LMFDB - Embedded newform 375.2.i.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, degree $4$, not 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.2
Root			$0.0898194i$ of defining polynomial
Character	$\chi$	$=$	375.49
Dual form			375.2.i.c.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0527945 + 0.0726655i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.615541 + 1.89444i) q^{4} +(0.0277557 - 0.0854234i) q^{6} +4.36070i q^{7} +(-0.341004 - 0.110799i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.0527945 + 0.0726655i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.615541 + 1.89444i) q^{4} +(0.0277557 - 0.0854234i) q^{6} +4.36070i q^{7} +(-0.341004 - 0.110799i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-3.55235 - 2.58093i) q^{11} +(-1.17083 - 1.61151i) q^{12} +(-1.16479 - 1.60319i) q^{13} +(-0.316872 - 0.230221i) q^{14} +(-3.19696 + 2.32273i) q^{16} +(0.948224 + 0.308097i) q^{17} +0.0898194i q^{18} +(-0.417468 + 1.28484i) q^{19} +(-1.34753 - 4.14727i) q^{21} +(0.375089 - 0.121874i) q^{22} +(-1.38512 + 1.90646i) q^{23} +0.358553 q^{24} +0.177991 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-8.26109 + 2.68419i) q^{28} +(2.46551 + 7.58806i) q^{29} +(-1.13645 + 3.49762i) q^{31} -1.07204i q^{32} +(4.17603 + 1.35688i) q^{33} +(-0.0724490 + 0.0526373i) q^{34} +(1.61151 + 1.17083i) q^{36} +(0.844681 + 1.16260i) q^{37} +(-0.0713231 - 0.0981678i) q^{38} +(1.60319 + 1.16479i) q^{39} +(4.83992 - 3.51641i) q^{41} +(0.372506 + 0.121034i) q^{42} -2.68554i q^{43} +(2.70280 - 8.31838i) q^{44} +(-0.0654066 - 0.201301i) q^{46} +(-10.4039 + 3.38042i) q^{47} +(2.32273 - 3.19696i) q^{48} -12.0157 q^{49} -0.997022 q^{51} +(2.32018 - 3.19345i) q^{52} +(10.5102 - 3.41496i) q^{53} +(-0.0277557 - 0.0854234i) q^{54} +(0.483161 - 1.48702i) q^{56} -1.35096i q^{57} +(-0.681555 - 0.221451i) q^{58} +(5.41147 - 3.93167i) q^{59} +(7.64982 + 5.55792i) q^{61} +(-0.194158 - 0.267235i) q^{62} +(2.56316 + 3.52788i) q^{63} +(-6.31602 - 4.58886i) q^{64} +(-0.319070 + 0.231818i) q^{66} +(12.2894 + 3.99307i) q^{67} +1.98600i q^{68} +(0.728201 - 2.24117i) q^{69} +(2.26280 + 6.96418i) q^{71} +(-0.341004 + 0.110799i) q^{72} +(0.249694 - 0.343674i) q^{73} -0.129076 q^{74} -2.69101 q^{76} +(11.2547 - 15.4907i) q^{77} +(-0.169280 + 0.0550023i) q^{78} +(1.96390 + 6.04425i) q^{79} +(0.309017 - 0.951057i) q^{81} +0.537343i q^{82} +(-0.700939 - 0.227749i) q^{83} +(7.02730 - 5.10563i) q^{84} +(0.195146 + 0.141782i) q^{86} +(-4.68968 - 6.45479i) q^{87} +(0.925401 + 1.27370i) q^{88} +(-7.91814 - 5.75286i) q^{89} +(6.99105 - 5.07929i) q^{91} +(-4.46427 - 1.45053i) q^{92} -3.67761i q^{93} +(0.303628 - 0.934470i) q^{94} +(0.331279 + 1.01957i) q^{96} +(-0.0320583 + 0.0104164i) q^{97} +(0.634365 - 0.873128i) q^{98} -4.39094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0527945	+	0.0726655i	−0.0373314	+	0.0513822i	−0.827275	−	0.561798i	$-0.810110\pi$
$2$	−0.0527945	+	0.0726655i	−0.0373314	+	0.0513822i	0.789943	+	0.613180i	$0.210110\pi$
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.615541	+	1.89444i	0.307770	+	0.947220i
$5$		0			0
$5$		0			0
$6$	0.0277557	−	0.0854234i	0.0113312	−	0.0348739i
$7$			4.36070i			1.64819i	0.566451	+	0.824095i	$0.308316\pi$
$7$			4.36070i			1.64819i	−0.566451	+	0.824095i	$0.691684\pi$
$8$	−0.341004	−	0.110799i	−0.120563	−	0.0391734i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$		0			0
$11$	−3.55235	−	2.58093i	−1.07107	−	0.778180i	−0.0949680	−	0.995480i	$-0.530275\pi$
$11$	−3.55235	−	2.58093i	−1.07107	−	0.778180i	−0.976105	+	0.217300i	$0.930275\pi$
$12$	−1.17083	−	1.61151i	−0.337989	−	0.465202i
$13$	−1.16479	−	1.60319i	−0.323054	−	0.444646i	0.616343	−	0.787478i	$-0.288614\pi$
$13$	−1.16479	−	1.60319i	−0.323054	−	0.444646i	−0.939397	+	0.342832i	$0.888614\pi$
$14$	−0.316872	−	0.230221i	−0.0846877	−	0.0615292i
$15$		0			0
$16$	−3.19696	+	2.32273i	−0.799240	+	0.580682i
$17$	0.948224	+	0.308097i	0.229978	+	0.0747244i	0.421739	−	0.906717i	$-0.361420\pi$
$17$	0.948224	+	0.308097i	0.229978	+	0.0747244i	−0.191761	+	0.981442i	$0.561420\pi$
$18$			0.0898194i			0.0211706i
$19$	−0.417468	+	1.28484i	−0.0957738	+	0.294761i	−0.987455	−	0.157903i	$-0.949527\pi$
$19$	−0.417468	+	1.28484i	−0.0957738	+	0.294761i	0.891681	+	0.452665i	$0.149527\pi$
$20$		0			0
$21$	−1.34753	−	4.14727i	−0.294055	−	0.905009i
$22$	0.375089	−	0.121874i	0.0799692	−	0.0259836i
$23$	−1.38512	+	1.90646i	−0.288818	+	0.397524i	−0.928630	−	0.371008i	$-0.879012\pi$
$23$	−1.38512	+	1.90646i	−0.288818	+	0.397524i	0.639812	+	0.768532i	$0.279012\pi$
$24$	0.358553			0.0731893
$25$		0			0
$26$	0.177991			0.0349069
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−8.26109	+	2.68419i	−1.56120	+	0.507264i
$29$	2.46551	+	7.58806i	0.457834	+	1.40907i	0.867776	+	0.496955i	$0.165549\pi$
$29$	2.46551	+	7.58806i	0.457834	+	1.40907i	−0.409942	+	0.912111i	$0.634451\pi$
$30$		0			0
$31$	−1.13645	+	3.49762i	−0.204112	+	0.628191i	0.795637	+	0.605774i	$0.207136\pi$
$31$	−1.13645	+	3.49762i	−0.204112	+	0.628191i	−0.999749	+	0.0224173i	$0.992864\pi$
$32$		−	1.07204i		−	0.189512i
$33$	4.17603	+	1.35688i	0.726954	+	0.236202i
$34$	−0.0724490	+	0.0526373i	−0.0124249	+	0.00902722i
$35$		0			0
$36$	1.61151	+	1.17083i	0.268585	+	0.195138i
$37$	0.844681	+	1.16260i	0.138865	+	0.191131i	0.872785	−	0.488105i	$-0.162312\pi$
$37$	0.844681	+	1.16260i	0.138865	+	0.191131i	−0.733920	+	0.679235i	$0.762312\pi$
$38$	−0.0713231	−	0.0981678i	−0.0115701	−	0.0159249i
$39$	1.60319	+	1.16479i	0.256716	+	0.186515i
$40$		0			0
$41$	4.83992	−	3.51641i	0.755869	−	0.549171i	−0.141771	−	0.989899i	$-0.545280\pi$
$41$	4.83992	−	3.51641i	0.755869	−	0.549171i	0.897641	+	0.440728i	$0.145280\pi$
$42$	0.372506	+	0.121034i	0.0574789	+	0.0186760i
$43$		−	2.68554i		−	0.409541i	−0.978810	−	0.204770i	$-0.934355\pi$
$43$		−	2.68554i		−	0.409541i	0.978810	−	0.204770i	$-0.0656447\pi$
$44$	2.70280	−	8.31838i	0.407463	−	1.25404i
$45$		0			0
$46$	−0.0654066	−	0.201301i	−0.00964368	−	0.0296802i
$47$	−10.4039	+	3.38042i	−1.51756	+	0.493086i	−0.945082	−	0.326833i	$-0.894018\pi$
$47$	−10.4039	+	3.38042i	−1.51756	+	0.493086i	−0.572480	+	0.819919i	$0.694018\pi$
$48$	2.32273	−	3.19696i	0.335257	−	0.461441i
$49$	−12.0157			−1.71653
$50$		0			0
$51$	−0.997022			−0.139611
$52$	2.32018	−	3.19345i	0.321751	−	0.442852i
$53$	10.5102	−	3.41496i	1.44368	−	0.469081i	0.520639	−	0.853777i	$-0.325694\pi$
$53$	10.5102	−	3.41496i	1.44368	−	0.469081i	0.923043	+	0.384696i	$0.125694\pi$
$54$	−0.0277557	−	0.0854234i	−0.00377708	−	0.0116246i
$55$		0			0
$56$	0.483161	−	1.48702i	0.0645652	−	0.198711i
$57$		−	1.35096i		−	0.178938i
$58$	−0.681555	−	0.221451i	−0.0894926	−	0.0290779i
$59$	5.41147	−	3.93167i	0.704514	−	0.511859i	−0.176885	−	0.984231i	$-0.556602\pi$
$59$	5.41147	−	3.93167i	0.704514	−	0.511859i	0.881399	+	0.472372i	$0.156602\pi$
$60$		0			0
$61$	7.64982	+	5.55792i	0.979460	+	0.711619i	0.957588	−	0.288142i	$-0.0930374\pi$
$61$	7.64982	+	5.55792i	0.979460	+	0.711619i	0.0218719	+	0.999761i	$0.493037\pi$
$62$	−0.194158	−	0.267235i	−0.0246581	−	0.0339389i
$63$	2.56316	+	3.52788i	0.322927	+	0.444471i
$64$	−6.31602	−	4.58886i	−0.789502	−	0.573607i
$65$		0			0
$66$	−0.319070	+	0.231818i	−0.0392748	+	0.0285348i
$67$	12.2894	+	3.99307i	1.50139	+	0.487831i	0.940423	−	0.340006i	$-0.110429\pi$
$67$	12.2894	+	3.99307i	1.50139	+	0.487831i	0.560968	+	0.827838i	$0.310429\pi$
$68$			1.98600i			0.240838i
$69$	0.728201	−	2.24117i	0.0876651	−	0.269806i
$70$		0			0
$71$	2.26280	+	6.96418i	0.268545	+	0.826496i	0.990856	+	0.134927i	$0.0430800\pi$
$71$	2.26280	+	6.96418i	0.268545	+	0.826496i	−0.722311	+	0.691569i	$0.756920\pi$
$72$	−0.341004	+	0.110799i	−0.0401877	+	0.0130578i
$73$	0.249694	−	0.343674i	0.0292244	−	0.0402240i	−0.794155	−	0.607716i	$-0.792086\pi$
$73$	0.249694	−	0.343674i	0.0292244	−	0.0402240i	0.823379	+	0.567492i	$0.192086\pi$
$74$	−0.129076			−0.0150047
$75$		0			0
$76$	−2.69101			−0.308680
$77$	11.2547	−	15.4907i	1.28259	−	1.76533i
$78$	−0.169280	+	0.0550023i	−0.0191671	+	0.00622778i
$79$	1.96390	+	6.04425i	0.220956	+	0.680032i	0.998677	+	0.0514225i	$0.0163755\pi$
