LMFDB - Embedded newform 273.2.bz.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.b.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02552 - 0.542736i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.07611 + 1.19864i) q^{4} +(0.220234 - 0.821926i) q^{5} +(-1.48278 - 1.48278i) q^{6} +(0.498246 + 2.59841i) q^{7} +(-0.589092 - 0.589092i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.02552 - 0.542736i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.07611 + 1.19864i) q^{4} +(0.220234 - 0.821926i) q^{5} +(-1.48278 - 1.48278i) q^{6} +(0.498246 + 2.59841i) q^{7} +(-0.589092 - 0.589092i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.892178 + 1.54530i) q^{10} +(-2.99793 + 0.803294i) q^{11} +(1.19864 + 2.07611i) q^{12} +(3.60505 - 0.0598320i) q^{13} +(0.401046 - 5.53355i) q^{14} +(0.601692 - 0.601692i) q^{15} +(-1.52379 - 2.63929i) q^{16} +(0.206711 - 0.358033i) q^{17} +(-0.542736 - 2.02552i) q^{18} +(-2.13893 + 7.98261i) q^{19} +(1.44243 - 1.44243i) q^{20} +(-0.867713 + 2.49941i) q^{21} +6.50834 q^{22} +(-0.426092 + 0.246004i) q^{23} +(-0.215623 - 0.804715i) q^{24} +(3.70307 + 2.13797i) q^{25} +(-7.33458 - 1.83540i) q^{26} +1.00000i q^{27} +(-2.08016 + 5.99182i) q^{28} +9.90597 q^{29} +(-1.54530 + 0.892178i) q^{30} +(4.18465 - 1.12127i) q^{31} +(2.08528 + 7.78237i) q^{32} +(-2.99793 - 0.803294i) q^{33} +(-0.613014 + 0.613014i) q^{34} +(2.24543 + 0.162739i) q^{35} +2.39729i q^{36} +(0.315519 - 1.17753i) q^{37} +(8.66490 - 15.0080i) q^{38} +(3.15199 + 1.75071i) q^{39} +(-0.613928 + 0.354452i) q^{40} +(2.61146 + 2.61146i) q^{41} +(3.11409 - 4.59167i) q^{42} -4.14927i q^{43} +(-7.18691 - 1.92573i) q^{44} +(0.821926 - 0.220234i) q^{45} +(0.996572 - 0.267031i) q^{46} +(-5.42098 - 1.45255i) q^{47} -3.04759i q^{48} +(-6.50350 + 2.58930i) q^{49} +(-6.34028 - 6.34028i) q^{50} +(0.358033 - 0.206711i) q^{51} +(7.55622 + 4.19696i) q^{52} +(-3.68892 + 6.38940i) q^{53} +(0.542736 - 2.02552i) q^{54} +2.64099i q^{55} +(1.23719 - 1.82422i) q^{56} +(-5.84367 + 5.84367i) q^{57} +(-20.0647 - 5.37633i) q^{58} +(0.904707 + 3.37641i) q^{59} +(1.97039 - 0.527965i) q^{60} +(2.20104 - 1.27077i) q^{61} -9.08463 q^{62} +(-2.00117 + 1.73070i) q^{63} -10.7999i q^{64} +(0.744780 - 2.97627i) q^{65} +(5.63639 + 3.25417i) q^{66} +(-3.67889 - 13.7298i) q^{67} +(0.858309 - 0.495545i) q^{68} -0.492008 q^{69} +(-4.45984 - 1.54831i) q^{70} +(-6.37812 + 6.37812i) q^{71} +(0.215623 - 0.804715i) q^{72} +(-3.62354 - 13.5232i) q^{73} +(-1.27818 + 2.21387i) q^{74} +(2.13797 + 3.70307i) q^{75} +(-14.0090 + 14.0090i) q^{76} +(-3.58100 - 7.38963i) q^{77} +(-5.43423 - 5.25679i) q^{78} +(-4.27606 - 7.40636i) q^{79} +(-2.50489 + 0.671183i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.87223 - 6.70690i) q^{82} +(-8.63202 - 8.63202i) q^{83} +(-4.79738 + 4.14899i) q^{84} +(-0.248752 - 0.248752i) q^{85} +(-2.25196 + 8.40443i) q^{86} +(8.57882 + 4.95299i) q^{87} +(2.23927 + 1.29284i) q^{88} +(6.52842 + 1.74928i) q^{89} -1.78436 q^{90} +(1.95167 + 9.33761i) q^{91} -1.17949 q^{92} +(4.18465 + 1.12127i) q^{93} +(10.1919 + 5.88432i) q^{94} +(6.09005 + 3.51609i) q^{95} +(-2.08528 + 7.78237i) q^{96} +(4.47968 + 4.47968i) q^{97} +(14.5783 - 1.71499i) q^{98} +(-2.19464 - 2.19464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.02552	−	0.542736i	−1.43226	−	0.383772i	−0.542443	−	0.840093i	$-0.682500\pi$
$2$	−2.02552	−	0.542736i	−1.43226	−	0.383772i	−0.889815	+	0.456321i	$0.849167\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	2.07611	+	1.19864i	1.03806	+	0.599322i
$5$	0.220234	−	0.821926i	0.0984918	−	0.367576i	−0.899034	−	0.437879i	$-0.855730\pi$
$5$	0.220234	−	0.821926i	0.0984918	−	0.367576i	0.997526	+	0.0703026i	$0.0223965\pi$
$6$	−1.48278	−	1.48278i	−0.605343	−	0.605343i
$7$	0.498246	+	2.59841i	0.188319	+	0.982108i
$7$	0.498246	+	2.59841i	0.188319	+	0.982108i
$8$	−0.589092	−	0.589092i	−0.208275	−	0.208275i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.892178	+	1.54530i	−0.282131	+	0.488666i
$11$	−2.99793	+	0.803294i	−0.903911	+	0.242202i	−0.680695	−	0.732567i	$-0.738322\pi$
$11$	−2.99793	+	0.803294i	−0.903911	+	0.242202i	−0.223216	+	0.974769i	$0.571655\pi$
$12$	1.19864	+	2.07611i	0.346019	+	0.599322i
$13$	3.60505	−	0.0598320i	0.999862	−	0.0165944i
$13$	3.60505	−	0.0598320i	0.999862	−	0.0165944i
$14$	0.401046	−	5.53355i	0.107184	−	1.47890i
$15$	0.601692	−	0.601692i	0.155356	−	0.155356i
$16$	−1.52379	−	2.63929i	−0.380948	−	0.659822i
$17$	0.206711	−	0.358033i	0.0501347	−	0.0868358i	−0.839869	−	0.542789i	$-0.817368\pi$
$17$	0.206711	−	0.358033i	0.0501347	−	0.0868358i	0.890004	+	0.455953i	$0.150702\pi$
$18$	−0.542736	−	2.02552i	−0.127924	−	0.477419i
$19$	−2.13893	+	7.98261i	−0.490705	+	1.83134i	0.0621617	+	0.998066i	$0.480201\pi$
$19$	−2.13893	+	7.98261i	−0.490705	+	1.83134i	−0.552867	+	0.833270i	$0.686466\pi$
$20$	1.44243	−	1.44243i	0.322537	−	0.322537i
$21$	−0.867713	+	2.49941i	−0.189350	+	0.545417i
$22$	6.50834			1.38758
$23$	−0.426092	+	0.246004i	−0.0888463	+	0.0512954i	−0.543765	−	0.839238i	$-0.683002\pi$
$23$	−0.426092	+	0.246004i	−0.0888463	+	0.0512954i	0.454919	+	0.890533i	$0.349668\pi$
$24$	−0.215623	−	0.804715i	−0.0440138	−	0.164262i
$25$	3.70307	+	2.13797i	0.740614	+	0.427593i
$26$	−7.33458	−	1.83540i	−1.43843	−	0.359952i
$27$			1.00000i			0.192450i
$28$	−2.08016	+	5.99182i	−0.393113	+	1.13235i
$29$	9.90597			1.83949			0.919746	−	0.392513i	$-0.128394\pi$
$29$	9.90597			1.83949			0.919746	+	0.392513i	$0.128394\pi$
$30$	−1.54530	+	0.892178i	−0.282131	+	0.162889i
$31$	4.18465	−	1.12127i	0.751584	−	0.201386i	0.137364	−	0.990521i	$-0.456137\pi$
$31$	4.18465	−	1.12127i	0.751584	−	0.201386i	0.614221	+	0.789134i	$0.289470\pi$
$32$	2.08528	+	7.78237i	0.368629	+	1.37574i
$33$	−2.99793	−	0.803294i	−0.521873	−	0.139835i
$34$	−0.613014	+	0.613014i	−0.105131	+	0.105131i
$35$	2.24543	+	0.162739i	0.379548	+	0.0275078i
$36$			2.39729i			0.399548i
$37$	0.315519	−	1.17753i	0.0518710	−	0.193585i	−0.935128	−	0.354309i	$-0.884716\pi$
$37$	0.315519	−	1.17753i	0.0518710	−	0.193585i	0.986999	+	0.160724i	$0.0513828\pi$
$38$	8.66490	−	15.0080i	1.40563	−	2.43463i
$39$	3.15199	+	1.75071i	0.504722	+	0.280338i
$40$	−0.613928	+	0.354452i	−0.0970706	+	0.0560437i
$41$	2.61146	+	2.61146i	0.407842	+	0.407842i	0.880985	−	0.473143i	$-0.156881\pi$
$41$	2.61146	+	2.61146i	0.407842	+	0.407842i	−0.473143	+	0.880985i	$0.656881\pi$
$42$	3.11409	−	4.59167i	0.480515	−	0.708510i
$43$		−	4.14927i		−	0.632758i	−0.948633	−	0.316379i	$-0.897533\pi$
$43$		−	4.14927i		−	0.632758i	0.948633	−	0.316379i	$-0.102467\pi$
$44$	−7.18691	−	1.92573i	−1.08347	−	0.290314i
$45$	0.821926	−	0.220234i	0.122525	−	0.0328306i
$46$	0.996572	−	0.267031i	0.146937	−	0.0393715i
$47$	−5.42098	−	1.45255i	−0.790731	−	0.211876i	−0.159220	−	0.987243i	$-0.550898\pi$
$47$	−5.42098	−	1.45255i	−0.790731	−	0.211876i	−0.631510	+	0.775367i	$0.717565\pi$
$48$		−	3.04759i		−	0.439881i
$49$	−6.50350	+	2.58930i	−0.929072	+	0.369900i
$50$	−6.34028	−	6.34028i	−0.896651	−	0.896651i
$51$	0.358033	−	0.206711i	0.0501347	−	0.0289453i
$52$	7.55622	+	4.19696i	1.04786	+	0.582014i
$53$	−3.68892	+	6.38940i	−0.506713	+	0.877652i	0.493257	+	0.869884i	$0.335806\pi$
$53$	−3.68892	+	6.38940i	−0.506713	+	0.877652i	−0.999970	+	0.00776859i	$0.997527\pi$
$54$	0.542736	−	2.02552i	0.0738570	−	0.275638i
$55$			2.64099i			0.356111i
$56$	1.23719	−	1.82422i	0.165327	−	0.243771i
$57$	−5.84367	+	5.84367i	−0.774014	+	0.774014i
$58$	−20.0647	−	5.37633i	−2.63463	−	0.705946i
$59$	0.904707	+	3.37641i	0.117783	+	0.439572i	0.999480	−	0.0322441i	$-0.0102654\pi$
$59$	0.904707	+	3.37641i	0.117783	+	0.439572i	−0.881697	+	0.471816i	$0.843599\pi$
$60$	1.97039	−	0.527965i	0.254377	−	0.0681600i
$61$	2.20104	−	1.27077i	0.281814	−	0.162705i	−0.352430	−	0.935838i	$-0.614645\pi$
$61$	2.20104	−	1.27077i	0.281814	−	0.162705i	0.634244	+	0.773133i	$0.281311\pi$
$62$	−9.08463			−1.15375
$63$	−2.00117	+	1.73070i	−0.252124	+	0.218048i
$64$		−	10.7999i		−	1.34999i
$65$	0.744780	−	2.97627i	0.0923785	−	0.369160i
$66$	5.63639	+	3.25417i	0.693792	+	0.400561i
$67$	−3.67889	−	13.7298i	−0.449448	−	1.67736i	−0.703917	−	0.710282i	$-0.748567\pi$
$67$	−3.67889	−	13.7298i	−0.449448	−	1.67736i	0.254469	−	0.967081i	$-0.418099\pi$
$68$	0.858309	−	0.495545i	0.104085	−	0.0600937i
$69$	−0.492008			−0.0592309
$70$	−4.45984	−	1.54831i	−0.533053	−	0.185058i
$71$	−6.37812	+	6.37812i	−0.756943	+	0.756943i	−0.975765	−	0.218822i	$-0.929779\pi$
$71$	−6.37812	+	6.37812i	−0.756943	+	0.756943i	0.218822	+	0.975765i	$0.429779\pi$
$72$	0.215623	−	0.804715i	0.0254114	−	0.0948365i
$73$	−3.62354	−	13.5232i	−0.424103	−	1.58277i	−0.765874	−	0.642991i	$-0.777693\pi$
$73$	−3.62354	−	13.5232i	−0.424103	−	1.58277i	0.341771	−	0.939783i	$-0.388973\pi$
$74$	−1.27818	+	2.21387i	−0.148585	+	0.257357i
$75$	2.13797	+	3.70307i	0.246871	+	0.427593i
$76$	−14.0090	+	14.0090i	−1.60694	+	1.60694i
$77$	−3.58100	−	7.38963i	−0.408092	−	0.842126i
$78$	−5.43423	−	5.25679i	−0.615305	−	0.595215i
$79$	−4.27606	−	7.40636i	−0.481095	−	0.833280i	0.518670	−	0.854974i	$-0.326427\pi$
