LMFDB - Embedded newform 750.2.h.c.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("750.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.809017 - 0.587785i) q^{6} -2.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.160734 - 0.494689i) q^{11} +(-0.951057 + 0.309017i) q^{12} +(2.07919 - 0.675571i) q^{13} +(-0.642040 + 1.97599i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.58450 - 2.18088i) q^{17} +1.00000i q^{18} +(-5.55899 + 4.03884i) q^{19} +(1.68088 + 1.22123i) q^{21} +(-0.305735 + 0.420808i) q^{22} +(-3.67171 - 1.19301i) q^{23} +1.00000 q^{24} -2.18619 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.22123 - 1.68088i) q^{28} +(-7.30844 - 5.30989i) q^{29} +(5.99083 - 4.35259i) q^{31} -1.00000i q^{32} +(0.305735 + 0.420808i) q^{33} +(0.833023 + 2.56378i) q^{34} +(0.309017 - 0.951057i) q^{36} +(5.04743 - 1.64001i) q^{37} +(6.53498 - 2.12334i) q^{38} +(-0.675571 + 2.07919i) q^{39} +(-0.996141 - 3.06581i) q^{41} +(-1.22123 - 1.68088i) q^{42} -9.53920i q^{43} +(0.420808 - 0.305735i) q^{44} +(3.12334 + 2.26924i) q^{46} +(-5.44627 + 7.49614i) q^{47} +(-0.951057 - 0.309017i) q^{48} +2.68323 q^{49} +2.69572 q^{51} +(2.07919 + 0.675571i) q^{52} +(1.43326 - 1.97271i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.68088 + 1.22123i) q^{56} -6.87129i q^{57} +(5.30989 + 7.30844i) q^{58} +(-2.67261 - 8.22545i) q^{59} +(3.88998 - 11.9721i) q^{61} +(-7.04264 + 2.28829i) q^{62} +(-1.97599 + 0.642040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.160734 - 0.494689i) q^{66} +(-3.93455 - 5.41544i) q^{67} -2.69572i q^{68} +(3.12334 - 2.26924i) q^{69} +(6.60886 + 4.80162i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-3.65537 - 1.18770i) q^{73} -5.30719 q^{74} -6.87129 q^{76} +(-1.02781 - 0.333955i) q^{77} +(1.28501 - 1.76867i) q^{78} +(2.84162 + 2.06455i) q^{79} +(-0.809017 + 0.587785i) q^{81} +3.22358i q^{82} +(-7.71827 - 10.6233i) q^{83} +(0.642040 + 1.97599i) q^{84} +(-2.94777 + 9.07232i) q^{86} +(8.59159 - 2.79158i) q^{87} +(-0.494689 + 0.160734i) q^{88} +(3.04654 - 9.37628i) q^{89} +(-1.40362 - 4.31990i) q^{91} +(-2.26924 - 3.12334i) q^{92} +7.40507i q^{93} +(7.49614 - 5.44627i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-6.32443 + 8.70483i) q^{97} +(-2.55190 - 0.829164i) q^{98} -0.520147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} - 2 q^{21} + 10 q^{23} + 8 q^{24} + 4 q^{26} + 10 q^{28} - 22 q^{29} + 24 q^{31} + 8 q^{34} - 2 q^{36}+ \cdots + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 - 2 * q^21 + 10 * q^23 + 8 * q^24 + 4 * q^26 + 10 * q^28 - 22 * q^29 + 24 * q^31 + 8 * q^34 - 2 * q^36 + 20 * q^37 + 10 * q^38 + 4 * q^39 + 22 * q^41 - 10 * q^42 + 10 * q^46 - 10 * q^47 + 8 * q^49 - 12 * q^51 + 20 * q^52 + 30 * q^53 - 2 * q^54 + 2 * q^56 - 30 * q^58 - 20 * q^59 - 10 * q^62 - 10 * q^63 + 2 * q^64 - 10 * q^66 - 10 * q^67 + 10 * q^69 + 20 * q^71 + 20 * q^73 - 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 2 * q^81 - 70 * q^83 + 2 * q^84 - 18 * q^86 + 30 * q^87 - 10 * q^88 - 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 + 2 * q^96 - 60 * q^97 - 20 * q^98 + 20 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$		−	2.07768i		−	0.785291i	−0.919690	−	0.392645i	$-0.871560\pi$
$7$		−	2.07768i		−	0.785291i	0.919690	−	0.392645i	$-0.128440\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−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	$0.0750140\pi$
$12$	−0.951057	+	0.309017i	−0.274546	+	0.0892055i
$13$	2.07919	−	0.675571i	0.576664	−	0.187370i	−0.00614146	−	0.999981i	$-0.501955\pi$
$13$	2.07919	−	0.675571i	0.576664	−	0.187370i	0.582806	+	0.812612i	$0.301955\pi$
$14$	−0.642040	+	1.97599i	−0.171592	+	0.528107i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.58450	−	2.18088i	−0.384298	−	0.528941i	0.572418	−	0.819962i	$-0.306005\pi$
$17$	−1.58450	−	2.18088i	−0.384298	−	0.528941i	−0.956717	+	0.291020i	$0.906005\pi$
$18$			1.00000i			0.235702i
$19$	−5.55899	+	4.03884i	−1.27532	+	0.926574i	−0.999401	−	0.0346072i	$-0.988982\pi$
$19$	−5.55899	+	4.03884i	−1.27532	+	0.926574i	−0.275919	+	0.961181i	$0.588982\pi$
$20$		0			0
$21$	1.68088	+	1.22123i	0.366798	+	0.266495i
$22$	−0.305735	+	0.420808i	−0.0651829	+	0.0897165i
$23$	−3.67171	−	1.19301i	−0.765605	−	0.248760i	−0.0999224	−	0.994995i	$-0.531859\pi$
$23$	−3.67171	−	1.19301i	−0.765605	−	0.248760i	−0.665682	+	0.746235i	$0.731859\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$	−2.18619			−0.428748
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	1.22123	−	1.68088i	0.230791	−	0.317657i
$29$	−7.30844	−	5.30989i	−1.35714	−	0.986022i	−0.998621	−	0.0525013i	$-0.983281\pi$
$29$	−7.30844	−	5.30989i	−1.35714	−	0.986022i	−0.358523	−	0.933521i	$-0.616719\pi$
$30$		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	$0.0684335\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.305735	+	0.420808i	0.0532216	+	0.0732532i
$34$	0.833023	+	2.56378i	0.142862	+	0.439685i
$35$		0			0
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	5.04743	−	1.64001i	0.829793	−	0.269616i	0.136835	−	0.990594i	$-0.456307\pi$
$37$	5.04743	−	1.64001i	0.829793	−	0.269616i	0.692958	+	0.720978i	$0.256307\pi$
$38$	6.53498	−	2.12334i	1.06011	−	0.344452i
$39$	−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	$0.980996\pi$
$42$	−1.22123	−	1.68088i	−0.188440	−	0.259366i
$43$		−	9.53920i		−	1.45471i	−0.686259	−	0.727357i	$-0.740748\pi$
$43$		−	9.53920i		−	1.45471i	0.686259	−	0.727357i	$-0.259252\pi$
$44$	0.420808	−	0.305735i	0.0634392	−	0.0460912i
$45$		0			0
$46$	3.12334	+	2.26924i	0.460512	+	0.334582i
$47$	−5.44627	+	7.49614i	−0.794419	+	1.09342i	0.199124	+	0.979974i	$0.436190\pi$
$47$	−5.44627	+	7.49614i	−0.794419	+	1.09342i	−0.993544	+	0.113450i	$0.963810\pi$
$48$	−0.951057	−	0.309017i	−0.137273	−	0.0446028i
$49$	2.68323			0.383319
$50$		0			0
$51$	2.69572			0.377476
$52$	2.07919	+	0.675571i	0.288332	+	0.0936848i
$53$	1.43326	−	1.97271i	0.196873	−	0.270973i	−0.699155	−	0.714970i	$-0.746440\pi$
$53$	1.43326	−	1.97271i	0.196873	−	0.270973i	0.896028	+	0.443998i	$0.146440\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$		0			0
$56$	−1.68088	+	1.22123i	−0.224617	+	0.163194i
$57$		−	6.87129i		−	0.910124i
$58$	5.30989	+	7.30844i	0.697223	+	0.959645i
$59$	−2.67261	−	8.22545i	−0.347944	−	1.07086i	−0.959989	−	0.280039i	$-0.909653\pi$
$59$	−2.67261	−	8.22545i	−0.347944	−	1.07086i	0.612045	−	0.790823i	$-0.290347\pi$
$60$		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	$-0.198307\pi$
$62$	−7.04264	+	2.28829i	−0.894417	+	0.290614i
$63$	−1.97599	+	0.642040i	−0.248952	+	0.0808894i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		0			0
$66$	−0.160734	−	0.494689i	−0.0197850	−	0.0608920i
$67$	−3.93455	−	5.41544i	−0.480682	−	0.661601i	0.497954	−	0.867203i	$-0.334085\pi$
$67$	−3.93455	−	5.41544i	−0.480682	−	0.661601i	−0.978636	+	0.205602i	$0.934085\pi$
$68$		−	2.69572i		−	0.326904i
$69$	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	$0.538914\pi$
$72$	−0.587785	+	0.809017i	−0.0692712	+	0.0953436i
$73$	−3.65537	−	1.18770i	−0.427828	−	0.139010i	0.0871848	−	0.996192i	$-0.472213\pi$
$73$	−3.65537	−	1.18770i	−0.427828	−	0.139010i	−0.515013	+	0.857182i	$0.672213\pi$
$74$	−5.30719			−0.616948
$75$		0			0
$76$	−6.87129			−0.788191
$77$	−1.02781	−	0.333955i	−0.117130	−	0.0380577i
$78$	1.28501	−	1.76867i	0.145499	−	0.200262i
