LMFDB - Embedded newform 750.2.h.a.649.1

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			649.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.649
Dual form			750.2.h.a.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{6} +2.00000i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−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	−0.868719	−	0.495306i	$-0.835056\pi$
$13$	−4.61653	+	1.50000i	−1.28039	+	0.416025i	−0.411675	+	0.911331i	$0.635056\pi$
$14$	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	$-0.798555\pi$
$17$	−4.61653	−	6.35410i	−1.11967	−	1.54110i	−0.313332	−	0.949644i	$-0.601445\pi$
$18$			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	−0.353835	−	0.935308i	$-0.615123\pi$
$23$	−5.70634	−	1.85410i	−1.18985	−	0.386607i	−0.836019	+	0.548701i	$0.815123\pi$
$24$	−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	−0.136413	−	0.990652i	$-0.543557\pi$
$37$	2.04087	−	0.663119i	0.335517	−	0.109016i	0.471930	+	0.881636i	$0.343557\pi$
$38$	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	$0.0300451\pi$
$43$			1.23607i			0.188499i	−0.995549	+	0.0942493i	$0.969955\pi$
$44$	−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	−0.554392	−	0.832256i	$-0.687049\pi$
$47$	2.80017	−	3.85410i	0.408447	−	0.562179i	0.962839	+	0.270077i	$0.0870492\pi$
$48$	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	$0.400109\pi$
$53$	−5.03280	+	6.92705i	−0.691308	+	0.951504i	−1.00000		0.000341607i	$0.999891\pi$
$54$	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	$0.00206567\pi$
$67$	5.70634	+	7.85410i	0.697140	+	0.959531i	−0.302839	+	0.953042i	$0.597934\pi$
$68$		−	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	0.478824	−	0.877911i	$-0.341063\pi$
$73$	2.99193	+	0.972136i	0.350179	+	0.113780i	−0.128646	+	0.991691i	$0.541063\pi$
$74$	−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	0.957450	−	0.288600i	$-0.0931897\pi$
$83$	3.52671	+	4.85410i	0.387107	+	0.532807i	−0.570343	+	0.821407i	$0.693190\pi$
$84$	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	$0.448307\pi$
$97$	−8.14324	+	11.2082i	−0.826820	+	1.13802i	−0.988506	+	0.151178i	$0.951693\pi$
$98$	−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	−0.737478	−	0.675372i	$-0.763983\pi$
$103$	1.34708	−	1.85410i	0.132732	−	0.182690i	0.870210	+	0.492682i	$0.163983\pi$
$104$	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	$0.177437\pi$
$107$			10.9443i			1.05802i	−0.848615	+	0.529011i	$0.822563\pi$
$108$	−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	−0.776550	−	0.630056i	$-0.783032\pi$
$113$	−10.9964	+	3.57295i	−1.03445	+	0.336115i	−0.257905	+	0.966170i	$0.583032\pi$
$114$	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	0.321304	−	0.946976i	$-0.395879\pi$
$127$	0.277515	+	0.0901699i	0.0246254	+	0.00800129i	−0.296678	+	0.954977i	$0.595879\pi$
$128$	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	0.373943	−	0.927452i	$-0.378005\pi$
$137$	14.2986	−	4.64590i	1.22161	−	0.396926i	0.847669	+	0.530526i	$0.178005\pi$
$138$	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	$0.252417\pi$
$157$			17.8541i			1.42491i	−0.701717	+	0.712456i	$0.747583\pi$
$158$		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	0.577824	−	0.816162i	$-0.303902\pi$
