LMFDB - Embedded newform 78.2.k.a.41.2

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			41.2
Root			$0.500000 - 2.00333i$ of defining polynomial
Character	$\chi$	$=$	78.41
Dual form			78.2.k.a.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.428520 + 0.428520i) q^{5} +(-1.69185 - 0.370982i) q^{6} +(-0.735180 + 0.196991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.428520 + 0.428520i) q^{5} +(-1.69185 - 0.370982i) q^{6} +(-0.735180 + 0.196991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) 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} +(-0.707349 + 0.775521i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62362 - 4.54424i) q^{17} +(0.507306 - 2.95680i) q^{18} +(0.882911 + 3.29507i) q^{19} +(-0.156849 - 0.585369i) q^{20} +(-0.399317 - 1.25636i) q^{21} +(-2.10121 + 3.63939i) q^{22} +(-0.933306 - 1.61653i) q^{23} +(1.27970 + 1.16721i) 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} +(-0.566020 - 0.883966i) q^{30} +(-2.68240 + 2.68240i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55902 + 7.10987i) q^{33} +(3.71035 + 3.71035i) q^{34} +(-0.399453 - 0.230625i) q^{35} +(2.72474 + 1.25529i) q^{36} +(1.52130 - 5.67758i) q^{37} -3.41130 q^{38} +(6.19889 + 0.757437i) q^{39} +0.606018 q^{40} +(-2.29545 + 8.56672i) q^{41} +(1.31690 - 0.0605415i) q^{42} +(1.68905 + 0.975173i) q^{43} +(-2.97155 - 2.97155i) q^{44} +(-1.39809 - 1.16218i) q^{45} +(1.80301 - 0.483115i) q^{46} +(-5.73474 + 5.73474i) q^{47} +(-1.45865 + 0.933998i) 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} +(5.15627 + 0.642559i) q^{54} +(1.27337 + 2.20554i) q^{55} +(-0.380557 + 0.659144i) q^{56} +(-5.63097 + 1.78973i) q^{57} +(-2.25335 - 8.40963i) q^{58} +(-2.23614 - 8.34539i) q^{59} +(1.00034 - 0.317946i) q^{60} +(4.06531 - 7.04132i) q^{61} +(-1.89674 - 3.28525i) q^{62} +(2.14201 - 0.790842i) 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} +(2.72273 - 1.74341i) q^{69} +(0.326152 - 0.326152i) q^{70} +(10.0749 - 2.69957i) q^{71} +(-1.91774 + 2.30701i) q^{72} +(5.57806 + 5.57806i) q^{73} +(5.09038 + 2.93893i) q^{74} +(8.01568 - 0.368503i) q^{75} +(0.882911 - 3.29507i) q^{76} -3.19851 q^{77} +(-2.33602 + 5.79163i) q^{78} -13.5805 q^{79} +(-0.156849 + 0.585369i) q^{80} +(8.84847 - 1.64456i) q^{81} +(-7.68071 - 4.43446i) q^{82} +(-0.996926 - 0.996926i) q^{83} +(-0.282360 + 1.28769i) q^{84} +(3.07156 - 0.823023i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(-8.13166 - 12.6994i) 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} +(-4.85451 - 4.42778i) q^{93} +(-4.05507 - 7.02359i) q^{94} +(-1.03366 + 1.79035i) q^{95} +(-0.524648 - 1.65068i) q^{96} +(4.07638 + 15.2132i) q^{97} +(-1.66180 - 6.20192i) q^{98} +(-12.4257 - 2.13191i) 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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

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

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
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$3$	0.0795432	+	1.73022i	0.0459243	+	0.998945i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.428520	+	0.428520i	0.191640	+	0.191640i	0.796404	−	0.604765i	$-0.206733\pi$
$5$	0.428520	+	0.428520i	0.191640	+	0.191640i	−0.604765	+	0.796404i	$0.706733\pi$
$6$	−1.69185	−	0.370982i	−0.690697	−	0.151453i
$7$	−0.735180	+	0.196991i	−0.277872	+	0.0744555i	−0.395064	−	0.918654i	$-0.629277\pi$
$7$	−0.735180	+	0.196991i	−0.277872	+	0.0744555i	0.117192	+	0.993109i	$0.462611\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.98735	+	0.275255i	−0.995782	+	0.0917517i
$10$	−0.524827	+	0.303009i	−0.165965	+	0.0958199i
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.812201	−	0.583377i	$-0.198269\pi$
$11$	4.05922	+	1.08766i	1.22390	+	0.327943i	0.411699	+	0.911320i	$0.364936\pi$
$12$	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
$15$	−0.707349	+	0.775521i	−0.182637	+	0.200239i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.62362	−	4.54424i	0.636320	−	1.10214i	−0.349914	−	0.936782i	$-0.613789\pi$
$17$	2.62362	−	4.54424i	0.636320	−	1.10214i	0.986234	−	0.165357i	$-0.0528776\pi$
$18$	0.507306	−	2.95680i	0.119573	−	0.696923i
$19$	0.882911	+	3.29507i	0.202554	+	0.755940i	0.990181	+	0.139789i	$0.0446424\pi$
$19$	0.882911	+	3.29507i	0.202554	+	0.755940i	−0.787628	+	0.616151i	$0.788691\pi$
$20$	−0.156849	−	0.585369i	−0.0350725	−	0.130892i
$21$	−0.399317	−	1.25636i	−0.0871381	−	0.274159i
$22$	−2.10121	+	3.63939i	−0.447978	+	0.775921i
$23$	−0.933306	−	1.61653i	−0.194608	−	0.337071i	0.752164	−	0.658976i	$-0.229010\pi$
$23$	−0.933306	−	1.61653i	−0.194608	−	0.337071i	−0.946772	+	0.321905i	$0.895677\pi$
$24$	1.27970	+	1.16721i	0.261217	+	0.238255i
$25$		−	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	$-0.966311\pi$
$29$	−7.53987	+	4.35315i	−1.40012	+	0.808359i	−0.405715	+	0.914000i	$0.632977\pi$
$30$	−0.566020	−	0.883966i	−0.103341	−	0.161389i
$31$	−2.68240	+	2.68240i	−0.481773	+	0.481773i	−0.905697	−	0.423925i	$-0.860652\pi$
$31$	−2.68240	+	2.68240i	−0.481773	+	0.481773i	0.423925	+	0.905697i	$0.360652\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.55902	+	7.10987i	−0.271390	+	1.23767i
$34$	3.71035	+	3.71035i	0.636320	+	0.636320i
$35$	−0.399453	−	0.230625i	−0.0675200	−	0.0389827i
$36$	2.72474	+	1.25529i	0.454124	+	0.209216i
$37$	1.52130	−	5.67758i	0.250101	−	0.933389i	−0.720650	−	0.693299i	$-0.756156\pi$
$37$	1.52130	−	5.67758i	0.250101	−	0.933389i	0.970751	−	0.240090i	$-0.0771769\pi$
$38$	−3.41130			−0.553387
$39$	6.19889	+	0.757437i	0.992617	+	0.121287i
$40$	0.606018			0.0958199
$41$	−2.29545	+	8.56672i	−0.358488	+	1.33790i	0.517549	+	0.855654i	$0.326845\pi$
$41$	−2.29545	+	8.56672i	−0.358488	+	1.33790i	−0.876037	+	0.482243i	$0.839822\pi$
$42$	1.31690	−	0.0605415i	0.203202	−	0.00934175i
$43$	1.68905	+	0.975173i	0.257578	+	0.148712i	0.623229	−	0.782039i	$-0.285820\pi$
$43$	1.68905	+	0.975173i	0.257578	+	0.148712i	−0.365651	+	0.930752i	$0.619154\pi$
$44$	−2.97155	−	2.97155i	−0.447978	−	0.447978i
$45$	−1.39809	−	1.16218i	−0.208415	−	0.173248i
$46$	1.80301	−	0.483115i	0.265839	−	0.0712314i
$47$	−5.73474	+	5.73474i	−0.836498	+	0.836498i	−0.988396	−	0.151898i	$-0.951461\pi$
$47$	−5.73474	+	5.73474i	−0.836498	+	0.836498i	0.151898	+	0.988396i	$0.451461\pi$
$48$	−1.45865	+	0.933998i	−0.210537	+	0.134811i
$49$	−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	$-0.212524\pi$
$54$	5.15627	+	0.642559i	0.701679	+	0.0874413i
$55$	1.27337	+	2.20554i	0.171701	+	0.297395i
$56$	−0.380557	+	0.659144i	−0.0508541	+	0.0880819i
$57$	−5.63097	+	1.78973i	−0.745841	+	0.237056i
$58$	−2.25335	−	8.40963i	−0.295880	−	1.10424i
$59$	−2.23614	−	8.34539i	−0.291121	−	1.08648i	−0.944249	−	0.329231i	$-0.893211\pi$
$59$	−2.23614	−	8.34539i	−0.291121	−	1.08648i	0.653129	−	0.757247i	$-0.273456\pi$
$60$	1.00034	−	0.317946i	0.129144	−	0.0410467i
$61$	4.06531	−	7.04132i	0.520509	−	0.901548i	−0.479206	−	0.877702i	$-0.659075\pi$
$61$	4.06531	−	7.04132i	0.520509	−	0.901548i	0.999716	−	0.0238462i	$-0.00759119\pi$
$62$	−1.89674	−	3.28525i	−0.240886	−	0.417227i
$63$	2.14201	−	0.790842i	0.269868	−	0.0996367i
$64$		−	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	0.252632	−	0.967563i	$-0.418704\pi$
$67$	−0.101205	−	0.0271179i	−0.0123642	−	0.00331297i	−0.264996	+	0.964250i	$0.585371\pi$
$68$	−4.54424	+	2.62362i	−0.551069	+	0.318160i
$69$	2.72273	−	1.74341i	0.327778	−	0.209882i
$70$	0.326152	−	0.326152i	0.0389827	−	0.0389827i
$71$	10.0749	−	2.69957i	1.19567	−	0.320380i	0.394548	−	0.918875i	$-0.370901\pi$
$71$	10.0749	−	2.69957i	1.19567	−	0.320380i	0.801126	+	0.598496i	$0.204235\pi$
$72$	−1.91774	+	2.30701i	−0.226008	+	0.271883i
$73$	5.57806	+	5.57806i	0.652863	+	0.652863i	0.953681	−	0.300819i	$-0.0972599\pi$
$73$	5.57806	+	5.57806i	0.652863	+	0.652863i	−0.300819	+	0.953681i	$0.597260\pi$
$74$	5.09038	+	2.93893i	0.591745	+	0.341644i
$75$	8.01568	−	0.368503i	0.925571	−	0.0425511i
$76$	0.882911	−	3.29507i	0.101277	−	0.377970i
$77$	−3.19851			−0.364505
$78$	−2.33602	+	5.79163i	−0.264502	+	0.655773i
$79$	−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
