LMFDB - Embedded newform 78.2.k.a.41.3

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			41.3
Root			$0.500000 - 0.589118i$ of defining polynomial
Character	$\chi$	$=$	78.41
Dual form			78.2.k.a.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.45865 - 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.02097 - 2.02097i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(3.46723 - 0.929042i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.45865 - 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.02097 - 2.02097i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(3.46723 - 0.929042i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +(-2.47517 + 1.42904i) q^{10} +(4.05922 + 1.08766i) q^{11} +(0.796225 + 1.53819i) q^{12} +(-3.60121 - 0.176977i) q^{13} -3.58954i q^{14} +(1.06030 + 4.83546i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.72704 - 2.99132i) q^{17} +(2.95680 - 0.507306i) q^{18} +(0.581191 + 2.16903i) q^{19} +(0.739726 + 2.76070i) q^{20} +(-5.92518 - 1.88324i) q^{21} +(2.10121 - 3.63939i) q^{22} +(1.51618 + 2.62611i) q^{23} +(1.69185 - 0.370982i) q^{24} +3.16864i q^{25} +(-1.10301 + 3.43269i) q^{26} +(0.713876 - 5.14688i) q^{27} +(-3.46723 - 0.929042i) q^{28} +(-1.74432 + 1.00708i) q^{29} +(4.94512 + 0.227341i) q^{30} +(1.21829 - 1.21829i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-4.90508 - 5.37782i) q^{33} +(-2.44240 - 2.44240i) q^{34} +(-8.88473 - 5.12960i) q^{35} +(0.275255 - 2.98735i) q^{36} +(-1.25335 + 4.67758i) q^{37} +2.24555 q^{38} +(5.08759 + 3.62167i) q^{39} +2.85808 q^{40} +(-2.05521 + 7.67015i) q^{41} +(-3.35262 + 5.23587i) q^{42} +(-1.68905 - 0.975173i) q^{43} +(-2.97155 - 2.97155i) q^{44} +(2.96971 - 8.04354i) q^{45} +(2.92904 - 0.784834i) q^{46} +(0.957390 - 0.957390i) q^{47} +(0.0795432 - 1.73022i) q^{48} +(5.09639 - 2.94240i) q^{49} +(3.06067 + 0.820104i) q^{50} +(-5.31303 + 2.75023i) q^{51} +(3.03025 + 1.95387i) q^{52} -7.22186i q^{53} +(-4.78674 - 2.02166i) q^{54} +(-6.00542 - 10.4017i) q^{55} +(-1.79477 + 3.10863i) q^{56} +(1.17812 - 3.70668i) q^{57} +(0.521304 + 1.94553i) q^{58} +(2.66284 + 9.93785i) q^{59} +(1.49949 - 4.71778i) q^{60} +(-0.137104 + 0.237470i) q^{61} +(-0.861464 - 1.49210i) q^{62} +(6.88380 + 8.28110i) q^{63} -1.00000i q^{64} +(6.92026 + 7.63559i) q^{65} +(-6.46410 + 3.34607i) q^{66} +(4.10121 + 1.09891i) q^{67} +(-2.99132 + 1.72704i) q^{68} +(0.241204 - 5.24667i) q^{69} +(-7.25436 + 7.25436i) q^{70} +(-10.6578 + 2.85575i) q^{71} +(-2.81431 - 1.03906i) q^{72} +(10.0822 + 10.0822i) q^{73} +(4.19381 + 2.42130i) q^{74} +(2.95950 - 4.62192i) q^{75} +(0.581191 - 2.16903i) q^{76} +15.0847 q^{77} +(4.81502 - 3.97688i) q^{78} +1.58051 q^{79} +(0.739726 - 2.76070i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(6.87686 + 3.97036i) q^{82} +(2.58938 + 2.58938i) q^{83} +(4.18974 + 4.59353i) q^{84} +(-9.53567 + 2.55507i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(3.48495 + 0.160213i) q^{87} +(-3.63939 + 2.10121i) q^{88} +(-9.50933 - 2.54802i) q^{89} +(-7.00085 - 4.95035i) q^{90} +(-12.6506 + 2.73205i) q^{91} -3.03237i q^{92} +(-2.91495 + 0.639175i) q^{93} +(-0.676977 - 1.17256i) q^{94} +(3.20898 - 5.55812i) q^{95} +(-1.65068 - 0.524648i) q^{96} +(-2.07638 - 7.74915i) q^{97} +(-1.52310 - 5.68429i) 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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

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

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
$3$	−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
$5$	−2.02097	−	2.02097i	−0.903805	−	0.903805i	0.0919576	−	0.995763i	$-0.470688\pi$
$5$	−2.02097	−	2.02097i	−0.903805	−	0.903805i	−0.995763	+	0.0919576i	$0.970688\pi$
$6$	−1.27970	+	1.16721i	−0.522435	+	0.476510i
$7$	3.46723	−	0.929042i	1.31049	−	0.351145i	0.465083	−	0.885267i	$-0.346025\pi$
$7$	3.46723	−	0.929042i	1.31049	−	0.351145i	0.845407	+	0.534122i	$0.179358\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.25529	+	2.72474i	0.418432	+	0.908248i
$10$	−2.47517	+	1.42904i	−0.782718	+	0.451903i
$11$	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
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$14$		−	3.58954i		−	0.959345i
$15$	1.06030	+	4.83546i	0.273768	+	1.24851i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.72704	−	2.99132i	0.418869	−	0.725502i	−0.576957	−	0.816774i	$-0.695760\pi$
$17$	1.72704	−	2.99132i	0.418869	−	0.725502i	0.995826	+	0.0912724i	$0.0290934\pi$
$18$	2.95680	−	0.507306i	0.696923	−	0.119573i
$19$	0.581191	+	2.16903i	0.133334	+	0.497611i	0.999999	−	0.00128023i	$-0.000407509\pi$
$19$	0.581191	+	2.16903i	0.133334	+	0.497611i	−0.866665	+	0.498891i	$0.833741\pi$
$20$	0.739726	+	2.76070i	0.165408	+	0.617310i
$21$	−5.92518	−	1.88324i	−1.29298	−	0.410958i
$22$	2.10121	−	3.63939i	0.447978	−	0.775921i
$23$	1.51618	+	2.62611i	0.316146	+	0.547581i	0.979680	−	0.200565i	$-0.0642777\pi$
$23$	1.51618	+	2.62611i	0.316146	+	0.547581i	−0.663534	+	0.748146i	$0.730944\pi$
$24$	1.69185	−	0.370982i	0.345348	−	0.0757264i
$25$			3.16864i			0.633728i
$26$	−1.10301	+	3.43269i	−0.216317	+	0.673206i
$27$	0.713876	−	5.14688i	0.137386	−	0.990518i
$28$	−3.46723	−	0.929042i	−0.655245	−	0.175572i
$29$	−1.74432	+	1.00708i	−0.323911	+	0.187010i	−0.653135	−	0.757242i	$-0.726546\pi$
$29$	−1.74432	+	1.00708i	−0.323911	+	0.187010i	0.329223	+	0.944252i	$0.393213\pi$
$30$	4.94512	+	0.227341i	0.902852	+	0.0415066i
$31$	1.21829	−	1.21829i	0.218812	−	0.218812i	−0.589186	−	0.807998i	$-0.700551\pi$
$31$	1.21829	−	1.21829i	0.218812	−	0.218812i	0.807998	+	0.589186i	$0.200551\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−4.90508	−	5.37782i	−0.853865	−	0.936158i
$34$	−2.44240	−	2.44240i	−0.418869	−	0.418869i
$35$	−8.88473	−	5.12960i	−1.50179	−	0.867061i
$36$	0.275255	−	2.98735i	0.0458759	−	0.497891i
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	0.783077	+	0.621925i	$0.213649\pi$
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	−0.989127	+	0.147065i	$0.953017\pi$
$38$	2.24555			0.364276
$39$	5.08759	+	3.62167i	0.814666	+	0.579931i
$40$	2.85808			0.451903
$41$	−2.05521	+	7.67015i	−0.320970	+	1.19788i	0.597332	+	0.801994i	$0.296228\pi$
$41$	−2.05521	+	7.67015i	−0.320970	+	1.19788i	−0.918302	+	0.395881i	$0.870439\pi$
$42$	−3.35262	+	5.23587i	−0.517321	+	0.807912i
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	0.365651	−	0.930752i	$-0.380846\pi$
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	−0.623229	+	0.782039i	$0.714180\pi$
$44$	−2.97155	−	2.97155i	−0.447978	−	0.447978i
$45$	2.96971	−	8.04354i	0.442699	−	1.19906i
$46$	2.92904	−	0.784834i	0.431864	−	0.115718i
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	−0.633826	−	0.773476i	$-0.718516\pi$
$47$	0.957390	−	0.957390i	0.139650	−	0.139650i	0.773476	+	0.633826i	$0.218516\pi$
$48$	0.0795432	−	1.73022i	0.0114811	−	0.249736i
$49$	5.09639	−	2.94240i	0.728056	−	0.420343i
$50$	3.06067	+	0.820104i	0.432844	+	0.115980i
$51$	−5.31303	+	2.75023i	−0.743973	+	0.385109i
$52$	3.03025	+	1.95387i	0.420220	+	0.270953i
$53$		−	7.22186i		−	0.991999i	−0.868323	−	0.495999i	$-0.834802\pi$
$53$		−	7.22186i		−	0.991999i	0.868323	−	0.495999i	$-0.165198\pi$
$54$	−4.78674	−	2.02166i	−0.651393	−	0.275113i
$55$	−6.00542	−	10.4017i	−0.809771	−	1.40256i
$56$	−1.79477	+	3.10863i	−0.239836	+	0.415409i
$57$	1.17812	−	3.70668i	0.156046	−	0.490962i
$58$	0.521304	+	1.94553i	0.0684505	+	0.255461i
$59$	2.66284	+	9.93785i	0.346672	+	1.29380i	0.890647	+	0.454696i	$0.150252\pi$
$59$	2.66284	+	9.93785i	0.346672	+	1.29380i	−0.543975	+	0.839101i	$0.683081\pi$
$60$	1.49949	−	4.71778i	0.193583	−	0.609063i
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	−0.874669	−	0.484720i	$-0.838921\pi$
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	0.857115	+	0.515125i	$0.172255\pi$
$62$	−0.861464	−	1.49210i	−0.109406	−	0.189497i
$63$	6.88380	+	8.28110i	0.867277	+	1.04332i
$64$		−	1.00000i		−	0.125000i
$65$	6.92026	+	7.63559i	0.858353	+	0.947079i
$66$	−6.46410	+	3.34607i	−0.795676	+	0.411872i
$67$	4.10121	+	1.09891i	0.501042	+	0.134254i	0.500484	−	0.865746i	$-0.333156\pi$
$67$	4.10121	+	1.09891i	0.501042	+	0.134254i	0.000558430		1.00000i	$0.499822\pi$
$68$	−2.99132	+	1.72704i	−0.362751	+	0.209434i
$69$	0.241204	−	5.24667i	0.0290376	−	0.631625i
$70$	−7.25436	+	7.25436i	−0.867061	+	0.867061i
$71$	−10.6578	+	2.85575i	−1.26485	+	0.338915i	−0.828055	−	0.560647i	$-0.810553\pi$
$71$	−10.6578	+	2.85575i	−1.26485	+	0.338915i	−0.436793	+	0.899562i	$0.643886\pi$
$72$	−2.81431	−	1.03906i	−0.331670	−	0.122454i
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.979735	+	0.200296i	$0.0641903\pi$
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.200296	+	0.979735i	$0.435810\pi$
$74$	4.19381	+	2.42130i	0.487520	+	0.281470i
$75$	2.95950	−	4.62192i	0.341734	−	0.533694i
$76$	0.581191	−	2.16903i	0.0666672	−	0.248805i
$77$	15.0847			1.71906
$78$	4.81502	−	3.97688i	0.545194	−	0.450292i
$79$	1.58051			0.177821			0.0889105	−	0.996040i	$-0.471661\pi$
$79$	1.58051			0.177821			0.0889105	+	0.996040i	$0.471661\pi$
$80$	0.739726	−	2.76070i	0.0827039	−	0.308655i
$81$	−5.84847	+	6.84072i	−0.649830	+	0.760080i
