LMFDB - Embedded newform 605.2.g.i.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.2
Root			$-0.535233 + 1.64728i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.i.366.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40126 + 1.01807i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.40126 + 1.01807i) q^{6} +(0.535233 + 1.64728i) q^{7} +(0.535233 - 1.64728i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})$	\(q+(1.40126 + 1.01807i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.40126 + 1.01807i) q^{6} +(0.535233 + 1.64728i) q^{7} +(0.535233 - 1.64728i) q^{8} +(1.61803 + 1.17557i) q^{9} +1.73205 q^{10} -1.00000 q^{12} +(2.80252 + 2.03615i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{15} +(4.04508 - 2.93893i) q^{16} +(-5.60503 + 4.07230i) q^{17} +(1.07047 + 3.29456i) q^{18} +(1.07047 - 3.29456i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.73205 q^{21} +(1.40126 + 1.01807i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.85410 + 5.70634i) q^{26} +(-4.04508 + 2.93893i) q^{27} +(-1.40126 + 1.01807i) q^{28} +(-0.535233 + 1.64728i) q^{30} +(6.47214 + 4.70228i) q^{31} +5.19615 q^{32} -12.0000 q^{34} +(1.40126 + 1.01807i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(4.85410 - 3.52671i) q^{38} +(-2.80252 + 2.03615i) q^{39} +(-0.535233 - 1.64728i) q^{40} +(-3.74663 + 11.5309i) q^{41} +(-2.42705 - 1.76336i) q^{42} -8.66025 q^{43} +2.00000 q^{45} +(2.78115 - 8.55951i) q^{47} +(1.54508 + 4.75528i) q^{48} +(3.23607 - 2.35114i) q^{49} +(1.40126 - 1.01807i) q^{50} +(-2.14093 - 6.58911i) q^{51} +(-1.07047 + 3.29456i) q^{52} +(-4.85410 - 3.52671i) q^{53} -8.66025 q^{54} +3.00000 q^{56} +(2.80252 + 2.03615i) q^{57} +(-3.70820 - 11.4127i) q^{59} +(-0.809017 + 0.587785i) q^{60} +(7.00629 - 5.09037i) q^{61} +(4.28187 + 13.1782i) q^{62} +(-1.07047 + 3.29456i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.46410 q^{65} -5.00000 q^{67} +(-5.60503 - 4.07230i) q^{68} +(0.927051 + 2.85317i) q^{70} +(9.70820 - 7.05342i) q^{71} +(2.80252 - 2.03615i) q^{72} +(4.28187 - 13.1782i) q^{74} +(0.809017 + 0.587785i) q^{75} +3.46410 q^{76} -6.00000 q^{78} +(-8.40755 - 6.10844i) q^{79} +(1.54508 - 4.75528i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-16.9894 + 12.3435i) q^{82} +(2.80252 - 2.03615i) q^{83} +(-0.535233 - 1.64728i) q^{84} +(-2.14093 + 6.58911i) q^{85} +(-12.1353 - 8.81678i) q^{86} +3.00000 q^{89} +(2.80252 + 2.03615i) q^{90} +(-1.85410 + 5.70634i) q^{91} +(-6.47214 + 4.70228i) q^{93} +(12.6113 - 9.16267i) q^{94} +(-1.07047 - 3.29456i) q^{95} +(-1.60570 + 4.94183i) q^{96} +(8.09017 + 5.87785i) q^{97} +6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9} - 8 q^{12} + 6 q^{14} - 2 q^{15} + 10 q^{16} + 2 q^{20} - 2 q^{25} - 12 q^{26} - 10 q^{27} + 16 q^{31} - 96 q^{34} + 4 q^{36} + 16 q^{37} + 12 q^{38} - 6 q^{42} + 16 q^{45} - 18 q^{47} - 10 q^{48} + 8 q^{49} - 12 q^{53} + 24 q^{56} + 24 q^{59} - 2 q^{60} - 2 q^{64} - 40 q^{67} - 6 q^{70} + 24 q^{71} + 2 q^{75} - 48 q^{78} - 10 q^{80} - 2 q^{81} - 42 q^{82} - 30 q^{86} + 24 q^{89} + 12 q^{91} - 16 q^{93} + 20 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9 - 8 * q^12 + 6 * q^14 - 2 * q^15 + 10 * q^16 + 2 * q^20 - 2 * q^25 - 12 * q^26 - 10 * q^27 + 16 * q^31 - 96 * q^34 + 4 * q^36 + 16 * q^37 + 12 * q^38 - 6 * q^42 + 16 * q^45 - 18 * q^47 - 10 * q^48 + 8 * q^49 - 12 * q^53 + 24 * q^56 + 24 * q^59 - 2 * q^60 - 2 * q^64 - 40 * q^67 - 6 * q^70 + 24 * q^71 + 2 * q^75 - 48 * q^78 - 10 * q^80 - 2 * q^81 - 42 * q^82 - 30 * q^86 + 24 * q^89 + 12 * q^91 - 16 * q^93 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.40126	+	1.01807i	0.990839	+	0.719887i	0.960105	−	0.279641i	$-0.0902153\pi$
$2$	1.40126	+	1.01807i	0.990839	+	0.719887i	0.0307347	+	0.999528i	$0.490215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	−0.999773	−	0.0213149i	$-0.993215\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i	0.821362	+	0.570408i	$0.193215\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−1.40126	+	1.01807i	−0.572061	+	0.415627i
$7$	0.535233	+	1.64728i	0.202299	+	0.622613i	0.999813	+	0.0193127i	$0.00614781\pi$
$7$	0.535233	+	1.64728i	0.202299	+	0.622613i	−0.797514	+	0.603300i	$0.793852\pi$
$8$	0.535233	−	1.64728i	0.189233	−	0.582401i
$9$	1.61803	+	1.17557i	0.539345	+	0.391857i
$10$	1.73205			0.547723
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	2.80252	+	2.03615i	0.777278	+	0.564726i	0.904161	−	0.427192i	$-0.140497\pi$
$13$	2.80252	+	2.03615i	0.777278	+	0.564726i	−0.126883	+	0.991918i	$0.540497\pi$
$14$	−0.927051	+	2.85317i	−0.247765	+	0.762542i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	4.04508	−	2.93893i	1.01127	−	0.734732i
$17$	−5.60503	+	4.07230i	−1.35942	+	0.987677i	−0.360939	+	0.932589i	$0.617544\pi$
$17$	−5.60503	+	4.07230i	−1.35942	+	0.987677i	−0.998482	+	0.0550873i	$0.982456\pi$
$18$	1.07047	+	3.29456i	0.252311	+	0.776534i
$19$	1.07047	−	3.29456i	0.245582	−	0.755823i	−0.749958	−	0.661485i	$-0.769927\pi$
$19$	1.07047	−	3.29456i	0.245582	−	0.755823i	0.995540	−	0.0943381i	$-0.0300735\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−1.73205			−0.377964
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	1.40126	+	1.01807i	0.286031	+	0.207813i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	1.85410	+	5.70634i	0.363619	+	1.11911i
$27$	−4.04508	+	2.93893i	−0.778477	+	0.565597i
$28$	−1.40126	+	1.01807i	−0.264813	+	0.192398i
$29$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$29$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$30$	−0.535233	+	1.64728i	−0.0977198	+	0.300750i
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.990083	−	0.140482i	$-0.0448651\pi$
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.172347	+	0.985036i	$0.444865\pi$
$32$	5.19615			0.918559
$33$		0			0
$34$	−12.0000			−2.05798
$35$	1.40126	+	1.01807i	0.236856	+	0.172086i
$36$	−0.618034	+	1.90211i	−0.103006	+	0.317019i
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	−0.919707	−	0.392607i	$-0.871573\pi$
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	0.513290	−	0.858215i	$-0.328427\pi$
$38$	4.85410	−	3.52671i	0.787439	−	0.572108i
$39$	−2.80252	+	2.03615i	−0.448762	+	0.326045i
$40$	−0.535233	−	1.64728i	−0.0846278	−	0.260458i
$41$	−3.74663	+	11.5309i	−0.585126	+	1.80083i	0.0136398	+	0.999907i	$0.495658\pi$
$41$	−3.74663	+	11.5309i	−0.585126	+	1.80083i	−0.598765	+	0.800924i	$0.704342\pi$
$42$	−2.42705	−	1.76336i	−0.374502	−	0.272092i
$43$	−8.66025			−1.32068			−0.660338	−	0.750968i	$-0.729587\pi$
$43$	−8.66025			−1.32068			−0.660338	+	0.750968i	$0.729587\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$	2.78115	−	8.55951i	0.405673	−	1.24853i	−0.514659	−	0.857395i	$-0.672082\pi$
$47$	2.78115	−	8.55951i	0.405673	−	1.24853i	0.920332	−	0.391138i	$-0.127918\pi$
$48$	1.54508	+	4.75528i	0.223014	+	0.686366i
$49$	3.23607	−	2.35114i	0.462295	−	0.335877i
$50$	1.40126	−	1.01807i	0.198168	−	0.143977i
$51$	−2.14093	−	6.58911i	−0.299791	−	0.922660i
$52$	−1.07047	+	3.29456i	−0.148447	+	0.456873i
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	0.202178	−	0.979349i	$-0.435198\pi$
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	−0.868940	+	0.494918i	$0.835198\pi$
$54$	−8.66025			−1.17851
$55$		0			0
$56$	3.00000			0.400892
$57$	2.80252	+	2.03615i	0.371202	+	0.269694i
$58$		0			0
$59$	−3.70820	−	11.4127i	−0.482767	−	1.48580i	−0.835189	−	0.549963i	$-0.814642\pi$
$59$	−3.70820	−	11.4127i	−0.482767	−	1.48580i	0.352422	−	0.935841i	$-0.385358\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	7.00629	−	5.09037i	0.897064	−	0.651755i	−0.0406463	−	0.999174i	$-0.512942\pi$
$61$	7.00629	−	5.09037i	0.897064	−	0.651755i	0.937710	+	0.347419i	$0.112942\pi$
$62$	4.28187	+	13.1782i	0.543797	+	1.67364i
$63$	−1.07047	+	3.29456i	−0.134866	+	0.415075i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.46410			0.429669
$66$		0			0
$67$	−5.00000			−0.610847			−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000			−0.610847			−0.305424	+	0.952217i	$0.598798\pi$
$68$	−5.60503	−	4.07230i	−0.679710	−	0.493838i