$79$	1.96390	+	6.04425i	0.220956	+	0.680032i	−0.777721	+	0.628609i	$0.783624\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$			0.537343i			0.0593396i
$83$	−0.700939	−	0.227749i	−0.0769381	−	0.0249987i	0.270295	−	0.962778i	$-0.412879\pi$
$83$	−0.700939	−	0.227749i	−0.0769381	−	0.0249987i	−0.347233	+	0.937779i	$0.612879\pi$
$84$	7.02730	−	5.10563i	0.766742	−	0.557070i
$85$		0			0
$86$	0.195146	+	0.141782i	0.0210431	+	0.0152887i
$87$	−4.68968	−	6.45479i	−0.502786	−	0.692026i
$88$	0.925401	+	1.27370i	0.0986481	+	0.135777i
$89$	−7.91814	−	5.75286i	−0.839321	−	0.609802i	0.0828599	−	0.996561i	$-0.473595\pi$
$89$	−7.91814	−	5.75286i	−0.839321	−	0.609802i	−0.922181	+	0.386759i	$0.873595\pi$
$90$		0			0
$91$	6.99105	−	5.07929i	0.732861	−	0.532455i
$92$	−4.46427	−	1.45053i	−0.465432	−	0.151228i
$93$		−	3.67761i		−	0.381351i
$94$	0.303628	−	0.934470i	0.0313168	−	0.0963833i
$95$		0			0
$96$	0.331279	+	1.01957i	0.0338110	+	0.104060i
$97$	−0.0320583	+	0.0104164i	−0.00325503	+	0.00105762i	−0.310644	−	0.950526i	$-0.600545\pi$
$97$	−0.0320583	+	0.0104164i	−0.00325503	+	0.00105762i	0.307389	+	0.951584i	$0.400545\pi$
$98$	0.634365	−	0.873128i	0.0640805	−	0.0881992i
$99$	−4.39094			−0.441306
$100$		0			0
$101$	3.19390			0.317805			0.158902	−	0.987294i	$-0.449204\pi$
$101$	3.19390			0.317805			0.158902	+	0.987294i	$0.449204\pi$
$102$	0.0526373	−	0.0724490i	0.00521187	−	0.00717352i
$103$	8.13479	−	2.64315i	0.801544	−	0.260438i	0.120532	−	0.992709i	$-0.461540\pi$
$103$	8.13479	−	2.64315i	0.801544	−	0.260438i	0.681012	+	0.732272i	$0.261540\pi$
$104$	0.219565	+	0.675753i	0.0215302	+	0.0662630i
$105$		0			0
$106$	−0.306730	+	0.944017i	−0.0297922	+	0.0916910i
$107$			2.22136i			0.214747i	0.994219	+	0.107373i	$0.0342440\pi$
$107$			2.22136i			0.214747i	−0.994219	+	0.107373i	$0.965756\pi$
$108$	−1.89444	−	0.615541i	−0.182293	−	0.0592305i
$109$	8.90108	−	6.46701i	0.852569	−	0.619427i	−0.0732844	−	0.997311i	$-0.523348\pi$
$109$	8.90108	−	6.46701i	0.852569	−	0.619427i	0.925853	+	0.377884i	$0.123348\pi$
$110$		0			0
$111$	−1.16260	−	0.844681i	−0.110349	−	0.0801735i
$112$	−10.1287	−	13.9410i	−0.957074	−	1.31730i
$113$	1.00524	+	1.38359i	0.0945646	+	0.130157i	0.853678	−	0.520802i	$-0.174367\pi$
$113$	1.00524	+	1.38359i	0.0945646	+	0.130157i	−0.759113	+	0.650959i	$0.774367\pi$
$114$	0.0981678	+	0.0713231i	0.00919426	+	0.00668002i
$115$		0			0
$116$	−12.8575	+	9.34152i	−1.19379	+	0.867338i
$117$	−1.88467	−	0.612365i	−0.174237	−	0.0566132i
$118$			0.600798i			0.0553079i
$119$	−1.34352	+	4.13492i	−0.123160	+	0.379048i
$120$		0			0
$121$	2.55877	+	7.87510i	0.232616	+	0.715918i
$122$	−0.807738	+	0.262450i	−0.0731292	+	0.0237611i
$123$	−3.51641	+	4.83992i	−0.317064	+	0.436401i
$124$	−7.32556			−0.657855
$125$		0			0
$126$	−0.391676			−0.0348933
$127$	−7.38079	+	10.1588i	−0.654939	+	0.901447i	−0.999301	−	0.0373905i	$-0.988095\pi$
$127$	−7.38079	+	10.1588i	−0.654939	+	0.901447i	0.344361	+	0.938837i	$0.388095\pi$
$128$	2.70605	−	0.879248i	0.239183	−	0.0777153i
$129$	0.829877	+	2.55410i	0.0730666	+	0.224876i
$130$		0			0
$131$	5.09006	−	15.6656i	0.444721	−	1.36871i	−0.438069	−	0.898942i	$-0.644337\pi$
$131$	5.09006	−	15.6656i	0.444721	−	1.36871i	0.882790	−	0.469769i	$-0.155663\pi$
$132$			8.74646i			0.761282i
$133$	−5.60278	−	1.82046i	−0.485823	−	0.157853i
$134$	−0.938972	+	0.682203i	−0.0811149	+	0.0589334i
$135$		0			0
$136$	−0.289212	−	0.210125i	−0.0247997	−	0.0180180i
$137$	5.68231	+	7.82102i	0.485472	+	0.668195i	0.979545	−	0.201225i	$-0.0644923\pi$
$137$	5.68231	+	7.82102i	0.485472	+	0.668195i	−0.494073	+	0.869421i	$0.664492\pi$
$138$	0.124411	+	0.171237i	0.0105906	+	0.0145766i
$139$	10.9482	+	7.95430i	0.928611	+	0.674675i	0.945652	−	0.325180i	$-0.105425\pi$
$139$	10.9482	+	7.95430i	0.928611	+	0.674675i	−0.0170416	+	0.999855i	$0.505425\pi$
$140$		0			0
$141$	8.85007	−	6.42995i	0.745310	−	0.541499i
$142$	−0.625518	−	0.203243i	−0.0524923	−	0.0170558i
$143$			8.70133i			0.727642i
$144$	−1.22113	+	3.75825i	−0.101761	+	0.313188i
$145$		0			0
$146$	0.0117907	+	0.0362882i	0.000975809	+	0.00300323i
$147$	11.4276	−	3.71306i	0.942535	−	0.306248i
$148$	−1.68255	+	2.31583i	−0.138304	+	0.190360i
$149$	−13.6843			−1.12106			−0.560529	−	0.828134i	$-0.689402\pi$
$149$	−13.6843			−1.12106			−0.560529	+	0.828134i	$0.689402\pi$
$150$		0			0
$151$	−11.3204			−0.921237			−0.460619	−	0.887598i	$-0.652372\pi$
$151$	−11.3204			−0.921237			−0.460619	+	0.887598i	$0.652372\pi$
$152$	0.284717	−	0.391879i	0.0230936	−	0.0317856i
$153$	0.948224	−	0.308097i	0.0766594	−	0.0249081i
$154$	0.531455	+	1.63565i	0.0428259	+	0.131805i
$155$		0			0
$156$	−1.21979	+	3.75413i	−0.0976614	+	0.300571i
$157$			8.56070i			0.683219i	0.939842	+	0.341609i	$0.110972\pi$
$157$			8.56070i			0.683219i	−0.939842	+	0.341609i	$0.889028\pi$
$158$	−0.542892	−	0.176396i	−0.0431901	−	0.0140333i
$159$	−8.94048	+	6.49564i	−0.709026	+	0.515138i
$160$		0			0
$161$	−8.31349	−	6.04010i	−0.655194	−	0.476027i
$162$	0.0527945	+	0.0726655i	0.00414793	+	0.00570914i
$163$	2.69505	+	3.70942i	0.211093	+	0.290544i	0.901413	−	0.432959i	$-0.142531\pi$
$163$	2.69505	+	3.70942i	0.211093	+	0.290544i	−0.690321	+	0.723503i	$0.742531\pi$
$164$	9.64080	+	7.00445i	0.752820	+	0.546956i
$165$		0			0
$166$	0.0535552	−	0.0389102i	0.00415669	−	0.00302001i
$167$	6.86465	+	2.23046i	0.531203	+	0.172598i	0.562323	−	0.826917i	$-0.309908\pi$
$167$	6.86465	+	2.23046i	0.531203	+	0.172598i	−0.0311206	+	0.999516i	$0.509908\pi$
$168$			1.56354i			0.120630i
$169$	2.80372	−	8.62898i	0.215671	−	0.663767i
$170$		0			0
$171$	0.417468	+	1.28484i	0.0319246	+	0.0982538i
$172$	5.08759	−	1.65306i	0.387925	−	0.126045i
$173$	2.73326	−	3.76201i	0.207806	−	0.286020i	−0.692374	−	0.721539i	$-0.743435\pi$
$173$	2.73326	−	3.76201i	0.207806	−	0.286020i	0.900180	+	0.435519i	$0.143435\pi$
$174$	0.716629			0.0543275
$175$		0			0
$176$	17.3515			1.30792
$177$	−3.93167	+	5.41147i	−0.295522	+	0.406751i
$178$	0.836069	−	0.271655i	0.0626660	−	0.0203614i
$179$	2.22597	+	6.85082i	0.166377	+	0.512055i	0.999135	−	0.0415819i	$-0.0132397\pi$
$179$	2.22597	+	6.85082i	0.166377	+	0.512055i	−0.832758	+	0.553636i	$0.813240\pi$
$180$		0			0
$181$	−1.17557	+	3.61804i	−0.0873797	+	0.268927i	−0.985193	−	0.171449i	$-0.945155\pi$
$181$	−1.17557	+	3.61804i	−0.0873797	+	0.268927i	0.897813	+	0.440376i	$0.145155\pi$
$182$			0.776167i			0.0575333i
$183$	−8.99291	−	2.92197i	−0.664775	−	0.215998i
$184$	0.683566	−	0.496640i	0.0503931	−	0.0366128i
$185$		0			0
$186$	0.267235	+	0.194158i	0.0195947	+	0.0142364i
$187$	−2.57324	−	3.54177i	−0.188174	−	0.259000i
$188$	−12.8080	−	17.6287i	−0.934121	−	1.28571i
$189$	−3.52788	−	2.56316i	−0.256616	−	0.186442i
$190$		0			0
$191$	−17.4377	+	12.6692i	−1.26174	+	0.916711i	−0.998842	−	0.0481112i	$-0.984680\pi$
$191$	−17.4377	+	12.6692i	−1.26174	+	0.916711i	−0.262903	+	0.964822i	$0.584680\pi$
$192$	7.42493	+	2.41250i	0.535848	+	0.174108i
$193$		−	3.15029i		−	0.226763i	−0.993552	−	0.113381i	$-0.963832\pi$
$193$		−	3.15029i		−	0.226763i	0.993552	−	0.113381i	$-0.0361682\pi$
$194$	0.000935592	−	0.00287946i	6.71716e−5	−	0.000206733i
$195$		0			0
$196$	−7.39617	−	22.7631i	−0.528298	−	1.62593i
$197$	−24.8071	+	8.06032i	−1.76743	+	0.574274i	−0.997927	−	0.0643637i	$-0.979498\pi$
$197$	−24.8071	+	8.06032i	−1.76743	+	0.574274i	−0.769507	+	0.638638i	$0.779498\pi$
$198$	0.231818	−	0.319070i	0.0164746	−	0.0226753i
$199$	24.2662			1.72018			0.860092	−	0.510139i	$-0.170406\pi$
$199$	24.2662			1.72018			0.860092	+	0.510139i	$0.170406\pi$
$200$		0			0
$201$	−12.9219			−0.911437
$202$	−0.168620	+	0.232086i	−0.0118641	+	0.0163295i
$203$	−33.0893	+	10.7514i	−2.32241	+	0.754597i
$204$	−0.613708	−	1.88880i	−0.0429681	−	0.132242i
$205$		0			0
$206$	−0.237406	+	0.730662i	−0.0165409	+	0.0509076i
$207$			2.35651i			0.163789i
$208$	7.44756	+	2.41986i	0.516395	+	0.167787i
$209$	4.79906	−	3.48672i	0.331958	−	0.241182i
$210$		0			0
$211$	−13.2503	−	9.62694i	−0.912192	−	0.662746i	0.0293766	−	0.999568i	$-0.490648\pi$
$211$	−13.2503	−	9.62694i	−0.912192	−	0.662746i	−0.941568	+	0.336822i	$0.890648\pi$