$82$	6.87686	+	3.97036i	0.759423	+	0.438453i
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	0.834790	−	0.550569i	$-0.185589\pi$
$83$	2.58938	+	2.58938i	0.284221	+	0.284221i	−0.550569	+	0.834790i	$0.685589\pi$
$84$	4.18974	+	4.59353i	0.457138	+	0.501195i
$85$	−9.53567	+	2.55507i	−1.03429	+	0.277137i
$86$	−1.37910	+	1.37910i	−0.148712	+	0.148712i
$87$	3.48495	+	0.160213i	0.373626	+	0.0171766i
$88$	−3.63939	+	2.10121i	−0.387961	+	0.223989i
$89$	−9.50933	−	2.54802i	−1.00799	−	0.270089i	−0.283199	−	0.959061i	$-0.591396\pi$
$89$	−9.50933	−	2.54802i	−1.00799	−	0.270089i	−0.724788	+	0.688972i	$0.758062\pi$
$90$	−7.00085	−	4.95035i	−0.737954	−	0.521812i
$91$	−12.6506	+	2.73205i	−1.32615	+	0.286397i
$92$		−	3.03237i		−	0.316146i
$93$	−2.91495	+	0.639175i	−0.302266	+	0.0662794i
$94$	−0.676977	−	1.17256i	−0.0698248	−	0.120940i
$95$	3.20898	−	5.55812i	0.329235	−	0.570251i
$96$	−1.65068	−	0.524648i	−0.168472	−	0.0535466i
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	−0.987595	−	0.157023i	$-0.949810\pi$
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	0.776771	−	0.629784i	$-0.216856\pi$
$98$	−1.52310	−	5.68429i	−0.153856	−	0.574200i
$99$	2.13191	+	12.4257i	0.214265	+	1.24883i
$100$	1.58432	−	2.74412i	0.158432	−	0.274412i
$101$	−1.05342	−	1.82458i	−0.104820	−	0.181553i	0.808845	−	0.588022i	$-0.200093\pi$
$101$	−1.05342	−	1.82458i	−0.104820	−	0.181553i	−0.913665	+	0.406469i	$0.866760\pi$
$102$	1.28140	+	5.84380i	0.126878	+	0.578623i
$103$		−	14.2629i		−	1.40537i	−0.711503	−	0.702683i	$-0.751985\pi$
$103$		−	14.2629i		−	1.40537i	0.711503	−	0.702683i	$-0.248015\pi$
$104$	2.67158	−	2.42130i	0.261970	−	0.237428i
$105$	8.16864	+	15.7806i	0.797178	+	1.54003i
$106$	−6.97578	−	1.86915i	−0.677548	−	0.181548i
$107$	11.9906	−	6.92275i	1.15917	−	0.669248i	0.208066	−	0.978115i	$-0.433283\pi$
$107$	11.9906	−	6.92275i	1.15917	−	0.669248i	0.951105	+	0.308867i	$0.0999497\pi$
$108$	−3.19168	+	4.10039i	−0.307119	+	0.394560i
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	−0.369607	−	0.929188i	$-0.620508\pi$
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	0.929188	+	0.369607i	$0.120508\pi$
$110$	−11.6016	+	3.10863i	−1.10617	+	0.296397i
$111$	6.19705	−	5.65231i	0.588198	−	0.536493i
$112$	2.53819	+	2.53819i	0.239836	+	0.239836i
$113$	−15.5920	−	9.00205i	−1.46677	−	0.846841i	−0.467463	−	0.884012i	$-0.654832\pi$
$113$	−15.5920	−	9.00205i	−1.46677	−	0.846841i	−0.999309	+	0.0371710i	$0.988165\pi$
$114$	−3.27546	−	2.09734i	−0.306775	−	0.196434i
$115$	2.24312	−	8.37145i	0.209172	−	0.780641i
$116$	2.01416			0.187010
$117$	−4.03836	−	10.0345i	−0.373346	−	0.927692i
$118$	10.2884			0.947125
$119$	3.20898	−	11.9761i	0.294167	−	1.09785i
$120$	−4.16893	−	2.66944i	−0.380570	−	0.243686i
$121$	5.76795	+	3.33013i	0.524359	+	0.302739i
$122$	0.193894	+	0.193894i	0.0175543	+	0.0175543i
$123$	10.1617	−	9.26846i	0.916252	−	0.835709i
$124$	−1.66422	+	0.445927i	−0.149452	+	0.0400454i
$125$	−3.70112	+	3.70112i	−0.331039	+	0.331039i
$126$	9.78058	−	4.50593i	0.871324	−	0.401420i
$127$	−17.9209	+	10.3466i	−1.59022	+	0.918114i	−0.596952	+	0.802277i	$0.703622\pi$
$127$	−17.9209	+	10.3466i	−1.59022	+	0.918114i	−0.993268	+	0.115837i	$0.963045\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	1.55291	+	3.00000i	0.136726	+	0.264135i
$130$	9.16651	−	4.70822i	0.803956	−	0.412939i
$131$		−	4.68295i		−	0.409151i	−0.978851	−	0.204576i	$-0.934419\pi$
$131$		−	4.68295i		−	0.409151i	0.978851	−	0.204576i	$-0.0655814\pi$
$132$	1.55902	+	7.10987i	0.135695	+	0.618835i
$133$	4.03025	+	6.98059i	0.349467	+	0.605294i
$134$	2.12294	−	3.67704i	0.183394	−	0.317648i
$135$	−11.8444	+	8.95897i	−1.01940	+	0.771065i
$136$	0.893982	+	3.33639i	0.0766583	+	0.286093i
$137$	1.41832	+	5.29326i	0.121176	+	0.452234i	0.999675	−	0.0255107i	$-0.00812118\pi$
$137$	1.41832	+	5.29326i	0.121176	+	0.452234i	−0.878499	+	0.477744i	$0.841455\pi$
$138$	−5.00547	−	1.59092i	−0.426094	−	0.135428i
$139$	−7.34662	+	12.7247i	−0.623132	+	1.07930i	0.365767	+	0.930706i	$0.380807\pi$
$139$	−7.34662	+	12.7247i	−0.623132	+	1.07930i	−0.988899	+	0.148590i	$0.952527\pi$
$140$	5.12960	+	8.88473i	0.433531	+	0.750897i
$141$	−2.29069	+	0.502292i	−0.192911	+	0.0423006i
$142$			11.0338i			0.925933i
$143$	−14.4256	−	4.63529i	−1.20633	−	0.387622i
$144$	−1.73205	+	2.44949i	−0.144338	+	0.204124i
$145$	5.56049	+	1.48993i	0.461774	+	0.123732i
$146$	12.3481	−	7.12919i	1.02194	−	0.590016i
$147$	−10.1820	−	0.468097i	−0.839800	−	0.0386080i
$148$	3.42423	−	3.42423i	0.281470	−	0.281470i
$149$	9.98255	−	2.67482i	0.817803	−	0.219130i	0.174417	−	0.984672i	$-0.444196\pi$
$149$	9.98255	−	2.67482i	0.817803	−	0.219130i	0.643386	+	0.765542i	$0.277529\pi$
$150$	−3.69846	−	4.05490i	−0.301978	−	0.331081i
$151$	−6.48932	−	6.48932i	−0.528094	−	0.528094i	0.391910	−	0.920004i	$-0.371814\pi$
$151$	−6.48932	−	6.48932i	−0.528094	−	0.528094i	−0.920004	+	0.391910i	$0.871814\pi$
$152$	−1.94470	−	1.12277i	−0.157736	−	0.0910691i
$153$	10.3185	+	0.950753i	0.834204	+	0.0768638i
$154$	3.90421	−	14.5707i	0.314611	−	1.17414i
$155$	−4.92427			−0.395527
$156$	−2.59515	−	5.68025i	−0.207778	−	0.454784i
$157$	−14.1431			−1.12874			−0.564372	−	0.825520i	$-0.690882\pi$
$157$	−14.1431			−1.12874			−0.564372	+	0.825520i	$0.690882\pi$
$158$	0.409066	−	1.52665i	0.0325435	−	0.121454i
$159$	−6.74520	+	10.5341i	−0.534929	+	0.835411i
$160$	−2.47517	−	1.42904i	−0.195680	−	0.112976i
$161$	7.69672	+	7.69672i	0.606587	+	0.606587i
$162$	5.09393	+	7.41970i	0.400217	+	0.582946i
$163$	1.07638	−	0.288415i	0.0843084	−	0.0225904i	−0.216418	−	0.976301i	$-0.569437\pi$
$163$	1.07638	−	0.288415i	0.0843084	−	0.0225904i	0.300727	+	0.953710i	$0.402771\pi$
$164$	5.61494	−	5.61494i	0.438453	−	0.438453i
$165$	−0.955381	+	20.7814i	−0.0743763	+	1.61783i
$166$	3.17133	−	1.83097i	0.246143	−	0.142110i
$167$	−5.39478	−	1.44553i	−0.417461	−	0.111858i	0.0439735	−	0.999033i	$-0.485998\pi$
$167$	−5.39478	−	1.44553i	−0.417461	−	0.111858i	−0.461434	+	0.887174i	$0.652665\pi$
$168$	5.52139	−	2.85808i	0.425985	−	0.220506i
$169$	12.9374	+	1.27466i	0.995181	+	0.0980507i
$170$			9.87205i			0.757152i
$171$	−5.18050	+	4.30638i	−0.396163	+	0.329317i
$172$	0.975173	+	1.68905i	0.0743562	+	0.128789i
$173$	−8.74765	+	15.1514i	−0.665072	+	1.15194i	0.314194	+	0.949359i	$0.398266\pi$
$173$	−8.74765	+	15.1514i	−0.665072	+	1.15194i	−0.979266	+	0.202579i	$0.935068\pi$
$174$	1.05673	−	3.32474i	0.0801102	−	0.252048i
$175$	2.94380	+	10.9864i	0.222530	+	0.830494i
$176$	1.08766	+	4.05922i	0.0819857	+	0.305975i
$177$	5.39779	−	16.9829i	0.405723	−	1.27651i
$178$	−4.92239	+	8.52583i	−0.368949	+	0.639038i
$179$	4.60754	+	7.98049i	0.344384	+	0.596490i	0.985242	−	0.171169i	$-0.0547545\pi$
$179$	4.60754	+	7.98049i	0.344384	+	0.596490i	−0.640858	+	0.767660i	$0.721421\pi$
$180$	−6.59362	+	5.48105i	−0.491459	+	0.408534i
$181$		−	13.8110i		−	1.02656i	−0.858220	−	0.513282i	$-0.828429\pi$
$181$		−	13.8110i		−	1.02656i	0.858220	−	0.513282i	$-0.171571\pi$
$182$	−0.635265	+	12.9267i	−0.0470890	+	0.958189i
$183$	0.421783	−	0.218331i	0.0311791	−	0.0161395i
$184$	−2.92904	−	0.784834i	−0.215932	−	0.0578588i
$185$	11.9862	−	6.92026i	0.881246	−	0.508788i
$186$	−0.137047	+	2.98105i	−0.0100488	+	0.218581i
$187$	10.2640	−	10.2640i	0.750577	−	0.750577i
$188$	−1.30782	+	0.350429i	−0.0953825	+	0.0255577i
$189$	−2.30649	−	18.5086i	−0.167773	−	1.34631i
$190$	−4.53819	−	4.53819i	−0.329235	−	0.329235i
$191$	19.6614	+	11.3515i	1.42265	+	0.821366i	0.996525	−	0.0832996i	$-0.0265458\pi$
$191$	19.6614	+	11.3515i	1.42265	+	0.821366i	0.426123	+	0.904665i	$0.359879\pi$
$192$	−0.933998	+	1.45865i	−0.0674055	+	0.105269i
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	0.482133	+	0.876098i	$0.339862\pi$
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	−0.855588	+	0.517657i	$0.826804\pi$
$194$	−8.02251			−0.575983
$195$	−2.96258	−	17.6011i	−0.212155	−	1.26044i
$196$	−5.88481			−0.420343
$197$	4.82369	−	18.0023i	0.343674	−	1.28261i	−0.550480	−	0.834849i	$-0.685555\pi$
$197$	4.82369	−	18.0023i	0.343674	−	1.28261i	0.894154	−	0.447760i	$-0.147778\pi$
$198$	12.5541	+	1.15674i	0.892178	+	0.0822056i
$199$	−3.90611	−	2.25519i	−0.276897	−	0.159866i	0.355121	−	0.934820i	$-0.384440\pi$
$199$	−3.90611	−	2.25519i	−0.276897	−	0.159866i	−0.632018	+	0.774954i	$0.717773\pi$
$200$	−2.24057	−	2.24057i	−0.158432	−	0.158432i
$201$	−4.95582	−	5.43345i	−0.349557	−	0.383246i
$202$	−2.03506	+	0.545293i	−0.143186	+	0.0383667i
$203$	−5.11233	+	5.11233i	−0.358815	+	0.358815i
$204$	5.97633	+	0.274749i	0.418427	+	0.0192363i
$205$	19.6547	−	11.3476i	1.37274	−	0.792552i
$206$	−13.7769	−	3.69151i	−0.959883	−	0.257200i
$207$	−5.25221	+	7.42775i	−0.365054	+	0.516264i
$208$	−1.64734	−	3.20722i	−0.114222	−	0.222381i
$209$			9.43672i			0.652752i
$210$	17.3571	−	3.80598i	1.19775	−	0.262638i
$211$	4.28841	+	7.42775i	0.295227	+	0.511348i	0.975038	−	0.222040i	$-0.0712715\pi$
$211$	4.28841	+	7.42775i	0.295227	+	0.511348i	−0.679811	+	0.733387i	$0.737938\pi$
$212$	−3.61093	+	6.25431i	−0.248000	+	0.429548i
$213$	18.2132	+	5.78884i	1.24795	+	0.396645i
$214$	−3.58348	−	13.3737i	−0.244962	−	0.914210i
$215$	1.44272	+	5.38431i	0.0983928	+	0.367207i
