LMFDB - Embedded newform 414.2.e.c.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (of order $3$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.1481180578947.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 6x^{8} - 11x^{7} + 22x^{6} - 45x^{5} + 66x^{4} - 99x^{3} + 162x^{2} - 162x + 243 $ x^10 - 2x^9 + 6x^8 - 11x^7 + 22x^6 - 45x^5 + 66x^4 - 99x^3 + 162x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$0.785454 + 1.54372i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.c.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.944171 - 1.45208i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.85973 + 3.22115i) q^{5} +(1.72963 - 0.0916356i) q^{6} +(2.00591 - 3.47433i) q^{7} +1.00000 q^{8} +(-1.21708 + 2.74203i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.944171 - 1.45208i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.85973 + 3.22115i) q^{5} +(1.72963 - 0.0916356i) q^{6} +(2.00591 - 3.47433i) q^{7} +1.00000 q^{8} +(-1.21708 + 2.74203i) q^{9} -3.71947 q^{10} +(-1.51845 + 2.63003i) q^{11} +(-0.785454 + 1.54372i) q^{12} +(-1.14519 - 1.98352i) q^{13} +(2.00591 + 3.47433i) q^{14} +(2.92147 - 5.74181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.43416 q^{17} +(-1.76612 - 2.42504i) q^{18} +8.38700 q^{19} +(1.85973 - 3.22115i) q^{20} +(-6.93894 + 0.367625i) q^{21} +(-1.51845 - 2.63003i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.944171 - 1.45208i) q^{24} +(-4.41722 + 7.65085i) q^{25} +2.29038 q^{26} +(5.13078 - 0.821643i) q^{27} -4.01181 q^{28} +(2.70102 - 4.67830i) q^{29} +(3.51181 + 5.40097i) q^{30} +(4.67744 + 8.10156i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.25270 - 0.278288i) q^{33} +(-1.21708 + 2.10805i) q^{34} +14.9218 q^{35} +(2.98321 - 0.316991i) q^{36} -1.87000 q^{37} +(-4.19350 + 7.26336i) q^{38} +(-1.79898 + 3.53569i) q^{39} +(1.85973 + 3.22115i) q^{40} +(5.97179 + 10.3435i) q^{41} +(3.15109 - 6.19311i) q^{42} +(3.27457 - 5.67172i) q^{43} +3.03690 q^{44} +(-11.0959 + 1.17904i) q^{45} +1.00000 q^{46} +(2.07091 - 3.58692i) q^{47} +(1.72963 - 0.0916356i) q^{48} +(-4.54733 - 7.87620i) q^{49} +(-4.41722 - 7.65085i) q^{50} +(-2.29827 - 3.53460i) q^{51} +(-1.14519 + 1.98352i) q^{52} -2.15706 q^{53} +(-1.85383 + 4.85421i) q^{54} -11.2957 q^{55} +(2.00591 - 3.47433i) q^{56} +(-7.91877 - 12.1786i) q^{57} +(2.70102 + 4.67830i) q^{58} +(-3.26089 - 5.64802i) q^{59} +(-6.43328 + 0.340836i) q^{60} +(-0.596144 + 1.03255i) q^{61} -9.35487 q^{62} +(7.08537 + 9.72880i) q^{63} +1.00000 q^{64} +(4.25949 - 7.37765i) q^{65} +(-2.38535 + 4.68812i) q^{66} +(-1.29121 - 2.23645i) q^{67} +(-1.21708 - 2.10805i) q^{68} +(-0.785454 + 1.54372i) q^{69} +(-7.46091 + 12.9227i) q^{70} -10.5880 q^{71} +(-1.21708 + 2.74203i) q^{72} -5.83619 q^{73} +(0.935000 - 1.61947i) q^{74} +(15.2803 - 0.809549i) q^{75} +(-4.19350 - 7.26336i) q^{76} +(6.09175 + 10.5512i) q^{77} +(-2.16251 - 3.32581i) q^{78} +(0.140266 - 0.242948i) q^{79} -3.71947 q^{80} +(-6.03743 - 6.67454i) q^{81} -11.9436 q^{82} +(0.717810 - 1.24328i) q^{83} +(3.78784 + 5.82548i) q^{84} +(4.52689 + 7.84081i) q^{85} +(3.27457 + 5.67172i) q^{86} +(-9.34349 + 0.495019i) q^{87} +(-1.51845 + 2.63003i) q^{88} -15.0586 q^{89} +(4.52689 - 10.1989i) q^{90} -9.18856 q^{91} +(-0.500000 + 0.866025i) q^{92} +(7.34782 - 14.4413i) q^{93} +(2.07091 + 3.58692i) q^{94} +(15.5976 + 27.0158i) q^{95} +(-0.785454 + 1.54372i) q^{96} +(-5.31080 + 9.19857i) q^{97} +9.09466 q^{98} +(-5.36355 - 7.36460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.944171	−	1.45208i	−0.545118	−	0.838360i
$3$	−0.944171	−	1.45208i	−0.545118	−	0.838360i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.85973	+	3.22115i	0.831698	+	1.44054i	0.896691	+	0.442658i	$0.145964\pi$
$5$	1.85973	+	3.22115i	0.831698	+	1.44054i	−0.0649924	+	0.997886i	$0.520702\pi$
$6$	1.72963	−	0.0916356i	0.706116	−	0.0374101i
$7$	2.00591	−	3.47433i	0.758162	−	1.31317i	−0.185625	−	0.982621i	$-0.559431\pi$
$7$	2.00591	−	3.47433i	0.758162	−	1.31317i	0.943787	−	0.330554i	$-0.107236\pi$
$8$	1.00000			0.353553
$9$	−1.21708	+	2.74203i	−0.405694	+	0.914009i
$10$	−3.71947			−1.17620
$11$	−1.51845	+	2.63003i	−0.457830	+	0.792985i	−0.998846	−	0.0480271i	$-0.984707\pi$
$11$	−1.51845	+	2.63003i	−0.457830	+	0.792985i	0.541016	+	0.841012i	$0.318040\pi$
$12$	−0.785454	+	1.54372i	−0.226741	+	0.445633i
$13$	−1.14519	−	1.98352i	−0.317618	−	0.550130i	0.662373	−	0.749175i	$-0.269550\pi$
$13$	−1.14519	−	1.98352i	−0.317618	−	0.550130i	−0.979991	+	0.199044i	$0.936216\pi$
$14$	2.00591	+	3.47433i	0.536101	+	0.928555i
$15$	2.92147	−	5.74181i	0.754320	−	1.48253i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.43416			0.590371			0.295186	−	0.955440i	$-0.404619\pi$
$17$	2.43416			0.590371			0.295186	+	0.955440i	$0.404619\pi$
$18$	−1.76612	−	2.42504i	−0.416280	−	0.571587i
$19$	8.38700			1.92411			0.962055	−	0.272854i	$-0.0879677\pi$
$19$	8.38700			1.92411			0.962055	+	0.272854i	$0.0879677\pi$
$20$	1.85973	−	3.22115i	0.415849	−	0.720272i
$21$	−6.93894	+	0.367625i	−1.51420	+	0.0802224i
$22$	−1.51845	−	2.63003i	−0.323735	−	0.560725i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.944171	−	1.45208i	−0.192728	−	0.296405i
$25$	−4.41722	+	7.65085i	−0.883444	+	1.53017i
$26$	2.29038			0.449180
$27$	5.13078	−	0.821643i	0.987419	−	0.158125i
$28$	−4.01181			−0.758162
$29$	2.70102	−	4.67830i	0.501566	−	0.868738i	−0.498432	−	0.866929i	$-0.666091\pi$
$29$	2.70102	−	4.67830i	0.501566	−	0.868738i	0.999998	−	0.00180935i	$-0.000575935\pi$
$30$	3.51181	+	5.40097i	0.641167	+	0.986078i
$31$	4.67744	+	8.10156i	0.840093	+	1.45508i	0.889816	+	0.456320i	$0.150833\pi$
$31$	4.67744	+	8.10156i	0.840093	+	1.45508i	−0.0497233	+	0.998763i	$0.515834\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.25270	−	0.278288i	0.914378	−	0.0484438i
$34$	−1.21708	+	2.10805i	−0.208728	+	0.361527i
$35$	14.9218			2.52225
$36$	2.98321	−	0.316991i	0.497201	−	0.0528318i
$37$	−1.87000			−0.307426			−0.153713	−	0.988116i	$-0.549123\pi$
$37$	−1.87000			−0.307426			−0.153713	+	0.988116i	$0.549123\pi$
$38$	−4.19350	+	7.26336i	−0.680276	+	1.17827i
$39$	−1.79898	+	3.53569i	−0.288068	+	0.566164i
$40$	1.85973	+	3.22115i	0.294050	+	0.509309i
$41$	5.97179	+	10.3435i	0.932638	+	1.61538i	0.778793	+	0.627281i	$0.215832\pi$
$41$	5.97179	+	10.3435i	0.932638	+	1.61538i	0.153844	+	0.988095i	$0.450835\pi$
$42$	3.15109	−	6.19311i	0.486224	−	0.955617i
$43$	3.27457	−	5.67172i	0.499367	−	0.864929i	−0.500633	−	0.865660i	$-0.666899\pi$
$43$	3.27457	−	5.67172i	0.499367	−	0.864929i	1.00000		0.000731034i	$0.000232696\pi$
$44$	3.03690			0.457830
$45$	−11.0959	+	1.17904i	−1.65408	+	0.175760i
$46$	1.00000			0.147442
$47$	2.07091	−	3.58692i	0.302073	−	0.523206i	−0.674532	−	0.738245i	$-0.735655\pi$
$47$	2.07091	−	3.58692i	0.302073	−	0.523206i	0.976605	+	0.215040i	$0.0689881\pi$
$48$	1.72963	−	0.0916356i	0.249650	−	0.0132265i
$49$	−4.54733	−	7.87620i	−0.649618	−	1.12517i
$50$	−4.41722	−	7.65085i	−0.624689	−	1.08199i
$51$	−2.29827	−	3.53460i	−0.321822	−	0.494943i
$52$	−1.14519	+	1.98352i	−0.158809	+	0.275065i
$53$	−2.15706			−0.296295			−0.148148	−	0.988965i	$-0.547331\pi$
$53$	−2.15706			−0.296295			−0.148148	+	0.988965i	$0.547331\pi$
$54$	−1.85383	+	4.85421i	−0.252274	+	0.660574i
$55$	−11.2957			−1.52311
$56$	2.00591	−	3.47433i	0.268051	−	0.464277i
$57$	−7.91877	−	12.1786i	−1.04887	−	1.61310i
$58$	2.70102	+	4.67830i	0.354661	+	0.614291i
$59$	−3.26089	−	5.64802i	−0.424532	−	0.735310i	0.571845	−	0.820362i	$-0.306228\pi$
$59$	−3.26089	−	5.64802i	−0.424532	−	0.735310i	−0.996377	+	0.0850515i	$0.972895\pi$
$60$	−6.43328	+	0.340836i	−0.830533	+	0.0440017i
$61$	−0.596144	+	1.03255i	−0.0763284	+	0.132205i	−0.901663	−	0.432439i	$-0.857653\pi$
$61$	−0.596144	+	1.03255i	−0.0763284	+	0.132205i	0.825335	+	0.564644i	$0.190986\pi$
$62$	−9.35487			−1.18807
$63$	7.08537	+	9.72880i	0.892672	+	1.22571i
$64$	1.00000			0.125000
$65$	4.25949	−	7.37765i	0.528324	−	0.915085i
$66$	−2.38535	+	4.68812i	−0.293616	+	0.577068i
$67$	−1.29121	−	2.23645i	−0.157747	−	0.273225i	0.776309	−	0.630353i	$-0.217090\pi$
$67$	−1.29121	−	2.23645i	−0.157747	−	0.273225i	−0.934056	+	0.357127i	$0.883756\pi$
$68$	−1.21708	−	2.10805i	−0.147593	−	0.255638i
$69$	−0.785454	+	1.54372i	−0.0945575	+	0.185842i
$70$	−7.46091	+	12.9227i	−0.891749	+	1.54455i
$71$	−10.5880			−1.25657			−0.628283	−	0.777985i	$-0.716242\pi$
$71$	−10.5880			−1.25657			−0.628283	+	0.777985i	$0.716242\pi$
$72$	−1.21708	+	2.74203i	−0.143434	+	0.323151i
$73$	−5.83619			−0.683075			−0.341537	−	0.939868i	$-0.610948\pi$
$73$	−5.83619			−0.683075			−0.341537	+	0.939868i	$0.610948\pi$
$74$	0.935000	−	1.61947i	0.108692	−	0.188259i
$75$	15.2803	−	0.809549i	1.76441	−	0.0934787i
$76$	−4.19350	−	7.26336i	−0.481028	−	0.833164i
$77$	6.09175	+	10.5512i	0.694219	+	1.20242i
$78$	−2.16251	−	3.32581i	−0.244856	−	0.376574i
$79$	0.140266	−	0.242948i	0.0157812	−	0.0273338i	−0.858027	−	0.513605i	$-0.828310\pi$
