LMFDB - Embedded newform 546.2.bn.e.173.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, 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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.3
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.25705 - 1.19156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.80315 - 1.04105i) q^{5} +(-0.403394 + 1.68442i) q^{6} +(1.78353 + 1.95424i) q^{7} +1.00000 q^{8} +(0.160371 + 2.99571i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.25705 - 1.19156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.80315 - 1.04105i) q^{5} +(-0.403394 + 1.68442i) q^{6} +(1.78353 + 1.95424i) q^{7} +1.00000 q^{8} +(0.160371 + 2.99571i) q^{9} +2.08210i q^{10} +2.15624 q^{11} +(1.66045 - 0.492861i) q^{12} +(-0.217235 + 3.59900i) q^{13} +(0.800654 - 2.52170i) q^{14} +(1.02618 + 3.45721i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.278635 - 0.482611i) q^{17} +(2.51418 - 1.63674i) q^{18} +3.89440 q^{19} +(1.80315 - 1.04105i) q^{20} +(0.0865985 - 4.58176i) q^{21} +(-1.07812 - 1.86736i) q^{22} +(-1.79756 + 1.03782i) q^{23} +(-1.25705 - 1.19156i) q^{24} +(-0.332437 - 0.575798i) q^{25} +(3.22544 - 1.61137i) q^{26} +(3.36797 - 3.95686i) q^{27} +(-2.58418 + 0.567461i) q^{28} +(6.10476 + 3.52458i) q^{29} +(2.48094 - 2.61731i) q^{30} +(-3.21742 - 5.57273i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.71052 - 2.56929i) q^{33} -0.557271 q^{34} +(-1.18151 - 5.38051i) q^{35} +(-2.67455 - 1.35897i) q^{36} +(7.20214 - 4.15815i) q^{37} +(-1.94720 - 3.37265i) q^{38} +(4.56150 - 4.26529i) q^{39} +(-1.80315 - 1.04105i) q^{40} +(-0.532863 - 0.307649i) q^{41} +(-4.01122 + 2.21588i) q^{42} +(4.33366 + 7.50612i) q^{43} +(-1.07812 + 1.86736i) q^{44} +(2.82951 - 5.56866i) q^{45} +(1.79756 + 1.03782i) q^{46} +(0.507011 + 0.292723i) q^{47} +(-0.403394 + 1.68442i) q^{48} +(-0.638069 + 6.97086i) q^{49} +(-0.332437 + 0.575798i) q^{50} +(-0.925319 + 0.274657i) q^{51} +(-3.00821 - 1.98763i) q^{52} +(6.68551 - 3.85988i) q^{53} +(-5.11073 - 0.938319i) q^{54} +(-3.88803 - 2.24475i) q^{55} +(1.78353 + 1.95424i) q^{56} +(-4.89547 - 4.64041i) q^{57} -7.04917i q^{58} +(-1.35587 - 0.782812i) q^{59} +(-3.50713 - 0.839905i) q^{60} -8.20222i q^{61} +(-3.21742 + 5.57273i) q^{62} +(-5.56830 + 5.65633i) q^{63} +1.00000 q^{64} +(4.13844 - 6.26338i) q^{65} +(-0.869816 + 3.63202i) q^{66} +14.2600i q^{67} +(0.278635 + 0.482611i) q^{68} +(3.49626 + 0.837303i) q^{69} +(-4.06891 + 3.71347i) q^{70} +(6.52888 + 11.3084i) q^{71} +(0.160371 + 2.99571i) q^{72} +(-0.198890 - 0.344488i) q^{73} +(-7.20214 - 4.15815i) q^{74} +(-0.268206 + 1.11993i) q^{75} +(-1.94720 + 3.37265i) q^{76} +(3.84572 + 4.21381i) q^{77} +(-5.97460 - 1.81773i) q^{78} +(5.73441 - 9.93228i) q^{79} +2.08210i q^{80} +(-8.94856 + 0.960850i) q^{81} +0.615297i q^{82} +12.4455i q^{83} +(3.92462 + 2.36588i) q^{84} +(-1.00484 + 0.580146i) q^{85} +(4.33366 - 7.50612i) q^{86} +(-3.47426 - 11.7048i) q^{87} +2.15624 q^{88} +(7.54080 - 4.35368i) q^{89} +(-6.23736 + 0.333908i) q^{90} +(-7.42074 + 5.99438i) q^{91} -2.07565i q^{92} +(-2.59577 + 10.8390i) q^{93} -0.585446i q^{94} +(-7.02218 - 4.05426i) q^{95} +(1.66045 - 0.492861i) q^{96} +(-1.64731 - 2.85322i) q^{97} +(6.35598 - 2.93285i) q^{98} +(0.345799 + 6.45949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.25705	−	1.19156i	−0.725761	−	0.687947i
$3$	−1.25705	−	1.19156i	−0.725761	−	0.687947i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.80315	−	1.04105i	−0.806393	−	0.465571i	0.0393090	−	0.999227i	$-0.487484\pi$
$5$	−1.80315	−	1.04105i	−0.806393	−	0.465571i	−0.845702	+	0.533656i	$0.820818\pi$
$6$	−0.403394	+	1.68442i	−0.164685	+	0.687662i
$7$	1.78353	+	1.95424i	0.674110	+	0.738631i
$7$	1.78353	+	1.95424i	0.674110	+	0.738631i
$8$	1.00000			0.353553
$9$	0.160371	+	2.99571i	0.0534570	+	0.998570i
$10$			2.08210i			0.658417i
$11$	2.15624			0.650132			0.325066	−	0.945691i	$-0.394613\pi$
$11$	2.15624			0.650132			0.325066	+	0.945691i	$0.394613\pi$
$12$	1.66045	−	0.492861i	0.479330	−	0.142277i
$13$	−0.217235	+	3.59900i	−0.0602501	+	0.998183i
$13$	−0.217235	+	3.59900i	−0.0602501	+	0.998183i
$14$	0.800654	−	2.52170i	0.213984	−	0.673952i
$15$	1.02618	+	3.45721i	0.264960	+	0.892649i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.278635	−	0.482611i	0.0675790	−	0.117050i	−0.830256	−	0.557382i	$-0.811806\pi$
$17$	0.278635	−	0.482611i	0.0675790	−	0.117050i	0.897835	+	0.440332i	$0.145139\pi$
$18$	2.51418	−	1.63674i	0.592597	−	0.385783i
$19$	3.89440			0.893436			0.446718	−	0.894675i	$-0.352593\pi$
$19$	3.89440			0.893436			0.446718	+	0.894675i	$0.352593\pi$
$20$	1.80315	−	1.04105i	0.403196	−	0.232785i
$21$	0.0865985	−	4.58176i	0.0188973	−	0.999821i
$22$	−1.07812	−	1.86736i	−0.229856	−	0.398123i
$23$	−1.79756	+	1.03782i	−0.374818	+	0.216401i	−0.675561	−	0.737304i	$-0.736099\pi$
$23$	−1.79756	+	1.03782i	−0.374818	+	0.216401i	0.300743	+	0.953705i	$0.402765\pi$
$24$	−1.25705	−	1.19156i	−0.256595	−	0.243226i
$25$	−0.332437	−	0.575798i	−0.0664874	−	0.115160i
$26$	3.22544	−	1.61137i	0.632562	−	0.316016i
$27$	3.36797	−	3.95686i	0.648167	−	0.761499i
$28$	−2.58418	+	0.567461i	−0.488364	+	0.107240i
$29$	6.10476	+	3.52458i	1.13363	+	0.654499i	0.944844	−	0.327520i	$-0.106213\pi$
$29$	6.10476	+	3.52458i	1.13363	+	0.654499i	0.188781	+	0.982019i	$0.439546\pi$
$30$	2.48094	−	2.61731i	0.452956	−	0.477853i
$31$	−3.21742	−	5.57273i	−0.577865	−	1.00089i	−0.995724	−	0.0923797i	$-0.970553\pi$
$31$	−3.21742	−	5.57273i	−0.577865	−	1.00089i	0.417859	−	0.908512i	$-0.362781\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.71052	−	2.56929i	−0.471840	−	0.447257i
$34$	−0.557271			−0.0955711
$35$	−1.18151	−	5.38051i	−0.199712	−	0.909473i
$36$	−2.67455	−	1.35897i	−0.445758	−	0.226495i
$37$	7.20214	−	4.15815i	1.18402	−	0.683596i	0.227082	−	0.973876i	$-0.427082\pi$
$37$	7.20214	−	4.15815i	1.18402	−	0.683596i	0.956942	+	0.290279i	$0.0937482\pi$
$38$	−1.94720	−	3.37265i	−0.315877	−	0.547116i
$39$	4.56150	−	4.26529i	0.730425	−	0.682993i
$40$	−1.80315	−	1.04105i	−0.285103	−	0.164604i
$41$	−0.532863	−	0.307649i	−0.0832192	−	0.0480466i	0.457813	−	0.889049i	$-0.348633\pi$
$41$	−0.532863	−	0.307649i	−0.0832192	−	0.0480466i	−0.541032	+	0.841002i	$0.681966\pi$
$42$	−4.01122	+	2.21588i	−0.618944	+	0.341918i
$43$	4.33366	+	7.50612i	0.660877	+	1.14467i	0.980386	+	0.197089i	$0.0631487\pi$
$43$	4.33366	+	7.50612i	0.660877	+	1.14467i	−0.319509	+	0.947583i	$0.603518\pi$
$44$	−1.07812	+	1.86736i	−0.162533	+	0.281516i
$45$	2.82951	−	5.56866i	0.421798	−	0.830128i
$46$	1.79756	+	1.03782i	0.265036	+	0.153019i
$47$	0.507011	+	0.292723i	0.0739551	+	0.0426980i	0.536522	−	0.843887i	$-0.319738\pi$
$47$	0.507011	+	0.292723i	0.0739551	+	0.0426980i	−0.462566	+	0.886585i	$0.653071\pi$
$48$	−0.403394	+	1.68442i	−0.0582249	+	0.243125i
$49$	−0.638069	+	6.97086i	−0.0911527	+	0.995837i
$50$	−0.332437	+	0.575798i	−0.0470137	+	0.0814301i
$51$	−0.925319	+	0.274657i	−0.129571	+	0.0384597i
$52$	−3.00821	−	1.98763i	−0.417164	−	0.275635i
$53$	6.68551	−	3.85988i	0.918325	−	0.530195i	0.0352249	−	0.999379i	$-0.488785\pi$
$53$	6.68551	−	3.85988i	0.918325	−	0.530195i	0.883100	+	0.469184i	$0.155452\pi$
$54$	−5.11073	−	0.938319i	−0.695482	−	0.127689i
$55$	−3.88803	−	2.24475i	−0.524262	−	0.302683i
$56$	1.78353	+	1.95424i	0.238334	+	0.261146i
$57$	−4.89547	−	4.64041i	−0.648421	−	0.614637i
$58$		−	7.04917i		−	0.925601i
$59$	−1.35587	−	0.782812i	−0.176519	−	0.101913i	0.409137	−	0.912473i	$-0.365830\pi$
$59$	−1.35587	−	0.782812i	−0.176519	−	0.101913i	−0.585656	+	0.810560i	$0.699163\pi$
$60$	−3.50713	−	0.839905i	−0.452768	−	0.108431i
$61$		−	8.20222i		−	1.05019i	−0.851045	−	0.525093i	$-0.824030\pi$
$61$		−	8.20222i		−	1.05019i	0.851045	−	0.525093i	$-0.175970\pi$
$62$	−3.21742	+	5.57273i	−0.408612	+	0.707737i
$63$	−5.56830	+	5.65633i	−0.701539	+	0.712631i
$64$	1.00000			0.125000
$65$	4.13844	−	6.26338i	0.513310	−	0.776877i
$66$	−0.869816	+	3.63202i	−0.107067	+	0.447071i
$67$			14.2600i			1.74213i	0.491165	+	0.871067i	$0.336571\pi$
$67$			14.2600i			1.74213i	−0.491165	+	0.871067i	$0.663429\pi$
$68$	0.278635	+	0.482611i	0.0337895	+	0.0585251i
$69$	3.49626	+	0.837303i	0.420900	+	0.100799i
$70$	−4.06891	+	3.71347i	−0.486327	+	0.443845i
$71$	6.52888	+	11.3084i	0.774836	+	1.34206i	0.934887	+	0.354946i	$0.115501\pi$
$71$	6.52888	+	11.3084i	0.774836	+	1.34206i	−0.160051	+	0.987109i	$0.551166\pi$
$72$	0.160371	+	2.99571i	0.0188999	+	0.353048i
$73$	−0.198890	−	0.344488i	−0.0232783	−	0.0403192i	0.854152	−	0.520024i	$-0.174077\pi$
$73$	−0.198890	−	0.344488i	−0.0232783	−	0.0403192i	−0.877430	+	0.479705i	$0.840744\pi$
$74$	−7.20214	−	4.15815i	−0.837231	−	0.483376i
$75$	−0.268206	+	1.11993i	−0.0309698	+	0.129318i
$76$	−1.94720	+	3.37265i	−0.223359	+	0.386869i
$77$	3.84572	+	4.21381i	0.438260	+	0.480208i
$78$	−5.97460	−	1.81773i	−0.676490	−	0.205817i