$163$	19.4702	−	6.32624i	1.52502	−	0.495509i	0.947197	+	0.320652i	$0.103902\pi$
$164$	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	0.636051	−	0.771647i	$-0.280567\pi$
$167$	−3.80423	−	5.23607i	−0.294380	−	0.405179i	−0.930431	+	0.366468i	$0.880567\pi$
$168$		−	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	0.675620	−	0.737250i	$-0.263876\pi$
$173$	10.3759	+	3.37132i	0.788862	+	0.256317i	0.113243	+	0.993567i	$0.463876\pi$
$174$	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	$-0.972678\pi$
$193$		−	2.38197i		−	0.171458i	0.996319	−	0.0857288i	$-0.0273219\pi$
$194$	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	−0.991080	−	0.133266i	$-0.957453\pi$
$197$	−7.83297	+	10.7812i	−0.558076	+	0.768125i	0.433005	+	0.901392i	$0.357453\pi$
$198$	−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	0.381085	−	0.924540i	$-0.375550\pi$
$223$	2.17963	+	0.708204i	0.145959	+	0.0474248i	−0.235127	+	0.971965i	$0.575550\pi$
$224$	2.00000			0.133631
$225$		0			0
$226$	11.5623			0.769113
$227$	−16.1150	−	5.23607i	−1.06959	−	0.347530i	−0.279261	−	0.960215i	$-0.590089\pi$
$227$	−16.1150	−	5.23607i	−1.06959	−	0.347530i	−0.790327	+	0.612685i	$0.790089\pi$
$228$	−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	$-0.942492\pi$
$233$	−12.9843	−	17.8713i	−0.850628	−	1.17079i	0.133096	−	0.991103i	$-0.457508\pi$
$234$	−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	$-0.881972\pi$
$257$		−	11.6180i		−	0.724713i	0.932040	−	0.362357i	$-0.118028\pi$
$258$	−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	−0.295140	−	0.955454i	$-0.595366\pi$
$263$	0.449028	−	0.145898i	0.0276883	−	0.00899646i	0.322828	+	0.946458i	$0.395366\pi$
$264$	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	−0.402044	−	0.915620i	$-0.631700\pi$
$277$	−21.0620	−	6.84346i	−1.26549	−	0.411184i	−0.863449	+	0.504437i	$0.831700\pi$
$278$	−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	0.861801	−	0.507247i	$-0.169337\pi$
$283$	1.90211	+	2.61803i	0.113069	+	0.155626i	−0.748732	+	0.662873i	$0.769337\pi$
$284$	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	$0.318156\pi$
$293$			28.7984i			1.68242i	−0.540709	+	0.841209i	$0.681844\pi$
$294$	−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	$-0.846086\pi$
$307$		−	16.2918i		−	0.929822i	0.885357	−	0.464911i	$-0.153914\pi$
$308$	−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	−0.914669	−	0.404203i	$-0.867549\pi$
$313$	−25.0705	+	8.14590i	−1.41707	+	0.460433i	−0.502399	+	0.864636i	$0.667549\pi$
$314$	5.51722	−	16.9803i	0.311355	−	0.958252i
$315$		0			0
$316$		0			0
$317$	4.08174	+	5.61803i	0.229253	+	0.315540i	0.908111	−	0.418730i	$-0.137525\pi$
$317$	4.08174	+	5.61803i	0.229253	+	0.315540i	−0.678857	+	0.734270i	$0.737525\pi$
$318$		−	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	−0.938188	−	0.346125i	$-0.887497\pi$
$337$	−27.4216	+	8.90983i	−1.49375	+	0.485349i	−0.555563	+	0.831474i	$0.687497\pi$
$338$	−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	−0.883596	−	0.468249i	$-0.844885\pi$
$347$	−3.07768	+	4.23607i	−0.165219	+	0.227404i	0.718378	+	0.695653i	$0.244885\pi$
$348$	−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	−0.998640	−	0.0521313i	$-0.983399\pi$
$353$	−12.0332	+	16.5623i	−0.640464	+	0.881523i	0.358177	+	0.933654i	$0.383399\pi$
