LMFDB - Embedded newform 418.2.h.b.65.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.2
Root			$2.37734i$ of defining polynomial
Character	$\chi$	$=$	418.65
Dual form			418.2.h.b.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-2.05883 - 1.18867i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.05852 - 3.56546i) q^{5} +(-2.05883 + 1.18867i) q^{6} -2.89251i q^{7} -1.00000 q^{8} +(1.32587 + 2.29647i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-2.05883 - 1.18867i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.05852 - 3.56546i) q^{5} +(-2.05883 + 1.18867i) q^{6} -2.89251i q^{7} -1.00000 q^{8} +(1.32587 + 2.29647i) q^{9} +(-2.05852 - 3.56546i) q^{10} +(2.64123 + 2.00597i) q^{11} +2.37734i q^{12} +(-0.104453 - 0.180918i) q^{13} +(-2.50499 - 1.44625i) q^{14} +(-8.47630 + 4.89380i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.81130 + 3.93250i) q^{17} +2.65173 q^{18} +(-4.34659 + 0.327327i) q^{19} -4.11704 q^{20} +(-3.43823 + 5.95520i) q^{21} +(3.05784 - 1.28438i) q^{22} +(-2.98645 - 5.17269i) q^{23} +(2.05883 + 1.18867i) q^{24} +(-5.97501 - 10.3490i) q^{25} -0.208906 q^{26} +0.827948i q^{27} +(-2.50499 + 1.44625i) q^{28} +(1.71091 + 2.96338i) q^{29} +9.78759i q^{30} +5.73486i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.05341 - 7.26951i) q^{33} +(6.81130 - 3.93250i) q^{34} +(-10.3131 - 5.95429i) q^{35} +(1.32587 - 2.29647i) q^{36} -1.38157i q^{37} +(-1.88982 + 3.92792i) q^{38} +0.496640i q^{39} +(-2.05852 + 3.56546i) q^{40} +(-0.769945 + 1.33358i) q^{41} +(3.43823 + 5.95520i) q^{42} +(8.75986 + 5.05751i) q^{43} +(0.416609 - 3.29036i) q^{44} +10.9173 q^{45} -5.97290 q^{46} +(1.26444 + 2.19008i) q^{47} +(2.05883 - 1.18867i) q^{48} -1.36661 q^{49} -11.9500 q^{50} +(-9.34889 - 16.1928i) q^{51} +(-0.104453 + 0.180918i) q^{52} +(4.55571 - 2.63024i) q^{53} +(0.717024 + 0.413974i) q^{54} +(12.5892 - 5.28786i) q^{55} +2.89251i q^{56} +(9.33800 + 4.49274i) q^{57} +3.42181 q^{58} +(-11.8771 - 6.85724i) q^{59} +(8.47630 + 4.89380i) q^{60} +(-0.468667 + 0.270585i) q^{61} +(4.96654 + 2.86743i) q^{62} +(6.64255 - 3.83508i) q^{63} +1.00000 q^{64} -0.860074 q^{65} +(-7.82228 - 0.990420i) q^{66} +(1.14713 - 0.662294i) q^{67} -7.86501i q^{68} +14.1996i q^{69} +(-10.3131 + 5.95429i) q^{70} +(8.85065 + 5.10993i) q^{71} +(-1.32587 - 2.29647i) q^{72} +(-0.652738 - 0.376859i) q^{73} +(-1.19647 - 0.690784i) q^{74} +28.4092i q^{75} +(2.45677 + 3.60059i) q^{76} +(5.80229 - 7.63977i) q^{77} +(0.430103 + 0.248320i) q^{78} +(5.12887 - 8.88347i) q^{79} +(2.05852 + 3.56546i) q^{80} +(4.96176 - 8.59401i) q^{81} +(0.769945 + 1.33358i) q^{82} -2.79434i q^{83} +6.87647 q^{84} +(28.0424 - 16.1903i) q^{85} +(8.75986 - 5.05751i) q^{86} -8.13481i q^{87} +(-2.64123 - 2.00597i) q^{88} +(-1.51651 + 0.875555i) q^{89} +(5.45865 - 9.45465i) q^{90} +(-0.523307 + 0.302131i) q^{91} +(-2.98645 + 5.17269i) q^{92} +(6.81685 - 11.8071i) q^{93} +2.52888 q^{94} +(-7.78047 + 16.1714i) q^{95} -2.37734i q^{96} +(6.47787 + 3.74000i) q^{97} +(-0.683304 + 1.18352i) q^{98} +(-1.10474 + 8.72514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−2.05883	−	1.18867i	−1.18867	−	0.686278i	−0.230665	−	0.973033i	$-0.574090\pi$
$3$	−2.05883	−	1.18867i	−1.18867	−	0.686278i	−0.958004	+	0.286755i	$0.907423\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.05852	−	3.56546i	0.920598	−	1.59452i	0.122106	−	0.992517i	$-0.461035\pi$
$5$	2.05852	−	3.56546i	0.920598	−	1.59452i	0.798492	−	0.602006i	$-0.205632\pi$
$6$	−2.05883	+	1.18867i	−0.840516	+	0.485272i
$7$		−	2.89251i		−	1.09327i	−0.837372	−	0.546633i	$-0.815909\pi$
$7$		−	2.89251i		−	1.09327i	0.837372	−	0.546633i	$-0.184091\pi$
$8$	−1.00000			−0.353553
$9$	1.32587	+	2.29647i	0.441955	+	0.765489i
$10$	−2.05852	−	3.56546i	−0.650961	−	1.12750i
$11$	2.64123	+	2.00597i	0.796360	+	0.604823i
$11$	2.64123	+	2.00597i	0.796360	+	0.604823i
$12$			2.37734i			0.686278i
$13$	−0.104453	−	0.180918i	−0.0289700	−	0.0501776i	0.851177	−	0.524879i	$-0.175889\pi$
$13$	−0.104453	−	0.180918i	−0.0289700	−	0.0501776i	−0.880147	+	0.474701i	$0.842556\pi$
$14$	−2.50499	−	1.44625i	−0.669486	−	0.386528i
$15$	−8.47630	+	4.89380i	−2.18857	+	1.26357i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.81130	+	3.93250i	1.65198	+	0.953772i	0.976256	+	0.216619i	$0.0695031\pi$
$17$	6.81130	+	3.93250i	1.65198	+	0.953772i	0.675726	+	0.737153i	$0.263830\pi$
$18$	2.65173			0.625019
$19$	−4.34659	+	0.327327i	−0.997176	+	0.0750940i
$19$	−4.34659	+	0.327327i	−0.997176	+	0.0750940i
$20$	−4.11704			−0.920598
$21$	−3.43823	+	5.95520i	−0.750284	+	1.29953i
$22$	3.05784	−	1.28438i	0.651933	−	0.273832i
$23$	−2.98645	−	5.17269i	−0.622718	−	1.07858i	−0.988977	−	0.148067i	$-0.952695\pi$
$23$	−2.98645	−	5.17269i	−0.622718	−	1.07858i	0.366259	−	0.930513i	$-0.380638\pi$
$24$	2.05883	+	1.18867i	0.420258	+	0.242636i
$25$	−5.97501	−	10.3490i	−1.19500	−	2.06980i
$26$	−0.208906			−0.0409698
$27$			0.827948i			0.159339i
$28$	−2.50499	+	1.44625i	−0.473398	+	0.273316i
$29$	1.71091	+	2.96338i	0.317708	+	0.550286i	0.980009	−	0.198952i	$-0.0637537\pi$
$29$	1.71091	+	2.96338i	0.317708	+	0.550286i	−0.662302	+	0.749237i	$0.730420\pi$
$30$			9.78759i			1.78696i
$31$			5.73486i			1.03001i	0.857187	+	0.515006i	$0.172210\pi$
$31$			5.73486i			1.03001i	−0.857187	+	0.515006i	$0.827790\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.05341	−	7.26951i	−0.531531	−	1.26546i
$34$	6.81130	−	3.93250i	1.16813	−	0.674419i
$35$	−10.3131	−	5.95429i	−1.74324	−	1.00646i
$36$	1.32587	−	2.29647i	0.220978	−	0.382745i
$37$		−	1.38157i		−	0.227128i	−0.993531	−	0.113564i	$-0.963773\pi$
$37$		−	1.38157i		−	0.227128i	0.993531	−	0.113564i	$-0.0362268\pi$
$38$	−1.88982	+	3.92792i	−0.306570	+	0.637193i
$39$			0.496640i			0.0795260i
$40$	−2.05852	+	3.56546i	−0.325481	+	0.563749i
$41$	−0.769945	+	1.33358i	−0.120245	+	0.208271i	−0.919864	−	0.392237i	$-0.871701\pi$
$41$	−0.769945	+	1.33358i	−0.120245	+	0.208271i	0.799619	+	0.600507i	$0.205035\pi$
$42$	3.43823	+	5.95520i	0.530531	+	0.918907i
$43$	8.75986	+	5.05751i	1.33587	+	0.771263i	0.986192	−	0.165609i	$-0.0529588\pi$
$43$	8.75986	+	5.05751i	1.33587	+	0.771263i	0.349675	+	0.936871i	$0.386292\pi$
$44$	0.416609	−	3.29036i	0.0628061	−	0.496040i
$45$	10.9173			1.62745
$46$	−5.97290			−0.880656
$47$	1.26444	+	2.19008i	0.184438	+	0.319455i	0.943387	−	0.331694i	$-0.107620\pi$
$47$	1.26444	+	2.19008i	0.184438	+	0.319455i	−0.758949	+	0.651150i	$0.774287\pi$
$48$	2.05883	−	1.18867i	0.297167	−	0.171570i
$49$	−1.36661			−0.195230
$50$	−11.9500			−1.68999
$51$	−9.34889	−	16.1928i	−1.30911	−	2.26744i
$52$	−0.104453	+	0.180918i	−0.0144850	+	0.0250888i
$53$	4.55571	−	2.63024i	0.625775	−	0.361291i	−0.153339	−	0.988174i	$-0.549003\pi$
$53$	4.55571	−	2.63024i	0.625775	−	0.361291i	0.779114	+	0.626882i	$0.215669\pi$
$54$	0.717024	+	0.413974i	0.0975746	+	0.0563347i
$55$	12.5892	−	5.28786i	1.69753	−	0.713015i
$56$			2.89251i			0.386528i
$57$	9.33800	+	4.49274i	1.23685	+	0.595079i
$58$	3.42181			0.449306
$59$	−11.8771	−	6.85724i	−1.54627	−	0.892737i	−0.998422	−	0.0561558i	$-0.982116\pi$
$59$	−11.8771	−	6.85724i	−1.54627	−	0.892737i	−0.547843	−	0.836581i	$-0.684551\pi$
$60$	8.47630	+	4.89380i	1.09429	+	0.631786i
$61$	−0.468667	+	0.270585i	−0.0600067	+	0.0346449i	−0.529703	−	0.848183i	$-0.677697\pi$
$61$	−0.468667	+	0.270585i	−0.0600067	+	0.0346449i	0.469696	+	0.882828i	$0.344363\pi$
$62$	4.96654	+	2.86743i	0.630751	+	0.364164i
$63$	6.64255	−	3.83508i	0.836883	−	0.483175i
$64$	1.00000			0.125000
$65$	−0.860074			−0.106679
$66$	−7.82228	−	0.990420i	−0.962857	−	0.121912i
$67$	1.14713	−	0.662294i	0.140144	−	0.0809121i	−0.428289	−	0.903642i	$-0.640883\pi$
$67$	1.14713	−	0.662294i	0.140144	−	0.0809121i	0.568433	+	0.822730i	$0.307550\pi$
$68$		−	7.86501i		−	0.953772i
$69$			14.1996i			1.70943i
$70$	−10.3131	+	5.95429i	−1.23265	+	0.711673i
$71$	8.85065	+	5.10993i	1.05038	+	0.606437i	0.922755	−	0.385386i	$-0.125932\pi$
$71$	8.85065	+	5.10993i	1.05038	+	0.606437i	0.127624	+	0.991823i	$0.459265\pi$
$72$	−1.32587	−	2.29647i	−0.156255	−	0.270641i
$73$	−0.652738	−	0.376859i	−0.0763973	−	0.0441080i	0.461315	−	0.887237i	$-0.347378\pi$
$73$	−0.652738	−	0.376859i	−0.0763973	−	0.0441080i	−0.537712	+	0.843129i	$0.680711\pi$
$74$	−1.19647	−	0.690784i	−0.139087	−	0.0803020i
$75$			28.4092i			3.28041i
$76$	2.45677	+	3.60059i	0.281811	+	0.413017i
$77$	5.80229	−	7.63977i	0.661232	−	0.870633i
$78$	0.430103	+	0.248320i	0.0486996	+	0.0281167i