$216$	3.13461	+	4.14418i	0.213283	+	0.281976i
$217$	3.09226	−	5.35596i	0.209916	−	0.363586i
$218$	−4.13106	−	7.15520i	−0.279791	−	0.484612i
$219$	−5.28960	−	24.1231i	−0.357438	−	1.63009i
$220$			12.0108i			0.809771i
$221$	−6.74882	+	10.4667i	−0.453975	+	0.704067i
$222$	−3.85579	−	7.44882i	−0.258784	−	0.499932i
$223$	20.3575	+	5.45476i	1.36324	+	0.365278i	0.865004	−	0.501765i	$-0.167316\pi$
$223$	20.3575	+	5.45476i	1.36324	+	0.365278i	0.498232	+	0.867043i	$0.333983\pi$
$224$	3.10863	−	1.79477i	0.207704	−	0.119918i
$225$	−8.63374	+	3.97758i	−0.575582	+	0.265172i
$226$	−12.7308	+	12.7308i	−0.846841	+	0.846841i
$227$	−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	$0.470016\pi$
$228$	−2.87363	+	2.62102i	−0.190311	+	0.173581i
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	0.298544	−	0.954396i	$-0.403499\pi$
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	−0.954396	+	0.298544i	$0.903499\pi$
$230$	−7.50563	−	4.33338i	−0.494907	−	0.285735i
$231$	−22.0033	−	14.0891i	−1.44771	−	0.926995i
$232$	0.521304	−	1.94553i	0.0342253	−	0.127730i
$233$	−18.7944			−1.23126			−0.615630	−	0.788035i	$-0.711098\pi$
$233$	−18.7944			−1.23126			−0.615630	+	0.788035i	$0.711098\pi$
$234$	−10.7378	+	1.30363i	−0.701953	+	0.0852209i
$235$	−3.86971			−0.252432
$236$	2.66284	−	9.93785i	0.173336	−	0.646899i
$237$	−2.30540	−	1.47619i	−0.149752	−	0.0958889i
$238$	−10.7375	−	6.19928i	−0.696007	−	0.401840i
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	0.451188	−	0.892429i	$-0.351000\pi$
$239$	−6.82142	−	6.82142i	−0.441241	−	0.441241i	−0.892429	+	0.451188i	$0.851000\pi$
$240$	−3.65748	+	3.33598i	−0.236090	+	0.215336i
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.0147390	−	0.999891i	$-0.495308\pi$
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.512710	+	0.858562i	$0.328642\pi$
$242$	4.70951	−	4.70951i	0.302739	−	0.302739i
$243$	14.9201	−	4.51572i	0.957122	−	0.289684i
$244$	0.237470	−	0.137104i	0.0152025	−	0.00877716i
$245$	−16.2462	−	4.35315i	−1.03793	−	0.278112i
$246$	−6.32260	−	12.2143i	−0.403114	−	0.778757i
$247$	−1.70912	−	7.91400i	−0.108749	−	0.503555i
$248$			1.72293i			0.109406i
$249$	−1.35851	−	6.19546i	−0.0860921	−	0.392621i
$250$	2.61709	+	4.53293i	0.165519	+	0.286688i
$251$	3.51988	−	6.09661i	0.222173	−	0.384814i	−0.733295	−	0.679911i	$-0.762018\pi$
$251$	3.51988	−	6.09661i	0.222173	−	0.384814i	0.955467	+	0.295096i	$0.0953518\pi$
$252$	−1.82100	−	10.6135i	−0.114712	−	0.668590i
$253$	3.29820	+	12.3090i	0.207356	+	0.773862i
$254$	5.35580	+	19.9881i	0.336053	+	1.25417i
$255$	16.2956	+	5.17935i	1.02047	+	0.324343i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.815993	+	1.41334i	0.0509003	+	0.0881618i	0.890353	−	0.455271i	$-0.150458\pi$
$257$	0.815993	+	1.41334i	0.0509003	+	0.0881618i	−0.839453	+	0.543433i	$0.817124\pi$
$258$	3.29970	−	0.723543i	0.205430	−	0.0450458i
$259$			17.3827i			1.08011i
$260$	−2.17533	−	10.0727i	−0.134908	−	0.624685i
$261$	−4.93367	−	3.48863i	−0.305387	−	0.215941i
$262$	−4.52338	−	1.21204i	−0.279455	−	0.0748799i
$263$	9.15209	−	5.28396i	0.564342	−	0.325823i	−0.190544	−	0.981679i	$-0.561025\pi$
$263$	9.15209	−	5.28396i	0.564342	−	0.325823i	0.754886	+	0.655856i	$0.227692\pi$
$264$	7.27111	+	0.334273i	0.447506	+	0.0205731i
$265$	−14.5952	+	14.5952i	−0.896574	+	0.896574i
$266$	7.78584	−	2.08621i	0.477380	−	0.127914i
$267$	11.4909	+	12.5983i	0.703231	+	0.771006i
$268$	−3.00229	−	3.00229i	−0.183394	−	0.183394i
$269$	7.46392	+	4.30930i	0.455083	+	0.262742i	0.709975	−	0.704227i	$-0.248706\pi$
$269$	7.46392	+	4.30930i	0.455083	+	0.262742i	−0.254891	+	0.966970i	$0.582040\pi$
$270$	5.58814	+	13.7596i	0.340083	+	0.837381i
$271$	5.13290	−	19.1563i	0.311802	−	1.16366i	−0.615129	−	0.788427i	$-0.710896\pi$
$271$	5.13290	−	19.1563i	0.311802	−	1.16366i	0.926930	−	0.375233i	$-0.122437\pi$
$272$	3.45408			0.209434
$273$	21.0045	+	7.83057i	1.27125	+	0.473928i
$274$	5.47999			0.331058
$275$	−3.44642	+	12.8622i	−0.207827	+	0.775620i
$276$	−2.83223	+	4.42315i	−0.170480	+	0.266242i
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	0.0391339	−	0.999234i	$-0.487540\pi$
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	−0.845795	+	0.533508i	$0.820873\pi$
$278$	10.3897	+	10.3897i	0.623132	+	0.623132i
$279$	4.84886	+	1.79022i	0.290294	+	0.107178i
$280$	9.90963	−	2.65528i	0.592214	−	0.158683i
$281$	11.9452	−	11.9452i	0.712591	−	0.712591i	−0.254486	−	0.967077i	$-0.581906\pi$
$281$	11.9452	−	11.9452i	0.712591	−	0.712591i	0.967077	+	0.254486i	$0.0819061\pi$
$282$	−0.107698	+	2.34264i	−0.00641331	+	0.139502i
$283$	−1.36808	+	0.789860i	−0.0813237	+	0.0469523i	−0.540110	−	0.841594i	$-0.681618\pi$
$283$	−1.36808	+	0.789860i	−0.0813237	+	0.0469523i	0.458787	+	0.888546i	$0.348284\pi$
$284$	10.6578	+	2.85575i	0.632424	+	0.169458i
$285$	−9.87205	+	5.11015i	−0.584770	+	0.302699i
$286$	−8.21096	+	12.7343i	−0.485524	+	0.752997i
$287$			28.5035i			1.68251i
$288$	1.91774	+	2.30701i	0.113004	+	0.135942i
$289$	2.53467	+	4.39017i	0.149098	+	0.258245i
$290$	2.87832	−	4.98540i	0.169021	−	0.292753i
$291$	−4.20899	+	13.2426i	−0.246735	+	0.776295i
$292$	−3.69034	−	13.7725i	−0.215961	−	0.805976i
$293$	1.01073	+	3.77209i	0.0590474	+	0.220368i	0.989145	−	0.146946i	$-0.0469442\pi$
$293$	1.01073	+	3.77209i	0.0590474	+	0.220368i	−0.930097	+	0.367314i	$0.880278\pi$
$294$	−3.08745	+	9.71393i	−0.180064	+	0.566528i
$295$	14.7026	−	25.4656i	0.856017	−	1.48266i
$296$	−2.42130	−	4.19381i	−0.140735	−	0.243760i
$297$	8.49585	−	20.1158i	0.492979	−	1.16724i
$298$		−	10.3347i		−	0.598673i
$299$	−4.99533	−	9.72548i	−0.288887	−	0.562439i
$300$	−4.87397	+	2.52295i	−0.281399	+	0.145663i
$301$	−6.76230	−	1.81195i	−0.389772	−	0.104439i
$302$	−7.94777	+	4.58864i	−0.457343	+	0.264047i
$303$	−0.167586	+	3.64532i	−0.00962754	+	0.209418i
$304$	−1.58784	+	1.58784i	−0.0910691	+	0.0910691i
$305$	0.757003	−	0.202838i	0.0433459	−	0.0116145i
$306$	3.58899	−	9.72086i	0.205169	−	0.555705i
$307$	21.7994	+	21.7994i	1.24416	+	1.24416i	0.958260	+	0.285899i	$0.0922920\pi$
$307$	21.7994	+	21.7994i	1.24416	+	1.24416i	0.285899	+	0.958260i	$0.407708\pi$
$308$	−13.0638	−	7.54236i	−0.744377	−	0.429766i
$309$	−13.3215	+	20.8045i	−0.757835	+	1.18353i
$310$	−1.27450	+	4.75648i	−0.0723865	+	0.270150i
$311$	20.9295			1.18681			0.593403	−	0.804906i	$-0.297784\pi$
$311$	20.9295			1.18681			0.593403	+	0.804906i	$0.297784\pi$
$312$	−6.15837	+	1.03656i	−0.348649	+	0.0586838i
$313$	−32.6685			−1.84653			−0.923267	−	0.384159i	$-0.874491\pi$
$313$	−32.6685			−1.84653			−0.923267	+	0.384159i	$0.874491\pi$
$314$	−3.66051	+	13.6612i	−0.206575	+	0.770947i
$315$	2.82390	−	30.6478i	0.159109	−	1.72681i
$316$	−1.36876	−	0.790254i	−0.0769988	−	0.0444553i
$317$	−5.21085	−	5.21085i	−0.292671	−	0.292671i	0.545464	−	0.838134i	$-0.316354\pi$
$317$	−5.21085	−	5.21085i	−0.292671	−	0.292671i	−0.838134	+	0.545464i	$0.816354\pi$
$318$	8.42940	+	9.24180i	0.472698	+	0.518254i
$319$	−8.17593	+	2.19073i	−0.457764	+	0.122657i
$320$	−2.02097	+	2.02097i	−0.112976	+	0.112976i
$321$	−23.9558	−	1.10132i	−1.33708	−	0.0614695i
$322$	9.42652	−	5.44240i	0.525319	−	0.303293i
$323$	7.49202	+	2.00748i	0.416867	+	0.111699i
$324$	8.48528	−	3.00000i	0.471405	−	0.166667i
$325$	0.560775	−	11.4109i	0.0311062	−	0.632964i
$326$		−	1.11435i		−	0.0617181i
$327$	−13.9783	+	3.06510i	−0.773002	+	0.169500i
$328$	−3.97036	−	6.87686i	−0.219226	−	0.379711i
$329$	2.43004	−	4.20895i	0.133972	−	0.232047i
$330$	19.8261	+	6.30146i	1.09139	+	0.346884i
$331$	4.72013	+	17.6158i	0.259442	+	0.968251i	0.965565	+	0.260162i	$0.0837759\pi$
$331$	4.72013	+	17.6158i	0.259442	+	0.968251i	−0.706123	+	0.708089i	$0.749557\pi$
$332$	−0.947777	−	3.53715i	−0.0520160	−	0.194127i
$333$	−14.3186	+	2.45667i	−0.784652	+	0.134625i
$334$	−2.79254	+	4.83683i	−0.152801	+	0.264660i
$335$	−6.06754	−	10.5093i	−0.331505	−	0.574184i
$336$	−1.33165	−	6.07298i	−0.0726477	−	0.331308i
$337$			4.92484i			0.268273i	0.990963	+	0.134136i	$0.0428260\pi$
$337$			4.92484i			0.268273i	−0.990963	+	0.134136i	$0.957174\pi$
$338$	4.57966	−	12.1666i	0.249101	−	0.661777i
$339$	14.3353	+	27.6937i	0.778587	+	1.50412i
$340$	9.53567	+	2.55507i	0.517144	+	0.138568i
$341$	6.27042	−	3.62023i	0.339562	−	0.196046i
$342$	2.81883	+	6.11855i	0.152425	+	0.330853i
$343$	−2.83057	+	2.83057i	−0.152836	+	0.152836i
$344$	1.88389	−	0.504787i	0.101572	−	0.0272163i
$345$	−11.0908	+	10.1159i	−0.597110	+	0.544622i
$346$	12.3711	+	12.3711i	0.665072	+	0.665072i
$347$	−12.9403	−	7.47108i	−0.694671	−	0.401069i	0.110688	−	0.993855i	$-0.464694\pi$
$347$	−12.9403	−	7.47108i	−0.694671	−	0.401069i	−0.805360	+	0.592787i	$0.798028\pi$
$348$	−2.93795	−	1.88122i	−0.157491	−	0.100844i
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	0.313636	+	0.949543i	$0.398453\pi$
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	−0.746388	+	0.665511i	$0.768214\pi$
$350$	11.3740			0.607964
$351$	−3.48169	+	18.4086i	−0.185839	+	0.982580i
$352$	4.20241			0.223989
$353$	2.67762	−	9.99302i	0.142515	−	0.531875i	−0.857338	−	0.514754i	$-0.827883\pi$
$353$	2.67762	−	9.99302i	0.142515	−	0.531875i	0.999853	−	0.0171211i	$-0.00545007\pi$
$354$	−15.0072	−	9.60936i	−0.797621	−	0.510732i