$354$	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	0.956290	−	0.292420i	$-0.0944606\pi$
$367$	7.33094	+	10.0902i	0.382672	+	0.526703i	−0.573618	+	0.819123i	$0.694461\pi$
$368$		−	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	0.244712	−	0.969596i	$-0.421307\pi$
$373$	−2.45714	−	0.798374i	−0.127226	−	0.0413382i	−0.371938	+	0.928258i	$0.621307\pi$
$374$	−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	0.996967	−	0.0778275i	$-0.0247983\pi$
$383$	12.0332	+	16.5623i	0.614869	+	0.846294i	−0.382098	+	0.924122i	$0.624798\pi$
$384$	−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	$-0.542514\pi$
$397$	16.9475	−	23.3262i	0.850571	−	1.17071i	0.983737	−	0.179617i	$-0.0574857\pi$
$398$	−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	0.345451	−	0.938437i	$-0.387726\pi$
$433$	−13.6048	−	18.7254i	−0.653806	−	0.899886i	−0.999257	+	0.0385504i	$0.987726\pi$
$434$	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	$-0.746742\pi$
$443$		−	30.0689i		−	1.42862i	0.699832	−	0.714308i	$-0.253258\pi$
$444$	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	$-0.905775\pi$
$457$		−	12.4721i		−	0.583422i	0.956507	−	0.291711i	$-0.0942245\pi$
$458$	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	−0.567789	−	0.823174i	$-0.692201\pi$
$463$	−11.6902	+	3.79837i	−0.543289	+	0.176525i	0.0244992	+	0.999700i	$0.492201\pi$
$464$	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	0.537733	−	0.843115i	$-0.319281\pi$
$467$	−9.29856	−	12.7984i	−0.430286	−	0.592238i	−0.968019	+	0.250877i	$0.919281\pi$
$468$			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	−0.522268	−	0.852781i	$-0.674914\pi$
$487$	−9.78808	+	3.18034i	−0.443540	+	0.144115i	0.0787282	+	0.996896i	$0.474914\pi$
$488$	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	−0.991853	−	0.127385i	$-0.959342\pi$
$503$	−12.6538	+	17.4164i	−0.564203	+	0.776559i	0.427650	+	0.903944i	$0.359342\pi$
$504$	−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	0.356283	−	0.934378i	$-0.384044\pi$
$523$	2.17963	+	0.708204i	0.0953085	+	0.0309676i	−0.260975	+	0.965346i	$0.584044\pi$
$524$	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	−0.783145	−	0.621839i	$-0.786386\pi$
$547$	1.17557	−	1.61803i	0.0502638	−	0.0691821i	0.833409	+	0.552657i	$0.186386\pi$
$548$	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	$-0.803933\pi$
$557$		−	27.2705i		−	1.15549i	0.816218	−	0.577744i	$-0.196067\pi$
$558$	−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	−0.0915256	−	0.995803i	$-0.529174\pi$
$563$	9.95959	−	3.23607i	0.419747	−	0.136384i	0.511272	+	0.859419i	$0.329174\pi$
$564$	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	0.817965	−	0.575268i	$-0.195102\pi$
$577$	27.4216	+	8.90983i	1.14158	+	0.370921i	0.323613	+	0.946190i	$0.395102\pi$
$578$	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	0.0199141	−	0.999802i	$-0.493661\pi$
$587$	15.1109	−	4.90983i	0.623694	−	0.202650i	0.603780	+	0.797151i	$0.293661\pi$
$588$	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	$0.0395410\pi$
$593$			6.03444i			0.247805i	−0.992294	+	0.123902i	$0.960459\pi$
$594$	−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	$-0.988243\pi$
$607$		−	1.81966i		−	0.0738577i	0.999318	−	0.0369289i	$-0.0117575\pi$
