LMFDB - Embedded newform 637.2.r.f.116.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 $ x^16 - 11x^14 + 85x^12 - 334x^10 + 952x^8 - 1050x^6 + 853x^4 - 93*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.2
Root			$1.84073 + 1.06275i$ of defining polynomial
Character	$\chi$	$=$	637.116
Dual form			637.2.r.f.324.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84073 + 1.06275i) q^{2} +(-0.0894272 + 0.154892i) q^{3} +(1.25885 - 2.18040i) q^{4} +(-3.12291 + 1.80301i) q^{5} -0.380153i q^{6} +1.10038i q^{8} +(1.48401 + 2.57037i) q^{9} +O(q^{10})$	\(q+(-1.84073 + 1.06275i) q^{2} +(-0.0894272 + 0.154892i) q^{3} +(1.25885 - 2.18040i) q^{4} +(-3.12291 + 1.80301i) q^{5} -0.380153i q^{6} +1.10038i q^{8} +(1.48401 + 2.57037i) q^{9} +(3.83229 - 6.63772i) q^{10} +(3.45748 + 1.99618i) q^{11} +(0.225152 + 0.389974i) q^{12} +(2.51771 + 2.58092i) q^{13} -0.644954i q^{15} +(1.34828 + 2.33529i) q^{16} +(-2.39458 + 4.14753i) q^{17} +(-5.46330 - 3.15424i) q^{18} +(2.72850 - 1.57530i) q^{19} +9.07892i q^{20} -8.48572 q^{22} +(-1.08943 - 1.88694i) q^{23} +(-0.170441 - 0.0984042i) q^{24} +(4.00171 - 6.93117i) q^{25} +(-7.37728 - 2.07509i) q^{26} -1.06740 q^{27} -6.57198 q^{29} +(0.685421 + 1.18718i) q^{30} +(1.28753 + 0.743358i) q^{31} +(-6.86956 - 3.96614i) q^{32} +(-0.618386 + 0.357025i) q^{33} -10.1793i q^{34} +7.47259 q^{36} +(-4.29984 + 2.48252i) q^{37} +(-3.34828 + 5.79939i) q^{38} +(-0.624916 + 0.159170i) q^{39} +(-1.98401 - 3.43640i) q^{40} +2.11931i q^{41} -1.43145 q^{43} +(8.70494 - 5.02580i) q^{44} +(-9.26883 - 5.35136i) q^{45} +(4.01068 + 2.31557i) q^{46} +(0.882417 - 0.509464i) q^{47} -0.482292 q^{48} +17.0112i q^{50} +(-0.428281 - 0.741804i) q^{51} +(8.79686 - 2.24061i) q^{52} +(-3.01771 + 5.22682i) q^{53} +(1.96480 - 1.13438i) q^{54} -14.3966 q^{55} +0.563498i q^{57} +(12.0972 - 6.98434i) q^{58} +(4.24631 + 2.45161i) q^{59} +(-1.40626 - 0.811902i) q^{60} +(-1.01771 - 1.76272i) q^{61} -3.16000 q^{62} +11.4669 q^{64} +(-12.5160 - 3.52052i) q^{65} +(0.758854 - 1.31437i) q^{66} +(-3.38694 - 1.95545i) q^{67} +(6.02885 + 10.4423i) q^{68} +0.389698 q^{69} -8.80684i q^{71} +(-2.82840 + 1.63297i) q^{72} +(-2.67497 - 1.54439i) q^{73} +(5.27656 - 9.13927i) q^{74} +(0.715724 + 1.23967i) q^{75} -7.93228i q^{76} +(0.981145 - 0.957115i) q^{78} +(-0.984006 - 1.70435i) q^{79} +(-8.42112 - 4.86194i) q^{80} +(-4.35656 + 7.54579i) q^{81} +(-2.25229 - 3.90108i) q^{82} -7.66020i q^{83} -17.2698i q^{85} +(2.63491 - 1.52126i) q^{86} +(0.587714 - 1.01795i) q^{87} +(-2.19656 + 3.80456i) q^{88} +(-11.0844 + 6.39960i) q^{89} +22.7485 q^{90} -5.48572 q^{92} +(-0.230281 + 0.132953i) q^{93} +(-1.08286 + 1.87557i) q^{94} +(-5.68057 + 9.83903i) q^{95} +(1.22865 - 0.709362i) q^{96} -1.35900i q^{97} +11.8494i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	$ 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) $ 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.84073	+	1.06275i	−1.30159	+	0.751474i	−0.980677	−	0.195634i	$-0.937324\pi$
$2$	−1.84073	+	1.06275i	−1.30159	+	0.751474i	−0.320915	+	0.947108i	$0.603990\pi$
$3$	−0.0894272	+	0.154892i	−0.0516308	+	0.0894272i	−0.890686	−	0.454620i	$-0.849775\pi$
$3$	−0.0894272	+	0.154892i	−0.0516308	+	0.0894272i	0.839055	+	0.544047i	$0.183109\pi$
$4$	1.25885	−	2.18040i	0.629427	−	1.09020i
$5$	−3.12291	+	1.80301i	−1.39661	+	0.806332i	−0.994036	−	0.109056i	$-0.965217\pi$
$5$	−3.12291	+	1.80301i	−1.39661	+	0.806332i	−0.402572	+	0.915388i	$0.631884\pi$
$6$		−	0.380153i		−	0.155197i
$7$		0			0
$7$		0			0
$8$			1.10038i			0.389044i
$9$	1.48401	+	2.57037i	0.494669	+	0.856791i
$10$	3.83229	−	6.63772i	1.21188	−	2.09903i
$11$	3.45748	+	1.99618i	1.04247	+	0.601871i	0.920532	−	0.390667i	$-0.127756\pi$
$11$	3.45748	+	1.99618i	1.04247	+	0.601871i	0.121939	+	0.992538i	$0.461089\pi$
$12$	0.225152	+	0.389974i	0.0649957	+	0.112576i
$13$	2.51771	+	2.58092i	0.698287	+	0.715818i
$13$	2.51771	+	2.58092i	0.698287	+	0.715818i
$14$		0			0
$15$		−	0.644954i		−	0.166526i
$16$	1.34828	+	2.33529i	0.337070	+	0.583823i
$17$	−2.39458	+	4.14753i	−0.580771	+	1.00592i	0.414618	+	0.909996i	$0.363915\pi$
$17$	−2.39458	+	4.14753i	−0.580771	+	1.00592i	−0.995388	+	0.0959284i	$0.969418\pi$
$18$	−5.46330	−	3.15424i	−1.28771	−	0.743461i
$19$	2.72850	−	1.57530i	0.625960	−	0.361398i	−0.153226	−	0.988191i	$-0.548966\pi$
$19$	2.72850	−	1.57530i	0.625960	−	0.361398i	0.779186	+	0.626793i	$0.215633\pi$
$20$			9.07892i			2.03011i
$21$		0			0
$22$	−8.48572			−1.80916
$23$	−1.08943	−	1.88694i	−0.227161	−	0.393455i	0.729804	−	0.683656i	$-0.239611\pi$
$23$	−1.08943	−	1.88694i	−0.227161	−	0.393455i	−0.956966	+	0.290201i	$0.906278\pi$
$24$	−0.170441	−	0.0984042i	−0.0347911	−	0.0200867i
$25$	4.00171	−	6.93117i	0.800343	−	1.38623i
$26$	−7.37728	−	2.07509i	−1.44680	−	0.406959i
$27$	−1.06740			−0.205422
$28$		0			0
$29$	−6.57198			−1.22039			−0.610193	−	0.792253i	$-0.708908\pi$
$29$	−6.57198			−1.22039			−0.610193	+	0.792253i	$0.708908\pi$
$30$	0.685421	+	1.18718i	0.125140	+	0.216749i
$31$	1.28753	+	0.743358i	0.231248	+	0.133511i	0.611148	−	0.791517i	$-0.290708\pi$
$31$	1.28753	+	0.743358i	0.231248	+	0.133511i	−0.379900	+	0.925028i	$0.624042\pi$
$32$	−6.86956	−	3.96614i	−1.21438	−	0.701121i
$33$	−0.618386	+	0.357025i	−0.107647	+	0.0621502i
$34$		−	10.1793i		−	1.74574i
$35$		0			0
$36$	7.47259			1.24543
$37$	−4.29984	+	2.48252i	−0.706890	+	0.408123i	−0.809908	−	0.586556i	$-0.800483\pi$
$37$	−4.29984	+	2.48252i	−0.706890	+	0.408123i	0.103019	+	0.994679i	$0.467150\pi$
$38$	−3.34828	+	5.79939i	−0.543163	+	0.940786i
$39$	−0.624916	+	0.159170i	−0.100067	+	0.0254875i
$40$	−1.98401	−	3.43640i	−0.313699	−	0.543342i
$41$			2.11931i			0.330981i	0.986211	+	0.165490i	$0.0529207\pi$
$41$			2.11931i			0.330981i	−0.986211	+	0.165490i	$0.947079\pi$
$42$		0			0
$43$	−1.43145			−0.218294			−0.109147	−	0.994026i	$-0.534812\pi$
$43$	−1.43145			−0.218294			−0.109147	+	0.994026i	$0.534812\pi$
$44$	8.70494	−	5.02580i	1.31232	−	0.757667i
$45$	−9.26883	−	5.35136i	−1.38172	−	0.797734i
$46$	4.01068	+	2.31557i	0.591342	+	0.341412i
$47$	0.882417	−	0.509464i	0.128714	−	0.0743129i	−0.434261	−	0.900787i	$-0.642990\pi$
$47$	0.882417	−	0.509464i	0.128714	−	0.0743129i	0.562974	+	0.826474i	$0.309657\pi$
$48$	−0.482292			−0.0696129
$49$		0			0
$50$			17.0112i			2.40575i
$51$	−0.428281	−	0.741804i	−0.0599713	−	0.103873i
$52$	8.79686	−	2.24061i	1.21991	−	0.310716i
$53$	−3.01771	+	5.22682i	−0.414514	+	0.717959i	−0.995377	−	0.0960417i	$-0.969382\pi$
$53$	−3.01771	+	5.22682i	−0.414514	+	0.717959i	0.580863	+	0.814001i	$0.302715\pi$
$54$	1.96480	−	1.13438i	0.267376	−	0.154369i
$55$	−14.3966			−1.94123
$56$		0			0
$57$			0.563498i			0.0746371i
$58$	12.0972	−	6.98434i	1.58844	−	0.917089i
$59$	4.24631	+	2.45161i	0.552823	+	0.319172i	0.750260	−	0.661143i	$-0.229928\pi$
$59$	4.24631	+	2.45161i	0.552823	+	0.319172i	−0.197437	+	0.980316i	$0.563262\pi$
$60$	−1.40626	−	0.811902i	−0.181547	−	0.104816i
$61$	−1.01771	−	1.76272i	−0.130304	−	0.225693i	0.793490	−	0.608584i	$-0.208262\pi$
$61$	−1.01771	−	1.76272i	−0.130304	−	0.225693i	−0.923794	+	0.382890i	$0.874929\pi$
$62$	−3.16000			−0.401320
$63$		0			0
$64$	11.4669			1.43336
$65$	−12.5160	−	3.52052i	−1.55242	−	0.436667i
$66$	0.758854	−	1.31437i	0.0934085	−	0.161788i
$67$	−3.38694	−	1.95545i	−0.413781	−	0.238896i	0.278632	−	0.960398i	$-0.410119\pi$
$67$	−3.38694	−	1.95545i	−0.413781	−	0.238896i	−0.692413	+	0.721501i	$0.743452\pi$
$68$	6.02885	+	10.4423i	0.731105	+	1.26631i
$69$	0.389698			0.0469141
$70$		0			0
$71$		−	8.80684i		−	1.04518i	−0.852584	−	0.522590i	$-0.824966\pi$
$71$		−	8.80684i		−	1.04518i	0.852584	−	0.522590i	$-0.175034\pi$
$72$	−2.82840	+	1.63297i	−0.333330	+	0.192448i
$73$	−2.67497	−	1.54439i	−0.313081	−	0.180757i	0.335223	−	0.942139i	$-0.391188\pi$
$73$	−2.67497	−	1.54439i	−0.313081	−	0.180757i	−0.648304	+	0.761381i	$0.724522\pi$
$74$	5.27656	−	9.13927i	0.613388	−	1.06242i
$75$	0.715724	+	1.23967i	0.0826447	+	0.143145i
$76$		−	7.93228i		−	0.909895i
$77$		0			0
$78$	0.981145	−	0.957115i	0.111093	−	0.108372i
$79$	−0.984006	−	1.70435i	−0.110709	−	0.191754i	0.805347	−	0.592803i	$-0.201979\pi$