$79$	5.12887	−	8.88347i	0.577043	−	0.999468i	−0.418773	−	0.908091i	$-0.637540\pi$
$79$	5.12887	−	8.88347i	0.577043	−	0.999468i	0.995816	−	0.0913775i	$-0.0291270\pi$
$80$	2.05852	+	3.56546i	0.230150	+	0.398631i
$81$	4.96176	−	8.59401i	0.551306	−	0.954890i
$82$	0.769945	+	1.33358i	0.0850262	+	0.147270i
$83$		−	2.79434i		−	0.306719i	−0.988170	−	0.153359i	$-0.950991\pi$
$83$		−	2.79434i		−	0.306719i	0.988170	−	0.153359i	$-0.0490092\pi$
$84$	6.87647			0.750284
$85$	28.0424	−	16.1903i	3.04162	−	1.75608i
$86$	8.75986	−	5.05751i	0.944600	−	0.545365i
$87$		−	8.13481i		−	0.872143i
$88$	−2.64123	−	2.00597i	−0.281556	−	0.213837i
$89$	−1.51651	+	0.875555i	−0.160749	+	0.0928087i	−0.578217	−	0.815883i	$-0.696251\pi$
$89$	−1.51651	+	0.875555i	−0.160749	+	0.0928087i	0.417467	+	0.908692i	$0.362918\pi$
$90$	5.45865	−	9.45465i	0.575392	−	0.996608i
$91$	−0.523307	+	0.302131i	−0.0548574	+	0.0316720i
$92$	−2.98645	+	5.17269i	−0.311359	+	0.539290i
$93$	6.81685	−	11.8071i	0.706875	−	1.22434i
$94$	2.52888			0.260834
$95$	−7.78047	+	16.1714i	−0.798260	+	1.65915i
$96$		−	2.37734i		−	0.242636i
$97$	6.47787	+	3.74000i	0.657729	+	0.379740i	0.791411	−	0.611284i	$-0.209347\pi$
$97$	6.47787	+	3.74000i	0.657729	+	0.379740i	−0.133682	+	0.991024i	$0.542680\pi$
$98$	−0.683304	+	1.18352i	−0.0690241	+	0.119553i
$99$	−1.10474	+	8.72514i	−0.111030	+	0.876910i
$100$	−5.97501	+	10.3490i	−0.597501	+	1.03490i
$101$	−6.35893	+	3.67133i	−0.632738	+	0.365311i	−0.781812	−	0.623515i	$-0.785704\pi$
$101$	−6.35893	+	3.67133i	−0.632738	+	0.365311i	0.149074	+	0.988826i	$0.452371\pi$
$102$	−18.6978			−1.85136
$103$		−	4.03124i		−	0.397210i	−0.980080	−	0.198605i	$-0.936359\pi$
$103$		−	4.03124i		−	0.397210i	0.980080	−	0.198605i	$-0.0636411\pi$
$104$	0.104453	+	0.180918i	0.0102425	+	0.0177405i
$105$	14.1553	+	24.5178i	1.38142	+	2.39269i
$106$		−	5.26048i		−	0.510943i
$107$	−14.6180			−1.41317			−0.706587	−	0.707627i	$-0.749766\pi$
$107$	−14.6180			−1.41317			−0.706587	+	0.707627i	$0.749766\pi$
$108$	0.717024	−	0.413974i	0.0689957	−	0.0398347i
$109$	−0.996756	+	1.72643i	−0.0954719	+	0.165362i	−0.909805	−	0.415035i	$-0.863769\pi$
$109$	−0.996756	+	1.72643i	−0.0954719	+	0.165362i	0.814334	+	0.580397i	$0.197103\pi$
$110$	1.71520	−	13.5465i	0.163537	−	1.29161i
$111$	−1.64223	+	2.84442i	−0.155873	+	0.269981i
$112$	2.50499	+	1.44625i	0.236699	+	0.136658i
$113$		−	8.43532i		−	0.793528i	−0.917921	−	0.396764i	$-0.870133\pi$
$113$		−	8.43532i		−	0.793528i	0.917921	−	0.396764i	$-0.129867\pi$
$114$	8.55983	−	5.84057i	0.801701	−	0.547019i
$115$	−24.5907			−2.29309
$116$	1.71091	−	2.96338i	0.158854	−	0.275143i
$117$	0.276981	−	0.479746i	0.0256069	−	0.0443525i
$118$	−11.8771	+	6.85724i	−1.09337	+	0.631260i
$119$	11.3748	−	19.7017i	1.04273	−	1.80606i
$120$	8.47630	−	4.89380i	0.773777	−	0.446740i
$121$	2.95216	+	10.5965i	0.268378	+	0.963314i
$122$			0.541171i			0.0489953i
$123$	3.17038	−	1.83042i	0.285863	−	0.165043i
$124$	4.96654	−	2.86743i	0.446008	−	0.257503i
$125$	−28.6135			−2.55927
$126$		−	7.67016i		−	0.683312i
$127$	−3.57594	−	6.19370i	−0.317313	−	0.549602i	0.662613	−	0.748962i	$-0.269447\pi$
$127$	−3.57594	−	6.19370i	−0.317313	−	0.549602i	−0.979926	+	0.199359i	$0.936114\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−12.0234	−	20.8251i	−1.05860	−	1.83355i
$130$	−0.430037	+	0.744846i	−0.0377167	+	0.0653273i
$131$	−11.9239	−	6.88425i	−1.04179	−	0.601479i	−0.121452	−	0.992597i	$-0.538755\pi$
$131$	−11.9239	−	6.88425i	−1.04179	−	0.601479i	−0.920341	+	0.391118i	$0.872088\pi$
$132$	−4.76887	+	6.27909i	−0.415077	+	0.546524i
$133$	0.946797	+	12.5726i	0.0820977	+	1.09018i
$134$		−	1.32459i		−	0.114427i
$135$	2.95202	+	1.70435i	0.254069	+	0.146687i
$136$	−6.81130	−	3.93250i	−0.584064	−	0.337209i
$137$	5.99847	+	10.3897i	0.512484	+	0.887649i	0.999895	+	0.0144761i	$0.00460803\pi$
$137$	5.99847	+	10.3897i	0.512484	+	0.887649i	−0.487411	+	0.873173i	$0.662059\pi$
$138$	12.2972	+	7.09980i	1.04681	+	0.604375i
$139$	−15.3546	+	8.86499i	−1.30236	+	0.751919i	−0.980809	−	0.194973i	$-0.937538\pi$
$139$	−15.3546	+	8.86499i	−1.30236	+	0.751919i	−0.321553	+	0.946892i	$0.604205\pi$
$140$			11.9086i			1.00646i
$141$		−	6.01201i		−	0.506302i
$142$	8.85065	−	5.10993i	0.742730	−	0.428815i
$143$	0.0870321	−	0.687375i	0.00727799	−	0.0574812i
$144$	−2.65173			−0.220978
$145$	14.0877			1.16992
$146$	−0.652738	+	0.376859i	−0.0540210	+	0.0311891i
$147$	2.81362	+	1.62444i	0.232063	+	0.133982i
$148$	−1.19647	+	0.690784i	−0.0983495	+	0.0567821i
$149$	−15.6937	−	9.06077i	−1.28568	−	0.742288i	−0.307799	−	0.951451i	$-0.599592\pi$
$149$	−15.6937	−	9.06077i	−1.28568	−	0.742288i	−0.977881	+	0.209164i	$0.932926\pi$
$150$	24.6031	+	14.2046i	2.00884	+	1.15980i
$151$	9.53361			0.775834			0.387917	−	0.921694i	$-0.373195\pi$
$151$	9.53361			0.775834			0.387917	+	0.921694i	$0.373195\pi$
$152$	4.34659	−	0.327327i	0.352555	−	0.0265497i
$153$			20.8559i			1.68610i
$154$	−3.71509	−	8.84482i	−0.299371	−	0.712736i
$155$	20.4474	+	11.8053i	1.64238	+	0.948227i
$156$	0.430103	−	0.248320i	0.0344358	−	0.0198815i
$157$	−0.550698	+	0.953837i	−0.0439505	+	0.0761245i	−0.887164	−	0.461455i	$-0.847328\pi$
$157$	−0.550698	+	0.953837i	−0.0439505	+	0.0761245i	0.843213	+	0.537579i	$0.180661\pi$
$158$	−5.12887	−	8.88347i	−0.408031	−	0.706731i
$159$	−12.5059			−0.991785
$160$	4.11704			0.325481
$161$	−14.9620	+	8.63834i	−1.17917	+	0.680796i
$162$	−4.96176	−	8.59401i	−0.389832	−	0.675209i
$163$	10.8417			0.849191			0.424595	−	0.905383i	$-0.360416\pi$
$163$	10.8417			0.849191			0.424595	+	0.905383i	$0.360416\pi$
$164$	1.53989			0.120245
$165$	−32.2047	−	4.07760i	−2.50713	−	0.317441i
$166$	−2.41997	−	1.39717i	−0.187826	−	0.108441i
$167$	7.98411	+	13.8289i	0.617829	+	1.07011i	0.989881	+	0.141899i	$0.0453209\pi$
$167$	7.98411	+	13.8289i	0.617829	+	1.07011i	−0.372052	+	0.928212i	$0.621346\pi$
$168$	3.43823	−	5.95520i	0.265266	−	0.459453i
$169$	6.47818	−	11.2205i	0.498321	−	0.863118i
$170$		−	32.3806i		−	2.48347i
$171$	−6.51470	−	9.54782i	−0.498191	−	0.730140i
$172$		−	10.1150i		−	0.771263i
$173$	8.03663	−	13.9199i	0.611014	−	1.05831i	−0.380056	−	0.924963i	$-0.624095\pi$
$173$	8.03663	−	13.9199i	0.611014	−	1.05831i	0.991070	−	0.133344i	$-0.0425714\pi$
$174$	−7.04495	−	4.06740i	−0.534076	−	0.308349i
$175$	−29.9346	+	17.2828i	−2.26285	+	1.30645i
$176$	−3.05784	+	1.28438i	−0.230493	+	0.0968141i
$177$	16.3020	+	28.2358i	1.22533	+	2.12234i
$178$			1.75111i			0.131251i
$179$			6.94472i			0.519073i	0.965733	+	0.259536i	$0.0835698\pi$
$179$			6.94472i			0.519073i	−0.965733	+	0.259536i	$0.916430\pi$
$180$	−5.45865	−	9.45465i	−0.406863	−	0.704708i
$181$	−8.39523	+	4.84699i	−0.624012	+	0.360274i	−0.778430	−	0.627732i	$-0.783983\pi$
$181$	−8.39523	+	4.84699i	−0.624012	+	0.360274i	0.154417	+	0.988006i	$0.450650\pi$
$182$			0.604262i			0.0447909i
$183$	1.28655			0.0951041
$184$	2.98645	+	5.17269i	0.220164	+	0.381335i
$185$	−4.92593	−	2.84399i	−0.362162	−	0.209094i
$186$	−6.81685	−	11.8071i	−0.499836	−	0.865741i
$187$	10.1017	+	24.0499i	0.738709	+	1.75870i
$188$	1.26444	−	2.19008i	0.0922188	−	0.159728i
$189$	2.39485			0.174200
$190$	10.1146	+	14.8238i	0.733791	+	1.07543i
$191$	9.48445			0.686270			0.343135	−	0.939286i	$-0.388511\pi$
$191$	9.48445			0.686270			0.343135	+	0.939286i	$0.388511\pi$
$192$	−2.05883	−	1.18867i	−0.148584	−	0.0857848i
$193$	−7.93328	+	13.7408i	−0.571050	+	0.989087i	0.425409	+	0.905001i	$0.360130\pi$
$193$	−7.93328	+	13.7408i	−0.571050	+	0.989087i	−0.996458	+	0.0840861i	$0.973203\pi$
$194$	6.47787	−	3.74000i	0.465084	−	0.268517i
$195$	1.77075	+	1.02234i	0.126806	+	0.0732115i
$196$	0.683304	+	1.18352i	0.0488074	+	0.0845369i
$197$			5.47690i			0.390213i	0.980782	+	0.195106i	$0.0625052\pi$
$197$			5.47690i			0.390213i	−0.980782	+	0.195106i	$0.937495\pi$
$198$	7.00383	+	5.31930i	0.497740	+	0.378026i
$199$	0.462834	+	0.801652i	0.0328095	+	0.0568276i	0.881964	−	0.471317i	$-0.156221\pi$
$199$	0.462834	+	0.801652i	0.0328095	+	0.0568276i	−0.849154	+	0.528145i	$0.822888\pi$
$200$	5.97501	+	10.3490i	0.422497	+	0.731786i
$201$	−3.14899			−0.222113
$202$			7.34266i			0.516628i
$203$	8.57160	−	4.94881i	0.601608	−	0.347339i
$204$	−9.34889	+	16.1928i	−0.654553	+	1.13372i
$205$	3.16989	+	5.49042i	0.221395	+	0.383467i
$206$	−3.49116	−	2.01562i	−0.243241	−	0.140435i
$207$	7.91927	−	13.7166i	0.550427	−	0.953368i
$208$	0.208906			0.0144850
$209$	−12.1369	−	7.85459i	−0.839530	−	0.543314i
$210$	28.3107			1.95362
$211$	−6.95552	+	12.0473i	−0.478838	+	0.829371i	−0.999706	−	0.0242662i	$-0.992275\pi$