$79$	5.73441	−	9.93228i	0.645171	−	1.11747i	−0.339091	−	0.940754i	$-0.610119\pi$
$79$	5.73441	−	9.93228i	0.645171	−	1.11747i	0.984262	−	0.176715i	$-0.0565472\pi$
$80$			2.08210i			0.232785i
$81$	−8.94856	+	0.960850i	−0.994285	+	0.106761i
$82$			0.615297i			0.0679482i
$83$			12.4455i			1.36607i	0.730385	+	0.683035i	$0.239340\pi$
$83$			12.4455i			1.36607i	−0.730385	+	0.683035i	$0.760660\pi$
$84$	3.92462	+	2.36588i	0.428211	+	0.258138i
$85$	−1.00484	+	0.580146i	−0.108990	+	0.0629256i
$86$	4.33366	−	7.50612i	0.467310	−	0.809405i
$87$	−3.47426	−	11.7048i	−0.372480	−	1.25488i
$88$	2.15624			0.229856
$89$	7.54080	−	4.35368i	0.799323	−	0.461489i	−0.0439115	−	0.999035i	$-0.513982\pi$
$89$	7.54080	−	4.35368i	0.799323	−	0.461489i	0.843234	+	0.537546i	$0.180649\pi$
$90$	−6.23736	+	0.333908i	−0.657475	+	0.0351970i
$91$	−7.42074	+	5.99438i	−0.777905	+	0.628382i
$92$		−	2.07565i		−	0.216401i
$93$	−2.59577	+	10.8390i	−0.269169	+	1.12395i
$94$		−	0.585446i		−	0.0603841i
$95$	−7.02218	−	4.05426i	−0.720460	−	0.415958i
$96$	1.66045	−	0.492861i	0.169469	−	0.0503024i
$97$	−1.64731	−	2.85322i	−0.167259	−	0.289701i	0.770196	−	0.637807i	$-0.220158\pi$
$97$	−1.64731	−	2.85322i	−0.167259	−	0.289701i	−0.937455	+	0.348106i	$0.886825\pi$
$98$	6.35598	−	2.93285i	0.642050	−	0.296262i
$99$	0.345799	+	6.45949i	0.0347541	+	0.649203i
$100$	0.664874			0.0664874
$101$	15.8907			1.58119			0.790594	−	0.612340i	$-0.209772\pi$
$101$	15.8907			1.58119			0.790594	+	0.612340i	$0.209772\pi$
$102$	0.700520	+	0.664021i	0.0693618	+	0.0657479i
$103$	−2.32058	−	1.33979i	−0.228653	−	0.132013i	0.381297	−	0.924452i	$-0.375477\pi$
$103$	−2.32058	−	1.33979i	−0.228653	−	0.132013i	−0.609951	+	0.792439i	$0.708811\pi$
$104$	−0.217235	+	3.59900i	−0.0213016	+	0.352911i
$105$	−4.92598	+	8.17144i	−0.480726	+	0.797450i
$106$	−6.68551	−	3.85988i	−0.649354	−	0.374905i
$107$	−11.8825	+	6.86037i	−1.14873	+	0.663217i	−0.948576	−	0.316549i	$-0.897476\pi$
$107$	−11.8825	+	6.86037i	−1.14873	+	0.663217i	−0.200149	+	0.979765i	$0.564143\pi$
$108$	1.74276	+	4.89518i	0.167697	+	0.471039i
$109$	2.51915	−	1.45443i	0.241291	−	0.139309i	−0.374479	−	0.927235i	$-0.622178\pi$
$109$	2.51915	−	1.45443i	0.241291	−	0.139309i	0.615770	+	0.787926i	$0.288845\pi$
$110$			4.48951i			0.428058i
$111$	−14.0082	−	3.35475i	−1.32960	−	0.318419i
$112$	0.800654	−	2.52170i	0.0756547	−	0.238278i
$113$	17.2893	−	9.98197i	1.62644	−	0.939025i	0.641295	−	0.767295i	$-0.278398\pi$
$113$	17.2893	−	9.98197i	1.62644	−	0.939025i	0.985144	−	0.171730i	$-0.0549357\pi$
$114$	−1.57098	+	6.55980i	−0.147135	+	0.614382i
$115$	4.32170			0.403000
$116$	−6.10476	+	3.52458i	−0.566813	+	0.327249i
$117$	−10.8164	−	0.0735973i	−0.999977	−	0.00680408i
$118$			1.56562i			0.144127i
$119$	1.44009	−	0.316230i	0.132013	−	0.0289887i
$120$	1.02618	+	3.45721i	0.0936774	+	0.315599i
$121$	−6.35061			−0.577328
$122$	−7.10333	+	4.10111i	−0.643105	+	0.371297i
$123$	0.303256	+	1.02167i	0.0273437	+	0.0921208i
$124$	6.43483			0.577865
$125$			11.7948i			1.05496i
$126$	7.68267	+	1.99412i	0.684427	+	0.177650i
$127$	−7.35797	+	12.7444i	−0.652915	+	1.13088i	0.329498	+	0.944156i	$0.393121\pi$
$127$	−7.35797	+	12.7444i	−0.652915	+	1.13088i	−0.982412	+	0.186725i	$0.940213\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.49634	−	14.5994i	0.307836	−	1.28541i
$130$	−7.49347	−	0.452304i	−0.657221	−	0.0396697i
$131$	−2.82161	+	4.88718i	−0.246526	+	0.426995i	−0.962559	−	0.271071i	$-0.912622\pi$
$131$	−2.82161	+	4.88718i	−0.246526	+	0.426995i	0.716034	+	0.698066i	$0.245956\pi$
$132$	3.58033	−	1.06273i	0.311628	−	0.0924987i
$133$	6.94576	+	7.61057i	0.602274	+	0.659920i
$134$	12.3495	−	7.12999i	1.06683	−	0.615937i
$135$	−10.1922	+	3.62859i	−0.877208	+	0.312299i
$136$	0.278635	−	0.482611i	0.0238928	−	0.0413835i
$137$	−6.40998	+	11.1024i	−0.547642	+	0.948544i	0.450794	+	0.892628i	$0.351141\pi$
$137$	−6.40998	+	11.1024i	−0.547642	+	0.948544i	−0.998436	+	0.0559154i	$0.982192\pi$
$138$	−1.02301	−	3.44650i	−0.0870840	−	0.293386i
$139$	3.54239	−	2.04520i	0.300462	−	0.173472i	−0.342189	−	0.939631i	$-0.611168\pi$
$139$	3.54239	−	2.04520i	0.300462	−	0.173472i	0.642650	+	0.766160i	$0.277835\pi$
$140$	5.25042	+	1.66704i	0.443741	+	0.140891i
$141$	−0.288543	−	0.972102i	−0.0242997	−	0.0818658i
$142$	6.52888	−	11.3084i	0.547892	−	0.948976i
$143$	−0.468412	+	7.76033i	−0.0391705	+	0.648951i
$144$	2.51418	−	1.63674i	0.209515	−	0.136395i
$145$	−7.33853	−	12.7107i	−0.609431	−	1.05557i
$146$	−0.198890	+	0.344488i	−0.0164603	+	0.0285100i
$147$	9.10828	−	8.00245i	0.751238	−	0.660031i
$148$			8.31631i			0.683596i
$149$	1.14705			0.0939704			0.0469852	−	0.998896i	$-0.485039\pi$
$149$	1.14705			0.0939704			0.0469852	+	0.998896i	$0.485039\pi$
$150$	1.10399	−	0.327690i	0.0901403	−	0.0267558i
$151$	4.15879	−	2.40108i	0.338438	−	0.195397i	−0.321143	−	0.947031i	$-0.604067\pi$
$151$	4.15879	−	2.40108i	0.338438	−	0.195397i	0.659581	+	0.751633i	$0.270734\pi$
$152$	3.89440			0.315877
$153$	1.49045	+	0.757314i	0.120495	+	0.0612252i
$154$	1.72641	−	5.43739i	0.139118	−	0.438158i
$155$			13.3979i			1.07615i
$156$	1.41310	+	6.08302i	0.113139	+	0.487031i
$157$	−6.04701	+	3.49124i	−0.482604	+	0.278631i	−0.721501	−	0.692414i	$-0.756547\pi$
$157$	−6.04701	+	3.49124i	−0.482604	+	0.278631i	0.238897	+	0.971045i	$0.423214\pi$
$158$	−11.4688			−0.912410
$159$	−13.0033	−	3.11410i	−1.03123	−	0.246964i
$160$	1.80315	−	1.04105i	0.142551	−	0.0823021i
$161$	−5.23415	−	1.66187i	−0.412509	−	0.130974i
$162$	5.30640	+	7.26926i	0.416910	+	0.571127i
$163$			19.6797i			1.54143i	0.637180	+	0.770715i	$0.280101\pi$
$163$			19.6797i			1.54143i	−0.637180	+	0.770715i	$0.719899\pi$
$164$	0.532863	−	0.307649i	0.0416096	−	0.0240233i
$165$	2.21270	+	7.45460i	0.172259	+	0.580340i
$166$	10.7781	−	6.22275i	0.836544	−	0.482979i
$167$	−11.1356	−	6.42913i	−0.861698	−	0.497501i	0.00288283	−	0.999996i	$-0.499082\pi$
$167$	−11.1356	−	6.42913i	−0.861698	−	0.497501i	−0.864580	+	0.502495i	$0.832416\pi$
$168$	0.0865985	−	4.58176i	0.00668122	−	0.353490i
$169$	−12.9056	−	1.56366i	−0.992740	−	0.120281i
$170$	1.00484	+	0.580146i	0.0770679	+	0.0444951i
$171$	0.624548	+	11.6665i	0.0477604	+	0.892159i
$172$	−8.66732			−0.660877
$173$	−4.43081			−0.336868			−0.168434	−	0.985713i	$-0.553871\pi$
$173$	−4.43081			−0.336868			−0.168434	+	0.985713i	$0.553871\pi$
$174$	−8.39951	+	8.86119i	−0.636765	+	0.671765i
$175$	0.532334	−	1.67661i	0.0402407	−	0.126740i
$176$	−1.07812	−	1.86736i	−0.0812665	−	0.140758i
$177$	0.771635	+	2.59964i	0.0579997	+	0.195401i
$178$	−7.54080	−	4.35368i	−0.565207	−	0.326322i
$179$		−	22.7295i		−	1.69889i	−0.527680	−	0.849443i	$-0.676938\pi$
$179$		−	22.7295i		−	1.69889i	0.527680	−	0.849443i	$-0.323062\pi$
$180$	3.40785	+	5.23476i	0.254006	+	0.390176i
$181$		−	10.2663i		−	0.763090i	−0.924350	−	0.381545i	$-0.875392\pi$
$181$		−	10.2663i		−	0.763090i	0.924350	−	0.381545i	$-0.124608\pi$
$182$	8.90166	+	3.42936i	0.659835	+	0.254201i
$183$	−9.77343	+	10.3106i	−0.722473	+	0.762184i
$184$	−1.79756	+	1.03782i	−0.132518	+	0.0765093i
$185$	−17.3154			−1.27305
$186$	10.6847	−	3.17148i	0.783441	−	0.232544i
$187$	0.600806	−	1.04063i	0.0439353	−	0.0760982i
$188$	−0.507011	+	0.292723i	−0.0369776	+	0.0213490i
$189$	13.7395	−	0.475357i	0.999402	−	0.0345771i
$190$			8.10851i			0.588253i
$191$		−	3.89397i		−	0.281757i	−0.990027	−	0.140879i	$-0.955007\pi$
$191$		−	3.89397i		−	0.281757i	0.990027	−	0.140879i	$-0.0449928\pi$
$192$	−1.25705	−	1.19156i	−0.0907201	−	0.0859934i
$193$		−	3.59888i		−	0.259053i	−0.991576	−	0.129526i	$-0.958654\pi$
$193$		−	3.59888i		−	0.259053i	0.991576	−	0.129526i	$-0.0413457\pi$
$194$	−1.64731	+	2.85322i	−0.118270	+	0.204849i
$195$	−12.6654	+	2.94221i	−0.906991	+	0.210696i
$196$	−5.71791	−	4.03801i	−0.408422	−	0.288430i
$197$	5.48497	−	9.50024i	0.390788	−	0.676864i	−0.601766	−	0.798673i	$-0.705536\pi$
$197$	5.48497	−	9.50024i	0.390788	−	0.676864i	0.992554	+	0.121808i	$0.0388693\pi$
$198$	5.42118	−	3.52921i	0.385266	−	0.250810i
$199$	17.5580	+	10.1371i	1.24466	+	0.718603i	0.970039	−	0.242951i	$-0.0781153\pi$
$199$	17.5580	+	10.1371i	1.24466	+	0.718603i	0.274618	+	0.961553i	$0.411449\pi$
$200$	−0.332437	−	0.575798i	−0.0235068	−	0.0407150i
$201$	16.9916	−	17.9256i	1.19850	−	1.26437i
$202$	−7.94537	−	13.7618i	−0.559035	−	0.968276i
$203$	4.00013	+	18.2163i	0.280754	+	1.27854i
$204$	0.224800	−	0.938678i	0.0157391	−	0.0657206i
$205$	0.640554	+	1.10947i	0.0447382	+	0.0774889i
$206$			2.67957i			0.186695i
$207$	−3.39729	−	5.21854i	−0.236128	−	0.362714i
$208$	3.22544	−	1.61137i	0.223644	−	0.111728i
$209$	8.39727			0.580852
$210$	9.53966	+	0.180306i	0.658299	+	0.0124423i
$211$	6.39897	−	11.0833i	0.440523	−	0.763009i	−0.557205	−	0.830375i	$-0.688126\pi$
$211$	6.39897	−	11.0833i	0.440523	−	0.763009i	0.997728	+	0.0673662i	$0.0214596\pi$
$212$			7.71976i			0.530195i