$608$	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	−0.692316	−	0.721594i	$-0.743410\pi$
$613$	−20.5070	+	6.66312i	−0.828269	+	0.269121i	−0.135953	+	0.990715i	$0.543410\pi$
$614$	−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	0.698246	−	0.715858i	$-0.253964\pi$
$617$	−4.92680	−	6.78115i	−0.198345	−	0.272999i	−0.896591	+	0.442859i	$0.853964\pi$
$618$			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	$0.286992\pi$
$643$			39.7771i			1.56866i	−0.620347	+	0.784328i	$0.713008\pi$
$644$	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	$0.449261\pi$
$647$	−21.0948	+	29.0344i	−0.829320	+	1.14146i	−0.988049	+	0.154139i	$0.950739\pi$
$648$	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	$-0.582919\pi$
$653$	18.9354	−	26.0623i	0.740998	−	1.01990i	0.998561	−	0.0536351i	$-0.0170808\pi$
$654$	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	0.632601	−	0.774478i	$-0.281987\pi$
$673$	17.8783	+	5.80902i	0.689158	+	0.223921i	0.0565578	+	0.998399i	$0.481987\pi$
$674$	28.8328			1.11060
$675$		0			0
$676$	10.5623			0.406243
$677$	34.6871	+	11.2705i	1.33313	+	0.433161i	0.886985	−	0.461799i	$-0.152796\pi$
$677$	34.6871	+	11.2705i	1.33313	+	0.433161i	0.446147	+	0.894960i	$0.352796\pi$
$678$	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	0.969473	−	0.245196i	$-0.0788525\pi$
$683$	11.4127	+	15.7082i	0.436694	+	0.601058i	−0.532779	+	0.846254i	$0.678852\pi$
$684$	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	0.484847	−	0.874599i	$-0.338875\pi$
$727$	9.78808	+	3.18034i	0.363020	+	0.117952i	−0.121827	+	0.992551i	$0.538875\pi$
$728$	−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	0.734370	−	0.678750i	$-0.237478\pi$
$733$	−3.73871	−	5.14590i	−0.138093	−	0.190068i	−0.872462	+	0.488682i	$0.837478\pi$
$734$	−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	$-0.961060\pi$
$743$		−	6.65248i		−	0.244056i	0.992527	−	0.122028i	$-0.0389397\pi$
$744$	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	$-0.824305\pi$
$757$		−	28.8541i		−	1.04872i	0.851497	−	0.524360i	$-0.175695\pi$
$758$	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	0.0579395	−	0.998320i	$-0.481547\pi$
$773$	−13.4005	−	4.35410i	−0.481984	−	0.156606i	−0.539924	+	0.841714i	$0.681547\pi$
$774$	−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	−0.776918	−	0.629602i	$-0.783218\pi$
$787$	−29.0462	+	9.43769i	−1.03539	+	0.336417i	−0.258469	+	0.966020i	$0.583218\pi$
$788$	−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	−0.924890	−	0.380235i	$-0.875843\pi$
$797$	−7.83297	+	10.7812i	−0.277458	+	0.381888i	0.647432	+	0.762123i	$0.275843\pi$
$798$	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	0.672811	−	0.739815i	$-0.265087\pi$
$823$	22.4418	+	7.29180i	0.782273	+	0.254176i	0.109463	+	0.993991i	$0.465087\pi$
$824$	−2.29180			−0.0798385
$825$		0			0
$826$	−17.8885			−0.622422
$827$	14.0413	+	4.56231i	0.488265	+	0.158647i	0.542795	−	0.839865i	$-0.317366\pi$
$827$	14.0413	+	4.56231i	0.488265	+	0.158647i	−0.0545300	+	0.998512i	$0.517366\pi$
$828$	−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	−0.941810	−	0.336147i	$-0.890876\pi$
$853$	−9.66957	+	13.3090i	−0.331080	+	0.455692i	0.610730	+	0.791839i	$0.290876\pi$