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$	−7.68071	−	4.43446i	−0.848193	−	0.489704i
$83$	−0.996926	−	0.996926i	−0.109427	−	0.109427i	0.650273	−	0.759700i	$-0.274654\pi$
$83$	−0.996926	−	0.996926i	−0.109427	−	0.109427i	−0.759700	+	0.650273i	$0.774654\pi$
$84$	−0.282360	+	1.28769i	−0.0308080	+	0.140499i
$85$	3.07156	−	0.823023i	0.333158	−	0.0892694i
$86$	−1.37910	+	1.37910i	−0.148712	+	0.148712i
$87$	−8.13166	−	12.6994i	−0.871806	−	1.36152i
$88$	3.63939	−	2.10121i	0.387961	−	0.223989i
$89$	6.32442	+	1.69462i	0.670388	+	0.179630i	0.577929	−	0.816087i	$-0.303861\pi$
$89$	6.32442	+	1.69462i	0.670388	+	0.179630i	0.0924582	+	0.995717i	$0.470528\pi$
$90$	1.48444	−	1.04965i	0.156473	−	0.110643i
$91$	0.258323	+	2.73205i	0.0270796	+	0.286397i
$92$			1.86661i			0.194608i
$93$	−4.85451	−	4.42778i	−0.503389	−	0.459139i
$94$	−4.05507	−	7.02359i	−0.418249	−	0.724428i
$95$	−1.03366	+	1.79035i	−0.106051	+	0.183686i
$96$	−0.524648	−	1.65068i	−0.0535466	−	0.168472i
$97$	4.07638	+	15.2132i	0.413893	+	1.54467i	0.787042	+	0.616900i	$0.211612\pi$
$97$	4.07638	+	15.2132i	0.413893	+	1.54467i	−0.373148	+	0.927772i	$0.621722\pi$
$98$	−1.66180	−	6.20192i	−0.167867	−	0.626489i
$99$	−12.4257	−	2.13191i	−1.24883	−	0.214265i
$100$	−2.31637	+	4.01207i	−0.231637	+	0.401207i
$101$	1.63630	+	2.83416i	0.162818	+	0.282009i	0.935878	−	0.352323i	$-0.114608\pi$
$101$	1.63630	+	2.83416i	0.162818	+	0.282009i	−0.773060	+	0.634333i	$0.781275\pi$
$102$	−6.12461	+	6.71487i	−0.606426	+	0.664871i
$103$			4.79880i			0.472840i	0.971651	+	0.236420i	$0.0759741\pi$
$103$			4.79880i			0.472840i	−0.971651	+	0.236420i	$0.924026\pi$
$104$	−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	$-0.714934\pi$
$107$	−2.70638	+	1.56253i	−0.261635	+	0.151055i	0.363445	+	0.931616i	$0.381600\pi$
$108$	−1.95521	+	4.81427i	−0.188140	+	0.463253i
$109$	−0.913996	+	0.913996i	−0.0875449	+	0.0875449i	−0.749523	−	0.661978i	$-0.769717\pi$
$109$	−0.913996	+	0.913996i	−0.0875449	+	0.0875449i	0.661978	+	0.749523i	$0.269717\pi$
$110$	−2.45996	+	0.659144i	−0.234548	+	0.0628469i
$111$	9.94450	+	2.18058i	0.943890	+	0.206972i
$112$	−0.538189	−	0.538189i	−0.0508541	−	0.0508541i
$113$	6.03730	+	3.48564i	0.567942	+	0.327901i	0.756327	−	0.654194i	$-0.226992\pi$
$113$	6.03730	+	3.48564i	0.567942	+	0.327901i	−0.188385	+	0.982095i	$0.560325\pi$
$114$	−0.271346	−	5.90232i	−0.0254139	−	0.552803i
$115$	0.292776	−	1.09266i	0.0273015	−	0.101891i
$116$	8.70629			0.808359
$117$	−0.817456	+	10.7857i	−0.0755738	+	0.997140i
$118$	8.63979			0.795357
$119$	−1.03366	+	3.85766i	−0.0947551	+	0.353631i
$120$	0.0482047	+	1.04855i	0.00440046	+	0.0957188i
$121$	5.76795	+	3.33013i	0.524359	+	0.302739i
$122$	5.74921	+	5.74921i	0.520509	+	0.520509i
$123$	−15.0049	−	3.29021i	−1.35295	−	0.296668i
$124$	3.66422	−	0.981825i	0.329057	−	0.0881705i
$125$	4.12782	−	4.12782i	0.369203	−	0.369203i
$126$	0.209501	+	2.27371i	0.0186638	+	0.202558i
$127$	−1.93554	+	1.11748i	−0.171751	+	0.0991607i	−0.583411	−	0.812177i	$-0.698282\pi$
$127$	−1.93554	+	1.11748i	−0.171751	+	0.0991607i	0.411660	+	0.911337i	$0.364949\pi$
$128$	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	$0.584692\pi$
$132$	4.90508	−	5.37782i	0.426933	−	0.468079i
$133$	−1.29820	−	2.24854i	−0.112568	−	0.194973i
$134$	0.0523877	−	0.0907381i	0.00452561	−	0.00783858i
$135$	1.89963	−	2.51145i	0.163494	−	0.216151i
$136$	−1.35808	−	5.06844i	−0.116455	−	0.434615i
$137$	−2.58408	−	9.64392i	−0.220773	−	0.823935i	−0.984054	−	0.177869i	$-0.943080\pi$
$137$	−2.58408	−	9.64392i	−0.220773	−	0.823935i	0.763281	−	0.646066i	$-0.223587\pi$
$138$	0.979314	+	3.08118i	0.0833647	+	0.262287i
$139$	1.88252	−	3.26061i	0.159673	−	0.276562i	−0.775078	−	0.631866i	$-0.782289\pi$
$139$	1.88252	−	3.26061i	0.159673	−	0.276562i	0.934751	+	0.355304i	$0.115623\pi$
$140$	0.230625	+	0.399453i	0.0194913	+	0.0337600i
$141$	−10.3785	−	9.46622i	−0.874031	−	0.797200i
$142$			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
$147$	−5.99693	−	9.36553i	−0.494618	−	0.772456i
$148$	−4.15628	+	4.15628i	−0.341644	+	0.341644i
$149$	8.42964	−	2.25872i	0.690583	−	0.185041i	0.103574	−	0.994622i	$-0.466972\pi$
$149$	8.42964	−	2.25872i	0.690583	−	0.185041i	0.587009	+	0.809581i	$0.300305\pi$
$150$	−1.71866	+	7.83793i	−0.140328	+	0.639964i
$151$	−17.3671	−	17.3671i	−1.41331	−	1.41331i	−0.731885	−	0.681429i	$-0.761359\pi$
$151$	−17.3671	−	17.3671i	−1.41331	−	1.41331i	−0.681429	−	0.731885i	$-0.738641\pi$
$152$	2.95428	+	1.70565i	0.239623	+	0.138347i
$153$	−6.58682	+	14.2974i	−0.532513	+	1.15587i
$154$	0.827836	−	3.08953i	0.0667090	−	0.248961i
$155$	−2.29892			−0.184654
$156$	−4.98968	−	3.75541i	−0.399494	−	0.300673i
$157$	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
$159$	15.5980	−	0.717083i	1.23700	−	0.0568684i
$160$	−0.524827	−	0.303009i	−0.0414912	−	0.0239550i
$161$	1.00459	+	1.00459i	0.0791728	+	0.0791728i
$162$	−0.701625	+	8.97261i	−0.0551249	+	0.704955i
$163$	−5.07638	+	1.36021i	−0.397613	+	0.106540i	−0.452084	−	0.891975i	$-0.649319\pi$
$163$	−5.07638	+	1.36021i	−0.397613	+	0.106540i	0.0544714	+	0.998515i	$0.482653\pi$
$164$	6.27128	−	6.27128i	0.489704	−	0.489704i
$165$	−3.71479	+	2.37865i	−0.289196	+	0.185178i
$166$	1.22098	−	0.704933i	0.0947664	−	0.0547134i
$167$	−15.1927	−	4.07088i	−1.17565	−	0.315014i	−0.382450	−	0.923976i	$-0.624920\pi$
$167$	−15.1927	−	4.07088i	−1.17565	−	0.315014i	−0.793200	+	0.608962i	$0.791586\pi$
$168$	−1.17074	−	0.606018i	−0.0903244	−	0.0467553i
$169$	−12.2771	−	4.27466i	−0.944393	−	0.328820i
$170$			3.17992i			0.243889i
$171$	−3.54454	−	9.60048i	−0.271058	−	0.734167i
$172$	−0.975173	−	1.68905i	−0.0743562	−	0.128789i
$173$	−2.71186	+	4.69708i	−0.206179	+	0.357113i	−0.950508	−	0.310701i	$-0.899436\pi$
$173$	−2.71186	+	4.69708i	−0.206179	+	0.357113i	0.744329	+	0.667813i	$0.232770\pi$
$174$	14.3713	−	4.56774i	1.08949	−	0.346279i
$175$	0.912608	+	3.40590i	0.0689867	+	0.257462i
$176$	1.08766	+	4.05922i	0.0819857	+	0.305975i
$177$	14.2615	−	4.53284i	1.07196	−	0.340709i
$178$	−3.27376	+	5.67032i	−0.245379	+	0.425009i
$179$	−5.19042	−	8.99007i	−0.387950	−	0.671949i	0.604224	−	0.796815i	$-0.293483\pi$
$179$	−5.19042	−	8.99007i	−0.387950	−	0.671949i	−0.992174	+	0.124866i	$0.960150\pi$
$180$	0.629688	+	1.70553i	0.0469342	+	0.127122i
$181$		−	11.1172i		−	0.826335i	−0.910655	−	0.413167i	$-0.864422\pi$
$181$		−	11.1172i		−	0.826335i	0.910655	−	0.413167i	$-0.135578\pi$
$182$	−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
$186$	5.53335	−	3.54310i	0.405725	−	0.259793i
$187$	15.5924	−	15.5924i	1.14023	−	1.14023i
$188$	7.83380	−	2.09906i	0.571339	−	0.153090i
$189$	1.53872	+	3.64326i	0.111925	+	0.265008i
$190$	−1.46181	−	1.46181i	−0.106051	−	0.106051i
$191$	4.96444	+	2.86622i	0.359214	+	0.207392i	0.668736	−	0.743500i	$-0.266836\pi$
$191$	4.96444	+	2.86622i	0.359214	+	0.207392i	−0.309522	+	0.950892i	$0.600169\pi$
$192$	1.73022	−	0.0795432i	0.124868	−	0.00574054i
$193$	−2.93615	+	10.9578i	−0.211348	+	0.788763i	0.776072	+	0.630645i	$0.217209\pi$
$193$	−2.93615	+	10.9578i	−0.211348	+	0.788763i	−0.987420	+	0.158118i	$0.949457\pi$
$194$	−15.7499			−1.13078
$195$	2.33177	+	2.98092i	0.166982	+	0.213468i
$196$	6.42071			0.458622
$197$	−1.21210	+	4.52361i	−0.0863584	+	0.322294i	−0.995568	−	0.0940449i	$-0.970020\pi$
$197$	−1.21210	+	4.52361i	−0.0863584	+	0.322294i	0.909210	+	0.416339i	$0.136687\pi$
$198$	5.27526	−	11.4505i	0.374897	−	0.813751i
$199$	11.1741	+	6.45135i	0.792108	+	0.457324i	0.840704	−	0.541495i	$-0.182141\pi$
$199$	11.1741	+	6.45135i	0.792108	+	0.457324i	−0.0485961	+	0.998819i	$0.515475\pi$
$200$	−3.27584	−	3.27584i	−0.231637	−	0.231637i
$201$	0.0388698	−	0.177265i	0.00274166	−	0.0125033i
$202$	−3.16109	+	0.847012i	−0.222414	+	0.0595956i
$203$	4.68563	−	4.68563i	0.328867	−	0.328867i
$204$	−4.90090	−	7.65385i	−0.343132	−	0.535877i
$205$	−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
$210$	0.590260	+	0.538373i	0.0407318	+	0.0371513i
$211$	2.63979	+	4.57225i	0.181731	+	0.314767i	0.942470	−	0.334291i	$-0.108497\pi$
$211$	2.63979	+	4.57225i	0.181731	+	0.314767i	−0.760739	+	0.649057i	$0.775163\pi$
