LMFDB - Embedded newform 171.3.z.a.101.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(5,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 16]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("171.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.z (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$38$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.32
Character	$\chi$	$=$	171.101
Dual form			171.3.z.a.149.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.90844 - 0.512836i) q^{2} +(2.18553 - 2.05511i) q^{3} +(4.43724 - 1.61502i) q^{4} +(0.765438 + 0.912213i) q^{5} +(5.30255 - 7.09796i) q^{6} +(-4.65346 - 8.06002i) q^{7} +(1.84664 - 1.06616i) q^{8} +(0.553083 - 8.98299i) q^{9} +O(q^{10})$	\(q+(2.90844 - 0.512836i) q^{2} +(2.18553 - 2.05511i) q^{3} +(4.43724 - 1.61502i) q^{4} +(0.765438 + 0.912213i) q^{5} +(5.30255 - 7.09796i) q^{6} +(-4.65346 - 8.06002i) q^{7} +(1.84664 - 1.06616i) q^{8} +(0.553083 - 8.98299i) q^{9} +(2.69404 + 2.26057i) q^{10} +16.9199i q^{11} +(6.37868 - 12.6487i) q^{12} +(3.60544 + 3.02532i) q^{13} +(-17.6678 - 21.0556i) q^{14} +(3.54758 + 0.420614i) q^{15} +(-9.64500 + 8.09312i) q^{16} +(17.0746 + 20.3487i) q^{17} +(-2.99819 - 26.4101i) q^{18} +(12.4490 + 14.3535i) q^{19} +(4.86967 + 2.81151i) q^{20} +(-26.7345 - 8.05208i) q^{21} +(8.67715 + 49.2106i) q^{22} +(-1.04132 - 2.86099i) q^{23} +(1.84482 - 6.12516i) q^{24} +(4.09497 - 23.2237i) q^{25} +(12.0377 + 6.94996i) q^{26} +(-17.2522 - 20.7692i) q^{27} +(-33.6656 - 28.2488i) q^{28} +(-15.1192 - 41.5396i) q^{29} +(10.5336 - 0.595998i) q^{30} -30.7708 q^{31} +(-29.3840 + 35.0184i) q^{32} +(34.7723 + 36.9790i) q^{33} +(60.0959 + 50.4265i) q^{34} +(3.79053 - 10.4144i) q^{35} +(-12.0536 - 40.7529i) q^{36} -31.3032 q^{37} +(43.5680 + 35.3620i) q^{38} +(14.0971 - 0.797624i) q^{39} +(2.38605 + 0.868452i) q^{40} +(-29.4928 + 5.20038i) q^{41} +(-81.8849 - 9.70857i) q^{42} +(54.5083 + 19.8394i) q^{43} +(27.3261 + 75.0778i) q^{44} +(8.61775 - 6.37139i) q^{45} +(-4.49583 - 7.78700i) q^{46} +(0.502536 + 1.38071i) q^{47} +(-4.44723 + 37.5093i) q^{48} +(-18.8093 + 32.5787i) q^{49} -69.6448i q^{50} +(79.1358 + 9.38262i) q^{51} +(20.8842 + 7.60121i) q^{52} +(1.44462 + 0.254725i) q^{53} +(-60.8282 - 51.5585i) q^{54} +(-15.4346 + 12.9512i) q^{55} +(-17.1865 - 9.92265i) q^{56} +(56.7056 + 5.78612i) q^{57} +(-65.2762 - 113.062i) q^{58} +(12.1242 - 33.3111i) q^{59} +(16.4208 - 3.86306i) q^{60} +(-52.5562 - 44.0999i) q^{61} +(-89.4949 + 15.7804i) q^{62} +(-74.9769 + 37.3441i) q^{63} +(-42.3214 + 73.3028i) q^{64} +5.60462i q^{65} +(120.097 + 89.7188i) q^{66} +(-6.93871 + 39.3514i) q^{67} +(108.628 + 62.7162i) q^{68} +(-8.15547 - 4.11277i) q^{69} +(5.68364 - 32.2335i) q^{70} +(125.015 - 22.0435i) q^{71} +(-8.55595 - 17.1780i) q^{72} +(-127.557 - 46.4268i) q^{73} +(-91.0433 + 16.0534i) q^{74} +(-38.7775 - 59.1717i) q^{75} +(78.4203 + 43.5846i) q^{76} +(136.375 - 78.7362i) q^{77} +(40.5916 - 9.54937i) q^{78} +(-31.7622 + 26.6517i) q^{79} +(-14.7653 - 2.60352i) q^{80} +(-80.3882 - 9.93667i) q^{81} +(-83.1111 + 30.2500i) q^{82} +(68.7627 - 39.7002i) q^{83} +(-131.631 + 7.44778i) q^{84} +(-5.49282 + 31.1513i) q^{85} +(168.708 + 29.7478i) q^{86} +(-118.412 - 59.7145i) q^{87} +(18.0393 + 31.2451i) q^{88} +(18.1751 + 49.9357i) q^{89} +(21.7967 - 22.9503i) q^{90} +(7.60641 - 43.1381i) q^{91} +(-9.24114 - 11.0132i) q^{92} +(-67.2505 + 63.2372i) q^{93} +(2.16967 + 3.75798i) q^{94} +(-3.56456 + 22.3428i) q^{95} +(7.74706 + 136.921i) q^{96} +(-10.9147 - 61.9004i) q^{97} +(-37.9982 + 104.399i) q^{98} +(151.992 + 9.35813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9}+O(q^{10}) $ 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9	\( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21} + 81 q^{22} + 207 q^{23} - 222 q^{24} - 3 q^{25} - 216 q^{26} - 33 q^{27} - 36 q^{28} - 9 q^{29} + 171 q^{30} - 6 q^{31} - 9 q^{32} + 30 q^{33} + 33 q^{34} + 225 q^{35} - 246 q^{36} - 24 q^{37} - 9 q^{38} - 60 q^{39} - 177 q^{40} - 9 q^{41} - 15 q^{42} + 93 q^{43} + 441 q^{44} - 57 q^{45} - 6 q^{46} - 9 q^{47} - 774 q^{48} - 543 q^{49} - 81 q^{51} + 213 q^{52} + 393 q^{54} + 63 q^{55} - 459 q^{56} + 84 q^{57} - 6 q^{58} + 126 q^{59} - 333 q^{60} - 24 q^{61} - 36 q^{62} + 369 q^{63} + 372 q^{64} + 894 q^{66} + 39 q^{67} + 747 q^{68} + 231 q^{69} + 291 q^{70} + 204 q^{72} - 51 q^{73} + 333 q^{74} + 324 q^{75} - 3 q^{76} - 18 q^{77} - 1569 q^{78} - 105 q^{79} - 756 q^{80} + 1050 q^{81} + 132 q^{82} + 99 q^{83} - 69 q^{84} - 3 q^{85} - 495 q^{86} - 483 q^{87} + 387 q^{88} - 648 q^{89} - 339 q^{90} + 225 q^{91} + 27 q^{92} + 396 q^{93} - 6 q^{94} - 1305 q^{95} - 663 q^{96} - 543 q^{97} + 1125 q^{98} - 300 q^{99}+O(q^{100}) \) 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.90844	−	0.512836i	1.45422	−	0.256418i	0.609993	−	0.792406i	$-0.291172\pi$
$2$	2.90844	−	0.512836i	1.45422	−	0.256418i	0.844225	+	0.535988i	$0.180061\pi$
$3$	2.18553	−	2.05511i	0.728510	−	0.685035i
$3$	2.18553	−	2.05511i	0.728510	−	0.685035i
$4$	4.43724	−	1.61502i	1.10931	−	0.403756i
$5$	0.765438	+	0.912213i	0.153088	+	0.182443i	0.837137	−	0.546993i	$-0.184227\pi$
$5$	0.765438	+	0.912213i	0.153088	+	0.182443i	−0.684050	+	0.729435i	$0.739783\pi$
$6$	5.30255	−	7.09796i	0.883758	−	1.18299i
$7$	−4.65346	−	8.06002i	−0.664780	−	1.15143i	−0.979345	−	0.202196i	$-0.935192\pi$
$7$	−4.65346	−	8.06002i	−0.664780	−	1.15143i	0.314566	−	0.949236i	$-0.398141\pi$
$8$	1.84664	−	1.06616i	0.230830	−	0.133270i
$9$	0.553083	−	8.98299i	0.0614536	−	0.998110i
$10$	2.69404	+	2.26057i	0.269404	+	0.226057i
$11$			16.9199i			1.53818i	0.639143	+	0.769088i	$0.279289\pi$
$11$			16.9199i			1.53818i	−0.639143	+	0.769088i	$0.720711\pi$
$12$	6.37868	−	12.6487i	0.531556	−	1.05406i
$13$	3.60544	+	3.02532i	0.277341	+	0.232717i	0.770839	−	0.637030i	$-0.219837\pi$
$13$	3.60544	+	3.02532i	0.277341	+	0.232717i	−0.493497	+	0.869747i	$0.664282\pi$
$14$	−17.6678	−	21.0556i	−1.26198	−	1.50397i
$15$	3.54758	+	0.420614i	0.236505	+	0.0280409i
$16$	−9.64500	+	8.09312i	−0.602813	+	0.505820i
$17$	17.0746	+	20.3487i	1.00439	+	1.19698i	0.980349	+	0.197272i	$0.0632081\pi$
$17$	17.0746	+	20.3487i	1.00439	+	1.19698i	0.0240387	+	0.999711i	$0.492347\pi$
$18$	−2.99819	−	26.4101i	−0.166566	−	1.46723i
$19$	12.4490	+	14.3535i	0.655208	+	0.755448i
$19$	12.4490	+	14.3535i	0.655208	+	0.755448i
$20$	4.86967	+	2.81151i	0.243484	+	0.140575i
$21$	−26.7345	−	8.05208i	−1.27307	−	0.383432i
$22$	8.67715	+	49.2106i	0.394416	+	2.23685i
$23$	−1.04132	−	2.86099i	−0.0452746	−	0.124391i	0.914995	−	0.403466i	$-0.132195\pi$
$23$	−1.04132	−	2.86099i	−0.0452746	−	0.124391i	−0.960269	+	0.279075i	$0.909972\pi$
$24$	1.84482	−	6.12516i	0.0768675	−	0.255215i
$25$	4.09497	−	23.2237i	0.163799	−	0.928948i
$26$	12.0377	+	6.94996i	0.462988	+	0.267306i
$27$	−17.2522	−	20.7692i	−0.638971	−	0.769231i
$28$	−33.6656	−	28.2488i	−1.20234	−	1.00889i
$29$	−15.1192	−	41.5396i	−0.521351	−	1.43240i	−0.869017	−	0.494782i	$-0.835248\pi$
$29$	−15.1192	−	41.5396i	−0.521351	−	1.43240i	0.347666	−	0.937618i	$-0.386974\pi$
$30$	10.5336	−	0.595998i	0.351121	−	0.0198666i
$31$	−30.7708			−0.992606			−0.496303	−	0.868149i	$-0.665309\pi$
$31$	−30.7708			−0.992606			−0.496303	+	0.868149i	$0.665309\pi$
$32$	−29.3840	+	35.0184i	−0.918249	+	1.09433i
$33$	34.7723	+	36.9790i	1.05370	+	1.12058i
$34$	60.0959	+	50.4265i	1.76753	+	1.48313i
$35$	3.79053	−	10.4144i	0.108301	−	0.297554i
$36$	−12.0536	−	40.7529i	−0.334821	−	1.13203i
$37$	−31.3032			−0.846031			−0.423016	−	0.906122i	$-0.639028\pi$
$37$	−31.3032			−0.846031			−0.423016	+	0.906122i	$0.639028\pi$
$38$	43.5680	+	35.3620i	1.14653	+	0.930580i
$39$	14.0971	−	0.797624i	0.361465	−	0.0204519i
$40$	2.38605	+	0.868452i	0.0596513	+	0.0217113i
$41$	−29.4928	+	5.20038i	−0.719337	+	0.126839i	−0.521322	−	0.853360i	$-0.674561\pi$
$41$	−29.4928	+	5.20038i	−0.719337	+	0.126839i	−0.198016	+	0.980199i	$0.563450\pi$
$42$	−81.8849	−	9.70857i	−1.94964	−	0.231156i
$43$	54.5083	+	19.8394i	1.26763	+	0.461381i	0.886324	−	0.463066i	$-0.153251\pi$
$43$	54.5083	+	19.8394i	1.26763	+	0.461381i	0.381311	+	0.924447i	$0.375473\pi$
$44$	27.3261	+	75.0778i	0.621047	+	1.70631i
$45$	8.61775	−	6.37139i	0.191506	−	0.141586i
$46$	−4.49583	−	7.78700i	−0.0977353	−	0.169283i
$47$	0.502536	+	1.38071i	0.0106923	+	0.0293767i	0.944924	−	0.327290i	$-0.106135\pi$
$47$	0.502536	+	1.38071i	0.0106923	+	0.0293767i	−0.934232	+	0.356667i	$0.883913\pi$
$48$	−4.44723	+	37.5093i	−0.0926507	+	0.781443i
$49$	−18.8093	+	32.5787i	−0.383864	+	0.664871i
$50$		−	69.6448i		−	1.39290i
$51$	79.1358	+	9.38262i	1.55168	+	0.183973i
$52$	20.8842	+	7.60121i	0.401618	+	0.146177i
$53$	1.44462	+	0.254725i	0.0272569	+	0.00480613i	0.187260	−	0.982310i	$-0.440039\pi$
$53$	1.44462	+	0.254725i	0.0272569	+	0.00480613i	−0.160003	+	0.987117i	$0.551150\pi$
$54$	−60.8282	−	51.5585i	−1.12645	−	0.954787i
$55$	−15.4346	+	12.9512i	−0.280629	+	0.235476i
$56$	−17.1865	−	9.92265i	−0.306902	−	0.177190i
$57$	56.7056	+	5.78612i	0.994834	+	0.101511i
$58$	−65.2762	−	113.062i	−1.12545	−	1.94934i
$59$	12.1242	−	33.3111i	0.205496	−	0.564595i	−0.793539	−	0.608519i	$-0.791764\pi$
$59$	12.1242	−	33.3111i	0.205496	−	0.564595i	0.999035	+	0.0439243i	$0.0139860\pi$
$60$	16.4208	−	3.86306i	0.273679	−	0.0643843i
$61$	−52.5562	−	44.0999i	−0.861577	−	0.722949i	0.100730	−	0.994914i	$-0.467882\pi$
$61$	−52.5562	−	44.0999i	−0.861577	−	0.722949i	−0.962307	+	0.271965i	$0.912327\pi$
$62$	−89.4949	+	15.7804i	−1.44347	+	0.254522i
$63$	−74.9769	+	37.3441i	−1.19011	+	0.592763i
$64$	−42.3214	+	73.3028i	−0.661272	+	1.14536i
$65$			5.60462i			0.0862250i
