LMFDB - Embedded newform 210.2.m.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(13,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("210.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.m (of order $4$, degree $2$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$3.16053i$ of defining polynomial
Character	$\chi$	$=$	210.13
Dual form			210.2.m.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.52773 + 1.63280i) q^{5} -1.00000i q^{6} +(2.33991 + 1.23483i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.52773 + 1.63280i) q^{5} -1.00000i q^{6} +(2.33991 + 1.23483i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.0743018 - 2.23483i) q^{10} -5.73528 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.41421 + 3.41421i) q^{13} +(-2.52773 + 0.781409i) q^{14} +(-0.0743018 - 2.23483i) q^{15} -1.00000 q^{16} +(-2.57474 - 2.57474i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.85140 q^{19} +(1.63280 + 1.52773i) q^{20} +(-2.52773 + 0.781409i) q^{21} +(4.05545 - 4.05545i) q^{22} +(6.46967 + 6.46967i) q^{23} -1.00000 q^{24} +(-0.332104 - 4.98896i) q^{25} -4.82843i q^{26} +(0.707107 + 0.707107i) q^{27} +(1.23483 - 2.33991i) q^{28} +3.47577i q^{29} +(1.63280 + 1.52773i) q^{30} +0.469666i q^{31} +(0.707107 - 0.707107i) q^{32} +(4.05545 - 4.05545i) q^{33} +3.64124 q^{34} +(-5.59099 + 1.93413i) q^{35} -1.00000 q^{36} +(0.574745 - 0.574745i) q^{37} +(1.30913 - 1.30913i) q^{38} -4.82843i q^{39} +(-2.23483 + 0.0743018i) q^{40} -1.03858i q^{41} +(1.23483 - 2.33991i) q^{42} +(6.17246 + 6.17246i) q^{43} +5.73528i q^{44} +(1.63280 + 1.52773i) q^{45} -9.14949 q^{46} +(3.85140 + 3.85140i) q^{47} +(0.707107 - 0.707107i) q^{48} +(3.95037 + 5.77880i) q^{49} +(3.76256 + 3.29289i) q^{50} +3.64124 q^{51} +(3.41421 + 3.41421i) q^{52} +(-1.85140 - 1.85140i) q^{53} -1.00000 q^{54} +(8.76193 - 9.36459i) q^{55} +(0.781409 + 2.52773i) q^{56} +(1.30913 - 1.30913i) q^{57} +(-2.45774 - 2.45774i) q^{58} +13.3306 q^{59} +(-2.23483 + 0.0743018i) q^{60} -8.53122i q^{61} +(-0.332104 - 0.332104i) q^{62} +(1.23483 - 2.33991i) q^{63} +1.00000i q^{64} +(-0.358761 - 10.7907i) q^{65} +5.73528i q^{66} +(-4.46967 + 4.46967i) q^{67} +(-2.57474 + 2.57474i) q^{68} -9.14949 q^{69} +(2.58579 - 5.32106i) q^{70} +5.13387 q^{71} +(0.707107 - 0.707107i) q^{72} +(-7.80177 + 7.80177i) q^{73} +0.812812i q^{74} +(3.76256 + 3.29289i) q^{75} +1.85140i q^{76} +(-13.4200 - 7.08211i) q^{77} +(3.41421 + 3.41421i) q^{78} +4.16422i q^{79} +(1.52773 - 1.63280i) q^{80} -1.00000 q^{81} +(0.734390 + 0.734390i) q^{82} +(-1.77297 + 1.77297i) q^{83} +(0.781409 + 2.52773i) q^{84} +(8.13756 - 0.270551i) q^{85} -8.72918 q^{86} +(-2.45774 - 2.45774i) q^{87} +(-4.05545 - 4.05545i) q^{88} -9.12563 q^{89} +(-2.23483 + 0.0743018i) q^{90} +(-12.2049 + 3.77297i) q^{91} +(6.46967 - 6.46967i) q^{92} +(-0.332104 - 0.332104i) q^{93} -5.44670 q^{94} +(2.82843 - 3.02297i) q^{95} +1.00000i q^{96} +(0.0119278 + 0.0119278i) q^{97} +(-6.87957 - 1.29289i) q^{98} +5.73528i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−1.52773	+	1.63280i	−0.683220	+	0.730213i
$5$	−1.52773	+	1.63280i	−0.683220	+	0.730213i
$6$		−	1.00000i		−	0.408248i
$7$	2.33991	+	1.23483i	0.884404	+	0.466723i
$7$	2.33991	+	1.23483i	0.884404	+	0.466723i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−0.0743018	−	2.23483i	−0.0234963	−	0.706716i
$11$	−5.73528			−1.72925			−0.864625	−	0.502417i	$-0.832444\pi$
$11$	−5.73528			−1.72925			−0.864625	+	0.502417i	$0.832444\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	−0.998661	−	0.0517287i	$-0.983527\pi$
$13$	−3.41421	+	3.41421i	−0.946932	+	0.946932i	0.0517287	+	0.998661i	$0.483527\pi$
$14$	−2.52773	+	0.781409i	−0.675563	+	0.208840i
$15$	−0.0743018	−	2.23483i	−0.0191846	−	0.577031i
$16$	−1.00000			−0.250000
$17$	−2.57474	−	2.57474i	−0.624467	−	0.624467i	0.322203	−	0.946671i	$-0.395577\pi$
$17$	−2.57474	−	2.57474i	−0.624467	−	0.624467i	−0.946671	+	0.322203i	$0.895577\pi$
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−1.85140			−0.424739			−0.212370	−	0.977189i	$-0.568118\pi$
$19$	−1.85140			−0.424739			−0.212370	+	0.977189i	$0.568118\pi$
$20$	1.63280	+	1.52773i	0.365106	+	0.341610i
$21$	−2.52773	+	0.781409i	−0.551595	+	0.170517i
$22$	4.05545	−	4.05545i	0.864625	−	0.864625i
$23$	6.46967	+	6.46967i	1.34902	+	1.34902i	0.886729	+	0.462290i	$0.152972\pi$
$23$	6.46967	+	6.46967i	1.34902	+	1.34902i	0.462290	+	0.886729i	$0.347028\pi$
$24$	−1.00000			−0.204124
$25$	−0.332104	−	4.98896i	−0.0664208	−	0.997792i
$26$		−	4.82843i		−	0.946932i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.23483	−	2.33991i	0.233362	−	0.442202i
$29$			3.47577i			0.645434i	0.946496	+	0.322717i	$0.104596\pi$
$29$			3.47577i			0.645434i	−0.946496	+	0.322717i	$0.895404\pi$
$30$	1.63280	+	1.52773i	0.298108	+	0.278923i
$31$			0.469666i			0.0843546i	0.999110	+	0.0421773i	$0.0134294\pi$
$31$			0.469666i			0.0843546i	−0.999110	+	0.0421773i	$0.986571\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	4.05545	−	4.05545i	0.705964	−	0.705964i
$34$	3.64124			0.624467
$35$	−5.59099	+	1.93413i	−0.945049	+	0.326928i
$36$	−1.00000			−0.166667
$37$	0.574745	−	0.574745i	0.0944875	−	0.0944875i	−0.658283	−	0.752771i	$-0.728717\pi$
$37$	0.574745	−	0.574745i	0.0944875	−	0.0944875i	0.752771	+	0.658283i	$0.228717\pi$
$38$	1.30913	−	1.30913i	0.212370	−	0.212370i
$39$		−	4.82843i		−	0.773167i
$40$	−2.23483	+	0.0743018i	−0.353358	+	0.0117481i
$41$		−	1.03858i		−	0.162200i	−0.996706	−	0.0810998i	$-0.974157\pi$
$41$		−	1.03858i		−	0.162200i	0.996706	−	0.0810998i	$-0.0258433\pi$
$42$	1.23483	−	2.33991i	0.190539	−	0.361056i
$43$	6.17246	+	6.17246i	0.941291	+	0.941291i	0.998370	−	0.0570785i	$-0.0181785\pi$
$43$	6.17246	+	6.17246i	0.941291	+	0.941291i	−0.0570785	+	0.998370i	$0.518179\pi$
$44$			5.73528i			0.864625i
$45$	1.63280	+	1.52773i	0.243404	+	0.227740i
$46$	−9.14949			−1.34902
$47$	3.85140	+	3.85140i	0.561784	+	0.561784i	0.929814	−	0.368030i	$-0.119968\pi$
$47$	3.85140	+	3.85140i	0.561784	+	0.561784i	−0.368030	+	0.929814i	$0.619968\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	3.95037	+	5.77880i	0.564339	+	0.825543i
$50$	3.76256	+	3.29289i	0.532106	+	0.465685i
$51$	3.64124			0.509875
$52$	3.41421	+	3.41421i	0.473466	+	0.473466i
$53$	−1.85140	−	1.85140i	−0.254309	−	0.254309i	0.568426	−	0.822735i	$-0.307553\pi$
$53$	−1.85140	−	1.85140i	−0.254309	−	0.254309i	−0.822735	+	0.568426i	$0.807553\pi$
$54$	−1.00000			−0.136083
$55$	8.76193	−	9.36459i	1.18146	−	1.26272i
$56$	0.781409	+	2.52773i	0.104420	+	0.337782i
$57$	1.30913	−	1.30913i	0.173399	−	0.173399i
$58$	−2.45774	−	2.45774i	−0.322717	−	0.322717i
$59$	13.3306			1.73549			0.867747	−	0.497007i	$-0.165568\pi$
$59$	13.3306			1.73549			0.867747	+	0.497007i	$0.165568\pi$
$60$	−2.23483	+	0.0743018i	−0.288516	+	0.00959232i
$61$		−	8.53122i		−	1.09231i	−0.837684	−	0.546155i	$-0.816091\pi$
$61$		−	8.53122i		−	1.09231i	0.837684	−	0.546155i	$-0.183909\pi$
$62$	−0.332104	−	0.332104i	−0.0421773	−	0.0421773i
$63$	1.23483	−	2.33991i	0.155574	−	0.294801i
$64$			1.00000i			0.125000i
$65$	−0.358761	−	10.7907i	−0.0444988	−	1.33843i
$66$			5.73528i			0.705964i
$67$	−4.46967	+	4.46967i	−0.546057	+	0.546057i	−0.925298	−	0.379241i	$-0.876185\pi$
$67$	−4.46967	+	4.46967i	−0.546057	+	0.546057i	0.379241	+	0.925298i	$0.376185\pi$
$68$	−2.57474	+	2.57474i	−0.312234	+	0.312234i
$69$	−9.14949			−1.10147
$70$	2.58579	−	5.32106i	0.309061	−	0.635989i
$71$	5.13387			0.609279			0.304639	−	0.952468i	$-0.401464\pi$
$71$	5.13387			0.609279			0.304639	+	0.952468i	$0.401464\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	−7.80177	+	7.80177i	−0.913128	+	0.913128i	−0.996517	−	0.0833889i	$-0.973426\pi$
$73$	−7.80177	+	7.80177i	−0.913128	+	0.913128i	0.0833889	+	0.996517i	$0.473426\pi$
$74$			0.812812i			0.0944875i
$75$	3.76256	+	3.29289i	0.434463	+	0.380231i
$76$			1.85140i			0.212370i
$77$	−13.4200	−	7.08211i	−1.52936	−	0.807081i
$78$	3.41421	+	3.41421i	0.386584	+	0.386584i
$79$			4.16422i			0.468511i	0.972175	+	0.234256i	$0.0752653\pi$
$79$			4.16422i			0.468511i	−0.972175	+	0.234256i	$0.924735\pi$
$80$	1.52773	−	1.63280i	0.170805	−	0.182553i
$81$	−1.00000			−0.111111
$82$	0.734390	+	0.734390i	0.0810998	+	0.0810998i
$83$	−1.77297	+	1.77297i	−0.194609	+	0.194609i	−0.797684	−	0.603075i	$-0.793942\pi$