$212$	12.9389	+	17.8088i	0.888645	+	1.22312i
$213$	−4.30410	−	5.92408i	−0.294912	−	0.405911i
$214$	−0.161416	−	0.117276i	−0.0110342	−	0.00801680i
$215$		0			0
$216$	0.290076	−	0.210752i	0.0197371	−	0.0143399i
$217$	−15.2521	−	4.95570i	−1.03538	−	0.336415i
$218$			0.988224i			0.0669310i
$219$	−0.131272	+	0.404013i	−0.00887052	+	0.0273006i
$220$		0			0
$221$	−0.610541	−	1.87905i	−0.0410695	−	0.126399i
$222$	0.122758	−	0.0398866i	0.00823899	−	0.00267701i
$223$	3.34035	−	4.59760i	0.223687	−	0.307878i	−0.682393	−	0.730985i	$-0.739061\pi$
$223$	3.34035	−	4.59760i	0.223687	−	0.307878i	0.906080	+	0.423107i	$0.139061\pi$
$224$	4.67486			0.312352
$225$		0			0
$226$	−0.153610			−0.0102180
$227$	2.14174	−	2.94785i	0.142152	−	0.195656i	−0.732004	−	0.681300i	$-0.761415\pi$
$227$	2.14174	−	2.94785i	0.142152	−	0.195656i	0.874157	+	0.485644i	$0.161415\pi$
$228$	2.55931	−	0.831569i	0.169494	−	0.0550720i
$229$	−0.513355	−	1.57994i	−0.0339235	−	0.104406i	0.932661	−	0.360754i	$-0.117481\pi$
$229$	−0.513355	−	1.57994i	−0.0339235	−	0.104406i	−0.966584	+	0.256348i	$0.917481\pi$
$230$		0			0
$231$	−5.91693	+	18.2104i	−0.389305	+	1.19816i
$232$		−	2.86074i		−	0.187817i
$233$	−7.47434	−	2.42856i	−0.489661	−	0.159100i	0.0537719	−	0.998553i	$-0.482876\pi$
$233$	−7.47434	−	2.42856i	−0.489661	−	0.159100i	−0.543432	+	0.839453i	$0.682876\pi$
$234$	0.143998	−	0.104621i	0.00941344	−	0.00683926i
$235$		0			0
$236$	10.7793	+	7.83161i	0.701672	+	0.509795i
$237$	−3.73555	−	5.14155i	−0.242650	−	0.333980i
$238$	−0.229536	−	0.315929i	−0.0148786	−	0.0204786i
$239$	−0.458956	−	0.333451i	−0.0296874	−	0.0215691i	0.572843	−	0.819665i	$-0.305841\pi$
$239$	−0.458956	−	0.333451i	−0.0296874	−	0.0215691i	−0.602530	+	0.798096i	$0.705841\pi$
$240$		0			0
$241$	15.3779	−	11.1727i	0.990578	−	0.719697i	0.0305304	−	0.999534i	$-0.490280\pi$
$241$	15.3779	−	11.1727i	0.990578	−	0.719697i	0.960048	+	0.279837i	$0.0902804\pi$
$242$	−0.707337	−	0.229828i	−0.0454693	−	0.0147739i
$243$			1.00000i			0.0641500i
$244$	−5.82037	+	17.9133i	−0.372611	+	1.14678i
$245$		0			0
$246$	−0.166048	−	0.511043i	−0.0105868	−	0.0325829i
$247$	2.54610	−	0.827278i	0.162005	−	0.0526385i
$248$	0.775065	−	1.06679i	0.0492167	−	0.0677410i
$249$	0.737011			0.0467062
$250$		0			0
$251$	3.02533			0.190957			0.0954787	−	0.995431i	$-0.469562\pi$
$251$	3.02533			0.190957			0.0954787	+	0.995431i	$0.469562\pi$
$252$	−5.10563	+	7.02730i	−0.321625	+	0.442678i
$253$	9.84086	−	3.19749i	0.618690	−	0.201024i
$254$	−0.348527	−	1.07266i	−0.0218686	−	0.0673045i
$255$		0			0
$256$	4.74604	−	14.6068i	0.296627	−	0.912925i
$257$		−	19.8613i		−	1.23891i	−0.785032	−	0.619456i	$-0.787353\pi$
$257$		−	19.8613i		−	1.23891i	0.785032	−	0.619456i	$-0.212647\pi$
$258$	−0.229408	−	0.0745391i	−0.0142823	−	0.00464060i
$259$	−5.06977	+	3.68340i	−0.315020	+	0.228875i
$260$		0			0
$261$	6.45479	+	4.68968i	0.399541	+	0.290284i
$262$	0.869621	+	1.19693i	0.0537253	+	0.0739466i
$263$	13.4191	+	18.4698i	0.827456	+	1.13890i	0.988391	+	0.151930i	$0.0485489\pi$
$263$	13.4191	+	18.4698i	0.827456	+	1.13890i	−0.160935	+	0.986965i	$0.551451\pi$
$264$	−1.27370	−	0.925401i	−0.0783911	−	0.0569545i
$265$		0			0
$266$	0.428081	−	0.311019i	0.0262473	−	0.0190698i
$267$	9.30833	+	3.02446i	0.569661	+	0.185094i
$268$			25.7395i			1.57229i
$269$	−4.58346	+	14.1065i	−0.279459	+	0.860086i	0.708546	+	0.705664i	$0.249351\pi$
$269$	−4.58346	+	14.1065i	−0.279459	+	0.860086i	−0.988005	+	0.154421i	$0.950649\pi$
$270$		0			0
$271$	−1.98920	−	6.12214i	−0.120835	−	0.371893i	0.872284	−	0.489000i	$-0.162638\pi$
$271$	−1.98920	−	6.12214i	−0.120835	−	0.371893i	−0.993119	+	0.117106i	$0.962638\pi$
$272$	−3.74706	+	1.21749i	−0.227199	+	0.0738214i
$273$	−5.07929	+	6.99105i	−0.307413	+	0.423117i
$274$	−0.868313			−0.0524567
$275$		0			0
$276$	4.69401			0.282546
$277$	3.94390	−	5.42831i	0.236966	−	0.326155i	−0.673927	−	0.738798i	$-0.735394\pi$
$277$	3.94390	−	5.42831i	0.236966	−	0.326155i	0.910893	+	0.412642i	$0.135394\pi$
$278$	−1.15601	+	0.375609i	−0.0693326	+	0.0225275i
$279$	1.13645	+	3.49762i	0.0680372	+	0.209397i
$280$		0			0
$281$	−6.33074	+	19.4840i	−0.377661	+	1.16232i	0.564006	+	0.825771i	$0.309260\pi$
$281$	−6.33074	+	19.4840i	−0.377661	+	1.16232i	−0.941666	+	0.336549i	$0.890740\pi$
$282$			0.982560i			0.0585106i
$283$	10.8589	+	3.52828i	0.645496	+	0.209734i	0.613427	−	0.789751i	$-0.289790\pi$
$283$	10.8589	+	3.52828i	0.645496	+	0.209734i	0.0320688	+	0.999486i	$0.489790\pi$
$284$	−11.8004	+	8.57347i	−0.700223	+	0.508742i
$285$		0			0
$286$	−0.632286	−	0.459383i	−0.0373879	−	0.0271639i
$287$	15.3340	+	21.1055i	0.905139	+	1.24582i
$288$	−0.630131	−	0.867300i	−0.0371308	−	0.0511062i
$289$	−12.9491	−	9.40806i	−0.761711	−	0.553415i
$290$		0			0
$291$	0.0272704	−	0.0198131i	0.00159862	−	0.00116147i
$292$	0.804766	+	0.261484i	0.0470954	+	0.0153022i
$293$		−	28.5505i		−	1.66794i	−0.551812	−	0.833968i	$-0.686063\pi$
$293$		−	28.5505i		−	1.66794i	0.551812	−	0.833968i	$-0.313937\pi$
$294$	−0.333505	+	1.02642i	−0.0194504	+	0.0598622i
$295$		0			0
$296$	−0.159224	−	0.490042i	−0.00925473	−	0.0284831i
$297$	4.17603	−	1.35688i	0.242318	−	0.0787339i
$298$	0.722455	−	0.994374i	0.0418507	−	0.0576025i
$299$	4.66979			0.270061
$300$		0			0
$301$	11.7108			0.675001
$302$	0.597653	−	0.822598i	0.0343910	−	0.0473352i
$303$	−3.03758	+	0.986969i	−0.174504	+	0.0566999i
$304$	−1.64969	−	5.07723i	−0.0946164	−	0.291199i
$305$		0			0
$306$	−0.0276731	+	0.0851689i	−0.00158196	+	0.00486878i
$307$		−	20.5417i		−	1.17238i	−0.810175	−	0.586188i	$-0.800628\pi$
$307$		−	20.5417i		−	1.17238i	0.810175	−	0.586188i	$-0.199372\pi$
$308$	36.2740	+	11.7861i	2.06690	+	0.671577i
$309$	−6.91986	+	5.02758i	−0.393657	+	0.286009i
$310$		0			0
$311$	−14.1979	−	10.3154i	−0.805090	−	0.584932i	0.107313	−	0.994225i	$-0.465775\pi$
$311$	−14.1979	−	10.3154i	−0.805090	−	0.584932i	−0.912403	+	0.409293i	$0.865775\pi$
$312$	−0.417638	−	0.574830i	−0.0236441	−	0.0325433i
$313$	−1.75491	−	2.41543i	−0.0991935	−	0.136528i	0.756535	−	0.653953i	$-0.226891\pi$
$313$	−1.75491	−	2.41543i	−0.0991935	−	0.136528i	−0.855729	+	0.517425i	$0.826891\pi$
$314$	−0.622067	−	0.451958i	−0.0351053	−	0.0255055i
$315$		0			0
$316$	−10.2416	+	7.44097i	−0.576136	+	0.418587i
$317$	−15.3794	−	4.99706i	−0.863791	−	0.280663i	−0.156580	−	0.987665i	$-0.550047\pi$
$317$	−15.3794	−	4.99706i	−0.863791	−	0.280663i	−0.707211	+	0.707003i	$0.750047\pi$
$318$		−	0.992598i		−	0.0556621i
$319$	10.8259	−	33.3187i	0.606134	−	1.86549i
$320$		0			0
$321$	−0.686438	−	2.11264i	−0.0383132	−	0.117916i
$322$	0.877813	−	0.285219i	0.0489186	−	0.0158946i
$323$	−0.791707	+	1.08969i	−0.0440518	+	0.0606320i
$324$	1.99193			0.110663
$325$		0			0
$326$	−0.411830			−0.0228092
$327$	−6.46701	+	8.90108i	−0.357627	+	0.492231i
$328$	−2.04005	+	0.662852i	−0.112643	+	0.0365999i
$329$	−14.7410	−	45.3682i	−0.812699	−	2.50123i
$330$		0			0
$331$	−4.03900	+	12.4307i	−0.222003	+	0.683256i	0.776579	+	0.630020i	$0.216953\pi$
$331$	−4.03900	+	12.4307i	−0.222003	+	0.683256i	−0.998582	+	0.0532356i	$0.983047\pi$
$332$		−	1.46808i		−	0.0805711i
$333$	1.36672	+	0.444075i	0.0748959	+	0.0243352i
$334$	−0.524494	+	0.381067i	−0.0286990	+	0.0208511i
$335$		0			0
$336$	13.9410	+	10.1287i	0.760543	+	0.552567i
$337$	−15.7555	−	21.6856i	−0.858257	−	1.18129i	−0.981982	−	0.188973i	$-0.939484\pi$
$337$	−15.7555	−	21.6856i	−0.858257	−	1.18129i	0.123725	−	0.992317i	$-0.460516\pi$
$338$	0.479007	+	0.659297i	0.0260545	+	0.0358610i
$339$	−1.38359	−	1.00524i	−0.0751462	−	0.0545969i
$340$		0			0
$341$	13.0642	−	9.49167i	0.707464	−	0.514003i
$342$	−0.115403	−	0.0374968i	−0.00624029	−	0.00202759i
$343$		−	21.8721i		−	1.18098i
$344$	−0.297555	+	0.915780i	−0.0160431	+	0.0493755i
$345$		0			0
$346$	0.129067	+	0.397227i	0.00693867	+	0.0213550i
$347$	24.2385	−	7.87558i	1.30119	−	0.422783i	0.425196	−	0.905101i	$-0.360205\pi$
$347$	24.2385	−	7.87558i	1.30119	−	0.422783i	0.875996	+	0.482318i	$0.160205\pi$
$348$	9.34152	−	12.8575i	0.500758	−	0.689234i
$349$	28.0435			1.50113			0.750566	−	0.660795i	$-0.229781\pi$
$349$	28.0435			1.50113			0.750566	+	0.660795i	$0.229781\pi$
$350$		0			0
