LMFDB - Embedded newform 750.2.h.a.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(49,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, 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("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.h (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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			649.2
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.649
Dual form			750.2.h.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -2.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -2.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.951057 + 0.309017i) q^{12} +(4.61653 - 1.50000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(0.309017 + 0.951057i) q^{16} +(4.61653 + 6.35410i) q^{17} -1.00000i q^{18} +(-2.23607 + 1.62460i) q^{19} +(1.61803 + 1.17557i) q^{21} +(-3.07768 + 4.23607i) q^{22} +(5.70634 + 1.85410i) q^{23} -1.00000 q^{24} +4.85410 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.17557 - 1.61803i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-3.00000 + 2.17963i) q^{31} +1.00000i q^{32} +(-3.07768 - 4.23607i) q^{33} +(2.42705 + 7.46969i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.04087 + 0.663119i) q^{37} +(-2.62866 + 0.854102i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(-1.88197 - 5.79210i) q^{41} +(1.17557 + 1.61803i) q^{42} -1.23607i q^{43} +(-4.23607 + 3.07768i) q^{44} +(4.85410 + 3.52671i) q^{46} +(-2.80017 + 3.85410i) q^{47} +(-0.951057 - 0.309017i) q^{48} +3.00000 q^{49} -7.85410 q^{51} +(4.61653 + 1.50000i) q^{52} +(5.03280 - 6.92705i) q^{53} +(0.809017 + 0.587785i) q^{54} +(1.61803 - 1.17557i) q^{56} -2.76393i q^{57} +(-0.812299 - 1.11803i) q^{58} +(-2.76393 - 8.50651i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(-3.52671 + 1.14590i) q^{62} +(-1.90211 + 0.618034i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-1.61803 - 4.97980i) q^{66} +(-5.70634 - 7.85410i) q^{67} +7.85410i q^{68} +(-4.85410 + 3.52671i) q^{69} +(11.4721 + 8.33499i) q^{71} +(0.587785 - 0.809017i) q^{72} +(-2.99193 - 0.972136i) q^{73} -2.14590 q^{74} -2.76393 q^{76} +(9.95959 + 3.23607i) q^{77} +(-2.85317 + 3.92705i) q^{78} +(-0.809017 + 0.587785i) q^{81} -6.09017i q^{82} +(-3.52671 - 4.85410i) q^{83} +(0.618034 + 1.90211i) q^{84} +(0.381966 - 1.17557i) q^{86} +(1.31433 - 0.427051i) q^{87} +(-4.97980 + 1.61803i) q^{88} +(-0.427051 + 1.31433i) q^{89} +(-3.00000 - 9.23305i) q^{91} +(3.52671 + 4.85410i) q^{92} -3.70820i q^{93} +(-3.85410 + 2.80017i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(8.14324 - 11.2082i) q^{97} +(2.85317 + 0.927051i) q^{98} +5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{21} - 8 q^{24} + 12 q^{26} - 24 q^{31} + 6 q^{34} - 2 q^{36} - 12 q^{39} - 24 q^{41} - 16 q^{44} + 12 q^{46} + 24 q^{49} - 36 q^{51} + 2 q^{54} + 4 q^{56} - 40 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{66} - 12 q^{69} + 56 q^{71} - 44 q^{74} - 40 q^{76} - 2 q^{81} - 4 q^{84} + 12 q^{86} + 10 q^{89} - 24 q^{91} - 4 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^21 - 8 * q^24 + 12 * q^26 - 24 * q^31 + 6 * q^34 - 2 * q^36 - 12 * q^39 - 24 * q^41 - 16 * q^44 + 12 * q^46 + 24 * q^49 - 36 * q^51 + 2 * q^54 + 4 * q^56 - 40 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^66 - 12 * q^69 + 56 * q^71 - 44 * q^74 - 40 * q^76 - 2 * q^81 - 4 * q^84 + 12 * q^86 + 10 * q^89 - 24 * q^91 - 4 * q^94 - 2 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	0.339946	+	0.940445i	$0.389591\pi$
$11$	−1.61803	+	4.97980i	−0.487856	+	1.50147i	−0.827802	+	0.561020i	$0.810409\pi$
$12$	−0.951057	+	0.309017i	−0.274546	+	0.0892055i
$13$	4.61653	−	1.50000i	1.28039	−	0.416025i	0.411675	−	0.911331i	$-0.364944\pi$
$13$	4.61653	−	1.50000i	1.28039	−	0.416025i	0.868719	+	0.495306i	$0.164944\pi$
$14$	0.618034	−	1.90211i	0.165177	−	0.508361i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.61653	+	6.35410i	1.11967	+	1.54110i	0.806340	+	0.591452i	$0.201445\pi$
$17$	4.61653	+	6.35410i	1.11967	+	1.54110i	0.313332	+	0.949644i	$0.398555\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−2.23607	+	1.62460i	−0.512989	+	0.372708i	−0.813956	−	0.580926i	$-0.802691\pi$
$19$	−2.23607	+	1.62460i	−0.512989	+	0.372708i	0.300967	+	0.953635i	$0.402691\pi$
$20$		0			0
$21$	1.61803	+	1.17557i	0.353084	+	0.256531i
$22$	−3.07768	+	4.23607i	−0.656164	+	0.903133i
$23$	5.70634	+	1.85410i	1.18985	+	0.386607i	0.836019	−	0.548701i	$-0.184877\pi$
$23$	5.70634	+	1.85410i	1.18985	+	0.386607i	0.353835	+	0.935308i	$0.384877\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	4.85410			0.951968
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	1.17557	−	1.61803i	0.222162	−	0.305780i
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	0.479120	−	0.877750i	$-0.340956\pi$
$29$	−1.11803	−	0.812299i	−0.207614	−	0.150840i	−0.686733	+	0.726909i	$0.740956\pi$
$30$		0			0
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	−0.823645	−	0.567106i	$-0.808063\pi$
$31$	−3.00000	+	2.17963i	−0.538816	+	0.391473i	0.284829	+	0.958578i	$0.408063\pi$
$32$			1.00000i			0.176777i
$33$	−3.07768	−	4.23607i	−0.535756	−	0.737405i
$34$	2.42705	+	7.46969i	0.416236	+	1.28104i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−2.04087	+	0.663119i	−0.335517	+	0.109016i	−0.471930	−	0.881636i	$-0.656443\pi$
$37$	−2.04087	+	0.663119i	−0.335517	+	0.109016i	0.136413	+	0.990652i	$0.456443\pi$
$38$	−2.62866	+	0.854102i	−0.426424	+	0.138554i
$39$	−1.50000	+	4.61653i	−0.240192	+	0.739236i
$40$		0			0
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	−0.983584	−	0.180450i	$-0.942245\pi$
$41$	−1.88197	−	5.79210i	−0.293914	−	0.904573i	0.689670	−	0.724123i	$-0.257755\pi$
$42$	1.17557	+	1.61803i	0.181394	+	0.249668i
$43$		−	1.23607i		−	0.188499i	−0.995549	−	0.0942493i	$-0.969955\pi$
$43$		−	1.23607i		−	0.188499i	0.995549	−	0.0942493i	$-0.0300451\pi$
$44$	−4.23607	+	3.07768i	−0.638611	+	0.463978i
$45$		0			0
$46$	4.85410	+	3.52671i	0.715698	+	0.519985i
$47$	−2.80017	+	3.85410i	−0.408447	+	0.562179i	−0.962839	−	0.270077i	$-0.912951\pi$
$47$	−2.80017	+	3.85410i	−0.408447	+	0.562179i	0.554392	+	0.832256i	$0.312951\pi$
$48$	−0.951057	−	0.309017i	−0.137273	−	0.0446028i
$49$	3.00000			0.428571
$50$		0			0
$51$	−7.85410			−1.09979
$52$	4.61653	+	1.50000i	0.640197	+	0.208013i
$53$	5.03280	−	6.92705i	0.691308	−	0.951504i	−0.308692	−	0.951162i	$-0.599891\pi$
$53$	5.03280	−	6.92705i	0.691308	−	0.951504i	1.00000		0.000341607i	$-0.000108737\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$		0			0
$56$	1.61803	−	1.17557i	0.216219	−	0.157092i
$57$		−	2.76393i		−	0.366092i
$58$	−0.812299	−	1.11803i	−0.106660	−	0.146805i
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	−0.953154	−	0.302487i	$-0.902183\pi$
$59$	−2.76393	−	8.50651i	−0.359833	−	1.10745i	0.593320	−	0.804966i	$-0.297817\pi$
$60$		0			0
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	0.608357	+	0.793663i	$0.291829\pi$
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	−0.958675	+	0.284504i	$0.908171\pi$
$62$	−3.52671	+	1.14590i	−0.447893	+	0.145529i
$63$	−1.90211	+	0.618034i	−0.239644	+	0.0778650i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		0			0
$66$	−1.61803	−	4.97980i	−0.199166	−	0.612971i
$67$	−5.70634	−	7.85410i	−0.697140	−	0.959531i	−0.999979	−	0.00648944i	$-0.997934\pi$
$67$	−5.70634	−	7.85410i	−0.697140	−	0.959531i	0.302839	−	0.953042i	$-0.402066\pi$
$68$			7.85410i			0.952450i
$69$	−4.85410	+	3.52671i	−0.584365	+	0.424566i
$70$		0			0
$71$	11.4721	+	8.33499i	1.36149	+	0.989182i	0.998348	+	0.0574487i	$0.0182966\pi$
$71$	11.4721	+	8.33499i	1.36149	+	0.989182i	0.363144	+	0.931733i	$0.381703\pi$
$72$	0.587785	−	0.809017i	0.0692712	−	0.0953436i
$73$	−2.99193	−	0.972136i	−0.350179	−	0.113780i	0.128646	−	0.991691i	$-0.458937\pi$
$73$	−2.99193	−	0.972136i	−0.350179	−	0.113780i	−0.478824	+	0.877911i	$0.658937\pi$
$74$	−2.14590			−0.249456
$75$		0			0
$76$	−2.76393			−0.317045
$77$	9.95959	+	3.23607i	1.13500	+	0.368784i
$78$	−2.85317	+	3.92705i	−0.323058	+	0.444651i