$79$	−0.984006	−	1.70435i	−0.110709	−	0.191754i	−0.916056	+	0.401049i	$0.868646\pi$
$80$	−8.42112	−	4.86194i	−0.941510	−	0.543581i
$81$	−4.35656	+	7.54579i	−0.484062	+	0.838421i
$82$	−2.25229	−	3.90108i	−0.248724	−	0.430802i
$83$		−	7.66020i		−	0.840816i	−0.907335	−	0.420408i	$-0.861887\pi$
$83$		−	7.66020i		−	0.840816i	0.907335	−	0.420408i	$-0.138113\pi$
$84$		0			0
$85$		−	17.2698i		−	1.87318i
$86$	2.63491	−	1.52126i	0.284129	−	0.164042i
$87$	0.587714	−	1.01795i	0.0630095	−	0.109136i
$88$	−2.19656	+	3.80456i	−0.234154	+	0.405567i
$89$	−11.0844	+	6.39960i	−1.17495	+	0.678356i	−0.954840	−	0.297120i	$-0.903974\pi$
$89$	−11.0844	+	6.39960i	−1.17495	+	0.678356i	−0.220107	+	0.975476i	$0.570641\pi$
$90$	22.7485			2.39791
$91$		0			0
$92$	−5.48572			−0.571926
$93$	−0.230281	+	0.132953i	−0.0238790	+	0.0137866i
$94$	−1.08286	+	1.87557i	−0.111689	+	0.193450i
$95$	−5.68057	+	9.83903i	−0.582814	+	1.00946i
$96$	1.22865	−	0.709362i	0.125399	−	0.0723989i
$97$		−	1.35900i		−	0.137986i	−0.997617	−	0.0689930i	$-0.978021\pi$
$97$		−	1.35900i		−	0.137986i	0.997617	−	0.0689930i	$-0.0219786\pi$
$98$		0			0
$99$			11.8494i			1.19091i
$100$	−10.0751	−	17.4507i	−1.00751	−	1.74507i
$101$	−2.14400	+	3.71353i	−0.213336	+	0.369510i	−0.952757	−	0.303735i	$-0.901766\pi$
$101$	−2.14400	+	3.71353i	−0.213336	+	0.369510i	0.739420	+	0.673244i	$0.235100\pi$
$102$	1.57670	+	0.910307i	0.156116	+	0.0901338i
$103$	−7.21744	−	12.5010i	−0.711155	−	1.23176i	−0.964424	−	0.264361i	$-0.914839\pi$
$103$	−7.21744	−	12.5010i	−0.711155	−	1.23176i	0.253269	−	0.967396i	$-0.418494\pi$
$104$	−2.84000	+	2.77044i	−0.278485	+	0.271664i
$105$		0			0
$106$		−	12.8282i		−	1.24599i
$107$	4.85942	+	8.41677i	0.469778	+	0.813680i	0.999403	−	0.0345525i	$-0.0110006\pi$
$107$	4.85942	+	8.41677i	0.469778	+	0.813680i	−0.529625	+	0.848232i	$0.677667\pi$
$108$	−1.34371	+	2.32737i	−0.129298	+	0.223951i
$109$	5.75782	+	3.32428i	0.551499	+	0.318408i	0.749726	−	0.661748i	$-0.230185\pi$
$109$	5.75782	+	3.32428i	0.551499	+	0.318408i	−0.198227	+	0.980156i	$0.563518\pi$
$110$	26.5001	−	15.2999i	2.52669	−	1.45878i
$111$		−	0.888018i		−	0.0842869i
$112$		0			0
$113$	17.5434			1.65035			0.825173	−	0.564880i	$-0.191078\pi$
$113$	17.5434			1.65035			0.825173	+	0.564880i	$0.191078\pi$
$114$	−0.598855	−	1.03725i	−0.0560879	−	0.0971471i
$115$	6.80437	+	3.92850i	0.634511	+	0.366335i
$116$	−8.27316	+	14.3295i	−0.768144	+	1.33046i
$117$	−2.89763	+	10.3015i	−0.267886	+	0.952378i
$118$	−10.4217			−0.959399
$119$		0			0
$120$	0.709696			0.0647861
$121$	2.46946	+	4.27724i	0.224497	+	0.388840i
$122$	3.74665	+	2.16313i	0.339206	+	0.195840i
$123$	−0.328265	−	0.189524i	−0.0295987	−	0.0170888i
$124$	3.24163	−	1.87156i	0.291107	−	0.168071i
$125$			10.8304i			0.968704i
$126$		0			0
$127$	−19.5143			−1.73162			−0.865809	−	0.500375i	$-0.833195\pi$
$127$	−19.5143			−1.73162			−0.865809	+	0.500375i	$0.833195\pi$
$128$	−7.36826	+	4.25407i	−0.651269	+	0.376010i
$129$	0.128010	−	0.221720i	0.0112707	−	0.0195214i
$130$	26.7800	−	6.82100i	2.34876	−	0.598242i
$131$	9.53713	+	16.5188i	0.833263	+	1.44325i	0.895437	+	0.445188i	$0.146863\pi$
$131$	9.53713	+	16.5188i	0.833263	+	1.44325i	−0.0621741	+	0.998065i	$0.519803\pi$
$132$			1.79777i			0.156476i
$133$		0			0
$134$	8.31259			0.718098
$135$	3.33341	−	1.92455i	0.286894	−	0.165638i
$136$	−4.56387	−	2.63495i	−0.391349	−	0.225945i
$137$	−5.56759	−	3.21445i	−0.475672	−	0.274629i	0.242939	−	0.970042i	$-0.421888\pi$
$137$	−5.56759	−	3.21445i	−0.475672	−	0.274629i	−0.718611	+	0.695412i	$0.755222\pi$
$138$	−0.717328	+	0.414149i	−0.0610630	+	0.0352547i
$139$	2.42854			0.205986			0.102993	−	0.994682i	$-0.467158\pi$
$139$	2.42854			0.205986			0.102993	+	0.994682i	$0.467158\pi$
$140$		0			0
$141$			0.182240i			0.0153473i
$142$	9.35942	+	16.2110i	0.785425	+	1.36040i
$143$	3.55296	+	13.9493i	0.297113	+	1.16650i
$144$	−4.00171	+	6.93117i	−0.333476	+	0.577598i
$145$	20.5237	−	11.8494i	1.70440	−	0.984036i
$146$	6.56518			0.543338
$147$		0			0
$148$			12.5005i			1.02753i
$149$	−0.0998984	+	0.0576764i	−0.00818400	+	0.00472503i	−0.504086	−	0.863653i	$-0.668171\pi$
$149$	−0.0998984	+	0.0576764i	−0.00818400	+	0.00472503i	0.495902	+	0.868378i	$0.334837\pi$
$150$	−2.63491	−	1.52126i	−0.215139	−	0.124211i
$151$	10.2218	+	5.90155i	0.831838	+	0.480262i	0.854481	−	0.519482i	$-0.173875\pi$
$151$	10.2218	+	5.90155i	0.831838	+	0.480262i	−0.0226438	+	0.999744i	$0.507208\pi$
$152$	1.73343	+	3.00239i	0.140600	+	0.243526i
$153$	−14.2143			−1.14916
$154$		0			0
$155$	−5.36114			−0.430617
$156$	−0.439626	+	1.56294i	−0.0351982	+	0.125135i
$157$	−6.57343	+	11.3855i	−0.524617	+	0.908663i	0.474972	+	0.880001i	$0.342458\pi$
$157$	−6.57343	+	11.3855i	−0.524617	+	0.908663i	−0.999589	+	0.0286625i	$0.990875\pi$
$158$	3.62257	+	2.09149i	0.288197	+	0.166390i
$159$	−0.539730	−	0.934840i	−0.0428034	−	0.0741377i
$160$	28.6040			2.26135
$161$		0			0
$162$		−	18.5197i		−	1.45504i
$163$	−16.1501	+	9.32424i	−1.26497	+	0.730331i	−0.974032	−	0.226411i	$-0.927301\pi$
$163$	−16.1501	+	9.32424i	−1.26497	+	0.730331i	−0.290938	+	0.956742i	$0.593967\pi$
$164$	4.62094	+	2.66790i	0.360835	+	0.208328i
$165$	1.28744	−	2.22992i	0.100227	−	0.173599i
$166$	8.14084	+	14.1003i	0.631852	+	1.09440i
$167$			0.972672i			0.0752676i	0.999292	+	0.0376338i	$0.0119820\pi$
$167$			0.972672i			0.0752676i	−0.999292	+	0.0376338i	$0.988018\pi$
$168$		0			0
$169$	−0.322293	+	12.9960i	−0.0247917	+	0.999693i
$170$	18.3534	+	31.7891i	1.40764	+	2.43811i
$171$	8.09821	+	4.67550i	0.619286	+	0.357545i
$172$	−1.80198	+	3.12113i	−0.137400	+	0.237984i
$173$	−1.22855	−	2.12791i	−0.0934050	−	0.161782i	0.815537	−	0.578705i	$-0.196442\pi$
$173$	−1.22855	−	2.12791i	−0.0934050	−	0.161782i	−0.908942	+	0.416923i	$0.863108\pi$
$174$			2.49836i			0.189400i
$175$		0			0
$176$			10.7656i			0.811491i
$177$	−0.759471	+	0.438481i	−0.0570854	+	0.0329583i
$178$	13.6023	−	23.5598i	1.01953	−	1.76588i
$179$	7.23629	−	12.5336i	0.540866	−	0.936807i	−0.457989	−	0.888958i	$-0.651430\pi$
$179$	7.23629	−	12.5336i	0.540866	−	0.936807i	0.998855	−	0.0478492i	$-0.0152367\pi$
$180$	−23.3362	+	13.4732i	−1.73938	+	1.00423i
$181$	9.17885			0.682259			0.341129	−	0.940016i	$-0.389191\pi$
$181$	9.17885			0.682259			0.341129	+	0.940016i	$0.389191\pi$
$182$		0			0
$183$	0.364043			0.0269108
$184$	2.07636	−	1.19879i	0.153071	−	0.0883758i
$185$	8.95202	−	15.5053i	0.658165	−	1.13998i
$186$	0.282590	−	0.489460i	0.0207205	−	0.0358889i
$187$	−16.5584	+	9.56002i	−1.21087	+	0.699098i
$188$		−	2.56536i		−	0.187098i
$189$		0			0
$190$		−	24.1480i		−	1.75188i
$191$	−8.79202	−	15.2282i	−0.636168	−	1.10188i	−0.986266	−	0.165162i	$-0.947185\pi$
$191$	−8.79202	−	15.2282i	−0.636168	−	1.10188i	0.350098	−	0.936713i	$-0.386148\pi$
$192$	−1.02545	+	1.77613i	−0.0740054	+	0.128181i
$193$	17.1090	+	9.87791i	1.23154	+	0.711028i	0.967350	−	0.253444i	$-0.0815633\pi$
$193$	17.1090	+	9.87791i	1.23154	+	0.711028i	0.264186	+	0.964472i	$0.414897\pi$
$194$	1.44428	+	2.50156i	0.103693	+	0.179601i
$195$	1.66457	−	1.62380i	0.119203	−	0.116283i
$196$		0			0
$197$		−	7.66020i		−	0.545767i	−0.962047	−	0.272883i	$-0.912023\pi$
$197$		−	7.66020i		−	0.545767i	0.962047	−	0.272883i	$-0.0879773\pi$
$198$	−12.5929	−	21.8115i	−0.894935	−	1.55007i
$199$	3.27171	−	5.66677i	0.231925	−	0.401706i	−0.726449	−	0.687220i	$-0.758831\pi$
$199$	3.27171	−	5.66677i	0.231925	−	0.401706i	0.958375	+	0.285514i	$0.0921642\pi$
$200$	7.62694	+	4.40342i	0.539306	+	0.311369i
$201$	0.605769	−	0.349741i	0.0427277	−	0.0246688i
$202$		−	9.11412i		−	0.641267i
$203$		0			0
$204$	−2.15657			−0.150990
$205$	−3.82115	−	6.61842i	−0.266880	−	0.462250i
$206$	26.5707	+	15.3406i	1.85127	+	1.06883i
$207$	3.23343	−	5.60047i	0.224739	−	0.389259i
$208$	−2.63262	+	9.35939i	−0.182539	+	0.648957i
$209$	12.5783			0.870060
$210$		0			0
$211$	20.0452			1.37997			0.689983	−	0.723825i	$-0.257618\pi$
$211$	20.0452			1.37997			0.689983	+	0.723825i	$0.257618\pi$
$212$	7.59771	+	13.1596i	0.521813	+	0.903806i
$213$	1.36411	+	0.787571i	0.0934674	+	0.0539635i
$214$	−17.8898	−	10.3287i	−1.22292	−	0.706052i
$215$	4.47028	−	2.58092i	0.304871	−	0.176017i
$216$		−	1.17455i		−	0.0799183i
$217$		0			0
