LMFDB - Embedded newform 756.2.ci.a.95.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(95,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17, 12]))

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

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

chi := DirichletCharacter("756.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ci (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.8
Character	$\chi$	$=$	756.95
Dual form			756.2.ci.a.191.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39122 - 0.253995i) q^{2} +(1.51307 + 0.842975i) q^{3} +(1.87097 + 0.706724i) q^{4} +(3.16384 + 0.557871i) q^{5} +(-1.89090 - 1.55707i) q^{6} +(0.270632 + 2.63187i) q^{7} +(-2.42343 - 1.45842i) q^{8} +(1.57879 + 2.55097i) q^{9} +O(q^{10})$	\(q+(-1.39122 - 0.253995i) q^{2} +(1.51307 + 0.842975i) q^{3} +(1.87097 + 0.706724i) q^{4} +(3.16384 + 0.557871i) q^{5} +(-1.89090 - 1.55707i) q^{6} +(0.270632 + 2.63187i) q^{7} +(-2.42343 - 1.45842i) q^{8} +(1.57879 + 2.55097i) q^{9} +(-4.25990 - 1.57972i) q^{10} +(-0.648104 - 3.67558i) q^{11} +(2.23517 + 2.64651i) q^{12} +(0.816647 - 4.63144i) q^{13} +(0.291975 - 3.73025i) q^{14} +(4.31686 + 3.51114i) q^{15} +(3.00108 + 2.64452i) q^{16} +(5.13403 - 2.96413i) q^{17} +(-1.54850 - 3.94995i) q^{18} +(1.22570 + 0.707658i) q^{19} +(5.52521 + 3.27973i) q^{20} +(-1.80912 + 4.21036i) q^{21} +(-0.0319246 + 5.27815i) q^{22} +(0.642780 + 0.539356i) q^{23} +(-2.43741 - 4.24959i) q^{24} +(5.00022 + 1.81993i) q^{25} +(-2.31249 + 6.23591i) q^{26} +(0.238416 + 5.19068i) q^{27} +(-1.35366 + 5.11543i) q^{28} +(5.73413 - 1.01108i) q^{29} +(-5.11388 - 5.98122i) q^{30} +(-8.17084 - 1.44074i) q^{31} +(-3.50346 - 4.44137i) q^{32} +(2.11779 - 6.10776i) q^{33} +(-7.89542 + 2.81974i) q^{34} +(-0.612009 + 8.47781i) q^{35} +(1.15103 + 5.88856i) q^{36} -9.29934 q^{37} +(-1.52547 - 1.29583i) q^{38} +(5.13983 - 6.31929i) q^{39} +(-6.85373 - 5.96619i) q^{40} +(-7.90132 - 1.39322i) q^{41} +(3.58629 - 5.39801i) q^{42} +(4.21585 + 5.02425i) q^{43} +(1.38504 - 7.33494i) q^{44} +(3.57192 + 8.95162i) q^{45} +(-0.757253 - 0.913625i) q^{46} +(0.260389 + 1.47674i) q^{47} +(2.31159 + 6.53120i) q^{48} +(-6.85352 + 1.42454i) q^{49} +(-6.49415 - 3.80195i) q^{50} +(10.2668 - 0.157093i) q^{51} +(4.80107 - 8.08815i) q^{52} +(-3.76130 - 2.17159i) q^{53} +(0.986717 - 7.28192i) q^{54} -11.9905i q^{55} +(3.18253 - 6.77285i) q^{56} +(1.25804 + 2.10397i) q^{57} +(-8.23424 - 0.0498043i) q^{58} +(-1.68390 + 0.612889i) q^{59} +(5.59532 + 9.62008i) q^{60} +(2.37309 + 13.4585i) q^{61} +(11.0015 + 4.07973i) q^{62} +(-6.28656 + 4.84554i) q^{63} +(3.74600 + 7.06877i) q^{64} +(5.16749 - 14.1976i) q^{65} +(-4.49765 + 7.95931i) q^{66} +(-9.03556 + 10.7682i) q^{67} +(11.7004 - 1.91747i) q^{68} +(0.517909 + 1.35793i) q^{69} +(3.00476 - 11.6390i) q^{70} +(-1.65180 + 2.86100i) q^{71} +(-0.105677 - 8.48462i) q^{72} -10.7512 q^{73} +(12.9374 + 2.36198i) q^{74} +(6.03155 + 6.96876i) q^{75} +(1.79313 + 2.19024i) q^{76} +(9.49826 - 2.70046i) q^{77} +(-8.75569 + 7.48602i) q^{78} +(-1.09487 - 1.30482i) q^{79} +(8.01965 + 10.0411i) q^{80} +(-4.01487 + 8.05486i) q^{81} +(10.6386 + 3.94516i) q^{82} +(0.380043 + 2.15533i) q^{83} +(-6.36037 + 6.59891i) q^{84} +(17.8969 - 6.51392i) q^{85} +(-4.58903 - 8.06063i) q^{86} +(9.52849 + 3.30389i) q^{87} +(-3.78992 + 9.85271i) q^{88} +(4.90703 + 2.83307i) q^{89} +(-2.69565 - 13.3609i) q^{90} +(12.4104 + 0.895898i) q^{91} +(0.821448 + 1.46339i) q^{92} +(-11.1486 - 9.06776i) q^{93} +(0.0128263 - 2.12060i) q^{94} +(3.48314 + 2.92270i) q^{95} +(-1.55704 - 9.67345i) q^{96} +(5.79844 - 4.86547i) q^{97} +(9.89656 - 0.241083i) q^{98} +(8.35307 - 7.45624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.39122	−	0.253995i	−0.983739	−	0.179601i
$2$	−1.39122	−	0.253995i	−0.983739	−	0.179601i
$3$	1.51307	+	0.842975i	0.873574	+	0.486692i
$3$	1.51307	+	0.842975i	0.873574	+	0.486692i
$4$	1.87097	+	0.706724i	0.935487	+	0.353362i
$5$	3.16384	+	0.557871i	1.41491	+	0.249488i	0.828257	−	0.560348i	$-0.189333\pi$
$5$	3.16384	+	0.557871i	1.41491	+	0.249488i	0.586657	+	0.809836i	$0.300444\pi$
$6$	−1.89090	−	1.55707i	−0.771958	−	0.635673i
$7$	0.270632	+	2.63187i	0.102289	+	0.994755i
$7$	0.270632	+	2.63187i	0.102289	+	0.994755i
$8$	−2.42343	−	1.45842i	−0.856811	−	0.515631i
$9$	1.57879	+	2.55097i	0.526262	+	0.850323i
$10$	−4.25990	−	1.57972i	−1.34710	−	0.499551i
$11$	−0.648104	−	3.67558i	−0.195411	−	1.10823i	−0.911833	−	0.410562i	$-0.865333\pi$
$11$	−0.648104	−	3.67558i	−0.195411	−	1.10823i	0.716422	−	0.697667i	$-0.245779\pi$
$12$	2.23517	+	2.64651i	0.645238	+	0.763982i
$13$	0.816647	−	4.63144i	0.226497	−	1.28453i	−0.633305	−	0.773902i	$-0.718302\pi$
$13$	0.816647	−	4.63144i	0.226497	−	1.28453i	0.859802	−	0.510627i	$-0.170587\pi$
$14$	0.291975	−	3.73025i	0.0780335	−	0.996951i
$15$	4.31686	+	3.51114i	1.11461	+	0.906573i
$16$	3.00108	+	2.64452i	0.750271	+	0.661131i
$17$	5.13403	−	2.96413i	1.24518	−	0.718907i	0.275039	−	0.961433i	$-0.411309\pi$
$17$	5.13403	−	2.96413i	1.24518	−	0.718907i	0.970145	+	0.242526i	$0.0779759\pi$
$18$	−1.54850	−	3.94995i	−0.364985	−	0.931013i
$19$	1.22570	+	0.707658i	0.281195	+	0.162348i	0.633964	−	0.773362i	$-0.281427\pi$
$19$	1.22570	+	0.707658i	0.281195	+	0.162348i	−0.352769	+	0.935710i	$0.614760\pi$
$20$	5.52521	+	3.27973i	1.23547	+	0.733369i
$21$	−1.80912	+	4.21036i	−0.394782	+	0.918775i
$22$	−0.0319246	+	5.27815i	−0.00680634	+	1.12530i
$23$	0.642780	+	0.539356i	0.134029	+	0.112464i	0.707338	−	0.706876i	$-0.249896\pi$
$23$	0.642780	+	0.539356i	0.134029	+	0.112464i	−0.573309	+	0.819339i	$0.694340\pi$
$24$	−2.43741	−	4.24959i	−0.497534	−	0.867445i
$25$	5.00022	+	1.81993i	1.00004	+	0.363987i
$26$	−2.31249	+	6.23591i	−0.453517	+	1.22296i
$27$	0.238416	+	5.19068i	0.0458833	+	0.998947i
$28$	−1.35366	+	5.11543i	−0.255818	+	0.966725i
$29$	5.73413	−	1.01108i	1.06480	−	0.187753i	0.386316	−	0.922367i	$-0.373747\pi$
$29$	5.73413	−	1.01108i	1.06480	−	0.187753i	0.678486	+	0.734613i	$0.262636\pi$
$30$	−5.11388	−	5.98122i	−0.933662	−	1.09202i
$31$	−8.17084	−	1.44074i	−1.46753	−	0.258764i	−0.617945	−	0.786222i	$-0.712034\pi$
$31$	−8.17084	−	1.44074i	−1.46753	−	0.258764i	−0.849582	+	0.527457i	$0.823145\pi$
$32$	−3.50346	−	4.44137i	−0.619331	−	0.785130i
$33$	2.11779	−	6.10776i	0.368661	−	1.06322i
$34$	−7.89542	+	2.81974i	−1.35405	+	0.483581i
$35$	−0.612009	+	8.47781i	−0.103448	+	1.43301i
$36$	1.15103	+	5.88856i	0.191839	+	0.981426i
$37$	−9.29934			−1.52880			−0.764401	−	0.644741i	$-0.776965\pi$
$37$	−9.29934			−1.52880			−0.764401	+	0.644741i	$0.776965\pi$
$38$	−1.52547	−	1.29583i	−0.247465	−	0.210211i
$39$	5.13983	−	6.31929i	0.823032	−	1.01190i
$40$	−6.85373	−	5.96619i	−1.08367	−	0.943337i
$41$	−7.90132	−	1.39322i	−1.23398	−	0.217584i	−0.481645	−	0.876366i	$-0.659961\pi$
$41$	−7.90132	−	1.39322i	−1.23398	−	0.217584i	−0.752334	+	0.658782i	$0.771072\pi$
$42$	3.58629	−	5.39801i	0.553376	−	0.832932i
$43$	4.21585	+	5.02425i	0.642911	+	0.766191i	0.984827	−	0.173539i	$-0.0555203\pi$
$43$	4.21585	+	5.02425i	0.642911	+	0.766191i	−0.341916	+	0.939731i	$0.611076\pi$
$44$	1.38504	−	7.33494i	0.208802	−	1.10578i
$45$	3.57192	+	8.95162i	0.532470	+	1.33443i
$46$	−0.757253	−	0.913625i	−0.111651	−	0.134707i
$47$	0.260389	+	1.47674i	0.0379816	+	0.215404i	0.997891	−	0.0649045i	$-0.0206743\pi$
$47$	0.260389	+	1.47674i	0.0379816	+	0.215404i	−0.959910	+	0.280309i	$0.909563\pi$
$48$	2.31159	+	6.53120i	0.333649	+	0.942697i
$49$	−6.85352	+	1.42454i	−0.979074	+	0.203505i
$50$	−6.49415	−	3.80195i	−0.918411	−	0.537677i
$51$	10.2668	−	0.157093i	1.43765	−	0.0219974i
$52$	4.80107	−	8.08815i	0.665789	−	1.12162i
$53$	−3.76130	−	2.17159i	−0.516655	−	0.298291i	0.218910	−	0.975745i	$-0.429750\pi$
$53$	−3.76130	−	2.17159i	−0.516655	−	0.298291i	−0.735565	+	0.677454i	$0.763083\pi$
$54$	0.986717	−	7.28192i	0.134275	−	0.990944i
$55$		−	11.9905i		−	1.61680i
$56$	3.18253	−	6.77285i	0.425284	−	0.905060i
$57$	1.25804	+	2.10397i	0.166631	+	0.278678i
$58$	−8.23424	−	0.0498043i	−1.08121	−	0.00653963i
$59$	−1.68390	+	0.612889i	−0.219225	+	0.0797914i	−0.449298	−	0.893382i	$-0.648326\pi$
$59$	−1.68390	+	0.612889i	−0.219225	+	0.0797914i	0.230073	+	0.973173i	$0.426104\pi$
$60$	5.59532	+	9.62008i	0.722352	+	1.24195i
$61$	2.37309	+	13.4585i	0.303843	+	1.72318i	0.628902	+	0.777485i	$0.283505\pi$
$61$	2.37309	+	13.4585i	0.303843	+	1.72318i	−0.325059	+	0.945694i	$0.605384\pi$
$62$	11.0015	+	4.07973i	1.39719	+	0.518127i
$63$	−6.28656	+	4.84554i	−0.792032	+	0.610480i
$64$	3.74600	+	7.06877i	0.468249	+	0.883596i
$65$	5.16749	−	14.1976i	0.640948	−	1.76099i
$66$	−4.49765	+	7.95931i	−0.553623	+	0.979724i
$67$	−9.03556	+	10.7682i	−1.10387	+	1.31554i	−0.159300	+	0.987230i	$0.550924\pi$
$67$	−9.03556	+	10.7682i	−1.10387	+	1.31554i	−0.944570	+	0.328311i	$0.893521\pi$
$68$	11.7004	−	1.91747i	1.41889	−	0.232527i
$69$	0.517909	+	1.35793i	0.0623490	+	0.163476i
$70$	3.00476	−	11.6390i	0.359137	−	1.39113i
$71$	−1.65180	+	2.86100i	−0.196033	+	0.339538i	−0.947239	−	0.320530i	$-0.896139\pi$
$71$	−1.65180	+	2.86100i	−0.196033	+	0.339538i	0.751206	+	0.660068i	$0.229472\pi$
$72$	−0.105677	−	8.48462i	−0.0124542	−	0.999922i
$73$	−10.7512			−1.25833			−0.629166	−	0.777271i	$-0.716604\pi$
$73$	−10.7512			−1.25833			−0.629166	+	0.777271i	$0.716604\pi$
$74$	12.9374	+	2.36198i	1.50394	+	0.274575i
$75$	6.03155	+	6.96876i	0.696463	+	0.804683i
$76$	1.79313	+	2.19024i	0.205686	+	0.251238i
$77$	9.49826	−	2.70046i	1.08243	−	0.307746i
$78$	−8.75569	+	7.48602i	−0.991387	+	0.847625i
