LMFDB - Embedded newform 775.2.j.a.156.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(156,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("775.156");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.j (of order $5$, degree $4$, 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:	$6.18840615665$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			156.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	775.156
Dual form			775.2.j.a.621.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 + 1.90211i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-5.23607 - 3.80423i) q^{6} -0.236068 q^{7} +(2.30902 - 7.10642i) q^{9} +O(q^{10})$	\(q+(0.618034 + 1.90211i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-5.23607 - 3.80423i) q^{6} -0.236068 q^{7} +(2.30902 - 7.10642i) q^{9} -4.47214 q^{10} +(-1.19098 - 3.66547i) q^{11} +(2.00000 - 6.15537i) q^{12} +(0.736068 - 2.26538i) q^{13} +(-0.145898 - 0.449028i) q^{14} +(-2.23607 - 6.88191i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.42705 - 2.48990i) q^{17} +14.9443 q^{18} +(-3.61803 - 2.62866i) q^{19} +(-1.38197 - 4.25325i) q^{20} +(0.618034 - 0.449028i) q^{21} +(6.23607 - 4.53077i) q^{22} +(1.16312 + 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +4.76393 q^{26} +(4.47214 + 13.7638i) q^{27} +(0.381966 - 0.277515i) q^{28} +(-1.80902 + 1.31433i) q^{29} +(11.7082 - 8.50651i) q^{30} +(-0.809017 - 0.587785i) q^{31} -8.00000 q^{32} +(10.0902 + 7.33094i) q^{33} +(2.61803 - 8.05748i) q^{34} +(0.163119 - 0.502029i) q^{35} +(4.61803 + 14.2128i) q^{36} +(-0.336881 + 1.03681i) q^{37} +(2.76393 - 8.50651i) q^{38} +(2.38197 + 7.33094i) q^{39} +(-0.336881 + 1.03681i) q^{41} +(1.23607 + 0.898056i) q^{42} +5.47214 q^{43} +(6.23607 + 4.53077i) q^{44} +(13.5172 + 9.82084i) q^{45} +(-6.09017 + 4.42477i) q^{46} +(-8.85410 + 6.43288i) q^{47} +(-4.00000 - 12.3107i) q^{48} -6.94427 q^{49} +(3.09017 - 9.51057i) q^{50} +13.7082 q^{51} +(1.47214 + 4.53077i) q^{52} +(9.35410 - 6.79615i) q^{53} +(-23.4164 + 17.0130i) q^{54} +8.61803 q^{55} +14.4721 q^{57} +(-3.61803 - 2.62866i) q^{58} +(-2.39919 + 7.38394i) q^{59} +(11.7082 + 8.50651i) q^{60} +(-4.54508 - 13.9883i) q^{61} +(0.618034 - 1.90211i) q^{62} +(-0.545085 + 1.67760i) q^{63} +(-2.47214 - 7.60845i) q^{64} +(4.30902 + 3.13068i) q^{65} +(-7.70820 + 23.7234i) q^{66} +(-7.73607 - 5.62058i) q^{67} +8.47214 q^{68} +(-9.85410 - 7.15942i) q^{69} +1.05573 q^{70} +(-2.73607 + 1.98787i) q^{71} +(1.59017 + 4.89404i) q^{73} -2.18034 q^{74} +16.1803 q^{75} +8.94427 q^{76} +(0.281153 + 0.865300i) q^{77} +(-12.4721 + 9.06154i) q^{78} +(-6.54508 + 4.75528i) q^{79} +(-7.23607 - 5.25731i) q^{80} +(-19.7533 - 14.3516i) q^{81} -2.18034 q^{82} +(-3.73607 - 2.71441i) q^{83} +(-0.472136 + 1.45309i) q^{84} +(7.66312 - 5.56758i) q^{85} +(3.38197 + 10.4086i) q^{86} +(2.23607 - 6.88191i) q^{87} +(-1.01722 - 3.13068i) q^{89} +(-10.3262 + 31.7809i) q^{90} +(-0.173762 + 0.534785i) q^{91} +(-6.09017 - 4.42477i) q^{92} +3.23607 q^{93} +(-17.7082 - 12.8658i) q^{94} +(8.09017 - 5.87785i) q^{95} +(20.9443 - 15.2169i) q^{96} +(-8.59017 + 6.24112i) q^{97} +(-4.29180 - 13.2088i) q^{98} -28.7984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9} - 7 q^{11} + 8 q^{12} - 6 q^{13} - 14 q^{14} + 4 q^{16} - 7 q^{17} + 24 q^{18} - 10 q^{19} - 10 q^{20} - 2 q^{21} + 16 q^{22} - 11 q^{23} - 5 q^{25} + 28 q^{26} + 6 q^{28} - 5 q^{29} + 20 q^{30} - q^{31} - 32 q^{32} + 18 q^{33} + 6 q^{34} - 15 q^{35} + 14 q^{36} - 17 q^{37} + 20 q^{38} + 14 q^{39} - 17 q^{41} - 4 q^{42} + 4 q^{43} + 16 q^{44} + 25 q^{45} - 2 q^{46} - 22 q^{47} - 16 q^{48} + 8 q^{49} - 10 q^{50} + 28 q^{51} - 12 q^{52} + 24 q^{53} - 40 q^{54} + 30 q^{55} + 40 q^{57} - 10 q^{58} + 15 q^{59} + 20 q^{60} - 7 q^{61} - 2 q^{62} + 9 q^{63} + 8 q^{64} + 15 q^{65} - 4 q^{66} - 22 q^{67} + 16 q^{68} - 26 q^{69} + 40 q^{70} - 2 q^{71} - 16 q^{73} + 36 q^{74} + 20 q^{75} - 19 q^{77} - 32 q^{78} - 15 q^{79} - 20 q^{80} - 41 q^{81} + 36 q^{82} - 6 q^{83} + 16 q^{84} + 15 q^{85} + 18 q^{86} + 25 q^{89} - 10 q^{90} - 32 q^{91} - 2 q^{92} + 4 q^{93} - 44 q^{94} + 10 q^{95} + 48 q^{96} - 12 q^{97} - 44 q^{98} - 66 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9 - 7 * q^11 + 8 * q^12 - 6 * q^13 - 14 * q^14 + 4 * q^16 - 7 * q^17 + 24 * q^18 - 10 * q^19 - 10 * q^20 - 2 * q^21 + 16 * q^22 - 11 * q^23 - 5 * q^25 + 28 * q^26 + 6 * q^28 - 5 * q^29 + 20 * q^30 - q^31 - 32 * q^32 + 18 * q^33 + 6 * q^34 - 15 * q^35 + 14 * q^36 - 17 * q^37 + 20 * q^38 + 14 * q^39 - 17 * q^41 - 4 * q^42 + 4 * q^43 + 16 * q^44 + 25 * q^45 - 2 * q^46 - 22 * q^47 - 16 * q^48 + 8 * q^49 - 10 * q^50 + 28 * q^51 - 12 * q^52 + 24 * q^53 - 40 * q^54 + 30 * q^55 + 40 * q^57 - 10 * q^58 + 15 * q^59 + 20 * q^60 - 7 * q^61 - 2 * q^62 + 9 * q^63 + 8 * q^64 + 15 * q^65 - 4 * q^66 - 22 * q^67 + 16 * q^68 - 26 * q^69 + 40 * q^70 - 2 * q^71 - 16 * q^73 + 36 * q^74 + 20 * q^75 - 19 * q^77 - 32 * q^78 - 15 * q^79 - 20 * q^80 - 41 * q^81 + 36 * q^82 - 6 * q^83 + 16 * q^84 + 15 * q^85 + 18 * q^86 + 25 * q^89 - 10 * q^90 - 32 * q^91 - 2 * q^92 + 4 * q^93 - 44 * q^94 + 10 * q^95 + 48 * q^96 - 12 * q^97 - 44 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.618034	+	1.90211i	0.437016	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$2$	0.618034	+	1.90211i	0.437016	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.546027	+	0.837768i	$0.683860\pi$
$3$	−2.61803	+	1.90211i	−1.51152	+	1.09819i	−0.965496	+	0.260418i	$0.916140\pi$
$4$	−1.61803	+	1.17557i	−0.809017	+	0.587785i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$5$	−0.690983	+	2.12663i	−0.309017	+	0.951057i
$6$	−5.23607	−	3.80423i	−2.13762	−	1.55307i
$7$	−0.236068			−0.0892253			−0.0446127	−	0.999004i	$-0.514205\pi$
$7$	−0.236068			−0.0892253			−0.0446127	+	0.999004i	$0.514205\pi$
$8$		0			0
$9$	2.30902	−	7.10642i	0.769672	−	2.36881i
$10$	−4.47214			−1.41421
$11$	−1.19098	−	3.66547i	−0.359095	−	1.10518i	−0.953597	−	0.301086i	$-0.902651\pi$
$11$	−1.19098	−	3.66547i	−0.359095	−	1.10518i	0.594502	−	0.804094i	$-0.297349\pi$
$12$	2.00000	−	6.15537i	0.577350	−	1.77690i
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	−0.795599	−	0.605824i	$-0.792844\pi$
$13$	0.736068	−	2.26538i	0.204149	−	0.628305i	0.999747	−	0.0224806i	$-0.00715641\pi$
$14$	−0.145898	−	0.449028i	−0.0389929	−	0.120008i
$15$	−2.23607	−	6.88191i	−0.577350	−	1.77690i
$16$	−1.23607	+	3.80423i	−0.309017	+	0.951057i
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	0.0887115	−	0.996057i	$-0.471725\pi$
$17$	−3.42705	−	2.48990i	−0.831182	−	0.603889i	−0.919893	+	0.392168i	$0.871725\pi$
$18$	14.9443			3.52240
$19$	−3.61803	−	2.62866i	−0.830034	−	0.603055i	0.0895350	−	0.995984i	$-0.471462\pi$
$19$	−3.61803	−	2.62866i	−0.830034	−	0.603055i	−0.919569	+	0.392929i	$0.871462\pi$
$20$	−1.38197	−	4.25325i	−0.309017	−	0.951057i
$21$	0.618034	−	0.449028i	0.134866	−	0.0979859i
$22$	6.23607	−	4.53077i	1.32953	−	0.965963i
$23$	1.16312	+	3.57971i	0.242527	+	0.746422i	0.996033	+	0.0889808i	$0.0283610\pi$
$23$	1.16312	+	3.57971i	0.242527	+	0.746422i	−0.753506	+	0.657441i	$0.771639\pi$
$24$		0			0
$25$	−4.04508	−	2.93893i	−0.809017	−	0.587785i
$26$	4.76393			0.934284
$27$	4.47214	+	13.7638i	0.860663	+	2.64885i
$28$	0.381966	−	0.277515i	0.0721848	−	0.0524453i
$29$	−1.80902	+	1.31433i	−0.335926	+	0.244065i	−0.742941	−	0.669357i	$-0.766570\pi$
$29$	−1.80902	+	1.31433i	−0.335926	+	0.244065i	0.407015	+	0.913422i	$0.366570\pi$
$30$	11.7082	−	8.50651i	2.13762	−	1.55307i
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i
$31$	−0.809017	−	0.587785i	−0.145304	−	0.105569i
$32$	−8.00000			−1.41421
$33$	10.0902	+	7.33094i	1.75647	+	1.27615i
$34$	2.61803	−	8.05748i	0.448989	−	1.38185i
$35$	0.163119	−	0.502029i	0.0275721	−	0.0848583i
$36$	4.61803	+	14.2128i	0.769672	+	2.36881i
$37$	−0.336881	+	1.03681i	−0.0553829	+	0.170451i	−0.974922	−	0.222548i	$-0.928563\pi$
$37$	−0.336881	+	1.03681i	−0.0553829	+	0.170451i	0.919539	+	0.392999i	$0.128563\pi$
$38$	2.76393	−	8.50651i	0.448369	−	1.37994i
$39$	2.38197	+	7.33094i	0.381420	+	1.17389i
$40$		0			0
$41$	−0.336881	+	1.03681i	−0.0526120	+	0.161923i	−0.973910	−	0.226934i	$-0.927130\pi$
$41$	−0.336881	+	1.03681i	−0.0526120	+	0.161923i	0.921298	+	0.388857i	$0.127130\pi$
$42$	1.23607	+	0.898056i	0.190729	+	0.138573i
$43$	5.47214			0.834493			0.417246	−	0.908793i	$-0.362995\pi$
$43$	5.47214			0.834493			0.417246	+	0.908793i	$0.362995\pi$
$44$	6.23607	+	4.53077i	0.940123	+	0.683039i
$45$	13.5172	+	9.82084i	2.01503	+	1.46400i
$46$	−6.09017	+	4.42477i	−0.897947	+	0.652396i
$47$	−8.85410	+	6.43288i	−1.29150	+	0.938332i	−0.999835	−	0.0181871i	$-0.994211\pi$
$47$	−8.85410	+	6.43288i	−1.29150	+	0.938332i	−0.291669	+	0.956519i	$0.594211\pi$
$48$	−4.00000	−	12.3107i	−0.577350	−	1.77690i
$49$	−6.94427			−0.992039
$50$	3.09017	−	9.51057i	0.437016	−	1.34500i
$51$	13.7082			1.91953
