LMFDB - Embedded newform 418.2.n.d.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	418.49
Dual form			418.2.n.d.273.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(-1.41989 + 0.632177i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.85966 + 2.06536i) q^{5} +(-1.52030 + 0.323150i) q^{6} +(3.87852 - 2.81791i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.390947 + 0.434190i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(-1.41989 + 0.632177i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.85966 + 2.06536i) q^{5} +(-1.52030 + 0.323150i) q^{6} +(3.87852 - 2.81791i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.390947 + 0.434190i) q^{9} +(1.38961 + 2.40687i) q^{10} +(-3.29653 - 0.364534i) q^{11} -1.55426 q^{12} +(1.70370 - 1.89216i) q^{13} +(4.37965 - 1.94994i) q^{14} +(-3.94619 - 1.75696i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.63707 + 4.03938i) q^{17} +(-0.472677 + 0.343420i) q^{18} +(-3.69367 + 2.31447i) q^{19} +(0.858826 + 2.64319i) q^{20} +(-3.72567 + 6.45304i) q^{21} +(-3.14870 - 1.04196i) q^{22} +(2.52974 + 4.38165i) q^{23} +(-1.52030 - 0.323150i) q^{24} +(-0.284742 + 2.70914i) q^{25} +(2.05988 - 1.49659i) q^{26} +(1.72150 - 5.29823i) q^{27} +(4.68936 - 0.996754i) q^{28} +(1.02427 + 0.456032i) q^{29} +(-3.49466 - 2.53902i) q^{30} +(-1.81168 - 5.57579i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.91117 - 1.56639i) q^{33} +(2.71776 + 4.70730i) q^{34} +(13.0328 + 2.77020i) q^{35} +(-0.533749 + 0.237640i) q^{36} +(-5.45882 + 3.96606i) q^{37} +(-4.09416 + 1.49594i) q^{38} +(-1.22290 + 3.76370i) q^{39} +(0.290507 + 2.76399i) q^{40} +(-3.80753 + 1.69522i) q^{41} +(-4.98591 + 5.53742i) q^{42} +(0.476736 - 0.825730i) q^{43} +(-2.86326 - 1.67384i) q^{44} -1.62379 q^{45} +(1.56347 + 4.81186i) q^{46} +(0.0555287 - 0.528320i) q^{47} +(-1.41989 - 0.632177i) q^{48} +(4.93920 - 15.2013i) q^{49} +(-0.841780 + 2.59073i) q^{50} +(-7.71785 - 3.43621i) q^{51} +(2.32602 - 1.03561i) q^{52} +(4.48402 - 4.98001i) q^{53} +(2.78545 - 4.82453i) q^{54} +(-5.37753 - 7.48644i) q^{55} +4.79412 q^{56} +(3.78146 - 5.62135i) q^{57} +(0.907068 + 0.659024i) q^{58} +(-0.462476 - 4.40017i) q^{59} +(-2.89041 - 3.21012i) q^{60} +(-9.87051 + 2.09804i) q^{61} +(-0.612822 - 5.83062i) q^{62} +(-0.292786 + 2.78567i) q^{63} +(0.309017 + 0.951057i) q^{64} +7.07630 q^{65} +(5.12952 - 0.511072i) q^{66} +(-3.27880 - 5.67905i) q^{67} +(1.67967 + 5.16949i) q^{68} +(-6.36194 - 4.62222i) q^{69} +(12.1720 + 5.41932i) q^{70} +(-10.1166 - 11.2356i) q^{71} +(-0.571493 + 0.121475i) q^{72} +(-1.10513 - 10.5146i) q^{73} +(-6.16412 + 2.74444i) q^{74} +(-1.30835 - 4.02669i) q^{75} +(-4.31572 + 0.612024i) q^{76} +(-13.8129 + 7.87548i) q^{77} +(-1.97869 + 3.42720i) q^{78} +(15.6120 + 3.31842i) q^{79} +(-0.290507 + 2.76399i) q^{80} +(0.721859 + 6.86803i) q^{81} +(-4.07678 + 0.866547i) q^{82} +(2.76900 - 8.52211i) q^{83} +(-6.02825 + 4.37978i) q^{84} +(-1.57906 + 15.0238i) q^{85} +(0.637997 - 0.708567i) q^{86} -1.74264 q^{87} +(-2.45268 - 2.23257i) q^{88} +(1.11645 + 1.93374i) q^{89} +(-1.58830 - 0.337604i) q^{90} +(1.27593 - 12.1397i) q^{91} +(0.528861 + 5.03177i) q^{92} +(6.09728 + 6.77171i) q^{93} +(0.164159 - 0.505230i) q^{94} +(-11.6492 - 3.32464i) q^{95} +(-1.25743 - 0.913574i) q^{96} +(-1.69678 - 0.360661i) q^{97} +(7.99179 - 13.8422i) q^{98} +(1.44704 - 1.28881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	−1.41989	+	0.632177i	−0.819775	+	0.364987i	−0.773385	−	0.633936i	$-0.781438\pi$
$3$	−1.41989	+	0.632177i	−0.819775	+	0.364987i	−0.0463895	+	0.998923i	$0.514772\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	1.85966	+	2.06536i	0.831665	+	0.923658i	0.998051	−	0.0624027i	$-0.0198763\pi$
$5$	1.85966	+	2.06536i	0.831665	+	0.923658i	−0.166386	+	0.986061i	$0.553210\pi$
$6$	−1.52030	+	0.323150i	−0.620660	+	0.131925i
$7$	3.87852	−	2.81791i	1.46594	−	1.06507i	0.484180	−	0.874968i	$-0.339118\pi$
$7$	3.87852	−	2.81791i	1.46594	−	1.06507i	0.981764	−	0.190103i	$-0.0608821\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.390947	+	0.434190i	−0.130316	+	0.144730i
$10$	1.38961	+	2.40687i	0.439433	+	0.761120i
$11$	−3.29653	−	0.364534i	−0.993941	−	0.109911i
$11$	−3.29653	−	0.364534i	−0.993941	−	0.109911i
$12$	−1.55426			−0.448678
$13$	1.70370	−	1.89216i	0.472523	−	0.524790i	−0.459018	−	0.888427i	$-0.651799\pi$
$13$	1.70370	−	1.89216i	0.472523	−	0.524790i	0.931541	+	0.363637i	$0.118465\pi$
$14$	4.37965	−	1.94994i	1.17051	−	0.521145i
$15$	−3.94619	−	1.75696i	−1.01890	−	0.453644i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	3.63707	+	4.03938i	0.882120	+	0.979694i	0.999911	−	0.0133447i	$-0.00424788\pi$
$17$	3.63707	+	4.03938i	0.882120	+	0.979694i	−0.117791	+	0.993038i	$0.537581\pi$
$18$	−0.472677	+	0.343420i	−0.111411	+	0.0809448i
$19$	−3.69367	+	2.31447i	−0.847387	+	0.530976i
$19$	−3.69367	+	2.31447i	−0.847387	+	0.530976i
$20$	0.858826	+	2.64319i	0.192039	+	0.591036i
$21$	−3.72567	+	6.45304i	−0.813007	+	1.40817i
$22$	−3.14870	−	1.04196i	−0.671306	−	0.222146i
$23$	2.52974	+	4.38165i	0.527488	+	0.913637i	0.999487	+	0.0320371i	$0.0101995\pi$
$23$	2.52974	+	4.38165i	0.527488	+	0.913637i	−0.471998	+	0.881599i	$0.656467\pi$
$24$	−1.52030	−	0.323150i	−0.310330	−	0.0659627i
$25$	−0.284742	+	2.70914i	−0.0569483	+	0.541827i
$26$	2.05988	−	1.49659i	0.403975	−	0.293505i
$27$	1.72150	−	5.29823i	0.331303	−	1.01965i
$28$	4.68936	−	0.996754i	0.886205	−	0.188369i
$29$	1.02427	+	0.456032i	0.190201	+	0.0846831i	0.499627	−	0.866240i	$-0.333470\pi$
$29$	1.02427	+	0.456032i	0.190201	+	0.0846831i	−0.309426	+	0.950923i	$0.600137\pi$
$30$	−3.49466	−	2.53902i	−0.638035	−	0.463560i
$31$	−1.81168	−	5.57579i	−0.325388	−	1.00144i	−0.971265	−	0.238000i	$-0.923508\pi$
$31$	−1.81168	−	5.57579i	−0.325388	−	1.00144i	0.645877	−	0.763441i	$-0.276492\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.91117	−	1.56639i	0.854924	−	0.272674i
$34$	2.71776	+	4.70730i	0.466092	+	0.807295i
$35$	13.0328	+	2.77020i	2.20294	+	0.468249i
$36$	−0.533749	+	0.237640i	−0.0889581	+	0.0396067i
$37$	−5.45882	+	3.96606i	−0.897424	+	0.652017i	−0.937803	−	0.347168i	$-0.887143\pi$
$37$	−5.45882	+	3.96606i	−0.897424	+	0.652017i	0.0403791	+	0.999184i	$0.487143\pi$
$38$	−4.09416	+	1.49594i	−0.664161	+	0.242673i
$39$	−1.22290	+	3.76370i	−0.195821	+	0.602674i
$40$	0.290507	+	2.76399i	0.0459333	+	0.437026i
$41$	−3.80753	+	1.69522i	−0.594636	+	0.264749i	−0.681911	−	0.731435i	$-0.738851\pi$
$41$	−3.80753	+	1.69522i	−0.594636	+	0.264749i	0.0872746	+	0.996184i	$0.472184\pi$
$42$	−4.98591	+	5.53742i	−0.769343	+	0.854442i
$43$	0.476736	−	0.825730i	0.0727015	−	0.125923i	−0.827383	−	0.561638i	$-0.810171\pi$
$43$	0.476736	−	0.825730i	0.0727015	−	0.125923i	0.900084	+	0.435716i	$0.143505\pi$
$44$	−2.86326	−	1.67384i	−0.431653	−	0.252341i
$45$	−1.62379			−0.242060
$46$	1.56347	+	4.81186i	0.230521	+	0.709470i
$47$	0.0555287	−	0.528320i	0.00809969	−	0.0770634i	−0.989725	−	0.142982i	$-0.954331\pi$
$47$	0.0555287	−	0.528320i	0.00809969	−	0.0770634i	0.997825	+	0.0659183i	$0.0209977\pi$
$48$	−1.41989	−	0.632177i	−0.204944	−	0.0912468i
$49$	4.93920	−	15.2013i	0.705600	−	2.17161i
$50$	−0.841780	+	2.59073i	−0.119046	+	0.366385i
$51$	−7.71785	−	3.43621i	−1.08072	−	0.481166i
$52$	2.32602	−	1.03561i	0.322561	−	0.143613i
$53$	4.48402	−	4.98001i	0.615928	−	0.684057i	−0.351794	−	0.936077i	$-0.614428\pi$
$53$	4.48402	−	4.98001i	0.615928	−	0.684057i	0.967722	+	0.252020i	$0.0810950\pi$
$54$	2.78545	−	4.82453i	0.379051	−	0.656536i
$55$	−5.37753	−	7.48644i	−0.725106	−	1.00947i
$56$	4.79412			0.640641
$57$	3.78146	−	5.62135i	0.500867	−	0.744566i
$58$	0.907068	+	0.659024i	0.119104	+	0.0865340i
$59$	−0.462476	−	4.40017i	−0.0602093	−	0.572853i	−0.982488	−	0.186327i	$-0.940342\pi$
$59$	−0.462476	−	4.40017i	−0.0602093	−	0.572853i	0.922278	−	0.386526i	$-0.126325\pi$
$60$	−2.89041	−	3.21012i	−0.373150	−	0.414425i
$61$	−9.87051	+	2.09804i	−1.26379	+	0.268627i	−0.790599	−	0.612334i	$-0.790231\pi$
$61$	−9.87051	+	2.09804i	−1.26379	+	0.268627i	−0.473190	+	0.880961i	$0.656897\pi$
$62$	−0.612822	−	5.83062i	−0.0778285	−	0.740489i
$63$	−0.292786	+	2.78567i	−0.0368875	+	0.350962i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	7.07630			0.877707
$66$	5.12952	−	0.511072i	0.631400	−	0.0629087i
$67$	−3.27880	−	5.67905i	−0.400569	−	0.693806i	0.593225	−	0.805036i	$-0.297854\pi$
$67$	−3.27880	−	5.67905i	−0.400569	−	0.693806i	−0.993795	+	0.111230i	$0.964521\pi$
$68$	1.67967	+	5.16949i	0.203690	+	0.626893i
$69$	−6.36194	−	4.62222i	−0.765887	−	0.556450i
$70$	12.1720	+	5.41932i	1.45483	+	0.647733i
$71$	−10.1166	−	11.2356i	−1.20062	−	1.33342i	−0.928577	−	0.371139i	$-0.878967\pi$
$71$	−10.1166	−	11.2356i	−1.20062	−	1.33342i	−0.272043	−	0.962285i	$-0.587699\pi$
$72$	−0.571493	+	0.121475i	−0.0673511	+	0.0143159i
$73$	−1.10513	−	10.5146i	−0.129345	−	1.23064i	−0.845990	−	0.533199i	$-0.820990\pi$
$73$	−1.10513	−	10.5146i	−0.129345	−	1.23064i	0.716645	−	0.697438i	$-0.245677\pi$
$74$	−6.16412	+	2.74444i	−0.716564	+	0.319035i
$75$	−1.30835	−	4.02669i	−0.151075	−	0.464962i
$76$	−4.31572	+	0.612024i	−0.495047	+	0.0702039i
$77$	−13.8129	+	7.87548i	−1.57413	+	0.897495i
$78$	−1.97869	+	3.42720i	−0.224043	+	0.388054i