$79$	−4.27606	−	7.40636i	−0.481095	−	0.833280i	−0.999765	+	0.0216943i	$0.993094\pi$
$80$	−2.50489	+	0.671183i	−0.280055	+	0.0750406i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.87223	−	6.70690i	−0.427617	−	0.740654i
$83$	−8.63202	−	8.63202i	−0.947487	−	0.947487i	0.0512011	−	0.998688i	$-0.483695\pi$
$83$	−8.63202	−	8.63202i	−0.947487	−	0.947487i	−0.998688	+	0.0512011i	$0.983695\pi$
$84$	−4.79738	+	4.14899i	−0.523437	+	0.452692i
$85$	−0.248752	−	0.248752i	−0.0269810	−	0.0269810i
$86$	−2.25196	+	8.40443i	−0.242835	+	0.906273i
$87$	8.57882	+	4.95299i	0.919746	+	0.531016i
$88$	2.23927	+	1.29284i	0.238707	+	0.137818i
$89$	6.52842	+	1.74928i	0.692011	+	0.185424i	0.587649	−	0.809116i	$-0.300053\pi$
$89$	6.52842	+	1.74928i	0.692011	+	0.185424i	0.104361	+	0.994539i	$0.466720\pi$
$90$	−1.78436			−0.188088
$91$	1.95167	+	9.33761i	0.204591	+	0.978848i
$92$	−1.17949			−0.122970
$93$	4.18465	+	1.12127i	0.433928	+	0.116271i
$94$	10.1919	+	5.88432i	1.05122	+	0.606921i
$95$	6.09005	+	3.51609i	0.624825	+	0.360743i
$96$	−2.08528	+	7.78237i	−0.212828	+	0.794285i
$97$	4.47968	+	4.47968i	0.454843	+	0.454843i	0.896958	−	0.442115i	$-0.145772\pi$
$97$	4.47968	+	4.47968i	0.454843	+	0.454843i	−0.442115	+	0.896958i	$0.645772\pi$
$98$	14.5783	−	1.71499i	1.47263	−	0.173240i
$99$	−2.19464	−	2.19464i	−0.220570	−	0.220570i
$100$	5.12532	+	8.87732i	0.512532	+	0.887732i
$101$	4.31959	−	7.48175i	0.429815	−	0.744462i	−0.567041	−	0.823689i	$-0.691912\pi$
$101$	4.31959	−	7.48175i	0.429815	−	0.744462i	0.996857	+	0.0792273i	$0.0252453\pi$
$102$	−0.837393	+	0.224379i	−0.0829142	+	0.0222168i
$103$	−4.65197	−	8.05745i	−0.458372	−	0.793924i	0.540503	−	0.841342i	$-0.318234\pi$
$103$	−4.65197	−	8.05745i	−0.458372	−	0.793924i	−0.998875	+	0.0474182i	$0.984901\pi$
$104$	−2.15896	−	2.08846i	−0.211703	−	0.204791i
$105$	1.86323	+	1.26365i	0.181833	+	0.123320i
$106$	10.9397	−	10.9397i	1.06256	−	1.06256i
$107$	4.62055	+	8.00303i	0.446686	+	0.773683i	0.998168	−	0.0605042i	$-0.0192709\pi$
$107$	4.62055	+	8.00303i	0.446686	+	0.773683i	−0.551482	+	0.834187i	$0.685938\pi$
$108$	−1.19864	+	2.07611i	−0.115340	+	0.199774i
$109$	0.669594	+	2.49896i	0.0641355	+	0.239357i	0.990551	−	0.137146i	$-0.0437931\pi$
$109$	0.669594	+	2.49896i	0.0641355	+	0.239357i	−0.926415	+	0.376503i	$0.877126\pi$
$110$	1.43336	−	5.34938i	0.136666	−	0.510043i
$111$	0.862014	−	0.862014i	0.0818188	−	0.0818188i
$112$	6.09873	−	5.27446i	0.576276	−	0.498389i
$113$	−9.92126			−0.933314			−0.466657	−	0.884438i	$-0.654542\pi$
$113$	−9.92126			−0.933314			−0.466657	+	0.884438i	$0.654542\pi$
$114$	15.0080	−	8.66490i	1.40563	−	0.811542i
$115$	0.108357	+	0.404395i	0.0101044	+	0.0377100i
$116$	20.5659	+	11.8737i	1.90950	+	1.10245i
$117$	1.85434	+	3.09215i	0.171434	+	0.285870i
$118$		−	7.33001i		−	0.674782i
$119$	1.03331	+	0.358731i	0.0947235	+	0.0328848i
$120$	−0.708903			−0.0647137
$121$	−1.18396	+	0.683560i	−0.107633	+	0.0621418i
$122$	−5.14794	+	1.37939i	−0.466072	+	0.124884i
$123$	0.955862	+	3.56733i	0.0861872	+	0.321655i
$124$	10.0318	+	2.68801i	0.900882	+	0.241391i
$125$	5.58125	−	5.58125i	0.499202	−	0.499202i
$126$	4.99272	−	2.41946i	0.444787	−	0.215543i
$127$			17.6691i			1.56788i	0.620838	+	0.783939i	$0.286793\pi$
$127$			17.6691i			1.56788i	−0.620838	+	0.783939i	$0.713207\pi$
$128$	−1.69095	+	6.31070i	−0.149460	+	0.557793i
$129$	2.07464	−	3.59338i	0.182662	−	0.316379i
$130$	−3.12389	+	5.62426i	−0.273983	+	0.493280i
$131$	16.3849	−	9.45984i	1.43156	−	0.826510i	0.434318	−	0.900760i	$-0.356989\pi$
$131$	16.3849	−	9.45984i	1.43156	−	0.826510i	0.997240	+	0.0742495i	$0.0236561\pi$
$132$	−5.26118	−	5.26118i	−0.457927	−	0.457927i
$133$	−21.8078	−	1.58053i	−1.89098	−	0.137049i
$134$			29.8067i			2.57490i
$135$	0.821926	+	0.220234i	0.0707401	+	0.0189548i
$136$	−0.332686	+	0.0891430i	−0.0285276	+	0.00764395i
$137$	10.8269	−	2.90106i	0.925003	−	0.247854i	0.235281	−	0.971928i	$-0.424399\pi$
$137$	10.8269	−	2.90106i	0.925003	−	0.247854i	0.689723	+	0.724074i	$0.257732\pi$
$138$	0.996572	+	0.267031i	0.0848339	+	0.0227312i
$139$		−	2.52712i		−	0.214347i	−0.994240	−	0.107174i	$-0.965820\pi$
$139$		−	2.52712i		−	0.214347i	0.994240	−	0.107174i	$-0.0341801\pi$
$140$	4.46671	+	3.02934i	0.377506	+	0.256026i
$141$	−3.96843	−	3.96843i	−0.334202	−	0.334202i
$142$	16.3806	−	9.45736i	1.37463	−	0.793644i
$143$	−10.7596	+	3.07529i	−0.899767	+	0.257169i
$144$	1.52379	−	2.63929i	0.126983	−	0.219941i
$145$	2.18164	−	8.14197i	0.181175	−	0.676154i
$146$			29.3582i			2.42970i
$147$	−6.92685	−	1.00935i	−0.571317	−	0.0832500i
$148$	2.06650	−	2.06650i	0.169865	−	0.169865i
$149$	−7.88614	−	2.11309i	−0.646058	−	0.173111i	−0.0791120	−	0.996866i	$-0.525208\pi$
$149$	−7.88614	−	2.11309i	−0.646058	−	0.173111i	−0.566946	+	0.823755i	$0.691875\pi$
$150$	−2.32070	−	8.66099i	−0.189485	−	0.707166i
$151$	−2.81480	+	0.754224i	−0.229065	+	0.0613779i	−0.371526	−	0.928423i	$-0.621165\pi$
$151$	−2.81480	+	0.754224i	−0.229065	+	0.0613779i	0.142460	+	0.989800i	$0.454499\pi$
$152$	5.96252	−	3.44246i	0.483624	−	0.279221i
$153$	0.413421			0.0334231
$154$	3.24276	+	16.9114i	0.261309	+	1.36276i
$155$		−	3.68641i		−	0.296100i
$156$	4.44540	+	7.41278i	0.355917	+	0.593498i
$157$	−9.56036	−	5.51968i	−0.763000	−	0.440518i	0.0673717	−	0.997728i	$-0.478539\pi$
$157$	−9.56036	−	5.51968i	−0.763000	−	0.440518i	−0.830372	+	0.557210i	$0.811872\pi$
$158$	4.64155	+	17.3225i	0.369262	+	1.37810i
$159$	−6.38940	+	3.68892i	−0.506713	+	0.292551i
$160$	6.85578			0.541997
$161$	−0.851519	−	0.984592i	−0.0671091	−	0.0775967i
$162$	1.48278	−	1.48278i	0.116498	−	0.116498i
$163$	0.586902	−	2.19035i	0.0459697	−	0.171561i	−0.939124	−	0.343577i	$-0.888361\pi$
$163$	0.586902	−	2.19035i	0.0459697	−	0.171561i	0.985094	+	0.172016i	$0.0550280\pi$
$164$	2.29148	+	8.55191i	0.178934	+	0.667792i
$165$	−1.32050	+	2.28717i	−0.102800	+	0.178056i
$166$	12.7994	+	22.1692i	0.993427	+	1.72067i
$167$	8.26961	−	8.26961i	0.639922	−	0.639922i	−0.310614	−	0.950536i	$-0.600535\pi$
$167$	8.26961	−	8.26961i	0.639922	−	0.639922i	0.950536	+	0.310614i	$0.100535\pi$
$168$	1.98355	−	0.961223i	0.153034	−	0.0741599i
$169$	12.9928	−	0.431396i	0.999449	−	0.0331843i
$170$	0.368845	+	0.638859i	0.0282891	+	0.0489982i
$171$	−7.98261	+	2.13893i	−0.610445	+	0.163568i
$172$	4.97350	−	8.61436i	0.379226	−	0.656839i
$173$	−9.65446	−	16.7220i	−0.734015	−	1.27135i	−0.955154	−	0.296109i	$-0.904311\pi$
$173$	−9.65446	−	16.7220i	−0.734015	−	1.27135i	0.221139	−	0.975242i	$-0.429023\pi$
$174$	−14.6884	−	14.6884i	−1.11352	−	1.11352i
$175$	−3.71028	+	10.6873i	−0.280471	+	0.807887i
$176$	6.68835	+	6.68835i	0.504153	+	0.504153i
$177$	−0.904707	+	3.37641i	−0.0680020	+	0.253787i
$178$	−12.2740	−	7.08641i	−0.919977	−	0.531149i
$179$	−11.5367	−	6.66069i	−0.862290	−	0.497843i	0.00248848	−	0.999997i	$-0.499208\pi$
$179$	−11.5367	−	6.66069i	−0.862290	−	0.497843i	−0.864778	+	0.502154i	$0.832541\pi$
$180$	1.97039	+	0.527965i	0.146864	+	0.0393522i
$181$	0.758135			0.0563517			0.0281759	−	0.999603i	$-0.491030\pi$
$181$	0.758135			0.0563517			0.0281759	+	0.999603i	$0.491030\pi$
$182$	1.11471	−	19.9727i	0.0826277	−	1.48048i
$183$	2.54154			0.187876
$184$	0.395926	+	0.106088i	0.0291881	+	0.00782092i
$185$	−0.898357	−	0.518667i	−0.0660485	−	0.0381331i
$186$	−7.86752	−	4.54232i	−0.576875	−	0.333059i
$187$	−0.332099	+	1.23941i	−0.0242855	+	0.0906346i
$188$	−9.51347	−	9.51347i	−0.693841	−	0.693841i
$189$	−2.59841	+	0.498246i	−0.189007	+	0.0362421i
$190$	−10.4272	−	10.4272i	−0.756468	−	0.756468i
$191$	11.4856	+	19.8936i	0.831068	+	1.43945i	0.897192	+	0.441641i	$0.145604\pi$
$191$	11.4856	+	19.8936i	0.831068	+	1.43945i	−0.0661232	+	0.997811i	$0.521063\pi$
$192$	5.39996	−	9.35301i	0.389709	−	0.674995i
$193$	6.21044	−	1.66408i	0.447037	−	0.119783i	−0.0282756	−	0.999600i	$-0.509002\pi$
$193$	6.21044	−	1.66408i	0.447037	−	0.119783i	0.475313	+	0.879817i	$0.342335\pi$
$194$	−6.64240	−	11.5050i	−0.476896	−	0.826009i
$195$	2.13313	−	2.20513i	0.152757	−	0.157913i
$196$	−16.6056	−	2.41971i	−1.18612	−	0.172836i
$197$	−0.897366	+	0.897366i	−0.0639347	+	0.0639347i	−0.738351	−	0.674416i	$-0.764395\pi$
$197$	−0.897366	+	0.897366i	−0.0639347	+	0.0639347i	0.674416	+	0.738351i	$0.264395\pi$
$198$	3.25417	+	5.63639i	0.231264	+	0.400561i
$199$	2.13922	−	3.70523i	0.151645	−	0.262657i	−0.780187	−	0.625546i	$-0.784876\pi$
$199$	2.13922	−	3.70523i	0.151645	−	0.262657i	0.931832	+	0.362889i	$0.118210\pi$
$200$	−0.921988	−	3.44091i	−0.0651944	−	0.243309i
$201$	3.67889	−	13.7298i	0.259489	−	0.968426i
$202$	−12.8100	+	12.8100i	−0.901311	+	0.901311i
$203$	4.93561	+	25.7398i	0.346412	+	1.80658i
$204$	0.991090			0.0693902
$205$	2.72156	−	1.57130i	0.190082	−	0.109744i
$206$	5.04958	+	18.8453i	0.351821	+	1.31301i
$207$	−0.426092	−	0.246004i	−0.0296154	−	0.0170985i
$208$	−5.65127	−	9.42360i	−0.391845	−	0.653409i
$209$		−	25.6495i		−	1.77421i
$210$	−3.08818	−	3.57080i	−0.213105	−	0.246408i
$211$	14.4403			0.994110			0.497055	−	0.867719i	$-0.334415\pi$
$211$	14.4403			0.994110			0.497055	+	0.867719i	$0.334415\pi$
