LMFDB - Embedded newform 252.2.ba.a.155.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.5
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26027 - 0.641659i) q^{2} +(0.953579 - 1.44592i) q^{3} +(1.17655 + 1.61732i) q^{4} +(0.898347 - 0.518661i) q^{5} +(-2.12955 + 1.21037i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +O(q^{10})$	\(q+(-1.26027 - 0.641659i) q^{2} +(0.953579 - 1.44592i) q^{3} +(1.17655 + 1.61732i) q^{4} +(0.898347 - 0.518661i) q^{5} +(-2.12955 + 1.21037i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +(-1.46496 + 0.0772186i) q^{10} +(1.75133 - 3.03339i) q^{11} +(3.46045 - 0.158947i) q^{12} +(2.39811 + 4.15365i) q^{13} +(0.770594 + 1.18583i) q^{14} +(0.106702 - 1.79352i) q^{15} +(-1.23148 + 3.80572i) q^{16} -1.35469i q^{17} +(-0.280593 + 4.23335i) q^{18} -5.14106i q^{19} +(1.89579 + 0.842690i) q^{20} +(-1.54878 + 0.775415i) q^{21} +(-4.15354 + 2.69912i) q^{22} +(-1.66445 - 2.88291i) q^{23} +(-4.46309 - 2.02012i) q^{24} +(-1.96198 + 3.39825i) q^{25} +(-0.357033 - 6.77349i) q^{26} +(-5.11380 - 0.921417i) q^{27} +(-0.210257 - 1.98892i) q^{28} +(-0.188235 - 0.108677i) q^{29} +(-1.28530 + 2.19185i) q^{30} +(-0.738509 + 0.426379i) q^{31} +(3.99396 - 4.00603i) q^{32} +(-2.71601 - 5.42485i) q^{33} +(-0.869251 + 1.70727i) q^{34} -1.03732 q^{35} +(3.06999 - 5.15511i) q^{36} +3.25692 q^{37} +(-3.29881 + 6.47911i) q^{38} +(8.29264 + 0.493356i) q^{39} +(-1.84848 - 2.27847i) q^{40} +(-1.19014 + 0.687125i) q^{41} +(2.44943 + 0.0165622i) q^{42} +(6.70351 + 3.87028i) q^{43} +(6.96649 - 0.736458i) q^{44} +(-2.49154 - 1.86455i) q^{45} +(0.247804 + 4.70124i) q^{46} +(-2.08223 + 3.60653i) q^{47} +(4.32845 + 5.40967i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.65314 - 3.02378i) q^{50} +(-1.95878 - 1.29181i) q^{51} +(-3.89631 + 8.76549i) q^{52} +13.4415i q^{53} +(5.85352 + 4.44255i) q^{54} -3.63338i q^{55} +(-1.01123 + 2.64148i) q^{56} +(-7.43356 - 4.90241i) q^{57} +(0.167492 + 0.257745i) q^{58} +(2.77105 + 4.79960i) q^{59} +(3.02625 - 1.93759i) q^{60} +(5.65678 - 9.79783i) q^{61} +(1.20431 - 0.0634795i) q^{62} +(-0.355700 + 2.97884i) q^{63} +(-7.60396 + 2.48591i) q^{64} +(4.30868 + 2.48761i) q^{65} +(-0.0580118 + 8.57952i) q^{66} +(-12.8327 + 7.40894i) q^{67} +(2.19098 - 1.59386i) q^{68} +(-5.75563 - 0.342421i) q^{69} +(1.30730 + 0.665607i) q^{70} +12.5490 q^{71} +(-7.17683 + 4.52693i) q^{72} +14.5146 q^{73} +(-4.10460 - 2.08984i) q^{74} +(3.04270 + 6.07737i) q^{75} +(8.31476 - 6.04870i) q^{76} +(-3.03339 + 1.75133i) q^{77} +(-10.1344 - 5.94281i) q^{78} +(12.2513 + 7.07327i) q^{79} +(0.867583 + 4.05757i) q^{80} +(-6.20871 + 6.51551i) q^{81} +(1.94079 - 0.102300i) q^{82} +(-6.05157 + 10.4816i) q^{83} +(-3.07631 - 1.59257i) q^{84} +(-0.702626 - 1.21698i) q^{85} +(-5.96482 - 9.17895i) q^{86} +(-0.336635 + 0.168540i) q^{87} +(-9.25219 - 3.54198i) q^{88} -5.72707i q^{89} +(1.94360 + 3.94855i) q^{90} -4.79623i q^{91} +(2.70429 - 6.08382i) q^{92} +(-0.0877175 + 1.47441i) q^{93} +(4.93833 - 3.20911i) q^{94} +(-2.66647 - 4.61846i) q^{95} +(-1.98384 - 9.59502i) q^{96} +(4.52430 - 7.83631i) q^{97} +(-0.0744403 - 1.41225i) q^{98} +(-10.4338 - 1.24589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	−1.26027	−	0.641659i	−0.891143	−	0.453722i
$2$	−1.26027	−	0.641659i	−0.891143	−	0.453722i
$3$	0.953579	−	1.44592i	0.550549	−	0.834803i
$3$	0.953579	−	1.44592i	0.550549	−	0.834803i
$4$	1.17655	+	1.61732i	0.588273	+	0.808662i
$5$	0.898347	−	0.518661i	0.401753	−	0.231952i	−0.285487	−	0.958383i	$-0.592155\pi$
$5$	0.898347	−	0.518661i	0.401753	−	0.231952i	0.687240	+	0.726430i	$0.258822\pi$
$6$	−2.12955	+	1.21037i	−0.869386	+	0.494133i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	−0.444992	−	2.79320i	−0.157328	−	0.987546i
$9$	−1.18137	−	2.75760i	−0.393791	−	0.919200i
$10$	−1.46496	+	0.0772186i	−0.463261	+	0.0244187i
$11$	1.75133	−	3.03339i	0.528045	−	0.914601i	−0.471421	−	0.881909i	$-0.656259\pi$
$11$	1.75133	−	3.03339i	0.528045	−	0.914601i	0.999465	−	0.0326921i	$-0.0104081\pi$
$12$	3.46045	−	0.158947i	0.998947	−	0.0458839i
$13$	2.39811	+	4.15365i	0.665117	+	1.15202i	0.979254	+	0.202639i	$0.0649516\pi$
$13$	2.39811	+	4.15365i	0.665117	+	1.15202i	−0.314137	+	0.949378i	$0.601715\pi$
$14$	0.770594	+	1.18583i	0.205950	+	0.316926i
$15$	0.106702	−	1.79352i	0.0275504	−	0.463086i
$16$	−1.23148	+	3.80572i	−0.307869	+	0.951429i
$17$		−	1.35469i		−	0.328561i	−0.986414	−	0.164281i	$-0.947470\pi$
$17$		−	1.35469i		−	0.328561i	0.986414	−	0.164281i	$-0.0525303\pi$
$18$	−0.280593	+	4.23335i	−0.0661364	+	0.997811i
$19$		−	5.14106i		−	1.17944i	−0.807608	−	0.589720i	$-0.799238\pi$
$19$		−	5.14106i		−	1.17944i	0.807608	−	0.589720i	$-0.200762\pi$
$20$	1.89579	+	0.842690i	0.423912	+	0.188431i
$21$	−1.54878	+	0.775415i	−0.337972	+	0.169209i
$22$	−4.15354	+	2.69912i	−0.885538	+	0.575455i
$23$	−1.66445	−	2.88291i	−0.347061	−	0.601127i	0.638665	−	0.769485i	$-0.279487\pi$
$23$	−1.66445	−	2.88291i	−0.347061	−	0.601127i	−0.985726	+	0.168358i	$0.946154\pi$
$24$	−4.46309	−	2.02012i	−0.911023	−	0.412355i
$25$	−1.96198	+	3.39825i	−0.392396	+	0.679650i
$26$	−0.357033	−	6.77349i	−0.0700199	−	1.32839i
$27$	−5.11380	−	0.921417i	−0.984152	−	0.177327i
$28$	−0.210257	−	1.98892i	−0.0397349	−	0.375870i
$29$	−0.188235	−	0.108677i	−0.0349543	−	0.0201809i	0.482421	−	0.875939i	$-0.339758\pi$
$29$	−0.188235	−	0.108677i	−0.0349543	−	0.0201809i	−0.517375	+	0.855759i	$0.673091\pi$
$30$	−1.28530	+	2.19185i	−0.234663	+	0.400175i
$31$	−0.738509	+	0.426379i	−0.132640	+	0.0765799i	−0.564852	−	0.825192i	$-0.691067\pi$
$31$	−0.738509	+	0.426379i	−0.132640	+	0.0765799i	0.432212	+	0.901772i	$0.357733\pi$
$32$	3.99396	−	4.00603i	0.706039	−	0.708173i
$33$	−2.71601	−	5.42485i	−0.472796	−	0.944346i
$34$	−0.869251	+	1.70727i	−0.149075	+	0.292795i
$35$	−1.03732			−0.175339
$36$	3.06999	−	5.15511i	0.511665	−	0.859185i
$37$	3.25692			0.535435			0.267718	−	0.963497i	$-0.413731\pi$
$37$	3.25692			0.535435			0.267718	+	0.963497i	$0.413731\pi$
$38$	−3.29881	+	6.47911i	−0.535137	+	1.05105i
$39$	8.29264	+	0.493356i	1.32789	+	0.0790002i
$40$	−1.84848	−	2.27847i	−0.292271	−	0.360257i
$41$	−1.19014	+	0.687125i	−0.185868	+	0.107311i	−0.590047	−	0.807369i	$-0.700891\pi$
$41$	−1.19014	+	0.687125i	−0.185868	+	0.107311i	0.404179	+	0.914680i	$0.367557\pi$
$42$	2.44943	+	0.0165622i	0.377956	+	0.00255561i
$43$	6.70351	+	3.87028i	1.02228	+	0.590212i	0.914762	−	0.403992i	$-0.132378\pi$
$43$	6.70351	+	3.87028i	1.02228	+	0.590212i	0.107514	+	0.994204i	$0.465711\pi$
$44$	6.96649	−	0.736458i	1.05024	−	0.111025i
$45$	−2.49154	−	1.86455i	−0.371417	−	0.277951i
$46$	0.247804	+	4.70124i	0.0365367	+	0.693160i
$47$	−2.08223	+	3.60653i	−0.303724	+	0.526066i	−0.976976	−	0.213347i	$-0.931564\pi$
$47$	−2.08223	+	3.60653i	−0.303724	+	0.526066i	0.673252	+	0.739413i	$0.264897\pi$
$48$	4.32845	+	5.40967i	0.624758	+	0.780818i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	4.65314	−	3.02378i	0.658054	−	0.427627i
$51$	−1.95878	−	1.29181i	−0.274284	−	0.180889i
$52$	−3.89631	+	8.76549i	−0.540321	+	1.21556i
$53$			13.4415i			1.84634i	0.384395	+	0.923169i	$0.374410\pi$
$53$			13.4415i			1.84634i	−0.384395	+	0.923169i	$0.625590\pi$
$54$	5.85352	+	4.44255i	0.796564	+	0.604555i
$55$		−	3.63338i		−	0.489925i
$56$	−1.01123	+	2.64148i	−0.135131	+	0.352983i
$57$	−7.43356	−	4.90241i	−0.984600	−	0.649340i
$58$	0.167492	+	0.257745i	0.0219928	+	0.0338436i
$59$	2.77105	+	4.79960i	0.360760	+	0.624854i	0.988086	−	0.153902i	$-0.0491841\pi$
$59$	2.77105	+	4.79960i	0.360760	+	0.624854i	−0.627326	+	0.778757i	$0.715851\pi$
$60$	3.02625	−	1.93759i	0.390687	−	0.250142i
$61$	5.65678	−	9.79783i	0.724276	−	1.25448i	−0.234995	−	0.971997i	$-0.575507\pi$
$61$	5.65678	−	9.79783i	0.724276	−	1.25448i	0.959271	−	0.282487i	$-0.0911594\pi$
$62$	1.20431	−	0.0634795i	0.152947	−	0.00806191i
$63$	−0.355700	+	2.97884i	−0.0448140	+	0.375298i
$64$	−7.60396	+	2.48591i	−0.950496	+	0.310738i
$65$	4.30868	+	2.48761i	0.534425	+	0.308551i
$66$	−0.0580118	+	8.57952i	−0.00714076	+	1.05607i
$67$	−12.8327	+	7.40894i	−1.56776	+	0.905146i	−0.571329	+	0.820721i	$0.693572\pi$
$67$	−12.8327	+	7.40894i	−1.56776	+	0.905146i	−0.996430	+	0.0844247i	$0.973095\pi$
$68$	2.19098	−	1.59386i	0.265695	−	0.193284i
$69$	−5.75563	−	0.342421i	−0.692897	−	0.0412227i
$70$	1.30730	+	0.665607i	0.156253	+	0.0795553i
$71$	12.5490			1.48929			0.744645	−	0.667460i	$-0.232619\pi$
$71$	12.5490			1.48929			0.744645	+	0.667460i	$0.232619\pi$
$72$	−7.17683	+	4.52693i	−0.845798	+	0.533503i
$73$	14.5146			1.69881			0.849405	−	0.527741i	$-0.176961\pi$
$73$	14.5146			1.69881			0.849405	+	0.527741i	$0.176961\pi$
$74$	−4.10460	−	2.08984i	−0.477149	−	0.242938i
$75$	3.04270	+	6.07737i	0.351341	+	0.701755i
$76$	8.31476	−	6.04870i	0.953768	−	0.693833i
$77$	−3.03339	+	1.75133i	−0.345687	+	0.199582i
$78$	−10.1344	−	5.94281i	−1.14749	−	0.672891i
$79$	12.2513	+	7.07327i	1.37838	+	0.795806i	0.991964	−	0.126521i	$-0.0403810\pi$
$79$	12.2513	+	7.07327i	1.37838	+	0.795806i	0.386412	+	0.922326i	$0.373714\pi$