$79$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$79$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		−	6.09017i		−	0.672547i
$83$	−3.52671	−	4.85410i	−0.387107	−	0.532807i	0.570343	−	0.821407i	$-0.306810\pi$
$83$	−3.52671	−	4.85410i	−0.387107	−	0.532807i	−0.957450	+	0.288600i	$0.906810\pi$
$84$	0.618034	+	1.90211i	0.0674330	+	0.207538i
$85$		0			0
$86$	0.381966	−	1.17557i	0.0411885	−	0.126765i
$87$	1.31433	−	0.427051i	0.140911	−	0.0457847i
$88$	−4.97980	+	1.61803i	−0.530848	+	0.172483i
$89$	−0.427051	+	1.31433i	−0.0452673	+	0.139318i	−0.971136	−	0.238528i	$-0.923335\pi$
$89$	−0.427051	+	1.31433i	−0.0452673	+	0.139318i	0.925868	+	0.377846i	$0.123335\pi$
$90$		0			0
$91$	−3.00000	−	9.23305i	−0.314485	−	0.967887i
$92$	3.52671	+	4.85410i	0.367685	+	0.506075i
$93$		−	3.70820i		−	0.384523i
$94$	−3.85410	+	2.80017i	−0.397520	+	0.288815i
$95$		0			0
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	8.14324	−	11.2082i	0.826820	−	1.13802i	−0.161686	−	0.986842i	$-0.551693\pi$
$97$	8.14324	−	11.2082i	0.826820	−	1.13802i	0.988506	−	0.151178i	$-0.0483068\pi$
$98$	2.85317	+	0.927051i	0.288214	+	0.0936463i
$99$	5.23607			0.526245
$100$		0			0
$101$	1.67376			0.166546			0.0832728	−	0.996527i	$-0.473463\pi$
$101$	1.67376			0.166546			0.0832728	+	0.996527i	$0.473463\pi$
$102$	−7.46969	−	2.42705i	−0.739610	−	0.240314i
$103$	−1.34708	+	1.85410i	−0.132732	+	0.182690i	−0.870210	−	0.492682i	$-0.836017\pi$
$103$	−1.34708	+	1.85410i	−0.132732	+	0.182690i	0.737478	+	0.675372i	$0.236017\pi$
$104$	3.92705	+	2.85317i	0.385079	+	0.279776i
$105$		0			0
$106$	6.92705	−	5.03280i	0.672815	−	0.488828i
$107$		−	10.9443i		−	1.05802i	−0.848615	−	0.529011i	$-0.822563\pi$
$107$		−	10.9443i		−	1.05802i	0.848615	−	0.529011i	$-0.177437\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−0.791796	−	2.43690i	−0.0758403	−	0.233412i	0.905949	−	0.423388i	$-0.139159\pi$
$109$	−0.791796	−	2.43690i	−0.0758403	−	0.233412i	−0.981789	+	0.189975i	$0.939159\pi$
$110$		0			0
$111$	0.663119	−	2.04087i	0.0629405	−	0.193711i
$112$	1.90211	−	0.618034i	0.179733	−	0.0583987i
$113$	10.9964	−	3.57295i	1.03445	−	0.336115i	0.257905	−	0.966170i	$-0.416968\pi$
$113$	10.9964	−	3.57295i	1.03445	−	0.336115i	0.776550	+	0.630056i	$0.216968\pi$
$114$	0.854102	−	2.62866i	0.0799940	−	0.246196i
$115$		0			0
$116$	−0.427051	−	1.31433i	−0.0396507	−	0.122032i
$117$	−2.85317	−	3.92705i	−0.263776	−	0.363056i
$118$		−	8.94427i		−	0.823387i
$119$	12.7082	−	9.23305i	1.16496	−	0.846392i
$120$		0			0
$121$	−13.2812	−	9.64932i	−1.20738	−	0.877211i
$122$	−5.20431	+	7.16312i	−0.471176	+	0.648518i
$123$	5.79210	+	1.88197i	0.522256	+	0.169691i
$124$	−3.70820			−0.333007
$125$		0			0
$126$	−2.00000			−0.178174
$127$	−0.277515	−	0.0901699i	−0.0246254	−	0.00800129i	0.296678	−	0.954977i	$-0.404121\pi$
$127$	−0.277515	−	0.0901699i	−0.0246254	−	0.00800129i	−0.321304	+	0.946976i	$0.604121\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	1.00000	+	0.726543i	0.0880451	+	0.0639685i
$130$		0			0
$131$	0.618034	−	0.449028i	0.0539979	−	0.0392318i	−0.560459	−	0.828182i	$-0.689375\pi$
$131$	0.618034	−	0.449028i	0.0539979	−	0.0392318i	0.614457	+	0.788950i	$0.289375\pi$
$132$		−	5.23607i		−	0.455741i
$133$	3.24920	+	4.47214i	0.281741	+	0.387783i
$134$	−3.00000	−	9.23305i	−0.259161	−	0.797614i
$135$		0			0
$136$	−2.42705	+	7.46969i	−0.208118	+	0.640521i
$137$	−14.2986	+	4.64590i	−1.22161	+	0.396926i	−0.847669	−	0.530526i	$-0.821995\pi$
$137$	−14.2986	+	4.64590i	−1.22161	+	0.396926i	−0.373943	+	0.927452i	$0.621995\pi$
$138$	−5.70634	+	1.85410i	−0.485756	+	0.157832i
$139$	4.14590	−	12.7598i	0.351650	−	1.08227i	−0.606276	−	0.795254i	$-0.707337\pi$
$139$	4.14590	−	12.7598i	0.351650	−	1.08227i	0.957926	−	0.287014i	$-0.0926628\pi$
$140$		0			0
$141$	−1.47214	−	4.53077i	−0.123976	−	0.381560i
$142$	8.33499	+	11.4721i	0.699457	+	0.962720i
$143$			25.4164i			2.12543i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$		0			0
$146$	−2.54508	−	1.84911i	−0.210633	−	0.153034i
$147$	−1.76336	+	2.42705i	−0.145439	+	0.200180i
$148$	−2.04087	−	0.663119i	−0.167759	−	0.0545080i
$149$	−7.03444			−0.576284			−0.288142	−	0.957588i	$-0.593038\pi$
$149$	−7.03444			−0.576284			−0.288142	+	0.957588i	$0.593038\pi$
$150$		0			0
$151$	−6.94427			−0.565117			−0.282558	−	0.959250i	$-0.591183\pi$
$151$	−6.94427			−0.565117			−0.282558	+	0.959250i	$0.591183\pi$
$152$	−2.62866	−	0.854102i	−0.213212	−	0.0692768i
$153$	4.61653	−	6.35410i	0.373224	−	0.513699i
$154$	8.47214	+	6.15537i	0.682704	+	0.496014i
$155$		0			0
$156$	−3.92705	+	2.85317i	−0.314416	+	0.228436i
$157$		−	17.8541i		−	1.42491i	−0.701717	−	0.712456i	$-0.747583\pi$
$157$		−	17.8541i		−	1.42491i	0.701717	−	0.712456i	$-0.252417\pi$
$158$		0			0
$159$	2.64590	+	8.14324i	0.209833	+	0.645801i
$160$		0			0
$161$	3.70820	−	11.4127i	0.292247	−	0.899445i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	−19.4702	+	6.32624i	−1.52502	+	0.495509i	−0.947197	−	0.320652i	$-0.896098\pi$
$163$	−19.4702	+	6.32624i	−1.52502	+	0.495509i	−0.577824	+	0.816162i	$0.696098\pi$
$164$	1.88197	−	5.79210i	0.146957	−	0.452287i
$165$		0			0
$166$	−1.85410	−	5.70634i	−0.143906	−	0.442898i
$167$	3.80423	+	5.23607i	0.294380	+	0.405179i	0.930431	−	0.366468i	$-0.119433\pi$
$167$	3.80423	+	5.23607i	0.294380	+	0.405179i	−0.636051	+	0.771647i	$0.719433\pi$
$168$			2.00000i			0.154303i
$169$	8.54508	−	6.20837i	0.657314	−	0.477567i
$170$		0			0
$171$	2.23607	+	1.62460i	0.170996	+	0.124236i
$172$	0.726543	−	1.00000i	0.0553983	−	0.0762493i
$173$	−10.3759	−	3.37132i	−0.788862	−	0.256317i	−0.113243	−	0.993567i	$-0.536124\pi$
$173$	−10.3759	−	3.37132i	−0.788862	−	0.256317i	−0.675620	+	0.737250i	$0.736124\pi$
$174$	1.38197			0.104767
$175$		0			0
$176$	−5.23607			−0.394683
$177$	8.50651	+	2.76393i	0.639388	+	0.207750i
$178$	−0.812299	+	1.11803i	−0.0608844	+	0.0838002i
$179$	−3.09017	−	2.24514i	−0.230970	−	0.167810i	0.466281	−	0.884637i	$-0.345594\pi$
$179$	−3.09017	−	2.24514i	−0.230970	−	0.167810i	−0.697251	+	0.716827i	$0.745594\pi$
$180$		0			0
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.210003	−	0.977701i	$-0.432653\pi$
$181$	16.2082	−	11.7759i	1.20475	−	0.875299i	0.994743	+	0.102401i	$0.0326526\pi$
$182$		−	9.70820i		−	0.719620i
$183$	−5.20431	−	7.16312i	−0.384714	−	0.529513i
$184$	1.85410	+	5.70634i	0.136686	+	0.420677i
$185$		0			0
$186$	1.14590	−	3.52671i	0.0840213	−	0.258591i
$187$	−39.1118	+	12.7082i	−2.86014	+	0.929316i
$188$	−4.53077	+	1.47214i	−0.330440	+	0.107367i
$189$	0.618034	−	1.90211i	0.0449554	−	0.138358i
$190$		0			0
$191$	−0.236068	−	0.726543i	−0.0170813	−	0.0525708i	0.942153	−	0.335184i	$-0.108799\pi$
$191$	−0.236068	−	0.726543i	−0.0170813	−	0.0525708i	−0.959234	+	0.282614i	$0.908799\pi$
$192$	−0.587785	−	0.809017i	−0.0424197	−	0.0583858i
$193$			2.38197i			0.171458i	0.996319	+	0.0857288i	$0.0273219\pi$
$193$			2.38197i			0.171458i	−0.996319	+	0.0857288i	$0.972678\pi$
$194$	11.2082	−	8.14324i	0.804702	−	0.584650i
$195$		0			0
$196$	2.42705	+	1.76336i	0.173361	+	0.125954i
$197$	7.83297	−	10.7812i	0.558076	−	0.768125i	−0.433005	−	0.901392i	$-0.642547\pi$
$197$	7.83297	−	10.7812i	0.558076	−	0.768125i	0.991080	+	0.133266i	$0.0425466\pi$
$198$	4.97980	+	1.61803i	0.353899	+	0.114989i
$199$	6.18034			0.438113			0.219056	−	0.975712i	$-0.429702\pi$
$199$	6.18034			0.438113			0.219056	+	0.975712i	$0.429702\pi$
$200$		0			0
$201$	9.70820			0.684764
$202$	1.59184	+	0.517221i	0.112002	+	0.0363915i
$203$	−1.62460	+	2.23607i	−0.114024	+	0.156941i
$204$	−6.35410	−	4.61653i	−0.444876	−	0.323221i
$205$		0			0
$206$	−1.85410	+	1.34708i	−0.129181	+	0.0938558i
$207$		−	6.00000i		−	0.417029i
$208$	2.85317	+	3.92705i	0.197832	+	0.272292i
$209$	−4.47214	−	13.7638i	−0.309344	−	0.952063i
$210$		0			0
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	−0.999381	−	0.0351760i	$-0.988801\pi$
$211$	−2.47214	+	7.60845i	−0.170189	+	0.523787i	0.829192	+	0.558963i	$0.188801\pi$
$212$	8.14324	−	2.64590i	0.559280	−	0.181721i
$213$	−13.4863	+	4.38197i	−0.924066	+	0.300247i