$52$	1.47214	+	4.53077i	0.204149	+	0.628305i
$53$	9.35410	−	6.79615i	1.28488	−	0.933523i	0.285196	−	0.958469i	$-0.407941\pi$
$53$	9.35410	−	6.79615i	1.28488	−	0.933523i	0.999689	+	0.0249458i	$0.00794133\pi$
$54$	−23.4164	+	17.0130i	−3.18657	+	2.31518i
$55$	8.61803			1.16206
$56$		0			0
$57$	14.4721			1.91688
$58$	−3.61803	−	2.62866i	−0.475071	−	0.345159i
$59$	−2.39919	+	7.38394i	−0.312348	+	0.961307i	0.664485	+	0.747302i	$0.268651\pi$
$59$	−2.39919	+	7.38394i	−0.312348	+	0.961307i	−0.976833	+	0.214005i	$0.931349\pi$
$60$	11.7082	+	8.50651i	1.51152	+	1.09819i
$61$	−4.54508	−	13.9883i	−0.581938	−	1.79102i	−0.611232	−	0.791452i	$-0.709326\pi$
$61$	−4.54508	−	13.9883i	−0.581938	−	1.79102i	0.0292932	−	0.999571i	$-0.490674\pi$
$62$	0.618034	−	1.90211i	0.0784904	−	0.241569i
$63$	−0.545085	+	1.67760i	−0.0686743	+	0.211358i
$64$	−2.47214	−	7.60845i	−0.309017	−	0.951057i
$65$	4.30902	+	3.13068i	0.534468	+	0.388314i
$66$	−7.70820	+	23.7234i	−0.948814	+	2.92015i
$67$	−7.73607	−	5.62058i	−0.945111	−	0.686663i	0.00453440	−	0.999990i	$-0.498557\pi$
$67$	−7.73607	−	5.62058i	−0.945111	−	0.686663i	−0.949646	+	0.313326i	$0.898557\pi$
$68$	8.47214			1.02740
$69$	−9.85410	−	7.15942i	−1.18629	−	0.861893i
$70$	1.05573			0.126184
$71$	−2.73607	+	1.98787i	−0.324712	+	0.235917i	−0.738183	−	0.674600i	$-0.764316\pi$
$71$	−2.73607	+	1.98787i	−0.324712	+	0.235917i	0.413472	+	0.910517i	$0.364316\pi$
$72$		0			0
$73$	1.59017	+	4.89404i	0.186115	+	0.572804i	0.999966	−	0.00827030i	$-0.00263255\pi$
$73$	1.59017	+	4.89404i	0.186115	+	0.572804i	−0.813850	+	0.581074i	$0.802633\pi$
$74$	−2.18034			−0.253459
$75$	16.1803			1.86834
$76$	8.94427			1.02598
$77$	0.281153	+	0.865300i	0.0320404	+	0.0986101i
$78$	−12.4721	+	9.06154i	−1.41219	+	1.02602i
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	−0.891575	−	0.452873i	$-0.850399\pi$
$79$	−6.54508	+	4.75528i	−0.736380	+	0.535011i	0.155196	+	0.987884i	$0.450399\pi$
$80$	−7.23607	−	5.25731i	−0.809017	−	0.587785i
$81$	−19.7533	−	14.3516i	−2.19481	−	1.59462i
$82$	−2.18034			−0.240778
$83$	−3.73607	−	2.71441i	−0.410087	−	0.297945i	0.363550	−	0.931575i	$-0.381565\pi$
$83$	−3.73607	−	2.71441i	−0.410087	−	0.297945i	−0.773637	+	0.633629i	$0.781565\pi$
$84$	−0.472136	+	1.45309i	−0.0515143	+	0.158545i
$85$	7.66312	−	5.56758i	0.831182	−	0.603889i
$86$	3.38197	+	10.4086i	0.364687	+	1.12239i
$87$	2.23607	−	6.88191i	0.239732	−	0.737818i
$88$		0			0
$89$	−1.01722	−	3.13068i	−0.107825	−	0.331852i	0.882558	−	0.470204i	$-0.155820\pi$
$89$	−1.01722	−	3.13068i	−0.107825	−	0.331852i	−0.990383	+	0.138352i	$0.955820\pi$
$90$	−10.3262	+	31.7809i	−1.08848	+	3.35000i
$91$	−0.173762	+	0.534785i	−0.0182152	+	0.0560607i
$92$	−6.09017	−	4.42477i	−0.634944	−	0.461314i
$93$	3.23607			0.335565
$94$	−17.7082	−	12.8658i	−1.82646	−	1.32700i
$95$	8.09017	−	5.87785i	0.830034	−	0.603055i
$96$	20.9443	−	15.2169i	2.13762	−	1.55307i
$97$	−8.59017	+	6.24112i	−0.872200	+	0.633690i	−0.931176	−	0.364569i	$-0.881216\pi$
$97$	−8.59017	+	6.24112i	−0.872200	+	0.633690i	0.0589767	+	0.998259i	$0.481216\pi$
$98$	−4.29180	−	13.2088i	−0.433537	−	1.33429i
$99$	−28.7984			−2.89435
$100$	10.0000			1.00000
$101$	5.94427			0.591477			0.295739	−	0.955269i	$-0.404434\pi$
$101$	5.94427			0.591477			0.295739	+	0.955269i	$0.404434\pi$
$102$	8.47214	+	26.0746i	0.838866	+	2.58177i
$103$	−9.16312	+	6.65740i	−0.902869	+	0.655973i	−0.939201	−	0.343367i	$-0.888433\pi$
$103$	−9.16312	+	6.65740i	−0.902869	+	0.655973i	0.0363323	+	0.999340i	$0.488433\pi$
$104$		0			0
$105$	0.527864	+	1.62460i	0.0515143	+	0.158545i
$106$	18.7082	+	13.5923i	1.81710	+	1.32020i
$107$	−0.236068			−0.0228216			−0.0114108	−	0.999935i	$-0.503632\pi$
$107$	−0.236068			−0.0228216			−0.0114108	+	0.999935i	$0.503632\pi$
$108$	−23.4164	−	17.0130i	−2.25324	−	1.63708i
$109$	5.00000	−	15.3884i	0.478913	−	1.47394i	−0.361694	−	0.932297i	$-0.617801\pi$
$109$	5.00000	−	15.3884i	0.478913	−	1.47394i	0.840607	−	0.541646i	$-0.182199\pi$
$110$	5.32624	+	16.3925i	0.507837	+	1.56296i
$111$	−1.09017	−	3.35520i	−0.103474	−	0.318461i
$112$	0.291796	−	0.898056i	0.0275721	−	0.0848583i
$113$	−0.909830	+	2.80017i	−0.0855896	+	0.263418i	−0.984687	−	0.174331i	$-0.944224\pi$
$113$	−0.909830	+	2.80017i	−0.0855896	+	0.263418i	0.899098	+	0.437748i	$0.144224\pi$
$114$	8.94427	+	27.5276i	0.837708	+	2.57820i
$115$	−8.41641			−0.784834
$116$	1.38197	−	4.25325i	0.128312	−	0.394905i
$117$	−14.3992	−	10.4616i	−1.33121	−	0.967177i
$118$	−15.5279			−1.42946
$119$	0.809017	+	0.587785i	0.0741625	+	0.0538822i
$120$		0			0
$121$	−3.11803	+	2.26538i	−0.283458	+	0.205944i
$122$	23.7984	−	17.2905i	2.15460	−	1.56541i
$123$	−1.09017	−	3.35520i	−0.0982973	−	0.302528i
$124$	2.00000			0.179605
$125$	9.04508	−	6.57164i	0.809017	−	0.587785i
$126$	−3.52786			−0.314287
$127$	5.25329	+	16.1680i	0.466154	+	1.43467i	0.857525	+	0.514442i	$0.172001\pi$
$127$	5.25329	+	16.1680i	0.466154	+	1.43467i	−0.391371	+	0.920233i	$0.627999\pi$
$128$		0			0
$129$	−14.3262	+	10.4086i	−1.26135	+	0.916428i
$130$	−3.29180	+	10.1311i	−0.288710	+	0.888557i
$131$	14.1353	+	10.2699i	1.23500	+	0.897282i	0.997255	−	0.0740447i	$-0.0235907\pi$
$131$	14.1353	+	10.2699i	1.23500	+	0.897282i	0.237748	+	0.971327i	$0.423591\pi$
$132$	−24.9443			−2.17112
$133$	0.854102	+	0.620541i	0.0740600	+	0.0538078i
$134$	5.90983	−	18.1886i	0.510532	−	1.57125i
$135$	−32.3607			−2.78516
$136$		0			0
$137$	5.25329	−	16.1680i	0.448819	−	1.38132i	−0.429422	−	0.903104i	$-0.641283\pi$
$137$	5.25329	−	16.1680i	0.448819	−	1.38132i	0.878241	−	0.478218i	$-0.158717\pi$
$138$	7.52786	−	23.1684i	0.640814	−	1.97222i
$139$	−3.45492	−	10.6331i	−0.293042	−	0.901891i	−0.983872	−	0.178874i	$-0.942755\pi$
$139$	−3.45492	−	10.6331i	−0.293042	−	0.901891i	0.690830	−	0.723017i	$-0.257245\pi$
$140$	0.326238	+	1.00406i	0.0275721	+	0.0848583i
$141$	10.9443	−	33.6830i	0.921674	−	2.83662i
$142$	−5.47214	−	3.97574i	−0.459211	−	0.333637i
$143$	−9.18034			−0.767699
$144$	24.1803	+	17.5680i	2.01503	+	1.46400i
$145$	−1.54508	−	4.75528i	−0.128312	−	0.394905i
$146$	−8.32624	+	6.04937i	−0.689084	+	0.500649i
$147$	18.1803	−	13.2088i	1.49949	−	1.08944i
$148$	−0.673762	−	2.07363i	−0.0553829	−	0.170451i
$149$	7.03444			0.576284			0.288142	−	0.957588i	$-0.406962\pi$
$149$	7.03444			0.576284			0.288142	+	0.957588i	$0.406962\pi$
$150$	10.0000	+	30.7768i	0.816497	+	2.51292i
$151$	−13.0000			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$152$		0			0
$153$	−25.6074	+	18.6049i	−2.07023	+	1.50411i
$154$	−1.47214	+	1.06957i	−0.118628	+	0.0861884i
$155$	1.80902	−	1.31433i	0.145304	−	0.105569i
$156$	−12.4721	−	9.06154i	−0.998570	−	0.725504i
$157$	−18.6525			−1.48863			−0.744315	−	0.667829i	$-0.767224\pi$
$157$	−18.6525			−1.48863			−0.744315	+	0.667829i	$0.767224\pi$
$158$	−13.0902	−	9.51057i	−1.04140	−	0.756620i
$159$	−11.5623	+	35.5851i	−0.916951	+	2.82208i
$160$	5.52786	−	17.0130i	0.437016	−	1.34500i
$161$	−0.274575	−	0.845055i	−0.0216396	−	0.0665997i
$162$	15.0902	−	46.4428i	1.18560	−	3.64889i
$163$	3.92705	−	12.0862i	0.307590	−	0.946666i	−0.671108	−	0.741360i	$-0.734181\pi$
$163$	3.92705	−	12.0862i	0.307590	−	0.946666i	0.978698	−	0.205306i	$-0.0658189\pi$
$164$	−0.673762	−	2.07363i	−0.0526120	−	0.161923i
$165$	−22.5623	+	16.3925i	−1.75647	+	1.27615i
$166$	2.85410	−	8.78402i	0.221521	−	0.681772i
$167$	0.881966	+	0.640786i	0.0682486	+	0.0495855i	0.621386	−	0.783504i	$-0.286570\pi$
$167$	0.881966	+	0.640786i	0.0682486	+	0.0495855i	−0.553138	+	0.833090i	$0.686570\pi$
$168$		0			0
$169$	5.92705	+	4.30625i	0.455927	+	0.331250i
$170$	15.3262	+	11.1352i	1.17547	+	0.854028i
$171$	−27.0344	+	19.6417i	−2.06738	+	1.50204i
$172$	−8.85410	+	6.43288i	−0.675119	+	0.490503i
$173$	7.70820	+	23.7234i	0.586044	+	1.80366i	0.595037	+	0.803698i	$0.297137\pi$
$173$	7.70820	+	23.7234i	0.586044	+	1.80366i	−0.00899341	+	0.999960i	$0.502863\pi$
$174$	14.4721			1.09713
$175$	0.954915	+	0.693786i	0.0721848	+	0.0524453i
$176$	15.4164			1.16206
$177$	−7.76393	−	23.8949i	−0.583573	−	1.79605i
$178$	5.32624	−	3.86974i	0.399218	−	0.290049i
$179$	−14.8992	+	10.8249i	−1.11362	+	0.809090i	−0.983230	−	0.182373i	$-0.941622\pi$
$179$	−14.8992	+	10.8249i	−1.11362	+	0.809090i	−0.130388	+	0.991463i	$0.541622\pi$
$180$	−33.4164			−2.49071
$181$	6.30902	+	4.58377i	0.468946	+	0.340709i	0.797030	−	0.603939i	$-0.206403\pi$
$181$	6.30902	+	4.58377i	0.468946	+	0.340709i	−0.328085	+	0.944648i	$0.606403\pi$
$182$	−1.12461			−0.0833618
$183$	38.5066	+	27.9767i	2.84649	+	2.06809i
$184$		0			0
$185$	−1.97214	−	1.43284i	−0.144994	−	0.105345i
$186$	2.00000	+	6.15537i	0.146647	+	0.451333i
$187$	−5.04508	+	15.5272i	−0.368933	+	1.13546i
$188$	6.76393	−	20.8172i	0.493310	−	1.51825i
$189$	−1.05573	−	3.24920i	−0.0767929	−	0.236344i
$190$	16.1803	+	11.7557i	1.17385	+	0.852848i
$191$	5.25329	−	16.1680i	0.380115	−	1.16987i	−0.559848	−	0.828595i	$-0.689140\pi$