$79$	0.140266	−	0.242948i	0.0157812	−	0.0273338i	0.873808	+	0.486271i	$0.161643\pi$
$80$	−3.71947			−0.415849
$81$	−6.03743	−	6.67454i	−0.670825	−	0.741615i
$82$	−11.9436			−1.31895
$83$	0.717810	−	1.24328i	0.0787899	−	0.136468i	−0.823938	−	0.566680i	$-0.808228\pi$
$83$	0.717810	−	1.24328i	0.0787899	−	0.136468i	0.902728	+	0.430212i	$0.141561\pi$
$84$	3.78784	+	5.82548i	0.413287	+	0.635612i
$85$	4.52689	+	7.84081i	0.491011	+	0.850455i
$86$	3.27457	+	5.67172i	0.353106	+	0.611597i
$87$	−9.34349	+	0.495019i	−1.00173	+	0.0530716i
$88$	−1.51845	+	2.63003i	−0.161867	+	0.280363i
$89$	−15.0586			−1.59620			−0.798102	−	0.602522i	$-0.794162\pi$
$89$	−15.0586			−1.59620			−0.798102	+	0.602522i	$0.794162\pi$
$90$	4.52689	−	10.1989i	0.477176	−	1.07506i
$91$	−9.18856			−0.963223
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$	7.34782	−	14.4413i	0.761934	−	1.49749i
$94$	2.07091	+	3.58692i	0.213598	+	0.369962i
$95$	15.5976	+	27.0158i	1.60028	+	2.77177i
$96$	−0.785454	+	1.54372i	−0.0801650	+	0.157555i
$97$	−5.31080	+	9.19857i	−0.539230	+	0.933974i	0.459716	+	0.888066i	$0.347951\pi$
$97$	−5.31080	+	9.19857i	−0.539230	+	0.933974i	−0.998946	+	0.0459075i	$0.985382\pi$
$98$	9.09466			0.918699
$99$	−5.36355	−	7.36460i	−0.539057	−	0.740170i
$100$	8.83444			0.883444
$101$	4.34378	−	7.52364i	0.432222	−	0.748630i	−0.564842	−	0.825199i	$-0.691063\pi$
$101$	4.34378	−	7.52364i	0.432222	−	0.748630i	0.997064	+	0.0765684i	$0.0243964\pi$
$102$	4.21019	−	0.223056i	0.416871	−	0.0220858i
$103$	−5.86154	−	10.1525i	−0.577555	−	1.00035i	−0.995759	−	0.0920010i	$-0.970674\pi$
$103$	−5.86154	−	10.1525i	−0.577555	−	1.00035i	0.418204	−	0.908353i	$-0.362660\pi$
$104$	−1.14519	−	1.98352i	−0.112295	−	0.194500i
$105$	−14.0887	−	21.6677i	−1.37492	−	2.11455i
$106$	1.07853	−	1.86807i	0.104756	−	0.181443i
$107$	−9.89085			−0.956185			−0.478092	−	0.878310i	$-0.658672\pi$
$107$	−9.89085			−0.956185			−0.478092	+	0.878310i	$0.658672\pi$
$108$	−3.27695	−	4.03256i	−0.315325	−	0.388034i
$109$	4.27605			0.409572			0.204786	−	0.978807i	$-0.434350\pi$
$109$	4.27605			0.409572			0.204786	+	0.978807i	$0.434350\pi$
$110$	5.64783	−	9.78233i	0.538500	−	0.932709i
$111$	1.76560	+	2.71539i	0.167583	+	0.257734i
$112$	2.00591	+	3.47433i	0.189540	+	0.328294i
$113$	0.249940	+	0.432909i	0.0235124	+	0.0407246i	0.877542	−	0.479499i	$-0.159182\pi$
$113$	0.249940	+	0.432909i	0.0235124	+	0.0407246i	−0.854030	+	0.520224i	$0.825848\pi$
$114$	14.5064	−	0.768548i	1.35865	−	0.0719811i
$115$	1.85973	−	3.22115i	0.173421	−	0.300374i
$116$	−5.40203			−0.501566
$117$	6.83266	−	0.726027i	0.631680	−	0.0671212i
$118$	6.52178			0.600378
$119$	4.88270	−	8.45709i	0.447597	−	0.775260i
$120$	2.92147	−	5.74181i	0.266692	−	0.524153i
$121$	0.888611	+	1.53912i	0.0807828	+	0.139920i
$122$	−0.596144	−	1.03255i	−0.0539723	−	0.0934828i
$123$	9.38114	−	18.4375i	0.845869	−	1.66246i
$124$	4.67744	−	8.10156i	0.420046	−	0.727541i
$125$	−14.2621			−1.27564
$126$	−11.9681	+	1.27171i	−1.06620	+	0.113293i
$127$	−15.2701			−1.35500			−0.677499	−	0.735523i	$-0.736936\pi$
$127$	−15.2701			−1.35500			−0.677499	+	0.735523i	$0.736936\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−11.3275	+	0.600134i	−0.997335	+	0.0528389i
$130$	4.25949	+	7.37765i	0.373582	+	0.647063i
$131$	2.87441	+	4.97862i	0.251138	+	0.434984i	0.963840	−	0.266483i	$-0.0858618\pi$
$131$	2.87441	+	4.97862i	0.251138	+	0.434984i	−0.712701	+	0.701468i	$0.752528\pi$
$132$	−2.86736	−	4.40983i	−0.249571	−	0.383826i
$133$	16.8236	−	29.1392i	1.45879	−	2.52669i
$134$	2.58243			0.223088
$135$	12.1885	+	14.9990i	1.04902	+	1.29091i
$136$	2.43416			0.208728
$137$	−1.48082	+	2.56485i	−0.126515	+	0.219130i	−0.922324	−	0.386417i	$-0.873712\pi$
$137$	−1.48082	+	2.56485i	−0.126515	+	0.219130i	0.795809	+	0.605547i	$0.207046\pi$
$138$	−0.944171	−	1.45208i	−0.0803732	−	0.123609i
$139$	−0.566363	−	0.980969i	−0.0480383	−	0.0832047i	0.841006	−	0.541025i	$-0.181964\pi$
$139$	−0.566363	−	0.980969i	−0.0480383	−	0.0832047i	−0.889045	+	0.457820i	$0.848630\pi$
$140$	−7.46091	−	12.9227i	−0.630562	−	1.09217i
$141$	−7.16379	+	0.379538i	−0.603300	+	0.0319629i
$142$	5.29400	−	9.16948i	0.444263	−	0.769486i
$143$	6.95565			0.581660
$144$	−1.76612	−	2.42504i	−0.147177	−	0.202086i
$145$	20.0927			1.66861
$146$	2.91810	−	5.05429i	0.241503	−	0.418296i
$147$	−7.14343	+	14.0396i	−0.589180	+	1.15796i
$148$	0.935000	+	1.61947i	0.0768565	+	0.133119i
$149$	−2.03225	−	3.51996i	−0.166488	−	0.288366i	0.770694	−	0.637205i	$-0.219909\pi$
$149$	−2.03225	−	3.51996i	−0.166488	−	0.288366i	−0.937183	+	0.348839i	$0.886576\pi$
$150$	−6.93904	+	13.6379i	−0.566571	+	1.11353i
$151$	−5.51633	+	9.55457i	−0.448913	+	0.777540i	−0.998316	−	0.0580179i	$-0.981522\pi$
$151$	−5.51633	+	9.55457i	−0.448913	+	0.777540i	0.549403	+	0.835558i	$0.314855\pi$
$152$	8.38700			0.680276
$153$	−2.96257	+	6.67454i	−0.239510	+	0.539604i
$154$	−12.1835			−0.981774
$155$	−17.3976	+	30.1335i	−1.39741	+	2.42038i
$156$	3.96149	−	0.209880i	0.317173	−	0.0168038i
$157$	−2.24694	−	3.89182i	−0.179326	−	0.310601i	0.762324	−	0.647195i	$-0.224058\pi$
$157$	−2.24694	−	3.89182i	−0.179326	−	0.310601i	−0.941650	+	0.336594i	$0.890725\pi$
$158$	0.140266	+	0.242948i	0.0111590	+	0.0193279i
$159$	2.03663	+	3.13223i	0.161516	+	0.248402i
$160$	1.85973	−	3.22115i	0.147025	−	0.254655i
$161$	−4.01181			−0.316175
$162$	8.79903	−	1.89130i	0.691317	−	0.148594i
$163$	20.5964			1.61323			0.806617	−	0.591074i	$-0.201296\pi$
$163$	20.5964			1.61323			0.806617	+	0.591074i	$0.201296\pi$
$164$	5.97179	−	10.3435i	0.466319	−	0.807688i
$165$	10.6650	+	16.4022i	0.830272	+	1.27691i
$166$	0.717810	+	1.24328i	0.0557129	+	0.0964976i
$167$	5.60595	+	9.70979i	0.433801	+	0.751366i	0.997197	−	0.0748213i	$-0.0238386\pi$
$167$	5.60595	+	9.70979i	0.433801	+	0.751366i	−0.563396	+	0.826187i	$0.690505\pi$
$168$	−6.93894	+	0.367625i	−0.535350	+	0.0283629i
$169$	3.87709	−	6.71532i	0.298238	−	0.516563i
$170$	−9.05379			−0.694394
$171$	−10.2077	+	22.9974i	−0.780600	+	1.75865i
$172$	−6.54913			−0.499367
$173$	−4.78385	+	8.28587i	−0.363709	+	0.629963i	−0.988568	−	0.150775i	$-0.951823\pi$
$173$	−4.78385	+	8.28587i	−0.363709	+	0.629963i	0.624859	+	0.780738i	$0.285156\pi$
$174$	4.24305	−	8.33921i	0.321665	−	0.632194i
$175$	17.7211	+	30.6938i	1.33959	+	2.32023i
$176$	−1.51845	−	2.63003i	−0.114458	−	0.198246i
$177$	−5.12255	+	10.0678i	−0.385035	+	0.756741i
$178$	7.52928	−	13.0411i	0.564343	−	0.977471i
$179$	−16.3828			−1.22451			−0.612255	−	0.790661i	$-0.709737\pi$
$179$	−16.3828			−1.22451			−0.612255	+	0.790661i	$0.709737\pi$
$180$	6.56904	+	9.01985i	0.489628	+	0.672300i
$181$	−5.05549			−0.375771			−0.187886	−	0.982191i	$-0.560163\pi$
$181$	−5.05549			−0.375771			−0.187886	+	0.982191i	$0.560163\pi$
$182$	4.59428	−	7.95753i	0.340551	−	0.589851i
$183$	2.06221	−	0.109256i	0.152443	−	0.00807644i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−3.47770	−	6.02356i	−0.255686	−	0.442861i
$186$	8.83260	+	13.5840i	0.647638	+	0.996030i
$187$	−3.69616	+	6.40193i	−0.270290	+	0.468156i
$188$	−4.14182			−0.302073
$189$	7.43721	−	19.4742i	0.540977	−	1.41654i
$190$	−31.1952			−2.26314
$191$	2.82774	−	4.89779i	0.204608	−	0.354392i	−0.745400	−	0.666618i	$-0.767741\pi$
$191$	2.82774	−	4.89779i	0.204608	−	0.354392i	0.950008	+	0.312226i	$0.101075\pi$
$192$	−0.944171	−	1.45208i	−0.0681397	−	0.104795i
$193$	9.81386	+	16.9981i	0.706417	+	1.22355i	0.966178	+	0.257877i	$0.0830229\pi$
$193$	9.81386	+	16.9981i	0.706417	+	1.22355i	−0.259761	+	0.965673i	$0.583644\pi$
$194$	−5.31080	−	9.19857i	−0.381293	−	0.660419i
$195$	−14.7346	+	0.780642i	−1.05517	+	0.0559029i
$196$	−4.54733	+	7.87620i	−0.324809	+	0.562586i
$197$	5.06647			0.360971			0.180486	−	0.983578i	$-0.442233\pi$
$197$	5.06647			0.360971			0.180486	+	0.983578i	$0.442233\pi$
$198$	9.05971	−	0.962670i	0.643845	−	0.0684139i
$199$	−7.25048			−0.513973			−0.256986	−	0.966415i	$-0.582730\pi$
$199$	−7.25048			−0.513973			−0.256986	+	0.966415i	$0.582730\pi$
$200$	−4.41722	+	7.65085i	−0.312345	+	0.540997i
$201$	−2.02838	+	3.98653i	−0.143071	+	0.281188i
$202$	4.34378	+	7.52364i	0.305627	+	0.529362i
$203$	−10.8360	−	18.7685i	−0.760536	−	1.31729i
$204$	−1.91192	+	3.75766i	−0.133861	+	0.263089i
$205$	−22.2119	+	38.4721i	−1.55135	+	2.68701i
$206$	11.7231			0.816786
$207$	2.98321	−	0.316991i	0.207347	−	0.0220324i
$208$	2.29038			0.158809
$209$	−12.7353	+	22.0581i	−0.880916	+	1.52579i
$210$	25.8091	−	1.36737i	1.78100	−	0.0943575i
$211$	−11.1244	−	19.2681i	−0.765838	−	1.32647i	−0.939802	−	0.341718i	$-0.888991\pi$
$211$	−11.1244	−	19.2681i	−0.765838	−	1.32647i	0.173965	−	0.984752i	$-0.444342\pi$
$212$	1.07853	+	1.86807i	0.0740738	+	0.128300i
$213$	9.99689	+	15.3747i	0.684976	+	1.05345i
$214$	4.94543	−	8.56573i	0.338062	−	0.585541i
$215$	24.3593			1.66129
$216$	5.13078	−	0.821643i	0.349105	−	0.0559057i
$217$	37.5300			2.54770
