LMFDB - Embedded newform 546.2.bi.f.257.9

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			257.9
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.9

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	0.0393090	−	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
$7$	−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	−0.981526	−	0.191330i	$-0.938720\pi$
$11$	−1.07812	+	1.86736i	−0.325066	+	0.563031i	0.656460	+	0.754361i	$0.272053\pi$
$12$	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	0.998170	−	0.0604682i	$-0.0192594\pi$
$19$	1.94720	+	3.37265i	0.446718	+	0.773738i	−0.551452	+	0.834207i	$0.685926\pi$
$20$	−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	$0.0694319\pi$
$23$			2.07565i			0.432802i	−0.976305	+	0.216401i	$0.930568\pi$
$24$	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	0.188781	−	0.982019i	$-0.439546\pi$
$29$	6.10476	−	3.52458i	1.13363	−	0.654499i	0.944844	+	0.327520i	$0.106213\pi$
$30$	1.02618	−	3.45721i	0.187355	−	0.631198i
$31$	3.21742	+	5.57273i	0.577865	+	1.00089i	0.995724	+	0.0923797i	$0.0294474\pi$
$31$	3.21742	+	5.57273i	0.577865	+	1.00089i	−0.417859	+	0.908512i	$0.637219\pi$
$32$	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	$-0.760415\pi$
$37$		−	8.31631i		−	1.36719i	0.729860	−	0.683596i	$-0.239585\pi$
$38$	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	−0.457813	−	0.889049i	$-0.651367\pi$
$41$	0.532863	−	0.307649i	0.0832192	−	0.0480466i	0.541032	+	0.841002i	$0.318034\pi$
$42$	−4.57058	−	0.331402i	−0.705255	−	0.0511364i
$43$	4.33366	−	7.50612i	0.660877	−	1.14467i	−0.319509	−	0.947583i	$-0.603518\pi$
$43$	4.33366	−	7.50612i	0.660877	−	1.14467i	0.980386	−	0.197089i	$-0.0631487\pi$
$44$	−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	0.536522	−	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
$49$	−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	−0.883100	−	0.469184i	$-0.844548\pi$
$53$	−6.68551	+	3.85988i	−0.918325	+	0.530195i	−0.0352249	+	0.999379i	$0.511215\pi$
$54$	−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	$0.0324965\pi$
$59$			1.56562i			0.203827i	−0.994793	+	0.101913i	$0.967504\pi$
$60$	1.02618	−	3.45721i	0.132480	−	0.446324i
$61$	−7.10333	+	4.10111i	−0.909488	+	0.525093i	−0.880266	−	0.474480i	$-0.842636\pi$
$61$	−7.10333	+	4.10111i	−0.909488	+	0.525093i	−0.0292218	+	0.999573i	$0.509303\pi$
$62$	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	0.999948	+	0.0101724i	$0.00323804\pi$
$67$	12.3495	+	7.12999i	1.50873	+	0.871067i	0.508784	+	0.860894i	$0.330095\pi$
$68$	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	−0.160051	−	0.987109i	$-0.551166\pi$
$71$	6.52888	−	11.3084i	0.774836	−	1.34206i	0.934887	−	0.354946i	$-0.115501\pi$
$72$	−2.67455	+	1.35897i	−0.315198	+	0.160156i
$73$	0.198890	+	0.344488i	0.0232783	+	0.0403192i	0.877430	−	0.479705i	$-0.159256\pi$
$73$	0.198890	+	0.344488i	0.0232783	+	0.0403192i	−0.854152	+	0.520024i	$0.825923\pi$
$74$		−	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	−0.339091	−	0.940754i	$-0.610119\pi$
$79$	5.73441	−	9.93228i	0.645171	−	1.11747i	0.984262	−	0.176715i	$-0.0565472\pi$
$80$	−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	$0.239340\pi$
$83$			12.4455i			1.36607i	−0.730385	+	0.683035i	$0.760660\pi$
$84$	−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	$0.152685\pi$
$89$			8.70736i			0.922978i	−0.887146	+	0.461489i	$0.847315\pi$
$90$	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	−0.770196	−	0.637807i	$-0.779842\pi$
$97$	1.64731	−	2.85322i	0.167259	−	0.289701i	0.937455	+	0.348106i	$0.113175\pi$