$218$	−14.1314			−0.957102
$219$	0.478429	−	0.276221i	0.0323293	−	0.0186653i
$220$	−18.1232	+	31.3902i	−1.22186	+	2.11633i
$221$	−16.7333	+	4.26206i	−1.12560	+	0.286697i
$222$	0.943736	+	1.63460i	0.0633394	+	0.109707i
$223$			27.7139i			1.85586i	0.372752	+	0.927931i	$0.378414\pi$
$223$			27.7139i			1.85586i	−0.372752	+	0.927931i	$0.621586\pi$
$224$		0			0
$225$	23.7543			1.58362
$226$	−32.2927	+	18.6442i	−2.14808	+	1.24019i
$227$	−9.84766	−	5.68555i	−0.653612	−	0.377363i	0.136227	−	0.990678i	$-0.456502\pi$
$227$	−9.84766	−	5.68555i	−0.653612	−	0.377363i	−0.789839	+	0.613315i	$0.789836\pi$
$228$	1.22865	+	0.709362i	0.0813694	+	0.0469786i
$229$	7.54406	−	4.35556i	0.498525	−	0.287824i	−0.229579	−	0.973290i	$-0.573735\pi$
$229$	7.54406	−	4.35556i	0.498525	−	0.287824i	0.728104	+	0.685466i	$0.240402\pi$
$230$	−16.7000			−1.10116
$231$		0			0
$232$		−	7.23170i		−	0.474784i
$233$	−1.68228	−	2.91380i	−0.110210	−	0.190889i	0.805645	−	0.592399i	$-0.201819\pi$
$233$	−1.68228	−	2.91380i	−0.110210	−	0.190889i	−0.915855	+	0.401510i	$0.868486\pi$
$234$	−5.61416	−	22.0418i	−0.367009	−	1.44092i
$235$	−1.83714	+	3.18202i	−0.119842	+	0.207572i
$236$	10.6910	−	6.17244i	0.695923	−	0.401791i
$237$	0.351987			0.0228640
$238$		0			0
$239$			19.8798i			1.28592i	0.765902	+	0.642958i	$0.222293\pi$
$239$			19.8798i			1.28592i	−0.765902	+	0.642958i	$0.777707\pi$
$240$	1.50615	−	0.869579i	0.0972219	−	0.0561311i
$241$	−16.3435	−	9.43595i	−1.05278	−	0.607823i	−0.129354	−	0.991599i	$-0.541290\pi$
$241$	−16.3435	−	9.43595i	−1.05278	−	0.607823i	−0.923426	+	0.383776i	$0.874624\pi$
$242$	−9.09123	−	5.24882i	−0.584406	−	0.337407i
$243$	−2.38030	−	4.12280i	−0.152696	−	0.264477i
$244$	−5.12458			−0.328068
$245$		0			0
$246$	0.805663			0.0513672
$247$	10.9353	+	3.07589i	0.695795	+	0.195714i
$248$	−0.817978	+	1.41678i	−0.0519417	+	0.0899656i
$249$	1.18651	+	0.685030i	0.0751918	+	0.0434120i
$250$	−11.5100	−	19.9359i	−0.727956	−	1.26086i
$251$	−9.79601			−0.618319			−0.309159	−	0.951010i	$-0.600048\pi$
$251$	−9.79601			−0.618319			−0.309159	+	0.951010i	$0.600048\pi$
$252$		0			0
$253$		−	8.69877i		−	0.546887i
$254$	35.9206	−	20.7388i	2.25386	−	1.30127i
$255$	2.67497	+	1.54439i	0.167513	+	0.0967136i
$256$	−2.42488	+	4.20002i	−0.151555	+	0.262501i
$257$	−10.4697	−	18.1341i	−0.653083	−	1.13117i	−0.982371	−	0.186944i	$-0.940142\pi$
$257$	−10.4697	−	18.1341i	−0.653083	−	1.13117i	0.329287	−	0.944230i	$-0.393192\pi$
$258$			0.544170i			0.0338785i
$259$		0			0
$260$	−23.4320	+	22.8581i	−1.45319	+	1.41760i
$261$	−9.75285	−	16.8924i	−0.603686	−	1.04562i
$262$	−35.1105	−	20.2711i	−2.16914	−	1.25235i
$263$	3.69340	−	6.39715i	0.227745	−	0.394465i	−0.729395	−	0.684093i	$-0.760198\pi$
$263$	3.69340	−	6.39715i	0.227745	−	0.394465i	0.957139	+	0.289628i	$0.0935316\pi$
$264$	−0.392865	−	0.680462i	−0.0241792	−	0.0418795i
$265$		−	21.7639i		−	1.33694i
$266$		0			0
$267$		−	2.28919i		−	0.140096i
$268$	−8.52733	+	4.92326i	−0.520890	+	0.300736i
$269$	11.3946	−	19.7360i	0.694740	−	1.20332i	−0.275529	−	0.961293i	$-0.588853\pi$
$269$	11.3946	−	19.7360i	0.694740	−	1.20332i	0.970268	−	0.242032i	$-0.0778138\pi$
$270$	−4.09060	+	7.08513i	−0.248946	+	0.431187i
$271$	3.60814	−	2.08316i	0.219179	−	0.126543i	−0.386391	−	0.922335i	$-0.626278\pi$
$271$	3.60814	−	2.08316i	0.219179	−	0.126543i	0.605570	+	0.795792i	$0.292945\pi$
$272$	−12.9143			−0.783042
$273$		0			0
$274$	13.6646			0.825507
$275$	27.6717	−	15.9763i	1.66867	−	0.963406i
$276$	0.490572	−	0.849696i	0.0295290	−	0.0511457i
$277$	0.388551	−	0.672989i	0.0233457	−	0.0404360i	−0.854116	−	0.520082i	$-0.825901\pi$
$277$	0.388551	−	0.672989i	0.0233457	−	0.0404360i	0.877462	+	0.479646i	$0.159235\pi$
$278$	−4.47028	+	2.58092i	−0.268110	+	0.154793i
$279$			4.41259i			0.264175i
$280$		0			0
$281$			11.8988i			0.709824i	0.934900	+	0.354912i	$0.115489\pi$
$281$			11.8988i			0.709824i	−0.934900	+	0.354912i	$0.884511\pi$
$282$	−0.193674	−	0.335454i	−0.0115331	−	0.0199760i
$283$	7.95202	−	13.7733i	0.472698	−	0.818738i	−0.526813	−	0.849981i	$-0.676613\pi$
$283$	7.95202	−	13.7733i	0.472698	−	0.818738i	0.999512	+	0.0312434i	$0.00994670\pi$
$284$	−19.2024	−	11.0865i	−1.13945	−	0.657864i
$285$	−1.01599	−	1.75975i	−0.0601823	−	0.104239i
$286$	−21.3646	−	21.9010i	−1.26331	−	1.29503i
$287$		0			0
$288$		−	23.5431i		−	1.38729i
$289$	−2.96801	−	5.14075i	−0.174589	−	0.302397i
$290$	−25.1857	+	43.6229i	−1.47896	+	2.56163i
$291$	0.210500	+	0.121532i	0.0123397	+	0.00712433i
$292$	−6.73478	+	3.88833i	−0.394123	+	0.227547i
$293$		−	6.73698i		−	0.393579i	−0.980446	−	0.196789i	$-0.936949\pi$
$293$		−	6.73698i		−	0.393579i	0.980446	−	0.196789i	$-0.0630515\pi$
$294$		0			0
$295$	−17.6811			−1.02944
$296$	−2.73172	−	4.73148i	−0.158778	−	0.275011i
$297$	−3.69054	−	2.13073i	−0.214147	−	0.123638i
$298$	0.122591	−	0.212333i	0.00710148	−	0.0123001i
$299$	2.12719	−	7.56250i	0.123019	−	0.437350i
$300$	3.60397			0.208075
$301$		0			0
$302$	−25.0874			−1.44362
$303$	−0.383465	−	0.664180i	−0.0220295	−	0.0381562i
$304$	7.35756	+	4.24789i	0.421985	+	0.243633i
$305$	6.35642	+	3.66988i	0.363968	+	0.210137i
$306$	26.1646	−	15.1061i	1.49573	−	0.863561i
$307$			14.7179i			0.839996i	0.907525	+	0.419998i	$0.137969\pi$
$307$			14.7179i			0.839996i	−0.907525	+	0.419998i	$0.862031\pi$
$308$		0			0
$309$	2.58174			0.146870
$310$	9.86840	−	5.69752i	0.560487	−	0.323597i
$311$	−14.3289	+	24.8184i	−0.812517	+	1.40732i	0.0985808	+	0.995129i	$0.468570\pi$
$311$	−14.3289	+	24.8184i	−0.812517	+	1.40732i	−0.911097	+	0.412191i	$0.864764\pi$
$312$	−0.175147	−	0.687648i	−0.00991577	−	0.0389304i
$313$	−16.4125	−	28.4274i	−0.927692	−	1.60681i	−0.787174	−	0.616732i	$-0.788456\pi$
$313$	−16.4125	−	28.4274i	−0.927692	−	1.60681i	−0.140518	−	0.990078i	$-0.544877\pi$
$314$		−	27.9435i		−	1.57694i
$315$		0			0
$316$	−4.95488			−0.278734
$317$	−9.01715	+	5.20605i	−0.506453	+	0.292401i	−0.731375	−	0.681976i	$-0.761121\pi$
$317$	−9.01715	+	5.20605i	−0.506453	+	0.292401i	0.224921	+	0.974377i	$0.427788\pi$
$318$	1.98699	+	1.14719i	0.111425	+	0.0643313i
$319$	−22.7225	−	13.1188i	−1.27222	−	0.734515i
$320$	−35.8100	+	20.6749i	−2.00184	+	1.15576i
$321$	−1.73826			−0.0970201
$322$		0			0
$323$			15.0887i			0.839558i
$324$	10.9686	+	18.9981i	0.609364	+	1.05545i
$325$	27.9639	−	7.12256i	1.55116	−	0.395089i
$326$	19.8186	−	34.3268i	1.09765	−	1.90118i
$327$	−1.02981	+	0.594562i	−0.0569487	+	0.0328793i
$328$	−2.33205			−0.128766
$329$		0			0
$330$			5.47290i			0.301273i
$331$	3.86260	−	2.23007i	0.212308	−	0.122576i	−0.390076	−	0.920783i	$-0.627551\pi$
$331$	3.86260	−	2.23007i	0.212308	−	0.122576i	0.602383	+	0.798207i	$0.294218\pi$
$332$	−16.7023	−	9.64307i	−0.916657	−	0.529232i
$333$	−12.7620	−	7.36813i	−0.699352	−	0.403771i
$334$	−1.03370	−	1.79043i	−0.0565617	−	0.0979677i
$335$	14.1028			0.770519
$336$		0			0
$337$	10.7949			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$337$	10.7949			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$338$	−13.2182	−	24.2646i	−0.718975	−	1.31982i
$339$	−1.56886	+	2.71734i	−0.0852087	+	0.147586i
$340$	−37.6551	−	21.7402i	−2.04214	−	1.17903i
$341$	2.96775	+	5.14030i	0.160713	+	0.278363i
$342$	−19.8755			−1.07474
$343$		0			0
$344$		−	1.57514i		−	0.0849259i
$345$	−1.21699	+	0.702630i	−0.0655206	+	0.0378283i
$346$	4.52286	+	2.61127i	0.243150	+	0.140383i
$347$	2.03516	−	3.52499i	0.109253	−	0.189232i	−0.806215	−	0.591623i	$-0.798487\pi$
$347$	2.03516	−	3.52499i	0.109253	−	0.189232i	0.915468	+	0.402391i	$0.131821\pi$
$348$	−1.47969	−	2.56290i	−0.0793198	−	0.137386i
$349$			23.8727i			1.27788i	0.769258	+	0.638938i	$0.220626\pi$
$349$			23.8727i			1.27788i	−0.769258	+	0.638938i	$0.779374\pi$
$350$		0			0
$351$	−2.68741	−	2.75489i	−0.143444	−	0.147045i
$352$	−15.8343	−	27.4257i	−0.843969	−	1.46180i
$353$	22.5894	+	13.0420i	1.20231	+	0.694154i	0.961068	−	0.276311i	$-0.0891119\pi$
$353$	22.5894	+	13.0420i	1.20231	+	0.694154i	0.241242	+	0.970465i	$0.422445\pi$
$354$	0.931987	−	1.61425i	0.0495346	−	0.0857964i
$355$	15.8788	+	27.5030i	0.842762	+	1.45971i
$356$			32.2246i			1.70790i
$357$		0			0
$358$			30.7613i			1.62579i
$359$	19.8271	−	11.4472i	1.04644	−	0.604160i	0.124786	−	0.992184i	$-0.460176\pi$