$79$	2.84162	+	2.06455i	0.319707	+	0.232281i	0.736050	−	0.676927i	$-0.236689\pi$
$79$	2.84162	+	2.06455i	0.319707	+	0.232281i	−0.416344	+	0.909207i	$0.636689\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$			3.22358i			0.355985i
$83$	−7.71827	−	10.6233i	−0.847190	−	1.16606i	−0.984475	−	0.175526i	$-0.943837\pi$
$83$	−7.71827	−	10.6233i	−0.847190	−	1.16606i	0.137285	−	0.990532i	$-0.456163\pi$
$84$	0.642040	+	1.97599i	0.0700523	+	0.215599i
$85$		0			0
$86$	−2.94777	+	9.07232i	−0.317867	+	0.978293i
$87$	8.59159	−	2.79158i	0.921115	−	0.299288i
$88$	−0.494689	+	0.160734i	−0.0527340	+	0.0171343i
$89$	3.04654	−	9.37628i	0.322932	−	0.993883i	−0.649433	−	0.760419i	$-0.724994\pi$
$89$	3.04654	−	9.37628i	0.322932	−	0.993883i	0.972365	−	0.233465i	$-0.0750063\pi$
$90$		0			0
$91$	−1.40362	−	4.31990i	−0.147140	−	0.452849i
$92$	−2.26924	−	3.12334i	−0.236585	−	0.325631i
$93$			7.40507i			0.767870i
$94$	7.49614	−	5.44627i	0.773168	−	0.561739i
$95$		0			0
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−6.32443	+	8.70483i	−0.642149	+	0.883842i	−0.998728	−	0.0504234i	$-0.983943\pi$
$97$	−6.32443	+	8.70483i	−0.642149	+	0.883842i	0.356579	+	0.934265i	$0.383943\pi$
$98$	−2.55190	−	0.829164i	−0.257781	−	0.0837582i
$99$	−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	$0.840871\pi$
$102$	−2.56378	−	0.833023i	−0.253852	−	0.0824815i
$103$	−5.11231	+	7.03649i	−0.503731	+	0.693326i	−0.982846	−	0.184426i	$-0.940957\pi$
$103$	−5.11231	+	7.03649i	−0.503731	+	0.693326i	0.479116	+	0.877752i	$0.340957\pi$
$104$	−1.76867	−	1.28501i	−0.173432	−	0.126006i
$105$		0			0
$106$	−1.97271	+	1.43326i	−0.191607	+	0.139210i
$107$			5.40977i			0.522983i	0.965206	+	0.261491i	$0.0842143\pi$
$107$			5.40977i			0.522983i	−0.965206	+	0.261491i	$0.915786\pi$
$108$	0.587785	+	0.809017i	0.0565597	+	0.0778477i
$109$	−0.891135	−	2.74263i	−0.0853553	−	0.262697i	0.899265	−	0.437404i	$-0.144102\pi$
$109$	−0.891135	−	2.74263i	−0.0853553	−	0.262697i	−0.984620	+	0.174707i	$0.944102\pi$
$110$		0			0
$111$	−1.64001	+	5.04743i	−0.155663	+	0.479081i
$112$	1.97599	−	0.642040i	0.186714	−	0.0606670i
$113$	6.05780	−	1.96830i	0.569870	−	0.185162i	−0.00988741	−	0.999951i	$-0.503147\pi$
$113$	6.05780	−	1.96830i	0.569870	−	0.185162i	0.579757	+	0.814789i	$0.303147\pi$
$114$	−2.12334	+	6.53498i	−0.198869	+	0.612057i
$115$		0			0
$116$	−2.79158	−	8.59159i	−0.259191	−	0.797709i
$117$	−1.28501	−	1.76867i	−0.118799	−	0.163513i
$118$			8.64875i			0.796182i
$119$	−4.53118	+	3.29210i	−0.415373	+	0.301786i
$120$		0			0
$121$	8.68031	+	6.30661i	0.789119	+	0.573328i
$122$	−7.39919	+	10.1841i	−0.669891	+	0.922026i
$123$	3.06581	+	0.996141i	0.276435	+	0.0898191i
$124$	7.40507			0.664995
$125$		0			0
$126$	2.07768			0.185095
$127$	14.2348	+	4.62515i	1.26313	+	0.410416i	0.862609	−	0.505871i	$-0.168829\pi$
$127$	14.2348	+	4.62515i	1.26313	+	0.410416i	0.400522	+	0.916287i	$0.368829\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	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	$0.506933\pi$
$132$			0.520147i			0.0452730i
$133$	8.39144	+	11.5498i	0.727630	+	1.00150i
$134$	2.06851	+	6.36623i	0.178692	+	0.549959i
$135$		0			0
$136$	−0.833023	+	2.56378i	−0.0714311	+	0.219842i
$137$	18.9202	−	6.14755i	1.61646	−	0.525221i	0.645359	−	0.763879i	$-0.276708\pi$
$137$	18.9202	−	6.14755i	1.61646	−	0.525221i	0.971103	+	0.238659i	$0.0767077\pi$
$138$	−3.67171	+	1.19301i	−0.312557	+	0.101556i
$139$	−1.74398	+	5.36743i	−0.147923	+	0.455259i	−0.997375	−	0.0724056i	$-0.976932\pi$
$139$	−1.74398	+	5.36743i	−0.147923	+	0.455259i	0.849453	+	0.527665i	$0.176932\pi$
$140$		0			0
$141$	−2.86327	−	8.81224i	−0.241131	−	0.742125i
$142$	−4.80162	−	6.60886i	−0.402943	−	0.554604i
$143$		−	1.13714i		−	0.0950925i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$		0			0
$146$	3.10944	+	2.25914i	0.257339	+	0.186968i
$147$	−1.57716	+	2.17078i	−0.130082	+	0.179043i
$148$	5.04743	+	1.64001i	0.414897	+	0.134808i
$149$	15.0956			1.23668			0.618339	−	0.785911i	$-0.287806\pi$
$149$	15.0956			1.23668			0.618339	+	0.785911i	$0.287806\pi$
$150$		0			0
$151$	−20.9353			−1.70369			−0.851847	−	0.523791i	$-0.824517\pi$
$151$	−20.9353			−1.70369			−0.851847	+	0.523791i	$0.824517\pi$
$152$	6.53498	+	2.12334i	0.530057	+	0.172226i
$153$	−1.58450	+	2.18088i	−0.128099	+	0.176314i
$154$	0.874305	+	0.635220i	0.0704535	+	0.0511875i
$155$		0			0
$156$	−1.76867	+	1.28501i	−0.141607	+	0.102883i
$157$		−	5.71998i		−	0.456504i	−0.973602	−	0.228252i	$-0.926699\pi$
$157$		−	5.71998i		−	0.456504i	0.973602	−	0.228252i	$-0.0733010\pi$
$158$	−2.06455	−	2.84162i	−0.164247	−	0.226067i
$159$	0.753509	+	2.31906i	0.0597572	+	0.183914i
$160$		0			0
$161$	−2.47870	+	7.62866i	−0.195349	+	0.601222i
$162$	0.951057	−	0.309017i	0.0747221	−	0.0242787i
$163$	−11.3129	+	3.67577i	−0.886091	+	0.287908i	−0.716484	−	0.697603i	$-0.754250\pi$
$163$	−11.3129	+	3.67577i	−0.886091	+	0.287908i	−0.169607	+	0.985512i	$0.554250\pi$
$164$	0.996141	−	3.06581i	0.0777856	−	0.239399i
$165$		0			0
$166$	4.05774	+	12.4884i	0.314941	+	0.969290i
$167$	5.25731	+	7.23607i	0.406823	+	0.559944i	0.962440	−	0.271495i	$-0.0875179\pi$
$167$	5.25731	+	7.23607i	0.406823	+	0.559944i	−0.555617	+	0.831438i	$0.687518\pi$
$168$		−	2.07768i		−	0.160297i
$169$	−6.65058	+	4.83193i	−0.511583	+	0.371687i
$170$		0			0
$171$	5.55899	+	4.03884i	0.425106	+	0.308858i
$172$	5.60700	−	7.71737i	0.427530	−	0.588444i
$173$	15.5394	+	5.04904i	1.18144	+	0.383872i	0.832900	−	0.553424i	$-0.186679\pi$
$173$	15.5394	+	5.04904i	1.18144	+	0.383872i	0.348536	+	0.937295i	$0.386679\pi$
$174$	−9.03373			−0.684845
$175$		0			0
$176$	0.520147			0.0392076
$177$	8.22545	+	2.67261i	0.618262	+	0.200886i
$178$	−5.79486	+	7.97594i	−0.434343	+	0.597822i
$179$	2.97599	+	2.16219i	0.222436	+	0.161609i	0.693423	−	0.720531i	$-0.256102\pi$
$179$	2.97599	+	2.16219i	0.222436	+	0.161609i	−0.470986	+	0.882140i	$0.656102\pi$
$180$		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	$-0.0274391\pi$
$182$			4.54222i			0.336691i
$183$	7.39919	+	10.1841i	0.546964	+	0.752831i
$184$	1.19301	+	3.67171i	0.0879500	+	0.270682i
$185$		0			0
$186$	2.28829	−	7.04264i	0.167786	−	0.516392i
$187$	−1.33354	+	0.433294i	−0.0975183	+	0.0316856i
$188$	−8.81224	+	2.86327i	−0.642699	+	0.208826i
$189$	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	$0.920601\pi$
$192$	−0.587785	−	0.809017i	−0.0424197	−	0.0583858i
$193$		−	6.60138i		−	0.475178i	−0.971366	−	0.237589i	$-0.923643\pi$
$193$		−	6.60138i		−	0.475178i	0.971366	−	0.237589i	$-0.0763571\pi$
$194$	8.70483	−	6.32443i	0.624970	−	0.454068i
$195$		0			0
$196$	2.17078	+	1.57716i	0.155056	+	0.112655i
$197$	−7.43989	+	10.2401i	−0.530070	+	0.729579i	−0.987141	−	0.159851i	$-0.948899\pi$
$197$	−7.43989	+	10.2401i	−0.530070	+	0.729579i	0.457071	+	0.889430i	$0.348899\pi$
$198$	0.494689	+	0.160734i	0.0351560	+	0.0114229i
$199$	−6.24148			−0.442447			−0.221223	−	0.975223i	$-0.571005\pi$
$199$	−6.24148			−0.442447			−0.221223	+	0.975223i	$0.571005\pi$
$200$		0			0
$201$	6.69385			0.472148
$202$	16.7766	+	5.45106i	1.18040	+	0.383535i
$203$	−11.0323	+	15.1846i	−0.774314	+	1.06575i
$204$	2.18088	+	1.58450i	0.152692	+	0.110937i
$205$		0			0
$206$	7.03649	−	5.11231i	0.490256	−	0.356192i
$207$			3.86067i			0.268335i
$208$	1.28501	+	1.76867i	0.0890995	+	0.122635i
$209$	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	$0.818392\pi$