$214$	3.38197	−	10.4086i	0.231186	−	0.711519i
$215$		0			0
$216$	0.309017	+	0.951057i	0.0210259	+	0.0647112i
$217$	4.35926	+	6.00000i	0.295926	+	0.407307i
$218$		−	2.56231i		−	0.173541i
$219$	2.54508	−	1.84911i	0.171981	−	0.124951i
$220$		0			0
$221$	30.8435	+	22.4091i	2.07476	+	1.50740i
$222$	1.26133	−	1.73607i	0.0846547	−	0.116517i
$223$	−2.17963	−	0.708204i	−0.145959	−	0.0474248i	0.235127	−	0.971965i	$-0.424450\pi$
$223$	−2.17963	−	0.708204i	−0.145959	−	0.0474248i	−0.381085	+	0.924540i	$0.624450\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	11.5623			0.769113
$227$	16.1150	+	5.23607i	1.06959	+	0.347530i	0.790327	−	0.612685i	$-0.209911\pi$
$227$	16.1150	+	5.23607i	1.06959	+	0.347530i	0.279261	+	0.960215i	$0.409911\pi$
$228$	1.62460	−	2.23607i	0.107592	−	0.148087i
$229$	−19.6353	−	14.2658i	−1.29753	−	0.942714i	−0.297606	−	0.954689i	$-0.596188\pi$
$229$	−19.6353	−	14.2658i	−1.29753	−	0.942714i	−0.999928	+	0.0119751i	$0.996188\pi$
$230$		0			0
$231$	−8.47214	+	6.15537i	−0.557426	+	0.404993i
$232$		−	1.38197i		−	0.0907305i
$233$	12.9843	+	17.8713i	0.850628	+	1.17079i	0.983724	+	0.179686i	$0.0575082\pi$
$233$	12.9843	+	17.8713i	0.850628	+	1.17079i	−0.133096	+	0.991103i	$0.542492\pi$
$234$	−1.50000	−	4.61653i	−0.0980581	−	0.301792i
$235$		0			0
$236$	2.76393	−	8.50651i	0.179917	−	0.553727i
$237$		0			0
$238$	14.9394	−	4.85410i	0.968377	−	0.314645i
$239$	−8.29180	+	25.5195i	−0.536352	+	1.65072i	0.204358	+	0.978896i	$0.434489\pi$
$239$	−8.29180	+	25.5195i	−0.536352	+	1.65072i	−0.740710	+	0.671825i	$0.765511\pi$
$240$		0			0
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	−0.989014	−	0.147824i	$-0.952773\pi$
$241$	−4.28115	−	13.1760i	−0.275773	−	0.848743i	0.713240	−	0.700919i	$-0.247227\pi$
$242$	−9.64932	−	13.2812i	−0.620282	−	0.853745i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.16312	+	5.20431i	−0.458572	+	0.333172i
$245$		0			0
$246$	4.92705	+	3.57971i	0.314137	+	0.228234i
$247$	−7.88597	+	10.8541i	−0.501772	+	0.690630i
$248$	−3.52671	−	1.14590i	−0.223946	−	0.0727646i
$249$	6.00000			0.380235
$250$		0			0
$251$	−12.4721			−0.787234			−0.393617	−	0.919274i	$-0.628776\pi$
$251$	−12.4721			−0.787234			−0.393617	+	0.919274i	$0.628776\pi$
$252$	−1.90211	−	0.618034i	−0.119822	−	0.0389325i
$253$	−18.4661	+	25.4164i	−1.16095	+	1.59792i
$254$	−0.236068	−	0.171513i	−0.0148122	−	0.0107617i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			11.6180i			0.724713i	0.932040	+	0.362357i	$0.118028\pi$
$257$			11.6180i			0.724713i	−0.932040	+	0.362357i	$0.881972\pi$
$258$	0.726543	+	1.00000i	0.0452326	+	0.0622573i
$259$	1.32624	+	4.08174i	0.0824084	+	0.253627i
$260$		0			0
$261$	−0.427051	+	1.31433i	−0.0264338	+	0.0813548i
$262$	0.726543	−	0.236068i	0.0448859	−	0.0145843i
$263$	−0.449028	+	0.145898i	−0.0276883	+	0.00899646i	−0.322828	−	0.946458i	$-0.604634\pi$
$263$	−0.449028	+	0.145898i	−0.0276883	+	0.00899646i	0.295140	+	0.955454i	$0.404634\pi$
$264$	1.61803	−	4.97980i	0.0995831	−	0.306485i
$265$		0			0
$266$	1.70820	+	5.25731i	0.104737	+	0.322346i
$267$	−0.812299	−	1.11803i	−0.0497119	−	0.0684226i
$268$		−	9.70820i		−	0.593023i
$269$	−1.54508	+	1.12257i	−0.0942055	+	0.0684443i	−0.633891	−	0.773422i	$-0.718543\pi$
$269$	−1.54508	+	1.12257i	−0.0942055	+	0.0684443i	0.539685	+	0.841867i	$0.318543\pi$
$270$		0			0
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.996403	−	0.0847417i	$-0.972993\pi$
$271$	−22.7984	−	16.5640i	−1.38490	−	1.00619i	−0.388500	−	0.921449i	$-0.627007\pi$
$272$	−4.61653	+	6.35410i	−0.279918	+	0.385274i
$273$	9.23305	+	3.00000i	0.558810	+	0.181568i
$274$	−15.0344			−0.908264
$275$		0			0
$276$	−6.00000			−0.361158
$277$	21.0620	+	6.84346i	1.26549	+	0.411184i	0.863449	−	0.504437i	$-0.168300\pi$
$277$	21.0620	+	6.84346i	1.26549	+	0.411184i	0.402044	+	0.915620i	$0.368300\pi$
$278$	7.88597	−	10.8541i	0.472969	−	0.650986i
$279$	3.00000	+	2.17963i	0.179605	+	0.130491i
$280$		0			0
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	−0.431044	−	0.902331i	$-0.641855\pi$
$281$	4.92705	−	3.57971i	0.293923	−	0.213548i	0.724968	+	0.688783i	$0.241855\pi$
$282$		−	4.76393i		−	0.283688i
$283$	−1.90211	−	2.61803i	−0.113069	−	0.155626i	0.748732	−	0.662873i	$-0.230663\pi$
$283$	−1.90211	−	2.61803i	−0.113069	−	0.155626i	−0.861801	+	0.507247i	$0.830663\pi$
$284$	4.38197	+	13.4863i	0.260022	+	0.800265i
$285$		0			0
$286$	−7.85410	+	24.1724i	−0.464423	+	1.42935i
$287$	−11.5842	+	3.76393i	−0.683793	+	0.222178i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	−13.8090	+	42.4998i	−0.812295	+	2.49999i
$290$		0			0
$291$	4.28115	+	13.1760i	0.250966	+	0.772393i
$292$	−1.84911	−	2.54508i	−0.108211	−	0.148940i
$293$		−	28.7984i		−	1.68242i	−0.540709	−	0.841209i	$-0.681844\pi$
$293$		−	28.7984i		−	1.68242i	0.540709	−	0.841209i	$-0.318156\pi$
$294$	−2.42705	+	1.76336i	−0.141548	+	0.102841i
$295$		0			0
$296$	−1.73607	−	1.26133i	−0.100907	−	0.0733132i
$297$	−3.07768	+	4.23607i	−0.178585	+	0.245802i
$298$	−6.69015	−	2.17376i	−0.387550	−	0.125923i
$299$	29.1246			1.68432
$300$		0			0
$301$	−2.47214			−0.142492
$302$	−6.60440	−	2.14590i	−0.380040	−	0.123483i
$303$	−0.983813	+	1.35410i	−0.0565186	+	0.0777911i
$304$	−2.23607	−	1.62460i	−0.128247	−	0.0931771i
$305$		0			0
$306$	6.35410	−	4.61653i	0.363240	−	0.263909i
$307$			16.2918i			0.929822i	0.885357	+	0.464911i	$0.153914\pi$
$307$			16.2918i			0.929822i	−0.885357	+	0.464911i	$0.846086\pi$
$308$	6.15537	+	8.47214i	0.350735	+	0.482745i
$309$	−0.708204	−	2.17963i	−0.0402883	−	0.123995i
$310$		0			0
$311$	−5.76393	+	17.7396i	−0.326843	+	1.00592i	0.643759	+	0.765228i	$0.277374\pi$
$311$	−5.76393	+	17.7396i	−0.326843	+	1.00592i	−0.970602	+	0.240690i	$0.922626\pi$
$312$	−4.61653	+	1.50000i	−0.261359	+	0.0849208i
$313$	25.0705	−	8.14590i	1.41707	−	0.460433i	0.502399	−	0.864636i	$-0.332451\pi$
$313$	25.0705	−	8.14590i	1.41707	−	0.460433i	0.914669	+	0.404203i	$0.132451\pi$
$314$	5.51722	−	16.9803i	0.311355	−	0.958252i
$315$		0			0
$316$		0			0
$317$	−4.08174	−	5.61803i	−0.229253	−	0.315540i	0.678857	−	0.734270i	$-0.262475\pi$
$317$	−4.08174	−	5.61803i	−0.229253	−	0.315540i	−0.908111	+	0.418730i	$0.862475\pi$
$318$			8.56231i			0.480150i
$319$	5.85410	−	4.25325i	0.327767	−	0.238137i
$320$		0			0
$321$	8.85410	+	6.43288i	0.494188	+	0.359048i
$322$	7.05342	−	9.70820i	0.393072	−	0.541017i
$323$	−20.6457	−	6.70820i	−1.14876	−	0.373254i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−20.4721			−1.13385
$327$	2.43690	+	0.791796i	0.134761	+	0.0437864i
$328$	3.57971	−	4.92705i	0.197657	−	0.272051i
$329$	7.70820	+	5.60034i	0.424967	+	0.308757i
$330$		0			0
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.456761	−	0.889589i	$-0.349009\pi$
$331$	26.2705	−	19.0866i	1.44396	−	1.04910i	0.987197	−	0.159507i	$-0.0509906\pi$
$332$		−	6.00000i		−	0.329293i
$333$	1.26133	+	1.73607i	0.0691203	+	0.0951359i
$334$	2.00000	+	6.15537i	0.109435	+	0.336807i
$335$		0			0
$336$	−0.618034	+	1.90211i	−0.0337165	+	0.103769i
$337$	27.4216	−	8.90983i	1.49375	−	0.485349i	0.555563	−	0.831474i	$-0.312503\pi$
$337$	27.4216	−	8.90983i	1.49375	−	0.485349i	0.938188	+	0.346125i	$0.112503\pi$
$338$	10.0453	−	3.26393i	0.546395	−	0.177534i
$339$	−3.57295	+	10.9964i	−0.194056	+	0.597243i
$340$		0			0
$341$	−6.00000	−	18.4661i	−0.324918	−	0.999995i
$342$	1.62460	+	2.23607i	0.0878482	+	0.120913i
$343$		−	20.0000i		−	1.07990i
$344$	1.00000	−	0.726543i	0.0539164	−	0.0391725i
$345$		0			0
$346$	−8.82624	−	6.41264i	−0.474501	−	0.344746i
$347$	3.07768	−	4.23607i	0.165219	−	0.227404i	−0.718378	−	0.695653i	$-0.755115\pi$
$347$	3.07768	−	4.23607i	0.165219	−	0.227404i	0.883596	+	0.468249i	$0.155115\pi$
$348$	1.31433	+	0.427051i	0.0704554	+	0.0228923i
$349$	−14.7984			−0.792139			−0.396069	−	0.918221i	$-0.629626\pi$
$349$	−14.7984			−0.792139			−0.396069	+	0.918221i	$0.629626\pi$
$350$		0			0
$351$	4.85410			0.259093
$352$	−4.97980	−	1.61803i	−0.265424	−	0.0862415i
$353$	12.0332	−	16.5623i	0.640464	−	0.881523i	−0.358177	−	0.933654i	$-0.616601\pi$