$351$	1.98166			0.105773
$352$	−2.76687	+	3.80826i	−0.147474	+	0.202981i
$353$	13.9489	−	4.53226i	0.742423	−	0.241228i	0.0867054	−	0.996234i	$-0.472366\pi$
$353$	13.9489	−	4.53226i	0.742423	−	0.241228i	0.655718	+	0.755006i	$0.272366\pi$
$354$	−0.185657	−	0.571393i	−0.00986754	−	0.0303692i
$355$		0			0
$356$	6.02452	−	18.5416i	0.319299	−	0.982701i
$357$		−	4.34771i		−	0.230105i
$358$	−0.615337	−	0.199935i	−0.0325216	−	0.0105669i
$359$	−11.8283	+	8.59373i	−0.624272	+	0.453560i	−0.854411	−	0.519598i	$-0.826082\pi$
$359$	−11.8283	+	8.59373i	−0.624272	+	0.453560i	0.230139	+	0.973158i	$0.426082\pi$
$360$		0			0
$361$	13.8948	+	10.0952i	0.731305	+	0.531324i
$362$	−0.200843	−	0.276437i	−0.0105561	−	0.0145292i
$363$	−4.86708	−	6.69896i	−0.255455	−	0.351604i
$364$	13.9257	+	10.1176i	0.729905	+	0.530307i
$365$		0			0
$366$	0.687103	−	0.499210i	0.0359154	−	0.0260941i
$367$	−16.8279	−	5.46773i	−0.878412	−	0.285413i	−0.165114	−	0.986274i	$-0.552799\pi$
$367$	−16.8279	−	5.46773i	−0.878412	−	0.285413i	−0.713298	+	0.700861i	$0.752799\pi$
$368$		−	9.31212i		−	0.485428i
$369$	1.84869	−	5.68967i	0.0962388	−	0.296193i
$370$		0			0
$371$	14.8916	+	45.8317i	0.773134	+	2.37946i
$372$	6.96702	−	2.26372i	0.361223	−	0.117369i
$373$	−7.18821	+	9.89372i	−0.372191	+	0.512278i	−0.953495	−	0.301409i	$-0.902543\pi$
$373$	−7.18821	+	9.89372i	−0.372191	+	0.512278i	0.581303	+	0.813687i	$0.302543\pi$
$374$	0.393217			0.0203328
$375$		0			0
$376$	3.92231			0.202278
$377$	9.29333	−	12.7912i	0.478631	−	0.658779i
$378$	0.372506	−	0.121034i	0.0191596	−	0.00622534i
$379$	−8.68186	−	26.7200i	−0.445957	−	1.37251i	−0.881431	−	0.472313i	$-0.843419\pi$
$379$	−8.68186	−	26.7200i	−0.445957	−	1.37251i	0.435474	−	0.900201i	$-0.356581\pi$
$380$		0			0
$381$	3.88031	−	11.9424i	0.198794	−	0.611826i
$382$		−	1.93598i		−	0.0990533i
$383$	−32.7481	−	10.6405i	−1.67335	−	0.543705i	−0.689748	−	0.724049i	$-0.742279\pi$
$383$	−32.7481	−	10.6405i	−1.67335	−	0.543705i	−0.983603	+	0.180345i	$0.942279\pi$
$384$	−2.30190	+	1.67243i	−0.117468	+	0.0853458i
$385$		0			0
$386$	0.228917	+	0.166318i	0.0116516	+	0.00846536i
$387$	−1.57852	−	2.17265i	−0.0802406	−	0.110442i
$388$	−0.0394664	−	0.0543208i	−0.00200360	−	0.00275772i
$389$	10.9399	+	7.94834i	0.554677	+	0.402997i	0.829507	−	0.558496i	$-0.188622\pi$
$389$	10.9399	+	7.94834i	0.554677	+	0.402997i	−0.274830	+	0.961493i	$0.588622\pi$
$390$		0			0
$391$	−1.90078	+	1.38100i	−0.0961265	+	0.0698400i
$392$	4.09741	+	1.33133i	0.206951	+	0.0672423i
$393$			16.4718i			0.830892i
$394$	0.723974	−	2.22816i	0.0364733	−	0.112253i
$395$		0			0
$396$	−2.70280	−	8.31838i	−0.135821	−	0.418014i
$397$	34.2136	−	11.1167i	1.71713	−	0.557931i	0.725639	−	0.688076i	$-0.241544\pi$
$397$	34.2136	−	11.1167i	1.71713	−	0.557931i	0.991495	+	0.130145i	$0.0415444\pi$
$398$	−1.28112	+	1.76331i	−0.0642169	+	0.0883869i
$399$	5.89112			0.294925
$400$		0			0
$401$	4.35977			0.217717			0.108858	−	0.994057i	$-0.465281\pi$
$401$	4.35977			0.217717			0.108858	+	0.994057i	$0.465281\pi$
$402$	0.682203	−	0.938972i	0.0340252	−	0.0468317i
$403$	6.93108	−	2.25204i	0.345261	−	0.112182i
$404$	1.96598	+	6.05065i	0.0978110	+	0.301031i
$405$		0			0
$406$	0.965680	−	2.97206i	0.0479259	−	0.147501i
$407$		−	6.31003i		−	0.312777i
$408$	0.339989	+	0.110469i	0.0168319	+	0.00546903i
$409$	−14.6543	+	10.6470i	−0.724610	+	0.526460i	−0.887854	−	0.460126i	$-0.847804\pi$
$409$	−14.6543	+	10.6470i	−0.724610	+	0.526460i	0.163243	+	0.986586i	$0.447804\pi$
$410$		0			0
$411$	−7.82102	−	5.68231i	−0.385783	−	0.280288i
$412$	10.0146	+	13.7839i	0.493383	+	0.679084i
$413$	17.1448	+	23.5978i	0.843642	+	1.16117i
$414$	−0.171237	−	0.124411i	−0.00841583	−	0.00611446i
$415$		0			0
$416$	−1.71869	+	1.24870i	−0.0842657	+	0.0612226i
$417$	−12.8703	−	4.18182i	−0.630263	−	0.204785i
$418$			0.532806i			0.0260604i
$419$	−0.163120	+	0.502031i	−0.00796892	+	0.0245258i	−0.954962	−	0.296728i	$-0.904104\pi$
$419$	−0.163120	+	0.502031i	−0.00796892	+	0.0245258i	0.946993	+	0.321254i	$0.104104\pi$
$420$		0			0
$421$	5.76583	+	17.7454i	0.281009	+	0.864857i	0.987567	+	0.157201i	$0.0502472\pi$
$421$	5.76583	+	17.7454i	0.281009	+	0.864857i	−0.706557	+	0.707656i	$0.749753\pi$
$422$	1.39909	−	0.454593i	0.0681067	−	0.0221292i
$423$	−6.42995	+	8.85007i	−0.312635	+	0.430305i
$424$	−3.96239			−0.192430
$425$		0			0
$426$	0.657709			0.0318661
$427$	−24.2364	+	33.3586i	−1.17288	+	1.61434i
$428$	−4.20823	+	1.36734i	−0.203413	+	0.0660928i
$429$	−2.68886	−	8.27546i	−0.129819	−	0.399543i
$430$		0			0
$431$	6.48668	−	19.9640i	0.312453	−	0.961630i	−0.664338	−	0.747432i	$-0.731286\pi$
$431$	6.48668	−	19.9640i	0.312453	−	0.961630i	0.976790	−	0.214198i	$-0.0687136\pi$
$432$		−	3.95166i		−	0.190124i
$433$	12.9952	+	4.22239i	0.624508	+	0.202915i	0.604141	−	0.796877i	$-0.293516\pi$
$433$	12.9952	+	4.22239i	0.624508	+	0.202915i	0.0203675	+	0.999793i	$0.493516\pi$
$434$	1.16533	−	0.846665i	0.0559378	−	0.0406412i
$435$		0			0
$436$	17.7303	+	12.8819i	0.849130	+	0.616929i
$437$	−1.87124	−	2.57554i	−0.0895134	−	0.123205i
$438$	−0.0224273	−	0.0308686i	−0.00107162	−	0.00147496i
$439$	−3.50578	−	2.54710i	−0.167322	−	0.121567i	0.500973	−	0.865463i	$-0.332976\pi$
$439$	−3.50578	−	2.54710i	−0.167322	−	0.121567i	−0.668295	+	0.743896i	$0.732976\pi$
$440$		0			0
$441$	−9.72092	+	7.06266i	−0.462901	+	0.336317i
$442$	0.168776	+	0.0548385i	0.00802783	+	0.00260840i
$443$			1.60742i			0.0763707i	0.999271	+	0.0381854i	$0.0121577\pi$
$443$			1.60742i			0.0763707i	−0.999271	+	0.0381854i	$0.987842\pi$
$444$	0.884567	−	2.72242i	0.0419797	−	0.129200i
$445$		0			0
$446$	0.157734	+	0.485456i	0.00746894	+	0.0229870i
$447$	13.0145	−	4.22867i	0.615565	−	0.200009i
$448$	20.0106	−	27.5423i	0.945414	−	1.30125i
$449$	13.8291			0.652634			0.326317	−	0.945260i	$-0.394192\pi$
$449$	13.8291			0.652634			0.326317	+	0.945260i	$0.394192\pi$
$450$		0			0
$451$	−26.2687			−1.23694
$452$	−2.00236	+	2.75601i	−0.0941832	+	0.129632i
$453$	10.7663	−	3.49818i	0.505845	−	0.164359i
$454$	0.101135	+	0.311261i	0.00474649	+	0.0146082i
$455$		0			0
$456$	−0.149685	+	0.460682i	−0.00700962	+	0.0215734i
$457$			20.1345i			0.941850i	0.882173	+	0.470925i	$0.156080\pi$
$457$			20.1345i			0.941850i	−0.882173	+	0.470925i	$0.843920\pi$
$458$	0.141910	+	0.0461093i	0.00663101	+	0.00215455i
$459$	−0.806607	+	0.586035i	−0.0376492	+	0.0273538i
$460$		0			0
$461$	−25.5054	−	18.5308i	−1.18791	−	0.863064i	−0.194865	−	0.980830i	$-0.562427\pi$
$461$	−25.5054	−	18.5308i	−1.18791	−	0.863064i	−0.993041	+	0.117766i	$0.962427\pi$
$462$	−1.01089	−	1.39137i	−0.0470308	−	0.0647323i
$463$	−0.0265501	−	0.0365431i	−0.00123389	−	0.00169830i	0.808400	−	0.588634i	$-0.200334\pi$
$463$	−0.0265501	−	0.0365431i	−0.00123389	−	0.00169830i	−0.809633	+	0.586936i	$0.800334\pi$
$464$	−25.5071	−	18.5320i	−1.18414	−	0.860327i
$465$		0			0
$466$	0.571077	−	0.414912i	0.0264546	−	0.0192204i
$467$	−31.2278	−	10.1465i	−1.44505	−	0.469525i	−0.521582	−	0.853201i	$-0.674658\pi$
$467$	−31.2278	−	10.1465i	−1.44505	−	0.469525i	−0.923468	+	0.383676i	$0.874658\pi$
$468$		−	3.94732i		−	0.182465i
$469$	−17.4126	+	53.5905i	−0.804039	+	2.47458i
$470$		0			0
$471$	−2.64540	−	8.14171i	−0.121894	−	0.375150i
$472$	−2.28096	+	0.741129i	−0.104990	+	0.0341132i
$473$	−6.93119	+	9.53996i	−0.318696	+	0.438648i
$474$	0.570830			0.0262191
$475$		0			0
$476$	−8.66035			−0.396947
$477$	6.49564	−	8.94048i	0.297415	−	0.409356i
$478$	0.0484607	−	0.0157458i	0.00221654	−	0.000720198i
$479$	−2.31323	−	7.11938i	−0.105694	−	0.325293i	0.884199	−	0.467111i	$-0.154705\pi$
$479$	−2.31323	−	7.11938i	−0.105694	−	0.325293i	−0.989893	+	0.141818i	$0.954705\pi$
$480$		0			0
$481$	0.880003	−	2.70837i	0.0401247	−	0.123491i
$482$			1.70730i			0.0777654i
$483$	9.77309	+	3.17547i	0.444691	+	0.144489i
$484$	−13.3439	+	9.69489i	−0.606540	+	0.440677i
$485$		0			0
$486$	−0.0726655	−	0.0527945i	−0.00329617	−	0.00239481i
$487$	14.9471	+	20.5729i	0.677316	+	0.932246i	0.999898	−	0.0142956i	$-0.00455060\pi$
$487$	14.9471	+	20.5729i	0.677316	+	0.932246i	−0.322581	+	0.946542i	$0.604551\pi$
$488$	−1.99281	−	2.74287i	−0.0902103	−	0.124164i