$359$	19.8271	−	11.4472i	1.04644	−	0.604160i	0.921649	+	0.388024i	$0.126842\pi$
$360$	5.88855	−	10.1993i	0.310354	−	0.537549i
$361$	−4.53687	+	7.85809i	−0.238783	+	0.413584i
$362$	−16.8958	+	9.75478i	−0.888022	+	0.512700i
$363$	−0.883349			−0.0463638
$364$		0			0
$365$	11.1382			0.583002
$366$	−0.670104	+	0.386885i	−0.0350269	+	0.0202228i
$367$	−9.08003	+	15.7271i	−0.473974	+	0.820946i	−0.999556	−	0.0297964i	$-0.990514\pi$
$367$	−9.08003	+	15.7271i	−0.473974	+	0.820946i	0.525582	+	0.850743i	$0.323847\pi$
$368$	2.93771	−	5.08826i	0.153139	−	0.265244i
$369$	−5.44742	+	3.14507i	−0.283581	+	0.163726i
$370$			38.0548i			1.97838i
$371$		0			0
$372$			0.669473i			0.0347105i
$373$	7.93457	+	13.7431i	0.410836	+	0.711590i	0.994981	−	0.100060i	$-0.0319034\pi$
$373$	7.93457	+	13.7431i	0.410836	+	0.711590i	−0.584145	+	0.811649i	$0.698570\pi$
$374$	20.3197	−	35.1948i	1.05071	−	1.81988i
$375$	−1.67755	−	0.968536i	−0.0866285	−	0.0500150i
$376$	0.560605	+	0.970997i	0.0289110	+	0.0500754i
$377$	−16.5463	−	16.9618i	−0.852179	−	0.873575i
$378$		0			0
$379$			27.7634i			1.42611i	0.701108	+	0.713055i	$0.252689\pi$
$379$			27.7634i			1.42611i	−0.701108	+	0.713055i	$0.747311\pi$
$380$	14.3020	+	24.7718i	0.733678	+	1.27077i
$381$	1.74511	−	3.02262i	0.0894048	−	0.154854i
$382$	32.3674	+	18.6873i	1.65606	+	0.956128i
$383$	22.7304	−	13.1234i	1.16147	−	0.670576i	0.209815	−	0.977741i	$-0.432714\pi$
$383$	22.7304	−	13.1234i	1.16147	−	0.670576i	0.951656	+	0.307165i	$0.0993804\pi$
$384$		−	1.52172i		−	0.0776548i
$385$		0			0
$386$	−41.9908			−2.13728
$387$	−2.12428	−	3.67936i	−0.107983	−	0.187032i
$388$	−2.96317	−	1.71079i	−0.150432	−	0.0868521i
$389$	−12.6277	+	21.8718i	−0.640250	+	1.10895i	0.345127	+	0.938556i	$0.387836\pi$
$389$	−12.6277	+	21.8718i	−0.640250	+	1.10895i	−0.985377	+	0.170389i	$0.945497\pi$
$390$	−1.33834	+	4.75800i	−0.0677693	+	0.240931i
$391$	10.4349			0.527714
$392$		0			0
$393$	−3.41151			−0.172088
$394$	8.14084	+	14.1003i	0.410129	+	0.710365i
$395$	6.14592	+	3.54835i	0.309235	+	0.178537i
$396$	25.8363	+	14.9166i	1.29833	+	0.749588i
$397$	−12.9701	+	7.48827i	−0.650949	+	0.375826i	−0.788820	−	0.614625i	$-0.789308\pi$
$397$	−12.9701	+	7.48827i	−0.650949	+	0.375826i	0.137871	+	0.990450i	$0.455974\pi$
$398$			13.9080i			0.697143i
$399$		0			0
$400$	21.5817			1.07909
$401$	4.62811	−	2.67204i	0.231117	−	0.133435i	−0.379970	−	0.924999i	$-0.624066\pi$
$401$	4.62811	−	2.67204i	0.231117	−	0.133435i	0.611087	+	0.791563i	$0.290733\pi$
$402$	−0.743371	+	1.28756i	−0.0370760	+	0.0642175i
$403$	1.32309	+	5.19458i	0.0659076	+	0.258760i
$404$	5.39798	+	9.34957i	0.268559	+	0.465159i
$405$		−	31.4198i		−	1.56126i
$406$		0			0
$407$	−19.8222			−0.982549
$408$	0.816269	−	0.471273i	0.0404113	−	0.0233315i
$409$	−2.91433	−	1.68259i	−0.144104	−	0.0831985i	0.426214	−	0.904622i	$-0.359847\pi$
$409$	−2.91433	−	1.68259i	−0.144104	−	0.0831985i	−0.570319	+	0.821424i	$0.693180\pi$
$410$	14.0674	+	8.12181i	0.694739	+	0.401107i
$411$	0.995789	−	0.574919i	0.0491186	−	0.0283587i
$412$	−36.3428			−1.79048
$413$		0			0
$414$			13.7453i			0.675542i
$415$	13.8114	+	23.9221i	0.677977	+	1.17429i
$416$	−7.05925	−	27.7154i	−0.346108	−	1.35886i
$417$	−0.217178	+	0.376163i	−0.0106352	+	0.0184208i
$418$	−23.1533	+	13.3675i	−1.13246	+	0.653828i
$419$	28.8639			1.41010			0.705048	−	0.709160i	$-0.250926\pi$
$419$	28.8639			1.41010			0.705048	+	0.709160i	$0.250926\pi$
$420$		0			0
$421$		−	16.6125i		−	0.809644i	−0.914395	−	0.404822i	$-0.867333\pi$
$421$		−	16.6125i		−	0.809644i	0.914395	−	0.404822i	$-0.132667\pi$
$422$	−36.8977	+	21.3029i	−1.79615	+	1.03701i
$423$	2.61902	+	1.51209i	0.127341	+	0.0735205i
$424$	−5.75151	−	3.32064i	−0.279318	−	0.161264i
$425$	19.1648	+	33.1945i	0.929631	+	1.61017i
$426$	−3.34795			−0.162209
$427$		0			0
$428$	24.4692			1.18276
$429$	−2.47837	−	0.697119i	−0.119657	−	0.0336572i
$430$	−5.48572	+	9.50154i	−0.264545	+	0.458205i
$431$	−17.8015	−	10.2777i	−0.857469	−	0.495060i	0.00569505	−	0.999984i	$-0.498187\pi$
$431$	−17.8015	−	10.2777i	−0.857469	−	0.495060i	−0.863164	+	0.504924i	$0.831521\pi$
$432$	−1.43916	−	2.49270i	−0.0692417	−	0.119930i
$433$	19.4092			0.932748			0.466374	−	0.884588i	$-0.345560\pi$
$433$	19.4092			0.932748			0.466374	+	0.884588i	$0.345560\pi$
$434$		0			0
$435$			4.23862i			0.203226i
$436$	14.4965	−	8.36956i	0.694257	−	0.400829i
$437$	−5.94500	−	3.43235i	−0.284388	−	0.164191i
$438$	−0.587106	+	1.01690i	−0.0280530	+	0.0485892i
$439$	−6.71256	−	11.6265i	−0.320373	−	0.554902i	0.660192	−	0.751097i	$-0.270475\pi$
$439$	−6.71256	−	11.6265i	−0.320373	−	0.554902i	−0.980565	+	0.196195i	$0.937142\pi$
$440$		−	15.8417i		−	0.755225i
$441$		0			0
$442$	26.2720	−	25.6285i	1.24963	−	1.21902i
$443$	16.7766	+	29.0579i	0.797080	+	1.38058i	0.921510	+	0.388354i	$0.126956\pi$
$443$	16.7766	+	29.0579i	0.797080	+	1.38058i	−0.124430	+	0.992228i	$0.539710\pi$
$444$	−1.93623	−	1.11788i	−0.0918895	−	0.0530524i
$445$	23.0771	−	39.9707i	1.09396	−	1.89479i
$446$	−29.4528	−	51.0138i	−1.39463	−	2.41557i
$447$		−	0.0206313i		−	0.000975829i
$448$		0			0
$449$		−	34.4284i		−	1.62478i	−0.583117	−	0.812388i	$-0.698167\pi$
$449$		−	34.4284i		−	1.62478i	0.583117	−	0.812388i	$-0.301833\pi$
$450$	−43.7251	+	25.2447i	−2.06122	+	1.19005i
$451$	−4.23052	+	7.32748i	−0.199208	+	0.345038i
$452$	22.0846	−	38.2517i	1.03877	−	1.79921i
$453$	−1.82821	+	1.05552i	−0.0858969	+	0.0495926i
$454$	24.1691			1.13431
$455$		0			0
$456$	−0.620064			−0.0290371
$457$	−11.6735	+	6.73967i	−0.546061	+	0.315269i	−0.747532	−	0.664226i	$-0.768761\pi$
$457$	−11.6735	+	6.73967i	−0.546061	+	0.315269i	0.201471	+	0.979495i	$0.435428\pi$
$458$	−9.25771	+	16.0348i	−0.432584	+	0.749258i
$459$	2.55598	−	4.42710i	0.119303	−	0.206639i
$460$	17.1314	−	9.89082i	0.798756	−	0.461162i
$461$			1.35900i			0.0632951i	0.999499	+	0.0316476i	$0.0100754\pi$
$461$			1.35900i			0.0632951i	−0.999499	+	0.0316476i	$0.989925\pi$
$462$		0			0
$463$		−	2.49836i		−	0.116109i	−0.998313	−	0.0580543i	$-0.981510\pi$
$463$		−	2.49836i		−	0.116109i	0.998313	−	0.0580543i	$-0.0184897\pi$
$464$	−8.86088	−	15.3475i	−0.411356	−	0.712489i
$465$	0.479431	−	0.830399i	0.0222331	−	0.0385088i
$466$	6.19325	+	3.57567i	0.286897	+	0.165640i
$467$	13.1091	+	22.7056i	0.606617	+	1.05069i	0.991794	+	0.127849i	$0.0408072\pi$
$467$	13.1091	+	22.7056i	0.606617	+	1.05069i	−0.385176	+	0.922843i	$0.625859\pi$
$468$	18.8138	+	19.2861i	0.869668	+	0.891502i
$469$		0			0
$470$		−	7.80965i		−	0.360232i
$471$	−1.17569	−	2.03635i	−0.0541728	−	0.0938301i
$472$	−2.69771	+	4.67257i	−0.124172	+	0.215072i
$473$	−4.94921	−	2.85743i	−0.227565	−	0.131385i
$474$	−0.647913	+	0.374073i	−0.0297596	+	0.0171817i
$475$		−	25.2156i		−	1.15697i
$476$		0			0
$477$	−17.9132			−0.820188
$478$	−21.1271	−	36.5933i	−0.966332	−	1.67374i
$479$	−20.6513	−	11.9230i	−0.943583	−	0.544778i	−0.0525011	−	0.998621i	$-0.516719\pi$
$479$	−20.6513	−	11.9230i	−0.943583	−	0.544778i	−0.891082	+	0.453843i	$0.850053\pi$
$480$	−2.55798	+	4.43055i	−0.116755	+	0.202226i
$481$	−17.2329	−	4.84730i	−0.785754	−	0.221018i
$482$	40.1120			1.82705
$483$		0			0
$484$	12.4348			0.565217
$485$	2.45030	+	4.24405i	0.111263	+	0.192712i
$486$	8.76296	+	5.05930i	0.397496	+	0.229494i
$487$	−9.17524	−	5.29733i	−0.415770	−	0.240045i	0.277496	−	0.960727i	$-0.410496\pi$
$487$	−9.17524	−	5.29733i	−0.415770	−	0.240045i	−0.693266	+	0.720682i	$0.743829\pi$
$488$	1.93967	−	1.11987i	0.0878047	−	0.0506941i
$489$		−	3.33536i		−	0.150830i
$490$		0			0
$491$	19.7704			0.892224			0.446112	−	0.894977i	$-0.352808\pi$
$491$	19.7704			0.892224			0.446112	+	0.894977i	$0.352808\pi$
$492$	−0.826476	+	0.477166i	−0.0372604	+	0.0215123i
$493$	15.7371	−	27.2575i	0.708764	−	1.22762i
$494$	−23.3978	+	5.95953i	−1.05272	+	0.268132i
$495$	−21.3646	−	37.0045i	−0.960266	−	1.66323i
$496$			4.00902i			0.180010i
$497$		0			0
$498$	−2.91205			−0.130492
$499$	−11.4234	+	6.59530i	−0.511381	+	0.295246i	−0.733401	−	0.679796i	$-0.762068\pi$
$499$	−11.4234	+	6.59530i	−0.511381	+	0.295246i	0.222020	+	0.975042i	$0.428735\pi$
$500$	23.6147	+	13.6339i	1.05608	+	0.609728i