$212$	−15.3172	+	8.84341i	−1.05199	+	0.607368i
$213$	−8.71267	+	2.33455i	−0.596982	+	0.159961i
$214$	−5.01548	−	18.7180i	−0.342851	−	1.27954i
$215$	−3.41040	−	0.913813i	−0.232587	−	0.0623215i
$216$	0.589092	−	0.589092i	0.0400826	−	0.0400826i
$217$	4.99851	+	10.3148i	0.339321	+	0.700212i
$218$		−	5.42510i		−	0.367434i
$219$	3.62354	−	13.5232i	0.244856	−	0.913815i
$220$	−3.16561	+	5.48300i	−0.213425	+	0.369663i
$221$	0.723781	−	1.30310i	0.0486868	−	0.0876558i
$222$	−2.21387	+	1.27818i	−0.148585	+	0.0857858i
$223$	0.913313	+	0.913313i	0.0611599	+	0.0611599i	0.737025	−	0.675865i	$-0.236230\pi$
$223$	0.913313	+	0.913313i	0.0611599	+	0.0611599i	−0.675865	+	0.737025i	$0.736230\pi$
$224$	−19.1828	+	9.29596i	−1.28171	+	0.621112i
$225$			4.27593i			0.285062i
$226$	20.0957	+	5.38463i	1.33675	+	0.358180i
$227$	7.03137	−	1.88405i	0.466688	−	0.125049i	−0.0178091	−	0.999841i	$-0.505669\pi$
$227$	7.03137	−	1.88405i	0.466688	−	0.125049i	0.484498	+	0.874793i	$0.339002\pi$
$228$	−19.1366	+	5.12764i	−1.26735	+	0.339586i
$229$	−9.48673	−	2.54196i	−0.626901	−	0.167977i	−0.0686377	−	0.997642i	$-0.521865\pi$
$229$	−9.48673	−	2.54196i	−0.626901	−	0.167977i	−0.558263	+	0.829664i	$0.688532\pi$
$230$		−	0.877918i		−	0.0578882i
$231$	0.593580	−	8.19011i	0.0390547	−	0.538869i
$232$	−5.83553	−	5.83553i	−0.383121	−	0.383121i
$233$	−0.958246	+	0.553244i	−0.0627768	+	0.0362442i	−0.531060	−	0.847334i	$-0.678206\pi$
$233$	−0.958246	+	0.553244i	−0.0627768	+	0.0362442i	0.468283	+	0.883578i	$0.344873\pi$
$234$	−2.07778	−	7.26963i	−0.135829	−	0.475231i
$235$	−2.38777	+	4.13574i	−0.155761	+	0.269786i
$236$	−2.16884	+	8.09424i	−0.141180	+	0.526890i
$237$		−	8.55212i		−	0.555520i
$238$	−1.89830	−	1.28743i	−0.123048	−	0.0834518i
$239$	−8.91696	+	8.91696i	−0.576790	+	0.576790i	−0.934018	−	0.357227i	$-0.883722\pi$
$239$	−8.91696	+	8.91696i	−0.576790	+	0.576790i	0.357227	+	0.934018i	$0.383722\pi$
$240$	−2.50489	−	0.671183i	−0.161690	−	0.0433247i
$241$	−4.49590	−	16.7789i	−0.289606	−	1.08082i	−0.945407	−	0.325891i	$-0.894336\pi$
$241$	−4.49590	−	16.7789i	−0.289606	−	1.08082i	0.655801	−	0.754934i	$-0.272331\pi$
$242$	2.76913	−	0.741985i	0.178006	−	0.0476966i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	6.09281			0.390052
$245$	0.695917	+	5.91565i	0.0444605	+	0.377937i
$246$		−	7.74446i		−	0.493769i
$247$	−7.23336	+	28.9057i	−0.460247	+	1.83923i
$248$	−3.12567	−	1.80461i	−0.198480	−	0.114593i
$249$	−3.15954	−	11.7916i	−0.200228	−	0.747260i
$250$	−14.3341	+	8.27578i	−0.906567	+	0.523406i
$251$	−13.4051			−0.846120			−0.423060	−	0.906102i	$-0.639044\pi$
$251$	−13.4051			−0.846120			−0.423060	+	0.906102i	$0.639044\pi$
$252$	−6.22915	+	1.19444i	−0.392399	+	0.0752426i
$253$	1.07978	−	1.07978i	0.0678853	−	0.0678853i
$254$	9.58965	−	35.7891i	0.601708	−	2.24561i
$255$	−0.0910496	−	0.339802i	−0.00570175	−	0.0212792i
$256$	−3.94983	+	6.84131i	−0.246864	+	0.427582i
$257$	−5.41754	−	9.38346i	−0.337937	−	0.585324i	0.646107	−	0.763246i	$-0.276396\pi$
$257$	−5.41754	−	9.38346i	−0.337937	−	0.585324i	−0.984045	+	0.177922i	$0.943062\pi$
$258$	−6.15247	+	6.15247i	−0.383036	+	0.383036i
$259$	3.21692	+	0.233148i	0.199890	+	0.0144871i
$260$	5.11373	−	5.28634i	0.317140	−	0.327845i
$261$	4.95299	+	8.57882i	0.306582	+	0.531016i
$262$	−38.3222	+	10.2684i	−2.36755	+	0.634384i
$263$	11.4819	−	19.8873i	0.708007	−	1.22630i	−0.257589	−	0.966255i	$-0.582928\pi$
$263$	11.4819	−	19.8873i	0.708007	−	1.22630i	0.965595	−	0.260049i	$-0.0837388\pi$
$264$	1.29284	+	2.23927i	0.0795691	+	0.137818i
$265$	4.43919	+	4.43919i	0.272697	+	0.272697i
$266$	43.3144	+	15.0373i	2.65577	+	0.921995i
$267$	4.77913	+	4.77913i	0.292478	+	0.292478i
$268$	8.81936	−	32.9143i	0.538728	−	2.01056i
$269$	−2.45827	−	1.41928i	−0.149883	−	0.0865353i	0.423183	−	0.906044i	$-0.360913\pi$
$269$	−2.45827	−	1.41928i	−0.149883	−	0.0865353i	−0.573066	+	0.819509i	$0.694246\pi$
$270$	−1.54530	−	0.892178i	−0.0940438	−	0.0542962i
$271$	27.8738	+	7.46876i	1.69321	+	0.453695i	0.971215	−	0.238203i	$-0.0765582\pi$
$271$	27.8738	+	7.46876i	1.69321	+	0.453695i	0.721996	+	0.691897i	$0.243225\pi$
$272$	−1.25994			−0.0763949
$273$	−2.97861	+	9.06244i	−0.180273	+	0.548484i
$274$	−23.5046			−1.41996
$275$	−12.8190	−	3.43483i	−0.773013	−	0.207128i
$276$	−1.02146	−	0.589743i	−0.0614850	−	0.0354984i
$277$	1.07397	+	0.620055i	0.0645284	+	0.0372555i	0.531917	−	0.846796i	$-0.321472\pi$
$277$	1.07397	+	0.620055i	0.0645284	+	0.0372555i	−0.467389	+	0.884052i	$0.654805\pi$
$278$	−1.37156	+	5.11872i	−0.0822606	+	0.307001i
$279$	3.06337	+	3.06337i	0.183399	+	0.183399i
$280$	−1.22690	−	1.41864i	−0.0733213	−	0.0847797i
$281$	−8.85289	−	8.85289i	−0.528119	−	0.528119i	0.391892	−	0.920011i	$-0.371821\pi$
$281$	−8.85289	−	8.85289i	−0.528119	−	0.528119i	−0.920011	+	0.391892i	$0.871821\pi$
$282$	5.88432	+	10.1919i	0.350406	+	0.606921i
$283$	1.47438	−	2.55370i	0.0876428	−	0.151802i	−0.818871	−	0.573977i	$-0.805400\pi$
$283$	1.47438	−	2.55370i	0.0876428	−	0.151802i	0.906514	+	0.422175i	$0.138733\pi$
$284$	−20.8868	+	5.59660i	−1.23940	+	0.332097i
$285$	3.51609	+	6.09005i	0.208275	+	0.360743i
$286$	23.4629	−	0.389408i	1.38739	−	0.0230262i
$287$	−5.48451	+	8.08681i	−0.323740	+	0.477349i
$288$	−5.69709	+	5.69709i	−0.335704	+	0.335704i
$289$	8.41454	+	14.5744i	0.494973	+	0.857318i
$290$	−8.83789	+	15.3077i	−0.518979	+	0.898897i
$291$	1.63968	+	6.11936i	0.0961196	+	0.358723i
$292$	8.68667	−	32.4191i	0.508349	−	1.89718i
$293$	19.9885	−	19.9885i	1.16774	−	1.16774i	0.184999	−	0.982739i	$-0.440772\pi$
$293$	19.9885	−	19.9885i	1.16774	−	1.16774i	0.982739	−	0.184999i	$-0.0592283\pi$
$294$	13.4826	+	5.80391i	0.786324	+	0.338491i
$295$	2.97441			0.173177
$296$	−0.879545	+	0.507806i	−0.0511225	+	0.0295156i
$297$	−0.803294	−	2.99793i	−0.0466118	−	0.173958i
$298$	14.8267	+	8.56019i	0.858886	+	0.495878i
$299$	−1.52137	+	0.912353i	−0.0879828	+	0.0527627i
$300$			10.2506i			0.591821i
$301$	10.7815	−	2.06736i	0.621437	−	0.119161i
$302$	6.11078			0.351636
$303$	7.48175	−	4.31959i	0.429815	−	0.248154i
$304$	24.3277	−	6.51858i	1.39529	−	0.373866i
$305$	−0.559735	−	2.08896i	−0.0320503	−	0.119613i
$306$	−0.837393	−	0.224379i	−0.0478705	−	0.0128269i
$307$	16.9481	−	16.9481i	0.967282	−	0.967282i	−0.0321997	−	0.999481i	$-0.510251\pi$
$307$	16.9481	−	16.9481i	0.967282	−	0.967282i	0.999481	+	0.0321997i	$0.0102513\pi$
$308$	1.42298	−	19.6340i	0.0810820	−	1.11875i
$309$		−	9.30394i		−	0.529283i
$310$	−2.00075	+	7.46689i	−0.113635	+	0.424091i
$311$	−14.2289	+	24.6452i	−0.806847	+	1.39750i	0.108190	+	0.994130i	$0.465495\pi$
$311$	−14.2289	+	24.6452i	−0.806847	+	1.39750i	−0.915037	+	0.403370i	$0.867839\pi$
$312$	−0.825479	−	2.88814i	−0.0467336	−	0.163509i
$313$	8.98398	−	5.18691i	0.507805	−	0.293181i	−0.224126	−	0.974560i	$-0.571953\pi$
$313$	8.98398	−	5.18691i	0.507805	−	0.293181i	0.731931	+	0.681379i	$0.238619\pi$
$314$	16.3690	+	16.3690i	0.923754	+	0.923754i
$315$	0.981781	+	2.02597i	0.0553171	+	0.114151i
$316$		−	20.5019i		−	1.15332i
$317$	5.36127	+	1.43655i	0.301119	+	0.0806845i	0.406215	−	0.913778i	$-0.366848\pi$
$317$	5.36127	+	1.43655i	0.301119	+	0.0806845i	−0.105096	+	0.994462i	$0.533515\pi$
$318$	14.9440	−	4.00422i	0.838016	−	0.224546i
$319$	−29.6974	+	7.95740i	−1.66274	+	0.445529i
$320$	−8.87674	−	2.37851i	−0.496225	−	0.132963i
$321$			9.24111i			0.515788i
$322$	1.19039	+	2.45646i	0.0663381	+	0.136893i
$323$	2.41590	+	2.41590i	0.134424	+	0.134424i
$324$	−2.07611	+	1.19864i	−0.115340	+	0.0665913i
$325$	13.4777	+	7.48593i	0.747607	+	0.415245i
$326$	−2.37756	+	4.11806i	−0.131681	+	0.228078i
$327$	−0.669594	+	2.49896i	−0.0370286	+	0.138193i
$328$		−	3.07678i		−	0.169887i
$329$	1.07333	−	14.8097i	0.0591749	−	0.816483i
$330$	3.91602	−	3.91602i	0.215570	−	0.215570i
$331$	1.73372	+	0.464548i	0.0952937	+	0.0255339i	0.306151	−	0.951983i	$-0.400959\pi$
$331$	1.73372	+	0.464548i	0.0952937	+	0.0255339i	−0.210857	+	0.977517i	$0.567625\pi$
$332$	−7.57432	−	28.2678i	−0.415695	−	1.55140i
$333$	1.17753	−	0.315519i	0.0645284	−	0.0172903i
$334$	−21.2385	+	12.2620i	−1.16212	+	0.670949i
$335$	−12.0951			−0.660826
$336$	7.91889	−	1.51845i	0.432011	−	0.0828381i
$337$			34.8975i			1.90099i	0.310741	+	0.950495i	$0.399423\pi$
$337$			34.8975i			1.90099i	−0.310741	+	0.950495i	$0.600577\pi$
$338$	−26.5514	−	6.17788i	−1.44420	−	0.336033i
$339$	−8.59207	−	4.96063i	−0.466657	−	0.269425i
$340$	−0.218272	−	0.814603i	−0.0118375	−	0.0441780i
$341$	−11.6446	+	6.72300i	−0.630589	+	0.364071i
$342$	17.3298			0.937088
$343$	−9.96841	−	15.6087i	−0.538244	−	0.842789i
$344$	−2.44430	+	2.44430i	−0.131788	+	0.131788i
$345$	−0.108357	+	0.404395i	−0.00583375	+	0.0217719i
$346$	10.4796	+	39.1106i	0.563389	+	2.10260i
$347$	8.36008	−	14.4801i	0.448793	−	0.777332i	−0.549515	−	0.835484i	$-0.685187\pi$
$347$	8.36008	−	14.4801i	0.448793	−	0.777332i	0.998308	+	0.0581520i	$0.0185208\pi$
$348$	11.8737	+	20.5659i	0.636499	+	1.10245i
$349$	−20.0733	+	20.0733i	−1.07450	+	1.07450i	−0.0775094	+	0.996992i	$0.524697\pi$
$349$	−20.0733	+	20.0733i	−1.07450	+	1.07450i	−0.996992	+	0.0775094i	$0.975303\pi$
