LMFDB - Embedded newform 585.2.i.f.196.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.4
Root			$-0.237622 + 0.411573i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.f.391.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.237622 + 0.411573i) q^{2} +(-1.28679 - 1.15939i) q^{3} +(0.887072 + 1.53645i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.782942 - 0.254110i) q^{6} +(-1.24774 + 2.16115i) q^{7} -1.79364 q^{8} +(0.311632 + 2.98377i) q^{9} +O(q^{10})$	\(q+(-0.237622 + 0.411573i) q^{2} +(-1.28679 - 1.15939i) q^{3} +(0.887072 + 1.53645i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.782942 - 0.254110i) q^{6} +(-1.24774 + 2.16115i) q^{7} -1.79364 q^{8} +(0.311632 + 2.98377i) q^{9} +0.475244 q^{10} +(1.50314 - 2.60351i) q^{11} +(0.639877 - 3.00555i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.592980 - 1.02707i) q^{14} +(-0.360668 + 1.69408i) q^{15} +(-1.34794 + 2.33469i) q^{16} -1.86238 q^{17} +(-1.30209 - 0.580750i) q^{18} -6.61778 q^{19} +(0.887072 - 1.53645i) q^{20} +(4.11119 - 1.33432i) q^{21} +(0.714357 + 1.23730i) q^{22} +(-2.00144 - 3.46660i) q^{23} +(2.30803 + 2.07952i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.475244 q^{26} +(3.05835 - 4.20077i) q^{27} -4.42734 q^{28} +(-3.77429 + 6.53727i) q^{29} +(-0.611536 - 0.550992i) q^{30} +(0.552970 + 0.957772i) q^{31} +(-2.43424 - 4.21622i) q^{32} +(-4.95270 + 1.60744i) q^{33} +(0.442542 - 0.766505i) q^{34} +2.49548 q^{35} +(-4.30798 + 3.12563i) q^{36} -10.2065 q^{37} +(1.57253 - 2.72370i) q^{38} +(-0.360668 + 1.69408i) q^{39} +(0.896819 + 1.55334i) q^{40} +(1.96768 + 3.40812i) q^{41} +(-0.427738 + 2.00912i) q^{42} +(-3.18735 + 5.52065i) q^{43} +5.33357 q^{44} +(2.42820 - 1.76177i) q^{45} +1.90235 q^{46} +(0.0661868 - 0.114639i) q^{47} +(4.44132 - 1.44147i) q^{48} +(0.386290 + 0.669074i) q^{49} +(-0.237622 - 0.411573i) q^{50} +(2.39648 + 2.15922i) q^{51} +(0.887072 - 1.53645i) q^{52} -6.91685 q^{53} +(1.00219 + 2.25693i) q^{54} -3.00628 q^{55} +(2.23799 - 3.87632i) q^{56} +(8.51566 + 7.67259i) q^{57} +(-1.79371 - 3.10680i) q^{58} +(-0.402461 - 0.697082i) q^{59} +(-2.92282 + 0.948624i) q^{60} +(2.39312 - 4.14500i) q^{61} -0.525591 q^{62} +(-6.83721 - 3.04949i) q^{63} -3.07804 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.515292 - 2.42036i) q^{66} +(-2.07699 - 3.59746i) q^{67} +(-1.65206 - 2.86146i) q^{68} +(-1.44371 + 6.78122i) q^{69} +(-0.592980 + 1.02707i) q^{70} -5.44325 q^{71} +(-0.558955 - 5.35180i) q^{72} -6.33787 q^{73} +(2.42528 - 4.20071i) q^{74} +(1.64745 - 0.534694i) q^{75} +(-5.87045 - 10.1679i) q^{76} +(3.75105 + 6.49701i) q^{77} +(-0.611536 - 0.550992i) q^{78} +(2.31771 - 4.01440i) q^{79} +2.69587 q^{80} +(-8.80577 + 1.85968i) q^{81} -1.87025 q^{82} +(7.26757 - 12.5878i) q^{83} +(5.69703 + 5.13301i) q^{84} +(0.931190 + 1.61287i) q^{85} +(-1.51477 - 2.62365i) q^{86} +(12.4359 - 4.03618i) q^{87} +(-2.69609 + 4.66976i) q^{88} +5.77819 q^{89} +(0.148101 + 1.41802i) q^{90} +2.49548 q^{91} +(3.55085 - 6.15025i) q^{92} +(0.398878 - 1.87356i) q^{93} +(0.0314549 + 0.0544814i) q^{94} +(3.30889 + 5.73117i) q^{95} +(-1.75590 + 8.24760i) q^{96} +(-3.03607 + 5.25864i) q^{97} -0.367164 q^{98} +(8.23671 + 3.67368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.237622	+	0.411573i	−0.168024	+	0.291026i	−0.937725	−	0.347378i	$-0.887072\pi$
$2$	−0.237622	+	0.411573i	−0.168024	+	0.291026i	0.769701	+	0.638404i	$0.220405\pi$
$3$	−1.28679	−	1.15939i	−0.742926	−	0.669374i
$3$	−1.28679	−	1.15939i	−0.742926	−	0.669374i
$4$	0.887072	+	1.53645i	0.443536	+	0.768227i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.782942	−	0.254110i	0.319635	−	0.103740i
$7$	−1.24774	+	2.16115i	−0.471601	+	0.816838i	−0.999472	−	0.0324871i	$-0.989657\pi$
$7$	−1.24774	+	2.16115i	−0.471601	+	0.816838i	0.527871	+	0.849325i	$0.322991\pi$
$8$	−1.79364			−0.634147
$9$	0.311632	+	2.98377i	0.103877	+	0.994590i
$10$	0.475244			0.150285
$11$	1.50314	−	2.60351i	0.453213	−	0.784989i	−0.545370	−	0.838195i	$-0.683611\pi$
$11$	1.50314	−	2.60351i	0.453213	−	0.784989i	0.998584	+	0.0532067i	$0.0169442\pi$
$12$	0.639877	−	3.00555i	0.184717	−	0.867627i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−0.592980	−	1.02707i	−0.158481	−	0.274497i
$15$	−0.360668	+	1.69408i	−0.0931241	+	0.437410i
$16$	−1.34794	+	2.33469i	−0.336984	+	0.583674i
$17$	−1.86238			−0.451693			−0.225847	−	0.974163i	$-0.572515\pi$
$17$	−1.86238			−0.451693			−0.225847	+	0.974163i	$0.572515\pi$
$18$	−1.30209	−	0.580750i	−0.306906	−	0.136884i
$19$	−6.61778			−1.51822			−0.759112	−	0.650960i	$-0.774366\pi$
$19$	−6.61778			−1.51822			−0.759112	+	0.650960i	$0.774366\pi$
$20$	0.887072	−	1.53645i	0.198355	−	0.343561i
$21$	4.11119	−	1.33432i	0.897135	−	0.291172i
$22$	0.714357	+	1.23730i	0.152301	+	0.263794i
$23$	−2.00144	−	3.46660i	−0.417330	−	0.722836i	0.578340	−	0.815796i	$-0.303701\pi$
$23$	−2.00144	−	3.46660i	−0.417330	−	0.722836i	−0.995670	+	0.0929594i	$0.970367\pi$
$24$	2.30803	+	2.07952i	0.471124	+	0.424481i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.475244			0.0932029
$27$	3.05835	−	4.20077i	0.588579	−	0.808439i
$28$	−4.42734			−0.836689
$29$	−3.77429	+	6.53727i	−0.700869	+	1.21394i	0.267293	+	0.963615i	$0.413871\pi$
$29$	−3.77429	+	6.53727i	−0.700869	+	1.21394i	−0.968162	+	0.250325i	$0.919462\pi$
$30$	−0.611536	−	0.550992i	−0.111651	−	0.100597i
$31$	0.552970	+	0.957772i	0.0993164	+	0.172021i	0.911402	−	0.411517i	$-0.135001\pi$
$31$	0.552970	+	0.957772i	0.0993164	+	0.172021i	−0.812086	+	0.583538i	$0.801668\pi$
$32$	−2.43424	−	4.21622i	−0.430316	−	0.745329i
$33$	−4.95270	+	1.60744i	−0.862155	+	0.279819i
$34$	0.442542	−	0.766505i	0.0758953	−	0.131455i
$35$	2.49548			0.421813
$36$	−4.30798	+	3.12563i	−0.717997	+	0.520938i
$37$	−10.2065			−1.67793			−0.838966	−	0.544183i	$-0.816840\pi$
$37$	−10.2065			−1.67793			−0.838966	+	0.544183i	$0.816840\pi$
$38$	1.57253	−	2.72370i	0.255098	−	0.441843i
$39$	−0.360668	+	1.69408i	−0.0577531	+	0.271270i
$40$	0.896819	+	1.55334i	0.141799	+	0.245604i
$41$	1.96768	+	3.40812i	0.307299	+	0.532258i	0.977771	−	0.209677i	$-0.0672413\pi$
$41$	1.96768	+	3.40812i	0.307299	+	0.532258i	−0.670471	+	0.741936i	$0.733908\pi$
$42$	−0.427738	+	2.00912i	−0.0660015	+	0.310013i
$43$	−3.18735	+	5.52065i	−0.486066	+	0.841891i	−0.999872	−	0.0160156i	$-0.994902\pi$
$43$	−3.18735	+	5.52065i	−0.486066	+	0.841891i	0.513806	+	0.857907i	$0.328235\pi$
$44$	5.33357			0.804066
$45$	2.42820	−	1.76177i	0.361975	−	0.262629i
$46$	1.90235			0.280486
$47$	0.0661868	−	0.114639i	0.00965434	−	0.0167218i	−0.861158	−	0.508338i	$-0.830260\pi$
$47$	0.0661868	−	0.114639i	0.00965434	−	0.0167218i	0.870812	+	0.491616i	$0.163594\pi$
$48$	4.44132	−	1.44147i	0.641050	−	0.208058i
$49$	0.386290	+	0.669074i	0.0551843	+	0.0955820i
$50$	−0.237622	−	0.411573i	−0.0336048	−	0.0582052i
$51$	2.39648	+	2.15922i	0.335575	+	0.302352i
$52$	0.887072	−	1.53645i	0.123015	−	0.213068i
$53$	−6.91685			−0.950102			−0.475051	−	0.879958i	$-0.657570\pi$
$53$	−6.91685			−0.950102			−0.475051	+	0.879958i	$0.657570\pi$
$54$	1.00219	+	2.25693i	0.136381	+	0.307129i
$55$	−3.00628			−0.405366
$56$	2.23799	−	3.87632i	0.299064	−	0.517995i
$57$	8.51566	+	7.67259i	1.12793	+	1.01626i
$58$	−1.79371	−	3.10680i	−0.235526	−	0.407942i
$59$	−0.402461	−	0.697082i	−0.0523959	−	0.0907524i	0.838638	−	0.544689i	$-0.183352\pi$
$59$	−0.402461	−	0.697082i	−0.0523959	−	0.0907524i	−0.891034	+	0.453937i	$0.850019\pi$
$60$	−2.92282	+	0.948624i	−0.377334	+	0.122467i
$61$	2.39312	−	4.14500i	0.306407	−	0.530713i	−0.671166	−	0.741307i	$-0.734206\pi$
$61$	2.39312	−	4.14500i	0.306407	−	0.530713i	0.977574	+	0.210594i	$0.0675397\pi$
$62$	−0.525591			−0.0667501
$63$	−6.83721	−	3.04949i	−0.861407	−	0.384199i
$64$	−3.07804			−0.384754
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	0.515292	−	2.42036i	0.0634280	−	0.297926i
$67$	−2.07699	−	3.59746i	−0.253745	−	0.439499i	0.710809	−	0.703385i	$-0.248329\pi$
$67$	−2.07699	−	3.59746i	−0.253745	−	0.439499i	−0.964554	+	0.263886i	$0.914996\pi$
$68$	−1.65206	−	2.86146i	−0.200342	−	0.347003i
$69$	−1.44371	+	6.78122i	−0.173803	+	0.816363i
$70$	−0.592980	+	1.02707i	−0.0708747	+	0.122759i
$71$	−5.44325			−0.645995			−0.322997	−	0.946400i	$-0.604690\pi$
$71$	−5.44325			−0.645995			−0.322997	+	0.946400i	$0.604690\pi$
$72$	−0.558955	−	5.35180i	−0.0658734	−	0.630716i
$73$	−6.33787			−0.741792			−0.370896	−	0.928674i	$-0.620949\pi$
$73$	−6.33787			−0.741792			−0.370896	+	0.928674i	$0.620949\pi$
$74$	2.42528	−	4.20071i	0.281933	−	0.488322i
$75$	1.64745	−	0.534694i	0.190232	−	0.0617411i
$76$	−5.87045	−	10.1679i	−0.673387	−	1.16634i
$77$	3.75105	+	6.49701i	0.427472	+	0.740403i
