LMFDB - Embedded newform 143.2.h.c.92.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			92.2
Character	$\chi$	$=$	143.92
Dual form			143.2.h.c.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.91083 - 1.38830i) q^{2} +(0.850654 - 2.61804i) q^{3} +(1.10586 + 3.40347i) q^{4} +(-1.81276 + 1.31704i) q^{5} +(-5.26007 + 3.82167i) q^{6} +(-1.38773 - 4.27098i) q^{7} +(1.15219 - 3.54608i) q^{8} +(-3.70349 - 2.69074i) q^{9} +O(q^{10})$	\(q+(-1.91083 - 1.38830i) q^{2} +(0.850654 - 2.61804i) q^{3} +(1.10586 + 3.40347i) q^{4} +(-1.81276 + 1.31704i) q^{5} +(-5.26007 + 3.82167i) q^{6} +(-1.38773 - 4.27098i) q^{7} +(1.15219 - 3.54608i) q^{8} +(-3.70349 - 2.69074i) q^{9} +5.29231 q^{10} +(-0.676812 + 3.24683i) q^{11} +9.85114 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-3.27768 + 10.0877i) q^{14} +(1.90605 + 5.86623i) q^{15} +(-1.33431 + 0.969432i) q^{16} +(0.419199 - 0.304566i) q^{17} +(3.34118 + 10.2831i) q^{18} +(0.949208 - 2.92136i) q^{19} +(-6.48717 - 4.71321i) q^{20} -12.3621 q^{21} +(5.80084 - 5.26452i) q^{22} +1.35723 q^{23} +(-8.30367 - 6.03297i) q^{24} +(0.00639465 - 0.0196807i) q^{25} +(0.729871 + 2.24631i) q^{26} +(-3.51375 + 2.55289i) q^{27} +(13.0015 - 9.44617i) q^{28} +(-2.80388 - 8.62945i) q^{29} +(4.50193 - 13.8555i) q^{30} +(3.14803 + 2.28717i) q^{31} -3.56164 q^{32} +(7.92462 + 4.53385i) q^{33} -1.22384 q^{34} +(8.14068 + 5.91455i) q^{35} +(5.06235 - 15.5803i) q^{36} +(-2.43358 - 7.48979i) q^{37} +(-5.86948 + 4.26443i) q^{38} +(-2.22704 + 1.61804i) q^{39} +(2.58170 + 7.94566i) q^{40} +(1.29923 - 3.99863i) q^{41} +(23.6218 + 17.1622i) q^{42} +1.55539 q^{43} +(-11.7990 + 1.28702i) q^{44} +10.2574 q^{45} +(-2.59343 - 1.88423i) q^{46} +(2.67844 - 8.24338i) q^{47} +(1.40298 + 4.31793i) q^{48} +(-10.6524 + 7.73940i) q^{49} +(-0.0395417 + 0.0287287i) q^{50} +(-0.440774 - 1.35656i) q^{51} +(1.10586 - 3.40347i) q^{52} +(-2.09713 - 1.52365i) q^{53} +10.2583 q^{54} +(-3.04933 - 6.77711i) q^{55} -16.7442 q^{56} +(-6.84080 - 4.97013i) q^{57} +(-6.62251 + 20.3820i) q^{58} +(1.47424 + 4.53725i) q^{59} +(-17.8577 + 12.9744i) q^{60} +(0.382928 - 0.278213i) q^{61} +(-2.84005 - 8.74078i) q^{62} +(-6.35268 + 19.5515i) q^{63} +(9.47430 + 6.88348i) q^{64} +2.24069 q^{65} +(-8.84823 - 19.6651i) q^{66} +3.47727 q^{67} +(1.50016 + 1.08993i) q^{68} +(1.15453 - 3.55328i) q^{69} +(-7.34428 - 22.6034i) q^{70} +(8.32068 - 6.04532i) q^{71} +(-13.8087 + 10.0326i) q^{72} +(4.22289 + 12.9967i) q^{73} +(-5.74790 + 17.6902i) q^{74} +(-0.0460853 - 0.0334829i) q^{75} +10.9925 q^{76} +(14.8064 - 1.61506i) q^{77} +6.50181 q^{78} +(6.99142 + 5.07957i) q^{79} +(1.14199 - 3.51469i) q^{80} +(-0.549236 - 1.69037i) q^{81} +(-8.03390 + 5.83697i) q^{82} +(-10.8671 + 7.89539i) q^{83} +(-13.6707 - 42.0740i) q^{84} +(-0.358779 + 1.10421i) q^{85} +(-2.97207 - 2.15934i) q^{86} -24.9774 q^{87} +(10.7337 + 6.14100i) q^{88} +4.60465 q^{89} +(-19.6000 - 14.2402i) q^{90} +(-1.38773 + 4.27098i) q^{91} +(1.50090 + 4.61929i) q^{92} +(8.66580 - 6.29607i) q^{93} +(-16.5623 + 12.0332i) q^{94} +(2.12688 + 6.54586i) q^{95} +(-3.02973 + 9.32454i) q^{96} +(6.24804 + 4.53947i) q^{97} +31.0994 q^{98} +(11.2430 - 10.2035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.91083	−	1.38830i	−1.35116	−	0.981674i	−0.998953	−	0.0457510i	$-0.985432\pi$
$2$	−1.91083	−	1.38830i	−1.35116	−	0.981674i	−0.352205	−	0.935923i	$-0.614568\pi$
$3$	0.850654	−	2.61804i	0.491125	−	1.51153i	−0.331784	−	0.943355i	$-0.607651\pi$
$3$	0.850654	−	2.61804i	0.491125	−	1.51153i	0.822909	−	0.568173i	$-0.192349\pi$
$4$	1.10586	+	3.40347i	0.552928	+	1.70174i
$5$	−1.81276	+	1.31704i	−0.810689	+	0.589000i	−0.914030	−	0.405646i	$-0.867047\pi$
$5$	−1.81276	+	1.31704i	−0.810689	+	0.589000i	0.103341	+	0.994646i	$0.467047\pi$
$6$	−5.26007	+	3.82167i	−2.14742	+	1.56019i
$7$	−1.38773	−	4.27098i	−0.524511	−	1.61428i	−0.765281	−	0.643697i	$-0.777400\pi$
$7$	−1.38773	−	4.27098i	−0.524511	−	1.61428i	0.240770	−	0.970582i	$-0.422600\pi$
$8$	1.15219	−	3.54608i	0.407361	−	1.25373i
$9$	−3.70349	−	2.69074i	−1.23450	−	0.896914i
$10$	5.29231			1.67358
$11$	−0.676812	+	3.24683i	−0.204066	+	0.978957i
$11$	−0.676812	+	3.24683i	−0.204066	+	0.978957i
$12$	9.85114			2.84378
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	−3.27768	+	10.0877i	−0.875998	+	2.69604i
$15$	1.90605	+	5.86623i	0.492141	+	1.51465i
$16$	−1.33431	+	0.969432i	−0.333577	+	0.242358i
$17$	0.419199	−	0.304566i	0.101671	−	0.0738681i	−0.535788	−	0.844352i	$-0.679986\pi$
$17$	0.419199	−	0.304566i	0.101671	−	0.0738681i	0.637459	+	0.770484i	$0.279986\pi$
$18$	3.34118	+	10.2831i	0.787523	+	2.42375i
$19$	0.949208	−	2.92136i	0.217763	−	0.670206i	−0.781183	−	0.624302i	$-0.785383\pi$
$19$	0.949208	−	2.92136i	0.217763	−	0.670206i	0.998946	−	0.0459036i	$-0.0146167\pi$
$20$	−6.48717	−	4.71321i	−1.45058	−	1.05391i
$21$	−12.3621			−2.69763
$22$	5.80084	−	5.26452i	1.23674	−	1.12240i
$23$	1.35723			0.283001			0.141501	−	0.989938i	$-0.454807\pi$
$23$	1.35723			0.283001			0.141501	+	0.989938i	$0.454807\pi$
$24$	−8.30367	−	6.03297i	−1.69498	−	1.23147i
$25$	0.00639465	−	0.0196807i	0.00127893	−	0.00393614i
$26$	0.729871	+	2.24631i	0.143139	+	0.440538i
$27$	−3.51375	+	2.55289i	−0.676221	+	0.491303i
$28$	13.0015	−	9.44617i	2.45706	−	1.78516i
$29$	−2.80388	−	8.62945i	−0.520667	−	1.60245i	−0.772728	−	0.634737i	$-0.781108\pi$
$29$	−2.80388	−	8.62945i	−0.520667	−	1.60245i	0.252061	−	0.967711i	$-0.418892\pi$
$30$	4.50193	−	13.8555i	0.821935	−	2.52966i
$31$	3.14803	+	2.28717i	0.565402	+	0.410789i	0.833432	−	0.552622i	$-0.186373\pi$
$31$	3.14803	+	2.28717i	0.565402	+	0.410789i	−0.268030	+	0.963411i	$0.586373\pi$
$32$	−3.56164			−0.629615
$33$	7.92462	+	4.53385i	1.37950	+	0.789243i
$34$	−1.22384			−0.209888
$35$	8.14068	+	5.91455i	1.37603	+	0.999742i
$36$	5.06235	−	15.5803i	0.843724	−	2.59672i
$37$	−2.43358	−	7.48979i	−0.400078	−	1.23131i	−0.924936	−	0.380124i	$-0.875881\pi$
$37$	−2.43358	−	7.48979i	−0.400078	−	1.23131i	0.524858	−	0.851190i	$-0.324119\pi$
$38$	−5.86948	+	4.26443i	−0.952156	+	0.691782i
$39$	−2.22704	+	1.61804i	−0.356612	+	0.259094i
$40$	2.58170	+	7.94566i	0.408203	+	1.25632i
$41$	1.29923	−	3.99863i	0.202906	−	0.624481i	−0.796887	−	0.604129i	$-0.793521\pi$
$41$	1.29923	−	3.99863i	0.202906	−	0.624481i	0.999793	−	0.0203524i	$-0.00647881\pi$
$42$	23.6218	+	17.1622i	3.64492	+	2.64819i
$43$	1.55539			0.237194			0.118597	−	0.992942i	$-0.462160\pi$
$43$	1.55539			0.237194			0.118597	+	0.992942i	$0.462160\pi$
$44$	−11.7990	+	1.28702i	−1.77876	+	0.194025i
$45$	10.2574			1.52908
$46$	−2.59343	−	1.88423i	−0.382380	−	0.277815i
$47$	2.67844	−	8.24338i	0.390690	−	1.20242i	−0.541578	−	0.840651i	$-0.682173\pi$
$47$	2.67844	−	8.24338i	0.390690	−	1.20242i	0.932268	−	0.361769i	$-0.117827\pi$
$48$	1.40298	+	4.31793i	0.202503	+	0.623239i
$49$	−10.6524	+	7.73940i	−1.52177	+	1.10563i
$50$	−0.0395417	+	0.0287287i	−0.00559204	+	0.00406285i
$51$	−0.440774	−	1.35656i	−0.0617207	−	0.189957i
$52$	1.10586	−	3.40347i	0.153355	−	0.471977i
$53$	−2.09713	−	1.52365i	−0.288063	−	0.209290i	0.434364	−	0.900738i	$-0.356973\pi$
$53$	−2.09713	−	1.52365i	−0.288063	−	0.209290i	−0.722427	+	0.691448i	$0.756973\pi$
$54$	10.2583			1.39598
$55$	−3.04933	−	6.77711i	−0.411172	−	0.913825i
$56$	−16.7442			−2.23753
$57$	−6.84080	−	4.97013i	−0.906086	−	0.658310i
$58$	−6.62251	+	20.3820i	−0.869578	+	2.67629i
$59$	1.47424	+	4.53725i	0.191930	+	0.590699i	0.999999	+	0.00161127i	$0.000512884\pi$
$59$	1.47424	+	4.53725i	0.191930	+	0.590699i	−0.808069	+	0.589088i	$0.799487\pi$
$60$	−17.8577	+	12.9744i	−2.30542	+	1.67499i
$61$	0.382928	−	0.278213i	0.0490289	−	0.0356216i	−0.563001	−	0.826456i	$-0.690353\pi$
$61$	0.382928	−	0.278213i	0.0490289	−	0.0356216i	0.612030	+	0.790835i	$0.290353\pi$
$62$	−2.84005	−	8.74078i	−0.360687	−	1.11008i
$63$	−6.35268	+	19.5515i	−0.800363	+	2.46326i
$64$	9.47430	+	6.88348i	1.18429	+	0.860435i
$65$	2.24069			0.277923
$66$	−8.84823	−	19.6651i	−1.08914	−	2.42061i
$67$	3.47727			0.424816			0.212408	−	0.977181i	$-0.431869\pi$
$67$	3.47727			0.424816			0.212408	+	0.977181i	$0.431869\pi$
$68$	1.50016	+	1.08993i	0.181921	+	0.132173i
$69$	1.15453	−	3.55328i	0.138989	−	0.427765i
$70$	−7.34428	−	22.6034i	−0.877809	−	2.70162i
$71$	8.32068	−	6.04532i	0.987482	−	0.717448i	0.0281142	−	0.999605i	$-0.491050\pi$
$71$	8.32068	−	6.04532i	0.987482	−	0.717448i	0.959368	+	0.282157i	$0.0910498\pi$
$72$	−13.8087	+	10.0326i	−1.62737	+	1.18235i
$73$	4.22289	+	12.9967i	0.494252	+	1.52115i	0.818119	+	0.575049i	$0.195017\pi$
$73$	4.22289	+	12.9967i	0.494252	+	1.52115i	−0.323867	+	0.946103i	$0.604983\pi$
$74$	−5.74790	+	17.6902i	−0.668180	+	2.05645i
$75$	−0.0460853	−	0.0334829i	−0.00532147	−	0.00386627i
$76$	10.9925			1.26092
$77$	14.8064	−	1.61506i	1.68734	−	0.184054i
