LMFDB - Embedded newform 78.2.k.a.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(11,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 7]))

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

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

chi := DirichletCharacter("78.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.k (of order $12$, degree $4$, 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:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.4
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	78.59
Dual form			78.2.k.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(1.45865 - 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.428520 + 0.428520i) q^{5} +(1.27970 + 1.16721i) q^{6} +(-0.735180 - 0.196991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(1.45865 - 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.428520 + 0.428520i) q^{5} +(1.27970 + 1.16721i) q^{6} +(-0.735180 - 0.196991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-0.524827 - 0.303009i) q^{10} +(-4.05922 + 1.08766i) q^{11} +(-0.796225 + 1.53819i) q^{12} +(0.601205 + 3.55507i) q^{13} -0.761114i q^{14} +(-0.224822 + 1.02529i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.62362 - 4.54424i) q^{17} +(2.95680 + 0.507306i) q^{18} +(0.882911 - 3.29507i) q^{19} +(0.156849 - 0.585369i) q^{20} +(-1.25636 + 0.399317i) q^{21} +(-2.10121 - 3.63939i) q^{22} +(0.933306 - 1.61653i) q^{23} +(-1.69185 - 0.370982i) q^{24} +4.63274i q^{25} +(-3.27833 + 1.50084i) q^{26} +(-0.713876 - 5.14688i) q^{27} +(0.735180 - 0.196991i) q^{28} +(7.53987 + 4.35315i) q^{29} +(-1.04855 + 0.0482047i) q^{30} +(-2.68240 - 2.68240i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-4.90508 + 5.37782i) q^{33} +(3.71035 - 3.71035i) q^{34} +(0.399453 - 0.230625i) q^{35} +(0.275255 + 2.98735i) q^{36} +(1.52130 + 5.67758i) q^{37} +3.41130 q^{38} +(4.19738 + 4.62407i) q^{39} +0.606018 q^{40} +(2.29545 + 8.56672i) q^{41} +(-0.710879 - 1.11020i) q^{42} +(1.68905 - 0.975173i) q^{43} +(2.97155 - 2.97155i) q^{44} +(0.629688 + 1.70553i) q^{45} +(1.80301 + 0.483115i) q^{46} +(5.73474 + 5.73474i) q^{47} +(-0.0795432 - 1.73022i) q^{48} +(-5.56049 - 3.21035i) q^{49} +(-4.47488 + 1.19904i) q^{50} +(-8.07123 - 4.17798i) q^{51} +(-2.29820 - 2.77818i) q^{52} -9.01501i q^{53} +(4.78674 - 2.02166i) q^{54} +(1.27337 - 2.20554i) q^{55} +(0.380557 + 0.659144i) q^{56} +(-1.78973 - 5.63097i) q^{57} +(-2.25335 + 8.40963i) q^{58} +(2.23614 - 8.34539i) q^{59} +(-0.317946 - 1.00034i) q^{60} +(4.06531 + 7.04132i) q^{61} +(1.89674 - 3.28525i) q^{62} +(-1.45962 + 1.75590i) q^{63} +1.00000i q^{64} +(-1.78105 - 1.26579i) q^{65} +(-6.46410 - 3.34607i) q^{66} +(-0.101205 + 0.0271179i) q^{67} +(4.54424 + 2.62362i) q^{68} +(-0.148476 - 3.22966i) q^{69} +(0.326152 + 0.326152i) q^{70} +(-10.0749 - 2.69957i) q^{71} +(-2.81431 + 1.03906i) q^{72} +(5.57806 - 5.57806i) q^{73} +(-5.09038 + 2.93893i) q^{74} +(4.32697 + 6.75753i) q^{75} +(0.882911 + 3.29507i) q^{76} +3.19851 q^{77} +(-3.38015 + 5.25115i) q^{78} -13.5805 q^{79} +(0.156849 + 0.585369i) q^{80} +(-5.84847 - 6.84072i) q^{81} +(-7.68071 + 4.43446i) q^{82} +(0.996926 - 0.996926i) q^{83} +(0.888378 - 0.973996i) q^{84} +(3.07156 + 0.823023i) q^{85} +(1.37910 + 1.37910i) q^{86} +(15.0638 - 0.692527i) q^{87} +(3.63939 + 2.10121i) q^{88} +(-6.32442 + 1.69462i) q^{89} +(-1.48444 + 1.04965i) q^{90} +(0.258323 - 2.73205i) q^{91} +1.86661i q^{92} +(-6.41802 - 1.40731i) q^{93} +(-4.05507 + 7.02359i) q^{94} +(1.03366 + 1.79035i) q^{95} +(1.65068 - 0.524648i) q^{96} +(4.07638 - 15.2132i) q^{97} +(1.66180 - 6.20192i) q^{98} +(-2.13191 + 12.4257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.45865	−	0.933998i	0.842150	−	0.539244i
$3$	1.45865	−	0.933998i	0.842150	−	0.539244i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.428520	+	0.428520i	−0.191640	+	0.191640i	−0.796404	−	0.604765i	$-0.793267\pi$
$5$	−0.428520	+	0.428520i	−0.191640	+	0.191640i	0.604765	+	0.796404i	$0.293267\pi$
$6$	1.27970	+	1.16721i	0.522435	+	0.476510i
$7$	−0.735180	−	0.196991i	−0.277872	−	0.0744555i	0.117192	−	0.993109i	$-0.462611\pi$
$7$	−0.735180	−	0.196991i	−0.277872	−	0.0744555i	−0.395064	+	0.918654i	$0.629277\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.25529	−	2.72474i	0.418432	−	0.908248i
$10$	−0.524827	−	0.303009i	−0.165965	−	0.0958199i
$11$	−4.05922	+	1.08766i	−1.22390	+	0.327943i	−0.812201	−	0.583377i	$-0.801731\pi$
$11$	−4.05922	+	1.08766i	−1.22390	+	0.327943i	−0.411699	+	0.911320i	$0.635064\pi$
$12$	−0.796225	+	1.53819i	−0.229850	+	0.444037i
$13$	0.601205	+	3.55507i	0.166744	+	0.986000i
$13$	0.601205	+	3.55507i	0.166744	+	0.986000i
$14$		−	0.761114i		−	0.203416i
$15$	−0.224822	+	1.02529i	−0.0580487	+	0.264730i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.62362	−	4.54424i	−0.636320	−	1.10214i	−0.986234	−	0.165357i	$-0.947122\pi$
$17$	−2.62362	−	4.54424i	−0.636320	−	1.10214i	0.349914	−	0.936782i	$-0.386211\pi$
$18$	2.95680	+	0.507306i	0.696923	+	0.119573i
$19$	0.882911	−	3.29507i	0.202554	−	0.755940i	−0.787628	−	0.616151i	$-0.788691\pi$
$19$	0.882911	−	3.29507i	0.202554	−	0.755940i	0.990181	−	0.139789i	$-0.0446424\pi$
$20$	0.156849	−	0.585369i	0.0350725	−	0.130892i
$21$	−1.25636	+	0.399317i	−0.274159	+	0.0871381i
$22$	−2.10121	−	3.63939i	−0.447978	−	0.775921i
$23$	0.933306	−	1.61653i	0.194608	−	0.337071i	−0.752164	−	0.658976i	$-0.770990\pi$
$23$	0.933306	−	1.61653i	0.194608	−	0.337071i	0.946772	+	0.321905i	$0.104323\pi$
$24$	−1.69185	−	0.370982i	−0.345348	−	0.0757264i
$25$			4.63274i			0.926548i
$26$	−3.27833	+	1.50084i	−0.642934	+	0.294339i
$27$	−0.713876	−	5.14688i	−0.137386	−	0.990518i
$28$	0.735180	−	0.196991i	0.138936	−	0.0372278i
$29$	7.53987	+	4.35315i	1.40012	+	0.808359i	0.994404	−	0.105641i	$-0.0336893\pi$
$29$	7.53987	+	4.35315i	1.40012	+	0.808359i	0.405715	+	0.914000i	$0.367023\pi$
$30$	−1.04855	+	0.0482047i	−0.191438	+	0.00880093i
$31$	−2.68240	−	2.68240i	−0.481773	−	0.481773i	0.423925	−	0.905697i	$-0.360652\pi$
$31$	−2.68240	−	2.68240i	−0.481773	−	0.481773i	−0.905697	+	0.423925i	$0.860652\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−4.90508	+	5.37782i	−0.853865	+	0.936158i
$34$	3.71035	−	3.71035i	0.636320	−	0.636320i
$35$	0.399453	−	0.230625i	0.0675200	−	0.0389827i
$36$	0.275255	+	2.98735i	0.0458759	+	0.497891i
$37$	1.52130	+	5.67758i	0.250101	+	0.933389i	0.970751	+	0.240090i	$0.0771769\pi$
$37$	1.52130	+	5.67758i	0.250101	+	0.933389i	−0.720650	+	0.693299i	$0.756156\pi$
$38$	3.41130			0.553387
$39$	4.19738	+	4.62407i	0.672118	+	0.740444i
$40$	0.606018			0.0958199
$41$	2.29545	+	8.56672i	0.358488	+	1.33790i	0.876037	+	0.482243i	$0.160178\pi$
$41$	2.29545	+	8.56672i	0.358488	+	1.33790i	−0.517549	+	0.855654i	$0.673155\pi$
$42$	−0.710879	−	1.11020i	−0.109691	−	0.171307i
$43$	1.68905	−	0.975173i	0.257578	−	0.148712i	−0.365651	−	0.930752i	$-0.619154\pi$
$43$	1.68905	−	0.975173i	0.257578	−	0.148712i	0.623229	+	0.782039i	$0.285820\pi$
$44$	2.97155	−	2.97155i	0.447978	−	0.447978i
$45$	0.629688	+	1.70553i	0.0938684	+	0.254245i
$46$	1.80301	+	0.483115i	0.265839	+	0.0712314i
$47$	5.73474	+	5.73474i	0.836498	+	0.836498i	0.988396	−	0.151898i	$-0.0485386\pi$
$47$	5.73474	+	5.73474i	0.836498	+	0.836498i	−0.151898	+	0.988396i	$0.548539\pi$
$48$	−0.0795432	−	1.73022i	−0.0114811	−	0.249736i
$49$	−5.56049	−	3.21035i	−0.794356	−	0.458622i
$50$	−4.47488	+	1.19904i	−0.632844	+	0.169570i
$51$	−8.07123	−	4.17798i	−1.13020	−	0.585034i
$52$	−2.29820	−	2.77818i	−0.318702	−	0.385265i
$53$		−	9.01501i		−	1.23831i	−0.785270	−	0.619153i	$-0.787476\pi$
$53$		−	9.01501i		−	1.23831i	0.785270	−	0.619153i	$-0.212524\pi$
$54$	4.78674	−	2.02166i	0.651393	−	0.275113i
$55$	1.27337	−	2.20554i	0.171701	−	0.297395i
$56$	0.380557	+	0.659144i	0.0508541	+	0.0880819i
$57$	−1.78973	−	5.63097i	−0.237056	−	0.745841i
$58$	−2.25335	+	8.40963i	−0.295880	+	1.10424i
$59$	2.23614	−	8.34539i	0.291121	−	1.08648i	−0.653129	−	0.757247i	$-0.726544\pi$
$59$	2.23614	−	8.34539i	0.291121	−	1.08648i	0.944249	−	0.329231i	$-0.106789\pi$
$60$	−0.317946	−	1.00034i	−0.0410467	−	0.129144i
$61$	4.06531	+	7.04132i	0.520509	+	0.901548i	0.999716	+	0.0238462i	$0.00759119\pi$
$61$	4.06531	+	7.04132i	0.520509	+	0.901548i	−0.479206	+	0.877702i	$0.659075\pi$
$62$	1.89674	−	3.28525i	0.240886	−	0.417227i
$63$	−1.45962	+	1.75590i	−0.183894	+	0.221222i
$64$			1.00000i			0.125000i
$65$	−1.78105	−	1.26579i	−0.220912	−	0.157002i
$66$	−6.46410	−	3.34607i	−0.795676	−	0.411872i
$67$	−0.101205	+	0.0271179i	−0.0123642	+	0.00331297i	−0.264996	−	0.964250i	$-0.585371\pi$
$67$	−0.101205	+	0.0271179i	−0.0123642	+	0.00331297i	0.252632	+	0.967563i	$0.418704\pi$
$68$	4.54424	+	2.62362i	0.551069	+	0.318160i
$69$	−0.148476	−	3.22966i	−0.0178745	−	0.388805i
$70$	0.326152	+	0.326152i	0.0389827	+	0.0389827i
$71$	−10.0749	−	2.69957i	−1.19567	−	0.320380i	−0.394548	−	0.918875i	$-0.629099\pi$
$71$	−10.0749	−	2.69957i	−1.19567	−	0.320380i	−0.801126	+	0.598496i	$0.795765\pi$
$72$	−2.81431	+	1.03906i	−0.331670	+	0.122454i
$73$	5.57806	−	5.57806i	0.652863	−	0.652863i	−0.300819	−	0.953681i	$-0.597260\pi$
$73$	5.57806	−	5.57806i	0.652863	−	0.652863i	0.953681	+	0.300819i	$0.0972599\pi$
$74$	−5.09038	+	2.93893i	−0.591745	+	0.341644i