$80$	0.867583	+	4.05757i	0.0969987	+	0.453650i
$81$	−6.20871	+	6.51551i	−0.689857	+	0.723946i
$82$	1.94079	−	0.102300i	0.214324	−	0.0112971i
$83$	−6.05157	+	10.4816i	−0.664246	+	1.15051i	0.315243	+	0.949011i	$0.397914\pi$
$83$	−6.05157	+	10.4816i	−0.664246	+	1.15051i	−0.979489	+	0.201497i	$0.935419\pi$
$84$	−3.07631	−	1.59257i	−0.335653	−	0.173764i
$85$	−0.702626	−	1.21698i	−0.0762105	−	0.132000i
$86$	−5.96482	−	9.17895i	−0.643203	−	0.989792i
$87$	−0.336635	+	0.168540i	−0.0360911	+	0.0180694i
$88$	−9.25219	−	3.54198i	−0.986287	−	0.377576i
$89$		−	5.72707i		−	0.607068i	−0.952821	−	0.303534i	$-0.901833\pi$
$89$		−	5.72707i		−	0.607068i	0.952821	−	0.303534i	$-0.0981667\pi$
$90$	1.94360	+	3.94855i	0.204874	+	0.416214i
$91$		−	4.79623i		−	0.502781i
$92$	2.70429	−	6.08382i	0.281942	−	0.634282i
$93$	−0.0877175	+	1.47441i	−0.00909588	+	0.152889i
$94$	4.93833	−	3.20911i	0.509349	−	0.330994i
$95$	−2.66647	−	4.61846i	−0.273574	−	0.473844i
$96$	−1.98384	−	9.59502i	−0.202475	−	0.979287i
$97$	4.52430	−	7.83631i	0.459373	−	0.795657i	−0.539555	−	0.841950i	$-0.681408\pi$
$97$	4.52430	−	7.83631i	0.459373	−	0.795657i	0.998928	+	0.0462932i	$0.0147408\pi$
$98$	−0.0744403	−	1.41225i	−0.00751961	−	0.142659i
$99$	−10.4338	−	1.24589i	−1.04864	−	0.125217i
$100$	−7.80444	+	0.825042i	−0.780444	+	0.0825042i
$101$	5.65839	+	3.26687i	0.563031	+	0.325066i	0.754361	−	0.656460i	$-0.227947\pi$
$101$	5.65839	+	3.26687i	0.563031	+	0.325066i	−0.191330	+	0.981526i	$0.561280\pi$
$102$	1.63968	+	2.88489i	0.162353	+	0.285647i
$103$	−8.31662	+	4.80160i	−0.819460	+	0.473116i	−0.850230	−	0.526411i	$-0.823537\pi$
$103$	−8.31662	+	4.80160i	−0.819460	+	0.473116i	0.0307699	+	0.999526i	$0.490204\pi$
$104$	10.5349	−	8.54676i	1.03303	−	0.838079i
$105$	−0.989168	+	1.49988i	−0.0965329	+	0.146374i
$106$	8.62489	−	16.9399i	0.837723	−	1.64535i
$107$	−13.6334			−1.31799			−0.658997	−	0.752145i	$-0.729019\pi$
$107$	−13.6334			−1.31799			−0.658997	+	0.752145i	$0.729019\pi$
$108$	−4.52640	−	9.35477i	−0.435553	−	0.900163i
$109$	−0.139445			−0.0133564			−0.00667821	−	0.999978i	$-0.502126\pi$
$109$	−0.139445			−0.0133564			−0.00667821	+	0.999978i	$0.502126\pi$
$110$	−2.33139	+	4.57903i	−0.222289	+	0.436593i
$111$	3.10574	−	4.70925i	0.294783	−	0.446983i
$112$	2.96935	−	2.68011i	0.280577	−	0.253246i
$113$	−7.31774	+	4.22490i	−0.688395	+	0.397445i	−0.803010	−	0.595965i	$-0.796770\pi$
$113$	−7.31774	+	4.22490i	−0.688395	+	0.397445i	0.114616	+	0.993410i	$0.463436\pi$
$114$	6.22260	+	10.9482i	0.582800	+	1.02539i
$115$	−2.99050	−	1.72657i	−0.278866	−	0.161003i
$116$	−0.0457004	−	0.432300i	−0.00424317	−	0.0401381i
$117$	8.62105	−	11.5201i	0.797016	−	1.06503i
$118$	−0.412556	−	7.82684i	−0.0379788	−	0.720519i
$119$	−0.677346	+	1.17320i	−0.0620922	+	0.107547i
$120$	−5.05715	+	0.500062i	−0.461653	+	0.0456492i
$121$	−0.634293	−	1.09863i	−0.0576630	−	0.0998752i
$122$	−13.4159	+	8.71816i	−1.21462	+	0.789305i
$123$	−0.141360	+	2.37607i	−0.0127460	+	0.214243i
$124$	−1.55848	−	0.692755i	−0.139956	−	0.0622112i
$125$			9.25702i			0.827973i
$126$	2.35968	−	3.52589i	0.210217	−	0.314112i
$127$			5.70398i			0.506146i	0.967447	+	0.253073i	$0.0814413\pi$
$127$			5.70398i			0.506146i	−0.967447	+	0.253073i	$0.918559\pi$
$128$	11.1781	+	1.74625i	0.988017	+	0.154348i
$129$	11.9884	−	6.00214i	1.05552	−	0.528459i
$130$	−3.83388	−	5.89976i	−0.336254	−	0.517443i
$131$	−10.2385	−	17.7336i	−0.894542	−	1.54939i	−0.834370	−	0.551204i	$-0.814168\pi$
$131$	−10.2385	−	17.7336i	−0.894542	−	1.54939i	−0.0601718	−	0.998188i	$-0.519165\pi$
$132$	5.57824	−	10.7753i	0.485523	−	0.937866i
$133$	−2.57053	+	4.45229i	−0.222893	+	0.386062i
$134$	20.9266	−	1.10305i	1.80778	−	0.0952888i
$135$	−5.07187	+	1.82458i	−0.436517	+	0.157035i
$136$	−3.78393	+	0.602827i	−0.324469	+	0.0516920i
$137$	−9.77658	−	5.64451i	−0.835270	−	0.482243i	0.0203840	−	0.999792i	$-0.493511\pi$
$137$	−9.77658	−	5.64451i	−0.835270	−	0.482243i	−0.855653	+	0.517549i	$0.826844\pi$
$138$	7.03392	+	4.12470i	0.598767	+	0.351118i
$139$	9.25578	−	5.34382i	0.785065	−	0.453257i	−0.0531575	−	0.998586i	$-0.516929\pi$
$139$	9.25578	−	5.34382i	0.785065	−	0.453257i	0.838222	+	0.545329i	$0.183595\pi$
$140$	−1.22046	−	1.67769i	−0.103147	−	0.141790i
$141$	3.22918	+	6.44985i	0.271946	+	0.543175i
$142$	−15.8151	−	8.05217i	−1.32717	−	0.675723i
$143$	16.7995			1.40485
$144$	11.9495	−	1.10005i	0.995789	−	0.0916712i
$145$	−0.225467			−0.0187240
$146$	−18.2923	−	9.31346i	−1.51388	−	0.770787i
$147$	1.72899	+	0.102863i	0.142605	+	0.00848403i
$148$	3.83192	+	5.26750i	0.314982	+	0.432986i
$149$	−5.65372	+	3.26417i	−0.463170	+	0.267412i	−0.713376	−	0.700781i	$-0.752835\pi$
$149$	−5.65372	+	3.26417i	−0.463170	+	0.267412i	0.250206	+	0.968193i	$0.419502\pi$
$150$	0.0649896	−	9.61149i	0.00530638	−	0.784775i
$151$	−2.81463	−	1.62503i	−0.229051	−	0.132243i	0.381083	−	0.924541i	$-0.375551\pi$
$151$	−2.81463	−	1.62503i	−0.229051	−	0.132243i	−0.610134	+	0.792298i	$0.708885\pi$
$152$	−14.3600	+	2.28773i	−1.16475	+	0.185559i
$153$	−3.73570	+	1.60040i	−0.302013	+	0.129385i
$154$	4.94663	−	0.260739i	0.398611	−	0.0210109i
$155$	−0.442292	+	0.766072i	−0.0355257	+	0.0615324i
$156$	8.95877	+	13.9924i	0.717275	+	1.12028i
$157$	−8.13937	−	14.0978i	−0.649592	−	1.12513i	−0.983220	−	0.182422i	$-0.941606\pi$
$157$	−8.13937	−	14.0978i	−0.649592	−	1.12513i	0.333628	−	0.942705i	$-0.391727\pi$
$158$	−10.9012	−	16.7754i	−0.867256	−	1.33458i
$159$	19.4354	+	12.8176i	1.54133	+	1.01650i
$160$	1.51019	−	5.67032i	0.119391	−	0.448278i
$161$			3.32889i			0.262353i
$162$	12.0054	−	4.22741i	0.943231	−	0.332136i
$163$		−	6.05547i		−	0.474301i	−0.971473	−	0.237151i	$-0.923787\pi$
$163$		−	6.05547i		−	0.474301i	0.971473	−	0.237151i	$-0.0762135\pi$
$164$	−2.51155	−	1.11640i	−0.196119	−	0.0871763i
$165$	−5.25358	−	3.46471i	−0.408991	−	0.269728i
$166$	14.3522	−	9.32660i	1.11395	−	0.723885i
$167$	2.63025	+	4.55572i	0.203534	+	0.352532i	0.949665	−	0.313268i	$-0.101424\pi$
$167$	2.63025	+	4.55572i	0.203534	+	0.352532i	−0.746130	+	0.665800i	$0.768090\pi$
$168$	2.85509	+	3.98101i	0.220275	+	0.307142i
$169$	−5.00189	+	8.66353i	−0.384761	+	0.666426i
$170$	0.104607	+	1.98457i	0.00802302	+	0.152210i
$171$	−14.1770	+	6.07351i	−1.08414	+	0.464453i
$172$	1.62751	+	15.3953i	0.124096	+	1.17388i
$173$	1.85192	+	1.06921i	0.140799	+	0.0812903i	0.568745	−	0.822514i	$-0.307429\pi$
$173$	1.85192	+	1.06921i	0.140799	+	0.0812903i	−0.427946	+	0.903804i	$0.640763\pi$
$174$	0.532396	+	0.00359988i	0.0403608	+	0.000272906i
$175$	3.39825	−	1.96198i	0.256884	−	0.148312i
$176$	9.38749	+	10.4006i	0.707609	+	0.783974i
$177$	9.58225	+	0.570079i	0.720246	+	0.0428497i
$178$	−3.67483	+	7.21764i	−0.275440	+	0.540985i
$179$	6.85809			0.512598			0.256299	−	0.966598i	$-0.417497\pi$
$179$	6.85809			0.512598			0.256299	+	0.966598i	$0.417497\pi$
$180$	0.0841643	−	6.22336i	0.00627324	−	0.463862i
$181$	−20.0689			−1.49171			−0.745855	−	0.666108i	$-0.767959\pi$
$181$	−20.0689			−1.49171			−0.745855	+	0.666108i	$0.767959\pi$
$182$	−3.07754	+	6.04453i	−0.228123	+	0.448050i
$183$	−8.77270	−	17.5223i	−0.648497	−	1.29528i
$184$	−7.31187	+	5.93201i	−0.539039	+	0.437313i
$185$	2.92585	−	1.68924i	0.215113	−	0.124195i
$186$	1.05662	−	1.80187i	0.0774750	−	0.132119i
$187$	−4.10931	−	2.37251i	−0.300502	−	0.173495i
$188$	−8.28276	+	0.875607i	−0.604083	+	0.0638602i
$189$	3.96798	+	3.35487i	0.288628	+	0.244031i
$190$	0.396985	+	7.53145i	0.0288003	+	0.546389i
$191$	−12.3006	+	21.3053i	−0.890040	+	1.54159i	−0.0502147	+	0.998738i	$0.515991\pi$
$191$	−12.3006	+	21.3053i	−0.890040	+	1.54159i	−0.839826	+	0.542856i	$0.817343\pi$
$192$	−3.65656	+	13.3652i	−0.263889	+	0.964553i
$193$	−1.04725	−	1.81389i	−0.0753829	−	0.130567i	0.825870	−	0.563861i	$-0.190685\pi$
$193$	−1.04725	−	1.81389i	−0.0753829	−	0.130567i	−0.901253	+	0.433294i	$0.857351\pi$
$194$	−10.7301	+	6.97279i	−0.770374	+	0.500617i
$195$	7.70556	−	3.85787i	0.551806	−	0.276267i
$196$	−0.812371	+	1.82758i	−0.0580265	+	0.130542i
$197$			14.3561i			1.02283i	0.859334	+	0.511415i	$0.170878\pi$
$197$			14.3561i			1.02283i	−0.859334	+	0.511415i	$0.829122\pi$
$198$	12.3500	+	8.26513i	0.877675	+	0.587377i
$199$		−	3.06244i		−	0.217090i	−0.994092	−	0.108545i	$-0.965381\pi$
$199$		−	3.06244i		−	0.217090i	0.994092	−	0.108545i	$-0.0346192\pi$
$200$	10.3651	+	3.96802i	0.732921	+	0.280581i
$201$	−1.52422	+	25.6200i	−0.107510	+	1.80710i
$202$	−5.03486	−	7.74789i	−0.354252	−	0.545139i
$203$	0.108677	+	0.188235i	0.00762765	+	0.0132115i
$204$	−0.215324	−	4.68785i	−0.0150757	−	0.328215i
$205$	−0.712770	+	1.23455i	−0.0497820	+	0.0862250i
$206$	13.5621	−	0.714866i	0.944920	−	0.0498070i
$207$	−5.98357	+	7.99567i	−0.415887	+	0.555737i
$208$	−18.7608	+	4.01141i	−1.30083	+	0.278141i
$209$	−15.5948	−	9.00368i	−1.07872	−	0.622797i
$210$	2.20903	−	1.25555i	0.152438	−	0.0866410i
$211$	−14.8672	+	8.58359i	−1.02350	+	0.590918i	−0.915116	−	0.403191i	$-0.867901\pi$
$211$	−14.8672	+	8.58359i	−1.02350	+	0.590918i	−0.108385	+	0.994109i	$0.534568\pi$