$854$	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	$0.130310\pi$
$857$			23.3050i			0.796082i	−0.917368	+	0.398041i	$0.869690\pi$
$858$	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	−0.105138	−	0.994458i	$-0.533529\pi$
$863$	11.5842	−	3.76393i	0.394330	−	0.128126i	0.499469	+	0.866332i	$0.333529\pi$
$864$	−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	0.583129	−	0.812380i	$-0.301828\pi$
$877$	17.0988	+	5.55573i	0.577385	+	0.187604i	−0.00574402	+	0.999984i	$0.501828\pi$
$878$	−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	$0.0511879\pi$
$883$	24.7930	+	34.1246i	0.834350	+	1.14838i	−0.152747	+	0.988265i	$0.548812\pi$
$884$	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	−0.690730	−	0.723112i	$-0.742711\pi$
$887$	−24.5560	+	7.97871i	−0.824508	+	0.267899i	−0.133778	+	0.991011i	$0.542711\pi$
$888$	−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	$0.109375\pi$
$907$			20.2918i			0.673778i	−0.941544	+	0.336889i	$0.890625\pi$
$908$	−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	−0.798339	−	0.602208i	$-0.794288\pi$
$937$	−33.3727	+	10.8435i	−1.09024	+	0.354240i	−0.291901	+	0.956449i	$0.594288\pi$
$938$	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	−0.691603	−	0.722278i	$-0.743095\pi$
$947$	6.43288	−	8.85410i	0.209041	−	0.287720i	0.900644	+	0.434558i	$0.143095\pi$
$948$		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	−0.371959	−	0.928249i	$-0.621314\pi$
$953$	19.3189	−	26.5902i	0.625800	−	0.861340i	0.997759	+	0.0669091i	$0.0213138\pi$
$954$	−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	$-0.971259\pi$
$967$	−24.0664	−	33.1246i	−0.773925	−	1.06522i	0.222002	−	0.975046i	$-0.428741\pi$
$968$			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	−0.0210023	−	0.999779i	$-0.506686\pi$
$977$	−19.5559	−	6.35410i	−0.625649	−	0.203286i	−0.604647	+	0.796494i	$0.706686\pi$
$978$	−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	$-0.962663\pi$
$983$	−25.0050	−	34.4164i	−0.797535	−	1.09771i	0.195594	−	0.980685i	$-0.437337\pi$
$984$	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	−0.821997	−	0.569492i	$-0.807140\pi$
$997$	−0.832544	+	1.14590i	−0.0263669	+	0.0362910i	0.795630	+	0.605783i	$0.207140\pi$
$998$	−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.649.1		8
5.2	odd	4		750.2.g.a.601.1		4
5.3	odd	4		150.2.g.b.121.1	yes	4
5.4	even	2	inner	750.2.h.a.649.2		8
15.8	even	4		450.2.h.b.271.1		4
25.6	even	5	inner	750.2.h.a.349.2		8
25.8	odd	20		150.2.g.b.31.1	✓	4
25.9	even	10		3750.2.c.c.1249.3		4
25.12	odd	20		3750.2.a.g.1.1		2
25.13	odd	20		3750.2.a.b.1.1		2
25.16	even	5		3750.2.c.c.1249.1		4
25.17	odd	20		750.2.g.a.151.1		4
25.19	even	10	inner	750.2.h.a.349.1		8
75.8	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	25.8	odd	20
150.2.g.b.121.1	yes	4	5.3	odd	4
450.2.h.b.181.1		4	75.8	even	20
450.2.h.b.271.1		4	15.8	even	4
750.2.g.a.151.1		4	25.17	odd	20
750.2.g.a.601.1		4	5.2	odd	4
750.2.h.a.349.1		8	25.19	even	10	inner
750.2.h.a.349.2		8	25.6	even	5	inner
750.2.h.a.649.1		8	1.1	even	1	trivial
750.2.h.a.649.2		8	5.4	even	2	inner
3750.2.a.b.1.1		2	25.13	odd	20
3750.2.a.g.1.1		2	25.12	odd	20
3750.2.c.c.1249.1		4	25.16	even	5
3750.2.c.c.1249.3		4	25.9	even	10

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more