LMFDB - Embedded newform 50.3.f.b.27.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.2
Character	$\chi$	$=$	50.27
Dual form			50.3.f.b.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39680 + 0.221232i) q^{2} +(-0.299213 - 0.587238i) q^{3} +(1.90211 + 0.618034i) q^{4} +(3.77205 + 3.28201i) q^{5} +(-0.288025 - 0.886451i) q^{6} +(-5.08008 - 5.08008i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.03475 - 6.92973i) q^{9} +O(q^{10})$	\(q+(1.39680 + 0.221232i) q^{2} +(-0.299213 - 0.587238i) q^{3} +(1.90211 + 0.618034i) q^{4} +(3.77205 + 3.28201i) q^{5} +(-0.288025 - 0.886451i) q^{6} +(-5.08008 - 5.08008i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.03475 - 6.92973i) q^{9} +(4.54273 + 5.41882i) q^{10} +(-15.3739 + 11.1698i) q^{11} +(-0.206203 - 1.30192i) q^{12} +(-15.1469 + 2.39904i) q^{13} +(-5.97199 - 8.21974i) q^{14} +(0.798677 - 3.19712i) q^{15} +(3.23607 + 2.35114i) q^{16} +(2.06006 - 4.04310i) q^{17} +(8.56562 - 8.56562i) q^{18} +(7.61807 - 2.47526i) q^{19} +(5.14648 + 8.57402i) q^{20} +(-1.46319 + 4.50324i) q^{21} +(-23.9455 + 12.2008i) q^{22} +(4.63577 - 29.2691i) q^{23} -1.86414i q^{24} +(3.45678 + 24.7599i) q^{25} -21.6880 q^{26} +(-11.4345 - 1.81105i) q^{27} +(-6.52322 - 12.8025i) q^{28} +(41.1843 + 13.3816i) q^{29} +(1.82290 - 4.28905i) q^{30} +(7.78864 + 23.9710i) q^{31} +(4.00000 + 4.00000i) q^{32} +(11.1594 + 5.68602i) q^{33} +(3.77196 - 5.19165i) q^{34} +(-2.48944 - 35.8352i) q^{35} +(13.8595 - 10.0695i) q^{36} +(-1.63663 - 10.3332i) q^{37} +(11.1885 - 1.77209i) q^{38} +(5.94097 + 8.17704i) q^{39} +(5.29177 + 13.1148i) q^{40} +(31.9797 + 23.2346i) q^{41} +(-3.04005 + 5.96643i) q^{42} +(-16.0163 + 16.0163i) q^{43} +(-36.1463 + 11.7446i) q^{44} +(41.7348 - 9.61523i) q^{45} +(12.9505 - 39.8576i) q^{46} +(14.0708 - 7.16942i) q^{47} +(0.412407 - 2.60384i) q^{48} +2.61434i q^{49} +(-0.649230 + 35.3494i) q^{50} -2.99066 q^{51} +(-30.2939 - 4.79808i) q^{52} +(-22.4011 - 43.9646i) q^{53} +(-15.5711 - 5.05935i) q^{54} +(-94.6509 - 8.32431i) q^{55} +(-6.27932 - 19.3258i) q^{56} +(-3.73299 - 3.73299i) q^{57} +(54.5659 + 27.8027i) q^{58} +(-8.28306 + 11.4007i) q^{59} +(3.49510 - 5.58767i) q^{60} +(-52.4160 + 38.0825i) q^{61} +(5.57605 + 35.2058i) q^{62} +(-60.7805 + 9.62668i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-65.0087 - 40.6631i) q^{65} +(14.3296 + 10.4111i) q^{66} +(1.12080 - 2.19970i) q^{67} +(6.41724 - 6.41724i) q^{68} +(-18.5750 + 6.03539i) q^{69} +(4.45062 - 50.6054i) q^{70} +(34.1821 - 105.202i) q^{71} +(21.5866 - 10.9989i) q^{72} +(-20.0687 + 126.709i) q^{73} -14.7956i q^{74} +(13.5056 - 9.43842i) q^{75} +16.0202 q^{76} +(134.844 + 21.3573i) q^{77} +(6.48934 + 12.7360i) q^{78} +(-52.5356 - 17.0699i) q^{79} +(4.49015 + 19.4894i) q^{80} +(-21.4645 - 66.0609i) q^{81} +(39.5291 + 39.5291i) q^{82} +(132.945 + 67.7386i) q^{83} +(-5.56631 + 7.66137i) q^{84} +(21.0401 - 8.48963i) q^{85} +(-25.9150 + 18.8283i) q^{86} +(-4.46469 - 28.1889i) q^{87} +(-53.0875 + 8.40824i) q^{88} +(-58.7326 - 80.8385i) q^{89} +(60.4225 - 4.19750i) q^{90} +(89.1349 + 64.7603i) q^{91} +(26.9071 - 52.8081i) q^{92} +(11.7462 - 11.7462i) q^{93} +(21.2402 - 6.90136i) q^{94} +(36.8596 + 15.6658i) q^{95} +(1.15210 - 3.54581i) q^{96} +(74.7286 - 38.0761i) q^{97} +(-0.578375 + 3.65172i) q^{98} +162.775i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$2$	1.39680	+	0.221232i	0.698401	+	0.110616i
$3$	−0.299213	−	0.587238i	−0.0997376	−	0.195746i	0.835746	−	0.549116i	$-0.185036\pi$
$3$	−0.299213	−	0.587238i	−0.0997376	−	0.195746i	−0.935484	+	0.353370i	$0.885036\pi$
$4$	1.90211	+	0.618034i	0.475528	+	0.154508i
$5$	3.77205	+	3.28201i	0.754411	+	0.656403i
$5$	3.77205	+	3.28201i	0.754411	+	0.656403i
$6$	−0.288025	−	0.886451i	−0.0480042	−	0.147742i
$7$	−5.08008	−	5.08008i	−0.725725	−	0.725725i	0.244040	−	0.969765i	$-0.421527\pi$
$7$	−5.08008	−	5.08008i	−0.725725	−	0.725725i	−0.969765	+	0.244040i	$0.921527\pi$
$8$	2.52015	+	1.28408i	0.315018	+	0.160510i
$9$	5.03475	−	6.92973i	0.559416	−	0.769970i
$10$	4.54273	+	5.41882i	0.454273	+	0.541882i
$11$	−15.3739	+	11.1698i	−1.39763	+	1.01544i	−0.402653	+	0.915353i	$0.631912\pi$
$11$	−15.3739	+	11.1698i	−1.39763	+	1.01544i	−0.994979	+	0.100086i	$0.968088\pi$
$12$	−0.206203	−	1.30192i	−0.0171836	−	0.108493i
$13$	−15.1469	+	2.39904i	−1.16515	+	0.184541i	−0.708899	−	0.705310i	$-0.750808\pi$
$13$	−15.1469	+	2.39904i	−1.16515	+	0.184541i	−0.456250	+	0.889852i	$0.650808\pi$
$14$	−5.97199	−	8.21974i	−0.426571	−	0.587124i
$15$	0.798677	−	3.19712i	0.0532451	−	0.213141i
$16$	3.23607	+	2.35114i	0.202254	+	0.146946i
$17$	2.06006	−	4.04310i	0.121180	−	0.237829i	−0.822446	−	0.568844i	$-0.807391\pi$
$17$	2.06006	−	4.04310i	0.121180	−	0.237829i	0.943626	+	0.331015i	$0.107391\pi$
$18$	8.56562	−	8.56562i	0.475868	−	0.475868i
$19$	7.61807	−	2.47526i	0.400951	−	0.130277i	−0.101598	−	0.994826i	$-0.532396\pi$
$19$	7.61807	−	2.47526i	0.400951	−	0.130277i	0.502549	+	0.864549i	$0.332396\pi$
$20$	5.14648	+	8.57402i	0.257324	+	0.428701i
$21$	−1.46319	+	4.50324i	−0.0696758	+	0.214440i
$22$	−23.9455	+	12.2008i	−1.08843	+	0.554583i
$23$	4.63577	−	29.2691i	0.201555	−	1.27257i	−0.654649	−	0.755933i	$-0.727184\pi$
$23$	4.63577	−	29.2691i	0.201555	−	1.27257i	0.856204	−	0.516637i	$-0.172816\pi$
$24$		−	1.86414i		−	0.0776725i
$25$	3.45678	+	24.7599i	0.138271	+	0.990394i
$26$	−21.6880			−0.834155
$27$	−11.4345	−	1.81105i	−0.423500	−	0.0670758i
$28$	−6.52322	−	12.8025i	−0.232972	−	0.457233i
$29$	41.1843	+	13.3816i	1.42015	+	0.461434i	0.915649	−	0.401979i	$-0.131677\pi$
$29$	41.1843	+	13.3816i	1.42015	+	0.461434i	0.504499	+	0.863412i	$0.331677\pi$
$30$	1.82290	−	4.28905i	0.0607632	−	0.142968i
$31$	7.78864	+	23.9710i	0.251246	+	0.773257i	0.994546	+	0.104298i	$0.0332597\pi$
$31$	7.78864	+	23.9710i	0.251246	+	0.773257i	−0.743300	+	0.668959i	$0.766740\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	11.1594	+	5.68602i	0.338165	+	0.172303i
$34$	3.77196	−	5.19165i	0.110940	−	0.152696i
$35$	−2.48944	−	35.8352i	−0.0711269	−	1.02386i
$36$	13.8595	−	10.0695i	0.384985	−	0.279708i
$37$	−1.63663	−	10.3332i	−0.0442331	−	0.279277i	0.955651	−	0.294502i	$-0.0951537\pi$
$37$	−1.63663	−	10.3332i	−0.0442331	−	0.279277i	−0.999884	+	0.0152247i	$0.995154\pi$
$38$	11.1885	−	1.77209i	0.294435	−	0.0466340i
$39$	5.94097	+	8.17704i	0.152332	+	0.209668i
$40$	5.29177	+	13.1148i	0.132294	+	0.327869i
$41$	31.9797	+	23.2346i	0.779992	+	0.566698i	0.904977	−	0.425461i	$-0.139888\pi$
$41$	31.9797	+	23.2346i	0.779992	+	0.566698i	−0.124984	+	0.992159i	$0.539888\pi$
$42$	−3.04005	+	5.96643i	−0.0723821	+	0.142058i
$43$	−16.0163	+	16.0163i	−0.372473	+	0.372473i	−0.868377	−	0.495904i	$-0.834837\pi$