$212$	−21.7393	+	15.8146i	−1.49306	+	1.08615i
$213$	11.9665	−	18.1448i	0.819928	−	1.24326i
$214$	17.1818	+	8.74803i	1.17452	+	0.598003i
$215$	8.02944			0.547603
$216$	−0.298102	+	14.6939i	−0.0202833	+	0.999794i
$217$	0.852757			0.0578889
$218$	0.175738	+	0.0894762i	0.0119025	+	0.00606009i
$219$	13.8409	−	20.9870i	0.935279	−	1.41817i
$220$	5.87635	−	4.27484i	0.396184	−	0.288210i
$221$	5.62692	−	3.24871i	0.378508	−	0.218532i
$222$	−6.93579	+	3.94210i	−0.465500	+	0.264576i
$223$	15.2826	+	8.82341i	1.02340	+	0.590860i	0.915087	−	0.403257i	$-0.132122\pi$
$223$	15.2826	+	8.82341i	1.02340	+	0.590860i	0.108312	+	0.994117i	$0.465455\pi$
$224$	−5.46189	+	1.47234i	−0.364938	+	0.0983751i
$225$	11.6889	+	1.39575i	0.779257	+	0.0930503i
$226$	11.9332	−	0.629006i	0.793788	−	0.0418408i
$227$	9.52462	−	16.4971i	0.632171	−	1.09495i	−0.354936	−	0.934891i	$-0.615497\pi$
$227$	9.52462	−	16.4971i	0.632171	−	1.09495i	0.987107	−	0.160062i	$-0.0511693\pi$
$228$	−0.817154	−	17.7904i	−0.0541173	−	1.17820i
$229$	3.50925	+	6.07820i	0.231898	+	0.401659i	0.958367	−	0.285541i	$-0.0921732\pi$
$229$	3.50925	+	6.07820i	0.231898	+	0.401659i	−0.726469	+	0.687199i	$0.758840\pi$
$230$	2.66096	+	4.09482i	0.175459	+	0.270004i
$231$	−0.360295	+	6.05607i	−0.0237057	+	0.398460i
$232$	−0.219795	+	0.574138i	−0.0144302	+	0.0376940i
$233$		−	20.0883i		−	1.31603i	−0.753006	−	0.658013i	$-0.771397\pi$
$233$		−	20.0883i		−	1.31603i	0.753006	−	0.658013i	$-0.228603\pi$
$234$	−18.2568	+	8.98657i	−1.19348	+	0.587470i
$235$			4.31988i			0.281798i
$236$	−4.50224	+	10.1286i	−0.293071	+	0.659318i
$237$	21.9100	−	10.9694i	1.42320	−	0.712542i
$238$	1.60643	−	1.04392i	0.104129	−	0.0676671i
$239$	0.563997	+	0.976872i	0.0364820	+	0.0631886i	0.883690	−	0.468073i	$-0.155052\pi$
$239$	0.563997	+	0.976872i	0.0364820	+	0.0631886i	−0.847208	+	0.531261i	$0.821718\pi$
$240$	6.69423	+	2.61476i	0.432111	+	0.168782i
$241$	4.67470	−	8.09682i	0.301124	−	0.521562i	−0.675267	−	0.737573i	$-0.735972\pi$
$241$	4.67470	−	8.09682i	0.301124	−	0.521562i	0.976391	+	0.216012i	$0.0693049\pi$
$242$	0.0944339	+	1.79156i	0.00607044	+	0.115166i
$243$	3.50041	+	15.1904i	0.224552	+	0.974462i
$244$	22.5017	−	2.37876i	1.44053	−	0.152284i
$245$	0.898347	+	0.518661i	0.0573933	+	0.0331360i
$246$	1.70278	−	2.90378i	0.108565	−	0.185138i
$247$	21.3542	−	12.3288i	1.35873	−	0.784465i
$248$	1.51959	+	1.87307i	0.0964942	+	0.118940i
$249$	9.38495	+	18.7451i	0.594747	+	1.18793i
$250$	5.93985	−	11.6663i	0.375669	−	0.737843i
$251$	−20.3965			−1.28741			−0.643707	−	0.765272i	$-0.722604\pi$
$251$	−20.3965			−1.28741			−0.643707	+	0.765272i	$0.722604\pi$
$252$	−5.23625	+	2.92946i	−0.329852	+	0.184539i
$253$	−11.6600			−0.733055
$254$	3.66001	−	7.18854i	0.229650	−	0.451049i
$255$	−2.42967	−	0.144549i	−0.152152	−	0.00905201i
$256$	−12.9669	−	9.37329i	−0.810433	−	0.585831i
$257$	4.36914	−	2.52253i	0.272540	−	0.157351i	−0.357502	−	0.933913i	$-0.616371\pi$
$257$	4.36914	−	2.52253i	0.272540	−	0.157351i	0.630041	+	0.776562i	$0.283038\pi$
$258$	−18.9600	−	0.128201i	−1.18040	−	0.00798144i
$259$	−2.82058	−	1.62846i	−0.175262	−	0.101188i
$260$	1.04608	+	9.89532i	0.0648750	+	0.613682i
$261$	−0.0773131	+	0.647464i	−0.00478556	+	0.0400770i
$262$	1.52432	+	28.9187i	0.0941725	+	1.78660i
$263$	12.0228	−	20.8241i	0.741357	−	1.28407i	−0.210520	−	0.977590i	$-0.567516\pi$
$263$	12.0228	−	20.8241i	0.741357	−	1.28407i	0.951877	−	0.306479i	$-0.0991509\pi$
$264$	−13.9441	+	10.0004i	−0.858201	+	0.615481i
$265$	6.97160	+	12.0752i	0.428262	+	0.741772i
$266$	6.09641	−	3.96167i	0.373795	−	0.242905i
$267$	−8.28089	−	5.46122i	−0.506782	−	0.334221i
$268$	−27.0809	−	12.0376i	−1.65423	−	0.735314i
$269$		−	28.5815i		−	1.74264i	−0.490712	−	0.871322i	$-0.663263\pi$
$269$		−	28.5815i		−	1.74264i	0.490712	−	0.871322i	$-0.336737\pi$
$270$	7.56267	+	0.954959i	0.460250	+	0.0581169i
$271$		−	16.5138i		−	1.00314i	−0.865117	−	0.501570i	$-0.832756\pi$
$271$		−	16.5138i		−	1.00314i	0.865117	−	0.501570i	$-0.167244\pi$
$272$	5.15557	+	1.66827i	0.312603	+	0.101154i
$273$	−6.93496	−	4.57358i	−0.419723	−	0.276806i
$274$	8.69925	+	13.3868i	0.525541	+	0.808728i
$275$	6.87214	+	11.9029i	0.414406	+	0.717772i
$276$	−6.21797	−	9.71160i	−0.374278	−	0.584570i
$277$	−3.71718	+	6.43834i	−0.223344	+	0.386842i	−0.955821	−	0.293949i	$-0.905031\pi$
$277$	−3.71718	+	6.43834i	−0.223344	+	0.386842i	0.732478	+	0.680791i	$0.238364\pi$
$278$	−15.0937	+	0.795592i	−0.905258	+	0.0477165i
$279$	2.04824	+	1.53280i	0.122625	+	0.0917664i
$280$	0.461600	+	2.89745i	0.0275859	+	0.173156i
$281$	−3.33471	−	1.92530i	−0.198932	−	0.114854i	0.397225	−	0.917721i	$-0.369973\pi$
$281$	−3.33471	−	1.92530i	−0.198932	−	0.114854i	−0.596157	+	0.802868i	$0.703307\pi$
$282$	0.0689727	−	10.2006i	0.00410727	−	0.607435i
$283$	−25.6543	+	14.8115i	−1.52499	+	0.880455i	−0.525431	+	0.850836i	$0.676096\pi$
$283$	−25.6543	+	14.8115i	−1.52499	+	0.880455i	−0.999561	+	0.0296181i	$0.990571\pi$
$284$	14.7645	+	20.2958i	0.876110	+	1.20433i
$285$	−9.22061	−	0.548563i	−0.546182	−	0.0324941i
$286$	−21.1719	−	10.7796i	−1.25192	−	0.637409i
$287$	1.37425			0.0811194
$288$	−15.7654	−	6.28113i	−0.928984	−	0.370119i
$289$	15.1648			0.892048
$290$	0.284148	+	0.144673i	0.0166858	+	0.00849548i
$291$	−7.01641	−	14.0143i	−0.411309	−	0.821534i
$292$	17.0772	+	23.4749i	0.999365	+	1.37376i
$293$	11.7995	−	6.81242i	0.689332	−	0.397986i	−0.114030	−	0.993477i	$-0.536376\pi$
$293$	11.7995	−	6.81242i	0.689332	−	0.397986i	0.803362	+	0.595491i	$0.203043\pi$
$294$	−2.11299	−	1.23906i	−0.123232	−	0.0722635i
$295$	4.97873	+	2.87447i	0.289873	+	0.167358i
$296$	−1.44931	−	9.09725i	−0.0842392	−	0.528767i
$297$	−11.7510	+	13.8984i	−0.681860	+	0.806470i
$298$	9.21968	−	0.485972i	0.534082	−	0.0281516i
$299$	7.98306	−	13.8271i	0.461672	−	0.799640i
$300$	−6.24921	+	12.0713i	−0.360798	+	0.696939i
$301$	−3.87028	−	6.70351i	−0.223079	−	0.386384i
$302$	2.50447	+	3.85400i	0.144116	+	0.221773i
$303$	10.1194	−	5.06636i	0.581342	−	0.291055i
$304$	19.5654	+	6.33109i	1.12215	+	0.363113i
$305$		−	11.7358i		−	0.671990i
$306$	5.73489	+	0.380117i	0.327842	+	0.0217299i
$307$		−	28.8685i		−	1.64761i	−0.566872	−	0.823806i	$-0.691847\pi$
$307$		−	28.8685i		−	1.64761i	0.566872	−	0.823806i	$-0.308153\pi$
$308$	−6.40139	−	2.84545i	−0.364753	−	0.162135i
$309$	−0.987818	+	16.6039i	−0.0561950	+	0.944561i
$310$	1.04896	−	0.681655i	0.0595771	−	0.0387154i
$311$	−7.99815	−	13.8532i	−0.453534	−	0.785544i	0.545069	−	0.838391i	$-0.316504\pi$
$311$	−7.99815	−	13.8532i	−0.453534	−	0.785544i	−0.998603	+	0.0528478i	$0.983170\pi$
$312$	−2.31212	−	23.3826i	−0.130898	−	1.32378i
$313$	−5.03324	+	8.71782i	−0.284495	+	0.492761i	−0.972487	−	0.232958i	$-0.925159\pi$
$313$	−5.03324	+	8.71782i	−0.284495	+	0.492761i	0.687991	+	0.725719i	$0.258493\pi$
$314$	1.21179	+	22.9897i	0.0683855	+	1.29738i
$315$	1.22546	+	2.86052i	0.0690471	+	0.161172i
$316$	2.97441	+	28.1363i	0.167324	+	1.58279i
$317$	5.18429	+	2.99315i	0.291179	+	0.168112i	0.638473	−	0.769644i	$-0.279566\pi$
$317$	5.18429	+	2.99315i	0.291179	+	0.168112i	−0.347295	+	0.937756i	$0.612900\pi$
$318$	−16.2693	−	28.6245i	−0.912336	−	1.60518i
$319$	−0.659321	+	0.380659i	−0.0369149	+	0.0213128i
$320$	−5.54166	+	6.17708i	−0.309788	+	0.345310i
$321$	−13.0006	+	19.7129i	−0.725621	+	1.10027i
$322$	2.13601	−	4.19529i	0.119035	−	0.233795i
$323$	−6.96455			−0.387518
$324$	−17.8425	−	2.37570i	−0.991252	−	0.131983i
$325$	−18.8202			−1.04396
$326$	−3.88555	+	7.63151i	−0.215201	+	0.422670i
$327$	−0.132972	+	0.201626i	−0.00735336	+	0.0111500i
$328$	2.44888	+	3.01853i	0.135217	+	0.166670i
$329$	3.60653	−	2.08223i	0.198834	−	0.114797i
$330$	4.39775	+	7.73747i	0.242088	+	0.425934i
$331$	7.64092	+	4.41149i	0.419983	+	0.242477i	0.695070	−	0.718942i	$-0.255373\pi$
$331$	7.64092	+	4.41149i	0.419983	+	0.242477i	−0.275087	+	0.961419i	$0.588707\pi$
$332$	−24.0721	+	2.54477i	−1.32113	+	0.139662i
$333$	−3.84764	−	8.98129i	−0.210850	−	0.492172i
$334$	−0.391593	−	7.42914i	−0.0214270	−	0.406505i
$335$	−7.68545	+	13.3116i	−0.419901	+	0.727290i
$336$	−1.04372	−	6.84914i	−0.0569394	−	0.373651i
$337$	−0.0365288	−	0.0632698i	−0.00198985	−	0.00344652i	0.865029	−	0.501722i	$-0.167300\pi$
$337$	−0.0365288	−	0.0632698i	−0.00198985	−	0.00344652i	−0.867019	+	0.498276i	$0.833967\pi$
$338$	11.8628	−	7.70886i	0.645249	−	0.419306i
$339$	−0.869174	+	14.6096i	−0.0472071	+	0.793487i
$340$	1.14159	−	2.56821i	0.0619112	−	0.139281i
$341$			2.98691i			0.161750i
$342$	21.7639	+	1.44255i	1.17686	+	0.0780039i
$343$		−	1.00000i		−	0.0539949i
$344$	7.82745	−	20.4465i	0.422028	−	1.10240i
$345$	−5.34816	+	2.67761i	−0.287935	+	0.144158i
$346$	−1.64785	−	2.53579i	−0.0885889	−	0.136325i
$347$	3.09654	+	5.36336i	0.166231	+	0.287920i	0.937092	−	0.349083i	$-0.113507\pi$
$347$	3.09654	+	5.36336i	0.166231	+	0.287920i	−0.770861	+	0.637004i	$0.780174\pi$
$348$	−0.668651	−	0.346154i	−0.0358435	−	0.0185558i
$349$	−3.08486	+	5.34314i	−0.165129	+	0.286012i	−0.936701	−	0.350130i	$-0.886137\pi$
$349$	−3.08486	+	5.34314i	−0.165129	+	0.286012i	0.771572	+	0.636142i	$0.219471\pi$