$212$	−4.50750	+	7.80723i	−0.309577	+	0.536203i
$213$	5.47225	+	17.2171i	0.374952	+	1.17970i
$214$	−0.808823	−	3.01857i	−0.0552900	−	0.206345i
$215$	0.305910	+	1.14167i	0.0208629	+	0.0778613i
$216$	−4.14418	−	3.13461i	−0.281976	−	0.213283i
$217$	1.44364	−	2.50045i	0.0980004	−	0.169742i
$218$	−0.646293	−	1.11941i	−0.0437725	−	0.0758161i
$219$	−9.20760	+	10.0950i	−0.622192	+	0.682156i
$220$		−	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	0.142164	−	0.989843i	$-0.454594\pi$
$223$	−3.42925	−	0.918866i	−0.229640	−	0.0615318i	−0.371804	+	0.928311i	$0.621261\pi$
$224$	0.659144	−	0.380557i	0.0440409	−	0.0254270i
$225$	1.27519	+	13.8396i	0.0850124	+	0.922640i
$226$	−4.92944	+	4.92944i	−0.327901	+	0.327901i
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	−0.416326	−	0.909215i	$-0.636682\pi$
$227$	−4.85544	+	1.30101i	−0.322267	+	0.0863512i	0.0940589	+	0.995567i	$0.470016\pi$
$228$	5.77143	+	1.26553i	0.382222	+	0.0838119i
$229$	11.3889	+	11.3889i	0.752602	+	0.752602i	0.974964	−	0.222362i	$-0.0713767\pi$
$229$	11.3889	+	11.3889i	0.752602	+	0.752602i	−0.222362	+	0.974964i	$0.571377\pi$
$230$	0.979649	+	0.565601i	0.0645961	+	0.0372946i
$231$	−0.254420	−	5.53414i	−0.0167396	−	0.364120i
$232$	−2.25335	+	8.40963i	−0.147940	+	0.552120i
$233$	−22.3807			−1.46621			−0.733103	−	0.680117i	$-0.761929\pi$
$233$	−22.3807			−1.46621			−0.733103	+	0.680117i	$0.761929\pi$
$234$	−10.2066	−	3.58115i	−0.667228	−	0.234107i
$235$	−4.91490			−0.320613
$236$	−2.23614	+	8.34539i	−0.145560	+	0.543239i
$237$	−1.08024	−	23.4973i	−0.0701690	−	1.52631i
$238$	−3.45868	−	1.99687i	−0.224193	−	0.129438i
$239$	6.08236	+	6.08236i	0.393435	+	0.393435i	0.875910	−	0.482475i	$-0.160262\pi$
$239$	6.08236	+	6.08236i	0.393435	+	0.393435i	−0.482475	+	0.875910i	$0.660262\pi$
$240$	−1.02529	−	0.224822i	−0.0661825	−	0.0145122i
$241$	5.93615	−	1.59059i	0.382381	−	0.102459i	−0.0625080	−	0.998044i	$-0.519910\pi$
$241$	5.93615	−	1.59059i	0.382381	−	0.102459i	0.444889	+	0.895586i	$0.353243\pi$
$242$	−4.70951	+	4.70951i	−0.302739	+	0.302739i
$243$	3.54930	+	15.1790i	0.227688	+	0.973734i
$244$	−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
$249$	1.64561	−	1.80420i	0.104286	−	0.114337i
$250$	2.91881	+	5.05553i	0.184602	+	0.319739i
$251$	−6.27808	+	10.8740i	−0.396269	+	0.686358i	−0.993262	−	0.115888i	$-0.963029\pi$
$251$	−6.27808	+	10.8740i	−0.396269	+	0.686358i	0.596993	+	0.802246i	$0.296362\pi$
$252$	−2.25046	−	0.386118i	−0.141766	−	0.0243231i
$253$	−2.03025	−	7.57698i	−0.127641	−	0.476361i
$254$	−0.578452	−	2.15881i	−0.0362953	−	0.135456i
$255$	1.66834	+	5.24903i	0.104475	+	0.328707i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.36891	+	4.10307i	0.147768	+	0.255942i	0.930402	−	0.366540i	$-0.119458\pi$
$257$	2.36891	+	4.10307i	0.147768	+	0.255942i	−0.782634	+	0.622482i	$0.786124\pi$
$258$	−2.49585	−	2.27646i	−0.155385	−	0.141726i
$259$			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	$-0.610745\pi$
$263$	4.90945	−	2.83447i	0.302730	−	0.174781i	0.643668	+	0.765304i	$0.277412\pi$
$264$	3.92504	+	6.12983i	0.241570	+	0.377265i
$265$	3.86311	−	3.86311i	0.237309	−	0.237309i
$266$	2.50792	−	0.671996i	0.153771	−	0.0412027i
$267$	−2.42901	+	11.0775i	−0.148653	+	0.677930i
$268$	0.0740874	+	0.0740874i	0.00452561	+	0.00452561i
$269$	6.32711	+	3.65296i	0.385770	+	0.222725i	0.680326	−	0.732910i	$-0.261838\pi$
$269$	6.32711	+	3.65296i	0.385770	+	0.222725i	−0.294555	+	0.955634i	$0.595172\pi$
$270$	1.93421	+	2.48491i	0.117712	+	0.151227i
$271$	−6.34829	+	23.6922i	−0.385631	+	1.43920i	0.451538	+	0.892252i	$0.350876\pi$
$271$	−6.34829	+	23.6922i	−0.385631	+	1.43920i	−0.837169	+	0.546944i	$0.815791\pi$
$272$	5.24723			0.318160
$273$	−4.70651	+	0.664273i	−0.284851	+	0.0402036i
$274$	9.98412			0.603162
$275$	5.03887	−	18.8053i	0.303855	−	1.13400i
$276$	−3.22966	+	0.148476i	−0.194402	+	0.00893723i
$277$	−7.57448	−	4.37313i	−0.455107	−	0.262756i	0.254878	−	0.966973i	$-0.417965\pi$
$277$	−7.57448	−	4.37313i	−0.455107	−	0.262756i	−0.709984	+	0.704217i	$0.751298\pi$
$278$	2.66228	+	2.66228i	0.159673	+	0.159673i
$279$	7.27490	−	8.75159i	0.435537	−	0.523944i
$280$	−0.445532	+	0.119380i	−0.0266257	+	0.00713432i
$281$	9.49571	−	9.49571i	0.566467	−	0.566467i	−0.364670	−	0.931137i	$-0.618818\pi$
$281$	9.49571	−	9.49571i	0.566467	−	0.566467i	0.931137	+	0.364670i	$0.118818\pi$
$282$	11.8298	−	7.57486i	0.704456	−	0.451077i
$283$	27.2245	−	15.7181i	1.61833	−	0.934342i	0.630975	−	0.775803i	$-0.282655\pi$
$283$	27.2245	−	15.7181i	1.61833	−	0.934342i	0.987353	−	0.158539i	$-0.0506782\pi$
$284$	−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
$288$	2.81431	−	1.03906i	0.165835	−	0.0612271i
$289$	−5.26672	−	9.12222i	−0.309807	−	0.536601i
$290$	2.63809	−	4.56930i	0.154914	−	0.268319i
$291$	−25.9981	+	8.26316i	−1.52403	+	0.484395i
$292$	−2.04171	−	7.61977i	−0.119482	−	0.445914i
$293$	−0.542185	−	2.02346i	−0.0316748	−	0.118212i	0.948278	−	0.317440i	$-0.102823\pi$
$293$	−0.542185	−	2.02346i	−0.0316748	−	0.118212i	−0.979953	+	0.199228i	$0.936157\pi$
$294$	10.5985	−	3.36861i	0.618119	−	0.196461i
$295$	2.61794	−	4.53440i	0.152422	−	0.264003i
$296$	−2.93893	−	5.09038i	−0.170822	−	0.295872i
$297$	2.70030	−	21.6688i	0.156687	−	1.25735i
$298$			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
$303$	−4.77357	+	3.05661i	−0.274234	+	0.175597i
$304$	−2.41216	+	2.41216i	−0.138347	+	0.138347i
$305$	4.75941	−	1.27528i	0.272523	−	0.0730223i
$306$	−12.1054	−	10.0628i	−0.692020	−	0.575253i
$307$	1.91340	+	1.91340i	0.109203	+	0.109203i	0.759597	−	0.650394i	$-0.225396\pi$
$307$	1.91340	+	1.91340i	0.109203	+	0.109203i	−0.650394	+	0.759597i	$0.725396\pi$
$308$	2.76999	+	1.59926i	0.157835	+	0.0911261i
$309$	−8.30300	+	0.381712i	−0.472341	+	0.0217149i
$310$	0.595004	−	2.22059i	0.0337940	−	0.126121i
$311$	7.19354			0.407908			0.203954	−	0.978980i	$-0.434621\pi$
$311$	7.19354			0.407908			0.203954	+	0.978980i	$0.434621\pi$
$312$	4.91887	−	3.84769i	0.278476	−	0.217833i
$313$	−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
$315$	1.25679	+	0.579004i	0.0708119	+	0.0326232i
$316$	11.7611	+	6.79025i	0.661612	+	0.381982i
$317$	3.93077	+	3.93077i	0.220774	+	0.220774i	0.808824	−	0.588050i	$-0.200104\pi$
$317$	3.93077	+	3.93077i	0.220774	+	0.220774i	−0.588050	+	0.808824i	$0.700104\pi$
$318$	−3.34441	+	15.2521i	−0.187545	+	0.855295i
$319$	−35.3407	+	9.46952i	−1.97870	+	0.530191i
$320$	0.428520	−	0.428520i	0.0239550	−	0.0239550i
$321$	−2.91879	−	4.55834i	−0.162911	−	0.254422i
$322$	−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
$327$	−1.65412	−	1.50871i	−0.0914730	−	0.0834321i
$328$	4.43446	+	7.68071i	0.244852	+	0.424096i
$329$	3.08637	−	5.34576i	0.170157	−	0.294721i
$330$	−1.33614	−	4.20385i	−0.0735521	−	0.231414i
$331$	−5.11244	−	19.0799i	−0.281005	−	1.04873i	−0.951709	−	0.307000i	$-0.900675\pi$
$331$	−5.11244	−	19.0799i	−0.281005	−	1.04873i	0.670704	−	0.741725i	$-0.265992\pi$
$332$	0.364900	+	1.36183i	0.0200265	+	0.0747399i
$333$	−2.98188	+	17.3797i	−0.163406	+	0.952399i
$334$	7.86434	−	13.6214i	0.430318	−	0.745332i
$335$	−0.0317479	−	0.0549890i	−0.00173457	−	0.00300437i
$336$	0.888378	−	0.973996i	0.0484650	−	0.0531359i
$337$		−	16.3889i		−	0.892762i	−0.894843	−	0.446381i	$-0.852713\pi$
$337$		−	16.3889i		−	0.892762i	0.894843	−	0.446381i	$-0.147287\pi$
$338$	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
$342$	10.1907	−	0.938979i	0.551052	−	0.0507742i
$343$	7.22288	−	7.22288i	0.389999	−	0.389999i
$344$	1.88389	−	0.504787i	0.101572	−	0.0272163i
$345$	1.91383	+	0.419655i	0.103037	+	0.0225935i
$346$	−3.83515	−	3.83515i	−0.206179	−	0.206179i
$347$	18.7272	+	10.8122i	1.00533	+	0.580427i	0.909821	−	0.415001i	$-0.136219\pi$
$347$	18.7272	+	10.8122i	1.00533	+	0.580427i	0.0955087	+	0.995429i	$0.469552\pi$
$348$	0.692527	+	15.0638i	0.0371233	+	0.807506i
$349$	−0.503975	+	1.88086i	−0.0269771	+	0.100680i	−0.978102	−	0.208127i	$-0.933263\pi$
$349$	−0.503975	+	1.88086i	−0.0269771	+	0.100680i	0.951125	+	0.308807i	$0.0999298\pi$
$350$	−3.52605			−0.188475
$351$	−18.7267	−	0.556450i	−0.999559	−	0.0297011i