$191$	5.25329	−	16.1680i	0.380115	−	1.16987i	0.939963	−	0.341277i	$-0.110860\pi$
$192$	20.9443	+	15.2169i	1.51152	+	1.09819i
$193$	−9.32624			−0.671317			−0.335659	−	0.941984i	$-0.608959\pi$
$193$	−9.32624			−0.671317			−0.335659	+	0.941984i	$0.608959\pi$
$194$	−17.1803	−	12.4822i	−1.23348	−	0.896173i
$195$	−17.2361			−1.23430
$196$	11.2361	−	8.16348i	0.802576	−	0.583106i
$197$	7.85410	−	5.70634i	0.559582	−	0.406560i	−0.271724	−	0.962375i	$-0.587594\pi$
$197$	7.85410	−	5.70634i	0.559582	−	0.406560i	0.831306	+	0.555815i	$0.187594\pi$
$198$	−17.7984	−	54.7778i	−1.26488	−	3.89289i
$199$	−15.6525			−1.10957			−0.554787	−	0.831992i	$-0.687200\pi$
$199$	−15.6525			−1.10957			−0.554787	+	0.831992i	$0.687200\pi$
$200$		0			0
$201$	30.9443			2.18264
$202$	3.67376	+	11.3067i	0.258485	+	0.795535i
$203$	0.427051	−	0.310271i	0.0299731	−	0.0217767i
$204$	−22.1803	+	16.1150i	−1.55293	+	1.12827i
$205$	−1.97214	−	1.43284i	−0.137740	−	0.100074i
$206$	−18.3262	−	13.3148i	−1.27685	−	0.927685i
$207$	28.1246			1.95480
$208$	7.70820	+	5.60034i	0.534468	+	0.388314i
$209$	−5.32624	+	16.3925i	−0.368424	+	1.13389i
$210$	−2.76393	+	2.00811i	−0.190729	+	0.138573i
$211$	2.69098	+	8.28199i	0.185255	+	0.570156i	0.999953	−	0.00972984i	$-0.00309715\pi$
$211$	2.69098	+	8.28199i	0.185255	+	0.570156i	−0.814698	+	0.579886i	$0.803097\pi$
$212$	−7.14590	+	21.9928i	−0.490782	+	1.51047i
$213$	3.38197	−	10.4086i	0.231728	−	0.713187i
$214$	−0.145898	−	0.449028i	−0.00997338	−	0.0306949i
$215$	−3.78115	+	11.6372i	−0.257872	+	0.793650i
$216$		0			0
$217$	0.190983	+	0.138757i	0.0129648	+	0.00941946i
$218$	32.3607			2.19174
$219$	−13.4721	−	9.78808i	−0.910363	−	0.661417i
$220$	−13.9443	+	10.1311i	−0.940123	+	0.683039i
$221$	−8.16312	+	5.93085i	−0.549111	+	0.398952i
$222$	5.70820	−	4.14725i	0.383110	−	0.278345i
$223$	−5.01722	−	15.4414i	−0.335978	−	1.03403i	−0.966238	−	0.257650i	$-0.917052\pi$
$223$	−5.01722	−	15.4414i	−0.335978	−	1.03403i	0.630260	−	0.776384i	$-0.282948\pi$
$224$	1.88854			0.126184
$225$	−30.2254	+	21.9601i	−2.01503	+	1.46400i
$226$	−5.88854			−0.391700
$227$	−3.48936	−	10.7391i	−0.231597	−	0.712782i	−0.997555	−	0.0698908i	$-0.977735\pi$
$227$	−3.48936	−	10.7391i	−0.231597	−	0.712782i	0.765958	−	0.642891i	$-0.222265\pi$
$228$	−23.4164	+	17.0130i	−1.55079	+	1.12671i
$229$	20.0623	−	14.5761i	1.32575	−	0.963217i	0.325913	−	0.945400i	$-0.394328\pi$
$229$	20.0623	−	14.5761i	1.32575	−	0.963217i	0.999841	−	0.0178173i	$-0.00567173\pi$
$230$	−5.20163	−	16.0090i	−0.342985	−	1.05560i
$231$	−2.38197	−	1.73060i	−0.156722	−	0.113865i
$232$		0			0
$233$	8.23607	+	5.98385i	0.539563	+	0.392015i	0.823923	−	0.566702i	$-0.191781\pi$
$233$	8.23607	+	5.98385i	0.539563	+	0.392015i	−0.284360	+	0.958718i	$0.591781\pi$
$234$	11.0000	−	33.8545i	0.719092	−	2.21314i
$235$	−7.56231	−	23.2744i	−0.493310	−	1.51825i
$236$	−4.79837	−	14.7679i	−0.312348	−	0.961307i
$237$	8.09017	−	24.8990i	0.525513	−	1.61736i
$238$	−0.618034	+	1.90211i	−0.0400612	+	0.123296i
$239$	−3.61803	−	11.1352i	−0.234031	−	0.720274i	−0.997248	−	0.0741319i	$-0.976381\pi$
$239$	−3.61803	−	11.1352i	−0.234031	−	0.720274i	0.763217	−	0.646142i	$-0.223619\pi$
$240$	28.9443			1.86834
$241$	−6.19098	+	19.0539i	−0.398796	+	1.22737i	0.527169	+	0.849760i	$0.323253\pi$
$241$	−6.19098	+	19.0539i	−0.398796	+	1.22737i	−0.925965	+	0.377608i	$0.876747\pi$
$242$	−6.23607	−	4.53077i	−0.400870	−	0.291249i
$243$	35.5967			2.28353
$244$	23.7984	+	17.2905i	1.52353	+	1.10691i
$245$	4.79837	−	14.7679i	0.306557	−	0.943485i
$246$	5.70820	−	4.14725i	0.363942	−	0.264419i
$247$	−8.61803	+	6.26137i	−0.548352	+	0.398401i
$248$		0			0
$249$	14.9443			0.947055
$250$	18.0902	+	13.1433i	1.14412	+	0.831254i
$251$	3.90983			0.246786			0.123393	−	0.992358i	$-0.460622\pi$
$251$	3.90983			0.246786			0.123393	+	0.992358i	$0.460622\pi$
$252$	−1.09017	−	3.35520i	−0.0686743	−	0.211358i
$253$	11.7361	−	8.52675i	0.737840	−	0.536072i
$254$	−27.5066	+	19.9847i	−1.72592	+	1.25395i
$255$	−9.47214	+	29.1522i	−0.593168	+	1.82558i
$256$	−12.9443	−	9.40456i	−0.809017	−	0.587785i
$257$	−27.7984			−1.73401			−0.867007	−	0.498295i	$-0.833960\pi$
$257$	−27.7984			−1.73401			−0.867007	+	0.498295i	$0.833960\pi$
$258$	−28.6525	−	20.8172i	−1.78383	−	1.29602i
$259$	0.0795268	−	0.244758i	0.00494156	−	0.0152085i
$260$	−10.6525			−0.660639
$261$	5.16312	+	15.8904i	0.319589	+	0.983594i
$262$	−10.7984	+	33.2340i	−0.667126	+	2.05320i
$263$	0.309017	−	0.951057i	0.0190548	−	0.0586447i	−0.941077	−	0.338192i	$-0.890185\pi$
$263$	0.309017	−	0.951057i	0.0190548	−	0.0586447i	0.960132	+	0.279548i	$0.0901845\pi$
$264$		0			0
$265$	7.98936	+	24.5887i	0.490782	+	1.51047i
$266$	−0.652476	+	2.00811i	−0.0400059	+	0.123125i
$267$	8.61803	+	6.26137i	0.527415	+	0.383190i
$268$	19.1246			1.16822
$269$	12.6631	+	9.20029i	0.772084	+	0.560952i	0.902593	−	0.430495i	$-0.141661\pi$
$269$	12.6631	+	9.20029i	0.772084	+	0.560952i	−0.130509	+	0.991447i	$0.541661\pi$
$270$	−20.0000	−	61.5537i	−1.21716	−	3.74604i
$271$	−0.0729490	+	0.0530006i	−0.00443134	+	0.00321955i	−0.589999	−	0.807404i	$-0.700872\pi$
$271$	−0.0729490	+	0.0530006i	−0.00443134	+	0.00321955i	0.585567	+	0.810624i	$0.300872\pi$
$272$	13.7082	−	9.95959i	0.831182	−	0.603889i
$273$	−0.562306	−	1.73060i	−0.0340323	−	0.104741i
$274$	34.0000			2.05402
$275$	−5.95492	+	18.3273i	−0.359095	+	1.10518i
$276$	24.3607			1.46634
$277$	0.517221	+	1.59184i	0.0310768	+	0.0956445i	0.965392	−	0.260804i	$-0.0839876\pi$
$277$	0.517221	+	1.59184i	0.0310768	+	0.0956445i	−0.934315	+	0.356448i	$0.883988\pi$
$278$	18.0902	−	13.1433i	1.08498	−	0.788281i
$279$	−6.04508	+	4.39201i	−0.361910	+	0.262943i
$280$		0			0
$281$	−19.6074	−	14.2456i	−1.16968	−	0.849821i	−0.178708	−	0.983902i	$-0.557192\pi$
$281$	−19.6074	−	14.2456i	−1.16968	−	0.849821i	−0.990970	+	0.134081i	$0.957192\pi$
$282$	70.8328			4.21803
$283$	−5.80902	−	4.22050i	−0.345310	−	0.250883i	0.401589	−	0.915820i	$-0.368458\pi$
$283$	−5.80902	−	4.22050i	−0.345310	−	0.250883i	−0.746899	+	0.664938i	$0.768458\pi$
$284$	2.09017	−	6.43288i	0.124029	−	0.381721i
$285$	−10.0000	+	30.7768i	−0.592349	+	1.82306i
$286$	−5.67376	−	17.4620i	−0.335497	−	1.03255i
$287$	0.0795268	−	0.244758i	0.00469432	−	0.0144476i
$288$	−18.4721	+	56.8514i	−1.08848	+	3.35000i
$289$	0.291796	+	0.898056i	0.0171645	+	0.0528268i
$290$	8.09017	−	5.87785i	0.475071	−	0.345159i
$291$	10.6180	−	32.6789i	0.622440	−	1.91567i
$292$	−8.32624	−	6.04937i	−0.487256	−	0.354012i
$293$	−9.32624			−0.544845			−0.272422	−	0.962178i	$-0.587825\pi$
$293$	−9.32624			−0.544845			−0.272422	+	0.962178i	$0.587825\pi$
$294$	36.3607	+	26.4176i	2.12060	+	1.54070i
$295$	−14.0451	−	10.2044i	−0.817736	−	0.594120i
$296$		0			0
$297$	45.1246	−	32.7849i	2.61840	−	1.90238i
$298$	4.34752	+	13.3803i	0.251845	+	0.775100i
$299$	8.96556			0.518492
$300$	−26.1803	+	19.0211i	−1.51152	+	1.09819i
$301$	−1.29180			−0.0744579
$302$	−8.03444	−	24.7275i	−0.462330	−	1.42291i
$303$	−15.5623	+	11.3067i	−0.894031	+	0.649552i
$304$	14.4721	−	10.5146i	0.830034	−	0.603055i
$305$	32.8885			1.88319
$306$	−51.2148	−	37.2097i	−2.92775	−	2.12714i
$307$	−16.0902			−0.918315			−0.459157	−	0.888355i	$-0.651849\pi$
$307$	−16.0902			−0.918315			−0.459157	+	0.888355i	$0.651849\pi$
$308$	−1.47214	−	1.06957i	−0.0838827	−	0.0609444i
$309$	11.3262	−	34.8586i	0.644327	−	1.98304i
$310$	3.61803	+	2.62866i	0.205491	+	0.149298i
$311$	10.2918	+	31.6749i	0.583594	+	1.79612i	0.604844	+	0.796344i	$0.293236\pi$
$311$	10.2918	+	31.6749i	0.583594	+	1.79612i	−0.0212496	+	0.999774i	$0.506764\pi$
$312$		0			0
$313$	2.74671	−	8.45351i	0.155253	−	0.477820i	−0.842933	−	0.538018i	$-0.819173\pi$
$313$	2.74671	−	8.45351i	0.155253	−	0.477820i	0.998186	+	0.0601978i	$0.0191731\pi$
$314$	−11.5279	−	35.4791i	−0.650555	−	2.00220i
$315$	−3.19098	−	2.31838i	−0.179792	−	0.130626i
$316$	5.00000	−	15.3884i	0.281272	−	0.865666i
$317$	26.3713	+	19.1599i	1.48116	+	1.07613i	0.977180	+	0.212412i	$0.0681318\pi$
$317$	26.3713	+	19.1599i	1.48116	+	1.07613i	0.503981	+	0.863715i	$0.331868\pi$
$318$	−74.8328			−4.19642
$319$	6.97214	+	5.06555i	0.390365	+	0.283617i
$320$	17.8885			1.00000
$321$	0.618034	−	0.449028i	0.0344953	−	0.0250623i
$322$	1.43769	−	1.04455i	0.0801196	−	0.0582103i
$323$	5.85410	+	18.0171i	0.325731	+	1.00250i
$324$	48.8328			2.71293
$325$	−9.63525	+	7.00042i	−0.534468	+	0.388314i
$326$	25.4164			1.40768
$327$	16.1803	+	49.7980i	0.894775	+	2.75383i
$328$		0			0
$329$	2.09017	−	1.51860i	0.115235	−	0.0837230i
$330$	−45.1246	−	32.7849i	−2.48403	−	1.80475i
$331$	12.7533	+	9.26581i	0.700984	+	0.509295i	0.880253	−	0.474505i	$-0.157373\pi$
$331$	12.7533	+	9.26581i	0.700984	+	0.509295i	−0.179268	+	0.983800i	$0.557373\pi$
$332$	9.23607			0.506895
$333$	6.59017	+	4.78804i	0.361139	+	0.262383i
$334$	−0.673762	+	2.07363i	−0.0368666	+	0.113464i
$335$	17.2984	−	12.5680i	0.945111	−	0.686663i