$218$	−2.13803	+	3.70317i	−0.144805	+	0.250810i
$219$	5.51037	+	8.47463i	0.372356	+	0.572662i
$220$	5.64783	+	9.78233i	0.380777	+	0.659525i
$221$	−2.78757	−	4.82822i	−0.187512	−	0.324781i
$222$	−3.23440	+	0.171359i	−0.217079	+	0.0115008i
$223$	12.3735	−	21.4315i	0.828591	−	1.43516i	−0.0705529	−	0.997508i	$-0.522476\pi$
$223$	12.3735	−	21.4315i	0.828591	−	1.43516i	0.899144	−	0.437653i	$-0.144190\pi$
$224$	−4.01181			−0.268051
$225$	−15.6027	−	21.4238i	−1.04018	−	1.42826i
$226$	−0.499880			−0.0332515
$227$	12.0404	−	20.8545i	0.799147	−	1.38416i	−0.121025	−	0.992649i	$-0.538618\pi$
$227$	12.0404	−	20.8545i	0.799147	−	1.38416i	0.920172	−	0.391514i	$-0.128049\pi$
$228$	−6.58760	+	12.9472i	−0.436275	+	0.857447i
$229$	−3.22849	−	5.59191i	−0.213345	−	0.369524i	0.739414	−	0.673251i	$-0.235102\pi$
$229$	−3.22849	−	5.59191i	−0.213345	−	0.369524i	−0.952759	+	0.303726i	$0.901769\pi$
$230$	1.85973	+	3.22115i	0.122627	+	0.212397i
$231$	9.56957	−	18.8079i	0.629631	−	1.23747i
$232$	2.70102	−	4.67830i	0.177330	−	0.307145i
$233$	−2.96838			−0.194465			−0.0972325	−	0.995262i	$-0.530999\pi$
$233$	−2.96838			−0.194465			−0.0972325	+	0.995262i	$0.530999\pi$
$234$	−2.78757	+	6.28027i	−0.182229	+	0.410554i
$235$	15.4053			1.00493
$236$	−3.26089	+	5.64802i	−0.212266	+	0.367655i
$237$	−0.485216	+	0.0257068i	−0.0315182	+	0.00166983i
$238$	4.88270	+	8.45709i	0.316499	+	0.548192i
$239$	−5.25766	−	9.10654i	−0.340090	−	0.589053i	0.644359	−	0.764723i	$-0.277124\pi$
$239$	−5.25766	−	9.10654i	−0.340090	−	0.589053i	−0.984449	+	0.175670i	$0.943791\pi$
$240$	3.51181	+	5.40097i	0.226687	+	0.348631i
$241$	8.48428	−	14.6952i	0.546521	−	0.946601i	−0.451989	−	0.892024i	$-0.649285\pi$
$241$	8.48428	−	14.6952i	0.546521	−	0.946601i	0.998510	−	0.0545778i	$-0.0173813\pi$
$242$	−1.77722			−0.114244
$243$	−3.99161	+	15.0687i	−0.256062	+	0.966660i
$244$	1.19229			0.0763284
$245$	16.9136	−	29.2953i	1.08057	−	1.87161i
$246$	11.2768	+	17.3431i	0.718982	+	1.10575i
$247$	−9.60469	−	16.6358i	−0.611132	−	1.05851i
$248$	4.67744	+	8.10156i	0.297018	+	0.514449i
$249$	−2.48309	+	0.131554i	−0.157359	+	0.00833690i
$250$	7.13104	−	12.3513i	0.451006	−	0.781166i
$251$	−27.8636			−1.75873			−0.879367	−	0.476144i	$-0.842034\pi$
$251$	−27.8636			−1.75873			−0.879367	+	0.476144i	$0.842034\pi$
$252$	4.88270	−	11.0005i	0.307581	−	0.692967i
$253$	3.03690			0.190928
$254$	7.63503	−	13.2243i	0.479064	−	0.829764i
$255$	7.11133	−	13.9765i	0.445329	−	0.875241i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.91696	+	5.05233i	0.181955	+	0.315156i	0.942546	−	0.334076i	$-0.108424\pi$
$257$	2.91696	+	5.05233i	0.181955	+	0.315156i	−0.760591	+	0.649231i	$0.775091\pi$
$258$	5.14404	−	10.1100i	0.320254	−	0.629422i
$259$	−3.75105	+	6.49700i	−0.233079	+	0.403704i
$260$	−8.51898			−0.528324
$261$	9.54066	+	13.1001i	0.590552	+	0.810878i
$262$	−5.74882			−0.355163
$263$	−1.53070	+	2.65125i	−0.0943871	+	0.163483i	−0.909353	−	0.416026i	$-0.863422\pi$
$263$	−1.53070	+	2.65125i	−0.0943871	+	0.163483i	0.814966	+	0.579509i	$0.196756\pi$
$264$	5.25270	−	0.278288i	0.323282	−	0.0171275i
$265$	−4.01156	−	6.94822i	−0.246428	−	0.426826i
$266$	16.8236	+	29.1392i	1.03152	+	1.78664i
$267$	14.2179	+	21.8663i	0.870119	+	1.33819i
$268$	−1.29121	+	2.23645i	−0.0788734	+	0.136613i
$269$	−18.1571			−1.10706			−0.553528	−	0.832831i	$-0.686719\pi$
$269$	−18.1571			−1.10706			−0.553528	+	0.832831i	$0.686719\pi$
$270$	−19.0838	+	3.05607i	−1.16140	+	0.185987i
$271$	−7.14262			−0.433884			−0.216942	−	0.976185i	$-0.569608\pi$
$271$	−7.14262			−0.433884			−0.216942	+	0.976185i	$0.569608\pi$
$272$	−1.21708	+	2.10805i	−0.0737964	+	0.127819i
$273$	8.67558	+	13.3425i	0.525070	+	0.807527i
$274$	−1.48082	−	2.56485i	−0.0894596	−	0.154949i
$275$	−13.4147	−	23.2349i	−0.808935	−	1.40112i
$276$	1.72963	−	0.0916356i	0.104111	−	0.00551582i
$277$	−9.39139	+	16.2664i	−0.564274	+	0.977351i	0.432843	+	0.901469i	$0.357510\pi$
$277$	−9.39139	+	16.2664i	−0.564274	+	0.977351i	−0.997117	+	0.0758817i	$0.975823\pi$
$278$	1.13273			0.0679364
$279$	−27.9075	+	2.96541i	−1.67078	+	0.177534i
$280$	14.9218			0.891749
$281$	−6.78965	+	11.7600i	−0.405036	+	0.701543i	−0.994326	−	0.106379i	$-0.966074\pi$
$281$	−6.78965	+	11.7600i	−0.405036	+	0.701543i	0.589289	+	0.807922i	$0.299408\pi$
$282$	3.25320	−	6.39379i	0.193725	−	0.380745i
$283$	−1.62575	−	2.81588i	−0.0966408	−	0.167387i	0.813651	−	0.581353i	$-0.197476\pi$
$283$	−1.62575	−	2.81588i	−0.0966408	−	0.167387i	−0.910292	+	0.413966i	$0.864143\pi$
$284$	5.29400	+	9.16948i	0.314141	+	0.544109i
$285$	24.5024	−	48.1565i	1.45140	−	2.85255i
$286$	−3.47782	+	6.02377i	−0.205648	+	0.356193i
$287$	47.9155			2.82836
$288$	2.98321	−	0.316991i	0.175787	−	0.0186788i
$289$	−11.0749			−0.651462
$290$	−10.0463	+	17.4008i	−0.589942	+	1.02181i
$291$	18.3714	−	0.973317i	1.07695	−	0.0570568i
$292$	2.91810	+	5.05429i	0.170769	+	0.295780i
$293$	2.51384	+	4.35410i	0.146860	+	0.254369i	0.930065	−	0.367394i	$-0.119750\pi$
$293$	2.51384	+	4.35410i	0.146860	+	0.254369i	−0.783205	+	0.621763i	$0.786417\pi$
$294$	−8.58691	−	13.2062i	−0.500799	−	0.770200i
$295$	12.1288	−	21.0076i	0.706164	−	1.22311i
$296$	−1.87000			−0.108692
$297$	−5.62989	+	14.7418i	−0.326679	+	0.855403i
$298$	4.06450			0.235450
$299$	−1.14519	+	1.98352i	−0.0662279	+	0.114710i
$300$	−8.34122	−	12.8283i	−0.481581	−	0.740644i
$301$	−13.1370	−	22.7539i	−0.757202	−	1.31151i
$302$	−5.51633	−	9.55457i	−0.317429	−	0.549804i
$303$	−15.0262	+	0.796090i	−0.863233	+	0.0457341i
$304$	−4.19350	+	7.26336i	−0.240514	+	0.416582i
$305$	−4.43468			−0.253929
$306$	−4.29903	−	5.90293i	−0.245759	−	0.337448i
$307$	−9.80716			−0.559724			−0.279862	−	0.960040i	$-0.590289\pi$
$307$	−9.80716			−0.559724			−0.279862	+	0.960040i	$0.590289\pi$
$308$	6.09175	−	10.5512i	0.347109	−	0.601211i
$309$	−9.20794	+	18.0971i	−0.523821	+	1.02951i
$310$	−17.3976	−	30.1335i	−0.988116	−	1.71147i
$311$	3.44317	+	5.96375i	0.195244	+	0.338173i	0.946981	−	0.321291i	$-0.104117\pi$
$311$	3.44317	+	5.96375i	0.195244	+	0.338173i	−0.751736	+	0.659464i	$0.770783\pi$
$312$	−1.79898	+	3.53569i	−0.101847	+	0.200169i
$313$	−6.33490	+	10.9724i	−0.358070	+	0.620195i	−0.987638	−	0.156750i	$-0.949898\pi$
$313$	−6.33490	+	10.9724i	−0.358070	+	0.620195i	0.629569	+	0.776945i	$0.283232\pi$
$314$	4.49389			0.253605
$315$	−18.1611	+	40.9160i	−1.02326	+	2.30536i
$316$	−0.280532			−0.0157812
$317$	3.71647	−	6.43712i	0.208738	−	0.361545i	−0.742579	−	0.669758i	$-0.766398\pi$
$317$	3.71647	−	6.43712i	0.208738	−	0.361545i	0.951317	+	0.308214i	$0.0997311\pi$
$318$	−3.73091	+	0.197664i	−0.209219	+	0.0110844i
$319$	8.20272	+	14.2075i	0.459264	+	0.795469i
$320$	1.85973	+	3.22115i	0.103962	+	0.180068i
$321$	9.33866	+	14.3623i	0.521233	+	0.801627i
$322$	2.00591	−	3.47433i	0.111785	−	0.193617i
$323$	20.4153			1.13594
$324$	−2.76161	+	8.56584i	−0.153423	+	0.475880i
$325$	20.2342			1.12239
$326$	−10.2982	+	17.8370i	−0.570364	+	0.987900i
$327$	−4.03733	−	6.20918i	−0.223265	−	0.343368i
$328$	5.97179	+	10.3435i	0.329737	+	0.571122i
$329$	−8.30810	−	14.3900i	−0.458040	−	0.793349i
$330$	−19.5373	+	1.03509i	−1.07549	+	0.0569796i
$331$	−4.19805	+	7.27123i	−0.230746	+	0.399663i	−0.958028	−	0.286676i	$-0.907450\pi$
$331$	−4.19805	+	7.27123i	−0.230746	+	0.399663i	0.727282	+	0.686339i	$0.240783\pi$
$332$	−1.43562			−0.0787899
$333$	2.27594	−	5.12759i	0.124721	−	0.280990i
$334$	−11.2119			−0.613488
$335$	4.80262	−	8.31839i	0.262395	−	0.454482i
$336$	3.15109	−	6.19311i	0.171906	−	0.337862i
$337$	−5.63348	−	9.75748i	−0.306875	−	0.531524i	0.670802	−	0.741637i	$-0.265950\pi$
$337$	−5.63348	−	9.75748i	−0.306875	−	0.531524i	−0.977677	+	0.210113i	$0.932617\pi$
$338$	3.87709	+	6.71532i	0.210886	+	0.365265i
$339$	0.392633	−	0.771673i	0.0213249	−	0.0419115i
$340$	4.52689	−	7.84081i	0.245505	−	0.425228i
$341$	−28.4098			−1.53848
$342$	−14.8125	−	20.3388i	−0.800968	−	1.09980i
$343$	−8.40337			−0.453740
$344$	3.27457	−	5.67172i	0.176553	−	0.305798i
$345$	−6.43328	+	0.340836i	−0.346356	+	0.0183500i
$346$	−4.78385	−	8.28587i	−0.257181	−	0.445451i
$347$	−14.7434	−	25.5362i	−0.791465	−	1.37086i	−0.925060	−	0.379821i	$-0.875986\pi$
$347$	−14.7434	−	25.5362i	−0.791465	−	1.37086i	0.133595	−	0.991036i	$-0.457348\pi$
$348$	5.10044	+	7.84419i	0.273413	+	0.420493i
$349$	14.9456	−	25.8866i	0.800020	−	1.38568i	−0.119582	−	0.992824i	$-0.538155\pi$
$349$	14.9456	−	25.8866i	0.800020	−	1.38568i	0.919602	−	0.392851i	$-0.128511\pi$
$350$	−35.4421			−1.89446
$351$	−7.50545	−	9.23609i	−0.400611	−	0.492986i
$352$	3.03690			0.161867
$353$	−2.60103	+	4.50511i	−0.138439	+	0.239783i	−0.926906	−	0.375294i	$-0.877542\pi$
$353$	−2.60103	+	4.50511i	−0.138439	+	0.239783i	0.788467	+	0.615077i	$0.210875\pi$
$354$	−6.15768	−	9.47015i	−0.327277	−	0.503333i
$355$	−19.6909	−	34.1056i	−1.04508	−	1.81014i
$356$	7.52928	+	13.0411i	0.399051	+	0.691177i
$357$	−16.8905	+	0.894859i	−0.893940	+	0.0473610i