$350$	−5.54163	+	0.292101i	−0.296213	+	0.0156135i
$351$	−8.43623	−	23.4506i	−0.450293	−	1.25170i
$352$	−5.15711	−	19.1311i	−0.274875	−	1.01969i
$353$	20.5409	+	11.8593i	1.09328	+	0.631207i	0.934449	−	0.356098i	$-0.115893\pi$
$353$	20.5409	+	11.8593i	1.09328	+	0.631207i	0.158835	+	0.987305i	$0.449226\pi$
$354$	−11.7104	−	6.86699i	−0.622401	−	0.364977i
$355$	11.2733	−	6.50867i	0.598327	−	0.345444i
$356$	9.26253	−	6.73817i	0.490913	−	0.357122i
$357$	1.05045	+	2.09813i	0.0555956	+	0.111045i
$358$	−8.64303	−	4.40056i	−0.456798	−	0.232577i
$359$	−19.5103			−1.02971			−0.514856	−	0.857277i	$-0.672155\pi$
$359$	−19.5103			−1.02971			−0.514856	+	0.857277i	$0.672155\pi$
$360$	−4.09935	+	7.78909i	−0.216055	+	0.410521i
$361$	−7.43049			−0.391079
$362$	25.2922	+	12.8774i	1.32933	+	0.676821i
$363$	−2.19338	−	0.130491i	−0.115122	−	0.00684900i
$364$	7.75705	−	5.64298i	0.406580	−	0.295773i
$365$	13.0392	−	7.52818i	0.682502	−	0.394043i
$366$	−0.187378	+	27.7118i	−0.00979440	+	1.44852i
$367$	−6.01843	−	3.47474i	−0.314160	−	0.181380i	0.334627	−	0.942351i	$-0.391390\pi$
$367$	−6.01843	−	3.47474i	−0.314160	−	0.181380i	−0.648786	+	0.760971i	$0.724723\pi$
$368$	13.0212	−	2.78418i	0.678779	−	0.145135i
$369$	3.30081	+	2.47017i	0.171833	+	0.128592i
$370$	−4.77127	+	0.251495i	−0.248046	+	0.0130746i
$371$	6.72077	−	11.6407i	0.348925	−	0.604356i
$372$	−2.48781	+	1.59285i	−0.128987	+	0.0825853i
$373$	−12.3478	−	21.3871i	−0.639347	−	1.10738i	−0.985576	−	0.169232i	$-0.945871\pi$
$373$	−12.3478	−	21.3871i	−0.639347	−	1.10738i	0.346229	−	0.938150i	$-0.387462\pi$
$374$	3.65648	+	5.62677i	0.189072	+	0.290953i
$375$	13.3849	+	8.82730i	0.691194	+	0.455840i
$376$	11.0003	+	4.21121i	0.567299	+	0.217177i
$377$		−	1.04248i		−	0.0536906i
$378$	−2.84802	−	6.77412i	−0.146487	−	0.348423i
$379$			21.9062i			1.12524i	0.826714	+	0.562622i	$0.190207\pi$
$379$			21.9062i			1.12524i	−0.826714	+	0.562622i	$0.809793\pi$
$380$	4.33232	−	9.74637i	0.222243	−	0.499978i
$381$	8.24750	+	5.43920i	0.422532	+	0.278658i
$382$	29.1728	−	18.9575i	1.49261	−	0.969952i
$383$	12.7967	+	22.1646i	0.653882	+	1.13256i	0.982173	+	0.187980i	$0.0601942\pi$
$383$	12.7967	+	22.1646i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606472\pi$
$384$	13.1842	−	14.4975i	0.672802	−	0.739823i
$385$	−1.81669	+	3.14660i	−0.0925871	+	0.160366i
$386$	0.155916	+	2.95797i	0.00793590	+	0.150557i
$387$	2.75332	−	23.0579i	0.139959	−	1.17210i
$388$	17.9969	−	1.90253i	0.913655	−	0.0965865i
$389$	−2.81098	−	1.62292i	−0.142522	−	0.0822853i	0.427043	−	0.904231i	$-0.359555\pi$
$389$	−2.81098	−	1.62292i	−0.142522	−	0.0822853i	−0.569566	+	0.821946i	$0.692889\pi$
$390$	−12.1865	−	0.0824009i	−0.617087	−	0.00417253i
$391$	−3.90545	+	2.25481i	−0.197507	+	0.114031i
$392$	2.19649	−	1.78198i	0.110939	−	0.0900034i
$393$	−35.4046	−	2.10633i	−1.78593	−	0.106250i
$394$	9.21172	−	18.0925i	0.464080	−	0.911488i
$395$	14.6745			0.738355
$396$	−10.2609	−	18.3408i	−0.515629	−	0.921658i
$397$	−20.0197			−1.00476			−0.502380	−	0.864647i	$-0.667542\pi$
$397$	−20.0197			−1.00476			−0.502380	+	0.864647i	$0.667542\pi$
$398$	−1.96504	+	3.85949i	−0.0984986	+	0.193459i
$399$	3.98645	+	7.96239i	0.199572	+	0.398618i
$400$	−10.5166	−	11.6516i	−0.525832	−	0.582580i
$401$	15.7412	−	9.08820i	0.786079	−	0.453843i	−0.0525012	−	0.998621i	$-0.516719\pi$
$401$	15.7412	−	9.08820i	0.786079	−	0.453843i	0.838580	+	0.544778i	$0.183386\pi$
$402$	18.3602	−	31.3100i	0.915726	−	1.56160i
$403$	−3.54206	−	2.04501i	−0.176442	−	0.101869i
$404$	1.37377	+	12.9951i	0.0683474	+	0.646529i
$405$	−2.19824	+	9.07341i	−0.109231	+	0.450861i
$406$	−0.0161800	−	0.306960i	−0.000802998	−	0.0152342i
$407$	5.70394	−	9.87951i	0.282734	−	0.489709i
$408$	−2.73664	+	6.04611i	−0.135484	+	0.299327i
$409$	14.6559	+	25.3847i	0.724687	+	1.25519i	0.959103	+	0.283058i	$0.0913490\pi$
$409$	14.6559	+	25.3847i	0.724687	+	1.25519i	−0.234416	+	0.972136i	$0.575318\pi$
$410$	1.69044	−	1.09851i	0.0834851	−	0.0542516i
$411$	−17.4843	+	8.75367i	−0.862435	+	0.431787i
$412$	−17.5506	−	7.80136i	−0.864658	−	0.384345i
$413$		−	5.54210i		−	0.272709i
$414$	12.6714	−	6.23726i	0.622765	−	0.306545i
$415$			12.5548i			0.616293i
$416$	26.2176	+	6.98262i	1.28543	+	0.342351i
$417$	1.09937	−	18.4789i	0.0538363	−	0.904915i
$418$	13.8764	+	21.3536i	0.678715	+	1.04444i
$419$	1.13615	+	1.96786i	0.0555043	+	0.0961363i	0.892443	−	0.451161i	$-0.148990\pi$
$419$	1.13615	+	1.96786i	0.0555043	+	0.0961363i	−0.836938	+	0.547297i	$0.815657\pi$
$420$	−3.58960	+	0.164879i	−0.175155	+	0.00804526i
$421$	−4.74134	+	8.21225i	−0.231079	+	0.400240i	−0.958126	−	0.286347i	$-0.907559\pi$
$421$	−4.74134	+	8.21225i	−0.231079	+	0.400240i	0.727047	+	0.686588i	$0.240892\pi$
$422$	24.2444	−	1.27793i	1.18020	−	0.0622087i
$423$	12.4052	+	1.48130i	0.603164	+	0.0720232i
$424$	37.5450	−	5.98138i	1.82334	−	0.290481i
$425$	4.60359	+	2.65788i	0.223307	+	0.128926i
$426$	−26.7237	+	15.1890i	−1.29477	+	0.735908i
$427$	−9.79783	+	5.65678i	−0.474150	+	0.273751i
$428$	−16.0404	−	22.0497i	−0.775341	−	1.06581i
$429$	16.0197	−	24.2908i	0.773437	−	1.17277i
$430$	−10.1192	−	5.15217i	−0.487993	−	0.248460i
$431$	−1.41743			−0.0682751			−0.0341376	−	0.999417i	$-0.510868\pi$
$431$	−1.41743			−0.0682751			−0.0341376	+	0.999417i	$0.510868\pi$
$432$	9.80418	−	18.3270i	0.471704	−	0.881757i
$433$	0.663345			0.0318783			0.0159392	−	0.999873i	$-0.494926\pi$
$433$	0.663345			0.0318783			0.0159392	+	0.999873i	$0.494926\pi$
$434$	−1.07470	−	0.547180i	−0.0515873	−	0.0262655i
$435$	−0.215000	+	0.326007i	−0.0103085	+	0.0156308i
$436$	−0.164064	−	0.225528i	−0.00785722	−	0.0108008i
$437$	−14.8212	+	8.55702i	−0.708994	+	0.409338i
$438$	−30.9097	+	17.5681i	−1.47692	+	0.839438i
$439$	−15.7489	−	9.09265i	−0.751656	−	0.433969i	0.0746362	−	0.997211i	$-0.476220\pi$
$439$	−15.7489	−	9.09265i	−0.751656	−	0.433969i	−0.826292	+	0.563242i	$0.809554\pi$
$440$	−10.1488	+	1.61682i	−0.483823	+	0.0770791i
$441$	1.79746	−	2.40190i	0.0855936	−	0.114376i
$442$	−9.17599	+	0.483670i	−0.436457	+	0.0230058i
$443$	−19.6157	+	33.9754i	−0.931969	+	1.61422i	−0.152018	+	0.988378i	$0.548577\pi$
$443$	−19.6157	+	33.9754i	−0.931969	+	1.61422i	−0.779951	+	0.625841i	$0.784756\pi$
$444$	11.2704	−	0.517677i	0.534871	−	0.0245679i
$445$	−2.97041	−	5.14490i	−0.140811	−	0.243892i
$446$	−13.5985	−	20.9261i	−0.643909	−	0.990879i
$447$	−0.671528	+	11.2875i	−0.0317622	+	0.533879i
$448$	7.82818	+	1.64912i	0.369847	+	0.0779138i
$449$		−	21.5206i		−	1.01562i	−0.861469	−	0.507810i	$-0.830455\pi$
$449$		−	21.5206i		−	1.01562i	0.861469	−	0.507810i	$-0.169545\pi$
$450$	−13.8355	−	9.25929i	−0.652211	−	0.436487i
$451$			4.81352i			0.226660i
$452$	−15.4427	−	6.86437i	−0.726363	−	0.322873i
$453$	−5.03363	+	2.52014i	−0.236501	+	0.118406i
$454$	−22.5891	+	14.6792i	−1.06016	+	0.688930i
$455$	−2.48761	−	4.30868i	−0.116621	−	0.201994i
$456$	−10.3855	+	22.9450i	−0.486347	+	1.07450i
$457$	−10.9063	+	18.8903i	−0.510175	+	0.883650i	0.489755	+	0.871860i	$0.337086\pi$
$457$	−10.9063	+	18.8903i	−0.510175	+	0.883650i	−0.999931	+	0.0117896i	$0.996247\pi$
$458$	−0.522459	−	9.91190i	−0.0244129	−	0.463152i
$459$	−1.24824	+	6.92763i	−0.0582627	+	0.323354i
$460$	−0.726046	−	6.86799i	−0.0338521	−	0.320222i
$461$	12.2310	+	7.06156i	0.569653	+	0.328889i	0.757011	−	0.653402i	$-0.226659\pi$
$461$	12.2310	+	7.06156i	0.569653	+	0.328889i	−0.187358	+	0.982292i	$0.559992\pi$
$462$	4.34000	−	7.40108i	0.201915	−	0.344329i
$463$	−1.08348	+	0.625550i	−0.0503538	+	0.0290718i	−0.524966	−	0.851123i	$-0.675922\pi$
$463$	−1.08348	+	0.625550i	−0.0503538	+	0.0290718i	0.474612	+	0.880195i	$0.342588\pi$
$464$	0.645401	−	0.582534i	0.0299620	−	0.0270435i
$465$	0.685919	+	1.37003i	0.0318087	+	0.0635336i
$466$	−12.8898	+	25.3166i	−0.597110	+	1.17277i
$467$	−9.78040			−0.452583			−0.226292	−	0.974060i	$-0.572660\pi$
$467$	−9.78040			−0.452583			−0.226292	+	0.974060i	$0.572660\pi$
$468$	28.7747	+	0.389148i	1.33011	+	0.0179884i
$469$	14.8179			0.684226
$470$	2.77189	−	5.44421i	0.127858	−	0.251122i
$471$	−28.1458	−	1.67449i	−1.29689	−	0.0771562i
$472$	12.1732	−	9.87588i	0.560315	−	0.454574i
$473$	23.4801	−	13.5562i	1.07962	−	0.623316i
$474$	−34.6510	−	0.234298i	−1.59157	−	0.0107617i
$475$	17.4706	+	10.0867i	0.801607	+	0.462808i
$476$	−2.69437	+	0.284834i	−0.123496	+	0.0130553i
$477$	37.0664	−	15.8795i	1.69715	−	0.727072i
$478$	−0.0839683	−	1.59301i	−0.00384062	−	0.0728628i
$479$	10.8984	−	18.8765i	0.497960	−	0.862491i	−0.502038	−	0.864846i	$-0.667416\pi$
$479$	10.8984	−	18.8765i	0.497960	−	0.862491i	0.999997	+	0.00235456i	$0.000749482\pi$
$480$	−6.75874	−	7.59071i	−0.308493	−	0.346467i
$481$	7.81047	+	13.5281i	0.356127	+	0.616830i
$482$	−11.0868	+	7.20459i	−0.504988	+	0.328160i
$483$	4.81331	+	3.17436i	0.219013	+	0.144438i
$484$	1.03056	−	2.31844i	0.0468437	−	0.105384i
$485$		−	9.38631i		−	0.426210i
$486$	5.33558	−	21.3900i	0.242027	−	0.970270i
$487$		−	6.60927i		−	0.299495i	−0.988724	−	0.149747i	$-0.952154\pi$
$487$		−	6.60927i		−	0.299495i	0.988724	−	0.149747i	$-0.0478460\pi$