$78$	−0.611536	−	0.550992i	−0.0692429	−	0.0623876i
$79$	2.31771	−	4.01440i	0.260763	−	0.451655i	−0.705682	−	0.708529i	$-0.749359\pi$
$79$	2.31771	−	4.01440i	0.260763	−	0.451655i	0.966445	+	0.256874i	$0.0826925\pi$
$80$	2.69587			0.301408
$81$	−8.80577	+	1.85968i	−0.978419	+	0.206631i
$82$	−1.87025			−0.206535
$83$	7.26757	−	12.5878i	0.797719	−	1.38169i	−0.123379	−	0.992360i	$-0.539373\pi$
$83$	7.26757	−	12.5878i	0.797719	−	1.38169i	0.921098	−	0.389331i	$-0.127294\pi$
$84$	5.69703	+	5.13301i	0.621597	+	0.560057i
$85$	0.931190	+	1.61287i	0.101002	+	0.174940i
$86$	−1.51477	−	2.62365i	−0.163341	−	0.282916i
$87$	12.4359	−	4.03618i	1.33327	−	0.432724i
$88$	−2.69609	+	4.66976i	−0.287404	+	0.497798i
$89$	5.77819			0.612487			0.306243	−	0.951953i	$-0.400928\pi$
$89$	5.77819			0.612487			0.306243	+	0.951953i	$0.400928\pi$
$90$	0.148101	+	1.41802i	0.0156112	+	0.149472i
$91$	2.49548			0.261597
$92$	3.55085	−	6.15025i	0.370201	−	0.641208i
$93$	0.398878	−	1.87356i	0.0413617	−	0.194279i
$94$	0.0314549	+	0.0544814i	0.00324432	+	0.00561933i
$95$	3.30889	+	5.73117i	0.339485	+	0.588005i
$96$	−1.75590	+	8.24760i	−0.179211	+	0.841767i
$97$	−3.03607	+	5.25864i	−0.308267	+	0.533934i	−0.977983	−	0.208683i	$-0.933082\pi$
$97$	−3.03607	+	5.25864i	−0.308267	+	0.533934i	0.669717	+	0.742617i	$0.266416\pi$
$98$	−0.367164			−0.0370891
$99$	8.23671	+	3.67368i	0.827821	+	0.369219i
$100$	−1.77414			−0.177414
$101$	2.32176	−	4.02141i	0.231024	−	0.400146i	−0.727086	−	0.686547i	$-0.759126\pi$
$101$	2.32176	−	4.02141i	0.231024	−	0.400146i	0.958110	+	0.286401i	$0.0924590\pi$
$102$	−1.45813	+	0.473249i	−0.144377	+	0.0468586i
$103$	6.38750	+	11.0635i	0.629379	+	1.09012i	0.987677	+	0.156509i	$0.0500239\pi$
$103$	6.38750	+	11.0635i	0.629379	+	1.09012i	−0.358298	+	0.933607i	$0.616643\pi$
$104$	0.896819	+	1.55334i	0.0879403	+	0.152317i
$105$	−3.21115	−	2.89323i	−0.313376	−	0.282351i
$106$	1.64359	−	2.84679i	0.159640	−	0.276505i
$107$	10.4025			1.00565			0.502826	−	0.864388i	$-0.332294\pi$
$107$	10.4025			1.00565			0.502826	+	0.864388i	$0.332294\pi$
$108$	9.16727	+	0.972622i	0.882121	+	0.0935906i
$109$	18.4320			1.76546			0.882732	−	0.469877i	$-0.155702\pi$
$109$	18.4320			1.76546			0.882732	+	0.469877i	$0.155702\pi$
$110$	0.714357	−	1.23730i	0.0681113	−	0.117972i
$111$	13.1335	+	11.8333i	1.24658	+	1.12316i
$112$	−3.36375	−	5.82618i	−0.317844	−	0.550522i
$113$	8.00969	+	13.8732i	0.753489	+	1.30508i	0.946122	+	0.323810i	$0.104964\pi$
$113$	8.00969	+	13.8732i	0.753489	+	1.30508i	−0.192634	+	0.981271i	$0.561703\pi$
$114$	−5.18134	+	1.68164i	−0.485277	+	0.157500i
$115$	−2.00144	+	3.46660i	−0.186636	+	0.323262i
$116$	−13.3923			−1.24344
$117$	2.42820	−	1.76177i	0.224488	−	0.162875i
$118$	0.382534			0.0352151
$119$	2.32377	−	4.02488i	0.213019	−	0.368960i
$120$	0.646908	−	3.03857i	0.0590543	−	0.277382i
$121$	0.981147	+	1.69940i	0.0891952	+	0.154491i
$122$	1.13731	+	1.96989i	0.102968	+	0.178345i
$123$	1.41936	−	6.66682i	0.127979	−	0.601127i
$124$	−0.981048	+	1.69923i	−0.0881008	+	0.152595i
$125$	1.00000			0.0894427
$126$	2.87976	−	2.08939i	0.256549	−	0.186137i
$127$	−2.77944			−0.246636			−0.123318	−	0.992367i	$-0.539353\pi$
$127$	−2.77944			−0.246636			−0.123318	+	0.992367i	$0.539353\pi$
$128$	5.59988	−	9.69928i	0.494964	−	0.857303i
$129$	10.5020	−	3.40851i	0.924651	−	0.300103i
$130$	−0.237622	−	0.411573i	−0.0208408	−	0.0360973i
$131$	−7.23156	−	12.5254i	−0.631824	−	1.09435i	−0.987179	−	0.159620i	$-0.948973\pi$
$131$	−7.23156	−	12.5254i	−0.631824	−	1.09435i	0.355354	−	0.934732i	$-0.384360\pi$
$132$	−6.86316	−	6.18368i	−0.597361	−	0.538221i
$133$	8.25727	−	14.3020i	0.715996	−	1.24014i
$134$	1.97416			0.170541
$135$	−5.16715	−	0.548221i	−0.444718	−	0.0471833i
$136$	3.34043			0.286440
$137$	−9.09964	+	15.7610i	−0.777434	+	1.34656i	0.155982	+	0.987760i	$0.450146\pi$
$137$	−9.09964	+	15.7610i	−0.777434	+	1.34656i	−0.933416	+	0.358796i	$0.883187\pi$
$138$	−2.44791	−	2.20556i	−0.208380	−	0.187750i
$139$	11.3373	+	19.6368i	0.961618	+	1.66557i	0.718439	+	0.695590i	$0.244857\pi$
$139$	11.3373	+	19.6368i	0.961618	+	1.66557i	0.243179	+	0.969982i	$0.421810\pi$
$140$	2.21367	+	3.83419i	0.187089	+	0.324048i
$141$	−0.218079	+	0.0707794i	−0.0183656	+	0.00596070i
$142$	1.29343	−	2.24029i	0.108543	−	0.188001i
$143$	−3.00628			−0.251398
$144$	−7.38625	−	3.29437i	−0.615521	−	0.274531i
$145$	7.54859			0.626876
$146$	1.50602	−	2.60850i	0.124639	−	0.215881i
$147$	0.278645	−	1.30881i	0.0229822	−	0.107949i
$148$	−9.05387	−	15.6818i	−0.744223	−	1.28903i
$149$	−9.19585	−	15.9277i	−0.753353	−	1.30485i	−0.946189	−	0.323615i	$-0.895102\pi$
$149$	−9.19585	−	15.9277i	−0.753353	−	1.30485i	0.192836	−	0.981231i	$-0.438232\pi$
$150$	−0.171405	+	0.805102i	−0.0139952	+	0.0657363i
$151$	3.82184	−	6.61962i	0.311017	−	0.538697i	−0.667566	−	0.744551i	$-0.732664\pi$
$151$	3.82184	−	6.61962i	0.311017	−	0.538697i	0.978583	+	0.205854i	$0.0659971\pi$
$152$	11.8699			0.962776
$153$	−0.580377	−	5.55691i	−0.0469207	−	0.449250i
$154$	−3.56533			−0.287302
$155$	0.552970	−	0.957772i	0.0444156	−	0.0769301i
$156$	−2.92282	+	0.948624i	−0.234013	+	0.0759507i
$157$	4.74578	+	8.21993i	0.378754	+	0.656022i	0.990881	−	0.134738i	$-0.0430192\pi$
$157$	4.74578	+	8.21993i	0.378754	+	0.656022i	−0.612127	+	0.790760i	$0.709686\pi$
$158$	1.10148	+	1.90782i	0.0876289	+	0.151778i
$159$	8.90050	+	8.01932i	0.705856	+	0.635974i
$160$	−2.43424	+	4.21622i	−0.192443	+	0.333321i
$161$	9.98912			0.787253
$162$	1.32705	−	4.06612i	0.104263	−	0.319464i
$163$	3.32480			0.260418			0.130209	−	0.991487i	$-0.458435\pi$
$163$	3.32480			0.260418			0.130209	+	0.991487i	$0.458435\pi$
$164$	−3.49094	+	6.04649i	−0.272597	+	0.472151i
$165$	3.86843	+	3.48545i	0.301157	+	0.271342i
$166$	3.45386	+	5.98227i	0.268072	+	0.464314i
$167$	−1.13639	−	1.96829i	−0.0879365	−	0.152311i	0.818702	−	0.574218i	$-0.194694\pi$
$167$	−1.13639	−	1.96829i	−0.0879365	−	0.152311i	−0.906639	+	0.421908i	$0.861361\pi$
$168$	−7.37398	+	2.39328i	−0.568915	+	0.184646i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.885084			−0.0678828
$171$	−2.06231	−	19.7459i	−0.157709	−	1.51001i
$172$	−11.3096			−0.862351
$173$	7.19723	−	12.4660i	0.547195	−	0.947770i	−0.451270	−	0.892388i	$-0.649029\pi$
$173$	7.19723	−	12.4660i	0.547195	−	0.947770i	0.998465	−	0.0553826i	$-0.0176379\pi$
$174$	−1.29387	+	6.07739i	−0.0980879	+	0.460725i
$175$	−1.24774	−	2.16115i	−0.0943203	−	0.163368i
$176$	4.05227	+	7.01874i	0.305451	+	0.529057i
$177$	−0.290310	+	1.36360i	−0.0218210	+	0.102495i
$178$	−1.37302	+	2.37815i	−0.102912	+	0.178250i
$179$	−19.8554			−1.48407			−0.742033	−	0.670364i	$-0.766138\pi$
$179$	−19.8554			−1.48407			−0.742033	+	0.670364i	$0.766138\pi$
$180$	4.86086	+	2.16801i	0.362307	+	0.161594i
$181$	−20.2602			−1.50593			−0.752964	−	0.658061i	$-0.771377\pi$
$181$	−20.2602			−1.50593			−0.752964	+	0.658061i	$0.771377\pi$
$182$	−0.592980	+	1.02707i	−0.0439546	+	0.0761317i
$183$	−7.88510	+	2.55917i	−0.582883	+	0.189179i
$184$	3.58986	+	6.21783i	0.264648	+	0.458384i
$185$	5.10323	+	8.83906i	0.375197	+	0.649861i
$186$	0.676323	+	0.609365i	0.0495904	+	0.0446808i
$187$	−2.79942	+	4.84873i	−0.204714	+	0.354574i
$188$	0.234850			0.0171282
$189$	5.26248	+	11.8510i	0.382789	+	0.862035i
$190$	−3.14506			−0.228167
$191$	−7.21227	+	12.4920i	−0.521862	+	0.903891i	0.477815	+	0.878461i	$0.341429\pi$
$191$	−7.21227	+	12.4920i	−0.521862	+	0.903891i	−0.999677	+	0.0254305i	$0.991904\pi$
$192$	3.96077	+	3.56864i	0.285844	+	0.257545i
$193$	12.1134	+	20.9810i	0.871942	+	1.51025i	0.859985	+	0.510319i	$0.170473\pi$
$193$	12.1134	+	20.9810i	0.871942	+	1.51025i	0.0119565	+	0.999929i	$0.496194\pi$
$194$	−1.44287	−	2.49913i	−0.103592	−	0.179427i
$195$	1.64745	−	0.534694i	0.117977	−	0.0382902i
$196$	−0.685334	+	1.18703i	−0.0489524	+	0.0847881i
$197$	1.94373			0.138485			0.0692426	−	0.997600i	$-0.477942\pi$
$197$	1.94373			0.138485			0.0692426	+	0.997600i	$0.477942\pi$
$198$	−3.46921	+	2.51706i	−0.246546	+	0.178880i
$199$	7.57304			0.536839			0.268419	−	0.963302i	$-0.413499\pi$
$199$	7.57304			0.536839			0.268419	+	0.963302i	$0.413499\pi$
$200$	0.896819	−	1.55334i	0.0634147	−	0.109837i
$201$	−1.49821	+	7.03720i	−0.105676	+	0.496366i
$202$	1.10340	+	1.91115i	0.0776352	+	0.134468i
$203$	−9.41868	−	16.3136i	−0.661061	−	1.14499i
$204$	−1.19169	+	5.59747i	−0.0834353	+	0.391901i
$205$	1.96768	−	3.40812i	0.137429	−	0.238033i
$206$	−6.07123			−0.423003
$207$	9.71983	−	7.05215i	0.675575	−	0.490158i
$208$	2.69587			0.186925
$209$	−9.94745	+	17.2295i	−0.688079	+	1.19179i
$210$	1.95381	−	0.634126i	0.134826	−	0.0437588i
$211$	−7.58831	−	13.1433i	−0.522401	−	0.904824i	−0.999660	−	0.0260620i	$-0.991703\pi$
