LMFDB - Embedded newform 378.2.ba.a.185.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(47,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("378.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.ba (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.19
Character	$\chi$	$=$	378.185
Dual form			378.2.ba.a.47.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(-0.0904059 + 1.72969i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.22429 - 0.445607i) q^{5} +(0.211325 + 1.71911i) q^{6} +(2.52854 - 0.778769i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98365 - 0.312748i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0904059 + 1.72969i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.22429 - 0.445607i) q^{5} +(0.211325 + 1.71911i) q^{6} +(2.52854 - 0.778769i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98365 - 0.312748i) q^{9} +(1.12832 - 0.651433i) q^{10} +(0.276337 - 0.759229i) q^{11} +(0.506635 + 1.65630i) q^{12} +(0.540542 + 1.48513i) q^{13} +(2.35489 - 1.20601i) q^{14} +(0.660078 + 2.15793i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.739475 + 1.28081i) q^{17} +(-2.99263 + 0.210109i) q^{18} +(0.492317 + 0.284240i) q^{19} +(0.998054 - 0.837467i) q^{20} +(1.11843 + 4.44400i) q^{21} +(0.140300 - 0.795680i) q^{22} +(-6.98333 - 1.23135i) q^{23} +(0.786551 + 1.54316i) q^{24} +(-2.52989 + 2.12283i) q^{25} +(0.790219 + 1.36870i) q^{26} +(0.810697 - 5.13252i) q^{27} +(2.10970 - 1.59662i) q^{28} +(-0.907392 + 2.49304i) q^{29} +(1.02477 + 2.01053i) q^{30} +(1.00327 + 2.75645i) q^{31} +(0.642788 - 0.766044i) q^{32} +(1.28825 + 0.546616i) q^{33} +(0.950650 + 1.13294i) q^{34} +(2.74865 - 2.08018i) q^{35} +(-2.91068 + 0.726582i) q^{36} +2.55189 q^{37} +(0.534196 + 0.194431i) q^{38} +(-2.61768 + 0.800706i) q^{39} +(0.837467 - 0.998054i) q^{40} +(4.20365 - 1.53000i) q^{41} +(1.87313 + 4.18227i) q^{42} +(-1.31851 - 7.47766i) q^{43} -0.807955i q^{44} +(-3.79223 + 0.946640i) q^{45} -7.09106 q^{46} +(-2.29476 - 0.835224i) q^{47} +(1.04257 + 1.38313i) q^{48} +(5.78704 - 3.93830i) q^{49} +(-2.12283 + 2.52989i) q^{50} +(-2.28225 + 1.16327i) q^{51} +(1.01589 + 1.21069i) q^{52} +(-7.73602 - 4.46640i) q^{53} +(-0.0928721 - 5.19532i) q^{54} -1.05266i q^{55} +(1.80040 - 1.93870i) q^{56} +(-0.536155 + 0.825859i) q^{57} +(-0.460695 + 2.61273i) q^{58} +(-10.7915 - 9.05515i) q^{59} +(1.35833 + 1.80204i) q^{60} +(2.35510 - 6.47059i) q^{61} +(1.46668 + 2.54036i) q^{62} +(-7.78785 + 1.53278i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.32356 + 1.57736i) q^{65} +(1.36360 + 0.314609i) q^{66} +(-1.97688 + 11.2115i) q^{67} +(1.13294 + 0.950650i) q^{68} +(2.76119 - 11.9677i) q^{69} +(2.34568 - 2.52587i) q^{70} +(-11.3732 - 6.56633i) q^{71} +(-2.74029 + 1.22098i) q^{72} +11.9595i q^{73} +(2.51312 - 0.443131i) q^{74} +(-3.44312 - 4.56784i) q^{75} +(0.559843 + 0.0987154i) q^{76} +(0.107465 - 2.13495i) q^{77} +(-2.43887 + 1.24310i) q^{78} +(-2.03605 - 11.5470i) q^{79} +(0.651433 - 1.12832i) q^{80} +(8.80438 + 1.86626i) q^{81} +(3.87410 - 2.23671i) q^{82} +(6.99087 + 2.54447i) q^{83} +(2.57092 + 3.79346i) q^{84} +(1.47607 + 1.23857i) q^{85} +(-2.59697 - 7.13510i) q^{86} +(-4.23015 - 1.79489i) q^{87} +(-0.140300 - 0.795680i) q^{88} +(0.961447 - 1.66527i) q^{89} +(-3.57024 + 1.59077i) q^{90} +(2.52335 + 3.33425i) q^{91} +(-6.98333 + 1.23135i) q^{92} +(-4.85851 + 1.48614i) q^{93} +(-2.40493 - 0.424054i) q^{94} +(0.729400 + 0.128613i) q^{95} +(1.26691 + 1.18108i) q^{96} +(15.6731 - 2.76360i) q^{97} +(5.01524 - 4.88338i) q^{98} +(-1.06194 + 2.17885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) $ 144 * q - 18 * q^6 + 24 * q^9	$ 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) $ 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−0.0904059	+	1.72969i	−0.0521958	+	0.998637i
$3$	−0.0904059	+	1.72969i	−0.0521958	+	0.998637i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	1.22429	−	0.445607i	0.547521	−	0.199281i	−0.0534237	−	0.998572i	$-0.517013\pi$
$5$	1.22429	−	0.445607i	0.547521	−	0.199281i	0.600945	+	0.799291i	$0.294791\pi$
$6$	0.211325	+	1.71911i	0.0862731	+	0.701824i
$7$	2.52854	−	0.778769i	0.955699	−	0.294347i
$7$	2.52854	−	0.778769i	0.955699	−	0.294347i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.98365	−	0.312748i	−0.994551	−	0.104249i
$10$	1.12832	−	0.651433i	0.356805	−	0.206001i
$11$	0.276337	−	0.759229i	0.0833187	−	0.228916i	−0.891037	−	0.453932i	$-0.850021\pi$
$11$	0.276337	−	0.759229i	0.0833187	−	0.228916i	0.974355	+	0.225015i	$0.0722432\pi$
$12$	0.506635	+	1.65630i	0.146253	+	0.478132i
$13$	0.540542	+	1.48513i	0.149919	+	0.411900i	0.991806	−	0.127755i	$-0.0407770\pi$
$13$	0.540542	+	1.48513i	0.149919	+	0.411900i	−0.841886	+	0.539655i	$0.818555\pi$
$14$	2.35489	−	1.20601i	0.629372	−	0.322321i
$15$	0.660078	+	2.15793i	0.170431	+	0.557176i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.739475	+	1.28081i	0.179349	+	0.310641i	0.941658	−	0.336572i	$-0.109268\pi$
$17$	0.739475	+	1.28081i	0.179349	+	0.310641i	−0.762309	+	0.647213i	$0.775934\pi$
$18$	−2.99263	+	0.210109i	−0.705370	+	0.0495232i
$19$	0.492317	+	0.284240i	0.112945	+	0.0652090i	0.555408	−	0.831578i	$-0.312562\pi$
$19$	0.492317	+	0.284240i	0.112945	+	0.0652090i	−0.442463	+	0.896787i	$0.645895\pi$
$20$	0.998054	−	0.837467i	0.223172	−	0.187263i
$21$	1.11843	+	4.44400i	0.244062	+	0.969760i
$22$	0.140300	−	0.795680i	0.0299120	−	0.169640i
$23$	−6.98333	−	1.23135i	−1.45612	−	0.256754i	−0.611130	−	0.791530i	$-0.709285\pi$
$23$	−6.98333	−	1.23135i	−1.45612	−	0.256754i	−0.844994	+	0.534776i	$0.820396\pi$
$24$	0.786551	+	1.54316i	0.160554	+	0.314996i
$25$	−2.52989	+	2.12283i	−0.505978	+	0.424566i
$26$	0.790219	+	1.36870i	0.154975	+	0.268424i
$27$	0.810697	−	5.13252i	0.156019	−	0.987754i
$28$	2.10970	−	1.59662i	0.398695	−	0.301732i
$29$	−0.907392	+	2.49304i	−0.168499	+	0.462946i	−0.994987	−	0.100008i	$-0.968113\pi$
$29$	−0.907392	+	2.49304i	−0.168499	+	0.462946i	0.826488	+	0.562954i	$0.190335\pi$
$30$	1.02477	+	2.01053i	0.187097	+	0.367071i
$31$	1.00327	+	2.75645i	0.180192	+	0.495073i	0.996599	−	0.0824036i	$-0.0262596\pi$
$31$	1.00327	+	2.75645i	0.180192	+	0.495073i	−0.816407	+	0.577477i	$0.804037\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	1.28825	+	0.546616i	0.224255	+	0.0951536i
$34$	0.950650	+	1.13294i	0.163035	+	0.194298i
$35$	2.74865	−	2.08018i	0.464607	−	0.351614i
$36$	−2.91068	+	0.726582i	−0.485114	+	0.121097i
$37$	2.55189			0.419528			0.209764	−	0.977752i	$-0.432730\pi$
$37$	2.55189			0.419528			0.209764	+	0.977752i	$0.432730\pi$
$38$	0.534196	+	0.194431i	0.0866580	+	0.0315409i
$39$	−2.61768	+	0.800706i	−0.419164	+	0.128215i
$40$	0.837467	−	0.998054i	0.132415	−	0.157806i
$41$	4.20365	−	1.53000i	0.656499	−	0.238946i	0.00777516	−	0.999970i	$-0.497525\pi$
$41$	4.20365	−	1.53000i	0.656499	−	0.238946i	0.648724	+	0.761024i	$0.275303\pi$
$42$	1.87313	+	4.18227i	0.289031	+	0.645338i
$43$	−1.31851	−	7.47766i	−0.201071	−	1.14033i	−0.903503	−	0.428582i	$-0.859013\pi$
$43$	−1.31851	−	7.47766i	−0.201071	−	1.14033i	0.702432	−	0.711751i	$-0.252098\pi$
$44$		−	0.807955i		−	0.121804i
$45$	−3.79223	+	0.946640i	−0.565313	+	0.141117i
$46$	−7.09106			−1.04552
$47$	−2.29476	−	0.835224i	−0.334725	−	0.121830i	0.169189	−	0.985584i	$-0.445885\pi$
$47$	−2.29476	−	0.835224i	−0.334725	−	0.121830i	−0.503914	+	0.863754i	$0.668107\pi$
$48$	1.04257	+	1.38313i	0.150482	+	0.199638i
$49$	5.78704	−	3.93830i	0.826720	−	0.562614i
$50$	−2.12283	+	2.52989i	−0.300214	+	0.357781i
$51$	−2.28225	+	1.16327i	−0.319579	+	0.162890i
$52$	1.01589	+	1.21069i	0.140878	+	0.167892i
$53$	−7.73602	−	4.46640i	−1.06262	−	0.613507i	−0.136468	−	0.990645i	$-0.543575\pi$
$53$	−7.73602	−	4.46640i	−1.06262	−	0.613507i	−0.926157	+	0.377138i	$0.876908\pi$
$54$	−0.0928721	−	5.19532i	−0.0126383	−	0.706994i
$55$		−	1.05266i		−	0.141940i
$56$	1.80040	−	1.93870i	0.240588	−	0.259070i
$57$	−0.536155	+	0.825859i	−0.0710154	+	0.109388i
$58$	−0.460695	+	2.61273i	−0.0604922	+	0.343069i
$59$	−10.7915	−	9.05515i	−1.40493	−	1.17888i	−0.958859	−	0.283884i	$-0.908377\pi$
$59$	−10.7915	−	9.05515i	−1.40493	−	1.17888i	−0.446075	−	0.894995i	$-0.647179\pi$
$60$	1.35833	+	1.80204i	0.175359	+	0.232642i
$61$	2.35510	−	6.47059i	0.301540	−	0.828475i	−0.692693	−	0.721233i	$-0.743576\pi$
$61$	2.35510	−	6.47059i	0.301540	−	0.828475i	0.994233	−	0.107242i	$-0.0342019\pi$
$62$	1.46668	+	2.54036i	0.186268	+	0.322626i
$63$	−7.78785	+	1.53278i	−0.981177	+	0.193112i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	1.32356	+	1.57736i	0.164168	+	0.195648i
$66$	1.36360	+	0.314609i	0.167847	+	0.0387258i
$67$	−1.97688	+	11.2115i	−0.241515	+	1.36970i	0.586934	+	0.809635i	$0.300335\pi$
$67$	−1.97688	+	11.2115i	−0.241515	+	1.36970i	−0.828449	+	0.560064i	$0.810776\pi$
$68$	1.13294	+	0.950650i	0.137389	+	0.115283i
$69$	2.76119	−	11.9677i	0.332408	−	1.44074i
$70$	2.34568	−	2.52587i	0.280362	−	0.301900i
$71$	−11.3732	−	6.56633i	−1.34975	−	0.779280i	−0.361538	−	0.932357i	$-0.617748\pi$
$71$	−11.3732	−	6.56633i	−1.34975	−	0.779280i	−0.988214	+	0.153078i	$0.951081\pi$
$72$	−2.74029	+	1.22098i	−0.322947	+	0.143894i
$73$			11.9595i			1.39975i	0.714266	+	0.699875i	$0.246761\pi$
$73$			11.9595i			1.39975i	−0.714266	+	0.699875i	$0.753239\pi$
$74$	2.51312	−	0.443131i	0.292144	−	0.0515129i