$69$		0			0
$70$	0.927051	+	2.85317i	0.110804	+	0.341019i
$71$	9.70820	−	7.05342i	1.15215	−	0.837087i	0.163386	−	0.986562i	$-0.447758\pi$
$71$	9.70820	−	7.05342i	1.15215	−	0.837087i	0.988766	+	0.149475i	$0.0477583\pi$
$72$	2.80252	−	2.03615i	0.330280	−	0.239962i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$	4.28187	−	13.1782i	0.497757	−	1.53194i
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$	3.46410			0.397360
$77$		0			0
$78$	−6.00000			−0.679366
$79$	−8.40755	−	6.10844i	−0.945923	−	0.687254i	0.00391577	−	0.999992i	$-0.498754\pi$
$79$	−8.40755	−	6.10844i	−0.945923	−	0.687254i	−0.949839	+	0.312739i	$0.898754\pi$
$80$	1.54508	−	4.75528i	0.172746	−	0.531657i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−16.9894	+	12.3435i	−1.87616	+	1.36311i
$83$	2.80252	−	2.03615i	0.307616	−	0.223496i	−0.423257	−	0.906010i	$-0.639113\pi$
$83$	2.80252	−	2.03615i	0.307616	−	0.223496i	0.730873	+	0.682514i	$0.239113\pi$
$84$	−0.535233	−	1.64728i	−0.0583987	−	0.179733i
$85$	−2.14093	+	6.58911i	−0.232217	+	0.714690i
$86$	−12.1353	−	8.81678i	−1.30858	−	0.950738i
$87$		0			0
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$	2.80252	+	2.03615i	0.295411	+	0.214629i
$91$	−1.85410	+	5.70634i	−0.194363	+	0.598187i
$92$		0			0
$93$	−6.47214	+	4.70228i	−0.671129	+	0.487604i
$94$	12.6113	−	9.16267i	1.30076	−	0.945057i
$95$	−1.07047	−	3.29456i	−0.109828	−	0.338014i
$96$	−1.60570	+	4.94183i	−0.163881	+	0.504374i
$97$	8.09017	+	5.87785i	0.821432	+	0.596806i	0.917122	−	0.398606i	$-0.130506\pi$
$97$	8.09017	+	5.87785i	0.821432	+	0.596806i	−0.0956901	+	0.995411i	$0.530506\pi$
$98$	6.92820			0.699854
$99$		0			0
$100$	1.00000			0.100000
$101$	−1.40126	−	1.01807i	−0.139430	−	0.101302i	0.515884	−	0.856659i	$-0.327464\pi$
$101$	−1.40126	−	1.01807i	−0.139430	−	0.101302i	−0.655314	+	0.755357i	$0.727464\pi$
$102$	3.70820	−	11.4127i	0.367167	−	1.13002i
$103$	−1.23607	−	3.80423i	−0.121793	−	0.374842i	0.871510	−	0.490378i	$-0.163141\pi$
$103$	−1.23607	−	3.80423i	−0.121793	−	0.374842i	−0.993303	+	0.115536i	$0.963141\pi$
$104$	4.85410	−	3.52671i	0.475984	−	0.345823i
$105$	−1.40126	+	1.01807i	−0.136749	+	0.0993538i
$106$	−3.21140	−	9.88367i	−0.311919	−	0.959987i
$107$	−0.535233	+	1.64728i	−0.0517429	+	0.159248i	−0.973589	−	0.228308i	$-0.926681\pi$
$107$	−0.535233	+	1.64728i	−0.0517429	+	0.159248i	0.921846	+	0.387556i	$0.126681\pi$
$108$	−4.04508	−	2.93893i	−0.389238	−	0.282798i
$109$	−1.73205			−0.165900			−0.0829502	−	0.996554i	$-0.526434\pi$
$109$	−1.73205			−0.165900			−0.0829502	+	0.996554i	$0.526434\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	7.00629	+	5.09037i	0.662032	+	0.480995i
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	−0.999606	−	0.0280521i	$-0.991070\pi$
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	0.825187	+	0.564859i	$0.191070\pi$
$114$	1.85410	+	5.70634i	0.173653	+	0.534448i
$115$		0			0
$116$		0			0
$117$	2.14093	+	6.58911i	0.197929	+	0.609164i
$118$	6.42280	−	19.7673i	0.591266	−	1.81973i
$119$	−9.70820	−	7.05342i	−0.889950	−	0.646586i
$120$	1.73205			0.158114
$121$		0			0
$122$	15.0000			1.35804
$123$	−9.80881	−	7.12652i	−0.884431	−	0.642576i
$124$	−2.47214	+	7.60845i	−0.222004	+	0.683259i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−4.85410	+	3.52671i	−0.432438	+	0.314184i
$127$	1.40126	−	1.01807i	0.124342	−	0.0903395i	−0.523876	−	0.851794i	$-0.675515\pi$
$127$	1.40126	−	1.01807i	0.124342	−	0.0903395i	0.648218	+	0.761455i	$0.275515\pi$
$128$	−3.74663	−	11.5309i	−0.331159	−	1.01920i
$129$	2.67617	−	8.23639i	0.235623	−	0.725174i
$130$	4.85410	+	3.52671i	0.425733	+	0.309313i
$131$	3.46410			0.302660			0.151330	−	0.988483i	$-0.451644\pi$
$131$	3.46410			0.302660			0.151330	+	0.988483i	$0.451644\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$	−7.00629	−	5.09037i	−0.605252	−	0.439741i
$135$	−1.54508	+	4.75528i	−0.132980	+	0.409270i
$136$	3.70820	+	11.4127i	0.317976	+	0.978629i
$137$	−14.5623	+	10.5801i	−1.24414	+	0.903922i	−0.997867	−	0.0652782i	$-0.979207\pi$
$137$	−14.5623	+	10.5801i	−1.24414	+	0.903922i	−0.246275	+	0.969200i	$0.579207\pi$
$138$		0			0
$139$	−4.28187	−	13.1782i	−0.363183	−	1.11776i	−0.951111	−	0.308849i	$-0.900056\pi$
$139$	−4.28187	−	13.1782i	−0.363183	−	1.11776i	0.587928	−	0.808913i	$-0.299944\pi$
$140$	−0.535233	+	1.64728i	−0.0452355	+	0.139220i
$141$	7.28115	+	5.29007i	0.613184	+	0.445504i
$142$	20.7846			1.74421
$143$		0			0
$144$	10.0000			0.833333
$145$		0			0
$146$		0			0
$147$	1.23607	+	3.80423i	0.101949	+	0.313767i
$148$	6.47214	−	4.70228i	0.532006	−	0.386525i
$149$	−15.4138	+	11.1988i	−1.26275	+	0.917443i	−0.998889	−	0.0471179i	$-0.984996\pi$
$149$	−15.4138	+	11.1988i	−1.26275	+	0.917443i	−0.263862	+	0.964560i	$0.584996\pi$
$150$	0.535233	+	1.64728i	0.0437016	+	0.134500i
$151$	6.42280	−	19.7673i	0.522680	−	1.60864i	−0.246179	−	0.969224i	$-0.579175\pi$
$151$	6.42280	−	19.7673i	0.522680	−	1.60864i	0.768859	−	0.639419i	$-0.220825\pi$
$152$	−4.85410	−	3.52671i	−0.393720	−	0.286054i
$153$	−13.8564			−1.12022
$154$		0			0
$155$	8.00000			0.642575
$156$	−2.80252	−	2.03615i	−0.224381	−	0.163022i
$157$	1.23607	−	3.80423i	0.0986490	−	0.303610i	−0.889538	−	0.456860i	$-0.848974\pi$
$157$	1.23607	−	3.80423i	0.0986490	−	0.303610i	0.988187	+	0.153250i	$0.0489740\pi$
$158$	−5.56231	−	17.1190i	−0.442513	−	1.36192i
$159$	4.85410	−	3.52671i	0.384955	−	0.279686i
$160$	4.20378	−	3.05422i	0.332338	−	0.241457i
$161$		0			0
$162$	−0.535233	+	1.64728i	−0.0420519	+	0.129422i
$163$	15.3713	+	11.1679i	1.20397	+	0.874739i	0.994670	−	0.103111i	$-0.0328798\pi$
$163$	15.3713	+	11.1679i	1.20397	+	0.874739i	0.209305	+	0.977850i	$0.432880\pi$
$164$	−12.1244			−0.946753
$165$		0			0
$166$	6.00000			0.465690
$167$	−4.20378	−	3.05422i	−0.325298	−	0.236343i	0.413135	−	0.910670i	$-0.364434\pi$
$167$	−4.20378	−	3.05422i	−0.325298	−	0.236343i	−0.738433	+	0.674327i	$0.764434\pi$
$168$	−0.927051	+	2.85317i	−0.0715235	+	0.220127i
$169$	−0.309017	−	0.951057i	−0.0237705	−	0.0731582i
$170$	−9.70820	+	7.05342i	−0.744585	+	0.540973i
$171$	5.60503	−	4.07230i	0.428628	−	0.311416i
$172$	−2.67617	−	8.23639i	−0.204056	−	0.628019i
$173$	−3.21140	+	9.88367i	−0.244158	+	0.751441i	0.751616	+	0.659601i	$0.229275\pi$
$173$	−3.21140	+	9.88367i	−0.244158	+	0.751441i	−0.995774	+	0.0918401i	$0.970725\pi$
$174$		0			0
$175$	1.73205			0.130931
$176$		0			0
$177$	12.0000			0.901975
$178$	4.20378	+	3.05422i	0.315086	+	0.228924i
$179$	−5.56231	+	17.1190i	−0.415746	+	1.27954i	0.495835	+	0.868416i	$0.334862\pi$
$179$	−5.56231	+	17.1190i	−0.415746	+	1.27954i	−0.911582	+	0.411119i	$0.865138\pi$
$180$	0.618034	+	1.90211i	0.0460655	+	0.141775i
$181$	−8.89919	+	6.46564i	−0.661471	+	0.480587i	−0.867160	−	0.498031i	$-0.834057\pi$
$181$	−8.89919	+	6.46564i	−0.661471	+	0.480587i	0.205688	+	0.978618i	$0.434057\pi$
$182$	−8.40755	+	6.10844i	−0.623209	+	0.452788i
$183$	2.67617	+	8.23639i	0.197828	+	0.608852i
$184$		0			0
$185$	−6.47214	−	4.70228i	−0.475841	−	0.345719i
$186$	−13.8564			−1.01600
$187$		0			0
$188$	9.00000			0.656392
$189$	−7.00629	−	5.09037i	−0.509633	−	0.370270i
$190$	1.85410	−	5.70634i	0.134511	−	0.413981i
$191$	−1.85410	−	5.70634i	−0.134158	−	0.412896i	0.861300	−	0.508097i	$-0.169651\pi$
$191$	−1.85410	−	5.70634i	−0.134158	−	0.412896i	−0.995458	+	0.0952005i	$0.969651\pi$
$192$	0.809017	−	0.587785i	0.0583858	−	0.0424197i
$193$	−2.80252	+	2.03615i	−0.201730	+	0.146565i	−0.684064	−	0.729422i	$-0.739789\pi$
$193$	−2.80252	+	2.03615i	−0.201730	+	0.146565i	0.482334	+	0.875987i	$0.339789\pi$
$194$	5.35233	+	16.4728i	0.384275	+	1.18268i
$195$	−1.07047	+	3.29456i	−0.0766577	+	0.235928i
$196$	3.23607	+	2.35114i	0.231148	+	0.167939i
$197$	10.3923			0.740421			0.370211	−	0.928948i	$-0.379286\pi$
$197$	10.3923			0.740421			0.370211	+	0.928948i	$0.379286\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	−1.40126	−	1.01807i	−0.0990839	−	0.0719887i
$201$	1.54508	−	4.75528i	0.108982	−	0.335412i
$202$	−0.927051	−	2.85317i	−0.0652271	−	0.200748i
$203$		0			0
$204$	5.60503	−	4.07230i	0.392431	−	0.285118i