$353$	12.0332	−	16.5623i	0.640464	−	0.881523i	0.998640	+	0.0521313i	$0.0166014\pi$
$354$	7.23607	+	5.25731i	0.384593	+	0.279423i
$355$		0			0
$356$	−1.11803	+	0.812299i	−0.0592557	+	0.0430518i
$357$			15.7082i			0.831366i
$358$	−2.24514	−	3.09017i	−0.118659	−	0.163321i
$359$	8.61803	+	26.5236i	0.454842	+	1.39986i	0.871320	+	0.490715i	$0.163264\pi$
$359$	8.61803	+	26.5236i	0.454842	+	1.39986i	−0.416478	+	0.909146i	$0.636736\pi$
$360$		0			0
$361$	−3.51064	+	10.8046i	−0.184771	+	0.568666i
$362$	19.0539	−	6.19098i	1.00145	−	0.325391i
$363$	15.6129	−	5.07295i	0.819466	−	0.266261i
$364$	3.00000	−	9.23305i	0.157243	−	0.483943i
$365$		0			0
$366$	−2.73607	−	8.42075i	−0.143017	−	0.440160i
$367$	−7.33094	−	10.0902i	−0.382672	−	0.526703i	0.573618	−	0.819123i	$-0.305539\pi$
$367$	−7.33094	−	10.0902i	−0.382672	−	0.526703i	−0.956290	+	0.292420i	$0.905539\pi$
$368$			6.00000i			0.312772i
$369$	−4.92705	+	3.57971i	−0.256492	+	0.186352i
$370$		0			0
$371$	−13.8541	−	10.0656i	−0.719269	−	0.522580i
$372$	2.17963	−	3.00000i	0.113008	−	0.155543i
$373$	2.45714	+	0.798374i	0.127226	+	0.0413382i	0.371938	−	0.928258i	$-0.378693\pi$
$373$	2.45714	+	0.798374i	0.127226	+	0.0413382i	−0.244712	+	0.969596i	$0.578693\pi$
$374$	−41.1246			−2.12650
$375$		0			0
$376$	−4.76393			−0.245681
$377$	−6.37988	−	2.07295i	−0.328581	−	0.106762i
$378$	1.17557	−	1.61803i	0.0604648	−	0.0832227i
$379$	−2.76393	−	2.00811i	−0.141974	−	0.103150i	0.514531	−	0.857472i	$-0.327966\pi$
$379$	−2.76393	−	2.00811i	−0.141974	−	0.103150i	−0.656505	+	0.754322i	$0.727966\pi$
$380$		0			0
$381$	0.236068	−	0.171513i	0.0120941	−	0.00878690i
$382$		−	0.763932i		−	0.0390862i
$383$	−12.0332	−	16.5623i	−0.614869	−	0.846294i	0.382098	−	0.924122i	$-0.375202\pi$
$383$	−12.0332	−	16.5623i	−0.614869	−	0.846294i	−0.996967	+	0.0778275i	$0.975202\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$		0			0
$386$	−0.736068	+	2.26538i	−0.0374649	+	0.115305i
$387$	−1.17557	+	0.381966i	−0.0597576	+	0.0194164i
$388$	13.1760	−	4.28115i	0.668912	−	0.217343i
$389$	−4.93769	+	15.1967i	−0.250351	+	0.770501i	0.744359	+	0.667780i	$0.232755\pi$
$389$	−4.93769	+	15.1967i	−0.250351	+	0.770501i	−0.994710	+	0.102722i	$0.967245\pi$
$390$		0			0
$391$	14.5623	+	44.8182i	0.736447	+	2.26655i
$392$	1.76336	+	2.42705i	0.0890629	+	0.122585i
$393$			0.763932i			0.0385353i
$394$	10.7812	−	7.83297i	0.543147	−	0.394619i
$395$		0			0
$396$	4.23607	+	3.07768i	0.212870	+	0.154659i
$397$	−16.9475	+	23.3262i	−0.850571	+	1.17071i	0.133166	+	0.991094i	$0.457486\pi$
$397$	−16.9475	+	23.3262i	−0.850571	+	1.17071i	−0.983737	+	0.179617i	$0.942514\pi$
$398$	5.87785	+	1.90983i	0.294630	+	0.0957311i
$399$	−5.52786			−0.276739
$400$		0			0
$401$	−26.0902			−1.30288			−0.651440	−	0.758700i	$-0.725835\pi$
$401$	−26.0902			−1.30288			−0.651440	+	0.758700i	$0.725835\pi$
$402$	9.23305	+	3.00000i	0.460503	+	0.149626i
$403$	−10.5801	+	14.5623i	−0.527034	+	0.725400i
$404$	1.35410	+	0.983813i	0.0673691	+	0.0489465i
$405$		0			0
$406$	−2.23607	+	1.62460i	−0.110974	+	0.0806275i
$407$		−	11.2361i		−	0.556951i
$408$	−4.61653	−	6.35410i	−0.228552	−	0.314575i
$409$	−6.48278	−	19.9519i	−0.320553	−	0.986560i	−0.973408	−	0.229077i	$-0.926429\pi$
$409$	−6.48278	−	19.9519i	−0.320553	−	0.986560i	0.652855	−	0.757483i	$-0.273571\pi$
$410$		0			0
$411$	4.64590	−	14.2986i	0.229165	−	0.705298i
$412$	−2.17963	+	0.708204i	−0.107383	+	0.0348907i
$413$	−17.0130	+	5.52786i	−0.837156	+	0.272008i
$414$	1.85410	−	5.70634i	0.0911241	−	0.280451i
$415$		0			0
$416$	1.50000	+	4.61653i	0.0735436	+	0.226344i
$417$	7.88597	+	10.8541i	0.386177	+	0.531528i
$418$		−	14.4721i		−	0.707855i
$419$	−30.6525	+	22.2703i	−1.49747	+	1.08798i	−0.526097	+	0.850425i	$0.676345\pi$
$419$	−30.6525	+	22.2703i	−1.49747	+	1.08798i	−0.971375	+	0.237552i	$0.923655\pi$
$420$		0			0
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	0.784551	−	0.620064i	$-0.212893\pi$
$421$	8.97214	+	6.51864i	0.437275	+	0.317699i	−0.347276	+	0.937763i	$0.612893\pi$
$422$	−4.70228	+	6.47214i	−0.228904	+	0.315059i
$423$	4.53077	+	1.47214i	0.220294	+	0.0715777i
$424$	8.56231			0.415822
$425$		0			0
$426$	−14.1803			−0.687040
$427$	16.8415	+	5.47214i	0.815017	+	0.264815i
$428$	6.43288	−	8.85410i	0.310945	−	0.427979i
$429$	−20.5623	−	14.9394i	−0.992757	−	0.721281i
$430$		0			0
$431$	−3.00000	+	2.17963i	−0.144505	+	0.104989i	−0.657689	−	0.753290i	$-0.728466\pi$
$431$	−3.00000	+	2.17963i	−0.144505	+	0.104989i	0.513184	+	0.858279i	$0.328466\pi$
$432$			1.00000i			0.0481125i
$433$	13.6048	+	18.7254i	0.653806	+	0.899886i	0.999257	−	0.0385504i	$-0.0122740\pi$
$433$	13.6048	+	18.7254i	0.653806	+	0.899886i	−0.345451	+	0.938437i	$0.612274\pi$
$434$	2.29180	+	7.05342i	0.110010	+	0.338575i
$435$		0			0
$436$	0.791796	−	2.43690i	0.0379202	−	0.116706i
$437$	−15.7719	+	5.12461i	−0.754474	+	0.245143i
$438$	2.99193	−	0.972136i	0.142960	−	0.0464505i
$439$	7.76393	−	23.8949i	0.370552	−	1.14044i	−0.575878	−	0.817535i	$-0.695340\pi$
$439$	7.76393	−	23.8949i	0.370552	−	1.14044i	0.946431	−	0.322907i	$-0.104660\pi$
$440$		0			0
$441$	−0.927051	−	2.85317i	−0.0441453	−	0.135865i
$442$	22.4091	+	30.8435i	1.06589	+	1.46707i
$443$			30.0689i			1.42862i	0.699832	+	0.714308i	$0.253258\pi$
$443$			30.0689i			1.42862i	−0.699832	+	0.714308i	$0.746742\pi$
$444$	1.73607	−	1.26133i	0.0823901	−	0.0598599i
$445$		0			0
$446$	−1.85410	−	1.34708i	−0.0877943	−	0.0637863i
$447$	4.13474	−	5.69098i	0.195567	−	0.269174i
$448$	1.90211	+	0.618034i	0.0898664	+	0.0291994i
$449$	−4.79837			−0.226449			−0.113225	−	0.993569i	$-0.536118\pi$
$449$	−4.79837			−0.226449			−0.113225	+	0.993569i	$0.536118\pi$
$450$		0			0
$451$	31.8885			1.50157
$452$	10.9964	+	3.57295i	0.517227	+	0.168057i
$453$	4.08174	−	5.61803i	0.191777	−	0.263958i
$454$	13.7082	+	9.95959i	0.643358	+	0.467427i
$455$		0			0
$456$	2.23607	−	1.62460i	0.104713	−	0.0760788i
$457$			12.4721i			0.583422i	0.956507	+	0.291711i	$0.0942245\pi$
$457$			12.4721i			0.583422i	−0.956507	+	0.291711i	$0.905775\pi$
$458$	−14.2658	−	19.6353i	−0.666599	−	0.917495i
$459$	2.42705	+	7.46969i	0.113285	+	0.348655i
$460$		0			0
$461$	7.75329	−	23.8622i	0.361107	−	1.11137i	−0.591277	−	0.806469i	$-0.701376\pi$
$461$	7.75329	−	23.8622i	0.361107	−	1.11137i	0.952383	−	0.304903i	$-0.0986241\pi$
$462$	−9.95959	+	3.23607i	−0.463362	+	0.150556i
$463$	11.6902	−	3.79837i	0.543289	−	0.176525i	−0.0244992	−	0.999700i	$-0.507799\pi$
$463$	11.6902	−	3.79837i	0.543289	−	0.176525i	0.567789	+	0.823174i	$0.307799\pi$
$464$	0.427051	−	1.31433i	0.0198253	−	0.0610161i
$465$		0			0
$466$	6.82624	+	21.0090i	0.316219	+	0.973223i
$467$	9.29856	+	12.7984i	0.430286	+	0.592238i	0.968019	−	0.250877i	$-0.0807191\pi$
$467$	9.29856	+	12.7984i	0.430286	+	0.592238i	−0.537733	+	0.843115i	$0.680719\pi$
$468$		−	4.85410i		−	0.224381i
$469$	−15.7082	+	11.4127i	−0.725337	+	0.526989i
$470$		0			0
$471$	14.4443	+	10.4944i	0.665557	+	0.483555i
$472$	5.25731	−	7.23607i	0.241987	−	0.333067i
$473$	6.15537	+	2.00000i	0.283024	+	0.0919601i
$474$		0			0
$475$		0			0
$476$	15.7082			0.719984
$477$	−8.14324	−	2.64590i	−0.372853	−	0.121147i
$478$	−15.7719	+	21.7082i	−0.721391	+	0.992910i
$479$	3.61803	+	2.62866i	0.165312	+	0.120106i	0.667366	−	0.744730i	$-0.267422\pi$
$479$	3.61803	+	2.62866i	0.165312	+	0.120106i	−0.502053	+	0.864837i	$0.667422\pi$
$480$		0			0
$481$	−8.42705	+	6.12261i	−0.384240	+	0.279167i
$482$		−	13.8541i		−	0.631037i
$483$	7.05342	+	9.70820i	0.320942	+	0.441739i
$484$	−5.07295	−	15.6129i	−0.230589	−	0.709679i
$485$		0			0
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	9.78808	−	3.18034i	0.443540	−	0.144115i	−0.0787282	−	0.996896i	$-0.525086\pi$
$487$	9.78808	−	3.18034i	0.443540	−	0.144115i	0.522268	+	0.852781i	$0.325086\pi$
$488$	−8.42075	+	2.73607i	−0.381190	+	0.123856i
$489$	6.32624	−	19.4702i	0.286082	−	0.880471i
$490$		0			0
$491$	9.23607	+	28.4257i	0.416818	+	1.28283i	0.910615	+	0.413256i	$0.135609\pi$
$491$	9.23607	+	28.4257i	0.416818	+	1.28283i	−0.493797	+	0.869577i	$0.664391\pi$