$213$	5.26742	−	21.9948i	0.360918	−	1.50706i
$214$	11.8825	+	6.86037i	0.812272	+	0.468965i
$215$		−	18.0462i		−	1.23074i
$216$	3.36797	−	3.95686i	0.229162	−	0.269230i
$217$	5.15208	−	16.2267i	0.349746	−	1.10154i
$218$	−2.51915	−	1.45443i	−0.170618	−	0.0985065i
$219$	−0.160462	+	0.670029i	−0.0108430	+	0.0452764i
$220$	3.88803	−	2.24475i	0.262131	−	0.151341i
$221$	1.67639	+	1.10765i	0.112766	+	0.0745085i
$222$	4.09879	+	13.8088i	0.275092	+	0.926786i
$223$	−6.84088	+	11.8488i	−0.458099	+	0.793451i	−0.998861	−	0.0477249i	$-0.984803\pi$
$223$	−6.84088	+	11.8488i	−0.458099	+	0.793451i	0.540761	+	0.841176i	$0.318136\pi$
$224$	−2.58418	+	0.567461i	−0.172663	+	0.0379151i
$225$	1.67161	−	1.08823i	0.111441	−	0.0725484i
$226$	−17.2893	−	9.98197i	−1.15007	−	0.663991i
$227$	3.24204	+	1.87179i	0.215182	+	0.124235i	0.603717	−	0.797199i	$-0.293686\pi$
$227$	3.24204	+	1.87179i	0.215182	+	0.124235i	−0.388536	+	0.921434i	$0.627019\pi$
$228$	6.46644	−	1.91940i	0.428251	−	0.127115i
$229$	4.38767	−	7.59967i	0.289946	−	0.502201i	−0.683851	−	0.729622i	$-0.739696\pi$
$229$	4.38767	−	7.59967i	0.289946	−	0.502201i	0.973796	+	0.227421i	$0.0730294\pi$
$230$	−2.16085	−	3.74270i	−0.142482	−	0.246786i
$231$	0.186728	−	9.87939i	0.0122858	−	0.650016i
$232$	6.10476	+	3.52458i	0.400797	+	0.231400i
$233$	−19.0891	−	11.0211i	−1.25057	−	0.722017i	−0.279347	−	0.960190i	$-0.590118\pi$
$233$	−19.0891	−	11.0211i	−1.25057	−	0.722017i	−0.971223	+	0.238173i	$0.923451\pi$
$234$	5.34446	+	9.40408i	0.349379	+	0.614764i
$235$	−0.609477	−	1.05565i	−0.0397579	−	0.0688627i
$236$	1.35587	−	0.782812i	0.0882596	−	0.0509567i
$237$	−19.0434	+	5.65253i	−1.23700	+	0.367171i
$238$	−0.993907	−	1.08904i	−0.0644254	−	0.0705918i
$239$	−12.3469			−0.798656			−0.399328	−	0.916808i	$-0.630757\pi$
$239$	−12.3469			−0.798656			−0.399328	+	0.916808i	$0.630757\pi$
$240$	2.48094	−	2.61731i	0.160144	−	0.168947i
$241$	−0.612290	+	1.06052i	−0.0394410	+	0.0683139i	−0.885072	−	0.465454i	$-0.845891\pi$
$241$	−0.612290	+	1.06052i	−0.0394410	+	0.0683139i	0.845631	+	0.533768i	$0.179224\pi$
$242$	3.17530	+	5.49979i	0.204116	+	0.353540i
$243$	12.3937	+	9.45491i	0.795059	+	0.606532i
$244$	7.10333	+	4.10111i	0.454744	+	0.262547i
$245$	8.40753	−	11.9052i	0.537138	−	0.760597i
$246$	0.733163	−	0.773462i	0.0467448	−	0.0493141i
$247$	−0.845999	+	14.0159i	−0.0538296	+	0.891813i
$248$	−3.21742	−	5.57273i	−0.204306	−	0.353869i
$249$	14.8296	−	15.6447i	0.939785	−	0.991440i
$250$	10.2146	−	5.89741i	0.646029	−	0.372985i
$251$	−6.93362	−	12.0094i	−0.437646	−	0.758026i	0.559861	−	0.828586i	$-0.310854\pi$
$251$	−6.93362	−	12.0094i	−0.437646	−	0.758026i	−0.997507	+	0.0705608i	$0.977521\pi$
$252$	−2.11438	−	7.65045i	−0.133193	−	0.481933i
$253$	−3.87598	+	2.23780i	−0.243681	+	0.140689i
$254$	14.7159			0.923361
$255$	1.95442	+	0.468054i	0.122390	+	0.0293107i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.32800	−	9.22836i	−0.332351	−	0.575650i	0.650621	−	0.759403i	$-0.274509\pi$
$257$	−5.32800	−	9.22836i	−0.332351	−	0.575650i	−0.982972	+	0.183753i	$0.941175\pi$
$258$	−14.3916	+	4.27178i	−0.895984	+	0.265950i
$259$	20.9712	+	6.65849i	1.30309	+	0.413738i
$260$	3.35503	+	6.71569i	0.208070	+	0.416489i
$261$	−9.57961	+	18.8533i	−0.592963	+	1.16699i
$262$	5.64323			0.348640
$263$		−	24.4779i		−	1.50937i	−0.656086	−	0.754686i	$-0.727789\pi$
$263$		−	24.4779i		−	1.50937i	0.656086	−	0.754686i	$-0.272211\pi$
$264$	−2.71052	−	2.56929i	−0.166821	−	0.158129i
$265$	−16.0733			−0.987374
$266$	3.11807	−	9.82049i	0.191181	−	0.602133i
$267$	−14.6669	−	3.51250i	−0.897597	−	0.214961i
$268$	−12.3495	−	7.12999i	−0.754366	−	0.435533i
$269$	−5.52050	+	9.56179i	−0.336591	+	0.582993i	−0.983789	−	0.179329i	$-0.942607\pi$
$269$	−5.52050	+	9.56179i	−0.336591	+	0.582993i	0.647198	+	0.762322i	$0.275941\pi$
$270$	8.23857	+	7.01244i	0.501383	+	0.426764i
$271$	7.12608	+	12.3427i	0.432879	+	0.749768i	0.997120	−	0.0758423i	$-0.0241646\pi$
$271$	7.12608	+	12.3427i	0.432879	+	0.749768i	−0.564241	+	0.825610i	$0.690831\pi$
$272$	−0.557271			−0.0337895
$273$	16.4709	+	1.30699i	0.996866	+	0.0791024i
$274$	12.8200			0.774483
$275$	−0.716815	−	1.24156i	−0.0432256	−	0.0748689i
$276$	−2.47326	+	2.60920i	−0.148873	+	0.157055i
$277$	4.88378	−	8.45896i	0.293438	−	0.508250i	−0.681182	−	0.732114i	$-0.738534\pi$
$277$	4.88378	−	8.45896i	0.293438	−	0.508250i	0.974620	+	0.223864i	$0.0718672\pi$
$278$	−3.54239	−	2.04520i	−0.212459	−	0.122663i
$279$	16.1783	−	10.5322i	0.968570	−	0.630544i
$280$	−1.18151	−	5.38051i	−0.0706087	−	0.321547i
$281$	−0.791501			−0.0472170			−0.0236085	−	0.999721i	$-0.507516\pi$
$281$	−0.791501			−0.0472170			−0.0236085	+	0.999721i	$0.507516\pi$
$282$	−0.697593	+	0.735937i	−0.0415411	+	0.0438244i
$283$		−	11.7612i		−	0.699130i	−0.936912	−	0.349565i	$-0.886329\pi$
$283$		−	11.7612i		−	0.699130i	0.936912	−	0.349565i	$-0.113671\pi$
$284$	−13.0578			−0.774836
$285$	3.99637	+	13.4638i	0.236725	+	0.797524i
$286$	6.95485	−	3.47451i	0.411249	−	0.205452i
$287$	−0.349157	−	1.59004i	−0.0206101	−	0.0938570i
$288$	−2.67455	−	1.35897i	−0.157599	−	0.0800781i
$289$	8.34472	+	14.4535i	0.490866	+	0.850205i
$290$	−7.33853	+	12.7107i	−0.430933	+	0.746398i
$291$	−1.32903	+	5.54952i	−0.0779090	+	0.325319i
$292$	0.397780			0.0232783
$293$	6.68038	−	3.85692i	0.390272	−	0.225324i	−0.292006	−	0.956416i	$-0.594323\pi$
$293$	6.68038	−	3.85692i	0.390272	−	0.225324i	0.682278	+	0.731093i	$0.260989\pi$
$294$	−11.4845	−	3.88678i	−0.669788	−	0.226681i
$295$	1.62989	+	2.82305i	0.0948959	+	0.164364i
$296$	7.20214	−	4.15815i	0.418616	−	0.241688i
$297$	7.26217	−	8.53196i	0.421394	−	0.495075i
$298$	−0.573527	−	0.993378i	−0.0332235	−	0.0575449i
$299$	−3.34463	−	6.69488i	−0.193425	−	0.387175i
$300$	−0.835783	−	0.792237i	−0.0482539	−	0.0457398i
$301$	−6.93952	+	21.8563i	−0.399987	+	1.25978i
$302$	−4.15879	−	2.40108i	−0.239312	−	0.138167i
$303$	−19.9755	−	18.9348i	−1.14756	−	1.08777i
$304$	−1.94720	−	3.37265i	−0.111680	−	0.193435i
$305$	−8.53891	+	14.7898i	−0.488936	+	0.846863i
$306$	−0.0893701	−	1.66942i	−0.00510895	−	0.0954345i
$307$	−22.5567			−1.28738			−0.643689	−	0.765287i	$-0.722597\pi$
$307$	−22.5567			−1.28738			−0.643689	+	0.765287i	$0.722597\pi$
$308$	−5.57213	+	1.22359i	−0.317501	+	0.0697203i
$309$	1.32066	+	4.44929i	0.0751296	+	0.253111i
$310$	11.6030	−	6.69897i	0.659004	−	0.380476i
$311$	−6.64375	−	11.5073i	−0.376733	−	0.652520i	0.613852	−	0.789421i	$-0.289619\pi$
$311$	−6.64375	−	11.5073i	−0.376733	−	0.652520i	−0.990585	+	0.136901i	$0.956286\pi$
$312$	4.56150	−	4.26529i	0.258244	−	0.241475i
$313$	14.7574	+	8.52018i	0.834137	+	0.481589i	0.855267	−	0.518188i	$-0.173393\pi$
$313$	14.7574	+	8.52018i	0.834137	+	0.481589i	−0.0211303	+	0.999777i	$0.506726\pi$
$314$	6.04701	+	3.49124i	0.341252	+	0.197022i
$315$	15.9290	−	4.40234i	0.897496	−	0.248044i
$316$	5.73441	+	9.93228i	0.322585	+	0.558734i
$317$	−7.60593	+	13.1739i	−0.427192	+	0.739918i	−0.996622	−	0.0821217i	$-0.973830\pi$
$317$	−7.60593	+	13.1739i	−0.427192	+	0.739918i	0.569431	+	0.822039i	$0.307164\pi$
$318$	3.80477	+	12.8183i	0.213361	+	0.718812i
$319$	13.1634	+	7.59987i	0.737006	+	0.425511i
$320$	−1.80315	−	1.04105i	−0.100799	−	0.0581964i
$321$	23.1115	+	5.53486i	1.28996	+	0.308926i
$322$	1.17785	+	5.36384i	0.0656390	+	0.298915i
$323$	1.08512	−	1.87948i	0.0603775	−	0.104577i
$324$	3.64216	−	8.23011i	0.202342	−	0.457228i
$325$	2.14451	−	1.07136i	0.118956	−	0.0594282i
$326$	17.0431	−	9.83983i	0.943929	−	0.544978i
$327$	−4.89975	−	1.17342i	−0.270957	−	0.0648901i
$328$	−0.532863	−	0.307649i	−0.0294224	−	0.0169871i
$329$	0.332218	+	1.51290i	0.0183158	+	0.0834087i
$330$	5.34952	−	5.64356i	0.294481	−	0.310668i
$331$			11.4277i			0.628123i	0.949403	+	0.314061i	$0.101690\pi$
$331$			11.4277i			0.628123i	−0.949403	+	0.314061i	$0.898310\pi$
$332$	−10.7781	−	6.22275i	−0.591526	−	0.341518i
$333$	13.6116	+	20.9087i	0.745913	+	1.14579i
$334$			12.8583i			0.703573i
$335$	14.8453	−	25.7129i	0.811087	−	1.40484i
$336$	−4.01122	+	2.21588i	−0.218830	+	0.120886i
$337$	0.692991			0.0377496			0.0188748	−	0.999822i	$-0.493992\pi$
$337$	0.692991			0.0377496			0.0188748	+	0.999822i	$0.493992\pi$
$338$	5.09864	+	11.9584i	0.277330	+	0.650452i
$339$	−33.6277	−	8.05333i	−1.82640	−	0.437397i
$340$		−	1.16029i		−	0.0629256i
$341$	−6.93754	−	12.0162i	−0.375689	−	0.650712i
$342$	9.79120	−	6.37412i	0.529447	−	0.344673i
$343$	−14.7607	+	11.1858i	−0.797003	+	0.603975i
$344$	4.33366	+	7.50612i	0.233655	+	0.404703i
$345$	−5.43261	−	5.14956i	−0.292482	−	0.277243i
$346$	2.21541	+	3.83719i	0.119101	+	0.206289i
$347$	−12.8531	−	7.42074i	−0.689991	−	0.398366i	0.113618	−	0.993525i	$-0.463756\pi$
$347$	−12.8531	−	7.42074i	−0.689991	−	0.398366i	−0.803609	+	0.595158i	$0.797089\pi$
$348$	11.8738	+	2.84359i	0.636501	+	0.152432i
$349$	9.35756	−	16.2078i	0.500899	−	0.867582i	−0.499101	−	0.866544i	$-0.666336\pi$