$205$	3.74663	+	11.5309i	0.261676	+	0.805356i
$206$	2.14093	−	6.58911i	0.149166	−	0.459085i
$207$		0			0
$208$	17.3205			1.20096
$209$		0			0
$210$	−3.00000			−0.207020
$211$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$211$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$212$	1.85410	−	5.70634i	0.127340	−	0.391913i
$213$	3.70820	+	11.4127i	0.254082	+	0.781984i
$214$	−2.42705	+	1.76336i	−0.165910	+	0.120541i
$215$	−7.00629	+	5.09037i	−0.477825	+	0.347160i
$216$	2.67617	+	8.23639i	0.182090	+	0.560415i
$217$	−4.28187	+	13.1782i	−0.290672	+	0.894596i
$218$	−2.42705	−	1.76336i	−0.164381	−	0.119430i
$219$		0			0
$220$		0			0
$221$	−24.0000			−1.61441
$222$	11.2101	+	8.14459i	0.752371	+	0.546629i
$223$	−5.87132	+	18.0701i	−0.393173	+	1.21006i	0.537203	+	0.843453i	$0.319481\pi$
$223$	−5.87132	+	18.0701i	−0.393173	+	1.21006i	−0.930375	+	0.366608i	$0.880519\pi$
$224$	2.78115	+	8.55951i	0.185824	+	0.571906i
$225$	1.61803	−	1.17557i	0.107869	−	0.0783714i
$226$	−8.40755	+	6.10844i	−0.559262	+	0.406328i
$227$	−5.88756	−	18.1201i	−0.390771	−	1.20267i	−0.932206	−	0.361928i	$-0.882119\pi$
$227$	−5.88756	−	18.1201i	−0.390771	−	1.20267i	0.541435	−	0.840743i	$-0.317881\pi$
$228$	−1.07047	+	3.29456i	−0.0708934	+	0.218187i
$229$	−5.66312	−	4.11450i	−0.374229	−	0.271894i	0.384733	−	0.923028i	$-0.374293\pi$
$229$	−5.66312	−	4.11450i	−0.374229	−	0.271894i	−0.758963	+	0.651134i	$0.774293\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.80252	−	2.03615i	−0.183599	−	0.133392i	0.492189	−	0.870488i	$-0.336197\pi$
$233$	−2.80252	−	2.03615i	−0.183599	−	0.133392i	−0.675788	+	0.737096i	$0.736197\pi$
$234$	−3.70820	+	11.4127i	−0.242413	+	0.746070i
$235$	−2.78115	−	8.55951i	−0.181422	−	0.558361i
$236$	9.70820	−	7.05342i	0.631950	−	0.459139i
$237$	8.40755	−	6.10844i	0.546129	−	0.396786i
$238$	−6.42280	−	19.7673i	−0.416328	−	1.28133i
$239$	−1.07047	+	3.29456i	−0.0692427	+	0.213107i	−0.979690	−	0.200518i	$-0.935738\pi$
$239$	−1.07047	+	3.29456i	−0.0692427	+	0.213107i	0.910447	+	0.413625i	$0.135738\pi$
$240$	4.04508	+	2.93893i	0.261109	+	0.189707i
$241$	19.0526			1.22728			0.613642	−	0.789585i	$-0.289704\pi$
$241$	19.0526			1.22728			0.613642	+	0.789585i	$0.289704\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$	7.00629	+	5.09037i	0.448532	+	0.325878i
$245$	1.23607	−	3.80423i	0.0789695	−	0.243043i
$246$	−6.48936	−	19.9722i	−0.413746	−	1.27338i
$247$	9.70820	−	7.05342i	0.617718	−	0.448799i
$248$	11.2101	−	8.14459i	0.711840	−	0.517182i
$249$	1.07047	+	3.29456i	0.0678380	+	0.208784i
$250$	0.535233	−	1.64728i	0.0338511	−	0.104183i
$251$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$251$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$252$	−3.46410			−0.218218
$253$		0			0
$254$	3.00000			0.188237
$255$	−5.60503	−	4.07230i	−0.351001	−	0.255017i
$256$	5.87132	−	18.0701i	0.366958	−	1.12938i
$257$	3.70820	+	11.4127i	0.231311	+	0.711903i	0.997589	+	0.0693940i	$0.0221066\pi$
$257$	3.70820	+	11.4127i	0.231311	+	0.711903i	−0.766278	+	0.642509i	$0.777893\pi$
$258$	12.1353	−	8.81678i	0.755508	−	0.548909i
$259$	11.2101	−	8.14459i	0.696560	−	0.506080i
$260$	1.07047	+	3.29456i	0.0663875	+	0.204320i
$261$		0			0
$262$	4.85410	+	3.52671i	0.299887	+	0.217881i
$263$	−24.2487			−1.49524			−0.747620	−	0.664127i	$-0.768803\pi$
$263$	−24.2487			−1.49524			−0.747620	+	0.664127i	$0.768803\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	8.40755	+	6.10844i	0.515500	+	0.374533i
$267$	−0.927051	+	2.85317i	−0.0567346	+	0.174611i
$268$	−1.54508	−	4.75528i	−0.0943811	−	0.290475i
$269$	12.1353	−	8.81678i	0.739900	−	0.537568i	−0.152780	−	0.988260i	$-0.548823\pi$
$269$	12.1353	−	8.81678i	0.739900	−	0.537568i	0.892680	+	0.450692i	$0.148823\pi$
$270$	−7.00629	+	5.09037i	−0.426389	+	0.309790i
$271$	4.28187	+	13.1782i	0.260105	+	0.800520i	0.992781	+	0.119943i	$0.0382711\pi$
$271$	4.28187	+	13.1782i	0.260105	+	0.800520i	−0.732676	+	0.680578i	$0.761729\pi$
$272$	−10.7047	+	32.9456i	−0.649066	+	1.99762i
$273$	−4.85410	−	3.52671i	−0.293784	−	0.213446i
$274$	−31.1769			−1.88347
$275$		0			0
$276$		0			0
$277$	8.40755	+	6.10844i	0.505161	+	0.367021i	0.810985	−	0.585067i	$-0.198932\pi$
$277$	8.40755	+	6.10844i	0.505161	+	0.367021i	−0.305824	+	0.952088i	$0.598932\pi$
$278$	7.41641	−	22.8254i	0.444807	−	1.36897i
$279$	4.94427	+	15.2169i	0.296006	+	0.911012i
$280$	2.42705	−	1.76336i	0.145044	−	0.105381i
$281$	−5.60503	+	4.07230i	−0.334368	+	0.242933i	−0.742282	−	0.670088i	$-0.766256\pi$
$281$	−5.60503	+	4.07230i	−0.334368	+	0.242933i	0.407914	+	0.913021i	$0.366256\pi$
$282$	4.81710	+	14.8255i	0.286854	+	0.882846i
$283$	1.60570	−	4.94183i	0.0954489	−	0.293762i	−0.891921	−	0.452190i	$-0.850643\pi$
$283$	1.60570	−	4.94183i	0.0954489	−	0.293762i	0.987370	+	0.158429i	$0.0506428\pi$
$284$	9.70820	+	7.05342i	0.576076	+	0.418544i
$285$	3.46410			0.205196
$286$		0			0
$287$	−21.0000			−1.23959
$288$	8.40755	+	6.10844i	0.495420	+	0.359943i
$289$	9.57953	−	29.4828i	0.563502	−	1.73428i
$290$		0			0
$291$	−8.09017	+	5.87785i	−0.474254	+	0.344566i
$292$		0			0
$293$	2.14093	+	6.58911i	0.125075	+	0.384940i	0.993915	−	0.110153i	$-0.0351340\pi$
$293$	2.14093	+	6.58911i	0.125075	+	0.384940i	−0.868840	+	0.495093i	$0.835134\pi$
$294$	−2.14093	+	6.58911i	−0.124862	+	0.384285i
$295$	−9.70820	−	7.05342i	−0.565233	−	0.410666i
$296$	−13.8564			−0.805387
$297$		0			0
$298$	−33.0000			−1.91164
$299$		0			0
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$	−4.63525	−	14.2658i	−0.267172	−	0.822270i
$302$	29.1246	−	21.1603i	1.67593	−	1.21764i
$303$	1.40126	−	1.01807i	0.0805002	−	0.0584868i
$304$	−5.35233	−	16.4728i	−0.306977	−	0.944779i
$305$	2.67617	−	8.23639i	0.153237	−	0.471614i
$306$	−19.4164	−	14.1068i	−1.10996	−	0.806435i
$307$	10.3923			0.593120			0.296560	−	0.955014i	$-0.404160\pi$
$307$	10.3923			0.593120			0.296560	+	0.955014i	$0.404160\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	11.2101	+	8.14459i	0.636689	+	0.462582i
$311$	−1.85410	+	5.70634i	−0.105136	+	0.323577i	−0.989762	−	0.142724i	$-0.954414\pi$
$311$	−1.85410	+	5.70634i	−0.105136	+	0.323577i	0.884626	+	0.466301i	$0.154414\pi$
$312$	1.85410	+	5.70634i	0.104968	+	0.323058i
$313$	−8.09017	+	5.87785i	−0.457283	+	0.332236i	−0.792465	−	0.609918i	$-0.791202\pi$
$313$	−8.09017	+	5.87785i	−0.457283	+	0.332236i	0.335181	+	0.942154i	$0.391202\pi$
$314$	5.60503	−	4.07230i	0.316310	−	0.229813i
$315$	1.07047	+	3.29456i	0.0603139	+	0.185627i
$316$	3.21140	−	9.88367i	0.180655	−	0.556000i
$317$	4.85410	+	3.52671i	0.272634	+	0.198080i	0.715698	−	0.698410i	$-0.246109\pi$
$317$	4.85410	+	3.52671i	0.272634	+	0.198080i	−0.443064	+	0.896490i	$0.646109\pi$
$318$	10.3923			0.582772
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	−1.40126	−	1.01807i	−0.0782106	−	0.0568233i
$322$		0			0
$323$	7.41641	+	22.8254i	0.412660	+	1.27004i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	2.80252	−	2.03615i	0.155456	−	0.112945i
$326$	10.1694	+	31.2983i	0.563233	+	1.73345i
$327$	0.535233	−	1.64728i	0.0295985	−	0.0910947i
$328$	16.9894	+	12.3435i	0.938080	+	0.681555i
$329$	15.5885			0.859419
$330$		0			0
$331$	−34.0000			−1.86881			−0.934405	−	0.356214i	$-0.884068\pi$
$331$	−34.0000			−1.86881			−0.934405	+	0.356214i	$0.884068\pi$
$332$	2.80252	+	2.03615i	0.153808	+	0.111748i
$333$	4.94427	−	15.2169i	0.270944	−	0.833881i
$334$	−2.78115	−	8.55951i	−0.152178	−	0.468355i
$335$	−4.04508	+	2.93893i	−0.221007	+	0.160571i
$336$	−7.00629	+	5.09037i	−0.382225	+	0.277702i
$337$	−3.21140	−	9.88367i	−0.174936	−	0.538398i	0.824694	−	0.565578i	$-0.191347\pi$
$337$	−3.21140	−	9.88367i	−0.174936	−	0.538398i	−0.999631	+	0.0271807i	$0.991347\pi$
$338$	0.535233	−	1.64728i	0.0291128	−	0.0896001i
$339$	−4.85410	−	3.52671i	−0.263639	−	0.191545i
$340$	−6.92820			−0.375735
$341$		0			0
$342$	12.0000			0.648886
$343$	15.4138	+	11.1988i	0.832269	+	0.604679i
$344$	−4.63525	+	14.2658i	−0.249916	+	0.769163i
$345$		0			0
$346$	−14.5623	+	10.5801i	−0.782874	+	0.568792i
$347$	−9.80881	+	7.12652i	−0.526564	+	0.382572i	−0.819071	−	0.573692i	$-0.805511\pi$