$350$	13.3156	−	19.6337i	0.711751	−	1.04946i
$351$	0.0598320	+	3.60505i	0.00319360	+	0.192424i
$352$	−12.5031	−	21.6559i	−0.666415	−	1.15427i
$353$	15.3915	−	4.12415i	0.819209	−	0.219506i	0.175208	−	0.984531i	$-0.443940\pi$
$353$	15.3915	−	4.12415i	0.819209	−	0.219506i	0.644000	+	0.765025i	$0.277273\pi$
$354$	3.66500	−	6.34797i	0.194793	−	0.337391i
$355$	3.83766	+	6.64702i	0.203682	+	0.352787i
$356$	11.4570	+	11.4570i	0.607217	+	0.607217i
$357$	0.715508	+	0.827326i	0.0378687	+	0.0437867i
$358$	19.7527	+	19.7527i	1.04396	+	1.04396i
$359$	−6.42338	+	23.9724i	−0.339013	+	1.26521i	0.560439	+	0.828196i	$0.310632\pi$
$359$	−6.42338	+	23.9724i	−0.339013	+	1.26521i	−0.899452	+	0.437019i	$0.856034\pi$
$360$	−0.613928	−	0.354452i	−0.0323569	−	0.0186812i
$361$	−42.6925	−	24.6485i	−2.24697	−	1.29729i
$362$	−1.53562	−	0.411467i	−0.0807102	−	0.0216262i
$363$	−1.36712			−0.0717552
$364$	−7.14058	+	21.7253i	−0.374268	+	1.13871i
$365$	−11.9131			−0.623561
$366$	−5.14794	−	1.37939i	−0.269087	−	0.0721017i
$367$	−27.5277	−	15.8931i	−1.43693	−	0.829615i	−0.439299	−	0.898341i	$-0.644773\pi$
$367$	−27.5277	−	15.8931i	−1.43693	−	0.829615i	−0.997636	+	0.0687263i	$0.978106\pi$
$368$	1.29855	+	0.749719i	0.0676917	+	0.0390818i
$369$	−0.955862	+	3.56733i	−0.0497602	+	0.185708i
$370$	1.53814	+	1.53814i	0.0799641	+	0.0799641i
$371$	−18.4403	−	6.40185i	−0.957373	−	0.332368i
$372$	7.34379	+	7.34379i	0.380758	+	0.380758i
$373$	1.03118	+	1.78606i	0.0533925	+	0.0924784i	0.891486	−	0.453048i	$-0.149663\pi$
$373$	1.03118	+	1.78606i	0.0533925	+	0.0924784i	−0.838094	+	0.545526i	$0.816330\pi$
$374$	1.34534	−	2.33020i	0.0695661	−	0.120492i
$375$	7.62413	−	2.04288i	0.393708	−	0.105494i
$376$	2.33777	+	4.04914i	0.120561	+	0.208818i
$377$	35.7116	−	0.592694i	1.83924	−	0.0305253i
$378$	5.53355	+	0.401046i	0.284615	+	0.0206276i
$379$	16.5343	−	16.5343i	0.849312	−	0.849312i	−0.140735	−	0.990047i	$-0.544947\pi$
$379$	16.5343	−	16.5343i	0.849312	−	0.849312i	0.990047	+	0.140735i	$0.0449466\pi$
$380$	8.42908	+	14.5996i	0.432403	+	0.748943i
$381$	−8.83454	+	15.3019i	−0.452607	+	0.783939i
$382$	−12.4673	−	46.5286i	−0.637882	−	2.38061i
$383$	4.24594	−	15.8461i	0.216957	−	0.809695i	−0.768511	−	0.639836i	$-0.779002\pi$
$383$	4.24594	−	15.8461i	0.216957	−	0.809695i	0.985468	−	0.169859i	$-0.0543312\pi$
$384$	−4.61976	+	4.61976i	−0.235751	+	0.235751i
$385$	−6.86239	+	1.31586i	−0.349740	+	0.0670626i
$386$	−13.4825			−0.686242
$387$	3.59338	−	2.07464i	0.182662	−	0.105460i
$388$	3.93078	+	14.6699i	0.199555	+	0.744750i
$389$	27.5754	+	15.9207i	1.39813	+	0.807210i	0.994196	−	0.107579i	$-0.0343100\pi$
$389$	27.5754	+	15.9207i	1.39813	+	0.807210i	0.403932	+	0.914789i	$0.367643\pi$
$390$	−5.51750	+	3.30881i	−0.279389	+	0.167548i
$391$			0.203407i			0.0102867i
$392$	5.35650	+	2.30583i	0.270544	+	0.116462i
$393$	18.9197			0.954372
$394$	2.30466	−	1.33060i	0.116107	−	0.0670346i
$395$	−7.02921	+	1.88347i	−0.353678	+	0.0947677i
$396$	−1.92573	−	7.18691i	−0.0967714	−	0.361156i
$397$	2.49070	+	0.667382i	0.125005	+	0.0334949i	0.320779	−	0.947154i	$-0.396055\pi$
$397$	2.49070	+	0.667382i	0.125005	+	0.0334949i	−0.195774	+	0.980649i	$0.562722\pi$
$398$	−6.34398	+	6.34398i	−0.317995	+	0.317995i
$399$	−18.0959	−	12.2727i	−0.905927	−	0.614403i
$400$		−	13.0313i		−	0.651564i
$401$	7.32742	−	27.3463i	0.365914	−	1.36561i	−0.500264	−	0.865873i	$-0.666764\pi$
$401$	7.32742	−	27.3463i	0.365914	−	1.36561i	0.866178	−	0.499736i	$-0.166570\pi$
$402$	−14.9033	+	25.8133i	−0.743310	+	1.28745i
$403$	15.0188	−	4.29262i	0.748139	−	0.213831i
$404$	17.9359	−	10.3553i	0.892345	−	0.515196i
$405$	0.601692	+	0.601692i	0.0298983	+	0.0298983i
$406$	3.97275	−	54.8152i	0.197164	−	2.72043i
$407$			3.78362i			0.187547i
$408$	−0.332686	−	0.0891430i	−0.0164704	−	0.00441324i
$409$	0.0618067	−	0.0165610i	0.00305614	−	0.000818891i	−0.257291	−	0.966334i	$-0.582830\pi$
$409$	0.0618067	−	0.0165610i	0.00305614	−	0.000818891i	0.260347	+	0.965515i	$0.416163\pi$
$410$	−6.36538	+	1.70560i	−0.314364	+	0.0842334i
$411$	10.8269	+	2.90106i	0.534051	+	0.143098i
$412$		−	22.3042i		−	1.09885i
$413$	−8.32255	+	4.03309i	−0.409526	+	0.198455i
$414$	0.729542	+	0.729542i	0.0358550	+	0.0358550i
$415$	−8.99595	+	5.19381i	−0.441594	+	0.254954i
$416$	7.98318	+	27.9311i	0.391408	+	1.36944i
$417$	1.26356	−	2.18855i	0.0618767	−	0.107174i
$418$	−13.9209	+	51.9536i	−0.680894	+	2.54113i
$419$			4.23556i			0.206921i	0.994634	+	0.103460i	$0.0329915\pi$
$419$			4.23556i			0.206921i	−0.994634	+	0.103460i	$0.967009\pi$
$420$	2.35361	+	4.85684i	0.114845	+	0.236989i
$421$	−13.3618	+	13.3618i	−0.651216	+	0.651216i	−0.953286	−	0.302070i	$-0.902322\pi$
$421$	−13.3618	+	13.3618i	−0.651216	+	0.651216i	0.302070	+	0.953286i	$0.402322\pi$
$422$	−29.2491	−	7.83726i	−1.42382	−	0.381512i
$423$	−1.45255	−	5.42098i	−0.0706252	−	0.263577i
$424$	5.93706	−	1.59083i	0.288329	−	0.0772576i
$425$	1.53093	−	0.883881i	0.0742609	−	0.0428745i
$426$	18.9147			0.916421
$427$	4.39865	+	5.08605i	0.212865	+	0.246131i
$428$			22.1536i			1.07083i
$429$	−10.8558	−	2.71655i	−0.524122	−	0.131156i
$430$	6.41186	+	3.70189i	0.309207	+	0.178521i
$431$	3.90135	+	14.5600i	0.187921	+	0.701332i	0.993986	+	0.109505i	$0.0349266\pi$
$431$	3.90135	+	14.5600i	0.187921	+	0.701332i	−0.806065	+	0.591827i	$0.798407\pi$
$432$	2.63929	−	1.52379i	0.126983	−	0.0733135i
$433$	−8.45509			−0.406326			−0.203163	−	0.979145i	$-0.565122\pi$
$433$	−8.45509			−0.406326			−0.203163	+	0.979145i	$0.565122\pi$
$434$	−4.52638	−	23.6056i	−0.217273	−	1.13311i
$435$	5.96034	−	5.96034i	0.285776	−	0.285776i
$436$	−1.60521	+	5.99072i	−0.0768756	+	0.286904i
$437$	−1.05237	−	3.92751i	−0.0503418	−	0.187878i
$438$	−14.6791	+	25.4249i	−0.701394	+	1.21485i
$439$	9.90274	+	17.1520i	0.472632	+	0.818623i	0.999509	−	0.0313187i	$-0.00997068\pi$
$439$	9.90274	+	17.1520i	0.472632	+	0.818623i	−0.526877	+	0.849941i	$0.676637\pi$
$440$	1.55579	−	1.55579i	0.0741692	−	0.0741692i
$441$	−5.49415	−	4.33755i	−0.261626	−	0.206550i
$442$	−2.17327	+	2.24663i	−0.103372	+	0.106861i
$443$	1.30200	+	2.25514i	0.0618601	+	0.107145i	0.895297	−	0.445470i	$-0.146963\pi$
$443$	1.30200	+	2.25514i	0.0618601	+	0.107145i	−0.833437	+	0.552615i	$0.813630\pi$
$444$	2.82289	−	0.756390i	0.133968	−	0.0358967i
$445$	2.87556	−	4.98062i	0.136315	−	0.236104i
$446$	−1.35424	−	2.34562i	−0.0641253	−	0.111068i
$447$	−5.77306	−	5.77306i	−0.273056	−	0.273056i
$448$	28.0627	−	5.38102i	1.32584	−	0.254229i
$449$	−20.6509	−	20.6509i	−0.974578	−	0.974578i	0.0251065	−	0.999685i	$-0.492008\pi$
$449$	−20.6509	−	20.6509i	−0.974578	−	0.974578i	−0.999685	+	0.0251065i	$0.992008\pi$
$450$	2.32070	−	8.66099i	0.109399	−	0.408283i
$451$	−9.92676	−	5.73122i	−0.467433	−	0.269873i
$452$	−20.5977	−	11.8921i	−0.968832	−	0.559356i
$453$	−2.81480	−	0.754224i	−0.132251	−	0.0354365i
$454$	−15.2647			−0.716409
$455$	8.10465	+	0.452332i	0.379952	+	0.0212057i
$456$	6.88492			0.322416
$457$	−20.1428	−	5.39726i	−0.942243	−	0.252473i	−0.245175	−	0.969479i	$-0.578845\pi$
$457$	−20.1428	−	5.39726i	−0.942243	−	0.252473i	−0.697067	+	0.717006i	$0.745512\pi$
$458$	17.8359	+	10.2976i	0.833418	+	0.481174i
$459$	0.358033	+	0.206711i	0.0167116	+	0.00964843i
$460$	−0.259763	+	0.969450i	−0.0121115	+	0.0452009i
$461$	25.6893	+	25.6893i	1.19647	+	1.19647i	0.975216	+	0.221256i	$0.0710155\pi$
$461$	25.6893	+	25.6893i	1.19647	+	1.19647i	0.221256	+	0.975216i	$0.428985\pi$
$462$	−5.64737	+	16.2671i	−0.262740	+	0.756812i
$463$	−16.4838	−	16.4838i	−0.766066	−	0.766066i	0.211345	−	0.977411i	$-0.432216\pi$
$463$	−16.4838	−	16.4838i	−0.766066	−	0.766066i	−0.977411	+	0.211345i	$0.932216\pi$
$464$	−15.0946	−	26.1447i	−0.700751	−	1.21374i
$465$	1.84321	−	3.19253i	0.0854766	−	0.148050i
$466$	2.24121	−	0.600531i	0.103822	−	0.0278190i
$467$	7.45050	+	12.9047i	0.344768	+	0.597156i	0.985312	−	0.170766i	$-0.0546242\pi$
$467$	7.45050	+	12.9047i	0.344768	+	0.597156i	−0.640543	+	0.767922i	$0.721291\pi$
$468$	0.143435	+	8.64236i	0.00663027	+	0.399493i
$469$	33.8427	−	16.4001i	1.56271	−	0.757287i
$470$	7.08109	−	7.08109i	0.326626	−	0.326626i
$471$	−5.51968	−	9.56036i	−0.254333	−	0.440518i
$472$	1.45606	−	2.52197i	0.0670207	−	0.116083i
$473$	3.33308	+	12.4392i	0.153255	+	0.571957i
$474$	−4.64155	+	17.3225i	−0.213193	+	0.795648i
$475$	−24.9872	+	24.9872i	−1.14649	+	1.14649i
$476$	1.71528	+	1.98334i	0.0786197	+	0.0909062i
$477$	−7.37785			−0.337808
$478$	22.9010	−	13.2219i	1.04747	−	0.604756i
$479$	3.76447	+	14.0492i	0.172003	+	0.641924i	0.997043	+	0.0768490i	$0.0244859\pi$
$479$	3.76447	+	14.0492i	0.172003	+	0.641924i	−0.825040	+	0.565075i	$0.808847\pi$
$480$	5.93728	+	3.42789i	0.270999	+	0.156461i
$481$	1.06701	−	4.26395i	0.0486514	−	0.194419i
$482$			36.4261i			1.65916i
$483$	−0.245141	−	1.27844i	−0.0111543	−	0.0581711i
$484$	−3.27738			−0.148972
$485$	4.66855	−	2.69539i	0.211988	−	0.122391i
$486$	2.02552	−	0.542736i	0.0918794	−	0.0246190i
$487$	7.61625	+	28.4242i	0.345125	+	1.28802i	0.892466	+	0.451115i	$0.148973\pi$