$79$	15.6120	+	3.31842i	1.75648	+	0.373352i	0.969780	−	0.243981i	$-0.0784533\pi$
$79$	15.6120	+	3.31842i	1.75648	+	0.373352i	0.786702	+	0.617333i	$0.211787\pi$
$80$	−0.290507	+	2.76399i	−0.0324797	+	0.309024i
$81$	0.721859	+	6.86803i	0.0802065	+	0.763114i
$82$	−4.07678	+	0.866547i	−0.450205	+	0.0956941i
$83$	2.76900	−	8.52211i	0.303937	−	0.935423i	−0.676134	−	0.736779i	$-0.736346\pi$
$83$	2.76900	−	8.52211i	0.303937	−	0.935423i	0.980072	−	0.198645i	$-0.0636540\pi$
$84$	−6.02825	+	4.37978i	−0.657737	+	0.477874i
$85$	−1.57906	+	15.0238i	−0.171273	+	1.62955i
$86$	0.637997	−	0.708567i	0.0687970	−	0.0764068i
$87$	−1.74264			−0.186830
$88$	−2.45268	−	2.23257i	−0.261457	−	0.237992i
$89$	1.11645	+	1.93374i	0.118343	+	0.204976i	0.919111	−	0.393998i	$-0.128908\pi$
$89$	1.11645	+	1.93374i	0.118343	+	0.204976i	−0.800768	+	0.598974i	$0.795575\pi$
$90$	−1.58830	−	0.337604i	−0.167422	−	0.0355866i
$91$	1.27593	−	12.1397i	0.133754	−	1.27258i
$92$	0.528861	+	5.03177i	0.0551375	+	0.524599i
$93$	6.09728	+	6.77171i	0.632258	+	0.702194i
$94$	0.164159	−	0.505230i	0.0169317	−	0.0521105i
$95$	−11.6492	−	3.32464i	−1.19518	−	0.341101i
$96$	−1.25743	−	0.913574i	−0.128336	−	0.0932413i
$97$	−1.69678	−	0.360661i	−0.172281	−	0.0366195i	0.120963	−	0.992657i	$-0.461402\pi$
$97$	−1.69678	−	0.360661i	−0.172281	−	0.0366195i	−0.293245	+	0.956037i	$0.594735\pi$
$98$	7.99179	−	13.8422i	0.807293	−	1.39827i
$99$	1.44704	−	1.28881i	0.145433	−	0.129530i
$100$	−1.36203	+	2.35910i	−0.136203	+	0.235910i
$101$	−11.6518	+	12.9406i	−1.15939	+	1.28764i	−0.208533	+	0.978015i	$0.566869\pi$
$101$	−11.6518	+	12.9406i	−1.15939	+	1.28764i	−0.950860	+	0.309621i	$0.899798\pi$
$102$	−6.83477	−	4.96575i	−0.676743	−	0.491683i
$103$	4.34051	−	3.15357i	0.427684	−	0.310730i	−0.353038	−	0.935609i	$-0.614852\pi$
$103$	4.34051	−	3.15357i	0.427684	−	0.310730i	0.780722	+	0.624879i	$0.214852\pi$
$104$	2.49051	−	0.529374i	0.244214	−	0.0519094i
$105$	−20.2563	+	4.30562i	−1.97682	+	0.420185i
$106$	5.42144	−	3.93890i	0.526577	−	0.382580i
$107$	−5.31087	−	3.85857i	−0.513421	−	0.373022i	0.300699	−	0.953719i	$-0.402780\pi$
$107$	−5.31087	−	3.85857i	−0.513421	−	0.373022i	−0.814120	+	0.580697i	$0.802780\pi$
$108$	3.72765	−	4.13998i	0.358694	−	0.398370i
$109$	1.78141	−	3.08549i	0.170628	−	0.295536i	−0.768012	−	0.640436i	$-0.778754\pi$
$109$	1.78141	−	3.08549i	0.170628	−	0.295536i	0.938640	+	0.344900i	$0.112087\pi$
$110$	−3.70350	−	8.44089i	−0.353115	−	0.804808i
$111$	5.24368	−	9.08232i	0.497708	−	0.862055i
$112$	4.68936	+	0.996754i	0.443103	+	0.0941844i
$113$	6.99163	+	5.07972i	0.657718	+	0.477860i	0.865891	−	0.500232i	$-0.166752\pi$
$113$	6.99163	+	5.07972i	0.657718	+	0.477860i	−0.208174	+	0.978092i	$0.566752\pi$
$114$	4.86757	−	4.71230i	0.455890	−	0.441348i
$115$	−4.34522	+	13.3732i	−0.405194	+	1.24706i
$116$	0.750228	+	0.833212i	0.0696569	+	0.0773618i
$117$	0.155498	+	1.47946i	0.0143758	+	0.136776i
$118$	0.462476	−	4.40017i	0.0425744	−	0.405068i
$119$	25.4891	+	5.41788i	2.33658	+	0.496656i
$120$	−2.15982	−	3.74092i	−0.197164	−	0.341498i
$121$	10.7342	+	2.40339i	0.975839	+	0.218490i
$122$	−10.0910			−0.913598
$123$	4.33460	−	4.81406i	0.390838	−	0.434069i
$124$	0.612822	−	5.83062i	0.0550331	−	0.523605i
$125$	5.11731	−	3.71794i	0.457706	−	0.332543i
$126$	−0.865561	+	2.66392i	−0.0771103	+	0.237321i
$127$	−7.03740	+	1.49585i	−0.624468	+	0.132735i	−0.509269	−	0.860608i	$-0.670084\pi$
$127$	−7.03740	+	1.49585i	−0.624468	+	0.132735i	−0.115199	+	0.993342i	$0.536751\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	−0.154906	+	1.47383i	−0.0136387	+	0.129763i
$130$	6.92167	+	1.47125i	0.607070	+	0.129037i
$131$	−0.608917	+	1.05468i	−0.0532013	+	0.0921474i	−0.891400	−	0.453218i	$-0.850276\pi$
$131$	−0.608917	+	1.05468i	−0.0532013	+	0.0921474i	0.838198	+	0.545366i	$0.183609\pi$
$132$	5.12368	+	0.566582i	0.445959	+	0.0493146i
$133$	−7.80402	+	19.3852i	−0.676694	+	1.68091i
$134$	−2.02641	−	6.23665i	−0.175055	−	0.538764i
$135$	14.1442	−	6.29739i	1.21734	−	0.541993i
$136$	0.568167	+	5.40575i	0.0487199	+	0.463539i
$137$	10.4701	−	2.22549i	0.894522	−	0.190137i	0.262358	−	0.964971i	$-0.415500\pi$
$137$	10.4701	−	2.22549i	0.894522	−	0.190137i	0.632165	+	0.774834i	$0.282167\pi$
$138$	−5.26190	−	5.84393i	−0.447923	−	0.497469i
$139$	5.42392	+	2.41489i	0.460051	+	0.204828i	0.623658	−	0.781698i	$-0.285646\pi$
$139$	5.42392	+	2.41489i	0.460051	+	0.204828i	−0.163606	+	0.986526i	$0.552313\pi$
$140$	10.7793	+	7.83160i	0.911015	+	0.661891i
$141$	0.255147	+	0.785261i	0.0214872	+	0.0661309i
$142$	−7.55952	−	13.0935i	−0.634381	−	1.09878i
$143$	−6.30607	+	5.61649i	−0.527340	+	0.469675i
$144$	−0.584260			−0.0486884
$145$	0.962914	+	2.96354i	0.0799656	+	0.246109i
$146$	1.10513	−	10.5146i	0.0914608	−	0.870192i
$147$	2.59677	+	24.7066i	0.214178	+	2.03777i
$148$	−6.60002	+	1.40288i	−0.542518	+	0.115316i
$149$	−6.18049	−	6.86413i	−0.506326	−	0.562331i	0.434740	−	0.900556i	$-0.356840\pi$
$149$	−6.18049	−	6.86413i	−0.506326	−	0.562331i	−0.941065	+	0.338225i	$0.890174\pi$
$150$	−0.442564	−	4.21071i	−0.0361352	−	0.343803i
$151$	2.84925	+	2.07010i	0.231868	+	0.168462i	0.697653	−	0.716436i	$-0.254228\pi$
$151$	2.84925	+	2.07010i	0.231868	+	0.168462i	−0.465784	+	0.884898i	$0.654228\pi$
$152$	−4.34866	−	0.298639i	−0.352723	−	0.0242228i
$153$	−3.17576			−0.256745
$154$	−15.1485	+	4.83152i	−1.22070	+	0.389335i
$155$	8.14691	−	14.1109i	0.654375	−	1.13341i
$156$	−2.64801	+	2.94091i	−0.212010	+	0.235461i
$157$	−16.7791	+	7.47054i	−1.33912	+	0.596214i	−0.946267	−	0.323387i	$-0.895178\pi$
$157$	−16.7791	+	7.47054i	−1.33912	+	0.596214i	−0.392853	+	0.919601i	$0.628512\pi$
$158$	14.5809	+	6.49182i	1.15999	+	0.516461i
$159$	−3.21858	+	9.90577i	−0.255250	+	0.785579i
$160$	−0.858826	+	2.64319i	−0.0678961	+	0.208963i
$161$	22.1588	+	9.86572i	1.74636	+	0.777528i
$162$	−0.721859	+	6.86803i	−0.0567146	+	0.539603i
$163$	0.760717	+	2.34124i	0.0595839	+	0.183380i	0.976418	−	0.215887i	$-0.0692644\pi$
$163$	0.760717	+	2.34124i	0.0595839	+	0.183380i	−0.916834	+	0.399268i	$0.869264\pi$
$164$	−4.16786			−0.325455
$165$	12.3683	+	7.23038i	0.962868	+	0.562884i
$166$	4.48034	−	7.76018i	0.347742	−	0.602306i
$167$	−2.10357	+	2.33625i	−0.162779	+	0.180785i	−0.819017	−	0.573770i	$-0.805480\pi$
$167$	−2.10357	+	2.33625i	−0.162779	+	0.180785i	0.656237	+	0.754555i	$0.272147\pi$
$168$	−6.80713	+	3.03073i	−0.525182	+	0.233826i
$169$	0.681226	+	6.48143i	0.0524020	+	0.498572i
$170$	−4.66817	+	14.3671i	−0.358032	+	1.10191i
$171$	0.439108	−	2.50859i	0.0335794	−	0.191837i
$172$	0.771374	−	0.560436i	0.0588168	−	0.0427329i
$173$	5.45526	−	2.42884i	0.414755	−	0.184661i	−0.188741	−	0.982027i	$-0.560441\pi$
$173$	5.45526	−	2.42884i	0.414755	−	0.184661i	0.603496	+	0.797366i	$0.293774\pi$
$174$	−1.70456	−	0.362315i	−0.129222	−	0.0274670i
$175$	6.52973	+	11.3098i	0.493601	+	0.854942i
$176$	−1.93491	−	2.69372i	−0.145849	−	0.203047i
$177$	3.43835	+	5.95540i	0.258442	+	0.447635i
$178$	0.690001	+	2.12361i	0.0517178	+	0.159171i
$179$	−17.7923	−	12.9269i	−1.32986	−	0.966200i	−0.999752	−	0.0222575i	$-0.992915\pi$
$179$	−17.7923	−	12.9269i	−1.32986	−	0.966200i	−0.330109	−	0.943943i	$-0.607085\pi$
$180$	−1.48340	−	0.660454i	−0.110566	−	0.0492273i
$181$	−7.22115	+	1.53490i	−0.536744	+	0.114088i	−0.468305	−	0.883567i	$-0.655135\pi$
$181$	−7.22115	+	1.53490i	−0.536744	+	0.114088i	−0.0684388	+	0.997655i	$0.521802\pi$
$182$	3.77203	−	11.6091i	0.279601	−	0.860524i
$183$	12.6887	−	9.21889i	0.937977	−	0.681480i
$184$	−0.528861	+	5.03177i	−0.0389881	+	0.370947i
$185$	−18.3429	−	3.89890i	−1.34860	−	0.286653i
$186$	4.55612	+	7.89143i	0.334071	+	0.578628i
$187$	−10.5172	−	14.6418i	−0.769097	−	1.07071i
$188$	0.265615	−	0.460059i	0.0193720	−	0.0335532i
$189$	−8.25308	−	25.4004i	−0.600323	−	1.84760i
$190$	−10.7034	−	5.67399i	−0.776507	−	0.411635i
$191$	−10.7437	+	7.80572i	−0.777383	+	0.564802i	−0.904193	−	0.427125i	$-0.859526\pi$
$191$	−10.7437	+	7.80572i	−0.777383	+	0.564802i	0.126809	+	0.991927i	$0.459526\pi$
$192$	−1.04001	−	1.15504i	−0.0750560	−	0.0833581i
$193$	−5.19023	−	5.76433i	−0.373601	−	0.414926i	0.526798	−	0.849990i	$-0.323392\pi$
$193$	−5.19023	−	5.76433i	−0.373601	−	0.414926i	−0.900399	+	0.435064i	$0.856726\pi$
$194$	−1.58471	−	0.705559i	−0.113776	−	0.0506562i
$195$	−10.0476	+	4.47347i	−0.719522	+	0.320352i
$196$	10.6951	−	11.8781i	0.763936	−	0.848437i
$197$	18.8372			1.34209			0.671046	−	0.741415i	$-0.265845\pi$
$197$	18.8372			1.34209			0.671046	+	0.741415i	$0.265845\pi$
$198$	1.68338	−	0.959787i	0.119633	−	0.0682091i
$199$	5.02661	+	8.70635i	0.356327	+	0.617177i	0.987344	−	0.158592i	$-0.0506955\pi$
$199$	5.02661	+	8.70635i	0.356327	+	0.617177i	−0.631017	+	0.775769i	$0.717362\pi$
$200$	−1.82275	+	2.02437i	−0.128888	+	0.143145i
$201$	8.24570	+	5.99085i	0.581607	+	0.422562i
$202$	−14.0876	+	10.2353i	−0.991202	+	0.720151i
$203$	5.25770	−	1.11756i	0.369018	−	0.0784372i
$204$	−5.65298	−	6.27827i	−0.395788	−	0.439567i
$205$	−10.5820	−	4.71139i	−0.739076	−	0.329058i
$206$	4.90133	−	2.18221i	0.341492	−	0.152042i
$207$	−2.89146	−	0.614599i	−0.200971	−	0.0427176i
$208$	2.54615			0.176544
$209$	13.0200	−	6.28326i	0.900613	−	0.434622i
$210$	−20.7089			−1.42905
$211$	18.1819	+	3.86469i	1.25170	+	0.266056i	0.785632	−	0.618695i	$-0.212338\pi$