$336$	0.944272	+	2.90617i	0.0515143	+	0.158545i
$337$	−9.18034	+	28.2542i	−0.500085	+	1.53910i	0.308794	+	0.951129i	$0.400074\pi$
$337$	−9.18034	+	28.2542i	−0.500085	+	1.53910i	−0.808879	+	0.587975i	$0.799926\pi$
$338$	−4.52786	+	13.9353i	−0.246283	+	0.757982i
$339$	−2.94427	−	9.06154i	−0.159911	−	0.492155i
$340$	−5.85410	+	18.0171i	−0.317483	+	0.977113i
$341$	−1.19098	+	3.66547i	−0.0644953	+	0.198496i
$342$	−54.0689	−	39.2833i	−2.92371	−	2.12420i
$343$	3.29180			0.177740
$344$		0			0
$345$	22.0344	−	16.0090i	1.18629	−	0.861893i
$346$	−40.3607	+	29.3238i	−2.16980	+	1.57645i
$347$	−20.7254	+	15.0579i	−1.11260	+	0.808351i	−0.983071	−	0.183225i	$-0.941346\pi$
$347$	−20.7254	+	15.0579i	−1.11260	+	0.808351i	−0.129528	+	0.991576i	$0.541346\pi$
$348$	4.47214	+	13.7638i	0.239732	+	0.737818i
$349$	−8.29180			−0.443850			−0.221925	−	0.975064i	$-0.571234\pi$
$349$	−8.29180			−0.443850			−0.221925	+	0.975064i	$0.571234\pi$
$350$	−0.729490	+	2.24514i	−0.0389929	+	0.120008i
$351$	34.4721			1.83999
$352$	9.52786	+	29.3238i	0.507837	+	1.56296i
$353$	−21.7254	+	15.7844i	−1.15633	+	0.840121i	−0.989309	−	0.145833i	$-0.953414\pi$
$353$	−21.7254	+	15.7844i	−1.15633	+	0.840121i	−0.167018	+	0.985954i	$0.553414\pi$
$354$	40.6525	−	29.5358i	2.16065	−	1.56981i
$355$	−2.33688	−	7.19218i	−0.124029	−	0.381721i
$356$	5.32624	+	3.86974i	0.282290	+	0.205096i
$357$	−3.23607			−0.171271
$358$	−29.7984	−	21.6498i	−1.57489	−	1.14423i
$359$	−4.79837	+	14.7679i	−0.253248	+	0.779419i	0.740921	+	0.671592i	$0.234389\pi$
$359$	−4.79837	+	14.7679i	−0.253248	+	0.779419i	−0.994170	+	0.107827i	$0.965611\pi$
$360$		0			0
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−4.81966	+	14.8334i	−0.253316	+	0.779626i
$363$	3.85410	−	11.8617i	0.202288	−	0.622578i
$364$	−0.347524	−	1.06957i	−0.0182152	−	0.0560607i
$365$	−11.5066			−0.602282
$366$	−29.4164	+	90.5344i	−1.53762	+	4.73231i
$367$	3.80902	+	2.76741i	0.198829	+	0.144458i	0.682745	−	0.730657i	$-0.260786\pi$
$367$	3.80902	+	2.76741i	0.198829	+	0.144458i	−0.483916	+	0.875114i	$0.660786\pi$
$368$	−15.0557			−0.784834
$369$	6.59017	+	4.78804i	0.343071	+	0.249255i
$370$	1.50658	−	4.63677i	0.0783233	−	0.241054i
$371$	−2.20820	+	1.60435i	−0.114644	+	0.0832939i
$372$	−5.23607	+	3.80423i	−0.271477	+	0.197240i
$373$	5.37132	+	16.5312i	0.278117	+	0.855955i	0.988378	+	0.152017i	$0.0485767\pi$
$373$	5.37132	+	16.5312i	0.278117	+	0.855955i	−0.710261	+	0.703938i	$0.751423\pi$
$374$	−32.6525			−1.68842
$375$	−11.1803	+	34.4095i	−0.577350	+	1.77690i
$376$		0			0
$377$	1.64590	+	5.06555i	0.0847681	+	0.260889i
$378$	5.52786	−	4.01623i	0.284323	−	0.206572i
$379$	−30.9164	+	22.4621i	−1.58807	+	1.15380i	−0.681438	+	0.731876i	$0.738645\pi$
$379$	−30.9164	+	22.4621i	−1.58807	+	1.15380i	−0.906631	+	0.421924i	$0.861355\pi$
$380$	−6.18034	+	19.0211i	−0.317045	+	0.975763i
$381$	−44.5066	−	32.3359i	−2.28014	−	1.65662i
$382$	34.0000			1.73959
$383$	3.92705	+	2.85317i	0.200663	+	0.145790i	0.683579	−	0.729876i	$-0.260422\pi$
$383$	3.92705	+	2.85317i	0.200663	+	0.145790i	−0.482916	+	0.875667i	$0.660422\pi$
$384$		0			0
$385$	−2.03444			−0.103685
$386$	−5.76393	−	17.7396i	−0.293376	−	0.902920i
$387$	12.6353	−	38.8873i	0.642286	−	1.97675i
$388$	6.56231	−	20.1967i	0.333151	−	1.02533i
$389$	−9.04508	−	27.8379i	−0.458604	−	1.41144i	−0.866851	−	0.498567i	$-0.833860\pi$
$389$	−9.04508	−	27.8379i	−0.458604	−	1.41144i	0.408247	−	0.912871i	$-0.366140\pi$
$390$	−10.6525	−	32.7849i	−0.539409	−	1.66013i
$391$	4.92705	−	15.1639i	0.249172	−	0.766872i
$392$		0			0
$393$	−56.5410			−2.85212
$394$	15.7082	+	11.4127i	0.791368	+	0.574962i
$395$	−5.59017	−	17.2048i	−0.281272	−	0.865666i
$396$	46.5967	−	33.8545i	2.34157	−	1.70125i
$397$	−31.2533	+	22.7068i	−1.56856	+	1.13962i	−0.640036	+	0.768345i	$0.721081\pi$
$397$	−31.2533	+	22.7068i	−1.56856	+	1.13962i	−0.928521	+	0.371279i	$0.878919\pi$
$398$	−9.67376	−	29.7728i	−0.484902	−	1.49237i
$399$	−3.41641			−0.171034
$400$	16.1803	−	11.7557i	0.809017	−	0.587785i
$401$	−11.6180			−0.580177			−0.290088	−	0.957000i	$-0.593685\pi$
$401$	−11.6180			−0.580177			−0.290088	+	0.957000i	$0.593685\pi$
$402$	19.1246	+	58.8595i	0.953849	+	2.93565i
$403$	−1.92705	+	1.40008i	−0.0959932	+	0.0697432i
$404$	−9.61803	+	6.98791i	−0.478515	+	0.347662i
$405$	44.1697	−	32.0912i	2.19481	−	1.59462i
$406$	0.854102	+	0.620541i	0.0423884	+	0.0307970i
$407$	4.20163			0.208267
$408$		0			0
$409$	2.23607	−	6.88191i	0.110566	−	0.340289i	−0.880430	−	0.474176i	$-0.842746\pi$
$409$	2.23607	−	6.88191i	0.110566	−	0.340289i	0.990997	+	0.133887i	$0.0427461\pi$
$410$	1.50658	−	4.63677i	0.0744046	−	0.228994i
$411$	17.0000	+	52.3206i	0.838548	+	2.58079i
$412$	7.00000	−	21.5438i	0.344865	−	1.06139i
$413$	0.566371	−	1.74311i	0.0278693	−	0.0857729i
$414$	17.3820	+	53.4962i	0.854277	+	2.62919i
$415$	8.35410	−	6.06961i	0.410087	−	0.297945i
$416$	−5.88854	+	18.1231i	−0.288710	+	0.888557i
$417$	29.2705	+	21.2663i	1.43338	+	1.04141i
$418$	−34.4721			−1.68609
$419$	10.1631	+	7.38394i	0.496501	+	0.360729i	0.807679	−	0.589623i	$-0.200724\pi$
$419$	10.1631	+	7.38394i	0.496501	+	0.360729i	−0.311178	+	0.950352i	$0.600724\pi$
$420$	−2.76393	−	2.00811i	−0.134866	−	0.0979859i
$421$	8.70820	−	6.32688i	0.424412	−	0.308353i	−0.354999	−	0.934867i	$-0.615519\pi$
$421$	8.70820	−	6.32688i	0.424412	−	0.308353i	0.779411	+	0.626514i	$0.215519\pi$
$422$	−14.0902	+	10.2371i	−0.685899	+	0.498335i
$423$	25.2705	+	77.7746i	1.22869	+	3.78153i
$424$		0			0
$425$	6.54508	+	20.1437i	0.317483	+	0.977113i
$426$	21.8885			1.06050
$427$	1.07295	+	3.30220i	0.0519236	+	0.159805i
$428$	0.381966	−	0.277515i	0.0184630	−	0.0134142i
$429$	24.0344	−	17.4620i	1.16039	−	0.843075i
$430$	−24.4721			−1.18015
$431$	7.85410	+	5.70634i	0.378319	+	0.274865i	0.760652	−	0.649160i	$-0.224879\pi$
$431$	7.85410	+	5.70634i	0.378319	+	0.274865i	−0.382333	+	0.924024i	$0.624879\pi$
$432$	−57.8885			−2.78516
$433$	−2.61803	−	1.90211i	−0.125815	−	0.0914097i	0.523098	−	0.852272i	$-0.324776\pi$
$433$	−2.61803	−	1.90211i	−0.125815	−	0.0914097i	−0.648913	+	0.760863i	$0.724776\pi$
$434$	−0.145898	+	0.449028i	−0.00700333	+	0.0215540i
$435$	13.0902	+	9.51057i	0.627626	+	0.455997i
$436$	10.0000	+	30.7768i	0.478913	+	1.47394i
$437$	5.20163	−	16.0090i	0.248828	−	0.765812i
$438$	10.2918	−	31.6749i	0.491761	−	1.51348i
$439$	−9.83688	−	30.2748i	−0.469489	−	1.44494i	−0.853248	−	0.521505i	$-0.825371\pi$
$439$	−9.83688	−	30.2748i	−0.469489	−	1.44494i	0.383760	−	0.923433i	$-0.374629\pi$
$440$		0			0
$441$	−16.0344	+	49.3489i	−0.763545	+	2.34995i
$442$	−16.3262	−	11.8617i	−0.776560	−	0.564204i
$443$	26.1246			1.24122			0.620609	−	0.784120i	$-0.286885\pi$
$443$	26.1246			1.24122			0.620609	+	0.784120i	$0.286885\pi$
$444$	5.70820	+	4.14725i	0.270899	+	0.196820i
$445$	7.36068			0.348930
$446$	26.2705	−	19.0866i	1.24394	−	0.903779i
$447$	−18.4164	+	13.3803i	−0.871066	+	0.632867i
$448$	0.583592	+	1.79611i	0.0275721	+	0.0848583i
$449$	−18.4164			−0.869124			−0.434562	−	0.900642i	$-0.643097\pi$
$449$	−18.4164			−0.869124			−0.434562	+	0.900642i	$0.643097\pi$
$450$	−60.4508	−	43.9201i	−2.84968	−	2.07041i
$451$	4.20163			0.197847
$452$	−1.81966	−	5.60034i	−0.0855896	−	0.263418i
$453$	34.0344	−	24.7275i	1.59908	−	1.16180i
$454$	18.2705	−	13.2743i	0.857478	−	0.622994i
$455$	−1.01722	−	0.739054i	−0.0476881	−	0.0346474i
$456$		0			0
$457$	−5.23607			−0.244933			−0.122466	−	0.992473i	$-0.539080\pi$
$457$	−5.23607			−0.244933			−0.122466	+	0.992473i	$0.539080\pi$
$458$	40.1246	+	29.1522i	1.87490	+	1.36219i
$459$	18.9443	−	58.3045i	0.884243	−	2.72142i
$460$	13.6180	−	9.89408i	0.634944	−	0.461314i
$461$	−5.01064	−	15.4212i	−0.233369	−	0.718236i	−0.997334	−	0.0729776i	$-0.976750\pi$
$461$	−5.01064	−	15.4212i	−0.233369	−	0.718236i	0.763965	−	0.645258i	$-0.223250\pi$
$462$	1.81966	−	5.60034i	0.0846583	−	0.260551i
$463$	−2.98278	+	9.18005i	−0.138621	+	0.426633i	−0.996136	−	0.0878271i	$-0.972008\pi$
$463$	−2.98278	+	9.18005i	−0.138621	+	0.426633i	0.857514	+	0.514460i	$0.172008\pi$
$464$	−2.76393	−	8.50651i	−0.128312	−	0.394905i
$465$	−2.23607	+	6.88191i	−0.103695	+	0.319141i
$466$	−6.29180	+	19.3642i	−0.291462	+	0.897027i
$467$	−13.0623	−	9.49032i	−0.604451	−	0.439160i	0.243005	−	0.970025i	$-0.421867\pi$
$467$	−13.0623	−	9.49032i	−0.604451	−	0.439160i	−0.847456	+	0.530865i	$0.821867\pi$
$468$	35.5967			1.64546
$469$	1.82624	+	1.32684i	0.0843278	+	0.0612678i
$470$	39.5967	−	28.7687i	1.82646	−	1.32700i
$471$	48.8328	−	35.4791i	2.25010	−	1.63479i
$472$		0			0
$473$	−6.51722	−	20.0579i	−0.299662	−	0.922265i
$474$	52.3607			2.40501
$475$	6.90983	+	21.2663i	0.317045	+	0.975763i
$476$	−2.00000			−0.0916698
$477$	−26.6976	−	82.1666i	−1.22240	−	3.76215i
$478$	18.9443	−	13.7638i	0.866491	−	0.629542i
$479$	30.4894	−	22.1518i	1.39309	−	1.01214i	0.397576	−	0.917569i	$-0.369851\pi$
$479$	30.4894	−	22.1518i	1.39309	−	1.01214i	0.995518	−	0.0945731i	$-0.0301486\pi$