$79$	−1.09487	−	1.30482i	−0.123183	−	0.146803i	0.700928	−	0.713232i	$-0.252769\pi$
$79$	−1.09487	−	1.30482i	−0.123183	−	0.146803i	−0.824111	+	0.566428i	$0.808325\pi$
$80$	8.01965	+	10.0411i	0.896624	+	1.12263i
$81$	−4.01487	+	8.05486i	−0.446097	+	0.894985i
$82$	10.6386	+	3.94516i	1.17484	+	0.435670i
$83$	0.380043	+	2.15533i	0.0417152	+	0.236578i	0.998535	−	0.0541018i	$-0.0172295\pi$
$83$	0.380043	+	2.15533i	0.0417152	+	0.236578i	−0.956820	+	0.290680i	$0.906118\pi$
$84$	−6.36037	+	6.59891i	−0.693973	+	0.720001i
$85$	17.8969	−	6.51392i	1.94119	−	0.706534i
$86$	−4.58903	−	8.06063i	−0.494848	−	0.869200i
$87$	9.52849	+	3.30389i	1.02156	+	0.354214i
$88$	−3.78992	+	9.85271i	−0.404007	+	1.05030i
$89$	4.90703	+	2.83307i	0.520144	+	0.300305i	0.736994	−	0.675900i	$-0.236245\pi$
$89$	4.90703	+	2.83307i	0.520144	+	0.300305i	−0.216850	+	0.976205i	$0.569578\pi$
$90$	−2.69565	−	13.3609i	−0.284147	−	1.40836i
$91$	12.4104	+	0.895898i	1.30096	+	0.0939157i
$92$	0.821448	+	1.46339i	0.0856418	+	0.152569i
$93$	−11.1486	−	9.06776i	−1.15605	−	0.940283i
$94$	0.0128263	−	2.12060i	0.00132293	−	0.218723i
$95$	3.48314	+	2.92270i	0.357363	+	0.299863i
$96$	−1.55704	−	9.67345i	−0.158914	−	0.987292i
$97$	5.79844	−	4.86547i	0.588743	−	0.494014i	−0.299062	−	0.954234i	$-0.596674\pi$
$97$	5.79844	−	4.86547i	0.588743	−	0.494014i	0.887805	+	0.460220i	$0.152229\pi$
$98$	9.89656	−	0.241083i	0.999703	−	0.0243531i
$99$	8.35307	−	7.45624i	0.839515	−	0.749381i
$100$	8.06910	+	6.93882i	0.806910	+	0.693882i
$101$	−1.90188	−	2.26657i	−0.189244	−	0.225532i	0.663077	−	0.748551i	$-0.269250\pi$
$101$	−1.90188	−	2.26657i	−0.189244	−	0.225532i	−0.852321	+	0.523019i	$0.824806\pi$
$102$	−14.3233	−	2.38918i	−1.41822	−	0.236564i
$103$	−13.5695	−	2.39267i	−1.33704	−	0.235757i	−0.541014	−	0.841013i	$-0.681959\pi$
$103$	−13.5695	−	2.39267i	−1.33704	−	0.235757i	−0.796031	+	0.605256i	$0.793071\pi$
$104$	−8.73368	+	10.0329i	−0.856408	+	0.983809i
$105$	−8.07260	+	12.3117i	−0.787805	+	1.20149i
$106$	4.68122	+	3.97651i	0.454680	+	0.386232i
$107$	−5.60382	−	9.70609i	−0.541741	−	0.938323i	−0.998804	−	0.0488891i	$-0.984432\pi$
$107$	−5.60382	−	9.70609i	−0.541741	−	0.938323i	0.457063	−	0.889434i	$-0.348901\pi$
$108$	−3.22231	+	9.88012i	−0.310067	+	0.950715i
$109$	3.32871	−	5.76549i	0.318832	−	0.552234i	−0.661412	−	0.750022i	$-0.730043\pi$
$109$	3.32871	−	5.76549i	0.318832	−	0.552234i	0.980245	+	0.197789i	$0.0633760\pi$
$110$	−3.04553	+	16.6814i	−0.290380	+	1.59051i
$111$	−14.0706	−	7.83911i	−1.33552	−	0.744055i
$112$	−6.14786	+	8.61416i	−0.580919	+	0.813962i
$113$	7.89450	−	9.40830i	0.742652	−	0.885058i	−0.253968	−	0.967213i	$-0.581736\pi$
$113$	7.89450	−	9.40830i	0.742652	−	0.885058i	0.996620	+	0.0821547i	$0.0261802\pi$
$114$	−1.21580	−	3.24662i	−0.113870	−	0.304074i
$115$	1.73276	+	2.06503i	0.161581	+	0.192565i
$116$	11.4430	+	2.16074i	1.06245	+	0.200620i
$117$	13.1040	−	5.22880i	1.21146	−	0.483403i
$118$	2.49834	−	0.424961i	0.229991	−	0.0391208i
$119$	9.19065	+	12.7099i	0.842505	+	1.16512i
$120$	−5.34085	−	14.8048i	−0.487551	−	1.35149i
$121$	−2.75323	+	1.00209i	−0.250294	+	0.0910995i
$122$	0.116895	−	19.3264i	0.0105831	−	1.74973i
$123$	−10.7808	−	8.76866i	−0.972075	−	0.790643i
$124$	−14.2692	−	8.47011i	−1.28141	−	0.760639i
$125$	0.893452	+	0.515835i	0.0799128	+	0.0461377i
$126$	9.97671	−	5.14444i	0.888796	−	0.458303i
$127$	13.8457	−	7.99382i	1.22861	−	0.709336i	0.261868	−	0.965104i	$-0.415661\pi$
$127$	13.8457	−	7.99382i	1.22861	−	0.709336i	0.966738	+	0.255767i	$0.0823281\pi$
$128$	−3.41606	−	10.7857i	−0.301940	−	0.953327i
$129$	2.14357	+	11.1559i	0.188731	+	0.982224i
$130$	−10.7952	+	18.4394i	−0.946802	+	1.61724i
$131$	−4.19342	−	3.51870i	−0.366381	−	0.307430i	0.440947	−	0.897533i	$-0.354643\pi$
$131$	−4.19342	−	3.51870i	−0.366381	−	0.307430i	−0.807328	+	0.590103i	$0.799087\pi$
$132$	8.27884	−	9.93076i	0.720580	−	0.864362i
$133$	−1.53075	+	3.41740i	−0.132733	+	0.296326i
$134$	15.3055	−	12.6859i	1.32219	−	1.09589i
$135$	−2.14142	+	16.5555i	−0.184304	+	1.42487i
$136$	−16.7649	−	0.304234i	−1.43758	−	0.0260879i
$137$	1.72905	−	4.75054i	0.147723	−	0.405866i	−0.843657	−	0.536882i	$-0.819602\pi$
$137$	1.72905	−	4.75054i	0.147723	−	0.405866i	0.991380	+	0.131016i	$0.0418241\pi$
$138$	−0.375617	−	2.02073i	−0.0319746	−	0.172016i
$139$	0.0788654	+	0.216681i	0.00668928	+	0.0183786i	0.942992	−	0.332814i	$-0.107998\pi$
$139$	0.0788654	+	0.216681i	0.00668928	+	0.0183786i	−0.936303	+	0.351193i	$0.885776\pi$
$140$	−7.13653	+	15.4292i	−0.603147	+	1.30401i
$141$	−0.850865	+	2.45391i	−0.0716558	+	0.206657i
$142$	3.02469	−	3.56073i	0.253827	−	0.298810i
$143$	−17.5525			−1.46781
$144$	−2.00803	+	11.8308i	−0.167336	+	0.985900i
$145$	18.7060			1.55345
$146$	14.9573	+	2.73075i	1.23787	+	0.225998i
$147$	−11.5707	−	3.62192i	−0.954337	−	0.298731i
$148$	−17.3988	−	6.57206i	−1.43017	−	0.540220i
$149$	2.58232	+	7.09486i	0.211552	+	0.581234i	0.999400	−	0.0346356i	$-0.0110271\pi$
$149$	2.58232	+	7.09486i	0.211552	+	0.581234i	−0.787848	+	0.615870i	$0.788805\pi$
$150$	−6.62117	−	11.2270i	−0.540616	−	0.916684i
$151$	−8.90037	+	1.56938i	−0.724302	+	0.127714i	−0.523631	−	0.851945i	$-0.675423\pi$
$151$	−8.90037	+	1.56938i	−0.724302	+	0.127714i	−0.200670	+	0.979659i	$0.564312\pi$
$152$	−1.93833	−	3.50255i	−0.157219	−	0.284094i
$153$	15.6669	+	8.41701i	1.26660	+	0.680475i
$154$	−13.9001	+	1.34441i	−1.12010	+	0.108336i
$155$	−25.0475	−	9.11655i	−2.01186	−	0.732259i
$156$	14.0825	−	8.19078i	1.12750	−	0.655787i
$157$	−2.48307	+	0.903762i	−0.198170	+	0.0721281i	−0.439199	−	0.898390i	$-0.644738\pi$
$157$	−2.48307	+	0.903762i	−0.198170	+	0.0721281i	0.241028	+	0.970518i	$0.422515\pi$
$158$	1.19179	+	2.09337i	0.0948135	+	0.166540i
$159$	−3.86053	−	6.45646i	−0.306160	−	0.512031i
$160$	−8.60670	−	16.0063i	−0.680419	−	1.26541i
$161$	−1.24556	+	1.83768i	−0.0981640	+	0.144830i
$162$	7.63146	−	10.1863i	0.599584	−	0.800312i
$163$	17.7319	−	10.2375i	1.38887	−	0.801865i	0.395683	−	0.918387i	$-0.370508\pi$
$163$	17.7319	−	10.2375i	1.38887	−	0.801865i	0.993188	+	0.116522i	$0.0371745\pi$
$164$	−13.7985	−	8.19072i	−1.07749	−	0.639588i
$165$	10.1077	−	18.1425i	0.786884	−	1.41239i
$166$	0.0187203	−	3.09506i	0.00145298	−	0.240224i
$167$	−4.63709	−	3.89098i	−0.358829	−	0.301093i	0.445495	−	0.895285i	$-0.353028\pi$
$167$	−4.63709	−	3.89098i	−0.358829	−	0.301093i	−0.804324	+	0.594191i	$0.797472\pi$
$168$	10.5248	−	7.56502i	0.812002	−	0.583654i
$169$	−8.56727	−	3.11823i	−0.659021	−	0.239864i
$170$	−26.5529	+	4.51658i	−2.03652	+	0.346406i
$171$	0.129904	+	4.24396i	0.00993401	+	0.324544i
$172$	4.33698	+	12.3797i	0.330692	+	0.943942i
$173$	1.42124	−	3.90483i	0.108055	−	0.296879i	−0.873867	−	0.486165i	$-0.838395\pi$
$173$	1.42124	−	3.90483i	0.108055	−	0.296879i	0.981922	+	0.189286i	$0.0606175\pi$
$174$	−12.4170	−	7.01662i	−0.941332	−	0.531928i
$175$	−3.43661	+	13.6525i	−0.259784	+	1.03203i
$176$	7.77515	−	12.7446i	0.586074	−	0.960664i
$177$	−3.06451	−	0.492139i	−0.230343	−	0.0369914i
$178$	−6.10716	−	5.18778i	−0.457751	−	0.388841i
$179$	3.93796	+	6.82075i	0.294337	+	0.509807i	0.974830	−	0.222947i	$-0.0715678\pi$
$179$	3.93796	+	6.82075i	0.294337	+	0.509807i	−0.680493	+	0.732754i	$0.738234\pi$
$180$	0.356639	+	19.2726i	0.0265823	+	1.43650i
$181$	10.0814	+	17.4615i	0.749343	+	1.29790i	0.948138	+	0.317859i	$0.102964\pi$
$181$	10.0814	+	17.4615i	0.749343	+	1.29790i	−0.198795	+	0.980041i	$0.563703\pi$
$182$	−17.0380	−	4.39856i	−1.26294	−	0.326043i
$183$	−7.75449	+	22.3641i	−0.573228	+	1.65320i
$184$	−0.771119	−	2.24454i	−0.0568477	−	0.165469i
$185$	−29.4216	−	5.18783i	−2.16312	−	0.381417i
$186$	13.2069	+	15.4469i	0.968379	+	1.13262i
$187$	−14.2223	−	16.9495i	−1.04004	−	1.23947i
$188$	−0.556466	+	2.94696i	−0.0405844	+	0.214929i
$189$	−13.5967	+	2.03224i	−0.989014	+	0.147824i
$190$	−4.10346	−	4.95081i	−0.297696	−	0.359170i
$191$	−3.61944	+	3.03707i	−0.261894	+	0.219755i	−0.764274	−	0.644892i	$-0.776902\pi$
$191$	−3.61944	+	3.03707i	−0.261894	+	0.219755i	0.502380	+	0.864647i	$0.332458\pi$
$192$	−0.290830	+	13.8534i	−0.0209889	+	0.999780i
$193$	−0.231958	+	1.31550i	−0.0166967	+	0.0946916i	−0.992017	−	0.126102i	$-0.959753\pi$
$193$	−0.231958	+	1.31550i	−0.0166967	+	0.0946916i	0.975321	+	0.220793i	$0.0708646\pi$
$194$	−9.30270	+	5.29616i	−0.667895	+	0.380242i
$195$	19.7870	−	17.1259i	1.41697	−	1.22641i
$196$	−13.8295	−	2.17828i	−0.987822	−	0.155591i
$197$	−17.8655	+	10.3146i	−1.27286	+	0.734887i	−0.975526	−	0.219886i	$-0.929432\pi$
$197$	−17.8655	+	10.3146i	−1.27286	+	0.734887i	−0.297336	+	0.954773i	$0.596098\pi$
$198$	−13.5148	+	8.25162i	−0.960454	+	0.586417i
$199$	−7.49351	+	4.32638i	−0.531201	+	0.306689i	−0.741505	−	0.670947i	$-0.765888\pi$
$199$	−7.49351	+	4.32638i	−0.531201	+	0.306689i	0.210304	+	0.977636i	$0.432555\pi$
$200$	−9.46344	−	11.7029i	−0.669166	−	0.827522i
$201$	−22.7488	+	8.67627i	−1.60457	+	0.611977i
$202$	2.07023	+	3.63636i	0.145661	+	0.255854i
$203$	4.21288	+	14.8179i	0.295686	+	1.04001i
$204$	19.3200	+	6.96191i	1.35267	+	0.487431i
$205$	−24.2213	−	8.81584i	−1.69169	−	0.615725i
$206$	18.2704	+	6.77532i	1.27296	+	0.472059i
$207$	−0.361069	+	2.49124i	−0.0250960	+	0.173153i
$208$	14.6988	−	11.7397i	1.01918	−	0.814000i
$209$	1.80667	−	4.96379i	0.124970	−	0.343353i
$210$	14.3578	−	15.0778i	0.990785	−	1.04047i
$211$	11.2586	−	13.4174i	0.775072	−	0.923695i	−0.223628	−	0.974675i	$-0.571790\pi$
$211$	11.2586	−	13.4174i	0.775072	−	0.923695i	0.998700	+	0.0509799i	$0.0162345\pi$
$212$	−5.50258	−	6.72119i	−0.377919	−	0.461613i
$213$	−4.91105	+	2.93648i	−0.336499	+	0.201204i
