LMFDB - Embedded newform 115.2.g.c.16.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	115.16
Dual form			115.2.g.c.36.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29801 - 1.49799i) q^{2} +(0.749526 - 0.481691i) q^{3} +(-0.274499 - 1.90918i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.251328 - 1.74802i) q^{6} +(-3.44343 + 1.01108i) q^{7} +(0.118700 + 0.0762838i) q^{8} +(-0.916482 + 2.00682i) q^{9} +O(q^{10})$	\(q+(1.29801 - 1.49799i) q^{2} +(0.749526 - 0.481691i) q^{3} +(-0.274499 - 1.90918i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.251328 - 1.74802i) q^{6} +(-3.44343 + 1.01108i) q^{7} +(0.118700 + 0.0762838i) q^{8} +(-0.916482 + 2.00682i) q^{9} +(1.90183 + 0.558429i) q^{10} +(-2.66540 - 3.07604i) q^{11} +(-1.12538 - 1.29876i) q^{12} +(0.453235 + 0.133082i) q^{13} +(-2.95503 + 6.47061i) q^{14} +(0.749526 + 0.481691i) q^{15} +(3.96971 - 1.16561i) q^{16} +(-0.293567 + 2.04180i) q^{17} +(1.81658 + 3.97776i) q^{18} +(-1.10343 - 7.67453i) q^{19} +(1.62262 - 1.04280i) q^{20} +(-2.09391 + 2.41650i) q^{21} -8.06760 q^{22} +(3.46199 + 3.31883i) q^{23} +0.125714 q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.787660 - 0.506199i) q^{26} +(0.660130 + 4.59131i) q^{27} +(2.87555 + 6.29659i) q^{28} +(0.637549 - 4.43425i) q^{29} +(1.69446 - 0.497540i) q^{30} +(4.14649 + 2.66479i) q^{31} +(3.28944 - 7.20288i) q^{32} +(-3.47949 - 1.02167i) q^{33} +(2.67754 + 3.09005i) q^{34} +(-2.35016 - 2.71223i) q^{35} +(4.08295 + 1.19886i) q^{36} +(0.140033 - 0.306630i) q^{37} +(-12.9286 - 8.30873i) q^{38} +(0.403815 - 0.118571i) q^{39} +(-0.0200805 + 0.139663i) q^{40} +(1.21337 + 2.65690i) q^{41} +(0.901965 + 6.27331i) q^{42} +(2.28003 - 1.46529i) q^{43} +(-5.14106 + 5.93310i) q^{44} -2.20618 q^{45} +(9.46528 - 0.878132i) q^{46} -9.09267 q^{47} +(2.41394 - 2.78583i) q^{48} +(4.94612 - 3.17868i) q^{49} +(0.282086 + 1.96195i) q^{50} +(0.763481 + 1.67179i) q^{51} +(0.129665 - 0.901838i) q^{52} +(-4.31033 + 1.26563i) q^{53} +(7.73459 + 4.97072i) q^{54} +(1.69081 - 3.70237i) q^{55} +(-0.485864 - 0.142662i) q^{56} +(-4.52380 - 5.22075i) q^{57} +(-5.81491 - 6.71076i) q^{58} +(-14.0334 - 4.12057i) q^{59} +(0.713892 - 1.56321i) q^{60} +(3.64525 + 2.34266i) q^{61} +(9.37404 - 2.75247i) q^{62} +(1.12678 - 7.83696i) q^{63} +(-3.08269 - 6.75014i) q^{64} +(0.0672251 + 0.467561i) q^{65} +(-6.04688 + 3.88609i) q^{66} +(-0.224710 + 0.259329i) q^{67} +3.97875 q^{68} +(4.19350 + 0.819940i) q^{69} -7.11344 q^{70} +(6.18554 - 7.13850i) q^{71} +(-0.261874 + 0.168296i) q^{72} +(-0.367582 - 2.55659i) q^{73} +(-0.277563 - 0.607779i) q^{74} +(-0.126797 + 0.881895i) q^{75} +(-14.3492 + 4.21330i) q^{76} +(12.2882 + 7.89717i) q^{77} +(0.346541 - 0.758818i) q^{78} +(16.5651 + 4.86395i) q^{79} +(2.70936 + 3.12677i) q^{80} +(-1.62785 - 1.87864i) q^{81} +(5.55498 + 1.63109i) q^{82} +(-1.07706 + 2.35843i) q^{83} +(5.18831 + 3.33433i) q^{84} +(-1.97924 + 0.581157i) q^{85} +(0.764532 - 5.31744i) q^{86} +(-1.65808 - 3.63069i) q^{87} +(-0.0817311 - 0.568452i) q^{88} +(-7.82017 + 5.02572i) q^{89} +(-2.86366 + 3.30484i) q^{90} -1.69524 q^{91} +(5.38594 - 7.52058i) q^{92} +4.39151 q^{93} +(-11.8024 + 13.6207i) q^{94} +(6.52262 - 4.19183i) q^{95} +(-1.00404 - 6.98324i) q^{96} +(6.27465 + 13.7396i) q^{97} +(1.65851 - 11.5352i) q^{98} +(8.61583 - 2.52984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	1.29801	−	1.49799i	0.917835	−	1.05924i	−0.0802123	−	0.996778i	$-0.525560\pi$
$2$	1.29801	−	1.49799i	0.917835	−	1.05924i	0.998047	−	0.0624605i	$-0.0198947\pi$
$3$	0.749526	−	0.481691i	0.432739	−	0.278105i	−0.306083	−	0.952005i	$-0.599019\pi$
$3$	0.749526	−	0.481691i	0.432739	−	0.278105i	0.738822	+	0.673900i	$0.235382\pi$
$4$	−0.274499	−	1.90918i	−0.137249	−	0.954591i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	0.251328	−	1.74802i	0.102604	−	0.713628i
$7$	−3.44343	+	1.01108i	−1.30149	+	0.382153i	−0.857780	−	0.514016i	$-0.828157\pi$
$7$	−3.44343	+	1.01108i	−1.30149	+	0.382153i	−0.443712	+	0.896169i	$0.646339\pi$
$8$	0.118700	+	0.0762838i	0.0419668	+	0.0269704i
$9$	−0.916482	+	2.00682i	−0.305494	+	0.668939i
$10$	1.90183	+	0.558429i	0.601413	+	0.176591i
$11$	−2.66540	−	3.07604i	−0.803649	−	0.927460i	0.194927	−	0.980818i	$-0.437553\pi$
$11$	−2.66540	−	3.07604i	−0.803649	−	0.927460i	−0.998575	+	0.0533578i	$0.983008\pi$
$12$	−1.12538	−	1.29876i	−0.324869	−	0.374919i
$13$	0.453235	+	0.133082i	0.125705	+	0.0369102i	0.343980	−	0.938977i	$-0.388225\pi$
$13$	0.453235	+	0.133082i	0.125705	+	0.0369102i	−0.218275	+	0.975887i	$0.570043\pi$
$14$	−2.95503	+	6.47061i	−0.789765	+	1.72934i
$15$	0.749526	+	0.481691i	0.193527	+	0.124372i
$16$	3.96971	−	1.16561i	0.992429	−	0.291403i
$17$	−0.293567	+	2.04180i	−0.0712004	+	0.495209i	0.922752	+	0.385395i	$0.125935\pi$
$17$	−0.293567	+	2.04180i	−0.0712004	+	0.495209i	−0.993952	+	0.109814i	$0.964974\pi$
$18$	1.81658	+	3.97776i	0.428172	+	0.937566i
$19$	−1.10343	−	7.67453i	−0.253144	−	1.76066i	−0.579084	−	0.815268i	$-0.696590\pi$
$19$	−1.10343	−	7.67453i	−0.253144	−	1.76066i	0.325940	−	0.945391i	$-0.394319\pi$
$20$	1.62262	−	1.04280i	0.362829	−	0.233176i
$21$	−2.09391	+	2.41650i	−0.456928	+	0.527323i
$22$	−8.06760			−1.72002
$23$	3.46199	+	3.31883i	0.721875	+	0.692024i
$23$	3.46199	+	3.31883i	0.721875	+	0.692024i
$24$	0.125714			0.0256612
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	0.787660	−	0.506199i	0.154473	−	0.0992737i
$27$	0.660130	+	4.59131i	0.127042	+	0.883597i
$28$	2.87555	+	6.29659i	0.543429	+	1.18994i
$29$	0.637549	−	4.43425i	0.118390	−	0.823419i	−0.840939	−	0.541129i	$-0.817997\pi$
$29$	0.637549	−	4.43425i	0.118390	−	0.823419i	0.959329	−	0.282290i	$-0.0910940\pi$
$30$	1.69446	−	0.497540i	0.309365	−	0.0908379i
$31$	4.14649	+	2.66479i	0.744732	+	0.478610i	0.857160	−	0.515049i	$-0.172226\pi$
$31$	4.14649	+	2.66479i	0.744732	+	0.478610i	−0.112428	+	0.993660i	$0.535863\pi$
$32$	3.28944	−	7.20288i	0.581497	−	1.27330i
$33$	−3.47949	−	1.02167i	−0.605701	−	0.177850i
$34$	2.67754	+	3.09005i	0.459194	+	0.529939i
$35$	−2.35016	−	2.71223i	−0.397250	−	0.458451i
$36$	4.08295	+	1.19886i	0.680492	+	0.199810i
$37$	0.140033	−	0.306630i	0.0230213	−	0.0504097i	−0.897772	−	0.440460i	$-0.854815\pi$
$37$	0.140033	−	0.306630i	0.0230213	−	0.0504097i	0.920793	+	0.390051i	$0.127543\pi$
$38$	−12.9286	−	8.30873i	−2.09730	−	1.34785i
$39$	0.403815	−	0.118571i	0.0646622	−	0.0189865i
$40$	−0.0200805	+	0.139663i	−0.00317500	+	0.0220826i
$41$	1.21337	+	2.65690i	0.189496	+	0.414939i	0.980404	−	0.196996i	$-0.0631187\pi$
$41$	1.21337	+	2.65690i	0.189496	+	0.414939i	−0.790908	+	0.611935i	$0.790391\pi$
$42$	0.901965	+	6.27331i	0.139176	+	0.967992i
$43$	2.28003	−	1.46529i	0.347702	−	0.223455i	−0.355119	−	0.934821i	$-0.615560\pi$
$43$	2.28003	−	1.46529i	0.347702	−	0.223455i	0.702821	+	0.711366i	$0.251923\pi$
$44$	−5.14106	+	5.93310i	−0.775045	+	0.894449i
$45$	−2.20618			−0.328879
$46$	9.46528	−	0.878132i	1.39558	−	0.129474i
$47$	−9.09267			−1.32630			−0.663151	−	0.748486i	$-0.730781\pi$
$47$	−9.09267			−1.32630			−0.663151	+	0.748486i	$0.730781\pi$
$48$	2.41394	−	2.78583i	0.348422	−	0.402100i
$49$	4.94612	−	3.17868i	0.706589	−	0.454097i
$50$	0.282086	+	1.96195i	0.0398929	+	0.277461i
$51$	0.763481	+	1.67179i	0.106909	+	0.234098i
$52$	0.129665	−	0.901838i	0.0179813	−	0.125062i
$53$	−4.31033	+	1.26563i	−0.592070	+	0.173847i	−0.564023	−	0.825759i	$-0.690747\pi$
$53$	−4.31033	+	1.26563i	−0.592070	+	0.173847i	−0.0280470	+	0.999607i	$0.508929\pi$
$54$	7.73459	+	4.97072i	1.05254	+	0.676429i
$55$	1.69081	−	3.70237i	0.227989	−	0.499227i
$56$	−0.485864	−	0.142662i	−0.0649262	−	0.0190641i
$57$	−4.52380	−	5.22075i	−0.599193	−	0.691505i
$58$	−5.81491	−	6.71076i	−0.763535	−	0.881166i
$59$	−14.0334	−	4.12057i	−1.82699	−	0.536453i	−0.827311	−	0.561744i	$-0.810131\pi$
$59$	−14.0334	−	4.12057i	−1.82699	−	0.536453i	−0.999680	+	0.0252909i	$0.991949\pi$
$60$	0.713892	−	1.56321i	0.0921630	−	0.201809i
$61$	3.64525	+	2.34266i	0.466727	+	0.299947i	0.752786	−	0.658265i	$-0.228709\pi$
$61$	3.64525	+	2.34266i	0.466727	+	0.299947i	−0.286060	+	0.958212i	$0.592346\pi$
$62$	9.37404	−	2.75247i	1.19050	−	0.349564i
$63$	1.12678	−	7.83696i	0.141962	−	0.987364i
$64$	−3.08269	−	6.75014i	−0.385336	−	0.843768i
$65$	0.0672251	+	0.467561i	0.00833825	+	0.0579938i
$66$	−6.04688	+	3.88609i	−0.744319	+	0.478345i
$67$	−0.224710	+	0.259329i	−0.0274527	+	0.0316821i	−0.769310	−	0.638876i	$-0.779400\pi$
$67$	−0.224710	+	0.259329i	−0.0274527	+	0.0316821i	0.741857	+	0.670558i	$0.233945\pi$
$68$	3.97875			0.482495
$69$	4.19350	+	0.819940i	0.504838	+	0.0987091i
$70$	−7.11344			−0.850219
$71$	6.18554	−	7.13850i	0.734089	−	0.847184i	−0.258837	−	0.965921i	$-0.583339\pi$
$71$	6.18554	−	7.13850i	0.734089	−	0.847184i	0.992926	+	0.118737i	$0.0378846\pi$
$72$	−0.261874	+	0.168296i	−0.0308621	+	0.0198339i
$73$	−0.367582	−	2.55659i	−0.0430223	−	0.299226i	−0.999960	−	0.00893348i	$-0.997156\pi$
$73$	−0.367582	−	2.55659i	−0.0430223	−	0.299226i	0.956938	−	0.290293i	$-0.0937527\pi$
$74$	−0.277563	−	0.607779i	−0.0322661	−	0.0706529i
$75$	−0.126797	+	0.881895i	−0.0146413	+	0.101832i
$76$	−14.3492	+	4.21330i	−1.64596	+	0.483299i
$77$	12.2882	+	7.89717i	1.40037	+	0.899966i
$78$	0.346541	−	0.758818i	0.0392380	−	0.0859192i