$43$	−16.0163	+	16.0163i	−0.372473	+	0.372473i	0.495904	+	0.868377i	$0.334837\pi$
$44$	−36.1463	+	11.7446i	−0.821507	+	0.266924i
$45$	41.7348	−	9.61523i	0.927440	−	0.213672i
$46$	12.9505	−	39.8576i	0.281533	−	0.866469i
$47$	14.0708	−	7.16942i	0.299378	−	0.152541i	−0.297849	−	0.954613i	$-0.596269\pi$
$47$	14.0708	−	7.16942i	0.299378	−	0.152541i	0.597227	+	0.802072i	$0.296269\pi$
$48$	0.412407	−	2.60384i	0.00859181	−	0.0542466i
$49$			2.61434i			0.0533539i
$50$	−0.649230	+	35.3494i	−0.0129846	+	0.706988i
$51$	−2.99066			−0.0586403
$52$	−30.2939	−	4.79808i	−0.582575	−	0.0922707i
$53$	−22.4011	−	43.9646i	−0.422662	−	0.829521i	−0.999916	−	0.0129566i	$-0.995876\pi$
$53$	−22.4011	−	43.9646i	−0.422662	−	0.829521i	0.577254	−	0.816565i	$-0.304124\pi$
$54$	−15.5711	−	5.05935i	−0.288353	−	0.0936916i
$55$	−94.6509	−	8.32431i	−1.72092	−	0.151351i
$56$	−6.27932	−	19.3258i	−0.112131	−	0.345103i
$57$	−3.73299	−	3.73299i	−0.0654911	−	0.0654911i
$58$	54.5659	+	27.8027i	0.940791	+	0.479357i
$59$	−8.28306	+	11.4007i	−0.140391	+	0.193231i	−0.873423	−	0.486963i	$-0.838105\pi$
$59$	−8.28306	+	11.4007i	−0.140391	+	0.193231i	0.733032	+	0.680194i	$0.238105\pi$
$60$	3.49510	−	5.58767i	0.0582517	−	0.0931278i
$61$	−52.4160	+	38.0825i	−0.859279	+	0.624303i	−0.927689	−	0.373355i	$-0.878207\pi$
$61$	−52.4160	+	38.0825i	−0.859279	+	0.624303i	0.0684097	+	0.997657i	$0.478207\pi$
$62$	5.57605	+	35.2058i	0.0899363	+	0.567835i
$63$	−60.7805	+	9.62668i	−0.964769	+	0.152804i
$64$	4.70228	+	6.47214i	0.0734732	+	0.101127i
$65$	−65.0087	−	40.6631i	−1.00013	−	0.625587i
$66$	14.3296	+	10.4111i	0.217115	+	0.157743i
$67$	1.12080	−	2.19970i	0.0167284	−	0.0328313i	−0.882491	−	0.470329i	$-0.844135\pi$
$67$	1.12080	−	2.19970i	0.0167284	−	0.0328313i	0.899219	+	0.437498i	$0.144135\pi$
$68$	6.41724	−	6.41724i	0.0943711	−	0.0943711i
$69$	−18.5750	+	6.03539i	−0.269203	+	0.0874695i
$70$	4.45062	−	50.6054i	0.0635803	−	0.722935i
$71$	34.1821	−	105.202i	0.481438	−	1.48172i	−0.355635	−	0.934625i	$-0.615735\pi$
$71$	34.1821	−	105.202i	0.481438	−	1.48172i	0.837074	−	0.547090i	$-0.184265\pi$
$72$	21.5866	−	10.9989i	0.299814	−	0.152763i
$73$	−20.0687	+	126.709i	−0.274914	+	1.73574i	0.334063	+	0.942551i	$0.391580\pi$
$73$	−20.0687	+	126.709i	−0.274914	+	1.73574i	−0.608977	+	0.793188i	$0.708420\pi$
$74$		−	14.7956i		−	0.199940i
$75$	13.5056	−	9.43842i	0.180075	−	0.125846i
$76$	16.0202			0.210792
$77$	134.844	+	21.3573i	1.75123	+	0.277367i
$78$	6.48934	+	12.7360i	0.0831966	+	0.163283i
$79$	−52.5356	−	17.0699i	−0.665008	−	0.216074i	−0.0429880	−	0.999076i	$-0.513688\pi$
$79$	−52.5356	−	17.0699i	−0.665008	−	0.216074i	−0.622020	+	0.783001i	$0.713688\pi$
$80$	4.49015	+	19.4894i	0.0561268	+	0.243618i
$81$	−21.4645	−	66.0609i	−0.264994	−	0.815566i
$82$	39.5291	+	39.5291i	0.482062	+	0.482062i
$83$	132.945	+	67.7386i	1.60174	+	0.816128i	0.999846	+	0.0175538i	$0.00558783\pi$
$83$	132.945	+	67.7386i	1.60174	+	0.816128i	0.601896	+	0.798574i	$0.294412\pi$
$84$	−5.56631	+	7.66137i	−0.0662656	+	0.0912068i
$85$	21.0401	−	8.48963i	0.247531	−	0.0998780i
$86$	−25.9150	+	18.8283i	−0.301337	+	0.218934i
$87$	−4.46469	−	28.1889i	−0.0513183	−	0.324011i
$88$	−53.0875	+	8.40824i	−0.603268	+	0.0955482i
$89$	−58.7326	−	80.8385i	−0.659917	−	0.908298i	0.339562	−	0.940584i	$-0.389721\pi$
$89$	−58.7326	−	80.8385i	−0.659917	−	0.908298i	−0.999479	+	0.0322861i	$0.989721\pi$
$90$	60.4225	−	4.19750i	0.671361	−	0.0466389i
$91$	89.1349	+	64.7603i	0.979504	+	0.711652i
$92$	26.9071	−	52.8081i	0.292468	−	0.574001i
$93$	11.7462	−	11.7462i	0.126303	−	0.126303i
$94$	21.2402	−	6.90136i	0.225960	−	0.0734187i
$95$	36.8596	+	15.6658i	0.387996	+	0.164903i
$96$	1.15210	−	3.54581i	0.0120011	−	0.0369355i
$97$	74.7286	−	38.0761i	0.770398	−	0.392537i	−0.0241739	−	0.999708i	$-0.507696\pi$
$97$	74.7286	−	38.0761i	0.770398	−	0.392537i	0.794572	+	0.607171i	$0.207696\pi$
$98$	−0.578375	+	3.65172i	−0.00590179	+	0.0372624i
$99$			162.775i			1.64419i
$100$	−8.72725	+	49.2325i	−0.0872725	+	0.492325i
$101$	−94.8804			−0.939410			−0.469705	−	0.882824i	$-0.655640\pi$
$101$	−94.8804			−0.939410			−0.469705	+	0.882824i	$0.655640\pi$
$102$	−4.17736	−	0.661628i	−0.0409545	−	0.00648655i
$103$	−7.55549	−	14.8285i	−0.0733543	−	0.143966i	0.851417	−	0.524489i	$-0.175744\pi$
$103$	−7.55549	−	14.8285i	−0.0733543	−	0.143966i	−0.924771	+	0.380524i	$0.875744\pi$
$104$	−41.2531	−	13.4039i	−0.396664	−	0.128884i
$105$	−20.2989	+	12.1842i	−0.193323	+	0.116040i
$106$	−21.5635	−	66.3657i	−0.203430	−	0.626092i
$107$	6.28336	+	6.28336i	0.0587230	+	0.0587230i	0.735858	−	0.677135i	$-0.236779\pi$
$107$	6.28336	+	6.28336i	0.0587230	+	0.0587230i	−0.677135	+	0.735858i	$0.736779\pi$
$108$	−20.6304	−	10.5117i	−0.191022	−	0.0973308i
$109$	34.7441	−	47.8211i	0.318753	−	0.438726i	−0.619333	−	0.785128i	$-0.712597\pi$
$109$	34.7441	−	47.8211i	0.318753	−	0.438726i	0.938086	+	0.346403i	$0.112597\pi$
$110$	−130.367	−	32.5672i	−1.18515	−	0.296065i
$111$	−5.57838	+	4.05293i	−0.0502557	+	0.0365129i
$112$	−4.49550	−	28.3834i	−0.0401384	−	0.253424i
$113$	−79.1815	+	12.5411i	−0.700722	+	0.110983i	−0.496622	−	0.867967i	$-0.665427\pi$
$113$	−79.1815	+	12.5411i	−0.700722	+	0.110983i	−0.204099	+	0.978950i	$0.565427\pi$
$114$	−4.38839	−	6.04011i	−0.0384947	−	0.0529834i
$115$	113.548	−	95.1900i	0.987374	−	0.827739i
$116$	70.0669	+	50.9066i	0.604025	+	0.438850i
$117$	−59.6363	+	117.043i	−0.509712	+	1.00037i
$118$	−14.0920	+	14.0920i	−0.119424	+	0.119424i
$119$	−31.0045	+	10.0740i	−0.260542	+	0.0846552i
$120$	6.11813	−	7.03164i	0.0509844	−	0.0585970i
$121$	74.2022	−	228.371i	0.613241	−	1.88736i
$122$	−81.6399	+	41.5976i	−0.669179	+	0.340964i
$123$	4.07552	−	25.7318i	0.0331343	−	0.209202i
$124$			50.4091i			0.406525i
$125$	−68.2230	+	104.741i	−0.545784	+	0.837926i
$126$	−87.0280			−0.690699
$127$	−173.820	−	27.5304i	−1.36866	−	0.216775i	−0.571530	−	0.820581i	$-0.693650\pi$
$127$	−173.820	−	27.5304i	−1.36866	−	0.216775i	−0.797131	+	0.603806i	$0.793650\pi$
$128$	5.13632	+	10.0806i	0.0401275	+	0.0787546i
$129$	14.1977	+	4.61311i	0.110060	+	0.0357606i
$130$	−81.8084	−	71.1804i	−0.629295	−	0.547541i
$131$	60.0918	+	184.943i	0.458716	+	1.41178i	0.866717	+	0.498800i	$0.166226\pi$
$131$	60.0918	+	184.943i	0.458716	+	1.41178i	−0.408001	+	0.912981i	$0.633774\pi$
$132$	17.7124	+	17.7124i	0.134184	+	0.134184i
$133$	−51.2749	−	26.1258i	−0.385525	−	0.196435i
$134$	2.05218	−	2.82459i	0.0153148	−	0.0210790i
$135$	−37.1877	−	44.3595i	−0.275464	−	0.328589i
$136$	10.3833	−	7.54391i	0.0763478	−	0.0554700i
$137$	13.0753	+	82.5544i	0.0954404	+	0.602587i	0.988332	+	0.152315i	$0.0486729\pi$
$137$	13.0753	+	82.5544i	0.0954404	+	0.602587i	−0.892892	+	0.450272i	$0.851327\pi$