$212$	2.31906	−	0.753509i	0.159274	−	0.0517512i
$213$	−7.76919	+	2.52436i	−0.532336	+	0.172966i
$214$	1.67171	−	5.14500i	0.114276	−	0.351705i
$215$		0			0
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	−9.04331	−	12.4471i	−0.613900	−	0.844961i
$218$			2.88377i			0.195314i
$219$	3.10944	−	2.25914i	0.210117	−	0.152659i
$220$		0			0
$221$	−4.76783	−	3.46403i	−0.320719	−	0.233016i
$222$	3.11949	−	4.29360i	0.209366	−	0.288168i
$223$	−17.0524	−	5.54065i	−1.14191	−	0.371029i	−0.323820	−	0.946119i	$-0.604967\pi$
$223$	−17.0524	−	5.54065i	−1.14191	−	0.371029i	−0.818091	+	0.575089i	$0.804967\pi$
$224$	−2.07768			−0.138821
$225$		0			0
$226$	−6.36955			−0.423696
$227$	8.42412	+	2.73716i	0.559129	+	0.181672i	0.574929	−	0.818203i	$-0.305030\pi$
$227$	8.42412	+	2.73716i	0.559129	+	0.181672i	−0.0158003	+	0.999875i	$0.505030\pi$
$228$	4.03884	−	5.55899i	0.267479	−	0.368153i
$229$	17.8490	+	12.9681i	1.17950	+	0.856953i	0.992115	−	0.125334i	$-0.0400003\pi$
$229$	17.8490	+	12.9681i	1.17950	+	0.856953i	0.187380	+	0.982287i	$0.440000\pi$
$230$		0			0
$231$	0.874305	−	0.635220i	0.0575251	−	0.0417944i
$232$			9.03373i			0.593093i
$233$	−6.78466	−	9.33828i	−0.444478	−	0.611771i	0.526722	−	0.850037i	$-0.323421\pi$
$233$	−6.78466	−	9.33828i	−0.444478	−	0.611771i	−0.971200	+	0.238267i	$0.923421\pi$
$234$	0.675571	+	2.07919i	0.0441634	+	0.135921i
$235$		0			0
$236$	2.67261	−	8.22545i	0.173972	−	0.535431i
$237$	−3.34052	+	1.08540i	−0.216990	+	0.0705043i
$238$	5.32672	−	1.73076i	0.345280	−	0.112188i
$239$	0.273457	−	0.841616i	0.0176885	−	0.0544396i	−0.941823	−	0.336110i	$-0.890889\pi$
$239$	0.273457	−	0.841616i	0.0176885	−	0.0544396i	0.959511	+	0.281671i	$0.0908885\pi$
$240$		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	$0.766160\pi$
$242$	−6.30661	−	8.68031i	−0.405404	−	0.557991i
$243$		−	1.00000i		−	0.0641500i
$244$	10.1841	−	7.39919i	0.651971	−	0.473684i
$245$		0			0
$246$	−2.60793	−	1.89477i	−0.166276	−	0.120806i
$247$	−8.82968	+	12.1530i	−0.561819	+	0.773278i
$248$	−7.04264	−	2.28829i	−0.447208	−	0.145307i
$249$	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	$0.306507\pi$
$252$	−1.97599	−	0.642040i	−0.124476	−	0.0404447i
$253$	−1.18034	+	1.62460i	−0.0742073	+	0.102138i
$254$	−12.1088	−	8.79756i	−0.759774	−	0.552008i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	1.28053i		−	0.0798774i	−0.999202	−	0.0399387i	$-0.987284\pi$
$257$		−	1.28053i		−	0.0798774i	0.999202	−	0.0399387i	$-0.0127163\pi$
$258$	−5.60700	−	7.71737i	−0.349077	−	0.480463i
$259$	−3.40742	−	10.4870i	−0.211727	−	0.651629i
$260$		0			0
$261$	−2.79158	+	8.59159i	−0.172794	+	0.531806i
$262$	13.1770	−	4.28147i	0.814079	−	0.264510i
$263$	6.76605	−	2.19842i	0.417213	−	0.135561i	−0.0928855	−	0.995677i	$-0.529609\pi$
$263$	6.76605	−	2.19842i	0.417213	−	0.135561i	0.510098	+	0.860116i	$0.329609\pi$
$264$	0.160734	−	0.494689i	0.00989251	−	0.0304460i
$265$		0			0
$266$	−4.41164	−	13.5776i	−0.270495	−	0.832498i
$267$	5.79486	+	7.97594i	0.354640	+	0.488119i
$268$		−	6.69385i		−	0.408892i
$269$	−7.62892	+	5.54274i	−0.465143	+	0.337947i	−0.795546	−	0.605894i	$-0.792816\pi$
$269$	−7.62892	+	5.54274i	−0.465143	+	0.337947i	0.330402	+	0.943840i	$0.392816\pi$
$270$		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	$0.713296\pi$
$272$	1.58450	−	2.18088i	0.0960746	−	0.132235i
$273$	4.31990	+	1.40362i	0.261452	+	0.0849511i
$274$	−19.8939			−1.20183
$275$		0			0
$276$	3.86067			0.232385
$277$	−18.6375	−	6.05571i	−1.11982	−	0.363852i	−0.310122	−	0.950697i	$-0.600370\pi$
$277$	−18.6375	−	6.05571i	−1.11982	−	0.363852i	−0.809700	+	0.586845i	$0.800370\pi$
$278$	3.31725	−	4.56581i	0.198956	−	0.273839i
$279$	−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	$0.273022\pi$
$282$			9.26574i			0.551767i
$283$	1.31285	+	1.80699i	0.0780411	+	0.107414i	0.846253	−	0.532781i	$-0.178853\pi$
$283$	1.31285	+	1.80699i	0.0780411	+	0.107414i	−0.768212	+	0.640196i	$0.778853\pi$
$284$	2.52436	+	7.76919i	0.149793	+	0.461016i
$285$		0			0
$286$	−0.351396	+	1.08149i	−0.0207785	+	0.0639496i
$287$	−6.36978	+	2.06967i	−0.375996	+	0.122169i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	3.00770	−	9.25673i	0.176923	−	0.544514i
$290$		0			0
$291$	−3.32495	−	10.2331i	−0.194912	−	0.599877i
$292$	−2.25914	−	3.10944i	−0.132206	−	0.181966i
$293$			24.0260i			1.40361i	0.712367	+	0.701807i	$0.247623\pi$
$293$			24.0260i			1.40361i	−0.712367	+	0.701807i	$0.752377\pi$
$294$	2.17078	−	1.57716i	0.126602	−	0.0919821i
$295$		0			0
$296$	−4.29360	−	3.11949i	−0.249561	−	0.181316i
$297$	0.305735	−	0.420808i	0.0177405	−	0.0244177i
$298$	−14.3568	−	4.66479i	−0.831664	−	0.270224i
$299$	−8.44016			−0.488107
$300$		0			0
$301$	−19.8194			−1.14237
$302$	19.9107	+	6.46937i	1.14573	+	0.372271i
$303$	10.3685	−	14.2711i	0.595656	−	0.819850i
$304$	−5.55899	−	4.03884i	−0.318830	−	0.231643i
$305$		0			0
$306$	2.18088	−	1.58450i	0.124673	−	0.0905800i
$307$		−	17.1204i		−	0.977111i	−0.872533	−	0.488556i	$-0.837524\pi$
$307$		−	17.1204i		−	0.977111i	0.872533	−	0.488556i	$-0.162476\pi$
$308$	−0.635220	−	0.874305i	−0.0361950	−	0.0498182i
$309$	−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	$0.906409\pi$
$312$	2.07919	−	0.675571i	0.117711	−	0.0382466i
$313$	24.2560	−	7.88127i	1.37103	−	0.445476i	0.471322	−	0.881961i	$-0.343777\pi$
$313$	24.2560	−	7.88127i	1.37103	−	0.445476i	0.899711	+	0.436486i	$0.143777\pi$
$314$	−1.76757	+	5.44002i	−0.0997498	+	0.306998i
$315$		0			0
$316$	1.08540	+	3.34052i	0.0610586	+	0.187919i
$317$	−18.5260	−	25.4988i	−1.04052	−	1.43215i	−0.896747	−	0.442544i	$-0.854076\pi$
$317$	−18.5260	−	25.4988i	−1.04052	−	1.43215i	−0.143775	−	0.989610i	$-0.545924\pi$
$318$		−	2.43841i		−	0.136739i
$319$	−3.80146	+	2.76193i	−0.212841	+	0.154638i
$320$		0			0
$321$	−4.37660	−	3.17979i	−0.244278	−	0.177478i
$322$	4.71477	−	6.48932i	0.262744	−	0.361636i
$323$	17.6165	+	5.72394i	0.980207	+	0.318488i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	11.8950			0.658805
$327$	2.74263	+	0.891135i	0.151668	+	0.0492799i
$328$	−1.89477	+	2.60793i	−0.104621	+	0.143999i
$329$	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	$0.235698\pi$
$332$		−	13.1311i		−	0.720663i
$333$	−3.11949	−	4.29360i	−0.170947	−	0.235288i
$334$	−2.76393	−	8.50651i	−0.151236	−	0.465455i
$335$		0			0
$336$	−0.642040	+	1.97599i	−0.0350261	+	0.107799i
$337$	−25.4358	+	8.26459i	−1.38558	+	0.450201i	−0.904498	−	0.426477i	$-0.859754\pi$
$337$	−25.4358	+	8.26459i	−1.38558	+	0.450201i	−0.481077	+	0.876678i	$0.659754\pi$
$338$	7.81822	−	2.54029i	0.425255	−	0.138174i
$339$	−1.96830	+	6.05780i	−0.106903	+	0.329015i
$340$		0			0
$341$	−1.19025	−	3.66321i	−0.0644556	−	0.198374i
$342$	−4.03884	−	5.55899i	−0.218396	−	0.300596i
$343$		−	20.1187i		−	1.08631i
$344$	−7.71737	+	5.60700i	−0.416093	+	0.302309i
$345$		0			0
$346$	−13.2186	−	9.60385i	−0.710635	−	0.516306i
$347$	2.86327	−	3.94095i	0.153708	−	0.211562i	−0.725217	−	0.688520i	$-0.758261\pi$
$347$	2.86327	−	3.94095i	0.153708	−	0.211562i	0.878926	+	0.476958i	$0.158261\pi$
$348$	8.59159	+	2.79158i	0.460557	+	0.149644i
$349$	−16.7173			−0.894855			−0.447428	−	0.894320i	$-0.647660\pi$
$349$	−16.7173			−0.894855			−0.447428	+	0.894320i	$0.647660\pi$
$350$		0			0
$351$	2.18619			0.116690
$352$	−0.494689	−	0.160734i	−0.0263670	−	0.00856717i
