LMFDB - Embedded newform 546.2.bi.f.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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			17.9
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.f.257.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.403394 - 1.68442i) q^{3} +1.00000 q^{4} +(-1.80315 + 1.04105i) q^{5} +(0.403394 - 1.68442i) q^{6} +(-0.800654 - 2.52170i) q^{7} +1.00000 q^{8} +(-2.67455 - 1.35897i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.403394 - 1.68442i) q^{3} +1.00000 q^{4} +(-1.80315 + 1.04105i) q^{5} +(0.403394 - 1.68442i) q^{6} +(-0.800654 - 2.52170i) q^{7} +1.00000 q^{8} +(-2.67455 - 1.35897i) q^{9} +(-1.80315 + 1.04105i) q^{10} +(-1.07812 - 1.86736i) q^{11} +(0.403394 - 1.68442i) q^{12} +(0.217235 - 3.59900i) q^{13} +(-0.800654 - 2.52170i) q^{14} +(1.02618 + 3.45721i) q^{15} +1.00000 q^{16} +0.557271 q^{17} +(-2.67455 - 1.35897i) q^{18} +(1.94720 - 3.37265i) q^{19} +(-1.80315 + 1.04105i) q^{20} +(-4.57058 + 0.331402i) q^{21} +(-1.07812 - 1.86736i) q^{22} -2.07565i q^{23} +(0.403394 - 1.68442i) q^{24} +(-0.332437 + 0.575798i) q^{25} +(0.217235 - 3.59900i) q^{26} +(-3.36797 + 3.95686i) q^{27} +(-0.800654 - 2.52170i) q^{28} +(6.10476 + 3.52458i) q^{29} +(1.02618 + 3.45721i) q^{30} +(3.21742 - 5.57273i) q^{31} +1.00000 q^{32} +(-3.58033 + 1.06273i) q^{33} +0.557271 q^{34} +(4.06891 + 3.71347i) q^{35} +(-2.67455 - 1.35897i) q^{36} +8.31631i q^{37} +(1.94720 - 3.37265i) q^{38} +(-5.97460 - 1.81773i) q^{39} +(-1.80315 + 1.04105i) q^{40} +(0.532863 + 0.307649i) q^{41} +(-4.57058 + 0.331402i) q^{42} +(4.33366 + 7.50612i) q^{43} +(-1.07812 - 1.86736i) q^{44} +(6.23736 - 0.333908i) q^{45} -2.07565i q^{46} +(0.507011 - 0.292723i) q^{47} +(0.403394 - 1.68442i) q^{48} +(-5.71791 + 4.03801i) q^{49} +(-0.332437 + 0.575798i) q^{50} +(0.224800 - 0.938678i) q^{51} +(0.217235 - 3.59900i) q^{52} +(-6.68551 - 3.85988i) q^{53} +(-3.36797 + 3.95686i) q^{54} +(3.88803 + 2.24475i) q^{55} +(-0.800654 - 2.52170i) q^{56} +(-4.89547 - 4.64041i) q^{57} +(6.10476 + 3.52458i) q^{58} -1.56562i q^{59} +(1.02618 + 3.45721i) q^{60} +(-7.10333 - 4.10111i) q^{61} +(3.21742 - 5.57273i) q^{62} +(-1.28552 + 7.83246i) q^{63} +1.00000 q^{64} +(3.35503 + 6.71569i) q^{65} +(-3.58033 + 1.06273i) q^{66} +(12.3495 - 7.12999i) q^{67} +0.557271 q^{68} +(-3.49626 - 0.837303i) q^{69} +(4.06891 + 3.71347i) q^{70} +(6.52888 + 11.3084i) q^{71} +(-2.67455 - 1.35897i) q^{72} +(0.198890 - 0.344488i) q^{73} +8.31631i q^{74} +(0.835783 + 0.792237i) 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} +(-1.80315 + 1.04105i) q^{80} +(5.30640 + 7.26926i) q^{81} +(0.532863 + 0.307649i) q^{82} -12.4455i q^{83} +(-4.57058 + 0.331402i) q^{84} +(-1.00484 + 0.580146i) q^{85} +(4.33366 + 7.50612i) q^{86} +(8.39951 - 8.86119i) q^{87} +(-1.07812 - 1.86736i) q^{88} -8.70736i q^{89} +(6.23736 - 0.333908i) q^{90} +(-9.24952 + 2.33375i) q^{91} -2.07565i q^{92} +(-8.08894 - 7.66749i) q^{93} +(0.507011 - 0.292723i) q^{94} +8.10851i q^{95} +(0.403394 - 1.68442i) q^{96} +(1.64731 + 2.85322i) q^{97} +(-5.71791 + 4.03801i) q^{98} +(0.345799 + 6.45949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.403394	−	1.68442i	0.232900	−	0.972501i
$3$	0.403394	−	1.68442i	0.232900	−	0.972501i
$4$	1.00000			0.500000
$5$	−1.80315	+	1.04105i	−0.806393	+	0.465571i	−0.845702	−	0.533656i	$-0.820818\pi$
$5$	−1.80315	+	1.04105i	−0.806393	+	0.465571i	0.0393090	+	0.999227i	$0.487484\pi$
$6$	0.403394	−	1.68442i	0.164685	−	0.687662i
$7$	−0.800654	−	2.52170i	−0.302619	−	0.953112i
$7$	−0.800654	−	2.52170i	−0.302619	−	0.953112i
$8$	1.00000			0.353553
$9$	−2.67455	−	1.35897i	−0.891516	−	0.452990i
$10$	−1.80315	+	1.04105i	−0.570206	+	0.329208i
$11$	−1.07812	−	1.86736i	−0.325066	−	0.563031i	0.656460	−	0.754361i	$-0.272053\pi$
$11$	−1.07812	−	1.86736i	−0.325066	−	0.563031i	−0.981526	+	0.191330i	$0.938720\pi$
$12$	0.403394	−	1.68442i	0.116450	−	0.486250i
$13$	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
$16$	1.00000			0.250000
$17$	0.557271			0.135158			0.0675790	−	0.997714i	$-0.478473\pi$
$17$	0.557271			0.135158			0.0675790	+	0.997714i	$0.478473\pi$
$18$	−2.67455	−	1.35897i	−0.630397	−	0.320312i
$19$	1.94720	−	3.37265i	0.446718	−	0.773738i	−0.551452	−	0.834207i	$-0.685926\pi$
$19$	1.94720	−	3.37265i	0.446718	−	0.773738i	0.998170	+	0.0604682i	$0.0192594\pi$
$20$	−1.80315	+	1.04105i	−0.403196	+	0.232785i
$21$	−4.57058	+	0.331402i	−0.997382	+	0.0723178i
$22$	−1.07812	−	1.86736i	−0.229856	−	0.398123i
$23$		−	2.07565i		−	0.432802i	−0.976305	−	0.216401i	$-0.930568\pi$
$23$		−	2.07565i		−	0.432802i	0.976305	−	0.216401i	$-0.0694319\pi$
$24$	0.403394	−	1.68442i	0.0823424	−	0.343831i
$25$	−0.332437	+	0.575798i	−0.0664874	+	0.115160i
$26$	0.217235	−	3.59900i	0.0426033	−	0.705822i
$27$	−3.36797	+	3.95686i	−0.648167	+	0.761499i
$28$	−0.800654	−	2.52170i	−0.151309	−	0.476556i
$29$	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	$0.439546\pi$
$30$	1.02618	+	3.45721i	0.187355	+	0.631198i
$31$	3.21742	−	5.57273i	0.577865	−	1.00089i	−0.417859	−	0.908512i	$-0.637219\pi$
$31$	3.21742	−	5.57273i	0.577865	−	1.00089i	0.995724	−	0.0923797i	$-0.0294474\pi$
$32$	1.00000			0.176777
$33$	−3.58033	+	1.06273i	−0.623256	+	0.184997i
$34$	0.557271			0.0955711
$35$	4.06891	+	3.71347i	0.687771	+	0.627692i
$36$	−2.67455	−	1.35897i	−0.445758	−	0.226495i
$37$			8.31631i			1.36719i	0.729860	+	0.683596i	$0.239585\pi$
$37$			8.31631i			1.36719i	−0.729860	+	0.683596i	$0.760415\pi$
$38$	1.94720	−	3.37265i	0.315877	−	0.547116i
$39$	−5.97460	−	1.81773i	−0.956702	−	0.291070i
$40$	−1.80315	+	1.04105i	−0.285103	+	0.164604i
$41$	0.532863	+	0.307649i	0.0832192	+	0.0480466i	0.541032	−	0.841002i	$-0.318034\pi$
$41$	0.532863	+	0.307649i	0.0832192	+	0.0480466i	−0.457813	+	0.889049i	$0.651367\pi$
$42$	−4.57058	+	0.331402i	−0.705255	+	0.0511364i
$43$	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
$45$	6.23736	−	0.333908i	0.929810	−	0.0497761i
$46$		−	2.07565i		−	0.306037i
$47$	0.507011	−	0.292723i	0.0739551	−	0.0426980i	−0.462566	−	0.886585i	$-0.653071\pi$
$47$	0.507011	−	0.292723i	0.0739551	−	0.0426980i	0.536522	+	0.843887i	$0.319738\pi$
$48$	0.403394	−	1.68442i	0.0582249	−	0.243125i
$49$	−5.71791	+	4.03801i	−0.816844	+	0.576859i
$50$	−0.332437	+	0.575798i	−0.0470137	+	0.0814301i
$51$	0.224800	−	0.938678i	0.0314782	−	0.131441i
$52$	0.217235	−	3.59900i	0.0301251	−	0.499092i
$53$	−6.68551	−	3.85988i	−0.918325	−	0.530195i	−0.0352249	−	0.999379i	$-0.511215\pi$
$53$	−6.68551	−	3.85988i	−0.918325	−	0.530195i	−0.883100	+	0.469184i	$0.844548\pi$
$54$	−3.36797	+	3.95686i	−0.458323	+	0.538461i
$55$	3.88803	+	2.24475i	0.524262	+	0.302683i
$56$	−0.800654	−	2.52170i	−0.106992	−	0.336976i
$57$	−4.89547	−	4.64041i	−0.648421	−	0.614637i
$58$	6.10476	+	3.52458i	0.801594	+	0.462801i
$59$		−	1.56562i		−	0.203827i	−0.994793	−	0.101913i	$-0.967504\pi$
$59$		−	1.56562i		−	0.203827i	0.994793	−	0.101913i	$-0.0324965\pi$
$60$	1.02618	+	3.45721i	0.132480	+	0.446324i
$61$	−7.10333	−	4.10111i	−0.909488	−	0.525093i	−0.0292218	−	0.999573i	$-0.509303\pi$
$61$	−7.10333	−	4.10111i	−0.909488	−	0.525093i	−0.880266	+	0.474480i	$0.842636\pi$
$62$	3.21742	−	5.57273i	0.408612	−	0.707737i
$63$	−1.28552	+	7.83246i	−0.161961	+	0.986797i
$64$	1.00000			0.125000
$65$	3.35503	+	6.71569i	0.416140	+	0.832978i
$66$	−3.58033	+	1.06273i	−0.440708	+	0.130813i
$67$	12.3495	−	7.12999i	1.50873	−	0.871067i	0.508784	−	0.860894i	$-0.330095\pi$
$67$	12.3495	−	7.12999i	1.50873	−	0.871067i	0.999948	−	0.0101724i	$-0.00323804\pi$
$68$	0.557271			0.0675790
$69$	−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	$0.551166\pi$
$72$	−2.67455	−	1.35897i	−0.315198	−	0.160156i
$73$	0.198890	−	0.344488i	0.0232783	−	0.0403192i	−0.854152	−	0.520024i	$-0.825923\pi$
$73$	0.198890	−	0.344488i	0.0232783	−	0.0403192i	0.877430	+	0.479705i	$0.159256\pi$
$74$			8.31631i			0.966751i
$75$	0.835783	+	0.792237i	0.0965079	+	0.0914796i
$76$	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	0.984262	+	0.176715i	$0.0565472\pi$
$79$	5.73441	+	9.93228i	0.645171	+	1.11747i	−0.339091	+	0.940754i	$0.610119\pi$
$80$	−1.80315	+	1.04105i	−0.201598	+	0.116393i
$81$	5.30640	+	7.26926i	0.589600	+	0.807695i
$82$	0.532863	+	0.307649i	0.0588449	+	0.0339741i