$211$	−6.95552	+	12.0473i	−0.478838	+	0.829371i	0.520868	+	0.853637i	$0.325608\pi$
$212$	−4.55571	−	2.63024i	−0.312887	−	0.180646i
$213$	−12.1480	−	21.0410i	−0.832369	−	1.44170i
$214$	−7.30899	+	12.6595i	−0.499632	+	0.865388i
$215$	36.0647	−	20.8220i	2.45959	−	1.42005i
$216$		−	0.827948i		−	0.0563347i
$217$	16.5881			1.12608
$218$	0.996756	+	1.72643i	0.0675089	+	0.116929i
$219$	0.895920	+	1.55178i	0.0605407	+	0.104860i
$220$	−10.8740	−	8.25866i	−0.733127	−	0.556799i
$221$		−	1.64305i		−	0.110523i
$222$	1.64223	+	2.84442i	0.110219	+	0.190905i
$223$	5.43448	+	3.13760i	0.363920	+	0.210109i	0.670799	−	0.741639i	$-0.265951\pi$
$223$	5.43448	+	3.13760i	0.363920	+	0.210109i	−0.306879	+	0.951749i	$0.599285\pi$
$224$	2.50499	−	1.44625i	0.167371	−	0.0966319i
$225$	15.8441	−	27.4428i	1.05628	−	1.82952i
$226$	−7.30520	−	4.21766i	−0.485935	−	0.280554i
$227$	24.1778			1.60474			0.802370	−	0.596827i	$-0.203572\pi$
$227$	24.1778			1.60474			0.802370	+	0.596827i	$0.203572\pi$
$228$	−0.778167	−	10.3333i	−0.0515354	−	0.684340i
$229$	11.6670			0.770978			0.385489	−	0.922712i	$-0.374033\pi$
$229$	11.6670			0.770978			0.385489	+	0.922712i	$0.374033\pi$
$230$	−12.2953	+	21.2962i	−0.810731	+	1.40423i
$231$	−21.0271	+	8.83203i	−1.38348	+	0.581105i
$232$	−1.71091	−	2.96338i	−0.112327	−	0.194555i
$233$	−20.5498	−	11.8644i	−1.34626	−	0.777264i	−0.358543	−	0.933513i	$-0.616726\pi$
$233$	−20.5498	−	11.8644i	−1.34626	−	0.777264i	−0.987718	+	0.156250i	$0.950060\pi$
$234$	−0.276981	−	0.479746i	−0.0181068	−	0.0313620i
$235$	10.4115			0.679172
$236$			13.7145i			0.892737i
$237$	−21.1190	+	12.1931i	−1.37183	+	0.792025i
$238$	−11.3748	−	19.7017i	−0.737319	−	1.27707i
$239$			1.94367i			0.125726i	0.998022	+	0.0628628i	$0.0200230\pi$
$239$			1.94367i			0.125726i	−0.998022	+	0.0628628i	$0.979977\pi$
$240$		−	9.78759i		−	0.631786i
$241$	0.426995	+	0.739577i	0.0275052	+	0.0476403i	0.879450	−	0.475991i	$-0.157910\pi$
$241$	0.426995	+	0.739577i	0.0275052	+	0.0476403i	−0.851945	+	0.523631i	$0.824577\pi$
$242$	10.6529	+	2.74158i	0.684793	+	0.176236i
$243$	−18.2798	+	10.5538i	−1.17265	+	0.677029i
$244$	0.468667	+	0.270585i	0.0300034	+	0.0173224i
$245$	−2.81319	+	4.87259i	−0.179728	+	0.311298i
$246$		−	3.66084i		−	0.233406i
$247$	0.513234	+	0.752186i	0.0326563	+	0.0478604i
$248$		−	5.73486i		−	0.364164i
$249$	−3.32155	+	5.75309i	−0.210494	+	0.364587i
$250$	−14.3067	+	24.7800i	−0.904838	+	1.56723i
$251$	−7.92898	−	13.7334i	−0.500473	−	0.866845i	−1.00000		0.000546231i	$-0.999826\pi$
$251$	−7.92898	−	13.7334i	−0.500473	−	0.866845i	0.499527	−	0.866298i	$-0.333507\pi$
$252$	−6.64255	−	3.83508i	−0.418442	−	0.241587i
$253$	2.48836	−	19.6530i	0.156442	−	1.23557i
$254$	−7.15187			−0.448748
$255$	−76.9795			−4.82064
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.4296	+	6.59891i	−0.712962	+	0.411629i	−0.812157	−	0.583439i	$-0.801707\pi$
$257$	−11.4296	+	6.59891i	−0.712962	+	0.411629i	0.0991951	+	0.995068i	$0.468373\pi$
$258$	−24.0468			−1.49709
$259$	−3.99620			−0.248312
$260$	0.430037	+	0.744846i	0.0266698	+	0.0461934i
$261$	−4.53687	+	7.85809i	−0.280825	+	0.486403i
$262$	−11.9239	+	6.88425i	−0.736659	+	0.425310i
$263$	4.87621	+	2.81528i	0.300680	+	0.173598i	0.642748	−	0.766077i	$-0.277794\pi$
$263$	4.87621	+	2.81528i	0.300680	+	0.173598i	−0.342068	+	0.939675i	$0.611127\pi$
$264$	3.05341	+	7.26951i	0.187925	+	0.447407i
$265$		−	21.6576i		−	1.33042i
$266$	11.3615	+	5.46633i	0.696621	+	0.335162i
$267$	4.16298			0.254770
$268$	−1.14713	−	0.662294i	−0.0700719	−	0.0404561i
$269$	2.27078	+	1.31103i	0.138452	+	0.0799351i	0.567626	−	0.823287i	$-0.307862\pi$
$269$	2.27078	+	1.31103i	0.138452	+	0.0799351i	−0.429174	+	0.903222i	$0.641195\pi$
$270$	2.95202	−	1.70435i	0.179654	−	0.103723i
$271$	11.6079	+	6.70182i	0.705129	+	0.407107i	0.809255	−	0.587458i	$-0.199871\pi$
$271$	11.6079	+	6.70182i	0.705129	+	0.407107i	−0.104126	+	0.994564i	$0.533204\pi$
$272$	−6.81130	+	3.93250i	−0.412996	+	0.238443i
$273$	1.43654			0.0869431
$274$	11.9969			0.724762
$275$	4.97848	−	39.3198i	0.300214	−	2.37107i
$276$	12.2972	−	7.09980i	0.740206	−	0.427358i
$277$		−	18.5185i		−	1.11267i	−0.830958	−	0.556335i	$-0.812207\pi$
$277$		−	18.5185i		−	1.11267i	0.830958	−	0.556335i	$-0.187793\pi$
$278$			17.7300i			1.06337i
$279$	−13.1699	+	7.60366i	−0.788463	+	0.455219i
$280$	10.3131	+	5.95429i	0.616327	+	0.355837i
$281$	2.05276	+	3.55549i	0.122458	+	0.212103i	0.920736	−	0.390185i	$-0.127589\pi$
$281$	2.05276	+	3.55549i	0.122458	+	0.212103i	−0.798279	+	0.602288i	$0.794256\pi$
$282$	−5.20655	−	3.00600i	−0.310046	−	0.179005i
$283$	6.72522	+	3.88280i	0.399773	+	0.230809i	0.686386	−	0.727238i	$-0.259196\pi$
$283$	6.72522	+	3.88280i	0.399773	+	0.230809i	−0.286613	+	0.958046i	$0.592529\pi$
$284$		−	10.2199i		−	0.606437i
$285$	35.2412	−	24.0459i	2.08751	−	1.42435i
$286$	−0.551768	−	0.419059i	−0.0326267	−	0.0247795i
$287$	3.85740	+	2.22707i	0.227695	+	0.131460i
$288$	−1.32587	+	2.29647i	−0.0781274	+	0.135321i
$289$	22.4292	+	38.8485i	1.31936	+	2.28520i
$290$	7.04387	−	12.2003i	0.413630	−	0.716429i
$291$	−8.89125	−	15.4001i	−0.521214	−	0.902769i
$292$			0.753717i			0.0441080i
$293$	−25.0826			−1.46534			−0.732669	−	0.680585i	$-0.761726\pi$
$293$	−25.0826			−1.46534			−0.732669	+	0.680585i	$0.761726\pi$
$294$	2.81362	−	1.62444i	0.164094	−	0.0947395i
$295$	−48.8985	+	28.2315i	−2.84698	+	1.64370i
$296$			1.38157i			0.0803020i
$297$	−1.66084	+	2.18680i	−0.0963717	+	0.126891i
$298$	−15.6937	+	9.06077i	−0.909113	+	0.524877i
$299$	−0.623888	+	1.08060i	−0.0360803	+	0.0624930i
$300$	24.6031	−	14.2046i	1.42046	−	0.820104i
$301$	14.6289	−	25.3380i	0.843195	−	1.46046i
$302$	4.76680	−	8.25635i	0.274299	−	0.475099i
$303$	17.4560			1.00282
$304$	1.88982	−	3.92792i	0.108389	−	0.225282i
$305$			2.22802i			0.127576i
$306$	18.0617	+	10.4280i	1.03252	+	0.596126i
$307$	16.5060	−	28.5892i	0.942047	−	1.63167i	0.180490	−	0.983577i	$-0.442232\pi$
$307$	16.5060	−	28.5892i	0.942047	−	1.63167i	0.761558	−	0.648097i	$-0.224435\pi$
$308$	−9.51738	−	1.20504i	−0.542303	−	0.0686638i
$309$	−4.79181	+	8.29966i	−0.272597	+	0.472151i
$310$	20.4474	−	11.8053i	1.16134	−	0.670498i
$311$	−14.9709			−0.848921			−0.424461	−	0.905446i	$-0.639536\pi$
$311$	−14.9709			−0.848921			−0.424461	+	0.905446i	$0.639536\pi$
$312$		−	0.496640i		−	0.0281167i
$313$	6.91074	+	11.9698i	0.390618	+	0.676571i	0.992531	−	0.121991i	$-0.0389279\pi$
$313$	6.91074	+	11.9698i	0.390618	+	0.676571i	−0.601913	+	0.798562i	$0.705595\pi$
$314$	0.550698	+	0.953837i	0.0310777	+	0.0538281i
$315$		−	31.5784i		−	1.77924i
$316$	−10.2577			−0.577043
$317$	12.7564	−	7.36491i	0.716470	−	0.413654i	−0.0969818	−	0.995286i	$-0.530919\pi$
$317$	12.7564	−	7.36491i	0.716470	−	0.413654i	0.813452	+	0.581632i	$0.197586\pi$
$318$	−6.25297	+	10.8305i	−0.350649	+	0.607342i
$319$	−1.42556	+	11.2590i	−0.0798159	+	0.630382i
$320$	2.05852	−	3.56546i	0.115075	−	0.199315i
$321$	30.0960	+	17.3759i	1.67979	+	0.969830i
$322$			17.2767i			0.962791i
$323$	−30.8931	−	14.8635i	−1.71894	−	0.827025i
$324$	−9.92351			−0.551306
$325$	−1.24821	+	2.16197i	−0.0692385	+	0.119925i
$326$	5.42087	−	9.38922i	0.300234	−	0.520021i
$327$	4.10431	−	2.36963i	0.226969	−	0.131041i
$328$	0.769945	−	1.33358i	0.0425131	−	0.0736348i
$329$	6.33481	−	3.65741i	0.349250	−	0.201639i
$330$	−19.6336	+	25.8513i	−1.08080	+	1.42306i
$331$		−	9.67374i		−	0.531717i	−0.964012	−	0.265859i	$-0.914345\pi$
$331$		−	9.67374i		−	0.531717i	0.964012	−	0.265859i	$-0.0856554\pi$
$332$	−2.41997	+	1.39717i	−0.132813	+	0.0766797i
$333$	3.17273	−	1.83178i	0.173864	−	0.100381i
$334$	15.9682			0.873742
$335$		−	5.45338i		−	0.297950i
$336$	−3.43823	−	5.95520i	−0.187571	−	0.324883i
$337$	−12.1374	+	21.0226i	−0.661165	+	1.14517i	0.319145	+	0.947706i	$0.396604\pi$
$337$	−12.1374	+	21.0226i	−0.661165	+	1.14517i	−0.980310	+	0.197466i	$0.936729\pi$
$338$	−6.47818	−	11.2205i	−0.352366	−	0.610317i
$339$	−10.0268	+	17.3669i	−0.544581	+	0.943242i
$340$	−28.0424	−	16.1903i	−1.52081	−	0.878041i
$341$	−11.5040	+	15.1471i	−0.622975	+	0.820260i
$342$	−11.5260	+	0.867985i	−0.623255	+	0.0469352i
$343$		−	16.2946i		−	0.879828i
$344$	−8.75986	−	5.05751i	−0.472300	−	0.272683i
$345$	50.6281	+	29.2302i	2.72573	+	1.57370i
$346$	−8.03663	−	13.9199i	−0.432052	−	0.748336i
$347$	4.56471	+	2.63543i	0.245046	+	0.141478i	0.617494	−	0.786576i	$-0.288148\pi$
$347$	4.56471	+	2.63543i	0.245046	+	0.141478i	−0.372448	+	0.928053i	$0.621481\pi$