$355$	27.3105	+	15.7677i	1.44949	+	0.836864i
$356$	6.96131	+	6.96131i	0.368949	+	0.368949i
$357$	−15.8664	+	14.4717i	−0.839740	+	0.765923i
$358$	8.90109	−	2.38504i	0.470437	−	0.126053i
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	−0.425321	−	0.905043i	$-0.639839\pi$
$359$	9.08944	−	9.08944i	0.479722	−	0.479722i	0.905043	+	0.425321i	$0.139839\pi$
$360$	3.58774	+	7.78755i	0.189090	+	0.410440i
$361$	12.0876	−	6.97875i	0.636187	−	0.367303i
$362$	−13.3404	−	3.57455i	−0.701156	−	0.187874i
$363$	−5.30306	−	10.2447i	−0.278339	−	0.537709i
$364$	12.3218	+	3.95929i	0.645837	+	0.207523i
$365$		−	40.7516i		−	2.13304i
$366$	−0.101726	−	0.463919i	−0.00531730	−	0.0242494i
$367$	−0.823475	−	1.42630i	−0.0429850	−	0.0744522i	0.843732	−	0.536764i	$-0.180353\pi$
$367$	−0.823475	−	1.42630i	−0.0429850	−	0.0744522i	−0.886717	+	0.462312i	$0.847020\pi$
$368$	−1.51618	+	2.62611i	−0.0790365	+	0.136895i
$369$	−23.4791	+	4.02837i	−1.22227	+	0.209709i
$370$	−3.58219	−	13.3689i	−0.186229	−	0.695017i
$371$	−6.70941	−	25.0398i	−0.348335	−	1.30000i
$372$	2.84400	+	0.903931i	0.147455	+	0.0468666i
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	−0.483290	−	0.875461i	$-0.660558\pi$
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	0.999816	−	0.0191892i	$-0.00610849\pi$
$374$	−7.25773	−	12.5708i	−0.375288	−	0.650018i
$375$	8.85547	−	1.94179i	0.457295	−	0.100273i
$376$			1.35395i			0.0698248i
$377$	6.45987	−	3.31800i	0.332700	−	0.170886i
$378$	−18.4749	−	2.56249i	−0.950248	−	0.131800i
$379$	−11.8923	−	3.18653i	−0.610865	−	0.163681i	−0.0598936	−	0.998205i	$-0.519076\pi$
$379$	−11.8923	−	3.18653i	−0.610865	−	0.163681i	−0.550972	+	0.834524i	$0.685743\pi$
$380$	−5.55812	+	3.20898i	−0.285126	+	0.164617i
$381$	35.8039	+	1.64601i	1.83429	+	0.0843275i
$382$	16.0534	−	16.0534i	0.821366	−	0.821366i
$383$	−27.3800	+	7.33645i	−1.39905	+	0.374875i	−0.878005	−	0.478652i	$-0.841125\pi$
$383$	−27.3800	+	7.33645i	−1.39905	+	0.374875i	−0.521048	+	0.853527i	$0.674459\pi$
$384$	1.16721	+	1.27970i	0.0595638	+	0.0653043i
$385$	−30.4858	−	30.4858i	−1.55370	−	1.55370i
$386$	17.3601	+	10.0229i	0.883605	+	0.510150i
$387$	0.536843	−	5.82636i	0.0272892	−	0.296170i
$388$	−2.07638	+	7.74915i	−0.105412	+	0.393403i
$389$	−15.9504			−0.808717			−0.404359	−	0.914601i	$-0.632505\pi$
$389$	−15.9504			−0.808717			−0.404359	+	0.914601i	$0.632505\pi$
$390$	−17.7682	−	1.69387i	−0.899726	−	0.0857726i
$391$	10.4740			0.529695
$392$	−1.52310	+	5.68429i	−0.0769282	+	0.287100i
$393$	−4.37387	+	6.83077i	−0.220632	+	0.344567i
$394$	−16.1404	−	9.31866i	−0.813141	−	0.469467i
$395$	−3.19416	−	3.19416i	−0.160716	−	0.160716i
$396$	4.36655	−	11.8269i	0.219427	−	0.594324i
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.552981	−	0.833194i	$-0.686510\pi$
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.0622992	+	0.998058i	$0.519843\pi$
$398$	−3.18933	+	3.18933i	−0.159866	+	0.159866i
$399$	0.641158	−	13.9465i	0.0320980	−	0.698196i
$400$	−2.74412	+	1.58432i	−0.137206	+	0.0792160i
$401$	15.8603	+	4.24976i	0.792027	+	0.212223i	0.632080	−	0.774903i	$-0.282201\pi$
$401$	15.8603	+	4.24976i	0.792027	+	0.212223i	0.159946	+	0.987126i	$0.448868\pi$
$402$	−6.53097	+	3.38068i	−0.325735	+	0.168613i
$403$	−4.60294	+	4.17172i	−0.229289	+	0.207808i
$404$			2.10685i			0.104820i
$405$	25.6445	−	2.00530i	1.27428	−	0.0996443i
$406$	3.61496	+	6.26130i	0.179408	+	0.310743i
$407$	−10.1753	+	17.6241i	−0.504370	+	0.873594i
$408$	1.81217	−	5.70158i	0.0897160	−	0.282270i
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	−0.738364	−	0.674403i	$-0.764401\pi$
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	0.302240	−	0.953232i	$-0.402266\pi$
$410$	−5.87396	−	21.9219i	−0.290094	−	1.08265i
$411$	2.87506	−	9.04570i	0.141816	−	0.446192i
$412$	−7.13145	+	12.3520i	−0.351341	+	0.608541i
$413$	18.4653	+	31.9829i	0.908620	+	1.57378i
$414$	5.81528	+	6.99569i	0.285806	+	0.343820i
$415$		−	10.4661i		−	0.513761i
$416$	−3.52430	+	0.761114i	−0.172793	+	0.0373167i
$417$	22.6010	−	11.6991i	1.10677	−	0.572909i
$418$	9.11517	+	2.44240i	0.445838	+	0.119462i
$419$	−28.4943	+	16.4512i	−1.39204	+	0.803693i	−0.993541	−	0.113477i	$-0.963801\pi$
$419$	−28.4943	+	16.4512i	−1.39204	+	0.803693i	−0.398496	+	0.917170i	$0.630468\pi$
$420$	0.816051	−	17.7507i	0.0398192	−	0.866147i
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	−0.154808	−	0.987945i	$-0.549476\pi$
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	0.987945	+	0.154808i	$0.0494759\pi$
$422$	8.28458	−	2.21985i	0.403287	−	0.108060i
$423$	3.81045	+	1.40684i	0.185270	+	0.0684027i
$424$	5.10662	+	5.10662i	0.248000	+	0.248000i
$425$	9.47842	+	5.47237i	0.459771	+	0.265449i
$426$	10.3055	−	16.0944i	0.499304	−	0.779774i
$427$	−0.254750	+	0.950740i	−0.0123282	+	0.0460095i
$428$	−13.8455			−0.669248
$429$	16.7125	+	20.2347i	0.806885	+	0.976941i
$430$	5.57425			0.268814
$431$	0.454427	−	1.69594i	0.0218890	−	0.0816908i	−0.954117	−	0.299433i	$-0.903203\pi$
$431$	0.454427	−	1.69594i	0.0218890	−	0.0816908i	0.976006	+	0.217742i	$0.0698692\pi$
$432$	4.81427	−	1.95521i	0.231627	−	0.0940699i
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	0.271451	−	0.962452i	$-0.412497\pi$
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	−0.697783	+	0.716309i	$0.745830\pi$
$434$	−4.37312	−	4.37312i	−0.209916	−	0.209916i
$435$	−6.71920	−	7.36677i	−0.322161	−	0.353210i
$436$	−7.98059	+	2.13839i	−0.382201	+	0.102410i
$437$	−4.81492	+	4.81492i	−0.230329	+	0.230329i
$438$	−24.6702	−	1.13416i	−1.17879	−	0.0541921i
$439$	−4.67848	+	2.70112i	−0.223292	+	0.128917i	−0.607473	−	0.794340i	$-0.707817\pi$
$439$	−4.67848	+	2.70112i	−0.223292	+	0.128917i	0.384182	+	0.923257i	$0.374484\pi$
$440$	11.6016	+	3.10863i	0.553084	+	0.148198i
$441$	14.4148	+	10.1928i	0.686418	+	0.485371i
$442$	8.36335	+	9.22784i	0.397804	+	0.438924i
$443$		−	13.5731i		−	0.644876i	−0.946591	−	0.322438i	$-0.895498\pi$
$443$		−	13.5731i		−	0.644876i	0.946591	−	0.322438i	$-0.104502\pi$
$444$	−8.19296	+	1.79651i	−0.388821	+	0.0852588i
$445$	14.0686	+	24.3675i	0.666916	+	1.15513i
$446$	10.5378	−	18.2520i	0.498979	−	0.864257i
$447$	−17.0593	−	5.42208i	−0.806877	−	0.256455i
$448$	−0.929042	−	3.46723i	−0.0438931	−	0.163811i
$449$	0.525222	+	1.96016i	0.0247868	+	0.0925055i	0.977211	−	0.212269i	$-0.0680854\pi$
$449$	0.525222	+	1.96016i	0.0247868	+	0.0925055i	−0.952424	+	0.304775i	$0.901419\pi$
$450$	1.60747	+	9.36902i	0.0757769	+	0.441660i
$451$	−16.6851	+	28.8994i	−0.785670	+	1.36082i
$452$	9.00205	+	15.5920i	0.423421	+	0.733386i
$453$	3.40461	+	15.5266i	0.159962	+	0.729505i
$454$			5.02672i			0.235916i
$455$	31.0879	+	20.0451i	1.45742	+	0.939731i
$456$	1.78796	+	3.45408i	0.0837291	+	0.161752i
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.492022	−	0.870583i	$-0.663742\pi$
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.861395	+	0.507936i	$0.830409\pi$
$458$	−12.1554	+	7.01792i	−0.567984	+	0.327926i
$459$	−14.1631	−	11.0243i	−0.661076	−	0.514570i
$460$	−6.12832	+	6.12832i	−0.285735	+	0.285735i
$461$	15.5621	−	4.16985i	0.724798	−	0.194209i	0.122487	−	0.992470i	$-0.460913\pi$
$461$	15.5621	−	4.16985i	0.724798	−	0.194209i	0.602312	+	0.798261i	$0.294246\pi$
$462$	−19.3039	+	17.6070i	−0.898099	+	0.819152i
$463$	−4.07041	−	4.07041i	−0.189168	−	0.189168i	0.606168	−	0.795336i	$-0.292706\pi$
$463$	−4.07041	−	4.07041i	−0.189168	−	0.189168i	−0.795336	+	0.606168i	$0.792706\pi$
$464$	−1.74432	−	1.00708i	−0.0809779	−	0.0467526i
$465$	7.18277	+	4.59926i	0.333093	+	0.213286i
$466$	−4.86434	+	18.1540i	−0.225336	+	0.840966i
$467$	36.8536			1.70538			0.852690	−	0.522417i	$-0.174970\pi$
$467$	36.8536			1.70538			0.852690	+	0.522417i	$0.174970\pi$
$468$	−1.51994	+	10.7093i	−0.0702593	+	0.495039i
$469$	15.2408			0.703753
$470$	−1.00155	+	3.73785i	−0.0461983	+	0.172414i
$471$	20.6298	+	13.2097i	0.950572	+	0.608669i
$472$	−8.91003	−	5.14421i	−0.410117	−	0.236781i
$473$	−5.79555	−	5.79555i	−0.266480	−	0.266480i
$474$	−2.02257	+	1.84478i	−0.0928999	+	0.0847336i
$475$	−6.87289	+	1.84159i	−0.315350	+	0.0844977i
$476$	−8.76711	+	8.76711i	−0.401840	+	0.401840i
$477$	19.6777	−	9.06556i	0.900981	−	0.415084i
$478$	−8.35450	+	4.82347i	−0.382126	+	0.220621i
$479$	14.5305	+	3.89342i	0.663913	+	0.177895i	0.575011	−	0.818145i	$-0.304998\pi$
$479$	14.5305	+	3.89342i	0.663913	+	0.177895i	0.0889019	+	0.996040i	$0.471664\pi$
$480$	2.27568	+	4.39627i	0.103870	+	0.200661i
$481$	5.34141	−	16.6231i	0.243547	−	0.757949i
$482$		−	8.47706i		−	0.386119i
$483$	−4.03807	−	18.4155i	−0.183738	−	0.837935i
$484$	−3.33013	−	5.76795i	−0.151369	−	0.262180i
$485$	−11.4645	+	19.8571i	−0.520576	+	0.901664i
$486$	−0.500258	−	15.5804i	−0.0226921	−	0.706743i
$487$	4.33018	+	16.1605i	0.196219	+	0.732301i	0.991948	+	0.126647i	$0.0404216\pi$
$487$	4.33018	+	16.1605i	0.196219	+	0.732301i	−0.795728	+	0.605654i	$0.792912\pi$
$488$	−0.0709701	−	0.264864i	−0.00321266	−	0.0119898i
$489$	−1.83943	−	0.584640i	−0.0831820	−	0.0264383i
$490$	−8.40963	+	14.5659i	−0.379909	+	0.658021i
$491$	−12.6333	−	21.8815i	−0.570132	−	0.987498i	−0.996552	−	0.0829727i	$-0.973559\pi$
$491$	−12.6333	−	21.8815i	−0.570132	−	0.987498i	0.426419	−	0.904526i	$-0.359775\pi$