$353$	15.9175	−	21.9086i	0.847203	−	1.16608i	−0.137269	−	0.990534i	$-0.543832\pi$
$353$	15.9175	−	21.9086i	0.847203	−	1.16608i	0.984472	−	0.175541i	$-0.0561676\pi$
$354$	−6.99698	−	5.08361i	−0.371885	−	0.270191i
$355$		0			0
$356$	7.97594	−	5.79486i	0.422724	−	0.307127i
$357$		−	5.60085i		−	0.296428i
$358$	−2.16219	−	2.97599i	−0.114275	−	0.157286i
$359$	2.62299	+	8.07273i	0.138436	+	0.426062i	0.996109	−	0.0881339i	$-0.0280903\pi$
$359$	2.62299	+	8.07273i	0.138436	+	0.426062i	−0.857673	+	0.514196i	$0.828090\pi$
$360$		0			0
$361$	8.71879	−	26.8337i	0.458884	−	1.41230i
$362$	−21.9211	+	7.12261i	−1.15215	+	0.374356i
$363$	−10.2043	+	3.31558i	−0.535587	+	0.174023i
$364$	1.40362	−	4.31990i	0.0735698	−	0.226424i
$365$		0			0
$366$	−3.88998	−	11.9721i	−0.203333	−	0.625794i
$367$	7.49289	+	10.3131i	0.391126	+	0.538339i	0.958489	−	0.285129i	$-0.0920365\pi$
$367$	7.49289	+	10.3131i	0.391126	+	0.538339i	−0.567363	+	0.823468i	$0.692036\pi$
$368$		−	3.86067i		−	0.201251i
$369$	−2.60793	+	1.89477i	−0.135764	+	0.0986380i
$370$		0			0
$371$	−4.09867	−	2.97786i	−0.212792	−	0.154603i
$372$	−4.35259	+	5.99083i	−0.225671	+	0.310610i
$373$	10.4051	+	3.38081i	0.538754	+	0.175052i	0.565740	−	0.824584i	$-0.308591\pi$
$373$	10.4051	+	3.38081i	0.538754	+	0.175052i	−0.0269853	+	0.999636i	$0.508591\pi$
$374$	1.40217			0.0725045
$375$		0			0
$376$	9.26574			0.477844
$377$	−18.7829	−	6.10292i	−0.967367	−	0.314316i
$378$	−1.22123	+	1.68088i	−0.0628134	+	0.0864552i
$379$	−11.5124	−	8.36427i	−0.591354	−	0.429644i	0.251446	−	0.967871i	$-0.419094\pi$
$379$	−11.5124	−	8.36427i	−0.591354	−	0.429644i	−0.842799	+	0.538228i	$0.819094\pi$
$380$		0			0
$381$	−12.1088	+	8.79756i	−0.620353	+	0.450713i
$382$			1.78768i			0.0914658i
$383$	4.21101	+	5.79595i	0.215172	+	0.296159i	0.902936	−	0.429776i	$-0.141407\pi$
$383$	4.21101	+	5.79595i	0.215172	+	0.296159i	−0.687763	+	0.725935i	$0.741407\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$		0			0
$386$	−2.03994	+	6.27828i	−0.103830	+	0.319556i
$387$	−9.07232	+	2.94777i	−0.461172	+	0.149844i
$388$	−10.2331	+	3.32495i	−0.519509	+	0.168799i
$389$	0.283978	−	0.873994i	0.0143982	−	0.0443133i	−0.943599	−	0.331090i	$-0.892584\pi$
$389$	0.283978	−	0.873994i	0.0143982	−	0.0443133i	0.957998	+	0.286776i	$0.0925837\pi$
$390$		0			0
$391$	3.21602	+	9.89790i	0.162641	+	0.500558i
$392$	−1.57716	−	2.17078i	−0.0796588	−	0.109641i
$393$		−	13.8551i		−	0.698899i
$394$	10.2401	−	7.43989i	0.515891	−	0.374816i
$395$		0			0
$396$	−0.420808	−	0.305735i	−0.0211464	−	0.0153637i
$397$	−12.8148	+	17.6381i	−0.643159	+	0.885232i	−0.998779	−	0.0493984i	$-0.984270\pi$
$397$	−12.8148	+	17.6381i	−0.643159	+	0.885232i	0.355620	+	0.934630i	$0.384270\pi$
$398$	5.93600	+	1.92872i	0.297545	+	0.0966782i
$399$	−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	$0.307185\pi$
$402$	−6.36623	−	2.06851i	−0.317519	−	0.103168i
$403$	9.51560	−	13.0971i	0.474006	−	0.652413i
$404$	−14.2711	−	10.3685i	−0.710011	−	0.515853i
$405$		0			0
$406$	15.1846	−	11.0323i	0.753600	−	0.547523i
$407$		−	2.76052i		−	0.136834i
$408$	−1.58450	−	2.18088i	−0.0784446	−	0.107970i
$409$	−1.54554	−	4.75668i	−0.0764220	−	0.235203i	0.905547	−	0.424247i	$-0.139461\pi$
$409$	−1.54554	−	4.75668i	−0.0764220	−	0.235203i	−0.981969	+	0.189044i	$0.939461\pi$
$410$		0			0
$411$	−6.14755	+	18.9202i	−0.303236	+	0.933265i
$412$	−8.27189	+	2.68770i	−0.407527	+	0.132414i
$413$	−17.0899	+	5.55284i	−0.840938	+	0.273237i
$414$	1.19301	−	3.67171i	0.0586333	−	0.180455i
$415$		0			0
$416$	−0.675571	−	2.07919i	−0.0331226	−	0.101941i
$417$	−3.31725	−	4.56581i	−0.162447	−	0.223589i
$418$		−	3.57408i		−	0.174814i
$419$	−18.4661	+	13.4164i	−0.902128	+	0.655434i	−0.939012	−	0.343885i	$-0.888257\pi$
$419$	−18.4661	+	13.4164i	−0.902128	+	0.655434i	0.0368836	+	0.999320i	$0.488257\pi$
$420$		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	$0.825079\pi$
$422$	13.2122	−	18.1850i	0.643160	−	0.885234i
$423$	8.81224	+	2.86327i	0.428466	+	0.139217i
$424$	−2.43841			−0.118419
$425$		0			0
$426$	8.16901			0.395790
$427$	−24.8743	−	8.08215i	−1.20375	−	0.391123i
$428$	−3.17979	+	4.37660i	−0.153701	+	0.211551i
$429$	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	$0.226073\pi$
$432$			1.00000i			0.0481125i
$433$	−4.77408	−	6.57096i	−0.229428	−	0.315780i	0.678747	−	0.734373i	$-0.262524\pi$
$433$	−4.77408	−	6.57096i	−0.229428	−	0.315780i	−0.908174	+	0.418593i	$0.862524\pi$
$434$	4.75435	+	14.6324i	0.228216	+	0.702377i
$435$		0			0
$436$	0.891135	−	2.74263i	0.0426776	−	0.131348i
$437$	25.2294	−	8.19753i	1.20689	−	0.392141i
$438$	−3.65537	+	1.18770i	−0.174660	+	0.0567505i
$439$	−2.84899	+	8.76829i	−0.135975	+	0.418488i	−0.995740	−	0.0922014i	$-0.970610\pi$
$439$	−2.84899	+	8.76829i	−0.135975	+	0.418488i	0.859766	+	0.510689i	$0.170610\pi$
$440$		0			0
$441$	−0.829164	−	2.55190i	−0.0394840	−	0.121519i
$442$	3.46403	+	4.76783i	0.164767	+	0.226782i
$443$			9.63232i			0.457645i	0.973468	+	0.228823i	$0.0734876\pi$
$443$			9.63232i			0.457645i	−0.973468	+	0.228823i	$0.926512\pi$
$444$	−4.29360	+	3.11949i	−0.203765	+	0.148044i
$445$		0			0
$446$	14.5056	+	10.5389i	0.686861	+	0.499033i
$447$	−8.87296	+	12.2126i	−0.419677	+	0.577635i
$448$	1.97599	+	0.642040i	0.0933570	+	0.0303335i
$449$	21.3096			1.00566			0.502831	−	0.864385i	$-0.332292\pi$
$449$	21.3096			1.00566			0.502831	+	0.864385i	$0.332292\pi$
$450$		0			0
$451$	−1.67674			−0.0789544
$452$	6.05780	+	1.96830i	0.284935	+	0.0925810i
$453$	12.3055	−	16.9370i	0.578162	−	0.795772i
$454$	−7.16599	−	5.20640i	−0.336317	−	0.244348i
$455$		0			0
$456$	−5.55899	+	4.03884i	−0.260324	+	0.189136i
$457$			13.4662i			0.629923i	0.949104	+	0.314961i	$0.101992\pi$
$457$			13.4662i			0.629923i	−0.949104	+	0.314961i	$0.898008\pi$
$458$	−12.9681	−	17.8490i	−0.605958	−	0.834029i
$459$	−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	$-0.177090\pi$
$462$	−1.02781	+	0.333955i	−0.0478179	+	0.0155370i
$463$	21.8083	−	7.08596i	1.01352	−	0.329312i	0.245264	−	0.969456i	$-0.421125\pi$
$463$	21.8083	−	7.08596i	1.01352	−	0.329312i	0.768255	+	0.640144i	$0.221125\pi$
$464$	2.79158	−	8.59159i	0.129596	−	0.398854i
$465$		0			0
$466$	3.56690	+	10.9778i	0.165234	+	0.508537i
$467$	12.2459	+	16.8551i	0.566674	+	0.779960i	0.992156	−	0.125007i	$-0.0398954\pi$
$467$	12.2459	+	16.8551i	0.566674	+	0.779960i	−0.425482	+	0.904967i	$0.639895\pi$
$468$		−	2.18619i		−	0.101057i
$469$	−11.2516	+	8.17475i	−0.519549	+	0.377475i
$470$		0			0
$471$	4.62756	+	3.36212i	0.213227	+	0.154918i
$472$	−5.08361	+	6.99698i	−0.233992	+	0.322062i
$473$	−4.71894	−	1.53328i	−0.216977	−	0.0705001i
$474$	3.51243			0.161331
$475$		0			0
$476$	−5.60085			−0.256714
$477$	−2.31906	−	0.753509i	−0.106183	−	0.0345008i
$478$	−0.520147	+	0.715921i	−0.0237910	+	0.0327455i
$479$	10.9401	+	7.94842i	0.499864	+	0.363172i	0.808965	−	0.587857i	$-0.200028\pi$
$479$	10.9401	+	7.94842i	0.499864	+	0.363172i	−0.309101	+	0.951029i	$0.600028\pi$
$480$		0			0
$481$	9.38664	−	6.81980i	0.427994	−	0.310956i
$482$		−	12.6736i		−	0.577269i
$483$	−4.71477	−	6.48932i	−0.214529	−	0.295274i
$484$	3.31558	+	10.2043i	0.150708	+	0.463832i
$485$		0			0
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	25.3198	−	8.22690i	1.14735	−	0.372796i	0.327205	−	0.944953i	$-0.393893\pi$
$487$	25.3198	−	8.22690i	1.14735	−	0.372796i	0.820144	+	0.572157i	$0.193893\pi$