$480$	17.8885	+	55.0553i	0.816497	+	2.51292i
$481$	2.10081	+	1.52633i	0.0957888	+	0.0695947i
$482$	−40.0689			−1.82509
$483$	2.32624	+	1.69011i	0.105847	+	0.0769027i
$484$	2.38197	−	7.33094i	0.108271	−	0.333224i
$485$	−7.33688	−	22.5806i	−0.333151	−	1.02533i
$486$	22.0000	+	67.7090i	0.997940	+	3.07134i
$487$	3.54508	−	10.9106i	0.160643	−	0.494409i	−0.838046	−	0.545600i	$-0.816302\pi$
$487$	3.54508	−	10.9106i	0.160643	−	0.494409i	0.998689	+	0.0511913i	$0.0163018\pi$
$488$		0			0
$489$	12.7082	+	39.1118i	0.574685	+	1.76870i
$490$	31.0557			1.40295
$491$	−4.21885	+	12.9843i	−0.190394	+	0.585972i	−0.999999	−	0.00100208i	$-0.999681\pi$
$491$	−4.21885	+	12.9843i	−0.190394	+	0.585972i	0.809606	+	0.586974i	$0.199681\pi$
$492$	5.70820	+	4.14725i	0.257346	+	0.186973i
$493$	9.47214			0.426604
$494$	−17.2361	−	12.5227i	−0.775487	−	0.563425i
$495$	19.8992	−	61.2434i	0.894402	−	2.75269i
$496$	3.23607	−	2.35114i	0.145304	−	0.105569i
$497$	0.645898	−	0.469272i	0.0289725	−	0.0210497i
$498$	9.23607	+	28.4257i	0.413878	+	1.27379i
$499$	−20.1246			−0.900901			−0.450451	−	0.892801i	$-0.648737\pi$
$499$	−20.1246			−0.900901			−0.450451	+	0.892801i	$0.648737\pi$
$500$	−6.90983	+	21.2663i	−0.309017	+	0.951057i
$501$	−3.52786			−0.157613
$502$	2.41641	+	7.43694i	0.107850	+	0.331927i
$503$	2.70820	−	1.96763i	0.120753	−	0.0877321i	−0.525770	−	0.850627i	$-0.676223\pi$
$503$	2.70820	−	1.96763i	0.120753	−	0.0877321i	0.646523	+	0.762895i	$0.276223\pi$
$504$		0			0
$505$	−4.10739	+	12.6412i	−0.182776	+	0.562528i
$506$	23.4721	+	17.0535i	1.04346	+	0.758121i
$507$	−23.7082			−1.05292
$508$	−27.5066	−	19.9847i	−1.22041	−	0.886678i
$509$	6.44427	−	19.8334i	0.285637	−	0.879101i	−0.700570	−	0.713584i	$-0.747071\pi$
$509$	6.44427	−	19.8334i	0.285637	−	0.879101i	0.986207	−	0.165517i	$-0.0529293\pi$
$510$	−61.3050			−2.71463
$511$	−0.375388	−	1.15533i	−0.0166062	−	0.0511086i
$512$	9.88854	−	30.4338i	0.437016	−	1.34500i
$513$	20.0000	−	61.5537i	0.883022	−	2.71766i
$514$	−17.1803	−	52.8756i	−0.757792	−	2.33224i
$515$	−7.82624	−	24.0867i	−0.344865	−	1.06139i
$516$	10.9443	−	33.6830i	0.481795	−	1.48281i
$517$	34.1246	+	24.7930i	1.50080	+	1.09039i
$518$	0.514708			0.0226150
$519$	−65.3050	−	47.4468i	−2.86657	−	2.08268i
$520$		0			0
$521$	31.3713	−	22.7926i	1.37440	−	0.998562i	0.377024	−	0.926204i	$-0.376947\pi$
$521$	31.3713	−	22.7926i	1.37440	−	0.998562i	0.997379	−	0.0723584i	$-0.0230525\pi$
$522$	−27.0344	+	19.6417i	−1.18327	+	0.859693i
$523$	5.20820	+	16.0292i	0.227739	+	0.700908i	0.998002	+	0.0631820i	$0.0201249\pi$
$523$	5.20820	+	16.0292i	0.227739	+	0.700908i	−0.770263	+	0.637726i	$0.779875\pi$
$524$	−34.9443			−1.52655
$525$	−3.81966			−0.166704
$526$	2.00000			0.0872041
$527$	1.30902	+	4.02874i	0.0570217	+	0.175495i
$528$	−40.3607	+	29.3238i	−1.75647	+	1.27615i
$529$	7.14590	−	5.19180i	0.310691	−	0.225730i
$530$	−41.8328	+	30.3933i	−1.81710	+	1.32020i
$531$	46.9336	+	34.0993i	2.03675	+	1.47978i
$532$	−2.11146			−0.0915432
$533$	2.10081	+	1.52633i	0.0909963	+	0.0661127i
$534$	−6.58359	+	20.2622i	−0.284900	+	0.876832i
$535$	0.163119	−	0.502029i	0.00705225	−	0.0217046i
$536$		0			0
$537$	18.4164	−	56.6799i	0.794727	−	2.44592i
$538$	−9.67376	+	29.7728i	−0.417065	+	1.28360i
$539$	8.27051	+	25.4540i	0.356236	+	1.09638i
$540$	52.3607	−	38.0423i	2.25324	−	1.63708i
$541$	0.618034	−	1.90211i	0.0265714	−	0.0817782i	−0.936891	−	0.349620i	$-0.886311\pi$
$541$	0.618034	−	1.90211i	0.0265714	−	0.0817782i	0.963463	+	0.267842i	$0.0863106\pi$
$542$	−0.145898	−	0.106001i	−0.00626686	−	0.00455314i
$543$	−25.2361			−1.08298
$544$	27.4164	+	19.9192i	1.17547	+	0.854028i
$545$	29.2705	+	21.2663i	1.25381	+	0.910947i
$546$	2.94427	−	2.13914i	0.126003	−	0.0915467i
$547$	−12.8992	+	9.37181i	−0.551529	+	0.400710i	−0.828349	−	0.560212i	$-0.810720\pi$
$547$	−12.8992	+	9.37181i	−0.551529	+	0.400710i	0.276820	+	0.960922i	$0.410720\pi$
$548$	10.5066	+	32.3359i	0.448819	+	1.38132i
$549$	−109.902			−4.69049
$550$	−38.5410			−1.64339
$551$	10.0000			0.426014
$552$		0			0
$553$	1.54508	−	1.12257i	0.0657037	−	0.0477365i
$554$	−2.70820	+	1.96763i	−0.115061	+	0.0835964i
$555$	7.88854			0.334850
$556$	18.0902	+	13.1433i	0.767194	+	0.557399i
$557$	−2.79837			−0.118571			−0.0592855	−	0.998241i	$-0.518882\pi$
$557$	−2.79837			−0.118571			−0.0592855	+	0.998241i	$0.518882\pi$
$558$	−12.0902	−	8.78402i	−0.511818	−	0.371857i
$559$	4.02786	−	12.3965i	0.170360	−	0.524316i
$560$	1.70820	+	1.24108i	0.0721848	+	0.0524453i
$561$	−16.3262	−	50.2470i	−0.689294	−	2.12143i
$562$	14.9787	−	46.0997i	0.631839	−	1.94460i
$563$	1.16312	−	3.57971i	0.0490196	−	0.150867i	−0.923550	−	0.383477i	$-0.874727\pi$
$563$	1.16312	−	3.57971i	0.0490196	−	0.150867i	0.972570	+	0.232610i	$0.0747266\pi$
$564$	21.8885	+	67.3660i	0.921674	+	2.83662i
$565$	−5.32624	−	3.86974i	−0.224077	−	0.162801i
$566$	4.43769	−	13.6578i	0.186530	−	0.574081i
$567$	4.66312	+	3.38795i	0.195833	+	0.142281i
$568$		0			0
$569$	−33.1525	−	24.0867i	−1.38982	−	1.00977i	−0.995885	−	0.0906299i	$-0.971112\pi$
$569$	−33.1525	−	24.0867i	−1.38982	−	1.00977i	−0.393939	−	0.919136i	$-0.628888\pi$
$570$	−64.7214			−2.71088
$571$	3.80902	−	2.76741i	0.159402	−	0.115813i	−0.505225	−	0.862988i	$-0.668590\pi$
$571$	3.80902	−	2.76741i	0.159402	−	0.115813i	0.664627	+	0.747175i	$0.268590\pi$
$572$	14.8541	−	10.7921i	0.621081	−	0.451242i
$573$	17.0000	+	52.3206i	0.710185	+	2.18573i
$574$	0.514708			0.0214835
$575$	5.81559	−	17.8986i	0.242527	−	0.746422i
$576$	−59.7771			−2.49071
$577$	3.44427	+	10.6004i	0.143387	+	0.441300i	0.996800	−	0.0799356i	$-0.0254715\pi$
$577$	3.44427	+	10.6004i	0.143387	+	0.441300i	−0.853413	+	0.521235i	$0.825471\pi$
$578$	−1.52786	+	1.11006i	−0.0635508	+	0.0461723i
$579$	24.4164	−	17.7396i	1.01471	−	0.737231i
$580$	8.09017	+	5.87785i	0.335926	+	0.244065i
$581$	0.881966	+	0.640786i	0.0365901	+	0.0265843i
$582$	68.7214			2.84859
$583$	−36.0517	−	26.1931i	−1.49311	−	1.08481i
$584$		0			0
$585$	32.1976	−	23.3929i	1.33121	−	0.967177i
$586$	−5.76393	−	17.7396i	−0.238106	−	0.732814i
$587$	7.62868	−	23.4787i	0.314869	−	0.969068i	−0.660939	−	0.750440i	$-0.729842\pi$
$587$	7.62868	−	23.4787i	0.314869	−	0.969068i	0.975808	−	0.218628i	$-0.0701582\pi$
$588$	−13.8885	+	42.7445i	−0.572754	+	1.76276i
$589$	1.38197	+	4.25325i	0.0569429	+	0.175252i
$590$	10.7295	−	33.0220i	0.441726	−	1.35949i
$591$	−9.70820	+	29.8788i	−0.399342	+	1.22905i
$592$	−3.52786	−	2.56314i	−0.144994	−	0.105345i
$593$	−32.6180			−1.33946			−0.669731	−	0.742604i	$-0.733591\pi$
$593$	−32.6180			−1.33946			−0.669731	+	0.742604i	$0.733591\pi$
$594$	90.2492	+	65.5699i	3.70297	+	2.69037i
$595$	−1.80902	+	1.31433i	−0.0741625	+	0.0538822i
$596$	−11.3820	+	8.26948i	−0.466223	+	0.338731i
$597$	40.9787	−	29.7728i	1.67715	−	1.21852i
$598$	5.54102	+	17.0535i	0.226589	+	0.697370i
$599$	16.7082			0.682679			0.341339	−	0.939940i	$-0.389119\pi$
$599$	16.7082			0.682679			0.341339	+	0.939940i	$0.389119\pi$
$600$		0			0
$601$	10.8197			0.441343			0.220672	−	0.975348i	$-0.429175\pi$
$601$	10.8197			0.441343			0.220672	+	0.975348i	$0.429175\pi$
$602$	−0.798374	−	2.45714i	−0.0325393	−	0.100146i
$603$	−57.8050	+	41.9978i	−2.35400	+	1.71028i
$604$	21.0344	−	15.2824i	0.855879	−	0.621833i
$605$	−2.66312	−	8.19624i	−0.108271	−	0.333224i
$606$	−31.1246	−	22.6134i	−1.26435	−	0.918605i
$607$	19.7639			0.802193			0.401097	−	0.916036i	$-0.368629\pi$
$607$	19.7639			0.802193			0.401097	+	0.916036i	$0.368629\pi$
$608$	28.9443	+	21.0292i	1.17385	+	0.852848i
$609$	−0.527864	+	1.62460i	−0.0213901	+	0.0658321i
$610$	20.3262	+	62.5577i	0.822985	+	2.53289i
$611$	8.05573	+	24.7930i	0.325900	+	1.00302i
$612$	19.5623	−	60.2066i	0.790759	−	2.43371i
$613$	6.52786	−	20.0907i	0.263658	−	0.811456i	−0.728342	−	0.685214i	$-0.759709\pi$
$613$	6.52786	−	20.0907i	0.263658	−	0.811456i	0.992000	−	0.126242i	$-0.0402914\pi$
$614$	−9.94427	−	30.6053i	−0.401318	−	1.23513i
$615$	7.88854			0.318097
$616$		0			0
$617$	−7.63525	−	5.54734i	−0.307384	−	0.223327i	0.423389	−	0.905948i	$-0.360840\pi$
$617$	−7.63525	−	5.54734i	−0.307384	−	0.223327i	−0.730773	+	0.682620i	$0.760840\pi$
$618$	73.3050			2.94876
$619$	29.8607	+	21.6951i	1.20020	+	0.871998i	0.994305	−	0.106576i	$-0.0339887\pi$
$619$	29.8607	+	21.6951i	1.20020	+	0.871998i	0.205897	+	0.978574i	$0.433989\pi$
$620$	−1.38197	+	4.25325i	−0.0555011	+	0.170815i
$621$	−44.0689	+	32.0179i	−1.76842	+	1.28483i
$622$	−53.8885	+	39.1523i	−2.16073	+	1.56986i
$623$	0.240133	+	0.739054i	0.00962074	+	0.0296096i
$624$	−30.8328			−1.23430
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$	17.7771			0.710515
$627$	−17.2361	−	53.0472i	−0.688342	−	2.11850i
$628$	30.1803	−	21.9273i	1.20433	−	0.874995i
$629$	3.73607	−	2.71441i	0.148967	−	0.108231i
$630$	2.43769	−	7.50245i	0.0971201	−	0.298905i
$631$	−26.9443	−	19.5762i	−1.07263	−	0.779315i	−0.0962506	−	0.995357i	$-0.530685\pi$