$75$	−3.44312	−	4.56784i	−0.397577	−	0.527449i
$76$	0.559843	+	0.0987154i	0.0642183	+	0.0113234i
$77$	0.107465	−	2.13495i	0.0122468	−	0.243300i
$78$	−2.43887	+	1.24310i	−0.276147	+	0.140753i
$79$	−2.03605	−	11.5470i	−0.229074	−	1.29914i	−0.854742	−	0.519053i	$-0.826285\pi$
$79$	−2.03605	−	11.5470i	−0.229074	−	1.29914i	0.625668	−	0.780089i	$-0.284826\pi$
$80$	0.651433	−	1.12832i	0.0728325	−	0.126150i
$81$	8.80438	+	1.86626i	0.978264	+	0.207363i
$82$	3.87410	−	2.23671i	0.427823	−	0.247004i
$83$	6.99087	+	2.54447i	0.767348	+	0.279292i	0.695887	−	0.718152i	$-0.255012\pi$
$83$	6.99087	+	2.54447i	0.767348	+	0.279292i	0.0714611	+	0.997443i	$0.477234\pi$
$84$	2.57092	+	3.79346i	0.280510	+	0.413901i
$85$	1.47607	+	1.23857i	0.160102	+	0.134342i
$86$	−2.59697	−	7.13510i	−0.280038	−	0.769398i
$87$	−4.23015	−	1.79489i	−0.453520	−	0.192433i
$88$	−0.140300	−	0.795680i	−0.0149560	−	0.0848198i
$89$	0.961447	−	1.66527i	0.101913	−	0.176519i	−0.810560	−	0.585656i	$-0.800837\pi$
$89$	0.961447	−	1.66527i	0.101913	−	0.176519i	0.912473	+	0.409137i	$0.134170\pi$
$90$	−3.57024	+	1.59077i	−0.376336	+	0.167682i
$91$	2.52335	+	3.33425i	0.264519	+	0.349524i
$92$	−6.98333	+	1.23135i	−0.728062	+	0.128377i
$93$	−4.85851	+	1.48614i	−0.503804	+	0.154106i
$94$	−2.40493	−	0.424054i	−0.248050	−	0.0437379i
$95$	0.729400	+	0.128613i	0.0748349	+	0.0131954i
$96$	1.26691	+	1.18108i	0.129303	+	0.120543i
$97$	15.6731	−	2.76360i	1.59137	−	0.280601i	0.693363	−	0.720589i	$-0.256128\pi$
$97$	15.6731	−	2.76360i	1.59137	−	0.280601i	0.898004	+	0.439988i	$0.145017\pi$
$98$	5.01524	−	4.88338i	0.506616	−	0.493295i
$99$	−1.06194	+	2.17885i	−0.106729	+	0.218983i
$100$	−1.65127	+	2.86008i	−0.165127	+	0.286008i
$101$	0.414354	+	2.34992i	0.0412298	+	0.233826i	0.998458	−	0.0555073i	$-0.0176776\pi$
$101$	0.414354	+	2.34992i	0.0412298	+	0.233826i	−0.957228	+	0.289333i	$0.906566\pi$
$102$	−2.04558	+	1.54191i	−0.202543	+	0.152671i
$103$	1.09854	+	3.01820i	0.108242	+	0.297393i	0.981974	−	0.189015i	$-0.0605294\pi$
$103$	1.09854	+	3.01820i	0.108242	+	0.297393i	−0.873732	+	0.486407i	$0.838307\pi$
$104$	1.21069	+	1.01589i	0.118718	+	0.0996158i
$105$	3.34957	+	4.94238i	0.326884	+	0.482327i
$106$	−8.39408	−	3.05519i	−0.815305	−	0.296747i
$107$	−5.18946	+	2.99614i	−0.501684	+	0.289648i	−0.729409	−	0.684078i	$-0.760205\pi$
$107$	−5.18946	+	2.99614i	−0.501684	+	0.289648i	0.227725	+	0.973726i	$0.426871\pi$
$108$	−0.993619	−	5.10027i	−0.0956111	−	0.490773i
$109$	−2.52779	+	4.37826i	−0.242118	+	0.419361i	−0.961317	−	0.275443i	$-0.911176\pi$
$109$	−2.52779	+	4.37826i	−0.242118	+	0.419361i	0.719199	+	0.694804i	$0.244509\pi$
$110$	−0.182792	−	1.03667i	−0.0174285	−	0.0988422i
$111$	−0.230706	+	4.41398i	−0.0218976	+	0.418956i
$112$	1.43639	−	2.22189i	0.135726	−	0.209949i
$113$	−11.2304	−	1.98023i	−1.05647	−	0.186284i	−0.381681	−	0.924294i	$-0.624655\pi$
$113$	−11.2304	−	1.98023i	−1.05647	−	0.186284i	−0.674790	+	0.738010i	$0.735766\pi$
$114$	−0.384600	+	0.906415i	−0.0360211	+	0.0848935i
$115$	−9.09834	+	1.60428i	−0.848425	+	0.149600i
$116$			2.65304i			0.246328i
$117$	−1.14832	−	4.60016i	−0.106162	−	0.425285i
$118$	−12.2000	−	7.04365i	−1.12310	−	0.648421i
$119$	2.86724	+	2.66269i	0.262840	+	0.244089i
$120$	1.65061	+	1.53879i	0.150680	+	0.140471i
$121$	7.92642	+	6.65106i	0.720584	+	0.604642i
$122$	1.19572	−	6.78125i	0.108255	−	0.613946i
$123$	2.26640	+	7.40933i	0.204354	+	0.668077i
$124$	1.88552	+	2.24708i	0.169325	+	0.201794i
$125$	−5.40855	+	9.36788i	−0.483755	+	0.837889i
$126$	−7.40337	+	2.86184i	−0.659545	+	0.254953i
$127$	2.09554	+	3.62958i	0.185949	+	0.322073i	0.943896	−	0.330243i	$-0.107131\pi$
$127$	2.09554	+	3.62958i	0.185949	+	0.322073i	−0.757947	+	0.652316i	$0.773797\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	13.0532	−	1.60460i	1.14927	−	0.141277i
$130$	1.57736	+	1.32356i	0.138344	+	0.116084i
$131$	1.04627	−	5.93368i	0.0914129	−	0.518428i	−0.904375	−	0.426739i	$-0.859662\pi$
$131$	1.04627	−	5.93368i	0.0914129	−	0.518428i	0.995788	−	0.0916891i	$-0.0292266\pi$
$132$	1.39751	+	0.0730439i	0.121638	+	0.00635765i
$133$	1.46620	+	0.335310i	0.127136	+	0.0290750i
$134$			11.3844i			0.983464i
$135$	−1.29455	−	6.64497i	−0.111417	−	0.571908i
$136$	1.28081	+	0.739475i	0.109828	+	0.0634094i
$137$	6.77641	+	8.07582i	0.578948	+	0.689964i	0.973442	−	0.228935i	$-0.0735244\pi$
$137$	6.77641	+	8.07582i	0.578948	+	0.689964i	−0.394493	+	0.918899i	$0.629080\pi$
$138$	0.641073	−	12.2653i	0.0545718	−	1.04409i
$139$	−6.86868	+	8.18577i	−0.582593	+	0.694308i	−0.974164	−	0.225840i	$-0.927487\pi$
$139$	−6.86868	+	8.18577i	−0.582593	+	0.694308i	0.391571	+	0.920148i	$0.371932\pi$
$140$	1.87143	−	2.89482i	0.158164	−	0.244657i
$141$	1.65214	−	3.89371i	0.139135	−	0.327910i
$142$	−12.3407	−	4.49163i	−1.03560	−	0.376929i
$143$	1.27692			0.106782
$144$	−2.48664	+	1.67828i	−0.207220	+	0.139856i
$145$			3.45655i			0.287051i
$146$	2.07674	+	11.7778i	0.171872	+	0.974735i
$147$	6.28885	+	10.3658i	0.518696	+	0.854959i
$148$	2.39799	−	0.872797i	0.197114	−	0.0717435i
$149$	−1.99736	+	2.38036i	−0.163630	+	0.195007i	−0.841629	−	0.540056i	$-0.818403\pi$
$149$	−1.99736	+	2.38036i	−0.163630	+	0.195007i	0.677999	+	0.735063i	$0.262847\pi$
$150$	−4.18401	−	3.90056i	−0.341623	−	0.318479i
$151$	22.6918	+	8.25914i	1.84663	+	0.672119i	0.986891	+	0.161388i	$0.0515970\pi$
$151$	22.6918	+	8.25914i	1.84663	+	0.672119i	0.859740	+	0.510731i	$0.170625\pi$
$152$	0.568479			0.0461097
$153$	−1.80577	−	4.05276i	−0.145988	−	0.327646i
$154$	−0.264897	−	2.12117i	−0.0213460	−	0.170929i
$155$	2.45659	+	2.92764i	0.197318	+	0.235154i
$156$	−2.18595	+	1.64772i	−0.175016	+	0.131923i
$157$	−1.81925	+	2.16810i	−0.145192	+	0.173033i	−0.833739	−	0.552158i	$-0.813804\pi$
$157$	−1.81925	+	2.16810i	−0.145192	+	0.173033i	0.688547	+	0.725192i	$0.258249\pi$
$158$	−4.01024	−	11.0180i	−0.319038	−	0.876549i
$159$	8.42486	−	12.9771i	0.668135	−	1.02915i
$160$	0.445607	−	1.22429i	0.0352283	−	0.0967890i
$161$	−18.6166	+	2.32488i	−1.46719	+	0.183226i
$162$	8.99469	+	0.309048i	0.706690	+	0.0242811i
$163$	−5.30279	−	9.18470i	−0.415347	−	0.719401i	0.580118	−	0.814532i	$-0.303006\pi$
$163$	−5.30279	−	9.18470i	−0.415347	−	0.719401i	−0.995465	+	0.0951309i	$0.969673\pi$
$164$	3.42684	−	2.87546i	0.267592	−	0.224536i
$165$	1.82077	+	0.0951664i	0.141747	+	0.00740870i
$166$	7.32651	+	1.29186i	0.568647	+	0.100268i
$167$	−1.93714	+	10.9861i	−0.149900	+	0.850127i	0.813401	+	0.581704i	$0.197614\pi$
$167$	−1.93714	+	10.9861i	−0.149900	+	0.850127i	−0.963301	+	0.268423i	$0.913497\pi$
$168$	3.19059	+	3.28940i	0.246159	+	0.253782i
$169$	8.04516	−	6.75069i	0.618859	−	0.519284i
$170$	1.66872	+	0.963437i	0.127985	+	0.0738922i
$171$	−1.38001	−	1.00204i	−0.105532	−	0.0766282i
$172$	−3.79651	−	6.57575i	−0.289481	−	0.501396i
$173$	14.3245	−	12.0197i	1.08907	−	0.913841i	0.0924314	−	0.995719i	$-0.470536\pi$
$173$	14.3245	−	12.0197i	1.08907	−	0.913841i	0.996642	+	0.0818777i	$0.0260917\pi$
$174$	−4.47757	−	1.03307i	−0.339443	−	0.0783165i
$175$	−4.74374	+	7.33786i	−0.358593	+	0.554690i
$176$	−0.276337	−	0.759229i	−0.0208297	−	0.0572291i
$177$	16.6382	−	17.8473i	1.25060	−	1.34149i
$178$	0.657668	−	1.80693i	0.0492943	−	0.135435i
$179$	−0.420042	+	0.242511i	−0.0313954	+	0.0181261i	−0.515616	−	0.856820i	$-0.672437\pi$
$179$	−0.420042	+	0.242511i	−0.0313954	+	0.0181261i	0.484220	+	0.874946i	$0.339103\pi$
$180$	−3.23976	+	2.18657i	−0.241478	+	0.162977i
$181$	−12.4653	+	7.19684i	−0.926538	+	0.534937i	−0.885715	−	0.464229i	$-0.846331\pi$
$181$	−12.4653	+	7.19684i	−0.926538	+	0.534937i	−0.0408233	+	0.999166i	$0.512998\pi$
$182$	3.06400	+	2.84542i	0.227119	+	0.210916i
$183$	10.9792	+	4.65858i	0.811606	+	0.344372i
$184$	−6.66341	+	2.42528i	−0.491233	+	0.178794i
$185$	3.12426	−	1.13714i	0.229700	−	0.0836041i
$186$	−4.52663	+	2.30723i	−0.331909	+	0.169175i
$187$	1.17677	−	0.207496i	0.0860540	−	0.0151736i
$188$	−2.44203			−0.178103
$189$	−1.94717	−	13.6091i	−0.141636	−	0.989919i
$190$	0.740652			0.0537326
$191$	8.59749	−	1.51597i	0.622093	−	0.109692i	0.146287	−	0.989242i	$-0.453268\pi$
$191$	8.59749	−	1.51597i	0.622093	−	0.109692i	0.475806	+	0.879550i	$0.342157\pi$
$192$	1.45275	+	0.943139i	0.104843	+	0.0680652i
$193$	−6.99113	+	2.54456i	−0.503233	+	0.183162i	−0.581147	−	0.813798i	$-0.697396\pi$
$193$	−6.99113	+	2.54456i	−0.503233	+	0.183162i	0.0779148	+	0.996960i	$0.475174\pi$
$194$	14.9551	−	5.44322i	1.07372	−	0.390801i
$195$	−2.84801	+	2.14675i	−0.203950	+	0.153732i
$196$	4.09106	−	5.68007i	0.292219	−	0.405720i
$197$	11.3911	−	6.57665i	0.811582	−	0.468567i	−0.0359233	−	0.999355i	$-0.511437\pi$
$197$	11.3911	−	6.57665i	0.811582	−	0.468567i	0.847505	+	0.530788i	$0.178104\pi$
$198$	−0.667454	+	2.33016i	−0.0474339	+	0.165597i
$199$	−7.63907	+	4.41042i	−0.541520	+	0.312647i	−0.745695	−	0.666288i	$-0.767882\pi$
$199$	−7.63907	+	4.41042i	−0.541520	+	0.312647i	0.204175	+	0.978934i	$0.434549\pi$
$200$	−1.12953	+	3.10337i	−0.0798702	+	0.219441i
$201$	−19.2136	−	4.43298i	−1.35523	−	0.312678i
$202$	0.816119	+	2.24227i	0.0574219	+	0.157765i
$203$	−0.352876	+	7.01040i	−0.0247671	+	0.492034i
$204$	−1.74675	+	1.87369i	−0.122297	+	0.131185i
$205$	4.46472	−	3.74635i	0.311830	−	0.261656i
$206$	1.60595	+	2.78159i	0.111892	+	0.193803i
$207$	20.4507	+	5.85794i	1.42142	+	0.407155i
