LMFDB - Embedded newform 750.2.g.e.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(151,750)]

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, 4]))

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

//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);

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: 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 $\Q(\zeta_{5})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			601.1
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	750.601
Dual form			750.2.g.e.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} -2.07768 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.160734 - 0.494689i) q^{11} +(0.309017 + 0.951057i) q^{12} +(0.675571 + 2.07919i) q^{13} +(0.642040 - 1.97599i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.18088 + 1.58450i) q^{17} -1.00000 q^{18} +(5.55899 - 4.03884i) q^{19} +(1.68088 + 1.22123i) q^{21} +(0.420808 + 0.305735i) q^{22} +(1.19301 - 3.67171i) q^{23} -1.00000 q^{24} -2.18619 q^{26} +(0.309017 - 0.951057i) q^{27} +(1.68088 + 1.22123i) q^{28} +(7.30844 + 5.30989i) q^{29} +(5.99083 - 4.35259i) q^{31} -1.00000 q^{32} +(-0.420808 + 0.305735i) q^{33} +(-0.833023 - 2.56378i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-1.64001 - 5.04743i) q^{37} +(2.12334 + 6.53498i) q^{38} +(0.675571 - 2.07919i) q^{39} +(-0.996141 - 3.06581i) q^{41} +(-1.68088 + 1.22123i) q^{42} +9.53920 q^{43} +(-0.420808 + 0.305735i) q^{44} +(3.12334 + 2.26924i) q^{46} +(7.49614 + 5.44627i) q^{47} +(0.309017 - 0.951057i) q^{48} -2.68323 q^{49} +2.69572 q^{51} +(0.675571 - 2.07919i) q^{52} +(1.97271 + 1.43326i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-1.68088 + 1.22123i) q^{56} -6.87129 q^{57} +(-7.30844 + 5.30989i) q^{58} +(2.67261 + 8.22545i) q^{59} +(3.88998 - 11.9721i) q^{61} +(2.28829 + 7.04264i) q^{62} +(-0.642040 - 1.97599i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.160734 - 0.494689i) q^{66} +(-5.41544 + 3.93455i) q^{67} +2.69572 q^{68} +(-3.12334 + 2.26924i) q^{69} +(6.60886 + 4.80162i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.18770 - 3.65537i) q^{73} +5.30719 q^{74} -6.87129 q^{76} +(-0.333955 + 1.02781i) q^{77} +(1.76867 + 1.28501i) q^{78} +(-2.84162 - 2.06455i) q^{79} +(-0.809017 + 0.587785i) q^{81} +3.22358 q^{82} +(10.6233 - 7.71827i) q^{83} +(-0.642040 - 1.97599i) q^{84} +(-2.94777 + 9.07232i) q^{86} +(-2.79158 - 8.59159i) q^{87} +(-0.160734 - 0.494689i) q^{88} +(-3.04654 + 9.37628i) q^{89} +(-1.40362 - 4.31990i) q^{91} +(-3.12334 + 2.26924i) q^{92} -7.40507 q^{93} +(-7.49614 + 5.44627i) q^{94} +(0.809017 + 0.587785i) q^{96} +(8.70483 + 6.32443i) q^{97} +(0.829164 - 2.55190i) q^{98} +0.520147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} + 2 q^{8} - 2 q^{9} + 10 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{21} + 10 q^{23} - 8 q^{24} + 4 q^{26}+ \cdots - 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 + 2 * q^8 - 2 * q^9 + 10 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 - 2 * q^21 + 10 * q^23 - 8 * q^24 + 4 * q^26 - 2 * q^27 - 2 * q^28 + 22 * q^29 + 24 * q^31 - 8 * q^32 - 8 * q^34 - 2 * q^36 - 14 * q^37 + 2 * q^38 - 4 * q^39 + 22 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^46 + 30 * q^47 - 2 * q^48 - 8 * q^49 - 12 * q^51 - 4 * q^52 + 12 * q^53 + 2 * q^54 + 2 * q^56 - 12 * q^57 - 22 * q^58 + 20 * q^59 + 6 * q^62 - 2 * q^63 - 2 * q^64 - 10 * q^66 + 18 * q^67 - 12 * q^68 - 10 * q^69 + 20 * q^71 + 2 * q^72 + 16 * q^73 + 4 * q^74 - 12 * q^76 - 6 * q^78 - 16 * q^79 - 2 * q^81 + 28 * q^82 + 6 * q^83 - 2 * q^84 - 18 * q^86 - 8 * q^87 - 10 * q^88 + 34 * q^89 - 24 * q^91 - 10 * q^92 - 36 * q^93 - 30 * q^94 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 20 * 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
$7$	−2.07768			−0.785291			−0.392645	−	0.919690i	$-0.628440\pi$
$7$	−2.07768			−0.785291			−0.392645	+	0.919690i	$0.628440\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	0.160734	−	0.494689i	0.0484632	−	0.149154i	−0.923896	−	0.382643i	$-0.875014\pi$
$11$	0.160734	−	0.494689i	0.0484632	−	0.149154i	0.972360	+	0.233488i	$0.0750140\pi$
$12$	0.309017	+	0.951057i	0.0892055	+	0.274546i
$13$	0.675571	+	2.07919i	0.187370	+	0.576664i	0.999981	−	0.00614146i	$-0.00195490\pi$
$13$	0.675571	+	2.07919i	0.187370	+	0.576664i	−0.812612	+	0.582806i	$0.801955\pi$
$14$	0.642040	−	1.97599i	0.171592	−	0.528107i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.18088	+	1.58450i	−0.528941	+	0.384298i	−0.819962	−	0.572418i	$-0.806005\pi$
$17$	−2.18088	+	1.58450i	−0.528941	+	0.384298i	0.291020	+	0.956717i	$0.406005\pi$
$18$	−1.00000			−0.235702
$19$	5.55899	−	4.03884i	1.27532	−	0.926574i	0.275919	−	0.961181i	$-0.411018\pi$
$19$	5.55899	−	4.03884i	1.27532	−	0.926574i	0.999401	+	0.0346072i	$0.0110180\pi$
$20$		0			0
$21$	1.68088	+	1.22123i	0.366798	+	0.266495i
$22$	0.420808	+	0.305735i	0.0897165	+	0.0651829i
$23$	1.19301	−	3.67171i	0.248760	−	0.765605i	−0.746235	−	0.665682i	$-0.768141\pi$
$23$	1.19301	−	3.67171i	0.248760	−	0.765605i	0.994995	−	0.0999224i	$-0.0318595\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$	−2.18619			−0.428748
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	1.68088	+	1.22123i	0.317657	+	0.230791i
$29$	7.30844	+	5.30989i	1.35714	+	0.986022i	0.998621	+	0.0525013i	$0.0167194\pi$
$29$	7.30844	+	5.30989i	1.35714	+	0.986022i	0.358523	+	0.933521i	$0.383281\pi$
$30$		0			0
$31$	5.99083	−	4.35259i	1.07598	−	0.781749i	0.0990065	−	0.995087i	$-0.468434\pi$
$31$	5.99083	−	4.35259i	1.07598	−	0.781749i	0.976978	+	0.213338i	$0.0684335\pi$
$32$	−1.00000			−0.176777
$33$	−0.420808	+	0.305735i	−0.0732532	+	0.0532216i
$34$	−0.833023	−	2.56378i	−0.142862	−	0.439685i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	−1.64001	−	5.04743i	−0.269616	−	0.829793i	−0.990594	−	0.136835i	$-0.956307\pi$
$37$	−1.64001	−	5.04743i	−0.269616	−	0.829793i	0.720978	−	0.692958i	$-0.243693\pi$
$38$	2.12334	+	6.53498i	0.344452	+	1.06011i
$39$	0.675571	−	2.07919i	0.108178	−	0.332937i
$40$		0			0
$41$	−0.996141	−	3.06581i	−0.155571	−	0.478799i	0.842647	−	0.538466i	$-0.180996\pi$
$41$	−0.996141	−	3.06581i	−0.155571	−	0.478799i	−0.998218	+	0.0596673i	$0.980996\pi$
$42$	−1.68088	+	1.22123i	−0.259366	+	0.188440i
$43$	9.53920			1.45471			0.727357	−	0.686259i	$-0.240748\pi$
$43$	9.53920			1.45471			0.727357	+	0.686259i	$0.240748\pi$
$44$	−0.420808	+	0.305735i	−0.0634392	+	0.0460912i
$45$		0			0
$46$	3.12334	+	2.26924i	0.460512	+	0.334582i
$47$	7.49614	+	5.44627i	1.09342	+	0.794419i	0.979974	−	0.199124i	$-0.0638097\pi$
$47$	7.49614	+	5.44627i	1.09342	+	0.794419i	0.113450	+	0.993544i	$0.463810\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−2.68323			−0.383319
$50$		0			0
$51$	2.69572			0.377476
$52$	0.675571	−	2.07919i	0.0936848	−	0.288332i
$53$	1.97271	+	1.43326i	0.270973	+	0.196873i	0.714970	−	0.699155i	$-0.246440\pi$
$53$	1.97271	+	1.43326i	0.270973	+	0.196873i	−0.443998	+	0.896028i	$0.646440\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$		0			0
$56$	−1.68088	+	1.22123i	−0.224617	+	0.163194i
$57$	−6.87129			−0.910124
$58$	−7.30844	+	5.30989i	−0.959645	+	0.697223i
$59$	2.67261	+	8.22545i	0.347944	+	1.07086i	0.959989	+	0.280039i	$0.0903473\pi$
$59$	2.67261	+	8.22545i	0.347944	+	1.07086i	−0.612045	+	0.790823i	$0.709653\pi$
$60$		0			0
$61$	3.88998	−	11.9721i	0.498061	−	1.53287i	−0.314070	−	0.949400i	$-0.601693\pi$
$61$	3.88998	−	11.9721i	0.498061	−	1.53287i	0.812131	−	0.583475i	$-0.198307\pi$
$62$	2.28829	+	7.04264i	0.290614	+	0.894417i
$63$	−0.642040	−	1.97599i	−0.0808894	−	0.248952i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$		0			0
$66$	−0.160734	−	0.494689i	−0.0197850	−	0.0608920i
$67$	−5.41544	+	3.93455i	−0.661601	+	0.480682i	−0.867203	−	0.497954i	$-0.834085\pi$
$67$	−5.41544	+	3.93455i	−0.661601	+	0.480682i	0.205602	+	0.978636i	$0.434085\pi$
$68$	2.69572			0.326904
$69$	−3.12334	+	2.26924i	−0.376007	+	0.273185i
$70$		0			0
$71$	6.60886	+	4.80162i	0.784328	+	0.569848i	0.906275	−	0.422689i	$-0.138914\pi$