$66$	120.097	+	89.7188i	1.81965	+	1.35938i
$67$	−6.93871	+	39.3514i	−0.103563	+	0.587334i	0.888222	+	0.459415i	$0.151941\pi$
$67$	−6.93871	+	39.3514i	−0.103563	+	0.587334i	−0.991785	+	0.127919i	$0.959170\pi$
$68$	108.628	+	62.7162i	1.59747	+	0.922297i
$69$	−8.15547	−	4.11277i	−0.118195	−	0.0596054i
$70$	5.68364	−	32.2335i	0.0811949	−	0.460479i
$71$	125.015	−	22.0435i	1.76077	−	0.310472i	0.802569	−	0.596560i	$-0.203466\pi$
$71$	125.015	−	22.0435i	1.76077	−	0.310472i	0.958203	+	0.286088i	$0.0923550\pi$
$72$	−8.55595	−	17.1780i	−0.118833	−	0.238584i
$73$	−127.557	−	46.4268i	−1.74735	−	0.635984i	−0.747743	−	0.663988i	$-0.768863\pi$
$73$	−127.557	−	46.4268i	−1.74735	−	0.635984i	−0.999608	+	0.0280040i	$0.991085\pi$
$74$	−91.0433	+	16.0534i	−1.23031	+	0.216938i
$75$	−38.7775	−	59.1717i	−0.517033	−	0.788956i
$76$	78.4203	+	43.5846i	1.03185	+	0.573482i
$77$	136.375	−	78.7362i	1.77111	−	1.02255i
$78$	40.5916	−	9.54937i	0.520405	−	0.122428i
$79$	−31.7622	+	26.6517i	−0.402053	+	0.337363i	−0.821287	−	0.570516i	$-0.806743\pi$
$79$	−31.7622	+	26.6517i	−0.402053	+	0.337363i	0.419233	+	0.907879i	$0.362299\pi$
$80$	−14.7653	−	2.60352i	−0.184566	−	0.0325440i
$81$	−80.3882	−	9.93667i	−0.992447	−	0.122675i
$82$	−83.1111	+	30.2500i	−1.01355	+	0.368902i
$83$	68.7627	−	39.7002i	0.828467	−	0.478315i	−0.0248607	−	0.999691i	$-0.507914\pi$
$83$	68.7627	−	39.7002i	0.828467	−	0.478315i	0.853327	+	0.521375i	$0.174581\pi$
$84$	−131.631	+	7.44778i	−1.56704	+	0.0886640i
$85$	−5.49282	+	31.1513i	−0.0646214	+	0.366486i
$86$	168.708	+	29.7478i	1.96172	+	0.345905i
$87$	−118.412	−	59.7145i	−1.36105	−	0.686374i
$88$	18.0393	+	31.2451i	0.204993	+	0.355057i
$89$	18.1751	+	49.9357i	0.204215	+	0.561075i	0.998947	−	0.0458853i	$-0.0146109\pi$
$89$	18.1751	+	49.9357i	0.204215	+	0.561075i	−0.794732	+	0.606960i	$0.792389\pi$
$90$	21.7967	−	22.9503i	0.242186	−	0.255003i
$91$	7.60641	−	43.1381i	0.0835870	−	0.474045i
$92$	−9.24114	−	11.0132i	−0.100447	−	0.119708i
$93$	−67.2505	+	63.2372i	−0.723123	+	0.679970i
$94$	2.16967	+	3.75798i	0.0230816	+	0.0399785i
$95$	−3.56456	+	22.3428i	−0.0375217	+	0.235188i
$96$	7.74706	+	136.921i	0.0806986	+	1.42626i
$97$	−10.9147	−	61.9004i	−0.112523	−	0.638148i	−0.987947	−	0.154793i	$-0.950529\pi$
$97$	−10.9147	−	61.9004i	−0.112523	−	0.638148i	0.875424	−	0.483355i	$-0.160582\pi$
$98$	−37.9982	+	104.399i	−0.387737	+	1.06530i
$99$	151.992	+	9.35813i	1.53527	+	0.0945265i
$100$	−19.3365	−	109.663i	−0.193365	−	1.09663i
$101$	6.58876	+	1.16178i	0.0652352	+	0.0115027i	0.206171	−	0.978516i	$-0.433900\pi$
$101$	6.58876	+	1.16178i	0.0652352	+	0.0115027i	−0.140935	+	0.990019i	$0.545011\pi$
$102$	234.973	−	13.2949i	2.30366	−	0.130342i
$103$	23.9999	−	41.5691i	0.233009	−	0.403584i	−0.725683	−	0.688029i	$-0.758476\pi$
$103$	23.9999	−	41.5691i	0.233009	−	0.403584i	0.958692	+	0.284445i	$0.0918095\pi$
$104$	9.88342	+	1.74271i	0.0950329	+	0.0167569i
$105$	−13.1184	−	30.5509i	−0.124937	−	0.290961i
$106$	4.33221			0.0408699
$107$	−19.6530	−	11.3466i	−0.183673	−	0.106043i	0.405344	−	0.914164i	$-0.367152\pi$
$107$	−19.6530	−	11.3466i	−0.183673	−	0.106043i	−0.589017	+	0.808121i	$0.700485\pi$
$108$	−110.095	−	64.2953i	−1.01940	−	0.595327i
$109$	15.9784	+	90.6180i	0.146591	+	0.831358i	0.966076	+	0.258258i	$0.0831484\pi$
$109$	15.9784	+	90.6180i	0.146591	+	0.831358i	−0.819485	+	0.573100i	$0.805741\pi$
$110$	−38.2487	+	45.5831i	−0.347716	+	0.414391i
$111$	−68.4140	+	64.3313i	−0.616342	+	0.579561i
$112$	110.113	+	40.0780i	0.983155	+	0.357839i
$113$	−76.6522	+	44.2552i	−0.678338	+	0.391639i	−0.799229	−	0.601027i	$-0.794758\pi$
$113$	−76.6522	+	44.2552i	−0.678338	+	0.391639i	0.120890	+	0.992666i	$0.461425\pi$
$114$	167.892	−	12.2521i	1.47274	−	0.107475i
$115$	1.81277	−	3.13982i	0.0157632	−	0.0273027i
$116$	−134.175	−	159.903i	−1.15668	−	1.37848i
$117$	29.1705	−	30.7144i	0.249321	−	0.262516i
$118$	18.1795	−	103.101i	0.154063	−	0.873737i
$119$	84.5552	−	232.313i	0.710548	−	1.95221i
$120$	6.99955	−	3.00556i	0.0583296	−	0.0250463i
$121$	−165.284			−1.36599
$122$	−175.472	−	101.309i	−1.43830	−	0.830402i
$123$	−53.7701	+	71.9765i	−0.437155	+	0.585174i
$124$	−136.537	+	49.6955i	−1.10111	+	0.400770i
$125$	50.1012	−	28.9259i	0.400810	−	0.231408i
$126$	−198.914	+	147.064i	−1.57868	+	1.16717i
$127$	−2.47324	+	0.900187i	−0.0194744	+	0.00708809i	−0.351739	−	0.936098i	$-0.614410\pi$
$127$	−2.47324	+	0.900187i	−0.0194744	+	0.00708809i	0.332265	+	0.943186i	$0.392187\pi$
$128$	−22.9573	+	63.0746i	−0.179354	+	0.492770i
$129$	159.902	−	68.6607i	1.23955	−	0.532253i
$130$	2.87425	+	16.3007i	0.0221096	+	0.125390i
$131$	57.4296	−	157.786i	0.438394	−	1.20448i	−0.502143	−	0.864785i	$-0.667455\pi$
$131$	57.4296	−	157.786i	0.438394	−	1.20448i	0.940537	−	0.339692i	$-0.110323\pi$
$132$	214.015	+	107.927i	1.62132	+	0.817627i
$133$	57.7590	−	167.132i	0.434278	−	1.25663i
$134$			118.009i			0.880667i
$135$	5.74048	−	31.6353i	0.0425221	−	0.234335i
$136$	53.2256	+	19.3725i	0.391365	+	0.142445i
$137$	−16.8765	+	20.1127i	−0.123186	+	0.146808i	−0.824113	−	0.566426i	$-0.808326\pi$
$137$	−16.8765	+	20.1127i	−0.123186	+	0.146808i	0.700926	+	0.713234i	$0.252770\pi$
$138$	−25.8289	−	7.77932i	−0.187166	−	0.0563719i
$139$	128.198	+	107.571i	0.922289	+	0.773892i	0.974417	−	0.224748i	$-0.0721560\pi$
$139$	128.198	+	107.571i	0.922289	+	0.773892i	−0.0521282	+	0.998640i	$0.516600\pi$
$140$		−	52.3329i		−	0.373807i
$141$	3.93581	+	1.98481i	0.0279135	+	0.0140767i
$142$	352.293	−	128.224i	2.48094	−	0.902987i
$143$	−51.1883	+	61.0038i	−0.357960	+	0.426600i
$144$	67.3659	+	91.1171i	0.467819	+	0.632758i
$145$	26.3202	−	45.5879i	0.181518	−	0.314399i
$146$	−394.800	−	69.6139i	−2.70411	−	0.476807i
$147$	25.8443	+	109.857i	0.175812	+	0.747325i
$148$	−138.900	+	50.5553i	−0.938510	+	0.341590i
$149$	156.375	−	27.5731i	1.04950	−	0.185054i	0.377804	−	0.925885i	$-0.376679\pi$
$149$	156.375	−	27.5731i	1.04950	−	0.185054i	0.671692	+	0.740831i	$0.265568\pi$
$150$	−143.127	−	152.211i	−0.954182	−	1.01474i
$151$	12.4844	−	21.6236i	0.0826782	−	0.143203i	−0.821721	−	0.569890i	$-0.806986\pi$
$151$	12.4844	−	21.6236i	0.0826782	−	0.143203i	0.904400	+	0.426687i	$0.140319\pi$
$152$	38.2919	+	13.2332i	0.251920	+	0.0870607i
$153$	192.236	−	142.126i	1.25644	−	0.928930i
$154$	356.260	−	298.937i	2.31337	−	1.94115i
$155$	−23.5531	−	28.0695i	−0.151956	−	0.181094i
$156$	61.2642	−	26.3065i	0.392719	−	0.168631i
$157$	155.678	−	130.629i	0.991577	−	0.832032i	0.00578186	−	0.999983i	$-0.498160\pi$
$157$	155.678	−	130.629i	0.991577	−	0.832032i	0.985795	+	0.167951i	$0.0537151\pi$
$158$	−78.7105	+	93.8035i	−0.498168	+	0.593693i
$159$	3.68074	−	2.41213i	0.0231493	−	0.0151706i
$160$	−54.4359			−0.340224
$161$	−18.2140	+	21.7065i	−0.113130	+	0.134823i
$162$	−238.900	+	12.3258i	−1.47469	+	0.0760850i
$163$	145.317	+	251.696i	0.891514	+	1.54415i	0.838060	+	0.545578i	$0.183690\pi$
$163$	145.317	+	251.696i	0.891514	+	1.54415i	0.0534541	+	0.998570i	$0.482977\pi$
$164$	−122.468	+	70.7069i	−0.746756	+	0.431140i
$165$	−7.11676	+	60.0249i	−0.0431319	+	0.363787i
$166$	179.632	−	150.730i	1.08212	−	0.908009i
$167$	94.8663	+	260.643i	0.568062	+	1.56074i	0.807526	+	0.589832i	$0.200806\pi$
$167$	94.8663	+	260.643i	0.568062	+	1.56074i	−0.239465	+	0.970905i	$0.576972\pi$
$168$	−57.9538	+	13.6339i	−0.344963	+	0.0811541i
$169$	−25.4999	−	144.617i	−0.150887	−	0.855724i
$170$			93.4186i			0.549521i
$171$	135.823	−	103.890i	0.794285	−	0.607545i
$172$	273.907			1.59248
$173$	4.52666	−	0.798172i	0.0261656	−	0.00461371i	−0.160550	−	0.987028i	$-0.551327\pi$
$173$	4.52666	−	0.798172i	0.0261656	−	0.00461371i	0.186716	+	0.982414i	$0.440216\pi$
$174$	−375.017	−	112.950i	−2.15527	−	0.649139i
$175$	−206.239	+	75.0650i	−1.17851	+	0.428943i
$176$	−136.935	−	163.193i	−0.778040	−	0.927232i
$177$	−41.9599	−	97.7190i	−0.237062	−	0.552085i
$178$	78.4700	+	135.914i	0.440843	+	0.763562i
$179$	−8.58287	+	4.95532i	−0.0479490	+	0.0276834i	−0.523783	−	0.851852i	$-0.675480\pi$
$179$	−8.58287	+	4.95532i	−0.0479490	+	0.0276834i	0.475834	+	0.879535i	$0.342146\pi$
$180$	27.9491	−	42.1892i	0.155273	−	0.234385i
$181$	25.1833	+	21.1313i	0.139134	+	0.116747i	0.709699	−	0.704505i	$-0.248831\pi$
$181$	25.1833	+	21.1313i	0.139134	+	0.116747i	−0.570565	+	0.821253i	$0.693276\pi$
$182$		−	129.365i		−	0.710799i
$183$	−205.493	+	11.6269i	−1.12291	+	0.0635350i
$184$	−4.97321	−	4.17302i	−0.0270283	−	0.0226795i
$185$	−23.9606	−	28.5551i	−0.129517	−	0.154352i
$186$	−163.163	+	218.410i	−0.877223	+	1.17425i
$187$	−344.299	+	288.901i	−1.84117	+	1.54493i
$188$	4.45975	+	5.31492i	0.0237221	+	0.0282708i
$189$	−87.1181	+	235.702i	−0.460942	+	1.24710i
$190$	1.09089	+	66.8108i	0.00574155	+	0.351636i
$191$	−235.141	−	135.759i	−1.23110	−	0.710778i	−0.263844	−	0.964565i	$-0.584990\pi$
$191$	−235.141	−	135.759i	−1.23110	−	0.710778i	−0.967260	+	0.253787i	$0.918324\pi$
$192$	58.1503	+	247.180i	0.302866	+	1.28740i
$193$	43.9857	+	249.455i	0.227905	+	1.29251i	0.857053	+	0.515228i	$0.172293\pi$
$193$	43.9857	+	249.455i	0.227905	+	1.29251i	−0.629148	+	0.777285i	$0.716596\pi$
$194$	−63.4895	−	174.436i	−0.327265	−	0.899154i
$195$	11.5181	+	12.2491i	0.0590671	+	0.0628158i
$196$	−30.8461	+	174.937i	−0.157378	+	0.892535i
$197$	−104.716	−	60.4580i	−0.531555	−	0.306893i	0.210095	−	0.977681i	$-0.432623\pi$
$197$	−104.716	−	60.4580i	−0.531555	−	0.306893i	−0.741649	+	0.670788i	$0.765956\pi$
$198$	446.857	−	50.7293i	2.25686	−	0.256208i
$199$	26.1757	+	21.9640i	0.131536	+	0.110372i	0.706182	−	0.708030i	$-0.250416\pi$
$199$	26.1757	+	21.9640i	0.131536	+	0.110372i	−0.574646	+	0.818402i	$0.694860\pi$
$200$	−17.1982	−	47.2517i	−0.0859911	−	0.236259i