$211$	−7.58831	−	13.1433i	−0.522401	−	0.904824i	0.477260	−	0.878762i	$-0.341630\pi$
$212$	−6.13574	−	10.6274i	−0.421405	−	0.729894i
$213$	7.00429	+	6.31084i	0.479926	+	0.432412i
$214$	−2.47187	+	4.28141i	−0.168974	+	0.292671i
$215$	6.37469			0.434751
$216$	−5.48557	+	7.53467i	−0.373246	+	0.512669i
$217$	−2.75985			−0.187351
$218$	−4.37984	+	7.58610i	−0.296640	+	0.513796i
$219$	8.15548	+	7.34807i	0.551096	+	0.496536i
$220$	−2.66678	−	4.61901i	−0.179795	−	0.311413i
$221$	0.931190	+	1.61287i	0.0626386	+	0.108493i
$222$	−7.99107	+	2.59356i	−0.536325	+	0.174069i
$223$	11.4679	−	19.8631i	0.767950	−	1.33013i	−0.170722	−	0.985319i	$-0.554610\pi$
$223$	11.4679	−	19.8631i	0.767950	−	1.33013i	0.938673	−	0.344810i	$-0.112057\pi$
$224$	12.1492			0.811751
$225$	−2.73984	−	1.22200i	−0.182656	−	0.0814669i
$226$	−7.61311			−0.506417
$227$	8.32539	−	14.4200i	0.552576	−	0.957089i	−0.445512	−	0.895276i	$-0.646978\pi$
$227$	8.32539	−	14.4200i	0.552576	−	0.957089i	0.998088	−	0.0618130i	$-0.0196883\pi$
$228$	−4.23457	+	19.8901i	−0.280441	+	1.31725i
$229$	6.35958	+	11.0151i	0.420253	+	0.727899i	0.995964	−	0.0897539i	$-0.0286081\pi$
$229$	6.35958	+	11.0151i	0.420253	+	0.727899i	−0.575711	+	0.817653i	$0.695275\pi$
$230$	−0.951173	−	1.64748i	−0.0627185	−	0.108632i
$231$	2.70577	−	12.7092i	0.178027	−	0.836203i
$232$	6.76972	−	11.7255i	0.444454	−	0.769816i
$233$	−19.7105			−1.29128			−0.645638	−	0.763644i	$-0.723409\pi$
$233$	−19.7105			−1.29128			−0.645638	+	0.763644i	$0.723409\pi$
$234$	0.148101	+	1.41802i	0.00968167	+	0.0926987i
$235$	−0.132374			−0.00863511
$236$	0.714023	−	1.23672i	0.0464789	−	0.0805039i
$237$	−7.63665	+	2.47853i	−0.496053	+	0.160998i
$238$	1.10435	+	1.91280i	0.0715847	+	0.123988i
$239$	−6.88845	−	11.9311i	−0.445577	−	0.771761i	0.552516	−	0.833503i	$-0.313668\pi$
$239$	−6.88845	−	11.9311i	−0.445577	−	0.771761i	−0.998092	+	0.0617412i	$0.980335\pi$
$240$	−3.46901	−	3.12557i	−0.223924	−	0.201754i
$241$	0.962799	−	1.66762i	0.0620194	−	0.107421i	−0.833349	−	0.552748i	$-0.813579\pi$
$241$	0.962799	−	1.66762i	0.0620194	−	0.107421i	0.895368	+	0.445327i	$0.146913\pi$
$242$	−0.932568			−0.0599477
$243$	13.4872	+	7.81631i	0.865206	+	0.501417i
$244$	8.49147			0.543611
$245$	0.386290	−	0.669074i	0.0246792	−	0.0427455i
$246$	2.40661	+	2.16835i	0.153440	+	0.138249i
$247$	3.30889	+	5.73117i	0.210540	+	0.364665i
$248$	−0.991828	−	1.71790i	−0.0629811	−	0.109087i
$249$	−23.9460	+	7.77185i	−1.51751	+	0.492521i
$250$	−0.237622	+	0.411573i	−0.0150285	+	0.0260302i
$251$	−11.5406			−0.728436			−0.364218	−	0.931314i	$-0.618664\pi$
$251$	−11.5406			−0.728436			−0.364218	+	0.931314i	$0.618664\pi$
$252$	−1.37970	−	13.2102i	−0.0869130	−	0.832162i
$253$	−12.0338			−0.756558
$254$	0.660457	−	1.14394i	0.0414407	−	0.0717774i
$255$	0.671701	−	3.15503i	0.0420636	−	0.197575i
$256$	−0.416729	−	0.721796i	−0.0260456	−	0.0451123i
$257$	8.98850	+	15.5685i	0.560687	+	0.971139i	0.997437	+	0.0715554i	$0.0227963\pi$
$257$	8.98850	+	15.5685i	0.560687	+	0.971139i	−0.436750	+	0.899583i	$0.643870\pi$
$258$	−1.09266	+	5.13228i	−0.0680258	+	0.319522i
$259$	12.7350	−	22.0577i	0.791315	−	1.37060i
$260$	−1.77414			−0.110028
$261$	−20.6819	−	9.22441i	−1.28018	−	0.570976i
$262$	6.87350			0.424647
$263$	2.96942	−	5.14319i	0.183102	−	0.317142i	−0.759833	−	0.650118i	$-0.774719\pi$
$263$	2.96942	−	5.14319i	0.183102	−	0.317142i	0.942935	+	0.332976i	$0.108053\pi$
$264$	8.88335	−	2.88316i	0.546733	−	0.177446i
$265$	3.45842	+	5.99017i	0.212449	+	0.367973i
$266$	3.92422	+	6.79694i	0.240609	+	0.416747i
$267$	−7.43529	−	6.69917i	−0.455032	−	0.409983i
$268$	3.68488	−	6.38241i	0.225090	−	0.389868i
$269$	−1.31308			−0.0800597			−0.0400299	−	0.999198i	$-0.512745\pi$
$269$	−1.31308			−0.0800597			−0.0400299	+	0.999198i	$0.512745\pi$
$270$	1.45346	−	1.99639i	0.0884548	−	0.121496i
$271$	−17.1495			−1.04176			−0.520879	−	0.853631i	$-0.674396\pi$
$271$	−17.1495			−1.04176			−0.520879	+	0.853631i	$0.674396\pi$
$272$	2.51037	−	4.34809i	0.152214	−	0.263642i
$273$	−3.21115	−	2.89323i	−0.194347	−	0.175106i
$274$	−4.32454	−	7.49033i	−0.261255	−	0.452507i
$275$	1.50314	+	2.60351i	0.0906427	+	0.156998i
$276$	−11.6997	+	3.79723i	−0.704240	+	0.228567i
$277$	−14.5936	+	25.2769i	−0.876847	+	1.51874i	−0.0220645	+	0.999757i	$0.507024\pi$
$277$	−14.5936	+	25.2769i	−0.876847	+	1.51874i	−0.854782	+	0.518987i	$0.826309\pi$
$278$	−10.7760			−0.646299
$279$	−2.68545	+	1.94841i	−0.160774	+	0.116648i
$280$	−4.47599			−0.267491
$281$	−6.76359	+	11.7149i	−0.403482	+	0.698852i	−0.994144	−	0.108068i	$-0.965534\pi$
$281$	−6.76359	+	11.7149i	−0.403482	+	0.698852i	0.590661	+	0.806920i	$0.298867\pi$
$282$	0.0226895	−	0.106574i	0.00135114	−	0.00634641i
$283$	8.63655	+	14.9590i	0.513390	+	0.889217i	0.999879	+	0.0155309i	$0.00494383\pi$
$283$	8.63655	+	14.9590i	0.513390	+	0.889217i	−0.486490	+	0.873686i	$0.661723\pi$
$284$	−4.82855	−	8.36330i	−0.286522	−	0.496270i
$285$	2.38682	−	11.2111i	0.141383	−	0.664087i
$286$	0.714357	−	1.23730i	0.0422408	−	0.0731632i
$287$	−9.82060			−0.579691
$288$	11.8216	−	8.57711i	0.696597	−	0.505411i
$289$	−13.5315			−0.795973
$290$	−1.79371	+	3.10680i	−0.105330	+	0.182437i
$291$	10.0036	−	3.24674i	0.586420	−	0.190327i
$292$	−5.62215	−	9.73785i	−0.329011	−	0.569865i
$293$	−3.46977	−	6.00982i	−0.202706	−	0.351098i	0.746693	−	0.665169i	$-0.231640\pi$
$293$	−3.46977	−	6.00982i	−0.202706	−	0.351098i	−0.949400	+	0.314071i	$0.898307\pi$
$294$	0.472461	+	0.425686i	0.0275545	+	0.0248265i
$295$	−0.402461	+	0.697082i	−0.0234322	+	0.0405857i
$296$	18.3067			1.06406
$297$	−6.33965	−	14.2768i	−0.367864	−	0.828424i
$298$	8.74053			0.506326
$299$	−2.00144	+	3.46660i	−0.115746	+	0.200479i
$300$	2.28294	+	2.05692i	0.131806	+	0.118757i
$301$	−7.95396	−	13.7767i	−0.458459	−	0.794074i
$302$	1.81630	+	3.14593i	0.104517	+	0.181028i
$303$	−7.65000	+	2.48287i	−0.439481	+	0.142637i
$304$	8.92035	−	15.4505i	0.511617	−	0.886147i
$305$	−4.78624			−0.274059
$306$	2.42499	+	1.08158i	0.138627	+	0.0618296i
$307$	−16.0084			−0.913645			−0.456823	−	0.889558i	$-0.651013\pi$
$307$	−16.0084			−0.913645			−0.456823	+	0.889558i	$0.651013\pi$
$308$	−6.65491	+	11.5266i	−0.379198	+	0.656791i
$309$	4.60753	−	21.6419i	0.262113	−	1.23116i
$310$	0.262796	+	0.455175i	0.0149258	+	0.0258522i
$311$	6.48175	+	11.2267i	0.367546	+	0.636609i	0.989181	−	0.146698i	$-0.0468646\pi$
$311$	6.48175	+	11.2267i	0.367546	+	0.636609i	−0.621635	+	0.783307i	$0.713531\pi$
$312$	0.646908	−	3.03857i	0.0366240	−	0.172025i
$313$	9.24933	−	16.0203i	0.522803	−	0.905522i	−0.476845	−	0.878988i	$-0.658220\pi$
$313$	9.24933	−	16.0203i	0.522803	−	0.905522i	0.999648	−	0.0265342i	$-0.00844709\pi$
$314$	−4.51080			−0.254559
$315$	0.777671	+	7.44594i	0.0438168	+	0.419531i
$316$	8.22391			0.462631
$317$	−15.5849	+	26.9938i	−0.875333	+	1.51612i	−0.0189261	+	0.999821i	$0.506025\pi$
$317$	−15.5849	+	26.9938i	−0.875333	+	1.51612i	−0.856407	+	0.516301i	$0.827309\pi$
$318$	−5.41549	+	1.75764i	−0.303686	+	0.0985635i
$319$	11.3466	+	19.6528i	0.635286	+	1.10035i
$320$	1.53902	+	2.66566i	0.0860337	+	0.149015i
$321$	−13.3858	−	12.0606i	−0.747125	−	0.673157i
$322$	−2.37363	+	4.11125i	−0.132277	+	0.229111i
$323$	12.3248			0.685772
$324$	−10.6687	−	11.8800i	−0.592703	−	0.659999i
$325$	1.00000			0.0554700
$326$	−0.790045	+	1.36840i	−0.0437565	+	0.0757886i
$327$	−23.7180	−	21.3698i	−1.31161	−	1.18175i
$328$	−3.52930	−	6.11292i	−0.194873	−	0.337530i
$329$	0.165168	+	0.286079i	0.00910600	+	0.0157721i
$330$	−2.35374	+	0.763925i	−0.129569	+	0.0420527i
$331$	10.7108	−	18.5516i	0.588716	−	1.01969i	−0.405684	−	0.914013i	$-0.632967\pi$
$331$	10.7108	−	18.5516i	0.588716	−	1.01969i	0.994401	−	0.105674i	$-0.0336999\pi$
$332$	25.7874			1.41527
$333$	−3.18066	−	30.4537i	−0.174299	−	1.66886i
$334$	1.08012			0.0591018
$335$	−2.07699	+	3.59746i	−0.113478	+	0.196550i
$336$	−2.42639	+	11.3969i	−0.132371	+	0.621754i
$337$	10.7896	+	18.6881i	0.587747	+	1.01801i	0.994527	+	0.104482i	$0.0333184\pi$
$337$	10.7896	+	18.6881i	0.587747	+	1.01801i	−0.406780	+	0.913526i	$0.633348\pi$
$338$	−0.237622	−	0.411573i	−0.0129249	−	0.0223866i
$339$	5.77768	−	27.1382i	0.313801	−	1.47394i
$340$	−1.65206	+	2.86146i	−0.0895958	+	0.155184i
$341$	3.32476			0.180046
$342$	8.61695	+	3.84327i	0.465951	+	0.207820i
$343$	−19.3963			−1.04730
$344$	5.71695	−	9.90204i	0.308237	−	0.533882i
$345$	6.59457	−	2.14032i	0.355040	−	0.115231i
$346$	3.42044	+	5.92437i	0.183884	+	0.318496i
$347$	0.00650665	+	0.0112698i	0.000349295	+	0.000604997i	0.866200	−	0.499697i	$-0.166555\pi$
$347$	0.00650665	+	0.0112698i	0.000349295	+	0.000604997i	−0.865851	+	0.500302i	$0.833222\pi$
$348$	17.2330	+	15.5269i	0.923785	+	0.832328i