$75$	4.32697	+	6.75753i	0.499636	+	0.780292i
$76$	0.882911	+	3.29507i	0.101277	+	0.377970i
$77$	3.19851			0.364505
$78$	−3.38015	+	5.25115i	−0.382726	+	0.594576i
$79$	−13.5805			−1.52793			−0.763963	−	0.645260i	$-0.776749\pi$
$79$	−13.5805			−1.52793			−0.763963	+	0.645260i	$0.776749\pi$
$80$	0.156849	+	0.585369i	0.0175363	+	0.0654462i
$81$	−5.84847	−	6.84072i	−0.649830	−	0.760080i
$82$	−7.68071	+	4.43446i	−0.848193	+	0.489704i
$83$	0.996926	−	0.996926i	0.109427	−	0.109427i	−0.650273	−	0.759700i	$-0.725346\pi$
$83$	0.996926	−	0.996926i	0.109427	−	0.109427i	0.759700	+	0.650273i	$0.225346\pi$
$84$	0.888378	−	0.973996i	0.0969300	−	0.106272i
$85$	3.07156	+	0.823023i	0.333158	+	0.0892694i
$86$	1.37910	+	1.37910i	0.148712	+	0.148712i
$87$	15.0638	−	0.692527i	1.61501	−	0.0742467i
$88$	3.63939	+	2.10121i	0.387961	+	0.223989i
$89$	−6.32442	+	1.69462i	−0.670388	+	0.179630i	−0.577929	−	0.816087i	$-0.696139\pi$
$89$	−6.32442	+	1.69462i	−0.670388	+	0.179630i	−0.0924582	+	0.995717i	$0.529472\pi$
$90$	−1.48444	+	1.04965i	−0.156473	+	0.110643i
$91$	0.258323	−	2.73205i	0.0270796	−	0.286397i
$92$			1.86661i			0.194608i
$93$	−6.41802	−	1.40731i	−0.665518	−	0.145932i
$94$	−4.05507	+	7.02359i	−0.418249	+	0.724428i
$95$	1.03366	+	1.79035i	0.106051	+	0.183686i
$96$	1.65068	−	0.524648i	0.168472	−	0.0535466i
$97$	4.07638	−	15.2132i	0.413893	−	1.54467i	−0.373148	−	0.927772i	$-0.621722\pi$
$97$	4.07638	−	15.2132i	0.413893	−	1.54467i	0.787042	−	0.616900i	$-0.211612\pi$
$98$	1.66180	−	6.20192i	0.167867	−	0.626489i
$99$	−2.13191	+	12.4257i	−0.214265	+	1.24883i
$100$	−2.31637	−	4.01207i	−0.231637	−	0.401207i
$101$	−1.63630	+	2.83416i	−0.162818	+	0.282009i	−0.935878	−	0.352323i	$-0.885392\pi$
$101$	−1.63630	+	2.83416i	−0.162818	+	0.282009i	0.773060	+	0.634333i	$0.218725\pi$
$102$	1.94663	−	8.87755i	0.192745	−	0.879009i
$103$		−	4.79880i		−	0.472840i	−0.971651	−	0.236420i	$-0.924026\pi$
$103$		−	4.79880i		−	0.472840i	0.971651	−	0.236420i	$-0.0759741\pi$
$104$	2.08870	−	2.93893i	0.204814	−	0.288186i
$105$	0.367258	−	0.709488i	0.0358407	−	0.0692390i
$106$	8.70783	−	2.33326i	0.845779	−	0.226626i
$107$	2.70638	+	1.56253i	0.261635	+	0.151055i	0.625080	−	0.780560i	$-0.285066\pi$
$107$	2.70638	+	1.56253i	0.261635	+	0.151055i	−0.363445	+	0.931616i	$0.618400\pi$
$108$	3.19168	+	4.10039i	0.307119	+	0.394560i
$109$	−0.913996	−	0.913996i	−0.0875449	−	0.0875449i	0.661978	−	0.749523i	$-0.269717\pi$
$109$	−0.913996	−	0.913996i	−0.0875449	−	0.0875449i	−0.749523	+	0.661978i	$0.769717\pi$
$110$	2.45996	+	0.659144i	0.234548	+	0.0628469i
$111$	7.52190	+	6.86069i	0.713947	+	0.651188i
$112$	−0.538189	+	0.538189i	−0.0508541	+	0.0508541i
$113$	−6.03730	+	3.48564i	−0.567942	+	0.327901i	−0.756327	−	0.654194i	$-0.773008\pi$
$113$	−6.03730	+	3.48564i	−0.567942	+	0.327901i	0.188385	+	0.982095i	$0.439675\pi$
$114$	4.97588	−	3.18615i	0.466034	−	0.298410i
$115$	0.292776	+	1.09266i	0.0273015	+	0.101891i
$116$	−8.70629			−0.808359
$117$	10.4414	+	2.82454i	0.965304	+	0.261128i
$118$	8.63979			0.795357
$119$	1.03366	+	3.85766i	0.0947551	+	0.353631i
$120$	0.883966	−	0.566020i	0.0806947	−	0.0516703i
$121$	5.76795	−	3.33013i	0.524359	−	0.302739i
$122$	−5.74921	+	5.74921i	−0.520509	+	0.520509i
$123$	11.3495	+	10.3519i	1.02335	+	0.933397i
$124$	3.66422	+	0.981825i	0.329057	+	0.0881705i
$125$	−4.12782	−	4.12782i	−0.369203	−	0.369203i
$126$	−2.07384	−	0.955423i	−0.184753	−	0.0851158i
$127$	−1.93554	−	1.11748i	−0.171751	−	0.0991607i	0.411660	−	0.911337i	$-0.364949\pi$
$127$	−1.93554	−	1.11748i	−0.171751	−	0.0991607i	−0.583411	+	0.812177i	$0.698282\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	1.55291	−	3.00000i	0.136726	−	0.264135i
$130$	0.761691	−	2.04797i	0.0668047	−	0.179619i
$131$			22.0856i			1.92963i	0.262938	+	0.964813i	$0.415308\pi$
$131$			22.0856i			1.92963i	−0.262938	+	0.964813i	$0.584692\pi$
$132$	1.55902	−	7.10987i	0.135695	−	0.618835i
$133$	−1.29820	+	2.24854i	−0.112568	+	0.194973i
$134$	−0.0523877	−	0.0907381i	−0.00452561	−	0.00783858i
$135$	2.51145	+	1.89963i	0.216151	+	0.163494i
$136$	−1.35808	+	5.06844i	−0.116455	+	0.434615i
$137$	2.58408	−	9.64392i	0.220773	−	0.823935i	−0.763281	−	0.646066i	$-0.776413\pi$
$137$	2.58408	−	9.64392i	0.220773	−	0.823935i	0.984054	−	0.177869i	$-0.0569204\pi$
$138$	3.08118	−	0.979314i	0.262287	−	0.0833647i
$139$	1.88252	+	3.26061i	0.159673	+	0.276562i	0.934751	−	0.355304i	$-0.115623\pi$
$139$	1.88252	+	3.26061i	0.159673	+	0.276562i	−0.775078	+	0.631866i	$0.782289\pi$
$140$	−0.230625	+	0.399453i	−0.0194913	+	0.0337600i
$141$	13.7212	+	3.00872i	1.15553	+	0.253380i
$142$		−	10.4303i		−	0.875294i
$143$	−6.30715	−	13.7769i	−0.527430	−	1.15208i
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$	−5.09639	+	1.36557i	−0.423232	+	0.113405i
$146$	6.83170	+	3.94429i	0.565396	+	0.326431i
$147$	−11.1093	+	0.510724i	−0.916276	+	0.0421238i
$148$	−4.15628	−	4.15628i	−0.341644	−	0.341644i
$149$	−8.42964	−	2.25872i	−0.690583	−	0.185041i	−0.103574	−	0.994622i	$-0.533028\pi$
$149$	−8.42964	−	2.25872i	−0.690583	−	0.185041i	−0.587009	+	0.809581i	$0.699695\pi$
$150$	−5.40737	+	5.92851i	−0.441510	+	0.484061i
$151$	−17.3671	+	17.3671i	−1.41331	+	1.41331i	−0.681429	+	0.731885i	$0.738641\pi$
$151$	−17.3671	+	17.3671i	−1.41331	+	1.41331i	−0.731885	+	0.681429i	$0.761359\pi$
$152$	−2.95428	+	1.70565i	−0.239623	+	0.138347i
$153$	−15.6753	+	1.44433i	−1.26727	+	0.116767i
$154$	0.827836	+	3.08953i	0.0667090	+	0.248961i
$155$	2.29892			0.184654
$156$	−5.94707	−	1.90587i	−0.476147	−	0.152592i
$157$	11.0713			0.883589			0.441794	−	0.897116i	$-0.354342\pi$
$157$	11.0713			0.883589			0.441794	+	0.897116i	$0.354342\pi$
$158$	−3.51489	−	13.1178i	−0.279630	−	1.04359i
$159$	−8.42000	−	13.1497i	−0.667750	−	1.04284i
$160$	−0.524827	+	0.303009i	−0.0414912	+	0.0239550i
$161$	−1.00459	+	1.00459i	−0.0791728	+	0.0791728i
$162$	5.09393	−	7.41970i	0.400217	−	0.582946i
$163$	−5.07638	−	1.36021i	−0.397613	−	0.106540i	0.0544714	−	0.998515i	$-0.482653\pi$
$163$	−5.07638	−	1.36021i	−0.397613	−	0.106540i	−0.452084	+	0.891975i	$0.649319\pi$
$164$	−6.27128	−	6.27128i	−0.489704	−	0.489704i
$165$	−0.202576	−	4.40643i	−0.0157705	−	0.343040i
$166$	1.22098	+	0.704933i	0.0947664	+	0.0547134i
$167$	15.1927	−	4.07088i	1.17565	−	0.315014i	0.382450	−	0.923976i	$-0.375080\pi$
$167$	15.1927	−	4.07088i	1.17565	−	0.315014i	0.793200	+	0.608962i	$0.208414\pi$
$168$	1.17074	+	0.606018i	0.0903244	+	0.0467553i
$169$	−12.2771	+	4.27466i	−0.944393	+	0.328820i
$170$			3.17992i			0.243889i
$171$	−7.86990	−	6.54199i	−0.601827	−	0.500278i
$172$	−0.975173	+	1.68905i	−0.0743562	+	0.128789i
$173$	2.71186	+	4.69708i	0.206179	+	0.357113i	0.950508	−	0.310701i	$-0.100564\pi$
$173$	2.71186	+	4.69708i	0.206179	+	0.357113i	−0.744329	+	0.667813i	$0.767230\pi$
$174$	4.56774	+	14.3713i	0.346279	+	1.08949i
$175$	0.912608	−	3.40590i	0.0689867	−	0.257462i
$176$	−1.08766	+	4.05922i	−0.0819857	+	0.305975i
$177$	−4.53284	−	14.2615i	−0.340709	−	1.07196i
$178$	−3.27376	−	5.67032i	−0.245379	−	0.425009i
$179$	5.19042	−	8.99007i	0.387950	−	0.671949i	−0.604224	−	0.796815i	$-0.706517\pi$
$179$	5.19042	−	8.99007i	0.387950	−	0.671949i	0.992174	+	0.124866i	$0.0398500\pi$
$180$	−1.39809	−	1.16218i	−0.104207	−	0.0866241i
$181$			11.1172i			0.826335i	0.910655	+	0.413167i	$0.135578\pi$
$181$			11.1172i			0.826335i	−0.910655	+	0.413167i	$0.864422\pi$
$182$	2.70582	−	0.457586i	0.200569	−	0.0339185i
$183$	12.5064	+	6.47380i	0.924501	+	0.478557i
$184$	−1.80301	+	0.483115i	−0.132920	+	0.0356157i
$185$	−3.08486	−	1.78105i	−0.226804	−	0.130945i
$186$	−0.301746	−	6.56357i	−0.0221251	−	0.481264i
$187$	15.5924	+	15.5924i	1.14023	+	1.14023i
$188$	−7.83380	−	2.09906i	−0.571339	−	0.153090i
$189$	−0.489061	+	3.92451i	−0.0355740	+	0.285466i
$190$	−1.46181	+	1.46181i	−0.106051	+	0.106051i
$191$	−4.96444	+	2.86622i	−0.359214	+	0.207392i	−0.668736	−	0.743500i	$-0.733164\pi$
$191$	−4.96444	+	2.86622i	−0.359214	+	0.207392i	0.309522	+	0.950892i	$0.399831\pi$
$192$	0.933998	+	1.45865i	0.0674055	+	0.105269i
$193$	−2.93615	−	10.9578i	−0.211348	−	0.788763i	−0.987420	−	0.158118i	$-0.949457\pi$
$193$	−2.93615	−	10.9578i	−0.211348	−	0.788763i	0.776072	−	0.630645i	$-0.217209\pi$
$194$	15.7499			1.13078
$195$	−3.78016	−	0.182846i	−0.270703	−	0.0130938i
$196$	6.42071			0.458622
$197$	1.21210	+	4.52361i	0.0863584	+	0.322294i	0.995568	−	0.0940449i	$-0.0299797\pi$
$197$	1.21210	+	4.52361i	0.0863584	+	0.322294i	−0.909210	+	0.416339i	$0.863313\pi$
$198$	−12.5541	+	1.15674i	−0.892178	+	0.0822056i
$199$	11.1741	−	6.45135i	0.792108	−	0.457324i	−0.0485961	−	0.998819i	$-0.515475\pi$
$199$	11.1741	−	6.45135i	0.792108	−	0.457324i	0.840704	+	0.541495i	$0.182141\pi$
$200$	3.27584	−	3.27584i	0.231637	−	0.231637i
$201$	−0.122295	+	0.134081i	−0.00862599	+	0.00945734i
$202$	−3.16109	−	0.847012i	−0.222414	−	0.0595956i
$203$	−4.68563	−	4.68563i	−0.328867	−	0.328867i
$204$	9.07888	−	0.417382i	0.635649	−	0.0292226i
$205$	−4.65465	−	2.68736i	−0.325095	−	0.187694i
$206$	4.63529	−	1.24202i	0.322956	−	0.0865357i
$207$	−3.23307	−	4.57225i	−0.224714	−	0.317793i
$208$	3.37939	+	1.25688i	0.234318	+	0.0871488i
$209$			14.3357i			0.991621i
$210$	0.780367	+	0.171115i	0.0538504	+	0.0118081i
$211$	2.63979	−	4.57225i	0.181731	−	0.314767i	−0.760739	−	0.649057i	$-0.775163\pi$