$138$	−27.2809	+	4.32087i	−0.197687	+	0.0313106i
$139$	59.6964	+	82.1651i	0.429471	+	0.591116i	0.967832	−	0.251599i	$-0.0809563\pi$
$139$	59.6964	+	82.1651i	0.429471	+	0.591116i	−0.538361	+	0.842714i	$0.680956\pi$
$140$	17.4122	−	69.7012i	0.124373	−	0.497865i
$141$	−8.42032	−	6.11772i	−0.0597185	−	0.0433881i
$142$	71.0197	−	139.384i	0.500138	−	0.981577i
$143$	206.071	−	206.071i	1.44106	−	1.44106i
$144$	32.5856	−	10.5877i	0.226289	−	0.0735256i
$145$	111.431	+	185.643i	0.768488	+	1.28030i
$146$	−56.0641	+	172.547i	−0.384000	+	1.18183i
$147$	1.53524	−	0.782244i	0.0104438	−	0.00532139i
$148$	3.27325	−	20.6665i	0.0221166	−	0.139639i
$149$		−	256.620i		−	1.72229i	−0.508363	−	0.861143i	$-0.669749\pi$
$149$		−	256.620i		−	1.72229i	0.508363	−	0.861143i	$-0.330251\pi$
$150$	20.9528	−	10.1957i	0.139685	−	0.0679716i
$151$	26.4378			0.175085			0.0875423	−	0.996161i	$-0.472099\pi$
$151$	26.4378			0.175085			0.0875423	+	0.996161i	$0.472099\pi$
$152$	22.3771	+	3.54418i	0.147218	+	0.0233170i
$153$	−17.6457	−	34.6316i	−0.115331	−	0.226350i
$154$	183.626	+	59.6637i	1.19238	+	0.387427i
$155$	−49.2939	+	115.982i	−0.318025	+	0.748272i
$156$	6.24670	+	19.2254i	0.0400430	+	0.123240i
$157$	−182.454	−	182.454i	−1.16213	−	1.16213i	−0.984009	−	0.178119i	$-0.942999\pi$
$157$	−182.454	−	182.454i	−1.16213	−	1.16213i	−0.178119	−	0.984009i	$-0.557001\pi$
$158$	−69.6055	−	35.4658i	−0.440541	−	0.224467i
$159$	−19.1150	+	26.3096i	−0.120220	+	0.165469i
$160$	1.96016	+	28.2163i	0.0122510	+	0.176352i
$161$	−172.239	+	125.139i	−1.06981	+	0.777262i
$162$	−15.3669	−	97.0226i	−0.0948572	−	0.598905i
$163$	119.678	−	18.9551i	0.734219	−	0.116289i	0.221882	−	0.975074i	$-0.428780\pi$
$163$	119.678	−	18.9551i	0.734219	−	0.116289i	0.512337	+	0.858785i	$0.328780\pi$
$164$	46.4692	+	63.9594i	0.283349	+	0.389996i
$165$	23.4324	+	58.0734i	0.142015	+	0.351960i
$166$	170.711	+	124.029i	1.02838	+	0.747163i
$167$	−122.784	+	240.977i	−0.735233	+	1.44298i	0.155210	+	0.987882i	$0.450395\pi$
$167$	−122.784	+	240.977i	−0.735233	+	1.44298i	−0.890443	+	0.455095i	$0.849605\pi$
$168$	−9.46997	+	9.46997i	−0.0563689	+	0.0563689i
$169$	62.9458	−	20.4523i	0.372460	−	0.121020i
$170$	31.2671	−	7.20358i	0.183924	−	0.0423740i
$171$	21.2021	−	65.2535i	0.123989	−	0.381599i
$172$	−40.3635	+	20.5662i	−0.234672	+	0.119571i
$173$	0.0332496	−	0.209930i	0.000192194	−	0.00121347i	−0.987592	−	0.157041i	$-0.949804\pi$
$173$	0.0332496	−	0.209930i	0.000192194	−	0.00121347i	0.987784	+	0.155828i	$0.0498045\pi$
$174$		−	40.3621i		−	0.231966i
$175$	108.221	−	143.343i	0.618407	−	0.819101i
$176$	−76.0130			−0.431892
$177$	9.17330	+	1.45291i	0.0518266	+	0.00820852i
$178$	−64.1538	−	125.909i	−0.360415	−	0.707353i
$179$	−61.8454	−	20.0948i	−0.345505	−	0.112261i	0.131124	−	0.991366i	$-0.458141\pi$
$179$	−61.8454	−	20.0948i	−0.345505	−	0.112261i	−0.476629	+	0.879105i	$0.658141\pi$
$180$	85.3269	+	7.50429i	0.474038	+	0.0416905i
$181$	−34.0403	−	104.765i	−0.188068	−	0.578813i	0.811920	−	0.583769i	$-0.198423\pi$
$181$	−34.0403	−	104.765i	−0.188068	−	0.578813i	−0.999988	+	0.00495553i	$0.998423\pi$
$182$	110.177	+	110.177i	0.605367	+	0.605367i
$183$	38.0470	+	19.3859i	0.207907	+	0.105934i
$184$	49.2667	−	67.8098i	0.267754	−	0.368531i
$185$	27.7404	−	44.3490i	0.149948	−	0.239724i
$186$	19.0058	−	13.8085i	0.102182	−	0.0742392i
$187$	13.4894	+	85.1688i	0.0721359	+	0.455448i
$188$	31.1951	−	4.94083i	0.165932	−	0.0262810i
$189$	48.8879	+	67.2884i	0.258666	+	0.356023i
$190$	48.0198	+	30.0365i	0.252736	+	0.158087i
$191$	45.3902	+	32.9779i	0.237645	+	0.172659i	0.700234	−	0.713914i	$-0.253079\pi$
$191$	45.3902	+	32.9779i	0.237645	+	0.172659i	−0.462588	+	0.886573i	$0.653079\pi$
$192$	2.39370	−	4.69791i	0.0124672	−	0.0244683i
$193$	34.9311	−	34.9311i	0.180990	−	0.180990i	−0.610797	−	0.791787i	$-0.709151\pi$
$193$	34.9311	−	34.9311i	0.180990	−	0.180990i	0.791787	+	0.610797i	$0.209151\pi$
$194$	112.805	−	36.6525i	0.581467	−	0.188930i
$195$	−4.42751	+	50.3426i	−0.0227052	+	0.258167i
$196$	−1.61575	+	4.97277i	−0.00824363	+	0.0253713i
$197$	30.7715	−	15.6789i	0.156201	−	0.0795882i	−0.374143	−	0.927371i	$-0.622063\pi$
$197$	30.7715	−	15.6789i	0.156201	−	0.0795882i	0.530343	+	0.847783i	$0.322063\pi$
$198$	−36.0109	+	227.364i	−0.181873	+	1.14830i
$199$		−	102.272i		−	0.513928i	−0.966421	−	0.256964i	$-0.917278\pi$
$199$		−	102.272i		−	0.513928i	0.966421	−	0.256964i	$-0.0827221\pi$
$200$	−23.0820	+	66.8373i	−0.115410	+	0.334186i
$201$	−1.62711			−0.00809505
$202$	−132.529	−	20.9906i	−0.656085	−	0.103914i
$203$	−141.240	−	277.199i	−0.695763	−	1.36551i
$204$	−5.68857	−	1.84833i	−0.0278851	−	0.00906043i
$205$	44.3728	+	192.600i	0.216453	+	0.939512i
$206$	−7.27299	−	22.3840i	−0.0353058	−	0.108660i
$207$	−179.487	−	179.487i	−0.867088	−	0.867088i
$208$	−54.6570	−	27.8491i	−0.262774	−	0.133890i
$209$	−89.4715	+	123.147i	−0.428093	+	0.589220i
$210$	−31.0491	+	12.5282i	−0.147853	+	0.0596582i
$211$	−184.212	+	133.838i	−0.873043	+	0.634303i	−0.931402	−	0.363993i	$-0.881413\pi$
$211$	−184.212	+	133.838i	−0.873043	+	0.634303i	0.0583587	+	0.998296i	$0.481413\pi$
$212$	−15.4378	−	97.4703i	−0.0728197	−	0.459766i
$213$	−72.0063	+	11.4047i	−0.338058	+	0.0535431i
$214$	7.38653	+	10.1667i	0.0345165	+	0.0475079i
$215$	−112.980	+	7.84865i	−0.525490	+	0.0365054i
$216$	−26.4911	−	19.2469i	−0.122644	−	0.0891060i
$217$	82.2075	−	161.341i	0.378836	−	0.743508i
$218$	59.1101	−	59.1101i	0.271147	−	0.271147i
$219$	80.4131	−	26.1278i	0.367183	−	0.119305i
$220$	−174.892	−	74.3312i	−0.794963	−	0.337869i
$221$	−21.5041	+	66.1827i	−0.0973034	+	0.299469i
$222$	−8.68853	+	4.42703i	−0.0391375	+	0.0199416i
$223$	−33.2206	+	209.747i	−0.148971	+	0.940567i	0.794054	+	0.607847i	$0.207967\pi$
$223$	−33.2206	+	209.747i	−0.148971	+	0.940567i	−0.943025	+	0.332720i	$0.892033\pi$
$224$		−	40.6406i		−	0.181431i
$225$	188.983	+	100.705i	0.839926	+	0.447578i
$226$	−113.375			−0.501661
$227$	162.584	+	25.7507i	0.716228	+	0.113439i	0.503904	−	0.863760i	$-0.331897\pi$
$227$	162.584	+	25.7507i	0.716228	+	0.113439i	0.212324	+	0.977199i	$0.431897\pi$
$228$	−4.79346	−	9.40769i	−0.0210239	−	0.0412618i
$229$	−123.207	−	40.0325i	−0.538023	−	0.174814i	0.0273861	−	0.999625i	$-0.491282\pi$
$229$	−123.207	−	40.0325i	−0.538023	−	0.174814i	−0.565409	+	0.824811i	$0.691282\pi$
$230$	179.663	−	107.841i	0.781144	−	0.468875i
$231$	−27.8054	−	85.5762i	−0.120370	−	0.370460i
$232$	86.6074	+	86.6074i	0.373308	+	0.373308i
$233$	−123.226	−	62.7869i	−0.528868	−	0.269472i	0.169102	−	0.985599i	$-0.445913\pi$
$233$	−123.226	−	62.7869i	−0.528868	−	0.269472i	−0.697970	+	0.716127i	$0.745913\pi$
$234$	−109.194	+	150.292i	−0.466640	+	0.642274i