$83$		−	12.4455i		−	1.36607i	−0.730385	−	0.683035i	$-0.760660\pi$
$83$		−	12.4455i		−	1.36607i	0.730385	−	0.683035i	$-0.239340\pi$
$84$	−4.57058	+	0.331402i	−0.498691	+	0.0361589i
$85$	−1.00484	+	0.580146i	−0.108990	+	0.0629256i
$86$	4.33366	+	7.50612i	0.467310	+	0.809405i
$87$	8.39951	−	8.86119i	0.900522	−	0.950019i
$88$	−1.07812	−	1.86736i	−0.114928	−	0.199062i
$89$		−	8.70736i		−	0.922978i	−0.887146	−	0.461489i	$-0.847315\pi$
$89$		−	8.70736i		−	0.922978i	0.887146	−	0.461489i	$-0.152685\pi$
$90$	6.23736	−	0.333908i	0.657475	−	0.0351970i
$91$	−9.24952	+	2.33375i	−0.969613	+	0.244644i
$92$		−	2.07565i		−	0.216401i
$93$	−8.08894	−	7.66749i	−0.838783	−	0.795081i
$94$	0.507011	−	0.292723i	0.0522942	−	0.0301921i
$95$			8.10851i			0.831916i
$96$	0.403394	−	1.68442i	0.0411712	−	0.171915i
$97$	1.64731	+	2.85322i	0.167259	+	0.289701i	0.937455	−	0.348106i	$-0.113175\pi$
$97$	1.64731	+	2.85322i	0.167259	+	0.289701i	−0.770196	+	0.637807i	$0.779842\pi$
$98$	−5.71791	+	4.03801i	−0.577596	+	0.407901i
$99$	0.345799	+	6.45949i	0.0347541	+	0.649203i
$100$	−0.332437	+	0.575798i	−0.0332437	+	0.0575798i
$101$	7.94537	+	13.7618i	0.790594	+	1.36935i	0.925599	+	0.378505i	$0.123562\pi$
$101$	7.94537	+	13.7618i	0.790594	+	1.36935i	−0.135005	+	0.990845i	$0.543105\pi$
$102$	0.224800	−	0.938678i	0.0222585	−	0.0929430i
$103$	−2.32058	+	1.33979i	−0.228653	+	0.132013i	−0.609951	−	0.792439i	$-0.708811\pi$
$103$	−2.32058	+	1.33979i	−0.228653	+	0.132013i	0.381297	+	0.924452i	$0.375477\pi$
$104$	0.217235	−	3.59900i	0.0213016	−	0.352911i
$105$	7.89642	−	5.35576i	0.770612	−	0.522668i
$106$	−6.68551	−	3.85988i	−0.649354	−	0.374905i
$107$		−	13.7207i		−	1.32643i	−0.748427	−	0.663217i	$-0.769191\pi$
$107$		−	13.7207i		−	1.32643i	0.748427	−	0.663217i	$-0.230809\pi$
$108$	−3.36797	+	3.95686i	−0.324083	+	0.380749i
$109$	−2.51915	−	1.45443i	−0.241291	−	0.139309i	0.374479	−	0.927235i	$-0.377822\pi$
$109$	−2.51915	−	1.45443i	−0.241291	−	0.139309i	−0.615770	+	0.787926i	$0.711155\pi$
$110$	3.88803	+	2.24475i	0.370709	+	0.214029i
$111$	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	$-0.0549357\pi$
$114$	−4.89547	−	4.64041i	−0.458503	−	0.434614i
$115$	2.16085	+	3.74270i	0.201500	+	0.349008i
$116$	6.10476	+	3.52458i	0.566813	+	0.327249i
$117$	−5.47194	+	9.33048i	−0.505881	+	0.862603i
$118$		−	1.56562i		−	0.144127i
$119$	−0.446181	−	1.40527i	−0.0409014	−	0.128821i
$120$	1.02618	+	3.45721i	0.0936774	+	0.315599i
$121$	3.17530	−	5.49979i	0.288664	−	0.499981i
$122$	−7.10333	−	4.10111i	−0.643105	−	0.371297i
$123$	0.733163	−	0.773462i	0.0661071	−	0.0697407i
$124$	3.21742	−	5.57273i	0.288933	−	0.500446i
$125$		−	11.7948i		−	1.05496i
$126$	−1.28552	+	7.83246i	−0.114523	+	0.697771i
$127$	−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	$0.940213\pi$
$128$	1.00000			0.0883883
$129$	14.3916	−	4.27178i	1.26711	−	0.376110i
$130$	3.35503	+	6.71569i	0.294255	+	0.589005i
$131$	2.82161	+	4.88718i	0.246526	+	0.426995i	0.962559	−	0.271071i	$-0.0873777\pi$
$131$	2.82161	+	4.88718i	0.246526	+	0.426995i	−0.716034	+	0.698066i	$0.754044\pi$
$132$	−3.58033	+	1.06273i	−0.311628	+	0.0924987i
$133$	−10.0638	−	2.20992i	−0.872644	−	0.191624i
$134$	12.3495	−	7.12999i	1.06683	−	0.615937i
$135$	1.95367	−	10.6410i	0.168145	−	0.915834i
$136$	0.557271			0.0477856
$137$	12.8200			1.09528			0.547642	−	0.836713i	$-0.315526\pi$
$137$	12.8200			1.09528			0.547642	+	0.836713i	$0.315526\pi$
$138$	−3.49626	−	0.837303i	−0.297622	−	0.0712759i
$139$	−3.54239	+	2.04520i	−0.300462	+	0.173472i	−0.642650	−	0.766160i	$-0.722165\pi$
$139$	−3.54239	+	2.04520i	−0.300462	+	0.173472i	0.342189	+	0.939631i	$0.388832\pi$
$140$	4.06891	+	3.71347i	0.343885	+	0.313846i
$141$	−0.288543	−	0.972102i	−0.0242997	−	0.0818658i
$142$	6.52888	+	11.3084i	0.547892	+	0.948976i
$143$	−6.95485	+	3.47451i	−0.581593	+	0.290553i
$144$	−2.67455	−	1.35897i	−0.222879	−	0.113247i
$145$	−14.6771			−1.21886
$146$	0.198890	−	0.344488i	0.0164603	−	0.0285100i
$147$	4.49515	+	11.2603i	0.370753	+	0.928731i
$148$			8.31631i			0.683596i
$149$	−0.573527	+	0.993378i	−0.0469852	+	0.0813807i	−0.888562	−	0.458757i	$-0.848295\pi$
$149$	−0.573527	+	0.993378i	−0.0469852	+	0.0813807i	0.841576	+	0.540138i	$0.181628\pi$
$150$	0.835783	+	0.792237i	0.0682414	+	0.0646859i
$151$	−4.15879	−	2.40108i	−0.338438	−	0.195397i	0.321143	−	0.947031i	$-0.395933\pi$
$151$	−4.15879	−	2.40108i	−0.338438	−	0.195397i	−0.659581	+	0.751633i	$0.729266\pi$
$152$	1.94720	−	3.37265i	0.157939	−	0.273558i
$153$	−1.49045	−	0.757314i	−0.120495	−	0.0612252i
$154$	−3.84572	+	4.21381i	−0.309897	+	0.339558i
$155$			13.3979i			1.07615i
$156$	−5.97460	−	1.81773i	−0.478351	−	0.145535i
$157$	−6.04701	−	3.49124i	−0.482604	−	0.278631i	0.238897	−	0.971045i	$-0.423214\pi$
$157$	−6.04701	−	3.49124i	−0.482604	−	0.278631i	−0.721501	+	0.692414i	$0.756547\pi$
$158$	5.73441	+	9.93228i	0.456205	+	0.790170i
$159$	−9.19856	+	9.70416i	−0.729493	+	0.769590i
$160$	−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
$163$	−17.0431	−	9.83983i	−1.33492	−	0.770715i	−0.348869	−	0.937171i	$-0.613434\pi$
$163$	−17.0431	−	9.83983i	−1.33492	−	0.770715i	−0.986049	+	0.166456i	$0.946768\pi$
$164$	0.532863	+	0.307649i	0.0416096	+	0.0240233i
$165$	5.34952	−	5.64356i	0.416459	−	0.439350i
$166$		−	12.4455i		−	0.965958i
$167$	11.1356	+	6.42913i	0.861698	+	0.497501i	0.864580	−	0.502495i	$-0.167584\pi$
$167$	11.1356	+	6.42913i	0.861698	+	0.497501i	−0.00288283	+	0.999996i	$0.500918\pi$
$168$	−4.57058	+	0.331402i	−0.352628	+	0.0255682i
$169$	−12.9056	−	1.56366i	−0.992740	−	0.120281i
$170$	−1.00484	+	0.580146i	−0.0770679	+	0.0444951i
$171$	−9.79120	+	6.37412i	−0.748752	+	0.487441i
$172$	4.33366	+	7.50612i	0.330438	+	0.572336i
$173$	−2.21541	+	3.83719i	−0.168434	+	0.291736i	−0.937869	−	0.346988i	$-0.887204\pi$
$173$	−2.21541	+	3.83719i	−0.168434	+	0.291736i	0.769435	+	0.638725i	$0.220538\pi$
$174$	8.39951	−	8.86119i	0.636765	−	0.671765i
$175$	1.71815	+	0.377290i	0.129880	+	0.0285205i
$176$	−1.07812	−	1.86736i	−0.0812665	−	0.140758i
$177$	−2.63717	−	0.631563i	−0.198222	−	0.0474712i
$178$		−	8.70736i		−	0.652644i
$179$	−19.6844	+	11.3648i	−1.47128	+	0.849443i	−0.999479	−	0.0322629i	$-0.989729\pi$
$179$	−19.6844	+	11.3648i	−1.47128	+	0.849443i	−0.471799	+	0.881706i	$0.656395\pi$
$180$	6.23736	−	0.333908i	0.464905	−	0.0248880i
$181$			10.2663i			0.763090i	0.924350	+	0.381545i	$0.124608\pi$
$181$			10.2663i			0.763090i	−0.924350	+	0.381545i	$0.875392\pi$
$182$	−9.24952	+	2.33375i	−0.685620	+	0.172989i
$183$	−9.77343	+	10.3106i	−0.722473	+	0.762184i
$184$		−	2.07565i		−	0.153019i
$185$	−8.65768	−	14.9955i	−0.636525	−	1.10249i
$186$	−8.08894	−	7.66749i	−0.593109	−	0.562208i
$187$	−0.600806	−	1.04063i	−0.0439353	−	0.0760982i
$188$	0.507011	−	0.292723i	0.0369776	−	0.0213490i
$189$	12.6746	+	5.32493i	0.921941	+	0.387331i
$190$			8.10851i			0.588253i
$191$	3.37227	+	1.94698i	0.244009	+	0.140879i	0.617018	−	0.786949i	$-0.288341\pi$
$191$	3.37227	+	1.94698i	0.244009	+	0.140879i	−0.373009	+	0.927828i	$0.621674\pi$
$192$	0.403394	−	1.68442i	0.0291124	−	0.121563i
$193$	−3.11672	+	1.79944i	−0.224346	+	0.129526i	−0.607961	−	0.793967i	$-0.708012\pi$
$193$	−3.11672	+	1.79944i	−0.224346	+	0.129526i	0.383615	+	0.923493i	$0.374679\pi$
$194$	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	$0.0388693\pi$
$198$	0.345799	+	6.45949i	0.0245749	+	0.459056i
$199$			20.2743i			1.43721i	0.695421	+	0.718603i	$0.255218\pi$
$199$			20.2743i			1.43721i	−0.695421	+	0.718603i	$0.744782\pi$
$200$	−0.332437	+	0.575798i	−0.0235068	+	0.0407150i
$201$	−7.02819	−	23.6780i	−0.495730	−	1.67011i
$202$	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
$205$	−1.28111			−0.0894765
$206$	−2.32058	+	1.33979i	−0.161682	+	0.0933474i
$207$	−2.82074	+	5.55141i	−0.196055	+	0.385850i
$208$	0.217235	−	3.59900i	0.0150625	−	0.249546i
$209$	−8.39727			−0.580852
$210$	7.89642	−	5.35576i	0.544905	−	0.369582i
$211$	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	$0.0214596\pi$
$212$	−6.68551	−	3.85988i	−0.459163	−	0.265098i
$213$	21.6817	−	6.43567i	1.48561	−	0.440965i
$214$		−	13.7207i		−	0.937930i
$215$	−15.6285	−	9.02310i	−1.06585	−	0.615370i
$216$	−3.36797	+	3.95686i	−0.229162	+	0.269230i