$348$	−7.04495	+	4.06740i	−0.377649	+	0.218036i
$349$			28.0429i			1.50110i	0.660814	+	0.750550i	$0.270211\pi$
$349$			28.0429i			1.50110i	−0.660814	+	0.750550i	$0.729789\pi$
$350$			34.5655i			1.84761i
$351$	0.149791	−	0.0864817i	0.00799523	−	0.00461605i
$352$	−0.416609	+	3.29036i	−0.0222053	+	0.175377i
$353$	−14.0652			−0.748613			−0.374307	−	0.927305i	$-0.622119\pi$
$353$	−14.0652			−0.748613			−0.374307	+	0.927305i	$0.622119\pi$
$354$	32.6039			1.73288
$355$	36.4385	−	21.0378i	1.93395	−	1.11657i
$356$	1.51651	+	0.875555i	0.0803747	+	0.0464043i
$357$	−46.8377	+	27.0417i	−2.47891	+	1.43120i
$358$	6.01430	+	3.47236i	0.317866	+	0.183520i
$359$	18.0546	+	10.4238i	0.952886	+	0.550149i	0.893976	−	0.448114i	$-0.147904\pi$
$359$	18.0546	+	10.4238i	0.952886	+	0.550149i	0.0589096	+	0.998263i	$0.481238\pi$
$360$	−10.9173			−0.575392
$361$	18.7857	−	2.84552i	0.988722	−	0.149764i
$362$			9.69398i			0.509504i
$363$	6.51767	−	25.3255i	0.342089	−	1.32924i
$364$	0.523307	+	0.302131i	0.0274287	+	0.0158360i
$365$	−2.68735	+	1.55154i	−0.140662	+	0.0812114i
$366$	0.643273	−	1.11418i	0.0336244	−	0.0582392i
$367$	11.1016	+	19.2285i	0.579498	+	1.00372i	0.995537	+	0.0943731i	$0.0300847\pi$
$367$	11.1016	+	19.2285i	0.579498	+	1.00372i	−0.416039	+	0.909347i	$0.636582\pi$
$368$	5.97290			0.311359
$369$	−4.08338			−0.212572
$370$	−4.92593	+	2.84399i	−0.256087	+	0.147852i
$371$	−7.60799	−	13.1774i	−0.394987	−	0.684138i
$372$	−13.6337			−0.706875
$373$	6.46707			0.334852			0.167426	−	0.985885i	$-0.446454\pi$
$373$	6.46707			0.334852			0.167426	+	0.985885i	$0.446454\pi$
$374$	25.8787	+	3.27663i	1.33815	+	0.169431i
$375$	58.9105	+	34.0120i	3.04212	+	1.75637i
$376$	−1.26444	−	2.19008i	−0.0652086	−	0.112945i
$377$	0.357419	−	0.619067i	0.0184080	−	0.0318836i
$378$	1.19742	−	2.07400i	0.0615888	−	0.106675i
$379$		−	0.426001i		−	0.0218822i	−0.999940	−	0.0109411i	$-0.996517\pi$
$379$		−	0.426001i		−	0.0218822i	0.999940	−	0.0109411i	$-0.00348273\pi$
$380$	17.8951	−	1.34762i	0.917999	−	0.0691314i
$381$			17.0024i			0.871060i
$382$	4.74222	−	8.21377i	0.242633	−	0.420253i
$383$	24.5478	+	14.1727i	1.25434	+	0.724192i	0.971968	−	0.235114i	$-0.0755465\pi$
$383$	24.5478	+	14.1727i	1.25434	+	0.724192i	0.282369	+	0.959306i	$0.408880\pi$
$384$	−2.05883	+	1.18867i	−0.105064	+	0.0606590i
$385$	−15.2952	−	36.4145i	−0.779515	−	1.85585i
$386$	7.93328	+	13.7408i	0.403793	+	0.699390i
$387$			26.8223i			1.36346i
$388$		−	7.48001i		−	0.379740i
$389$	14.1486	+	24.5061i	0.717362	+	1.24251i	0.962041	+	0.272904i	$0.0879841\pi$
$389$	14.1486	+	24.5061i	0.717362	+	1.24251i	−0.244679	+	0.969604i	$0.578683\pi$
$390$	1.77075	−	1.02234i	0.0896654	−	0.0517684i
$391$		−	46.9769i		−	2.37573i
$392$	1.36661			0.0690241
$393$	16.3662	+	28.3470i	0.825564	+	1.42992i
$394$	4.74313	+	2.73845i	0.238956	+	0.137961i
$395$	−21.1158	−	36.5736i	−1.06245	−	1.84022i
$396$	8.10856	−	3.40584i	0.407471	−	0.171150i
$397$	2.81213	−	4.87076i	0.141137	−	0.244456i	−0.786788	−	0.617223i	$-0.788258\pi$
$397$	2.81213	−	4.87076i	0.141137	−	0.244456i	0.927925	+	0.372767i	$0.121591\pi$
$398$	0.925669			0.0463996
$399$	12.9953	−	27.0102i	0.650579	−	1.35220i
$400$	11.9500			0.597501
$401$	−23.1090	−	13.3420i	−1.15401	−	0.666267i	−0.204147	−	0.978940i	$-0.565442\pi$
$401$	−23.1090	−	13.3420i	−1.15401	−	0.666267i	−0.949861	+	0.312673i	$0.898775\pi$
$402$	−1.57450	+	2.72711i	−0.0785288	+	0.136016i
$403$	1.03754	−	0.599024i	0.0516835	−	0.0298395i
$404$	6.35893	+	3.67133i	0.316369	+	0.182656i
$405$	−20.4277	−	35.3819i	−1.01506	−	1.75814i
$406$		−	9.89763i		−	0.491211i
$407$	2.77139	−	3.64904i	0.137373	−	0.180876i
$408$	9.34889	+	16.1928i	0.462839	+	0.801661i
$409$	−10.3114	−	17.8599i	−0.509866	−	0.883113i	−0.999935	−	0.0114297i	$-0.996362\pi$
$409$	−10.3114	−	17.8599i	−0.509866	−	0.883113i	0.490069	−	0.871684i	$-0.336972\pi$
$410$	6.33979			0.313100
$411$		−	28.5208i		−	1.40683i
$412$	−3.49116	+	2.01562i	−0.171997	+	0.0993025i
$413$	−19.8346	+	34.3546i	−0.975998	+	1.69048i
$414$	−7.91927	−	13.7166i	−0.389211	−	0.674133i
$415$	−9.96312	−	5.75221i	−0.489070	−	0.282365i
$416$	0.104453	−	0.180918i	0.00512123	−	0.00887023i
$417$	42.1502			2.06410
$418$	−12.8707	+	6.58360i	−0.629529	+	0.322015i
$419$	−10.4193			−0.509017			−0.254508	−	0.967071i	$-0.581914\pi$
$419$	−10.4193			−0.509017			−0.254508	+	0.967071i	$0.581914\pi$
$420$	14.1553	−	24.5178i	0.690710	−	1.19635i
$421$	22.8027	+	13.1652i	1.11134	+	0.641631i	0.939176	−	0.343437i	$-0.111591\pi$
$421$	22.8027	+	13.1652i	1.11134	+	0.641631i	0.172162	+	0.985069i	$0.444925\pi$
$422$	6.95552	+	12.0473i	0.338589	+	0.586454i
$423$	−3.35296	+	5.80750i	−0.163026	+	0.282370i
$424$	−4.55571	+	2.63024i	−0.221245	+	0.127736i
$425$		−	93.9870i		−	4.55904i
$426$	−24.2960			−1.17715
$427$	0.782670	+	1.35562i	0.0378761	+	0.0656033i
$428$	7.30899	+	12.6595i	0.353293	+	0.611922i
$429$	−0.996246	+	1.31174i	−0.0480992	+	0.0633313i
$430$		−	41.6439i		−	2.00825i
$431$	5.62366	+	9.74047i	0.270882	+	0.469182i	0.969088	−	0.246715i	$-0.0793513\pi$
$431$	5.62366	+	9.74047i	0.270882	+	0.469182i	−0.698206	+	0.715897i	$0.746018\pi$
$432$	−0.717024	−	0.413974i	−0.0344978	−	0.0199173i
$433$	−8.79087	+	5.07541i	−0.422462	+	0.243909i	−0.696130	−	0.717916i	$-0.745096\pi$
$433$	−8.79087	+	5.07541i	−0.422462	+	0.243909i	0.273668	+	0.961824i	$0.411763\pi$
$434$	8.29407	−	14.3658i	0.398128	−	0.689578i
$435$	−29.0043	−	16.7457i	−1.39065	−	0.802893i
$436$	1.99351			0.0954719
$437$	14.6740	+	21.5060i	0.701955	+	1.02877i
$438$	1.79184			0.0856175
$439$	−2.36184	+	4.09083i	−0.112725	+	0.195245i	−0.916868	−	0.399191i	$-0.869291\pi$
$439$	−2.36184	+	4.09083i	−0.112725	+	0.195245i	0.804143	+	0.594435i	$0.202624\pi$
$440$	−12.5892	+	5.28786i	−0.600168	+	0.252089i
$441$	−1.81194	−	3.13837i	−0.0862828	−	0.149446i
$442$	−1.42292	−	0.821524i	−0.0676814	−	0.0390759i
$443$	4.66895	+	8.08686i	0.221828	+	0.384218i	0.955363	−	0.295434i	$-0.0954642\pi$
$443$	4.66895	+	8.08686i	0.221828	+	0.384218i	−0.733535	+	0.679652i	$0.762131\pi$
$444$	3.28445			0.155873
$445$			7.20939i			0.341758i
$446$	5.43448	−	3.13760i	0.257330	−	0.148570i
$447$	21.5405	+	37.3093i	1.01883	+	1.76467i
$448$		−	2.89251i		−	0.136658i
$449$			40.1504i			1.89481i	0.320033	+	0.947406i	$0.396306\pi$
$449$			40.1504i			1.89481i	−0.320033	+	0.947406i	$0.603694\pi$
$450$	−15.8441	−	27.4428i	−0.746899	−	1.29367i
$451$	−4.70873	+	1.97781i	−0.221725	+	0.0931314i
$452$	−7.30520	+	4.21766i	−0.343608	+	0.198382i
$453$	−19.6281	−	11.3323i	−0.922210	−	0.532438i
$454$	12.0889	−	20.9386i	0.567361	−	0.982698i
$455$			2.48777i			0.116629i
$456$	−9.33800	−	4.49274i	−0.437292	−	0.210392i
$457$			5.85807i			0.274029i	0.990569	+	0.137014i	$0.0437507\pi$
$457$			5.85807i			0.274029i	−0.990569	+	0.137014i	$0.956249\pi$
$458$	5.83351	−	10.1039i	0.272582	−	0.472126i
$459$	−3.25591	+	5.63940i	−0.151973	+	0.263225i
$460$	12.2953	+	21.2962i	0.573273	+	0.992938i
$461$	−2.97342	−	1.71670i	−0.138486	−	0.0799548i	0.429156	−	0.903230i	$-0.358811\pi$
$461$	−2.97342	−	1.71670i	−0.138486	−	0.0799548i	−0.567642	+	0.823275i	$0.692144\pi$
$462$	−2.86480	+	22.6260i	−0.133282	+	1.05266i
$463$	38.2076			1.77566			0.887830	−	0.460172i	$-0.152212\pi$
$463$	38.2076			1.77566			0.887830	+	0.460172i	$0.152212\pi$
$464$	−3.42181			−0.158854
$465$	−28.0652	−	48.6104i	−1.30149	−	2.25426i
$466$	−20.5498	+	11.8644i	−0.951950	+	0.549608i
$467$	23.8110			1.10184			0.550920	−	0.834558i	$-0.314277\pi$
$467$	23.8110			1.10184			0.550920	+	0.834558i	$0.314277\pi$
$468$	−0.553963			−0.0256069
$469$	−1.91569	−	3.31808i	−0.0884584	−	0.153214i
$470$	5.20575	−	9.01663i	0.240124	−	0.415906i
$471$	2.26759	−	1.30920i	0.104485	−	0.0603245i
$472$	11.8771	+	6.85724i	0.546687	+	0.315630i
$473$	12.9916	+	30.9301i	0.597353	+	1.42217i
$474$			24.3861i			1.12009i
$475$	29.3584	+	43.0272i	1.34706	+	1.97422i
$476$	−22.7496			−1.04273
$477$	12.0805	+	6.97469i	0.553129	+	0.319349i
$478$	1.68327	+	0.971835i	0.0769908	+	0.0444507i
$479$	9.02381	−	5.20990i	0.412308	−	0.238046i	−0.279473	−	0.960154i	$-0.590160\pi$
$479$	9.02381	−	5.20990i	0.412308	−	0.238046i	0.691781	+	0.722107i	$0.256826\pi$
$480$	−8.47630	−	4.89380i	−0.386889	−	0.223370i
$481$	−0.249950	+	0.144309i	−0.0113968	+	0.00657992i
$482$	0.853990			0.0388982
$483$	41.0725			1.86886
$484$	7.70072	−	7.85487i	0.350033	−	0.357039i
$485$	26.6697	−	15.3977i	1.21101	−	0.699175i
$486$			21.1077i			0.957464i
$487$		−	34.0280i		−	1.54196i	−0.636861	−	0.770979i	$-0.719768\pi$