$211$	2.63979	−	4.57225i	0.181731	−	0.314767i	0.942470	+	0.334291i	$0.108497\pi$
$212$	4.50750	+	7.80723i	0.309577	+	0.536203i
$213$	−17.2171	+	5.47225i	−1.17970	+	0.374952i
$214$	−0.808823	+	3.01857i	−0.0552900	+	0.206345i
$215$	−0.305910	+	1.14167i	−0.0208629	+	0.0778613i
$216$	−3.13461	+	4.14418i	−0.213283	+	0.281976i
$217$	1.44364	+	2.50045i	0.0980004	+	0.169742i
$218$	0.646293	−	1.11941i	0.0437725	−	0.0758161i
$219$	2.92652	−	13.3463i	0.197756	−	0.901860i
$220$			2.54674i			0.171701i
$221$	14.5778	−	12.0592i	0.980606	−	0.811187i
$222$	−4.68011	+	9.04127i	−0.314108	+	0.606810i
$223$	−3.42925	+	0.918866i	−0.229640	+	0.0615318i	−0.371804	−	0.928311i	$-0.621261\pi$
$223$	−3.42925	+	0.918866i	−0.229640	+	0.0615318i	0.142164	+	0.989843i	$0.454594\pi$
$224$	−0.659144	−	0.380557i	−0.0440409	−	0.0254270i
$225$	12.6230	+	5.81546i	0.841536	+	0.387697i
$226$	−4.92944	−	4.92944i	−0.327901	−	0.327901i
$227$	4.85544	+	1.30101i	0.322267	+	0.0863512i	0.416326	−	0.909215i	$-0.363318\pi$
$227$	4.85544	+	1.30101i	0.322267	+	0.0863512i	−0.0940589	+	0.995567i	$0.529984\pi$
$228$	4.36544	+	3.98170i	0.289108	+	0.263694i
$229$	11.3889	−	11.3889i	0.752602	−	0.752602i	−0.222362	−	0.974964i	$-0.571377\pi$
$229$	11.3889	−	11.3889i	0.752602	−	0.752602i	0.974964	+	0.222362i	$0.0713767\pi$
$230$	−0.979649	+	0.565601i	−0.0645961	+	0.0372946i
$231$	4.66550	−	2.98741i	0.306967	−	0.196557i
$232$	−2.25335	−	8.40963i	−0.147940	−	0.552120i
$233$	22.3807			1.46621			0.733103	−	0.680117i	$-0.238071\pi$
$233$	22.3807			1.46621			0.733103	+	0.680117i	$0.238071\pi$
$234$	−0.0258691	+	10.8166i	−0.00169112	+	0.707105i
$235$	−4.91490			−0.320613
$236$	2.23614	+	8.34539i	0.145560	+	0.543239i
$237$	−19.8092	+	12.6842i	−1.28674	+	0.823925i
$238$	−3.45868	+	1.99687i	−0.224193	+	0.129438i
$239$	−6.08236	+	6.08236i	−0.393435	+	0.393435i	−0.875910	−	0.482475i	$-0.839738\pi$
$239$	−6.08236	+	6.08236i	−0.393435	+	0.393435i	0.482475	+	0.875910i	$0.339738\pi$
$240$	0.775521	+	0.707349i	0.0500596	+	0.0456592i
$241$	5.93615	+	1.59059i	0.382381	+	0.102459i	0.444889	−	0.895586i	$-0.353243\pi$
$241$	5.93615	+	1.59059i	0.382381	+	0.102459i	−0.0625080	+	0.998044i	$0.519910\pi$
$242$	4.70951	+	4.70951i	0.302739	+	0.302739i
$243$	−14.9201	−	4.51572i	−0.957122	−	0.289684i
$244$	−7.04132	−	4.06531i	−0.450774	−	0.260255i
$245$	3.75848	−	1.00708i	0.240120	−	0.0643401i
$246$	−7.06166	+	13.6421i	−0.450235	+	0.869787i
$247$	12.2450	+	1.15780i	0.779132	+	0.0736691i
$248$			3.79348i			0.240886i
$249$	0.523035	−	2.38529i	0.0331460	−	0.151162i
$250$	2.91881	−	5.05553i	0.184602	−	0.319739i
$251$	6.27808	+	10.8740i	0.396269	+	0.686358i	0.993262	−	0.115888i	$-0.0369714\pi$
$251$	6.27808	+	10.8740i	0.396269	+	0.686358i	−0.596993	+	0.802246i	$0.703638\pi$
$252$	0.386118	−	2.25046i	0.0243231	−	0.141766i
$253$	−2.03025	+	7.57698i	−0.127641	+	0.476361i
$254$	0.578452	−	2.15881i	0.0362953	−	0.135456i
$255$	5.24903	−	1.66834i	0.328707	−	0.104475i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.36891	+	4.10307i	−0.147768	+	0.255942i	−0.930402	−	0.366540i	$-0.880542\pi$
$257$	−2.36891	+	4.10307i	−0.147768	+	0.255942i	0.782634	+	0.622482i	$0.213876\pi$
$258$	3.29970	+	0.723543i	0.205430	+	0.0450458i
$259$		−	4.47373i		−	0.277984i
$260$	2.17533	+	0.205683i	0.134908	+	0.0127559i
$261$	21.3260	−	15.0797i	1.32004	−	0.933413i
$262$	−21.3330	+	5.71617i	−1.31796	+	0.353146i
$263$	−4.90945	−	2.83447i	−0.302730	−	0.174781i	0.340939	−	0.940085i	$-0.389255\pi$
$263$	−4.90945	−	2.83447i	−0.302730	−	0.174781i	−0.643668	+	0.765304i	$0.722588\pi$
$264$	7.27111	−	0.334273i	0.447506	−	0.0205731i
$265$	3.86311	+	3.86311i	0.237309	+	0.237309i
$266$	−2.50792	−	0.671996i	−0.153771	−	0.0412027i
$267$	−7.64232	+	8.37886i	−0.467702	+	0.512778i
$268$	0.0740874	−	0.0740874i	0.00452561	−	0.00452561i
$269$	−6.32711	+	3.65296i	−0.385770	+	0.222725i	−0.680326	−	0.732910i	$-0.738162\pi$
$269$	−6.32711	+	3.65296i	−0.385770	+	0.222725i	0.294555	+	0.955634i	$0.404828\pi$
$270$	−1.18489	+	2.91753i	−0.0721101	+	0.177555i
$271$	−6.34829	−	23.6922i	−0.385631	−	1.43920i	−0.837169	−	0.546944i	$-0.815791\pi$
$271$	−6.34829	−	23.6922i	−0.385631	−	1.43920i	0.451538	−	0.892252i	$-0.350876\pi$
$272$	−5.24723			−0.318160
$273$	−2.17493	−	4.22637i	−0.131633	−	0.255791i
$274$	9.98412			0.603162
$275$	−5.03887	−	18.8053i	−0.303855	−	1.13400i
$276$	1.74341	+	2.72273i	0.104941	+	0.163889i
$277$	−7.57448	+	4.37313i	−0.455107	+	0.262756i	−0.709984	−	0.704217i	$-0.751298\pi$
$277$	−7.57448	+	4.37313i	−0.455107	+	0.262756i	0.254878	+	0.966973i	$0.417965\pi$
$278$	−2.66228	+	2.66228i	−0.159673	+	0.159673i
$279$	−10.6760	+	3.94165i	−0.639158	+	0.235980i
$280$	−0.445532	−	0.119380i	−0.0266257	−	0.00713432i
$281$	−9.49571	−	9.49571i	−0.566467	−	0.566467i	0.364670	−	0.931137i	$-0.381182\pi$
$281$	−9.49571	−	9.49571i	−0.566467	−	0.566467i	−0.931137	+	0.364670i	$0.881182\pi$
$282$	0.645107	+	14.0324i	0.0384156	+	0.835615i
$283$	27.2245	+	15.7181i	1.61833	+	0.934342i	0.987353	+	0.158539i	$0.0506782\pi$
$283$	27.2245	+	15.7181i	1.61833	+	0.934342i	0.630975	+	0.775803i	$0.282655\pi$
$284$	10.0749	−	2.69957i	0.597837	−	0.160190i
$285$	3.17992	+	1.64605i	0.188362	+	0.0975034i
$286$	11.6751	−	9.65796i	0.690361	−	0.571087i
$287$		−	6.75026i		−	0.398455i
$288$	1.91774	−	2.30701i	0.113004	−	0.135942i
$289$	−5.26672	+	9.12222i	−0.309807	+	0.536601i
$290$	−2.63809	−	4.56930i	−0.154914	−	0.268319i
$291$	−8.26316	−	25.9981i	−0.484395	−	1.52403i
$292$	−2.04171	+	7.61977i	−0.119482	+	0.445914i
$293$	0.542185	−	2.02346i	0.0316748	−	0.118212i	−0.948278	−	0.317440i	$-0.897177\pi$
$293$	0.542185	−	2.02346i	0.0316748	−	0.118212i	0.979953	+	0.199228i	$0.0638435\pi$
$294$	−3.36861	−	10.5985i	−0.196461	−	0.618119i
$295$	2.61794	+	4.53440i	0.152422	+	0.264003i
$296$	2.93893	−	5.09038i	0.170822	−	0.295872i
$297$	8.49585	+	20.1158i	0.492979	+	1.16724i
$298$		−	8.72701i		−	0.505542i
$299$	6.30801	+	2.34610i	0.364801	+	0.135679i
$300$	−7.12603	−	3.68871i	−0.411422	−	0.212968i
$301$	−1.43385	+	0.384200i	−0.0826460	+	0.0221449i
$302$	−21.2702	−	12.2804i	−1.22397	−	0.706657i
$303$	0.260313	+	5.66234i	0.0149546	+	0.325293i
$304$	−2.41216	−	2.41216i	−0.138347	−	0.138347i
$305$	−4.75941	−	1.27528i	−0.272523	−	0.0730223i
$306$	−5.45218	−	14.7674i	−0.311680	−	0.844193i
$307$	1.91340	−	1.91340i	0.109203	−	0.109203i	−0.650394	−	0.759597i	$-0.725396\pi$
$307$	1.91340	−	1.91340i	0.109203	−	0.109203i	0.759597	+	0.650394i	$0.225396\pi$
$308$	−2.76999	+	1.59926i	−0.157835	+	0.0911261i
$309$	−4.48207	−	6.99975i	−0.254976	−	0.398202i
$310$	0.595004	+	2.22059i	0.0337940	+	0.126121i
$311$	−7.19354			−0.407908			−0.203954	−	0.978980i	$-0.565379\pi$
$311$	−7.19354			−0.407908			−0.203954	+	0.978980i	$0.565379\pi$
$312$	0.301716	−	6.23771i	0.0170813	−	0.353141i
$313$	−14.6520			−0.828180			−0.414090	−	0.910236i	$-0.635900\pi$
$313$	−14.6520			−0.828180			−0.414090	+	0.910236i	$0.635900\pi$
$314$	2.86547	+	10.6941i	0.161708	+	0.603502i
$315$	−0.126961	−	1.37791i	−0.00715345	−	0.0776365i
$316$	11.7611	−	6.79025i	0.661612	−	0.381982i
$317$	−3.93077	+	3.93077i	−0.220774	+	0.220774i	−0.808824	−	0.588050i	$-0.799896\pi$
$317$	−3.93077	+	3.93077i	−0.220774	+	0.220774i	0.588050	+	0.808824i	$0.299896\pi$
$318$	10.5224	−	11.5365i	0.590066	−	0.646934i
$319$	−35.3407	−	9.46952i	−1.97870	−	0.530191i
$320$	−0.428520	−	0.428520i	−0.0239550	−	0.0239550i
$321$	5.40704	−	0.248577i	0.301792	−	0.0138742i
$322$	−1.23037	−	0.710353i	−0.0685657	−	0.0395864i
$323$	−17.2900	+	4.63284i	−0.962040	+	0.257778i
$324$	8.48528	+	3.00000i	0.471405	+	0.166667i
$325$	−16.4697	+	2.78523i	−0.913577	+	0.154497i
$326$		−	5.25545i		−	0.291073i
$327$	−2.18687	−	0.479526i	−0.120934	−	0.0265178i
$328$	4.43446	−	7.68071i	0.244852	−	0.424096i
$329$	−3.08637	−	5.34576i	−0.170157	−	0.294721i
$330$	4.20385	−	1.33614i	0.231414	−	0.0735521i
$331$	−5.11244	+	19.0799i	−0.281005	+	1.04873i	0.670704	+	0.741725i	$0.265992\pi$
$331$	−5.11244	+	19.0799i	−0.281005	+	1.04873i	−0.951709	+	0.307000i	$0.900675\pi$
$332$	−0.364900	+	1.36183i	−0.0200265	+	0.0747399i
$333$	17.3797	+	2.98188i	0.952399	+	0.163406i
$334$	7.86434	+	13.6214i	0.430318	+	0.745332i
$335$	0.0317479	−	0.0549890i	0.00173457	−	0.00300437i
$336$	−0.282360	+	1.28769i	−0.0154040	+	0.0702495i
$337$			16.3889i			0.892762i	0.894843	+	0.446381i	$0.147287\pi$
$337$			16.3889i			0.892762i	−0.894843	+	0.446381i	$0.852713\pi$
$338$	−7.30655	−	10.7524i	−0.397424	−	0.584854i
$339$	−5.55071	+	10.7231i	−0.301473	+	0.582401i
$340$	−3.07156	+	0.823023i	−0.166579	+	0.0446347i
$341$	13.8060	+	7.97088i	0.747635	+	0.431647i
$342$	4.28219	−	9.29493i	0.231554	−	0.502612i
$343$	7.22288	+	7.22288i	0.389999	+	0.389999i
$344$	−1.88389	−	0.504787i	−0.101572	−	0.0272163i
$345$	1.44760	+	1.32035i	0.0779360	+	0.0710851i
$346$	−3.83515	+	3.83515i	−0.206179	+	0.206179i
$347$	−18.7272	+	10.8122i	−1.00533	+	0.580427i	−0.909821	−	0.415001i	$-0.863781\pi$
$347$	−18.7272	+	10.8122i	−1.00533	+	0.580427i	−0.0955087	+	0.995429i	$0.530448\pi$
$348$	−12.6994	+	8.13166i	−0.680759	+	0.435903i
$349$	−0.503975	−	1.88086i	−0.0269771	−	0.100680i	0.951125	−	0.308807i	$-0.0999298\pi$
$349$	−0.503975	−	1.88086i	−0.0269771	−	0.100680i	−0.978102	+	0.208127i	$0.933263\pi$