$501$	−0.150660	−	0.0869833i	−0.00673097	−	0.00388613i
$502$	18.0318	−	10.4107i	0.804798	−	0.464651i
$503$	−37.9046			−1.69008			−0.845040	−	0.534703i	$-0.820424\pi$
$503$	−37.9046			−1.69008			−0.845040	+	0.534703i	$0.820424\pi$
$504$		0			0
$505$		−	15.4627i		−	0.688080i
$506$	9.24457	+	16.0121i	0.410971	+	0.711823i
$507$	−1.98416	−	1.21212i	−0.0881197	−	0.0538320i
$508$	−24.5657	+	42.5490i	−1.08993	+	1.88781i
$509$	23.9565	−	13.8313i	1.06185	−	0.613062i	0.135909	−	0.990721i	$-0.456604\pi$
$509$	23.9565	−	13.8313i	1.06185	−	0.613062i	0.925944	+	0.377660i	$0.123271\pi$
$510$	−6.56518			−0.290711
$511$		0			0
$512$		−	27.3244i		−	1.20758i
$513$	−2.91241	+	1.68148i	−0.128586	+	0.0742392i
$514$	38.5438	+	22.2533i	1.70010	+	0.981551i
$515$	45.0788	+	26.0263i	1.98641	+	1.14685i
$516$	−0.322293	−	0.558227i	−0.0141881	−	0.0245746i
$517$	4.06792			0.178907
$518$		0			0
$519$	0.439464			0.0192903
$520$	3.87392	−	13.7724i	0.169883	−	0.603960i
$521$	7.78339	−	13.4812i	0.340996	−	0.590623i	−0.643622	−	0.765344i	$-0.722569\pi$
$521$	7.78339	−	13.4812i	0.340996	−	0.590623i	0.984618	+	0.174721i	$0.0559022\pi$
$522$	35.9047	+	20.7296i	1.57151	+	0.907310i
$523$	13.6169	+	23.5852i	0.595425	+	1.03131i	0.993487	+	0.113948i	$0.0363498\pi$
$523$	13.6169	+	23.5852i	0.595425	+	1.03131i	−0.398061	+	0.917359i	$0.630317\pi$
$524$	48.0234			2.09791
$525$		0			0
$526$			15.7005i			0.684577i
$527$	−6.16620	+	3.56006i	−0.268604	+	0.155079i
$528$	−1.66752	−	0.962741i	−0.0725694	−	0.0418979i
$529$	9.12630	−	15.8072i	0.396796	−	0.687270i
$530$	23.1294	+	40.0614i	1.00468	+	1.74015i
$531$			14.5528i			0.631538i
$532$		0			0
$533$	−5.46977	+	5.33581i	−0.236922	+	0.231119i
$534$	2.43283	+	4.21378i	0.105279	+	0.182348i
$535$	−30.3511	−	17.5232i	−1.31219	−	0.757594i
$536$	2.15175	−	3.72693i	0.0929413	−	0.160979i
$537$	1.29424	+	2.24169i	0.0558507	+	0.0967362i
$538$			48.4381i			2.08832i
$539$		0			0
$540$		−	9.69089i		−	0.417029i
$541$	20.9626	−	12.1027i	0.901251	−	0.520338i	0.0236453	−	0.999720i	$-0.492473\pi$
$541$	20.9626	−	12.1027i	0.901251	−	0.520338i	0.877606	+	0.479383i	$0.159139\pi$
$542$	−4.42774	+	7.66907i	−0.190188	+	0.329415i
$543$	−0.820839	+	1.42174i	−0.0352256	+	0.0610125i
$544$	32.8994	−	18.9945i	1.41055	−	0.814381i
$545$	−23.9749			−1.02697
$546$		0			0
$547$	−22.2177			−0.949960			−0.474980	−	0.879997i	$-0.657545\pi$
$547$	−22.2177			−0.949960			−0.474980	+	0.879997i	$0.657545\pi$
$548$	−14.0176	+	8.09305i	−0.598801	+	0.345718i
$549$	3.02057	−	5.23178i	0.128915	−	0.223287i
$550$	−33.9574	+	58.8160i	−1.44795	+	2.50792i
$551$	−17.9316	+	10.3528i	−0.763913	+	0.441045i
$552$			0.428817i			0.0182517i
$553$		0			0
$554$			1.65172i			0.0701749i
$555$	1.60111	+	2.77320i	0.0679632	+	0.117716i
$556$	3.05718	−	5.29519i	0.129653	−	0.224566i
$557$	19.3300	+	11.1602i	0.819040	+	0.472873i	0.850085	−	0.526645i	$-0.176550\pi$
$557$	19.3300	+	11.1602i	0.819040	+	0.472873i	−0.0310455	+	0.999518i	$0.509884\pi$
$558$	−4.68946	−	8.12238i	−0.198521	−	0.343848i
$559$	−3.60397	−	3.69445i	−0.152432	−	0.156259i
$560$		0			0
$561$		−	3.41970i		−	0.144380i
$562$	−12.6454	−	21.9025i	−0.533415	−	0.923901i
$563$	−13.3519	+	23.1262i	−0.562717	+	0.974655i	0.434541	+	0.900652i	$0.356911\pi$
$563$	−13.3519	+	23.1262i	−0.562717	+	0.974655i	−0.997258	+	0.0740027i	$0.976423\pi$
$564$	0.397355	+	0.229413i	0.0167317	+	0.00966004i
$565$	−54.7865	+	31.6310i	−2.30489	+	1.33073i
$566$			33.8039i			1.42088i
$567$		0			0
$568$	9.69090			0.406621
$569$	3.30510	+	5.72461i	0.138557	+	0.239988i	0.926951	−	0.375183i	$-0.122420\pi$
$569$	3.30510	+	5.72461i	0.138557	+	0.239988i	−0.788393	+	0.615171i	$0.789087\pi$
$570$	3.74034	+	2.15949i	0.156666	+	0.0904509i
$571$	−21.0643	+	36.4844i	−0.881513	+	1.52683i	−0.0318546	+	0.999493i	$0.510141\pi$
$571$	−21.0643	+	36.4844i	−0.881513	+	1.52683i	−0.849659	+	0.527333i	$0.823192\pi$
$572$	34.8877	+	9.81325i	1.45873	+	0.410313i
$573$	3.14498			0.131383
$574$		0			0
$575$	−17.4383			−0.727227
$576$	17.0169	+	29.4741i	0.709037	+	1.22809i
$577$	−13.7559	−	7.94195i	−0.572664	−	0.330628i	0.185549	−	0.982635i	$-0.440594\pi$
$577$	−13.7559	−	7.94195i	−0.572664	−	0.330628i	−0.758213	+	0.652007i	$0.773927\pi$
$578$	10.9266	+	6.30848i	0.454487	+	0.262398i
$579$	−3.06003	+	1.76671i	−0.127170	+	0.0734219i
$580$		−	59.6665i		−	2.47752i
$581$		0			0
$582$	−0.516630			−0.0214150
$583$	−20.8674	+	12.0478i	−0.864238	+	0.498968i
$584$	1.69942	−	2.94349i	0.0703226	−	0.121802i
$585$	−9.52478	−	37.3953i	−0.393801	−	1.54610i
$586$	7.15969	+	12.4010i	0.295764	+	0.512279i
$587$			18.5676i			0.766366i	0.923672	+	0.383183i	$0.125172\pi$
$587$			18.5676i			0.766366i	−0.923672	+	0.383183i	$0.874828\pi$
$588$		0			0
$589$	4.68404			0.193003
$590$	32.5462	−	18.7905i	1.33990	−	0.773594i
$591$	1.18651	+	0.685030i	0.0488064	+	0.0281784i
$592$	−11.5948	−	6.69426i	−0.476543	−	0.275132i
$593$	17.8487	−	10.3050i	0.732960	−	0.423175i	−0.0865442	−	0.996248i	$-0.527582\pi$
$593$	17.8487	−	10.3050i	0.732960	−	0.423175i	0.819504	+	0.573073i	$0.194249\pi$
$594$	9.05770			0.371642
$595$		0			0
$596$			0.290425i			0.0118963i
$597$	0.585159	+	1.01353i	0.0239490	+	0.0414809i
$598$	4.12143	+	16.1812i	0.168538	+	0.661697i
$599$	6.80224	−	11.7818i	0.277932	−	0.481393i	−0.692939	−	0.720997i	$-0.743684\pi$
$599$	6.80224	−	11.7818i	0.277932	−	0.481393i	0.970871	+	0.239604i	$0.0770176\pi$
$600$	−1.36411	+	0.787571i	−0.0556897	+	0.0321524i
$601$	12.1503			0.495621			0.247810	−	0.968809i	$-0.420289\pi$
$601$	12.1503			0.495621			0.247810	+	0.968809i	$0.420289\pi$
$602$		0			0
$603$		−	11.6076i		−	0.472698i
$604$	25.7355	−	14.8584i	1.04716	−	0.604579i
$605$	−15.4238	−	8.90496i	−0.627068	−	0.362038i
$606$	1.41171	+	0.815050i	0.0573467	+	0.0331092i
$607$	17.6166	+	30.5128i	0.715035	+	1.23848i	0.962946	+	0.269695i	$0.0869228\pi$
$607$	17.6166	+	30.5128i	0.715035	+	1.23848i	−0.247911	+	0.968783i	$0.579744\pi$
$608$	−24.9914			−1.01354
$609$		0			0
$610$	−15.6006			−0.631650
$611$	3.53655	+	0.994767i	0.143074	+	0.0402440i
$612$	−17.8937	+	30.9928i	−0.723310	+	1.25281i
$613$	26.0345	+	15.0310i	1.05152	+	0.607097i	0.923075	−	0.384619i	$-0.125667\pi$
$613$	26.0345	+	15.0310i	1.05152	+	0.607097i	0.128448	+	0.991716i	$0.459000\pi$
$614$	−15.6414	−	27.0917i	−0.631236	−	1.09333i
$615$	1.36686			0.0551170
$616$		0			0
$617$			7.01712i			0.282499i	0.989974	+	0.141249i	$0.0451119\pi$
$617$			7.01712i			0.282499i	−0.989974	+	0.141249i	$0.954888\pi$
$618$	−4.75228	+	2.74373i	−0.191165	+	0.110369i
$619$	37.9736	+	21.9241i	1.52629	+	0.881203i	0.999513	+	0.0311993i	$0.00993266\pi$
$619$	37.9736	+	21.9241i	1.52629	+	0.881203i	0.526776	+	0.850004i	$0.323401\pi$
$620$	−6.74889	+	11.6894i	−0.271042	+	0.469458i
$621$	1.16286	+	2.01413i	0.0466640	+	0.0808244i
$622$		−	60.9118i		−	2.44234i
$623$		0			0
$624$	−1.21427	−	1.24476i	−0.0486097	−	0.0498302i
$625$	0.481145	+	0.833367i	0.0192458	+	0.0333347i
$626$	60.4221	+	34.8847i	2.41495	+	1.39427i
$627$	−1.12484	+	1.94829i	−0.0449219	+	0.0778070i
$628$	16.5500	+	28.6654i	0.660416	+	1.14387i
$629$		−	23.7783i		−	0.948103i
$630$		0			0
$631$			23.4936i			0.935267i	0.883922	+	0.467634i	$0.154893\pi$
$631$			23.4936i			0.935267i	−0.883922	+	0.467634i	$0.845107\pi$
$632$	1.87544	−	1.08278i	0.0746008	−	0.0430708i
$633$	−1.79258	+	3.10485i	−0.0712488	+	0.123407i
$634$	11.0654	−	19.1659i	0.439464	−	0.761173i
$635$	60.9415	−	35.1846i	2.41839	−	1.39626i
$636$	−2.71777			−0.107766
$637$		0			0
$638$	55.7680			2.20788
$639$	22.6369	−	13.0694i	0.895500	−	0.517017i
$640$	15.3403	−	26.5702i	0.606378	−	1.05028i
$641$	3.70233	−	6.41262i	0.146233	−	0.253283i	−0.783599	−	0.621267i	$-0.786618\pi$
$641$	3.70233	−	6.41262i	0.146233	−	0.253283i	0.929832	+	0.367983i	$0.119952\pi$
$642$	3.19966	−	1.84732i	0.126281	−	0.0729081i
$643$		−	39.9607i		−	1.57590i	−0.615742	−	0.787948i	$-0.711144\pi$
$643$		−	39.9607i		−	1.57590i	0.615742	−	0.787948i	$-0.288856\pi$
$644$		0			0
$645$			0.923218i			0.0363517i
$646$	−16.0354	−	27.7742i	−0.630906	−	1.09276i
$647$	−13.6234	+	23.5964i	−0.535591	+	0.927670i	0.463544	+	0.886074i	$0.346578\pi$
$647$	−13.6234	+	23.5964i	−0.535591	+	0.927670i	−0.999134	+	0.0415963i	$0.986756\pi$