$492$	−13.4345	+	2.94586i	−0.605676	+	0.132810i
$493$			6.95708i			0.313331i
$494$	−8.08669	−	0.397410i	−0.363837	−	0.0178803i
$495$	20.8034	−	29.4204i	0.935043	−	1.32235i
$496$	1.66422	+	0.445927i	0.0747258	+	0.0200227i
$497$	−34.3000	+	19.8031i	−1.53856	+	0.888290i
$498$	−6.33596	−	0.291282i	−0.283921	−	0.0130527i
$499$	1.37946	−	1.37946i	0.0617533	−	0.0617533i	−0.675556	−	0.737309i	$-0.736096\pi$
$499$	1.37946	−	1.37946i	0.0617533	−	0.0617533i	0.737309	+	0.675556i	$0.236096\pi$
$500$	5.05583	−	1.35471i	0.226104	−	0.0605843i
$501$	6.51896	+	7.14723i	0.291245	+	0.319315i
$502$	−4.97786	−	4.97786i	−0.222173	−	0.222173i
$503$	9.77777	+	5.64520i	0.435969	+	0.251707i	0.701886	−	0.712289i	$-0.252341\pi$
$503$	9.77777	+	5.64520i	0.435969	+	0.251707i	−0.265917	+	0.963996i	$0.585675\pi$
$504$	−10.7232	−	0.988040i	−0.477649	−	0.0440108i
$505$	−1.55849	+	5.81637i	−0.0693520	+	0.258825i
$506$	12.7433			0.566507
$507$	−17.6805	−	13.9427i	−0.785218	−	0.619219i
$508$	20.6932			0.918114
$509$	−9.73260	+	36.3226i	−0.431390	+	1.60997i	0.318171	+	0.948033i	$0.396931\pi$
$509$	−9.73260	+	36.3226i	−0.431390	+	1.60997i	−0.749561	+	0.661936i	$0.769735\pi$
$510$	9.22047	−	14.3998i	0.408289	−	0.637635i
$511$	44.3241	+	25.5905i	1.96078	+	1.13206i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	11.5787	−	1.44290i	0.511210	−	0.0637056i
$514$	1.57638	−	0.422389i	0.0695311	−	0.0186308i
$515$	−28.8249	+	28.8249i	−1.27018	+	1.27018i
$516$	0.155137	−	3.37453i	0.00682952	−	0.148556i
$517$	4.92757	−	2.84493i	0.216714	−	0.125120i
$518$	16.7904	+	4.49897i	0.737727	+	0.197673i
$519$	26.9111	−	13.9302i	1.18127	−	0.611468i
$520$	−10.2925	−	0.505814i	−0.451358	−	0.0221814i
$521$			18.2111i			0.797843i	0.916985	+	0.398922i	$0.130615\pi$
$521$			18.2111i			0.797843i	−0.916985	+	0.398922i	$0.869385\pi$
$522$	−4.64669	+	3.86264i	−0.203380	+	0.169063i
$523$	−16.9049	−	29.2801i	−0.739199	−	1.28033i	−0.952857	−	0.303421i	$-0.901871\pi$
$523$	−16.9049	−	29.2801i	−0.739199	−	1.28033i	0.213658	−	0.976909i	$-0.431462\pi$
$524$	−2.34147	+	4.05555i	−0.102288	+	0.177168i
$525$	5.96732	−	18.7748i	0.260435	−	0.819398i
$526$	−2.73518	−	10.2078i	−0.119260	−	0.445083i
$527$	−1.54027	−	5.74835i	−0.0670951	−	0.250402i
$528$	2.20478	−	6.93684i	0.0959509	−	0.301887i
$529$	6.90238	−	11.9553i	0.300103	−	0.519794i
$530$	10.3203	+	17.8753i	0.448287	+	0.776455i
$531$	−23.7354	+	19.7305i	−1.03003	+	0.856230i
$532$		−	8.06049i		−	0.349467i
$533$	8.75867	−	27.2580i	0.379380	−	1.18068i
$534$	15.1431	−	7.83866i	0.655307	−	0.339212i
$535$	−38.2233	−	10.2419i	−1.65254	−	0.442795i
$536$	−3.67704	+	2.12294i	−0.158824	+	0.0916970i
$537$	0.732997	−	15.9441i	0.0316312	−	0.688041i
$538$	6.09426	−	6.09426i	0.262742	−	0.262742i
$539$	23.8877	−	6.40069i	1.02892	−	0.275697i
$540$	14.7370	−	1.83649i	0.634182	−	0.0790299i
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	0.592063	−	0.805892i	$-0.298314\pi$
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	−0.805892	+	0.592063i	$0.798314\pi$
$542$	−17.1750	−	9.91601i	−0.737731	−	0.425929i
$543$	−12.8995	+	20.1454i	−0.553569	+	0.864521i
$544$	0.893982	−	3.33639i	0.0383291	−	0.143046i
$545$	−23.6138			−1.01150
$546$	13.0001	−	18.2621i	0.556354	−	0.781546i
$547$	−2.15870			−0.0922995			−0.0461497	−	0.998935i	$-0.514695\pi$
$547$	−2.15870			−0.0922995			−0.0461497	+	0.998935i	$0.514695\pi$
$548$	1.41832	−	5.29326i	0.0605878	−	0.226117i
$549$	−0.819152	−	0.0754770i	−0.0349606	−	0.00322128i
$550$	11.5319	+	6.65796i	0.491723	+	0.283897i
$551$	−3.19818	−	3.19818i	−0.136247	−	0.136247i
$552$	3.53940	+	3.88051i	0.150647	+	0.165166i
$553$	5.47999	−	1.46836i	0.233033	−	0.0624409i
$554$	−10.9619	+	10.9619i	−0.465726	+	0.465726i
$555$	−23.9472	−	1.10092i	−1.01650	−	0.0467315i
$556$	12.7247	−	7.34662i	0.539648	−	0.311566i
$557$	2.17782	+	0.583545i	0.0922772	+	0.0247256i	0.304662	−	0.952460i	$-0.401456\pi$
$557$	2.17782	+	0.583545i	0.0922772	+	0.0247256i	−0.212385	+	0.977186i	$0.568123\pi$
$558$	2.98420	−	4.22030i	0.126331	−	0.178659i
$559$	5.91003	+	3.81072i	0.249968	+	0.161176i
$560$		−	10.2592i		−	0.433531i
$561$	−24.5581	+	5.38497i	−1.03684	+	0.227354i
$562$	−8.44653	−	14.6298i	−0.356296	−	0.617122i
$563$	18.1490	−	31.4349i	0.764888	−	1.32482i	−0.175418	−	0.984494i	$-0.556128\pi$
$563$	18.1490	−	31.4349i	0.764888	−	1.32482i	0.940306	−	0.340330i	$-0.110539\pi$
$564$	2.23494	+	0.710348i	0.0941081	+	0.0299111i
$565$	13.3181	+	49.7038i	0.560297	+	2.09106i
$566$	0.408861	+	1.52589i	0.0171857	+	0.0641380i
$567$	−13.9227	+	29.1518i	−0.584698	+	1.22426i
$568$	5.51689	−	9.55553i	0.231483	−	0.400941i
$569$	−19.5376	−	33.8400i	−0.819057	−	1.41865i	−0.906378	−	0.422468i	$-0.861164\pi$
$569$	−19.5376	−	33.8400i	−0.819057	−	1.41865i	0.0873209	−	0.996180i	$-0.472169\pi$
$570$	2.38095	+	10.8583i	0.0997270	+	0.454803i
$571$		−	31.9061i		−	1.33523i	−0.744508	−	0.667614i	$-0.767316\pi$
$571$		−	31.9061i		−	1.33523i	0.744508	−	0.667614i	$-0.232684\pi$
$572$	10.1753	+	11.2271i	0.425450	+	0.469427i
$573$	−18.0767	−	34.9215i	−0.755165	−	1.45887i
$574$	27.5323	+	7.37726i	1.14918	+	0.307921i
$575$	−8.32119	+	4.80424i	−0.347018	+	0.200351i
$576$	2.72474	−	1.25529i	0.113531	−	0.0523040i
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	−0.486240	−	0.873825i	$-0.661632\pi$
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	0.873825	+	0.486240i	$0.161632\pi$
$578$	4.89660	−	1.31204i	0.203672	−	0.0545736i
$579$	25.6525	−	23.3975i	1.06608	−	0.972366i
$580$	−4.07056	−	4.07056i	−0.169021	−	0.169021i
$581$	11.3836	+	6.57233i	0.472271	+	0.272666i
$582$	11.7020	+	7.49301i	0.485063	+	0.310595i
$583$	7.85495	−	29.3151i	0.325319	−	1.21411i
$584$	−14.2584			−0.590016
$585$	−12.1181	+	28.4409i	−0.501021	+	1.17589i
$586$	3.90516			0.161321
$587$	−7.58008	+	28.2892i	−0.312863	+	1.16762i	0.613099	+	0.790006i	$0.289923\pi$
$587$	−7.58008	+	28.2892i	−0.312863	+	1.16762i	−0.925962	+	0.377615i	$0.876744\pi$
$588$	8.58385	+	5.49640i	0.353992	+	0.226668i
$589$	3.35059	+	1.93446i	0.138058	+	0.0797081i
$590$	−20.7926	−	20.7926i	−0.856017	−	0.856017i
$591$	−23.8501	+	21.7536i	−0.981064	+	0.894824i
$592$	−4.67758	+	1.25335i	−0.192247	+	0.0515126i
$593$	12.7368	−	12.7368i	0.523037	−	0.523037i	−0.395450	−	0.918487i	$-0.629411\pi$
$593$	12.7368	−	12.7368i	0.523037	−	0.523037i	0.918487	+	0.395450i	$0.129411\pi$
$594$	−17.2315	−	13.4127i	−0.707018	−	0.550331i
$595$	−30.6886	+	17.7181i	−1.25811	+	0.726370i
$596$	−9.98255	−	2.67482i	−0.408901	−	0.109565i
$597$	3.59128	+	6.93783i	0.146981	+	0.283946i
$598$	−10.6870	+	2.30798i	−0.437023	+	0.0943802i
$599$		−	15.6579i		−	0.639764i	−0.947457	−	0.319882i	$-0.896357\pi$
$599$		−	15.6579i		−	0.639764i	0.947457	−	0.319882i	$-0.103643\pi$
$600$	1.17551	+	5.36088i	0.0479899	+	0.218857i
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	0.772882	−	0.634549i	$-0.218814\pi$
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	−0.935977	+	0.352061i	$0.885481\pi$
$602$	−3.50042	+	6.06291i	−0.142667	+	0.247106i
$603$	2.15396	+	12.5542i	0.0877160	+	0.511247i
$604$	2.37526	+	8.86458i	0.0966478	+	0.360695i
$605$	−4.92677	−	18.3869i	−0.200302	−	0.747535i
$606$	3.47773	+	1.10535i	0.141273	+	0.0449019i
$607$	−2.24581	+	3.88985i	−0.0911545	+	0.157884i	−0.907997	−	0.418976i	$-0.862389\pi$
$607$	−2.24581	+	3.88985i	−0.0911545	+	0.157884i	0.816843	+	0.576860i	$0.195722\pi$
$608$	1.12277	+	1.94470i	0.0455345	+	0.0788681i
$609$	12.2320	−	2.68217i	0.495665	−	0.108687i
$610$		−	0.783707i		−	0.0317314i
$611$	−3.61719	+	3.27832i	−0.146336	+	0.132627i
$612$	−8.46073	−	5.98264i	−0.342005	−	0.241834i
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.815489	−	0.578773i	$-0.196468\pi$
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.416848	+	0.908976i	$0.363135\pi$
$614$	26.6987	−	15.4145i	1.07747	−	0.622079i
$615$	−39.2678	−	1.80525i	−1.58343	−	0.0727948i
$616$	−10.6665	+	10.6665i	−0.429766	+	0.429766i
$617$	5.23513	−	1.40275i	0.210758	−	0.0564725i	−0.151895	−	0.988397i	$-0.548538\pi$
$617$	5.23513	−	1.40275i	0.210758	−	0.0564725i	0.362653	+	0.931924i	$0.381871\pi$
$618$	16.6478	+	18.2522i	0.669671	+	0.734212i
$619$	7.22455	+	7.22455i	0.290379	+	0.290379i	0.837230	−	0.546851i	$-0.184174\pi$
$619$	7.22455	+	7.22455i	0.290379	+	0.290379i	−0.546851	+	0.837230i	$0.684174\pi$
$620$	4.26455	+	2.46214i	0.171268	+	0.0988818i
$621$	14.5986	−	5.92890i	0.585823	−	0.237919i
$622$	5.41696	−	20.2164i	0.217200	−	0.810603i
$623$	−35.3382			−1.41580
$624$	−0.592661	+	6.21681i	−0.0237254	+	0.248872i
$625$	30.8029			1.23212
$626$	−8.45523	+	31.5554i	−0.337939	+	1.26121i
$627$	8.81388	−	13.7648i	0.351992	−	0.549715i
$628$	12.2483	+	7.07156i	0.488761	+	0.282186i
$629$	11.8276	+	11.8276i	0.471596	+	0.471596i
$630$	−28.8726	−	10.6599i	−1.15031	−	0.424701i
$631$	−20.2844	+	5.43520i	−0.807511	+	0.216372i	−0.638879	−	0.769307i	$-0.720602\pi$
$631$	−20.2844	+	5.43520i	−0.807511	+	0.216372i	−0.168632	+	0.985679i	$0.553935\pi$
$632$	−1.11759	+	1.11759i	−0.0444553	+	0.0444553i
$633$	0.682229	−	14.8398i	0.0271162	−	0.589830i
$634$	−6.38197	+	3.68463i	−0.253460	+	0.146335i
$635$	57.1277	+	15.3073i	2.26705	+	0.607453i
$636$	11.1086	−	5.75023i	0.440484	−	0.228011i