$78$	6.50181			0.736185
$79$	6.99142	+	5.07957i	0.786596	+	0.571496i	0.906951	−	0.421235i	$-0.138403\pi$
$79$	6.99142	+	5.07957i	0.786596	+	0.571496i	−0.120355	+	0.992731i	$0.538403\pi$
$80$	1.14199	−	3.51469i	0.127679	−	0.392954i
$81$	−0.549236	−	1.69037i	−0.0610262	−	0.187819i
$82$	−8.03390	+	5.83697i	−0.887195	+	0.644585i
$83$	−10.8671	+	7.89539i	−1.19282	+	0.866632i	−0.993559	−	0.113315i	$-0.963853\pi$
$83$	−10.8671	+	7.89539i	−1.19282	+	0.866632i	−0.199257	+	0.979947i	$0.563853\pi$
$84$	−13.6707	−	42.0740i	−1.49159	−	4.59065i
$85$	−0.358779	+	1.10421i	−0.0389150	+	0.119768i
$86$	−2.97207	−	2.15934i	−0.320487	−	0.232847i
$87$	−24.9774			−2.67786
$88$	10.7337	+	6.14100i	1.14422	+	0.654633i
$89$	4.60465			0.488092			0.244046	−	0.969764i	$-0.421525\pi$
$89$	4.60465			0.488092			0.244046	+	0.969764i	$0.421525\pi$
$90$	−19.6000	−	14.2402i	−2.06602	−	1.50105i
$91$	−1.38773	+	4.27098i	−0.145473	+	0.447720i
$92$	1.50090	+	4.61929i	0.156479	+	0.481594i
$93$	8.66580	−	6.29607i	0.898602	−	0.652872i
$94$	−16.5623	+	12.0332i	−1.70827	+	1.24113i
$95$	2.12688	+	6.54586i	0.218213	+	0.671592i
$96$	−3.02973	+	9.32454i	−0.309220	+	0.951681i
$97$	6.24804	+	4.53947i	0.634393	+	0.460913i	0.857919	−	0.513785i	$-0.171757\pi$
$97$	6.24804	+	4.53947i	0.634393	+	0.460913i	−0.223527	+	0.974698i	$0.571757\pi$
$98$	31.0994			3.14152
$99$	11.2430	−	10.2035i	1.12996	−	1.02549i
$100$	0.0740543			0.00740543
$101$	7.35218	+	5.34167i	0.731570	+	0.531516i	0.890060	−	0.455844i	$-0.150663\pi$
$101$	7.35218	+	5.34167i	0.731570	+	0.531516i	−0.158490	+	0.987361i	$0.550663\pi$
$102$	−1.04107	+	3.20408i	−0.103081	+	0.317251i
$103$	−1.53345	−	4.71948i	−0.151096	−	0.465024i	0.846649	−	0.532152i	$-0.178617\pi$
$103$	−1.53345	−	4.71948i	−0.151096	−	0.465024i	−0.997744	+	0.0671277i	$0.978617\pi$
$104$	−3.01647	+	2.19160i	−0.295790	+	0.214904i
$105$	22.4095	−	16.2814i	2.18694	−	1.58890i
$106$	1.89197	+	5.82288i	0.183764	+	0.565568i
$107$	0.891648	−	2.74421i	0.0861989	−	0.265293i	−0.898661	−	0.438643i	$-0.855459\pi$
$107$	0.891648	−	2.74421i	0.0861989	−	0.265293i	0.984860	+	0.173350i	$0.0554592\pi$
$108$	−12.5744	−	9.13582i	−1.20997	−	0.879095i
$109$	14.7956			1.41716			0.708579	−	0.705632i	$-0.249337\pi$
$109$	14.7956			1.41716			0.708579	+	0.705632i	$0.249337\pi$
$110$	−3.58190	+	17.1833i	−0.341521	+	1.63836i
$111$	−21.6787			−2.05765
$112$	5.99208	+	4.35350i	0.566198	+	0.411367i
$113$	−0.0699832	+	0.215386i	−0.00658346	+	0.0202618i	−0.954294	−	0.298869i	$-0.903391\pi$
$113$	−0.0699832	+	0.215386i	−0.00658346	+	0.0202618i	0.947711	+	0.319130i	$0.103391\pi$
$114$	6.17156	+	18.9941i	0.578020	+	1.77896i
$115$	−2.46032	+	1.78753i	−0.229426	+	0.166688i
$116$	26.2694	−	19.0858i	2.43905	−	1.77208i
$117$	1.41461	+	4.35371i	0.130780	+	0.402501i
$118$	3.48203	−	10.7166i	0.320546	−	0.986541i
$119$	−1.88253	−	1.36774i	−0.172571	−	0.125380i
$120$	22.9982			2.09944
$121$	−10.0839	−	4.39499i	−0.916714	−	0.399545i
$122$	−1.11795			−0.101215
$123$	−9.36339	−	6.80290i	−0.844269	−	0.613397i
$124$	−4.30307	+	13.2435i	−0.386427	+	1.18930i
$125$	−3.44773	−	10.6110i	−0.308374	−	0.949078i
$126$	39.2822	−	28.5402i	3.49954	−	2.54256i
$127$	−3.60189	+	2.61693i	−0.319616	+	0.232215i	−0.736012	−	0.676969i	$-0.763293\pi$
$127$	−3.60189	+	2.61693i	−0.319616	+	0.232215i	0.416396	+	0.909184i	$0.363293\pi$
$128$	−6.34621	−	19.5316i	−0.560931	−	1.72637i
$129$	1.32310	−	4.07207i	0.116492	−	0.358526i
$130$	−4.28157	−	3.11074i	−0.375518	−	0.272830i
$131$	3.12082			0.272667			0.136334	−	0.990663i	$-0.456468\pi$
$131$	3.12082			0.272667			0.136334	+	0.990663i	$0.456468\pi$
$132$	−6.66737	+	31.9850i	−0.580320	+	2.78394i
$133$	−13.7943			−1.19612
$134$	−6.64446	−	4.82748i	−0.573994	−	0.417031i
$135$	3.00730	−	9.25552i	0.258827	−	0.796589i
$136$	−0.597017	−	1.83743i	−0.0511938	−	0.157558i
$137$	5.55876	−	4.03867i	0.474917	−	0.345047i	−0.324438	−	0.945907i	$-0.605175\pi$
$137$	5.55876	−	4.03867i	0.474917	−	0.345047i	0.799354	+	0.600860i	$0.205175\pi$
$138$	−7.13911	+	5.18687i	−0.607722	+	0.441536i
$139$	−0.360403	−	1.10921i	−0.0305690	−	0.0940816i	0.934608	−	0.355680i	$-0.115751\pi$
$139$	−0.360403	−	1.10921i	−0.0305690	−	0.0940816i	−0.965177	+	0.261598i	$0.915751\pi$
$140$	−11.1276	+	34.2472i	−0.940454	+	2.89442i
$141$	−19.3031	−	14.0245i	−1.62561	−	1.18108i
$142$	−24.2921			−2.03854
$143$	2.45599	−	2.22892i	0.205380	−	0.186392i
$144$	7.55009			0.629174
$145$	16.4481	+	11.9503i	1.36594	+	0.992415i
$146$	9.97410	−	30.6971i	0.825462	−	2.54051i
$147$	11.2006	+	34.4719i	0.923811	+	2.84320i
$148$	22.8001	−	16.5652i	1.87416	−	1.36165i
$149$	−7.66538	+	5.56922i	−0.627972	+	0.456248i	−0.855697	−	0.517477i	$-0.826871\pi$
$149$	−7.66538	+	5.56922i	−0.627972	+	0.456248i	0.227725	+	0.973725i	$0.426871\pi$
$150$	0.0415768	+	0.127960i	0.00339473	+	0.0104479i
$151$	1.33742	−	4.11615i	0.108838	−	0.334967i	−0.881774	−	0.471671i	$-0.843651\pi$
$151$	1.33742	−	4.11615i	0.108838	−	0.334967i	0.990612	+	0.136704i	$0.0436509\pi$
$152$	−9.26570	−	6.73193i	−0.751548	−	0.546031i
$153$	−2.37201			−0.191766
$154$	−30.5346	−	17.4696i	−2.46055	−	1.40774i
$155$	−8.71891			−0.700320
$156$	−7.96974	−	5.79035i	−0.638090	−	0.463599i
$157$	−0.597498	+	1.83891i	−0.0476855	+	0.146761i	−0.972064	−	0.234715i	$-0.924584\pi$
$157$	−0.597498	+	1.83891i	−0.0476855	+	0.146761i	0.924379	+	0.381476i	$0.124584\pi$
$158$	−6.30745	−	19.4123i	−0.501794	−	1.54436i
$159$	−5.77293	+	4.19428i	−0.457823	+	0.332628i
$160$	6.45639	−	4.69084i	0.510423	−	0.370844i
$161$	−1.88346	−	5.79669i	−0.148437	−	0.456843i
$162$	−1.29725	+	3.99251i	−0.101921	+	0.313681i
$163$	5.34578	+	3.88394i	0.418714	+	0.304213i	0.777120	−	0.629352i	$-0.216680\pi$
$163$	5.34578	+	3.88394i	0.418714	+	0.304213i	−0.358406	+	0.933566i	$0.616680\pi$
$164$	15.0460			1.17489
$165$	−20.3367	+	2.21830i	−1.58321	+	0.172695i
$166$	31.7262			2.46243
$167$	5.09677	+	3.70302i	0.394400	+	0.286548i	0.767256	−	0.641341i	$-0.221621\pi$
$167$	5.09677	+	3.70302i	0.394400	+	0.286548i	−0.372856	+	0.927889i	$0.621621\pi$
$168$	−14.2435	+	43.8369i	−1.09891	+	3.38209i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	2.21853	−	1.61186i	0.170154	−	0.123624i
$171$	−11.3760	+	8.26515i	−0.869945	+	0.632052i
$172$	1.72003	+	5.29372i	0.131151	+	0.403642i
$173$	−5.19875	+	16.0001i	−0.395254	+	1.21647i	0.533510	+	0.845794i	$0.320873\pi$
$173$	−5.19875	+	16.0001i	−0.395254	+	1.21647i	−0.928764	+	0.370672i	$0.879127\pi$
$174$	47.7275	+	34.6760i	3.61821	+	2.62878i
$175$	−0.0929299			−0.00702484
$176$	−2.24451	−	4.98840i	−0.169186	−	0.376015i
$177$	13.1328			0.987120
$178$	−8.79868	−	6.39262i	−0.659489	−	0.479147i
$179$	−1.58148	+	4.86730i	−0.118205	+	0.363799i	−0.992602	−	0.121413i	$-0.961257\pi$
$179$	−1.58148	+	4.86730i	−0.118205	+	0.363799i	0.874397	+	0.485212i	$0.161257\pi$
$180$	11.3431	+	34.9106i	0.845468	+	2.60208i
$181$	−20.6968	+	15.0371i	−1.53838	+	1.11770i	−0.587046	+	0.809554i	$0.699709\pi$
$181$	−20.6968	+	15.0371i	−1.53838	+	1.11770i	−0.951339	+	0.308148i	$0.900291\pi$
$182$	8.58109	−	6.23453i	0.636073	−	0.462134i
$183$	−0.402636	−	1.23919i	−0.0297637	−	0.0916032i
$184$	1.56378	−	4.81283i	0.115284	−	0.354807i
$185$	14.2759	+	10.3720i	1.04958	+	0.762567i
$186$	−25.2997			−1.85506
$187$	0.705156	+	1.56720i	0.0515661	+	0.114605i
$188$	31.0181			2.26223
$189$	15.7794	+	11.4644i	1.14779	+	0.833915i
$190$	5.02350	−	15.4607i	0.364443	−	1.12164i
$191$	1.09526	+	3.37088i	0.0792506	+	0.243908i	0.982830	−	0.184512i	$-0.0590704\pi$
$191$	1.09526	+	3.37088i	0.0792506	+	0.243908i	−0.903580	+	0.428420i	$0.859070\pi$
$192$	26.0806	−	18.9487i	1.88221	−	1.36750i
$193$	14.6251	−	10.6258i	1.05274	−	0.764861i	0.0800090	−	0.996794i	$-0.474505\pi$
$193$	14.6251	−	10.6258i	1.05274	−	0.764861i	0.972732	+	0.231933i	$0.0745051\pi$
$194$	−5.63680	−	17.3483i	−0.404698	−	1.24553i
$195$	1.90605	−	5.86623i	0.136495	−	0.420089i
$196$	−38.1208	−	27.6964i	−2.72292	−	1.97831i
$197$	−20.0091			−1.42559			−0.712793	−	0.701374i	$-0.752570\pi$
$197$	−20.0091			−1.42559			−0.712793	+	0.701374i	$0.752570\pi$
$198$	−35.6488	+	3.88853i	−2.53345	+	0.276346i
$199$	17.9988			1.27590			0.637950	−	0.770078i	$-0.279783\pi$
$199$	17.9988			1.27590			0.637950	+	0.770078i	$0.279783\pi$
$200$	−0.0624214	−	0.0453518i	−0.00441386	−	0.00320686i
$201$	2.95795	−	9.10364i	0.208638	−	0.642122i
$202$	−6.63292	−	20.4140i	−0.466690	−	1.43633i
$203$	−32.9652	+	23.9506i	−2.31370	+	1.68100i
$204$	4.12959	−	3.00032i	0.289129	−	0.210065i
$205$	2.91118	+	8.95969i	0.203326	+	0.625772i
$206$	−3.62188	+	11.1470i	−0.252348	+	0.776648i
$207$	−5.02648	−	3.65195i	−0.349364	−	0.253828i
$208$	1.64930			0.114358
$209$	8.84274	+	5.05913i	0.611665	+	0.349947i
$210$	−65.4240			−4.51469