$349$	6.51289	−	11.2807i	0.348627	−	0.603840i	−0.637379	−	0.770551i	$-0.719981\pi$
$349$	6.51289	−	11.2807i	0.348627	−	0.603840i	0.986006	+	0.166711i	$0.0533147\pi$
$350$	1.18596			0.0633923
$351$	−5.16715	−	0.548221i	−0.275802	−	0.0292618i
$352$	−14.6360			−0.780100
$353$	−7.29075	+	12.6280i	−0.388048	+	0.672118i	−0.992187	−	0.124760i	$-0.960184\pi$
$353$	−7.29075	+	12.6280i	−0.388048	+	0.672118i	0.604139	+	0.796879i	$0.293517\pi$
$354$	−0.492239	−	0.443506i	−0.0261622	−	0.0235721i
$355$	2.72162	+	4.71399i	0.144449	+	0.250193i
$356$	5.12567	+	8.87792i	0.271660	+	0.470529i
$357$	−7.65659	+	2.48501i	−0.405230	+	0.131521i
$358$	4.71808	−	8.17196i	0.249359	−	0.431902i
$359$	−28.3828			−1.49799			−0.748995	−	0.662576i	$-0.769463\pi$
$359$	−28.3828			−1.49799			−0.748995	+	0.662576i	$0.769463\pi$
$360$	−4.35532	+	3.15997i	−0.229545	+	0.166545i
$361$	24.7950			1.30500
$362$	4.81426	−	8.33855i	0.253032	−	0.438265i
$363$	0.707737	−	3.32429i	0.0371466	−	0.174480i
$364$	2.21367	+	3.83419i	0.116028	+	0.200966i
$365$	3.16894	+	5.48876i	0.165870	+	0.287295i
$366$	0.820386	−	3.85341i	0.0428823	−	0.201421i
$367$	−2.40226	+	4.16084i	−0.125397	+	0.217194i	−0.921888	−	0.387456i	$-0.873354\pi$
$367$	−2.40226	+	4.16084i	−0.125397	+	0.217194i	0.796491	+	0.604650i	$0.206687\pi$
$368$	10.7913			0.562534
$369$	−9.55585	+	6.93317i	−0.497457	+	0.360927i
$370$	−4.85056			−0.252168
$371$	8.63043	−	14.9483i	0.448070	−	0.776079i
$372$	3.23246	−	1.04912i	0.167595	−	0.0543944i
$373$	2.06426	+	3.57540i	0.106883	+	0.185127i	0.914506	−	0.404572i	$-0.132580\pi$
$373$	2.06426	+	3.57540i	0.106883	+	0.185127i	−0.807623	+	0.589699i	$0.799246\pi$
$374$	−1.33040	−	2.30433i	−0.0687936	−	0.119154i
$375$	−1.28679	−	1.15939i	−0.0664493	−	0.0598706i
$376$	−0.118715	+	0.205621i	−0.00612227	+	0.0106041i
$377$	7.54859			0.388772
$378$	−6.12804	−	0.650168i	−0.315192	−	0.0334410i
$379$	15.4974			0.796050			0.398025	−	0.917375i	$-0.369696\pi$
$379$	15.4974			0.796050			0.398025	+	0.917375i	$0.369696\pi$
$380$	−5.87045	+	10.1679i	−0.301148	+	0.521603i
$381$	3.57655	+	3.22246i	0.183232	+	0.165092i
$382$	−3.42759	−	5.93675i	−0.175371	−	0.303751i
$383$	−1.07069	−	1.85449i	−0.0547099	−	0.0947602i	0.837373	−	0.546631i	$-0.184090\pi$
$383$	−1.07069	−	1.85449i	−0.0547099	−	0.0947602i	−0.892083	+	0.451871i	$0.850757\pi$
$384$	−18.4511	+	5.98844i	−0.941578	+	0.305596i
$385$	3.75105	−	6.49701i	0.191171	−	0.331119i
$386$	−11.5136			−0.586028
$387$	−17.4656	−	7.78990i	−0.887828	−	0.395983i
$388$	−10.7729			−0.546909
$389$	−8.29210	+	14.3623i	−0.420426	+	0.728199i	−0.995981	−	0.0895637i	$-0.971453\pi$
$389$	−8.29210	+	14.3623i	−0.420426	+	0.728199i	0.575555	+	0.817763i	$0.304786\pi$
$390$	−0.171405	+	0.805102i	−0.00867944	+	0.0407679i
$391$	3.72745	+	6.45613i	0.188505	+	0.326500i
$392$	−0.692864	−	1.20008i	−0.0349949	−	0.0606130i
$393$	−5.21639	+	24.5017i	−0.263132	+	1.23595i
$394$	−0.461873	+	0.799988i	−0.0232688	+	0.0403028i
$395$	−4.63542			−0.233234
$396$	1.66211	+	15.9141i	0.0835242	+	0.799716i
$397$	4.60300			0.231018			0.115509	−	0.993306i	$-0.463150\pi$
$397$	4.60300			0.231018			0.115509	+	0.993306i	$0.463150\pi$
$398$	−1.79952	+	3.11686i	−0.0902018	+	0.156234i
$399$	−27.2069	+	8.83022i	−1.36205	+	0.442064i
$400$	−1.34794	−	2.33469i	−0.0673968	−	0.116735i
$401$	−5.21156	−	9.02668i	−0.260253	−	0.450771i	0.706056	−	0.708156i	$-0.250473\pi$
$401$	−5.21156	−	9.02668i	−0.260253	−	0.450771i	−0.966309	+	0.257385i	$0.917139\pi$
$402$	−2.54031	−	2.28882i	−0.126699	−	0.114156i
$403$	0.552970	−	0.957772i	0.0275454	−	0.0477100i
$404$	8.23829			0.409870
$405$	6.01341	+	6.69618i	0.298809	+	0.332736i
$406$	8.95233			0.444297
$407$	−15.3417	+	26.5727i	−0.760462	+	1.31716i
$408$	−4.29842	−	3.87286i	−0.212804	−	0.191735i
$409$	−18.3965	−	31.8638i	−0.909651	−	1.57556i	−0.814550	−	0.580093i	$-0.803016\pi$
$409$	−18.3965	−	31.8638i	−0.909651	−	1.57556i	−0.0951006	−	0.995468i	$-0.530317\pi$
$410$	0.935126	+	1.61969i	0.0461826	+	0.0799906i
$411$	29.9825	−	9.73104i	1.47893	−	0.479997i
$412$	−11.3323	+	19.6282i	−0.558304	+	0.967011i
$413$	2.00867			0.0988399
$414$	0.592832	+	5.67616i	0.0291361	+	0.278968i
$415$	−14.5351			−0.713502
$416$	−2.43424	+	4.21622i	−0.119348	+	0.206717i
$417$	8.17801	−	38.4127i	0.400479	−	1.88108i
$418$	−4.72746	−	8.18820i	−0.231228	−	0.400498i
$419$	12.8064	+	22.1813i	0.625634	+	1.08363i	0.988418	+	0.151756i	$0.0484929\pi$
$419$	12.8064	+	22.1813i	0.625634	+	1.08363i	−0.362784	+	0.931873i	$0.618174\pi$
$420$	1.59680	−	7.50028i	0.0779159	−	0.365976i
$421$	−4.15123	+	7.19014i	−0.202318	+	0.350426i	−0.949275	−	0.314447i	$-0.898181\pi$
$421$	−4.15123	+	7.19014i	−0.202318	+	0.350426i	0.746957	+	0.664873i	$0.231514\pi$
$422$	7.21259			0.351103
$423$	0.362682	+	0.161761i	0.0176342	+	0.00786510i
$424$	12.4063			0.602504
$425$	0.931190	−	1.61287i	0.0451693	−	0.0782356i
$426$	−4.26174	+	1.38318i	−0.206482	+	0.0670154i
$427$	5.97198	+	10.3438i	0.289004	+	0.500570i
$428$	9.22781	+	15.9830i	0.446043	+	0.772569i
$429$	3.86843	+	3.48545i	0.186770	+	0.168279i
$430$	−1.51477	+	2.62365i	−0.0730485	+	0.126524i
$431$	−1.12921			−0.0543923			−0.0271961	−	0.999630i	$-0.508658\pi$
$431$	−1.12921			−0.0543923			−0.0271961	+	0.999630i	$0.508658\pi$
$432$	5.68506	+	12.8027i	0.273523	+	0.615969i
$433$	24.7868			1.19118			0.595588	−	0.803290i	$-0.296919\pi$
$433$	24.7868			1.19118			0.595588	+	0.803290i	$0.296919\pi$
$434$	0.655801	−	1.13588i	0.0314795	−	0.0545240i
$435$	−9.71341	−	8.75175i	−0.465722	−	0.419615i
$436$	16.3505	+	28.3199i	0.783046	+	1.35628i
$437$	13.2451	+	22.9412i	0.633600	+	1.09743i
$438$	−4.96219	+	1.61052i	−0.237102	+	0.0769534i
$439$	17.1709	−	29.7408i	0.819520	−	1.41945i	−0.0865163	−	0.996250i	$-0.527573\pi$
$439$	17.1709	−	29.7408i	0.819520	−	1.41945i	0.906036	−	0.423200i	$-0.139093\pi$
$440$	5.39217			0.257062
$441$	−1.87598	+	1.36110i	−0.0893325	+	0.0648145i
$442$	−0.885084			−0.0420992
$443$	−8.58860	+	14.8759i	−0.408057	+	0.706775i	−0.994672	−	0.103091i	$-0.967127\pi$
$443$	−8.58860	+	14.8759i	−0.408057	+	0.706775i	0.586615	+	0.809866i	$0.300460\pi$
$444$	−6.53088	+	30.6760i	−0.309942	+	1.45582i
$445$	−2.88910	−	5.00406i	−0.136956	−	0.237215i
$446$	5.45007	+	9.43979i	0.258068	+	0.446987i
$447$	−6.63330	+	31.1571i	−0.313744	+	1.47368i
$448$	3.84059	−	6.65209i	0.181451	−	0.314282i
$449$	7.37552			0.348072			0.174036	−	0.984739i	$-0.444319\pi$
$449$	7.37552			0.348072			0.174036	+	0.984739i	$0.444319\pi$
$450$	1.15399	−	0.837268i	0.0543996	−	0.0394692i
$451$	11.8308			0.557089
$452$	−14.2103	+	24.6130i	−0.668398	+	1.15770i
$453$	−12.5926	+	4.08703i	−0.591652	+	0.192025i
$454$	3.95659	+	6.85301i	0.185692	+	0.321628i
$455$	−1.24774	−	2.16115i	−0.0584950	−	0.101316i
$456$	−15.2740	−	13.7618i	−0.715271	−	0.644457i
$457$	−8.88483	+	15.3890i	−0.415615	+	0.719866i	−0.995493	−	0.0948374i	$-0.969767\pi$
$457$	−8.88483	+	15.3890i	−0.415615	+	0.719866i	0.579878	+	0.814703i	$0.303100\pi$
$458$	−6.04470			−0.282450
$459$	−5.69581	+	7.82344i	−0.265858	+	0.365167i
$460$	−7.10170			−0.331118
$461$	7.79084	−	13.4941i	0.362856	−	0.628485i	−0.625574	−	0.780165i	$-0.715135\pi$
$461$	7.79084	−	13.4941i	0.362856	−	0.628485i	0.988430	+	0.151680i	$0.0484685\pi$
$462$	4.58781	+	4.13360i	0.213444	+	0.192313i
$463$	−1.91706	−	3.32045i	−0.0890935	−	0.154314i	0.818035	−	0.575169i	$-0.195064\pi$
$463$	−1.91706	−	3.32045i	−0.0890935	−	0.154314i	−0.907128	+	0.420854i	$0.861730\pi$
$464$	−10.1750	−	17.6236i	−0.472363	−	0.818157i
$465$	−1.82199	+	0.591340i	−0.0844925	+	0.0274227i
$466$	4.68364	−	8.11230i	0.216965	−	0.375795i
$467$	−15.3789			−0.711652			−0.355826	−	0.934552i	$-0.615800\pi$
$467$	−15.3789			−0.711652			−0.355826	+	0.934552i	$0.615800\pi$
$468$	4.86086	+	2.16801i	0.224694	+	0.100216i
$469$	10.3662			0.478666
$470$	0.0314549	−	0.0544814i	0.00145090	−	0.00251304i
$471$	3.42330	−	16.0795i	0.157737	−	0.740904i
$472$	0.721868	+	1.25031i	0.0332267	+	0.0575503i
$473$	9.58205	+	16.5966i	0.440583	+	0.763112i
$474$	0.794536	−	3.73199i	0.0364943	−	0.171416i
$475$	3.30889	−	5.73117i	0.151822	−	0.262964i
$476$	8.24539			0.377927
$477$	−2.15551	−	20.6383i	−0.0986941	−	0.944962i
$478$	6.54738			0.299470
$479$	−10.8178	+	18.7370i	−0.494278	+	0.856115i	−0.999978	−	0.00659439i	$-0.997901\pi$
$479$	−10.8178	+	18.7370i	−0.494278	+	0.856115i	0.505700	+	0.862709i	$0.331234\pi$
$480$	8.02058	−	2.60314i	0.366088	−	0.118817i
$481$	5.10323	+	8.83906i	0.232687	+	0.403026i
$482$	0.457564	+	0.792524i	0.0208415	+	0.0360985i
$483$	−12.8539	−	11.5813i	−0.584871	−	0.526967i
$484$	−1.74070	+	3.01497i	−0.0791225	+	0.137044i
$485$	6.07215			0.275722