$349$	9.35756	−	16.2078i	0.500899	−	0.867582i	0.999999	−	0.00103797i	$-0.000330396\pi$
$350$	−1.71815	+	0.377290i	−0.0918392	+	0.0201670i
$351$	13.5091	+	12.9809i	0.721063	+	0.692870i
$352$	−1.07812	+	1.86736i	−0.0574641	+	0.0995308i
$353$			24.3746i			1.29733i	0.761075	+	0.648664i	$0.224672\pi$
$353$			24.3746i			1.29733i	−0.761075	+	0.648664i	$0.775328\pi$
$354$	1.86553	−	1.96807i	0.0991520	−	0.104602i
$355$		−	27.1875i		−	1.44296i
$356$			8.70736i			0.461489i
$357$	−2.18708	−	1.31843i	−0.115752	−	0.0697789i
$358$	−19.6844	+	11.3648i	−1.04035	+	0.600647i
$359$	−2.79005	+	4.83250i	−0.147253	+	0.255050i	−0.930211	−	0.367025i	$-0.880377\pi$
$359$	−2.79005	+	4.83250i	−0.147253	+	0.255050i	0.782958	+	0.622074i	$0.213710\pi$
$360$	2.82951	−	5.56866i	0.149128	−	0.293494i
$361$	−3.83367			−0.201772
$362$	−8.89090	+	5.13316i	−0.467295	+	0.269793i
$363$	7.98306	+	7.56713i	0.419002	+	0.397171i
$364$	−1.48092	−	9.42374i	−0.0776213	−	0.493938i
$365$			0.828216i			0.0433508i
$366$	13.8160	+	3.30872i	0.722173	+	0.172950i
$367$		−	32.9869i		−	1.72190i	−0.508689	−	0.860951i	$-0.669870\pi$
$367$		−	32.9869i		−	1.72190i	0.508689	−	0.860951i	$-0.330130\pi$
$368$	1.79756	+	1.03782i	0.0937044	+	0.0541003i
$369$	0.836170	−	1.64564i	0.0435293	−	0.0856687i
$370$	8.65768	+	14.9955i	0.450091	+	0.779581i
$371$	19.4669	+	6.18086i	1.01067	+	0.320894i
$372$	−8.08894	−	7.66749i	−0.419392	−	0.397541i
$373$	19.2542			0.996943			0.498471	−	0.866906i	$-0.333895\pi$
$373$	19.2542			0.996943			0.498471	+	0.866906i	$0.333895\pi$
$374$	−1.20161			−0.0621339
$375$	14.0542	−	14.8267i	0.725757	−	0.765649i
$376$	0.507011	+	0.292723i	0.0261471	+	0.0150960i
$377$	−14.0112	+	21.2054i	−0.721611	+	1.09213i
$378$	−7.28142	−	11.6611i	−0.374516	−	0.599781i
$379$	10.8971	+	6.29144i	0.559746	+	0.323169i	0.753043	−	0.657971i	$-0.228585\pi$
$379$	10.8971	+	6.29144i	0.559746	+	0.323169i	−0.193298	+	0.981140i	$0.561918\pi$
$380$	7.02218	−	4.05426i	0.360230	−	0.207979i
$381$	24.4351	−	7.25292i	1.25185	−	0.371578i
$382$	−3.37227	+	1.94698i	−0.172541	+	0.0996163i
$383$			1.19512i			0.0610680i	0.999534	+	0.0305340i	$0.00972079\pi$
$383$			1.19512i			0.0610680i	−0.999534	+	0.0305340i	$0.990279\pi$
$384$	−0.403394	+	1.68442i	−0.0205856	+	0.0859577i
$385$	−2.54762	−	11.6017i	−0.129839	−	0.591278i
$386$	−3.11672	+	1.79944i	−0.158637	+	0.0915890i
$387$	−21.7912	+	14.1862i	−1.10771	+	0.721123i
$388$	3.29462			0.167259
$389$	13.1871	−	7.61359i	0.668614	−	0.386024i	−0.126937	−	0.991911i	$-0.540515\pi$
$389$	13.1871	−	7.61359i	0.668614	−	0.386024i	0.795551	+	0.605886i	$0.207181\pi$
$390$	8.88075	+	9.49748i	0.449694	+	0.480924i
$391$			1.15670i			0.0584967i
$392$	−0.638069	+	6.97086i	−0.0322274	+	0.352082i
$393$	9.37029	−	2.78133i	0.472668	−	0.140299i
$394$	−10.9699			−0.552657
$395$	−20.6800	+	11.9396i	−1.04052	+	0.600746i
$396$	−5.76698	−	2.93027i	−0.289802	−	0.147252i
$397$	−26.0287			−1.30634			−0.653172	−	0.757210i	$-0.726562\pi$
$397$	−26.0287			−1.30634			−0.653172	+	0.757210i	$0.726562\pi$
$398$		−	20.2743i		−	1.01626i
$399$	0.337249	−	17.8432i	0.0168836	−	0.893277i
$400$	−0.332437	+	0.575798i	−0.0166218	+	0.0287899i
$401$	−18.3498	−	31.7828i	−0.916347	−	1.58716i	−0.804917	−	0.593387i	$-0.797790\pi$
$401$	−18.3498	−	31.7828i	−0.916347	−	1.58716i	−0.111430	−	0.993772i	$-0.535543\pi$
$402$	−24.0198	−	5.75239i	−1.19800	−	0.286903i
$403$	20.7552	−	10.3689i	1.03389	−	0.516511i
$404$	−7.94537	+	13.7618i	−0.395297	+	0.684675i
$405$	17.1359	+	7.58333i	0.851489	+	0.376819i
$406$	13.7757	−	12.5724i	0.683678	−	0.623957i
$407$	15.5296	−	8.96600i	0.769772	−	0.444428i
$408$	−0.925319	+	0.274657i	−0.0458101	+	0.0135976i
$409$	−14.6580	+	25.3884i	−0.724791	+	1.25537i	0.234269	+	0.972172i	$0.424730\pi$
$409$	−14.6580	+	25.3884i	−0.724791	+	1.25537i	−0.959060	+	0.283203i	$0.908603\pi$
$410$	0.640554	−	1.10947i	0.0316347	−	0.0547929i
$411$	21.2869	−	6.31846i	1.05001	−	0.311667i
$412$	2.32058	−	1.33979i	0.114327	−	0.0660065i
$413$	−0.888431	−	4.04585i	−0.0437168	−	0.199084i
$414$	−2.82074	+	5.55141i	−0.138632	+	0.272837i
$415$	12.9564	−	22.4411i	0.636003	−	1.10159i
$416$	−3.00821	−	1.98763i	−0.147490	−	0.0974517i
$417$	−6.88996	−	1.65004i	−0.337403	−	0.0808030i
$418$	−4.19864	−	7.27225i	−0.205362	−	0.355698i
$419$	−18.5356	+	32.1046i	−0.905523	+	1.56841i	−0.0853087	+	0.996355i	$0.527188\pi$
$419$	−18.5356	+	32.1046i	−0.905523	+	1.56841i	−0.820214	+	0.572057i	$0.806146\pi$
$420$	−4.61368	−	8.35174i	−0.225125	−	0.407523i
$421$		−	15.9315i		−	0.776451i	−0.921564	−	0.388226i	$-0.873088\pi$
$421$		−	15.9315i		−	0.776451i	0.921564	−	0.388226i	$-0.126912\pi$
$422$	−12.7979			−0.622994
$423$	−0.795603	+	1.56580i	−0.0386835	+	0.0761319i
$424$	6.68551	−	3.85988i	0.324677	−	0.187452i
$425$	−0.370515			−0.0179726
$426$	−21.6817	+	6.43567i	−1.05048	+	0.311809i
$427$	16.0291	−	14.6289i	0.775701	−	0.707941i
$428$		−	13.7207i		−	0.663217i
$429$	9.83571	−	9.19701i	0.474873	−	0.444036i
$430$	−15.6285	+	9.02310i	−0.753671	+	0.435132i
$431$	−28.1808			−1.35742			−0.678710	−	0.734407i	$-0.737461\pi$
$431$	−28.1808			−1.35742			−0.678710	+	0.734407i	$0.737461\pi$
$432$	−5.11073	−	0.938319i	−0.245890	−	0.0451449i
$433$	−10.7990	+	6.23481i	−0.518967	+	0.299626i	−0.736512	−	0.676425i	$-0.763528\pi$
$433$	−10.7990	+	6.23481i	−0.518967	+	0.299626i	0.217545	+	0.976050i	$0.430195\pi$
$434$	−16.6288	+	3.65152i	−0.798206	+	0.175279i
$435$	−5.92063	+	24.7223i	−0.283873	+	1.18534i
$436$			2.90886i			0.139309i
$437$	−7.00042	+	4.04170i	−0.334876	+	0.193341i
$438$	0.660493	−	0.196050i	0.0315596	−	0.00936764i
$439$	−31.5375	+	18.2082i	−1.50520	+	0.869029i	−0.505221	+	0.862990i	$0.668589\pi$
$439$	−31.5375	+	18.2082i	−1.50520	+	0.869029i	−0.999982	+	0.00603872i	$0.998078\pi$
$440$	−3.88803	−	2.24475i	−0.185355	−	0.107014i
$441$	−20.9850	−	0.793547i	−0.999286	−	0.0377879i
$442$	0.121059	−	2.00562i	0.00575817	−	0.0953975i
$443$	11.6506	+	6.72648i	0.553537	+	0.319585i	0.750547	−	0.660817i	$-0.229790\pi$
$443$	11.6506	+	6.72648i	0.553537	+	0.319585i	−0.197011	+	0.980401i	$0.563123\pi$
$444$	9.90938	−	10.4541i	0.470278	−	0.496127i
$445$	−18.1296			−0.859424
$446$	13.6818			0.647850
$447$	−1.44191	−	1.36678i	−0.0682000	−	0.0646467i
$448$	1.78353	+	1.95424i	0.0842637	+	0.0923289i
$449$	10.8390	+	18.7736i	0.511522	+	0.885982i	0.999911	+	0.0133556i	$0.00425136\pi$
$449$	10.8390	+	18.7736i	0.511522	+	0.885982i	−0.488389	+	0.872626i	$0.662415\pi$
$450$	−1.77824	−	0.903544i	−0.0838269	−	0.0425935i
$451$	−1.14898	−	0.663366i	−0.0541035	−	0.0312367i
$452$			19.9639i			0.939025i
$453$	−8.08886	−	1.93716i	−0.380048	−	0.0910158i
$454$		−	3.74358i		−	0.175695i
$455$	19.6211	−	3.08342i	0.919853	−	0.144553i
$456$	−4.89547	−	4.64041i	−0.229251	−	0.217307i
$457$	−12.5219	+	7.22952i	−0.585750	+	0.338183i	−0.763415	−	0.645908i	$-0.776479\pi$
$457$	−12.5219	+	7.22952i	−0.585750	+	0.338183i	0.177665	+	0.984091i	$0.443146\pi$
$458$	−8.77535			−0.410045
$459$	−0.971187	−	2.72794i	−0.0453311	−	0.127329i
$460$	−2.16085	+	3.74270i	−0.100750	+	0.174504i
$461$	29.7738	−	17.1899i	1.38670	−	0.800614i	0.393762	−	0.919212i	$-0.371173\pi$
$461$	29.7738	−	17.1899i	1.38670	−	0.800614i	0.992942	+	0.118598i	$0.0378400\pi$
$462$	−8.64917	+	4.77798i	−0.402396	+	0.222292i
$463$			3.55647i			0.165283i	0.996579	+	0.0826415i	$0.0263357\pi$
$463$			3.55647i			0.165283i	−0.996579	+	0.0826415i	$0.973664\pi$
$464$		−	7.04917i		−	0.327249i
$465$	15.9645	−	16.8419i	0.740334	−	0.781026i
$466$			22.0422i			1.02109i
$467$	−0.408159	+	0.706953i	−0.0188874	+	0.0327139i	−0.875315	−	0.483554i	$-0.839346\pi$
$467$	−0.408159	+	0.706953i	−0.0188874	+	0.0327139i	0.856427	+	0.516268i	$0.172679\pi$
$468$	5.47194	−	9.33048i	0.252940	−	0.431302i
$469$	−27.8673	+	25.4330i	−1.28679	+	1.17439i
$470$	−0.609477	+	1.05565i	−0.0281131	+	0.0486933i
$471$	11.7614	+	2.81669i	0.541938	+	0.129786i
$472$	−1.35587	−	0.782812i	−0.0624090	−	0.0360318i
$473$	9.34443	+	16.1850i	0.429657	+	0.744188i
$474$	14.4169	+	13.6658i	0.662191	+	0.627690i
$475$	−1.29464	−	2.24239i	−0.0594022	−	0.102888i
$476$	−0.446181	+	1.40527i	−0.0204507	+	0.0644103i
$477$	12.6352	+	19.4088i	0.578528	+	0.888670i
$478$	6.17346	+	10.6927i	0.282368	+	0.489075i
$479$			37.0189i			1.69144i	0.533628	+	0.845719i	$0.320828\pi$
$479$			37.0189i			1.69144i	−0.533628	+	0.845719i	$0.679172\pi$
$480$	−3.50713	−	0.839905i	−0.160078	−	0.0383362i
$481$	13.4006	+	26.8238i	0.611017	+	1.22306i
$482$	1.22458			0.0557781
$483$	4.59939	+	8.32587i	0.209279	+	0.378840i
$484$	3.17530	−	5.49979i	0.144332	−	0.249990i
$485$			6.85971i			0.311483i
$486$	1.99132	−	15.4607i	0.0903280	−	0.701314i
$487$	−18.8435	−	10.8793i	−0.853881	−	0.492989i	0.00807726	−	0.999967i	$-0.497429\pi$
$487$	−18.8435	−	10.8793i	−0.853881	−	0.492989i	−0.861959	+	0.506979i	$0.830762\pi$
$488$		−	8.20222i		−	0.371297i