$211$	−7.58094	−	5.50787i	−0.521893	−	0.379178i	0.295423	−	0.955366i	$-0.404539\pi$
$211$	−7.58094	−	5.50787i	−0.521893	−	0.379178i	−0.817317	+	0.576189i	$0.804539\pi$
$212$	2.86659	−	8.82247i	0.196878	−	0.605929i
$213$	−8.74891	−	26.9264i	−0.599465	−	1.84496i
$214$	−5.51356	+	4.00584i	−0.376899	+	0.273833i
$215$	−2.81954	+	2.04851i	−0.192291	+	0.139708i
$216$	5.00423	+	15.4014i	0.340495	+	1.04793i
$217$	5.39988	−	16.6191i	0.366568	−	1.12818i
$218$	−28.2717	−	20.5406i	−1.91480	−	1.39119i
$219$	37.6182			2.54200
$220$	19.6936	−	17.8728i	1.32774	−	1.20498i
$221$	−0.518159			−0.0348551
$222$	41.4243	+	30.0965i	2.78022	+	2.01994i
$223$	6.06912	−	18.6788i	0.406419	−	1.25083i	−0.513286	−	0.858217i	$-0.671572\pi$
$223$	6.06912	−	18.6788i	0.406419	−	1.25083i	0.919705	−	0.392610i	$-0.128428\pi$
$224$	4.94258	+	15.2117i	0.330240	+	1.01637i
$225$	−0.0766382	+	0.0556809i	−0.00510921	+	0.00371206i
$226$	0.432745	−	0.314408i	0.0287858	−	0.0209141i
$227$	4.76007	+	14.6500i	0.315937	+	0.972355i	0.975367	+	0.220589i	$0.0707978\pi$
$227$	4.76007	+	14.6500i	0.315937	+	0.972355i	−0.659430	+	0.751766i	$0.729202\pi$
$228$	9.35078	−	28.7787i	0.619270	−	1.90592i
$229$	−22.0278	−	16.0042i	−1.45564	−	1.05758i	−0.984472	−	0.175541i	$-0.943833\pi$
$229$	−22.0278	−	16.0042i	−1.45564	−	1.05758i	−0.471168	−	0.882044i	$-0.656167\pi$
$230$	7.18287			0.473624
$231$	8.36681	−	40.1376i	0.550496	−	2.64086i
$232$	−33.8313			−2.22113
$233$	2.65326	+	1.92771i	0.173821	+	0.126288i	0.671294	−	0.741191i	$-0.265739\pi$
$233$	2.65326	+	1.92771i	0.173821	+	0.126288i	−0.497473	+	0.867479i	$0.665739\pi$
$234$	3.34118	−	10.2831i	0.218420	−	0.672226i
$235$	6.00155	+	18.4709i	0.391498	+	1.20491i
$236$	−13.8121	+	10.0351i	−0.899091	+	0.653228i
$237$	19.2458	−	13.9829i	1.25015	−	0.908287i
$238$	1.69836	+	5.22702i	0.110088	+	0.338817i
$239$	5.06374	−	15.5846i	0.327546	−	1.00808i	−0.642732	−	0.766091i	$-0.722199\pi$
$239$	5.06374	−	15.5846i	0.327546	−	1.00808i	0.970278	−	0.241992i	$-0.0778008\pi$
$240$	−8.23017	−	5.97957i	−0.531255	−	0.385979i
$241$	−14.7660			−0.951162			−0.475581	−	0.879672i	$-0.657762\pi$
$241$	−14.7660			−0.951162			−0.475581	+	0.879672i	$0.657762\pi$
$242$	13.1669	+	22.3974i	0.846403	+	1.43976i
$243$	−17.9224			−1.14972
$244$	1.37035	+	0.995621i	0.0877280	+	0.0637381i
$245$	9.11702	−	28.0593i	0.582465	−	1.79264i
$246$	8.44737	+	25.9983i	0.538585	+	1.65759i
$247$	−2.48506	+	1.80550i	−0.158120	+	0.114881i
$248$	11.7376	−	8.52788i	0.745340	−	0.541521i
$249$	11.4264	+	35.1667i	0.724116	+	2.22860i
$250$	−8.14323	+	25.0623i	−0.515023	+	1.58508i
$251$	4.90862	+	3.56632i	0.309829	+	0.225104i	0.731823	−	0.681494i	$-0.238670\pi$
$251$	4.90862	+	3.56632i	0.309829	+	0.225104i	−0.421994	+	0.906599i	$0.638670\pi$
$252$	−73.5683			−4.63437
$253$	−0.918588	+	4.40669i	−0.0577511	+	0.277046i
$254$	10.5156			0.659811
$255$	2.58567	+	1.87860i	0.161921	+	0.117642i
$256$	−7.75146	+	23.8565i	−0.484466	+	1.49103i
$257$	−5.18832	−	15.9680i	−0.323639	−	0.996058i	−0.972051	−	0.234768i	$-0.924567\pi$
$257$	−5.18832	−	15.9680i	−0.323639	−	0.996058i	0.648413	−	0.761289i	$-0.275433\pi$
$258$	−8.18145	+	5.94417i	−0.509355	+	0.370068i
$259$	−28.6116	+	20.7875i	−1.77784	+	1.29168i
$260$	2.47788	+	7.62613i	0.153672	+	0.472952i
$261$	−12.8355	+	39.5036i	−0.794497	+	2.44521i
$262$	−5.96334	−	4.33262i	−0.368416	−	0.267670i
$263$	−12.0349			−0.742102			−0.371051	−	0.928612i	$-0.621003\pi$
$263$	−12.0349			−0.742102			−0.371051	+	0.928612i	$0.621003\pi$
$264$	25.2081	−	22.8774i	1.55145	−	1.40801i
$265$	5.80831			0.356801
$266$	26.3585	+	19.1506i	1.61615	+	1.17420i
$267$	3.91696	−	12.0552i	0.239714	−	0.737764i
$268$	3.84536	+	11.8348i	0.234893	+	0.722925i
$269$	21.2034	−	15.4051i	1.29279	−	0.939268i	0.292934	−	0.956133i	$-0.405368\pi$
$269$	21.2034	−	15.4051i	1.29279	−	0.939268i	0.999858	+	0.0168646i	$0.00536842\pi$
$270$	−18.5958	+	13.5107i	−1.13171	+	0.822233i
$271$	3.05566	+	9.40434i	0.185618	+	0.571273i	0.999958	−	0.00911422i	$-0.00290119\pi$
$271$	3.05566	+	9.40434i	0.185618	+	0.571273i	−0.814341	+	0.580387i	$0.802901\pi$
$272$	−0.264085	+	0.812770i	−0.0160125	+	0.0492814i
$273$	10.0011	+	7.26625i	0.605296	+	0.439774i
$274$	−16.2287			−0.980411
$275$	0.0595720	+	0.0340825i	0.00359232	+	0.00205525i
$276$	13.3702			0.804794
$277$	−14.4462	−	10.4958i	−0.867987	−	0.630629i	0.0620592	−	0.998072i	$-0.480233\pi$
$277$	−14.4462	−	10.4958i	−0.867987	−	0.630629i	−0.930046	+	0.367443i	$0.880233\pi$
$278$	−0.851240	+	2.61985i	−0.0510540	+	0.157128i
$279$	−5.50448	−	16.9411i	−0.329545	−	1.01423i
$280$	30.3531	−	22.0528i	1.81394	−	1.31791i
$281$	15.4065	−	11.1934i	0.919072	−	0.667745i	−0.0242206	−	0.999707i	$-0.507710\pi$
$281$	15.4065	−	11.1934i	0.919072	−	0.667745i	0.943293	+	0.331962i	$0.107710\pi$
$282$	17.4147	+	53.5968i	1.03703	+	3.19165i
$283$	0.629188	−	1.93644i	0.0374013	−	0.115109i	−0.930613	−	0.366005i	$-0.880725\pi$
$283$	0.629188	−	1.93644i	0.0374013	−	0.115109i	0.968014	+	0.250896i	$0.0807252\pi$
$284$	29.7766	+	21.6339i	1.76691	+	1.28374i
$285$	18.9466			1.12230
$286$	−7.78738	+	0.849438i	−0.460478	+	0.0502283i
$287$	−18.8811			−1.11451
$288$	13.1905	+	9.58346i	0.777258	+	0.564711i
$289$	−5.17032	+	15.9126i	−0.304137	+	0.936036i
$290$	−14.8390	−	45.6697i	−0.871376	−	2.68182i
$291$	17.1995	−	12.4961i	1.00825	−	0.732536i
$292$	−39.5641	+	28.7450i	−2.31531	+	1.68217i
$293$	7.72789	+	23.7840i	0.451468	+	1.38948i	0.875232	+	0.483703i	$0.160708\pi$
$293$	7.72789	+	23.7840i	0.451468	+	1.38948i	−0.423764	+	0.905772i	$0.639292\pi$
$294$	26.4548	−	81.4196i	1.54288	−	4.74849i
$295$	−8.64820	−	6.28328i	−0.503518	−	0.365827i
$296$	−29.3633			−1.70671
$297$	−5.91065	−	13.1364i	−0.342971	−	0.762250i
$298$	22.3789			1.29638
$299$	−1.09802	−	0.797758i	−0.0635001	−	0.0461356i
$300$	0.0629946	−	0.193877i	0.00363699	−	0.0111935i
$301$	−2.15845	−	6.64303i	−0.124411	−	0.382898i
$302$	−8.27001	+	6.00851i	−0.475885	+	0.345751i
$303$	20.2389	−	14.7044i	1.16269	−	0.844747i
$304$	1.56552	+	4.81819i	0.0897890	+	0.276342i
$305$	−0.327736	+	1.00867i	−0.0187661	+	0.0577561i
$306$	4.53250	+	3.29305i	0.259106	+	0.188251i
$307$	19.0543			1.08748			0.543742	−	0.839252i	$-0.317007\pi$
$307$	19.0543			1.08748			0.543742	+	0.839252i	$0.317007\pi$
$308$	21.8706	+	48.6071i	1.24619	+	2.76965i
$309$	−13.6602			−0.777104
$310$	16.6603	+	12.1044i	0.946243	+	0.687486i
$311$	0.377613	−	1.16217i	0.0214125	−	0.0659009i	−0.939779	−	0.341782i	$-0.888970\pi$
$311$	0.377613	−	1.16217i	0.0214125	−	0.0659009i	0.961192	+	0.275881i	$0.0889696\pi$
$312$	3.17172	+	9.76155i	0.179563	+	0.552639i
$313$	0.0129205	−	0.00938730i	0.000730311	−	0.000530602i	−0.587420	−	0.809282i	$-0.699856\pi$
$313$	0.0129205	−	0.00938730i	0.000730311	−	0.000530602i	0.588150	+	0.808752i	$0.299856\pi$
$314$	3.69467	−	2.68433i	0.208502	−	0.151486i
$315$	−14.2344	−	43.8090i	−0.802017	−	2.46836i
$316$	−9.55666	+	29.4124i	−0.537604	+	1.65458i
$317$	−10.8209	−	7.86183i	−0.607761	−	0.441564i	0.240864	−	0.970559i	$-0.422569\pi$
$317$	−10.8209	−	7.86183i	−0.607761	−	0.441564i	−0.848625	+	0.528994i	$0.822569\pi$
$318$	16.8540			0.945123
$319$	29.9161	−	3.26321i	1.67498	−	0.182705i
$320$	−26.2404			−1.46689
$321$	−6.42598	−	4.66875i	−0.358663	−	0.260584i
$322$	−4.44856	+	13.6913i	−0.247909	+	0.762985i
$323$	−0.491840	−	1.51373i	−0.0273667	−	0.0842261i
$324$	5.14576	−	3.73862i	0.285876	−	0.207701i
$325$	−0.0167414	+	0.0121633i	−0.000928646	+	0.000674701i
$326$	−4.82280	−	14.8431i	−0.267110	−	0.822081i
$327$	12.5859	−	38.7354i	0.696002	−	2.14207i
$328$	−12.6825	−	9.21437i	−0.700273	−	0.508778i
$329$	−38.9242			−2.14596
$330$	41.9395	+	23.9946i	2.30870	+	1.32086i
$331$	11.2602			0.618918			0.309459	−	0.950913i	$-0.399852\pi$
$331$	11.2602			0.618918			0.309459	+	0.950913i	$0.399852\pi$
$332$	−38.8892	−	28.2546i	−2.13432	−	1.55067i
$333$	−11.1404	+	34.2865i	−0.610488	+	1.87889i
$334$	−4.59815	−	14.1517i	−0.251600	−	0.774344i
$335$	−6.30344	+	4.57972i	−0.344394	+	0.250217i
$336$	16.4948	−	11.9842i	0.899867	−	0.653792i
$337$	−4.05694	−	12.4860i	−0.220996	−	0.680154i	−0.998673	−	0.0514914i	$-0.983603\pi$
$337$	−4.05694	−	12.4860i	−0.220996	−	0.680154i	0.777678	−	0.628663i	$-0.216397\pi$
$338$	0.729871	−	2.24631i	0.0396997	−	0.122183i
$339$	0.504359	+	0.366438i	0.0273930	+	0.0199022i
$340$	−4.15490			−0.225331
$341$	−9.55669	+	8.67313i	−0.517524	+	0.469676i
$342$	33.2121			1.79590
$343$	22.4056	+	16.2786i	1.20979	+	0.878964i
$344$	1.79210	−	5.51552i	0.0966237	−	0.297377i
$345$	2.58695	+	7.96180i	0.139277	+	0.428649i
$346$	32.1468	−	23.3560i	1.72822	−	1.25563i
$347$	21.7218	−	15.7818i	1.16609	−	0.847213i	0.175553	−	0.984470i	$-0.443829\pi$
$347$	21.7218	−	15.7818i	1.16609	−	0.847213i	0.990535	+	0.137257i	$0.0438286\pi$