$488$	−11.9721	+	3.88998i	−0.541953	+	0.176091i
$489$	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	$0.987449\pi$
$492$	1.89477	+	2.60793i	0.0854230	+	0.117575i
$493$			24.3524i			1.09678i
$494$	12.1530	−	8.82968i	0.546790	−	0.397266i
$495$		0			0
$496$	5.99083	+	4.35259i	0.268996	+	0.195437i
$497$	9.97625	−	13.7311i	0.447496	−	0.615925i
$498$	−12.4884	−	4.05774i	−0.559620	−	0.181831i
$499$	27.3600			1.22480			0.612400	−	0.790548i	$-0.290204\pi$
$499$	27.3600			1.22480			0.612400	+	0.790548i	$0.290204\pi$
$500$		0			0
$501$	−8.94427			−0.399601
$502$	−17.2109	−	5.59216i	−0.768161	−	0.249590i
$503$	−5.38563	+	7.41268i	−0.240133	+	0.330515i	−0.912025	−	0.410134i	$-0.865482\pi$
$503$	−5.38563	+	7.41268i	−0.240133	+	0.330515i	0.671892	+	0.740649i	$0.265482\pi$
$504$	1.68088	+	1.22123i	0.0748724	+	0.0543980i
$505$		0			0
$506$	1.62460	−	1.18034i	0.0722222	−	0.0524725i
$507$		−	8.22056i		−	0.365088i
$508$	8.79756	+	12.1088i	0.390329	+	0.537241i
$509$	0.725667	+	2.23337i	0.0321646	+	0.0989925i	0.965850	−	0.259102i	$-0.0834266\pi$
$509$	0.725667	+	2.23337i	0.0321646	+	0.0989925i	−0.933685	+	0.358094i	$0.883427\pi$
$510$		0			0
$511$	−2.46767	+	7.59470i	−0.109163	+	0.335970i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−6.53498	+	2.12334i	−0.288527	+	0.0937480i
$514$	−0.395706	+	1.21786i	−0.0174538	+	0.0537174i
$515$		0			0
$516$	2.94777	+	9.07232i	0.129769	+	0.399386i
$517$	2.83286	+	3.89910i	0.124589	+	0.171482i
$518$			11.0267i			0.484483i
$519$	−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	$0.689300\pi$
$522$	5.30989	−	7.30844i	0.232408	−	0.319882i
$523$	−39.5506	−	12.8508i	−1.72943	−	0.561926i	−0.736062	−	0.676914i	$-0.763317\pi$
$523$	−39.5506	−	12.8508i	−1.72943	−	0.561926i	−0.993367	+	0.114988i	$0.963317\pi$
$524$	−13.8551			−0.605265
$525$		0			0
$526$	−7.11425			−0.310196
$527$	−18.9850	−	6.16859i	−0.826999	−	0.268708i
$528$	−0.305735	+	0.420808i	−0.0133054	+	0.0183133i
$529$	−6.54920	−	4.75827i	−0.284748	−	0.206881i
$530$		0			0
$531$	−6.99698	+	5.08361i	−0.303643	+	0.220610i
$532$			14.2764i			0.618959i
$533$	−4.14234	−	5.70144i	−0.179425	−	0.246957i
$534$	−3.04654	−	9.37628i	−0.131837	−	0.405751i
$535$		0			0
$536$	−2.06851	+	6.36623i	−0.0893462	+	0.274979i
$537$	−3.49849	+	1.13673i	−0.150971	+	0.0490535i
$538$	8.96833	−	2.91399i	0.386652	−	0.125631i
$539$	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	$0.765760\pi$
$542$	0.808141	+	1.11231i	0.0347126	+	0.0477778i
$543$			23.0493i			0.989138i
$544$	−2.18088	+	1.58450i	−0.0935045	+	0.0679350i
$545$		0			0
$546$	−3.67473	−	2.66985i	−0.157264	−	0.114259i
$547$	16.0588	−	22.1030i	0.686624	−	0.945057i	−0.313365	−	0.949633i	$-0.601456\pi$
$547$	16.0588	−	22.1030i	0.686624	−	0.945057i	0.999990	+	0.00457542i	$0.00145641\pi$
$548$	18.9202	+	6.14755i	0.808231	+	0.262610i
$549$	−12.5882			−0.537253
$550$		0			0
$551$	62.0734			2.64441
$552$	−3.67171	−	1.19301i	−0.156278	−	0.0507779i
$553$	4.28949	−	5.90398i	0.182408	−	0.251063i
$554$	15.8540	+	11.5186i	0.673574	+	0.489380i
$555$		0			0
$556$	−4.56581	+	3.31725i	−0.193633	+	0.140683i
$557$		−	9.89921i		−	0.419443i	−0.977761	−	0.209721i	$-0.932744\pi$
$557$		−	9.89921i		−	0.419443i	0.977761	−	0.209721i	$-0.0672557\pi$
$558$	4.35259	+	5.99083i	0.184260	+	0.253612i
$559$	−6.44440	−	19.8338i	−0.272569	−	0.838881i
$560$		0			0
$561$	0.433294	−	1.33354i	0.0182937	−	0.0563022i
$562$	−2.69916	+	0.877011i	−0.113857	+	0.0369945i
$563$	1.91338	−	0.621694i	0.0806392	−	0.0262013i	−0.268420	−	0.963302i	$-0.586501\pi$
$563$	1.91338	−	0.621694i	0.0806392	−	0.0262013i	0.349059	+	0.937101i	$0.386501\pi$
$564$	2.86327	−	8.81224i	0.120565	−	0.371062i
$565$		0			0
$566$	−0.690208	−	2.12424i	−0.0290116	−	0.0892886i
$567$	1.22123	+	1.68088i	0.0512869	+	0.0705904i
$568$		−	8.16901i		−	0.342764i
$569$	19.0969	−	13.8747i	0.800585	−	0.581659i	−0.110501	−	0.993876i	$-0.535245\pi$
$569$	19.0969	−	13.8747i	0.800585	−	0.581659i	0.911086	+	0.412217i	$0.135245\pi$
$570$		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	$0.846546\pi$
$572$	0.668395	−	0.919967i	0.0279470	−	0.0384657i
$573$	1.70019	+	0.552424i	0.0710263	+	0.0230779i
$574$	6.69758			0.279552
$575$		0			0
$576$	1.00000			0.0416667
$577$	43.1167	+	14.0095i	1.79497	+	0.583222i	0.999734	−	0.0230749i	$-0.00734563\pi$
$577$	43.1167	+	14.0095i	1.79497	+	0.583222i	0.795238	+	0.606297i	$0.207346\pi$
$578$	−5.72098	+	7.87425i	−0.237961	+	0.327526i
$579$	5.34063	+	3.88019i	0.221949	+	0.161255i
$580$		0			0
$581$	−22.0718	+	16.0361i	−0.915694	+	0.665291i
$582$			10.7598i			0.446006i
$583$	−0.745506	−	1.02610i	−0.0308757	−	0.0424967i
$584$	1.18770	+	3.65537i	0.0491474	+	0.151260i
$585$		0			0
$586$	7.42445	−	22.8501i	0.306701	−	0.943929i
$587$	15.5245	−	5.04421i	0.640764	−	0.208197i	0.0294265	−	0.999567i	$-0.490632\pi$
$587$	15.5245	−	5.04421i	0.640764	−	0.208197i	0.611337	+	0.791370i	$0.290632\pi$
$588$	−2.55190	+	0.829164i	−0.105239	+	0.0341941i
$589$	−15.7235	+	48.3920i	−0.647877	+	1.99396i
$590$		0			0
$591$	−3.91138	−	12.0380i	−0.160893	−	0.495177i
$592$	3.11949	+	4.29360i	0.128210	+	0.176466i
$593$			32.8357i			1.34840i	0.738549	+	0.674199i	$0.235511\pi$
$593$			32.8357i			1.34840i	−0.738549	+	0.674199i	$0.764489\pi$
$594$	−0.420808	+	0.305735i	−0.0172660	+	0.0125444i
$595$		0			0
$596$	12.2126	+	8.87296i	0.500247	+	0.363451i
$597$	3.66865	−	5.04946i	0.150148	−	0.206661i
$598$	8.02707	+	2.60815i	0.328251	+	0.106655i
$599$	13.1905			0.538947			0.269474	−	0.963008i	$-0.413150\pi$
$599$	13.1905			0.538947			0.269474	+	0.963008i	$0.413150\pi$
$600$		0			0
$601$	−19.1992			−0.783152			−0.391576	−	0.920146i	$-0.628070\pi$
$601$	−19.1992			−0.783152			−0.391576	+	0.920146i	$0.628070\pi$
$602$	18.8494	+	6.12454i	0.768244	+	0.249618i
$603$	−3.93455	+	5.41544i	−0.160227	+	0.220534i
$604$	−16.9370	−	12.3055i	−0.689158	−	0.500703i
$605$		0			0
$606$	−14.2711	+	10.3685i	−0.579722	+	0.421193i
$607$			6.54268i			0.265559i	0.991146	+	0.132779i	$0.0423902\pi$
$607$			6.54268i			0.265559i	−0.991146	+	0.132779i	$0.957610\pi$
$608$	4.03884	+	5.55899i	0.163797	+	0.225447i
$609$	−5.80001	−	17.8506i	−0.235028	−	0.723343i
$610$		0			0
$611$	−6.25966	+	19.2653i	−0.253239	+	0.779389i
$612$	−2.56378	+	0.833023i	−0.103635	+	0.0336729i
$613$	−8.87528	+	2.88375i	−0.358469	+	0.116474i	−0.482714	−	0.875778i	$-0.660349\pi$
$613$	−8.87528	+	2.88375i	−0.358469	+	0.116474i	0.124245	+	0.992252i	$0.460349\pi$
$614$	−5.29049	+	16.2824i	−0.213507	+	0.657106i
$615$		0			0
$616$	0.333955	+	1.02781i	0.0134554	+	0.0414115i
$617$	19.3979	+	26.6989i	0.780929	+	1.07486i	0.995179	+	0.0980778i	$0.0312694\pi$
$617$	19.3979	+	26.6989i	0.780929	+	1.07486i	−0.214250	+	0.976779i	$0.568731\pi$
$618$			8.69758i			0.349868i
$619$	22.7569	−	16.5339i	0.914678	−	0.664553i	−0.0275155	−	0.999621i	$-0.508760\pi$
$619$	22.7569	−	16.5339i	0.914678	−	0.664553i	0.942194	+	0.335069i	$0.108760\pi$
$620$		0			0
$621$	−3.12334	−	2.26924i	−0.125336	−	0.0910616i
$622$	11.8455	−	16.3039i	0.474961	−	0.653727i
$623$	−19.4809	−	6.32974i	−0.780487	−	0.253596i
$624$	−2.18619			−0.0875177
$625$		0			0
$626$	−25.5043			−1.01936
$627$	−3.39915	−	1.10445i	−0.135749	−	0.0441075i
$628$	3.36212	−	4.62756i	0.134163	−	0.184660i
$629$	−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	$0.284808\pi$
$632$		−	3.51243i		−	0.139717i
$633$	−13.2122	−	18.1850i	−0.525138	−	0.722790i