$489$	23.4495	−	24.7384i	1.06042	−	1.11871i
$490$	−14.5140	−	1.32852i	−0.655676	−	0.0600165i
$491$	−25.7673	−	14.8768i	−1.16286	−	0.671379i	−0.210875	−	0.977513i	$-0.567631\pi$
$491$	−25.7673	−	14.8768i	−1.16286	−	0.671379i	−0.951989	+	0.306134i	$0.900965\pi$
$492$	−1.03642	−	0.248207i	−0.0467254	−	0.0111900i
$493$	3.40200	−	1.96415i	0.153219	−	0.0884608i
$494$	12.5612	−	6.27531i	0.565153	−	0.282340i
$495$	6.10111	−	12.0074i	0.274224	−	0.539693i
$496$	−3.21742	+	5.57273i	−0.144466	+	0.250223i
$497$	−10.4548	+	32.9277i	−0.468960	+	1.47701i
$498$	−20.9635	−	5.02044i	−0.939395	−	0.224971i
$499$	9.70337	+	5.60224i	0.434383	+	0.250791i	0.701212	−	0.712953i	$-0.252643\pi$
$499$	9.70337	+	5.60224i	0.434383	+	0.250791i	−0.266829	+	0.963744i	$0.585976\pi$
$500$	−10.2146	−	5.89741i	−0.456811	−	0.263740i
$501$	6.33734	+	21.3505i	0.283131	+	0.953869i
$502$	−6.93362	+	12.0094i	−0.309463	+	0.536005i
$503$	−13.0943	−	22.6800i	−0.583847	−	1.01125i	−0.995018	−	0.0996945i	$-0.968213\pi$
$503$	−13.0943	−	22.6800i	−0.583847	−	1.01125i	0.411171	−	0.911558i	$-0.365120\pi$
$504$	−5.56830	+	5.65633i	−0.248032	+	0.251953i
$505$	−28.6534	−	16.5430i	−1.27506	−	0.736155i
$506$	3.87598	+	2.23780i	0.172309	+	0.0994824i
$507$	14.3599	+	17.3434i	0.637744	+	0.770248i
$508$	−7.35797	−	12.7444i	−0.326457	−	0.565441i
$509$	−8.93202	+	5.15690i	−0.395905	+	0.228576i	−0.684715	−	0.728811i	$-0.740073\pi$
$509$	−8.93202	+	5.15690i	−0.395905	+	0.228576i	0.288811	+	0.957386i	$0.406740\pi$
$510$	−0.571863	−	1.92660i	−0.0253225	−	0.0853114i
$511$	0.318484	−	1.00308i	0.0140889	−	0.0443737i
$512$	1.00000			0.0441942
$513$	13.1162	−	15.4096i	0.579095	−	0.680350i
$514$	−5.32800	+	9.22836i	−0.235008	+	0.407046i
$515$	2.78957	+	4.83167i	0.122923	+	0.212909i
$516$	10.8953	+	10.3276i	0.479638	+	0.454648i
$517$	1.09324	+	0.631182i	0.0480806	+	0.0277594i
$518$	−4.71918	−	21.4908i	−0.207349	−	0.944253i
$519$	5.56977	+	5.27958i	0.244486	+	0.231748i
$520$	4.13844	−	6.26338i	0.181483	−	0.274667i
$521$	17.8124	+	30.8520i	0.780376	+	1.35165i	0.931723	+	0.363171i	$0.118306\pi$
$521$	17.8124	+	30.8520i	0.780376	+	1.35165i	−0.151346	+	0.988481i	$0.548361\pi$
$522$	21.1173	−	1.13048i	0.924278	−	0.0494799i
$523$	−9.62328	+	5.55600i	−0.420797	+	0.242947i	−0.695418	−	0.718605i	$-0.744781\pi$
$523$	−9.62328	+	5.55600i	−0.420797	+	0.242947i	0.274621	+	0.961552i	$0.411447\pi$
$524$	−2.82161	−	4.88718i	−0.123263	−	0.213497i
$525$	−2.66695	+	1.47328i	−0.116395	+	0.0642993i
$526$	−21.1985	+	12.2389i	−0.924298	+	0.533644i
$527$	−3.58594			−0.156206
$528$	−0.869816	+	3.63202i	−0.0378539	+	0.158064i
$529$	−9.34585	+	16.1875i	−0.406341	+	0.703804i
$530$	8.03664	+	13.9199i	0.349090	+	0.604641i
$531$	2.12764	−	4.18734i	0.0923315	−	0.181715i
$532$	−10.0638	+	2.20992i	−0.436322	+	0.0958122i
$533$	1.22298	−	1.85094i	0.0529733	−	0.0801732i
$534$	4.29152	+	14.4581i	0.185712	+	0.625664i
$535$	28.5679			1.23510
$536$			14.2600i			0.615937i
$537$	−27.0836	+	28.5723i	−1.16874	+	1.23298i
$538$	11.0410			0.476012
$539$	−1.37583	+	15.0309i	−0.0592613	+	0.647426i
$540$	1.95367	−	10.6410i	0.0840726	−	0.457917i
$541$	−14.2432	−	8.22331i	−0.612363	−	0.353548i	0.161527	−	0.986868i	$-0.448358\pi$
$541$	−14.2432	−	8.22331i	−0.612363	−	0.353548i	−0.773890	+	0.633320i	$0.781692\pi$
$542$	7.12608	−	12.3427i	0.306091	−	0.530166i
$543$	−12.2329	+	12.9053i	−0.524966	+	0.553821i
$544$	0.278635	+	0.482611i	0.0119464	+	0.0206918i
$545$	−6.05653			−0.259433
$546$	−7.10359	−	14.9177i	−0.304005	−	0.638420i
$547$	38.7499			1.65683			0.828414	−	0.560116i	$-0.189243\pi$
$547$	38.7499			1.65683			0.828414	+	0.560116i	$0.189243\pi$
$548$	−6.40998	−	11.1024i	−0.273821	−	0.474272i
$549$	24.5715	−	1.31540i	1.04869	−	0.0561398i
$550$	−0.716815	+	1.24156i	−0.0305651	+	0.0529403i
$551$	23.7744	+	13.7261i	1.01282	+	0.584753i
$552$	3.49626	+	0.837303i	0.148811	+	0.0356380i
$553$	29.6375	−	6.50811i	1.26031	−	0.276753i
$554$	−9.76756			−0.414984
$555$	21.7663	+	20.6323i	0.923930	+	0.875792i
$556$			4.09040i			0.173472i
$557$	−26.2909			−1.11398			−0.556992	−	0.830518i	$-0.688044\pi$
$557$	−26.2909			−1.11398			−0.556992	+	0.830518i	$0.688044\pi$
$558$	−17.2103	−	8.74474i	−0.728569	−	0.370195i
$559$	−27.9559	+	13.9663i	−1.18241	+	0.590710i
$560$	−4.06891	+	3.71347i	−0.171943	+	0.156923i
$561$	−1.99521	+	0.592228i	−0.0842380	+	0.0250039i
$562$	0.395750	+	0.685460i	0.0166937	+	0.0289144i
$563$	−9.43940	+	16.3495i	−0.397823	+	0.689050i	−0.993457	−	0.114206i	$-0.963568\pi$
$563$	−9.43940	+	16.3495i	−0.397823	+	0.689050i	0.595634	+	0.803256i	$0.296901\pi$
$564$	0.986137	+	0.236165i	0.0415239	+	0.00994435i
$565$	−41.5669			−1.74873
$566$	−10.1855	+	5.88059i	−0.428128	+	0.247180i
$567$	−17.8377	−	15.7739i	−0.749114	−	0.662441i
$568$	6.52888	+	11.3084i	0.273946	+	0.474488i
$569$	36.2914	−	20.9528i	1.52141	−	0.878388i	0.521733	−	0.853109i	$-0.325286\pi$
$569$	36.2914	−	20.9528i	1.52141	−	0.878388i	0.999680	−	0.0252796i	$-0.00804760\pi$
$570$	9.66178	−	10.1928i	0.404687	−	0.426931i
$571$	3.92765	+	6.80288i	0.164367	+	0.284692i	0.936430	−	0.350854i	$-0.114109\pi$
$571$	3.92765	+	6.80288i	0.164367	+	0.284692i	−0.772063	+	0.635546i	$0.780775\pi$
$572$	−6.48643	−	4.28582i	−0.271211	−	0.179199i
$573$	−4.63989	+	4.89493i	−0.193834	+	0.204488i
$574$	−1.20244	+	1.09740i	−0.0501887	+	0.0458045i
$575$	1.19515	+	0.690021i	0.0498413	+	0.0287759i
$576$	0.160371	+	2.99571i	0.00668213	+	0.124821i
$577$	11.6409	+	20.1626i	0.484617	+	0.839381i	0.999844	−	0.0176727i	$-0.00562569\pi$
$577$	11.6409	+	20.1626i	0.484617	+	0.839381i	−0.515227	+	0.857054i	$0.672292\pi$
$578$	8.34472	−	14.4535i	0.347095	−	0.601186i
$579$	−4.28827	+	4.52398i	−0.178215	+	0.188010i
$580$	14.6771			0.609431
$581$	−24.3214	+	22.1969i	−1.00902	+	0.920881i
$582$	5.47054	−	1.62379i	0.226761	−	0.0673082i
$583$	14.4156	−	8.32285i	0.597033	−	0.344697i
$584$	−0.198890	−	0.344488i	−0.00823013	−	0.0142550i
$585$	19.4270	+	11.3931i	0.803206	+	0.471047i
$586$	−6.68038	−	3.85692i	−0.275964	−	0.159328i
$587$	−20.2618	−	11.6981i	−0.836294	−	0.482834i	0.0197091	−	0.999806i	$-0.493726\pi$
$587$	−20.2618	−	11.6981i	−0.836294	−	0.482834i	−0.856003	+	0.516971i	$0.827059\pi$
$588$	2.37618	+	11.8892i	0.0979922	+	0.490304i
$589$	−12.5299	−	21.7024i	−0.516286	−	0.894233i
$590$	1.62989	−	2.82305i	0.0671015	−	0.116223i
$591$	−18.2150	+	5.40665i	−0.749265	+	0.222400i
$592$	−7.20214	−	4.15815i	−0.296006	−	0.170899i
$593$	−4.32543	−	2.49729i	−0.177624	−	0.102551i	0.408552	−	0.912735i	$-0.366034\pi$
$593$	−4.32543	−	2.49729i	−0.177624	−	0.102551i	−0.586176	+	0.810184i	$0.699367\pi$
$594$	−11.0200	−	2.02325i	−0.452155	−	0.0830148i
$595$	−2.92590	−	0.928992i	−0.119950	−	0.0380850i
$596$	−0.573527	+	0.993378i	−0.0234926	+	0.0406904i
$597$	−9.99240	−	33.6644i	−0.408962	−	1.37779i
$598$	−4.12562	+	6.24398i	−0.168709	+	0.255335i
$599$	7.43793	−	4.29429i	0.303905	−	0.175460i	−0.340291	−	0.940320i	$-0.610525\pi$
$599$	7.43793	−	4.29429i	0.303905	−	0.175460i	0.644196	+	0.764860i	$0.277192\pi$
$600$	−0.268206	+	1.11993i	−0.0109495	+	0.0457208i
$601$	−42.0105	−	24.2548i	−1.71364	−	0.989373i	−0.929523	−	0.368765i	$-0.879781\pi$
$601$	−42.0105	−	24.2548i	−1.71364	−	0.989373i	−0.784121	−	0.620608i	$-0.786886\pi$
$602$	22.3979	−	4.91837i	0.912871	−	0.200458i
$603$	−42.7188	+	2.28689i	−1.73964	+	0.0931292i
$604$			4.80216i			0.195397i
$605$	11.4511	+	6.61129i	0.465553	+	0.268787i
$606$	−6.41023	+	26.7667i	−0.260398	+	1.08732i
$607$		−	8.10700i		−	0.329053i	−0.986373	−	0.164527i	$-0.947390\pi$
$607$		−	8.10700i		−	0.329053i	0.986373	−	0.164527i	$-0.0526096\pi$
$608$	−1.94720	+	3.37265i	−0.0789693	+	0.136779i
$609$	16.6775	−	27.6653i	0.675805	−	1.12105i
$610$	17.0778			0.691460
$611$	−1.16365	+	1.76114i	−0.0470762	+	0.0712482i
$612$	−1.40108	+	0.912108i	−0.0566352	+	0.0368698i
$613$		−	0.507258i		−	0.0204880i	−0.999948	−	0.0102440i	$-0.996739\pi$
$613$		−	0.507258i		−	0.0204880i	0.999948	−	0.0102440i	$-0.00326082\pi$
$614$	11.2783	+	19.5347i	0.455157	+	0.788355i
$615$	0.516791	−	2.15793i	0.0208390	−	0.0870160i
$616$	3.84572	+	4.21381i	0.154948	+	0.169779i
$617$	−14.0828	−	24.3922i	−0.566954	−	0.981993i	−0.996865	−	0.0791221i	$-0.974788\pi$
$617$	−14.0828	−	24.3922i	−0.566954	−	0.981993i	0.429911	−	0.902871i	$-0.358545\pi$
$618$	3.19287	−	3.36837i	0.128436	−	0.135496i
$619$	−12.3365	−	21.3674i	−0.495846	−	0.858830i	0.504143	−	0.863620i	$-0.331809\pi$
$619$	−12.3365	−	21.3674i	−0.495846	−	0.858830i	−0.999989	+	0.00479018i	$0.998475\pi$
$620$	−11.6030	−	6.69897i	−0.465986	−	0.269037i
$621$	−1.94762	+	10.6081i	−0.0781552	+	0.425687i
$622$	−6.64375	+	11.5073i	−0.266390	+	0.461401i
$623$	21.9573	+	6.97158i	0.879702	+	0.279311i
$624$	−5.97460	−	1.81773i	−0.239175	−	0.0727674i
$625$	10.6168	−	18.3888i	0.424671	−	0.735553i
$626$		−	17.0404i		−	0.681070i
$627$	−10.5558	−	10.0059i	−0.421559	−	0.399595i