$211$	18.1819	+	3.86469i	1.25170	+	0.266056i	0.466064	+	0.884751i	$0.345672\pi$
$212$	6.12191	−	2.72565i	0.420455	−	0.187198i
$213$	21.4674	+	9.55790i	1.47092	+	0.654896i
$214$	−4.39257	−	4.87845i	−0.300270	−	0.333484i
$215$	2.59200	−	0.550946i	0.176773	−	0.0375742i
$216$	4.50695	−	3.27449i	0.306659	−	0.222801i
$217$	−22.7388	−	16.5207i	−1.54361	−	1.12150i
$218$	2.38399	−	2.64769i	0.161464	−	0.179324i
$219$	8.21622	+	14.2309i	0.555201	+	0.961636i
$220$	−1.86761	−	9.02644i	−0.125914	−	0.608563i
$221$	13.8396			0.930955
$222$	7.01741	−	7.79362i	0.470978	−	0.523074i
$223$	−24.4570	+	10.8889i	−1.63776	+	0.729178i	−0.999184	−	0.0403819i	$-0.987143\pi$
$223$	−24.4570	+	10.8889i	−1.63776	+	0.729178i	−0.638575	+	0.769559i	$0.720476\pi$
$224$	4.37965	+	1.94994i	0.292627	+	0.130286i
$225$	−1.06496	−	1.18276i	−0.0709974	−	0.0788506i
$226$	5.78272	+	6.42236i	0.384661	+	0.427209i
$227$	−21.0973	+	15.3281i	−1.40027	+	1.01736i	−0.405626	+	0.914039i	$0.632946\pi$
$227$	−21.0973	+	15.3281i	−1.40027	+	1.01736i	−0.994648	+	0.103319i	$0.967054\pi$
$228$	5.74095	−	3.59730i	0.380203	−	0.238237i
$229$	−2.00027	−	6.15620i	−0.132182	−	0.406813i	0.862959	−	0.505273i	$-0.168608\pi$
$229$	−2.00027	−	6.15620i	−0.132182	−	0.406813i	−0.995141	+	0.0984601i	$0.968608\pi$
$230$	−7.03072	+	12.1776i	−0.463592	+	0.802964i
$231$	14.6341	−	19.9145i	0.962855	−	1.31028i
$232$	0.560599	+	0.970986i	0.0368051	+	0.0637483i
$233$	−3.07761	−	0.654166i	−0.201621	−	0.0428558i	0.105994	−	0.994367i	$-0.466198\pi$
$233$	−3.07761	−	0.654166i	−0.201621	−	0.0428558i	−0.307615	+	0.951511i	$0.599531\pi$
$234$	−0.155498	+	1.47946i	−0.0101652	+	0.0967156i
$235$	1.19444	−	0.867809i	0.0779165	−	0.0566096i
$236$	1.36722	−	4.20786i	0.0889982	−	0.273908i
$237$	−24.2651	+	5.15771i	−1.57619	+	0.335029i
$238$	23.8057	+	10.5990i	1.54309	+	0.687029i
$239$	22.8011	+	16.5659i	1.47488	+	1.07156i	0.979163	+	0.203076i	$0.0650939\pi$
$239$	22.8011	+	16.5659i	1.47488	+	1.07156i	0.495715	+	0.868485i	$0.334906\pi$
$240$	−1.33484	−	4.10822i	−0.0861637	−	0.265185i
$241$	−13.8802	−	24.0413i	−0.894105	−	1.54863i	−0.834909	−	0.550388i	$-0.814480\pi$
$241$	−13.8802	−	24.0413i	−0.894105	−	1.54863i	−0.0591958	−	0.998246i	$-0.518854\pi$
$242$	9.99997	+	4.58265i	0.642822	+	0.294584i
$243$	2.98957	+	5.17809i	0.191781	+	0.332174i
$244$	−9.87051	−	2.09804i	−0.631894	−	0.134313i
$245$	40.5814	−	18.0680i	2.59265	−	1.15432i
$246$	5.24078	−	3.80765i	0.334140	−	0.242767i
$247$	−1.91359	+	10.9322i	−0.121759	+	0.695598i
$248$	1.81168	−	5.57579i	0.115042	−	0.354063i
$249$	1.45580	+	13.8510i	0.0922573	+	0.877770i
$250$	5.77849	−	2.57275i	0.365464	−	0.162715i
$251$	−14.2151	+	15.7874i	−0.897247	+	0.996494i	0.102751	+	0.994707i	$0.467236\pi$
$251$	−14.2151	+	15.7874i	−0.897247	+	0.996494i	−0.999998	+	0.00178706i	$0.999431\pi$
$252$	−1.40051	+	2.42575i	−0.0882237	+	0.152808i
$253$	−6.74212	−	15.3664i	−0.423874	−	0.966078i
$254$	−7.19462			−0.451430
$255$	−7.25557	−	22.3303i	−0.454361	−	1.39838i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	13.0743	+	5.82106i	0.815554	+	0.363108i	0.771745	−	0.635932i	$-0.219384\pi$
$257$	13.0743	+	5.82106i	0.815554	+	0.363108i	0.0438086	+	0.999040i	$0.486051\pi$
$258$	−0.457947	+	1.40942i	−0.0285105	+	0.0877464i
$259$	−9.99614	+	30.7649i	−0.621130	+	1.91164i
$260$	6.46452	+	2.87819i	0.400913	+	0.178498i
$261$	−0.598438	+	0.266442i	−0.0370424	+	0.0164923i
$262$	−0.814890	+	0.905027i	−0.0503441	+	0.0559128i
$263$	2.35223	−	4.07418i	0.145045	−	0.251225i	−0.784345	−	0.620325i	$-0.787001\pi$
$263$	2.35223	−	4.07418i	0.145045	−	0.251225i	0.929390	+	0.369100i	$0.120334\pi$
$264$	4.89392	+	1.61947i	0.301200	+	0.0996718i
$265$	18.6243			1.14408
$266$	−11.6639	+	17.3390i	−0.715159	+	1.06312i
$267$	−2.80770	−	2.03991i	−0.171828	−	0.124841i
$268$	−0.685456	−	6.52168i	−0.0418709	−	0.398375i
$269$	11.7213	+	13.0178i	0.714658	+	0.793708i	0.985637	−	0.168877i	$-0.0540140\pi$
$269$	11.7213	+	13.0178i	0.714658	+	0.793708i	−0.270979	+	0.962585i	$0.587347\pi$
$270$	15.1444	−	3.21904i	0.921658	−	0.195904i
$271$	−1.22186	−	11.6252i	−0.0742226	−	0.706181i	−0.966843	−	0.255372i	$-0.917802\pi$
$271$	−1.22186	−	11.6252i	−0.0742226	−	0.706181i	0.892620	−	0.450809i	$-0.148864\pi$
$272$	−0.568167	+	5.40575i	−0.0344502	+	0.327772i
$273$	5.86273	+	18.0436i	0.354828	+	1.09205i
$274$	10.7040			0.646654
$275$	1.92623	−	8.82695i	0.116156	−	0.532285i
$276$	−3.93189	−	6.81024i	−0.236672	−	0.409928i
$277$	2.29320	+	7.05774i	0.137785	+	0.424058i	0.996013	−	0.0892104i	$-0.0284344\pi$
$277$	2.29320	+	7.05774i	0.137785	+	0.424058i	−0.858228	+	0.513269i	$0.828434\pi$
$278$	4.80332	+	3.48981i	0.288084	+	0.209305i
$279$	3.12922	+	1.39322i	0.187342	+	0.0834099i
$280$	8.91544	+	9.90159i	0.532799	+	0.591733i
$281$	−1.67042	+	0.355059i	−0.0996488	+	0.0211810i	−0.257466	−	0.966287i	$-0.582888\pi$
$281$	−1.67042	+	0.355059i	−0.0996488	+	0.0211810i	0.157817	+	0.987468i	$0.449554\pi$
$282$	0.0863063	+	0.821149i	0.00513946	+	0.0488987i
$283$	−27.5744	+	12.2769i	−1.63913	+	0.729786i	−0.999251	−	0.0386943i	$-0.987680\pi$
$283$	−27.5744	+	12.2769i	−1.63913	+	0.729786i	−0.639874	+	0.768480i	$0.721013\pi$
$284$	−4.67204	−	14.3791i	−0.277234	−	0.853240i
$285$	18.6424	−	2.64372i	1.10428	−	0.156601i
$286$	−7.33600	+	4.18265i	−0.433787	+	0.247325i
$287$	−9.99061	+	17.3043i	−0.589727	+	1.02144i
$288$	−0.571493	−	0.121475i	−0.0336755	−	0.00715796i
$289$	−1.31130	+	12.4762i	−0.0771353	+	0.733893i
$290$	0.325716	+	3.09898i	0.0191267	+	0.181979i
$291$	2.63724	−	0.560562i	0.154598	−	0.0328607i
$292$	3.26708	−	10.0550i	0.191191	−	0.588426i
$293$	−11.6876	+	8.49154i	−0.682797	+	0.496081i	−0.874284	−	0.485414i	$-0.838669\pi$
$293$	−11.6876	+	8.49154i	−0.682797	+	0.496081i	0.191487	+	0.981495i	$0.438669\pi$
$294$	−2.59677	+	24.7066i	−0.151447	+	1.44092i
$295$	8.22789	−	9.13800i	0.479046	−	0.532035i
$296$	−6.74747			−0.392189
$297$	−7.60636	+	16.8382i	−0.441366	+	0.977054i
$298$	−4.61830	−	7.99913i	−0.267531	−	0.463377i
$299$	12.6007	+	2.67836i	0.728717	+	0.154894i
$300$	0.442564	−	4.21071i	0.0255514	−	0.243106i
$301$	−0.477805	−	4.54602i	−0.0275402	−	0.262028i
$302$	2.35659	+	2.61725i	0.135606	+	0.150606i
$303$	8.36349	−	25.7402i	0.480470	−	1.47874i
$304$	−4.19154	−	1.19625i	−0.240401	−	0.0686096i
$305$	−22.6890	−	16.4845i	−1.29917	−	0.943901i
$306$	−3.10636	−	0.660278i	−0.177579	−	0.0377456i
$307$	−10.1028	+	17.4986i	−0.576598	+	0.998697i	0.419268	+	0.907863i	$0.362287\pi$
$307$	−10.1028	+	17.4986i	−0.576598	+	0.998697i	−0.995866	+	0.0908347i	$0.971047\pi$
$308$	−15.8220	+	1.57640i	−0.901540	+	0.0898237i
$309$	−4.16945	+	7.22170i	−0.237192	+	0.410828i
$310$	10.9027	−	12.1087i	0.619231	−	0.687726i
$311$	10.3808	+	7.54211i	0.588643	+	0.427674i	0.841830	−	0.539743i	$-0.181479\pi$
$311$	10.3808	+	7.54211i	0.588643	+	0.427674i	−0.253187	+	0.967417i	$0.581479\pi$
$312$	−3.20159	+	2.32609i	−0.181255	+	0.131689i
$313$	32.5957	−	6.92843i	1.84242	−	0.391618i	0.851308	−	0.524666i	$-0.175810\pi$
$313$	32.5957	−	6.92843i	1.84242	−	0.391618i	0.991110	+	0.133048i	$0.0424765\pi$
$314$	−17.9657	+	3.81872i	−1.01386	+	0.215503i
$315$	−6.29790	+	4.57569i	−0.354847	+	0.257811i
$316$	12.9125	+	9.38149i	0.726385	+	0.527750i
$317$	−4.85222	+	5.38894i	−0.272528	+	0.302673i	−0.863836	−	0.503773i	$-0.831945\pi$
$317$	−4.85222	+	5.38894i	−0.272528	+	0.302673i	0.591308	+	0.806446i	$0.298612\pi$
$318$	−5.20777	+	9.02012i	−0.292037	+	0.505823i
$319$	−3.21028	−	1.87670i	−0.179741	−	0.105075i
$320$	−1.38961	+	2.40687i	−0.0776815	+	0.134548i
$321$	9.98016	+	2.12135i	0.557038	+	0.118402i
$322$	19.6234	+	14.2572i	1.09357	+	0.794523i
$323$	−22.7832	−	6.50224i	−1.26769	−	0.361794i
$324$	−2.13403	+	6.56786i	−0.118557	+	0.364881i
$325$	4.64099	+	5.15434i	0.257436	+	0.285911i
$326$	0.257321	+	2.44825i	0.0142517	+	0.135596i
$327$	−0.578833	+	5.50723i	−0.0320095	+	0.304550i
$328$	−4.07678	−	0.866547i	−0.225103	−	0.0478471i
$329$	−1.27339	−	2.20558i	−0.0702043	−	0.121597i
$330$	10.5947	+	9.64389i	0.583220	+	0.530879i
$331$	33.3859			1.83506			0.917528	−	0.397671i	$-0.130181\pi$
$331$	33.3859			1.83506			0.917528	+	0.397671i	$0.130181\pi$
$332$	5.99587	−	6.65908i	0.329066	−	0.365465i
$333$	0.412080	−	3.92068i	0.0225819	−	0.214852i
$334$	−2.54334	+	1.84784i	−0.139165	+	0.101109i
$335$	5.63184	−	17.3330i	0.307700	−	0.947004i
$336$	−7.28850	+	1.54922i	−0.397620	+	0.0845168i
$337$	0.913359	+	8.69003i	0.0497538	+	0.473376i	0.990823	+	0.135163i	$0.0431558\pi$
$337$	0.913359	+	8.69003i	0.0497538	+	0.473376i	−0.941070	+	0.338213i	$0.890178\pi$
$338$	−0.681226	+	6.48143i	−0.0370538	+	0.352544i
$339$	−13.1386	−	2.79270i	−0.713593	−	0.151679i
$340$	−7.55325	+	13.0826i	−0.409633	+	0.709505i
$341$	3.93971	+	19.0412i	0.213347	+	1.03114i
$342$	0.951078	−	2.36248i	0.0514284	−	0.127748i
$343$	−13.3089	−	40.9605i	−0.718611	−	2.21166i
$344$	0.871039	−	0.387812i	0.0469633	−	0.0209094i
$345$	−2.28449	−	21.7355i	−0.122993	−	1.17020i
$346$	5.84103	−	1.24155i	0.314016	−	0.0667461i
$347$	15.5470	+	17.2667i	0.834609	+	0.926927i	0.998222	−	0.0595977i	$-0.0189818\pi$
$347$	15.5470	+	17.2667i	0.834609	+	0.926927i	−0.163614	+	0.986524i	$0.552315\pi$
$348$	−1.59198	−	0.708795i	−0.0853391	−	0.0379954i