$71$	6.60886	+	4.80162i	0.784328	+	0.569848i	−0.121947	+	0.992537i	$0.538914\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.18770	−	3.65537i	0.139010	−	0.427828i	−0.857182	−	0.515013i	$-0.827787\pi$
$73$	1.18770	−	3.65537i	0.139010	−	0.427828i	0.996192	+	0.0871848i	$0.0277870\pi$
$74$	5.30719			0.616948
$75$		0			0
$76$	−6.87129			−0.788191
$77$	−0.333955	+	1.02781i	−0.0380577	+	0.117130i
$78$	1.76867	+	1.28501i	0.200262	+	0.145499i
$79$	−2.84162	−	2.06455i	−0.319707	−	0.232281i	0.416344	−	0.909207i	$-0.363311\pi$
$79$	−2.84162	−	2.06455i	−0.319707	−	0.232281i	−0.736050	+	0.676927i	$0.763311\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	3.22358			0.355985
$83$	10.6233	−	7.71827i	1.16606	−	0.847190i	0.175526	−	0.984475i	$-0.443837\pi$
$83$	10.6233	−	7.71827i	1.16606	−	0.847190i	0.990532	+	0.137285i	$0.0438375\pi$
$84$	−0.642040	−	1.97599i	−0.0700523	−	0.215599i
$85$		0			0
$86$	−2.94777	+	9.07232i	−0.317867	+	0.978293i
$87$	−2.79158	−	8.59159i	−0.299288	−	0.921115i
$88$	−0.160734	−	0.494689i	−0.0171343	−	0.0527340i
$89$	−3.04654	+	9.37628i	−0.322932	+	0.993883i	0.649433	+	0.760419i	$0.275006\pi$
$89$	−3.04654	+	9.37628i	−0.322932	+	0.993883i	−0.972365	+	0.233465i	$0.924994\pi$
$90$		0			0
$91$	−1.40362	−	4.31990i	−0.147140	−	0.452849i
$92$	−3.12334	+	2.26924i	−0.325631	+	0.236585i
$93$	−7.40507			−0.767870
$94$	−7.49614	+	5.44627i	−0.773168	+	0.561739i
$95$		0			0
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	8.70483	+	6.32443i	0.883842	+	0.642149i	0.934265	−	0.356579i	$-0.116057\pi$
$97$	8.70483	+	6.32443i	0.883842	+	0.642149i	−0.0504234	+	0.998728i	$0.516057\pi$
$98$	0.829164	−	2.55190i	0.0837582	−	0.257781i
$99$	0.520147			0.0522767
$100$		0			0
$101$	−17.6400			−1.75524			−0.877622	−	0.479353i	$-0.840871\pi$
$101$	−17.6400			−1.75524			−0.877622	+	0.479353i	$0.840871\pi$
$102$	−0.833023	+	2.56378i	−0.0824815	+	0.253852i
$103$	−7.03649	−	5.11231i	−0.693326	−	0.503731i	0.184426	−	0.982846i	$-0.440957\pi$
$103$	−7.03649	−	5.11231i	−0.693326	−	0.503731i	−0.877752	+	0.479116i	$0.840957\pi$
$104$	1.76867	+	1.28501i	0.173432	+	0.126006i
$105$		0			0
$106$	−1.97271	+	1.43326i	−0.191607	+	0.139210i
$107$	5.40977			0.522983			0.261491	−	0.965206i	$-0.415786\pi$
$107$	5.40977			0.522983			0.261491	+	0.965206i	$0.415786\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	0.891135	+	2.74263i	0.0853553	+	0.262697i	0.984620	−	0.174707i	$-0.0558980\pi$
$109$	0.891135	+	2.74263i	0.0853553	+	0.262697i	−0.899265	+	0.437404i	$0.855898\pi$
$110$		0			0
$111$	−1.64001	+	5.04743i	−0.155663	+	0.479081i
$112$	−0.642040	−	1.97599i	−0.0606670	−	0.186714i
$113$	1.96830	+	6.05780i	0.185162	+	0.569870i	0.999951	−	0.00988741i	$-0.00314731\pi$
$113$	1.96830	+	6.05780i	0.185162	+	0.569870i	−0.814789	+	0.579757i	$0.803147\pi$
$114$	2.12334	−	6.53498i	0.198869	−	0.612057i
$115$		0			0
$116$	−2.79158	−	8.59159i	−0.259191	−	0.797709i
$117$	−1.76867	+	1.28501i	−0.163513	+	0.118799i
$118$	−8.64875			−0.796182
$119$	4.53118	−	3.29210i	0.415373	−	0.301786i
$120$		0			0
$121$	8.68031	+	6.30661i	0.789119	+	0.573328i
$122$	10.1841	+	7.39919i	0.922026	+	0.669891i
$123$	−0.996141	+	3.06581i	−0.0898191	+	0.276435i
$124$	−7.40507			−0.664995
$125$		0			0
$126$	2.07768			0.185095
$127$	4.62515	−	14.2348i	0.410416	−	1.26313i	−0.505871	−	0.862609i	$-0.668829\pi$
$127$	4.62515	−	14.2348i	0.410416	−	1.26313i	0.916287	−	0.400522i	$-0.131171\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−7.71737	−	5.60700i	−0.679477	−	0.493669i
$130$		0			0
$131$	−11.2090	+	8.14385i	−0.979339	+	0.711531i	−0.957561	−	0.288232i	$-0.906933\pi$
$131$	−11.2090	+	8.14385i	−0.979339	+	0.711531i	−0.0217781	+	0.999763i	$0.506933\pi$
$132$	0.520147			0.0452730
$133$	−11.5498	+	8.39144i	−1.00150	+	0.727630i
$134$	−2.06851	−	6.36623i	−0.178692	−	0.549959i
$135$		0			0
$136$	−0.833023	+	2.56378i	−0.0714311	+	0.219842i
$137$	−6.14755	−	18.9202i	−0.525221	−	1.61646i	−0.763879	−	0.645359i	$-0.776708\pi$
$137$	−6.14755	−	18.9202i	−0.525221	−	1.61646i	0.238659	−	0.971103i	$-0.423292\pi$
$138$	−1.19301	−	3.67171i	−0.101556	−	0.312557i
$139$	1.74398	−	5.36743i	0.147923	−	0.455259i	−0.849453	−	0.527665i	$-0.823068\pi$
$139$	1.74398	−	5.36743i	0.147923	−	0.455259i	0.997375	+	0.0724056i	$0.0230676\pi$
$140$		0			0
$141$	−2.86327	−	8.81224i	−0.241131	−	0.742125i
$142$	−6.60886	+	4.80162i	−0.554604	+	0.402943i
$143$	1.13714			0.0950925
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$		0			0
$146$	3.10944	+	2.25914i	0.257339	+	0.186968i
$147$	2.17078	+	1.57716i	0.179043	+	0.130082i
$148$	−1.64001	+	5.04743i	−0.134808	+	0.414897i
$149$	−15.0956			−1.23668			−0.618339	−	0.785911i	$-0.712194\pi$
$149$	−15.0956			−1.23668			−0.618339	+	0.785911i	$0.712194\pi$
$150$		0			0
$151$	−20.9353			−1.70369			−0.851847	−	0.523791i	$-0.824517\pi$
$151$	−20.9353			−1.70369			−0.851847	+	0.523791i	$0.824517\pi$
$152$	2.12334	−	6.53498i	0.172226	−	0.530057i
$153$	−2.18088	−	1.58450i	−0.176314	−	0.128099i
$154$	−0.874305	−	0.635220i	−0.0704535	−	0.0511875i
$155$		0			0
$156$	−1.76867	+	1.28501i	−0.141607	+	0.102883i
$157$	−5.71998			−0.456504			−0.228252	−	0.973602i	$-0.573301\pi$
$157$	−5.71998			−0.456504			−0.228252	+	0.973602i	$0.573301\pi$
$158$	2.84162	−	2.06455i	0.226067	−	0.164247i
$159$	−0.753509	−	2.31906i	−0.0597572	−	0.183914i
$160$		0			0
$161$	−2.47870	+	7.62866i	−0.195349	+	0.601222i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−3.67577	−	11.3129i	−0.287908	−	0.886091i	−0.985512	−	0.169607i	$-0.945750\pi$
$163$	−3.67577	−	11.3129i	−0.287908	−	0.886091i	0.697603	−	0.716484i	$-0.254250\pi$
$164$	−0.996141	+	3.06581i	−0.0777856	+	0.239399i
$165$		0			0
$166$	4.05774	+	12.4884i	0.314941	+	0.969290i
$167$	7.23607	−	5.25731i	0.559944	−	0.406823i	−0.271495	−	0.962440i	$-0.587518\pi$
$167$	7.23607	−	5.25731i	0.559944	−	0.406823i	0.831438	+	0.555617i	$0.187518\pi$
$168$	2.07768			0.160297
$169$	6.65058	−	4.83193i	0.511583	−	0.371687i
$170$		0			0
$171$	5.55899	+	4.03884i	0.425106	+	0.308858i
$172$	−7.71737	−	5.60700i	−0.588444	−	0.427530i
$173$	−5.04904	+	15.5394i	−0.383872	+	1.18144i	0.553424	+	0.832900i	$0.313321\pi$
$173$	−5.04904	+	15.5394i	−0.383872	+	1.18144i	−0.937295	+	0.348536i	$0.886679\pi$
$174$	9.03373			0.684845
$175$		0			0
$176$	0.520147			0.0392076
$177$	2.67261	−	8.22545i	0.200886	−	0.618262i
$178$	−7.97594	−	5.79486i	−0.597822	−	0.434343i
$179$	−2.97599	−	2.16219i	−0.222436	−	0.161609i	0.470986	−	0.882140i	$-0.343898\pi$
$179$	−2.97599	−	2.16219i	−0.222436	−	0.161609i	−0.693423	+	0.720531i	$0.743898\pi$
$180$		0			0
$181$	18.6472	−	13.5480i	1.38604	−	1.00702i	0.389751	−	0.920920i	$-0.372561\pi$
$181$	18.6472	−	13.5480i	1.38604	−	1.00702i	0.996287	−	0.0860956i	$-0.0274391\pi$
$182$	4.54222			0.336691
$183$	−10.1841	+	7.39919i	−0.752831	+	0.546964i
$184$	−1.19301	−	3.67171i	−0.0879500	−	0.270682i
$185$		0			0
$186$	2.28829	−	7.04264i	0.167786	−	0.516392i
$187$	0.433294	+	1.33354i	0.0316856	+	0.0975183i
$188$	−2.86327	−	8.81224i	−0.208826	−	0.642699i
$189$	−0.642040	+	1.97599i	−0.0467015	+	0.143732i
$190$		0			0
$191$	−0.552424	−	1.70019i	−0.0399720	−	0.123021i	0.929079	−	0.369881i	$-0.120601\pi$
$191$	−0.552424	−	1.70019i	−0.0399720	−	0.123021i	−0.969051	+	0.246859i	$0.920601\pi$
$192$	−0.809017	+	0.587785i	−0.0583858	+	0.0424197i
$193$	6.60138			0.475178			0.237589	−	0.971366i	$-0.423643\pi$
$193$	6.60138			0.475178			0.237589	+	0.971366i	$0.423643\pi$
$194$	−8.70483	+	6.32443i	−0.624970	+	0.454068i
$195$		0			0
$196$	2.17078	+	1.57716i	0.155056	+	0.112655i
$197$	10.2401	+	7.43989i	0.729579	+	0.530070i	0.889430	−	0.457071i	$-0.151101\pi$
$197$	10.2401	+	7.43989i	0.729579	+	0.530070i	−0.159851	+	0.987141i	$0.551101\pi$
$198$	−0.160734	+	0.494689i	−0.0114229	+	0.0351560i
$199$	6.24148			0.442447			0.221223	−	0.975223i	$-0.428995\pi$
$199$	6.24148			0.442447			0.221223	+	0.975223i	$0.428995\pi$
$200$		0			0
$201$	6.69385			0.472148
$202$	5.45106	−	16.7766i	0.383535	−	1.18040i
$203$	−15.1846	−	11.0323i	−1.06575	−	0.774314i
$204$	−2.18088	−	1.58450i	−0.152692	−	0.110937i
$205$		0			0
$206$	7.03649	−	5.11231i	0.490256	−	0.356192i
$207$	3.86067			0.268335
