LMFDB - Embedded newform 750.2.g.b.601.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [750,2,Mod(151,750)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("750.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(750, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [4,1,-1,-1,0,1,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	750.601
Dual form			750.2.g.b.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.809017 - 0.587785i) q^{6} -0.381966 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.427051 - 1.31433i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-0.763932 - 2.35114i) q^{13} +(0.118034 - 0.363271i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.61803 + 1.90211i) q^{17} -1.00000 q^{18} +(-6.23607 + 4.53077i) q^{19} +(0.309017 + 0.224514i) q^{21} +(1.11803 + 0.812299i) q^{22} +(1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +2.47214 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 + 0.224514i) q^{28} +(0.381966 + 0.277515i) q^{29} +(-3.54508 + 2.57565i) q^{31} -1.00000 q^{32} +(-1.11803 + 0.812299i) q^{33} +(-1.00000 - 3.07768i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(-2.38197 - 7.33094i) q^{38} +(-0.763932 + 2.35114i) q^{39} +(-2.38197 - 7.33094i) q^{41} +(-0.309017 + 0.224514i) q^{42} -5.70820 q^{43} +(-1.11803 + 0.812299i) q^{44} +(3.61803 + 2.62866i) q^{46} +(-9.47214 - 6.88191i) q^{47} +(0.309017 - 0.951057i) q^{48} -6.85410 q^{49} +3.23607 q^{51} +(-0.763932 + 2.35114i) q^{52} +(7.35410 + 5.34307i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.309017 + 0.224514i) q^{56} +7.70820 q^{57} +(-0.381966 + 0.277515i) q^{58} +(-0.427051 - 1.31433i) q^{59} +(2.23607 - 6.88191i) q^{61} +(-1.35410 - 4.16750i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.427051 - 1.31433i) q^{66} +(-8.47214 + 6.15537i) q^{67} +3.23607 q^{68} +(-3.61803 + 2.62866i) q^{69} +(-11.7082 - 8.50651i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-3.85410 + 11.8617i) q^{73} +8.00000 q^{74} +7.70820 q^{76} +(-0.163119 + 0.502029i) q^{77} +(-2.00000 - 1.45309i) q^{78} +(2.73607 + 1.98787i) q^{79} +(-0.809017 + 0.587785i) q^{81} +7.70820 q^{82} +(7.16312 - 5.20431i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(1.76393 - 5.42882i) q^{86} +(-0.145898 - 0.449028i) q^{87} +(-0.427051 - 1.31433i) q^{88} +(3.85410 - 11.8617i) q^{89} +(0.291796 + 0.898056i) q^{91} +(-3.61803 + 2.62866i) q^{92} +4.38197 q^{93} +(9.47214 - 6.88191i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-4.54508 - 3.30220i) q^{97} +(2.11803 - 6.51864i) q^{98} +1.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9} - 5 q^{11} - q^{12} - 12 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 4 q^{18} - 16 q^{19} - q^{21} + 10 q^{23} - 4 q^{24} - 8 q^{26} - q^{27}+ \cdots + 10 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9 - 5 * q^11 - q^12 - 12 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 4 * q^18 - 16 * q^19 - q^21 + 10 * q^23 - 4 * q^24 - 8 * q^26 - q^27 - q^28 + 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - q^36 + 8 * q^37 - 14 * q^38 - 12 * q^39 - 14 * q^41 + q^42 + 4 * q^43 + 10 * q^46 - 20 * q^47 - q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 + 16 * q^53 + q^54 + q^56 + 4 * q^57 - 6 * q^58 + 5 * q^59 + 8 * q^62 + 4 * q^63 - q^64 + 5 * q^66 - 16 * q^67 + 4 * q^68 - 10 * q^69 - 20 * q^71 + q^72 - 2 * q^73 + 32 * q^74 + 4 * q^76 + 15 * q^77 - 8 * q^78 + 2 * q^79 - q^81 + 4 * q^82 + 13 * q^83 + 4 * q^84 + 16 * q^86 - 14 * q^87 + 5 * q^88 + 2 * q^89 + 28 * q^91 - 10 * q^92 + 22 * q^93 + 20 * q^94 + q^96 - 7 * q^97 + 4 * q^98 + 10 * q^99

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$		0			0
$5$		0			0
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	−0.381966			−0.144370			−0.0721848	−	0.997391i	$-0.522997\pi$
$7$	−0.381966			−0.144370			−0.0721848	+	0.997391i	$0.522997\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	0.427051	−	1.31433i	0.128761	−	0.396285i	−0.865807	−	0.500378i	$-0.833194\pi$
$11$	0.427051	−	1.31433i	0.128761	−	0.396285i	0.994567	+	0.104094i	$0.0331942\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	−0.763932	−	2.35114i	−0.211877	−	0.652089i	−0.999361	−	0.0357541i	$-0.988617\pi$
$13$	−0.763932	−	2.35114i	−0.211877	−	0.652089i	0.787484	−	0.616335i	$-0.211383\pi$
$14$	0.118034	−	0.363271i	0.0315459	−	0.0970883i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.61803	+	1.90211i	−0.634967	+	0.461330i	−0.858117	−	0.513454i	$-0.828366\pi$
$17$	−2.61803	+	1.90211i	−0.634967	+	0.461330i	0.223151	+	0.974784i	$0.428366\pi$
$18$	−1.00000			−0.235702
$19$	−6.23607	+	4.53077i	−1.43065	+	1.03943i	−0.440757	+	0.897626i	$0.645290\pi$
$19$	−6.23607	+	4.53077i	−1.43065	+	1.03943i	−0.989895	+	0.141803i	$0.954710\pi$
$20$		0			0
$21$	0.309017	+	0.224514i	0.0674330	+	0.0489930i
$22$	1.11803	+	0.812299i	0.238366	+	0.173183i
$23$	1.38197	−	4.25325i	0.288160	−	0.886865i	−0.697274	−	0.716805i	$-0.745604\pi$
$23$	1.38197	−	4.25325i	0.288160	−	0.886865i	0.985434	−	0.170060i	$-0.0543961\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	2.47214			0.484826
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	0.309017	+	0.224514i	0.0583987	+	0.0424292i
$29$	0.381966	+	0.277515i	0.0709293	+	0.0515332i	0.622685	−	0.782473i	$-0.286042\pi$
$29$	0.381966	+	0.277515i	0.0709293	+	0.0515332i	−0.551756	+	0.834006i	$0.686042\pi$
$30$		0			0
$31$	−3.54508	+	2.57565i	−0.636716	+	0.462601i	−0.858720	−	0.512444i	$-0.828740\pi$
$31$	−3.54508	+	2.57565i	−0.636716	+	0.462601i	0.222004	+	0.975046i	$0.428740\pi$
$32$	−1.00000			−0.176777
$33$	−1.11803	+	0.812299i	−0.194625	+	0.141403i
$34$	−1.00000	−	3.07768i	−0.171499	−	0.527818i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	−0.919707	−	0.392607i	$-0.871573\pi$
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	0.513290	−	0.858215i	$-0.328427\pi$
$38$	−2.38197	−	7.33094i	−0.386406	−	1.18924i
$39$	−0.763932	+	2.35114i	−0.122327	+	0.376484i
$40$		0			0
$41$	−2.38197	−	7.33094i	−0.372001	−	1.14490i	−0.945480	−	0.325680i	$-0.894407\pi$
$41$	−2.38197	−	7.33094i	−0.372001	−	1.14490i	0.573479	−	0.819220i	$-0.305593\pi$
$42$	−0.309017	+	0.224514i	−0.0476824	+	0.0346433i
$43$	−5.70820			−0.870493			−0.435246	−	0.900311i	$-0.643339\pi$
$43$	−5.70820			−0.870493			−0.435246	+	0.900311i	$0.643339\pi$
$44$	−1.11803	+	0.812299i	−0.168550	+	0.122459i
$45$		0			0
$46$	3.61803	+	2.62866i	0.533450	+	0.387574i
$47$	−9.47214	−	6.88191i	−1.38165	−	1.00383i	−0.996724	−	0.0808837i	$-0.974226\pi$
$47$	−9.47214	−	6.88191i	−1.38165	−	1.00383i	−0.384929	−	0.922946i	$-0.625774\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−6.85410			−0.979157
$50$		0			0
$51$	3.23607			0.453140
$52$	−0.763932	+	2.35114i	−0.105938	+	0.326045i
$53$	7.35410	+	5.34307i	1.01016	+	0.733927i	0.964243	−	0.265018i	$-0.0853780\pi$
$53$	7.35410	+	5.34307i	1.01016	+	0.733927i	0.0459202	+	0.998945i	$0.485378\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$		0			0
$56$	−0.309017	+	0.224514i	−0.0412941	+	0.0300019i
$57$	7.70820			1.02098
$58$	−0.381966	+	0.277515i	−0.0501546	+	0.0364394i
$59$	−0.427051	−	1.31433i	−0.0555973	−	0.171111i	0.919402	−	0.393320i	$-0.128673\pi$
$59$	−0.427051	−	1.31433i	−0.0555973	−	0.171111i	−0.974999	+	0.222209i	$0.928673\pi$
$60$		0			0
$61$	2.23607	−	6.88191i	0.286299	−	0.881138i	−0.699707	−	0.714430i	$-0.746686\pi$
$61$	2.23607	−	6.88191i	0.286299	−	0.881138i	0.986006	−	0.166708i	$-0.0533138\pi$
$62$	−1.35410	−	4.16750i	−0.171971	−	0.529273i
$63$	−0.118034	−	0.363271i	−0.0148709	−	0.0457679i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$	−0.427051	−	1.31433i	−0.0525663	−	0.161783i
$67$	−8.47214	+	6.15537i	−1.03504	+	0.751998i	−0.969310	−	0.245840i	$-0.920936\pi$
$67$	−8.47214	+	6.15537i	−1.03504	+	0.751998i	−0.0657257	+	0.997838i	$0.520936\pi$
$68$	3.23607			0.392431
$69$	−3.61803	+	2.62866i	−0.435560	+	0.316453i
$70$		0			0
$71$	−11.7082	−	8.50651i	−1.38951	−	1.00954i	−0.995919	−	0.0902503i	$-0.971233\pi$