$201$	65.7065	+	100.263i	0.326898	+	0.498823i
$202$	19.7588			0.0978158
$203$	−264.454	+	315.164i	−1.30273	+	1.55253i
$204$	366.297	−	86.1731i	1.79558	−	0.422417i
$205$	−27.3188	−	22.9232i	−0.133262	−	0.111820i
$206$	48.4842	−	133.209i	0.235360	−	0.646647i
$207$	−26.2762	+	7.77177i	−0.126938	+	0.0375448i
$208$	−59.2587			−0.284898
$209$	−242.861	+	210.636i	−1.16201	+	1.00783i
$210$	−53.8215	−	82.1278i	−0.256293	−	0.391085i
$211$	−22.8897	−	8.33115i	−0.108482	−	0.0394841i	0.287209	−	0.957868i	$-0.407273\pi$
$211$	−22.8897	−	8.33115i	−0.108482	−	0.0394841i	−0.395691	+	0.918384i	$0.629495\pi$
$212$	6.82149	−	1.20281i	0.0321768	−	0.00567364i
$213$	227.922	−	305.095i	1.07006	−	1.43237i
$214$	−62.9784	−	22.9223i	−0.294291	−	0.107113i
$215$	23.6249	+	64.9090i	0.109883	+	0.301902i
$216$	−54.0019	−	19.9597i	−0.250009	−	0.0924062i
$217$	143.190	+	248.013i	0.659864	+	1.14292i
$218$	92.9444	+	255.363i	0.426350	+	1.17139i
$219$	−374.191	+	160.675i	−1.70863	+	0.733676i
$220$	−47.5705	+	82.3946i	−0.216230	+	0.374521i
$221$			125.022i			0.565711i
$222$	−165.986	+	222.189i	−0.747686	+	1.00085i
$223$	−218.948	−	79.6907i	−0.981831	−	0.357357i	−0.199279	−	0.979943i	$-0.563860\pi$
$223$	−218.948	−	79.6907i	−0.981831	−	0.357357i	−0.782552	+	0.622585i	$0.786082\pi$
$224$	418.986	+	73.8786i	1.87048	+	0.329815i
$225$	−206.353	−	49.6297i	−0.917127	−	0.220576i
$226$	−200.243	+	168.023i	−0.886029	+	0.743467i
$227$	139.424	+	80.4967i	0.614204	+	0.354611i	0.774609	−	0.632440i	$-0.217947\pi$
$227$	139.424	+	80.4967i	0.614204	+	0.354611i	−0.160405	+	0.987051i	$0.551280\pi$
$228$	260.961	−	65.9064i	1.14456	−	0.289063i
$229$	55.9715	+	96.9455i	0.244417	+	0.423343i	0.961968	−	0.273164i	$-0.0880701\pi$
$229$	55.9715	+	96.9455i	0.244417	+	0.423343i	−0.717551	+	0.696506i	$0.754737\pi$
$230$	3.66213	−	10.0616i	0.0159223	−	0.0437461i
$231$	136.241	−	452.346i	0.589787	−	1.95821i
$232$	−72.2075	−	60.5893i	−0.311239	−	0.261161i
$233$	−62.2560	+	10.9774i	−0.267193	+	0.0471134i	−0.305640	−	0.952147i	$-0.598870\pi$
$233$	−62.2560	+	10.9774i	−0.267193	+	0.0471134i	0.0384463	+	0.999261i	$0.487759\pi$
$234$	69.0893	−	104.290i	0.295253	−	0.445686i
$235$	−0.874839	+	1.51527i	−0.00372272	+	0.00644794i
$236$		−	167.390i		−	0.709281i
$237$	−14.6453	+	123.523i	−0.0617945	+	0.521193i
$238$	126.785	−	719.032i	0.532709	−	3.02114i
$239$	355.928	+	205.495i	1.48924	+	0.859812i	0.999924	−	0.0122952i	$-0.00391379\pi$
$239$	355.928	+	205.495i	1.48924	+	0.859812i	0.489314	+	0.872108i	$0.337247\pi$
$240$	−37.6205	+	24.6542i	−0.156752	+	0.102726i
$241$	39.2114	−	222.379i	0.162703	−	0.922733i	−0.788699	−	0.614780i	$-0.789245\pi$
$241$	39.2114	−	222.379i	0.162703	−	0.922733i	0.951401	−	0.307953i	$-0.0996441\pi$
$242$	−480.719	+	84.7638i	−1.98644	+	0.350264i
$243$	−196.112	+	143.489i	−0.807044	+	0.590491i
$244$	−304.427	−	110.802i	−1.24765	−	0.454108i
$245$	−44.1161	+	7.77885i	−0.180066	+	0.0317504i
$246$	−119.475	+	236.914i	−0.485670	+	0.963066i
$247$	1.45994	+	89.4128i	0.00591070	+	0.361995i
$248$	−56.8226	+	32.8065i	−0.229123	+	0.132284i
$249$	68.6950	−	228.081i	0.275883	−	0.915986i
$250$	130.882	−	109.823i	0.523528	−	0.439292i
$251$	−204.641	−	36.0837i	−0.815301	−	0.143760i	−0.249578	−	0.968355i	$-0.580292\pi$
$251$	−204.641	−	36.0837i	−0.815301	−	0.143760i	−0.565723	+	0.824595i	$0.691403\pi$
$252$	−272.379	+	286.794i	−1.08087	+	1.13807i
$253$	48.4078	−	17.6190i	0.191335	−	0.0696404i
$254$	−6.73163	+	3.88651i	−0.0265025	+	0.0153012i
$255$	52.0145	+	79.3705i	0.203979	+	0.311257i
$256$	24.3694	−	138.206i	0.0951928	−	0.539865i
$257$	−88.9508	−	15.6844i	−0.346112	−	0.0610289i	−0.00210995	−	0.999998i	$-0.500672\pi$
$257$	−88.9508	−	15.6844i	−0.346112	−	0.0610289i	−0.344002	+	0.938969i	$0.611783\pi$
$258$	429.852	−	281.699i	1.66609	−	1.09186i
$259$	145.668	+	252.304i	0.562424	+	0.974147i
$260$	9.05159	+	24.8690i	0.0348138	+	0.0956502i
$261$	−381.512	+	112.841i	−1.46173	+	0.432339i
$262$	86.1117	−	488.364i	0.328671	−	1.86398i
$263$	318.296	+	379.330i	1.21025	+	1.44232i	0.863491	+	0.504364i	$0.168273\pi$
$263$	318.296	+	379.330i	1.21025	+	1.44232i	0.346758	+	0.937955i	$0.387282\pi$
$264$	103.637	+	31.2143i	0.392566	+	0.118236i
$265$	0.873400	+	1.51277i	0.00329585	+	0.00570858i
$266$	82.2769	−	515.715i	0.309312	−	1.93878i
$267$	142.345	+	71.7842i	0.533129	+	0.268855i
$268$	32.7647	+	185.818i	0.122256	+	0.693349i
$269$	123.038	−	338.044i	0.457391	−	1.25667i	−0.470030	−	0.882651i	$-0.655757\pi$
$269$	123.038	−	338.044i	0.457391	−	1.25667i	0.927421	−	0.374020i	$-0.122021\pi$
$270$	0.472122	−	94.9531i	0.00174860	−	0.351678i
$271$	8.96651	+	50.8516i	0.0330868	+	0.187644i	0.996872	−	0.0790362i	$-0.0251843\pi$
$271$	8.96651	+	50.8516i	0.0330868	+	0.187644i	−0.963785	+	0.266681i	$0.914073\pi$
$272$	−329.369	−	58.0766i	−1.21092	−	0.213517i
$273$	−72.0293	−	109.912i	−0.263844	−	0.402607i
$274$	−38.7698	+	67.1513i	−0.141496	+	0.245078i
$275$	392.944	+	69.2866i	1.42889	+	0.251951i
$276$	−42.8300	−	5.07808i	−0.155181	−	0.0183988i
$277$	−391.643			−1.41387			−0.706937	−	0.707277i	$-0.749924\pi$
$277$	−391.643			−1.41387			−0.706937	+	0.707277i	$0.749924\pi$
$278$	428.023	+	247.119i	1.53965	+	0.888917i
$279$	−17.0188	+	276.414i	−0.0609992	+	0.990730i
$280$	−4.10365	−	23.2729i	−0.0146559	−	0.0831177i
$281$	130.447	−	155.460i	0.464223	−	0.553240i	−0.482245	−	0.876036i	$-0.660179\pi$
$281$	130.447	−	155.460i	0.464223	−	0.553240i	0.946468	+	0.322797i	$0.104623\pi$
$282$	12.4649	+	3.75428i	0.0442019	+	0.0133130i
$283$	−84.2981	−	30.6820i	−0.297873	−	0.108417i	0.188760	−	0.982023i	$-0.439553\pi$
$283$	−84.2981	−	30.6820i	−0.297873	−	0.108417i	−0.486634	+	0.873606i	$0.661775\pi$
$284$	519.120	−	299.714i	1.82789	−	1.05533i
$285$	38.1264	+	56.1565i	0.133777	+	0.197040i
$286$	−117.593	+	203.677i	−0.411164	+	0.712157i
$287$	179.159	+	213.513i	0.624247	+	0.743948i
$288$	298.319	+	283.324i	1.03583	+	0.983763i
$289$	−72.3438	+	410.282i	−0.250325	+	1.41966i
$290$	53.1715	−	146.087i	0.183350	−	0.503750i
$291$	−151.066	−	112.854i	−0.519128	−	0.387815i
$292$	−640.980			−2.19514
$293$	−401.821	−	231.991i	−1.37140	−	0.791780i	−0.380298	−	0.924864i	$-0.624179\pi$
$293$	−401.821	−	231.991i	−1.37140	−	0.791780i	−0.991105	+	0.133084i	$0.957512\pi$
$294$	131.505	+	306.258i	0.447296	+	1.04169i
$295$	39.6672	−	14.4377i	0.134465	−	0.0489413i
$296$	−57.8057	+	33.3741i	−0.195289	+	0.112750i
$297$	351.414	−	291.906i	1.18321	−	0.982850i
$298$	440.666	−	160.389i	1.47875	−	0.538219i
$299$	4.90102	−	13.4655i	0.0163914	−	0.0450350i
$300$	−267.629	−	199.932i	−0.892096	−	0.666441i
$301$	−93.7460	−	531.660i	−0.311448	−	1.76631i
$302$	25.2208	−	69.2935i	0.0835124	−	0.229449i
$303$	16.7875	−	11.0015i	0.0554043	−	0.0363086i
$304$	−236.235	−	37.6888i	−0.777089	−	0.123976i
$305$		−	81.6982i		−	0.267863i
$306$	486.218	−	511.951i	1.58895	−	1.67304i
$307$	−333.395	−	121.346i	−1.08598	−	0.395264i	−0.263848	−	0.964564i	$-0.584992\pi$
$307$	−333.395	−	121.346i	−1.08598	−	0.395264i	−0.822129	+	0.569301i	$0.807214\pi$
$308$	477.968	−	569.620i	1.55184	−	1.84942i
$309$	−32.9763	−	140.173i	−0.106720	−	0.453634i
$310$	−82.8978	−	69.5595i	−0.267412	−	0.224386i
$311$		−	373.853i		−	1.20210i	−0.799212	−	0.601049i	$-0.794749\pi$
$311$		−	373.853i		−	1.20210i	0.799212	−	0.601049i	$-0.205251\pi$
$312$	25.1820	−	16.5027i	0.0807115	−	0.0528933i
$313$	184.487	−	67.1476i	0.589414	−	0.214529i	−0.0300577	−	0.999548i	$-0.509569\pi$
$313$	184.487	−	67.1476i	0.589414	−	0.214529i	0.619472	+	0.785019i	$0.287347\pi$
$314$	385.787	−	459.763i	1.22862	−	1.46421i
$315$	−91.4559	−	39.8103i	−0.290336	−	0.126382i
$316$	−97.8935	+	169.557i	−0.309790	+	0.536571i
$317$	36.6323	+	6.45926i	0.115559	+	0.0203762i	0.231129	−	0.972923i	$-0.425758\pi$
$317$	36.6323	+	6.45926i	0.115559	+	0.0203762i	−0.115569	+	0.993299i	$0.536869\pi$
$318$	9.46816	−	8.90314i	0.0297741	−	0.0279973i
$319$	702.848	−	255.816i	2.20328	−	0.801930i
$320$	−99.2621	+	17.5026i	−0.310194	+	0.0546956i
$321$	−66.2707	+	15.5905i	−0.206451	+	0.0485685i
$322$	−41.8423	+	72.4729i	−0.129945	+	0.225071i
$323$	−79.5146	+	498.401i	−0.246175	+	1.54304i
$324$	−372.750	+	85.7374i	−1.15046	+	0.264622i
$325$	85.0233	−	71.3430i	0.261610	−	0.219517i
$326$	551.724	+	657.519i	1.69240	+	2.01693i
$327$	221.151	+	165.211i	0.676302	+	0.505233i
$328$	−48.9182	+	41.0473i	−0.149141	+	0.125144i
$329$	8.79000	−	10.4755i	0.0267173	−	0.0318405i
$330$	10.0843	+	178.228i	0.0305583	+	0.540086i
$331$	284.306			0.858929			0.429465	−	0.903084i	$-0.358702\pi$
$331$	284.306			0.858929			0.429465	+	0.903084i	$0.358702\pi$
$332$	241.000	−	287.213i	0.725903	−	0.865098i
$333$	−17.3132	+	281.196i	−0.0519917	+	0.844432i
$334$	409.580	+	709.413i	1.22629	+	2.12399i
$335$	−41.2080	+	23.7914i	−0.123009	+	0.0710192i
$336$	323.020	−	138.703i	0.961370	−	0.412806i
$337$	11.6534	−	9.77834i	0.0345797	−	0.0290158i	−0.625334	−	0.780357i	$-0.715037\pi$
$337$	11.6534	−	9.77834i	0.0345797	−	0.0290158i	0.659914	+	0.751341i	$0.270593\pi$
$338$	−148.330	−	407.533i	−0.438846	−	1.20572i
$339$	−76.5767	+	254.249i	−0.225890	+	0.749998i
$340$	25.9372	+	147.097i	0.0762857	+	0.432638i
$341$		−	520.640i		−	1.52680i
$342$	341.753	−	371.813i	0.999279	−	1.08717i
$343$	−105.925			−0.308820
$344$	121.809	−	21.4782i	0.354096	−	0.0624368i
$345$	−2.49078	−	10.5876i	−0.00721966	−	0.0306887i
$346$	12.7562	−	4.64286i	0.0368675	−	0.0134187i
$347$	370.415	+	441.443i	1.06748	+	1.27217i	0.960611	+	0.277897i	$0.0896374\pi$
$347$	370.415	+	441.443i	1.06748	+	1.27217i	0.106867	+	0.994273i	$0.465918\pi$
$348$	−621.861	−	73.7301i	−1.78696	−	0.211868i
$349$	74.5255	+	129.082i	0.213540	+	0.369863i	0.952820	−	0.303536i	$-0.0981672\pi$