$83$	−1.77297	+	1.77297i	−0.194609	+	0.194609i	0.603075	+	0.797684i	$0.293942\pi$
$84$	0.781409	+	2.52773i	0.0852587	+	0.275798i
$85$	8.13756	−	0.270551i	0.882643	−	0.0293453i
$86$	−8.72918			−0.941291
$87$	−2.45774	−	2.45774i	−0.263497	−	0.263497i
$88$	−4.05545	−	4.05545i	−0.432313	−	0.432313i
$89$	−9.12563			−0.967315			−0.483658	−	0.875257i	$-0.660692\pi$
$89$	−9.12563			−0.967315			−0.483658	+	0.875257i	$0.660692\pi$
$90$	−2.23483	+	0.0743018i	−0.235572	+	0.00783210i
$91$	−12.2049	+	3.77297i	−1.27943	+	0.395515i
$92$	6.46967	−	6.46967i	0.674509	−	0.674509i
$93$	−0.332104	−	0.332104i	−0.0344376	−	0.0344376i
$94$	−5.44670			−0.561784
$95$	2.82843	−	3.02297i	0.290191	−	0.310150i
$96$			1.00000i			0.102062i
$97$	0.0119278	+	0.0119278i	0.00121108	+	0.00121108i	0.707712	−	0.706501i	$-0.249727\pi$
$97$	0.0119278	+	0.0119278i	0.00121108	+	0.00121108i	−0.706501	+	0.707712i	$0.749727\pi$
$98$	−6.87957	−	1.29289i	−0.694941	−	0.130602i
$99$			5.73528i			0.576417i
$100$	−4.98896	+	0.332104i	−0.498896	+	0.0332104i
$101$		−	6.25088i		−	0.621986i	−0.950412	−	0.310993i	$-0.899338\pi$
$101$		−	6.25088i		−	0.621986i	0.950412	−	0.310993i	$-0.100662\pi$
$102$	−2.57474	+	2.57474i	−0.254938	+	0.254938i
$103$	−1.36459	+	1.36459i	−0.134457	+	0.134457i	−0.771132	−	0.636675i	$-0.780309\pi$
$103$	−1.36459	+	1.36459i	−0.134457	+	0.134457i	0.636675	+	0.771132i	$0.280309\pi$
$104$	−4.82843			−0.473466
$105$	2.58579	−	5.32106i	0.252347	−	0.519283i
$106$	2.61827			0.254309
$107$	11.2981	−	11.2981i	1.09223	−	1.09223i	0.0969374	−	0.995290i	$-0.469095\pi$
$107$	11.2981	−	11.2981i	1.09223	−	1.09223i	0.995290	−	0.0969374i	$-0.0309047\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$		−	1.91295i		−	0.183227i	−0.995795	−	0.0916137i	$-0.970798\pi$
$109$		−	1.91295i		−	0.183227i	0.995795	−	0.0916137i	$-0.0292025\pi$
$110$	0.426141	+	12.8174i	0.0406310	+	1.22209i
$111$			0.812812i			0.0771487i
$112$	−2.33991	−	1.23483i	−0.221101	−	0.116681i
$113$	−2.37563	−	2.37563i	−0.223480	−	0.223480i	0.586482	−	0.809962i	$-0.300512\pi$
$113$	−2.37563	−	2.37563i	−0.223480	−	0.223480i	−0.809962	+	0.586482i	$0.800512\pi$
$114$			1.85140i			0.173399i
$115$	−20.4476	+	0.679824i	−1.90675	+	0.0633939i
$116$	3.47577			0.322717
$117$	3.41421	+	3.41421i	0.315644	+	0.315644i
$118$	−9.42614	+	9.42614i	−0.867747	+	0.867747i
$119$	−2.84530	−	9.20406i	−0.260828	−	0.843734i
$120$	1.52773	−	1.63280i	0.139462	−	0.149054i
$121$	21.8934			1.99031
$122$	6.03248	+	6.03248i	0.546155	+	0.546155i
$123$	0.734390	+	0.734390i	0.0662177	+	0.0662177i
$124$	0.469666			0.0421773
$125$	8.65336	+	7.07950i	0.773980	+	0.633210i
$126$	0.781409	+	2.52773i	0.0696134	+	0.225188i
$127$	−13.3802	+	13.3802i	−1.18730	+	1.18730i	−0.209490	+	0.977811i	$0.567180\pi$
$127$	−13.3802	+	13.3802i	−1.18730	+	1.18730i	−0.977811	+	0.209490i	$0.932820\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−8.72918			−0.768561
$130$	7.88388	+	7.37652i	0.691462	+	0.646963i
$131$			11.5646i			1.01040i	0.863001	+	0.505201i	$0.168582\pi$
$131$			11.5646i			1.01040i	−0.863001	+	0.505201i	$0.831418\pi$
$132$	−4.05545	−	4.05545i	−0.352982	−	0.352982i
$133$	−4.33210	−	2.28617i	−0.375641	−	0.198236i
$134$		−	6.32106i		−	0.546057i
$135$	−2.23483	+	0.0743018i	−0.192344	+	0.00639488i
$136$		−	3.64124i		−	0.312234i
$137$	−8.03248	+	8.03248i	−0.686261	+	0.686261i	−0.961404	−	0.275142i	$-0.911275\pi$
$137$	−8.03248	+	8.03248i	−0.686261	+	0.686261i	0.275142	+	0.961404i	$0.411275\pi$
$138$	6.46967	−	6.46967i	0.550735	−	0.550735i
$139$	7.02297			0.595680			0.297840	−	0.954616i	$-0.403734\pi$
$139$	7.02297			0.595680			0.297840	+	0.954616i	$0.403734\pi$
$140$	1.93413	+	5.59099i	0.163464	+	0.472525i
$141$	−5.44670			−0.458695
$142$	−3.63020	+	3.63020i	−0.304639	+	0.304639i
$143$	19.5815	−	19.5815i	1.63748	−	1.63748i
$144$			1.00000i			0.0833333i
$145$	−5.67525	−	5.31002i	−0.471304	−	0.440973i
$146$		−	11.0334i		−	0.913128i
$147$	−6.87957	−	1.29289i	−0.567417	−	0.106636i
$148$	−0.574745	−	0.574745i	−0.0472437	−	0.0472437i
$149$		−	1.88388i		−	0.154333i	−0.997018	−	0.0771667i	$-0.975413\pi$
$149$		−	1.88388i		−	0.154333i	0.997018	−	0.0771667i	$-0.0245874\pi$
$150$	−4.98896	+	0.332104i	−0.407347	+	0.0271162i
$151$	3.28248			0.267124			0.133562	−	0.991040i	$-0.457358\pi$
$151$	3.28248			0.267124			0.133562	+	0.991040i	$0.457358\pi$
$152$	−1.30913	−	1.30913i	−0.106185	−	0.106185i
$153$	−2.57474	+	2.57474i	−0.208156	+	0.208156i
$154$	14.4972	−	4.48159i	1.16822	−	0.361137i
$155$	−0.766874	−	0.717522i	−0.0615968	−	0.0576327i
$156$	−4.82843			−0.386584
$157$	7.57106	+	7.57106i	0.604236	+	0.604236i	0.941434	−	0.337198i	$-0.109479\pi$
$157$	7.57106	+	7.57106i	0.604236	+	0.604236i	−0.337198	+	0.941434i	$0.609479\pi$
$158$	−2.94455	−	2.94455i	−0.234256	−	0.234256i
$159$	2.61827			0.207642
$160$	0.0743018	+	2.23483i	0.00587407	+	0.176679i
$161$	7.14949	+	23.1274i	0.563459	+	1.82269i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−10.3367	−	10.3367i	−0.809631	−	0.809631i	0.174947	−	0.984578i	$-0.444025\pi$
$163$	−10.3367	−	10.3367i	−0.809631	−	0.809631i	−0.984578	+	0.174947i	$0.944025\pi$
$164$	−1.03858			−0.0810998
$165$	0.426141	+	12.8174i	0.0331751	+	0.997832i
$166$		−	2.50736i		−	0.194609i
$167$	−9.85140	−	9.85140i	−0.762324	−	0.762324i	0.214418	−	0.976742i	$-0.431215\pi$
$167$	−9.85140	−	9.85140i	−0.762324	−	0.762324i	−0.976742	+	0.214418i	$0.931215\pi$
$168$	−2.33991	−	1.23483i	−0.180528	−	0.0952694i
$169$		−	10.3137i		−	0.793362i
$170$	−5.56282	+	5.94543i	−0.426649	+	0.455994i
$171$			1.85140i			0.141580i
$172$	6.17246	−	6.17246i	0.470646	−	0.470646i
$173$	8.83947	−	8.83947i	0.672052	−	0.672052i	−0.286137	−	0.958189i	$-0.592371\pi$
$173$	8.83947	−	8.83947i	0.672052	−	0.672052i	0.958189	+	0.286137i	$0.0923711\pi$
$174$	3.47577			0.263497
$175$	5.38344	−	12.0838i	0.406950	−	0.913451i
$176$	5.73528			0.432313
$177$	−9.42614	+	9.42614i	−0.708512	+	0.708512i
$178$	6.45280	−	6.45280i	0.483658	−	0.483658i
$179$		−	7.68934i		−	0.574728i	−0.957821	−	0.287364i	$-0.907221\pi$
$179$		−	7.68934i		−	0.574728i	0.957821	−	0.287364i	$-0.0927789\pi$
$180$	1.52773	−	1.63280i	0.113870	−	0.121702i
$181$		−	10.7071i		−	0.795852i	−0.917418	−	0.397926i	$-0.869730\pi$
$181$		−	10.7071i		−	0.795852i	0.917418	−	0.397926i	$-0.130270\pi$
$182$	5.96230	−	11.2981i	0.441955	−	0.837470i
$183$	6.03248	+	6.03248i	0.445934	+	0.445934i
$184$			9.14949i			0.674509i
$185$	0.0603934	+	1.81650i	0.00444021	+	0.133552i
$186$	0.469666			0.0344376
$187$	14.7669	+	14.7669i	1.07986	+	1.07986i
$188$	3.85140	−	3.85140i	0.280892	−	0.280892i
$189$	0.781409	+	2.52773i	0.0568391	+	0.183865i
$190$	0.137562	+	4.13756i	0.00997980	+	0.300170i
$191$	−4.91206			−0.355424			−0.177712	−	0.984082i	$-0.556870\pi$
$191$	−4.91206			−0.355424			−0.177712	+	0.984082i	$0.556870\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	16.4706	+	16.4706i	1.18558	+	1.18558i	0.978278	+	0.207299i	$0.0664672\pi$
$193$	16.4706	+	16.4706i	1.18558	+	1.18558i	0.207299	+	0.978278i	$0.433533\pi$
$194$	−0.0168684			−0.00121108
$195$	7.88388	+	7.37652i	0.564576	+	0.528243i
$196$	5.77880	−	3.95037i	0.412772	−	0.282170i
$197$	−5.13387	+	5.13387i	−0.365773	+	0.365773i	−0.865933	−	0.500160i	$-0.833275\pi$
$197$	−5.13387	+	5.13387i	−0.365773	+	0.365773i	0.500160	+	0.865933i	$0.333275\pi$
$198$	−4.05545	−	4.05545i	−0.288208	−	0.288208i
$199$	8.63388			0.612040			0.306020	−	0.952025i	$-0.401003\pi$
$199$	8.63388			0.612040			0.306020	+	0.952025i	$0.401003\pi$
$200$	3.29289	−	3.76256i	0.232843	−	0.266053i
$201$		−	6.32106i		−	0.445853i
$202$	4.42004	+	4.42004i	0.310993	+	0.310993i
$203$	−4.29199	+	8.13299i	−0.301239	+	0.570824i
$204$		−	3.64124i		−	0.254938i
$205$	1.69581	+	1.58667i	0.118440	+	0.110818i
$206$		−	1.92982i		−	0.134457i
$207$	6.46967	−	6.46967i	0.449673	−	0.449673i
$208$	3.41421	−	3.41421i	0.236733	−	0.236733i
$209$	10.6183			0.734481
$210$	1.93413	+	5.59099i	0.133468	+	0.385815i
$211$	7.73402			0.532432			0.266216	−	0.963913i	$-0.414227\pi$
$211$	7.73402			0.532432			0.266216	+	0.963913i	$0.414227\pi$
$212$	−1.85140	+	1.85140i	−0.127154	+	0.127154i
$213$	−3.63020	+	3.63020i	−0.248737	+	0.248737i
$214$			15.9779i			1.09223i
$215$	−19.5083	+	0.648593i	−1.33045	+	0.0442337i
$216$			1.00000i			0.0680414i
$217$	−0.579960	+	1.09898i	−0.0393702	+	0.0746035i
$218$	1.35266	+	1.35266i	0.0916137	+	0.0916137i