$214$	5.33083	+	14.9266i	0.364408	+	1.02036i
$215$	10.5354	+	18.2479i	0.718508	+	1.24449i
$216$	6.99243	−	12.9269i	0.475775	−	0.879567i
$217$	1.58056	−	21.8945i	0.107295	−	1.48630i
$218$	−6.09536	+	7.17557i	−0.412830	+	0.485991i
$219$	−16.2674	−	9.06299i	−1.09925	−	0.612420i
$220$	8.47399	−	22.4339i	0.571316	−	1.51250i
$221$	−9.53549	−	26.1986i	−0.641427	−	1.76231i
$222$	17.5842	+	14.4798i	1.18017	+	0.971818i
$223$	1.70046	−	4.67198i	0.113871	−	0.312859i	−0.869645	−	0.493677i	$-0.835652\pi$
$223$	1.70046	−	4.67198i	0.113871	−	0.312859i	0.983517	+	0.180818i	$0.0578746\pi$
$224$	10.7410	−	10.4226i	0.717661	−	0.696392i
$225$	3.25169	+	15.6287i	0.216779	+	1.04191i
$226$	−13.3726	+	11.0838i	−0.889534	+	0.737285i
$227$	−1.92824	−	10.9356i	−0.127982	−	0.725821i	−0.979492	−	0.201483i	$-0.935424\pi$
$227$	−1.92824	−	10.9356i	−0.127982	−	0.725821i	0.851510	−	0.524338i	$-0.175687\pi$
$228$	0.866823	+	4.82556i	0.0574068	+	0.319581i
$229$	8.22471	−	2.99355i	0.543504	−	0.197819i	−0.0556538	−	0.998450i	$-0.517724\pi$
$229$	8.22471	−	2.99355i	0.543504	−	0.197819i	0.599158	+	0.800631i	$0.295502\pi$
$230$	−1.88615	−	3.31302i	−0.124369	−	0.218454i
$231$	16.6480	+	3.92081i	1.09536	+	0.257970i
$232$	−15.3708	−	5.91252i	−1.00915	−	0.388176i
$233$		−	7.10076i		−	0.465186i	−0.972574	−	0.232593i	$-0.925279\pi$
$233$		−	7.10076i		−	0.465186i	0.972574	−	0.232593i	$-0.0747210\pi$
$234$	−19.5585	+	3.94607i	−1.27858	+	0.257962i
$235$			4.81743i			0.314254i
$236$	−3.58367	−	0.0433529i	−0.233277	−	0.00282203i
$237$	−0.556693	−	2.89723i	−0.0361611	−	0.188195i
$238$	−9.55794	−	20.0166i	−0.619549	−	1.29749i
$239$	−18.3606	+	6.68270i	−1.18765	+	0.432268i	−0.858897	−	0.512149i	$-0.828850\pi$
$239$	−18.3606	+	6.68270i	−1.18765	+	0.432268i	−0.328750	+	0.944417i	$0.606627\pi$
$240$	3.66995	+	21.9533i	0.236894	+	1.41708i
$241$	24.8308	+	9.03768i	1.59949	+	0.582168i	0.979324	−	0.202299i	$-0.0648413\pi$
$241$	24.8308	+	9.03768i	1.59949	+	0.582168i	0.620170	+	0.784467i	$0.287064\pi$
$242$	4.08487	−	0.694825i	0.262585	−	0.0446650i
$243$	−12.8648	+	8.80316i	−0.825280	+	0.564723i
$244$	−5.07143	+	26.8575i	−0.324665	+	1.71938i
$245$	−22.4782	+	0.683634i	−1.43608	+	0.0436758i
$246$	12.7713	+	14.9374i	0.814268	+	0.952373i
$247$	4.27844	−	5.09884i	0.272230	−	0.324432i
$248$	17.7002	+	15.4081i	1.12397	+	0.978414i
$249$	−1.24186	+	3.58154i	−0.0786996	+	0.226971i
$250$	−1.11197	−	0.944571i	−0.0703270	−	0.0597399i
$251$	3.19296	+	5.53037i	0.201538	+	0.349074i	0.949024	−	0.315203i	$-0.102073\pi$
$251$	3.19296	+	5.53037i	0.201538	+	0.349074i	−0.747486	+	0.664277i	$0.768739\pi$
$252$	−15.1864	+	4.62301i	−0.956655	+	0.291222i
$253$	1.56586	−	2.71215i	0.0984447	−	0.170511i
$254$	−21.2928	+	7.60440i	−1.33603	+	0.477143i
$255$	32.5703	+	5.23056i	2.03963	+	0.327550i
$256$	2.01299	+	15.8729i	0.125812	+	0.992054i
$257$	−2.59439	−	7.12803i	−0.161834	−	0.444634i	0.832099	−	0.554628i	$-0.187139\pi$
$257$	−2.59439	−	7.12803i	−0.161834	−	0.444634i	−0.993932	+	0.109993i	$0.964917\pi$
$258$	−0.148626	−	16.0648i	−0.00925307	−	1.00015i
$259$	−2.51670	−	24.4747i	−0.156380	−	1.52078i
$260$	19.7020	−	22.9113i	1.22187	−	1.42090i
$261$	11.6322	+	13.0313i	0.720016	+	0.806618i
$262$	4.94023	+	5.96038i	0.305209	+	0.368234i
$263$	−0.0894409	+	0.0750499i	−0.00551516	+	0.00462777i	−0.645541	−	0.763726i	$-0.723368\pi$
$263$	−0.0894409	+	0.0750499i	−0.00551516	+	0.00462777i	0.640026	+	0.768353i	$0.278924\pi$
$264$	−14.0400	+	11.7131i	−0.864104	+	0.720889i
$265$	−10.6887	−	8.96889i	−0.656602	−	0.550955i
$266$	2.99761	−	4.36555i	0.183795	−	0.267669i
$267$	5.03648	+	8.42315i	0.308228	+	0.515489i
$268$	−24.5154	+	13.7613i	−1.49752	+	0.840605i
$269$	−13.4291	−	7.75331i	−0.818789	−	0.472728i	0.0312100	−	0.999513i	$-0.490064\pi$
$269$	−13.4291	−	7.75331i	−0.818789	−	0.472728i	−0.849999	+	0.526785i	$0.823397\pi$
$270$	7.18419	−	22.4884i	0.437216	−	1.36860i
$271$	18.0136	−	10.4002i	1.09425	−	0.631766i	0.159546	−	0.987191i	$-0.448997\pi$
$271$	18.0136	−	10.4002i	1.09425	−	0.631766i	0.934705	+	0.355424i	$0.115664\pi$
$272$	23.2463	+	4.68145i	1.40952	+	0.283855i
$273$	18.0226	+	11.8172i	1.09078	+	0.715209i
$274$	−3.61210	+	6.16986i	−0.218215	+	0.372735i
$275$	3.44864	−	19.5582i	0.207961	−	1.17941i
$276$	0.00931028	+	2.90668i	0.000560413	+	0.174961i
$277$	−15.4794	+	12.9888i	−0.930068	+	0.780420i	−0.975830	−	0.218532i	$-0.929873\pi$
$277$	−15.4794	+	12.9888i	−0.930068	+	0.780420i	0.0457612	+	0.998952i	$0.485429\pi$
$278$	−0.0546831	−	0.321482i	−0.00327968	−	0.0192812i
$279$	−9.22472	−	23.1182i	−0.552270	−	1.38405i
$280$	13.8474	−	19.6528i	0.827541	−	1.17448i
$281$	16.2248	+	19.3360i	0.967893	+	1.15349i	0.988118	+	0.153694i	$0.0491171\pi$
$281$	16.2248	+	19.3360i	0.967893	+	1.15349i	−0.0202258	+	0.999795i	$0.506439\pi$
$282$	1.80702	−	3.19781i	0.107606	−	0.190427i
$283$	21.0047	−	25.0325i	1.24860	−	1.48803i	0.441905	−	0.897062i	$-0.354303\pi$
$283$	21.0047	−	25.0325i	1.24860	−	1.48803i	0.806697	−	0.590965i	$-0.201253\pi$
$284$	−5.11241	+	4.18549i	−0.303366	+	0.248363i
$285$	2.80648	+	7.35847i	0.166242	+	0.435878i
$286$	24.4193	+	4.45824i	1.44394	+	0.263621i
$287$	1.52842	−	21.1723i	0.0902198	−	1.24976i
$288$	5.79857	−	15.9492i	0.341684	−	0.939815i
$289$	9.07215	−	15.7134i	0.533656	−	0.924319i
$290$	−26.0241	−	4.75122i	−1.52819	−	0.279001i
$291$	12.8749	−	2.47387i	0.754743	−	0.145021i
$292$	−20.1152	−	7.59813i	−1.17715	−	0.444647i
$293$	5.77179	+	15.8579i	0.337191	+	0.926426i	0.986187	+	0.165634i	$0.0529670\pi$
$293$	5.77179	+	15.8579i	0.337191	+	0.926426i	−0.648996	+	0.760792i	$0.724811\pi$
$294$	15.1775	+	7.97778i	0.885167	+	0.465273i
$295$	−5.66951	+	0.999687i	−0.330091	+	0.0582040i
$296$	22.5363	+	13.5624i	1.30989	+	0.788297i
$297$	18.9242	−	4.24042i	1.09810	−	0.246054i
$298$	−1.79051	−	10.5264i	−0.103721	−	0.609778i
$299$	3.02292	−	2.53653i	0.174820	−	0.146691i
$300$	6.35988	+	17.3010i	0.367188	+	0.998874i
$301$	−12.0823	+	12.4553i	−0.696410	+	0.717912i
$302$	12.7810	+	0.0773049i	0.735462	+	0.00444840i
$303$	−0.967021	−	5.03273i	−0.0555539	−	0.289123i
$304$	1.80701	+	5.36513i	0.103639	+	0.307711i
$305$			43.9043i			2.51395i
$306$	−19.6582	−	15.6892i	−1.12379	−	0.896892i
$307$	−6.81834	−	3.93657i	−0.389143	−	0.224672i	0.292646	−	0.956221i	$-0.405464\pi$
$307$	−6.81834	−	3.93657i	−0.389143	−	0.224672i	−0.681789	+	0.731549i	$0.738798\pi$
$308$	19.6795	+	1.66017i	1.12134	+	0.0945970i
$309$	−18.5147	−	15.0591i	−1.05327	−	0.856680i
$310$	32.5310	+	19.0450i	1.84764	+	1.08169i
$311$	15.2233	+	12.7738i	0.863232	+	0.724337i	0.962662	−	0.270707i	$-0.0872575\pi$
$311$	15.2233	+	12.7738i	0.863232	+	0.724337i	−0.0994300	+	0.995045i	$0.531702\pi$
$312$	−21.6722	+	7.81828i	−1.22695	+	0.442623i
$313$	10.1457	+	3.69273i	0.573468	+	0.208725i	0.612443	−	0.790515i	$-0.290187\pi$
$313$	10.1457	+	3.69273i	0.573468	+	0.208725i	−0.0389746	+	0.999240i	$0.512409\pi$
$314$	3.68404	−	0.626644i	0.207902	−	0.0353636i
$315$	−22.5929	+	11.8234i	−1.27296	+	0.666175i
$316$	−1.12633	−	3.21505i	−0.0633609	−	0.180861i
$317$	−15.8307	+	2.79138i	−0.889140	+	0.156779i	−0.599518	−	0.800362i	$-0.704641\pi$
$317$	−15.8307	+	2.79138i	−0.889140	+	0.156779i	−0.289623	+	0.957141i	$0.593530\pi$
$318$	3.73094	+	9.96290i	0.209220	+	0.558692i
$319$	−7.43263	−	20.4210i	−0.416147	−	1.14336i
$320$	7.90828	+	24.4543i	0.442086	+	1.36704i
$321$	−0.296991	−	19.4099i	−0.0165764	−	1.08336i
$322$	2.19961	−	2.24025i	0.122579	−	0.124844i
$323$	8.39037			0.466852
$324$	−13.2043	+	12.2330i	−0.733571	+	0.679612i
$325$	12.5123	−	21.6720i	0.694059	−	1.20214i
$326$	−27.2692	+	9.73882i	−1.51030	+	0.539383i
$327$	9.89674	−	5.91759i	0.547291	−	0.327244i
$328$	17.1164	+	14.8998i	0.945094	+	0.822706i
$329$	−3.81612	+	1.08496i	−0.210389	+	0.0598159i
$330$	−18.6701	+	22.6729i	−1.02776	+	1.24810i
$331$	7.69825	−	1.35741i	0.423134	−	0.0746099i	0.0419733	−	0.999119i	$-0.486636\pi$
$331$	7.69825	−	1.35741i	0.423134	−	0.0746099i	0.381161	+	0.924509i	$0.375524\pi$
$332$	−0.812174	+	4.30115i	−0.0445739	+	0.236056i
$333$	−14.6817	−	23.7223i	−0.804550	−	1.29997i
$334$	5.46292	+	6.59100i	0.298917	+	0.360644i
$335$	−34.5944	+	29.0281i	−1.89009	+	1.58598i
$336$	−16.5637	+	7.85136i	−0.903624	+	0.428327i
$337$	−2.30376	+	13.0653i	−0.125494	+	0.711711i	0.855520	+	0.517771i	$0.173238\pi$
$337$	−2.30376	+	13.0653i	−0.125494	+	0.711711i	−0.981013	+	0.193940i	$0.937873\pi$
$338$	11.1269	+	6.51418i	0.605225	+	0.354325i
$339$	19.8759	−	7.58058i	1.07951	−	0.411721i
$340$	38.0881	+	0.460764i	2.06562	+	0.0249884i
$341$			30.9663i			1.67692i
$342$	0.897219	−	5.93727i	0.0485161	−	0.321051i
$343$	−5.60398	−	17.6521i	−0.302586	−	0.953122i
$344$	−2.88931	−	18.3244i	−0.155781	−	0.987986i
$345$	0.881033	+	4.58522i	0.0474332	+	0.246860i
$346$	−2.96907	+	5.07148i	−0.159618	+	0.272645i
$347$	5.24781	−	29.7618i	0.281717	−	1.59770i	−0.435064	−	0.900399i	$-0.643274\pi$
$347$	5.24781	−	29.7618i	0.281717	−	1.59770i	0.716781	−	0.697298i	$-0.245615\pi$
$348$	15.4926	+	12.9155i	0.830491	+	0.692344i
$349$	−0.861877	−	4.88795i	−0.0461352	−	0.261646i	0.953012	−	0.302932i	$-0.0979655\pi$
$349$	−0.861877	−	4.88795i	−0.0461352	−	0.261646i	−0.999147	+	0.0412863i	$0.986854\pi$
$350$	8.24874	−	18.1207i	0.440914	−	0.968592i
$351$	24.2350	+	3.13474i	1.29357	+	0.167320i
$352$	−14.0540	+	15.7557i	−0.749080	+	0.839783i
$353$	−0.148784	+	0.408781i	−0.00791897	+	0.0217572i	−0.943589	−	0.331119i	$-0.892574\pi$
$353$	−0.148784	+	0.408781i	−0.00791897	+	0.0217572i	0.935670	+	0.352876i	$0.114796\pi$
