	0.102767	+	0.250177i
$799$			18.3133i			0.647880i
$800$	−15.8147	+	20.8578i	−0.559135	+	0.737436i
$801$	−37.4983	+	3.63135i	−1.32494	+	0.128307i
$802$	38.0227	+	18.0822i	1.34263	+	0.638503i
$803$	40.1919	−	40.1919i	1.41834	−	1.41834i
$804$	−1.91731	−	0.103916i	−0.0676183	−	0.00366483i
$805$	8.00000	+	8.00000i	0.281963	+	0.281963i
$806$	−2.07819	+	0.738623i	−0.0732012	+	0.0260169i
$807$	26.9547	−	29.6911i	0.948850	−	1.04518i
$808$	−0.378326	+	0.622190i	−0.0133095	+	0.0218886i
$809$	48.5934			1.70845			0.854227	−	0.519900i	$-0.174031\pi$
$809$	48.5934			1.70845			0.854227	+	0.519900i	$0.174031\pi$
$810$	−3.95920	−	6.68702i	−0.139112	−	0.234958i
$811$	19.2197	−	19.2197i	0.674894	−	0.674894i	−0.283946	−	0.958840i	$-0.591644\pi$
$811$	19.2197	−	19.2197i	0.674894	−	0.674894i	0.958840	+	0.283946i	$0.0916436\pi$
$812$	−2.56713	+	24.9781i	−0.0900886	+	0.876561i
$813$	−23.0901	+	1.11542i	−0.809806	+	0.0391195i
$814$	11.6272	+	5.52946i	0.407534	+	0.193808i
$815$	13.5567			0.474869
$816$	−2.62445	+	16.6259i	−0.0918740	+	0.582023i
$817$	−1.01056			−0.0353551
$818$	−20.0072	−	9.51467i	−0.699536	−	0.332673i
$819$	17.5955	−	21.3688i	0.614837	−	0.746688i
$820$	−2.20555	−	0.226676i	−0.0770212	−	0.00791585i
$821$	33.7881	−	33.7881i	1.17921	−	1.17921i	0.199268	−	0.979945i	$-0.436143\pi$
$821$	33.7881	−	33.7881i	1.17921	−	1.17921i	0.979945	−	0.199268i	$-0.0638565\pi$
$822$	−29.9721	−	12.5182i	−1.04540	−	0.436621i
$823$	−4.37833			−0.152619			−0.0763094	−	0.997084i	$-0.524314\pi$
$823$	−4.37833			−0.152619			−0.0763094	+	0.997084i	$0.524314\pi$
$824$	−17.4695	+	4.25796i	−0.608577	+	0.148333i
$825$	−25.0586	−	22.7491i	−0.872429	−	0.792024i
$826$	0.470539	−	0.167237i	0.0163721	−	0.00581892i
$827$	−14.2044	−	14.2044i	−0.493934	−	0.493934i	0.415609	−	0.909543i	$-0.363568\pi$
$827$	−14.2044	−	14.2044i	−0.493934	−	0.493934i	−0.909543	+	0.415609i	$0.863568\pi$
$828$	25.4858	−	25.1880i	0.885691	−	0.875343i
$829$	14.8483	−	14.8483i	0.515704	−	0.515704i	−0.400564	−	0.916269i	$-0.631186\pi$
$829$	14.8483	−	14.8483i	0.515704	−	0.515704i	0.916269	+	0.400564i	$0.131186\pi$
$830$	−5.01985	−	2.38725i	−0.174242	−	0.0828627i
$831$	−17.5860	+	19.3713i	−0.610053	+	0.671984i
$832$	7.19499	−	22.6761i	0.249441	−	0.786152i
$833$		−	6.38269i		−	0.221147i
$834$	26.8903	−	11.0459i	0.931133	−	0.382487i
$835$	−8.26499	−	8.26499i	−0.286022	−	0.286022i
$836$	−6.58584	+	5.35828i	−0.227776	+	0.185320i
$837$	−2.69654	+	0.393236i	−0.0932060	+	0.0135922i
$838$	9.48110	+	26.6761i	0.327519	+	0.921510i
$839$			3.11543i			0.107557i	0.998553	+	0.0537784i	$0.0171265\pi$
