LMFDB - Embedded newform 546.2.o.a.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$1.91681i$ of defining polynomial
Character	$\chi$	$=$	546.307
Dual form			546.2.o.a.265.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -3.62760 q^{10} +(-1.64828 + 1.64828i) q^{11} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} +(1.35539 - 2.27220i) q^{14} +(2.56510 + 2.56510i) q^{15} -1.00000 q^{16} -7.15945 q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.86167 + 2.86167i) q^{19} +(-2.56510 - 2.56510i) q^{20} +(-2.56510 + 0.648285i) q^{21} -2.33103 q^{22} +4.45602i q^{23} +(0.707107 + 0.707107i) q^{24} -8.15945i q^{25} +(-0.707107 + 3.53553i) q^{26} +1.00000i q^{27} +(2.56510 - 0.648285i) q^{28} -9.75259 q^{29} +3.62760i q^{30} +(3.91681 - 3.91681i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.64828 + 1.64828i) q^{33} +(-5.06250 - 5.06250i) q^{34} +(8.24264 + 4.91681i) q^{35} -1.00000i q^{36} +(2.48191 - 2.48191i) q^{37} -4.04701 q^{38} +(3.00000 - 2.00000i) q^{39} -3.62760i q^{40} +(7.53921 - 7.53921i) q^{41} +(-2.27220 - 1.35539i) q^{42} +8.62240i q^{43} +(-1.64828 - 1.64828i) q^{44} +(2.56510 - 2.56510i) q^{45} +(-3.15088 + 3.15088i) q^{46} +(-0.703431 - 0.703431i) q^{47} +1.00000i q^{48} +(-6.15945 + 3.32583i) q^{49} +(5.76961 - 5.76961i) q^{50} +7.15945i q^{51} +(-3.00000 + 2.00000i) q^{52} +2.42677 q^{53} +(-0.707107 + 0.707107i) q^{54} -8.45602i q^{55} +(2.27220 + 1.35539i) q^{56} +(2.86167 + 2.86167i) q^{57} +(-6.89612 - 6.89612i) q^{58} +(10.4560 + 10.4560i) q^{59} +(-2.56510 + 2.56510i) q^{60} +7.15945i q^{61} +5.53921 q^{62} +(0.648285 + 2.56510i) q^{63} -1.00000i q^{64} +(-12.8255 - 2.56510i) q^{65} +2.33103i q^{66} +(-4.53921 - 4.53921i) q^{67} -7.15945i q^{68} +4.45602 q^{69} +(2.35172 + 9.30514i) q^{70} +(-0.456023 - 0.456023i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.48191 + 2.48191i) q^{73} +3.50995 q^{74} -8.15945 q^{75} +(-2.86167 - 2.86167i) q^{76} +(5.29657 + 3.15945i) q^{77} +(3.53553 + 0.707107i) q^{78} +12.0422 q^{79} +(2.56510 - 2.56510i) q^{80} +1.00000 q^{81} +10.6621 q^{82} +(2.70343 - 2.70343i) q^{83} +(-0.648285 - 2.56510i) q^{84} +(18.3647 - 18.3647i) q^{85} +(-6.09696 + 6.09696i) q^{86} +9.75259i q^{87} -2.33103i q^{88} +(4.75044 + 4.75044i) q^{89} +3.62760 q^{90} +(6.39872 - 7.07505i) q^{91} -4.45602 q^{92} +(-3.91681 - 3.91681i) q^{93} -0.994801i q^{94} -14.6809i q^{95} +(-0.707107 + 0.707107i) q^{96} +(-4.49220 + 4.49220i) q^{97} +(-6.70711 - 2.00368i) q^{98} +(1.64828 - 1.64828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^9	$ 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$			1.00000i			0.500000i
$5$	−2.56510	+	2.56510i	−1.14715	+	1.14715i	−0.160035	+	0.987111i	$0.551161\pi$
$5$	−2.56510	+	2.56510i	−1.14715	+	1.14715i	−0.987111	+	0.160035i	$0.948839\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−0.648285	−	2.56510i	−0.245029	−	0.969516i
$7$	−0.648285	−	2.56510i	−0.245029	−	0.969516i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.62760			−1.14715
$11$	−1.64828	+	1.64828i	−0.496977	+	0.496977i	−0.910496	−	0.413519i	$-0.864300\pi$
$11$	−1.64828	+	1.64828i	−0.496977	+	0.496977i	0.413519	+	0.910496i	$0.364300\pi$
$12$	1.00000			0.288675
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$	1.35539	−	2.27220i	0.362244	−	0.607272i
$15$	2.56510	+	2.56510i	0.662305	+	0.662305i
$16$	−1.00000			−0.250000
$17$	−7.15945			−1.73642			−0.868211	−	0.496195i	$-0.834730\pi$
$17$	−7.15945			−1.73642			−0.868211	+	0.496195i	$0.834730\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−2.86167	+	2.86167i	−0.656512	+	0.656512i	−0.954553	−	0.298041i	$-0.903667\pi$
$19$	−2.86167	+	2.86167i	−0.656512	+	0.656512i	0.298041	+	0.954553i	$0.403667\pi$
$20$	−2.56510	−	2.56510i	−0.573573	−	0.573573i
$21$	−2.56510	+	0.648285i	−0.559750	+	0.141467i
$22$	−2.33103			−0.496977
$23$			4.45602i			0.929145i	0.885535	+	0.464573i	$0.153792\pi$
$23$			4.45602i			0.929145i	−0.885535	+	0.464573i	$0.846208\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$		−	8.15945i		−	1.63189i
$26$	−0.707107	+	3.53553i	−0.138675	+	0.693375i
$27$			1.00000i			0.192450i
$28$	2.56510	−	0.648285i	0.484758	−	0.122514i
$29$	−9.75259			−1.81101			−0.905506	−	0.424335i	$-0.860508\pi$
$29$	−9.75259			−1.81101			−0.905506	+	0.424335i	$0.860508\pi$
$30$			3.62760i			0.662305i
$31$	3.91681	−	3.91681i	0.703480	−	0.703480i	−0.261676	−	0.965156i	$-0.584275\pi$
$31$	3.91681	−	3.91681i	0.703480	−	0.703480i	0.965156	+	0.261676i	$0.0842750\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.64828	+	1.64828i	0.286930	+	0.286930i
$34$	−5.06250	−	5.06250i	−0.868211	−	0.868211i
$35$	8.24264	+	4.91681i	1.39326	+	0.831093i
$36$		−	1.00000i		−	0.166667i
$37$	2.48191	−	2.48191i	0.408024	−	0.408024i	−0.473025	−	0.881049i	$-0.656838\pi$
$37$	2.48191	−	2.48191i	0.408024	−	0.408024i	0.881049	+	0.473025i	$0.156838\pi$
$38$	−4.04701			−0.656512
$39$	3.00000	−	2.00000i	0.480384	−	0.320256i
$40$		−	3.62760i		−	0.573573i
$41$	7.53921	−	7.53921i	1.17743	−	1.17743i	0.197029	−	0.980398i	$-0.436871\pi$
$41$	7.53921	−	7.53921i	1.17743	−	1.17743i	0.980398	−	0.197029i	$-0.0631294\pi$
$42$	−2.27220	−	1.35539i	−0.350609	−	0.209141i
$43$			8.62240i			1.31490i	0.753497	+	0.657452i	$0.228366\pi$
$43$			8.62240i			1.31490i	−0.753497	+	0.657452i	$0.771634\pi$
$44$	−1.64828	−	1.64828i	−0.248488	−	0.248488i
$45$	2.56510	−	2.56510i	0.382382	−	0.382382i
$46$	−3.15088	+	3.15088i	−0.464573	+	0.464573i
$47$	−0.703431	−	0.703431i	−0.102606	−	0.102606i	0.653940	−	0.756546i	$-0.273115\pi$
$47$	−0.703431	−	0.703431i	−0.102606	−	0.102606i	−0.756546	+	0.653940i	$0.773115\pi$
$48$			1.00000i			0.144338i
$49$	−6.15945	+	3.32583i	−0.879922	+	0.475118i
$50$	5.76961	−	5.76961i	0.815945	−	0.815945i
$51$			7.15945i			1.00252i
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	2.42677			0.333342			0.166671	−	0.986013i	$-0.446698\pi$
$53$	2.42677			0.333342			0.166671	+	0.986013i	$0.446698\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$		−	8.45602i		−	1.14021i
$56$	2.27220	+	1.35539i	0.303636	+	0.181122i
$57$	2.86167	+	2.86167i	0.379037	+	0.379037i
$58$	−6.89612	−	6.89612i	−0.905506	−	0.905506i
$59$	10.4560	+	10.4560i	1.36126	+	1.36126i	0.872316	+	0.488942i	$0.162617\pi$
$59$	10.4560	+	10.4560i	1.36126	+	1.36126i	0.488942	+	0.872316i	$0.337383\pi$
$60$	−2.56510	+	2.56510i	−0.331153	+	0.331153i
$61$			7.15945i			0.916674i	0.888778	+	0.458337i	$0.151555\pi$
$61$			7.15945i			0.916674i	−0.888778	+	0.458337i	$0.848445\pi$
$62$	5.53921			0.703480
$63$	0.648285	+	2.56510i	0.0816762	+	0.323172i
$64$		−	1.00000i		−	0.125000i
$65$	−12.8255	−	2.56510i	−1.59081	−	0.318161i
$66$			2.33103i			0.286930i
$67$	−4.53921	−	4.53921i	−0.554553	−	0.554553i	0.373199	−	0.927751i	$-0.378261\pi$
$67$	−4.53921	−	4.53921i	−0.554553	−	0.554553i	−0.927751	+	0.373199i	$0.878261\pi$
$68$		−	7.15945i		−	0.868211i
$69$	4.45602			0.536442
$70$	2.35172	+	9.30514i	0.281084	+	1.11218i
$71$	−0.456023	−	0.456023i	−0.0541200	−	0.0541200i	0.679529	−	0.733649i	$-0.262184\pi$
$71$	−0.456023	−	0.456023i	−0.0541200	−	0.0541200i	−0.733649	+	0.679529i	$0.762184\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	2.48191	+	2.48191i	0.290486	+	0.290486i	0.837272	−	0.546786i	$-0.184149\pi$
$73$	2.48191	+	2.48191i	0.290486	+	0.290486i	−0.546786	+	0.837272i	$0.684149\pi$
$74$	3.50995			0.408024
$75$	−8.15945			−0.942173
$76$	−2.86167	−	2.86167i	−0.328256	−	0.328256i
$77$	5.29657	+	3.15945i	0.603600	+	0.360053i
$78$	3.53553	+	0.707107i	0.400320	+	0.0800641i
$79$	12.0422			1.35486			0.677429	−	0.735588i	$-0.263094\pi$
$79$	12.0422			1.35486			0.677429	+	0.735588i	$0.263094\pi$
$80$	2.56510	−	2.56510i	0.286787	−	0.286787i
$81$	1.00000			0.111111
$82$	10.6621			1.17743
$83$	2.70343	−	2.70343i	0.296740	−	0.296740i	−0.542996	−	0.839736i	$-0.682710\pi$
$83$	2.70343	−	2.70343i	0.296740	−	0.296740i	0.839736	+	0.542996i	$0.182710\pi$
$84$	−0.648285	−	2.56510i	−0.0707337	−	0.279875i
$85$	18.3647	−	18.3647i	1.99193	−	1.99193i
$86$	−6.09696	+	6.09696i	−0.657452	+	0.657452i
$87$			9.75259i			1.04559i
$88$		−	2.33103i		−	0.248488i
$89$	4.75044	+	4.75044i	0.503546	+	0.503546i	0.912538	−	0.408992i	$-0.134120\pi$