$217$	−16.6288	−	3.65152i	−1.12883	−	0.247881i
$218$	−2.51915	−	1.45443i	−0.170618	−	0.0985065i
$219$	−0.500031	−	0.473979i	−0.0337890	−	0.0320285i
$220$	3.88803	+	2.24475i	0.262131	+	0.151341i
$221$	0.121059	−	2.00562i	0.00814328	−	0.134912i
$222$	14.0082	+	3.35475i	0.940166	+	0.225156i
$223$	6.84088	−	11.8488i	0.458099	−	0.793451i	−0.540761	−	0.841176i	$-0.681864\pi$
$223$	6.84088	−	11.8488i	0.458099	−	0.793451i	0.998861	+	0.0477249i	$0.0151971\pi$
$224$	−0.800654	−	2.52170i	−0.0534960	−	0.168488i
$225$	1.67161	−	1.08823i	0.111441	−	0.0725484i
$226$	17.2893	−	9.98197i	1.15007	−	0.663991i
$227$			3.74358i			0.248470i	0.992253	+	0.124235i	$0.0396477\pi$
$227$			3.74358i			0.248470i	−0.992253	+	0.124235i	$0.960352\pi$
$228$	−4.89547	−	4.64041i	−0.324210	−	0.307318i
$229$	−4.38767	−	7.59967i	−0.289946	−	0.502201i	0.683851	−	0.729622i	$-0.260304\pi$
$229$	−4.38767	−	7.59967i	−0.289946	−	0.502201i	−0.973796	+	0.227421i	$0.926971\pi$
$230$	2.16085	+	3.74270i	0.142482	+	0.246786i
$231$	5.54649	+	8.17763i	0.364932	+	0.538049i
$232$	6.10476	+	3.52458i	0.400797	+	0.231400i
$233$	19.0891	−	11.0211i	1.25057	−	0.722017i	0.279347	−	0.960190i	$-0.409882\pi$
$233$	19.0891	−	11.0211i	1.25057	−	0.722017i	0.971223	+	0.238173i	$0.0765487\pi$
$234$	−5.47194	+	9.33048i	−0.357712	+	0.609953i
$235$	−0.609477	+	1.05565i	−0.0397579	+	0.0688627i
$236$		−	1.56562i		−	0.101913i
$237$	19.0434	−	5.65253i	1.23700	−	0.367171i
$238$	−0.446181	−	1.40527i	−0.0289216	−	0.0910900i
$239$	−12.3469			−0.798656			−0.399328	−	0.916808i	$-0.630757\pi$
$239$	−12.3469			−0.798656			−0.399328	+	0.916808i	$0.630757\pi$
$240$	1.02618	+	3.45721i	0.0662399	+	0.223162i
$241$	−1.22458			−0.0788821			−0.0394410	−	0.999222i	$-0.512558\pi$
$241$	−1.22458			−0.0788821			−0.0394410	+	0.999222i	$0.512558\pi$
$242$	3.17530	−	5.49979i	0.204116	−	0.353540i
$243$	14.3851	−	6.00584i	0.922802	−	0.385275i
$244$	−7.10333	−	4.10111i	−0.454744	−	0.262547i
$245$	6.10647	−	13.2338i	0.390128	−	0.845474i
$246$	0.733163	−	0.773462i	0.0467448	−	0.0493141i
$247$	−11.7152	−	7.74063i	−0.745418	−	0.492524i
$248$	3.21742	−	5.57273i	0.204306	−	0.353869i
$249$	−20.9635	−	5.02044i	−1.32850	−	0.318157i
$250$		−	11.7948i		−	0.745970i
$251$	6.93362	+	12.0094i	0.437646	+	0.758026i	0.997507	−	0.0705608i	$-0.0224789\pi$
$251$	6.93362	+	12.0094i	0.437646	+	0.758026i	−0.559861	+	0.828586i	$0.689146\pi$
$252$	−1.28552	+	7.83246i	−0.0809803	+	0.493399i
$253$	−3.87598	+	2.23780i	−0.243681	+	0.140689i
$254$	−7.35797	+	12.7444i	−0.461680	+	0.799654i
$255$	0.571863	+	1.92660i	0.0358114	+	0.120649i
$256$	1.00000			0.0625000
$257$	−10.6560			−0.664703			−0.332351	−	0.943156i	$-0.607842\pi$
$257$	−10.6560			−0.664703			−0.332351	+	0.943156i	$0.607842\pi$
$258$	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
$261$	−11.5377	−	17.7229i	−0.714163	−	1.09702i
$262$	2.82161	+	4.88718i	0.174320	+	0.301931i
$263$	−21.1985	+	12.2389i	−1.30715	+	0.754686i	−0.981620	−	0.190844i	$-0.938877\pi$
$263$	−21.1985	+	12.2389i	−1.30715	+	0.754686i	−0.325534	+	0.945530i	$0.605544\pi$
$264$	−3.58033	+	1.06273i	−0.220354	+	0.0654065i
$265$	16.0733			0.987374
$266$	−10.0638	−	2.20992i	−0.617053	−	0.135499i
$267$	−14.6669	−	3.51250i	−0.897597	−	0.214961i
$268$	12.3495	−	7.12999i	0.754366	−	0.435533i
$269$	−11.0410			−0.673182			−0.336591	−	0.941651i	$-0.609274\pi$
$269$	−11.0410			−0.673182			−0.336591	+	0.941651i	$0.609274\pi$
$270$	1.95367	−	10.6410i	0.118897	−	0.647593i
$271$	14.2522			0.865757			0.432879	−	0.901452i	$-0.357498\pi$
$271$	14.2522			0.865757			0.432879	+	0.901452i	$0.357498\pi$
$272$	0.557271			0.0337895
$273$	0.199826	+	16.5215i	0.0120940	+	0.999927i
$274$	12.8200			0.774483
$275$	1.43363			0.0864512
$276$	−3.49626	−	0.837303i	−0.210450	−	0.0503997i
$277$	−9.76756			−0.586876			−0.293438	−	0.955978i	$-0.594799\pi$
$277$	−9.76756			−0.586876			−0.293438	+	0.955978i	$0.594799\pi$
$278$	−3.54239	+	2.04520i	−0.212459	+	0.122663i
$279$	−16.1783	+	10.5322i	−0.968570	+	0.630544i
$280$	4.06891	+	3.71347i	0.243164	+	0.221922i
$281$	−0.791501			−0.0472170			−0.0236085	−	0.999721i	$-0.507516\pi$
$281$	−0.791501			−0.0472170			−0.0236085	+	0.999721i	$0.507516\pi$
$282$	−0.288543	−	0.972102i	−0.0171825	−	0.0578878i
$283$	10.1855	−	5.88059i	0.605464	−	0.349565i	−0.165724	−	0.986172i	$-0.552996\pi$
$283$	10.1855	−	5.88059i	0.605464	−	0.349565i	0.771188	+	0.636607i	$0.219663\pi$
$284$	6.52888	+	11.3084i	0.387418	+	0.671028i
$285$	13.6581	+	3.27092i	0.809039	+	0.193753i
$286$	−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
$289$	−16.6894			−0.981732
$290$	−14.6771			−0.861866
$291$	5.47054	−	1.62379i	0.320689	−	0.0951882i
$292$	0.198890	−	0.344488i	0.0116392	−	0.0201596i
$293$	−6.68038	+	3.85692i	−0.390272	+	0.225324i	−0.682278	−	0.731093i	$-0.739011\pi$
$293$	−6.68038	+	3.85692i	−0.390272	+	0.225324i	0.292006	+	0.956416i	$0.405677\pi$
$294$	4.49515	+	11.2603i	0.262162	+	0.656712i
$295$	1.62989	+	2.82305i	0.0948959	+	0.164364i
$296$			8.31631i			0.483376i
$297$	11.0200	+	2.02325i	0.639444	+	0.117401i
$298$	−0.573527	+	0.993378i	−0.0332235	+	0.0575449i
$299$	−7.47025	−	0.450903i	−0.432016	−	0.0260764i
$300$	0.835783	+	0.792237i	0.0482539	+	0.0457398i
$301$	15.4584	−	16.9380i	0.891007	−	0.976289i
$302$	−4.15879	−	2.40108i	−0.239312	−	0.138167i
$303$	26.3858	−	7.83193i	1.51582	−	0.449933i
$304$	1.94720	−	3.37265i	0.111680	−	0.193435i
$305$	17.0778			0.977873
$306$	−1.49045	−	0.757314i	−0.0852032	−	0.0432928i
$307$	22.5567			1.28738			0.643689	−	0.765287i	$-0.277403\pi$
$307$	22.5567			1.28738			0.643689	+	0.765287i	$0.277403\pi$
$308$	−3.84572	+	4.21381i	−0.219130	+	0.240104i
$309$	1.32066	+	4.44929i	0.0751296	+	0.253111i
$310$			13.3979i			0.760952i
$311$	6.64375	−	11.5073i	0.376733	−	0.652520i	−0.613852	−	0.789421i	$-0.710381\pi$
$311$	6.64375	−	11.5073i	0.376733	−	0.652520i	0.990585	+	0.136901i	$0.0437143\pi$
$312$	−5.97460	−	1.81773i	−0.338245	−	0.102909i
$313$	14.7574	−	8.52018i	0.834137	−	0.481589i	−0.0211303	−	0.999777i	$-0.506726\pi$
$313$	14.7574	−	8.52018i	0.834137	−	0.481589i	0.855267	+	0.518188i	$0.173393\pi$
$314$	−6.04701	−	3.49124i	−0.341252	−	0.197022i
$315$	−5.83598	−	15.4614i	−0.328820	−	0.871150i
$316$	5.73441	+	9.93228i	0.322585	+	0.558734i
$317$	−7.60593	−	13.1739i	−0.427192	−	0.739918i	0.569431	−	0.822039i	$-0.307164\pi$
$317$	−7.60593	−	13.1739i	−0.427192	−	0.739918i	−0.996622	+	0.0821217i	$0.973830\pi$
$318$	−9.19856	+	9.70416i	−0.515829	+	0.544182i
$319$		−	15.1997i		−	0.851022i
$320$	−1.80315	+	1.04105i	−0.100799	+	0.0581964i
$321$	−23.1115	−	5.53486i	−1.28996	−	0.308926i
$322$	−5.23415	+	1.66187i	−0.291688	+	0.0926126i
$323$	1.08512	−	1.87948i	0.0603775	−	0.104577i
$324$	5.30640	+	7.26926i	0.294800	+	0.403848i
$325$	2.00008	+	1.32152i	0.110944	+	0.0733050i
$326$	−17.0431	−	9.83983i	−0.943929	−	0.544978i
$327$	−3.46608	+	3.65660i	−0.191675	+	0.202210i
$328$	0.532863	+	0.307649i	0.0294224	+	0.0169871i
$329$	−1.14410	−	1.04416i	−0.0630762	−	0.0575663i
$330$	5.34952	−	5.64356i	0.294481	−	0.310668i
$331$	−9.89667	−	5.71384i	−0.543970	−	0.314061i	0.202716	−	0.979238i	$-0.435023\pi$
$331$	−9.89667	−	5.71384i	−0.543970	−	0.314061i	−0.746686	+	0.665176i	$0.768356\pi$
$332$		−	12.4455i		−	0.683035i
$333$	11.3016	−	22.2424i	0.619325	−	1.21887i
$334$	11.1356	+	6.42913i	0.609312	+	0.351787i
$335$	−14.8453	+	25.7129i	−0.811087	+	1.40484i
$336$	−4.57058	+	0.331402i	−0.249345	+	0.0180794i
$337$	0.692991			0.0377496			0.0188748	−	0.999822i	$-0.493992\pi$
$337$	0.692991			0.0377496			0.0188748	+	0.999822i	$0.493992\pi$
$338$	−12.9056	−	1.56366i	−0.701973	−	0.0850517i
$339$	−9.83945	−	33.1491i	−0.534406	−	1.80041i
$340$	−1.00484	+	0.580146i	−0.0544952	+	0.0314628i
$341$	−13.8751			−0.751377
$342$	−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
$345$	7.17595	−	2.13000i	0.386340	−	0.114675i
$346$	−2.21541	+	3.83719i	−0.119101	+	0.206289i
$347$			14.8415i			0.796733i	0.917226	+	0.398366i	$0.130423\pi$
$347$			14.8415i			0.796733i	−0.917226	+	0.398366i	$0.869577\pi$
$348$	8.39951	−	8.86119i	0.450261	−	0.475010i
$349$	−9.35756	+	16.2078i	−0.500899	+	0.867582i	0.499101	+	0.866544i	$0.333664\pi$
$349$	−9.35756	+	16.2078i	−0.500899	+	0.867582i	−0.999999	+	0.00103797i	$0.999670\pi$