$350$	3.52605			0.188475
$351$	17.8684	−	5.63221i	0.953742	−	0.300625i
$352$	−4.20241			−0.223989
$353$	−6.02369	−	22.4807i	−0.320609	−	1.19653i	−0.918653	−	0.395065i	$-0.870722\pi$
$353$	−6.02369	−	22.4807i	−0.320609	−	1.19653i	0.598045	−	0.801463i	$-0.295945\pi$
$354$	12.6024	−	8.06955i	0.669810	−	0.428892i
$355$	5.47412	−	3.16049i	0.290536	−	0.167741i
$356$	4.62980	−	4.62980i	0.245379	−	0.245379i
$357$	5.11078	+	4.66152i	0.270491	+	0.246714i
$358$	10.0271	+	2.68676i	0.529950	+	0.142000i
$359$	15.8859	+	15.8859i	0.838428	+	0.838428i	0.988652	−	0.150224i	$-0.0479996\pi$
$359$	15.8859	+	15.8859i	0.838428	+	0.838428i	−0.150224	+	0.988652i	$0.548000\pi$
$360$	0.760732	−	1.65125i	0.0400941	−	0.0870283i
$361$	6.37655	+	3.68150i	0.335608	+	0.193763i
$362$	−10.7384	+	2.87734i	−0.564397	+	0.151230i
$363$	5.30306	−	10.2447i	0.278339	−	0.537709i
$364$	1.14231	+	2.49519i	0.0598734	+	0.130783i
$365$			4.78062i			0.250229i
$366$	−3.01631	+	13.7558i	−0.157665	+	0.719028i
$367$	−0.300881	+	0.521141i	−0.0157059	+	0.0272034i	−0.873772	−	0.486337i	$-0.838333\pi$
$367$	−0.300881	+	0.521141i	−0.0157059	+	0.0272034i	0.858066	+	0.513540i	$0.171666\pi$
$368$	−0.933306	−	1.61653i	−0.0486519	−	0.0842676i
$369$	26.2236	+	4.49926i	1.36515	+	0.234222i
$370$	0.921938	−	3.44072i	0.0479293	−	0.178874i
$371$	−1.77587	+	6.62765i	−0.0921988	+	0.344091i
$372$	6.26182	−	1.99024i	0.324660	−	0.103189i
$373$	−5.70783	−	9.88625i	−0.295540	−	0.511891i	0.679570	−	0.733611i	$-0.262166\pi$
$373$	−5.70783	−	9.88625i	−0.295540	−	0.511891i	−0.975110	+	0.221720i	$0.928833\pi$
$374$	−11.0255	+	19.0967i	−0.570116	+	0.987469i
$375$	−9.87640	−	2.16565i	−0.510015	−	0.111834i
$376$		−	8.11015i		−	0.418249i
$377$	−10.9427	+	29.4219i	−0.563580	+	1.51531i
$378$	−3.91736	+	0.543341i	−0.201487	+	0.0279465i
$379$	36.2846	−	9.72242i	1.86381	−	0.499407i	0.863823	−	0.503795i	$-0.168063\pi$
$379$	36.2846	−	9.72242i	1.86381	−	0.499407i	0.999990	+	0.00438723i	$0.00139650\pi$
$380$	−1.79035	−	1.03366i	−0.0918428	−	0.0530255i
$381$	−3.86699	+	0.177777i	−0.198112	+	0.00910777i
$382$	−4.05345	−	4.05345i	−0.207392	−	0.207392i
$383$	12.2026	+	3.26967i	0.623523	+	0.167073i	0.556729	−	0.830694i	$-0.312056\pi$
$383$	12.2026	+	3.26967i	0.623523	+	0.167073i	0.0667943	+	0.997767i	$0.478723\pi$
$384$	−1.16721	+	1.27970i	−0.0595638	+	0.0653043i
$385$	−1.37063	+	1.37063i	−0.0698536	+	0.0698536i
$386$	9.82453	−	5.67220i	0.500056	−	0.288707i
$387$	−0.536843	−	5.82636i	−0.0272892	−	0.296170i
$388$	4.07638	+	15.2132i	0.206947	+	0.772336i
$389$	−18.8229			−0.954361			−0.477180	−	0.878805i	$-0.658341\pi$
$389$	−18.8229			−0.954361			−0.477180	+	0.878805i	$0.658341\pi$
$390$	−0.801763	−	3.69868i	−0.0405989	−	0.187290i
$391$	−9.79455			−0.495332
$392$	1.66180	+	6.20192i	0.0839336	+	0.313245i
$393$	20.6279	+	32.2150i	1.04054	+	1.62503i
$394$	−4.05576	+	2.34159i	−0.204326	+	0.117968i
$395$	5.81951	−	5.81951i	0.292812	−	0.292812i
$396$	−4.36655	−	11.8269i	−0.219427	−	0.594324i
$397$	11.5273	+	3.08874i	0.578540	+	0.155019i	0.536210	−	0.844084i	$-0.319855\pi$
$397$	11.5273	+	3.08874i	0.578540	+	0.155019i	0.0423297	+	0.999104i	$0.486522\pi$
$398$	9.12358	+	9.12358i	0.457324	+	0.457324i
$399$	0.206525	+	4.49234i	0.0103392	+	0.224898i
$400$	4.01207	+	2.31637i	0.200604	+	0.115819i
$401$	23.3959	−	6.26891i	1.16833	−	0.313054i	0.378045	−	0.925787i	$-0.376597\pi$
$401$	23.3959	−	6.26891i	1.16833	−	0.313054i	0.790290	+	0.612733i	$0.209930\pi$
$402$	−0.161164	−	0.0834248i	−0.00803815	−	0.00416085i
$403$	7.92345	−	11.1488i	0.394695	−	0.555361i
$404$		−	3.27260i		−	0.162818i
$405$	5.43757	+	0.425198i	0.270195	+	0.0211282i
$406$	3.31324	−	5.73870i	0.164433	−	0.284807i
$407$	−12.3506	−	21.3919i	−0.612197	−	1.06036i
$408$	2.75295	+	8.66150i	0.136291	+	0.428808i
$409$	6.94441	−	25.9169i	0.343379	−	1.28151i	−0.551116	−	0.834429i	$-0.685798\pi$
$409$	6.94441	−	25.9169i	0.343379	−	1.28151i	0.894495	−	0.447078i	$-0.147535\pi$
$410$	1.39108	−	5.19159i	0.0687007	−	0.256394i
$411$	−5.23814	−	16.4806i	−0.258379	−	0.812927i
$412$	2.39940	+	4.15589i	0.118210	+	0.204746i
$413$	−3.28793	+	5.69487i	−0.161789	+	0.280226i
$414$	3.57967	−	4.30629i	0.175931	−	0.211643i
$415$			0.854405i			0.0419411i
$416$	−0.339401	+	3.58954i	−0.0166405	+	0.175992i
$417$	5.79133	+	2.99781i	0.283603	+	0.146804i
$418$	−13.8472	+	3.71035i	−0.677290	+	0.181479i
$419$	−9.38488	−	5.41836i	−0.458481	−	0.264704i	0.252924	−	0.967486i	$-0.418608\pi$
$419$	−9.38488	−	5.41836i	−0.458481	−	0.264704i	−0.711405	+	0.702782i	$0.751941\pi$
$420$	0.0366892	+	0.798064i	0.00179025	+	0.0389415i
$421$	−22.8984	−	22.8984i	−1.11600	−	1.11600i	−0.992323	−	0.123676i	$-0.960532\pi$
$421$	−22.8984	−	22.8984i	−1.11600	−	1.11600i	−0.123676	−	0.992323i	$-0.539468\pi$
$422$	5.09968	+	1.36646i	0.248249	+	0.0665180i
$423$	22.8245	−	8.42691i	1.10977	−	0.409731i
$424$	−6.37457	+	6.37457i	−0.309577	+	0.309577i
$425$	21.0523	−	12.1545i	1.02119	−	0.589581i
$426$	−9.74191	−	15.2142i	−0.471997	−	0.737128i
$427$	−1.60166	−	5.97746i	−0.0775096	−	0.289270i
$428$	−3.12505			−0.151055
$429$	−22.0675	−	14.2048i	−1.06543	−	0.685812i
$430$	−1.18195			−0.0569985
$431$	8.68719	+	32.4210i	0.418447	+	1.56167i	0.777829	+	0.628476i	$0.216321\pi$
$431$	8.68719	+	32.4210i	0.418447	+	1.56167i	−0.359381	+	0.933191i	$0.617012\pi$
$432$	−4.81427	−	1.95521i	−0.231627	−	0.0940699i
$433$	−20.5735	+	11.8781i	−0.988698	+	0.570825i	−0.904885	−	0.425657i	$-0.860043\pi$
$433$	−20.5735	+	11.8781i	−0.988698	+	0.570825i	−0.0838130	+	0.996482i	$0.526710\pi$
$434$	−2.04161	+	2.04161i	−0.0980004	+	0.0980004i
$435$	−6.15839	+	6.75191i	−0.295272	+	0.323729i
$436$	1.24854	+	0.334546i	0.0597943	+	0.0160218i
$437$	−4.50256	−	4.50256i	−0.215387	−	0.215387i
$438$	13.6490	−	0.627482i	0.652174	−	0.0299823i
$439$	12.8746	+	7.43317i	0.614473	+	0.354766i	0.774714	−	0.632312i	$-0.217894\pi$
$439$	12.8746	+	7.43317i	0.614473	+	0.354766i	−0.160241	+	0.987078i	$0.551227\pi$
$440$	−2.45996	+	0.659144i	−0.117274	+	0.0314235i
$441$	−15.7275	+	11.1210i	−0.748926	+	0.529571i
$442$	15.4213	+	10.9599i	0.733515	+	0.521309i
$443$		−	40.3416i		−	1.91669i	−0.285619	−	0.958343i	$-0.592199\pi$
$443$		−	40.3416i		−	1.91669i	0.285619	−	0.958343i	$-0.407801\pi$
$444$	−9.94450	−	2.18058i	−0.471945	−	0.103486i
$445$	1.98396	−	3.43632i	0.0940487	−	0.162897i
$446$	−1.77511	−	3.07458i	−0.0840540	−	0.145586i
$447$	−14.4055	+	4.57860i	−0.681357	+	0.216560i
$448$	0.196991	−	0.735180i	0.00930694	−	0.0347340i
$449$	−1.18156	+	4.40965i	−0.0557613	+	0.208104i	−0.988186	−	0.153261i	$-0.951022\pi$
$449$	−1.18156	+	4.40965i	−0.0557613	+	0.208104i	0.932424	+	0.361365i	$0.117689\pi$
$450$	−2.35022	+	13.6981i	−0.110790	+	0.645733i
$451$	−18.6354	−	32.2775i	−0.877508	−	1.51989i
$452$	3.48564	−	6.03730i	0.163951	−	0.283971i
$453$	−9.11160	+	41.5532i	−0.428100	+	1.95234i
$454$			5.02672i			0.235916i
$455$	1.06004	+	1.28143i	0.0496955	+	0.0600746i
$456$	−2.71617	+	5.24723i	−0.127196	+	0.245724i
$457$	25.3969	−	6.80507i	1.18801	−	0.318328i	0.389914	−	0.920851i	$-0.372505\pi$
$457$	25.3969	−	6.80507i	1.18801	−	0.318328i	0.798101	+	0.602524i	$0.205838\pi$
$458$	13.9485	+	8.05319i	0.651773	+	0.376301i
$459$	−21.5157	+	16.7475i	−1.00427	+	0.781704i
$460$	−0.799880	−	0.799880i	−0.0372946	−	0.0372946i
$461$	14.5525	+	3.89933i	0.677778	+	0.181610i	0.581256	−	0.813721i	$-0.302562\pi$
$461$	14.5525	+	3.89933i	0.677778	+	0.181610i	0.0965219	+	0.995331i	$0.469228\pi$
$462$	4.09313	+	3.73333i	0.190430	+	0.173690i
$463$	−12.8578	+	12.8578i	−0.597552	+	0.597552i	−0.939661	−	0.342108i	$-0.888859\pi$
$463$	−12.8578	+	12.8578i	−0.597552	+	0.597552i	0.342108	+	0.939661i	$0.388859\pi$
$464$	7.53987	−	4.35315i	0.350030	−	0.202090i
$465$	3.35331	−	2.14719i	0.155506	−	0.0995734i
$466$	5.79254	+	21.6181i	0.268334	+	1.00144i
$467$	−12.7104			−0.588168			−0.294084	−	0.955780i	$-0.595015\pi$
$467$	−12.7104			−0.588168			−0.294084	+	0.955780i	$0.595015\pi$
$468$	−10.4548	+	2.77456i	−0.483271	+	0.128254i
$469$	0.0797460			0.00368233
$470$	−1.27207	−	4.74743i	−0.0586762	−	0.218982i
$471$	16.1492	−	10.3406i	0.744114	−	0.476470i
$472$	−7.48228	+	4.31989i	−0.344400	+	0.198839i
$473$	−5.79555	+	5.79555i	−0.266480	+	0.266480i
$474$	−17.3790	−	15.8513i	−0.798242	−	0.728073i
$475$	15.2652	+	4.09030i	0.700415	+	0.187676i
$476$	−2.82400	−	2.82400i	−0.129438	−	0.129438i
$477$	−24.5636	−	11.3165i	−1.12469	−	0.518147i
$478$	−7.44934	−	4.30088i	−0.340725	−	0.196718i
$479$	−34.6068	+	9.27288i	−1.58123	+	0.423689i	−0.939306	−	0.343082i	$-0.888529\pi$
$479$	−34.6068	+	9.27288i	−1.58123	+	0.423689i	−0.641922	+	0.766770i	$0.721863\pi$
$480$	−0.482527	+	0.932171i	−0.0220242	+	0.0425476i
$481$	−19.2696	+	8.82174i	−0.878619	+	0.402237i
$482$			6.14555i			0.279922i
$483$	−0.527056	+	2.40363i	−0.0239819	+	0.109369i
$484$	−3.33013	+	5.76795i	−0.151369	+	0.262180i
$485$	4.77237	+	8.26598i	0.216702	+	0.375339i
$486$	0.500258	−	15.5804i	0.0226921	−	0.706743i
$487$	−1.74173	+	6.50021i	−0.0789252	+	0.294553i	−0.994095	−	0.108517i	$-0.965390\pi$
$487$	−1.74173	+	6.50021i	−0.0789252	+	0.294553i	0.915169	+	0.403069i	$0.132057\pi$
$488$	2.10436	−	7.85357i	0.0952598	−	0.355514i
$489$	−8.67507	+	2.75726i	−0.392300	+	0.124688i
$490$	1.94553	+	3.36976i	0.0878902	+	0.152230i