$208$	1.36870	+	0.790219i	0.0949023	+	0.0547918i
$209$	0.351848	−	0.295236i	0.0243379	−	0.0204219i
$210$	4.15691	+	4.28565i	0.286854	+	0.295738i
$211$	2.05923	−	11.6785i	0.141763	−	0.803979i	−0.828146	−	0.560512i	$-0.810604\pi$
$211$	2.05923	−	11.6785i	0.141763	−	0.803979i	0.969909	−	0.243467i	$-0.0782847\pi$
$212$	−8.79708	−	1.55116i	−0.604186	−	0.106534i
$213$	12.3859	−	19.0785i	0.848669	−	1.30724i
$214$	−4.59035	+	3.85176i	−0.313790	+	0.263301i
$215$	−4.94635	−	8.56732i	−0.337338	−	0.584287i
$216$	−1.86418	−	4.85024i	−0.126841	−	0.330017i
$217$	4.68344	+	6.18849i	0.317932	+	0.420102i
$218$	−1.72911	+	4.75069i	−0.117110	+	0.321757i
$219$	−20.6862	−	1.08121i	−1.39784	−	0.0730611i
$220$	−0.360030	−	0.989175i	−0.0242732	−	0.0666901i
$221$	−1.50244	+	1.79054i	−0.101065	+	0.120445i
$222$	0.539278	+	4.38698i	0.0361940	+	0.294435i
$223$	−13.9462	−	16.6205i	−0.933908	−	1.11299i	−0.993393	−	0.114760i	$-0.963390\pi$
$223$	−13.9462	−	16.6205i	−0.933908	−	1.11299i	0.0594848	−	0.998229i	$-0.481054\pi$
$224$	1.02874	−	2.43756i	0.0687358	−	0.162866i
$225$	8.21223	−	5.54257i	0.547482	−	0.369505i
$226$	−11.4037			−0.758561
$227$	16.1399	+	5.87446i	1.07125	+	0.389902i	0.816643	−	0.577144i	$-0.195833\pi$
$227$	16.1399	+	5.87446i	1.07125	+	0.389902i	0.254604	+	0.967046i	$0.418055\pi$
$228$	−0.221360	+	0.959430i	−0.0146599	+	0.0635398i
$229$	1.54466	−	1.84086i	0.102074	−	0.121647i	−0.712589	−	0.701582i	$-0.752477\pi$
$229$	1.54466	−	1.84086i	0.102074	−	0.121647i	0.814663	+	0.579935i	$0.196922\pi$
$230$	−8.68154	+	3.15982i	−0.572444	+	0.208352i
$231$	3.68308	+	0.378892i	0.242329	+	0.0249293i
$232$	0.460695	+	2.61273i	0.0302461	+	0.171534i
$233$			18.0270i			1.18099i	0.807042	+	0.590493i	$0.201067\pi$
$233$			18.0270i			1.18099i	−0.807042	+	0.590493i	$0.798933\pi$
$234$	−1.92968	−	4.33087i	−0.126147	−	0.283118i
$235$	−3.18164			−0.207547
$236$	−13.2377	−	4.81814i	−0.861703	−	0.313634i
$237$	20.1569	−	2.47782i	1.30933	−	0.160952i
$238$	3.28606	+	2.12435i	0.213003	+	0.137701i
$239$	−6.82430	+	8.13288i	−0.441427	+	0.526072i	−0.940183	−	0.340670i	$-0.889346\pi$
$239$	−6.82430	+	8.13288i	−0.441427	+	0.526072i	0.498756	+	0.866743i	$0.333791\pi$
$240$	1.89274	+	1.22878i	0.122176	+	0.0793177i
$241$	13.1348	+	15.6534i	0.846086	+	1.00833i	0.999796	+	0.0202103i	$0.00643359\pi$
$241$	13.1348	+	15.6534i	0.846086	+	1.00833i	−0.153709	+	0.988116i	$0.549122\pi$
$242$	8.96095	+	5.17360i	0.576031	+	0.332572i
$243$	−4.02403	+	15.0601i	−0.258141	+	0.966107i
$244$		−	6.88586i		−	0.440822i
$245$	5.33011	−	7.40038i	0.340528	−	0.472793i
$246$	3.51858	+	6.90321i	0.224336	+	0.440132i
$247$	−0.156014	+	0.884797i	−0.00992690	+	0.0562983i
$248$	2.24708	+	1.88552i	0.142690	+	0.119731i
$249$	−5.03316	+	11.8620i	−0.318963	+	0.751724i
$250$	−3.69967	+	10.1647i	−0.233987	+	0.642875i
$251$	12.1854	+	21.1057i	0.769136	+	1.33218i	0.938032	+	0.346548i	$0.112646\pi$
$251$	12.1854	+	21.1057i	0.769136	+	1.33218i	−0.168896	+	0.985634i	$0.554020\pi$
$252$	−6.79394	+	4.10394i	−0.427978	+	0.258524i
$253$	−2.86463	+	4.96168i	−0.180098	+	0.311938i
$254$	2.69397	+	3.21055i	0.169035	+	0.201448i
$255$	−2.27579	+	2.44117i	−0.142515	+	0.152872i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	12.8891	+	10.8153i	0.804003	+	0.674638i	0.949168	−	0.314769i	$-0.101927\pi$
$257$	12.8891	+	10.8153i	0.804003	+	0.674638i	−0.145166	+	0.989407i	$0.546372\pi$
$258$	12.5763	−	3.84689i	0.782966	−	0.239497i
$259$	6.45256	−	1.98733i	0.400942	−	0.123487i
$260$	1.78323	+	1.02955i	0.110591	+	0.0638500i
$261$	3.48704	−	7.15458i	0.215842	−	0.442858i
$262$		−	6.02522i		−	0.372239i
$263$	30.0944	−	5.30645i	1.85570	−	0.327210i	0.869651	−	0.493666i	$-0.164344\pi$
$263$	30.0944	−	5.30645i	1.85570	−	0.327210i	0.986049	+	0.166456i	$0.0532325\pi$
$264$	1.38896	−	0.170741i	0.0854848	−	0.0105084i
$265$	−11.4614	−	2.02096i	−0.704070	−	0.124147i
$266$	1.50215	+	0.0756125i	0.0921029	+	0.00463610i
$267$	2.79349	+	1.81356i	0.170959	+	0.110988i
$268$	1.97688	+	11.2115i	0.120757	+	0.684849i
$269$	−13.7756	+	23.8600i	−0.839913	+	1.45477i	0.0500543	+	0.998746i	$0.484061\pi$
$269$	−13.7756	+	23.8600i	−0.839913	+	1.45477i	−0.889967	+	0.456025i	$0.849273\pi$
$270$	−2.42877	−	6.31922i	−0.147810	−	0.384575i
$271$	−6.29412	+	3.63391i	−0.382340	+	0.220744i	−0.678836	−	0.734290i	$-0.737515\pi$
$271$	−6.29412	+	3.63391i	−0.382340	+	0.220744i	0.296496	+	0.955034i	$0.404182\pi$
$272$	1.38976	+	0.505830i	0.0842664	+	0.0306705i
$273$	−5.99534	+	4.06318i	−0.362854	+	0.245915i
$274$	8.07582	+	6.77641i	0.487878	+	0.409378i
$275$	0.912613	+	2.50738i	0.0550326	+	0.151201i
$276$	−1.49852	−	12.1903i	−0.0902002	−	0.733770i
$277$	−2.01612	−	11.4340i	−0.121137	−	0.687000i	−0.983528	−	0.180758i	$-0.942145\pi$
$277$	−2.01612	−	11.4340i	−0.121137	−	0.687000i	0.862391	−	0.506243i	$-0.168966\pi$
$278$	−5.34288	+	9.25414i	−0.320445	+	0.555027i
$279$	−2.13132	−	8.53806i	−0.127599	−	0.511161i
$280$	1.34032	−	3.17581i	0.0800992	−	0.189791i
$281$	−24.5862	+	4.33522i	−1.46669	+	0.258617i	−0.849247	−	0.527996i	$-0.822944\pi$
$281$	−24.5862	+	4.33522i	−1.46669	+	0.258617i	−0.617446	+	0.786613i	$0.711832\pi$
$282$	0.950903	−	4.12145i	0.0566254	−	0.245429i
$283$	−17.3806	−	3.06467i	−1.03317	−	0.182176i	−0.368746	−	0.929530i	$-0.620213\pi$
$283$	−17.3806	−	3.06467i	−1.03317	−	0.182176i	−0.664426	+	0.747354i	$0.731324\pi$
$284$	−12.9331	−	2.28046i	−0.767441	−	0.135320i
$285$	−0.288403	+	1.25001i	−0.0170835	+	0.0740441i
$286$	1.25752	−	0.221735i	0.0743589	−	0.0131115i
$287$	9.43758	−	7.14234i	0.557083	−	0.421599i
$288$	−2.15743	+	2.08458i	−0.127128	+	0.122835i
$289$	7.40635	−	12.8282i	0.435668	−	0.754599i
$290$	0.600224	+	3.40404i	0.0352464	+	0.199892i
$291$	3.36322	+	27.3595i	0.197156	+	1.60384i
$292$	4.09038	+	11.2382i	0.239371	+	0.657667i
$293$	9.47733	+	7.95242i	0.553672	+	0.464586i	0.876182	−	0.481980i	$-0.160082\pi$
$293$	9.47733	+	7.95242i	0.553672	+	0.464586i	−0.322511	+	0.946566i	$0.604527\pi$
$294$	7.99332	+	9.11630i	0.466180	+	0.531673i
$295$	−17.2470	−	6.27740i	−1.00416	−	0.365484i
$296$	2.21000	−	1.27594i	0.128454	−	0.0741628i
$297$	−3.67273	−	2.03381i	−0.213114	−	0.118014i
$298$	−1.55367	+	2.69104i	−0.0900017	+	0.155887i
$299$	−1.94607	−	11.0367i	−0.112544	−	0.638270i
$300$	−4.79777	−	3.11475i	−0.276999	−	0.179830i
$301$	−9.15729	−	17.8808i	−0.527817	−	1.03063i
$302$	23.7812	+	4.19327i	1.36846	+	0.241296i
$303$	−4.10209	+	0.504258i	−0.235659	+	0.0289689i
$304$	0.559843	−	0.0987154i	0.0321092	−	0.00566171i
$305$		−	8.97136i		−	0.513699i
$306$	−2.48209	−	3.67762i	−0.141891	−	0.210235i
$307$	−23.4925	−	13.5634i	−1.34079	−	0.774103i	−0.353863	−	0.935297i	$-0.615132\pi$
$307$	−23.4925	−	13.5634i	−1.34079	−	0.774103i	−0.986923	+	0.161194i	$0.948465\pi$
$308$	−0.629210	−	2.04295i	−0.0358526	−	0.116408i
$309$	−5.31987	+	1.62726i	−0.302637	+	0.0925718i
$310$	2.92764	+	2.45659i	0.166279	+	0.139525i
$311$	2.15340	−	12.2126i	0.122108	−	0.692510i	−0.860875	−	0.508816i	$-0.830083\pi$
$311$	2.15340	−	12.2126i	0.122108	−	0.692510i	0.982983	−	0.183694i	$-0.0588056\pi$
$312$	−1.86662	+	2.00227i	−0.105677	+	0.113356i
$313$	9.40818	+	11.2122i	0.531782	+	0.633753i	0.963324	−	0.268340i	$-0.0864750\pi$
$313$	9.40818	+	11.2122i	0.531782	+	0.633753i	−0.431543	+	0.902092i	$0.642031\pi$
$314$	−1.41513	+	2.45107i	−0.0798602	+	0.138322i
$315$	−8.85160	+	5.34689i	−0.498731	+	0.301263i
$316$	−5.86258	−	10.1543i	−0.329796	−	0.571223i
$317$	2.34792	−	6.45086i	0.131872	−	0.362316i	−0.856129	−	0.516762i	$-0.827137\pi$
$317$	2.34792	−	6.45086i	0.131872	−	0.362316i	0.988001	+	0.154446i	$0.0493593\pi$
$318$	6.04341	−	14.2429i	0.338898	−	0.798705i
$319$	1.64204	+	1.37784i	0.0919368	+	0.0771441i
$320$	0.226240	−	1.28307i	0.0126472	−	0.0717260i
$321$	−4.71323	−	9.24703i	−0.263067	−	0.516119i
$322$	−17.9300	+	5.52229i	−0.999201	+	0.307745i
$323$			0.840752i			0.0467807i
$324$	8.91171	−	1.25756i	0.495095	−	0.0698644i
$325$	−4.52018	−	2.60973i	−0.250735	−	0.144762i
$326$	−6.81714	−	8.12435i	−0.377566	−	0.449966i
$327$	−7.34450	−	4.76811i	−0.406152	−	0.263677i
$328$	2.87546	−	3.42684i	0.158771	−	0.189216i
$329$	−6.45284	−	0.324811i	−0.355757	−	0.0179074i
$330$	1.80964	−	0.222453i	0.0996171	−	0.0122456i
$331$	−32.8233	−	11.9467i	−1.80413	−	0.656650i	−0.997880	−	0.0650742i	$-0.979272\pi$
$331$	−32.8233	−	11.9467i	−1.80413	−	0.656650i	−0.806250	−	0.591575i	$-0.798506\pi$
$332$	7.43953			0.408297
$333$	−7.61395	−	0.798099i	−0.417242	−	0.0437355i
$334$			11.1555i			0.610404i
$335$	2.57562	+	14.6071i	0.140721	+	0.798068i
$336$	3.71332	+	2.68538i	0.202578	+	0.146500i
$337$	19.6162	−	7.13972i	1.06856	−	0.388926i	0.252925	−	0.967486i	$-0.418608\pi$
$337$	19.6162	−	7.13972i	1.06856	−	0.388926i	0.815640	+	0.578560i	$0.196385\pi$
$338$	6.75069	−	8.04516i	0.367189	−	0.437599i
$339$	4.44048	−	19.2461i	0.241174	−	1.04531i
$340$	1.81067	+	0.659030i	0.0981973	+	0.0357409i
$341$	2.37002			0.128344
$342$	−1.53305	−	0.747184i	−0.0828977	−	0.0404031i
$343$	11.5657	−	14.4649i	0.624491	−	0.781032i
$344$	−4.88070	−	5.81659i	−0.263150	−	0.313610i
$345$	−1.95237	−	15.8823i	−0.105112	−	0.855077i
$346$	12.0197	−	14.3245i	0.646183	−	0.770091i
$347$	−2.86139	−	7.86161i	−0.153608	−	0.422033i	0.838889	−	0.544302i	$-0.183205\pi$
$347$	−2.86139	−	7.86161i	−0.153608	−	0.422033i	−0.992497	+	0.122268i	$0.960983\pi$