$349$	74.5255	+	129.082i	0.213540	+	0.369863i	−0.739280	+	0.673398i	$0.764834\pi$
$350$	−561.338	+	324.089i	−1.60382	+	0.925968i
$351$	0.631841	−	127.076i	0.00180012	−	0.362039i
$352$	−592.510	−	497.175i	−1.68327	−	1.41243i
$353$			273.148i			0.773791i	0.922124	+	0.386896i	$0.126453\pi$
$353$			273.148i			0.773791i	−0.922124	+	0.386896i	$0.873547\pi$
$354$	−172.152	−	262.691i	−0.486304	−	0.742065i
$355$	115.799	+	97.1672i	0.326196	+	0.273711i
$356$	161.295	+	192.223i	0.453075	+	0.539953i
$357$	−292.631	−	681.498i	−0.819694	−	1.90896i
$358$	−22.4215	+	18.8139i	−0.0626298	+	0.0525527i
$359$	−73.2709	−	87.3209i	−0.204097	−	0.243234i	0.654280	−	0.756252i	$-0.272972\pi$
$359$	−73.2709	−	87.3209i	−0.204097	−	0.243234i	−0.858378	+	0.513019i	$0.828527\pi$
$360$	9.12098	−	20.9536i	0.0253361	−	0.0582043i
$361$	−51.0469	+	357.373i	−0.141404	+	0.989952i
$362$	84.0808	+	48.5441i	0.232267	+	0.134100i
$363$	−361.234	+	339.677i	−0.995135	+	0.935749i
$364$	−35.9176	−	203.699i	−0.0986746	−	0.559612i
$365$	−55.2855	−	151.896i	−0.151467	−	0.416153i
$366$	−591.701	+	139.200i	−1.61667	+	0.380329i
$367$	−34.9213	+	198.048i	−0.0951533	+	0.539641i	0.899547	+	0.436824i	$0.143897\pi$
$367$	−34.9213	+	198.048i	−0.0951533	+	0.539641i	−0.994700	+	0.102817i	$0.967214\pi$
$368$	33.1979	+	19.1668i	0.0902116	+	0.0520837i
$369$	30.4030	+	267.810i	0.0823929	+	0.725772i
$370$	−84.3321	−	70.7630i	−0.227924	−	0.191251i
$371$	−4.66937	−	12.8290i	−0.0125859	−	0.0345795i
$372$	−196.277	+	389.209i	−0.527626	+	1.04626i
$373$	357.840			0.959357			0.479678	−	0.877444i	$-0.340753\pi$
$373$	357.840			0.959357			0.479678	+	0.877444i	$0.340753\pi$
$374$	−853.213	+	1016.82i	−2.28132	+	2.71877i
$375$	50.0518	−	166.182i	0.133472	−	0.443151i
$376$	2.40006	+	2.01389i	0.00638313	+	0.00535608i
$377$	71.1594	−	195.509i	0.188752	−	0.518591i
$378$	−132.501	+	730.202i	−0.350532	+	1.93175i
$379$	−617.280			−1.62871			−0.814353	−	0.580370i	$-0.802908\pi$
$379$	−617.280			−1.62871			−0.814353	+	0.580370i	$0.802908\pi$
$380$	20.2674	+	104.897i	0.0533351	+	0.276046i
$381$	−3.55537	+	7.05017i	−0.00933168	+	0.0185044i
$382$	−753.515	−	274.257i	−1.97255	−	0.717950i
$383$	−311.484	+	54.9231i	−0.813275	+	0.143402i	−0.564791	−	0.825234i	$-0.691043\pi$
$383$	−311.484	+	54.9231i	−0.813275	+	0.143402i	−0.248484	+	0.968636i	$0.579932\pi$
$384$	79.4511	+	185.031i	0.206904	+	0.481852i
$385$	176.211	+	64.1355i	0.457691	+	0.166586i
$386$	255.859	+	702.967i	0.662847	+	1.82116i
$387$	208.365	−	478.675i	0.538410	−	1.23689i
$388$	−148.402	−	257.039i	−0.382478	−	0.662472i
$389$	−44.4787	−	122.204i	−0.114341	−	0.314150i	0.869301	−	0.494283i	$-0.164569\pi$
$389$	−44.4787	−	122.204i	−0.114341	−	0.314150i	−0.983642	+	0.180133i	$0.942347\pi$
$390$	39.7814	+	29.7188i	0.102004	+	0.0762020i
$391$	40.4375	−	70.0397i	0.103421	−	0.179130i
$392$			80.2149i			0.204630i
$393$	−198.754	−	462.871i	−0.505735	−	1.17779i
$394$	−335.566	−	122.136i	−0.851690	−	0.309990i
$395$	−48.6240	−	8.57372i	−0.123099	−	0.0217056i
$396$	689.537	−	203.946i	1.74125	−	0.515014i
$397$	308.189	−	258.601i	0.776295	−	0.651389i	−0.166018	−	0.986123i	$-0.553091\pi$
$397$	308.189	−	258.601i	0.776295	−	0.651389i	0.942313	+	0.334734i	$0.108646\pi$
$398$	87.3943	+	50.4571i	0.219584	+	0.126777i
$399$	−217.241	−	483.974i	−0.544463	−	1.21297i
$400$	148.456	+	257.134i	0.371141	+	0.642835i
$401$	−194.729	+	535.014i	−0.485609	+	1.33420i	0.419012	+	0.907981i	$0.362377\pi$
$401$	−194.729	+	535.014i	−0.485609	+	1.33420i	−0.904620	+	0.426218i	$0.859846\pi$
$402$	242.522	+	257.913i	0.603288	+	0.641575i
$403$	−110.942	−	93.0915i	−0.275291	−	0.230996i
$404$	31.1122	−	5.48592i	0.0770104	−	0.0135790i
$405$	−52.4678	−	80.9371i	−0.129550	−	0.199845i
$406$	−607.520	+	1052.26i	−1.49635	+	2.59176i
$407$		−	529.647i		−	1.30135i
$408$	156.139	−	67.0450i	0.382693	−	0.164326i
$409$	1.49899	−	8.50121i	0.00366502	−	0.0207854i	−0.982920	−	0.184031i	$-0.941085\pi$
$409$	1.49899	−	8.50121i	0.00366502	−	0.0207854i	0.986585	+	0.163246i	$0.0521964\pi$
$410$	−91.2108	−	52.6606i	−0.222465	−	0.128440i
$411$	4.44949	+	78.6399i	0.0108260	+	0.191338i
$412$	39.3584	−	223.213i	0.0955301	−	0.541778i
$413$	−324.908	+	57.2900i	−0.786702	+	0.138717i
$414$	−72.4371	+	36.0791i	−0.174969	+	0.0871476i
$415$	88.8486	+	32.3383i	0.214093	+	0.0779235i
$416$	−211.884	+	37.3609i	−0.509337	+	0.0898098i
$417$	501.251	−	28.3610i	1.20204	−	0.0680120i
$418$	−598.323	+	737.168i	−1.43140	+	1.76356i
$419$	124.165	−	71.6864i	0.296335	−	0.171089i	−0.344460	−	0.938801i	$-0.611938\pi$
$419$	124.165	−	71.6864i	0.296335	−	0.171089i	0.640795	+	0.767712i	$0.278605\pi$
$420$	−107.550	−	114.375i	−0.256071	−	0.272322i
$421$	−429.188	+	360.131i	−1.01945	+	0.855419i	−0.989558	−	0.144134i	$-0.953960\pi$
$421$	−429.188	+	360.131i	−1.01945	+	0.855419i	−0.0298906	+	0.999553i	$0.509516\pi$
$422$	−70.8457	−	12.4920i	−0.167881	−	0.0296019i
$423$	12.6808	−	3.75063i	0.0299783	−	0.00886674i
$424$	2.93926	−	1.06980i	0.00693222	−	0.00252312i
$425$	542.492	−	313.208i	1.27645	−	0.736960i
$426$	506.433	−	1004.24i	1.18881	−	2.35736i
$427$	−110.878	+	628.821i	−0.259668	+	1.47265i
$428$	−105.530	−	18.6078i	−0.246565	−	0.0434761i
$429$	13.4958	+	238.523i	0.0314586	+	0.555997i
$430$	101.999	+	176.668i	0.237208	+	0.410856i
$431$	−174.774	−	480.188i	−0.405508	−	1.11413i	−0.959526	−	0.281620i	$-0.909128\pi$
$431$	−174.774	−	480.188i	−0.405508	−	1.11413i	0.554018	−	0.832505i	$-0.313094\pi$
$432$	334.486	+	60.6952i	0.774272	+	0.140498i
$433$	98.3197	−	557.599i	0.227066	−	1.28776i	−0.631629	−	0.775271i	$-0.717613\pi$
$433$	98.3197	−	557.599i	0.227066	−	1.28776i	0.858695	−	0.512486i	$-0.171275\pi$
$434$	543.651	+	647.898i	1.25265	+	1.49285i
$435$	−36.1644	−	153.724i	−0.0831365	−	0.353390i
$436$	217.250	+	376.288i	0.498280	+	0.863047i
$437$	28.1020	−	50.5630i	0.0643067	−	0.115705i
$438$	−1005.91	+	659.212i	−2.29660	+	1.50505i
$439$	33.2122	+	188.356i	0.0756542	+	0.429056i	0.998985	+	0.0450501i	$0.0143448\pi$
$439$	33.2122	+	188.356i	0.0756542	+	0.429056i	−0.923331	+	0.384006i	$0.874544\pi$
$440$	−14.6942	+	40.3719i	−0.0333958	+	0.0917543i
$441$	282.251	+	186.983i	0.640025	+	0.423997i
$442$	64.1158	+	363.619i	0.145058	+	0.822667i
$443$	201.656	+	35.5574i	0.455205	+	0.0802650i	0.396550	−	0.918013i	$-0.370207\pi$
$443$	201.656	+	35.5574i	0.455205	+	0.0802650i	0.0586557	+	0.998278i	$0.481319\pi$
$444$	−199.673	+	395.943i	−0.449713	+	0.891764i
$445$	−31.6401	+	54.8022i	−0.0711013	+	0.123151i
$446$	−677.666	−	119.491i	−1.51943	−	0.267916i
$447$	285.096	−	381.629i	0.637799	−	0.853756i
$448$	787.763			1.75840
$449$	467.872	+	270.126i	1.04203	+	0.601617i	0.920408	−	0.390959i	$-0.127857\pi$
$449$	467.872	+	270.126i	1.04203	+	0.601617i	0.121624	+	0.992576i	$0.461190\pi$
$450$	−625.618	−	38.5193i	−1.39026	−	0.0855985i
$451$	−87.9901	−	499.017i	−0.195100	−	1.10647i
$452$	−268.651	+	320.166i	−0.594361	+	0.708332i
$453$	−17.1538	−	72.9159i	−0.0378671	−	0.160962i
$454$	446.788	+	162.618i	0.984116	+	0.358189i
$455$	45.1734	−	26.0809i	0.0992822	−	0.0573206i
$456$	110.884	−	49.7722i	0.243166	−	0.109150i
$457$	455.914	−	789.667i	0.997624	−	1.72794i	0.439153	−	0.898412i	$-0.355278\pi$
$457$	455.914	−	789.667i	0.997624	−	1.72794i	0.558471	−	0.829524i	$-0.311388\pi$
$458$	212.507	+	253.256i	0.463989	+	0.552960i
$459$	128.053	−	705.686i	0.278982	−	1.53744i
$460$	2.97283	−	16.8598i	0.00646268	−	0.0366517i
$461$	−29.9111	+	82.1801i	−0.0648831	+	0.178265i	−0.967897	−	0.251346i	$-0.919127\pi$
$461$	−29.9111	+	82.1801i	−0.0648831	+	0.178265i	0.903014	+	0.429611i	$0.141349\pi$
$462$	164.268	−	1385.49i	0.355559	−	2.99889i
$463$	352.413			0.761150			0.380575	−	0.924750i	$-0.375726\pi$
$463$	352.413			0.761150			0.380575	+	0.924750i	$0.375726\pi$
$464$	482.009	+	278.288i	1.03881	+	0.599759i
$465$	−109.162	−	12.9426i	−0.234757	−	0.0278336i
$466$	−175.438	+	63.8543i	−0.376477	+	0.137026i
$467$	−581.725	+	335.859i	−1.24566	+	0.719184i	−0.970242	−	0.242139i	$-0.922151\pi$
$467$	−581.725	+	335.859i	−1.24566	+	0.719184i	−0.275422	+	0.961323i	$0.588818\pi$
$468$	79.8322	−	183.398i	0.170582	−	0.391876i
$469$	349.462	−	127.194i	0.745121	−	0.271202i
$470$	−1.76733	+	4.85570i	−0.00376028	+	0.0103313i
$471$	71.7817	−	605.428i	0.152403	−	1.28541i
$472$	−13.1258	−	74.4400i	−0.0278089	−	0.157712i
$473$	−335.681	+	922.277i	−0.709686	+	1.94985i
$474$	20.7520	+	366.769i	0.0437805	+	0.773774i
$475$	384.320	−	230.334i	0.809095	−	0.484913i
$476$		−	1167.39i		−	2.45250i
$477$	3.08718	−	12.8361i	0.00647208	−	0.0269100i
$478$	1140.58	+	415.137i	2.38615	+	0.868488i
$479$	−293.263	+	349.497i	−0.612240	+	0.729639i	−0.979715	−	0.200394i	$-0.935778\pi$
$479$	−293.263	+	349.497i	−0.612240	+	0.729639i	0.367476	+	0.930033i	$0.380222\pi$
$480$	−118.971	+	111.871i	−0.247857	+	0.233066i
$481$	−112.862	−	94.7021i	−0.234639	−	0.196886i
$482$		−	666.884i		−	1.38358i
$483$	4.80210	+	84.8719i	0.00994223	+	0.175718i
$484$	−733.406	+	266.938i	−1.51530	+	0.551525i
$485$	48.1118	−	57.3374i	0.0991996	−	0.118221i
$486$	−496.792	+	517.903i	−1.02221	+	1.06564i
$487$	−198.987	+	344.656i	−0.408598	+	0.707712i	−0.994733	−	0.102501i	$-0.967315\pi$
$487$	−198.987	+	344.656i	−0.408598	+	0.707712i	0.586135	+	0.810213i	$0.300649\pi$
$488$	−144.070	−	25.4034i	−0.295225	−	0.0520562i
$489$	834.856	+	251.448i	1.70727	+	0.514209i
$490$	−124.320	+	45.2486i	−0.253713	+	0.0923441i
$491$	416.614	−	73.4603i	0.848501	−	0.149614i	0.267542	−	0.963546i	$-0.413789\pi$
$491$	416.614	−	73.4603i	0.848501	−	0.149614i	0.580959	+	0.813933i	$0.302678\pi$
$492$	−122.347	+	406.217i	−0.248673	+	0.825644i