$89$	4.75044	+	4.75044i	0.503546	+	0.503546i	−0.408992	+	0.912538i	$0.634120\pi$
$90$	3.62760			0.382382
$91$	6.39872	−	7.07505i	0.670769	−	0.741667i
$92$	−4.45602			−0.464573
$93$	−3.91681	−	3.91681i	−0.406155	−	0.406155i
$94$		−	0.994801i		−	0.102606i
$95$		−	14.6809i		−	1.50623i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−4.49220	+	4.49220i	−0.456114	+	0.456114i	−0.897378	−	0.441264i	$-0.854530\pi$
$97$	−4.49220	+	4.49220i	−0.456114	+	0.456114i	0.441264	+	0.897378i	$0.354530\pi$
$98$	−6.70711	−	2.00368i	−0.677520	−	0.202402i
$99$	1.64828	−	1.64828i	0.165659	−	0.165659i
$100$	8.15945			0.815945
$101$	3.55696			0.353931			0.176965	−	0.984217i	$-0.443372\pi$
$101$	3.55696			0.353931			0.176965	+	0.984217i	$0.443372\pi$
$102$	−5.06250	+	5.06250i	−0.501262	+	0.501262i
$103$	−9.80437			−0.966053			−0.483027	−	0.875606i	$-0.660463\pi$
$103$	−9.80437			−0.966053			−0.483027	+	0.875606i	$0.660463\pi$
$104$	−3.53553	−	0.707107i	−0.346688	−	0.0693375i
$105$	4.91681	−	8.24264i	0.479832	−	0.804399i
$106$	1.71598	+	1.71598i	0.166671	+	0.166671i
$107$	−0.332748			−0.0321679			−0.0160840	−	0.999871i	$-0.505120\pi$
$107$	−0.332748			−0.0321679			−0.0160840	+	0.999871i	$0.505120\pi$
$108$	−1.00000			−0.0962250
$109$	−12.9672	−	12.9672i	−1.24203	−	1.24203i	−0.959157	−	0.282875i	$-0.908712\pi$
$109$	−12.9672	−	12.9672i	−1.24203	−	1.24203i	−0.282875	−	0.959157i	$-0.591288\pi$
$110$	5.97931	−	5.97931i	0.570105	−	0.570105i
$111$	−2.48191	−	2.48191i	−0.235573	−	0.235573i
$112$	0.648285	+	2.56510i	0.0612572	+	0.242379i
$113$	−12.6872			−1.19351			−0.596754	−	0.802425i	$-0.703543\pi$
$113$	−12.6872			−1.19351			−0.596754	+	0.802425i	$0.703543\pi$
$114$			4.04701i			0.379037i
$115$	−11.4301	−	11.4301i	−1.06587	−	1.06587i
$116$		−	9.75259i		−	0.905506i
$117$	−2.00000	−	3.00000i	−0.184900	−	0.277350i
$118$			14.7870i			1.36126i
$119$	4.64136	+	18.3647i	0.425473	+	1.68349i
$120$	−3.62760			−0.331153
$121$			5.56631i			0.506029i
$122$	−5.06250	+	5.06250i	−0.458337	+	0.458337i
$123$	−7.53921	−	7.53921i	−0.679788	−	0.679788i
$124$	3.91681	+	3.91681i	0.351740	+	0.351740i
$125$	8.10431	+	8.10431i	0.724871	+	0.724871i
$126$	−1.35539	+	2.27220i	−0.120748	+	0.202424i
$127$		−	5.94822i		−	0.527820i	−0.964547	−	0.263910i	$-0.914988\pi$
$127$		−	5.94822i		−	0.527820i	0.964547	−	0.263910i	$-0.0850121\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	8.62240			0.759160
$130$	−7.25519	−	10.8828i	−0.636322	−	0.954484i
$131$			0.0292581i			0.00255629i	0.999999	+	0.00127815i	$0.000406847\pi$
$131$			0.0292581i			0.00255629i	−0.999999	+	0.00127815i	$0.999593\pi$
$132$	−1.64828	+	1.64828i	−0.143465	+	0.143465i
$133$	9.19563	+	5.48528i	0.797362	+	0.475634i
$134$		−	6.41941i		−	0.554553i
$135$	−2.56510	−	2.56510i	−0.220768	−	0.220768i
$136$	5.06250	−	5.06250i	0.434106	−	0.434106i
$137$	4.56510	−	4.56510i	0.390023	−	0.390023i	−0.484673	−	0.874695i	$-0.661061\pi$
$137$	4.56510	−	4.56510i	0.390023	−	0.390023i	0.874695	+	0.484673i	$0.161061\pi$
$138$	3.15088	+	3.15088i	0.268221	+	0.268221i
$139$			12.6872i			1.07611i	0.842910	+	0.538055i	$0.180841\pi$
$139$			12.6872i			1.07611i	−0.842910	+	0.538055i	$0.819159\pi$
$140$	−4.91681	+	8.24264i	−0.415547	+	0.696630i
$141$	−0.703431	+	0.703431i	−0.0592395	+	0.0592395i
$142$		−	0.644914i		−	0.0541200i
$143$	−8.24142	−	1.64828i	−0.689182	−	0.137836i
$144$	1.00000			0.0833333
$145$	25.0164	−	25.0164i	2.07750	−	2.07750i
$146$			3.50995i			0.290486i
$147$	3.32583	+	6.15945i	0.274310	+	0.508023i
$148$	2.48191	+	2.48191i	0.204012	+	0.204012i
$149$	13.4021	+	13.4021i	1.09794	+	1.09794i	0.994651	+	0.103291i	$0.0329374\pi$
$149$	13.4021	+	13.4021i	1.09794	+	1.09794i	0.103291	+	0.994651i	$0.467063\pi$
$150$	−5.76961	−	5.76961i	−0.471086	−	0.471086i
$151$	3.02804	−	3.02804i	0.246418	−	0.246418i	−0.573081	−	0.819499i	$-0.694252\pi$
$151$	3.02804	−	3.02804i	0.246418	−	0.246418i	0.819499	+	0.573081i	$0.194252\pi$
$152$		−	4.04701i		−	0.328256i
$153$	7.15945			0.578808
$154$	1.51117	+	5.97931i	0.121773	+	0.481827i
$155$			20.0940i			1.61399i
$156$	2.00000	+	3.00000i	0.160128	+	0.240192i
$157$		−	11.4198i		−	0.911403i	−0.890133	−	0.455701i	$-0.849388\pi$
$157$		−	11.4198i		−	0.911403i	0.890133	−	0.455701i	$-0.150612\pi$
$158$	8.51515	+	8.51515i	0.677429	+	0.677429i
$159$		−	2.42677i		−	0.192455i
$160$	3.62760			0.286787
$161$	11.4301	−	2.88877i	0.900821	−	0.227667i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−9.07627	+	9.07627i	−0.710908	+	0.710908i	−0.966725	−	0.255817i	$-0.917656\pi$
$163$	−9.07627	+	9.07627i	−0.710908	+	0.710908i	0.255817	+	0.966725i	$0.417656\pi$
$164$	7.53921	+	7.53921i	0.588713	+	0.588713i
$165$	−8.45602			−0.658301
$166$	3.82323			0.296740
$167$	3.31554	+	3.31554i	0.256564	+	0.256564i	0.823655	−	0.567091i	$-0.191931\pi$
$167$	3.31554	+	3.31554i	0.256564	+	0.256564i	−0.567091	+	0.823655i	$0.691931\pi$
$168$	1.35539	−	2.27220i	0.104571	−	0.175304i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	25.9716			1.99193
$171$	2.86167	−	2.86167i	0.218837	−	0.218837i
$172$	−8.62240			−0.657452
$173$	−6.05852			−0.460620			−0.230310	−	0.973117i	$-0.573974\pi$
$173$	−6.05852			−0.460620			−0.230310	+	0.973117i	$0.573974\pi$
$174$	−6.89612	+	6.89612i	−0.522794	+	0.522794i
$175$	−20.9298	+	5.28965i	−1.58214	+	0.399860i
$176$	1.64828	−	1.64828i	0.124244	−	0.124244i
$177$	10.4560	−	10.4560i	0.785923	−	0.785923i
$178$			6.71814i			0.503546i
$179$			13.5570i			1.01329i	0.862153	+	0.506647i	$0.169115\pi$
$179$			13.5570i			1.01329i	−0.862153	+	0.506647i	$0.830885\pi$
$180$	2.56510	+	2.56510i	0.191191	+	0.191191i
$181$	−14.5793			−1.08367			−0.541835	−	0.840485i	$-0.682270\pi$
$181$	−14.5793			−1.08367			−0.541835	+	0.840485i	$0.682270\pi$
$182$	9.52740	−	0.478235i	0.706218	−	0.0354491i
$183$	7.15945			0.529242
$184$	−3.15088	−	3.15088i	−0.232286	−	0.232286i
$185$			12.7327i			0.936126i
$186$		−	5.53921i		−	0.406155i
$187$	11.8008	−	11.8008i	0.862961	−	0.862961i
$188$	0.703431	−	0.703431i	0.0513029	−	0.0513029i
$189$	2.56510	−	0.648285i	0.186583	−	0.0471558i
$190$	10.3810	−	10.3810i	0.753115	−	0.753115i
$191$	−26.3837			−1.90906			−0.954528	−	0.298123i	$-0.903640\pi$
$191$	−26.3837			−1.90906			−0.954528	+	0.298123i	$0.903640\pi$
$192$	−1.00000			−0.0721688
$193$	2.86288	−	2.86288i	0.206075	−	0.206075i	−0.596522	−	0.802597i	$-0.703451\pi$
$193$	2.86288	−	2.86288i	0.206075	−	0.206075i	0.802597	+	0.596522i	$0.203451\pi$
$194$	−6.35293			−0.456114
$195$	−2.56510	+	12.8255i	−0.183690	+	0.918452i
$196$	−3.32583	−	6.15945i	−0.237559	−	0.439961i
$197$	−6.21338	−	6.21338i	−0.442685	−	0.442685i	0.450228	−	0.892913i	$-0.351343\pi$
$197$	−6.21338	−	6.21338i	−0.442685	−	0.442685i	−0.892913	+	0.450228i	$0.851343\pi$
$198$	2.33103			0.165659
$199$	−1.63799			−0.116114			−0.0580572	−	0.998313i	$-0.518491\pi$
$199$	−1.63799			−0.116114			−0.0580572	+	0.998313i	$0.518491\pi$
$200$	5.76961	+	5.76961i	0.407973	+	0.407973i
$201$	−4.53921	+	4.53921i	−0.320171	+	0.320171i
$202$	2.51515	+	2.51515i	0.176965	+	0.176965i
$203$	6.32246	+	25.0164i	0.443749	+	1.75580i
$204$	−7.15945			−0.501262
$205$			38.6776i			2.70136i
$206$	−6.93274	−	6.93274i	−0.483027	−	0.483027i
$207$		−	4.45602i		−	0.309715i
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$		−	9.43369i		−	0.652542i
$210$	9.30514	−	2.35172i	0.642116	−	0.162284i
$211$	0.622397			0.0428476			0.0214238	−	0.999770i	$-0.493180\pi$
$211$	0.622397			0.0428476			0.0214238	+	0.999770i	$0.493180\pi$
$212$			2.42677i			0.166671i
$213$	−0.456023	+	0.456023i	−0.0312462	+	0.0312462i
$214$	−0.235288	−	0.235288i	−0.0160840	−	0.0160840i
$215$	−22.1173	−	22.1173i	−1.50839	−	1.50839i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−12.5862	−	7.50780i	−0.854408	−	0.509663i
$218$		−	18.3384i		−	1.24203i
$219$	2.48191	−	2.48191i	0.167712	−	0.167712i
$220$	8.45602			0.570105
$221$	−14.3189	−	21.4784i	−0.963194	−	1.44479i
$222$		−	3.50995i		−	0.235573i
$223$	−15.5615	+	15.5615i	−1.04208	+	1.04208i	−0.0430034	+	0.999075i	$0.513693\pi$
$223$	−15.5615	+	15.5615i	−1.04208	+	1.04208i	−0.999075	+	0.0430034i	$0.986307\pi$
$224$	−1.35539	+	2.27220i	−0.0905609	+	0.151818i
$225$			8.15945i			0.543964i
$226$	−8.97117	−	8.97117i	−0.596754	−	0.596754i