$71$	−11.7082	−	8.50651i	−1.38951	−	1.00954i	−0.393589	−	0.919286i	$-0.628767\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	−3.85410	+	11.8617i	−0.451089	+	1.38831i	0.424578	+	0.905391i	$0.360422\pi$
$73$	−3.85410	+	11.8617i	−0.451089	+	1.38831i	−0.875667	+	0.482916i	$0.839578\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	7.70820			0.884192
$77$	−0.163119	+	0.502029i	−0.0185891	+	0.0572115i
$78$	−2.00000	−	1.45309i	−0.226455	−	0.164529i
$79$	2.73607	+	1.98787i	0.307832	+	0.223653i	0.730966	−	0.682414i	$-0.239070\pi$
$79$	2.73607	+	1.98787i	0.307832	+	0.223653i	−0.423134	+	0.906067i	$0.639070\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	7.70820			0.851229
$83$	7.16312	−	5.20431i	0.786254	−	0.571247i	−0.120595	−	0.992702i	$-0.538480\pi$
$83$	7.16312	−	5.20431i	0.786254	−	0.571247i	0.906850	+	0.421454i	$0.138480\pi$
$84$	−0.118034	−	0.363271i	−0.0128786	−	0.0396361i
$85$		0			0
$86$	1.76393	−	5.42882i	0.190210	−	0.585405i
$87$	−0.145898	−	0.449028i	−0.0156419	−	0.0481409i
$88$	−0.427051	−	1.31433i	−0.0455238	−	0.140108i
$89$	3.85410	−	11.8617i	0.408534	−	1.25734i	−0.509374	−	0.860545i	$-0.670123\pi$
$89$	3.85410	−	11.8617i	0.408534	−	1.25734i	0.917908	−	0.396793i	$-0.129877\pi$
$90$		0			0
$91$	0.291796	+	0.898056i	0.0305885	+	0.0941418i
$92$	−3.61803	+	2.62866i	−0.377206	+	0.274056i
$93$	4.38197			0.454389
$94$	9.47214	−	6.88191i	0.976976	−	0.709815i
$95$		0			0
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−4.54508	−	3.30220i	−0.461483	−	0.335287i	0.332629	−	0.943058i	$-0.392064\pi$
$97$	−4.54508	−	3.30220i	−0.461483	−	0.335287i	−0.794113	+	0.607770i	$0.792064\pi$
$98$	2.11803	−	6.51864i	0.213954	−	0.658482i
$99$	1.38197			0.138893
$100$		0			0
$101$	6.61803			0.658519			0.329259	−	0.944239i	$-0.393201\pi$
$101$	6.61803			0.658519			0.329259	+	0.944239i	$0.393201\pi$
$102$	−1.00000	+	3.07768i	−0.0990148	+	0.304736i
$103$	−1.07295	−	0.779543i	−0.105721	−	0.0768107i	0.533669	−	0.845694i	$-0.320813\pi$
$103$	−1.07295	−	0.779543i	−0.105721	−	0.0768107i	−0.639390	+	0.768883i	$0.720813\pi$
$104$	−2.00000	−	1.45309i	−0.196116	−	0.142487i
$105$		0			0
$106$	−7.35410	+	5.34307i	−0.714294	+	0.518965i
$107$	9.38197			0.906989			0.453494	−	0.891259i	$-0.350177\pi$
$107$	9.38197			0.906989			0.453494	+	0.891259i	$0.350177\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	3.94427	+	12.1392i	0.377793	+	1.16273i	0.941575	+	0.336803i	$0.109346\pi$
$109$	3.94427	+	12.1392i	0.377793	+	1.16273i	−0.563782	+	0.825923i	$0.690654\pi$
$110$		0			0
$111$	−2.47214	+	7.60845i	−0.234645	+	0.722162i
$112$	−0.118034	−	0.363271i	−0.0111532	−	0.0343259i
$113$	4.56231	+	14.0413i	0.429186	+	1.32090i	0.898929	+	0.438095i	$0.144346\pi$
$113$	4.56231	+	14.0413i	0.429186	+	1.32090i	−0.469743	+	0.882803i	$0.655654\pi$
$114$	−2.38197	+	7.33094i	−0.223092	+	0.686605i
$115$		0			0
$116$	−0.145898	−	0.449028i	−0.0135463	−	0.0416912i
$117$	2.00000	−	1.45309i	0.184900	−	0.134338i
$118$	1.38197			0.127220
$119$	1.00000	−	0.726543i	0.0916698	−	0.0666020i
$120$		0			0
$121$	7.35410	+	5.34307i	0.668555	+	0.485733i
$122$	5.85410	+	4.25325i	0.530005	+	0.385072i
$123$	−2.38197	+	7.33094i	−0.214775	+	0.661008i
$124$	4.38197			0.393512
$125$		0			0
$126$	0.381966			0.0340282
$127$	−3.51722	+	10.8249i	−0.312103	+	0.960554i	0.664828	+	0.746997i	$0.268505\pi$
$127$	−3.51722	+	10.8249i	−0.312103	+	0.960554i	−0.976931	+	0.213557i	$0.931495\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	4.61803	+	3.35520i	0.406595	+	0.295409i
$130$		0			0
$131$	−14.4721	+	10.5146i	−1.26444	+	0.918667i	−0.998967	−	0.0454523i	$-0.985527\pi$
$131$	−14.4721	+	10.5146i	−1.26444	+	0.918667i	−0.265470	+	0.964119i	$0.585527\pi$
$132$	1.38197			0.120285
$133$	2.38197	−	1.73060i	0.206543	−	0.150062i
$134$	−3.23607	−	9.95959i	−0.279554	−	0.860378i
$135$		0			0
$136$	−1.00000	+	3.07768i	−0.0857493	+	0.263909i
$137$	−3.14590	−	9.68208i	−0.268772	−	0.827196i	−0.990800	−	0.135332i	$-0.956790\pi$
$137$	−3.14590	−	9.68208i	−0.268772	−	0.827196i	0.722028	−	0.691864i	$-0.243210\pi$
$138$	−1.38197	−	4.25325i	−0.117641	−	0.362061i
$139$	0.472136	−	1.45309i	0.0400460	−	0.123249i	−0.929035	−	0.369992i	$-0.879360\pi$
$139$	0.472136	−	1.45309i	0.0400460	−	0.123249i	0.969081	+	0.246743i	$0.0793604\pi$
$140$		0			0
$141$	3.61803	+	11.1352i	0.304693	+	0.937750i
$142$	11.7082	−	8.50651i	0.982531	−	0.713850i
$143$	−3.41641			−0.285694
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$		0			0
$146$	−10.0902	−	7.33094i	−0.835068	−	0.606713i
$147$	5.54508	+	4.02874i	0.457351	+	0.332285i
$148$	−2.47214	+	7.60845i	−0.203208	+	0.625411i
$149$	10.9098			0.893768			0.446884	−	0.894592i	$-0.352534\pi$
$149$	10.9098			0.893768			0.446884	+	0.894592i	$0.352534\pi$
$150$		0			0
$151$	2.67376			0.217588			0.108794	−	0.994064i	$-0.465301\pi$
$151$	2.67376			0.217588			0.108794	+	0.994064i	$0.465301\pi$
$152$	−2.38197	+	7.33094i	−0.193203	+	0.594618i
$153$	−2.61803	−	1.90211i	−0.211656	−	0.153777i
$154$	−0.427051	−	0.310271i	−0.0344127	−	0.0250023i
$155$		0			0
$156$	2.00000	−	1.45309i	0.160128	−	0.116340i
$157$	22.6525			1.80786			0.903932	−	0.427676i	$-0.140668\pi$
$157$	22.6525			1.80786			0.903932	+	0.427676i	$0.140668\pi$
$158$	−2.73607	+	1.98787i	−0.217670	+	0.158146i
$159$	−2.80902	−	8.64527i	−0.222770	−	0.685614i
$160$		0			0
$161$	−0.527864	+	1.62460i	−0.0416015	+	0.128036i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−2.61803	−	8.05748i	−0.205060	−	0.631111i	−0.999711	−	0.0240436i	$-0.992346\pi$
$163$	−2.61803	−	8.05748i	−0.205060	−	0.631111i	0.794651	−	0.607067i	$-0.207654\pi$
$164$	−2.38197	+	7.33094i	−0.186000	+	0.572450i
$165$		0			0
$166$	2.73607	+	8.42075i	0.212360	+	0.653577i
$167$	−1.38197	+	1.00406i	−0.106940	+	0.0776963i	−0.639970	−	0.768400i	$-0.721053\pi$
$167$	−1.38197	+	1.00406i	−0.106940	+	0.0776963i	0.533030	+	0.846096i	$0.321053\pi$
$168$	0.381966			0.0294693
$169$	5.57295	−	4.04898i	0.428688	−	0.311460i
$170$		0			0
$171$	−6.23607	−	4.53077i	−0.476884	−	0.346477i
$172$	4.61803	+	3.35520i	0.352122	+	0.255831i
$173$	1.88197	−	5.79210i	0.143083	−	0.440365i	−0.853676	−	0.520804i	$-0.825632\pi$
$173$	1.88197	−	5.79210i	0.143083	−	0.440365i	0.996760	+	0.0804391i	$0.0256322\pi$
$174$	0.472136			0.0357925
$175$		0			0
$176$	1.38197			0.104170
$177$	−0.427051	+	1.31433i	−0.0320991	+	0.0987909i
$178$	10.0902	+	7.33094i	0.756290	+	0.549477i
$179$	−2.54508	−	1.84911i	−0.190229	−	0.138209i	0.488595	−	0.872511i	$-0.337510\pi$
$179$	−2.54508	−	1.84911i	−0.190229	−	0.138209i	−0.678823	+	0.734302i	$0.737510\pi$
$180$		0			0
$181$	−19.9443	+	14.4904i	−1.48245	+	1.07706i	−0.505688	+	0.862717i	$0.668761\pi$
$181$	−19.9443	+	14.4904i	−1.48245	+	1.07706i	−0.976758	+	0.214344i	$0.931239\pi$
$182$	−0.944272			−0.0699941
$183$	−5.85410	+	4.25325i	−0.432748	+	0.314410i
$184$	−1.38197	−	4.25325i	−0.101880	−	0.313554i
$185$		0			0
$186$	−1.35410	+	4.16750i	−0.0992876	+	0.305576i
$187$	1.38197	+	4.25325i	0.101059	+	0.311029i
$188$	3.61803	+	11.1352i	0.263872	+	0.812115i
$189$	−0.118034	+	0.363271i	−0.00858571	+	0.0264241i
$190$		0			0
$191$	5.47214	+	16.8415i	0.395950	+	1.21861i	0.928219	+	0.372033i	$0.121339\pi$
$191$	5.47214	+	16.8415i	0.395950	+	1.21861i	−0.532269	+	0.846575i	$0.678661\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	−11.1459			−0.802299			−0.401150	−	0.916013i	$-0.631389\pi$
$193$	−11.1459			−0.802299			−0.401150	+	0.916013i	$0.631389\pi$
$194$	4.54508	−	3.30220i	0.326318	−	0.237084i
$195$		0			0
$196$	5.54508	+	4.02874i	0.396077	+	0.287767i
$197$	−4.78115	−	3.47371i	−0.340643	−	0.247492i	0.404290	−	0.914631i	$-0.367519\pi$
$197$	−4.78115	−	3.47371i	−0.340643	−	0.247492i	−0.744933	+	0.667139i	$0.767519\pi$
$198$	−0.427051	+	1.31433i	−0.0303492	+	0.0934052i
$199$	−18.5066			−1.31190			−0.655948	−	0.754806i	$-0.727731\pi$
$199$	−18.5066			−1.31190			−0.655948	+	0.754806i	$0.727731\pi$
$200$		0			0
$201$	10.4721			0.738648
$202$	−2.04508	+	6.29412i	−0.143892	+	0.442853i
$203$	−0.145898	−	0.106001i	−0.0102400	−	0.00743982i
$204$	−2.61803	−	1.90211i	−0.183299	−	0.133175i
$205$		0			0
$206$	1.07295	−	0.779543i	0.0747559	−	0.0543133i
$207$	4.47214			0.310835