$350$	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
$353$	−21.1090	+	12.1873i	−1.12352	+	0.648664i	−0.942297	−	0.334778i	$-0.891339\pi$
$353$	−21.1090	+	12.1873i	−1.12352	+	0.648664i	−0.181222	+	0.983442i	$0.558005\pi$
$354$	−2.63717	−	0.631563i	−0.140164	−	0.0335672i
$355$	−23.5451	−	13.5938i	−1.24964	−	0.721482i
$356$		−	8.70736i		−	0.461489i
$357$	−2.54705	+	0.184680i	−0.134804	+	0.00977433i
$358$	−19.6844	+	11.3648i	−1.04035	+	0.600647i
$359$	−2.79005	−	4.83250i	−0.147253	−	0.255050i	0.782958	−	0.622074i	$-0.213710\pi$
$359$	−2.79005	−	4.83250i	−0.147253	−	0.255050i	−0.930211	+	0.367025i	$0.880377\pi$
$360$	6.23736	−	0.333908i	0.328738	−	0.0175985i
$361$	1.91683	+	3.32005i	0.100886	+	0.174740i
$362$			10.2663i			0.539586i
$363$	−7.98306	−	7.56713i	−0.419002	−	0.397171i
$364$	−9.24952	+	2.33375i	−0.484806	+	0.122322i
$365$			0.828216i			0.0433508i
$366$	−9.77343	+	10.3106i	−0.510866	+	0.538946i
$367$	28.5675	−	16.4934i	1.49121	−	0.860951i	0.491261	−	0.871013i	$-0.336536\pi$
$367$	28.5675	−	16.4934i	1.49121	−	0.860951i	0.999949	+	0.0100621i	$0.00320291\pi$
$368$		−	2.07565i		−	0.108201i
$369$	−1.00708	−	1.54697i	−0.0524266	−	0.0805318i
$370$	−8.65768	−	14.9955i	−0.450091	−	0.779581i
$371$	−4.38067	+	19.9493i	−0.227433	+	1.03571i
$372$	−8.08894	−	7.66749i	−0.419392	−	0.397541i
$373$	−9.62708	+	16.6746i	−0.498471	+	0.863378i	−0.999998	−	0.00176408i	$-0.999438\pi$
$373$	−9.62708	+	16.6746i	−0.498471	+	0.863378i	0.501527	+	0.865142i	$0.332772\pi$
$374$	−0.600806	−	1.04063i	−0.0310669	−	0.0538095i
$375$	−19.8674	−	4.75796i	−1.02595	−	0.245700i
$376$	0.507011	−	0.292723i	0.0261471	−	0.0150960i
$377$	14.0112	−	21.2054i	0.721611	−	1.09213i
$378$	12.6746	+	5.32493i	0.651910	+	0.273885i
$379$	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	$0.561918\pi$
$380$			8.10851i			0.415958i
$381$	18.4987	+	17.5349i	0.947720	+	0.898342i
$382$	3.37227	+	1.94698i	0.172541	+	0.0996163i
$383$	1.03501	+	0.597562i	0.0528864	+	0.0305340i	0.526210	−	0.850355i	$-0.323613\pi$
$383$	1.03501	+	0.597562i	0.0528864	+	0.0305340i	−0.473324	+	0.880889i	$0.656946\pi$
$384$	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
$387$	−1.38999	−	25.9648i	−0.0706570	−	1.31986i
$388$	1.64731	+	2.85322i	0.0836294	+	0.144850i
$389$	−13.1871	−	7.61359i	−0.668614	−	0.386024i	0.126937	−	0.991911i	$-0.459485\pi$
$389$	−13.1871	−	7.61359i	−0.668614	−	0.386024i	−0.795551	+	0.605886i	$0.792819\pi$
$390$	12.6654	−	2.94221i	0.641339	−	0.148985i
$391$		−	1.15670i		−	0.0584967i
$392$	−5.71791	+	4.03801i	−0.288798	+	0.203950i
$393$	9.37029	−	2.78133i	0.472668	−	0.140299i
$394$	5.48497	−	9.50024i	0.276329	−	0.478615i
$395$	−20.6800	−	11.9396i	−1.04052	−	0.600746i
$396$	0.345799	+	6.45949i	0.0173771	+	0.324601i
$397$	−13.0144	+	22.5415i	−0.653172	+	1.13133i	0.329177	+	0.944268i	$0.393229\pi$
$397$	−13.0144	+	22.5415i	−0.653172	+	1.13133i	−0.982349	+	0.187058i	$0.940105\pi$
$398$			20.2743i			1.01626i
$399$	−7.78212	+	16.0602i	−0.389593	+	0.804018i
$400$	−0.332437	+	0.575798i	−0.0166218	+	0.0287899i
$401$	36.6997			1.83269			0.916347	−	0.400385i	$-0.131124\pi$
$401$	36.6997			1.83269			0.916347	+	0.400385i	$0.131124\pi$
$402$	−7.02819	−	23.6780i	−0.350534	−	1.18095i
$403$	−19.3573	−	12.7901i	−0.964257	−	0.637119i
$404$	7.94537	+	13.7618i	0.395297	+	0.684675i
$405$	−17.1359	−	7.58333i	−0.851489	−	0.376819i
$406$	4.00013	−	18.2163i	0.198523	−	0.904061i
$407$	15.5296	−	8.96600i	0.769772	−	0.444428i
$408$	0.224800	−	0.938678i	0.0111292	−	0.0464715i
$409$	−29.3160			−1.44958			−0.724791	−	0.688969i	$-0.758064\pi$
$409$	−29.3160			−1.44958			−0.724791	+	0.688969i	$0.758064\pi$
$410$	−1.28111			−0.0632694
$411$	5.17150	−	21.5942i	0.255091	−	1.06516i
$412$	−2.32058	+	1.33979i	−0.114327	+	0.0660065i
$413$	−3.94803	+	1.25352i	−0.194270	+	0.0616819i
$414$	−2.82074	+	5.55141i	−0.138632	+	0.272837i
$415$	12.9564	+	22.4411i	0.636003	+	1.10159i
$416$	0.217235	−	3.59900i	0.0106508	−	0.176456i
$417$	2.01600	+	6.79190i	0.0987240	+	0.332601i
$418$	−8.39727			−0.410724
$419$	18.5356	−	32.1046i	0.905523	−	1.56841i	0.0853087	−	0.996355i	$-0.472812\pi$
$419$	18.5356	−	32.1046i	0.905523	−	1.56841i	0.820214	−	0.572057i	$-0.193854\pi$
$420$	7.89642	−	5.35576i	0.385306	−	0.261334i
$421$		−	15.9315i		−	0.776451i	−0.921564	−	0.388226i	$-0.873088\pi$
$421$		−	15.9315i		−	0.776451i	0.921564	−	0.388226i	$-0.126912\pi$
$422$	6.39897	−	11.0833i	0.311497	−	0.539529i
$423$	−1.75383	+	0.0938885i	−0.0852739	+	0.00456502i
$424$	−6.68551	−	3.85988i	−0.324677	−	0.187452i
$425$	−0.185257	+	0.320875i	−0.00898630	+	0.0155647i
$426$	21.6817	−	6.43567i	1.05048	−	0.311809i
$427$	−4.65444	+	21.1960i	−0.225244	+	1.02575i
$428$		−	13.7207i		−	0.663217i
$429$	3.04699	+	13.1165i	0.147110	+	0.633270i
$430$	−15.6285	−	9.02310i	−0.753671	−	0.435132i
$431$	14.0904	+	24.4053i	0.678710	+	1.17556i	0.975370	+	0.220576i	$0.0707938\pi$
$431$	14.0904	+	24.4053i	0.678710	+	1.17556i	−0.296660	+	0.954983i	$0.595873\pi$
$432$	−3.36797	+	3.95686i	−0.162042	+	0.190375i
$433$	10.7990	−	6.23481i	0.518967	−	0.299626i	−0.217545	−	0.976050i	$-0.569805\pi$
$433$	10.7990	−	6.23481i	0.518967	−	0.299626i	0.736512	+	0.676425i	$0.236472\pi$
$434$	−16.6288	−	3.65152i	−0.798206	−	0.175279i
$435$	−5.92063	+	24.7223i	−0.283873	+	1.18534i
$436$	−2.51915	−	1.45443i	−0.120645	−	0.0696546i
$437$	−7.00042	−	4.04170i	−0.334876	−	0.193341i
$438$	−0.500031	−	0.473979i	−0.0238924	−	0.0226476i
$439$			36.4164i			1.73806i	0.494761	+	0.869029i	$0.335256\pi$
$439$			36.4164i			1.73806i	−0.494761	+	0.869029i	$0.664744\pi$
$440$	3.88803	+	2.24475i	0.185355	+	0.107014i
$441$	20.7803	−	3.02939i	0.989540	−	0.144257i
$442$	0.121059	−	2.00562i	0.00575817	−	0.0953975i
$443$	−11.6506	+	6.72648i	−0.553537	+	0.319585i	−0.750547	−	0.660817i	$-0.770210\pi$
$443$	−11.6506	+	6.72648i	−0.553537	+	0.319585i	0.197011	+	0.980401i	$0.436877\pi$
$444$	14.0082	+	3.35475i	0.664798	+	0.159209i
$445$	9.06478	+	15.7007i	0.429712	+	0.744283i
$446$	6.84088	−	11.8488i	0.323925	−	0.561055i
$447$	1.44191	+	1.36678i	0.0682000	+	0.0646467i
$448$	−0.800654	−	2.52170i	−0.0378274	−	0.119139i
$449$	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	$0.662415\pi$
$450$	1.67161	−	1.08823i	0.0788004	−	0.0512995i
$451$		−	1.32673i		−	0.0624733i
$452$	17.2893	−	9.98197i	0.813219	−	0.469512i
$453$	−5.72206	+	6.03658i	−0.268846	+	0.283623i
$454$			3.74358i			0.175695i
$455$	14.2487	−	13.8373i	0.667990	−	0.648703i
$456$	−4.89547	−	4.64041i	−0.229251	−	0.217307i
$457$		−	14.4590i		−	0.676366i	−0.941080	−	0.338183i	$-0.890188\pi$
$457$		−	14.4590i		−	0.676366i	0.941080	−	0.338183i	$-0.109812\pi$
$458$	−4.38767	−	7.59967i	−0.205023	−	0.355109i
$459$	−1.87687	+	2.20504i	−0.0876049	+	0.102923i
$460$	2.16085	+	3.74270i	0.100750	+	0.174504i
$461$	−29.7738	+	17.1899i	−1.38670	+	0.800614i	−0.992942	−	0.118598i	$-0.962160\pi$
$461$	−29.7738	+	17.1899i	−1.38670	+	0.800614i	−0.393762	+	0.919212i	$0.628827\pi$
$462$	5.54649	+	8.17763i	0.258046	+	0.380458i
$463$			3.55647i			0.165283i	0.996579	+	0.0826415i	$0.0263357\pi$
$463$			3.55647i			0.165283i	−0.996579	+	0.0826415i	$0.973664\pi$
$464$	6.10476	+	3.52458i	0.283406	+	0.163625i
$465$	22.5678	+	5.40465i	1.04656	+	0.250635i
$466$	19.0891	−	11.0211i	0.884286	−	0.510543i
$467$	0.408159	+	0.706953i	0.0188874	+	0.0327139i	0.875315	−	0.483554i	$-0.160654\pi$
$467$	0.408159	+	0.706953i	0.0188874	+	0.0327139i	−0.856427	+	0.516268i	$0.827321\pi$
$468$	−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
$471$	−8.32004	+	8.77736i	−0.383367	+	0.404439i
$472$		−	1.56562i		−	0.0720637i
$473$	9.34443	−	16.1850i	0.429657	−	0.744188i
$474$	19.0434	−	5.65253i	0.874691	−	0.259629i
$475$	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
$478$	−12.3469			−0.564735
$479$	−32.0593	+	18.5095i	−1.46483	+	0.845719i	−0.999228	−	0.0392758i	$-0.987495\pi$
$479$	−32.0593	+	18.5095i	−1.46483	+	0.845719i	−0.465600	+	0.884995i	$0.654162\pi$
$480$	1.02618	+	3.45721i	0.0468387	+	0.157799i
$481$	29.9304	+	1.80659i	1.36471	+	0.0823735i
$482$	−1.22458			−0.0557781
$483$	0.687873	+	9.48690i	0.0312993	+	0.431669i
$484$	3.17530	−	5.49979i	0.144332	−	0.249990i
$485$	−5.94069	−	3.42986i	−0.269753	−	0.155742i