$98$	−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	−0.135005	−	0.990845i	$-0.543105\pi$
$101$	7.94537	−	13.7618i	0.790594	−	1.36935i	0.925599	−	0.378505i	$-0.123562\pi$
$102$	0.224800	+	0.938678i	0.0222585	+	0.0929430i
$103$	−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
$105$	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	$0.230809\pi$
$107$			13.7207i			1.32643i	−0.748427	+	0.663217i	$0.769191\pi$
$108$	−3.36797	−	3.95686i	−0.324083	−	0.380749i
$109$	−2.51915	+	1.45443i	−0.241291	+	0.139309i	−0.615770	−	0.787926i	$-0.711155\pi$
$109$	−2.51915	+	1.45443i	−0.241291	+	0.139309i	0.374479	+	0.927235i	$0.377822\pi$
$110$	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	0.985144	+	0.171730i	$0.0549357\pi$
$113$	17.2893	+	9.98197i	1.62644	+	0.939025i	0.641295	+	0.767295i	$0.278398\pi$
$114$	−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	−0.982412	−	0.186725i	$-0.940213\pi$
$127$	−7.35797	−	12.7444i	−0.652915	−	1.13088i	0.329498	−	0.944156i	$-0.393121\pi$
$128$	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	−0.716034	−	0.698066i	$-0.754044\pi$
$131$	2.82161	−	4.88718i	0.246526	−	0.426995i	0.962559	+	0.271071i	$0.0873777\pi$
$132$	−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	0.342189	−	0.939631i	$-0.388832\pi$
$139$	−3.54239	−	2.04520i	−0.300462	−	0.173472i	−0.642650	+	0.766160i	$0.722165\pi$
$140$	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	0.841576	−	0.540138i	$-0.181628\pi$
$149$	−0.573527	−	0.993378i	−0.0469852	−	0.0813807i	−0.888562	+	0.458757i	$0.848295\pi$
$150$	0.835783	−	0.792237i	0.0682414	−	0.0646859i
$151$	−4.15879	+	2.40108i	−0.338438	+	0.195397i	−0.659581	−	0.751633i	$-0.729266\pi$
$151$	−4.15879	+	2.40108i	−0.338438	+	0.195397i	0.321143	+	0.947031i	$0.395933\pi$
$152$	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	−0.721501	−	0.692414i	$-0.756547\pi$
$157$	−6.04701	+	3.49124i	−0.482604	+	0.278631i	0.238897	+	0.971045i	$0.423214\pi$
$158$	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	−0.986049	−	0.166456i	$-0.946768\pi$
$163$	−17.0431	+	9.83983i	−1.33492	+	0.770715i	−0.348869	+	0.937171i	$0.613434\pi$
$164$	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	−0.00288283	−	0.999996i	$-0.500918\pi$
$167$	11.1356	−	6.42913i	0.861698	−	0.497501i	0.864580	+	0.502495i	$0.167584\pi$
$168$	−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	0.769435	−	0.638725i	$-0.220538\pi$
$173$	−2.21541	−	3.83719i	−0.168434	−	0.291736i	−0.937869	+	0.346988i	$0.887204\pi$
$174$	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	−0.471799	−	0.881706i	$-0.656395\pi$
$179$	−19.6844	−	11.3648i	−1.47128	−	0.849443i	−0.999479	+	0.0322629i	$0.989729\pi$
$180$	6.23736	+	0.333908i	0.464905	+	0.0248880i
$181$		−	10.2663i		−	0.763090i	−0.924350	−	0.381545i	$-0.875392\pi$
$181$		−	10.2663i		−	0.763090i	0.924350	−	0.381545i	$-0.124608\pi$
$182$	−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	−0.373009	−	0.927828i	$-0.621674\pi$
$191$	3.37227	−	1.94698i	0.244009	−	0.140879i	0.617018	+	0.786949i	$0.288341\pi$
$192$	0.403394	+	1.68442i	0.0291124	+	0.121563i
$193$	−3.11672	−	1.79944i	−0.224346	−	0.129526i	0.383615	−	0.923493i	$-0.374679\pi$
$193$	−3.11672	−	1.79944i	−0.224346	−	0.129526i	−0.607961	+	0.793967i	$0.708012\pi$
$194$	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	0.992554	−	0.121808i	$-0.0388693\pi$
$197$	5.48497	+	9.50024i	0.390788	+	0.676864i	−0.601766	+	0.798673i	$0.705536\pi$
$198$	0.345799	−	6.45949i	0.0245749	−	0.459056i
$199$		−	20.2743i		−	1.43721i	−0.695421	−	0.718603i	$-0.744782\pi$
