LMFDB - Embedded newform 435.2.q.c.41.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	435.41
Dual form			435.2.q.c.191.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48848 + 1.48848i) q^{2} +(-1.36422 + 1.06719i) q^{3} -2.43117i q^{4} -1.00000 q^{5} +(0.442117 - 3.61912i) q^{6} -1.31013 q^{7} +(0.641785 + 0.641785i) q^{8} +(0.722191 - 2.91178i) q^{9} +O(q^{10})$	\(q+(-1.48848 + 1.48848i) q^{2} +(-1.36422 + 1.06719i) q^{3} -2.43117i q^{4} -1.00000 q^{5} +(0.442117 - 3.61912i) q^{6} -1.31013 q^{7} +(0.641785 + 0.641785i) q^{8} +(0.722191 - 2.91178i) q^{9} +(1.48848 - 1.48848i) q^{10} +(1.11414 - 1.11414i) q^{11} +(2.59453 + 3.31665i) q^{12} +0.320703i q^{13} +(1.95011 - 1.95011i) q^{14} +(1.36422 - 1.06719i) q^{15} +2.95176 q^{16} +(0.771447 - 0.771447i) q^{17} +(3.25916 + 5.40910i) q^{18} +(-0.562790 - 0.562790i) q^{19} +2.43117i q^{20} +(1.78731 - 1.39817i) q^{21} +3.31677i q^{22} -1.90150i q^{23} +(-1.56045 - 0.190626i) q^{24} +1.00000 q^{25} +(-0.477361 - 0.477361i) q^{26} +(2.12220 + 4.74302i) q^{27} +3.18515i q^{28} +(0.168557 - 5.38253i) q^{29} +(-0.442117 + 3.61912i) q^{30} +(3.49362 + 3.49362i) q^{31} +(-5.67722 + 5.67722i) q^{32} +(-0.330928 + 2.70894i) q^{33} +2.29657i q^{34} +1.31013 q^{35} +(-7.07901 - 1.75577i) q^{36} +(0.254763 - 0.254763i) q^{37} +1.67541 q^{38} +(-0.342252 - 0.437509i) q^{39} +(-0.641785 - 0.641785i) q^{40} +(0.109398 + 0.109398i) q^{41} +(-0.579232 + 4.74153i) q^{42} +(3.91113 + 3.91113i) q^{43} +(-2.70867 - 2.70867i) q^{44} +(-0.722191 + 2.91178i) q^{45} +(2.83035 + 2.83035i) q^{46} +(5.63289 + 5.63289i) q^{47} +(-4.02685 + 3.15010i) q^{48} -5.28355 q^{49} +(-1.48848 + 1.48848i) q^{50} +(-0.229139 + 1.87571i) q^{51} +0.779682 q^{52} -6.38664i q^{53} +(-10.2188 - 3.90104i) q^{54} +(-1.11414 + 1.11414i) q^{55} +(-0.840823 - 0.840823i) q^{56} +(1.36838 + 0.167163i) q^{57} +(7.76091 + 8.26270i) q^{58} +1.03228i q^{59} +(-2.59453 - 3.31665i) q^{60} +(4.99878 + 4.99878i) q^{61} -10.4004 q^{62} +(-0.946166 + 3.81481i) q^{63} -10.9974i q^{64} -0.320703i q^{65} +(-3.53964 - 4.52480i) q^{66} -11.6027i q^{67} +(-1.87552 - 1.87552i) q^{68} +(2.02927 + 2.59406i) q^{69} +(-1.95011 + 1.95011i) q^{70} +10.0463 q^{71} +(2.33223 - 1.40524i) q^{72} +(9.52688 - 9.52688i) q^{73} +0.758422i q^{74} +(-1.36422 + 1.06719i) q^{75} +(-1.36824 + 1.36824i) q^{76} +(-1.45968 + 1.45968i) q^{77} +(1.16066 + 0.141788i) q^{78} +(-2.05510 - 2.05510i) q^{79} -2.95176 q^{80} +(-7.95688 - 4.20572i) q^{81} -0.325673 q^{82} -7.00231i q^{83} +(-3.39918 - 4.34525i) q^{84} +(-0.771447 + 0.771447i) q^{85} -11.6433 q^{86} +(5.51425 + 7.52283i) q^{87} +1.43008 q^{88} +(9.17721 - 9.17721i) q^{89} +(-3.25916 - 5.40910i) q^{90} -0.420163i q^{91} -4.62286 q^{92} +(-8.49443 - 1.03769i) q^{93} -16.7689 q^{94} +(0.562790 + 0.562790i) q^{95} +(1.68628 - 13.8037i) q^{96} +(12.7339 - 12.7339i) q^{97} +(7.86448 - 7.86448i) q^{98} +(-2.43951 - 4.04876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.48848	+	1.48848i	−1.05252	+	1.05252i	−0.0539746	+	0.998542i	$0.517189\pi$
$2$	−1.48848	+	1.48848i	−1.05252	+	1.05252i	−0.998542	+	0.0539746i	$0.982811\pi$
$3$	−1.36422	+	1.06719i	−0.787633	+	0.616145i
$3$	−1.36422	+	1.06719i	−0.787633	+	0.616145i
$4$		−	2.43117i		−	1.21558i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.442117	−	3.61912i	0.180493	−	1.47750i
$7$	−1.31013			−0.495183			−0.247592	−	0.968864i	$-0.579639\pi$
$7$	−1.31013			−0.495183			−0.247592	+	0.968864i	$0.579639\pi$
$8$	0.641785	+	0.641785i	0.226905	+	0.226905i
$9$	0.722191	−	2.91178i	0.240730	−	0.970592i
$10$	1.48848	−	1.48848i	0.470700	−	0.470700i
$11$	1.11414	−	1.11414i	0.335927	−	0.335927i	−0.518905	−	0.854832i	$-0.673660\pi$
$11$	1.11414	−	1.11414i	0.335927	−	0.335927i	0.854832	+	0.518905i	$0.173660\pi$
$12$	2.59453	+	3.31665i	0.748976	+	0.957433i
$13$			0.320703i			0.0889470i	0.999011	+	0.0444735i	$0.0141610\pi$
$13$			0.320703i			0.0889470i	−0.999011	+	0.0444735i	$0.985839\pi$
$14$	1.95011	−	1.95011i	0.521189	−	0.521189i
$15$	1.36422	−	1.06719i	0.352240	−	0.275548i
$16$	2.95176			0.737940
$17$	0.771447	−	0.771447i	0.187103	−	0.187103i	−0.607339	−	0.794443i	$-0.707763\pi$
$17$	0.771447	−	0.771447i	0.187103	−	0.187103i	0.794443	+	0.607339i	$0.207763\pi$
$18$	3.25916	+	5.40910i	0.768192	+	1.27494i
$19$	−0.562790	−	0.562790i	−0.129113	−	0.129113i	0.639597	−	0.768710i	$-0.279101\pi$
$19$	−0.562790	−	0.562790i	−0.129113	−	0.129113i	−0.768710	+	0.639597i	$0.779101\pi$
$20$			2.43117i			0.543625i
$21$	1.78731	−	1.39817i	0.390023	−	0.305105i
$22$			3.31677i			0.707137i
$23$		−	1.90150i		−	0.396490i	−0.980153	−	0.198245i	$-0.936476\pi$
$23$		−	1.90150i		−	0.396490i	0.980153	−	0.198245i	$-0.0635241\pi$
$24$	−1.56045	−	0.190626i	−0.318525	−	0.0389114i
$25$	1.00000			0.200000
$26$	−0.477361	−	0.477361i	−0.0936182	−	0.0936182i
$27$	2.12220	+	4.74302i	0.408419	+	0.912795i
$28$			3.18515i			0.601937i
$29$	0.168557	−	5.38253i	0.0313003	−	0.999510i
$29$	0.168557	−	5.38253i	0.0313003	−	0.999510i
$30$	−0.442117	+	3.61912i	−0.0807191	+	0.660758i
$31$	3.49362	+	3.49362i	0.627472	+	0.627472i	0.947431	−	0.319959i	$-0.103669\pi$
$31$	3.49362	+	3.49362i	0.627472	+	0.627472i	−0.319959	+	0.947431i	$0.603669\pi$
$32$	−5.67722	+	5.67722i	−1.00360	+	1.00360i
$33$	−0.330928	+	2.70894i	−0.0576072	+	0.471567i
$34$			2.29657i			0.393859i
$35$	1.31013			0.221453
$36$	−7.07901	−	1.75577i	−1.17984	−	0.292628i
$37$	0.254763	−	0.254763i	0.0418829	−	0.0418829i	−0.685855	−	0.727738i	$-0.740572\pi$
$37$	0.254763	−	0.254763i	0.0418829	−	0.0418829i	0.727738	+	0.685855i	$0.240572\pi$
$38$	1.67541			0.271787
$39$	−0.342252	−	0.437509i	−0.0548042	−	0.0700575i
$40$	−0.641785	−	0.641785i	−0.101475	−	0.101475i
$41$	0.109398	+	0.109398i	0.0170850	+	0.0170850i	0.715598	−	0.698513i	$-0.246154\pi$
$41$	0.109398	+	0.109398i	0.0170850	+	0.0170850i	−0.698513	+	0.715598i	$0.746154\pi$
$42$	−0.579232	+	4.74153i	−0.0893774	+	0.731633i
$43$	3.91113	+	3.91113i	0.596441	+	0.596441i	0.939364	−	0.342923i	$-0.111417\pi$
$43$	3.91113	+	3.91113i	0.596441	+	0.596441i	−0.342923	+	0.939364i	$0.611417\pi$
$44$	−2.70867	−	2.70867i	−0.408347	−	0.408347i
$45$	−0.722191	+	2.91178i	−0.107658	+	0.434062i
$46$	2.83035	+	2.83035i	0.417312	+	0.417312i
$47$	5.63289	+	5.63289i	0.821641	+	0.821641i	0.986343	−	0.164702i	$-0.0526663\pi$
$47$	5.63289	+	5.63289i	0.821641	+	0.821641i	−0.164702	+	0.986343i	$0.552666\pi$
$48$	−4.02685	+	3.15010i	−0.581226	+	0.454678i
$49$	−5.28355			−0.754793
$50$	−1.48848	+	1.48848i	−0.210503	+	0.210503i
$51$	−0.229139	+	1.87571i	−0.0320859	+	0.262652i
$52$	0.779682			0.108122
$53$		−	6.38664i		−	0.877273i	−0.898665	−	0.438636i	$-0.855462\pi$
$53$		−	6.38664i		−	0.877273i	0.898665	−	0.438636i	$-0.144538\pi$
$54$	−10.2188	−	3.90104i	−1.39060	−	0.530865i
$55$	−1.11414	+	1.11414i	−0.150231	+	0.150231i
$56$	−0.840823	−	0.840823i	−0.112360	−	0.112360i
$57$	1.36838	+	0.167163i	0.181246	+	0.0221412i
$58$	7.76091	+	8.26270i	1.01906	+	1.08495i
$59$			1.03228i			0.134392i	0.997740	+	0.0671959i	$0.0214053\pi$
$59$			1.03228i			0.134392i	−0.997740	+	0.0671959i	$0.978595\pi$
$60$	−2.59453	−	3.31665i	−0.334952	−	0.428177i
$61$	4.99878	+	4.99878i	0.640028	+	0.640028i	0.950562	−	0.310534i	$-0.100508\pi$
$61$	4.99878	+	4.99878i	0.640028	+	0.640028i	−0.310534	+	0.950562i	$0.600508\pi$
$62$	−10.4004			−1.32085
$63$	−0.946166	+	3.81481i	−0.119206	+	0.480621i
$64$		−	10.9974i		−	1.37467i
$65$		−	0.320703i		−	0.0397783i
$66$	−3.53964	−	4.52480i	−0.435699	−	0.556964i
$67$		−	11.6027i		−	1.41750i	−0.705461	−	0.708748i	$-0.749260\pi$
$67$		−	11.6027i		−	1.41750i	0.705461	−	0.708748i	$-0.250740\pi$
$68$	−1.87552	−	1.87552i	−0.227440	−	0.227440i
$69$	2.02927	+	2.59406i	0.244295	+	0.312288i
$70$	−1.95011	+	1.95011i	−0.233083	+	0.233083i
$71$	10.0463			1.19228			0.596141	−	0.802880i	$-0.296700\pi$
$71$	10.0463			1.19228			0.596141	+	0.802880i	$0.296700\pi$
$72$	2.33223	−	1.40524i	0.274855	−	0.165610i
$73$	9.52688	−	9.52688i	1.11504	−	1.11504i	0.122578	−	0.992459i	$-0.460884\pi$
$73$	9.52688	−	9.52688i	1.11504	−	1.11504i	0.992459	−	0.122578i	$-0.0391163\pi$
$74$			0.758422i			0.0881648i
$75$	−1.36422	+	1.06719i	−0.157527	+	0.123229i
$76$	−1.36824	+	1.36824i	−0.156948	+	0.156948i
$77$	−1.45968	+	1.45968i	−0.166345	+	0.166345i
$78$	1.16066	+	0.141788i	0.131419	+	0.0160543i