$492$	3.57971	+	4.92705i	0.161386	+	0.222129i
$493$		−	10.8541i		−	0.488844i
$494$	−10.8541	+	7.88597i	−0.488349	+	0.354806i
$495$		0			0
$496$	−3.00000	−	2.17963i	−0.134704	−	0.0978682i
$497$	16.6700	−	22.9443i	0.747751	−	1.02919i
$498$	5.70634	+	1.85410i	0.255707	+	0.0830843i
$499$	33.4164			1.49592			0.747962	−	0.663742i	$-0.231033\pi$
$499$	33.4164			1.49592			0.747962	+	0.663742i	$0.231033\pi$
$500$		0			0
$501$	−6.47214			−0.289154
$502$	−11.8617	−	3.85410i	−0.529414	−	0.172017i
$503$	12.6538	−	17.4164i	0.564203	−	0.776559i	−0.427650	−	0.903944i	$-0.640658\pi$
$503$	12.6538	−	17.4164i	0.564203	−	0.776559i	0.991853	+	0.127385i	$0.0406584\pi$
$504$	−1.61803	−	1.17557i	−0.0720730	−	0.0523641i
$505$		0			0
$506$	−25.4164	+	18.4661i	−1.12990	+	0.820918i
$507$			10.5623i			0.469088i
$508$	−0.171513	−	0.236068i	−0.00760968	−	0.0104738i
$509$	4.24671	+	13.0700i	0.188232	+	0.579319i	0.999989	−	0.00467647i	$-0.00148857\pi$
$509$	4.24671	+	13.0700i	0.188232	+	0.579319i	−0.811757	+	0.583995i	$0.801489\pi$
$510$		0			0
$511$	−1.94427	+	5.98385i	−0.0860095	+	0.264710i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−2.62866	+	0.854102i	−0.116058	+	0.0377095i
$514$	−3.59017	+	11.0494i	−0.158356	+	0.487368i
$515$		0			0
$516$	0.381966	+	1.17557i	0.0168151	+	0.0517516i
$517$	−14.6619	−	20.1803i	−0.644829	−	0.887530i
$518$			4.29180i			0.188571i
$519$	8.82624	−	6.41264i	0.387429	−	0.281484i
$520$		0			0
$521$	−5.07295	−	3.68571i	−0.222250	−	0.161474i	0.471089	−	0.882086i	$-0.343861\pi$
$521$	−5.07295	−	3.68571i	−0.222250	−	0.161474i	−0.693339	+	0.720612i	$0.743861\pi$
$522$	−0.812299	+	1.11803i	−0.0355534	+	0.0489350i
$523$	−2.17963	−	0.708204i	−0.0953085	−	0.0309676i	0.260975	−	0.965346i	$-0.415956\pi$
$523$	−2.17963	−	0.708204i	−0.0953085	−	0.0309676i	−0.356283	+	0.934378i	$0.615956\pi$
$524$	0.763932			0.0333725
$525$		0			0
$526$	−0.472136			−0.0205861
$527$	−27.6992	−	9.00000i	−1.20659	−	0.392046i
$528$	3.07768	−	4.23607i	0.133939	−	0.184351i
$529$	10.5172	+	7.64121i	0.457270	+	0.332226i
$530$		0			0
$531$	−7.23607	+	5.25731i	−0.314019	+	0.228148i
$532$			5.52786i			0.239663i
$533$	−17.3763	−	23.9164i	−0.752651	−	1.03593i
$534$	−0.427051	−	1.31433i	−0.0184803	−	0.0568765i
$535$		0			0
$536$	3.00000	−	9.23305i	0.129580	−	0.398807i
$537$	3.63271	−	1.18034i	0.156763	−	0.0509354i
$538$	−1.81636	+	0.590170i	−0.0783087	+	0.0254440i
$539$	−4.85410	+	14.9394i	−0.209081	+	0.643485i
$540$		0			0
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	0.987110	+	0.160045i	$0.0511639\pi$
$541$	6.57295	+	20.2295i	0.282593	+	0.869732i	−0.704517	+	0.709688i	$0.748836\pi$
$542$	−16.5640	−	22.7984i	−0.711484	−	0.979274i
$543$			20.0344i			0.859760i
$544$	−6.35410	+	4.61653i	−0.272430	+	0.197932i
$545$		0			0
$546$	7.85410	+	5.70634i	0.336125	+	0.244209i
$547$	−1.17557	+	1.61803i	−0.0502638	+	0.0691821i	−0.833409	−	0.552657i	$-0.813614\pi$
$547$	−1.17557	+	1.61803i	−0.0502638	+	0.0691821i	0.783145	+	0.621839i	$0.213614\pi$
$548$	−14.2986	−	4.64590i	−0.610806	−	0.198463i
$549$	8.85410			0.377884
$550$		0			0
$551$	3.81966			0.162723
$552$	−5.70634	−	1.85410i	−0.242878	−	0.0789158i
$553$		0			0
$554$	17.9164	+	13.0170i	0.761195	+	0.553041i
$555$		0			0
$556$	10.8541	−	7.88597i	0.460316	−	0.334439i
$557$			27.2705i			1.15549i	0.816218	+	0.577744i	$0.196067\pi$
$557$			27.2705i			1.15549i	−0.816218	+	0.577744i	$0.803933\pi$
$558$	2.17963	+	3.00000i	0.0922710	+	0.127000i
$559$	−1.85410	−	5.70634i	−0.0784202	−	0.241352i
$560$		0			0
$561$	12.7082	−	39.1118i	0.536541	−	1.65130i
$562$	5.79210	−	1.88197i	0.244325	−	0.0793859i
$563$	−9.95959	+	3.23607i	−0.419747	+	0.136384i	−0.511272	−	0.859419i	$-0.670826\pi$
$563$	−9.95959	+	3.23607i	−0.419747	+	0.136384i	0.0915256	+	0.995803i	$0.470826\pi$
$564$	1.47214	−	4.53077i	0.0619881	−	0.190780i
$565$		0			0
$566$	−1.00000	−	3.07768i	−0.0420331	−	0.129365i
$567$	1.17557	+	1.61803i	0.0493693	+	0.0679510i
$568$			14.1803i			0.594994i
$569$	17.2984	−	12.5680i	0.725186	−	0.526878i	−0.162851	−	0.986651i	$-0.552069\pi$
$569$	17.2984	−	12.5680i	0.725186	−	0.526878i	0.888037	+	0.459772i	$0.152069\pi$
$570$		0			0
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.153944	−	0.988080i	$-0.549198\pi$
$571$	−27.2705	−	19.8132i	−1.14124	−	0.829156i	−0.987291	+	0.158924i	$0.949198\pi$
$572$	−14.9394	+	20.5623i	−0.624647	+	0.859753i
$573$	0.726543	+	0.236068i	0.0303517	+	0.00986188i
$574$	−12.1803			−0.508398
$575$		0			0
$576$	1.00000			0.0416667
$577$	−27.4216	−	8.90983i	−1.14158	−	0.370921i	−0.323613	−	0.946190i	$-0.604898\pi$
$577$	−27.4216	−	8.90983i	−1.14158	−	0.370921i	−0.817965	+	0.575268i	$0.804898\pi$
$578$	−26.2663	+	36.1525i	−1.09253	+	1.50374i
$579$	−1.92705	−	1.40008i	−0.0800855	−	0.0581855i
$580$		0			0
$581$	−9.70820	+	7.05342i	−0.402764	+	0.292625i
$582$			13.8541i			0.574271i
$583$	26.3521	+	36.2705i	1.09139	+	1.50217i
$584$	−0.972136	−	2.99193i	−0.0402273	−	0.123807i
$585$		0			0
$586$	8.89919	−	27.3889i	0.367622	−	1.13142i
$587$	−15.1109	+	4.90983i	−0.623694	+	0.202650i	−0.603780	−	0.797151i	$-0.706339\pi$
$587$	−15.1109	+	4.90983i	−0.623694	+	0.202650i	−0.0199141	+	0.999802i	$0.506339\pi$
$588$	−2.85317	+	0.927051i	−0.117663	+	0.0382309i
$589$	3.16718	−	9.74759i	0.130502	−	0.401642i
$590$		0			0
$591$	4.11803	+	12.6740i	0.169393	+	0.521339i
$592$	−1.26133	−	1.73607i	−0.0518402	−	0.0713520i
$593$		−	6.03444i		−	0.247805i	−0.992294	−	0.123902i	$-0.960459\pi$
$593$		−	6.03444i		−	0.247805i	0.992294	−	0.123902i	$-0.0395410\pi$
$594$	−4.23607	+	3.07768i	−0.173808	+	0.126279i
$595$		0			0
$596$	−5.69098	−	4.13474i	−0.233112	−	0.169366i
$597$	−3.63271	+	5.00000i	−0.148677	+	0.204636i
$598$	27.6992	+	9.00000i	1.13270	+	0.368037i
$599$	−1.05573			−0.0431359			−0.0215679	−	0.999767i	$-0.506866\pi$
$599$	−1.05573			−0.0431359			−0.0215679	+	0.999767i	$0.506866\pi$
$600$		0			0
$601$	7.32624			0.298843			0.149422	−	0.988774i	$-0.452259\pi$
$601$	7.32624			0.298843			0.149422	+	0.988774i	$0.452259\pi$
$602$	−2.35114	−	0.763932i	−0.0958254	−	0.0311355i
$603$	−5.70634	+	7.85410i	−0.232380	+	0.319844i
$604$	−5.61803	−	4.08174i	−0.228595	−	0.166084i
$605$		0			0
$606$	−1.35410	+	0.983813i	−0.0550066	+	0.0399647i
$607$			1.81966i			0.0738577i	0.999318	+	0.0369289i	$0.0117575\pi$
$607$			1.81966i			0.0738577i	−0.999318	+	0.0369289i	$0.988243\pi$
$608$	−1.62460	−	2.23607i	−0.0658862	−	0.0906845i
$609$	−0.854102	−	2.62866i	−0.0346100	−	0.106518i
$610$		0			0
$611$	−7.14590	+	21.9928i	−0.289092	+	0.889734i
$612$	7.46969	−	2.42705i	0.301945	−	0.0981077i
$613$	20.5070	−	6.66312i	0.828269	−	0.269121i	0.135953	−	0.990715i	$-0.456590\pi$
$613$	20.5070	−	6.66312i	0.828269	−	0.269121i	0.692316	+	0.721594i	$0.256590\pi$
$614$	−5.03444	+	15.4944i	−0.203174	+	0.625304i
$615$		0			0
$616$	3.23607	+	9.95959i	0.130385	+	0.401283i
$617$	4.92680	+	6.78115i	0.198345	+	0.272999i	0.896591	−	0.442859i	$-0.146036\pi$
$617$	4.92680	+	6.78115i	0.198345	+	0.272999i	−0.698246	+	0.715858i	$0.746036\pi$
$618$		−	2.29180i		−	0.0921896i
$619$	2.76393	−	2.00811i	0.111092	−	0.0807129i	−0.530852	−	0.847464i	$-0.678128\pi$
$619$	2.76393	−	2.00811i	0.111092	−	0.0807129i	0.641944	+	0.766751i	$0.278128\pi$
$620$		0			0
$621$	4.85410	+	3.52671i	0.194788	+	0.141522i
$622$	−10.9637	+	15.0902i	−0.439602	+	0.605061i
$623$	2.62866	+	0.854102i	0.105315	+	0.0342189i
$624$	−4.85410			−0.194320
$625$		0			0
$626$	26.3607			1.05358
$627$	13.7638	+	4.47214i	0.549674	+	0.178600i
$628$	10.4944	−	14.4443i	0.418771	−	0.576389i
$629$	−13.6353	−	9.90659i	−0.543673	−	0.395002i
$630$		0			0
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.392905	−	0.919579i	$-0.371470\pi$
$631$	34.8885	−	25.3480i	1.38889	−	1.00909i	0.995986	−	0.0895093i	$-0.0285299\pi$
$632$		0			0
$633$	−4.70228	−	6.47214i	−0.186899	−	0.257244i
$634$	−2.14590	−	6.60440i	−0.0852245	−	0.262294i
$635$		0			0
$636$	−2.64590	+	8.14324i	−0.104917	+	0.322900i
$637$	13.8496	−	4.50000i	0.548740	−	0.178296i
$638$	6.88191	−	2.23607i	0.272457	−	0.0885268i