$199$		−	20.2743i		−	1.43721i	0.695421	−	0.718603i	$-0.255218\pi$
$200$	−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	0.997728	−	0.0673662i	$-0.0214596\pi$
$211$	6.39897	+	11.0833i	0.440523	+	0.763009i	−0.557205	+	0.830375i	$0.688126\pi$
$212$	−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	0.998861	−	0.0477249i	$-0.0151971\pi$
$223$	6.84088	+	11.8488i	0.458099	+	0.793451i	−0.540761	+	0.841176i	$0.681864\pi$
$224$	−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	$-0.960352\pi$
$227$		−	3.74358i		−	0.248470i	0.992253	−	0.124235i	$-0.0396477\pi$
$228$	−4.89547	+	4.64041i	−0.324210	+	0.307318i
$229$	−4.38767	+	7.59967i	−0.289946	+	0.502201i	−0.973796	−	0.227421i	$-0.926971\pi$
$229$	−4.38767	+	7.59967i	−0.289946	+	0.502201i	0.683851	+	0.729622i	$0.260304\pi$
$230$	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	0.971223	−	0.238173i	$-0.0765487\pi$
$233$	19.0891	+	11.0211i	1.25057	+	0.722017i	0.279347	+	0.960190i	$0.409882\pi$
$234$	−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	−0.559861	−	0.828586i	$-0.689146\pi$
$251$	6.93362	−	12.0094i	0.437646	−	0.758026i	0.997507	+	0.0705608i	$0.0224789\pi$
$252$	−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	−0.325534	−	0.945530i	$-0.605544\pi$
$263$	−21.1985	−	12.2389i	−1.30715	−	0.754686i	−0.981620	+	0.190844i	$0.938877\pi$
$264$	−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	0.771188	−	0.636607i	$-0.219663\pi$
$283$	10.1855	+	5.88059i	0.605464	+	0.349565i	−0.165724	+	0.986172i	$0.552996\pi$
$284$	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	0.292006	−	0.956416i	$-0.405677\pi$
$293$	−6.68038	−	3.85692i	−0.390272	−	0.225324i	−0.682278	+	0.731093i	$0.739011\pi$
$294$	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	0.990585	−	0.136901i	$-0.0437143\pi$
$311$	6.64375	+	11.5073i	0.376733	+	0.652520i	−0.613852	+	0.789421i	$0.710381\pi$
$312$	−5.97460	+	1.81773i	−0.338245	+	0.102909i
$313$	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
$315$	−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	−0.996622	−	0.0821217i	$-0.973830\pi$
$317$	−7.60593	+	13.1739i	−0.427192	+	0.739918i	0.569431	+	0.822039i	$0.307164\pi$
$318$	−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	−0.746686	−	0.665176i	$-0.768356\pi$
$331$	−9.89667	+	5.71384i	−0.543970	+	0.314061i	0.202716	+	0.979238i	$0.435023\pi$
$332$			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	$-0.869577\pi$
$347$		−	14.8415i		−	0.796733i	0.917226	−	0.398366i	$-0.130423\pi$
$348$	8.39951	+	8.86119i	0.450261	+	0.475010i
$349$	−9.35756	−	16.2078i	−0.500899	−	0.867582i	−0.999999	−	0.00103797i	$-0.999670\pi$
$349$	−9.35756	−	16.2078i	−0.500899	−	0.867582i	0.499101	−	0.866544i	$-0.333664\pi$
$350$	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	−0.181222	−	0.983442i	$-0.558005\pi$
$353$	−21.1090	−	12.1873i	−1.12352	−	0.648664i	−0.942297	+	0.334778i	$0.891339\pi$
$354$	−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	−0.930211	−	0.367025i	$-0.880377\pi$
$359$	−2.79005	+	4.83250i	−0.147253	+	0.255050i	0.782958	+	0.622074i	$0.213710\pi$
$360$	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	0.999949	−	0.0100621i	$-0.00320291\pi$
$367$	28.5675	+	16.4934i	1.49121	+	0.860951i	0.491261	+	0.871013i	$0.336536\pi$
$368$			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	0.501527	−	0.865142i	$-0.332772\pi$
$373$	−9.62708	−	16.6746i	−0.498471	−	0.863378i	−0.999998	+	0.00176408i	$0.999438\pi$
$374$	−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	−0.193298	−	0.981140i	$-0.561918\pi$