$631$	−26.9443	−	19.5762i	−1.07263	−	0.779315i	−0.976384	+	0.216043i	$0.930685\pi$
$632$		0			0
$633$	−22.7984	−	16.5640i	−0.906154	−	0.658359i
$634$	−20.1459	+	62.0027i	−0.800096	+	2.46244i
$635$	−38.0132			−1.50851
$636$	−23.1246	−	71.1702i	−0.916951	−	2.82208i
$637$	−5.11146	+	15.7314i	−0.202523	+	0.623303i
$638$	−5.32624	+	16.3925i	−0.210868	+	0.648984i
$639$	7.80902	+	24.0337i	0.308920	+	0.950758i
$640$		0			0
$641$	7.75329	−	23.8622i	0.306236	−	0.942499i	−0.672976	−	0.739664i	$-0.734984\pi$
$641$	7.75329	−	23.8622i	0.306236	−	0.942499i	0.979213	−	0.202835i	$-0.0650155\pi$
$642$	1.23607	+	0.898056i	0.0487837	+	0.0354434i
$643$	16.2016			0.638930			0.319465	−	0.947598i	$-0.396497\pi$
$643$	16.2016			0.638930			0.319465	+	0.947598i	$0.396497\pi$
$644$	1.43769	+	1.04455i	0.0566531	+	0.0411609i
$645$	−12.2361	−	37.6587i	−0.481795	−	1.48281i
$646$	−30.6525	+	22.2703i	−1.20601	+	0.876214i
$647$	−11.5172	+	8.36775i	−0.452789	+	0.328970i	−0.790696	−	0.612209i	$-0.790281\pi$
$647$	−11.5172	+	8.36775i	−0.452789	+	0.328970i	0.337907	+	0.941179i	$0.390281\pi$
$648$		0			0
$649$	29.9230			1.17458
$650$	−19.2705	−	14.0008i	−0.755852	−	0.549158i
$651$	−0.763932			−0.0299409
$652$	7.85410	+	24.1724i	0.307590	+	0.946666i
$653$	9.35410	−	6.79615i	0.366054	−	0.265954i	−0.389519	−	0.921019i	$-0.627359\pi$
$653$	9.35410	−	6.79615i	0.366054	−	0.265954i	0.755573	+	0.655065i	$0.227359\pi$
$654$	−84.7214	+	61.5537i	−3.31287	+	2.40694i
$655$	−31.6074	+	22.9641i	−1.23500	+	0.897282i
$656$	−3.52786	−	2.56314i	−0.137740	−	0.100074i
$657$	38.4508			1.50011
$658$	4.18034	+	3.03719i	0.162967	+	0.118402i
$659$	−11.4443	+	35.2218i	−0.445806	+	1.37205i	0.435792	+	0.900047i	$0.356468\pi$
$659$	−11.4443	+	35.2218i	−0.445806	+	1.37205i	−0.881598	+	0.472001i	$0.843532\pi$
$660$	17.2361	−	53.0472i	0.670913	−	2.06486i
$661$	−3.03851	−	9.35156i	−0.118184	−	0.363734i	0.874414	−	0.485181i	$-0.161246\pi$
$661$	−3.03851	−	9.35156i	−0.118184	−	0.363734i	−0.992598	+	0.121448i	$0.961246\pi$
$662$	−9.74265	+	29.9848i	−0.378659	+	1.16539i
$663$	10.0902	−	31.0543i	0.391870	−	1.20605i
$664$		0			0
$665$	−1.90983	+	1.38757i	−0.0740600	+	0.0538078i
$666$	−5.03444	+	15.4944i	−0.195081	+	0.600397i
$667$	−6.80902	−	4.94704i	−0.263646	−	0.191550i
$668$	−2.18034			−0.0843599
$669$	42.5066	+	30.8828i	1.64340	+	1.19400i
$670$	34.5967	+	25.1360i	1.33659	+	0.971089i
$671$	−45.8607	+	33.3197i	−1.77043	+	1.28629i
$672$	−4.94427	+	3.59222i	−0.190729	+	0.138573i
$673$	9.15248	+	28.1684i	0.352802	+	1.08581i	0.957273	+	0.289186i	$0.0933845\pi$
$673$	9.15248	+	28.1684i	0.352802	+	1.08581i	−0.604471	+	0.796627i	$0.706615\pi$
$674$	−59.4164			−2.28863
$675$	22.3607	−	68.8191i	0.860663	−	2.64885i
$676$	−14.6525			−0.563557
$677$	−4.28115	−	13.1760i	−0.164538	−	0.506396i	0.834464	−	0.551063i	$-0.185777\pi$
$677$	−4.28115	−	13.1760i	−0.164538	−	0.506396i	−0.999002	+	0.0446665i	$0.985777\pi$
$678$	15.4164	−	11.2007i	0.592064	−	0.430159i
$679$	2.02786	−	1.47333i	0.0778223	−	0.0565412i
$680$		0			0
$681$	29.5623	+	21.4783i	1.13283	+	0.823049i
$682$	−7.70820			−0.295162
$683$	−11.1353	−	8.09024i	−0.426079	−	0.309564i	0.354000	−	0.935245i	$-0.384821\pi$
$683$	−11.1353	−	8.09024i	−0.426079	−	0.309564i	−0.780079	+	0.625681i	$0.784821\pi$
$684$	20.6525	−	63.5618i	0.789667	−	2.43035i
$685$	30.7533	+	22.3436i	1.17502	+	0.853704i
$686$	2.03444	+	6.26137i	0.0776754	+	0.239060i
$687$	−24.7984	+	76.3215i	−0.946117	+	2.91185i
$688$	−6.76393	+	20.8172i	−0.257872	+	0.793650i
$689$	−8.51064	−	26.1931i	−0.324230	−	0.997876i
$690$	44.0689	+	32.0179i	1.67767	+	1.21890i
$691$	−3.26393	+	10.0453i	−0.124166	+	0.382143i	−0.993748	−	0.111645i	$-0.964388\pi$
$691$	−3.26393	+	10.0453i	−0.124166	+	0.382143i	0.869582	+	0.493788i	$0.164388\pi$
$692$	−40.3607	−	29.3238i	−1.53428	−	1.11472i
$693$	6.79837			0.258249
$694$	−41.4508	−	30.1158i	−1.57345	−	1.14318i
$695$	25.0000			0.948304
$696$		0			0
$697$	3.73607	−	2.71441i	0.141514	−	0.102816i
$698$	−5.12461	−	15.7719i	−0.193969	−	0.596976i
$699$	−32.9443			−1.24607
$700$	−2.36068			−0.0892253
$701$	−36.6180			−1.38304			−0.691522	−	0.722355i	$-0.743060\pi$
$701$	−36.6180			−1.38304			−0.691522	+	0.722355i	$0.743060\pi$
$702$	21.3050	+	65.5699i	0.804104	+	2.47478i
$703$	3.94427	−	2.86568i	0.148761	−	0.108081i
$704$	−24.9443	+	18.1231i	−0.940123	+	0.683039i
$705$	64.0689	+	46.5488i	2.41297	+	1.75313i
$706$	−43.4508	−	31.5689i	−1.63529	−	1.18811i
$707$	−1.40325			−0.0527747
$708$	40.6525	+	29.5358i	1.52781	+	1.11002i
$709$	−1.70820	+	5.25731i	−0.0641529	+	0.197442i	−0.977995	−	0.208626i	$-0.933101\pi$
$709$	−1.70820	+	5.25731i	−0.0641529	+	0.197442i	0.913842	+	0.406069i	$0.133101\pi$
$710$	12.2361	−	8.89002i	0.459211	−	0.333637i
$711$	18.6803	+	57.4922i	0.700567	+	2.15612i
$712$		0			0
$713$	1.16312	−	3.57971i	0.0435591	−	0.134061i
$714$	−2.00000	−	6.15537i	−0.0748481	−	0.230359i
$715$	6.34346	−	19.5232i	0.237232	−	0.730125i
$716$	11.3820	−	35.0301i	0.425364	−	1.30914i
$717$	30.6525	+	22.2703i	1.14474	+	0.831701i
$718$	−31.0557			−1.15899
$719$	−3.35410	−	2.43690i	−0.125087	−	0.0908809i	0.523483	−	0.852036i	$-0.324632\pi$
$719$	−3.35410	−	2.43690i	−0.125087	−	0.0908809i	−0.648570	+	0.761155i	$0.724632\pi$
$720$	−54.0689	+	39.2833i	−2.01503	+	1.46400i
$721$	2.16312	−	1.57160i	0.0805588	−	0.0585294i
$722$	−1.61803	+	1.17557i	−0.0602170	+	0.0437502i
$723$	−20.0344	−	61.6597i	−0.745089	−	2.29315i
$724$	−15.5967			−0.579649
$725$	11.1803			0.415227
$726$	24.9443			0.925769
$727$	−13.6910	−	42.1365i	−0.507770	−	1.56276i	−0.796063	−	0.605214i	$-0.793087\pi$
$727$	−13.6910	−	42.1365i	−0.507770	−	1.56276i	0.288292	−	0.957542i	$-0.406913\pi$
$728$		0			0
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	−7.11146	−	21.8868i	−0.263207	−	0.810067i
$731$	−18.7533	−	13.6251i	−0.693615	−	0.503941i
$732$	−95.1935			−3.51845
$733$	21.3885	+	15.5397i	0.790004	+	0.573971i	0.907965	−	0.419047i	$-0.137636\pi$
$733$	21.3885	+	15.5397i	0.790004	+	0.573971i	−0.117961	+	0.993018i	$0.537636\pi$
$734$	−2.90983	+	8.95554i	−0.107404	+	0.330555i
$735$	15.5279	+	47.7899i	0.572754	+	1.76276i
$736$	−9.30495	−	28.6377i	−0.342985	−	1.05560i
$737$	−11.3885	+	35.0503i	−0.419502	+	1.29110i
$738$	−5.03444	+	15.4944i	−0.185320	+	0.570357i
$739$	−11.4443	−	35.2218i	−0.420984	−	1.29566i	−0.906787	−	0.421588i	$-0.861473\pi$
$739$	−11.4443	−	35.2218i	−0.420984	−	1.29566i	0.485803	−	0.874068i	$-0.338527\pi$
$740$	4.87539			0.179223
$741$	10.6525	−	32.7849i	0.391328	−	1.20439i
$742$	−4.41641	−	3.20871i	−0.162131	−	0.117795i
$743$	6.52786			0.239484			0.119742	−	0.992805i	$-0.461793\pi$
$743$	6.52786			0.239484			0.119742	+	0.992805i	$0.461793\pi$
$744$		0			0
$745$	−4.86068	+	14.9596i	−0.178082	+	0.548079i
$746$	−28.1246	+	20.4337i	−1.02972	+	0.748132i
$747$	−27.9164	+	20.2825i	−1.02141	+	0.742096i
$748$	−10.0902	−	31.0543i	−0.368933	−	1.13546i
$749$	0.0557281			0.00203626
$750$	−72.3607			−2.64224
$751$	0.0901699			0.00329035			0.00164517	−	0.999999i	$-0.499476\pi$
$751$	0.0901699			0.00329035			0.00164517	+	0.999999i	$0.499476\pi$
$752$	−13.5279	−	41.6345i	−0.493310	−	1.51825i
$753$	−10.2361	+	7.43694i	−0.373023	+	0.271017i
$754$	−8.61803	+	6.26137i	−0.313850	+	0.228026i
$755$	8.98278	−	27.6462i	0.326917	−	1.00615i
$756$	5.52786	+	4.01623i	0.201046	+	0.146069i
$757$	−25.2361			−0.917220			−0.458610	−	0.888638i	$-0.651653\pi$
$757$	−25.2361			−0.917220			−0.458610	+	0.888638i	$0.651653\pi$
$758$	−61.8328	−	44.9242i	−2.24587	−	1.63172i
$759$	−14.5066	+	44.6467i	−0.526555	+	1.62057i
$760$		0			0
$761$	14.2984	+	44.0059i	0.518316	+	1.59521i	0.777167	+	0.629294i	$0.216656\pi$
$761$	14.2984	+	44.0059i	0.518316	+	1.59521i	−0.258851	+	0.965917i	$0.583344\pi$
$762$	34.0000	−	104.641i	1.23169	−	3.79075i
$763$	−1.18034	+	3.63271i	−0.0427312	+	0.131513i
$764$	10.5066	+	32.3359i	0.380115	+	1.16987i
$765$	−21.8713	−	67.3130i	−0.790759	−	2.43371i
$766$	−3.00000	+	9.23305i	−0.108394	+	0.333604i
$767$	14.9615	+	10.8702i	0.540228	+	0.392499i
$768$	51.7771			1.86834
$769$	21.2812	+	15.4617i	0.767418	+	0.557562i	0.901177	−	0.433452i	$-0.142705\pi$
$769$	21.2812	+	15.4617i	0.767418	+	0.557562i	−0.133759	+	0.991014i	$0.542705\pi$
$770$	−1.25735	−	3.86974i	−0.0453119	−	0.139456i
$771$	72.7771	−	52.8756i	2.62100	−	1.90427i
$772$	15.0902	−	10.9637i	0.543107	−	0.394590i
$773$	6.52786	+	20.0907i	0.234791	+	0.722612i	0.997149	+	0.0754569i	$0.0240415\pi$
$773$	6.52786	+	20.0907i	0.234791	+	0.722612i	−0.762358	+	0.647155i	$0.775958\pi$
$774$	81.7771			2.93942
$775$	1.54508	+	4.75528i	0.0555011	+	0.170815i
$776$		0			0
$777$	0.257354	+	0.792055i	0.00923253	+	0.0284148i
$778$	47.3607	−	34.4095i	1.69796	−	1.23364i
$779$	3.94427	−	2.86568i	0.141318	−	0.102674i
$780$	27.8885	−	20.2622i	0.998570	−	0.725504i
$781$	10.5451	+	7.66145i	0.377333	+	0.274148i
$782$	31.8885			1.14033