$639$	4.38197	−	13.4863i	0.173348	−	0.533510i
$640$		0			0
$641$	−8.32624	−	25.6255i	−0.328867	−	1.01215i	−0.969665	−	0.244438i	$-0.921397\pi$
$641$	−8.32624	−	25.6255i	−0.328867	−	1.01215i	0.640798	−	0.767709i	$-0.278603\pi$
$642$	6.43288	+	8.85410i	0.253886	+	0.349444i
$643$		−	39.7771i		−	1.56866i	−0.620347	−	0.784328i	$-0.713008\pi$
$643$		−	39.7771i		−	1.56866i	0.620347	−	0.784328i	$-0.286992\pi$
$644$	9.70820	−	7.05342i	0.382557	−	0.277944i
$645$		0			0
$646$	−17.5623	−	12.7598i	−0.690980	−	0.502026i
$647$	21.0948	−	29.0344i	0.829320	−	1.14146i	−0.158729	−	0.987322i	$-0.550739\pi$
$647$	21.0948	−	29.0344i	0.829320	−	1.14146i	0.988049	−	0.154139i	$-0.0492605\pi$
$648$	−0.951057	−	0.309017i	−0.0373610	−	0.0121393i
$649$	46.8328			1.83835
$650$		0			0
$651$	−7.41641			−0.290672
$652$	−19.4702	−	6.32624i	−0.762510	−	0.247755i
$653$	−18.9354	+	26.0623i	−0.740998	+	1.01990i	0.257562	+	0.966262i	$0.417081\pi$
$653$	−18.9354	+	26.0623i	−0.740998	+	1.01990i	−0.998561	+	0.0536351i	$0.982919\pi$
$654$	2.07295	+	1.50609i	0.0810587	+	0.0588926i
$655$		0			0
$656$	4.92705	−	3.57971i	0.192369	−	0.139764i
$657$			3.14590i			0.122733i
$658$	5.60034	+	7.70820i	0.218324	+	0.300497i
$659$	−12.0344	−	37.0382i	−0.468795	−	1.44280i	−0.854146	−	0.520033i	$-0.825920\pi$
$659$	−12.0344	−	37.0382i	−0.468795	−	1.44280i	0.385351	−	0.922770i	$-0.374080\pi$
$660$		0			0
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	0.704262	+	0.709940i	$0.251278\pi$
$661$	−7.27051	+	22.3763i	−0.282790	+	0.870338i	−0.987052	+	0.160398i	$0.948722\pi$
$662$	30.8828	−	10.0344i	1.20030	−	0.390000i
$663$	−36.2587	+	11.7812i	−1.40817	+	0.457542i
$664$	1.85410	−	5.70634i	0.0719531	−	0.221449i
$665$		0			0
$666$	0.663119	+	2.04087i	0.0256953	+	0.0790821i
$667$	−4.87380	−	6.70820i	−0.188714	−	0.259743i
$668$			6.47214i			0.250414i
$669$	1.85410	−	1.34708i	0.0716837	−	0.0520813i
$670$		0			0
$671$	−37.5066	−	27.2501i	−1.44793	−	1.05198i
$672$	−1.17557	+	1.61803i	−0.0453486	+	0.0624170i
$673$	−17.8783	−	5.80902i	−0.689158	−	0.223921i	−0.0565578	−	0.998399i	$-0.518013\pi$
$673$	−17.8783	−	5.80902i	−0.689158	−	0.223921i	−0.632601	+	0.774478i	$0.718013\pi$
$674$	28.8328			1.11060
$675$		0			0
$676$	10.5623			0.406243
$677$	−34.6871	−	11.2705i	−1.33313	−	0.433161i	−0.446147	−	0.894960i	$-0.647204\pi$
$677$	−34.6871	−	11.2705i	−1.33313	−	0.433161i	−0.886985	+	0.461799i	$0.847204\pi$
$678$	−6.79615	+	9.35410i	−0.261005	+	0.359242i
$679$	−22.4164	−	16.2865i	−0.860263	−	0.625017i
$680$		0			0
$681$	−13.7082	+	9.95959i	−0.525300	+	0.381652i
$682$		−	19.4164i		−	0.743493i
$683$	−11.4127	−	15.7082i	−0.436694	−	0.601058i	0.532779	−	0.846254i	$-0.321148\pi$
$683$	−11.4127	−	15.7082i	−0.436694	−	0.601058i	−0.969473	+	0.245196i	$0.921148\pi$
$684$	0.854102	+	2.62866i	0.0326574	+	0.100509i
$685$		0			0
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	23.0826	−	7.50000i	0.880657	−	0.286143i
$688$	1.17557	−	0.381966i	0.0448182	−	0.0145623i
$689$	12.8435	−	39.5281i	0.489297	−	1.50590i
$690$		0			0
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	−0.986621	−	0.163028i	$-0.947874\pi$
$691$	−7.47214	−	22.9969i	−0.284253	−	0.874842i	0.702368	−	0.711814i	$-0.252126\pi$
$692$	−6.41264	−	8.82624i	−0.243772	−	0.335523i
$693$		−	10.4721i		−	0.397804i
$694$	4.23607	−	3.07768i	0.160799	−	0.116827i
$695$		0			0
$696$	1.11803	+	0.812299i	0.0423790	+	0.0307901i
$697$	28.1154	−	38.6976i	1.06495	−	1.46577i
$698$	−14.0741	−	4.57295i	−0.532712	−	0.173089i
$699$	−22.0902			−0.835527
$700$		0			0
$701$	−20.1591			−0.761397			−0.380698	−	0.924699i	$-0.624316\pi$
$701$	−20.1591			−0.761397			−0.380698	+	0.924699i	$0.624316\pi$
$702$	4.61653	+	1.50000i	0.174240	+	0.0566139i
$703$	3.48622	−	4.79837i	0.131485	−	0.180974i
$704$	−4.23607	−	3.07768i	−0.159653	−	0.115995i
$705$		0			0
$706$	16.5623	−	12.0332i	0.623331	−	0.452876i
$707$		−	3.34752i		−	0.125897i
$708$	5.25731	+	7.23607i	0.197582	+	0.271948i
$709$	9.20820	+	28.3399i	0.345821	+	1.06433i	0.961143	+	0.276052i	$0.0890263\pi$
$709$	9.20820	+	28.3399i	0.345821	+	1.06433i	−0.615321	+	0.788276i	$0.710974\pi$
$710$		0			0
$711$		0			0
$712$	−1.31433	+	0.427051i	−0.0492565	+	0.0160044i
$713$	−21.1603	+	6.87539i	−0.792458	+	0.257485i
$714$	−4.85410	+	14.9394i	−0.181660	+	0.559093i
$715$		0			0
$716$	−1.18034	−	3.63271i	−0.0441114	−	0.135761i
$717$	−15.7719	−	21.7082i	−0.589014	−	0.810708i
$718$			27.8885i			1.04079i
$719$	18.0902	−	13.1433i	0.674649	−	0.490162i	−0.196929	−	0.980418i	$-0.563097\pi$
$719$	18.0902	−	13.1433i	0.674649	−	0.490162i	0.871578	+	0.490256i	$0.163097\pi$
$720$		0			0
$721$	3.70820	+	2.69417i	0.138101	+	0.100336i
$722$	−6.67764	+	9.19098i	−0.248516	+	0.342053i
$723$	13.1760	+	4.28115i	0.490022	+	0.159218i
$724$	20.0344			0.744574
$725$		0			0
$726$	16.4164			0.609270
$727$	−9.78808	−	3.18034i	−0.363020	−	0.117952i	0.121827	−	0.992551i	$-0.461125\pi$
$727$	−9.78808	−	3.18034i	−0.363020	−	0.117952i	−0.484847	+	0.874599i	$0.661125\pi$
$728$	5.70634	−	7.85410i	0.211491	−	0.291092i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	7.85410	−	5.70634i	0.290494	−	0.211057i
$732$		−	8.85410i		−	0.327257i
$733$	3.73871	+	5.14590i	0.138093	+	0.190068i	0.872462	−	0.488682i	$-0.162522\pi$
$733$	3.73871	+	5.14590i	0.138093	+	0.190068i	−0.734370	+	0.678750i	$0.762522\pi$
$734$	−3.85410	−	11.8617i	−0.142257	−	0.437824i
$735$		0			0
$736$	−1.85410	+	5.70634i	−0.0683431	+	0.210338i
$737$	48.3449	−	15.7082i	1.78081	−	0.578619i
$738$	−5.79210	+	1.88197i	−0.213210	+	0.0692761i
$739$	−2.56231	+	7.88597i	−0.0942559	+	0.290090i	−0.987059	−	0.160357i	$-0.948735\pi$
$739$	−2.56231	+	7.88597i	−0.0942559	+	0.290090i	0.892803	+	0.450447i	$0.148735\pi$
$740$		0			0
$741$	−4.14590	−	12.7598i	−0.152303	−	0.468742i
$742$	−10.0656	−	13.8541i	−0.369520	−	0.508600i
$743$			6.65248i			0.244056i	0.992527	+	0.122028i	$0.0389397\pi$
$743$			6.65248i			0.244056i	−0.992527	+	0.122028i	$0.961060\pi$
$744$	3.00000	−	2.17963i	0.109985	−	0.0799090i
$745$		0			0
$746$	2.09017	+	1.51860i	0.0765266	+	0.0555998i
$747$	−3.52671	+	4.85410i	−0.129036	+	0.177602i
$748$	−39.1118	−	12.7082i	−1.43007	−	0.464658i
$749$	−21.8885			−0.799790
$750$		0			0
$751$	14.7639			0.538744			0.269372	−	0.963036i	$-0.413184\pi$
$751$	14.7639			0.538744			0.269372	+	0.963036i	$0.413184\pi$
$752$	−4.53077	−	1.47214i	−0.165220	−	0.0536833i
$753$	7.33094	−	10.0902i	0.267154	−	0.367706i
$754$	−5.42705	−	3.94298i	−0.197642	−	0.143595i
$755$		0			0
$756$	1.61803	−	1.17557i	0.0588473	−	0.0427551i
$757$			28.8541i			1.04872i	0.851497	+	0.524360i	$0.175695\pi$
$757$			28.8541i			1.04872i	−0.851497	+	0.524360i	$0.824305\pi$
$758$	−2.00811	−	2.76393i	−0.0729380	−	0.100391i
$759$	−9.70820	−	29.8788i	−0.352385	−	1.08453i
$760$		0			0
$761$	7.46556	−	22.9766i	0.270626	−	0.832902i	−0.719717	−	0.694267i	$-0.755729\pi$
$761$	7.46556	−	22.9766i	0.270626	−	0.832902i	0.990344	−	0.138635i	$-0.0442714\pi$
$762$	0.277515	−	0.0901699i	0.0100533	−	0.00326651i
$763$	−4.87380	+	1.58359i	−0.176443	+	0.0573299i
$764$	0.236068	−	0.726543i	0.00854064	−	0.0262854i
$765$		0			0
$766$	−6.32624	−	19.4702i	−0.228576	−	0.703485i
$767$	−25.5195	−	35.1246i	−0.921457	−	1.26828i
$768$		−	1.00000i		−	0.0360844i
$769$	−1.90983	+	1.38757i	−0.0688702	+	0.0500372i	−0.621688	−	0.783265i	$-0.713553\pi$
$769$	−1.90983	+	1.38757i	−0.0688702	+	0.0500372i	0.552817	+	0.833302i	$0.313553\pi$
$770$		0			0
$771$	−9.39919	−	6.82891i	−0.338503	−	0.245937i
$772$	−1.40008	+	1.92705i	−0.0503901	+	0.0693561i
$773$	13.4005	+	4.35410i	0.481984	+	0.156606i	0.539924	−	0.841714i	$-0.318453\pi$
$773$	13.4005	+	4.35410i	0.481984	+	0.156606i	−0.0579395	+	0.998320i	$0.518453\pi$
$774$	−1.23607			−0.0444295
$775$		0			0
$776$	13.8541			0.497333
$777$	−4.08174	−	1.32624i	−0.146432	−	0.0475785i
$778$	−9.39205	+	12.9271i	−0.336721	+	0.463457i
$779$	13.6180	+	9.89408i	0.487917	+	0.354492i
$780$		0			0
$781$	−60.0689	+	43.6426i	−2.14943	+	1.56165i
$782$			47.1246i			1.68517i
$783$	−0.812299	−	1.11803i	−0.0290292	−	0.0399553i