$352$	−4.20241			−0.223989
$353$	6.02369	−	22.4807i	0.320609	−	1.19653i	−0.598045	−	0.801463i	$-0.704055\pi$
$353$	6.02369	−	22.4807i	0.320609	−	1.19653i	0.918653	−	0.395065i	$-0.129278\pi$
$354$	0.687237	+	14.9488i	0.0365262	+	0.794518i
$355$	5.47412	+	3.16049i	0.290536	+	0.167741i
$356$	−4.62980	−	4.62980i	−0.245379	−	0.245379i
$357$	−6.75683	−	1.48161i	−0.357609	−	0.0784149i
$358$	10.0271	−	2.68676i	0.529950	−	0.142000i
$359$	−15.8859	+	15.8859i	−0.838428	+	0.838428i	−0.988652	−	0.150224i	$-0.952000\pi$
$359$	−15.8859	+	15.8859i	−0.838428	+	0.838428i	0.150224	+	0.988652i	$0.452000\pi$
$360$	−1.81039	+	0.166810i	−0.0954157	+	0.00879164i
$361$	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
$366$	−9.49011	+	10.4047i	−0.496056	+	0.543864i
$367$	−0.300881	−	0.521141i	−0.0157059	−	0.0272034i	0.858066	−	0.513540i	$-0.171666\pi$
$367$	−0.300881	−	0.521141i	−0.0157059	−	0.0272034i	−0.873772	+	0.486337i	$0.838333\pi$
$368$	0.933306	−	1.61653i	0.0486519	−	0.0842676i
$369$	4.49926	−	26.2236i	0.234222	−	1.36515i
$370$	0.921938	+	3.44072i	0.0479293	+	0.178874i
$371$	1.77587	+	6.62765i	0.0921988	+	0.344091i
$372$	1.99024	+	6.26182i	0.103189	+	0.324660i
$373$	−5.70783	+	9.88625i	−0.295540	+	0.511891i	−0.975110	−	0.221720i	$-0.928833\pi$
$373$	−5.70783	+	9.88625i	−0.295540	+	0.511891i	0.679570	+	0.733611i	$0.262166\pi$
$374$	11.0255	+	19.0967i	0.570116	+	0.987469i
$375$	7.47039	+	6.81371i	0.385769	+	0.351858i
$376$			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	0.999990	−	0.00438723i	$-0.00139650\pi$
$379$	36.2846	+	9.72242i	1.86381	+	0.499407i	0.863823	+	0.503795i	$0.168063\pi$
$380$	1.79035	−	1.03366i	0.0918428	−	0.0530255i
$381$	−2.08746	−	3.26003i	−0.106944	−	0.167016i
$382$	−4.05345	+	4.05345i	−0.207392	+	0.207392i
$383$	−12.2026	+	3.26967i	−0.623523	+	0.167073i	−0.556729	−	0.830694i	$-0.687944\pi$
$383$	−12.2026	+	3.26967i	−0.623523	+	0.167073i	−0.0667943	+	0.997767i	$0.521277\pi$
$384$	−0.370982	+	1.69185i	−0.0189316	+	0.0863371i
$385$	−1.37063	−	1.37063i	−0.0698536	−	0.0698536i
$386$	−9.82453	−	5.67220i	−0.500056	−	0.288707i
$387$	−5.31419	−	2.44826i	−0.270136	−	0.124452i
$388$	4.07638	−	15.2132i	0.206947	−	0.772336i
$389$	18.8229			0.954361			0.477180	−	0.878805i	$-0.341659\pi$
$389$	18.8229			0.954361			0.477180	+	0.878805i	$0.341659\pi$
$390$	−3.48286	+	1.48080i	−0.176361	+	0.0749831i
$391$	−9.79455			−0.495332
$392$	−1.66180	+	6.20192i	−0.0839336	+	0.313245i
$393$	−38.2130	+	1.75676i	−1.92759	+	0.0886167i
$394$	−4.05576	−	2.34159i	−0.204326	−	0.117968i
$395$	−5.81951	−	5.81951i	−0.292812	−	0.292812i
$396$	9.69499	+	8.05912i	0.487192	+	0.404986i
$397$	11.5273	−	3.08874i	0.578540	−	0.155019i	0.0423297	−	0.999104i	$-0.486522\pi$
$397$	11.5273	−	3.08874i	0.578540	−	0.155019i	0.536210	+	0.844084i	$0.319855\pi$
$398$	−9.12358	+	9.12358i	−0.457324	+	0.457324i
$399$	3.78722	−	2.42503i	0.189598	−	0.121403i
$400$	4.01207	−	2.31637i	0.200604	−	0.115819i
$401$	−23.3959	−	6.26891i	−1.16833	−	0.313054i	−0.378045	−	0.925787i	$-0.623403\pi$
$401$	−23.3959	−	6.26891i	−1.16833	−	0.313054i	−0.790290	+	0.612733i	$0.790070\pi$
$402$	0.161164	+	0.0834248i	0.00803815	+	0.00416085i
$403$	7.92345	+	11.1488i	0.394695	+	0.555361i
$404$		−	3.27260i		−	0.162818i
$405$	4.49647	+	3.08701i	0.223431	+	0.153395i
$406$	3.31324	+	5.73870i	0.164433	+	0.284807i
$407$	12.3506	−	21.3919i	0.612197	−	1.06036i
$408$	8.66150	−	2.75295i	0.428808	−	0.136291i
$409$	6.94441	+	25.9169i	0.343379	+	1.28151i	0.894495	+	0.447078i	$0.147535\pi$
$409$	6.94441	+	25.9169i	0.343379	+	1.28151i	−0.551116	+	0.834429i	$0.685798\pi$
$410$	−1.39108	−	5.19159i	−0.0687007	−	0.256394i
$411$	16.4806	−	5.23814i	0.812927	−	0.258379i
$412$	2.39940	−	4.15589i	0.118210	−	0.204746i
$413$	3.28793	+	5.69487i	0.161789	+	0.280226i
$414$	−5.25323	+	1.93952i	−0.258182	+	0.0953221i
$415$		−	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	$-0.581392\pi$
$419$	9.38488	−	5.41836i	0.458481	−	0.264704i	0.711405	+	0.702782i	$0.248059\pi$
$420$	−0.672799	+	0.430806i	−0.0328292	+	0.0210212i
$421$	−22.8984	+	22.8984i	−1.11600	+	1.11600i	−0.123676	+	0.992323i	$0.539468\pi$
$421$	−22.8984	+	22.8984i	−1.11600	+	1.11600i	−0.992323	+	0.123676i	$0.960532\pi$
$422$	−5.09968	+	1.36646i	−0.248249	+	0.0665180i
$423$	15.5531	−	18.7102i	0.756219	−	0.909720i
$424$	−6.37457	−	6.37457i	−0.309577	−	0.309577i
$425$	−21.0523	−	12.1545i	−1.02119	−	0.589581i
$426$	−18.0468	+	0.829662i	−0.874370	+	0.0401973i
$427$	−1.60166	+	5.97746i	−0.0775096	+	0.289270i
$428$	3.12505			0.151055
$429$	24.3388	+	9.81692i	1.17509	+	0.473965i
$430$	−1.18195			−0.0569985
$431$	−8.68719	+	32.4210i	−0.418447	+	1.56167i	0.359381	+	0.933191i	$0.382988\pi$
$431$	−8.68719	+	32.4210i	−0.418447	+	1.56167i	−0.777829	+	0.628476i	$0.783679\pi$
$432$	4.10039	−	3.19168i	0.197280	−	0.153560i
$433$	−20.5735	−	11.8781i	−0.988698	−	0.570825i	−0.0838130	−	0.996482i	$-0.526710\pi$
$433$	−20.5735	−	11.8781i	−0.988698	−	0.570825i	−0.904885	+	0.425657i	$0.860043\pi$
$434$	2.04161	+	2.04161i	0.0980004	+	0.0980004i
$435$	1.95736	−	8.92652i	0.0938485	−	0.427994i
$436$	1.24854	−	0.334546i	0.0597943	−	0.0160218i
$437$	4.50256	−	4.50256i	0.215387	−	0.215387i
$438$	−7.36791	−	11.5066i	−0.352052	−	0.549808i
$439$	12.8746	−	7.43317i	0.614473	−	0.354766i	−0.160241	−	0.987078i	$-0.551227\pi$
$439$	12.8746	−	7.43317i	0.614473	−	0.354766i	0.774714	+	0.632312i	$0.217894\pi$
$440$	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	$-0.407801\pi$
$444$	−7.52190	−	6.86069i	−0.356973	−	0.325594i
$445$	1.98396	+	3.43632i	0.0940487	+	0.162897i
$446$	1.77511	−	3.07458i	0.0840540	−	0.145586i
$447$	4.57860	+	14.4055i	0.216560	+	0.681357i
$448$	0.196991	+	0.735180i	0.00930694	+	0.0347340i
$449$	1.18156	+	4.40965i	0.0557613	+	0.208104i	0.988186	−	0.153261i	$-0.0489775\pi$
$449$	1.18156	+	4.40965i	0.0557613	+	0.208104i	−0.932424	+	0.361365i	$0.882311\pi$
$450$	−13.6981	−	2.35022i	−0.645733	−	0.110790i
$451$	−18.6354	+	32.2775i	−0.877508	+	1.51989i
$452$	−3.48564	−	6.03730i	−0.163951	−	0.283971i
$453$	28.6675	−	31.4304i	1.34692	−	1.47673i
$454$		−	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	0.798101	−	0.602524i	$-0.205838\pi$
$457$	25.3969	+	6.80507i	1.18801	+	0.318328i	0.389914	+	0.920851i	$0.372505\pi$
$458$	−13.9485	+	8.05319i	−0.651773	+	0.376301i
$459$	−25.2616	−	10.2594i	−1.17911	−	0.478869i
$460$	−0.799880	+	0.799880i	−0.0372946	+	0.0372946i
$461$	−14.5525	+	3.89933i	−0.677778	+	0.181610i	−0.581256	−	0.813721i	$-0.697438\pi$
$461$	−14.5525	+	3.89933i	−0.677778	+	0.181610i	−0.0965219	+	0.995331i	$0.530772\pi$
$462$	5.41142	+	1.18659i	0.251762	+	0.0552052i
$463$	−12.8578	−	12.8578i	−0.597552	−	0.597552i	0.342108	−	0.939661i	$-0.388859\pi$
$463$	−12.8578	−	12.8578i	−0.597552	−	0.597552i	−0.939661	+	0.342108i	$0.888859\pi$
$464$	−7.53987	−	4.35315i	−0.350030	−	0.202090i
$465$	−0.182863	−	3.97764i	−0.00848009	−	0.184459i
$466$	5.79254	−	21.6181i	0.268334	−	1.00144i
$467$	12.7104			0.588168			0.294084	−	0.955780i	$-0.404985\pi$
$467$	12.7104			0.588168			0.294084	+	0.955780i	$0.404985\pi$
$468$	6.10080	−	8.93198i	0.282009	−	0.412881i
$469$	0.0797460			0.00368233
$470$	1.27207	−	4.74743i	0.0586762	−	0.218982i
$471$	0.880650	+	19.1559i	0.0405782	+	0.882656i
$472$	−7.48228	−	4.31989i	−0.344400	−	0.198839i
$473$	5.79555	+	5.79555i	0.266480	+	0.266480i
$474$	22.9762	+	5.03812i	1.05533	+	0.231409i
$475$	15.2652	−	4.09030i	0.700415	−	0.187676i
$476$	2.82400	−	2.82400i	0.129438	−	0.129438i
$477$	2.48143	+	26.9309i	0.113617	+	1.23308i
$478$	−7.44934	+	4.30088i	−0.340725	+	0.196718i
$479$	34.6068	+	9.27288i	1.58123	+	0.423689i	0.939306	−	0.343082i	$-0.111471\pi$
$479$	34.6068	+	9.27288i	1.58123	+	0.423689i	0.641922	+	0.766770i	$0.278137\pi$
$480$	0.482527	−	0.932171i	0.0220242	−	0.0425476i
$481$	−19.2696	−	8.82174i	−0.878619	−	0.402237i
$482$			6.14555i			0.279922i
$483$	−1.65826	+	1.81807i	−0.0754533	+	0.0827252i
$484$	−3.33013	−	5.76795i	−0.151369	−	0.262180i
$485$	−4.77237	+	8.26598i	−0.216702	+	0.375339i
$486$	−15.5804	−	0.500258i	−0.706743	−	0.0226921i