$347$	−9.80881	+	7.12652i	−0.526564	+	0.382572i	0.292507	+	0.956263i	$0.405511\pi$
$348$		0			0
$349$	−10.7047	+	32.9456i	−0.573007	+	1.76354i	0.0698585	+	0.997557i	$0.477745\pi$
$349$	−10.7047	+	32.9456i	−0.573007	+	1.76354i	−0.642866	+	0.765979i	$0.722255\pi$
$350$	2.42705	+	1.76336i	0.129731	+	0.0942553i
$351$	−17.3205			−0.924500
$352$		0			0
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$	16.8151	+	12.2169i	0.893713	+	0.649320i
$355$	3.70820	−	11.4127i	0.196811	−	0.605722i
$356$	0.927051	+	2.85317i	0.0491336	+	0.151218i
$357$	9.70820	−	7.05342i	0.513813	−	0.373307i
$358$	−25.2227	+	18.3253i	−1.33306	+	0.968524i
$359$	1.07047	+	3.29456i	0.0564970	+	0.173880i	0.975323	−	0.220783i	$-0.0708613\pi$
$359$	1.07047	+	3.29456i	0.0564970	+	0.173880i	−0.918826	+	0.394663i	$0.870861\pi$
$360$	1.07047	−	3.29456i	0.0564185	−	0.173638i
$361$	5.66312	+	4.11450i	0.298059	+	0.216552i
$362$	−19.0526			−1.00138
$363$		0			0
$364$	−6.00000			−0.314485
$365$		0			0
$366$	−4.63525	+	14.2658i	−0.242289	+	0.745688i
$367$	5.25329	+	16.1680i	0.274219	+	0.843961i	0.989425	+	0.145046i	$0.0463331\pi$
$367$	5.25329	+	16.1680i	0.274219	+	0.843961i	−0.715205	+	0.698914i	$0.753667\pi$
$368$		0			0
$369$	−19.6176	+	14.2530i	−1.02125	+	0.741983i
$370$	−4.28187	−	13.1782i	−0.222604	−	0.685103i
$371$	3.21140	−	9.88367i	0.166728	−	0.513135i
$372$	−6.47214	−	4.70228i	−0.335565	−	0.243802i
$373$	13.8564			0.717458			0.358729	−	0.933442i	$-0.383210\pi$
$373$	13.8564			0.717458			0.358729	+	0.933442i	$0.383210\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$	−12.6113	−	9.16267i	−0.650380	−	0.472528i
$377$		0			0
$378$	−4.63525	−	14.2658i	−0.238412	−	0.733756i
$379$	27.5066	−	19.9847i	1.41292	−	1.02655i	0.420028	−	0.907511i	$-0.362020\pi$
$379$	27.5066	−	19.9847i	1.41292	−	1.02655i	0.992890	−	0.119034i	$-0.0379797\pi$
$380$	2.80252	−	2.03615i	0.143766	−	0.104452i
$381$	0.535233	+	1.64728i	0.0274208	+	0.0843926i
$382$	3.21140	−	9.88367i	0.164309	−	0.505693i
$383$	−19.4164	−	14.1068i	−0.992132	−	0.720826i	−0.0317451	−	0.999496i	$-0.510106\pi$
$383$	−19.4164	−	14.1068i	−0.992132	−	0.720826i	−0.960387	+	0.278670i	$0.910106\pi$
$384$	12.1244			0.618718
$385$		0			0
$386$	−6.00000			−0.305392
$387$	−14.0126	−	10.1807i	−0.712300	−	0.517516i
$388$	−3.09017	+	9.51057i	−0.156880	+	0.482826i
$389$	0.927051	+	2.85317i	0.0470034	+	0.144661i	0.971804	−	0.235791i	$-0.0757682\pi$
$389$	0.927051	+	2.85317i	0.0470034	+	0.144661i	−0.924800	+	0.380453i	$0.875768\pi$
$390$	−4.85410	+	3.52671i	−0.245797	+	0.178582i
$391$		0			0
$392$	−2.14093	−	6.58911i	−0.108133	−	0.332800i
$393$	−1.07047	+	3.29456i	−0.0539979	+	0.166188i
$394$	14.5623	+	10.5801i	0.733638	+	0.533019i
$395$	−10.3923			−0.522894
$396$		0			0
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$	−19.6176	−	14.2530i	−0.983342	−	0.714440i
$399$	−1.85410	+	5.70634i	−0.0928212	+	0.285674i
$400$	−1.54508	−	4.75528i	−0.0772542	−	0.237764i
$401$	−21.8435	+	15.8702i	−1.09081	+	0.792520i	−0.979536	−	0.201270i	$-0.935493\pi$
$401$	−21.8435	+	15.8702i	−1.09081	+	0.792520i	−0.111274	+	0.993790i	$0.535493\pi$
$402$	7.00629	−	5.09037i	0.349442	−	0.253885i
$403$	8.56373	+	26.3565i	0.426590	+	1.31291i
$404$	0.535233	−	1.64728i	0.0266288	−	0.0819552i
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$		0			0
$407$		0			0
$408$	−12.0000			−0.594089
$409$	4.20378	+	3.05422i	0.207863	+	0.151022i	0.686846	−	0.726803i	$-0.258994\pi$
$409$	4.20378	+	3.05422i	0.207863	+	0.151022i	−0.478983	+	0.877824i	$0.658994\pi$
$410$	−6.48936	+	19.9722i	−0.320486	+	0.986356i
$411$	−5.56231	−	17.1190i	−0.274368	−	0.844419i
$412$	3.23607	−	2.35114i	0.159430	−	0.115832i
$413$	16.8151	−	12.2169i	0.827417	−	0.601154i
$414$		0			0
$415$	1.07047	−	3.29456i	0.0525471	−	0.161723i
$416$	14.5623	+	10.5801i	0.713976	+	0.518734i
$417$	13.8564			0.678551
$418$		0			0
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$	−1.40126	−	1.01807i	−0.0683744	−	0.0496769i
$421$	−5.25329	+	16.1680i	−0.256030	+	0.787978i	0.737595	+	0.675243i	$0.235961\pi$
$421$	−5.25329	+	16.1680i	−0.256030	+	0.787978i	−0.993625	+	0.112735i	$0.964039\pi$
$422$		0			0
$423$	14.5623	−	10.5801i	0.708044	−	0.514424i
$424$	−8.40755	+	6.10844i	−0.408307	+	0.296652i
$425$	2.14093	+	6.58911i	0.103850	+	0.319619i
$426$	−6.42280	+	19.7673i	−0.311186	+	0.957731i
$427$	12.1353	+	8.81678i	0.587266	+	0.426674i
$428$	−1.73205			−0.0837218
$429$		0			0
$430$	−15.0000			−0.723364
$431$	30.8277	+	22.3976i	1.48492	+	1.07886i	0.975931	+	0.218081i	$0.0699798\pi$
$431$	30.8277	+	22.3976i	1.48492	+	1.07886i	0.508987	+	0.860774i	$0.330020\pi$
$432$	−7.72542	+	23.7764i	−0.371690	+	1.14394i
$433$	9.88854	+	30.4338i	0.475213	+	1.46256i	0.845670	+	0.533706i	$0.179201\pi$
$433$	9.88854	+	30.4338i	0.475213	+	1.46256i	−0.370457	+	0.928850i	$0.620799\pi$
$434$	−19.4164	+	14.1068i	−0.932017	+	0.677150i
$435$		0			0
$436$	−0.535233	−	1.64728i	−0.0256330	−	0.0788903i
$437$		0			0
$438$		0			0
$439$	27.7128			1.32266			0.661330	−	0.750095i	$-0.269992\pi$
$439$	27.7128			1.32266			0.661330	+	0.750095i	$0.269992\pi$
$440$		0			0
$441$	8.00000			0.380952
$442$	−33.6302	−	24.4338i	−1.59963	−	1.16220i
$443$	−4.63525	+	14.2658i	−0.220228	+	0.677791i	0.778513	+	0.627628i	$0.215974\pi$
$443$	−4.63525	+	14.2658i	−0.220228	+	0.677791i	−0.998741	+	0.0501629i	$0.984026\pi$
$444$	2.47214	+	7.60845i	0.117322	+	0.361081i
$445$	2.42705	−	1.76336i	0.115053	−	0.0835911i
$446$	−26.6239	+	19.3434i	−1.26068	+	0.915937i
$447$	−5.88756	−	18.1201i	−0.278472	−	0.857049i
$448$	0.535233	−	1.64728i	0.0252874	−	0.0778266i
$449$	12.1353	+	8.81678i	0.572698	+	0.416090i	0.836084	−	0.548601i	$-0.184839\pi$
$449$	12.1353	+	8.81678i	0.572698	+	0.416090i	−0.263386	+	0.964690i	$0.584839\pi$
$450$	3.46410			0.163299
$451$		0			0
$452$	−6.00000			−0.282216
$453$	16.8151	+	12.2169i	0.790042	+	0.573999i
$454$	10.1976	−	31.3849i	0.478595	−	1.47296i
$455$	1.85410	+	5.70634i	0.0869216	+	0.267517i
$456$	4.85410	−	3.52671i	0.227314	−	0.165153i
$457$	16.8151	−	12.2169i	0.786577	−	0.571482i	−0.120368	−	0.992729i	$-0.538408\pi$
$457$	16.8151	−	12.2169i	0.786577	−	0.571482i	0.906946	+	0.421247i	$0.138408\pi$
$458$	−3.74663	−	11.5309i	−0.175069	−	0.538806i
$459$	10.7047	−	32.9456i	0.499651	−	1.53777i
$460$		0			0
$461$	12.1244			0.564688			0.282344	−	0.959313i	$-0.408888\pi$
$461$	12.1244			0.564688			0.282344	+	0.959313i	$0.408888\pi$
$462$		0			0
$463$	41.0000			1.90543			0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000			1.90543			0.952716	+	0.303863i	$0.0982765\pi$
$464$		0			0
$465$	−2.47214	+	7.60845i	−0.114643	+	0.352834i
$466$	−1.85410	−	5.70634i	−0.0858896	−	0.264341i
$467$	−2.42705	+	1.76336i	−0.112311	+	0.0815984i	−0.642523	−	0.766267i	$-0.722112\pi$
$467$	−2.42705	+	1.76336i	−0.112311	+	0.0815984i	0.530212	+	0.847865i	$0.322112\pi$
$468$	−5.60503	+	4.07230i	−0.259093	+	0.188242i
$469$	−2.67617	−	8.23639i	−0.123574	−	0.380321i
$470$	4.81710	−	14.8255i	0.222196	−	0.683849i
$471$	3.23607	+	2.35114i	0.149110	+	0.108335i
$472$	−20.7846			−0.956689
$473$		0			0
$474$	18.0000			0.826767
$475$	−2.80252	−	2.03615i	−0.128588	−	0.0934249i
$476$	3.70820	−	11.4127i	0.169965	−	0.523099i
$477$	−3.70820	−	11.4127i	−0.169787	−	0.522551i
$478$	−4.85410	+	3.52671i	−0.222021	+	0.161308i
$479$	8.40755	−	6.10844i	0.384151	−	0.279102i	−0.378904	−	0.925436i	$-0.623699\pi$
$479$	8.40755	−	6.10844i	0.384151	−	0.279102i	0.763054	+	0.646334i	$0.223699\pi$
$480$	1.60570	+	4.94183i	0.0732898	+	0.225563i
$481$	8.56373	−	26.3565i	0.390472	−	1.20175i
$482$	26.6976	+	19.3969i	1.21604	+	0.883505i
$483$		0			0
$484$		0			0
$485$	10.0000			0.454077
$486$	−22.4201	−	16.2892i	−1.01700	−	0.738892i
$487$	−6.18034	+	19.0211i	−0.280058	+	0.861930i	0.707779	+	0.706434i	$0.249697\pi$
$487$	−6.18034	+	19.0211i	−0.280058	+	0.861930i	−0.987837	+	0.155495i	$0.950303\pi$
$488$	−4.63525	−	14.2658i	−0.209828	−	0.645785i
$489$	−15.3713	+	11.1679i	−0.695115	+	0.505031i
$490$	5.60503	−	4.07230i	0.253210	−	0.183968i