$379$	10.8971	−	6.29144i	0.559746	−	0.323169i	0.753043	+	0.657971i	$0.228585\pi$
$380$		−	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	−0.473324	−	0.880889i	$-0.656946\pi$
$383$	1.03501	−	0.597562i	0.0528864	−	0.0305340i	0.526210	+	0.850355i	$0.323613\pi$
$384$	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	−0.795551	−	0.605886i	$-0.792819\pi$
$389$	−13.1871	+	7.61359i	−0.668614	+	0.386024i	0.126937	+	0.991911i	$0.459485\pi$
$390$	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	−0.982349	−	0.187058i	$-0.940105\pi$
$397$	−13.0144	−	22.5415i	−0.653172	−	1.13133i	0.329177	−	0.944268i	$-0.393229\pi$
$398$		−	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	0.820214	+	0.572057i	$0.193854\pi$
$419$	18.5356	+	32.1046i	0.905523	+	1.56841i	0.0853087	+	0.996355i	$0.472812\pi$
$420$	7.89642	+	5.35576i	0.385306	+	0.261334i
$421$			15.9315i			0.776451i	0.921564	+	0.388226i	$0.126912\pi$
$421$			15.9315i			0.776451i	−0.921564	+	0.388226i	$0.873088\pi$
$422$	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	−0.296660	−	0.954983i	$-0.595873\pi$
$431$	14.0904	−	24.4053i	0.678710	−	1.17556i	0.975370	−	0.220576i	$-0.0707938\pi$
$432$	−3.36797	−	3.95686i	−0.162042	−	0.190375i
$433$	10.7990	+	6.23481i	0.518967	+	0.299626i	0.736512	−	0.676425i	$-0.236472\pi$
$433$	10.7990	+	6.23481i	0.518967	+	0.299626i	−0.217545	+	0.976050i	$0.569805\pi$
$434$	−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	$-0.664744\pi$
$439$		−	36.4164i		−	1.73806i	0.494761	−	0.869029i	$-0.335256\pi$
$440$	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	0.197011	−	0.980401i	$-0.436877\pi$
$443$	−11.6506	−	6.72648i	−0.553537	−	0.319585i	−0.750547	+	0.660817i	$0.770210\pi$
$444$	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	−0.488389	−	0.872626i	$-0.662415\pi$
$449$	10.8390	−	18.7736i	0.511522	−	0.885982i	0.999911	−	0.0133556i	$-0.00425136\pi$
$450$	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	$0.109812\pi$
$457$			14.4590i			0.676366i	−0.941080	+	0.338183i	$0.890188\pi$
$458$	−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	−0.393762	−	0.919212i	$-0.628827\pi$
$461$	−29.7738	−	17.1899i	−1.38670	−	0.800614i	−0.992942	+	0.118598i	$0.962160\pi$
$462$	5.54649	−	8.17763i	0.258046	−	0.380458i
$463$		−	3.55647i		−	0.165283i	−0.996579	−	0.0826415i	$-0.973664\pi$
$463$		−	3.55647i		−	0.165283i	0.996579	−	0.0826415i	$-0.0263357\pi$
$464$	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	−0.856427	−	0.516268i	$-0.827321\pi$
$467$	0.408159	−	0.706953i	0.0188874	−	0.0327139i	0.875315	+	0.483554i	$0.160654\pi$
$468$	−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	−0.465600	−	0.884995i	$-0.654162\pi$
$479$	−32.0593	−	18.5095i	−1.46483	−	0.845719i	−0.999228	+	0.0392758i	$0.987495\pi$
$480$	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	$-0.835904\pi$
$487$		−	21.7586i		−	0.985977i	0.870036	−	0.492989i	$-0.164096\pi$
$488$	−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	−0.951989	−	0.306134i	$-0.900965\pi$
$491$	−25.7673	+	14.8768i	−1.16286	+	0.671379i	−0.210875	+	0.977513i	$0.567631\pi$
$492$	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	0.266829	−	0.963744i	$-0.414024\pi$
$499$	−9.70337	−	5.60224i	−0.434383	−	0.250791i	−0.701212	+	0.712953i	$0.747357\pi$
$500$			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	−0.411171	−	0.911558i	$-0.634880\pi$
$503$	13.0943	−	22.6800i	0.583847	−	1.01125i	0.995018	−	0.0996945i	$-0.0317866\pi$
$504$	−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	$-0.926593\pi$
$509$		−	10.3138i		−	0.457151i	0.973526	−	0.228576i	$-0.0734068\pi$