$487$		−	34.0280i		−	1.54196i	0.636861	−	0.770979i	$-0.280232\pi$
$488$	0.468667	−	0.270585i	0.0212156	−	0.0122488i
$489$	−22.3214	−	12.8872i	−1.00941	−	0.582781i
$490$	2.81319	+	4.87259i	0.127087	+	0.220121i
$491$	13.8599	+	8.00204i	0.625490	+	0.361127i	0.779003	−	0.627020i	$-0.215725\pi$
$491$	13.8599	+	8.00204i	0.625490	+	0.361127i	−0.153513	+	0.988147i	$0.549059\pi$
$492$	−3.17038	−	1.83042i	−0.142932	−	0.0825216i
$493$			26.9126i			1.21208i
$494$	0.908029	−	0.0683806i	0.0408542	−	0.00307659i
$495$	28.8350	+	21.8998i	1.29604	+	0.984322i
$496$	−4.96654	−	2.86743i	−0.223004	−	0.128751i
$497$	14.7805	−	25.6006i	0.662996	−	1.14834i
$498$	3.32155	+	5.75309i	0.148842	+	0.257802i
$499$	−11.3717	+	19.6964i	−0.509069	+	0.881734i	0.490876	+	0.871230i	$0.336677\pi$
$499$	−11.3717	+	19.6964i	−0.509069	+	0.881734i	−0.999945	+	0.0105041i	$0.996656\pi$
$500$	14.3067	+	24.7800i	0.639817	+	1.10820i
$501$		−	37.9618i		−	1.69601i
$502$	−15.8580			−0.707776
$503$	−6.92306	+	3.99703i	−0.308684	+	0.178219i	−0.646337	−	0.763052i	$-0.723700\pi$
$503$	−6.92306	+	3.99703i	−0.308684	+	0.178219i	0.337654	+	0.941270i	$0.390367\pi$
$504$	−6.64255	+	3.83508i	−0.295883	+	0.170828i
$505$			30.2300i			1.34522i
$506$	−15.7758	−	11.9815i	−0.701319	−	0.532641i
$507$	−26.6750	+	15.4008i	−1.18468	+	0.683974i
$508$	−3.57594	+	6.19370i	−0.158656	+	0.274801i
$509$	−14.5797	+	8.41761i	−0.646235	+	0.373104i	−0.787012	−	0.616937i	$-0.788373\pi$
$509$	−14.5797	+	8.41761i	−0.646235	+	0.373104i	0.140777	+	0.990041i	$0.455040\pi$
$510$	−38.4897	+	66.6662i	−1.70435	+	2.95203i
$511$	−1.09007	+	1.88805i	−0.0482217	+	0.0835225i
$512$	−1.00000			−0.0441942
$513$	−0.271010	−	3.59875i	−0.0119654	−	0.158889i
$514$			13.1978i			0.582131i
$515$	−14.3732	−	8.29839i	−0.633361	−	0.365671i
$516$	−12.0234	+	20.8251i	−0.529301	+	0.916776i
$517$	−1.05355	+	8.32092i	−0.0463353	+	0.365954i
$518$	−1.99810	+	3.46081i	−0.0877915	+	0.152059i
$519$	−33.0922	+	19.1058i	−1.45259	+	0.838651i
$520$	0.860074			0.0377167
$521$		−	16.4377i		−	0.720147i	−0.932924	−	0.360074i	$-0.882752\pi$
$521$		−	16.4377i		−	0.720147i	0.932924	−	0.360074i	$-0.117248\pi$
$522$	4.53687	+	7.85809i	0.198573	+	0.343939i
$523$	−8.40588	−	14.5594i	−0.367563	−	0.636639i	0.621621	−	0.783319i	$-0.286475\pi$
$523$	−8.40588	−	14.5594i	−0.367563	−	0.636639i	−0.989184	+	0.146680i	$0.953141\pi$
$524$			13.7685i			0.601479i
$525$	82.1739			3.58636
$526$	4.87621	−	2.81528i	0.212613	−	0.122752i
$527$	−22.5524	+	39.0619i	−0.982397	+	1.70156i
$528$	7.82228	+	0.990420i	0.340421	+	0.0431025i
$529$	−6.33779	+	10.9774i	−0.275556	+	0.477277i
$530$	−18.7560	−	10.8288i	−0.814710	−	0.470373i
$531$		−	36.3671i		−	1.57820i
$532$	10.4148	−	7.10623i	0.451537	−	0.308094i
$533$	0.321692			0.0139340
$534$	2.08149	−	3.60525i	0.0900749	−	0.156014i
$535$	−30.0914	+	52.1198i	−1.30096	+	2.25334i
$536$	−1.14713	+	0.662294i	−0.0495483	+	0.0286067i
$537$	8.25497	−	14.2980i	0.356228	−	0.617006i
$538$	2.27078	−	1.31103i	0.0979001	−	0.0565227i
$539$	−3.60952	−	2.74138i	−0.155473	−	0.118079i
$540$		−	3.40870i		−	0.146687i
$541$	−20.9237	+	12.0803i	−0.899579	+	0.519372i	−0.877064	−	0.480374i	$-0.840501\pi$
$541$	−20.9237	+	12.0803i	−0.899579	+	0.519372i	−0.0225155	+	0.999746i	$0.507168\pi$
$542$	11.6079	−	6.70182i	0.498602	−	0.287868i
$543$	23.0458			0.988992
$544$			7.86501i			0.337209i
$545$	4.10369	+	7.10779i	0.175783	+	0.304464i
$546$	0.718268	−	1.24408i	0.0307390	−	0.0532415i
$547$	0.638424	+	1.10578i	0.0272970	+	0.0472799i	0.879351	−	0.476174i	$-0.157977\pi$
$547$	0.638424	+	1.10578i	0.0272970	+	0.0472799i	−0.852054	+	0.523454i	$0.824643\pi$
$548$	5.99847	−	10.3897i	0.256242	−	0.443824i
$549$	−1.24278	−	0.717520i	−0.0530406	−	0.0306230i
$550$	−31.5627	−	23.9714i	−1.34584	−	1.02214i
$551$	−8.40661	−	12.3206i	−0.358134	−	0.524874i
$552$		−	14.1996i		−	0.604375i
$553$	−25.6955	−	14.8353i	−1.09268	−	0.630862i
$554$	−16.0375	−	9.25926i	−0.681369	−	0.393388i
$555$	6.76112	+	11.7106i	0.286993	+	0.497087i
$556$	15.3546	+	8.86499i	0.651181	+	0.375959i
$557$	−14.8404	+	8.56810i	−0.628807	+	0.363042i	−0.780290	−	0.625418i	$-0.784929\pi$
$557$	−14.8404	+	8.56810i	−0.628807	+	0.363042i	0.151483	+	0.988460i	$0.451595\pi$
$558$			15.2073i			0.643777i
$559$		−	2.11309i		−	0.0893741i
$560$	10.3131	−	5.95429i	0.435809	−	0.251615i
$561$	7.78966	−	61.5223i	0.328880	−	2.59747i
$562$	4.10553			0.173181
$563$	−14.2144			−0.599064			−0.299532	−	0.954086i	$-0.596830\pi$
$563$	−14.2144			−0.599064			−0.299532	+	0.954086i	$0.596830\pi$
$564$	−5.20655	+	3.00600i	−0.219235	+	0.126576i
$565$	−30.0758	−	17.3643i	−1.26530	−	0.730520i
$566$	6.72522	−	3.88280i	0.282682	−	0.163206i
$567$	−24.8583	−	14.3519i	−1.04395	−	0.602724i
$568$	−8.85065	−	5.10993i	−0.371365	−	0.214408i
$569$	−5.08546			−0.213193			−0.106597	−	0.994302i	$-0.533995\pi$
$569$	−5.08546			−0.213193			−0.106597	+	0.994302i	$0.533995\pi$
$570$	−3.20375	−	42.5427i	−0.134190	−	1.78192i
$571$		−	22.1623i		−	0.927462i	−0.885976	−	0.463731i	$-0.846510\pi$
$571$		−	22.1623i		−	0.927462i	0.885976	−	0.463731i	$-0.153490\pi$
$572$	−0.638800	+	0.268315i	−0.0267096	+	0.0112188i
$573$	−19.5269	−	11.2739i	−0.815748	−	0.470972i
$574$	3.85740	−	2.22707i	0.161005	−	0.0929562i
$575$	−35.6881	+	61.8137i	−1.48830	+	2.57781i
$576$	1.32587	+	2.29647i	0.0552444	+	0.0956862i
$577$	−15.8208			−0.658629			−0.329315	−	0.944220i	$-0.606818\pi$
$577$	−15.8208			−0.658629			−0.329315	+	0.944220i	$0.606818\pi$
$578$	44.8584			1.86586
$579$	32.6666	−	18.8601i	1.35758	−	0.783798i
$580$	−7.04387	−	12.2003i	−0.292481	−	0.506592i
$581$	−8.08266			−0.335325
$582$	−17.7825			−0.737108
$583$	17.3088	+	2.19156i	0.716859	+	0.0907652i
$584$	0.652738	+	0.376859i	0.0270105	+	0.0155945i
$585$	−1.14034	−	1.97513i	−0.0471474	−	0.0816617i
$586$	−12.5413	+	21.7221i	−0.518075	+	0.897333i
$587$	−12.4134	+	21.5007i	−0.512358	+	0.887429i	0.487540	+	0.873101i	$0.337894\pi$
$587$	−12.4134	+	21.5007i	−0.512358	+	0.887429i	−0.999897	+	0.0143285i	$0.995439\pi$
$588$		−	3.24889i		−	0.133982i
$589$	−1.87718	−	24.9271i	−0.0773477	−	1.02710i
$590$			56.4631i			2.32455i
$591$	6.51022	−	11.2760i	0.267795	−	0.463834i
$592$	1.19647	+	0.690784i	0.0491748	+	0.0283911i
$593$	−5.09675	+	2.94261i	−0.209298	+	0.120838i	−0.600985	−	0.799260i	$-0.705225\pi$
$593$	−5.09675	+	2.94261i	−0.209298	+	0.120838i	0.391687	+	0.920099i	$0.371892\pi$
$594$	1.06340	+	2.53173i	0.0436320	+	0.103878i
$595$	−46.8305	−	81.1128i	−1.91986	−	3.32530i
$596$			18.1215i			0.742288i
$597$		−	2.20063i		−	0.0900656i
$598$	0.623888	+	1.08060i	0.0255127	+	0.0441892i
$599$	9.66182	−	5.57826i	0.394771	−	0.227921i	−0.289454	−	0.957192i	$-0.593474\pi$
$599$	9.66182	−	5.57826i	0.394771	−	0.227921i	0.684225	+	0.729271i	$0.260140\pi$
$600$		−	28.4092i		−	1.15980i
$601$	25.4755			1.03917			0.519584	−	0.854419i	$-0.326087\pi$
$601$	25.4755			1.03917			0.519584	+	0.854419i	$0.326087\pi$
$602$	−14.6289	−	25.3380i	−0.596229	−	1.03270i
$603$	3.04187	+	1.75623i	0.123875	+	0.0715191i
$604$	−4.76680	−	8.25635i	−0.193958	−	0.335946i
$605$	43.8583	+	11.2872i	1.78309	+	0.458890i
$606$	8.72800	−	15.1173i	0.354551	−	0.614100i
$607$	3.07959			0.124997			0.0624983	−	0.998045i	$-0.480093\pi$
$607$	3.07959			0.124997			0.0624983	+	0.998045i	$0.480093\pi$
$608$	−2.45677	−	3.60059i	−0.0996352	−	0.146023i
$609$	−23.5300			−0.953484
$610$	1.92952	+	1.11401i	0.0781241	+	0.0451050i
$611$	0.264149	−	0.457520i	0.0106863	−	0.0185093i
$612$	18.0617	−	10.4280i	0.730103	−	0.421525i
$613$	−11.7968	−	6.81088i	−0.476468	−	0.275089i	0.242476	−	0.970157i	$-0.422041\pi$
$613$	−11.7968	−	6.81088i	−0.476468	−	0.275089i	−0.718943	+	0.695069i	$0.755374\pi$
$614$	−16.5060	−	28.5892i	−0.666128	−	1.15377i
$615$		−	15.0718i		−	0.607754i
$616$	−5.80229	+	7.63977i	−0.233781	+	0.307815i
$617$	−22.9455	−	39.7428i	−0.923753	−	1.59999i	−0.793555	−	0.608498i	$-0.791772\pi$
$617$	−22.9455	−	39.7428i	−0.923753	−	1.59999i	−0.130197	−	0.991488i	$-0.541561\pi$
$618$	4.79181	+	8.29966i	0.192755	+	0.333861i
$619$	−21.7810			−0.875451			−0.437726	−	0.899109i	$-0.644216\pi$
$619$	−21.7810			−0.875451			−0.437726	+	0.899109i	$0.644216\pi$
$620$		−	23.6107i		−	0.948227i
$621$	4.28272	−	2.47263i	0.171859	−	0.0992231i
$622$	−7.48545	+	12.9652i	−0.300139	+	0.519856i
$623$	2.53255	+	4.38651i	0.101465	+	0.175742i
$624$	−0.430103	−	0.248320i	−0.0172179	−	0.00994075i
$625$	−29.0264	+	50.2752i	−1.16106	+	2.01101i
$626$	13.8215			0.552418