$489$	−3.70942	−	2.69505i	−0.167746	−	0.121874i
$490$		0			0
$491$	8.95323	−	6.50490i	0.404053	−	0.293562i	−0.367137	−	0.930167i	$-0.619662\pi$
$491$	8.95323	−	6.50490i	0.404053	−	0.293562i	0.771190	+	0.636605i	$0.219662\pi$
$492$	−11.3334	−	3.68246i	−0.510951	−	0.166018i
$493$			7.95479i			0.358266i
$494$	−0.0743057	+	0.228689i	−0.00334317	+	0.0102892i
$495$		0			0
$496$	−4.49084	−	13.8214i	−0.201645	−	0.620599i
$497$	−30.3687	+	9.86739i	−1.36222	+	0.442613i
$498$	−0.0389102	+	0.0535552i	−0.00174361	+	0.00239987i
$499$	−4.68157			−0.209576			−0.104788	−	0.994495i	$-0.533416\pi$
$499$	−4.68157			−0.209576			−0.104788	+	0.994495i	$0.533416\pi$
$500$		0			0
$501$	−7.21792			−0.322473
$502$	−0.159721	+	0.219837i	−0.00712870	+	0.00981182i
$503$	10.2985	−	3.34618i	0.459187	−	0.149199i	−0.0702839	−	0.997527i	$-0.522391\pi$
$503$	10.2985	−	3.34618i	0.459187	−	0.149199i	0.529471	+	0.848328i	$0.322391\pi$
$504$	−0.483161	−	1.48702i	−0.0215217	−	0.0662371i
$505$		0			0
$506$	−0.287197	+	0.883901i	−0.0127675	+	0.0392942i
$507$			9.07304i			0.402948i
$508$	−23.7884	−	7.72932i	−1.05544	−	0.342933i
$509$	9.30422	−	6.75991i	0.412402	−	0.299628i	−0.362171	−	0.932112i	$-0.617964\pi$
$509$	9.30422	−	6.75991i	0.412402	−	0.299628i	0.774574	+	0.632484i	$0.217964\pi$
$510$		0			0
$511$	1.49866	+	1.08884i	0.0662967	+	0.0481674i
$512$	4.15570	+	5.71984i	0.183658	+	0.252783i
$513$	−0.794072	−	1.09295i	−0.0350591	−	0.0482548i
$514$	1.44323	+	1.04857i	0.0636580	+	0.0462503i
$515$		0			0
$516$	−4.32776	+	3.14430i	−0.190519	+	0.138420i
$517$	45.6828	+	14.8432i	2.00913	+	0.652805i
$518$		−	0.562860i		−	0.0247307i
$519$	−1.43696	+	4.42250i	−0.0630755	+	0.194126i
$520$		0			0
$521$	0.246536	+	0.758759i	0.0108009	+	0.0332418i	0.956312	−	0.292349i	$-0.0944368\pi$
$521$	0.246536	+	0.758759i	0.0108009	+	0.0332418i	−0.945511	+	0.325591i	$0.894437\pi$
$522$	−0.681555	+	0.221451i	−0.0298309	+	0.00969263i
$523$	−23.5954	+	32.4763i	−1.03175	+	1.42009i	−0.128133	+	0.991757i	$0.540898\pi$
$523$	−23.5954	+	32.4763i	−1.03175	+	1.42009i	−0.903622	+	0.428331i	$0.859102\pi$
$524$	32.8107			1.43334
$525$		0			0
$526$	−2.05057			−0.0894090
$527$	−2.15521	+	2.96639i	−0.0938824	+	0.129218i
$528$	−16.5023	+	5.36191i	−0.718169	+	0.233347i
$529$	5.39138	+	16.5930i	0.234408	+	0.721433i
$530$		0			0
$531$	2.06700	−	6.36157i	0.0897001	−	0.276069i
$532$		−	11.7347i		−	0.508764i
$533$	−11.2750	−	3.66346i	−0.488373	−	0.158682i
$534$	−0.711203	+	0.516719i	−0.0307768	+	0.0223606i
$535$		0			0
$536$	−3.74831	−	2.72331i	−0.161903	−	0.117629i
$537$	−4.23404	−	5.82766i	−0.182712	−	0.251482i
$538$	−0.783070	−	1.07780i	−0.0337605	−	0.0464674i
$539$	42.6840	+	31.0117i	1.83853	+	1.33577i
$540$		0			0
$541$	−1.14085	+	0.828873i	−0.0490488	+	0.0356360i	−0.612040	−	0.790827i	$-0.709651\pi$
$541$	−1.14085	+	0.828873i	−0.0490488	+	0.0356360i	0.562991	+	0.826463i	$0.309651\pi$
$542$	0.549887	+	0.178669i	0.0236197	+	0.00767449i
$543$		−	3.80424i		−	0.163255i
$544$	0.330293	−	1.01654i	0.0141612	−	0.0435836i
$545$		0			0
$546$	−0.239849	−	0.738178i	−0.0102646	−	0.0315911i
$547$	−14.7053	+	4.77804i	−0.628753	+	0.204294i	−0.606023	−	0.795447i	$-0.707236\pi$
$547$	−14.7053	+	4.77804i	−0.628753	+	0.204294i	−0.0227302	+	0.999742i	$0.507236\pi$
$548$	−11.3188	+	15.5790i	−0.483514	+	0.665500i
$549$	9.45570			0.403560
$550$		0			0
$551$	−10.7787			−0.459187
$552$	−0.496640	+	0.683566i	−0.0211384	+	0.0290945i
$553$	−26.3572	+	8.56397i	−1.12082	+	0.364177i
$554$	0.186234	+	0.573170i	0.00791234	+	0.0243517i
$555$		0			0
$556$	−8.32991	+	25.6368i	−0.353267	+	1.08724i
$557$		−	18.0445i		−	0.764568i	−0.924045	−	0.382284i	$-0.875138\pi$
$557$		−	18.0445i		−	0.764568i	0.924045	−	0.382284i	$-0.124862\pi$
$558$	−0.314154	−	0.102075i	−0.0132992	−	0.00432117i
$559$	−4.30543	+	3.12808i	−0.182100	+	0.132304i
$560$		0			0
$561$	3.54177	+	2.57324i	0.149533	+	0.108642i
$562$	−1.08159	−	1.48868i	−0.0456240	−	0.0627960i
$563$	−16.7711	−	23.0834i	−0.706816	−	0.972849i	−0.999860	−	0.0167502i	$-0.994668\pi$
$563$	−16.7711	−	23.0834i	−0.706816	−	0.972849i	0.293043	−	0.956099i	$-0.405332\pi$
$564$	17.6287	+	12.8080i	0.742304	+	0.539315i
$565$		0			0
$566$	−0.829676	+	0.602795i	−0.0348739	+	0.0253374i
$567$	4.14727	+	1.34753i	0.174169	+	0.0565910i
$568$		−	2.62553i		−	0.110165i
$569$	−5.07011	+	15.6042i	−0.212550	+	0.654162i	0.786768	+	0.617248i	$0.211753\pi$
$569$	−5.07011	+	15.6042i	−0.212550	+	0.654162i	−0.999318	+	0.0369135i	$0.988247\pi$
$570$		0			0
$571$	−2.57938	−	7.93852i	−0.107944	−	0.332217i	0.882466	−	0.470376i	$-0.155882\pi$
$571$	−2.57938	−	7.93852i	−0.107944	−	0.332217i	−0.990410	+	0.138159i	$0.955882\pi$
$572$	−16.4842	+	5.35603i	−0.689237	+	0.223947i
$573$	12.6692	−	17.4377i	0.529263	−	0.728469i
$574$	−2.34319			−0.0978029
$575$		0			0
$576$	−7.80703			−0.325293
$577$	4.95815	−	6.82431i	0.206411	−	0.284100i	−0.693243	−	0.720704i	$-0.743819\pi$
$577$	4.95815	−	6.82431i	0.206411	−	0.284100i	0.899654	+	0.436604i	$0.143819\pi$
$578$	1.36728	−	0.444257i	0.0568714	−	0.0184786i
$579$	0.973492	+	2.99610i	0.0404570	+	0.124514i
$580$		0			0
$581$	0.993145	−	3.05659i	0.0412026	−	0.126809i
$582$			0.00302764i			0.000125500i
$583$	−46.1495	−	14.9949i	−1.91132	−	0.621025i
$584$	−0.123225	+	0.0895284i	−0.00509910	+	0.00370471i
$585$		0			0
$586$	2.07463	+	1.50731i	0.0857023	+	0.0622664i
$587$	14.2745	+	19.6471i	0.589171	+	0.810925i	0.994663	−	0.103174i	$-0.0328998\pi$
$587$	14.2745	+	19.6471i	0.589171	+	0.810925i	−0.405492	+	0.914099i	$0.632900\pi$
$588$	14.0684	+	19.3634i	0.580169	+	0.798534i
$589$	−4.01943	−	2.92029i	−0.165618	−	0.120328i
$590$		0			0
$591$	21.1022	−	15.3316i	0.868028	−	0.630659i
$592$	−5.40082	−	1.75483i	−0.221972	−	0.0721232i
$593$			28.4653i			1.16893i	0.811418	+	0.584466i	$0.198696\pi$
$593$			28.4653i			1.16893i	−0.811418	+	0.584466i	$0.801304\pi$
$594$	−0.121874	+	0.375089i	−0.00500054	+	0.0153901i
$595$		0			0
$596$	−8.42323	−	25.9240i	−0.345029	−	1.06189i
$597$	−23.0785	+	7.49866i	−0.944541	+	0.306900i
$598$	−0.246539	+	0.339332i	−0.0100817	+	0.0138763i
$599$	−16.0387			−0.655323			−0.327662	−	0.944795i	$-0.606261\pi$
$599$	−16.0387			−0.655323			−0.327662	+	0.944795i	$0.606261\pi$
$600$		0			0
$601$	−8.09005			−0.330000			−0.165000	−	0.986294i	$-0.552762\pi$
$601$	−8.09005			−0.330000			−0.165000	+	0.986294i	$0.552762\pi$
$602$	−0.618268	+	0.850973i	−0.0251987	+	0.0346831i
$603$	12.2894	−	3.99307i	0.500464	−	0.162610i
$604$	−6.96814	−	21.4457i	−0.283530	−	0.872614i
$605$		0			0
$606$	0.0886490	−	0.272834i	0.00360112	−	0.0110831i
$607$		−	0.434608i		−	0.0176402i	−0.999961	−	0.00882010i	$-0.997192\pi$
$607$		−	0.434608i		−	0.0176402i	0.999961	−	0.00882010i	$-0.00280756\pi$
$608$	1.37740	+	0.447544i	0.0558609	+	0.0181503i
$609$	28.1474	−	20.4503i	1.14059	−	0.828687i
$610$		0			0
$611$	17.5378	+	12.7419i	0.709503	+	0.515484i
$612$	1.16734	+	1.60671i	0.0471870	+	0.0649473i
$613$	−23.1565	−	31.8722i	−0.935282	−	1.28731i	−0.957763	−	0.287558i	$-0.907156\pi$
$613$	−23.1565	−	31.8722i	−0.935282	−	1.28731i	0.0224808	−	0.999747i	$-0.492844\pi$
$614$	1.49267	+	1.08449i	0.0602393	+	0.0437664i
$615$		0			0
$616$	−5.55425	+	4.03540i	−0.223787	+	0.162591i
$617$	14.6602	+	4.76337i	0.590196	+	0.191766i	0.588863	−	0.808233i	$-0.299576\pi$
$617$	14.6602	+	4.76337i	0.590196	+	0.191766i	0.00133273	+	0.999999i	$0.499576\pi$
$618$		−	0.768264i		−	0.0309041i
$619$	3.29776	−	10.1495i	0.132548	−	0.407942i	−0.862652	−	0.505797i	$-0.831198\pi$
$619$	3.29776	−	10.1495i	0.132548	−	0.407942i	0.995201	+	0.0978556i	$0.0311983\pi$
$620$		0			0
$621$	−0.728201	−	2.24117i	−0.0292217	−	0.0899352i
$622$	1.49914	−	0.487102i	0.0601102	−	0.0195310i
$623$	25.0865	−	34.5286i	1.00507	−	1.38336i
$624$	−7.83083			−0.313484
$625$		0			0
$626$	0.268168			0.0107182
$627$	−3.48672	+	4.79906i	−0.139246	+	0.191656i
$628$	−16.2177	+	5.26946i	−0.647158	+	0.210275i
$629$	0.442752	+	1.36265i	0.0176537	+	0.0543325i
$630$		0			0
$631$	−5.69664	+	17.5324i	−0.226780	+	0.697956i	0.771327	+	0.636440i	$0.219594\pi$
$631$	−5.69664	+	17.5324i	−0.226780	+	0.697956i	−0.998106	+	0.0615162i	$0.980406\pi$