$487$	7.61625	+	28.4242i	0.345125	+	1.28802i	−0.547341	+	0.836910i	$0.684360\pi$
$488$	−2.04522	−	0.548014i	−0.0925826	−	0.0248074i
$489$	1.60345	−	1.60345i	0.0725103	−	0.0725103i
$490$	1.80104	−	12.3600i	0.0813629	−	0.558366i
$491$		−	25.7337i		−	1.16135i	−0.814137	−	0.580673i	$-0.802790\pi$
$491$		−	25.7337i		−	1.16135i	0.814137	−	0.580673i	$-0.197210\pi$
$492$	−2.29148	+	8.55191i	−0.103308	+	0.385550i
$493$	2.04767	−	3.54667i	0.0922224	−	0.159734i
$494$	30.3395	−	54.6233i	1.36504	−	2.45762i
$495$	−2.28717	+	1.32050i	−0.102800	+	0.0593519i
$496$	−9.33589	−	9.33589i	−0.419194	−	0.419194i
$497$	−19.7509	−	13.3951i	−0.885947	−	0.600853i
$498$			25.5988i			1.14711i
$499$	34.2285	+	9.17150i	1.53228	+	0.410573i	0.923762	−	0.382968i	$-0.125098\pi$
$499$	34.2285	+	9.17150i	1.53228	+	0.410573i	0.608517	+	0.793541i	$0.291765\pi$
$500$	18.2772	−	4.89737i	0.817383	−	0.219017i
$501$	11.2965	−	3.02689i	0.504691	−	0.135231i
$502$	27.1522	+	7.27541i	1.21186	+	0.324717i
$503$			29.3220i			1.30740i	0.756753	+	0.653701i	$0.226785\pi$
$503$			29.3220i			1.30740i	−0.756753	+	0.653701i	$0.773215\pi$
$504$	2.19841	+	0.159331i	0.0979252	+	0.00709716i
$505$	−5.19812	−	5.19812i	−0.231313	−	0.231313i
$506$	−2.77315	+	1.60108i	−0.123282	+	0.0711767i
$507$	11.4678	+	6.12282i	0.509304	+	0.271924i
$508$	−21.1789	+	36.6830i	−0.939664	+	1.62755i
$509$	7.58614	−	28.3119i	0.336250	−	1.25490i	−0.566258	−	0.824228i	$-0.691609\pi$
$509$	7.58614	−	28.3119i	0.336250	−	1.25490i	0.902508	−	0.430674i	$-0.141724\pi$
$510$			0.737691i			0.0326655i
$511$	33.3335	−	16.1533i	1.47459	−	0.714582i
$512$	20.9530	−	20.9530i	0.926000	−	0.926000i
$513$	−7.98261	−	2.13893i	−0.352441	−	0.0944362i
$514$	5.88059	+	21.9467i	0.259382	+	0.968026i
$515$	−7.64715	+	2.04905i	−0.336974	+	0.0902918i
$516$	8.61436	−	4.97350i	0.379226	−	0.218946i
$517$	17.4185			0.766066
$518$	−6.38940	−	2.21819i	−0.280734	−	0.0974615i
$519$		−	19.3089i		−	0.847568i
$520$	−2.19204	+	1.31455i	−0.0961272	+	0.0576468i
$521$	−8.32208	−	4.80476i	−0.364597	−	0.210500i	0.306498	−	0.951871i	$-0.400843\pi$
$521$	−8.32208	−	4.80476i	−0.364597	−	0.210500i	−0.671095	+	0.741371i	$0.734176\pi$
$522$	−5.37633	−	20.0647i	−0.235315	−	0.878209i
$523$	4.36673	−	2.52113i	0.190944	−	0.110241i	−0.401481	−	0.915868i	$-0.631504\pi$
$523$	4.36673	−	2.52113i	0.190944	−	0.110241i	0.592424	+	0.805626i	$0.298171\pi$
$524$	45.3559			1.98138
$525$	−8.55687	+	7.40036i	−0.373452	+	0.322978i
$526$	−34.0504	+	34.0504i	−1.48467	+	1.48467i
$527$	0.463558	−	1.73002i	0.0201929	−	0.0753609i
$528$	2.44811	+	9.13646i	0.106540	+	0.397613i
$529$	−11.3790	+	19.7089i	−0.494738	+	0.856911i
$530$	−6.58235	−	11.4010i	−0.285919	−	0.495226i
$531$	−2.47171	+	2.47171i	−0.107263	+	0.107263i
$532$	−43.3810	−	29.4212i	−1.88081	−	1.27557i
$533$	9.57072	+	9.25822i	0.414554	+	0.401018i
$534$	−7.08641	−	12.2740i	−0.306659	−	0.531149i
$535$	7.59551	−	2.03521i	0.328382	−	0.0879898i
$536$	−5.92092	+	10.2553i	−0.255745	+	0.442963i
$537$	−6.66069	−	11.5367i	−0.287430	−	0.497843i
$538$	4.20898	+	4.20898i	0.181462	+	0.181462i
$539$	17.4171	−	12.9868i	0.750207	−	0.559380i
$540$	1.44243	+	1.44243i	0.0620722	+	0.0620722i
$541$	−3.72582	+	13.9049i	−0.160185	+	0.597820i	0.838420	+	0.545025i	$0.183480\pi$
$541$	−3.72582	+	13.9049i	−0.160185	+	0.597820i	−0.998605	+	0.0527954i	$0.983187\pi$
$542$	−52.4053	−	30.2562i	−2.25100	−	1.29962i
$543$	0.656564	+	0.379067i	0.0281759	+	0.0162673i
$544$	3.21740	+	0.862099i	0.137945	+	0.0369622i
$545$	2.20143			0.0942987
$546$	10.9517	−	16.7396i	0.468691	−	0.716387i
$547$	18.1309			0.775223			0.387612	−	0.921823i	$-0.373300\pi$
$547$	18.1309			0.775223			0.387612	+	0.921823i	$0.373300\pi$
$548$	25.9552	+	6.95467i	1.10875	+	0.297089i
$549$	2.20104	+	1.27077i	0.0939381	+	0.0542352i
$550$	24.1008	+	13.9146i	1.02766	+	0.593322i
$551$	−21.1882	+	79.0755i	−0.902648	+	3.36873i
$552$	0.289838	+	0.289838i	0.0123363	+	0.0123363i
$553$	17.1142	−	14.8012i	0.727772	−	0.629409i
$554$	−1.83881	−	1.83881i	−0.0781237	−	0.0781237i
$555$	−0.518667	−	0.898357i	−0.0220162	−	0.0381331i
$556$	3.02911	−	5.24658i	0.128463	−	0.222505i
$557$	−30.3793	+	8.14011i	−1.28721	+	0.344907i	−0.836601	−	0.547813i	$-0.815461\pi$
$557$	−30.3793	+	8.14011i	−1.28721	+	0.344907i	−0.450611	+	0.892720i	$0.648794\pi$
$558$	−4.54232	−	7.86752i	−0.192292	−	0.333059i
$559$	−0.248259	−	14.9584i	−0.0105003	−	0.632671i
$560$	−2.99206	−	6.17432i	−0.126438	−	0.260913i
$561$	−0.907311	+	0.907311i	−0.0383067	+	0.0383067i
$562$	13.1269	+	22.7365i	0.553725	+	0.959080i
$563$	15.3955	−	26.6658i	0.648844	−	1.12383i	−0.334555	−	0.942376i	$-0.608586\pi$
$563$	15.3955	−	26.6658i	0.648844	−	1.12383i	0.983399	−	0.181455i	$-0.0580806\pi$
$564$	−3.48217	−	12.9956i	−0.146626	−	0.547215i
$565$	−2.18500	+	8.15454i	−0.0919238	+	0.343064i
$566$	−4.37237	+	4.37237i	−0.183784	+	0.183784i
$567$	−2.49941	−	0.867713i	−0.104966	−	0.0364405i
$568$	7.51460			0.315306
$569$	−15.6802	+	9.05299i	−0.657350	+	0.379521i	−0.791266	−	0.611471i	$-0.790578\pi$
$569$	−15.6802	+	9.05299i	−0.657350	+	0.379521i	0.133917	+	0.990993i	$0.457245\pi$
$570$	−3.81662	−	14.2438i	−0.159861	−	0.596608i
$571$	−4.25643	−	2.45745i	−0.178126	−	0.102841i	0.408286	−	0.912854i	$-0.366127\pi$
$571$	−4.25643	−	2.45745i	−0.178126	−	0.102841i	−0.586412	+	0.810013i	$0.699460\pi$
$572$	−26.0244	−	6.51234i	−1.08814	−	0.272295i
$573$			22.9712i			0.959635i
$574$	15.4980	−	13.4033i	0.646873	−	0.559445i
$575$	−2.10380			−0.0877344
$576$	9.35301	−	5.39996i	0.389709	−	0.224998i
$577$	21.6694	−	5.80630i	0.902109	−	0.241719i	0.222187	−	0.975004i	$-0.428680\pi$
$577$	21.6694	−	5.80630i	0.902109	−	0.241719i	0.679922	+	0.733285i	$0.262014\pi$
$578$	−9.13375	−	34.0876i	−0.379914	−	1.41786i
$579$	6.21044	+	1.66408i	0.258097	+	0.0691569i
$580$	14.2887	−	14.2887i	0.593304	−	0.593304i
$581$	18.1287	−	26.7304i	0.752104	−	1.10896i
$582$		−	13.2848i		−	0.550672i
$583$	5.92658	−	22.1183i	0.245454	−	0.916046i
$584$	−5.83183	+	10.1010i	−0.241323	+	0.417983i
$585$	2.94991	−	0.843135i	0.121964	−	0.0348593i
$586$	−51.3354	+	29.6385i	−2.12065	+	1.22436i
$587$	−22.0551	−	22.0551i	−0.910312	−	0.910312i	0.0859844	−	0.996296i	$-0.472596\pi$
$587$	−22.0551	−	22.0551i	−0.910312	−	0.910312i	−0.996296	+	0.0859844i	$0.972596\pi$
$588$	−13.1711	−	10.3984i	−0.543165	−	0.428821i
$589$			35.8027i			1.47522i
$590$	−6.02472	−	1.61432i	−0.248034	−	0.0664605i
$591$	−1.22582	+	0.328459i	−0.0504237	+	0.0135110i
$592$	−3.58863	+	0.961571i	−0.147492	+	0.0395203i
$593$	3.72580	+	0.998325i	0.153000	+	0.0409963i	0.334506	−	0.942394i	$-0.391430\pi$
$593$	3.72580	+	0.998325i	0.153000	+	0.0409963i	−0.181506	+	0.983390i	$0.558097\pi$
$594$			6.50834i			0.267041i
$595$	0.522421	−	0.770301i	0.0214172	−	0.0315792i
$596$	−13.8397	−	13.8397i	−0.566895	−	0.566895i
$597$	3.70523	−	2.13922i	0.151645	−	0.0875523i
$598$	3.57672	−	1.02229i	0.146263	−	0.0418044i
$599$	−5.92981	+	10.2707i	−0.242285	+	0.419651i	−0.961365	−	0.275277i	$-0.911230\pi$
$599$	−5.92981	+	10.2707i	−0.242285	+	0.419651i	0.719080	+	0.694928i	$0.244564\pi$
$600$	0.921988	−	3.44091i	0.0376400	−	0.140474i
$601$		−	4.00550i		−	0.163388i	−0.996657	−	0.0816939i	$-0.973967\pi$
$601$		−	4.00550i		−	0.163388i	0.996657	−	0.0816939i	$-0.0260330\pi$
$602$	−22.9602	−	1.66405i	−0.935788	−	0.0678216i
$603$	10.0509	−	10.0509i	0.409305	−	0.409305i
$604$	−6.74789	−	1.80809i	−0.274568	−	0.0735702i
$605$	0.301087	+	1.12367i	0.0122409	+	0.0456837i
$606$	−17.4988	+	4.68880i	−0.710841	+	0.190469i
$607$	−21.2877	+	12.2904i	−0.864040	+	0.498854i	−0.865363	−	0.501145i	$-0.832912\pi$
$607$	−21.2877	+	12.2904i	−0.864040	+	0.498854i	0.00132321	+	0.999999i	$0.499579\pi$
$608$	−66.5839			−2.70033
$609$	−8.59554	+	24.7591i	−0.348309	+	1.00329i
$610$			4.53501i			0.183617i
$611$	−19.6298	−	4.91216i	−0.794138	−	0.198725i
$612$	0.858309	+	0.495545i	0.0346951	+	0.0200312i
$613$	4.78193	+	17.8464i	0.193140	+	0.720809i	0.992740	+	0.120277i	$0.0383781\pi$
$613$	4.78193	+	17.8464i	0.193140	+	0.720809i	−0.799600	+	0.600533i	$0.794955\pi$
$614$	−43.5272	+	25.1304i	−1.75661	+	1.01418i
$615$	3.14259			0.126721
$616$	−2.24364	+	6.46271i	−0.0903986	+	0.260390i
$617$	−21.0606	+	21.0606i	−0.847867	+	0.847867i	−0.989867	−	0.142000i	$-0.954647\pi$
$617$	−21.0606	+	21.0606i	−0.847867	+	0.847867i	0.142000	+	0.989867i	$0.454647\pi$
$618$	−5.04958	+	18.8453i	−0.203124	+	0.758069i
$619$	3.54712	+	13.2380i	0.142571	+	0.532082i	0.999852	+	0.0172324i	$0.00548550\pi$
$619$	3.54712	+	13.2380i	0.142571	+	0.532082i	−0.857281	+	0.514849i	$0.827848\pi$
$620$	4.41870	−	7.65340i	0.177459	−	0.307368i
$621$	−0.246004	−	0.426092i	−0.00987181	−	0.0170985i
$622$	42.1967	−	42.1967i	1.69194	−	1.69194i
$623$	−1.29260	+	17.8351i	−0.0517871	+	0.714548i
$624$	−0.182343	−	10.9867i	−0.00729957	−	0.439821i
$625$	7.33164	+	12.6988i	0.293266	+	0.507951i
$626$	−21.0123	+	5.63024i	−0.839822	+	0.225030i
$627$	12.8248	−	22.2131i	0.512171	−	0.887107i
$628$	−13.2323	−	22.9190i	−0.528025	−	0.914566i
$629$	−0.356375	−	0.356375i	−0.0142096	−	0.0142096i
$630$	−0.889048	−	4.63649i	−0.0354205	−	0.184722i