$235$	76.6058	+	19.1370i	0.325982	+	0.0814342i
$236$	−22.8013	+	16.5661i	−0.0966157	+	0.0701954i
$237$	5.69526	+	35.9585i	0.0240306	+	0.151723i
$238$	−45.5358	+	7.21217i	−0.191327	+	0.0303032i
$239$	−124.760	−	171.718i	−0.522009	−	0.718484i	0.463877	−	0.885900i	$-0.346458\pi$
$239$	−124.760	−	171.718i	−0.522009	−	0.718484i	−0.985886	+	0.167415i	$0.946458\pi$
$240$	10.1014	−	8.46828i	0.0420893	−	0.0352845i
$241$	−211.841	−	153.912i	−0.879009	−	0.638637i	0.0539800	−	0.998542i	$-0.482809\pi$
$241$	−211.841	−	153.912i	−0.879009	−	0.638637i	−0.932989	+	0.359905i	$0.882809\pi$
$242$	154.169	−	302.573i	0.637060	−	1.25030i
$243$	−106.047	+	106.047i	−0.436407	+	0.436407i
$244$	−123.237	+	40.0423i	−0.505072	+	0.164108i
$245$	−8.58030	+	9.86143i	−0.0350216	+	0.0402507i
$246$	11.3854	−	35.0406i	0.0462820	−	0.142441i
$247$	−109.452	+	55.7686i	−0.443126	+	0.225784i
$248$	−11.1521	+	70.4116i	−0.0449681	+	0.283918i
$249$		−	98.3384i		−	0.394933i
$250$	−118.466	+	131.209i	−0.473864	+	0.524836i
$251$	257.619			1.02637			0.513185	−	0.858278i	$-0.328465\pi$
$251$	257.619			1.02637			0.513185	+	0.858278i	$0.328465\pi$
$252$	−121.561	−	19.2534i	−0.482385	−	0.0764022i
$253$	255.661	+	501.763i	1.01052	+	1.98325i
$254$	−236.702	−	76.9090i	−0.931896	−	0.302791i
$255$	−11.2809	−	9.81538i	−0.0442389	−	0.0384917i
$256$	4.94427	+	15.2169i	0.0193136	+	0.0594410i
$257$	253.093	+	253.093i	0.984798	+	0.984798i	0.999886	−	0.0150882i	$-0.00480290\pi$
$257$	253.093	+	253.093i	0.984798	+	0.984798i	−0.0150882	+	0.999886i	$0.504803\pi$
$258$	18.8108	+	9.58459i	0.0729101	+	0.0371496i
$259$	−44.1795	+	60.8079i	−0.170577	+	0.234779i
$260$	−98.5228	−	117.524i	−0.378934	−	0.452014i
$261$	300.083	−	218.023i	1.14974	−	0.835338i
$262$	43.0210	+	271.624i	0.164202	+	1.03673i
$263$	403.221	−	63.8639i	1.53316	−	0.242829i	0.667938	−	0.744217i	$-0.267177\pi$
$263$	403.221	−	63.8639i	1.53316	−	0.242829i	0.865222	+	0.501388i	$0.167177\pi$
$264$	20.8221	+	28.6592i	0.0788717	+	0.108558i
$265$	59.7944	−	239.358i	0.225639	−	0.903236i
$266$	−65.8410	−	47.8363i	−0.247522	−	0.179836i
$267$	−29.8979	+	58.6780i	−0.111977	+	0.219768i
$268$	3.49138	−	3.49138i	0.0130275	−	0.0130275i
$269$	159.892	−	51.9520i	0.594393	−	0.193130i	0.00365486	−	0.999993i	$-0.498837\pi$
$269$	159.892	−	51.9520i	0.594393	−	0.193130i	0.590738	+	0.806863i	$0.298837\pi$
$270$	−42.1301	−	70.1886i	−0.156037	−	0.259958i
$271$	−10.8829	+	33.4942i	−0.0401584	+	0.123595i	−0.969126	−	0.246567i	$-0.920698\pi$
$271$	−10.8829	+	33.4942i	−0.0401584	+	0.123595i	0.928967	+	0.370161i	$0.120698\pi$
$272$	16.1724	−	8.24024i	0.0594573	−	0.0302950i
$273$	11.3594	−	71.7205i	0.0416096	−	0.262713i
$274$			118.205i			0.431405i
$275$	−329.708	−	342.045i	−1.19894	−	1.24380i
$276$	−39.0619			−0.141529
$277$	485.638	+	76.9174i	1.75320	+	0.277680i	0.948680	−	0.316239i	$-0.102420\pi$
$277$	485.638	+	76.9174i	1.75320	+	0.277680i	0.804525	+	0.593919i	$0.202420\pi$
$278$	65.2066	+	127.975i	0.234556	+	0.460342i
$279$	205.326	+	66.7146i	0.735936	+	0.239120i
$280$	39.7415	−	93.5066i	0.141934	−	0.333952i
$281$	88.8094	+	273.327i	0.316048	+	0.972695i	0.975321	+	0.220791i	$0.0708640\pi$
$281$	88.8094	+	273.327i	0.316048	+	0.972695i	−0.659273	+	0.751903i	$0.729136\pi$
$282$	−10.4081	−	10.4081i	−0.0369081	−	0.0369081i
$283$	−180.911	−	92.1790i	−0.639263	−	0.325721i	0.104142	−	0.994562i	$-0.466790\pi$
$283$	−180.911	−	92.1790i	−0.639263	−	0.325721i	−0.743405	+	0.668842i	$0.766790\pi$
$284$	130.037	−	178.980i	0.457875	−	0.630211i
$285$	−1.82932	−	26.3328i	−0.00641866	−	0.0923957i
$286$	333.430	−	242.251i	1.16584	−	0.847033i
$287$	−44.4257	−	280.493i	−0.154793	−	0.977327i
$288$	47.8579	−	7.57995i	0.166173	−	0.0263193i
$289$	157.767	+	217.148i	0.545907	+	0.751377i
$290$	114.577	+	283.959i	0.395092	+	0.979170i
$291$	−44.7195	−	32.4906i	−0.153675	−	0.111652i
$292$	−116.483	+	228.611i	−0.398916	+	0.782916i
$293$	−131.312	+	131.312i	−0.448164	+	0.448164i	−0.894744	−	0.446580i	$-0.852642\pi$
$293$	−131.312	+	131.312i	−0.448164	+	0.448164i	0.446580	+	0.894744i	$0.352642\pi$
$294$	2.31749	−	0.752997i	0.00788260	−	0.00256121i
$295$	−68.6613	+	15.8188i	−0.232750	+	0.0536229i
$296$	9.14417	−	28.1429i	0.0308925	−	0.0950772i
$297$	196.022	−	99.8784i	0.660008	−	0.336291i
$298$	56.7726	−	358.448i	0.190512	−	1.20285i
$299$			454.459i			1.51993i
$300$	31.5225	−	9.60601i	0.105075	−	0.0320200i
$301$	162.728			0.540626
$302$	36.9283	+	5.84887i	0.122279	+	0.0193671i
$303$	28.3894	+	55.7174i	0.0936945	+	0.183886i
$304$	30.4723	+	9.90104i	0.100238	+	0.0325692i
$305$	−322.703	−	28.3810i	−1.05804	−	0.0930523i
$306$	−16.9859	−	52.2773i	−0.0555096	−	0.170841i
$307$	−226.711	−	226.711i	−0.738472	−	0.738472i	0.233810	−	0.972282i	$-0.424881\pi$
$307$	−226.711	−	226.711i	−0.738472	−	0.738472i	−0.972282	+	0.233810i	$0.924881\pi$
$308$	243.290	+	123.962i	0.789902	+	0.402475i
$309$	−6.44715	+	8.87375i	−0.0208646	+	0.0287176i
$310$	−94.5127	+	151.099i	−0.304880	+	0.487416i
$311$	178.706	−	129.837i	0.574617	−	0.417483i	−0.262163	−	0.965024i	$-0.584436\pi$
$311$	178.706	−	129.837i	0.574617	−	0.417483i	0.836779	+	0.547540i	$0.184436\pi$
$312$	4.47215	+	28.2360i	0.0143338	+	0.0905000i
$313$	−288.434	+	45.6834i	−0.921514	+	0.145953i	−0.599126	−	0.800654i	$-0.704485\pi$
$313$	−288.434	+	45.6834i	−0.921514	+	0.145953i	−0.322387	+	0.946608i	$0.604485\pi$
$314$	−214.488	−	295.217i	−0.683082	−	0.940181i
$315$	−260.862	−	163.170i	−0.828134	−	0.518000i
$316$	−89.3789	−	64.9376i	−0.282845	−	0.205499i
$317$	−85.6031	+	168.006i	−0.270041	+	0.529986i	−0.985709	−	0.168455i	$-0.946122\pi$
$317$	−85.6031	+	168.006i	−0.270041	+	0.529986i	0.715668	+	0.698441i	$0.246122\pi$
$318$	−32.5204	+	32.5204i	−0.102265	+	0.102265i
$319$	−782.635	+	254.294i	−2.45340	+	0.797158i
$320$	−3.50438	+	39.8462i	−0.0109512	+	0.124519i
$321$	1.80977	−	5.56989i	0.00563791	−	0.0173517i
$322$	−268.269	+	136.690i	−0.833134	+	0.424503i
$323$	5.68596	−	35.8997i	0.0176036	−	0.111145i
$324$		−	138.921i		−	0.428768i
$325$	−111.759	−	366.743i	−0.343875	−	1.12844i
$326$	171.359			0.525643
$327$	−38.4783	−	6.09436i	−0.117671	−	0.0186372i
$328$	50.7584	+	99.6190i	0.154751	+	0.303717i
$329$	−107.902	−	35.0594i	−0.327969	−	0.106564i
$330$	19.8828	+	86.3010i	0.0602508	+	0.261518i
$331$	6.22386	+	19.1551i	0.0188032	+	0.0578703i	0.960018	−	0.279939i	$-0.0903142\pi$
$331$	6.22386	+	19.1551i	0.0188032	+	0.0578703i	−0.941215	+	0.337809i	$0.890314\pi$
$332$	211.011	+	211.011i	0.635575	+	0.635575i
$333$	−79.8467	−	40.6839i	−0.239780	−	0.122174i
$334$	−224.817	+	309.434i	−0.673104	+	0.926448i
$335$	11.4472	−	4.61889i	0.0341706	−	0.0137877i