$219$		−	11.0334i		−	0.745566i
$220$	−9.36459	−	8.76193i	−0.631360	−	0.590729i
$221$	17.5815			1.18266
$222$	−0.574745	−	0.574745i	−0.0385744	−	0.0385744i
$223$	−8.63883	+	8.63883i	−0.578499	+	0.578499i	−0.934489	−	0.355991i	$-0.884143\pi$
$223$	−8.63883	+	8.63883i	−0.578499	+	0.578499i	0.355991	+	0.934489i	$0.384143\pi$
$224$	2.52773	−	0.781409i	0.168891	−	0.0522101i
$225$	−4.98896	+	0.332104i	−0.332597	+	0.0221403i
$226$	3.35965			0.223480
$227$	4.08705	+	4.08705i	0.271267	+	0.271267i	0.829610	−	0.558343i	$-0.188563\pi$
$227$	4.08705	+	4.08705i	0.271267	+	0.271267i	−0.558343	+	0.829610i	$0.688563\pi$
$228$	−1.30913	−	1.30913i	−0.0866996	−	0.0866996i
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$	13.9779	−	14.9393i	0.921677	−	0.985070i
$231$	14.4972	−	4.48159i	0.953846	−	0.294867i
$232$	−2.45774	+	2.45774i	−0.161358	+	0.161358i
$233$	−5.22791	−	5.22791i	−0.342492	−	0.342492i	0.514812	−	0.857303i	$-0.327862\pi$
$233$	−5.22791	−	5.22791i	−0.342492	−	0.342492i	−0.857303	+	0.514812i	$0.827862\pi$
$234$	−4.82843			−0.315644
$235$	−12.1725	+	0.404699i	−0.794044	+	0.0263997i
$236$		−	13.3306i		−	0.867747i
$237$	−2.94455	−	2.94455i	−0.191269	−	0.191269i
$238$	8.52018	+	4.49632i	0.552281	+	0.291453i
$239$			7.38514i			0.477705i	0.971056	+	0.238853i	$0.0767713\pi$
$239$			7.38514i			0.477705i	−0.971056	+	0.238853i	$0.923229\pi$
$240$	0.0743018	+	2.23483i	0.00479616	+	0.144258i
$241$			4.44417i			0.286274i	0.989703	+	0.143137i	$0.0457190\pi$
$241$			4.44417i			0.286274i	−0.989703	+	0.143137i	$0.954281\pi$
$242$	−15.4810	+	15.4810i	−0.995154	+	0.995154i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−8.53122			−0.546155
$245$	−15.4707	−	2.37824i	−0.988390	−	0.151940i
$246$	−1.03858			−0.0662177
$247$	6.32106	−	6.32106i	0.402200	−	0.402200i
$248$	−0.332104	+	0.332104i	−0.0210886	+	0.0210886i
$249$		−	2.50736i		−	0.158898i
$250$	−11.1248	+	1.11289i	−0.703595	+	0.0703851i
$251$			14.1400i			0.892507i	0.894907	+	0.446254i	$0.147242\pi$
$251$			14.1400i			0.892507i	−0.894907	+	0.446254i	$0.852758\pi$
$252$	−2.33991	−	1.23483i	−0.147401	−	0.0777872i
$253$	−37.1053	−	37.1053i	−2.33279	−	2.33279i
$254$		−	18.9225i		−	1.18730i
$255$	−5.56282	+	5.94543i	−0.348357	+	0.372317i
$256$	1.00000			0.0625000
$257$	6.67400	+	6.67400i	0.416312	+	0.416312i	0.883931	−	0.467618i	$-0.154888\pi$
$257$	6.67400	+	6.67400i	0.416312	+	0.416312i	−0.467618	+	0.883931i	$0.654888\pi$
$258$	6.17246	−	6.17246i	0.384281	−	0.384281i
$259$	2.05457	−	0.635138i	0.127665	−	0.0394656i
$260$	−10.7907	+	0.358761i	−0.669213	+	0.0222494i
$261$	3.47577			0.215145
$262$	−8.17740	−	8.17740i	−0.505201	−	0.505201i
$263$	2.21016	+	2.21016i	0.136284	+	0.136284i	0.771958	−	0.635674i	$-0.219278\pi$
$263$	2.21016	+	2.21016i	0.136284	+	0.136284i	−0.635674	+	0.771958i	$0.719278\pi$
$264$	5.73528			0.352982
$265$	5.85140	−	0.194542i	0.359448	−	0.0119506i
$266$	4.67982	−	1.44670i	0.286938	−	0.0887027i
$267$	6.45280	−	6.45280i	0.394905	−	0.394905i
$268$	4.46967	+	4.46967i	0.273028	+	0.273028i
$269$	16.2362			0.989937			0.494968	−	0.868911i	$-0.335180\pi$
$269$	16.2362			0.989937			0.494968	+	0.868911i	$0.335180\pi$
$270$	1.52773	−	1.63280i	0.0929745	−	0.0993693i
$271$		−	30.1841i		−	1.83355i	−0.399399	−	0.916777i	$-0.630781\pi$
$271$		−	30.1841i		−	1.83355i	0.399399	−	0.916777i	$-0.369219\pi$
$272$	2.57474	+	2.57474i	0.156117	+	0.156117i
$273$	5.96230	−	11.2981i	0.360855	−	0.683792i
$274$		−	11.3596i		−	0.686261i
$275$	1.90471	+	28.6131i	0.114858	+	1.72543i
$276$			9.14949i			0.550735i
$277$	12.3646	−	12.3646i	0.742916	−	0.742916i	−0.230222	−	0.973138i	$-0.573945\pi$
$277$	12.3646	−	12.3646i	0.742916	−	0.742916i	0.973138	+	0.230222i	$0.0739453\pi$
$278$	−4.96599	+	4.96599i	−0.297840	+	0.297840i
$279$	0.469666			0.0281182
$280$	−5.32106	−	2.58579i	−0.317994	−	0.154530i
$281$	−22.1127			−1.31913			−0.659566	−	0.751647i	$-0.729260\pi$
$281$	−22.1127			−1.31913			−0.659566	+	0.751647i	$0.729260\pi$
$282$	3.85140	−	3.85140i	0.229347	−	0.229347i
$283$	−14.9172	+	14.9172i	−0.886738	+	0.886738i	−0.994208	−	0.107470i	$-0.965725\pi$
$283$	−14.9172	+	14.9172i	−0.886738	+	0.886738i	0.107470	+	0.994208i	$0.465725\pi$
$284$		−	5.13387i		−	0.304639i
$285$	0.137562	+	4.13756i	0.00814847	+	0.245088i
$286$			27.6924i			1.63748i
$287$	1.28248	−	2.43020i	0.0757023	−	0.143450i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$		−	3.74138i		−	0.220081i
$290$	7.76776	−	0.258256i	0.456139	−	0.0151653i
$291$	−0.0168684			−0.000988844
$292$	7.80177	+	7.80177i	0.456564	+	0.456564i
$293$	−11.5977	+	11.5977i	−0.677546	+	0.677546i	−0.959444	−	0.281899i	$-0.909036\pi$
$293$	−11.5977	+	11.5977i	−0.677546	+	0.677546i	0.281899	+	0.959444i	$0.409036\pi$
$294$	5.77880	−	3.95037i	0.337027	−	0.230390i
$295$	−20.3655	+	21.7662i	−1.18572	+	1.26728i
$296$	0.812812			0.0472437
$297$	−4.05545	−	4.05545i	−0.235321	−	0.235321i
$298$	1.33210	+	1.33210i	0.0771667	+	0.0771667i
$299$	−44.1776			−2.55486
$300$	3.29289	−	3.76256i	0.190115	−	0.217231i
$301$	6.82105	+	22.0650i	0.393159	+	1.27180i
$302$	−2.32106	+	2.32106i	−0.133562	+	0.133562i
$303$	4.42004	+	4.42004i	0.253925	+	0.253925i
$304$	1.85140			0.106185
$305$	13.9298	+	13.0334i	0.797619	+	0.746289i
$306$		−	3.64124i		−	0.208156i
$307$	−12.4164	−	12.4164i	−0.708639	−	0.708639i	0.257610	−	0.966249i	$-0.417065\pi$
$307$	−12.4164	−	12.4164i	−0.708639	−	0.708639i	−0.966249	+	0.257610i	$0.917065\pi$
$308$	−7.08211	+	13.4200i	−0.403541	+	0.764678i
$309$		−	1.92982i		−	0.109784i
$310$	1.04963	−	0.0348971i	0.0596147	−	0.00198202i
$311$			9.81370i			0.556484i	0.960511	+	0.278242i	$0.0897517\pi$
$311$			9.81370i			0.556484i	−0.960511	+	0.278242i	$0.910248\pi$
$312$	3.41421	−	3.41421i	0.193292	−	0.193292i
$313$	13.4586	−	13.4586i	0.760726	−	0.760726i	−0.215727	−	0.976454i	$-0.569212\pi$
$313$	13.4586	−	13.4586i	0.760726	−	0.760726i	0.976454	+	0.215727i	$0.0692122\pi$
$314$	−10.7071			−0.604236
$315$	1.93413	+	5.59099i	0.108976	+	0.315016i
$316$	4.16422			0.234256
$317$	−8.01040	+	8.01040i	−0.449909	+	0.449909i	−0.895324	−	0.445415i	$-0.853056\pi$
$317$	−8.01040	+	8.01040i	−0.449909	+	0.449909i	0.445415	+	0.895324i	$0.353056\pi$
$318$	−1.85140	+	1.85140i	−0.103821	+	0.103821i
$319$		−	19.9345i		−	1.11612i
$320$	−1.63280	−	1.52773i	−0.0912766	−	0.0854025i
$321$			15.9779i			0.891800i
$322$	−21.4090	−	11.2981i	−1.19308	−	0.629618i
$323$	4.76687	+	4.76687i	0.265236	+	0.265236i
$324$			1.00000i			0.0555556i
$325$	18.1672	+	15.8995i	1.00774	+	0.881945i
$326$	14.6183			0.809631
$327$	1.35266	+	1.35266i	0.0748023	+	0.0748023i
$328$	0.734390	−	0.734390i	0.0405499	−	0.0405499i
$329$	4.25610	+	13.7678i	0.234646	+	0.759041i
$330$	−9.36459	−	8.76193i	−0.515504	−	0.482329i
$331$	−13.6906			−0.752503			−0.376251	−	0.926518i	$-0.622787\pi$
$331$	−13.6906			−0.752503			−0.376251	+	0.926518i	$0.622787\pi$
$332$	1.77297	+	1.77297i	0.0973046	+	0.0973046i
$333$	−0.574745	−	0.574745i	−0.0314958	−	0.0314958i
$334$	13.9320			0.762324
$335$	−0.469666	−	14.1265i	−0.0256606	−	0.771814i
$336$	2.52773	−	0.781409i	0.137899	−	0.0426293i
$337$	−4.47055	+	4.47055i	−0.243527	+	0.243527i	−0.818307	−	0.574781i	$-0.805087\pi$
$337$	−4.47055	+	4.47055i	−0.243527	+	0.243527i	0.574781	+	0.818307i	$0.305087\pi$
$338$	7.29289	+	7.29289i	0.396681	+	0.396681i
$339$	3.35965			0.182471
$340$	−0.270551	−	8.13756i	−0.0146727	−	0.441321i
$341$		−	2.69367i		−	0.145870i
$342$	−1.30913	−	1.30913i	−0.0707899	−	0.0707899i
$343$	2.10767	+	18.3999i	0.113804	+	0.993503i
$344$			8.72918i			0.470646i
$345$	13.9779	−	14.9393i	0.752546	−	0.804307i
$346$			12.5009i			0.672052i
$347$	12.9103	−	12.9103i	0.693059	−	0.693059i	−0.269845	−	0.962904i	$-0.586972\pi$
$347$	12.9103	−	12.9103i	0.693059	−	0.693059i	0.962904	+	0.269845i	$0.0869724\pi$
$348$	−2.45774	+	2.45774i	−0.131749	+	0.131749i
$349$	13.5937			0.727652			0.363826	−	0.931467i	$-0.381470\pi$
$349$	13.5937			0.727652			0.363826	+	0.931467i	$0.381470\pi$
$350$	4.73788	+	12.3512i	0.253251	+	0.660200i
$351$	−4.82843			−0.257722
$352$	−4.05545	+	4.05545i	−0.216156	+	0.216156i
$353$	17.4032	−	17.4032i	0.926277	−	0.926277i	−0.0711857	−	0.997463i	$-0.522678\pi$
$353$	17.4032	−	17.4032i	0.926277	−	0.926277i	0.997463	+	0.0711857i	$0.0226783\pi$
$354$		−	13.3306i		−	0.708512i
$355$	−7.84316	+	8.38262i	−0.416271	+	0.444903i