$227$	1.15945	−	1.15945i	0.0769556	−	0.0769556i	−0.667581	−	0.744537i	$-0.732670\pi$
$227$	1.15945	−	1.15945i	0.0769556	−	0.0769556i	0.744537	+	0.667581i	$0.232670\pi$
$228$	−2.86167	+	2.86167i	−0.189519	+	0.189519i
$229$	4.15945	+	4.15945i	0.274864	+	0.274864i	0.831055	−	0.556190i	$-0.187737\pi$
$229$	4.15945	+	4.15945i	0.274864	+	0.274864i	−0.556190	+	0.831055i	$0.687737\pi$
$230$		−	16.1647i		−	1.06587i
$231$	3.15945	−	5.29657i	0.207877	−	0.348489i
$232$	6.89612	−	6.89612i	0.452753	−	0.452753i
$233$		−	10.7974i		−	0.707364i	−0.935366	−	0.353682i	$-0.884929\pi$
$233$		−	10.7974i		−	0.707364i	0.935366	−	0.353682i	$-0.115071\pi$
$234$	0.707107	−	3.53553i	0.0462250	−	0.231125i
$235$	3.60874			0.235408
$236$	−10.4560	+	10.4560i	−0.680629	+	0.680629i
$237$		−	12.0422i		−	0.782228i
$238$	−9.70386	+	16.2677i	−0.629008	+	1.05448i
$239$	16.1501	+	16.1501i	1.04466	+	1.04466i	0.998955	+	0.0457083i	$0.0145545\pi$
$239$	16.1501	+	16.1501i	1.04466	+	1.04466i	0.0457083	+	0.998955i	$0.485446\pi$
$240$	−2.56510	−	2.56510i	−0.165576	−	0.165576i
$241$	3.45602	+	3.45602i	0.222622	+	0.222622i	0.809602	−	0.586980i	$-0.199683\pi$
$241$	3.45602	+	3.45602i	0.222622	+	0.222622i	−0.586980	+	0.809602i	$0.699683\pi$
$242$	−3.93598	+	3.93598i	−0.253014	+	0.253014i
$243$		−	1.00000i		−	0.0641500i
$244$	−7.15945			−0.458337
$245$	7.26853	−	24.3307i	0.464369	−	1.55443i
$246$		−	10.6621i		−	0.679788i
$247$	−14.3083	−	2.86167i	−0.910418	−	0.182084i
$248$			5.53921i			0.351740i
$249$	−2.70343	−	2.70343i	−0.171323	−	0.171323i
$250$			11.4612i			0.724871i
$251$	−5.64230			−0.356139			−0.178069	−	0.984018i	$-0.556985\pi$
$251$	−5.64230			−0.356139			−0.178069	+	0.984018i	$0.556985\pi$
$252$	−2.56510	+	0.648285i	−0.161586	+	0.0408381i
$253$	−7.34480	−	7.34480i	−0.461763	−	0.461763i
$254$	4.20603	−	4.20603i	0.263910	−	0.263910i
$255$	−18.3647	−	18.3647i	−1.15004	−	1.15004i
$256$	1.00000			0.0625000
$257$	25.0199			1.56070			0.780349	−	0.625344i	$-0.215041\pi$
$257$	25.0199			1.56070			0.780349	+	0.625344i	$0.215041\pi$
$258$	6.09696	+	6.09696i	0.379580	+	0.379580i
$259$	−7.97533	−	4.75736i	−0.495563	−	0.295608i
$260$	2.56510	−	12.8255i	0.159081	−	0.795403i
$261$	9.75259			0.603670
$262$	−0.0206886	+	0.0206886i	−0.00127815	+	0.00127815i
$263$	−12.1525			−0.749357			−0.374679	−	0.927155i	$-0.622247\pi$
$263$	−12.1525			−0.749357			−0.374679	+	0.927155i	$0.622247\pi$
$264$	−2.33103			−0.143465
$265$	−6.22489	+	6.22489i	−0.382392	+	0.382392i
$266$	2.62361	+	10.3810i	0.160864	+	0.636498i
$267$	4.75044	−	4.75044i	0.290722	−	0.290722i
$268$	4.53921	−	4.53921i	0.277276	−	0.277276i
$269$		−	19.9482i		−	1.21626i	−0.793836	−	0.608132i	$-0.791919\pi$
$269$		−	19.9482i		−	1.21626i	0.793836	−	0.608132i	$-0.208081\pi$
$270$		−	3.62760i		−	0.220768i
$271$	−8.31432	−	8.31432i	−0.505059	−	0.505059i	0.407947	−	0.913006i	$-0.366245\pi$
$271$	−8.31432	−	8.31432i	−0.505059	−	0.505059i	−0.913006	+	0.407947i	$0.866245\pi$
$272$	7.15945			0.434106
$273$	−7.07505	−	6.39872i	−0.428201	−	0.387268i
$274$	6.45602			0.390023
$275$	13.4491	+	13.4491i	0.811011	+	0.811011i
$276$			4.45602i			0.268221i
$277$			5.55696i			0.333885i	0.985967	+	0.166943i	$0.0533895\pi$
$277$			5.55696i			0.333885i	−0.985967	+	0.166943i	$0.946611\pi$
$278$	−8.97117	+	8.97117i	−0.538055	+	0.538055i
$279$	−3.91681	+	3.91681i	−0.234493	+	0.234493i
$280$	−9.30514	+	2.35172i	−0.556088	+	0.140542i
$281$	−11.4807	+	11.4807i	−0.684881	+	0.684881i	−0.961096	−	0.276215i	$-0.910920\pi$
$281$	−11.4807	+	11.4807i	−0.684881	+	0.684881i	0.276215	+	0.961096i	$0.410920\pi$
$282$	−0.994801			−0.0592395
$283$	6.44735			0.383255			0.191627	−	0.981468i	$-0.438623\pi$
$283$	6.44735			0.383255			0.191627	+	0.981468i	$0.438623\pi$
$284$	0.456023	−	0.456023i	0.0270600	−	0.0270600i
$285$	−14.6809			−0.869622
$286$	−4.66205	−	6.99308i	−0.275673	−	0.413509i
$287$	−24.2264	−	14.4513i	−1.43004	−	0.853031i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	34.2578			2.01516
$290$	35.3785			2.07750
$291$	4.49220	+	4.49220i	0.263338	+	0.263338i
$292$	−2.48191	+	2.48191i	−0.145243	+	0.145243i
$293$	−22.1703	−	22.1703i	−1.29520	−	1.29520i	−0.931525	−	0.363677i	$-0.881521\pi$
$293$	−22.1703	−	22.1703i	−1.29520	−	1.29520i	−0.363677	−	0.931525i	$-0.618479\pi$
$294$	−2.00368	+	6.70711i	−0.116857	+	0.391166i
$295$	−53.6414			−3.12313
$296$			3.50995i			0.204012i
$297$	−1.64828	−	1.64828i	−0.0956432	−	0.0956432i
$298$			18.9534i			1.09794i
$299$	−13.3681	+	8.91205i	−0.773095	+	0.515397i
$300$		−	8.15945i		−	0.471086i
$301$	22.1173	−	5.58977i	1.27482	−	0.322189i
$302$	4.28230			0.246418
$303$		−	3.55696i		−	0.204342i
$304$	2.86167	−	2.86167i	0.164128	−	0.164128i
$305$	−18.3647	−	18.3647i	−1.05156	−	1.05156i
$306$	5.06250	+	5.06250i	0.289404	+	0.289404i
$307$	5.54613	+	5.54613i	0.316534	+	0.316534i	0.847434	−	0.530900i	$-0.178146\pi$
$307$	5.54613	+	5.54613i	0.316534	+	0.316534i	−0.530900	+	0.847434i	$0.678146\pi$
$308$	−3.15945	+	5.29657i	−0.180027	+	0.301800i
$309$			9.80437i			0.557751i
$310$	−14.2086	+	14.2086i	−0.806995	+	0.806995i
$311$	−15.6648			−0.888270			−0.444135	−	0.895960i	$-0.646489\pi$
$311$	−15.6648			−0.888270			−0.444135	+	0.895960i	$0.646489\pi$
$312$	−0.707107	+	3.53553i	−0.0400320	+	0.200160i
$313$			2.58640i			0.146192i	0.997325	+	0.0730959i	$0.0232879\pi$
$313$			2.58640i			0.146192i	−0.997325	+	0.0730959i	$0.976712\pi$
$314$	8.07505	−	8.07505i	0.455701	−	0.455701i
$315$	−8.24264	−	4.91681i	−0.464420	−	0.277031i
$316$			12.0422i			0.677429i
$317$	5.33059	+	5.33059i	0.299396	+	0.299396i	0.840777	−	0.541381i	$-0.182098\pi$
$317$	5.33059	+	5.33059i	0.299396	+	0.299396i	−0.541381	+	0.840777i	$0.682098\pi$
$318$	1.71598	−	1.71598i	0.0962275	−	0.0962275i
$319$	16.0750	−	16.0750i	0.900030	−	0.900030i
$320$	2.56510	+	2.56510i	0.143393	+	0.143393i
$321$			0.332748i			0.0185722i
$322$	10.1250	+	6.03966i	0.564244	+	0.336577i
$323$	20.4880	−	20.4880i	1.13998	−	1.13998i
$324$			1.00000i			0.0555556i
$325$	24.4784	−	16.3189i	1.35782	−	0.905210i
$326$	−12.8358			−0.710908
$327$	−12.9672	+	12.9672i	−0.717087	+	0.717087i
$328$			10.6621i			0.588713i
$329$	−1.34834	+	2.26039i	−0.0743367	+	0.124619i
$330$	−5.97931	−	5.97931i	−0.329150	−	0.329150i
$331$	17.3927	+	17.3927i	0.955991	+	0.955991i	0.999072	−	0.0430801i	$-0.0137171\pi$
$331$	17.3927	+	17.3927i	0.955991	+	0.955991i	−0.0430801	+	0.999072i	$0.513717\pi$
$332$	2.70343	+	2.70343i	0.148370	+	0.148370i
$333$	−2.48191	+	2.48191i	−0.136008	+	0.136008i
$334$			4.68888i			0.256564i
$335$	23.2870			1.27231
$336$	2.56510	−	0.648285i	0.139938	−	0.0353668i
$337$			9.75259i			0.531258i	0.964075	+	0.265629i	$0.0855795\pi$
$337$			9.75259i			0.531258i	−0.964075	+	0.265629i	$0.914420\pi$
$338$	−12.0208	+	4.94975i	−0.653846	+	0.269231i
$339$			12.6872i			0.689072i
$340$	18.3647	+	18.3647i	0.995966	+	0.995966i
$341$			12.9120i			0.699227i
$342$	4.04701			0.218837
$343$	12.5242	+	13.6435i	0.676241	+	0.736681i
$344$	−6.09696	−	6.09696i	−0.328726	−	0.328726i
$345$	−11.4301	+	11.4301i	−0.615378	+	0.615378i
$346$	−4.28402	−	4.28402i	−0.230310	−	0.230310i
$347$	2.38696			0.128139			0.0640693	−	0.997945i	$-0.479592\pi$
$347$	2.38696			0.128139			0.0640693	+	0.997945i	$0.479592\pi$
$348$	−9.75259			−0.522794
$349$	1.27667	+	1.27667i	0.0683383	+	0.0683383i	0.740450	−	0.672112i	$-0.234612\pi$
$349$	1.27667	+	1.27667i	0.0683383	+	0.0683383i	−0.672112	+	0.740450i	$0.734612\pi$
$350$	−18.5399	−	11.0593i	−0.991002	−	0.591142i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	2.33103			0.124244
$353$	−16.3074	+	16.3074i	−0.867955	+	0.867955i	−0.992246	−	0.124291i	$-0.960335\pi$
$353$	−16.3074	+	16.3074i	−0.867955	+	0.867955i	0.124291	+	0.992246i	$0.460335\pi$
$354$	14.7870			0.785923
$355$	2.33949			0.124167
$356$	−4.75044	+	4.75044i	−0.251773	+	0.251773i
$357$	18.3647	−	4.64136i	0.971963	−	0.245647i
$358$	−9.58622	+	9.58622i	−0.506647	+	0.506647i
$359$	16.0130	−	16.0130i	0.845133	−	0.845133i	−0.144388	−	0.989521i	$-0.546121\pi$
$359$	16.0130	−	16.0130i	0.845133	−	0.845133i	0.989521	+	0.144388i	$0.0461214\pi$
$360$			3.62760i			0.191191i
$361$			2.62172i			0.137985i
$362$	−10.3091	−	10.3091i	−0.541835	−	0.541835i
$363$	5.56631			0.292156