$336$	−15.3227	+	11.1326i	−0.0456034	+	0.0331328i
$337$	0.112139	+	0.708016i	0.000332756	+	0.00210094i	0.987854	−	0.155384i	$-0.0496615\pi$
$337$	0.112139	+	0.708016i	0.000332756	+	0.00210094i	−0.987521	+	0.157485i	$0.949661\pi$
$338$	92.4475	−	14.6423i	0.273513	−	0.0433203i
$339$	31.0568	+	42.7460i	0.0916129	+	0.126094i
$340$	45.2676	−	3.14471i	0.133140	−	0.00924914i
$341$	−387.494	−	281.531i	−1.13635	−	0.825603i
$342$	44.0513	−	86.4556i	0.128805	−	0.252794i
$343$	−235.643	+	235.643i	−0.687005	+	0.687005i
$344$	−60.9297	+	19.7973i	−0.177121	+	0.0575502i
$345$	−89.8743	−	38.1977i	−0.260505	−	0.110718i
$346$	0.0928863	−	0.285875i	0.000268457	−	0.000826227i
$347$	301.742	−	153.745i	0.869573	−	0.443069i	0.0385166	−	0.999258i	$-0.487737\pi$
$347$	301.742	−	153.745i	0.869573	−	0.443069i	0.831056	+	0.556188i	$0.187737\pi$
$348$	8.92938	−	56.3779i	0.0256591	−	0.162005i
$349$		−	16.5208i		−	0.0473377i	−0.999720	−	0.0236688i	$-0.992465\pi$
$349$		−	16.5208i		−	0.0473377i	0.999720	−	0.0236688i	$-0.00753473\pi$
$350$	182.876	−	176.279i	0.522502	−	0.503655i
$351$	177.542			0.505819
$352$	−106.175	−	16.8165i	−0.301634	−	0.0477741i
$353$	79.4588	+	155.947i	0.225096	+	0.441776i	0.975740	−	0.218931i	$-0.0702569\pi$
$353$	79.4588	+	155.947i	0.225096	+	0.441776i	−0.750645	+	0.660706i	$0.770257\pi$
$354$	12.4919	+	4.05885i	0.0352877	+	0.0114657i
$355$	474.210	−	284.641i	1.33580	−	0.801804i
$356$	−61.7551	−	190.063i	−0.173469	−	0.533884i
$357$	15.1928	+	15.1928i	0.0425568	+	0.0425568i
$358$	−81.9402	−	41.7506i	−0.228883	−	0.116622i
$359$	256.595	−	353.173i	0.714751	−	0.983770i	−0.284931	−	0.958548i	$-0.591971\pi$
$359$	256.595	−	353.173i	0.714751	−	0.983770i	0.999682	−	0.0252219i	$-0.00802924\pi$
$360$	117.525	+	29.3590i	0.326457	+	0.0815528i
$361$	−240.147	+	174.477i	−0.665227	+	0.483316i
$362$	−24.3702	−	153.867i	−0.0673209	−	0.425047i
$363$	−156.310	+	24.7571i	−0.430607	+	0.0682014i
$364$	129.521	+	178.270i	0.355826	+	0.489752i
$365$	−491.561	+	412.087i	−1.34674	+	1.12901i
$366$	48.8554	+	35.4955i	0.133485	+	0.0969823i
$367$	3.80774	−	7.47312i	0.0103753	−	0.0203627i	−0.885761	−	0.464142i	$-0.846363\pi$
$367$	3.80774	−	7.47312i	0.0103753	−	0.0203627i	0.896136	+	0.443779i	$0.146363\pi$
$368$	83.8175	−	83.8175i	0.227765	−	0.227765i
$369$	322.019	−	104.630i	0.872681	−	0.283551i
$370$	48.5593	−	55.8097i	0.131241	−	0.150837i
$371$	−109.544	+	337.143i	−0.295268	+	0.908741i
$372$	29.6022	−	15.0831i	0.0795758	−	0.0405459i
$373$	60.0619	−	379.216i	0.161024	−	1.01667i	−0.766321	−	0.642458i	$-0.777915\pi$
$373$	60.0619	−	379.216i	0.161024	−	1.01667i	0.927345	−	0.374207i	$-0.122085\pi$
$374$			121.948i			0.326065i
$375$	81.9210	+	8.72341i	0.218456	+	0.0232624i
$376$	44.6665			0.118794
$377$	−655.919	−	103.887i	−1.73984	−	0.275563i
$378$	53.4003	+	104.804i	0.141271	+	0.277259i
$379$	323.639	+	105.157i	0.853928	+	0.277458i	0.703090	−	0.711101i	$-0.251803\pi$
$379$	323.639	+	105.157i	0.853928	+	0.277458i	0.150838	+	0.988559i	$0.451803\pi$
$380$	60.4291	+	52.5786i	0.159024	+	0.138365i
$381$	35.8423	+	110.311i	0.0940742	+	0.289531i
$382$	56.1054	+	56.1054i	0.146873	+	0.146873i
$383$	67.0852	+	34.1816i	0.175157	+	0.0892470i	0.539371	−	0.842068i	$-0.318662\pi$
$383$	67.0852	+	34.1816i	0.175157	+	0.0892470i	−0.364214	+	0.931315i	$0.618662\pi$
$384$	4.38286	−	6.03248i	0.0114137	−	0.0157096i
$385$	438.545	+	523.122i	1.13908	+	1.35876i
$386$	56.5197	−	41.0639i	0.146424	−	0.106383i
$387$	30.3507	+	191.627i	0.0784257	+	0.495160i
$388$	165.675	−	26.2403i	0.426996	−	0.0676295i
$389$	−3.14213	−	4.32477i	−0.00807745	−	0.0111177i	0.804959	−	0.593330i	$-0.202187\pi$
$389$	−3.14213	−	4.32477i	−0.00807745	−	0.0111177i	−0.813037	+	0.582213i	$0.802187\pi$
$390$	−17.3217	+	69.3391i	−0.0444147	+	0.177793i
$391$	−108.788	−	79.0390i	−0.278230	−	0.202146i
$392$	−3.35702	+	6.58852i	−0.00856383	+	0.0168075i
$393$	90.6256	−	90.6256i	0.230600	−	0.230600i
$394$	46.4504	−	15.0926i	0.117894	−	0.0383062i
$395$	−142.144	−	236.811i	−0.359857	−	0.599522i
$396$	−100.600	+	309.616i	−0.254041	+	0.781858i
$397$	255.655	−	130.263i	0.643968	−	0.328118i	−0.101327	−	0.994853i	$-0.532309\pi$
$397$	255.655	−	130.263i	0.643968	−	0.328118i	0.745295	+	0.666735i	$0.232309\pi$
$398$	22.6257	−	142.853i	0.0568485	−	0.358928i
$399$			37.9278i			0.0950570i
$400$	−47.0276	+	88.2520i	−0.117569	+	0.220630i
$401$	369.494			0.921432			0.460716	−	0.887548i	$-0.347593\pi$
$401$	369.494			0.921432			0.460716	+	0.887548i	$0.347593\pi$
$402$	−2.27274	−	0.359967i	−0.00565359	−	0.000895441i
$403$	−175.481	−	344.402i	−0.435438	−	0.854594i
$404$	−180.473	−	58.6393i	−0.446716	−	0.145147i
$405$	135.847	−	319.632i	0.335426	−	0.789214i
$406$	−135.959	−	418.439i	−0.334874	−	1.03064i
$407$	140.582	+	140.582i	0.345410	+	0.345410i
$408$	−7.53690	−	3.84024i	−0.0184728	−	0.00941235i
$409$	195.858	−	269.576i	0.478871	−	0.659110i	−0.499416	−	0.866362i	$-0.666452\pi$
$409$	195.858	−	269.576i	0.478871	−	0.659110i	0.978288	+	0.207252i	$0.0664521\pi$
$410$	19.3708	+	278.841i	0.0472460	+	0.680099i
$411$	44.5668	−	32.3797i	0.108435	−	0.0787827i
$412$	−5.20689	−	32.8750i	−0.0126381	−	0.0797937i
$413$	99.9948	−	15.8376i	0.242118	−	0.0383477i
$414$	−211.000	−	290.416i	−0.509662	−	0.701489i
$415$	279.155	+	691.840i	0.672663	+	1.66708i
$416$	−70.1839	−	50.9916i	−0.168711	−	0.122576i
$417$	30.3885	−	59.6409i	0.0728742	−	0.143024i
$418$	−152.218	+	152.218i	−0.364158	+	0.364158i
$419$	547.856	−	178.009i	1.30753	−	0.424843i	0.429337	−	0.903145i	$-0.358747\pi$
$419$	547.856	−	178.009i	1.30753	−	0.424843i	0.878196	+	0.478302i	$0.158747\pi$
$420$	−46.1411	+	10.6304i	−0.109860	+	0.0253105i
$421$	−239.932	+	738.435i	−0.569910	+	1.75400i	0.0829823	+	0.996551i	$0.473556\pi$
$421$	−239.932	+	738.435i	−0.569910	+	1.75400i	−0.652892	+	0.757451i	$0.726444\pi$
$422$	−286.917	+	146.192i	−0.679898	+	0.346425i
$423$	21.1606	−	133.603i	0.0500251	−	0.315846i
$424$		−	139.562i		−	0.329156i
$425$	107.228	+	37.0307i	0.252300	+	0.0871311i
$426$	−103.102			−0.242023
$427$	459.739	+	72.8155i	1.07667	+	0.170528i
$428$	8.06833	+	15.8350i	0.0188512	+	0.0369977i
$429$	−182.672	−	59.3538i	−0.425809	−	0.138354i
$430$	−159.547	−	14.0318i	−0.371041	−	0.0326321i
$431$	95.6942	+	294.516i	0.222028	+	0.683333i	0.998580	+	0.0532789i	$0.0169672\pi$
$431$	95.6942	+	294.516i	0.222028	+	0.683333i	−0.776551	+	0.630054i	$0.783033\pi$
$432$	−32.7448	−	32.7448i	−0.0757981	−	0.0757981i
$433$	23.0174	+	11.7280i	0.0531581	+	0.0270854i	0.480368	−	0.877067i	$-0.340503\pi$
$433$	23.0174	+	11.7280i	0.0531581	+	0.0270854i	−0.427209	+	0.904153i	$0.640503\pi$
$434$	150.521	−	207.175i	0.346823	−	0.477361i
$435$	75.6754	−	120.983i	0.173966	−	0.278123i