$488$	−29.8846	−	11.4406i	−1.35281	−	0.517891i
$489$	−8.75573	−	5.77437i	−0.395948	−	0.261126i
$490$	−0.799354	−	1.23008i	−0.0361111	−	0.0555695i
$491$	15.6065	+	27.0312i	0.704310	+	1.21990i	0.966940	+	0.255004i	$0.0820767\pi$
$491$	15.6065	+	27.0312i	0.704310	+	1.21990i	−0.262630	+	0.964897i	$0.584590\pi$
$492$	−4.00919	+	2.56693i	−0.180748	+	0.115726i
$493$	−0.147224	+	0.255000i	−0.00663065	+	0.0114846i
$494$	−34.8229	+	1.83553i	−1.56676	+	0.0825842i
$495$	−10.0194	+	4.29238i	−0.450339	+	0.192928i
$496$	−0.713219	−	3.33563i	−0.0320245	−	0.149774i
$497$	−10.8677	−	6.27449i	−0.487485	−	0.281449i
$498$	0.200455	−	29.6458i	0.00898260	−	1.32846i
$499$	7.57908	−	4.37578i	0.339286	−	0.195887i	−0.320670	−	0.947191i	$-0.603908\pi$
$499$	7.57908	−	4.37578i	0.339286	−	0.195887i	0.659956	+	0.751304i	$0.270575\pi$
$500$	−14.9716	+	10.8913i	−0.669551	+	0.487075i
$501$	9.09535	+	0.541112i	0.406350	+	0.0241751i
$502$	25.7050	+	13.0876i	1.14727	+	0.584128i
$503$	−23.2222			−1.03543			−0.517713	−	0.855555i	$-0.673216\pi$
$503$	−23.2222			−1.03543			−0.517713	+	0.855555i	$0.673216\pi$
$504$	8.47878	−	0.332016i	0.377675	−	0.0147892i
$505$	6.77759			0.301599
$506$	14.6947	+	7.48172i	0.653257	+	0.332603i
$507$	7.75708	+	15.4937i	0.344504	+	0.688100i
$508$	−9.22518	+	6.71100i	−0.409301	+	0.297752i
$509$	−24.9560	+	14.4083i	−1.10615	+	0.638638i	−0.937830	−	0.347094i	$-0.887168\pi$
$509$	−24.9560	+	14.4083i	−1.10615	+	0.638638i	−0.168323	+	0.985732i	$0.553835\pi$
$510$	2.96928	+	1.74119i	0.131482	+	0.0771013i
$511$	−12.5701	−	7.25732i	−0.556066	−	0.321045i
$512$	10.3273	+	20.1332i	0.456408	+	0.889770i
$513$	−4.73706	+	26.2904i	−0.209146	+	1.16075i
$514$	−7.12489	+	0.375555i	−0.314265	+	0.0165650i
$515$	−4.98080	+	8.62701i	−0.219480	+	0.380151i
$516$	23.8124	+	12.3274i	1.04828	+	0.542684i
$517$	7.29333	+	12.6324i	0.320760	+	0.555573i
$518$	2.50977	+	3.86215i	0.110273	+	0.169693i
$519$	3.31194	−	1.65816i	0.145378	−	0.0727850i
$520$	5.03109	−	13.1420i	0.220628	−	0.576314i
$521$		−	12.0996i		−	0.530094i	−0.964235	−	0.265047i	$-0.914612\pi$
$521$		−	12.0996i		−	0.530094i	0.964235	−	0.265047i	$-0.0853875\pi$
$522$	0.512887	−	0.766369i	0.0224484	−	0.0335431i
$523$		−	7.58603i		−	0.331714i	−0.986150	−	0.165857i	$-0.946961\pi$
$523$		−	7.58603i		−	0.331714i	0.986150	−	0.165857i	$-0.0530390\pi$
$524$	16.6349	−	37.4234i	0.726700	−	1.63485i
$525$	0.403632	−	6.78451i	0.0176160	−	0.296100i
$526$	−28.5139	+	18.5294i	−1.24327	+	0.807919i
$527$	0.577612	+	1.00045i	0.0251612	+	0.0435804i
$528$	23.9902	−	3.65578i	1.04404	−	0.159097i
$529$	5.95924	−	10.3217i	0.259097	−	0.448770i
$530$	−1.03794	−	19.6913i	−0.0450851	−	0.855337i
$531$	9.96172	−	13.3116i	0.432302	−	0.577673i
$532$	−10.2251	+	1.08094i	−0.443316	+	0.0468649i
$533$	−5.70816	−	3.29561i	−0.247248	−	0.142749i
$534$	6.93190	+	12.1961i	0.299972	+	0.527777i
$535$	−12.2476	+	7.07113i	−0.529508	+	0.305712i
$536$	26.4051	+	32.5473i	1.14053	+	1.40583i
$537$	6.53974	−	9.91626i	0.282210	−	0.427918i
$538$	−18.3396	+	36.0203i	−0.790675	+	1.55295i
$539$	3.50265			0.150870
$540$	−8.91823	−	6.05616i	−0.383779	−	0.260616i
$541$	−1.63666			−0.0703654			−0.0351827	−	0.999381i	$-0.511201\pi$
$541$	−1.63666			−0.0703654			−0.0351827	+	0.999381i	$0.511201\pi$
$542$	−10.5962	+	20.8117i	−0.455146	+	0.893941i
$543$	−19.1373	+	29.0181i	−0.821260	+	1.24528i
$544$	−5.42694	−	5.41059i	−0.232678	−	0.231977i
$545$	−0.125270	+	0.0723247i	−0.00536598	+	0.00309805i
$546$	5.80523	+	10.2138i	0.248441	+	0.437111i
$547$	8.45182	+	4.87966i	0.361374	+	0.208639i	0.669683	−	0.742647i	$-0.266430\pi$
$547$	8.45182	+	4.87966i	0.361374	+	0.208639i	−0.308310	+	0.951286i	$0.599763\pi$
$548$	−2.37360	−	22.4529i	−0.101395	−	0.959142i
$549$	−33.7013	−	4.02424i	−1.43834	−	0.171750i
$550$	−1.02313	−	19.4104i	−0.0436264	−	0.827663i
$551$	−0.558717	+	0.967726i	−0.0238021	+	0.0412265i
$552$	1.60476	+	16.2290i	0.0683031	+	0.690753i
$553$	−7.07327	−	12.2513i	−0.300786	−	0.520977i
$554$	8.81586	−	5.72887i	0.374550	−	0.243396i
$555$	0.347522	−	5.84137i	0.0147515	−	0.247952i
$556$	19.5325	+	8.68233i	0.828365	+	0.368213i
$557$			43.1522i			1.82842i	0.405243	+	0.914209i	$0.367187\pi$
$557$			43.1522i			1.82842i	−0.405243	+	0.914209i	$0.632813\pi$
$558$	−1.59779	−	3.24601i	−0.0676399	−	0.137415i
$559$			37.1254i			1.57024i
$560$	1.27744	−	3.94775i	0.0539815	−	0.166823i
$561$	−7.34901	+	3.67936i	−0.310275	+	0.155343i
$562$	2.96725	+	4.56614i	0.125166	+	0.192611i
$563$	1.30493	+	2.26020i	0.0549961	+	0.0952560i	0.892213	−	0.451615i	$-0.149152\pi$
$563$	1.30493	+	2.26020i	0.0549961	+	0.0952560i	−0.837217	+	0.546871i	$0.815819\pi$
$564$	−6.63221	+	12.8112i	−0.279266	+	0.539448i
$565$	−4.38258	+	7.59085i	−0.184376	+	0.319349i
$566$	41.8353	−	2.20515i	1.75847	−	0.0926894i
$567$	8.63466	−	2.53824i	0.362622	−	0.106596i
$568$	−5.58420	−	35.0519i	−0.234308	−	1.47074i
$569$	−19.6204	−	11.3278i	−0.822529	−	0.474888i	0.0287586	−	0.999586i	$-0.490845\pi$
$569$	−19.6204	−	11.3278i	−0.822529	−	0.474888i	−0.851288	+	0.524699i	$0.824178\pi$
$570$	11.2684	+	6.60782i	0.471983	+	0.276771i
$571$	14.1425	−	8.16520i	0.591847	−	0.341703i	−0.173980	−	0.984749i	$-0.555663\pi$
$571$	14.1425	−	8.16520i	0.591847	−	0.341703i	0.765828	+	0.643046i	$0.222330\pi$
$572$	19.7654	+	27.1703i	0.826434	+	1.13605i
$573$	19.0761	+	38.1020i	0.796917	+	1.59173i
$574$	−1.73192	−	0.881801i	−0.0722891	−	0.0368056i
$575$	13.0625			0.544742
$576$	15.8383	+	18.0319i	0.659927	+	0.751329i
$577$	−3.85191			−0.160357			−0.0801786	−	0.996781i	$-0.525549\pi$
$577$	−3.85191			−0.160357			−0.0801786	+	0.996781i	$0.525549\pi$
$578$	−19.1117	−	9.73064i	−0.794942	−	0.404741i
$579$	−3.62138	−	0.215448i	−0.150500	−	0.00895371i
$580$	−0.265272	−	0.364653i	−0.0110148	−	0.0151414i
$581$	10.4816	−	6.05157i	0.434851	−	0.251061i
$582$	−0.149865	+	22.1639i	−0.00621210	+	0.918725i
$583$	40.7734	+	23.5405i	1.68866	+	0.974949i
$584$	−6.45890	−	40.5424i	−0.267271	−	1.67765i
$585$	1.76969	−	14.8204i	0.0731677	−	0.612748i
$586$	−19.2417	+	1.01424i	−0.794868	+	0.0418978i
$587$	11.3059	−	19.5823i	0.466643	−	0.808250i	−0.532631	−	0.846348i	$-0.678797\pi$
$587$	11.3059	−	19.5823i	0.466643	−	0.808250i	0.999274	+	0.0380980i	$0.0121299\pi$
$588$	1.86788	+	2.91737i	0.0770300	+	0.120310i
$589$	2.19204	+	3.79672i	0.0903214	+	0.156441i
$590$	−4.43010	−	6.81724i	−0.182384	−	0.280662i
$591$	20.7578	+	13.6897i	0.853861	+	0.563118i
$592$	−4.01082	+	12.3949i	−0.164844	+	0.509428i
$593$			0.678737i			0.0278724i	0.999903	+	0.0139362i	$0.00443617\pi$
$593$			0.678737i			0.0278724i	−0.999903	+	0.0139362i	$0.995564\pi$
$594$	23.7274	−	9.97564i	0.973548	−	0.409306i
$595$			1.40525i			0.0576097i
$596$	−11.9311	−	5.30344i	−0.488716	−	0.217237i
$597$	−4.42804	−	2.92028i	−0.181228	−	0.119519i
$598$	−18.9331	+	12.3034i	−0.774230	+	0.503123i
$599$	9.15979	+	15.8652i	0.374259	+	0.648235i	0.990216	−	0.139545i	$-0.0445639\pi$
$599$	9.15979	+	15.8652i	0.374259	+	0.648235i	−0.615957	+	0.787780i	$0.711231\pi$
$600$	15.6214	−	11.2033i	0.637739	−	0.457371i
$601$	16.3104	−	28.2504i	0.665314	−	1.15236i	−0.313886	−	0.949461i	$-0.601631\pi$
$601$	16.3104	−	28.2504i	0.665314	−	1.15236i	0.979200	−	0.202897i	$-0.0650357\pi$
$602$	0.576209	+	10.9316i	0.0234845	+	0.445539i
$603$	35.5911	+	26.6346i	1.44938	+	1.08465i
$604$	−0.683347	−	6.46408i	−0.0278050	−	0.263020i
$605$	−1.13963	−	0.657965i	−0.0463325	−	0.0267501i
$606$	−16.0040	−	0.108213i	−0.650117	−	0.00439587i
$607$	−30.1157	+	17.3873i	−1.22236	+	0.705728i	−0.965420	−	0.260700i	$-0.916047\pi$
$607$	−30.1157	+	17.3873i	−1.22236	+	0.705728i	−0.256937	+	0.966428i	$0.582713\pi$
$608$	−20.5952	−	20.5332i	−0.835247	−	0.832731i
$609$	0.375805	+	0.0223578i	0.0152284	+	0.000905985i
$610$	−7.53039	+	14.7902i	−0.304896	+	0.598840i
$611$	−19.9737			−0.808049
$612$	−6.98359	−	4.15889i	−0.282295	−	0.168113i
$613$	13.6778			0.552443			0.276221	−	0.961094i	$-0.410918\pi$
$613$	13.6778			0.552443			0.276221	+	0.961094i	$0.410918\pi$
$614$	−18.5237	+	36.3820i	−0.747557	+	1.46826i
$615$	1.10538	+	2.20785i	0.0445734	+	0.0890293i
$616$	6.24164	+	7.69354i	0.251483	+	0.309982i
$617$	4.95281	−	2.85951i	0.199393	−	0.115119i	−0.396980	−	0.917827i	$-0.629942\pi$
$617$	4.95281	−	2.85951i	0.199393	−	0.115119i	0.596372	+	0.802708i	$0.296608\pi$
$618$	11.8989	−	20.2915i	0.478646	−	0.816243i
$619$	−7.04976	−	4.07018i	−0.283354	−	0.163594i	0.351587	−	0.936155i	$-0.385642\pi$
$619$	−7.04976	−	4.07018i	−0.283354	−	0.163594i	−0.634941	+	0.772561i	$0.718975\pi$
$620$	−1.75936	+	0.185990i	−0.0706577	+	0.00746954i
$621$	5.85529	+	16.2763i	0.234965	+	0.653144i
$622$	1.19077	+	22.5908i	0.0477456	+	0.905810i
$623$	−2.86354	+	4.95979i	−0.114725	+	0.198710i
$624$	−12.0898	+	30.9519i	−0.483978	+	1.23907i
$625$	−5.00865	−	8.67524i	−0.200346	−	0.347010i
$626$	11.9371	−	7.75716i	0.477102	−	0.310039i
$627$	−27.8895	+	13.9632i	−1.11380	+	0.557635i
$628$	13.2244	−	29.7507i	0.527710	−	1.18718i
$629$		−	4.41213i		−	0.175923i
$630$	0.291065	−	4.39135i	0.0115963	−	0.174955i