$348$	−27.6214	−	85.0099i	−1.48066	−	4.55701i
$349$	−4.07912	+	12.5542i	−0.218350	+	0.672013i	0.780548	+	0.625095i	$0.214940\pi$
$349$	−4.07912	+	12.5542i	−0.218350	+	0.672013i	−0.998899	+	0.0469180i	$0.985060\pi$
$350$	0.177573	+	0.129014i	0.00949167	+	0.00689610i
$351$	4.34323			0.231824
$352$	2.41056	−	11.5641i	0.128483	−	0.616366i
$353$	29.6666			1.57900			0.789498	−	0.613753i	$-0.210341\pi$
$353$	29.6666			1.57900			0.789498	+	0.613753i	$0.210341\pi$
$354$	−25.0945	−	18.2322i	−1.33376	−	0.969030i
$355$	−7.12140	+	21.9174i	−0.377964	+	1.16326i
$356$	5.09207	+	15.6718i	0.269879	+	0.830603i
$357$	−5.18218	+	3.76507i	−0.274270	+	0.199269i
$358$	9.77918	−	7.10499i	0.516846	−	0.375511i
$359$	3.97687	+	12.2395i	0.209891	+	0.645978i	0.999477	+	0.0323380i	$0.0102953\pi$
$359$	3.97687	+	12.2395i	0.209891	+	0.645978i	−0.789586	+	0.613640i	$0.789705\pi$
$360$	11.8184	−	36.3734i	0.622886	−	1.91705i
$361$	7.73797	+	5.62196i	0.407262	+	0.295893i
$362$	60.4241			3.17582
$363$	−20.0841	+	22.6613i	−1.05414	+	1.18941i
$364$	−16.0708			−0.842338
$365$	−24.7724	−	17.9982i	−1.29664	−	0.942067i
$366$	−0.950990	+	2.92685i	−0.0497090	+	0.152989i
$367$	−1.17120	−	3.60459i	−0.0611363	−	0.188158i	0.915824	−	0.401580i	$-0.131539\pi$
$367$	−1.17120	−	3.60459i	−0.0611363	−	0.188158i	−0.976960	+	0.213422i	$0.931539\pi$
$368$	−1.81096	+	1.31574i	−0.0944028	+	0.0685877i
$369$	−15.5710	+	11.3130i	−0.810593	+	0.588930i
$370$	−12.8793	−	39.6383i	−0.669561	−	2.06070i
$371$	−3.59726	+	11.0712i	−0.186760	+	0.574789i
$372$	31.0116	+	22.5313i	1.60788	+	1.16819i
$373$	17.1966			0.890406			0.445203	−	0.895430i	$-0.353132\pi$
$373$	17.1966			0.890406			0.445203	+	0.895430i	$0.353132\pi$
$374$	0.828312	−	3.97362i	0.0428310	−	0.205471i
$375$	−30.7129			−1.58601
$376$	−26.1456	−	18.9959i	−1.34836	−	0.979638i
$377$	−2.80388	+	8.62945i	−0.144407	+	0.444439i
$378$	−14.2357	−	43.8131i	−0.732207	−	2.25350i
$379$	−13.4008	+	9.73622i	−0.688351	+	0.500116i	−0.876118	−	0.482098i	$-0.839875\pi$
$379$	−13.4008	+	9.73622i	−0.688351	+	0.500116i	0.187767	+	0.982214i	$0.439875\pi$
$380$	−19.9266	+	14.4776i	−1.02222	+	0.742683i
$381$	3.78726	+	11.6560i	0.194027	+	0.597155i
$382$	2.58692	−	7.96171i	0.132358	−	0.407357i
$383$	−1.80806	−	1.31363i	−0.0923877	−	0.0671236i	0.540632	−	0.841259i	$-0.318185\pi$
$383$	−1.80806	−	1.31363i	−0.0923877	−	0.0671236i	−0.633020	+	0.774135i	$0.718185\pi$
$384$	−56.5331			−2.88494
$385$	−24.7133	+	22.4284i	−1.25950	+	1.14306i
$386$	−42.6978			−2.17326
$387$	−5.76036	−	4.18515i	−0.292815	−	0.212743i
$388$	−8.54053	+	26.2850i	−0.433580	+	1.33442i
$389$	5.47627	+	16.8542i	0.277658	+	0.854543i	0.988504	+	0.151195i	$0.0483122\pi$
$389$	5.47627	+	16.8542i	0.277658	+	0.854543i	−0.710846	+	0.703347i	$0.751688\pi$
$390$	−11.7862	+	8.56317i	−0.596817	+	0.433613i
$391$	0.568949	−	0.413365i	0.0287730	−	0.0209048i
$392$	15.1710	+	46.6914i	0.766249	+	2.35827i
$393$	2.65474	−	8.17044i	0.133914	−	0.412144i
$394$	38.2338	+	27.7785i	1.92619	+	1.39946i
$395$	−19.3638			−0.974297
$396$	47.1604	+	26.9815i	2.36990	+	1.35587i
$397$	−12.4080			−0.622742			−0.311371	−	0.950288i	$-0.600788\pi$
$397$	−12.4080			−0.622742			−0.311371	+	0.950288i	$0.600788\pi$
$398$	−34.3925	−	24.9876i	−1.72394	−	1.25252i
$399$	−11.7342	+	36.1141i	−0.587444	+	1.80797i
$400$	0.0105467	+	0.0324593i	0.000527333	+	0.00162296i
$401$	12.4106	−	9.01681i	0.619754	−	0.450278i	−0.233081	−	0.972457i	$-0.574881\pi$
$401$	12.4106	−	9.01681i	0.619754	−	0.450278i	0.852836	+	0.522179i	$0.174881\pi$
$402$	−18.2907	+	13.2890i	−0.912257	+	0.662793i
$403$	−1.20244	−	3.70073i	−0.0598977	−	0.184346i
$404$	−10.0498	+	30.9301i	−0.499996	+	1.53883i
$405$	3.22193	+	2.34087i	0.160099	+	0.116319i
$406$	96.2413			4.77638
$407$	25.9652	−	2.83225i	1.28705	−	0.140389i
$408$	−5.31833			−0.263297
$409$	−31.3674	−	22.7897i	−1.55102	−	1.12688i	−0.942921	−	0.333017i	$-0.891933\pi$
$409$	−31.3674	−	22.7897i	−1.55102	−	1.12688i	−0.608097	−	0.793863i	$-0.708067\pi$
$410$	6.87595	−	21.1620i	0.339579	−	1.04512i
$411$	−5.84484	−	17.9886i	−0.288305	−	0.887311i
$412$	14.3668	−	10.4381i	0.707804	−	0.514250i
$413$	17.3327	−	12.5929i	0.852884	−	0.619657i
$414$	4.53474	+	13.9565i	0.222870	+	0.685924i
$415$	9.30078	−	28.6249i	0.456557	−	1.40514i
$416$	2.88143	+	2.09348i	0.141274	+	0.102641i
$417$	−3.21053			−0.157220
$418$	−9.87336	−	21.9435i	−0.482922	−	1.07329i
$419$	22.3649			1.09260			0.546298	−	0.837591i	$-0.316037\pi$
$419$	22.3649			1.09260			0.546298	+	0.837591i	$0.316037\pi$
$420$	80.1950	+	58.2651i	3.91312	+	2.84304i
$421$	−6.36174	+	19.5794i	−0.310052	+	0.954243i	0.667691	+	0.744438i	$0.267283\pi$
$421$	−6.36174	+	19.5794i	−0.310052	+	0.954243i	−0.977743	+	0.209804i	$0.932717\pi$
$422$	6.83929	+	21.0492i	0.332932	+	1.02466i
$423$	−32.1004	+	23.3223i	−1.56077	+	1.13397i
$424$	−7.81929	+	5.68105i	−0.379738	+	0.275896i
$425$	−0.00331344	−	0.0101977i	−0.000160725	−	0.000494662i
$426$	−20.6641	+	63.5977i	−1.00118	+	3.08132i
$427$	−1.71964	−	1.24939i	−0.0832194	−	0.0604624i
$428$	10.3259			0.499120
$429$	−3.74622	−	8.32594i	−0.180869	−	0.401980i
$430$	8.23159			0.396963
$431$	−14.6579	−	10.6496i	−0.706044	−	0.512971i	0.175851	−	0.984417i	$-0.443732\pi$
$431$	−14.6579	−	10.6496i	−0.706044	−	0.512971i	−0.881895	+	0.471446i	$0.843732\pi$
$432$	2.21357	−	6.81268i	0.106501	−	0.327775i
$433$	−4.10978	−	12.6486i	−0.197503	−	0.607853i	−0.999938	−	0.0111133i	$-0.996462\pi$
$433$	−4.10978	−	12.6486i	−0.197503	−	0.607853i	0.802435	−	0.596740i	$-0.203538\pi$
$434$	−33.3905	+	24.2596i	−1.60280	+	1.16450i
$435$	45.2780	−	32.8964i	2.17091	−	1.57726i
$436$	16.3617	+	50.3563i	0.783585	+	2.41163i
$437$	1.28829	−	3.96495i	0.0616273	−	0.189669i
$438$	−71.8819	−	52.2252i	−3.43465	−	2.49542i
$439$	−0.565731			−0.0270009			−0.0135004	−	0.999909i	$-0.504297\pi$
$439$	−0.565731			−0.0270009			−0.0135004	+	0.999909i	$0.504297\pi$
$440$	−27.5456	+	3.00464i	−1.31318	+	0.143240i
$441$	60.2757			2.87027
$442$	0.990111	+	0.719358i	0.0470948	+	0.0342164i
$443$	4.11607	−	12.6680i	0.195560	−	0.601873i	−0.804409	−	0.594076i	$-0.797518\pi$
$443$	4.11607	−	12.6680i	0.195560	−	0.601873i	0.999970	−	0.00779755i	$-0.00248206\pi$
$444$	−23.9735	−	73.7830i	−1.13773	−	3.50158i
$445$	−8.34711	+	6.06453i	−0.395691	+	0.287486i
$446$	−37.5288	+	27.2663i	−1.77704	+	1.29110i
$447$	8.05988	+	24.8058i	0.381219	+	1.17327i
$448$	16.2515	−	50.0169i	0.767810	−	2.36308i
$449$	−11.5371	−	8.38217i	−0.544468	−	0.395579i	0.281274	−	0.959628i	$-0.409243\pi$
$449$	−11.5371	−	8.38217i	−0.544468	−	0.395579i	−0.825742	+	0.564049i	$0.809243\pi$
$450$	0.223744			0.0105474
$451$	12.1036	+	6.92472i	0.569934	+	0.326072i
$452$	−0.810452			−0.0381204
$453$	−9.63858	−	7.00284i	−0.452860	−	0.329022i
$454$	11.2429	−	34.6020i	0.527654	−	1.62395i
$455$	−3.10946	−	9.56995i	−0.145774	−	0.448646i
$456$	−25.5064	+	18.5315i	−1.19445	+	0.867816i
$457$	−12.2285	+	8.88454i	−0.572026	+	0.415601i	−0.835841	−	0.548972i	$-0.815019\pi$
$457$	−12.2285	+	8.88454i	−0.572026	+	0.415601i	0.263815	+	0.964573i	$0.415019\pi$
$458$	19.8728	+	61.1623i	0.928597	+	2.85793i
$459$	−0.695437	+	2.14034i	−0.0324602	+	0.0999023i
$460$	−8.80457	−	6.39689i	−0.410515	−	0.298257i
$461$	−32.5875			−1.51775			−0.758875	−	0.651236i	$-0.774251\pi$
$461$	−32.5875			−1.51775			−0.758875	+	0.651236i	$0.774251\pi$
$462$	−71.7105	+	65.0804i	−3.33627	+	3.02782i
$463$	25.4090			1.18086			0.590428	−	0.807090i	$-0.298959\pi$
$463$	25.4090			1.18086			0.590428	+	0.807090i	$0.298959\pi$
$464$	12.1069	+	8.79618i	0.562049	+	0.408353i
$465$	−7.41678	+	22.8265i	−0.343945	+	1.05855i
$466$	−2.39369	−	7.36702i	−0.110886	−	0.341271i
$467$	−3.41505	+	2.48118i	−0.158030	+	0.114815i	−0.663990	−	0.747741i	$-0.731138\pi$
$467$	−3.41505	+	2.48118i	−0.158030	+	0.114815i	0.505960	+	0.862557i	$0.331138\pi$
$468$	−13.2534	+	9.62915i	−0.612638	+	0.445108i
$469$	−4.82550	−	14.8514i	−0.222821	−	0.685772i
$470$	14.1751	−	43.6265i	0.653849	−	2.01234i
$471$	4.30608	+	3.12855i	0.198414	+	0.144156i
$472$	17.7880			0.818761
$473$	−1.05270	+	5.05008i	−0.0484034	+	0.232203i
$474$	−56.1878			−2.58079
$475$	−0.0514246	−	0.0373621i	−0.00235952	−	0.00171429i
$476$	2.57325	−	7.91966i	0.117945	−	0.362997i
$477$	3.66694	+	11.2857i	0.167898	+	0.516736i
$478$	−31.3119	+	22.7495i	−1.43218	+	1.04054i
$479$	−12.6825	+	9.21434i	−0.579476	+	0.421014i	−0.838535	−	0.544847i	$-0.816588\pi$
$479$	−12.6825	+	9.21434i	−0.579476	+	0.421014i	0.259059	+	0.965861i	$0.416588\pi$
$480$	−6.78868	−	20.8934i	−0.309859	−	0.953649i
$481$	−2.43358	+	7.48979i	−0.110962	+	0.341505i
$482$	28.2153	+	20.4996i	1.28517	+	0.933731i
$483$	−16.7782			−0.763433
$484$	3.80695	−	39.1803i	0.173043	−	1.78092i
$485$	−17.3049			−0.785774