$348$	−4.58893	−	0.239850i	−0.245993	−	0.0128573i
$349$	−3.28308	+	9.02019i	−0.175739	+	0.482840i	−0.996021	−	0.0891202i	$-0.971594\pi$
$349$	−3.28308	+	9.02019i	−0.175739	+	0.482840i	0.820282	+	0.571960i	$0.193817\pi$
$350$	−3.39746	+	8.05013i	−0.181602	+	0.430297i
$351$	8.06066	−	1.57035i	0.430246	−	0.0838193i
$352$	−0.403978	−	0.699710i	−0.0215321	−	0.0372946i
$353$	−11.8179	+	9.91643i	−0.629006	+	0.527798i	−0.900620	−	0.434608i	$-0.856887\pi$
$353$	−11.8179	+	9.91643i	−0.629006	+	0.527798i	0.271614	+	0.962406i	$0.412443\pi$
$354$	13.2863	−	20.4654i	0.706158	−	1.08772i
$355$	−16.8502	−	2.97114i	−0.894313	−	0.157692i
$356$	0.333907	−	1.89368i	0.0176970	−	0.100365i
$357$	−4.86485	+	4.71872i	−0.257475	+	0.249741i
$358$	−0.371549	+	0.311766i	−0.0196370	+	0.0164774i
$359$	17.3730	+	10.0303i	0.916914	+	0.529380i	0.882649	−	0.470032i	$-0.155758\pi$
$359$	17.3730	+	10.0303i	0.916914	+	0.529380i	0.0342646	+	0.999413i	$0.489091\pi$
$360$	−2.81085	+	2.71593i	−0.148145	+	0.143142i
$361$	−9.33842	−	16.1746i	−0.491496	−	0.851295i
$362$	−11.0262	+	9.25208i	−0.579524	+	0.486279i
$363$	−12.2209	+	13.1090i	−0.641429	+	0.688042i
$364$	3.51155	+	2.27013i	0.184055	+	0.118987i
$365$	5.32922	+	14.6419i	0.278944	+	0.766392i
$366$	11.6214	+	2.68129i	0.607458	+	0.140153i
$367$	−8.94043	+	24.5636i	−0.466687	+	1.28221i	0.453683	+	0.891163i	$0.350110\pi$
$367$	−8.94043	+	24.5636i	−0.466687	+	1.28221i	−0.920370	+	0.391049i	$0.872112\pi$
$368$	−6.14103	+	3.54553i	−0.320124	+	0.184823i
$369$	−13.0207	+	3.25031i	−0.677832	+	0.169205i
$370$	2.87934	−	1.66239i	0.149690	−	0.0864233i
$371$	−23.0391	−	5.26889i	−1.19613	−	0.273547i
$372$	−4.05721	+	3.05822i	−0.210357	+	0.158561i
$373$	0.418407	−	0.152288i	0.0216643	−	0.00788517i	−0.331165	−	0.943573i	$-0.607442\pi$
$373$	0.418407	−	0.152288i	0.0216643	−	0.00788517i	0.352830	+	0.935688i	$0.385220\pi$
$374$	1.12286	−	0.408688i	0.0580618	−	0.0211328i
$375$	−15.7146	−	10.2020i	−0.811497	−	0.526830i
$376$	−2.40493	+	0.424054i	−0.124025	+	0.0218689i
$377$	−4.19296			−0.215949
$378$	−4.28079	−	13.0643i	−0.220180	−	0.671953i
$379$	−23.1712			−1.19022			−0.595112	−	0.803643i	$-0.702892\pi$
$379$	−23.1712			−1.19022			−0.595112	+	0.803643i	$0.702892\pi$
$380$	0.729400	−	0.128613i	0.0374174	−	0.00659770i
$381$	−6.46749	+	3.29649i	−0.331340	+	0.168885i
$382$	8.20363	−	2.98588i	0.419734	−	0.152771i
$383$	27.3157	−	9.94210i	1.39577	−	0.508017i	0.468848	−	0.883279i	$-0.344669\pi$
$383$	27.3157	−	9.94210i	1.39577	−	0.508017i	0.926919	+	0.375262i	$0.122447\pi$
$384$	1.59446	+	0.676542i	0.0813667	+	0.0345247i
$385$	−0.819777	−	2.66169i	−0.0417797	−	0.135652i
$386$	−6.44306	+	3.71990i	−0.327943	+	0.189338i
$387$	1.59536	+	22.7231i	0.0810969	+	1.15508i
$388$	13.7827	−	7.95746i	0.699712	−	0.403979i
$389$	10.7809	−	29.6203i	0.546614	−	1.50181i	−0.291639	−	0.956529i	$-0.594200\pi$
$389$	10.7809	−	29.6203i	0.546614	−	1.50181i	0.838253	−	0.545282i	$-0.183577\pi$
$390$	−2.43196	+	2.60869i	−0.123147	+	0.132096i
$391$	−3.58687	−	9.85485i	−0.181396	−	0.498381i
$392$	3.04257	−	6.30419i	0.153673	−	0.318409i
$393$	10.1688	+	2.34616i	0.512950	+	0.118348i
$394$	10.0760	−	8.45478i	0.507622	−	0.425945i
$395$	−7.63816	−	13.2297i	−0.384318	−	0.665658i
$396$	−0.252686	+	2.41066i	−0.0126980	+	0.121140i
$397$	21.7651	+	12.5661i	1.09236	+	0.630674i	0.934204	−	0.356740i	$-0.116112\pi$
$397$	21.7651	+	12.5661i	1.09236	+	0.630674i	0.158156	+	0.987414i	$0.449445\pi$
$398$	−6.75716	+	5.66993i	−0.338706	+	0.284208i
$399$	−0.712535	+	2.50576i	−0.0356714	+	0.125445i
$400$	−0.573480	+	3.25237i	−0.0286740	+	0.162618i
$401$	10.5465	+	1.85964i	0.526668	+	0.0928658i	0.430659	−	0.902515i	$-0.358281\pi$
$401$	10.5465	+	1.85964i	0.526668	+	0.0928658i	0.0960091	+	0.995380i	$0.469392\pi$
$402$	−19.6915	−	1.02922i	−0.982124	−	0.0513328i
$403$	−3.55137	+	2.97995i	−0.176906	+	0.148442i
$404$	1.19309	+	2.06649i	0.0593582	+	0.102811i
$405$	11.6108	−	1.63843i	0.576944	−	0.0814143i
$406$	0.869828	+	6.96518i	0.0431688	+	0.345676i
$407$	0.705181	−	1.93747i	0.0349545	−	0.0960368i
$408$	−1.39485	+	2.14855i	−0.0690556	+	0.106369i
$409$	5.03090	+	13.8223i	0.248762	+	0.683468i	0.999732	+	0.0231322i	$0.00736385\pi$
$409$	5.03090	+	13.8223i	0.248762	+	0.683468i	−0.750970	+	0.660336i	$0.770414\pi$
$410$	3.74635	−	4.46472i	0.185019	−	0.220497i
$411$	−14.5813	+	10.9910i	−0.719242	+	0.542146i
$412$	2.06457	+	2.46046i	0.101714	+	0.121218i
$413$	−34.3386	−	14.4922i	−1.68969	−	0.713115i
$414$	21.1573	+	2.21772i	1.03982	+	0.108995i
$415$	9.69272			0.475797
$416$	1.48513	+	0.540542i	0.0728143	+	0.0265022i
$417$	−13.5379	−	12.6207i	−0.662952	−	0.618039i
$418$	0.295236	−	0.351848i	0.0144405	−	0.0172095i
$419$	−0.645023	+	0.234769i	−0.0315115	+	0.0114692i	−0.357728	−	0.933826i	$-0.616448\pi$
$419$	−0.645023	+	0.234769i	−0.0315115	+	0.0114692i	0.326216	+	0.945295i	$0.394226\pi$
$420$	4.83796	+	3.49870i	0.236068	+	0.170719i
$421$	−4.15971	−	23.5909i	−0.202732	−	1.14975i	−0.900969	−	0.433884i	$-0.857143\pi$
$421$	−4.15971	−	23.5909i	−0.202732	−	1.14975i	0.698237	−	0.715867i	$-0.253968\pi$
$422$		−	11.8586i		−	0.577269i
$423$	6.58555	+	3.20970i	0.320201	+	0.156061i
$424$	−8.93279			−0.433815
$425$	−4.58973	−	1.67052i	−0.222634	−	0.0810323i
$426$	8.88480	−	20.9394i	0.430470	−	1.01452i
$427$	0.915878	−	18.1952i	0.0443224	−	0.880530i
$428$	−3.85176	+	4.59035i	−0.186182	+	0.221883i
$429$	−0.115441	+	2.20868i	−0.00557356	+	0.106636i
$430$	−6.35890	−	7.57824i	−0.306653	−	0.365455i
$431$	2.32833	+	1.34426i	0.112152	+	0.0647507i	0.555027	−	0.831833i	$-0.312708\pi$
$431$	2.32833	+	1.34426i	0.112152	+	0.0647507i	−0.442875	+	0.896583i	$0.646041\pi$
$432$	−2.67809	−	4.45285i	−0.128850	−	0.214238i
$433$			17.4112i			0.836730i	0.908279	+	0.418365i	$0.137397\pi$
$433$			17.4112i			0.836730i	−0.908279	+	0.418365i	$0.862603\pi$
$434$	5.68690	+	5.28120i	0.272980	+	0.253506i
$435$	−5.97877	−	0.312493i	−0.286660	−	0.0149829i
$436$	−0.877892	+	4.97877i	−0.0420434	+	0.238440i
$437$	−3.08801	−	2.59115i	−0.147720	−	0.123952i
$438$	−20.5596	+	2.52733i	−0.982378	+	0.120761i
$439$	10.1167	−	27.7955i	0.482846	−	1.32661i	−0.424197	−	0.905570i	$-0.639444\pi$
$439$	10.1167	−	27.7955i	0.482846	−	1.32661i	0.907043	−	0.421038i	$-0.138334\pi$
$440$	−0.526329	−	0.911628i	−0.0250917	−	0.0434602i
$441$	−18.4982	+	9.94063i	−0.880867	+	0.473363i
$442$	−1.16869	+	2.02424i	−0.0555891	+	0.0962832i
$443$	4.79675	+	5.71655i	0.227901	+	0.271601i	0.867862	−	0.496806i	$-0.165494\pi$
$443$	4.79675	+	5.71655i	0.227901	+	0.271601i	−0.639961	+	0.768407i	$0.721050\pi$
$444$	1.29288	+	4.22669i	0.0613572	+	0.200590i
$445$	0.435036	−	2.46721i	0.0206227	−	0.116957i
$446$	−16.6205	−	13.9462i	−0.787002	−	0.660373i
$447$	−3.93671	−	3.67001i	−0.186200	−	0.173586i
$448$	0.589837	−	2.57917i	0.0278672	−	0.121854i
$449$	−16.6235	−	9.59759i	−0.784512	−	0.452938i	0.0535149	−	0.998567i	$-0.482958\pi$
$449$	−16.6235	−	9.59759i	−0.784512	−	0.452938i	−0.838027	+	0.545629i	$0.816291\pi$
$450$	7.12501	−	6.88441i	0.335876	−	0.324534i
$451$		−	3.61433i		−	0.170192i
$452$	−11.2304	+	1.98023i	−0.528235	+	0.0931421i
$453$	−16.3372	+	38.5031i	−0.767589	+	1.80903i
$454$	16.9148	+	2.98254i	0.793853	+	0.139978i
$455$	4.57509	+	2.95768i	0.214483	+	0.138658i
$456$	−0.0513938	+	0.983292i	−0.00240674	+	0.0460469i
$457$	1.96319	+	11.1338i	0.0918341	+	0.520817i	0.995672	+	0.0929411i	$0.0296268\pi$
$457$	1.96319	+	11.1338i	0.0918341	+	0.520817i	−0.903838	+	0.427876i	$0.859262\pi$
$458$	1.20153	−	2.08112i	0.0561440	−	0.0972442i
$459$	7.17326	−	2.75702i	0.334819	−	0.128687i
$460$	−8.00095	+	4.61935i	−0.373046	+	0.215378i
$461$	−12.9724	−	4.72157i	−0.604185	−	0.219905i	0.0217720	−	0.999763i	$-0.493069\pi$
$461$	−12.9724	−	4.72157i	−0.604185	−	0.219905i	−0.625957	+	0.779858i	$0.715291\pi$
$462$	3.69292	−	0.266423i	0.171810	−	0.0123951i
$463$	4.08406	+	3.42693i	0.189802	+	0.159263i	0.732737	−	0.680512i	$-0.238242\pi$
$463$	4.08406	+	3.42693i	0.189802	+	0.159263i	−0.542935	+	0.839775i	$0.682687\pi$
$464$	0.907392	+	2.49304i	0.0421246	+	0.115736i
$465$	−5.28601	+	3.98445i	−0.245133	+	0.184775i
$466$	3.13035	+	17.7531i	0.145011	+	0.822397i
$467$	6.59622	−	11.4250i	0.305237	−	0.528685i	−0.672077	−	0.740481i	$-0.734598\pi$
$467$	6.59622	−	11.4250i	0.305237	−	0.528685i	0.977314	+	0.211796i	$0.0679311\pi$
$468$	−2.65241	−	3.92998i	−0.122608	−	0.181664i
$469$	3.73251	+	29.8882i	0.172351	+	1.38011i
$470$	−3.13331	+	0.552486i	−0.144529	+	0.0254843i
$471$	−3.58567	−	3.34275i	−0.165219	−	0.154026i
$472$	−13.8733	−	2.44623i	−0.638570	−	0.112597i
$473$	−6.04162	−	1.06530i	−0.277794	−	0.0489825i
$474$	19.4204	−	5.94038i	0.892006	−	0.272851i
$475$	−1.84890	+	0.326011i	−0.0848334	+	0.0149584i
$476$	3.60502	+	1.52146i	0.165236	+	0.0697359i
$477$	21.6848	+	15.7456i	0.992877	+	0.720942i
$478$	−5.30836	+	9.19435i	−0.242799	+	0.420540i
$479$	1.00589	+	5.70471i	0.0459605	+	0.260655i	0.999126	−	0.0417935i	$-0.0133071\pi$
$479$	1.00589	+	5.70471i	0.0459605	+	0.260655i	−0.953166	+	0.302448i	$0.902196\pi$
$480$	2.07736	+	0.881445i	0.0948183	+	0.0402323i
$481$	1.37940	+	3.78988i	0.0628953	+	0.172804i
$482$	15.6534	+	13.1348i	0.712994	+	0.598273i
$483$	−2.33828	−	32.4111i	−0.106395	−	1.47475i
$484$	9.72320	+	3.53895i	0.441963	+	0.160862i