$628$		−	6.98248i		−	0.278631i
$629$		−	4.63444i		−	0.184787i
$630$	−11.7770	−	11.5937i	−0.469208	−	0.461905i
$631$	35.8457	−	20.6955i	1.42699	−	0.823875i	0.430111	−	0.902776i	$-0.358474\pi$
$631$	35.8457	−	20.6955i	1.42699	−	0.823875i	0.996882	+	0.0789008i	$0.0251410\pi$
$632$	5.73441	−	9.93228i	0.228102	−	0.395085i
$633$	−21.2503	+	6.30761i	−0.844624	+	0.250705i
$634$	15.2119			0.604140
$635$	26.5350	−	15.3200i	1.05301	−	0.607956i
$636$	9.19856	−	9.70416i	0.364746	−	0.384795i
$637$	−24.9495	−	3.81072i	−0.988536	−	0.150986i
$638$		−	15.1997i		−	0.601763i
$639$	−32.8295	+	21.3722i	−1.29872	+	0.845470i
$640$			2.08210i			0.0823021i
$641$	−23.1368	−	13.3581i	−0.913850	−	0.527612i	−0.0321822	−	0.999482i	$-0.510246\pi$
$641$	−23.1368	−	13.3581i	−0.913850	−	0.527612i	−0.881668	+	0.471870i	$0.843579\pi$
$642$	−6.76242	−	22.7826i	−0.266891	−	0.899156i
$643$	22.0044	+	38.1127i	0.867769	+	1.50302i	0.864272	+	0.503025i	$0.167780\pi$
$643$	22.0044	+	38.1127i	0.867769	+	1.50302i	0.00349687	+	0.999994i	$0.498887\pi$
$644$	4.05630	−	3.70197i	0.159841	−	0.145878i
$645$	−21.5031	+	22.6850i	−0.846684	+	0.893223i
$646$	−2.17023			−0.0853867
$647$	15.5467			0.611203			0.305601	−	0.952160i	$-0.401142\pi$
$647$	15.5467			0.611203			0.305601	+	0.952160i	$0.401142\pi$
$648$	−8.94856	+	0.960850i	−0.351533	+	0.0377458i
$649$	−2.92359	−	1.68793i	−0.114761	−	0.0662572i
$650$	−2.00008	−	1.32152i	−0.0784496	−	0.0518344i
$651$	−25.8115	+	14.2588i	−1.01163	+	0.558848i
$652$	−17.0431	−	9.83983i	−0.667459	−	0.385358i
$653$	24.1143	−	13.9224i	0.943667	−	0.544826i	0.0525588	−	0.998618i	$-0.483262\pi$
$653$	24.1143	−	13.9224i	0.943667	−	0.544826i	0.891108	+	0.453792i	$0.149929\pi$
$654$	1.43366	+	4.83001i	0.0560607	+	0.188868i
$655$	10.1756	−	5.87487i	0.397593	−	0.229550i
$656$			0.615297i			0.0240233i
$657$	1.00009	−	0.651063i	0.0390172	−	0.0254004i
$658$	1.14410	−	1.04416i	0.0446016	−	0.0407055i
$659$	37.5062	−	21.6542i	1.46103	−	0.843528i	0.461974	−	0.886893i	$-0.347141\pi$
$659$	37.5062	−	21.6542i	1.46103	−	0.843528i	0.999059	+	0.0433655i	$0.0138080\pi$
$660$	−7.56222	−	1.81104i	−0.294359	−	0.0704947i
$661$	19.3405			0.752257			0.376129	−	0.926567i	$-0.377255\pi$
$661$	19.3405			0.752257			0.376129	+	0.926567i	$0.377255\pi$
$662$	9.89667	−	5.71384i	0.384645	−	0.222075i
$663$	−0.787480	−	3.38989i	−0.0305832	−	0.131652i
$664$			12.4455i			0.482979i
$665$	−4.60127	−	20.9539i	−0.178430	−	0.812556i
$666$	11.3016	−	22.2424i	0.437929	−	0.861874i
$667$	−14.6316			−0.566537
$668$	11.1356	−	6.42913i	0.430849	−	0.248751i
$669$	22.7179	−	6.74321i	0.878323	−	0.260707i
$670$	−29.6907			−1.14705
$671$		−	17.6860i		−	0.682760i
$672$	3.92462	+	2.36588i	0.151395	+	0.0912656i
$673$	11.4777	−	19.8800i	0.442434	−	0.766319i	−0.555435	−	0.831560i	$-0.687448\pi$
$673$	11.4777	−	19.8800i	0.442434	−	0.766319i	0.997870	+	0.0652410i	$0.0207816\pi$
$674$	−0.346495	−	0.600147i	−0.0133465	−	0.0231168i
$675$	−3.39799	−	0.623864i	−0.130789	−	0.0240125i
$676$	7.80698	−	10.3948i	0.300268	−	0.399799i
$677$	1.50584	−	2.60819i	0.0578740	−	0.100241i	−0.835637	−	0.549282i	$-0.814901\pi$
$677$	1.50584	−	2.60819i	0.0578740	−	0.100241i	0.893511	+	0.449042i	$0.148234\pi$
$678$	9.83945	+	33.1491i	0.377882	+	1.27308i
$679$	2.63785	−	8.30803i	0.101231	−	0.318833i
$680$	−1.00484	+	0.580146i	−0.0385339	+	0.0222476i
$681$	−1.84507	−	6.21602i	−0.0707031	−	0.238199i
$682$	−6.93754	+	12.0162i	−0.265652	+	0.460123i
$683$	−15.5595	+	26.9499i	−0.595368	+	1.03121i	0.398127	+	0.917331i	$0.369660\pi$
$683$	−15.5595	+	26.9499i	−0.595368	+	1.03121i	−0.993495	+	0.113878i	$0.963673\pi$
$684$	−10.4157	−	5.29237i	−0.398256	−	0.202359i
$685$	23.1163	−	13.3462i	0.883229	−	0.509932i
$686$	17.0675	+	7.19026i	0.651641	+	0.274526i
$687$	−14.5710	+	4.32503i	−0.555919	+	0.165010i
$688$	4.33366	−	7.50612i	0.165219	−	0.286168i
$689$	12.4394	+	24.8997i	0.473903	+	0.948601i
$690$	−1.74335	+	7.27955i	−0.0663680	+	0.277128i
$691$	−23.4332	−	40.5876i	−0.891442	−	1.54402i	−0.838147	−	0.545444i	$-0.816361\pi$
$691$	−23.4332	−	40.5876i	−0.891442	−	1.54402i	−0.0532952	−	0.998579i	$-0.516972\pi$
$692$	2.21541	−	3.83719i	0.0842171	−	0.145868i
$693$	−12.0066	+	12.1964i	−0.456093	+	0.463304i
$694$			14.8415i			0.563375i
$695$	−8.51661			−0.323054
$696$	−3.47426	−	11.7048i	−0.131692	−	0.443669i
$697$	−0.296949	+	0.171444i	−0.0112477	+	0.00649389i
$698$	−18.7151			−0.708378
$699$	10.8638	+	36.6000i	0.410905	+	1.38434i
$700$	1.18582	+	1.29932i	0.0448198	+	0.0491097i
$701$		−	27.7719i		−	1.04893i	−0.851433	−	0.524464i	$-0.824266\pi$
$701$		−	27.7719i		−	1.04893i	0.851433	−	0.524464i	$-0.175734\pi$
$702$	4.48724	−	18.1897i	0.169360	−	0.686525i
$703$	28.0480	−	16.1935i	1.05785	−	0.610750i
$704$	2.15624			0.0812665
$705$	−0.491719	+	2.05323i	−0.0185192	+	0.0773292i
$706$	21.1090	−	12.1873i	0.794448	−	0.458675i
$707$	28.3416	+	31.0543i	1.06589	+	1.16792i
$708$	−2.63717	−	0.631563i	−0.0991109	−	0.0237356i
$709$			32.1210i			1.20633i	0.797617	+	0.603165i	$0.206094\pi$
$709$			32.1210i			1.20633i	−0.797617	+	0.603165i	$0.793906\pi$
$710$	−23.5451	+	13.5938i	−0.883632	+	0.510165i
$711$	30.6739	+	15.5858i	1.15036	+	0.584512i
$712$	7.54080	−	4.35368i	0.282603	−	0.163161i
$713$	11.5670	+	6.67822i	0.433188	+	0.250101i
$714$	−0.0482588	+	2.55328i	−0.00180604	+	0.0955541i
$715$	8.92349	−	13.5054i	0.333720	−	0.505073i
$716$	19.6844	+	11.3648i	0.735639	+	0.424722i
$717$	15.5208	+	14.7121i	0.579633	+	0.549433i
$718$	5.58009			0.208247
$719$	37.0497			1.38172			0.690861	−	0.722987i	$-0.257232\pi$
$719$	37.0497			1.38172			0.690861	+	0.722987i	$0.257232\pi$
$720$	−6.23736	+	0.333908i	−0.232453	+	0.0124440i
$721$	−1.52055	−	6.92450i	−0.0566284	−	0.257882i
$722$	1.91683	+	3.32005i	0.0713372	+	0.123560i
$723$	2.03335	−	0.603548i	0.0756211	−	0.0224462i
$724$	8.89090	+	5.13316i	0.330428	+	0.190773i
$725$		−	4.68681i		−	0.174064i
$726$	2.56180	−	10.6971i	0.0950772	−	0.397007i
$727$		−	8.65396i		−	0.320957i	−0.987039	−	0.160479i	$-0.948696\pi$
$727$		−	8.65396i		−	0.320957i	0.987039	−	0.160479i	$-0.0513038\pi$
$728$	−7.42074	+	5.99438i	−0.275031	+	0.222167i
$729$	−4.31352	−	26.6532i	−0.159760	−	0.987156i
$730$	0.717256	−	0.414108i	0.0265468	−	0.0153268i
$731$	4.83004			0.178646
$732$	−4.04256	−	13.6194i	−0.149417	−	0.503386i
$733$	11.2469	−	19.4802i	0.415413	−	0.719516i	−0.580059	−	0.814574i	$-0.696971\pi$
$733$	11.2469	−	19.4802i	0.415413	−	0.719516i	0.995472	+	0.0950586i	$0.0303039\pi$
$734$	−28.5675	+	16.4934i	−1.05444	+	0.608784i
$735$	−24.7545	+	4.94745i	−0.913084	+	0.182489i
$736$		−	2.07565i		−	0.0765093i
$737$			30.7480i			1.13262i
$738$	−1.84325	+	0.0986758i	−0.0678511	+	0.00363231i
$739$		−	22.8275i		−	0.839724i	−0.907588	−	0.419862i	$-0.862078\pi$
$739$		−	22.8275i		−	0.839724i	0.907588	−	0.419862i	$-0.137922\pi$
$740$	8.65768	−	14.9955i	0.318263	−	0.551247i
$741$	17.7643	−	16.6107i	0.652588	−	0.610211i
$742$	−4.38067	−	19.9493i	−0.160819	−	0.732360i
$743$	−5.89495	+	10.2104i	−0.216265	+	0.374582i	−0.953663	−	0.300877i	$-0.902721\pi$
$743$	−5.89495	+	10.2104i	−0.216265	+	0.374582i	0.737398	+	0.675458i	$0.236054\pi$
$744$	−2.59577	+	10.8390i	−0.0951656	+	0.397376i
$745$	−2.06831	−	1.19414i	−0.0757770	−	0.0437499i
$746$	−9.62708	−	16.6746i	−0.352473	−	0.610500i
$747$	−37.2831	+	1.99590i	−1.36412	+	0.0730260i
$748$	0.600806	+	1.04063i	0.0219676	+	0.0380491i
$749$	−34.5995	−	10.9856i	−1.26424	−	0.401404i
$750$	−19.8674	−	4.75796i	−0.725456	−	0.173736i
$751$	−2.07414	−	3.59252i	−0.0756864	−	0.131093i	0.825698	−	0.564112i	$-0.190781\pi$
$751$	−2.07414	−	3.59252i	−0.0756864	−	0.131093i	−0.901385	+	0.433019i	$0.857448\pi$
$752$		−	0.585446i		−	0.0213490i
$753$	−5.59396	+	23.3583i	−0.203855	+	0.851223i
$754$	25.3700	+	1.53133i	0.923920	+	0.0557676i
$755$	−9.99856			−0.363885
$756$	−6.45808	+	12.1364i	−0.234878	+	0.441398i
$757$	16.7609	−	29.0308i	0.609186	−	1.05514i	−0.382189	−	0.924084i	$-0.624830\pi$
$757$	16.7609	−	29.0308i	0.609186	−	1.05514i	0.991375	−	0.131057i	$-0.0418372\pi$
$758$		−	12.5829i		−	0.457031i
$759$	7.53880	+	1.80543i	0.273641	+	0.0655329i
$760$	−7.02218	−	4.05426i	−0.254721	−	0.147063i
$761$			7.07273i			0.256386i	0.991749	+	0.128193i	$0.0409178\pi$
$761$			7.07273i			0.256386i	−0.991749	+	0.128193i	$0.959082\pi$
$762$	−18.4987	−	17.5349i	−0.670139	−	0.635224i
$763$	7.33526	+	2.32899i	0.265554	+	0.0843152i
$764$	3.37227	+	1.94698i	0.122005	+	0.0704394i
$765$	−1.89910	−	2.91718i	−0.0686620	−	0.105471i
$766$	1.03501	−	0.597562i	0.0373964	−	0.0215908i
$767$	3.11188	−	4.70972i	0.112364	−	0.170058i
$768$	1.66045	−	0.492861i	0.0599163	−	0.0177846i
$769$	3.05595	−	5.29306i	0.110200	−	0.190872i	−0.805651	−	0.592391i	$-0.798184\pi$
$769$	3.05595	−	5.29306i	0.110200	−	0.190872i	0.915851	+	0.401518i	$0.131517\pi$
$770$	−8.77356	+	8.00716i	−0.316177	+	0.288558i