$627$	15.6514	+	30.5981i	0.625059	+	1.22197i
$628$	1.10140			0.0439505
$629$	5.43302	−	9.41027i	0.216629	−	0.375212i
$630$	−27.3477	−	15.7892i	−1.08956	−	0.629056i
$631$	4.81721	+	8.34366i	0.191770	+	0.332156i	0.945837	−	0.324642i	$-0.105244\pi$
$631$	4.81721	+	8.34366i	0.191770	+	0.332156i	−0.754067	+	0.656798i	$0.771910\pi$
$632$	−5.12887	+	8.88347i	−0.204016	+	0.353365i
$633$	28.6405	−	16.5356i	1.13836	−	0.657232i
$634$		−	14.7298i		−	0.584996i
$635$	−29.4445			−1.16847
$636$	6.25297	+	10.8305i	0.247946	+	0.429455i
$637$	0.142746	+	0.247244i	0.00565581	+	0.00979615i
$638$	9.03779	+	6.86406i	0.357809	+	0.271751i
$639$			27.1003i			1.07207i
$640$	−2.05852	−	3.56546i	−0.0813701	−	0.140937i
$641$	15.1184	+	8.72863i	0.597142	+	0.344760i	0.767916	−	0.640550i	$-0.221294\pi$
$641$	15.1184	+	8.72863i	0.597142	+	0.344760i	−0.170774	+	0.985310i	$0.554627\pi$
$642$	30.0960	−	17.3759i	1.18779	−	0.685773i
$643$	−0.277171	+	0.480075i	−0.0109306	+	0.0189323i	−0.871439	−	0.490504i	$-0.836813\pi$
$643$	−0.277171	+	0.480075i	−0.0109306	+	0.0189323i	0.860508	+	0.509436i	$0.170146\pi$
$644$	14.9620	+	8.63834i	0.589587	+	0.340398i
$645$	−99.0016			−3.89819
$646$	−28.3187	+	19.3225i	−1.11418	+	0.760234i
$647$	10.0434			0.394846			0.197423	−	0.980318i	$-0.436743\pi$
$647$	10.0434			0.394846			0.197423	+	0.980318i	$0.436743\pi$
$648$	−4.96176	+	8.59401i	−0.194916	+	0.337605i
$649$	−17.6147	−	41.9366i	−0.691436	−	1.64616i
$650$	1.24821	+	2.16197i	0.0489590	+	0.0847995i
$651$	−34.1522	−	19.7178i	−1.33853	−	0.772802i
$652$	−5.42087	−	9.38922i	−0.212298	−	0.367710i
$653$	4.90757			0.192048			0.0960241	−	0.995379i	$-0.469387\pi$
$653$	4.90757			0.192048			0.0960241	+	0.995379i	$0.469387\pi$
$654$		−	4.73925i		−	0.185319i
$655$	−49.0910	+	28.3427i	−1.91814	+	1.10744i
$656$	−0.769945	−	1.33358i	−0.0300613	−	0.0520677i
$657$		−	1.99866i		−	0.0779751i
$658$		−	7.31481i		−	0.285161i
$659$	−11.8707	−	20.5607i	−0.462417	−	0.800930i	0.536664	−	0.843796i	$-0.319684\pi$
$659$	−11.8707	−	20.5607i	−0.462417	−	0.800930i	−0.999081	+	0.0428661i	$0.986351\pi$
$660$	12.5710	+	29.9288i	0.489326	+	1.16498i
$661$	3.90579	−	2.25501i	0.151918	−	0.0877097i	−0.422114	−	0.906543i	$-0.638712\pi$
$661$	3.90579	−	2.25501i	0.151918	−	0.0877097i	0.574032	+	0.818833i	$0.305379\pi$
$662$	−8.37771	−	4.83687i	−0.325609	−	0.187990i
$663$	−1.95304	+	3.38276i	−0.0758497	+	0.131376i
$664$			2.79434i			0.108441i
$665$	46.7760	+	22.5051i	1.81389	+	0.872710i
$666$		−	3.66355i		−	0.141960i
$667$	10.2191	−	17.7000i	0.395684	−	0.685346i
$668$	7.98411	−	13.8289i	0.308914	−	0.535055i
$669$	−7.45913	−	12.9196i	−0.288387	−	0.499500i
$670$	−4.72277	−	2.72669i	−0.182456	−	0.105341i
$671$	−1.78064	−	0.225456i	−0.0687410	−	0.00870365i
$672$	−6.87647			−0.265266
$673$	18.7039			0.720982			0.360491	−	0.932763i	$-0.382609\pi$
$673$	18.7039			0.720982			0.360491	+	0.932763i	$0.382609\pi$
$674$	12.1374	+	21.0226i	0.467514	+	0.809759i
$675$	8.56845	−	4.94700i	0.329800	−	0.190410i
$676$	−12.9564			−0.498321
$677$	−34.5108			−1.32636			−0.663179	−	0.748461i	$-0.730793\pi$
$677$	−34.5108			−1.32636			−0.663179	+	0.748461i	$0.730793\pi$
$678$	10.0268	+	17.3669i	0.385077	+	0.666972i
$679$	10.8180	−	18.7373i	0.415156	−	0.719072i
$680$	−28.0424	+	16.1903i	−1.07538	+	0.620869i
$681$	−49.7782	−	28.7394i	−1.90750	−	1.10130i
$682$	7.36576	+	17.5363i	0.282050	+	0.671498i
$683$		−	11.3951i		−	0.436023i	−0.975946	−	0.218011i	$-0.930043\pi$
$683$		−	11.3951i		−	0.436023i	0.975946	−	0.218011i	$-0.0699570\pi$
$684$	−5.01130	+	10.4158i	−0.191612	+	0.398258i
$685$	49.3919			1.88717
$686$	−14.1116	−	8.14732i	−0.538782	−	0.311066i
$687$	−24.0204	−	13.8682i	−0.916437	−	0.529105i
$688$	−8.75986	+	5.05751i	−0.333967	+	0.192816i
$689$	−0.951715	−	0.549473i	−0.0362574	−	0.0209332i
$690$	50.6281	−	29.2302i	1.92738	−	1.11277i
$691$	−6.53957			−0.248777			−0.124388	−	0.992234i	$-0.539697\pi$
$691$	−6.53957			−0.248777			−0.124388	+	0.992234i	$0.539697\pi$
$692$	−16.0733			−0.611014
$693$	25.2376	+	3.19546i	0.958695	+	0.121385i
$694$	4.56471	−	2.63543i	0.173274	−	0.100040i
$695$			72.9951i			2.76886i
$696$			8.13481i			0.308349i
$697$	−10.4886	+	6.05562i	−0.397286	+	0.229373i
$698$	24.2858	+	14.0214i	0.919232	+	0.530719i
$699$	28.2057	+	48.8537i	1.06684	+	1.84782i
$700$	29.9346	+	17.2828i	1.13142	+	0.653227i
$701$	6.55712	+	3.78576i	0.247659	+	0.142986i	0.618692	−	0.785634i	$-0.287663\pi$
$701$	6.55712	+	3.78576i	0.247659	+	0.142986i	−0.371033	+	0.928620i	$0.620996\pi$
$702$		−	0.172963i		−	0.00652808i
$703$	0.452225	+	6.00511i	0.0170560	+	0.226487i
$704$	2.64123	+	2.00597i	0.0995450	+	0.0756029i
$705$	−21.4356	−	12.3758i	−0.807310	−	0.466101i
$706$	−7.03258	+	12.1808i	−0.264675	+	0.458430i
$707$	10.6194	+	18.3933i	0.399382	+	0.691750i
$708$	16.3020	−	28.2358i	0.612666	−	1.06117i
$709$	−23.6585	−	40.9777i	−0.888512	−	1.53895i	−0.841634	−	0.540048i	$-0.818406\pi$
$709$	−23.6585	−	40.9777i	−0.888512	−	1.53895i	−0.0468779	−	0.998901i	$-0.514927\pi$
$710$		−	42.0755i		−	1.57907i
$711$	27.2008			1.02011
$712$	1.51651	−	0.875555i	0.0568335	−	0.0328128i
$713$	29.6646	−	17.1269i	1.11095	−	0.641407i
$714$			54.0835i			2.02402i
$715$	−2.27165	−	1.72528i	−0.0849549	−	0.0645220i
$716$	6.01430	−	3.47236i	0.224765	−	0.129768i
$717$	2.31038	−	4.00169i	0.0862827	−	0.149446i
$718$	18.0546	−	10.4238i	0.673792	−	0.389014i
$719$	17.1946	−	29.7820i	0.641251	−	1.11068i	−0.343902	−	0.939005i	$-0.611749\pi$
$719$	17.1946	−	29.7820i	0.641251	−	1.11068i	0.985154	−	0.171674i	$-0.0549177\pi$
$720$	−5.45865	+	9.45465i	−0.203432	+	0.352354i
$721$	−11.6604			−0.434256
$722$	6.92857	−	17.6917i	0.257855	−	0.658416i
$723$		−	2.03022i		−	0.0755047i
$724$	8.39523	+	4.84699i	0.312006	+	0.180137i
$725$	20.4454	−	35.4124i	0.759322	−	1.31518i
$726$	−18.6737	−	18.3072i	−0.693045	−	0.679444i
$727$	2.74546	−	4.75527i	0.101823	−	0.176363i	−0.810613	−	0.585583i	$-0.800866\pi$
$727$	2.74546	−	4.75527i	0.101823	−	0.176363i	0.912436	+	0.409220i	$0.134199\pi$
$728$	0.523307	−	0.302131i	0.0193950	−	0.0111977i
$729$	20.4096			0.755910
$730$			3.10308i			0.114850i
$731$	39.7773	+	68.8964i	1.47122	+	2.54822i
$732$	−0.643273	−	1.11418i	−0.0237760	−	0.0411813i
$733$			8.14616i			0.300885i	0.988619	+	0.150443i	$0.0480699\pi$
$733$			8.14616i			0.300885i	−0.988619	+	0.150443i	$0.951930\pi$
$734$	22.2032			0.819534
$735$	11.5838	−	6.68790i	0.427274	−	0.246687i
$736$	2.98645	−	5.17269i	0.110082	−	0.190668i
$737$	4.35837	+	0.551835i	0.160542	+	0.0203271i
$738$	−2.04169	+	3.53631i	−0.0751556	+	0.130173i
$739$	15.5031	+	8.95072i	0.570291	+	0.329258i	0.757266	−	0.653107i	$-0.226535\pi$
$739$	15.5031	+	8.95072i	0.570291	+	0.329258i	−0.186975	+	0.982365i	$0.559868\pi$
$740$			5.68797i			0.209094i
$741$	−0.162564	−	2.15869i	−0.00597193	−	0.0793015i
$742$	−15.2160			−0.558596
$743$	5.42069	−	9.38892i	0.198866	−	0.344446i	−0.749295	−	0.662236i	$-0.769607\pi$
$743$	5.42069	−	9.38892i	0.198866	−	0.344446i	0.948161	+	0.317790i	$0.102941\pi$
$744$	−6.81685	+	11.8071i	−0.249918	+	0.432871i
$745$	−64.6117	+	37.3036i	−2.36719	+	1.36670i
$746$	3.23353	−	5.60065i	0.118388	−	0.205054i
$747$	6.41712	−	3.70492i	0.234790	−	0.135556i
$748$	15.7770	−	20.7733i	0.576864	−	0.759546i
$749$			42.2826i			1.54497i
$750$	58.9105	−	34.0120i	2.15111	−	1.24194i
$751$	−33.0185	+	19.0632i	−1.20486	+	0.695628i	−0.961632	−	0.274341i	$-0.911540\pi$
$751$	−33.0185	+	19.0632i	−1.20486	+	0.695628i	−0.243230	+	0.969969i	$0.578207\pi$
$752$	−2.52888			−0.0922188
$753$			37.6997i			1.37385i
$754$	−0.357419	−	0.619067i	−0.0130164	−	0.0225451i
$755$	19.6251	−	33.9917i	0.714231	−	1.23708i
$756$	−1.19742	−	2.07400i	−0.0435499	−	0.0754306i
$757$	4.46473	−	7.73314i	0.162273	−	0.281066i	−0.773410	−	0.633906i	$-0.781451\pi$
$757$	4.46473	−	7.73314i	0.162273	−	0.281066i	0.935684	+	0.352840i	$0.114784\pi$
$758$	−0.368928	−	0.213001i	−0.0134001	−	0.00773653i
$759$	−28.4840	+	37.5044i	−1.03390	+	1.36132i
$760$	7.78047	−	16.1714i	0.282227	−	0.586599i
$761$		−	0.813615i		−	0.0294935i	−0.999891	−	0.0147468i	$-0.995306\pi$
$761$		−	0.813615i		−	0.0294935i	0.999891	−	0.0147468i	$-0.00469421\pi$
$762$	14.7245	+	8.50120i	0.533413	+	0.307966i
$763$	4.99372	+	2.88313i	0.180785	+	0.104376i
$764$	−4.74222	−	8.21377i	−0.171568	−	0.297164i
$765$	74.3609	+	42.9323i	2.68852	+	1.55222i
$766$	24.5478	−	14.1727i	0.886950	−	0.512081i
$767$			2.86504i			0.103450i
$768$			2.37734i			0.0857848i