$208$	2.00000	−	1.45309i	0.138675	−	0.100753i
$209$	3.29180	+	10.1311i	0.227698	+	0.700783i
$210$		0			0
$211$	7.23607	−	22.2703i	0.498151	−	1.53315i	−0.313836	−	0.949477i	$-0.601614\pi$
$211$	7.23607	−	22.2703i	0.498151	−	1.53315i	0.811987	−	0.583675i	$-0.198386\pi$
$212$	−2.80902	−	8.64527i	−0.192924	−	0.593759i
$213$	4.47214	+	13.7638i	0.306426	+	0.943081i
$214$	−2.89919	+	8.92278i	−0.198184	+	0.609949i
$215$		0			0
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	1.35410	−	0.983813i	0.0919224	−	0.0667856i
$218$	−12.7639			−0.864483
$219$	10.0902	−	7.33094i	0.681830	−	0.495379i
$220$		0			0
$221$	6.47214	+	4.70228i	0.435363	+	0.316310i
$222$	−6.47214	−	4.70228i	−0.434381	−	0.315597i
$223$	−0.954915	+	2.93893i	−0.0639458	+	0.196805i	−0.977925	−	0.208956i	$-0.932993\pi$
$223$	−0.954915	+	2.93893i	−0.0639458	+	0.196805i	0.913979	+	0.405761i	$0.132993\pi$
$224$	0.381966			0.0255212
$225$		0			0
$226$	−14.7639			−0.982082
$227$	−3.48278	+	10.7189i	−0.231160	+	0.711438i	0.766447	+	0.642307i	$0.222023\pi$
$227$	−3.48278	+	10.7189i	−0.231160	+	0.711438i	−0.997608	+	0.0691308i	$0.977977\pi$
$228$	−6.23607	−	4.53077i	−0.412994	−	0.300057i
$229$	11.7082	+	8.50651i	0.773700	+	0.562126i	0.903082	−	0.429469i	$-0.141299\pi$
$229$	11.7082	+	8.50651i	0.773700	+	0.562126i	−0.129382	+	0.991595i	$0.541299\pi$
$230$		0			0
$231$	0.427051	−	0.310271i	0.0280979	−	0.0204143i
$232$	0.472136			0.0309972
$233$	−10.2361	+	7.43694i	−0.670587	+	0.487210i	−0.870222	−	0.492660i	$-0.836024\pi$
$233$	−10.2361	+	7.43694i	−0.670587	+	0.487210i	0.199635	+	0.979870i	$0.436024\pi$
$234$	0.763932	+	2.35114i	0.0499398	+	0.153699i
$235$		0			0
$236$	−0.427051	+	1.31433i	−0.0277987	+	0.0855555i
$237$	−1.04508	−	3.21644i	−0.0678856	−	0.208930i
$238$	0.381966	+	1.17557i	0.0247592	+	0.0762009i
$239$	7.94427	−	24.4500i	0.513872	−	1.58154i	−0.271452	−	0.962452i	$-0.587504\pi$
$239$	7.94427	−	24.4500i	0.513872	−	1.58154i	0.785325	−	0.619084i	$-0.212496\pi$
$240$		0			0
$241$	−3.26393	−	10.0453i	−0.210248	−	0.647078i	−0.999457	−	0.0329526i	$-0.989509\pi$
$241$	−3.26393	−	10.0453i	−0.210248	−	0.647078i	0.789209	−	0.614125i	$-0.210491\pi$
$242$	−7.35410	+	5.34307i	−0.472740	+	0.343465i
$243$	1.00000			0.0641500
$244$	−5.85410	+	4.25325i	−0.374770	+	0.272287i
$245$		0			0
$246$	−6.23607	−	4.53077i	−0.397597	−	0.288871i
$247$	15.4164	+	11.2007i	0.980923	+	0.712682i
$248$	−1.35410	+	4.16750i	−0.0859856	+	0.264636i
$249$	−8.85410			−0.561106
$250$		0			0
$251$	−6.56231			−0.414209			−0.207105	−	0.978319i	$-0.566404\pi$
$251$	−6.56231			−0.414209			−0.207105	+	0.978319i	$0.566404\pi$
$252$	−0.118034	+	0.363271i	−0.00743544	+	0.0228839i
$253$	−5.00000	−	3.63271i	−0.314347	−	0.228387i
$254$	−9.20820	−	6.69015i	−0.577774	−	0.419777i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$	−4.61803	+	3.35520i	−0.287506	+	0.208886i
$259$	0.944272	+	2.90617i	0.0586742	+	0.180581i
$260$		0			0
$261$	−0.145898	+	0.449028i	−0.00903086	+	0.0277941i
$262$	−5.52786	−	17.0130i	−0.341513	−	1.05107i
$263$	−0.527864	−	1.62460i	−0.0325495	−	0.100177i	0.933462	−	0.358677i	$-0.116772\pi$
$263$	−0.527864	−	1.62460i	−0.0325495	−	0.100177i	−0.966011	+	0.258500i	$0.916772\pi$
$264$	−0.427051	+	1.31433i	−0.0262832	+	0.0808913i
$265$		0			0
$266$	0.909830	+	2.80017i	0.0557853	+	0.171689i
$267$	−10.0902	+	7.33094i	−0.617508	+	0.448646i
$268$	10.4721			0.639688
$269$	−1.69098	+	1.22857i	−0.103101	+	0.0749073i	−0.638141	−	0.769919i	$-0.720296\pi$
$269$	−1.69098	+	1.22857i	−0.103101	+	0.0749073i	0.535040	+	0.844827i	$0.320296\pi$
$270$		0			0
$271$	−8.92705	−	6.48588i	−0.542280	−	0.393989i	0.282651	−	0.959223i	$-0.408786\pi$
$271$	−8.92705	−	6.48588i	−0.542280	−	0.393989i	−0.824931	+	0.565233i	$0.808786\pi$
$272$	−2.61803	−	1.90211i	−0.158742	−	0.115333i
$273$	0.291796	−	0.898056i	0.0176603	−	0.0543528i
$274$	10.1803			0.615017
$275$		0			0
$276$	4.47214			0.269191
$277$	0.291796	−	0.898056i	0.0175323	−	0.0539590i	−0.941908	−	0.335872i	$-0.890969\pi$
$277$	0.291796	−	0.898056i	0.0175323	−	0.0539590i	0.959440	+	0.281913i	$0.0909690\pi$
$278$	1.23607	+	0.898056i	0.0741344	+	0.0538618i
$279$	−3.54508	−	2.57565i	−0.212239	−	0.154200i
$280$		0			0
$281$	24.1803	−	17.5680i	1.44248	−	1.04802i	0.454961	−	0.890511i	$-0.349653\pi$
$281$	24.1803	−	17.5680i	1.44248	−	1.04802i	0.987517	−	0.157510i	$-0.0503467\pi$
$282$	−11.7082			−0.697213
$283$	25.4164	−	18.4661i	1.51085	−	1.09770i	0.545050	−	0.838404i	$-0.316511\pi$
$283$	25.4164	−	18.4661i	1.51085	−	1.09770i	0.965799	−	0.259292i	$-0.0834892\pi$
$284$	4.47214	+	13.7638i	0.265372	+	0.816732i
$285$		0			0
$286$	1.05573	−	3.24920i	0.0624265	−	0.192129i
$287$	0.909830	+	2.80017i	0.0537056	+	0.165289i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−2.01722	+	6.20837i	−0.118660	+	0.365198i
$290$		0			0
$291$	1.73607	+	5.34307i	0.101770	+	0.313216i
$292$	10.0902	−	7.33094i	0.590483	−	0.429011i
$293$	10.9098			0.637359			0.318680	−	0.947863i	$-0.396761\pi$
$293$	10.9098			0.637359			0.318680	+	0.947863i	$0.396761\pi$
$294$	−5.54508	+	4.02874i	−0.323396	+	0.234961i
$295$		0			0
$296$	−6.47214	−	4.70228i	−0.376185	−	0.273315i
$297$	−1.11803	−	0.812299i	−0.0648749	−	0.0471344i
$298$	−3.37132	+	10.3759i	−0.195295	+	0.601058i
$299$	−11.0557			−0.639369
$300$		0			0
$301$	2.18034			0.125673
$302$	−0.826238	+	2.54290i	−0.0475446	+	0.146327i
$303$	−5.35410	−	3.88998i	−0.307585	−	0.223474i
$304$	−6.23607	−	4.53077i	−0.357663	−	0.259857i
$305$		0			0
$306$	2.61803	−	1.90211i	0.149663	−	0.108737i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$	0.427051	−	0.310271i	0.0243335	−	0.0176793i
$309$	0.409830	+	1.26133i	0.0233144	+	0.0717544i
$310$		0			0
$311$	−5.85410	+	18.0171i	−0.331956	+	1.02165i	0.636247	+	0.771486i	$0.280486\pi$
$311$	−5.85410	+	18.0171i	−0.331956	+	1.02165i	−0.968202	+	0.250169i	$0.919514\pi$
$312$	0.763932	+	2.35114i	0.0432491	+	0.133107i
$313$	−5.33688	−	16.4252i	−0.301658	−	0.928409i	−0.980903	−	0.194497i	$-0.937693\pi$
$313$	−5.33688	−	16.4252i	−0.301658	−	0.928409i	0.679245	−	0.733912i	$-0.262307\pi$
$314$	−7.00000	+	21.5438i	−0.395033	+	1.21579i
$315$		0			0
$316$	−1.04508	−	3.21644i	−0.0587906	−	0.180939i
$317$	−0.354102	+	0.257270i	−0.0198883	+	0.0144497i	−0.597685	−	0.801731i	$-0.703913\pi$
$317$	−0.354102	+	0.257270i	−0.0198883	+	0.0144497i	0.577797	+	0.816181i	$0.303913\pi$
$318$	9.09017			0.509751
$319$	0.527864	−	0.383516i	0.0295547	−	0.0214728i
$320$		0			0
$321$	−7.59017	−	5.51458i	−0.423642	−	0.307794i
$322$	−1.38197	−	1.00406i	−0.0770140	−	0.0559539i
$323$	7.70820	−	23.7234i	0.428896	−	1.32001i
$324$	1.00000			0.0555556
$325$		0			0
$326$	8.47214			0.469228
$327$	3.94427	−	12.1392i	0.218119	−	0.671300i
$328$	−6.23607	−	4.53077i	−0.344329	−	0.250170i
$329$	3.61803	+	2.62866i	0.199469	+	0.144922i
$330$		0			0
$331$	14.5623	−	10.5801i	0.800417	−	0.581537i	−0.110620	−	0.993863i	$-0.535284\pi$
$331$	14.5623	−	10.5801i	0.800417	−	0.581537i	0.911036	+	0.412326i	$0.135284\pi$
$332$	−8.85410			−0.485932
$333$	6.47214	−	4.70228i	0.354671	−	0.257683i
$334$	−0.527864	−	1.62460i	−0.0288834	−	0.0888941i
$335$		0			0
$336$	−0.118034	+	0.363271i	−0.00643928	+	0.0198181i
$337$	−3.73607	−	11.4984i	−0.203517	−	0.626360i	−0.999771	−	0.0213978i	$-0.993188\pi$
$337$	−3.73607	−	11.4984i	−0.203517	−	0.626360i	0.796254	−	0.604962i	$-0.206812\pi$
$338$	2.12868	+	6.55139i	0.115785	+	0.356349i
$339$	4.56231	−	14.0413i	0.247790	−	0.762621i
$340$		0			0
$341$	1.87132	+	5.75934i	0.101338	+	0.311886i
$342$	6.23607	−	4.53077i	0.337208	−	0.244996i
$343$	5.29180			0.285730
$344$	−4.61803	+	3.35520i	−0.248988	+	0.180900i
$345$		0			0
$346$	4.92705	+	3.57971i	0.264880	+	0.192447i
$347$	0.354102	+	0.257270i	0.0190092	+	0.0138110i	0.597249	−	0.802056i	$-0.296260\pi$
$347$	0.354102	+	0.257270i	0.0190092	+	0.0138110i	−0.578240	+	0.815867i	$0.696260\pi$
$348$	−0.145898	+	0.449028i	−0.00782096	+	0.0240704i
$349$	7.88854			0.422264			0.211132	−	0.977458i	$-0.432285\pi$
$349$	7.88854			0.422264			0.211132	+	0.977458i	$0.432285\pi$
$350$		0			0
$351$	−2.47214			−0.131953