$487$	−1.74173	−	6.50021i	−0.0789252	−	0.294553i	0.915169	−	0.403069i	$-0.132057\pi$
$487$	−1.74173	−	6.50021i	−0.0789252	−	0.294553i	−0.994095	+	0.108517i	$0.965390\pi$
$488$	−2.10436	−	7.85357i	−0.0952598	−	0.355514i
$489$	−2.75726	−	8.67507i	−0.124688	−	0.392300i
$490$	1.94553	−	3.36976i	0.0878902	−	0.152230i
$491$	−14.9069	−	25.8195i	−0.672740	−	1.16522i	−0.977124	−	0.212670i	$-0.931784\pi$
$491$	−14.9069	−	25.8195i	−0.672740	−	1.16522i	0.304385	−	0.952549i	$-0.401549\pi$
$492$	11.3495	+	10.3519i	0.511677	+	0.466698i
$493$			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
$498$	1.31681	+	2.05649i	0.0590078	+	0.0921537i
$499$	25.5487	−	25.5487i	1.14372	−	1.14372i	0.155954	−	0.987764i	$-0.450155\pi$
$499$	25.5487	−	25.5487i	1.14372	−	1.14372i	0.987764	−	0.155954i	$-0.0498453\pi$
$500$	−5.63871	+	1.51089i	−0.252171	+	0.0675689i
$501$	5.83506	−	26.6106i	0.260691	−	1.18888i
$502$	−8.87855	−	8.87855i	−0.396269	−	0.396269i
$503$	−36.8913	−	21.2992i	−1.64490	−	0.949684i	−0.979055	−	0.203594i	$-0.934738\pi$
$503$	−36.8913	−	21.2992i	−1.64490	−	0.949684i	−0.665845	−	0.746090i	$-0.731929\pi$
$504$	0.955423	−	2.07384i	0.0425579	−	0.0923763i
$505$	−0.513305	+	1.91568i	−0.0228418	+	0.0852466i
$506$	7.84427			0.348720
$507$	6.41955	−	21.5822i	0.285102	−	0.958497i
$508$	2.23497			0.0991607
$509$	4.37237	−	16.3179i	0.193802	−	0.723279i	−0.798772	−	0.601634i	$-0.794517\pi$
$509$	4.37237	−	16.3179i	0.193802	−	0.723279i	0.992574	−	0.121645i	$-0.0388168\pi$
$510$	−5.50197	+	0.252941i	−0.243631	+	0.0112004i
$511$	−5.19971	−	3.00205i	−0.230021	−	0.132803i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	16.3290	−	6.89650i	0.720944	−	0.304488i
$514$	−4.57638	+	1.22624i	−0.201855	+	0.0540870i
$515$	−2.05638	+	2.05638i	−0.0906150	+	0.0906150i
$516$	2.84486	−	1.82162i	0.125238	−	0.0801923i
$517$	−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	$-0.135382\pi$
$522$	9.04634	+	24.5022i	0.395948	+	1.07243i
$523$	5.97667	+	10.3519i	0.261342	+	0.452657i	0.966599	−	0.256295i	$-0.0825017\pi$
$523$	5.97667	+	10.3519i	0.261342	+	0.452657i	−0.705257	+	0.708952i	$0.749168\pi$
$524$	11.0428	−	19.1267i	0.482406	−	0.835552i
$525$	−5.82037	+	1.84993i	−0.254022	+	0.0807376i
$526$	1.46723	+	5.47578i	0.0639743	+	0.238755i
$527$	5.15186	+	19.2270i	0.224419	+	0.837542i
$528$	−6.93684	+	2.20478i	−0.301887	+	0.0959509i
$529$	9.75788	−	16.9011i	0.424256	−	0.734832i
$530$	2.73163	+	4.73132i	0.118654	+	0.205516i
$531$	8.97724	+	24.3151i	0.389579	+	1.05518i
$532$			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
$537$	15.1420	−	9.69568i	0.653424	−	0.418400i
$538$	−5.16606	+	5.16606i	−0.222725	+	0.222725i
$539$	−26.0630	+	6.98357i	−1.12261	+	0.300804i
$540$	−2.90085	+	1.22516i	−0.124833	+	0.0527227i
$541$	13.7056	+	13.7056i	0.589250	+	0.589250i	0.937428	−	0.348179i	$-0.113200\pi$
$541$	13.7056	+	13.7056i	0.589250	+	0.589250i	−0.348179	+	0.937428i	$0.613200\pi$
$542$	−21.2418	−	12.2640i	−0.912414	−	0.526782i
$543$	19.2352	−	0.884298i	0.825463	−	0.0379488i
$544$	−1.35808	+	5.06844i	−0.0582273	+	0.217307i
$545$	−0.783330			−0.0335542
$546$	0.576496	−	4.71807i	0.0246718	−	0.201915i
$547$	−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
$549$	−10.2063	+	22.1538i	−0.435595	+	0.945503i
$550$	16.8604	+	9.73434i	0.718929	+	0.415074i
$551$	−21.0009	−	21.0009i	−0.894670	−	0.894670i
$552$	0.692479	−	3.15804i	0.0294739	−	0.134415i
$553$	9.98412	−	2.67524i	0.424568	−	0.113763i
$554$	6.18454	−	6.18454i	0.262756	−	0.262756i
$555$	3.32699	+	5.19583i	0.141223	+	0.220551i
$556$	−3.26061	+	1.88252i	−0.138281	+	0.0798365i
$557$	−1.16825	−	0.313031i	−0.0495002	−	0.0132635i	0.233984	−	0.972240i	$-0.424824\pi$
$557$	−1.16825	−	0.313031i	−0.0495002	−	0.0132635i	−0.283484	+	0.958977i	$0.591490\pi$
$558$	6.57050	+	9.29209i	0.278152	+	0.393366i
$559$	4.48228	−	5.41841i	0.189580	−	0.229175i
$560$		−	0.461249i		−	0.0194913i
$561$	28.2186	+	25.7381i	1.19139	+	1.08666i
$562$	6.71448	+	11.6298i	0.283233	+	0.490575i
$563$	−12.2059	+	21.1412i	−0.514416	+	0.890994i	0.485444	+	0.874267i	$0.338658\pi$
$563$	−12.2059	+	21.1412i	−0.514416	+	0.890994i	−0.999860	+	0.0167265i	$0.994676\pi$
$564$	4.25497	+	13.3873i	0.179167	+	0.563705i
$565$	1.09344	+	4.08077i	0.0460013	+	0.171679i
$566$	8.13627	+	30.3650i	0.341993	+	1.27633i
$567$	−6.18125	+	2.95212i	−0.259588	+	0.123977i
$568$	5.21517	−	9.03293i	0.218823	−	0.379013i
$569$	2.98833	+	5.17593i	0.125277	+	0.216986i	0.921841	−	0.387568i	$-0.126685\pi$
$569$	2.98833	+	5.17593i	0.125277	+	0.216986i	−0.796564	+	0.604554i	$0.793351\pi$
$570$	2.41298	−	2.64554i	0.101069	−	0.110809i
$571$		−	35.8068i		−	1.49847i	−0.662307	−	0.749233i	$-0.730422\pi$
$571$		−	35.8068i		−	1.49847i	0.662307	−	0.749233i	$-0.269578\pi$
$572$	−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
$576$	0.275255	+	2.98735i	0.0114690	+	0.124473i
$577$	13.8142	−	13.8142i	0.575094	−	0.575094i	−0.358453	−	0.933548i	$-0.616696\pi$
$577$	13.8142	−	13.8142i	0.575094	−	0.575094i	0.933548	+	0.358453i	$0.116696\pi$
$578$	10.1745	−	2.72625i	0.423204	−	0.113397i
$579$	−19.1931	−	4.20856i	−0.797637	−	0.174902i
$580$	3.73082	+	3.73082i	0.154914	+	0.154914i
$581$	0.929305	+	0.536534i	0.0385541	+	0.0222592i
$582$	−1.25280	−	27.2509i	−0.0519302	−	1.12958i
$583$	9.80530	−	36.5939i	0.406094	−	1.51556i
$584$	7.88857			0.326431
$585$	−4.97219	+	4.27160i	−0.205575	+	0.176609i
$586$	2.09484			0.0865371
$587$	−3.99377	+	14.9050i	−0.164841	+	0.615194i	0.833220	+	0.552942i	$0.186495\pi$
$587$	−3.99377	+	14.9050i	−0.164841	+	0.615194i	−0.998060	+	0.0622518i	$0.980172\pi$
$588$	0.510724	+	11.1093i	0.0210619	+	0.458138i
$589$	−11.2070	−	6.47036i	−0.461776	−	0.266607i
$590$	3.70232	+	3.70232i	0.152422	+	0.152422i
$591$	−7.92327	−	1.73738i	−0.325920	−	0.0714661i
$592$	5.67758	−	1.52130i	0.233347	−	0.0625252i
$593$	−19.1066	+	19.1066i	−0.784613	+	0.784613i	−0.980605	−	0.195992i	$-0.937207\pi$
$593$	−19.1066	+	19.1066i	−0.784613	+	0.784613i	0.195992	+	0.980605i	$0.437207\pi$
$594$	20.2315	+	8.21658i	0.830110	+	0.337130i
$595$	−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	$0.896357\pi$
$600$	5.40737	−	5.92851i	0.220755	−	0.242030i
$601$	6.65857	+	11.5330i	0.271609	+	0.470440i	0.969274	−	0.245984i	$-0.0791110\pi$
$601$	6.65857	+	11.5330i	0.271609	+	0.470440i	−0.697665	+	0.716424i	$0.745778\pi$
$602$	0.742218	−	1.28556i	0.0302505	−	0.0523955i
$603$	0.309799	+	0.0531532i	0.0126160	+	0.00216456i
$604$	6.35679	+	23.7239i	0.258654	+	0.965311i
$605$	1.04465	+	3.89870i	0.0424713	+	0.158505i
$606$	−1.71696	−	5.40202i	−0.0697469	−	0.219442i
$607$	−6.14650	+	10.6460i	−0.249479	+	0.432110i	−0.963381	−	0.268135i	$-0.913593\pi$
$607$	−6.14650	+	10.6460i	−0.249479	+	0.432110i	0.713903	+	0.700245i	$0.246926\pi$
$608$	−1.70565	−	2.95428i	−0.0691733	−	0.119812i
$609$	8.47990	+	7.73448i	0.343623	+	0.313417i
$610$			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	0.0428820	−	0.999080i	$-0.486346\pi$
$613$	−10.3869	−	2.78315i	−0.419521	−	0.112410i	−0.462403	+	0.886670i	$0.653013\pi$
$614$	−2.34342	+	1.35298i	−0.0945728	+	0.0546017i
$615$	−5.01999	−	7.83983i	−0.202425	−	0.316132i
$616$	−2.26169	+	2.26169i	−0.0911261	+	0.0911261i
$617$	12.1675	−	3.26027i	0.489845	−	0.131254i	−0.00543815	−	0.999985i	$-0.501731\pi$
$617$	12.1675	−	3.26027i	0.489845	−	0.131254i	0.495283	+	0.868732i	$0.335064\pi$
$618$	1.78027	−	8.11888i	0.0716129	−	0.326589i
$619$	−5.08096	−	5.08096i	−0.204221	−	0.204221i	0.597585	−	0.801806i	$-0.296127\pi$
$619$	−5.08096	−	5.08096i	−0.204221	−	0.204221i	−0.801806	+	0.597585i	$0.796127\pi$
$620$	1.99092	+	1.14946i	0.0799574	+	0.0461634i
$621$	−7.65384	+	5.95762i	−0.307138	+	0.239071i
$622$	−1.86183	+	6.94843i	−0.0746524	+	0.278607i
$623$	−4.98342			−0.199656
$624$	2.44349	+	5.74712i	0.0978178	+	0.230069i
$625$	−19.6260			−0.785040
$626$	3.79222	−	14.1527i	0.151567	−	0.565657i
$627$	−24.8040	+	1.14031i	−0.990575	+	0.0455395i
$628$	−9.58806	−	5.53567i	−0.382605	−	0.220897i
$629$	−21.8090	−	21.8090i	−0.869580	−	0.869580i
$630$	−0.884555	+	1.06411i	−0.0352415	+	0.0423950i
$631$	−23.9643	+	6.42121i	−0.954002	+	0.255624i	−0.702060	−	0.712118i	$-0.747736\pi$