$485$	17.9571	−	10.3675i	0.815388	−	0.470764i
$486$	−1.34773	+	15.5301i	−0.0611343	+	0.704459i
$487$	19.3632	−	33.5381i	0.877431	−	1.51975i	0.0232799	−	0.999729i	$-0.492589\pi$
$487$	19.3632	−	33.5381i	0.877431	−	1.51975i	0.854151	−	0.520025i	$-0.174078\pi$
$488$	−1.19572	−	6.78125i	−0.0541276	−	0.306973i
$489$	16.3661	−	8.34183i	0.740100	−	0.377231i
$490$	3.96407	−	8.21351i	0.179078	−	0.371049i
$491$	−33.8230	−	5.96390i	−1.52641	−	0.269147i	−0.653461	−	0.756960i	$-0.726684\pi$
$491$	−33.8230	−	5.96390i	−1.52641	−	0.269147i	−0.872948	+	0.487813i	$0.837795\pi$
$492$	4.66385	+	6.18734i	0.210263	+	0.278947i
$493$	−3.86410	+	0.681345i	−0.174030	+	0.0306862i
$494$			0.898446i			0.0404230i
$495$	−0.329217	+	3.14077i	−0.0147972	+	0.141167i
$496$	2.54036	+	1.46668i	0.114065	+	0.0658557i
$497$	−33.8713	−	7.74612i	−1.51933	−	0.347461i
$498$	−2.89688	+	12.5558i	−0.129812	+	0.562638i
$499$	32.6894	+	27.4297i	1.46338	+	1.22792i	0.922028	+	0.387124i	$0.126532\pi$
$499$	32.6894	+	27.4297i	1.46338	+	1.22792i	0.541351	+	0.840796i	$0.317913\pi$
$500$	−1.87837	+	10.6528i	−0.0840033	+	0.476406i
$501$	−18.8273	−	4.34385i	−0.841144	−	0.194069i
$502$	15.6653	+	18.6691i	0.699174	+	0.833244i
$503$	21.5885	−	37.3924i	0.962583	−	1.66724i	0.246611	−	0.969115i	$-0.420683\pi$
$503$	21.5885	−	37.3924i	0.962583	−	1.66724i	0.715972	−	0.698129i	$-0.245984\pi$
$504$	−5.97808	+	5.22135i	−0.266285	+	0.232577i
$505$	1.55443	+	2.69235i	0.0691713	+	0.119808i
$506$	−1.95952	+	5.38374i	−0.0871113	+	0.239336i
$507$	10.9493	+	14.5259i	0.486274	+	0.645120i
$508$	3.21055	+	2.69397i	0.142445	+	0.119526i
$509$	−0.671015	+	3.80551i	−0.0297422	+	0.168676i	−0.996061	−	0.0886720i	$-0.971738\pi$
$509$	−0.671015	+	3.80551i	−0.0297422	+	0.168676i	0.966319	+	0.257348i	$0.0828488\pi$
$510$	−1.81731	+	2.79927i	−0.0804718	+	0.123954i
$511$	9.31366	+	30.2400i	0.412012	+	1.33774i
$512$		−	1.00000i		−	0.0441942i
$513$	1.85799	−	2.29640i	0.0820321	−	0.101388i
$514$	14.5714	+	8.41279i	0.642716	+	0.371072i
$515$	2.68986	+	3.20566i	0.118530	+	0.141258i
$516$	11.7172	−	5.97230i	0.515822	−	0.262916i
$517$	−1.26825	+	1.51145i	−0.0557777	+	0.0664733i
$518$	6.00943	−	3.07761i	0.264039	−	0.135223i
$519$	19.4953	+	25.8636i	0.855751	+	1.13529i
$520$	1.93492	+	0.704254i	0.0848519	+	0.0308836i
$521$	−27.2107			−1.19212			−0.596061	−	0.802939i	$-0.703268\pi$
$521$	−27.2107			−1.19212			−0.596061	+	0.802939i	$0.703268\pi$
$522$	2.19168	−	7.65141i	0.0959273	−	0.334893i
$523$			37.3531i			1.63334i	0.577108	+	0.816668i	$0.304181\pi$
$523$			37.3531i			1.63334i	−0.577108	+	0.816668i	$0.695819\pi$
$524$	−1.04627	−	5.93368i	−0.0457064	−	0.259214i
$525$	−12.2634	−	8.86858i	−0.535217	−	0.387057i
$526$	28.7157	−	10.4517i	1.25207	−	0.455715i
$527$	−2.78859	+	3.32332i	−0.121473	+	0.144766i
$528$	1.33821	−	0.409338i	0.0582383	−	0.0178142i
$529$	25.6377	+	9.33136i	1.11468	+	0.405711i
$530$	−11.6382			−0.505533
$531$	29.3661	+	30.3924i	1.27438	+	1.31892i
$532$	1.49246	−	0.186382i	0.0647064	−	0.00808069i
$533$	4.54449	+	5.41592i	0.196844	+	0.234589i
$534$	3.06597	+	1.30092i	0.132677	+	0.0562963i
$535$	−5.01833	+	5.98061i	−0.216961	+	0.258564i
$536$	3.89370	+	10.6979i	0.168182	+	0.462077i
$537$	−0.381495	−	0.748466i	−0.0164627	−	0.0322987i
$538$	−9.42306	+	25.8896i	−0.406257	+	1.11618i
$539$	−1.39090	−	5.48199i	−0.0599103	−	0.236126i
$540$	−3.48920	−	5.80146i	−0.150151	−	0.249655i
$541$	11.9770	+	20.7447i	0.514930	+	0.891885i	0.999850	+	0.0173261i	$0.00551535\pi$
$541$	11.9770	+	20.7447i	0.514930	+	0.891885i	−0.484920	+	0.874558i	$0.661151\pi$
$542$	−5.56747	+	4.67167i	−0.239143	+	0.200665i
$543$	−11.3214	−	22.2117i	−0.485847	−	0.953197i
$544$	1.45648	+	0.256817i	0.0624461	+	0.0110109i
$545$	−1.14378	+	6.48667i	−0.0489940	+	0.277859i
$546$	−5.19869	+	5.04253i	−0.222483	+	0.215800i
$547$	17.8362	−	14.9664i	0.762622	−	0.639916i	−0.176186	−	0.984357i	$-0.556376\pi$
$547$	17.8362	−	14.9664i	0.762622	−	0.639916i	0.938808	+	0.344441i	$0.111931\pi$
$548$	9.12984	+	5.27111i	0.390007	+	0.225171i
$549$	−9.05048	+	18.5695i	−0.386265	+	0.792525i
$550$	1.33415	+	2.31082i	0.0568884	+	0.0985336i
$551$	−1.15535	+	0.969450i	−0.0492194	+	0.0413000i
$552$	−3.59258	−	11.7449i	−0.152910	−	0.499896i
$553$	−14.1407	−	27.6115i	−0.601324	−	1.17416i
$554$	−3.97097	−	10.9102i	−0.168711	−	0.463528i
$555$	1.68445	+	5.50681i	0.0715007	+	0.233751i
$556$	−3.65475	+	10.0413i	−0.154996	+	0.425847i
$557$	−3.16086	+	1.82493i	−0.133930	+	0.0773246i	−0.565468	−	0.824770i	$-0.691304\pi$
$557$	−3.16086	+	1.82493i	−0.133930	+	0.0773246i	0.431538	+	0.902095i	$0.357971\pi$
$558$	−3.58156	−	8.03825i	−0.151620	−	0.340286i
$559$	10.3926	−	6.00015i	0.439559	−	0.253779i
$560$	0.768479	−	3.36031i	0.0324741	−	0.141999i
$561$	0.252517	+	2.05421i	0.0106613	+	0.0867287i
$562$	−23.4599	+	8.53871i	−0.989597	+	0.360184i
$563$	32.9570	−	11.9954i	1.38897	−	0.505544i	0.464086	−	0.885790i	$-0.346383\pi$
$563$	32.9570	−	11.9954i	1.38897	−	0.505544i	0.924885	+	0.380246i	$0.124161\pi$
$564$	0.220774	−	4.22396i	0.00929626	−	0.177861i
$565$	−14.6318	+	2.57997i	−0.615563	+	0.108540i
$566$	−17.6488			−0.741833
$567$	23.7156	−	2.13765i	0.995962	−	0.0897728i
$568$	−13.1327			−0.551034
$569$	−4.06857	+	0.717399i	−0.170563	+	0.0300749i	−0.258278	−	0.966071i	$-0.583155\pi$
$569$	−4.06857	+	0.717399i	−0.170563	+	0.0300749i	0.0877141	+	0.996146i	$0.472044\pi$
$570$	−0.0669593	+	1.28110i	−0.00280462	+	0.0536593i
$571$	0.717947	−	0.261311i	0.0300452	−	0.0109355i	−0.326954	−	0.945040i	$-0.606022\pi$
$571$	0.717947	−	0.261311i	0.0300452	−	0.0109355i	0.356999	+	0.934105i	$0.383800\pi$
$572$	1.19992	−	0.436733i	0.0501710	−	0.0182607i
$573$	1.84489	+	15.0080i	0.0770716	+	0.626970i
$574$	8.05394	−	8.67265i	0.336165	−	0.361990i
$575$	20.2810	−	11.7092i	0.845776	−	0.488309i
$576$	−1.76267	+	2.42755i	−0.0734448	+	0.101148i
$577$	39.4565	−	22.7802i	1.64260	−	0.948353i	0.662690	−	0.748893i	$-0.269415\pi$
$577$	39.4565	−	22.7802i	1.64260	−	0.948353i	0.979906	−	0.199460i	$-0.0639188\pi$
$578$	5.06625	−	13.9194i	0.210728	−	0.578970i
$579$	−3.76927	−	12.3225i	−0.156645	−	0.512107i
$580$	1.18221	+	3.24810i	0.0490887	+	0.134870i
$581$	19.6583	+	0.989520i	0.815562	+	0.0410522i
$582$	8.06306	+	26.3598i	0.334225	+	1.09265i
$583$	−5.52877	+	4.63919i	−0.228978	+	0.192135i
$584$	5.97973	+	10.3572i	0.247443	+	0.428584i
$585$	−3.45574	−	5.12025i	−0.142877	−	0.211696i
$586$	10.7143	+	6.18589i	0.442602	+	0.255537i
$587$	20.8889	−	17.5279i	0.862177	−	0.723452i	−0.100259	−	0.994961i	$-0.531967\pi$
$587$	20.8889	−	17.5279i	0.862177	−	0.723452i	0.962436	+	0.271509i	$0.0875227\pi$
$588$	9.45491	+	7.58978i	0.389914	+	0.312997i
$589$	−0.289567	+	1.64222i	−0.0119314	+	0.0676663i
$590$	−18.0750	−	3.18712i	−0.744138	−	0.131212i
$591$	10.3457	+	20.2976i	0.425567	+	0.834932i
$592$	1.95486	−	1.64032i	0.0803443	−	0.0674168i
$593$	19.7076	+	34.1345i	0.809293	+	1.40174i	0.913354	+	0.407166i	$0.133483\pi$
$593$	19.7076	+	34.1345i	0.809293	+	1.40174i	−0.104061	+	0.994571i	$0.533184\pi$
$594$	−3.97011	−	1.36515i	−0.162895	−	0.0560127i
$595$	4.69687	+	1.98226i	0.192553	+	0.0812647i
$596$	−1.06277	+	2.91994i	−0.0435329	+	0.119606i
$597$	−6.93804	−	13.6120i	−0.283955	−	0.557100i
$598$	−3.83301	−	10.5311i	−0.156744	−	0.430649i
$599$	−16.6556	+	19.8494i	−0.680531	+	0.811025i	−0.990176	−	0.139827i	$-0.955345\pi$
$599$	−16.6556	+	19.8494i	−0.680531	+	0.811025i	0.309645	+	0.950852i	$0.399790\pi$
$600$	−5.26575	−	2.23431i	−0.214973	−	0.0912152i
$601$	−12.6672	−	15.0962i	−0.516707	−	0.615788i	0.443092	−	0.896476i	$-0.353882\pi$
$601$	−12.6672	−	15.0962i	−0.516707	−	0.615788i	−0.959799	+	0.280689i	$0.909437\pi$
$602$	−12.1231	−	16.0190i	−0.494102	−	0.652884i
$603$	9.40471	−	32.8329i	0.382989	−	1.33706i
$604$	24.1481			0.982572
$605$	12.6680	+	4.61079i	0.515029	+	0.187455i
$606$	−3.95221	+	1.20892i	−0.160548	+	0.0491089i
$607$	12.0233	−	14.3288i	0.488009	−	0.581586i	−0.464701	−	0.885468i	$-0.653838\pi$
$607$	12.0233	−	14.3288i	0.488009	−	0.581586i	0.952710	+	0.303881i	$0.0982827\pi$
$608$	0.534196	−	0.194431i	0.0216645	−	0.00788523i
$609$	−12.0939	−	1.24415i	−0.490070	−	0.0504154i
$610$	−1.55786	−	8.83507i	−0.0630759	−	0.357721i
$611$		−	3.85948i		−	0.156138i
$612$	−3.08299	−	3.19074i	−0.124622	−	0.128978i
$613$	−28.7433			−1.16093			−0.580465	−	0.814285i	$-0.697129\pi$
$613$	−28.7433			−1.16093			−0.580465	+	0.814285i	$0.697129\pi$
$614$	−25.4908	−	9.27790i	−1.02873	−	0.374426i
$615$	6.07638	+	8.06128i	0.245023	+	0.325062i
$616$	−0.974405	−	1.90265i	−0.0392599	−	0.0766599i
$617$	−5.81133	+	6.92568i	−0.233956	+	0.278817i	−0.870230	−	0.492645i	$-0.836030\pi$
$617$	−5.81133	+	6.92568i	−0.233956	+	0.278817i	0.636275	+	0.771463i	$0.280474\pi$
$618$	−4.95648	+	2.52633i	−0.199379	+	0.101624i
$619$	18.2900	+	21.7971i	0.735136	+	0.876101i	0.996007	−	0.0892730i	$-0.0284544\pi$
$619$	18.2900	+	21.7971i	0.735136	+	0.876101i	−0.260872	+	0.965374i	$0.584010\pi$
$620$	3.30975	+	1.91088i	0.132923	+	0.0767430i
$621$	−11.9813	+	34.8438i	−0.480793	+	1.39823i
$622$		−	12.4010i		−	0.497233i
$623$	1.13419	−	4.95946i	0.0454405	−	0.198697i
$624$	−1.49057	+	2.29599i	−0.0596707	+	0.0919130i
$625$	0.420133	−	2.38269i	0.0168053	−	0.0953078i
$626$	11.2122	+	9.40818i	0.448131	+	0.376026i
$627$	0.478857	+	0.635280i	0.0191237	+	0.0253706i