$352$	−0.427051	+	1.31433i	−0.0227619	+	0.0700539i
$353$	−7.09017	−	5.15131i	−0.377372	−	0.274177i	0.382889	−	0.923794i	$-0.374929\pi$
$353$	−7.09017	−	5.15131i	−0.377372	−	0.274177i	−0.760261	+	0.649618i	$0.774929\pi$
$354$	−1.11803	−	0.812299i	−0.0594228	−	0.0431732i
$355$		0			0
$356$	−10.0902	+	7.33094i	−0.534778	+	0.388539i
$357$	−1.23607			−0.0654197
$358$	2.54508	−	1.84911i	0.134512	−	0.0977286i
$359$	−0.0557281	−	0.171513i	−0.00294122	−	0.00905213i	0.949575	−	0.313540i	$-0.101515\pi$
$359$	−0.0557281	−	0.171513i	−0.00294122	−	0.00905213i	−0.952516	+	0.304487i	$0.901515\pi$
$360$		0			0
$361$	12.4894	−	38.4383i	0.657335	−	2.02307i
$362$	−7.61803	−	23.4459i	−0.400395	−	1.23229i
$363$	−2.80902	−	8.64527i	−0.147435	−	0.453759i
$364$	0.291796	−	0.898056i	0.0152943	−	0.0470709i
$365$		0			0
$366$	−2.23607	−	6.88191i	−0.116881	−	0.359723i
$367$	−22.9615	+	16.6825i	−1.19858	+	0.870819i	−0.994144	−	0.108060i	$-0.965536\pi$
$367$	−22.9615	+	16.6825i	−1.19858	+	0.870819i	−0.204436	+	0.978880i	$0.565536\pi$
$368$	4.47214			0.233126
$369$	6.23607	−	4.53077i	0.324637	−	0.235862i
$370$		0			0
$371$	−2.80902	−	2.04087i	−0.145837	−	0.105957i
$372$	−3.54508	−	2.57565i	−0.183804	−	0.133541i
$373$	6.32624	−	19.4702i	0.327560	−	1.00813i	−0.642712	−	0.766108i	$-0.722191\pi$
$373$	6.32624	−	19.4702i	0.327560	−	1.00813i	0.970272	−	0.242018i	$-0.0778094\pi$
$374$	−4.47214			−0.231249
$375$		0			0
$376$	−11.7082			−0.603805
$377$	0.360680	−	1.11006i	0.0185760	−	0.0571709i
$378$	−0.309017	−	0.224514i	−0.0158941	−	0.0115478i
$379$	−1.76393	−	1.28157i	−0.0906071	−	0.0658299i	0.541559	−	0.840662i	$-0.317834\pi$
$379$	−1.76393	−	1.28157i	−0.0906071	−	0.0658299i	−0.632166	+	0.774833i	$0.717834\pi$
$380$		0			0
$381$	9.20820	−	6.69015i	0.471751	−	0.342747i
$382$	−17.7082			−0.906031
$383$	−16.1803	+	11.7557i	−0.826777	+	0.600688i	−0.918646	−	0.395083i	$-0.870716\pi$
$383$	−16.1803	+	11.7557i	−0.826777	+	0.600688i	0.0918688	+	0.995771i	$0.470716\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$		0			0
$386$	3.44427	−	10.6004i	0.175309	−	0.539545i
$387$	−1.76393	−	5.42882i	−0.0896657	−	0.275963i
$388$	1.73607	+	5.34307i	0.0881355	+	0.271253i
$389$	−4.51722	+	13.9026i	−0.229032	+	0.704889i	0.768825	+	0.639459i	$0.220842\pi$
$389$	−4.51722	+	13.9026i	−0.229032	+	0.704889i	−0.997857	+	0.0654294i	$0.979158\pi$
$390$		0			0
$391$	4.47214	+	13.7638i	0.226166	+	0.696066i
$392$	−5.54508	+	4.02874i	−0.280069	+	0.203482i
$393$	17.8885			0.902358
$394$	4.78115	−	3.47371i	0.240871	−	0.175003i
$395$		0			0
$396$	−1.11803	−	0.812299i	−0.0561833	−	0.0408196i
$397$	−28.5066	−	20.7112i	−1.43070	−	1.03947i	−0.989885	−	0.141871i	$-0.954688\pi$
$397$	−28.5066	−	20.7112i	−1.43070	−	1.03947i	−0.440819	−	0.897596i	$-0.645312\pi$
$398$	5.71885	−	17.6008i	0.286660	−	0.882248i
$399$	−2.94427			−0.147398
$400$		0			0
$401$	12.2918			0.613823			0.306912	−	0.951738i	$-0.400704\pi$
$401$	12.2918			0.613823			0.306912	+	0.951738i	$0.400704\pi$
$402$	−3.23607	+	9.95959i	−0.161400	+	0.496739i
$403$	8.76393	+	6.36737i	0.436563	+	0.317181i
$404$	−5.35410	−	3.88998i	−0.266377	−	0.193534i
$405$		0			0
$406$	0.145898	−	0.106001i	0.00724080	−	0.00526075i
$407$	−11.0557			−0.548012
$408$	2.61803	−	1.90211i	0.129612	−	0.0941686i
$409$	−5.80902	−	17.8783i	−0.287237	−	0.884026i	−0.985719	−	0.168398i	$-0.946141\pi$
$409$	−5.80902	−	17.8783i	−0.287237	−	0.884026i	0.698482	−	0.715628i	$-0.253859\pi$
$410$		0			0
$411$	−3.14590	+	9.68208i	−0.155176	+	0.477582i
$412$	0.409830	+	1.26133i	0.0201909	+	0.0621411i
$413$	0.163119	+	0.502029i	0.00802656	+	0.0247032i
$414$	−1.38197	+	4.25325i	−0.0679199	+	0.209036i
$415$		0			0
$416$	0.763932	+	2.35114i	0.0374548	+	0.115274i
$417$	−1.23607	+	0.898056i	−0.0605305	+	0.0439780i
$418$	−10.6525			−0.521030
$419$	−6.54508	+	4.75528i	−0.319748	+	0.232311i	−0.736068	−	0.676908i	$-0.763320\pi$
$419$	−6.54508	+	4.75528i	−0.319748	+	0.232311i	0.416320	+	0.909218i	$0.363320\pi$
$420$		0			0
$421$	22.0344	+	16.0090i	1.07389	+	0.780229i	0.976608	−	0.215028i	$-0.0689842\pi$
$421$	22.0344	+	16.0090i	1.07389	+	0.780229i	0.0972850	+	0.995257i	$0.468984\pi$
$422$	18.9443	+	13.7638i	0.922193	+	0.670012i
$423$	3.61803	−	11.1352i	0.175915	−	0.541410i
$424$	9.09017			0.441458
$425$		0			0
$426$	−14.4721			−0.701177
$427$	−0.854102	+	2.62866i	−0.0413329	+	0.127210i
$428$	−7.59017	−	5.51458i	−0.366885	−	0.266557i
$429$	2.76393	+	2.00811i	0.133444	+	0.0969527i
$430$		0			0
$431$	29.7984	−	21.6498i	1.43534	−	1.04283i	0.446346	−	0.894861i	$-0.352725\pi$
$431$	29.7984	−	21.6498i	1.43534	−	1.04283i	0.988991	−	0.147973i	$-0.0472748\pi$
$432$	1.00000			0.0481125
$433$	−18.2082	+	13.2290i	−0.875030	+	0.635747i	−0.931932	−	0.362633i	$-0.881878\pi$
$433$	−18.2082	+	13.2290i	−0.875030	+	0.635747i	0.0569016	+	0.998380i	$0.481878\pi$
$434$	0.517221	+	1.59184i	0.0248274	+	0.0764109i
$435$		0			0
$436$	3.94427	−	12.1392i	0.188896	−	0.581363i
$437$	10.6525	+	32.7849i	0.509577	+	1.56832i
$438$	3.85410	+	11.8617i	0.184156	+	0.566774i
$439$	4.48278	−	13.7966i	0.213951	−	0.658475i	−0.785275	−	0.619147i	$-0.787478\pi$
$439$	4.48278	−	13.7966i	0.213951	−	0.658475i	0.999226	−	0.0393275i	$-0.0125216\pi$
$440$		0			0
$441$	−2.11803	−	6.51864i	−0.100859	−	0.310411i
$442$	−6.47214	+	4.70228i	−0.307848	+	0.223665i
$443$	−14.3820			−0.683308			−0.341654	−	0.939826i	$-0.610987\pi$
$443$	−14.3820			−0.683308			−0.341654	+	0.939826i	$0.610987\pi$
$444$	6.47214	−	4.70228i	0.307154	−	0.223160i
$445$		0			0
$446$	−2.50000	−	1.81636i	−0.118378	−	0.0860070i
$447$	−8.82624	−	6.41264i	−0.417467	−	0.303307i
$448$	−0.118034	+	0.363271i	−0.00557658	+	0.0171630i
$449$	−14.2918			−0.674472			−0.337236	−	0.941420i	$-0.609492\pi$
$449$	−14.2918			−0.674472			−0.337236	+	0.941420i	$0.609492\pi$
$450$		0			0
$451$	−10.6525			−0.501605
$452$	4.56231	−	14.0413i	0.214593	−	0.660449i
$453$	−2.16312	−	1.57160i	−0.101632	−	0.0738401i
$454$	−9.11803	−	6.62464i	−0.427931	−	0.310910i
$455$		0			0
$456$	6.23607	−	4.53077i	0.292031	−	0.212173i
$457$	−7.09017			−0.331664			−0.165832	−	0.986154i	$-0.553031\pi$
$457$	−7.09017			−0.331664			−0.165832	+	0.986154i	$0.553031\pi$
$458$	−11.7082	+	8.50651i	−0.547088	+	0.397483i
$459$	1.00000	+	3.07768i	0.0466760	+	0.143654i
$460$		0			0
$461$	−3.88197	+	11.9475i	−0.180801	+	0.556449i	−0.999851	−	0.0172739i	$-0.994501\pi$
$461$	−3.88197	+	11.9475i	−0.180801	+	0.556449i	0.819050	+	0.573723i	$0.194501\pi$
$462$	0.163119	+	0.502029i	0.00758898	+	0.0233565i
$463$	−9.52786	−	29.3238i	−0.442797	−	1.36279i	−0.884881	−	0.465817i	$-0.845761\pi$
$463$	−9.52786	−	29.3238i	−0.442797	−	1.36279i	0.442084	−	0.896974i	$-0.354239\pi$
$464$	−0.145898	+	0.449028i	−0.00677315	+	0.0208456i
$465$		0			0
$466$	−3.90983	−	12.0332i	−0.181119	−	0.557428i
$467$	21.2984	−	15.4742i	0.985571	−	0.716059i	0.0266244	−	0.999646i	$-0.491524\pi$
$467$	21.2984	−	15.4742i	0.985571	−	0.716059i	0.958947	+	0.283586i	$0.0915242\pi$
$468$	−2.47214			−0.114275
$469$	3.23607	−	2.35114i	0.149428	−	0.108566i
$470$		0			0
$471$	−18.3262	−	13.3148i	−0.844428	−	0.613513i
$472$	−1.11803	−	0.812299i	−0.0514617	−	0.0373891i
$473$	−2.43769	+	7.50245i	−0.112085	+	0.344963i
$474$	3.38197			0.155339
$475$		0			0
$476$	−1.23607			−0.0566551
$477$	−2.80902	+	8.64527i	−0.128616	+	0.395840i
$478$	20.7984	+	15.1109i	0.951295	+	0.691157i
$479$	−9.00000	−	6.53888i	−0.411220	−	0.298769i	0.362875	−	0.931838i	$-0.381795\pi$
$479$	−9.00000	−	6.53888i	−0.411220	−	0.298769i	−0.774096	+	0.633069i	$0.781795\pi$
$480$		0			0
$481$	−16.0000	+	11.6247i	−0.729537	+	0.530040i
$482$	10.5623			0.481100
$483$	1.38197	−	1.00406i	0.0628816	−	0.0456862i
$484$	−2.80902	−	8.64527i	−0.127683	−	0.392967i
$485$		0			0
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	2.10081	+	6.46564i	0.0951969	+	0.292986i	0.987305	−	0.158836i	$-0.0507742\pi$
$487$	2.10081	+	6.46564i	0.0951969	+	0.292986i	−0.892108	+	0.451822i	$0.850774\pi$
$488$	−2.23607	−	6.88191i	−0.101222	−	0.311529i
$489$	−2.61803	+	8.05748i	−0.118392	+	0.364372i
$490$		0			0