$486$	34.2465	+	24.8816i	1.55345	+	1.12865i
$487$	−13.3630	+	41.1270i	−0.605534	+	1.86364i	−0.112457	+	0.993657i	$0.535872\pi$
$487$	−13.3630	+	41.1270i	−0.605534	+	1.86364i	−0.493077	+	0.869986i	$0.664128\pi$
$488$	−0.545361	−	1.67845i	−0.0246873	−	0.0759797i
$489$	14.7157	−	10.6916i	0.665468	−	0.483491i
$490$	−56.3757	+	40.9593i	−2.54679	+	1.85035i
$491$	−7.65950	−	23.5735i	−0.345668	−	1.06386i	−0.961225	−	0.275765i	$-0.911069\pi$
$491$	−7.65950	−	23.5735i	−0.345668	−	1.06386i	0.615557	−	0.788093i	$-0.288931\pi$
$492$	12.7989	−	39.3911i	0.577021	−	1.77589i
$493$	−3.80362	−	2.76349i	−0.171306	−	0.124461i
$494$	7.25508			0.326422
$495$	−6.94230	+	33.3039i	−0.312033	+	1.49690i
$496$	−6.41770			−0.288163
$497$	−37.3663	−	27.1482i	−1.67611	−	1.21776i
$498$	26.9880	−	83.0607i	1.20936	−	3.72204i
$499$	−10.6899	−	32.9003i	−0.478548	−	1.47282i	−0.841112	−	0.540860i	$-0.818099\pi$
$499$	−10.6899	−	32.9003i	−0.478548	−	1.47282i	0.362565	−	0.931959i	$-0.381901\pi$
$500$	32.3016	−	23.4685i	1.44457	−	1.04954i
$501$	14.0303	−	10.1936i	0.626826	−	0.455416i
$502$	−4.42841	−	13.6292i	−0.197650	−	0.608303i
$503$	3.92851	−	12.0907i	0.175164	−	0.539098i	−0.824477	−	0.565895i	$-0.808531\pi$
$503$	3.92851	−	12.0907i	0.175164	−	0.539098i	0.999641	+	0.0267971i	$0.00853079\pi$
$504$	62.0118	+	45.0542i	2.76222	+	2.00687i
$505$	−20.3629			−0.906139
$506$	7.87305	−	7.14515i	0.350000	−	0.317641i
$507$	2.75277			0.122255
$508$	−12.8898	−	9.36499i	−0.571892	−	0.415504i
$509$	−4.68298	+	14.4127i	−0.207569	+	0.638833i	0.792029	+	0.610484i	$0.209025\pi$
$509$	−4.68298	+	14.4127i	−0.207569	+	0.638833i	−0.999598	+	0.0283490i	$0.990975\pi$
$510$	−2.33271	−	7.17935i	−0.103294	−	0.317907i
$511$	49.6486	−	36.0718i	2.19632	−	1.59572i
$512$	14.7024	−	10.6820i	0.649763	−	0.472080i
$513$	4.12263	+	12.6881i	0.182018	+	0.560195i
$514$	−12.2544	+	37.7150i	−0.540517	+	1.66354i
$515$	8.99554	+	6.53564i	0.396391	+	0.287995i
$516$	15.3223			0.674528
$517$	24.9521	+	14.2756i	1.09739	+	0.627842i
$518$	83.5311			3.67014
$519$	37.4667	+	27.2211i	1.64460	+	1.19487i
$520$	2.58170	−	7.94566i	0.113215	−	0.348440i
$521$	6.24008	+	19.2050i	0.273383	+	0.841386i	0.989643	+	0.143552i	$0.0458525\pi$
$521$	6.24008	+	19.2050i	0.273383	+	0.841386i	−0.716260	+	0.697834i	$0.754147\pi$
$522$	79.3691	−	57.6650i	3.47389	−	2.52393i
$523$	8.83298	−	6.41753i	0.386239	−	0.280619i	−0.377674	−	0.925939i	$-0.623276\pi$
$523$	8.83298	−	6.41753i	0.386239	−	0.280619i	0.763913	+	0.645320i	$0.223276\pi$
$524$	3.45117	+	10.6216i	0.150765	+	0.464007i
$525$	−0.0790512	+	0.243294i	−0.00345008	+	0.0106182i
$526$	22.9966	+	16.7080i	1.00270	+	0.728502i
$527$	2.01624			0.0878290
$528$	−14.9692	+	1.63282i	−0.651449	+	0.0710593i
$529$	−21.1579			−0.919910
$530$	−11.0987	−	8.06365i	−0.482095	−	0.350263i
$531$	6.74873	−	20.7705i	0.292870	−	0.901361i
$532$	−15.2545	−	46.9486i	−0.661367	−	2.03548i
$533$	−3.40144	+	2.47129i	−0.147333	+	0.107043i
$534$	−24.2208	+	17.5974i	−1.04814	+	0.761515i
$535$	1.99791	+	6.14893i	0.0863771	+	0.265841i
$536$	4.00648	−	12.3307i	0.173053	−	0.532604i
$537$	11.3975	+	8.28077i	0.491839	+	0.357342i
$538$	−61.9028			−2.66882
$539$	−17.9189	−	39.8246i	−0.771821	−	1.71537i
$540$	34.8266			1.49870
$541$	13.7318	+	9.97671i	0.590375	+	0.428932i	0.842449	−	0.538776i	$-0.181113\pi$
$541$	13.7318	+	9.97671i	0.590375	+	0.428932i	−0.252075	+	0.967708i	$0.581113\pi$
$542$	7.21719	−	22.2122i	0.310005	−	0.954096i
$543$	21.7620	+	66.9766i	0.933898	+	2.87424i
$544$	−1.49304	+	1.08476i	−0.0640135	+	0.0465085i
$545$	−26.8207	+	19.4864i	−1.14887	+	0.834706i
$546$	−9.02272	−	27.7691i	−0.386137	−	1.18841i
$547$	−0.530537	+	1.63283i	−0.0226841	+	0.0698146i	−0.961758	−	0.273901i	$-0.911686\pi$
$547$	−0.530537	+	1.63283i	−0.0226841	+	0.0698146i	0.939074	+	0.343716i	$0.111686\pi$
$548$	19.8927	+	14.4529i	0.849774	+	0.617397i
$549$	−2.16677			−0.0924755
$550$	−0.0665151	−	0.147829i	−0.00283621	−	0.00630346i
$551$	−27.8712			−1.18735
$552$	−11.2700	−	8.18811i	−0.479682	−	0.348509i
$553$	11.9926	−	36.9093i	0.509975	−	1.56954i
$554$	13.0329	+	40.1112i	0.553715	+	1.70416i
$555$	39.2983	−	28.5519i	1.66812	−	1.21196i
$556$	3.37660	−	2.45324i	0.143200	−	0.104041i
$557$	−12.1449	−	37.3780i	−0.514594	−	1.58376i	−0.784019	−	0.620737i	$-0.786834\pi$
$557$	−12.1449	−	37.3780i	−0.514594	−	1.58376i	0.269425	−	0.963021i	$-0.413166\pi$
$558$	−13.0011	+	40.0133i	−0.550380	+	1.69390i
$559$	−1.25833	−	0.914233i	−0.0532219	−	0.0386680i
$560$	−16.5959			−0.701306
$561$	4.70285	−	0.512981i	0.198555	−	0.0216581i
$562$	−44.9789			−1.89732
$563$	10.5585	+	7.67120i	0.444988	+	0.323303i	0.787614	−	0.616169i	$-0.211316\pi$
$563$	10.5585	+	7.67120i	0.444988	+	0.323303i	−0.342626	+	0.939472i	$0.611316\pi$
$564$	26.3856	−	81.2067i	1.11104	−	3.41942i
$565$	−0.156811	−	0.482613i	−0.00659707	−	0.0203037i
$566$	−3.89062	+	2.82670i	−0.163535	+	0.118815i
$567$	−6.45736	+	4.69155i	−0.271184	+	0.197027i
$568$	−11.8502	−	36.4711i	−0.497223	−	1.53029i
$569$	11.6376	−	35.8167i	0.487871	−	1.50151i	−0.339907	−	0.940459i	$-0.610396\pi$
$569$	11.6376	−	35.8167i	0.487871	−	1.50151i	0.827779	−	0.561055i	$-0.189604\pi$
$570$	−36.2037	−	26.3035i	−1.51640	−	1.10173i
$571$	17.9056			0.749327			0.374663	−	0.927161i	$-0.377758\pi$
$571$	17.9056			0.749327			0.374663	+	0.927161i	$0.377758\pi$
$572$	10.3021	+	5.89404i	0.430750	+	0.246442i
$573$	9.75679			0.407596
$574$	36.0784	+	26.2125i	1.50588	+	1.09409i
$575$	0.00867899	−	0.0267112i	0.000361939	−	0.00111393i
$576$	−16.5663	−	50.9858i	−0.690262	−	2.12441i
$577$	−1.52879	+	1.11073i	−0.0636445	+	0.0462405i	−0.619153	−	0.785271i	$-0.712524\pi$
$577$	−1.52879	+	1.11073i	−0.0636445	+	0.0462405i	0.555508	+	0.831511i	$0.312524\pi$
$578$	31.9710	−	23.2283i	1.32982	−	0.966170i
$579$	−15.3778	−	47.3281i	−0.639081	−	1.96689i
$580$	−22.4831	+	69.1960i	−0.933562	+	2.87321i
$581$	48.8016	+	35.4564i	2.02463	+	1.47098i
$582$	−50.2135			−2.08142
$583$	6.36641	−	5.77780i	0.263670	−	0.239292i
$584$	50.9530			2.10845
$585$	−8.29837	−	6.02912i	−0.343096	−	0.249273i
$586$	18.2526	−	56.1757i	0.754007	−	2.32060i
$587$	6.14593	+	18.9152i	0.253670	+	0.780715i	0.994089	+	0.108570i	$0.0346271\pi$
$587$	6.14593	+	18.9152i	0.253670	+	0.780715i	−0.740419	+	0.672145i	$0.765373\pi$
$588$	−104.938	+	76.2419i	−4.32757	+	3.14416i
$589$	9.66979	−	7.02551i	0.398437	−	0.289481i
$590$	7.80214	+	24.0125i	0.321209	+	0.988580i
$591$	−17.0208	+	52.3846i	−0.700141	+	2.15481i
$592$	10.5080	+	7.63450i	0.431876	+	0.313776i
$593$	−20.9160			−0.858918			−0.429459	−	0.903086i	$-0.641296\pi$
$593$	−20.9160			−0.858918			−0.429459	+	0.903086i	$0.641296\pi$
$594$	−6.94295	+	33.3071i	−0.284873	+	1.36661i
$595$	5.21394			0.213751
$596$	−27.4315	−	19.9301i	−1.12364	−	0.816370i
$597$	15.3107	−	47.1216i	0.626626	−	1.92856i
$598$	0.990600	+	3.04875i	0.0405087	+	0.124673i
$599$	24.2791	−	17.6398i	0.992017	−	0.720742i	0.0316549	−	0.999499i	$-0.489922\pi$
$599$	24.2791	−	17.6398i	0.992017	−	0.720742i	0.960362	+	0.278757i	$0.0899222\pi$
$600$	−0.171832	+	0.124843i	−0.00701502	+	0.00509671i
$601$	6.97041	+	21.4527i	0.284329	+	0.875075i	0.986599	+	0.163164i	$0.0521700\pi$
$601$	6.97041	+	21.4527i	0.284329	+	0.875075i	−0.702270	+	0.711911i	$0.747830\pi$
$602$	−5.09807	+	15.6902i	−0.207782	+	0.639486i
$603$	−12.8780	−	9.35644i	−0.524434	−	0.381024i
$604$	15.4882			0.630205
$605$	24.0680	−	5.31384i	0.978502	−	0.216038i
$606$	−59.0871			−2.40025
$607$	32.2459	+	23.4281i	1.30882	+	0.950915i	1.00000		0.000204425i	$-6.50706e-5\pi$
$607$	32.2459	+	23.4281i	1.30882	+	0.950915i	0.308823	+	0.951120i	$0.400065\pi$
$608$	−3.38074	+	10.4048i	−0.137107	+	0.421972i
$609$	34.6618	+	106.678i	1.40457	+	4.32281i
$610$	2.02657	−	1.47239i	0.0820536	−	0.0596154i
$611$	−7.01224	+	5.09469i	−0.283685	+	0.206109i
$612$	−2.62310	−	8.07307i	−0.106032	−	0.326334i
$613$	−10.7132	+	32.9718i	−0.432702	+	1.33172i	0.462722	+	0.886504i	$0.346873\pi$
$613$	−10.7132	+	32.9718i	−0.432702	+	1.33172i	−0.895424	+	0.445215i	$0.853127\pi$
$614$	−36.4094	−	26.4530i	−1.46936	−	1.06755i
$615$	25.9333			1.04573
$616$	11.3326	−	54.3655i	0.456605	−	2.19045i
$617$	39.5459			1.59206			0.796029	−	0.605259i	$-0.206930\pi$
$617$	39.5459			1.59206			0.796029	+	0.605259i	$0.206930\pi$
$618$	26.1023	+	18.9645i	1.04999	+	0.762863i
$619$	−9.52568	+	29.3170i	−0.382870	+	1.17835i	0.555144	+	0.831754i	$0.312663\pi$
$619$	−9.52568	+	29.3170i	−0.382870	+	1.17835i	−0.938014	+	0.346597i	$0.887337\pi$
$620$	−9.64186	−	29.6746i	−0.387226	−	1.19176i
$621$	−4.76895	+	3.46485i	−0.191372	+	0.139040i
$622$	−2.33500	+	1.69647i	−0.0936248	+	0.0680224i
$623$	−6.38999	−	19.6664i	−0.256010	−	0.787916i
$624$	1.40298	−	4.31793i	0.0561642	−	0.172856i
$625$	20.3088	+	14.7552i	0.812351	+	0.590208i