$632$		−	2.27871i		−	0.0906424i
$633$	15.5767	+	5.06118i	0.619119	+	0.201164i
$634$	1.17506	−	0.853731i	0.0466676	−	0.0339060i
$635$		0			0
$636$	−17.8088	−	12.9389i	−0.706166	−	0.513060i
$637$	13.9958	+	19.2635i	0.554533	+	0.763249i
$638$	1.84957	+	2.54572i	0.0732252	+	0.100786i
$639$	5.92408	+	4.30410i	0.234353	+	0.170267i
$640$		0			0
$641$	−10.0546	+	7.30508i	−0.397132	+	0.288533i	−0.768372	−	0.640004i	$-0.778933\pi$
$641$	−10.0546	+	7.30508i	−0.397132	+	0.288533i	0.371240	+	0.928537i	$0.378933\pi$
$642$	0.189756	+	0.0616554i	0.00748907	+	0.00243335i
$643$			1.84657i			0.0728218i	0.999337	+	0.0364109i	$0.0115925\pi$
$643$			1.84657i			0.0728218i	−0.999337	+	0.0364109i	$0.988407\pi$
$644$	6.32532	−	19.4673i	0.249253	−	0.767120i
$645$		0			0
$646$	−0.0373851	−	0.115059i	−0.00147090	−	0.00452695i
$647$	37.0683	−	12.0442i	1.45731	−	0.473508i	0.530061	−	0.847960i	$-0.322169\pi$
$647$	37.0683	−	12.0442i	1.45731	−	0.473508i	0.927246	+	0.374452i	$0.122169\pi$
$648$	−0.210752	+	0.290076i	−0.00827913	+	0.0113952i
$649$	−29.3708			−1.15290
$650$		0			0
$651$	16.0370			0.628539
$652$	−5.36836	+	7.38891i	−0.210241	+	0.289372i
$653$	26.9519	−	8.75719i	1.05471	−	0.342695i	0.270193	−	0.962806i	$-0.412912\pi$
$653$	26.9519	−	8.75719i	1.05471	−	0.342695i	0.784514	+	0.620111i	$0.212912\pi$
$654$	−0.305378	−	0.939857i	−0.0119412	−	0.0367513i
$655$		0			0
$656$	−7.30538	+	22.4836i	−0.285227	+	0.877839i
$657$		−	0.424804i		−	0.0165732i
$658$	4.07495	+	1.32403i	0.158858	+	0.0516161i
$659$	−18.0864	+	13.1406i	−0.704547	+	0.511883i	−0.881410	−	0.472352i	$-0.843405\pi$
$659$	−18.0864	+	13.1406i	−0.704547	+	0.511883i	0.176863	+	0.984236i	$0.443405\pi$
$660$		0			0
$661$	−23.6349	−	17.1717i	−0.919290	−	0.667903i	0.0240570	−	0.999711i	$-0.492342\pi$
$661$	−23.6349	−	17.1717i	−0.919290	−	0.667903i	−0.943347	+	0.331807i	$0.892342\pi$
$662$	−0.690049	−	0.949771i	−0.0268195	−	0.0369139i
$663$	1.16132	+	1.59842i	0.0451019	+	0.0620774i
$664$	0.213789	+	0.155327i	0.00829662	+	0.00602785i
$665$		0			0
$666$	−0.104424	+	0.0758687i	−0.00404636	+	0.00293985i
$667$	−17.8813	−	5.81000i	−0.692368	−	0.224964i
$668$			14.3776i			0.556287i
$669$	−1.75613	+	5.40480i	−0.0678958	+	0.208962i
$670$		0			0
$671$	−12.8302	−	39.4873i	−0.495305	−	1.52439i
$672$	−4.44605	+	1.44461i	−0.171510	+	0.0557270i
$673$	−1.89000	+	2.60136i	−0.0728542	+	0.100275i	−0.843889	−	0.536518i	$-0.819739\pi$
$673$	−1.89000	+	2.60136i	−0.0728542	+	0.100275i	0.771035	+	0.636793i	$0.219739\pi$
$674$	2.40760			0.0927372
$675$		0			0
$676$	18.0729			0.695111
$677$	−27.7711	+	38.2236i	−1.06733	+	1.46905i	−0.194579	+	0.980887i	$0.562334\pi$
$677$	−27.7711	+	38.2236i	−1.06733	+	1.46905i	−0.872751	+	0.488166i	$0.837666\pi$
$678$	0.146092	−	0.0474681i	0.00561062	−	0.00182300i
$679$	−0.0454227	−	0.139797i	−0.00174316	−	0.00536490i
$680$		0			0
$681$	−1.12598	+	3.46541i	−0.0431476	+	0.132795i
$682$			1.45042i			0.0555395i
$683$	35.4294	+	11.5117i	1.35567	+	0.440483i	0.894595	−	0.446879i	$-0.147464\pi$
$683$	35.4294	+	11.5117i	1.35567	+	0.440483i	0.461074	+	0.887362i	$0.347464\pi$
$684$	−2.17708	+	1.58174i	−0.0832426	+	0.0604793i
$685$		0			0
$686$	1.58934	+	1.15473i	0.0606814	+	0.0440876i
$687$	0.976460	+	1.34398i	0.0372543	+	0.0512761i
$688$	6.23777	+	8.58556i	0.237813	+	0.327321i
$689$	−17.7170	−	12.8721i	−0.674962	−	0.490389i
$690$		0			0
$691$	8.88522	−	6.45549i	0.338010	−	0.245578i	−0.405812	−	0.913957i	$-0.633011\pi$
$691$	8.88522	−	6.45549i	0.338010	−	0.245578i	0.743822	+	0.668378i	$0.233011\pi$
$692$	8.80933	+	2.86232i	0.334880	+	0.108809i
$693$		−	19.1476i		−	0.727357i
$694$	−0.707380	+	2.17709i	−0.0268518	+	0.0826412i
$695$		0			0
$696$	0.884016	+	2.72072i	0.0335085	+	0.103129i
$697$	5.67273	−	1.84318i	0.214870	−	0.0698154i
$698$	−1.48054	+	2.03779i	−0.0560394	+	0.0771316i
$699$	7.85899			0.297254
$700$		0			0
$701$	22.4086			0.846361			0.423180	−	0.906046i	$-0.360914\pi$
$701$	22.4086			0.846361			0.423180	+	0.906046i	$0.360914\pi$
$702$	−0.104621	+	0.143998i	−0.00394865	+	0.00543485i
$703$	−1.84638	+	0.599926i	−0.0696376	+	0.0226266i
$704$	10.5932	+	32.6024i	0.399245	+	1.22875i
$705$		0			0
$706$	−0.407085	+	1.25288i	−0.0153209	+	0.0471527i
$707$			13.9276i			0.523803i
$708$	−12.6718	−	4.11732i	−0.476236	−	0.154738i
$709$	−11.8357	+	8.59914i	−0.444499	+	0.322948i	−0.787420	−	0.616417i	$-0.788584\pi$
$709$	−11.8357	+	8.59914i	−0.444499	+	0.322948i	0.342921	+	0.939364i	$0.388584\pi$
$710$		0			0
$711$	5.14155	+	3.73555i	0.192823	+	0.140094i
$712$	2.06271	+	2.83907i	0.0773032	+	0.106399i
$713$	−5.09394	−	7.01121i	−0.190770	−	0.262572i
$714$	0.315929	+	0.229536i	0.0118233	+	0.00859015i
$715$		0			0
$716$	−11.6083	+	8.43392i	−0.433823	+	0.315191i
$717$	0.539535	+	0.175305i	0.0201493	+	0.00654690i
$718$		−	1.31321i		−	0.0490085i
$719$	8.80627	−	27.1029i	0.328419	−	1.01077i	−0.641455	−	0.767160i	$-0.721669\pi$
$719$	8.80627	−	27.1029i	0.328419	−	1.01077i	0.969874	−	0.243608i	$-0.0783310\pi$
$720$		0			0
$721$	11.5260	+	35.4734i	0.429251	+	1.32110i
$722$	−1.46714	+	0.476702i	−0.0546013	+	0.0177410i
$723$	−11.1727	+	15.3779i	−0.415517	+	0.571910i
$724$	−7.57778			−0.281626
$725$		0			0
$726$	0.743738			0.0276027
$727$	25.8663	−	35.6019i	0.959329	−	1.32040i	0.0120725	−	0.999927i	$-0.496157\pi$
$727$	25.8663	−	35.6019i	0.959329	−	1.32040i	0.947257	−	0.320476i	$-0.103843\pi$
$728$	−2.94676	+	0.957460i	−0.109214	+	0.0354858i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$		0			0
$731$	0.827405	−	2.54649i	0.0306027	−	0.0941854i
$732$		−	18.8351i		−	0.696166i
$733$	25.9854	+	8.44317i	0.959793	+	0.311856i	0.746689	−	0.665174i	$-0.231643\pi$
$733$	25.9854	+	8.44317i	0.959793	+	0.311856i	0.213104	+	0.977029i	$0.431643\pi$
$734$	1.28574	−	0.934144i	0.0474575	−	0.0344799i
$735$		0			0
$736$	2.04380	+	1.48491i	0.0753355	+	0.0547344i
$737$	−33.3504	−	45.9029i	−1.22848	−	1.69086i
$738$	0.315842	+	0.434719i	0.0116263	+	0.0160022i
$739$	13.3227	+	9.67951i	0.490083	+	0.356066i	0.805216	−	0.592981i	$-0.202049\pi$
$739$	13.3227	+	9.67951i	0.490083	+	0.356066i	−0.315133	+	0.949048i	$0.602049\pi$
$740$		0			0
$741$	−2.16584	+	1.57358i	−0.0795642	+	0.0578068i
$742$	−4.11658	−	1.33756i	−0.151124	−	0.0491033i
$743$			35.6012i			1.30608i	0.757322	+	0.653041i	$0.226507\pi$
$743$			35.6012i			1.30608i	−0.757322	+	0.653041i	$0.773493\pi$
$744$	−0.407476	+	1.25408i	−0.0149388	+	0.0459769i
$745$		0			0
$746$	−0.339434	−	1.04467i	−0.0124275	−	0.0382481i
$747$	−0.700939	+	0.227749i	−0.0256460	+	0.00833290i
$748$	5.12573	−	7.05496i	0.187415	−	0.257955i
$749$	−9.68668			−0.353944
$750$		0			0
$751$	46.0748			1.68129			0.840647	−	0.541583i	$-0.182175\pi$
$751$	46.0748			1.68129			0.840647	+	0.541583i	$0.182175\pi$
$752$	25.4090	−	34.9725i	0.926570	−	1.27531i
$753$	−2.87726	+	0.934879i	−0.104853	+	0.0340689i
$754$	0.438839	+	1.35061i	0.0159816	+	0.0491862i
$755$		0			0
$756$	2.68419	−	8.26109i	0.0976231	−	0.300453i
$757$			36.6482i			1.33200i	0.745951	+	0.666000i	$0.231995\pi$
$757$			36.6482i			1.33200i	−0.745951	+	0.666000i	$0.768005\pi$
$758$	2.39998	+	0.779800i	0.0871711	+	0.0283236i
$759$	−8.37114	+	6.08199i	−0.303853	+	0.220762i
$760$		0			0
$761$	22.0116	+	15.9923i	0.797919	+	0.579722i	0.910303	−	0.413943i	$-0.135849\pi$
$761$	22.0116	+	15.9923i	0.797919	+	0.579722i	−0.112384	+	0.993665i	$0.535849\pi$
$762$	0.662939	+	0.912457i	0.0240157	+	0.0330548i
$763$	28.2007	+	38.8149i	1.02093	+	1.40520i
$764$	−34.7346	−	25.2362i	−1.25666	−	0.913013i
$765$		0			0
$766$	2.50212	−	1.81790i	0.0904053	−	0.0656833i
$767$	−12.6064	−	4.09608i	−0.455192	−	0.147901i
$768$			15.3585i			0.554202i
$769$	−8.19906	+	25.2341i	−0.295666	+	0.909965i	0.687331	+	0.726344i	$0.258782\pi$
$769$	−8.19906	+	25.2341i	−0.295666	+	0.909965i	−0.982997	+	0.183621i	$0.941218\pi$
$770$		0			0
$771$	6.13747	+	18.8892i	0.221035	+	0.680277i
$772$	5.96803	−	1.93913i	0.214794	−	0.0697908i
$773$	16.9092	−	23.2736i	0.608183	−	0.837092i	−0.388244	−	0.921557i	$-0.626918\pi$
$773$	16.9092	−	23.2736i	0.608183	−	0.837092i	0.996426	+	0.0844651i	$0.0269181\pi$
$774$	0.241213			0.00867024