$631$		−	21.8309i		−	0.869075i	−0.900654	−	0.434538i	$-0.856912\pi$
$631$		−	21.8309i		−	0.869075i	0.900654	−	0.434538i	$-0.143088\pi$
$632$	14.3054	−	37.3678i	0.569037	−	1.48641i
$633$	−1.76587	+	29.6819i	−0.0701872	+	1.17975i
$634$	−4.61301	−	7.09872i	−0.183206	−	0.281926i
$635$	2.95843	+	5.12415i	0.117402	+	0.203346i
$636$	2.13649	+	46.5138i	0.0847172	+	1.84439i
$637$	−2.39811	+	4.15365i	−0.0950167	+	0.164574i
$638$	1.07517	−	0.0566728i	0.0425665	−	0.00224370i
$639$	−14.8250	−	34.6051i	−0.586470	−	1.36896i
$640$	10.9476	−	4.22892i	0.432740	−	0.167163i
$641$	−20.0771	−	11.5915i	−0.792998	−	0.457838i	0.0480189	−	0.998846i	$-0.484709\pi$
$641$	−20.0771	−	11.5915i	−0.792998	−	0.457838i	−0.841017	+	0.541009i	$0.818043\pi$
$642$	29.0331	−	16.5016i	1.14585	−	0.651265i
$643$	9.84261	−	5.68263i	0.388155	−	0.224101i	−0.293206	−	0.956049i	$-0.594722\pi$
$643$	9.84261	−	5.68263i	0.388155	−	0.224101i	0.681360	+	0.731948i	$0.261389\pi$
$644$	−5.38390	+	3.91660i	−0.212155	+	0.154336i
$645$	7.65671	−	11.6099i	0.301483	−	0.457141i
$646$	8.77720	+	4.46887i	0.345334	+	0.175825i
$647$	−4.43372			−0.174307			−0.0871537	−	0.996195i	$-0.527777\pi$
$647$	−4.43372			−0.174307			−0.0871537	+	0.996195i	$0.527777\pi$
$648$	20.9620	+	14.4428i	0.823464	+	0.567368i
$649$	19.4120			0.761990
$650$	23.7185	+	12.0762i	0.930316	+	0.473666i
$651$	0.813172	−	1.23302i	0.0318707	−	0.0483258i
$652$	9.79366	−	7.12454i	0.383549	−	0.279019i
$653$	−38.6732	+	22.3280i	−1.51340	+	0.873761i	−0.513521	+	0.858077i	$0.671659\pi$
$653$	−38.6732	+	22.3280i	−1.51340	+	0.873761i	−0.999877	+	0.0156838i	$0.995007\pi$
$654$	0.296956	−	0.168781i	0.0116119	−	0.00659984i
$655$	−18.3955	−	10.6206i	−0.718770	−	0.414982i
$656$	−1.14938	−	5.37550i	−0.0448757	−	0.209878i
$657$	−17.1472	−	40.0256i	−0.668977	−	1.56155i
$658$	−5.88127	+	0.310004i	−0.229276	+	0.0120852i
$659$	5.15687	−	8.93196i	0.200883	−	0.347940i	−0.747930	−	0.663778i	$-0.768952\pi$
$659$	5.15687	−	8.93196i	0.200883	−	0.347940i	0.948813	+	0.315838i	$0.102286\pi$
$660$	−0.577513	−	12.5731i	−0.0224797	−	0.489409i
$661$	−8.31721	−	14.4058i	−0.323502	−	0.560322i	0.657706	−	0.753275i	$-0.271527\pi$
$661$	−8.31721	−	14.4058i	−0.323502	−	0.560322i	−0.981208	+	0.192953i	$0.938194\pi$
$662$	−6.79893	−	10.4625i	−0.264248	−	0.406638i
$663$	0.668346	−	11.2340i	0.0259564	−	0.436292i
$664$	31.9702	+	12.2390i	1.24068	+	0.474966i
$665$			5.33293i			0.206802i
$666$	−0.913870	+	13.7877i	−0.0354118	+	0.534263i
$667$			0.723550i			0.0280160i
$668$	−4.27347	+	9.61397i	−0.165345	+	0.371976i
$669$	27.3311	−	13.6836i	1.05668	−	0.529039i
$670$	18.2272	−	11.8447i	0.704179	−	0.457602i
$671$	−19.8137	−	34.3184i	−0.764901	−	1.32485i
$672$	−3.07945	+	9.30145i	−0.118792	+	0.358811i
$673$	21.3572	−	36.9917i	0.823258	−	1.42592i	−0.0799851	−	0.996796i	$-0.525487\pi$
$673$	21.3572	−	36.9917i	0.823258	−	1.42592i	0.903243	−	0.429129i	$-0.141179\pi$
$674$	0.00543844	+	0.103176i	0.000209481	+	0.00397419i
$675$	13.1644	−	15.5702i	0.506698	−	0.599297i
$676$	−19.8967	+	2.10337i	−0.765258	+	0.0808988i
$677$	7.25220	+	4.18706i	0.278725	+	0.160922i	0.632846	−	0.774278i	$-0.281887\pi$
$677$	7.25220	+	4.18706i	0.278725	+	0.160922i	−0.354121	+	0.935200i	$0.615220\pi$
$678$	10.4698	−	17.8543i	0.402090	−	0.685692i
$679$	−7.83631	+	4.52430i	−0.300730	+	0.173627i
$680$	−3.08662	+	2.50412i	−0.118366	+	0.0960288i
$681$	−14.7711	−	29.5032i	−0.566028	−	1.13056i
$682$	1.91658	−	3.76431i	0.0733897	−	0.144143i
$683$	30.2783			1.15857			0.579283	−	0.815127i	$-0.303333\pi$
$683$	30.2783			1.15857			0.579283	+	0.815127i	$0.303333\pi$
$684$	−26.5027	−	15.7830i	−1.01336	−	0.603478i
$685$	−11.7103			−0.447429
$686$	−0.641659	+	1.26027i	−0.0244987	+	0.0481172i
$687$	12.1349	+	0.721946i	0.462977	+	0.0275440i
$688$	−22.9844	+	20.7455i	−0.876271	+	0.790915i
$689$	−55.8315	+	32.2343i	−2.12701	+	1.22803i
$690$	8.45822	+	0.0571916i	0.321999	+	0.00217725i
$691$	−12.9887	−	7.49902i	−0.494113	−	0.285276i	0.232166	−	0.972676i	$-0.425419\pi$
$691$	−12.9887	−	7.49902i	−0.494113	−	0.285276i	−0.726279	+	0.687400i	$0.758752\pi$
$692$	0.449617	+	4.25313i	0.0170919	+	0.161680i
$693$	8.41302	+	6.29590i	0.319584	+	0.239161i
$694$	−0.461015	−	8.74619i	−0.0174999	−	0.332001i
$695$	5.54327	−	9.60122i	0.210268	−	0.364195i
$696$	0.620566	+	0.865292i	0.0235225	+	0.0327988i
$697$	0.930843	+	1.61227i	0.0352582	+	0.0610690i
$698$	7.31623	−	4.75435i	0.276923	−	0.179955i
$699$	−29.0461	−	19.1558i	−1.09862	−	0.724537i
$700$	7.17136	+	3.18771i	0.271052	+	0.120484i
$701$			50.3732i			1.90257i	0.308316	+	0.951284i	$0.400235\pi$
$701$			50.3732i			1.90257i	−0.308316	+	0.951284i	$0.599765\pi$
$702$	−4.41541	+	34.9673i	−0.166649	+	1.31975i
$703$		−	16.7440i		−	0.631514i
$704$	−5.77631	+	27.4194i	−0.217703	+	1.03341i
$705$	6.24621	+	4.11935i	0.235246	+	0.155144i
$706$	−18.2774	−	28.1262i	−0.687880	−	1.05854i
$707$	−3.26687	−	5.65839i	−0.122863	−	0.212806i
$708$	10.3520	+	16.1683i	0.389051	+	0.607643i
$709$	−19.7109	+	34.1403i	−0.740258	+	1.28217i	0.212119	+	0.977244i	$0.431964\pi$
$709$	−19.7109	+	34.1403i	−0.740258	+	1.28217i	−0.952378	+	0.304921i	$0.901370\pi$
$710$	−18.3838	+	0.969015i	−0.689931	+	0.0363665i
$711$	5.03193	−	42.1403i	0.188712	−	1.58038i
$712$	−15.9969	+	2.54850i	−0.599508	+	0.0955091i
$713$	2.45842	+	1.41937i	0.0920685	+	0.0531558i
$714$	0.0224367	−	3.31823i	0.000839674	−	0.124182i
$715$	15.0918	−	8.71325i	0.564401	−	0.325857i
$716$	8.06887	+	11.0918i	0.301548	+	0.414519i
$717$	1.95030	+	0.116029i	0.0728351	+	0.00433320i
$718$	24.5881	+	12.5189i	0.917621	+	0.467203i
$719$	−5.11873			−0.190896			−0.0954482	−	0.995434i	$-0.530428\pi$
$719$	−5.11873			−0.190896			−0.0954482	+	0.995434i	$0.530428\pi$
$720$	10.1642	−	7.18595i	0.378798	−	0.267805i
$721$	9.60320			0.357642
$722$	9.36441	+	4.76785i	0.348507	+	0.177441i
$723$	−7.24966	−	14.4802i	−0.269618	−	0.538524i
$724$	−23.6120	−	32.4579i	−0.877534	−	1.20629i
$725$	0.738626	−	0.426446i	0.0274319	−	0.0158378i
$726$	2.68051	+	1.57185i	0.0994830	+	0.0583370i
$727$	−16.2868	−	9.40317i	−0.604043	−	0.348744i	0.166588	−	0.986027i	$-0.446725\pi$
$727$	−16.2868	−	9.40317i	−0.604043	−	0.348744i	−0.770630	+	0.637282i	$0.780058\pi$
$728$	−13.3968	+	2.13428i	−0.496520	+	0.0791018i
$729$	25.3020	+	9.42389i	0.937110	+	0.349033i
$730$	−21.2634	+	1.12080i	−0.786993	+	0.0414827i
$731$	5.24303	−	9.08120i	0.193921	−	0.335880i
$732$	18.0177	−	34.8041i	0.665953	−	1.28640i
$733$	−17.9418	−	31.0762i	−0.662697	−	1.14782i	−0.979904	−	0.199468i	$-0.936079\pi$
$733$	−17.9418	−	31.0762i	−0.662697	−	1.14782i	0.317208	−	0.948356i	$-0.397255\pi$
$734$	5.35523	+	8.24089i	0.197665	+	0.304177i
$735$	1.60659	−	0.804354i	0.0592599	−	0.0296691i
$736$	−18.1967	−	4.84639i	−0.670741	−	0.178640i
$737$			51.9019i			1.91183i
$738$	−2.57490	−	5.23107i	−0.0947834	−	0.192558i
$739$		−	36.4538i		−	1.34097i	−0.741922	−	0.670486i	$-0.766085\pi$
$739$		−	36.4538i		−	1.34097i	0.741922	−	0.670486i	$-0.233915\pi$
$740$	6.17444	+	2.74458i	0.226977	+	0.100893i
$741$	2.53637	−	42.6330i	0.0931760	−	1.56616i
$742$	−15.9393	+	10.3580i	−0.585152	+	0.380253i
$743$	−16.8124	−	29.1198i	−0.616785	−	1.06830i	−0.990068	−	0.140586i	$-0.955101\pi$
$743$	−16.8124	−	29.1198i	−0.616785	−	1.06830i	0.373283	−	0.927717i	$-0.378232\pi$
$744$	4.15737	−	0.411089i	0.152416	−	0.0150712i
$745$	−3.38600	+	5.86472i	−0.124053	+	0.214867i
$746$	1.83836	+	34.8766i	0.0673070	+	1.27692i
$747$	36.0533	+	4.30509i	1.31912	+	0.157515i
$748$	−0.997674	−	9.43745i	−0.0364786	−	0.345067i
$749$	11.8069	+	6.81672i	0.431415	+	0.249078i
$750$	−11.2045	−	19.7133i	−0.409129	−	0.719829i
$751$	20.3676	−	11.7593i	0.743225	−	0.429101i	−0.0800155	−	0.996794i	$-0.525497\pi$
$751$	20.3676	−	11.7593i	0.743225	−	0.429101i	0.823241	+	0.567692i	$0.192164\pi$
$752$	−11.1612	−	12.3657i	−0.407007	−	0.450931i
$753$	−19.4496	+	29.4917i	−0.708785	+	1.07474i
$754$	−0.668918	+	1.31381i	−0.0243606	+	0.0478460i
$755$	−3.37135			−0.122696
$756$	−0.757408	+	10.3647i	−0.0275467	+	0.376959i
$757$	29.6018			1.07590			0.537948	−	0.842978i	$-0.319200\pi$
$757$	29.6018			1.07590			0.537948	+	0.842978i	$0.319200\pi$
$758$	14.0563	−	27.6076i	0.510548	−	1.00275i
$759$	−11.1187	+	16.8594i	−0.403583	+	0.611957i
$760$	−11.7137	+	9.50316i	−0.424901	+	0.344716i
$761$	10.7836	−	6.22589i	0.390904	−	0.225688i	−0.291648	−	0.956526i	$-0.594204\pi$
$761$	10.7836	−	6.22589i	0.390904	−	0.225688i	0.682552	+	0.730837i	$0.260870\pi$
$762$	−6.90395	−	12.1469i	−0.250104	−	0.440037i
$763$	0.120763	+	0.0697225i	0.00437191	+	0.00252412i
$764$	−48.9298	+	5.17258i	−1.77022	+	0.187137i
$765$	−2.52589	+	3.37527i	−0.0913238	+	0.122033i
$766$	−1.90519	−	36.1444i	−0.0688372	−	1.30595i
$767$	−13.2906	+	23.0200i	−0.479895	+	0.831202i
$768$	−25.9180	+	9.81099i	−0.935237	+	0.354023i
$769$	4.89062	+	8.47080i	0.176360	+	0.305465i	0.940631	−	0.339431i	$-0.110234\pi$
$769$	4.89062	+	8.47080i	0.176360	+	0.305465i	−0.764271	+	0.644895i	$0.776901\pi$
$770$	4.30856	−	2.79986i	0.155270	−	0.100900i