$491$	2.55573	+	7.86572i	0.115338	+	0.354975i	0.992017	−	0.126101i	$-0.0402462\pi$
$491$	2.55573	+	7.86572i	0.115338	+	0.354975i	−0.876679	+	0.481076i	$0.840246\pi$
$492$	6.23607	−	4.53077i	0.281144	−	0.204263i
$493$	−1.52786			−0.0688115
$494$	−15.4164	+	11.2007i	−0.693617	+	0.503942i
$495$		0			0
$496$	−3.54508	−	2.57565i	−0.159179	−	0.115650i
$497$	4.47214	+	3.24920i	0.200603	+	0.145746i
$498$	2.73607	−	8.42075i	0.122606	−	0.377343i
$499$	−13.5967			−0.608674			−0.304337	−	0.952564i	$-0.598435\pi$
$499$	−13.5967			−0.608674			−0.304337	+	0.952564i	$0.598435\pi$
$500$		0			0
$501$	1.70820			0.0763169
$502$	2.02786	−	6.24112i	0.0905080	−	0.278555i
$503$	−9.61803	−	6.98791i	−0.428847	−	0.311576i	0.352341	−	0.935872i	$-0.385386\pi$
$503$	−9.61803	−	6.98791i	−0.428847	−	0.311576i	−0.781188	+	0.624296i	$0.785386\pi$
$504$	−0.309017	−	0.224514i	−0.0137647	−	0.0100006i
$505$		0			0
$506$	5.00000	−	3.63271i	0.222277	−	0.161494i
$507$	−6.88854			−0.305931
$508$	9.20820	−	6.69015i	0.408548	−	0.296827i
$509$	6.33688	+	19.5029i	0.280877	+	0.864451i	0.987604	+	0.156965i	$0.0501710\pi$
$509$	6.33688	+	19.5029i	0.280877	+	0.864451i	−0.706727	+	0.707487i	$0.749829\pi$
$510$		0			0
$511$	1.47214	−	4.53077i	0.0651235	−	0.200429i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	2.38197	+	7.33094i	0.105166	+	0.323669i
$514$	−6.79837	+	20.9232i	−0.299863	+	0.922885i
$515$		0			0
$516$	−1.76393	−	5.42882i	−0.0776528	−	0.238991i
$517$	−13.0902	+	9.51057i	−0.575705	+	0.418274i
$518$	−3.05573			−0.134261
$519$	−4.92705	+	3.57971i	−0.216274	+	0.157132i
$520$		0			0
$521$	6.61803	+	4.80828i	0.289941	+	0.210655i	0.723242	−	0.690595i	$-0.242651\pi$
$521$	6.61803	+	4.80828i	0.289941	+	0.210655i	−0.433301	+	0.901249i	$0.642651\pi$
$522$	−0.381966	−	0.277515i	−0.0167182	−	0.0121465i
$523$	−8.94427	+	27.5276i	−0.391106	+	1.20370i	0.540847	+	0.841121i	$0.318104\pi$
$523$	−8.94427	+	27.5276i	−0.391106	+	1.20370i	−0.931953	+	0.362579i	$0.881896\pi$
$524$	17.8885			0.781465
$525$		0			0
$526$	1.70820			0.0744812
$527$	4.38197	−	13.4863i	0.190881	−	0.587473i
$528$	−1.11803	−	0.812299i	−0.0486562	−	0.0353508i
$529$	2.42705	+	1.76336i	0.105524	+	0.0766676i
$530$		0			0
$531$	1.11803	−	0.812299i	0.0485185	−	0.0352508i
$532$	−2.94427			−0.127650
$533$	−15.4164	+	11.2007i	−0.667759	+	0.485155i
$534$	−3.85410	−	11.8617i	−0.166783	−	0.513306i
$535$		0			0
$536$	−3.23607	+	9.95959i	−0.139777	+	0.430189i
$537$	0.972136	+	2.99193i	0.0419508	+	0.129111i
$538$	−0.645898	−	1.98787i	−0.0278466	−	0.0857032i
$539$	−2.92705	+	9.00854i	−0.126077	+	0.388025i
$540$		0			0
$541$	−1.18034	−	3.63271i	−0.0507468	−	0.156183i	0.922472	−	0.386065i	$-0.126166\pi$
$541$	−1.18034	−	3.63271i	−0.0507468	−	0.156183i	−0.973218	+	0.229882i	$0.926166\pi$
$542$	8.92705	−	6.48588i	0.383450	−	0.278592i
$543$	24.6525			1.05794
$544$	2.61803	−	1.90211i	0.112247	−	0.0815524i
$545$		0			0
$546$	0.763932	+	0.555029i	0.0326933	+	0.0237531i
$547$	−3.00000	−	2.17963i	−0.128271	−	0.0931941i	0.521800	−	0.853068i	$-0.325261\pi$
$547$	−3.00000	−	2.17963i	−0.128271	−	0.0931941i	−0.650071	+	0.759874i	$0.725261\pi$
$548$	−3.14590	+	9.68208i	−0.134386	+	0.413598i
$549$	7.23607			0.308828
$550$		0			0
$551$	−3.63932			−0.155040
$552$	−1.38197	+	4.25325i	−0.0588204	+	0.181031i
$553$	−1.04508	−	0.759299i	−0.0444415	−	0.0322887i
$554$	0.763932	+	0.555029i	0.0324564	+	0.0235809i
$555$		0			0
$556$	−1.23607	+	0.898056i	−0.0524210	+	0.0380861i
$557$	2.67376			0.113291			0.0566455	−	0.998394i	$-0.481960\pi$
$557$	2.67376			0.113291			0.0566455	+	0.998394i	$0.481960\pi$
$558$	3.54508	−	2.57565i	0.150075	−	0.109036i
$559$	4.36068	+	13.4208i	0.184437	+	0.567639i
$560$		0			0
$561$	1.38197	−	4.25325i	0.0583467	−	0.179573i
$562$	9.23607	+	28.4257i	0.389600	+	1.19907i
$563$	3.79180	+	11.6699i	0.159805	+	0.491830i	0.998616	−	0.0525933i	$-0.0167487\pi$
$563$	3.79180	+	11.6699i	0.159805	+	0.491830i	−0.838811	+	0.544423i	$0.816749\pi$
$564$	3.61803	−	11.1352i	0.152347	−	0.468875i
$565$		0			0
$566$	9.70820	+	29.8788i	0.408066	+	1.25590i
$567$	0.309017	−	0.224514i	0.0129775	−	0.00942870i
$568$	−14.4721			−0.607237
$569$	−35.4164	+	25.7315i	−1.48473	+	1.07872i	−0.508740	+	0.860920i	$0.669889\pi$
$569$	−35.4164	+	25.7315i	−1.48473	+	1.07872i	−0.975993	+	0.217801i	$0.930111\pi$
$570$		0			0
$571$	22.5623	+	16.3925i	0.944203	+	0.686004i	0.949429	−	0.313983i	$-0.101663\pi$
$571$	22.5623	+	16.3925i	0.944203	+	0.686004i	−0.00522561	+	0.999986i	$0.501663\pi$
$572$	2.76393	+	2.00811i	0.115566	+	0.0839635i
$573$	5.47214	−	16.8415i	0.228602	−	0.703564i
$574$	−2.94427			−0.122892
$575$		0			0
$576$	1.00000			0.0416667
$577$	11.7361	−	36.1199i	0.488579	−	1.50369i	−0.338151	−	0.941092i	$-0.609801\pi$
$577$	11.7361	−	36.1199i	0.488579	−	1.50369i	0.826730	−	0.562599i	$-0.190199\pi$
$578$	−5.28115	−	3.83698i	−0.219667	−	0.159597i
$579$	9.01722	+	6.55139i	0.374743	+	0.272267i
$580$		0			0
$581$	−2.73607	+	1.98787i	−0.113511	+	0.0824707i
$582$	−5.61803			−0.232875
$583$	10.1631	−	7.38394i	0.420913	−	0.305811i
$584$	3.85410	+	11.8617i	0.159484	+	0.490841i
$585$		0			0
$586$	−3.37132	+	10.3759i	−0.139268	+	0.428623i
$587$	9.28115	+	28.5645i	0.383074	+	1.17898i	0.937868	+	0.346993i	$0.112797\pi$
$587$	9.28115	+	28.5645i	0.383074	+	1.17898i	−0.554794	+	0.831988i	$0.687203\pi$
$588$	−2.11803	−	6.51864i	−0.0873462	−	0.268824i
$589$	10.4377	−	32.1239i	0.430078	−	1.32364i
$590$		0			0
$591$	1.82624	+	5.62058i	0.0751214	+	0.231200i
$592$	6.47214	−	4.70228i	0.266003	−	0.193263i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	1.11803	−	0.812299i	0.0458735	−	0.0333290i
$595$		0			0
$596$	−8.82624	−	6.41264i	−0.361537	−	0.262672i
$597$	14.9721	+	10.8779i	0.612769	+	0.445203i
$598$	3.41641	−	10.5146i	0.139707	−	0.429975i
$599$	−8.47214			−0.346162			−0.173081	−	0.984908i	$-0.555372\pi$
$599$	−8.47214			−0.346162			−0.173081	+	0.984908i	$0.555372\pi$
$600$		0			0
$601$	−41.2705			−1.68346			−0.841730	−	0.539899i	$-0.818462\pi$
$601$	−41.2705			−1.68346			−0.841730	+	0.539899i	$0.818462\pi$
$602$	−0.673762	+	2.07363i	−0.0274605	+	0.0845147i
$603$	−8.47214	−	6.15537i	−0.345012	−	0.250666i
$604$	−2.16312	−	1.57160i	−0.0880161	−	0.0639474i
$605$		0			0
$606$	5.35410	−	3.88998i	0.217496	−	0.158020i
$607$	13.5623			0.550477			0.275239	−	0.961376i	$-0.411243\pi$
$607$	13.5623			0.550477			0.275239	+	0.961376i	$0.411243\pi$
$608$	6.23607	−	4.53077i	0.252906	−	0.183747i
$609$	0.0557281	+	0.171513i	0.00225822	+	0.00695007i
$610$		0			0
$611$	−8.94427	+	27.5276i	−0.361847	+	1.11365i
$612$	1.00000	+	3.07768i	0.0404226	+	0.124408i
$613$	9.96556	+	30.6708i	0.402505	+	1.23878i	0.922961	+	0.384895i	$0.125762\pi$
$613$	9.96556	+	30.6708i	0.402505	+	1.23878i	−0.520455	+	0.853889i	$0.674238\pi$
$614$	3.09017	−	9.51057i	0.124709	−	0.383815i
$615$		0			0
$616$	0.163119	+	0.502029i	0.00657225	+	0.0202273i
$617$	30.6525	−	22.2703i	1.23402	−	0.896570i	0.236837	−	0.971549i	$-0.423889\pi$
$617$	30.6525	−	22.2703i	1.23402	−	0.896570i	0.997185	+	0.0749797i	$0.0238892\pi$
$618$	−1.32624			−0.0533491
$619$	−14.0902	+	10.2371i	−0.566332	+	0.411464i	−0.833771	−	0.552111i	$-0.813823\pi$
$619$	−14.0902	+	10.2371i	−0.566332	+	0.411464i	0.267439	+	0.963575i	$0.413823\pi$
$620$		0			0
$621$	−3.61803	−	2.62866i	−0.145187	−	0.105484i
$622$	−15.3262	−	11.1352i	−0.614526	−	0.446479i
$623$	−1.47214	+	4.53077i	−0.0589799	+	0.181521i
$624$	−2.47214			−0.0989646
$625$		0			0
$626$	17.2705			0.690268
$627$	3.29180	−	10.1311i	0.131462	−	0.404597i
$628$	−18.3262	−	13.3148i	−0.731297	−	0.531318i
$629$	20.9443	+	15.2169i	0.835103	+	0.606738i
$630$		0			0
$631$	−30.3607	+	22.0583i	−1.20864	+	0.878128i	−0.995107	−	0.0988078i	$-0.968497\pi$
$631$	−30.3607	+	22.0583i	−1.20864	+	0.878128i	−0.213533	+	0.976936i	$0.568497\pi$
$632$	3.38197			0.134527
$633$	−18.9443	+	13.7638i	−0.752967	+	0.547063i
$634$	−0.135255	−	0.416272i	−0.00537166	−	0.0165323i
$635$		0			0
$636$	−2.80902	+	8.64527i	−0.111385	+	0.342807i
$637$	5.23607	+	16.1150i	0.207461	+	0.638498i
$638$	0.201626	+	0.620541i	0.00798245	+	0.0245675i
$639$	4.47214	−	13.7638i	0.176915	−	0.544488i