$358$	8.19141	−	14.1879i	0.432929	−	0.749856i
$359$	34.8499			1.83931			0.919654	−	0.392729i	$-0.128469\pi$
$359$	34.8499			1.83931			0.919654	+	0.392729i	$0.128469\pi$
$360$	−11.0959	+	1.17904i	−0.584807	+	0.0621407i
$361$	51.3418			2.70220
$362$	2.52774	−	4.37818i	0.132855	−	0.230112i
$363$	1.39593	−	2.74353i	0.0732671	−	0.143998i
$364$	4.59428	+	7.95753i	0.240806	+	0.417088i
$365$	−10.8538	−	18.7993i	−0.568112	−	0.983999i
$366$	−0.936487	+	1.84055i	−0.0489509	+	0.0962073i
$367$	3.86994	−	6.70294i	0.202009	−	0.349890i	−0.747166	−	0.664637i	$-0.768586\pi$
$367$	3.86994	−	6.70294i	0.202009	−	0.349890i	0.949176	+	0.314747i	$0.101920\pi$
$368$	1.00000			0.0521286
$369$	−35.6302	+	3.78600i	−1.85483	+	0.197092i
$370$	6.95540			0.361594
$371$	−4.32686	+	7.49435i	−0.224640	+	0.389087i
$372$	−16.1804	+	0.857240i	−0.838916	+	0.0444458i
$373$	0.582842	+	1.00951i	0.0301784	+	0.0522706i	0.880720	−	0.473637i	$-0.157059\pi$
$373$	0.582842	+	1.00951i	0.0301784	+	0.0522706i	−0.850542	+	0.525908i	$0.823726\pi$
$374$	−3.69616	−	6.40193i	−0.191124	−	0.331036i
$375$	13.4658	+	20.7097i	0.695373	+	1.06944i
$376$	2.07091	−	3.58692i	0.106799	−	0.184981i
$377$	−12.3727			−0.637225
$378$	13.1465	+	16.1779i	0.676185	+	0.832101i
$379$	35.2059			1.80841			0.904203	−	0.427103i	$-0.140466\pi$
$379$	35.2059			1.80841			0.904203	+	0.427103i	$0.140466\pi$
$380$	15.5976	−	27.0158i	0.800140	−	1.38588i
$381$	14.4176	+	22.1734i	0.738634	+	1.13598i
$382$	2.82774	+	4.89779i	0.144680	+	0.250593i
$383$	14.7387	+	25.5282i	0.753112	+	1.30443i	0.946307	+	0.323268i	$0.104782\pi$
$383$	14.7387	+	25.5282i	0.753112	+	1.30443i	−0.193195	+	0.981160i	$0.561885\pi$
$384$	1.72963	−	0.0916356i	0.0882646	−	0.00467626i
$385$	−22.6581	+	39.2449i	−1.15476	+	2.00010i
$386$	−19.6277			−0.999024
$387$	11.5666	+	15.8819i	0.587963	+	0.807322i
$388$	10.6216			0.539230
$389$	0.0897001	−	0.155365i	0.00454797	−	0.00787732i	−0.863742	−	0.503933i	$-0.831886\pi$
$389$	0.0897001	−	0.155365i	0.00454797	−	0.00787732i	0.868290	+	0.496056i	$0.165219\pi$
$390$	6.69126	−	13.1509i	0.338825	−	0.665921i
$391$	−1.21708	−	2.10805i	−0.0615504	−	0.106608i
$392$	−4.54733	−	7.87620i	−0.229675	−	0.397808i
$393$	4.51543	−	8.87455i	0.227773	−	0.447662i
$394$	−2.53324	+	4.38769i	−0.127623	+	0.221049i
$395$	1.04343			0.0525007
$396$	−3.69616	+	8.32727i	−0.185739	+	0.418461i
$397$	15.1549			0.760602			0.380301	−	0.924863i	$-0.375820\pi$
$397$	15.1549			0.760602			0.380301	+	0.924863i	$0.375820\pi$
$398$	3.62524	−	6.27910i	0.181717	−	0.314743i
$399$	−58.1969	+	3.08327i	−2.91349	+	0.154357i
$400$	−4.41722	−	7.65085i	−0.220861	−	0.382542i
$401$	13.7000	+	23.7290i	0.684143	+	1.18497i	0.973705	+	0.227812i	$0.0731571\pi$
$401$	13.7000	+	23.7290i	0.684143	+	1.18497i	−0.289562	+	0.957159i	$0.593510\pi$
$402$	−2.43825	−	3.74989i	−0.121609	−	0.187028i
$403$	10.7131	−	18.5556i	0.533657	−	0.924321i
$404$	−8.68755			−0.432222
$405$	10.2717	−	31.8603i	0.510405	−	1.58315i
$406$	21.6720			1.07556
$407$	2.83950	−	4.91816i	0.140749	−	0.243784i
$408$	−2.29827	−	3.53460i	−0.113781	−	0.174989i
$409$	−5.17995	−	8.97193i	−0.256132	−	0.443633i	0.709071	−	0.705138i	$-0.249115\pi$
$409$	−5.17995	−	8.97193i	−0.256132	−	0.443633i	−0.965202	+	0.261504i	$0.915781\pi$
$410$	−22.2119	−	38.4721i	−1.09697	−	1.90000i
$411$	5.12252	−	0.271392i	0.252675	−	0.0133868i
$412$	−5.86154	+	10.1525i	−0.288777	+	0.500177i
$413$	−26.1642			−1.28745
$414$	−1.21708	+	2.74203i	−0.0598163	+	0.134763i
$415$	5.33975			0.262118
$416$	−1.14519	+	1.98352i	−0.0561474	+	0.0972502i
$417$	−0.889703	+	1.74861i	−0.0435690	+	0.0856297i
$418$	−12.7353	−	22.0581i	−0.622902	−	1.07890i
$419$	15.5174	+	26.8769i	0.758074	+	1.31302i	0.943832	+	0.330427i	$0.107193\pi$
$419$	15.5174	+	26.8769i	0.758074	+	1.31302i	−0.185758	+	0.982596i	$0.559474\pi$
$420$	−11.7204	+	23.0351i	−0.571897	+	1.12400i
$421$	−8.39865	+	14.5469i	−0.409325	+	0.708972i	−0.994814	−	0.101708i	$-0.967569\pi$
$421$	−8.39865	+	14.5469i	−0.409325	+	0.708972i	0.585489	+	0.810680i	$0.300902\pi$
$422$	22.2489			1.08306
$423$	7.31496	+	10.0441i	0.355666	+	0.488359i
$424$	−2.15706			−0.104756
$425$	−10.7522	+	18.6234i	−0.521560	+	0.903368i
$426$	−18.3133	+	0.970239i	−0.887282	+	0.0470082i
$427$	2.39162	+	4.14240i	0.115739	+	0.200465i
$428$	4.94543	+	8.56573i	0.239046	+	0.414040i
$429$	−6.56732	−	10.1002i	−0.317073	−	0.487641i
$430$	−12.1796	+	21.0958i	−0.587355	+	1.01733i
$431$	−13.8232			−0.665841			−0.332920	−	0.942955i	$-0.608034\pi$
$431$	−13.8232			−0.665841			−0.332920	+	0.942955i	$0.608034\pi$
$432$	−1.85383	+	4.85421i	−0.0891923	+	0.233548i
$433$	−20.6527			−0.992505			−0.496252	−	0.868178i	$-0.665291\pi$
$433$	−20.6527			−0.992505			−0.496252	+	0.868178i	$0.665291\pi$
$434$	−18.7650	+	32.5020i	−0.900749	+	1.56014i
$435$	−18.9709	−	29.1762i	−0.909587	−	1.39889i
$436$	−2.13803	−	3.70317i	−0.102393	−	0.177350i
$437$	−4.19350	−	7.26336i	−0.200602	−	0.347454i
$438$	−10.0944	+	0.534803i	−0.482330	+	0.0255539i
$439$	1.89987	−	3.29068i	0.0906761	−	0.157056i	−0.817120	−	0.576468i	$-0.804431\pi$
$439$	1.89987	−	3.29068i	0.0906761	−	0.157056i	0.907796	+	0.419412i	$0.137764\pi$
$440$	−11.2957			−0.538500
$441$	27.1312	−	2.88292i	1.29196	−	0.137282i
$442$	5.57514			0.265183
$443$	7.16075	−	12.4028i	0.340218	−	0.589274i	−0.644255	−	0.764810i	$-0.722833\pi$
$443$	7.16075	−	12.4028i	0.340218	−	0.589274i	0.984473	+	0.175536i	$0.0561659\pi$
$444$	1.46880	−	2.88675i	0.0697061	−	0.136999i
$445$	−28.0049	−	48.5059i	−1.32756	−	2.29940i
$446$	12.3735	+	21.4315i	0.585902	+	1.01481i
$447$	−3.19248	+	6.27444i	−0.150999	+	0.296771i
$448$	2.00591	−	3.47433i	0.0947702	−	0.164147i
$449$	9.70335			0.457930			0.228965	−	0.973435i	$-0.426466\pi$
$449$	9.70335			0.457930			0.228965	+	0.973435i	$0.426466\pi$
$450$	26.3550	−	2.80043i	1.24238	−	0.132014i
$451$	−36.2715			−1.70796
$452$	0.249940	−	0.432909i	0.0117562	−	0.0203623i
$453$	19.0824	−	1.01099i	0.896568	−	0.0475002i
$454$	12.0404	+	20.8545i	0.565082	+	0.978751i
$455$	−17.0883	−	29.5978i	−0.801111	−	1.38756i
$456$	−7.91877	−	12.1786i	−0.370830	−	0.570316i
$457$	−8.52899	+	14.7726i	−0.398969	+	0.691035i	−0.993599	−	0.112965i	$-0.963965\pi$
$457$	−8.52899	+	14.7726i	−0.398969	+	0.691035i	0.594630	+	0.804000i	$0.297299\pi$
$458$	6.45699			0.301715
$459$	12.4891	−	2.00001i	0.582944	−	0.0933525i
$460$	−3.71947			−0.173421
$461$	3.22774	−	5.59060i	0.150331	−	0.260380i	−0.781018	−	0.624508i	$-0.785300\pi$
$461$	3.22774	−	5.59060i	0.150331	−	0.260380i	0.931349	+	0.364128i	$0.118633\pi$
$462$	11.5033	+	17.6914i	0.535182	+	0.823079i
$463$	5.76085	+	9.97809i	0.267729	+	0.463721i	0.968275	−	0.249887i	$-0.0803933\pi$
$463$	5.76085	+	9.97809i	0.267729	+	0.463721i	−0.700546	+	0.713608i	$0.747060\pi$
$464$	2.70102	+	4.67830i	0.125392	+	0.217185i
$465$	60.1826	−	3.18848i	2.79090	−	0.147862i
$466$	1.48419	−	2.57069i	0.0687538	−	0.119085i
$467$	14.1465			0.654622			0.327311	−	0.944917i	$-0.393857\pi$
$467$	14.1465			0.654622			0.327311	+	0.944917i	$0.393857\pi$
$468$	−4.04509	−	5.55424i	−0.186984	−	0.256745i
$469$	−10.3602			−0.478390
$470$	−7.70267	+	13.3414i	−0.355298	+	0.615394i
$471$	−3.52974	+	6.93729i	−0.162642	+	0.319654i
$472$	−3.26089	−	5.64802i	−0.150095	−	0.259971i
$473$	9.94454	+	17.2245i	0.457250	+	0.791981i
$474$	0.220345	−	0.433063i	0.0101208	−	0.0198912i
$475$	−37.0472	+	64.1677i	−1.69984	+	2.94422i
$476$	−9.76541			−0.447597
$477$	2.62532	−	5.91472i	0.120205	−	0.270816i
$478$	10.5153			0.480960
$479$	1.02238	−	1.77081i	0.0467135	−	0.0809102i	−0.841723	−	0.539909i	$-0.818459\pi$
$479$	1.02238	−	1.77081i	0.0467135	−	0.0809102i	0.888437	+	0.458999i	$0.151792\pi$
$480$	−6.43328	+	0.340836i	−0.293638	+	0.0155570i
$481$	2.14150	+	3.70919i	0.0976440	+	0.169124i
$482$	8.48428	+	14.6952i	0.386448	+	0.669348i
$483$	3.78784	+	5.82548i	0.172353	+	0.265069i
$484$	0.888611	−	1.53912i	0.0403914	−	0.0699600i
$485$	−39.5067			−1.79391
$486$	−11.0541	−	10.9912i	−0.501425	−	0.498571i
$487$	−36.3892			−1.64895			−0.824477	−	0.565896i	$-0.808530\pi$
$487$	−36.3892			−1.64895			−0.824477	+	0.565896i	$0.808530\pi$
$488$	−0.596144	+	1.03255i	−0.0269862	+	0.0467414i
$489$	−19.4465	−	29.9076i	−0.879402	−	1.35247i
$490$	16.9136	+	29.2953i	0.764080	+	1.32343i
$491$	−8.25835	−	14.3039i	−0.372694	−	0.645525i	0.617285	−	0.786740i	$-0.288233\pi$
$491$	−8.25835	−	14.3039i	−0.372694	−	0.645525i	−0.989979	+	0.141214i	$0.954899\pi$
$492$	−20.6579	+	1.09446i	−0.931331	+	0.0493420i
$493$	6.57471	−	11.3877i	0.296110	−	0.512878i
$494$	19.2094			0.864271
$495$	13.7477	−	30.9730i	0.617915	−	1.39213i
$496$	−9.35487			−0.420046
$497$	−21.2386	+	36.7863i	−0.952680	+	1.65009i
$498$	1.12761	−	2.21619i	0.0505296	−	0.0993100i
$499$	16.6059	+	28.7623i	0.743383	+	1.28758i	0.950946	+	0.309356i	$0.100114\pi$
$499$	16.6059	+	28.7623i	0.743383	+	1.28758i	−0.207563	+	0.978222i	$0.566553\pi$
$500$	7.13104	+	12.3513i	0.318910	+	0.552368i