$486$	−6.42184	+	3.69365i	−0.291301	+	0.167547i
$487$	−13.1986			−0.598086			−0.299043	−	0.954240i	$-0.596667\pi$
$487$	−13.1986			−0.598086			−0.299043	+	0.954240i	$0.596667\pi$
$488$	−4.29239	+	7.43463i	−0.194307	+	0.336550i
$489$	−4.27830	−	3.85474i	−0.193472	−	0.174317i
$490$	0.183582	+	0.317973i	0.00829338	+	0.0143646i
$491$	15.1570	+	26.2526i	0.684024	+	1.18476i	0.973743	+	0.227652i	$0.0731048\pi$
$491$	15.1570	+	26.2526i	0.684024	+	1.18476i	−0.289719	+	0.957112i	$0.593562\pi$
$492$	11.5023	−	3.73317i	0.518565	−	0.168304i
$493$	7.02917	−	12.1749i	0.316578	−	0.548329i
$494$	−3.14506			−0.141503
$495$	−0.936852	−	8.97004i	−0.0421084	−	0.403173i
$496$	−2.98147			−0.133872
$497$	6.79176	−	11.7637i	0.304652	−	0.527673i
$498$	2.49140	−	11.7023i	0.111642	−	0.524391i
$499$	−18.2081	−	31.5373i	−0.815106	−	1.41181i	−0.909252	−	0.416247i	$-0.863345\pi$
$499$	−18.2081	−	31.5373i	−0.815106	−	1.41181i	0.0941452	−	0.995558i	$-0.469988\pi$
$500$	0.887072	+	1.53645i	0.0396711	+	0.0687123i
$501$	−0.819720	+	3.85028i	−0.0366224	+	0.172018i
$502$	2.74230	−	4.74980i	0.122395	−	0.211994i
$503$	−3.37170			−0.150337			−0.0751684	−	0.997171i	$-0.523949\pi$
$503$	−3.37170			−0.150337			−0.0751684	+	0.997171i	$0.523949\pi$
$504$	12.2635	+	5.46967i	0.546258	+	0.243639i
$505$	−4.64353			−0.206634
$506$	2.85949	−	4.95278i	0.127120	−	0.220178i
$507$	1.64745	−	0.534694i	0.0731660	−	0.0237466i
$508$	−2.46557	−	4.27049i	−0.109392	−	0.189472i
$509$	−14.5760	−	25.2464i	−0.646072	−	1.11903i	−0.984053	−	0.177876i	$-0.943077\pi$
$509$	−14.5760	−	25.2464i	−0.646072	−	1.11903i	0.337981	−	0.941153i	$-0.390256\pi$
$510$	1.13891	+	1.02616i	0.0504319	+	0.0454390i
$511$	7.90802	−	13.6971i	0.349830	−	0.605924i
$512$	22.7956			1.00743
$513$	−20.2395	+	27.7998i	−0.893595	+	1.22739i
$514$	−8.54345			−0.376835
$515$	6.38750	−	11.0635i	0.281467	−	0.487515i
$516$	14.5531	+	13.1123i	0.640663	+	0.577235i
$517$	−0.198976	−	0.344637i	−0.00875096	−	0.0151571i
$518$	6.05223	+	10.4828i	0.265920	+	0.460587i
$519$	−23.7142	+	7.69663i	−1.04094	+	0.337845i
$520$	0.896819	−	1.55334i	0.0393281	−	0.0681183i
$521$	−3.09509			−0.135598			−0.0677991	−	0.997699i	$-0.521598\pi$
$521$	−3.09509			−0.135598			−0.0677991	+	0.997699i	$0.521598\pi$
$522$	8.71099	−	6.32019i	0.381270	−	0.276627i
$523$	11.6267			0.508400			0.254200	−	0.967152i	$-0.418188\pi$
$523$	11.6267			0.508400			0.254200	+	0.967152i	$0.418188\pi$
$524$	12.8298	−	22.2219i	0.560474	−	0.970769i
$525$	−0.900040	+	4.22755i	−0.0392810	+	0.184505i
$526$	1.41120	+	2.44427i	0.0615311	+	0.106575i
$527$	−1.02984	−	1.78374i	−0.0448606	−	0.0777008i
$528$	2.92305	−	13.7298i	0.127209	−	0.597512i
$529$	3.48845	−	6.04217i	0.151672	−	0.262703i
$530$	−3.28719			−0.142786
$531$	1.95451	−	1.41808i	0.0848187	−	0.0615396i
$532$	29.2992			1.27028
$533$	1.96768	−	3.40812i	0.0852295	−	0.147622i
$534$	4.52399	−	1.46829i	0.195772	−	0.0635393i
$535$	−5.20127	−	9.00887i	−0.224871	−	0.389487i
$536$	3.72537	+	6.45254i	0.160912	+	0.278707i
$537$	25.5497	+	23.0202i	1.10255	+	0.993394i
$538$	0.312016	−	0.540427i	0.0134520	−	0.0232995i
$539$	2.32259			0.100041
$540$	−3.74132	−	8.42540i	−0.161001	−	0.362571i
$541$	19.7270			0.848132			0.424066	−	0.905631i	$-0.360603\pi$
$541$	19.7270			0.848132			0.424066	+	0.905631i	$0.360603\pi$
$542$	4.07509	−	7.05827i	0.175040	−	0.303179i
$543$	26.0705	+	23.4895i	1.11879	+	1.00803i
$544$	4.53347	+	7.85220i	0.194371	+	0.336660i
$545$	−9.21599	−	15.9626i	−0.394770	−	0.683761i
$546$	1.95381	−	0.634126i	0.0836156	−	0.0271381i
$547$	5.38353	−	9.32455i	0.230183	−	0.398689i	−0.727679	−	0.685918i	$-0.759401\pi$
$547$	5.38353	−	9.32455i	0.230183	−	0.398689i	0.957862	+	0.287229i	$0.0927342\pi$
$548$	−32.2881			−1.37928
$549$	13.1135	+	5.84880i	0.559671	+	0.249621i
$550$	−1.42871			−0.0609206
$551$	24.9775	−	43.2622i	1.06408	−	1.84303i
$552$	2.58950	−	12.1631i	0.110216	−	0.517694i
$553$	5.78380	+	10.0178i	0.245952	+	0.426002i
$554$	−6.93553	−	12.0127i	−0.294663	−	0.510371i
$555$	3.68115	−	17.2906i	0.156256	−	0.733945i
$556$	−20.1140	+	34.8385i	−0.853024	+	1.47748i
$557$	34.4423			1.45937			0.729683	−	0.683786i	$-0.239668\pi$
$557$	34.4423			1.45937			0.729683	+	0.683786i	$0.239668\pi$
$558$	−0.163791	−	1.56824i	−0.00693382	−	0.0663890i
$559$	6.37469			0.269621
$560$	−3.36375	+	5.82618i	−0.142144	+	0.246201i
$561$	9.22381	−	2.99366i	0.389430	−	0.126392i
$562$	−3.21435	−	5.56742i	−0.135589	−	0.234848i
$563$	−10.7378	−	18.5984i	−0.452544	−	0.783828i	0.546000	−	0.837785i	$-0.316150\pi$
$563$	−10.7378	−	18.5984i	−0.452544	−	0.783828i	−0.998543	+	0.0539570i	$0.982817\pi$
$564$	−0.302201	−	0.272283i	−0.0127250	−	0.0114652i
$565$	8.00969	−	13.8732i	0.336970	−	0.583650i
$566$	−8.20893			−0.345047
$567$	6.96827	−	21.3510i	0.292640	−	0.896657i
$568$	9.76321			0.409655
$569$	22.9248	−	39.7070i	0.961059	−	1.66460i	0.241208	−	0.970474i	$-0.422457\pi$
$569$	22.9248	−	39.7070i	0.961059	−	1.66460i	0.719851	−	0.694129i	$-0.244210\pi$
$570$	4.04701	+	3.64635i	0.169511	+	0.152729i
$571$	22.9690	+	39.7834i	0.961221	+	1.66488i	0.719443	+	0.694552i	$0.244397\pi$
$571$	22.9690	+	39.7834i	0.961221	+	1.66488i	0.241778	+	0.970332i	$0.422269\pi$
$572$	−2.66678	−	4.61901i	−0.111504	−	0.193130i
$573$	23.7638	−	7.71272i	0.992746	−	0.322203i
$574$	2.33359	−	4.04189i	0.0974021	−	0.168705i
$575$	4.00289			0.166932
$576$	−0.959214	−	9.18415i	−0.0399673	−	0.382673i
$577$	−44.0303			−1.83301			−0.916503	−	0.400028i	$-0.869000\pi$
$577$	−44.0303			−1.83301			−0.916503	+	0.400028i	$0.869000\pi$
$578$	3.21539	−	5.56922i	0.133743	−	0.231649i
$579$	8.73784	−	41.0422i	0.363132	−	1.70566i
$580$	6.69614	+	11.5981i	0.278042	+	0.481583i
$581$	18.1361	+	31.4126i	0.752411	+	1.30321i
$582$	−1.04080	+	4.88870i	−0.0431425	+	0.202643i
$583$	−10.3970	+	18.0081i	−0.430599	+	0.745820i
$584$	11.3678			0.470405
$585$	−2.73984	−	1.22200i	−0.113278	−	0.0505236i
$586$	3.29798			0.136238
$587$	11.0945	−	19.2162i	0.457917	−	0.793136i	−0.540934	−	0.841065i	$-0.681929\pi$
$587$	11.0945	−	19.2162i	0.457917	−	0.793136i	0.998851	+	0.0479296i	$0.0152623\pi$
$588$	2.25811	−	0.732887i	0.0931229	−	0.0302238i
$589$	−3.65944	−	6.33833i	−0.150784	−	0.261166i
$590$	−0.191267	−	0.331284i	−0.00787433	−	0.0136387i
$591$	−2.50117	−	2.25354i	−0.102884	−	0.0926984i
$592$	13.7577	−	23.8290i	0.565437	−	0.979365i
$593$	−8.38651			−0.344392			−0.172196	−	0.985063i	$-0.555086\pi$
$593$	−8.38651			−0.344392			−0.172196	+	0.985063i	$0.555086\pi$
$594$	7.38238	+	0.783250i	0.302903	+	0.0321372i
$595$	−4.64753			−0.190530
$596$	16.3148	−	28.2580i	0.668278	−	1.15749i
$597$	−9.74488	−	8.78010i	−0.398831	−	0.359346i
$598$	−0.951173	−	1.64748i	−0.0388964	−	0.0673705i
$599$	−20.4216	−	35.3712i	−0.834402	−	1.44523i	−0.894516	−	0.447035i	$-0.852480\pi$
$599$	−20.4216	−	35.3712i	−0.834402	−	1.44523i	0.0601143	−	0.998192i	$-0.480853\pi$
$600$	−2.95493	+	0.959047i	−0.120635	+	0.0391529i
$601$	4.18193	−	7.24331i	0.170584	−	0.295461i	−0.768040	−	0.640402i	$-0.778768\pi$
$601$	4.18193	−	7.24331i	0.170584	−	0.295461i	0.938624	+	0.344941i	$0.112101\pi$
$602$	7.56014			0.308128
$603$	10.0867	−	7.31835i	0.410763	−	0.298026i
$604$	13.5610			0.551789
$605$	0.981147	−	1.69940i	0.0398893	−	0.0690903i
$606$	0.795925	−	3.73852i	0.0323323	−	0.151867i
$607$	−15.0802	−	26.1197i	−0.612087	−	1.06017i	−0.990888	−	0.134688i	$-0.956997\pi$
$607$	−15.0802	−	26.1197i	−0.612087	−	1.06017i	0.378801	−	0.925478i	$-0.376337\pi$
$608$	16.1092	+	27.9020i	0.653316	+	1.13158i
$609$	−6.79403	+	31.9120i	−0.275308	+	1.29314i
$610$	1.13731	−	1.96989i	0.0460485	−	0.0797583i
$611$	−0.132374			−0.00535527
$612$	8.02310	−	5.82110i	0.324315	−	0.235304i
$613$	−6.73660			−0.272089			−0.136044	−	0.990703i	$-0.543439\pi$
$613$	−6.73660			−0.272089			−0.136044	+	0.990703i	$0.543439\pi$
$614$	3.80393	−	6.58861i	0.153514	−	0.265895i
$615$	−6.48331	+	2.10421i	−0.261432	+	0.0848499i
$616$	−6.72803	−	11.6533i	−0.271080	−	0.469524i
$617$	3.48508	+	6.03634i	0.140304	+	0.243014i	0.927611	−	0.373547i	$-0.121859\pi$
$617$	3.48508	+	6.03634i	0.140304	+	0.243014i	−0.787307	+	0.616561i	$0.788525\pi$
$618$	7.81237	+	7.03892i	0.314260	+	0.283147i
$619$	−17.6414	+	30.5557i	−0.709066	+	1.22814i	0.256138	+	0.966640i	$0.417550\pi$
$619$	−17.6414	+	30.5557i	−0.709066	+	1.22814i	−0.965204	+	0.261498i	$0.915783\pi$
$620$	1.96210			0.0787997
$621$	−20.6835	−	2.19446i	−0.830001	−	0.0880608i
$622$	−6.16082			−0.247026
$623$	−7.20968	+	12.4875i	−0.288850	+	0.500302i
$624$	−3.46901	−	3.12557i	−0.138871	−	0.125123i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.39569	+	7.61355i	0.175687	+	0.304299i
$627$	32.7759	−	10.6377i	1.30894	−	0.424828i
$628$	−8.41969	+	14.5833i	−0.335982	+	0.581938i