$491$	−7.49326	−	23.0619i	−0.338166	−	1.04077i	−0.965141	−	0.261729i	$-0.915707\pi$
$491$	−7.49326	−	23.0619i	−0.338166	−	1.04077i	0.626975	−	0.779039i	$-0.284293\pi$
$492$	3.74663	−	11.5309i	0.168911	−	0.519855i
$493$		0			0
$494$	20.7846			0.935144
$495$		0			0
$496$	40.0000			1.79605
$497$	16.8151	+	12.2169i	0.754260	+	0.548002i
$498$	−1.85410	+	5.70634i	−0.0830843	+	0.255707i
$499$	−11.7426	−	36.1401i	−0.525673	−	1.61786i	−0.762981	−	0.646421i	$-0.776265\pi$
$499$	−11.7426	−	36.1401i	−0.525673	−	1.61786i	0.237308	−	0.971434i	$-0.423735\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	4.20378	−	3.05422i	0.187811	−	0.136453i
$502$		0			0
$503$	−2.67617	+	8.23639i	−0.119324	+	0.367243i	−0.992824	−	0.119582i	$-0.961845\pi$
$503$	−2.67617	+	8.23639i	−0.119324	+	0.367243i	0.873500	+	0.486824i	$0.161845\pi$
$504$	4.85410	+	3.52671i	0.216219	+	0.157092i
$505$	−1.73205			−0.0770752
$506$		0			0
$507$	1.00000			0.0444116
$508$	1.40126	+	1.01807i	0.0621708	+	0.0451697i
$509$	4.63525	−	14.2658i	0.205454	−	0.632323i	−0.794240	−	0.607604i	$-0.792131\pi$
$509$	4.63525	−	14.2658i	0.205454	−	0.632323i	0.999694	−	0.0247189i	$-0.00786908\pi$
$510$	−3.70820	−	11.4127i	−0.164202	−	0.505362i
$511$		0			0
$512$	7.00629	−	5.09037i	0.309637	−	0.224965i
$513$	5.35233	+	16.4728i	0.236311	+	0.727291i
$514$	−6.42280	+	19.7673i	−0.283297	+	0.871900i
$515$	−3.23607	−	2.35114i	−0.142598	−	0.103604i
$516$	8.66025			0.381246
$517$		0			0
$518$	24.0000			1.05450
$519$	−8.40755	−	6.10844i	−0.369051	−	0.268131i
$520$	1.85410	−	5.70634i	0.0813077	−	0.250240i
$521$	4.63525	+	14.2658i	0.203074	+	0.624998i	0.999787	+	0.0206400i	$0.00657038\pi$
$521$	4.63525	+	14.2658i	0.203074	+	0.624998i	−0.796713	+	0.604358i	$0.793430\pi$
$522$		0			0
$523$	−14.0126	+	10.1807i	−0.612728	+	0.445173i	−0.850374	−	0.526179i	$-0.823624\pi$
$523$	−14.0126	+	10.1807i	−0.612728	+	0.445173i	0.237646	+	0.971352i	$0.423624\pi$
$524$	1.07047	+	3.29456i	0.0467635	+	0.143923i
$525$	−0.535233	+	1.64728i	−0.0233595	+	0.0718931i
$526$	−33.9787	−	24.6870i	−1.48154	−	1.07640i
$527$	−55.4256			−2.41438
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−8.40755	−	6.10844i	−0.365201	−	0.265334i
$531$	7.41641	−	22.8254i	0.321845	−	0.990536i
$532$	1.85410	+	5.70634i	0.0803855	+	0.247401i
$533$	−33.9787	+	24.6870i	−1.47178	+	1.06931i
$534$	−4.20378	+	3.05422i	−0.181915	+	0.132169i
$535$	0.535233	+	1.64728i	0.0231401	+	0.0712180i
$536$	−2.67617	+	8.23639i	−0.115593	+	0.355758i
$537$	−14.5623	−	10.5801i	−0.628410	−	0.456567i
$538$	25.9808			1.12011
$539$		0			0
$540$	−5.00000			−0.215166
$541$	−4.20378	−	3.05422i	−0.180734	−	0.131311i	0.493740	−	0.869610i	$-0.335630\pi$
$541$	−4.20378	−	3.05422i	−0.180734	−	0.131311i	−0.674474	+	0.738299i	$0.735630\pi$
$542$	−7.41641	+	22.8254i	−0.318562	+	0.980433i
$543$	−3.39919	−	10.4616i	−0.145873	−	0.448951i
$544$	−29.1246	+	21.1603i	−1.24871	+	0.907239i
$545$	−1.40126	+	1.01807i	−0.0600233	+	0.0436095i
$546$	−3.21140	−	9.88367i	−0.137435	−	0.422982i
$547$	13.9161	−	42.8292i	0.595008	−	1.83125i	0.0403207	−	0.999187i	$-0.487162\pi$
$547$	13.9161	−	42.8292i	0.595008	−	1.83125i	0.554687	−	0.832059i	$-0.312838\pi$
$548$	−14.5623	−	10.5801i	−0.622071	−	0.451961i
$549$	17.3205			0.739221
$550$		0			0
$551$		0			0
$552$		0			0
$553$	5.56231	−	17.1190i	0.236533	−	0.727975i
$554$	5.56231	+	17.1190i	0.236320	+	0.727317i
$555$	6.47214	−	4.70228i	0.274727	−	0.199601i
$556$	11.2101	−	8.14459i	0.475413	−	0.345408i
$557$	2.14093	+	6.58911i	0.0907142	+	0.279190i	0.986113	−	0.166075i	$-0.0531095\pi$
$557$	2.14093	+	6.58911i	0.0907142	+	0.279190i	−0.895399	+	0.445265i	$0.853109\pi$
$558$	−8.56373	+	26.3565i	−0.362532	+	1.11576i
$559$	−24.2705	−	17.6336i	−1.02653	−	0.745820i
$560$	8.66025			0.365963
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−12.6113	−	9.16267i	−0.531504	−	0.386160i	0.289416	−	0.957203i	$-0.406539\pi$
$563$	−12.6113	−	9.16267i	−0.531504	−	0.386160i	−0.820920	+	0.571043i	$0.806539\pi$
$564$	−2.78115	+	8.55951i	−0.117108	+	0.360420i
$565$	1.85410	+	5.70634i	0.0780027	+	0.240067i
$566$	7.28115	−	5.29007i	0.306050	−	0.222358i
$567$	−1.40126	+	1.01807i	−0.0588473	+	0.0427551i
$568$	−6.42280	−	19.7673i	−0.269495	−	0.829419i
$569$	0.535233	−	1.64728i	0.0224381	−	0.0690575i	−0.939210	−	0.343342i	$-0.888441\pi$
$569$	0.535233	−	1.64728i	0.0224381	−	0.0690575i	0.961649	+	0.274285i	$0.0884410\pi$
$570$	4.85410	+	3.52671i	0.203316	+	0.147718i
$571$	3.46410			0.144968			0.0724841	−	0.997370i	$-0.476907\pi$
$571$	3.46410			0.144968			0.0724841	+	0.997370i	$0.476907\pi$
$572$		0			0
$573$	6.00000			0.250654
$574$	−29.4264	−	21.3796i	−1.22824	−	0.892365i
$575$		0			0
$576$	−0.618034	−	1.90211i	−0.0257514	−	0.0792547i
$577$	16.1803	−	11.7557i	0.673596	−	0.489396i	−0.197631	−	0.980277i	$-0.563325\pi$
$577$	16.1803	−	11.7557i	0.673596	−	0.489396i	0.871227	+	0.490880i	$0.163325\pi$
$578$	43.4390	−	31.5603i	1.80682	−	1.31274i
$579$	−1.07047	−	3.29456i	−0.0444871	−	0.136917i
$580$		0			0
$581$	4.85410	+	3.52671i	0.201382	+	0.146313i
$582$	−17.3205			−0.717958
$583$		0			0
$584$		0			0
$585$	5.60503	+	4.07230i	0.231740	+	0.168369i
$586$	−3.70820	+	11.4127i	−0.153184	+	0.471453i
$587$	6.48936	+	19.9722i	0.267844	+	0.824340i	0.991024	+	0.133681i	$0.0426797\pi$
$587$	6.48936	+	19.9722i	0.267844	+	0.824340i	−0.723180	+	0.690660i	$0.757320\pi$
$588$	−3.23607	+	2.35114i	−0.133453	+	0.0969594i
$589$	22.4201	−	16.2892i	0.923806	−	0.671184i
$590$	−6.42280	−	19.7673i	−0.264422	−	0.813808i
$591$	−3.21140	+	9.88367i	−0.132099	+	0.406560i
$592$	−32.3607	−	23.5114i	−1.33002	−	0.966313i
$593$	−24.2487			−0.995775			−0.497888	−	0.867242i	$-0.665891\pi$
$593$	−24.2487			−0.995775			−0.497888	+	0.867242i	$0.665891\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	−15.4138	−	11.1988i	−0.631376	−	0.458721i
$597$	4.32624	−	13.3148i	0.177061	−	0.544938i
$598$		0			0
$599$	−24.2705	+	17.6336i	−0.991666	+	0.720488i	−0.960285	−	0.279020i	$-0.909990\pi$
$599$	−24.2705	+	17.6336i	−0.991666	+	0.720488i	−0.0313808	+	0.999508i	$0.509990\pi$
$600$	1.40126	−	1.01807i	0.0572061	−	0.0415627i
$601$	−6.42280	−	19.7673i	−0.261991	−	0.806327i	−0.992371	−	0.123285i	$-0.960657\pi$
$601$	−6.42280	−	19.7673i	−0.261991	−	0.806327i	0.730380	−	0.683041i	$-0.239343\pi$
$602$	8.02850	−	24.7092i	0.327217	−	1.00707i
$603$	−8.09017	−	5.87785i	−0.329457	−	0.239365i
$604$	20.7846			0.845714
$605$		0			0
$606$	3.00000			0.121867
$607$	−2.80252	−	2.03615i	−0.113751	−	0.0826447i	0.529456	−	0.848338i	$-0.322396\pi$
$607$	−2.80252	−	2.03615i	−0.113751	−	0.0826447i	−0.643206	+	0.765693i	$0.722396\pi$
$608$	5.56231	−	17.1190i	0.225581	−	0.694268i
$609$		0			0
$610$	12.1353	−	8.81678i	0.491342	−	0.356981i
$611$	25.2227	−	18.3253i	1.02040	−	0.741364i
$612$	−4.28187	−	13.1782i	−0.173084	−	0.532698i
$613$	3.21140	−	9.88367i	0.129707	−	0.399198i	−0.865022	−	0.501734i	$-0.832696\pi$
$613$	3.21140	−	9.88367i	0.129707	−	0.399198i	0.994729	+	0.102536i	$0.0326957\pi$
$614$	14.5623	+	10.5801i	0.587687	+	0.426979i
$615$	−12.1244			−0.488901
$616$		0			0
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$	5.60503	+	4.07230i	0.225468	+	0.163812i
$619$	6.18034	−	19.0211i	0.248409	−	0.764524i	−0.746648	−	0.665219i	$-0.768338\pi$
$619$	6.18034	−	19.0211i	0.248409	−	0.764524i	0.995057	−	0.0993047i	$-0.0316619\pi$
$620$	2.47214	+	7.60845i	0.0992834	+	0.305563i
$621$		0			0
$622$	−8.40755	+	6.10844i	−0.337112	+	0.244926i
$623$	1.60570	+	4.94183i	0.0643310	+	0.197990i
$624$	−5.35233	+	16.4728i	−0.214265	+	0.659439i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−17.3205			−0.692267
$627$		0			0
$628$	4.00000			0.159617
$629$	44.8403	+	32.5784i	1.78790	+	1.29898i
$630$	−1.85410	+	5.70634i	−0.0738692	+	0.227346i
$631$	8.65248	+	26.6296i	0.344450	+	1.06011i	0.961878	+	0.273480i	$0.0881746\pi$
$631$	8.65248	+	26.6296i	0.344450	+	1.06011i	−0.617428	+	0.786627i	$0.711825\pi$
$632$	−14.5623	+	10.5801i	−0.579257	+	0.420855i
$633$		0			0
$634$	3.21140	+	9.88367i	0.127541	+	0.392531i
$635$	0.535233	−	1.64728i	0.0212401	−	0.0653702i