$354$	4.13841	+	1.46304i	0.219954	+	0.0777598i
$355$	−6.82211	+	8.13027i	−0.362080	+	0.431510i
$356$	7.17872	+	8.76852i	0.380471	+	0.464731i
$357$	3.19198	+	26.9785i	0.168938	+	1.42786i
$358$	−3.74613	−	10.4894i	−0.197989	−	0.554381i
$359$	−0.288205	+	0.499186i	−0.0152109	+	0.0263460i	−0.873531	−	0.486769i	$-0.838175\pi$
$359$	−0.288205	+	0.499186i	−0.0152109	+	0.0263460i	0.858320	+	0.513115i	$0.171509\pi$
$360$	4.39898	−	26.9030i	0.231847	−	1.41791i
$361$	−8.49844	−	14.7197i	−0.447286	−	0.774723i
$362$	−9.59027	−	26.8533i	−0.504053	−	1.41138i
$363$	−5.01058	−	0.804663i	−0.262987	−	0.0422339i
$364$	22.5863	+	10.4469i	1.18384	+	0.547567i
$365$	−34.0151	−	5.99778i	−1.78043	−	0.313938i
$366$	16.4685	−	29.1437i	0.860824	−	1.52337i
$367$	−14.1614	+	2.49704i	−0.739220	+	0.130344i	−0.530564	−	0.847645i	$-0.678020\pi$
$367$	−14.1614	+	2.49704i	−0.739220	+	0.130344i	−0.208655	+	0.977989i	$0.566909\pi$
$368$	0.502694	+	3.31850i	0.0262048	+	0.172989i
$369$	−8.92044	−	22.3556i	−0.464380	−	1.16379i
$370$	39.6142	+	14.6903i	2.05945	+	0.763715i
$371$	4.69742	−	10.4870i	0.243878	−	0.544457i
$372$	−14.4503	−	24.8445i	−0.749212	−	1.28813i
$373$	−3.32932	+	18.8815i	−0.172386	+	0.977648i	0.768733	+	0.639570i	$0.220888\pi$
$373$	−3.32932	+	18.8815i	−0.172386	+	0.977648i	−0.941118	+	0.338078i	$0.890223\pi$
$374$	15.4812	+	27.1928i	0.800515	+	1.40610i
$375$	0.917023	+	1.53365i	0.0473549	+	0.0791976i
$376$	1.52268	−	3.95852i	0.0785261	−	0.204145i
$377$		−	27.3830i		−	1.41029i
$378$	19.4321	+	0.626194i	0.999481	+	0.0322079i
$379$			20.0522i			1.03001i	0.857186	+	0.515006i	$0.172210\pi$
$379$			20.0522i			1.03001i	−0.857186	+	0.515006i	$0.827790\pi$
$380$	4.45132	+	7.92992i	0.228348	+	0.406796i
$381$	27.6881	−	0.423656i	1.41851	−	0.0217046i
$382$	5.80683	−	3.30591i	0.297103	−	0.169145i
$383$	6.13778	−	34.8091i	0.313626	−	1.77866i	−0.266199	−	0.963918i	$-0.585768\pi$
$383$	6.13778	−	34.8091i	0.313626	−	1.77866i	0.579824	−	0.814741i	$-0.303121\pi$
$384$	3.92329	−	19.1992i	0.200209	−	0.979753i
$385$	31.5575	−	3.24501i	1.60832	−	0.165381i
$386$	0.656833	−	1.77123i	0.0334319	−	0.0901531i
$387$	−6.16079	+	18.6867i	−0.313170	+	0.949899i
$388$	14.2873	−	5.00527i	0.725327	−	0.254104i
$389$	3.37204	−	0.594582i	0.170969	−	0.0301465i	−0.0875081	−	0.996164i	$-0.527890\pi$
$389$	3.37204	−	0.594582i	0.170969	−	0.0301465i	0.258477	+	0.966017i	$0.416779\pi$
$390$	−31.8779	+	18.8000i	−1.61420	+	0.951977i
$391$	4.89877	+	0.863785i	0.247741	+	0.0436835i
$392$	18.6866	+	6.54308i	0.943815	+	0.330475i
$393$	−3.37878	−	8.85900i	−0.170437	−	0.446878i
$394$	27.4746	−	9.81216i	1.38415	−	0.494330i
$395$	−2.73608	−	4.73903i	−0.137667	−	0.238446i
$396$	20.8979	−	8.04712i	1.05016	−	0.404383i
$397$	−11.4533	+	19.8376i	−0.574823	+	0.995623i	0.421238	+	0.906950i	$0.361596\pi$
$397$	−11.4533	+	19.8376i	−0.574823	+	0.995623i	−0.996061	+	0.0886727i	$0.971737\pi$
$398$	11.5240	−	4.11563i	0.577645	−	0.206298i
$399$	−5.19693	+	3.88039i	−0.260172	+	0.194263i
$400$	10.1932	+	18.6850i	0.509661	+	0.934249i
$401$	−2.62189	+	3.12465i	−0.130931	+	0.156038i	−0.827527	−	0.561426i	$-0.810253\pi$
$401$	−2.62189	+	3.12465i	−0.130931	+	0.156038i	0.696596	+	0.717464i	$0.254697\pi$
$402$	33.8522	−	6.29252i	1.68840	−	0.313842i
$403$	−13.3454	+	36.6661i	−0.664781	+	1.82647i
$404$	−1.95653	−	5.58480i	−0.0973408	−	0.277854i
$405$	−17.1960	+	23.2445i	−0.854476	+	1.15503i
$406$	−2.09737	−	21.6850i	−0.104091	−	1.07621i
$407$	6.02694	+	34.1805i	0.298744	+	1.69426i
$408$	−25.1101	−	14.5927i	−1.24313	−	0.722447i
$409$	0.390371	−	2.21390i	0.0193026	−	0.109470i	−0.973634	−	0.228115i	$-0.926744\pi$
$409$	0.390371	−	2.21390i	0.0193026	−	0.109470i	0.992937	+	0.118645i	$0.0378549\pi$
$410$	31.4579	+	18.4168i	1.55360	+	0.909543i
$411$	6.62077	−	5.73037i	0.326579	−	0.282658i
$412$	−23.6973	−	14.0665i	−1.16748	−	0.693008i
$413$	−2.06876	−	4.26594i	−0.101797	−	0.209913i
$414$	1.13509	−	3.37415i	0.0557865	−	0.165830i
$415$			7.03115i			0.345145i
$416$	−23.4310	+	12.5990i	−1.14880	+	0.617718i
$417$	−0.0633275	+	0.394336i	−0.00310116	+	0.0193107i
$418$	−3.77425	+	6.44683i	−0.184605	+	0.315325i
$419$	2.21290	−	12.5500i	0.108107	−	0.613106i	−0.881827	−	0.471574i	$-0.843686\pi$
$419$	2.21290	−	12.5500i	0.108107	−	0.613106i	0.989934	−	0.141532i	$-0.0452028\pi$
$420$	−23.8046	+	17.3297i	−1.16154	+	0.845601i
$421$	−12.9191	+	10.8404i	−0.629638	+	0.528329i	−0.900816	−	0.434200i	$-0.857031\pi$
$421$	−12.9191	+	10.8404i	−0.629638	+	0.528329i	0.271179	+	0.962529i	$0.412587\pi$
$422$	−19.0711	+	15.8070i	−0.928366	+	0.769471i
$423$	−3.35601	+	2.99569i	−0.163175	+	0.145656i
$424$	5.94814	+	10.7483i	0.288867	+	0.521982i
$425$	31.0658	−	5.47774i	1.50691	−	0.265709i
$426$	7.57819	−	2.83790i	0.367164	−	0.137497i
$427$	−34.7787	+	9.88795i	−1.68306	+	0.478512i
$428$	−3.62506	−	22.1202i	−0.175224	−	1.06922i
$429$	−26.5582	−	14.7963i	−1.28224	−	0.714372i
$430$	−10.0222	−	28.0627i	−0.483312	−	1.35330i
$431$	−5.45098	+	9.44137i	−0.262564	+	0.454775i	−0.966923	−	0.255070i	$-0.917902\pi$
$431$	−5.45098	+	9.44137i	−0.262564	+	0.454775i	0.704358	+	0.709845i	$0.251235\pi$
$432$	−13.0114	+	16.2082i	−0.626010	+	0.779815i
$433$	−17.6119			−0.846374			−0.423187	−	0.906042i	$-0.639089\pi$
$433$	−17.6119			−0.846374			−0.423187	+	0.906042i	$0.639089\pi$
$434$	−7.75999	+	30.0586i	−0.372492	+	1.44286i
$435$	28.3035	+	15.7687i	1.35705	+	0.756049i
$436$	10.3025	−	8.43460i	0.493402	−	0.403944i
$437$	0.406175	+	1.11596i	0.0194300	+	0.0533835i
$438$	20.3295	+	16.7404i	0.971380	+	0.799888i
$439$	32.2887	−	5.69336i	1.54105	−	0.271729i	0.662386	−	0.749163i	$-0.269544\pi$
$439$	32.2887	−	5.69336i	1.54105	−	0.271729i	0.878668	+	0.477433i	$0.158433\pi$
$440$	−17.4873	+	29.0581i	−0.833673	+	1.38529i
$441$	−14.4542	−	15.2341i	−0.688294	−	0.725432i
$442$	6.61165	+	38.8699i	0.314484	+	1.84885i
$443$	11.2832	+	4.10674i	0.536079	+	0.195117i	0.595851	−	0.803095i	$-0.296815\pi$
$443$	11.2832	+	4.10674i	0.536079	+	0.195117i	−0.0597715	+	0.998212i	$0.519037\pi$
$444$	−20.7856	−	24.6108i	−0.986441	−	1.16798i
$445$	13.9446	+	11.7009i	0.661036	+	0.554675i
$446$	−3.55237	+	6.06784i	−0.168210	+	0.287320i
$447$	−2.07355	+	12.9119i	−0.0980758	+	0.610711i
$448$	−17.5903	+	11.7720i	−0.831065	+	0.556176i
$449$	5.46357	+	3.15439i	0.257842	+	0.148865i	0.623350	−	0.781943i	$-0.285771\pi$
$449$	5.46357	+	3.15439i	0.257842	+	0.148865i	−0.365508	+	0.930808i	$0.619105\pi$
$450$	−0.554204	−	22.5688i	−0.0261254	−	1.06390i
$451$			29.9449i			1.41005i
$452$	21.4195	−	12.0234i	1.00749	−	0.565535i
$453$	−14.7899	−	5.12821i	−0.694888	−	0.240944i
$454$	−0.0949820	+	15.7035i	−0.00445773	+	0.737004i
$455$	38.7647	+	9.75786i	1.81731	+	0.457456i
$456$	0.0197283	−	6.93358i	0.000923860	−	0.324695i
$457$	13.1991	−	11.0753i	0.617426	−	0.518082i	−0.279567	−	0.960126i	$-0.590191\pi$
$457$	13.1991	−	11.0753i	0.617426	−	0.518082i	0.896993	+	0.442044i	$0.145746\pi$
$458$	−12.2027	+	2.07565i	−0.570195	+	0.0969886i
$459$	16.6099	+	25.9424i	0.775283	+	1.21089i
$460$	1.78255	+	5.08820i	0.0831118	+	0.237238i
$461$	40.1495	−	7.07944i	1.86995	−	0.329722i	0.880435	−	0.474166i	$-0.157250\pi$
$461$	40.1495	−	7.07944i	1.86995	−	0.329722i	0.989513	+	0.144444i	$0.0461393\pi$
$462$	−22.1651	−	9.68321i	−1.03121	−	0.450504i
$463$	3.86339	+	10.6146i	0.179547	+	0.493302i	0.996518	−	0.0833772i	$-0.0265706\pi$
$463$	3.86339	+	10.6146i	0.179547	+	0.493302i	−0.816971	+	0.576679i	$0.804348\pi$
$464$	19.8824	+	12.1297i	0.923019	+	0.563108i
$465$	−30.2137	−	34.9084i	−1.40113	−	1.61884i
$466$	−1.80356	+	9.87870i	−0.0835481	+	0.457622i
$467$	1.64818	−	2.85474i	0.0762689	−	0.132102i	−0.825368	−	0.564594i	$-0.809033\pi$
$467$	1.64818	−	2.85474i	0.0762689	−	0.132102i	0.901637	+	0.432493i	$0.142366\pi$
$468$	28.2125	−	0.522071i	1.30412	−	0.0241327i
$469$	−30.7858	−	20.8663i	−1.42155	−	0.963514i
$470$	1.22360	−	6.70209i	0.0564405	−	0.309144i
$471$	−4.51891	−	0.725705i	−0.208221	−	0.0334387i
$472$	4.97466	+	0.970548i	0.228977	+	0.0446731i
$473$	15.7347	−	18.7519i	0.723484	−	0.862215i
$474$	0.0385988	+	4.17208i	0.00177290	+	0.191630i
$475$	4.84088	+	5.76914i	0.222115	+	0.264706i
$476$	8.21305	+	30.2752i	0.376445	+	1.38766i
$477$	−0.398636	−	13.0234i	−0.0182523	−	0.596302i
$478$	27.2409	−	4.63360i	1.24597	−	0.211936i
$479$	11.3406	−	9.51593i	0.518167	−	0.434794i	−0.345825	−	0.938299i	$-0.612401\pi$
$479$	11.3406	−	9.51593i	0.518167	−	0.434794i	0.863992	+	0.503505i	$0.167956\pi$
$480$	0.470320	−	31.4739i	0.0214671	−	1.43658i
$481$	−7.59427	+	43.0693i	−0.346269	+	1.96379i
$482$	−32.2496	−	18.8803i	−1.46893	−	0.859973i
$483$	−3.43375	+	1.73057i	−0.156241	+	0.0787437i
$484$	−5.85943	−	0.0708834i	−0.266338	−	0.00322197i
$485$	21.0597	−	12.1588i	0.956271	−	0.552103i
$486$	20.1338	−	8.97951i	0.913286	−	0.407319i
$487$	−7.73291	−	4.46460i	−0.350411	−	0.202310i	0.314455	−	0.949272i	$-0.398178\pi$
$487$	−7.73291	−	4.46460i	−0.350411	−	0.202310i	−0.664866	+	0.746962i	$0.731512\pi$
$488$	13.8771	−	36.0766i	0.628188	−	1.63311i
$489$	35.4597	−	0.542568i	1.60354	−	0.0245358i
$490$	31.4457	+	4.75825i	1.42057	+	0.214956i
$491$	−16.6774	−	13.9940i	−0.752641	−	0.631540i	0.183559	−	0.983009i	$-0.441238\pi$
$491$	−16.6774	−	13.9940i	−0.752641	−	0.631540i	−0.936200	+	0.351468i	$0.885683\pi$
$492$	−13.9736	−	24.0250i	−0.629980	−	1.08313i
$493$	26.4422	−	22.1876i	1.19090	−	0.999281i
$494$	−7.24732	+	6.00690i	−0.326072	+	0.270263i
$495$	30.5874	−	18.9305i	1.37480	−	0.850861i
$496$	−20.7113	−	25.9318i	−0.929964	−	1.16437i
$497$	−7.97682	−	3.57305i	−0.357809	−	0.160273i