$493$	587.123	−	1016.93i	1.19092	−	2.06273i
$494$	50.1003	+	259.303i	0.101418	+	0.524905i
$495$	107.804	+	145.812i	0.217785	+	0.294569i
$496$	296.784	−	249.032i	0.598355	−	0.502080i
$497$	−759.422	−	905.044i	−1.52801	−	1.82101i
$498$	82.8270	−	698.587i	0.166319	−	1.40279i
$499$	−228.198	+	191.481i	−0.457311	+	0.383729i	−0.842140	−	0.539258i	$-0.818705\pi$
$499$	−228.198	+	191.481i	−0.457311	+	0.383729i	0.384830	+	0.922988i	$0.374260\pi$
$500$	175.595	−	209.266i	0.351190	−	0.418532i
$501$	742.982	+	374.683i	1.48300	+	0.747870i
$502$	−613.690			−1.22249
$503$	−51.3607	+	61.2093i	−0.102109	+	0.121688i	−0.814679	−	0.579913i	$-0.803087\pi$
$503$	−51.3607	+	61.2093i	−0.102109	+	0.121688i	0.712570	+	0.701601i	$0.247531\pi$
$504$	−98.6406	+	148.898i	−0.195715	+	0.295433i
$505$	3.98350	+	6.89962i	0.00788811	+	0.0136626i
$506$	131.756	−	76.0691i	0.260386	−	0.150334i
$507$	−352.935	−	263.660i	−0.696124	−	0.520040i
$508$	−9.52055	+	7.98869i	−0.0187412	+	0.0157258i
$509$	194.928	+	535.561i	0.382963	+	1.05218i	0.970102	+	0.242696i	$0.0780318\pi$
$509$	194.928	+	535.561i	0.382963	+	1.05218i	−0.587139	+	0.809486i	$0.699746\pi$
$510$	191.985	+	204.169i	0.376441	+	0.400332i
$511$	219.378	+	1244.15i	0.429311	+	2.43474i
$512$		−	682.950i		−	1.33389i
$513$	83.3395	−	506.185i	0.162455	−	0.986716i
$514$	−266.751			−0.518972
$515$	56.2904	−	9.92551i	0.109302	−	0.0192728i
$516$	598.633	−	562.908i	1.16014	−	1.09091i
$517$	−23.3615	+	8.50288i	−0.0451866	+	0.0164466i
$518$	553.057	+	659.107i	1.06768	+	1.27241i
$519$	8.25282	−	11.0472i	0.0159014	−	0.0212855i
$520$	5.97542	+	10.3497i	0.0114912	+	0.0199033i
$521$	−447.248	+	258.219i	−0.858442	+	0.495622i	−0.863490	−	0.504365i	$-0.831726\pi$
$521$	−447.248	+	258.219i	−0.858442	+	0.495622i	0.00504819	+	0.999987i	$0.498393\pi$
$522$	−1051.74	+	523.843i	−2.01482	+	1.00353i
$523$	−367.855	−	308.667i	−0.703356	−	0.590186i	0.219370	−	0.975642i	$-0.429600\pi$
$523$	−367.855	−	308.667i	−0.703356	−	0.590186i	−0.922726	+	0.385456i	$0.874044\pi$
$524$		−	792.886i		−	1.51314i
$525$	−296.476	+	587.900i	−0.564716	+	1.11981i
$526$	1120.28	+	940.024i	2.12980	+	1.78712i
$527$	−525.398	−	626.145i	−0.996961	−	1.18813i
$528$	−634.654	−	75.2469i	−1.20200	−	0.142513i
$529$	398.137	−	334.076i	0.752621	−	0.631524i
$530$	3.31603	+	3.95189i	0.00625667	+	0.00745641i
$531$	−292.528	−	127.336i	−0.550899	−	0.239804i
$532$	−13.6322	−	834.888i	−0.0256244	−	1.56934i
$533$	−122.067	−	70.4756i	−0.229019	−	0.132224i
$534$	450.816	+	135.780i	0.844225	+	0.254270i
$535$	−4.69256	−	26.6128i	−0.00877114	−	0.0497436i
$536$	29.1415	+	80.0656i	0.0543685	+	0.149376i
$537$	−8.57441	+	28.4687i	−0.0159672	+	0.0530144i
$538$	184.487	−	1046.28i	0.342913	−	1.94476i
$539$	−551.229	−	318.252i	−1.02269	−	0.590450i
$540$	−25.6198	−	149.644i	−0.0474440	−	0.277119i
$541$	−665.764	−	558.642i	−1.23062	−	1.03261i	−0.998199	−	0.0599938i	$-0.980892\pi$
$541$	−665.764	−	558.642i	−1.23062	−	1.03261i	−0.232418	−	0.972616i	$-0.574664\pi$
$542$	52.1571	+	143.300i	0.0962308	+	0.264392i
$543$	98.4657	−	5.57124i	0.181337	−	0.0102601i
$544$	−1214.30			−2.23217
$545$	−70.4325	+	83.9382i	−0.129234	+	0.154015i
$546$	−265.859	−	282.732i	−0.486922	−	0.517824i
$547$	−455.271	−	382.018i	−0.832305	−	0.698387i	0.123514	−	0.992343i	$-0.460584\pi$
$547$	−455.271	−	382.018i	−0.832305	−	0.698387i	−0.955819	+	0.293956i	$0.905028\pi$
$548$	−42.4028	+	116.501i	−0.0773773	+	0.212593i
$549$	−425.217	+	447.721i	−0.774530	+	0.815521i
$550$	1178.39			2.14252
$551$	408.021	−	734.138i	0.740511	−	1.33237i
$552$	−19.4451	+	1.10021i	−0.0352266	+	0.00199314i
$553$	362.617	+	131.982i	0.655727	+	0.238665i
$554$	−1139.07	+	200.849i	−2.05608	+	0.362543i
$555$	−111.050	−	13.1665i	−0.200091	−	0.0237235i
$556$	742.575	+	270.275i	1.33557	+	0.486107i
$557$	211.500	+	581.091i	0.379712	+	1.04325i	0.971476	+	0.237140i	$0.0762099\pi$
$557$	211.500	+	581.091i	0.379712	+	1.04325i	−0.591763	+	0.806112i	$0.701568\pi$
$558$	92.2568	+	812.659i	0.165335	+	1.45638i
$559$	136.506	+	236.435i	0.244196	+	0.422960i
$560$	47.7252	+	131.124i	0.0852237	+	0.234150i
$561$	−158.753	+	1338.97i	−0.282983	+	2.38676i
$562$	299.671	−	519.045i	0.533222	−	0.923567i
$563$		−	439.779i		−	0.781135i	−0.920574	−	0.390567i	$-0.872279\pi$
$563$		−	439.779i		−	0.781135i	0.920574	−	0.390567i	$-0.127721\pi$
$564$	20.6696	+	2.45067i	0.0366483	+	0.00434515i
$565$	−99.0427	−	36.0486i	−0.175297	−	0.0638028i
$566$	−260.911	−	46.0056i	−0.460973	−	0.0812820i
$567$	293.993	+	694.171i	0.518506	+	1.22429i
$568$	207.356	−	173.992i	0.365063	−	0.306324i
$569$	380.108	+	219.456i	0.668028	+	0.385686i	0.795329	−	0.606178i	$-0.207298\pi$
$569$	380.108	+	219.456i	0.668028	+	0.385686i	−0.127301	+	0.991864i	$0.540631\pi$
$570$	139.687	+	143.775i	0.245066	+	0.252237i
$571$	403.585	+	699.030i	0.706805	+	1.22422i	0.966036	+	0.258406i	$0.0831973\pi$
$571$	403.585	+	699.030i	0.706805	+	1.22422i	−0.259232	+	0.965815i	$0.583469\pi$
$572$	−128.612	+	353.359i	−0.224846	+	0.617760i
$573$	−792.906	+	186.535i	−1.38378	+	0.325541i
$574$	630.569	+	529.111i	1.09855	+	0.921795i
$575$	−70.7070	+	12.4676i	−0.122969	+	0.0216827i
$576$	635.071	+	420.715i	1.10255	+	0.730408i
$577$	−493.685	+	855.088i	−0.855607	+	1.48195i	0.0204739	+	0.999790i	$0.493483\pi$
$577$	−493.685	+	855.088i	−0.855607	+	1.48195i	−0.876081	+	0.482164i	$0.839851\pi$
$578$			1230.38i			2.12869i
$579$	608.788	+	454.796i	1.05145	+	0.785486i
$580$	43.1634	−	244.792i	0.0744197	−	0.422055i
$581$	−639.969	−	369.486i	−1.10150	−	0.635949i
$582$	−497.242	−	250.757i	−0.854368	−	0.430854i
$583$	−4.30993	+	24.4428i	−0.00739267	+	0.0419259i
$584$	−285.050	+	50.2620i	−0.488099	+	0.0860650i
$585$	50.3463	+	3.09982i	0.0860620	+	0.00529884i
$586$	−1287.65	−	468.664i	−2.19735	−	0.799769i
$587$	−352.117	+	62.0877i	−0.599858	+	0.105771i	−0.465328	−	0.885138i	$-0.654064\pi$
$587$	−352.117	+	62.0877i	−0.599858	+	0.105771i	−0.134530	+	0.990910i	$0.542952\pi$
$588$	292.099	+	445.722i	0.496767	+	0.758030i
$589$	−383.064	−	441.669i	−0.650364	−	0.749862i
$590$	107.965	−	62.3338i	0.182992	−	0.105651i
$591$	−353.108	+	83.0703i	−0.597475	+	0.140559i
$592$	301.919	−	253.340i	0.509998	−	0.427939i
$593$	66.0939	+	11.6541i	0.111457	+	0.0196529i	0.229098	−	0.973403i	$-0.426422\pi$
$593$	66.0939	+	11.6541i	0.111457	+	0.0196529i	−0.117641	+	0.993056i	$0.537533\pi$
$594$	872.366	−	1029.21i	1.46863	−	1.73268i
$595$	276.641	−	100.689i	0.464943	−	0.169225i
$596$	649.341	−	374.897i	1.08950	−	0.629023i
$597$	102.346	−	5.79080i	0.171434	−	0.00969983i
$598$	7.34875	−	41.6769i	0.0122889	−	0.0696937i
$599$	585.454	+	103.231i	0.977386	+	0.172340i	0.639453	−	0.768830i	$-0.279161\pi$
$599$	585.454	+	103.231i	0.977386	+	0.172340i	0.337933	+	0.941170i	$0.390272\pi$
$600$	−134.695	−	67.9259i	−0.224491	−	0.113210i
$601$	−314.004	−	543.871i	−0.522469	−	0.904943i	−0.999658	−	0.0261423i	$-0.991678\pi$
$601$	−314.004	−	543.871i	−0.522469	−	0.904943i	0.477189	−	0.878801i	$-0.341656\pi$
$602$	−545.309	−	1498.22i	−0.905828	−	2.48874i
$603$	349.655	+	84.0949i	0.579859	+	0.139461i
$604$	20.4737	−	116.112i	0.0338968	−	0.192238i
$605$	−126.515	−	150.775i	−0.209116	−	0.249214i
$606$	43.1834	−	40.6064i	0.0712598	−	0.0670073i
$607$	−5.39599	−	9.34612i	−0.00888960	−	0.0153972i	0.861546	−	0.507679i	$-0.169496\pi$
$607$	−5.39599	−	9.34612i	−0.00888960	−	0.0153972i	−0.870436	+	0.492282i	$0.836163\pi$
$608$	−868.437	+	14.1800i	−1.42835	+	0.0233223i
$609$	69.7231	+	1232.28i	0.114488	+	2.02345i
$610$	−41.8978	−	237.614i	−0.0686849	−	0.389531i
$611$	−2.36522	+	6.49839i	−0.00387106	+	0.0106357i
$612$	623.459	−	941.114i	1.01872	−	1.53777i
$613$	−62.9451	−	356.979i	−0.102684	−	0.582348i	−0.992120	−	0.125289i	$-0.960014\pi$
$613$	−62.9451	−	356.979i	−0.102684	−	0.582348i	0.889437	−	0.457059i	$-0.151097\pi$
$614$	−1031.89	−	181.950i	−1.68060	−	0.296335i
$615$	−106.816	+	6.04368i	−0.173684	+	0.00982712i
$616$	167.891	−	290.795i	0.272550	−	0.472070i
$617$	603.514	+	106.416i	0.978142	+	0.172473i	0.639793	−	0.768548i	$-0.279020\pi$
$617$	603.514	+	106.416i	0.978142	+	0.172473i	0.338350	+	0.941020i	$0.390131\pi$
$618$	−167.795	−	390.773i	−0.271513	−	0.632319i
$619$	66.0182			0.106653			0.0533265	−	0.998577i	$-0.483018\pi$
$619$	66.0182			0.106653			0.0533265	+	0.998577i	$0.483018\pi$
$620$	−149.844	−	86.5123i	−0.241683	−	0.139536i
$621$	−41.4556	+	70.9858i	−0.0667563	+	0.114309i
$622$	−191.725	−	1087.33i	−0.308240	−	1.74811i
$623$	317.906	−	378.865i	0.510282	−	0.608131i
$624$	−129.512	+	121.783i	−0.207551	+	0.195165i
$625$	−489.259	−	178.076i	−0.782815	−	0.284921i
$626$	502.132	−	289.906i	0.802128	−	0.463109i
$627$	−97.9008	+	959.455i	−0.156142	+	1.53023i
$628$	479.810	−	831.055i	0.764028	−	1.32334i
$629$	−534.488	−	636.979i	−0.849743	−	1.01268i
$630$	−286.410	−	68.8839i	−0.454619	−	0.109340i
$631$	−2.83805	+	16.0954i	−0.00449771	+	0.0255078i	−0.986974	−	0.160880i	$-0.948567\pi$
$631$	−2.83805	+	16.0954i	−0.00449771	+	0.0255078i	0.982476	+	0.186387i	$0.0596780\pi$
$632$	−30.2385	+	83.0796i	−0.0478458	+	0.131455i
$633$	−67.1474	+	28.8327i	−0.106078	+	0.0455492i
$634$	109.855			0.173273
$635$	−2.71428	−	1.56709i	−0.00427445	−	0.00246786i
$636$	12.4367	−	16.6477i	0.0195545	−	0.0261756i
$637$	−166.377	+	60.5562i	−0.261188	+	0.0950647i
$638$	1913.00	−	1104.47i	2.99843	−	1.73114i
$639$	−128.873	−	1135.20i	−0.201679	−	1.77652i
$640$	−75.1098	+	27.3377i	−0.117359	+	0.0427152i
$641$	−357.276	+	981.609i	−0.557373	+	1.53137i	0.266059	+	0.963957i	$0.414278\pi$
$641$	−357.276	+	981.609i	−0.557373	+	1.53137i	−0.823432	+	0.567414i	$0.807944\pi$
$642$	−184.749	+	79.3299i	−0.287771	+	0.123567i