$510$	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	−0.931723	−	0.363171i	$-0.881694\pi$
$521$	−17.8124	−	30.8520i	−0.780376	−	1.35165i	0.151346	−	0.988481i	$-0.451639\pi$
$522$	−11.5377	+	17.7229i	−0.504990	+	0.775708i
$523$		−	11.1120i		−	0.485894i	−0.970040	−	0.242947i	$-0.921886\pi$
$523$		−	11.1120i		−	0.485894i	0.970040	−	0.242947i	$-0.0781141\pi$
$524$	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	0.773890	−	0.633320i	$-0.218308\pi$
$541$	14.2432	+	8.22331i	0.612363	+	0.353548i	−0.161527	+	0.986868i	$0.551642\pi$
$542$	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	−0.440754	−	0.897628i	$-0.645289\pi$
$557$	13.1455	−	22.7686i	0.556992	−	0.964738i	0.997746	−	0.0671098i	$-0.0213778\pi$
$558$	−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	$-0.658619\pi$
$569$		−	41.9057i		−	1.75678i	0.477947	−	0.878388i	$-0.341381\pi$
$570$	13.6581	−	3.27092i	0.572077	−	0.137004i
$571$	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	$0.780775\pi$
$572$	−6.95485	−	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	0.515227	−	0.857054i	$-0.327708\pi$
$577$	−11.6409	−	20.1626i	−0.484617	−	0.839381i	−0.999844	+	0.0176727i	$0.994374\pi$
$578$	−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	−0.0197091	−	0.999806i	$-0.506274\pi$
$587$	20.2618	−	11.6981i	0.836294	−	0.482834i	0.856003	+	0.516971i	$0.172941\pi$
$588$	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	0.408552	−	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
$595$	2.26748	−	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	−0.644196	−	0.764860i	$-0.722808\pi$
$599$	−7.43793	+	4.29429i	−0.303905	+	0.175460i	0.340291	+	0.940320i	$0.389475\pi$
$600$	0.835783	−	0.792237i	0.0341207	−	0.0323429i
$601$	42.0105	−	24.2548i	1.71364	−	0.989373i	0.784121	−	0.620608i	$-0.213114\pi$
$601$	42.0105	−	24.2548i	1.71364	−	0.989373i	0.929523	−	0.368765i	$-0.120219\pi$
$602$	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	−0.635670	−	0.771961i	$-0.719276\pi$
$607$	−7.02087	+	4.05350i	−0.284968	+	0.164527i	0.350702	+	0.936487i	$0.385943\pi$
$608$	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	0.491102	−	0.871102i	$-0.336594\pi$
$613$	−0.439299	−	0.253629i	−0.0177431	−	0.0102440i	−0.508845	+	0.860858i	$0.669927\pi$
$614$	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	0.429911	+	0.902871i	$0.358545\pi$
$617$	−14.0828	+	24.3922i	−0.566954	+	0.981993i	−0.996865	+	0.0791221i	$0.974788\pi$
$618$	1.32066	−	4.44929i	0.0531246	−	0.178977i
$619$	12.3365	+	21.3674i	0.495846	+	0.858830i	0.999989	−	0.00479018i	$-0.00152477\pi$
$619$	12.3365	+	21.3674i	0.495846	+	0.858830i	−0.504143	+	0.863620i	$0.668191\pi$
$620$		−	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	0.996882	−	0.0789008i	$-0.0251410\pi$
$631$	35.8457	+	20.6955i	1.42699	+	0.823875i	0.430111	+	0.902776i	$0.358474\pi$
$632$	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	$-0.823088\pi$
$641$		−	26.7161i		−	1.05522i	0.849486	−	0.527612i	$-0.176912\pi$
$642$	−23.1115	+	5.53486i	−0.912138	+	0.218444i
$643$	−22.0044	+	38.1127i	−0.867769	+	1.50302i	−0.00349687	+	0.999994i	$0.501113\pi$
$643$	−22.0044	+	38.1127i	−0.867769	+	1.50302i	−0.864272	+	0.503025i	$0.832220\pi$
$644$	−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	−0.671794	−	0.740738i	$-0.734476\pi$
$647$	7.77334	−	13.4638i	0.305601	−	0.529317i	0.977395	+	0.211421i	$0.0678091\pi$
$648$	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	$-0.816596\pi$
$653$		−	27.8448i		−	1.08965i	0.838549	−	0.544826i	$-0.183404\pi$