$771$	−4.29856	+	17.9492i	−0.154809	+	0.646424i
$772$	3.11672	+	1.79944i	0.112173	+	0.0647632i
$773$	−33.4359	−	19.3042i	−1.20261	−	0.694324i	−0.241471	−	0.970408i	$-0.577630\pi$
$773$	−33.4359	−	19.3042i	−1.20261	−	0.694324i	−0.961134	+	0.276084i	$0.910963\pi$
$774$	23.1811	+	11.7786i	0.833229	+	0.423374i
$775$	−2.13918	+	3.70516i	−0.0768415	+	0.133093i
$776$	−1.64731	−	2.85322i	−0.0591349	−	0.102425i
$777$	−18.4280	−	33.3585i	−0.661099	−	1.19673i
$778$	−13.1871	−	7.61359i	−0.472781	−	0.272960i
$779$	−2.07518	−	1.19811i	−0.0743511	−	0.0429266i
$780$	3.78469	−	12.4397i	0.135514	−	0.445413i
$781$	14.0779	+	24.3836i	0.503746	+	0.872513i
$782$	1.00173	−	0.578348i	0.0358217	−	0.0206817i
$783$	34.5070	−	12.2850i	1.23318	−	0.439030i
$784$	6.35598	−	2.93285i	0.226999	−	0.104744i
$785$	14.5382			0.518891
$786$	−7.09384	−	6.72424i	−0.253029	−	0.239846i
$787$	7.27190	−	12.5953i	0.259215	−	0.448974i	−0.706817	−	0.707397i	$-0.749869\pi$
$787$	7.27190	−	12.5953i	0.259215	−	0.448974i	0.966032	+	0.258423i	$0.0832028\pi$
$788$	5.48497	+	9.50024i	0.195394	+	0.338432i
$789$	−29.1669	+	30.7700i	−1.03837	+	1.09544i
$790$	20.6800	+	11.9396i	0.735760	+	0.424791i
$791$	50.3430	+	15.9842i	1.78999	+	0.568333i
$792$	0.345799	+	6.45949i	0.0122874	+	0.229528i
$793$	29.5198	+	1.78181i	1.04828	+	0.0632739i
$794$	13.0144	+	22.5415i	0.461862	+	0.799969i
$795$	20.2050	+	19.1523i	0.716597	+	0.679261i
$796$	−17.5580	+	10.1371i	−0.622328	+	0.359301i
$797$	11.4623	+	19.8532i	0.406014	+	0.703237i	0.994439	−	0.105315i	$-0.0335851\pi$
$797$	11.4623	+	19.8532i	0.406014	+	0.703237i	−0.588425	+	0.808552i	$0.700252\pi$
$798$	−15.6213	+	8.62953i	−0.552987	+	0.305482i
$799$	0.282542	−	0.163126i	0.00999563	−	0.00577098i
$800$	0.664874			0.0235068
$801$	14.2517	+	21.8918i	0.503559	+	0.773510i
$802$	−18.3498	+	31.7828i	−0.647955	+	1.12229i
$803$	−0.428855	−	0.742799i	−0.0151340	−	0.0262128i
$804$	7.02819	+	23.6780i	0.247865	+	0.835057i
$805$	7.70786	+	8.44561i	0.271666	+	0.297669i
$806$	−19.3573	−	12.7901i	−0.681833	−	0.450511i
$807$	18.3330	−	5.44168i	0.645353	−	0.191556i
$808$	15.8907			0.559035
$809$		−	35.8600i		−	1.26077i	−0.776282	−	0.630386i	$-0.782897\pi$
$809$		−	35.8600i		−	1.26077i	0.776282	−	0.630386i	$-0.217103\pi$
$810$	−2.00058	−	18.6318i	−0.0702933	−	0.654654i
$811$	48.6802			1.70939			0.854696	−	0.519129i	$-0.173743\pi$
$811$	48.6802			1.70939			0.854696	+	0.519129i	$0.173743\pi$
$812$	−17.7759	−	5.64395i	−0.623811	−	0.198064i
$813$	5.74923	−	24.0066i	0.201634	−	0.841949i
$814$	−15.5296	−	8.96600i	−0.544311	−	0.314258i
$815$	20.4875	−	35.4854i	0.717645	−	1.24300i
$816$	0.700520	+	0.664021i	0.0245231	+	0.0232454i
$817$	16.8770	+	29.2318i	0.590451	+	1.02269i
$818$	29.3160			1.02501
$819$	−19.1475	−	21.2691i	−0.669068	−	0.743201i
$820$	−1.28111			−0.0447382
$821$	−27.9725	−	48.4498i	−0.976246	−	1.69091i	−0.675759	−	0.737122i	$-0.736184\pi$
$821$	−27.9725	−	48.4498i	−0.976246	−	1.69091i	−0.300487	−	0.953786i	$-0.597149\pi$
$822$	−16.1154	−	15.2758i	−0.562089	−	0.532803i
$823$	−14.5755	+	25.2456i	−0.508071	+	0.880005i	0.491885	+	0.870660i	$0.336308\pi$
$823$	−14.5755	+	25.2456i	−0.508071	+	0.880005i	−0.999956	+	0.00934521i	$0.997025\pi$
$824$	−2.32058	−	1.33979i	−0.0808412	−	0.0466737i
$825$	−0.578318	+	2.41484i	−0.0201344	+	0.0840739i
$826$	−3.05960	+	2.79233i	−0.106457	+	0.0971576i
$827$	21.9052			0.761718			0.380859	−	0.924633i	$-0.375628\pi$
$827$	21.9052			0.761718			0.380859	+	0.924633i	$0.375628\pi$
$828$	6.21803	−	0.332873i	0.216092	−	0.0115682i
$829$			2.43272i			0.0844919i	0.999107	+	0.0422460i	$0.0134513\pi$
$829$			2.43272i			0.0844919i	−0.999107	+	0.0422460i	$0.986549\pi$
$830$	−25.9127			−0.899444
$831$	−16.2185	+	4.81405i	−0.562615	+	0.166998i
$832$	−0.217235	+	3.59900i	−0.00753126	+	0.124773i
$833$	3.18642	+	2.25027i	0.110403	+	0.0779671i
$834$	2.01600	+	6.79190i	0.0698084	+	0.235184i
$835$	13.3861	+	23.1854i	0.463244	+	0.802363i
$836$	−4.19864	+	7.27225i	−0.145213	+	0.251516i
$837$	−32.8867	−	6.03793i	−1.13673	−	0.208701i
$838$	37.0712			1.28060
$839$	44.9506	−	25.9522i	1.55187	−	0.895970i	0.553876	−	0.832599i	$-0.313148\pi$
$839$	44.9506	−	25.9522i	1.55187	−	0.895970i	0.997990	−	0.0633716i	$-0.0201853\pi$
$840$	−4.92598	+	8.17144i	−0.169962	+	0.281941i
$841$	10.3454	+	17.9187i	0.356738	+	0.617888i
$842$	−13.7970	+	7.96573i	−0.475477	+	0.274517i
$843$	0.994960	+	0.943121i	0.0342682	+	0.0324828i
$844$	6.39897	+	11.0833i	0.220262	+	0.381504i
$845$	21.6429	+	16.2549i	0.744539	+	0.559185i
$846$	1.75383	−	0.0938885i	0.0602978	−	0.00322795i
$847$	−11.3265	−	12.4106i	−0.389182	−	0.426433i
$848$	−6.68551	−	3.85988i	−0.229581	−	0.132549i
$849$	−14.0142	+	14.7845i	−0.480965	+	0.507401i
$850$	0.185257	+	0.320875i	0.00635428	+	0.0110059i
$851$	−8.63086	+	14.9491i	−0.295862	+	0.512448i
$852$	16.4143	+	15.5591i	0.562345	+	0.533046i
$853$	48.0179			1.64410			0.822051	−	0.569413i	$-0.192830\pi$
$853$	48.0179			1.64410			0.822051	+	0.569413i	$0.192830\pi$
$854$	−20.6835	−	6.56714i	−0.707775	−	0.224723i
$855$	11.0192	−	21.6866i	0.376849	−	0.741666i
$856$	−11.8825	+	6.86037i	−0.406136	+	0.234483i
$857$	−4.00763	−	6.94143i	−0.136898	−	0.237115i	0.789423	−	0.613850i	$-0.210380\pi$
$857$	−4.00763	−	6.94143i	−0.136898	−	0.237115i	−0.926321	+	0.376735i	$0.877047\pi$
$858$	−12.8827	−	3.91947i	−0.439808	−	0.133809i
$859$	10.3210	+	5.95884i	0.352148	+	0.203313i	0.665631	−	0.746281i	$-0.268162\pi$
$859$	10.3210	+	5.95884i	0.352148	+	0.203313i	−0.313483	+	0.949594i	$0.601496\pi$
$860$	15.6285	+	9.02310i	0.532926	+	0.307685i
$861$	−1.45572	+	2.41481i	−0.0496107	+	0.0822964i
$862$	14.0904	+	24.4053i	0.479920	+	0.831246i
$863$	−13.8281	+	23.9509i	−0.470713	+	0.815299i	−0.999439	−	0.0334938i	$-0.989337\pi$
$863$	−13.8281	+	23.9509i	−0.470713	+	0.815299i	0.528726	+	0.848793i	$0.322670\pi$
$864$	1.74276	+	4.89518i	0.0592898	+	0.166537i
$865$	7.98941	+	4.61269i	0.271648	+	0.156836i
$866$	10.7990	+	6.23481i	0.366965	+	0.211867i
$867$	6.73242	−	28.1121i	0.228645	−	0.954735i
$868$	11.4767	+	12.5752i	0.389544	+	0.426829i
$869$	12.3648	−	21.4164i	0.419446	−	0.726503i
$870$	24.3705	−	7.23375i	0.826237	−	0.245247i
$871$	−51.3217	−	3.09776i	−1.73897	−	0.104964i
$872$	2.51915	−	1.45443i	0.0853091	−	0.0492532i
$873$	8.28325	−	5.39243i	0.280345	−	0.182506i
$874$	7.00042	+	4.04170i	0.236793	+	0.136712i
$875$	−23.0498	+	21.0364i	−0.779227	+	0.711159i
$876$	−0.500031	−	0.473979i	−0.0168945	−	0.0160143i
$877$		−	26.9329i		−	0.909460i	−0.890629	−	0.454730i	$-0.849736\pi$
$877$		−	26.9329i		−	0.909460i	0.890629	−	0.454730i	$-0.150264\pi$
$878$	31.5375	+	18.2082i	1.06434	+	0.614496i
$879$	−12.9933	−	3.11171i	−0.438255	−	0.104956i
$880$			4.48951i			0.151341i
$881$	28.8939	−	50.0457i	0.973460	−	1.68608i	0.288533	−	0.957470i	$-0.406833\pi$
$881$	28.8939	−	50.0457i	0.973460	−	1.68608i	0.684927	−	0.728612i	$-0.259834\pi$
$882$	9.80527	+	18.5703i	0.330161	+	0.625295i
$883$	−31.0838			−1.04605			−0.523027	−	0.852316i	$-0.675197\pi$
$883$	−31.0838			−1.04605			−0.523027	+	0.852316i	$0.675197\pi$
$884$	−1.79745	+	0.897969i	−0.0604546	+	0.0302020i
$885$	1.31498	−	5.49084i	0.0442024	−	0.184573i
$886$		−	13.4530i		−	0.451961i
$887$	22.0060	+	38.1155i	0.738889	+	1.27979i	0.952996	+	0.302983i	$0.0979824\pi$
$887$	22.0060	+	38.1155i	0.738889	+	1.27979i	−0.214107	+	0.976810i	$0.568684\pi$
$888$	−14.0082	−	3.35475i	−0.470083	−	0.112578i
$889$	−38.0287	+	8.35073i	−1.27544	+	0.280075i
$890$	9.06478	+	15.7007i	0.303852	+	0.526288i
$891$	−19.2953	+	2.07183i	−0.646417	+	0.0694089i
$892$	−6.84088	−	11.8488i	−0.229050	−	0.396726i
$893$	1.97450	+	1.13998i	0.0660742	+	0.0381479i
$894$	−0.462715	+	1.93212i	−0.0154755	+	0.0646198i
$895$	−23.6626	+	40.9848i	−0.790952	+	1.36997i
$896$	0.800654	−	2.52170i	0.0267480	−	0.0842440i
$897$	−3.77296	+	12.4012i	−0.125976	+	0.414063i
$898$	10.8390	−	18.7736i	0.361700	−	0.626484i
$899$		−	45.3602i		−	1.51285i
$900$	0.106626	+	1.99177i	0.00355422	+	0.0663923i
$901$		−	4.30200i		−	0.143320i
$902$			1.32673i			0.0441753i
$903$	34.7665	−	19.2058i	1.15696	−	0.639127i
$904$	17.2893	−	9.98197i	0.575033	−	0.331995i
$905$	−10.6877	+	18.5117i	−0.355273	+	0.615350i
$906$	2.36680	+	7.97374i	0.0786316	+	0.264910i
$907$	14.8323			0.492500			0.246250	−	0.969206i	$-0.420802\pi$
$907$	14.8323			0.492500			0.246250	+	0.969206i	$0.420802\pi$
$908$	−3.24204	+	1.87179i	−0.107591	+	0.0621176i
$909$	2.54842	+	47.6041i	0.0845256	+	1.57893i
$910$	−12.4809	−	15.4507i	−0.413737	−	0.512185i
$911$			10.4486i			0.346178i	0.984906	+	0.173089i	$0.0553749\pi$
$911$			10.4486i			0.346178i	−0.984906	+	0.173089i	$0.944625\pi$
$912$	−1.57098	+	6.55980i	−0.0520202	+	0.217217i
$913$			26.8355i			0.888127i
$914$	12.5219	+	7.22952i	0.414188	+	0.239131i
$915$	28.3568	−	8.41699i	0.937448	−	0.278257i
$916$	4.38767	+	7.59967i	0.144973	+	0.251100i