$643$	−192.353	−	1090.89i	−0.299149	−	1.69656i	−0.649843	−	0.760069i	$-0.725165\pi$
$643$	−192.353	−	1090.89i	−0.299149	−	1.69656i	0.350694	−	0.936490i	$-0.385946\pi$
$644$	−45.7631	+	125.733i	−0.0710607	+	0.195238i
$645$	185.028	+	93.3088i	0.286865	+	0.144665i
$646$	24.3345	+	1490.34i	0.0376696	+	2.30704i
$647$			650.620i			1.00559i	0.864404	+	0.502797i	$0.167696\pi$
$647$			650.620i			1.00559i	−0.864404	+	0.502797i	$0.832304\pi$
$648$	−159.042	+	67.3571i	−0.245436	+	0.103946i
$649$	563.622	+	205.142i	0.868447	+	0.316089i
$650$	210.698	−	251.100i	0.324150	−	0.386307i
$651$	822.640	+	247.769i	1.26366	+	0.380597i
$652$	1051.30	+	882.146i	1.61242	+	1.35298i
$653$		−	234.187i		−	0.358632i	−0.983792	−	0.179316i	$-0.942612\pi$
$653$		−	234.187i		−	0.358632i	0.983792	−	0.179316i	$-0.0573885\pi$
$654$	727.930	+	367.092i	1.11304	+	0.561303i
$655$	187.894	−	68.3877i	0.286860	−	0.104409i
$656$	242.371	−	288.847i	0.369468	−	0.440315i
$657$	−487.601	+	1120.16i	−0.742163	+	1.70497i
$658$	20.1929	−	34.9752i	0.0306884	−	0.0531538i
$659$	556.566	+	98.1376i	0.844561	+	0.148919i	0.579155	−	0.815218i	$-0.303383\pi$
$659$	556.566	+	98.1376i	0.844561	+	0.148919i	0.265406	+	0.964137i	$0.414494\pi$
$660$	65.3627	+	277.838i	0.0990345	+	0.420967i
$661$	623.759	−	227.030i	0.943659	−	0.343464i	0.176049	−	0.984381i	$-0.443668\pi$
$661$	623.759	−	227.030i	0.943659	−	0.343464i	0.767610	+	0.640918i	$0.221446\pi$
$662$	826.885	−	145.802i	1.24907	−	0.220245i
$663$	256.934	+	273.240i	0.387532	+	0.412126i
$664$	84.6534	−	146.624i	0.127490	−	0.220819i
$665$	196.671	−	75.2409i	0.295746	−	0.113144i
$666$	93.8529	+	826.720i	0.140920	+	1.24132i
$667$	−103.101	+	86.5118i	−0.154574	+	0.129703i
$668$	841.889	+	1003.32i	1.26031	+	1.50198i
$669$	−642.291	+	275.796i	−0.960076	+	0.412250i
$670$	−107.650	+	90.3289i	−0.160671	+	0.134819i
$671$	746.168	−	889.248i	1.11202	−	1.32526i
$672$	1067.54	−	699.597i	1.58859	−	1.04107i
$673$	−604.022			−0.897507			−0.448753	−	0.893656i	$-0.648132\pi$
$673$	−604.022			−0.897507			−0.448753	+	0.893656i	$0.648132\pi$
$674$	28.8784	−	34.4160i	0.0428463	−	0.0510623i
$675$	−552.986	+	315.611i	−0.819238	+	0.467572i
$676$	−346.709	−	600.518i	−0.512884	−	0.888341i
$677$	−40.3230	+	23.2805i	−0.0595613	+	0.0343877i	−0.529485	−	0.848319i	$-0.677615\pi$
$677$	−40.3230	+	23.2805i	−0.0595613	+	0.0343877i	0.469924	+	0.882707i	$0.344281\pi$
$678$	−92.3302	+	778.740i	−0.136180	+	1.14858i
$679$	−448.127	+	376.023i	−0.659981	+	0.553790i
$680$	23.0690	+	63.3815i	0.0339250	+	0.0932082i
$681$	470.145	−	110.604i	0.690375	−	0.162414i
$682$	−267.003	−	1514.25i	−0.391500	−	2.22031i
$683$		−	673.719i		−	0.986411i	−0.869913	−	0.493205i	$-0.835825\pi$
$683$		−	673.719i		−	0.986411i	0.869913	−	0.493205i	$-0.164175\pi$
$684$	434.893	−	680.342i	0.635809	−	0.994653i
$685$	−31.2650			−0.0456423
$686$	−308.077	+	54.3224i	−0.449092	+	0.0791871i
$687$	321.561	+	96.8499i	0.468065	+	0.140975i
$688$	−686.295	+	249.791i	−0.997522	+	0.363068i
$689$	4.43785	+	5.28882i	0.00644100	+	0.00767608i
$690$	−12.6740	−	29.5160i	−0.0183681	−	0.0427768i
$691$	−72.6446	−	125.824i	−0.105130	−	0.182090i	0.808661	−	0.588274i	$-0.200192\pi$
$691$	−72.6446	−	125.824i	−0.105130	−	0.182090i	−0.913791	+	0.406184i	$0.866859\pi$
$692$	18.7968	−	10.8523i	0.0271630	−	0.0156826i
$693$	−631.860	−	1268.60i	−0.911775	−	1.83060i
$694$	1303.72	+	1093.95i	1.87855	+	1.57629i
$695$			199.283i			0.286738i
$696$	−282.329	+	15.9743i	−0.405645	+	0.0229516i
$697$	−609.399	−	511.346i	−0.874317	−	0.733639i
$698$	282.951	+	337.208i	0.405374	+	0.483105i
$699$	−113.503	+	151.934i	−0.162379	+	0.217359i
$700$	−793.902	+	666.163i	−1.13415	+	0.951661i
$701$	120.805	+	143.970i	0.172333	+	0.205378i	0.845297	−	0.534297i	$-0.179424\pi$
$701$	120.805	+	143.970i	0.172333	+	0.205378i	−0.672964	+	0.739675i	$0.734979\pi$
$702$	−63.3313	−	369.916i	−0.0902156	−	0.526945i
$703$	−389.692	−	449.310i	−0.554327	−	0.639133i
$704$	−1240.28	−	716.075i	−1.76176	−	1.01715i
$705$	1.20204	+	5.10954i	0.00170503	+	0.00724758i
$706$	140.080	+	794.435i	0.198414	+	1.12526i
$707$	−21.2966	−	58.5118i	−0.0301224	−	0.0827607i
$708$	−344.005	−	365.836i	−0.485882	−	0.516718i
$709$	−146.697	+	831.960i	−0.206907	+	1.17343i	0.687504	+	0.726181i	$0.258706\pi$
$709$	−146.697	+	831.960i	−0.206907	+	1.17343i	−0.894411	+	0.447246i	$0.852405\pi$
$710$	386.626	+	223.219i	0.544544	+	0.314393i
$711$	221.845	+	300.060i	0.312018	+	0.422026i
$712$	86.8023	+	72.8357i	0.121913	+	0.102297i
$713$	32.0421	+	88.0350i	0.0449399	+	0.123471i
$714$	−1200.59	−	1832.02i	−1.68151	−	2.56586i
$715$	−94.8299			−0.132629
$716$	−30.0813	+	35.8495i	−0.0420130	+	0.0500691i
$717$	1200.21	−	282.354i	1.67393	−	0.393799i
$718$	−257.885	−	216.391i	−0.359172	−	0.301381i
$719$	144.197	−	396.178i	0.200552	−	0.551013i	−0.798122	−	0.602496i	$-0.794173\pi$
$719$	144.197	−	396.178i	0.200552	−	0.551013i	0.998674	+	0.0514837i	$0.0163950\pi$
$720$	−31.5538	+	131.197i	−0.0438248	+	0.182217i
$721$	−446.731			−0.619599
$722$	34.8070	+	1065.57i	0.0482091	+	1.47587i
$723$	−371.314	−	566.599i	−0.513574	−	0.783678i
$724$	145.872	+	53.0929i	0.201480	+	0.0733327i
$725$	−1026.62	+	181.020i	−1.41602	+	0.249683i
$726$	−876.428	+	1173.18i	−1.20720	+	1.61595i
$727$	−1172.50	−	426.755i	−1.61279	−	0.587009i	−0.630803	−	0.775943i	$-0.717275\pi$
$727$	−1172.50	−	426.755i	−1.61279	−	0.587009i	−0.981990	+	0.188934i	$0.939497\pi$
$728$	−31.9458	−	87.7703i	−0.0438815	−	0.120564i
$729$	−133.722	+	716.631i	−0.183433	+	0.983032i
$730$	−238.692	−	413.427i	−0.326975	−	0.566338i
$731$	527.001	+	1447.92i	0.720931	+	1.98074i
$732$	−893.044	+	383.467i	−1.22001	+	0.523863i
$733$	−328.905	+	569.680i	−0.448711	+	0.777190i	−0.998302	−	0.0582435i	$-0.981450\pi$
$733$	−328.905	+	569.680i	−0.448711	+	0.777190i	0.549592	+	0.835433i	$0.314783\pi$
$734$			593.920i			0.809156i
$735$	−80.4306	+	107.664i	−0.109429	+	0.146482i
$736$	130.786	+	47.6020i	0.177698	+	0.0646767i
$737$	−665.823	−	117.403i	−0.903423	−	0.159298i
$738$	225.768	+	763.317i	0.305918	+	1.03430i
$739$	607.917	−	510.103i	0.822620	−	0.690261i	−0.130964	−	0.991387i	$-0.541807\pi$
$739$	607.917	−	510.103i	0.822620	−	0.690261i	0.953584	+	0.301127i	$0.0973627\pi$
$740$	−152.436	−	88.0091i	−0.205995	−	0.118931i
$741$	186.944	+	192.414i	0.252285	+	0.259668i
$742$	−20.1597	−	34.9177i	−0.0271694	−	0.0470589i
$743$	162.905	−	447.577i	0.219253	−	0.602391i	−0.780488	−	0.625171i	$-0.785029\pi$
$743$	162.905	−	447.577i	0.219253	−	0.602391i	0.999741	+	0.0227793i	$0.00725152\pi$
$744$	−56.7666	+	188.476i	−0.0762991	+	0.253328i
$745$	144.848	+	121.542i	0.194427	+	0.163143i
$746$	1040.76	−	183.513i	1.39511	−	0.245996i
$747$	−318.595	−	639.652i	−0.426499	−	0.856295i
$748$	−1061.15	+	1837.97i	−1.41866	+	2.45718i
$749$			211.204i			0.281982i
$750$	60.3486	−	508.998i	0.0804648	−	0.678664i
$751$	119.508	−	677.766i	0.159132	−	0.902484i	−0.795778	−	0.605589i	$-0.792938\pi$
$751$	119.508	−	677.766i	0.159132	−	0.902484i	0.954910	−	0.296895i	$-0.0959512\pi$
$752$	−16.0212	−	9.24984i	−0.0213048	−	0.0123003i
$753$	−521.404	+	341.696i	−0.692436	+	0.453780i
$754$	106.699	−	605.118i	0.141510	−	0.802544i
$755$	29.2814	−	5.16310i	0.0387833	−	0.00683855i
$756$	−5.89978	+	1186.56i	−0.00780395	+	1.56953i
$757$	854.482	+	311.006i	1.12877	+	0.410840i	0.837847	−	0.545905i	$-0.183814\pi$
$757$	854.482	+	311.006i	1.12877	+	0.410840i	0.290927	+	0.956745i	$0.406036\pi$
$758$	−1795.32	+	316.563i	−2.36849	+	0.417630i
$759$	69.5879	−	137.990i	0.0916836	−	0.181805i
$760$	17.2385	+	45.0596i	0.0226823	+	0.0592889i
$761$	−90.4690	+	52.2323i	−0.118882	+	0.0686364i	−0.558262	−	0.829665i	$-0.688531\pi$
$761$	−90.4690	+	52.2323i	−0.118882	+	0.0686364i	0.439380	+	0.898301i	$0.355198\pi$
$762$	−6.72499	+	22.3283i	−0.00882545	+	0.0293022i
$763$	656.029	−	550.473i	0.859802	−	0.721459i
$764$	−1262.63	−	222.636i	−1.65266	−	0.291408i
$765$	276.794	+	66.5712i	0.361822	+	0.0870212i
$766$	−877.766	+	319.481i	−1.14591	+	0.417077i
$767$	144.490	−	83.4213i	0.188383	−	0.108763i
$768$	−230.767	−	352.134i	−0.300478	−	0.458508i
$769$	171.349	−	971.767i	0.222820	−	1.26368i	−0.643989	−	0.765035i	$-0.722722\pi$
$769$	171.349	−	971.767i	0.222820	−	1.26368i	0.866809	−	0.498641i	$-0.166167\pi$
$770$	545.389	+	96.1668i	0.708298	+	0.124892i
$771$	−226.638	+	148.524i	−0.293953	+	0.192639i
$772$	598.050	+	1035.85i	0.774677	+	1.34178i
$773$	218.844	+	601.268i	0.283109	+	0.777837i	0.996987	+	0.0775664i	$0.0247150\pi$
$773$	218.844	+	601.268i	0.283109	+	0.777837i	−0.713878	+	0.700270i	$0.753063\pi$
$774$	360.534	−	1499.05i	0.465806	−	1.93676i
$775$	−126.005	+	714.612i	−0.162587	+	0.922079i
$776$	−86.1511	−	102.671i	−0.111020	−	0.132308i
$777$	836.873	+	252.055i	1.07706	+	0.324396i
$778$	−192.034	−	332.613i	−0.246831	−	0.427523i
$779$	−441.799	−	358.586i	−0.567136	−	0.460316i
$780$	70.8910	+	35.7501i	0.0908860	+	0.0458334i
$781$	372.974	+	2115.24i	0.477560	+	2.70838i
$782$	81.6909	−	224.444i	0.104464	−	0.287013i
$783$	−601.907	+	1030.66i	−0.768718	+	1.31630i
$784$	−82.2473	−	466.448i	−0.104907	−	0.594959i
$785$	238.323	+	42.0228i	0.303596	+	0.0535322i
$786$	−815.440	−	1244.30i	−1.03746	−	1.58308i
$787$	−101.121	+	175.146i	−0.128489	+	0.222549i	−0.923091	−	0.384581i	$-0.874346\pi$
$787$	−101.121	+	175.146i	−0.128489	+	0.222549i	0.794603	+	0.607130i	$0.207679\pi$
$788$	−562.292	−	99.1472i	−0.713568	−	0.125821i
$789$	1475.21	+	174.906i	1.86972	+	0.221680i
$790$	−145.817			−0.184578
$791$	713.396	+	411.879i	0.901891	+	0.520707i
$792$	290.651	−	144.766i	0.366984	−	0.182785i
$793$	−56.0718	−	317.999i	−0.0707084	−	0.401007i
$794$	763.729	−	910.176i	0.961875	−	1.14632i