$79$	16.5651	+	4.86395i	1.86372	+	0.547238i	0.998987	+	0.0450060i	$0.0143307\pi$
$79$	16.5651	+	4.86395i	1.86372	+	0.547238i	0.864733	+	0.502232i	$0.167487\pi$
$80$	2.70936	+	3.12677i	0.302915	+	0.349583i
$81$	−1.62785	−	1.87864i	−0.180873	−	0.208738i
$82$	5.55498	+	1.63109i	0.613445	+	0.180124i
$83$	−1.07706	+	2.35843i	−0.118223	+	0.258872i	−0.959487	−	0.281752i	$-0.909084\pi$
$83$	−1.07706	+	2.35843i	−0.118223	+	0.258872i	0.841264	+	0.540624i	$0.181812\pi$
$84$	5.18831	+	3.33433i	0.566091	+	0.363805i
$85$	−1.97924	+	0.581157i	−0.214679	+	0.0630353i
$86$	0.764532	−	5.31744i	0.0824416	−	0.573394i
$87$	−1.65808	−	3.63069i	−0.177765	−	0.389250i
$88$	−0.0817311	−	0.568452i	−0.00871256	−	0.0605972i
$89$	−7.82017	+	5.02572i	−0.828936	+	0.532725i	−0.884940	−	0.465706i	$-0.845800\pi$
$89$	−7.82017	+	5.02572i	−0.828936	+	0.532725i	0.0560037	+	0.998431i	$0.482164\pi$
$90$	−2.86366	+	3.30484i	−0.301856	+	0.348361i
$91$	−1.69524			−0.177709
$92$	5.38594	−	7.52058i	0.561523	−	0.784075i
$93$	4.39151			0.455379
$94$	−11.8024	+	13.6207i	−1.21733	+	1.40487i
$95$	6.52262	−	4.19183i	0.669207	−	0.430073i
$96$	−1.00404	−	6.98324i	−0.102474	−	0.712724i
$97$	6.27465	+	13.7396i	0.637094	+	1.39504i	0.902409	+	0.430880i	$0.141797\pi$
$97$	6.27465	+	13.7396i	0.637094	+	1.39504i	−0.265315	+	0.964162i	$0.585476\pi$
$98$	1.65851	−	11.5352i	0.167535	−	1.16523i
$99$	8.61583	−	2.52984i	0.865924	−	0.254258i
$100$	1.62262	+	1.04280i	0.162262	+	0.104280i
$101$	−4.48225	+	9.81476i	−0.446001	+	0.976606i	0.544457	+	0.838789i	$0.316736\pi$
$101$	−4.48225	+	9.81476i	−0.446001	+	0.976606i	−0.990458	+	0.137817i	$0.955991\pi$
$102$	3.49534	+	1.02632i	0.346090	+	0.101621i
$103$	5.95998	+	6.87818i	0.587254	+	0.677728i	0.969148	−	0.246479i	$-0.0792735\pi$
$103$	5.95998	+	6.87818i	0.587254	+	0.677728i	−0.381894	+	0.924206i	$0.624728\pi$
$104$	0.0436469	+	0.0503712i	0.00427993	+	0.00493931i
$105$	−3.06797	−	0.900836i	−0.299403	−	0.0879126i
$106$	−3.69898	+	8.09964i	−0.359277	+	0.786706i
$107$	−3.88764	−	2.49844i	−0.375832	−	0.241533i	0.339064	−	0.940763i	$-0.389890\pi$
$107$	−3.88764	−	2.49844i	−0.375832	−	0.241533i	−0.714896	+	0.699231i	$0.753526\pi$
$108$	8.58443	−	2.52062i	0.826037	−	0.242546i
$109$	2.10468	−	14.6384i	0.201592	−	1.40210i	−0.597970	−	0.801518i	$-0.704026\pi$
$109$	2.10468	−	14.6384i	0.201592	−	1.40210i	0.799562	−	0.600583i	$-0.205065\pi$
$110$	−3.35140	−	7.33855i	−0.319544	−	0.699703i
$111$	−0.0427424	−	0.297280i	−0.00405693	−	0.0282166i
$112$	−12.4909	+	8.02741i	−1.18028	+	0.758519i
$113$	−11.1628	+	12.8826i	−1.05011	+	1.21189i	−0.0734057	+	0.997302i	$0.523387\pi$
$113$	−11.1628	+	12.8826i	−1.05011	+	1.21189i	−0.976704	+	0.214589i	$0.931159\pi$
$114$	−13.6926			−1.28243
$115$	−1.58075	+	4.52783i	−0.147406	+	0.422222i
$116$	−8.64079			−0.802277
$117$	−0.682452	+	0.787591i	−0.0630927	+	0.0728129i
$118$	−24.3881	+	15.6733i	−2.24511	+	1.44284i
$119$	−1.05355	−	7.32761i	−0.0965789	−	0.671721i
$120$	0.0522234	+	0.114353i	0.00476733	+	0.0104390i
$121$	−0.792176	+	5.50971i	−0.0720160	+	0.500883i
$122$	8.24087	−	2.41974i	0.746093	−	0.219073i
$123$	2.18926	+	1.40695i	0.197399	+	0.126860i
$124$	3.94936	−	8.64789i	0.354663	−	0.776604i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	−10.2771	−	11.8604i	−0.915557	−	1.05661i
$127$	0.680229	+	0.785026i	0.0603606	+	0.0696598i	0.785127	−	0.619335i	$-0.212598\pi$
$127$	0.680229	+	0.785026i	0.0603606	+	0.0696598i	−0.724766	+	0.688995i	$0.758052\pi$
$128$	1.08238	+	0.317816i	0.0956699	+	0.0280912i
$129$	1.00313	−	2.19655i	0.0883206	−	0.193395i
$130$	0.787660	+	0.506199i	0.0690824	+	0.0443966i
$131$	2.07273	−	0.608608i	0.181095	−	0.0531743i	−0.189928	−	0.981798i	$-0.560825\pi$
$131$	2.07273	−	0.608608i	0.181095	−	0.0531743i	0.371023	+	0.928624i	$0.379007\pi$
$132$	−0.995438	+	6.92342i	−0.0866417	+	0.602606i
$133$	11.5592	+	25.3110i	1.00231	+	2.19474i
$134$	0.0967954	+	0.673226i	0.00836185	+	0.0581579i
$135$	−3.90217	+	2.50777i	−0.335845	+	0.215835i
$136$	−0.190603	+	0.219967i	−0.0163440	+	0.0188620i
$137$	18.2672			1.56068			0.780338	−	0.625358i	$-0.215047\pi$
$137$	18.2672			1.56068			0.780338	+	0.625358i	$0.215047\pi$
$138$	6.67149	−	5.21753i	0.567915	−	0.444145i
$139$	−2.12975			−0.180643			−0.0903213	−	0.995913i	$-0.528789\pi$
$139$	−2.12975			−0.180643			−0.0903213	+	0.995913i	$0.528789\pi$
$140$	−4.53303	+	5.23139i	−0.383111	+	0.442133i
$141$	−6.81519	+	4.37986i	−0.573943	+	0.368851i
$142$	−2.66446	−	18.5318i	−0.223597	−	1.55515i
$143$	−0.798688	−	1.74888i	−0.0667896	−	0.146249i
$144$	−1.29900	+	9.03475i	−0.108250	+	0.752896i
$145$	4.29838	−	1.26212i	0.356961	−	0.104813i
$146$	−4.30687	−	2.76786i	−0.356439	−	0.229070i
$147$	2.17611	−	4.76501i	0.179482	−	0.393011i
$148$	−0.623852	−	0.183179i	−0.0512803	−	0.0150573i
$149$	10.3520	+	11.9468i	0.848068	+	0.978723i	0.999953	−	0.00967556i	$-0.00307988\pi$
$149$	10.3520	+	11.9468i	0.848068	+	0.978723i	−0.151885	+	0.988398i	$0.548534\pi$
$150$	1.15648	+	1.33465i	0.0944265	+	0.108974i
$151$	−14.9174	−	4.38015i	−1.21396	−	0.356452i	−0.388787	−	0.921328i	$-0.627106\pi$
$151$	−14.9174	−	4.38015i	−1.21396	−	0.356452i	−0.825176	+	0.564876i	$0.808924\pi$
$152$	0.454465	−	0.995140i	0.0368620	−	0.0807165i
$153$	−3.82847	−	2.46041i	−0.309513	−	0.198912i
$154$	27.7802	−	8.15700i	2.23859	−	0.657310i
$155$	−0.701462	+	4.87878i	−0.0563428	+	0.391873i
$156$	−0.337220	−	0.738410i	−0.0269992	−	0.0591201i
$157$	−1.76049	−	12.2444i	−0.140502	−	0.977213i	−0.931070	−	0.364840i	$-0.881124\pi$
$157$	−1.76049	−	12.2444i	−0.140502	−	0.977213i	0.790568	−	0.612374i	$-0.209785\pi$
$158$	28.7879	−	18.5009i	2.29024	−	1.47185i
$159$	−2.62107	+	3.02487i	−0.207864	+	0.239888i
$160$	7.91845			0.626008
$161$	−15.2767	−	7.92779i	−1.20397	−	0.624798i
$162$	−4.92717			−0.387115
$163$	6.97482	−	8.04937i	0.546310	−	0.630476i	−0.413709	−	0.910409i	$-0.635767\pi$
$163$	6.97482	−	8.04937i	0.546310	−	0.630476i	0.960019	+	0.279934i	$0.0903124\pi$
$164$	4.73944	−	3.04586i	0.370088	−	0.237841i
$165$	−0.516088	−	3.58947i	−0.0401774	−	0.279440i
$166$	2.13487	+	4.67471i	0.165698	+	0.362828i
$167$	1.55167	−	10.7921i	0.120072	−	0.835117i	−0.837400	−	0.546590i	$-0.815926\pi$
$167$	1.55167	−	10.7921i	0.120072	−	0.835117i	0.957472	−	0.288527i	$-0.0931654\pi$
$168$	−0.432887	+	0.127107i	−0.0333979	+	0.00980652i
$169$	−10.7486	−	6.90770i	−0.826814	−	0.531361i
$170$	−1.69851	+	3.71923i	−0.130270	+	0.285252i
$171$	16.4126	+	4.81919i	1.25511	+	0.368533i
$172$	−3.42337	−	3.95078i	−0.261030	−	0.301244i
$173$	5.23781	+	6.04475i	0.398223	+	0.459574i	0.919081	−	0.394070i	$-0.128933\pi$
$173$	5.23781	+	6.04475i	0.398223	+	0.459574i	−0.520858	+	0.853644i	$0.674388\pi$
$174$	−7.59094	−	2.22890i	−0.575468	−	0.168973i
$175$	1.49084	−	3.26449i	0.112697	−	0.246772i
$176$	−14.1663	−	9.10416i	−1.06783	−	0.686252i
$177$	−12.5032	+	3.67128i	−0.939801	+	0.275950i
$178$	−2.62223	+	18.2380i	−0.196544	+	1.36699i
$179$	−5.84398	−	12.7965i	−0.436799	−	0.956457i	−0.992175	−	0.124857i	$-0.960153\pi$
$179$	−5.84398	−	12.7965i	−0.436799	−	0.956457i	0.555375	−	0.831600i	$-0.312575\pi$
$180$	0.605595	+	4.21201i	0.0451384	+	0.313944i
$181$	5.03489	−	3.23572i	0.374240	−	0.240509i	−0.339977	−	0.940434i	$-0.610419\pi$
$181$	5.03489	−	3.23572i	0.374240	−	0.240509i	0.714217	+	0.699924i	$0.246783\pi$
$182$	−2.20044	+	2.53945i	−0.163108	+	0.188236i
$183$	3.86065			0.285387
$184$	0.157765	+	0.658038i	0.0116306	+	0.0485112i
$185$	0.337093			0.0247835
$186$	5.70025	−	6.57844i	0.417962	−	0.482354i
$187$	7.06313	−	4.53920i	0.516507	−	0.331939i
$188$	2.49593	+	17.3596i	0.182034	+	1.26608i
$189$	−6.91529	−	15.1424i	−0.503014	−	1.10145i
$190$	2.18714	−	15.2119i	0.158672	−	1.10359i
$191$	6.55327	−	1.92421i	0.474178	−	0.139231i	−0.0359072	−	0.999355i	$-0.511432\pi$
$191$	6.55327	−	1.92421i	0.474178	−	0.139231i	0.510085	+	0.860124i	$0.329614\pi$
$192$	−5.56204	−	3.57451i	−0.401406	−	0.257968i
$193$	6.20837	−	13.5944i	0.446888	−	0.978549i	−0.543394	−	0.839478i	$-0.682861\pi$
$193$	6.20837	−	13.5944i	0.446888	−	0.978549i	0.990282	−	0.139071i	$-0.0444117\pi$
$194$	28.7263	+	8.43481i	2.06243	+	0.605584i
$195$	0.275607	+	0.318067i	0.0197366	+	0.0227773i
$196$	−7.42639	−	8.57051i	−0.530456	−	0.612179i
$197$	11.6767	+	3.42860i	0.831933	+	0.244277i	0.669847	−	0.742499i	$-0.266360\pi$
$197$	11.6767	+	3.42860i	0.831933	+	0.244277i	0.162086	+	0.986777i	$0.448178\pi$
$198$	7.39381	−	16.1902i	0.525455	−	1.15059i
$199$	3.42670	+	2.20221i	0.242913	+	0.156110i	0.656433	−	0.754384i	$-0.272065\pi$
$199$	3.42670	+	2.20221i	0.242913	+	0.156110i	−0.413520	+	0.910495i	$0.635701\pi$
$200$	−0.135383	+	0.0397521i	−0.00957305	+	0.00281090i
$201$	−0.0435095	+	0.302615i	−0.00306892	+	0.0213448i
$202$	8.88438	+	19.4541i	0.625103	+	1.36878i
$203$	2.28803	+	15.9136i	0.160588	+	1.11692i
$204$	2.98218	−	1.91653i	0.208794	−	0.134184i
$205$	−1.91275	+	2.20743i	−0.133592	+	0.154174i
$206$	18.0396			1.25688
$207$	−9.83313	+	3.90593i	−0.683450	+	0.271481i
$208$	1.95433			0.135509
$209$	−20.6661	+	23.8499i	−1.42950	+	1.64973i
$210$	−5.33171	+	3.42648i	−0.367923	+	0.236450i
$211$	−2.39847	−	16.6817i	−0.165117	−	1.14842i	−0.888804	−	0.458288i	$-0.848463\pi$