$783$	−26.1803	−	19.0211i	−0.935609	−	0.679760i
$784$	8.58359	−	26.4176i	0.306557	−	0.943485i
$785$	12.8885	−	39.6669i	0.460012	−	1.41577i
$786$	−34.9443	−	107.547i	−1.24642	−	3.83609i
$787$	1.04508	−	3.21644i	0.0372533	−	0.114654i	−0.930701	−	0.365782i	$-0.880802\pi$
$787$	1.04508	−	3.21644i	0.0372533	−	0.114654i	0.967954	+	0.251128i	$0.0808016\pi$
$788$	−6.00000	+	18.4661i	−0.213741	+	0.657828i
$789$	1.00000	+	3.07768i	0.0356009	+	0.109568i
$790$	29.2705	−	21.2663i	1.04140	−	0.756620i
$791$	0.214782	−	0.661030i	0.00763676	−	0.0235035i
$792$		0			0
$793$	−35.0344			−1.24411
$794$	−62.5066	−	45.4137i	−2.21828	−	1.61167i
$795$	−67.6869	−	49.1774i	−2.40061	−	1.74414i
$796$	25.3262	−	18.4006i	0.897665	−	0.652192i
$797$	−6.09017	+	4.42477i	−0.215725	+	0.156733i	−0.690400	−	0.723428i	$-0.742566\pi$
$797$	−6.09017	+	4.42477i	−0.215725	+	0.156733i	0.474675	+	0.880161i	$0.342566\pi$
$798$	−2.11146	−	6.49839i	−0.0747447	−	0.230041i
$799$	46.3607			1.64012
$800$	32.3607	+	23.5114i	1.14412	+	0.831254i
$801$	−24.5967			−0.869083
$802$	−7.18034	−	22.0988i	−0.253547	−	0.780336i
$803$	16.0451	−	11.6574i	0.566219	−	0.411382i
$804$	−50.0689	+	36.3772i	−1.76579	+	1.28292i
$805$	1.98684			0.0700271
$806$	−3.85410	−	2.80017i	−0.135755	−	0.0986317i
$807$	−50.6525			−1.78305
$808$		0			0
$809$	−15.8926	+	48.9124i	−0.558754	+	1.71967i	0.127062	+	0.991895i	$0.459445\pi$
$809$	−15.8926	+	48.9124i	−0.558754	+	1.71967i	−0.685817	+	0.727774i	$0.740555\pi$
$810$	88.3394	+	64.1823i	3.10393	+	2.25514i
$811$	−16.7812	−	51.6471i	−0.589266	−	1.81357i	−0.581418	−	0.813605i	$-0.697502\pi$
$811$	−16.7812	−	51.6471i	−0.589266	−	1.81357i	−0.00784797	−	0.999969i	$-0.502498\pi$
$812$	−0.326238	+	1.00406i	−0.0114487	+	0.0352355i
$813$	0.0901699	−	0.277515i	0.00316240	−	0.00973286i
$814$	2.59675	+	7.99197i	0.0910160	+	0.280118i
$815$	22.9894	+	16.7027i	0.805282	+	0.585072i
$816$	−16.9443	+	52.1491i	−0.593168	+	1.82558i
$817$	−19.7984	−	14.3844i	−0.692657	−	0.503245i
$818$	14.4721			0.506006
$819$	3.39919	+	2.46965i	0.118777	+	0.0862967i
$820$	4.87539			0.170256
$821$	−0.600813	+	0.436516i	−0.0209685	+	0.0152345i	−0.598220	−	0.801332i	$-0.704125\pi$
$821$	−0.600813	+	0.436516i	−0.0209685	+	0.0152345i	0.577252	+	0.816566i	$0.304125\pi$
$822$	−89.0132	+	64.6718i	−3.10469	+	2.25569i
$823$	−2.41641	−	7.43694i	−0.0842307	−	0.259235i	0.900067	−	0.435751i	$-0.143517\pi$
$823$	−2.41641	−	7.43694i	−0.0842307	−	0.259235i	−0.984298	+	0.176516i	$0.943517\pi$
$824$		0			0
$825$	−19.2705	−	59.3085i	−0.670913	−	2.06486i
$826$	3.66563			0.127544
$827$	−6.45492	−	19.8662i	−0.224459	−	0.690815i	−0.998346	−	0.0574908i	$-0.981690\pi$
$827$	−6.45492	−	19.8662i	−0.224459	−	0.690815i	0.773887	−	0.633324i	$-0.218310\pi$
$828$	−45.5066	+	33.0625i	−1.58146	+	1.14900i
$829$	18.2533	−	13.2618i	0.633963	−	0.460601i	−0.223808	−	0.974633i	$-0.571849\pi$
$829$	18.2533	−	13.2618i	0.633963	−	0.460601i	0.857771	+	0.514032i	$0.171849\pi$
$830$	16.7082	+	12.1392i	0.579950	+	0.421359i
$831$	−4.38197	−	3.18368i	−0.152009	−	0.110441i
$832$	−19.0557			−0.660639
$833$	23.7984	+	17.2905i	0.824565	+	0.599081i
$834$	−22.3607	+	68.8191i	−0.774287	+	2.38301i
$835$	−1.97214	+	1.43284i	−0.0682486	+	0.0495855i
$836$	−10.6525	−	32.7849i	−0.368424	−	1.13389i
$837$	4.47214	−	13.7638i	0.154580	−	0.475747i
$838$	−7.76393	+	23.8949i	−0.268201	+	0.825437i
$839$	17.2984	+	53.2389i	0.597206	+	1.83801i	0.543423	+	0.839459i	$0.317128\pi$
$839$	17.2984	+	53.2389i	0.597206	+	1.83801i	0.0537832	+	0.998553i	$0.482872\pi$
$840$		0			0
$841$	−7.41641	+	22.8254i	−0.255738	+	0.787081i
$842$	17.4164	+	12.6538i	0.600209	+	0.436077i
$843$	78.4296			2.70126
$844$	−14.0902	−	10.2371i	−0.485004	−	0.352376i
$845$	−13.2533	+	9.62908i	−0.455927	+	0.331250i
$846$	−132.318	+	96.1347i	−4.54919	+	3.30518i
$847$	0.736068	−	0.534785i	0.0252916	−	0.0183754i
$848$	14.2918	+	43.9856i	0.490782	+	1.51047i
$849$	23.2361			0.797460
$850$	−34.2705	+	24.8990i	−1.17547	+	0.854028i
$851$	−4.10333			−0.140660
$852$	6.76393	+	20.8172i	0.231728	+	0.713187i
$853$	−9.91641	+	7.20469i	−0.339531	+	0.246684i	−0.744464	−	0.667663i	$-0.767295\pi$
$853$	−9.91641	+	7.20469i	−0.339531	+	0.246684i	0.404933	+	0.914346i	$0.367295\pi$
$854$	−5.61803	+	4.08174i	−0.192245	+	0.139674i
$855$	−23.0902	−	71.0642i	−0.789667	−	2.43035i
$856$		0			0
$857$	24.0344			0.821001			0.410500	−	0.911860i	$-0.365354\pi$
$857$	24.0344			0.821001			0.410500	+	0.911860i	$0.365354\pi$
$858$	48.0689	+	34.9241i	1.64104	+	1.19229i
$859$	0.652476	−	2.00811i	0.0222622	−	0.0685160i	−0.939308	−	0.343074i	$-0.888532\pi$
$859$	0.652476	−	2.00811i	0.0222622	−	0.0685160i	0.961570	+	0.274558i	$0.0885317\pi$
$860$	−7.56231	−	23.2744i	−0.257872	−	0.793650i
$861$	0.257354	+	0.792055i	0.00877061	+	0.0269932i
$862$	−6.00000	+	18.4661i	−0.204361	+	0.628958i
$863$	1.38854	−	4.27350i	0.0472666	−	0.145472i	−0.924638	−	0.380848i	$-0.875632\pi$
$863$	1.38854	−	4.27350i	0.0472666	−	0.145472i	0.971904	+	0.235376i	$0.0756322\pi$
$864$	−35.7771	−	110.111i	−1.21716	−	3.74604i
$865$	−55.7771			−1.89648
$866$	2.00000	−	6.15537i	0.0679628	−	0.209168i
$867$	−2.47214	−	1.79611i	−0.0839581	−	0.0609992i
$868$	−0.472136			−0.0160253
$869$	25.2254	+	18.3273i	0.855714	+	0.621713i
$870$	−10.0000	+	30.7768i	−0.339032	+	1.04343i
$871$	−18.4271	+	13.3880i	−0.624377	+	0.453636i
$872$		0			0
$873$	24.5172	+	75.4562i	0.829782	+	2.55381i
$874$	33.6656			1.13876
$875$	−2.13525	+	1.55135i	−0.0721848	+	0.0524453i
$876$	33.3050			1.12527
$877$	0.982779	+	3.02468i	0.0331861	+	0.102136i	0.966277	−	0.257503i	$-0.0828997\pi$
$877$	0.982779	+	3.02468i	0.0331861	+	0.102136i	−0.933091	+	0.359639i	$0.882900\pi$
$878$	51.5066	−	37.4217i	1.73826	−	1.26292i
$879$	24.4164	−	17.7396i	0.823545	−	0.598340i
$880$	−10.6525	+	32.7849i	−0.359095	+	1.10518i
$881$	−30.2984	−	22.0131i	−1.02078	−	0.741639i	−0.0543359	−	0.998523i	$-0.517304\pi$
$881$	−30.2984	−	22.0131i	−1.02078	−	0.741639i	−0.966442	+	0.256884i	$0.917304\pi$
$882$	−103.777			−3.49436
$883$	−0.545085	−	0.396027i	−0.0183436	−	0.0133274i	0.578576	−	0.815629i	$-0.303609\pi$
$883$	−0.545085	−	0.396027i	−0.0183436	−	0.0133274i	−0.596919	+	0.802301i	$0.703609\pi$
$884$	6.23607	−	19.1926i	0.209742	−	0.645518i
$885$	56.1803			1.88848
$886$	16.1459	+	49.6920i	0.542432	+	1.66943i
$887$	−15.5238	+	47.7773i	−0.521238	+	1.60421i	0.250399	+	0.968143i	$0.419438\pi$
$887$	−15.5238	+	47.7773i	−0.521238	+	1.60421i	−0.771637	+	0.636063i	$0.780562\pi$
$888$		0			0
$889$	−1.24013	−	3.81674i	−0.0415927	−	0.128009i
$890$	4.54915	+	14.0008i	0.152488	+	0.469309i
$891$	−29.0795	+	89.4976i	−0.974201	+	2.99828i
$892$	26.2705	+	19.0866i	0.879602	+	0.639068i
$893$	48.9443			1.63786
$894$	−36.8328	−	26.7606i	−1.23187	−	0.895009i
$895$	−12.7254	−	39.1648i	−0.425364	−	1.30914i
$896$		0			0
$897$	−23.4721	+	17.0535i	−0.783712	+	0.569400i
$898$	−11.3820	−	35.0301i	−0.379821	−	1.16897i
$899$	2.23607			0.0745770
$900$	23.0902	−	71.0642i	0.769672	−	2.36881i
$901$	−48.9787			−1.63172
$902$	2.59675	+	7.99197i	0.0864622	+	0.266103i
$903$	3.38197	−	2.45714i	0.112545	−	0.0817686i
$904$		0			0
$905$	−14.1074	+	10.2496i	−0.468946	+	0.340709i
$906$	68.0689	+	49.4549i	2.26144	+	1.64303i
$907$	45.0902			1.49719			0.748597	−	0.663025i	$-0.230728\pi$
$907$	45.0902			1.49719			0.748597	+	0.663025i	$0.230728\pi$
$908$	18.2705	+	13.2743i	0.606328	+	0.440523i
$909$	13.7254	−	42.2425i	0.455244	−	1.40110i
$910$	0.777088	−	2.39163i	0.0257602	−	0.0792818i
$911$	−4.70820	−	14.4904i	−0.155990	−	0.480087i	0.842270	−	0.539056i	$-0.181219\pi$
$911$	−4.70820	−	14.4904i	−0.155990	−	0.480087i	−0.998260	+	0.0589687i	$0.981219\pi$
$912$	−17.8885	+	55.0553i	−0.592349	+	1.82306i
$913$	−5.50000	+	16.9273i	−0.182023	+	0.560211i
$914$	−3.23607	−	9.95959i	−0.107040	−	0.329434i
$915$	−86.1033	+	62.5577i	−2.84649	+	2.06809i
$916$	−15.3262	+	47.1693i	−0.506393	+	1.55852i
$917$	−3.33688	−	2.42439i	−0.110194	−	0.0800603i
$918$	122.610			4.04673
$919$	44.9615	+	32.6664i	1.48314	+	1.07757i	0.976527	+	0.215394i	$0.0691037\pi$
$919$	44.9615	+	32.6664i	1.48314	+	1.07757i	0.506616	+	0.862172i	$0.330896\pi$
$920$		0			0
$921$	42.1246	−	30.6053i	1.38805	−	1.00848i
$922$	26.2361	−	19.0616i	0.864039	−	0.627761i
$923$	2.48936	+	7.66145i	0.0819382	+	0.252180i
$924$	5.88854			0.193719
$925$	4.40983	−	3.20393i	0.144994	−	0.105345i
$926$	−19.3050			−0.634400
$927$	26.1525	+	80.4890i	0.858960	+	2.64361i
$928$	14.4721	−	10.5146i	0.475071	−	0.345159i
$929$	30.3885	−	22.0786i	0.997016	−	0.724374i	0.0355695	−	0.999367i	$-0.488675\pi$
$929$	30.3885	−	22.0786i	0.997016	−	0.724374i	0.961446	+	0.274993i	$0.0886755\pi$
$930$	−14.4721			−0.474560
$931$	25.1246	+	18.2541i	0.823426	+	0.598254i
$932$	−20.3607			−0.666936
$933$	−87.1935	−	63.3498i	−2.85459	−	2.07398i
$934$	9.97871	−	30.7113i	0.326513	−	1.00491i
$935$	−29.5344	−	21.4580i	−0.965880	−	0.701753i