$501$	8.80643	−	17.3080i	0.393442	−	0.773264i
$502$	13.9318	−	24.1306i	0.621807	−	1.07700i
$503$	8.08665			0.360566			0.180283	−	0.983615i	$-0.442299\pi$
$503$	8.08665			0.360566			0.180283	+	0.983615i	$0.442299\pi$
$504$	7.08537	+	9.72880i	0.315607	+	0.433355i
$505$	32.3131			1.43791
$506$	−1.51845	+	2.63003i	−0.0675034	+	0.116919i
$507$	−13.4118	+	0.710559i	−0.595640	+	0.0315570i
$508$	7.63503	+	13.2243i	0.338750	+	0.586732i
$509$	6.22947	+	10.7898i	0.276116	+	0.478247i	0.970416	−	0.241438i	$-0.0776192\pi$
$509$	6.22947	+	10.7898i	0.276116	+	0.478247i	−0.694300	+	0.719686i	$0.744286\pi$
$510$	8.54833	+	13.1468i	0.378526	+	0.582152i
$511$	−11.7069	+	20.2769i	−0.517881	+	0.896997i
$512$	1.00000			0.0441942
$513$	43.0319	−	6.89112i	1.89990	−	0.304250i
$514$	−5.83393			−0.257323
$515$	21.8018	−	37.7618i	0.960702	−	1.66399i
$516$	6.18350	+	9.50988i	0.272214	+	0.418649i
$517$	6.28914	+	10.8931i	0.276596	+	0.479079i
$518$	−3.75105	−	6.49700i	−0.164811	−	0.285462i
$519$	16.5485	−	0.876742i	0.726400	−	0.0384847i
$520$	4.25949	−	7.37765i	0.186791	−	0.323531i
$521$	3.72673			0.163271			0.0816354	−	0.996662i	$-0.473986\pi$
$521$	3.72673			0.163271			0.0816354	+	0.996662i	$0.473986\pi$
$522$	−16.1154	+	1.71239i	−0.705351	+	0.0749494i
$523$	−36.7362			−1.60636			−0.803182	−	0.595734i	$-0.796861\pi$
$523$	−36.7362			−1.60636			−0.803182	+	0.595734i	$0.796861\pi$
$524$	2.87441	−	4.97862i	0.125569	−	0.217492i
$525$	27.8382	−	54.7126i	1.21496	−	2.38785i
$526$	−1.53070	−	2.65125i	−0.0667417	−	0.115600i
$527$	11.3856	+	19.7205i	0.495966	+	0.859039i
$528$	−2.38535	+	4.68812i	−0.103809	+	0.204024i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	8.02312			0.348502
$531$	19.4558	−	2.06734i	0.844310	−	0.0897150i
$532$	−33.6471			−1.45879
$533$	13.6776	−	23.6904i	0.592445	−	1.02614i
$534$	−26.0457	+	1.37990i	−1.12711	+	0.0597141i
$535$	−18.3943	−	31.8599i	−0.795257	−	1.37743i
$536$	−1.29121	−	2.23645i	−0.0557719	−	0.0965998i
$537$	15.4682	+	23.7892i	0.667502	+	1.02658i
$538$	9.07853	−	15.7245i	0.391403	−	0.677930i
$539$	27.6196			1.18966
$540$	6.89525	−	18.0551i	0.296724	−	0.776966i
$541$	−28.9731			−1.24565			−0.622825	−	0.782361i	$-0.714015\pi$
$541$	−28.9731			−1.24565			−0.622825	+	0.782361i	$0.714015\pi$
$542$	3.57131	−	6.18569i	0.153401	−	0.265698i
$543$	4.77324	+	7.34098i	0.204840	+	0.315031i
$544$	−1.21708	−	2.10805i	−0.0521819	−	0.0903817i
$545$	7.95232	+	13.7738i	0.340640	+	0.590006i
$546$	−15.8928	+	0.842000i	−0.680148	+	0.0360343i
$547$	−8.24013	+	14.2723i	−0.352322	+	0.610240i	−0.986656	−	0.162819i	$-0.947941\pi$
$547$	−8.24013	+	14.2723i	−0.352322	+	0.610240i	0.634334	+	0.773059i	$0.281275\pi$
$548$	2.96164			0.126515
$549$	−2.10573	−	2.89134i	−0.0898703	−	0.123399i
$550$	26.8293			1.14401
$551$	22.6534	−	39.2369i	0.965069	−	1.67155i
$552$	−0.785454	+	1.54372i	−0.0334311	+	0.0657050i
$553$	−0.562722	−	0.974663i	−0.0239294	−	0.0414469i
$554$	−9.39139	−	16.2664i	−0.399002	−	0.691092i
$555$	−5.46315	+	10.7372i	−0.231898	+	0.455768i
$556$	−0.566363	+	0.980969i	−0.0240191	+	0.0416024i
$557$	−3.39248			−0.143744			−0.0718721	−	0.997414i	$-0.522897\pi$
$557$	−3.39248			−0.143744			−0.0718721	+	0.997414i	$0.522897\pi$
$558$	11.3856	−	25.6513i	0.481993	−	1.08591i
$559$	−15.0000			−0.634431
$560$	−7.46091	+	12.9227i	−0.315281	+	0.546083i
$561$	12.7859	−	0.677399i	0.539822	−	0.0285998i
$562$	−6.78965	−	11.7600i	−0.286404	−	0.496066i
$563$	−10.1387	−	17.5608i	−0.427296	−	0.740098i	0.569336	−	0.822105i	$-0.307200\pi$
$563$	−10.1387	−	17.5608i	−0.427296	−	0.740098i	−0.996632	+	0.0820070i	$0.973867\pi$
$564$	3.91058	+	6.01425i	0.164665	+	0.253246i
$565$	−0.929644	+	1.61019i	−0.0391104	+	0.0677412i
$566$	3.25150			0.136671
$567$	−35.3001	+	7.58753i	−1.48246	+	0.318646i
$568$	−10.5880			−0.444263
$569$	3.83516	−	6.64269i	0.160778	−	0.278476i	−0.774370	−	0.632733i	$-0.781933\pi$
$569$	3.83516	−	6.64269i	0.160778	−	0.278476i	0.935148	+	0.354257i	$0.115266\pi$
$570$	29.4536	+	45.2980i	1.23368	+	1.89732i
$571$	14.1312	+	24.4760i	0.591373	+	1.02429i	0.994048	+	0.108945i	$0.0347473\pi$
$571$	14.1312	+	24.4760i	0.591373	+	1.02429i	−0.402674	+	0.915343i	$0.631919\pi$
$572$	−3.47782	−	6.02377i	−0.145415	−	0.251866i
$573$	−9.78186	+	0.518244i	−0.408643	+	0.0216499i
$574$	−23.9577	+	41.4960i	−0.999976	+	1.73201i
$575$	8.83444			0.368422
$576$	−1.21708	+	2.74203i	−0.0507117	+	0.114251i
$577$	−24.0389			−1.00075			−0.500375	−	0.865809i	$-0.666805\pi$
$577$	−24.0389			−1.00075			−0.500375	+	0.865809i	$0.666805\pi$
$578$	5.53743	−	9.59111i	0.230327	−	0.398937i
$579$	15.4167	−	30.2996i	0.640695	−	1.25921i
$580$	−10.0463	−	17.4008i	−0.417152	−	0.722528i
$581$	−2.87972	−	4.98783i	−0.119471	−	0.206930i
$582$	−8.34277	+	16.3967i	−0.345819	+	0.679667i
$583$	3.27539	−	5.67314i	0.135653	−	0.234958i
$584$	−5.83619			−0.241503
$585$	15.0456	+	20.6588i	0.622058	+	0.854138i
$586$	−5.02768			−0.207691
$587$	−5.74420	+	9.94925i	−0.237089	+	0.410650i	−0.959878	−	0.280419i	$-0.909527\pi$
$587$	−5.74420	+	9.94925i	−0.237089	+	0.410650i	0.722789	+	0.691069i	$0.242860\pi$
$588$	15.7303	−	0.833395i	0.648709	−	0.0343686i
$589$	39.2297	+	67.9478i	1.61643	+	2.79974i
$590$	12.1288	+	21.0076i	0.499334	+	0.864871i
$591$	−4.78362	−	7.35693i	−0.196772	−	0.302624i
$592$	0.935000	−	1.61947i	0.0384283	−	0.0665597i
$593$	12.4563			0.511518			0.255759	−	0.966741i	$-0.417675\pi$
$593$	12.4563			0.511518			0.255759	+	0.966741i	$0.417675\pi$
$594$	−9.95179	−	12.2465i	−0.408327	−	0.502480i
$595$	36.3221			1.48906
$596$	−2.03225	+	3.51996i	−0.0832442	+	0.144183i
$597$	6.84569	+	10.5283i	0.280175	+	0.430894i
$598$	−1.14519	−	1.98352i	−0.0468302	−	0.0811123i
$599$	−7.12263	−	12.3368i	−0.291023	−	0.504067i	0.683029	−	0.730391i	$-0.260662\pi$
$599$	−7.12263	−	12.3368i	−0.291023	−	0.504067i	−0.974052	+	0.226325i	$0.927329\pi$
$600$	15.2803	−	0.809549i	0.623814	−	0.0330497i
$601$	18.4220	−	31.9078i	0.751448	−	1.30155i	−0.195672	−	0.980669i	$-0.562689\pi$
$601$	18.4220	−	31.9078i	0.751448	−	1.30155i	0.947121	−	0.320878i	$-0.103978\pi$
$602$	26.2739			1.07084
$603$	7.70391	−	0.818605i	0.313727	−	0.0333362i
$604$	11.0327			0.448913
$605$	−3.30516	+	5.72470i	−0.134374	+	0.232742i
$606$	6.82367	−	13.4111i	0.277193	−	0.544790i
$607$	−9.18478	−	15.9085i	−0.372799	−	0.645707i	0.617196	−	0.786809i	$-0.288269\pi$
$607$	−9.18478	−	15.9085i	−0.372799	−	0.645707i	−0.989995	+	0.141103i	$0.954935\pi$
$608$	−4.19350	−	7.26336i	−0.170069	−	0.294568i
$609$	−17.0223	+	33.4554i	−0.689779	+	1.35568i
$610$	2.21734	−	3.84054i	0.0897774	−	0.155499i
$611$	−9.48631			−0.383775
$612$	7.26161	−	0.771606i	0.293533	−	0.0311903i
$613$	19.4182			0.784295			0.392148	−	0.919902i	$-0.371732\pi$
$613$	19.4182			0.784295			0.392148	+	0.919902i	$0.371732\pi$
$614$	4.90358	−	8.49325i	0.197892	−	0.342760i
$615$	76.8365	−	4.07080i	3.09835	−	0.164151i
$616$	6.09175	+	10.5512i	0.245443	+	0.425120i
$617$	1.97016	+	3.41242i	0.0793157	+	0.137379i	0.902955	−	0.429735i	$-0.141393\pi$
$617$	1.97016	+	3.41242i	0.0793157	+	0.137379i	−0.823639	+	0.567114i	$0.808060\pi$
$618$	−11.0686	−	17.0229i	−0.445244	−	0.684760i
$619$	12.7431	−	22.0717i	0.512188	−	0.887135i	−0.487712	−	0.873004i	$-0.662169\pi$
$619$	12.7431	−	22.0717i	0.512188	−	0.887135i	0.999900	−	0.0141308i	$-0.00449812\pi$
$620$	34.7952			1.39741
$621$	−3.27695	−	4.03256i	−0.131500	−	0.161821i
$622$	−6.88635			−0.276117
$623$	−30.2061	+	52.3185i	−1.21018	+	2.09609i
$624$	−2.16251	−	3.32581i	−0.0865695	−	0.133139i
$625$	−4.43756	−	7.68608i	−0.177502	−	0.307443i
$626$	−6.33490	−	10.9724i	−0.253194	−	0.438544i
$627$	44.0544	−	2.33401i	1.75936	−	0.0932112i
$628$	−2.24694	+	3.89182i	−0.0896628	+	0.155301i
$629$	−4.55188			−0.181495
$630$	−26.3538	−	36.1859i	−1.04996	−	1.44168i
$631$	6.73846			0.268254			0.134127	−	0.990964i	$-0.457177\pi$
$631$	6.73846			0.268254			0.134127	+	0.990964i	$0.457177\pi$
$632$	0.140266	−	0.242948i	0.00557949	−	0.00966396i
$633$	−17.4755	+	34.3460i	−0.694587	+	1.36513i
$634$	3.71647	+	6.43712i	0.147600	+	0.255651i
$635$	−28.3982	−	49.1872i	−1.12695	−	1.95193i
$636$	1.69427	−	3.32989i	0.0671822	−	0.132039i
$637$	−10.4151	+	18.0395i	−0.412661	+	0.714749i
$638$	−16.4054			−0.649498
$639$	12.8865	−	29.0326i	0.509781	−	1.14851i
$640$	−3.71947			−0.147025
$641$	−18.4876	+	32.0215i	−0.730217	+	1.26477i	0.226573	+	0.973994i	$0.427248\pi$
$641$	−18.4876	+	32.0215i	−0.730217	+	1.26477i	−0.956790	+	0.290779i	$0.906085\pi$
$642$	−17.1075	+	0.906354i	−0.675178	+	0.0357710i
$643$	−2.30376	−	3.99023i	−0.0908514	−	0.157359i	0.817018	−	0.576612i	$-0.195625\pi$
$643$	−2.30376	−	3.99023i	−0.0908514	−	0.157359i	−0.907870	+	0.419253i	$0.862292\pi$
$644$	2.00591	+	3.47433i	0.0790438	+	0.136908i
$645$	−22.9993	−	35.3717i	−0.905598	−	1.39276i
$646$	−10.2077	+	17.6802i	−0.401615	+	0.695618i
$647$	8.89668			0.349765			0.174882	−	0.984589i	$-0.444046\pi$