$486$	14.3851	−	6.00584i	0.652519	−	0.272430i
$487$			21.7586i			0.985977i	0.870036	+	0.492989i	$0.164096\pi$
$487$			21.7586i			0.985977i	−0.870036	+	0.492989i	$0.835904\pi$
$488$	−7.10333	−	4.10111i	−0.321553	−	0.185649i
$489$	−23.4495	+	24.7384i	−1.06042	+	1.11871i
$490$	6.10647	−	13.2338i	0.275862	−	0.597840i
$491$	−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	$0.900965\pi$
$492$	0.733163	−	0.773462i	0.0330536	−	0.0348704i
$493$	3.40200	+	1.96415i	0.153219	+	0.0884608i
$494$	−11.7152	−	7.74063i	−0.527090	−	0.348267i
$495$	−7.34816	−	11.2874i	−0.330275	−	0.507332i
$496$	3.21742	−	5.57273i	0.144466	−	0.250223i
$497$	23.2889	−	25.5179i	1.04465	−	1.14464i
$498$	−20.9635	−	5.02044i	−0.939395	−	0.224971i
$499$	−9.70337	+	5.60224i	−0.434383	+	0.250791i	−0.701212	−	0.712953i	$-0.747357\pi$
$499$	−9.70337	+	5.60224i	−0.434383	+	0.250791i	0.266829	+	0.963744i	$0.414024\pi$
$500$		−	11.7948i		−	0.527480i
$501$	15.3214	−	16.1635i	0.684509	−	0.722134i
$502$	6.93362	+	12.0094i	0.309463	+	0.536005i
$503$	13.0943	+	22.6800i	0.583847	+	1.01125i	0.995018	+	0.0996945i	$0.0317866\pi$
$503$	13.0943	+	22.6800i	0.583847	+	1.01125i	−0.411171	+	0.911558i	$0.634880\pi$
$504$	−1.28552	+	7.83246i	−0.0572617	+	0.348886i
$505$	−28.6534	−	16.5430i	−1.27506	−	0.736155i
$506$	−3.87598	+	2.23780i	−0.172309	+	0.0994824i
$507$	−7.83990	+	21.1077i	−0.348182	+	0.937427i
$508$	−7.35797	+	12.7444i	−0.326457	+	0.565441i
$509$			10.3138i			0.457151i	0.973526	+	0.228576i	$0.0734068\pi$
$509$			10.3138i			0.457151i	−0.973526	+	0.228576i	$0.926593\pi$
$510$	0.571863	+	1.92660i	0.0253225	+	0.0853114i
$511$	−1.02794	−	0.225725i	−0.0454732	−	0.00998548i
$512$	1.00000			0.0441942
$513$	6.78699	+	19.0638i	0.299653	+	0.841686i
$514$	−10.6560			−0.470016
$515$	2.78957	−	4.83167i	0.122923	−	0.212909i
$516$	14.3916	−	4.27178i	0.633556	−	0.188055i
$517$	−1.09324	−	0.631182i	−0.0480806	−	0.0277594i
$518$	20.9712	−	6.65849i	0.921422	−	0.292557i
$519$	5.56977	+	5.27958i	0.244486	+	0.231748i
$520$	3.35503	+	6.71569i	0.147128	+	0.294502i
$521$	−17.8124	+	30.8520i	−0.780376	+	1.35165i	0.151346	+	0.988481i	$0.451639\pi$
$521$	−17.8124	+	30.8520i	−0.780376	+	1.35165i	−0.931723	+	0.363171i	$0.881694\pi$
$522$	−11.5377	−	17.7229i	−0.504990	−	0.775708i
$523$			11.1120i			0.485894i	0.970040	+	0.242947i	$0.0781141\pi$
$523$			11.1120i			0.485894i	−0.970040	+	0.242947i	$0.921886\pi$
$524$	2.82161	+	4.88718i	0.123263	+	0.213497i
$525$	1.32861	−	2.74190i	0.0579852	−	0.119666i
$526$	−21.1985	+	12.2389i	−0.924298	+	0.533644i
$527$	1.79297	−	3.10552i	0.0781031	−	0.135279i
$528$	−3.58033	+	1.06273i	−0.155814	+	0.0462494i
$529$	18.6917			0.812682
$530$	16.0733			0.698179
$531$	−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
$534$	−14.6669	−	3.51250i	−0.634697	−	0.152001i
$535$	14.2840	+	24.7405i	0.617549	+	1.06963i
$536$	12.3495	−	7.12999i	0.533417	−	0.307969i
$537$	11.2025	+	37.7412i	0.483424	+	1.62865i
$538$	−11.0410			−0.476012
$539$	13.7050	+	6.32393i	0.590318	+	0.272391i
$540$	1.95367	−	10.6410i	0.0840726	−	0.457917i
$541$	14.2432	−	8.22331i	0.612363	−	0.353548i	−0.161527	−	0.986868i	$-0.551642\pi$
$541$	14.2432	−	8.22331i	0.612363	−	0.353548i	0.773890	+	0.633320i	$0.218308\pi$
$542$	14.2522			0.612183
$543$	17.2928	+	4.14137i	0.742106	+	0.177723i
$544$	0.557271			0.0238928
$545$	6.05653			0.259433
$546$	0.199826	+	16.5215i	0.00855178	+	0.707055i
$547$	38.7499			1.65683			0.828414	−	0.560116i	$-0.189243\pi$
$547$	38.7499			1.65683			0.828414	+	0.560116i	$0.189243\pi$
$548$	12.8200			0.547642
$549$	13.4249	+	20.6218i	0.572961	+	0.880118i
$550$	1.43363			0.0611302
$551$	23.7744	−	13.7261i	1.01282	−	0.584753i
$552$	−3.49626	−	0.837303i	−0.148811	−	0.0356380i
$553$	20.4549	−	22.4128i	0.869832	−	0.953087i
$554$	−9.76756			−0.414984
$555$	−28.7513	+	8.53407i	−1.22042	+	0.362251i
$556$	−3.54239	+	2.04520i	−0.150231	+	0.0867359i
$557$	13.1455	+	22.7686i	0.556992	+	0.964738i	0.997746	+	0.0671098i	$0.0213778\pi$
$557$	13.1455	+	22.7686i	0.556992	+	0.964738i	−0.440754	+	0.897628i	$0.645289\pi$
$558$	−16.1783	+	10.5322i	−0.684882	+	0.445862i
$559$	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
$562$	−0.791501			−0.0333875
$563$	−18.8788			−0.795646			−0.397823	−	0.917462i	$-0.630234\pi$
$563$	−18.8788			−0.795646			−0.397823	+	0.917462i	$0.630234\pi$
$564$	−0.288543	−	0.972102i	−0.0121499	−	0.0409329i
$565$	−20.7834	+	35.9979i	−0.874365	+	1.51445i
$566$	10.1855	−	5.88059i	0.428128	−	0.247180i
$567$	14.0823	−	19.2013i	0.591400	−	0.806379i
$568$	6.52888	+	11.3084i	0.273946	+	0.474488i
$569$			41.9057i			1.75678i	0.477947	+	0.878388i	$0.341381\pi$
$569$			41.9057i			1.75678i	−0.477947	+	0.878388i	$0.658619\pi$
$570$	13.6581	+	3.27092i	0.572077	+	0.137004i
$571$	3.92765	−	6.80288i	0.164367	−	0.284692i	−0.772063	−	0.635546i	$-0.780775\pi$
$571$	3.92765	−	6.80288i	0.164367	−	0.284692i	0.936430	+	0.350854i	$0.114109\pi$
$572$	−6.95485	+	3.47451i	−0.290797	+	0.145276i
$573$	4.63989	−	4.89493i	0.193834	−	0.204488i
$574$	0.349157	−	1.59004i	0.0145736	−	0.0663669i
$575$	1.19515	+	0.690021i	0.0498413	+	0.0287759i
$576$	−2.67455	−	1.35897i	−0.111439	−	0.0566237i
$577$	−11.6409	+	20.1626i	−0.484617	+	0.839381i	−0.999844	−	0.0176727i	$-0.994374\pi$
$577$	−11.6409	+	20.1626i	−0.484617	+	0.839381i	0.515227	+	0.857054i	$0.327708\pi$
$578$	−16.6894			−0.694190
$579$	1.77375	+	5.97575i	0.0737144	+	0.248344i
$580$	−14.6771			−0.609431
$581$	−31.3838	+	9.96454i	−1.30202	+	0.413399i
$582$	5.47054	−	1.62379i	0.226761	−	0.0673082i
$583$			16.6457i			0.689394i
$584$	0.198890	−	0.344488i	0.00823013	−	0.0142550i
$585$	0.153237	−	22.5208i	0.00633556	−	0.931120i
$586$	−6.68038	+	3.85692i	−0.275964	+	0.159328i
$587$	20.2618	+	11.6981i	0.836294	+	0.482834i	0.856003	−	0.516971i	$-0.172941\pi$
$587$	20.2618	+	11.6981i	0.836294	+	0.482834i	−0.0197091	+	0.999806i	$0.506274\pi$
$588$	4.49515	+	11.2603i	0.185377	+	0.464366i
$589$	−12.5299	−	21.7024i	−0.516286	−	0.894233i
$590$	1.62989	+	2.82305i	0.0671015	+	0.116223i
$591$	−13.7898	−	13.0713i	−0.567237	−	0.537683i
$592$			8.31631i			0.341798i
$593$	−4.32543	+	2.49729i	−0.177624	+	0.102551i	−0.586176	−	0.810184i	$-0.699367\pi$
$593$	−4.32543	+	2.49729i	−0.177624	+	0.102551i	0.408552	+	0.912735i	$0.366034\pi$
$594$	11.0200	+	2.02325i	0.452155	+	0.0830148i
$595$	2.26748	+	2.06941i	0.0929577	+	0.0848375i
$596$	−0.573527	+	0.993378i	−0.0234926	+	0.0406904i
$597$	34.1504	+	8.17852i	1.39768	+	0.334724i
$598$	−7.47025	−	0.450903i	−0.305481	−	0.0184388i
$599$	−7.43793	−	4.29429i	−0.303905	−	0.175460i	0.340291	−	0.940320i	$-0.389475\pi$
$599$	−7.43793	−	4.29429i	−0.303905	−	0.175460i	−0.644196	+	0.764860i	$0.722808\pi$
$600$	0.835783	+	0.792237i	0.0341207	+	0.0323429i
$601$	42.0105	+	24.2548i	1.71364	+	0.989373i	0.929523	+	0.368765i	$0.120219\pi$
$601$	42.0105	+	24.2548i	1.71364	+	0.989373i	0.784121	+	0.620608i	$0.213114\pi$
$602$	15.4584	−	16.9380i	0.630037	−	0.690340i
$603$	−42.7188	+	2.28689i	−1.73964	+	0.0931292i
$604$	−4.15879	−	2.40108i	−0.169219	−	0.0976986i
$605$			13.2226i			0.537574i
$606$	26.3858	−	7.83193i	1.07185	−	0.318150i
$607$	−7.02087	−	4.05350i	−0.284968	−	0.164527i	0.350702	−	0.936487i	$-0.385943\pi$
$607$	−7.02087	−	4.05350i	−0.284968	−	0.164527i	−0.635670	+	0.771961i	$0.719276\pi$
$608$	1.94720	−	3.37265i	0.0789693	−	0.136779i
$609$	−29.0703	−	14.0863i	−1.17799	−	0.570804i
$610$	17.0778			0.691460
$611$	−0.943369	−	1.88832i	−0.0381646	−	0.0763933i
$612$	−1.49045	−	0.757314i	−0.0602477	−	0.0306126i
$613$	−0.439299	+	0.253629i	−0.0177431	+	0.0102440i	−0.508845	−	0.860858i	$-0.669927\pi$
$613$	−0.439299	+	0.253629i	−0.0177431	+	0.0102440i	0.491102	+	0.871102i	$0.336594\pi$
$614$	22.5567			0.910314
$615$	−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	$-0.358545\pi$
$618$	1.32066	+	4.44929i	0.0531246	+	0.178977i
$619$	12.3365	−	21.3674i	0.495846	−	0.858830i	−0.504143	−	0.863620i	$-0.668191\pi$
$619$	12.3365	−	21.3674i	0.495846	−	0.858830i	0.999989	+	0.00479018i	$0.00152477\pi$
$620$			13.3979i			0.538074i
$621$	8.21305	+	6.99072i	0.329578	+	0.280528i
$622$	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
$626$	14.7574	−	8.52018i	0.589824	−	0.340535i
$627$	−3.38741	+	14.1445i	−0.135280	+	0.564879i