$839$			3.11543i			0.107557i	−0.998553	+	0.0537784i	$0.982874\pi$
$840$	8.15333	+	4.43359i	0.281317	+	0.152973i
$841$		−	12.6272i		−	0.435421i
$842$	−13.8647	+	4.92775i	−0.477810	+	0.169821i
$843$	−1.47041	−	30.4387i	−0.0506436	−	1.04837i
$844$	−1.78891	+	17.4061i	−0.0615768	+	0.599142i
$845$	1.79457	+	1.79457i	0.0617352	+	0.0617352i
$846$	10.8872	−	30.0711i	0.374309	−	1.03386i
$847$		−	21.2005i		−	0.728459i
$848$	−27.4076	−	41.7812i	−0.941180	−	1.43477i
$849$	−31.1502	−	28.2793i	−1.06907	−	0.970544i
$850$	6.82774	−	14.3572i	0.234190	−	0.492448i
$851$	9.10404	−	9.10404i	0.312082	−	0.312082i
$852$	11.6126	+	12.9435i	0.397841	+	0.443437i
$853$	35.4550	+	35.4550i	1.21395	+	1.21395i	0.969715	+	0.244240i	$0.0785383\pi$
$853$	35.4550	+	35.4550i	1.21395	+	1.21395i	0.244240	+	0.969715i	$0.421462\pi$
$854$	−11.9080	−	33.5045i	−0.407484	−	1.14650i
$855$	1.83276	−	0.177486i	0.0626792	−	0.00606988i
$856$	−5.62721	−	3.42166i	−0.192334	−	0.116950i
$857$	14.0817			0.481021			0.240511	−	0.970646i	$-0.422685\pi$
$857$	14.0817			0.481021			0.240511	+	0.970646i	$0.422685\pi$
$858$	28.3842	+	11.8550i	0.969022	+	0.404722i
$859$	−30.9547	+	30.9547i	−1.05616	+	1.05616i	−0.0578344	+	0.998326i	$0.518420\pi$
$859$	−30.9547	+	30.9547i	−1.05616	+	1.05616i	−0.998326	+	0.0578344i	$0.981580\pi$
$860$	−0.952209	+	0.774723i	−0.0324701	+	0.0264179i
$861$	−0.470820	−	9.74637i	−0.0160455	−	0.332155i
$862$	−12.5783	+	26.4494i	−0.428420	+	0.900871i
$863$	−14.4458			−0.491740			−0.245870	−	0.969303i	$-0.579074\pi$
$863$	−14.4458			−0.491740			−0.245870	+	0.969303i	$0.579074\pi$
$864$	14.1934	−	25.7400i	0.482870	−	0.875692i
$865$	11.5083			0.391295
$866$	−14.2126	+	29.8860i	−0.482965	+	1.01557i
$867$	0.927474	+	19.1995i	0.0314987	+	0.652049i
$868$	2.52444	−	2.05390i	0.0856850	−	0.0697139i
$869$	10.3781	−	10.3781i	0.352054	−	0.352054i
$870$	5.58408	+	2.33225i	0.189318	+	0.0790706i
$871$	−1.64834			−0.0558518
$872$	−13.6606	+	22.4660i	−0.462607	+	0.760796i
$873$	25.9071	−	2.50885i	0.876822	−	0.0849118i
$874$	2.84333	+	8.00000i	0.0961769	+	0.270604i
$875$	−12.8963	−	12.8963i	−0.435976	−	0.435976i
$876$	−31.1374	−	34.7061i	−1.05204	−	1.17261i
$877$	11.3672	−	11.3672i	0.383845	−	0.383845i	−0.488641	−	0.872485i	$-0.662507\pi$
$877$	11.3672	−	11.3672i	0.383845	−	0.383845i	0.872485	+	0.488641i	$0.162507\pi$
$878$	12.3049	−	25.8743i	0.415269	−	0.873217i
$879$	−6.75506	−	6.13249i	−0.227842	−	0.206844i
$880$	−2.09775	+	10.0978i	−0.0707152	+	0.340395i
$881$		−	10.2172i		−	0.344226i	−0.985077	−	0.172113i	$-0.944941\pi$