$634$	9.73967	+	29.9756i	0.386812	+	1.19048i
$635$		0			0
$636$	−0.753509	+	2.31906i	−0.0298786	+	0.0919568i
$637$	5.57895	−	1.81271i	0.221046	−	0.0718223i
$638$	4.46889	−	1.45203i	0.176925	−	0.0574864i
$639$	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	$0.822704\pi$
$642$	3.17979	+	4.37660i	0.125496	+	0.172731i
$643$		−	27.0249i		−	1.06576i	−0.846192	−	0.532878i	$-0.821110\pi$
$643$		−	27.0249i		−	1.06576i	0.846192	−	0.532878i	$-0.178890\pi$
$644$	−6.48932	+	4.71477i	−0.255715	+	0.185788i
$645$		0			0
$646$	−14.9855	−	10.8876i	−0.589595	−	0.428366i
$647$	19.9375	−	27.4417i	0.783826	−	1.07884i	−0.211024	−	0.977481i	$-0.567680\pi$
$647$	19.9375	−	27.4417i	0.783826	−	1.07884i	0.994850	−	0.101363i	$-0.0323203\pi$
$648$	0.951057	+	0.309017i	0.0373610	+	0.0121393i
$649$	−4.49862			−0.176586
$650$		0			0
$651$	15.3854			0.603001
$652$	−11.3129	−	3.67577i	−0.443046	−	0.143954i
$653$	−8.73039	+	12.0163i	−0.341646	+	0.470236i	−0.944921	−	0.327297i	$-0.893862\pi$
$653$	−8.73039	+	12.0163i	−0.341646	+	0.470236i	0.603275	+	0.797533i	$0.293862\pi$
$654$	−2.33302	−	1.69504i	−0.0912284	−	0.0662813i
$655$		0			0
$656$	2.60793	−	1.89477i	0.101823	−	0.0739785i
$657$			3.84348i			0.149948i
$658$	−11.3156	−	15.5746i	−0.441129	−	0.607162i
$659$	−1.45835	−	4.48835i	−0.0568094	−	0.174841i	0.918625	−	0.395129i	$-0.129300\pi$
$659$	−1.45835	−	4.48835i	−0.0568094	−	0.174841i	−0.975435	+	0.220288i	$0.929300\pi$
$660$		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	$0.0783363\pi$
$662$	−6.94330	+	2.25602i	−0.269859	+	0.0876826i
$663$	5.60491	−	1.82115i	0.217677	−	0.0707275i
$664$	−4.05774	+	12.4884i	−0.157471	+	0.484645i
$665$		0			0
$666$	1.64001	+	5.04743i	0.0635491	+	0.195584i
$667$	20.4997	+	28.2155i	0.793753	+	1.09251i
$668$			8.94427i			0.346064i
$669$	14.5056	−	10.5389i	0.560819	−	0.407459i
$670$		0			0
$671$	−5.29723	−	3.84867i	−0.204497	−	0.148576i
$672$	1.22123	−	1.68088i	0.0471100	−	0.0648414i
$673$	23.4287	+	7.61244i	0.903110	+	0.293438i	0.723520	−	0.690303i	$-0.242523\pi$
$673$	23.4287	+	7.61244i	0.903110	+	0.293438i	0.179590	+	0.983742i	$0.442523\pi$
$674$	26.7448			1.03017
$675$		0			0
$676$	−8.22056			−0.316176
$677$	−28.3655	−	9.21651i	−1.09017	−	0.354219i	−0.291861	−	0.956461i	$-0.594274\pi$
$677$	−28.3655	−	9.21651i	−1.09017	−	0.354219i	−0.798314	+	0.602242i	$0.794274\pi$
$678$	3.74393	−	5.15307i	0.143785	−	0.197903i
$679$	18.0859	+	13.1402i	0.694072	+	0.504273i
$680$		0			0
$681$	−7.16599	+	5.20640i	−0.274601	+	0.199510i
$682$			3.85173i			0.147490i
$683$	15.3138	+	21.0776i	0.585964	+	0.806511i	0.994333	−	0.106306i	$-0.0339023\pi$
$683$	15.3138	+	21.0776i	0.585964	+	0.806511i	−0.408369	+	0.912817i	$0.633902\pi$
$684$	2.12334	+	6.53498i	0.0811881	+	0.249871i
$685$		0			0
$686$	−6.21702	+	19.1340i	−0.237367	+	0.730540i
$687$	−20.9828	+	6.81771i	−0.800542	+	0.260112i
$688$	9.07232	−	2.94777i	0.345879	−	0.112383i
$689$	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	$0.672928\pi$
$692$	9.60385	+	13.2186i	0.365084	+	0.502495i
$693$			1.08070i			0.0410524i
$694$	−3.94095	+	2.86327i	−0.149597	+	0.108688i
$695$		0			0
$696$	−7.30844	−	5.30989i	−0.277026	−	0.201271i
$697$	−5.10777	+	7.03025i	−0.193471	+	0.266290i
$698$	15.8991	+	5.16592i	0.601789	+	0.195533i
$699$	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	$0.419225\pi$
$702$	−2.07919	−	0.675571i	−0.0784741	−	0.0254978i
$703$	−21.4349	+	29.5026i	−0.808432	+	1.11271i
$704$	0.420808	+	0.305735i	0.0158598	+	0.0115228i
$705$		0			0
$706$	−21.9086	+	15.9175i	−0.824540	+	0.599063i
$707$			36.6503i			1.37838i
$708$	5.08361	+	6.99698i	0.191054	+	0.262963i
$709$	2.24820	+	6.91924i	0.0844329	+	0.259858i	0.984356	−	0.176191i	$-0.0563776\pi$
$709$	2.24820	+	6.91924i	0.0844329	+	0.259858i	−0.899923	+	0.436049i	$0.856378\pi$
$710$		0			0
$711$	1.08540	−	3.34052i	0.0407057	−	0.125279i
$712$	−9.37628	+	3.04654i	−0.351391	+	0.114174i
$713$	−27.1893	+	8.83434i	−1.01825	+	0.330849i
$714$	−1.73076	+	5.32672i	−0.0647720	+	0.199348i
$715$		0			0
$716$	1.13673	+	3.49849i	0.0424815	+	0.130745i
$717$	0.520147	+	0.715921i	0.0194252	+	0.0267366i
$718$		−	8.48817i		−	0.316776i
$719$	−26.0071	+	18.8953i	−0.969902	+	0.704675i	−0.955429	−	0.295220i	$-0.904607\pi$
$719$	−26.0071	+	18.8953i	−0.969902	+	0.704675i	−0.0144727	+	0.999895i	$0.504607\pi$
$720$		0			0
$721$	14.6196	+	10.6218i	0.544462	+	0.395575i
$722$	−16.5841	+	22.8261i	−0.617197	+	0.849499i
$723$	−12.0534	−	3.91637i	−0.448269	−	0.145651i
$724$	23.0493			0.856619
$725$		0			0
$726$	10.7294			0.398207
$727$	−2.97260	−	0.965858i	−0.110248	−	0.0358217i	0.253374	−	0.967369i	$-0.418460\pi$
$727$	−2.97260	−	0.965858i	−0.110248	−	0.0358217i	−0.363621	+	0.931547i	$0.618460\pi$
$728$	−2.66985	+	3.67473i	−0.0989511	+	0.136195i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	−20.8039	+	15.1149i	−0.769458	+	0.559044i
$732$			12.5882i			0.465275i
$733$	27.2488	+	37.5047i	1.00646	+	1.38527i	0.921279	+	0.388902i	$0.127146\pi$
$733$	27.2488	+	37.5047i	1.00646	+	1.38527i	0.0851773	+	0.996366i	$0.472854\pi$
$734$	−3.93925	−	12.1238i	−0.145400	−	0.447496i
$735$		0			0
$736$	−1.19301	+	3.67171i	−0.0439750	+	0.135341i
$737$	−3.31138	+	1.07593i	−0.121976	+	0.0396324i
$738$	3.06581	−	0.996141i	0.112854	−	0.0366685i
$739$	14.8417	−	45.6779i	0.545959	−	1.68029i	−0.172739	−	0.984968i	$-0.555262\pi$
$739$	14.8417	−	45.6779i	0.545959	−	1.68029i	0.718698	−	0.695322i	$-0.244738\pi$
$740$		0			0
$741$	−4.64204	−	14.2867i	−0.170530	−	0.524836i
$742$	2.97786	+	4.09867i	0.109321	+	0.150467i
$743$		−	2.88963i		−	0.106010i	−0.998594	−	0.0530051i	$-0.983120\pi$
$743$		−	2.88963i		−	0.106010i	0.998594	−	0.0530051i	$-0.0168799\pi$
$744$	5.99083	−	4.35259i	0.219635	−	0.159574i
$745$		0			0
$746$	−8.85108	−	6.43069i	−0.324061	−	0.235444i
$747$	−7.71827	+	10.6233i	−0.282397	+	0.388686i
$748$	−1.33354	−	0.433294i	−0.0487591	−	0.0158428i
$749$	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	$0.756144\pi$
$752$	−8.81224	−	2.86327i	−0.321349	−	0.104413i
$753$	−10.6369	+	14.6405i	−0.387631	+	0.533529i
$754$	15.9777	+	11.6084i	0.581872	+	0.422755i
$755$		0			0
$756$	1.68088	−	1.22123i	0.0611331	−	0.0444158i
$757$		−	25.4654i		−	0.925555i	−0.886475	−	0.462777i	$-0.846853\pi$
$757$		−	25.4654i		−	0.925555i	0.886475	−	0.462777i	$-0.153147\pi$
$758$	8.36427	+	11.5124i	0.303804	+	0.418150i
$759$	−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	$-0.172498\pi$
$762$	14.2348	−	4.62515i	0.515671	−	0.167552i
$763$	−5.69832	+	1.85150i	−0.206293	+	0.0670287i
$764$	0.552424	−	1.70019i	0.0199860	−	0.0615106i
$765$		0			0
$766$	−2.21386	−	6.81355i	−0.0799899	−	0.246184i
$767$	−11.1137	−	15.2967i	−0.401294	−	0.552334i
$768$		−	1.00000i		−	0.0360844i
$769$	1.67667	−	1.21817i	0.0604621	−	0.0439283i	−0.557144	−	0.830416i	$-0.688103\pi$
$769$	1.67667	−	1.21817i	0.0604621	−	0.0439283i	0.617606	+	0.786488i	$0.288103\pi$
$770$		0			0
$771$	1.03597	+	0.752678i	0.0373096	+	0.0271070i
$772$	3.88019	−	5.34063i	0.139651	−	0.192213i
$773$	−7.59855	−	2.46892i	−0.273301	−	0.0888009i	0.169160	−	0.985589i	$-0.445895\pi$
$773$	−7.59855	−	2.46892i	−0.273301	−	0.0888009i	−0.442461	+	0.896788i	$0.645895\pi$
$774$	9.53920			0.342879
$775$		0			0
$776$	10.7598			0.386253
$777$	10.4870	+	3.40742i	0.376218	+	0.122241i
$778$	−0.540158	+	0.743464i	−0.0193656	+	0.0266545i