$629$	19.0083			0.757911
$630$	−3.24934	−	1.44925i	−0.129457	−	0.0577395i
$631$	6.42382			0.255728			0.127864	−	0.991792i	$-0.459188\pi$
$631$	6.42382			0.255728			0.127864	+	0.991792i	$0.459188\pi$
$632$	−4.15714	+	7.20037i	−0.165362	+	0.286415i
$633$	−5.47372	+	25.7104i	−0.217561	+	1.02190i
$634$	−7.40661	−	12.8286i	−0.294154	−	0.509490i
$635$	1.38972	+	2.40707i	0.0551494	+	0.0955216i
$636$	−4.42593	+	20.7889i	−0.175500	+	0.824334i
$637$	0.386290	−	0.669074i	0.0153054	−	0.0265097i
$638$	−10.7848			−0.426973
$639$	−1.69629	−	16.2414i	−0.0671042	−	0.642500i
$640$	−11.1998			−0.442709
$641$	−24.7537	+	42.8746i	−0.977711	+	1.69345i	−0.307029	+	0.951700i	$0.599335\pi$
$641$	−24.7537	+	42.8746i	−0.977711	+	1.69345i	−0.670682	+	0.741745i	$0.733998\pi$
$642$	8.14459	−	2.64339i	0.321441	−	0.104326i
$643$	19.0192	+	32.9423i	0.750046	+	1.29912i	0.947800	+	0.318866i	$0.103302\pi$
$643$	19.0192	+	32.9423i	0.750046	+	1.29912i	−0.197754	+	0.980252i	$0.563365\pi$
$644$	8.86107	+	15.3478i	0.349175	+	0.604789i
$645$	−8.20286	−	7.39075i	−0.322987	−	0.291011i
$646$	−2.92865	+	5.07257i	−0.115226	+	0.199577i
$647$	44.2290			1.73882			0.869410	−	0.494091i	$-0.164499\pi$
$647$	44.2290			1.73882			0.869410	+	0.494091i	$0.164499\pi$
$648$	15.7944	−	3.33558i	0.620461	−	0.131034i
$649$	−2.41982			−0.0949861
$650$	−0.237622	+	0.411573i	−0.00932029	+	0.0161432i
$651$	3.55134	+	3.19974i	0.139188	+	0.125408i
$652$	2.94934	+	5.10840i	0.115505	+	0.200060i
$653$	−18.3836	−	31.8414i	−0.719407	−	1.24605i	−0.961235	−	0.275731i	$-0.911080\pi$
$653$	−18.3836	−	31.8414i	−0.719407	−	1.24605i	0.241828	−	0.970319i	$-0.422253\pi$
$654$	14.4312	−	4.68375i	0.564303	−	0.183149i
$655$	−7.23156	+	12.5254i	−0.282560	+	0.489409i
$656$	−10.6092			−0.414220
$657$	−1.97508	−	18.9108i	−0.0770554	−	0.737779i
$658$	−0.156990			−0.00612011
$659$	−13.9797	+	24.2135i	−0.544570	+	0.943224i	0.454063	+	0.890969i	$0.349974\pi$
$659$	−13.9797	+	24.2135i	−0.544570	+	0.943224i	−0.998634	+	0.0522543i	$0.983359\pi$
$660$	−1.92365	+	9.03551i	−0.0748779	+	0.351707i
$661$	−1.33600	−	2.31401i	−0.0519642	−	0.0900046i	0.838873	−	0.544327i	$-0.183215\pi$
$661$	−1.33600	−	2.31401i	−0.0519642	−	0.0900046i	−0.890837	+	0.454322i	$0.849881\pi$
$662$	5.09022	+	8.81652i	0.197837	+	0.342664i
$663$	0.671701	−	3.15503i	0.0260867	−	0.122531i
$664$	−13.0354	+	22.5779i	−0.505871	+	0.876194i
$665$	−16.5145			−0.640407
$666$	13.2897	+	5.92740i	0.514967	+	0.229682i
$667$	30.2161			1.16997
$668$	2.01612	−	3.49202i	0.0780060	−	0.135110i
$669$	−37.7858	+	12.2637i	−1.46088	+	0.474141i
$670$	−0.987078	−	1.70967i	−0.0381341	−	0.0660503i
$671$	−7.19438	−	12.4610i	−0.277736	−	0.481053i
$672$	−15.6334	−	14.0856i	−0.603070	−	0.543365i
$673$	11.2433	−	19.4740i	0.433398	−	0.750668i	−0.563765	−	0.825935i	$-0.690648\pi$
$673$	11.2433	−	19.4740i	0.433398	−	0.750668i	0.997163	+	0.0752673i	$0.0239810\pi$
$674$	−10.2554			−0.395022
$675$	2.10880	+	4.74899i	0.0811679	+	0.182789i
$676$	−1.77414			−0.0682363
$677$	−18.6555	+	32.3124i	−0.716991	+	1.24186i	0.245196	+	0.969474i	$0.421148\pi$
$677$	−18.6555	+	32.3124i	−0.716991	+	1.24186i	−0.962187	+	0.272391i	$0.912186\pi$
$678$	9.79644	+	8.82656i	0.376230	+	0.338982i
$679$	−7.57646	−	13.1228i	−0.290758	−	0.503608i
$680$	−1.67022	−	2.89290i	−0.0640499	−	0.110938i
$681$	−27.4314	+	8.90307i	−1.05117	+	0.341166i
$682$	−0.790036	+	1.36838i	−0.0302521	+	0.0523981i
$683$	−21.6591			−0.828762			−0.414381	−	0.910103i	$-0.636002\pi$
$683$	−21.6591			−0.828762			−0.414381	+	0.910103i	$0.636002\pi$
$684$	28.5093	−	20.6847i	1.09008	−	0.790900i
$685$	18.1993			0.695358
$686$	4.60899	−	7.98300i	0.175972	−	0.304792i
$687$	4.58740	−	21.5473i	0.175020	−	0.822081i
$688$	−8.59268	−	14.8830i	−0.327593	−	0.567408i
$689$	3.45842	+	5.99017i	0.131755	+	0.228207i
$690$	−0.686116	+	3.22273i	−0.0261200	+	0.122687i
$691$	−15.0718	+	26.1051i	−0.573357	+	0.993084i	0.422861	+	0.906195i	$0.361026\pi$
$691$	−15.0718	+	26.1051i	−0.573357	+	0.993084i	−0.996218	+	0.0868893i	$0.972307\pi$
$692$	25.5378			0.970803
$693$	−18.2167	+	13.2170i	−0.691993	+	0.502071i
$694$	−0.00618448			−0.000234760
$695$	11.3373	−	19.6368i	0.430049	−	0.744866i
$696$	−22.3056	+	7.23945i	−0.845491	+	0.274411i
$697$	−3.66456	−	6.34721i	−0.138805	−	0.240418i
$698$	3.09521	+	5.36106i	0.117155	+	0.202919i
$699$	25.3631	+	22.8521i	0.959322	+	0.864346i
$700$	2.21367	−	3.83419i	0.0836689	−	0.144919i
$701$	−10.1845			−0.384664			−0.192332	−	0.981330i	$-0.561605\pi$
$701$	−10.1845			−0.384664			−0.192332	+	0.981330i	$0.561605\pi$
$702$	1.45346	−	1.99639i	0.0548573	−	0.0753489i
$703$	67.5442			2.54748
$704$	−4.62672	+	8.01371i	−0.174376	+	0.302028i
$705$	0.170336	+	0.153473i	0.00641524	+	0.00578011i
$706$	−3.46488	−	6.00135i	−0.130403	−	0.225864i
$707$	5.79392	+	10.0354i	0.217903	+	0.377419i
$708$	−2.35264	+	0.763567i	−0.0884176	+	0.0286966i
$709$	−16.2836	+	28.2040i	−0.611543	+	1.05922i	0.379438	+	0.925217i	$0.376117\pi$
$709$	−16.2836	+	28.2040i	−0.611543	+	1.05922i	−0.990981	+	0.134006i	$0.957216\pi$
$710$	−2.58687			−0.0970834
$711$	12.7003	+	5.66451i	0.476299	+	0.212436i
$712$	−10.3640			−0.388407
$713$	2.21348	−	3.83385i	0.0828954	−	0.143579i
$714$	0.796611	−	3.74174i	0.0298124	−	0.140031i
$715$	1.50314	+	2.60351i	0.0562142	+	0.0973659i
$716$	−17.6132	−	30.5070i	−0.658236	−	1.14010i
$717$	−4.96889	+	23.3392i	−0.185567	+	0.871619i
$718$	6.74438	−	11.6816i	0.251698	−	0.435954i
$719$	−28.8233			−1.07493			−0.537464	−	0.843287i	$-0.680618\pi$
$719$	−28.8233			−1.07493			−0.537464	+	0.843287i	$0.680618\pi$
$720$	0.840120	+	8.04386i	0.0313094	+	0.299777i
$721$	−31.8797			−1.18726
$722$	−5.89184	+	10.2050i	−0.219272	+	0.379790i
$723$	−3.17233	+	1.02961i	−0.117980	+	0.0382914i
$724$	−17.9723	−	31.1289i	−0.667933	−	1.15689i
$725$	−3.77429	−	6.53727i	−0.140174	−	0.242788i
$726$	1.20001	+	1.08121i	0.0445367	+	0.0401274i
$727$	−11.8436	+	20.5138i	−0.439256	+	0.760813i	−0.997632	−	0.0687744i	$-0.978091\pi$
$727$	−11.8436	+	20.5138i	−0.439256	+	0.760813i	0.558376	+	0.829588i	$0.311424\pi$
$728$	−4.47599			−0.165891
$729$	−8.29301	−	25.6949i	−0.307148	−	0.951662i
$730$	−3.01203			−0.111480
$731$	5.93605	−	10.2815i	0.219553	−	0.380277i
$732$	−10.9267	−	9.84492i	−0.403862	−	0.363879i
$733$	−11.3349	−	19.6326i	−0.418664	−	0.725148i	0.577141	−	0.816644i	$-0.304168\pi$
$733$	−11.3349	−	19.6326i	−0.418664	−	0.725148i	−0.995805	+	0.0914967i	$0.970835\pi$
$734$	−1.14166	−	1.97741i	−0.0421394	−	0.0729876i
$735$	−1.27279	+	0.413094i	−0.0469475	+	0.0152372i
$736$	−9.74397	+	16.8770i	−0.359167	+	0.622096i
$737$	−12.4880			−0.460003
$738$	−0.582830	−	5.58040i	−0.0214543	−	0.205417i
$739$	5.54302			0.203903			0.101952	−	0.994789i	$-0.467491\pi$
$739$	5.54302			0.203903			0.101952	+	0.994789i	$0.467491\pi$
$740$	−9.05387	+	15.6818i	−0.332827	+	0.576473i
$741$	2.38682	−	11.2111i	0.0876822	−	0.411849i
$742$	4.10156	+	7.10410i	0.150573	+	0.260800i
$743$	−22.0684	−	38.2235i	−0.809610	−	1.40229i	−0.913134	−	0.407659i	$-0.866345\pi$
$743$	−22.0684	−	38.2235i	−0.809610	−	1.40229i	0.103524	−	0.994627i	$-0.466988\pi$
$744$	−0.715442	+	3.36048i	−0.0262294	+	0.123201i
$745$	−9.19585	+	15.9277i	−0.336910	+	0.583545i
$746$	−1.96205			−0.0718358
$747$	39.8239	+	17.7620i	1.45708	+	0.649877i
$748$	−9.93313			−0.363191
$749$	−12.9797	+	22.4815i	−0.474267	+	0.821455i
$750$	0.782942	−	0.254110i	0.0285890	−	0.00927878i
$751$	−12.0674	−	20.9014i	−0.440347	−	0.762704i	0.557368	−	0.830266i	$-0.311811\pi$
$751$	−12.0674	−	20.9014i	−0.440347	−	0.762704i	−0.997715	+	0.0675620i	$0.978478\pi$
$752$	0.178431	+	0.309052i	0.00650672	+	0.0112700i
$753$	14.8503	+	13.3800i	0.541174	+	0.487596i
$754$	−1.79371	+	3.10680i	−0.0653230	+	0.113143i
$755$	−7.64368			−0.278182
$756$	−13.5403	+	18.5983i	−0.492458	+	0.676412i
$757$	−10.9814			−0.399126			−0.199563	−	0.979885i	$-0.563952\pi$
$757$	−10.9814			−0.399126			−0.199563	+	0.979885i	$0.563952\pi$
$758$	−3.68253	+	6.37832i	−0.133755	+	0.231671i
$759$	15.4849	+	13.9518i	0.562066	+	0.506420i
$760$	−5.93495	−	10.2796i	−0.215283	−	0.372882i
$761$	−20.6439	−	35.7562i	−0.748339	−	1.29616i	−0.948618	−	0.316422i	$-0.897518\pi$
$761$	−20.6439	−	35.7562i	−0.748339	−	1.29616i	0.200279	−	0.979739i	$-0.435815\pi$
$762$	−2.17614	+	0.706284i	−0.0788333	+	0.0255860i
$763$	−22.9983	+	39.8343i	−0.832595	+	1.44210i
$764$	−25.5912			−0.925858
$765$	−4.52224	+	3.28108i	−0.163502	+	0.118628i
$766$	1.01768			0.0367703
$767$	−0.402461	+	0.697082i	−0.0145320	+	0.0251702i
$768$	−0.300602	+	1.41195i	−0.0108470	+	0.0509493i
$769$	16.9547	+	29.3664i	0.611403	+	1.05898i	0.991004	+	0.133830i	$0.0427278\pi$