$881$		−	10.2172i		−	0.344226i	0.985077	−	0.172113i	$-0.0550594\pi$
$882$	−3.79447	+	10.4806i	−0.127766	+	0.352899i
$883$	0.230246	+	0.230246i	0.00774840	+	0.00774840i	0.710970	−	0.703222i	$-0.248256\pi$
$883$	0.230246	+	0.230246i	0.00774840	+	0.00774840i	−0.703222	+	0.710970i	$0.748256\pi$
$884$	−1.47725	+	14.3736i	−0.0496851	+	0.483436i
$885$	−0.00580708	−	0.120211i	−0.000195203	−	0.00404087i
$886$	−7.63726	+	2.71440i	−0.256579	+	0.0911921i
$887$			34.2664i			1.15055i	0.817959	+	0.575276i	$0.195105\pi$
$887$			34.2664i			1.15055i	−0.817959	+	0.575276i	$0.804895\pi$
$888$	5.04545	−	9.27853i	0.169314	−	0.311367i
$889$		−	48.9583i		−	1.64201i
$890$	−3.63135	−	10.2172i	−0.121723	−	0.342481i
$891$	31.5316	+	21.2182i	1.05635	+	0.710837i
$892$	−12.7058	+	10.3375i	−0.425422	+	0.346126i
$893$	5.35828	+	5.35828i	0.179308	+	0.179308i
$894$	18.5529	−	7.62108i	0.620502	−	0.254887i
$895$			7.93051i			0.265088i
$896$	1.20190	+	35.0833i	0.0401525	+	1.17205i
$897$	20.6761	−	22.7751i	0.690355	−	0.760438i
$898$	−6.87610	−	3.27001i	−0.229458	−	0.109122i
$899$	1.50052	−	1.50052i	0.0500450	−	0.0500450i
$900$	−19.7466	+	19.5159i	−0.658221	+	0.650530i
$901$	21.4600	+	21.4600i	0.714935	+	0.714935i
$902$	10.2172	−	3.63135i	0.340195	−	0.120911i
$903$	−4.00000	−	3.63135i	−0.133112	−	0.120844i
$904$	5.56777	+	22.8433i	0.185181	+	0.759758i
$905$	−14.2592			−0.473991
$906$	22.4809	+	9.38936i	0.746877	+	0.311941i
$907$	−26.5436	+	26.5436i	−0.881366	+	0.881366i	−0.993673	−	0.112308i	$-0.964176\pi$
$907$	−26.5436	+	26.5436i	−0.881366	+	0.881366i	0.112308	+	0.993673i	$0.464176\pi$
$908$	−27.8837	−	2.86575i	−0.925353	−	0.0951032i
$909$	−0.490953	+	0.596236i	−0.0162839	+	0.0197759i
$910$	7.19499	+	3.42166i	0.238512	+	0.113427i
$911$	24.1636			0.800576			0.400288	−	0.916389i	$-0.368910\pi$
$911$	24.1636			0.800576			0.400288	+	0.916389i	$0.368910\pi$
$912$	4.09667	+	5.63244i	0.135654	+	0.186509i
$913$	27.1849			0.899690
$914$	35.8580	+	17.0527i	1.18608	+	0.564054i
$915$	−8.55960	+	0.413491i	−0.282972	+	0.0136696i
$916$	2.06803	−	20.1219i	0.0683297	−	0.664847i
$917$	−0.249687	+	0.249687i	−0.00824540	+	0.00824540i
$918$	−5.26046	+	17.0602i	−0.173621	+	0.563069i
$919$	−25.8272			−0.851961			−0.425981	−	0.904732i	$-0.640071\pi$
$919$	−25.8272			−0.851961			−0.425981	+	0.904732i	$0.640071\pi$
$920$	8.81215	+	5.35828i	0.290528	+	0.176657i
$921$	22.1298	−	24.3764i	0.729201	−	0.803228i
$922$	42.9597	−	15.2686i	1.41480	−	0.502843i
$923$	10.5556	+	10.5556i	0.347443	+	0.347443i
$924$	−45.3224	−	2.45642i	−1.49100	−	0.0808103i