$364$	7.07505	+	6.39872i	0.370833	+	0.335384i
$365$	−12.7327			−0.666459
$366$	5.06250	+	5.06250i	0.264621	+	0.264621i
$367$			2.42677i			0.126676i	0.997992	+	0.0633381i	$0.0201746\pi$
$367$			2.42677i			0.126676i	−0.997992	+	0.0633381i	$0.979825\pi$
$368$		−	4.45602i		−	0.232286i
$369$	−7.53921	+	7.53921i	−0.392476	+	0.392476i
$370$	−9.00337	+	9.00337i	−0.468063	+	0.468063i
$371$	−1.57323	−	6.22489i	−0.0816783	−	0.323180i
$372$	3.91681	−	3.91681i	0.203077	−	0.203077i
$373$	−11.8759			−0.614909			−0.307455	−	0.951563i	$-0.599477\pi$
$373$	−11.8759			−0.614909			−0.307455	+	0.951563i	$0.599477\pi$
$374$	16.6889			0.862961
$375$	8.10431	−	8.10431i	0.418505	−	0.418505i
$376$	0.994801			0.0513029
$377$	−19.5052	−	29.2578i	−1.00457	−	1.50685i
$378$	2.27220	+	1.35539i	0.116870	+	0.0697138i
$379$	14.4021	+	14.4021i	0.739786	+	0.739786i	0.972536	−	0.232751i	$-0.0747726\pi$
$379$	14.4021	+	14.4021i	0.739786	+	0.739786i	−0.232751	+	0.972536i	$0.574773\pi$
$380$	14.6809			0.753115
$381$	−5.94822			−0.304737
$382$	−18.6561	−	18.6561i	−0.954528	−	0.954528i
$383$	18.6121	−	18.6121i	0.951034	−	0.951034i	−0.0478217	−	0.998856i	$-0.515228\pi$
$383$	18.6121	−	18.6121i	0.951034	−	0.951034i	0.998856	+	0.0478217i	$0.0152279\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−21.6905	+	5.48191i	−1.10545	+	0.279384i
$386$	4.04873			0.206075
$387$		−	8.62240i		−	0.438301i
$388$	−4.49220	−	4.49220i	−0.228057	−	0.228057i
$389$		−	0.107858i		−	0.00546860i	−0.999996	−	0.00273430i	$-0.999130\pi$
$389$		−	0.107858i		−	0.00546860i	0.999996	−	0.00273430i	$-0.000870356\pi$
$390$	−10.8828	+	7.25519i	−0.551071	+	0.367381i
$391$		−	31.9027i		−	1.61339i
$392$	2.00368	−	6.70711i	0.101201	−	0.338760i
$393$	0.0292581			0.00147588
$394$		−	8.78705i		−	0.442685i
$395$	−30.8895	+	30.8895i	−1.55422	+	1.55422i
$396$	1.64828	+	1.64828i	0.0828294	+	0.0828294i
$397$	18.9320	+	18.9320i	0.950167	+	0.950167i	0.998816	−	0.0486486i	$-0.0154914\pi$
$397$	18.9320	+	18.9320i	0.950167	+	0.950167i	−0.0486486	+	0.998816i	$0.515491\pi$
$398$	−1.15824	−	1.15824i	−0.0580572	−	0.0580572i
$399$	5.48528	−	9.19563i	0.274608	−	0.460357i
$400$			8.15945i			0.407973i
$401$	1.33059	−	1.33059i	0.0664467	−	0.0664467i	−0.673103	−	0.739549i	$-0.735039\pi$
$401$	1.33059	−	1.33059i	0.0664467	−	0.0664467i	0.739549	+	0.673103i	$0.235039\pi$
$402$	−6.41941			−0.320171
$403$	19.5841	+	3.91681i	0.975552	+	0.195110i
$404$			3.55696i			0.176965i
$405$	−2.56510	+	2.56510i	−0.127461	+	0.127461i
$406$	−13.2186	+	22.1599i	−0.656027	+	1.09978i
$407$			8.18179i			0.405556i
$408$	−5.06250	−	5.06250i	−0.250631	−	0.250631i
$409$	−21.6543	+	21.6543i	−1.07074	+	1.07074i	−0.0734389	+	0.997300i	$0.523397\pi$
$409$	−21.6543	+	21.6543i	−1.07074	+	1.07074i	−0.997300	+	0.0734389i	$0.976603\pi$
$410$	−27.3492	+	27.3492i	−1.35068	+	1.35068i
$411$	−4.56510	−	4.56510i	−0.225180	−	0.225180i
$412$		−	9.80437i		−	0.483027i
$413$	20.0422	−	33.5992i	0.986214	−	1.65331i
$414$	3.15088	−	3.15088i	0.154858	−	0.154858i
$415$			13.8691i			0.680809i
$416$	0.707107	−	3.53553i	0.0346688	−	0.173344i
$417$	12.6872			0.621293
$418$	6.67062	−	6.67062i	0.326271	−	0.326271i
$419$			3.41741i			0.166951i	0.996510	+	0.0834757i	$0.0266021\pi$
$419$			3.41741i			0.166951i	−0.996510	+	0.0834757i	$0.973398\pi$
$420$	8.24264	+	4.91681i	0.402200	+	0.239916i
$421$	−1.36201	−	1.36201i	−0.0663801	−	0.0663801i	0.673137	−	0.739517i	$-0.264946\pi$
$421$	−1.36201	−	1.36201i	−0.0663801	−	0.0663801i	−0.739517	+	0.673137i	$0.764946\pi$
$422$	0.440101	+	0.440101i	0.0214238	+	0.0214238i
$423$	0.703431	+	0.703431i	0.0342020	+	0.0342020i
$424$	−1.71598	+	1.71598i	−0.0833355	+	0.0833355i
$425$			58.4172i			2.83365i
$426$	−0.644914			−0.0312462
$427$	18.3647	−	4.64136i	0.888730	−	0.224611i
$428$		−	0.332748i		−	0.0160840i
$429$	−1.64828	+	8.24142i	−0.0795799	+	0.397900i
$430$		−	31.2786i		−	1.50839i
$431$	11.1302	+	11.1302i	0.536123	+	0.536123i	0.922388	−	0.386265i	$-0.126235\pi$
$431$	11.1302	+	11.1302i	0.536123	+	0.536123i	−0.386265	+	0.922388i	$0.626235\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−19.7843			−0.950772			−0.475386	−	0.879777i	$-0.657692\pi$
$433$	−19.7843			−0.950772			−0.475386	+	0.879777i	$0.657692\pi$
$434$	−3.59099	−	14.2086i	−0.172373	−	0.682035i
$435$	−25.0164	−	25.0164i	−1.19944	−	1.19944i
$436$	12.9672	−	12.9672i	0.621016	−	0.621016i
$437$	−12.7517	−	12.7517i	−0.609994	−	0.609994i
$438$	3.50995			0.167712
$439$	26.7749			1.27790			0.638949	−	0.769249i	$-0.279370\pi$
$439$	26.7749			1.27790			0.638949	+	0.769249i	$0.279370\pi$
$440$	5.97931	+	5.97931i	0.285052	+	0.285052i
$441$	6.15945	−	3.32583i	0.293307	−	0.158373i
$442$	5.06250	−	25.3125i	0.240798	−	1.20399i
$443$	28.3587			1.34736			0.673682	−	0.739022i	$-0.264712\pi$
$443$	28.3587			1.34736			0.673682	+	0.739022i	$0.264712\pi$
$444$	2.48191	−	2.48191i	0.117786	−	0.117786i
$445$	−24.3707			−1.15528
$446$	−22.0074			−1.04208
$447$	13.4021	−	13.4021i	0.633897	−	0.633897i
$448$	−2.56510	+	0.648285i	−0.121189	+	0.0306286i
$449$	2.28843	−	2.28843i	0.107998	−	0.107998i	−0.651043	−	0.759041i	$-0.725668\pi$
$449$	2.28843	−	2.28843i	0.107998	−	0.107998i	0.759041	+	0.651043i	$0.225668\pi$
$450$	−5.76961	+	5.76961i	−0.271982	+	0.271982i
$451$			24.8535i			1.17031i
$452$		−	12.6872i		−	0.596754i
$453$	−3.02804	−	3.02804i	−0.142270	−	0.142270i
$454$	1.63972			0.0769556
$455$	1.73484	+	34.5615i	0.0813307	+	1.62027i
$456$	−4.04701			−0.189519
$457$	−5.68091	−	5.68091i	−0.265742	−	0.265742i	0.561640	−	0.827382i	$-0.310171\pi$
$457$	−5.68091	−	5.68091i	−0.265742	−	0.265742i	−0.827382	+	0.561640i	$0.810171\pi$
$458$			5.88236i			0.274864i
$459$		−	7.15945i		−	0.334175i
$460$	11.4301	−	11.4301i	0.532933	−	0.532933i
$461$	−15.6953	+	15.6953i	−0.731003	+	0.731003i	−0.970818	−	0.239816i	$-0.922913\pi$
$461$	−15.6953	+	15.6953i	−0.731003	+	0.731003i	0.239816	+	0.970818i	$0.422913\pi$
$462$	5.97931	−	1.51117i	0.278183	−	0.0703059i
$463$	−11.2324	+	11.2324i	−0.522012	+	0.522012i	−0.918179	−	0.396167i	$-0.870340\pi$
$463$	−11.2324	+	11.2324i	−0.522012	+	0.522012i	0.396167	+	0.918179i	$0.370340\pi$
$464$	9.75259			0.452753
$465$	20.0940			0.931838
$466$	7.63495	−	7.63495i	0.353682	−	0.353682i
$467$	2.81997			0.130492			0.0652462	−	0.997869i	$-0.479217\pi$
$467$	2.81997			0.130492			0.0652462	+	0.997869i	$0.479217\pi$
$468$	3.00000	−	2.00000i	0.138675	−	0.0924500i
$469$	−8.70082	+	14.5862i	−0.401766	+	0.673529i
$470$	2.55176	+	2.55176i	0.117704	+	0.117704i
$471$	−11.4198			−0.526199
$472$	−14.7870			−0.680629
$473$	−14.2122	−	14.2122i	−0.653476	−	0.653476i
$474$	8.51515	−	8.51515i	0.391114	−	0.391114i
$475$	23.3496	+	23.3496i	1.07136	+	1.07136i
$476$	−18.3647	+	4.64136i	−0.841745	+	0.212737i
$477$	−2.42677			−0.111114
$478$			22.8397i			1.04466i
$479$	−23.0456	−	23.0456i	−1.05298	−	1.05298i	−0.998516	−	0.0544653i	$-0.982655\pi$
$479$	−23.0456	−	23.0456i	−1.05298	−	1.05298i	−0.0544653	−	0.998516i	$-0.517345\pi$
$480$		−	3.62760i		−	0.165576i
$481$	12.4096	+	2.48191i	0.565827	+	0.113165i
$482$			4.88755i			0.222622i
$483$	−2.88877	−	11.4301i	−0.131444	−	0.520089i
$484$	−5.56631			−0.253014
$485$		−	23.0459i		−	1.04646i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	26.3503	+	26.3503i	1.19405	+	1.19405i	0.975921	+	0.218126i	$0.0699945\pi$
$487$	26.3503	+	26.3503i	1.19405	+	1.19405i	0.218126	+	0.975921i	$0.430005\pi$
$488$	−5.06250	−	5.06250i	−0.229169	−	0.229169i
$489$	9.07627	+	9.07627i	0.410443	+	0.410443i
$490$	22.3440	−	12.0648i	1.00940	−	0.545030i
$491$			11.7819i			0.531707i	0.964013	+	0.265854i	$0.0856538\pi$
$491$			11.7819i			0.531707i	−0.964013	+	0.265854i	$0.914346\pi$
$492$	7.53921	−	7.53921i	0.339894	−	0.339894i
$493$	69.8232			3.14468
$494$	−8.09402	−	12.1410i	−0.364167	−	0.546251i
$495$			8.45602i			0.380070i
$496$	−3.91681	+	3.91681i	−0.175870	+	0.175870i
$497$	−0.874111	+	1.46538i	−0.0392093	+	0.0657312i
$498$		−	3.82323i		−	0.171323i
$499$	−25.6014	−	25.6014i	−1.14607	−	1.14607i	−0.987318	−	0.158756i	$-0.949252\pi$
$499$	−25.6014	−	25.6014i	−1.14607	−	1.14607i	−0.158756	−	0.987318i	$-0.550748\pi$
$500$	−8.10431	+	8.10431i	−0.362436	+	0.362436i
$501$	3.31554	−	3.31554i	0.148127	−	0.148127i