$211$	−2.39847	−	16.6817i	−0.165117	−	1.14842i	0.723687	−	0.690129i	$-0.242446\pi$
$212$	3.59950	+	7.88180i	0.247214	+	0.541324i
$213$	1.19767	−	8.33001i	0.0820633	−	0.570763i
$214$	−8.78884	+	2.58064i	−0.600793	+	0.176409i
$215$	2.28003	+	1.46529i	0.155497	+	0.0999319i
$216$	−0.271885	+	0.595345i	−0.0184994	+	0.0405081i
$217$	−16.9725	−	4.98357i	−1.15217	−	0.338307i
$218$	−19.1962	−	22.1536i	−1.30013	−	1.50043i
$219$	−1.50700	−	1.73917i	−0.101834	−	0.117522i
$220$	−7.53262	−	2.21178i	−0.507849	−	0.149118i
$221$	−0.404781	+	0.886346i	−0.0272285	+	0.0596221i
$222$	−0.500803	−	0.321846i	−0.0336117	−	0.0216009i
$223$	−23.6597	+	6.94711i	−1.58437	+	0.465213i	−0.951142	−	0.308754i	$-0.900088\pi$
$223$	−23.6597	+	6.94711i	−1.58437	+	0.465213i	−0.633227	+	0.773966i	$0.718270\pi$
$224$	−4.04426	+	28.1285i	−0.270219	+	1.87941i
$225$	−0.916482	−	2.00682i	−0.0610988	−	0.133788i
$226$	4.80846	+	33.4436i	0.319854	+	2.22463i
$227$	−19.2830	+	12.3924i	−1.27986	+	0.822514i	−0.990870	−	0.134819i	$-0.956955\pi$
$227$	−19.2830	+	12.3924i	−1.27986	+	0.822514i	−0.288986	+	0.957333i	$0.593318\pi$
$228$	−8.72558	+	10.0699i	−0.577866	+	0.666892i
$229$	−4.84115			−0.319912			−0.159956	−	0.987124i	$-0.551135\pi$
$229$	−4.84115			−0.319912			−0.159956	+	0.987124i	$0.551135\pi$
$230$	4.73080	+	8.24514i	0.311940	+	0.543668i
$231$	13.0143			0.856281
$232$	0.413938	−	0.477710i	0.0271764	−	0.0313632i
$233$	1.60936	−	1.03427i	0.105433	−	0.0677574i	−0.486862	−	0.873479i	$-0.661859\pi$
$233$	1.60936	−	1.03427i	0.105433	−	0.0677574i	0.592295	+	0.805722i	$0.298222\pi$
$234$	0.293971	+	2.04461i	0.0192175	+	0.133660i
$235$	−3.77723	−	8.27098i	−0.246399	−	0.539539i
$236$	−4.01478	+	27.9234i	−0.261340	+	1.81766i
$237$	14.7589	−	4.33360i	0.958694	−	0.281498i
$238$	−12.3442	−	7.93314i	−0.800156	−	0.514229i
$239$	−7.24646	+	15.8675i	−0.468734	+	1.02638i	0.516675	+	0.856182i	$0.327170\pi$
$239$	−7.24646	+	15.8675i	−0.468734	+	1.02638i	−0.985409	+	0.170203i	$0.945558\pi$
$240$	3.53687	+	1.03852i	0.228304	+	0.0670361i
$241$	−16.6272	−	19.1888i	−1.07105	−	1.23606i	−0.970494	−	0.241126i	$-0.922483\pi$
$241$	−16.6272	−	19.1888i	−1.07105	−	1.23606i	−0.100556	−	0.994931i	$-0.532062\pi$
$242$	7.22523	+	8.33836i	0.464455	+	0.536010i
$243$	−15.4769	−	4.54444i	−0.992845	−	0.291526i
$244$	3.47195	−	7.60251i	0.222269	−	0.486701i
$245$	4.94612	+	3.17868i	0.315996	+	0.203079i
$246$	4.94928	−	1.45324i	0.315555	−	0.0926553i
$247$	0.521227	−	3.62521i	0.0331649	−	0.230667i
$248$	0.288908	+	0.632621i	0.0183457	+	0.0401715i
$249$	0.328752	+	2.28652i	0.0208338	+	0.144902i
$250$	−1.66747	+	1.07162i	−0.105460	+	0.0677750i
$251$	−1.75119	+	2.02098i	−0.110534	+	0.127563i	−0.808320	−	0.588743i	$-0.799623\pi$
$251$	−1.75119	+	2.02098i	−0.110534	+	0.127563i	0.697786	+	0.716306i	$0.254169\pi$
$252$	−15.2715			−0.962013
$253$	0.981251	−	19.4952i	0.0616907	−	1.22565i
$254$	2.05891			0.129187
$255$	−1.20355	+	1.38897i	−0.0753694	+	0.0869809i
$256$	14.3665	−	9.23278i	0.897905	−	0.577048i
$257$	−1.60934	−	11.1932i	−0.100388	−	0.698214i	−0.976407	−	0.215938i	$-0.930719\pi$
$257$	−1.60934	−	11.1932i	−0.100388	−	0.698214i	0.876019	−	0.482277i	$-0.160190\pi$
$258$	−1.98833	−	4.35382i	−0.123788	−	0.271057i
$259$	−0.172166	+	1.19744i	−0.0106979	+	0.0744055i
$260$	0.874206	−	0.256690i	0.0542159	−	0.0159192i
$261$	8.31442	+	5.34335i	0.514650	+	0.330745i
$262$	1.77874	−	3.89491i	0.109891	−	0.240628i
$263$	−27.9603	−	8.20989i	−1.72411	−	0.506243i	−0.738349	−	0.674418i	$-0.764394\pi$
$263$	−27.9603	−	8.20989i	−1.72411	−	0.506243i	−0.985757	+	0.168175i	$0.946213\pi$
$264$	−0.335078	−	0.386701i	−0.0206226	−	0.0237998i
$265$	−2.94183	−	3.39506i	−0.180715	−	0.208557i
$266$	52.9196	+	15.5386i	3.24471	+	0.952733i
$267$	−3.44058	+	7.53381i	−0.210560	+	0.461062i
$268$	0.556789	+	0.357827i	0.0340113	+	0.0218577i
$269$	−2.63877	+	0.774814i	−0.160889	+	0.0472412i	−0.361185	−	0.932494i	$-0.617628\pi$
$269$	−2.63877	+	0.774814i	−0.160889	+	0.0472412i	0.200296	+	0.979735i	$0.435810\pi$
$270$	−1.30846	+	9.10054i	−0.0796303	+	0.553841i
$271$	10.7308	+	23.4972i	0.651850	+	1.42735i	0.889926	+	0.456106i	$0.150756\pi$
$271$	10.7308	+	23.4972i	0.651850	+	1.42735i	−0.238076	+	0.971247i	$0.576517\pi$
$272$	1.21457	+	8.44755i	0.0736444	+	0.512208i
$273$	−1.27062	+	0.816580i	−0.0769017	+	0.0494217i
$274$	23.7111	−	27.3641i	1.43244	−	1.65313i
$275$	4.07018			0.245441
$276$	0.414302	−	8.23123i	0.0249380	−	0.495462i
$277$	23.4579			1.40945			0.704725	−	0.709480i	$-0.251070\pi$
$277$	23.4579			1.40945			0.704725	+	0.709480i	$0.251070\pi$
$278$	−2.76444	+	3.19034i	−0.165800	+	0.191344i
$279$	−9.14793	+	5.87902i	−0.547672	+	0.351968i
$280$	−0.0720647	−	0.501221i	−0.00430669	−	0.0299537i
$281$	5.00230	+	10.9535i	0.298412	+	0.653432i	0.998139	−	0.0609789i	$-0.0194222\pi$
$281$	5.00230	+	10.9535i	0.298412	+	0.653432i	−0.699727	+	0.714410i	$0.746695\pi$
$282$	−2.28524	+	15.8942i	−0.136084	+	0.946486i
$283$	−9.08138	+	2.66653i	−0.539832	+	0.158509i	−0.540271	−	0.841491i	$-0.681678\pi$
$283$	−9.08138	+	2.66653i	−0.539832	+	0.158509i	0.000439237		1.00000i	$0.499860\pi$
$284$	−15.3266	−	9.84982i	−0.909467	−	0.584479i
$285$	2.86970	−	6.28377i	0.169987	−	0.372219i
$286$	−3.65652	−	1.07365i	−0.216214	−	0.0634863i
$287$	−6.86448	−	7.92204i	−0.405198	−	0.467623i
$288$	11.4401	+	13.2026i	0.674116	+	0.777971i
$289$	12.2286	+	3.59064i	0.719330	+	0.211214i
$290$	3.68872	−	8.07718i	0.216609	−	0.474308i
$291$	11.3212	+	7.27572i	0.663663	+	0.426510i
$292$	−4.78010	+	1.40356i	−0.279734	+	0.0821373i
$293$	1.26023	−	8.76511i	0.0736236	−	0.512063i	−0.919323	−	0.393503i	$-0.871263\pi$
$293$	1.26023	−	8.76511i	0.0736236	−	0.512063i	0.992947	−	0.118560i	$-0.0378279\pi$
$294$	−4.31331	−	9.44484i	−0.251558	−	0.550834i
$295$	−2.08147	−	14.4770i	−0.121188	−	0.842882i
$296$	0.0400129	−	0.0257147i	0.00232570	−	0.00149464i
$297$	12.3635	−	14.2683i	0.717404	−	0.827928i
$298$	31.3333			1.81509
$299$	1.12742	+	1.96494i	0.0652003	+	0.113635i
$300$	1.71850			0.0992178
$301$	−6.36961	+	7.35092i	−0.367138	+	0.423700i
$302$	−25.9245	+	16.6606i	−1.49178	+	0.958712i
$303$	1.36812	+	9.51548i	0.0785964	+	0.546650i
$304$	−13.3258	−	29.1795i	−0.764289	−	1.67356i
$305$	−0.616667	+	4.28901i	−0.0353103	+	0.245588i
$306$	−8.65507	+	2.54136i	−0.494778	+	0.145280i
$307$	22.2590	+	14.3050i	1.27039	+	0.816430i	0.989671	−	0.143360i	$-0.0457908\pi$
$307$	22.2590	+	14.3050i	1.27039	+	0.816430i	0.280719	+	0.959790i	$0.409427\pi$
$308$	11.7040	−	25.6282i	0.666899	−	1.46030i
$309$	7.78032	+	2.28451i	0.442607	+	0.129961i
$310$	6.39785	+	7.38351i	0.363373	+	0.419355i
$311$	12.7067	+	14.6644i	0.720533	+	0.831539i	0.991371	−	0.131086i	$-0.0418463\pi$
$311$	12.7067	+	14.6644i	0.720533	+	0.831539i	−0.270838	+	0.962625i	$0.587301\pi$
$312$	0.0569779	+	0.0167302i	0.00322574	+	0.000947162i
$313$	−6.52980	+	14.2983i	−0.369086	+	0.808186i	0.630404	+	0.776267i	$0.282889\pi$
$313$	−6.52980	+	14.2983i	−0.369086	+	0.808186i	−0.999490	+	0.0319188i	$0.989838\pi$
$314$	−20.6272	−	13.2563i	−1.16406	−	0.748096i
$315$	7.59683	−	2.23063i	0.428033	−	0.125682i
$316$	4.73907	−	32.9609i	0.266593	−	1.85420i
$317$	−10.1095	−	22.1366i	−0.567804	−	1.24332i	−0.947958	−	0.318394i	$-0.896856\pi$
$317$	−10.1095	−	22.1366i	−0.567804	−	1.24332i	0.380154	−	0.924923i	$-0.375871\pi$
$318$	1.12904	+	7.85265i	0.0633135	+	0.440355i
$319$	−15.3392	+	9.85793i	−0.858832	+	0.551938i
$320$	4.85955	−	5.60822i	0.271657	−	0.313509i
$321$	−4.11736			−0.229809
$322$	−31.7051	+	12.5940i	−1.76686	+	0.701834i
$323$	15.9938			0.889918
$324$	−3.13983	+	3.62356i	−0.174435	+	0.201309i
$325$	−0.397382	+	0.255382i	−0.0220428	+	0.0141660i
$326$	−3.00445	−	20.8964i	−0.166401	−	1.15735i
$327$	−5.47366	−	11.9856i	−0.302694	−	0.662808i
$328$	−0.0586521	+	0.407934i	−0.00323852	+	0.0225244i
$329$	31.3099	−	9.19343i	1.72617	−	0.506850i
$330$	−6.04688	−	3.88609i	−0.332870	−	0.213922i
$331$	5.42441	−	11.8778i	0.298153	−	0.652863i	−0.699966	−	0.714176i	$-0.746802\pi$
$331$	5.42441	−	11.8778i	0.298153	−	0.652863i	0.998119	+	0.0613130i	$0.0195288\pi$
$332$	4.79833	+	1.40892i	0.263343	+	0.0773244i
$333$	0.487012	+	0.562042i	0.0266881	+	0.0307997i
$334$	−14.1523	−	16.3327i	−0.774382	−	0.893684i
$335$	−0.329242	−	0.0966742i	−0.0179884	−	0.00528188i
$336$	−5.49552	+	12.0335i	−0.299805	+	0.656481i
$337$	−2.13386	−	1.37135i	−0.116239	−	0.0747021i	0.481230	−	0.876595i	$-0.340190\pi$
$337$	−2.13386	−	1.37135i	−0.116239	−	0.0747021i	−0.597468	+	0.801892i	$0.703827\pi$
$338$	−24.2995	+	7.13497i	−1.32172	+	0.388091i
$339$	−2.16140	+	15.0329i	−0.117391	+	0.816473i
$340$	1.65283	+	3.61920i	0.0896375	+	0.196279i
$341$	−2.85508	−	19.8575i	−0.154611	−	1.07534i
$342$	28.5230	−	18.3306i	1.54234	−	0.991205i
$343$	2.63343	−	3.03914i	0.142192	−	0.164098i
$344$	0.382418			0.0206186
$345$	0.996201	+	4.15516i	0.0536336	+	0.223706i
$346$	15.8537			0.852301
$347$	−15.6084	+	18.0131i	−0.837904	+	0.966993i	−0.999804	−	0.0198141i	$-0.993693\pi$
$347$	−15.6084	+	18.0131i	−0.837904	+	0.966993i	0.161899	+	0.986807i	$0.448238\pi$
$348$	−6.47650	+	4.16219i	−0.347177	+	0.223117i
$349$	−0.874471	−	6.08208i	−0.0468094	−	0.325566i	−0.999749	−	0.0224061i	$-0.992867\pi$
$349$	−0.874471	−	6.08208i	−0.0468094	−	0.325566i	0.952940	−	0.303160i	$-0.0980418\pi$