$631$	−32.1535	−	32.1535i	−1.28001	−	1.28001i	−0.940660	−	0.339350i	$-0.889793\pi$
$631$	−32.1535	−	32.1535i	−1.28001	−	1.28001i	−0.339350	−	0.940660i	$-0.610207\pi$
$632$	−1.84403	+	6.88202i	−0.0733516	+	0.273752i
$633$	12.5056	+	7.22014i	0.497055	+	0.286975i
$634$	−10.0797	−	5.81951i	−0.400315	−	0.231122i
$635$	14.5227	+	3.89134i	0.576315	+	0.154423i
$636$	−17.6868			−0.701328
$637$	−23.2906	+	9.72368i	−0.922805	+	0.385266i
$638$	64.4715			2.55245
$639$	−8.71267	−	2.33455i	−0.344668	−	0.0923535i
$640$	4.81453	+	2.77967i	0.190311	+	0.109876i
$641$	−25.6992	−	14.8374i	−1.01506	−	0.586044i	−0.102389	−	0.994744i	$-0.532649\pi$
$641$	−25.6992	−	14.8374i	−1.01506	−	0.586044i	−0.912669	+	0.408700i	$0.865982\pi$
$642$	5.01548	−	18.7180i	0.197945	−	0.738742i
$643$	−24.1967	−	24.1967i	−0.954225	−	0.954225i	0.0447727	−	0.998997i	$-0.485744\pi$
$643$	−24.1967	−	24.1967i	−0.954225	−	0.954225i	−0.998997	+	0.0447727i	$0.985744\pi$
$644$	−0.587674	−	3.06479i	−0.0231576	−	0.120770i
$645$	−2.49658	−	2.49658i	−0.0983028	−	0.0983028i
$646$	−3.58225	−	6.20465i	−0.140942	−	0.244119i
$647$	2.61599	−	4.53103i	0.102845	−	0.178133i	−0.810011	−	0.586415i	$-0.800539\pi$
$647$	2.61599	−	4.53103i	0.102845	−	0.178133i	0.912856	+	0.408282i	$0.133872\pi$
$648$	0.804715	−	0.215623i	0.0316122	−	0.00847046i
$649$	−5.42450	−	9.39552i	−0.212930	−	0.368806i
$650$	−23.2364	−	22.4777i	−0.911407	−	0.881648i
$651$	−0.828545	+	11.4321i	−0.0324733	+	0.448060i
$652$	3.84392	−	3.84392i	0.150540	−	0.150540i
$653$	9.75711	+	16.8998i	0.381825	+	0.661341i	0.991323	−	0.131447i	$-0.0419622\pi$
$653$	9.75711	+	16.8998i	0.381825	+	0.661341i	−0.609498	+	0.792788i	$0.708629\pi$
$654$	2.71255	−	4.69827i	0.106069	−	0.183717i
$655$	−4.16676	−	15.5506i	−0.162809	−	0.607611i
$656$	2.91307	−	10.8717i	0.113736	−	0.424470i
$657$	9.89969	−	9.89969i	0.386224	−	0.386224i
$658$	−10.2118	+	29.4147i	−0.398097	+	1.14670i
$659$	32.6455			1.27169			0.635844	−	0.771817i	$-0.280652\pi$
$659$	32.6455			1.27169			0.635844	+	0.771817i	$0.280652\pi$
$660$	−5.48300	+	3.16561i	−0.213425	+	0.123221i
$661$	−8.62585	−	32.1921i	−0.335506	−	1.25213i	−0.903319	−	0.428969i	$-0.858877\pi$
$661$	−8.62585	−	32.1921i	−0.335506	−	1.25213i	0.567813	−	0.823158i	$-0.307790\pi$
$662$	−3.25955	−	1.88190i	−0.126686	−	0.0731422i
$663$	1.27836	−	0.766625i	0.0496475	−	0.0297733i
$664$			10.1701i			0.394677i
$665$	−6.10191	+	17.5763i	−0.236622	+	0.681581i
$666$	−2.55636			−0.0990569
$667$	−4.22085	+	2.43691i	−0.163432	+	0.0943576i
$668$	27.0810	−	7.25633i	1.04779	−	0.280756i
$669$	0.334296	+	1.24761i	0.0129246	+	0.0482353i
$670$	24.4989	+	6.56445i	0.946474	+	0.253607i
$671$	−5.57777	+	5.57777i	−0.215327	+	0.215327i
$672$	−21.2608	−	1.54088i	−0.820153	−	0.0594408i
$673$			34.9465i			1.34709i	0.739147	+	0.673544i	$0.235229\pi$
$673$			34.9465i			1.34709i	−0.739147	+	0.673544i	$0.764771\pi$
$674$	18.9401	−	70.6856i	0.729547	−	2.72271i
$675$	−2.13797	+	3.70307i	−0.0822904	+	0.142531i
$676$	27.4917	+	14.6782i	1.05737	+	0.564545i
$677$	3.10994	−	1.79552i	0.119525	−	0.0690075i	−0.439046	−	0.898465i	$-0.644683\pi$
$677$	3.10994	−	1.79552i	0.119525	−	0.0690075i	0.558570	+	0.829457i	$0.311350\pi$
$678$	14.7111	+	14.7111i	0.564976	+	0.564976i
$679$	−9.40809	+	13.8721i	−0.361049	+	0.532361i
$680$			0.293076i			0.0112389i
$681$	7.03137	+	1.88405i	0.269443	+	0.0721970i
$682$	27.2351	−	7.29763i	1.04289	−	0.279441i
$683$	−28.9083	+	7.74595i	−1.10614	+	0.296390i	−0.765264	−	0.643716i	$-0.777392\pi$
$683$	−28.9083	+	7.74595i	−1.10614	+	0.296390i	−0.340880	+	0.940107i	$0.610725\pi$
$684$	−19.1366	−	5.12764i	−0.731707	−	0.196060i
$685$		−	9.53781i		−	0.364421i
$686$	11.7198	+	37.0259i	0.447465	+	1.41365i
$687$	−6.94477	−	6.94477i	−0.264959	−	0.264959i
$688$	−10.9511	+	6.32263i	−0.417508	+	0.241048i
$689$	−12.9165	+	23.2549i	−0.492079	+	0.885940i
$690$	0.438959	−	0.760299i	0.0167109	−	0.0289441i
$691$	1.25007	−	4.66531i	0.0475547	−	0.177477i	−0.938064	−	0.346463i	$-0.887383\pi$
$691$	1.25007	−	4.66531i	0.0475547	−	0.177477i	0.985618	+	0.168986i	$0.0540493\pi$
$692$		−	46.2890i		−	1.75965i
$693$	4.60911	−	6.79605i	0.175086	−	0.258161i
$694$	−24.7924	+	24.7924i	−0.941105	+	0.941105i
$695$	−2.07710	−	0.556558i	−0.0787890	−	0.0211115i
$696$	−2.13595	−	7.97148i	−0.0809630	−	0.302158i
$697$	1.47481	−	0.395174i	0.0558623	−	0.0149683i
$698$	51.5534	−	29.7644i	1.95133	−	1.12660i
$699$	−1.10649			−0.0418512
$700$	−20.5133	+	17.7408i	−0.775329	+	0.670539i
$701$		−	37.4256i		−	1.41355i	−0.707440	−	0.706773i	$-0.750150\pi$
$701$		−	37.4256i		−	1.41355i	0.707440	−	0.706773i	$-0.249850\pi$
$702$	1.83540	−	7.33458i	0.0692728	−	0.276826i
$703$	8.72491	+	5.03733i	0.329066	+	0.189986i
$704$	8.67551	+	32.3774i	0.326971	+	1.22027i
$705$	−4.13574	+	2.38777i	−0.155761	+	0.0899286i
$706$	−33.4142			−1.25756
$707$	21.5929	+	7.49633i	0.812085	+	0.281928i
$708$	−5.92539	+	5.92539i	−0.222690	+	0.222690i
$709$	−0.476195	+	1.77718i	−0.0178839	+	0.0667435i	−0.974291	−	0.225293i	$-0.927666\pi$
$709$	−0.476195	+	1.77718i	−0.0178839	+	0.0667435i	0.956407	+	0.292036i	$0.0943328\pi$
$710$	−4.16567	−	15.5465i	−0.156335	−	0.583450i
$711$	4.27606	−	7.40636i	0.160365	−	0.277760i
$712$	−2.81535	−	4.87633i	−0.105510	−	0.182748i
$713$	−1.50721	+	1.50721i	−0.0564453	+	0.0564453i
$714$	−1.00026	−	2.06410i	−0.0374336	−	0.0772469i
$715$	0.158016	+	9.52092i	0.00590946	+	0.356062i
$716$	−15.9676	−	27.6567i	−0.596737	−	1.03358i
$717$	−12.1808	+	3.26383i	−0.454900	+	0.121890i
$718$	26.0214	−	45.0703i	0.971109	−	1.68201i
$719$	−15.2707	−	26.4497i	−0.569502	−	0.986407i	−0.996615	−	0.0822086i	$-0.973803\pi$
$719$	−15.2707	−	26.4497i	−0.569502	−	0.986407i	0.427113	−	0.904198i	$-0.359531\pi$
$720$	−1.83371	−	1.83371i	−0.0683382	−	0.0683382i
$721$	18.6188	−	16.1023i	0.693399	−	0.599682i
$722$	73.0968	+	73.0968i	2.72038	+	2.72038i
$723$	4.49590	−	16.7789i	0.167204	−	0.624015i
$724$	1.57397	+	0.908734i	0.0584963	+	0.0337728i
$725$	36.6825	+	21.1786i	1.36235	+	0.786555i
$726$	2.76913	+	0.741985i	0.102772	+	0.0275376i
$727$	13.0799			0.485108			0.242554	−	0.970138i	$-0.422015\pi$
$727$	13.0799			0.485108			0.242554	+	0.970138i	$0.422015\pi$
$728$	4.35100	−	6.65043i	0.161259	−	0.246481i
$729$	−1.00000			−0.0370370
$730$	24.1302	+	6.46568i	0.893101	+	0.239306i
$731$	−1.48558	−	0.857699i	−0.0549461	−	0.0317231i
$732$	5.27653	+	3.04640i	0.195026	+	0.112598i
$733$	3.21831	−	12.0109i	0.118871	−	0.443632i	−0.880676	−	0.473718i	$-0.842911\pi$
$733$	3.21831	−	12.0109i	0.118871	−	0.443632i	0.999547	+	0.0300861i	$0.00957816\pi$
$734$	47.1321	+	47.1321i	1.73968	+	1.73968i
$735$	−2.35514	+	5.47106i	−0.0868708	+	0.201803i
$736$	−2.80302	−	2.80302i	−0.103321	−	0.103321i
$737$	22.0581	+	38.2058i	0.812522	+	1.40733i
$738$	3.87223	−	6.70690i	0.142539	−	0.246885i
$739$	18.9414	−	5.07533i	0.696770	−	0.186699i	0.106987	−	0.994260i	$-0.465880\pi$
$739$	18.9414	−	5.07533i	0.696770	−	0.186699i	0.589784	+	0.807561i	$0.299213\pi$
$740$	−1.24339	−	2.15362i	−0.0457080	−	0.0791687i
$741$	−20.7171	+	21.4164i	−0.761063	+	0.786751i
$742$	33.8767	+	22.9753i	1.24365	+	0.843449i
$743$	15.1899	−	15.1899i	0.557264	−	0.557264i	−0.371263	−	0.928528i	$-0.621075\pi$
$743$	15.1899	−	15.1899i	0.557264	−	0.557264i	0.928528	+	0.371263i	$0.121075\pi$
$744$	−1.80461	−	3.12567i	−0.0661602	−	0.114593i
$745$	−3.47360	+	6.01645i	−0.127263	+	0.220426i
$746$	−1.11932	−	4.17735i	−0.0409811	−	0.152944i
$747$	3.15954	−	11.7916i	0.115601	−	0.431431i
$748$	−2.17508	+	2.17508i	−0.0795290	+	0.0795290i
$749$	−18.4930	+	15.9936i	−0.675720	+	0.584393i
$750$	−16.5516			−0.604378
$751$	20.2091	−	11.6677i	0.737442	−	0.425762i	−0.0836967	−	0.996491i	$-0.526673\pi$
$751$	20.2091	−	11.6677i	0.737442	−	0.425762i	0.821138	+	0.570729i	$0.193339\pi$
$752$	4.42676	+	16.5209i	0.161427	+	0.602455i
$753$	−11.6091	−	6.70253i	−0.423060	−	0.244254i
$754$	−72.6561	−	18.1814i	−2.64598	−	0.662129i
$755$			2.47967i			0.0902443i
$756$	−5.99182	−	2.08016i	−0.217920	−	0.0756546i
$757$	−31.8412			−1.15729			−0.578644	−	0.815580i	$-0.696418\pi$
$757$	−31.8412			−1.15729			−0.578644	+	0.815580i	$0.696418\pi$
$758$	−42.4644	+	24.5168i	−1.54238	+	0.890492i
$759$	1.47501	−	0.395227i	0.0535394	−	0.0143458i
$760$	−1.51630	−	5.65890i	−0.0550019	−	0.205270i
$761$	43.9024	+	11.7636i	1.59146	+	0.426430i	0.942449	−	0.334349i	$-0.108516\pi$
$761$	43.9024	+	11.7636i	1.59146	+	0.426430i	0.649011	+	0.760779i	$0.275183\pi$
$762$	26.1994	−	26.1994i	0.949105	−	0.949105i
$763$	−6.15970	+	2.98498i	−0.222996	+	0.108063i
$764$			55.0686i			1.99231i
$765$	0.0910496	−	0.339802i	0.00329190	−	0.0122856i
$766$	−17.2004	+	29.7921i	−0.621478	+	1.07643i
$767$	3.46354	+	12.1180i	0.125061	+	0.437557i
$768$	−6.84131	+	3.94983i	−0.246864	+	0.142527i
$769$	−24.5113	−	24.5113i	−0.883898	−	0.883898i	0.110030	−	0.993928i	$-0.464905\pi$
$769$	−24.5113	−	24.5113i	−0.883898	−	0.883898i	−0.993928	+	0.110030i	$0.964905\pi$
$770$	14.6141	+	1.05916i	0.526654	+	0.0381694i
$771$		−	10.8351i		−	0.390216i
$772$	14.8882	+	3.98928i	0.535838	+	0.143577i