$769$	−26.8508	+	15.5023i	−0.968266	+	0.559029i	−0.898707	−	0.438549i	$-0.855492\pi$
$769$	−26.8508	+	15.5023i	−0.968266	+	0.559029i	−0.0695588	+	0.997578i	$0.522159\pi$
$770$	−39.1834	−	4.96122i	−1.41207	−	0.178790i
$771$	31.3757			1.12997
$772$	15.8666			0.571050
$773$	−40.1948	+	23.2065i	−1.44571	+	0.834678i	−0.998222	−	0.0596140i	$-0.981013\pi$
$773$	−40.1948	+	23.2065i	−1.44571	+	0.834678i	−0.447484	+	0.894292i	$0.647680\pi$
$774$	23.2288	+	13.4112i	0.834942	+	0.482054i
$775$	59.3502	−	34.2659i	2.13192	−	1.23087i
$776$	−6.47787	−	3.74000i	−0.232542	−	0.134258i
$777$	8.22751	+	4.75016i	0.295160	+	0.170411i
$778$	28.2972			1.01450
$779$	2.91012	−	6.04857i	0.104266	−	0.216712i
$780$		−	2.04469i		−	0.0732115i
$781$	13.1262	+	31.2506i	0.469693	+	1.11824i
$782$	−40.6832	−	23.4885i	−1.45483	−	0.839946i
$783$	−2.45352	+	1.41654i	−0.0876818	+	0.0506231i
$784$	0.683304	−	1.18352i	0.0244037	−	0.0422685i
$785$	2.26725	+	3.92699i	0.0809215	+	0.140160i
$786$	32.7323			1.16752
$787$	35.7984			1.27608			0.638038	−	0.770005i	$-0.279746\pi$
$787$	35.7984			1.27608			0.638038	+	0.770005i	$0.279746\pi$
$788$	4.74313	−	2.73845i	0.168967	−	0.0975532i
$789$	−6.69287	−	11.5924i	−0.238272	−	0.412700i
$790$	−42.2316			−1.50253
$791$	−24.3992			−0.867537
$792$	1.10474	−	8.72514i	0.0392551	−	0.310034i
$793$	0.0979074	+	0.0565269i	0.00347679	+	0.00200733i
$794$	−2.81213	−	4.87076i	−0.0997989	−	0.172857i
$795$	−25.7437	+	44.5894i	−0.913035	+	1.58142i
$796$	0.462834	−	0.801652i	0.0164047	−	0.0284138i
$797$		−	23.2256i		−	0.822691i	−0.911479	−	0.411346i	$-0.865059\pi$
$797$		−	23.2256i		−	0.822691i	0.911479	−	0.411346i	$-0.134941\pi$
$798$	−16.8939	−	24.7594i	−0.598038	−	0.876473i
$799$			19.8897i			0.703646i
$800$	5.97501	−	10.3490i	0.211248	−	0.365893i
$801$	−4.02137	−	2.32174i	−0.142088	−	0.0820346i
$802$	−23.1090	+	13.3420i	−0.816007	+	0.471122i
$803$	−0.968063	−	2.30474i	−0.0341622	−	0.0813327i
$804$	1.57450	+	2.72711i	0.0555282	+	0.0961777i
$805$			71.1288i			2.50696i
$806$		−	1.19805i		−	0.0421994i
$807$	−3.11677	−	5.39840i	−0.109715	−	0.190033i
$808$	6.35893	−	3.67133i	0.223707	−	0.129157i
$809$		−	6.59290i		−	0.231794i	−0.993261	−	0.115897i	$-0.963026\pi$
$809$		−	6.59290i		−	0.231794i	0.993261	−	0.115897i	$-0.0369742\pi$
$810$	−40.8555			−1.43552
$811$	−7.58726	−	13.1415i	−0.266425	−	0.461461i	0.701511	−	0.712659i	$-0.252509\pi$
$811$	−7.58726	−	13.1415i	−0.266425	−	0.461461i	−0.967936	+	0.251197i	$0.919176\pi$
$812$	−8.57160	−	4.94881i	−0.300804	−	0.173669i
$813$	−15.9325	−	27.5959i	−0.558777	−	0.967830i
$814$	−1.77446	−	4.22461i	−0.0621949	−	0.148072i
$815$	22.3179	−	38.6558i	0.781763	−	1.35405i
$816$	18.6978			0.654553
$817$	−39.7310	−	19.1156i	−1.39001	−	0.668769i
$818$	−20.6228			−0.721059
$819$	−1.38767	−	0.801171i	−0.0484891	−	0.0279952i
$820$	3.16989	−	5.49042i	0.110697	−	0.191734i
$821$	−7.60682	+	4.39180i	−0.265480	+	0.153275i	−0.626832	−	0.779155i	$-0.715649\pi$
$821$	−7.60682	+	4.39180i	−0.265480	+	0.153275i	0.361352	+	0.932429i	$0.382315\pi$
$822$	−24.6997	−	14.2604i	−0.861502	−	0.497388i
$823$	16.1381	+	27.9520i	0.562538	+	0.974345i	0.997274	+	0.0737867i	$0.0235084\pi$
$823$	16.1381	+	27.9520i	0.562538	+	0.974345i	−0.434736	+	0.900558i	$0.643158\pi$
$824$			4.03124i			0.140435i
$825$	−56.9881	+	75.0352i	−1.98407	+	2.61239i
$826$	19.8346	+	34.3546i	0.690135	+	1.19535i
$827$	2.99933	+	5.19500i	0.104297	+	0.180648i	0.913451	−	0.406949i	$-0.133407\pi$
$827$	2.99933	+	5.19500i	0.104297	+	0.180648i	−0.809154	+	0.587597i	$0.800074\pi$
$828$	−15.8385			−0.550427
$829$			20.8779i			0.725120i	0.931960	+	0.362560i	$0.118097\pi$
$829$			20.8779i			0.725120i	−0.931960	+	0.362560i	$0.881903\pi$
$830$	−9.96312	+	5.75221i	−0.345825	+	0.199662i
$831$	−22.0124	+	38.1266i	−0.763601	+	1.32260i
$832$	−0.104453	−	0.180918i	−0.00362126	−	0.00627220i
$833$	−9.30837	−	5.37419i	−0.322516	−	0.186205i
$834$	21.0751	−	36.5031i	0.729770	−	1.26400i
$835$	65.7418			2.27509
$836$	−0.733805	+	14.4382i	−0.0253792	+	0.499355i
$837$	−4.74817			−0.164121
$838$	−5.20966	+	9.02339i	−0.179965	+	0.311708i
$839$	4.85591	+	2.80356i	0.167645	+	0.0967897i	0.581475	−	0.813564i	$-0.302476\pi$
$839$	4.85591	+	2.80356i	0.167645	+	0.0967897i	−0.413830	+	0.910354i	$0.635809\pi$
$840$	−14.1553	−	24.5178i	−0.488406	−	0.845944i
$841$	8.64559	−	14.9746i	0.298124	−	0.516366i
$842$	22.8027	−	13.1652i	0.785835	−	0.453702i
$843$		−	9.76022i		−	0.336160i
$844$	13.9110			0.478838
$845$	−26.6709	−	46.1954i	−0.917508	−	1.58917i
$846$	3.35296	+	5.80750i	0.115277	+	0.199666i
$847$	30.6503	−	8.53914i	1.05316	−	0.293408i
$848$			5.26048i			0.180646i
$849$	−9.23074	−	15.9881i	−0.316798	−	0.548710i
$850$	−81.3951	−	46.9935i	−2.79183	−	1.61186i
$851$	−7.14642	+	4.12599i	−0.244976	+	0.141437i
$852$	−12.1480	+	21.0410i	−0.416184	+	0.720852i
$853$	−5.37659	−	3.10418i	−0.184091	−	0.106285i	0.405122	−	0.914262i	$-0.367229\pi$
$853$	−5.37659	−	3.10418i	−0.184091	−	0.106285i	−0.589213	+	0.807978i	$0.700562\pi$
$854$	1.56534			0.0535649
$855$	−47.4530	+	3.57353i	−1.62286	+	0.122212i
$856$	14.6180			0.499632
$857$	−22.3151	+	38.6508i	−0.762268	+	1.32029i	0.179411	+	0.983774i	$0.442581\pi$
$857$	−22.3151	+	38.6508i	−0.762268	+	1.32029i	−0.941679	+	0.336513i	$0.890753\pi$
$858$	0.637876	+	1.51864i	0.0217767	+	0.0518456i
$859$	8.64218	+	14.9687i	0.294867	+	0.510725i	0.974954	−	0.222406i	$-0.0713912\pi$
$859$	8.64218	+	14.9687i	0.294867	+	0.510725i	−0.680087	+	0.733132i	$0.738058\pi$
$860$	−36.0647	−	20.8220i	−1.22980	−	0.710023i
$861$	−5.29450	−	9.17035i	−0.180436	−	0.312525i
$862$	11.2473			0.383085
$863$		−	50.6123i		−	1.72286i	−0.507874	−	0.861431i	$-0.669569\pi$
$863$		−	50.6123i		−	1.72286i	0.507874	−	0.861431i	$-0.330431\pi$
$864$	−0.717024	+	0.413974i	−0.0243937	+	0.0140837i
$865$	−33.0871	−	57.3086i	−1.12500	−	1.94855i
$866$			10.1508i			0.344939i
$867$		−	106.643i		−	3.62180i
$868$	−8.29407	−	14.3658i	−0.281519	−	0.487605i
$869$	31.3665	−	13.1749i	1.06404	−	0.446927i
$870$	−29.0043	+	16.7457i	−0.983339	+	0.567731i
$871$	−0.239642	−	0.138357i	−0.00811995	−	0.00468805i
$872$	0.996756	−	1.72643i	0.0337544	−	0.0584644i
$873$			19.8350i			0.671312i
$874$	25.9618	−	1.95509i	0.878170	−	0.0661320i
$875$			82.7648i			2.79796i
$876$	0.895920	−	1.55178i	0.0302703	−	0.0524298i
$877$	24.5696	−	42.5557i	0.829655	−	1.43701i	−0.0686532	−	0.997641i	$-0.521870\pi$
$877$	24.5696	−	42.5557i	0.829655	−	1.43701i	0.898309	−	0.439365i	$-0.144796\pi$
$878$	2.36184	+	4.09083i	0.0797083	+	0.138059i
$879$	51.6408	+	29.8149i	1.74180	+	1.00563i
$880$	−1.71520	+	13.5465i	−0.0578192	+	0.456653i
$881$	−46.6885			−1.57298			−0.786488	−	0.617605i	$-0.788103\pi$
$881$	−46.6885			−1.57298			−0.786488	+	0.617605i	$0.788103\pi$
$882$	−3.62388			−0.122022
$883$	−7.33269	−	12.7006i	−0.246765	−	0.427409i	0.715862	−	0.698242i	$-0.246034\pi$
$883$	−7.33269	−	12.7006i	−0.246765	−	0.427409i	−0.962626	+	0.270833i	$0.912701\pi$
$884$	−1.42292	+	0.821524i	−0.0478580	+	0.0276308i
$885$	134.232			4.51215
$886$	9.33790			0.313713
$887$	17.2362	+	29.8539i	0.578734	+	1.00240i	0.995625	+	0.0934401i	$0.0297864\pi$
$887$	17.2362	+	29.8539i	0.578734	+	1.00240i	−0.416891	+	0.908957i	$0.636880\pi$
$888$	1.64223	−	2.84442i	0.0551095	−	0.0954525i
$889$	−17.9153	+	10.3434i	−0.600861	+	0.346907i
$890$	6.24352	+	3.60470i	0.209283	+	0.120830i
$891$	30.3445	−	12.7456i	1.01658	−	0.426994i
$892$		−	6.27520i		−	0.210109i
$893$	−6.21288	−	9.10548i	−0.207906	−	0.304703i
$894$	43.0810			1.44085
$895$	24.7611	+	14.2958i	0.827673	+	0.477857i
$896$	−2.50499	−	1.44625i	−0.0836857	−	0.0483160i
$897$	2.56896	−	1.48319i	0.0857752	−	0.0495223i
$898$	34.7712	+	20.0752i	1.16033	+	0.669918i
$899$	−16.9946	+	9.81182i	−0.566801	+	0.327242i
$900$	−31.6883			−1.05628
$901$	41.3737			1.37836
$902$	−0.641532	+	5.06678i	−0.0213607	+	0.168705i
$903$	−60.2369	+	34.7778i	−2.00456	+	1.15733i
$904$			8.43532i			0.280554i
$905$			39.9105i			1.32667i
$906$	−19.6281	+	11.3323i	−0.652101	+	0.376490i
$907$	20.2340	+	11.6821i	0.671860	+	0.387898i	0.796781	−	0.604268i	$-0.206535\pi$
$907$	20.2340	+	11.6821i	0.671860	+	0.387898i	−0.124921	+	0.992167i	$0.539868\pi$
$908$	−12.0889	−	20.9386i	−0.401185	−	0.694872i
$909$	−16.8622	−	9.73539i	−0.559284	−	0.322903i
$910$	2.15447	+	1.24389i	0.0714201	+	0.0412344i
$911$		−	12.8623i		−	0.426147i	−0.977036	−	0.213073i	$-0.931653\pi$
$911$		−	12.8623i		−	0.426147i	0.977036	−	0.213073i	$-0.0683473\pi$
$912$	−8.55983	+	5.84057i	−0.283444	+	0.193401i