$628$	−0.968003	+	2.65957i	−0.0386275	+	0.106128i
$629$	1.88706	+	3.26848i	0.0752419	+	0.130323i
$630$	−7.78865	+	6.80272i	−0.310307	+	0.271027i
$631$	12.9293	−	22.3941i	0.514706	−	0.891497i	−0.485148	−	0.874432i	$-0.661234\pi$
$631$	12.9293	−	22.3941i	0.514706	−	0.891497i	0.999854	−	0.0170651i	$-0.00543225\pi$
$632$	−7.53679	−	8.98199i	−0.299797	−	0.357285i
$633$	20.0140	+	4.61763i	0.795484	+	0.183534i
$634$	1.19207	−	6.76057i	0.0473432	−	0.268496i
$635$	4.18292	+	3.50989i	0.165994	+	0.139286i
$636$	3.47834	−	15.0760i	0.137925	−	0.597802i
$637$	8.97701	+	6.46567i	0.355682	+	0.256179i
$638$	1.85636	+	1.07177i	0.0734938	+	0.0424317i
$639$	31.8801	+	23.1486i	1.26116	+	0.915744i
$640$		−	1.30287i		−	0.0515003i
$641$	19.9010	−	3.50908i	0.786042	−	0.138600i	0.233800	−	0.972285i	$-0.424884\pi$
$641$	19.9010	−	3.50908i	0.786042	−	0.138600i	0.552241	+	0.833684i	$0.313773\pi$
$642$	−6.24736	−	8.28810i	−0.246563	−	0.327105i
$643$	−13.4353	−	2.36901i	−0.529837	−	0.0934246i	−0.0976715	−	0.995219i	$-0.531139\pi$
$643$	−13.4353	−	2.36901i	−0.529837	−	0.0934246i	−0.432166	+	0.901794i	$0.642251\pi$
$644$	−16.6987	+	8.55191i	−0.658021	+	0.336993i
$645$	15.2660	−	7.78111i	0.601098	−	0.306381i
$646$	0.145995	+	0.827979i	0.00574410	+	0.0325764i
$647$	13.6339	−	23.6146i	0.536004	−	0.928386i	−0.463110	−	0.886301i	$-0.653266\pi$
$647$	13.6339	−	23.6146i	0.536004	−	0.928386i	0.999114	−	0.0420856i	$-0.0134002\pi$
$648$	8.55795	−	2.78596i	0.336188	−	0.109443i
$649$	−9.85702	+	5.69095i	−0.386922	+	0.223389i
$650$	−4.90469	−	1.78516i	−0.192378	−	0.0700197i
$651$	−11.1276	+	7.54142i	−0.436124	+	0.295572i
$652$	−8.12435	−	6.81714i	−0.318174	−	0.266980i
$653$	7.71778	+	21.2044i	0.302020	+	0.829793i	0.994149	+	0.108019i	$0.0344508\pi$
$653$	7.71778	+	21.2044i	0.302020	+	0.829793i	−0.692129	+	0.721774i	$0.743327\pi$
$654$	−8.06089	−	3.42031i	−0.315206	−	0.133745i
$655$	−1.36315	−	7.73080i	−0.0532626	−	0.302067i
$656$	2.23671	−	3.87410i	0.0873290	−	0.151258i
$657$	3.74030	−	35.6829i	0.145923	−	1.39212i
$658$	−6.41121	+	0.800648i	−0.249935	+	0.0312125i
$659$	−28.6283	+	5.04794i	−1.11520	+	0.196640i	−0.700732	−	0.713425i	$-0.747143\pi$
$659$	−28.6283	+	5.04794i	−1.11520	+	0.196640i	−0.414467	+	0.910064i	$0.636032\pi$
$660$	1.74351	−	0.533313i	0.0678662	−	0.0207592i
$661$	−35.0476	−	6.17983i	−1.36319	−	0.240368i	−0.556259	−	0.831009i	$-0.687764\pi$
$661$	−35.0476	−	6.17983i	−1.36319	−	0.240368i	−0.806934	+	0.590641i	$0.798875\pi$
$662$	−34.3991	−	6.06550i	−1.33696	−	0.235742i
$663$	−2.96125	−	2.76064i	−0.115006	−	0.107214i
$664$	7.32651	−	1.29186i	0.284324	−	0.0501339i
$665$	1.94448	−	0.242831i	0.0754036	−	0.00941659i
$666$	−7.63687	+	0.536175i	−0.295923	+	0.0207764i
$667$	9.40642	−	16.2924i	0.364218	−	0.630844i
$668$	1.93714	+	10.9861i	0.0749502	+	0.425063i
$669$	30.0091	−	22.6201i	1.16022	−	0.874542i
$670$	5.07298	+	13.9379i	0.195986	+	0.538467i
$671$	−4.26186	−	3.57613i	−0.164527	−	0.138055i
$672$	4.12321	+	1.99978i	0.159056	+	0.0771430i
$673$	−21.6515	−	7.88049i	−0.834603	−	0.303771i	−0.110856	−	0.993836i	$-0.535359\pi$
$673$	−21.6515	−	7.88049i	−0.834603	−	0.303771i	−0.723747	+	0.690066i	$0.757582\pi$
$674$	18.0784	−	10.4376i	0.696355	−	0.402040i
$675$	8.84450	+	14.7057i	0.340425	+	0.566022i
$676$	5.25111	−	9.09518i	0.201966	−	0.349815i
$677$	2.90482	+	16.4740i	0.111641	+	0.633149i	0.988359	+	0.152143i	$0.0486173\pi$
$677$	2.90482	+	16.4740i	0.111641	+	0.633149i	−0.876717	+	0.481006i	$0.840272\pi$
$678$	1.03096	−	19.7248i	0.0395938	−	0.757527i
$679$	37.4780	−	19.1936i	1.43827	−	0.736584i
$680$	1.89760	+	0.334598i	0.0727696	+	0.0128313i
$681$	−11.6201	+	27.3860i	−0.445285	+	1.04943i
$682$	2.33401	−	0.411549i	0.0893739	−	0.0157590i
$683$			20.4158i			0.781191i	0.920562	+	0.390595i	$0.127731\pi$
$683$			20.4158i			0.781191i	−0.920562	+	0.390595i	$0.872269\pi$
$684$	−1.63950	−	0.469622i	−0.0626880	−	0.0179565i
$685$	11.8950	+	6.86756i	0.454483	+	0.262396i
$686$	8.87822	−	16.2535i	0.338972	−	0.620563i
$687$	3.04446	+	2.83821i	0.116154	+	0.108284i
$688$	−5.81659	−	4.88070i	−0.221755	−	0.186075i
$689$	2.45152	−	13.9032i	0.0933954	−	0.529672i
$690$	−4.68065	−	15.3020i	−0.178189	−	0.582539i
$691$	−19.2393	−	22.9285i	−0.731898	−	0.872242i	0.263831	−	0.964569i	$-0.415014\pi$
$691$	−19.2393	−	22.9285i	−0.731898	−	0.872242i	−0.995729	+	0.0923271i	$0.970569\pi$
$692$	9.34967	−	16.1941i	0.355421	−	0.615608i
$693$	−0.988338	+	6.33633i	−0.0375439	+	0.240697i
$694$	−4.18308	−	7.24530i	−0.158787	−	0.275028i
$695$	−4.76165	+	13.0825i	−0.180620	+	0.496248i
$696$	−4.56087	+	0.560653i	−0.172879	+	0.0212515i
$697$	5.06813	+	4.25267i	0.191969	+	0.161081i
$698$	−1.66686	+	9.45325i	−0.0630917	+	0.357811i
$699$	−31.1811	−	1.62975i	−1.17938	−	0.0616426i
$700$	−1.94796	+	8.51779i	−0.0736259	+	0.321942i
$701$		−	48.5497i		−	1.83370i	−0.399236	−	0.916848i	$-0.630725\pi$
$701$		−	48.5497i		−	1.83370i	0.399236	−	0.916848i	$-0.369275\pi$
$702$	7.66551	−	2.94622i	0.289316	−	0.111198i
$703$	1.25634	+	0.725348i	0.0473837	+	0.0273570i
$704$	−0.519343	−	0.618929i	−0.0195735	−	0.0233268i
$705$	0.287639	−	5.50325i	0.0108331	−	0.207265i
$706$	−9.91643	+	11.8179i	−0.373210	+	0.444774i
$707$	2.87776	+	5.61918i	0.108229	+	0.211331i
$708$	9.53066	−	22.4616i	0.358184	−	0.844158i
$709$	33.0345	+	12.0236i	1.24064	+	0.451555i	0.877228	−	0.480074i	$-0.159390\pi$
$709$	33.0345	+	12.0236i	1.24064	+	0.451555i	0.363410	+	0.931629i	$0.381613\pi$
$710$	−17.1101			−0.642130
$711$	2.46356	+	35.0891i	0.0923909	+	1.31594i
$712$		−	1.92289i		−	0.0720635i
$713$	−3.61198	−	20.4846i	−0.135270	−	0.767153i
$714$	−3.97155	+	5.49181i	−0.148631	+	0.205526i
$715$	1.56333	−	0.569005i	0.0584652	−	0.0212796i
$716$	−0.311766	+	0.371549i	−0.0116513	+	0.0138854i
$717$	−13.4504	−	12.5392i	−0.502315	−	0.468284i
$718$	18.8508	+	6.86115i	0.703507	+	0.256056i
$719$	−5.25697			−0.196052			−0.0980260	−	0.995184i	$-0.531253\pi$
$719$	−5.25697			−0.196052			−0.0980260	+	0.995184i	$0.531253\pi$
$720$	−2.29653	+	3.16277i	−0.0855866	+	0.117869i
$721$	5.12818	+	6.77615i	0.190983	+	0.252357i
$722$	−12.0052	−	14.3073i	−0.446789	−	0.532462i
$723$	−28.2631	+	21.3040i	−1.05111	+	0.792303i
$724$	−9.25208	+	11.0262i	−0.343851	+	0.409786i
$725$	−2.99670	−	8.23336i	−0.111295	−	0.305779i
$726$	−9.75885	+	15.0319i	−0.362185	+	0.557887i
$727$	−7.20103	+	19.7847i	−0.267071	+	0.733773i	0.731575	+	0.681761i	$0.238786\pi$
$727$	−7.20103	+	19.7847i	−0.267071	+	0.733773i	−0.998646	+	0.0520118i	$0.983437\pi$
$728$	3.85241	+	1.62587i	0.142780	+	0.0602586i
$729$	−25.6855	−	8.32184i	−0.951316	−	0.308216i
$730$	7.79079	+	13.4940i	0.288350	+	0.499437i
$731$	8.60244	−	7.21831i	0.318173	−	0.266979i
$732$	11.9104	+	0.622522i	0.440221	+	0.0230091i
$733$	−44.4711	−	7.84146i	−1.64258	−	0.289631i	−0.725466	−	0.688258i	$-0.758376\pi$
$733$	−44.4711	−	7.84146i	−1.64258	−	0.289631i	−0.917113	+	0.398627i	$0.869487\pi$
$734$	−4.53918	+	25.7430i	−0.167544	+	0.950190i
$735$	12.3185	+	9.88847i	0.454374	+	0.364742i
$736$	−5.43206	+	4.55804i	−0.200229	+	0.168012i
$737$	7.96579	+	4.59905i	0.293424	+	0.169408i
$738$	−12.2585	+	5.46196i	−0.451242	+	0.201058i
$739$	6.85264	+	11.8691i	0.252079	+	0.436613i	0.964098	−	0.265547i	$-0.0855525\pi$
$739$	6.85264	+	11.8691i	0.252079	+	0.436613i	−0.712019	+	0.702160i	$0.752219\pi$
$740$	2.54692	−	2.13712i	0.0936267	−	0.0785622i
$741$	−1.51632	−	0.349846i	−0.0557034	−	0.0128519i
$742$	−23.6041	−	1.18814i	−0.866532	−	0.0436179i
$743$	11.9620	+	32.8654i	0.438844	+	1.20572i	0.940245	+	0.340500i	$0.110596\pi$
$743$	11.9620	+	32.8654i	0.438844	+	1.20572i	−0.501400	+	0.865215i	$0.667182\pi$
$744$	−3.46452	+	3.71629i	−0.127015	+	0.136246i
$745$	−1.38465	+	3.80430i	−0.0507297	+	0.139379i
$746$	0.385606	−	0.222630i	0.0141181	−	0.00815106i
$747$	−20.0626	−	9.77820i	−0.734051	−	0.357765i
$748$	1.03483	−	0.597462i	0.0378373	−	0.0218454i
$749$	−10.7885	+	11.6172i	−0.394202	+	0.424485i
$750$	−17.2474	−	7.31823i	−0.629786	−	0.267224i
$751$	−12.7616	+	4.64483i	−0.465676	+	0.169492i	−0.564192	−	0.825643i	$-0.690812\pi$
$751$	−12.7616	+	4.64483i	−0.465676	+	0.169492i	0.0985168	+	0.995135i	$0.468590\pi$
$752$	−2.29476	+	0.835224i	−0.0836813	+	0.0304575i
$753$	−37.6080	+	19.1689i	−1.37051	+	0.698553i
$754$	−4.12926	+	0.728100i	−0.150379	+	0.0265159i
$755$	31.4618			1.14501
$756$	−6.48434	−	12.1224i	−0.235833	−	0.440889i
$757$	22.7604			0.827241			0.413620	−	0.910449i	$-0.364264\pi$
$757$	22.7604			0.827241			0.413620	+	0.910449i	$0.364264\pi$
$758$	−22.8191	+	4.02363i	−0.828829	+	0.146145i
$759$	−8.32319	−	5.40348i	−0.302113	−	0.196134i
$760$	0.695986	−	0.253318i	0.0252461	−	0.00918881i
$761$	−22.0842	+	8.03801i	−0.800553	+	0.291377i	−0.709716	−	0.704488i	$-0.751177\pi$
$761$	−22.0842	+	8.03801i	−0.800553	+	0.291377i	−0.0908374	+	0.995866i	$0.528954\pi$
$762$	−5.79681	+	4.36948i	−0.209996	+	0.158290i
$763$	−2.98196	+	13.0392i	−0.107954	+	0.472049i
$764$	7.56051	−	4.36506i	0.273530	−	0.157922i
$765$	−4.01672	−	4.15710i	−0.145225	−	0.150300i
$766$	25.1743	−	14.5344i	0.909583	−	0.525148i
$767$	7.61478	−	20.9214i	0.274954	−	0.755429i
$768$	1.68771	+	0.389390i	0.0609001	+	0.0140509i
$769$	−14.3419	−	39.4041i	−0.517183	−	1.42095i	−0.873611	−	0.486625i	$-0.838228\pi$