$769$	16.9547	+	29.3664i	0.611403	+	1.05898i	−0.379602	+	0.925150i	$0.623939\pi$
$770$	1.78266	+	3.08766i	0.0642427	+	0.111272i
$771$	6.48373	−	30.4545i	0.233506	−	1.09679i
$772$	−21.4909	+	37.2234i	−0.773475	+	1.33970i
$773$	38.5022			1.38483			0.692414	−	0.721500i	$-0.256547\pi$
$773$	38.5022			1.38483			0.692414	+	0.721500i	$0.256547\pi$
$774$	7.35633	−	5.33733i	0.264418	−	0.191846i
$775$	−1.10594			−0.0397266
$776$	5.44562	−	9.43209i	0.195486	−	0.338592i
$777$	−41.9607	+	13.6187i	−1.50533	+	0.488567i
$778$	−3.94077	−	6.82561i	−0.141283	−	0.244710i
$779$	−13.0217	−	22.5542i	−0.466549	−	0.808087i
$780$	2.28294	+	2.05692i	0.0817424	+	0.0736497i
$781$	−8.18196	+	14.1716i	−0.292773	+	0.507098i
$782$	−3.54289			−0.126694
$783$	15.9185	+	35.8482i	0.568880	+	1.28111i
$784$	−2.08278			−0.0743849
$785$	4.74578	−	8.21993i	0.169384	−	0.293382i
$786$	−8.84472	−	7.96907i	−0.315481	−	0.284247i
$787$	−3.56557	−	6.17575i	−0.127099	−	0.220142i	0.795452	−	0.606016i	$-0.207233\pi$
$787$	−3.56557	−	6.17575i	−0.127099	−	0.220142i	−0.922551	+	0.385874i	$0.873900\pi$
$788$	1.72423	+	2.98645i	0.0614231	+	0.106388i
$789$	−9.78396	+	3.17546i	−0.348318	+	0.113049i
$790$	1.10148	−	1.90782i	0.0391888	−	0.0678770i
$791$	−39.9761			−1.42138
$792$	−14.7737	−	6.58926i	−0.524960	−	0.234139i
$793$	−4.78624			−0.169964
$794$	−1.09377	+	1.89447i	−0.0388165	+	0.0672322i
$795$	2.49469	−	11.7177i	0.0884775	−	0.415585i
$796$	6.71783	+	11.6356i	0.238107	+	0.412414i
$797$	−1.42162	−	2.46232i	−0.0503564	−	0.0872199i	0.839748	−	0.542976i	$-0.182702\pi$
$797$	−1.42162	−	2.46232i	−0.0503564	−	0.0872199i	−0.890105	+	0.455756i	$0.849369\pi$
$798$	2.83068	−	13.2959i	0.100205	−	0.470670i
$799$	−0.123265	+	0.213501i	−0.00436080	+	0.00755313i
$800$	4.86847			0.172126
$801$	1.80067	+	17.2408i	0.0636235	+	0.609173i
$802$	4.95352			0.174915
$803$	−9.52671	+	16.5007i	−0.336190	+	0.582298i
$804$	−12.1414	+	3.94057i	−0.428192	+	0.138973i
$805$	−4.99456	−	8.65083i	−0.176035	−	0.304902i
$806$	0.262796	+	0.455175i	0.00925658	+	0.0160329i
$807$	1.68965	+	1.52237i	0.0594784	+	0.0535899i
$808$	−4.16440	+	7.21296i	−0.146503	+	0.253751i
$809$	49.2285			1.73078			0.865391	−	0.501098i	$-0.167070\pi$
$809$	49.2285			1.73078			0.865391	+	0.501098i	$0.167070\pi$
$810$	−4.18489	+	0.883799i	−0.147042	+	0.0310535i
$811$	14.4236			0.506480			0.253240	−	0.967404i	$-0.418504\pi$
$811$	14.4236			0.506480			0.253240	+	0.967404i	$0.418504\pi$
$812$	16.7101	−	28.9427i	0.586409	−	1.01569i
$813$	22.0677	+	19.8829i	0.773949	+	0.697325i
$814$	−7.29106	−	12.6285i	−0.255552	−	0.442628i
$815$	−1.66240	−	2.87936i	−0.0582313	−	0.100860i
$816$	−8.27143	+	2.68456i	−0.289558	+	0.0939783i
$817$	21.0932	−	36.5344i	0.737957	−	1.27818i
$818$	17.4857			0.611372
$819$	0.777671	+	7.44594i	0.0271740	+	0.260182i
$820$	6.98188			0.243818
$821$	15.3555	−	26.5966i	0.535912	−	0.928227i	−0.463206	−	0.886250i	$-0.653301\pi$
$821$	15.3555	−	26.5966i	0.535912	−	0.928227i	0.999119	−	0.0419768i	$-0.0133655\pi$
$822$	−3.11945	+	14.6523i	−0.108803	+	0.511057i
$823$	19.8972	+	34.4629i	0.693572	+	1.20130i	0.970660	+	0.240457i	$0.0772973\pi$
$823$	19.8972	+	34.4629i	0.693572	+	1.20130i	−0.277088	+	0.960845i	$0.589369\pi$
$824$	−11.4569	−	19.8439i	−0.399118	−	0.691293i
$825$	1.08427	−	5.09289i	0.0377494	−	0.177311i
$826$	−0.477303	+	0.826712i	−0.0166075	+	0.0287650i
$827$	−31.7524			−1.10414			−0.552069	−	0.833798i	$-0.686162\pi$
$827$	−31.7524			−1.10414			−0.552069	+	0.833798i	$0.686162\pi$
$828$	19.4575	+	8.67830i	0.676194	+	0.301592i
$829$	6.91750			0.240255			0.120127	−	0.992758i	$-0.461670\pi$
$829$	6.91750			0.240255			0.120127	+	0.992758i	$0.461670\pi$
$830$	3.45386	−	5.98227i	0.119885	−	0.207648i
$831$	48.0847	−	15.6063i	1.66804	−	0.541375i
$832$	1.53902	+	2.66566i	0.0533558	+	0.0924150i
$833$	−0.719418	−	1.24607i	−0.0249264	−	0.0431737i
$834$	13.8664	+	12.4935i	0.480153	+	0.432616i
$835$	−1.13639	+	1.96829i	−0.0393264	+	0.0681153i
$836$	−35.2964			−1.22075
$837$	5.71456	+	0.606299i	0.197524	+	0.0209568i
$838$	−12.1723			−0.420486
$839$	−16.0617	+	27.8198i	−0.554513	+	0.960445i	0.443428	+	0.896310i	$0.353762\pi$
$839$	−16.0617	+	27.8198i	−0.554513	+	0.960445i	−0.997941	+	0.0641348i	$0.979571\pi$
$840$	5.75963	+	5.18941i	0.198726	+	0.179052i
$841$	−13.9906	−	24.2324i	−0.482434	−	0.835601i
$842$	−1.97284	−	3.41707i	−0.0679887	−	0.117760i
$843$	22.2854	−	7.23290i	0.767550	−	0.249114i
$844$	13.4627	−	23.3182i	0.463407	−	0.802644i
$845$	1.00000			0.0344010
$846$	−0.152758	+	0.110832i	−0.00525192	+	0.00381049i
$847$	−4.89687			−0.168258
$848$	9.32347	−	16.1487i	0.320169	−	0.554550i
$849$	6.22986	−	29.2621i	0.213808	−	1.00427i
$850$	0.442542	+	0.766505i	0.0151791	+	0.0262909i
$851$	20.4277	+	35.3817i	0.700251	+	1.21287i
$852$	−3.48301	+	16.3599i	−0.119326	+	0.560482i
$853$	−19.8130	+	34.3171i	−0.678384	+	1.17500i	0.297083	+	0.954852i	$0.403986\pi$
$853$	−19.8130	+	34.3171i	−0.678384	+	1.17500i	−0.975467	+	0.220144i	$0.929347\pi$
$854$	−5.67629			−0.194239
$855$	−16.0693	+	11.6590i	−0.549560	+	0.398729i
$856$	−18.6584			−0.637731
$857$	1.12803	−	1.95380i	0.0385327	−	0.0667405i	−0.846116	−	0.532999i	$-0.821065\pi$
$857$	1.12803	−	1.95380i	0.0385327	−	0.0667405i	0.884649	+	0.466258i	$0.154398\pi$
$858$	−2.35374	+	0.763925i	−0.0803554	+	0.0260800i
$859$	−6.67248	−	11.5571i	−0.227662	−	0.394322i	0.729453	−	0.684031i	$-0.239775\pi$
$859$	−6.67248	−	11.5571i	−0.227662	−	0.394322i	−0.957115	+	0.289709i	$0.906441\pi$
$860$	5.65481	+	9.79442i	0.192827	+	0.333987i
$861$	12.6370	+	11.3859i	0.430668	+	0.388030i
$862$	0.268326	−	0.464754i	0.00913921	−	0.0158296i
$863$	45.5215			1.54957			0.774786	−	0.632224i	$-0.217858\pi$
$863$	45.5215			1.54957			0.774786	+	0.632224i	$0.217858\pi$
$864$	−25.1561	−	2.66900i	−0.855829	−	0.0908011i
$865$	−14.3945			−0.489426
$866$	−5.88987	+	10.2016i	−0.200146	+	0.346663i
$867$	17.4122	+	15.6883i	0.591349	+	0.532804i
$868$	−2.44819	−	4.24038i	−0.0830969	−	0.143928i
$869$	−6.96769	−	12.0684i	−0.236363	−	0.409392i
$870$	5.91010	−	1.91817i	0.200371	−	0.0650321i
$871$	−2.07699	+	3.59746i	−0.0703762	+	0.121895i
$872$	−33.0603			−1.11956
$873$	−16.6367	−	7.42019i	−0.563067	−	0.251135i
$874$	−12.5893			−0.425840
$875$	−1.24774	+	2.16115i	−0.0421813	+	0.0730602i
$876$	−4.05546	+	19.0488i	−0.137021	+	0.643599i
$877$	−26.1599	−	45.3103i	−0.883358	−	1.53002i	−0.847584	−	0.530661i	$-0.821944\pi$
$877$	−26.1599	−	45.3103i	−0.883358	−	1.53002i	−0.0357738	−	0.999360i	$-0.511390\pi$
$878$	8.16034	+	14.1341i	0.275398	+	0.477003i
$879$	−2.50287	+	11.7562i	−0.0844199	+	0.396526i
$880$	4.05227	−	7.01874i	0.136602	−	0.236602i
$881$	−45.1831			−1.52226			−0.761128	−	0.648601i	$-0.775354\pi$
$881$	−45.1831			−1.52226			−0.761128	+	0.648601i	$0.775354\pi$
$882$	−0.114420	−	1.09553i	−0.00385272	−	0.0368885i
$883$	−7.24302			−0.243747			−0.121873	−	0.992546i	$-0.538890\pi$
$883$	−7.24302			−0.243747			−0.121873	+	0.992546i	$0.538890\pi$
$884$	−1.65206	+	2.86146i	−0.0555649	+	0.0962413i
$885$	1.32607	−	0.430386i	0.0445754	−	0.0144673i
$886$	−4.08168	−	7.06967i	−0.137127	−	0.237510i
$887$	−15.2434	−	26.4023i	−0.511823	−	0.886504i	−0.999906	−	0.0137067i	$-0.995637\pi$
$887$	−15.2434	−	26.4023i	−0.511823	−	0.886504i	0.488083	−	0.872797i	$-0.337696\pi$
$888$	−23.5568	−	21.2246i	−0.790514	−	0.712251i
$889$	3.46802	−	6.00679i	0.116314	−	0.201461i
$890$	2.74605			0.0920477
$891$	−8.39461	+	25.7213i	−0.281230	+	0.861696i
$892$	40.6916			1.36245
$893$	−0.438010	+	0.758656i	−0.0146574	+	0.0253874i
$894$	−11.2472	−	10.1337i	−0.376162	−	0.338921i
$895$	9.92772	+	17.1953i	0.331847	+	0.574776i
$896$	13.9744	+	24.2043i	0.466851	+	0.808610i
$897$	6.59457	−	2.14032i	0.220186	−	0.0714632i
$898$	−1.75258	+	3.03557i	−0.0584845	+	0.101298i
$899$	−8.34829			−0.278431
$900$	−0.552880	−	5.29364i	−0.0184293	−	0.176455i
$901$	12.8818			0.429155
$902$	−2.81125	+	4.86922i	−0.0936043	+	0.162127i
$903$	−5.73748	+	26.9493i	−0.190931	+	0.896818i
$904$	−14.3665	−	24.8835i	−0.477822	−	0.827612i
$905$	10.1301	+	17.5458i	0.336736	+	0.583244i
$906$	1.31017	−	6.15394i	0.0435274	−	0.204451i
$907$	−6.72909	+	11.6551i	−0.223436	+	0.387002i	−0.955849	−	0.293858i	$-0.905061\pi$
$907$	−6.72909	+	11.6551i	−0.223436	+	0.387002i	0.732413	+	0.680860i	$0.238394\pi$
$908$	29.5409			0.980348
$909$	12.7225	+	5.67441i	0.421979	+	0.188208i
$910$	1.18596			0.0393142
$911$	15.3374	−	26.5651i	0.508149	−	0.880140i	−0.491806	−	0.870705i	$-0.663663\pi$
$911$	15.3374	−	26.5651i	0.508149	−	0.880140i	0.999955	−	0.00943566i	$-0.00300351\pi$
$912$	−29.3917	+	9.53931i	−0.973257	+	0.315878i
$913$	−21.8483	−	37.8424i	−0.723074	−	1.25240i
$914$	−4.22246	−	7.31351i	−0.139666	−	0.241909i