$936$		0			0
$937$	2.42705	−	7.46969i	0.0792883	−	0.244024i	−0.903553	−	0.428476i	$-0.859051\pi$
$937$	2.42705	−	7.46969i	0.0792883	−	0.244024i	0.982842	+	0.184451i	$0.0590508\pi$
$938$	−1.39512	+	4.29374i	−0.0455523	+	0.140196i
$939$	8.88854	+	27.3561i	0.290067	+	0.892733i
$940$	39.5967	+	28.7687i	1.29150	+	0.938332i
$941$	−7.00658	+	21.5640i	−0.228408	+	0.702967i	0.769520	+	0.638623i	$0.220496\pi$
$941$	−7.00658	+	21.5640i	−0.228408	+	0.702967i	−0.997928	+	0.0643444i	$0.979504\pi$
$942$	97.6656	+	70.9582i	3.18212	+	2.31194i
$943$	−4.10333			−0.133623
$944$	−25.1246	−	18.2541i	−0.817736	−	0.594120i
$945$	7.63932			0.248507
$946$	34.1246	−	24.7930i	1.10949	−	0.806089i
$947$	35.7426	−	25.9686i	1.16148	−	0.843865i	0.171516	−	0.985181i	$-0.445134\pi$
$947$	35.7426	−	25.9686i	1.16148	−	0.843865i	0.989964	+	0.141317i	$0.0451336\pi$
$948$	16.1803	+	49.7980i	0.525513	+	1.61736i
$949$	12.2574			0.397891
$950$	−36.1803	+	26.2866i	−1.17385	+	0.852848i
$951$	−105.485			−3.42059
$952$		0			0
$953$	−40.2426	+	29.2380i	−1.30359	+	0.947112i	−0.999984	−	0.00568700i	$-0.998190\pi$
$953$	−40.2426	+	29.2380i	−1.30359	+	0.947112i	−0.303603	+	0.952799i	$0.598190\pi$
$954$	139.790	−	101.564i	4.52588	−	3.28824i
$955$	30.7533	+	22.3436i	0.995153	+	0.723021i
$956$	18.9443	+	13.7638i	0.612702	+	0.445154i
$957$	−27.8885			−0.901509
$958$	60.9787	+	44.3036i	1.97013	+	1.43139i
$959$	−1.24013	+	3.81674i	−0.0400460	+	0.123249i
$960$	−46.8328	+	34.0260i	−1.51152	+	1.09819i
$961$	0.309017	+	0.951057i	0.00996829	+	0.0306792i
$962$	−1.60488	+	4.93931i	−0.0517434	+	0.159250i
$963$	−0.545085	+	1.67760i	−0.0175651	+	0.0540599i
$964$	−12.3820	−	38.1078i	−0.398796	−	1.22737i
$965$	6.44427	−	19.8334i	0.207448	−	0.638461i
$966$	−1.77709	+	5.46931i	−0.0571769	+	0.175972i
$967$	40.3156	+	29.2910i	1.29646	+	0.941935i	0.999914	−	0.0130832i	$-0.00416462\pi$
$967$	40.3156	+	29.2910i	1.29646	+	0.941935i	0.296548	+	0.955018i	$0.404165\pi$
$968$		0			0
$969$	−49.5967	−	36.0341i	−1.59328	−	1.15758i
$970$	38.4164	−	27.9112i	1.23348	−	0.896173i
$971$	3.11803	−	2.26538i	0.100062	−	0.0726996i	−0.536629	−	0.843818i	$-0.680303\pi$
$971$	3.11803	−	2.26538i	0.100062	−	0.0726996i	0.636691	+	0.771119i	$0.280303\pi$
$972$	−57.5967	+	41.8465i	−1.84742	+	1.34223i
$973$	0.815595	+	2.51014i	0.0261468	+	0.0804715i
$974$	22.9443			0.735182
$975$	11.9098	−	36.6547i	0.381420	−	1.17389i
$976$	58.8328			1.88319
$977$	5.65654	+	17.4090i	0.180969	+	0.556965i	0.999856	−	0.0169903i	$-0.00540844\pi$
$977$	5.65654	+	17.4090i	0.180969	+	0.556965i	−0.818887	+	0.573955i	$0.805408\pi$
$978$	−66.5410	+	48.3449i	−2.12775	+	1.54590i
$979$	−10.2639	+	7.45718i	−0.328037	+	0.238333i
$980$	9.59675	+	29.5358i	0.306557	+	0.943485i
$981$	−97.8115	−	71.0642i	−3.12288	−	2.26891i
$982$	−27.3050			−0.871336
$983$	−5.70820	−	4.14725i	−0.182063	−	0.132277i	0.493021	−	0.870018i	$-0.335893\pi$
$983$	−5.70820	−	4.14725i	−0.182063	−	0.132277i	−0.675084	+	0.737741i	$0.735893\pi$
$984$		0			0
$985$	6.70820	+	20.6457i	0.213741	+	0.657828i
$986$	5.85410	+	18.0171i	0.186433	+	0.573781i
$987$	−2.58359	+	7.95148i	−0.0822366	+	0.253098i
$988$	6.58359	−	20.2622i	0.209452	−	0.644627i
$989$	6.36475	+	19.5887i	0.202387	+	0.622884i
$990$	128.790			4.09322
$991$	15.5795	−	47.9489i	0.494900	−	1.52315i	−0.322213	−	0.946667i	$-0.604427\pi$
$991$	15.5795	−	47.9489i	0.494900	−	1.52315i	0.817113	−	0.576478i	$-0.195573\pi$
$992$	6.47214	+	4.70228i	0.205491	+	0.149298i
$993$	−51.0132			−1.61885
$994$	1.29180	+	0.938545i	0.0409733	+	0.0297688i
$995$	10.8156	−	33.2870i	0.342877	−	1.05527i
$996$	−24.1803	+	17.5680i	−0.766183	+	0.556665i
$997$	−26.5172	+	19.2659i	−0.839809	+	0.610157i	−0.922317	−	0.386434i	$-0.873707\pi$
$997$	−26.5172	+	19.2659i	−0.839809	+	0.610157i	0.0825084	+	0.996590i	$0.473707\pi$
$998$	−12.4377	−	38.2793i	−0.393708	−	1.21171i
$999$	−15.7771			−0.499165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.j.a.156.1	✓	4
25.21	even	5	inner	775.2.j.a.621.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.j.a.156.1	✓	4	1.1	even	1	trivial
775.2.j.a.621.1	yes	4	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 + 1.90211i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-5.23607 - 3.80423i) q^{6} -0.236068 q^{7} +(2.30902 - 7.10642i) q^{9} +O(q^{10})\)	\(q+(0.618034 + 1.90211i) q^{2} +(-2.61803 + 1.90211i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-5.23607 - 3.80423i) q^{6} -0.236068 q^{7} +(2.30902 - 7.10642i) q^{9} -4.47214 q^{10} +(-1.19098 - 3.66547i) q^{11} +(2.00000 - 6.15537i) q^{12} +(0.736068 - 2.26538i) q^{13} +(-0.145898 - 0.449028i) q^{14} +(-2.23607 - 6.88191i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-3.42705 - 2.48990i) q^{17} +14.9443 q^{18} +(-3.61803 - 2.62866i) q^{19} +(-1.38197 - 4.25325i) q^{20} +(0.618034 - 0.449028i) q^{21} +(6.23607 - 4.53077i) q^{22} +(1.16312 + 3.57971i) q^{23} +(-4.04508 - 2.93893i) q^{25} +4.76393 q^{26} +(4.47214 + 13.7638i) q^{27} +(0.381966 - 0.277515i) q^{28} +(-1.80902 + 1.31433i) q^{29} +(11.7082 - 8.50651i) q^{30} +(-0.809017 - 0.587785i) q^{31} -8.00000 q^{32} +(10.0902 + 7.33094i) q^{33} +(2.61803 - 8.05748i) q^{34} +(0.163119 - 0.502029i) q^{35} +(4.61803 + 14.2128i) q^{36} +(-0.336881 + 1.03681i) q^{37} +(2.76393 - 8.50651i) q^{38} +(2.38197 + 7.33094i) q^{39} +(-0.336881 + 1.03681i) q^{41} +(1.23607 + 0.898056i) q^{42} +5.47214 q^{43} +(6.23607 + 4.53077i) q^{44} +(13.5172 + 9.82084i) q^{45} +(-6.09017 + 4.42477i) q^{46} +(-8.85410 + 6.43288i) q^{47} +(-4.00000 - 12.3107i) q^{48} -6.94427 q^{49} +(3.09017 - 9.51057i) q^{50} +13.7082 q^{51} +(1.47214 + 4.53077i) q^{52} +(9.35410 - 6.79615i) q^{53} +(-23.4164 + 17.0130i) q^{54} +8.61803 q^{55} +14.4721 q^{57} +(-3.61803 - 2.62866i) q^{58} +(-2.39919 + 7.38394i) q^{59} +(11.7082 + 8.50651i) q^{60} +(-4.54508 - 13.9883i) q^{61} +(0.618034 - 1.90211i) q^{62} +(-0.545085 + 1.67760i) q^{63} +(-2.47214 - 7.60845i) q^{64} +(4.30902 + 3.13068i) q^{65} +(-7.70820 + 23.7234i) q^{66} +(-7.73607 - 5.62058i) q^{67} +8.47214 q^{68} +(-9.85410 - 7.15942i) q^{69} +1.05573 q^{70} +(-2.73607 + 1.98787i) q^{71} +(1.59017 + 4.89404i) q^{73} -2.18034 q^{74} +16.1803 q^{75} +8.94427 q^{76} +(0.281153 + 0.865300i) q^{77} +(-12.4721 + 9.06154i) q^{78} +(-6.54508 + 4.75528i) q^{79} +(-7.23607 - 5.25731i) q^{80} +(-19.7533 - 14.3516i) q^{81} -2.18034 q^{82} +(-3.73607 - 2.71441i) q^{83} +(-0.472136 + 1.45309i) q^{84} +(7.66312 - 5.56758i) q^{85} +(3.38197 + 10.4086i) q^{86} +(2.23607 - 6.88191i) q^{87} +(-1.01722 - 3.13068i) q^{89} +(-10.3262 + 31.7809i) q^{90} +(-0.173762 + 0.534785i) q^{91} +(-6.09017 - 4.42477i) q^{92} +3.23607 q^{93} +(-17.7082 - 12.8658i) q^{94} +(8.09017 - 5.87785i) q^{95} +(20.9443 - 15.2169i) q^{96} +(-8.59017 + 6.24112i) q^{97} +(-4.29180 - 13.2088i) q^{98} -28.7984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9} - 7 q^{11} + 8 q^{12} - 6 q^{13} - 14 q^{14} + 4 q^{16} - 7 q^{17} + 24 q^{18} - 10 q^{19} - 10 q^{20} - 2 q^{21} + 16 q^{22} - 11 q^{23} - 5 q^{25} + 28 q^{26} + 6 q^{28} - 5 q^{29} + 20 q^{30} - q^{31} - 32 q^{32} + 18 q^{33} + 6 q^{34} - 15 q^{35} + 14 q^{36} - 17 q^{37} + 20 q^{38} + 14 q^{39} - 17 q^{41} - 4 q^{42} + 4 q^{43} + 16 q^{44} + 25 q^{45} - 2 q^{46} - 22 q^{47} - 16 q^{48} + 8 q^{49} - 10 q^{50} + 28 q^{51} - 12 q^{52} + 24 q^{53} - 40 q^{54} + 30 q^{55} + 40 q^{57} - 10 q^{58} + 15 q^{59} + 20 q^{60} - 7 q^{61} - 2 q^{62} + 9 q^{63} + 8 q^{64} + 15 q^{65} - 4 q^{66} - 22 q^{67} + 16 q^{68} - 26 q^{69} + 40 q^{70} - 2 q^{71} - 16 q^{73} + 36 q^{74} + 20 q^{75} - 19 q^{77} - 32 q^{78} - 15 q^{79} - 20 q^{80} - 41 q^{81} + 36 q^{82} - 6 q^{83} + 16 q^{84} + 15 q^{85} + 18 q^{86} + 25 q^{89} - 10 q^{90} - 32 q^{91} - 2 q^{92} + 4 q^{93} - 44 q^{94} + 10 q^{95} + 48 q^{96} - 12 q^{97} - 44 q^{98} - 66 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9 - 7 * q^11 + 8 * q^12 - 6 * q^13 - 14 * q^14 + 4 * q^16 - 7 * q^17 + 24 * q^18 - 10 * q^19 - 10 * q^20 - 2 * q^21 + 16 * q^22 - 11 * q^23 - 5 * q^25 + 28 * q^26 + 6 * q^28 - 5 * q^29 + 20 * q^30 - q^31 - 32 * q^32 + 18 * q^33 + 6 * q^34 - 15 * q^35 + 14 * q^36 - 17 * q^37 + 20 * q^38 + 14 * q^39 - 17 * q^41 - 4 * q^42 + 4 * q^43 + 16 * q^44 + 25 * q^45 - 2 * q^46 - 22 * q^47 - 16 * q^48 + 8 * q^49 - 10 * q^50 + 28 * q^51 - 12 * q^52 + 24 * q^53 - 40 * q^54 + 30 * q^55 + 40 * q^57 - 10 * q^58 + 15 * q^59 + 20 * q^60 - 7 * q^61 - 2 * q^62 + 9 * q^63 + 8 * q^64 + 15 * q^65 - 4 * q^66 - 22 * q^67 + 16 * q^68 - 26 * q^69 + 40 * q^70 - 2 * q^71 - 16 * q^73 + 36 * q^74 + 20 * q^75 - 19 * q^77 - 32 * q^78 - 15 * q^79 - 20 * q^80 - 41 * q^81 + 36 * q^82 - 6 * q^83 + 16 * q^84 + 15 * q^85 + 18 * q^86 + 25 * q^89 - 10 * q^90 - 32 * q^91 - 2 * q^92 + 4 * q^93 - 44 * q^94 + 10 * q^95 + 48 * q^96 - 12 * q^97 - 44 * q^98 - 66 * q^99

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