$769$	−14.3419	−	39.4041i	−0.517183	−	1.42095i	0.356428	−	0.934323i	$-0.383994\pi$
$770$	−1.26952	−	2.47890i	−0.0457503	−	0.0893333i
$771$	−19.8723	+	21.3165i	−0.715684	+	0.767693i
$772$	−5.69922	+	4.78221i	−0.205119	+	0.172116i
$773$	−9.09053	−	15.7453i	−0.326964	−	0.566318i	0.654944	−	0.755677i	$-0.272692\pi$
$773$	−9.09053	−	15.7453i	−0.326964	−	0.566318i	−0.981908	+	0.189359i	$0.939359\pi$
$774$	5.51695	+	22.1009i	0.198303	+	0.794400i
$775$	−8.38963	−	4.84376i	−0.301364	−	0.173993i
$776$	12.1915	−	10.2299i	0.437651	−	0.367233i
$777$	2.85412	+	11.3406i	0.102391	+	0.406841i
$778$	5.47362	−	31.0424i	0.196239	−	1.11292i
$779$	2.50442	+	0.441596i	0.0897300	+	0.0158218i
$780$	−1.94202	+	2.99136i	−0.0695354	+	0.107108i
$781$	−8.12819	+	6.82036i	−0.290849	+	0.244052i
$782$	−5.24366	−	9.08228i	−0.187513	−	0.324782i
$783$	12.0600	+	6.67831i	0.430988	+	0.238663i
$784$	1.90164	−	6.73675i	0.0679157	−	0.240598i
$785$	−1.26118	+	3.46506i	−0.0450134	+	0.123673i
$786$	10.4218	+	0.544715i	0.371732	+	0.0194293i
$787$	−10.4215	−	28.6329i	−0.371487	−	1.02065i	−0.974787	−	0.223137i	$-0.928370\pi$
$787$	−10.4215	−	28.6329i	−0.371487	−	1.02065i	0.603301	−	0.797514i	$-0.293852\pi$
$788$	8.45478	−	10.0760i	0.301189	−	0.358943i
$789$	6.45781	+	52.5337i	0.229904	+	1.87025i
$790$	−9.81943	−	11.7023i	−0.349360	−	0.416351i
$791$	−29.9387	+	3.73882i	−1.06450	+	0.132937i
$792$	0.169759	+	2.41791i	0.00603211	+	0.0859168i
$793$	10.8827			0.386455
$794$	23.6165	+	8.59572i	0.838120	+	0.305051i
$795$	4.53181	−	19.6420i	0.160727	−	0.696630i
$796$	−5.66993	+	6.75716i	−0.200965	+	0.239501i
$797$	−20.8200	+	7.57787i	−0.737483	+	0.268422i	−0.683329	−	0.730111i	$-0.739469\pi$
$797$	−20.8200	+	7.57787i	−0.737483	+	0.268422i	−0.0541543	+	0.998533i	$0.517246\pi$
$798$	−0.266590	+	2.59142i	−0.00943717	+	0.0917353i
$799$	−0.627155	−	3.55677i	−0.0221871	−	0.125830i
$800$			3.30254i			0.116762i
$801$	−3.38944	+	4.66791i	−0.119760	+	0.164933i
$802$	10.7092			0.378156
$803$	9.07997	+	3.30484i	0.320425	+	0.116625i
$804$	−19.5711	+	2.40581i	−0.690219	+	0.0848465i
$805$	−21.7562	+	11.1420i	−0.766804	+	0.392704i
$806$	−2.97995	+	3.55137i	−0.104964	+	0.125092i
$807$	−40.0250	−	25.9846i	−1.40895	−	0.914701i
$808$	1.53380	+	1.82791i	0.0539590	+	0.0643058i
$809$	8.45014	+	4.87869i	0.297091	+	0.171526i	0.641135	−	0.767428i	$-0.278464\pi$
$809$	8.45014	+	4.87869i	0.297091	+	0.171526i	−0.344044	+	0.938953i	$0.611797\pi$
$810$	11.1499	−	3.62973i	0.391766	−	0.127536i
$811$			4.56357i			0.160249i	0.996785	+	0.0801243i	$0.0255317\pi$
$811$			4.56357i			0.160249i	−0.996785	+	0.0801243i	$0.974468\pi$
$812$	2.06610	+	6.70831i	0.0725060	+	0.235416i
$813$	−5.71651	−	11.2154i	−0.200487	−	0.393341i
$814$	0.358030	−	2.03049i	0.0125489	−	0.0711686i
$815$	−10.5849	−	8.88182i	−0.370774	−	0.311117i
$816$	−1.00057	+	2.35812i	−0.0350270	+	0.0825507i
$817$	1.47632	−	4.05616i	0.0516499	−	0.141907i
$818$	7.35468	+	12.7387i	0.257151	+	0.445398i
$819$	−6.48603	−	10.7374i	−0.226640	−	0.375195i
$820$	2.91414	−	5.04744i	0.101766	−	0.176264i
$821$	−19.6278	−	23.3914i	−0.685013	−	0.816367i	0.305730	−	0.952118i	$-0.401100\pi$
$821$	−19.6278	−	23.3914i	−0.685013	−	0.816367i	−0.990743	+	0.135751i	$0.956655\pi$
$822$	−12.4512	+	13.3560i	−0.434285	+	0.465845i
$823$	−4.12730	+	23.4071i	−0.143869	+	0.815920i	0.824400	+	0.566008i	$0.191513\pi$
$823$	−4.12730	+	23.4071i	−0.143869	+	0.815920i	−0.968269	+	0.249912i	$0.919598\pi$
$824$	2.46046	+	2.06457i	0.0857143	+	0.0719228i
$825$	−4.41950	+	1.35186i	−0.153867	+	0.0470656i
$826$	−36.3335	−	8.30921i	−1.26420	−	0.289114i
$827$	30.9584	+	17.8738i	1.07653	+	0.621534i	0.929958	−	0.367666i	$-0.119843\pi$
$827$	30.9584	+	17.8738i	1.07653	+	0.621534i	0.146571	+	0.989200i	$0.453176\pi$
$828$	21.2209	−	1.48990i	0.737478	−	0.0517775i
$829$		−	22.6294i		−	0.785952i	−0.919549	−	0.392976i	$-0.871446\pi$
$829$		−	22.6294i		−	0.785952i	0.919549	−	0.392976i	$-0.128554\pi$
$830$	9.54546	−	1.68312i	0.331328	−	0.0584220i
$831$	19.9595	−	2.45356i	0.692387	−	0.0851130i
$832$	1.55643	+	0.274440i	0.0539594	+	0.00951450i
$833$	9.32357	+	4.49981i	0.323043	+	0.155909i
$834$	−15.5238	−	10.0782i	−0.537544	−	0.348978i
$835$	2.52383	+	14.3134i	0.0873409	+	0.495335i
$836$	0.229653	−	0.397770i	0.00794271	−	0.0137572i
$837$	14.9609	−	2.91464i	0.517124	−	0.100745i
$838$	−0.594457	+	0.343210i	−0.0205352	+	0.0118560i
$839$	−38.1491	−	13.8852i	−1.31705	−	0.479369i	−0.414541	−	0.910031i	$-0.636058\pi$
$839$	−38.1491	−	13.8852i	−1.31705	−	0.479369i	−0.902513	+	0.430662i	$0.858280\pi$
$840$	5.37200	+	2.60544i	0.185352	+	0.0898963i
$841$	16.8234	+	14.1165i	0.580117	+	0.486776i
$842$	−8.19304	−	22.5102i	−0.282351	−	0.775752i
$843$	−5.27584	−	42.9185i	−0.181710	−	1.47819i
$844$	−2.05923	−	11.6785i	−0.0708816	−	0.401990i
$845$	6.84149	−	11.8498i	0.235355	−	0.407646i
$846$	7.04286	+	2.01737i	0.242139	+	0.0693586i
$847$	25.2219	+	10.6446i	0.866635	+	0.365753i
$848$	−8.79708	+	1.55116i	−0.302093	+	0.0532672i
$849$	6.87225	−	29.7860i	0.235855	−	1.02225i
$850$	−4.81008	−	0.848147i	−0.164984	−	0.0290912i
$851$	−17.8207	−	3.14227i	−0.610885	−	0.107715i
$852$	5.11372	−	22.1642i	0.175193	−	0.759331i
$853$	15.4616	−	2.72630i	0.529396	−	0.0933468i	0.0974398	−	0.995241i	$-0.468935\pi$
$853$	15.4616	−	2.72630i	0.529396	−	0.0933468i	0.431956	+	0.901895i	$0.357824\pi$
$854$	−2.25761	−	18.0779i	−0.0772537	−	0.618612i
$855$	−2.13605	−	0.611855i	−0.0730515	−	0.0209250i
$856$	−2.99614	+	5.18946i	−0.102406	+	0.177372i
$857$	0.817199	+	4.63457i	0.0279150	+	0.158314i	0.995579	−	0.0939294i	$-0.0299428\pi$
$857$	0.817199	+	4.63457i	0.0279150	+	0.158314i	−0.967664	+	0.252243i	$0.918832\pi$
$858$	0.269846	+	2.19517i	0.00921239	+	0.0749419i
$859$	5.18439	+	14.2440i	0.176889	+	0.485998i	0.996174	−	0.0873874i	$-0.0278518\pi$
$859$	5.18439	+	14.2440i	0.176889	+	0.485998i	−0.819285	+	0.573386i	$0.805630\pi$
$860$	−7.57824	−	6.35890i	−0.258416	−	0.216837i
$861$	11.5008	+	16.9698i	0.391947	+	0.578329i
$862$	2.52638	+	0.919528i	0.0860490	+	0.0313193i
$863$	26.3262	−	15.1994i	0.896154	−	0.517395i	0.0202037	−	0.999796i	$-0.493569\pi$
$863$	26.3262	−	15.1994i	0.896154	−	0.517395i	0.875951	+	0.482401i	$0.160235\pi$
$864$	−3.41063	−	3.92015i	−0.116032	−	0.133366i
$865$	12.1814	−	21.0988i	0.414179	−	0.717379i
$866$	3.02343	+	17.1467i	0.102740	+	0.582669i
$867$	21.5192	+	13.9704i	0.730830	+	0.474461i
$868$	6.51758	+	4.21344i	0.221221	+	0.143014i
$869$	−9.32948	−	1.64504i	−0.316481	−	0.0558041i
$870$	−5.94220	+	0.730457i	−0.201459	+	0.0247648i
$871$	−17.7190	+	3.12434i	−0.600387	+	0.105864i
$872$			5.05558i			0.171203i
$873$	−47.6275	+	3.34387i	−1.61195	+	0.113173i
$874$	−3.49105	−	2.01556i	−0.118087	−	0.0681773i
$875$	−6.38032	+	27.8991i	−0.215694	+	0.943161i
$876$	−19.8084	+	6.05908i	−0.669265	+	0.204717i
$877$	−0.113813	−	0.0955007i	−0.00384320	−	0.00322483i	0.640864	−	0.767654i	$-0.278576\pi$
$877$	−0.113813	−	0.0955007i	−0.00384320	−	0.00322483i	−0.644707	+	0.764430i	$0.723021\pi$
$878$	5.13641	−	29.1300i	0.173345	−	0.983090i
$879$	−14.6120	+	15.6739i	−0.492852	+	0.528667i
$880$	−0.676635	−	0.806383i	−0.0228094	−	0.0271832i
$881$	−4.14619	+	7.18141i	−0.139689	+	0.241948i	−0.927379	−	0.374124i	$-0.877944\pi$
$881$	−4.14619	+	7.18141i	−0.139689	+	0.241948i	0.787690	+	0.616072i	$0.211277\pi$
$882$	−16.4910	+	13.0018i	−0.555281	+	0.437793i
$883$	4.64089	+	8.03826i	0.156178	+	0.270509i	0.933488	−	0.358610i	$-0.116749\pi$
$883$	4.64089	+	8.03826i	0.156178	+	0.270509i	−0.777309	+	0.629119i	$0.783416\pi$
$884$	−0.799434	+	2.19643i	−0.0268879	+	0.0738738i
$885$	12.4172	−	29.2645i	0.417399	−	0.983714i
$886$	5.71655	+	4.79675i	0.192051	+	0.161150i
$887$	5.75377	−	32.6313i	0.193193	−	1.09565i	−0.721776	−	0.692126i	$-0.756674\pi$
$887$	5.75377	−	32.6313i	0.193193	−	1.09565i	0.914969	−	0.403524i	$-0.132215\pi$
$888$	2.00719	+	3.93797i	0.0673569	+	0.132150i
$889$	8.12525	+	7.54560i	0.272512	+	0.253071i
$890$		−	2.50527i		−	0.0839770i
$891$	3.84990	−	6.16882i	0.128976	−	0.206663i
$892$	−18.7897	−	10.8482i	−0.629126	−	0.363226i
$893$	−0.892346	−	1.06346i	−0.0298612	−	0.0355872i
$894$	−4.51420	−	2.93065i	−0.150977	−	0.0980157i
$895$	−0.406190	+	0.484078i	−0.0135774	+	0.0161810i
$896$	0.133008	−	2.64241i	0.00444350	−	0.0882766i
$897$	19.2660	−	2.36832i	0.643274	−	0.0790758i
$898$	−18.0376	−	6.56514i	−0.601921	−	0.219081i
$899$	−7.78230			−0.259554
$900$	5.82130	−	8.01706i	0.194043	−	0.267235i
$901$		−	13.2111i		−	0.440127i
$902$	−0.627622	−	3.55942i	−0.0208975	−	0.118516i
$903$	31.7560	−	14.2227i	1.05677	−	0.473303i
$904$	−10.7160	+	3.90029i	−0.356407	+	0.129722i
$905$	−12.0542	+	14.3657i	−0.400696	+	0.477531i
$906$	−9.40302	+	40.7551i	−0.312395	+	1.35400i
$907$	3.45774	+	1.25851i	0.114812	+	0.0417882i	0.398787	−	0.917043i	$-0.369431\pi$
$907$	3.45774	+	1.25851i	0.114812	+	0.0417882i	−0.283975	+	0.958832i	$0.591653\pi$
$908$	17.1758			0.569998
$909$	−0.501356	−	7.14094i	−0.0166289	−	0.236850i
$910$	5.01918	+	2.11829i	0.166384	+	0.0702205i
$911$	24.9022	+	29.6773i	0.825046	+	0.983252i	0.999999	−	0.00132505i	$-0.000421776\pi$
$911$	24.9022	+	29.6773i	0.825046	+	0.983252i	−0.174953	+	0.984577i	$0.555977\pi$
$912$	0.120134	+	0.977278i	0.00397803	+	0.0323609i
$913$	3.86367	−	4.60454i	0.127869	−	0.152388i
$914$	3.86673	+	10.6237i	0.127900	+	0.351402i