$79$	−2.05510	−	2.05510i	−0.231217	−	0.231217i	0.581983	−	0.813201i	$-0.302277\pi$
$79$	−2.05510	−	2.05510i	−0.231217	−	0.231217i	−0.813201	+	0.581983i	$0.802277\pi$
$80$	−2.95176			−0.330017
$81$	−7.95688	−	4.20572i	−0.884098	−	0.467302i
$82$	−0.325673			−0.0359646
$83$		−	7.00231i		−	0.768604i	−0.923208	−	0.384302i	$-0.874442\pi$
$83$		−	7.00231i		−	0.768604i	0.923208	−	0.384302i	$-0.125558\pi$
$84$	−3.39918	−	4.34525i	−0.370880	−	0.474105i
$85$	−0.771447	+	0.771447i	−0.0836752	+	0.0836752i
$86$	−11.6433			−1.25553
$87$	5.51425	+	7.52283i	0.591190	+	0.806532i
$88$	1.43008			0.152447
$89$	9.17721	−	9.17721i	0.972783	−	0.972783i	−0.0268565	−	0.999639i	$-0.508550\pi$
$89$	9.17721	−	9.17721i	0.972783	−	0.972783i	0.999639	+	0.0268565i	$0.00854971\pi$
$90$	−3.25916	−	5.40910i	−0.343546	−	0.570169i
$91$		−	0.420163i		−	0.0440451i
$92$	−4.62286			−0.481967
$93$	−8.49443	−	1.03769i	−0.880831	−	0.107604i
$94$	−16.7689			−1.72958
$95$	0.562790	+	0.562790i	0.0577410	+	0.0577410i
$96$	1.68628	−	13.8037i	0.172105	−	1.40883i
$97$	12.7339	−	12.7339i	1.29293	−	1.29293i	0.359960	−	0.932968i	$-0.382790\pi$
$97$	12.7339	−	12.7339i	1.29293	−	1.29293i	0.932968	−	0.359960i	$-0.117210\pi$
$98$	7.86448	−	7.86448i	0.794433	−	0.794433i
$99$	−2.43951	−	4.04876i	−0.245180	−	0.406916i
$100$		−	2.43117i		−	0.243117i
$101$	5.00642	−	5.00642i	0.498157	−	0.498157i	−0.412707	−	0.910864i	$-0.635417\pi$
$101$	5.00642	−	5.00642i	0.498157	−	0.498157i	0.910864	+	0.412707i	$0.135417\pi$
$102$	−2.45089	−	3.13303i	−0.242674	−	0.310216i
$103$	0.376151			0.0370632			0.0185316	−	0.999828i	$-0.494101\pi$
$103$	0.376151			0.0370632			0.0185316	+	0.999828i	$0.494101\pi$
$104$	−0.205822	+	0.205822i	−0.0201825	+	0.0201825i
$105$	−1.78731	+	1.39817i	−0.174423	+	0.136447i
$106$	9.50641	+	9.50641i	0.923344	+	0.923344i
$107$			4.71119i			0.455448i	0.973726	+	0.227724i	$0.0731284\pi$
$107$			4.71119i			0.455448i	−0.973726	+	0.227724i	$0.926872\pi$
$108$	11.5311	−	5.15943i	1.10958	−	0.496467i
$109$		−	14.6413i		−	1.40238i	−0.712975	−	0.701190i	$-0.752653\pi$
$109$		−	14.6413i		−	1.40238i	0.712975	−	0.701190i	$-0.247347\pi$
$110$		−	3.31677i		−	0.316241i
$111$	−0.0756711	+	0.619435i	−0.00718238	+	0.0587942i
$112$	−3.86720			−0.365416
$113$	−1.40534	−	1.40534i	−0.132203	−	0.132203i	0.637909	−	0.770112i	$-0.279800\pi$
$113$	−1.40534	−	1.40534i	−0.132203	−	0.132203i	−0.770112	+	0.637909i	$0.779800\pi$
$114$	−2.28562	+	1.78799i	−0.214068	+	0.167460i
$115$			1.90150i			0.177316i
$116$	−13.0858	−	0.409791i	−1.21499	−	0.0380481i
$117$	0.933815	+	0.231609i	0.0863312	+	0.0214122i
$118$	−1.53654	−	1.53654i	−0.141450	−	0.141450i
$119$	−1.01070	+	1.01070i	−0.0926505	+	0.0926505i
$120$	1.56045	+	0.190626i	0.142449	+	0.0174017i
$121$			8.51737i			0.774306i
$122$	−14.8812			−1.34728
$123$	−0.265991	−	0.0324938i	−0.0239836	−	0.00292987i
$124$	8.49357	−	8.49357i	0.762745	−	0.762745i
$125$	−1.00000			−0.0894427
$126$	−4.26993	−	7.08664i	−0.380396	−	0.631328i
$127$	−3.99666	−	3.99666i	−0.354647	−	0.354647i	0.507189	−	0.861835i	$-0.330685\pi$
$127$	−3.99666	−	3.99666i	−0.354647	−	0.354647i	−0.861835	+	0.507189i	$0.830685\pi$
$128$	5.01497	+	5.01497i	0.443265	+	0.443265i
$129$	−9.50957	−	1.16170i	−0.837271	−	0.102282i
$130$	0.477361	+	0.477361i	0.0418673	+	0.0418673i
$131$	11.7786	+	11.7786i	1.02910	+	1.02910i	0.999564	+	0.0295363i	$0.00940307\pi$
$131$	11.7786	+	11.7786i	1.02910	+	1.02910i	0.0295363	+	0.999564i	$0.490597\pi$
$132$	6.58590	+	0.804542i	0.573229	+	0.0700264i
$133$	0.737329	+	0.737329i	0.0639346	+	0.0639346i
$134$	17.2704	+	17.2704i	1.49194	+	1.49194i
$135$	−2.12220	−	4.74302i	−0.182650	−	0.408214i
$136$	0.990206			0.0849095
$137$	6.21543	−	6.21543i	0.531020	−	0.531020i	−0.389856	−	0.920876i	$-0.627475\pi$
$137$	6.21543	−	6.21543i	0.531020	−	0.531020i	0.920876	+	0.389856i	$0.127475\pi$
$138$	−6.88175	−	0.840685i	−0.585814	−	0.0715638i
$139$	−7.97233			−0.676204			−0.338102	−	0.941109i	$-0.609785\pi$
$139$	−7.97233			−0.676204			−0.338102	+	0.941109i	$0.609785\pi$
$140$		−	3.18515i		−	0.269194i
$141$	−13.6959	−	1.67311i	−1.15340	−	0.140901i
$142$	−14.9538	+	14.9538i	−1.25490	+	1.25490i
$143$	0.357309	+	0.357309i	0.0298797	+	0.0298797i
$144$	2.13173	−	8.59487i	0.177645	−	0.716239i
$145$	−0.168557	+	5.38253i	−0.0139979	+	0.446994i
$146$			28.3612i			2.34719i
$147$	7.20793	−	5.63858i	0.594500	−	0.465062i
$148$	−0.619372	−	0.619372i	−0.0509121	−	0.0509121i
$149$	−19.7304			−1.61638			−0.808190	−	0.588921i	$-0.799553\pi$
$149$	−19.7304			−1.61638			−0.808190	+	0.588921i	$0.799553\pi$
$150$	0.442117	−	3.61912i	0.0360987	−	0.295500i
$151$			4.29567i			0.349576i	0.984606	+	0.174788i	$0.0559241\pi$
$151$			4.29567i			0.349576i	−0.984606	+	0.174788i	$0.944076\pi$
$152$		−	0.722381i		−	0.0585928i
$153$	−1.68915	−	2.80341i	−0.136560	−	0.226642i
$154$		−	4.34540i		−	0.350163i
$155$	−3.49362	−	3.49362i	−0.280614	−	0.280614i
$156$	−1.06366	+	0.832073i	−0.0851608	+	0.0666191i
$157$	0.337898	−	0.337898i	0.0269672	−	0.0269672i	−0.693495	−	0.720462i	$-0.743930\pi$
$157$	0.337898	−	0.337898i	0.0269672	−	0.0269672i	0.720462	+	0.693495i	$0.243930\pi$
$158$	6.11797			0.486720
$159$	6.81579	+	8.71278i	0.540527	+	0.690969i
$160$	5.67722	−	5.67722i	0.448823	−	0.448823i
$161$			2.49121i			0.196335i
$162$	18.1038	−	5.58355i	1.42237	−	0.438685i
$163$	−13.5451	+	13.5451i	−1.06093	+	1.06093i	−0.0629129	+	0.998019i	$0.520039\pi$
$163$	−13.5451	+	13.5451i	−1.06093	+	1.06093i	−0.998019	+	0.0629129i	$0.979961\pi$
$164$	0.265964	−	0.265964i	0.0207683	−	0.0207683i
$165$	0.330928	−	2.70894i	0.0257627	−	0.210891i
$166$	10.4228	+	10.4228i	0.808968	+	0.808968i
$167$	17.3298			1.34102			0.670509	−	0.741901i	$-0.266076\pi$
$167$	17.3298			1.34102			0.670509	+	0.741901i	$0.266076\pi$
$168$	2.04439	+	0.249746i	0.157728	+	0.0192683i
$169$	12.8971			0.992088
$170$		−	2.29657i		−	0.176139i
$171$	−2.04516	+	1.23228i	−0.156397	+	0.0942346i
$172$	9.50860	−	9.50860i	0.725024	−	0.725024i
$173$	−17.4438			−1.32623			−0.663113	−	0.748519i	$-0.730765\pi$
$173$	−17.4438			−1.32623			−0.663113	+	0.748519i	$0.730765\pi$
$174$	−19.4055	−	2.98973i	−1.47113	−	0.226651i
$175$	−1.31013			−0.0990367
$176$	3.28868	−	3.28868i	0.247894	−	0.247894i
$177$	−1.10165	−	1.40826i	−0.0828049	−	0.105851i
$178$			27.3203i			2.04774i
$179$	16.2861			1.21728			0.608639	−	0.793447i	$-0.291716\pi$
$179$	16.2861			1.21728			0.608639	+	0.793447i	$0.291716\pi$
$180$	7.07901	+	1.75577i	0.527639	+	0.130867i
$181$	−13.8578			−1.03004			−0.515020	−	0.857178i	$-0.672215\pi$
$181$	−13.8578			−1.03004			−0.515020	+	0.857178i	$0.672215\pi$
$182$	0.625406	+	0.625406i	0.0463582	+	0.0463582i
$183$	−12.1541	−	1.48476i	−0.898458	−	0.109757i
$184$	1.22035	−	1.22035i	0.0899657	−	0.0899657i
$185$	−0.254763	+	0.254763i	−0.0187306	+	0.0187306i
$186$	14.1884	−	11.0992i	1.04034	−	0.813835i
$187$		−	1.71900i		−	0.125706i
$188$	13.6945	−	13.6945i	0.998774	−	0.998774i
$189$	−2.78037	−	6.21398i	−0.202242	−	0.452001i
$190$	−1.67541			−0.121547
$191$	−1.13648	+	1.13648i	−0.0822327	+	0.0822327i	−0.747027	−	0.664794i	$-0.768519\pi$
$191$	−1.13648	+	1.13648i	−0.0822327	+	0.0822327i	0.664794	+	0.747027i	$0.268519\pi$
$192$	11.7363	+	15.0028i	0.846997	+	1.08274i
$193$	−9.68489	−	9.68489i	−0.697134	−	0.697134i	0.266658	−	0.963791i	$-0.414081\pi$
$193$	−9.68489	−	9.68489i	−0.697134	−	0.697134i	−0.963791	+	0.266658i	$0.914081\pi$
$194$			37.9083i			2.72166i
$195$	0.342252	+	0.437509i	0.0245092	+	0.0313307i
$196$			12.8452i			0.917514i
$197$		−	12.8295i		−	0.914061i	−0.889451	−	0.457031i	$-0.848913\pi$
$197$		−	12.8295i		−	0.914061i	0.889451	−	0.457031i	$-0.151087\pi$
$198$	9.65769	+	2.39534i	0.686342	+	0.170229i
$199$	−2.61214			−0.185170			−0.0925850	−	0.995705i	$-0.529513\pi$
$199$	−2.61214			−0.185170			−0.0925850	+	0.995705i	$0.529513\pi$
$200$	0.641785	+	0.641785i	0.0453811	+	0.0453811i
$201$	12.3824	+	15.8286i	0.873384	+	1.11647i
$202$			14.9039i			1.04864i
$203$	−0.220832	+	7.05182i	−0.0154994	+	0.494941i
$204$	4.56016	+	0.557075i	0.319275	+	0.0390031i
$205$	−0.109398	−	0.109398i	−0.00764066	−	0.00764066i
$206$	−0.559894	+	0.559894i	−0.0390097	+	0.0390097i
$207$	−5.53674	−	1.37324i	−0.384830	−	0.0954471i
$208$			0.946638i			0.0656375i
$209$	−1.25406			−0.0867450
$210$	0.579232	−	4.74153i	0.0399708	−	0.327196i
$211$	−8.86770	+	8.86770i	−0.610478	+	0.610478i	−0.943070	−	0.332593i	$-0.892076\pi$