$491$	14.9069	−	25.8195i	0.672740	−	1.16522i	−0.304385	−	0.952549i	$-0.598451\pi$
$491$	14.9069	−	25.8195i	0.672740	−	1.16522i	0.977124	−	0.212670i	$-0.0682159\pi$
$492$	−15.0049	−	3.29021i	−0.676474	−	0.148334i
$493$		−	45.6839i		−	2.05750i
$494$	2.05089	+	12.1274i	0.0922741	+	0.545639i
$495$	−4.41108	−	6.23821i	−0.198263	−	0.280387i
$496$	−3.66422	+	0.981825i	−0.164528	+	0.0440853i
$497$	6.87509	+	3.96934i	0.308390	+	0.178049i
$498$	2.43938	−	0.112145i	0.109311	−	0.00502535i
$499$	25.5487	+	25.5487i	1.14372	+	1.14372i	0.987764	+	0.155954i	$0.0498453\pi$
$499$	25.5487	+	25.5487i	1.14372	+	1.14372i	0.155954	+	0.987764i	$0.450155\pi$
$500$	5.63871	+	1.51089i	0.252171	+	0.0675689i
$501$	18.3586	−	20.1280i	0.820203	−	0.899251i
$502$	−8.87855	+	8.87855i	−0.396269	+	0.396269i
$503$	36.8913	−	21.2992i	1.64490	−	0.949684i	0.665845	−	0.746090i	$-0.268071\pi$
$503$	36.8913	−	21.2992i	1.64490	−	0.949684i	0.979055	−	0.203594i	$-0.0652623\pi$
$504$	2.27371	−	0.209501i	0.101279	−	0.00933190i
$505$	−0.513305	−	1.91568i	−0.0228418	−	0.0852466i
$506$	−7.84427			−0.348720
$507$	−13.9154	+	17.7020i	−0.618006	+	0.786174i
$508$	2.23497			0.0991607
$509$	−4.37237	−	16.3179i	−0.193802	−	0.723279i	−0.992574	−	0.121645i	$-0.961183\pi$
$509$	−4.37237	−	16.3179i	−0.193802	−	0.723279i	0.798772	−	0.601634i	$-0.205483\pi$
$510$	2.97004	+	4.63837i	0.131515	+	0.205391i
$511$	−5.19971	+	3.00205i	−0.230021	+	0.132803i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.5896	−	2.19197i	−0.776600	−	0.0967777i
$514$	−4.57638	−	1.22624i	−0.201855	−	0.0540870i
$515$	2.05638	+	2.05638i	0.0906150	+	0.0906150i
$516$	0.155137	+	3.37453i	0.00682952	+	0.148556i
$517$	−29.5160	−	17.0411i	−1.29811	−	0.749466i
$518$	4.32129	−	1.15789i	0.189867	−	0.0508746i
$519$	8.34271	+	4.31851i	0.366204	+	0.189561i
$520$	0.364341	+	2.15444i	0.0159774	+	0.0944784i
$521$		−	18.8358i		−	0.825213i	−0.910909	−	0.412607i	$-0.864618\pi$
$521$		−	18.8358i		−	0.825213i	0.910909	−	0.412607i	$-0.135382\pi$
$522$	20.0855	+	16.6964i	0.879118	+	0.730781i
$523$	5.97667	−	10.3519i	0.261342	−	0.452657i	−0.705257	−	0.708952i	$-0.749168\pi$
$523$	5.97667	−	10.3519i	0.261342	−	0.452657i	0.966599	+	0.256295i	$0.0825017\pi$
$524$	−11.0428	−	19.1267i	−0.482406	−	0.835552i
$525$	−1.84993	−	5.82037i	−0.0807376	−	0.254022i
$526$	1.46723	−	5.47578i	0.0639743	−	0.238755i
$527$	−5.15186	+	19.2270i	−0.224419	+	0.837542i
$528$	2.20478	+	6.93684i	0.0959509	+	0.301887i
$529$	9.75788	+	16.9011i	0.424256	+	0.734832i
$530$	−2.73163	+	4.73132i	−0.118654	+	0.205516i
$531$	−19.9321	−	16.5688i	−0.864977	−	0.719027i
$532$		−	2.59639i		−	0.112568i
$533$	−29.0753	+	13.3108i	−1.25939	+	0.576556i
$534$	−10.0713	−	5.21331i	−0.435829	−	0.225602i
$535$	−1.82931	+	0.490162i	−0.0790879	+	0.0211915i
$536$	0.0907381	+	0.0523877i	0.00391929	+	0.00226280i
$537$	−0.825725	−	17.9612i	−0.0356327	−	0.775081i
$538$	−5.16606	−	5.16606i	−0.222725	−	0.222725i
$539$	26.0630	+	6.98357i	1.12261	+	0.300804i
$540$	−3.12479	−	0.389403i	−0.134470	−	0.0167572i
$541$	13.7056	−	13.7056i	0.589250	−	0.589250i	−0.348179	−	0.937428i	$-0.613200\pi$
$541$	13.7056	−	13.7056i	0.589250	−	0.589250i	0.937428	+	0.348179i	$0.113200\pi$
$542$	21.2418	−	12.2640i	0.912414	−	0.526782i
$543$	10.3834	+	16.2160i	0.445596	+	0.695897i
$544$	−1.35808	−	5.06844i	−0.0582273	−	0.217307i
$545$	0.783330			0.0335542
$546$	3.51944	−	3.19468i	0.150618	−	0.136720i
$547$	−14.6259			−0.625359			−0.312679	−	0.949859i	$-0.601227\pi$
$547$	−14.6259			−0.625359			−0.312679	+	0.949859i	$0.601227\pi$
$548$	2.58408	+	9.64392i	0.110386	+	0.411968i
$549$	24.2890	−	2.23799i	1.03663	−	0.0955152i
$550$	16.8604	−	9.73434i	0.718929	−	0.415074i
$551$	21.0009	−	21.0009i	0.894670	−	0.894670i
$552$	−2.17872	+	2.38870i	−0.0927326	+	0.101670i
$553$	9.98412	+	2.67524i	0.424568	+	0.113763i
$554$	−6.18454	−	6.18454i	−0.262756	−	0.262756i
$555$	−6.16322	+	0.283341i	−0.261614	+	0.0120271i
$556$	−3.26061	−	1.88252i	−0.138281	−	0.0798365i
$557$	1.16825	−	0.313031i	0.0495002	−	0.0132635i	−0.233984	−	0.972240i	$-0.575176\pi$
$557$	1.16825	−	0.313031i	0.0495002	−	0.0132635i	0.283484	+	0.958977i	$0.408510\pi$
$558$	−6.57050	−	9.29209i	−0.278152	−	0.393366i
$559$	4.48228	+	5.41841i	0.189580	+	0.229175i
$560$		−	0.461249i		−	0.0194913i
$561$	37.3071	+	8.18053i	1.57511	+	0.345382i
$562$	6.71448	−	11.6298i	0.283233	−	0.490575i
$563$	12.2059	+	21.1412i	0.514416	+	0.890994i	0.999860	+	0.0167265i	$0.00532446\pi$
$563$	12.2059	+	21.1412i	0.514416	+	0.890994i	−0.485444	+	0.874267i	$0.661342\pi$
$564$	−13.3873	+	4.25497i	−0.563705	+	0.179167i
$565$	1.09344	−	4.08077i	0.0460013	−	0.171679i
$566$	−8.13627	+	30.3650i	−0.341993	+	1.27633i
$567$	2.95212	+	6.18125i	0.123977	+	0.259588i
$568$	5.21517	+	9.03293i	0.218823	+	0.379013i
$569$	−2.98833	+	5.17593i	−0.125277	+	0.216986i	−0.921841	−	0.387568i	$-0.873315\pi$
$569$	−2.98833	+	5.17593i	−0.125277	+	0.216986i	0.796564	+	0.604554i	$0.206649\pi$
$570$	−0.766936	+	3.49759i	−0.0321234	+	0.146498i
$571$			35.8068i			1.49847i	0.662307	+	0.749233i	$0.269578\pi$
$571$			35.8068i			1.49847i	−0.662307	+	0.749233i	$0.730422\pi$
$572$	12.3506	+	8.77758i	0.516405	+	0.367009i
$573$	−4.56431	+	8.81758i	−0.190677	+	0.368360i
$574$	6.52025	−	1.74710i	0.272150	−	0.0729224i
$575$	7.48898	+	4.32377i	0.312312	+	0.180314i
$576$	2.72474	+	1.25529i	0.113531	+	0.0523040i
$577$	13.8142	+	13.8142i	0.575094	+	0.575094i	0.933548	−	0.358453i	$-0.116696\pi$
$577$	13.8142	+	13.8142i	0.575094	+	0.575094i	−0.358453	+	0.933548i	$0.616696\pi$
$578$	−10.1745	−	2.72625i	−0.423204	−	0.113397i
$579$	−14.5174	−	13.2413i	−0.603323	−	0.550288i
$580$	3.73082	−	3.73082i	0.154914	−	0.154914i
$581$	−0.929305	+	0.536534i	−0.0385541	+	0.0222592i
$582$	22.9735	−	14.7104i	0.952284	−	0.609765i
$583$	9.80530	+	36.5939i	0.406094	+	1.51556i
$584$	−7.88857			−0.326431
$585$	−5.68470	+	3.26396i	−0.235033	+	0.134948i
$586$	2.09484			0.0865371
$587$	3.99377	+	14.9050i	0.164841	+	0.615194i	0.998060	+	0.0622518i	$0.0198282\pi$
$587$	3.99377	+	14.9050i	0.164841	+	0.615194i	−0.833220	+	0.552942i	$0.813505\pi$
$588$	9.36553	−	5.99693i	0.386228	−	0.247309i
$589$	−11.2070	+	6.47036i	−0.461776	+	0.266607i
$590$	−3.70232	+	3.70232i	−0.152422	+	0.152422i
$591$	5.99306	+	5.46625i	0.246522	+	0.224851i
$592$	5.67758	+	1.52130i	0.233347	+	0.0625252i
$593$	19.1066	+	19.1066i	0.784613	+	0.784613i	0.980605	−	0.195992i	$-0.0627927\pi$
$593$	19.1066	+	19.1066i	0.784613	+	0.784613i	−0.195992	+	0.980605i	$0.562793\pi$
$594$	−17.2315	+	13.4127i	−0.707018	+	0.550331i
$595$	−2.09602	−	1.21014i	−0.0859286	−	0.0496109i
$596$	8.42964	−	2.25872i	0.345292	−	0.0925206i
$597$	10.2734	−	19.8468i	0.420464	−	0.812275i
$598$	−0.633531	+	6.70028i	−0.0259070	+	0.273995i
$599$			15.6579i			0.639764i	0.947457	+	0.319882i	$0.103643\pi$
$599$			15.6579i			0.639764i	−0.947457	+	0.319882i	$0.896357\pi$
$600$	1.71866	−	7.83793i	0.0701641	−	0.319982i
$601$	6.65857	−	11.5330i	0.271609	−	0.470440i	−0.697665	−	0.716424i	$-0.745778\pi$
$601$	6.65857	−	11.5330i	0.271609	−	0.470440i	0.969274	+	0.245984i	$0.0791110\pi$
$602$	−0.742218	−	1.28556i	−0.0302505	−	0.0523955i
$603$	−0.0531532	+	0.309799i	−0.00216456	+	0.0126160i
$604$	6.35679	−	23.7239i	0.258654	−	0.965311i
$605$	−1.04465	+	3.89870i	−0.0424713	+	0.158505i
$606$	−5.40202	+	1.71696i	−0.219442	+	0.0697469i
$607$	−6.14650	−	10.6460i	−0.249479	−	0.432110i	0.713903	−	0.700245i	$-0.246926\pi$
$607$	−6.14650	−	10.6460i	−0.249479	−	0.432110i	−0.963381	+	0.268135i	$0.913593\pi$
$608$	1.70565	−	2.95428i	0.0691733	−	0.119812i
$609$	−11.2110	−	2.45831i	−0.454295	−	0.0996156i
$610$		−	4.92730i		−	0.199501i
$611$	−16.9397	+	23.8352i	−0.685306	+	0.964268i
$612$	12.8530	−	9.08847i	0.519553	−	0.367380i
$613$	−10.3869	+	2.78315i	−0.419521	+	0.112410i	−0.462403	−	0.886670i	$-0.653013\pi$
$613$	−10.3869	+	2.78315i	−0.419521	+	0.112410i	0.0428820	+	0.999080i	$0.486346\pi$
$614$	2.34342	+	1.35298i	0.0945728	+	0.0546017i
$615$	−9.29948	+	0.427523i	−0.374991	+	0.0172394i
$616$	−2.26169	−	2.26169i	−0.0911261	−	0.0911261i
$617$	−12.1675	−	3.26027i	−0.489845	−	0.131254i	0.00543815	−	0.999985i	$-0.498269\pi$
$617$	−12.1675	−	3.26027i	−0.489845	−	0.131254i	−0.495283	+	0.868732i	$0.664936\pi$
$618$	5.60120	−	6.14102i	0.225313	−	0.247028i
$619$	−5.08096	+	5.08096i	−0.204221	+	0.204221i	−0.801806	−	0.597585i	$-0.796127\pi$
$619$	−5.08096	+	5.08096i	−0.204221	+	0.204221i	0.597585	+	0.801806i	$0.296127\pi$
$620$	−1.99092	+	1.14946i	−0.0799574	+	0.0461634i
$621$	−8.98637	−	3.64961i	−0.360611	−	0.146454i
$622$	−1.86183	−	6.94843i	−0.0746524	−	0.278607i
$623$	4.98342			0.199656
$624$	6.10325	−	1.32300i	0.244326	−	0.0529624i
$625$	−19.6260			−0.785040
$626$	−3.79222	−	14.1527i	−0.151567	−	0.565657i
$627$	13.3895	+	20.9107i	0.534726	+	0.835093i
$628$	−9.58806	+	5.53567i	−0.382605	+	0.220897i
$629$	21.8090	−	21.8090i	0.869580	−	0.869580i
$630$	1.29810	−	0.479265i	0.0517175	−	0.0190944i
$631$	−23.9643	−	6.42121i	−0.954002	−	0.255624i	−0.251943	−	0.967742i	$-0.581069\pi$
$631$	−23.9643	−	6.42121i	−0.954002	−	0.255624i	−0.702060	+	0.712118i	$0.747736\pi$
$632$	9.60287	+	9.60287i	0.381982	+	0.381982i
$633$	−0.419955	−	9.13485i	−0.0166917	−	0.363078i
$634$	−4.81419	−	2.77947i	−0.191196	−	0.110387i