$925$	−7.05390	+	7.05390i	−0.231931	+	0.231931i
$926$	−0.945134	−	0.449470i	−0.0310590	−	0.0147705i
$927$	−18.9828	+	1.83830i	−0.623477	+	0.0603778i
$928$	3.11836	+	22.6761i	0.102365	+	0.744379i
$929$			29.6272i			0.972036i	0.873949	+	0.486018i	$0.161551\pi$
$929$			29.6272i			0.972036i	−0.873949	+	0.486018i	$0.838449\pi$
$930$	−0.298021	−	0.725507i	−0.00977248	−	0.0237903i
$931$	−1.86751	−	1.86751i	−0.0612050	−	0.0612050i
$932$	24.7939	+	30.4741i	0.812152	+	0.998212i
$933$	−23.9298	+	1.15598i	−0.783427	+	0.0378452i
$934$	−6.51890	−	18.3416i	−0.213305	−	0.600156i
$935$		−	6.26395i		−	0.204853i
$936$	10.9707	−	22.7236i	0.358588	−	0.742745i
$937$			33.4005i			1.09115i	0.838063	+	0.545574i	$0.183688\pi$
$937$			33.4005i			1.09115i	−0.838063	+	0.545574i	$0.816312\pi$
$938$	2.29178	−	0.814535i	0.0748293	−	0.0265955i
$939$	6.81730	−	0.329325i	0.222474	−	0.0107471i
$940$	9.15667	+	0.941078i	0.298658	+	0.0306946i
$941$	−15.6688	−	15.6688i	−0.510788	−	0.510788i	0.403980	−	0.914768i	$-0.367626\pi$
$941$	−15.6688	−	15.6688i	−0.510788	−	0.510788i	−0.914768	+	0.403980i	$0.867626\pi$
$942$	−29.3246	+	12.0458i	−0.955446	+	0.392474i
$943$		−	10.8433i		−	0.353107i
$944$	0.380633	−	0.249687i	0.0123885	−	0.00812663i
$945$	7.89220	+	5.88332i	0.256733	+	0.191384i
$946$	2.57834	−	5.42166i	0.0838290	−	0.176273i
$947$	−21.4040	+	21.4040i	−0.695536	+	0.695536i	−0.963444	−	0.267908i	$-0.913668\pi$
$947$	−21.4040	+	21.4040i	−0.695536	+	0.695536i	0.267908	+	0.963444i	$0.413668\pi$
$948$	−8.04014	−	8.96161i	−0.261132	−	0.291060i
$949$	−28.3033	−	28.3033i	−0.918764	−	0.918764i
$950$	−2.20304	−	6.19848i	−0.0714760	−	0.201105i
$951$	−14.6897	+	16.1810i	−0.476346	+	0.524704i
$952$	−5.04888	−	20.7144i	−0.163635	−	0.671358i
$953$	−30.7403			−0.995777			−0.497888	−	0.867241i	$-0.665891\pi$
$953$	−30.7403			−0.995777			−0.497888	+	0.867241i	$0.665891\pi$
$954$	−22.4801	−	47.9957i	−0.727820	−	1.55392i
$955$	−1.37227	+	1.37227i	−0.0444056	+	0.0444056i
$956$	−11.9185	−	14.6489i	−0.385471	−	0.473780i
$957$	−29.5614	+	1.42803i	−0.955585	+	0.0461616i
$958$	−17.1567	+	36.0766i	−0.554307	+	1.16558i
$959$	41.1441			1.32861
$960$	8.17808	+	2.16659i	0.263946	+	0.0699263i
$961$	30.7250			0.991128
$962$	3.89387	−	8.18793i	0.125543	−	0.263989i
$963$	−5.39249	−	4.44028i	−0.173770	−	0.143086i
$964$	−20.9739	−	25.7789i	−0.675522	−	0.830281i
$965$	−4.94765	+	4.94765i	−0.159271	+	0.159271i
$966$	−17.4927	+	41.8827i	−0.562819	+	1.34755i
$967$	−15.8172			−0.508646			−0.254323	−	0.967119i	$-0.581853\pi$
$967$	−15.8172			−0.508646			−0.254323	+	0.967119i	$0.581853\pi$