$356$			9.12563i			0.483658i
$357$	8.52018	+	4.49632i	0.450936	+	0.237971i
$358$	5.43718	+	5.43718i	0.287364	+	0.287364i
$359$		−	7.02297i		−	0.370658i	−0.982677	−	0.185329i	$-0.940665\pi$
$359$		−	7.02297i		−	0.370658i	0.982677	−	0.185329i	$-0.0593351\pi$
$360$	0.0743018	+	2.23483i	0.00391605	+	0.117786i
$361$	−15.5723			−0.819596
$362$	7.57106	+	7.57106i	0.397926	+	0.397926i
$363$	−15.4810	+	15.4810i	−0.812540	+	0.812540i
$364$	3.77297	+	12.2049i	0.197758	+	0.639713i
$365$	−0.819799	−	24.6577i	−0.0429103	−	1.29065i
$366$	−8.53122			−0.445934
$367$	−23.0609	−	23.0609i	−1.20377	−	1.20377i	−0.973011	−	0.230759i	$-0.925879\pi$
$367$	−23.0609	−	23.0609i	−1.20377	−	1.20377i	−0.230759	−	0.973011i	$-0.574121\pi$
$368$	−6.46967	−	6.46967i	−0.337255	−	0.337255i
$369$	−1.03858			−0.0540665
$370$	−1.32716	−	1.24175i	−0.0689959	−	0.0645557i
$371$	−2.04594	−	6.61827i	−0.106220	−	0.343603i
$372$	−0.332104	+	0.332104i	−0.0172188	+	0.0172188i
$373$	−8.04352	−	8.04352i	−0.416478	−	0.416478i	0.467510	−	0.883988i	$-0.345151\pi$
$373$	−8.04352	−	8.04352i	−0.416478	−	0.416478i	−0.883988	+	0.467510i	$0.845151\pi$
$374$	−20.8835			−1.07986
$375$	−11.1248	+	1.11289i	−0.574483	+	0.0574692i
$376$			5.44670i			0.280892i
$377$	−11.8670	−	11.8670i	−0.611182	−	0.611182i
$378$	−2.33991	−	1.23483i	−0.120352	−	0.0635130i
$379$		−	11.4368i		−	0.587470i	−0.955887	−	0.293735i	$-0.905102\pi$
$379$		−	11.4368i		−	0.587470i	0.955887	−	0.293735i	$-0.0948983\pi$
$380$	−3.02297	−	2.82843i	−0.155075	−	0.145095i
$381$		−	18.9225i		−	0.969427i
$382$	3.47335	−	3.47335i	0.177712	−	0.177712i
$383$	5.71841	−	5.71841i	0.292197	−	0.292197i	−0.545751	−	0.837948i	$-0.683755\pi$
$383$	5.71841	−	5.71841i	0.292197	−	0.292197i	0.837948	+	0.545751i	$0.183755\pi$
$384$	1.00000			0.0510310
$385$	32.0659	−	11.0928i	1.63423	−	0.565341i
$386$	−23.2929			−1.18558
$387$	6.17246	−	6.17246i	0.313764	−	0.313764i
$388$	0.0119278	−	0.0119278i	0.000605541	−	0.000605541i
$389$			32.4151i			1.64351i	0.569840	+	0.821755i	$0.307005\pi$
$389$			32.4151i			1.64351i	−0.569840	+	0.821755i	$0.692995\pi$
$390$	−10.7907	+	0.358761i	−0.546410	+	0.0181666i
$391$		−	33.3155i		−	1.68484i
$392$	−1.29289	+	6.87957i	−0.0653010	+	0.347471i
$393$	−8.17740	−	8.17740i	−0.412495	−	0.412495i
$394$		−	7.26040i		−	0.365773i
$395$	−6.79936	−	6.36179i	−0.342113	−	0.320096i
$396$	5.73528			0.288208
$397$	25.6023	+	25.6023i	1.28494	+	1.28494i	0.937820	+	0.347122i	$0.112841\pi$
$397$	25.6023	+	25.6023i	1.28494	+	1.28494i	0.347122	+	0.937820i	$0.387159\pi$
$398$	−6.10508	+	6.10508i	−0.306020	+	0.306020i
$399$	4.67982	−	1.44670i	0.234284	−	0.0724254i
$400$	0.332104	+	4.98896i	0.0166052	+	0.249448i
$401$	−12.8597			−0.642181			−0.321090	−	0.947049i	$-0.604049\pi$
$401$	−12.8597			−0.642181			−0.321090	+	0.947049i	$0.604049\pi$
$402$	4.46967	+	4.46967i	0.222927	+	0.222927i
$403$	−1.60354	−	1.60354i	−0.0798781	−	0.0798781i
$404$	−6.25088			−0.310993
$405$	1.52773	−	1.63280i	0.0759133	−	0.0811347i
$406$	−2.71599	−	8.78579i	−0.134793	−	0.436031i
$407$	−3.29632	+	3.29632i	−0.163393	+	0.163393i
$408$	2.57474	+	2.57474i	0.127469	+	0.127469i
$409$	−7.67894			−0.379699			−0.189850	−	0.981813i	$-0.560800\pi$
$409$	−7.67894			−0.379699			−0.189850	+	0.981813i	$0.560800\pi$
$410$	−2.32106	+	0.0771687i	−0.114629	+	0.00381109i
$411$		−	11.3596i		−	0.560330i
$412$	1.36459	+	1.36459i	0.0672284	+	0.0672284i
$413$	31.1924	+	16.4610i	1.53488	+	0.809995i
$414$			9.14949i			0.449673i
$415$	−0.186302	−	5.60354i	−0.00914519	−	0.275067i
$416$			4.82843i			0.236733i
$417$	−4.96599	+	4.96599i	−0.243186	+	0.243186i
$418$	−7.50825	+	7.50825i	−0.367241	+	0.367241i
$419$	15.2534			0.745178			0.372589	−	0.927997i	$-0.378470\pi$
$419$	15.2534			0.745178			0.372589	+	0.927997i	$0.378470\pi$
$420$	−5.32106	−	2.58579i	−0.259641	−	0.126173i
$421$	16.5264			0.805447			0.402724	−	0.915322i	$-0.368064\pi$
$421$	16.5264			0.805447			0.402724	+	0.915322i	$0.368064\pi$
$422$	−5.46878	+	5.46878i	−0.266216	+	0.266216i
$423$	3.85140	−	3.85140i	0.187261	−	0.187261i
$424$		−	2.61827i		−	0.127154i
$425$	−11.9902	+	13.7004i	−0.581611	+	0.664566i
$426$		−	5.13387i		−	0.248737i
$427$	10.5346	−	19.9623i	0.509807	−	0.966043i
$428$	−11.2981	−	11.2981i	−0.546114	−	0.546114i
$429$			27.6924i			1.33700i
$430$	13.3358	−	14.2530i	0.643109	−	0.687343i
$431$	7.22830			0.348175			0.174087	−	0.984730i	$-0.444302\pi$
$431$	7.22830			0.348175			0.174087	+	0.984730i	$0.444302\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	13.0916	−	13.0916i	0.629143	−	0.629143i	−0.318709	−	0.947853i	$-0.603249\pi$
$433$	13.0916	−	13.0916i	0.629143	−	0.629143i	0.947853	+	0.318709i	$0.103249\pi$
$434$	−0.367001	−	1.18719i	−0.0176166	−	0.0569868i
$435$	7.76776	−	0.258256i	0.372436	−	0.0123824i
$436$	−1.91295			−0.0916137
$437$	−11.9779	−	11.9779i	−0.572981	−	0.572981i
$438$	7.80177	+	7.80177i	0.372783	+	0.372783i
$439$	24.9034			1.18857			0.594287	−	0.804253i	$-0.297434\pi$
$439$	24.9034			1.18857			0.594287	+	0.804253i	$0.297434\pi$
$440$	12.8174	−	0.426141i	0.611045	−	0.0203155i
$441$	5.77880	−	3.95037i	0.275181	−	0.188113i
$442$	−12.4320	+	12.4320i	−0.591328	+	0.591328i
$443$	12.2821	+	12.2821i	0.583541	+	0.583541i	0.935874	−	0.352334i	$-0.114612\pi$
$443$	12.2821	+	12.2821i	0.583541	+	0.583541i	−0.352334	+	0.935874i	$0.614612\pi$
$444$	0.812812			0.0385744
$445$	13.9415	−	14.9004i	0.660889	−	0.706346i
$446$		−	12.2171i		−	0.578499i
$447$	1.33210	+	1.33210i	0.0630064	+	0.0630064i
$448$	−1.23483	+	2.33991i	−0.0583404	+	0.110550i
$449$			4.53122i			0.213841i	0.994268	+	0.106921i	$0.0340991\pi$
$449$			4.53122i			0.213841i	−0.994268	+	0.106921i	$0.965901\pi$
$450$	3.29289	−	3.76256i	0.155228	−	0.177369i
$451$			5.95657i			0.280484i
$452$	−2.37563	+	2.37563i	−0.111740	+	0.111740i
$453$	−2.32106	+	2.32106i	−0.109053	+	0.109053i
$454$	−5.77996			−0.271267
$455$	12.4853	−	25.6924i	0.585319	−	1.20448i
$456$	1.85140			0.0866996
$457$	−5.34315	+	5.34315i	−0.249942	+	0.249942i	−0.820947	−	0.571005i	$-0.806554\pi$
$457$	−5.34315	+	5.34315i	−0.249942	+	0.249942i	0.571005	+	0.820947i	$0.306554\pi$
$458$	6.58579	−	6.58579i	0.307734	−	0.307734i
$459$		−	3.64124i		−	0.169958i
$460$	0.679824	+	20.4476i	0.0316969	+	0.953373i
$461$			12.9004i			0.600831i	0.953808	+	0.300415i	$0.0971253\pi$
$461$			12.9004i			0.600831i	−0.953808	+	0.300415i	$0.902875\pi$
$462$	−7.08211	+	13.4200i	−0.329490	+	0.624357i
$463$	11.9452	+	11.9452i	0.555139	+	0.555139i	0.927919	−	0.372781i	$-0.121596\pi$
$463$	11.9452	+	11.9452i	0.555139	+	0.555139i	−0.372781	+	0.927919i	$0.621596\pi$
$464$		−	3.47577i		−	0.161358i
$465$	1.04963	−	0.0348971i	0.0486752	−	0.00161831i
$466$	7.39338			0.342492
$467$	25.1204	+	25.1204i	1.16243	+	1.16243i	0.983941	+	0.178493i	$0.0571223\pi$
$467$	25.1204	+	25.1204i	1.16243	+	1.16243i	0.178493	+	0.983941i	$0.442878\pi$
$468$	3.41421	−	3.41421i	0.157822	−	0.157822i
$469$	−15.9779	+	4.93933i	−0.737792	+	0.228077i
$470$	8.32106	−	8.89339i	0.383822	−	0.410222i
$471$	−10.7071			−0.493357
$472$	9.42614	+	9.42614i	0.433873	+	0.433873i
$473$	−35.4008	−	35.4008i	−1.62773	−	1.62773i
$474$	4.16422			0.191269
$475$	0.614857	+	9.23654i	0.0282116	+	0.423802i
$476$	−9.20406	+	2.84530i	−0.421867	+	0.130414i
$477$	−1.85140	+	1.85140i	−0.0847696	+	0.0847696i
$478$	−5.22208	−	5.22208i	−0.238853	−	0.238853i
$479$	−1.17157			−0.0535305			−0.0267653	−	0.999642i	$-0.508521\pi$
$479$	−1.17157			−0.0535305			−0.0267653	+	0.999642i	$0.508521\pi$
$480$	−1.63280	−	1.52773i	−0.0745270	−	0.0697308i
$481$			3.92460i			0.178947i
$482$	−3.14250	−	3.14250i	−0.143137	−	0.143137i
$483$	−21.4090	−	11.2981i	−0.974143	−	0.514081i
$484$		−	21.8934i		−	0.995154i
$485$	−0.0376981	+	0.00125335i	−0.00171178	+	5.69118e-5i
$486$			1.00000i			0.0453609i
$487$	5.67741	−	5.67741i	0.257268	−	0.257268i	−0.566674	−	0.823942i	$-0.691770\pi$
$487$	5.67741	−	5.67741i	0.257268	−	0.257268i	0.823942	+	0.566674i	$0.191770\pi$
$488$	6.03248	−	6.03248i	0.273078	−	0.273078i
$489$	14.6183			0.661061
$490$	12.6211	−	9.25780i	0.570165	−	0.418225i
$491$	−21.3462			−0.963340			−0.481670	−	0.876353i	$-0.659970\pi$
$491$	−21.3462			−0.963340			−0.481670	+	0.876353i	$0.659970\pi$
$492$	0.734390	−	0.734390i	0.0331089	−	0.0331089i
$493$	8.94921	−	8.94921i	0.403052	−	0.403052i
$494$			8.93933i			0.402200i