$640$		0			0
$641$	−11.1803	−	34.4095i	−0.441597	−	1.35910i	−0.886173	−	0.463354i	$-0.846646\pi$
$641$	−11.1803	−	34.4095i	−0.441597	−	1.35910i	0.444576	−	0.895741i	$-0.353354\pi$
$642$	7.59017	−	5.51458i	0.299560	−	0.217643i
$643$	13.8885			0.547711			0.273855	−	0.961771i	$-0.411701\pi$
$643$	13.8885			0.547711			0.273855	+	0.961771i	$0.411701\pi$
$644$	1.38197	−	1.00406i	0.0544571	−	0.0395654i
$645$		0			0
$646$	20.1803	+	14.6619i	0.793985	+	0.576864i
$647$	−4.09017	−	2.97168i	−0.160801	−	0.116829i	0.504475	−	0.863426i	$-0.331686\pi$
$647$	−4.09017	−	2.97168i	−0.160801	−	0.116829i	−0.665276	+	0.746598i	$0.731686\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	−1.90983			−0.0749674
$650$		0			0
$651$	−1.67376			−0.0655999
$652$	−2.61803	+	8.05748i	−0.102530	+	0.315555i
$653$	2.30902	+	1.67760i	0.0903588	+	0.0656495i	0.632047	−	0.774930i	$-0.282215\pi$
$653$	2.30902	+	1.67760i	0.0903588	+	0.0656495i	−0.541689	+	0.840579i	$0.682215\pi$
$654$	10.3262	+	7.50245i	0.403788	+	0.293369i
$655$		0			0
$656$	6.23607	−	4.53077i	0.243478	−	0.176897i
$657$	−12.4721			−0.486584
$658$	−3.61803	+	2.62866i	−0.141046	+	0.102476i
$659$	−5.68034	−	17.4823i	−0.221275	−	0.681013i	−0.998648	−	0.0519743i	$-0.983449\pi$
$659$	−5.68034	−	17.4823i	−0.221275	−	0.681013i	0.777374	−	0.629039i	$-0.216551\pi$
$660$		0			0
$661$	−6.65248	+	20.4742i	−0.258751	+	0.796355i	0.734316	+	0.678808i	$0.237503\pi$
$661$	−6.65248	+	20.4742i	−0.258751	+	0.796355i	−0.993067	+	0.117547i	$0.962497\pi$
$662$	5.56231	+	17.1190i	0.216185	+	0.665350i
$663$	−2.47214	−	7.60845i	−0.0960098	−	0.295488i
$664$	2.73607	−	8.42075i	0.106180	−	0.326789i
$665$		0			0
$666$	2.47214	+	7.60845i	0.0957933	+	0.294822i
$667$	1.70820	−	1.24108i	0.0661419	−	0.0480549i
$668$	1.70820			0.0660924
$669$	2.50000	−	1.81636i	0.0966556	−	0.0702244i
$670$		0			0
$671$	−8.09017	−	5.87785i	−0.312318	−	0.226912i
$672$	−0.309017	−	0.224514i	−0.0119206	−	0.00866082i
$673$	−7.55573	+	23.2541i	−0.291252	+	0.896381i	0.693203	+	0.720743i	$0.256199\pi$
$673$	−7.55573	+	23.2541i	−0.291252	+	0.896381i	−0.984455	+	0.175639i	$0.943801\pi$
$674$	12.0902			0.465696
$675$		0			0
$676$	−6.88854			−0.264944
$677$	−5.53444	+	17.0333i	−0.212706	+	0.654641i	0.786603	+	0.617460i	$0.211838\pi$
$677$	−5.53444	+	17.0333i	−0.212706	+	0.654641i	−0.999309	+	0.0371818i	$0.988162\pi$
$678$	11.9443	+	8.67802i	0.458717	+	0.333277i
$679$	1.73607	+	1.26133i	0.0666242	+	0.0484053i
$680$		0			0
$681$	9.11803	−	6.62464i	0.349404	−	0.253857i
$682$	−6.05573			−0.231886
$683$	−3.64590	+	2.64890i	−0.139506	+	0.101357i	−0.655350	−	0.755326i	$-0.727479\pi$
$683$	−3.64590	+	2.64890i	−0.139506	+	0.101357i	0.515843	+	0.856683i	$0.327479\pi$
$684$	2.38197	+	7.33094i	0.0910767	+	0.280305i
$685$		0			0
$686$	−1.63525	+	5.03280i	−0.0624343	+	0.192153i
$687$	−4.47214	−	13.7638i	−0.170623	−	0.525122i
$688$	−1.76393	−	5.42882i	−0.0672493	−	0.206972i
$689$	6.94427	−	21.3723i	0.264556	−	0.814219i
$690$		0			0
$691$	2.09017	+	6.43288i	0.0795138	+	0.244718i	0.982909	−	0.184090i	$-0.0589337\pi$
$691$	2.09017	+	6.43288i	0.0795138	+	0.244718i	−0.903396	+	0.428808i	$0.858934\pi$
$692$	−4.92705	+	3.57971i	−0.187298	+	0.136080i
$693$	−0.527864			−0.0200519
$694$	−0.354102	+	0.257270i	−0.0134415	+	0.00976584i
$695$		0			0
$696$	−0.381966	−	0.277515i	−0.0144784	−	0.0105192i
$697$	20.1803	+	14.6619i	0.764385	+	0.555358i
$698$	−2.43769	+	7.50245i	−0.0922681	+	0.283972i
$699$	12.6525			0.478561
$700$		0			0
$701$	−12.8328			−0.484689			−0.242344	−	0.970190i	$-0.577916\pi$
$701$	−12.8328			−0.484689			−0.242344	+	0.970190i	$0.577916\pi$
$702$	0.763932	−	2.35114i	0.0288328	−	0.0887381i
$703$	49.8885	+	36.2461i	1.88158	+	1.36705i
$704$	−1.11803	−	0.812299i	−0.0421375	−	0.0306147i
$705$		0			0
$706$	7.09017	−	5.15131i	0.266842	−	0.193872i
$707$	−2.52786			−0.0950701
$708$	1.11803	−	0.812299i	0.0420183	−	0.0305281i
$709$	−9.36068	−	28.8092i	−0.351548	−	1.08195i	−0.957984	−	0.286821i	$-0.907402\pi$
$709$	−9.36068	−	28.8092i	−0.351548	−	1.08195i	0.606437	−	0.795132i	$-0.292598\pi$
$710$		0			0
$711$	−1.04508	+	3.21644i	−0.0391937	+	0.120626i
$712$	−3.85410	−	11.8617i	−0.144439	−	0.444536i
$713$	6.05573	+	18.6376i	0.226789	+	0.697984i
$714$	0.381966	−	1.17557i	0.0142947	−	0.0439946i
$715$		0			0
$716$	0.972136	+	2.99193i	0.0363304	+	0.111814i
$717$	−20.7984	+	15.1109i	−0.776730	+	0.564327i
$718$	0.180340			0.00673022
$719$	35.1246	−	25.5195i	1.30993	−	0.951718i	0.309927	−	0.950760i	$-0.399695\pi$
$719$	35.1246	−	25.5195i	1.30993	−	0.951718i	1.00000		0.000957448i	$-0.000304765\pi$
$720$		0			0
$721$	0.409830	+	0.297759i	0.0152629	+	0.0110891i
$722$	32.6976	+	23.7562i	1.21688	+	0.884113i
$723$	−3.26393	+	10.0453i	−0.121387	+	0.373591i
$724$	24.6525			0.916202
$725$		0			0
$726$	9.09017			0.337368
$727$	10.9443	−	33.6830i	0.405901	−	1.24923i	−0.514240	−	0.857646i	$-0.671926\pi$
$727$	10.9443	−	33.6830i	0.405901	−	1.24923i	0.920141	−	0.391587i	$-0.128074\pi$
$728$	0.763932	+	0.555029i	0.0283132	+	0.0205707i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	14.9443	−	10.8576i	0.552734	−	0.401585i
$732$	7.23607			0.267453
$733$	−0.0901699	+	0.0655123i	−0.00333050	+	0.00241975i	−0.589449	−	0.807805i	$-0.700655\pi$
$733$	−0.0901699	+	0.0655123i	−0.00333050	+	0.00241975i	0.586119	+	0.810225i	$0.300655\pi$
$734$	−8.77051	−	26.9929i	−0.323725	−	0.996324i
$735$		0			0
$736$	−1.38197	+	4.25325i	−0.0509399	+	0.156777i
$737$	4.47214	+	13.7638i	0.164733	+	0.506997i
$738$	2.38197	+	7.33094i	0.0876814	+	0.269856i
$739$	−7.97871	+	24.5560i	−0.293502	+	0.903305i	0.690219	+	0.723601i	$0.257514\pi$
$739$	−7.97871	+	24.5560i	−0.293502	+	0.903305i	−0.983721	+	0.179705i	$0.942486\pi$
$740$		0			0
$741$	−5.88854	−	18.1231i	−0.216321	−	0.665768i
$742$	2.80902	−	2.04087i	0.103122	−	0.0749227i
$743$	−37.0132			−1.35788			−0.678940	−	0.734193i	$-0.737561\pi$
$743$	−37.0132			−1.35788			−0.678940	+	0.734193i	$0.737561\pi$
$744$	3.54508	−	2.57565i	0.129969	−	0.0944281i
$745$		0			0
$746$	16.5623	+	12.0332i	0.606389	+	0.440567i
$747$	7.16312	+	5.20431i	0.262085	+	0.190416i
$748$	1.38197	−	4.25325i	0.0505297	−	0.155514i
$749$	−3.58359			−0.130942
$750$		0			0
$751$	0.201626			0.00735744			0.00367872	−	0.999993i	$-0.498829\pi$
$751$	0.201626			0.00735744			0.00367872	+	0.999993i	$0.498829\pi$
$752$	3.61803	−	11.1352i	0.131936	−	0.406058i
$753$	5.30902	+	3.85723i	0.193471	+	0.140565i
$754$	0.944272	+	0.686054i	0.0343884	+	0.0249846i
$755$		0			0
$756$	0.309017	−	0.224514i	0.0112388	−	0.00816549i
$757$	−23.1246			−0.840478			−0.420239	−	0.907413i	$-0.638054\pi$
$757$	−23.1246			−0.840478			−0.420239	+	0.907413i	$0.638054\pi$
$758$	1.76393	−	1.28157i	0.0640689	−	0.0465488i
$759$	1.90983	+	5.87785i	0.0693224	+	0.213353i
$760$		0			0
$761$	−7.85410	+	24.1724i	−0.284711	+	0.876250i	0.701774	+	0.712399i	$0.252392\pi$
$761$	−7.85410	+	24.1724i	−0.284711	+	0.876250i	−0.986485	+	0.163851i	$0.947608\pi$
$762$	3.51722	+	10.8249i	0.127415	+	0.392144i
$763$	−1.50658	−	4.63677i	−0.0545418	−	0.167862i
$764$	5.47214	−	16.8415i	0.197975	−	0.609304i
$765$		0			0
$766$	−6.18034	−	19.0211i	−0.223305	−	0.687261i
$767$	−2.76393	+	2.00811i	−0.0997998	+	0.0725088i
$768$	1.00000			0.0360844
$769$	28.8713	−	20.9762i	1.04113	−	0.756423i	0.0706214	−	0.997503i	$-0.477502\pi$
$769$	28.8713	−	20.9762i	1.04113	−	0.756423i	0.970505	+	0.241080i	$0.0775018\pi$
$770$		0			0
$771$	−17.7984	−	12.9313i	−0.640993	−	0.465709i
$772$	9.01722	+	6.55139i	0.324537	+	0.235790i
$773$	2.42705	−	7.46969i	0.0872950	−	0.268666i	−0.897874	−	0.440252i	$-0.854889\pi$
$773$	2.42705	−	7.46969i	0.0872950	−	0.268666i	0.985169	+	0.171586i	$0.0548891\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−5.61803			−0.201676
$777$	0.944272	−	2.90617i	0.0338756	−	0.104258i
$778$	−11.8262	−	8.59226i	−0.423991	−	0.308048i
$779$	48.0689	+	34.9241i	1.72225	+	1.25129i
$780$		0			0
$781$	−16.1803	+	11.7557i	−0.578978	+	0.420652i
$782$	−14.4721			−0.517523
$783$	0.381966	−	0.277515i	0.0136504	−	0.00991756i
$784$	−2.11803	−	6.51864i	−0.0756441	−	0.232809i