$636$	4.85410	+	3.52671i	0.192478	+	0.139843i
$637$	13.8564			0.549011
$638$		0			0
$639$	24.0000			0.949425
$640$	−9.80881	−	7.12652i	−0.387727	−	0.281700i
$641$	9.27051	−	28.5317i	0.366163	−	1.12693i	−0.583086	−	0.812410i	$-0.698155\pi$
$641$	9.27051	−	28.5317i	0.366163	−	1.12693i	0.949250	−	0.314524i	$-0.101845\pi$
$642$	−0.927051	−	2.85317i	−0.0365878	−	0.112606i
$643$	25.0795	−	18.2213i	0.989040	−	0.718580i	0.0293293	−	0.999570i	$-0.490663\pi$
$643$	25.0795	−	18.2213i	0.989040	−	0.718580i	0.959711	+	0.280990i	$0.0906628\pi$
$644$		0			0
$645$	−2.67617	−	8.23639i	−0.105374	−	0.324308i
$646$	−12.8456	+	39.5347i	−0.505403	+	1.55547i
$647$	−26.6976	−	19.3969i	−1.04959	−	0.762571i	−0.0774551	−	0.996996i	$-0.524679\pi$
$647$	−26.6976	−	19.3969i	−1.04959	−	0.762571i	−0.972134	+	0.234424i	$0.924679\pi$
$648$	1.73205			0.0680414
$649$		0			0
$650$	6.00000			0.235339
$651$	−11.2101	−	8.14459i	−0.439357	−	0.319212i
$652$	−5.87132	+	18.0701i	−0.229939	+	0.707679i
$653$	−9.27051	−	28.5317i	−0.362783	−	1.11653i	−0.951358	−	0.308089i	$-0.900311\pi$
$653$	−9.27051	−	28.5317i	−0.362783	−	1.11653i	0.588575	−	0.808443i	$-0.299689\pi$
$654$	2.42705	−	1.76336i	0.0949052	−	0.0689527i
$655$	2.80252	−	2.03615i	0.109503	−	0.0795589i
$656$	18.7332	+	57.6547i	0.731407	+	2.25104i
$657$		0			0
$658$	21.8435	+	15.8702i	0.851547	+	0.618685i
$659$	−3.46410			−0.134942			−0.0674711	−	0.997721i	$-0.521493\pi$
$659$	−3.46410			−0.134942			−0.0674711	+	0.997721i	$0.521493\pi$
$660$		0			0
$661$	37.0000			1.43913			0.719567	−	0.694423i	$-0.244340\pi$
$661$	37.0000			1.43913			0.719567	+	0.694423i	$0.244340\pi$
$662$	−47.6428	−	34.6145i	−1.85169	−	1.34533i
$663$	7.41641	−	22.8254i	0.288029	−	0.886463i
$664$	−1.85410	−	5.70634i	−0.0719531	−	0.221449i
$665$	4.85410	−	3.52671i	0.188234	−	0.136760i
$666$	22.4201	−	16.2892i	0.868763	−	0.631193i
$667$		0			0
$668$	1.60570	−	4.94183i	0.0621264	−	0.191205i
$669$	−15.3713	−	11.1679i	−0.594290	−	0.431777i
$670$	−8.66025			−0.334575
$671$		0			0
$672$	−9.00000			−0.347183
$673$	−16.8151	−	12.2169i	−0.648175	−	0.470926i	0.214474	−	0.976730i	$-0.431196\pi$
$673$	−16.8151	−	12.2169i	−0.648175	−	0.470926i	−0.862649	+	0.505803i	$0.831196\pi$
$674$	5.56231	−	17.1190i	0.214252	−	0.659400i
$675$	1.54508	+	4.75528i	0.0594703	+	0.183031i
$676$	0.809017	−	0.587785i	0.0311160	−	0.0226071i
$677$	22.4201	−	16.2892i	0.861676	−	0.626044i	−0.0666645	−	0.997775i	$-0.521236\pi$
$677$	22.4201	−	16.2892i	0.861676	−	0.626044i	0.928340	+	0.371731i	$0.121236\pi$
$678$	−3.21140	−	9.88367i	−0.123333	−	0.379580i
$679$	−5.35233	+	16.4728i	−0.205404	+	0.632167i
$680$	9.70820	+	7.05342i	0.372293	+	0.270486i
$681$	19.0526			0.730096
$682$		0			0
$683$	−21.0000			−0.803543			−0.401771	−	0.915740i	$-0.631605\pi$
$683$	−21.0000			−0.803543			−0.401771	+	0.915740i	$0.631605\pi$
$684$	5.60503	+	4.07230i	0.214314	+	0.155708i
$685$	−5.56231	+	17.1190i	−0.212525	+	0.654084i
$686$	10.1976	+	31.3849i	0.389345	+	1.19828i
$687$	5.66312	−	4.11450i	0.216061	−	0.156978i
$688$	−35.0315	+	25.4518i	−1.33556	+	0.970343i
$689$	−6.42280	−	19.7673i	−0.244689	−	0.753076i
$690$		0			0
$691$	8.09017	+	5.87785i	0.307765	+	0.223604i	0.730937	−	0.682445i	$-0.239083\pi$
$691$	8.09017	+	5.87785i	0.307765	+	0.223604i	−0.423172	+	0.906049i	$0.639083\pi$
$692$	−10.3923			−0.395056
$693$		0			0
$694$	−21.0000			−0.797149
$695$	−11.2101	−	8.14459i	−0.425222	−	0.308942i
$696$		0			0
$697$	−25.9574	−	79.8887i	−0.983208	−	3.02600i
$698$	−48.5410	+	35.2671i	−1.83730	+	1.33488i
$699$	2.80252	−	2.03615i	0.106001	−	0.0770142i
$700$	0.535233	+	1.64728i	0.0202299	+	0.0622613i
$701$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$701$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$702$	−24.2705	−	17.6336i	−0.916031	−	0.665536i
$703$	−27.7128			−1.04521
$704$		0			0
$705$	9.00000			0.338960
$706$	33.6302	+	24.4338i	1.26569	+	0.919577i
$707$	0.927051	−	2.85317i	0.0348653	−	0.107304i
$708$	3.70820	+	11.4127i	0.139363	+	0.428915i
$709$	−20.2254	+	14.6946i	−0.759582	+	0.551868i	−0.898782	−	0.438396i	$-0.855547\pi$
$709$	−20.2254	+	14.6946i	−0.759582	+	0.551868i	0.139200	+	0.990264i	$0.455547\pi$
$710$	16.8151	−	12.2169i	0.631060	−	0.458492i
$711$	−6.42280	−	19.7673i	−0.240874	−	0.741333i
$712$	1.60570	−	4.94183i	0.0601761	−	0.185203i
$713$		0			0
$714$	20.7846			0.777844
$715$		0			0
$716$	−18.0000			−0.672692
$717$	−2.80252	−	2.03615i	−0.104662	−	0.0760413i
$718$	−1.85410	+	5.70634i	−0.0691945	+	0.212959i
$719$	1.85410	+	5.70634i	0.0691463	+	0.212811i	0.979659	−	0.200672i	$-0.0643124\pi$
$719$	1.85410	+	5.70634i	0.0691463	+	0.212811i	−0.910512	+	0.413482i	$0.864312\pi$
$720$	8.09017	−	5.87785i	0.301503	−	0.219055i
$721$	5.60503	−	4.07230i	0.208742	−	0.151660i
$722$	3.74663	+	11.5309i	0.139435	+	0.429137i
$723$	−5.88756	+	18.1201i	−0.218961	+	0.673892i
$724$	−8.89919	−	6.46564i	−0.330736	−	0.240294i
$725$		0			0
$726$		0			0
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$	8.40755	+	6.10844i	0.311605	+	0.226394i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$		0			0
$731$	48.5410	−	35.2671i	1.79535	−	1.30440i
$732$	−7.00629	+	5.09037i	−0.258960	+	0.188145i
$733$	6.42280	+	19.7673i	0.237231	+	0.730123i	0.996818	+	0.0797166i	$0.0254015\pi$
$733$	6.42280	+	19.7673i	0.237231	+	0.730123i	−0.759586	+	0.650407i	$0.774598\pi$
$734$	−9.09896	+	28.0037i	−0.335849	+	1.03364i
$735$	3.23607	+	2.35114i	0.119364	+	0.0867231i
$736$		0			0
$737$		0			0
$738$	−42.0000			−1.54604
$739$	2.80252	+	2.03615i	0.103092	+	0.0749009i	0.638137	−	0.769923i	$-0.279705\pi$
$739$	2.80252	+	2.03615i	0.103092	+	0.0749009i	−0.535045	+	0.844824i	$0.679705\pi$
$740$	2.47214	−	7.60845i	0.0908775	−	0.279692i
$741$	3.70820	+	11.4127i	0.136224	+	0.419255i
$742$	14.5623	−	10.5801i	0.534599	−	0.388409i
$743$	4.20378	−	3.05422i	0.154222	−	0.112049i	−0.507998	−	0.861358i	$-0.669614\pi$
$743$	4.20378	−	3.05422i	0.154222	−	0.112049i	0.662220	+	0.749309i	$0.269614\pi$
$744$	4.28187	+	13.1782i	0.156981	+	0.483137i
$745$	−5.88756	+	18.1201i	−0.215704	+	0.663868i
$746$	19.4164	+	14.1068i	0.710885	+	0.516488i
$747$	6.92820			0.253490
$748$		0			0
$749$	−3.00000			−0.109618
$750$	1.40126	+	1.01807i	0.0511667	+	0.0371748i
$751$	−4.32624	+	13.3148i	−0.157867	+	0.485864i	−0.998440	−	0.0558340i	$-0.982218\pi$
$751$	−4.32624	+	13.3148i	−0.157867	+	0.485864i	0.840573	+	0.541698i	$0.182218\pi$
$752$	−13.9058	−	42.7975i	−0.507091	−	1.56067i
$753$		0			0
$754$		0			0
$755$	−6.42280	−	19.7673i	−0.233750	−	0.719407i
$756$	2.67617	−	8.23639i	0.0973312	−	0.299555i
$757$	1.61803	+	1.17557i	0.0588084	+	0.0427268i	0.616801	−	0.787119i	$-0.288428\pi$
$757$	1.61803	+	1.17557i	0.0588084	+	0.0427268i	−0.557993	+	0.829846i	$0.688428\pi$
$758$	58.8897			2.13897
$759$		0			0
$760$	−6.00000			−0.217643
$761$	28.0252	+	20.3615i	1.01591	+	0.738103i	0.965441	−	0.260623i	$-0.0839278\pi$
$761$	28.0252	+	20.3615i	1.01591	+	0.738103i	0.0504709	+	0.998726i	$0.483928\pi$
$762$	−0.927051	+	2.85317i	−0.0335835	+	0.103359i
$763$	−0.927051	−	2.85317i	−0.0335615	−	0.103292i
$764$	4.85410	−	3.52671i	0.175615	−	0.127592i
$765$	−11.2101	+	8.14459i	−0.405301	+	0.294468i
$766$	−12.8456	−	39.5347i	−0.464130	−	1.42845i
$767$	12.8456	−	39.5347i	0.463828	−	1.42751i
$768$	15.3713	+	11.1679i	0.554665	+	0.402988i
$769$	−27.7128			−0.999350			−0.499675	−	0.866213i	$-0.666547\pi$
$769$	−27.7128			−0.999350			−0.499675	+	0.866213i	$0.666547\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−2.80252	−	2.03615i	−0.100865	−	0.0732826i
$773$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$773$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$774$	−9.27051	−	28.5317i	−0.333222	−	1.02555i
$775$	6.47214	−	4.70228i	0.232486	−	0.168911i
$776$	14.0126	−	10.1807i	0.503023	−	0.365467i
$777$	4.28187	+	13.1782i	0.153611	+	0.472766i
$778$	−1.60570	+	4.94183i	−0.0575671	+	0.177173i
$779$	33.9787	+	24.6870i	1.21741	+	0.884503i
$780$	−3.46410			−0.124035
$781$		0			0
$782$		0			0
$783$		0			0
$784$	6.18034	−	19.0211i	0.220726	−	0.679326i