$795$	5.01775	+	1.51128i	0.00631163	+	0.00190098i
$796$	151.620	+	55.1852i	0.190478	+	0.0693282i
$797$	−590.702	+	341.042i	−0.741157	+	0.427907i	−0.822490	−	0.568780i	$-0.807416\pi$
$797$	−590.702	+	341.042i	−0.741157	+	0.427907i	0.0813326	+	0.996687i	$0.474082\pi$
$798$	−880.030	−	1296.20i	−1.10279	−	1.62431i
$799$	−19.5150	+	33.8010i	−0.0244243	+	0.0423041i
$800$	692.932	+	825.804i	0.866165	+	1.03225i
$801$	458.624	−	135.648i	0.572564	−	0.169349i
$802$	−291.983	+	1655.92i	−0.364069	+	2.06474i
$803$	785.539	−	2158.25i	0.978255	−	2.68773i
$804$	453.483	+	338.775i	0.564033	+	0.421362i
$805$	−33.7426			−0.0419163
$806$	−370.409	−	213.856i	−0.459564	−	0.265330i
$807$	−425.814	−	991.663i	−0.527650	−	1.22883i
$808$	13.4057	−	4.87928i	0.0165912	−	0.00603871i
$809$	−524.543	+	302.845i	−0.648384	+	0.374345i	−0.787837	−	0.615884i	$-0.788799\pi$
$809$	−524.543	+	302.845i	−0.648384	+	0.374345i	0.139453	+	0.990229i	$0.455466\pi$
$810$	−194.107	−	208.493i	−0.239638	−	0.257399i
$811$	1175.30	−	427.775i	1.44920	−	0.527466i	0.506833	−	0.862044i	$-0.330816\pi$
$811$	1175.30	−	427.775i	1.44920	−	0.527466i	0.942368	+	0.334578i	$0.108594\pi$
$812$	−664.448	+	1825.56i	−0.818285	+	2.24822i
$813$	124.102	+	92.7106i	0.152647	+	0.114035i
$814$	−271.622	−	1540.45i	−0.333688	−	1.89244i
$815$	−118.370	+	325.218i	−0.145239	+	0.399040i
$816$	−839.199	+	549.960i	−1.02843	+	0.673970i
$817$	393.806	+	1029.37i	0.482015	+	1.25993i
$818$		−	25.4940i		−	0.0311662i
$819$	−383.302	−	92.1873i	−0.468013	−	0.112561i
$820$	−158.241	−	57.5952i	−0.192977	−	0.0702380i
$821$	932.311	−	1111.09i	1.13558	−	1.35333i	0.208698	−	0.977980i	$-0.433078\pi$
$821$	932.311	−	1111.09i	1.13558	−	1.35333i	0.926883	−	0.375352i	$-0.122478\pi$
$822$	53.2704	+	226.437i	0.0648059	+	0.275471i
$823$	592.953	+	497.546i	0.720477	+	0.604552i	0.927517	−	0.373780i	$-0.121939\pi$
$823$	592.953	+	497.546i	0.720477	+	0.604552i	−0.207040	+	0.978332i	$0.566383\pi$
$824$		−	102.351i		−	0.124212i
$825$	1001.18	−	656.113i	1.21355	−	0.795288i
$826$	−915.594	+	333.249i	−1.10847	+	0.403449i
$827$	−88.9336	+	105.987i	−0.107538	+	0.128158i	−0.817128	−	0.576456i	$-0.804435\pi$
$827$	−88.9336	+	105.987i	−0.107538	+	0.128158i	0.709591	+	0.704614i	$0.248880\pi$
$828$	−104.042	+	76.9219i	−0.125655	+	0.0929008i
$829$	440.462	−	762.903i	0.531318	−	0.920270i	−0.468014	−	0.883721i	$-0.655030\pi$
$829$	440.462	−	762.903i	0.531318	−	0.920270i	0.999332	−	0.0365485i	$-0.0116363\pi$
$830$	274.995	+	48.4890i	0.331319	+	0.0584205i
$831$	−855.948	+	804.868i	−1.03002	+	0.968553i
$832$	−374.352	+	136.253i	−0.449942	+	0.163765i
$833$	−984.095	+	173.523i	−1.18139	+	0.208310i
$834$	1443.31	−	339.546i	1.73059	−	0.407129i
$835$	−165.148	+	286.044i	−0.197782	+	0.342568i
$836$	−737.449	+	1326.87i	−0.882116	+	1.58716i
$837$	530.864	+	639.086i	0.634246	+	0.763543i
$838$	324.362	−	272.172i	0.387066	−	0.324787i
$839$	169.261	+	201.717i	0.201741	+	0.240426i	0.857424	−	0.514611i	$-0.172064\pi$
$839$	169.261	+	201.717i	0.201741	+	0.240426i	−0.655683	+	0.755037i	$0.727619\pi$
$840$	−56.7970	−	42.4303i	−0.0676155	−	0.0505123i
$841$	−852.706	+	715.505i	−1.01392	+	0.850779i
$842$	−1063.58	+	1267.52i	−1.26316	+	1.50537i
$843$	−34.3922	−	607.845i	−0.0407974	−	0.721050i
$844$	−115.022			−0.136282
$845$	112.403	−	133.957i	0.133022	−	0.158529i
$846$	34.9579	−	17.4117i	0.0413214	−	0.0205812i
$847$	769.144	+	1332.20i	0.908080	+	1.57284i
$848$	−15.9948	+	9.23462i	−0.0188618	+	0.0108899i
$849$	−247.291	+	106.185i	−0.291273	+	0.125071i
$850$	1417.18	−	1189.16i	1.66727	−	1.39901i
$851$	32.5965	+	89.5581i	0.0383038	+	0.105239i
$852$	518.608	−	1721.88i	0.608695	−	2.02099i
$853$	−281.871	−	1598.57i	−0.330447	−	1.87406i	−0.468247	−	0.883598i	$-0.655114\pi$
$853$	−281.871	−	1598.57i	−0.330447	−	1.87406i	0.137800	−	0.990460i	$-0.455997\pi$
$854$			1885.75i			2.20814i
$855$	198.734	+	44.3779i	0.232437	+	0.0519039i
$856$	−48.3893			−0.0565295
$857$	−996.160	+	175.650i	−1.16238	+	0.204959i	−0.721375	−	0.692545i	$-0.756489\pi$
$857$	−996.160	+	175.650i	−1.16238	+	0.204959i	−0.441006	+	0.897504i	$0.645378\pi$
$858$	161.575	+	686.808i	0.188315	+	0.800475i
$859$	−39.7230	+	14.4580i	−0.0462433	+	0.0168312i	−0.365038	−	0.930993i	$-0.618944\pi$
$859$	−39.7230	+	14.4580i	−0.0462433	+	0.0168312i	0.318795	+	0.947824i	$0.396722\pi$
$860$	209.659	+	249.862i	0.243790	+	0.290537i
$861$	830.349	+	98.4491i	0.964401	+	0.114343i
$862$	−754.577	−	1306.97i	−0.875380	−	1.51620i
$863$	−277.243	+	160.066i	−0.321254	+	0.185476i	−0.651952	−	0.758261i	$-0.726049\pi$
$863$	−277.243	+	160.066i	−0.321254	+	0.185476i	0.330697	+	0.943737i	$0.392716\pi$
$864$	1234.24	+	6.13686i	1.42852	+	0.00710285i
$865$	4.19298	+	3.51832i	0.00484737	+	0.00406743i
$866$		−	1672.16i		−	1.93090i
$867$	685.063	+	1045.36i	0.790154	+	1.20572i
$868$	1035.92	+	869.238i	1.19345	+	1.00143i
$869$	−450.945	−	537.415i	−0.518924	−	0.618429i
$870$	−184.017	−	428.552i	−0.211514	−	0.492588i
$871$	−144.068	+	120.887i	−0.165405	+	0.138791i
$872$	126.120	+	150.303i	0.144633	+	0.172366i
$873$	−562.087	+	63.8106i	−0.643857	+	0.0730935i
$874$	55.8025	−	161.471i	0.0638472	−	0.184749i
$875$	−466.288	−	269.211i	−0.532900	−	0.307670i
$876$	−1400.88	+	1317.28i	−1.59918	+	1.50375i
$877$	−256.191	−	1452.93i	−0.292122	−	1.65670i	−0.678677	−	0.734437i	$-0.737446\pi$
$877$	−256.191	−	1452.93i	−0.292122	−	1.65670i	0.386555	−	0.922266i	$-0.373665\pi$
$878$	193.191	+	530.788i	0.220036	+	0.604543i
$879$	−1354.96	+	318.760i	−1.54148	+	0.362640i
$880$	44.0514	−	249.828i	0.0500584	−	0.283895i
$881$	707.250	+	408.331i	0.802781	+	0.463486i	0.844443	−	0.535646i	$-0.179932\pi$
$881$	707.250	+	408.331i	0.802781	+	0.463486i	−0.0416619	+	0.999132i	$0.513265\pi$
$882$	916.801	+	399.079i	1.03946	+	0.452470i
$883$	239.399	+	200.879i	0.271120	+	0.227497i	0.768203	−	0.640206i	$-0.221151\pi$
$883$	239.399	+	200.879i	0.271120	+	0.227497i	−0.497083	+	0.867703i	$0.665596\pi$
$884$	201.914	+	554.753i	0.228409	+	0.627549i
$885$	57.0229	−	113.074i	0.0644326	−	0.127767i
$886$	604.739			0.682549
$887$	756.929	−	902.072i	0.853358	−	1.01699i	−0.146257	−	0.989247i	$-0.546723\pi$
$887$	756.929	−	902.072i	0.853358	−	1.01699i	0.999615	−	0.0277458i	$-0.00883289\pi$
$888$	−57.7487	+	191.737i	−0.0650323	+	0.215920i
$889$	18.7647	+	15.7454i	0.0211076	+	0.0177114i
$890$	−63.9186	+	175.615i	−0.0718187	+	0.197320i
$891$	168.128	−	1360.16i	0.188696	−	1.52656i
$892$	−1100.23			−1.23344
$893$	−13.5619	+	24.4015i	−0.0151870	+	0.0273253i
$894$	633.472	−	1256.15i	0.708582	−	1.40509i
$895$	−11.0900	−	4.03642i	−0.0123910	−	0.00450996i
$896$	615.213	−	108.479i	0.686622	−	0.121070i
$897$	−16.9616	−	39.5013i	−0.0189092	−	0.0440371i
$898$	1499.31	+	545.703i	1.66961	+	0.607688i
$899$	465.229	+	1278.21i	0.517496	+	1.42181i
$900$	−995.793	+	113.047i	−1.10644	+	0.125608i
$901$	19.4829	+	33.7454i	0.0216236	+	0.0374532i
$902$	−511.828	−	1406.23i	−0.567436	−	1.55902i
$903$	−1297.50	−	969.301i	−1.43688	−	1.07342i
$904$	−94.3661	+	163.447i	−0.104387	+	0.180804i
$905$			39.1472i			0.0432565i
$906$	−87.2846	−	203.274i	−0.0963407	−	0.224365i
$907$	−145.207	−	52.8509i	−0.160095	−	0.0582700i	0.260729	−	0.965412i	$-0.416037\pi$
$907$	−145.207	−	52.8509i	−0.160095	−	0.0582700i	−0.420825	+	0.907142i	$0.638259\pi$
$908$	748.663	+	132.009i	0.824519	+	0.145385i
$909$	14.0803	−	58.5442i	0.0154899	−	0.0644051i
$910$	118.009	−	99.0211i	0.129680	−	0.108814i
$911$	−1008.56	−	582.294i	−1.10709	−	0.639182i	−0.169019	−	0.985613i	$-0.554060\pi$
$911$	−1008.56	−	582.294i	−1.10709	−	0.639182i	−0.938075	+	0.346431i	$0.887393\pi$
$912$	−593.753	+	403.118i	−0.651045	+	0.442015i
$913$	671.725	+	1163.46i	0.735734	+	1.27433i
$914$	921.029	−	2530.51i	1.00769	−	2.76861i
$915$	−167.898	−	178.554i	−0.183496	−	0.195141i
$916$	404.928	+	339.775i	0.442061	+	0.370933i
$917$	−1539.01	+	271.369i	−1.67831	+	0.295931i
$918$	10.5316	−	2118.11i	0.0114723	−	2.30731i
$919$	138.825	−	240.451i	0.151061	−	0.261645i	−0.780557	−	0.625085i	$-0.785064\pi$
$919$	138.825	−	240.451i	0.151061	−	0.261645i	0.931618	+	0.363440i	$0.118398\pi$
$920$		−	7.73082i		−	0.00840306i
$921$	−978.024	+	419.957i	−1.06191	+	0.455979i
$922$	−44.8497	+	254.355i	−0.0486439	+	0.275873i
$923$	517.422	+	298.734i	0.560587	+	0.323655i
$924$	−126.016	−	2227.20i	−0.136381	−	2.41039i
$925$	−128.185	+	726.975i	−0.138579	+	0.785919i
$926$	1024.97	−	180.730i	1.10688	−	0.195173i
$927$	−360.141	−	238.582i	−0.388502	−	0.257370i
$928$	1898.91	+	691.148i	2.04624	+	0.744771i
$929$	−21.2211	+	3.74185i	−0.0228429	+	0.00402783i	−0.185058	−	0.982728i	$-0.559247\pi$
$929$	−21.2211	+	3.74185i	−0.0228429	+	0.00402783i	0.162215	+	0.986755i	$0.448136\pi$
$930$	−324.128	+	18.3393i	−0.348525	+	0.0197197i
$931$	−701.775	+	135.591i	−0.753786	+	0.145640i
$932$	−258.516	+	149.254i	−0.277378	+	0.160144i
$933$	−768.307	−	817.066i	−0.823480	−	0.875741i
$934$	−1519.67	+	1275.15i	−1.62706	+	1.36526i
$935$	−527.079	−	92.9382i	−0.563720	−	0.0993991i
$936$	21.1211	−	87.8188i	0.0225653	−	0.0938235i
$937$	228.025	−	82.9942i	0.243356	−	0.0885744i	−0.217463	−	0.976069i	$-0.569778\pi$
$937$	228.025	−	82.9942i	0.243356	−	0.0885744i	0.460819	+	0.887494i	$0.347556\pi$
$938$	951.159	−	549.152i	1.01403	−	0.585450i
$939$	265.205	−	525.893i	0.282434	−	0.560056i
$940$	−1.43468	+	8.13648i	−0.00152626	+	0.00865583i
$941$	39.9853	+	7.05049i	0.0424923	+	0.00749255i	0.194854	−	0.980832i	$-0.437577\pi$
$941$	39.9853	+	7.05049i	0.0424923	+	0.00749255i	−0.152362	+	0.988325i	$0.548688\pi$
$942$	−101.713	−	1797.66i	−0.107975	−	1.90834i
$943$	45.5896	+	78.9636i	0.0483453	+	0.0837365i
$944$	152.652	+	419.409i	0.161708	+	0.444289i