$648$	−8.30326	−	4.79389i	−0.326183	−	0.188322i
$649$	9.78770	+	16.9528i	0.384201	+	0.665456i
$650$	−43.9046	+	42.8292i	−1.72208	+	1.67990i
$651$		0			0
$652$			46.9514i			1.83876i
$653$	−9.57255	−	16.5801i	−0.374603	−	0.648831i	0.615665	−	0.788008i	$-0.288888\pi$
$653$	−9.57255	−	16.5801i	−0.374603	−	0.648831i	−0.990267	+	0.139177i	$0.955554\pi$
$654$	1.26373	−	2.18885i	0.0494159	−	0.0855909i
$655$	−59.5672	−	34.3911i	−2.32748	−	1.34377i
$656$	−4.94921	+	2.85743i	−0.193234	+	0.111564i
$657$		−	9.16755i		−	0.357660i
$658$		0			0
$659$	41.5725			1.61943			0.809717	−	0.586820i	$-0.199620\pi$
$659$	41.5725			1.61943			0.809717	+	0.586820i	$0.199620\pi$
$660$	−3.24141	−	5.61428i	−0.126172	−	0.218536i
$661$	−29.6221	−	17.1023i	−1.15217	−	0.665203i	−0.202752	−	0.979230i	$-0.564988\pi$
$661$	−29.6221	−	17.1023i	−1.15217	−	0.665203i	−0.949414	+	0.314027i	$0.898322\pi$
$662$	−4.74000	+	8.20992i	−0.184225	+	0.319088i
$663$	0.836251	−	2.97300i	0.0324773	−	0.115462i
$664$	8.42915			0.327115
$665$		0			0
$666$	31.3218			1.21369
$667$	7.15969	+	12.4010i	0.277224	+	0.480167i
$668$	2.12081	+	1.22445i	0.0820567	+	0.0473755i
$669$	−4.29268	−	2.47838i	−0.165965	−	0.0958197i
$670$	−25.9595	+	14.9877i	−1.00290	+	0.579025i
$671$		−	8.12611i		−	0.313705i
$672$		0			0
$673$	−21.4308			−0.826098			−0.413049	−	0.910709i	$-0.635536\pi$
$673$	−21.4308			−0.826098			−0.413049	+	0.910709i	$0.635536\pi$
$674$	−19.8704	+	11.4722i	−0.765381	+	0.441893i
$675$	−4.27145	+	7.39837i	−0.164408	+	0.284763i
$676$	27.9308	+	17.0628i	1.07426	+	0.656261i
$677$	4.89083	+	8.47117i	0.187970	+	0.325573i	0.944573	−	0.328301i	$-0.106476\pi$
$677$	4.89083	+	8.47117i	0.187970	+	0.325573i	−0.756603	+	0.653874i	$0.773143\pi$
$678$		−	6.66919i		−	0.256129i
$679$		0			0
$680$	19.0034			0.728748
$681$	1.76130	−	1.01688i	0.0674930	−	0.0389671i
$682$	−10.9256	−	6.30793i	−0.418365	−	0.241543i
$683$	13.2297	+	7.63818i	0.506221	+	0.292267i	0.731279	−	0.682079i	$-0.238924\pi$
$683$	13.2297	+	7.63818i	0.506221	+	0.292267i	−0.225058	+	0.974345i	$0.572257\pi$
$684$	20.3889	−	11.7716i	0.779590	−	0.450097i
$685$	23.1828			0.885769
$686$		0			0
$687$			1.55802i			0.0594423i
$688$	−1.92999	−	3.34285i	−0.0735803	−	0.127445i
$689$	−21.0877	+	5.37115i	−0.803378	+	0.204625i
$690$	1.49343	−	2.58670i	0.0568540	−	0.0984741i
$691$	−36.7690	+	21.2286i	−1.39876	+	0.807573i	−0.994263	−	0.106967i	$-0.965886\pi$
$691$	−36.7690	+	21.2286i	−1.39876	+	0.807573i	−0.404496	+	0.914540i	$0.632553\pi$
$692$	−6.18627			−0.235167
$693$		0			0
$694$			8.65141i			0.328403i
$695$	−7.58412	+	4.37869i	−0.287682	+	0.166093i
$696$	1.12013	+	0.646710i	0.0424586	+	0.0245135i
$697$	−8.78991	−	5.07486i	−0.332942	−	0.192224i
$698$	−25.3706	−	43.9432i	−0.960291	−	1.66327i
$699$	0.601767			0.0227609
$700$		0			0
$701$	2.79985			0.105749			0.0528744	−	0.998601i	$-0.483162\pi$
$701$	2.79985			0.105749			0.0528744	+	0.998601i	$0.483162\pi$
$702$	7.87454	+	2.21496i	0.297205	+	0.0835983i
$703$	−7.82141	+	13.5471i	−0.294990	+	0.510937i
$704$	39.6465	+	22.8899i	1.49423	+	0.862696i
$705$	−0.328581	−	0.569118i	−0.0123751	−	0.0214342i
$706$	−55.4412			−2.08656
$707$		0			0
$708$			2.20793i			0.0829793i
$709$	12.6149	−	7.28319i	0.473761	−	0.273526i	−0.244052	−	0.969762i	$-0.578477\pi$
$709$	12.6149	−	7.28319i	0.473761	−	0.273526i	0.717813	+	0.696236i	$0.245143\pi$
$710$	−58.4573	−	33.7503i	−2.19386	−	1.26663i
$711$	2.92054	−	5.05852i	0.109529	−	0.189709i
$712$	−7.04201	−	12.1971i	−0.263910	−	0.457106i
$713$		−	3.23934i		−	0.121314i
$714$		0			0
$715$	−36.2463	−	37.1563i	−1.35554	−	1.38957i
$716$	−18.2189	−	31.5560i	−0.680871	−	1.17930i
$717$	−3.07923	−	1.77779i	−0.114996	−	0.0663928i
$718$	−24.3309	+	42.1423i	−0.908021	+	1.57274i
$719$	−17.2529	−	29.8828i	−0.643423	−	1.11444i	−0.984663	−	0.174465i	$-0.944180\pi$
$719$	−17.2529	−	29.8828i	−0.643423	−	1.11444i	0.341240	−	0.939976i	$-0.389153\pi$
$720$		−	28.8606i		−	1.07557i
$721$		0			0
$722$		−	19.2861i		−	0.717756i
$723$	2.92311	−	1.68766i	0.108712	−	0.0627648i
$724$	11.5548	−	20.0136i	0.429432	−	0.743798i
$725$	−26.2992	+	45.5515i	−0.976727	+	1.69174i
$726$	1.62601	−	0.938775i	0.0603467	−	0.0348412i
$727$	35.7571			1.32616			0.663078	−	0.748550i	$-0.269250\pi$
$727$	35.7571			1.32616			0.663078	+	0.748550i	$0.269250\pi$
$728$		0			0
$729$	−25.2879			−0.936590
$730$	−20.5025	+	11.8371i	−0.758830	+	0.438111i
$731$	3.42771	−	5.93698i	0.126779	−	0.219587i
$732$	0.458277	−	0.793759i	0.0169384	−	0.0293382i
$733$	35.5504	−	20.5250i	1.31308	−	0.758108i	0.330477	−	0.943814i	$-0.392790\pi$
$733$	35.5504	−	20.5250i	1.31308	−	0.758108i	0.982605	+	0.185706i	$0.0594571\pi$
$734$		−	38.5990i		−	1.42472i
$735$		0			0
$736$			17.2833i			0.637071i
$737$	−7.80686	−	13.5219i	−0.287570	−	0.498085i
$738$	6.68481	−	11.5784i	0.246071	−	0.426208i
$739$	−0.629089	−	0.363205i	−0.0231414	−	0.0133607i	0.488385	−	0.872628i	$-0.337586\pi$
$739$	−0.629089	−	0.363205i	−0.0231414	−	0.0133607i	−0.511526	+	0.859268i	$0.670920\pi$
$740$	−22.5386	−	39.0379i	−0.828534	−	1.43506i
$741$	−1.45434	+	1.41872i	−0.0534266	+	0.0521181i
$742$		0			0
$743$			16.4547i			0.603664i	0.953361	+	0.301832i	$0.0975981\pi$
$743$			16.4547i			0.603664i	−0.953361	+	0.301832i	$0.902402\pi$
$744$	−0.146299	−	0.253397i	−0.00536358	−	0.00929000i
$745$	0.207983	−	0.360236i	0.00761989	−	0.0131980i
$746$	−29.2108	−	16.8648i	−1.06948	−	0.617466i
$747$	19.6896	−	11.3678i	0.720404	−	0.415925i
$748$			48.1387i			1.76012i
$749$		0			0
$750$	4.11723			0.150340
$751$	12.5854	+	21.7985i	0.459247	+	0.795439i	0.998921	−	0.0464350i	$-0.0147860\pi$
$751$	12.5854	+	21.7985i	0.459247	+	0.795439i	−0.539675	+	0.841874i	$0.681453\pi$
$752$	2.37949	+	1.37380i	0.0867712	+	0.0500974i
$753$	0.876030	−	1.51733i	0.0319243	−	0.0552945i
$754$	48.4833	+	13.6375i	1.76566	+	0.496647i
$755$	−42.5623			−1.54900
$756$		0			0
$757$	44.0743			1.60191			0.800953	−	0.598727i	$-0.204327\pi$
$757$	44.0743			1.60191			0.800953	+	0.598727i	$0.204327\pi$
$758$	−29.5054	−	51.1049i	−1.07168	−	1.85621i
$759$	1.34737	+	0.777906i	0.0489066	+	0.0282362i
$760$	−10.8267	−	6.25080i	−0.392726	−	0.226740i
$761$	−33.5171	+	19.3511i	−1.21499	+	0.701477i	−0.963843	−	0.266471i	$-0.914142\pi$
$761$	−33.5171	+	19.3511i	−1.21499	+	0.701477i	−0.251151	+	0.967948i	$0.580809\pi$
$762$			7.41844i			0.268742i
$763$		0			0
$764$	−44.2715			−1.60169
$765$	44.3899	−	25.6285i	1.60492	−	0.926601i
$766$	−27.8937	+	48.3133i	−1.00784	+	1.74563i
$767$	4.36357	+	17.1318i	0.157559	+	0.618594i
$768$	−0.433701	−	0.751191i	−0.0156498	−	0.0271063i
$769$			36.1506i			1.30362i	0.758381	+	0.651811i	$0.225991\pi$
$769$			36.1506i			1.30362i	−0.758381	+	0.651811i	$0.774009\pi$
$770$		0			0
$771$	3.74511			0.134877
$772$	43.0756	−	24.8697i	1.55032	−	0.895080i
$773$	26.0441	+	15.0366i	0.936740	+	0.540827i	0.888937	−	0.458030i	$-0.151445\pi$
$773$	26.0441	+	15.0366i	0.936740	+	0.540827i	0.0478033	+	0.998857i	$0.484778\pi$
$774$	7.82043	+	4.51513i	0.281100	+	0.162293i
$775$	10.3047	−	5.94941i	0.370155	−	0.213709i
$776$	1.49543			0.0536827
$777$		0			0
$778$		−	53.6801i		−	1.92453i
$779$	3.33855	+	5.78253i	0.119616	+	0.207181i
$780$	−1.44509	−	5.67357i	−0.0517424	−	0.203146i
$781$	17.5800	−	30.4495i	0.629063	−	1.08957i
$782$	−19.2078	+	11.0896i	−0.686868	+	0.396564i
$783$	7.01496			0.250694
$784$		0			0
$785$		−	47.4079i		−	1.69206i
$786$	6.27967	−	3.62557i	0.223988	−	0.129320i
$787$	31.9106	+	18.4236i	1.13749	+	0.656730i	0.945808	−	0.324727i	$-0.105272\pi$
$787$	31.9106	+	18.4236i	1.13749	+	0.656730i	0.191682	+	0.981457i	$0.438606\pi$
$788$	−16.7023	−	9.64307i	−0.594994	−	0.343520i
$789$	0.660580	+	1.14416i	0.0235173	+	0.0407331i
$790$	−15.0840			−0.536663
$791$		0			0
$792$	−13.0388			−0.463315
$793$	1.98715	−	7.06464i	0.0705658	−	0.250873i
$794$	15.9163	−	27.5678i	0.564847	−	0.978343i
$795$	3.37106	+	1.94628i	0.119559	+	0.0690275i
$796$	−8.23721	−	14.2673i	−0.291960	−	0.505690i
$797$	27.5910			0.977323			0.488661	−	0.872474i	$-0.337485\pi$
$797$	27.5910			0.977323			0.488661	+	0.872474i	$0.337485\pi$
$798$		0			0
$799$			4.87980i			0.172635i
$800$	−54.9800	+	31.7427i	−1.94384	+	1.12227i