$785$		0			0
$786$	−5.52786	+	17.0130i	−0.197172	+	0.606834i
$787$	9.29180	+	28.5972i	0.331217	+	1.01938i	0.968556	+	0.248797i	$0.0800351\pi$
$787$	9.29180	+	28.5972i	0.331217	+	1.01938i	−0.637339	+	0.770584i	$0.719965\pi$
$788$	1.82624	+	5.62058i	0.0650570	+	0.200225i
$789$	−0.527864	+	1.62460i	−0.0187925	+	0.0578372i
$790$		0			0
$791$	−1.74265	−	5.36331i	−0.0619614	−	0.190697i
$792$	1.11803	−	0.812299i	0.0397276	−	0.0288638i
$793$	−17.8885			−0.635241
$794$	28.5066	−	20.7112i	1.01166	−	0.735014i
$795$		0			0
$796$	14.9721	+	10.8779i	0.530673	+	0.385557i
$797$	−29.5344	−	21.4580i	−1.04616	−	0.760082i	−0.0746844	−	0.997207i	$-0.523795\pi$
$797$	−29.5344	−	21.4580i	−1.04616	−	0.760082i	−0.971479	+	0.237125i	$0.923795\pi$
$798$	0.909830	−	2.80017i	0.0322076	−	0.0991249i
$799$	37.8885			1.34040
$800$		0			0
$801$	12.4721			0.440681
$802$	−3.79837	+	11.6902i	−0.134125	+	0.412795i
$803$	13.9443	+	10.1311i	0.492083	+	0.357519i
$804$	−8.47214	−	6.15537i	−0.298789	−	0.217083i
$805$		0			0
$806$	−8.76393	+	6.36737i	−0.308696	+	0.224281i
$807$	2.09017			0.0735775
$808$	5.35410	−	3.88998i	0.188357	−	0.136849i
$809$	7.05573	+	21.7153i	0.248066	+	0.763469i	0.995117	+	0.0987023i	$0.0314692\pi$
$809$	7.05573	+	21.7153i	0.248066	+	0.763469i	−0.747051	+	0.664767i	$0.768531\pi$
$810$		0			0
$811$	2.38197	−	7.33094i	0.0836421	−	0.257424i	−0.900486	−	0.434886i	$-0.856789\pi$
$811$	2.38197	−	7.33094i	0.0836421	−	0.257424i	0.984128	+	0.177462i	$0.0567887\pi$
$812$	0.0557281	+	0.171513i	0.00195567	+	0.00601894i
$813$	3.40983	+	10.4944i	0.119588	+	0.368054i
$814$	3.41641	−	10.5146i	0.119745	−	0.368537i
$815$		0			0
$816$	1.00000	+	3.07768i	0.0350070	+	0.107740i
$817$	35.5967	−	25.8626i	1.24537	−	0.904816i
$818$	18.7984			0.657270
$819$	−0.763932	+	0.555029i	−0.0266939	+	0.0193943i
$820$		0			0
$821$	27.4336	+	19.9317i	0.957440	+	0.695621i	0.952555	−	0.304367i	$-0.0984449\pi$
$821$	27.4336	+	19.9317i	0.957440	+	0.695621i	0.00488541	+	0.999988i	$0.498445\pi$
$822$	−8.23607	−	5.98385i	−0.287266	−	0.208711i
$823$	−9.89919	+	30.4666i	−0.345064	+	1.06200i	0.616486	+	0.787366i	$0.288556\pi$
$823$	−9.89919	+	30.4666i	−0.345064	+	1.06200i	−0.961550	+	0.274631i	$0.911444\pi$
$824$	−1.32624			−0.0462017
$825$		0			0
$826$	−0.527864			−0.0183667
$827$	13.3197	−	40.9937i	0.463170	−	1.42549i	−0.398100	−	0.917342i	$-0.630330\pi$
$827$	13.3197	−	40.9937i	0.463170	−	1.42549i	0.861270	−	0.508148i	$-0.169670\pi$
$828$	−3.61803	−	2.62866i	−0.125735	−	0.0913521i
$829$	8.00000	+	5.81234i	0.277851	+	0.201871i	0.717980	−	0.696064i	$-0.245067\pi$
$829$	8.00000	+	5.81234i	0.277851	+	0.201871i	−0.440128	+	0.897935i	$0.645067\pi$
$830$		0			0
$831$	−0.763932	+	0.555029i	−0.0265005	+	0.0192537i
$832$	−2.47214			−0.0857059
$833$	17.9443	−	13.0373i	0.621732	−	0.451715i
$834$	−0.472136	−	1.45309i	−0.0163487	−	0.0503162i
$835$		0			0
$836$	3.29180	−	10.1311i	0.113849	−	0.350392i
$837$	1.35410	+	4.16750i	0.0468046	+	0.144050i
$838$	−2.50000	−	7.69421i	−0.0863611	−	0.265792i
$839$	−11.8541	+	36.4832i	−0.409249	+	1.25954i	0.508046	+	0.861330i	$0.330368\pi$
$839$	−11.8541	+	36.4832i	−0.409249	+	1.25954i	−0.917295	+	0.398209i	$0.869632\pi$
$840$		0			0
$841$	−8.89261	−	27.3686i	−0.306642	−	0.943746i
$842$	−22.0344	+	16.0090i	−0.759357	+	0.551705i
$843$	−29.8885			−1.02942
$844$	−18.9443	+	13.7638i	−0.652089	+	0.473770i
$845$		0			0
$846$	9.47214	+	6.88191i	0.325659	+	0.236605i
$847$	−2.80902	−	2.04087i	−0.0965190	−	0.0701251i
$848$	−2.80902	+	8.64527i	−0.0964620	+	0.296880i
$849$	−31.4164			−1.07821
$850$		0			0
$851$	−35.7771			−1.22642
$852$	4.47214	−	13.7638i	0.153213	−	0.471541i
$853$	4.52786	+	3.28969i	0.155031	+	0.112637i	0.662597	−	0.748977i	$-0.269454\pi$
$853$	4.52786	+	3.28969i	0.155031	+	0.112637i	−0.507565	+	0.861613i	$0.669454\pi$
$854$	−2.23607	−	1.62460i	−0.0765167	−	0.0555926i
$855$		0			0
$856$	7.59017	−	5.51458i	0.259427	−	0.188485i
$857$	−42.0689			−1.43705			−0.718523	−	0.695503i	$-0.755181\pi$
$857$	−42.0689			−1.43705			−0.718523	+	0.695503i	$0.755181\pi$
$858$	−2.76393	+	2.00811i	−0.0943591	+	0.0685559i
$859$	−4.85410	−	14.9394i	−0.165620	−	0.509725i	0.833462	−	0.552577i	$-0.186356\pi$
$859$	−4.85410	−	14.9394i	−0.165620	−	0.509725i	−0.999081	+	0.0428520i	$0.986356\pi$
$860$		0			0
$861$	0.909830	−	2.80017i	0.0310069	−	0.0954295i
$862$	11.3820	+	35.0301i	0.387671	+	1.19313i
$863$	−3.76393	−	11.5842i	−0.128126	−	0.394330i	0.866332	−	0.499469i	$-0.166471\pi$
$863$	−3.76393	−	11.5842i	−0.128126	−	0.394330i	−0.994458	+	0.105138i	$0.966471\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$		0			0
$866$	−6.95492	−	21.4050i	−0.236338	−	0.727372i
$867$	5.28115	−	3.83698i	0.179357	−	0.130311i
$868$	−1.67376			−0.0568112
$869$	3.78115	−	2.74717i	0.128267	−	0.0931913i
$870$		0			0
$871$	20.9443	+	15.2169i	0.709670	+	0.515605i
$872$	10.3262	+	7.50245i	0.349691	+	0.254065i
$873$	1.73607	−	5.34307i	0.0587570	−	0.180835i
$874$	−34.4721			−1.16604
$875$		0			0
$876$	−12.4721			−0.421394
$877$	−0.965558	+	2.97168i	−0.0326046	+	0.100347i	−0.966034	−	0.258413i	$-0.916800\pi$
$877$	−0.965558	+	2.97168i	−0.0326046	+	0.100347i	0.933430	+	0.358760i	$0.116800\pi$
$878$	11.7361	+	8.52675i	0.396073	+	0.287764i
$879$	−8.82624	−	6.41264i	−0.297702	−	0.216293i
$880$		0			0
$881$	−20.7082	+	15.0454i	−0.697677	+	0.506892i	−0.879175	−	0.476499i	$-0.841905\pi$
$881$	−20.7082	+	15.0454i	−0.697677	+	0.506892i	0.181498	+	0.983391i	$0.441905\pi$
$882$	6.85410			0.230790
$883$	22.7082	−	16.4985i	0.764192	−	0.555218i	−0.136001	−	0.990709i	$-0.543425\pi$
$883$	22.7082	−	16.4985i	0.764192	−	0.555218i	0.900193	+	0.435491i	$0.143425\pi$
$884$	−2.47214	−	7.60845i	−0.0831469	−	0.255900i
$885$		0			0
$886$	4.44427	−	13.6781i	0.149308	−	0.459523i
$887$	1.05573	+	3.24920i	0.0354479	+	0.109097i	0.967215	−	0.253960i	$-0.0817330\pi$
$887$	1.05573	+	3.24920i	0.0354479	+	0.109097i	−0.931767	+	0.363057i	$0.881733\pi$
$888$	2.47214	+	7.60845i	0.0829595	+	0.255323i
$889$	1.34346	−	4.13474i	0.0450582	−	0.138675i
$890$		0			0
$891$	0.427051	+	1.31433i	0.0143067	+	0.0440316i
$892$	2.50000	−	1.81636i	0.0837062	−	0.0608161i
$893$	90.2492			3.02008
$894$	8.82624	−	6.41264i	0.295194	−	0.214471i
$895$		0			0
$896$	−0.309017	−	0.224514i	−0.0103235	−	0.00750049i
$897$	8.94427	+	6.49839i	0.298641	+	0.216975i
$898$	4.41641	−	13.5923i	0.147377	−	0.453581i
$899$	−2.06888			−0.0690011
$900$		0			0
$901$	−29.4164			−0.980003
$902$	3.29180	−	10.1311i	0.109605	−	0.337329i
$903$	−1.76393	−	1.28157i	−0.0587000	−	0.0426480i
$904$	11.9443	+	8.67802i	0.397261	+	0.288627i
$905$		0			0
$906$	2.16312	−	1.57160i	0.0718648	−	0.0522128i
$907$	−21.5279			−0.714821			−0.357410	−	0.933947i	$-0.616340\pi$
$907$	−21.5279			−0.714821			−0.357410	+	0.933947i	$0.616340\pi$
$908$	9.11803	−	6.62464i	0.302593	−	0.219846i
$909$	2.04508	+	6.29412i	0.0678312	+	0.208763i
$910$		0			0
$911$	−1.29180	+	3.97574i	−0.0427991	+	0.131722i	−0.970173	−	0.242414i	$-0.922061\pi$
$911$	−1.29180	+	3.97574i	−0.0427991	+	0.131722i	0.927374	+	0.374136i	$0.122061\pi$
$912$	2.38197	+	7.33094i	0.0788748	+	0.242752i
$913$	−3.78115	−	11.6372i	−0.125138	−	0.385135i
$914$	2.19098	−	6.74315i	0.0724713	−	0.223044i
$915$		0			0
$916$	−4.47214	−	13.7638i	−0.147764	−	0.454769i
$917$	5.52786	−	4.01623i	0.182546	−	0.132628i
$918$	−3.23607			−0.106806
$919$	−39.4164	+	28.6377i	−1.30023	+	0.944670i	−0.999958	−	0.00918396i	$-0.997077\pi$
$919$	−39.4164	+	28.6377i	−1.30023	+	0.944670i	−0.300269	+	0.953854i	$0.597077\pi$
$920$		0			0
$921$	8.09017	+	5.87785i	0.266580	+	0.193682i
$922$	−10.1631	−	7.38394i	−0.334704	−	0.243177i
$923$	−11.0557	+	34.0260i	−0.363904	+	1.11998i
$924$	−0.527864			−0.0173655
$925$		0			0
$926$	30.8328			1.01323
$927$	0.409830	−	1.26133i	0.0134606	−	0.0414274i
$928$	−0.381966	−	0.277515i	−0.0125386	−	0.00910986i
$929$	−46.1246	−	33.5115i	−1.51330	−	1.09948i	−0.964687	−	0.263400i	$-0.915156\pi$
$929$	−46.1246	−	33.5115i	−1.51330	−	1.09948i	−0.548613	−	0.836077i	$-0.684844\pi$
$930$		0			0
$931$	42.7426	−	31.0543i	1.40083	−	1.01777i