$436$	95.6422	−	69.4881i	0.219363	−	0.159376i
$437$	−37.1330	−	234.449i	−0.0849726	−	0.536496i
$438$	118.102	−	18.7055i	0.269638	−	0.0427065i
$439$	−173.704	−	239.083i	−0.395682	−	0.544609i	0.563972	−	0.825794i	$-0.309273\pi$
$439$	−173.704	−	239.083i	−0.395682	−	0.544609i	−0.959654	+	0.281185i	$0.909273\pi$
$440$	−227.845	−	142.518i	−0.517830	−	0.323904i
$441$	18.1167	+	13.1625i	0.0410809	+	0.0298470i
$442$	−44.6786	+	87.6867i	−0.101083	+	0.198386i
$443$	−497.721	+	497.721i	−1.12352	+	1.12352i	−0.132316	+	0.991208i	$0.542241\pi$
$443$	−497.721	+	497.721i	−1.12352	+	1.12352i	−0.991208	+	0.132316i	$0.957759\pi$
$444$	−13.1156	+	4.26150i	−0.0295396	+	0.00959798i
$445$	43.7705	−	497.688i	0.0983606	−	1.11840i
$446$	−92.8052	+	285.625i	−0.208083	+	0.640415i
$447$	−150.697	+	76.7842i	−0.337131	+	0.171777i
$448$	8.99099	−	56.7669i	0.0200692	−	0.126712i
$449$			99.6032i			0.221833i	0.993830	+	0.110917i	$0.0353787\pi$
$449$			99.6032i			0.221833i	−0.993830	+	0.110917i	$0.964621\pi$
$450$	241.693	+	182.474i	0.537096	+	0.405498i
$451$	−751.180			−1.66559
$452$	−158.363	−	25.0822i	−0.350361	−	0.0554917i
$453$	−7.91052	−	15.5253i	−0.0174625	−	0.0342721i
$454$	221.400	+	71.9374i	0.487666	+	0.158452i
$455$	123.677	+	536.821i	0.271819	+	1.17983i
$456$	−4.61423	−	14.2011i	−0.0101189	−	0.0311429i
$457$	−479.543	−	479.543i	−1.04933	−	1.04933i	−0.998718	−	0.0506104i	$-0.983883\pi$
$457$	−479.543	−	479.543i	−1.04933	−	1.04933i	−0.0506104	−	0.998718i	$-0.516117\pi$
$458$	−163.240	−	83.1748i	−0.356419	−	0.181604i
$459$	−30.8780	+	42.4999i	−0.0672723	+	0.0925924i
$460$	274.812	−	110.886i	0.597417	−	0.241056i
$461$	73.4943	−	53.3967i	0.159424	−	0.115828i	−0.505213	−	0.862994i	$-0.668586\pi$
$461$	73.4943	−	53.3967i	0.159424	−	0.115828i	0.664637	+	0.747166i	$0.268586\pi$
$462$	−19.9065	−	125.684i	−0.0430876	−	0.272044i
$463$	536.515	−	84.9756i	1.15878	−	0.183533i	0.452699	−	0.891664i	$-0.350461\pi$
$463$	536.515	−	84.9756i	1.15878	−	0.183533i	0.706081	+	0.708131i	$0.250461\pi$
$464$	101.813	+	140.134i	0.219425	+	0.302012i
$465$	82.8586	−	5.75612i	0.178190	−	0.0123788i
$466$	−158.232	−	114.962i	−0.339554	−	0.246700i
$467$	138.860	−	272.527i	0.297344	−	0.583570i	−0.693203	−	0.720742i	$-0.743801\pi$
$467$	138.860	−	272.527i	0.297344	−	0.583570i	0.990547	+	0.137172i	$0.0438013\pi$
$468$	−185.771	+	185.771i	−0.396947	+	0.396947i
$469$	−16.8684	+	5.48087i	−0.0359667	+	0.0116863i
$470$	102.769	+	43.6783i	0.218659	+	0.0929326i
$471$	−52.5514	+	161.737i	−0.111574	+	0.343390i
$472$	−35.5139	+	18.0952i	−0.0752413	+	0.0383373i
$473$	67.3346	−	425.134i	0.142356	−	0.898803i
$474$			51.4868i			0.108622i
$475$	87.6211	+	180.066i	0.184465	+	0.379086i
$476$	−65.2001			−0.136975
$477$	−417.447	−	66.1171i	−0.875151	−	0.138610i
$478$	−136.276	−	267.457i	−0.285096	−	0.559533i
$479$	433.715	+	140.923i	0.905459	+	0.294201i	0.724488	−	0.689287i	$-0.242076\pi$
$479$	433.715	+	140.923i	0.905459	+	0.294201i	0.180971	+	0.983488i	$0.442076\pi$
$480$	15.9832	−	9.59375i	0.0332983	−	0.0199870i
$481$	49.5797	+	152.591i	0.103076	+	0.317237i
$482$	−261.850	−	261.850i	−0.543257	−	0.543257i
$483$	125.023	+	63.7023i	0.258846	+	0.131889i
$484$	282.282	−	388.528i	0.583227	−	0.802743i
$485$	406.846	+	101.635i	0.838859	+	0.209557i
$486$	−171.587	+	124.665i	−0.353060	+	0.256513i
$487$	58.1185	+	366.946i	0.119340	+	0.753482i	0.972684	+	0.232134i	$0.0745707\pi$
$487$	58.1185	+	366.946i	0.119340	+	0.753482i	−0.853344	+	0.521348i	$0.825429\pi$
$488$	−180.997	+	28.6671i	−0.370895	+	0.0587441i
$489$	−46.9402	−	64.6077i	−0.0959923	−	0.132122i
$490$	−14.1666	+	11.8762i	−0.0289115	+	0.0242372i
$491$	−665.953	−	483.843i	−1.35632	−	0.985425i	−0.998669	−	0.0515692i	$-0.983578\pi$
$491$	−665.953	−	483.843i	−1.35632	−	0.985425i	−0.357651	−	0.933855i	$-0.616422\pi$
$492$	23.6552	−	46.4260i	0.0480797	−	0.0943617i
$493$	138.945	−	138.945i	0.281836	−	0.281836i
$494$	−165.221	+	53.6835i	−0.334455	+	0.108671i
$495$	−534.228	+	613.995i	−1.07925	+	1.24039i
$496$	−31.1546	+	95.8839i	−0.0628116	+	0.193314i
$497$	−708.081	+	360.785i	−1.42471	+	0.725926i
$498$	21.7556	−	137.359i	0.0436859	−	0.275822i
$499$		−	564.641i		−	1.13154i	−0.824562	−	0.565772i	$-0.808578\pi$
$499$		−	564.641i		−	1.13154i	0.824562	−	0.565772i	$-0.191422\pi$
$500$	−194.501	+	157.065i	−0.389002	+	0.314129i
$501$	178.250			0.355788
$502$	359.843	+	56.9935i	0.716818	+	0.113533i
$503$	87.1140	+	170.971i	0.173189	+	0.339902i	0.961243	−	0.275704i	$-0.0889110\pi$
$503$	87.1140	+	170.971i	0.173189	+	0.339902i	−0.788054	+	0.615607i	$0.788911\pi$
$504$	−165.537	−	53.7863i	−0.328447	−	0.106719i
$505$	−357.894	−	311.399i	−0.708701	−	0.616631i
$506$	246.102	+	757.423i	0.486367	+	1.49688i
$507$	−30.8446	−	30.8446i	−0.0608375	−	0.0608375i
$508$	−313.611	−	159.793i	−0.617344	−	0.314552i
$509$	−457.051	+	629.076i	−0.897938	+	1.23591i	0.0731825	+	0.997319i	$0.476684\pi$
$509$	−457.051	+	629.076i	−0.897938	+	1.23591i	−0.971121	+	0.238588i	$0.923316\pi$
$510$	−13.5857	−	16.2058i	−0.0266387	−	0.0317762i
$511$	745.641	−	541.740i	1.45918	−	1.06016i
$512$	3.53971	+	22.3488i	0.00691349	+	0.0436501i
$513$	−91.5916	+	14.5067i	−0.178541	+	0.0282781i
$514$	297.529	+	409.513i	0.578850	+	0.796718i
$515$	20.1676	−	80.7311i	0.0391603	−	0.156759i
$516$	24.1546	+	17.5493i	0.0468112	+	0.0340103i
$517$	−136.242	+	267.390i	−0.263525	+	0.517196i
$518$	−75.1627	+	75.1627i	−0.145102	+	0.145102i
$519$	−0.133228	+	0.0432883i	−0.000256701	+	8.34071e-5i
$520$	−111.617	−	185.953i	−0.214648	−	0.357603i
$521$	165.034	−	507.924i	0.316765	−	0.974901i	−0.658257	−	0.752793i	$-0.728706\pi$
$521$	165.034	−	507.924i	0.316765	−	0.974901i	0.975022	−	0.222108i	$-0.0712939\pi$
$522$	467.391	−	238.147i	0.895384	−	0.456221i
$523$	94.2656	−	595.170i	0.180240	−	1.13799i	−0.717204	−	0.696864i	$-0.754578\pi$
$523$	94.2656	−	595.170i	0.180240	−	1.13799i	0.897444	−	0.441129i	$-0.145422\pi$
$524$			388.922i			0.742218i
$525$	−116.558	−	20.6617i	−0.222014	−	0.0393556i
$526$	577.349			1.09762
$527$	112.962	+	17.8914i	0.214349	+	0.0339496i
$528$	22.7441	+	44.6377i	0.0430759	+	0.0845412i
$529$	−332.082	−	107.900i	−0.627754	−	0.203970i
$530$	136.474	−	321.107i	0.257499	−	0.605862i
$531$	37.3004	+	114.799i	0.0702456	+	0.216194i
$532$	−81.3839	−	81.3839i	−0.152977	−	0.152977i
$533$	−540.135	−	275.213i	−1.01339	−	0.516346i
$534$	−54.7429	+	75.3471i	−0.102515	+	0.141100i
$535$	3.07910	+	44.3233i	0.00575533	+	0.0828472i
$536$	5.64917	−	4.10436i	0.0105395	−	0.00765739i
$537$	6.70451	+	42.3306i	0.0124851	+	0.0788280i
$538$	234.831	−	37.1935i	0.436488	−	0.0691329i
$539$	−29.2017	−	40.1927i	−0.0541776	−	0.0745691i
$540$	−43.3194	−	107.360i	−0.0802212	−	0.198815i