$502$	−3.98971	−	3.98971i	−0.178069	−	0.178069i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−2.27220	−	1.35539i	−0.101212	−	0.0603739i
$505$	−9.12395	+	9.12395i	−0.406011	+	0.406011i
$506$		−	10.3871i		−	0.461763i
$507$	12.0000	+	5.00000i	0.532939	+	0.222058i
$508$	5.94822			0.263910
$509$	−24.4927	+	24.4927i	−1.08562	+	1.08562i	−0.0896482	+	0.995973i	$0.528574\pi$
$509$	−24.4927	+	24.4927i	−1.08562	+	1.08562i	−0.995973	+	0.0896482i	$0.971426\pi$
$510$		−	25.9716i		−	1.15004i
$511$	4.75736	−	7.97533i	0.210453	−	0.352808i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.86167	−	2.86167i	−0.126346	−	0.126346i
$514$	17.6917	+	17.6917i	0.780349	+	0.780349i
$515$	25.1492	−	25.1492i	1.10820	−	1.10820i
$516$			8.62240i			0.379580i
$517$	2.31891			0.101985
$518$	−2.27545	−	9.00337i	−0.0999775	−	0.395585i
$519$			6.05852i			0.265939i
$520$	10.8828	−	7.25519i	0.477242	−	0.318161i
$521$			24.7188i			1.08295i	0.840716	+	0.541476i	$0.182134\pi$
$521$			24.7188i			1.08295i	−0.840716	+	0.541476i	$0.817866\pi$
$522$	6.89612	+	6.89612i	0.301835	+	0.301835i
$523$		−	8.22489i		−	0.359649i	−0.983699	−	0.179825i	$-0.942447\pi$
$523$		−	8.22489i		−	0.359649i	0.983699	−	0.179825i	$-0.0575530\pi$
$524$	−0.0292581			−0.00127815
$525$	5.28965	+	20.9298i	0.230859	+	0.913451i
$526$	−8.59314	−	8.59314i	−0.374679	−	0.374679i
$527$	−28.0422	+	28.0422i	−1.22154	+	1.22154i
$528$	−1.64828	−	1.64828i	−0.0717324	−	0.0717324i
$529$	3.14386			0.136689
$530$	−8.80332			−0.382392
$531$	−10.4560	−	10.4560i	−0.453753	−	0.453753i
$532$	−5.48528	+	9.19563i	−0.237817	+	0.398681i
$533$	37.6961	+	7.53921i	1.63280	+	0.326559i
$534$	6.71814			0.290722
$535$	0.853530	−	0.853530i	0.0369013	−	0.0369013i
$536$	6.41941			0.277276
$537$	13.5570			0.585026
$538$	14.1055	−	14.1055i	0.608132	−	0.608132i
$539$	4.67062	−	15.6344i	0.201178	−	0.673423i
$540$	2.56510	−	2.56510i	0.110384	−	0.110384i
$541$	15.1691	−	15.1691i	0.652169	−	0.652169i	−0.301346	−	0.953515i	$-0.597436\pi$
$541$	15.1691	−	15.1691i	0.652169	−	0.652169i	0.953515	+	0.301346i	$0.0974358\pi$
$542$		−	11.7582i		−	0.505059i
$543$			14.5793i			0.625658i
$544$	5.06250	+	5.06250i	0.217053	+	0.217053i
$545$	66.5242			2.84959
$546$	−0.478235	−	9.52740i	−0.0204666	−	0.407735i
$547$	−15.2261			−0.651020			−0.325510	−	0.945539i	$-0.605536\pi$
$547$	−15.2261			−0.651020			−0.325510	+	0.945539i	$0.605536\pi$
$548$	4.56510	+	4.56510i	0.195011	+	0.195011i
$549$		−	7.15945i		−	0.305558i
$550$			19.0199i			0.811011i
$551$	27.9087	−	27.9087i	1.18895	−	1.18895i
$552$	−3.15088	+	3.15088i	−0.134111	+	0.134111i
$553$	−7.80680	−	30.8895i	−0.331979	−	1.31356i
$554$	−3.92936	+	3.92936i	−0.166943	+	0.166943i
$555$	12.7327			0.540473
$556$	−12.6872			−0.538055
$557$	24.0893	−	24.0893i	1.02069	−	1.02069i	0.0209130	−	0.999781i	$-0.493343\pi$
$557$	24.0893	−	24.0893i	1.02069	−	1.02069i	0.999781	−	0.0209130i	$-0.00665731\pi$
$558$	−5.53921			−0.234493
$559$	−25.8672	+	17.2448i	−1.09407	+	0.729377i
$560$	−8.24264	−	4.91681i	−0.348315	−	0.207773i
$561$	−11.8008	−	11.8008i	−0.498231	−	0.498231i
$562$	−16.2362			−0.684881
$563$	31.8346			1.34167			0.670835	−	0.741607i	$-0.265936\pi$
$563$	31.8346			1.34167			0.670835	+	0.741607i	$0.265936\pi$
$564$	−0.703431	−	0.703431i	−0.0296198	−	0.0296198i
$565$	32.5438	−	32.5438i	1.36913	−	1.36913i
$566$	4.55896	+	4.55896i	0.191627	+	0.191627i
$567$	−0.648285	−	2.56510i	−0.0272254	−	0.107724i
$568$	0.644914			0.0270600
$569$			15.2218i			0.638130i	0.947733	+	0.319065i	$0.103369\pi$
$569$			15.2218i			0.638130i	−0.947733	+	0.319065i	$0.896631\pi$
$570$	−10.3810	−	10.3810i	−0.434811	−	0.434811i
$571$			2.53462i			0.106071i	0.998593	+	0.0530353i	$0.0168896\pi$
$571$			2.53462i			0.106071i	−0.998593	+	0.0530353i	$0.983110\pi$
$572$	1.64828	−	8.24142i	0.0689182	−	0.344591i
$573$			26.3837i			1.10219i
$574$	−6.91205	−	27.3492i	−0.288503	−	1.14153i
$575$	36.3587			1.51626
$576$			1.00000i			0.0416667i
$577$	14.6380	−	14.6380i	0.609388	−	0.609388i	−0.333398	−	0.942786i	$-0.608195\pi$
$577$	14.6380	−	14.6380i	0.609388	−	0.609388i	0.942786	+	0.333398i	$0.108195\pi$
$578$	24.2239	+	24.2239i	1.00758	+	1.00758i
$579$	−2.86288	−	2.86288i	−0.118977	−	0.118977i
$580$	25.0164	+	25.0164i	1.03875	+	1.03875i
$581$	−8.68716	−	5.18197i	−0.360404	−	0.214984i
$582$			6.35293i			0.263338i
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	−3.50995			−0.145243
$585$	12.8255	+	2.56510i	0.530269	+	0.106054i
$586$		−	31.3535i		−	1.29520i
$587$	21.2017	−	21.2017i	0.875088	−	0.875088i	−0.117934	−	0.993021i	$-0.537627\pi$
$587$	21.2017	−	21.2017i	0.875088	−	0.875088i	0.993021	+	0.117934i	$0.0376271\pi$
$588$	−6.15945	+	3.32583i	−0.254012	+	0.137155i
$589$			22.4172i			0.923686i
$590$	−37.9302	−	37.9302i	−1.56156	−	1.56156i
$591$	−6.21338	+	6.21338i	−0.255584	+	0.255584i
$592$	−2.48191	+	2.48191i	−0.102006	+	0.102006i
$593$	−13.9952	−	13.9952i	−0.574715	−	0.574715i	0.358727	−	0.933442i	$-0.383211\pi$
$593$	−13.9952	−	13.9952i	−0.574715	−	0.574715i	−0.933442	+	0.358727i	$0.883211\pi$
$594$		−	2.33103i		−	0.0956432i
$595$	−59.0128	−	35.2017i	−2.41929	−	1.44313i
$596$	−13.4021	+	13.4021i	−0.548971	+	0.548971i
$597$			1.63799i			0.0670386i
$598$	−15.7544	−	3.15088i	−0.644246	−	0.128849i
$599$	26.4603			1.08114			0.540570	−	0.841299i	$-0.318209\pi$
$599$	26.4603			1.08114			0.540570	+	0.841299i	$0.318209\pi$
$600$	5.76961	−	5.76961i	0.235543	−	0.235543i
$601$		−	8.65166i		−	0.352908i	−0.984309	−	0.176454i	$-0.943537\pi$
$601$		−	8.65166i		−	0.352908i	0.984309	−	0.176454i	$-0.0564627\pi$
$602$	19.5919	+	11.6867i	0.798504	+	0.476315i
$603$	4.53921	+	4.53921i	0.184851	+	0.184851i
$604$	3.02804	+	3.02804i	0.123209	+	0.123209i
$605$	−14.2781	−	14.2781i	−0.580489	−	0.580489i
$606$	2.51515	−	2.51515i	0.102171	−	0.102171i
$607$			2.46556i			0.100074i	0.998747	+	0.0500369i	$0.0159339\pi$
$607$			2.46556i			0.100074i	−0.998747	+	0.0500369i	$0.984066\pi$
$608$	4.04701			0.164128
$609$	25.0164	−	6.32246i	1.01371	−	0.256199i
$610$		−	25.9716i		−	1.05156i
$611$	0.703431	−	3.51715i	0.0284578	−	0.142289i
$612$			7.15945i			0.289404i
$613$	−6.36488	−	6.36488i	−0.257075	−	0.257075i	0.566788	−	0.823863i	$-0.308186\pi$
$613$	−6.36488	−	6.36488i	−0.257075	−	0.257075i	−0.823863	+	0.566788i	$0.808186\pi$
$614$			7.84341i			0.316534i
$615$	38.6776			1.55963
$616$	−5.97931	+	1.51117i	−0.240913	+	0.0608867i
$617$	−21.1065	−	21.1065i	−0.849714	−	0.849714i	0.140383	−	0.990097i	$-0.455167\pi$
$617$	−21.1065	−	21.1065i	−0.849714	−	0.849714i	−0.990097	+	0.140383i	$0.955167\pi$
$618$	−6.93274	+	6.93274i	−0.278876	+	0.278876i
$619$	20.3108	+	20.3108i	0.816359	+	0.816359i	0.985578	−	0.169220i	$-0.0541247\pi$
$619$	20.3108	+	20.3108i	0.816359	+	0.816359i	−0.169220	+	0.985578i	$0.554125\pi$
$620$	−20.0940			−0.806995
$621$	−4.45602			−0.178814
$622$	−11.0767	−	11.0767i	−0.444135	−	0.444135i
$623$	9.10570	−	15.2650i	0.364812	−	0.611578i
$624$	−3.00000	+	2.00000i	−0.120096	+	0.0800641i
$625$	−0.779417			−0.0311767
$626$	−1.82886	+	1.82886i	−0.0730959	+	0.0730959i
$627$	−9.43369			−0.376745
$628$	11.4198			0.455701
$629$	−17.7691	+	17.7691i	−0.708501	+	0.708501i
$630$	−2.35172	−	9.30514i	−0.0936946	−	0.370726i
$631$	−10.3788	+	10.3788i	−0.413174	+	0.413174i	−0.882843	−	0.469669i	$-0.844373\pi$
$631$	−10.3788	+	10.3788i	−0.413174	+	0.413174i	0.469669	+	0.882843i	$0.344373\pi$
$632$	−8.51515	+	8.51515i	−0.338715	+	0.338715i
$633$		−	0.622397i		−	0.0247381i
$634$			7.53860i			0.299396i
$635$	15.2578	+	15.2578i	0.605486	+	0.605486i
$636$	2.42677			0.0962275
$637$	−22.2964	−	11.8267i	−0.883415	−	0.468591i
$638$	22.7336			0.900030
$639$	0.456023	+	0.456023i	0.0180400	+	0.0180400i
$640$			3.62760i			0.143393i
$641$			0.168808i			0.00666750i	0.999994	+	0.00333375i	$0.00106117\pi$
$641$			0.168808i			0.00666750i	−0.999994	+	0.00333375i	$0.998939\pi$
$642$	−0.235288	+	0.235288i	−0.00928608	+	0.00928608i
$643$	−23.4995	+	23.4995i	−0.926729	+	0.926729i	−0.997493	−	0.0707640i	$-0.977456\pi$
$643$	−23.4995	+	23.4995i	−0.926729	+	0.926729i	0.0707640	+	0.997493i	$0.477456\pi$
$644$	2.88877	+	11.4301i	0.113834	+	0.450410i
$645$	−22.1173	+	22.1173i	−0.870868	+	0.870868i
$646$	28.9744			1.13998