$211$	−8.86770	+	8.86770i	−0.610478	+	0.610478i	0.332593	+	0.943070i	$0.392076\pi$
$212$	−15.5270			−1.06640
$213$	−13.7054	+	10.7214i	−0.939080	+	0.734618i
$214$	−7.01253	−	7.01253i	−0.479367	−	0.479367i
$215$	−3.91113	−	3.91113i	−0.266737	−	0.266737i
$216$	−1.68200	+	4.40600i	−0.114446	+	0.299790i
$217$	−4.57710	−	4.57710i	−0.310714	−	0.310714i
$218$	21.7933	+	21.7933i	1.47603	+	1.47603i
$219$	−2.82972	+	23.1638i	−0.191215	+	1.56526i
$220$	2.70867	+	2.70867i	0.182618	+	0.182618i
$221$	0.247405	+	0.247405i	0.0166423	+	0.0166423i
$222$	−0.809384	−	1.03465i	−0.0543223	−	0.0694415i
$223$	4.88866			0.327369			0.163684	−	0.986513i	$-0.447662\pi$
$223$	4.88866			0.327369			0.163684	+	0.986513i	$0.447662\pi$
$224$	7.43791	−	7.43791i	0.496966	−	0.496966i
$225$	0.722191	−	2.91178i	0.0481461	−	0.194118i
$226$	4.18365			0.278292
$227$		−	6.23494i		−	0.413828i	−0.978359	−	0.206914i	$-0.933658\pi$
$227$		−	6.23494i		−	0.413828i	0.978359	−	0.206914i	$-0.0663420\pi$
$228$	0.406401	−	3.32675i	0.0269145	−	0.220319i
$229$	−6.56453	+	6.56453i	−0.433796	+	0.433796i	−0.889918	−	0.456121i	$-0.849238\pi$
$229$	−6.56453	+	6.56453i	−0.433796	+	0.433796i	0.456121	+	0.889918i	$0.349238\pi$
$230$	−2.83035	−	2.83035i	−0.186628	−	0.186628i
$231$	0.433560	−	3.54907i	0.0285262	−	0.233512i
$232$	3.56260	−	3.34625i	0.233896	−	0.219692i
$233$			24.7489i			1.62135i	0.585494	+	0.810677i	$0.300901\pi$
$233$			24.7489i			1.62135i	−0.585494	+	0.810677i	$0.699099\pi$
$234$	−1.73471	+	1.04522i	−0.113402	+	0.0683283i
$235$	−5.63289	−	5.63289i	−0.367449	−	0.367449i
$236$	2.50965			0.163364
$237$	4.99681	+	0.610417i	0.324577	+	0.0396508i
$238$		−	3.00881i		−	0.195032i
$239$			14.2271i			0.920275i	0.887848	+	0.460137i	$0.152200\pi$
$239$			14.2271i			0.920275i	−0.887848	+	0.460137i	$0.847800\pi$
$240$	4.02685	−	3.15010i	0.259932	−	0.203338i
$241$		−	12.6599i		−	0.815494i	−0.913095	−	0.407747i	$-0.866315\pi$
$241$		−	12.6599i		−	0.815494i	0.913095	−	0.407747i	$-0.133685\pi$
$242$	−12.6780	−	12.6780i	−0.814970	−	0.814970i
$243$	15.3433	−	2.75402i	0.984270	−	0.176670i
$244$	12.1529	−	12.1529i	0.778008	−	0.778008i
$245$	5.28355			0.337554
$246$	0.444290	−	0.347557i	0.0283269	−	0.0221594i
$247$	0.180488	−	0.180488i	0.0114842	−	0.0114842i
$248$			4.48430i			0.284753i
$249$	7.47283	+	9.55269i	0.473571	+	0.605377i
$250$	1.48848	−	1.48848i	0.0941400	−	0.0941400i
$251$	9.74488	−	9.74488i	0.615092	−	0.615092i	−0.329177	−	0.944268i	$-0.606771\pi$
$251$	9.74488	−	9.74488i	0.615092	−	0.615092i	0.944268	+	0.329177i	$0.106771\pi$
$252$	9.27445	+	2.30029i	0.584235	+	0.144904i
$253$	−2.11854	−	2.11854i	−0.133192	−	0.133192i
$254$	11.8979			0.746543
$255$	0.229139	−	1.87571i	0.0143492	−	0.117461i
$256$	7.06534			0.441584
$257$		−	12.2887i		−	0.766546i	−0.923635	−	0.383273i	$-0.874797\pi$
$257$		−	12.2887i		−	0.766546i	0.923635	−	0.383273i	$-0.125203\pi$
$258$	15.8840	−	12.4257i	0.988895	−	0.773588i
$259$	−0.333774	+	0.333774i	−0.0207397	+	0.0207397i
$260$	−0.779682			−0.0483538
$261$	−15.5510	−	4.37801i	−0.962582	−	0.270992i
$262$	−35.0645			−2.16629
$263$	4.82134	−	4.82134i	0.297296	−	0.297296i	−0.542658	−	0.839954i	$-0.682582\pi$
$263$	4.82134	−	4.82134i	0.297296	−	0.297296i	0.839954	+	0.542658i	$0.182582\pi$
$264$	−1.95094	+	1.52618i	−0.120072	+	0.0939296i
$265$			6.38664i			0.392328i
$266$	−2.19501			−0.134584
$267$	−2.72586	+	22.3136i	−0.166820	+	1.36557i
$268$	−28.2081			−1.72309
$269$	17.9121	+	17.9121i	1.09212	+	1.09212i	0.995302	+	0.0968192i	$0.0308669\pi$
$269$	17.9121	+	17.9121i	1.09212	+	1.09212i	0.0968192	+	0.995302i	$0.469133\pi$
$270$	10.2188	+	3.90104i	0.621895	+	0.237410i
$271$	15.7605	−	15.7605i	0.957383	−	0.957383i	−0.0417454	−	0.999128i	$-0.513292\pi$
$271$	15.7605	−	15.7605i	0.957383	−	0.957383i	0.999128	+	0.0417454i	$0.0132918\pi$
$272$	2.27713	−	2.27713i	0.138071	−	0.138071i
$273$	0.448396	+	0.573195i	0.0271382	+	0.0346913i
$274$			18.5031i			1.11781i
$275$	1.11414	−	1.11414i	0.0671854	−	0.0671854i
$276$	6.30660	−	4.93349i	0.379613	−	0.296961i
$277$	1.75738			0.105591			0.0527955	−	0.998605i	$-0.483187\pi$
$277$	1.75738			0.105591			0.0527955	+	0.998605i	$0.483187\pi$
$278$	11.8667	−	11.8667i	0.711716	−	0.711716i
$279$	12.6957	−	7.64957i	0.760071	−	0.457968i
$280$	0.840823	+	0.840823i	0.0502488	+	0.0502488i
$281$		−	21.6158i		−	1.28949i	−0.764398	−	0.644744i	$-0.776964\pi$
$281$		−	21.6158i		−	1.28949i	0.764398	−	0.644744i	$-0.223036\pi$
$282$	22.8765	−	17.8957i	1.36228	−	1.06567i
$283$		−	30.5753i		−	1.81751i	−0.417327	−	0.908757i	$-0.637033\pi$
$283$		−	30.5753i		−	1.81751i	0.417327	−	0.908757i	$-0.362967\pi$
$284$		−	24.4243i		−	1.44932i
$285$	−1.36838	−	0.167163i	−0.0810556	−	0.00990187i
$286$	−1.06370			−0.0628977
$287$	−0.143325	−	0.143325i	−0.00846023	−	0.00846023i
$288$	12.4308	+	20.6308i	0.732489	+	1.21568i
$289$			15.8097i			0.929985i
$290$	−7.76091	−	8.26270i	−0.455736	−	0.485202i
$291$	−3.78228	+	30.9613i	−0.221721	+	1.81498i
$292$	−23.1614	−	23.1614i	−1.35542	−	1.35542i
$293$	−19.9204	+	19.9204i	−1.16376	+	1.16376i	−0.180118	+	0.983645i	$0.557648\pi$
$293$	−19.9204	+	19.9204i	−1.16376	+	1.16376i	−0.983645	+	0.180118i	$0.942352\pi$
$294$	−2.33595	+	19.1218i	−0.136235	+	1.11521i
$295$		−	1.03228i		−	0.0601019i
$296$	0.327007			0.0190069
$297$	7.64885	+	2.91996i	0.443831	+	0.169434i
$298$	29.3684	−	29.3684i	1.70127	−	1.70127i
$299$	0.609816			0.0352666
$300$	2.59453	+	3.31665i	0.149795	+	0.191487i
$301$	−5.12409	−	5.12409i	−0.295348	−	0.295348i
$302$	−6.39403	−	6.39403i	−0.367935	−	0.367935i
$303$	−1.48703	+	12.1727i	−0.0854277	+	0.699302i
$304$	−1.66122	−	1.66122i	−0.0952776	−	0.0952776i
$305$	−4.99878	−	4.99878i	−0.286229	−	0.286229i
$306$	6.68710	+	1.65856i	0.382276	+	0.0948138i
$307$	−9.77936	−	9.77936i	−0.558138	−	0.558138i	0.370639	−	0.928777i	$-0.379139\pi$
$307$	−9.77936	−	9.77936i	−0.558138	−	0.558138i	−0.928777	+	0.370639i	$0.879139\pi$
$308$	3.54871	+	3.54871i	0.202207	+	0.202207i
$309$	−0.513152	+	0.401426i	−0.0291922	+	0.0228363i
$310$	10.4004			0.590702
$311$	−20.0155	+	20.0155i	−1.13497	+	1.13497i	−0.145634	+	0.989339i	$0.546522\pi$
$311$	−20.0155	+	20.0155i	−1.13497	+	1.13497i	−0.989339	+	0.145634i	$0.953478\pi$
$312$	0.0611344	−	0.500439i	0.00346105	−	0.0283318i
$313$	−10.2828			−0.581219			−0.290610	−	0.956842i	$-0.593858\pi$
$313$	−10.2828			−0.581219			−0.290610	+	0.956842i	$0.593858\pi$
$314$			1.00591i			0.0567668i
$315$	0.946166	−	3.81481i	0.0533104	−	0.214940i
$316$	−4.99630	+	4.99630i	−0.281064	+	0.281064i
$317$	−8.49331	−	8.49331i	−0.477032	−	0.477032i	0.427149	−	0.904181i	$-0.359518\pi$
$317$	−8.49331	−	8.49331i	−0.477032	−	0.477032i	−0.904181	+	0.427149i	$0.859518\pi$
$318$	−23.1140	−	2.82364i	−1.29617	−	0.158342i
$319$	−5.80911	−	6.18470i	−0.325248	−	0.346277i
$320$			10.9974i			0.614772i
$321$	−5.02776	−	6.42710i	−0.280622	−	0.358726i
$322$	−3.70813	−	3.70813i	−0.206646	−	0.206646i
$323$	−0.868325			−0.0483149
$324$	−10.2248	+	19.3445i	−0.568044	+	1.07469i
$325$			0.320703i			0.0177894i
$326$		−	40.3232i		−	2.23330i
$327$	15.6251	+	19.9739i	0.864070	+	1.10456i
$328$			0.140420i			0.00775337i
$329$	−7.37983	−	7.37983i	−0.406863	−	0.406863i
$330$	3.53964	+	4.52480i	0.194851	+	0.249082i
$331$	3.37379	−	3.37379i	0.185440	−	0.185440i	−0.608281	−	0.793722i	$-0.708141\pi$
$331$	3.37379	−	3.37379i	0.185440	−	0.185440i	0.793722	+	0.608281i	$0.208141\pi$
$332$	−17.0238			−0.934302
$333$	−0.557826	−	0.925802i	−0.0305687	−	0.0507336i
$334$	−25.7951	+	25.7951i	−1.41144	+	1.41144i
$335$			11.6027i			0.633924i
$336$	5.27571	−	4.12705i	0.287813	−	0.225149i
$337$	−2.24484	+	2.24484i	−0.122284	+	0.122284i	−0.765601	−	0.643316i	$-0.777558\pi$
$337$	−2.24484	+	2.24484i	−0.122284	+	0.122284i	0.643316	+	0.765601i	$0.277558\pi$
$338$	−19.1972	+	19.1972i	−1.04419	+	1.04419i
$339$	3.41696	+	0.417421i	0.185584	+	0.0226712i
$340$	1.87552	+	1.87552i	0.101714	+	0.101714i
$341$	7.78478			0.421569
$342$	1.20996	−	4.87841i	0.0654274	−	0.263794i
$343$	16.0931			0.868945
$344$			5.02020i			0.270671i
$345$	−2.02927	−	2.59406i	−0.109252	−	0.139660i
$346$	25.9648	−	25.9648i	1.39588	−	1.39588i
$347$	−17.0200			−0.913684			−0.456842	−	0.889548i	$-0.651020\pi$
$347$	−17.0200			−0.913684			−0.456842	+	0.889548i	$0.651020\pi$
$348$	18.2893	−	13.4061i	0.980407	−	0.718641i