$541$	267.054	+	194.026i	0.493631	+	0.358644i	0.806579	−	0.591126i	$-0.201317\pi$
$541$	267.054	+	194.026i	0.493631	+	0.358644i	−0.312948	+	0.949770i	$0.601317\pi$
$542$	−22.6113	+	44.3771i	−0.0417182	+	0.0818767i
$543$	−51.3369	+	51.3369i	−0.0945430	+	0.0945430i
$544$	24.4126	−	7.93214i	0.0448761	−	0.0145811i
$545$	288.006	−	66.3533i	0.528451	−	0.121749i
$546$	31.7337	−	97.6664i	0.0581204	−	0.178876i
$547$	51.5761	−	26.2793i	0.0942890	−	0.0480426i	−0.406210	−	0.913780i	$-0.633150\pi$
$547$	51.5761	−	26.2793i	0.0942890	−	0.0480426i	0.500499	+	0.865737i	$0.333150\pi$
$548$	−26.1507	+	165.109i	−0.0477202	+	0.301294i
$549$			554.965i			1.01086i
$550$	−384.865	−	550.711i	−0.699755	−	1.00129i
$551$	346.867			0.629524
$552$	−54.5617	−	8.64173i	−0.0988437	−	0.0156553i
$553$	180.169	+	353.601i	0.325803	+	0.639423i
$554$	661.323	+	214.877i	1.19372	+	0.387864i
$555$	−34.3437	−	3.02045i	−0.0618806	−	0.00544225i
$556$	62.7685	+	193.182i	0.112893	+	0.347449i
$557$	292.810	+	292.810i	0.525692	+	0.525692i	0.919285	−	0.393593i	$-0.128768\pi$
$557$	292.810	+	292.810i	0.525692	+	0.525692i	−0.393593	+	0.919285i	$0.628768\pi$
$558$	272.041	+	138.612i	0.487528	+	0.248408i
$559$	204.175	−	281.022i	0.365250	−	0.502723i
$560$	76.1976	−	121.818i	0.136067	−	0.217532i
$561$	45.9782	−	33.4051i	0.0819576	−	0.0595457i
$562$	63.5805	+	401.432i	0.113133	+	0.714291i
$563$	−294.479	+	46.6408i	−0.523053	+	0.0828434i	−0.412377	−	0.911013i	$-0.635301\pi$
$563$	−294.479	+	46.6408i	−0.523053	+	0.0828434i	−0.110675	+	0.993857i	$0.535301\pi$
$564$	−12.2354	−	16.8406i	−0.0216940	−	0.0298593i
$565$	−339.837	−	212.569i	−0.601482	−	0.376228i
$566$	−232.305	−	168.779i	−0.410432	−	0.298196i
$567$	−226.553	+	444.635i	−0.399564	+	0.784189i
$568$	221.231	−	221.231i	0.389492	−	0.389492i
$569$	−400.352	+	130.082i	−0.703607	+	0.228616i	−0.638901	−	0.769289i	$-0.720611\pi$
$569$	−400.352	+	130.082i	−0.703607	+	0.228616i	−0.0647055	+	0.997904i	$0.520611\pi$
$570$	3.27045	−	37.1864i	0.00573763	−	0.0652393i
$571$	−93.2408	+	286.966i	−0.163294	+	0.502567i	−0.998907	−	0.0467522i	$-0.985113\pi$
$571$	−93.2408	+	286.966i	−0.163294	+	0.502567i	0.835613	+	0.549319i	$0.185113\pi$
$572$	519.330	−	264.612i	0.907920	−	0.462608i
$573$	5.78457	−	36.5223i	0.0100952	−	0.0637388i
$574$		−	401.621i		−	0.699689i
$575$	740.724	+	13.6042i	1.28822	+	0.0236595i
$576$	68.5250			0.118967
$577$	132.165	+	20.9329i	0.229056	+	0.0362788i	0.269907	−	0.962886i	$-0.413007\pi$
$577$	132.165	+	20.9329i	0.229056	+	0.0362788i	−0.0408514	+	0.999165i	$0.513007\pi$
$578$	172.330	+	338.216i	0.298148	+	0.585148i
$579$	−30.9647	−	10.0610i	−0.0534796	−	0.0173766i
$580$	97.2200	+	421.983i	0.167621	+	0.727557i
$581$	−331.251	−	1019.49i	−0.570140	−	1.75471i
$582$	−55.2763	−	55.2763i	−0.0949765	−	0.0949765i
$583$	835.471	+	425.694i	1.43305	+	0.730178i
$584$	−213.280	+	293.555i	−0.365206	+	0.502663i
$585$	−609.087	+	245.765i	−1.04117	+	0.420111i
$586$	−212.467	+	154.366i	−0.362572	+	0.263424i
$587$	−43.1900	−	272.691i	−0.0735775	−	0.464550i	−0.996777	−	0.0802279i	$-0.974435\pi$
$587$	−43.1900	−	272.691i	−0.0735775	−	0.464550i	0.923199	−	0.384322i	$-0.125565\pi$
$588$	3.40366	−	0.539086i	0.00578853	−	0.000916813i
$589$	118.669	+	163.334i	0.201475	+	0.277306i
$590$	−99.4058	+	6.90564i	−0.168484	+	0.0117045i
$591$	−18.4145	−	13.3789i	−0.0311582	−	0.0226377i
$592$	18.9987	−	37.2870i	0.0320924	−	0.0629849i
$593$	617.372	−	617.372i	1.04110	−	1.04110i	0.0419820	−	0.999118i	$-0.486633\pi$
$593$	617.372	−	617.372i	1.04110	−	1.04110i	0.999118	−	0.0419820i	$-0.0133672\pi$
$594$	295.901	−	96.1440i	0.498149	−	0.161859i
$595$	−150.013	−	63.7576i	−0.252124	−	0.107156i
$596$	158.600	−	488.121i	0.266108	−	0.818995i
$597$	−60.0578	+	30.6010i	−0.100599	+	0.0512579i
$598$	−100.541	+	634.789i	−0.168128	+	1.06152i
$599$		−	194.492i		−	0.324695i	−0.986734	−	0.162348i	$-0.948093\pi$
$599$		−	194.492i		−	0.324695i	0.986734	−	0.162348i	$-0.0519066\pi$
$600$	46.1558	−	6.44392i	0.0769264	−	0.0107399i
$601$	−5.84871			−0.00973163			−0.00486581	−	0.999988i	$-0.501549\pi$
$601$	−5.84871			−0.00973163			−0.00486581	+	0.999988i	$0.501549\pi$
$602$	227.299	+	36.0007i	0.377574	+	0.0598018i
$603$	−9.60037	−	18.8418i	−0.0159210	−	0.0312467i
$604$	50.2876	+	16.3394i	0.0832576	+	0.0270520i
$605$	1029.41	−	617.894i	1.70150	−	1.02131i
$606$	27.3280	+	84.1068i	0.0450957	+	0.138790i
$607$	368.811	+	368.811i	0.607597	+	0.607597i	0.942317	−	0.334721i	$-0.108642\pi$
$607$	368.811	+	368.811i	0.607597	+	0.607597i	−0.334721	+	0.942317i	$0.608642\pi$
$608$	40.3733	+	20.5712i	0.0664035	+	0.0338343i
$609$	−120.521	+	165.883i	−0.197900	+	0.272386i
$610$	−444.474	−	111.035i	−0.728646	−	0.182024i
$611$	−195.929	+	142.351i	−0.320670	+	0.232980i
$612$	−12.1606	−	76.7789i	−0.0198702	−	0.125456i
$613$	211.132	−	33.4401i	0.344425	−	0.0545515i	0.0181741	−	0.999835i	$-0.494215\pi$
$613$	211.132	−	33.4401i	0.344425	−	0.0545515i	0.326251	+	0.945283i	$0.394215\pi$
$614$	−266.515	−	366.826i	−0.434063	−	0.597437i
$615$	99.8251	−	83.6858i	0.162317	−	0.136074i
$616$	312.403	+	226.974i	0.507148	+	0.368465i
$617$	104.841	−	205.762i	0.169921	−	0.333488i	−0.790305	−	0.612714i	$-0.790078\pi$
$617$	104.841	−	205.762i	0.169921	−	0.333488i	0.960225	+	0.279226i	$0.0900779\pi$
$618$	−10.9686	+	10.9686i	−0.0177485	+	0.0177485i
$619$	−1081.59	+	351.431i	−1.74732	+	0.567739i	−0.995766	−	0.0919290i	$-0.970697\pi$
$619$	−1081.59	+	351.431i	−1.74732	+	0.567739i	−0.751557	+	0.659668i	$0.770697\pi$
$620$	−165.443	+	190.146i	−0.266844	+	0.306687i
$621$	−106.015	+	326.282i	−0.170717	+	0.525414i
$622$	278.341	−	141.822i	0.447493	−	0.228009i
$623$	−112.300	+	709.032i	−0.180256	+	1.13809i
$624$			40.4295i			0.0647909i
$625$	−601.101	+	171.179i	−0.961762	+	0.273886i
$626$	−412.992			−0.659731
$627$	99.0877	+	15.6939i	0.158035	+	0.0250302i
$628$	−234.285	−	459.811i	−0.373066	−	0.732183i
$629$	−45.1499	−	14.6701i	−0.0717804	−	0.0233229i
$630$	−328.274	−	285.627i	−0.521070	−	0.453376i
$631$	−385.541	−	1186.57i	−0.611000	−	1.88047i	−0.448577	−	0.893744i	$-0.648069\pi$
$631$	−385.541	−	1186.57i	−0.611000	−	1.88047i	−0.162423	−	0.986721i	$-0.551931\pi$
$632$	−110.478	−	110.478i	−0.174808	−	0.174808i
$633$	133.713	+	68.1304i	0.211238	+	0.107631i
$634$	−156.739	+	215.732i	−0.247222	+	0.340272i
$635$	−565.303	−	674.326i	−0.890241	−	1.06193i
$636$	−52.6191	+	38.2300i	−0.0827345	+	0.0601101i
$637$	−6.27191	−	39.5993i	−0.00984601	−	0.0621652i
$638$	−1149.44	+	182.054i	−1.80164	+	0.285351i
$639$	−556.922	−	766.537i	−0.871553	−	1.19959i
$640$	−13.7102	+	54.8820i	−0.0214221	+	0.0857531i
$641$	774.288	+	562.553i	1.20794	+	0.877618i	0.995042	−	0.0994564i	$-0.0317104\pi$