$915$	15.5177	+	0.811064i	0.512998	+	0.0268129i
$916$	0.821898	−	2.25814i	0.0271563	−	0.0746112i
$917$	−1.97544	−	15.8184i	−0.0652346	−	0.522368i
$918$	6.58553	−	3.96076i	0.217355	−	0.130725i
$919$	−18.4384	−	31.9362i	−0.608226	−	1.05348i	−0.991533	−	0.129857i	$-0.958548\pi$
$919$	−18.4384	−	31.9362i	−0.608226	−	1.05348i	0.383307	−	0.923621i	$-0.374785\pi$
$920$	−7.07726	+	5.93852i	−0.233330	+	0.195787i
$921$	25.5843	−	39.4085i	0.843031	−	1.29855i
$922$	−13.5952	−	2.39720i	−0.447734	−	0.0789477i
$923$	3.60413	−	20.4400i	0.118631	−	0.672792i
$924$	3.59055	−	0.903644i	0.118120	−	0.0297277i
$925$	−6.45600	+	5.41723i	−0.212272	+	0.178117i
$926$	4.61709	+	2.66568i	0.151727	+	0.0875997i
$927$	−2.33371	−	9.34884i	−0.0766492	−	0.307056i
$928$	1.32652	+	2.29760i	0.0435451	+	0.0754224i
$929$	18.0744	−	15.1662i	0.593001	−	0.497587i	−0.296187	−	0.955130i	$-0.595715\pi$
$929$	18.0744	−	15.1662i	0.593001	−	0.497587i	0.889187	+	0.457543i	$0.151271\pi$
$930$	−4.51381	+	4.84183i	−0.148014	+	0.158770i
$931$	3.96848	−	0.293988i	0.130062	−	0.00963505i
$932$	6.16559	+	16.9398i	0.201961	+	0.554882i
$933$	20.9293	+	4.82881i	0.685193	+	0.158088i
$934$	4.51208	−	12.3968i	0.147640	−	0.405637i
$935$	1.34825	−	0.778414i	0.0440926	−	0.0254568i
$936$	−3.29455	−	3.40969i	−0.107686	−	0.111449i
$937$	−30.5436	+	17.6344i	−0.997817	+	0.576090i	−0.907602	−	0.419832i	$-0.862089\pi$
$937$	−30.5436	+	17.6344i	−0.997817	+	0.576090i	−0.0902154	+	0.995922i	$0.528756\pi$
$938$	8.86584	+	28.7860i	0.289480	+	0.939896i
$939$	−20.2442	+	15.2596i	−0.660645	+	0.497977i
$940$	−2.98977	+	1.08819i	−0.0975154	+	0.0354927i
$941$	41.3447	−	15.0482i	1.34780	−	0.490559i	0.435539	−	0.900170i	$-0.356558\pi$
$941$	41.3447	−	15.0482i	1.34780	−	0.490559i	0.912260	+	0.409611i	$0.134336\pi$
$942$	−4.11166	−	2.66932i	−0.133965	−	0.0869712i
$943$	−31.2394	+	5.50835i	−1.01730	+	0.179377i
$944$	−14.0873			−0.458503
$945$	−8.44823	−	15.7939i	−0.274821	−	0.513776i
$946$	−6.13482			−0.199460
$947$	−59.5729	+	10.5043i	−1.93586	+	0.341344i	−0.999941	−	0.0108690i	$-0.996540\pi$
$947$	−59.5729	+	10.5043i	−1.93586	+	0.341344i	−0.935920	+	0.352213i	$0.885429\pi$
$948$	18.0938	−	9.22244i	0.587659	−	0.299531i
$949$	−17.7613	+	6.46459i	−0.576557	+	0.209849i
$950$	−1.76420	+	0.642117i	−0.0572383	+	0.0208330i
$951$	10.9457	+	4.64437i	0.354939	+	0.150604i
$952$	3.81445	+	0.872339i	0.123627	+	0.0282727i
$953$	12.0840	−	6.97668i	0.391438	−	0.225997i	−0.291345	−	0.956618i	$-0.594103\pi$
$953$	12.0840	−	6.97668i	0.391438	−	0.225997i	0.682783	+	0.730621i	$0.260769\pi$
$954$	24.0895	+	11.7409i	0.779927	+	0.380125i
$955$	9.85033	−	5.68709i	0.318749	−	0.184030i
$956$	−3.63113	+	9.97646i	−0.117439	+	0.322662i
$957$	−2.53168	+	2.71566i	−0.0818377	+	0.0877848i
$958$	1.98122	+	5.44337i	0.0640105	+	0.175867i
$959$	23.4236	+	15.1428i	0.756389	+	0.488986i
$960$	2.19887	+	0.507323i	0.0709681	+	0.0163738i
$961$	17.1559	−	14.3955i	0.553416	−	0.464371i
$962$	2.01655	+	3.49277i	0.0650162	+	0.112611i
$963$	16.4206	−	7.31644i	0.529146	−	0.235769i
$964$	17.6965	+	10.2171i	0.569965	+	0.329069i
$965$	−7.42533	+	6.23059i	−0.239030	+	0.200570i
$966$	−7.93088	−	31.5126i	−0.255172	−	1.01390i
$967$	−2.69054	+	15.2588i	−0.0865218	+	0.490689i	0.910496	+	0.413518i	$0.135700\pi$
$967$	−2.69054	+	15.2588i	−0.0865218	+	0.490689i	−0.997018	+	0.0771716i	$0.975411\pi$
$968$	10.1900	+	1.79677i	0.327519	+	0.0577505i
$969$	−1.45424	−	0.0760089i	−0.0467169	−	0.00244176i
$970$	15.8840	−	13.3282i	0.510003	−	0.427943i
$971$	−5.19485	−	8.99775i	−0.166711	−	0.288752i	0.770551	−	0.637379i	$-0.219981\pi$
$971$	−5.19485	−	8.99775i	−0.166711	−	0.288752i	−0.937261	+	0.348627i	$0.886648\pi$
$972$	1.36952	+	15.5282i	0.0439273	+	0.498067i
$973$	−10.9929	+	26.0472i	−0.352416	+	0.835034i
$974$	13.2452	−	36.3909i	0.424404	−	1.16604i
$975$	4.92267	−	7.58258i	0.157652	−	0.242837i
$976$	−2.35510	−	6.47059i	−0.0753850	−	0.207119i
$977$	−33.9502	+	40.4603i	−1.08616	+	1.29444i	−0.133289	+	0.991077i	$0.542554\pi$
$977$	−33.9502	+	40.4603i	−1.08616	+	1.29444i	−0.952875	+	0.303363i	$0.901891\pi$
$978$	14.6689	−	11.0570i	0.469060	−	0.353565i
$979$	−0.998642	−	1.19014i	−0.0319167	−	0.0380369i
$980$	2.47758	−	8.77708i	0.0791435	−	0.280374i
$981$	8.91134	−	12.2726i	0.284517	−	0.391835i
$982$	−34.3448			−1.09599
$983$	39.5826	+	14.4069i	1.26249	+	0.459509i	0.884604	−	0.466344i	$-0.154429\pi$
$983$	39.5826	+	14.4069i	1.26249	+	0.459509i	0.377886	+	0.925852i	$0.376651\pi$
$984$	5.66742	+	5.28347i	0.180671	+	0.168431i
$985$	11.0154	−	13.1277i	0.350981	−	0.418283i
$986$	−3.68708	+	1.34199i	−0.117421	+	0.0427376i
$987$	1.14520	−	11.1320i	0.0364520	−	0.354337i
$988$	0.156014	+	0.884797i	0.00496345	+	0.0281491i
$989$			53.8425i			1.71209i
$990$	0.221173	+	3.15022i	0.00702934	+	0.100121i
$991$	8.14833			0.258840			0.129420	−	0.991590i	$-0.458688\pi$
$991$	8.14833			0.258840			0.129420	+	0.991590i	$0.458688\pi$
$992$	2.75645	+	1.00327i	0.0875174	+	0.0318537i
$993$	23.6315	−	55.6940i	0.749923	−	1.76740i
$994$	−34.7018	−	1.74675i	−1.10067	−	0.0554037i
$995$	−7.38716	+	8.80368i	−0.234189	+	0.279095i
$996$	−0.672577	+	12.8681i	−0.0213114	+	0.407741i
$997$	−13.4404	−	16.0177i	−0.425662	−	0.507284i	0.510003	−	0.860172i	$-0.329644\pi$
$997$	−13.4404	−	16.0177i	−0.425662	−	0.507284i	−0.935666	+	0.352888i	$0.885200\pi$
$998$	36.9559	+	21.3365i	1.16982	+	0.675395i
$999$	2.06881	−	13.0976i	0.0654542	−	0.414390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.ba.a.185.19	yes	144
7.5	odd	6		378.2.bf.a.131.10	yes	144
27.20	odd	18		378.2.bf.a.101.10	yes	144
189.47	even	18	inner	378.2.ba.a.47.19	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.19	✓	144	189.47	even	18	inner
378.2.ba.a.185.19	yes	144	1.1	even	1	trivial
378.2.bf.a.101.10	yes	144	27.20	odd	18
378.2.bf.a.131.10	yes	144	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0904059 + 1.72969i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.22429 - 0.445607i) q^{5} +(0.211325 + 1.71911i) q^{6} +(2.52854 - 0.778769i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98365 - 0.312748i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(-0.0904059 + 1.72969i) q^{3} +(0.939693 - 0.342020i) q^{4} +(1.22429 - 0.445607i) q^{5} +(0.211325 + 1.71911i) q^{6} +(2.52854 - 0.778769i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.98365 - 0.312748i) q^{9} +(1.12832 - 0.651433i) q^{10} +(0.276337 - 0.759229i) q^{11} +(0.506635 + 1.65630i) q^{12} +(0.540542 + 1.48513i) q^{13} +(2.35489 - 1.20601i) q^{14} +(0.660078 + 2.15793i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.739475 + 1.28081i) q^{17} +(-2.99263 + 0.210109i) q^{18} +(0.492317 + 0.284240i) q^{19} +(0.998054 - 0.837467i) q^{20} +(1.11843 + 4.44400i) q^{21} +(0.140300 - 0.795680i) q^{22} +(-6.98333 - 1.23135i) q^{23} +(0.786551 + 1.54316i) q^{24} +(-2.52989 + 2.12283i) q^{25} +(0.790219 + 1.36870i) q^{26} +(0.810697 - 5.13252i) q^{27} +(2.10970 - 1.59662i) q^{28} +(-0.907392 + 2.49304i) q^{29} +(1.02477 + 2.01053i) q^{30} +(1.00327 + 2.75645i) q^{31} +(0.642788 - 0.766044i) q^{32} +(1.28825 + 0.546616i) q^{33} +(0.950650 + 1.13294i) q^{34} +(2.74865 - 2.08018i) q^{35} +(-2.91068 + 0.726582i) q^{36} +2.55189 q^{37} +(0.534196 + 0.194431i) q^{38} +(-2.61768 + 0.800706i) q^{39} +(0.837467 - 0.998054i) q^{40} +(4.20365 - 1.53000i) q^{41} +(1.87313 + 4.18227i) q^{42} +(-1.31851 - 7.47766i) q^{43} -0.807955i q^{44} +(-3.79223 + 0.946640i) q^{45} -7.09106 q^{46} +(-2.29476 - 0.835224i) q^{47} +(1.04257 + 1.38313i) q^{48} +(5.78704 - 3.93830i) q^{49} +(-2.12283 + 2.52989i) q^{50} +(-2.28225 + 1.16327i) q^{51} +(1.01589 + 1.21069i) q^{52} +(-7.73602 - 4.46640i) q^{53} +(-0.0928721 - 5.19532i) q^{54} -1.05266i q^{55} +(1.80040 - 1.93870i) q^{56} +(-0.536155 + 0.825859i) q^{57} +(-0.460695 + 2.61273i) q^{58} +(-10.7915 - 9.05515i) q^{59} +(1.35833 + 1.80204i) q^{60} +(2.35510 - 6.47059i) q^{61} +(1.46668 + 2.54036i) q^{62} +(-7.78785 + 1.53278i) q^{63} +(0.500000 - 0.866025i) q^{64} +(1.32356 + 1.57736i) q^{65} +(1.36360 + 0.314609i) q^{66} +(-1.97688 + 11.2115i) q^{67} +(1.13294 + 0.950650i) q^{68} +(2.76119 - 11.9677i) q^{69} +(2.34568 - 2.52587i) q^{70} +(-11.3732 - 6.56633i) q^{71} +(-2.74029 + 1.22098i) q^{72} +11.9595i q^{73} +(2.51312 - 0.443131i) q^{74} +(-3.44312 - 4.56784i) q^{75} +(0.559843 + 0.0987154i) q^{76} +(0.107465 - 2.13495i) q^{77} +(-2.43887 + 1.24310i) q^{78} +(-2.03605 - 11.5470i) q^{79} +(0.651433 - 1.12832i) q^{80} +(8.80438 + 1.86626i) q^{81} +(3.87410 - 2.23671i) q^{82} +(6.99087 + 2.54447i) q^{83} +(2.57092 + 3.79346i) q^{84} +(1.47607 + 1.23857i) q^{85} +(-2.59697 - 7.13510i) q^{86} +(-4.23015 - 1.79489i) q^{87} +(-0.140300 - 0.795680i) q^{88} +(0.961447 - 1.66527i) q^{89} +(-3.57024 + 1.59077i) q^{90} +(2.52335 + 3.33425i) q^{91} +(-6.98333 + 1.23135i) q^{92} +(-4.85851 + 1.48614i) q^{93} +(-2.40493 - 0.424054i) q^{94} +(0.729400 + 0.128613i) q^{95} +(1.26691 + 1.18108i) q^{96} +(15.6731 - 2.76360i) q^{97} +(5.01524 - 4.88338i) q^{98} +(-1.06194 + 2.17885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) \) 144 * q - 18 * q^6 + 24 * q^9	\( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) \) 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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