$349$	−0.147528			−0.00789698			−0.00394849	−	0.999992i	$-0.501257\pi$
$349$	−0.147528			−0.00789698			−0.00394849	+	0.999992i	$0.501257\pi$
$350$	1.95011	−	1.95011i	0.104238	−	0.104238i
$351$	−1.52110	+	0.680597i	−0.0811903	+	0.0363276i
$352$			12.6505i			0.674272i
$353$	−17.4259			−0.927485			−0.463743	−	0.885970i	$-0.653494\pi$
$353$	−17.4259			−0.927485			−0.463743	+	0.885970i	$0.653494\pi$
$354$	3.73596	+	0.456390i	0.198564	+	0.0242568i
$355$	−10.0463			−0.533204
$356$	−22.3113	−	22.3113i	−1.18250	−	1.18250i
$357$	0.300202	−	2.45742i	0.0158884	−	0.130061i
$358$	−24.2415	+	24.2415i	−1.28121	+	1.28121i
$359$	−5.45728	+	5.45728i	−0.288024	+	0.288024i	−0.836299	−	0.548274i	$-0.815285\pi$
$359$	−5.45728	+	5.45728i	−0.288024	+	0.288024i	0.548274	+	0.836299i	$0.315285\pi$
$360$	−2.33223	+	1.40524i	−0.122919	+	0.0740628i
$361$		−	18.3665i		−	0.966660i
$362$	20.6271	−	20.6271i	1.08413	−	1.08413i
$363$	−9.08969	−	11.6196i	−0.477085	−	0.609869i
$364$	−1.02149			−0.0535405
$365$	−9.52688	+	9.52688i	−0.498660	+	0.498660i
$366$	20.3012	−	15.8811i	1.06116	−	0.830121i
$367$	6.93520	+	6.93520i	0.362015	+	0.362015i	0.864554	−	0.502540i	$-0.167601\pi$
$367$	6.93520	+	6.93520i	0.362015	+	0.362015i	−0.502540	+	0.864554i	$0.667601\pi$
$368$		−	5.61277i		−	0.292586i
$369$	0.397547	−	0.239535i	0.0206955	−	0.0124697i
$370$		−	0.758422i		−	0.0394285i
$371$			8.36735i			0.434411i
$372$	−2.52280	+	20.6514i	−0.130801	+	1.07072i
$373$	30.2323			1.56537			0.782684	−	0.622419i	$-0.213850\pi$
$373$	30.2323			1.56537			0.782684	+	0.622419i	$0.213850\pi$
$374$	2.55871	+	2.55871i	0.132308	+	0.132308i
$375$	1.36422	−	1.06719i	0.0704480	−	0.0551097i
$376$			7.23021i			0.372870i
$377$	1.72619	+	0.0540568i	0.0889034	+	0.00278406i
$378$	13.3879	+	5.11088i	0.688602	+	0.262875i
$379$	−7.43882	−	7.43882i	−0.382107	−	0.382107i	0.489754	−	0.871861i	$-0.337087\pi$
$379$	−7.43882	−	7.43882i	−0.382107	−	0.382107i	−0.871861	+	0.489754i	$0.837087\pi$
$380$	1.36824	−	1.36824i	0.0701891	−	0.0701891i
$381$	9.71754	+	1.18711i	0.497845	+	0.0608174i
$382$		−	3.38326i		−	0.173103i
$383$	−25.1306			−1.28411			−0.642056	−	0.766658i	$-0.721918\pi$
$383$	−25.1306			−1.28411			−0.642056	+	0.766658i	$0.721918\pi$
$384$	−12.1935	−	1.48957i	−0.622245	−	0.0760144i
$385$	1.45968	−	1.45968i	0.0743919	−	0.0743919i
$386$	28.8316			1.46749
$387$	14.2129	−	8.56374i	0.722482	−	0.435319i
$388$	−30.9582	−	30.9582i	−1.57166	−	1.57166i
$389$	−16.0651	−	16.0651i	−0.814532	−	0.814532i	0.170778	−	0.985310i	$-0.445372\pi$
$389$	−16.0651	−	16.0651i	−0.814532	−	0.814532i	−0.985310	+	0.170778i	$0.945372\pi$
$390$	−1.16066	−	0.141788i	−0.0587724	−	0.00717972i
$391$	−1.46690	−	1.46690i	−0.0741846	−	0.0741846i
$392$	−3.39091	−	3.39091i	−0.171267	−	0.171267i
$393$	−28.6386	−	3.49854i	−1.44463	−	0.176478i
$394$	19.0964	+	19.0964i	0.962065	+	0.962065i
$395$	2.05510	+	2.05510i	0.103403	+	0.103403i
$396$	−9.84321	+	5.93086i	−0.494640	+	0.298037i
$397$	34.1752			1.71521			0.857603	−	0.514313i	$-0.171953\pi$
$397$	34.1752			1.71521			0.857603	+	0.514313i	$0.171953\pi$
$398$	3.88813	−	3.88813i	0.194894	−	0.194894i
$399$	−1.79275	−	0.219005i	−0.0897499	−	0.0109640i
$400$	2.95176			0.147588
$401$		−	34.8871i		−	1.74218i	−0.491126	−	0.871089i	$-0.663415\pi$
$401$		−	34.8871i		−	1.74218i	0.491126	−	0.871089i	$-0.336585\pi$
$402$	−41.9916	−	5.12975i	−2.09435	−	0.255849i
$403$	−1.12041	+	1.12041i	−0.0558117	+	0.0558117i
$404$	−12.1714	−	12.1714i	−0.605551	−	0.605551i
$405$	7.95688	+	4.20572i	0.395381	+	0.208984i
$406$	−10.1678	−	10.8252i	−0.504620	−	0.537247i
$407$		−	0.567686i		−	0.0281391i
$408$	−1.35086	+	1.05674i	−0.0668775	+	0.0523166i
$409$	13.9706	+	13.9706i	0.690800	+	0.690800i	0.962408	−	0.271608i	$-0.0875554\pi$
$409$	13.9706	+	13.9706i	0.690800	+	0.690800i	−0.271608	+	0.962408i	$0.587555\pi$
$410$	0.325673			0.0160838
$411$	−1.84614	+	15.1123i	−0.0910633	+	0.745434i
$412$		−	0.914485i		−	0.0450535i
$413$		−	1.35243i		−	0.0665486i
$414$	10.2854	−	6.19729i	0.505500	−	0.304580i
$415$			7.00231i			0.343730i
$416$	−1.82070	−	1.82070i	−0.0892672	−	0.0892672i
$417$	10.8760	−	8.50803i	0.532601	−	0.416640i
$418$	1.86664	−	1.86664i	0.0913006	−	0.0913006i
$419$	5.01829			0.245160			0.122580	−	0.992459i	$-0.460883\pi$
$419$	5.01829			0.245160			0.122580	+	0.992459i	$0.460883\pi$
$420$	3.39918	+	4.34525i	0.165863	+	0.212026i
$421$	−27.9727	+	27.9727i	−1.36330	+	1.36330i	−0.493634	+	0.869670i	$0.664332\pi$
$421$	−27.9727	+	27.9727i	−1.36330	+	1.36330i	−0.869670	+	0.493634i	$0.835668\pi$
$422$		−	26.3988i		−	1.28508i
$423$	20.4697	−	12.3337i	0.995272	−	0.599685i
$424$	4.09885	−	4.09885i	0.199058	−	0.199058i
$425$	0.771447	−	0.771447i	0.0374207	−	0.0374207i
$426$	4.44166	−	36.3589i	0.215199	−	1.76160i
$427$	−6.54906	−	6.54906i	−0.316931	−	0.316931i
$428$	11.4537			0.553635
$429$	−0.868766	−	0.106130i	−0.0419444	−	0.00512399i
$430$	11.6433			0.561489
$431$		−	5.66882i		−	0.273058i	−0.990636	−	0.136529i	$-0.956405\pi$
$431$		−	5.66882i		−	0.273058i	0.990636	−	0.136529i	$-0.0435946\pi$
$432$	6.26424	+	14.0003i	0.301388	+	0.673588i
$433$	17.4659	−	17.4659i	0.839355	−	0.839355i	−0.149419	−	0.988774i	$-0.547740\pi$
$433$	17.4659	−	17.4659i	0.839355	−	0.839355i	0.988774	+	0.149419i	$0.0477402\pi$
$434$	13.6259			0.654063
$435$	−5.51425	−	7.52283i	−0.264388	−	0.360692i
$436$	−35.5954			−1.70471
$437$	−1.07014	+	1.07014i	−0.0511920	+	0.0511920i
$438$	−30.2669	−	38.6909i	−1.44621	−	1.84872i
$439$		−	0.172919i		−	0.00825298i	−0.999991	−	0.00412649i	$-0.998686\pi$
$439$		−	0.172919i		−	0.00825298i	0.999991	−	0.00412649i	$-0.00131351\pi$
$440$	−1.43008			−0.0681764
$441$	−3.81573	+	15.3845i	−0.181702	+	0.732596i
$442$	−0.736517			−0.0350326
$443$	5.27876	+	5.27876i	0.250802	+	0.250802i	0.821299	−	0.570498i	$-0.193250\pi$
$443$	5.27876	+	5.27876i	0.250802	+	0.250802i	−0.570498	+	0.821299i	$0.693250\pi$
$444$	1.50595	+	0.183969i	0.0714693	+	0.00873079i
$445$	−9.17721	+	9.17721i	−0.435042	+	0.435042i
$446$	−7.27669	+	7.27669i	−0.344561	+	0.344561i
$447$	26.9167	−	21.0562i	1.27311	−	0.995925i
$448$			14.4080i			0.680714i
$449$	25.0789	−	25.0789i	1.18355	−	1.18355i	0.204728	−	0.978819i	$-0.434369\pi$
$449$	25.0789	−	25.0789i	1.18355	−	1.18355i	0.978819	−	0.204728i	$-0.0656311\pi$
$450$	3.25916	+	5.40910i	0.153638	+	0.254987i
$451$	0.243769			0.0114786
$452$	−3.41662	+	3.41662i	−0.160704	+	0.160704i
$453$	−4.58431	−	5.86023i	−0.215390	−	0.275338i
$454$	9.28061	+	9.28061i	0.435560	+	0.435560i
$455$			0.420163i			0.0196976i
$456$	0.770921	+	0.985486i	0.0361017	+	0.0461496i
$457$			19.0649i			0.891820i	0.895078	+	0.445910i	$0.147120\pi$
$457$			19.0649i			0.891820i	−0.895078	+	0.445910i	$0.852880\pi$
$458$		−	19.5424i		−	0.913156i
$459$	5.29616	+	2.02182i	0.247203	+	0.0943705i
$460$	4.62286			0.215542
$461$	−4.22235	−	4.22235i	−0.196654	−	0.196654i	0.601910	−	0.798564i	$-0.294407\pi$
$461$	−4.22235	−	4.22235i	−0.196654	−	0.196654i	−0.798564	+	0.601910i	$0.794407\pi$
$462$	4.63739	+	5.92809i	0.215751	+	0.275800i
$463$			36.6998i			1.70558i	0.522251	+	0.852792i	$0.325092\pi$
$463$			36.6998i			1.70558i	−0.522251	+	0.852792i	$0.674908\pi$
$464$	0.497540	−	15.8879i	0.0230977	−	0.737579i
$465$	8.49443	+	1.03769i	0.393920	+	0.0481218i
$466$	−36.8383	−	36.8383i	−1.70650	−	1.70650i
$467$	−23.5624	+	23.5624i	−1.09034	+	1.09034i	−0.0948462	+	0.995492i	$0.530236\pi$
$467$	−23.5624	+	23.5624i	−1.09034	+	1.09034i	−0.995492	+	0.0948462i	$0.969764\pi$
$468$	0.563079	−	2.27026i	0.0260284	−	0.104943i
$469$			15.2011i			0.701921i
$470$	16.7689			0.773493
$471$	−0.100364	+	0.821570i	−0.00462453	+	0.0378559i
$472$	−0.662504	+	0.662504i	−0.0304942	+	0.0304942i
$473$	8.71511			0.400721
$474$	−8.34626	+	6.52907i	−0.383356	+	0.299890i
$475$	−0.562790	−	0.562790i	−0.0258226	−	0.0258226i
$476$	2.45717	+	2.45717i	0.112624	+	0.112624i
$477$	−18.5965	−	4.61237i	−0.851474	−	0.211186i
$478$	−21.1768	−	21.1768i	−0.968605	−	0.968605i
$479$	−23.8415	−	23.8415i	−1.08935	−	1.08935i	−0.995596	−	0.0937499i	$-0.970115\pi$
$479$	−23.8415	−	23.8415i	−1.08935	−	1.08935i	−0.0937499	−	0.995596i	$-0.529885\pi$
$480$	−1.68628	+	13.8037i	−0.0769676	+	0.630048i
$481$	0.0817034	+	0.0817034i	0.00372535	+	0.00372535i
$482$	18.8440	+	18.8440i	0.858321	+	0.858321i
$483$	−2.65861	−	3.39856i	−0.120971	−	0.154640i
$484$	20.7071			0.941234
$485$	−12.7339	+	12.7339i	−0.578215	+	0.578215i