$631$	−23.9643	+	6.42121i	−0.954002	+	0.255624i	−0.251943	+	0.967742i	$0.581069\pi$
$632$	−9.60287	+	9.60287i	−0.381982	+	0.381982i
$633$	−7.70103	+	4.93112i	−0.306089	+	0.195994i
$634$	−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
$639$	−29.3542	+	10.8377i	−1.16123	+	0.428734i
$640$	0.303009	+	0.524827i	0.0119775	+	0.0207456i
$641$	5.92602	−	10.2642i	0.234064	−	0.405410i	−0.724936	−	0.688816i	$-0.758131\pi$
$641$	5.92602	−	10.2642i	0.234064	−	0.405410i	0.959000	+	0.283406i	$0.0914642\pi$
$642$	5.15846	−	1.63955i	0.203588	−	0.0647079i
$643$	−7.18682	−	26.8216i	−0.283420	−	1.05774i	−0.949986	−	0.312293i	$-0.898903\pi$
$643$	−7.18682	−	26.8216i	−0.283420	−	1.05774i	0.666566	−	0.745446i	$-0.267764\pi$
$644$	−0.367706	−	1.37230i	−0.0144896	−	0.0540760i
$645$	−1.95101	+	0.620105i	−0.0768211	+	0.0244166i
$646$	−8.94995	+	15.5018i	−0.352131	+	0.609909i
$647$	9.84613	+	17.0540i	0.387091	+	0.670462i	0.992057	−	0.125790i	$-0.0401465\pi$
$647$	9.84613	+	17.0540i	0.387091	+	0.670462i	−0.604966	+	0.796251i	$0.706813\pi$
$648$	5.09393	−	7.41970i	0.200108	−	0.291473i
$649$		−	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	0.669455	−	0.742853i	$-0.266528\pi$
$653$	42.1003	−	24.3066i	1.64751	−	0.951191i	0.978057	−	0.208339i	$-0.0668056\pi$
$654$	1.88542	−	1.20727i	0.0737259	−	0.0472081i
$655$	−9.46410	+	9.46410i	−0.369793	+	0.369793i
$656$	−8.56672	+	2.29545i	−0.334474	+	0.0896221i
$657$	−18.1990	−	15.1282i	−0.710010	−	0.590208i
$658$	4.36479	+	4.36479i	0.170157	+	0.170157i
$659$	3.21116	+	1.85397i	0.125089	+	0.0722202i	0.561239	−	0.827654i	$-0.310325\pi$
$659$	3.21116	+	1.85397i	0.125089	+	0.0722202i	−0.436150	+	0.899874i	$0.643658\pi$
$660$	4.40643	−	0.202576i	0.171520	−	0.00788525i
$661$	1.66416	−	6.21075i	0.0647285	−	0.241570i	−0.925980	−	0.377573i	$-0.876759\pi$
$661$	1.66416	−	6.21075i	0.0647285	−	0.241570i	0.990708	+	0.136003i	$0.0434255\pi$
$662$	19.7529			0.767720
$663$	19.7055	−	26.1820i	0.765298	−	1.01682i
$664$	−1.40987			−0.0547134
$665$	0.407242	−	1.51985i	0.0157922	−	0.0589371i
$666$	−16.0157	−	7.37846i	−0.620595	−	0.285909i
$667$	14.0740	+	8.12564i	0.544948	+	0.314626i
$668$	11.1219	+	11.1219i	0.430318	+	0.430318i
$669$	1.31707	−	6.00646i	0.0509208	−	0.232223i
$670$	0.0613322	−	0.0164339i	0.00236947	−	0.000634898i
$671$	24.1605	−	24.1605i	0.932708	−	0.932708i
$672$	0.710879	+	1.11020i	0.0274228	+	0.0428267i
$673$	5.14268	−	2.96913i	0.198236	−	0.114451i	−0.397597	−	0.917560i	$-0.630156\pi$
$673$	5.14268	−	2.96913i	0.198236	−	0.114451i	0.595832	+	0.803109i	$0.296822\pi$
$674$	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	$-0.156243\pi$
$678$	−8.92113	−	8.13692i	−0.342614	−	0.312497i
$679$	−5.99374	−	10.3815i	−0.230019	−	0.398404i
$680$	1.58996	−	2.75389i	0.0609721	−	0.105607i
$681$	−2.63726	−	8.29751i	−0.101060	−	0.317961i
$682$	−4.12603	−	15.3986i	−0.157994	−	0.589641i
$683$	6.94368	+	25.9142i	0.265693	+	0.991578i	0.961825	+	0.273665i	$0.0882359\pi$
$683$	6.94368	+	25.9142i	0.265693	+	0.991578i	−0.696133	+	0.717913i	$0.745097\pi$
$684$	−1.73057	+	10.0865i	−0.0661702	+	0.385668i
$685$	3.02528	−	5.23994i	0.115590	−	0.200208i
$686$	5.10734	+	8.84618i	0.194999	+	0.337749i
$687$	−18.7995	+	20.6113i	−0.717245	+	0.786371i
$688$			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	0.0599568	−	0.998201i	$-0.480904\pi$
$691$	−10.1788	−	2.72740i	−0.387220	−	0.103755i	−0.447176	+	0.894446i	$0.647570\pi$
$692$	4.69708	−	2.71186i	0.178556	−	0.103090i
$693$	9.55507	−	0.880407i	0.362967	−	0.0334439i
$694$	−15.2907	+	15.2907i	−0.580427	+	0.580427i
$695$	2.20393	−	0.590542i	0.0835999	−	0.0224005i
$696$	−14.7298	−	3.22988i	−0.558331	−	0.122428i
$697$	32.9068	+	32.9068i	1.24644	+	1.24644i
$698$	−1.68633	−	0.973604i	−0.0638286	−	0.0368515i
$699$	−1.78023	−	38.7236i	−0.0673345	−	1.46466i
$700$	0.912608	−	3.40590i	0.0344933	−	0.128731i
$701$	48.3500			1.82616			0.913078	−	0.407785i	$-0.133699\pi$
$701$	48.3500			1.82616			0.913078	+	0.407785i	$0.133699\pi$
$702$	5.38432	−	17.9446i	0.203218	−	0.677276i
$703$	20.0512			0.756245
$704$	1.08766	−	4.05922i	0.0409929	−	0.152987i
$705$	−0.390947	−	8.50387i	−0.0147239	−	0.320274i
$706$	20.1557	+	11.6369i	0.758568	+	0.437959i
$707$	−1.76128	−	1.76128i	−0.0662397	−	0.0662397i
$708$	−14.6173	−	3.20521i	−0.549351	−	0.120459i
$709$	28.4274	−	7.61709i	1.06761	−	0.286066i	0.318100	−	0.948057i	$-0.396955\pi$
$709$	28.4274	−	7.61709i	1.06761	−	0.286066i	0.749512	+	0.661991i	$0.230288\pi$
$710$	−4.46960	+	4.46960i	−0.167741	+	0.167741i
$711$	40.5697	−	3.73810i	1.52148	−	0.140190i
$712$	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
$717$	−10.0400	+	11.0077i	−0.374952	+	0.411089i
$718$	−11.2331	−	19.4562i	−0.419214	−	0.726100i
$719$	21.4236	−	37.1068i	0.798966	−	1.38385i	−0.121324	−	0.992613i	$-0.538714\pi$
$719$	21.4236	−	37.1068i	0.798966	−	1.38385i	0.920290	−	0.391237i	$-0.127953\pi$
$720$	0.307437	−	1.79187i	0.0114575	−	0.0667791i
$721$	−0.945320	−	3.52798i	−0.0352056	−	0.131389i
$722$	1.90569	+	7.11211i	0.0709223	+	0.264685i
$723$	3.22425	+	10.1443i	0.119911	+	0.377272i
$724$	−5.55860	+	9.62777i	−0.206584	+	0.357813i
$725$	20.1670	+	34.9303i	0.748984	+	1.29728i
$726$	−8.52312	−	7.77390i	−0.316322	−	0.288516i
$727$			1.92620i			0.0714389i	0.999362	+	0.0357194i	$0.0113723\pi$
$727$			1.92620i			0.0714389i	−0.999362	+	0.0357194i	$0.988628\pi$
$728$	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
$732$	−7.59398	−	11.8597i	−0.280682	−	0.438347i
$733$	−22.6065	+	22.6065i	−0.834990	+	0.834990i	−0.988195	−	0.153204i	$-0.951041\pi$
$733$	−22.6065	+	22.6065i	−0.834990	+	0.834990i	0.153204	+	0.988195i	$0.451041\pi$
$734$	0.581258	−	0.155748i	0.0214546	−	0.00574875i
$735$	1.44351	−	6.58312i	0.0532448	−	0.242822i
$736$	1.31989	+	1.31989i	0.0486519	+	0.0486519i
$737$	−0.381319	−	0.220155i	−0.0140461	−	0.00810950i
$738$	24.1656	+	11.1331i	0.889546	+	0.409816i
$739$	−0.376096	+	1.40361i	−0.0138349	+	0.0516325i	−0.972498	−	0.232910i	$-0.925175\pi$
$739$	−0.376096	+	1.40361i	−0.0138349	+	0.0516325i	0.958663	+	0.284543i	$0.0918418\pi$
$740$	−3.56209			−0.130945
$741$	2.97726	+	21.0945i	0.109372	+	0.774927i
$742$	−6.86145			−0.251892
$743$	9.58365	−	35.7667i	0.351590	−	1.31215i	−0.533132	−	0.846032i	$-0.678985\pi$
$743$	9.58365	−	35.7667i	0.351590	−	1.31215i	0.884722	−	0.466119i	$-0.154348\pi$
$744$	−6.56357	+	0.301746i	−0.240632	+	0.0110625i
$745$	4.58017	+	2.64436i	0.167804	+	0.0968820i
$746$	−8.07209	−	8.07209i	−0.295540	−	0.295540i
$747$	3.25257	+	2.70375i	0.119005	+	0.0989251i
$748$	−21.2996	+	5.70722i	−0.778792	+	0.208677i
$749$	1.68187	−	1.68187i	0.0614542	−	0.0614542i
$750$	−8.51502	+	5.45232i	−0.310924	+	0.199091i
$751$	−13.2882	+	7.67193i	−0.484892	+	0.279953i	−0.722453	−	0.691420i	$-0.756985\pi$
$751$	−13.2882	+	7.67193i	−0.484892	+	0.279953i	0.237561	+	0.971373i	$0.423652\pi$
$752$	−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
$756$	0.489061	−	3.92451i	0.0177870	−	0.142733i
$757$	−11.2354	−	19.4603i	−0.408357	−	0.707296i	0.586349	−	0.810059i	$-0.300565\pi$
$757$	−11.2354	−	19.4603i	−0.408357	−	0.707296i	−0.994706	+	0.102763i	$0.967232\pi$
$758$	−18.7823	+	32.5319i	−0.682203	+	1.18161i
$759$	12.9484	−	4.11548i	0.469997	−	0.149382i
$760$	0.535060	+	1.99687i	0.0194087	+	0.0724341i
$761$	−0.210189	−	0.784436i	−0.00761934	−	0.0284358i	0.962012	−	0.273009i	$-0.0880188\pi$
$761$	−0.210189	−	0.784436i	−0.00761934	−	0.0284358i	−0.969631	+	0.244573i	$0.921352\pi$
$762$	3.68922	−	1.17257i	0.133646	−	0.0424777i
$763$	0.491903	−	0.852000i	0.0178081	−	0.0308445i
$764$	−2.86622	−	4.96444i	−0.103696	−	0.179607i
$765$	−8.94929	+	3.30412i	−0.323562	+	0.119461i
$766$		−	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	0.0343269	−	0.999411i	$-0.489071\pi$
$769$	−12.0810	−	3.23708i	−0.435651	−	0.116732i	−0.469977	+	0.882678i	$0.655738\pi$
$770$	1.67867	−	0.969179i	0.0604950	−	0.0349268i
$771$	−6.91079	+	4.42511i	−0.248886	+	0.159366i
$772$	8.02170	−	8.02170i	0.288707	−	0.288707i
$773$	−14.6654	+	3.92957i	−0.527476	+	0.141337i	−0.512723	−	0.858554i	$-0.671363\pi$