$626$	−0.0377212			−0.00150764
$627$	20.7671	−	18.8471i	0.829359	−	0.752681i
$628$	−6.91943			−0.276115
$629$	−3.30129	−	2.39853i	−0.131631	−	0.0956355i
$630$	−33.6204	+	103.473i	−1.33947	+	4.12246i
$631$	9.53779	+	29.3543i	0.379693	+	1.16858i	0.940257	+	0.340465i	$0.110584\pi$
$631$	9.53779	+	29.3543i	0.379693	+	1.16858i	−0.560564	+	0.828111i	$0.689416\pi$
$632$	26.0680	−	18.9395i	1.03693	−	0.753373i
$633$	−20.8686	+	15.1619i	−0.829453	+	0.602633i
$634$	9.76227	+	30.0452i	0.387709	+	1.19325i
$635$	3.08274	−	9.48770i	0.122335	−	0.376508i
$636$	−20.6591	−	15.0097i	−0.819187	−	0.595175i
$637$	13.1671			0.521698
$638$	−61.6947	−	35.2970i	−2.44252	−	1.39742i
$639$	−47.0819			−1.86253
$640$	37.2281	+	27.0478i	1.47157	+	1.06916i
$641$	−5.19983	+	16.0034i	−0.205381	+	0.632097i	0.794317	+	0.607504i	$0.207829\pi$
$641$	−5.19983	+	16.0034i	−0.205381	+	0.632097i	−0.999698	+	0.0245934i	$0.992171\pi$
$642$	5.79733	+	17.8423i	0.228802	+	0.704181i
$643$	−7.85551	+	5.70736i	−0.309791	+	0.225076i	−0.731807	−	0.681512i	$-0.761323\pi$
$643$	−7.85551	+	5.70736i	−0.309791	+	0.225076i	0.422016	+	0.906588i	$0.361323\pi$
$644$	17.6460	−	12.8206i	0.695352	−	0.505203i
$645$	2.96465	+	9.12425i	0.116733	+	0.359267i
$646$	−1.16168	+	3.57529i	−0.0457058	+	0.140668i
$647$	−15.8482	−	11.5144i	−0.623059	−	0.452679i	0.230930	−	0.972970i	$-0.425823\pi$
$647$	−15.8482	−	11.5144i	−0.623059	−	0.452679i	−0.853989	+	0.520292i	$0.825823\pi$
$648$	−6.62702			−0.260334
$649$	−15.7295	+	1.71575i	−0.617436	+	0.0673492i
$650$	0.0488762			0.00191708
$651$	−38.9162	−	28.2742i	−1.52524	−	1.10816i
$652$	−7.30721	+	22.4893i	−0.286173	+	0.880749i
$653$	6.98405	+	21.4947i	0.273307	+	0.841153i	0.989662	+	0.143417i	$0.0458090\pi$
$653$	6.98405	+	21.4947i	0.273307	+	0.841153i	−0.716355	+	0.697736i	$0.754191\pi$
$654$	−77.8257	+	56.5437i	−3.04323	+	2.21103i
$655$	−5.65728	+	4.11026i	−0.221048	+	0.160601i
$656$	2.14282	+	6.59493i	0.0836631	+	0.257489i
$657$	19.3314	−	59.4960i	0.754190	−	2.32116i
$658$	74.3775	+	54.0384i	2.89953	+	2.10664i
$659$	18.2018			0.709043			0.354522	−	0.935048i	$-0.384644\pi$
$659$	18.2018			0.709043			0.354522	+	0.935048i	$0.384644\pi$
$660$	−30.0394	−	66.7623i	−1.16928	−	2.59872i
$661$	1.10670			0.0430456			0.0215228	−	0.999768i	$-0.493149\pi$
$661$	1.10670			0.0430456			0.0215228	+	0.999768i	$0.493149\pi$
$662$	−21.5163	−	15.6325i	−0.836256	−	0.607576i
$663$	−0.440774	+	1.35656i	−0.0171182	+	0.0526845i
$664$	15.4767	+	47.6325i	0.600614	+	1.84850i
$665$	25.0057	−	18.1677i	0.969681	−	0.704514i
$666$	68.8871	−	50.0494i	2.66932	−	1.93938i
$667$	−3.80550	−	11.7121i	−0.147350	−	0.453495i
$668$	−6.96684	+	21.4417i	−0.269555	+	0.829606i
$669$	−43.7393	−	31.7785i	−1.69106	−	1.22863i
$670$	18.4028			0.710962
$671$	0.644142	+	1.43160i	0.0248668	+	0.0552664i
$672$	44.0293			1.69847
$673$	11.1729	+	8.11759i	0.430684	+	0.312910i	0.781922	−	0.623376i	$-0.214239\pi$
$673$	11.1729	+	8.11759i	0.430684	+	0.312910i	−0.351238	+	0.936286i	$0.614239\pi$
$674$	−9.58213	+	29.4908i	−0.369090	+	1.13594i
$675$	0.0277734	+	0.0854778i	0.00106900	+	0.00329004i
$676$	−2.89517	+	2.10346i	−0.111353	+	0.0809024i
$677$	−9.25375	+	6.72324i	−0.355650	+	0.258395i	−0.751236	−	0.660034i	$-0.770542\pi$
$677$	−9.25375	+	6.72324i	−0.355650	+	0.258395i	0.395585	+	0.918429i	$0.370542\pi$
$678$	−0.455017	−	1.40040i	−0.0174748	−	0.0537820i
$679$	10.7174	−	32.9848i	0.411297	−	1.26584i
$680$	3.50223	+	2.54452i	0.134304	+	0.0975777i
$681$	42.4035			1.62491
$682$	30.3020	−	3.30531i	1.16033	−	0.126567i
$683$	23.6893			0.906445			0.453222	−	0.891397i	$-0.350274\pi$
$683$	23.6893			0.906445			0.453222	+	0.891397i	$0.350274\pi$
$684$	−40.7104	−	29.5779i	−1.55660	−	1.13094i
$685$	−4.75756	+	14.6423i	−0.181777	+	0.559452i
$686$	−20.2137	−	62.2113i	−0.771761	−	2.37524i
$687$	−60.6376	+	44.0558i	−2.31347	+	1.68083i
$688$	−2.07537	+	1.50784i	−0.0791226	+	0.0574859i
$689$	0.801032	+	2.46532i	0.0305169	+	0.0939214i
$690$	6.11014	−	18.8051i	0.232609	−	0.715897i
$691$	−32.1030	−	23.3242i	−1.22126	−	0.887294i	−0.225052	−	0.974347i	$-0.572255\pi$
$691$	−32.1030	−	23.3242i	−1.22126	−	0.887294i	−0.996204	+	0.0870530i	$0.972255\pi$
$692$	−60.2050			−2.28865
$693$	−59.1810	−	33.8588i	−2.24810	−	1.28619i
$694$	−63.4165			−2.40726
$695$	2.11420	+	1.53605i	0.0801961	+	0.0582659i
$696$	−28.7787	+	88.5718i	−1.09086	+	3.35731i
$697$	−0.673209	−	2.07193i	−0.0254996	−	0.0784798i
$698$	25.2235	−	18.3260i	0.954724	−	0.693647i
$699$	7.30382	−	5.30654i	0.276256	−	0.200712i
$700$	−0.102767	−	0.316284i	−0.00388423	−	0.0119544i
$701$	−6.90700	+	21.2576i	−0.260874	+	0.802887i	0.731742	+	0.681582i	$0.238708\pi$
$701$	−6.90700	+	21.2576i	−0.260874	+	0.802887i	−0.992615	+	0.121305i	$0.961292\pi$
$702$	−8.29916	−	6.02969i	−0.313231	−	0.227576i
$703$	−24.1903			−0.912356
$704$	−28.7618	+	26.1026i	−1.08400	+	0.983780i
$705$	53.4627			2.01352
$706$	−56.6878	−	41.1861i	−2.13347	−	1.55006i
$707$	12.6114	−	38.8138i	0.474299	−	1.45974i
$708$	14.5230	+	44.6971i	0.545806	+	1.67982i
$709$	38.7891	−	28.1820i	1.45676	−	1.05840i	0.472563	−	0.881297i	$-0.343329\pi$
$709$	38.7891	−	28.1820i	1.45676	−	1.05840i	0.984193	−	0.177099i	$-0.0566712\pi$
$710$	44.0356	−	31.9937i	1.65263	−	1.20070i
$711$	−12.2249	−	37.6242i	−0.458468	−	1.41102i
$712$	5.30543	−	16.3284i	0.198829	−	0.611934i
$713$	4.27259	+	3.10422i	0.160010	+	0.116254i
$714$	15.1293			0.566199
$715$	−1.51653	+	7.27515i	−0.0567149	+	0.272075i
$716$	−18.3146			−0.684449
$717$	−36.4936	−	26.5142i	−1.36288	−	0.990190i
$718$	9.39300	−	28.9087i	0.350544	−	1.07886i
$719$	−4.42774	−	13.6272i	−0.165127	−	0.508208i	0.833919	−	0.551887i	$-0.186092\pi$
$719$	−4.42774	−	13.6272i	−0.165127	−	0.508208i	−0.999046	+	0.0436790i	$0.986092\pi$
$720$	−13.6865	+	9.94381i	−0.510065	+	0.370584i
$721$	−18.0288	+	13.0987i	−0.671428	+	0.487821i
$722$	−6.98096	−	21.4852i	−0.259805	−	0.799596i
$723$	−12.5608	+	38.6580i	−0.467140	+	1.43771i
$724$	−74.0662	−	53.8122i	−2.75265	−	1.99992i
$725$	−0.187763			−0.00697336
$726$	69.8380	−	15.4191i	2.59193	−	0.572258i
$727$	−15.6688			−0.581123			−0.290562	−	0.956856i	$-0.593842\pi$
$727$	−15.6688			−0.581123			−0.290562	+	0.956856i	$0.593842\pi$
$728$	13.5463	+	9.84197i	0.502059	+	0.364768i
$729$	−13.5980	+	41.8504i	−0.503631	+	1.55002i
$730$	22.3489	+	68.7827i	0.827169	+	2.54576i
$731$	0.652017	−	0.473718i	0.0241157	−	0.0175211i
$732$	3.77228	−	2.74072i	0.139427	−	0.101300i
$733$	−0.743308	−	2.28767i	−0.0274547	−	0.0844969i	0.936390	−	0.350960i	$-0.114145\pi$
$733$	−0.743308	−	2.28767i	−0.0274547	−	0.0844969i	−0.963845	+	0.266463i	$0.914145\pi$
$734$	−2.76628	+	8.51373i	−0.102105	+	0.314247i
$735$	−65.7051	−	47.7375i	−2.42357	−	1.76082i
$736$	−4.83396			−0.178182
$737$	−2.35346	+	11.2901i	−0.0866907	+	0.415877i
$738$	45.4592			1.67338
$739$	25.0867	+	18.2266i	0.922830	+	0.670475i	0.944227	−	0.329296i	$-0.106811\pi$
$739$	25.0867	+	18.2266i	0.922830	+	0.670475i	−0.0213968	+	0.999771i	$0.506811\pi$
$740$	−19.5139	+	60.0575i	−0.717344	+	2.20776i
$741$	2.61295	+	8.04185i	0.0959893	+	0.295425i
$742$	22.2439	−	16.1611i	0.816598	−	0.593293i
$743$	−0.0642147	+	0.0466547i	−0.00235581	+	0.00171160i	−0.588963	−	0.808160i	$-0.700463\pi$
$743$	−0.0642147	+	0.0466547i	−0.00235581	+	0.00171160i	0.586607	+	0.809872i	$0.300463\pi$
$744$	−12.3417	−	37.9839i	−0.452469	−	1.39256i
$745$	6.56055	−	20.1913i	0.240360	−	0.739751i
$746$	−32.8597	−	23.8740i	−1.20308	−	0.874088i
$747$	61.4906			2.24982
$748$	−4.55413	+	4.13308i	−0.166516	+	0.151120i
$749$	−12.9578			−0.473469
$750$	58.6871	+	42.6387i	2.14295	+	1.55694i
$751$	5.45157	−	16.7782i	0.198931	−	0.612246i	−0.800978	−	0.598694i	$-0.795686\pi$
$751$	5.45157	−	16.7782i	0.198931	−	0.612246i	0.999908	−	0.0135511i	$-0.00431359\pi$
$752$	4.41753	+	13.5958i	0.161091	+	0.495787i
$753$	13.5123	−	9.81728i	0.492417	−	0.357762i
$754$	17.3380	−	12.5968i	0.631411	−	0.458747i
$755$	2.99674	+	9.22301i	0.109062	+	0.335660i
$756$	−21.5691	+	66.3829i	−0.784461	+	2.41432i
$757$	−26.5854	−	19.3154i	−0.966261	−	0.702030i	−0.0116649	−	0.999932i	$-0.503713\pi$
$757$	−26.5854	−	19.3154i	−0.966261	−	0.702030i	−0.954596	+	0.297902i	$0.903713\pi$
$758$	39.1233			1.42102
$759$	10.7555	+	6.15347i	0.390400	+	0.223357i
$760$	25.6627			0.930884
$761$	−9.44313	−	6.86084i	−0.342313	−	0.248705i	0.403324	−	0.915057i	$-0.367855\pi$
$761$	−9.44313	−	6.86084i	−0.342313	−	0.248705i	−0.745637	+	0.666352i	$0.767855\pi$
$762$	8.94518	−	27.5304i	0.324050	−	0.997322i
$763$	−20.5322	−	63.1915i	−0.743315	−	2.28769i
$764$	−10.2615	+	7.45540i	−0.371247	+	0.269727i
$765$	4.29987	−	3.12404i	0.155462	−	0.112950i
$766$	1.63118	+	5.02025i	0.0589369	+	0.181389i
$767$	1.47424	−	4.53725i	0.0532318	−	0.163831i