$208$	−1.76867	+	1.28501i	−0.122635	+	0.0890995i
$209$	−1.10445	−	3.39915i	−0.0763965	−	0.235124i
$210$		0			0
$211$	−6.94607	+	21.3778i	−0.478187	+	1.47171i	0.363424	+	0.931624i	$0.381608\pi$
$211$	−6.94607	+	21.3778i	−0.478187	+	1.47171i	−0.841611	+	0.540084i	$0.818392\pi$
$212$	−0.753509	−	2.31906i	−0.0517512	−	0.159274i
$213$	−2.52436	−	7.76919i	−0.172966	−	0.532336i
$214$	−1.67171	+	5.14500i	−0.114276	+	0.351705i
$215$		0			0
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−12.4471	+	9.04331i	−0.844961	+	0.613900i
$218$	−2.88377			−0.195314
$219$	−3.10944	+	2.25914i	−0.210117	+	0.152659i
$220$		0			0
$221$	−4.76783	−	3.46403i	−0.320719	−	0.233016i
$222$	−4.29360	−	3.11949i	−0.288168	−	0.209366i
$223$	5.54065	−	17.0524i	0.371029	−	1.14191i	−0.575089	−	0.818091i	$-0.695033\pi$
$223$	5.54065	−	17.0524i	0.371029	−	1.14191i	0.946119	−	0.323820i	$-0.104967\pi$
$224$	2.07768			0.138821
$225$		0			0
$226$	−6.36955			−0.423696
$227$	2.73716	−	8.42412i	0.181672	−	0.559129i	−0.818203	−	0.574929i	$-0.805030\pi$
$227$	2.73716	−	8.42412i	0.181672	−	0.559129i	0.999875	+	0.0158003i	$0.00502961\pi$
$228$	5.55899	+	4.03884i	0.368153	+	0.267479i
$229$	−17.8490	−	12.9681i	−1.17950	−	0.856953i	−0.187380	−	0.982287i	$-0.560000\pi$
$229$	−17.8490	−	12.9681i	−1.17950	−	0.856953i	−0.992115	+	0.125334i	$0.960000\pi$
$230$		0			0
$231$	0.874305	−	0.635220i	0.0575251	−	0.0417944i
$232$	9.03373			0.593093
$233$	9.33828	−	6.78466i	0.611771	−	0.444478i	−0.238267	−	0.971200i	$-0.576579\pi$
$233$	9.33828	−	6.78466i	0.611771	−	0.444478i	0.850037	+	0.526722i	$0.176579\pi$
$234$	−0.675571	−	2.07919i	−0.0441634	−	0.135921i
$235$		0			0
$236$	2.67261	−	8.22545i	0.173972	−	0.535431i
$237$	1.08540	+	3.34052i	0.0705043	+	0.216990i
$238$	1.73076	+	5.32672i	0.112188	+	0.345280i
$239$	−0.273457	+	0.841616i	−0.0176885	+	0.0544396i	−0.959511	−	0.281671i	$-0.909111\pi$
$239$	−0.273457	+	0.841616i	−0.0176885	+	0.0544396i	0.941823	+	0.336110i	$0.109111\pi$
$240$		0			0
$241$	3.91637	+	12.0534i	0.252276	+	0.776425i	0.994354	+	0.106112i	$0.0338402\pi$
$241$	3.91637	+	12.0534i	0.252276	+	0.776425i	−0.742078	+	0.670313i	$0.766160\pi$
$242$	−8.68031	+	6.30661i	−0.557991	+	0.405404i
$243$	1.00000			0.0641500
$244$	−10.1841	+	7.39919i	−0.651971	+	0.473684i
$245$		0			0
$246$	−2.60793	−	1.89477i	−0.166276	−	0.120806i
$247$	12.1530	+	8.82968i	0.773278	+	0.561819i
$248$	2.28829	−	7.04264i	0.145307	−	0.447208i
$249$	−13.1311			−0.832150
$250$		0			0
$251$	18.0966			1.14225			0.571124	−	0.820864i	$-0.306507\pi$
$251$	18.0966			1.14225			0.571124	+	0.820864i	$0.306507\pi$
$252$	−0.642040	+	1.97599i	−0.0404447	+	0.124476i
$253$	−1.62460	−	1.18034i	−0.102138	−	0.0742073i
$254$	12.1088	+	8.79756i	0.759774	+	0.552008i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−1.28053			−0.0798774			−0.0399387	−	0.999202i	$-0.512716\pi$
$257$	−1.28053			−0.0798774			−0.0399387	+	0.999202i	$0.512716\pi$
$258$	7.71737	−	5.60700i	0.480463	−	0.349077i
$259$	3.40742	+	10.4870i	0.211727	+	0.651629i
$260$		0			0
$261$	−2.79158	+	8.59159i	−0.172794	+	0.531806i
$262$	−4.28147	−	13.1770i	−0.264510	−	0.814079i
$263$	2.19842	+	6.76605i	0.135561	+	0.417213i	0.995677	−	0.0928855i	$-0.0296091\pi$
$263$	2.19842	+	6.76605i	0.135561	+	0.417213i	−0.860116	+	0.510098i	$0.829609\pi$
$264$	−0.160734	+	0.494689i	−0.00989251	+	0.0304460i
$265$		0			0
$266$	−4.41164	−	13.5776i	−0.270495	−	0.832498i
$267$	7.97594	−	5.79486i	0.488119	−	0.354640i
$268$	6.69385			0.408892
$269$	7.62892	−	5.54274i	0.465143	−	0.337947i	−0.330402	−	0.943840i	$-0.607184\pi$
$269$	7.62892	−	5.54274i	0.465143	−	0.337947i	0.795546	+	0.605894i	$0.207184\pi$
$270$		0			0
$271$	−1.11231	−	0.808141i	−0.0675681	−	0.0490911i	0.553488	−	0.832857i	$-0.313296\pi$
$271$	−1.11231	−	0.808141i	−0.0675681	−	0.0490911i	−0.621057	+	0.783766i	$0.713296\pi$
$272$	−2.18088	−	1.58450i	−0.132235	−	0.0960746i
$273$	−1.40362	+	4.31990i	−0.0849511	+	0.261452i
$274$	19.8939			1.20183
$275$		0			0
$276$	3.86067			0.232385
$277$	−6.05571	+	18.6375i	−0.363852	+	1.11982i	0.586845	+	0.809700i	$0.300370\pi$
$277$	−6.05571	+	18.6375i	−0.363852	+	1.11982i	−0.950697	+	0.310122i	$0.899630\pi$
$278$	4.56581	+	3.31725i	0.273839	+	0.198956i
$279$	5.99083	+	4.35259i	0.358662	+	0.260583i
$280$		0			0
$281$	2.29605	−	1.66817i	0.136971	−	0.0995150i	−0.517190	−	0.855871i	$-0.673022\pi$
$281$	2.29605	−	1.66817i	0.136971	−	0.0995150i	0.654161	+	0.756356i	$0.273022\pi$
$282$	9.26574			0.551767
$283$	−1.80699	+	1.31285i	−0.107414	+	0.0780411i	−0.640196	−	0.768212i	$-0.721147\pi$
$283$	−1.80699	+	1.31285i	−0.107414	+	0.0780411i	0.532781	+	0.846253i	$0.321147\pi$
$284$	−2.52436	−	7.76919i	−0.149793	−	0.461016i
$285$		0			0
$286$	−0.351396	+	1.08149i	−0.0207785	+	0.0639496i
$287$	2.06967	+	6.36978i	0.122169	+	0.375996i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	−3.00770	+	9.25673i	−0.176923	+	0.544514i
$290$		0			0
$291$	−3.32495	−	10.2331i	−0.194912	−	0.599877i
$292$	−3.10944	+	2.25914i	−0.181966	+	0.132206i
$293$	−24.0260			−1.40361			−0.701807	−	0.712367i	$-0.747623\pi$
$293$	−24.0260			−1.40361			−0.701807	+	0.712367i	$0.747623\pi$
$294$	−2.17078	+	1.57716i	−0.126602	+	0.0919821i
$295$		0			0
$296$	−4.29360	−	3.11949i	−0.249561	−	0.181316i
$297$	−0.420808	−	0.305735i	−0.0244177	−	0.0177405i
$298$	4.66479	−	14.3568i	0.270224	−	0.831664i
$299$	8.44016			0.488107
$300$		0			0
$301$	−19.8194			−1.14237
$302$	6.46937	−	19.9107i	0.372271	−	1.14573i
$303$	14.2711	+	10.3685i	0.819850	+	0.595656i
$304$	5.55899	+	4.03884i	0.318830	+	0.231643i
$305$		0			0
$306$	2.18088	−	1.58450i	0.124673	−	0.0905800i
$307$	−17.1204			−0.977111			−0.488556	−	0.872533i	$-0.662476\pi$
$307$	−17.1204			−0.977111			−0.488556	+	0.872533i	$0.662476\pi$
$308$	0.874305	−	0.635220i	0.0498182	−	0.0361950i
$309$	2.68770	+	8.27189i	0.152898	+	0.470572i
$310$		0			0
$311$	−6.22754	+	19.1664i	−0.353131	+	1.08683i	0.603954	+	0.797020i	$0.293591\pi$
$311$	−6.22754	+	19.1664i	−0.353131	+	1.08683i	−0.957085	+	0.289807i	$0.906409\pi$
$312$	−0.675571	−	2.07919i	−0.0382466	−	0.117711i
$313$	7.88127	+	24.2560i	0.445476	+	1.37103i	0.881961	+	0.471322i	$0.156223\pi$
$313$	7.88127	+	24.2560i	0.445476	+	1.37103i	−0.436486	+	0.899711i	$0.643777\pi$
$314$	1.76757	−	5.44002i	0.0997498	−	0.306998i
$315$		0			0
$316$	1.08540	+	3.34052i	0.0610586	+	0.187919i
$317$	−25.4988	+	18.5260i	−1.43215	+	1.04052i	−0.442544	+	0.896747i	$0.645924\pi$
$317$	−25.4988	+	18.5260i	−1.43215	+	1.04052i	−0.989610	+	0.143775i	$0.954076\pi$
$318$	2.43841			0.136739
$319$	3.80146	−	2.76193i	0.212841	−	0.154638i
$320$		0			0
$321$	−4.37660	−	3.17979i	−0.244278	−	0.177478i
$322$	−6.48932	−	4.71477i	−0.361636	−	0.262744i
$323$	−5.72394	+	17.6165i	−0.318488	+	0.980207i
$324$	1.00000			0.0555556
$325$		0			0
$326$	11.8950			0.658805
$327$	0.891135	−	2.74263i	0.0492799	−	0.151668i
$328$	−2.60793	−	1.89477i	−0.143999	−	0.104621i
$329$	−15.5746	−	11.3156i	−0.858656	−	0.623850i
$330$		0			0
$331$	5.90633	−	4.29120i	0.324641	−	0.235866i	−0.413512	−	0.910499i	$-0.635698\pi$
$331$	5.90633	−	4.29120i	0.324641	−	0.235866i	0.738153	+	0.674633i	$0.235698\pi$
$332$	−13.1311			−0.720663
$333$	4.29360	−	3.11949i	0.235288	−	0.170947i
$334$	2.76393	+	8.50651i	0.151236	+	0.465455i
$335$		0			0
$336$	−0.642040	+	1.97599i	−0.0350261	+	0.107799i
$337$	8.26459	+	25.4358i	0.450201	+	1.38558i	0.876678	+	0.481077i	$0.159754\pi$
$337$	8.26459	+	25.4358i	0.450201	+	1.38558i	−0.426477	+	0.904498i	$0.640246\pi$
$338$	2.54029	+	7.81822i	0.138174	+	0.425255i
$339$	1.96830	−	6.05780i	0.106903	−	0.329015i
$340$		0			0
$341$	−1.19025	−	3.66321i	−0.0644556	−	0.198374i
$342$	−5.55899	+	4.03884i	−0.300596	+	0.218396i
$343$	20.1187			1.08631
$344$	7.71737	−	5.60700i	0.416093	−	0.302309i
$345$		0			0
$346$	−13.2186	−	9.60385i	−0.710635	−	0.516306i
$347$	−3.94095	−	2.86327i	−0.211562	−	0.153708i	0.476958	−	0.878926i	$-0.341739\pi$
$347$	−3.94095	−	2.86327i	−0.211562	−	0.153708i	−0.688520	+	0.725217i	$0.741739\pi$
$348$	−2.79158	+	8.59159i	−0.149644	+	0.460557i
$349$	16.7173			0.894855			0.447428	−	0.894320i	$-0.352340\pi$