$773$	−14.6654	+	3.92957i	−0.527476	+	0.141337i	−0.0147536	+	0.999891i	$0.504696\pi$
$774$	3.74025	−	4.49946i	0.134441	−	0.161730i
$775$	12.4268	+	12.4268i	0.446386	+	0.446386i
$776$	13.6398	+	7.87496i	0.489641	+	0.282695i
$777$	−7.74055	+	0.355855i	−0.277691	+	0.0127662i
$778$	−4.87173	+	18.1816i	−0.174660	+	0.651840i
$779$	−30.2546			−1.08398
$780$	−0.528911	−	3.74744i	−0.0189380	−	0.134180i
$781$	43.8325			1.56845
$782$	2.53502	−	9.46081i	0.0906520	−	0.338318i
$783$	27.7877	+	35.6992i	0.993050	+	1.27579i
$784$	−5.56049	−	3.21035i	−0.198589	−	0.114655i
$785$	4.74428	+	4.74428i	0.169331	+	0.169331i
$786$	8.19335	−	37.3656i	0.292247	−	1.33279i
$787$	−26.9442	+	7.21968i	−0.960458	+	0.257354i	−0.704794	−	0.709412i	$-0.748961\pi$
$787$	−26.9442	+	7.21968i	−0.960458	+	0.257354i	−0.255664	+	0.966766i	$0.582294\pi$
$788$	3.31151	−	3.31151i	0.117968	−	0.117968i
$789$	5.29478	+	8.26898i	0.188499	+	0.294384i
$790$	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
$795$	6.99132	+	6.37676i	0.247957	+	0.226160i
$796$	−6.45135	−	11.1741i	−0.228662	−	0.396054i
$797$	−21.9041	+	37.9390i	−0.775883	+	1.34387i	0.158414	+	0.987373i	$0.449362\pi$
$797$	−21.9041	+	37.9390i	−0.775883	+	1.34387i	−0.934297	+	0.356496i	$0.883971\pi$
$798$	1.36219	+	4.28581i	0.0482210	+	0.151716i
$799$	11.0143	+	41.1058i	0.389656	+	1.45422i
$800$	1.19904	+	4.47488i	0.0423925	+	0.158211i
$801$	−19.3597	−	3.32160i	−0.684041	−	0.117363i
$802$	12.1106	−	20.9762i	0.427640	−	0.740694i
$803$	16.5755	+	28.7096i	0.584937	+	1.01314i
$804$	−0.122295	+	0.134081i	−0.00431300	+	0.00472867i
$805$			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	$-0.664493\pi$
$809$	0.336378	−	0.194208i	0.0118264	−	0.00682798i	0.505902	+	0.862591i	$0.331160\pi$
$810$	−4.14560	+	3.54428i	−0.145662	+	0.124533i
$811$	−5.70744	+	5.70744i	−0.200415	+	0.200415i	−0.800178	−	0.599763i	$-0.795262\pi$
$811$	−5.70744	+	5.70744i	−0.200415	+	0.200415i	0.599763	+	0.800178i	$0.295262\pi$
$812$	−6.40069	+	1.71506i	−0.224620	+	0.0601868i
$813$	−41.4977	−	9.09942i	−1.45539	−	0.319130i
$814$	17.4664	+	17.4664i	0.612197	+	0.612197i
$815$	−2.75821	−	1.59245i	−0.0966157	−	0.0557811i
$816$	0.417382	+	9.07888i	0.0146113	+	0.317824i
$817$	−1.72198	+	6.42652i	−0.0602445	+	0.224835i
$818$	−26.8311			−0.938128
$819$	−1.52371	−	8.09048i	−0.0532428	−	0.282704i
$820$	5.37473			0.187694
$821$	−8.85384	+	33.0430i	−0.309001	+	1.15321i	0.620445	+	0.784250i	$0.286952\pi$
$821$	−8.85384	+	33.0430i	−0.309001	+	1.15321i	−0.929446	+	0.368958i	$0.879715\pi$
$822$	0.794169	+	17.2748i	0.0276998	+	0.602526i
$823$	32.3186	+	18.6592i	1.12656	+	0.650418i	0.943067	−	0.332604i	$-0.107927\pi$
$823$	32.3186	+	18.6592i	1.12656	+	0.650418i	0.183490	+	0.983022i	$0.441260\pi$
$824$	3.39327	+	3.39327i	0.118210	+	0.118210i
$825$	32.9382	+	7.22253i	1.14676	+	0.251456i
$826$	−6.35180	+	1.70196i	−0.221007	+	0.0592187i
$827$	8.16295	−	8.16295i	0.283854	−	0.283854i	−0.550790	−	0.834644i	$-0.685674\pi$
$827$	8.16295	−	8.16295i	0.283854	−	0.283854i	0.834644	+	0.550790i	$0.185674\pi$
$828$	−0.513795	−	5.57622i	−0.0178556	−	0.193787i
$829$	28.1823	−	16.2711i	0.978813	−	0.565118i	0.0769017	−	0.997039i	$-0.475497\pi$
$829$	28.1823	−	16.2711i	0.978813	−	0.565118i	0.901912	+	0.431921i	$0.142164\pi$
$830$	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
$834$	−4.39457	+	4.81811i	−0.152172	+	0.166837i
$835$	−4.76593	−	8.25484i	−0.164932	−	0.285671i
$836$	7.16785	−	12.4151i	0.247905	−	0.429385i
$837$	15.7209	+	11.8911i	0.543393	+	0.411016i
$838$	2.80475	+	10.4675i	0.0968885	+	0.361593i
$839$	3.48230	+	12.9961i	0.120222	+	0.448676i	0.999624	−	0.0274036i	$-0.00872393\pi$
$839$	3.48230	+	12.9961i	0.120222	+	0.448676i	−0.879402	+	0.476080i	$0.842057\pi$
$840$	−0.241993	−	0.761375i	−0.00834956	−	0.0262699i
$841$	23.3998	−	40.5296i	0.806889	−	1.39757i
$842$	−16.1916	−	28.0447i	−0.557999	−	0.966483i
$843$	17.1850	+	15.6744i	0.591884	+	0.539854i
$844$		−	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
$849$	29.3613	+	45.8542i	1.00768	+	1.57371i
$850$	17.1891	−	17.1891i	0.589581	−	0.589581i
$851$	−10.5978	+	2.83968i	−0.363290	+	0.0973431i
$852$	3.86946	−	17.6466i	0.132566	−	0.604563i
$853$	−8.09779	−	8.09779i	−0.277263	−	0.277263i	0.554752	−	0.832015i	$-0.312813\pi$
$853$	−8.09779	−	8.09779i	−0.277263	−	0.277263i	−0.832015	+	0.554752i	$0.812813\pi$
$854$	−5.35925	−	3.09416i	−0.183390	−	0.105880i
$855$	2.59509	−	5.63290i	0.0887501	−	0.192641i
$856$	−0.808823	+	3.01857i	−0.0276450	+	0.103173i
$857$	2.81672			0.0962173			0.0481086	−	0.998842i	$-0.484681\pi$
$857$	2.81672			0.0962173			0.0481086	+	0.998842i	$0.484681\pi$
$858$	−15.7818	+	20.9687i	−0.538780	+	0.715859i
$859$	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
$861$	11.6795	−	0.536938i	0.398035	−	0.0182988i
$862$	−29.0679	−	16.7824i	−0.990057	−	0.571610i
$863$	16.9992	+	16.9992i	0.578658	+	0.578658i	0.934534	−	0.355875i	$-0.115817\pi$
$863$	16.9992	+	16.9992i	0.578658	+	0.578658i	−0.355875	+	0.934534i	$0.615817\pi$
$864$	2.02166	+	4.78674i	0.0687783	+	0.162848i
$865$	−3.17488	+	0.850706i	−0.107949	+	0.0289249i
$866$	16.7982	−	16.7982i	0.570825	−	0.570825i
$867$	15.3645	−	9.83821i	0.521807	−	0.334123i
$868$	−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
$873$	−16.3651	−	44.3252i	−0.553874	−	1.50018i
$874$	3.18379	+	5.51449i	0.107693	+	0.186530i
$875$	−2.22155	+	3.84783i	−0.0751020	+	0.130080i
$876$	13.0215	−	4.13872i	0.439956	−	0.139834i
$877$	−7.98650	−	29.8060i	−0.269685	−	1.00648i	−0.959320	−	0.282321i	$-0.908896\pi$
$877$	−7.98650	−	29.8060i	−0.269685	−	1.00648i	0.689635	−	0.724157i	$-0.257771\pi$
$878$	3.84769	+	14.3598i	0.129853	+	0.484619i
$879$	3.45791	−	1.09905i	0.116633	−	0.0370702i
$880$	−1.27337	+	2.20554i	−0.0429253	+	0.0743487i
$881$	−23.1312	−	40.0644i	−0.779310	−	1.34980i	−0.932340	−	0.361583i	$-0.882236\pi$
$881$	−23.1312	−	40.0644i	−0.779310	−	1.34980i	0.153030	−	0.988222i	$-0.451097\pi$
$882$	6.67149	+	18.0699i	0.224641	+	0.608444i
$883$			31.0867i			1.04615i	0.852286	+	0.523076i	$0.175216\pi$
$883$			31.0867i			1.04615i	−0.852286	+	0.523076i	$0.824784\pi$
$884$	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	$-0.458410\pi$
$887$	31.3930	−	18.1248i	1.05407	−	0.608570i	0.923787	+	0.382907i	$0.125077\pi$
$888$	8.57373	−	5.48992i	0.287715	−	0.184230i
$889$	1.20283	−	1.20283i	0.0403418	−	0.0403418i
$890$	−3.83272	+	1.02697i	−0.128473	+	0.0344242i
$891$	37.7066	+	2.94852i	1.26322	+	0.0987790i
$892$	2.51039	+	2.51039i	0.0840540	+	0.0840540i
$893$	−23.9596	−	13.8331i	−0.801778	−	0.462907i
$894$	−15.0997	+	0.694174i	−0.505008	+	0.0232167i
$895$	1.62822	−	6.07662i	0.0544255	−	0.203119i
$896$	−0.761114			−0.0254270
$897$	−4.56104	−	10.7276i	−0.152289	−	0.358186i
$898$	−4.56520			−0.152343
$899$	8.54806	−	31.9018i	0.285094	−	1.06398i
$900$	5.81546	−	12.6230i	0.193849	−	0.420768i
$901$	−40.9663	−	23.6519i	−1.36479	−	0.787960i
$902$	−26.3545	−	26.3545i	−0.877508	−	0.877508i
$903$	0.550699	−	2.51145i	0.0183261	−	0.0835758i
$904$	6.73373	−	1.80430i	0.223961	−	0.0600101i
$905$	4.76394	−	4.76394i	0.158359	−	0.158359i
$906$	22.9397	+	35.8255i	0.762121	+	1.19022i
$907$	−47.4882	+	27.4174i	−1.57682	+	0.910378i	−0.581522	+	0.813531i	$0.697543\pi$
$907$	−47.4882	+	27.4174i	−1.57682	+	0.910378i	−0.995299	+	0.0968476i	$0.969124\pi$
$908$	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	$0.933626\pi$
$912$	−4.36544	−	3.98170i	−0.144554	−	0.131847i
$913$	−2.96242	−	5.13106i	−0.0980417	−	0.169813i
$914$	−13.1464	+	22.7702i	−0.434844	+	0.753171i
$915$	2.58510	+	8.13340i	0.0854607	+	0.268882i
$916$	−4.16864	−	15.5576i	−0.137736	−	0.514037i
$917$	−4.35066	−	16.2369i	−0.143671	−	0.536189i
$918$	16.4480	−	21.7455i	0.542865	−	0.717708i
$919$	−15.2143	+	26.3520i	−0.501874	+	0.869272i	0.498123	+	0.867106i	$0.334023\pi$
$919$	−15.2143	+	26.3520i	−0.501874	+	0.869272i	−0.999998	+	0.00216566i	$0.999311\pi$
$920$	−0.565601	−	0.979649i	−0.0186473	−	0.0322981i
$921$	−3.15841	+	3.46280i	−0.104073	+	0.114103i
$922$		−	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
$927$	−1.32090	−	14.3357i	−0.0433839	−	0.470846i