$349$	14.8759	+	10.8080i	0.796288	+	0.578537i	0.909823	−	0.414997i	$-0.136217\pi$
$349$	14.8759	+	10.8080i	0.796288	+	0.578537i	−0.113535	+	0.993534i	$0.536217\pi$
$350$	4.03560	+	12.4203i	0.215712	+	0.663892i
$351$	−7.09215	−	12.2840i	−0.378551	−	0.655670i
$352$	−1.33257	−	3.03715i	−0.0710262	−	0.161880i
$353$	−10.5713			−0.562655			−0.281327	−	0.959612i	$-0.590775\pi$
$353$	−10.5713			−0.562655			−0.281327	+	0.959612i	$0.590775\pi$
$354$	2.12502	+	6.54013i	0.112943	+	0.347604i
$355$	4.39219	−	41.7889i	0.233113	−	2.21793i
$356$	0.233401	+	2.22066i	0.0123702	+	0.117695i
$357$	−39.6168	+	8.42082i	−2.09674	+	0.445677i
$358$	−14.7159	−	16.3436i	−0.777758	−	0.863788i
$359$	−2.66546	−	25.3602i	−0.140678	−	1.33846i	−0.806005	−	0.591909i	$-0.798375\pi$
$359$	−2.66546	−	25.3602i	−0.140678	−	1.33846i	0.665327	−	0.746552i	$-0.268292\pi$
$360$	−1.31367	−	0.954439i	−0.0692366	−	0.0503033i
$361$	8.28644	−	17.0978i	0.436128	−	0.899885i
$362$	−7.38247			−0.388014
$363$	−16.7608	+	3.37337i	−0.879715	+	0.177056i
$364$	6.10327	−	10.5712i	0.319898	−	0.554080i
$365$	19.6612	−	21.8360i	1.02912	−	1.14295i
$366$	14.3282	−	6.37931i	0.748945	−	0.333452i
$367$	−33.3034	−	14.8276i	−1.73842	−	0.773997i	−0.994380	−	0.105867i	$-0.966238\pi$
$367$	−33.3034	−	14.8276i	−1.73842	−	0.773997i	−0.744045	−	0.668130i	$-0.767095\pi$
$368$	−1.56347	+	4.81186i	−0.0815014	+	0.250836i
$369$	0.752493	−	2.31593i	0.0391732	−	0.120563i
$370$	−17.1314	−	7.62741i	−0.890621	−	0.396530i
$371$	3.35815	−	31.9507i	0.174347	−	1.65880i
$372$	2.81584	+	8.66626i	0.145994	+	0.449324i
$373$	−23.0274			−1.19231			−0.596157	−	0.802868i	$-0.703306\pi$
$373$	−23.0274			−1.19231			−0.596157	+	0.802868i	$0.703306\pi$
$374$	−7.24321	−	16.5085i	−0.374538	−	0.853633i
$375$	−4.91563	+	8.51412i	−0.253842	+	0.439667i
$376$	0.355462	−	0.394781i	0.0183316	−	0.0203593i
$377$	2.60793	−	1.16113i	0.134315	−	0.0598010i
$378$	−2.79170	−	26.5612i	−0.143589	−	1.36616i
$379$	6.44040	−	19.8215i	0.330821	−	1.01816i	−0.637923	−	0.770100i	$-0.720206\pi$
$379$	6.44040	−	19.8215i	0.330821	−	1.01816i	0.968744	−	0.248062i	$-0.0797938\pi$
$380$	−9.28982	−	7.77537i	−0.476558	−	0.398868i
$381$	9.04670	−	6.57282i	0.463477	−	0.336736i
$382$	−12.1318	+	5.40142i	−0.620716	+	0.276360i
$383$	12.2881	+	2.61192i	0.627893	+	0.133463i	0.510858	−	0.859665i	$-0.329328\pi$
$383$	12.2881	+	2.61192i	0.627893	+	0.133463i	0.117035	+	0.993128i	$0.462661\pi$
$384$	−0.777132	−	1.34603i	−0.0396579	−	0.0686895i
$385$	−41.9530	−	13.8829i	−2.13812	−	0.707539i
$386$	−3.87834	−	6.71748i	−0.197402	−	0.341911i
$387$	0.172146	+	0.529810i	0.00875066	+	0.0269318i
$388$	−1.40339	−	1.01962i	−0.0712462	−	0.0517634i
$389$	13.3692	+	5.95236i	0.677846	+	0.301797i	0.716633	−	0.697451i	$-0.245682\pi$
$389$	13.3692	+	5.95236i	0.677846	+	0.301797i	−0.0387863	+	0.999248i	$0.512349\pi$
$390$	−10.7581	+	2.28671i	−0.544758	+	0.115792i
$391$	−8.49827	+	26.1550i	−0.429776	+	1.32271i
$392$	12.9310	−	9.39492i	0.653114	−	0.474515i
$393$	0.197855	−	1.88247i	0.00998048	−	0.0949579i
$394$	18.4255	+	3.91647i	0.928265	+	0.197309i
$395$	22.1792	+	38.4155i	1.11596	+	1.93289i
$396$	1.84615	−	0.588819i	0.0927723	−	0.0295893i
$397$	8.07897	−	13.9932i	0.405472	−	0.702298i	−0.588904	−	0.808203i	$-0.700441\pi$
$397$	8.07897	−	13.9932i	0.405472	−	0.702298i	0.994376	+	0.105905i	$0.0337739\pi$
$398$	3.10662	+	9.56119i	0.155721	+	0.479259i
$399$	−1.17400	−	32.4584i	−0.0587734	−	1.62495i
$400$	−2.20381	+	1.60116i	−0.110190	+	0.0800581i
$401$	8.57672	+	9.52541i	0.428301	+	0.475676i	0.918208	−	0.396098i	$-0.129636\pi$
$401$	8.57672	+	9.52541i	0.428301	+	0.475676i	−0.489907	+	0.871775i	$0.662969\pi$
$402$	6.81995	+	7.57432i	0.340148	+	0.377773i
$403$	−13.6368	−	6.07151i	−0.679299	−	0.302444i
$404$	−15.9078	+	7.08262i	−0.791443	+	0.352373i
$405$	−12.8426	+	14.2631i	−0.638152	+	0.708739i
$406$	5.37516			0.266765
$407$	19.4409	−	11.0843i	0.963651	−	0.549430i
$408$	−4.22412	−	7.31639i	−0.209125	−	0.362215i
$409$	−4.01424	+	4.45827i	−0.198492	+	0.220447i	−0.834171	−	0.551506i	$-0.814053\pi$
$409$	−4.01424	+	4.45827i	−0.198492	+	0.220447i	0.635679	+	0.771953i	$0.280720\pi$
$410$	−9.37117	−	6.80855i	−0.462809	−	0.336250i
$411$	−13.4595	+	9.77892i	−0.663909	+	0.482358i
$412$	5.24793	−	1.11548i	0.258547	−	0.0549558i
$413$	−14.1930	−	15.7629i	−0.698393	−	0.775644i
$414$	−2.70050	−	1.20234i	−0.132722	−	0.0590917i
$415$	22.7507	−	10.1292i	1.11679	−	0.497225i
$416$	2.49051	+	0.529374i	0.122107	+	0.0259547i
$417$	−9.22802			−0.451898
$418$	14.0419	−	3.43894i	0.686810	−	0.168204i
$419$	10.4523			0.510629			0.255314	−	0.966858i	$-0.417821\pi$
$419$	10.4523			0.510629			0.255314	+	0.966858i	$0.417821\pi$
$420$	−20.2563	−	4.30562i	−0.988409	−	0.210093i
$421$	26.4445	−	11.7739i	1.28883	−	0.573823i	0.356114	−	0.934442i	$-0.384101\pi$
$421$	26.4445	−	11.7739i	1.28883	−	0.573823i	0.932713	+	0.360620i	$0.117435\pi$
$422$	16.9811	+	7.56047i	0.826627	+	0.368038i
$423$	0.207683	+	0.230655i	0.0100979	+	0.0112148i
$424$	6.55483	−	1.39327i	0.318331	−	0.0676632i
$425$	−11.9789	+	8.70315i	−0.581060	+	0.422165i
$426$	19.0111	+	13.8124i	0.921090	+	0.669211i
$427$	−32.3709	+	35.9515i	−1.56654	+	1.73982i
$428$	−3.28230	−	5.68511i	−0.158656	−	0.274800i
$429$	5.40332	−	11.9614i	0.260875	−	0.577500i
$430$	2.64991			0.127790
$431$	−5.46303	+	6.06731i	−0.263145	+	0.292252i	−0.860209	−	0.509941i	$-0.829667\pi$
$431$	−5.46303	+	6.06731i	−0.263145	+	0.292252i	0.597064	+	0.802193i	$0.296334\pi$
$432$	5.08926	−	2.26589i	0.244857	−	0.109017i
$433$	6.24580	+	2.78081i	0.300154	+	0.133637i	0.551288	−	0.834315i	$-0.314137\pi$
$433$	6.24580	+	2.78081i	0.300154	+	0.133637i	−0.251134	+	0.967952i	$0.580803\pi$
$434$	−18.8070	−	20.8873i	−0.902766	−	1.00262i
$435$	−3.24072	−	3.59918i	−0.155380	−	0.172567i
$436$	2.88238	−	2.09417i	0.138041	−	0.100293i
$437$	−19.4852	−	10.3293i	−0.932106	−	0.494120i
$438$	5.07790	+	15.6282i	0.242632	+	0.746743i
$439$	−19.3824	+	33.5713i	−0.925071	+	1.60227i	−0.133625	+	0.991032i	$0.542662\pi$
$439$	−19.3824	+	33.5713i	−0.925071	+	1.60227i	−0.791446	+	0.611239i	$0.790672\pi$
$440$	0.0499024	−	9.21749i	0.00237900	−	0.439427i
$441$	4.66929	+	8.08745i	0.222347	+	0.385117i
$442$	13.5372	+	2.87742i	0.643899	+	0.136865i
$443$	−2.86983	+	27.3046i	−0.136350	+	1.29728i	0.685708	+	0.727876i	$0.259493\pi$
$443$	−2.86983	+	27.3046i	−0.136350	+	1.29728i	−0.822058	+	0.569404i	$0.807174\pi$
$444$	8.48445	−	6.16431i	0.402654	−	0.292545i
$445$	−1.91766	+	5.90197i	−0.0909060	+	0.279780i
$446$	−26.1865	+	5.56610i	−1.23996	+	0.263563i
$447$	13.1150	+	5.83916i	0.620317	+	0.276183i
$448$	3.87852	+	2.81791i	0.183243	+	0.133134i
$449$	−6.28365	−	19.3391i	−0.296544	−	0.912668i	−0.982699	−	0.185212i	$-0.940703\pi$
$449$	−6.28365	−	19.3391i	−0.296544	−	0.912668i	0.686155	−	0.727456i	$-0.259297\pi$
$450$	−0.795780	−	1.37833i	−0.0375134	−	0.0649751i
$451$	13.1696	−	4.20038i	0.620133	−	0.197788i
$452$	4.32107	+	7.48431i	0.203246	+	0.352032i
$453$	−5.35429	−	1.13809i	−0.251567	−	0.0534721i
$454$	−23.8231	+	10.6067i	−1.11807	+	0.497799i
$455$	27.4456	−	19.9404i	1.28667	−	0.934820i
$456$	6.36341	−	2.32508i	0.297994	−	0.108882i
$457$	−0.0240194	+	0.0739242i	−0.00112358	+	0.00345803i	−0.951617	−	0.307287i	$-0.900579\pi$
$457$	−0.0240194	+	0.0739242i	−0.00112358	+	0.00345803i	0.950493	+	0.310745i	$0.100579\pi$
$458$	−0.676614	−	6.43755i	−0.0316161	−	0.300807i
$459$	27.6628	−	12.3163i	1.29119	−	0.574874i
$460$	−9.40893	+	10.4497i	−0.438694	+	0.487219i
$461$	9.96989	−	17.2684i	0.464344	−	0.804267i	−0.534828	−	0.844961i	$-0.679623\pi$
$461$	9.96989	−	17.2684i	0.464344	−	0.804267i	0.999172	+	0.0406938i	$0.0129568\pi$
$462$	18.4548	−	16.4367i	0.858595	−	0.764706i
$463$	−17.9340			−0.833465			−0.416732	−	0.909029i	$-0.636825\pi$
$463$	−17.9340			−0.833465			−0.416732	+	0.909029i	$0.636825\pi$
$464$	0.346469	+	1.06632i	0.0160844	+	0.0495028i
$465$	−2.64717	+	25.1862i	−0.122760	+	1.16798i
$466$	−2.87435	−	1.27974i	−0.133152	−	0.0592829i
$467$	10.0444	−	30.9134i	0.464798	−	1.43050i	−0.394439	−	0.918922i	$-0.629061\pi$
$467$	10.0444	−	30.9134i	0.464798	−	1.43050i	0.859237	−	0.511578i	$-0.170939\pi$
$468$	−0.459698	+	1.41480i	−0.0212495	+	0.0653993i
$469$	−28.7200	−	12.7870i	−1.32617	−	0.590447i
$470$	1.34876	−	0.600508i	0.0622138	−	0.0276994i
$471$	19.1018	−	21.2147i	0.880166	−	0.977523i
$472$	2.21220	−	3.83165i	0.101825	−	0.176366i
$473$	−1.87258	+	2.54826i	−0.0861013	+	0.117169i
$474$	−24.8072			−1.13943
$475$	−5.21848	−	10.6657i	−0.239440	−	0.489375i
$476$	21.0818	+	15.3168i	0.966283	+	0.702046i
$477$	0.409259	+	3.89384i	0.0187387	+	0.178287i
$478$	18.8585	+	20.9445i	0.862570	+	0.957981i
$479$	−27.2446	+	5.79102i	−1.24484	+	0.264599i	−0.782807	−	0.622265i	$-0.786213\pi$
$479$	−27.2446	+	5.79102i	−1.24484	+	0.264599i	−0.462032	+	0.886863i	$0.652879\pi$
$480$	−0.451526	−	4.29598i	−0.0206092	−	0.196084i
$481$	−1.79580	+	17.0859i	−0.0818816	+	0.779052i
$482$	−8.57846	−	26.4018i	−0.390738	−	1.20257i
$483$	−37.6999			−1.71541
$484$	8.82866	+	6.56161i	0.401303	+	0.298255i
$485$	−2.41053	−	4.17516i	−0.109457	−	0.189584i
$486$	1.84766	+	5.68650i	0.0838113	+	0.257945i
$487$	4.23113	+	3.07410i	0.191731	+	0.139301i	0.679509	−	0.733667i	$-0.262193\pi$