$349$	16.7173			0.894855			0.447428	+	0.894320i	$0.352340\pi$
$350$		0			0
$351$	2.18619			0.116690
$352$	−0.160734	+	0.494689i	−0.00856717	+	0.0263670i
$353$	21.9086	+	15.9175i	1.16608	+	0.847203i	0.990534	−	0.137269i	$-0.0438324\pi$
$353$	21.9086	+	15.9175i	1.16608	+	0.847203i	0.175541	+	0.984472i	$0.443832\pi$
$354$	6.99698	+	5.08361i	0.371885	+	0.270191i
$355$		0			0
$356$	7.97594	−	5.79486i	0.422724	−	0.307127i
$357$	−5.60085			−0.296428
$358$	2.97599	−	2.16219i	0.157286	−	0.114275i
$359$	−2.62299	−	8.07273i	−0.138436	−	0.426062i	0.857673	−	0.514196i	$-0.171910\pi$
$359$	−2.62299	−	8.07273i	−0.138436	−	0.426062i	−0.996109	+	0.0881339i	$0.971910\pi$
$360$		0			0
$361$	8.71879	−	26.8337i	0.458884	−	1.41230i
$362$	7.12261	+	21.9211i	0.374356	+	1.15215i
$363$	−3.31558	−	10.2043i	−0.174023	−	0.535587i
$364$	−1.40362	+	4.31990i	−0.0735698	+	0.226424i
$365$		0			0
$366$	−3.88998	−	11.9721i	−0.203333	−	0.625794i
$367$	10.3131	−	7.49289i	0.538339	−	0.391126i	−0.285129	−	0.958489i	$-0.592036\pi$
$367$	10.3131	−	7.49289i	0.538339	−	0.391126i	0.823468	+	0.567363i	$0.192036\pi$
$368$	3.86067			0.201251
$369$	2.60793	−	1.89477i	0.135764	−	0.0986380i
$370$		0			0
$371$	−4.09867	−	2.97786i	−0.212792	−	0.154603i
$372$	5.99083	+	4.35259i	0.310610	+	0.225671i
$373$	−3.38081	+	10.4051i	−0.175052	+	0.538754i	−0.999636	−	0.0269853i	$-0.991409\pi$
$373$	−3.38081	+	10.4051i	−0.175052	+	0.538754i	0.824584	+	0.565740i	$0.191409\pi$
$374$	−1.40217			−0.0725045
$375$		0			0
$376$	9.26574			0.477844
$377$	−6.10292	+	18.7829i	−0.314316	+	0.967367i
$378$	−1.68088	−	1.22123i	−0.0864552	−	0.0628134i
$379$	11.5124	+	8.36427i	0.591354	+	0.429644i	0.842799	−	0.538228i	$-0.180906\pi$
$379$	11.5124	+	8.36427i	0.591354	+	0.429644i	−0.251446	+	0.967871i	$0.580906\pi$
$380$		0			0
$381$	−12.1088	+	8.79756i	−0.620353	+	0.450713i
$382$	1.78768			0.0914658
$383$	−5.79595	+	4.21101i	−0.296159	+	0.215172i	−0.725935	−	0.687763i	$-0.758593\pi$
$383$	−5.79595	+	4.21101i	−0.296159	+	0.215172i	0.429776	+	0.902936i	$0.358593\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$		0			0
$386$	−2.03994	+	6.27828i	−0.103830	+	0.319556i
$387$	2.94777	+	9.07232i	0.149844	+	0.461172i
$388$	−3.32495	−	10.2331i	−0.168799	−	0.519509i
$389$	−0.283978	+	0.873994i	−0.0143982	+	0.0443133i	−0.957998	−	0.286776i	$-0.907416\pi$
$389$	−0.283978	+	0.873994i	−0.0143982	+	0.0443133i	0.943599	+	0.331090i	$0.107416\pi$
$390$		0			0
$391$	3.21602	+	9.89790i	0.162641	+	0.500558i
$392$	−2.17078	+	1.57716i	−0.109641	+	0.0796588i
$393$	13.8551			0.698899
$394$	−10.2401	+	7.43989i	−0.515891	+	0.374816i
$395$		0			0
$396$	−0.420808	−	0.305735i	−0.0211464	−	0.0153637i
$397$	17.6381	+	12.8148i	0.885232	+	0.643159i	0.934630	−	0.355620i	$-0.115730\pi$
$397$	17.6381	+	12.8148i	0.885232	+	0.643159i	−0.0493984	+	0.998779i	$0.515730\pi$
$398$	−1.92872	+	5.93600i	−0.0966782	+	0.297545i
$399$	14.2764			0.714712
$400$		0			0
$401$	22.8035			1.13875			0.569375	−	0.822078i	$-0.307185\pi$
$401$	22.8035			1.13875			0.569375	+	0.822078i	$0.307185\pi$
$402$	−2.06851	+	6.36623i	−0.103168	+	0.317519i
$403$	13.0971	+	9.51560i	0.652413	+	0.474006i
$404$	14.2711	+	10.3685i	0.710011	+	0.515853i
$405$		0			0
$406$	15.1846	−	11.0323i	0.753600	−	0.547523i
$407$	−2.76052			−0.136834
$408$	2.18088	−	1.58450i	0.107970	−	0.0784446i
$409$	1.54554	+	4.75668i	0.0764220	+	0.235203i	0.981969	−	0.189044i	$-0.0605389\pi$
$409$	1.54554	+	4.75668i	0.0764220	+	0.235203i	−0.905547	+	0.424247i	$0.860539\pi$
$410$		0			0
$411$	−6.14755	+	18.9202i	−0.303236	+	0.933265i
$412$	2.68770	+	8.27189i	0.132414	+	0.407527i
$413$	−5.55284	−	17.0899i	−0.273237	−	0.840938i
$414$	−1.19301	+	3.67171i	−0.0586333	+	0.180455i
$415$		0			0
$416$	−0.675571	−	2.07919i	−0.0331226	−	0.101941i
$417$	−4.56581	+	3.31725i	−0.223589	+	0.162447i
$418$	3.57408			0.174814
$419$	18.4661	−	13.4164i	0.902128	−	0.655434i	−0.0368836	−	0.999320i	$-0.511743\pi$
$419$	18.4661	−	13.4164i	0.902128	−	0.655434i	0.939012	+	0.343885i	$0.111743\pi$
$420$		0			0
$421$	−12.7124	−	9.23612i	−0.619566	−	0.450141i	0.233204	−	0.972428i	$-0.425079\pi$
$421$	−12.7124	−	9.23612i	−0.619566	−	0.450141i	−0.852770	+	0.522287i	$0.825079\pi$
$422$	−18.1850	−	13.2122i	−0.885234	−	0.643160i
$423$	−2.86327	+	8.81224i	−0.139217	+	0.428466i
$424$	2.43841			0.118419
$425$		0			0
$426$	8.16901			0.395790
$427$	−8.08215	+	24.8743i	−0.391123	+	1.20375i
$428$	−4.37660	−	3.17979i	−0.211551	−	0.153701i
$429$	−0.919967	−	0.668395i	−0.0444164	−	0.0322704i
$430$		0			0
$431$	7.73154	−	5.61729i	0.372415	−	0.270576i	−0.385796	−	0.922584i	$-0.626073\pi$
$431$	7.73154	−	5.61729i	0.372415	−	0.270576i	0.758212	+	0.652008i	$0.226073\pi$
$432$	1.00000			0.0481125
$433$	6.57096	−	4.77408i	0.315780	−	0.229428i	−0.418593	−	0.908174i	$-0.637476\pi$
$433$	6.57096	−	4.77408i	0.315780	−	0.229428i	0.734373	+	0.678747i	$0.237476\pi$
$434$	−4.75435	−	14.6324i	−0.228216	−	0.702377i
$435$		0			0
$436$	0.891135	−	2.74263i	0.0426776	−	0.131348i
$437$	−8.19753	−	25.2294i	−0.392141	−	1.20689i
$438$	−1.18770	−	3.65537i	−0.0567505	−	0.174660i
$439$	2.84899	−	8.76829i	0.135975	−	0.418488i	−0.859766	−	0.510689i	$-0.829390\pi$
$439$	2.84899	−	8.76829i	0.135975	−	0.418488i	0.995740	+	0.0922014i	$0.0293904\pi$
$440$		0			0
$441$	−0.829164	−	2.55190i	−0.0394840	−	0.121519i
$442$	4.76783	−	3.46403i	0.226782	−	0.164767i
$443$	−9.63232			−0.457645			−0.228823	−	0.973468i	$-0.573488\pi$
$443$	−9.63232			−0.457645			−0.228823	+	0.973468i	$0.573488\pi$
$444$	4.29360	−	3.11949i	0.203765	−	0.148044i
$445$		0			0
$446$	14.5056	+	10.5389i	0.686861	+	0.499033i
$447$	12.2126	+	8.87296i	0.577635	+	0.419677i
$448$	−0.642040	+	1.97599i	−0.0303335	+	0.0933570i
$449$	−21.3096			−1.00566			−0.502831	−	0.864385i	$-0.667708\pi$
$449$	−21.3096			−1.00566			−0.502831	+	0.864385i	$0.667708\pi$
$450$		0			0
$451$	−1.67674			−0.0789544
$452$	1.96830	−	6.05780i	0.0925810	−	0.284935i
$453$	16.9370	+	12.3055i	0.795772	+	0.578162i
$454$	7.16599	+	5.20640i	0.336317	+	0.244348i
$455$		0			0
$456$	−5.55899	+	4.03884i	−0.260324	+	0.189136i
$457$	13.4662			0.629923			0.314961	−	0.949104i	$-0.398008\pi$
$457$	13.4662			0.629923			0.314961	+	0.949104i	$0.398008\pi$
$458$	17.8490	−	12.9681i	0.834029	−	0.605958i
$459$	0.833023	+	2.56378i	0.0388822	+	0.119667i
$460$		0			0
$461$	10.1468	−	31.2286i	0.472582	−	1.45446i	−0.376608	−	0.926373i	$-0.622910\pi$
$461$	10.1468	−	31.2286i	0.472582	−	1.45446i	0.849191	−	0.528086i	$-0.177090\pi$
$462$	0.333955	+	1.02781i	0.0155370	+	0.0478179i
$463$	7.08596	+	21.8083i	0.329312	+	1.01352i	0.969456	+	0.245264i	$0.0788747\pi$
$463$	7.08596	+	21.8083i	0.329312	+	1.01352i	−0.640144	+	0.768255i	$0.721125\pi$
$464$	−2.79158	+	8.59159i	−0.129596	+	0.398854i
$465$		0			0
$466$	3.56690	+	10.9778i	0.165234	+	0.508537i
$467$	16.8551	−	12.2459i	0.779960	−	0.566674i	−0.125007	−	0.992156i	$-0.539895\pi$
$467$	16.8551	−	12.2459i	0.779960	−	0.566674i	0.904967	+	0.425482i	$0.139895\pi$
$468$	2.18619			0.101057
$469$	11.2516	−	8.17475i	0.519549	−	0.377475i
$470$		0			0
$471$	4.62756	+	3.36212i	0.213227	+	0.154918i
$472$	6.99698	+	5.08361i	0.322062	+	0.233992i
$473$	1.53328	−	4.71894i	0.0705001	−	0.216977i
$474$	−3.51243			−0.161331
$475$		0			0
$476$	−5.60085			−0.256714
$477$	−0.753509	+	2.31906i	−0.0345008	+	0.106183i
$478$	−0.715921	−	0.520147i	−0.0327455	−	0.0237910i
$479$	−10.9401	−	7.94842i	−0.499864	−	0.363172i	0.309101	−	0.951029i	$-0.399972\pi$
$479$	−10.9401	−	7.94842i	−0.499864	−	0.363172i	−0.808965	+	0.587857i	$0.799972\pi$
$480$		0			0
$481$	9.38664	−	6.81980i	0.427994	−	0.310956i
$482$	−12.6736			−0.577269
$483$	6.48932	−	4.71477i	0.295274	−	0.214529i
$484$	−3.31558	−	10.2043i	−0.150708	−	0.463832i
$485$		0			0
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−8.22690	−	25.3198i	−0.372796	−	1.14735i	−0.944953	−	0.327205i	$-0.893893\pi$
$487$	−8.22690	−	25.3198i	−0.372796	−	1.14735i	0.572157	−	0.820144i	$-0.306107\pi$
$488$	−3.88998	−	11.9721i	−0.176091	−	0.541953i
$489$	−3.67577	+	11.3129i	−0.166224	+	0.511585i
$490$		0			0