$647$	8.89668			0.349765			0.174882	+	0.984589i	$0.444046\pi$
$648$	−6.03743	−	6.67454i	−0.237173	−	0.262201i
$649$	19.8060			0.777454
$650$	−10.1171	+	17.5233i	−0.396825	+	0.687321i
$651$	−35.4348	−	54.4966i	−1.38880	−	2.13589i
$652$	−10.2982	−	17.8370i	−0.403308	−	0.698551i
$653$	0.187190	+	0.324222i	0.00732530	+	0.0126878i	0.869665	−	0.493643i	$-0.164335\pi$
$653$	0.187190	+	0.324222i	0.00732530	+	0.0126878i	−0.862340	+	0.506330i	$0.831002\pi$
$654$	7.39597	−	0.391839i	0.289205	−	0.0153221i
$655$	−10.6913	+	18.5178i	−0.417743	+	0.723551i
$656$	−11.9436			−0.466319
$657$	7.10312	−	16.0030i	0.277119	−	0.624337i
$658$	16.6162			0.647767
$659$	12.5306	−	21.7036i	0.488121	−	0.845451i	−0.511785	−	0.859113i	$-0.671016\pi$
$659$	12.5306	−	21.7036i	0.488121	−	0.845451i	0.999907	+	0.0136624i	$0.00434901\pi$
$660$	8.87222	−	17.4373i	0.345351	−	0.678746i
$661$	13.0625	+	22.6248i	0.508071	+	0.880004i	0.999956	+	0.00934446i	$0.00297448\pi$
$661$	13.0625	+	22.6248i	0.508071	+	0.880004i	−0.491886	+	0.870660i	$0.663692\pi$
$662$	−4.19805	−	7.27123i	−0.163162	−	0.282604i
$663$	−4.37902	+	8.60645i	−0.170067	+	0.334247i
$664$	0.717810	−	1.24328i	0.0278564	−	0.0482488i
$665$	125.149			4.85308
$666$	3.30265	+	4.53482i	0.127975	+	0.175721i
$667$	−5.40203			−0.209168
$668$	5.60595	−	9.70979i	0.216901	−	0.375683i
$669$	−42.8030	+	2.26771i	−1.65486	+	0.0876746i
$670$	4.80262	+	8.31839i	0.185542	+	0.321367i
$671$	−1.81043	−	3.13576i	−0.0698909	−	0.121055i
$672$	3.78784	+	5.82548i	0.146119	+	0.224723i
$673$	1.45588	−	2.52166i	0.0561200	−	0.0972027i	−0.836601	−	0.547813i	$-0.815460\pi$
$673$	1.45588	−	2.52166i	0.0561200	−	0.0972027i	0.892721	+	0.450611i	$0.148794\pi$
$674$	11.2670			0.433987
$675$	−16.3775	+	42.8842i	−0.630371	+	1.65061i
$676$	−7.75418			−0.298238
$677$	4.21217	−	7.29569i	0.161887	−	0.280396i	−0.773658	−	0.633603i	$-0.781575\pi$
$677$	4.21217	−	7.29569i	0.161887	−	0.280396i	0.935545	+	0.353206i	$0.114909\pi$
$678$	0.471972	+	0.725866i	0.0181260	+	0.0278767i
$679$	21.3059	+	36.9030i	0.817647	+	1.41621i
$680$	4.52689	+	7.84081i	0.173598	+	0.300681i
$681$	−41.6506	+	2.20665i	−1.59606	+	0.0845591i
$682$	14.2049	−	24.6036i	0.543935	−	0.942122i
$683$	−44.3011			−1.69514			−0.847568	−	0.530687i	$-0.821934\pi$
$683$	−44.3011			−1.69514			−0.847568	+	0.530687i	$0.821934\pi$
$684$	25.0202	−	2.65860i	0.956670	−	0.101654i
$685$	−11.0157			−0.420889
$686$	4.20169	−	7.27754i	0.160421	−	0.277858i
$687$	−5.07166	+	9.96776i	−0.193496	+	0.380294i
$688$	3.27457	+	5.67172i	0.124842	+	0.216232i
$689$	2.47024	+	4.27858i	0.0941086	+	0.163001i
$690$	2.92147	−	5.74181i	0.111218	−	0.218587i
$691$	6.44077	−	11.1557i	0.245019	−	0.424385i	−0.717118	−	0.696951i	$-0.754539\pi$
$691$	6.44077	−	11.1557i	0.245019	−	0.424385i	0.962137	+	0.272567i	$0.0878726\pi$
$692$	9.56769			0.363709
$693$	−36.3459	+	3.86205i	−1.38067	+	0.146707i
$694$	29.4867			1.11930
$695$	2.10657	−	3.64868i	0.0799067	−	0.138402i
$696$	−9.34349	+	0.495019i	−0.354164	+	0.0187636i
$697$	14.5363	+	25.1776i	0.550602	+	0.953671i
$698$	14.9456	+	25.8866i	0.565700	+	0.979821i
$699$	2.80266	+	4.31033i	0.106006	+	0.163032i
$700$	17.7211	−	30.6938i	0.669793	−	1.16012i
$701$	27.0240			1.02068			0.510342	−	0.859972i	$-0.329519\pi$
$701$	27.0240			1.02068			0.510342	+	0.859972i	$0.329519\pi$
$702$	11.7514	−	1.88187i	0.443528	−	0.0710266i
$703$	−15.6837			−0.591522
$704$	−1.51845	+	2.63003i	−0.0572288	+	0.0991232i
$705$	−14.5453	−	22.3698i	−0.547807	−	0.842496i
$706$	−2.60103	−	4.50511i	−0.0978909	−	0.169552i
$707$	−17.4264	−	30.1835i	−0.655388	−	1.13517i
$708$	11.2802	−	0.597627i	0.423937	−	0.0224602i
$709$	−23.8572	+	41.3220i	−0.895978	+	1.55188i	−0.0633876	+	0.997989i	$0.520190\pi$
$709$	−23.8572	+	41.3220i	−0.895978	+	1.55188i	−0.832590	+	0.553890i	$0.813143\pi$
$710$	39.3818			1.47797
$711$	0.495455	+	0.680301i	0.0185810	+	0.0255133i
$712$	−15.0586			−0.564343
$713$	4.67744	−	8.10156i	0.175171	−	0.303406i
$714$	7.67028	−	15.0750i	0.287053	−	0.564169i
$715$	12.9357	+	22.4052i	0.483766	+	0.837907i
$716$	8.19141	+	14.1879i	0.306127	+	0.530228i
$717$	−8.25930	+	16.2327i	−0.308449	+	0.606221i
$718$	−17.4250	+	30.1809i	−0.650294	+	1.12634i
$719$	−23.2822			−0.868279			−0.434140	−	0.900846i	$-0.642948\pi$
$719$	−23.2822			−0.868279			−0.434140	+	0.900846i	$0.642948\pi$
$720$	4.52689	−	10.1989i	0.168707	−	0.380090i
$721$	−47.0308			−1.75152
$722$	−25.6709	+	44.4633i	−0.955373	+	1.65475i
$723$	−29.3492	+	1.55492i	−1.09151	+	0.0578283i
$724$	2.52774	+	4.37818i	0.0939428	+	0.162714i
$725$	23.8620	+	41.3301i	0.886211	+	1.53496i
$726$	1.67800	+	2.58067i	0.0622765	+	0.0957777i
$727$	−16.2016	+	28.0619i	−0.600883	+	1.04076i	0.391805	+	0.920048i	$0.371851\pi$
$727$	−16.2016	+	28.0619i	−0.600883	+	1.04076i	−0.992688	+	0.120711i	$0.961482\pi$
$728$	−9.18856			−0.340551
$729$	25.6498	−	8.43134i	0.949993	−	0.312272i
$730$	21.7075			0.803432
$731$	7.97083	−	13.8059i	0.294812	−	0.510629i
$732$	−1.12572	−	1.73130i	−0.0416079	−	0.0639906i
$733$	−8.66105	−	15.0014i	−0.319903	−	0.554088i	0.660565	−	0.750769i	$-0.270317\pi$
$733$	−8.66105	−	15.0014i	−0.319903	−	0.554088i	−0.980468	+	0.196681i	$0.936984\pi$
$734$	3.86994	+	6.70294i	0.142842	+	0.247410i
$735$	−58.5085	+	3.09978i	−2.15812	+	0.114337i
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	7.84258			0.288885
$738$	14.5363	−	32.7496i	0.535089	−	1.20553i
$739$	−35.4786			−1.30510			−0.652550	−	0.757746i	$-0.726301\pi$
$739$	−35.4786			−1.30510			−0.652550	+	0.757746i	$0.726301\pi$
$740$	−3.47770	+	6.02356i	−0.127843	+	0.221430i
$741$	−15.0881	+	29.6539i	−0.554275	+	1.08936i
$742$	−4.32686	−	7.49435i	−0.158844	−	0.275126i
$743$	−15.0746	−	26.1100i	−0.553035	−	0.957884i	−0.998054	−	0.0623631i	$-0.980136\pi$
$743$	−15.0746	−	26.1100i	−0.553035	−	0.957884i	0.445019	−	0.895521i	$-0.353197\pi$
$744$	7.34782	−	14.4413i	0.269384	−	0.529443i
$745$	7.55889	−	13.0924i	0.276936	−	0.479668i
$746$	−1.16568			−0.0426787
$747$	2.53549	+	3.48143i	0.0927686	+	0.127379i
$748$	7.39231			0.270290
$749$	−19.8401	+	34.3641i	−0.724943	+	1.25564i
$750$	−24.6680	+	1.30691i	−0.900749	+	0.0477218i
$751$	−11.0957	−	19.2183i	−0.404888	−	0.701286i	0.589421	−	0.807826i	$-0.299356\pi$
$751$	−11.0957	−	19.2183i	−0.404888	−	0.701286i	−0.994308	+	0.106540i	$0.966023\pi$
$752$	2.07091	+	3.58692i	0.0755182	+	0.130801i
$753$	26.3080	+	40.4602i	0.958717	+	1.47445i
$754$	6.18634	−	10.7151i	0.225293	−	0.390219i
$755$	−41.0356			−1.49344
$756$	−20.5837	+	3.29628i	−0.748623	+	0.119884i
$757$	40.4615			1.47060			0.735299	−	0.677743i	$-0.237042\pi$
$757$	40.4615			1.47060			0.735299	+	0.677743i	$0.237042\pi$
$758$	−17.6030	+	30.4892i	−0.639368	+	1.10742i
$759$	−2.86736	−	4.40983i	−0.104078	−	0.160067i
$760$	15.5976	+	27.0158i	0.565784	+	0.979967i
$761$	−10.1340	−	17.5527i	−0.367358	−	0.636283i	0.621793	−	0.783181i	$-0.286404\pi$
$761$	−10.1340	−	17.5527i	−0.367358	−	0.636283i	−0.989152	+	0.146898i	$0.953071\pi$
$762$	−26.4115	+	1.39928i	−0.956787	+	0.0506906i
$763$	8.57736	−	14.8564i	0.310521	−	0.537839i
$764$	−5.65548			−0.204608
$765$	−27.0093	+	2.86997i	−0.976524	+	0.103764i
$766$	−29.4774			−1.06506
$767$	−7.46866	+	12.9361i	−0.269678	+	0.467095i
$768$	−0.785454	+	1.54372i	−0.0283426	+	0.0557041i
$769$	14.3030	+	24.7735i	0.515779	+	0.893355i	0.999832	+	0.0183166i	$0.00583068\pi$
$769$	14.3030	+	24.7735i	0.515779	+	0.893355i	−0.484053	+	0.875038i	$0.660836\pi$
$770$	−22.6581	−	39.2449i	−0.816539	−	1.41429i
$771$	4.58228	−	9.00593i	0.165027	−	0.324341i
$772$	9.81386	−	16.9981i	0.353208	−	0.611775i
$773$	1.25682			0.0452048			0.0226024	−	0.999745i	$-0.492805\pi$
$773$	1.25682			0.0452048			0.0226024	+	0.999745i	$0.492805\pi$
$774$	−19.5374	+	2.07601i	−0.702258	+	0.0746208i
$775$	−82.6451			−2.96870
$776$	−5.31080	+	9.19857i	−0.190647	+	0.330210i
$777$	12.9758	−	0.687459i	0.465504	−	0.0246625i
$778$	0.0897001	+	0.155365i	0.00321590	+	0.00557011i
$779$	50.0855	+	86.7506i	1.79450	+	3.10816i
$780$	8.04337	+	12.3702i	0.287999	+	0.442926i
$781$	16.0774	−	27.8468i	0.575294	−	0.996438i
$782$	2.43416			0.0870455
$783$	10.0144	−	26.2226i	0.357887	−	0.937119i
$784$	9.09466			0.324809
$785$	8.35744	−	14.4755i	0.298290	−	0.516653i
$786$	5.42787	+	8.34775i	0.193606	+	0.297755i
$787$	3.59511	+	6.22691i	0.128152	+	0.221965i	0.922961	−	0.384895i	$-0.125762\pi$
$787$	3.59511	+	6.22691i	0.128152	+	0.221965i	−0.794809	+	0.606860i	$0.792429\pi$
$788$	−2.53324	−	4.38769i	−0.0902428	−	0.156305i
$789$	5.29508	−	0.280533i	0.188510	−	0.00998726i
$790$	−0.521716	+	0.903638i	−0.0185618	+	0.0321500i
$791$	2.00543			0.0713047
$792$	−5.36355	−	7.36460i	−0.190585	−	0.261690i
$793$	2.73079			0.0969731
$794$	−7.57745	+	13.1245i	−0.268914	+	0.465772i
$795$	−6.30179	+	12.3854i	−0.223501	+	0.439266i
$796$	3.62524	+	6.27910i	0.128493	+	0.222557i
$797$	−23.6706	−	40.9987i	−0.838456	−	1.45225i	−0.891185	−	0.453640i	$-0.850125\pi$