$487$	4.23113	+	3.07410i	0.191731	+	0.139301i	−0.487779	+	0.872967i	$0.662193\pi$
$488$	−9.21861	−	4.10439i	−0.417307	−	0.185797i
$489$	−2.56022	−	2.84341i	−0.115777	−	0.128583i
$490$	43.4512	−	9.23583i	1.96292	−	0.417232i
$491$	3.35206	+	31.8927i	0.151276	+	1.43930i	0.762063	+	0.647503i	$0.224187\pi$
$491$	3.35206	+	31.8927i	0.151276	+	1.43930i	−0.610787	+	0.791795i	$0.709147\pi$
$492$	5.91791	−	2.63482i	0.266800	−	0.118787i
$493$	1.88324	+	5.79602i	0.0848169	+	0.261040i
$494$	−4.14470	+	10.2954i	−0.186479	+	0.463213i
$495$	5.35287	+	0.591926i	0.240593	+	0.0266051i
$496$	2.93137	−	5.07728i	0.131622	−	0.227976i
$497$	−70.8985	−	15.0700i	−3.18023	−	0.675980i
$498$	−1.45580	+	13.8510i	−0.0652358	+	0.620677i
$499$	−0.384142	−	3.65487i	−0.0171966	−	0.163614i	0.982553	−	0.185981i	$-0.0595464\pi$
$499$	−0.384142	−	3.65487i	−0.0171966	−	0.163614i	−0.999750	+	0.0223670i	$0.992880\pi$
$500$	6.18712	−	1.31511i	0.276696	−	0.0588136i
$501$	1.50992	−	4.64705i	0.0674582	−	0.207615i
$502$	−17.1868	+	12.4870i	−0.767086	+	0.557320i
$503$	3.58329	−	34.0928i	0.159771	−	1.52012i	−0.561505	−	0.827473i	$-0.689777\pi$
$503$	3.58329	−	34.0928i	0.159771	−	1.52012i	0.721276	−	0.692648i	$-0.243556\pi$
$504$	−1.87424	+	2.08156i	−0.0834855	+	0.0927200i
$505$	−48.3953			−2.15356
$506$	−3.39994	−	16.4324i	−0.151146	−	0.730509i
$507$	−5.06468	−	8.77228i	−0.224930	−	0.389591i
$508$	−7.03740	−	1.49585i	−0.312234	−	0.0663674i
$509$	0.937001	−	8.91497i	0.0415318	−	0.395149i	−0.953933	−	0.300020i	$-0.903007\pi$
$509$	0.937001	−	8.91497i	0.0415318	−	0.395149i	0.995465	−	0.0951296i	$-0.0303265\pi$
$510$	−2.45428	−	23.3509i	−0.108677	−	1.03399i
$511$	−33.9154	−	37.6669i	−1.50033	−	1.66628i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	5.90395	+	23.5543i	0.260666	+	1.03995i
$514$	11.5783	+	8.41216i	0.510699	+	0.371045i
$515$	14.5851	+	3.10017i	0.642698	+	0.136610i
$516$	−0.740973	+	1.28340i	−0.0326195	+	0.0564987i
$517$	−0.375643	+	1.72138i	−0.0165207	+	0.0757063i
$518$	−16.1741	+	28.0143i	−0.710649	+	1.23088i
$519$	−6.21042	+	6.89737i	−0.272607	+	0.302761i
$520$	5.72485	+	4.15934i	0.251051	+	0.182399i
$521$	−10.5582	+	7.67099i	−0.462564	+	0.336072i	−0.794536	−	0.607217i	$-0.792286\pi$
$521$	−10.5582	+	7.67099i	−0.462564	+	0.336072i	0.331972	+	0.943289i	$0.392286\pi$
$522$	−0.640757	+	0.136197i	−0.0280452	+	0.00596118i
$523$	14.9573	−	3.17927i	0.654036	−	0.139020i	0.131070	−	0.991373i	$-0.458159\pi$
$523$	14.9573	−	3.17927i	0.654036	−	0.139020i	0.522966	+	0.852353i	$0.324825\pi$
$524$	−0.985248	+	0.715825i	−0.0430408	+	0.0312710i
$525$	−16.4213	−	11.9308i	−0.716685	−	0.520702i
$526$	3.14790	−	3.49610i	0.137255	−	0.152437i
$527$	15.9335	−	27.5976i	0.694075	−	1.20217i
$528$	4.45027	+	2.60159i	0.193673	+	0.113220i
$529$	−1.29922	+	2.25031i	−0.0564878	+	0.0978397i
$530$	18.2173	+	3.87221i	0.791309	+	0.168198i
$531$	2.09131	+	1.51943i	0.0907553	+	0.0659376i
$532$	−15.0140	+	14.5351i	−0.650939	+	0.630175i
$533$	−3.27928	+	10.0926i	−0.142042	+	0.437159i
$534$	−2.32222	−	2.57909i	−0.100492	−	0.111608i
$535$	−1.90707	−	18.1445i	−0.0824496	−	0.784456i
$536$	0.685456	−	6.52168i	0.0296072	−	0.281694i
$537$	33.4352	+	7.10688i	1.44284	+	0.306685i
$538$	8.75858	+	15.1703i	0.377609	+	0.654038i
$539$	−21.8236	+	48.3110i	−0.940010	+	2.08090i
$540$	15.4827			0.666270
$541$	−8.07971	+	8.97342i	−0.347374	+	0.385798i	−0.891360	−	0.453297i	$-0.850248\pi$
$541$	−8.07971	+	8.97342i	−0.347374	+	0.385798i	0.543986	+	0.839094i	$0.316914\pi$
$542$	1.22186	−	11.6252i	0.0524833	−	0.499345i
$543$	9.28292	−	6.74444i	0.398368	−	0.289431i
$544$	−1.67967	+	5.16949i	−0.0720152	+	0.221640i
$545$	9.68547	−	2.05871i	0.414880	−	0.0881855i
$546$	1.98313	+	18.8683i	0.0848703	+	0.807487i
$547$	−1.79611	+	17.0889i	−0.0767962	+	0.730667i	0.886591	+	0.462554i	$0.153067\pi$
$547$	−1.79611	+	17.0889i	−0.0767962	+	0.730667i	−0.963387	+	0.268113i	$0.913600\pi$
$548$	10.4701	+	2.22549i	0.447261	+	0.0950683i
$549$	2.94789	−	5.10590i	0.125813	−	0.217914i
$550$	3.71936	−	8.23357i	0.158594	−	0.351081i
$551$	−4.83877	+	0.686200i	−0.206139	+	0.0292331i
$552$	−2.43004	−	7.47891i	−0.103430	−	0.318323i
$553$	69.9024	−	31.1226i	2.97255	−	1.32347i
$554$	0.775700	+	7.38029i	0.0329563	+	0.313559i
$555$	28.5097	−	6.05993i	1.21017	−	0.257230i
$556$	3.97278	+	4.41222i	0.168483	+	0.187120i
$557$	38.0965	+	16.9617i	1.61420	+	0.718688i	0.997643	−	0.0686211i	$-0.0218600\pi$
$557$	38.0965	+	16.9617i	1.61420	+	0.718688i	0.616558	+	0.787310i	$0.288527\pi$
$558$	2.77118	+	2.01338i	0.117313	+	0.0852331i
$559$	−0.750194	−	2.30886i	−0.0317298	−	0.0976543i
$560$	6.66195	+	11.5388i	0.281519	+	0.487605i
$561$	24.1895	+	14.1410i	1.02128	+	0.597033i
$562$	−1.70774			−0.0720365
$563$	7.42039	+	22.8376i	0.312732	+	0.962491i	0.976678	+	0.214710i	$0.0688806\pi$
$563$	7.42039	+	22.8376i	0.312732	+	0.962491i	−0.663946	+	0.747781i	$0.731119\pi$
$564$	−0.0863063	+	0.821149i	−0.00363415	+	0.0345766i
$565$	2.51060	+	23.8868i	0.105622	+	1.00493i
$566$	−29.5243	+	6.27558i	−1.24100	+	0.263782i
$567$	22.1533	+	24.6037i	0.930349	+	1.03326i
$568$	−1.58037	−	15.0362i	−0.0663108	−	0.630905i
$569$	4.44435	+	3.22901i	0.186317	+	0.135367i	0.677034	−	0.735952i	$-0.263265\pi$
$569$	4.44435	+	3.22901i	0.186317	+	0.135367i	−0.490717	+	0.871319i	$0.663265\pi$
$570$	18.7846	+	1.29001i	0.786802	+	0.0540327i
$571$	13.3540			0.558846			0.279423	−	0.960168i	$-0.409857\pi$
$571$	13.3540			0.558846			0.279423	+	0.960168i	$0.409857\pi$
$572$	−8.04532	+	2.56601i	−0.336392	+	0.107290i
$573$	10.3202	−	17.8752i	0.431134	−	0.746746i
$574$	−13.3701	+	14.8489i	−0.558055	+	0.619783i
$575$	−12.5908	+	5.60578i	−0.525073	+	0.233777i
$576$	−0.533749	−	0.237640i	−0.0222395	−	0.00990167i
$577$	5.41145	−	16.6547i	0.225282	−	0.693346i	−0.772981	−	0.634429i	$-0.781235\pi$
$577$	5.41145	−	16.6547i	0.225282	−	0.693346i	0.998263	−	0.0589167i	$-0.0187646\pi$
$578$	−3.87659	+	11.9309i	−0.161245	+	0.496261i
$579$	11.0136	+	4.90359i	0.457711	+	0.203786i
$580$	−0.325716	+	3.09898i	−0.0135246	+	0.128678i
$581$	−13.2749	−	40.8560i	−0.550737	−	1.69499i
$582$	2.69616			0.111759
$583$	−16.5971	+	14.7822i	−0.687382	+	0.612215i
$584$	5.28624	−	9.15604i	0.218746	−	0.378880i
$585$	−2.76646	+	3.07246i	−0.114379	+	0.127031i
$586$	−13.1977	+	5.87599i	−0.545192	+	0.242735i
$587$	0.891790	+	8.48482i	0.0368081	+	0.350206i	0.997390	+	0.0722075i	$0.0230044\pi$
$587$	0.891790	+	8.48482i	0.0368081	+	0.350206i	−0.960582	+	0.277999i	$0.910329\pi$
$588$	−7.67683	+	23.6268i	−0.316587	+	0.974355i
$589$	19.5968	+	16.4021i	0.807471	+	0.675835i
$590$	9.94799	−	7.22764i	0.409552	−	0.297557i
$591$	−26.7467	+	11.9084i	−1.10021	+	0.489847i
$592$	−6.60002	−	1.40288i	−0.271259	−	0.0576579i
$593$	8.13184	+	14.0848i	0.333935	+	0.578392i	0.983280	−	0.182102i	$-0.0582902\pi$
$593$	8.13184	+	14.0848i	0.333935	+	0.578392i	−0.649345	+	0.760494i	$0.724957\pi$
$594$	−10.9410	+	14.8888i	−0.448915	+	0.610896i
$595$	36.2112	+	62.7197i	1.48451	+	2.57126i
$596$	−2.85427	−	8.78453i	−0.116915	−	0.359828i
$597$	−12.6412	−	9.18437i	−0.517370	−	0.375891i
$598$	11.7685	+	5.23966i	0.481249	+	0.214266i
$599$	8.04568	−	1.71016i	0.328737	−	0.0698753i	−0.0405865	−	0.999176i	$-0.512923\pi$
$599$	8.04568	−	1.71016i	0.328737	−	0.0698753i	0.369324	+	0.929301i	$0.379589\pi$
$600$	1.30835	−	4.02669i	0.0534131	−	0.164389i
$601$	−17.2838	+	12.5574i	−0.705019	+	0.512226i	−0.881563	−	0.472066i	$-0.843508\pi$
$601$	−17.2838	+	12.5574i	−0.705019	+	0.512226i	0.176544	+	0.984293i	$0.443508\pi$
$602$	0.477805	−	4.54602i	0.0194739	−	0.185282i
$603$	3.74762	+	0.796582i	0.152615	+	0.0324393i
$604$	1.76093	+	3.05002i	0.0716513	+	0.124104i
$605$	14.9981	+	26.6396i	0.609761	+	1.08305i
$606$	13.5324	−	23.4388i	0.549717	−	0.952138i
$607$	4.95382	+	15.2463i	0.201069	+	0.618828i	0.999852	+	0.0172081i	$0.00547779\pi$
$607$	4.95382	+	15.2463i	0.201069	+	0.618828i	−0.798783	+	0.601620i	$0.794522\pi$
$608$	−3.85123	−	2.04158i	−0.156188	−	0.0827969i
$609$	−6.75887	+	4.91060i	−0.273883	+	0.198988i
$610$	−18.7659	−	20.8416i	−0.759808	−	0.843852i
$611$	−0.905060	−	1.00517i	−0.0366148	−	0.0406648i
$612$	−2.90120	−	1.29170i	−0.117274	−	0.0522138i
$613$	31.9613	−	14.2301i	1.29090	−	0.574747i	0.357613	−	0.933870i	$-0.383591\pi$
$613$	31.9613	−	14.2301i	1.29090	−	0.574747i	0.933290	+	0.359123i	$0.116924\pi$
$614$	−13.5202	+	15.0157i	−0.545631	+	0.605985i
$615$	18.0037			0.725978
$616$	−15.8040	−	1.74762i	−0.636760	−	0.0704136i
$617$	−1.47558	−	2.55578i	−0.0594047	−	0.102892i	0.834794	−	0.550563i	$-0.185587\pi$
$617$	−1.47558	−	2.55578i	−0.0594047	−	0.102892i	−0.894198	+	0.447671i	$0.852254\pi$
$618$	−5.57981	+	6.19701i	−0.224453	+	0.249280i
$619$	7.68044	+	5.58017i	0.308703	+	0.224286i	0.731340	−	0.682013i	$-0.238895\pi$
$619$	7.68044	+	5.58017i	0.308703	+	0.224286i	−0.422637	+	0.906299i	$0.638895\pi$
$620$	13.1820	−	9.57727i	0.529401	−	0.384632i
$621$	27.5699	−	5.86017i	1.10634	−	0.235161i
$622$	8.58589	+	9.53560i	0.344263	+	0.382343i
$623$	9.77927	+	4.35401i	0.391798	+	0.174440i
$624$	−3.61525	+	1.60961i	−0.144726	+	0.0644361i
$625$	30.5180	+	6.48680i	1.22072	+	0.259472i
$626$	33.3239			1.33189
$627$	−14.5149	+	17.1525i	−0.579668	+	0.685005i
$628$	−18.3670			−0.732924