$498$	2.63739	−	4.66728i	0.118184	−	0.209146i
$499$	11.6002	+	31.8713i	0.519296	+	1.42675i	0.871298	+	0.490755i	$0.163279\pi$
$499$	11.6002	+	31.8713i	0.519296	+	1.42675i	−0.352002	+	0.935999i	$0.614499\pi$
$500$	1.30707	+	1.59654i	0.0584540	+	0.0713993i
$501$	−3.73626	−	9.79630i	−0.166924	−	0.437666i
$502$	−3.03742	−	8.50494i	−0.135567	−	0.379594i
$503$	−10.3356	+	17.9017i	−0.460839	+	0.798197i	−0.999003	−	0.0446431i	$-0.985785\pi$
$503$	−10.3356	+	17.9017i	−0.460839	+	0.798197i	0.538164	+	0.842840i	$0.319118\pi$
$504$	22.3019	−	2.57434i	0.993404	−	0.114670i
$505$	−4.75280	−	8.23209i	−0.211497	−	0.366323i
$506$	−2.86732	+	3.37547i	−0.127468	+	0.150058i
$507$	−10.3343	−	11.9401i	−0.458964	−	0.530279i
$508$	31.5543	−	5.17113i	1.40000	−	0.229432i
$509$	−2.44443	+	2.91316i	−0.108348	+	0.129124i	−0.817493	−	0.575939i	$-0.804637\pi$
$509$	−2.44443	+	2.91316i	−0.108348	+	0.129124i	0.709145	+	0.705063i	$0.249081\pi$
$510$	−43.9839	−	15.5495i	−1.94764	−	0.688545i
$511$	−2.90962	−	28.2958i	−0.128714	−	1.25173i
$512$	1.23112	−	22.5939i	0.0544084	−	0.998519i
$513$	−3.38100	+	6.53093i	−0.149275	+	0.288348i
$514$	1.79888	+	10.5756i	0.0793452	+	0.466470i
$515$	−41.5970	−	15.1401i	−1.83298	−	0.667152i
$516$	−3.87360	+	22.3873i	−0.170526	+	0.985548i
$517$	5.25911	−	1.91416i	0.231295	−	0.0841846i
$518$	−2.71517	+	34.6888i	−0.119298	+	1.52414i
$519$	5.44212	−	4.71023i	0.238883	−	0.206756i
$520$	−33.2291	+	26.8703i	−1.45719	+	1.17834i
$521$		−	9.66709i		−	0.423523i	−0.977321	−	0.211761i	$-0.932080\pi$
$521$		−	9.66709i		−	0.423523i	0.977321	−	0.211761i	$-0.0679200\pi$
$522$	−12.8730	−	21.0839i	−0.563438	−	0.922818i
$523$			5.64342i			0.246770i	0.992359	+	0.123385i	$0.0393750\pi$
$523$			5.64342i			0.246770i	−0.992359	+	0.123385i	$0.960625\pi$
$524$	−5.35903	−	9.54698i	−0.234110	−	0.417062i
$525$	−16.7086	+	17.7602i	−0.729221	+	0.775121i
$526$	0.143494	−	0.0816932i	0.00625664	−	0.00356199i
$527$	−46.2198	+	16.8226i	−2.01337	+	0.732806i
$528$	22.5078	−	12.7293i	0.979526	−	0.553973i
$529$	−3.87165	−	21.9572i	−0.168332	−	0.954661i
$530$	12.5923	+	15.1926i	0.546973	+	0.659923i
$531$	−4.22198	−	3.32795i	−0.183218	−	0.144421i
$532$	−5.27916	+	5.31205i	−0.228881	+	0.230306i
$533$	−12.9052	+	35.4567i	−0.558985	+	1.53580i
$534$	−4.86741	−	12.9977i	−0.210633	−	0.562465i
$535$	−12.3148	−	33.8348i	−0.532417	−	1.46280i
$536$	37.6016	−	12.9182i	1.62414	−	0.557980i
$537$	0.208704	+	13.6399i	0.00900624	+	0.588605i
$538$	16.7135	+	14.1975i	0.720572	+	0.612097i
$539$	9.67779	+	24.2674i	0.416852	+	1.04527i
$540$	−15.7067	+	29.4615i	−0.675909	+	1.26782i
$541$	15.2984	+	26.4976i	0.657730	+	1.13922i	0.981202	+	0.192984i	$0.0618166\pi$
$541$	15.2984	+	26.4976i	0.657730	+	1.13922i	−0.323472	+	0.946238i	$0.604850\pi$
$542$	−27.7025	+	9.89355i	−1.18992	+	0.424964i
$543$	0.534293	+	34.9188i	0.0229287	+	1.49851i
$544$	−31.1517	−	12.4174i	−1.33562	−	0.532390i
$545$	13.7479	−	16.3841i	0.588895	−	0.701818i
$546$	−22.0718	−	21.0179i	−0.944587	−	0.899484i
$547$	5.82814	−	16.0127i	0.249193	−	0.684652i	−0.750523	−	0.660844i	$-0.770199\pi$
$547$	5.82814	−	16.0127i	0.249193	−	0.684652i	0.999717	−	0.0238086i	$-0.00757923\pi$
$548$	6.59234	−	7.66617i	0.281611	−	0.327482i
$549$	−30.5855	+	27.3017i	−1.30536	+	1.16521i
$550$	−9.76550	+	26.3338i	−0.416402	+	1.12288i
$551$	7.74383	+	2.81852i	0.329898	+	0.120073i
$552$	0.725328	−	4.04618i	0.0308720	−	0.172217i
$553$	3.13780	−	3.23469i	0.133433	−	0.137553i
$554$	24.8343	−	14.1385i	1.05511	−	0.600688i
$555$	−40.1439	−	32.6513i	−1.70401	−	1.38597i
$556$	−0.00557857	+	0.461140i	−0.000236584	+	0.0195567i
$557$	−27.7137	+	16.0005i	−1.17427	+	0.677964i	−0.954681	−	0.297629i	$-0.903804\pi$
$557$	−27.7137	+	16.0005i	−1.17427	+	0.677964i	−0.219586	+	0.975593i	$0.570471\pi$
$558$	6.96170	+	34.5054i	0.294712	+	1.46073i
$559$	26.7124	−	15.4224i	1.12981	−	0.652298i
$560$	−24.2565	+	23.8241i	−1.02502	+	1.00675i
$561$	−7.23139	−	37.6348i	−0.305310	−	1.58894i
$562$	−17.6610	−	31.0216i	−0.744986	−	1.30857i
$563$	5.03737	−	28.5684i	0.212300	−	1.20401i	−0.673231	−	0.739432i	$-0.735094\pi$
$563$	5.03737	−	28.5684i	0.212300	−	1.20401i	0.885531	−	0.464581i	$-0.153795\pi$
$564$	−3.32619	+	3.98988i	−0.140058	+	0.168004i
$565$	30.2256	−	25.3623i	1.27160	−	1.06700i
$566$	−35.5803	+	29.4905i	−1.49555	+	1.23958i
$567$	−22.2859	−	8.38674i	−0.935921	−	0.352210i
$568$	8.17557	−	4.52440i	0.343039	−	0.189840i
$569$	−9.18826	−	10.9501i	−0.385192	−	0.459054i	0.538254	−	0.842783i	$-0.319084\pi$
$569$	−9.18826	−	10.9501i	−0.385192	−	0.459054i	−0.923446	+	0.383729i	$0.874640\pi$
$570$	−2.03542	−	10.9501i	−0.0852543	−	0.458648i
$571$	−27.7272	−	4.88906i	−1.16035	−	0.204601i	−0.439860	−	0.898067i	$-0.644972\pi$
$571$	−27.7272	−	4.88906i	−1.16035	−	0.204601i	−0.720490	+	0.693466i	$0.756083\pi$
$572$	−32.8402	−	12.4048i	−1.37312	−	0.518669i
$573$	−8.03666	+	1.54422i	−0.335736	+	0.0645105i
$574$	−7.50403	+	29.0671i	−0.313212	+	1.21324i
$575$	2.23245	+	3.86672i	0.0930996	+	0.161253i
$576$	−12.1181	+	20.7160i	−0.504920	+	0.863166i
$577$	8.77887	+	15.2055i	0.365469	+	0.633011i	0.988851	−	0.148906i	$-0.0475752\pi$
$577$	8.77887	+	15.2055i	0.365469	+	0.633011i	−0.623382	+	0.781917i	$0.714242\pi$
$578$	−16.6125	+	19.5565i	−0.690987	+	0.813443i
$579$	−1.45990	+	1.79491i	−0.0606714	+	0.0745939i
$580$	34.9983	+	13.2200i	1.45323	+	0.548929i
$581$	−5.56971	+	1.58353i	−0.231070	+	0.0656958i
$582$	−18.5402	+	0.171528i	−0.768516	+	0.00711007i
$583$	−5.54414	+	15.2324i	−0.229615	+	0.630861i
$584$	26.0547	+	15.6798i	1.07815	+	0.648835i
$585$	44.3759	−	9.23280i	1.83472	−	0.381729i
$586$	−4.00200	−	23.5277i	−0.165321	−	0.971922i
$587$	6.94506	+	2.52779i	0.286653	+	0.104333i	0.481345	−	0.876531i	$-0.340148\pi$
$587$	6.94506	+	2.52779i	0.286653	+	0.104333i	−0.194692	+	0.980864i	$0.562371\pi$
$588$	−19.0888	−	14.9538i	−0.787210	−	0.616685i
$589$	−8.99545	−	7.54808i	−0.370651	−	0.311013i
$590$	8.14143	+	0.0492430i	0.335178	+	0.00202730i
$591$	−35.7267	+	0.546655i	−1.46960	+	0.0224864i
$592$	−27.9081	−	24.5923i	−1.14701	−	1.01074i
$593$	40.3128	−	23.2746i	1.65545	−	0.955773i	0.680671	−	0.732590i	$-0.261689\pi$
$593$	40.3128	−	23.2746i	1.65545	−	0.955773i	0.974777	−	0.223183i	$-0.0716448\pi$
$594$	−27.4048	+	1.09269i	−1.12443	+	0.0448335i
$595$	21.9873	+	45.3394i	0.901391	+	1.85873i
$596$	−0.182661	+	15.0993i	−0.00748209	+	0.618491i
$597$	−14.9853	+	0.229289i	−0.613306	+	0.00938419i
$598$	−4.84980	+	2.76106i	−0.198323	+	0.112908i
$599$	−28.0300	+	10.2021i	−1.14527	+	0.416846i	−0.843816	−	0.536633i	$-0.819696\pi$
$599$	−28.0300	+	10.2021i	−1.14527	+	0.416846i	−0.301459	+	0.953479i	$0.597474\pi$
$600$	−4.45361	−	25.6848i	−0.181818	−	1.04858i
$601$	15.8974	+	5.78620i	0.648470	+	0.236024i	0.645251	−	0.763971i	$-0.276753\pi$
$601$	15.8974	+	5.78620i	0.648470	+	0.236024i	0.00321967	+	0.999995i	$0.498975\pi$
$602$	19.9726	−	14.2592i	0.814024	−	0.581162i
$603$	−41.7345	−	6.04881i	−1.69956	−	0.246327i
$604$	−17.7615	−	3.35385i	−0.722704	−	0.136466i
$605$	−9.26983	+	1.63452i	−0.376872	+	0.0664527i
$606$	0.0670492	+	7.24724i	0.00272369	+	0.294399i
$607$	−10.1926	−	28.0039i	−0.413704	−	1.13664i	−0.955206	−	0.295942i	$-0.904366\pi$
$607$	−10.1926	−	28.0039i	−0.413704	−	1.13664i	0.541502	−	0.840699i	$-0.317856\pi$
$608$	−1.15122	−	7.92304i	−0.0466883	−	0.321322i
$609$	−6.11671	+	25.9719i	−0.247862	+	1.05243i
$610$	11.1515	−	61.0805i	0.451510	−	2.47308i
$611$	7.05206			0.285296
$612$	23.3639	+	26.8202i	0.944430	+	1.08414i
$613$	6.60842			0.266912			0.133456	−	0.991055i	$-0.457393\pi$
$613$	6.60842			0.266912			0.133456	+	0.991055i	$0.457393\pi$
$614$	8.48593	+	7.20845i	0.342464	+	0.290909i
$615$	−29.2171	−	33.7570i	−1.17815	−	1.36121i
$616$	−26.9568	−	7.30814i	−1.08612	−	0.294454i
$617$	1.55823	+	4.28120i	0.0627319	+	0.172354i	0.967099	−	0.254402i	$-0.0818785\pi$
$617$	1.55823	+	4.28120i	0.0627319	+	0.172354i	−0.904367	+	0.426756i	$0.859656\pi$
$618$	21.9331	+	25.6531i	0.882278	+	1.03192i
$619$	−4.71146	+	12.9446i	−0.189369	+	0.520288i	−0.997651	−	0.0685086i	$-0.978176\pi$
$619$	−4.71146	+	12.9446i	−0.189369	+	0.520288i	0.808281	+	0.588797i	$0.200398\pi$
$620$	−40.4203	−	34.7585i	−1.62332	−	1.39594i
$621$	−2.64638	+	3.46506i	−0.106195	+	0.139048i
$622$	−17.9344	−	21.6378i	−0.719103	−	0.867597i
$623$	−6.12829	+	13.6814i	−0.245525	+	0.548134i
$624$	32.1366	−	5.37230i	1.28649	−	0.215064i
$625$	−17.8421	−	14.9713i	−0.713685	−	0.598853i
$626$	−13.1769	−	7.71434i	−0.526656	−	0.308327i
$627$	6.91799	−	5.98761i	0.276278	−	0.239122i
$628$	−5.28446	−	0.0639279i	−0.210873	−	0.00255100i
$629$	−47.7430	+	27.5645i	−1.90364	+	1.09907i
$630$	34.4347	−	10.7105i	1.37191	−	0.426717i
$631$	1.18298	+	0.682993i	0.0470936	+	0.0271895i	0.523362	−	0.852110i	$-0.324678\pi$
$631$	1.18298	+	0.682993i	0.0470936	+	0.0271895i	−0.476268	+	0.879300i	$0.658011\pi$
$632$	0.750363	+	4.75891i	0.0298478	+	0.189299i
$633$	28.3456	−	10.8109i	1.12664	−	0.429694i
$634$	22.7329	+	0.137499i	0.902840	+	0.00546078i
$635$	48.2651	−	17.5671i	1.91534	−	0.697128i
$636$	−2.66002	−	14.8082i	−0.105477	−	0.587183i
$637$	1.00075	+	32.9050i	0.0396510	+	1.30374i
$638$	5.15358	+	30.2979i	0.204032	+	1.19950i
$639$	−9.90616	+	0.303219i	−0.391882	+	0.0119952i
$640$	−4.79089	−	36.0299i	−0.189376	−	1.42421i
$641$	0.0725512	+	0.0864632i	0.00286560	+	0.00341509i	0.767475	−	0.641078i	$-0.221513\pi$
$641$	0.0725512	+	0.0864632i	0.00286560	+	0.00341509i	−0.764610	+	0.644494i	$0.777068\pi$
$642$	−4.51684	+	27.0789i	−0.178265	+	1.06872i