$932$	12.6525			0.414446
$933$	15.3262	−	11.1352i	0.501759	−	0.364549i
$934$	8.13525	+	25.0377i	0.266194	+	0.819260i
$935$		0			0
$936$	0.763932	−	2.35114i	0.0249699	−	0.0768494i
$937$	−15.9721	−	49.1572i	−0.521787	−	1.60590i	−0.770583	−	0.637339i	$-0.780035\pi$
$937$	−15.9721	−	49.1572i	−0.521787	−	1.60590i	0.248796	−	0.968556i	$-0.419965\pi$
$938$	1.23607	+	3.80423i	0.0403591	+	0.124212i
$939$	−5.33688	+	16.4252i	−0.174163	+	0.536017i
$940$		0			0
$941$	−7.59017	−	23.3601i	−0.247432	−	0.761519i	−0.995227	−	0.0975885i	$-0.968887\pi$
$941$	−7.59017	−	23.3601i	−0.247432	−	0.761519i	0.747794	−	0.663930i	$-0.231113\pi$
$942$	18.3262	−	13.3148i	0.597101	−	0.433819i
$943$	−34.4721			−1.12257
$944$	1.11803	−	0.812299i	0.0363889	−	0.0264381i
$945$		0			0
$946$	−6.38197	−	4.63677i	−0.207496	−	0.150754i
$947$	−10.8713	−	7.89848i	−0.353271	−	0.256666i	0.396969	−	0.917832i	$-0.370062\pi$
$947$	−10.8713	−	7.89848i	−0.353271	−	0.256666i	−0.750240	+	0.661166i	$0.770062\pi$
$948$	−1.04508	+	3.21644i	−0.0339428	+	0.104465i
$949$	30.8328			1.00088
$950$		0			0
$951$	0.437694			0.0141932
$952$	0.381966	−	1.17557i	0.0123796	−	0.0381005i
$953$	−46.3607	−	33.6830i	−1.50177	−	1.09110i	−0.969670	−	0.244418i	$-0.921403\pi$
$953$	−46.3607	−	33.6830i	−1.50177	−	1.09110i	−0.532100	−	0.846682i	$-0.678597\pi$
$954$	−7.35410	−	5.34307i	−0.238098	−	0.172988i
$955$		0			0
$956$	−20.7984	+	15.1109i	−0.672667	+	0.488722i
$957$	−0.652476			−0.0210915
$958$	9.00000	−	6.53888i	0.290777	−	0.211262i
$959$	1.20163	+	3.69822i	0.0388025	+	0.119422i
$960$		0			0
$961$	−3.64590	+	11.2209i	−0.117610	+	0.361965i
$962$	−6.11146	−	18.8091i	−0.197041	−	0.606431i
$963$	2.89919	+	8.92278i	0.0934250	+	0.287533i
$964$	−3.26393	+	10.0453i	−0.105124	+	0.323539i
$965$		0			0
$966$	0.527864	+	1.62460i	0.0169837	+	0.0522706i
$967$	17.8713	−	12.9843i	0.574703	−	0.417546i	−0.262108	−	0.965039i	$-0.584418\pi$
$967$	17.8713	−	12.9843i	0.574703	−	0.417546i	0.836811	+	0.547492i	$0.184418\pi$
$968$	9.09017			0.292169
$969$	−20.1803	+	14.6619i	−0.648286	+	0.471007i
$970$		0			0
$971$	−30.1074	−	21.8743i	−0.966192	−	0.701980i	−0.0116116	−	0.999933i	$-0.503696\pi$
$971$	−30.1074	−	21.8743i	−0.966192	−	0.701980i	−0.954581	+	0.297953i	$0.903696\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−0.180340	+	0.555029i	−0.00578143	+	0.0177934i
$974$	−6.79837			−0.217834
$975$		0			0
$976$	7.23607			0.231621
$977$	1.61803	−	4.97980i	0.0517655	−	0.159318i	−0.921832	−	0.387590i	$-0.873308\pi$
$977$	1.61803	−	4.97980i	0.0517655	−	0.159318i	0.973597	+	0.228272i	$0.0733076\pi$
$978$	−6.85410	−	4.97980i	−0.219170	−	0.159236i
$979$	−13.9443	−	10.1311i	−0.445661	−	0.323792i
$980$		0			0
$981$	−10.3262	+	7.50245i	−0.329691	+	0.239535i
$982$	−8.27051			−0.263923
$983$	14.4164	−	10.4741i	0.459812	−	0.334073i	−0.333646	−	0.942699i	$-0.608279\pi$
$983$	14.4164	−	10.4741i	0.459812	−	0.334073i	0.793458	+	0.608626i	$0.208279\pi$
$984$	2.38197	+	7.33094i	0.0759343	+	0.233702i
$985$		0			0
$986$	0.472136	−	1.45309i	0.0150359	−	0.0462757i
$987$	−1.38197	−	4.25325i	−0.0439885	−	0.135383i
$988$	−5.88854	−	18.1231i	−0.187340	−	0.576572i
$989$	−7.88854	+	24.2784i	−0.250841	+	0.772010i
$990$		0			0
$991$	−8.17376	−	25.1563i	−0.259648	−	0.799115i	−0.992878	−	0.119134i	$-0.961988\pi$
$991$	−8.17376	−	25.1563i	−0.259648	−	0.799115i	0.733230	−	0.679981i	$-0.238012\pi$
$992$	3.54508	−	2.57565i	0.112557	−	0.0817771i
$993$	−18.0000			−0.571213
$994$	−4.47214	+	3.24920i	−0.141848	+	0.103058i
$995$		0			0
$996$	7.16312	+	5.20431i	0.226972	+	0.164905i
$997$	35.2705	+	25.6255i	1.11703	+	0.811569i	0.983756	−	0.179511i	$-0.0574515\pi$
$997$	35.2705	+	25.6255i	1.11703	+	0.811569i	0.133272	+	0.991079i	$0.457452\pi$
$998$	4.20163	−	12.9313i	0.133000	−	0.409332i
$999$	−8.00000			−0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.b.601.1		4
5.2	odd	4		750.2.h.b.649.1		8
5.3	odd	4		750.2.h.b.649.2		8
5.4	even	2		150.2.g.a.121.1	yes	4
15.14	odd	2		450.2.h.c.271.1		4
25.6	even	5	inner	750.2.g.b.151.1		4
25.8	odd	20		750.2.h.b.349.1		8
25.9	even	10		3750.2.a.f.1.1		2
25.12	odd	20		3750.2.c.b.1249.2		4
25.13	odd	20		3750.2.c.b.1249.3		4
25.16	even	5		3750.2.a.d.1.2		2
25.17	odd	20		750.2.h.b.349.2		8
25.19	even	10		150.2.g.a.31.1	✓	4
75.44	odd	10		450.2.h.c.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.g.a.31.1	✓	4	25.19	even	10
150.2.g.a.121.1	yes	4	5.4	even	2
450.2.h.c.181.1		4	75.44	odd	10
450.2.h.c.271.1		4	15.14	odd	2
750.2.g.b.151.1		4	25.6	even	5	inner
750.2.g.b.601.1		4	1.1	even	1	trivial
750.2.h.b.349.1		8	25.8	odd	20
750.2.h.b.349.2		8	25.17	odd	20
750.2.h.b.649.1		8	5.2	odd	4
750.2.h.b.649.2		8	5.3	odd	4
3750.2.a.d.1.2		2	25.16	even	5
3750.2.a.f.1.1		2	25.9	even	10
3750.2.c.b.1249.2		4	25.12	odd	20
3750.2.c.b.1249.3		4	25.13	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.809017 - 0.587785i) q^{6} -0.381966 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.427051 - 1.31433i) q^{11} +(0.309017 + 0.951057i) q^{12} +(-0.763932 - 2.35114i) q^{13} +(0.118034 - 0.363271i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.61803 + 1.90211i) q^{17} -1.00000 q^{18} +(-6.23607 + 4.53077i) q^{19} +(0.309017 + 0.224514i) q^{21} +(1.11803 + 0.812299i) q^{22} +(1.38197 - 4.25325i) q^{23} -1.00000 q^{24} +2.47214 q^{26} +(0.309017 - 0.951057i) q^{27} +(0.309017 + 0.224514i) q^{28} +(0.381966 + 0.277515i) q^{29} +(-3.54508 + 2.57565i) q^{31} -1.00000 q^{32} +(-1.11803 + 0.812299i) q^{33} +(-1.00000 - 3.07768i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(-2.38197 - 7.33094i) q^{38} +(-0.763932 + 2.35114i) q^{39} +(-2.38197 - 7.33094i) q^{41} +(-0.309017 + 0.224514i) q^{42} -5.70820 q^{43} +(-1.11803 + 0.812299i) q^{44} +(3.61803 + 2.62866i) q^{46} +(-9.47214 - 6.88191i) q^{47} +(0.309017 - 0.951057i) q^{48} -6.85410 q^{49} +3.23607 q^{51} +(-0.763932 + 2.35114i) q^{52} +(7.35410 + 5.34307i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.309017 + 0.224514i) q^{56} +7.70820 q^{57} +(-0.381966 + 0.277515i) q^{58} +(-0.427051 - 1.31433i) q^{59} +(2.23607 - 6.88191i) q^{61} +(-1.35410 - 4.16750i) q^{62} +(-0.118034 - 0.363271i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.427051 - 1.31433i) q^{66} +(-8.47214 + 6.15537i) q^{67} +3.23607 q^{68} +(-3.61803 + 2.62866i) q^{69} +(-11.7082 - 8.50651i) q^{71} +(0.809017 + 0.587785i) q^{72} +(-3.85410 + 11.8617i) q^{73} +8.00000 q^{74} +7.70820 q^{76} +(-0.163119 + 0.502029i) q^{77} +(-2.00000 - 1.45309i) q^{78} +(2.73607 + 1.98787i) q^{79} +(-0.809017 + 0.587785i) q^{81} +7.70820 q^{82} +(7.16312 - 5.20431i) q^{83} +(-0.118034 - 0.363271i) q^{84} +(1.76393 - 5.42882i) q^{86} +(-0.145898 - 0.449028i) q^{87} +(-0.427051 - 1.31433i) q^{88} +(3.85410 - 11.8617i) q^{89} +(0.291796 + 0.898056i) q^{91} +(-3.61803 + 2.62866i) q^{92} +4.38197 q^{93} +(9.47214 - 6.88191i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-4.54508 - 3.30220i) q^{97} +(2.11803 - 6.51864i) q^{98} +1.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + q^{6} - 6 q^{7} + q^{8} - q^{9} - 5 q^{11} - q^{12} - 12 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 4 q^{18} - 16 q^{19} - q^{21} + 10 q^{23} - 4 q^{24} - 8 q^{26} - q^{27}+ \cdots + 10 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + q^6 - 6 * q^7 + q^8 - q^9 - 5 * q^11 - q^12 - 12 * q^13 - 4 * q^14 - q^16 - 6 * q^17 - 4 * q^18 - 16 * q^19 - q^21 + 10 * q^23 - 4 * q^24 - 8 * q^26 - q^27 - q^28 + 6 * q^29 - 3 * q^31 - 4 * q^32 - 4 * q^34 - q^36 + 8 * q^37 - 14 * q^38 - 12 * q^39 - 14 * q^41 + q^42 + 4 * q^43 + 10 * q^46 - 20 * q^47 - q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 + 16 * q^53 + q^54 + q^56 + 4 * q^57 - 6 * q^58 + 5 * q^59 + 8 * q^62 + 4 * q^63 - q^64 + 5 * q^66 - 16 * q^67 + 4 * q^68 - 10 * q^69 - 20 * q^71 + q^72 - 2 * q^73 + 32 * q^74 + 4 * q^76 + 15 * q^77 - 8 * q^78 + 2 * q^79 - q^81 + 4 * q^82 + 13 * q^83 + 4 * q^84 + 16 * q^86 - 14 * q^87 + 5 * q^88 + 2 * q^89 + 28 * q^91 - 10 * q^92 + 22 * q^93 + 20 * q^94 + q^96 - 7 * q^97 + 4 * q^98 + 10 * q^99

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