$495$	−9.36459	−	8.76193i	−0.420907	−	0.393820i
$496$		−	0.469666i		−	0.0210886i
$497$	12.0128	+	6.33948i	0.538848	+	0.284364i
$498$	1.77297	+	1.77297i	0.0794489	+	0.0794489i
$499$			33.4411i			1.49703i	0.663118	+	0.748515i	$0.269233\pi$
$499$			33.4411i			1.49703i	−0.663118	+	0.748515i	$0.730767\pi$
$500$	7.07950	−	8.65336i	0.316605	−	0.386990i
$501$	13.9320			0.622435
$502$	−9.99847	−	9.99847i	−0.446254	−	0.446254i
$503$	9.00089	−	9.00089i	0.401330	−	0.401330i	−0.477372	−	0.878701i	$-0.658410\pi$
$503$	9.00089	−	9.00089i	0.401330	−	0.401330i	0.878701	+	0.477372i	$0.158410\pi$
$504$	2.52773	−	0.781409i	0.112594	−	0.0348067i
$505$	10.2065	+	9.54964i	0.454182	+	0.424953i
$506$	52.4749			2.33279
$507$	7.29289	+	7.29289i	0.323889	+	0.323889i
$508$	13.3802	+	13.3802i	0.593651	+	0.593651i
$509$	24.7938			1.09896			0.549482	−	0.835506i	$-0.314825\pi$
$509$	24.7938			1.09896			0.549482	+	0.835506i	$0.314825\pi$
$510$	−0.270551	−	8.13756i	−0.0119802	−	0.360337i
$511$	−27.8893	+	8.62157i	−1.23375	+	0.381396i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.30913	−	1.30913i	−0.0577997	−	0.0577997i
$514$	−9.43846			−0.416312
$515$	−0.143389	−	4.31282i	−0.00631847	−	0.190046i
$516$			8.72918i			0.384281i
$517$	−22.0888	−	22.0888i	−0.971465	−	0.971465i
$518$	−1.00369	+	1.90191i	−0.0440995	+	0.0835651i
$519$			12.5009i			0.548728i
$520$	7.37652	−	7.88388i	0.323482	−	0.345731i
$521$		−	36.4871i		−	1.59853i	−0.600981	−	0.799263i	$-0.705223\pi$
$521$		−	36.4871i		−	1.59853i	0.600981	−	0.799263i	$-0.294777\pi$
$522$	−2.45774	+	2.45774i	−0.107572	+	0.107572i
$523$	22.9887	−	22.9887i	1.00522	−	1.00522i	0.00523871	−	0.999986i	$-0.498332\pi$
$523$	22.9887	−	22.9887i	1.00522	−	1.00522i	0.999986	−	0.00523871i	$-0.00166754\pi$
$524$	11.5646			0.505201
$525$	4.73788	+	12.3512i	0.206778	+	0.539051i
$526$	−3.12563			−0.136284
$527$	1.20927	−	1.20927i	0.0526767	−	0.0526767i
$528$	−4.05545	+	4.05545i	−0.176491	+	0.176491i
$529$			60.7132i			2.63970i
$530$	−4.00000	+	4.27512i	−0.173749	+	0.185700i
$531$		−	13.3306i		−	0.578498i
$532$	−2.28617	+	4.33210i	−0.0991179	+	0.187821i
$533$	3.54595	+	3.54595i	0.153592	+	0.153592i
$534$			9.12563i			0.394905i
$535$	1.18719	+	35.7080i	0.0513266	+	1.54379i
$536$	−6.32106			−0.273028
$537$	5.43718	+	5.43718i	0.234632	+	0.234632i
$538$	−11.4807	+	11.4807i	−0.494968	+	0.494968i
$539$	−22.6565	−	33.1430i	−0.975884	−	1.42757i
$540$	0.0743018	+	2.23483i	0.00319744	+	0.0961719i
$541$	−17.9896			−0.773432			−0.386716	−	0.922199i	$-0.626391\pi$
$541$	−17.9896			−0.773432			−0.386716	+	0.922199i	$0.626391\pi$
$542$	21.3434	+	21.3434i	0.916777	+	0.916777i
$543$	7.57106	+	7.57106i	0.324905	+	0.324905i
$544$	−3.64124			−0.156117
$545$	3.12347	+	2.92246i	0.133795	+	0.125185i
$546$	3.77297	+	12.2049i	0.161468	+	0.522323i
$547$	22.6044	−	22.6044i	0.966496	−	0.966496i	−0.0329611	−	0.999457i	$-0.510494\pi$
$547$	22.6044	−	22.6044i	0.966496	−	0.966496i	0.999457	+	0.0329611i	$0.0104937\pi$
$548$	8.03248	+	8.03248i	0.343131	+	0.343131i
$549$	−8.53122			−0.364104
$550$	−21.5793	−	18.8857i	−0.920145	−	0.805287i
$551$		−	6.43502i		−	0.274141i
$552$	−6.46967	−	6.46967i	−0.275367	−	0.275367i
$553$	−5.14212	+	9.74390i	−0.218665	+	0.414353i
$554$			17.4862i			0.742916i
$555$	−1.32716	−	1.24175i	−0.0563350	−	0.0527095i
$556$		−	7.02297i		−	0.297840i
$557$	11.1240	−	11.1240i	0.471339	−	0.471339i	−0.431009	−	0.902348i	$-0.641842\pi$
$557$	11.1240	−	11.1240i	0.471339	−	0.471339i	0.902348	+	0.431009i	$0.141842\pi$
$558$	−0.332104	+	0.332104i	−0.0140591	+	0.0140591i
$559$	−42.1482			−1.78268
$560$	5.59099	−	1.93413i	0.236262	−	0.0817320i
$561$	−20.8835			−0.881703
$562$	15.6360	−	15.6360i	0.659566	−	0.659566i
$563$	−29.1274	+	29.1274i	−1.22757	+	1.22757i	−0.262695	+	0.964879i	$0.584611\pi$
$563$	−29.1274	+	29.1274i	−1.22757	+	1.22757i	−0.964879	+	0.262695i	$0.915389\pi$
$564$			5.44670i			0.229347i
$565$	7.50825	−	0.249628i	0.315874	−	0.0105019i
$566$		−	21.0962i		−	0.886738i
$567$	−2.33991	−	1.23483i	−0.0982671	−	0.0518581i
$568$	3.63020	+	3.63020i	0.152320	+	0.152320i
$569$		−	8.70532i		−	0.364946i	−0.983211	−	0.182473i	$-0.941590\pi$
$569$		−	8.70532i		−	0.364946i	0.983211	−	0.182473i	$-0.0584102\pi$
$570$	−3.02297	−	2.82843i	−0.126618	−	0.118470i
$571$	−35.9454			−1.50427			−0.752134	−	0.659010i	$-0.770975\pi$
$571$	−35.9454			−1.50427			−0.752134	+	0.659010i	$0.770975\pi$
$572$	−19.5815	−	19.5815i	−0.818742	−	0.818742i
$573$	3.47335	−	3.47335i	0.145101	−	0.145101i
$574$	0.811559	+	2.62526i	0.0338738	+	0.109576i
$575$	30.1283	−	34.4255i	1.25644	−	1.43564i
$576$	1.00000			0.0416667
$577$	22.5860	+	22.5860i	0.940269	+	0.940269i	0.998314	−	0.0580452i	$-0.0184867\pi$
$577$	22.5860	+	22.5860i	0.940269	+	0.940269i	−0.0580452	+	0.998314i	$0.518487\pi$
$578$	2.64555	+	2.64555i	0.110041	+	0.110041i
$579$	−23.2929			−0.968019
$580$	−5.31002	+	5.67525i	−0.220487	+	0.235652i
$581$	−6.33793	+	1.95928i	−0.262942	+	0.0812845i
$582$	0.0119278	−	0.0119278i	0.000494422	−	0.000494422i
$583$	10.6183	+	10.6183i	0.439764	+	0.439764i
$584$	−11.0334			−0.456564
$585$	−10.7907	+	0.358761i	−0.446142	+	0.0148329i
$586$		−	16.4016i		−	0.677546i
$587$	25.9727	+	25.9727i	1.07201	+	1.07201i	0.997198	+	0.0748104i	$0.0238351\pi$
$587$	25.9727	+	25.9727i	1.07201	+	1.07201i	0.0748104	+	0.997198i	$0.476165\pi$
$588$	−1.29289	+	6.87957i	−0.0533180	+	0.283709i
$589$		−	0.869539i		−	0.0358287i
$590$	−0.990486	−	29.7916i	−0.0407777	−	1.22650i
$591$		−	7.26040i		−	0.298653i
$592$	−0.574745	+	0.574745i	−0.0236219	+	0.0236219i
$593$	−24.4656	+	24.4656i	−1.00468	+	1.00468i	−0.00469328	+	0.999989i	$0.501494\pi$
$593$	−24.4656	+	24.4656i	−1.00468	+	1.00468i	−0.999989	+	0.00469328i	$0.998506\pi$
$594$	5.73528			0.235321
$595$	19.3753	+	9.41547i	0.794308	+	0.385997i
$596$	−1.88388			−0.0771667
$597$	−6.10508	+	6.10508i	−0.249864	+	0.249864i
$598$	31.2383	−	31.2383i	1.27743	−	1.27743i
$599$		−	6.72576i		−	0.274807i	−0.990515	−	0.137404i	$-0.956124\pi$
$599$		−	6.72576i		−	0.274807i	0.990515	−	0.137404i	$-0.0438757\pi$
$600$	0.332104	+	4.98896i	0.0135581	+	0.203673i
$601$			44.3830i			1.81042i	0.424965	+	0.905210i	$0.360286\pi$
$601$			44.3830i			1.81042i	−0.424965	+	0.905210i	$0.639714\pi$
$602$	−20.4255	−	10.7791i	−0.832481	−	0.439322i
$603$	4.46967	+	4.46967i	0.182019	+	0.182019i
$604$		−	3.28248i		−	0.133562i
$605$	−33.4471	+	35.7476i	−1.35982	+	1.45335i
$606$	−6.25088			−0.253925
$607$	−7.20378	−	7.20378i	−0.292393	−	0.292393i	0.545632	−	0.838025i	$-0.316290\pi$
$607$	−7.20378	−	7.20378i	−0.292393	−	0.292393i	−0.838025	+	0.545632i	$0.816290\pi$
$608$	−1.30913	+	1.30913i	−0.0530924	+	0.0530924i
$609$	−2.71599	−	8.78579i	−0.110058	−	0.356018i
$610$	−19.0659	+	0.633885i	−0.771954	+	0.0256653i
$611$	−26.2990			−1.06394
$612$	2.57474	+	2.57474i	0.104078	+	0.104078i
$613$	21.6324	+	21.6324i	0.873723	+	0.873723i	0.992876	−	0.119153i	$-0.0380180\pi$
$613$	21.6324	+	21.6324i	0.873723	+	0.873723i	−0.119153	+	0.992876i	$0.538018\pi$
$614$	17.5594			0.708639
$615$	−2.32106	+	0.0771687i	−0.0935943	+	0.00311174i
$616$	−4.48159	−	14.4972i	−0.180569	−	0.584109i
$617$	29.8652	−	29.8652i	1.20233	−	1.20233i	0.228871	−	0.973457i	$-0.426496\pi$
$617$	29.8652	−	29.8652i	1.20233	−	1.20233i	0.973457	−	0.228871i	$-0.0735035\pi$
$618$	1.36459	+	1.36459i	0.0548918	+	0.0548918i
$619$	−12.6963			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$619$	−12.6963			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$620$	−0.717522	+	0.766874i	−0.0288164	+	0.0307984i
$621$			9.14949i			0.367156i
$622$	−6.93933	−	6.93933i	−0.278242	−	0.278242i
$623$	−21.3532	−	11.2686i	−0.855497	−	0.451468i
$624$			4.82843i			0.193292i
$625$	−24.7794	+	3.31371i	−0.991177	+	0.132548i
$626$			19.0334i			0.760726i
$627$	−7.50825	+	7.50825i	−0.299851	+	0.299851i
$628$	7.57106	−	7.57106i	0.302118	−	0.302118i
$629$	−2.95964			−0.118009
$630$	−5.32106	−	2.58579i	−0.211996	−	0.103020i
$631$	36.4650			1.45165			0.725824	−	0.687881i	$-0.241459\pi$
$631$	36.4650			1.45165			0.725824	+	0.687881i	$0.241459\pi$
$632$	−2.94455	+	2.94455i	−0.117128	+	0.117128i
$633$	−5.46878	+	5.46878i	−0.217364	+	0.217364i
$634$		−	11.3284i		−	0.449909i
$635$	−1.40597	−	42.2886i	−0.0557943	−	1.67817i
$636$		−	2.61827i		−	0.103821i
$637$	−33.2175	−	6.24264i	−1.31612	−	0.247342i