$491$	−3.71521	−	11.4342i	−0.167665	−	0.516020i	0.831558	−	0.555438i	$-0.187449\pi$
$491$	−3.71521	−	11.4342i	−0.167665	−	0.516020i	−0.999223	+	0.0394184i	$0.987449\pi$
$492$	2.60793	−	1.89477i	0.117575	−	0.0854230i
$493$	−24.3524			−1.09678
$494$	−12.1530	+	8.82968i	−0.546790	+	0.397266i
$495$		0			0
$496$	5.99083	+	4.35259i	0.268996	+	0.195437i
$497$	−13.7311	−	9.97625i	−0.615925	−	0.447496i
$498$	4.05774	−	12.4884i	0.181831	−	0.559620i
$499$	−27.3600			−1.22480			−0.612400	−	0.790548i	$-0.709796\pi$
$499$	−27.3600			−1.22480			−0.612400	+	0.790548i	$0.709796\pi$
$500$		0			0
$501$	−8.94427			−0.399601
$502$	−5.59216	+	17.2109i	−0.249590	+	0.768161i
$503$	−7.41268	−	5.38563i	−0.330515	−	0.240133i	0.410134	−	0.912025i	$-0.365482\pi$
$503$	−7.41268	−	5.38563i	−0.330515	−	0.240133i	−0.740649	+	0.671892i	$0.765482\pi$
$504$	−1.68088	−	1.22123i	−0.0748724	−	0.0543980i
$505$		0			0
$506$	1.62460	−	1.18034i	0.0722222	−	0.0524725i
$507$	−8.22056			−0.365088
$508$	−12.1088	+	8.79756i	−0.537241	+	0.390329i
$509$	−0.725667	−	2.23337i	−0.0321646	−	0.0989925i	0.933685	−	0.358094i	$-0.116573\pi$
$509$	−0.725667	−	2.23337i	−0.0321646	−	0.0989925i	−0.965850	+	0.259102i	$0.916573\pi$
$510$		0			0
$511$	−2.46767	+	7.59470i	−0.109163	+	0.335970i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−2.12334	−	6.53498i	−0.0937480	−	0.288527i
$514$	0.395706	−	1.21786i	0.0174538	−	0.0537174i
$515$		0			0
$516$	2.94777	+	9.07232i	0.129769	+	0.399386i
$517$	3.89910	−	2.83286i	0.171482	−	0.124589i
$518$	−11.0267			−0.484483
$519$	13.2186	−	9.60385i	0.580231	−	0.421562i
$520$		0			0
$521$	1.24129	+	0.901848i	0.0543818	+	0.0395107i	0.614644	−	0.788805i	$-0.289300\pi$
$521$	1.24129	+	0.901848i	0.0543818	+	0.0395107i	−0.560262	+	0.828315i	$0.689300\pi$
$522$	−7.30844	−	5.30989i	−0.319882	−	0.232408i
$523$	12.8508	−	39.5506i	0.561926	−	1.72943i	−0.114988	−	0.993367i	$-0.536683\pi$
$523$	12.8508	−	39.5506i	0.561926	−	1.72943i	0.676914	−	0.736062i	$-0.263317\pi$
$524$	13.8551			0.605265
$525$		0			0
$526$	−7.11425			−0.310196
$527$	−6.16859	+	18.9850i	−0.268708	+	0.826999i
$528$	−0.420808	−	0.305735i	−0.0183133	−	0.0133054i
$529$	6.54920	+	4.75827i	0.284748	+	0.206881i
$530$		0			0
$531$	−6.99698	+	5.08361i	−0.303643	+	0.220610i
$532$	14.2764			0.618959
$533$	5.70144	−	4.14234i	0.246957	−	0.179425i
$534$	3.04654	+	9.37628i	0.131837	+	0.405751i
$535$		0			0
$536$	−2.06851	+	6.36623i	−0.0893462	+	0.274979i
$537$	1.13673	+	3.49849i	0.0490535	+	0.150971i
$538$	2.91399	+	8.96833i	0.125631	+	0.386652i
$539$	−0.431287	+	1.32737i	−0.0185769	+	0.0571737i
$540$		0			0
$541$	5.88428	+	18.1100i	0.252985	+	0.778608i	0.994220	+	0.107362i	$0.0342404\pi$
$541$	5.88428	+	18.1100i	0.252985	+	0.778608i	−0.741235	+	0.671246i	$0.765760\pi$
$542$	1.11231	−	0.808141i	0.0477778	−	0.0347126i
$543$	−23.0493			−0.989138
$544$	2.18088	−	1.58450i	0.0935045	−	0.0679350i
$545$		0			0
$546$	−3.67473	−	2.66985i	−0.157264	−	0.114259i
$547$	−22.1030	−	16.0588i	−0.945057	−	0.686624i	0.00457542	−	0.999990i	$-0.498544\pi$
$547$	−22.1030	−	16.0588i	−0.945057	−	0.686624i	−0.949633	+	0.313365i	$0.898544\pi$
$548$	−6.14755	+	18.9202i	−0.262610	+	0.808231i
$549$	12.5882			0.537253
$550$		0			0
$551$	62.0734			2.64441
$552$	−1.19301	+	3.67171i	−0.0507779	+	0.156278i
$553$	5.90398	+	4.28949i	0.251063	+	0.182408i
$554$	−15.8540	−	11.5186i	−0.673574	−	0.489380i
$555$		0			0
$556$	−4.56581	+	3.31725i	−0.193633	+	0.140683i
$557$	−9.89921			−0.419443			−0.209721	−	0.977761i	$-0.567256\pi$
$557$	−9.89921			−0.419443			−0.209721	+	0.977761i	$0.567256\pi$
$558$	−5.99083	+	4.35259i	−0.253612	+	0.184260i
$559$	6.44440	+	19.8338i	0.272569	+	0.838881i
$560$		0			0
$561$	0.433294	−	1.33354i	0.0182937	−	0.0563022i
$562$	0.877011	+	2.69916i	0.0369945	+	0.113857i
$563$	0.621694	+	1.91338i	0.0262013	+	0.0806392i	0.963302	−	0.268420i	$-0.0865013\pi$
$563$	0.621694	+	1.91338i	0.0262013	+	0.0806392i	−0.937101	+	0.349059i	$0.886501\pi$
$564$	−2.86327	+	8.81224i	−0.120565	+	0.371062i
$565$		0			0
$566$	−0.690208	−	2.12424i	−0.0290116	−	0.0892886i
$567$	1.68088	−	1.22123i	0.0705904	−	0.0512869i
$568$	8.16901			0.342764
$569$	−19.0969	+	13.8747i	−0.800585	+	0.581659i	−0.911086	−	0.412217i	$-0.864755\pi$
$569$	−19.0969	+	13.8747i	−0.800585	+	0.581659i	0.110501	+	0.993876i	$0.464755\pi$
$570$		0			0
$571$	−17.1782	−	12.4807i	−0.718886	−	0.522301i	0.167142	−	0.985933i	$-0.446546\pi$
$571$	−17.1782	−	12.4807i	−0.718886	−	0.522301i	−0.886028	+	0.463631i	$0.846546\pi$
$572$	−0.919967	−	0.668395i	−0.0384657	−	0.0279470i
$573$	−0.552424	+	1.70019i	−0.0230779	+	0.0710263i
$574$	−6.69758			−0.279552
$575$		0			0
$576$	1.00000			0.0416667
$577$	14.0095	−	43.1167i	0.583222	−	1.79497i	−0.0230749	−	0.999734i	$-0.507346\pi$
$577$	14.0095	−	43.1167i	0.583222	−	1.79497i	0.606297	−	0.795238i	$-0.292654\pi$
$578$	−7.87425	−	5.72098i	−0.327526	−	0.237961i
$579$	−5.34063	−	3.88019i	−0.221949	−	0.161255i
$580$		0			0
$581$	−22.0718	+	16.0361i	−0.915694	+	0.665291i
$582$	10.7598			0.446006
$583$	1.02610	−	0.745506i	0.0424967	−	0.0308757i
$584$	−1.18770	−	3.65537i	−0.0491474	−	0.151260i
$585$		0			0
$586$	7.42445	−	22.8501i	0.306701	−	0.943929i
$587$	−5.04421	−	15.5245i	−0.208197	−	0.640764i	−0.999567	−	0.0294265i	$-0.990632\pi$
$587$	−5.04421	−	15.5245i	−0.208197	−	0.640764i	0.791370	−	0.611337i	$-0.209368\pi$
$588$	−0.829164	−	2.55190i	−0.0341941	−	0.105239i
$589$	15.7235	−	48.3920i	0.647877	−	1.99396i
$590$		0			0
$591$	−3.91138	−	12.0380i	−0.160893	−	0.495177i
$592$	4.29360	−	3.11949i	0.176466	−	0.128210i
$593$	−32.8357			−1.34840			−0.674199	−	0.738549i	$-0.735511\pi$
$593$	−32.8357			−1.34840			−0.674199	+	0.738549i	$0.735511\pi$
$594$	0.420808	−	0.305735i	0.0172660	−	0.0125444i
$595$		0			0
$596$	12.2126	+	8.87296i	0.500247	+	0.363451i
$597$	−5.04946	−	3.66865i	−0.206661	−	0.150148i
$598$	−2.60815	+	8.02707i	−0.106655	+	0.328251i
$599$	−13.1905			−0.538947			−0.269474	−	0.963008i	$-0.586850\pi$
$599$	−13.1905			−0.538947			−0.269474	+	0.963008i	$0.586850\pi$
$600$		0			0
$601$	−19.1992			−0.783152			−0.391576	−	0.920146i	$-0.628070\pi$
$601$	−19.1992			−0.783152			−0.391576	+	0.920146i	$0.628070\pi$
$602$	6.12454	−	18.8494i	0.249618	−	0.768244i
$603$	−5.41544	−	3.93455i	−0.220534	−	0.160227i
$604$	16.9370	+	12.3055i	0.689158	+	0.500703i
$605$		0			0
$606$	−14.2711	+	10.3685i	−0.579722	+	0.421193i
$607$	6.54268			0.265559			0.132779	−	0.991146i	$-0.457610\pi$
$607$	6.54268			0.265559			0.132779	+	0.991146i	$0.457610\pi$
$608$	−5.55899	+	4.03884i	−0.225447	+	0.163797i
$609$	5.80001	+	17.8506i	0.235028	+	0.723343i
$610$		0			0
$611$	−6.25966	+	19.2653i	−0.253239	+	0.779389i
$612$	0.833023	+	2.56378i	0.0336729	+	0.103635i
$613$	−2.88375	−	8.87528i	−0.116474	−	0.358469i	0.875778	−	0.482714i	$-0.160349\pi$
$613$	−2.88375	−	8.87528i	−0.116474	−	0.358469i	−0.992252	+	0.124245i	$0.960349\pi$
$614$	5.29049	−	16.2824i	0.213507	−	0.657106i
$615$		0			0
$616$	0.333955	+	1.02781i	0.0134554	+	0.0414115i
$617$	26.6989	−	19.3979i	1.07486	−	0.780929i	0.0980778	−	0.995179i	$-0.468731\pi$
$617$	26.6989	−	19.3979i	1.07486	−	0.780929i	0.976779	+	0.214250i	$0.0687306\pi$
$618$	−8.69758			−0.349868
$619$	−22.7569	+	16.5339i	−0.914678	+	0.664553i	−0.942194	−	0.335069i	$-0.891240\pi$
$619$	−22.7569	+	16.5339i	−0.914678	+	0.664553i	0.0275155	+	0.999621i	$0.491240\pi$
$620$		0			0
$621$	−3.12334	−	2.26924i	−0.125336	−	0.0910616i
$622$	−16.3039	−	11.8455i	−0.653727	−	0.474961i
$623$	6.32974	−	19.4809i	0.253596	−	0.780487i
$624$	2.18619			0.0875177
$625$		0			0
$626$	−25.5043			−1.01936
$627$	−1.10445	+	3.39915i	−0.0441075	+	0.135749i
$628$	4.62756	+	3.36212i	0.184660	+	0.134163i
$629$	11.5743	+	8.40925i	0.461499	+	0.335299i
$630$		0			0
$631$	1.93909	−	1.40883i	0.0771940	−	0.0560847i	−0.548519	−	0.836138i	$-0.684808\pi$
$631$	1.93909	−	1.40883i	0.0771940	−	0.0560847i	0.625713	+	0.780053i	$0.284808\pi$
$632$	−3.51243			−0.139717
$633$	18.1850	−	13.2122i	0.722790	−	0.525138i
$634$	−9.73967	−	29.9756i	−0.386812	−	1.19048i
$635$		0			0
$636$	−0.753509	+	2.31906i	−0.0298786	+	0.0919568i