$768$	55.8636	+	40.5873i	2.01581	+	1.46457i
$769$	14.4295			0.520343			0.260171	−	0.965562i	$-0.416221\pi$
$769$	14.4295			0.520343			0.260171	+	0.965562i	$0.416221\pi$
$770$	78.3600	−	8.54742i	2.82390	−	0.308028i
$771$	−46.2184			−1.66452
$772$	52.3379	+	38.0257i	1.88368	+	1.36857i
$773$	−12.1925	+	37.5246i	−0.438533	+	1.34967i	0.450889	+	0.892580i	$0.351107\pi$
$773$	−12.1925	+	37.5246i	−0.438533	+	1.34967i	−0.889422	+	0.457086i	$0.848893\pi$
$774$	5.19682	+	15.9942i	0.186796	+	0.574899i
$775$	0.0651437	−	0.0473297i	0.00234003	−	0.00170013i
$776$	23.2962	−	16.9257i	0.836287	−	0.607598i
$777$	30.0841	+	92.5894i	1.07926	+	3.32163i
$778$	12.9345	−	39.8082i	0.463723	−	1.42719i
$779$	−10.4482	−	7.59106i	−0.374346	−	0.271978i
$780$	22.0734			0.790353
$781$	13.9966	+	31.1074i	0.500839	+	1.11311i
$782$	−1.66104			−0.0593985
$783$	31.8821	+	23.1637i	1.13937	+	0.827804i
$784$	6.71073	−	20.6535i	0.239669	−	0.737625i
$785$	−1.33881	−	4.12043i	−0.0477841	−	0.147064i
$786$	−16.4157	+	11.9267i	−0.585529	+	0.425412i
$787$	−29.9779	+	21.7802i	−1.06860	+	0.776381i	−0.975659	−	0.219291i	$-0.929625\pi$
$787$	−29.9779	+	21.7802i	−1.06860	+	0.776381i	−0.0929367	+	0.995672i	$0.529625\pi$
$788$	−22.1271	−	68.1003i	−0.788246	−	2.42597i
$789$	−10.2375	+	31.5078i	−0.364465	+	1.12171i
$790$	37.0008	+	26.8826i	1.31643	+	0.956441i
$791$	1.01703			0.0361613
$792$	−23.2283	−	51.6248i	−0.825383	−	1.83441i
$793$	−0.473325			−0.0168083
$794$	23.7096	+	17.2260i	0.841422	+	0.611329i
$795$	4.94086	−	15.2064i	0.175234	−	0.539315i
$796$	19.9040	+	61.2583i	0.705480	+	2.17124i
$797$	1.83840	−	1.33568i	0.0651195	−	0.0473121i	−0.554749	−	0.832018i	$-0.687186\pi$
$797$	1.83840	−	1.33568i	0.0651195	−	0.0473121i	0.619869	+	0.784706i	$0.287186\pi$
$798$	72.5591	−	52.7173i	2.56856	−	1.86617i
$799$	−1.38785	−	4.27138i	−0.0490988	−	0.151110i
$800$	−0.0227754	+	0.0700956i	−0.000805233	+	0.00247825i
$801$	−17.0533	−	12.3899i	−0.602548	−	0.437776i
$802$	−36.2324			−1.27941
$803$	−45.0563	+	4.91469i	−1.59000	+	0.173436i
$804$	34.2551			1.20808
$805$	11.0488	+	8.02739i	0.389417	+	0.282928i
$806$	−2.84005	+	8.74078i	−0.100037	+	0.307881i
$807$	−22.2946	−	68.6158i	−0.784808	−	2.41539i
$808$	27.4131	−	19.9168i	0.964390	−	0.700670i
$809$	15.1845	−	11.0322i	0.533859	−	0.387872i	−0.287940	−	0.957648i	$-0.592970\pi$
$809$	15.1845	−	11.0322i	0.533859	−	0.387872i	0.821799	+	0.569777i	$0.192970\pi$
$810$	−2.90673	−	8.94598i	−0.102132	−	0.314330i
$811$	−5.50041	+	16.9285i	−0.193145	+	0.594440i	0.806848	+	0.590759i	$0.201172\pi$
$811$	−5.50041	+	16.9285i	−0.193145	+	0.594440i	−0.999993	+	0.00368100i	$0.998828\pi$
$812$	−117.970	−	85.7102i	−4.13994	−	3.00784i
$813$	27.2203			0.954657
$814$	−53.5469	−	30.6354i	−1.87682	−	1.07377i
$815$	−14.8059			−0.518629
$816$	1.90322	+	1.38277i	0.0666261	+	0.0484067i
$817$	1.47638	−	4.54385i	0.0516522	−	0.158969i
$818$	28.2987	+	87.0945i	0.989441	+	3.04519i
$819$	16.6315	−	12.0835i	0.581153	−	0.422232i
$820$	−27.2747	+	19.8163i	−0.952475	+	0.692014i
$821$	7.05976	+	21.7277i	0.246387	+	0.758302i	0.995405	+	0.0957525i	$0.0305257\pi$
$821$	7.05976	+	21.7277i	0.246387	+	0.758302i	−0.749018	+	0.662550i	$0.769474\pi$
$822$	−13.8050	+	42.4874i	−0.481505	+	1.48192i
$823$	10.7139	+	7.78411i	0.373463	+	0.271337i	0.758646	−	0.651504i	$-0.225861\pi$
$823$	10.7139	+	7.78411i	0.373463	+	0.271337i	−0.385182	+	0.922840i	$0.625861\pi$
$824$	−18.5025			−0.644564
$825$	0.139905	−	0.126970i	0.00487085	−	0.00442051i
$826$	−50.6024			−1.76068
$827$	25.4213	+	18.4696i	0.883985	+	0.642252i	0.934303	−	0.356481i	$-0.116023\pi$
$827$	25.4213	+	18.4696i	0.883985	+	0.642252i	−0.0503180	+	0.998733i	$0.516023\pi$
$828$	6.87075	−	21.1460i	0.238775	−	0.734875i
$829$	−11.0463	−	33.9969i	−0.383653	−	1.18076i	−0.937453	−	0.348112i	$-0.886823\pi$
$829$	−11.0463	−	33.9969i	−0.383653	−	1.18076i	0.553800	−	0.832650i	$-0.313177\pi$
$830$	−57.5119	+	41.7849i	−1.99627	+	1.45037i
$831$	−39.7671	+	28.8925i	−1.37950	+	1.00227i
$832$	−3.61886	−	11.1377i	−0.125461	−	0.386130i
$833$	−2.10831	+	6.48870i	−0.0730485	+	0.224820i
$834$	6.13476	+	4.45717i	0.212429	+	0.154339i
$835$	−14.1163			−0.488513
$836$	−7.43983	+	35.6907i	−0.257312	+	1.23439i
$837$	−16.9003			−0.584158
$838$	−42.7354	−	31.0491i	−1.47627	−	1.07257i
$839$	−17.4097	+	53.5816i	−0.601050	+	1.84984i	−0.0791001	+	0.996867i	$0.525205\pi$
$839$	−17.4097	+	53.5816i	−0.601050	+	1.84984i	−0.521950	+	0.852976i	$0.674795\pi$
$840$	−31.9152	−	98.2250i	−1.10118	−	3.38908i
$841$	−43.1442	+	31.3461i	−1.48773	+	1.08090i
$842$	39.3382	−	28.5809i	1.35568	−	0.984963i
$843$	−16.1994	−	49.8565i	−0.557936	−	1.71715i
$844$	10.3625	−	31.8924i	0.356691	−	1.09778i
$845$	−1.81276	−	1.31704i	−0.0623607	−	0.0453077i
$846$	93.7165			3.22204
$847$	−4.77730	+	49.1670i	−0.164150	+	1.68940i
$848$	4.27530			0.146814
$849$	−4.53447	−	3.29448i	−0.155622	−	0.113066i
$850$	−0.00782605	+	0.0240861i	−0.000268431	+	0.000826147i
$851$	−3.30292	−	10.1653i	−0.113223	−	0.348464i
$852$	81.9681	−	59.5533i	2.80818	−	2.04026i
$853$	2.91957	−	2.12119i	0.0999641	−	0.0726282i	−0.536680	−	0.843786i	$-0.680322\pi$
$853$	2.91957	−	2.12119i	0.0999641	−	0.0726282i	0.636644	+	0.771157i	$0.280322\pi$
$854$	1.55141	+	4.77475i	0.0530882	+	0.163389i
$855$	9.73636	−	29.9654i	0.332976	−	1.02480i
$856$	−8.70384	−	6.32371i	−0.297491	−	0.216140i
$857$	23.2328			0.793617			0.396808	−	0.917901i	$-0.370118\pi$
$857$	23.2328			0.793617			0.396808	+	0.917901i	$0.370118\pi$
$858$	−4.40050	+	21.1103i	−0.150231	+	0.720693i
$859$	21.7751			0.742957			0.371479	−	0.928442i	$-0.378851\pi$
$859$	21.7751			0.742957			0.371479	+	0.928442i	$0.378851\pi$
$860$	−10.0901	−	7.33086i	−0.344068	−	0.249980i
$861$	−16.0612	+	49.4314i	−0.547366	+	1.68462i
$862$	13.2239	+	40.6989i	0.450407	+	1.38621i
$863$	5.66114	−	4.11306i	0.192707	−	0.140010i	−0.487248	−	0.873264i	$-0.661999\pi$
$863$	5.66114	−	4.11306i	0.192707	−	0.140010i	0.679955	+	0.733254i	$0.261999\pi$
$864$	12.5147	−	9.09247i	0.425759	−	0.309332i
$865$	−11.6488	−	35.8513i	−0.396071	−	1.21898i
$866$	−9.70693	+	29.8749i	−0.329855	+	1.01519i
$867$	37.2618	+	27.0723i	1.26548	+	0.919422i
$868$	62.5342			2.12255
$869$	−21.2244	+	19.2621i	−0.719988	+	0.653421i
$870$	−132.188			−4.48160
$871$	−2.81317	−	2.04389i	−0.0953206	−	0.0692545i
$872$	17.0473	−	52.4662i	0.577294	−	1.77673i
$873$	−10.9250	−	33.6238i	−0.369756	−	1.13799i
$874$	−7.96623	+	5.78780i	−0.269462	+	0.195775i
$875$	−40.5349	+	29.4504i	−1.37033	+	0.995604i
$876$	41.6003	+	128.033i	1.40554	+	4.32582i
$877$	16.0404	−	49.3673i	0.541647	−	1.66702i	−0.187186	−	0.982325i	$-0.559937\pi$
$877$	16.0404	−	49.3673i	0.541647	−	1.66702i	0.728832	−	0.684692i	$-0.240063\pi$
$878$	1.08101	+	0.785403i	0.0364825	+	0.0265061i
$879$	68.8413			2.32196
$880$	10.6387	+	6.08664i	0.358630	+	0.205181i
$881$	−10.4780			−0.353012			−0.176506	−	0.984300i	$-0.556479\pi$
$881$	−10.4780			−0.353012			−0.176506	+	0.984300i	$0.556479\pi$
$882$	−115.176	−	83.6805i	−3.87819	−	2.81767i
$883$	9.36250	−	28.8148i	0.315073	−	0.969696i	−0.660651	−	0.750693i	$-0.729720\pi$
$883$	9.36250	−	28.8148i	0.315073	−	0.969696i	0.975724	−	0.219002i	$-0.0702803\pi$
$884$	−0.573008	−	1.76354i	−0.0192724	−	0.0593142i
$885$	−23.8065	+	17.2965i	−0.800248	+	0.581414i
$886$	−25.4520	+	18.4920i	−0.855076	+	0.621249i
$887$	13.5088	+	41.5757i	0.453580	+	1.39598i	0.872794	+	0.488088i	$0.162306\pi$
$887$	13.5088	+	41.5757i	0.453580	+	1.39598i	−0.419214	+	0.907887i	$0.637694\pi$
$888$	−24.9780	+	76.8745i	−0.838208	+	2.57974i
$889$	16.1753	+	11.7520i	0.542501	+	0.394150i
$890$	24.3692			0.816859
$891$	5.86009	−	0.639212i	0.196320	−	0.0214144i
$892$	70.2845			2.35330
$893$	−21.5395	−	15.6494i	−0.720791	−	0.523686i
$894$	19.0367	−	58.5890i	0.636683	−	1.95951i
$895$	−3.54361	−	10.9061i	−0.118450	−	0.364551i
$896$	−74.6124	+	54.2091i	−2.49262	+	1.81100i
$897$	−3.02260	+	2.19605i	−0.100922	+	0.0733239i
$898$	10.4084	+	32.0337i	0.347332	+	1.06898i
$899$	10.9104	−	33.5787i	0.363881	−	1.11991i
$900$	−0.274259	−	0.199261i	−0.00914197	−	0.00664203i
$901$	−1.34317			−0.0447474
$902$	−13.5142	−	30.0352i	−0.449974	−	1.00006i
$903$	−19.2278			−0.639862
$904$	0.683142	+	0.496331i	0.0227210	+	0.0165077i
$905$	17.7138	−	54.5173i	0.588825	−	1.81222i
$906$	8.69563	+	26.7624i	0.288893	+	0.889121i
$907$	−27.5540	+	20.0191i	−0.914914	+	0.664724i	−0.942253	−	0.334902i	$-0.891297\pi$
$907$	−27.5540	+	20.0191i	−0.914914	+	0.664724i	0.0273387	+	0.999626i	$0.491297\pi$
$908$	−44.5969	+	32.4016i	−1.48000	+	1.07528i
$909$	−12.8557	−	39.5657i	−0.426395	−	1.31231i
$910$	−7.34428	+	22.6034i	−0.243460	+	0.749294i
$911$	33.2004	+	24.1215i	1.09998	+	0.799180i	0.981056	−	0.193724i	$-0.0620565\pi$
$911$	33.2004	+	24.1215i	1.09998	+	0.799180i	0.118921	+	0.992904i	$0.462057\pi$