$784$	0.927051	+	2.85317i	0.0331090	+	0.101899i
$785$		0			0
$786$	−0.236068	+	0.726543i	−0.00842027	+	0.0259149i
$787$	29.0462	−	9.43769i	1.03539	−	0.336417i	0.258469	−	0.966020i	$-0.416782\pi$
$787$	29.0462	−	9.43769i	1.03539	−	0.336417i	0.776918	+	0.629602i	$0.216782\pi$
$788$	12.6740	−	4.11803i	0.451493	−	0.146699i
$789$	0.145898	−	0.449028i	0.00519411	−	0.0159858i
$790$		0			0
$791$	−7.14590	−	21.9928i	−0.254079	−	0.781974i
$792$	3.07768	+	4.23607i	0.109361	+	0.150522i
$793$			42.9787i			1.52622i
$794$	−23.3262	+	16.9475i	−0.827817	+	0.601444i
$795$		0			0
$796$	5.00000	+	3.63271i	0.177220	+	0.128758i
$797$	7.83297	−	10.7812i	0.277458	−	0.381888i	−0.647432	−	0.762123i	$-0.724157\pi$
$797$	7.83297	−	10.7812i	0.277458	−	0.381888i	0.924890	+	0.380235i	$0.124157\pi$
$798$	−5.25731	−	1.70820i	−0.186107	−	0.0604698i
$799$	−37.4164			−1.32370
$800$		0			0
$801$	1.38197			0.0488294
$802$	−24.8132	−	8.06231i	−0.876185	−	0.284690i
$803$	9.68208	−	13.3262i	0.341673	−	0.470273i
$804$	7.85410	+	5.70634i	0.276993	+	0.201247i
$805$		0			0
$806$	−14.5623	+	10.5801i	−0.512935	+	0.372669i
$807$		−	1.90983i		−	0.0672292i
$808$	0.983813	+	1.35410i	0.0346104	+	0.0476371i
$809$	−2.53851	−	7.81272i	−0.0892492	−	0.274681i	0.896463	−	0.443118i	$-0.146128\pi$
$809$	−2.53851	−	7.81272i	−0.0892492	−	0.274681i	−0.985712	+	0.168438i	$0.946128\pi$
$810$		0			0
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	−0.879563	−	0.475783i	$-0.842165\pi$
$811$	3.18034	−	9.78808i	0.111677	−	0.343706i	0.991239	+	0.132077i	$0.0421647\pi$
$812$	−2.62866	+	0.854102i	−0.0922477	+	0.0299731i
$813$	26.8011	−	8.70820i	0.939955	−	0.305410i
$814$	3.47214	−	10.6861i	0.121698	−	0.374549i
$815$		0			0
$816$	−2.42705	−	7.46969i	−0.0849638	−	0.261492i
$817$	2.00811	+	2.76393i	0.0702550	+	0.0966977i
$818$		−	20.9787i		−	0.733504i
$819$	−7.85410	+	5.70634i	−0.274445	+	0.199396i
$820$		0			0
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.999029	−	0.0440528i	$-0.0140270\pi$
$821$	36.2705	+	26.3521i	1.26585	+	0.919694i	0.266820	+	0.963746i	$0.414027\pi$
$822$	8.83702	−	12.1631i	0.308227	−	0.424237i
$823$	−22.4418	−	7.29180i	−0.782273	−	0.254176i	−0.109463	−	0.993991i	$-0.534913\pi$
$823$	−22.4418	−	7.29180i	−0.782273	−	0.254176i	−0.672811	+	0.739815i	$0.734913\pi$
$824$	−2.29180			−0.0798385
$825$		0			0
$826$	−17.8885			−0.622422
$827$	−14.0413	−	4.56231i	−0.488265	−	0.158647i	0.0545300	−	0.998512i	$-0.482634\pi$
$827$	−14.0413	−	4.56231i	−0.488265	−	0.158647i	−0.542795	+	0.839865i	$0.682634\pi$
$828$	3.52671	−	4.85410i	0.122562	−	0.168692i
$829$	31.6697	+	23.0094i	1.09993	+	0.799149i	0.981049	−	0.193759i	$-0.0620680\pi$
$829$	31.6697	+	23.0094i	1.09993	+	0.799149i	0.118885	+	0.992908i	$0.462068\pi$
$830$		0			0
$831$	−17.9164	+	13.0170i	−0.621513	+	0.451556i
$832$			4.85410i			0.168286i
$833$	13.8496	+	19.0623i	0.479859	+	0.660470i
$834$	4.14590	+	12.7598i	0.143561	+	0.441834i
$835$		0			0
$836$	4.47214	−	13.7638i	0.154672	−	0.476032i
$837$	−3.52671	+	1.14590i	−0.121901	+	0.0396080i
$838$	−36.0341	+	11.7082i	−1.24478	+	0.404453i
$839$	1.58359	−	4.87380i	0.0546717	−	0.168262i	−0.919992	−	0.391937i	$-0.871805\pi$
$839$	1.58359	−	4.87380i	0.0546717	−	0.168262i	0.974664	+	0.223674i	$0.0718053\pi$
$840$		0			0
$841$	−8.37132	−	25.7643i	−0.288666	−	0.888424i
$842$	6.51864	+	8.97214i	0.224647	+	0.309200i
$843$			6.09017i			0.209757i
$844$	−6.47214	+	4.70228i	−0.222780	+	0.161859i
$845$		0			0
$846$	3.85410	+	2.80017i	0.132507	+	0.0962718i
$847$	−19.2986	+	26.5623i	−0.663109	+	0.912692i
$848$	8.14324	+	2.64590i	0.279640	+	0.0908605i
$849$	3.23607			0.111062
$850$		0			0
$851$	−12.8754			−0.441363
$852$	−13.4863	−	4.38197i	−0.462033	−	0.150124i
$853$	9.66957	−	13.3090i	0.331080	−	0.455692i	−0.610730	−	0.791839i	$-0.709124\pi$
$853$	9.66957	−	13.3090i	0.331080	−	0.455692i	0.941810	+	0.336147i	$0.109124\pi$
$854$	14.3262	+	10.4086i	0.490234	+	0.356176i
$855$		0			0
$856$	8.85410	−	6.43288i	0.302627	−	0.219871i
$857$		−	23.3050i		−	0.796082i	−0.917368	−	0.398041i	$-0.869690\pi$
$857$		−	23.3050i		−	0.796082i	0.917368	−	0.398041i	$-0.130310\pi$
$858$	−14.9394	−	20.5623i	−0.510022	−	0.701986i
$859$	−14.0689	−	43.2996i	−0.480024	−	1.47736i	−0.839060	−	0.544039i	$-0.816894\pi$
$859$	−14.0689	−	43.2996i	−0.480024	−	1.47736i	0.359036	−	0.933324i	$-0.383106\pi$
$860$		0			0
$861$	3.76393	−	11.5842i	0.128274	−	0.394788i
$862$	−3.52671	+	1.14590i	−0.120120	+	0.0390294i
$863$	−11.5842	+	3.76393i	−0.394330	+	0.128126i	−0.499469	−	0.866332i	$-0.666471\pi$
$863$	−11.5842	+	3.76393i	−0.394330	+	0.128126i	0.105138	+	0.994458i	$0.466471\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$		0			0
$866$	7.15248	+	22.0131i	0.243051	+	0.748034i
$867$	−26.2663	−	36.1525i	−0.892051	−	1.22780i
$868$			7.41641i			0.251729i
$869$		0			0
$870$		0			0
$871$	−38.1246	−	27.6992i	−1.29180	−	0.938550i
$872$	1.50609	−	2.07295i	0.0510025	−	0.0701989i
$873$	−13.1760	−	4.28115i	−0.445941	−	0.144895i
$874$	−16.5836			−0.560948
$875$		0			0
$876$	3.14590			0.106290
$877$	−17.0988	−	5.55573i	−0.577385	−	0.187604i	0.00574402	−	0.999984i	$-0.498172\pi$
$877$	−17.0988	−	5.55573i	−0.577385	−	0.187604i	−0.583129	+	0.812380i	$0.698172\pi$
$878$	14.7679	−	20.3262i	0.498392	−	0.685977i
$879$	23.2984	+	16.9273i	0.785835	+	0.570942i
$880$		0			0
$881$	−37.7984	+	27.4621i	−1.27346	+	0.925223i	−0.999335	−	0.0364716i	$-0.988388\pi$
$881$	−37.7984	+	27.4621i	−1.27346	+	0.925223i	−0.274125	+	0.961694i	$0.588388\pi$
$882$		−	3.00000i		−	0.101015i
$883$	−24.7930	−	34.1246i	−0.834350	−	1.14838i	−0.987098	−	0.160119i	$-0.948812\pi$
$883$	−24.7930	−	34.1246i	−0.834350	−	1.14838i	0.152747	−	0.988265i	$-0.451188\pi$
$884$	11.7812	+	36.2587i	0.396243	+	1.21951i
$885$		0			0
$886$	−9.29180	+	28.5972i	−0.312164	+	0.960742i
$887$	24.5560	−	7.97871i	0.824508	−	0.267899i	0.133778	−	0.991011i	$-0.457289\pi$
$887$	24.5560	−	7.97871i	0.824508	−	0.267899i	0.690730	+	0.723112i	$0.257289\pi$
$888$	2.04087	−	0.663119i	0.0684871	−	0.0222528i
$889$	−0.180340	+	0.555029i	−0.00604841	+	0.0186151i
$890$		0			0
$891$	−1.61803	−	4.97980i	−0.0542062	−	0.166829i
$892$	−1.34708	−	1.85410i	−0.0451037	−	0.0620799i
$893$		−	13.1672i		−	0.440623i
$894$	5.69098	−	4.13474i	0.190335	−	0.138286i
$895$		0			0
$896$	1.61803	+	1.17557i	0.0540547	+	0.0392731i
$897$	−17.1190	+	23.5623i	−0.571587	+	0.786722i
$898$	−4.56352	−	1.48278i	−0.152287	−	0.0494810i
$899$	5.12461			0.170915
$900$		0			0
$901$	67.2492			2.24040
$902$	30.3278	+	9.85410i	1.00981	+	0.328106i
$903$	1.45309	−	2.00000i	0.0483556	−	0.0665558i
$904$	9.35410	+	6.79615i	0.311113	+	0.226037i
$905$		0			0
$906$	5.61803	−	4.08174i	0.186647	−	0.135607i
$907$		−	20.2918i		−	0.673778i	−0.941544	−	0.336889i	$-0.890625\pi$
$907$		−	20.2918i		−	0.673778i	0.941544	−	0.336889i	$-0.109375\pi$
$908$	9.95959	+	13.7082i	0.330521	+	0.454923i
$909$	−0.517221	−	1.59184i	−0.0171551	−	0.0527981i
$910$		0			0
$911$	17.3262	−	53.3247i	0.574044	−	1.76673i	−0.0653683	−	0.997861i	$-0.520822\pi$
$911$	17.3262	−	53.3247i	0.574044	−	1.76673i	0.639412	−	0.768864i	$-0.279178\pi$
$912$	2.62866	−	0.854102i	0.0870435	−	0.0282821i
$913$	29.8788	−	9.70820i	0.988843	−	0.321295i
$914$	−3.85410	+	11.8617i	−0.127482	+	0.392350i
$915$		0			0
$916$	−7.50000	−	23.0826i	−0.247807	−	0.762671i
$917$	−0.898056	−	1.23607i	−0.0296564	−	0.0408186i
$918$			7.85410i			0.259224i
$919$	−0.854102	+	0.620541i	−0.0281742	+	0.0204698i	−0.601783	−	0.798659i	$-0.705543\pi$
$919$	−0.854102	+	0.620541i	−0.0281742	+	0.0204698i	0.573609	+	0.819129i	$0.305543\pi$
$920$		0			0
$921$	−13.1803	−	9.57608i	−0.434307	−	0.315542i
$922$	14.7476	−	20.2984i	0.485687	−	0.668491i
$923$	65.4639	+	21.2705i	2.15477	+	0.700127i
$924$	−10.4721			−0.344508
$925$		0			0
$926$	12.2918			0.403933
$927$	2.17963	+	0.708204i	0.0715884	+	0.0232605i
$928$	0.812299	−	1.11803i	0.0266650	−	0.0367013i
$929$	−25.0623	−	18.2088i	−0.822268	−	0.597412i	0.0950935	−	0.995468i	$-0.469685\pi$
$929$	−25.0623	−	18.2088i	−0.822268	−	0.597412i	−0.917361	+	0.398056i	$0.869685\pi$