$801$	−32.8987	−	18.9941i	−1.16242	−	0.671123i
$802$	−5.67939	+	9.83700i	−0.200546	+	0.347356i
$803$	−6.16577	−	10.6794i	−0.217585	−	0.376869i
$804$		−	1.76109i		−	0.0621089i
$805$		0			0
$806$	−7.95596	−	8.15570i	−0.280237	−	0.287272i
$807$	2.03797	+	3.52987i	0.0717399	+	0.124257i
$808$	−4.08630	−	2.35923i	−0.143756	−	0.0829973i
$809$	−17.8551	+	30.9260i	−0.627752	+	1.08730i	0.360250	+	0.932856i	$0.382692\pi$
$809$	−17.8551	+	30.9260i	−0.627752	+	1.08730i	−0.988002	+	0.154443i	$0.950642\pi$
$810$	33.3912	+	57.8352i	1.17325	+	2.03212i
$811$		−	2.22418i		−	0.0781015i	−0.999237	−	0.0390508i	$-0.987567\pi$
$811$		−	2.22418i		−	0.0781015i	0.999237	−	0.0390508i	$-0.0124334\pi$
$812$		0			0
$813$			0.745166i			0.0261341i
$814$	36.4873	−	21.0659i	1.27888	−	0.738360i
$815$	33.6234	−	58.2375i	1.17778	−	2.03997i
$816$	1.15489	−	2.00032i	0.0404291	−	0.0700252i
$817$	−3.90570	+	2.25496i	−0.136643	+	0.0788910i
$818$	7.15264			0.250086
$819$		0			0
$820$	−19.2411			−0.671927
$821$	−46.2192	+	26.6847i	−1.61306	+	0.931302i	−0.624407	+	0.781099i	$0.714659\pi$
$821$	−46.2192	+	26.6847i	−1.61306	+	0.931302i	−0.988655	+	0.150203i	$0.952007\pi$
$822$	−1.22198	+	2.11654i	−0.0426216	+	0.0738228i
$823$	25.6043	−	44.3479i	0.892509	−	1.54587i	0.0556519	−	0.998450i	$-0.482276\pi$
$823$	25.6043	−	44.3479i	0.892509	−	1.54587i	0.836857	−	0.547421i	$-0.184390\pi$
$824$	13.7559	−	7.94195i	0.479208	−	0.276671i
$825$			5.71485i			0.198966i
$826$		0			0
$827$		−	8.97196i		−	0.311986i	−0.987758	−	0.155993i	$-0.950142\pi$
$827$		−	8.97196i		−	0.311986i	0.987758	−	0.155993i	$-0.0498577\pi$
$828$	−8.14084	−	14.1003i	−0.282914	−	0.490021i
$829$	−20.2858	+	35.1360i	−0.704554	+	1.22032i	0.262298	+	0.964987i	$0.415520\pi$
$829$	−20.2858	+	35.1360i	−0.704554	+	1.22032i	−0.966852	+	0.255337i	$0.917814\pi$
$830$	−50.8462	−	29.3561i	−1.76490	−	1.01896i
$831$	0.0694940	+	0.120367i	0.00241072	+	0.00417549i
$832$	28.8702	+	29.5951i	1.00089	+	1.02602i
$833$		0			0
$834$		−	0.923218i		−	0.0319684i
$835$	−1.75374	−	3.03757i	−0.0606907	−	0.105119i
$836$	15.8343	−	27.4257i	0.547639	−	0.948539i
$837$	−1.37432	−	0.793464i	−0.0475034	−	0.0274261i
$838$	−53.1307	+	30.6750i	−1.83537	+	1.05965i
$839$		−	32.3005i		−	1.11514i	−0.830131	−	0.557568i	$-0.811734\pi$
$839$		−	32.3005i		−	1.11514i	0.830131	−	0.557568i	$-0.188266\pi$
$840$		0			0
$841$	14.1909			0.489342
$842$	17.6549	+	30.5791i	0.608427	+	1.05383i
$843$	−1.84304	−	1.06408i	−0.0634776	−	0.0366488i
$844$	25.2340	−	43.7065i	0.868588	−	1.50444i
$845$	−22.4255	−	41.1665i	−0.771460	−	1.41617i
$846$	−6.42788			−0.220995
$847$		0			0
$848$	−16.2749			−0.558882
$849$	1.42225	+	2.46341i	0.0488116	+	0.0845442i
$850$	−70.5545	−	40.7347i	−2.42000	−	1.39719i
$851$	9.36873	+	5.40904i	0.321156	+	0.185419i
$852$	3.43444	−	1.98287i	0.117662	−	0.0679321i
$853$			35.5887i			1.21853i	0.792965	+	0.609267i	$0.208536\pi$
$853$			35.5887i			1.21853i	−0.792965	+	0.609267i	$0.791464\pi$
$854$		0			0
$855$	−33.7200			−1.15320
$856$	−9.26167	+	5.34723i	−0.316557	+	0.182764i
$857$	−23.0114	+	39.8570i	−0.786055	+	1.36149i	0.142311	+	0.989822i	$0.454547\pi$
$857$	−23.0114	+	39.8570i	−0.786055	+	1.36149i	−0.928367	+	0.371666i	$0.878787\pi$
$858$	5.30287	−	1.35067i	0.181037	−	0.0461110i
$859$	12.6229	+	21.8635i	0.430689	+	0.745975i	0.996933	−	0.0782630i	$-0.0249374\pi$
$859$	12.6229	+	21.8635i	0.430689	+	0.745975i	−0.566244	+	0.824238i	$0.691604\pi$
$860$		−	12.9960i		−	0.443160i
$861$		0			0
$862$	43.6903			1.48810
$863$	11.9803	−	6.91684i	0.407815	−	0.235452i	−0.282036	−	0.959404i	$-0.591010\pi$
$863$	11.9803	−	6.91684i	0.407815	−	0.235452i	0.689850	+	0.723952i	$0.257676\pi$
$864$	7.33260	+	4.23348i	0.249460	+	0.144026i
$865$	7.67331	+	4.43019i	0.260900	+	0.150631i
$866$	−35.7271	+	20.6271i	−1.21406	+	0.700936i
$867$	1.06168			0.0360567
$868$		0			0
$869$		−	7.85701i		−	0.266531i
$870$	−4.50457	−	7.80215i	−0.152719	−	0.264518i
$871$	−3.48047	−	13.6647i	−0.117931	−	0.463010i
$872$	−3.65798	+	6.33581i	−0.123875	+	0.214557i
$873$	3.49315	−	2.01677i	0.118225	−	0.0682573i
$874$	14.5908			0.493542
$875$		0			0
$876$		−	1.39089i		−	0.0469938i
$877$	−3.16459	+	1.82708i	−0.106861	+	0.0616961i	−0.552478	−	0.833528i	$-0.686318\pi$
$877$	−3.16459	+	1.82708i	−0.106861	+	0.0616961i	0.445617	+	0.895224i	$0.352984\pi$
$878$	24.7120	+	14.2675i	0.833989	+	0.481504i
$879$	1.04351	+	0.602469i	0.0351966	+	0.0203208i
$880$	−19.4106	−	33.6201i	−0.654331	−	1.13333i
$881$	36.6320			1.23416			0.617082	−	0.786899i	$-0.288315\pi$
$881$	36.6320			1.23416			0.617082	+	0.786899i	$0.288315\pi$
$882$		0			0
$883$	7.11145			0.239319			0.119660	−	0.992815i	$-0.461820\pi$
$883$	7.11145			0.239319			0.119660	+	0.992815i	$0.461820\pi$
$884$	−11.7718	+	41.8506i	−0.395928	+	1.40759i
$885$	1.58117	−	2.73867i	0.0531506	−	0.0920595i
$886$	−61.7623	−	35.6585i	−2.07494	−	1.19797i
$887$	−3.36773	−	5.83308i	−0.113077	−	0.195856i	0.803932	−	0.594721i	$-0.202737\pi$
$887$	−3.36773	−	5.83308i	−0.113077	−	0.195856i	−0.917010	+	0.398865i	$0.869404\pi$
$888$	0.977160			0.0327913
$889$		0			0
$890$			98.1004i			3.28833i
$891$	−30.1255	+	17.3930i	−1.00924	+	0.582686i
$892$	60.4274	+	34.8878i	2.02326	+	1.16813i
$893$	1.60512	−	2.78014i	0.0537131	−	0.0930339i
$894$	0.0219259	+	0.0379767i	0.000733311	+	0.00127013i
$895$			52.1885i			1.74447i
$896$		0			0
$897$	0.981145	+	1.00578i	0.0327595	+	0.0335820i
$898$	36.5886	+	63.3733i	1.22098	+	2.11479i
$899$	−8.46164	−	4.88533i	−0.282212	−	0.162935i
$900$	29.9031	−	51.7938i	0.996772	−	1.72646i
$901$	−14.4523	−	25.0321i	−0.481475	−	0.833939i
$902$		−	17.9839i		−	0.598798i
$903$		0			0
$904$			19.3045i			0.642058i
$905$	−28.6647	+	16.5496i	−0.952848	+	0.550127i
$906$	2.24350	−	3.88585i	0.0745351	−	0.129099i
$907$	−2.46630	+	4.27175i	−0.0818921	+	0.141841i	−0.904063	−	0.427400i	$-0.859430\pi$
$907$	−2.46630	+	4.27175i	−0.0818921	+	0.141841i	0.822171	+	0.569241i	$0.192763\pi$
$908$	−24.7935	+	14.3145i	−0.822802	+	0.475045i
$909$	−12.7269			−0.422123
$910$		0			0
$911$	−26.6258			−0.882152			−0.441076	−	0.897470i	$-0.645403\pi$
$911$	−26.6258			−0.882152			−0.441076	+	0.897470i	$0.645403\pi$
$912$	−1.31593	+	0.759754i	−0.0435749	+	0.0251580i
$913$	15.2911	−	26.4850i	0.506063	−	0.876526i
$914$	14.3251	−	24.8118i	0.473833	−	0.820702i
$915$	−1.13687	+	0.656374i	−0.0375839	+	0.0216991i
$916$		−	21.9321i		−	0.724656i
$917$		0			0
$918$			10.8654i			0.358613i
$919$	16.1918	+	28.0450i	0.534118	+	0.925119i	0.999205	+	0.0398544i	$0.0126894\pi$
$919$	16.1918	+	28.0450i	0.534118	+	0.925119i	−0.465088	+	0.885265i	$0.653977\pi$
$920$	−4.32286	+	7.48741i	−0.142520	+	0.246853i
$921$	−2.27970	−	1.31618i	−0.0751185	−	0.0433697i
$922$	−1.44428	−	2.50156i	−0.0475647	−	0.0823844i
$923$	22.7297	−	22.1730i	0.748158	−	0.729835i
$924$		0			0
$925$			39.7373i			1.30655i
$926$	2.65512	+	4.59880i	0.0872526	+	0.151126i
$927$	21.4214	−	37.1030i	0.703572	−	1.21862i
$928$	45.1466	+	26.0654i	1.48201	+	0.855639i
$929$	−24.2722	+	14.0135i	−0.796344	+	0.459769i	−0.842191	−	0.539179i	$-0.818735\pi$
$929$	−24.2722	+	14.0135i	−0.796344	+	0.459769i	0.0458472	+	0.998948i	$0.485401\pi$
$930$			2.03805i			0.0668304i
$931$		0			0
$932$	−8.47099			−0.277476
$933$	−2.56278	−	4.43887i	−0.0839018	−	0.145322i
$934$	−48.2606	−	27.8633i	−1.57914	−	0.911714i
$935$	34.4737	−	59.7102i	1.12741	−	1.95273i
$936$	−11.3357	−	3.18851i	−0.370517	−	0.104220i
$937$	−14.1324			−0.461686			−0.230843	−	0.972991i	$-0.574148\pi$
$937$	−14.1324			−0.461686			−0.230843	+	0.972991i	$0.574148\pi$
$938$		0			0
$939$	5.87091			0.191590
$940$	4.62538	+	8.01140i	0.150863	+	0.261303i
$941$	7.77080	+	4.48647i	0.253321	+	0.146255i	0.621284	−	0.783586i	$-0.286611\pi$
$941$	7.77080	+	4.48647i	0.253321	+	0.146255i	−0.367963	+	0.929840i	$0.619945\pi$
$942$	4.32824	+	2.49891i	0.141022	+	0.0814189i
$943$	3.99902	−	2.30883i	0.130226	−	0.0751860i
$944$			13.2218i			0.430334i
$945$		0			0
$946$	12.1469			0.394929
$947$	40.0933	−	23.1479i	1.30286	−	0.752205i	0.321964	−	0.946752i	$-0.395657\pi$
$947$	40.0933	−	23.1479i	1.30286	−	0.752205i	0.980893	+	0.194546i	$0.0623235\pi$
$948$	0.443101	−	0.767473i	0.0143912	−	0.0249264i