$775$		0			0
$776$	0.0120861			0.000433867
$777$	3.68340	−	5.06977i	0.132141	−	0.181877i
$778$	−1.15514	+	0.375327i	−0.0414137	+	0.0134561i
$779$	2.49749	+	7.68650i	0.0894820	+	0.275397i
$780$		0			0
$781$	9.93581	−	30.5793i	0.355531	−	1.09421i
$782$		−	0.211030i		−	0.00754641i
$783$	−7.58806	−	2.46551i	−0.271175	−	0.0881101i
$784$	38.4138	−	27.9092i	1.37192	−	0.996759i
$785$		0			0
$786$	−1.19693	−	0.869621i	−0.0426931	−	0.0310183i
$787$	−14.6160	−	20.1172i	−0.521005	−	0.717102i	0.464721	−	0.885457i	$-0.346155\pi$
$787$	−14.6160	−	20.1172i	−0.521005	−	0.717102i	−0.985726	+	0.168355i	$0.946155\pi$
$788$	−30.5396	−	42.0341i	−1.08793	−	1.49740i
$789$	−18.4698	−	13.4191i	−0.657541	−	0.477732i
$790$		0			0
$791$	−6.03342	+	4.38353i	−0.214524	+	0.155861i
$792$	1.49733	+	0.486512i	0.0532053	+	0.0172875i
$793$		−	18.7379i		−	0.665404i
$794$	−0.998495	+	3.07305i	−0.0354352	+	0.109058i
$795$		0			0
$796$	14.9368	+	45.9708i	0.529422	+	1.62939i
$797$	29.8828	−	9.70951i	1.05850	−	0.343928i	0.272503	−	0.962155i	$-0.412149\pi$
$797$	29.8828	−	9.70951i	1.05850	−	0.343928i	0.786000	+	0.618226i	$0.212149\pi$
$798$	−0.311019	+	0.428081i	−0.0110099	+	0.0151539i
$799$	−10.9067			−0.385851
$800$		0			0
$801$	−9.78736			−0.345819
$802$	−0.230172	+	0.316805i	−0.00812766	+	0.0111868i
$803$	−1.77400	+	0.576406i	−0.0626030	+	0.0203409i
$804$	−7.95393	−	24.4797i	−0.280513	−	0.863332i
$805$		0			0
$806$	−0.202277	+	0.622545i	−0.00712491	+	0.0219282i
$807$		−	14.8324i		−	0.522125i
$808$	−1.08913	−	0.353881i	−0.0383156	−	0.0124495i
$809$	40.8575	−	29.6847i	1.43647	−	1.04366i	0.447710	−	0.894179i	$-0.352240\pi$
$809$	40.8575	−	29.6847i	1.43647	−	1.04366i	0.988765	−	0.149481i	$-0.0477603\pi$
$810$		0			0
$811$	−20.3558	−	14.7894i	−0.714789	−	0.519325i	0.169926	−	0.985457i	$-0.445647\pi$
$811$	−20.3558	−	14.7894i	−0.714789	−	0.519325i	−0.884715	+	0.466132i	$0.845647\pi$
$812$	−40.7356	−	56.0677i	−1.42954	−	1.96759i
$813$	3.78369	+	5.20780i	0.132700	+	0.182646i
$814$	0.458521	+	0.333135i	0.0160712	+	0.0116764i
$815$		0			0
$816$	3.18744	−	2.31581i	0.111583	−	0.0810696i
$817$	3.45047	+	1.12113i	0.120717	+	0.0392233i
$818$		−	1.62697i		−	0.0568856i
$819$	2.67034	−	8.21847i	0.0933093	−	0.287177i
$820$		0			0
$821$	−6.37524	−	19.6210i	−0.222498	−	0.684777i	−0.998536	−	0.0540914i	$-0.982774\pi$
$821$	−6.37524	−	19.6210i	−0.222498	−	0.684777i	0.776038	−	0.630686i	$-0.217226\pi$
$822$	0.825815	−	0.268324i	0.0288036	−	0.00935886i
$823$	21.0790	−	29.0128i	0.734769	−	1.01132i	−0.264133	−	0.964486i	$-0.585086\pi$
$823$	21.0790	−	29.0128i	0.734769	−	1.01132i	0.998903	−	0.0468368i	$-0.0149141\pi$
$824$	−3.06686			−0.106839
$825$		0			0
$826$	−2.61990			−0.0911580
$827$	2.78400	−	3.83184i	0.0968090	−	0.133246i	−0.757865	−	0.652412i	$-0.773757\pi$
$827$	2.78400	−	3.83184i	0.0968090	−	0.133246i	0.854674	+	0.519166i	$0.173757\pi$
$828$	−4.46427	+	1.45053i	−0.155144	+	0.0504093i
$829$	8.79981	+	27.0830i	0.305630	+	0.940632i	0.979441	+	0.201729i	$0.0646560\pi$
$829$	8.79981	+	27.0830i	0.305630	+	0.940632i	−0.673811	+	0.738903i	$0.735344\pi$
$830$		0			0
$831$	−2.07343	+	6.38136i	−0.0719265	+	0.221367i
$832$			15.4708i			0.536355i
$833$	−11.3936	−	3.70200i	−0.394765	−	0.128267i
$834$	0.983357	−	0.714451i	0.0340509	−	0.0247394i
$835$		0			0
$836$	9.55941	+	6.94532i	0.330619	+	0.240209i
$837$	−2.16165	−	2.97525i	−0.0747175	−	0.102840i
$838$	−0.0278685	−	0.0383577i	−0.000962700	−	0.00132504i
$839$	−0.619476	−	0.450076i	−0.0213867	−	0.0155383i	0.577041	−	0.816715i	$-0.304207\pi$
$839$	−0.619476	−	0.450076i	−0.0213867	−	0.0155383i	−0.598427	+	0.801177i	$0.704207\pi$
$840$		0			0
$841$	−28.0384	+	20.3711i	−0.966841	+	0.702451i
$842$	−1.59388	−	0.517883i	−0.0549287	−	0.0178474i
$843$		−	20.4867i		−	0.705600i
$844$	10.0815	−	31.0278i	0.347021	−	1.06802i
$845$		0			0
$846$	−0.303628	−	0.934470i	−0.0104389	−	0.0321278i
$847$	−34.3410	+	11.1581i	−1.17997	+	0.383395i
$848$	−25.6686	+	35.3297i	−0.881462	+	1.21323i
$849$	−11.4177			−0.391856
$850$		0			0
$851$	−3.38644			−0.116086
$852$	8.57347	−	11.8004i	0.293722	−	0.404274i
$853$	33.0292	−	10.7318i	1.13090	−	0.367451i	0.316981	−	0.948432i	$-0.397331\pi$
$853$	33.0292	−	10.7318i	1.13090	−	0.367451i	0.813917	+	0.580981i	$0.197331\pi$
$854$	−1.14447	−	3.52230i	−0.0391628	−	0.120531i
$855$		0			0
$856$	0.246124	−	0.757493i	0.00841236	−	0.0258906i
$857$			54.2561i			1.85335i	0.375860	+	0.926676i	$0.377347\pi$
$857$			54.2561i			1.85335i	−0.375860	+	0.926676i	$0.622653\pi$
$858$	0.743297	+	0.241512i	0.0253757	+	0.00824508i
$859$	12.8710	−	9.35134i	0.439154	−	0.319064i	−0.346145	−	0.938181i	$-0.612509\pi$
$859$	12.8710	−	9.35134i	0.439154	−	0.319064i	0.785299	+	0.619117i	$0.212509\pi$
$860$		0			0
$861$	−21.1055	−	15.3340i	−0.719272	−	0.522582i
$862$	1.10823	+	1.52535i	0.0377464	+	0.0519535i
$863$	13.2083	+	18.1797i	0.449617	+	0.618845i	0.972315	−	0.233673i	$-0.0750744\pi$
$863$	13.2083	+	18.1797i	0.449617	+	0.618845i	−0.522698	+	0.852518i	$0.675074\pi$
$864$	0.867300	+	0.630131i	0.0295062	+	0.0214375i
$865$		0			0
$866$	−0.992896	+	0.721381i	−0.0337400	+	0.0245135i
$867$	15.2226	+	4.94611i	0.516985	+	0.167979i
$868$		−	31.9446i		−	1.08427i
$869$	8.62336	−	26.5400i	0.292527	−	0.900307i
$870$		0			0
$871$	−7.91289	−	24.3534i	−0.268118	−	0.825183i
$872$	−3.75184	+	1.21905i	−0.127053	+	0.0412822i
$873$	−0.0198131	+	0.0272704i	−0.000670572	+	0.000922963i
$874$	0.285944			0.00967219
$875$		0			0
$876$	−0.846181			−0.0285898
$877$	15.9146	−	21.9046i	0.537399	−	0.739667i	−0.450836	−	0.892607i	$-0.648874\pi$
$877$	15.9146	−	21.9046i	0.537399	−	0.739667i	0.988235	+	0.152940i	$0.0488741\pi$
$878$	0.370173	−	0.120276i	0.0124927	−	0.00405913i
$879$	8.82258	+	27.1531i	0.297578	+	0.915852i
$880$		0			0
$881$	−2.41440	+	7.43077i	−0.0813433	+	0.250349i	−0.983455	−	0.181154i	$-0.942017\pi$
$881$	−2.41440	+	7.43077i	−0.0813433	+	0.250349i	0.902111	+	0.431503i	$0.142017\pi$
$882$		−	1.07925i		−	0.0363401i
$883$	55.4476	+	18.0160i	1.86596	+	0.606287i	0.992942	+	0.118599i	$0.0378402\pi$
$883$	55.4476	+	18.0160i	1.86596	+	0.606287i	0.873018	+	0.487688i	$0.162160\pi$
$884$	3.18394	−	2.31327i	0.107088	−	0.0778036i
$885$		0			0
$886$	−0.116804	−	0.0848629i	−0.00392410	−	0.00285102i
$887$	5.08205	+	6.99484i	0.170638	+	0.234864i	0.885768	−	0.464128i	$-0.153632\pi$
$887$	5.08205	+	6.99484i	0.170638	+	0.234864i	−0.715130	+	0.698992i	$0.753632\pi$
$888$	0.302863	+	0.416855i	0.0101634	+	0.0139887i
$889$	−44.2994	−	32.1854i	−1.48576	−	1.07946i
$890$		0			0
$891$	−3.55235	+	2.58093i	−0.119008	+	0.0864644i
$892$	10.7660	+	3.49809i	0.360472	+	0.117125i
$893$		−	14.7785i		−	0.494543i
$894$	−0.379817	+	1.16896i	−0.0127030	+	0.0390957i
$895$		0			0
$896$	3.83414	+	11.8003i	0.128090	+	0.394219i
$897$	−4.44123	+	1.44304i	−0.148288	+	0.0481818i
$898$	−0.730099	+	1.00490i	−0.0243637	+	0.0335338i
$899$	−29.3420			−0.978612
$900$		0			0
$901$	11.0181			0.367067
$902$	1.38684	−	1.90883i	0.0461769	−	0.0635570i
$903$	−11.1377	+	3.61885i	−0.370638	+	0.120428i
$904$	−0.189490	−	0.583189i	−0.00630233	−	0.0193966i
$905$		0			0
$906$	−0.314205	+	0.967022i	−0.0104387	+	0.0321272i
$907$		−	40.4367i		−	1.34268i	−0.741151	−	0.671339i	$-0.765720\pi$
$907$		−	40.4367i		−	1.34268i	0.741151	−	0.671339i	$-0.234280\pi$
$908$	6.90285	+	2.24287i	0.229079	+	0.0744324i
$909$	2.58392	−	1.87733i	0.0857032	−	0.0622670i
$910$		0			0
$911$	40.9074	+	29.7210i	1.35532	+	0.984700i	0.998727	+	0.0504407i	$0.0160626\pi$
$911$	40.9074	+	29.7210i	1.35532	+	0.984700i	0.356596	+	0.934259i	$0.383937\pi$
$912$	3.13790	+	4.31895i	0.103906	+	0.143015i
$913$	1.90217	+	2.61812i	0.0629528	+	0.0866471i
$914$	−1.46308	−	1.06299i	−0.0483944	−	0.0351606i
$915$		0			0
$916$	2.67712	−	1.94504i	0.0884545	−	0.0642660i
$917$	68.3130	+	22.1962i	2.25590	+	0.732985i
$918$		−	0.0895519i		−	0.00295565i
$919$	13.3979	−	41.2346i	0.441957	−	1.36020i	−0.443831	−	0.896111i	$-0.646381\pi$
$919$	13.3979	−	41.2346i	0.441957	−	1.36020i	0.885787	−	0.464092i	$-0.153619\pi$
$920$		0			0
$921$	6.34773	+	19.5363i	0.209165	+	0.643743i
$922$	2.69309	−	0.875039i	0.0886923	−	0.0288179i