$637$	−18.8739	+	9.69426i	−0.747811	+	0.384100i
$638$			8.46434i			0.335106i
$639$	−21.1599	−	25.4550i	−0.837072	−	1.00698i
$640$	1.42904	+	2.47517i	0.0564878	+	0.0978398i
$641$	21.3437	−	36.9683i	0.843024	−	1.46016i	−0.0443019	−	0.999018i	$-0.514106\pi$
$641$	21.3437	−	36.9683i	0.843024	−	1.46016i	0.887326	−	0.461143i	$-0.152560\pi$
$642$	−7.26401	+	22.8545i	−0.286688	+	0.901995i
$643$	−0.813185	−	3.03485i	−0.0320689	−	0.119683i	0.948036	−	0.318163i	$-0.103066\pi$
$643$	−0.813185	−	3.03485i	−0.0320689	−	0.119683i	−0.980105	+	0.198481i	$0.936399\pi$
$644$	−2.81720	−	10.5139i	−0.111013	−	0.414306i
$645$	2.92452	−	9.20130i	0.115153	−	0.362301i
$646$	3.87815	−	6.71716i	0.152584	−	0.264283i
$647$	−18.2351	−	31.5841i	−0.716895	−	1.24170i	−0.962224	−	0.272258i	$-0.912229\pi$
$647$	−18.2351	−	31.5841i	−0.716895	−	1.24170i	0.245329	−	0.969440i	$-0.421104\pi$
$648$	−0.701625	−	8.97261i	−0.0275624	−	0.352477i
$649$			43.2361i			1.69717i
$650$	−10.8770	−	3.49503i	−0.426630	−	0.137086i
$651$	−9.51297	+	4.92427i	−0.372843	+	0.192998i
$652$	−1.07638	−	0.288415i	−0.0421542	−	0.0112952i
$653$	−39.3421	+	22.7142i	−1.53957	+	0.888874i	−0.540711	+	0.841208i	$0.681845\pi$
$653$	−39.3421	+	22.7142i	−1.53957	+	0.888874i	−0.998863	+	0.0476658i	$0.984822\pi$
$654$	−0.657196	+	14.2953i	−0.0256984	+	0.558991i
$655$	−9.46410	+	9.46410i	−0.369793	+	0.369793i
$656$	−7.67015	+	2.05521i	−0.299469	+	0.0802424i
$657$	−14.8153	+	40.1275i	−0.577999	+	1.56552i
$658$	−3.43659	−	3.43659i	−0.133972	−	0.133972i
$659$	−11.4858	−	6.63132i	−0.447422	−	0.258319i	0.259319	−	0.965792i	$-0.416502\pi$
$659$	−11.4858	−	6.63132i	−0.447422	−	0.258319i	−0.706741	+	0.707472i	$0.749835\pi$
$660$	11.2181	−	17.5196i	0.436664	−	0.681948i
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	−0.903165	−	0.429294i	$-0.858762\pi$
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	0.996811	+	0.0798025i	$0.0254290\pi$
$662$	18.2372			0.708809
$663$	19.6200	−	8.96385i	0.761979	−	0.348127i
$664$	−3.66193			−0.142110
$665$	5.96256	−	22.2526i	0.231218	−	0.862918i
$666$	−1.33295	+	14.4665i	−0.0516507	+	0.560565i
$667$	−5.28941	−	3.05384i	−0.204807	−	0.118245i
$668$	3.94925	+	3.94925i	0.152801	+	0.152801i
$669$	−24.5996	−	26.9704i	−0.951075	−	1.04274i
$670$	−11.7216	+	3.14079i	−0.452844	+	0.121339i
$671$	−0.814821	+	0.814821i	−0.0314558	+	0.0314558i
$672$	−6.21071	−	0.285524i	−0.239583	−	0.0110143i
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.871904	−	0.489678i	$-0.837114\pi$
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.0118785	+	0.999929i	$0.503781\pi$
$674$	4.75703	+	1.27464i	0.183234	+	0.0490973i
$675$	16.3086	+	2.26202i	0.627719	+	0.0870650i
$676$	−10.5668	−	7.57257i	−0.406414	−	0.291253i
$677$			41.0789i			1.57879i	0.613885	+	0.789396i	$0.289606\pi$
$677$			41.0789i			1.57879i	−0.613885	+	0.789396i	$0.710394\pi$
$678$	30.4603	−	6.67919i	1.16982	−	0.256513i
$679$	−14.3986	−	24.9390i	−0.552566	−	0.957073i
$680$	4.93602	−	8.54944i	0.189288	−	0.327856i
$681$	8.29751	+	2.63726i	0.317961	+	0.101060i
$682$	−1.87397	−	6.99374i	−0.0717579	−	0.267804i
$683$	−1.54160	−	5.75334i	−0.0589878	−	0.220145i	0.930140	−	0.367206i	$-0.119685\pi$
$683$	−1.54160	−	5.75334i	−0.0589878	−	0.220145i	−0.989128	+	0.147060i	$0.953019\pi$
$684$	6.63963	−	1.13918i	0.253873	−	0.0435577i
$685$	7.83113	−	13.5639i	0.299212	−	0.518250i
$686$	2.00152	+	3.46673i	0.0764182	+	0.132360i
$687$	5.20704	+	23.7466i	0.198661	+	0.905989i
$688$		−	1.95035i		−	0.0743562i
$689$	−1.27810	+	26.0074i	−0.0486917	+	0.990803i
$690$	6.90069	+	13.3311i	0.262705	+	0.507507i
$691$	27.6429	+	7.40689i	1.05159	+	0.281771i	0.742907	−	0.669395i	$-0.233447\pi$
$691$	27.6429	+	7.40689i	1.05159	+	0.281771i	0.308679	+	0.951166i	$0.400113\pi$
$692$	15.1514	−	8.74765i	0.575969	−	0.332536i
$693$	18.9358	+	41.1020i	0.719311	+	1.56134i
$694$	−10.5657	+	10.5657i	−0.401069	+	0.401069i
$695$	40.5636	−	10.8690i	1.53866	−	0.412284i
$696$	−2.57752	+	2.35095i	−0.0977007	+	0.0891124i
$697$	19.3944	+	19.3944i	0.734617	+	0.734617i
$698$	27.0512	+	15.6180i	1.02390	+	0.591151i
$699$	27.4143	+	17.5539i	1.03691	+	0.663950i
$700$	2.94380	−	10.9864i	0.111265	−	0.415247i
$701$	0.672924			0.0254160			0.0127080	−	0.999919i	$-0.495955\pi$
$701$	0.672924			0.0254160			0.0127080	+	0.999919i	$0.495955\pi$
$702$	16.8802	+	8.12756i	0.637104	+	0.306755i
$703$	−10.8743			−0.410131
$704$	1.08766	−	4.05922i	0.0409929	−	0.152987i
$705$	5.64454	+	3.61430i	0.212586	+	0.136123i
$706$	−8.95950	−	5.17277i	−0.337195	−	0.194680i
$707$	−5.34758	−	5.34758i	−0.201116	−	0.201116i
$708$	−13.1661	+	12.0087i	−0.494811	+	0.451315i
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.343111	−	0.939295i	$-0.388519\pi$
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.766790	+	0.641898i	$0.221853\pi$
$710$	22.2989	−	22.2989i	0.836864	−	0.836864i
$711$	1.98400	+	4.30648i	0.0744060	+	0.161506i
$712$	8.52583	−	4.92239i	0.319519	−	0.184474i
$713$	5.04653	+	1.35221i	0.188994	+	0.0506408i
$714$	9.87205	+	19.0713i	0.369452	+	0.713727i
$715$	19.7859	+	38.5214i	0.739950	+	1.44062i
$716$		−	9.21508i		−	0.344384i
$717$	3.57884	+	16.3212i	0.133654	+	0.609528i
$718$	−6.42720	−	11.1322i	−0.239861	−	0.415452i
$719$	−11.5566	+	20.0165i	−0.430987	+	0.746491i	−0.996959	−	0.0779336i	$-0.975168\pi$
$719$	−11.5566	+	20.0165i	−0.430987	+	0.746491i	0.565972	+	0.824425i	$0.308501\pi$
$720$	8.45077	−	1.44992i	0.314942	−	0.0540354i
$721$	−13.2508	−	49.4528i	−0.493487	−	1.84172i
$722$	−3.61247	−	13.4819i	−0.134442	−	0.501745i
$723$	−13.9929	−	4.44747i	−0.520402	−	0.165403i
$724$	−6.90550	+	11.9607i	−0.256641	+	0.444515i
$725$	−3.19108	−	5.52711i	−0.118514	−	0.205272i
$726$	−11.2682	+	2.47083i	−0.418201	+	0.0917012i
$727$			11.5379i			0.427917i	0.976843	+	0.213959i	$0.0686357\pi$
$727$			11.5379i			0.427917i	−0.976843	+	0.213959i	$0.931364\pi$
$728$	7.01349	−	10.8772i	0.259937	−	0.403136i
$729$	−25.9808	−	7.34847i	−0.962250	−	0.272166i
$730$	−39.3630	−	10.5473i	−1.45689	−	0.390373i
$731$	−5.83411	+	3.36832i	−0.215782	+	0.124582i
$732$	−0.474440	−	0.0218113i	−0.0175358	−	0.000806170i
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	−0.723716	−	0.690098i	$-0.757567\pi$
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	0.690098	+	0.723716i	$0.257567\pi$
$734$	−1.59083	+	0.426262i	−0.0587186	+	0.0157336i
$735$	19.6316	+	21.5236i	0.724121	+	0.793909i
$736$	2.14421	+	2.14421i	0.0790365	+	0.0790365i
$737$	15.4524	+	8.92147i	0.569198	+	0.328626i
$738$	−2.18572	+	23.7217i	−0.0804576	+	0.873207i
$739$	−3.23160	+	12.0605i	−0.118876	+	0.443652i	−0.999548	−	0.0300754i	$-0.990425\pi$
$739$	−3.23160	+	12.0605i	−0.118876	+	0.443652i	0.880671	+	0.473728i	$0.157092\pi$
$740$	−13.8405			−0.508788
$741$	−4.89866	+	13.1400i	−0.179957	+	0.482711i
$742$	−25.9232			−0.951669
$743$	11.8573	−	44.2519i	0.435001	−	1.62345i	−0.306063	−	0.952011i	$-0.599012\pi$
$743$	11.8573	−	44.2519i	0.435001	−	1.62345i	0.741064	−	0.671435i	$-0.234322\pi$
$744$	1.60921	−	2.51314i	0.0589966	−	0.0921363i
$745$	−25.5802	−	14.7687i	−0.937185	−	0.541084i
$746$	−14.1079	−	14.1079i	−0.516526	−	0.516526i
$747$	−3.80496	+	10.3058i	−0.139216	+	0.377070i
$748$	−14.0209	+	3.75688i	−0.512653	+	0.137365i
$749$	35.1425	−	35.1425i	1.28408	−	1.28408i
$750$	0.416344	−	9.05630i	0.0152027	−	0.330689i
$751$	13.8766	−	8.01168i	0.506366	−	0.292350i	−0.224973	−	0.974365i	$-0.572229\pi$
$751$	13.8766	−	8.01168i	0.506366	−	0.292350i	0.731338	+	0.682015i	$0.238896\pi$
$752$	1.30782	+	0.350429i	0.0476912	+	0.0127788i
$753$	−10.8285	+	5.60523i	−0.394611	+	0.204266i
$754$	−1.53301	−	7.09852i	−0.0558289	−	0.258513i
$755$			26.2295i			0.954588i
$756$	−7.25684	+	17.1822i	−0.263929	+	0.624911i
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	0.996764	+	0.0803861i	$0.0256153\pi$
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	−0.428765	+	0.903416i	$0.641051\pi$
$758$	−6.15590	+	10.6623i	−0.223592	+	0.387273i
$759$	6.68572	−	21.0350i	0.242676	−	0.763523i
$760$	1.66109	+	6.19928i	0.0602542	+	0.224872i
$761$	−4.45283	−	16.6182i	−0.161415	−	0.602409i	−0.998470	−	0.0552906i	$-0.982391\pi$
$761$	−4.45283	−	16.6182i	−0.161415	−	0.602409i	0.837055	−	0.547118i	$-0.184275\pi$
$762$	10.8567	−	34.1579i	0.393295	−	1.23741i
$763$	14.8286	−	25.6839i	0.536832	−	0.929820i
$764$	−11.3515	−	19.6614i	−0.410683	−	0.711324i
$765$	−18.9320	−	22.7749i	−0.684488	−	0.823428i
$766$			28.3459i			1.02418i
$767$	−7.83066	−	36.2595i	−0.282749	−	1.30925i
$768$	1.53819	−	0.796225i	0.0555046	−	0.0287313i
$769$	0.224553	+	0.0601687i	0.00809758	+	0.00216974i	0.262866	−	0.964832i	$-0.415332\pi$
$769$	0.224553	+	0.0601687i	0.00809758	+	0.00216974i	−0.254768	+	0.967002i	$0.581999\pi$
$770$	−37.3373	+	21.5567i	−1.34554	+	0.776850i
$771$	0.129813	−	2.82370i	0.00467512	−	0.101693i
$772$	14.1745	−	14.1745i	0.510150	−	0.510150i
$773$	−42.7466	+	11.4539i	−1.53749	+	0.411968i	−0.925453	−	0.378863i	$-0.876315\pi$
$773$	−42.7466	+	11.4539i	−1.53749	+	0.411968i	−0.612034	+	0.790831i	$0.709648\pi$
$774$	−5.48888	−	2.02652i	−0.197294	−	0.0728418i
$775$	3.86034	+	3.86034i	0.138667	+	0.138667i
$776$	6.94770	+	4.01125i	0.249408	+	0.143996i
$777$	16.2354	−	25.3552i	0.582441	−	0.909612i