$643$	−11.3006	+	13.4675i	−0.445651	+	0.531107i	−0.941370	−	0.337377i	$-0.890460\pi$
$643$	−11.3006	+	13.4675i	−0.445651	+	0.531107i	0.495718	+	0.868483i	$0.334905\pi$
$644$	−3.62915	+	2.55799i	−0.143008	+	0.100799i
$645$	0.558355	+	36.4914i	0.0219852	+	1.43685i
$646$	−11.6728	−	2.13111i	−0.459261	−	0.0838474i
$647$	−13.1395	+	22.7582i	−0.516565	+	0.894718i	0.483250	+	0.875483i	$0.339456\pi$
$647$	−13.1395	+	22.7582i	−0.516565	+	0.894718i	−0.999815	+	0.0192350i	$0.993877\pi$
$648$	21.4772	−	13.6650i	0.843702	−	0.536811i
$649$	3.34406	+	5.79209i	0.131266	+	0.227359i
$650$	−22.9119	+	26.9724i	−0.898680	+	1.05794i
$651$	20.8480	−	31.7957i	0.817099	−	1.24617i
$652$	40.4111	−	6.62257i	1.58262	−	0.259360i
$653$	−22.7418	−	4.00999i	−0.889955	−	0.156923i	−0.290066	−	0.957007i	$-0.593677\pi$
$653$	−22.7418	−	4.00999i	−0.889955	−	0.156923i	−0.599889	+	0.800084i	$0.704788\pi$
$654$	−15.2716	+	5.71894i	−0.597165	+	0.223628i
$655$	−11.3044	−	13.4720i	−0.441698	−	0.526395i
$656$	−20.0281	−	25.0764i	−0.781967	−	0.979068i
$657$	−16.9738	−	27.4260i	−0.662212	−	1.06999i
$658$	5.58462	−	0.540144i	0.217711	−	0.0210570i
$659$	8.22719	−	6.90343i	0.320486	−	0.268920i	−0.468324	−	0.883557i	$-0.655142\pi$
$659$	8.22719	−	6.90343i	0.320486	−	0.268920i	0.788810	+	0.614637i	$0.210698\pi$
$660$	31.7330	−	26.8008i	1.23521	−	1.04322i
$661$	35.3720	+	29.6806i	1.37581	+	1.15444i	0.970733	+	0.240162i	$0.0772004\pi$
$661$	35.3720	+	29.6806i	1.37581	+	1.15444i	0.405079	+	0.914282i	$0.367244\pi$
$662$	−11.0547	−	0.0668638i	−0.429654	−	0.00259874i
$663$	7.65683	−	47.6785i	0.297366	−	1.85168i
$664$	2.22238	−	5.77755i	0.0862452	−	0.224213i
$665$	−6.74953	+	9.95816i	−0.261736	+	0.386161i
$666$	14.4000	+	36.7320i	0.557990	+	1.42333i
$667$	4.23112	+	2.44284i	0.163830	+	0.0945871i
$668$	−5.92602	−	10.5571i	−0.229285	−	0.408465i
$669$	6.51129	−	5.63561i	0.251741	−	0.217885i
$670$	55.5013	−	31.5976i	2.14420	−	1.22072i
$671$	47.9296	−	17.4450i	1.85030	−	0.673455i
$672$	25.0379	−	6.71586i	0.965859	−	0.259070i
$673$	−0.595850	−	3.37923i	−0.0229683	−	0.130260i	0.971168	−	0.238398i	$-0.0766222\pi$
$673$	−0.595850	−	3.37923i	−0.0229683	−	0.130260i	−0.994136	+	0.108138i	$0.965511\pi$
$674$	6.52354	−	17.5915i	0.251278	−	0.677599i
$675$	−8.25455	+	26.3885i	−0.317718	+	1.01569i
$676$	−13.8254	−	11.8888i	−0.531747	−	0.457263i
$677$	16.5690	+	19.7462i	0.636799	+	0.758908i	0.983861	−	0.178934i	$-0.0572650\pi$
$677$	16.5690	+	19.7462i	0.636799	+	0.758908i	−0.347062	+	0.937842i	$0.612821\pi$
$678$	−29.5772	+	5.49786i	−1.13590	+	0.211144i
$679$	14.3746	+	13.9440i	0.551645	+	0.535122i
$680$	−52.8718	−	10.3152i	−2.02754	−	0.395570i
$681$	6.30086	−	18.1718i	0.241450	−	0.696345i
$682$	7.86529	−	43.0809i	0.301177	−	1.64965i
$683$	−25.6289			−0.980663			−0.490332	−	0.871536i	$-0.663124\pi$
$683$	−25.6289			−0.980663			−0.490332	+	0.871536i	$0.663124\pi$
$684$	−2.75626	+	8.03214i	−0.105388	+	0.307117i
$685$	8.12065	−	14.0654i	0.310274	−	0.537410i
$686$	3.31282	+	25.9812i	0.126484	+	0.991969i
$687$	14.9681	+	2.40377i	0.571068	+	0.0917094i
$688$	−0.634649	+	26.2271i	−0.0241958	+	0.999899i
$689$	−13.1292	+	15.6468i	−0.500184	+	0.596096i
$690$	−0.0610871	−	6.60281i	−0.00232555	−	0.251365i
$691$	−8.67576	+	23.8365i	−0.330042	+	0.906782i	0.658058	+	0.752967i	$0.271378\pi$
$691$	−8.67576	+	23.8365i	−0.330042	+	0.906782i	−0.988100	+	0.153815i	$0.950844\pi$
$692$	5.41875	−	6.30141i	0.205990	−	0.239544i
$693$	21.8845	+	19.9663i	0.831323	+	0.758458i
$694$	−14.8602	+	40.0722i	−0.564085	+	1.52112i
$695$	0.128638	+	0.729542i	0.00487951	+	0.0276731i
$696$	−18.2731	−	21.9033i	−0.692641	−	0.830243i
$697$	−44.6953	+	16.2677i	−1.69295	+	0.616185i
$698$	−0.0424547	+	7.01911i	−0.00160693	+	0.265677i
$699$	5.98576	−	10.7440i	0.226402	−	0.406374i
$700$	−16.0784	+	23.1147i	−0.607705	+	0.873654i
$701$		−	4.49026i		−	0.169595i	−0.996398	−	0.0847973i	$-0.972976\pi$
$701$		−	4.49026i		−	0.169595i	0.996398	−	0.0847973i	$-0.0270243\pi$
$702$	−32.9200	−	10.5167i	−1.24248	−	0.396926i
$703$	−11.3982	−	6.58075i	−0.429891	−	0.248198i
$704$	23.5540	−	18.3500i	0.887726	−	0.691592i
$705$	−4.06097	+	7.28912i	−0.152945	+	0.274524i
$706$	0.310819	−	0.530912i	0.0116978	−	0.0199811i
$707$	5.45062	−	5.61892i	0.204992	−	0.211321i
$708$	−5.38582	−	3.08654i	−0.202411	−	0.115999i
$709$	−1.51619	−	8.59872i	−0.0569416	−	0.322932i	0.943010	−	0.332764i	$-0.107981\pi$
$709$	−1.51619	−	8.59872i	−0.0569416	−	0.322932i	−0.999952	+	0.00983238i	$0.996870\pi$
$710$	11.5561	−	9.57819i	0.433692	−	0.359463i
$711$	1.59998	−	4.85300i	0.0600038	−	0.182002i
$712$	−7.76000	−	14.0223i	−0.290818	−	0.525507i
$713$	−4.47498	−	5.33307i	−0.167589	−	0.199725i
$714$	2.41166	−	38.3438i	0.0902542	−	1.43498i
$715$	−55.5333	−	9.79202i	−2.07683	−	0.366201i
$716$	2.54743	+	15.5445i	0.0952021	+	0.580925i
$717$	−33.4142	−	5.36609i	−1.24788	−	0.200400i
$718$	0.527746	−	0.621273i	0.0196953	−	0.0231857i
$719$	16.4168			0.612242			0.306121	−	0.951993i	$-0.400969\pi$
$719$	16.4168			0.612242			0.306121	+	0.951993i	$0.400969\pi$
$720$	−12.9532	+	36.3106i	−0.482736	+	1.35322i
$721$	2.62487	−	36.3608i	0.0977552	−	1.35415i
$722$	8.08445	+	22.6369i	0.300872	+	0.842458i
$723$	29.9523	+	34.6064i	1.11394	+	1.28703i
$724$	6.52155	+	39.7947i	0.242372	+	1.47896i
$725$	30.5121	+	5.38010i	1.13319	+	0.199812i
$726$	6.76643	+	2.39212i	0.251126	+	0.0887800i
$727$	7.61331	−	1.34243i	0.282362	−	0.0497880i	−0.0306736	−	0.999529i	$-0.509765\pi$
$727$	7.61331	−	1.34243i	0.282362	−	0.0497880i	0.313035	+	0.949741i	$0.398654\pi$
$728$	−28.7690	−	20.2707i	−1.06625	−	0.751283i
$729$	−26.8863	+	2.47509i	−0.995789	+	0.0916699i
$730$	45.7990	+	16.9839i	1.69510	+	0.628602i
$731$	36.5368	+	13.2983i	1.35136	+	0.491856i
$732$	−30.3137	+	36.3623i	−1.12043	+	1.34399i
$733$	−11.4282	−	9.58944i	−0.422112	−	0.354194i	0.406854	−	0.913493i	$-0.366626\pi$
$733$	−11.4282	−	9.58944i	−0.422112	−	0.354194i	−0.828966	+	0.559299i	$0.811070\pi$
$734$	20.3358	+	0.123000i	0.750609	+	0.00454002i
$735$	−34.5874	−	17.9141i	−1.27578	−	0.660773i
$736$	0.143524	−	4.74444i	0.00529037	−	0.174882i
$737$	45.4352	+	26.2320i	1.67363	+	0.966270i
$738$	6.73207	+	33.3673i	0.247811	+	1.22827i
$739$	40.7732	−	23.5404i	1.49987	−	0.865949i	0.499868	−	0.866102i	$-0.333382\pi$
$739$	40.7732	−	23.5404i	1.49987	−	0.865949i	1.00000		0.000152790i	$4.86347e-5\pi$
$740$	−51.3807	−	30.4993i	−1.88879	−	1.12118i
$741$	10.7718	−	4.10831i	0.395712	−	0.150923i
$742$	−9.19877	+	13.3965i	−0.337698	+	0.491803i
$743$	−0.384292	+	2.17943i	−0.0140983	+	0.0799556i	−0.991045	−	0.133527i	$-0.957370\pi$
$743$	−0.384292	+	2.17943i	−0.0140983	+	0.0799556i	0.976947	+	0.213483i	$0.0684807\pi$
$744$	13.7931	+	38.2344i	0.505680	+	1.40174i
$745$	4.21204	+	23.8876i	0.154317	+	0.875176i
$746$	9.42762	−	25.4227i	0.345170	−	0.930790i
$747$	−4.89818	+	4.37228i	−0.179215	+	0.159974i
$748$	−14.6309	−	41.7632i	−0.534959	−	1.52701i
$749$	24.0286	−	17.3753i	0.877987	−	0.634880i
$750$	−0.886239	−	2.36657i	−0.0323609	−	0.0864148i
$751$	33.2962	+	5.87102i	1.21500	+	0.214237i	0.744171	−	0.667989i	$-0.232845\pi$
$751$	33.2962	+	5.87102i	1.21500	+	0.214237i	0.470826	+	0.882226i	$0.343956\pi$
$752$	−3.12382	+	5.12041i	−0.113914	+	0.186722i
$753$	0.169220	+	11.0594i	0.00616674	+	0.403029i
$754$	−6.95513	+	38.0957i	−0.253291	+	1.38736i
$755$	−29.0349			−1.05669
$756$	−26.8753	−	5.80683i	−0.977444	−	0.211192i
$757$	−10.7622			−0.391158			−0.195579	−	0.980688i	$-0.562659\pi$
$757$	−10.7622			−0.391158			−0.195579	+	0.980688i	$0.562659\pi$
$758$	5.09316	−	27.8970i	0.184992	−	1.01326i
$759$	4.65553	−	2.78370i	0.168985	−	0.101042i
$760$	−4.17860	−	12.1629i	−0.151574	−	0.441193i
$761$	−34.6695	−	6.11316i	−1.25677	−	0.221602i	−0.494679	−	0.869076i	$-0.664714\pi$
$761$	−34.6695	−	6.11316i	−1.25677	−	0.221602i	−0.762088	+	0.647474i	$0.775826\pi$
$762$	−38.6278	−	6.44325i	−1.39934	−	0.233414i
$763$	16.0749	+	7.20041i	0.581950	+	0.260672i
$764$	−8.91825	+	3.12433i	−0.322651	+	0.113034i
$765$	44.8721	+	35.3702i	1.62235	+	1.27881i
$766$	−17.3803	+	46.8680i	−0.627976	+	1.69341i
$767$	1.46341	+	8.29938i	0.0528405	+	0.299673i
$768$	−10.3346	+	25.7137i	−0.372919	+	0.927864i
$769$	4.35219	−	24.6825i	0.156944	−	0.890073i	−0.800043	−	0.599943i	$-0.795190\pi$
$769$	4.35219	−	24.6825i	0.156944	−	0.890073i	0.956987	−	0.290131i	$-0.0936988\pi$
$770$	−44.7276	−	3.50093i	−1.61187	−	0.126165i
$771$	2.08325	−	12.9722i	0.0750263	−	0.467184i
$772$	−1.36368	+	2.29733i	−0.0490799	+	0.0826827i
$773$	30.2653	−	17.4737i	1.08857	−	0.628485i	0.155373	−	0.987856i	$-0.450342\pi$
$773$	30.2653	−	17.4737i	1.08857	−	0.628485i	0.933195	+	0.359371i	$0.117009\pi$
$774$	13.3173	−	24.4325i	0.478681	−	0.878207i
$775$	−38.2340	−	22.0744i	−1.37341	−	0.792936i
$776$	−21.1480	+	3.33452i	−0.759170	+	0.119702i
$777$	16.8236	−	39.1535i	0.603543	−	1.40462i
$778$	−4.84226	−	0.0292881i	−0.173604	−	0.00105003i
$779$	−8.69873	−	7.29910i	−0.311664	−	0.261517i
$780$	49.1242	−	18.0581i	1.75893	−	0.646585i
$781$	11.5864	+	4.21710i	0.414593	+	0.150900i
$782$	−6.59586	−	2.44598i	−0.235867	−	0.0874679i
$783$	6.61532	+	29.5230i	0.236412	+	1.05507i
$784$	−24.3352	−	13.8491i	−0.869114	−	0.494612i
$785$	−8.36022	+	1.47413i	−0.298389	+	0.0526140i
$786$	2.45048	+	13.1830i	0.0874057	+	0.470222i
$787$	6.87055	+	1.21146i	0.244909	+	0.0431840i	0.294755	−	0.955573i	$-0.404762\pi$
$787$	6.87055	+	1.21146i	0.244909	+	0.0431840i	−0.0498462	+	0.998757i	$0.515873\pi$
$788$	−40.7154	+	6.67244i	−1.45043	+	0.237696i
$789$	−0.198596	+	0.0381595i	−0.00707020	+	0.00135851i