$968$	−4.57648	−	18.7763i	−0.147094	−	0.603493i
$969$	−3.13198	−	2.84333i	−0.100614	−	0.0913408i
$970$	2.50885	+	7.05892i	0.0805544	+	0.226648i
$971$	−13.8170	−	13.8170i	−0.443409	−	0.443409i	0.449747	−	0.893156i	$-0.351514\pi$
$971$	−13.8170	−	13.8170i	−0.443409	−	0.443409i	−0.893156	+	0.449747i	$0.851514\pi$
$972$	18.7800	−	24.8860i	0.602369	−	0.798218i
$973$	−26.0383	+	26.0383i	−0.834750	+	0.834750i
$974$	11.9708	−	25.1718i	0.383568	−	0.806557i
$975$	−16.0200	+	17.6464i	−0.513052	+	0.565136i
$976$	−17.7789	−	27.1028i	−0.569088	−	0.867539i
$977$		−	16.1005i		−	0.515101i	−0.966265	−	0.257550i	$-0.917085\pi$
$977$		−	16.1005i		−	0.515101i	0.966265	−	0.257550i	$-0.0829154\pi$
$978$	20.6654	+	50.3083i	0.660807	+	1.60868i
$979$	37.4983	+	37.4983i	1.19845	+	1.19845i
$980$	−3.19135	−	0.327991i	−0.101944	−	0.0104773i
$981$	−17.7273	+	21.5289i	−0.565990	+	0.687365i
$982$	55.4827	−	19.7194i	1.77052	−	0.629272i
$983$			37.0765i			1.18256i	0.806468	+	0.591278i	$0.201376\pi$
$983$			37.0765i			1.18256i	−0.806468	+	0.591278i	$0.798624\pi$
$984$	−2.52090	−	8.53026i	−0.0803633	−	0.271935i
$985$		−	12.7839i		−	0.407329i
$986$	−4.65576	−	13.0995i	−0.148270	−	0.417172i
$987$	1.95468	+	40.4635i	0.0622182	+	1.28797i
$988$	3.77332	+	4.63778i	0.120045	+	0.147547i
$989$	−4.24513	−	4.24513i	−0.134987	−	0.134987i
$990$	−3.72388	+	10.2856i	−0.118353	+	0.326898i
$991$		−	40.7089i		−	1.29316i	−0.762846	−	0.646580i	$-0.776199\pi$
$991$		−	40.7089i		−	1.29316i	0.762846	−	0.646580i	$-0.223801\pi$
$992$	1.79241	−	2.36398i	0.0569089	−	0.0750565i
$993$	17.1219	+	15.5439i	0.543348	+	0.493272i
$994$	−19.8922	−	9.45998i	−0.630942	−	0.300052i
$995$	−10.5580	+	10.5580i	−0.334712	+	0.334712i
$996$	1.20687	−	22.2676i	0.0382413	−	0.705575i
$997$	9.52444	+	9.52444i	0.301642	+	0.301642i	0.841656	−	0.540014i	$-0.181581\pi$
$997$	9.52444	+	9.52444i	0.301642	+	0.301642i	−0.540014	+	0.841656i	$0.681581\pi$
$998$	8.34887	−	2.96732i	0.264279	−	0.0939289i
$999$	6.69525	−	8.98136i	0.211828	−	0.284158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.2.k.a.11.5	yes	12
3.2	odd	2	inner	48.2.k.a.11.2	✓	12
4.3	odd	2		192.2.k.a.143.3		12
8.3	odd	2		384.2.k.a.287.4		12
8.5	even	2		384.2.k.b.287.3		12
12.11	even	2		192.2.k.a.143.1		12
16.3	odd	4	inner	48.2.k.a.35.2	yes	12
16.5	even	4		384.2.k.a.95.6		12
16.11	odd	4		384.2.k.b.95.1		12
16.13	even	4		192.2.k.a.47.1		12
24.5	odd	2		384.2.k.b.287.1		12
24.11	even	2		384.2.k.a.287.6		12
48.5	odd	4		384.2.k.a.95.4		12
48.11	even	4		384.2.k.b.95.3		12
48.29	odd	4		192.2.k.a.47.3		12