$628$	−6.04701	−	3.49124i	−0.241302	−	0.139316i
$629$			4.63444i			0.184787i
$630$	−5.83598	−	15.4614i	−0.232511	−	0.615996i
$631$	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
$633$	−16.0877	−	15.2495i	−0.639429	−	0.606114i
$634$	−7.60593	−	13.1739i	−0.302070	−	0.523201i
$635$		−	30.6400i		−	1.21591i
$636$	−9.19856	+	9.70416i	−0.364746	+	0.384795i
$637$	13.2907	+	21.4559i	0.526596	+	0.850116i
$638$		−	15.1997i		−	0.601763i
$639$	−2.09409	−	39.1173i	−0.0828408	−	1.54746i
$640$	−1.80315	+	1.04105i	−0.0712757	+	0.0411510i
$641$			26.7161i			1.05522i	0.849486	+	0.527612i	$0.176912\pi$
$641$			26.7161i			1.05522i	−0.849486	+	0.527612i	$0.823088\pi$
$642$	−23.1115	−	5.53486i	−0.912138	−	0.218444i
$643$	−22.0044	−	38.1127i	−0.867769	−	1.50302i	−0.864272	−	0.503025i	$-0.832220\pi$
$643$	−22.0044	−	38.1127i	−0.867769	−	1.50302i	−0.00349687	−	0.999994i	$-0.501113\pi$
$644$	−5.23415	+	1.66187i	−0.206254	+	0.0654870i
$645$	−21.5031	+	22.6850i	−0.846684	+	0.893223i
$646$	1.08512	−	1.87948i	0.0426934	−	0.0739471i
$647$	7.77334	+	13.4638i	0.305601	+	0.529317i	0.977395	−	0.211421i	$-0.0678091\pi$
$647$	7.77334	+	13.4638i	0.305601	+	0.529317i	−0.671794	+	0.740738i	$0.734476\pi$
$648$	5.30640	+	7.26926i	0.208455	+	0.285563i
$649$	−2.92359	+	1.68793i	−0.114761	+	0.0662572i
$650$	2.00008	+	1.32152i	0.0784496	+	0.0518344i
$651$	−12.8586	+	26.5368i	−0.503970	+	1.04006i
$652$	−17.0431	−	9.83983i	−0.667459	−	0.385358i
$653$			27.8448i			1.08965i	0.838549	+	0.544826i	$0.183404\pi$
$653$			27.8448i			1.08965i	−0.838549	+	0.544826i	$0.816596\pi$
$654$	−3.46608	+	3.65660i	−0.135535	+	0.142984i
$655$	−10.1756	−	5.87487i	−0.397593	−	0.229550i
$656$	0.532863	+	0.307649i	0.0208048	+	0.0120117i
$657$	−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	$0.0138080\pi$
$660$	5.34952	−	5.64356i	0.208230	−	0.219675i
$661$	9.67024	+	16.7493i	0.376129	+	0.651474i	0.990495	−	0.137547i	$-0.0439218\pi$
$661$	9.67024	+	16.7493i	0.376129	+	0.651474i	−0.614367	+	0.789021i	$0.710588\pi$
$662$	−9.89667	−	5.71384i	−0.384645	−	0.222075i
$663$	−3.32947	−	1.01297i	−0.129306	−	0.0393404i
$664$		−	12.4455i		−	0.482979i
$665$	20.4472	−	6.49211i	0.792909	−	0.251753i
$666$	11.3016	−	22.2424i	0.437929	−	0.861874i
$667$	7.31579	−	12.6713i	0.283269	−	0.490635i
$668$	11.1356	+	6.42913i	0.430849	+	0.248751i
$669$	−17.1987	−	16.3026i	−0.664941	−	0.630296i
$670$	−14.8453	+	25.7129i	−0.573525	+	0.993374i
$671$			17.6860i			0.682760i
$672$	−4.57058	+	0.331402i	−0.176314	+	0.0127841i
$673$	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	$0.0207816\pi$
$674$	0.692991			0.0266930
$675$	−1.15871	−	3.25468i	−0.0445989	−	0.125273i
$676$	−12.9056	−	1.56366i	−0.496370	−	0.0601407i
$677$	−1.50584	−	2.60819i	−0.0578740	−	0.100241i	0.835637	−	0.549282i	$-0.185099\pi$
$677$	−1.50584	−	2.60819i	−0.0578740	−	0.100241i	−0.893511	+	0.449042i	$0.851766\pi$
$678$	−9.83945	−	33.1491i	−0.377882	−	1.27308i
$679$	5.87604	−	6.43846i	0.225502	−	0.247085i
$680$	−1.00484	+	0.580146i	−0.0385339	+	0.0222476i
$681$	6.30577	+	1.51014i	0.241638	+	0.0578686i
$682$	−13.8751			−0.531304
$683$	31.1190			1.19074			0.595368	−	0.803453i	$-0.297006\pi$
$683$	31.1190			1.19074			0.595368	+	0.803453i	$0.297006\pi$
$684$	−9.79120	+	6.37412i	−0.374376	+	0.243721i
$685$	−23.1163	+	13.3462i	−0.883229	+	0.509932i
$686$	14.7607	+	11.1858i	0.563566	+	0.427075i
$687$	−14.5710	+	4.32503i	−0.555919	+	0.165010i
$688$	4.33366	+	7.50612i	0.165219	+	0.286168i
$689$	−15.3440	+	23.2227i	−0.584561	+	0.884713i
$690$	7.17595	−	2.13000i	0.273184	−	0.0810875i
$691$	−46.8665			−1.78288			−0.891442	−	0.453134i	$-0.850306\pi$
$691$	−46.8665			−1.78288			−0.891442	+	0.453134i	$0.850306\pi$
$692$	−2.21541	+	3.83719i	−0.0842171	+	0.145868i
$693$	16.0120	−	6.04381i	0.608245	−	0.229585i
$694$			14.8415i			0.563375i
$695$	4.25831	−	7.37560i	0.161527	−	0.279773i
$696$	8.39951	−	8.86119i	0.318382	−	0.335882i
$697$	0.296949	+	0.171444i	0.0112477	+	0.00649389i
$698$	−9.35756	+	16.2078i	−0.354189	+	0.613473i
$699$	−10.8638	−	36.6000i	−0.410905	−	1.38434i
$700$	1.71815	+	0.377290i	0.0649401	+	0.0142602i
$701$		−	27.7719i		−	1.04893i	−0.851433	−	0.524464i	$-0.824266\pi$
$701$		−	27.7719i		−	1.04893i	0.851433	−	0.524464i	$-0.175734\pi$
$702$	13.5091	+	12.9809i	0.509869	+	0.489933i
$703$	28.0480	+	16.1935i	1.05785	+	0.610750i
$704$	−1.07812	−	1.86736i	−0.0406333	−	0.0703789i
$705$	1.53229	+	1.45246i	0.0577094	+	0.0547027i
$706$	−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
$709$	−27.8176	−	16.0605i	−1.04471	−	0.603165i	−0.123548	−	0.992339i	$-0.539427\pi$
$709$	−27.8176	−	16.0605i	−1.04471	−	0.603165i	−0.921164	+	0.389174i	$0.872761\pi$
$710$	−23.5451	−	13.5938i	−0.883632	−	0.510165i
$711$	−1.83926	−	34.3572i	−0.0689778	−	1.28850i
$712$		−	8.70736i		−	0.326322i
$713$	−11.5670	−	6.67822i	−0.433188	−	0.250101i
$714$	−2.54705	+	0.184680i	−0.0953209	+	0.00691149i
$715$	8.92349	−	13.5054i	0.333720	−	0.505073i
$716$	−19.6844	+	11.3648i	−0.735639	+	0.424722i
$717$	−4.98067	+	20.7974i	−0.186007	+	0.776694i
$718$	−2.79005	−	4.83250i	−0.104124	−	0.180347i
$719$	18.5249	−	32.0860i	0.690861	−	1.19661i	−0.280695	−	0.959797i	$-0.590565\pi$
$719$	18.5249	−	32.0860i	0.690861	−	1.19661i	0.971556	−	0.236810i	$-0.0761018\pi$
$720$	6.23736	−	0.333908i	0.232453	−	0.0124440i
$721$	5.23652	+	4.77909i	0.195018	+	0.177983i
$722$	1.91683	+	3.32005i	0.0713372	+	0.123560i
$723$	−0.493988	+	2.06271i	−0.0183716	+	0.0767129i
$724$			10.2663i			0.381545i
$725$	−4.05890	+	2.34340i	−0.150744	+	0.0870318i
$726$	−7.98306	−	7.56713i	−0.296279	−	0.280842i
$727$			8.65396i			0.320957i	0.987039	+	0.160479i	$0.0513038\pi$
$727$			8.65396i			0.320957i	−0.987039	+	0.160479i	$0.948696\pi$
$728$	−9.24952	+	2.33375i	−0.342810	+	0.0864947i
$729$	−4.31352	−	26.6532i	−0.159760	−	0.987156i
$730$			0.828216i			0.0306537i
$731$	2.41502	+	4.18294i	0.0893228	+	0.154712i
$732$	−9.77343	+	10.3106i	−0.361237	+	0.381092i
$733$	−11.2469	−	19.4802i	−0.415413	−	0.719516i	0.580059	−	0.814574i	$-0.303029\pi$
$733$	−11.2469	−	19.4802i	−0.415413	−	0.719516i	−0.995472	+	0.0950586i	$0.969696\pi$
$734$	28.5675	−	16.4934i	1.05444	−	0.608784i
$735$	−19.8279	−	15.6243i	−0.731363	−	0.576310i
$736$		−	2.07565i		−	0.0765093i
$737$	−26.6286	−	15.3740i	−0.980875	−	0.566309i
$738$	−1.00708	−	1.54697i	−0.0370712	−	0.0569446i
$739$	−19.7692	+	11.4138i	−0.727223	+	0.419862i	−0.817405	−	0.576063i	$-0.804588\pi$
$739$	−19.7692	+	11.4138i	−0.727223	+	0.419862i	0.0901827	+	0.995925i	$0.471255\pi$
$740$	−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	$0.236054\pi$
$744$	−8.08894	−	7.66749i	−0.296555	−	0.281104i
$745$		−	2.38828i		−	0.0874997i
$746$	−9.62708	+	16.6746i	−0.352473	+	0.610500i
$747$	−16.9131	+	33.2861i	−0.618816	+	1.21787i
$748$	−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
$751$	4.14828			0.151373			0.0756864	−	0.997132i	$-0.475885\pi$
$751$	4.14828			0.151373			0.0756864	+	0.997132i	$0.475885\pi$
$752$	0.507011	−	0.292723i	0.0184888	−	0.0106745i
$753$	23.0258	−	6.83462i	0.839108	−	0.249068i
$754$	14.0112	−	21.2054i	0.510256	−	0.772254i
$755$	9.99856			0.363885
$756$	12.6746	+	5.32493i	0.460970	+	0.193666i
$757$	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	$-0.0418372\pi$
$758$	10.8971	+	6.29144i	0.395800	+	0.228515i
$759$	2.20585	+	7.43150i	0.0800673	+	0.269746i
$760$			8.10851i			0.294127i
$761$	6.12517	+	3.53637i	0.222037	+	0.128193i	0.606893	−	0.794783i	$-0.292416\pi$
$761$	6.12517	+	3.53637i	0.222037	+	0.128193i	−0.384856	+	0.922977i	$0.625749\pi$
$762$	18.4987	+	17.5349i	0.670139	+	0.635224i
$763$	−1.65067	+	7.51702i	−0.0597581	+	0.272134i
$764$	3.37227	+	1.94698i	0.122005	+	0.0704394i
$765$	3.47590	−	0.186077i	0.125671	−	0.00672763i
$766$	1.03501	+	0.597562i	0.0373964	+	0.0215908i
$767$	−5.63468	−	0.340108i	−0.203457	−	0.0122806i
$768$	0.403394	−	1.68442i	0.0145562	−	0.0607813i
$769$	−3.05595	+	5.29306i	−0.110200	+	0.190872i	−0.915851	−	0.401518i	$-0.868483\pi$
$769$	−3.05595	+	5.29306i	−0.110200	+	0.190872i	0.805651	+	0.592391i	$0.201816\pi$
$770$	2.54762	−	11.6017i	0.0918100	−	0.418096i
$771$	−4.29856	+	17.9492i	−0.154809	+	0.646424i
$772$	−3.11672	+	1.79944i	−0.112173	+	0.0647632i