$350$	−2.95503	−	6.47061i	−0.157953	−	0.345869i
$351$	−0.311825	+	2.16879i	−0.0166440	+	0.115761i
$352$	−30.9240	+	9.08010i	−1.64825	+	0.483971i
$353$	0.162231	+	0.104259i	0.00863468	+	0.00554917i	0.544951	−	0.838468i	$-0.316548\pi$
$353$	0.162231	+	0.104259i	0.00863468	+	0.00554917i	−0.536316	+	0.844017i	$0.680185\pi$
$354$	−10.7298	+	23.4951i	−0.570285	+	1.24875i
$355$	9.06297	+	2.66113i	0.481013	+	0.141238i
$356$	11.7416	+	13.5506i	0.622305	+	0.718178i
$357$	−4.31931	−	4.98475i	−0.228602	−	0.263821i
$358$	−26.7546	−	7.85587i	−1.41403	−	0.415195i
$359$	−4.30929	+	9.43603i	−0.227436	+	0.498014i	−0.988604	−	0.150540i	$-0.951899\pi$
$359$	−4.30929	+	9.43603i	−0.227436	+	0.498014i	0.761168	+	0.648554i	$0.224626\pi$
$360$	−0.261874	−	0.168296i	−0.0138020	−	0.00886998i
$361$	−39.4505	+	11.5837i	−2.07634	+	0.609669i
$362$	1.68828	−	11.7422i	0.0887339	−	0.617157i
$363$	2.06022	+	4.51125i	0.108134	+	0.236779i
$364$	0.465341	+	3.23651i	0.0243905	+	0.169639i
$365$	2.17286	−	1.39641i	0.113733	−	0.0730915i
$366$	5.01118	−	5.78321i	0.261939	−	0.302293i
$367$	11.7540			0.613555			0.306777	−	0.951781i	$-0.400749\pi$
$367$	11.7540			0.613555			0.306777	+	0.951781i	$0.400749\pi$
$368$	17.6116	+	9.13946i	0.918067	+	0.476427i
$369$	−6.44394			−0.335458
$370$	0.437551	−	0.504961i	0.0227472	−	0.0262517i
$371$	13.5627	−	8.71619i	0.704138	−	0.452522i
$372$	−1.20547	−	8.38419i	−0.0625005	−	0.434700i
$373$	0.0581291	+	0.127285i	0.00300981	+	0.00659057i	0.911131	−	0.412117i	$-0.135211\pi$
$373$	0.0581291	+	0.127285i	0.00300981	+	0.00659057i	−0.908121	+	0.418708i	$0.862483\pi$
$374$	2.36838	−	16.4724i	0.122466	−	0.851769i
$375$	−0.854873	+	0.251013i	−0.0441455	+	0.0129623i
$376$	−1.07930	−	0.693623i	−0.0556606	−	0.0357709i
$377$	0.879076	−	1.92491i	0.0452747	−	0.0991379i
$378$	−31.6593	−	9.29600i	−1.62838	−	0.478135i
$379$	15.8275	+	18.2659i	0.813005	+	0.938258i	0.999019	−	0.0442893i	$-0.0141023\pi$
$379$	15.8275	+	18.2659i	0.813005	+	0.938258i	−0.186014	+	0.982547i	$0.559557\pi$
$380$	−9.79342	−	11.3022i	−0.502392	−	0.579791i
$381$	0.887989	+	0.260737i	0.0454931	+	0.0133580i
$382$	5.62379	−	12.3144i	0.287738	−	0.630059i
$383$	4.28464	+	2.75357i	0.218935	+	0.140701i	0.645511	−	0.763751i	$-0.276644\pi$
$383$	4.28464	+	2.75357i	0.218935	+	0.140701i	−0.426577	+	0.904451i	$0.640281\pi$
$384$	0.964362	−	0.283162i	0.0492124	−	0.0144501i
$385$	−2.07880	+	14.4584i	−0.105945	+	0.736867i
$386$	−12.3058	−	26.9459i	−0.626347	−	1.37151i
$387$	0.850955	+	5.91852i	0.0432565	+	0.300855i
$388$	24.5089	−	15.7509i	1.24425	−	0.799633i
$389$	1.28513	−	1.48312i	0.0651589	−	0.0751973i	−0.722234	−	0.691648i	$-0.756885\pi$
$389$	1.28513	−	1.48312i	0.0651589	−	0.0751973i	0.787393	+	0.616451i	$0.211430\pi$
$390$	0.834203			0.0422415
$391$	−7.79271	+	6.09439i	−0.394094	+	0.308207i
$392$	0.829587			0.0419004
$393$	1.26040	−	1.45458i	0.0635789	−	0.0733740i
$394$	20.2926	−	13.0412i	1.02233	−	0.657008i
$395$	2.45699	+	17.0887i	0.123624	+	0.859826i
$396$	−7.19495	−	15.7548i	−0.361560	−	0.791706i
$397$	−3.93466	+	27.3662i	−0.197475	+	1.37347i	0.614104	+	0.789225i	$0.289518\pi$
$397$	−3.93466	+	27.3662i	−0.197475	+	1.37347i	−0.811579	+	0.584243i	$0.801391\pi$
$398$	7.74680	−	2.27466i	0.388312	−	0.114019i
$399$	20.8560	+	13.4033i	1.04411	+	0.671006i
$400$	−1.71870	+	3.76342i	−0.0859349	+	0.188171i
$401$	−9.33822	−	2.74195i	−0.466328	−	0.136926i	0.0401232	−	0.999195i	$-0.487225\pi$
$401$	−9.33822	−	2.74195i	−0.466328	−	0.136926i	−0.506452	+	0.862268i	$0.669043\pi$
$402$	0.396838	+	0.457975i	0.0197925	+	0.0228417i
$403$	1.52470	+	1.75960i	0.0759507	+	0.0876518i
$404$	19.9685	+	5.86329i	0.993472	+	0.291710i
$405$	1.03264	−	2.26117i	0.0513123	−	0.112358i
$406$	26.8083	+	17.2287i	1.33048	+	0.855045i
$407$	−1.31645	+	0.386545i	−0.0652541	+	0.0191603i
$408$	−0.0369054	+	0.256683i	−0.00182709	+	0.0127077i
$409$	−6.30724	−	13.8109i	−0.311873	−	0.682906i	0.687177	−	0.726490i	$-0.258850\pi$
$409$	−6.30724	−	13.8109i	−0.311873	−	0.682906i	−0.999050	+	0.0435839i	$0.986122\pi$
$410$	0.823931	+	5.73057i	0.0406911	+	0.283013i
$411$	13.6918	−	8.79917i	0.675365	−	0.434031i
$412$	11.4957	−	13.2667i	0.566352	−	0.653605i
$413$	52.4892			2.58282
$414$	−6.91251	+	19.7999i	−0.339732	+	0.973111i
$415$	−2.59273			−0.127272
$416$	2.44946	−	2.82683i	0.120095	−	0.138597i
$417$	−1.59630	+	1.02588i	−0.0781711	+	0.0502375i
$418$	8.90204	+	61.9151i	0.435413	+	3.02836i
$419$	−4.62997	−	10.1382i	−0.226189	−	0.495285i	0.762179	−	0.647366i	$-0.224130\pi$
$419$	−4.62997	−	10.1382i	−0.226189	−	0.495285i	−0.988368	+	0.152082i	$0.951402\pi$
$420$	−0.877707	+	6.10458i	−0.0428277	+	0.297873i
$421$	−9.25746	+	2.71823i	−0.451181	+	0.132479i	−0.499425	−	0.866357i	$-0.666456\pi$
$421$	−9.25746	+	2.71823i	−0.451181	+	0.132479i	0.0482445	+	0.998836i	$0.484637\pi$
$422$	−28.1023	−	18.0602i	−1.36800	−	0.879159i
$423$	8.33327	−	18.2473i	0.405177	−	0.887215i
$424$	−0.608183	−	0.178579i	−0.0295360	−	0.00867255i
$425$	−1.35084	−	1.55896i	−0.0655256	−	0.0756206i
$426$	−10.9237	−	12.6066i	−0.529253	−	0.610791i
$427$	−14.9208	−	4.38113i	−0.722067	−	0.212018i
$428$	−3.70281	+	8.10803i	−0.178982	+	0.391916i
$429$	−1.44106	−	0.926112i	−0.0695750	−	0.0447131i
$430$	5.15451	−	1.51350i	0.248572	−	0.0729874i
$431$	3.17776	−	22.1018i	0.153067	−	1.06460i	−0.757973	−	0.652286i	$-0.773810\pi$
$431$	3.17776	−	22.1018i	0.153067	−	1.06460i	0.911040	−	0.412319i	$-0.135281\pi$
$432$	7.97221	+	17.4567i	0.383563	+	0.839887i
$433$	−5.34816	−	37.1973i	−0.257016	−	1.78759i	−0.553806	−	0.832646i	$-0.686825\pi$
$433$	−5.34816	−	37.1973i	−0.257016	−	1.78759i	0.296790	−	0.954943i	$-0.404084\pi$
$434$	−29.4958	+	18.9558i	−1.41585	+	0.909909i
$435$	2.61380	−	3.01648i	0.125322	−	0.144629i
$436$	−28.5250			−1.36610
$437$	21.6504	−	30.2312i	1.03568	−	1.44616i
$438$	−4.56137			−0.217951
$439$	0.0289701	−	0.0334333i	0.00138267	−	0.00159568i	−0.755058	−	0.655658i	$-0.772391\pi$
$439$	0.0289701	−	0.0334333i	0.00138267	−	0.00159568i	0.756440	+	0.654063i	$0.226937\pi$
$440$	0.483130	−	0.310489i	0.0230323	−	0.0148020i
$441$	1.84599	+	12.8392i	0.0879044	+	0.611389i
$442$	0.802326	+	1.75685i	0.0381627	+	0.0835647i
$443$	−1.21543	+	8.45349i	−0.0577467	+	0.401637i	0.940363	+	0.340174i	$0.110486\pi$
$443$	−1.21543	+	8.45349i	−0.0577467	+	0.401637i	−0.998109	+	0.0614636i	$0.980423\pi$
$444$	−0.555829	+	0.163206i	−0.0263785	+	0.00774542i
$445$	−7.82017	−	5.02572i	−0.370711	−	0.238242i
$446$	−20.3039	+	44.4594i	−0.961418	+	2.10521i
$447$	13.5138	+	3.96800i	0.639179	+	0.187680i
$448$	17.4399	+	20.1268i	0.823960	+	0.950901i
$449$	14.0485	+	16.2128i	0.662990	+	0.765132i	0.983263	−	0.182194i	$-0.0583199\pi$
$449$	14.0485	+	16.2128i	0.662990	+	0.765132i	−0.320272	+	0.947326i	$0.603774\pi$
$450$	−4.19580	−	1.23200i	−0.197792	−	0.0580769i
$451$	4.93862	−	10.8141i	0.232551	−	0.509215i
$452$	27.6594	+	17.7756i	1.30099	+	0.836094i
$453$	−13.2909	+	3.90255i	−0.624460	+	0.183358i
$454$	−6.46589	+	44.9712i	−0.303459	+	2.11061i
$455$	−0.704227	−	1.54204i	−0.0330147	−	0.0722920i
$456$	−0.138717	−	0.964795i	−0.00649600	−	0.0451807i
$457$	2.49837	−	1.60561i	0.116869	−	0.0751072i	−0.480900	−	0.876775i	$-0.659690\pi$
$457$	2.49837	−	1.60561i	0.116869	−	0.0751072i	0.597769	+	0.801668i	$0.296054\pi$
$458$	−6.28388	+	7.25198i	−0.293626	+	0.338863i
$459$	−9.56832			−0.446611
$460$	9.07836	+	1.77506i	0.423281	+	0.0827625i
$461$	−4.08019			−0.190033			−0.0950166	−	0.995476i	$-0.530290\pi$
$461$	−4.08019			−0.190033			−0.0950166	+	0.995476i	$0.530290\pi$
$462$	16.8928	−	19.4954i	0.785925	−	0.907006i
$463$	−9.50000	+	6.10528i	−0.441502	+	0.283736i	−0.742446	−	0.669905i	$-0.766335\pi$
$463$	−9.50000	+	6.10528i	−0.441502	+	0.283736i	0.300944	+	0.953642i	$0.402698\pi$
$464$	−2.63773	−	18.3458i	−0.122454	−	0.851684i
$465$	1.82430	+	3.99466i	0.0845999	+	0.185248i
$466$	0.539643	−	3.75330i	0.0249985	−	0.173868i
$467$	−24.5994	+	7.22304i	−1.13833	+	0.334242i	−0.795975	−	0.605330i	$-0.793041\pi$
$467$	−24.5994	+	7.22304i	−1.13833	+	0.334242i	−0.342351	+	0.939572i	$0.611223\pi$
$468$	1.69099	+	1.08673i	0.0781659	+	0.0502342i
$469$	0.511570	−	1.12018i	0.0236221	−	0.0517252i
$470$	−17.2927	−	5.07761i	−0.797655	−	0.234213i
$471$	−7.21757	−	8.32952i	−0.332568	−	0.383804i
$472$	−1.35143	−	1.55963i	−0.0622045	−	0.0717879i
$473$	−10.5845	−	3.10789i	−0.486675	−	0.142901i
$474$	12.6656	−	27.7338i	0.581749	−	1.27385i
$475$	6.52262	+	4.19183i	0.299278	+	0.192334i
$476$	−13.7005	+	4.02284i	−0.627963	+	0.184387i
$477$	1.41046	−	9.80997i	0.0645806	−	0.449168i
$478$	14.3634	+	31.4514i	0.656965	+	1.43855i
$479$	−0.556576	−	3.87107i	−0.0254306	−	0.176874i	0.973147	−	0.230183i	$-0.0739324\pi$
$479$	−0.556576	−	3.87107i	−0.0254306	−	0.176874i	−0.998578	+	0.0533087i	$0.983023\pi$
$480$	5.93509	−	3.81425i	0.270898	−	0.174096i
$481$	0.104275	−	0.120340i	0.00475452	−	0.00548701i
$482$	−50.3269			−2.29233
$483$	−15.2690	+	1.41657i	−0.694765	+	0.0644562i
$484$	10.7365			0.488022
$485$	−9.89137	+	11.4152i	−0.449144	+	0.518340i
$486$	−26.8968	+	17.2855i	−1.22006	+	0.784087i
$487$	2.34269	+	16.2938i	0.106158	+	0.738343i	0.971479	+	0.237125i	$0.0762052\pi$
$487$	2.34269	+	16.2938i	0.106158	+	0.738343i	−0.865321	+	0.501217i	$0.832886\pi$