$797$	−23.6706	−	40.9987i	−0.838456	−	1.45225i	0.0527287	−	0.998609i	$-0.483208\pi$
$798$	26.4282	−	51.9416i	0.935550	−	1.83871i
$799$	5.04092	−	8.73114i	0.178335	−	0.308885i
$800$	8.83444			0.312345
$801$	18.3275	−	41.2910i	0.647570	−	1.45895i
$802$	−27.3999			−0.967525
$803$	8.86198	−	15.3494i	0.312732	−	0.541668i
$804$	4.46663	−	0.236642i	0.157526	−	0.00834573i
$805$	−7.46091	−	12.9227i	−0.262962	−	0.455464i
$806$	10.7131	+	18.5556i	0.377352	+	0.653593i
$807$	17.1434	+	26.3655i	0.603475	+	0.928111i
$808$	4.34378	−	7.52364i	0.152814	−	0.264681i
$809$	1.70654			0.0599989			0.0299994	−	0.999550i	$-0.490449\pi$
$809$	1.70654			0.0599989			0.0299994	+	0.999550i	$0.490449\pi$
$810$	22.4560	+	24.8257i	0.789024	+	0.872287i
$811$	10.1889			0.357782			0.178891	−	0.983869i	$-0.442749\pi$
$811$	10.1889			0.357782			0.178891	+	0.983869i	$0.442749\pi$
$812$	−10.8360	+	18.7685i	−0.380268	+	0.658644i
$813$	6.74386	+	10.3717i	0.236518	+	0.363750i
$814$	2.83950	+	4.91816i	0.0995245	+	0.172382i
$815$	38.3038	+	66.3441i	1.34172	+	2.32393i
$816$	4.21019	−	0.223056i	0.147386	−	0.00780852i
$817$	27.4638	−	47.5687i	0.960837	−	1.66422i
$818$	10.3599			0.362225
$819$	11.1832	−	25.1953i	0.390773	−	0.880394i
$820$	44.4238			1.55135
$821$	14.6055	−	25.2974i	0.509735	−	0.882886i	−0.490202	−	0.871609i	$-0.663077\pi$
$821$	14.6055	−	25.2974i	0.509735	−	0.882886i	0.999936	−	0.0112772i	$-0.00358972\pi$
$822$	−2.32623	+	4.57193i	−0.0811366	+	0.159464i
$823$	−13.9739	−	24.2035i	−0.487100	−	0.843683i	0.512790	−	0.858514i	$-0.328612\pi$
$823$	−13.9739	−	24.2035i	−0.487100	−	0.843683i	−0.999890	+	0.0148317i	$0.995279\pi$
$824$	−5.86154	−	10.1525i	−0.204196	−	0.353679i
$825$	−21.0732	+	41.4169i	−0.733675	+	1.44195i
$826$	13.0821	−	22.6588i	0.455184	−	0.788401i
$827$	−15.0913			−0.524776			−0.262388	−	0.964962i	$-0.584510\pi$
$827$	−15.0913			−0.524776			−0.262388	+	0.964962i	$0.584510\pi$
$828$	−1.76612	−	2.42504i	−0.0613771	−	0.0842759i
$829$	31.6202			1.09821			0.549107	−	0.835752i	$-0.314968\pi$
$829$	31.6202			1.09821			0.549107	+	0.835752i	$0.314968\pi$
$830$	−2.66987	+	4.62436i	−0.0926726	+	0.160514i
$831$	32.4872	−	1.72117i	1.12697	−	0.0597068i
$832$	−1.14519	−	1.98352i	−0.0397022	−	0.0687663i
$833$	−11.0689	−	19.1720i	−0.383516	−	0.664269i
$834$	−1.06949	−	1.64481i	−0.0370333	−	0.0569551i
$835$	−20.8511	+	36.1152i	−0.721584	+	1.24982i
$836$	25.4705			0.880916
$837$	30.6555	+	37.7241i	1.05961	+	1.30394i
$838$	−31.0348			−1.07208
$839$	17.0906	−	29.6018i	0.590033	−	1.02197i	−0.404194	−	0.914673i	$-0.632448\pi$
$839$	17.0906	−	29.6018i	0.590033	−	1.02197i	0.994227	−	0.107294i	$-0.0342187\pi$
$840$	−14.0887	−	21.6677i	−0.486108	−	0.747606i
$841$	−0.0909775	−	0.157578i	−0.00313716	−	0.00543371i
$842$	−8.39865	−	14.5469i	−0.289436	−	0.501319i
$843$	23.4871	−	1.24435i	0.808938	−	0.0428576i
$844$	−11.1244	+	19.2681i	−0.382919	+	0.663235i
$845$	28.8414			0.992175
$846$	−12.3559	+	1.31292i	−0.424804	+	0.0451390i
$847$	7.12988			0.244986
$848$	1.07853	−	1.86807i	0.0370369	−	0.0641498i
$849$	−2.55390	+	5.01940i	−0.0876497	+	0.172265i
$850$	−10.7522	−	18.6234i	−0.368798	−	0.638778i
$851$	0.935000	+	1.61947i	0.0320514	+	0.0555146i
$852$	8.31639	−	16.3449i	0.284915	−	0.559967i
$853$	8.13306	−	14.0869i	0.278471	−	0.482325i	−0.692534	−	0.721385i	$-0.743506\pi$
$853$	8.13306	−	14.0869i	0.278471	−	0.482325i	0.971005	+	0.239060i	$0.0768392\pi$
$854$	−4.78324			−0.163679
$855$	−93.0617	+	9.88858i	−3.18264	+	0.338182i
$856$	−9.89085			−0.338062
$857$	−21.5965	+	37.4062i	−0.737722	+	1.27777i	0.215796	+	0.976438i	$0.430765\pi$
$857$	−21.5965	+	37.4062i	−0.737722	+	1.27777i	−0.953519	+	0.301334i	$0.902568\pi$
$858$	12.0307	−	0.637385i	0.410720	−	0.0217600i
$859$	4.72117	+	8.17731i	0.161084	+	0.279006i	0.935258	−	0.353967i	$-0.115168\pi$
$859$	4.72117	+	8.17731i	0.161084	+	0.279006i	−0.774174	+	0.632973i	$0.781834\pi$
$860$	−12.1796	−	21.0958i	−0.415322	−	0.719360i
$861$	−45.2404	−	69.5772i	−1.54179	−	2.37118i
$862$	6.91161	−	11.9713i	0.235410	−	0.407743i
$863$	12.0578			0.410453			0.205227	−	0.978714i	$-0.434207\pi$
$863$	12.0578			0.410453			0.205227	+	0.978714i	$0.434207\pi$
$864$	−3.27695	−	4.03256i	−0.111484	−	0.137191i
$865$	−35.5867			−1.20998
$866$	10.3263	−	17.8857i	0.350903	−	0.607783i
$867$	10.4566	+	16.0816i	0.355123	+	0.546159i
$868$	−18.7650	−	32.5020i	−0.636926	−	1.10319i
$869$	0.425975	+	0.737810i	0.0144502	+	0.0250285i
$870$	34.7528	−	1.84121i	1.17823	−	0.0624227i
$871$	−2.95736	+	5.12230i	−0.100206	+	0.173563i
$872$	4.27605			0.144805
$873$	−18.7591	−	25.7578i	−0.634898	−	0.871768i
$874$	8.38700			0.283695
$875$	−28.6084	+	49.5512i	−0.967140	+	1.67514i
$876$	4.58406	−	9.00943i	0.154881	−	0.304401i
$877$	−16.7129	−	28.9475i	−0.564353	−	0.977488i	−0.997110	−	0.0759771i	$-0.975792\pi$
$877$	−16.7129	−	28.9475i	−0.564353	−	0.977488i	0.432757	−	0.901511i	$-0.357541\pi$
$878$	1.89987	+	3.29068i	0.0641177	+	0.111055i
$879$	3.94901	−	7.76131i	0.133197	−	0.261782i
$880$	5.64783	−	9.78233i	0.190388	−	0.329762i
$881$	−11.8765			−0.400130			−0.200065	−	0.979783i	$-0.564115\pi$
$881$	−11.8765			−0.400130			−0.200065	+	0.979783i	$0.564115\pi$
$882$	−11.0689	+	24.9378i	−0.372710	+	0.839699i
$883$	38.5733			1.29809			0.649047	−	0.760748i	$-0.275168\pi$
$883$	38.5733			1.29809			0.649047	+	0.760748i	$0.275168\pi$
$884$	−2.78757	+	4.82822i	−0.0937562	+	0.162390i
$885$	−41.9564	+	2.22285i	−1.41035	+	0.0747205i
$886$	7.16075	+	12.4028i	0.240570	+	0.416680i
$887$	−23.9053	−	41.4051i	−0.802660	−	1.39025i	−0.917860	−	0.396905i	$-0.870084\pi$
$887$	−23.9053	−	41.4051i	−0.802660	−	1.39025i	0.115200	−	0.993342i	$-0.463249\pi$
$888$	1.76560	+	2.71539i	0.0592497	+	0.0911226i
$889$	−30.6303	+	53.0533i	−1.02731	+	1.77935i
$890$	56.0098			1.87745
$891$	26.7218	−	5.74368i	0.895214	−	0.192421i
$892$	−24.7470			−0.828591
$893$	17.3687	−	30.0835i	0.581222	−	1.00671i
$894$	−3.83758	−	5.90198i	−0.128348	−	0.197392i
$895$	−30.4677	−	52.7716i	−1.01842	−	1.76396i
$896$	2.00591	+	3.47433i	0.0670127	+	0.116069i
$897$	3.96149	−	0.209880i	0.132270	−	0.00700769i
$898$	−4.85168	+	8.40335i	−0.161903	+	0.280423i
$899$	50.5353			1.68545
$900$	−10.7522	+	24.2243i	−0.358408	+	0.807476i
$901$	−5.25063			−0.174924
$902$	18.1358	−	31.4121i	0.603855	−	1.04591i
$903$	−20.6369	+	40.5595i	−0.686754	+	1.34974i
$904$	0.249940	+	0.432909i	0.00831288	+	0.0143983i
$905$	−9.40186	−	16.2845i	−0.312528	−	0.541315i
$906$	−8.66565	+	17.0313i	−0.287897	+	0.565828i
$907$	−0.282486	+	0.489280i	−0.00937979	+	0.0162463i	−0.870677	−	0.491855i	$-0.836319\pi$
$907$	−0.282486	+	0.489280i	−0.00937979	+	0.0162463i	0.861297	+	0.508101i	$0.169652\pi$
$908$	−24.0807			−0.799147
$909$	15.3433	+	21.0676i	0.508905	+	0.698769i
$910$	34.1766			1.13294
$911$	−1.29271	+	2.23904i	−0.0428294	+	0.0741828i	−0.886645	−	0.462450i	$-0.846971\pi$
$911$	−1.29271	+	2.23904i	−0.0428294	+	0.0741828i	0.843816	+	0.536633i	$0.180304\pi$
$912$	14.5064	−	0.768548i	0.480354	−	0.0254492i
$913$	2.17992	+	3.77573i	0.0721448	+	0.124959i
$914$	−8.52899	−	14.7726i	−0.282114	−	0.488635i
$915$	4.18709	+	6.43951i	0.138421	+	0.212884i
$916$	−3.22849	+	5.59191i	−0.106672	+	0.184762i
$917$	23.0632			0.761614
$918$	−4.51251	+	11.8159i	−0.148935	+	0.389984i
$919$	−41.0191			−1.35309			−0.676547	−	0.736399i	$-0.736525\pi$
$919$	−41.0191			−1.35309			−0.676547	+	0.736399i	$0.736525\pi$
$920$	1.85973	−	3.22115i	0.0613136	−	0.106198i
$921$	9.25964	+	14.2408i	0.305116	+	0.469250i
$922$	3.22774	+	5.59060i	0.106300	+	0.184117i
$923$	12.1253	+	21.0016i	0.399108	+	0.691275i
$924$	−21.0729	+	1.11644i	−0.693247	+	0.0367282i
$925$	8.26020	−	14.3071i	0.271594	−	0.470414i
$926$	−11.5217			−0.378627
$927$	34.9724	−	3.71611i	1.14864	−	0.122053i
$928$	−5.40203			−0.177330
$929$	−11.5411	+	19.9898i	−0.378651	+	0.655843i	−0.990866	−	0.134848i	$-0.956945\pi$
$929$	−11.5411	+	19.9898i	−0.378651	+	0.655843i	0.612215	+	0.790691i	$0.290279\pi$
$930$	−27.3300	+	53.7139i	−0.896185	+	1.76135i
$931$	−38.1385	−	66.0578i	−1.24994	−	2.16496i
$932$	1.48419	+	2.57069i	0.0486163	+	0.0842058i
$933$	5.40891	−	10.6306i	0.177080	−	0.348029i
$934$	−7.07325	+	12.2512i	−0.231444	+	0.400873i
$935$	−27.4955			−0.899198
$936$	6.83266	−	0.726027i	0.223332	−	0.0237309i
$937$	10.2885			0.336111			0.168055	−	0.985778i	$-0.446251\pi$
$937$	10.2885			0.336111			0.168055	+	0.985778i	$0.446251\pi$
$938$	5.18011	−	8.97221i	0.169136	−	0.292953i
$939$	21.9140	−	1.16101i	0.715137	−	0.0378880i
$940$	−7.70267	−	13.3414i	−0.251234	−	0.435149i
$941$	−28.3625	−	49.1253i	−0.924592	−	1.60144i	−0.792217	−	0.610240i	$-0.791073\pi$
$941$	−28.3625	−	49.1253i	−0.924592	−	1.60144i	−0.132375	−	0.991200i	$-0.542260\pi$
$942$	−4.24300	−	6.52549i	−0.138244	−	0.212612i
$943$	5.97179	−	10.3435i	0.194468	−	0.336829i
$944$	6.52178			0.212266
$945$	76.5605	−	12.2604i	2.49051	−	0.398831i
$946$	−19.8891			−0.646650