$945$	−281.694	+	100.945i	−0.298089	+	0.106820i
$946$	−503.331	+	2854.53i	−0.532063	+	3.01748i
$947$	237.590	+	283.149i	0.250887	+	0.298996i	0.876759	−	0.480931i	$-0.159701\pi$
$947$	237.590	+	283.149i	0.250887	+	0.298996i	−0.625872	+	0.779926i	$0.715257\pi$
$948$	134.507	+	571.752i	0.141885	+	0.603114i
$949$	−319.441	−	553.289i	−0.336608	−	0.583023i
$950$	999.647	−	867.005i	1.05226	−	0.912637i
$951$	93.3354	−	61.1663i	0.0981445	−	0.0643179i
$952$	−91.5399	−	519.149i	−0.0961554	−	0.545324i
$953$	68.8496	−	189.163i	0.0722451	−	0.198492i	−0.898314	−	0.439353i	$-0.855208\pi$
$953$	68.8496	−	189.163i	0.0722451	−	0.198492i	0.970560	+	0.240861i	$0.0774299\pi$
$954$	2.39607	−	38.9162i	0.00251160	−	0.0407926i
$955$	−56.1449	−	318.413i	−0.0587904	−	0.333417i
$956$	1911.22	+	336.999i	1.99918	+	0.352510i
$957$	1010.37	−	2003.52i	1.05576	−	2.09354i
$958$	−673.702	+	1166.89i	−0.703238	+	1.21804i
$959$	240.643	+	42.4318i	0.250931	+	0.0442459i
$960$	−180.971	+	242.247i	−0.188511	+	0.252340i
$961$	−14.1594			−0.0147340
$962$	−376.817	−	217.556i	−0.391702	−	0.226149i
$963$	−112.796	+	170.267i	−0.117130	+	0.176809i
$964$	−185.156	−	1050.07i	−0.192071	−	1.08929i
$965$	−193.888	+	231.067i	−0.200920	+	0.239447i
$966$	57.4920	+	244.382i	0.0595155	+	0.252983i
$967$	−622.442	−	226.551i	−0.643684	−	0.234282i	−0.000507615	−	1.00000i	$-0.500162\pi$
$967$	−622.442	−	226.551i	−0.643684	−	0.234282i	−0.643176	+	0.765718i	$0.722384\pi$
$968$	−305.221	+	176.219i	−0.315311	+	0.182045i
$969$	850.484	+	1252.68i	0.877693	+	1.29276i
$970$	110.525	−	191.436i	0.113944	−	0.197356i
$971$	−777.330	−	926.386i	−0.800546	−	0.954053i	0.199118	−	0.979975i	$-0.436192\pi$
$971$	−777.330	−	926.386i	−0.800546	−	0.954053i	−0.999664	+	0.0259221i	$0.991748\pi$
$972$	−638.456	+	953.421i	−0.656848	+	0.980886i
$973$	270.460	−	1533.86i	0.277965	−	1.57642i
$974$	−401.990	+	1104.46i	−0.412720	+	1.13394i
$975$	39.2036	−	330.654i	0.0402088	−	0.339133i
$976$	863.811			0.885052
$977$	1272.64	+	734.760i	1.30260	+	0.752057i	0.980850	−	0.194767i	$-0.0623951\pi$
$977$	1272.64	+	734.760i	1.30260	+	0.752057i	0.321751	+	0.946824i	$0.395728\pi$
$978$	2557.08	+	303.176i	2.61460	+	0.309996i
$979$	−844.909	+	307.522i	−0.863033	+	0.314118i
$980$	−183.191	+	105.765i	−0.186929	+	0.107924i
$981$	822.858	−	93.4146i	0.838795	−	0.0952238i
$982$	1174.02	−	427.309i	1.19554	−	0.435142i
$983$	−107.701	+	295.906i	−0.109564	+	0.301024i	−0.982342	−	0.187092i	$-0.940094\pi$
$983$	−107.701	+	295.906i	−0.109564	+	0.301024i	0.872779	+	0.488116i	$0.162316\pi$
$984$	−22.5558	+	190.242i	−0.0229226	+	0.193336i
$985$	−25.0032	−	141.800i	−0.0253840	−	0.143960i
$986$	1186.09	−	3258.77i	1.20294	−	3.30504i
$987$	−2.31748	−	40.9589i	−0.00234800	−	0.0414984i
$988$	150.882	+	394.388i	0.152714	+	0.399178i
$989$		−	176.607i		−	0.178571i
$990$	388.317	+	368.799i	0.392240	+	0.372524i
$991$	−250.872	−	91.3098i	−0.253150	−	0.0921391i	0.212328	−	0.977198i	$-0.431895\pi$
$991$	−250.872	−	91.3098i	−0.253150	−	0.0921391i	−0.465478	+	0.885059i	$0.654118\pi$
$992$	904.167	−	1077.54i	0.911459	−	1.08623i
$993$	621.359	−	584.278i	0.625739	−	0.588397i
$994$	−2672.87	−	2242.80i	−2.68900	−	2.25634i
$995$			40.6899i			0.0408944i
$996$	−63.5395	−	1122.99i	−0.0637947	−	1.12750i
$997$	796.341	−	289.844i	0.798737	−	0.290716i	0.0897739	−	0.995962i	$-0.471386\pi$
$997$	796.341	−	289.844i	0.798737	−	0.290716i	0.708963	+	0.705246i	$0.249163\pi$
$998$	−565.502	+	673.939i	−0.566635	+	0.675289i
$999$	540.049	+	650.143i	0.540589	+	0.650793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.z.a.101.32	✓	228
9.5	odd	6		171.3.bf.a.158.32	yes	228
19.16	even	9		171.3.bf.a.92.32	yes	228
171.149	odd	18	inner	171.3.z.a.149.32	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.z.a.101.32	✓	228	1.1	even	1	trivial
171.3.z.a.149.32	yes	228	171.149	odd	18	inner
171.3.bf.a.92.32	yes	228	19.16	even	9
171.3.bf.a.158.32	yes	228	9.5	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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.90844 - 0.512836i) q^{2} +(2.18553 - 2.05511i) q^{3} +(4.43724 - 1.61502i) q^{4} +(0.765438 + 0.912213i) q^{5} +(5.30255 - 7.09796i) q^{6} +(-4.65346 - 8.06002i) q^{7} +(1.84664 - 1.06616i) q^{8} +(0.553083 - 8.98299i) q^{9} +O(q^{10})\)	\(q+(2.90844 - 0.512836i) q^{2} +(2.18553 - 2.05511i) q^{3} +(4.43724 - 1.61502i) q^{4} +(0.765438 + 0.912213i) q^{5} +(5.30255 - 7.09796i) q^{6} +(-4.65346 - 8.06002i) q^{7} +(1.84664 - 1.06616i) q^{8} +(0.553083 - 8.98299i) q^{9} +(2.69404 + 2.26057i) q^{10} +16.9199i q^{11} +(6.37868 - 12.6487i) q^{12} +(3.60544 + 3.02532i) q^{13} +(-17.6678 - 21.0556i) q^{14} +(3.54758 + 0.420614i) q^{15} +(-9.64500 + 8.09312i) q^{16} +(17.0746 + 20.3487i) q^{17} +(-2.99819 - 26.4101i) q^{18} +(12.4490 + 14.3535i) q^{19} +(4.86967 + 2.81151i) q^{20} +(-26.7345 - 8.05208i) q^{21} +(8.67715 + 49.2106i) q^{22} +(-1.04132 - 2.86099i) q^{23} +(1.84482 - 6.12516i) q^{24} +(4.09497 - 23.2237i) q^{25} +(12.0377 + 6.94996i) q^{26} +(-17.2522 - 20.7692i) q^{27} +(-33.6656 - 28.2488i) q^{28} +(-15.1192 - 41.5396i) q^{29} +(10.5336 - 0.595998i) q^{30} -30.7708 q^{31} +(-29.3840 + 35.0184i) q^{32} +(34.7723 + 36.9790i) q^{33} +(60.0959 + 50.4265i) q^{34} +(3.79053 - 10.4144i) q^{35} +(-12.0536 - 40.7529i) q^{36} -31.3032 q^{37} +(43.5680 + 35.3620i) q^{38} +(14.0971 - 0.797624i) q^{39} +(2.38605 + 0.868452i) q^{40} +(-29.4928 + 5.20038i) q^{41} +(-81.8849 - 9.70857i) q^{42} +(54.5083 + 19.8394i) q^{43} +(27.3261 + 75.0778i) q^{44} +(8.61775 - 6.37139i) q^{45} +(-4.49583 - 7.78700i) q^{46} +(0.502536 + 1.38071i) q^{47} +(-4.44723 + 37.5093i) q^{48} +(-18.8093 + 32.5787i) q^{49} -69.6448i q^{50} +(79.1358 + 9.38262i) q^{51} +(20.8842 + 7.60121i) q^{52} +(1.44462 + 0.254725i) q^{53} +(-60.8282 - 51.5585i) q^{54} +(-15.4346 + 12.9512i) q^{55} +(-17.1865 - 9.92265i) q^{56} +(56.7056 + 5.78612i) q^{57} +(-65.2762 - 113.062i) q^{58} +(12.1242 - 33.3111i) q^{59} +(16.4208 - 3.86306i) q^{60} +(-52.5562 - 44.0999i) q^{61} +(-89.4949 + 15.7804i) q^{62} +(-74.9769 + 37.3441i) q^{63} +(-42.3214 + 73.3028i) q^{64} +5.60462i q^{65} +(120.097 + 89.7188i) q^{66} +(-6.93871 + 39.3514i) q^{67} +(108.628 + 62.7162i) q^{68} +(-8.15547 - 4.11277i) q^{69} +(5.68364 - 32.2335i) q^{70} +(125.015 - 22.0435i) q^{71} +(-8.55595 - 17.1780i) q^{72} +(-127.557 - 46.4268i) q^{73} +(-91.0433 + 16.0534i) q^{74} +(-38.7775 - 59.1717i) q^{75} +(78.4203 + 43.5846i) q^{76} +(136.375 - 78.7362i) q^{77} +(40.5916 - 9.54937i) q^{78} +(-31.7622 + 26.6517i) q^{79} +(-14.7653 - 2.60352i) q^{80} +(-80.3882 - 9.93667i) q^{81} +(-83.1111 + 30.2500i) q^{82} +(68.7627 - 39.7002i) q^{83} +(-131.631 + 7.44778i) q^{84} +(-5.49282 + 31.1513i) q^{85} +(168.708 + 29.7478i) q^{86} +(-118.412 - 59.7145i) q^{87} +(18.0393 + 31.2451i) q^{88} +(18.1751 + 49.9357i) q^{89} +(21.7967 - 22.9503i) q^{90} +(7.60641 - 43.1381i) q^{91} +(-9.24114 - 11.0132i) q^{92} +(-67.2505 + 63.2372i) q^{93} +(2.16967 + 3.75798i) q^{94} +(-3.56456 + 22.3428i) q^{95} +(7.74706 + 136.921i) q^{96} +(-10.9147 - 61.9004i) q^{97} +(-37.9982 + 104.399i) q^{98} +(151.992 + 9.35813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9}+O(q^{10}) \) 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9	\( 228 q - 9 q^{2} + 6 q^{3} - 3 q^{4} - 9 q^{5} - 30 q^{6} + 3 q^{7} + 30 q^{9} - 12 q^{10} - 3 q^{12} + 12 q^{13} - 9 q^{14} - 48 q^{15} + 9 q^{16} - 81 q^{17} - 60 q^{18} - 33 q^{19} - 18 q^{20} + 21 q^{21} + 81 q^{22} + 207 q^{23} - 222 q^{24} - 3 q^{25} - 216 q^{26} - 33 q^{27} - 36 q^{28} - 9 q^{29} + 171 q^{30} - 6 q^{31} - 9 q^{32} + 30 q^{33} + 33 q^{34} + 225 q^{35} - 246 q^{36} - 24 q^{37} - 9 q^{38} - 60 q^{39} - 177 q^{40} - 9 q^{41} - 15 q^{42} + 93 q^{43} + 441 q^{44} - 57 q^{45} - 6 q^{46} - 9 q^{47} - 774 q^{48} - 543 q^{49} - 81 q^{51} + 213 q^{52} + 393 q^{54} + 63 q^{55} - 459 q^{56} + 84 q^{57} - 6 q^{58} + 126 q^{59} - 333 q^{60} - 24 q^{61} - 36 q^{62} + 369 q^{63} + 372 q^{64} + 894 q^{66} + 39 q^{67} + 747 q^{68} + 231 q^{69} + 291 q^{70} + 204 q^{72} - 51 q^{73} + 333 q^{74} + 324 q^{75} - 3 q^{76} - 18 q^{77} - 1569 q^{78} - 105 q^{79} - 756 q^{80} + 1050 q^{81} + 132 q^{82} + 99 q^{83} - 69 q^{84} - 3 q^{85} - 495 q^{86} - 483 q^{87} + 387 q^{88} - 648 q^{89} - 339 q^{90} + 225 q^{91} + 27 q^{92} + 396 q^{93} - 6 q^{94} - 1305 q^{95} - 663 q^{96} - 543 q^{97} + 1125 q^{98} - 300 q^{99}+O(q^{100}) \) 228 * q - 9 * q^2 + 6 * q^3 - 3 * q^4 - 9 * q^5 - 30 * q^6 + 3 * q^7 + 30 * q^9 - 12 * q^10 - 3 * q^12 + 12 * q^13 - 9 * q^14 - 48 * q^15 + 9 * q^16 - 81 * q^17 - 60 * q^18 - 33 * q^19 - 18 * q^20 + 21 * q^21 + 81 * q^22 + 207 * q^23 - 222 * q^24 - 3 * q^25 - 216 * q^26 - 33 * q^27 - 36 * q^28 - 9 * q^29 + 171 * q^30 - 6 * q^31 - 9 * q^32 + 30 * q^33 + 33 * q^34 + 225 * q^35 - 246 * q^36 - 24 * q^37 - 9 * q^38 - 60 * q^39 - 177 * q^40 - 9 * q^41 - 15 * q^42 + 93 * q^43 + 441 * q^44 - 57 * q^45 - 6 * q^46 - 9 * q^47 - 774 * q^48 - 543 * q^49 - 81 * q^51 + 213 * q^52 + 393 * q^54 + 63 * q^55 - 459 * q^56 + 84 * q^57 - 6 * q^58 + 126 * q^59 - 333 * q^60 - 24 * q^61 - 36 * q^62 + 369 * q^63 + 372 * q^64 + 894 * q^66 + 39 * q^67 + 747 * q^68 + 231 * q^69 + 291 * q^70 + 204 * q^72 - 51 * q^73 + 333 * q^74 + 324 * q^75 - 3 * q^76 - 18 * q^77 - 1569 * q^78 - 105 * q^79 - 756 * q^80 + 1050 * q^81 + 132 * q^82 + 99 * q^83 - 69 * q^84 - 3 * q^85 - 495 * q^86 - 483 * q^87 + 387 * q^88 - 648 * q^89 - 339 * q^90 + 225 * q^91 + 27 * q^92 + 396 * q^93 - 6 * q^94 - 1305 * q^95 - 663 * q^96 - 543 * q^97 + 1125 * q^98 - 300 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more