$773$	−21.9374	+	5.87810i	−0.789033	+	0.211421i	−0.630763	−	0.775975i	$-0.717258\pi$
$773$	−21.9374	+	5.87810i	−0.789033	+	0.211421i	−0.158269	+	0.987396i	$0.550591\pi$
$774$	−8.40443	+	2.25196i	−0.302091	+	0.0809450i
$775$	17.8933	+	4.79449i	0.642745	+	0.172223i
$776$		−	5.27789i		−	0.189465i
$777$	2.66936	+	1.81037i	0.0957629	+	0.0649468i
$778$	−47.2138	−	47.2138i	−1.69270	−	1.69270i
$779$	−26.4320	+	15.2605i	−0.947026	+	0.546766i
$780$	7.07179	−	2.02124i	0.253211	−	0.0723719i
$781$	13.9977	−	24.2447i	0.500876	−	0.867543i
$782$	0.110396	−	0.412004i	0.00394776	−	0.0147332i
$783$			9.90597i			0.354011i
$784$	16.7439	+	13.2191i	0.597996	+	0.472109i
$785$	−6.64229	+	6.64229i	−0.237073	+	0.237073i
$786$	−38.3222	−	10.2684i	−1.36691	−	0.366261i
$787$	−4.57290	−	17.0663i	−0.163006	−	0.608348i	−0.998286	−	0.0585226i	$-0.981361\pi$
$787$	−4.57290	−	17.0663i	−0.163006	−	0.608348i	0.835280	−	0.549825i	$-0.185306\pi$
$788$	−2.93866	+	0.787410i	−0.104685	+	0.0280503i
$789$	19.8873	−	11.4819i	0.708007	−	0.408768i
$790$	15.2600			0.542927
$791$	−4.94323	−	25.7795i	−0.175761	−	0.916615i
$792$			2.58569i			0.0918784i
$793$	7.85883	−	4.71289i	0.279075	−	0.167360i
$794$	−4.68275	−	2.70359i	−0.166185	−	0.0959467i
$795$	1.62486	+	6.06404i	0.0576277	+	0.215070i
$796$	8.88250	−	5.12832i	0.314832	−	0.181768i
$797$	22.9818			0.814058			0.407029	−	0.913415i	$-0.366565\pi$
$797$	22.9818			0.814058			0.407029	+	0.913415i	$0.366565\pi$
$798$	29.9927	+	34.6798i	1.06173	+	1.22765i
$799$	−1.64063	+	1.64063i	−0.0580414	+	0.0580414i
$800$	−8.91652	+	33.2769i	−0.315247	+	1.17652i
$801$	1.74928	+	6.52842i	0.0618079	+	0.230670i
$802$	−29.6837	+	51.4136i	−1.04817	+	1.81548i
$803$	21.7262	+	37.6310i	0.766703	+	1.32797i
$804$	24.0950	−	24.0950i	0.849763	−	0.849763i
$805$	−0.996796	+	0.483045i	−0.0351324	+	0.0170251i
$806$	−32.7506	+	0.543552i	−1.15359	+	0.0191458i
$807$	−1.41928	−	2.45827i	−0.0499612	−	0.0865353i
$808$	−6.95208	+	1.86280i	−0.244573	+	0.0655332i
$809$	−20.7877	+	36.0053i	−0.730856	+	1.26588i	0.225661	+	0.974206i	$0.427546\pi$
$809$	−20.7877	+	36.0053i	−0.730856	+	1.26588i	−0.956518	+	0.291674i	$0.905788\pi$
$810$	−0.892178	−	1.54530i	−0.0313479	−	0.0542962i
$811$	−16.0291	−	16.0291i	−0.562859	−	0.562859i	0.367259	−	0.930119i	$-0.380296\pi$
$811$	−16.0291	−	16.0291i	−0.562859	−	0.562859i	−0.930119	+	0.367259i	$0.880296\pi$
$812$	−20.6060	+	59.3548i	−0.723128	+	2.08294i
$813$	20.4050	+	20.4050i	0.715635	+	0.715635i
$814$	2.05351	−	7.66379i	0.0719754	−	0.268616i
$815$	−1.67105	−	0.964780i	−0.0585342	−	0.0337948i
$816$	−1.09114	−	0.629968i	−0.0381974	−	0.0220533i
$817$	33.1220	+	8.87502i	1.15879	+	0.310498i
$818$	−0.134179			−0.00469145
$819$	−7.11077	+	6.35900i	−0.248470	+	0.222202i
$820$	7.53370			0.263088
$821$	54.2832	+	14.5451i	1.89450	+	0.507629i	0.997899	+	0.0647853i	$0.0206363\pi$
$821$	54.2832	+	14.5451i	1.89450	+	0.507629i	0.896599	+	0.442844i	$0.146030\pi$
$822$	−20.3555	−	11.7523i	−0.709981	−	0.409908i
$823$	7.43047	+	4.28998i	0.259010	+	0.149539i	0.623883	−	0.781518i	$-0.285554\pi$
$823$	7.43047	+	4.28998i	0.259010	+	0.149539i	−0.364873	+	0.931057i	$0.618888\pi$
$824$	−2.00614	+	7.48702i	−0.0698872	+	0.260823i
$825$	−9.38413	−	9.38413i	−0.326714	−	0.326714i
$826$	19.0464	−	3.65215i	0.662709	−	0.127074i
$827$	−12.1796	−	12.1796i	−0.423527	−	0.423527i	0.462889	−	0.886416i	$-0.346813\pi$
$827$	−12.1796	−	12.1796i	−0.423527	−	0.423527i	−0.886416	+	0.462889i	$0.846813\pi$
$828$	−0.589743	−	1.02146i	−0.0204950	−	0.0354984i
$829$	−10.1278	+	17.5419i	−0.351754	+	0.609255i	−0.986557	−	0.163419i	$-0.947748\pi$
$829$	−10.1278	+	17.5419i	−0.351754	+	0.609255i	0.634803	+	0.772674i	$0.281081\pi$
$830$	21.0403	−	5.63774i	0.730321	−	0.195689i
$831$	0.620055	+	1.07397i	0.0215095	+	0.0372555i
$832$	−0.646181	−	38.9343i	−0.0224023	−	1.34980i
$833$	−0.417288	+	2.86371i	−0.0144582	+	0.0992215i
$834$	−3.74717	+	3.74717i	−0.129754	+	0.129754i
$835$	−4.97576	−	8.61826i	−0.172193	−	0.298247i
$836$	30.7446	−	53.2513i	1.06333	−	1.84173i
$837$	1.12127	+	4.18465i	0.0387568	+	0.144643i
$838$	2.29879	−	8.57921i	0.0794105	−	0.296364i
$839$	6.54394	−	6.54394i	0.225922	−	0.225922i	−0.585065	−	0.810987i	$-0.698931\pi$
$839$	6.54394	−	6.54394i	0.225922	−	0.225922i	0.810987	+	0.585065i	$0.198931\pi$
$840$	−0.353208	−	1.84202i	−0.0121868	−	0.0635559i
$841$	69.1283			2.38373
$842$	34.3166	−	19.8127i	1.18263	−	0.682791i
$843$	−3.24038	−	12.0933i	−0.111605	−	0.416514i
$844$	29.9796	+	17.3088i	1.03194	+	0.595792i
$845$	2.50690	−	10.7742i	0.0862398	−	0.370642i
$846$			11.7686i			0.404614i
$847$	−2.36607	−	2.73584i	−0.0812993	−	0.0940045i
$848$	22.4846			0.772125
$849$	2.55370	−	1.47438i	0.0876428	−	0.0506006i
$850$	−3.58064	+	0.959428i	−0.122815	+	0.0329081i
$851$	0.155238	+	0.579356i	0.00532149	+	0.0198601i
$852$	−20.8868	−	5.59660i	−0.715569	−	0.191736i
$853$	−26.9552	+	26.9552i	−0.922928	+	0.922928i	−0.997235	−	0.0743069i	$-0.976326\pi$
$853$	−26.9552	+	26.9552i	−0.922928	+	0.922928i	0.0743069	+	0.997235i	$0.476326\pi$
$854$	−6.14916	−	12.6892i	−0.210420	−	0.434215i
$855$			7.03218i			0.240495i
$856$	1.99259	−	7.43646i	0.0681054	−	0.254173i
$857$	−27.5423	+	47.7047i	−0.940828	+	1.62956i	−0.176932	+	0.984223i	$0.556617\pi$
$857$	−27.5423	+	47.7047i	−0.940828	+	1.62956i	−0.763896	+	0.645339i	$0.776716\pi$
$858$	20.5142	+	11.3942i	0.700343	+	0.388993i
$859$	40.4711	−	23.3660i	1.38086	−	0.797237i	0.388595	−	0.921409i	$-0.372961\pi$
$859$	40.4711	−	23.3660i	1.38086	−	0.797237i	0.992261	+	0.124172i	$0.0396273\pi$
$860$	−5.98503	−	5.98503i	−0.204088	−	0.204088i
$861$	−8.79313	+	4.26113i	−0.299669	+	0.145219i
$862$		−	31.6090i		−	1.07661i
$863$	32.4993	+	8.70817i	1.10629	+	0.296430i	0.765324	−	0.643646i	$-0.222579\pi$
$863$	32.4993	+	8.70817i	1.10629	+	0.296430i	0.340967	+	0.940075i	$0.389246\pi$
$864$	−7.78237	+	2.08528i	−0.264762	+	0.0709427i
$865$	−15.8705	+	4.25249i	−0.539613	+	0.144589i
$866$	17.1259	+	4.58888i	0.581963	+	0.155937i
$867$			16.8291i			0.571546i
$868$	−1.98626	+	27.4061i	−0.0674181	+	0.930222i
$869$	18.7688	+	18.7688i	0.636689	+	0.636689i
$870$	−15.3077	+	8.83789i	−0.518979	+	0.299632i
$871$	−14.0841	−	49.2766i	−0.477221	−	1.66967i
$872$	1.07766	−	1.86657i	0.0364943	−	0.0632100i
$873$	−1.63968	+	6.11936i	−0.0554947	+	0.207109i
$874$			8.52641i			0.288410i
$875$	17.2832	+	11.7216i	0.584280	+	0.396261i
$876$	23.7324	−	23.7324i	0.801844	−	0.801844i
$877$	−45.8348	−	12.2814i	−1.54773	−	0.414713i	−0.618977	−	0.785409i	$-0.712452\pi$
$877$	−45.8348	−	12.2814i	−1.54773	−	0.414713i	−0.928754	+	0.370696i	$0.879119\pi$
$878$	−10.7491	−	40.1164i	−0.362766	−	1.35386i
$879$	27.3047	−	7.31628i	0.920966	−	0.246772i
$880$	6.97033	−	4.02432i	0.234970	−	0.135660i
$881$	−38.1764			−1.28620			−0.643099	−	0.765783i	$-0.722351\pi$
$881$	−38.1764			−1.28620			−0.643099	+	0.765783i	$0.722351\pi$
$882$	8.77436	+	11.7677i	0.295448	+	0.396238i
$883$		−	40.9343i		−	1.37755i	−0.724976	−	0.688775i	$-0.758149\pi$
$883$		−	40.9343i		−	1.37755i	0.724976	−	0.688775i	$-0.241851\pi$
$884$	3.06460	−	1.83782i	0.103074	−	0.0618126i
$885$	2.57591	+	1.48720i	0.0865884	+	0.0499918i
$886$	−1.41329	−	5.27447i	−0.0474804	−	0.177199i
$887$	6.85775	−	3.95932i	0.230261	−	0.132941i	−0.380432	−	0.924809i	$-0.624225\pi$
$887$	6.85775	−	3.95932i	0.230261	−	0.132941i	0.610692	+	0.791868i	$0.290891\pi$
$888$	−1.01561			−0.0340817
$889$	−45.9116	+	8.80356i	−1.53983	+	0.295262i
$890$	−8.52767	+	8.52767i	−0.285848	+	0.285848i
$891$	0.803294	−	2.99793i	0.0269113	−	0.100435i
$892$	0.801403	+	2.99088i	0.0268330	+	0.100142i
$893$	23.1902	−	40.1666i	0.776031	−	1.34412i
$894$	8.56019	+	14.8267i	0.286295	+	0.495878i
$895$	−8.01536	+	8.01536i	−0.267924	+	0.267924i
$896$	−17.2403	−	1.24950i	−0.575959	−	0.0417428i
$897$	−1.77372	+	0.0294379i	−0.0592227	+	0.000982902i
$898$	30.6209	+	53.0369i	1.02183	+	1.76986i
$899$	41.4530	−	11.1073i	1.38253	−	0.370449i
$900$	−5.12532	+	8.87732i	−0.170844	+	0.295911i
$901$	1.52508	+	2.64152i	0.0508078	+	0.0880017i
$902$	16.9963	+	16.9963i	0.565915	+	0.565915i
$903$	10.3708	+	3.60038i	0.345117	+	0.119813i
$904$	5.84454	+	5.84454i	0.194386	+	0.194386i
$905$	0.166967	−	0.623131i	0.00555018	−	0.0207136i
$906$	5.29209	+	3.05539i	0.175818	+	0.101509i
$907$	5.92117	+	3.41859i	0.196609	+	0.113512i	0.595073	−	0.803672i	$-0.297123\pi$
$907$	5.92117	+	3.41859i	0.196609	+	0.113512i	−0.398464	+	0.917184i	$0.630457\pi$
$908$	16.8562	+	4.51661i	0.559393	+	0.149889i
$909$	8.63918			0.286544
$910$	−16.1706	−	5.31489i	−0.536051	−	0.176187i
$911$	−59.0374			−1.95600			−0.977998	−	0.208613i	$-0.933105\pi$
$911$	−59.0374			−1.95600			−0.977998	+	0.208613i	$0.933105\pi$
$912$	24.3277	+	6.51858i	0.805570	+	0.215852i
$913$	32.8123	+	18.9442i	1.08593	+	0.626960i
$914$	37.8704	+	21.8645i	1.25264	+	0.723213i
$915$	0.559735	−	2.08896i	0.0185043	−	0.0690588i
$916$	−16.6486	−	16.6486i	−0.550085	−	0.550085i
$917$	32.7443	+	37.8615i	1.08131	+	1.25030i
$918$	−0.613014	−	0.613014i	−0.0202325	−	0.0202325i