$637$	−1.81271	−	5.57895i	−0.0718223	−	0.221046i
$638$	1.45203	+	4.46889i	0.0574864	+	0.176925i
$639$	−2.52436	+	7.76919i	−0.0998622	+	0.307344i
$640$		0			0
$641$	3.76246	+	11.5797i	0.148608	+	0.457370i	0.997457	−	0.0712658i	$-0.0227039\pi$
$641$	3.76246	+	11.5797i	0.148608	+	0.457370i	−0.848849	+	0.528635i	$0.822704\pi$
$642$	4.37660	−	3.17979i	0.172731	−	0.125496i
$643$	27.0249			1.06576			0.532878	−	0.846192i	$-0.321110\pi$
$643$	27.0249			1.06576			0.532878	+	0.846192i	$0.321110\pi$
$644$	6.48932	−	4.71477i	0.255715	−	0.185788i
$645$		0			0
$646$	−14.9855	−	10.8876i	−0.589595	−	0.428366i
$647$	−27.4417	−	19.9375i	−1.07884	−	0.783826i	−0.101363	−	0.994850i	$-0.532320\pi$
$647$	−27.4417	−	19.9375i	−1.07884	−	0.783826i	−0.977481	+	0.211024i	$0.932320\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	4.49862			0.176586
$650$		0			0
$651$	15.3854			0.603001
$652$	−3.67577	+	11.3129i	−0.143954	+	0.443046i
$653$	−12.0163	−	8.73039i	−0.470236	−	0.341646i	0.327297	−	0.944921i	$-0.393862\pi$
$653$	−12.0163	−	8.73039i	−0.470236	−	0.341646i	−0.797533	+	0.603275i	$0.793862\pi$
$654$	2.33302	+	1.69504i	0.0912284	+	0.0662813i
$655$		0			0
$656$	2.60793	−	1.89477i	0.101823	−	0.0739785i
$657$	3.84348			0.149948
$658$	15.5746	−	11.3156i	0.607162	−	0.441129i
$659$	1.45835	+	4.48835i	0.0568094	+	0.174841i	0.975435	−	0.220288i	$-0.0706997\pi$
$659$	1.45835	+	4.48835i	0.0568094	+	0.174841i	−0.918625	+	0.395129i	$0.870700\pi$
$660$		0			0
$661$	1.08059	−	3.32571i	0.0420300	−	0.129355i	−0.927840	−	0.372979i	$-0.878336\pi$
$661$	1.08059	−	3.32571i	0.0420300	−	0.129355i	0.969870	+	0.243624i	$0.0783363\pi$
$662$	2.25602	+	6.94330i	0.0876826	+	0.269859i
$663$	1.82115	+	5.60491i	0.0707275	+	0.217677i
$664$	4.05774	−	12.4884i	0.157471	−	0.484645i
$665$		0			0
$666$	1.64001	+	5.04743i	0.0635491	+	0.195584i
$667$	28.2155	−	20.4997i	1.09251	−	0.793753i
$668$	−8.94427			−0.346064
$669$	−14.5056	+	10.5389i	−0.560819	+	0.407459i
$670$		0			0
$671$	−5.29723	−	3.84867i	−0.204497	−	0.148576i
$672$	−1.68088	−	1.22123i	−0.0648414	−	0.0471100i
$673$	−7.61244	+	23.4287i	−0.293438	+	0.903110i	0.690303	+	0.723520i	$0.257477\pi$
$673$	−7.61244	+	23.4287i	−0.293438	+	0.903110i	−0.983742	+	0.179590i	$0.942523\pi$
$674$	−26.7448			−1.03017
$675$		0			0
$676$	−8.22056			−0.316176
$677$	−9.21651	+	28.3655i	−0.354219	+	1.09017i	0.602242	+	0.798314i	$0.294274\pi$
$677$	−9.21651	+	28.3655i	−0.354219	+	1.09017i	−0.956461	+	0.291861i	$0.905726\pi$
$678$	5.15307	+	3.74393i	0.197903	+	0.143785i
$679$	−18.0859	−	13.1402i	−0.694072	−	0.504273i
$680$		0			0
$681$	−7.16599	+	5.20640i	−0.274601	+	0.199510i
$682$	3.85173			0.147490
$683$	−21.0776	+	15.3138i	−0.806511	+	0.585964i	−0.912817	−	0.408369i	$-0.866098\pi$
$683$	−21.0776	+	15.3138i	−0.806511	+	0.585964i	0.106306	+	0.994333i	$0.466098\pi$
$684$	−2.12334	−	6.53498i	−0.0811881	−	0.249871i
$685$		0			0
$686$	−6.21702	+	19.1340i	−0.237367	+	0.730540i
$687$	6.81771	+	20.9828i	0.260112	+	0.800542i
$688$	2.94777	+	9.07232i	0.112383	+	0.345879i
$689$	−1.64732	+	5.06992i	−0.0627577	+	0.193148i
$690$		0			0
$691$	10.6313	+	32.7197i	0.404432	+	1.24471i	0.921368	+	0.388690i	$0.127072\pi$
$691$	10.6313	+	32.7197i	0.404432	+	1.24471i	−0.516936	+	0.856024i	$0.672928\pi$
$692$	13.2186	−	9.60385i	0.502495	−	0.365084i
$693$	−1.08070			−0.0410524
$694$	3.94095	−	2.86327i	0.149597	−	0.108688i
$695$		0			0
$696$	−7.30844	−	5.30989i	−0.277026	−	0.201271i
$697$	7.03025	+	5.10777i	0.266290	+	0.193471i
$698$	−5.16592	+	15.8991i	−0.195533	+	0.601789i
$699$	−11.5427			−0.436587
$700$		0			0
$701$	13.2937			0.502095			0.251047	−	0.967975i	$-0.419225\pi$
$701$	13.2937			0.502095			0.251047	+	0.967975i	$0.419225\pi$
$702$	−0.675571	+	2.07919i	−0.0254978	+	0.0784741i
$703$	−29.5026	−	21.4349i	−1.11271	−	0.808432i
$704$	−0.420808	−	0.305735i	−0.0158598	−	0.0115228i
$705$		0			0
$706$	−21.9086	+	15.9175i	−0.824540	+	0.599063i
$707$	36.6503			1.37838
$708$	−6.99698	+	5.08361i	−0.262963	+	0.191054i
$709$	−2.24820	−	6.91924i	−0.0844329	−	0.259858i	0.899923	−	0.436049i	$-0.143622\pi$
$709$	−2.24820	−	6.91924i	−0.0844329	−	0.259858i	−0.984356	+	0.176191i	$0.943622\pi$
$710$		0			0
$711$	1.08540	−	3.34052i	0.0407057	−	0.125279i
$712$	3.04654	+	9.37628i	0.114174	+	0.351391i
$713$	−8.83434	−	27.1893i	−0.330849	−	1.01825i
$714$	1.73076	−	5.32672i	0.0647720	−	0.199348i
$715$		0			0
$716$	1.13673	+	3.49849i	0.0424815	+	0.130745i
$717$	0.715921	−	0.520147i	0.0267366	−	0.0194252i
$718$	8.48817			0.316776
$719$	26.0071	−	18.8953i	0.969902	−	0.704675i	0.0144727	−	0.999895i	$-0.495393\pi$
$719$	26.0071	−	18.8953i	0.969902	−	0.704675i	0.955429	+	0.295220i	$0.0953930\pi$
$720$		0			0
$721$	14.6196	+	10.6218i	0.544462	+	0.395575i
$722$	22.8261	+	16.5841i	0.849499	+	0.617197i
$723$	3.91637	−	12.0534i	0.145651	−	0.448269i
$724$	−23.0493			−0.856619
$725$		0			0
$726$	10.7294			0.398207
$727$	−0.965858	+	2.97260i	−0.0358217	+	0.110248i	−0.967369	−	0.253374i	$-0.918460\pi$
$727$	−0.965858	+	2.97260i	−0.0358217	+	0.110248i	0.931547	+	0.363621i	$0.118460\pi$
$728$	−3.67473	−	2.66985i	−0.136195	−	0.0989511i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	−20.8039	+	15.1149i	−0.769458	+	0.559044i
$732$	12.5882			0.465275
$733$	−37.5047	+	27.2488i	−1.38527	+	1.00646i	−0.388902	+	0.921279i	$0.627146\pi$
$733$	−37.5047	+	27.2488i	−1.38527	+	1.00646i	−0.996366	+	0.0851773i	$0.972854\pi$
$734$	3.93925	+	12.1238i	0.145400	+	0.447496i
$735$		0			0
$736$	−1.19301	+	3.67171i	−0.0439750	+	0.135341i
$737$	1.07593	+	3.31138i	0.0396324	+	0.121976i
$738$	0.996141	+	3.06581i	0.0366685	+	0.112854i
$739$	−14.8417	+	45.6779i	−0.545959	+	1.68029i	0.172739	+	0.984968i	$0.444738\pi$
$739$	−14.8417	+	45.6779i	−0.545959	+	1.68029i	−0.718698	+	0.695322i	$0.755262\pi$
$740$		0			0
$741$	−4.64204	−	14.2867i	−0.170530	−	0.524836i
$742$	4.09867	−	2.97786i	0.150467	−	0.109321i
$743$	2.88963			0.106010			0.0530051	−	0.998594i	$-0.483120\pi$
$743$	2.88963			0.106010			0.0530051	+	0.998594i	$0.483120\pi$
$744$	−5.99083	+	4.35259i	−0.219635	+	0.159574i
$745$		0			0
$746$	−8.85108	−	6.43069i	−0.324061	−	0.235444i
$747$	10.6233	+	7.71827i	0.388686	+	0.282397i
$748$	0.433294	−	1.33354i	0.0158428	−	0.0487591i
$749$	−11.2398			−0.410693
$750$		0			0
$751$	−39.4965			−1.44125			−0.720624	−	0.693326i	$-0.756144\pi$
$751$	−39.4965			−1.44125			−0.720624	+	0.693326i	$0.756144\pi$
$752$	−2.86327	+	8.81224i	−0.104413	+	0.321349i
$753$	−14.6405	−	10.6369i	−0.533529	−	0.387631i
$754$	−15.9777	−	11.6084i	−0.581872	−	0.422755i
$755$		0			0
$756$	1.68088	−	1.22123i	0.0611331	−	0.0444158i
$757$	−25.4654			−0.925555			−0.462777	−	0.886475i	$-0.653147\pi$
$757$	−25.4654			−0.925555			−0.462777	+	0.886475i	$0.653147\pi$
$758$	−11.5124	+	8.36427i	−0.418150	+	0.303804i
$759$	0.620541	+	1.90983i	0.0225242	+	0.0693224i
$760$		0			0
$761$	12.8769	−	39.6310i	0.466787	−	1.43662i	−0.389934	−	0.920843i	$-0.627502\pi$
$761$	12.8769	−	39.6310i	0.466787	−	1.43662i	0.856721	−	0.515780i	$-0.172498\pi$
$762$	−4.62515	−	14.2348i	−0.167552	−	0.515671i
$763$	−1.85150	−	5.69832i	−0.0670287	−	0.206293i
$764$	−0.552424	+	1.70019i	−0.0199860	+	0.0615106i
$765$		0			0
$766$	−2.21386	−	6.81355i	−0.0799899	−	0.246184i
$767$	−15.2967	+	11.1137i	−0.552334	+	0.401294i
$768$	1.00000			0.0360844
$769$	−1.67667	+	1.21817i	−0.0604621	+	0.0439283i	−0.617606	−	0.786488i	$-0.711897\pi$
$769$	−1.67667	+	1.21817i	−0.0604621	+	0.0439283i	0.557144	+	0.830416i	$0.311897\pi$
$770$		0			0
$771$	1.03597	+	0.752678i	0.0373096	+	0.0271070i
$772$	−5.34063	−	3.88019i	−0.192213	−	0.139651i
$773$	2.46892	−	7.59855i	0.0888009	−	0.273301i	−0.896788	−	0.442461i	$-0.854105\pi$
$773$	2.46892	−	7.59855i	0.0888009	−	0.273301i	0.985589	+	0.169160i	$0.0541055\pi$
$774$	−9.53920			−0.342879
$775$		0			0
$776$	10.7598			0.386253
$777$	3.40742	−	10.4870i	0.122241	−	0.376218i
$778$	−0.743464	−	0.540158i	−0.0266545	−	0.0193656i
$779$	−17.9199	−	13.0195i	−0.642045	−	0.466473i
$780$		0			0
$781$	3.43758	−	2.49755i	0.123006	−	0.0893693i
$782$	−10.4073			−0.372163
$783$	7.30844	−	5.30989i	0.261182	−	0.189760i