$779$	17.9199	+	13.0195i	0.642045	+	0.466473i
$780$		0			0
$781$	3.43758	−	2.49755i	0.123006	−	0.0893693i
$782$		−	10.4073i		−	0.372163i
$783$	−5.30989	−	7.30844i	−0.189760	−	0.261182i
$784$	0.829164	+	2.55190i	0.0296130	+	0.0911394i
$785$		0			0
$786$	−4.28147	+	13.1770i	−0.152715	+	0.470009i
$787$	−17.0337	+	5.53459i	−0.607186	+	0.197287i	−0.596443	−	0.802656i	$-0.703420\pi$
$787$	−17.0337	+	5.53459i	−0.607186	+	0.197287i	−0.0107432	+	0.999942i	$0.503420\pi$
$788$	−12.0380	+	3.91138i	−0.428836	+	0.139337i
$789$	−2.19842	+	6.76605i	−0.0782659	+	0.240878i
$790$		0			0
$791$	−4.08950	−	12.5862i	−0.145406	−	0.447514i
$792$	0.305735	+	0.420808i	0.0108638	+	0.0149528i
$793$		−	27.5203i		−	0.977276i
$794$	17.6381	−	12.8148i	0.625954	−	0.454782i
$795$		0			0
$796$	−5.04946	−	3.66865i	−0.178973	−	0.130032i
$797$	15.4319	−	21.2401i	0.546625	−	0.752364i	−0.442925	−	0.896559i	$-0.646059\pi$
$797$	15.4319	−	21.2401i	0.546625	−	0.752364i	0.989549	+	0.144195i	$0.0460591\pi$
$798$	13.5776	+	4.41164i	0.480643	+	0.156170i
$799$	24.9778			0.883652
$800$		0			0
$801$	−9.85880			−0.348344
$802$	−21.6874	−	7.04666i	−0.765808	−	0.248826i
$803$	−1.17509	+	1.61737i	−0.0414679	+	0.0570756i
$804$	5.41544	+	3.93455i	0.190988	+	0.138761i
$805$		0			0
$806$	−13.0971	+	9.51560i	−0.461326	+	0.335173i
$807$		−	9.42986i		−	0.331947i
$808$	10.3685	+	14.2711i	0.364763	+	0.502054i
$809$	−9.12577	−	28.0862i	−0.320845	−	0.987459i	−0.973281	−	0.229616i	$-0.926253\pi$
$809$	−9.12577	−	28.0862i	−0.320845	−	0.987459i	0.652436	−	0.757844i	$-0.273747\pi$
$810$		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	$-0.0731348\pi$
$812$	−17.8506	+	5.80001i	−0.626433	+	0.203540i
$813$	1.30760	−	0.424865i	0.0458595	−	0.0149007i
$814$	−0.853047	+	2.62541i	−0.0298993	+	0.0920205i
$815$		0			0
$816$	0.833023	+	2.56378i	0.0291616	+	0.0897502i
$817$	38.5273	+	53.0283i	1.34790	+	1.85523i
$818$			5.00147i			0.174872i
$819$	−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	$0.985835\pi$
$822$	11.6933	−	16.0945i	0.407852	−	0.561360i
$823$	−20.6983	−	6.72529i	−0.721498	−	0.234429i	−0.0748255	−	0.997197i	$-0.523840\pi$
$823$	−20.6983	−	6.72529i	−0.721498	−	0.234429i	−0.646673	+	0.762768i	$0.723840\pi$
$824$	8.69758			0.302995
$825$		0			0
$826$	17.9694			0.625234
$827$	−18.1721	−	5.90446i	−0.631905	−	0.205318i	−0.0244861	−	0.999700i	$-0.507795\pi$
$827$	−18.1721	−	5.90446i	−0.631905	−	0.205318i	−0.607419	+	0.794382i	$0.707795\pi$
$828$	−2.26924	+	3.12334i	−0.0788616	+	0.108544i
$829$	−29.3862	−	21.3503i	−1.02063	−	0.741528i	−0.0542146	−	0.998529i	$-0.517265\pi$
$829$	−29.3862	−	21.3503i	−1.02063	−	0.741528i	−0.966411	+	0.257001i	$0.917265\pi$
$830$		0			0
$831$	15.8540	−	11.5186i	0.549971	−	0.399577i
$832$			2.18619i			0.0757926i
$833$	−4.25159	−	5.85181i	−0.147309	−	0.202753i
$834$	1.74398	+	5.36743i	0.0603892	+	0.185859i
$835$		0			0
$836$	−1.10445	+	3.39915i	−0.0381983	+	0.117562i
$837$	7.04264	−	2.28829i	0.243429	−	0.0790950i
$838$	21.7082	−	7.05342i	0.749897	−	0.243656i
$839$	−6.13673	+	18.8869i	−0.211863	+	0.652049i	0.787498	+	0.616317i	$0.211376\pi$
$839$	−6.13673	+	18.8869i	−0.211863	+	0.652049i	−0.999361	+	0.0357313i	$0.988624\pi$
$840$		0			0
$841$	16.2568	+	50.0334i	0.560581	+	1.72529i
$842$	9.23612	+	12.7124i	0.318298	+	0.438099i
$843$			2.83807i			0.0977483i
$844$	−18.1850	+	13.2122i	−0.625955	+	0.454783i
$845$		0			0
$846$	−7.49614	−	5.44627i	−0.257723	−	0.187246i
$847$	13.1031	−	18.0349i	0.450229	−	0.619687i
$848$	2.31906	+	0.753509i	0.0796369	+	0.0258756i
$849$	−2.23356			−0.0766556
$850$		0			0
$851$	−20.4893			−0.702363
$852$	−7.76919	−	2.52436i	−0.266168	−	0.0864832i
$853$	−15.3025	+	21.0621i	−0.523948	+	0.721153i	−0.986193	−	0.165600i	$-0.947044\pi$
$853$	−15.3025	+	21.0621i	−0.523948	+	0.721153i	0.462245	+	0.886752i	$0.347044\pi$
$854$	21.1594	+	15.3732i	0.724058	+	0.526059i
$855$		0			0
$856$	4.37660	−	3.17979i	0.149589	−	0.108683i
$857$			34.8614i			1.19084i	0.803414	+	0.595421i	$0.203015\pi$
$857$			34.8614i			1.19084i	−0.803414	+	0.595421i	$0.796985\pi$
$858$	−0.668395	−	0.919967i	−0.0228186	−	0.0314071i
$859$	4.67229	+	14.3798i	0.159417	+	0.490634i	0.998582	−	0.0532431i	$-0.0169558\pi$
$859$	4.67229	+	14.3798i	0.159417	+	0.490634i	−0.839165	+	0.543877i	$0.816956\pi$
$860$		0			0
$861$	2.06967	−	6.36978i	0.0705341	−	0.217081i
$862$	−9.08897	+	2.95319i	−0.309572	+	0.100586i
$863$	21.7819	−	7.07738i	0.741466	−	0.240917i	0.0861610	−	0.996281i	$-0.472540\pi$
$863$	21.7819	−	7.07738i	0.741466	−	0.240917i	0.655305	+	0.755364i	$0.272540\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$		0			0
$866$	2.50988	+	7.72462i	0.0852892	+	0.262493i
$867$	5.72098	+	7.87425i	0.194295	+	0.267424i
$868$		−	15.3854i		−	0.522215i
$869$	1.47806	−	1.07387i	0.0501397	−	0.0364286i
$870$		0			0
$871$	−11.8392	−	8.60168i	−0.401156	−	0.291457i
$872$	−1.69504	+	2.33302i	−0.0574013	+	0.0790061i
$873$	10.2331	+	3.32495i	0.346339	+	0.112532i
$874$	−26.5278			−0.897315
$875$		0			0
$876$	3.84348			0.129859
$877$	−15.6806	−	5.09493i	−0.529495	−	0.172043i	0.0320550	−	0.999486i	$-0.489795\pi$
$877$	−15.6806	−	5.09493i	−0.529495	−	0.172043i	−0.561550	+	0.827443i	$0.689795\pi$
$878$	5.41910	−	7.45875i	0.182886	−	0.251721i
$879$	−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	$0.427756\pi$
$882$			2.68323i			0.0903491i
$883$	14.3841	+	19.7980i	0.484062	+	0.666254i	0.979279	−	0.202515i	$-0.0649114\pi$
$883$	14.3841	+	19.7980i	0.484062	+	0.666254i	−0.495217	+	0.868769i	$0.664911\pi$
$884$	−1.82115	−	5.60491i	−0.0612518	−	0.188514i
$885$		0			0
$886$	2.97655	−	9.16088i	0.0999991	−	0.307766i
$887$	−3.75624	+	1.22048i	−0.126122	+	0.0409796i	−0.371398	−	0.928474i	$-0.621121\pi$
$887$	−3.75624	+	1.22048i	−0.126122	+	0.0409796i	0.245276	+	0.969453i	$0.421121\pi$
$888$	5.04743	−	1.64001i	0.169381	−	0.0550352i
$889$	9.60960	−	29.5753i	0.322296	−	0.991924i
$890$		0			0
$891$	0.160734	+	0.494689i	0.00538480	+	0.0165727i
$892$	−10.5389	−	14.5056i	−0.352870	−	0.485684i
$893$		−	63.6676i		−	2.13055i
$894$	12.2126	−	8.87296i	0.408450	−	0.296756i
$895$		0			0
$896$	−1.68088	−	1.22123i	−0.0561543	−	0.0407985i
$897$	4.96100	−	6.82823i	0.165643	−	0.227988i
$898$	−20.2666	−	6.58502i	−0.676306	−	0.219745i
$899$	−66.8954			−2.23109
$900$		0			0
$901$	−6.57325			−0.218987
$902$	1.59467	+	0.518140i	0.0530967	+	0.0172522i
$903$	11.6496	−	16.0343i	0.387673	−	0.533587i
$904$	−5.15307	−	3.74393i	−0.171389	−	0.124521i
$905$		0			0
$906$	−16.9370	+	12.3055i	−0.562695	+	0.408822i
$907$		−	52.8637i		−	1.75531i	−0.479291	−	0.877656i	$-0.659106\pi$
$907$		−	52.8637i		−	1.75531i	0.479291	−	0.877656i	$-0.340894\pi$
$908$	5.20640	+	7.16599i	0.172780	+	0.237812i
$909$	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	$0.0389377\pi$
$912$	6.53498	−	2.12334i	0.216395	−	0.0703110i
$913$	−6.49582	+	2.11062i	−0.214980	+	0.0698513i
$914$	4.16129	−	12.8071i	0.137643	−	0.423622i
$915$		0			0
$916$	6.81771	+	20.9828i	0.225264	+	0.693290i
$917$	16.9203	+	23.2888i	0.558759	+	0.769066i
$918$			2.69572i			0.0889719i
$919$	25.1008	−	18.2368i	0.828000	−	0.601577i	−0.0909927	−	0.995852i	$-0.529004\pi$
$919$	25.1008	−	18.2368i	0.828000	−	0.601577i	0.918993	+	0.394274i	$0.129004\pi$
$920$		0			0
$921$	13.8507	+	10.0631i	0.456395	+	0.331590i
$922$	−19.3003	+	26.5646i	−0.635622	+	0.874858i