$778$	−4.12827	+	15.4069i	−0.148006	+	0.552364i
$779$	−17.8313			−0.638872
$780$	−6.23490	+	16.7243i	−0.223245	+	0.598827i
$781$	−46.3684			−1.65919
$782$	2.71088	−	10.1171i	0.0969409	−	0.361788i
$783$	3.93810	+	9.69672i	0.140736	+	0.346533i
$784$	5.09639	+	2.94240i	0.182014	+	0.105086i
$785$	28.5828	+	28.5828i	1.02017	+	1.02017i
$786$	5.46597	+	5.99276i	0.194965	+	0.213755i
$787$	20.4083	−	5.46839i	0.727478	−	0.194927i	0.123972	−	0.992286i	$-0.460437\pi$
$787$	20.4083	−	5.46839i	0.727478	−	0.194927i	0.603506	+	0.797358i	$0.293770\pi$
$788$	−13.1786	+	13.1786i	−0.469467	+	0.469467i
$789$	−18.2849	−	0.840607i	−0.650959	−	0.0299264i
$790$	−3.91203	+	2.25861i	−0.139184	+	0.0803578i
$791$	−62.4244	−	16.7266i	−2.21955	−	0.594728i
$792$	−10.2938	−	7.27879i	−0.365773	−	0.258640i
$793$	0.535765	−	0.830916i	0.0190256	−	0.0295067i
$794$			12.6918i			0.450417i
$795$	34.9210	−	7.65732i	1.23852	−	0.271577i
$796$	2.25519	+	3.90611i	0.0799332	+	0.138448i
$797$	12.0370	−	20.8487i	0.426373	−	0.738501i	−0.570174	−	0.821524i	$-0.693124\pi$
$797$	12.0370	−	20.8487i	0.426373	−	0.738501i	0.996548	+	0.0830233i	$0.0264576\pi$
$798$	−13.3053	−	4.22892i	−0.471002	−	0.149702i
$799$	−1.21041	−	4.51731i	−0.0428212	−	0.159811i
$800$	0.820104	+	3.06067i	0.0289951	+	0.108211i
$801$	−4.99431	−	29.1090i	−0.176465	−	1.02852i
$802$	8.20991	−	14.2200i	0.289902	−	0.502125i
$803$	29.9598	+	51.8918i	1.05726	+	1.83122i
$804$	1.57514	+	7.18341i	0.0555511	+	0.253339i
$805$		−	31.1097i		−	1.09647i
$806$	2.83824	+	5.52582i	0.0999729	+	0.194639i
$807$	−6.86234	−	13.2570i	−0.241566	−	0.466669i
$808$	2.03506	+	0.545293i	0.0715932	+	0.0191833i
$809$	22.2703	−	12.8578i	0.782982	−	0.452055i	−0.0545042	−	0.998514i	$-0.517358\pi$
$809$	22.2703	−	12.8578i	0.782982	−	0.452055i	0.837486	+	0.546459i	$0.184025\pi$
$810$	4.70030	−	25.2897i	0.165152	−	0.888588i
$811$	5.99463	−	5.99463i	0.210500	−	0.210500i	−0.593980	−	0.804480i	$-0.702444\pi$
$811$	5.99463	−	5.99463i	0.210500	−	0.210500i	0.804480	+	0.593980i	$0.202444\pi$
$812$	6.98357	−	1.87124i	0.245075	−	0.0656677i
$813$	−25.3790	+	23.1481i	−0.890080	+	0.811838i
$814$	14.3900	+	14.3900i	0.504370	+	0.504370i
$815$	−2.75821	−	1.59245i	−0.0966157	−	0.0557811i
$816$	−5.03828	−	3.22610i	−0.176375	−	0.112936i
$817$	1.13352	−	4.23037i	0.0396570	−	0.148002i
$818$	−34.0781			−1.19151
$819$	−23.3244	−	31.0402i	−0.815021	−	1.08463i
$820$	−22.6952			−0.792552
$821$	−13.7528	+	51.3262i	−0.479977	+	1.79130i	0.121710	+	0.992566i	$0.461162\pi$
$821$	−13.7528	+	51.3262i	−0.479977	+	1.79130i	−0.601687	+	0.798732i	$0.705504\pi$
$822$	−7.99336	−	5.11830i	−0.278800	−	0.178521i
$823$	−9.92634	−	5.73097i	−0.346010	−	0.199769i	0.316916	−	0.948454i	$-0.397353\pi$
$823$	−9.92634	−	5.73097i	−0.346010	−	0.199769i	−0.662927	+	0.748684i	$0.730686\pi$
$824$	10.0854	+	10.0854i	0.351341	+	0.351341i
$825$	17.0404	−	15.5424i	0.593269	−	0.541118i
$826$	35.6723	−	9.55837i	1.24120	−	0.332578i
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	−0.623042	−	0.782188i	$-0.714104\pi$
$827$	4.57665	−	4.57665i	0.159146	−	0.159146i	0.782188	+	0.623042i	$0.214104\pi$
$828$	8.26243	−	3.80652i	0.287139	−	0.132286i
$829$	43.2625	−	24.9776i	1.50257	−	0.867509i	0.502574	−	0.864534i	$-0.332387\pi$
$829$	43.2625	−	24.9776i	1.50257	−	0.867509i	0.999996	−	0.00297446i	$-0.000946803\pi$
$830$	−10.1095	−	2.70883i	−0.350905	−	0.0940248i
$831$	12.3434	+	23.8457i	0.428189	+	0.827198i
$832$	−0.176977	+	3.60121i	−0.00613556	+	0.124849i
$833$		−	20.3266i		−	0.704275i
$834$	−5.45092	−	24.8588i	−0.188750	−	0.860791i
$835$	7.98133	+	13.8241i	0.276205	+	0.478401i
$836$	4.71836	−	8.17244i	0.163188	−	0.282650i
$837$	−5.40071	−	7.14013i	−0.186676	−	0.246799i
$838$	8.51576	+	31.7812i	0.294172	+	1.09786i
$839$	3.00183	+	11.2030i	0.103635	+	0.386770i	0.998187	−	0.0601939i	$-0.0191719\pi$
$839$	3.00183	+	11.2030i	0.103635	+	0.386770i	−0.894552	+	0.446964i	$0.852505\pi$
$840$	−16.9347	−	5.38247i	−0.584302	−	0.185713i
$841$	−12.4716	+	21.6014i	−0.430054	+	0.744876i
$842$	−12.0877	−	20.9364i	−0.416568	−	0.721517i
$843$	−28.5806	+	6.26702i	−0.984369	+	0.215848i
$844$		−	8.57683i		−	0.295227i
$845$	−23.5700	−	28.7221i	−0.810832	−	0.988069i
$846$	2.34512	−	3.31649i	0.0806267	−	0.114023i
$847$	23.0926	+	6.18765i	0.793472	+	0.212610i
$848$	6.25431	−	3.61093i	0.214774	−	0.124000i
$849$	2.73327	+	0.125656i	0.0938055	+	0.00431250i
$850$	7.73910	−	7.73910i	0.265449	−	0.265449i
$851$	−14.1841	+	3.80063i	−0.486226	+	0.130284i
$852$	−12.8787	−	14.1199i	−0.441217	−	0.483740i
$853$	−1.56247	−	1.56247i	−0.0534978	−	0.0534978i	0.679852	−	0.733350i	$-0.262044\pi$
$853$	−1.56247	−	1.56247i	−0.0534978	−	0.0534978i	−0.733350	+	0.679852i	$0.762044\pi$
$854$	0.852410	+	0.492139i	0.0291689	+	0.0168407i
$855$	19.1727	+	1.76658i	0.655692	+	0.0604157i
$856$	−3.58348	+	13.3737i	−0.122481	+	0.457105i
$857$	21.5804			0.737174			0.368587	−	0.929593i	$-0.379842\pi$
$857$	21.5804			0.737174			0.368587	+	0.929593i	$0.379842\pi$
$858$	23.8707	−	10.9059i	0.814933	−	0.372320i
$859$	10.5544			0.360110			0.180055	−	0.983657i	$-0.442372\pi$
$859$	10.5544			0.360110			0.180055	+	0.983657i	$0.442372\pi$
$860$	1.44272	−	5.38431i	0.0491964	−	0.183604i
$861$	26.6223	−	41.5766i	0.907284	−	1.41693i
$862$	−1.52054	−	0.877885i	−0.0517899	−	0.0299009i
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	0.970434	−	0.241368i	$-0.0775960\pi$
$863$	21.4177	+	21.4177i	0.729066	+	0.729066i	−0.241368	+	0.970434i	$0.577596\pi$
$864$	−0.642559	−	5.15627i	−0.0218603	−	0.175420i
$865$	48.2992	−	12.9417i	1.64222	−	0.440032i
$866$	−7.24346	+	7.24346i	−0.246143	+	0.246143i
$867$	0.403231	−	8.77108i	0.0136944	−	0.297881i
$868$	−5.35596	+	3.09226i	−0.181793	+	0.104958i
$869$	6.41562	+	1.71906i	0.217635	+	0.0583152i
$870$	−8.85481	+	4.58359i	−0.300206	+	0.155398i
$871$	−14.5748	−	4.68323i	−0.493848	−	0.158685i
$872$			8.26212i			0.279791i
$873$	18.5080	−	15.3851i	0.626400	−	0.520706i
$874$	3.40467	+	5.89705i	0.115165	+	0.199471i
$875$	−9.39415	+	16.2711i	−0.317580	+	0.550065i
$876$	−7.48062	+	23.5360i	−0.252747	+	0.795208i
$877$	10.1109	+	37.7342i	0.341420	+	1.27419i	0.896740	+	0.442558i	$0.145929\pi$
$877$	10.1109	+	37.7342i	0.341420	+	1.27419i	−0.555320	+	0.831637i	$0.687404\pi$
$878$	1.39820	+	5.21816i	0.0471871	+	0.176105i
$879$	2.04883	−	6.44617i	0.0691054	−	0.217424i
$880$	6.00542	−	10.4017i	0.202443	−	0.350641i
$881$	3.39708	+	5.88391i	0.114450	+	0.198234i	0.917560	−	0.397598i	$-0.130156\pi$
$881$	3.39708	+	5.88391i	0.114450	+	0.198234i	−0.803110	+	0.595831i	$0.796823\pi$
$882$	13.5763	−	11.2855i	0.457138	−	0.380003i
$883$		−	40.6560i		−	1.36818i	−0.729397	−	0.684091i	$-0.760199\pi$
$883$		−	40.6560i		−	1.36818i	0.729397	−	0.684091i	$-0.239801\pi$
$884$	11.0780	−	5.69003i	0.372594	−	0.191376i
$885$	−45.2307	+	23.4131i	−1.52041	+	0.787023i
$886$	−13.1106	−	3.51297i	−0.440458	−	0.118020i
$887$	9.04299	−	5.22097i	0.303634	−	0.175303i	−0.340440	−	0.940266i	$-0.610576\pi$
$887$	9.04299	−	5.22097i	0.303634	−	0.175303i	0.644074	+	0.764963i	$0.277243\pi$
$888$	−0.385195	+	8.37876i	−0.0129263	+	0.281173i
$889$	−52.5233	+	52.5233i	−1.76158	+	1.76158i
$890$	27.1784	−	7.28244i	0.911024	−	0.244108i
$891$	−31.1806	+	21.4068i	−1.04459	+	0.717154i
$892$	−14.9027	−	14.9027i	−0.498979	−	0.498979i
$893$	2.63304	+	1.52018i	0.0881112	+	0.0508710i
$894$	−9.65259	+	15.0747i	−0.322831	+	0.504172i
$895$	6.81664	−	25.4400i	0.227855	−	0.850367i
$896$	−3.58954			−0.119918
$897$	−1.79716	+	18.8517i	−0.0600056	+	0.629438i
$898$	2.02930			0.0677187
$899$	−0.898169	+	3.35201i	−0.0299556	+	0.111796i
$900$	9.46582	+	0.872184i	0.315527	+	0.0290728i
$901$	−21.6029	−	12.4724i	−0.719697	−	0.415517i
$902$	23.5963	+	23.5963i	0.785670	+	0.785670i
$903$	8.17144	+	8.95897i	0.271928	+	0.298136i
$904$	17.3906	−	4.65980i	0.578403	−	0.154983i
$905$	−27.9116	+	27.9116i	−0.927814	+	0.927814i
$906$	15.8788	+	0.729991i	0.527536	+	0.0242523i
$907$	−33.9759	+	19.6160i	−1.12815	+	0.651338i	−0.943469	−	0.331461i	$-0.892458\pi$
$907$	−33.9759	+	19.6160i	−1.12815	+	0.651338i	−0.184681	+	0.982799i	$0.559125\pi$
$908$	4.85544	+	1.30101i	0.161134	+	0.0431756i
$909$	3.64917	−	5.16071i	0.121035	−	0.171170i
$910$	27.4083	−	24.8406i	0.908575	−	0.823457i
$911$			32.0923i			1.06326i	0.846975	+	0.531632i	$0.178421\pi$
$911$			32.0923i			1.06326i	−0.846975	+	0.531632i	$0.821579\pi$
$912$	3.79914	−	0.833058i	0.125802	−	0.0275853i
$913$	7.69447	+	13.3272i	0.254650	+	0.441066i
$914$	−14.9767	+	25.9404i	−0.495385	+	0.858032i
$915$	−1.29365	−	0.411170i	−0.0427667	−	0.0135929i
$916$	3.63274	+	13.5576i	0.120029	+	0.447955i
$917$	−4.35066	−	16.2369i	−0.143671	−	0.536189i
$918$	−14.3143	+	10.8272i	−0.472443	+	0.357350i
$919$	−16.6421	+	28.8249i	−0.548972	+	0.950847i	0.449374	+	0.893344i	$0.351647\pi$
$919$	−16.6421	+	28.8249i	−0.548972	+	0.950847i	−0.998345	+	0.0575028i	$0.981686\pi$
$920$	4.33338	+	7.50563i	0.142867	+	0.247453i
$921$	−11.4370	−	52.1582i	−0.376862	−	1.71867i
$922$		−	16.1111i		−	0.530589i
$923$	38.8863	−	8.39796i	1.27996	−	0.276422i
$924$	12.0108	+	23.2032i	0.395128	+	0.763328i
$925$	−14.8216	−	3.97143i	−0.487330	−	0.130580i