$635$	1.30828	−	0.350553i	0.0519175	−	0.0139113i
$636$	13.8668	+	7.17798i	0.549854	+	0.284625i
$637$	8.07004	−	21.6980i	0.319747	−	0.859708i
$638$		−	36.5874i		−	1.44851i
$639$	−20.0026	+	24.0628i	−0.791292	+	0.951912i
$640$	0.303009	−	0.524827i	0.0119775	−	0.0207456i
$641$	−5.92602	−	10.2642i	−0.234064	−	0.405410i	0.724936	−	0.688816i	$-0.241869\pi$
$641$	−5.92602	−	10.2642i	−0.234064	−	0.405410i	−0.959000	+	0.283406i	$0.908536\pi$
$642$	1.63955	+	5.15846i	0.0647079	+	0.203588i
$643$	−7.18682	+	26.8216i	−0.283420	+	1.05774i	0.666566	+	0.745446i	$0.267764\pi$
$643$	−7.18682	+	26.8216i	−0.283420	+	1.05774i	−0.949986	+	0.312293i	$0.898903\pi$
$644$	0.367706	−	1.37230i	0.0144896	−	0.0540760i
$645$	0.620105	+	1.95101i	0.0244166	+	0.0768211i
$646$	−8.94995	−	15.5018i	−0.352131	−	0.609909i
$647$	−9.84613	+	17.0540i	−0.387091	+	0.670462i	−0.992057	−	0.125790i	$-0.959853\pi$
$647$	−9.84613	+	17.0540i	−0.387091	+	0.670462i	0.604966	+	0.796251i	$0.293187\pi$
$648$	−0.701625	+	8.97261i	−0.0275624	+	0.352477i
$649$			36.3079i			1.42521i
$650$	−6.95301	−	15.1877i	−0.272719	−	0.595710i
$651$	4.44117	+	2.29892i	0.174063	+	0.0901017i
$652$	5.07638	−	1.36021i	0.198806	−	0.0532700i
$653$	−42.1003	−	24.3066i	−1.64751	−	0.951191i	−0.978057	−	0.208339i	$-0.933194\pi$
$653$	−42.1003	−	24.3066i	−1.64751	−	0.951191i	−0.669455	−	0.742853i	$-0.733472\pi$
$654$	−0.102816	−	2.23646i	−0.00402044	−	0.0874526i
$655$	−9.46410	−	9.46410i	−0.369793	−	0.369793i
$656$	8.56672	+	2.29545i	0.334474	+	0.0896221i
$657$	−8.19668	−	22.2009i	−0.319783	−	0.866140i
$658$	4.36479	−	4.36479i	0.170157	−	0.170157i
$659$	−3.21116	+	1.85397i	−0.125089	+	0.0722202i	−0.561239	−	0.827654i	$-0.689675\pi$
$659$	−3.21116	+	1.85397i	−0.125089	+	0.0722202i	0.436150	+	0.899874i	$0.356342\pi$
$660$	2.37865	+	3.71479i	0.0925888	+	0.144598i
$661$	1.66416	+	6.21075i	0.0647285	+	0.241570i	0.990708	−	0.136003i	$-0.0434255\pi$
$661$	1.66416	+	6.21075i	0.0647285	+	0.241570i	−0.925980	+	0.377573i	$0.876759\pi$
$662$	−19.7529			−0.767720
$663$	10.0006	−	31.2057i	0.388389	−	1.21193i
$664$	−1.40987			−0.0547134
$665$	−0.407242	−	1.51985i	−0.0157922	−	0.0589371i
$666$	1.61791	+	17.5592i	0.0626929	+	0.680406i
$667$	14.0740	−	8.12564i	0.544948	−	0.314626i
$668$	−11.1219	+	11.1219i	−0.430318	+	0.430318i
$669$	−4.14385	+	4.54322i	−0.160210	+	0.175651i
$670$	0.0613322	+	0.0164339i	0.00236947	+	0.000634898i
$671$	−24.1605	−	24.1605i	−0.932708	−	0.932708i
$672$	−1.31690	+	0.0605415i	−0.0508004	+	0.00233544i
$673$	5.14268	+	2.96913i	0.198236	+	0.114451i	0.595832	−	0.803109i	$-0.296822\pi$
$673$	5.14268	+	2.96913i	0.198236	+	0.114451i	−0.397597	+	0.917560i	$0.630156\pi$
$674$	−15.8305	+	4.24177i	−0.609768	+	0.163387i
$675$	23.8442	−	3.30720i	0.917763	−	0.127294i
$676$	8.49496	−	9.84052i	0.326729	−	0.378481i
$677$		−	24.5297i		−	0.942753i	−0.881932	−	0.471376i	$-0.843757\pi$
$677$		−	24.5297i		−	0.942753i	0.881932	−	0.471376i	$-0.156243\pi$
$678$	−11.7944	−	2.58622i	−0.452961	−	0.0993231i
$679$	−5.99374	+	10.3815i	−0.230019	+	0.398404i
$680$	−1.58996	−	2.75389i	−0.0609721	−	0.105607i
$681$	8.29751	−	2.63726i	0.317961	−	0.101060i
$682$	−4.12603	+	15.3986i	−0.157994	+	0.589641i
$683$	−6.94368	+	25.9142i	−0.265693	+	0.991578i	0.696133	+	0.717913i	$0.254903\pi$
$683$	−6.94368	+	25.9142i	−0.265693	+	0.991578i	−0.961825	+	0.273665i	$0.911764\pi$
$684$	10.0865	+	1.73057i	0.385668	+	0.0661702i
$685$	3.02528	+	5.23994i	0.115590	+	0.200208i
$686$	−5.10734	+	8.84618i	−0.194999	+	0.337749i
$687$	5.97518	−	27.2497i	0.227967	−	1.03964i
$688$		−	1.95035i		−	0.0743562i
$689$	32.0490	−	5.41987i	1.22097	−	0.206481i
$690$	−0.900691	+	1.74000i	−0.0342887	+	0.0662407i
$691$	−10.1788	+	2.72740i	−0.387220	+	0.103755i	−0.447176	−	0.894446i	$-0.647570\pi$
$691$	−10.1788	+	2.72740i	−0.387220	+	0.103755i	0.0599568	+	0.998201i	$0.480904\pi$
$692$	−4.69708	−	2.71186i	−0.178556	−	0.103090i
$693$	4.01508	−	8.71514i	0.152520	−	0.331061i
$694$	−15.2907	−	15.2907i	−0.580427	−	0.580427i
$695$	−2.20393	−	0.590542i	−0.0835999	−	0.0224005i
$696$	−11.1414	−	10.1620i	−0.422315	−	0.385191i
$697$	32.9068	−	32.9068i	1.24644	−	1.24644i
$698$	1.68633	−	0.973604i	0.0638286	−	0.0368515i
$699$	32.6455	−	20.9035i	1.23477	−	0.790643i
$700$	0.912608	+	3.40590i	0.0344933	+	0.128731i
$701$	−48.3500			−1.82616			−0.913078	−	0.407785i	$-0.866301\pi$
$701$	−48.3500			−1.82616			−0.913078	+	0.407785i	$0.866301\pi$
$702$	10.0650	+	15.8018i	0.379878	+	0.596400i
$703$	20.0512			0.756245
$704$	−1.08766	−	4.05922i	−0.0409929	−	0.152987i
$705$	−7.16910	+	4.59051i	−0.270004	+	0.172888i
$706$	20.1557	−	11.6369i	0.758568	−	0.437959i
$707$	1.76128	−	1.76128i	0.0662397	−	0.0662397i
$708$	11.0563	+	10.0844i	0.415522	+	0.378996i
$709$	28.4274	+	7.61709i	1.06761	+	0.286066i	0.749512	−	0.661991i	$-0.230288\pi$
$709$	28.4274	+	7.61709i	1.06761	+	0.286066i	0.318100	+	0.948057i	$0.396955\pi$
$710$	4.46960	+	4.46960i	0.167741	+	0.167741i
$711$	−17.0475	+	37.0034i	−0.639333	+	1.38774i
$712$	5.67032	+	3.27376i	0.212504	+	0.122689i
$713$	−6.83968	+	1.83269i	−0.256148	+	0.0686347i
$714$	−3.17992	+	6.14313i	−0.119005	+	0.229901i
$715$	8.60641	+	3.20094i	0.321862	+	0.119708i
$716$			10.3808i			0.387950i
$717$	−3.19110	+	14.5529i	−0.119174	+	0.543489i
$718$	−11.2331	+	19.4562i	−0.419214	+	0.726100i
$719$	−21.4236	−	37.1068i	−0.798966	−	1.38385i	−0.920290	−	0.391237i	$-0.872047\pi$
$719$	−21.4236	−	37.1068i	−0.798966	−	1.38385i	0.121324	−	0.992613i	$-0.461286\pi$
$720$	1.79187	+	0.307437i	0.0667791	+	0.0114575i
$721$	−0.945320	+	3.52798i	−0.0352056	+	0.131389i
$722$	−1.90569	+	7.11211i	−0.0709223	+	0.264685i
$723$	10.1443	−	3.22425i	0.377272	−	0.119911i
$724$	−5.55860	−	9.62777i	−0.206584	−	0.357813i
$725$	−20.1670	+	34.9303i	−0.748984	+	1.29728i
$726$	11.2682	+	2.47083i	0.418201	+	0.0917012i
$727$		−	1.92620i		−	0.0714389i	−0.999362	−	0.0357194i	$-0.988628\pi$
$727$		−	1.92620i		−	0.0714389i	0.999362	−	0.0357194i	$-0.0113723\pi$
$728$	−2.11451	+	1.74919i	−0.0783691	+	0.0648293i
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	−4.61772	+	1.23732i	−0.170910	+	0.0457951i
$731$	−8.86283	−	5.11696i	−0.327804	−	0.189257i
$732$	−14.0678	+	0.646735i	−0.519960	+	0.0239040i
$733$	−22.6065	−	22.6065i	−0.834990	−	0.834990i	0.153204	−	0.988195i	$-0.451041\pi$
$733$	−22.6065	−	22.6065i	−0.834990	−	0.834990i	−0.988195	+	0.153204i	$0.951041\pi$
$734$	−0.581258	−	0.155748i	−0.0214546	−	0.00574875i
$735$	4.54168	−	4.97939i	0.167522	−	0.183668i
$736$	1.31989	−	1.31989i	0.0486519	−	0.0486519i
$737$	0.381319	−	0.220155i	0.0140461	−	0.00810950i
$738$	2.44122	+	26.4945i	0.0898624	+	0.975277i
$739$	−0.376096	−	1.40361i	−0.0138349	−	0.0516325i	0.958663	−	0.284543i	$-0.0918418\pi$
$739$	−0.376096	−	1.40361i	−0.0138349	−	0.0516325i	−0.972498	+	0.232910i	$0.925175\pi$
$740$	3.56209			0.130945
$741$	18.9425	−	9.74800i	0.695871	−	0.358102i
$742$	−6.86145			−0.251892
$743$	−9.58365	−	35.7667i	−0.351590	−	1.31215i	−0.884722	−	0.466119i	$-0.845652\pi$
$743$	−9.58365	−	35.7667i	−0.351590	−	1.31215i	0.533132	−	0.846032i	$-0.321015\pi$
$744$	3.54310	+	5.53335i	0.129897	+	0.202862i
$745$	4.58017	−	2.64436i	0.167804	−	0.0968820i
$746$	8.07209	−	8.07209i	0.295540	−	0.295540i
$747$	−1.46493	−	3.96780i	−0.0535991	−	0.145174i
$748$	−21.2996	−	5.70722i	−0.778792	−	0.208677i
$749$	−1.68187	−	1.68187i	−0.0614542	−	0.0614542i
$750$	−0.464343	−	10.1004i	−0.0169554	−	0.368814i
$751$	−13.2882	−	7.67193i	−0.484892	−	0.279953i	0.237561	−	0.971373i	$-0.423652\pi$
$751$	−13.2882	−	7.67193i	−0.484892	−	0.279953i	−0.722453	+	0.691420i	$0.756985\pi$
$752$	7.83380	−	2.09906i	0.285669	−	0.0765449i
$753$	19.3138	+	9.99753i	0.703832	+	0.364330i
$754$	−31.2516	−	2.95493i	−1.13812	−	0.107612i
$755$		−	14.8843i		−	0.541694i
$756$	−1.53872	−	3.64326i	−0.0559625	−	0.132504i
$757$	−11.2354	+	19.4603i	−0.408357	+	0.707296i	−0.994706	−	0.102763i	$-0.967232\pi$
$757$	−11.2354	+	19.4603i	−0.408357	+	0.707296i	0.586349	+	0.810059i	$0.300565\pi$
$758$	18.7823	+	32.5319i	0.682203	+	1.18161i
$759$	4.11548	+	12.9484i	0.149382	+	0.469997i
$760$	0.535060	−	1.99687i	0.0194087	−	0.0724341i
$761$	0.210189	−	0.784436i	0.00761934	−	0.0284358i	−0.962012	−	0.273009i	$-0.911981\pi$
$761$	0.210189	−	0.784436i	0.00761934	−	0.0284358i	0.969631	+	0.244573i	$0.0786478\pi$
$762$	−1.17257	−	3.68922i	−0.0424777	−	0.133646i
$763$	0.491903	+	0.852000i	0.0178081	+	0.0308445i
$764$	2.86622	−	4.96444i	0.103696	−	0.179607i
$765$	6.09825	−	7.33609i	0.220483	−	0.265237i
$766$			12.6331i			0.456451i
$767$	31.0129	+	2.93235i	1.11981	+	0.105881i
$768$	−1.53819	−	0.796225i	−0.0555046	−	0.0287313i
$769$	−12.0810	+	3.23708i	−0.435651	+	0.116732i	−0.469977	−	0.882678i	$-0.655738\pi$
$769$	−12.0810	+	3.23708i	−0.435651	+	0.116732i	0.0343269	+	0.999411i	$0.489071\pi$
$770$	−1.67867	−	0.969179i	−0.0604950	−	0.0349268i
$771$	0.376861	+	8.19748i	0.0135723	+	0.295225i
$772$	8.02170	+	8.02170i	0.288707	+	0.288707i
$773$	14.6654	+	3.92957i	0.527476	+	0.141337i	0.512723	−	0.858554i	$-0.328637\pi$
$773$	14.6654	+	3.92957i	0.527476	+	0.141337i	0.0147536	+	0.999891i	$0.495304\pi$
$774$	5.48888	−	2.02652i	0.197294	−	0.0728418i
$775$	12.4268	−	12.4268i	0.446386	−	0.446386i
$776$	−13.6398	+	7.87496i	−0.489641	+	0.282695i