$629$	−35.8746	−	7.62537i	−1.43041	−	0.304044i
$630$	−7.11162	+	3.16630i	−0.283334	+	0.126148i
$631$	9.38135	+	4.17685i	0.373466	+	0.166278i	0.584882	−	0.811118i	$-0.301141\pi$
$631$	9.38135	+	4.17685i	0.373466	+	0.166278i	−0.211416	+	0.977396i	$0.567808\pi$
$632$	10.6798	+	11.8611i	0.424820	+	0.471811i
$633$	−28.2595	+	6.00675i	−1.12322	+	0.238747i
$634$	−5.86661	+	4.26235i	−0.232993	+	0.169279i
$635$	−16.1766	−	11.7530i	−0.641950	−	0.466404i
$636$	−6.96936	+	7.74026i	−0.276353	+	0.306921i
$637$	−20.3483	−	35.2443i	−0.806228	−	1.39643i
$638$	−2.74994	−	2.50315i	−0.108871	−	0.0991006i
$639$	8.83345			0.349446
$640$	−1.85966	+	2.06536i	−0.0735095	+	0.0816406i
$641$	0.770337	−	0.342976i	0.0304265	−	0.0135467i	−0.391467	−	0.920192i	$-0.628032\pi$
$641$	0.770337	−	0.342976i	0.0304265	−	0.0135467i	0.421893	+	0.906645i	$0.361366\pi$
$642$	9.32102	+	4.14998i	0.367871	+	0.163787i
$643$	−5.28706	−	5.87188i	−0.208501	−	0.231564i	0.629819	−	0.776742i	$-0.283129\pi$
$643$	−5.28706	−	5.87188i	−0.208501	−	0.231564i	−0.838321	+	0.545177i	$0.816462\pi$
$644$	16.2303	+	18.0256i	0.639563	+	0.710307i
$645$	−3.33206	+	2.42088i	−0.131200	+	0.0953222i
$646$	−20.9334	−	11.0970i	−0.823615	−	0.436607i
$647$	−11.8883	−	36.5883i	−0.467376	−	1.43843i	−0.855970	−	0.517025i	$-0.827039\pi$
$647$	−11.8883	−	36.5883i	−0.467376	−	1.43843i	0.388595	−	0.921409i	$-0.372961\pi$
$648$	−3.45293	+	5.98065i	−0.135644	+	0.234942i
$649$	−0.0794427	+	14.6739i	−0.00311840	+	0.576000i
$650$	3.46793	+	6.00662i	0.136023	+	0.235599i
$651$	42.7305	+	9.08266i	1.67474	+	0.355977i
$652$	−0.257321	+	2.44825i	−0.0100775	+	0.0958807i
$653$	13.4413	−	9.76570i	0.526000	−	0.382161i	−0.292859	−	0.956156i	$-0.594607\pi$
$653$	13.4413	−	9.76570i	0.526000	−	0.382161i	0.818859	+	0.573994i	$0.194607\pi$
$654$	−1.71120	+	5.26654i	−0.0669133	+	0.205938i
$655$	−3.31067	+	0.703704i	−0.129358	+	0.0274960i
$656$	−3.80753	−	1.69522i	−0.148659	−	0.0661873i
$657$	4.99737	+	3.63080i	0.194966	+	0.141651i
$658$	−0.786999	−	2.42213i	−0.0306804	−	0.0944246i
$659$	−6.02698	−	10.4390i	−0.234778	−	0.406647i	0.724430	−	0.689348i	$-0.242103\pi$
$659$	−6.02698	−	10.4390i	−0.234778	−	0.406647i	−0.959208	+	0.282701i	$0.908770\pi$
$660$	8.35811	+	11.6359i	0.325339	+	0.452927i
$661$	3.41377	+	5.91282i	0.132780	+	0.229982i	0.924747	−	0.380582i	$-0.124276\pi$
$661$	3.41377	+	5.91282i	0.132780	+	0.229982i	−0.791967	+	0.610564i	$0.790943\pi$
$662$	32.6564	+	6.94132i	1.26923	+	0.269782i
$663$	−19.6508	+	8.74910i	−0.763173	+	0.339787i
$664$	7.24934	−	5.26696i	0.281329	−	0.204398i
$665$	−54.5503	+	19.9317i	−2.11537	+	0.772920i
$666$	1.21823	−	3.74933i	0.0472055	−	0.145284i
$667$	0.592957	+	5.64161i	0.0229594	+	0.218444i
$668$	−2.87195	+	1.27867i	−0.111119	+	0.0494734i
$669$	27.8425	−	30.9222i	1.07645	−	1.19552i
$670$	9.11250	−	15.7833i	0.352047	−	0.609763i
$671$	33.3032	−	3.31812i	1.28566	−	0.128095i
$672$	−7.45133			−0.287441
$673$	13.1622	+	40.5092i	0.507367	+	1.56152i	0.796754	+	0.604304i	$0.206549\pi$
$673$	13.1622	+	40.5092i	0.507367	+	1.56152i	−0.289387	+	0.957212i	$0.593451\pi$
$674$	−0.913359	+	8.69003i	−0.0351813	+	0.334728i
$675$	13.8634	+	6.17240i	0.533604	+	0.237576i
$676$	−2.01391	+	6.19816i	−0.0774579	+	0.238391i
$677$	12.6095	−	38.8082i	0.484624	−	1.49152i	−0.347900	−	0.937532i	$-0.613105\pi$
$677$	12.6095	−	38.8082i	0.484624	−	1.49152i	0.832525	−	0.553988i	$-0.186895\pi$
$678$	−12.2709	−	5.46335i	−0.471261	−	0.209819i
$679$	−7.59730	+	3.38253i	−0.291557	+	0.129810i
$680$	−10.1082	+	11.2263i	−0.387633	+	0.430510i
$681$	20.2658	−	35.1014i	0.776586	−	1.34509i
$682$	−0.105269	+	19.4442i	−0.00403094	+	0.744557i
$683$	−23.2924			−0.891257			−0.445629	−	0.895218i	$-0.647020\pi$
$683$	−23.2924			−0.891257			−0.445629	+	0.895218i	$0.647020\pi$
$684$	1.42148	−	2.11311i	0.0543517	−	0.0807968i
$685$	24.0673	+	17.4859i	0.919565	+	0.668103i
$686$	−4.50187	−	42.8325i	−0.171882	−	1.63535i
$687$	6.73197	+	7.47662i	0.256841	+	0.285251i
$688$	0.932636	−	0.198238i	0.0355564	−	0.00755775i
$689$	−1.78351	−	16.9689i	−0.0679462	−	0.646465i
$690$	2.28449	−	21.7355i	0.0869690	−	0.827455i
$691$	−5.62220	−	17.3033i	−0.213878	−	0.658250i	−0.999231	−	0.0392019i	$-0.987518\pi$
$691$	−5.62220	−	17.3033i	−0.213878	−	0.658250i	0.785353	−	0.619048i	$-0.212482\pi$
$692$	5.97152			0.227003
$693$	1.98065	−	9.07632i	0.0752386	−	0.344781i
$694$	11.6173	+	20.1218i	0.440988	+	0.763814i
$695$	5.09904	+	15.6932i	0.193418	+	0.595278i
$696$	−1.40982	−	1.02430i	−0.0534392	−	0.0388259i
$697$	−20.6959	−	9.21442i	−0.783914	−	0.349021i
$698$	12.3037	+	13.6647i	0.465702	+	0.517215i
$699$	4.78342	−	1.01675i	0.180926	−	0.0384569i
$700$	1.36509	+	12.9879i	0.0515954	+	0.490897i
$701$	−18.1068	+	8.06165i	−0.683883	+	0.304484i	−0.719111	−	0.694895i	$-0.755451\pi$
$701$	−18.1068	+	8.06165i	−0.683883	+	0.304484i	0.0352282	+	0.999379i	$0.488784\pi$
$702$	−4.38319	−	13.4901i	−0.165433	−	0.509150i
$703$	10.9837	−	27.2836i	0.414260	−	1.02902i
$704$	−0.671992	−	3.24783i	−0.0253266	−	0.122407i
$705$	−1.14736	+	1.98729i	−0.0432122	+	0.0748457i
$706$	−10.3403	−	2.19790i	−0.389163	−	0.0827191i
$707$	−8.72617	+	83.0240i	−0.328182	+	3.12244i
$708$	0.718811	+	6.83903i	0.0270146	+	0.257026i
$709$	−28.9667	+	6.15707i	−1.08787	+	0.231234i	−0.716735	−	0.697346i	$-0.754364\pi$
$709$	−28.9667	+	6.15707i	−1.08787	+	0.231234i	−0.371134	+	0.928579i	$0.621031\pi$
$710$	12.9846	−	39.9625i	0.487304	−	1.49977i
$711$	−7.54427	+	5.48123i	−0.282932	+	0.205562i
$712$	−0.233401	+	2.22066i	−0.00874706	+	0.0832227i
$713$	19.8480	−	22.0435i	0.743315	−	0.825535i
$714$	−40.5019			−1.51575
$715$	−23.3272	−	2.57955i	−0.872389	−	0.0964697i
$716$	−10.9963	−	19.0461i	−0.410950	−	0.711786i
$717$	−42.8476	−	9.10755i	−1.60017	−	0.340128i
$718$	2.66546	−	25.3602i	0.0994743	−	0.946434i
$719$	4.87330	+	46.3664i	0.181744	+	1.72917i	0.582362	+	0.812929i	$0.302129\pi$
$719$	4.87330	+	46.3664i	0.181744	+	1.72917i	−0.400619	+	0.916245i	$0.631205\pi$
$720$	−1.08653	−	1.20671i	−0.0404924	−	0.0449714i
$721$	7.94831	−	24.4624i	0.296010	−	0.911027i
$722$	11.6602	−	15.0013i	0.433947	−	0.558292i
$723$	34.9068	+	25.3612i	1.29820	+	0.943195i
$724$	−7.22115	−	1.53490i	−0.268372	−	0.0570442i
$725$	−1.52710	+	2.64502i	−0.0567152	+	0.0982336i
$726$	−17.0959	−	0.185116i	−0.634489	−	0.00687030i
$727$	11.8725	−	20.5637i	0.440326	−	0.762667i	−0.557387	−	0.830252i	$-0.688196\pi$
$727$	11.8725	−	20.5637i	0.440326	−	0.762667i	0.997713	+	0.0675855i	$0.0215295\pi$
$728$	8.16777	−	9.07122i	0.302718	−	0.336202i
$729$	−24.2792	−	17.6399i	−0.899230	−	0.653329i
$730$	23.7715	−	17.2710i	0.879824	−	0.639230i
$731$	5.06936	−	1.07753i	0.187497	−	0.0398537i
$732$	15.3414	−	3.26091i	0.567034	−	0.120527i
$733$	13.5291	−	9.82948i	0.499709	−	0.363060i	−0.309197	−	0.950998i	$-0.600060\pi$
$733$	13.5291	−	9.82948i	0.499709	−	0.363060i	0.808906	+	0.587938i	$0.200060\pi$
$734$	−29.4928	−	21.4278i	−1.08860	−	0.790914i
$735$	−46.1990	+	51.3092i	−1.70408	+	1.89257i
$736$	−2.52974	+	4.38165i	−0.0932476	+	0.161510i
$737$	8.73846	+	19.9164i	0.321885	+	0.733630i
$738$	1.21756	−	2.10887i	0.0448189	−	0.0776287i
$739$	0.323564	+	0.0687757i	0.0119025	+	0.00252995i	0.213859	−	0.976865i	$-0.431397\pi$
$739$	0.323564	+	0.0687757i	0.0119025	+	0.00252995i	−0.201957	+	0.979394i	$0.564730\pi$
$740$	−15.1712	−	11.0226i	−0.557706	−	0.405197i
$741$	−4.19398	−	16.7322i	−0.154070	−	0.614674i
$742$	9.92769	−	30.5543i	0.364457	−	1.12168i
$743$	5.71626	+	6.34855i	0.209709	+	0.232906i	0.838818	−	0.544411i	$-0.183247\pi$
$743$	5.71626	+	6.34855i	0.209709	+	0.232906i	−0.629109	+	0.777317i	$0.716580\pi$
$744$	0.952488	+	9.06232i	0.0349199	+	0.332241i
$745$	2.68330	−	25.5299i	0.0983085	−	0.935343i
$746$	−22.5242	−	4.78766i	−0.824669	−	0.175289i
$747$	2.61769	+	4.53396i	0.0957761	+	0.165889i
$748$	−3.65263	−	17.6537i	−0.133553	−	0.645482i
$749$	−31.4715			−1.14994
$750$	−6.57839	+	7.30605i	−0.240209	+	0.266779i
$751$	−2.78283	+	26.4768i	−0.101547	+	0.966153i	0.818543	+	0.574445i	$0.194782\pi$
$751$	−2.78283	+	26.4768i	−0.101547	+	0.966153i	−0.920090	+	0.391708i	$0.871884\pi$
$752$	0.429774	−	0.312249i	0.0156723	−	0.0113866i
$753$	10.2034	−	31.4029i	0.371833	−	1.14438i
$754$	2.79235	−	0.593533i	0.101691	−	0.0216152i
$755$	1.02313	+	9.73441i	0.0372354	+	0.354271i
$756$	2.79170	−	26.5612i	0.101533	−	0.966022i
$757$	33.8126	+	7.18710i	1.22894	+	0.261220i	0.776237	−	0.630441i	$-0.217126\pi$
$757$	33.8126	+	7.18710i	1.22894	+	0.261220i	0.452704	+	0.891661i	$0.350459\pi$
$758$	10.4208	−	18.0493i	0.378500	−	0.655581i
$759$	19.2874	+	17.5564i	0.700087	+	0.637258i
$760$	−7.47023	−	9.53692i	−0.270974	−	0.345940i
$761$	−8.07527	−	24.8531i	−0.292728	−	0.900925i	−0.983975	−	0.178306i	$-0.942938\pi$
$761$	−8.07527	−	24.8531i	−0.292728	−	0.900925i	0.691247	−	0.722619i	$-0.257062\pi$
$762$	10.2156	−	4.54827i	0.370071	−	0.164766i
$763$	−1.78541	−	16.9870i	−0.0646361	−	0.614971i
$764$	−12.9897	+	2.76104i	−0.469950	+	0.0998910i
$765$	−5.90584	−	6.55910i	−0.213526	−	0.237145i
$766$	11.4765	+	5.10968i	0.414664	+	0.184620i
$767$	−9.11373	−	6.62151i	−0.329078	−	0.239089i
$768$	−0.480294	−	1.47819i	−0.0173311	−	0.0533397i
$769$	−5.61498	−	9.72542i	−0.202481	−	0.350708i	0.746846	−	0.664997i	$-0.231567\pi$