$638$	14.0958	+	14.0958i	0.558058	+	0.558058i
$639$		−	5.13387i		−	0.203093i
$640$	2.23483	−	0.0743018i	0.0883395	−	0.00293704i
$641$	−0.862164			−0.0340534			−0.0170267	−	0.999855i	$-0.505420\pi$
$641$	−0.862164			−0.0340534			−0.0170267	+	0.999855i	$0.505420\pi$
$642$	−11.2981	−	11.2981i	−0.445900	−	0.445900i
$643$	8.58057	−	8.58057i	0.338385	−	0.338385i	−0.517374	−	0.855759i	$-0.673091\pi$
$643$	8.58057	−	8.58057i	0.338385	−	0.338385i	0.855759	+	0.517374i	$0.173091\pi$
$644$	23.1274	−	7.14949i	0.911347	−	0.281729i
$645$	13.3358	−	14.2530i	0.525096	−	0.561213i
$646$	−6.74138			−0.265236
$647$	1.35623	+	1.35623i	0.0533191	+	0.0533191i	0.733264	−	0.679945i	$-0.237996\pi$
$647$	1.35623	+	1.35623i	0.0533191	+	0.0533191i	−0.679945	+	0.733264i	$0.737996\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−76.4545			−3.00110
$650$	−24.0888	+	1.60354i	−0.944841	+	0.0628961i
$651$	−0.367001	−	1.18719i	−0.0143839	−	0.0465296i
$652$	−10.3367	+	10.3367i	−0.404816	+	0.404816i
$653$	−15.8873	−	15.8873i	−0.621718	−	0.621718i	0.324253	−	0.945971i	$-0.394887\pi$
$653$	−15.8873	−	15.8873i	−0.621718	−	0.621718i	−0.945971	+	0.324253i	$0.894887\pi$
$654$	−1.91295			−0.0748023
$655$	−18.8827	−	17.6675i	−0.737809	−	0.690327i
$656$			1.03858i			0.0405499i
$657$	7.80177	+	7.80177i	0.304376	+	0.304376i
$658$	−12.7448	−	6.72576i	−0.496844	−	0.262198i
$659$			25.8315i			1.00625i	0.864213	+	0.503126i	$0.167817\pi$
$659$			25.8315i			1.00625i	−0.864213	+	0.503126i	$0.832183\pi$
$660$	12.8174	−	0.426141i	0.498916	−	0.0165875i
$661$		−	30.7383i		−	1.19558i	−0.801652	−	0.597791i	$-0.796045\pi$
$661$		−	30.7383i		−	1.19558i	0.801652	−	0.597791i	$-0.203955\pi$
$662$	9.68071	−	9.68071i	0.376251	−	0.376251i
$663$	−12.4320	+	12.4320i	−0.482818	+	0.482818i
$664$	−2.50736			−0.0973046
$665$	10.3511	−	3.58085i	0.401400	−	0.138859i
$666$	0.812812			0.0314958
$667$	−22.4871	+	22.4871i	−0.870702	+	0.870702i
$668$	−9.85140	+	9.85140i	−0.381162	+	0.381162i
$669$		−	12.2171i		−	0.472342i
$670$	10.3211	+	9.65685i	0.398737	+	0.373077i
$671$			48.9289i			1.88888i
$672$	−1.23483	+	2.33991i	−0.0476347	+	0.0902641i
$673$	−4.05024	−	4.05024i	−0.156125	−	0.156125i	0.624722	−	0.780847i	$-0.285212\pi$
$673$	−4.05024	−	4.05024i	−0.156125	−	0.156125i	−0.780847	+	0.624722i	$0.785212\pi$
$674$		−	6.32232i		−	0.243527i
$675$	3.29289	−	3.76256i	0.126744	−	0.144821i
$676$	−10.3137			−0.396681
$677$	−2.32222	−	2.32222i	−0.0892503	−	0.0892503i	0.661072	−	0.750322i	$-0.270102\pi$
$677$	−2.32222	−	2.32222i	−0.0892503	−	0.0892503i	−0.750322	+	0.661072i	$0.770102\pi$
$678$	−2.37563	+	2.37563i	−0.0912355	+	0.0912355i
$679$	0.0131811	+	0.0426387i	0.000505845	+	0.00163632i
$680$	5.94543	+	5.56282i	0.227997	+	0.213324i
$681$	−5.77996			−0.221489
$682$	1.90471	+	1.90471i	0.0729351	+	0.0729351i
$683$	−13.2028	−	13.2028i	−0.505191	−	0.505191i	0.407855	−	0.913047i	$-0.366277\pi$
$683$	−13.2028	−	13.2028i	−0.505191	−	0.505191i	−0.913047	+	0.407855i	$0.866277\pi$
$684$	1.85140			0.0707899
$685$	−0.844042	−	25.3869i	−0.0322492	−	0.969984i
$686$	−14.5011	−	11.5204i	−0.553653	−	0.439850i
$687$	6.58579	−	6.58579i	0.251263	−	0.251263i
$688$	−6.17246	−	6.17246i	−0.235323	−	0.235323i
$689$	12.6421			0.481627
$690$	0.679824	+	20.4476i	0.0258804	+	0.778426i
$691$			49.4659i			1.88177i	0.338726	+	0.940885i	$0.390004\pi$
$691$			49.4659i			1.88177i	−0.338726	+	0.940885i	$0.609996\pi$
$692$	−8.83947	−	8.83947i	−0.336026	−	0.336026i
$693$	−7.08211	+	13.4200i	−0.269027	+	0.509785i
$694$			18.2579i			0.693059i
$695$	−10.7292	+	11.4671i	−0.406981	+	0.434973i
$696$		−	3.47577i		−	0.131749i
$697$	−2.67409	+	2.67409i	−0.101288	+	0.101288i
$698$	−9.61217	+	9.61217i	−0.363826	+	0.363826i
$699$	7.39338			0.279643
$700$	−12.0838	−	5.38344i	−0.456725	−	0.203475i
$701$	31.2773			1.18133			0.590663	−	0.806918i	$-0.298866\pi$
$701$	31.2773			1.18133			0.590663	+	0.806918i	$0.298866\pi$
$702$	3.41421	−	3.41421i	0.128861	−	0.128861i
$703$	−1.06408	+	1.06408i	−0.0401326	+	0.0401326i
$704$		−	5.73528i		−	0.216156i
$705$	8.32106	−	8.89339i	0.313389	−	0.334945i
$706$			24.6118i			0.926277i
$707$	7.71880	−	14.6265i	0.290295	−	0.550087i
$708$	9.42614	+	9.42614i	0.354256	+	0.354256i
$709$		−	42.4051i		−	1.59256i	−0.604931	−	0.796278i	$-0.706799\pi$
$709$		−	42.4051i		−	1.59256i	0.604931	−	0.796278i	$-0.293201\pi$
$710$	−0.381456	−	11.4734i	−0.0143158	−	0.430587i
$711$	4.16422			0.156170
$712$	−6.45280	−	6.45280i	−0.241829	−	0.241829i
$713$	−3.03858	+	3.03858i	−0.113796	+	0.113796i
$714$	−9.20406	+	2.84530i	−0.344453	+	0.106483i
$715$	2.05759	+	61.8878i	0.0769496	+	2.31447i
$716$	−7.68934			−0.287364
$717$	−5.22208	−	5.22208i	−0.195022	−	0.195022i
$718$	4.96599	+	4.96599i	0.185329	+	0.185329i
$719$	31.0675			1.15862			0.579311	−	0.815107i	$-0.303322\pi$
$719$	31.0675			1.15862			0.579311	+	0.815107i	$0.303322\pi$
$720$	−1.63280	−	1.52773i	−0.0608510	−	0.0569350i
$721$	−4.87805	+	1.50798i	−0.181668	+	0.0561600i
$722$	11.0113	−	11.0113i	0.409798	−	0.409798i
$723$	−3.14250	−	3.14250i	−0.116871	−	0.116871i
$724$	−10.7071			−0.397926
$725$	17.3405	−	1.15432i	0.644008	−	0.0428703i
$726$		−	21.8934i		−	0.812540i
$727$	6.60937	+	6.60937i	0.245128	+	0.245128i	0.818968	−	0.573840i	$-0.194547\pi$
$727$	6.60937	+	6.60937i	0.245128	+	0.245128i	−0.573840	+	0.818968i	$0.694547\pi$
$728$	−11.2981	−	5.96230i	−0.418735	−	0.220978i
$729$			1.00000i			0.0370370i
$730$	18.0153	+	16.8560i	0.666778	+	0.623867i
$731$		−	31.7850i		−	1.17561i
$732$	6.03248	−	6.03248i	0.222967	−	0.222967i
$733$	3.30331	−	3.30331i	0.122010	−	0.122010i	−0.643465	−	0.765476i	$-0.722504\pi$
$733$	3.30331	−	3.30331i	0.122010	−	0.122010i	0.765476	+	0.643465i	$0.222504\pi$
$734$	32.6131			1.20377
$735$	12.6211	−	9.25780i	0.465538	−	0.341479i
$736$	9.14949			0.337255
$737$	25.6348	−	25.6348i	0.944269	−	0.944269i
$738$	0.734390	−	0.734390i	0.0270333	−	0.0270333i
$739$			8.70709i			0.320296i	0.987093	+	0.160148i	$0.0511971\pi$
$739$			8.70709i			0.320296i	−0.987093	+	0.160148i	$0.948803\pi$
$740$	1.81650	−	0.0603934i	0.0667758	−	0.00222011i
$741$			8.93933i			0.328395i
$742$	6.12652	+	3.23313i	0.224912	+	0.118692i
$743$	33.9264	+	33.9264i	1.24464	+	1.24464i	0.958056	+	0.286582i	$0.0925192\pi$
$743$	33.9264	+	33.9264i	1.24464	+	1.24464i	0.286582	+	0.958056i	$0.407481\pi$
$744$		−	0.469666i		−	0.0172188i
$745$	3.07601	+	2.87805i	0.112696	+	0.105444i
$746$	11.3753			0.416478
$747$	1.77297	+	1.77297i	0.0648697	+	0.0648697i
$748$	14.7669	−	14.7669i	0.539930	−	0.539930i
$749$	40.3878	−	12.4853i	1.47574	−	0.456202i
$750$	7.07950	−	8.65336i	0.258507	−	0.315976i
$751$	40.1365			1.46460			0.732301	−	0.680981i	$-0.238446\pi$
$751$	40.1365			1.46460			0.732301	+	0.680981i	$0.238446\pi$
$752$	−3.85140	−	3.85140i	−0.140446	−	0.140446i
$753$	−9.99847	−	9.99847i	−0.364365	−	0.364365i
$754$	16.7825			0.611182
$755$	−5.01473	+	5.35965i	−0.182505	+	0.195058i
$756$	2.52773	−	0.781409i	0.0919325	−	0.0284196i
$757$	7.01659	−	7.01659i	0.255022	−	0.255022i	−0.568004	−	0.823026i	$-0.692284\pi$
$757$	7.01659	−	7.01659i	0.255022	−	0.255022i	0.823026	+	0.568004i	$0.192284\pi$
$758$	8.08705	+	8.08705i	0.293735	+	0.293735i
$759$	52.4749			1.90472
$760$	4.13756	−	0.137562i	0.150085	−	0.00498990i
$761$		−	35.9693i		−	1.30388i	−0.758269	−	0.651942i	$-0.773954\pi$
$761$		−	35.9693i		−	1.30388i	0.758269	−	0.651942i	$-0.226046\pi$
$762$	13.3802	+	13.3802i	0.484714	+	0.484714i
$763$	2.36217	−	4.47613i	0.0855164	−	0.162047i
$764$			4.91206i			0.177712i
$765$	−0.270551	−	8.13756i	−0.00978178	−	0.294214i
$766$			8.08705i			0.292197i
$767$	−45.5134	+	45.5134i	−1.64339	+	1.64339i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	29.0018			1.04583			0.522916	−	0.852384i	$-0.324844\pi$
$769$	29.0018			1.04583			0.522916	+	0.852384i	$0.324844\pi$
$770$	−14.8302	+	30.5178i	−0.534443	+	1.09978i
$771$	−9.43846			−0.339918
$772$	16.4706	−	16.4706i	0.592788	−	0.592788i
$773$	−33.1042	+	33.1042i	−1.19067	+	1.19067i	−0.213796	+	0.976878i	$0.568583\pi$
$773$	−33.1042	+	33.1042i	−1.19067	+	1.19067i	−0.976878	+	0.213796i	$0.931417\pi$
$774$			8.72918i			0.313764i
$775$	2.34315	−	0.155978i	0.0841683	−	0.00560290i
$776$			0.0168684i			0.000605541i
$777$	−1.00369	+	1.90191i	−0.0360071	+	0.0682306i
$778$	−22.9209	−	22.9209i	−0.821755	−	0.821755i
$779$			1.92283i			0.0688926i