$647$	−7.68783			−0.302240			−0.151120	−	0.988515i	$-0.548288\pi$
$647$	−7.68783			−0.302240			−0.151120	+	0.988515i	$0.548288\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−34.4690			−1.35303
$650$	28.8480	+	5.76961i	1.13151	+	0.226303i
$651$	−7.50780	+	12.5862i	−0.294254	+	0.493293i
$652$	−9.07627	−	9.07627i	−0.355454	−	0.355454i
$653$	15.9545			0.624347			0.312173	−	0.950025i	$-0.398943\pi$
$653$	15.9545			0.624347			0.312173	+	0.950025i	$0.398943\pi$
$654$	−18.3384			−0.717087
$655$	−0.0750499	−	0.0750499i	−0.00293244	−	0.00293244i
$656$	−7.53921	+	7.53921i	−0.294357	+	0.294357i
$657$	−2.48191	−	2.48191i	−0.0968286	−	0.0968286i
$658$	−2.55176	+	0.644914i	−0.0994780	+	0.0251414i
$659$	−24.5438			−0.956091			−0.478045	−	0.878335i	$-0.658655\pi$
$659$	−24.5438			−0.956091			−0.478045	+	0.878335i	$0.658655\pi$
$660$		−	8.45602i		−	0.329150i
$661$	−3.34817	−	3.34817i	−0.130229	−	0.130229i	0.638988	−	0.769217i	$-0.279353\pi$
$661$	−3.34817	−	3.34817i	−0.130229	−	0.130229i	−0.769217	+	0.638988i	$0.779353\pi$
$662$			24.5970i			0.955991i
$663$	−21.4784	+	14.3189i	−0.834150	+	0.556100i
$664$			3.82323i			0.148370i
$665$	−37.6580	+	9.51741i	−1.46031	+	0.369069i
$666$	−3.50995			−0.136008
$667$		−	43.4578i		−	1.68269i
$668$	−3.31554	+	3.31554i	−0.128282	+	0.128282i
$669$	15.5615	+	15.5615i	0.601644	+	0.601644i
$670$	16.4664	+	16.4664i	0.636153	+	0.636153i
$671$	−11.8008	−	11.8008i	−0.455566	−	0.455566i
$672$	2.27220	+	1.35539i	0.0876522	+	0.0522854i
$673$		−	11.5369i		−	0.444714i	−0.974965	−	0.222357i	$-0.928625\pi$
$673$		−	11.5369i		−	0.444714i	0.974965	−	0.222357i	$-0.0713750\pi$
$674$	−6.89612	+	6.89612i	−0.265629	+	0.265629i
$675$	8.15945			0.314058
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	12.8958i		−	0.495625i	−0.968808	−	0.247812i	$-0.920288\pi$
$677$		−	12.8958i		−	0.495625i	0.968808	−	0.247812i	$-0.0797117\pi$
$678$	−8.97117	+	8.97117i	−0.344536	+	0.344536i
$679$	14.4352	+	8.61071i	0.553971	+	0.330449i
$680$			25.9716i			0.995966i
$681$	−1.15945	−	1.15945i	−0.0444304	−	0.0444304i
$682$	−9.13020	+	9.13020i	−0.349613	+	0.349613i
$683$	14.7785	−	14.7785i	0.565483	−	0.565483i	−0.365377	−	0.930860i	$-0.619060\pi$
$683$	14.7785	−	14.7785i	0.565483	−	0.565483i	0.930860	+	0.365377i	$0.119060\pi$
$684$	2.86167	+	2.86167i	0.109419	+	0.109419i
$685$			23.4198i			0.894826i
$686$	−0.791511	+	18.5033i	−0.0302200	+	0.706461i
$687$	4.15945	−	4.15945i	0.158693	−	0.158693i
$688$		−	8.62240i		−	0.328726i
$689$	4.85353	+	7.28030i	0.184905	+	0.277357i
$690$	−16.1647			−0.615378
$691$	13.4220	−	13.4220i	0.510597	−	0.510597i	−0.404112	−	0.914709i	$-0.632420\pi$
$691$	13.4220	−	13.4220i	0.510597	−	0.510597i	0.914709	+	0.404112i	$0.132420\pi$
$692$		−	6.05852i		−	0.230310i
$693$	−5.29657	−	3.15945i	−0.201200	−	0.120018i
$694$	1.68783	+	1.68783i	0.0640693	+	0.0640693i
$695$	−32.5438	−	32.5438i	−1.23446	−	1.23446i
$696$	−6.89612	−	6.89612i	−0.261397	−	0.261397i
$697$	−53.9766	+	53.9766i	−2.04451	+	2.04451i
$698$			1.80548i			0.0683383i
$699$	−10.7974			−0.408397
$700$	−5.28965	−	20.9298i	−0.199930	−	0.791072i
$701$		−	19.5009i		−	0.736538i	−0.929719	−	0.368269i	$-0.879951\pi$
$701$		−	19.5009i		−	0.736538i	0.929719	−	0.368269i	$-0.120049\pi$
$702$	−3.53553	−	0.707107i	−0.133440	−	0.0266880i
$703$			14.2048i			0.535744i
$704$	1.64828	+	1.64828i	0.0621221	+	0.0621221i
$705$		−	3.60874i		−	0.135913i
$706$	−23.0621			−0.867955
$707$	−2.30592	−	9.12395i	−0.0867232	−	0.343142i
$708$	10.4560	+	10.4560i	0.392961	+	0.392961i
$709$	36.2084	−	36.2084i	1.35984	−	1.35984i	0.485724	−	0.874112i	$-0.338556\pi$
$709$	36.2084	−	36.2084i	1.35984	−	1.35984i	0.874112	−	0.485724i	$-0.161444\pi$
$710$	1.65427	+	1.65427i	0.0620836	+	0.0620836i
$711$	−12.0422			−0.451619
$712$	−6.71814			−0.251773
$713$	17.4534	+	17.4534i	0.653635	+	0.653635i
$714$	16.2677	+	9.70386i	0.608805	+	0.363158i
$715$	25.3681	−	16.9120i	0.948712	−	0.632475i
$716$	−13.5570			−0.506647
$717$	16.1501	−	16.1501i	0.603137	−	0.603137i
$718$	22.6458			0.845133
$719$	31.8404			1.18745			0.593723	−	0.804670i	$-0.297658\pi$
$719$	31.8404			1.18745			0.593723	+	0.804670i	$0.297658\pi$
$720$	−2.56510	+	2.56510i	−0.0955956	+	0.0955956i
$721$	6.35602	+	25.1492i	0.236711	+	0.936604i
$722$	−1.85384	+	1.85384i	−0.0689926	+	0.0689926i
$723$	3.45602	−	3.45602i	0.128531	−	0.128531i
$724$		−	14.5793i		−	0.541835i
$725$			79.5758i			2.95537i
$726$	3.93598	+	3.93598i	0.146078	+	0.146078i
$727$	0.263681			0.00977940			0.00488970	−	0.999988i	$-0.498444\pi$
$727$	0.263681			0.00977940			0.00488970	+	0.999988i	$0.498444\pi$
$728$	0.478235	+	9.52740i	0.0177246	+	0.353109i
$729$	−1.00000			−0.0370370
$730$	−9.00337	−	9.00337i	−0.333230	−	0.333230i
$731$		−	61.7317i		−	2.28323i
$732$			7.15945i			0.264621i
$733$	14.4266	−	14.4266i	0.532858	−	0.532858i	−0.388564	−	0.921422i	$-0.627029\pi$
$733$	14.4266	−	14.4266i	0.532858	−	0.532858i	0.921422	+	0.388564i	$0.127029\pi$
$734$	−1.71598	+	1.71598i	−0.0633381	+	0.0633381i
$735$	−24.3307	−	7.26853i	−0.897450	−	0.268104i
$736$	3.15088	−	3.15088i	0.116143	−	0.116143i
$737$	14.9638			0.551199
$738$	−10.6621			−0.392476
$739$	6.59099	−	6.59099i	0.242453	−	0.242453i	−0.575411	−	0.817864i	$-0.695158\pi$
$739$	6.59099	−	6.59099i	0.242453	−	0.242453i	0.817864	+	0.575411i	$0.195158\pi$
$740$	−12.7327			−0.468063
$741$	−2.86167	+	14.3083i	−0.105126	+	0.525630i
$742$	3.28922	−	5.51411i	0.120751	−	0.202429i
$743$	18.2311	+	18.2311i	0.668835	+	0.668835i	0.957446	−	0.288611i	$-0.0931934\pi$
$743$	18.2311	+	18.2311i	0.668835	+	0.668835i	−0.288611	+	0.957446i	$0.593193\pi$
$744$	5.53921			0.203077
$745$	−68.7554			−2.51900
$746$	−8.39751	−	8.39751i	−0.307455	−	0.307455i
$747$	−2.70343	+	2.70343i	−0.0989133	+	0.0989133i
$748$	11.8008	+	11.8008i	0.431481	+	0.431481i
$749$	0.215715	+	0.853530i	0.00788206	+	0.0311873i
$750$	11.4612			0.418505
$751$			17.5282i			0.639613i	0.947483	+	0.319807i	$0.103618\pi$
$751$			17.5282i			0.639613i	−0.947483	+	0.319807i	$0.896382\pi$
$752$	0.703431	+	0.703431i	0.0256515	+	0.0256515i
$753$			5.64230i			0.205617i
$754$	6.89612	−	34.4806i	0.251142	−	1.25571i
$755$			15.5344i			0.565356i
$756$	0.648285	+	2.56510i	0.0235779	+	0.0932917i
$757$	31.7843			1.15522			0.577610	−	0.816313i	$-0.303986\pi$
$757$	31.7843			1.15522			0.577610	+	0.816313i	$0.303986\pi$
$758$			20.3676i			0.739786i
$759$	−7.34480	+	7.34480i	−0.266599	+	0.266599i
$760$	10.3810	+	10.3810i	0.376557	+	0.376557i
$761$	−1.82886	−	1.82886i	−0.0662961	−	0.0662961i	0.673181	−	0.739477i	$-0.264927\pi$
$761$	−1.82886	−	1.82886i	−0.0662961	−	0.0662961i	−0.739477	+	0.673181i	$0.764927\pi$
$762$	−4.20603	−	4.20603i	−0.152368	−	0.152368i
$763$	−24.8557	+	41.6685i	−0.899836	+	1.50850i
$764$		−	26.3837i		−	0.954528i
$765$	−18.3647	+	18.3647i	−0.663977	+	0.663977i
$766$	26.3215			0.951034
$767$	−10.4560	+	52.2801i	−0.377545	+	1.88773i
$768$		−	1.00000i		−	0.0360844i
$769$	1.20162	−	1.20162i	0.0433314	−	0.0433314i	−0.685109	−	0.728440i	$-0.740245\pi$
$769$	1.20162	−	1.20162i	0.0433314	−	0.0433314i	0.728440	+	0.685109i	$0.240245\pi$
$770$	−19.2138	−	11.4612i	−0.692418	−	0.413034i
$771$		−	25.0199i		−	0.901070i
$772$	2.86288	+	2.86288i	0.103037	+	0.103037i
$773$	2.61687	−	2.61687i	0.0941224	−	0.0941224i	−0.658478	−	0.752600i	$-0.728799\pi$
$773$	2.61687	−	2.61687i	0.0941224	−	0.0941224i	0.752600	+	0.658478i	$0.228799\pi$
$774$	6.09696	−	6.09696i	0.219151	−	0.219151i
$775$	−31.9591	−	31.9591i	−1.14800	−	1.14800i
$776$		−	6.35293i		−	0.228057i
$777$	−4.75736	+	7.97533i	−0.170669	+	0.286113i
$778$	0.0762669	−	0.0762669i	0.00273430	−	0.00273430i
$779$			43.1494i			1.54599i
$780$	−12.8255	−	2.56510i	−0.459226	−	0.0918452i
$781$	1.50331			0.0537927
$782$	22.5586	−	22.5586i	0.806694	−	0.806694i
$783$		−	9.75259i		−	0.348529i
$784$	6.15945	−	3.32583i	0.219980	−	0.118780i
$785$	29.2930	+	29.2930i	1.04551	+	1.04551i
$786$	0.0206886	+	0.0206886i	0.000737938	+	0.000737938i
$787$	23.2324	+	23.2324i	0.828144	+	0.828144i	0.987260	−	0.159116i	$-0.0508644\pi$
$787$	23.2324	+	23.2324i	0.828144	+	0.828144i	−0.159116	+	0.987260i	$0.550864\pi$
$788$	6.21338	−	6.21338i	0.221343	−	0.221343i
$789$			12.1525i			0.432642i
$790$	−43.6844			−1.55422
$791$	8.22489	+	32.5438i	0.292443	+	1.15712i