$790$	2.60279	+	7.28797i	0.0926033	+	0.259294i
$791$	26.8979	+	18.2311i	0.956381	+	0.648225i
$792$	−31.1174	+	5.88734i	−1.10571	+	0.209198i
$793$	64.2699			2.28229
$794$	20.9727	−	24.6894i	0.744292	−	0.876195i
$795$	−8.61225	−	22.5809i	−0.305445	−	0.800862i
$796$	−17.0777	+	2.79870i	−0.605304	+	0.0991972i
$797$	19.3329	+	3.40890i	0.684805	+	0.120750i	0.505217	−	0.862992i	$-0.331412\pi$
$797$	19.3329	+	3.40890i	0.684805	+	0.120750i	0.179588	+	0.983742i	$0.442524\pi$
$798$	8.21566	−	4.07848i	0.290831	−	0.144377i
$799$	5.71408	+	6.80978i	0.202150	+	0.240913i
$800$	−9.43511	−	28.5839i	−0.333582	−	1.01059i
$801$	0.520064	+	16.9905i	0.0183756	+	0.600329i
$802$	4.44127	−	3.68112i	0.156827	−	0.129985i
$803$	6.96789	+	39.5169i	0.245892	+	1.39452i
$804$	−48.6941	+	0.155970i	−1.71731	+	0.00550065i
$805$	−4.96595	+	5.11928i	−0.175027	+	0.180431i
$806$	27.8793	−	47.6209i	0.982008	−	1.67738i
$807$	−13.7834	−	23.0518i	−0.485199	−	0.811460i
$808$	1.30344	+	8.26662i	0.0458550	+	0.290819i
$809$	5.53347	+	3.19475i	0.194547	+	0.112322i	0.594109	−	0.804384i	$-0.297505\pi$
$809$	5.53347	+	3.19475i	0.194547	+	0.112322i	−0.399563	+	0.916706i	$0.630838\pi$
$810$	29.8274	−	27.9705i	1.04803	−	0.982784i
$811$			34.8460i			1.22361i	0.791009	+	0.611804i	$0.209556\pi$
$811$			34.8460i			1.22361i	−0.791009	+	0.611804i	$0.790444\pi$
$812$	−2.58997	+	30.7012i	−0.0908902	+	1.07740i
$813$	36.0231	−	0.551189i	1.26338	−	0.0193310i
$814$	0.296877	−	49.0833i	0.0104055	−	1.72037i
$815$	61.8122	−	22.4978i	2.16519	−	0.788064i
$816$	31.2271	+	26.6795i	1.09317	+	0.933969i
$817$	1.61191	+	9.14161i	0.0563937	+	0.319824i
$818$	−1.10541	+	2.98087i	−0.0386498	+	0.104224i
$819$	17.3079	+	33.0729i	0.604787	+	1.15566i
$820$	−39.0871	−	33.6120i	−1.36498	−	1.17378i
$821$	−2.61497	+	7.18457i	−0.0912630	+	0.250743i	−0.976923	−	0.213591i	$-0.931484\pi$
$821$	−2.61497	+	7.18457i	−0.0912630	+	0.250743i	0.885660	+	0.464334i	$0.153706\pi$
$822$	−10.6664	+	6.29054i	−0.372034	+	0.219408i
$823$	4.96948	−	5.92240i	0.173225	−	0.206442i	−0.672446	−	0.740146i	$-0.734756\pi$
$823$	4.96948	−	5.92240i	0.173225	−	0.206442i	0.845671	+	0.533705i	$0.179201\pi$
$824$	29.3952	+	25.5886i	1.02403	+	0.891421i
$825$	21.7052	−	26.6859i	0.755677	−	0.929085i
$826$	1.79457	+	6.46031i	0.0624412	+	0.224783i
$827$	19.7895	−	34.2765i	0.688149	−	1.19191i	−0.284287	−	0.958739i	$-0.591757\pi$
$827$	19.7895	−	34.2765i	0.688149	−	1.19191i	0.972436	−	0.233170i	$-0.0749099\pi$
$828$	−2.43617	+	4.40586i	−0.0846627	+	0.153114i
$829$	−24.9344			−0.866008			−0.433004	−	0.901392i	$-0.642546\pi$
$829$	−24.9344			−0.866008			−0.433004	+	0.901392i	$0.642546\pi$
$830$	1.78588	−	9.78186i	0.0619886	−	0.339533i
$831$	−34.3707	+	6.60421i	−1.19231	+	0.229098i
$832$	35.7977	−	11.5766i	1.24106	−	0.401348i
$833$	−30.9636	+	27.6283i	−1.07283	+	0.957265i
$834$	0.188262	−	0.532522i	0.00651897	−	0.0184397i
$835$	−12.5004	−	14.8974i	−0.432593	−	0.515544i
$836$	6.88827	−	8.01031i	0.238236	−	0.277042i
$837$	5.53035	−	42.7557i	0.191157	−	1.47785i
$838$	−6.26625	+	16.8977i	−0.216464	+	0.583720i
$839$	1.23644	+	7.01218i	0.0426865	+	0.242087i	0.998684	−	0.0512879i	$-0.0163326\pi$
$839$	1.23644	+	7.01218i	0.0426865	+	0.242087i	−0.955997	+	0.293375i	$0.905221\pi$
$840$	37.5190	−	18.0631i	1.29453	−	0.623236i
$841$	4.60692	−	1.67678i	0.158859	−	0.0578201i
$842$	20.7267	−	11.8000i	0.714288	−	0.406654i
$843$	8.24960	+	42.9339i	0.284131	+	1.47872i
$844$	30.5469	−	17.1470i	1.05147	−	0.590223i
$845$	−25.3659	−	14.6450i	−0.872615	−	0.503805i
$846$	5.42983	−	3.31525i	0.186681	−	0.113981i
$847$	−3.38250	−	6.97496i	−0.116224	−	0.239662i
$848$	−5.54516	−	16.4640i	−0.190422	−	0.565375i
$849$	52.8835	−	20.1695i	1.81496	−	0.692216i
$850$	−44.6106	−	0.269825i	−1.53013	−	0.00925491i
$851$	−5.97743	−	5.01566i	−0.204904	−	0.171934i
$852$	−11.2637	+	2.02332i	−0.385889	+	0.0693178i
$853$	−14.8461	+	12.4573i	−0.508320	+	0.426531i	−0.860538	−	0.509387i	$-0.829872\pi$
$853$	−14.8461	+	12.4573i	−0.508320	+	0.426531i	0.352218	+	0.935918i	$0.385428\pi$
$854$	50.8963	−	4.92268i	1.74163	−	0.168451i
$855$	−1.95659	+	13.4997i	−0.0669139	+	0.461680i
$856$	−0.575168	+	31.6948i	−0.0196588	+	1.08330i
$857$	22.0427	+	26.2694i	0.752963	+	0.897347i	0.997381	−	0.0723232i	$-0.0230413\pi$
$857$	22.0427	+	26.2694i	0.752963	+	0.897347i	−0.244418	+	0.969670i	$0.578597\pi$
$858$	33.1901	+	27.3305i	1.13309	+	0.933049i
$859$	−9.44905	−	1.66612i	−0.322397	−	0.0568473i	0.0101075	−	0.999949i	$-0.496783\pi$
$859$	−9.44905	−	1.66612i	−0.322397	−	0.0568473i	−0.332505	+	0.943102i	$0.607894\pi$
$860$	6.81526	+	41.5869i	0.232398	+	1.41810i
$861$	20.1604	−	30.7469i	0.687063	−	1.04785i
$862$	9.98156	−	11.7505i	0.339973	−	0.400223i
$863$	−15.5598	−	26.9504i	−0.529662	−	0.917401i	−0.999401	−	0.0345958i	$-0.988986\pi$
$863$	−15.5598	−	26.9504i	−0.529662	−	0.917401i	0.469740	−	0.882805i	$-0.344348\pi$
$864$	22.2184	−	19.2443i	0.755886	−	0.654703i
$865$	6.67498	−	11.5614i	0.226956	−	0.393100i
$866$	24.5020	+	4.47333i	0.832611	+	0.152010i
$867$	26.9729	−	16.1280i	0.916046	−	0.547735i
$868$	18.4306	−	39.8471i	0.625574	−	1.35250i
$869$	−4.08636	+	4.86994i	−0.138620	+	0.165201i
$870$	−35.3712	−	29.1266i	−1.19919	−	0.987484i
$871$	42.4932	+	50.6414i	1.43983	+	1.71592i
$872$	−16.4754	+	9.11757i	−0.557928	+	0.308760i
$873$	21.5662	+	7.11011i	0.729904	+	0.240641i
$874$	−0.281631	−	1.65571i	−0.00952630	−	0.0560051i
$875$	−1.11582	+	2.49105i	−0.0377214	+	0.0842130i
$876$	−24.0308	−	28.4532i	−0.811924	−	0.961343i
$877$	−26.3565	+	9.59297i	−0.889995	+	0.323932i	−0.746236	−	0.665681i	$-0.768141\pi$
$877$	−26.3565	+	9.59297i	−0.889995	+	0.323932i	−0.143758	+	0.989613i	$0.545919\pi$
$878$	−46.3667	−	0.280446i	−1.56480	−	0.00946460i
$879$	−4.63464	+	28.8596i	−0.156323	+	0.973410i
$880$	31.7092	−	35.9845i	1.06892	−	1.21304i
$881$	47.7389	+	27.5621i	1.60836	+	0.928589i	0.989736	+	0.142905i	$0.0456443\pi$
$881$	47.7389	+	27.5621i	1.60836	+	0.928589i	0.618627	+	0.785685i	$0.287689\pi$
$882$	16.2395	+	24.8652i	0.546814	+	0.837254i
$883$	−11.7267	+	6.77041i	−0.394635	+	0.227843i	−0.684166	−	0.729326i	$-0.739834\pi$
$883$	−11.7267	+	6.77041i	−0.394635	+	0.227843i	0.289532	+	0.957168i	$0.406500\pi$
$884$	0.674496	−	55.7558i	0.0226857	−	1.87527i
$885$	−9.42109	−	3.26665i	−0.316687	−	0.109807i
$886$	−14.6542	−	8.57923i	−0.492319	−	0.288225i
$887$	3.40286	+	2.85534i	0.114257	+	0.0958730i	0.698126	−	0.715975i	$-0.254017\pi$
$887$	3.40286	+	2.85534i	0.114257	+	0.0958730i	−0.583869	+	0.811848i	$0.698462\pi$
$888$	22.6663	+	39.5184i	0.760630	+	1.32615i
$889$	24.7858	+	34.2767i	0.831289	+	1.14960i
$890$	−16.4280	−	19.8203i	−0.550667	−	0.664379i
$891$	32.2083	+	9.53660i	1.07902	+	0.319488i
$892$	6.48333	−	7.53940i	0.217078	−	0.252438i
$893$	−0.725867	+	1.99430i	−0.0242902	+	0.0667368i
$894$	6.16432	−	17.4366i	0.206166	−	0.583166i
$895$	8.65400	+	23.7767i	0.289271	+	0.794766i
$896$	27.4620	−	11.9096i	0.917441	−	0.397872i
$897$	6.71213	−	1.28971i	0.224111	−	0.0430622i
$898$	−6.79981	−	5.77616i	−0.226913	−	0.192753i
$899$	−48.3094			−1.61121
$900$	−4.96135	+	31.5389i	−0.165378	+	1.05130i
$901$	−25.7475			−0.857774
$902$	7.60585	−	41.6599i	0.253247	−	1.38712i
$903$	−28.7809	+	8.66075i	−0.957767	+	0.288212i
$904$	−32.8530	+	11.2868i	−1.09268	+	0.375393i
$905$	22.1547	+	60.8694i	0.736446	+	2.02337i
$906$	19.2734	+	10.8910i	0.640315	+	0.361829i
$907$	−28.2572	+	4.98251i	−0.938266	+	0.165442i	−0.621812	−	0.783166i	$-0.713603\pi$
$907$	−28.2572	+	4.98251i	−0.938266	+	0.165442i	−0.316454	+	0.948608i	$0.602492\pi$
$908$	4.12076	−	21.8229i	0.136752	−	0.724219i
$909$	2.77929	−	8.43007i	0.0921833	−	0.279608i
$910$	−51.4516	−	23.4213i	−1.70560	−	0.776410i
$911$	36.6378	+	13.3351i	1.21386	+	0.441810i	0.868042	−	0.496490i	$-0.165378\pi$
$911$	36.6378	+	13.3351i	1.21386	+	0.441810i	0.345821	+	0.938300i	$0.387600\pi$
$912$	−1.78854	+	9.64110i	−0.0592244	+	0.319249i
$913$	7.67579	−	2.79376i	0.254031	−	0.0924599i
$914$	−21.1759	+	12.0557i	−0.700435	+	0.398767i
$915$	−37.0103	+	66.4305i	−1.22352	+	2.19612i
$916$	17.5038	+	0.211750i	0.578343	+	0.00699640i
$917$	8.12590	−	11.9888i	0.268341	−	0.395906i
$918$	−16.5187	−	40.3103i	−0.545200	−	1.33044i
$919$	−3.00168	+	1.73302i	−0.0990163	+	0.0571671i	−0.548690	−	0.836026i	$-0.684873\pi$
$919$	−3.00168	+	1.73302i	−0.0990163	+	0.0571671i	0.449674	+	0.893193i	$0.351540\pi$
$920$	−1.18754	−	7.53155i	−0.0391520	−	0.248308i
$921$	−6.99822	−	11.7040i	−0.230599	−	0.385661i
$922$	−57.6548	−	0.348722i	−1.89876	−	0.0114845i
$923$	11.9016	+	9.98663i	0.391746	+	0.328714i
$924$	28.3770	+	19.1013i	0.933535	+	0.628386i
$925$	−46.4988	−	16.9242i	−1.52887	−	0.556463i
$926$	−2.67877	−	15.7485i	−0.0880299	−	0.517527i
$927$	−15.3197	−	38.3929i	−0.503166	−	1.26099i
$928$	−24.5799	−	21.9251i	−0.806875	−	0.719727i
$929$	17.9787	−	49.3961i	0.589863	−	1.62063i	−0.180892	−	0.983503i	$-0.557898\pi$
$929$	17.9787	−	49.3961i	0.589863	−	1.62063i	0.770755	−	0.637132i	$-0.219879\pi$
$930$	33.1673	+	56.2394i	1.08760	+	1.84416i
$931$	−9.40844	−	3.10389i	−0.308349	−	0.101726i
$932$	5.01828	−	13.2853i	0.164379	−	0.435175i
$933$	12.2659	+	32.1606i	0.401567	+	1.05289i
$934$	−3.01807	+	3.55293i	−0.0987543	+	0.116255i
$935$	−35.5415	−	61.5596i	−1.16233	−	2.01322i
$936$	−39.3823	−	6.43951i	−1.28725	−	0.210482i
$937$	5.59448	+	9.68993i	0.182764	+	0.316556i	0.942821	−	0.333300i	$-0.108162\pi$
$937$	5.59448	+	9.68993i	0.182764	+	0.316556i	−0.760057	+	0.649857i	$0.774829\pi$
$938$	37.5298	+	36.8489i	1.22539	+	1.20316i
$939$	12.2383	+	14.1399i	0.399382	+	0.461439i