$777$	−4.17845	−	6.52558i	−0.149901	−	0.234104i
$778$	−4.87173	−	18.1816i	−0.174660	−	0.651840i
$779$	30.2546			1.08398
$780$	3.36514	−	1.73173i	0.120491	−	0.0620060i
$781$	43.8325			1.56845
$782$	−2.53502	−	9.46081i	−0.0906520	−	0.338318i
$783$	17.0226	−	41.9144i	0.608338	−	1.49790i
$784$	−5.56049	+	3.21035i	−0.198589	+	0.114655i
$785$	−4.74428	+	4.74428i	−0.169331	+	0.169331i
$786$	−25.7784	+	28.2629i	−0.919486	+	1.00810i
$787$	−26.9442	−	7.21968i	−0.960458	−	0.257354i	−0.255664	−	0.966766i	$-0.582294\pi$
$787$	−26.9442	−	7.21968i	−0.960458	−	0.257354i	−0.704794	+	0.709412i	$0.748961\pi$
$788$	−3.31151	−	3.31151i	−0.117968	−	0.117968i
$789$	−9.80854	+	0.450926i	−0.349193	+	0.0160534i
$790$	7.12742	+	4.11502i	0.253582	+	0.146406i
$791$	5.12514	−	1.37328i	0.182229	−	0.0488281i
$792$	10.2938	−	7.27879i	0.365773	−	0.258640i
$793$	−22.5883	+	18.6857i	−0.802135	+	0.663550i
$794$			11.9340i			0.423521i
$795$	9.24304	+	2.02677i	0.327817	+	0.0718822i
$796$	−6.45135	+	11.1741i	−0.228662	+	0.396054i
$797$	21.9041	+	37.9390i	0.775883	+	1.34387i	0.934297	+	0.356496i	$0.116029\pi$
$797$	21.9041	+	37.9390i	0.775883	+	1.34387i	−0.158414	+	0.987373i	$0.550638\pi$
$798$	−4.28581	+	1.36219i	−0.151716	+	0.0482210i
$799$	11.0143	−	41.1058i	0.389656	−	1.45422i
$800$	−1.19904	+	4.47488i	−0.0423925	+	0.158211i
$801$	−3.32160	+	19.3597i	−0.117363	+	0.684041i
$802$	12.1106	+	20.9762i	0.427640	+	0.740694i
$803$	−16.5755	+	28.7096i	−0.584937	+	1.01314i
$804$	0.0388698	−	0.177265i	0.00137083	−	0.00625165i
$805$		−	0.860973i		−	0.0303453i
$806$	12.8196	+	4.76794i	0.451553	+	0.167944i
$807$	−5.81715	+	11.2379i	−0.204773	+	0.395592i
$808$	3.16109	−	0.847012i	0.111207	−	0.0297978i
$809$	−0.336378	−	0.194208i	−0.0118264	−	0.00682798i	0.494075	−	0.869419i	$-0.335507\pi$
$809$	−0.336378	−	0.194208i	−0.0118264	−	0.00682798i	−0.505902	+	0.862591i	$0.668840\pi$
$810$	0.996636	+	5.36233i	0.0350182	+	0.188413i
$811$	−5.70744	−	5.70744i	−0.200415	−	0.200415i	0.599763	−	0.800178i	$-0.295262\pi$
$811$	−5.70744	−	5.70744i	−0.200415	−	0.200415i	−0.800178	+	0.599763i	$0.795262\pi$
$812$	6.40069	+	1.71506i	0.224620	+	0.0601868i
$813$	−31.3883	−	28.6292i	−1.10084	−	1.00407i
$814$	17.4664	−	17.4664i	0.612197	−	0.612197i
$815$	2.75821	−	1.59245i	0.0966157	−	0.0557811i
$816$	−7.65385	+	4.90090i	−0.267938	+	0.171566i
$817$	−1.72198	−	6.42652i	−0.0602445	−	0.224835i
$818$	26.8311			0.938128
$819$	−7.11987	−	4.13339i	−0.248788	−	0.144432i
$820$	5.37473			0.187694
$821$	8.85384	+	33.0430i	0.309001	+	1.15321i	0.929446	+	0.368958i	$0.120285\pi$
$821$	8.85384	+	33.0430i	0.309001	+	1.15321i	−0.620445	+	0.784250i	$0.713048\pi$
$822$	14.5633	−	9.32515i	0.507953	−	0.325252i
$823$	32.3186	−	18.6592i	1.12656	−	0.650418i	0.183490	−	0.983022i	$-0.441260\pi$
$823$	32.3186	−	18.6592i	1.12656	−	0.650418i	0.943067	+	0.332604i	$0.107927\pi$
$824$	−3.39327	+	3.39327i	−0.118210	+	0.118210i
$825$	−24.9140	−	22.7240i	−0.867396	−	0.791148i
$826$	−6.35180	−	1.70196i	−0.221007	−	0.0592187i
$827$	−8.16295	−	8.16295i	−0.283854	−	0.283854i	0.550790	−	0.834644i	$-0.314326\pi$
$827$	−8.16295	−	8.16295i	−0.283854	−	0.283854i	−0.834644	+	0.550790i	$0.814326\pi$
$828$	5.08604	+	2.34315i	0.176752	+	0.0814301i
$829$	28.1823	+	16.2711i	0.978813	+	0.565118i	0.901912	−	0.431921i	$-0.142164\pi$
$829$	28.1823	+	16.2711i	0.978813	+	0.565118i	0.0769017	+	0.997039i	$0.475497\pi$
$830$	−0.825291	+	0.221136i	−0.0286463	+	0.00767575i
$831$	−6.96399	+	13.4534i	−0.241578	+	0.466693i
$832$	−3.55507	+	0.601205i	−0.123250	+	0.0208430i
$833$			33.6909i			1.16732i
$834$	−1.39676	+	6.36989i	−0.0483658	+	0.220571i
$835$	−4.76593	+	8.25484i	−0.164932	+	0.285671i
$836$	−7.16785	−	12.4151i	−0.247905	−	0.429385i
$837$	−11.8911	+	15.7209i	−0.411016	+	0.543393i
$838$	2.80475	−	10.4675i	0.0968885	−	0.361593i
$839$	−3.48230	+	12.9961i	−0.120222	+	0.448676i	−0.999624	−	0.0274036i	$-0.991276\pi$
$839$	−3.48230	+	12.9961i	−0.120222	+	0.448676i	0.879402	+	0.476080i	$0.157943\pi$
$840$	−0.761375	+	0.241993i	−0.0262699	+	0.00834956i
$841$	23.3998	+	40.5296i	0.806889	+	1.39757i
$842$	16.1916	−	28.0447i	0.557999	−	0.966483i
$843$	−22.7199	−	4.98190i	−0.782513	−	0.171586i
$844$			5.27958i			0.181731i
$845$	3.42921	−	7.09276i	0.117968	−	0.243998i
$846$	14.0472	+	19.8657i	0.482952	+	0.682998i
$847$	−4.89648	+	1.31201i	−0.168245	+	0.0450812i
$848$	−7.80723	−	4.50750i	−0.268101	−	0.154788i
$849$	54.3915	−	2.50053i	1.86671	−	0.0858180i
$850$	17.1891	+	17.1891i	0.589581	+	0.589581i
$851$	10.5978	+	2.83968i	0.363290	+	0.0973431i
$852$	12.1744	−	13.3477i	0.417087	−	0.457284i
$853$	−8.09779	+	8.09779i	−0.277263	+	0.277263i	−0.832015	−	0.554752i	$-0.812813\pi$
$853$	−8.09779	+	8.09779i	−0.277263	+	0.277263i	0.554752	+	0.832015i	$0.312813\pi$
$854$	5.35925	−	3.09416i	0.183390	−	0.105880i
$855$	6.17578	−	0.569038i	0.211207	−	0.0194607i
$856$	−0.808823	−	3.01857i	−0.0276450	−	0.103173i
$857$	−2.81672			−0.0962173			−0.0481086	−	0.998842i	$-0.515319\pi$
$857$	−2.81672			−0.0962173			−0.0481086	+	0.998842i	$0.515319\pi$
$858$	8.00926	−	24.9920i	0.273432	−	0.853214i
$859$	18.5174			0.631807			0.315903	−	0.948791i	$-0.397692\pi$
$859$	18.5174			0.631807			0.315903	+	0.948791i	$0.397692\pi$
$860$	−0.305910	−	1.14167i	−0.0104314	−	0.0389307i
$861$	−6.30473	−	9.84624i	−0.214865	−	0.335559i
$862$	−29.0679	+	16.7824i	−0.990057	+	0.571610i
$863$	−16.9992	+	16.9992i	−0.578658	+	0.578658i	−0.934534	−	0.355875i	$-0.884183\pi$
$863$	−16.9992	+	16.9992i	−0.578658	+	0.578658i	0.355875	+	0.934534i	$0.384183\pi$
$864$	0.642559	−	5.15627i	0.0218603	−	0.175420i
$865$	−3.17488	−	0.850706i	−0.107949	−	0.0289249i
$866$	−16.7982	−	16.7982i	−0.570825	−	0.570825i
$867$	0.837863	+	18.2252i	0.0284553	+	0.618960i
$868$	−2.50045	−	1.44364i	−0.0848708	−	0.0490002i
$869$	55.1262	−	14.7710i	1.87003	−	0.501073i
$870$	−8.11575	−	4.20102i	−0.275150	−	0.142428i
$871$	−0.157251	−	0.343489i	−0.00532825	−	0.0116387i
$872$			1.29259i			0.0437725i
$873$	−36.3352	−	30.2042i	−1.22976	−	1.02226i
$874$	3.18379	−	5.51449i	0.107693	−	0.186530i
$875$	2.22155	+	3.84783i	0.0751020	+	0.130080i
$876$	4.13872	+	13.0215i	0.139834	+	0.439956i
$877$	−7.98650	+	29.8060i	−0.269685	+	1.00648i	0.689635	+	0.724157i	$0.257771\pi$
$877$	−7.98650	+	29.8060i	−0.269685	+	1.00648i	−0.959320	+	0.282321i	$0.908896\pi$
$878$	−3.84769	+	14.3598i	−0.129853	+	0.484619i
$879$	−1.09905	−	3.45791i	−0.0370702	−	0.116633i
$880$	−1.27337	−	2.20554i	−0.0429253	−	0.0743487i
$881$	23.1312	−	40.0644i	0.779310	−	1.34980i	−0.153030	−	0.988222i	$-0.548903\pi$
$881$	23.1312	−	40.0644i	0.779310	−	1.34980i	0.932340	−	0.361583i	$-0.117764\pi$
$882$	−14.8126	−	12.3132i	−0.498767	−	0.414608i
$883$		−	31.0867i		−	1.04615i	−0.852286	−	0.523076i	$-0.824784\pi$
$883$		−	31.0867i		−	1.04615i	0.852286	−	0.523076i	$-0.175216\pi$
$884$	−6.59513	+	17.7324i	−0.221818	+	0.596406i
$885$	8.05376	+	4.16893i	0.270724	+	0.140137i
$886$	38.9670	−	10.4412i	1.30912	−	0.350778i
$887$	−31.3930	−	18.1248i	−1.05407	−	0.608570i	−0.130287	−	0.991476i	$-0.541590\pi$
$887$	−31.3930	−	18.1248i	−1.05407	−	0.608570i	−0.923787	+	0.382907i	$0.874923\pi$
$888$	−0.467545	−	10.1700i	−0.0156898	−	0.341284i
$889$	1.20283	+	1.20283i	0.0403418	+	0.0403418i
$890$	3.83272	+	1.02697i	0.128473	+	0.0344242i
$891$	31.1806	+	21.4068i	1.04459	+	0.717154i
$892$	2.51039	−	2.51039i	0.0840540	−	0.0840540i
$893$	23.9596	−	13.8331i	0.801778	−	0.462907i
$894$	−8.15101	−	12.7296i	−0.272610	−	0.425742i
$895$	1.62822	+	6.07662i	0.0544255	+	0.203119i
$896$	0.761114			0.0254270
$897$	11.3924	−	2.46953i	0.380381	−	0.0824552i
$898$	−4.56520			−0.152343
$899$	−8.54806	−	31.9018i	−0.285094	−	1.06398i
$900$	−13.8396	+	1.27519i	−0.461320	+	0.0425062i
$901$	−40.9663	+	23.6519i	−1.36479	+	0.787960i
$902$	26.3545	−	26.3545i	0.877508	−	0.877508i
$903$	−1.73264	+	1.89963i	−0.0576588	+	0.0632157i
$904$	6.73373	+	1.80430i	0.223961	+	0.0600101i
$905$	−4.76394	−	4.76394i	−0.158359	−	0.158359i
$906$	−42.4956	+	1.95364i	−1.41182	+	0.0649054i
$907$	−47.4882	−	27.4174i	−1.57682	−	0.910378i	−0.995299	−	0.0968476i	$-0.969124\pi$
$907$	−47.4882	−	27.4174i	−1.57682	−	0.910378i	−0.581522	−	0.813531i	$-0.697543\pi$
$908$	−4.85544	+	1.30101i	−0.161134	+	0.0431756i
$909$	5.66832	+	8.01621i	0.188006	+	0.265881i
$910$	−0.963411	+	1.35558i	−0.0319368	+	0.0449371i
$911$			12.4963i			0.414022i	0.978339	+	0.207011i	$0.0663737\pi$
$911$			12.4963i			0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$912$	−5.77143	−	1.26553i	−0.191111	−	0.0419060i
$913$	−2.96242	+	5.13106i	−0.0980417	+	0.169813i
$914$	13.1464	+	22.7702i	0.434844	+	0.753171i
$915$	−8.13340	+	2.58510i	−0.268882	+	0.0854607i
$916$	−4.16864	+	15.5576i	−0.137736	+	0.514037i
$917$	4.35066	−	16.2369i	0.143671	−	0.536189i
$918$	−21.7455	−	16.4480i	−0.717708	−	0.542865i
$919$	−15.2143	−	26.3520i	−0.501874	−	0.869272i	−0.999998	−	0.00216566i	$-0.999311\pi$
$919$	−15.2143	−	26.3520i	−0.501874	−	0.869272i	0.498123	−	0.867106i	$-0.334023\pi$
$920$	0.565601	−	0.979649i	0.0186473	−	0.0322981i
$921$	1.00386	−	4.57808i	0.0330783	−	0.150853i
$922$			15.0659i			0.496168i
$923$	3.54007	−	37.4401i	0.116523	−	1.23236i
$924$	−2.54674	+	4.91992i	−0.0837815	+	0.161853i
$925$	−26.3028	+	7.04781i	−0.864830	+	0.231730i