$926$	−4.98521	+	2.87821i	−0.163824	+	0.0945840i
$927$	38.8628	−	17.9042i	1.27642	−	0.588049i
$928$	−1.42423	+	1.42423i	−0.0467526	+	0.0467526i
$929$	21.2156	−	5.68470i	0.696060	−	0.186509i	0.106595	−	0.994303i	$-0.466005\pi$
$929$	21.2156	−	5.68470i	0.696060	−	0.186509i	0.589465	+	0.807794i	$0.299338\pi$
$930$	6.30159	−	5.74765i	0.206637	−	0.188473i
$931$	9.34415	+	9.34415i	0.306242	+	0.306242i
$932$	16.2764	+	9.39719i	0.533151	+	0.307815i
$933$	−30.5288	−	19.5481i	−0.999467	−	0.639978i
$934$	9.53841	−	35.5978i	0.312106	−	1.16480i
$935$	−41.4864			−1.35675
$936$	9.95103	+	4.23993i	0.325260	+	0.138586i
$937$	55.9423			1.82755			0.913777	−	0.406216i	$-0.133152\pi$
$937$	55.9423			1.82755			0.913777	+	0.406216i	$0.133152\pi$
$938$	3.94460	−	14.7214i	0.128796	−	0.480672i
$939$	47.6518	+	30.5123i	1.55506	+	0.995732i
$940$	3.35127	+	1.93486i	0.109306	+	0.0631080i
$941$	−17.1600	−	17.1600i	−0.559401	−	0.559401i	0.369736	−	0.929137i	$-0.379448\pi$
$941$	−17.1600	−	17.1600i	−0.559401	−	0.559401i	−0.929137	+	0.369736i	$0.879448\pi$
$942$	18.0989	−	16.5080i	0.589695	−	0.537858i
$943$	−23.2587	+	6.23215i	−0.757407	+	0.202947i
$944$	−7.27501	+	7.27501i	−0.236781	+	0.236781i
$945$	−32.7441	+	42.0668i	−1.06516	+	1.36843i
$946$	−7.09808	+	4.09808i	−0.230778	+	0.133240i
$947$	−46.0604	−	12.3419i	−1.49676	−	0.401056i	−0.584748	−	0.811215i	$-0.698807\pi$
$947$	−46.0604	−	12.3419i	−1.49676	−	0.401056i	−0.912014	+	0.410159i	$0.865473\pi$
$948$	1.25844	+	2.43112i	0.0408722	+	0.0789591i
$949$	−34.5237	−	38.0924i	−1.12069	−	1.23653i
$950$			7.11534i			0.230852i
$951$	2.73386	+	12.4677i	0.0886516	+	0.404293i
$952$	6.19928	+	10.7375i	0.200920	+	0.348003i
$953$	−21.5278	+	37.2872i	−0.697353	+	1.20785i	0.272029	+	0.962289i	$0.412305\pi$
$953$	−21.5278	+	37.2872i	−0.697353	+	1.20785i	−0.969381	+	0.245561i	$0.921028\pi$
$954$	−3.66369	−	21.3536i	−0.118616	−	0.691347i
$955$	−16.7940	−	62.6761i	−0.543441	−	2.02815i
$956$	2.49681	+	9.31824i	0.0807527	+	0.301373i
$957$	13.9719	+	4.44080i	0.451648	+	0.143551i
$958$	7.52152	−	13.0276i	0.243009	−	0.420904i
$959$	9.83532	+	17.0353i	0.317599	+	0.550098i
$960$	4.83546	−	1.06030i	0.156064	−	0.0342209i
$961$			28.0315i			0.904242i
$962$	−14.6742	−	9.46179i	−0.473117	−	0.305060i
$963$	33.9144	+	23.9811i	1.09288	+	0.772781i
$964$	−8.18821	−	2.19402i	−0.263724	−	0.0706648i
$965$	49.6166	−	28.6461i	1.59721	−	0.922152i
$966$	−18.8331	−	0.865813i	−0.605947	−	0.0278571i
$967$	−4.96226	+	4.96226i	−0.159576	+	0.159576i	−0.782379	−	0.622803i	$-0.785994\pi$
$967$	−4.96226	+	4.96226i	−0.159576	+	0.159576i	0.622803	+	0.782379i	$0.285994\pi$
$968$	−6.43331	+	1.72380i	−0.206774	+	0.0554050i
$969$	−9.05322	−	9.92573i	−0.290831	−	0.318861i
$970$	16.2132	+	16.2132i	0.520576	+	0.520576i
$971$	27.5285	+	15.8936i	0.883432	+	0.510050i	0.871789	−	0.489882i	$-0.162960\pi$
$971$	27.5285	+	15.8936i	0.883432	+	0.510050i	0.0116437	+	0.999932i	$0.496294\pi$
$972$	−15.1790	−	3.54930i	−0.486867	−	0.113844i
$973$	−13.6506	+	50.9448i	−0.437619	+	1.63322i
$974$	16.7305			0.536081
$975$	−11.4758	+	16.1207i	−0.367518	+	0.516277i
$976$	−0.274207			−0.00877716
$977$	−1.80392	+	6.73232i	−0.0577125	+	0.215386i	−0.988760	−	0.149512i	$-0.952230\pi$
$977$	−1.80392	+	6.73232i	−0.0577125	+	0.215386i	0.931047	+	0.364898i	$0.118896\pi$
$978$	−1.04080	+	1.62544i	−0.0332811	+	0.0519758i
$979$	−35.8290	−	20.6859i	−1.14510	−	0.661124i
$980$	11.8930	+	11.8930i	0.379909	+	0.379909i
$981$	23.2522	+	8.58482i	0.742385	+	0.274092i
$982$	−24.4056	+	6.53947i	−0.778815	+	0.208683i
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	−0.855209	−	0.518283i	$-0.826571\pi$
$983$	−10.5636	+	10.5636i	−0.336926	+	0.336926i	0.518283	+	0.855209i	$0.326571\pi$
$984$	−0.631631	+	13.7392i	−0.0201356	+	0.437990i
$985$	−46.1306	+	26.6335i	−1.46984	+	0.848614i
$986$	6.72002	+	1.80063i	0.214009	+	0.0573436i
$987$	−7.47571	+	3.86971i	−0.237954	+	0.123174i
$988$	−2.47686	+	7.70828i	−0.0787993	+	0.245233i
$989$		−	5.91416i		−	0.188059i
$990$	−23.0336	−	27.7091i	−0.732057	−	0.880653i
$991$	−13.1927	−	22.8505i	−0.419081	−	0.725870i	0.576766	−	0.816909i	$-0.304314\pi$
$991$	−13.1927	−	22.8505i	−0.419081	−	0.725870i	−0.995847	+	0.0910396i	$0.970981\pi$
$992$	0.861464	−	1.49210i	0.0273515	−	0.0473742i
$993$	9.56810	−	30.1038i	0.303635	−	0.955315i
$994$	10.2508	+	38.2566i	0.325137	+	1.21343i
$995$	3.33645	+	12.4518i	0.105773	+	0.394749i
$996$	−1.92122	+	6.04468i	−0.0608763	+	0.191533i
$997$	−14.6325	+	25.3443i	−0.463416	+	0.802660i	−0.999129	−	0.0417401i	$-0.986710\pi$
$997$	−14.6325	+	25.3443i	−0.463416	+	0.802660i	0.535712	+	0.844401i	$0.320043\pi$
$998$	−0.975428	−	1.68949i	−0.0308766	−	0.0534799i
$999$	23.1802	+	9.79008i	0.733390	+	0.309744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.41.3	yes	16
3.2	odd	2	inner	78.2.k.a.41.1	✓	16
4.3	odd	2		624.2.cn.d.353.4		16
12.11	even	2		624.2.cn.d.353.3		16
13.2	odd	12		1014.2.g.d.437.8		16
13.3	even	3		1014.2.g.c.239.8		16
13.7	odd	12	inner	78.2.k.a.59.1	yes	16
13.10	even	6		1014.2.g.d.239.4		16
13.11	odd	12		1014.2.g.c.437.4		16
39.2	even	12		1014.2.g.d.437.4		16
39.11	even	12		1014.2.g.c.437.8		16
39.20	even	12	inner	78.2.k.a.59.3	yes	16
39.23	odd	6		1014.2.g.d.239.8		16
39.29	odd	6		1014.2.g.c.239.4		16
52.7	even	12		624.2.cn.d.449.3		16
156.59	odd	12		624.2.cn.d.449.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.1	✓	16	3.2	odd	2	inner
78.2.k.a.41.3	yes	16	1.1	even	1	trivial
78.2.k.a.59.1	yes	16	13.7	odd	12	inner
78.2.k.a.59.3	yes	16	39.20	even	12	inner
624.2.cn.d.353.3		16	12.11	even	2
624.2.cn.d.353.4		16	4.3	odd	2
624.2.cn.d.449.3		16	52.7	even	12
624.2.cn.d.449.4		16	156.59	odd	12
1014.2.g.c.239.4		16	39.29	odd	6
1014.2.g.c.239.8		16	13.3	even	3
1014.2.g.c.437.4		16	13.11	odd	12
1014.2.g.c.437.8		16	39.11	even	12
1014.2.g.d.239.4		16	13.10	even	6
1014.2.g.d.239.8		16	39.23	odd	6
1014.2.g.d.437.4		16	39.2	even	12
1014.2.g.d.437.8		16	13.2	odd	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.45865 - 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.02097 - 2.02097i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(3.46723 - 0.929042i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.45865 - 0.933998i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.02097 - 2.02097i) q^{5} +(-1.27970 + 1.16721i) q^{6} +(3.46723 - 0.929042i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.25529 + 2.72474i) q^{9} +(-2.47517 + 1.42904i) q^{10} +(4.05922 + 1.08766i) q^{11} +(0.796225 + 1.53819i) q^{12} +(-3.60121 - 0.176977i) q^{13} -3.58954i q^{14} +(1.06030 + 4.83546i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.72704 - 2.99132i) q^{17} +(2.95680 - 0.507306i) q^{18} +(0.581191 + 2.16903i) q^{19} +(0.739726 + 2.76070i) q^{20} +(-5.92518 - 1.88324i) q^{21} +(2.10121 - 3.63939i) q^{22} +(1.51618 + 2.62611i) q^{23} +(1.69185 - 0.370982i) q^{24} +3.16864i q^{25} +(-1.10301 + 3.43269i) q^{26} +(0.713876 - 5.14688i) q^{27} +(-3.46723 - 0.929042i) q^{28} +(-1.74432 + 1.00708i) q^{29} +(4.94512 + 0.227341i) q^{30} +(1.21829 - 1.21829i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-4.90508 - 5.37782i) q^{33} +(-2.44240 - 2.44240i) q^{34} +(-8.88473 - 5.12960i) q^{35} +(0.275255 - 2.98735i) q^{36} +(-1.25335 + 4.67758i) q^{37} +2.24555 q^{38} +(5.08759 + 3.62167i) q^{39} +2.85808 q^{40} +(-2.05521 + 7.67015i) q^{41} +(-3.35262 + 5.23587i) q^{42} +(-1.68905 - 0.975173i) q^{43} +(-2.97155 - 2.97155i) q^{44} +(2.96971 - 8.04354i) q^{45} +(2.92904 - 0.784834i) q^{46} +(0.957390 - 0.957390i) q^{47} +(0.0795432 - 1.73022i) q^{48} +(5.09639 - 2.94240i) q^{49} +(3.06067 + 0.820104i) q^{50} +(-5.31303 + 2.75023i) q^{51} +(3.03025 + 1.95387i) q^{52} -7.22186i q^{53} +(-4.78674 - 2.02166i) q^{54} +(-6.00542 - 10.4017i) q^{55} +(-1.79477 + 3.10863i) q^{56} +(1.17812 - 3.70668i) q^{57} +(0.521304 + 1.94553i) q^{58} +(2.66284 + 9.93785i) q^{59} +(1.49949 - 4.71778i) q^{60} +(-0.137104 + 0.237470i) q^{61} +(-0.861464 - 1.49210i) q^{62} +(6.88380 + 8.28110i) q^{63} -1.00000i q^{64} +(6.92026 + 7.63559i) q^{65} +(-6.46410 + 3.34607i) q^{66} +(4.10121 + 1.09891i) q^{67} +(-2.99132 + 1.72704i) q^{68} +(0.241204 - 5.24667i) q^{69} +(-7.25436 + 7.25436i) q^{70} +(-10.6578 + 2.85575i) q^{71} +(-2.81431 - 1.03906i) q^{72} +(10.0822 + 10.0822i) q^{73} +(4.19381 + 2.42130i) q^{74} +(2.95950 - 4.62192i) q^{75} +(0.581191 - 2.16903i) q^{76} +15.0847 q^{77} +(4.81502 - 3.97688i) q^{78} +1.58051 q^{79} +(0.739726 - 2.76070i) q^{80} +(-5.84847 + 6.84072i) q^{81} +(6.87686 + 3.97036i) q^{82} +(2.58938 + 2.58938i) q^{83} +(4.18974 + 4.59353i) q^{84} +(-9.53567 + 2.55507i) q^{85} +(-1.37910 + 1.37910i) q^{86} +(3.48495 + 0.160213i) q^{87} +(-3.63939 + 2.10121i) q^{88} +(-9.50933 - 2.54802i) q^{89} +(-7.00085 - 4.95035i) q^{90} +(-12.6506 + 2.73205i) q^{91} -3.03237i q^{92} +(-2.91495 + 0.639175i) q^{93} +(-0.676977 - 1.17256i) q^{94} +(3.20898 - 5.55812i) q^{95} +(-1.65068 - 0.524648i) q^{96} +(-2.07638 - 7.74915i) q^{97} +(-1.52310 - 5.68429i) 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

Varieties

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Database

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