$917$	−14.5831	+	3.20231i	−0.481577	+	0.105750i
$918$	−1.87687	+	2.20504i	−0.0619460	+	0.0727773i
$919$	−45.9594			−1.51606			−0.758030	−	0.652219i	$-0.773838\pi$
$919$	−45.9594			−1.51606			−0.758030	+	0.652219i	$0.773838\pi$
$920$	4.32170			0.142482
$921$	28.3550	+	26.8777i	0.934329	+	0.885649i
$922$	−29.7738	−	17.1899i	−0.980548	−	0.566120i
$923$	−42.1171	+	21.0409i	−1.38630	+	0.692569i
$924$	8.46244	+	5.10141i	0.278394	+	0.167824i
$925$	−4.78851	−	2.76465i	−0.157445	−	0.0909011i
$926$	3.07999	−	1.77823i	0.101215	−	0.0584364i
$927$	3.64146	−	7.16664i	0.119601	−	0.235383i
$928$	−6.10476	+	3.52458i	−0.200399	+	0.115700i
$929$		−	17.4133i		−	0.571311i	−0.958332	−	0.285655i	$-0.907789\pi$
$929$		−	17.4133i		−	0.571311i	0.958332	−	0.285655i	$-0.0922113\pi$
$930$	−22.5678	−	5.40465i	−0.740027	−	0.177225i
$931$	−2.48489	+	27.1473i	−0.0814391	+	0.889717i
$932$	19.0891	−	11.0211i	0.625285	−	0.361008i
$933$	−5.36010	+	22.3817i	−0.175482	+	0.732745i
$934$	0.816319			0.0267108
$935$	−2.16669	+	1.25094i	−0.0708582	+	0.0409100i
$936$	−10.8164	−	0.0735973i	−0.353545	−	0.00240560i
$937$			0.922295i			0.0301301i	0.999887	+	0.0150650i	$0.00479553\pi$
$937$			0.922295i			0.0301301i	−0.999887	+	0.0150650i	$0.995204\pi$
$938$	35.9593	+	11.4173i	1.17411	+	0.372788i
$939$	−8.39853	−	28.2946i	−0.274076	−	0.923360i
$940$	1.21895			0.0397579
$941$	9.53735	−	5.50639i	0.310909	−	0.179503i	−0.336424	−	0.941711i	$-0.609218\pi$
$941$	9.53735	−	5.50639i	0.310909	−	0.179503i	0.647333	+	0.762207i	$0.275884\pi$
$942$	−3.44139	−	11.5940i	−0.112127	−	0.377754i
$943$	1.27714			0.0415894
$944$			1.56562i			0.0509567i
$945$	−25.2692	−	13.4464i	−0.822008	−	0.437410i
$946$	9.34443	−	16.1850i	0.303814	−	0.526221i
$947$	5.08808	+	8.81281i	0.165340	+	0.286378i	0.936776	−	0.349929i	$-0.113794\pi$
$947$	5.08808	+	8.81281i	0.165340	+	0.286378i	−0.771436	+	0.636307i	$0.780461\pi$
$948$	4.62645	−	19.3183i	0.150260	−	0.627429i
$949$	1.28302	−	0.640971i	0.0416485	−	0.0208068i
$950$	−1.29464	+	2.24239i	−0.0420037	+	0.0727526i
$951$	25.2585	−	7.49734i	0.819063	−	0.243118i
$952$	1.44009	−	0.316230i	0.0466735	−	0.0102491i
$953$	−2.74974	+	1.58756i	−0.0890727	+	0.0514261i	−0.543875	−	0.839166i	$-0.683043\pi$
$953$	−2.74974	+	1.58756i	−0.0890727	+	0.0514261i	0.454802	+	0.890593i	$0.349710\pi$
$954$	10.4909	−	20.6469i	0.339656	−	0.668467i
$955$	−4.05381	+	7.02140i	−0.131178	+	0.227207i
$956$	6.17346	−	10.6927i	0.199664	−	0.345828i
$957$	−7.49136	−	25.2384i	−0.242161	−	0.815841i
$958$	32.0593	−	18.5095i	1.03579	−	0.598014i
$959$	−33.1291	+	7.27484i	−1.06979	+	0.234917i
$960$	1.02618	+	3.45721i	0.0331200	+	0.111581i
$961$	−5.20354	+	9.01280i	−0.167856	+	0.290735i
$962$	16.5298	−	25.0172i	0.532941	−	0.806587i
$963$	−22.4573	−	34.4963i	−0.723676	−	1.11163i
$964$	−0.612290	−	1.06052i	−0.0197205	−	0.0341569i
$965$	−3.74660	+	6.48931i	−0.120607	+	0.208898i
$966$	4.91072	−	8.14612i	0.158000	−	0.262097i
$967$		−	43.4041i		−	1.39578i	−0.716204	−	0.697891i	$-0.754122\pi$
$967$		−	43.4041i		−	1.39578i	0.716204	−	0.697891i	$-0.245878\pi$
$968$	−6.35061			−0.204116
$969$	−3.60356	+	1.06962i	−0.115763	+	0.0343613i
$970$	5.94069	−	3.42986i	0.190744	−	0.110126i
$971$	−2.49676			−0.0801248			−0.0400624	−	0.999197i	$-0.512756\pi$
$971$	−2.49676			−0.0801248			−0.0400624	+	0.999197i	$0.512756\pi$
$972$	−14.3851	+	6.00584i	−0.461401	+	0.192637i
$973$	10.3148	+	3.27500i	0.330676	+	0.104992i
$974$			21.7586i			0.697191i
$975$	−3.97236	−	1.20856i	−0.127217	−	0.0387049i
$976$	−7.10333	+	4.10111i	−0.227372	+	0.131273i
$977$	−26.4812			−0.847208			−0.423604	−	0.905847i	$-0.639235\pi$
$977$	−26.4812			−0.847208			−0.423604	+	0.905847i	$0.639235\pi$
$978$	−33.1488	−	7.93866i	−1.05998	−	0.253850i
$979$	16.2598	−	9.38760i	0.519666	−	0.300029i
$980$	6.10647	+	13.2338i	0.195064	+	0.422737i
$981$	4.76105	+	7.31339i	0.152009	+	0.233499i
$982$			29.7535i			0.949474i
$983$	40.2588	−	23.2434i	1.28406	−	0.741351i	0.306470	−	0.951880i	$-0.400852\pi$
$983$	40.2588	−	23.2434i	1.28406	−	0.741351i	0.977587	+	0.210530i	$0.0675188\pi$
$984$	0.303256	+	1.02167i	0.00966745	+	0.0325696i
$985$	−19.7804	+	11.4202i	−0.630257	+	0.363879i
$986$	−3.40200	−	1.96415i	−0.108342	−	0.0625512i
$987$	1.38509	−	2.29765i	0.0440879	−	0.0731350i
$988$	−11.7152	−	7.74063i	−0.372709	−	0.246262i
$989$	−15.5800	−	8.99514i	−0.495417	−	0.286029i
$990$	−13.4493	+	0.719987i	−0.427446	+	0.0228827i
$991$	−31.7381			−1.00820			−0.504098	−	0.863647i	$-0.668175\pi$
$991$	−31.7381			−1.00820			−0.504098	+	0.863647i	$0.668175\pi$
$992$	6.43483			0.204306
$993$	13.6168	−	14.3652i	0.432115	−	0.455867i
$994$	33.7436	−	7.40978i	1.07028	−	0.235024i
$995$	−21.1065	−	36.5575i	−0.669121	−	1.15895i
$996$	6.13390	+	20.6651i	0.194360	+	0.654799i
$997$	−50.8072	−	29.3335i	−1.60908	−	0.929002i	−0.989577	−	0.144007i	$-0.954001\pi$
$997$	−50.8072	−	29.3335i	−1.60908	−	0.929002i	−0.619502	−	0.784995i	$-0.712665\pi$
$998$		−	11.2045i		−	0.354672i
$999$	7.80335	−	42.5024i	0.246887	−	1.34472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.3	yes	34
3.2	odd	2		546.2.bn.f.173.15	yes	34
7.3	odd	6		546.2.bi.f.17.9	yes	34
13.10	even	6		546.2.bi.e.257.15	yes	34
21.17	even	6		546.2.bi.e.17.15	✓	34
39.23	odd	6		546.2.bi.f.257.9	yes	34
91.10	odd	6		546.2.bn.f.101.15	yes	34
273.101	even	6	inner	546.2.bn.e.101.3	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.15	✓	34	21.17	even	6
546.2.bi.e.257.15	yes	34	13.10	even	6
546.2.bi.f.17.9	yes	34	7.3	odd	6
546.2.bi.f.257.9	yes	34	39.23	odd	6
546.2.bn.e.101.3	yes	34	273.101	even	6	inner
546.2.bn.e.173.3	yes	34	1.1	even	1	trivial
546.2.bn.f.101.15	yes	34	91.10	odd	6
546.2.bn.f.173.15	yes	34	3.2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.25705 - 1.19156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.80315 - 1.04105i) q^{5} +(-0.403394 + 1.68442i) q^{6} +(1.78353 + 1.95424i) q^{7} +1.00000 q^{8} +(0.160371 + 2.99571i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.25705 - 1.19156i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.80315 - 1.04105i) q^{5} +(-0.403394 + 1.68442i) q^{6} +(1.78353 + 1.95424i) q^{7} +1.00000 q^{8} +(0.160371 + 2.99571i) q^{9} +2.08210i q^{10} +2.15624 q^{11} +(1.66045 - 0.492861i) q^{12} +(-0.217235 + 3.59900i) q^{13} +(0.800654 - 2.52170i) q^{14} +(1.02618 + 3.45721i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.278635 - 0.482611i) q^{17} +(2.51418 - 1.63674i) q^{18} +3.89440 q^{19} +(1.80315 - 1.04105i) q^{20} +(0.0865985 - 4.58176i) q^{21} +(-1.07812 - 1.86736i) q^{22} +(-1.79756 + 1.03782i) q^{23} +(-1.25705 - 1.19156i) q^{24} +(-0.332437 - 0.575798i) q^{25} +(3.22544 - 1.61137i) q^{26} +(3.36797 - 3.95686i) q^{27} +(-2.58418 + 0.567461i) q^{28} +(6.10476 + 3.52458i) q^{29} +(2.48094 - 2.61731i) q^{30} +(-3.21742 - 5.57273i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.71052 - 2.56929i) q^{33} -0.557271 q^{34} +(-1.18151 - 5.38051i) q^{35} +(-2.67455 - 1.35897i) q^{36} +(7.20214 - 4.15815i) q^{37} +(-1.94720 - 3.37265i) q^{38} +(4.56150 - 4.26529i) q^{39} +(-1.80315 - 1.04105i) q^{40} +(-0.532863 - 0.307649i) q^{41} +(-4.01122 + 2.21588i) q^{42} +(4.33366 + 7.50612i) q^{43} +(-1.07812 + 1.86736i) q^{44} +(2.82951 - 5.56866i) q^{45} +(1.79756 + 1.03782i) q^{46} +(0.507011 + 0.292723i) q^{47} +(-0.403394 + 1.68442i) q^{48} +(-0.638069 + 6.97086i) q^{49} +(-0.332437 + 0.575798i) q^{50} +(-0.925319 + 0.274657i) q^{51} +(-3.00821 - 1.98763i) q^{52} +(6.68551 - 3.85988i) q^{53} +(-5.11073 - 0.938319i) q^{54} +(-3.88803 - 2.24475i) q^{55} +(1.78353 + 1.95424i) q^{56} +(-4.89547 - 4.64041i) q^{57} -7.04917i q^{58} +(-1.35587 - 0.782812i) q^{59} +(-3.50713 - 0.839905i) q^{60} -8.20222i q^{61} +(-3.21742 + 5.57273i) q^{62} +(-5.56830 + 5.65633i) q^{63} +1.00000 q^{64} +(4.13844 - 6.26338i) q^{65} +(-0.869816 + 3.63202i) q^{66} +14.2600i q^{67} +(0.278635 + 0.482611i) q^{68} +(3.49626 + 0.837303i) q^{69} +(-4.06891 + 3.71347i) q^{70} +(6.52888 + 11.3084i) q^{71} +(0.160371 + 2.99571i) q^{72} +(-0.198890 - 0.344488i) q^{73} +(-7.20214 - 4.15815i) q^{74} +(-0.268206 + 1.11993i) q^{75} +(-1.94720 + 3.37265i) q^{76} +(3.84572 + 4.21381i) q^{77} +(-5.97460 - 1.81773i) q^{78} +(5.73441 - 9.93228i) q^{79} +2.08210i q^{80} +(-8.94856 + 0.960850i) q^{81} +0.615297i q^{82} +12.4455i q^{83} +(3.92462 + 2.36588i) q^{84} +(-1.00484 + 0.580146i) q^{85} +(4.33366 - 7.50612i) q^{86} +(-3.47426 - 11.7048i) q^{87} +2.15624 q^{88} +(7.54080 - 4.35368i) q^{89} +(-6.23736 + 0.333908i) q^{90} +(-7.42074 + 5.99438i) q^{91} -2.07565i q^{92} +(-2.59577 + 10.8390i) q^{93} -0.585446i q^{94} +(-7.02218 - 4.05426i) q^{95} +(1.66045 - 0.492861i) q^{96} +(-1.64731 - 2.85322i) q^{97} +(6.35598 - 2.93285i) q^{98} +(0.345799 + 6.45949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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