$488$	0.253984	+	0.556147i	0.0114973	+	0.0251756i
$489$	1.35050	−	9.39293i	0.0610717	−	0.424763i
$490$	11.1818	−	3.28327i	0.505141	−	0.148323i
$491$	−7.54939	−	4.85170i	−0.340699	−	0.218954i	0.359091	−	0.933303i	$-0.383087\pi$
$491$	−7.54939	−	4.85170i	−0.340699	−	0.218954i	−0.699790	+	0.714349i	$0.746723\pi$
$492$	2.08517	−	4.56590i	0.0940069	−	0.205846i
$493$	8.86669	+	2.60349i	0.399335	+	0.117255i
$494$	−4.75397	−	5.48637i	−0.213891	−	0.246843i
$495$	5.88037	+	6.78630i	0.264303	+	0.305022i
$496$	19.5665	+	5.74525i	0.878562	+	0.257969i
$497$	−14.0819	+	30.8350i	−0.631658	+	1.38314i
$498$	3.85191	+	2.47547i	0.172608	+	0.110928i
$499$	−13.9790	+	4.10461i	−0.625787	+	0.183748i	−0.579225	−	0.815168i	$-0.696645\pi$
$499$	−13.9790	+	4.10461i	−0.625787	+	0.183748i	−0.0465620	+	0.998915i	$0.514826\pi$
$500$	−0.274499	+	1.90918i	−0.0122760	+	0.0853812i
$501$	−4.03544	−	8.83638i	−0.180290	−	0.394780i
$502$	0.754336	+	5.24652i	0.0336677	+	0.234164i
$503$	19.7231	−	12.6753i	0.879409	−	0.565162i	−0.0212084	−	0.999775i	$-0.506751\pi$
$503$	19.7231	−	12.6753i	0.879409	−	0.565162i	0.900617	+	0.434613i	$0.143115\pi$
$504$	0.731582	−	0.844291i	0.0325873	−	0.0376077i
$505$	−10.7898			−0.480141
$506$	−27.9299	−	26.7750i	−1.24164	−	1.19029i
$507$	−11.3837			−0.505569
$508$	1.31204	−	1.51417i	0.0582121	−	0.0671804i
$509$	29.4305	−	18.9138i	1.30448	−	0.838341i	0.310792	−	0.950478i	$-0.399406\pi$
$509$	29.4305	−	18.9138i	1.30448	−	0.838341i	0.993693	+	0.112137i	$0.0357695\pi$
$510$	0.518438	+	3.60582i	0.0229568	+	0.159668i
$511$	3.85066	+	8.43178i	0.170343	+	0.373000i
$512$	4.49622	−	31.2719i	0.198707	−	1.38204i
$513$	34.5077	−	10.1324i	1.52355	−	0.447356i
$514$	−18.8563	−	12.1182i	−0.831715	−	0.534511i
$515$	−3.78075	+	8.27869i	−0.166600	+	0.364803i
$516$	−4.46896	−	1.31221i	−0.196735	−	0.0577666i
$517$	24.2356	+	27.9694i	1.06588	+	1.23009i
$518$	1.57028	+	1.81220i	0.0689943	+	0.0796237i
$519$	6.83757	+	2.00769i	0.300136	+	0.0881279i
$520$	−0.0276877	+	0.0606276i	−0.00121419	+	0.00265870i
$521$	−11.8224	−	7.59781i	−0.517950	−	0.332866i	0.255411	−	0.966833i	$-0.417789\pi$
$521$	−11.8224	−	7.59781i	−0.517950	−	0.332866i	−0.773360	+	0.633967i	$0.781426\pi$
$522$	18.7965	−	5.51916i	0.822701	−	0.241567i
$523$	1.77117	−	12.3188i	0.0774479	−	0.538662i	−0.913750	−	0.406276i	$-0.866827\pi$
$523$	1.77117	−	12.3188i	0.0774479	−	0.538662i	0.991198	−	0.132386i	$-0.0422638\pi$
$524$	−1.73091	−	3.79015i	−0.0756149	−	0.165574i
$525$	−0.455050	−	3.16494i	−0.0198600	−	0.138129i
$526$	−48.5912	+	31.2277i	−2.11868	+	1.36159i
$527$	−6.65824	+	7.68402i	−0.290038	+	0.334721i
$528$	−15.0034			−0.652941
$529$	0.970742	+	22.9795i	0.0422062	+	0.999109i
$530$	−8.90430			−0.386778
$531$	21.1306	−	24.3860i	0.916989	−	1.05826i
$532$	45.1504	−	29.0164i	1.95752	−	1.25802i
$533$	0.196355	+	1.36568i	0.00850507	+	0.0591541i
$534$	6.81965	+	14.9329i	0.295115	+	0.646212i
$535$	0.657672	−	4.57421i	0.0284336	−	0.197760i
$536$	−0.0464557	+	0.0136406i	−0.00200658	+	0.000589185i
$537$	−10.5442	−	6.77634i	−0.455015	−	0.292420i
$538$	−2.26450	+	4.95857i	−0.0976297	+	0.213779i
$539$	−22.9611	−	6.74200i	−0.989007	−	0.290399i
$540$	5.85894	+	6.76157i	0.252128	+	0.290972i
$541$	19.4868	+	22.4889i	0.837802	+	0.966875i	0.999802	−	0.0199155i	$-0.00633972\pi$
$541$	19.4868	+	22.4889i	0.837802	+	0.966875i	−0.161999	+	0.986791i	$0.551794\pi$
$542$	49.1273	+	14.4251i	2.11020	+	0.619610i
$543$	2.21516	−	4.85052i	0.0950615	−	0.208156i
$544$	13.7412	+	8.83091i	0.589148	+	0.378622i
$545$	14.1898	−	4.16651i	0.607826	−	0.178474i
$546$	−0.426060	+	2.96331i	−0.0182337	+	0.126818i
$547$	−10.7728	−	23.5892i	−0.460614	−	1.00860i	−0.987347	−	0.158573i	$-0.949311\pi$
$547$	−10.7728	−	23.5892i	−0.460614	−	1.00860i	0.526734	−	0.850030i	$-0.323416\pi$
$548$	−5.01434	−	34.8755i	−0.214202	−	1.48981i
$549$	−8.04210	+	5.16834i	−0.343228	+	0.220579i
$550$	5.28315	−	6.09709i	0.225274	−	0.259981i
$551$	−34.7343			−1.47973
$552$	0.435220	+	0.417223i	0.0185242	+	0.0177582i
$553$	−61.9586			−2.63475
$554$	30.4487	−	35.1397i	1.29364	−	1.49294i
$555$	0.252660	−	0.162375i	0.0107248	−	0.00689242i
$556$	0.584613	+	4.06607i	0.0247931	+	0.172440i
$557$	−5.42786	−	11.8854i	−0.229986	−	0.503599i	0.759094	−	0.650981i	$-0.225642\pi$
$557$	−5.42786	−	11.8854i	−0.229986	−	0.503599i	−0.989080	+	0.147383i	$0.952915\pi$
$558$	−3.06745	+	21.3346i	−0.129855	+	0.903164i
$559$	1.22839	−	0.360689i	0.0519555	−	0.0152555i
$560$	−12.4909	−	8.02741i	−0.527836	−	0.339220i
$561$	3.10751	−	6.80449i	0.131199	−	0.287286i
$562$	22.9013	+	6.72443i	0.966033	+	0.283653i
$563$	0.853135	+	0.984570i	0.0359554	+	0.0414947i	0.773442	−	0.633867i	$-0.218533\pi$
$563$	0.853135	+	0.984570i	0.0359554	+	0.0414947i	−0.737487	+	0.675361i	$0.763988\pi$
$564$	10.2327	+	11.8092i	0.430875	+	0.497256i
$565$	−16.3556	−	4.80244i	−0.688086	−	0.202040i
$566$	−7.79333	+	17.0650i	−0.327578	+	0.717296i
$567$	7.50486	+	4.82308i	0.315174	+	0.202550i
$568$	1.27878	−	0.375482i	0.0536562	−	0.0157549i
$569$	2.72792	−	18.9731i	0.114360	−	0.795394i	−0.849232	−	0.528020i	$-0.822935\pi$
$569$	2.72792	−	18.9731i	0.114360	−	0.795394i	0.963593	−	0.267375i	$-0.0861561\pi$
$570$	−5.68811	−	12.4552i	−0.238249	−	0.521692i
$571$	3.62499	+	25.2124i	0.151701	+	1.05510i	0.913368	+	0.407136i	$0.133472\pi$
$571$	3.62499	+	25.2124i	0.151701	+	1.05510i	−0.761667	+	0.647969i	$0.775619\pi$
$572$	−3.11970	+	2.00491i	−0.130441	+	0.0838294i
$573$	3.98497	−	4.59890i	0.166474	−	0.192122i
$574$	−20.7773			−0.867229
$575$	−4.77532	+	0.443026i	−0.199145	+	0.0184755i
$576$	16.3715			0.682147
$577$	18.1867	−	20.9886i	0.757122	−	0.873765i	−0.238116	−	0.971237i	$-0.576530\pi$
$577$	18.1867	−	20.9886i	0.757122	−	0.873765i	0.995238	+	0.0974712i	$0.0310754\pi$
$578$	21.2517	−	13.6576i	0.883953	−	0.568082i
$579$	−1.89498	−	13.1799i	−0.0787528	−	0.547738i
$580$	−3.58951	−	7.85994i	−0.149046	−	0.326366i
$581$	1.32421	−	9.21009i	0.0549375	−	0.382099i
$582$	25.5941	−	7.51510i	1.06091	−	0.311511i
$583$	15.3819	+	9.88534i	0.637053	+	0.409409i
$584$	0.151395	−	0.331508i	0.00626475	−	0.0137179i
$585$	−0.999919	−	0.293603i	−0.0413416	−	0.0121390i
$586$	−11.4942	−	13.2651i	−0.474823	−	0.547975i
$587$	18.0146	+	20.7900i	0.743544	+	0.858096i	0.993926	−	0.110052i	$-0.0351016\pi$
$587$	18.0146	+	20.7900i	0.743544	+	0.858096i	−0.250382	+	0.968147i	$0.580556\pi$
$588$	−9.69461	−	2.84659i	−0.399799	−	0.117392i
$589$	15.8756	−	34.7628i	0.654145	−	1.43238i
$590$	−24.3881	−	15.6733i	−1.00404	−	0.645259i
$591$	10.4035	−	3.05475i	0.427944	−	0.125656i
$592$	0.198480	−	1.38046i	0.00815748	−	0.0567365i
$593$	−9.26005	−	20.2767i	−0.380264	−	0.832663i	−0.998896	−	0.0469816i	$-0.985040\pi$
$593$	−9.26005	−	20.2767i	−0.380264	−	0.832663i	0.618631	−	0.785681i	$-0.287687\pi$
$594$	−5.32567	−	37.0408i	−0.218515	−	1.51980i
$595$	6.22777	−	4.00234i	0.255314	−	0.164080i
$596$	19.9671	−	23.0432i	0.817883	−	0.943887i
$597$	3.62919			0.148533
$598$	4.40686	+	0.861656i	0.180210	+	0.0352357i
$599$	−4.40142			−0.179837			−0.0899186	−	0.995949i	$-0.528661\pi$
$599$	−4.40142			−0.179837			−0.0899186	+	0.995949i	$0.528661\pi$
$600$	−0.0823251	+	0.0950082i	−0.00336091	+	0.00387869i
$601$	27.8022	−	17.8674i	1.13408	−	0.728827i	0.167669	−	0.985843i	$-0.446376\pi$
$601$	27.8022	−	17.8674i	1.13408	−	0.728827i	0.966407	+	0.257017i	$0.0827395\pi$
$602$	2.74375	+	19.0832i	0.111827	+	0.777773i
$603$	−0.314483	−	0.688622i	−0.0128067	−	0.0280429i
$604$	−4.26769	+	29.6824i	−0.173650	+	1.20776i
$605$	−5.34089	+	1.56823i	−0.217138	+	0.0637575i
$606$	16.0299	+	10.3018i	0.651171	+	0.418482i
$607$	−16.8176	+	36.8254i	−0.682605	+	1.49470i	0.177253	+	0.984165i	$0.443279\pi$
$607$	−16.8176	+	36.8254i	−0.682605	+	1.49470i	−0.859859	+	0.510532i	$0.829448\pi$
$608$	−58.9084	−	17.2971i	−2.38905	−	0.701488i
$609$	9.38039	+	10.8255i	0.380113	+	0.438673i
$610$	5.62445	+	6.49096i	0.227727	+	0.262811i
$611$	−4.12111	−	1.21007i	−0.166722	−	0.0489541i
$612$	−3.64645	+	7.98462i	−0.147399	+	0.322759i
$613$	−13.6464	−	8.77003i	−0.551174	−	0.354218i	0.235221	−	0.971942i	$-0.424419\pi$
$613$	−13.6464	−	8.77003i	−0.551174	−	0.354218i	−0.786395	+	0.617724i	$0.788055\pi$
$614$	50.3213	−	14.7757i	2.03080	−	0.596297i
$615$	−0.370357	+	2.57589i	−0.0149342	+	0.103870i
$616$	0.856186	+	1.87479i	0.0344967	+	0.0755373i
$617$	−0.536310	−	3.73011i	−0.0215910	−	0.150169i	0.976174	−	0.216989i	$-0.0696236\pi$
$617$	−0.536310	−	3.73011i	−0.0215910	−	0.150169i	−0.997765	+	0.0668204i	$0.978715\pi$
$618$	13.5211	−	8.68951i	0.543900	−	0.349543i
$619$	2.88793	−	3.33285i	0.116076	−	0.133958i	−0.694738	−	0.719263i	$-0.744480\pi$
$619$	2.88793	−	3.33285i	0.116076	−	0.133958i	0.810814	+	0.585305i	$0.199025\pi$
$620$	9.50702			0.381811
$621$	−12.9524	+	18.0859i	−0.519762	+	0.725763i
$622$	38.4606			1.54213
$623$	21.8468	−	25.2125i	0.875272	−	1.01012i
$624$	1.46482	−	0.941385i	0.0586399	−	0.0376856i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	12.9429	+	28.3409i	0.517301	+	1.13273i
$627$	−4.00146	+	27.8308i	−0.159803	+	1.11145i
$628$	−22.8936	+	6.72218i	−0.913555	+	0.268244i
$629$	0.584969	+	0.375937i	0.0233242	+	0.0149896i
$630$	6.51934	−	14.2754i	0.259737	−	0.568744i