$654$	−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	0.999059	−	0.0433655i	$-0.0138080\pi$
$659$	37.5062	+	21.6542i	1.46103	+	0.843528i	0.461974	+	0.886893i	$0.347141\pi$
$660$	5.34952	+	5.64356i	0.208230	+	0.219675i
$661$	9.67024	−	16.7493i	0.376129	−	0.651474i	−0.614367	−	0.789021i	$-0.710588\pi$
$661$	9.67024	−	16.7493i	0.376129	−	0.651474i	0.990495	+	0.137547i	$0.0439218\pi$
$662$	−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	0.997870	−	0.0652410i	$-0.0207816\pi$
$673$	11.4777	+	19.8800i	0.442434	+	0.766319i	−0.555435	+	0.831560i	$0.687448\pi$
$674$	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	−0.893511	−	0.449042i	$-0.851766\pi$
$677$	−1.50584	+	2.60819i	−0.0578740	+	0.100241i	0.835637	+	0.549282i	$0.185099\pi$
$678$	−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	$0.175734\pi$
$701$			27.7719i			1.04893i	−0.851433	+	0.524464i	$0.824266\pi$
$702$	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	−0.921164	−	0.389174i	$-0.872761\pi$
$709$	−27.8176	+	16.0605i	−1.04471	+	0.603165i	−0.123548	+	0.992339i	$0.539427\pi$
$710$	−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	0.971556	+	0.236810i	$0.0761018\pi$
$719$	18.5249	+	32.0860i	0.690861	+	1.19661i	−0.280695	+	0.959797i	$0.590565\pi$
$720$	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	$-0.948696\pi$
$727$		−	8.65396i		−	0.320957i	0.987039	−	0.160479i	$-0.0513038\pi$
$728$	−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	−0.995472	−	0.0950586i	$-0.969696\pi$
$733$	−11.2469	+	19.4802i	−0.415413	+	0.719516i	0.580059	+	0.814574i	$0.303029\pi$
$734$	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	0.0901827	−	0.995925i	$-0.471255\pi$
$739$	−19.7692	−	11.4138i	−0.727223	−	0.419862i	−0.817405	+	0.576063i	$0.804588\pi$
$740$	−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	0.737398	−	0.675458i	$-0.236054\pi$
$743$	−5.89495	−	10.2104i	−0.216265	−	0.374582i	−0.953663	+	0.300877i	$0.902721\pi$
$744$	−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	0.991375	+	0.131057i	$0.0418372\pi$
$757$	16.7609	+	29.0308i	0.609186	+	1.05514i	−0.382189	+	0.924084i	$0.624830\pi$
$758$	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	−0.384856	−	0.922977i	$-0.625749\pi$
$761$	6.12517	−	3.53637i	0.222037	−	0.128193i	0.606893	+	0.794783i	$0.292416\pi$
$762$	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	0.805651	−	0.592391i	$-0.201816\pi$
$769$	−3.05595	−	5.29306i	−0.110200	−	0.190872i	−0.915851	+	0.401518i	$0.868483\pi$
$770$	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	$0.244297\pi$
$773$			38.6084i			1.38865i	−0.719662	+	0.694324i	$0.755703\pi$
$774$	−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	−0.994439	−	0.105315i	$-0.966415\pi$
$797$	−11.4623	+	19.8532i	−0.406014	+	0.703237i	0.588425	+	0.808552i	$0.299748\pi$
$798$	−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	−0.157789	−	0.987473i	$-0.550437\pi$
$809$	−31.0557	−	17.9300i	−1.09186	−	0.630386i	−0.934071	+	0.357087i	$0.883770\pi$
$810$	−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	0.462968	−	0.886375i	$-0.346785\pi$
$829$	−2.10680	−	1.21636i	−0.0731722	−	0.0422460i	−0.536140	+	0.844129i	$0.680118\pi$
$830$	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	−0.997990	−	0.0633716i	$-0.979815\pi$
$839$	−44.9506	−	25.9522i	−1.55187	−	0.895970i	−0.553876	−	0.832599i	$-0.686852\pi$
$840$	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	0.926321	−	0.376735i	$-0.122953\pi$
$857$	4.00763	+	6.94143i	0.136898	+	0.237115i	−0.789423	+	0.613850i	$0.789620\pi$
$858$	3.04699	−	13.1165i	0.104023	−	0.447789i