$771$	0.518951	−	8.72286i	0.0186896	−	0.314146i
$772$	1.70151	−	3.82788i	0.0612388	−	0.137768i
$773$			27.6321i			0.993857i	0.867792	+	0.496928i	$0.165539\pi$
$773$			27.6321i			0.993857i	−0.867792	+	0.496928i	$0.834461\pi$
$774$	−18.2652	+	27.2924i	−0.656529	+	0.981004i
$775$		−	3.34619i		−	0.120199i
$776$	−23.9017	−	9.15018i	−0.858021	−	0.328472i
$777$	−5.04427	+	2.52547i	−0.180962	+	0.0906006i
$778$	2.50122	+	3.84900i	0.0896732	+	0.137993i
$779$	3.53255	+	6.11856i	0.126567	+	0.219220i
$780$	15.3054	+	7.92342i	0.548020	+	0.283704i
$781$	21.9774	−	38.0659i	0.786412	−	1.36211i
$782$	6.36873	−	0.335698i	0.227745	−	0.0120045i
$783$	0.862458	+	0.729197i	0.0308217	+	0.0260594i
$784$	−3.91158	+	0.836368i	−0.139699	+	0.0298703i
$785$	−14.6240	−	8.44314i	−0.521951	−	0.301349i
$786$	43.2677	+	25.3722i	1.54331	+	0.904998i
$787$	27.3188	−	15.7725i	0.973810	−	0.562229i	0.0734143	−	0.997302i	$-0.476610\pi$
$787$	27.3188	−	15.7725i	0.973810	−	0.562229i	0.900396	+	0.435072i	$0.143277\pi$
$788$	−23.2185	+	16.8906i	−0.827123	+	0.601703i
$789$	−18.6453	−	37.2414i	−0.663790	−	1.32583i
$790$	−18.4938	−	9.41604i	−0.657981	−	0.335008i
$791$	8.44980			0.300440
$792$	1.16294	+	29.6982i	0.0413232	+	1.05528i
$793$	54.2624			1.92691
$794$	25.2302	+	12.8458i	0.895385	+	0.455881i
$795$	24.1077	+	1.43424i	0.855012	+	0.0508674i
$796$	4.95295	−	3.60310i	0.175553	−	0.127709i
$797$	−16.7768	+	9.68607i	−0.594264	+	0.343098i	−0.766782	−	0.641908i	$-0.778143\pi$
$797$	−16.7768	+	9.68607i	−0.594264	+	0.343098i	0.172518	+	0.985006i	$0.444810\pi$
$798$	0.0851474	−	12.5927i	0.00301419	−	0.445776i
$799$	4.88573	+	2.82078i	0.172845	+	0.0997920i
$800$	5.77742	+	21.4322i	0.204263	+	0.757744i
$801$	−15.7930	+	6.76581i	−0.558017	+	0.239058i
$802$	−25.6697	+	1.35306i	−0.906428	+	0.0477781i
$803$	25.4199	−	44.0285i	0.897049	−	1.55373i
$804$	−43.2292	+	27.6780i	−1.52458	+	0.976128i
$805$	1.72657	+	2.99050i	0.0608535	+	0.105401i
$806$	3.15174	+	4.85005i	0.111015	+	0.170836i
$807$	−41.3266	−	27.2547i	−1.45476	−	0.959411i
$808$	6.60710	−	17.2588i	0.232437	−	0.607161i
$809$		−	21.4126i		−	0.752828i	−0.926452	−	0.376414i	$-0.877157\pi$
$809$		−	21.4126i		−	0.752828i	0.926452	−	0.376414i	$-0.122843\pi$
$810$	8.59240	−	10.0244i	0.301906	−	0.352221i
$811$			32.7084i			1.14855i	0.818663	+	0.574274i	$0.194715\pi$
$811$			32.7084i			1.14855i	−0.818663	+	0.574274i	$0.805285\pi$
$812$	−0.176573	+	0.397233i	−0.00619648	+	0.0139402i
$813$	−23.8776	−	15.7472i	−0.837424	−	0.552278i
$814$	−13.5278	+	8.79084i	−0.474148	+	0.308119i
$815$	−3.14074	−	5.43991i	−0.110015	−	0.190552i
$816$	7.32844	−	5.86372i	0.256547	−	0.205271i
$817$	19.8973	−	34.4632i	0.696119	−	1.20571i
$818$	−2.18198	−	41.3956i	−0.0762911	−	1.44736i
$819$	−13.2261	+	5.66614i	−0.462156	+	0.197991i
$820$	−2.83528	+	0.299730i	−0.0990123	+	0.0104670i
$821$	38.1467	+	22.0240i	1.33133	+	0.768644i	0.985504	−	0.169654i	$-0.0542651\pi$
$821$	38.1467	+	22.0240i	1.33133	+	0.768644i	0.345827	+	0.938298i	$0.387598\pi$
$822$	27.6517	+	0.186971i	0.964464	+	0.00652138i
$823$	15.5963	−	9.00455i	0.543654	−	0.313879i	−0.202904	−	0.979199i	$-0.565038\pi$
$823$	15.5963	−	9.00455i	0.543654	−	0.313879i	0.746559	+	0.665320i	$0.231705\pi$
$824$	17.1127	+	21.0933i	0.596148	+	0.734821i
$825$	23.7638	+	1.41378i	0.827349	+	0.0492216i
$826$	−3.55614	+	6.98452i	−0.123734	+	0.243023i
$827$	−48.5077			−1.68678			−0.843389	−	0.537303i	$-0.819443\pi$
$827$	−48.5077			−1.68678			−0.843389	+	0.537303i	$0.819443\pi$
$828$	−19.9715	−	0.270094i	−0.694059	−	0.00938640i
$829$	−27.8358			−0.966777			−0.483389	−	0.875406i	$-0.660594\pi$
$829$	−27.8358			−0.966777			−0.483389	+	0.875406i	$0.660594\pi$
$830$	8.05593	−	15.8225i	0.279626	−	0.549206i
$831$	5.76471	+	11.5142i	0.199975	+	0.399424i
$832$	−28.5608	−	25.6228i	−0.990166	−	0.888309i
$833$	1.17320	−	0.677346i	0.0406489	−	0.0234687i
$834$	−13.2426	+	22.5829i	−0.458555	+	0.781982i
$835$	4.72575	+	2.72841i	0.163541	+	0.0944205i
$836$	−3.78618	−	35.8151i	−0.130948	−	1.23869i
$837$	4.16947	−	1.49994i	0.144118	−	0.0518456i
$838$	−0.169150	−	3.20905i	−0.00584319	−	0.110855i
$839$	−3.69402	+	6.39822i	−0.127532	+	0.220891i	−0.922720	−	0.385472i	$-0.874039\pi$
$839$	−3.69402	+	6.39822i	−0.127532	+	0.220891i	0.795188	+	0.606363i	$0.207372\pi$
$840$	4.62965	+	2.09551i	0.159738	+	0.0723020i
$841$	−14.4764	−	25.0738i	−0.499185	−	0.864615i
$842$	11.2448	−	7.30730i	0.387522	−	0.251826i
$843$	−5.96374	+	2.98581i	−0.205402	+	0.102837i
$844$	−31.3744	−	13.9461i	−1.07995	−	0.480045i
$845$			10.3771i			0.356985i
$846$	−14.6834	−	9.82677i	−0.504827	−	0.337851i
$847$			1.26859i			0.0435891i
$848$	−51.1547	−	16.5529i	−1.75666	−	0.568430i
$849$	−3.04713	+	51.2181i	−0.104577	+	1.75780i
$850$	−4.09629	−	6.30358i	−0.140502	−	0.216211i
$851$	−5.42098	−	9.38941i	−0.185829	−	0.321865i
$852$	43.4252	−	1.99462i	1.48772	−	0.0683345i
$853$	26.8805	−	46.5584i	0.920371	−	1.59413i	0.121529	−	0.992588i	$-0.461220\pi$
$853$	26.8805	−	46.5584i	0.920371	−	1.59413i	0.798842	−	0.601541i	$-0.205446\pi$
$854$	15.9776	−	0.842185i	0.546743	−	0.0288190i
$855$	−9.58576	+	12.8092i	−0.327826	+	0.438064i
$856$	6.06677	+	38.0810i	0.207358	+	1.30158i
$857$	43.9316	+	25.3639i	1.50068	+	0.866416i	1.00000		0.000781209i	$0.000248666\pi$
$857$	43.9316	+	25.3639i	1.50068	+	0.866416i	0.500676	+	0.865635i	$0.333085\pi$
$858$	−35.7755	+	20.3337i	−1.22135	+	0.694181i
$859$	1.97520	−	1.14038i	0.0673930	−	0.0389094i	−0.465925	−	0.884824i	$-0.654278\pi$
$859$	1.97520	−	1.14038i	0.0673930	−	0.0389094i	0.533318	+	0.845915i	$0.320945\pi$
$860$	9.44701	+	12.9862i	0.322140	+	0.442826i
$861$	1.31046	−	1.98706i	0.0446602	−	0.0677187i
$862$	1.78634	+	0.909506i	0.0608429	+	0.0309779i
$863$	12.2604			0.417350			0.208675	−	0.977985i	$-0.433085\pi$
$863$	12.2604			0.417350			0.208675	+	0.977985i	$0.433085\pi$
$864$	−24.1156	+	16.8059i	−0.820428	+	0.571750i
$865$	2.21822			0.0754219
$866$	−0.835992	−	0.425641i	−0.0284082	−	0.0144639i
$867$	14.4608	−	21.9271i	0.491116	−	0.744684i
$868$	1.00331	+	1.37919i	0.0340545	+	0.0468126i
$869$	42.9120	−	24.7752i	1.45569	−	0.840442i
$870$	0.480143	−	0.272899i	0.0162784	−	0.00925214i
$871$	−61.5483	−	35.5349i	−2.08549	−	1.20406i
$872$	0.0620519	+	0.389498i	0.00210134	+	0.0131901i
$873$	−26.9543	−	3.21859i	−0.912265	−	0.108933i
$874$	24.1693	−	1.27397i	0.817540	−	0.0430928i
$875$	4.62851	−	8.01682i	0.156472	−	0.271018i
$876$	50.2273	−	2.30705i	1.69702	−	0.0779481i
$877$	−7.38684	−	12.7944i	−0.249436	−	0.432036i	0.713933	−	0.700214i	$-0.246912\pi$
$877$	−7.38684	−	12.7944i	−0.249436	−	0.432036i	−0.963369	+	0.268178i	$0.913579\pi$
$878$	14.0135	+	21.5646i	0.472932	+	0.727771i
$879$	1.40150	−	23.5573i	0.0472713	−	0.794567i
$880$	13.8276	+	4.47442i	0.466128	+	0.150833i
$881$		−	23.5253i		−	0.792589i	−0.918124	−	0.396294i	$-0.870296\pi$
$881$		−	23.5253i		−	0.792589i	0.918124	−	0.396294i	$-0.129704\pi$
$882$	−3.80649	+	1.87368i	−0.128171	+	0.0630899i
$883$			13.0569i			0.439401i	0.975567	+	0.219700i	$0.0705080\pi$
$883$			13.0569i			0.439401i	−0.975567	+	0.219700i	$0.929492\pi$
$884$	11.8745	+	5.27831i	0.399384	+	0.177529i
$885$	8.90386	−	4.45781i	0.299300	−	0.149848i
$886$	46.5216	−	30.2314i	1.56292	−	1.01565i
$887$	−5.09668	−	8.82771i	−0.171130	−	0.296405i	0.767685	−	0.640827i	$-0.221408\pi$
$887$	−5.09668	−	8.82771i	−0.171130	−	0.296405i	−0.938815	+	0.344422i	$0.888075\pi$
$888$	−14.5359	−	6.57937i	−0.487794	−	0.220789i
$889$	2.85199	−	4.93979i	0.0956527	−	0.165675i
$890$	0.442236	+	8.38993i	0.0148238	+	0.281231i
$891$	8.89058	+	30.2442i	0.297846	+	1.01322i
$892$	3.71037	+	35.0981i	0.124232	+	1.17517i
$893$	18.5414	+	10.7049i	0.620463	+	0.358225i
$894$	8.08902	−	13.7943i	0.270537	−	0.461352i
$895$	6.16095	−	3.55703i	0.205938	−	0.118898i
$896$	−8.80742	−	7.10136i	−0.294235	−	0.237240i
$897$	−12.3804	−	24.7281i	−0.413368	−	0.825646i
$898$	−13.8089	+	27.1217i	−0.460809	+	0.905064i
$899$	0.185351			0.00618179
$900$	11.4951	+	20.5468i	0.383170	+	0.684895i
$901$	18.2092			0.606635
$902$	3.08864	−	6.06633i	0.102841	−	0.201987i
$903$	−13.3834	−	0.796219i	−0.445370	−	0.0264965i
$904$	15.0573	+	18.5599i	0.500799	+	0.617292i
$905$	−18.0288	+	10.4090i	−0.599299	+	0.346006i
$906$	7.96079	+	0.0538281i	0.264479	+	0.00178832i
$907$	25.7954	+	14.8930i	0.856523	+	0.494514i	0.862846	−	0.505466i	$-0.168679\pi$
$907$	25.7954	+	14.8930i	0.856523	+	0.494514i	−0.00632328	+	0.999980i	$0.502013\pi$
$908$	37.8873	−	4.00524i	1.25734	−	0.132919i
$909$	2.32405	−	19.4630i	0.0770840	−	0.645546i
$910$	0.370358	+	7.02628i	0.0122772	+	0.232919i
$911$	−18.7781	+	32.5246i	−0.622146	+	1.07759i	0.366939	+	0.930245i	$0.380406\pi$
$911$	−18.7781	+	32.5246i	−0.622146	+	1.07759i	−0.989085	+	0.147344i	$0.952928\pi$
$912$	27.8114	−	22.2528i	0.920928	−	0.736865i
$913$	21.1965	+	36.7135i	0.701503	+	1.21504i
$914$	25.8660	−	16.8087i	0.855570	−	0.555981i
$915$	−16.9690	−	11.1910i	−0.560979	−	0.369964i
$916$	−5.70162	+	12.8269i	−0.188387	+	0.423812i
$917$			20.4770i			0.676210i