$769$	−5.61498	−	9.72542i	−0.202481	−	0.350708i	−0.949327	+	0.314289i	$0.898234\pi$
$770$	−38.1498	−	22.3021i	−1.37482	−	0.803711i
$771$	−22.2441			−0.801100
$772$	−2.39695	−	7.37704i	−0.0862679	−	0.265505i
$773$	−4.46543	+	42.4857i	−0.160610	+	1.52811i	0.556324	+	0.830965i	$0.312211\pi$
$773$	−4.46543	+	42.4857i	−0.160610	+	1.52811i	−0.716935	+	0.697140i	$0.754455\pi$
$774$	0.0582303	+	0.554024i	0.00209304	+	0.0199140i
$775$	15.6214	−	3.32044i	0.561138	−	0.119274i
$776$	−1.16073	−	1.28912i	−0.0416677	−	0.0462767i
$777$	−5.25544	−	50.0022i	−0.188538	−	1.79382i
$778$	11.8395	+	8.60190i	0.424467	+	0.308393i
$779$	10.1402	−	15.0740i	0.363311	−	0.540083i
$780$	−10.9984			−0.393808
$781$	29.2539	+	40.7265i	1.04679	+	1.45731i
$782$	−13.7505	+	23.8165i	−0.491716	+	0.851678i
$783$	4.17944	−	4.64173i	0.149361	−	0.165882i
$784$	14.6017	−	6.50111i	0.521491	−	0.232183i
$785$	−46.6328	−	20.7623i	−1.66440	−	0.741037i
$786$	0.584919	−	1.80019i	0.0208634	−	0.0642108i
$787$	12.7033	−	39.0966i	0.452822	−	1.39364i	−0.420851	−	0.907130i	$-0.638268\pi$
$787$	12.7033	−	39.0966i	0.452822	−	1.39364i	0.873673	−	0.486513i	$-0.161732\pi$
$788$	17.2086	+	7.66177i	0.613031	+	0.272939i
$789$	−0.764310	+	7.27193i	−0.0272102	+	0.258887i
$790$	13.7075	+	42.1873i	0.487691	+	1.50096i
$791$	41.4314			1.47313
$792$	1.92823	−	0.192116i	0.0685165	−	0.00682655i
$793$	−12.8466	+	22.2510i	−0.456197	+	0.790156i
$794$	10.8118	−	12.0077i	0.383695	−	0.426137i
$795$	−26.4445	+	11.7738i	−0.937889	+	0.417575i
$796$	1.05085	+	9.99815i	0.0372463	+	0.354375i
$797$	−5.35821	+	16.4909i	−0.189797	+	0.584136i	−0.999998	−	0.00201647i	$-0.999358\pi$
$797$	−5.35821	+	16.4909i	−0.189797	+	0.584136i	0.810201	+	0.586153i	$0.199358\pi$
$798$	5.60013	−	31.9932i	0.198243	−	1.13255i
$799$	2.33605	−	1.69724i	0.0826434	−	0.0600440i
$800$	−2.48855	+	1.10797i	−0.0879836	+	0.0391728i
$801$	−1.27608	−	0.271240i	−0.0450881	−	0.00958378i
$802$	6.40885	+	11.1005i	0.226304	+	0.391971i
$803$	−0.189835	+	35.0644i	−0.00669913	+	1.23740i
$804$	5.09612	+	8.82675i	0.179726	+	0.311295i
$805$	20.8315	+	64.1128i	0.734214	+	2.25968i
$806$	−12.0765	−	8.77409i	−0.425377	−	0.309054i
$807$	−24.8725	−	11.0739i	−0.875552	−	0.389821i
$808$	−17.0328	+	3.62042i	−0.599210	+	0.127366i
$809$	−12.9002	+	39.7027i	−0.453547	+	1.39587i	0.419286	+	0.907854i	$0.362280\pi$
$809$	−12.9002	+	39.7027i	−0.453547	+	1.39587i	−0.872833	+	0.488019i	$0.837720\pi$
$810$	−15.5274	+	11.2813i	−0.545576	+	0.396384i
$811$	−3.71185	+	35.3159i	−0.130341	+	1.24011i	0.712394	+	0.701780i	$0.247611\pi$
$811$	−3.71185	+	35.3159i	−0.130341	+	1.24011i	−0.842735	+	0.538329i	$0.819056\pi$
$812$	5.25770	+	1.11756i	0.184509	+	0.0392186i
$813$	9.08409	+	15.7341i	0.318593	+	0.551819i
$814$	21.3207	−	6.80011i	0.747288	−	0.238344i
$815$	−3.42084	+	5.92508i	−0.119827	+	0.207546i
$816$	−2.61065	−	8.03476i	−0.0913910	−	0.281273i
$817$	0.150225	+	4.15337i	0.00525569	+	0.145308i
$818$	−4.85345	+	3.52624i	−0.169697	+	0.123292i
$819$	4.77210	+	5.29996i	0.166751	+	0.185195i
$820$	−7.75081	−	8.60814i	−0.270670	−	0.300609i
$821$	3.50564	+	1.56081i	0.122348	+	0.0544727i	0.466998	−	0.884259i	$-0.345336\pi$
$821$	3.50564	+	1.56081i	0.122348	+	0.0544727i	−0.344650	+	0.938731i	$0.612002\pi$
$822$	−15.1986	+	6.76683i	−0.530110	+	0.236020i
$823$	−7.41868	+	8.23928i	−0.258599	+	0.287203i	−0.858438	−	0.512917i	$-0.828565\pi$
$823$	−7.41868	+	8.23928i	−0.258599	+	0.287203i	0.599839	+	0.800121i	$0.295231\pi$
$824$	5.36517			0.186905
$825$	2.84515	+	13.7510i	0.0990555	+	0.478749i
$826$	−10.6056	−	18.3694i	−0.369015	−	0.639153i
$827$	−35.1278	+	39.0133i	−1.22151	+	1.35663i	−0.307185	+	0.951650i	$0.599387\pi$
$827$	−35.1278	+	39.0133i	−1.22151	+	1.35663i	−0.914327	+	0.404977i	$0.867280\pi$
$828$	−2.39150	−	1.73753i	−0.0831105	−	0.0603833i
$829$	27.7338	−	20.1498i	0.963236	−	0.699832i	0.00933562	−	0.999956i	$-0.497028\pi$
$829$	27.7338	−	20.1498i	0.963236	−	0.699832i	0.953900	+	0.300125i	$0.0970283\pi$
$830$	24.3595	−	5.17777i	0.845530	−	0.179723i
$831$	−7.71783	−	8.57152i	−0.267729	−	0.297343i
$832$	2.32602	+	1.03561i	0.0806403	+	0.0359034i
$833$	79.3681	−	35.3369i	2.74994	−	1.22435i
$834$	−9.02636	−	1.91861i	−0.312557	−	0.0664361i
$835$	−8.73714			−0.302361
$836$	14.4500	−	0.444329i	0.499764	−	0.0153675i
$837$	−32.6606			−1.12892
$838$	10.2239	+	2.17316i	0.353179	+	0.0750704i
$839$	−45.8191	+	20.4000i	−1.58185	+	0.704285i	−0.994469	−	0.105026i	$-0.966507\pi$
$839$	−45.8191	+	20.4000i	−1.58185	+	0.704285i	−0.587380	+	0.809311i	$0.699841\pi$
$840$	−18.9185	−	8.42306i	−0.652751	−	0.290623i
$841$	−18.5636	−	20.6170i	−0.640125	−	0.710931i
$842$	28.3146	−	6.01845i	0.975784	−	0.207409i
$843$	2.14735	−	1.56014i	0.0739588	−	0.0537342i
$844$	15.0381	+	10.9258i	0.517633	+	0.376083i
$845$	−12.1197	+	13.4602i	−0.416929	+	0.463047i
$846$	0.155188	+	0.268794i	0.00533549	+	0.00924134i
$847$	48.4055	−	20.9265i	1.66323	−	0.719043i
$848$	6.70127			0.230122
$849$	31.3914	−	34.8637i	1.07735	−	1.19652i
$850$	−13.5266	+	6.02242i	−0.463958	+	0.206567i
$851$	−31.1873	−	13.8855i	−1.06909	−	0.475988i
$852$	15.7239	+	17.4631i	0.538692	+	0.598278i
$853$	20.8197	+	23.1226i	0.712854	+	0.791704i	0.985367	−	0.170448i	$-0.0545214\pi$
$853$	20.8197	+	23.1226i	0.712854	+	0.791704i	−0.272513	+	0.962152i	$0.587855\pi$
$854$	−39.1383	+	28.4356i	−1.33928	+	0.973047i
$855$	5.99774	−	3.75821i	0.205118	−	0.128528i
$856$	−2.02857	−	6.24330i	−0.0693352	−	0.213392i
$857$	−5.36819	+	9.29797i	−0.183374	+	0.317613i	−0.943027	−	0.332715i	$-0.892035\pi$
$857$	−5.36819	+	9.29797i	−0.183374	+	0.317613i	0.759654	+	0.650328i	$0.225369\pi$
$858$	7.77215	−	10.5766i	0.265337	−	0.361078i
$859$	−20.9386	−	36.2668i	−0.714417	−	1.23741i	−0.963184	−	0.268843i	$-0.913359\pi$
$859$	−20.9386	−	36.2668i	−0.714417	−	1.23741i	0.248767	−	0.968563i	$-0.419975\pi$
$860$	2.59200	+	0.550946i	0.0883864	+	0.0187871i
$861$	3.24625	−	30.8860i	0.110632	−	1.05259i
$862$	−6.60511	+	4.79889i	−0.224971	+	0.163451i
$863$	−7.54958	+	23.2352i	−0.256991	+	0.790936i	0.736440	+	0.676503i	$0.236505\pi$
$863$	−7.54958	+	23.2352i	−0.256991	+	0.790936i	−0.993431	+	0.114434i	$0.963495\pi$
$864$	5.44915	−	1.15825i	0.185384	−	0.0394046i
$865$	15.1614	+	6.75027i	0.515501	+	0.229516i
$866$	5.53115	+	4.01862i	0.187956	+	0.136558i
$867$	−6.02525	−	18.5438i	−0.204628	−	0.629781i
$868$	−14.0533	−	24.3411i	−0.477001	−	0.826190i
$869$	−50.2556	−	16.6304i	−1.70481	−	0.564147i
$870$	−2.42159	−	4.19431i	−0.0820995	−	0.142200i
$871$	−16.3318	−	3.47142i	−0.553380	−	0.117625i
$872$	3.25480	−	1.44913i	0.110221	−	0.0490737i
$873$	0.819944	−	0.595724i	0.0277509	−	0.0201622i
$874$	−16.9119	−	14.1548i	−0.572052	−	0.478794i
$875$	9.37077	−	28.8403i	0.316790	−	0.974979i
$876$	1.71766	+	16.3424i	0.0580343	+	0.552159i
$877$	−29.0872	+	12.9505i	−0.982206	+	0.437306i	−0.834069	−	0.551660i	$-0.813994\pi$
$877$	−29.0872	+	12.9505i	−0.982206	+	0.437306i	−0.148137	+	0.988967i	$0.547328\pi$
$878$	−25.9387	+	28.8079i	−0.875389	+	0.972218i
$879$	11.2270	−	19.4457i	0.378677	−	0.655887i
$880$	1.96524	−	9.00569i	0.0662481	−	0.303582i
$881$	23.4275			0.789293			0.394647	−	0.918833i	$-0.370867\pi$
$881$	23.4275			0.789293			0.394647	+	0.918833i	$0.370867\pi$
$882$	2.88578	+	8.88152i	0.0971693	+	0.299056i
$883$	2.39845	−	22.8197i	0.0807143	−	0.767946i	−0.877052	−	0.480396i	$-0.840493\pi$
$883$	2.39845	−	22.8197i	0.0807143	−	0.767946i	0.957766	−	0.287549i	$-0.0928405\pi$
$884$	12.6431	+	5.62909i	0.425235	+	0.189327i
$885$	−5.90589	+	18.1765i	−0.198524	+	0.610995i
$886$	−8.48406	+	26.1113i	−0.285028	+	0.877225i
$887$	−16.5052	−	7.34858i	−0.554190	−	0.246741i	0.110480	−	0.993878i	$-0.464761\pi$
$887$	−16.5052	−	7.34858i	−0.554190	−	0.246741i	−0.664670	+	0.747137i	$0.731428\pi$
$888$	9.58068	−	4.26559i	0.321506	−	0.143144i
$889$	−23.0796	+	25.6324i	−0.774064	+	0.859685i
$890$	−3.10285	+	5.37429i	−0.104008	+	0.180147i
$891$	0.123999	−	22.9038i	0.00415411	−	0.767306i
$892$	−26.7715			−0.896375
$893$	1.01768	+	2.07996i	0.0340553	+	0.0696032i
$894$	11.6143	+	8.43832i	0.388442	+	0.282220i
$895$	−6.38899	−	60.7872i	−0.213560	−	2.03189i
$896$	3.20789	+	3.56273i	0.107168	+	0.119022i
$897$	−19.5848	+	4.16288i	−0.653918	+	0.138995i
$898$	−2.12552	−	20.2229i	−0.0709294	−	0.674848i
$899$	0.687095	−	6.53727i	0.0229159	−	0.218030i
$900$	−0.491819	−	1.51366i	−0.0163940	−	0.0504554i
$901$	36.4249			1.21349
$902$	13.7551	−	1.37047i	0.457996	−	0.0456318i
$903$	3.55232	+	6.15279i	0.118214	+	0.204752i
$904$	2.67057	+	8.21916i	0.0888217	+	0.273365i
$905$	−16.5990	−	12.0599i	−0.551770	−	0.400884i
$906$	−5.00066	−	2.22644i	−0.166136	−	0.0739685i
$907$	9.19805	+	10.2155i	0.305416	+	0.339199i	0.876241	−	0.481873i	$-0.160043\pi$
$907$	9.19805	+	10.2155i	0.305416	+	0.339199i	−0.570825	+	0.821072i	$0.693377\pi$
$908$	−25.5078	+	5.42185i	−0.846505	+	0.179930i
$909$	−1.06346	−	10.1182i	−0.0352728	−	0.335598i
$910$	30.9917	−	13.7984i	1.02736	−	0.457412i
$911$	12.9548	+	39.8707i	0.429211	+	1.32097i	0.898904	+	0.438145i	$0.144364\pi$
$911$	12.9548	+	39.8707i	0.429211	+	1.32097i	−0.469694	+	0.882829i	$0.655636\pi$
$912$	6.70777	−	0.951247i	0.222116	−	0.0314989i
$913$	−12.2347	+	27.0840i	−0.404909	+	0.896350i
$914$	−0.0388642	+	0.0673148i	−0.00128551	+	0.00222658i