$784$	−0.829164	−	2.55190i	−0.0296130	−	0.0911394i
$785$		0			0
$786$	−4.28147	+	13.1770i	−0.152715	+	0.470009i
$787$	5.53459	+	17.0337i	0.197287	+	0.607186i	0.999942	+	0.0107432i	$0.00341974\pi$
$787$	5.53459	+	17.0337i	0.197287	+	0.607186i	−0.802656	+	0.596443i	$0.796580\pi$
$788$	−3.91138	−	12.0380i	−0.139337	−	0.428836i
$789$	2.19842	−	6.76605i	0.0782659	−	0.240878i
$790$		0			0
$791$	−4.08950	−	12.5862i	−0.145406	−	0.447514i
$792$	0.420808	−	0.305735i	0.0149528	−	0.0108638i
$793$	27.5203			0.977276
$794$	−17.6381	+	12.8148i	−0.625954	+	0.454782i
$795$		0			0
$796$	−5.04946	−	3.66865i	−0.178973	−	0.130032i
$797$	−21.2401	−	15.4319i	−0.752364	−	0.546625i	0.144195	−	0.989549i	$-0.453941\pi$
$797$	−21.2401	−	15.4319i	−0.752364	−	0.546625i	−0.896559	+	0.442925i	$0.853941\pi$
$798$	−4.41164	+	13.5776i	−0.156170	+	0.480643i
$799$	−24.9778			−0.883652
$800$		0			0
$801$	−9.85880			−0.348344
$802$	−7.04666	+	21.6874i	−0.248826	+	0.765808i
$803$	−1.61737	−	1.17509i	−0.0570756	−	0.0414679i
$804$	−5.41544	−	3.93455i	−0.190988	−	0.138761i
$805$		0			0
$806$	−13.0971	+	9.51560i	−0.461326	+	0.335173i
$807$	−9.42986			−0.331947
$808$	−14.2711	+	10.3685i	−0.502054	+	0.364763i
$809$	9.12577	+	28.0862i	0.320845	+	0.987459i	0.973281	+	0.229616i	$0.0737470\pi$
$809$	9.12577	+	28.0862i	0.320845	+	0.987459i	−0.652436	+	0.757844i	$0.726253\pi$
$810$		0			0
$811$	9.10810	−	28.0318i	0.319829	−	0.984331i	−0.653893	−	0.756587i	$-0.726865\pi$
$811$	9.10810	−	28.0318i	0.319829	−	0.984331i	0.973721	−	0.227744i	$-0.0731348\pi$
$812$	5.80001	+	17.8506i	0.203540	+	0.626433i
$813$	0.424865	+	1.30760i	0.0149007	+	0.0458595i
$814$	0.853047	−	2.62541i	0.0298993	−	0.0920205i
$815$		0			0
$816$	0.833023	+	2.56378i	0.0291616	+	0.0897502i
$817$	53.0283	−	38.5273i	1.85523	−	1.34790i
$818$	−5.00147			−0.174872
$819$	3.67473	−	2.66985i	0.128405	−	0.0932920i
$820$		0			0
$821$	−36.2580	−	26.3430i	−1.26541	−	0.919377i	−0.266404	−	0.963862i	$-0.585835\pi$
$821$	−36.2580	−	26.3430i	−1.26541	−	0.919377i	−0.999010	+	0.0444846i	$0.985835\pi$
$822$	−16.0945	−	11.6933i	−0.561360	−	0.407852i
$823$	6.72529	−	20.6983i	0.234429	−	0.721498i	−0.762768	−	0.646673i	$-0.776160\pi$
$823$	6.72529	−	20.6983i	0.234429	−	0.721498i	0.997197	−	0.0748255i	$-0.0238400\pi$
$824$	−8.69758			−0.302995
$825$		0			0
$826$	17.9694			0.625234
$827$	−5.90446	+	18.1721i	−0.205318	+	0.631905i	0.794382	+	0.607419i	$0.207795\pi$
$827$	−5.90446	+	18.1721i	−0.205318	+	0.631905i	−0.999700	+	0.0244861i	$0.992205\pi$
$828$	−3.12334	−	2.26924i	−0.108544	−	0.0788616i
$829$	29.3862	+	21.3503i	1.02063	+	0.741528i	0.966411	−	0.257001i	$-0.0827345\pi$
$829$	29.3862	+	21.3503i	1.02063	+	0.741528i	0.0542146	+	0.998529i	$0.482735\pi$
$830$		0			0
$831$	15.8540	−	11.5186i	0.549971	−	0.399577i
$832$	2.18619			0.0757926
$833$	5.85181	−	4.25159i	0.202753	−	0.147309i
$834$	−1.74398	−	5.36743i	−0.0603892	−	0.185859i
$835$		0			0
$836$	−1.10445	+	3.39915i	−0.0381983	+	0.117562i
$837$	−2.28829	−	7.04264i	−0.0790950	−	0.243429i
$838$	7.05342	+	21.7082i	0.243656	+	0.749897i
$839$	6.13673	−	18.8869i	0.211863	−	0.652049i	−0.787498	−	0.616317i	$-0.788624\pi$
$839$	6.13673	−	18.8869i	0.211863	−	0.652049i	0.999361	−	0.0357313i	$-0.0113761\pi$
$840$		0			0
$841$	16.2568	+	50.0334i	0.560581	+	1.72529i
$842$	12.7124	−	9.23612i	0.438099	−	0.318298i
$843$	−2.83807			−0.0977483
$844$	18.1850	−	13.2122i	0.625955	−	0.454783i
$845$		0			0
$846$	−7.49614	−	5.44627i	−0.257723	−	0.187246i
$847$	−18.0349	−	13.1031i	−0.619687	−	0.450229i
$848$	−0.753509	+	2.31906i	−0.0258756	+	0.0796369i
$849$	2.23356			0.0766556
$850$		0			0
$851$	−20.4893			−0.702363
$852$	−2.52436	+	7.76919i	−0.0864832	+	0.266168i
$853$	−21.0621	−	15.3025i	−0.721153	−	0.523948i	0.165600	−	0.986193i	$-0.447044\pi$
$853$	−21.0621	−	15.3025i	−0.721153	−	0.523948i	−0.886752	+	0.462245i	$0.847044\pi$
$854$	−21.1594	−	15.3732i	−0.724058	−	0.526059i
$855$		0			0
$856$	4.37660	−	3.17979i	0.149589	−	0.108683i
$857$	34.8614			1.19084			0.595421	−	0.803414i	$-0.296985\pi$
$857$	34.8614			1.19084			0.595421	+	0.803414i	$0.296985\pi$
$858$	0.919967	−	0.668395i	0.0314071	−	0.0228186i
$859$	−4.67229	−	14.3798i	−0.159417	−	0.490634i	0.839165	−	0.543877i	$-0.183044\pi$
$859$	−4.67229	−	14.3798i	−0.159417	−	0.490634i	−0.998582	+	0.0532431i	$0.983044\pi$
$860$		0			0
$861$	2.06967	−	6.36978i	0.0705341	−	0.217081i
$862$	2.95319	+	9.08897i	0.100586	+	0.309572i
$863$	7.07738	+	21.7819i	0.240917	+	0.741466i	0.996281	+	0.0861610i	$0.0274599\pi$
$863$	7.07738	+	21.7819i	0.240917	+	0.741466i	−0.755364	+	0.655305i	$0.772540\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$		0			0
$866$	2.50988	+	7.72462i	0.0852892	+	0.262493i
$867$	7.87425	−	5.72098i	0.267424	−	0.194295i
$868$	15.3854			0.522215
$869$	−1.47806	+	1.07387i	−0.0501397	+	0.0364286i
$870$		0			0
$871$	−11.8392	−	8.60168i	−0.401156	−	0.291457i
$872$	2.33302	+	1.69504i	0.0790061	+	0.0574013i
$873$	−3.32495	+	10.2331i	−0.112532	+	0.346339i
$874$	26.5278			0.897315
$875$		0			0
$876$	3.84348			0.129859
$877$	−5.09493	+	15.6806i	−0.172043	+	0.529495i	−0.999486	−	0.0320550i	$-0.989795\pi$
$877$	−5.09493	+	15.6806i	−0.172043	+	0.529495i	0.827443	+	0.561550i	$0.189795\pi$
$878$	7.45875	+	5.41910i	0.251721	+	0.182886i
$879$	19.4375	+	14.1221i	0.655609	+	0.476328i
$880$		0			0
$881$	−18.7621	+	13.6315i	−0.632112	+	0.459257i	−0.857131	−	0.515098i	$-0.827756\pi$
$881$	−18.7621	+	13.6315i	−0.632112	+	0.459257i	0.225019	+	0.974354i	$0.427756\pi$
$882$	2.68323			0.0903491
$883$	−19.7980	+	14.3841i	−0.666254	+	0.484062i	−0.868769	−	0.495217i	$-0.835089\pi$
$883$	−19.7980	+	14.3841i	−0.666254	+	0.484062i	0.202515	+	0.979279i	$0.435089\pi$
$884$	1.82115	+	5.60491i	0.0612518	+	0.188514i
$885$		0			0
$886$	2.97655	−	9.16088i	0.0999991	−	0.307766i
$887$	1.22048	+	3.75624i	0.0409796	+	0.126122i	0.969453	−	0.245276i	$-0.0788785\pi$
$887$	1.22048	+	3.75624i	0.0409796	+	0.126122i	−0.928474	+	0.371398i	$0.878879\pi$
$888$	1.64001	+	5.04743i	0.0550352	+	0.169381i
$889$	−9.60960	+	29.5753i	−0.322296	+	0.991924i
$890$		0			0
$891$	0.160734	+	0.494689i	0.00538480	+	0.0165727i
$892$	−14.5056	+	10.5389i	−0.485684	+	0.352870i
$893$	63.6676			2.13055
$894$	−12.2126	+	8.87296i	−0.408450	+	0.296756i
$895$		0			0
$896$	−1.68088	−	1.22123i	−0.0561543	−	0.0407985i
$897$	−6.82823	−	4.96100i	−0.227988	−	0.165643i
$898$	6.58502	−	20.2666i	0.219745	−	0.676306i
$899$	66.8954			2.23109
$900$		0			0
$901$	−6.57325			−0.218987
$902$	0.518140	−	1.59467i	0.0172522	−	0.0530967i
$903$	16.0343	+	11.6496i	0.533587	+	0.387673i
$904$	5.15307	+	3.74393i	0.171389	+	0.124521i
$905$		0			0
$906$	−16.9370	+	12.3055i	−0.562695	+	0.408822i
$907$	−52.8637			−1.75531			−0.877656	−	0.479291i	$-0.840894\pi$
$907$	−52.8637			−1.75531			−0.877656	+	0.479291i	$0.840894\pi$
$908$	−7.16599	+	5.20640i	−0.237812	+	0.172780i
$909$	−5.45106	−	16.7766i	−0.180800	−	0.556446i
$910$		0			0
$911$	3.55654	−	10.9459i	0.117833	−	0.362654i	−0.874694	−	0.484676i	$-0.838938\pi$
$911$	3.55654	−	10.9459i	0.117833	−	0.362654i	0.992527	+	0.122021i	$0.0389377\pi$
$912$	−2.12334	−	6.53498i	−0.0703110	−	0.216395i
$913$	−2.11062	−	6.49582i	−0.0698513	−	0.214980i
$914$	−4.16129	+	12.8071i	−0.137643	+	0.423622i
$915$		0			0
$916$	6.81771	+	20.9828i	0.225264	+	0.693290i
$917$	23.2888	−	16.9203i	0.769066	−	0.558759i
$918$	−2.69572			−0.0889719
$919$	−25.1008	+	18.2368i	−0.828000	+	0.601577i	−0.918993	−	0.394274i	$-0.870996\pi$
$919$	−25.1008	+	18.2368i	−0.828000	+	0.601577i	0.0909927	+	0.995852i	$0.470996\pi$
$920$		0			0
$921$	13.8507	+	10.0631i	0.456395	+	0.331590i
$922$	26.5646	+	19.3003i	0.874858	+	0.635622i
$923$	−5.51874	+	16.9849i	−0.181652	+	0.559066i
$924$	−1.08070			−0.0355524
$925$		0			0
$926$	−22.9306			−0.753547
$927$	2.68770	−	8.27189i	0.0882757	−	0.271685i
$928$	−7.30844	−	5.30989i	−0.239911	−	0.174306i
$929$	9.67177	+	7.02695i	0.317320	+	0.230547i	0.735031	−	0.678033i	$-0.237167\pi$
$929$	9.67177	+	7.02695i	0.317320	+	0.230547i	−0.417711	+	0.908580i	$0.637167\pi$
$930$		0			0
$931$	−14.9161	+	10.8371i	−0.488854	+	0.355173i
$932$	−11.5427			−0.378095