48.35	even	4	inner	48.2.k.a.35.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.2.k.a.11.2	✓	12	3.2	odd	2	inner
48.2.k.a.11.5	yes	12	1.1	even	1	trivial
48.2.k.a.35.2	yes	12	16.3	odd	4	inner
48.2.k.a.35.5	yes	12	48.35	even	4	inner
192.2.k.a.47.1		12	16.13	even	4
192.2.k.a.47.3		12	48.29	odd	4
192.2.k.a.143.1		12	12.11	even	2
192.2.k.a.143.3		12	4.3	odd	2
384.2.k.a.95.4		12	48.5	odd	4
384.2.k.a.95.6		12	16.5	even	4
384.2.k.a.287.4		12	8.3	odd	2
384.2.k.a.287.6		12	24.11	even	2
384.2.k.b.95.1		12	16.11	odd	4
384.2.k.b.95.3		12	48.11	even	4
384.2.k.b.287.1		12	24.5	odd	2
384.2.k.b.287.3		12	8.5	even	2

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.607364 - 1.27715i) q^{2} +(0.0835731 + 1.73003i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(0.431733 - 0.431733i) q^{5} +(2.26027 + 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 + 0.669785i) q^{8} +(-2.98603 + 0.289169i) q^{9} +O(q^{10})\)	\(q+(0.607364 - 1.27715i) q^{2} +(0.0835731 + 1.73003i) q^{3} +(-1.26222 - 1.55139i) q^{4} +(0.431733 - 0.431733i) q^{5} +(2.26027 + 0.944024i) q^{6} -3.10278 q^{7} +(-2.74798 + 0.669785i) q^{8} +(-2.98603 + 0.289169i) q^{9} +(-0.289169 - 0.813607i) q^{10} +(2.98603 + 2.98603i) q^{11} +(2.57846 - 2.31334i) q^{12} +(2.10278 - 2.10278i) q^{13} +(-1.88451 + 3.96271i) q^{14} +(0.782994 + 0.710831i) q^{15} +(-0.813607 + 3.91638i) q^{16} -2.42945i q^{17} +(-1.44430 + 3.98924i) q^{18} +(-0.710831 - 0.710831i) q^{19} +(-1.21473 - 0.124844i) q^{20} +(-0.259309 - 5.36790i) q^{21} +(5.62721 - 2.00000i) q^{22} -5.97206i q^{23} +(-1.38841 - 4.69812i) q^{24} +4.62721i q^{25} +(-1.40841 - 3.96271i) q^{26} +(-0.749823 - 5.14177i) q^{27} +(3.91638 + 4.81361i) q^{28} +(2.86119 + 2.86119i) q^{29} +(1.38340 - 0.568267i) q^{30} -0.524438i q^{31} +(4.50765 + 3.41776i) q^{32} +(-4.91638 + 5.41549i) q^{33} +(-3.10278 - 1.47556i) q^{34} +(-1.33957 + 1.33957i) q^{35} +(4.21764 + 4.26750i) q^{36} +(1.52444 + 1.52444i) q^{37} +(-1.33957 + 0.476105i) q^{38} +(3.81361 + 3.46214i) q^{39} +(-0.897225 + 1.47556i) q^{40} +1.81568 q^{41} +(-7.01311 - 2.92909i) q^{42} +(0.710831 - 0.710831i) q^{43} +(0.863466 - 8.40152i) q^{44} +(-1.16432 + 1.41401i) q^{45} +(-7.62721 - 3.62721i) q^{46} -7.53805 q^{47} +(-6.84347 - 1.08026i) q^{48} +2.62721 q^{49} +(5.90964 + 2.81040i) q^{50} +(4.20304 - 0.203037i) q^{51} +(-5.91638 - 0.608056i) q^{52} +(-8.83325 + 8.83325i) q^{53} +(-7.02222 - 2.16529i) q^{54} +2.57834 q^{55} +(8.52636 - 2.07819i) q^{56} +(1.17036 - 1.28917i) q^{57} +(5.39194 - 1.91638i) q^{58} +(-0.0804722 - 0.0804722i) q^{59} +(0.114465 - 2.11195i) q^{60} +(-5.72999 + 5.72999i) q^{61} +(-0.669785 - 0.318525i) q^{62} +(9.26498 - 0.897225i) q^{63} +(7.10278 - 3.68111i) q^{64} -1.81568i q^{65} +(3.93035 + 9.56812i) q^{66} +(-0.391944 - 0.391944i) q^{67} +(-3.76903 + 3.06650i) q^{68} +(10.3319 - 0.499104i) q^{69} +(0.897225 + 2.52444i) q^{70} +5.01985i q^{71} +(8.01187 - 2.79463i) q^{72} -13.4600i q^{73} +(2.87282 - 1.02105i) q^{74} +(-8.00523 + 0.386711i) q^{75} +(-0.205550 + 2.00000i) q^{76} +(-9.26498 - 9.26498i) q^{77} +(6.73791 - 2.76777i) q^{78} -3.47556i q^{79} +(1.33957 + 2.04209i) q^{80} +(8.83276 - 1.72693i) q^{81} +(1.10278 - 2.31889i) q^{82} +(4.55202 - 4.55202i) q^{83} +(-8.00040 + 7.17776i) q^{84} +(-1.04888 - 1.04888i) q^{85} +(-0.476105 - 1.33957i) q^{86} +(-4.71083 + 5.18907i) q^{87} +(-10.2056 - 6.20555i) q^{88} +12.5579 q^{89} +(1.09874 + 2.34584i) q^{90} +(-6.52444 + 6.52444i) q^{91} +(-9.26498 + 7.53805i) q^{92} +(0.907295 - 0.0438289i) q^{93} +(-4.57834 + 9.62721i) q^{94} -0.613779 q^{95} +(-5.53613 + 8.08401i) q^{96} -8.67609 q^{97} +(1.59567 - 3.35534i) q^{98} +(-9.77985 - 8.05292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7	\( 12 q - 2 q^{3} - 4 q^{4} - 8 q^{6} - 8 q^{7} - 8 q^{12} - 4 q^{13} + 16 q^{16} + 4 q^{18} - 12 q^{19} - 8 q^{21} + 16 q^{22} + 24 q^{24} + 10 q^{27} - 8 q^{28} + 28 q^{30} - 4 q^{33} - 8 q^{34} + 20 q^{36} - 4 q^{37} + 20 q^{39} - 40 q^{40} - 24 q^{42} + 12 q^{43} - 12 q^{45} - 40 q^{46} - 48 q^{48} - 20 q^{49} + 24 q^{51} - 16 q^{52} - 52 q^{54} + 24 q^{55} + 32 q^{58} - 16 q^{60} + 12 q^{61} + 56 q^{64} + 28 q^{66} + 28 q^{67} + 4 q^{69} + 40 q^{70} + 40 q^{72} - 34 q^{75} + 56 q^{76} + 60 q^{78} - 4 q^{81} - 16 q^{82} + 16 q^{84} + 32 q^{85} - 60 q^{87} - 64 q^{88} - 16 q^{90} - 56 q^{91} + 28 q^{93} - 48 q^{94} - 56 q^{96} - 8 q^{97} - 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^4 - 8 * q^6 - 8 * q^7 - 8 * q^12 - 4 * q^13 + 16 * q^16 + 4 * q^18 - 12 * q^19 - 8 * q^21 + 16 * q^22 + 24 * q^24 + 10 * q^27 - 8 * q^28 + 28 * q^30 - 4 * q^33 - 8 * q^34 + 20 * q^36 - 4 * q^37 + 20 * q^39 - 40 * q^40 - 24 * q^42 + 12 * q^43 - 12 * q^45 - 40 * q^46 - 48 * q^48 - 20 * q^49 + 24 * q^51 - 16 * q^52 - 52 * q^54 + 24 * q^55 + 32 * q^58 - 16 * q^60 + 12 * q^61 + 56 * q^64 + 28 * q^66 + 28 * q^67 + 4 * q^69 + 40 * q^70 + 40 * q^72 - 34 * q^75 + 56 * q^76 + 60 * q^78 - 4 * q^81 - 16 * q^82 + 16 * q^84 + 32 * q^85 - 60 * q^87 - 64 * q^88 - 16 * q^90 - 56 * q^91 + 28 * q^93 - 48 * q^94 - 56 * q^96 - 8 * q^97 - 52 * q^99

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