$631$	21.3504	+	6.26904i	0.849946	+	0.249567i	0.677564	−	0.735464i	$-0.263036\pi$
$631$	21.3504	+	6.26904i	0.849946	+	0.249567i	0.172382	+	0.985030i	$0.444854\pi$
$632$	1.59524	+	1.84100i	0.0634551	+	0.0732310i
$633$	−9.83315	−	11.3481i	−0.390833	−	0.451045i
$634$	−46.2827	−	13.5898i	−1.83812	−	0.539721i
$635$	−0.431507	+	0.944870i	−0.0171239	+	0.0374960i
$636$	6.49451	+	4.17377i	0.257524	+	0.165501i
$637$	2.66478	−	0.782450i	0.105582	−	0.0310018i
$638$	−5.14349	+	35.7737i	−0.203633	+	1.41630i
$639$	8.65671	+	18.9556i	0.342454	+	0.749870i
$640$	0.160542	+	1.11659i	0.00634598	+	0.0441372i
$641$	−9.16472	+	5.88981i	−0.361985	+	0.232634i	−0.708972	−	0.705236i	$-0.750841\pi$
$641$	−9.16472	+	5.88981i	−0.361985	+	0.232634i	0.346988	+	0.937870i	$0.387205\pi$
$642$	−5.34440	+	6.16776i	−0.210927	+	0.243422i
$643$	−16.3283			−0.643924			−0.321962	−	0.946753i	$-0.604342\pi$
$643$	−16.3283			−0.643924			−0.321962	+	0.946753i	$0.604342\pi$
$644$	−10.9422	+	31.3422i	−0.431181	+	1.23506i
$645$	2.41476			0.0950812
$646$	20.7602	−	23.9585i	0.816798	−	0.942636i
$647$	−15.5265	+	9.97830i	−0.610411	+	0.392288i	−0.809011	−	0.587793i	$-0.799997\pi$
$647$	−15.5265	+	9.97830i	−0.610411	+	0.392288i	0.198600	+	0.980081i	$0.436361\pi$
$648$	−0.0499160	−	0.347174i	−0.00196089	−	0.0136383i
$649$	24.7296	+	54.1502i	0.970720	+	2.12558i
$650$	−0.133248	+	0.926764i	−0.00522644	+	0.0363507i
$651$	−15.1218	+	4.44017i	−0.592672	+	0.174024i
$652$	−17.2823	−	11.1067i	−0.676827	−	0.434970i
$653$	−12.4981	+	27.3670i	−0.489089	+	1.07095i	0.490775	+	0.871286i	$0.336714\pi$
$653$	−12.4981	+	27.3670i	−0.489089	+	1.07095i	−0.979864	+	0.199668i	$0.936013\pi$
$654$	−25.0593	−	7.35806i	−0.979895	−	0.287723i
$655$	1.41465	+	1.63260i	0.0552750	+	0.0637908i
$656$	7.91364	+	9.13283i	0.308976	+	0.356577i
$657$	5.46749	+	1.60540i	0.213307	+	0.0626326i
$658$	26.8691	−	58.8352i	1.04747	−	2.29363i
$659$	39.8554	+	25.6135i	1.55255	+	0.997762i	0.984625	+	0.174679i	$0.0558889\pi$
$659$	39.8554	+	25.6135i	1.55255	+	0.997762i	0.567922	+	0.823082i	$0.307748\pi$
$660$	−6.71129	+	1.97061i	−0.261236	+	0.0767059i
$661$	2.32397	−	16.1636i	0.0903921	−	0.628691i	−0.893385	−	0.449293i	$-0.851676\pi$
$661$	2.32397	−	16.1636i	0.0903921	−	0.628691i	0.983777	−	0.179398i	$-0.0574149\pi$
$662$	−10.7519	−	23.5433i	−0.417883	−	0.915036i
$663$	0.123551	+	0.859319i	0.00479834	+	0.0333732i
$664$	−0.307757	+	0.197784i	−0.0119433	+	0.00767550i
$665$	−18.2219	+	21.0292i	−0.706614	+	0.815476i
$666$	1.47408			0.0571195
$667$	16.9237	−	13.2354i	0.655288	−	0.512477i
$668$	−21.0300			−0.813675
$669$	−14.3872	+	16.6037i	−0.556241	+	0.641936i
$670$	−0.572178	+	0.367717i	−0.0221052	+	0.0142061i
$671$	−2.50995	−	17.4571i	−0.0968954	−	0.673922i
$672$	10.5180	+	23.0311i	0.405739	+	0.888444i
$673$	4.64548	−	32.3100i	0.179070	−	1.24546i	−0.679850	−	0.733351i	$-0.737955\pi$
$673$	4.64548	−	32.3100i	0.179070	−	1.24546i	0.858921	−	0.512109i	$-0.171136\pi$
$674$	−4.82405	+	1.41647i	−0.185815	+	0.0545603i
$675$	−3.90217	−	2.50777i	−0.150195	−	0.0965242i
$676$	−10.2376	+	22.4172i	−0.393753	+	0.862198i
$677$	−31.5479	−	9.26331i	−1.21249	−	0.356018i	−0.387871	−	0.921714i	$-0.626789\pi$
$677$	−31.5479	−	9.26331i	−1.21249	−	0.356018i	−0.824614	+	0.565696i	$0.808608\pi$
$678$	19.7135	+	22.7506i	0.757094	+	0.873733i
$679$	−35.4981	−	40.9670i	−1.36229	−	1.57217i
$680$	−0.279268	−	0.0820006i	−0.0107095	−	0.00314458i
$681$	−8.48378	+	18.5769i	−0.325099	+	0.711868i
$682$	−33.4523	−	21.4985i	−1.28095	−	0.823219i
$683$	6.90998	−	2.02895i	0.264403	−	0.0776358i	−0.146844	−	0.989160i	$-0.546912\pi$
$683$	6.90998	−	2.02895i	0.264403	−	0.0776358i	0.411247	+	0.911524i	$0.365093\pi$
$684$	4.69545	−	32.6576i	0.179535	−	1.24869i
$685$	7.58848	+	16.6165i	0.289941	+	0.634882i
$686$	−1.13437	−	7.88969i	−0.0433103	−	0.301230i
$687$	−3.62857	+	2.33194i	−0.138438	+	0.0889690i
$688$	7.34313	−	8.47442i	0.279954	−	0.323084i
$689$	−2.12202			−0.0808427
$690$	7.51747	+	3.90116i	0.286185	+	0.148515i
$691$	−16.5959			−0.631337			−0.315668	−	0.948870i	$-0.602229\pi$
$691$	−16.5959			−0.631337			−0.315668	+	0.948870i	$0.602229\pi$
$692$	10.1028	−	11.6592i	0.384049	−	0.443216i
$693$	−27.1101	+	17.4226i	−1.02983	+	0.661830i
$694$	6.72343	+	46.7625i	0.255218	+	1.77508i
$695$	−0.884728	−	1.93728i	−0.0335597	−	0.0734854i
$696$	0.0801487	−	0.557447i	0.00303803	−	0.0211300i
$697$	−5.78107	+	1.69748i	−0.218974	+	0.0642965i
$698$	−10.2460	−	6.58469i	−0.387816	−	0.249234i
$699$	0.708056	−	1.55043i	0.0267812	−	0.0586425i
$700$	−6.64173	−	1.95019i	−0.251034	−	0.0737102i
$701$	23.0026	+	26.5464i	0.868796	+	1.00264i	0.999936	+	0.0112802i	$0.00359067\pi$
$701$	23.0026	+	26.5464i	0.868796	+	1.00264i	−0.131140	+	0.991364i	$0.541864\pi$
$702$	2.84407	+	3.28223i	0.107343	+	0.123880i
$703$	−2.50776	−	0.736345i	−0.0945820	−	0.0277718i
$704$	−12.5471	+	27.4743i	−0.472886	+	1.03548i
$705$	−6.81519	−	4.37986i	−0.256675	−	0.164955i
$706$	0.366758	−	0.107690i	0.0138031	−	0.00405296i
$707$	5.51078	−	38.3283i	0.207254	−	1.44149i
$708$	10.4413	+	22.8632i	0.392407	+	0.859251i
$709$	2.99316	+	20.8179i	0.112411	+	0.781832i	0.965563	+	0.260170i	$0.0837787\pi$
$709$	2.99316	+	20.8179i	0.112411	+	0.781832i	−0.853152	+	0.521662i	$0.825312\pi$
$710$	15.7502	−	10.1221i	0.591095	−	0.379874i
$711$	−24.9427	+	28.7854i	−0.935424	+	1.07954i
$712$	−1.31163			−0.0491555
$713$	5.51114	+	22.9870i	0.206394	+	0.860869i
$714$	−13.0736			−0.489268
$715$	1.25905	−	1.45302i	0.0470859	−	0.0543400i
$716$	−22.8267	+	14.6698i	−0.853075	+	0.548238i
$717$	2.21184	+	15.3837i	0.0826026	+	0.574514i
$718$	8.54154	+	18.7034i	0.318768	+	0.698004i
$719$	2.68004	−	18.6401i	0.0999485	−	0.695157i	−0.876814	−	0.480830i	$-0.840335\pi$
$719$	2.68004	−	18.6401i	0.0999485	−	0.695157i	0.976762	−	0.214326i	$-0.0687556\pi$
$720$	−8.75792	+	2.57156i	−0.326388	+	0.0958363i
$721$	−27.4772	−	17.6585i	−1.02330	−	0.657637i
$722$	−33.8551	+	74.1323i	−1.25996	+	2.75892i
$723$	−21.7056	−	6.37332i	−0.807238	−	0.237027i
$724$	−7.55966	−	8.72431i	−0.280952	−	0.324236i
$725$	2.93368	+	3.38564i	0.108954	+	0.125740i
$726$	9.43201	+	2.76949i	0.350055	+	0.102785i
$727$	11.1758	−	24.4716i	0.414487	−	0.907600i	−0.581107	−	0.813827i	$-0.697380\pi$
$727$	11.1758	−	24.4716i	0.414487	−	0.907600i	0.995594	−	0.0937724i	$-0.0298926\pi$
$728$	−0.201224	−	0.129319i	−0.00745787	−	0.00479288i
$729$	−6.63405	+	1.94793i	−0.245705	+	0.0721456i
$730$	0.728594	−	5.06748i	0.0269665	−	0.187556i
$731$	2.32249	+	5.08554i	0.0859003	+	0.188095i
$732$	−1.05974	−	7.37068i	−0.0391693	−	0.272428i
$733$	28.4046	−	18.2546i	1.04915	−	0.674247i	0.101916	−	0.994793i	$-0.467503\pi$
$733$	28.4046	−	18.2546i	1.04915	−	0.674247i	0.947233	+	0.320546i	$0.103866\pi$
$734$	15.2569	−	17.6074i	0.563142	−	0.649901i
$735$	5.23839			0.193221
$736$	35.2931	−	14.0192i	1.30092	−	0.516754i
$737$	1.39665			0.0514462
$738$	−8.36434	+	9.65296i	−0.307895	+	0.355330i
$739$	−30.4979	+	19.5998i	−1.12188	+	0.720991i	−0.963851	−	0.266443i	$-0.914151\pi$
$739$	−30.4979	+	19.5998i	−1.12188	+	0.720991i	−0.158033	+	0.987434i	$0.550515\pi$
$740$	−0.0925316	−	0.643571i	−0.00340153	−	0.0236581i
$741$	−1.35556	−	2.96826i	−0.0497977	−	0.109042i
$742$	4.54777	−	31.6305i	0.166954	−	1.16119i
$743$	3.86527	−	1.13495i	0.141803	−	0.0416371i	−0.210061	−	0.977688i	$-0.567366\pi$
$743$	3.86527	−	1.13495i	0.141803	−	0.0416371i	0.351864	+	0.936051i	$0.385548\pi$
$744$	0.521272	+	0.335001i	0.0191108	+	0.0122817i
$745$	−6.56685	+	14.3794i	−0.240591	+	0.526820i
$746$	0.266124	+	0.0781411i	0.00974350	+	0.00286095i
$747$	−3.74584	−	4.32293i	−0.137053	−	0.158168i
$748$	−10.6050	−	12.2388i	−0.387756	−	0.447494i
$749$	15.9129	+	4.67246i	0.581446	+	0.170728i
$750$	−0.733623	+	1.60641i	−0.0267881	+	0.0586578i
$751$	26.6229	+	17.1095i	0.971482	+	0.624334i	0.927153	−	0.374683i	$-0.122249\pi$
$751$	26.6229	+	17.1095i	0.971482	+	0.624334i	0.0443295	+	0.999017i	$0.485885\pi$
$752$	−36.0953	+	10.5985i	−1.31626	+	0.386489i
$753$	−0.339074	+	2.35831i	−0.0123565	+	0.0859415i
$754$	−1.74244	−	3.81541i	−0.0634559	−	0.138949i
$755$	−2.21260	−	15.3889i	−0.0805246	−	0.560061i
$756$	−27.0113	+	17.3591i	−0.982392	+	0.631345i
$757$	−7.83752	+	9.04498i	−0.284859	+	0.328745i	−0.880087	−	0.474812i	$-0.842516\pi$
$757$	−7.83752	+	9.04498i	−0.284859	+	0.328745i	0.595228	+	0.803557i	$0.297062\pi$
$758$	47.9065			1.74004
$759$	−8.65520	−	15.0848i	−0.314164	−	0.547545i
$760$	1.09400			0.0396837
$761$	11.6170	−	13.4067i	0.421116	−	0.485994i	−0.505061	−	0.863084i	$-0.668530\pi$
$761$	11.6170	−	13.4067i	0.421116	−	0.485994i	0.926177	+	0.377090i	$0.123075\pi$
$762$	1.54320	−	0.991758i	0.0559044	−	0.0359276i
$763$	7.55327	+	52.5342i	0.273447	+	1.90186i
$764$	−5.47254	−	11.9832i	−0.197989	−	0.433536i
$765$	0.647662	−	4.50459i	0.0234163	−	0.162864i
$766$	9.68634	−	2.84416i	0.349982	−	0.102764i
$767$	−5.81204	−	3.73517i	−0.209861	−	0.134869i
$768$	6.32070	−	13.8404i	0.228079	−	0.499423i
$769$	11.0894	+	3.25615i	0.399895	+	0.117420i	0.475495	−	0.879718i	$-0.342269\pi$
$769$	11.0894	+	3.25615i	0.399895	+	0.117420i	−0.0756000	+	0.997138i	$0.524087\pi$
$770$	18.9602	+	21.8812i	0.683277	+	0.788544i
$771$	−6.59792	−	7.61441i	−0.237618	−	0.274226i
$772$	−27.6584	−	8.12125i	−0.995449	−	0.292290i