$923$	8.52924	−	11.7395i	0.280743	−	0.386410i
$924$	−38.1407			−1.25474
$925$		0			0
$926$	0.00405712			0.000133325
$927$	5.02758	−	6.91986i	0.165127	−	0.227278i
$928$	8.13472	−	2.64313i	0.267035	−	0.0867650i
$929$	10.5605	+	32.5020i	0.346480	+	1.06636i	0.960787	+	0.277289i	$0.0894358\pi$
$929$	10.5605	+	32.5020i	0.346480	+	1.06636i	−0.614307	+	0.789067i	$0.710564\pi$
$930$		0			0
$931$	5.01618	−	15.4382i	0.164399	−	0.505967i
$932$		−	15.6546i		−	0.512783i
$933$	16.6907	+	5.42312i	0.546427	+	0.177545i
$934$	2.38596	−	1.73350i	0.0780710	−	0.0567219i
$935$		0			0
$936$	0.574830	+	0.417638i	0.0187889	+	0.0136509i
$937$	−16.3990	−	22.5713i	−0.535731	−	0.737371i	0.452259	−	0.891887i	$-0.350618\pi$
$937$	−16.3990	−	22.5713i	−0.535731	−	0.737371i	−0.987990	+	0.154516i	$0.950618\pi$
$938$	−2.97489	−	4.09458i	−0.0971334	−	0.133693i
$939$	2.41543	+	1.75491i	0.0788246	+	0.0572694i
$940$		0			0
$941$	43.9507	−	31.9321i	1.43275	−	1.04096i	0.443257	−	0.896395i	$-0.353823\pi$
$941$	43.9507	−	31.9321i	1.43275	−	1.04096i	0.989496	−	0.144561i	$-0.0461769\pi$
$942$	0.731284	+	0.237609i	0.0238265	+	0.00774171i
$943$			14.0978i			0.459086i
$944$	−8.16808	+	25.1388i	−0.265848	+	0.818197i
$945$		0			0
$946$	−0.327297	−	1.00732i	−0.0106413	−	0.0327507i
$947$	−4.02460	+	1.30767i	−0.130782	+	0.0424936i	−0.373677	−	0.927559i	$-0.621903\pi$
$947$	−4.02460	+	1.30767i	−0.130782	+	0.0424936i	0.242895	+	0.970053i	$0.421903\pi$
$948$	7.44097	−	10.2416i	0.241672	−	0.332632i
$949$	−0.841815			−0.0273265
$950$		0			0
$951$	16.1708			0.524375
$952$	0.916291	−	1.26117i	0.0296971	−	0.0408746i
$953$	−45.5848	+	14.8114i	−1.47664	+	0.479788i	−0.933106	−	0.359601i	$-0.882913\pi$
$953$	−45.5848	+	14.8114i	−1.47664	+	0.479788i	−0.543531	+	0.839389i	$0.682913\pi$
$954$	0.306730	+	0.944017i	0.00993074	+	0.0305637i
$955$		0			0
$956$	0.349197	−	1.07472i	0.0112938	−	0.0347588i
$957$			35.0334i			1.13247i
$958$	0.639459	+	0.207773i	0.0206600	+	0.00671284i
$959$	−34.1052	+	24.7788i	−1.10131	+	0.800151i
$960$		0			0
$961$	14.1377	+	10.2716i	0.456055	+	0.331343i
$962$	0.150346	+	0.206933i	0.00484734	+	0.00667179i
$963$	1.30568	+	1.79712i	0.0420750	+	0.0579113i
$964$	30.6318	+	22.2553i	0.986582	+	0.716794i
$965$		0			0
$966$	−0.746713	+	0.542518i	−0.0240251	+	0.0174552i
$967$	−19.8607	−	6.45312i	−0.638676	−	0.207518i	−0.0282614	−	0.999601i	$-0.508997\pi$
$967$	−19.8607	−	6.45312i	−0.638676	−	0.207518i	−0.610414	+	0.792082i	$0.708997\pi$
$968$		−	2.96895i		−	0.0954257i
$969$	0.416225	−	1.28101i	0.0133711	−	0.0411519i
$970$		0			0
$971$	4.96713	+	15.2872i	0.159403	+	0.490591i	0.998580	−	0.0532663i	$-0.0169632\pi$
$971$	4.96713	+	15.2872i	0.159403	+	0.490591i	−0.839178	+	0.543857i	$0.816963\pi$
$972$	−1.89444	+	0.615541i	−0.0607642	+	0.0197435i
$973$	−34.6863	+	47.7417i	−1.11199	+	1.53053i
$974$	−2.28406			−0.0731860
$975$		0			0
$976$	−37.3657			−1.19605
$977$	−20.9055	+	28.7739i	−0.668826	+	0.920560i	−0.999733	−	0.0231034i	$-0.992645\pi$
$977$	−20.9055	+	28.7739i	−0.668826	+	0.920560i	0.330907	+	0.943663i	$0.392645\pi$
$978$	0.391674	−	0.127263i	0.0125244	−	0.00406941i
$979$	13.2802	+	40.8723i	0.424438	+	1.30629i
$980$		0			0
$981$	3.39991	−	10.4638i	0.108551	−	0.334085i
$982$			0.994014i			0.0317202i
$983$	−17.5671	−	5.70790i	−0.560303	−	0.182054i	0.0151542	−	0.999885i	$-0.495176\pi$
$983$	−17.5671	−	5.70790i	−0.560303	−	0.182054i	−0.575458	+	0.817832i	$0.695176\pi$
$984$	1.73537	−	1.26082i	0.0553216	−	0.0401935i
$985$		0			0
$986$	−0.578039	−	0.419970i	−0.0184085	−	0.0133746i
$987$	28.0391	+	38.5925i	0.892494	+	1.22841i
$988$	3.13446	+	4.31421i	0.0997204	+	0.137253i
$989$	5.11986	+	3.71979i	0.162802	+	0.118283i
$990$		0			0
$991$	33.6476	−	24.4464i	1.06885	−	0.776566i	0.0931455	−	0.995653i	$-0.470308\pi$
$991$	33.6476	−	24.4464i	1.06885	−	0.776566i	0.975705	+	0.219087i	$0.0703078\pi$
$992$	3.74959	+	1.21832i	0.119050	+	0.0386816i
$993$		−	13.0705i		−	0.414779i
$994$	0.886283	−	2.72770i	0.0281112	−	0.0865174i
$995$		0			0
$996$	0.453660	+	1.39622i	0.0143748	+	0.0442410i
$997$	−30.2792	+	9.83830i	−0.958952	+	0.311582i	−0.746348	−	0.665556i	$-0.768194\pi$
$997$	−30.2792	+	9.83830i	−0.958952	+	0.311582i	−0.212604	+	0.977138i	$0.568194\pi$
$998$	0.247161	−	0.340189i	0.00782376	−	0.0107685i
$999$	−1.43706			−0.0454665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.49.2		16
5.2	odd	4		375.2.g.e.76.2		16
5.3	odd	4		375.2.g.d.76.3		16
5.4	even	2		75.2.i.a.34.3	✓	16
15.14	odd	2		225.2.m.b.109.2		16
25.2	odd	20		375.2.g.e.301.2		16
25.6	even	5		1875.2.b.h.1249.8		16
25.8	odd	20		1875.2.a.p.1.4		8
25.11	even	5		75.2.i.a.64.3	yes	16
25.14	even	10	inner	375.2.i.c.199.2		16
25.17	odd	20		1875.2.a.m.1.5		8
25.19	even	10		1875.2.b.h.1249.9		16
25.23	odd	20		375.2.g.d.301.3		16
75.8	even	20		5625.2.a.t.1.5		8
75.11	odd	10		225.2.m.b.64.2		16
75.17	even	20		5625.2.a.bd.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.3	✓	16	5.4	even	2
75.2.i.a.64.3	yes	16	25.11	even	5
225.2.m.b.64.2		16	75.11	odd	10
225.2.m.b.109.2		16	15.14	odd	2
375.2.g.d.76.3		16	5.3	odd	4
375.2.g.d.301.3		16	25.23	odd	20
375.2.g.e.76.2		16	5.2	odd	4
375.2.g.e.301.2		16	25.2	odd	20
375.2.i.c.49.2		16	1.1	even	1	trivial
375.2.i.c.199.2		16	25.14	even	10	inner
1875.2.a.m.1.5		8	25.17	odd	20
1875.2.a.p.1.4		8	25.8	odd	20
1875.2.b.h.1249.8		16	25.6	even	5
1875.2.b.h.1249.9		16	25.19	even	10
5625.2.a.t.1.5		8	75.8	even	20
5625.2.a.bd.1.4		8	75.17	even	20

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0527945 + 0.0726655i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.615541 + 1.89444i) q^{4} +(0.0277557 - 0.0854234i) q^{6} +4.36070i q^{7} +(-0.341004 - 0.110799i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.0527945 + 0.0726655i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.615541 + 1.89444i) q^{4} +(0.0277557 - 0.0854234i) q^{6} +4.36070i q^{7} +(-0.341004 - 0.110799i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-3.55235 - 2.58093i) q^{11} +(-1.17083 - 1.61151i) q^{12} +(-1.16479 - 1.60319i) q^{13} +(-0.316872 - 0.230221i) q^{14} +(-3.19696 + 2.32273i) q^{16} +(0.948224 + 0.308097i) q^{17} +0.0898194i q^{18} +(-0.417468 + 1.28484i) q^{19} +(-1.34753 - 4.14727i) q^{21} +(0.375089 - 0.121874i) q^{22} +(-1.38512 + 1.90646i) q^{23} +0.358553 q^{24} +0.177991 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-8.26109 + 2.68419i) q^{28} +(2.46551 + 7.58806i) q^{29} +(-1.13645 + 3.49762i) q^{31} -1.07204i q^{32} +(4.17603 + 1.35688i) q^{33} +(-0.0724490 + 0.0526373i) q^{34} +(1.61151 + 1.17083i) q^{36} +(0.844681 + 1.16260i) q^{37} +(-0.0713231 - 0.0981678i) q^{38} +(1.60319 + 1.16479i) q^{39} +(4.83992 - 3.51641i) q^{41} +(0.372506 + 0.121034i) q^{42} -2.68554i q^{43} +(2.70280 - 8.31838i) q^{44} +(-0.0654066 - 0.201301i) q^{46} +(-10.4039 + 3.38042i) q^{47} +(2.32273 - 3.19696i) q^{48} -12.0157 q^{49} -0.997022 q^{51} +(2.32018 - 3.19345i) q^{52} +(10.5102 - 3.41496i) q^{53} +(-0.0277557 - 0.0854234i) q^{54} +(0.483161 - 1.48702i) q^{56} -1.35096i q^{57} +(-0.681555 - 0.221451i) q^{58} +(5.41147 - 3.93167i) q^{59} +(7.64982 + 5.55792i) q^{61} +(-0.194158 - 0.267235i) q^{62} +(2.56316 + 3.52788i) q^{63} +(-6.31602 - 4.58886i) q^{64} +(-0.319070 + 0.231818i) q^{66} +(12.2894 + 3.99307i) q^{67} +1.98600i q^{68} +(0.728201 - 2.24117i) q^{69} +(2.26280 + 6.96418i) q^{71} +(-0.341004 + 0.110799i) q^{72} +(0.249694 - 0.343674i) q^{73} -0.129076 q^{74} -2.69101 q^{76} +(11.2547 - 15.4907i) q^{77} +(-0.169280 + 0.0550023i) q^{78} +(1.96390 + 6.04425i) q^{79} +(0.309017 - 0.951057i) q^{81} +0.537343i q^{82} +(-0.700939 - 0.227749i) q^{83} +(7.02730 - 5.10563i) q^{84} +(0.195146 + 0.141782i) q^{86} +(-4.68968 - 6.45479i) q^{87} +(0.925401 + 1.27370i) q^{88} +(-7.91814 - 5.75286i) q^{89} +(6.99105 - 5.07929i) q^{91} +(-4.46427 - 1.45053i) q^{92} -3.67761i q^{93} +(0.303628 - 0.934470i) q^{94} +(0.331279 + 1.01957i) q^{96} +(-0.0320583 + 0.0104164i) q^{97} +(0.634365 - 0.873128i) q^{98} -4.39094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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