$792$			2.33103i			0.0828294i
$793$	−21.4784	+	14.3189i	−0.762719	+	0.508479i
$794$			26.7738i			0.950167i
$795$	6.22489	+	6.22489i	0.220774	+	0.220774i
$796$		−	1.63799i		−	0.0580572i
$797$	−33.6371			−1.19149			−0.595744	−	0.803174i	$-0.703143\pi$
$797$	−33.6371			−1.19149			−0.595744	+	0.803174i	$0.703143\pi$
$798$	10.3810	−	2.62361i	0.367482	−	0.0928749i
$799$	5.03618	+	5.03618i	0.178167	+	0.178167i
$800$	−5.76961	+	5.76961i	−0.203986	+	0.203986i
$801$	−4.75044	−	4.75044i	−0.167849	−	0.167849i
$802$	1.88174			0.0664467
$803$	−8.18179			−0.288729
$804$	−4.53921	−	4.53921i	−0.160086	−	0.160086i
$805$	−21.9094	+	36.7294i	−0.772206	+	1.29454i
$806$	11.0784	+	16.6176i	0.390221	+	0.585331i
$807$	−19.9482			−0.702211
$808$	−2.51515	+	2.51515i	−0.0884827	+	0.0884827i
$809$	−20.3165			−0.714289			−0.357145	−	0.934049i	$-0.616250\pi$
$809$	−20.3165			−0.714289			−0.357145	+	0.934049i	$0.616250\pi$
$810$	−3.62760			−0.127461
$811$	11.7152	−	11.7152i	0.411376	−	0.411376i	−0.470842	−	0.882218i	$-0.656050\pi$
$811$	11.7152	−	11.7152i	0.411376	−	0.411376i	0.882218	+	0.470842i	$0.156050\pi$
$812$	−25.0164	+	6.32246i	−0.877902	+	0.221875i
$813$	−8.31432	+	8.31432i	−0.291596	+	0.291596i
$814$	−5.78540	+	5.78540i	−0.202778	+	0.202778i
$815$		−	46.5630i		−	1.63103i
$816$		−	7.15945i		−	0.250631i
$817$	−24.6744	−	24.6744i	−0.863249	−	0.863249i
$818$	−30.6239			−1.07074
$819$	−6.39872	+	7.07505i	−0.223590	+	0.247222i
$820$	−38.6776			−1.35068
$821$	3.79529	+	3.79529i	0.132457	+	0.132457i	0.770227	−	0.637770i	$-0.220143\pi$
$821$	3.79529	+	3.79529i	0.132457	+	0.132457i	−0.637770	+	0.770227i	$0.720143\pi$
$822$		−	6.45602i		−	0.225180i
$823$		−	42.2235i		−	1.47182i	−0.677079	−	0.735910i	$-0.736755\pi$
$823$		−	42.2235i		−	1.47182i	0.677079	−	0.735910i	$-0.263245\pi$
$824$	6.93274	−	6.93274i	0.241513	−	0.241513i
$825$	13.4491	−	13.4491i	0.468238	−	0.468238i
$826$	37.9302	−	9.58622i	1.31976	−	0.333547i
$827$	8.55602	−	8.55602i	0.297522	−	0.297522i	−0.542520	−	0.840043i	$-0.682530\pi$
$827$	8.55602	−	8.55602i	0.297522	−	0.297522i	0.840043	+	0.542520i	$0.182530\pi$
$828$	4.45602			0.154858
$829$	−40.5026			−1.40671			−0.703356	−	0.710838i	$-0.748316\pi$
$829$	−40.5026			−1.40671			−0.703356	+	0.710838i	$0.748316\pi$
$830$	−9.80695	+	9.80695i	−0.340404	+	0.340404i
$831$	5.55696			0.192769
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	44.0983	−	23.8111i	1.52792	−	0.825006i
$834$	8.97117	+	8.97117i	0.310646	+	0.310646i
$835$	−17.0094			−0.588633
$836$	9.43369			0.326271
$837$	3.91681	+	3.91681i	0.135385	+	0.135385i
$838$	−2.41647	+	2.41647i	−0.0834757	+	0.0834757i
$839$	−13.3882	−	13.3882i	−0.462210	−	0.462210i	0.437169	−	0.899379i	$-0.355981\pi$
$839$	−13.3882	−	13.3882i	−0.462210	−	0.462210i	−0.899379	+	0.437169i	$0.855981\pi$
$840$	2.35172	+	9.30514i	0.0811419	+	0.321058i
$841$	66.1131			2.27976
$842$		−	1.92617i		−	0.0663801i
$843$	11.4807	+	11.4807i	0.395416	+	0.395416i
$844$			0.622397i			0.0214238i
$845$	−17.9557	−	43.6067i	−0.617694	−	1.50011i
$846$			0.994801i			0.0342020i
$847$	14.2781	−	3.60856i	0.490603	−	0.123991i
$848$	−2.42677			−0.0833355
$849$		−	6.44735i		−	0.221272i
$850$	−41.3072	+	41.3072i	−1.41683	+	1.41683i
$851$	11.0595	+	11.0595i	0.379113	+	0.379113i
$852$	−0.456023	−	0.456023i	−0.0156231	−	0.0156231i
$853$	−3.51211	−	3.51211i	−0.120252	−	0.120252i	0.644420	−	0.764672i	$-0.277099\pi$
$853$	−3.51211	−	3.51211i	−0.120252	−	0.120252i	−0.764672	+	0.644420i	$0.777099\pi$
$854$	16.2677	+	9.70386i	0.556671	+	0.332059i
$855$			14.6809i			0.502077i
$856$	0.235288	−	0.235288i	0.00804198	−	0.00804198i
$857$	24.3679			0.832391			0.416196	−	0.909275i	$-0.363363\pi$
$857$	24.3679			0.832391			0.416196	+	0.909275i	$0.363363\pi$
$858$	−6.99308	+	4.66205i	−0.238740	+	0.159160i
$859$			2.26749i			0.0773658i	0.999252	+	0.0386829i	$0.0123162\pi$
$859$			2.26749i			0.0773658i	−0.999252	+	0.0386829i	$0.987684\pi$
$860$	22.1173	−	22.1173i	0.754193	−	0.754193i
$861$	−14.4513	+	24.2264i	−0.492498	+	0.825632i
$862$			15.7405i			0.536123i
$863$	−24.0154	−	24.0154i	−0.817494	−	0.817494i	0.168250	−	0.985744i	$-0.446188\pi$
$863$	−24.0154	−	24.0154i	−0.817494	−	0.817494i	−0.985744	+	0.168250i	$0.946188\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	15.5407	−	15.5407i	0.528399	−	0.528399i
$866$	−13.9896	−	13.9896i	−0.475386	−	0.475386i
$867$		−	34.2578i		−	1.16346i
$868$	7.50780	−	12.5862i	0.254831	−	0.427204i
$869$	−19.8490	+	19.8490i	−0.673333	+	0.673333i
$870$		−	35.3785i		−	1.19944i
$871$	4.53921	−	22.6961i	0.153805	−	0.769026i
$872$	18.3384			0.621016
$873$	4.49220	−	4.49220i	0.152038	−	0.152038i
$874$		−	18.0336i		−	0.609994i
$875$	15.5344	−	26.0422i	0.525160	−	0.880388i
$876$	2.48191	+	2.48191i	0.0838560	+	0.0838560i
$877$	−38.9474	−	38.9474i	−1.31516	−	1.31516i	−0.917559	−	0.397601i	$-0.869843\pi$
$877$	−38.9474	−	38.9474i	−1.31516	−	1.31516i	−0.397601	−	0.917559i	$-0.630157\pi$
$878$	18.9327	+	18.9327i	0.638949	+	0.638949i
$879$	−22.1703	+	22.1703i	−0.747785	+	0.747785i
$880$			8.45602i			0.285052i
$881$	−19.7569			−0.665627			−0.332813	−	0.942993i	$-0.607998\pi$
$881$	−19.7569			−0.665627			−0.332813	+	0.942993i	$0.607998\pi$
$882$	6.70711	+	2.00368i	0.225840	+	0.0674673i
$883$			19.9027i			0.669779i	0.942257	+	0.334889i	$0.108699\pi$
$883$			19.9027i			0.669779i	−0.942257	+	0.334889i	$0.891301\pi$
$884$	21.4784	−	14.3189i	0.722395	−	0.481597i
$885$			53.6414i			1.80314i
$886$	20.0526	+	20.0526i	0.673682	+	0.673682i
$887$		−	1.87156i		−	0.0628409i	−0.999506	−	0.0314204i	$-0.989997\pi$
$887$		−	1.87156i		−	0.0628409i	0.999506	−	0.0314204i	$-0.0100031\pi$
$888$	3.50995			0.117786
$889$	−15.2578	+	3.85614i	−0.511729	+	0.129331i
$890$	−17.2327	−	17.2327i	−0.577641	−	0.577641i
$891$	−1.64828	+	1.64828i	−0.0552196	+	0.0552196i
$892$	−15.5615	−	15.5615i	−0.521039	−	0.521039i
$893$	4.02597			0.134724
$894$	18.9534			0.633897
$895$	−34.7749	−	34.7749i	−1.16240	−	1.16240i
$896$	−2.27220	−	1.35539i	−0.0759090	−	0.0452805i
$897$	8.91205	+	13.3681i	0.297565	+	0.446347i
$898$	3.23633			0.107998
$899$	−38.1991	+	38.1991i	−1.27401	+	1.27401i
$900$	−8.15945			−0.271982
$901$	−17.3743			−0.578822
$902$	−17.5741	+	17.5741i	−0.585154	+	0.585154i
$903$	−5.58977	−	22.1173i	−0.186016	−	0.736017i
$904$	8.97117	−	8.97117i	0.298377	−	0.298377i
$905$	37.3973	−	37.3973i	1.24313	−	1.24313i
$906$		−	4.28230i		−	0.142270i
$907$			35.5637i			1.18087i	0.807084	+	0.590437i	$0.201044\pi$
$907$			35.5637i			1.18087i	−0.807084	+	0.590437i	$0.798956\pi$
$908$	1.15945	+	1.15945i	0.0384778	+	0.0384778i
$909$	−3.55696			−0.117977
$910$	−23.2120	+	25.6654i	−0.769470	+	0.850801i
$911$	−19.6150			−0.649873			−0.324937	−	0.945736i	$-0.605343\pi$
$911$	−19.6150			−0.649873			−0.324937	+	0.945736i	$0.605343\pi$
$912$	−2.86167	−	2.86167i	−0.0947593	−	0.0947593i
$913$			8.91205i			0.294946i
$914$		−	8.03402i		−	0.265742i
$915$	−18.3647	+	18.3647i	−0.607118	+	0.607118i
$916$	−4.15945	+	4.15945i	−0.137432	+	0.137432i
$917$	0.0750499	−	0.0189676i	0.00247837	−	0.000626365i
$918$	5.06250	−	5.06250i	0.167087	−	0.167087i
$919$	−34.3682			−1.13370			−0.566852	−	0.823820i	$-0.691839\pi$
$919$	−34.3682			−1.13370			−0.566852	+	0.823820i	$0.691839\pi$
$920$	16.1647			0.532933
$921$	5.54613	−	5.54613i	0.182751	−	0.182751i
$922$	−22.1965			−0.731003
$923$	0.456023	−	2.28012i	0.0150102	−	0.0750509i
$924$	5.29657	+	3.15945i	0.174244	+	0.103938i
$925$	−20.2510	−	20.2510i	−0.665850	−	0.665850i
$926$	−15.8849			−0.522012
$927$	9.80437			0.322018
$928$	6.89612	+	6.89612i	0.226376	+	0.226376i
$929$	−21.5546	+	21.5546i	−0.707184	+	0.707184i	−0.965942	−	0.258758i	$-0.916687\pi$
$929$	−21.5546	+	21.5546i	−0.707184	+	0.707184i	0.258758	+	0.965942i	$0.416687\pi$
$930$	14.2086	+	14.2086i	0.465919	+	0.465919i
$931$	8.10890	−	27.1437i	0.265758	−	0.889599i
$932$	10.7974			0.353682
$933$			15.6648i			0.512843i
$934$	1.99402	+	1.99402i	0.0652462	+	0.0652462i
$935$			60.5405i			1.97989i
$936$	3.53553	+	0.707107i	0.115563	+	0.0231125i
$937$		−	15.9071i		−	0.519661i	−0.965654	−	0.259831i	$-0.916333\pi$
$937$		−	15.9071i		−	0.519661i	0.965654	−	0.259831i	$-0.0836667\pi$
$938$	−16.4664	+	4.16161i	−0.537648	+	0.135881i