$928$	6.15628	−	6.15628i	0.202090	−	0.202090i
$929$	−11.3485	+	3.04082i	−0.372332	+	0.0997662i	−0.440133	−	0.897933i	$-0.645069\pi$
$929$	−11.3485	+	3.04082i	−0.372332	+	0.0997662i	0.0678003	+	0.997699i	$0.478402\pi$
$930$	3.88944	+	0.852857i	0.127540	+	0.0279663i
$931$	−15.4877	−	15.4877i	−0.507590	−	0.507590i
$932$	19.3822	+	11.1903i	0.634886	+	0.366552i
$933$	0.572198	+	12.4464i	0.0187329	+	0.407478i
$934$	−3.28970	+	12.2773i	−0.107642	+	0.401726i
$935$	13.3633			0.437027
$936$	7.04863	+	8.20468i	0.230392	+	0.268179i
$937$	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
$939$	−1.16547	−	25.3512i	−0.0380336	−	0.827306i
$940$	4.25643	+	2.45745i	0.138829	+	0.0801532i
$941$	35.4161	+	35.4161i	1.15453	+	1.15453i	0.985634	+	0.168897i	$0.0540204\pi$
$941$	35.4161	+	35.4161i	1.15453	+	1.15453i	0.168897	+	0.985634i	$0.445980\pi$
$942$	−18.7311	−	4.10726i	−0.610292	−	0.133822i
$943$	15.9907	−	4.28471i	0.520730	−	0.139529i
$944$	6.10925	−	6.10925i	0.198839	−	0.198839i
$945$	−0.901837	+	2.22058i	−0.0293368	+	0.0722354i
$946$	−7.09808	+	4.09808i	−0.230778	+	0.133240i
$947$	−54.5457	−	14.6155i	−1.77250	−	0.474939i	−0.783314	−	0.621626i	$-0.786472\pi$
$947$	−54.5457	−	14.6155i	−1.77250	−	0.474939i	−0.989183	+	0.146687i	$0.953139\pi$
$948$	−10.8131	+	20.8894i	−0.351195	+	0.678456i
$949$	23.1840	−	16.4769i	0.752584	−	0.534862i
$950$			15.8037i			0.512739i
$951$	−6.48844	+	7.11377i	−0.210402	+	0.230680i
$952$	1.99687	+	3.45868i	0.0647190	+	0.112097i
$953$	3.27175	−	5.66683i	0.105982	−	0.183567i	−0.808157	−	0.588967i	$-0.799535\pi$
$953$	3.27175	−	5.66683i	0.105982	−	0.183567i	0.914139	+	0.405401i	$0.132868\pi$
$954$	−26.6555	−	4.57337i	−0.863005	−	0.148068i
$955$	0.899128	+	3.35559i	0.0290951	+	0.108584i
$956$	−2.22630	−	8.30866i	−0.0720037	−	0.268721i
$957$	−19.1955	−	60.3941i	−0.620502	−	1.95226i
$958$	−17.9138	+	31.0276i	−0.578769	+	1.00246i
$959$	3.79953	+	6.58097i	0.122693	+	0.212511i
$960$	0.775521	+	0.707349i	0.0250298	+	0.0228296i
$961$			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
$966$	−1.32694	−	2.07231i	−0.0426935	−	0.0666753i
$967$	−10.8941	+	10.8941i	−0.350332	+	0.350332i	−0.860233	−	0.509901i	$-0.829682\pi$
$967$	−10.8941	+	10.8941i	−0.350332	+	0.350332i	0.509901	+	0.860233i	$0.329682\pi$
$968$	6.43331	−	1.72380i	0.206774	−	0.0554050i
$969$	−6.64054	+	30.2840i	−0.213325	+	0.972863i
$970$	−6.74915	−	6.74915i	−0.216702	−	0.216702i
$971$	2.07268	+	1.19666i	0.0665153	+	0.0384027i	0.532889	−	0.846185i	$-0.321106\pi$
$971$	2.07268	+	1.19666i	0.0665153	+	0.0384027i	−0.466373	+	0.884588i	$0.654440\pi$
$972$	4.51572	−	14.9201i	0.144842	−	0.478561i
$973$	−0.741677	+	2.76798i	−0.0237771	+	0.0887372i
$974$	6.72951			0.215628
$975$	3.50901	−	28.7179i	0.112378	−	0.919708i
$976$	8.13061			0.260255
$977$	8.71475	−	32.5239i	0.278810	−	1.04053i	−0.674436	−	0.738334i	$-0.735613\pi$
$977$	8.71475	−	32.5239i	0.278810	−	1.04053i	0.953245	−	0.302198i	$-0.0977203\pi$
$978$	9.09311	−	0.418036i	0.290766	−	0.0133673i
$979$	23.8290	+	13.7577i	0.761579	+	0.439698i
$980$	2.75140	+	2.75140i	0.0878902	+	0.0878902i
$981$	2.47884	−	2.98200i	0.0791433	−	0.0952081i
$982$	28.7979	−	7.71639i	0.918979	−	0.246240i
$983$	−26.5732	+	26.5732i	−0.847553	+	0.847553i	−0.989827	−	0.142274i	$-0.954558\pi$
$983$	−26.5732	+	26.5732i	−0.847553	+	0.847553i	0.142274	+	0.989827i	$0.454558\pi$
$984$	−12.9366	+	8.28356i	−0.412404	+	0.264070i
$985$	−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
$990$	7.16732	−	2.64621i	0.227792	−	0.0841020i
$991$	−10.8598	−	18.8098i	−0.344974	−	0.597512i	0.640375	−	0.768062i	$-0.278779\pi$
$991$	−10.8598	−	18.8098i	−0.344974	−	0.597512i	−0.985349	+	0.170550i	$0.945445\pi$
$992$	1.89674	−	3.28525i	0.0602216	−	0.104307i
$993$	32.6058	−	10.3633i	1.03471	−	0.328871i
$994$	−2.05468	−	7.66817i	−0.0651705	−	0.243220i
$995$	2.02378	+	7.55283i	0.0641580	+	0.239441i
$996$	−2.32724	+	0.739683i	−0.0737413	+	0.0234377i
$997$	5.77610	−	10.0045i	0.182931	−	0.316846i	−0.759946	−	0.649986i	$-0.774775\pi$
$997$	5.77610	−	10.0045i	0.182931	−	0.316846i	0.942877	+	0.333140i	$0.108108\pi$
$998$	18.0657	+	31.2907i	0.571859	+	0.990489i
$999$	−30.3079	−	3.77688i	−0.958898	−	0.119495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.41.2	✓	16
3.2	odd	2	inner	78.2.k.a.41.4	yes	16
4.3	odd	2		624.2.cn.d.353.2		16
12.11	even	2		624.2.cn.d.353.1		16
13.2	odd	12		1014.2.g.d.437.1		16
13.3	even	3		1014.2.g.c.239.1		16
13.7	odd	12	inner	78.2.k.a.59.4	yes	16
13.10	even	6		1014.2.g.d.239.5		16
13.11	odd	12		1014.2.g.c.437.5		16
39.2	even	12		1014.2.g.d.437.5		16
39.11	even	12		1014.2.g.c.437.1		16
39.20	even	12	inner	78.2.k.a.59.2	yes	16
39.23	odd	6		1014.2.g.d.239.1		16
39.29	odd	6		1014.2.g.c.239.5		16
52.7	even	12		624.2.cn.d.449.1		16
156.59	odd	12		624.2.cn.d.449.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.2	✓	16	1.1	even	1	trivial
78.2.k.a.41.4	yes	16	3.2	odd	2	inner
78.2.k.a.59.2	yes	16	39.20	even	12	inner
78.2.k.a.59.4	yes	16	13.7	odd	12	inner
624.2.cn.d.353.1		16	12.11	even	2
624.2.cn.d.353.2		16	4.3	odd	2
624.2.cn.d.449.1		16	52.7	even	12
624.2.cn.d.449.2		16	156.59	odd	12
1014.2.g.c.239.1		16	13.3	even	3
1014.2.g.c.239.5		16	39.29	odd	6
1014.2.g.c.437.1		16	39.11	even	12
1014.2.g.c.437.5		16	13.11	odd	12
1014.2.g.d.239.1		16	39.23	odd	6
1014.2.g.d.239.5		16	13.10	even	6
1014.2.g.d.437.1		16	13.2	odd	12
1014.2.g.d.437.5		16	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.428520 + 0.428520i) q^{5} +(-1.69185 - 0.370982i) q^{6} +(-0.735180 + 0.196991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.0795432 + 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.428520 + 0.428520i) q^{5} +(-1.69185 - 0.370982i) q^{6} +(-0.735180 + 0.196991i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) 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} +(-0.707349 + 0.775521i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62362 - 4.54424i) q^{17} +(0.507306 - 2.95680i) q^{18} +(0.882911 + 3.29507i) q^{19} +(-0.156849 - 0.585369i) q^{20} +(-0.399317 - 1.25636i) q^{21} +(-2.10121 + 3.63939i) q^{22} +(-0.933306 - 1.61653i) q^{23} +(1.27970 + 1.16721i) 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} +(-0.566020 - 0.883966i) q^{30} +(-2.68240 + 2.68240i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55902 + 7.10987i) q^{33} +(3.71035 + 3.71035i) q^{34} +(-0.399453 - 0.230625i) q^{35} +(2.72474 + 1.25529i) q^{36} +(1.52130 - 5.67758i) q^{37} -3.41130 q^{38} +(6.19889 + 0.757437i) q^{39} +0.606018 q^{40} +(-2.29545 + 8.56672i) q^{41} +(1.31690 - 0.0605415i) q^{42} +(1.68905 + 0.975173i) q^{43} +(-2.97155 - 2.97155i) q^{44} +(-1.39809 - 1.16218i) q^{45} +(1.80301 - 0.483115i) q^{46} +(-5.73474 + 5.73474i) q^{47} +(-1.45865 + 0.933998i) 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} +(5.15627 + 0.642559i) q^{54} +(1.27337 + 2.20554i) q^{55} +(-0.380557 + 0.659144i) q^{56} +(-5.63097 + 1.78973i) q^{57} +(-2.25335 - 8.40963i) q^{58} +(-2.23614 - 8.34539i) q^{59} +(1.00034 - 0.317946i) q^{60} +(4.06531 - 7.04132i) q^{61} +(-1.89674 - 3.28525i) q^{62} +(2.14201 - 0.790842i) 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} +(2.72273 - 1.74341i) q^{69} +(0.326152 - 0.326152i) q^{70} +(10.0749 - 2.69957i) q^{71} +(-1.91774 + 2.30701i) q^{72} +(5.57806 + 5.57806i) q^{73} +(5.09038 + 2.93893i) q^{74} +(8.01568 - 0.368503i) q^{75} +(0.882911 - 3.29507i) q^{76} -3.19851 q^{77} +(-2.33602 + 5.79163i) q^{78} -13.5805 q^{79} +(-0.156849 + 0.585369i) q^{80} +(8.84847 - 1.64456i) q^{81} +(-7.68071 - 4.43446i) q^{82} +(-0.996926 - 0.996926i) q^{83} +(-0.282360 + 1.28769i) q^{84} +(3.07156 - 0.823023i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(-8.13166 - 12.6994i) 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} +(-4.85451 - 4.42778i) q^{93} +(-4.05507 - 7.02359i) q^{94} +(-1.03366 + 1.79035i) q^{95} +(-0.524648 - 1.65068i) q^{96} +(4.07638 + 15.2132i) q^{97} +(-1.66180 - 6.20192i) q^{98} +(-12.4257 - 2.13191i) 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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