$785$	−1.23607	−	3.80423i	−0.0441172	−	0.135779i
$786$	−4.85410	+	3.52671i	−0.173140	+	0.125794i
$787$	−21.0189	+	15.2711i	−0.749242	+	0.544356i	−0.895592	−	0.444877i	$-0.853248\pi$
$787$	−21.0189	+	15.2711i	−0.749242	+	0.544356i	0.146350	+	0.989233i	$0.453248\pi$
$788$	3.21140	+	9.88367i	0.114401	+	0.352091i
$789$	7.49326	−	23.0619i	0.266767	−	0.821025i
$790$	−14.5623	−	10.5801i	−0.518104	−	0.376424i
$791$	−10.3923			−0.369508
$792$		0			0
$793$	30.0000			1.06533
$794$	28.0252	+	20.3615i	0.994576	+	0.722602i
$795$	1.85410	−	5.70634i	0.0657582	−	0.202383i
$796$	−4.32624	−	13.3148i	−0.153339	−	0.471930i
$797$	9.70820	−	7.05342i	0.343882	−	0.249845i	−0.402416	−	0.915457i	$-0.631829\pi$
$797$	9.70820	−	7.05342i	0.343882	−	0.249845i	0.746298	+	0.665612i	$0.231829\pi$
$798$	−8.40755	+	6.10844i	−0.297624	+	0.216237i
$799$	19.2684	+	59.3020i	0.681667	+	2.09795i
$800$	1.60570	−	4.94183i	0.0567700	−	0.174720i
$801$	4.85410	+	3.52671i	0.171511	+	0.124610i
$802$	−46.7654			−1.65134
$803$		0			0
$804$	5.00000			0.176336
$805$		0			0
$806$	−14.8328	+	45.6507i	−0.522464	+	1.60798i
$807$	4.63525	+	14.2658i	0.163169	+	0.502182i
$808$	−2.42705	+	1.76336i	−0.0853834	+	0.0620346i
$809$	−39.2352	+	28.5061i	−1.37944	+	1.00222i	−0.382505	+	0.923953i	$0.624939\pi$
$809$	−39.2352	+	28.5061i	−1.37944	+	1.00222i	−0.996932	+	0.0782667i	$0.975061\pi$
$810$	0.535233	+	1.64728i	0.0188062	+	0.0578795i
$811$	−2.14093	+	6.58911i	−0.0751783	+	0.231375i	−0.981583	−	0.191035i	$-0.938816\pi$
$811$	−2.14093	+	6.58911i	−0.0751783	+	0.231375i	0.906405	+	0.422410i	$0.138816\pi$
$812$		0			0
$813$	−13.8564			−0.485965
$814$		0			0
$815$	19.0000			0.665541
$816$	−28.0252	−	20.3615i	−0.981077	−	0.712794i
$817$	−9.27051	+	28.5317i	−0.324334	+	0.998198i
$818$	2.78115	+	8.55951i	0.0972407	+	0.299276i
$819$	−9.70820	+	7.05342i	−0.339232	+	0.246467i
$820$	−9.80881	+	7.12652i	−0.342538	+	0.248869i
$821$	−9.09896	−	28.0037i	−0.317556	−	0.977337i	−0.974690	−	0.223563i	$-0.928231\pi$
$821$	−9.09896	−	28.0037i	−0.317556	−	0.977337i	0.657134	−	0.753774i	$-0.271769\pi$
$822$	9.63420	−	29.6510i	0.336031	−	1.03420i
$823$	−13.7533	−	9.99235i	−0.479410	−	0.348311i	0.321688	−	0.946846i	$-0.395750\pi$
$823$	−13.7533	−	9.99235i	−0.479410	−	0.348311i	−0.801097	+	0.598534i	$0.795750\pi$
$824$	−6.92820			−0.241355
$825$		0			0
$826$	36.0000			1.25260
$827$	23.8214	+	17.3073i	0.828351	+	0.601832i	0.919092	−	0.394042i	$-0.128924\pi$
$827$	23.8214	+	17.3073i	0.828351	+	0.601832i	−0.0907413	+	0.995875i	$0.528924\pi$
$828$		0			0
$829$	8.96149	+	27.5806i	0.311246	+	0.957915i	0.977272	+	0.211987i	$0.0679936\pi$
$829$	8.96149	+	27.5806i	0.311246	+	0.957915i	−0.666027	+	0.745928i	$0.732006\pi$
$830$	4.85410	−	3.52671i	0.168488	−	0.122414i
$831$	−8.40755	+	6.10844i	−0.291655	+	0.211900i
$832$	−1.07047	−	3.29456i	−0.0371117	−	0.114218i
$833$	−8.56373	+	26.3565i	−0.296716	+	0.913197i
$834$	19.4164	+	14.1068i	0.672335	+	0.488480i
$835$	−5.19615			−0.179820
$836$		0			0
$837$	−40.0000			−1.38260
$838$	25.2227	+	18.3253i	0.871302	+	0.633038i
$839$	−12.9787	+	39.9444i	−0.448075	+	1.37903i	0.431001	+	0.902351i	$0.358161\pi$
$839$	−12.9787	+	39.9444i	−0.448075	+	1.37903i	−0.879076	+	0.476682i	$0.841839\pi$
$840$	0.927051	+	2.85317i	0.0319863	+	0.0984437i
$841$	23.4615	−	17.0458i	0.809017	−	0.587785i
$842$	−23.8214	+	17.3073i	−0.820939	+	0.596447i
$843$	−2.14093	−	6.58911i	−0.0737376	−	0.226941i
$844$		0			0
$845$	−0.809017	−	0.587785i	−0.0278310	−	0.0202204i
$846$	31.1769			1.07188
$847$		0			0
$848$	−30.0000			−1.03020
$849$	4.20378	+	3.05422i	0.144273	+	0.104821i
$850$	−3.70820	+	11.4127i	−0.127190	+	0.391452i
$851$		0			0
$852$	−9.70820	+	7.05342i	−0.332598	+	0.241646i
$853$	−28.0252	+	20.3615i	−0.959564	+	0.697164i	−0.953049	−	0.302815i	$-0.902074\pi$
$853$	−28.0252	+	20.3615i	−0.959564	+	0.697164i	−0.00651423	+	0.999979i	$0.502074\pi$
$854$	8.02850	+	24.7092i	0.274730	+	0.845530i
$855$	2.14093	−	6.58911i	0.0732183	−	0.225343i
$856$	2.42705	+	1.76336i	0.0829549	+	0.0602703i
$857$	10.3923			0.354994			0.177497	−	0.984121i	$-0.443200\pi$
$857$	10.3923			0.354994			0.177497	+	0.984121i	$0.443200\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−7.00629	−	5.09037i	−0.238913	−	0.173580i
$861$	6.48936	−	19.9722i	0.221157	−	0.680650i
$862$	20.3951	+	62.7697i	0.694661	+	2.13795i
$863$	−16.9894	+	12.3435i	−0.578324	+	0.420177i	−0.838120	−	0.545486i	$-0.816345\pi$
$863$	−16.9894	+	12.3435i	−0.578324	+	0.420177i	0.259795	+	0.965664i	$0.416345\pi$
$864$	−21.0189	+	15.2711i	−0.715077	+	0.519534i
$865$	3.21140	+	9.88367i	0.109191	+	0.336055i
$866$	−17.1275	+	52.7129i	−0.582015	+	1.79126i
$867$	25.0795	+	18.2213i	0.851745	+	0.618829i
$868$	−13.8564			−0.470317
$869$		0			0
$870$		0			0
$871$	−14.0126	−	10.1807i	−0.474798	−	0.344961i
$872$	−0.927051	+	2.85317i	−0.0313939	+	0.0966205i
$873$	6.18034	+	19.0211i	0.209173	+	0.643768i
$874$		0			0
$875$	1.40126	−	1.01807i	0.0473712	−	0.0344172i
$876$		0			0
$877$	8.56373	−	26.3565i	0.289177	−	0.889994i	−0.695939	−	0.718101i	$-0.745012\pi$
$877$	8.56373	−	26.3565i	0.289177	−	0.889994i	0.985116	−	0.171893i	$-0.0549884\pi$
$878$	38.8328	+	28.2137i	1.31054	+	0.952166i
$879$	−6.92820			−0.233682
$880$		0			0
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$	11.2101	+	8.14459i	0.377463	+	0.274243i
$883$	−17.3050	+	53.2592i	−0.582358	+	1.79231i	0.0272727	+	0.999628i	$0.491318\pi$
$883$	−17.3050	+	53.2592i	−0.582358	+	1.79231i	−0.609631	+	0.792686i	$0.708682\pi$
$884$	−7.41641	−	22.8254i	−0.249441	−	0.767700i
$885$	9.70820	−	7.05342i	0.326338	−	0.237098i
$886$	−21.0189	+	15.2711i	−0.706143	+	0.513043i
$887$	10.1694	+	31.2983i	0.341456	+	1.05089i	0.963454	+	0.267875i	$0.0863213\pi$
$887$	10.1694	+	31.2983i	0.341456	+	1.05089i	−0.621998	+	0.783019i	$0.713679\pi$
$888$	4.28187	−	13.1782i	0.143690	−	0.442232i
$889$	2.42705	+	1.76336i	0.0814007	+	0.0591411i
$890$	5.19615			0.174175
$891$		0			0
$892$	−19.0000			−0.636167
$893$	−25.2227	−	18.3253i	−0.844044	−	0.613234i
$894$	10.1976	−	31.3849i	0.341057	−	1.04967i
$895$	5.56231	+	17.1190i	0.185927	+	0.572226i
$896$	16.9894	−	12.3435i	0.567575	−	0.412367i
$897$		0			0
$898$	8.02850	+	24.7092i	0.267914	+	0.824556i
$899$		0			0
$900$	1.61803	+	1.17557i	0.0539345	+	0.0391857i
$901$	41.5692			1.38487
$902$		0			0
$903$	15.0000			0.499169
$904$	8.40755	+	6.10844i	0.279631	+	0.203164i
$905$	−3.39919	+	10.4616i	−0.112993	+	0.347756i
$906$	11.1246	+	34.2380i	0.369590	+	1.13748i
$907$	−13.7533	+	9.99235i	−0.456670	+	0.331791i	−0.792224	−	0.610231i	$-0.791077\pi$
$907$	−13.7533	+	9.99235i	−0.456670	+	0.331791i	0.335553	+	0.942021i	$0.391077\pi$
$908$	15.4138	−	11.1988i	0.511526	−	0.371646i
$909$	−1.07047	−	3.29456i	−0.0355051	−	0.109274i
$910$	−3.21140	+	9.88367i	−0.106457	+	0.327640i
$911$	−4.85410	−	3.52671i	−0.160824	−	0.116845i	0.504463	−	0.863433i	$-0.331691\pi$
$911$	−4.85410	−	3.52671i	−0.160824	−	0.116845i	−0.665286	+	0.746588i	$0.731691\pi$
$912$	17.3205			0.573539
$913$		0			0
$914$	36.0000			1.19077
$915$	7.00629	+	5.09037i	0.231621	+	0.168282i
$916$	2.16312	−	6.65740i	0.0714715	−	0.219967i
$917$	1.85410	+	5.70634i	0.0612278	+	0.188440i
$918$	48.5410	−	35.2671i	1.60209	−	1.16399i
$919$	30.8277	−	22.3976i	1.01691	−	0.738830i	0.0512641	−	0.998685i	$-0.483675\pi$
$919$	30.8277	−	22.3976i	1.01691	−	0.738830i	0.965647	+	0.259856i	$0.0836750\pi$
$920$		0			0
$921$	−3.21140	+	9.88367i	−0.105819	+	0.325678i
$922$	16.9894	+	12.3435i	0.559515	+	0.406511i
$923$	41.5692			1.36827
$924$		0			0
$925$	−8.00000			−0.263038
$926$	57.4516	+	41.7410i	1.88798	+	1.37170i
$927$	2.47214	−	7.60845i	0.0811956	−	0.249894i
$928$		0			0
$929$	−14.5623	+	10.5801i	−0.477774	+	0.347123i	−0.800463	−	0.599382i	$-0.795413\pi$
$929$	−14.5623	+	10.5801i	−0.477774	+	0.347123i	0.322689	+	0.946505i	$0.395413\pi$
$930$	−11.2101	+	8.14459i	−0.367593	+	0.267072i
$931$	−4.28187	−	13.1782i	−0.140332	−	0.431899i
$932$	1.07047	−	3.29456i	0.0350643	−	0.107917i
$933$	−4.85410	−	3.52671i	−0.158916	−	0.115459i
$934$	−5.19615			−0.170023