$486$	−18.7389	+	26.9375i	−0.850012	+	1.22191i
$487$	25.3173			1.14724			0.573619	−	0.819123i	$-0.305539\pi$
$487$	25.3173			1.14724			0.573619	+	0.819123i	$0.305539\pi$
$488$			6.41629i			0.290452i
$489$	4.02323	−	32.9337i	0.181937	−	1.48931i
$490$	−7.86448	+	7.86448i	−0.355281	+	0.355281i
$491$	7.97339	+	7.97339i	0.359834	+	0.359834i	0.863752	−	0.503918i	$-0.168109\pi$
$491$	7.97339	+	7.97339i	0.359834	+	0.359834i	−0.503918	+	0.863752i	$0.668109\pi$
$492$	−0.0789979	+	0.646668i	−0.00356150	+	0.0291541i
$493$	−4.02230	−	4.28237i	−0.181155	−	0.192868i
$494$			0.537308i			0.0241746i
$495$	2.43951	+	4.04876i	0.109648	+	0.181978i
$496$	10.3123	+	10.3123i	0.463037	+	0.463037i
$497$	−13.1620			−0.590398
$498$	−25.3422	−	3.09584i	−1.13561	−	0.138728i
$499$		−	6.11551i		−	0.273768i	−0.990587	−	0.136884i	$-0.956291\pi$
$499$		−	6.11551i		−	0.273768i	0.990587	−	0.136884i	$-0.0437087\pi$
$500$			2.43117i			0.108725i
$501$	−23.6416	+	18.4942i	−1.05623	+	0.826262i
$502$			29.0102i			1.29479i
$503$	22.1736	+	22.1736i	0.988670	+	0.988670i	0.999937	−	0.0112662i	$-0.00358622\pi$
$503$	22.1736	+	22.1736i	0.988670	+	0.988670i	−0.0112662	+	0.999937i	$0.503586\pi$
$504$	−3.05552	+	1.84105i	−0.136104	+	0.0820071i
$505$	−5.00642	+	5.00642i	−0.222783	+	0.222783i
$506$	6.30683			0.280373
$507$	−17.5945	+	13.7638i	−0.781401	+	0.611270i
$508$	−9.71656	+	9.71656i	−0.431102	+	0.431102i
$509$			28.3255i			1.25551i	0.778413	+	0.627753i	$0.216025\pi$
$509$			28.3255i			1.25551i	−0.778413	+	0.627753i	$0.783975\pi$
$510$	2.45089	+	3.13303i	0.108527	+	0.138733i
$511$	−12.4815	+	12.4815i	−0.552148	+	0.552148i
$512$	−20.5466	+	20.5466i	−0.908039	+	0.908039i
$513$	1.47497	−	3.86368i	0.0651215	−	0.170586i
$514$	18.2915	+	18.2915i	0.806803	+	0.806803i
$515$	−0.376151			−0.0165752
$516$	−2.82429	+	23.1193i	−0.124333	+	1.01777i
$517$	12.5517			0.552023
$518$		−	0.993634i		−	0.0436578i
$519$	23.7972	−	18.6159i	1.04458	−	0.817148i
$520$	0.205822	−	0.205822i	0.00902591	−	0.00902591i
$521$	−16.6369			−0.728877			−0.364438	−	0.931228i	$-0.618739\pi$
$521$	−16.6369			−0.728877			−0.364438	+	0.931228i	$0.618739\pi$
$522$	29.6640	−	16.6308i	1.29836	−	0.727910i
$523$	26.3304			1.15135			0.575674	−	0.817680i	$-0.304740\pi$
$523$	26.3304			1.15135			0.575674	+	0.817680i	$0.304740\pi$
$524$	28.6357	−	28.6357i	1.25096	−	1.25096i
$525$	1.78731	−	1.39817i	0.0780045	−	0.0610210i
$526$			14.3530i			0.625819i
$527$	5.39028			0.234804
$528$	−0.976822	+	7.99615i	−0.0425107	+	0.347988i
$529$	19.3843			0.842796
$530$	−9.50641	−	9.50641i	−0.412932	−	0.412932i
$531$	3.00578	+	0.745506i	0.130440	+	0.0323522i
$532$	1.79257	−	1.79257i	0.0777178	−	0.0777178i
$533$	−0.0350841	+	0.0350841i	−0.00151966	+	0.00151966i
$534$	−29.1560	−	37.2708i	−1.26171	−	1.61287i
$535$		−	4.71119i		−	0.203683i
$536$	7.44645	−	7.44645i	0.321638	−	0.321638i
$537$	−22.2178	+	17.3804i	−0.958768	+	0.750020i
$538$	−53.3238			−2.29895
$539$	−5.88664	+	5.88664i	−0.253555	+	0.253555i
$540$	−11.5311	+	5.15943i	−0.496219	+	0.222027i
$541$	7.94784	+	7.94784i	0.341704	+	0.341704i	0.857008	−	0.515303i	$-0.172321\pi$
$541$	7.94784	+	7.94784i	0.341704	+	0.341704i	−0.515303	+	0.857008i	$0.672321\pi$
$542$			46.9185i			2.01532i
$543$	18.9050	−	14.7889i	0.811293	−	0.634654i
$544$			8.75934i			0.375554i
$545$			14.6413i			0.627163i
$546$	−1.52062	−	0.185761i	−0.0650766	−	0.00794985i
$547$	6.77236			0.289565			0.144783	−	0.989463i	$-0.453752\pi$
$547$	6.77236			0.289565			0.144783	+	0.989463i	$0.453752\pi$
$548$	−15.1107	−	15.1107i	−0.645499	−	0.645499i
$549$	18.1654	−	10.9453i	0.775281	−	0.467132i
$550$			3.31677i			0.141427i
$551$	−3.12409	+	2.93437i	−0.133091	+	0.125008i
$552$	−0.362476	+	2.96719i	−0.0154280	+	0.126292i
$553$	2.69246	+	2.69246i	0.114495	+	0.114495i
$554$	−2.61584	+	2.61584i	−0.111136	+	0.111136i
$555$	0.0756711	−	0.619435i	0.00321206	−	0.0262936i
$556$			19.3821i			0.821983i
$557$	−38.3481			−1.62486			−0.812431	−	0.583058i	$-0.801856\pi$
$557$	−38.3481			−1.62486			−0.812431	+	0.583058i	$0.801856\pi$
$558$	−7.51106	+	30.2836i	−0.317969	+	1.28201i
$559$	−1.25431	+	1.25431i	−0.0530516	+	0.0530516i
$560$	3.86720			0.163419
$561$	1.83451	+	2.34510i	0.0774532	+	0.0990102i
$562$	32.1747	+	32.1747i	1.35721	+	1.35721i
$563$	17.2850	+	17.2850i	0.728476	+	0.728476i	0.970316	−	0.241840i	$-0.0777509\pi$
$563$	17.2850	+	17.2850i	0.728476	+	0.728476i	−0.241840	+	0.970316i	$0.577751\pi$
$564$	−4.06761	+	33.2970i	−0.171277	+	1.40206i
$565$	1.40534	+	1.40534i	0.0591231	+	0.0591231i
$566$	45.5108	+	45.5108i	1.91296	+	1.91296i
$567$	10.4246	+	5.51005i	0.437791	+	0.231400i
$568$	6.44759	+	6.44759i	0.270535	+	0.270535i
$569$	9.57727	+	9.57727i	0.401500	+	0.401500i	0.878761	−	0.477261i	$-0.158370\pi$
$569$	9.57727	+	9.57727i	0.401500	+	0.401500i	−0.477261	+	0.878761i	$0.658370\pi$
$570$	2.28562	−	1.78799i	0.0957343	−	0.0748905i
$571$	−17.9363			−0.750612			−0.375306	−	0.926901i	$-0.622462\pi$
$571$	−17.9363			−0.750612			−0.375306	+	0.926901i	$0.622462\pi$
$572$	0.868678	−	0.868678i	0.0363212	−	0.0363212i
$573$	0.337562	−	2.76325i	0.0141019	−	0.115436i
$574$	0.426675			0.0178091
$575$		−	1.90150i		−	0.0792980i
$576$	−32.0219	−	7.94220i	−1.33425	−	0.330925i
$577$	−0.342156	+	0.342156i	−0.0142441	+	0.0142441i	−0.714193	−	0.699949i	$-0.753206\pi$
$577$	−0.342156	+	0.342156i	−0.0142441	+	0.0142441i	0.699949	+	0.714193i	$0.253206\pi$
$578$	−23.5325	−	23.5325i	−0.978825	−	0.978825i
$579$	23.5480	+	2.87665i	0.978621	+	0.119550i
$580$	13.0858	+	0.409791i	0.543359	+	0.0170156i
$581$			9.17396i			0.380600i
$582$	−40.4555	−	51.7152i	−1.67694	−	2.14367i
$583$	−7.11563	−	7.11563i	−0.294699	−	0.294699i
$584$	12.2284			0.506016
$585$	−0.933815	−	0.231609i	−0.0386085	−	0.00957584i
$586$		−	59.3024i		−	2.44976i
$587$			15.0468i			0.621049i	0.950565	+	0.310525i	$0.100505\pi$
$587$			15.0468i			0.621049i	−0.950565	+	0.310525i	$0.899495\pi$
$588$	−13.7083	−	17.5237i	−0.565322	−	0.722664i
$589$		−	3.93235i		−	0.162029i
$590$	1.53654	+	1.53654i	0.0632582	+	0.0632582i
$591$	13.6915	+	17.5022i	0.563194	+	0.719944i
$592$	0.752001	−	0.752001i	0.0309070	−	0.0309070i
$593$	28.6722			1.17742			0.588712	−	0.808343i	$-0.299635\pi$
$593$	28.6722			1.17742			0.588712	+	0.808343i	$0.299635\pi$
$594$	−15.7315	+	7.03886i	−0.645471	+	0.288808i
$595$	1.01070	−	1.01070i	0.0414346	−	0.0414346i
$596$			47.9680i			1.96485i
$597$	3.56354	−	2.78767i	0.145846	−	0.114092i
$598$	−0.907701	+	0.907701i	−0.0371187	+	0.0371187i
$599$	19.8711	−	19.8711i	0.811913	−	0.811913i	−0.173008	−	0.984921i	$-0.555348\pi$
$599$	19.8711	−	19.8711i	0.811913	−	0.811913i	0.984921	+	0.173008i	$0.0553485\pi$
$600$	−1.56045	−	0.190626i	−0.0637049	−	0.00778228i
$601$	−15.9176	−	15.9176i	−0.649292	−	0.649292i	0.303530	−	0.952822i	$-0.401835\pi$
$601$	−15.9176	−	15.9176i	−0.649292	−	0.649292i	−0.952822	+	0.303530i	$0.901835\pi$
$602$	15.2543			0.621717
$603$	−33.7845	−	8.37937i	−1.37581	−	0.341234i
$604$	10.4435			0.424939
$605$		−	8.51737i		−	0.346280i
$606$	−15.9054	−	20.3322i	−0.646113	−	0.825941i
$607$	11.4732	−	11.4732i	0.465683	−	0.465683i	−0.434830	−	0.900513i	$-0.643191\pi$
$607$	11.4732	−	11.4732i	0.465683	−	0.465683i	0.900513	+	0.434830i	$0.143191\pi$
$608$	6.39016			0.259155
$609$	−7.22440	−	9.85590i	−0.292748	−	0.399381i
$610$	14.8812			0.602523
$611$	−1.80648	+	1.80648i	−0.0730825	+	0.0730825i
$612$	−6.81556	+	4.10660i	−0.275503	+	0.166000i
$613$		−	3.17364i		−	0.128182i	−0.997944	−	0.0640911i	$-0.979585\pi$
$613$		−	3.17364i		−	0.128182i	0.997944	−	0.0640911i	$-0.0204148\pi$
$614$	29.1128			1.17490
$615$	0.265991	+	0.0324938i	0.0107258	+	0.00131028i
$616$	−1.87360			−0.0754893
$617$	18.2098	+	18.2098i	0.733098	+	0.733098i	0.971232	−	0.238134i	$-0.0765358\pi$
$617$	18.2098	+	18.2098i	0.733098	+	0.733098i	−0.238134	+	0.971232i	$0.576536\pi$
$618$	0.166303	−	1.36134i	0.00668967	−	0.0547609i
$619$	18.5659	−	18.5659i	0.746225	−	0.746225i	−0.227543	−	0.973768i	$-0.573069\pi$
$619$	18.5659	−	18.5659i	0.746225	−	0.746225i	0.973768	+	0.227543i	$0.0730692\pi$
$620$	−8.49357	+	8.49357i	−0.341110	+	0.341110i
$621$	9.01885	−	4.03537i	0.361914	−	0.161934i
$622$		−	59.5854i		−	2.38916i
$623$	−12.0234	+	12.0234i	−0.481706	+	0.481706i
$624$	−1.01025	−	1.29142i	−0.0404423	−	0.0516983i
$625$	1.00000			0.0400000
$626$	15.3058	−	15.3058i	0.611743	−	0.611743i