$913$	5.60537	−	7.38049i	0.185511	−	0.244259i
$914$	5.07323	+	2.92903i	0.167808	+	0.0968838i
$915$	2.64838	−	4.58713i	0.0875527	−	0.151646i
$916$	−5.83351	−	10.1039i	−0.192744	−	0.333843i
$917$	−19.9127	+	34.4899i	−0.657577	+	1.13896i
$918$	3.25591	+	5.63940i	0.107461	+	0.186128i
$919$		−	44.5460i		−	1.46944i	−0.678373	−	0.734718i	$-0.737314\pi$
$919$		−	44.5460i		−	1.46944i	0.678373	−	0.734718i	$-0.262686\pi$
$920$	24.5907			0.810731
$921$	−67.9663	+	39.2403i	−2.23956	+	1.29301i
$922$	−2.97342	+	1.71670i	−0.0979243	+	0.0565366i
$923$		−	2.13499i		−	0.0702740i
$924$	18.1623	+	13.7940i	0.597496	+	0.453789i
$925$	−14.2979	+	8.25488i	−0.470111	+	0.271419i
$926$	19.1038	−	33.0888i	0.627790	−	1.08736i
$927$	9.25762	−	5.34489i	0.304060	−	0.175549i
$928$	−1.71091	+	2.96338i	−0.0561633	+	0.0972777i
$929$	−9.83916	+	17.0419i	−0.322812	+	0.559127i	−0.981067	−	0.193668i	$-0.937962\pi$
$929$	−9.83916	+	17.0419i	−0.322812	+	0.559127i	0.658255	+	0.752795i	$0.271295\pi$
$930$	−56.1305			−1.84059
$931$	5.94009	−	0.447328i	0.194678	−	0.0146606i
$932$			23.7288i			0.777264i
$933$	30.8226	+	17.7954i	1.00909	+	0.582596i
$934$	11.9055	−	20.6209i	0.389560	−	0.674737i
$935$	106.544	+	13.4900i	3.48435	+	0.441171i
$936$	−0.276981	+	0.479746i	−0.00905342	+	0.0156810i
$937$	6.58265	−	3.80050i	0.215046	−	0.124157i	−0.388608	−	0.921403i	$-0.627044\pi$
$937$	6.58265	−	3.80050i	0.215046	−	0.124157i	0.603654	+	0.797246i	$0.293711\pi$
$938$	−3.83138			−0.125099
$939$		−	32.8583i		−	1.07229i
$940$	−5.20575	−	9.01663i	−0.169793	−	0.294090i
$941$	6.13080	+	10.6189i	0.199858	+	0.346165i	0.948482	−	0.316830i	$-0.102618\pi$
$941$	6.13080	+	10.6189i	0.199858	+	0.346165i	−0.748624	+	0.662995i	$0.769285\pi$
$942$		−	2.61839i		−	0.0853118i
$943$	9.19761			0.299515
$944$	11.8771	−	6.85724i	0.386566	−	0.223184i
$945$	4.92984	−	8.53874i	0.160368	−	0.277765i
$946$	33.2820	+	4.21400i	1.08209	+	0.137009i
$947$	−25.9053	+	44.8692i	−0.841808	+	1.45805i	0.0465563	+	0.998916i	$0.485175\pi$
$947$	−25.9053	+	44.8692i	−0.841808	+	1.45805i	−0.888364	+	0.459139i	$0.848158\pi$
$948$	21.1190	+	12.1931i	0.685913	+	0.396012i
$949$			0.157456i			0.00511124i
$950$	51.9418	−	3.91157i	1.68522	−	0.126908i
$951$	−35.0177			−1.13553
$952$	−11.3748	+	19.7017i	−0.368659	+	0.638537i
$953$	−11.2127	+	19.4209i	−0.363214	+	0.629106i	−0.988488	−	0.151300i	$-0.951654\pi$
$953$	−11.2127	+	19.4209i	−0.363214	+	0.629106i	0.625273	+	0.780406i	$0.284987\pi$
$954$	12.0805	−	6.97469i	0.391121	−	0.225814i
$955$	19.5239	−	33.8164i	0.631779	−	1.09427i
$956$	1.68327	−	0.971835i	0.0544407	−	0.0314314i
$957$	16.3182	−	21.4859i	0.527492	−	0.694540i
$958$		−	10.4198i		−	0.336648i
$959$	30.0522	−	17.3506i	0.970436	−	0.560281i
$960$	−8.47630	+	4.89380i	−0.273572	+	0.157947i
$961$	−1.88865			−0.0609242
$962$			0.288618i			0.00930542i
$963$	−19.3815	−	33.5697i	−0.624560	−	1.08177i
$964$	0.426995	−	0.739577i	0.0137526	−	0.0238202i
$965$	32.6616	+	56.5716i	1.05141	+	1.82110i
$966$	20.5362	−	35.5698i	0.660743	−	1.14444i
$967$	−12.3065	−	7.10519i	−0.395752	−	0.228487i	0.288897	−	0.957360i	$-0.406711\pi$
$967$	−12.3065	−	7.10519i	−0.395752	−	0.228487i	−0.684649	+	0.728873i	$0.740045\pi$
$968$	−2.95216	−	10.5965i	−0.0948859	−	0.340583i
$969$	45.9361	+	67.3231i	1.47568	+	2.16273i
$970$		−	30.7955i		−	0.988783i
$971$	0.975925	+	0.563451i	0.0313189	+	0.0180820i	0.515578	−	0.856843i	$-0.327577\pi$
$971$	0.975925	+	0.563451i	0.0313189	+	0.0180820i	−0.484259	+	0.874925i	$0.660911\pi$
$972$	18.2798	+	10.5538i	0.586325	+	0.338515i
$973$	25.6421	+	44.4134i	0.822047	+	1.42383i
$974$	−29.4691	−	17.0140i	−0.944252	−	0.545164i
$975$	5.13974	−	2.96743i	0.164603	−	0.0950338i
$976$		−	0.541171i		−	0.0173224i
$977$		−	15.3081i		−	0.489750i	−0.969555	−	0.244875i	$-0.921253\pi$
$977$		−	15.3081i		−	0.489750i	0.969555	−	0.244875i	$-0.0787468\pi$
$978$	−22.3214	+	12.8872i	−0.713758	+	0.412088i
$979$	−5.76178	−	0.729528i	−0.184147	−	0.0233158i
$980$	5.62638			0.179728
$981$	−5.28626			−0.168777
$982$	13.8599	−	8.00204i	0.442288	−	0.255355i
$983$	−34.7437	−	20.0593i	−1.10815	−	0.639791i	−0.169801	−	0.985478i	$-0.554313\pi$
$983$	−34.7437	−	20.0593i	−1.10815	−	0.639791i	−0.938350	+	0.345687i	$0.887646\pi$
$984$	−3.17038	+	1.83042i	−0.101068	+	0.0583516i
$985$	19.5277	+	11.2743i	0.622203	+	0.359229i
$986$	23.3070	+	13.4563i	0.742246	+	0.428536i
$987$	−17.3898			−0.553523
$988$	0.394795	−	0.820566i	0.0125601	−	0.0261057i
$989$		−	60.4160i		−	1.92112i
$990$	33.3833	−	14.0220i	1.06099	−	0.445648i
$991$	−28.2642	−	16.3184i	−0.897843	−	0.518370i	−0.0213431	−	0.999772i	$-0.506794\pi$
$991$	−28.2642	−	16.3184i	−0.897843	−	0.518370i	−0.876500	+	0.481402i	$0.840128\pi$
$992$	−4.96654	+	2.86743i	−0.157688	+	0.0910410i
$993$	−11.4989	+	19.9166i	−0.364906	+	0.632035i
$994$	−14.7805	−	25.6006i	−0.468809	−	0.812001i
$995$	3.81101			0.120817
$996$	6.64309			0.210494
$997$	−19.9958	+	11.5446i	−0.633273	+	0.365620i	−0.782018	−	0.623255i	$-0.785810\pi$
$997$	−19.9958	+	11.5446i	−0.633273	+	0.365620i	0.148746	+	0.988875i	$0.452476\pi$
$998$	11.3717	+	19.6964i	0.359966	+	0.623480i
$999$	1.14387			0.0361904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.65.2	yes	20
11.10	odd	2		418.2.h.a.65.2	✓	20
19.12	odd	6		418.2.h.a.373.2	yes	20
209.164	even	6	inner	418.2.h.b.373.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.2	✓	20	11.10	odd	2
418.2.h.a.373.2	yes	20	19.12	odd	6
418.2.h.b.65.2	yes	20	1.1	even	1	trivial
418.2.h.b.373.2	yes	20	209.164	even	6	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.05883 - 1.18867i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.05852 - 3.56546i) q^{5} +(-2.05883 + 1.18867i) q^{6} -2.89251i q^{7} -1.00000 q^{8} +(1.32587 + 2.29647i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-2.05883 - 1.18867i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.05852 - 3.56546i) q^{5} +(-2.05883 + 1.18867i) q^{6} -2.89251i q^{7} -1.00000 q^{8} +(1.32587 + 2.29647i) q^{9} +(-2.05852 - 3.56546i) q^{10} +(2.64123 + 2.00597i) q^{11} +2.37734i q^{12} +(-0.104453 - 0.180918i) q^{13} +(-2.50499 - 1.44625i) q^{14} +(-8.47630 + 4.89380i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.81130 + 3.93250i) q^{17} +2.65173 q^{18} +(-4.34659 + 0.327327i) q^{19} -4.11704 q^{20} +(-3.43823 + 5.95520i) q^{21} +(3.05784 - 1.28438i) q^{22} +(-2.98645 - 5.17269i) q^{23} +(2.05883 + 1.18867i) q^{24} +(-5.97501 - 10.3490i) q^{25} -0.208906 q^{26} +0.827948i q^{27} +(-2.50499 + 1.44625i) q^{28} +(1.71091 + 2.96338i) q^{29} +9.78759i q^{30} +5.73486i q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.05341 - 7.26951i) q^{33} +(6.81130 - 3.93250i) q^{34} +(-10.3131 - 5.95429i) q^{35} +(1.32587 - 2.29647i) q^{36} -1.38157i q^{37} +(-1.88982 + 3.92792i) q^{38} +0.496640i q^{39} +(-2.05852 + 3.56546i) q^{40} +(-0.769945 + 1.33358i) q^{41} +(3.43823 + 5.95520i) q^{42} +(8.75986 + 5.05751i) q^{43} +(0.416609 - 3.29036i) q^{44} +10.9173 q^{45} -5.97290 q^{46} +(1.26444 + 2.19008i) q^{47} +(2.05883 - 1.18867i) q^{48} -1.36661 q^{49} -11.9500 q^{50} +(-9.34889 - 16.1928i) q^{51} +(-0.104453 + 0.180918i) q^{52} +(4.55571 - 2.63024i) q^{53} +(0.717024 + 0.413974i) q^{54} +(12.5892 - 5.28786i) q^{55} +2.89251i q^{56} +(9.33800 + 4.49274i) q^{57} +3.42181 q^{58} +(-11.8771 - 6.85724i) q^{59} +(8.47630 + 4.89380i) q^{60} +(-0.468667 + 0.270585i) q^{61} +(4.96654 + 2.86743i) q^{62} +(6.64255 - 3.83508i) q^{63} +1.00000 q^{64} -0.860074 q^{65} +(-7.82228 - 0.990420i) q^{66} +(1.14713 - 0.662294i) q^{67} -7.86501i q^{68} +14.1996i q^{69} +(-10.3131 + 5.95429i) q^{70} +(8.85065 + 5.10993i) q^{71} +(-1.32587 - 2.29647i) q^{72} +(-0.652738 - 0.376859i) q^{73} +(-1.19647 - 0.690784i) q^{74} +28.4092i q^{75} +(2.45677 + 3.60059i) q^{76} +(5.80229 - 7.63977i) q^{77} +(0.430103 + 0.248320i) q^{78} +(5.12887 - 8.88347i) q^{79} +(2.05852 + 3.56546i) q^{80} +(4.96176 - 8.59401i) q^{81} +(0.769945 + 1.33358i) q^{82} -2.79434i q^{83} +6.87647 q^{84} +(28.0424 - 16.1903i) q^{85} +(8.75986 - 5.05751i) q^{86} -8.13481i q^{87} +(-2.64123 - 2.00597i) q^{88} +(-1.51651 + 0.875555i) q^{89} +(5.45865 - 9.45465i) q^{90} +(-0.523307 + 0.302131i) q^{91} +(-2.98645 + 5.17269i) q^{92} +(6.81685 - 11.8071i) q^{93} +2.52888 q^{94} +(-7.78047 + 16.1714i) q^{95} -2.37734i q^{96} +(6.47787 + 3.74000i) q^{97} +(-0.683304 + 1.18352i) q^{98} +(-1.10474 + 8.72514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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