$935$		0			0
$936$	12.0000			0.392232
$937$	−19.6176	−	14.2530i	−0.640880	−	0.465626i	0.219273	−	0.975664i	$-0.429632\pi$
$937$	−19.6176	−	14.2530i	−0.640880	−	0.465626i	−0.860152	+	0.510037i	$0.829632\pi$
$938$	4.63525	−	14.2658i	0.151346	−	0.465796i
$939$	−3.09017	−	9.51057i	−0.100844	−	0.310366i
$940$	7.28115	−	5.29007i	0.237485	−	0.172543i
$941$	−40.6365	+	29.5241i	−1.32471	+	0.962460i	−0.324851	+	0.945765i	$0.605314\pi$
$941$	−40.6365	+	29.5241i	−1.32471	+	0.962460i	−0.999861	+	0.0166945i	$0.994686\pi$
$942$	2.14093	+	6.58911i	0.0697554	+	0.214685i
$943$		0			0
$944$	−48.5410	−	35.2671i	−1.57988	−	1.14785i
$945$	−8.66025			−0.281718
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	8.40755	+	6.10844i	0.273065	+	0.198393i
$949$		0			0
$950$	−1.85410	−	5.70634i	−0.0601550	−	0.185138i
$951$	−4.85410	+	3.52671i	−0.157405	+	0.114361i
$952$	−16.8151	+	12.2169i	−0.544981	+	0.395952i
$953$	−17.1275	−	52.7129i	−0.554813	−	1.70754i	−0.696437	−	0.717618i	$-0.745232\pi$
$953$	−17.1275	−	52.7129i	−0.554813	−	1.70754i	0.141624	−	0.989920i	$-0.454768\pi$
$954$	6.42280	−	19.7673i	0.207946	−	0.639991i
$955$	−4.85410	−	3.52671i	−0.157075	−	0.114122i
$956$	−3.46410			−0.112037
$957$		0			0
$958$	18.0000			0.581554
$959$	−25.2227	−	18.3253i	−0.814482	−	0.591756i
$960$	0.309017	−	0.951057i	0.00997348	−	0.0306952i
$961$	10.1976	+	31.3849i	0.328954	+	1.01242i
$962$	38.8328	−	28.2137i	1.25202	−	0.909646i
$963$	−2.80252	+	2.03615i	−0.0903099	+	0.0656139i
$964$	5.88756	+	18.1201i	0.189626	+	0.583608i
$965$	−1.07047	+	3.29456i	−0.0344595	+	0.106056i
$966$		0			0
$967$	−38.1051			−1.22538			−0.612689	−	0.790324i	$-0.709912\pi$
$967$	−38.1051			−1.22538			−0.612689	+	0.790324i	$0.709912\pi$
$968$		0			0
$969$	−24.0000			−0.770991
$970$	14.0126	+	10.1807i	0.449917	+	0.326884i
$971$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$971$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$972$	−4.94427	−	15.2169i	−0.158588	−	0.488082i
$973$	19.4164	−	14.1068i	0.622461	−	0.452245i
$974$	−28.0252	+	20.3615i	−0.897984	+	0.652424i
$975$	1.07047	+	3.29456i	0.0342824	+	0.105510i
$976$	13.3808	−	41.1820i	0.428310	−	1.31820i
$977$	19.4164	+	14.1068i	0.621186	+	0.451318i	0.853336	−	0.521362i	$-0.174576\pi$
$977$	19.4164	+	14.1068i	0.621186	+	0.451318i	−0.232150	+	0.972680i	$0.574576\pi$
$978$	−32.9090			−1.05231
$979$		0			0
$980$	4.00000			0.127775
$981$	−2.80252	−	2.03615i	−0.0894775	−	0.0650092i
$982$	12.9787	−	39.9444i	0.414167	−	1.27468i
$983$	−0.927051	−	2.85317i	−0.0295683	−	0.0910020i	0.935183	−	0.354164i	$-0.115235\pi$
$983$	−0.927051	−	2.85317i	−0.0295683	−	0.0910020i	−0.964752	+	0.263162i	$0.915235\pi$
$984$	−16.9894	+	12.3435i	−0.541601	+	0.393496i
$985$	8.40755	−	6.10844i	0.267887	−	0.194631i
$986$		0			0
$987$	−4.81710	+	14.8255i	−0.153330	+	0.471901i
$988$	9.70820	+	7.05342i	0.308859	+	0.224399i
$989$		0			0
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	33.6302	+	24.4338i	1.06776	+	0.775773i
$993$	10.5066	−	32.3359i	0.333416	−	1.02615i
$994$	11.1246	+	34.2380i	0.352851	+	1.08596i
$995$	−11.3262	+	8.22899i	−0.359066	+	0.260877i
$996$	−2.80252	+	2.03615i	−0.0888012	+	0.0645178i
$997$	13.9161	+	42.8292i	0.440726	+	1.35642i	0.887103	+	0.461571i	$0.152714\pi$
$997$	13.9161	+	42.8292i	0.440726	+	1.35642i	−0.446377	+	0.894845i	$0.647286\pi$
$998$	20.3389	−	62.5966i	0.643815	−	1.98146i
$999$	32.3607	+	23.5114i	1.02385	+	0.743868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.i.81.2		8
11.2	odd	10	inner	605.2.g.i.511.2		8
11.3	even	5	inner	605.2.g.i.366.2		8
11.4	even	5	inner	605.2.g.i.251.1		8
11.5	even	5		605.2.a.e.1.1	✓	2
11.6	odd	10		605.2.a.e.1.2	yes	2
11.7	odd	10	inner	605.2.g.i.251.2		8
11.8	odd	10	inner	605.2.g.i.366.1		8
11.9	even	5	inner	605.2.g.i.511.1		8
11.10	odd	2	inner	605.2.g.i.81.1		8
33.5	odd	10		5445.2.a.u.1.2		2
33.17	even	10		5445.2.a.u.1.1		2
44.27	odd	10		9680.2.a.bu.1.1		2
44.39	even	10		9680.2.a.bu.1.2		2
55.39	odd	10		3025.2.a.l.1.1		2
55.49	even	10		3025.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.e.1.1	✓	2	11.5	even	5
605.2.a.e.1.2	yes	2	11.6	odd	10
605.2.g.i.81.1		8	11.10	odd	2	inner
605.2.g.i.81.2		8	1.1	even	1	trivial
605.2.g.i.251.1		8	11.4	even	5	inner
605.2.g.i.251.2		8	11.7	odd	10	inner
605.2.g.i.366.1		8	11.8	odd	10	inner
605.2.g.i.366.2		8	11.3	even	5	inner
605.2.g.i.511.1		8	11.9	even	5	inner
605.2.g.i.511.2		8	11.2	odd	10	inner
3025.2.a.l.1.1		2	55.39	odd	10
3025.2.a.l.1.2		2	55.49	even	10
5445.2.a.u.1.1		2	33.17	even	10
5445.2.a.u.1.2		2	33.5	odd	10
9680.2.a.bu.1.1		2	44.27	odd	10
9680.2.a.bu.1.2		2	44.39	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40126 + 1.01807i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.40126 + 1.01807i) q^{6} +(0.535233 + 1.64728i) q^{7} +(0.535233 - 1.64728i) q^{8} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\)	\(q+(1.40126 + 1.01807i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-1.40126 + 1.01807i) q^{6} +(0.535233 + 1.64728i) q^{7} +(0.535233 - 1.64728i) q^{8} +(1.61803 + 1.17557i) q^{9} +1.73205 q^{10} -1.00000 q^{12} +(2.80252 + 2.03615i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{15} +(4.04508 - 2.93893i) q^{16} +(-5.60503 + 4.07230i) q^{17} +(1.07047 + 3.29456i) q^{18} +(1.07047 - 3.29456i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.73205 q^{21} +(1.40126 + 1.01807i) q^{24} +(0.309017 - 0.951057i) q^{25} +(1.85410 + 5.70634i) q^{26} +(-4.04508 + 2.93893i) q^{27} +(-1.40126 + 1.01807i) q^{28} +(-0.535233 + 1.64728i) q^{30} +(6.47214 + 4.70228i) q^{31} +5.19615 q^{32} -12.0000 q^{34} +(1.40126 + 1.01807i) q^{35} +(-0.618034 + 1.90211i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(4.85410 - 3.52671i) q^{38} +(-2.80252 + 2.03615i) q^{39} +(-0.535233 - 1.64728i) q^{40} +(-3.74663 + 11.5309i) q^{41} +(-2.42705 - 1.76336i) q^{42} -8.66025 q^{43} +2.00000 q^{45} +(2.78115 - 8.55951i) q^{47} +(1.54508 + 4.75528i) q^{48} +(3.23607 - 2.35114i) q^{49} +(1.40126 - 1.01807i) q^{50} +(-2.14093 - 6.58911i) q^{51} +(-1.07047 + 3.29456i) q^{52} +(-4.85410 - 3.52671i) q^{53} -8.66025 q^{54} +3.00000 q^{56} +(2.80252 + 2.03615i) q^{57} +(-3.70820 - 11.4127i) q^{59} +(-0.809017 + 0.587785i) q^{60} +(7.00629 - 5.09037i) q^{61} +(4.28187 + 13.1782i) q^{62} +(-1.07047 + 3.29456i) q^{63} +(-0.809017 - 0.587785i) q^{64} +3.46410 q^{65} -5.00000 q^{67} +(-5.60503 - 4.07230i) q^{68} +(0.927051 + 2.85317i) q^{70} +(9.70820 - 7.05342i) q^{71} +(2.80252 - 2.03615i) q^{72} +(4.28187 - 13.1782i) q^{74} +(0.809017 + 0.587785i) q^{75} +3.46410 q^{76} -6.00000 q^{78} +(-8.40755 - 6.10844i) q^{79} +(1.54508 - 4.75528i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-16.9894 + 12.3435i) q^{82} +(2.80252 - 2.03615i) q^{83} +(-0.535233 - 1.64728i) q^{84} +(-2.14093 + 6.58911i) q^{85} +(-12.1353 - 8.81678i) q^{86} +3.00000 q^{89} +(2.80252 + 2.03615i) q^{90} +(-1.85410 + 5.70634i) q^{91} +(-6.47214 + 4.70228i) q^{93} +(12.6113 - 9.16267i) q^{94} +(-1.07047 - 3.29456i) q^{95} +(-1.60570 + 4.94183i) q^{96} +(8.09017 + 5.87785i) q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9} - 8 q^{12} + 6 q^{14} - 2 q^{15} + 10 q^{16} + 2 q^{20} - 2 q^{25} - 12 q^{26} - 10 q^{27} + 16 q^{31} - 96 q^{34} + 4 q^{36} + 16 q^{37} + 12 q^{38} - 6 q^{42} + 16 q^{45} - 18 q^{47} - 10 q^{48} + 8 q^{49} - 12 q^{53} + 24 q^{56} + 24 q^{59} - 2 q^{60} - 2 q^{64} - 40 q^{67} - 6 q^{70} + 24 q^{71} + 2 q^{75} - 48 q^{78} - 10 q^{80} - 2 q^{81} - 42 q^{82} - 30 q^{86} + 24 q^{89} + 12 q^{91} - 16 q^{93} + 20 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9 - 8 * q^12 + 6 * q^14 - 2 * q^15 + 10 * q^16 + 2 * q^20 - 2 * q^25 - 12 * q^26 - 10 * q^27 + 16 * q^31 - 96 * q^34 + 4 * q^36 + 16 * q^37 + 12 * q^38 - 6 * q^42 + 16 * q^45 - 18 * q^47 - 10 * q^48 + 8 * q^49 - 12 * q^53 + 24 * q^56 + 24 * q^59 - 2 * q^60 - 2 * q^64 - 40 * q^67 - 6 * q^70 + 24 * q^71 + 2 * q^75 - 48 * q^78 - 10 * q^80 - 2 * q^81 - 42 * q^82 - 30 * q^86 + 24 * q^89 + 12 * q^91 - 16 * q^93 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more