$773$		−	38.6084i		−	1.38865i	−0.719662	−	0.694324i	$-0.755703\pi$
$773$		−	38.6084i		−	1.38865i	0.719662	−	0.694324i	$-0.244297\pi$
$774$	−1.38999	−	25.9648i	−0.0499620	−	0.933285i
$775$	2.13918	+	3.70516i	0.0768415	+	0.133093i
$776$	1.64731	+	2.85322i	0.0591349	+	0.102425i
$777$	−2.75604	−	38.0103i	−0.0988723	−	1.36361i
$778$	−13.1871	−	7.61359i	−0.472781	−	0.272960i
$779$	2.07518	−	1.19811i	0.0743511	−	0.0429266i
$780$	12.6654	−	2.94221i	0.453495	−	0.105348i
$781$	14.0779	−	24.3836i	0.503746	−	0.872513i
$782$		−	1.15670i		−	0.0413634i
$783$	−34.5070	+	12.2850i	−1.23318	+	0.439030i
$784$	−5.71791	+	4.03801i	−0.204211	+	0.144215i
$785$	14.5382			0.518891
$786$	9.37029	−	2.78133i	0.334227	−	0.0992067i
$787$	14.5438			0.518430			0.259215	−	0.965820i	$-0.416536\pi$
$787$	14.5438			0.518430			0.259215	+	0.965820i	$0.416536\pi$
$788$	5.48497	−	9.50024i	0.195394	−	0.338432i
$789$	12.0642	+	40.6443i	0.429497	+	1.44697i
$790$	−20.6800	−	11.9396i	−0.735760	−	0.424791i
$791$	−39.0142	−	35.6062i	−1.38719	−	1.26601i
$792$	0.345799	+	6.45949i	0.0122874	+	0.229528i
$793$	−16.3030	+	24.6740i	−0.578936	+	0.876199i
$794$	−13.0144	+	22.5415i	−0.461862	+	0.799969i
$795$	6.48386	−	27.0742i	0.229959	−	0.960222i
$796$			20.2743i			0.718603i
$797$	−11.4623	−	19.8532i	−0.406014	−	0.703237i	0.588425	−	0.808552i	$-0.299748\pi$
$797$	−11.4623	−	19.8532i	−0.406014	−	0.703237i	−0.994439	+	0.105315i	$0.966415\pi$
$798$	−7.78212	+	16.0602i	−0.275484	+	0.568527i
$799$	0.282542	−	0.163126i	0.00999563	−	0.00577098i
$800$	−0.332437	+	0.575798i	−0.0117534	+	0.0203575i
$801$	−11.8330	+	23.2882i	−0.418100	+	0.822850i
$802$	36.6997			1.29591
$803$	−0.857711			−0.0302680
$804$	−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
$807$	−4.45387	+	18.5977i	−0.156784	+	0.654670i
$808$	7.94537	+	13.7618i	0.279517	+	0.484138i
$809$	−31.0557	+	17.9300i	−1.09186	+	0.630386i	−0.934071	−	0.357087i	$-0.883770\pi$
$809$	−31.0557	+	17.9300i	−1.09186	+	0.630386i	−0.157789	+	0.987473i	$0.550437\pi$
$810$	−17.1359	−	7.58333i	−0.602093	−	0.266451i
$811$	−48.6802			−1.70939			−0.854696	−	0.519129i	$-0.826257\pi$
$811$	−48.6802			−1.70939			−0.854696	+	0.519129i	$0.826257\pi$
$812$	4.00013	−	18.2163i	0.140377	−	0.639268i
$813$	5.74923	−	24.0066i	0.201634	−	0.841949i
$814$	15.5296	−	8.96600i	0.544311	−	0.314258i
$815$	40.9750			1.43529
$816$	0.224800	−	0.938678i	0.00786956	−	0.0328603i
$817$	33.7540			1.18090
$818$	−29.3160			−1.02501
$819$	27.9098	+	6.32808i	0.975246	+	0.221121i
$820$	−1.28111			−0.0447382
$821$	55.9450			1.95249			0.976246	−	0.216664i	$-0.0695175\pi$
$821$	55.9450			1.95249			0.976246	+	0.216664i	$0.0695175\pi$
$822$	5.17150	−	21.5942i	0.180377	−	0.753185i
$823$	29.1511			1.01614			0.508071	−	0.861315i	$-0.330359\pi$
$823$	29.1511			1.01614			0.508071	+	0.861315i	$0.330359\pi$
$824$	−2.32058	+	1.33979i	−0.0808412	+	0.0466737i
$825$	0.578318	−	2.41484i	0.0201344	−	0.0840739i
$826$	−3.94803	+	1.25352i	−0.137369	+	0.0436157i
$827$	21.9052			0.761718			0.380859	−	0.924633i	$-0.375628\pi$
$827$	21.9052			0.761718			0.380859	+	0.924633i	$0.375628\pi$
$828$	−2.82074	+	5.55141i	−0.0980275	+	0.192925i
$829$	−2.10680	+	1.21636i	−0.0731722	+	0.0422460i	−0.536140	−	0.844129i	$-0.680118\pi$
$829$	−2.10680	+	1.21636i	−0.0731722	+	0.0422460i	0.462968	+	0.886375i	$0.346785\pi$
$830$	12.9564	+	22.4411i	0.449722	+	0.778941i
$831$	−3.94017	+	16.4527i	−0.136683	+	0.570737i
$832$	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
$835$	−26.7722			−0.926489
$836$	−8.39727			−0.290426
$837$	11.2144	+	31.4997i	0.387625	+	1.08879i
$838$	18.5356	−	32.1046i	0.640301	−	1.10903i
$839$	−44.9506	+	25.9522i	−1.55187	+	0.895970i	−0.553876	+	0.832599i	$0.686852\pi$
$839$	−44.9506	+	25.9522i	−1.55187	+	0.895970i	−0.997990	+	0.0633716i	$0.979815\pi$
$840$	7.89642	−	5.35576i	0.272453	−	0.184791i
$841$	10.3454	+	17.9187i	0.356738	+	0.617888i
$842$		−	15.9315i		−	0.549034i
$843$	−0.319287	+	1.33322i	−0.0109968	+	0.0459186i
$844$	6.39897	−	11.0833i	0.220262	−	0.381504i
$845$	24.8986	−	10.6159i	0.856537	−	0.365197i
$846$	−1.75383	+	0.0938885i	−0.0602978	+	0.00322795i
$847$	−16.4111	−	3.60373i	−0.563893	−	0.123825i
$848$	−6.68551	−	3.85988i	−0.229581	−	0.132549i
$849$	−5.79663	−	19.5288i	−0.198940	−	0.670228i
$850$	−0.185257	+	0.320875i	−0.00635428	+	0.0110059i
$851$	17.2617			0.591724
$852$	21.6817	−	6.43567i	0.742804	−	0.220482i
$853$	−48.0179			−1.64410			−0.822051	−	0.569413i	$-0.807170\pi$
$853$	−48.0179			−1.64410			−0.822051	+	0.569413i	$0.807170\pi$
$854$	−4.65444	+	21.1960i	−0.159272	+	0.725313i
$855$	11.0192	−	21.6866i	0.376849	−	0.741666i
$856$		−	13.7207i		−	0.468965i
$857$	4.00763	−	6.94143i	0.136898	−	0.237115i	−0.789423	−	0.613850i	$-0.789620\pi$
$857$	4.00763	−	6.94143i	0.136898	−	0.237115i	0.926321	+	0.376735i	$0.122953\pi$
$858$	3.04699	+	13.1165i	0.104023	+	0.447789i
$859$	10.3210	−	5.95884i	0.352148	−	0.203313i	−0.313483	−	0.949594i	$-0.601496\pi$
$859$	10.3210	−	5.95884i	0.352148	−	0.203313i	0.665631	+	0.746281i	$0.268162\pi$
$860$	−15.6285	−	9.02310i	−0.532926	−	0.307685i
$861$	−2.53745	−	1.22954i	−0.0864760	−	0.0419026i
$862$	14.0904	+	24.4053i	0.479920	+	0.831246i
$863$	−13.8281	−	23.9509i	−0.470713	−	0.815299i	0.528726	−	0.848793i	$-0.322670\pi$
$863$	−13.8281	−	23.9509i	−0.470713	−	0.815299i	−0.999439	+	0.0334938i	$0.989337\pi$
$864$	−3.36797	+	3.95686i	−0.114581	+	0.134615i
$865$		−	9.22538i		−	0.313672i
$866$	10.7990	−	6.23481i	0.366965	−	0.211867i
$867$	−6.73242	+	28.1121i	−0.228645	+	0.954735i
$868$	−16.6288	−	3.65152i	−0.564417	−	0.123941i
$869$	12.3648	−	21.4164i	0.419446	−	0.726503i
$870$	−5.92063	+	24.7223i	−0.200728	+	0.838165i
$871$	−22.9781	−	45.9948i	−0.778583	−	1.55847i
$872$	−2.51915	−	1.45443i	−0.0853091	−	0.0492532i
$873$	−0.528361	−	9.86972i	−0.0178823	−	0.334039i
$874$	−7.00042	−	4.04170i	−0.236793	−	0.136712i
$875$	−29.7429	+	9.44357i	−1.00549	+	0.319251i
$876$	−0.500031	−	0.473979i	−0.0168945	−	0.0160143i
$877$	23.3246	+	13.4665i	0.787615	+	0.454730i	0.839122	−	0.543943i	$-0.183069\pi$
$877$	23.3246	+	13.4665i	0.787615	+	0.454730i	−0.0515070	+	0.998673i	$0.516402\pi$
$878$			36.4164i			1.22899i
$879$	3.80185	+	12.8084i	0.128233	+	0.432018i
$880$	3.88803	+	2.24475i	0.131065	+	0.0756707i
$881$	−28.8939	+	50.0457i	−0.973460	+	1.68608i	−0.288533	+	0.957470i	$0.593167\pi$
$881$	−28.8939	+	50.0457i	−0.973460	+	1.68608i	−0.684927	+	0.728612i	$0.740166\pi$
$882$	20.7803	−	3.02939i	0.699711	−	0.102005i
$883$	−31.0838			−1.04605			−0.523027	−	0.852316i	$-0.675197\pi$
$883$	−31.0838			−1.04605			−0.523027	+	0.852316i	$0.675197\pi$
$884$	0.121059	−	2.00562i	0.00407164	−	0.0674562i
$885$	5.41270	−	1.60662i	0.181946	−	0.0540059i
$886$	−11.6506	+	6.72648i	−0.391409	+	0.225980i
$887$	44.0120			1.47778			0.738889	−	0.673828i	$-0.235351\pi$
$887$	44.0120			1.47778			0.738889	+	0.673828i	$0.235351\pi$
$888$	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
$891$	7.85339	−	17.7461i	0.263098	−	0.594518i
$892$	6.84088	−	11.8488i	0.229050	−	0.396726i
$893$		−	2.27996i		−	0.0762959i
$894$	1.44191	+	1.36678i	0.0482247	+	0.0457121i
$895$	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
$899$	39.2831	−	22.6801i	1.31017	−	0.756424i
$900$	1.67161	−	1.08823i	0.0557203	−	0.0362742i
$901$	−3.72564	−	2.15100i	−0.124119	−	0.0716601i
$902$		−	1.32673i		−	0.0441753i
$903$	−22.2949	−	32.8711i	−0.741926	−	1.09388i
$904$	17.2893	−	9.98197i	0.575033	−	0.331995i
$905$	−10.6877	−	18.5117i	−0.355273	−	0.615350i
$906$	−5.72206	+	6.03658i	−0.190103	+	0.200552i
$907$	−7.41617	−	12.8452i	−0.246250	−	0.426518i	0.716232	−	0.697862i	$-0.245865\pi$
$907$	−7.41617	−	12.8452i	−0.246250	−	0.426518i	−0.962482	+	0.271344i	$0.912532\pi$
$908$			3.74358i			0.124235i
$909$	−2.54842	−	47.6041i	−0.0845256	−	1.57893i
$910$	14.2487	−	13.8373i	0.472340	−	0.458702i
$911$			10.4486i			0.346178i	0.984906	+	0.173089i	$0.0553749\pi$
$911$			10.4486i			0.346178i	−0.984906	+	0.173089i	$0.944625\pi$
$912$	−4.89547	−	4.64041i	−0.162105	−	0.153659i
$913$	−23.2403	+	13.4178i	−0.769140	+	0.444063i
$914$		−	14.4590i		−	0.478263i
$915$	6.88908	−	28.7662i	0.227746	−	0.950982i
$916$	−4.38767	−	7.59967i	−0.144973	−	0.251100i
$917$	10.0648	−	11.0282i	0.332370	−	0.364183i