$923$	16.9849	+	5.51874i	0.559066	+	0.181652i
$924$	1.08070			0.0355524
$925$		0			0
$926$	−22.9306			−0.753547
$927$	8.27189	+	2.68770i	0.271685	+	0.0882757i
$928$	−5.30989	+	7.30844i	−0.174306	+	0.239911i
$929$	−9.67177	−	7.02695i	−0.317320	−	0.230547i	0.417711	−	0.908580i	$-0.362833\pi$
$929$	−9.67177	−	7.02695i	−0.317320	−	0.230547i	−0.735031	+	0.678033i	$0.762833\pi$
$930$		0			0
$931$	−14.9161	+	10.8371i	−0.488854	+	0.355173i
$932$		−	11.5427i		−	0.378095i
$933$	−11.8455	−	16.3039i	−0.387804	−	0.533766i
$934$	−6.43806	−	19.8143i	−0.210660	−	0.648344i
$935$		0			0
$936$	−0.675571	+	2.07919i	−0.0220817	+	0.0679605i
$937$	13.9740	−	4.54042i	0.456510	−	0.148329i	−0.0717304	−	0.997424i	$-0.522852\pi$
$937$	13.9740	−	4.54042i	0.456510	−	0.148329i	0.528240	+	0.849095i	$0.322852\pi$
$938$	13.2270	−	4.29772i	0.431877	−	0.140325i
$939$	−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	$0.591838\pi$
$942$	−3.36212	−	4.62756i	−0.109544	−	0.150774i
$943$			12.4452i			0.405271i
$944$	6.99698	−	5.08361i	0.227732	−	0.165457i
$945$		0			0
$946$	4.01417	+	2.91646i	0.130512	+	0.0948224i
$947$	23.3247	−	32.1037i	0.757952	−	1.04323i	−0.239430	−	0.970914i	$-0.576960\pi$
$947$	23.3247	−	32.1037i	0.757952	−	1.04323i	0.997382	−	0.0723177i	$-0.0230395\pi$
$948$	−3.34052	−	1.08540i	−0.108495	−	0.0352522i
$949$	−8.40259			−0.272759
$950$		0			0
$951$	31.5182			1.02205
$952$	5.32672	+	1.73076i	0.172640	+	0.0560942i
$953$	29.7563	−	40.9560i	0.963901	−	1.32670i	0.0188330	−	0.999823i	$-0.494005\pi$
$953$	29.7563	−	40.9560i	0.963901	−	1.32670i	0.945068	−	0.326873i	$-0.105995\pi$
$954$	1.97271	+	1.43326i	0.0638689	+	0.0464035i
$955$		0			0
$956$	0.715921	−	0.520147i	0.0231545	−	0.0168228i
$957$		−	4.69887i		−	0.151893i
$958$	−7.94842	−	10.9401i	−0.256802	−	0.353457i
$959$	−12.7727	−	39.3102i	−0.412451	−	1.26939i
$960$		0			0
$961$	7.36546	−	22.6685i	0.237595	−	0.731243i
$962$	−11.0347	+	3.58538i	−0.355772	+	0.115597i
$963$	5.14500	−	1.67171i	0.165795	−	0.0538702i
$964$	−3.91637	+	12.0534i	−0.126138	+	0.388212i
$965$		0			0
$966$	2.47870	+	7.62866i	0.0797509	+	0.245448i
$967$	−6.49628	−	8.94137i	−0.208906	−	0.287535i	0.691687	−	0.722197i	$-0.256868\pi$
$967$	−6.49628	−	8.94137i	−0.208906	−	0.287535i	−0.900594	+	0.434662i	$0.856868\pi$
$968$		−	10.7294i		−	0.344857i
$969$	−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	$0.829488\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	11.1518	+	3.62345i	0.357511	+	0.116162i
$974$	−26.6228			−0.853050
$975$		0			0
$976$	12.5882			0.402940
$977$	−7.71967	−	2.50827i	−0.246974	−	0.0802467i	0.182914	−	0.983129i	$-0.441447\pi$
$977$	−7.71967	−	2.50827i	−0.246974	−	0.0802467i	−0.429888	+	0.902882i	$0.641447\pi$
$978$	−6.99173	+	9.62329i	−0.223571	+	0.307719i
$979$	−4.14866	−	3.01418i	−0.132592	−	0.0963336i
$980$		0			0
$981$	−2.33302	+	1.69504i	−0.0744877	+	0.0541185i
$982$			12.0227i			0.383659i
$983$	−15.6954	−	21.6028i	−0.500605	−	0.689023i	0.481695	−	0.876339i	$-0.340021\pi$
$983$	−15.6954	−	21.6028i	−0.500605	−	0.689023i	−0.982300	+	0.187316i	$0.940021\pi$
$984$	−0.996141	−	3.06581i	−0.0317558	−	0.0977344i
$985$		0			0
$986$	7.52530	−	23.1605i	0.239654	−	0.737580i
$987$	−18.3091	+	5.94897i	−0.582784	+	0.189358i
$988$	−14.2867	+	4.64204i	−0.454521	+	0.147683i
$989$	−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	$-0.417706\pi$
$992$	−4.35259	−	5.99083i	−0.138195	−	0.190209i
$993$			7.30062i			0.231678i
$994$	−13.7311	+	9.97625i	−0.435525	+	0.316427i
$995$		0			0
$996$	10.6233	+	7.71827i	0.336612	+	0.244563i
$997$	16.6169	−	22.8712i	0.526262	−	0.724337i	−0.460293	−	0.887767i	$-0.652256\pi$
$997$	16.6169	−	22.8712i	0.526262	−	0.724337i	0.986555	+	0.163430i	$0.0522557\pi$
$998$	−26.0209	−	8.45469i	−0.823676	−	0.267629i
$999$	5.30719			0.167912

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.19.2	✓	8	25.6	even	5
150.2.h.a.79.2	yes	8	5.4	even	2
450.2.l.a.19.1		8	75.56	odd	10
450.2.l.a.379.1		8	15.14	odd	2
750.2.g.c.151.2		8	25.17	odd	20
750.2.g.c.601.2		8	5.2	odd	4
750.2.g.e.151.1		8	25.8	odd	20
750.2.g.e.601.1		8	5.3	odd	4
750.2.h.c.349.1		8	25.19	even	10	inner
750.2.h.c.649.1		8	1.1	even	1	trivial
3750.2.a.m.1.1		4	25.13	odd	20
3750.2.a.o.1.4		4	25.12	odd	20
3750.2.c.e.1249.1		8	25.16	even	5
3750.2.c.e.1249.8		8	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.809017 - 0.587785i) q^{6} -2.07768i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(0.160734 - 0.494689i) q^{11} +(-0.951057 + 0.309017i) q^{12} +(2.07919 - 0.675571i) q^{13} +(-0.642040 + 1.97599i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.58450 - 2.18088i) q^{17} +1.00000i q^{18} +(-5.55899 + 4.03884i) q^{19} +(1.68088 + 1.22123i) q^{21} +(-0.305735 + 0.420808i) q^{22} +(-3.67171 - 1.19301i) q^{23} +1.00000 q^{24} -2.18619 q^{26} +(0.951057 + 0.309017i) q^{27} +(1.22123 - 1.68088i) q^{28} +(-7.30844 - 5.30989i) q^{29} +(5.99083 - 4.35259i) q^{31} -1.00000i q^{32} +(0.305735 + 0.420808i) q^{33} +(0.833023 + 2.56378i) q^{34} +(0.309017 - 0.951057i) q^{36} +(5.04743 - 1.64001i) q^{37} +(6.53498 - 2.12334i) q^{38} +(-0.675571 + 2.07919i) q^{39} +(-0.996141 - 3.06581i) q^{41} +(-1.22123 - 1.68088i) q^{42} -9.53920i q^{43} +(0.420808 - 0.305735i) q^{44} +(3.12334 + 2.26924i) q^{46} +(-5.44627 + 7.49614i) q^{47} +(-0.951057 - 0.309017i) q^{48} +2.68323 q^{49} +2.69572 q^{51} +(2.07919 + 0.675571i) q^{52} +(1.43326 - 1.97271i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.68088 + 1.22123i) q^{56} -6.87129i q^{57} +(5.30989 + 7.30844i) q^{58} +(-2.67261 - 8.22545i) q^{59} +(3.88998 - 11.9721i) q^{61} +(-7.04264 + 2.28829i) q^{62} +(-1.97599 + 0.642040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.160734 - 0.494689i) q^{66} +(-3.93455 - 5.41544i) q^{67} -2.69572i q^{68} +(3.12334 - 2.26924i) q^{69} +(6.60886 + 4.80162i) q^{71} +(-0.587785 + 0.809017i) q^{72} +(-3.65537 - 1.18770i) q^{73} -5.30719 q^{74} -6.87129 q^{76} +(-1.02781 - 0.333955i) q^{77} +(1.28501 - 1.76867i) q^{78} +(2.84162 + 2.06455i) q^{79} +(-0.809017 + 0.587785i) q^{81} +3.22358i q^{82} +(-7.71827 - 10.6233i) q^{83} +(0.642040 + 1.97599i) q^{84} +(-2.94777 + 9.07232i) q^{86} +(8.59159 - 2.79158i) q^{87} +(-0.494689 + 0.160734i) q^{88} +(3.04654 - 9.37628i) q^{89} +(-1.40362 - 4.31990i) q^{91} +(-2.26924 - 3.12334i) q^{92} +7.40507i q^{93} +(7.49614 - 5.44627i) q^{94} +(0.809017 + 0.587785i) q^{96} +(-6.32443 + 8.70483i) q^{97} +(-2.55190 - 0.829164i) q^{98} -0.520147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} - 8 q^{19} - 2 q^{21} + 10 q^{23} + 8 q^{24} + 4 q^{26} + 10 q^{28} - 22 q^{29} + 24 q^{31} + 8 q^{34} - 2 q^{36}+ \cdots + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 - 8 * q^19 - 2 * q^21 + 10 * q^23 + 8 * q^24 + 4 * q^26 + 10 * q^28 - 22 * q^29 + 24 * q^31 + 8 * q^34 - 2 * q^36 + 20 * q^37 + 10 * q^38 + 4 * q^39 + 22 * q^41 - 10 * q^42 + 10 * q^46 - 10 * q^47 + 8 * q^49 - 12 * q^51 + 20 * q^52 + 30 * q^53 - 2 * q^54 + 2 * q^56 - 30 * q^58 - 20 * q^59 - 10 * q^62 - 10 * q^63 + 2 * q^64 - 10 * q^66 - 10 * q^67 + 10 * q^69 + 20 * q^71 + 20 * q^73 - 4 * q^74 - 12 * q^76 + 20 * q^77 + 16 * q^79 - 2 * q^81 - 70 * q^83 + 2 * q^84 - 18 * q^86 + 30 * q^87 - 10 * q^88 - 34 * q^89 - 24 * q^91 - 30 * q^92 + 30 * q^94 + 2 * q^96 - 60 * q^97 - 20 * q^98 + 20 * q^99

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