$933$	16.3039	−	11.8455i	0.533766	−	0.387804i
$934$	6.43806	+	19.8143i	0.210660	+	0.648344i
$935$		0			0
$936$	−0.675571	+	2.07919i	−0.0220817	+	0.0679605i
$937$	−4.54042	−	13.9740i	−0.148329	−	0.456510i	0.849095	−	0.528240i	$-0.177148\pi$
$937$	−4.54042	−	13.9740i	−0.148329	−	0.456510i	−0.997424	+	0.0717304i	$0.977148\pi$
$938$	4.29772	+	13.2270i	0.140325	+	0.431877i
$939$	7.88127	−	24.2560i	0.257195	−	0.791566i
$940$		0			0
$941$	15.6185	+	48.0688i	0.509149	+	1.56700i	0.793682	+	0.608333i	$0.208162\pi$
$941$	15.6185	+	48.0688i	0.509149	+	1.56700i	−0.284533	+	0.958666i	$0.591838\pi$
$942$	−4.62756	+	3.36212i	−0.150774	+	0.109544i
$943$	−12.4452			−0.405271
$944$	−6.99698	+	5.08361i	−0.227732	+	0.165457i
$945$		0			0
$946$	4.01417	+	2.91646i	0.130512	+	0.0948224i
$947$	−32.1037	−	23.3247i	−1.04323	−	0.757952i	−0.0723177	−	0.997382i	$-0.523040\pi$
$947$	−32.1037	−	23.3247i	−1.04323	−	0.757952i	−0.970914	+	0.239430i	$0.923040\pi$
$948$	1.08540	−	3.34052i	0.0352522	−	0.108495i
$949$	8.40259			0.272759
$950$		0			0
$951$	31.5182			1.02205
$952$	1.73076	−	5.32672i	0.0560942	−	0.172640i
$953$	40.9560	+	29.7563i	1.32670	+	0.963901i	0.999823	+	0.0188330i	$0.00599509\pi$
$953$	40.9560	+	29.7563i	1.32670	+	0.963901i	0.326873	+	0.945068i	$0.394005\pi$
$954$	−1.97271	−	1.43326i	−0.0638689	−	0.0464035i
$955$		0			0
$956$	0.715921	−	0.520147i	0.0231545	−	0.0168228i
$957$	−4.69887			−0.151893
$958$	10.9401	−	7.94842i	0.353457	−	0.256802i
$959$	12.7727	+	39.3102i	0.412451	+	1.26939i
$960$		0			0
$961$	7.36546	−	22.6685i	0.237595	−	0.731243i
$962$	3.58538	+	11.0347i	0.115597	+	0.355772i
$963$	1.67171	+	5.14500i	0.0538702	+	0.165795i
$964$	3.91637	−	12.0534i	0.126138	−	0.388212i
$965$		0			0
$966$	2.47870	+	7.62866i	0.0797509	+	0.245448i
$967$	−8.94137	+	6.49628i	−0.287535	+	0.208906i	−0.722197	−	0.691687i	$-0.756868\pi$
$967$	−8.94137	+	6.49628i	−0.287535	+	0.208906i	0.434662	+	0.900594i	$0.356868\pi$
$968$	10.7294			0.344857
$969$	14.9855	−	10.8876i	0.481402	−	0.349759i
$970$		0			0
$971$	−19.9495	−	14.4942i	−0.640211	−	0.465140i	0.219712	−	0.975565i	$-0.429488\pi$
$971$	−19.9495	−	14.4942i	−0.640211	−	0.465140i	−0.859923	+	0.510424i	$0.829488\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−3.62345	+	11.1518i	−0.116162	+	0.357511i
$974$	26.6228			0.853050
$975$		0			0
$976$	12.5882			0.402940
$977$	−2.50827	+	7.71967i	−0.0802467	+	0.246974i	−0.983129	−	0.182914i	$-0.941447\pi$
$977$	−2.50827	+	7.71967i	−0.0802467	+	0.246974i	0.902882	+	0.429888i	$0.141447\pi$
$978$	−9.62329	−	6.99173i	−0.307719	−	0.223571i
$979$	4.14866	+	3.01418i	0.132592	+	0.0963336i
$980$		0			0
$981$	−2.33302	+	1.69504i	−0.0744877	+	0.0541185i
$982$	12.0227			0.383659
$983$	21.6028	−	15.6954i	0.689023	−	0.500605i	−0.187316	−	0.982300i	$-0.559979\pi$
$983$	21.6028	−	15.6954i	0.689023	−	0.500605i	0.876339	+	0.481695i	$0.159979\pi$
$984$	0.996141	+	3.06581i	0.0317558	+	0.0977344i
$985$		0			0
$986$	7.52530	−	23.1605i	0.239654	−	0.737580i
$987$	5.94897	+	18.3091i	0.189358	+	0.582784i
$988$	−4.64204	−	14.2867i	−0.147683	−	0.454521i
$989$	11.3804	−	35.0252i	0.361875	−	1.11374i
$990$		0			0
$991$	−16.3515	−	50.3248i	−0.519423	−	1.59862i	−0.775088	−	0.631854i	$-0.782294\pi$
$991$	−16.3515	−	50.3248i	−0.519423	−	1.59862i	0.255665	−	0.966765i	$-0.417706\pi$
$992$	−5.99083	+	4.35259i	−0.190209	+	0.138195i
$993$	−7.30062			−0.231678
$994$	13.7311	−	9.97625i	0.435525	−	0.316427i
$995$		0			0
$996$	10.6233	+	7.71827i	0.336612	+	0.244563i
$997$	−22.8712	−	16.6169i	−0.724337	−	0.526262i	0.163430	−	0.986555i	$-0.447744\pi$
$997$	−22.8712	−	16.6169i	−0.724337	−	0.526262i	−0.887767	+	0.460293i	$0.847744\pi$
$998$	8.45469	−	26.0209i	0.267629	−	0.823676i
$999$	−5.30719			−0.167912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.g.e.601.1		8
5.2	odd	4		750.2.h.c.649.1		8
5.3	odd	4		150.2.h.a.79.2	yes	8
5.4	even	2		750.2.g.c.601.2		8
15.8	even	4		450.2.l.a.379.1		8
25.6	even	5	inner	750.2.g.e.151.1		8
25.8	odd	20		750.2.h.c.349.1		8
25.9	even	10		3750.2.a.o.1.4		4
25.12	odd	20		3750.2.c.e.1249.1		8
25.13	odd	20		3750.2.c.e.1249.8		8
25.16	even	5		3750.2.a.m.1.1		4
25.17	odd	20		150.2.h.a.19.2	✓	8
25.19	even	10		750.2.g.c.151.2		8
75.17	even	20		450.2.l.a.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.2	✓	8	25.17	odd	20
150.2.h.a.79.2	yes	8	5.3	odd	4
450.2.l.a.19.1		8	75.17	even	20
450.2.l.a.379.1		8	15.8	even	4
750.2.g.c.151.2		8	25.19	even	10
750.2.g.c.601.2		8	5.4	even	2
750.2.g.e.151.1		8	25.6	even	5	inner
750.2.g.e.601.1		8	1.1	even	1	trivial
750.2.h.c.349.1		8	25.8	odd	20
750.2.h.c.649.1		8	5.2	odd	4
3750.2.a.m.1.1		4	25.16	even	5
3750.2.a.o.1.4		4	25.9	even	10
3750.2.c.e.1249.1		8	25.12	odd	20
3750.2.c.e.1249.8		8	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 $\F_{q}$

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} -2.07768 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.160734 - 0.494689i) q^{11} +(0.309017 + 0.951057i) q^{12} +(0.675571 + 2.07919i) q^{13} +(0.642040 - 1.97599i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.18088 + 1.58450i) q^{17} -1.00000 q^{18} +(5.55899 - 4.03884i) q^{19} +(1.68088 + 1.22123i) q^{21} +(0.420808 + 0.305735i) q^{22} +(1.19301 - 3.67171i) q^{23} -1.00000 q^{24} -2.18619 q^{26} +(0.309017 - 0.951057i) q^{27} +(1.68088 + 1.22123i) q^{28} +(7.30844 + 5.30989i) q^{29} +(5.99083 - 4.35259i) q^{31} -1.00000 q^{32} +(-0.420808 + 0.305735i) q^{33} +(-0.833023 - 2.56378i) q^{34} +(0.309017 - 0.951057i) q^{36} +(-1.64001 - 5.04743i) q^{37} +(2.12334 + 6.53498i) q^{38} +(0.675571 - 2.07919i) q^{39} +(-0.996141 - 3.06581i) q^{41} +(-1.68088 + 1.22123i) q^{42} +9.53920 q^{43} +(-0.420808 + 0.305735i) q^{44} +(3.12334 + 2.26924i) q^{46} +(7.49614 + 5.44627i) q^{47} +(0.309017 - 0.951057i) q^{48} -2.68323 q^{49} +2.69572 q^{51} +(0.675571 - 2.07919i) q^{52} +(1.97271 + 1.43326i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-1.68088 + 1.22123i) q^{56} -6.87129 q^{57} +(-7.30844 + 5.30989i) q^{58} +(2.67261 + 8.22545i) q^{59} +(3.88998 - 11.9721i) q^{61} +(2.28829 + 7.04264i) q^{62} +(-0.642040 - 1.97599i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.160734 - 0.494689i) q^{66} +(-5.41544 + 3.93455i) q^{67} +2.69572 q^{68} +(-3.12334 + 2.26924i) q^{69} +(6.60886 + 4.80162i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.18770 - 3.65537i) q^{73} +5.30719 q^{74} -6.87129 q^{76} +(-0.333955 + 1.02781i) q^{77} +(1.76867 + 1.28501i) q^{78} +(-2.84162 - 2.06455i) q^{79} +(-0.809017 + 0.587785i) q^{81} +3.22358 q^{82} +(10.6233 - 7.71827i) q^{83} +(-0.642040 - 1.97599i) q^{84} +(-2.94777 + 9.07232i) q^{86} +(-2.79158 - 8.59159i) q^{87} +(-0.160734 - 0.494689i) q^{88} +(-3.04654 + 9.37628i) q^{89} +(-1.40362 - 4.31990i) q^{91} +(-3.12334 + 2.26924i) q^{92} -7.40507 q^{93} +(-7.49614 + 5.44627i) q^{94} +(0.809017 + 0.587785i) q^{96} +(8.70483 + 6.32443i) q^{97} +(0.829164 - 2.55190i) q^{98} +0.520147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 8 q^{7} + 2 q^{8} - 2 q^{9} + 10 q^{11} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 2 q^{16} - 2 q^{17} - 8 q^{18} + 8 q^{19} - 2 q^{21} + 10 q^{23} - 8 q^{24} + 4 q^{26}+ \cdots - 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 8 * q^7 + 2 * q^8 - 2 * q^9 + 10 * q^11 - 2 * q^12 - 4 * q^13 + 2 * q^14 - 2 * q^16 - 2 * q^17 - 8 * q^18 + 8 * q^19 - 2 * q^21 + 10 * q^23 - 8 * q^24 + 4 * q^26 - 2 * q^27 - 2 * q^28 + 22 * q^29 + 24 * q^31 - 8 * q^32 - 8 * q^34 - 2 * q^36 - 14 * q^37 + 2 * q^38 - 4 * q^39 + 22 * q^41 + 2 * q^42 + 28 * q^43 + 10 * q^46 + 30 * q^47 - 2 * q^48 - 8 * q^49 - 12 * q^51 - 4 * q^52 + 12 * q^53 + 2 * q^54 + 2 * q^56 - 12 * q^57 - 22 * q^58 + 20 * q^59 + 6 * q^62 - 2 * q^63 - 2 * q^64 - 10 * q^66 + 18 * q^67 - 12 * q^68 - 10 * q^69 + 20 * q^71 + 2 * q^72 + 16 * q^73 + 4 * q^74 - 12 * q^76 - 6 * q^78 - 16 * q^79 - 2 * q^81 + 28 * q^82 + 6 * q^83 - 2 * q^84 - 18 * q^86 - 8 * q^87 - 10 * q^88 + 34 * q^89 - 24 * q^91 - 10 * q^92 - 36 * q^93 - 30 * q^94 + 2 * q^96 - 4 * q^97 - 22 * q^98 - 20 * q^99

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