$915$	6.15886	+	5.54911i	0.203606	+	0.183448i
$916$	−11.2828	+	19.5424i	−0.372794	+	0.645699i
$917$	36.0924			1.19188
$918$	−1.86647	−	4.20326i	−0.0616026	−	0.138728i
$919$	−19.6999			−0.649839			−0.324919	−	0.945742i	$-0.605337\pi$
$919$	−19.6999			−0.649839			−0.324919	+	0.945742i	$0.605337\pi$
$920$	3.58986	−	6.21783i	0.118354	−	0.204996i
$921$	20.5993	+	18.5599i	0.678771	+	0.611570i
$922$	3.70255	+	6.41300i	0.121937	+	0.211201i
$923$	2.72162	+	4.71399i	0.0895833	+	0.155163i
$924$	21.9273	−	7.11668i	0.721355	−	0.234121i
$925$	5.10323	−	8.83906i	0.167793	−	0.290626i
$926$	1.82214			0.0598794
$927$	−31.0203	+	22.5066i	−1.01884	+	0.739212i
$928$	36.7501			1.20638
$929$	−1.45936	+	2.52769i	−0.0478802	+	0.0829309i	−0.888972	−	0.457961i	$-0.848580\pi$
$929$	−1.45936	+	2.52769i	−0.0478802	+	0.0829309i	0.841092	+	0.540892i	$0.181913\pi$
$930$	0.189564	−	0.890395i	0.00621605	−	0.0291972i
$931$	−2.55638	−	4.42778i	−0.0837820	−	0.145115i
$932$	−17.4846	−	30.2842i	−0.572727	−	0.991993i
$933$	4.67552	−	21.9613i	0.153070	−	0.718979i
$934$	3.65437	−	6.32955i	0.119575	−	0.207109i
$935$	5.59883			0.183101
$936$	−4.35532	+	3.15997i	−0.142358	+	0.103287i
$937$	−34.7949			−1.13670			−0.568351	−	0.822786i	$-0.692418\pi$
$937$	−34.7949			−1.13670			−0.568351	+	0.822786i	$0.692418\pi$
$938$	−2.46323	+	4.26644i	−0.0804274	+	0.139304i
$939$	−30.4757	+	9.89112i	−0.994537	+	0.322785i
$940$	−0.117425	−	0.203386i	−0.00382998	−	0.00663372i
$941$	0.357443	+	0.619109i	0.0116523	+	0.0201824i	0.871793	−	0.489875i	$-0.162958\pi$
$941$	0.357443	+	0.619109i	0.0116523	+	0.0201824i	−0.860140	+	0.510057i	$0.829624\pi$
$942$	5.80443	+	5.22978i	0.189119	+	0.170395i
$943$	7.87639	−	13.6423i	0.256490	−	0.444255i
$944$	2.16997			0.0706264
$945$	7.63205	−	10.4829i	0.248271	−	0.341010i
$946$	−9.10762			−0.296114
$947$	−8.19183	+	14.1887i	−0.266199	+	0.461070i	−0.967877	−	0.251424i	$-0.919101\pi$
$947$	−8.19183	+	14.1887i	−0.266199	+	0.461070i	0.701678	+	0.712494i	$0.252434\pi$
$948$	−10.5824	−	9.53471i	−0.343701	−	0.309673i
$949$	3.16894	+	5.48876i	0.102868	+	0.178173i
$950$	1.57253	+	2.72370i	0.0510196	+	0.0883685i
$951$	51.3507	−	16.6663i	1.66516	−	0.540441i
$952$	−4.16799	+	7.21918i	−0.135085	+	0.233975i
$953$	8.97837			0.290838			0.145419	−	0.989370i	$-0.453547\pi$
$953$	8.97837			0.290838			0.145419	+	0.989370i	$0.453547\pi$
$954$	9.00636	+	4.01696i	0.291592	+	0.130054i
$955$	14.4245			0.466767
$956$	12.2211	−	21.1676i	0.395258	−	0.684608i
$957$	8.18470	−	38.4441i	0.264574	−	1.24272i
$958$	−5.14109	−	8.90463i	−0.166101	−	0.287696i
$959$	−22.7080	−	39.3313i	−0.733278	−	1.27008i
$960$	1.11015	−	5.21445i	0.0358299	−	0.168296i
$961$	14.8884	−	25.7875i	0.480273	−	0.831856i
$962$	−4.85056			−0.156388
$963$	3.24177	+	31.0388i	0.104464	+	1.00021i
$964$	3.41629			0.110031
$965$	12.1134	−	20.9810i	0.389944	−	0.675403i
$966$	7.82090	−	2.53833i	0.251633	−	0.0816696i
$967$	−0.152998	−	0.265000i	−0.00492008	−	0.00852182i	0.863555	−	0.504255i	$-0.168233\pi$
$967$	−0.152998	−	0.265000i	−0.00492008	−	0.00852182i	−0.868475	+	0.495733i	$0.834899\pi$
$968$	−1.75982	−	3.04810i	−0.0565628	−	0.0979697i
$969$	−15.8594	−	14.2893i	−0.509477	−	0.459038i
$970$	−1.44287	+	2.49913i	−0.0463279	+	0.0802423i
$971$	24.9695			0.801310			0.400655	−	0.916229i	$-0.368783\pi$
$971$	24.9695			0.801310			0.400655	+	0.916229i	$0.368783\pi$
$972$	−0.0452670	+	27.6561i	−0.00145194	+	0.887071i
$973$	−56.5841			−1.81400
$974$	3.13628	−	5.43219i	0.100493	−	0.174059i
$975$	−1.28679	−	1.15939i	−0.0412101	−	0.0371302i
$976$	6.45154	+	11.1744i	0.206509	+	0.357684i
$977$	−11.7457	−	20.3442i	−0.375780	−	0.650870i	0.614664	−	0.788789i	$-0.289292\pi$
$977$	−11.7457	−	20.3442i	−0.375780	−	0.650870i	−0.990443	+	0.137920i	$0.955958\pi$
$978$	2.60312	−	0.844864i	0.0832387	−	0.0270158i
$979$	8.68542	−	15.0436i	0.277587	−	0.480795i
$980$	1.37067			0.0437844
$981$	5.74399	+	54.9968i	0.183392	+	1.75591i
$982$	−14.4065			−0.459729
$983$	2.20491	−	3.81902i	0.0703257	−	0.121808i	−0.828718	−	0.559666i	$-0.810929\pi$
$983$	2.20491	−	3.81902i	0.0703257	−	0.121808i	0.899044	+	0.437858i	$0.144263\pi$
$984$	−2.54581	+	11.9579i	−0.0811575	+	0.381202i
$985$	−0.971866	−	1.68332i	−0.0309662	−	0.0536351i
$986$	3.34057	+	5.78603i	0.106385	+	0.184265i
$987$	0.119142	−	0.559616i	0.00379232	−	0.0178128i
$988$	−5.87045	+	10.1679i	−0.186764	+	0.323484i
$989$	25.5172			0.811399
$990$	3.91444	+	1.74589i	0.124409	+	0.0554882i
$991$	−55.1403			−1.75159			−0.875794	−	0.482685i	$-0.839662\pi$
$991$	−55.1403			−1.75159			−0.875794	+	0.482685i	$0.839662\pi$
$992$	2.69212	−	4.66289i	0.0854749	−	0.148047i
$993$	−35.2909	+	11.4540i	−1.11992	+	0.363480i
$994$	3.22774	+	5.59061i	0.102378	+	0.177323i
$995$	−3.78652	−	6.55845i	−0.120041	−	0.207917i
$996$	−33.1829	−	29.8977i	−1.05144	−	0.947344i
$997$	17.5331	−	30.3683i	0.555280	−	0.961772i	−0.442602	−	0.896718i	$-0.645945\pi$
$997$	17.5331	−	30.3683i	0.555280	−	0.961772i	0.997882	−	0.0650543i	$-0.0207221\pi$
$998$	17.3066			0.547830
$999$	−31.2149	+	42.8751i	−0.987597	+	1.35651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.f.196.4	✓	16
3.2	odd	2		1755.2.i.e.586.5		16
9.2	odd	6		5265.2.a.be.1.4		8
9.4	even	3	inner	585.2.i.f.391.4	yes	16
9.5	odd	6		1755.2.i.e.1171.5		16
9.7	even	3		5265.2.a.bb.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.4	✓	16	1.1	even	1	trivial
585.2.i.f.391.4	yes	16	9.4	even	3	inner
1755.2.i.e.586.5		16	3.2	odd	2
1755.2.i.e.1171.5		16	9.5	odd	6
5265.2.a.bb.1.5		8	9.7	even	3
5265.2.a.be.1.4		8	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.237622 + 0.411573i) q^{2} +(-1.28679 - 1.15939i) q^{3} +(0.887072 + 1.53645i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.782942 - 0.254110i) q^{6} +(-1.24774 + 2.16115i) q^{7} -1.79364 q^{8} +(0.311632 + 2.98377i) q^{9} +O(q^{10})\)	\(q+(-0.237622 + 0.411573i) q^{2} +(-1.28679 - 1.15939i) q^{3} +(0.887072 + 1.53645i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.782942 - 0.254110i) q^{6} +(-1.24774 + 2.16115i) q^{7} -1.79364 q^{8} +(0.311632 + 2.98377i) q^{9} +0.475244 q^{10} +(1.50314 - 2.60351i) q^{11} +(0.639877 - 3.00555i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-0.592980 - 1.02707i) q^{14} +(-0.360668 + 1.69408i) q^{15} +(-1.34794 + 2.33469i) q^{16} -1.86238 q^{17} +(-1.30209 - 0.580750i) q^{18} -6.61778 q^{19} +(0.887072 - 1.53645i) q^{20} +(4.11119 - 1.33432i) q^{21} +(0.714357 + 1.23730i) q^{22} +(-2.00144 - 3.46660i) q^{23} +(2.30803 + 2.07952i) q^{24} +(-0.500000 + 0.866025i) q^{25} +0.475244 q^{26} +(3.05835 - 4.20077i) q^{27} -4.42734 q^{28} +(-3.77429 + 6.53727i) q^{29} +(-0.611536 - 0.550992i) q^{30} +(0.552970 + 0.957772i) q^{31} +(-2.43424 - 4.21622i) q^{32} +(-4.95270 + 1.60744i) q^{33} +(0.442542 - 0.766505i) q^{34} +2.49548 q^{35} +(-4.30798 + 3.12563i) q^{36} -10.2065 q^{37} +(1.57253 - 2.72370i) q^{38} +(-0.360668 + 1.69408i) q^{39} +(0.896819 + 1.55334i) q^{40} +(1.96768 + 3.40812i) q^{41} +(-0.427738 + 2.00912i) q^{42} +(-3.18735 + 5.52065i) q^{43} +5.33357 q^{44} +(2.42820 - 1.76177i) q^{45} +1.90235 q^{46} +(0.0661868 - 0.114639i) q^{47} +(4.44132 - 1.44147i) q^{48} +(0.386290 + 0.669074i) q^{49} +(-0.237622 - 0.411573i) q^{50} +(2.39648 + 2.15922i) q^{51} +(0.887072 - 1.53645i) q^{52} -6.91685 q^{53} +(1.00219 + 2.25693i) q^{54} -3.00628 q^{55} +(2.23799 - 3.87632i) q^{56} +(8.51566 + 7.67259i) q^{57} +(-1.79371 - 3.10680i) q^{58} +(-0.402461 - 0.697082i) q^{59} +(-2.92282 + 0.948624i) q^{60} +(2.39312 - 4.14500i) q^{61} -0.525591 q^{62} +(-6.83721 - 3.04949i) q^{63} -3.07804 q^{64} +(-0.500000 + 0.866025i) q^{65} +(0.515292 - 2.42036i) q^{66} +(-2.07699 - 3.59746i) q^{67} +(-1.65206 - 2.86146i) q^{68} +(-1.44371 + 6.78122i) q^{69} +(-0.592980 + 1.02707i) q^{70} -5.44325 q^{71} +(-0.558955 - 5.35180i) q^{72} -6.33787 q^{73} +(2.42528 - 4.20071i) q^{74} +(1.64745 - 0.534694i) q^{75} +(-5.87045 - 10.1679i) q^{76} +(3.75105 + 6.49701i) q^{77} +(-0.611536 - 0.550992i) q^{78} +(2.31771 - 4.01440i) q^{79} +2.69587 q^{80} +(-8.80577 + 1.85968i) q^{81} -1.87025 q^{82} +(7.26757 - 12.5878i) q^{83} +(5.69703 + 5.13301i) q^{84} +(0.931190 + 1.61287i) q^{85} +(-1.51477 - 2.62365i) q^{86} +(12.4359 - 4.03618i) q^{87} +(-2.69609 + 4.66976i) q^{88} +5.77819 q^{89} +(0.148101 + 1.41802i) q^{90} +2.49548 q^{91} +(3.55085 - 6.15025i) q^{92} +(0.398878 - 1.87356i) q^{93} +(0.0314549 + 0.0544814i) q^{94} +(3.30889 + 5.73117i) q^{95} +(-1.75590 + 8.24760i) q^{96} +(-3.03607 + 5.25864i) q^{97} -0.367164 q^{98} +(8.23671 + 3.67368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

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