$930$		0			0
$931$	−6.70820	+	4.87380i	−0.219853	+	0.159732i
$932$			22.0902i			0.723588i
$933$	−10.9637	−	15.0902i	−0.358934	−	0.494030i
$934$	4.88854	+	15.0454i	0.159958	+	0.492300i
$935$		0			0
$936$	1.50000	−	4.61653i	0.0490290	−	0.150896i
$937$	33.3727	−	10.8435i	1.09024	−	0.354240i	0.291901	−	0.956449i	$-0.405712\pi$
$937$	33.3727	−	10.8435i	1.09024	−	0.354240i	0.798339	+	0.602208i	$0.205712\pi$
$938$	−18.4661	+	6.00000i	−0.602940	+	0.195907i
$939$	−8.14590	+	25.0705i	−0.265831	+	0.818145i
$940$		0			0
$941$	6.69756	+	20.6130i	0.218334	+	0.671964i	0.998900	+	0.0468901i	$0.0149311\pi$
$941$	6.69756	+	20.6130i	0.218334	+	0.671964i	−0.780566	+	0.625074i	$0.785069\pi$
$942$	10.4944	+	14.4443i	0.341925	+	0.470620i
$943$		−	36.5410i		−	1.18994i
$944$	7.23607	−	5.25731i	0.235514	−	0.171111i
$945$		0			0
$946$	5.23607	+	3.80423i	0.170239	+	0.123686i
$947$	−6.43288	+	8.85410i	−0.209041	+	0.287720i	−0.900644	−	0.434558i	$-0.856905\pi$
$947$	−6.43288	+	8.85410i	−0.209041	+	0.287720i	0.691603	+	0.722278i	$0.256905\pi$
$948$		0			0
$949$	−15.2705			−0.495702
$950$		0			0
$951$	6.94427			0.225183
$952$	14.9394	+	4.85410i	0.484188	+	0.157322i
$953$	−19.3189	+	26.5902i	−0.625800	+	0.861340i	−0.997759	−	0.0669091i	$-0.978686\pi$
$953$	−19.3189	+	26.5902i	−0.625800	+	0.861340i	0.371959	+	0.928249i	$0.378686\pi$
$954$	−6.92705	−	5.03280i	−0.224272	−	0.162943i
$955$		0			0
$956$	−21.7082	+	15.7719i	−0.702093	+	0.510101i
$957$			7.23607i			0.233909i
$958$	2.62866	+	3.61803i	0.0849280	+	0.116893i
$959$	9.29180	+	28.5972i	0.300048	+	0.923452i
$960$		0			0
$961$	−5.33030	+	16.4050i	−0.171945	+	0.529193i
$962$	−9.90659	+	3.21885i	−0.319401	+	0.103780i
$963$	−10.4086	+	3.38197i	−0.335413	+	0.108982i
$964$	4.28115	−	13.1760i	0.137887	−	0.424371i
$965$		0			0
$966$	3.70820	+	11.4127i	0.119310	+	0.367197i
$967$	24.0664	+	33.1246i	0.773925	+	1.06522i	0.995926	+	0.0901695i	$0.0287409\pi$
$967$	24.0664	+	33.1246i	0.773925	+	1.06522i	−0.222002	+	0.975046i	$0.571259\pi$
$968$		−	16.4164i		−	0.527643i
$969$	17.5623	−	12.7598i	0.564183	−	0.409903i
$970$		0			0
$971$	27.3262	+	19.8537i	0.876941	+	0.637135i	0.932440	−	0.361324i	$-0.117675\pi$
$971$	27.3262	+	19.8537i	0.876941	+	0.637135i	−0.0554996	+	0.998459i	$0.517675\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	−25.5195	−	8.29180i	−0.818118	−	0.265823i
$974$	10.2918			0.329770
$975$		0			0
$976$	−8.85410			−0.283413
$977$	19.5559	+	6.35410i	0.625649	+	0.203286i	0.604647	−	0.796494i	$-0.293314\pi$
$977$	19.5559	+	6.35410i	0.625649	+	0.203286i	0.0210023	+	0.999779i	$0.493314\pi$
$978$	12.0332	−	16.5623i	0.384780	−	0.529604i
$979$	−5.85410	−	4.25325i	−0.187098	−	0.135935i
$980$		0			0
$981$	−2.07295	+	1.50609i	−0.0661842	+	0.0480856i
$982$			29.8885i			0.953782i
$983$	25.0050	+	34.4164i	0.797535	+	1.09771i	0.993129	+	0.117028i	$0.0373367\pi$
$983$	25.0050	+	34.4164i	0.797535	+	1.09771i	−0.195594	+	0.980685i	$0.562663\pi$
$984$	1.88197	+	5.79210i	0.0599949	+	0.184645i
$985$		0			0
$986$	3.35410	−	10.3229i	0.106816	−	0.328747i
$987$	−9.06154	+	2.94427i	−0.288432	+	0.0937172i
$988$	−12.7598	+	4.14590i	−0.405942	+	0.131899i
$989$	2.29180	−	7.05342i	0.0728749	−	0.224286i
$990$		0			0
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.558250	+	0.829673i	$0.311473\pi$
$991$	18.7082	+	57.5779i	0.594286	+	1.82902i	0.0360356	+	0.999351i	$0.488527\pi$
$992$	−2.17963	−	3.00000i	−0.0692032	−	0.0952501i
$993$			32.4721i			1.03047i
$994$	22.9443	−	16.6700i	0.727748	−	0.528740i
$995$		0			0
$996$	4.85410	+	3.52671i	0.153808	+	0.111748i
$997$	0.832544	−	1.14590i	0.0263669	−	0.0362910i	−0.795630	−	0.605783i	$-0.792860\pi$
$997$	0.832544	−	1.14590i	0.0263669	−	0.0362910i	0.821997	+	0.569492i	$0.192860\pi$
$998$	31.7809	+	10.3262i	1.00601	+	0.326871i
$999$	−2.14590			−0.0678932

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.h.a.649.2		8
5.2	odd	4		150.2.g.b.121.1	yes	4
5.3	odd	4		750.2.g.a.601.1		4
5.4	even	2	inner	750.2.h.a.649.1		8
15.2	even	4		450.2.h.b.271.1		4
25.6	even	5	inner	750.2.h.a.349.1		8
25.8	odd	20		750.2.g.a.151.1		4
25.9	even	10		3750.2.c.c.1249.1		4
25.12	odd	20		3750.2.a.b.1.1		2
25.13	odd	20		3750.2.a.g.1.1		2
25.16	even	5		3750.2.c.c.1249.3		4
25.17	odd	20		150.2.g.b.31.1	✓	4
25.19	even	10	inner	750.2.h.a.349.2		8
75.17	even	20		450.2.h.b.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.b.31.1	✓	4	25.17	odd	20
150.2.g.b.121.1	yes	4	5.2	odd	4
450.2.h.b.181.1		4	75.17	even	20
450.2.h.b.271.1		4	15.2	even	4
750.2.g.a.151.1		4	25.8	odd	20
750.2.g.a.601.1		4	5.3	odd	4
750.2.h.a.349.1		8	25.6	even	5	inner
750.2.h.a.349.2		8	25.19	even	10	inner
750.2.h.a.649.1		8	5.4	even	2	inner
750.2.h.a.649.2		8	1.1	even	1	trivial
3750.2.a.b.1.1		2	25.12	odd	20
3750.2.a.g.1.1		2	25.13	odd	20
3750.2.c.c.1249.1		4	25.9	even	10
3750.2.c.c.1249.3		4	25.16	even	5

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.h (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -2.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} -2.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(-1.61803 + 4.97980i) q^{11} +(-0.951057 + 0.309017i) q^{12} +(4.61653 - 1.50000i) q^{13} +(0.618034 - 1.90211i) q^{14} +(0.309017 + 0.951057i) q^{16} +(4.61653 + 6.35410i) q^{17} -1.00000i q^{18} +(-2.23607 + 1.62460i) q^{19} +(1.61803 + 1.17557i) q^{21} +(-3.07768 + 4.23607i) q^{22} +(5.70634 + 1.85410i) q^{23} -1.00000 q^{24} +4.85410 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.17557 - 1.61803i) q^{28} +(-1.11803 - 0.812299i) q^{29} +(-3.00000 + 2.17963i) q^{31} +1.00000i q^{32} +(-3.07768 - 4.23607i) q^{33} +(2.42705 + 7.46969i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.04087 + 0.663119i) q^{37} +(-2.62866 + 0.854102i) q^{38} +(-1.50000 + 4.61653i) q^{39} +(-1.88197 - 5.79210i) q^{41} +(1.17557 + 1.61803i) q^{42} -1.23607i q^{43} +(-4.23607 + 3.07768i) q^{44} +(4.85410 + 3.52671i) q^{46} +(-2.80017 + 3.85410i) q^{47} +(-0.951057 - 0.309017i) q^{48} +3.00000 q^{49} -7.85410 q^{51} +(4.61653 + 1.50000i) q^{52} +(5.03280 - 6.92705i) q^{53} +(0.809017 + 0.587785i) q^{54} +(1.61803 - 1.17557i) q^{56} -2.76393i q^{57} +(-0.812299 - 1.11803i) q^{58} +(-2.76393 - 8.50651i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(-3.52671 + 1.14590i) q^{62} +(-1.90211 + 0.618034i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-1.61803 - 4.97980i) q^{66} +(-5.70634 - 7.85410i) q^{67} +7.85410i q^{68} +(-4.85410 + 3.52671i) q^{69} +(11.4721 + 8.33499i) q^{71} +(0.587785 - 0.809017i) q^{72} +(-2.99193 - 0.972136i) q^{73} -2.14590 q^{74} -2.76393 q^{76} +(9.95959 + 3.23607i) q^{77} +(-2.85317 + 3.92705i) q^{78} +(-0.809017 + 0.587785i) q^{81} -6.09017i q^{82} +(-3.52671 - 4.85410i) q^{83} +(0.618034 + 1.90211i) q^{84} +(0.381966 - 1.17557i) q^{86} +(1.31433 - 0.427051i) q^{87} +(-4.97980 + 1.61803i) q^{88} +(-0.427051 + 1.31433i) q^{89} +(-3.00000 - 9.23305i) q^{91} +(3.52671 + 4.85410i) q^{92} -3.70820i q^{93} +(-3.85410 + 2.80017i) q^{94} +(-0.809017 - 0.587785i) q^{96} +(8.14324 - 11.2082i) q^{97} +(2.85317 + 0.927051i) q^{98} +5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 4 q^{11} - 4 q^{14} - 2 q^{16} + 4 q^{21} - 8 q^{24} + 12 q^{26} - 24 q^{31} + 6 q^{34} - 2 q^{36} - 12 q^{39} - 24 q^{41} - 16 q^{44} + 12 q^{46} + 24 q^{49} - 36 q^{51} + 2 q^{54} + 4 q^{56} - 40 q^{59} - 4 q^{61} + 2 q^{64} - 4 q^{66} - 12 q^{69} + 56 q^{71} - 44 q^{74} - 40 q^{76} - 2 q^{81} - 4 q^{84} + 12 q^{86} + 10 q^{89} - 24 q^{91} - 4 q^{94} - 2 q^{96} + 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 4 * q^11 - 4 * q^14 - 2 * q^16 + 4 * q^21 - 8 * q^24 + 12 * q^26 - 24 * q^31 + 6 * q^34 - 2 * q^36 - 12 * q^39 - 24 * q^41 - 16 * q^44 + 12 * q^46 + 24 * q^49 - 36 * q^51 + 2 * q^54 + 4 * q^56 - 40 * q^59 - 4 * q^61 + 2 * q^64 - 4 * q^66 - 12 * q^69 + 56 * q^71 - 44 * q^74 - 40 * q^76 - 2 * q^81 - 4 * q^84 + 12 * q^86 + 10 * q^89 - 24 * q^91 - 4 * q^94 - 2 * q^96 + 24 * q^99

Introduction

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