$773$	−1.25614	+	2.75056i	−0.0451801	+	0.0989307i	−0.930876	−	0.365335i	$-0.880954\pi$
$773$	−1.25614	+	2.75056i	−0.0451801	+	0.0989307i	0.885696	+	0.464266i	$0.153682\pi$
$774$	9.97043	+	6.40761i	0.358380	+	0.230317i
$775$	−4.72929	+	1.38864i	−0.169881	+	0.0498816i
$776$	−0.303306	+	2.10954i	−0.0108880	+	0.0757280i
$777$	0.447755	+	0.980446i	0.0160631	+	0.0351733i
$778$	−0.553580	−	3.85023i	−0.0198468	−	0.138038i
$779$	19.0516	−	12.2437i	0.682595	−	0.438677i
$780$	0.531595	−	0.613493i	0.0190341	−	0.0219666i
$781$	−38.4452			−1.37568
$782$	−0.985721	+	19.5840i	−0.0352493	+	0.700323i
$783$	20.7799			0.742611
$784$	15.9296	−	18.3837i	0.568914	−	0.656562i
$785$	10.4066	−	6.68792i	0.371428	−	0.238702i
$786$	−0.542927	−	3.77614i	−0.0193656	−	0.134690i
$787$	−10.7548	−	23.5498i	−0.383368	−	0.839460i	−0.998689	−	0.0511831i	$-0.983701\pi$
$787$	−10.7548	−	23.5498i	−0.383368	−	0.839460i	0.615321	−	0.788277i	$-0.289026\pi$
$788$	3.34057	−	23.2341i	0.119003	−	0.827682i
$789$	−24.9116	+	7.31471i	−0.886877	+	0.260411i
$790$	28.7879	+	18.5009i	1.02423	+	0.658231i
$791$	25.4130	−	55.6467i	0.903583	−	1.97857i
$792$	1.21568	+	0.356957i	0.0431975	+	0.0126839i
$793$	1.34039	+	1.54689i	0.0475986	+	0.0549317i
$794$	35.8870	+	41.4158i	1.27358	+	1.46979i
$795$	−3.84035	−	1.12763i	−0.136203	−	0.0399928i
$796$	3.26379	−	7.14670i	0.115682	−	0.253308i
$797$	4.68326	+	3.00975i	0.165889	+	0.106611i	0.620951	−	0.783849i	$-0.286746\pi$
$797$	4.68326	+	3.00975i	0.165889	+	0.106611i	−0.455062	+	0.890460i	$0.650383\pi$
$798$	47.1494	−	13.8443i	1.66907	−	0.490084i
$799$	2.66930	−	18.5654i	0.0944332	−	0.656797i
$800$	3.28944	+	7.20288i	0.116299	+	0.254660i
$801$	−2.91864	−	20.2996i	−0.103125	−	0.717251i
$802$	−16.2286	+	10.4295i	−0.573050	+	0.368277i
$803$	−6.88442	+	7.94504i	−0.242946	+	0.280374i
$804$	0.589690			0.0207968
$805$	0.865198	−	17.1895i	0.0304942	−	0.605851i
$806$	4.61494			0.162554
$807$	−1.60461	+	1.85182i	−0.0564849	+	0.0651870i
$808$	−1.28075	+	0.823088i	−0.0450566	+	0.0289561i
$809$	4.07960	+	28.3743i	0.143431	+	0.997586i	0.926673	+	0.375869i	$0.122656\pi$
$809$	4.07960	+	28.3743i	0.143431	+	0.997586i	−0.783242	+	0.621717i	$0.786435\pi$
$810$	−2.04682	−	4.48191i	−0.0719179	−	0.157478i
$811$	−1.78928	+	12.4447i	−0.0628301	+	0.436993i	0.933989	+	0.357301i	$0.116303\pi$
$811$	−1.78928	+	12.4447i	−0.0628301	+	0.436993i	−0.996820	+	0.0796924i	$0.974606\pi$
$812$	29.7539	−	8.73654i	1.04416	−	0.306593i
$813$	19.3614	+	12.4428i	0.679034	+	0.436389i
$814$	−1.12973	+	2.47377i	−0.0395971	+	0.0867056i
$815$	10.2194	+	3.00069i	0.357970	+	0.105110i
$816$	4.97946	+	5.74661i	0.174316	+	0.201172i
$817$	−13.7613	−	15.8814i	−0.481446	−	0.555618i
$818$	−28.8755	−	8.47861i	−1.00961	−	0.296448i
$819$	1.55365	−	3.40203i	0.0542891	−	0.118876i
$820$	4.73944	+	3.04586i	0.165509	+	0.106366i
$821$	45.2182	−	13.2773i	1.57813	−	0.463380i	0.628773	−	0.777589i	$-0.283557\pi$
$821$	45.2182	−	13.2773i	1.57813	−	0.463380i	0.949354	+	0.314209i	$0.101739\pi$
$822$	4.59107	−	31.9316i	0.160132	−	1.11374i
$823$	−16.4884	−	36.1046i	−0.574749	−	1.25853i	−0.944230	−	0.329287i	$-0.893192\pi$
$823$	−16.4884	−	36.1046i	−0.574749	−	1.25853i	0.369480	−	0.929239i	$-0.379536\pi$
$824$	0.182755	+	1.27109i	0.00636658	+	0.0442805i
$825$	3.05071	−	1.96057i	0.106212	−	0.0682583i
$826$	68.1317	−	78.6282i	2.37061	−	2.73583i
$827$	−1.92063			−0.0667867			−0.0333934	−	0.999442i	$-0.510631\pi$
$827$	−1.92063			−0.0667867			−0.0333934	+	0.999442i	$0.510631\pi$
$828$	10.1563	+	17.7011i	0.352956	+	0.615154i
$829$	−8.49181			−0.294933			−0.147466	−	0.989067i	$-0.547112\pi$
$829$	−8.49181			−0.294933			−0.147466	+	0.989067i	$0.547112\pi$
$830$	−3.36541	+	3.88389i	−0.116815	+	0.134812i
$831$	17.5823	−	11.2995i	0.609924	−	0.391974i
$832$	−0.498860	−	3.46965i	−0.0172949	−	0.120288i
$833$	5.03822	+	11.0322i	0.174564	+	0.382241i
$834$	−0.535265	+	3.72285i	−0.0185347	+	0.128912i
$835$	10.4614	−	3.07175i	0.362032	−	0.106302i
$836$	51.2066	+	32.9085i	1.77102	+	1.13816i
$837$	−9.49764	+	20.7969i	−0.328287	+	0.718847i
$838$	−21.1967	−	6.22392i	−0.732229	−	0.215002i
$839$	−17.0467	−	19.6730i	−0.588518	−	0.679186i	0.380896	−	0.924618i	$-0.375616\pi$
$839$	−17.0467	−	19.6730i	−0.588518	−	0.679186i	−0.969414	+	0.245432i	$0.921070\pi$
$840$	−0.295448	−	0.340965i	−0.0101939	−	0.0117644i
$841$	8.56921	+	2.51615i	0.295490	+	0.0867637i
$842$	−7.94443	+	17.3959i	−0.273783	+	0.599502i
$843$	9.02556	+	5.80038i	0.310857	+	0.199776i
$844$	−31.1900	+	9.15822i	−1.07361	+	0.315239i
$845$	1.81834	−	12.6468i	0.0625527	−	0.435064i
$846$	−16.5176	−	36.1684i	−0.567886	−	1.24350i
$847$	−2.84296	−	19.7732i	−0.0976853	−	0.679416i
$848$	−15.6356	+	10.0484i	−0.536927	+	0.345062i
$849$	−5.52229	+	6.37306i	−0.189524	+	0.218723i
$850$	−4.08872			−0.140242
$851$	1.50245	−	0.596804i	0.0515032	−	0.0204582i
$852$	−16.2323			−0.556108
$853$	−22.9266	+	26.4587i	−0.784991	+	0.905928i	−0.997459	−	0.0712401i	$-0.977304\pi$
$853$	−22.9266	+	26.4587i	−0.784991	+	0.905928i	0.212468	+	0.977168i	$0.431850\pi$
$854$	−25.9303	+	16.6644i	−0.887316	+	0.570243i
$855$	2.43437	+	16.9314i	0.0832538	+	0.579043i
$856$	−0.270873	−	0.593128i	−0.00925823	−	0.0202727i
$857$	−3.30842	+	23.0106i	−0.113013	+	0.786025i	0.851947	+	0.523629i	$0.175422\pi$
$857$	−3.30842	+	23.0106i	−0.113013	+	0.786025i	−0.964960	+	0.262397i	$0.915487\pi$
$858$	−3.25782	+	0.956583i	−0.111220	+	0.0326572i
$859$	15.2004	+	9.76872i	0.518632	+	0.333304i	0.773630	−	0.633637i	$-0.218439\pi$
$859$	15.2004	+	9.76872i	0.518632	+	0.333304i	−0.254999	+	0.966941i	$0.582075\pi$
$860$	2.17164	−	4.75522i	0.0740522	−	0.162152i
$861$	−8.96109	−	2.63121i	−0.305393	−	0.0896715i
$862$	−28.9834	−	33.4487i	−0.987180	−	1.13927i
$863$	−3.79128	−	4.37537i	−0.129057	−	0.148939i	0.687543	−	0.726143i	$-0.258689\pi$
$863$	−3.79128	−	4.37537i	−0.129057	−	0.148939i	−0.816600	+	0.577204i	$0.804144\pi$
$864$	35.2421	+	10.3480i	1.19896	+	0.352046i
$865$	−3.32263	+	7.27555i	−0.112973	+	0.247376i
$866$	−62.6632	−	40.2712i	−2.12938	−	1.36847i
$867$	10.8952	−	3.19913i	0.370022	−	0.108648i
$868$	−4.85561	+	33.7715i	−0.164810	+	1.14628i
$869$	−29.1909	−	63.9193i	−0.990235	−	2.16831i
$870$	−1.12591	−	7.83088i	−0.0381719	−	0.265492i
$871$	−0.136358	+	0.0876322i	−0.00462033	+	0.00296930i
$872$	1.36650	−	1.57702i	0.0462754	−	0.0534046i
$873$	−33.3234			−1.12783
$874$	−17.1835	−	71.6727i	−0.581242	−	2.42436i
$875$	3.58880			0.121324
$876$	−2.90672	+	3.35454i	−0.0982091	+	0.113339i
$877$	3.39556	−	2.18219i	0.114660	−	0.0736875i	−0.482054	−	0.876142i	$-0.660109\pi$
$877$	3.39556	−	2.18219i	0.114660	−	0.0736875i	0.596714	+	0.802454i	$0.296473\pi$
$878$	−0.0124791	−	0.0867938i	−0.000421148	−	0.00292915i
$879$	−3.27750	−	7.17672i	−0.110547	−	0.242065i
$880$	2.39652	−	16.6682i	0.0807867	−	0.561884i
$881$	4.32504	−	1.26995i	0.145714	−	0.0427856i	−0.208062	−	0.978116i	$-0.566716\pi$
$881$	4.32504	−	1.26995i	0.145714	−	0.0427856i	0.353776	+	0.935330i	$0.384897\pi$
$882$	21.6291	+	13.9002i	0.728288	+	0.468042i
$883$	12.2263	−	26.7719i	0.411449	−	0.900947i	−0.584531	−	0.811371i	$-0.698722\pi$
$883$	12.2263	−	26.7719i	0.411449	−	0.900947i	0.995980	−	0.0895756i	$-0.0285511\pi$
$884$	1.80331	+	0.529499i	0.0606518	+	0.0178090i
$885$	−8.53354	−	9.84824i	−0.286852	−	0.331045i
$886$	11.0856	+	12.7935i	0.372428	+	0.429804i
$887$	−17.1154	−	5.02554i	−0.574679	−	0.168741i	−0.0185369	−	0.999828i	$-0.505901\pi$
$887$	−17.1154	−	5.02554i	−0.574679	−	0.168741i	−0.556142	+	0.831087i	$0.687719\pi$
$888$	0.0176041	−	0.0385477i	0.000590756	−	0.00129358i
$889$	−3.13604	−	2.01541i	−0.105180	−	0.0675948i
$890$	−17.6792	+	5.19107i	−0.592607	+	0.174005i
$891$	−1.43989	+	10.0147i	−0.0482382	+	0.335504i
$892$	19.7578	+	43.2636i	0.661542	+	1.44857i
$893$	10.0331	+	69.7820i	0.335746	+	2.33516i
$894$	23.4851	−	15.0930i	0.785459	−	0.504784i
$895$	9.21245	−	10.6317i	0.307938	−	0.355380i
$896$	−4.04844			−0.135249
$897$	1.79152	+	0.929703i	0.0598172	+	0.0310419i
$898$	42.5219			1.41897
$899$	14.4599	−	16.6877i	0.482266	−	0.556564i
$900$	−3.57980	+	2.30060i	−0.119327	+	0.0766867i
$901$	−1.31879	−	9.17239i	−0.0439353	−	0.305576i
$902$	−9.78896	−	21.4348i	−0.325937	−	0.713702i
$903$	−1.23331	+	8.57789i	−0.0410421	+	0.285454i
$904$	−2.30776	+	0.677619i	−0.0767549	+	0.0225373i
$905$	5.03489	+	3.23572i	0.167365	+	0.107559i
$906$	−11.4058	+	24.9752i	−0.378931	+	0.829744i
$907$	28.8439	+	8.46934i	0.957746	+	0.281220i	0.723009	−	0.690839i	$-0.242759\pi$
$907$	28.8439	+	8.46934i	0.957746	+	0.281220i	0.234738	+	0.972059i	$0.424577\pi$
$908$	28.9525	+	33.4130i	0.960824	+	1.10885i
$909$	−15.5885	−	17.9901i	−0.517039	−	0.596694i
$910$	−3.22406	−	0.946669i	−0.106876	−	0.0313818i
$911$	−15.6728	+	34.3187i	−0.519263	+	1.13703i	0.450454	+	0.892799i	$0.351262\pi$
$911$	−15.6728	+	34.3187i	−0.519263	+	1.13703i	−0.969718	+	0.244229i	$0.921465\pi$
$912$	−24.0436	−	15.4519i	−0.796163	−	0.511663i
$913$	10.1254	−	2.97309i	0.335103	−	0.0983951i
$914$	0.837744	−	5.82664i	0.0277101	−	0.192728i
$915$	1.60377	+	3.51177i	0.0530191	+	0.116096i
$916$	1.32889	+	9.24263i	0.0439077	+	0.305385i
$917$	−6.52194	+	4.19139i	−0.215373	+	0.138412i
$918$	−12.4198	+	14.3332i	−0.409915	+	0.473068i