$926$	−15.7475	−	9.09183i	−0.517496	−	0.298776i
$927$	−13.0755	−	6.02391i	−0.429456	−	0.197851i
$928$	6.15628	+	6.15628i	0.202090	+	0.202090i
$929$	11.3485	+	3.04082i	0.372332	+	0.0997662i	0.440133	−	0.897933i	$-0.354931\pi$
$929$	11.3485	+	3.04082i	0.372332	+	0.0997662i	−0.0678003	+	0.997699i	$0.521598\pi$
$930$	2.94192	+	2.68331i	0.0964694	+	0.0879894i
$931$	−15.4877	+	15.4877i	−0.507590	+	0.507590i
$932$	−19.3822	+	11.1903i	−0.634886	+	0.366552i
$933$	−10.4928	+	6.71876i	−0.343520	+	0.219962i
$934$	−3.28970	−	12.2773i	−0.107642	−	0.401726i
$935$	−13.3633			−0.437027
$936$	−5.38591	−	9.38040i	−0.176044	−	0.306608i
$937$	4.30645			0.140686			0.0703429	−	0.997523i	$-0.477591\pi$
$937$	4.30645			0.140686			0.0703429	+	0.997523i	$0.477591\pi$
$938$	0.0206398	+	0.0770288i	0.000673913	+	0.00251508i
$939$	−21.3721	+	13.6849i	−0.697451	+	0.446591i
$940$	4.25643	−	2.45745i	0.138829	−	0.0801532i
$941$	−35.4161	+	35.4161i	−1.15453	+	1.15453i	−0.168897	+	0.985634i	$0.554020\pi$
$941$	−35.4161	+	35.4161i	−1.15453	+	1.15453i	−0.985634	+	0.168897i	$0.945980\pi$
$942$	14.1680	+	12.9225i	0.461617	+	0.421039i
$943$	15.9907	+	4.28471i	0.520730	+	0.139529i
$944$	−6.10925	−	6.10925i	−0.198839	−	0.198839i
$945$	−1.47216	−	1.89130i	−0.0478893	−	0.0615241i
$946$	−7.09808	−	4.09808i	−0.230778	−	0.133240i
$947$	54.5457	−	14.6155i	1.77250	−	0.474939i	0.783314	−	0.621626i	$-0.213528\pi$
$947$	54.5457	−	14.6155i	1.77250	−	0.474939i	0.989183	+	0.146687i	$0.0468611\pi$
$948$	10.8131	−	20.8894i	0.351195	−	0.678456i
$949$	23.1840	+	16.4769i	0.752584	+	0.534862i
$950$			15.8037i			0.512739i
$951$	−2.06227	+	9.40492i	−0.0668736	+	0.304976i
$952$	1.99687	−	3.45868i	0.0647190	−	0.112097i
$953$	−3.27175	−	5.66683i	−0.105982	−	0.183567i	0.808157	−	0.588967i	$-0.200465\pi$
$953$	−3.27175	−	5.66683i	−0.105982	−	0.183567i	−0.914139	+	0.405401i	$0.867132\pi$
$954$	4.57337	−	26.6555i	0.148068	−	0.863005i
$955$	0.899128	−	3.35559i	0.0290951	−	0.108584i
$956$	2.22630	−	8.30866i	0.0720037	−	0.268721i
$957$	−60.3941	+	19.1955i	−1.95226	+	0.620502i
$958$	−17.9138	−	31.0276i	−0.578769	−	1.00246i
$959$	−3.79953	+	6.58097i	−0.122693	+	0.212511i
$960$	−1.02529	−	0.224822i	−0.0330913	−	0.00725609i
$961$		−	16.6095i		−	0.535790i
$962$	−13.5085	−	16.3298i	−0.435531	−	0.526493i
$963$	7.65478	−	5.41275i	0.246672	−	0.174423i
$964$	−5.93615	+	1.59059i	−0.191190	+	0.0512293i
$965$	5.95385	+	3.43746i	0.191661	+	0.110656i
$966$	−2.45814	+	0.113007i	−0.0790893	+	0.00363596i
$967$	−10.8941	−	10.8941i	−0.350332	−	0.350332i	0.509901	−	0.860233i	$-0.329682\pi$
$967$	−10.8941	−	10.8941i	−0.350332	−	0.350332i	−0.860233	+	0.509901i	$0.829682\pi$
$968$	−6.43331	−	1.72380i	−0.206774	−	0.0554050i
$969$	−20.8929	+	22.9065i	−0.671176	+	0.735862i
$970$	−6.74915	+	6.74915i	−0.216702	+	0.216702i
$971$	−2.07268	+	1.19666i	−0.0665153	+	0.0384027i	−0.532889	−	0.846185i	$-0.678894\pi$
$971$	−2.07268	+	1.19666i	−0.0665153	+	0.0384027i	0.466373	+	0.884588i	$0.345560\pi$
$972$	15.1790	−	3.54930i	0.486867	−	0.113844i
$973$	−0.741677	−	2.76798i	−0.0237771	−	0.0887372i
$974$	−6.72951			−0.215628
$975$	−21.4221	+	19.4454i	−0.686057	+	0.622750i
$976$	8.13061			0.260255
$977$	−8.71475	−	32.5239i	−0.278810	−	1.04053i	−0.953245	−	0.302198i	$-0.902280\pi$
$977$	−8.71475	−	32.5239i	−0.278810	−	1.04053i	0.674436	−	0.738334i	$-0.264387\pi$
$978$	−4.90858	−	7.66584i	−0.156959	−	0.245127i
$979$	23.8290	−	13.7577i	0.761579	−	0.439698i
$980$	−2.75140	+	2.75140i	−0.0878902	+	0.0878902i
$981$	−3.63774	+	1.34307i	−0.116144	+	0.0428810i
$982$	28.7979	+	7.71639i	0.918979	+	0.246240i
$983$	26.5732	+	26.5732i	0.847553	+	0.847553i	0.989827	−	0.142274i	$-0.0454415\pi$
$983$	26.5732	+	26.5732i	0.847553	+	0.847553i	−0.142274	+	0.989827i	$0.545442\pi$
$984$	−0.705463	−	15.3452i	−0.0224893	−	0.489188i
$985$	−2.45786	−	1.41905i	−0.0783140	−	0.0452146i
$986$	44.1273	−	11.8239i	1.40530	−	0.376549i
$987$	−9.49485	−	4.91490i	−0.302225	−	0.156443i
$988$	−11.1834	+	5.11982i	−0.355791	+	0.162883i
$989$		−	3.64054i		−	0.115762i
$990$	4.88397	−	5.87534i	0.155223	−	0.186731i
$991$	−10.8598	+	18.8098i	−0.344974	+	0.597512i	−0.985349	−	0.170550i	$-0.945445\pi$
$991$	−10.8598	+	18.8098i	−0.344974	+	0.597512i	0.640375	+	0.768062i	$0.278779\pi$
$992$	−1.89674	−	3.28525i	−0.0602216	−	0.104307i
$993$	10.3633	+	32.6058i	0.328871	+	1.03471i
$994$	−2.05468	+	7.66817i	−0.0651705	+	0.243220i
$995$	−2.02378	+	7.55283i	−0.0641580	+	0.239441i
$996$	0.739683	+	2.32724i	0.0234377	+	0.0737413i
$997$	5.77610	+	10.0045i	0.182931	+	0.316846i	0.942877	−	0.333140i	$-0.108108\pi$
$997$	5.77610	+	10.0045i	0.182931	+	0.316846i	−0.759946	+	0.649986i	$0.774775\pi$
$998$	−18.0657	+	31.2907i	−0.571859	+	0.990489i
$999$	28.1358	−	11.8831i	0.890178	−	0.375963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.59.4	yes	16
3.2	odd	2	inner	78.2.k.a.59.2	yes	16
4.3	odd	2		624.2.cn.d.449.1		16
12.11	even	2		624.2.cn.d.449.2		16
13.2	odd	12	inner	78.2.k.a.41.2	✓	16
13.4	even	6		1014.2.g.d.437.1		16
13.6	odd	12		1014.2.g.c.239.1		16
13.7	odd	12		1014.2.g.d.239.5		16
13.9	even	3		1014.2.g.c.437.5		16
39.2	even	12	inner	78.2.k.a.41.4	yes	16
39.17	odd	6		1014.2.g.d.437.5		16
39.20	even	12		1014.2.g.d.239.1		16
39.32	even	12		1014.2.g.c.239.5		16
39.35	odd	6		1014.2.g.c.437.1		16
52.15	even	12		624.2.cn.d.353.2		16
156.119	odd	12		624.2.cn.d.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.2	✓	16	13.2	odd	12	inner
78.2.k.a.41.4	yes	16	39.2	even	12	inner
78.2.k.a.59.2	yes	16	3.2	odd	2	inner
78.2.k.a.59.4	yes	16	1.1	even	1	trivial
624.2.cn.d.353.1		16	156.119	odd	12
624.2.cn.d.353.2		16	52.15	even	12
624.2.cn.d.449.1		16	4.3	odd	2
624.2.cn.d.449.2		16	12.11	even	2
1014.2.g.c.239.1		16	13.6	odd	12
1014.2.g.c.239.5		16	39.32	even	12
1014.2.g.c.437.1		16	39.35	odd	6
1014.2.g.c.437.5		16	13.9	even	3
1014.2.g.d.239.1		16	39.20	even	12
1014.2.g.d.239.5		16	13.7	odd	12
1014.2.g.d.437.1		16	13.4	even	6
1014.2.g.d.437.5		16	39.17	odd	6

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.45865 - 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.428520 + 0.428520i) q^{5} +(1.27970 + 1.16721i) q^{6} +(-0.735180 - 0.196991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.45865 - 0.933998i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.428520 + 0.428520i) q^{5} +(1.27970 + 1.16721i) q^{6} +(-0.735180 - 0.196991i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.25529 - 2.72474i) q^{9} +(-0.524827 - 0.303009i) q^{10} +(-4.05922 + 1.08766i) q^{11} +(-0.796225 + 1.53819i) q^{12} +(0.601205 + 3.55507i) q^{13} -0.761114i q^{14} +(-0.224822 + 1.02529i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.62362 - 4.54424i) q^{17} +(2.95680 + 0.507306i) q^{18} +(0.882911 - 3.29507i) q^{19} +(0.156849 - 0.585369i) q^{20} +(-1.25636 + 0.399317i) q^{21} +(-2.10121 - 3.63939i) q^{22} +(0.933306 - 1.61653i) q^{23} +(-1.69185 - 0.370982i) q^{24} +4.63274i q^{25} +(-3.27833 + 1.50084i) q^{26} +(-0.713876 - 5.14688i) q^{27} +(0.735180 - 0.196991i) q^{28} +(7.53987 + 4.35315i) q^{29} +(-1.04855 + 0.0482047i) q^{30} +(-2.68240 - 2.68240i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-4.90508 + 5.37782i) q^{33} +(3.71035 - 3.71035i) q^{34} +(0.399453 - 0.230625i) q^{35} +(0.275255 + 2.98735i) q^{36} +(1.52130 + 5.67758i) q^{37} +3.41130 q^{38} +(4.19738 + 4.62407i) q^{39} +0.606018 q^{40} +(2.29545 + 8.56672i) q^{41} +(-0.710879 - 1.11020i) q^{42} +(1.68905 - 0.975173i) q^{43} +(2.97155 - 2.97155i) q^{44} +(0.629688 + 1.70553i) q^{45} +(1.80301 + 0.483115i) q^{46} +(5.73474 + 5.73474i) q^{47} +(-0.0795432 - 1.73022i) q^{48} +(-5.56049 - 3.21035i) q^{49} +(-4.47488 + 1.19904i) q^{50} +(-8.07123 - 4.17798i) q^{51} +(-2.29820 - 2.77818i) q^{52} -9.01501i q^{53} +(4.78674 - 2.02166i) q^{54} +(1.27337 - 2.20554i) q^{55} +(0.380557 + 0.659144i) q^{56} +(-1.78973 - 5.63097i) q^{57} +(-2.25335 + 8.40963i) q^{58} +(2.23614 - 8.34539i) q^{59} +(-0.317946 - 1.00034i) q^{60} +(4.06531 + 7.04132i) q^{61} +(1.89674 - 3.28525i) q^{62} +(-1.45962 + 1.75590i) q^{63} +1.00000i q^{64} +(-1.78105 - 1.26579i) q^{65} +(-6.46410 - 3.34607i) q^{66} +(-0.101205 + 0.0271179i) q^{67} +(4.54424 + 2.62362i) q^{68} +(-0.148476 - 3.22966i) q^{69} +(0.326152 + 0.326152i) q^{70} +(-10.0749 - 2.69957i) q^{71} +(-2.81431 + 1.03906i) q^{72} +(5.57806 - 5.57806i) q^{73} +(-5.09038 + 2.93893i) q^{74} +(4.32697 + 6.75753i) q^{75} +(0.882911 + 3.29507i) q^{76} +3.19851 q^{77} +(-3.38015 + 5.25115i) q^{78} -13.5805 q^{79} +(0.156849 + 0.585369i) q^{80} +(-5.84847 - 6.84072i) q^{81} +(-7.68071 + 4.43446i) q^{82} +(0.996926 - 0.996926i) q^{83} +(0.888378 - 0.973996i) q^{84} +(3.07156 + 0.823023i) q^{85} +(1.37910 + 1.37910i) q^{86} +(15.0638 - 0.692527i) q^{87} +(3.63939 + 2.10121i) q^{88} +(-6.32442 + 1.69462i) q^{89} +(-1.48444 + 1.04965i) q^{90} +(0.258323 - 2.73205i) q^{91} +1.86661i q^{92} +(-6.41802 - 1.40731i) q^{93} +(-4.05507 + 7.02359i) q^{94} +(1.03366 + 1.79035i) q^{95} +(1.65068 - 0.524648i) q^{96} +(4.07638 - 15.2132i) q^{97} +(1.66180 - 6.20192i) q^{98} +(-2.13191 + 12.4257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Introduction

L-functions

Modular forms

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