$918$	6.01829	−	7.92972i	0.198633	−	0.261720i
$919$			39.5435i			1.30442i	0.758038	+	0.652210i	$0.226158\pi$
$919$			39.5435i			1.30442i	−0.758038	+	0.652210i	$0.773842\pi$
$920$	−3.49190	+	9.12138i	−0.115125	+	0.300723i
$921$	−41.7415	−	27.5284i	−1.37543	−	0.907091i
$922$	−10.8832	−	16.7476i	−0.358418	−	0.551552i
$923$	30.0939	+	52.1241i	0.990552	+	1.71569i
$924$	−10.2185	+	6.54253i	−0.336165	+	0.215233i
$925$	−6.39003	+	11.0679i	−0.210103	+	0.363909i
$926$	1.76687	−	0.0931323i	0.0580630	−	0.00306052i
$927$	23.0659	+	17.2614i	0.757584	+	0.566939i
$928$	−1.18717	+	0.320021i	−0.0389706	+	0.0105052i
$929$	−27.7644	−	16.0298i	−0.910920	−	0.525920i	−0.0301929	−	0.999544i	$-0.509612\pi$
$929$	−27.7644	−	16.0298i	−0.910920	−	0.525920i	−0.880727	+	0.473624i	$0.842946\pi$
$930$	0.0146507	−	2.16673i	0.000480415	−	0.0710498i
$931$	4.45229	−	2.57053i	0.145918	−	0.0842457i
$932$	32.4893	−	23.6348i	1.06422	−	0.774183i
$933$	−27.6575	−	1.64543i	−0.905467	−	0.0538691i
$934$	12.3259	+	6.27569i	0.403316	+	0.205347i
$935$	−4.92211			−0.160970
$936$	−36.0141	−	18.9540i	−1.17716	−	0.619531i
$937$	−41.0972			−1.34259			−0.671294	−	0.741191i	$-0.734261\pi$
$937$	−41.0972			−1.34259			−0.671294	+	0.741191i	$0.734261\pi$
$938$	−18.6745	−	9.50803i	−0.609744	−	0.310448i
$939$	7.80569	+	15.5908i	0.254729	+	0.508786i
$940$	−6.98665	+	5.08254i	−0.227879	+	0.165774i
$941$	−28.3042	+	16.3415i	−0.922692	+	0.532716i	−0.884493	−	0.466554i	$-0.845495\pi$
$941$	−28.3042	+	16.3415i	−0.922692	+	0.532716i	−0.0381990	+	0.999270i	$0.512162\pi$
$942$	34.3968	+	20.1703i	1.12071	+	0.657185i
$943$	3.96183	+	2.28737i	0.129015	+	0.0744869i
$944$	−21.6784	+	4.63523i	−0.705571	+	0.150864i
$945$	5.30466	+	0.955806i	0.172561	+	0.0310924i
$946$	−38.2897	+	2.01826i	−1.24490	+	0.0656194i
$947$	−5.32129	+	9.21675i	−0.172919	+	0.299504i	−0.939439	−	0.342716i	$-0.888653\pi$
$947$	−5.32129	+	9.21675i	−0.172919	+	0.299504i	0.766520	+	0.642220i	$0.221986\pi$
$948$	43.5192	+	22.5294i	1.41344	+	0.731722i
$949$	34.8078	+	60.2888i	1.12991	+	1.95706i
$950$	−15.5454	−	23.9221i	−0.504361	−	0.776135i
$951$	9.27149	−	4.64186i	0.300649	−	0.150523i
$952$	3.57839	+	1.36990i	0.115976	+	0.0443988i
$953$		−	12.8664i		−	0.416782i	−0.978046	−	0.208391i	$-0.933177\pi$
$953$		−	12.8664i		−	0.416782i	0.978046	−	0.208391i	$-0.0668227\pi$
$954$	−56.9028	−	3.77160i	−1.84230	−	0.122110i
$955$			25.5194i			0.825787i
$956$	−0.916350	+	2.06150i	−0.0296369	+	0.0666737i
$957$	−0.0783118	+	1.31631i	−0.00253146	+	0.0425504i
$958$	−25.8472	+	16.7964i	−0.835084	+	0.542668i
$959$	5.64451	+	9.77658i	0.182271	+	0.315702i
$960$	3.64717	+	13.9031i	0.117712	+	0.448722i
$961$	−15.1364	+	26.2170i	−0.488271	+	0.845710i
$962$	−1.16283	−	22.0607i	−0.0374911	−	0.711266i
$963$	16.1062	+	37.5956i	0.519015	+	1.21150i
$964$	18.5952	−	1.96578i	0.598910	−	0.0633135i
$965$	−1.88159	−	1.08634i	−0.0605706	−	0.0349704i
$966$	−4.02920	−	7.08905i	−0.129637	−	0.228087i
$967$	32.3882	−	18.6994i	1.04154	−	0.601331i	0.121268	−	0.992620i	$-0.461304\pi$
$967$	32.3882	−	18.6994i	1.04154	−	0.601331i	0.920268	+	0.391289i	$0.127971\pi$
$968$	−2.78643	+	2.26059i	−0.0895593	+	0.0726581i
$969$	−6.64125	+	10.0702i	−0.213348	+	0.323501i
$970$	−6.02281	+	11.8293i	−0.193381	+	0.379814i
$971$	45.2767			1.45300			0.726500	−	0.687167i	$-0.241146\pi$
$971$	45.2767			1.45300			0.726500	+	0.687167i	$0.241146\pi$
$972$	−20.4493	+	23.5335i	−0.655913	+	0.754837i
$973$	−10.6876			−0.342630
$974$	−4.24090	+	8.32945i	−0.135887	+	0.266893i
$975$	−17.9466	+	27.2125i	−0.574750	+	0.871499i
$976$	30.3216	+	33.5939i	0.970570	+	1.07531i
$977$	−24.9988	+	14.4331i	−0.799782	+	0.461755i	−0.843395	−	0.537294i	$-0.819447\pi$
$977$	−24.9988	+	14.4331i	−0.799782	+	0.461755i	0.0436127	+	0.999049i	$0.486113\pi$
$978$	7.32938	+	12.8954i	0.234368	+	0.412351i
$979$	−17.3724	−	10.0300i	−0.555225	−	0.320559i
$980$	0.218104	+	2.06315i	0.00696709	+	0.0659048i
$981$	0.164737	+	0.384534i	0.00525964	+	0.0122772i
$982$	−2.32350	−	44.0805i	−0.0741459	−	1.40667i
$983$	−28.6347	+	49.5967i	−0.913304	+	1.58189i	−0.103937	+	0.994584i	$0.533144\pi$
$983$	−28.6347	+	49.5967i	−0.913304	+	1.58189i	−0.809366	+	0.587304i	$0.800189\pi$
$984$	6.69975	−	0.662485i	0.213580	−	0.0211193i
$985$	7.44594	+	12.8968i	0.237248	+	0.410925i
$986$	0.349165	−	0.226900i	0.0111197	−	0.00722598i
$987$	0.428370	−	7.20032i	0.0136352	−	0.229189i
$988$	45.0639	+	20.0312i	1.43367	+	0.637277i
$989$		−	25.7675i		−	0.819358i
$990$	15.3814	+	1.01950i	0.488852	+	0.0324019i
$991$			33.6933i			1.07030i	0.844756	+	0.535152i	$0.179745\pi$
$991$			33.6933i			1.07030i	−0.844756	+	0.535152i	$0.820255\pi$
$992$	−1.24149	+	4.66143i	−0.0394174	+	0.148001i
$993$	13.6649	−	6.84147i	0.433642	−	0.217107i
$994$	9.67017	+	14.8809i	0.306719	+	0.471994i
$995$	−1.58837	−	2.75113i	−0.0503546	−	0.0872167i
$996$	−19.2751	+	37.2330i	−0.610756	+	1.17977i
$997$	−11.9494	+	20.6969i	−0.378440	+	0.655478i	−0.990836	−	0.135074i	$-0.956873\pi$
$997$	−11.9494	+	20.6969i	−0.378440	+	0.655478i	0.612395	+	0.790552i	$0.290206\pi$
$998$	−12.3594	+	0.651470i	−0.391231	+	0.0206219i
$999$	−16.6553	−	3.00099i	−0.526950	−	0.0949470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.5	✓	72
3.2	odd	2		756.2.ba.a.575.32		72
4.3	odd	2	inner	252.2.ba.a.155.7	yes	72
9.4	even	3		756.2.ba.a.71.30		72
9.5	odd	6	inner	252.2.ba.a.239.7	yes	72
12.11	even	2		756.2.ba.a.575.30		72
36.23	even	6	inner	252.2.ba.a.239.5	yes	72
36.31	odd	6		756.2.ba.a.71.32		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.5	✓	72	1.1	even	1	trivial
252.2.ba.a.155.7	yes	72	4.3	odd	2	inner
252.2.ba.a.239.5	yes	72	36.23	even	6	inner
252.2.ba.a.239.7	yes	72	9.5	odd	6	inner
756.2.ba.a.71.30		72	9.4	even	3
756.2.ba.a.71.32		72	36.31	odd	6
756.2.ba.a.575.30		72	12.11	even	2
756.2.ba.a.575.32		72	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26027 - 0.641659i) q^{2} +(0.953579 - 1.44592i) q^{3} +(1.17655 + 1.61732i) q^{4} +(0.898347 - 0.518661i) q^{5} +(-2.12955 + 1.21037i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +O(q^{10})\)	\(q+(-1.26027 - 0.641659i) q^{2} +(0.953579 - 1.44592i) q^{3} +(1.17655 + 1.61732i) q^{4} +(0.898347 - 0.518661i) q^{5} +(-2.12955 + 1.21037i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(-0.444992 - 2.79320i) q^{8} +(-1.18137 - 2.75760i) q^{9} +(-1.46496 + 0.0772186i) q^{10} +(1.75133 - 3.03339i) q^{11} +(3.46045 - 0.158947i) q^{12} +(2.39811 + 4.15365i) q^{13} +(0.770594 + 1.18583i) q^{14} +(0.106702 - 1.79352i) q^{15} +(-1.23148 + 3.80572i) q^{16} -1.35469i q^{17} +(-0.280593 + 4.23335i) q^{18} -5.14106i q^{19} +(1.89579 + 0.842690i) q^{20} +(-1.54878 + 0.775415i) q^{21} +(-4.15354 + 2.69912i) q^{22} +(-1.66445 - 2.88291i) q^{23} +(-4.46309 - 2.02012i) q^{24} +(-1.96198 + 3.39825i) q^{25} +(-0.357033 - 6.77349i) q^{26} +(-5.11380 - 0.921417i) q^{27} +(-0.210257 - 1.98892i) q^{28} +(-0.188235 - 0.108677i) q^{29} +(-1.28530 + 2.19185i) q^{30} +(-0.738509 + 0.426379i) q^{31} +(3.99396 - 4.00603i) q^{32} +(-2.71601 - 5.42485i) q^{33} +(-0.869251 + 1.70727i) q^{34} -1.03732 q^{35} +(3.06999 - 5.15511i) q^{36} +3.25692 q^{37} +(-3.29881 + 6.47911i) q^{38} +(8.29264 + 0.493356i) q^{39} +(-1.84848 - 2.27847i) q^{40} +(-1.19014 + 0.687125i) q^{41} +(2.44943 + 0.0165622i) q^{42} +(6.70351 + 3.87028i) q^{43} +(6.96649 - 0.736458i) q^{44} +(-2.49154 - 1.86455i) q^{45} +(0.247804 + 4.70124i) q^{46} +(-2.08223 + 3.60653i) q^{47} +(4.32845 + 5.40967i) q^{48} +(0.500000 + 0.866025i) q^{49} +(4.65314 - 3.02378i) q^{50} +(-1.95878 - 1.29181i) q^{51} +(-3.89631 + 8.76549i) q^{52} +13.4415i q^{53} +(5.85352 + 4.44255i) q^{54} -3.63338i q^{55} +(-1.01123 + 2.64148i) q^{56} +(-7.43356 - 4.90241i) q^{57} +(0.167492 + 0.257745i) q^{58} +(2.77105 + 4.79960i) q^{59} +(3.02625 - 1.93759i) q^{60} +(5.65678 - 9.79783i) q^{61} +(1.20431 - 0.0634795i) q^{62} +(-0.355700 + 2.97884i) q^{63} +(-7.60396 + 2.48591i) q^{64} +(4.30868 + 2.48761i) q^{65} +(-0.0580118 + 8.57952i) q^{66} +(-12.8327 + 7.40894i) q^{67} +(2.19098 - 1.59386i) q^{68} +(-5.75563 - 0.342421i) q^{69} +(1.30730 + 0.665607i) q^{70} +12.5490 q^{71} +(-7.17683 + 4.52693i) q^{72} +14.5146 q^{73} +(-4.10460 - 2.08984i) q^{74} +(3.04270 + 6.07737i) q^{75} +(8.31476 - 6.04870i) q^{76} +(-3.03339 + 1.75133i) q^{77} +(-10.1344 - 5.94281i) q^{78} +(12.2513 + 7.07327i) q^{79} +(0.867583 + 4.05757i) q^{80} +(-6.20871 + 6.51551i) q^{81} +(1.94079 - 0.102300i) q^{82} +(-6.05157 + 10.4816i) q^{83} +(-3.07631 - 1.59257i) q^{84} +(-0.702626 - 1.21698i) q^{85} +(-5.96482 - 9.17895i) q^{86} +(-0.336635 + 0.168540i) q^{87} +(-9.25219 - 3.54198i) q^{88} -5.72707i q^{89} +(1.94360 + 3.94855i) q^{90} -4.79623i q^{91} +(2.70429 - 6.08382i) q^{92} +(-0.0877175 + 1.47441i) q^{93} +(4.93833 - 3.20911i) q^{94} +(-2.66647 - 4.61846i) q^{95} +(-1.98384 - 9.59502i) q^{96} +(4.52430 - 7.83631i) q^{97} +(-0.0744403 - 1.41225i) q^{98} +(-10.4338 - 1.24589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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