$919$	1.66310			0.0548606			0.0274303	−	0.999624i	$-0.491268\pi$
$919$	1.66310			0.0548606			0.0274303	+	0.999624i	$0.491268\pi$
$920$	−0.533035	+	0.416867i	−0.0175736	+	0.0137437i
$921$	23.5743			0.776800
$922$	−5.29614	+	6.11207i	−0.174419	+	0.201290i
$923$	3.75351	−	2.41223i	0.123548	−	0.0793996i
$924$	−3.57242	−	24.8468i	−0.117524	−	0.817398i
$925$	0.140033	+	0.306630i	0.00460427	+	0.0100819i
$926$	−3.18550	+	22.1556i	−0.104682	+	0.728080i
$927$	−19.2655	+	5.65685i	−0.632761	+	0.185795i
$928$	−29.8422	−	19.1784i	−0.979617	−	0.629562i
$929$	18.3388	−	40.1565i	0.601678	−	1.31749i	−0.326445	−	0.945216i	$-0.605851\pi$
$929$	18.3388	−	40.1565i	0.601678	−	1.31749i	0.928123	−	0.372275i	$-0.121422\pi$
$930$	8.35192	+	2.45235i	0.273870	+	0.0804156i
$931$	−29.8526	−	34.4517i	−0.978380	−	1.12911i
$932$	−2.41638	−	2.78865i	−0.0791512	−	0.0913453i
$933$	16.5877	+	4.87059i	0.543057	+	0.159456i
$934$	−21.1104	+	46.2253i	−0.690753	+	1.51254i
$935$	7.06313	+	4.53920i	0.230989	+	0.148448i
$936$	−0.141087	+	0.0414270i	−0.00461159	+	0.00135408i
$937$	0.391712	−	2.72442i	0.0127967	−	0.0890029i	−0.982422	−	0.186672i	$-0.940230\pi$
$937$	0.391712	−	2.72442i	0.0127967	−	0.0890029i	0.995219	+	0.0976695i	$0.0311388\pi$
$938$	−1.01399	−	2.22034i	−0.0331081	−	0.0724966i
$939$	1.99309	+	13.8623i	0.0650421	+	0.452378i
$940$	−14.7540	+	9.48180i	−0.481221	+	0.309262i
$941$	−5.79052	+	6.68261i	−0.188765	+	0.217847i	−0.842242	−	0.539100i	$-0.818764\pi$
$941$	−5.79052	+	6.68261i	−0.188765	+	0.217847i	0.653476	+	0.756947i	$0.273310\pi$
$942$	−21.8461			−0.711783
$943$	−4.61714	+	13.2251i	−0.150355	+	0.430669i
$944$	−60.5115			−1.96948
$945$	10.9013	−	12.5807i	0.354619	−	0.409252i
$946$	−18.3944	+	11.8214i	−0.598054	+	0.384346i
$947$	−2.88044	−	20.0339i	−0.0936017	−	0.651014i	−0.981569	−	0.191108i	$-0.938792\pi$
$947$	−2.88044	−	20.0339i	−0.0936017	−	0.651014i	0.887967	−	0.459906i	$-0.152117\pi$
$948$	−12.3249	−	26.9879i	−0.400295	−	0.876525i
$949$	0.173634	−	1.20765i	0.00563641	−	0.0392021i
$950$	14.7458	−	4.32975i	0.478416	−	0.140476i
$951$	−18.2403	−	11.7223i	−0.591483	−	0.380123i
$952$	0.433921	−	0.950155i	0.0140635	−	0.0307947i
$953$	46.2932	+	13.5929i	1.49958	+	0.440318i	0.925586	−	0.378538i	$-0.123573\pi$
$953$	46.2932	+	13.5929i	1.49958	+	0.440318i	0.573999	+	0.818856i	$0.305391\pi$
$954$	−12.8644	−	14.8463i	−0.416501	−	0.480668i
$955$	4.47265	+	5.16172i	0.144732	+	0.167029i
$956$	32.2831	+	9.47918i	1.04411	+	0.306579i
$957$	−6.74868	+	14.7775i	−0.218154	+	0.477690i
$958$	−6.52127	−	4.19097i	−0.210693	−	0.135404i
$959$	−62.9019	+	18.4697i	−2.03121	+	0.596416i
$960$	0.940930	−	6.54431i	0.0303684	−	0.211217i
$961$	−2.78556	−	6.09952i	−0.0898566	−	0.196759i
$962$	−0.0449171	−	0.312405i	−0.00144818	−	0.0100723i
$963$	8.57685	−	5.51201i	0.276385	−	0.177622i
$964$	−32.0707	+	37.0116i	−1.03293	+	1.19206i
$965$	14.9450			0.481096
$966$	−17.6974	+	24.7116i	−0.569406	+	0.795082i
$967$	−0.229589			−0.00738309			−0.00369154	−	0.999993i	$-0.501175\pi$
$967$	−0.229589			−0.00738309			−0.00369154	+	0.999993i	$0.501175\pi$
$968$	−0.514333	+	0.593572i	−0.0165313	+	0.0190781i
$969$	11.9878	−	7.70407i	0.385102	−	0.247490i
$970$	4.26077	+	29.6343i	0.136805	+	0.951501i
$971$	11.7475	+	25.7235i	0.376996	+	0.825505i	0.999094	+	0.0425658i	$0.0135532\pi$
$971$	11.7475	+	25.7235i	0.376996	+	0.825505i	−0.622098	+	0.782939i	$0.713720\pi$
$972$	−4.42775	+	30.7957i	−0.142020	+	0.987773i
$973$	7.33362	−	2.15335i	0.235105	−	0.0690331i
$974$	27.4488	+	17.6403i	0.879516	+	0.565231i
$975$	−0.174833	+	0.382831i	−0.00559914	+	0.0122604i
$976$	17.2012	+	5.05074i	0.550598	+	0.161670i
$977$	−8.04399	−	9.28326i	−0.257350	−	0.296998i	0.612342	−	0.790593i	$-0.290228\pi$
$977$	−8.04399	−	9.28326i	−0.257350	−	0.296998i	−0.869692	+	0.493596i	$0.835682\pi$
$978$	−12.3175	−	14.2152i	−0.393871	−	0.454552i
$979$	36.3032	+	10.6596i	1.16025	+	0.340681i
$980$	4.71097	−	10.3156i	0.150487	−	0.329520i
$981$	27.4476	+	17.6395i	0.876335	+	0.563186i
$982$	−17.0670	+	5.01133i	−0.544630	+	0.159918i
$983$	−3.33266	+	23.1791i	−0.106295	+	0.739300i	0.865060	+	0.501668i	$0.167280\pi$
$983$	−3.33266	+	23.1791i	−0.106295	+	0.739300i	−0.971355	+	0.237631i	$0.923629\pi$
$984$	0.152537	+	0.334010i	0.00486271	+	0.0106478i
$985$	1.73193	+	12.0458i	0.0551838	+	0.383812i
$986$	15.4091	−	9.90283i	0.490726	−	0.315370i
$987$	19.0392	−	21.9724i	0.606025	−	0.699390i
$988$	−7.06426			−0.224744
$989$	12.7565	+	2.49423i	0.405633	+	0.0793119i
$990$	17.7986			0.565677
$991$	−14.0692	+	16.2367i	−0.446922	+	0.515775i	−0.933849	−	0.357667i	$-0.883572\pi$
$991$	−14.0692	+	16.2367i	−0.446922	+	0.515775i	0.486927	+	0.873442i	$0.338118\pi$
$992$	32.8338	−	21.1010i	1.04247	−	0.669958i
$993$	−1.65570	−	11.5156i	−0.0525419	−	0.365437i
$994$	27.9120	+	61.1187i	0.885315	+	1.93857i
$995$	−0.579695	+	4.03187i	−0.0183776	+	0.127819i
$996$	4.27514	−	1.25529i	0.135463	−	0.0397755i
$997$	40.7856	+	26.2113i	1.29169	+	0.830120i	0.992282	−	0.124005i	$-0.0395739\pi$
$997$	40.7856	+	26.2113i	1.29169	+	0.830120i	0.299410	+	0.954125i	$0.403210\pi$
$998$	−11.9963	+	26.2683i	−0.379737	+	0.831507i
$999$	1.50027	+	0.440520i	0.0474666	+	0.0139374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.16.5	✓	50
5.2	odd	4		575.2.p.d.499.9		100
5.3	odd	4		575.2.p.d.499.2		100
5.4	even	2		575.2.k.d.476.1		50
23.6	even	11		2645.2.a.y.1.5		25
23.13	even	11	inner	115.2.g.c.36.5	yes	50
23.17	odd	22		2645.2.a.x.1.5		25
115.13	odd	44		575.2.p.d.174.9		100
115.59	even	22		575.2.k.d.151.1		50
115.82	odd	44		575.2.p.d.174.2		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.16.5	✓	50	1.1	even	1	trivial
115.2.g.c.36.5	yes	50	23.13	even	11	inner
575.2.k.d.151.1		50	115.59	even	22
575.2.k.d.476.1		50	5.4	even	2
575.2.p.d.174.2		100	115.82	odd	44
575.2.p.d.174.9		100	115.13	odd	44
575.2.p.d.499.2		100	5.3	odd	4
575.2.p.d.499.9		100	5.2	odd	4
2645.2.a.x.1.5		25	23.17	odd	22
2645.2.a.y.1.5		25	23.6	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29801 - 1.49799i) q^{2} +(0.749526 - 0.481691i) q^{3} +(-0.274499 - 1.90918i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.251328 - 1.74802i) q^{6} +(-3.44343 + 1.01108i) q^{7} +(0.118700 + 0.0762838i) q^{8} +(-0.916482 + 2.00682i) q^{9} +O(q^{10})\)	\(q+(1.29801 - 1.49799i) q^{2} +(0.749526 - 0.481691i) q^{3} +(-0.274499 - 1.90918i) q^{4} +(0.415415 + 0.909632i) q^{5} +(0.251328 - 1.74802i) q^{6} +(-3.44343 + 1.01108i) q^{7} +(0.118700 + 0.0762838i) q^{8} +(-0.916482 + 2.00682i) q^{9} +(1.90183 + 0.558429i) q^{10} +(-2.66540 - 3.07604i) q^{11} +(-1.12538 - 1.29876i) q^{12} +(0.453235 + 0.133082i) q^{13} +(-2.95503 + 6.47061i) q^{14} +(0.749526 + 0.481691i) q^{15} +(3.96971 - 1.16561i) q^{16} +(-0.293567 + 2.04180i) q^{17} +(1.81658 + 3.97776i) q^{18} +(-1.10343 - 7.67453i) q^{19} +(1.62262 - 1.04280i) q^{20} +(-2.09391 + 2.41650i) q^{21} -8.06760 q^{22} +(3.46199 + 3.31883i) q^{23} +0.125714 q^{24} +(-0.654861 + 0.755750i) q^{25} +(0.787660 - 0.506199i) q^{26} +(0.660130 + 4.59131i) q^{27} +(2.87555 + 6.29659i) q^{28} +(0.637549 - 4.43425i) q^{29} +(1.69446 - 0.497540i) q^{30} +(4.14649 + 2.66479i) q^{31} +(3.28944 - 7.20288i) q^{32} +(-3.47949 - 1.02167i) q^{33} +(2.67754 + 3.09005i) q^{34} +(-2.35016 - 2.71223i) q^{35} +(4.08295 + 1.19886i) q^{36} +(0.140033 - 0.306630i) q^{37} +(-12.9286 - 8.30873i) q^{38} +(0.403815 - 0.118571i) q^{39} +(-0.0200805 + 0.139663i) q^{40} +(1.21337 + 2.65690i) q^{41} +(0.901965 + 6.27331i) q^{42} +(2.28003 - 1.46529i) q^{43} +(-5.14106 + 5.93310i) q^{44} -2.20618 q^{45} +(9.46528 - 0.878132i) q^{46} -9.09267 q^{47} +(2.41394 - 2.78583i) q^{48} +(4.94612 - 3.17868i) q^{49} +(0.282086 + 1.96195i) q^{50} +(0.763481 + 1.67179i) q^{51} +(0.129665 - 0.901838i) q^{52} +(-4.31033 + 1.26563i) q^{53} +(7.73459 + 4.97072i) q^{54} +(1.69081 - 3.70237i) q^{55} +(-0.485864 - 0.142662i) q^{56} +(-4.52380 - 5.22075i) q^{57} +(-5.81491 - 6.71076i) q^{58} +(-14.0334 - 4.12057i) q^{59} +(0.713892 - 1.56321i) q^{60} +(3.64525 + 2.34266i) q^{61} +(9.37404 - 2.75247i) q^{62} +(1.12678 - 7.83696i) q^{63} +(-3.08269 - 6.75014i) q^{64} +(0.0672251 + 0.467561i) q^{65} +(-6.04688 + 3.88609i) q^{66} +(-0.224710 + 0.259329i) q^{67} +3.97875 q^{68} +(4.19350 + 0.819940i) q^{69} -7.11344 q^{70} +(6.18554 - 7.13850i) q^{71} +(-0.261874 + 0.168296i) q^{72} +(-0.367582 - 2.55659i) q^{73} +(-0.277563 - 0.607779i) q^{74} +(-0.126797 + 0.881895i) q^{75} +(-14.3492 + 4.21330i) q^{76} +(12.2882 + 7.89717i) q^{77} +(0.346541 - 0.758818i) q^{78} +(16.5651 + 4.86395i) q^{79} +(2.70936 + 3.12677i) q^{80} +(-1.62785 - 1.87864i) q^{81} +(5.55498 + 1.63109i) q^{82} +(-1.07706 + 2.35843i) q^{83} +(5.18831 + 3.33433i) q^{84} +(-1.97924 + 0.581157i) q^{85} +(0.764532 - 5.31744i) q^{86} +(-1.65808 - 3.63069i) q^{87} +(-0.0817311 - 0.568452i) q^{88} +(-7.82017 + 5.02572i) q^{89} +(-2.86366 + 3.30484i) q^{90} -1.69524 q^{91} +(5.38594 - 7.52058i) q^{92} +4.39151 q^{93} +(-11.8024 + 13.6207i) q^{94} +(6.52262 - 4.19183i) q^{95} +(-1.00404 - 6.98324i) q^{96} +(6.27465 + 13.7396i) q^{97} +(1.65851 - 11.5352i) q^{98} +(8.61583 - 2.52984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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