$780$	7.37652	−	7.88388i	0.264122	−	0.282288i
$781$	−29.4442			−1.05360
$782$	23.5576	+	23.5576i	0.842418	+	0.842418i
$783$	−2.45774	+	2.45774i	−0.0878324	+	0.0878324i
$784$	−3.95037	−	5.77880i	−0.141085	−	0.206386i
$785$	−23.9286	+	0.795556i	−0.854047	+	0.0283946i
$786$	11.5646			0.412495
$787$	0.532861	+	0.532861i	0.0189944	+	0.0189944i	0.716540	−	0.697546i	$-0.245725\pi$
$787$	0.532861	+	0.532861i	0.0189944	+	0.0189944i	−0.697546	+	0.716540i	$0.745725\pi$
$788$	5.13387	+	5.13387i	0.182887	+	0.182887i
$789$	−3.12563			−0.111276
$790$	9.30633	−	0.309409i	0.331105	−	0.0110083i
$791$	−2.62526	−	8.49227i	−0.0933434	−	0.301950i
$792$	−4.05545	+	4.05545i	−0.144104	+	0.144104i
$793$	29.1274	+	29.1274i	1.03434	+	1.03434i
$794$	−36.2071			−1.28494
$795$	−4.00000	+	4.27512i	−0.141865	+	0.151623i
$796$		−	8.63388i		−	0.306020i
$797$	−22.6961	−	22.6961i	−0.803935	−	0.803935i	0.179773	−	0.983708i	$-0.442464\pi$
$797$	−22.6961	−	22.6961i	−0.803935	−	0.803935i	−0.983708	+	0.179773i	$0.942464\pi$
$798$	−2.28617	+	4.33210i	−0.0809294	+	0.153355i
$799$		−	19.8327i		−	0.701631i
$800$	−3.76256	−	3.29289i	−0.133027	−	0.116421i
$801$			9.12563i			0.322438i
$802$	9.09315	−	9.09315i	0.321090	−	0.321090i
$803$	44.7453	−	44.7453i	1.57903	−	1.57903i
$804$	−6.32106			−0.222927
$805$	−48.6850	−	23.6586i	−1.71592	−	0.833857i
$806$	2.26775			0.0798781
$807$	−11.4807	+	11.4807i	−0.404140	+	0.404140i
$808$	4.42004	−	4.42004i	0.155496	−	0.155496i
$809$			16.6404i			0.585044i	0.956259	+	0.292522i	$0.0944944\pi$
$809$			16.6404i			0.585044i	−0.956259	+	0.292522i	$0.905506\pi$
$810$	0.0743018	+	2.23483i	0.00261070	+	0.0785240i
$811$		−	13.7933i		−	0.484347i	−0.970233	−	0.242173i	$-0.922140\pi$
$811$		−	13.7933i		−	0.484347i	0.970233	−	0.242173i	$-0.0778603\pi$
$812$	8.13299	+	4.29199i	0.285412	+	0.150619i
$813$	21.3434	+	21.3434i	0.748545	+	0.748545i
$814$		−	4.66170i		−	0.163393i
$815$	32.6694	−	1.08616i	1.14436	−	0.0380467i
$816$	−3.64124			−0.127469
$817$	−11.4277	−	11.4277i	−0.399804	−	0.399804i
$818$	5.42983	−	5.42983i	0.189850	−	0.189850i
$819$	3.77297	+	12.2049i	0.131838	+	0.426475i
$820$	1.58667	−	1.69581i	0.0554090	−	0.0592201i
$821$	−25.2001			−0.879489			−0.439745	−	0.898123i	$-0.644931\pi$
$821$	−25.2001			−0.879489			−0.439745	+	0.898123i	$0.644931\pi$
$822$	8.03248	+	8.03248i	0.280165	+	0.280165i
$823$	4.45075	+	4.45075i	0.155143	+	0.155143i	0.780411	−	0.625267i	$-0.215010\pi$
$823$	4.45075	+	4.45075i	0.155143	+	0.155143i	−0.625267	+	0.780411i	$0.715010\pi$
$824$	−1.92982			−0.0672284
$825$	−21.5793	−	18.8857i	−0.751295	−	0.657514i
$826$	−33.6961	+	10.4166i	−1.17244	+	0.362441i
$827$	−21.7665	+	21.7665i	−0.756896	+	0.756896i	−0.975756	−	0.218861i	$-0.929766\pi$
$827$	−21.7665	+	21.7665i	−0.756896	+	0.756896i	0.218861	+	0.975756i	$0.429766\pi$
$828$	−6.46967	−	6.46967i	−0.224836	−	0.224836i
$829$	30.3787			1.05509			0.527547	−	0.849526i	$-0.323112\pi$
$829$	30.3787			1.05509			0.527547	+	0.849526i	$0.323112\pi$
$830$	4.09404	+	3.83057i	0.142106	+	0.132961i
$831$			17.4862i			0.606588i
$832$	−3.41421	−	3.41421i	−0.118367	−	0.118367i
$833$	4.70773	−	25.0501i	0.163113	−	0.867936i
$834$		−	7.02297i		−	0.243186i
$835$	31.1356	−	1.03517i	1.07749	−	0.0358236i
$836$		−	10.6183i		−	0.367241i
$837$	−0.332104	+	0.332104i	−0.0114792	+	0.0114792i
$838$	−10.7858	+	10.7858i	−0.372589	+	0.372589i
$839$	−16.1464			−0.557436			−0.278718	−	0.960373i	$-0.589910\pi$
$839$	−16.1464			−0.557436			−0.278718	+	0.960373i	$0.589910\pi$
$840$	5.59099	−	1.93413i	0.192907	−	0.0667339i
$841$	16.9190			0.583415
$842$	−11.6859	+	11.6859i	−0.402724	+	0.402724i
$843$	15.6360	−	15.6360i	0.538533	−	0.538533i
$844$		−	7.73402i		−	0.266216i
$845$	16.8403	+	15.7565i	0.579323	+	0.542041i
$846$			5.44670i			0.187261i
$847$	51.2286	+	27.0347i	1.76024	+	0.928923i
$848$	1.85140	+	1.85140i	0.0635772	+	0.0635772i
$849$		−	21.0962i		−	0.724019i
$850$	−1.20927	−	18.1660i	−0.0414777	−	0.623088i
$851$	7.43682			0.254931
$852$	3.63020	+	3.63020i	0.124369	+	0.124369i
$853$	26.8216	−	26.8216i	0.918353	−	0.918353i	−0.0785565	−	0.996910i	$-0.525031\pi$
$853$	26.8216	−	26.8216i	0.918353	−	0.918353i	0.996910	+	0.0785565i	$0.0250311\pi$
$854$	6.66637	+	21.5646i	0.228118	+	0.737925i
$855$	−3.02297	−	2.82843i	−0.103383	−	0.0967302i
$856$	15.9779			0.546114
$857$	−18.6709	−	18.6709i	−0.637787	−	0.637787i	0.312222	−	0.950009i	$-0.398927\pi$
$857$	−18.6709	−	18.6709i	−0.637787	−	0.637787i	−0.950009	+	0.312222i	$0.898927\pi$
$858$	−19.5815	−	19.5815i	−0.668500	−	0.668500i
$859$	8.11664			0.276936			0.138468	−	0.990367i	$-0.455782\pi$
$859$	8.11664			0.276936			0.138468	+	0.990367i	$0.455782\pi$
$860$	0.648593	+	19.5083i	0.0221169	+	0.665226i
$861$	0.811559	+	2.62526i	0.0276578	+	0.0894685i
$862$	−5.11118	+	5.11118i	−0.174087	+	0.174087i
$863$	6.62651	+	6.62651i	0.225569	+	0.225569i	0.810839	−	0.585270i	$-0.199011\pi$
$863$	6.62651	+	6.62651i	0.225569	+	0.225569i	−0.585270	+	0.810839i	$0.699011\pi$
$864$	1.00000			0.0340207
$865$	0.928839	+	27.9374i	0.0315815	+	0.949901i
$866$			18.5144i			0.629143i
$867$	2.64555	+	2.64555i	0.0898477	+	0.0898477i
$868$	1.09898	+	0.579960i	0.0373017	+	0.0196851i
$869$		−	23.8829i		−	0.810173i
$870$	−5.31002	+	5.67525i	−0.180027	+	0.192409i
$871$		−	30.5208i		−	1.03416i
$872$	1.35266	−	1.35266i	0.0458068	−	0.0458068i
$873$	0.0119278	−	0.0119278i	0.000403694	−	0.000403694i
$874$	16.9393			0.572981
$875$	11.5061	+	27.2509i	0.388977	+	0.921247i
$876$	−11.0334			−0.372783
$877$	−27.9123	+	27.9123i	−0.942532	+	0.942532i	−0.998436	−	0.0559044i	$-0.982196\pi$
$877$	−27.9123	+	27.9123i	−0.942532	+	0.942532i	0.0559044	+	0.998436i	$0.482196\pi$
$878$	−17.6094	+	17.6094i	−0.594287	+	0.594287i
$879$		−	16.4016i		−	0.553214i
$880$	−8.76193	+	9.36459i	−0.295365	+	0.315680i
$881$		−	34.6317i		−	1.16677i	−0.812195	−	0.583386i	$-0.801728\pi$
$881$		−	34.6317i		−	1.16677i	0.812195	−	0.583386i	$-0.198272\pi$
$882$	−1.29289	+	6.87957i	−0.0435340	+	0.231647i
$883$	5.61001	+	5.61001i	0.188792	+	0.188792i	0.795174	−	0.606382i	$-0.207380\pi$
$883$	5.61001	+	5.61001i	0.188792	+	0.188792i	−0.606382	+	0.795174i	$0.707380\pi$
$884$		−	17.5815i		−	0.591328i
$885$	−0.990486	−	29.7916i	−0.0332948	−	1.00143i
$886$	−17.3695			−0.583541
$887$	−24.0494	−	24.0494i	−0.807498	−	0.807498i	0.176756	−	0.984255i	$-0.443440\pi$
$887$	−24.0494	−	24.0494i	−0.807498	−	0.807498i	−0.984255	+	0.176756i	$0.943440\pi$
$888$	−0.574745	+	0.574745i	−0.0192872	+	0.0192872i
$889$	−47.8308	+	14.7862i	−1.60419	+	0.495912i
$890$	0.678051	+	20.3943i	0.0227283	+	0.683617i
$891$	5.73528			0.192139
$892$	8.63883	+	8.63883i	0.289249	+	0.289249i
$893$	−7.13046	−	7.13046i	−0.238612	−	0.238612i
$894$	−1.88388			−0.0630064
$895$	12.5552	+	11.7472i	0.419674	+	0.392666i
$896$	−0.781409	−	2.52773i	−0.0261050	−	0.0844454i
$897$	31.2383	−	31.2383i	1.04302	−	1.04302i
$898$	−3.20406	−	3.20406i	−0.106921	−	0.106921i
$899$	−1.63245			−0.0544453
$900$	0.332104	+	4.98896i	0.0110701	+	0.166299i
$901$			9.53375i			0.317615i
$902$	−4.21193	−	4.21193i	−0.140242	−	0.140242i
$903$	−20.4255	−	10.7791i	−0.679718	−	0.358705i
$904$		−	3.35965i		−	0.111740i
$905$	17.4826	+	16.3575i	0.581141	+	0.543742i
$906$		−	3.28248i		−	0.109053i
$907$	34.2153	−	34.2153i	1.13610	−	1.13610i	0.146959	−	0.989143i	$-0.453051\pi$
$907$	34.2153	−	34.2153i	1.13610	−	1.13610i	0.989143	−	0.146959i	$-0.0469486\pi$
$908$	4.08705	−	4.08705i	0.135634	−	0.135634i
$909$	−6.25088			−0.207329
$910$	9.33882	+	26.9957i	0.309579	+	0.894898i
$911$	56.4059			1.86881			0.934406	−	0.356210i	$-0.115931\pi$
$911$	56.4059			1.86881			0.934406	+	0.356210i	$0.115931\pi$
$912$	−1.30913	+	1.30913i	−0.0433498	+	0.0433498i
$913$	10.1685	−	10.1685i	0.336528	−	0.336528i
$914$		−	7.55635i		−	0.249942i
$915$	−19.0659	+	0.633885i	−0.630298	+	0.0209556i
$916$			9.31371i			0.307734i
$917$	−14.2803	+	27.0601i	−0.471578	+	0.893604i
$918$	2.57474	+	2.57474i	0.0849792	+	0.0849792i
$919$		−	37.1036i		−	1.22393i	−0.790884	−	0.611967i	$-0.790379\pi$
$919$		−	37.1036i		−	1.22393i	0.790884	−	0.611967i	$-0.209621\pi$
$920$	−14.9393	−	13.9779i	−0.492535	−	0.460838i
$921$	17.5594			0.578601
$922$	−9.12195	−	9.12195i	−0.300415	−	0.300415i
$923$	−17.5281	+	17.5281i	−0.576946	+	0.576946i
$924$	−4.48159	−	14.4972i	−0.147434	−	0.476923i
$925$	−3.05825	−	2.67650i	−0.100555	−	0.0880029i