$627$	1.71081	−	1.33832i	0.0683232	−	0.0534475i
$628$	−0.821486	−	0.821486i	−0.0327809	−	0.0327809i
$629$		−	0.393073i		−	0.0156728i
$630$	4.26993	+	7.08664i	0.170118	+	0.282338i
$631$			7.81015i			0.310917i	0.987842	+	0.155459i	$0.0496855\pi$
$631$			7.81015i			0.310917i	−0.987842	+	0.155459i	$0.950314\pi$
$632$		−	2.63787i		−	0.104929i
$633$	2.63393	−	21.5611i	0.104689	−	0.856975i
$634$	25.2843			1.00417
$635$	3.99666	+	3.99666i	0.158603	+	0.158603i
$636$	21.1822	−	16.5703i	0.839930	−	0.657056i
$637$		−	1.69445i		−	0.0671366i
$638$	17.8526	+	0.559065i	0.706791	+	0.0221336i
$639$	7.25538	−	29.2527i	0.287018	−	1.15722i
$640$	−5.01497	−	5.01497i	−0.198234	−	0.198234i
$641$	−3.20794	+	3.20794i	−0.126706	+	0.126706i	−0.767616	−	0.640910i	$-0.778557\pi$
$641$	−3.20794	+	3.20794i	−0.126706	+	0.126706i	0.640910	+	0.767616i	$0.278557\pi$
$642$	17.0504	+	2.08290i	0.672925	+	0.0822054i
$643$		−	45.7452i		−	1.80402i	−0.431719	−	0.902008i	$-0.642093\pi$
$643$		−	45.7452i		−	1.80402i	0.431719	−	0.902008i	$-0.357907\pi$
$644$	6.05656			0.238662
$645$	9.50957	+	1.16170i	0.374439	+	0.0457420i
$646$	1.29249	−	1.29249i	0.0508523	−	0.0508523i
$647$	7.40835			0.291252			0.145626	−	0.989340i	$-0.453480\pi$
$647$	7.40835			0.291252			0.145626	+	0.989340i	$0.453480\pi$
$648$	−2.40744	−	7.80577i	−0.0945732	−	0.306640i
$649$	1.15011	+	1.15011i	0.0451458	+	0.0451458i
$650$	−0.477361	−	0.477361i	−0.0187236	−	0.0187236i
$651$	11.1288	+	1.35951i	0.436173	+	0.0532835i
$652$	32.9303	+	32.9303i	1.28965	+	1.28965i
$653$	25.9833	+	25.9833i	1.01680	+	1.01680i	0.999856	+	0.0169479i	$0.00539494\pi$
$653$	25.9833	+	25.9833i	1.01680	+	1.01680i	0.0169479	+	0.999856i	$0.494605\pi$
$654$	−52.9885	−	6.47316i	−2.07202	−	0.253120i
$655$	−11.7786	−	11.7786i	−0.460228	−	0.460228i
$656$	0.322916	+	0.322916i	0.0126077	+	0.0126077i
$657$	−20.8599	−	34.6204i	−0.813823	−	1.35067i
$658$	21.9695			0.856461
$659$	−12.3271	+	12.3271i	−0.480197	+	0.480197i	−0.905195	−	0.424997i	$-0.860275\pi$
$659$	−12.3271	+	12.3271i	−0.480197	+	0.480197i	0.424997	+	0.905195i	$0.360275\pi$
$660$	−6.58590	−	0.804542i	−0.256356	−	0.0313168i
$661$	45.6191			1.77438			0.887188	−	0.461409i	$-0.152656\pi$
$661$	45.6191			1.77438			0.887188	+	0.461409i	$0.152656\pi$
$662$			10.0437i			0.390358i
$663$	−0.601545	−	0.0734855i	−0.0233621	−	0.00285394i
$664$	4.49398	−	4.49398i	0.174400	−	0.174400i
$665$	−0.737329	−	0.737329i	−0.0285924	−	0.0285924i
$666$	2.20836	+	0.547726i	0.0855721	+	0.0212239i
$667$	−10.2349	−	0.320511i	−0.396296	−	0.0124102i
$668$		−	42.1316i		−	1.63012i
$669$	−6.66921	+	5.21715i	−0.257846	+	0.201707i
$670$	−17.2704	−	17.2704i	−0.667215	−	0.667215i
$671$	11.1387			0.430005
$672$	−2.20924	+	18.0846i	−0.0852235	+	0.697630i
$673$		−	18.4565i		−	0.711446i	−0.934591	−	0.355723i	$-0.884235\pi$
$673$		−	18.4565i		−	0.711446i	0.934591	−	0.355723i	$-0.115765\pi$
$674$		−	6.68282i		−	0.257412i
$675$	2.12220	+	4.74302i	0.0816837	+	0.182559i
$676$		−	31.3551i		−	1.20597i
$677$	12.0354	+	12.0354i	0.462556	+	0.462556i	0.899492	−	0.436936i	$-0.143936\pi$
$677$	12.0354	+	12.0354i	0.462556	+	0.462556i	−0.436936	+	0.899492i	$0.643936\pi$
$678$	−5.70742	+	4.46477i	−0.219192	+	0.171468i
$679$	−16.6830	+	16.6830i	−0.640237	+	0.640237i
$680$	−0.990206			−0.0379727
$681$	6.65390	+	8.50583i	0.254978	+	0.325944i
$682$	−11.5875	+	11.5875i	−0.443709	+	0.443709i
$683$		−	44.5490i		−	1.70462i	−0.523037	−	0.852310i	$-0.675201\pi$
$683$		−	44.5490i		−	1.70462i	0.523037	−	0.852310i	$-0.324799\pi$
$684$	2.99587	+	4.97213i	0.114550	+	0.190114i
$685$	−6.21543	+	6.21543i	−0.237479	+	0.237479i
$686$	−23.9543	+	23.9543i	−0.914579	+	0.914579i
$687$	1.94983	−	15.9611i	0.0743906	−	0.608954i
$688$	11.5447	+	11.5447i	0.440138	+	0.440138i
$689$	2.04821			0.0780308
$690$	6.88175	+	0.840685i	0.261984	+	0.0320043i
$691$	−24.8348			−0.944760			−0.472380	−	0.881395i	$-0.656605\pi$
$691$	−24.8348			−0.944760			−0.472380	+	0.881395i	$0.656605\pi$
$692$			42.4087i			1.61214i
$693$	3.19608	+	5.30441i	0.121409	+	0.201498i
$694$	25.3341	−	25.3341i	0.961668	−	0.961668i
$695$	7.97233			0.302408
$696$	−1.28908	+	8.36701i	−0.0488623	+	0.317151i
$697$	0.168789			0.00639333
$698$	0.219593	−	0.219593i	0.00831171	−	0.00831171i
$699$	−26.4119	−	33.7629i	−0.998989	−	1.27703i
$700$			3.18515i			0.120387i
$701$	−16.4573			−0.621582			−0.310791	−	0.950478i	$-0.600594\pi$
$701$	−16.4573			−0.621582			−0.310791	+	0.950478i	$0.600594\pi$
$702$	1.25108	−	3.27719i	0.0472188	−	0.123690i
$703$	−0.286757			−0.0108152
$704$	−12.2526	−	12.2526i	−0.461789	−	0.461789i
$705$	13.6959	+	1.67311i	0.515817	+	0.0630129i
$706$	25.9381	−	25.9381i	0.976194	−	0.976194i
$707$	−6.55907	+	6.55907i	−0.246679	+	0.246679i
$708$	−3.42372	+	2.67829i	−0.128671	+	0.100656i
$709$			21.7736i			0.817725i	0.912596	+	0.408862i	$0.134074\pi$
$709$			21.7736i			0.817725i	−0.912596	+	0.408862i	$0.865926\pi$
$710$	14.9538	−	14.9538i	0.561207	−	0.561207i
$711$	−7.46817	+	4.49982i	−0.280078	+	0.168757i
$712$	11.7796			0.441459
$713$	6.64311	−	6.64311i	0.248786	−	0.248786i
$714$	3.21099	+	4.10468i	0.120168	+	0.153614i
$715$	−0.357309	−	0.357309i	−0.0133626	−	0.0133626i
$716$		−	39.5942i		−	1.47970i
$717$	−15.1831	−	19.4089i	−0.567023	−	0.724838i
$718$		−	16.2461i		−	0.606301i
$719$			41.8447i			1.56055i	0.625440	+	0.780273i	$0.284920\pi$
$719$			41.8447i			1.56055i	−0.625440	+	0.780273i	$0.715080\pi$
$720$	−2.13173	+	8.59487i	−0.0794451	+	0.320312i
$721$	−0.492807			−0.0183531
$722$	27.3383	+	27.3383i	1.01743	+	1.01743i
$723$	13.5105	+	17.2708i	0.502462	+	0.642309i
$724$			33.6905i			1.25210i
$725$	0.168557	−	5.38253i	0.00626006	−	0.199902i
$726$	30.8254	+	3.76567i	1.14404	+	0.139757i
$727$	−10.8410	−	10.8410i	−0.402069	−	0.402069i	0.476893	−	0.878962i	$-0.341763\pi$
$727$	−10.8410	−	10.8410i	−0.402069	−	0.402069i	−0.878962	+	0.476893i	$0.841763\pi$
$728$	0.269654	−	0.269654i	0.00999406	−	0.00999406i
$729$	−17.9925	+	20.1313i	−0.666389	+	0.745605i
$730$		−	28.3612i		−	1.04970i
$731$	6.03445			0.223192
$732$	−3.60971	+	29.5487i	−0.133419	+	1.09215i
$733$	12.8829	−	12.8829i	0.475841	−	0.475841i	−0.427957	−	0.903799i	$-0.640767\pi$
$733$	12.8829	−	12.8829i	0.475841	−	0.475841i	0.903799	+	0.427957i	$0.140767\pi$
$734$	−20.6459			−0.762053
$735$	−7.20793	+	5.63858i	−0.265868	+	0.207982i
$736$	10.7952	+	10.7952i	0.397917	+	0.397917i
$737$	−12.9271	−	12.9271i	−0.476175	−	0.476175i
$738$	−0.235198	+	0.948287i	−0.00865776	+	0.0349069i
$739$	−28.1281	−	28.1281i	−1.03471	−	1.03471i	−0.999376	−	0.0353323i	$-0.988751\pi$
$739$	−28.1281	−	28.1281i	−1.03471	−	1.03471i	−0.0353323	−	0.999376i	$-0.511249\pi$
$740$	0.619372	+	0.619372i	0.0227686	+	0.0227686i
$741$	−0.0536096	+	0.438842i	−0.00196940	+	0.0161213i
$742$	−12.4547	−	12.4547i	−0.457225	−	0.457225i
$743$	−17.7691	−	17.7691i	−0.651884	−	0.651884i	0.301563	−	0.953446i	$-0.402492\pi$
$743$	−17.7691	−	17.7691i	−0.651884	−	0.651884i	−0.953446	+	0.301563i	$0.902492\pi$
$744$	−4.78562	−	6.11757i	−0.175449	−	0.224281i
$745$	19.7304			0.722867
$746$	−45.0002	+	45.0002i	−1.64758	+	1.64758i
$747$	−20.3892	−	5.05701i	−0.746001	−	0.185026i
$748$	−4.17919			−0.152806
$749$		−	6.17229i		−	0.225530i
$750$	−0.442117	+	3.61912i	−0.0161438	+	0.132152i
$751$	7.71808	−	7.71808i	0.281637	−	0.281637i	−0.552125	−	0.833761i	$-0.686183\pi$
$751$	7.71808	−	7.71808i	0.281637	−	0.281637i	0.833761	+	0.552125i	$0.186183\pi$
$752$	16.6269	+	16.6269i	0.606322	+	0.606322i
$753$	−2.89447	+	23.6939i	−0.105481	+	0.863452i
$754$	−2.64987	+	2.48895i	−0.0965026	+	0.0906420i
$755$		−	4.29567i		−	0.156335i
$756$	−15.1072	+	6.75954i	−0.549445	+	0.245842i
$757$	6.26971	+	6.26971i	0.227876	+	0.227876i	0.811805	−	0.583929i	$-0.198485\pi$
$757$	6.26971	+	6.26971i	0.227876	+	0.227876i	−0.583929	+	0.811805i	$0.698485\pi$
$758$	22.1451			0.804347
$759$	5.15105	+	0.629260i	0.186971	+	0.0228407i
$760$			0.722381i			0.0262035i
$761$		−	5.60419i		−	0.203152i	−0.994828	−	0.101576i	$-0.967612\pi$
$761$		−	5.60419i		−	0.203152i	0.994828	−	0.101576i	$-0.0323884\pi$
$762$	−16.2314	+	12.6974i	−0.588002	+	0.459979i
$763$			19.1820i			0.694435i
$764$	2.76297	+	2.76297i	0.0999607	+	0.0999607i
$765$	1.68915	+	2.80341i	0.0610713	+	0.101358i
$766$	37.4065	−	37.4065i	1.35155	−	1.35155i
$767$	−0.331056			−0.0119537
$768$	−9.63868	+	7.54009i	−0.347806	+	0.272080i