$949$	−2.74883	−	10.7922i	−0.0892308	−	0.350330i
$950$	26.7977	+	46.4150i	0.869433	+	1.50590i
$951$		−	1.86225i		−	0.0603876i
$952$		0			0
$953$	−19.1097			−0.619023			−0.309512	−	0.950896i	$-0.600166\pi$
$953$	−19.1097			−0.619023			−0.309512	+	0.950896i	$0.600166\pi$
$954$	32.9733	−	19.0371i	1.06755	−	0.616350i
$955$	54.9134	+	31.7042i	1.77695	+	1.02593i
$956$	43.3458	+	25.0257i	1.40190	+	0.809390i
$957$	4.06402	−	2.34636i	0.131371	−	0.0758472i
$958$	50.6846			1.63755
$959$		0			0
$960$		−	7.39560i		−	0.238692i
$961$	−14.3948	−	24.9326i	−0.464350	−	0.804277i
$962$	36.8726	−	9.39164i	1.18882	−	0.302799i
$963$	−14.4228	+	24.9811i	−0.464769	+	0.805003i
$964$	−41.1483	+	23.7570i	−1.32530	+	0.765160i
$965$	−71.2400			−2.29330
$966$		0			0
$967$			22.5432i			0.724942i	0.931995	+	0.362471i	$0.118067\pi$
$967$			22.5432i			0.724942i	−0.931995	+	0.362471i	$0.881933\pi$
$968$	−4.70660	+	2.71736i	−0.151276	+	0.0873392i
$969$	−2.33713	−	1.34934i	−0.0750793	−	0.0433471i
$970$	−9.02068	−	5.20809i	−0.289637	−	0.167222i
$971$	13.6429	+	23.6301i	0.437820	+	0.758327i	0.997521	−	0.0703679i	$-0.0224173\pi$
$971$	13.6429	+	23.6301i	0.437820	+	0.758327i	−0.559701	+	0.828695i	$0.689084\pi$
$972$	−11.9858			−0.384444
$973$		0			0
$974$	22.5188			0.721550
$975$	−1.39751	+	4.96835i	−0.0447560	+	0.159115i
$976$	2.74431	−	4.75329i	0.0878433	−	0.152149i
$977$	48.6568	+	28.0920i	1.55667	+	0.898744i	0.997572	+	0.0696427i	$0.0221859\pi$
$977$	48.6568	+	28.0920i	1.55667	+	0.898744i	0.559098	+	0.829101i	$0.311147\pi$
$978$	3.54464	+	6.13949i	0.113345	+	0.196319i
$979$	−51.0990			−1.63313
$980$		0			0
$981$			19.7330i			0.630026i
$982$	−36.3919	+	21.0108i	−1.16131	+	0.670483i
$983$	−22.9402	−	13.2445i	−0.731678	−	0.422435i	0.0873577	−	0.996177i	$-0.472158\pi$
$983$	−22.9402	−	13.2445i	−0.731678	−	0.422435i	−0.819036	+	0.573742i	$0.805491\pi$
$984$	0.208549	−	0.361218i	0.00664830	−	0.0115152i
$985$	13.8114	+	23.9221i	0.440069	+	0.762222i
$986$			66.8982i			2.13047i
$987$		0			0
$988$	20.4726	−	19.9712i	0.651320	−	0.635368i
$989$	1.55946	+	2.70106i	0.0495879	+	0.0858887i
$990$	78.6527	+	45.4102i	2.49975	+	1.44323i
$991$	−2.55629	+	4.42763i	−0.0812033	+	0.140648i	−0.903767	−	0.428025i	$-0.859210\pi$
$991$	−2.55629	+	4.42763i	−0.0812033	+	0.140648i	0.822564	+	0.568673i	$0.192543\pi$
$992$	−5.89652	−	10.2131i	−0.187215	−	0.324266i
$993$			0.797717i			0.0253148i
$994$		0			0
$995$			23.5957i			0.748035i
$996$	2.98728	−	1.72471i	0.0946555	−	0.0546494i
$997$	1.01771	−	1.76272i	0.0322311	−	0.0558260i	−0.849460	−	0.527653i	$-0.823072\pi$
$997$	1.01771	−	1.76272i	0.0322311	−	0.0558260i	0.881691	+	0.471827i	$0.156405\pi$
$998$	14.0182	−	24.2803i	0.443740	−	0.768580i
$999$	4.58967	−	2.64985i	0.145211	−	0.0838375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.f.116.2		16
7.2	even	3	inner	637.2.r.f.324.7		16
7.3	odd	6		637.2.c.f.246.2		8
7.4	even	3		637.2.c.e.246.2		8
7.5	odd	6		91.2.r.a.51.7	yes	16
7.6	odd	2		91.2.r.a.25.2	✓	16
13.12	even	2	inner	637.2.r.f.116.7		16
21.5	even	6		819.2.dl.e.415.2		16
21.20	even	2		819.2.dl.e.298.7		16
91.5	even	12		1183.2.e.i.170.7		16
91.12	odd	6		91.2.r.a.51.2	yes	16
91.18	odd	12		8281.2.a.cj.1.2		8
91.25	even	6		637.2.c.e.246.7		8
91.31	even	12		8281.2.a.ck.1.2		8
91.34	even	4		1183.2.e.i.508.2		16
91.38	odd	6		637.2.c.f.246.7		8
91.47	even	12		1183.2.e.i.170.2		16
91.51	even	6	inner	637.2.r.f.324.2		16
91.60	odd	12		8281.2.a.cj.1.7		8
91.73	even	12		8281.2.a.ck.1.7		8
91.83	even	4		1183.2.e.i.508.7		16
91.90	odd	2		91.2.r.a.25.7	yes	16
273.194	even	6		819.2.dl.e.415.7		16
273.272	even	2		819.2.dl.e.298.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.r.a.25.2	✓	16	7.6	odd	2
91.2.r.a.25.7	yes	16	91.90	odd	2
91.2.r.a.51.2	yes	16	91.12	odd	6
91.2.r.a.51.7	yes	16	7.5	odd	6
637.2.c.e.246.2		8	7.4	even	3
637.2.c.e.246.7		8	91.25	even	6
637.2.c.f.246.2		8	7.3	odd	6
637.2.c.f.246.7		8	91.38	odd	6
637.2.r.f.116.2		16	1.1	even	1	trivial
637.2.r.f.116.7		16	13.12	even	2	inner
637.2.r.f.324.2		16	91.51	even	6	inner
637.2.r.f.324.7		16	7.2	even	3	inner
819.2.dl.e.298.2		16	273.272	even	2
819.2.dl.e.298.7		16	21.20	even	2
819.2.dl.e.415.2		16	21.5	even	6
819.2.dl.e.415.7		16	273.194	even	6
1183.2.e.i.170.2		16	91.47	even	12
1183.2.e.i.170.7		16	91.5	even	12
1183.2.e.i.508.2		16	91.34	even	4
1183.2.e.i.508.7		16	91.83	even	4
8281.2.a.cj.1.2		8	91.18	odd	12
8281.2.a.cj.1.7		8	91.60	odd	12
8281.2.a.ck.1.2		8	91.31	even	12
8281.2.a.ck.1.7		8	91.73	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.84073 + 1.06275i) q^{2} +(-0.0894272 + 0.154892i) q^{3} +(1.25885 - 2.18040i) q^{4} +(-3.12291 + 1.80301i) q^{5} -0.380153i q^{6} +1.10038i q^{8} +(1.48401 + 2.57037i) q^{9} +O(q^{10})\)	\(q+(-1.84073 + 1.06275i) q^{2} +(-0.0894272 + 0.154892i) q^{3} +(1.25885 - 2.18040i) q^{4} +(-3.12291 + 1.80301i) q^{5} -0.380153i q^{6} +1.10038i q^{8} +(1.48401 + 2.57037i) q^{9} +(3.83229 - 6.63772i) q^{10} +(3.45748 + 1.99618i) q^{11} +(0.225152 + 0.389974i) q^{12} +(2.51771 + 2.58092i) q^{13} -0.644954i q^{15} +(1.34828 + 2.33529i) q^{16} +(-2.39458 + 4.14753i) q^{17} +(-5.46330 - 3.15424i) q^{18} +(2.72850 - 1.57530i) q^{19} +9.07892i q^{20} -8.48572 q^{22} +(-1.08943 - 1.88694i) q^{23} +(-0.170441 - 0.0984042i) q^{24} +(4.00171 - 6.93117i) q^{25} +(-7.37728 - 2.07509i) q^{26} -1.06740 q^{27} -6.57198 q^{29} +(0.685421 + 1.18718i) q^{30} +(1.28753 + 0.743358i) q^{31} +(-6.86956 - 3.96614i) q^{32} +(-0.618386 + 0.357025i) q^{33} -10.1793i q^{34} +7.47259 q^{36} +(-4.29984 + 2.48252i) q^{37} +(-3.34828 + 5.79939i) q^{38} +(-0.624916 + 0.159170i) q^{39} +(-1.98401 - 3.43640i) q^{40} +2.11931i q^{41} -1.43145 q^{43} +(8.70494 - 5.02580i) q^{44} +(-9.26883 - 5.35136i) q^{45} +(4.01068 + 2.31557i) q^{46} +(0.882417 - 0.509464i) q^{47} -0.482292 q^{48} +17.0112i q^{50} +(-0.428281 - 0.741804i) q^{51} +(8.79686 - 2.24061i) q^{52} +(-3.01771 + 5.22682i) q^{53} +(1.96480 - 1.13438i) q^{54} -14.3966 q^{55} +0.563498i q^{57} +(12.0972 - 6.98434i) q^{58} +(4.24631 + 2.45161i) q^{59} +(-1.40626 - 0.811902i) q^{60} +(-1.01771 - 1.76272i) q^{61} -3.16000 q^{62} +11.4669 q^{64} +(-12.5160 - 3.52052i) q^{65} +(0.758854 - 1.31437i) q^{66} +(-3.38694 - 1.95545i) q^{67} +(6.02885 + 10.4423i) q^{68} +0.389698 q^{69} -8.80684i q^{71} +(-2.82840 + 1.63297i) q^{72} +(-2.67497 - 1.54439i) q^{73} +(5.27656 - 9.13927i) q^{74} +(0.715724 + 1.23967i) q^{75} -7.93228i q^{76} +(0.981145 - 0.957115i) q^{78} +(-0.984006 - 1.70435i) q^{79} +(-8.42112 - 4.86194i) q^{80} +(-4.35656 + 7.54579i) q^{81} +(-2.25229 - 3.90108i) q^{82} -7.66020i q^{83} -17.2698i q^{85} +(2.63491 - 1.52126i) q^{86} +(0.587714 - 1.01795i) q^{87} +(-2.19656 + 3.80456i) q^{88} +(-11.0844 + 6.39960i) q^{89} +22.7485 q^{90} -5.48572 q^{92} +(-0.230281 + 0.132953i) q^{93} +(-1.08286 + 1.87557i) q^{94} +(-5.68057 + 9.83903i) q^{95} +(1.22865 - 0.709362i) q^{96} -1.35900i q^{97} +11.8494i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9	\( 16 q + 4 q^{3} + 6 q^{4} - 12 q^{9} + 6 q^{10} - 18 q^{12} + 12 q^{13} + 2 q^{16} - 8 q^{17} - 36 q^{22} - 12 q^{23} + 6 q^{26} - 32 q^{27} - 16 q^{29} + 38 q^{30} - 56 q^{36} - 34 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{43} - 36 q^{48} + 16 q^{51} + 42 q^{52} - 20 q^{53} - 24 q^{55} + 12 q^{61} - 44 q^{62} + 88 q^{64} - 30 q^{65} - 2 q^{66} + 2 q^{68} + 56 q^{69} + 42 q^{74} - 8 q^{75} + 20 q^{78} + 20 q^{79} - 24 q^{81} + 16 q^{82} + 68 q^{87} + 4 q^{88} + 216 q^{90} + 12 q^{92} + 26 q^{94} - 16 q^{95}+O(q^{100}) \) 16 * q + 4 * q^3 + 6 * q^4 - 12 * q^9 + 6 * q^10 - 18 * q^12 + 12 * q^13 + 2 * q^16 - 8 * q^17 - 36 * q^22 - 12 * q^23 + 6 * q^26 - 32 * q^27 - 16 * q^29 + 38 * q^30 - 56 * q^36 - 34 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^43 - 36 * q^48 + 16 * q^51 + 42 * q^52 - 20 * q^53 - 24 * q^55 + 12 * q^61 - 44 * q^62 + 88 * q^64 - 30 * q^65 - 2 * q^66 + 2 * q^68 + 56 * q^69 + 42 * q^74 - 8 * q^75 + 20 * q^78 + 20 * q^79 - 24 * q^81 + 16 * q^82 + 68 * q^87 + 4 * q^88 + 216 * q^90 + 12 * q^92 + 26 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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