$912$	13.9459			0.461797
$913$	−18.2801	−	40.6273i	−0.604982	−	1.34457i
$914$	35.7009			1.18088
$915$	2.36194	+	1.71605i	0.0780834	+	0.0567309i
$916$	30.1101	−	92.6694i	0.994866	−	3.06188i
$917$	−4.33084	−	13.3289i	−0.143017	−	0.440161i
$918$	4.30028	−	3.12434i	0.141930	−	0.103118i
$919$	45.0546	−	32.7341i	1.48621	−	1.07980i	0.510726	−	0.859743i	$-0.329377\pi$
$919$	45.0546	−	32.7341i	1.48621	−	1.07980i	0.975488	−	0.220054i	$-0.0706234\pi$
$920$	3.50396	+	10.7841i	0.115522	+	0.355540i
$921$	16.2086	−	49.8849i	0.534091	−	1.64376i
$922$	62.2690	+	45.2411i	2.05072	+	1.48994i
$923$	−10.2849			−0.338532
$924$	145.860	−	15.9102i	4.79844	−	0.523408i
$925$	−0.162966			−0.00535829
$926$	−48.5522	−	35.2752i	−1.59552	−	1.15922i
$927$	−7.01978	+	21.6047i	−0.230560	+	0.709591i
$928$	9.98641	+	30.7350i	0.327820	+	1.00893i
$929$	33.3103	−	24.2014i	1.09288	−	0.794021i	0.112994	−	0.993596i	$-0.463956\pi$
$929$	33.3103	−	24.2014i	1.09288	−	0.794021i	0.979883	+	0.199574i	$0.0639560\pi$
$930$	45.8621	−	33.3208i	1.50388	−	1.09263i
$931$	12.4983	+	38.4657i	0.409614	+	1.26066i
$932$	−3.62677	+	11.1621i	−0.118799	+	0.365625i
$933$	−2.72141	−	1.97722i	−0.0890948	−	0.0647312i
$934$	9.97019			0.326235
$935$	−3.34235	−	1.91224i	−0.109307	−	0.0625368i
$936$	17.0685			0.557901
$937$	17.4610	+	12.6862i	0.570426	+	0.414439i	0.835260	−	0.549855i	$-0.185317\pi$
$937$	17.4610	+	12.6862i	0.570426	+	0.414439i	−0.264834	+	0.964294i	$0.585317\pi$
$938$	−11.3974	+	35.0776i	−0.372138	+	1.14532i
$939$	−0.0135855	−	0.0418118i	−0.000443346	−	0.00136448i
$940$	−56.2282	+	40.8522i	−1.83396	+	1.33245i
$941$	43.6232	−	31.6941i	1.42207	−	1.03320i	0.430650	−	0.902519i	$-0.358284\pi$
$941$	43.6232	−	31.6941i	1.42207	−	1.03320i	0.991425	−	0.130678i	$-0.0417155\pi$
$942$	−3.88482	−	11.9562i	−0.126574	−	0.389555i
$943$	1.76336	−	5.42705i	0.0574228	−	0.176729i
$944$	−6.36565	−	4.62491i	−0.207184	−	0.150528i
$945$	−43.7035			−1.42167
$946$	9.02254	−	8.18836i	0.293348	−	0.266227i
$947$	−37.1797			−1.20818			−0.604090	−	0.796916i	$-0.706463\pi$
$947$	−37.1797			−1.20818			−0.604090	+	0.796916i	$0.706463\pi$
$948$	68.8735	+	50.0395i	2.23691	+	1.62521i
$949$	4.22289	−	12.9967i	0.137081	−	0.421892i
$950$	0.0463937	+	0.142785i	0.00150521	+	0.00463256i
$951$	−29.7874	+	21.6418i	−0.965924	+	0.701785i
$952$	−7.01913	+	5.09970i	−0.227491	+	0.165282i
$953$	−5.02583	−	15.4679i	−0.162803	−	0.501055i	0.836065	−	0.548630i	$-0.184851\pi$
$953$	−5.02583	−	15.4679i	−0.162803	−	0.501055i	−0.998868	+	0.0475752i	$0.984851\pi$
$954$	8.66098	−	26.6558i	0.280410	−	0.863012i
$955$	−6.42504	−	4.66807i	−0.207910	−	0.151055i
$956$	58.6415			1.89660
$957$	16.9050	−	81.0975i	0.546461	−	2.62151i
$958$	37.0262			1.19626
$959$	−24.9631	−	18.1368i	−0.806101	−	0.585667i
$960$	−22.3215	+	68.6986i	−0.720425	+	2.21724i
$961$	−4.90063	−	15.0826i	−0.158085	−	0.486535i
$962$	15.0482	−	10.9332i	0.485173	−	0.352499i
$963$	−10.6862	+	7.76396i	−0.344357	+	0.250190i
$964$	−16.3291	−	50.2557i	−0.525924	−	1.61863i
$965$	−12.5172	+	38.5239i	−0.402942	+	1.24013i
$966$	32.0602	+	23.2931i	1.03152	+	0.749442i
$967$	1.42787			0.0459171			0.0229586	−	0.999736i	$-0.492691\pi$
$967$	1.42787			0.0459171			0.0229586	+	0.999736i	$0.492691\pi$
$968$	−27.2035	+	30.6943i	−0.874353	+	0.986551i
$969$	−4.38139			−0.140751
$970$	33.0666	+	24.0243i	1.06170	+	0.771373i
$971$	−5.47054	+	16.8366i	−0.175558	+	0.540312i	−0.999659	−	0.0261314i	$-0.991681\pi$
$971$	−5.47054	+	16.8366i	−0.175558	+	0.540312i	0.824100	+	0.566444i	$0.191681\pi$
$972$	−19.8195	−	60.9983i	−0.635712	−	1.95652i
$973$	−4.23726	+	3.07855i	−0.135840	+	0.0986937i
$974$	82.6308	−	60.0348i	2.64766	−	1.92364i
$975$	0.0176030	+	0.0541765i	0.000563748	+	0.00173504i
$976$	−0.241235	+	0.742445i	−0.00772175	+	0.0237651i
$977$	−37.9525	−	27.5741i	−1.21421	−	0.882174i	−0.218602	−	0.975814i	$-0.570150\pi$
$977$	−37.9525	−	27.5741i	−1.21421	−	0.882174i	−0.995606	+	0.0936398i	$0.970150\pi$
$978$	−42.9623			−1.37378
$979$	−3.11648	+	14.9505i	−0.0996032	+	0.477821i
$980$	105.581			3.37267
$981$	−54.7952	−	39.8110i	−1.74948	−	1.27107i
$982$	−18.0911	+	55.6785i	−0.577309	+	1.77677i
$983$	10.5878	+	32.5858i	0.337697	+	1.03933i	0.965378	+	0.260855i	$0.0840044\pi$
$983$	10.5878	+	32.5858i	0.337697	+	1.03933i	−0.627681	+	0.778471i	$0.715996\pi$
$984$	−34.9120	+	25.3651i	−1.11295	+	0.808609i
$985$	36.2715	−	26.3528i	1.15571	−	0.839671i
$986$	3.43151	+	10.5611i	0.109282	+	0.336334i
$987$	−33.1111	+	101.905i	−1.05394	+	3.24368i
$988$	−8.89308	−	6.46120i	−0.282927	−	0.205558i
$989$	2.11101			0.0671263
$990$	59.5012	−	54.0000i	1.89107	−	1.71623i
$991$	27.7347			0.881023			0.440511	−	0.897747i	$-0.354797\pi$
$991$	27.7347			0.881023			0.440511	+	0.897747i	$0.354797\pi$
$992$	−11.2121	−	8.14610i	−0.355986	−	0.258639i
$993$	9.57856	−	29.4798i	0.303966	−	0.935512i
$994$	33.7107	+	103.751i	1.06924	+	3.29078i
$995$	−32.6274	+	23.7052i	−1.03436	+	0.751505i
$996$	−107.053	+	77.7786i	−3.39211	+	2.46451i
$997$	8.67914	+	26.7116i	0.274871	+	0.845966i	0.989253	+	0.146211i	$0.0467077\pi$
$997$	8.67914	+	26.7116i	0.274871	+	0.845966i	−0.714382	+	0.699755i	$0.753292\pi$
$998$	−25.2487	+	77.7075i	−0.799234	+	2.45979i
$999$	27.6716	+	20.1046i	0.875490	+	0.636080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.92.2	yes	28
11.3	even	5	inner	143.2.h.c.14.2	✓	28
11.5	even	5		1573.2.a.s.1.12		14
11.6	odd	10		1573.2.a.r.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.2	✓	28	11.3	even	5	inner
143.2.h.c.92.2	yes	28	1.1	even	1	trivial
1573.2.a.r.1.3		14	11.6	odd	10
1573.2.a.s.1.12		14	11.5	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91083 - 1.38830i) q^{2} +(0.850654 - 2.61804i) q^{3} +(1.10586 + 3.40347i) q^{4} +(-1.81276 + 1.31704i) q^{5} +(-5.26007 + 3.82167i) q^{6} +(-1.38773 - 4.27098i) q^{7} +(1.15219 - 3.54608i) q^{8} +(-3.70349 - 2.69074i) q^{9} +O(q^{10})\)	\(q+(-1.91083 - 1.38830i) q^{2} +(0.850654 - 2.61804i) q^{3} +(1.10586 + 3.40347i) q^{4} +(-1.81276 + 1.31704i) q^{5} +(-5.26007 + 3.82167i) q^{6} +(-1.38773 - 4.27098i) q^{7} +(1.15219 - 3.54608i) q^{8} +(-3.70349 - 2.69074i) q^{9} +5.29231 q^{10} +(-0.676812 + 3.24683i) q^{11} +9.85114 q^{12} +(-0.809017 - 0.587785i) q^{13} +(-3.27768 + 10.0877i) q^{14} +(1.90605 + 5.86623i) q^{15} +(-1.33431 + 0.969432i) q^{16} +(0.419199 - 0.304566i) q^{17} +(3.34118 + 10.2831i) q^{18} +(0.949208 - 2.92136i) q^{19} +(-6.48717 - 4.71321i) q^{20} -12.3621 q^{21} +(5.80084 - 5.26452i) q^{22} +1.35723 q^{23} +(-8.30367 - 6.03297i) q^{24} +(0.00639465 - 0.0196807i) q^{25} +(0.729871 + 2.24631i) q^{26} +(-3.51375 + 2.55289i) q^{27} +(13.0015 - 9.44617i) q^{28} +(-2.80388 - 8.62945i) q^{29} +(4.50193 - 13.8555i) q^{30} +(3.14803 + 2.28717i) q^{31} -3.56164 q^{32} +(7.92462 + 4.53385i) q^{33} -1.22384 q^{34} +(8.14068 + 5.91455i) q^{35} +(5.06235 - 15.5803i) q^{36} +(-2.43358 - 7.48979i) q^{37} +(-5.86948 + 4.26443i) q^{38} +(-2.22704 + 1.61804i) q^{39} +(2.58170 + 7.94566i) q^{40} +(1.29923 - 3.99863i) q^{41} +(23.6218 + 17.1622i) q^{42} +1.55539 q^{43} +(-11.7990 + 1.28702i) q^{44} +10.2574 q^{45} +(-2.59343 - 1.88423i) q^{46} +(2.67844 - 8.24338i) q^{47} +(1.40298 + 4.31793i) q^{48} +(-10.6524 + 7.73940i) q^{49} +(-0.0395417 + 0.0287287i) q^{50} +(-0.440774 - 1.35656i) q^{51} +(1.10586 - 3.40347i) q^{52} +(-2.09713 - 1.52365i) q^{53} +10.2583 q^{54} +(-3.04933 - 6.77711i) q^{55} -16.7442 q^{56} +(-6.84080 - 4.97013i) q^{57} +(-6.62251 + 20.3820i) q^{58} +(1.47424 + 4.53725i) q^{59} +(-17.8577 + 12.9744i) q^{60} +(0.382928 - 0.278213i) q^{61} +(-2.84005 - 8.74078i) q^{62} +(-6.35268 + 19.5515i) q^{63} +(9.47430 + 6.88348i) q^{64} +2.24069 q^{65} +(-8.84823 - 19.6651i) q^{66} +3.47727 q^{67} +(1.50016 + 1.08993i) q^{68} +(1.15453 - 3.55328i) q^{69} +(-7.34428 - 22.6034i) q^{70} +(8.32068 - 6.04532i) q^{71} +(-13.8087 + 10.0326i) q^{72} +(4.22289 + 12.9967i) q^{73} +(-5.74790 + 17.6902i) q^{74} +(-0.0460853 - 0.0334829i) q^{75} +10.9925 q^{76} +(14.8064 - 1.61506i) q^{77} +6.50181 q^{78} +(6.99142 + 5.07957i) q^{79} +(1.14199 - 3.51469i) q^{80} +(-0.549236 - 1.69037i) q^{81} +(-8.03390 + 5.83697i) q^{82} +(-10.8671 + 7.89539i) q^{83} +(-13.6707 - 42.0740i) q^{84} +(-0.358779 + 1.10421i) q^{85} +(-2.97207 - 2.15934i) q^{86} -24.9774 q^{87} +(10.7337 + 6.14100i) q^{88} +4.60465 q^{89} +(-19.6000 - 14.2402i) q^{90} +(-1.38773 + 4.27098i) q^{91} +(1.50090 + 4.61929i) q^{92} +(8.66580 - 6.29607i) q^{93} +(-16.5623 + 12.0332i) q^{94} +(2.12688 + 6.54586i) q^{95} +(-3.02973 + 9.32454i) q^{96} +(6.24804 + 4.53947i) q^{97} +31.0994 q^{98} +(11.2430 - 10.2035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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