$859$	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
$861$	−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	−0.999439	−	0.0334938i	$-0.989337\pi$
$863$	−13.8281	+	23.9509i	−0.470713	+	0.815299i	0.528726	+	0.848793i	$0.322670\pi$
$864$	−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	−0.0515070	−	0.998673i	$-0.516402\pi$
$877$	23.3246	−	13.4665i	0.787615	−	0.454730i	0.839122	+	0.543943i	$0.183069\pi$
$878$		−	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	−0.684927	−	0.728612i	$-0.740166\pi$
$881$	−28.8939	−	50.0457i	−0.973460	−	1.68608i	−0.288533	−	0.957470i	$-0.593167\pi$
$882$	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	−0.962482	−	0.271344i	$-0.912532\pi$
$907$	−7.41617	+	12.8452i	−0.246250	+	0.426518i	0.716232	+	0.697862i	$0.245865\pi$
$908$		−	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	$-0.944625\pi$
$911$		−	10.4486i		−	0.346178i	0.984906	−	0.173089i	$-0.0553749\pi$
$912$	−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	0.943854	+	0.330364i	$0.107171\pi$
$919$	22.9797	+	39.8020i	0.758030	+	1.31295i	−0.185823	+	0.982583i	$0.559495\pi$
$920$	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	−0.726551	−	0.687112i	$-0.758878\pi$
$929$	−15.0803	+	8.70664i	−0.494770	+	0.285655i	0.231781	+	0.972768i	$0.425545\pi$
$930$	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	$0.00479553\pi$
$937$			0.922295i			0.0301301i	−0.999887	+	0.0150650i	$0.995204\pi$
$938$	−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	−0.336424	−	0.941711i	$-0.609218\pi$
$941$	9.53735	−	5.50639i	0.310909	−	0.179503i	0.647333	+	0.762207i	$0.275884\pi$
$942$	−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	0.454802	−	0.890593i	$-0.349710\pi$
$953$	−2.74974	−	1.58756i	−0.0890727	−	0.0514261i	−0.543875	+	0.839166i	$0.683043\pi$
$954$	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	$0.245878\pi$
$967$			43.4041i			1.39578i	−0.716204	+	0.697891i	$0.754122\pi$
$968$	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	0.845299	−	0.534294i	$-0.179422\pi$
$971$	−1.24838	−	2.16226i	−0.0400624	−	0.0693901i	−0.885361	+	0.464904i	$0.846089\pi$
$972$	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	−0.572685	−	0.819776i	$-0.694098\pi$
$977$	13.2406	−	22.9334i	0.423604	−	0.733704i	0.996289	+	0.0860718i	$0.0274315\pi$
$978$	−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	0.306470	−	0.951880i	$-0.400852\pi$
$983$	40.2588	−	23.2434i	1.28406	−	0.741351i	0.977587	+	0.210530i	$0.0675188\pi$
$984$	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	−0.495891	−	0.868385i	$-0.665159\pi$
$991$	15.8691	−	27.4860i	0.504098	−	0.873123i	0.999989	−	0.00473799i	$-0.00150816\pi$
$992$	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	$0.379332\pi$
$997$			58.6671i			1.85800i	−0.370075	+	0.929002i	$0.620668\pi$
$998$	−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.257.9	yes	34
3.2	odd	2		546.2.bi.e.257.15	yes	34
7.3	odd	6		546.2.bn.e.101.3	yes	34
13.4	even	6		546.2.bn.f.173.15	yes	34
21.17	even	6		546.2.bn.f.101.15	yes	34
39.17	odd	6		546.2.bn.e.173.3	yes	34
91.17	odd	6		546.2.bi.e.17.15	✓	34
273.17	even	6	inner	546.2.bi.f.17.9	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.15	✓	34	91.17	odd	6
546.2.bi.e.257.15	yes	34	3.2	odd	2
546.2.bi.f.17.9	yes	34	273.17	even	6	inner
546.2.bi.f.257.9	yes	34	1.1	even	1	trivial
546.2.bn.e.101.3	yes	34	7.3	odd	6
546.2.bn.e.173.3	yes	34	39.17	odd	6
546.2.bn.f.101.15	yes	34	21.17	even	6
546.2.bn.f.173.15	yes	34	13.4	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more