$939$	2.58640			0.0844039
$940$			3.60874i			0.117704i
$941$	−10.1348	+	10.1348i	−0.330384	+	0.330384i	−0.852732	−	0.522348i	$-0.825056\pi$
$941$	−10.1348	+	10.1348i	−0.330384	+	0.330384i	0.522348	+	0.852732i	$0.325056\pi$
$942$	−8.07505	−	8.07505i	−0.263099	−	0.263099i
$943$	33.5949	+	33.5949i	1.09400	+	1.09400i
$944$	−10.4560	−	10.4560i	−0.340315	−	0.340315i
$945$	−4.91681	+	8.24264i	−0.159944	+	0.268133i
$946$		−	20.0990i		−	0.653476i
$947$	8.77848	−	8.77848i	0.285262	−	0.285262i	−0.549941	−	0.835203i	$-0.685350\pi$
$947$	8.77848	−	8.77848i	0.285262	−	0.285262i	0.835203	+	0.549941i	$0.185350\pi$
$948$	12.0422			0.391114
$949$	−2.48191	+	12.4096i	−0.0805662	+	0.402831i
$950$			33.0214i			1.07136i
$951$	5.33059	−	5.33059i	0.172856	−	0.172856i
$952$	−16.2677	−	9.70386i	−0.527241	−	0.314504i
$953$			41.5076i			1.34456i	0.740295	+	0.672282i	$0.234686\pi$
$953$			41.5076i			1.34456i	−0.740295	+	0.672282i	$0.765314\pi$
$954$	−1.71598	−	1.71598i	−0.0555570	−	0.0555570i
$955$	67.6767	−	67.6767i	2.18997	−	2.18997i
$956$	−16.1501	+	16.1501i	−0.522332	+	0.522332i
$957$	−16.0750	−	16.0750i	−0.519633	−	0.519633i
$958$		−	32.5914i		−	1.05298i
$959$	−14.6694	−	8.75044i	−0.473700	−	0.282566i
$960$	2.56510	−	2.56510i	0.0827882	−	0.0827882i
$961$			0.317151i			0.0102307i
$962$	7.01990	+	10.5299i	0.226331	+	0.339496i
$963$	0.332748			0.0107226
$964$	−3.45602	+	3.45602i	−0.111311	+	0.111311i
$965$			14.6872i			0.472796i
$966$	6.03966	−	10.1250i	0.194323	−	0.325766i
$967$	−14.2124	−	14.2124i	−0.457041	−	0.457041i	0.440642	−	0.897683i	$-0.354751\pi$
$967$	−14.2124	−	14.2124i	−0.457041	−	0.457041i	−0.897683	+	0.440642i	$0.854751\pi$
$968$	−3.93598	−	3.93598i	−0.126507	−	0.126507i
$969$	−20.4880	−	20.4880i	−0.658169	−	0.658169i
$970$	16.2959	−	16.2959i	0.523230	−	0.523230i
$971$			48.8259i			1.56690i	0.621457	+	0.783448i	$0.286541\pi$
$971$			48.8259i			1.56690i	−0.621457	+	0.783448i	$0.713459\pi$
$972$	1.00000			0.0320750
$973$	32.5438	−	8.22489i	1.04331	−	0.263678i
$974$			37.2650i			1.19405i
$975$	−16.3189	−	24.4784i	−0.522623	−	0.783935i
$976$		−	7.15945i		−	0.229169i
$977$	−28.0635	−	28.0635i	−0.897832	−	0.897832i	0.0974119	−	0.995244i	$-0.468944\pi$
$977$	−28.0635	−	28.0635i	−0.897832	−	0.897832i	−0.995244	+	0.0974119i	$0.968944\pi$
$978$			12.8358i			0.410443i
$979$	−15.6602			−0.500501
$980$	24.3307	+	7.26853i	0.777215	+	0.232185i
$981$	12.9672	+	12.9672i	0.414011	+	0.414011i
$982$	−8.33103	+	8.33103i	−0.265854	+	0.265854i
$983$	24.2698	+	24.2698i	0.774087	+	0.774087i	0.978818	−	0.204731i	$-0.0656320\pi$
$983$	24.2698	+	24.2698i	0.774087	+	0.774087i	−0.204731	+	0.978818i	$0.565632\pi$
$984$	10.6621			0.339894
$985$	31.8759			1.01565
$986$	49.3725	+	49.3725i	1.57234	+	1.57234i
$987$	2.26039	+	1.34834i	0.0719490	+	0.0429183i
$988$	2.86167	−	14.3083i	0.0910418	−	0.455209i
$989$	−38.4216			−1.22174
$990$	−5.97931	+	5.97931i	−0.190035	+	0.190035i
$991$	46.7432			1.48485			0.742424	−	0.669930i	$-0.233676\pi$
$991$	46.7432			1.48485			0.742424	+	0.669930i	$0.233676\pi$
$992$	−5.53921			−0.175870
$993$	17.3927	−	17.3927i	0.551942	−	0.551942i
$994$	−1.65427	+	0.418088i	−0.0524702	+	0.0132609i
$995$	4.20162	−	4.20162i	0.133200	−	0.133200i
$996$	2.70343	−	2.70343i	0.0856615	−	0.0856615i
$997$		−	30.1568i		−	0.955077i	−0.878611	−	0.477538i	$-0.841529\pi$
$997$		−	30.1568i		−	0.955077i	0.878611	−	0.477538i	$-0.158471\pi$
$998$		−	36.2058i		−	1.14607i
$999$	2.48191	+	2.48191i	0.0785242	+	0.0785242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.a.307.3	yes	8
3.2	odd	2		1638.2.x.d.307.2		8
7.6	odd	2		546.2.o.d.307.4	yes	8
13.5	odd	4		546.2.o.d.265.4	yes	8
21.20	even	2		1638.2.x.b.307.1		8
39.5	even	4		1638.2.x.b.811.1		8
91.83	even	4	inner	546.2.o.a.265.3	✓	8
273.83	odd	4		1638.2.x.d.811.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.3	✓	8	91.83	even	4	inner
546.2.o.a.307.3	yes	8	1.1	even	1	trivial
546.2.o.d.265.4	yes	8	13.5	odd	4
546.2.o.d.307.4	yes	8	7.6	odd	2
1638.2.x.b.307.1		8	21.20	even	2
1638.2.x.b.811.1		8	39.5	even	4
1638.2.x.d.307.2		8	3.2	odd	2
1638.2.x.d.811.2		8	273.83	odd	4

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(-2.56510 + 2.56510i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.648285 - 2.56510i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -3.62760 q^{10} +(-1.64828 + 1.64828i) q^{11} +1.00000 q^{12} +(2.00000 + 3.00000i) q^{13} +(1.35539 - 2.27220i) q^{14} +(2.56510 + 2.56510i) q^{15} -1.00000 q^{16} -7.15945 q^{17} +(-0.707107 - 0.707107i) q^{18} +(-2.86167 + 2.86167i) q^{19} +(-2.56510 - 2.56510i) q^{20} +(-2.56510 + 0.648285i) q^{21} -2.33103 q^{22} +4.45602i q^{23} +(0.707107 + 0.707107i) q^{24} -8.15945i q^{25} +(-0.707107 + 3.53553i) q^{26} +1.00000i q^{27} +(2.56510 - 0.648285i) q^{28} -9.75259 q^{29} +3.62760i q^{30} +(3.91681 - 3.91681i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.64828 + 1.64828i) q^{33} +(-5.06250 - 5.06250i) q^{34} +(8.24264 + 4.91681i) q^{35} -1.00000i q^{36} +(2.48191 - 2.48191i) q^{37} -4.04701 q^{38} +(3.00000 - 2.00000i) q^{39} -3.62760i q^{40} +(7.53921 - 7.53921i) q^{41} +(-2.27220 - 1.35539i) q^{42} +8.62240i q^{43} +(-1.64828 - 1.64828i) q^{44} +(2.56510 - 2.56510i) q^{45} +(-3.15088 + 3.15088i) q^{46} +(-0.703431 - 0.703431i) q^{47} +1.00000i q^{48} +(-6.15945 + 3.32583i) q^{49} +(5.76961 - 5.76961i) q^{50} +7.15945i q^{51} +(-3.00000 + 2.00000i) q^{52} +2.42677 q^{53} +(-0.707107 + 0.707107i) q^{54} -8.45602i q^{55} +(2.27220 + 1.35539i) q^{56} +(2.86167 + 2.86167i) q^{57} +(-6.89612 - 6.89612i) q^{58} +(10.4560 + 10.4560i) q^{59} +(-2.56510 + 2.56510i) q^{60} +7.15945i q^{61} +5.53921 q^{62} +(0.648285 + 2.56510i) q^{63} -1.00000i q^{64} +(-12.8255 - 2.56510i) q^{65} +2.33103i q^{66} +(-4.53921 - 4.53921i) q^{67} -7.15945i q^{68} +4.45602 q^{69} +(2.35172 + 9.30514i) q^{70} +(-0.456023 - 0.456023i) q^{71} +(0.707107 - 0.707107i) q^{72} +(2.48191 + 2.48191i) q^{73} +3.50995 q^{74} -8.15945 q^{75} +(-2.86167 - 2.86167i) q^{76} +(5.29657 + 3.15945i) q^{77} +(3.53553 + 0.707107i) q^{78} +12.0422 q^{79} +(2.56510 - 2.56510i) q^{80} +1.00000 q^{81} +10.6621 q^{82} +(2.70343 - 2.70343i) q^{83} +(-0.648285 - 2.56510i) q^{84} +(18.3647 - 18.3647i) q^{85} +(-6.09696 + 6.09696i) q^{86} +9.75259i q^{87} -2.33103i q^{88} +(4.75044 + 4.75044i) q^{89} +3.62760 q^{90} +(6.39872 - 7.07505i) q^{91} -4.45602 q^{92} +(-3.91681 - 3.91681i) q^{93} -0.994801i q^{94} -14.6809i q^{95} +(-0.707107 + 0.707107i) q^{96} +(-4.49220 + 4.49220i) q^{97} +(-6.70711 - 2.00368i) q^{98} +(1.64828 - 1.64828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^9	\( 8 q - 4 q^{5} - 8 q^{9} + 4 q^{10} - 8 q^{11} + 8 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} - 12 q^{17} + 4 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 4 q^{28} - 12 q^{29} + 20 q^{31} + 8 q^{33} - 24 q^{34} + 32 q^{35} - 8 q^{37} + 12 q^{38} + 24 q^{39} + 16 q^{41} + 4 q^{42} - 8 q^{44} + 4 q^{45} - 20 q^{46} - 16 q^{47} - 4 q^{49} + 24 q^{50} - 24 q^{52} - 24 q^{53} - 4 q^{56} - 4 q^{57} - 16 q^{58} + 28 q^{59} - 4 q^{60} - 20 q^{65} + 8 q^{67} - 20 q^{69} + 24 q^{70} + 52 q^{71} - 8 q^{73} - 4 q^{74} - 20 q^{75} + 4 q^{76} + 32 q^{77} - 48 q^{79} + 4 q^{80} + 8 q^{81} + 40 q^{82} + 32 q^{83} + 20 q^{85} - 20 q^{86} + 4 q^{89} - 4 q^{90} + 12 q^{91} + 20 q^{92} - 20 q^{93} - 36 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^9 + 4 * q^10 - 8 * q^11 + 8 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 - 12 * q^17 + 4 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 4 * q^28 - 12 * q^29 + 20 * q^31 + 8 * q^33 - 24 * q^34 + 32 * q^35 - 8 * q^37 + 12 * q^38 + 24 * q^39 + 16 * q^41 + 4 * q^42 - 8 * q^44 + 4 * q^45 - 20 * q^46 - 16 * q^47 - 4 * q^49 + 24 * q^50 - 24 * q^52 - 24 * q^53 - 4 * q^56 - 4 * q^57 - 16 * q^58 + 28 * q^59 - 4 * q^60 - 20 * q^65 + 8 * q^67 - 20 * q^69 + 24 * q^70 + 52 * q^71 - 8 * q^73 - 4 * q^74 - 20 * q^75 + 4 * q^76 + 32 * q^77 - 48 * q^79 + 4 * q^80 + 8 * q^81 + 40 * q^82 + 32 * q^83 + 20 * q^85 - 20 * q^86 + 4 * q^89 - 4 * q^90 + 12 * q^91 + 20 * q^92 - 20 * q^93 - 36 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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