$926$	−16.8930			−0.555139
$927$	1.36459	+	1.36459i	0.0448189	+	0.0448189i
$928$	2.45774	+	2.45774i	0.0806792	+	0.0806792i
$929$	−0.164219			−0.00538784			−0.00269392	−	0.999996i	$-0.500858\pi$
$929$	−0.164219			−0.00538784			−0.00269392	+	0.999996i	$0.500858\pi$
$930$	−0.717522	+	0.766874i	−0.0235285	+	0.0251468i
$931$	−7.31371	−	10.6989i	−0.239697	−	0.350641i
$932$	−5.22791	+	5.22791i	−0.171246	+	0.171246i
$933$	−6.93933	−	6.93933i	−0.227184	−	0.227184i
$934$	−35.5256			−1.16243
$935$	−46.6712	+	1.55168i	−1.52631	+	0.0507454i
$936$			4.82843i			0.157822i
$937$	−25.1804	−	25.1804i	−0.822609	−	0.822609i	0.163872	−	0.986482i	$-0.447602\pi$
$937$	−25.1804	−	25.1804i	−0.822609	−	0.822609i	−0.986482	+	0.163872i	$0.947602\pi$
$938$	7.80546	−	14.7907i	0.254857	−	0.482934i
$939$			19.0334i			0.621131i
$940$	0.404699	+	12.1725i	0.0131998	+	0.397022i
$941$			46.5762i			1.51834i	0.650892	+	0.759171i	$0.274395\pi$
$941$			46.5762i			1.51834i	−0.650892	+	0.759171i	$0.725605\pi$
$942$	7.57106	−	7.57106i	0.246678	−	0.246678i
$943$	6.71929	−	6.71929i	0.218810	−	0.218810i
$944$	−13.3306			−0.433873
$945$	−5.32106	−	2.58579i	−0.173094	−	0.0841156i
$946$	50.0642			1.62773
$947$	15.2362	−	15.2362i	0.495108	−	0.495108i	−0.414803	−	0.909911i	$-0.636149\pi$
$947$	15.2362	−	15.2362i	0.495108	−	0.495108i	0.909911	+	0.414803i	$0.136149\pi$
$948$	−2.94455	+	2.94455i	−0.0956344	+	0.0956344i
$949$		−	53.2738i		−	1.72934i
$950$	−6.96599	−	6.09645i	−0.226007	−	0.197795i
$951$		−	11.3284i		−	0.367349i
$952$	4.49632	−	8.52018i	0.145727	−	0.276141i
$953$	−2.21318	−	2.21318i	−0.0716920	−	0.0716920i	0.670352	−	0.742044i	$-0.266143\pi$
$953$	−2.21318	−	2.21318i	−0.0716920	−	0.0716920i	−0.742044	+	0.670352i	$0.766143\pi$
$954$		−	2.61827i		−	0.0847696i
$955$	7.50429	−	8.02044i	0.242833	−	0.259535i
$956$	7.38514			0.238853
$957$	14.0958	+	14.0958i	0.455653	+	0.455653i
$958$	0.828427	−	0.828427i	0.0267653	−	0.0267653i
$959$	−28.7141	+	8.87653i	−0.927226	+	0.286638i
$960$	2.23483	−	0.0743018i	0.0721289	−	0.00239808i
$961$	30.7794			0.992884
$962$	−2.77511	−	2.77511i	−0.0894733	−	0.0894733i
$963$	−11.2981	−	11.2981i	−0.364076	−	0.364076i
$964$	4.44417			0.143137
$965$	−52.0557	+	1.73070i	−1.67573	+	0.0557133i
$966$	23.1274	−	7.14949i	0.744112	−	0.230031i
$967$	4.58606	−	4.58606i	0.147478	−	0.147478i	−0.629513	−	0.776990i	$-0.716745\pi$
$967$	4.58606	−	4.58606i	0.147478	−	0.147478i	0.776990	+	0.629513i	$0.216745\pi$
$968$	15.4810	+	15.4810i	0.497577	+	0.497577i
$969$	−6.74138			−0.216564
$970$	0.0257703	−	0.0275428i	0.000827435	−	0.000884347i
$971$			37.1737i			1.19296i	0.802627	+	0.596481i	$0.203435\pi$
$971$			37.1737i			1.19296i	−0.802627	+	0.596481i	$0.796565\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	16.4331	+	8.67220i	0.526822	+	0.278018i
$974$			8.02907i			0.257268i
$975$	−24.0888	+	1.60354i	−0.771460	+	0.0513544i
$976$			8.53122i			0.273078i
$977$	−42.4680	+	42.4680i	−1.35867	+	1.35867i	−0.483114	+	0.875557i	$0.660494\pi$
$977$	−42.4680	+	42.4680i	−1.35867	+	1.35867i	−0.875557	+	0.483114i	$0.839506\pi$
$978$	−10.3367	+	10.3367i	−0.330531	+	0.330531i
$979$	52.3380			1.67273
$980$	−2.37824	+	15.4707i	−0.0759700	+	0.494195i
$981$	−1.91295			−0.0610758
$982$	15.0940	−	15.0940i	0.481670	−	0.481670i
$983$	−31.8722	+	31.8722i	−1.01657	+	1.01657i	−0.0167048	+	0.999860i	$0.505318\pi$
$983$	−31.8722	+	31.8722i	−1.01657	+	1.01657i	−0.999860	+	0.0167048i	$0.994682\pi$
$984$			1.03858i			0.0331089i
$985$	−0.539460	−	16.2258i	−0.0171886	−	0.516996i
$986$			12.6561i			0.403052i
$987$	−12.7448	−	6.72576i	−0.405671	−	0.214083i
$988$	−6.32106	−	6.32106i	−0.201100	−	0.201100i
$989$			79.8675i			2.53964i
$990$	12.8174	−	0.426141i	0.407363	−	0.0135437i
$991$	12.2660			0.389642			0.194821	−	0.980839i	$-0.437587\pi$
$991$	12.2660			0.389642			0.194821	+	0.980839i	$0.437587\pi$
$992$	0.332104	+	0.332104i	0.0105443	+	0.0105443i
$993$	9.68071	−	9.68071i	0.307208	−	0.307208i
$994$	−12.9770	+	4.01165i	−0.411606	+	0.127242i
$995$	−13.1902	+	14.0975i	−0.418158	+	0.446919i
$996$	−2.50736			−0.0794489
$997$	−18.0221	−	18.0221i	−0.570764	−	0.570764i	0.361578	−	0.932342i	$-0.382238\pi$
$997$	−18.0221	−	18.0221i	−0.570764	−	0.570764i	−0.932342	+	0.361578i	$0.882238\pi$
$998$	−23.6464	−	23.6464i	−0.748515	−	0.748515i
$999$	0.812812			0.0257162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.m.a.13.1	✓	8
3.2	odd	2		630.2.p.b.433.4		8
4.3	odd	2		1680.2.cz.b.433.3		8
5.2	odd	4		210.2.m.b.97.2	yes	8
5.3	odd	4		1050.2.m.a.307.4		8
5.4	even	2		1050.2.m.b.643.3		8
7.6	odd	2		210.2.m.b.13.2	yes	8
15.2	even	4		630.2.p.c.307.3		8
20.7	even	4		1680.2.cz.a.97.2		8
21.20	even	2		630.2.p.c.433.3		8
28.27	even	2		1680.2.cz.a.433.2		8
35.13	even	4		1050.2.m.b.307.3		8
35.27	even	4	inner	210.2.m.a.97.1	yes	8
35.34	odd	2		1050.2.m.a.643.4		8
105.62	odd	4		630.2.p.b.307.4		8
140.27	odd	4		1680.2.cz.b.97.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.1	✓	8	1.1	even	1	trivial
210.2.m.a.97.1	yes	8	35.27	even	4	inner
210.2.m.b.13.2	yes	8	7.6	odd	2
210.2.m.b.97.2	yes	8	5.2	odd	4
630.2.p.b.307.4		8	105.62	odd	4
630.2.p.b.433.4		8	3.2	odd	2
630.2.p.c.307.3		8	15.2	even	4
630.2.p.c.433.3		8	21.20	even	2
1050.2.m.a.307.4		8	5.3	odd	4
1050.2.m.a.643.4		8	35.34	odd	2
1050.2.m.b.307.3		8	35.13	even	4
1050.2.m.b.643.3		8	5.4	even	2
1680.2.cz.a.97.2		8	20.7	even	4
1680.2.cz.a.433.2		8	28.27	even	2
1680.2.cz.b.97.3		8	140.27	odd	4
1680.2.cz.b.433.3		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.52773 + 1.63280i) q^{5} -1.00000i q^{6} +(2.33991 + 1.23483i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +(-1.52773 + 1.63280i) q^{5} -1.00000i q^{6} +(2.33991 + 1.23483i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-0.0743018 - 2.23483i) q^{10} -5.73528 q^{11} +(0.707107 + 0.707107i) q^{12} +(-3.41421 + 3.41421i) q^{13} +(-2.52773 + 0.781409i) q^{14} +(-0.0743018 - 2.23483i) q^{15} -1.00000 q^{16} +(-2.57474 - 2.57474i) q^{17} +(0.707107 + 0.707107i) q^{18} -1.85140 q^{19} +(1.63280 + 1.52773i) q^{20} +(-2.52773 + 0.781409i) q^{21} +(4.05545 - 4.05545i) q^{22} +(6.46967 + 6.46967i) q^{23} -1.00000 q^{24} +(-0.332104 - 4.98896i) q^{25} -4.82843i q^{26} +(0.707107 + 0.707107i) q^{27} +(1.23483 - 2.33991i) q^{28} +3.47577i q^{29} +(1.63280 + 1.52773i) q^{30} +0.469666i q^{31} +(0.707107 - 0.707107i) q^{32} +(4.05545 - 4.05545i) q^{33} +3.64124 q^{34} +(-5.59099 + 1.93413i) q^{35} -1.00000 q^{36} +(0.574745 - 0.574745i) q^{37} +(1.30913 - 1.30913i) q^{38} -4.82843i q^{39} +(-2.23483 + 0.0743018i) q^{40} -1.03858i q^{41} +(1.23483 - 2.33991i) q^{42} +(6.17246 + 6.17246i) q^{43} +5.73528i q^{44} +(1.63280 + 1.52773i) q^{45} -9.14949 q^{46} +(3.85140 + 3.85140i) q^{47} +(0.707107 - 0.707107i) q^{48} +(3.95037 + 5.77880i) q^{49} +(3.76256 + 3.29289i) q^{50} +3.64124 q^{51} +(3.41421 + 3.41421i) q^{52} +(-1.85140 - 1.85140i) q^{53} -1.00000 q^{54} +(8.76193 - 9.36459i) q^{55} +(0.781409 + 2.52773i) q^{56} +(1.30913 - 1.30913i) q^{57} +(-2.45774 - 2.45774i) q^{58} +13.3306 q^{59} +(-2.23483 + 0.0743018i) q^{60} -8.53122i q^{61} +(-0.332104 - 0.332104i) q^{62} +(1.23483 - 2.33991i) q^{63} +1.00000i q^{64} +(-0.358761 - 10.7907i) q^{65} +5.73528i q^{66} +(-4.46967 + 4.46967i) q^{67} +(-2.57474 + 2.57474i) q^{68} -9.14949 q^{69} +(2.58579 - 5.32106i) q^{70} +5.13387 q^{71} +(0.707107 - 0.707107i) q^{72} +(-7.80177 + 7.80177i) q^{73} +0.812812i q^{74} +(3.76256 + 3.29289i) q^{75} +1.85140i q^{76} +(-13.4200 - 7.08211i) q^{77} +(3.41421 + 3.41421i) q^{78} +4.16422i q^{79} +(1.52773 - 1.63280i) q^{80} -1.00000 q^{81} +(0.734390 + 0.734390i) q^{82} +(-1.77297 + 1.77297i) q^{83} +(0.781409 + 2.52773i) q^{84} +(8.13756 - 0.270551i) q^{85} -8.72918 q^{86} +(-2.45774 - 2.45774i) q^{87} +(-4.05545 - 4.05545i) q^{88} -9.12563 q^{89} +(-2.23483 + 0.0743018i) q^{90} +(-12.2049 + 3.77297i) q^{91} +(6.46967 - 6.46967i) q^{92} +(-0.332104 - 0.332104i) q^{93} -5.44670 q^{94} +(2.82843 - 3.02297i) q^{95} +1.00000i q^{96} +(0.0119278 + 0.0119278i) q^{97} +(-6.87957 - 1.29289i) q^{98} +5.73528i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

Introduction

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Modular forms

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Database

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