$919$	0.228793	+	0.396282i	0.00754720	+	0.0130721i	0.869774	−	0.493450i	$-0.164264\pi$
$919$	0.228793	+	0.396282i	0.00754720	+	0.0130721i	−0.862227	+	0.506522i	$0.830931\pi$
$920$	0.174393	−	0.302058i	0.00574958	−	0.00995856i
$921$	23.1516	−	6.20345i	0.762871	−	0.204411i
$922$	−38.0917	−	65.9767i	−1.25448	−	2.17283i
$923$	−22.6119	+	23.3751i	−0.744278	+	0.769400i
$924$	11.0494	−	16.2921i	0.363497	−	0.535970i
$925$	3.68592	−	3.68592i	0.121192	−	0.121192i
$926$	24.4419	+	42.3345i	0.803209	+	1.39120i
$927$	4.65197	−	8.05745i	0.152791	−	0.264641i
$928$	20.6567	+	77.0919i	0.678090	+	2.53067i
$929$	−4.14397	+	15.4655i	−0.135959	+	0.507407i	0.864033	+	0.503435i	$0.167931\pi$
$929$	−4.14397	+	15.4655i	−0.135959	+	0.507407i	−0.999992	+	0.00397147i	$0.998736\pi$
$930$	−5.46615	+	5.46615i	−0.179242	+	0.179242i
$931$	−6.75880	−	57.4532i	−0.221511	−	1.88295i
$932$	−2.65257			−0.0868878
$933$	−24.6452	+	14.2289i	−0.806847	+	0.465833i
$934$	−8.08731	−	30.1823i	−0.264625	−	0.987594i
$935$	0.945563	+	0.545921i	0.0309232	+	0.0178535i
$936$	0.729184	−	2.91394i	0.0238341	−	0.0952452i
$937$			21.9493i			0.717052i	0.933520	+	0.358526i	$0.116721\pi$
$937$			21.9493i			0.717052i	−0.933520	+	0.358526i	$0.883279\pi$
$938$	−77.4500	+	14.8511i	−2.52883	+	0.484904i
$939$	10.3738			0.338537
$940$	−9.91456	+	5.72417i	−0.323377	+	0.186702i
$941$	−6.19114	+	1.65891i	−0.201825	+	0.0540789i	−0.358315	−	0.933601i	$-0.616649\pi$
$941$	−6.19114	+	1.65891i	−0.201825	+	0.0540789i	0.156490	+	0.987680i	$0.449982\pi$
$942$	5.99146	+	22.3604i	0.195212	+	0.728542i
$943$	−1.75515	−	0.470292i	−0.0571557	−	0.0153148i
$944$	7.53274	−	7.53274i	0.245170	−	0.245170i
$945$	−0.162739	+	2.24543i	−0.00529388	+	0.0730440i
$946$		−	27.0049i		−	0.878005i
$947$	4.17686	−	15.5883i	0.135730	−	0.506551i	−0.864264	−	0.503039i	$-0.832215\pi$
$947$	4.17686	−	15.5883i	0.135730	−	0.506551i	0.999994	−	0.00351220i	$-0.00111797\pi$
$948$	10.2510	−	17.7552i	0.332935	−	0.576661i
$949$	−13.8722	−	48.5352i	−0.450310	−	1.57552i
$950$	64.1734	−	37.0505i	2.08206	−	1.20208i
$951$	3.92472	+	3.92472i	0.127268	+	0.127268i
$952$	−0.397390	−	0.820041i	−0.0128795	−	0.0265777i
$953$		−	29.0712i		−	0.941710i	−0.882211	−	0.470855i	$-0.843946\pi$
$953$		−	29.0712i		−	0.941710i	0.882211	−	0.470855i	$-0.156054\pi$
$954$	14.9440	+	4.00422i	0.483829	+	0.129642i
$955$	18.8806	−	5.05905i	0.610962	−	0.163707i
$956$	−29.2009	+	7.82435i	−0.944424	+	0.253058i
$957$	−29.6974	−	7.95740i	−0.959982	−	0.257226i
$958$		−	30.5000i		−	0.985410i
$959$	12.9326	+	26.6873i	0.417615	+	0.861777i
$960$	−6.49822	−	6.49822i	−0.209729	−	0.209729i
$961$	−10.5928	+	6.11575i	−0.341703	+	0.197282i
$962$	−4.47545	+	8.05760i	−0.144294	+	0.259788i
$963$	−4.62055	+	8.00303i	−0.148895	+	0.257894i
$964$	10.7780	−	40.2239i	0.347135	−	1.29552i
$965$		−	5.47101i		−	0.176118i
$966$	−0.197318	+	2.72255i	−0.00634860	+	0.0875967i
$967$	−13.9005	+	13.9005i	−0.447009	+	0.447009i	−0.894359	−	0.447350i	$-0.852368\pi$
$967$	−13.9005	+	13.9005i	−0.447009	+	0.447009i	0.447350	+	0.894359i	$0.352368\pi$
$968$	1.10014	+	0.294782i	0.0353599	+	0.00947465i
$969$	0.884281	+	3.30018i	0.0284072	+	0.106017i
$970$	−10.9191	+	2.92577i	−0.350592	+	0.0939408i
$971$	−13.3914	+	7.73151i	−0.429750	+	0.248116i	−0.699240	−	0.714887i	$-0.746478\pi$
$971$	−13.3914	+	7.73151i	−0.429750	+	0.248116i	0.269490	+	0.963003i	$0.413145\pi$
$972$	−2.39729			−0.0768931
$973$	6.56649	−	1.25913i	0.210512	−	0.0403657i
$974$		−	61.7074i		−	1.97723i
$975$	7.92905	+	13.2218i	0.253933	+	0.423438i
$976$	−6.70786	−	3.87278i	−0.214713	−	0.123965i
$977$	10.2795	+	38.3637i	0.328871	+	1.22736i	0.910363	+	0.413811i	$0.135802\pi$
$977$	10.2795	+	38.3637i	0.328871	+	1.22736i	−0.581492	+	0.813552i	$0.697531\pi$
$978$	−4.11806	+	2.37756i	−0.131681	+	0.0760260i
$979$	−20.9769			−0.670426
$980$	−5.64596	+	13.1157i	−0.180353	+	0.418966i
$981$	−1.82936	+	1.82936i	−0.0584071	+	0.0584071i
$982$	−13.9666	+	52.1241i	−0.445692	+	1.66335i
$983$	−4.41721	−	16.4852i	−0.140887	−	0.525798i	−0.999904	−	0.0138507i	$-0.995591\pi$
$983$	−4.41721	−	16.4852i	−0.140887	−	0.525798i	0.859017	−	0.511947i	$-0.171076\pi$
$984$	1.53839	−	2.66457i	0.0490422	−	0.0849435i
$985$	0.539938	+	0.935199i	0.0172038	+	0.0297979i
$986$	−6.07250	+	6.07250i	−0.193388	+	0.193388i
$987$	8.33436	−	12.2889i	0.265286	−	0.391159i
$988$	−49.6649	+	51.3413i	−1.58005	+	1.63338i
$989$	1.02074	+	1.76797i	0.0324576	+	0.0562182i
$990$	5.34938	−	1.43336i	0.170014	−	0.0455552i
$991$	0.801895	−	1.38892i	0.0254730	−	0.0441206i	−0.853008	−	0.521898i	$-0.825224\pi$
$991$	0.801895	−	1.38892i	0.0254730	−	0.0441206i	0.878481	+	0.477777i	$0.158557\pi$
$992$	17.4523	+	30.2283i	0.554112	+	0.959749i
$993$	1.26917	+	1.26917i	0.0402759	+	0.0402759i
$994$	32.7357	+	37.8516i	1.03831	+	1.20058i
$995$	−2.57430	−	2.57430i	−0.0816107	−	0.0816107i
$996$	7.57432	−	28.2678i	0.240002	−	0.895698i
$997$	−3.73168	−	2.15449i	−0.118184	−	0.0682333i	0.439743	−	0.898124i	$-0.355070\pi$
$997$	−3.73168	−	2.15449i	−0.118184	−	0.0682333i	−0.557926	+	0.829890i	$0.688403\pi$
$998$	−64.3528	−	37.1541i	−2.03705	−	1.17609i
$999$	1.17753	+	0.315519i	0.0372555	+	0.00998258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.31.2	yes	36
3.2	odd	2		819.2.fn.g.577.8		36
7.5	odd	6		273.2.bz.a.187.8	yes	36
13.8	odd	4		273.2.bz.a.73.8	✓	36
21.5	even	6		819.2.fn.f.460.2		36
39.8	even	4		819.2.fn.f.73.2		36
91.47	even	12	inner	273.2.bz.b.229.2	yes	36
273.47	odd	12		819.2.fn.g.775.8		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.8	✓	36	13.8	odd	4
273.2.bz.a.187.8	yes	36	7.5	odd	6
273.2.bz.b.31.2	yes	36	1.1	even	1	trivial
273.2.bz.b.229.2	yes	36	91.47	even	12	inner
819.2.fn.f.73.2		36	39.8	even	4
819.2.fn.f.460.2		36	21.5	even	6
819.2.fn.g.577.8		36	3.2	odd	2
819.2.fn.g.775.8		36	273.47	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.02552 - 0.542736i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.07611 + 1.19864i) q^{4} +(0.220234 - 0.821926i) q^{5} +(-1.48278 - 1.48278i) q^{6} +(0.498246 + 2.59841i) q^{7} +(-0.589092 - 0.589092i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.02552 - 0.542736i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.07611 + 1.19864i) q^{4} +(0.220234 - 0.821926i) q^{5} +(-1.48278 - 1.48278i) q^{6} +(0.498246 + 2.59841i) q^{7} +(-0.589092 - 0.589092i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.892178 + 1.54530i) q^{10} +(-2.99793 + 0.803294i) q^{11} +(1.19864 + 2.07611i) q^{12} +(3.60505 - 0.0598320i) q^{13} +(0.401046 - 5.53355i) q^{14} +(0.601692 - 0.601692i) q^{15} +(-1.52379 - 2.63929i) q^{16} +(0.206711 - 0.358033i) q^{17} +(-0.542736 - 2.02552i) q^{18} +(-2.13893 + 7.98261i) q^{19} +(1.44243 - 1.44243i) q^{20} +(-0.867713 + 2.49941i) q^{21} +6.50834 q^{22} +(-0.426092 + 0.246004i) q^{23} +(-0.215623 - 0.804715i) q^{24} +(3.70307 + 2.13797i) q^{25} +(-7.33458 - 1.83540i) q^{26} +1.00000i q^{27} +(-2.08016 + 5.99182i) q^{28} +9.90597 q^{29} +(-1.54530 + 0.892178i) q^{30} +(4.18465 - 1.12127i) q^{31} +(2.08528 + 7.78237i) q^{32} +(-2.99793 - 0.803294i) q^{33} +(-0.613014 + 0.613014i) q^{34} +(2.24543 + 0.162739i) q^{35} +2.39729i q^{36} +(0.315519 - 1.17753i) q^{37} +(8.66490 - 15.0080i) q^{38} +(3.15199 + 1.75071i) q^{39} +(-0.613928 + 0.354452i) q^{40} +(2.61146 + 2.61146i) q^{41} +(3.11409 - 4.59167i) q^{42} -4.14927i q^{43} +(-7.18691 - 1.92573i) q^{44} +(0.821926 - 0.220234i) q^{45} +(0.996572 - 0.267031i) q^{46} +(-5.42098 - 1.45255i) q^{47} -3.04759i q^{48} +(-6.50350 + 2.58930i) q^{49} +(-6.34028 - 6.34028i) q^{50} +(0.358033 - 0.206711i) q^{51} +(7.55622 + 4.19696i) q^{52} +(-3.68892 + 6.38940i) q^{53} +(0.542736 - 2.02552i) q^{54} +2.64099i q^{55} +(1.23719 - 1.82422i) q^{56} +(-5.84367 + 5.84367i) q^{57} +(-20.0647 - 5.37633i) q^{58} +(0.904707 + 3.37641i) q^{59} +(1.97039 - 0.527965i) q^{60} +(2.20104 - 1.27077i) q^{61} -9.08463 q^{62} +(-2.00117 + 1.73070i) q^{63} -10.7999i q^{64} +(0.744780 - 2.97627i) q^{65} +(5.63639 + 3.25417i) q^{66} +(-3.67889 - 13.7298i) q^{67} +(0.858309 - 0.495545i) q^{68} -0.492008 q^{69} +(-4.45984 - 1.54831i) q^{70} +(-6.37812 + 6.37812i) q^{71} +(0.215623 - 0.804715i) q^{72} +(-3.62354 - 13.5232i) q^{73} +(-1.27818 + 2.21387i) q^{74} +(2.13797 + 3.70307i) q^{75} +(-14.0090 + 14.0090i) q^{76} +(-3.58100 - 7.38963i) q^{77} +(-5.43423 - 5.25679i) q^{78} +(-4.27606 - 7.40636i) q^{79} +(-2.50489 + 0.671183i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.87223 - 6.70690i) q^{82} +(-8.63202 - 8.63202i) q^{83} +(-4.79738 + 4.14899i) q^{84} +(-0.248752 - 0.248752i) q^{85} +(-2.25196 + 8.40443i) q^{86} +(8.57882 + 4.95299i) q^{87} +(2.23927 + 1.29284i) q^{88} +(6.52842 + 1.74928i) q^{89} -1.78436 q^{90} +(1.95167 + 9.33761i) q^{91} -1.17949 q^{92} +(4.18465 + 1.12127i) q^{93} +(10.1919 + 5.88432i) q^{94} +(6.09005 + 3.51609i) q^{95} +(-2.08528 + 7.78237i) q^{96} +(4.47968 + 4.47968i) q^{97} +(14.5783 - 1.71499i) q^{98} +(-2.19464 - 2.19464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Introduction

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