$915$	42.6371	+	9.06279i	1.40954	+	0.299607i
$916$	0.676614	−	6.43755i	0.0223560	−	0.212703i
$917$	0.610283	+	5.80646i	0.0201533	+	0.191746i
$918$	29.6190	−	6.29571i	0.977573	−	0.207789i
$919$	8.66328	−	26.6628i	0.285775	−	0.879526i	−0.700390	−	0.713760i	$-0.746991\pi$
$919$	8.66328	−	26.6628i	0.285775	−	0.879526i	0.986165	−	0.165765i	$-0.0530094\pi$
$920$	−11.3759	+	8.26510i	−0.375053	+	0.272492i
$921$	3.28271	−	31.2329i	0.108169	−	1.02916i
$922$	13.3423	−	14.8181i	0.439406	−	0.488009i
$923$	−38.4953			−1.26709
$924$	21.4689	−	12.2406i	0.706275	−	0.402686i
$925$	−9.19025	−	15.9180i	−0.302174	−	0.523380i
$926$	−17.5421	−	3.72869i	−0.576470	−	0.122532i
$927$	−0.327661	+	3.11748i	−0.0107618	+	0.102392i
$928$	0.117197	+	1.11506i	0.00384718	+	0.0366035i
$929$	0.746553	+	0.829131i	0.0244936	+	0.0272029i	0.755267	−	0.655417i	$-0.227507\pi$
$929$	0.746553	+	0.829131i	0.0244936	+	0.0272029i	−0.730774	+	0.682620i	$0.760840\pi$
$930$	−7.82583	+	24.0854i	−0.256619	+	0.789792i
$931$	16.9392	+	67.5803i	0.555159	+	2.21485i
$932$	−2.54546	−	1.84939i	−0.0833794	−	0.0605787i
$933$	−19.5076	−	4.14647i	−0.638650	−	0.135749i
$934$	16.2521	−	28.1495i	0.531786	−	0.921080i
$935$	10.6821	−	48.9506i	0.349342	−	1.60086i
$936$	−0.743807	+	1.28831i	−0.0243121	+	0.0421098i
$937$	10.0655	−	11.1789i	0.328826	−	0.365198i	−0.555949	−	0.831216i	$-0.687645\pi$
$937$	10.0655	−	11.1789i	0.328826	−	0.365198i	0.884775	+	0.466018i	$0.154312\pi$
$938$	−25.4338	−	18.4787i	−0.830444	−	0.603353i
$939$	−41.9024	+	30.4439i	−1.36743	+	0.993498i
$940$	1.44414	−	0.306962i	0.0471027	−	0.0100120i
$941$	6.90114	−	1.46688i	0.224971	−	0.0478190i	−0.0940469	−	0.995568i	$-0.529980\pi$
$941$	6.90114	−	1.46688i	0.224971	−	0.0478190i	0.319018	+	0.947749i	$0.396647\pi$
$942$	23.0952	−	16.7796i	0.752482	−	0.546710i
$943$	−17.0599	−	12.3948i	−0.555548	−	0.403629i
$944$	2.96051	−	3.28797i	0.0963563	−	0.107014i
$945$	37.1130	−	64.2816i	1.20729	−	2.09108i
$946$	−2.36147	+	2.10324i	−0.0767781	+	0.0683823i
$947$	8.18808	−	14.1822i	0.266077	−	0.460859i	−0.701768	−	0.712405i	$-0.747606\pi$
$947$	8.18808	−	14.1822i	0.266077	−	0.460859i	0.967845	+	0.251547i	$0.0809392\pi$
$948$	−24.2651	−	5.15771i	−0.788094	−	0.167515i
$949$	−21.7780	−	15.8226i	−0.706944	−	0.513625i
$950$	−2.88692	−	11.5176i	−0.0936640	−	0.373680i
$951$	3.48287	−	10.7192i	0.112940	−	0.347593i
$952$	17.4366	+	19.3653i	0.565123	+	0.627632i
$953$	−3.07564	−	29.2627i	−0.0996296	−	0.947912i	−0.924137	−	0.382061i	$-0.875214\pi$
$953$	−3.07564	−	29.2627i	−0.0996296	−	0.947912i	0.824507	−	0.565851i	$-0.191452\pi$
$954$	−0.409259	+	3.89384i	−0.0132502	+	0.126068i
$955$	−36.1012	−	7.67354i	−1.16821	−	0.248310i
$956$	14.0918	+	24.4078i	0.455762	+	0.789404i
$957$	5.74466	+	0.635251i	0.185699	+	0.0205347i
$958$	−27.8533			−0.899899
$959$	34.3374	−	38.1355i	1.10881	−	1.23146i
$960$	0.451526	−	4.29598i	0.0145729	−	0.138652i
$961$	−2.72771	+	1.98180i	−0.0879907	+	0.0639289i
$962$	−5.30893	+	16.3392i	−0.171167	+	0.526797i
$963$	3.75162	−	0.797432i	0.120894	−	0.0256969i
$964$	−2.90176	−	27.6084i	−0.0934594	−	0.889207i
$965$	2.25337	−	21.4394i	0.0725386	−	0.690159i
$966$	−36.8761	−	7.83826i	−1.18647	−	0.252192i
$967$	−22.5129	+	38.9934i	−0.723965	+	1.25394i	0.235434	+	0.971890i	$0.424349\pi$
$967$	−22.5129	+	38.9934i	−0.723965	+	1.25394i	−0.959399	+	0.282054i	$0.908984\pi$
$968$	7.27150	+	8.25381i	0.233715	+	0.265287i
$969$	36.4602	−	5.17052i	1.17127	−	0.166101i
$970$	−1.48979	−	4.58510i	−0.0478343	−	0.147219i
$971$	0.496329	−	0.220980i	0.0159280	−	0.00709159i	−0.398757	−	0.917057i	$-0.630558\pi$
$971$	0.496329	−	0.220980i	0.0159280	−	0.00709159i	0.414685	+	0.909965i	$0.363892\pi$
$972$	0.624990	+	5.94638i	0.0200466	+	0.190730i
$973$	27.8418	−	5.91795i	0.892566	−	0.189721i
$974$	3.49953	+	3.88662i	0.112132	+	0.124535i
$975$	−9.84816	−	4.38468i	−0.315393	−	0.140422i
$976$	−8.16381	−	5.93135i	−0.261317	−	0.189858i
$977$	−0.810395	−	2.49414i	−0.0259268	−	0.0797946i	0.937256	−	0.348642i	$-0.113357\pi$
$977$	−0.810395	−	2.49414i	−0.0259268	−	0.0797946i	−0.963183	+	0.268848i	$0.913357\pi$
$978$	−1.91309	−	3.31357i	−0.0611739	−	0.105956i
$979$	−2.97548	−	6.78162i	−0.0950969	−	0.216741i
$980$	44.4219			1.41901
$981$	0.643254	+	1.97973i	0.0205375	+	0.0632080i
$982$	−3.35206	+	31.8927i	−0.106968	+	1.01774i
$983$	0.793943	+	7.55386i	0.0253228	+	0.240931i	0.999860	+	0.0167066i	$0.00531811\pi$
$983$	0.793943	+	7.55386i	0.0253228	+	0.240931i	−0.974538	+	0.224224i	$0.928015\pi$
$984$	6.33640	−	1.34684i	0.201997	−	0.0429358i
$985$	35.0307	+	38.9056i	1.11617	+	1.23963i
$986$	0.637027	+	6.06091i	0.0202871	+	0.193019i
$987$	3.20239	+	2.32667i	0.101933	+	0.0740588i
$988$	−6.19467	+	9.20872i	−0.197079	+	0.292968i
$989$	4.82408			0.153397
$990$	5.11283	+	1.69191i	0.162496	+	0.0537726i
$991$	23.6432	−	40.9512i	0.751051	−	1.30086i	−0.196262	−	0.980551i	$-0.562880\pi$
$991$	23.6432	−	40.9512i	0.751051	−	1.30086i	0.947314	−	0.320308i	$-0.103786\pi$
$992$	3.92293	−	4.35686i	0.124553	−	0.138330i
$993$	−47.4044	+	21.1058i	−1.50433	+	0.669772i
$994$	−66.2160	−	29.4813i	−2.10024	−	0.935089i
$995$	−8.63397	+	26.5726i	−0.273715	+	0.842409i
$996$	−4.30376	+	13.2456i	−0.136370	+	0.419704i
$997$	−7.35062	−	3.27271i	−0.232797	−	0.103648i	0.287023	−	0.957924i	$-0.407334\pi$
$997$	−7.35062	−	3.27271i	−0.232797	−	0.103648i	−0.519820	+	0.854276i	$0.674001\pi$
$998$	0.384142	−	3.65487i	0.0121598	−	0.115693i
$999$	11.6158	+	35.7497i	0.367507	+	1.13107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.49.2	✓	64
11.9	even	5	inner	418.2.n.d.163.7	yes	64
19.7	even	3	inner	418.2.n.d.159.7	yes	64
209.64	even	15	inner	418.2.n.d.273.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.49.2	✓	64	1.1	even	1	trivial
418.2.n.d.159.7	yes	64	19.7	even	3	inner
418.2.n.d.163.7	yes	64	11.9	even	5	inner
418.2.n.d.273.2	yes	64	209.64	even	15	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(-1.41989 + 0.632177i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.85966 + 2.06536i) q^{5} +(-1.52030 + 0.323150i) q^{6} +(3.87852 - 2.81791i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.390947 + 0.434190i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(-1.41989 + 0.632177i) q^{3} +(0.913545 + 0.406737i) q^{4} +(1.85966 + 2.06536i) q^{5} +(-1.52030 + 0.323150i) q^{6} +(3.87852 - 2.81791i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.390947 + 0.434190i) q^{9} +(1.38961 + 2.40687i) q^{10} +(-3.29653 - 0.364534i) q^{11} -1.55426 q^{12} +(1.70370 - 1.89216i) q^{13} +(4.37965 - 1.94994i) q^{14} +(-3.94619 - 1.75696i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.63707 + 4.03938i) q^{17} +(-0.472677 + 0.343420i) q^{18} +(-3.69367 + 2.31447i) q^{19} +(0.858826 + 2.64319i) q^{20} +(-3.72567 + 6.45304i) q^{21} +(-3.14870 - 1.04196i) q^{22} +(2.52974 + 4.38165i) q^{23} +(-1.52030 - 0.323150i) q^{24} +(-0.284742 + 2.70914i) q^{25} +(2.05988 - 1.49659i) q^{26} +(1.72150 - 5.29823i) q^{27} +(4.68936 - 0.996754i) q^{28} +(1.02427 + 0.456032i) q^{29} +(-3.49466 - 2.53902i) q^{30} +(-1.81168 - 5.57579i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.91117 - 1.56639i) q^{33} +(2.71776 + 4.70730i) q^{34} +(13.0328 + 2.77020i) q^{35} +(-0.533749 + 0.237640i) q^{36} +(-5.45882 + 3.96606i) q^{37} +(-4.09416 + 1.49594i) q^{38} +(-1.22290 + 3.76370i) q^{39} +(0.290507 + 2.76399i) q^{40} +(-3.80753 + 1.69522i) q^{41} +(-4.98591 + 5.53742i) q^{42} +(0.476736 - 0.825730i) q^{43} +(-2.86326 - 1.67384i) q^{44} -1.62379 q^{45} +(1.56347 + 4.81186i) q^{46} +(0.0555287 - 0.528320i) q^{47} +(-1.41989 - 0.632177i) q^{48} +(4.93920 - 15.2013i) q^{49} +(-0.841780 + 2.59073i) q^{50} +(-7.71785 - 3.43621i) q^{51} +(2.32602 - 1.03561i) q^{52} +(4.48402 - 4.98001i) q^{53} +(2.78545 - 4.82453i) q^{54} +(-5.37753 - 7.48644i) q^{55} +4.79412 q^{56} +(3.78146 - 5.62135i) q^{57} +(0.907068 + 0.659024i) q^{58} +(-0.462476 - 4.40017i) q^{59} +(-2.89041 - 3.21012i) q^{60} +(-9.87051 + 2.09804i) q^{61} +(-0.612822 - 5.83062i) q^{62} +(-0.292786 + 2.78567i) q^{63} +(0.309017 + 0.951057i) q^{64} +7.07630 q^{65} +(5.12952 - 0.511072i) q^{66} +(-3.27880 - 5.67905i) q^{67} +(1.67967 + 5.16949i) q^{68} +(-6.36194 - 4.62222i) q^{69} +(12.1720 + 5.41932i) q^{70} +(-10.1166 - 11.2356i) q^{71} +(-0.571493 + 0.121475i) q^{72} +(-1.10513 - 10.5146i) q^{73} +(-6.16412 + 2.74444i) q^{74} +(-1.30835 - 4.02669i) q^{75} +(-4.31572 + 0.612024i) q^{76} +(-13.8129 + 7.87548i) q^{77} +(-1.97869 + 3.42720i) q^{78} +(15.6120 + 3.31842i) q^{79} +(-0.290507 + 2.76399i) q^{80} +(0.721859 + 6.86803i) q^{81} +(-4.07678 + 0.866547i) q^{82} +(2.76900 - 8.52211i) q^{83} +(-6.02825 + 4.37978i) q^{84} +(-1.57906 + 15.0238i) q^{85} +(0.637997 - 0.708567i) q^{86} -1.74264 q^{87} +(-2.45268 - 2.23257i) q^{88} +(1.11645 + 1.93374i) q^{89} +(-1.58830 - 0.337604i) q^{90} +(1.27593 - 12.1397i) q^{91} +(0.528861 + 5.03177i) q^{92} +(6.09728 + 6.77171i) q^{93} +(0.164159 - 0.505230i) q^{94} +(-11.6492 - 3.32464i) q^{95} +(-1.25743 - 0.913574i) q^{96} +(-1.69678 - 0.360661i) q^{97} +(7.99179 - 13.8422i) q^{98} +(1.44704 - 1.28881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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