$769$	−30.8478	+	30.8478i	−1.11240	+	1.11240i	−0.119576	+	0.992825i	$0.538153\pi$
$769$	−30.8478	+	30.8478i	−1.11240	+	1.11240i	−0.992825	+	0.119576i	$0.961847\pi$
$770$			4.34540i			0.156598i
$771$	13.1144	+	16.7644i	0.472304	+	0.603757i
$772$	−23.5456	+	23.5456i	−0.847424	+	0.847424i
$773$	5.86761	−	5.86761i	0.211043	−	0.211043i	−0.593667	−	0.804711i	$-0.702320\pi$
$773$	5.86761	−	5.86761i	0.211043	−	0.211043i	0.804711	+	0.593667i	$0.202320\pi$
$774$	−8.40868	+	33.9027i	−0.302244	+	1.21861i
$775$	3.49362	+	3.49362i	0.125494	+	0.125494i
$776$	16.3448			0.586744
$777$	0.0991392	−	0.811542i	0.00355660	−	0.0291139i
$778$	47.8252			1.71462
$779$		−	0.123136i		−	0.00441180i
$780$	1.06366	−	0.832073i	0.0380851	−	0.0297930i
$781$	11.1931	−	11.1931i	0.400519	−	0.400519i
$782$	4.36693			0.156161
$783$	25.8871	−	10.6234i	0.925131	−	0.379648i
$784$	−15.5958			−0.556992
$785$	−0.337898	+	0.337898i	−0.0120601	+	0.0120601i
$786$	47.8356	−	37.4206i	1.70624	−	1.33475i
$787$			41.6867i			1.48597i	0.669308	+	0.742985i	$0.266591\pi$
$787$			41.6867i			1.48597i	−0.669308	+	0.742985i	$0.733409\pi$
$788$	−31.1906			−1.11112
$789$	−1.43206	+	11.7227i	−0.0509826	+	0.417338i
$790$	−6.11797			−0.217668
$791$	1.84118	+	1.84118i	0.0654649	+	0.0654649i
$792$	1.03279	−	4.16408i	0.0366987	−	0.147964i
$793$	−1.60312	+	1.60312i	−0.0569286	+	0.0569286i
$794$	−50.8693	+	50.8693i	−1.80528	+	1.80528i
$795$	−6.81579	−	8.71278i	−0.241731	−	0.309011i
$796$			6.35056i			0.225089i
$797$	−15.2640	+	15.2640i	−0.540679	+	0.540679i	−0.923728	−	0.383049i	$-0.874874\pi$
$797$	−15.2640	+	15.2640i	−0.540679	+	0.540679i	0.383049	+	0.923728i	$0.374874\pi$
$798$	2.99447	−	2.34250i	0.106003	−	0.0829235i
$799$	8.69095			0.307464
$800$	−5.67722	+	5.67722i	−0.200720	+	0.200720i
$801$	−20.0943	−	33.3497i	−0.709997	−	1.17835i
$802$	51.9288	+	51.9288i	1.83367	+	1.83367i
$803$		−	21.2286i		−	0.749142i
$804$	38.4821	−	30.1036i	1.35716	−	1.06167i
$805$		−	2.49121i		−	0.0878038i
$806$		−	3.33543i		−	0.117486i
$807$	−43.5518	−	5.32035i	−1.53310	−	0.187285i
$808$	6.42609			0.226069
$809$	17.0762	+	17.0762i	0.600368	+	0.600368i	0.940410	−	0.340042i	$-0.110441\pi$
$809$	17.0762	+	17.0762i	0.600368	+	0.600368i	−0.340042	+	0.940410i	$0.610441\pi$
$810$	−18.1038	+	5.58355i	−0.636104	+	0.196186i
$811$		−	7.97534i		−	0.280052i	−0.990148	−	0.140026i	$-0.955281\pi$
$811$		−	7.97534i		−	0.280052i	0.990148	−	0.140026i	$-0.0447186\pi$
$812$	17.1442	+	0.536880i	0.601642	+	0.0188408i
$813$	−4.68127	+	38.3203i	−0.164179	+	1.34395i
$814$	0.844991	+	0.844991i	0.0296169	+	0.0296169i
$815$	13.5451	−	13.5451i	0.474463	−	0.474463i
$816$	−0.676364	+	5.53664i	−0.0236775	+	0.193821i
$817$		−	4.40229i		−	0.154016i
$818$	−41.5899			−1.45416
$819$	−1.22342	−	0.303438i	−0.0427498	−	0.0106030i
$820$	−0.265964	+	0.265964i	−0.00928786	+	0.00928786i
$821$	−4.39119			−0.153254			−0.0766268	−	0.997060i	$-0.524415\pi$
$821$	−4.39119			−0.153254			−0.0766268	+	0.997060i	$0.524415\pi$
$822$	−19.7464	−	25.2423i	−0.688736	−	0.880427i
$823$	−6.33746	−	6.33746i	−0.220910	−	0.220910i	0.587972	−	0.808882i	$-0.299927\pi$
$823$	−6.33746	−	6.33746i	−0.220910	−	0.220910i	−0.808882	+	0.587972i	$0.799927\pi$
$824$	0.241408	+	0.241408i	0.00840985	+	0.00840985i
$825$	−0.330928	+	2.70894i	−0.0115214	+	0.0943133i
$826$	2.01307	+	2.01307i	0.0700435	+	0.0700435i
$827$	−19.0119	−	19.0119i	−0.661108	−	0.661108i	0.294533	−	0.955641i	$-0.404836\pi$
$827$	−19.0119	−	19.0119i	−0.661108	−	0.661108i	−0.955641	+	0.294533i	$0.904836\pi$
$828$	−3.33859	+	13.4607i	−0.116024	+	0.467793i
$829$	4.89760	+	4.89760i	0.170101	+	0.170101i	0.787024	−	0.616923i	$-0.211621\pi$
$829$	4.89760	+	4.89760i	0.170101	+	0.170101i	−0.616923	+	0.787024i	$0.711621\pi$
$830$	−10.4228	−	10.4228i	−0.361782	−	0.361782i
$831$	−2.39746	+	1.87547i	−0.0831669	+	0.0650593i
$832$	3.52689			0.122273
$833$	−4.07598	+	4.07598i	−0.141224	+	0.141224i
$834$	−3.52470	+	28.8528i	−0.122050	+	0.999092i
$835$	−17.3298			−0.599722
$836$			3.04882i			0.105446i
$837$	−9.15613	+	23.9845i	−0.316482	+	0.829024i
$838$	−7.46965	+	7.46965i	−0.258035	+	0.258035i
$839$	−14.0915	−	14.0915i	−0.486491	−	0.486491i	0.420706	−	0.907197i	$-0.361782\pi$
$839$	−14.0915	−	14.0915i	−0.486491	−	0.486491i	−0.907197	+	0.420706i	$0.861782\pi$
$840$	−2.04439	−	0.249746i	−0.0705382	−	0.00861704i
$841$	−28.9432	−	1.81453i	−0.998041	−	0.0625699i
$842$		−	83.2737i		−	2.86980i
$843$	23.0682	+	29.4887i	0.794512	+	1.01564i
$844$	21.5589	+	21.5589i	0.742086	+	0.742086i
$845$	−12.8971			−0.443675
$846$	−12.1104	+	48.8274i	−0.416363	+	1.67872i
$847$		−	11.1589i		−	0.383424i
$848$		−	18.8518i		−	0.647375i
$849$	32.6298	+	41.7114i	1.11985	+	1.43153i
$850$			2.29657i			0.0787718i
$851$	−0.484432	−	0.484432i	−0.0166061	−	0.0166061i
$852$	26.0655	+	33.3202i	0.892990	+	1.14153i
$853$	−34.5823	+	34.5823i	−1.18408	+	1.18408i	−0.205397	+	0.978679i	$0.565849\pi$
$853$	−34.5823	+	34.5823i	−1.18408	+	1.18408i	−0.978679	+	0.205397i	$0.934151\pi$
$854$	19.4964			0.667151
$855$	2.04516	−	1.23228i	0.0699430	−	0.0421430i
$856$	−3.02357	+	3.02357i	−0.103344	+	0.103344i
$857$		−	34.3731i		−	1.17416i	−0.809527	−	0.587082i	$-0.800277\pi$
$857$		−	34.3731i		−	1.17416i	0.809527	−	0.587082i	$-0.199723\pi$
$858$	1.45112	−	1.13517i	0.0495403	−	0.0387541i
$859$	−24.4432	+	24.4432i	−0.833991	+	0.833991i	−0.988060	−	0.154069i	$-0.950762\pi$
$859$	−24.4432	+	24.4432i	−0.833991	+	0.833991i	0.154069	+	0.988060i	$0.450762\pi$
$860$	−9.50860	+	9.50860i	−0.324241	+	0.324241i
$861$	0.348483	+	0.0425712i	0.0118763	+	0.00145082i
$862$	8.43795	+	8.43795i	0.287398	+	0.287398i
$863$	8.62298			0.293530			0.146765	−	0.989171i	$-0.453114\pi$
$863$	8.62298			0.293530			0.146765	+	0.989171i	$0.453114\pi$
$864$	−38.9754	−	14.8789i	−1.32597	−	0.506192i
$865$	17.4438			0.593106
$866$			51.9953i			1.76687i
$867$	−16.8721	−	21.5680i	−0.573006	−	0.732486i
$868$	−11.1277	+	11.1277i	−0.377699	+	0.377699i
$869$	−4.57936			−0.155344
$870$	19.4055	+	2.98973i	0.657908	+	0.101361i
$871$	3.72102			0.126082
$872$	9.39655	−	9.39655i	0.318207	−	0.318207i
$873$	−27.8819	−	46.2744i	−0.943659	−	1.56615i
$874$		−	3.18579i		−	0.107761i
$875$	1.31013			0.0442906
$876$	56.3151	+	6.87953i	1.90271	+	0.232438i
$877$	−47.7453			−1.61224			−0.806122	−	0.591750i	$-0.798437\pi$
$877$	−47.7453			−1.61224			−0.806122	+	0.591750i	$0.798437\pi$
$878$	0.257387	+	0.257387i	0.00868640	+	0.00868640i
$879$	5.91686	−	48.4348i	0.199571	−	1.63367i
$880$	−3.28868	+	3.28868i	−0.110862	+	0.110862i
$881$	27.1581	−	27.1581i	0.914978	−	0.914978i	−0.0816802	−	0.996659i	$-0.526029\pi$
$881$	27.1581	−	27.1581i	0.914978	−	0.914978i	0.996659	+	0.0816802i	$0.0260286\pi$
$882$	−17.2200	−	28.5793i	−0.579826	−	0.962314i
$883$			14.6003i			0.491338i	0.969354	+	0.245669i	$0.0790076\pi$
$883$			14.6003i			0.491338i	−0.969354	+	0.245669i	$0.920992\pi$
$884$	0.601483	−	0.601483i	0.0202301	−	0.0202301i
$885$	1.10165	+	1.40826i	0.0370315	+	0.0473382i
$886$	−15.7147			−0.527946
$887$	9.98930	−	9.98930i	0.335408	−	0.335408i	−0.519228	−	0.854636i	$-0.673780\pi$
$887$	9.98930	−	9.98930i	0.335408	−	0.335408i	0.854636	+	0.519228i	$0.173780\pi$
$888$	−0.446109	+	0.348980i	−0.0149704	+	0.0117110i
$889$	5.23616	+	5.23616i	0.175615	+	0.175615i
$890$		−	27.3203i		−	0.915777i
$891$	−13.5509	+	4.17933i	−0.453971	+	0.140013i
$892$		−	11.8851i		−	0.397944i
$893$		−	6.34027i		−	0.212169i
$894$	−8.72316	+	71.4068i	−0.291746	+	2.38820i
$895$	−16.2861			−0.544383
$896$	−6.57027	−	6.57027i	−0.219497	−	0.219497i
$897$	−0.831923	+	0.650792i	−0.0277771	+	0.0217293i
$898$			74.6591i			2.49141i
$899$	19.3934	−	18.2156i	0.646805	−	0.607525i
$900$	−7.07901	−	1.75577i	−0.235967	−	0.0585256i
$901$	−4.92695	−	4.92695i	−0.164141	−	0.164141i
$902$	−0.362847	+	0.362847i	−0.0120815	+	0.0120815i
$903$	12.4588	+	1.52198i	0.414603	+	0.0506484i
$904$		−	1.80385i		−	0.0599952i
$905$	13.8578			0.460648
$906$	15.5465	+	1.89919i	0.516499	+	0.0630963i
$907$	−23.3075	+	23.3075i	−0.773914	+	0.773914i	−0.978788	−	0.204875i	$-0.934321\pi$
$907$	−23.3075	+	23.3075i	−0.773914	+	0.773914i	0.204875	+	0.978788i	$0.434321\pi$
$908$	−15.1582			−0.503042
$909$	−10.9620	−	18.1932i	−0.363586	−	0.603429i
$910$	−0.625406	−	0.625406i	−0.0207320	−	0.0207320i
$911$	−7.53322	−	7.53322i	−0.249587	−	0.249587i	0.571214	−	0.820801i	$-0.306473\pi$