$940$	−3.40459	+	9.01328i	−0.111046	+	0.293981i
$941$	−54.2145	−	9.55949i	−1.76734	−	0.311630i	−0.807021	−	0.590522i	$-0.798922\pi$
$941$	−54.2145	−	9.55949i	−1.76734	−	0.311630i	−0.960322	+	0.278892i	$0.910033\pi$
$942$	6.10247	+	2.15739i	0.198829	+	0.0702917i
$943$	−4.32737	−	5.15716i	−0.140919	−	0.167940i
$944$	−6.67432	−	2.61378i	−0.217231	−	0.0850713i
$945$	−44.1515	−	1.15550i	−1.43625	−	0.0375883i
$946$	−26.6533	+	22.0915i	−0.866575	+	0.718256i
$947$	25.5206	−	21.4143i	0.829308	−	0.695872i	−0.125824	−	0.992053i	$-0.540157\pi$
$947$	25.5206	−	21.4143i	0.829308	−	0.695872i	0.955132	+	0.296180i	$0.0957129\pi$
$948$	1.00599	−	5.81407i	0.0326729	−	0.188832i
$949$	−8.77993	+	49.7935i	−0.285009	+	1.61636i
$950$	−5.26939	−	9.25569i	−0.170962	−	0.300294i
$951$	−26.3061	−	9.12132i	−0.853033	−	0.295779i
$952$	−3.73641	−	44.2054i	−0.121098	−	1.43271i
$953$	−2.98099	+	1.72108i	−0.0965638	+	0.0557512i	−0.547504	−	0.836803i	$-0.684422\pi$
$953$	−2.98099	+	1.72108i	−0.0965638	+	0.0557512i	0.450940	+	0.892554i	$0.351089\pi$
$954$	−2.75330	+	18.2197i	−0.0891412	+	0.589884i
$955$	−13.1456	+	7.58964i	−0.425383	+	0.245595i
$956$	−39.0750	−	0.472703i	−1.26377	−	0.0152883i
$957$	5.96826	−	37.1640i	0.192927	−	1.20134i
$958$	−18.1943	+	10.3583i	−0.587831	+	0.334660i
$959$	12.9708	+	3.26501i	0.418848	+	0.105433i
$960$	−8.64853	+	43.6676i	−0.279130	+	1.40937i
$961$	35.5564	+	12.9415i	1.14698	+	0.417467i
$962$	21.5047	−	57.9898i	0.693338	−	1.86967i
$963$	15.9127	−	29.6190i	0.512780	−	0.954459i
$964$	40.0707	+	34.4578i	1.29059	+	1.10981i
$965$	−1.46776	+	4.03263i	−0.0472487	+	0.129815i
$966$	5.21664	−	1.53545i	0.167843	−	0.0494022i
$967$	32.5972	−	38.8478i	1.04825	−	1.24926i	0.0806619	−	0.996742i	$-0.474297\pi$
$967$	32.5972	−	38.8478i	1.04825	−	1.24926i	0.967592	−	0.252519i	$-0.0812589\pi$
$968$	8.13373	+	1.58688i	0.261428	+	0.0510042i
$969$	12.6952	+	7.07287i	0.407830	+	0.227213i
$970$	−32.3869	+	11.5665i	−1.03988	+	0.371378i
$971$	4.59442	+	7.95777i	0.147442	+	0.255377i	0.930281	−	0.366847i	$-0.119563\pi$
$971$	4.59442	+	7.95777i	0.147442	+	0.255377i	−0.782839	+	0.622224i	$0.786229\pi$
$972$	−30.2912	+	7.37858i	−0.971591	+	0.236668i
$973$	−0.548933	+	0.266205i	−0.0175980	+	0.00853413i
$974$	9.62417	+	8.17534i	0.308378	+	0.261955i
$975$	37.2010	−	22.2437i	1.19139	−	0.712369i
$976$	−28.4694	+	46.6656i	−0.911282	+	1.49373i
$977$	6.79096	+	18.6580i	0.217262	+	0.596923i	0.999666	−	0.0258488i	$-0.00822883\pi$
$977$	6.79096	+	18.6580i	0.217262	+	0.596923i	−0.782404	+	0.622772i	$0.786007\pi$
$978$	−49.4700	−	8.25175i	−1.58187	−	0.263862i
$979$	7.23293	−	19.8723i	0.231165	−	0.635121i
$980$	−42.5392	−	14.6068i	−1.35886	−	0.466597i
$981$	19.9629	−	0.611047i	0.637366	−	0.0195092i
$982$	19.6475	+	23.7047i	0.626977	+	0.756447i
$983$	1.12593	+	6.38547i	0.0359116	+	0.203665i	0.997485	−	0.0708849i	$-0.0225823\pi$
$983$	1.12593	+	6.38547i	0.0359116	+	0.203665i	−0.961573	+	0.274550i	$0.911471\pi$
$984$	13.3381	+	36.9732i	0.425204	+	1.17866i
$985$	−62.2778	+	22.6673i	−1.98433	+	0.722239i
$986$	−42.4224	+	24.1517i	−1.35101	+	0.769146i
$987$	−6.68866	−	1.57526i	−0.212902	−	0.0501412i
$988$	11.6083	−	6.51612i	0.369310	−	0.207305i
$989$			5.50333i			0.174996i
$990$	−47.3620	+	18.5673i	−1.50526	+	0.590109i
$991$			56.6873i			1.80073i	0.435135	+	0.900365i	$0.356701\pi$
$991$			56.6873i			1.80073i	−0.435135	+	0.900365i	$0.643299\pi$
$992$	22.2274	+	41.3373i	0.705720	+	1.31246i
$993$	12.7923	+	4.43557i	0.405951	+	0.140759i
$994$	10.1900	+	6.99696i	0.323206	+	0.221930i
$995$	−26.1219	+	9.50758i	−0.828119	+	0.301411i
$996$	−4.85465	+	5.82332i	−0.153825	+	0.184519i
$997$	−32.2224	−	11.7280i	−1.02049	−	0.371429i	−0.223040	−	0.974809i	$-0.571598\pi$
$997$	−32.2224	−	11.7280i	−1.02049	−	0.371429i	−0.797454	+	0.603380i	$0.793820\pi$
$998$	−8.04326	−	47.2863i	−0.254605	−	1.49682i
$999$	−2.21711	−	48.2699i	−0.0701464	−	1.52719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ci.a.95.8	yes	840
4.3	odd	2	inner	756.2.ci.a.95.71	yes	840
7.2	even	3		756.2.bs.a.527.87	yes	840
27.2	odd	18		756.2.bs.a.515.23	✓	840
28.23	odd	6		756.2.bs.a.527.23	yes	840
108.83	even	18		756.2.bs.a.515.87	yes	840
189.2	odd	18	inner	756.2.ci.a.191.71	yes	840
756.191	even	18	inner	756.2.ci.a.191.8	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bs.a.515.23	✓	840	27.2	odd	18
756.2.bs.a.515.87	yes	840	108.83	even	18
756.2.bs.a.527.23	yes	840	28.23	odd	6
756.2.bs.a.527.87	yes	840	7.2	even	3
756.2.ci.a.95.8	yes	840	1.1	even	1	trivial
756.2.ci.a.95.71	yes	840	4.3	odd	2	inner
756.2.ci.a.191.8	yes	840	756.191	even	18	inner
756.2.ci.a.191.71	yes	840	189.2	odd	18	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39122 - 0.253995i) q^{2} +(1.51307 + 0.842975i) q^{3} +(1.87097 + 0.706724i) q^{4} +(3.16384 + 0.557871i) q^{5} +(-1.89090 - 1.55707i) q^{6} +(0.270632 + 2.63187i) q^{7} +(-2.42343 - 1.45842i) q^{8} +(1.57879 + 2.55097i) q^{9} +O(q^{10})\)	\(q+(-1.39122 - 0.253995i) q^{2} +(1.51307 + 0.842975i) q^{3} +(1.87097 + 0.706724i) q^{4} +(3.16384 + 0.557871i) q^{5} +(-1.89090 - 1.55707i) q^{6} +(0.270632 + 2.63187i) q^{7} +(-2.42343 - 1.45842i) q^{8} +(1.57879 + 2.55097i) q^{9} +(-4.25990 - 1.57972i) q^{10} +(-0.648104 - 3.67558i) q^{11} +(2.23517 + 2.64651i) q^{12} +(0.816647 - 4.63144i) q^{13} +(0.291975 - 3.73025i) q^{14} +(4.31686 + 3.51114i) q^{15} +(3.00108 + 2.64452i) q^{16} +(5.13403 - 2.96413i) q^{17} +(-1.54850 - 3.94995i) q^{18} +(1.22570 + 0.707658i) q^{19} +(5.52521 + 3.27973i) q^{20} +(-1.80912 + 4.21036i) q^{21} +(-0.0319246 + 5.27815i) q^{22} +(0.642780 + 0.539356i) q^{23} +(-2.43741 - 4.24959i) q^{24} +(5.00022 + 1.81993i) q^{25} +(-2.31249 + 6.23591i) q^{26} +(0.238416 + 5.19068i) q^{27} +(-1.35366 + 5.11543i) q^{28} +(5.73413 - 1.01108i) q^{29} +(-5.11388 - 5.98122i) q^{30} +(-8.17084 - 1.44074i) q^{31} +(-3.50346 - 4.44137i) q^{32} +(2.11779 - 6.10776i) q^{33} +(-7.89542 + 2.81974i) q^{34} +(-0.612009 + 8.47781i) q^{35} +(1.15103 + 5.88856i) q^{36} -9.29934 q^{37} +(-1.52547 - 1.29583i) q^{38} +(5.13983 - 6.31929i) q^{39} +(-6.85373 - 5.96619i) q^{40} +(-7.90132 - 1.39322i) q^{41} +(3.58629 - 5.39801i) q^{42} +(4.21585 + 5.02425i) q^{43} +(1.38504 - 7.33494i) q^{44} +(3.57192 + 8.95162i) q^{45} +(-0.757253 - 0.913625i) q^{46} +(0.260389 + 1.47674i) q^{47} +(2.31159 + 6.53120i) q^{48} +(-6.85352 + 1.42454i) q^{49} +(-6.49415 - 3.80195i) q^{50} +(10.2668 - 0.157093i) q^{51} +(4.80107 - 8.08815i) q^{52} +(-3.76130 - 2.17159i) q^{53} +(0.986717 - 7.28192i) q^{54} -11.9905i q^{55} +(3.18253 - 6.77285i) q^{56} +(1.25804 + 2.10397i) q^{57} +(-8.23424 - 0.0498043i) q^{58} +(-1.68390 + 0.612889i) q^{59} +(5.59532 + 9.62008i) q^{60} +(2.37309 + 13.4585i) q^{61} +(11.0015 + 4.07973i) q^{62} +(-6.28656 + 4.84554i) q^{63} +(3.74600 + 7.06877i) q^{64} +(5.16749 - 14.1976i) q^{65} +(-4.49765 + 7.95931i) q^{66} +(-9.03556 + 10.7682i) q^{67} +(11.7004 - 1.91747i) q^{68} +(0.517909 + 1.35793i) q^{69} +(3.00476 - 11.6390i) q^{70} +(-1.65180 + 2.86100i) q^{71} +(-0.105677 - 8.48462i) q^{72} -10.7512 q^{73} +(12.9374 + 2.36198i) q^{74} +(6.03155 + 6.96876i) q^{75} +(1.79313 + 2.19024i) q^{76} +(9.49826 - 2.70046i) q^{77} +(-8.75569 + 7.48602i) q^{78} +(-1.09487 - 1.30482i) q^{79} +(8.01965 + 10.0411i) q^{80} +(-4.01487 + 8.05486i) q^{81} +(10.6386 + 3.94516i) q^{82} +(0.380043 + 2.15533i) q^{83} +(-6.36037 + 6.59891i) q^{84} +(17.8969 - 6.51392i) q^{85} +(-4.58903 - 8.06063i) q^{86} +(9.52849 + 3.30389i) q^{87} +(-3.78992 + 9.85271i) q^{88} +(4.90703 + 2.83307i) q^{89} +(-2.69565 - 13.3609i) q^{90} +(12.4104 + 0.895898i) q^{91} +(0.821448 + 1.46339i) q^{92} +(-11.1486 - 9.06776i) q^{93} +(0.0128263 - 2.12060i) q^{94} +(3.48314 + 2.92270i) q^{95} +(-1.55704 - 9.67345i) q^{96} +(5.79844 - 4.86547i) q^{97} +(9.89656 - 0.241083i) q^{98} +(8.35307 - 7.45624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{9} + 3 q^{10} - 3 q^{12} - 24 q^{13} + 24 q^{14} - 3 q^{16} - 18 q^{17} - 3 q^{18} - 12 q^{20} - 12 q^{21} - 12 q^{22} + 48 q^{24} - 6 q^{25} - 12 q^{28} - 12 q^{29} - 21 q^{30} - 63 q^{32} - 6 q^{33} - 6 q^{34} - 42 q^{36} - 12 q^{37} + 45 q^{38} - 33 q^{40} - 24 q^{41} - 21 q^{42} + 6 q^{45} - 6 q^{46} - 78 q^{48} - 12 q^{49} - 27 q^{50} - 3 q^{52} + 39 q^{54} - 27 q^{56} - 6 q^{57} - 3 q^{58} - 63 q^{60} - 6 q^{61} - 117 q^{62} - 6 q^{64} - 54 q^{65} - 3 q^{66} - 12 q^{68} - 48 q^{69} - 21 q^{70} - 9 q^{72} - 12 q^{73} + 15 q^{74} + 12 q^{77} + 6 q^{78} - 54 q^{81} - 6 q^{82} - 39 q^{84} + 6 q^{85} - 9 q^{86} - 27 q^{88} - 18 q^{89} - 39 q^{90} + 48 q^{92} - 6 q^{93} - 3 q^{94} + 213 q^{96} - 24 q^{97} + 162 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 12 * q^6 - 18 * q^8 - 6 * q^9 + 3 * q^10 - 3 * q^12 - 24 * q^13 + 24 * q^14 - 3 * q^16 - 18 * q^17 - 3 * q^18 - 12 * q^20 - 12 * q^21 - 12 * q^22 + 48 * q^24 - 6 * q^25 - 12 * q^28 - 12 * q^29 - 21 * q^30 - 63 * q^32 - 6 * q^33 - 6 * q^34 - 42 * q^36 - 12 * q^37 + 45 * q^38 - 33 * q^40 - 24 * q^41 - 21 * q^42 + 6 * q^45 - 6 * q^46 - 78 * q^48 - 12 * q^49 - 27 * q^50 - 3 * q^52 + 39 * q^54 - 27 * q^56 - 6 * q^57 - 3 * q^58 - 63 * q^60 - 6 * q^61 - 117 * q^62 - 6 * q^64 - 54 * q^65 - 3 * q^66 - 12 * q^68 - 48 * q^69 - 21 * q^70 - 9 * q^72 - 12 * q^73 + 15 * q^74 + 12 * q^77 + 6 * q^78 - 54 * q^81 - 6 * q^82 - 39 * q^84 + 6 * q^85 - 9 * q^86 - 27 * q^88 - 18 * q^89 - 39 * q^90 + 48 * q^92 - 6 * q^93 - 3 * q^94 + 213 * q^96 - 24 * q^97 + 162 * q^98

Introduction

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