$947$	−27.6486	+	47.8888i	−0.898459	+	1.55618i	−0.0689951	+	0.997617i	$0.521979\pi$
$947$	−27.6486	+	47.8888i	−0.898459	+	1.55618i	−0.829464	+	0.558560i	$0.811354\pi$
$948$	0.264871	+	0.407356i	0.00860260	+	0.0132303i
$949$	6.68354	+	11.5762i	0.216957	+	0.375780i
$950$	−37.0472	−	64.1677i	−1.20197	−	2.08188i
$951$	−12.8562	+	0.681122i	−0.416891	+	0.0220869i
$952$	4.88270	−	8.45709i	0.158249	−	0.274096i
$953$	52.1203			1.68834			0.844171	−	0.536074i	$-0.180093\pi$
$953$	52.1203			1.68834			0.844171	+	0.536074i	$0.180093\pi$
$954$	3.80964	+	5.23095i	0.123342	+	0.169358i
$955$	21.0354			0.680689
$956$	−5.25766	+	9.10654i	−0.170045	+	0.294527i
$957$	12.8857	−	25.3254i	0.416536	−	0.818653i
$958$	1.02238	+	1.77081i	0.0330314	+	0.0572121i
$959$	5.94077	+	10.2897i	0.191838	+	0.332272i
$960$	2.92147	−	5.74181i	0.0942900	−	0.185316i
$961$	−28.2568	+	48.9423i	−0.911511	+	1.57878i
$962$	−4.28300			−0.138089
$963$	12.0380	−	27.1210i	0.387918	−	0.873961i
$964$	−16.9686			−0.546521
$965$	−36.5023	+	63.2239i	−1.17505	+	2.03525i
$966$	−6.93894	+	0.367625i	−0.223257	+	0.0118281i
$967$	14.9802	+	25.9465i	0.481731	+	0.834382i	0.999780	−	0.0209687i	$-0.00667503\pi$
$967$	14.9802	+	25.9465i	0.481731	+	0.834382i	−0.518049	+	0.855351i	$0.673342\pi$
$968$	0.888611	+	1.53912i	0.0285610	+	0.0494692i
$969$	−19.2756	−	29.6447i	−0.619220	−	0.952326i
$970$	19.7533	−	34.2138i	0.634242	−	1.09854i
$971$	−53.3700			−1.71273			−0.856363	−	0.516374i	$-0.827281\pi$
$971$	−53.3700			−1.71273			−0.856363	+	0.516374i	$0.827281\pi$
$972$	15.0457	−	4.07754i	0.482592	−	0.130787i
$973$	−4.54428			−0.145683
$974$	18.1946	−	31.5140i	0.582993	−	1.00977i
$975$	−19.1045	−	29.3817i	−0.611835	−	0.940967i
$976$	−0.596144	−	1.03255i	−0.0190821	−	0.0330512i
$977$	1.89912	+	3.28938i	0.0607583	+	0.105236i	0.894805	−	0.446458i	$-0.147315\pi$
$977$	1.89912	+	3.28938i	0.0607583	+	0.105236i	−0.834046	+	0.551694i	$0.813981\pi$
$978$	35.6240	−	1.88736i	1.13913	−	0.0603512i
$979$	22.8657	−	39.6045i	0.730791	−	1.26577i
$980$	−33.8273			−1.08057
$981$	−5.20430	+	11.7251i	−0.166161	+	0.374352i
$982$	16.5167			0.527069
$983$	−17.4868	+	30.2881i	−0.557744	+	0.966040i	0.439941	+	0.898027i	$0.354999\pi$
$983$	−17.4868	+	30.2881i	−0.557744	+	0.966040i	−0.997684	+	0.0680136i	$0.978334\pi$
$984$	9.38114	−	18.4375i	0.299060	−	0.587767i
$985$	9.42229	+	16.3199i	0.300219	+	0.519995i
$986$	6.57471	+	11.3877i	0.209381	+	0.362659i
$987$	−13.0513	+	25.6507i	−0.415426	+	0.816471i
$988$	−9.60469	+	16.6358i	−0.305566	+	0.529256i
$989$	−6.54913			−0.208250
$990$	19.9495	+	27.3924i	0.634038	+	0.870587i
$991$	16.9687			0.539029			0.269514	−	0.962996i	$-0.413137\pi$
$991$	16.9687			0.539029			0.269514	+	0.962996i	$0.413137\pi$
$992$	4.67744	−	8.10156i	0.148509	−	0.257225i
$993$	14.5221	−	0.769381i	0.460845	−	0.0244156i
$994$	−21.2386	−	36.7863i	−0.673646	−	1.16679i
$995$	−13.4840	−	23.3549i	−0.427470	−	0.740400i
$996$	1.35547	+	2.08464i	0.0429498	+	0.0660543i
$997$	11.3644	−	19.6837i	0.359915	−	0.623390i	−0.628032	−	0.778188i	$-0.716139\pi$
$997$	11.3644	−	19.6837i	0.359915	−	0.623390i	0.987946	+	0.154797i	$0.0494725\pi$
$998$	−33.2119			−1.05130
$999$	−9.59456	+	1.53647i	−0.303558	+	0.0486118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.c.277.2	yes	10
3.2	odd	2		1242.2.e.c.829.1		10
9.2	odd	6		3726.2.a.s.1.5		5
9.4	even	3	inner	414.2.e.c.139.2	✓	10
9.5	odd	6		1242.2.e.c.415.1		10
9.7	even	3		3726.2.a.t.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.c.139.2	✓	10	9.4	even	3	inner
414.2.e.c.277.2	yes	10	1.1	even	1	trivial
1242.2.e.c.415.1		10	9.5	odd	6
1242.2.e.c.829.1		10	3.2	odd	2
3726.2.a.s.1.5		5	9.2	odd	6
3726.2.a.t.1.1		5	9.7	even	3

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.944171 - 1.45208i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.85973 + 3.22115i) q^{5} +(1.72963 - 0.0916356i) q^{6} +(2.00591 - 3.47433i) q^{7} +1.00000 q^{8} +(-1.21708 + 2.74203i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.944171 - 1.45208i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.85973 + 3.22115i) q^{5} +(1.72963 - 0.0916356i) q^{6} +(2.00591 - 3.47433i) q^{7} +1.00000 q^{8} +(-1.21708 + 2.74203i) q^{9} -3.71947 q^{10} +(-1.51845 + 2.63003i) q^{11} +(-0.785454 + 1.54372i) q^{12} +(-1.14519 - 1.98352i) q^{13} +(2.00591 + 3.47433i) q^{14} +(2.92147 - 5.74181i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.43416 q^{17} +(-1.76612 - 2.42504i) q^{18} +8.38700 q^{19} +(1.85973 - 3.22115i) q^{20} +(-6.93894 + 0.367625i) q^{21} +(-1.51845 - 2.63003i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.944171 - 1.45208i) q^{24} +(-4.41722 + 7.65085i) q^{25} +2.29038 q^{26} +(5.13078 - 0.821643i) q^{27} -4.01181 q^{28} +(2.70102 - 4.67830i) q^{29} +(3.51181 + 5.40097i) q^{30} +(4.67744 + 8.10156i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.25270 - 0.278288i) q^{33} +(-1.21708 + 2.10805i) q^{34} +14.9218 q^{35} +(2.98321 - 0.316991i) q^{36} -1.87000 q^{37} +(-4.19350 + 7.26336i) q^{38} +(-1.79898 + 3.53569i) q^{39} +(1.85973 + 3.22115i) q^{40} +(5.97179 + 10.3435i) q^{41} +(3.15109 - 6.19311i) q^{42} +(3.27457 - 5.67172i) q^{43} +3.03690 q^{44} +(-11.0959 + 1.17904i) q^{45} +1.00000 q^{46} +(2.07091 - 3.58692i) q^{47} +(1.72963 - 0.0916356i) q^{48} +(-4.54733 - 7.87620i) q^{49} +(-4.41722 - 7.65085i) q^{50} +(-2.29827 - 3.53460i) q^{51} +(-1.14519 + 1.98352i) q^{52} -2.15706 q^{53} +(-1.85383 + 4.85421i) q^{54} -11.2957 q^{55} +(2.00591 - 3.47433i) q^{56} +(-7.91877 - 12.1786i) q^{57} +(2.70102 + 4.67830i) q^{58} +(-3.26089 - 5.64802i) q^{59} +(-6.43328 + 0.340836i) q^{60} +(-0.596144 + 1.03255i) q^{61} -9.35487 q^{62} +(7.08537 + 9.72880i) q^{63} +1.00000 q^{64} +(4.25949 - 7.37765i) q^{65} +(-2.38535 + 4.68812i) q^{66} +(-1.29121 - 2.23645i) q^{67} +(-1.21708 - 2.10805i) q^{68} +(-0.785454 + 1.54372i) q^{69} +(-7.46091 + 12.9227i) q^{70} -10.5880 q^{71} +(-1.21708 + 2.74203i) q^{72} -5.83619 q^{73} +(0.935000 - 1.61947i) q^{74} +(15.2803 - 0.809549i) q^{75} +(-4.19350 - 7.26336i) q^{76} +(6.09175 + 10.5512i) q^{77} +(-2.16251 - 3.32581i) q^{78} +(0.140266 - 0.242948i) q^{79} -3.71947 q^{80} +(-6.03743 - 6.67454i) q^{81} -11.9436 q^{82} +(0.717810 - 1.24328i) q^{83} +(3.78784 + 5.82548i) q^{84} +(4.52689 + 7.84081i) q^{85} +(3.27457 + 5.67172i) q^{86} +(-9.34349 + 0.495019i) q^{87} +(-1.51845 + 2.63003i) q^{88} -15.0586 q^{89} +(4.52689 - 10.1989i) q^{90} -9.18856 q^{91} +(-0.500000 + 0.866025i) q^{92} +(7.34782 - 14.4413i) q^{93} +(2.07091 + 3.58692i) q^{94} +(15.5976 + 27.0158i) q^{95} +(-0.785454 + 1.54372i) q^{96} +(-5.31080 + 9.19857i) q^{97} +9.09466 q^{98} +(-5.36355 - 7.36460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9	\( 10 q - 5 q^{2} + q^{3} - 5 q^{4} + 5 q^{5} + q^{6} + 5 q^{7} + 10 q^{8} + q^{9} - 10 q^{10} + 3 q^{11} - 2 q^{12} + 8 q^{13} + 5 q^{14} + 11 q^{15} - 5 q^{16} - 2 q^{17} - 8 q^{18} - 2 q^{19} + 5 q^{20} - 15 q^{21} + 3 q^{22} - 5 q^{23} + q^{24} - 16 q^{26} - 5 q^{27} - 10 q^{28} + 18 q^{29} + 5 q^{30} + 8 q^{31} - 5 q^{32} + 24 q^{33} + q^{34} + 2 q^{35} + 7 q^{36} - 12 q^{37} + q^{38} - 27 q^{39} + 5 q^{40} + 24 q^{41} - 3 q^{42} - 11 q^{43} - 6 q^{44} - 7 q^{45} + 10 q^{46} + 9 q^{47} + q^{48} - 4 q^{49} + 2 q^{51} + 8 q^{52} - 58 q^{53} - 20 q^{54} - 28 q^{55} + 5 q^{56} + 2 q^{57} + 18 q^{58} + 21 q^{59} - 16 q^{60} + 17 q^{61} - 16 q^{62} + 6 q^{63} + 10 q^{64} + 21 q^{65} + 21 q^{66} + 3 q^{67} + q^{68} - 2 q^{69} - q^{70} - 18 q^{71} + q^{72} - 14 q^{73} + 6 q^{74} + 13 q^{75} + q^{76} + 17 q^{77} + 15 q^{79} - 10 q^{80} + q^{81} - 48 q^{82} + 21 q^{83} + 18 q^{84} - 7 q^{85} - 11 q^{86} - 9 q^{87} + 3 q^{88} - 18 q^{89} - 7 q^{90} + 34 q^{91} - 5 q^{92} + 5 q^{93} + 9 q^{94} + 11 q^{95} - 2 q^{96} - 32 q^{97} + 8 q^{98}+O(q^{100}) \) 10 * q - 5 * q^2 + q^3 - 5 * q^4 + 5 * q^5 + q^6 + 5 * q^7 + 10 * q^8 + q^9 - 10 * q^10 + 3 * q^11 - 2 * q^12 + 8 * q^13 + 5 * q^14 + 11 * q^15 - 5 * q^16 - 2 * q^17 - 8 * q^18 - 2 * q^19 + 5 * q^20 - 15 * q^21 + 3 * q^22 - 5 * q^23 + q^24 - 16 * q^26 - 5 * q^27 - 10 * q^28 + 18 * q^29 + 5 * q^30 + 8 * q^31 - 5 * q^32 + 24 * q^33 + q^34 + 2 * q^35 + 7 * q^36 - 12 * q^37 + q^38 - 27 * q^39 + 5 * q^40 + 24 * q^41 - 3 * q^42 - 11 * q^43 - 6 * q^44 - 7 * q^45 + 10 * q^46 + 9 * q^47 + q^48 - 4 * q^49 + 2 * q^51 + 8 * q^52 - 58 * q^53 - 20 * q^54 - 28 * q^55 + 5 * q^56 + 2 * q^57 + 18 * q^58 + 21 * q^59 - 16 * q^60 + 17 * q^61 - 16 * q^62 + 6 * q^63 + 10 * q^64 + 21 * q^65 + 21 * q^66 + 3 * q^67 + q^68 - 2 * q^69 - q^70 - 18 * q^71 + q^72 - 14 * q^73 + 6 * q^74 + 13 * q^75 + q^76 + 17 * q^77 + 15 * q^79 - 10 * q^80 + q^81 - 48 * q^82 + 21 * q^83 + 18 * q^84 - 7 * q^85 - 11 * q^86 - 9 * q^87 + 3 * q^88 - 18 * q^89 - 7 * q^90 + 34 * q^91 - 5 * q^92 + 5 * q^93 + 9 * q^94 + 11 * q^95 - 2 * q^96 - 32 * q^97 + 8 * q^98

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