$911$	−7.53322	−	7.53322i	−0.249587	−	0.249587i	−0.820801	+	0.571214i	$0.806473\pi$
$912$	4.03912	+	0.493424i	0.133749	+	0.0163389i
$913$	−7.80158	−	7.80158i	−0.258195	−	0.258195i
$914$	−28.3778	−	28.3778i	−0.938656	−	0.938656i
$915$	12.1541	+	1.48476i	0.401802	+	0.0490848i
$916$	15.9595	+	15.9595i	0.527316	+	0.527316i
$917$	−15.4315	−	15.4315i	−0.509593	−	0.509593i
$918$	−10.8927	+	4.87380i	−0.359512	+	0.160859i
$919$	−40.1084			−1.32305			−0.661527	−	0.749921i	$-0.730092\pi$
$919$	−40.1084			−1.32305			−0.661527	+	0.749921i	$0.730092\pi$
$920$	−1.22035	+	1.22035i	−0.0402339	+	0.0402339i
$921$	23.7777	+	2.90472i	0.783501	+	0.0957136i
$922$	12.5698			0.413964
$923$			3.22189i			0.106050i
$924$	−8.62839	−	1.05406i	−0.283853	−	0.0346759i
$925$	0.254763	−	0.254763i	0.00837657	−	0.00837657i
$926$	−54.6270	−	54.6270i	−1.79516	−	1.79516i
$927$	0.271653	−	1.09527i	0.00892224	−	0.0359733i
$928$	29.6008	+	31.5147i	0.971695	+	1.03452i
$929$		−	24.5237i		−	0.804598i	−0.915508	−	0.402299i	$-0.868211\pi$
$929$		−	24.5237i		−	0.804598i	0.915508	−	0.402299i	$-0.131789\pi$
$930$	−14.1884	+	11.0992i	−0.465256	+	0.363958i
$931$	2.97353	+	2.97353i	0.0974536	+	0.0974536i
$932$	60.1687			1.97089
$933$	5.94509	−	48.6659i	0.194634	−	1.59325i
$934$		−	70.1445i		−	2.29520i
$935$			1.71900i			0.0562175i
$936$	0.450666	+	0.747952i	0.0147305	+	0.0244476i
$937$			22.3297i			0.729480i	0.931109	+	0.364740i	$0.118842\pi$
$937$			22.3297i			0.729480i	−0.931109	+	0.364740i	$0.881158\pi$
$938$	−22.6266	−	22.6266i	−0.738784	−	0.738784i
$939$	14.0280	−	10.9738i	0.457787	−	0.358115i
$940$	−13.6945	+	13.6945i	−0.446665	+	0.446665i
$941$	−8.30153			−0.270622			−0.135311	−	0.990803i	$-0.543203\pi$
$941$	−8.30153			−0.270622			−0.135311	+	0.990803i	$0.543203\pi$
$942$	−1.07350	−	1.37228i	−0.0349766	−	0.0447114i
$943$	0.208019	−	0.208019i	0.00677404	−	0.00677404i
$944$			3.04705i			0.0991731i
$945$	2.78037	+	6.21398i	0.0904454	+	0.202141i
$946$	−12.9723	+	12.9723i	−0.421766	+	0.421766i
$947$	34.6700	−	34.6700i	1.12663	−	1.12663i	0.135903	−	0.990722i	$-0.456606\pi$
$947$	34.6700	−	34.6700i	1.12663	−	1.12663i	0.990722	−	0.135903i	$-0.0433936\pi$
$948$	1.48403	−	12.1481i	0.0481989	−	0.394551i
$949$	3.05530	+	3.05530i	0.0991792	+	0.0991792i
$950$	1.67541			0.0543574
$951$	20.6508	+	2.52273i	0.669647	+	0.0818050i
$952$	−1.29730			−0.0420458
$953$			23.4267i			0.758866i	0.925219	+	0.379433i	$0.123881\pi$
$953$			23.4267i			0.758866i	−0.925219	+	0.379433i	$0.876119\pi$
$954$	34.5460	−	20.8151i	1.11847	−	0.673914i
$955$	1.13648	−	1.13648i	0.0367756	−	0.0367756i
$956$	34.5885			1.11867
$957$	14.5252	+	2.23784i	0.469532	+	0.0723392i
$958$	70.9753			2.29311
$959$	−8.14303	+	8.14303i	−0.262952	+	0.262952i
$960$	−11.7363	−	15.0028i	−0.378789	−	0.484214i
$961$		−	6.58929i		−	0.212558i
$962$	−0.243228			−0.00784199
$963$	13.7179	+	3.40238i	0.442054	+	0.109640i
$964$	−30.7782			−0.991301
$965$	9.68489	+	9.68489i	0.311768	+	0.311768i
$966$	9.01601	+	1.10141i	0.290085	+	0.0354372i
$967$	20.0087	−	20.0087i	0.643436	−	0.643436i	−0.307962	−	0.951399i	$-0.599647\pi$
$967$	20.0087	−	20.0087i	0.643436	−	0.643436i	0.951399	+	0.307962i	$0.0996471\pi$
$968$	−5.46632	+	5.46632i	−0.175694	+	0.175694i
$969$	1.18459	−	0.926672i	0.0380544	−	0.0297690i
$970$		−	37.9083i		−	1.21716i
$971$	−31.9016	+	31.9016i	−1.02377	+	1.02377i	−0.0240599	+	0.999711i	$0.507659\pi$
$971$	−31.9016	+	31.9016i	−1.02377	+	1.02377i	−0.999711	+	0.0240599i	$0.992341\pi$
$972$	−6.69548	−	37.3020i	−0.214758	−	1.19646i
$973$	10.4448			0.334845
$974$	−37.6844	+	37.6844i	−1.20749	+	1.20749i
$975$	−0.342252	−	0.437509i	−0.0109608	−	0.0140115i
$976$	14.7552	+	14.7552i	0.472303	+	0.472303i
$977$		−	19.1885i		−	0.613896i	−0.951726	−	0.306948i	$-0.900692\pi$
$977$		−	19.1885i		−	0.613896i	0.951726	−	0.306948i	$-0.0993077\pi$
$978$	43.0327	+	55.0098i	1.37604	+	1.75902i
$979$		−	20.4495i		−	0.653568i
$980$		−	12.8452i		−	0.410325i
$981$	−42.6321	−	10.5738i	−1.36114	−	0.337595i
$982$	−23.7365			−0.757462
$983$	14.6004	+	14.6004i	0.465680	+	0.465680i	0.900512	−	0.434832i	$-0.143192\pi$
$983$	14.6004	+	14.6004i	0.465680	+	0.465680i	−0.434832	+	0.900512i	$0.643192\pi$
$984$	−0.149855	−	0.191563i	−0.00477720	−	0.00610681i
$985$			12.8295i			0.408781i
$986$	12.3614	+	0.387104i	0.393666	+	0.0123279i
$987$	17.9434	+	2.19199i	0.571145	+	0.0697719i
$988$	−0.438797	−	0.438797i	−0.0139600	−	0.0139600i
$989$	7.43700	−	7.43700i	0.236483	−	0.236483i
$990$	−9.65769	−	2.39534i	−0.306941	−	0.0761289i
$991$			57.5391i			1.82779i	0.405952	+	0.913894i	$0.366940\pi$
$991$			57.5391i			1.82779i	−0.405952	+	0.913894i	$0.633060\pi$
$992$	−39.6680			−1.25946
$993$	−1.00210	+	8.20309i	−0.0318007	+	0.260317i
$994$	19.5915	−	19.5915i	0.621404	−	0.621404i
$995$	2.61214			0.0828105
$996$	23.2242	−	18.1677i	0.735887	−	0.575666i
$997$	−2.27654	−	2.27654i	−0.0720989	−	0.0720989i	0.670138	−	0.742237i	$-0.266235\pi$
$997$	−2.27654	−	2.27654i	−0.0720989	−	0.0720989i	−0.742237	+	0.670138i	$0.766235\pi$
$998$	9.10283	+	9.10283i	0.288145	+	0.288145i
$999$	1.74901	+	0.667688i	0.0553362	+	0.0211247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.41.3	✓	36
3.2	odd	2		435.2.q.d.41.16	yes	36
29.17	odd	4		435.2.q.d.191.16	yes	36
87.17	even	4	inner	435.2.q.c.191.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.3	✓	36	1.1	even	1	trivial
435.2.q.c.191.3	yes	36	87.17	even	4	inner
435.2.q.d.41.16	yes	36	3.2	odd	2
435.2.q.d.191.16	yes	36	29.17	odd	4

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.48848 + 1.48848i) q^{2} +(-1.36422 + 1.06719i) q^{3} -2.43117i q^{4} -1.00000 q^{5} +(0.442117 - 3.61912i) q^{6} -1.31013 q^{7} +(0.641785 + 0.641785i) q^{8} +(0.722191 - 2.91178i) q^{9} +O(q^{10})\)	\(q+(-1.48848 + 1.48848i) q^{2} +(-1.36422 + 1.06719i) q^{3} -2.43117i q^{4} -1.00000 q^{5} +(0.442117 - 3.61912i) q^{6} -1.31013 q^{7} +(0.641785 + 0.641785i) q^{8} +(0.722191 - 2.91178i) q^{9} +(1.48848 - 1.48848i) q^{10} +(1.11414 - 1.11414i) q^{11} +(2.59453 + 3.31665i) q^{12} +0.320703i q^{13} +(1.95011 - 1.95011i) q^{14} +(1.36422 - 1.06719i) q^{15} +2.95176 q^{16} +(0.771447 - 0.771447i) q^{17} +(3.25916 + 5.40910i) q^{18} +(-0.562790 - 0.562790i) q^{19} +2.43117i q^{20} +(1.78731 - 1.39817i) q^{21} +3.31677i q^{22} -1.90150i q^{23} +(-1.56045 - 0.190626i) q^{24} +1.00000 q^{25} +(-0.477361 - 0.477361i) q^{26} +(2.12220 + 4.74302i) q^{27} +3.18515i q^{28} +(0.168557 - 5.38253i) q^{29} +(-0.442117 + 3.61912i) q^{30} +(3.49362 + 3.49362i) q^{31} +(-5.67722 + 5.67722i) q^{32} +(-0.330928 + 2.70894i) q^{33} +2.29657i q^{34} +1.31013 q^{35} +(-7.07901 - 1.75577i) q^{36} +(0.254763 - 0.254763i) q^{37} +1.67541 q^{38} +(-0.342252 - 0.437509i) q^{39} +(-0.641785 - 0.641785i) q^{40} +(0.109398 + 0.109398i) q^{41} +(-0.579232 + 4.74153i) q^{42} +(3.91113 + 3.91113i) q^{43} +(-2.70867 - 2.70867i) q^{44} +(-0.722191 + 2.91178i) q^{45} +(2.83035 + 2.83035i) q^{46} +(5.63289 + 5.63289i) q^{47} +(-4.02685 + 3.15010i) q^{48} -5.28355 q^{49} +(-1.48848 + 1.48848i) q^{50} +(-0.229139 + 1.87571i) q^{51} +0.779682 q^{52} -6.38664i q^{53} +(-10.2188 - 3.90104i) q^{54} +(-1.11414 + 1.11414i) q^{55} +(-0.840823 - 0.840823i) q^{56} +(1.36838 + 0.167163i) q^{57} +(7.76091 + 8.26270i) q^{58} +1.03228i q^{59} +(-2.59453 - 3.31665i) q^{60} +(4.99878 + 4.99878i) q^{61} -10.4004 q^{62} +(-0.946166 + 3.81481i) q^{63} -10.9974i q^{64} -0.320703i q^{65} +(-3.53964 - 4.52480i) q^{66} -11.6027i q^{67} +(-1.87552 - 1.87552i) q^{68} +(2.02927 + 2.59406i) q^{69} +(-1.95011 + 1.95011i) q^{70} +10.0463 q^{71} +(2.33223 - 1.40524i) q^{72} +(9.52688 - 9.52688i) q^{73} +0.758422i q^{74} +(-1.36422 + 1.06719i) q^{75} +(-1.36824 + 1.36824i) q^{76} +(-1.45968 + 1.45968i) q^{77} +(1.16066 + 0.141788i) q^{78} +(-2.05510 - 2.05510i) q^{79} -2.95176 q^{80} +(-7.95688 - 4.20572i) q^{81} -0.325673 q^{82} -7.00231i q^{83} +(-3.39918 - 4.34525i) q^{84} +(-0.771447 + 0.771447i) q^{85} -11.6433 q^{86} +(5.51425 + 7.52283i) q^{87} +1.43008 q^{88} +(9.17721 - 9.17721i) q^{89} +(-3.25916 - 5.40910i) q^{90} -0.420163i q^{91} -4.62286 q^{92} +(-8.49443 - 1.03769i) q^{93} -16.7689 q^{94} +(0.562790 + 0.562790i) q^{95} +(1.68628 - 13.8037i) q^{96} +(12.7339 - 12.7339i) q^{97} +(7.86448 - 7.86448i) q^{98} +(-2.43951 - 4.04876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

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