$918$	−1.87687	+	2.20504i	−0.0619460	+	0.0727773i
$919$	22.9797	−	39.8020i	0.758030	−	1.31295i	−0.185823	−	0.982583i	$-0.559495\pi$
$919$	22.9797	−	39.8020i	0.758030	−	1.31295i	0.943854	−	0.330364i	$-0.107171\pi$
$920$	2.16085	+	3.74270i	0.0712410	+	0.123393i
$921$	9.09923	−	37.9950i	0.299830	−	1.25198i
$922$	−29.7738	+	17.1899i	−0.980548	+	0.566120i
$923$	42.1171	−	21.0409i	1.38630	−	0.692569i
$924$	5.54649	+	8.17763i	0.182466	+	0.269024i
$925$	−4.78851	−	2.76465i	−0.157445	−	0.0909011i
$926$			3.55647i			0.116873i
$927$	8.02723	−	0.429726i	0.263649	−	0.0141140i
$928$	6.10476	+	3.52458i	0.200399	+	0.115700i
$929$	−15.0803	−	8.70664i	−0.494770	−	0.285655i	0.231781	−	0.972768i	$-0.425545\pi$
$929$	−15.0803	−	8.70664i	−0.494770	−	0.285655i	−0.726551	+	0.687112i	$0.758878\pi$
$930$	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
$933$	−16.7031	−	15.8329i	−0.546835	−	0.518344i
$934$	0.408159	+	0.706953i	0.0133554	+	0.0231322i
$935$	2.16669	+	1.25094i	0.0708582	+	0.0409100i
$936$	−5.47194	+	9.33048i	−0.178856	+	0.304976i
$937$		−	0.922295i		−	0.0301301i	−0.999887	−	0.0150650i	$-0.995204\pi$
$937$		−	0.922295i		−	0.0301301i	0.999887	−	0.0150650i	$-0.00479553\pi$
$938$	−27.8673	−	25.4330i	−0.909901	−	0.830418i
$939$	−8.39853	−	28.2946i	−0.274076	−	0.923360i
$940$	−0.609477	+	1.05565i	−0.0198790	+	0.0344314i
$941$	9.53735	+	5.50639i	0.310909	+	0.179503i	0.647333	−	0.762207i	$-0.275884\pi$
$941$	9.53735	+	5.50639i	0.310909	+	0.179503i	−0.336424	+	0.941711i	$0.609218\pi$
$942$	−8.32004	+	8.77736i	−0.271082	+	0.285982i
$943$	0.638570	−	1.10604i	0.0207947	−	0.0360175i
$944$		−	1.56562i		−	0.0509567i
$945$	−28.3977	+	3.59322i	−0.923776	+	0.116888i
$946$	9.34443	−	16.1850i	0.303814	−	0.526221i
$947$	−10.1762			−0.330681			−0.165340	−	0.986237i	$-0.552872\pi$
$947$	−10.1762			−0.330681			−0.165340	+	0.986237i	$0.552872\pi$
$948$	19.0434	−	5.65253i	0.618500	−	0.183586i
$949$	−1.19661	−	0.790640i	−0.0388434	−	0.0256653i
$950$	1.29464	+	2.24239i	0.0420037	+	0.0727526i
$951$	−25.2585	+	7.49734i	−0.819063	+	0.243118i
$952$	−0.446181	−	1.40527i	−0.0144608	−	0.0455450i
$953$	−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	$0.349710\pi$
$954$	12.6352	+	19.4088i	0.409081	+	0.628384i
$955$	−8.10761			−0.262356
$956$	−12.3469			−0.399328
$957$	−25.6027	−	6.13148i	−0.827619	−	0.198203i
$958$	−32.0593	+	18.5095i	−1.03579	+	0.598014i
$959$	−10.2644	−	32.3281i	−0.331454	−	1.04393i
$960$	1.02618	+	3.45721i	0.0331200	+	0.111581i
$961$	−5.20354	−	9.01280i	−0.167856	−	0.290735i
$962$	29.9304	+	1.80659i	0.964995	+	0.0582469i
$963$	−18.6461	+	36.6968i	−0.600861	+	1.18254i
$964$	−1.22458			−0.0394410
$965$	3.74660	−	6.48931i	0.120607	−	0.208898i
$966$	0.687873	+	9.48690i	0.0221319	+	0.305236i
$967$		−	43.4041i		−	1.39578i	−0.716204	−	0.697891i	$-0.754122\pi$
$967$		−	43.4041i		−	1.39578i	0.716204	−	0.697891i	$-0.245878\pi$
$968$	3.17530	−	5.49979i	0.102058	−	0.176770i
$969$	−2.72810	−	2.58596i	−0.0876392	−	0.0830731i
$970$	−5.94069	−	3.42986i	−0.190744	−	0.110126i
$971$	−1.24838	+	2.16226i	−0.0400624	+	0.0693901i	−0.885361	−	0.464904i	$-0.846089\pi$
$971$	−1.24838	+	2.16226i	−0.0400624	+	0.0693901i	0.845299	+	0.534294i	$0.179422\pi$
$972$	14.3851	−	6.00584i	0.461401	−	0.192637i
$973$	7.99361	+	7.29534i	0.256263	+	0.233878i
$974$			21.7586i			0.697191i
$975$	3.03282	−	2.83588i	0.0971281	−	0.0908209i
$976$	−7.10333	−	4.10111i	−0.227372	−	0.131273i
$977$	13.2406	+	22.9334i	0.423604	+	0.733704i	0.996289	−	0.0860718i	$-0.0274315\pi$
$977$	13.2406	+	22.9334i	0.423604	+	0.733704i	−0.572685	+	0.819776i	$0.694098\pi$
$978$	−23.4495	+	24.7384i	−0.749832	+	0.791047i
$979$	−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
$982$	−25.7673	−	14.8768i	−0.822269	−	0.474737i
$983$	40.2588	+	23.2434i	1.28406	+	0.741351i	0.977587	−	0.210530i	$-0.0675188\pi$
$983$	40.2588	+	23.2434i	1.28406	+	0.741351i	0.306470	+	0.951880i	$0.400852\pi$
$984$	0.733163	−	0.773462i	0.0233724	−	0.0246571i
$985$			22.8405i			0.727758i
$986$	3.40200	+	1.96415i	0.108342	+	0.0625512i
$987$	−2.22032	+	1.50594i	−0.0706737	+	0.0479345i
$988$	−11.7152	−	7.74063i	−0.372709	−	0.246262i
$989$	15.5800	−	8.99514i	0.495417	−	0.286029i
$990$	−7.34816	−	11.2874i	−0.233540	−	0.358738i
$991$	15.8691	+	27.4860i	0.504098	+	0.873123i	0.999989	+	0.00473799i	$0.00150816\pi$
$991$	15.8691	+	27.4860i	0.504098	+	0.873123i	−0.495891	+	0.868385i	$0.665159\pi$
$992$	3.21742	−	5.57273i	0.102153	−	0.176934i
$993$	−13.6168	+	14.3652i	−0.432115	+	0.455867i
$994$	23.2889	−	25.5179i	0.738678	−	0.809380i
$995$	−21.1065	−	36.5575i	−0.669121	−	1.15895i
$996$	−20.9635	−	5.02044i	−0.664252	−	0.159079i
$997$		−	58.6671i		−	1.85800i	−0.370075	−	0.929002i	$-0.620668\pi$
$997$		−	58.6671i		−	1.85800i	0.370075	−	0.929002i	$-0.379332\pi$
$998$	−9.70337	+	5.60224i	−0.307155	+	0.177336i
$999$	−32.9065	−	28.0091i	−1.04112	−	0.886169i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.15	✓	34	3.2	odd	2
546.2.bi.e.257.15	yes	34	91.75	odd	6
546.2.bi.f.17.9	yes	34	1.1	even	1	trivial
546.2.bi.f.257.9	yes	34	273.257	even	6	inner
546.2.bn.e.101.3	yes	34	39.23	odd	6
546.2.bn.e.173.3	yes	34	7.5	odd	6
546.2.bn.f.101.15	yes	34	13.10	even	6
546.2.bn.f.173.15	yes	34	21.5	even	6

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.403394 - 1.68442i) q^{3} +1.00000 q^{4} +(-1.80315 + 1.04105i) q^{5} +(0.403394 - 1.68442i) q^{6} +(-0.800654 - 2.52170i) q^{7} +1.00000 q^{8} +(-2.67455 - 1.35897i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.403394 - 1.68442i) q^{3} +1.00000 q^{4} +(-1.80315 + 1.04105i) q^{5} +(0.403394 - 1.68442i) q^{6} +(-0.800654 - 2.52170i) q^{7} +1.00000 q^{8} +(-2.67455 - 1.35897i) q^{9} +(-1.80315 + 1.04105i) q^{10} +(-1.07812 - 1.86736i) q^{11} +(0.403394 - 1.68442i) q^{12} +(0.217235 - 3.59900i) q^{13} +(-0.800654 - 2.52170i) q^{14} +(1.02618 + 3.45721i) q^{15} +1.00000 q^{16} +0.557271 q^{17} +(-2.67455 - 1.35897i) q^{18} +(1.94720 - 3.37265i) q^{19} +(-1.80315 + 1.04105i) q^{20} +(-4.57058 + 0.331402i) q^{21} +(-1.07812 - 1.86736i) q^{22} -2.07565i q^{23} +(0.403394 - 1.68442i) q^{24} +(-0.332437 + 0.575798i) q^{25} +(0.217235 - 3.59900i) q^{26} +(-3.36797 + 3.95686i) q^{27} +(-0.800654 - 2.52170i) q^{28} +(6.10476 + 3.52458i) q^{29} +(1.02618 + 3.45721i) q^{30} +(3.21742 - 5.57273i) q^{31} +1.00000 q^{32} +(-3.58033 + 1.06273i) q^{33} +0.557271 q^{34} +(4.06891 + 3.71347i) q^{35} +(-2.67455 - 1.35897i) q^{36} +8.31631i q^{37} +(1.94720 - 3.37265i) q^{38} +(-5.97460 - 1.81773i) q^{39} +(-1.80315 + 1.04105i) q^{40} +(0.532863 + 0.307649i) q^{41} +(-4.57058 + 0.331402i) q^{42} +(4.33366 + 7.50612i) q^{43} +(-1.07812 - 1.86736i) q^{44} +(6.23736 - 0.333908i) q^{45} -2.07565i q^{46} +(0.507011 - 0.292723i) q^{47} +(0.403394 - 1.68442i) q^{48} +(-5.71791 + 4.03801i) q^{49} +(-0.332437 + 0.575798i) q^{50} +(0.224800 - 0.938678i) q^{51} +(0.217235 - 3.59900i) q^{52} +(-6.68551 - 3.85988i) q^{53} +(-3.36797 + 3.95686i) q^{54} +(3.88803 + 2.24475i) q^{55} +(-0.800654 - 2.52170i) q^{56} +(-4.89547 - 4.64041i) q^{57} +(6.10476 + 3.52458i) q^{58} -1.56562i q^{59} +(1.02618 + 3.45721i) q^{60} +(-7.10333 - 4.10111i) q^{61} +(3.21742 - 5.57273i) q^{62} +(-1.28552 + 7.83246i) q^{63} +1.00000 q^{64} +(3.35503 + 6.71569i) q^{65} +(-3.58033 + 1.06273i) q^{66} +(12.3495 - 7.12999i) q^{67} +0.557271 q^{68} +(-3.49626 - 0.837303i) q^{69} +(4.06891 + 3.71347i) q^{70} +(6.52888 + 11.3084i) q^{71} +(-2.67455 - 1.35897i) q^{72} +(0.198890 - 0.344488i) q^{73} +8.31631i q^{74} +(0.835783 + 0.792237i) 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} +(-1.80315 + 1.04105i) q^{80} +(5.30640 + 7.26926i) q^{81} +(0.532863 + 0.307649i) q^{82} -12.4455i q^{83} +(-4.57058 + 0.331402i) q^{84} +(-1.00484 + 0.580146i) q^{85} +(4.33366 + 7.50612i) q^{86} +(8.39951 - 8.86119i) q^{87} +(-1.07812 - 1.86736i) q^{88} -8.70736i q^{89} +(6.23736 - 0.333908i) q^{90} +(-9.24952 + 2.33375i) q^{91} -2.07565i q^{92} +(-8.08894 - 7.66749i) q^{93} +(0.507011 - 0.292723i) q^{94} +8.10851i q^{95} +(0.403394 - 1.68442i) q^{96} +(1.64731 + 2.85322i) q^{97} +(-5.71791 + 4.03801i) q^{98} +(0.345799 + 6.45949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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