$641$	774.288	+	562.553i	1.20794	+	0.877618i	0.212896	+	0.977075i	$0.431710\pi$
$642$	3.76013	−	7.37966i	0.00585689	−	0.0114948i
$643$	−564.710	+	564.710i	−0.878243	+	0.878243i	−0.993353	−	0.115109i	$-0.963278\pi$
$643$	−564.710	+	564.710i	−0.878243	+	0.878243i	0.115109	+	0.993353i	$0.463278\pi$
$644$	−404.959	+	131.579i	−0.628819	+	0.204316i
$645$	38.4142	+	63.9979i	0.0595569	+	0.0992216i
$646$	15.8843	−	48.8869i	0.0245887	−	0.0756764i
$647$	−438.612	+	223.484i	−0.677916	+	0.345415i	−0.758814	−	0.651307i	$-0.774221\pi$
$647$	−438.612	+	223.484i	−0.677916	+	0.345415i	0.0808985	+	0.996722i	$0.474221\pi$
$648$	30.7337	−	194.045i	0.0474286	−	0.299452i
$649$		−	267.793i		−	0.412625i
$650$	−74.9707	−	536.992i	−0.115340	−	0.826142i
$651$	−119.343			−0.183323
$652$	239.355	+	37.9102i	0.367109	+	0.0581444i
$653$	245.470	+	481.761i	0.375911	+	0.737766i	0.999015	−	0.0443726i	$-0.0141289\pi$
$653$	245.470	+	481.761i	0.375911	+	0.737766i	−0.623104	+	0.782139i	$0.714129\pi$
$654$	−52.3983	−	17.0252i	−0.0801196	−	0.0260325i
$655$	−380.317	+	894.838i	−0.580637	+	1.36617i
$656$	48.8606	+	150.377i	0.0744826	+	0.229234i
$657$	777.018	+	777.018i	1.18268	+	1.18268i
$658$	−142.961	−	72.8424i	−0.217266	−	0.110703i
$659$	−247.804	+	341.073i	−0.376030	+	0.517561i	−0.954527	−	0.298123i	$-0.903639\pi$
$659$	−247.804	+	341.073i	−0.376030	+	0.517561i	0.578497	+	0.815684i	$0.303639\pi$
$660$	8.67977	+	124.944i	0.0131512	+	0.189309i
$661$	355.368	−	258.190i	0.537622	−	0.390606i	−0.285579	−	0.958355i	$-0.592186\pi$
$661$	355.368	−	258.190i	0.537622	−	0.390606i	0.823201	+	0.567750i	$0.192186\pi$
$662$	4.45579	+	28.1328i	0.00673081	+	0.0424966i
$663$	45.2993	−	7.17470i	0.0683247	−	0.0108216i
$664$	248.058	+	341.423i	0.373581	+	0.514191i
$665$	−107.666	−	266.833i	−0.161904	−	0.401252i
$666$	−102.529	−	74.4920i	−0.153948	−	0.111850i
$667$	582.588	−	1143.39i	0.873446	−	1.71423i
$668$	−382.481	+	382.481i	−0.572576	+	0.572576i
$669$	133.111	−	43.2505i	0.198970	−	0.0646494i
$670$	17.0113	−	3.91920i	0.0253899	−	0.00584955i
$671$	380.467	−	1170.96i	0.567014	−	1.74509i
$672$	−23.8657	+	12.1602i	−0.0355145	+	0.0180955i
$673$	−192.174	+	1213.34i	−0.285548	+	1.80288i	0.260877	+	0.965372i	$0.415988\pi$
$673$	−192.174	+	1213.34i	−0.285548	+	1.80288i	−0.546425	+	0.837508i	$0.684012\pi$
$674$			1.01377i			0.00150411i
$675$	5.31473	−	289.377i	0.00787367	−	0.428707i
$676$	132.370			0.195814
$677$	−383.123	−	60.6808i	−0.565913	−	0.0896319i	−0.133079	−	0.991105i	$-0.542486\pi$
$677$	−383.123	−	60.6808i	−0.565913	−	0.0896319i	−0.432834	+	0.901474i	$0.642486\pi$
$678$	33.9234	+	66.5784i	0.0500345	+	0.0981983i
$679$	−573.056	−	186.197i	−0.843971	−	0.274223i
$680$	63.9256	+	5.62210i	0.0940083	+	0.00826780i
$681$	−33.5253	−	103.180i	−0.0492296	−	0.151513i
$682$	−478.969	−	478.969i	−0.702300	−	0.702300i
$683$	−621.402	−	316.620i	−0.909812	−	0.463572i	−0.0645440	−	0.997915i	$-0.520559\pi$
$683$	−621.402	−	316.620i	−0.909812	−	0.463572i	−0.845268	+	0.534342i	$0.820559\pi$
$684$	80.6577	−	111.016i	0.117921	−	0.162304i
$685$	−221.624	+	354.313i	−0.323538	+	0.517246i
$686$	−381.278	+	277.015i	−0.555799	+	0.403811i
$687$	13.3566	+	84.3302i	0.0194419	+	0.122751i
$688$	−89.4866	+	14.1733i	−0.130068	+	0.0206007i
$689$	444.781	+	612.188i	0.645546	+	0.888517i
$690$	−117.086	−	73.2376i	−0.169690	−	0.106141i
$691$	66.3377	+	48.1971i	0.0960024	+	0.0697498i	0.634751	−	0.772717i	$-0.281103\pi$
$691$	66.3377	+	48.1971i	0.0960024	+	0.0697498i	−0.538749	+	0.842467i	$0.681103\pi$
$692$	0.192988	−	0.378761i	0.000278885	−	0.000547342i
$693$	826.907	−	826.907i	1.19323	−	1.19323i
$694$	455.487	−	147.997i	0.656321	−	0.213252i
$695$	−44.4887	+	505.855i	−0.0640126	+	0.727850i
$696$	24.9451	−	76.7733i	0.0358407	−	0.110306i
$697$	159.820	−	81.4322i	0.229297	−	0.116832i
$698$	3.65493	−	23.0764i	0.00523630	−	0.0330607i
$699$			91.1498i			0.130400i
$700$	294.440	−	205.770i	0.420628	−	0.293956i
$701$	88.2963			0.125958			0.0629788	−	0.998015i	$-0.479940\pi$
$701$	88.2963			0.125958			0.0629788	+	0.998015i	$0.479940\pi$
$702$	247.992	+	39.2780i	0.353264	+	0.0559516i
$703$	−38.0454	−	74.6683i	−0.0541186	−	0.106214i
$704$	−144.585	−	46.9786i	−0.205377	−	0.0667310i
$705$	−11.6835	−	50.7119i	−0.0165723	−	0.0719318i
$706$	76.4879	+	235.406i	0.108340	+	0.333436i
$707$	482.000	+	482.000i	0.681753	+	0.681753i
$708$	16.5507	+	8.43301i	0.0233767	+	0.0119110i
$709$	176.056	−	242.321i	0.248317	−	0.341778i	−0.666604	−	0.745412i	$-0.732253\pi$
$709$	176.056	−	242.321i	0.248317	−	0.341778i	0.914921	+	0.403633i	$0.132253\pi$
$710$	725.350	−	292.676i	1.02162	−	0.412220i
$711$	−382.793	+	278.116i	−0.538387	+	0.391161i
$712$	−44.2118	−	279.142i	−0.0620952	−	0.392054i
$713$	737.715	−	116.843i	1.03466	−	0.163875i
$714$	17.8602	+	24.5824i	0.0250142	+	0.0344291i
$715$	1453.64	−	100.983i	2.03306	−	0.141235i
$716$	−105.218	−	76.4452i	−0.146952	−	0.106767i
$717$	−63.5094	+	124.644i	−0.0885765	+	0.173841i
$718$	436.546	−	436.546i	0.608003	−	0.608003i
$719$	956.744	−	310.865i	1.33066	−	0.432357i	0.444517	−	0.895771i	$-0.353375\pi$
$719$	956.744	−	310.865i	1.33066	−	0.432357i	0.886142	+	0.463413i	$0.153375\pi$
$720$	157.663	+	67.0089i	0.218977	+	0.0930679i
$721$	−36.9474	+	113.712i	−0.0512446	+	0.157715i
$722$	−374.038	+	190.582i	−0.518058	+	0.263964i
$723$	−26.9972	+	170.454i	−0.0373405	+	0.235759i
$724$		−	220.313i		−	0.304300i
$725$	−188.961	+	1065.97i	−0.260636	+	1.47031i
$726$	−223.812			−0.308281
$727$	−175.309	−	27.7663i	−0.241141	−	0.0381930i	0.0346941	−	0.999398i	$-0.488954\pi$
$727$	−175.309	−	27.7663i	−0.241141	−	0.0381930i	−0.275835	+	0.961205i	$0.588954\pi$
$728$	141.476	+	277.662i	0.194335	+	0.381403i
$729$	−500.542	−	162.636i	−0.686615	−	0.223095i
$730$	−777.780	+	466.855i	−1.06545	+	0.639528i
$731$	31.7609	+	97.7501i	0.0434486	+	0.133721i
$732$	60.3886	+	60.3886i	0.0824981	+	0.0824981i
$733$	−88.9443	−	45.3194i	−0.121343	−	0.0618273i	0.392265	−	0.919852i	$-0.371691\pi$
$733$	−88.9443	−	45.3194i	−0.121343	−	0.0618273i	−0.513608	+	0.858025i	$0.671691\pi$
$734$	6.97196	−	9.59608i	0.00949858	−	0.0130737i
$735$	8.35835	+	2.08801i	0.0113719	+	0.00284084i
$736$	135.620	−	98.5334i	0.184266	−	0.133877i
$737$	7.33909	+	46.3372i	0.00995806	+	0.0628727i
$738$	472.945	−	74.9071i	0.640846	−	0.101500i
$739$	297.186	+	409.042i	0.402147	+	0.553507i	0.961281	−	0.275570i	$-0.0888664\pi$
$739$	297.186	+	409.042i	0.402147	+	0.553507i	−0.559134	+	0.829077i	$0.688866\pi$
$740$	80.1746	−	67.2123i	0.108344	−	0.0908274i
$741$	65.4990	+	47.5878i	0.0883927	+	0.0642210i
$742$	−227.599	+	446.687i	−0.306737	+	0.602005i
$743$	−477.643	+	477.643i	−0.642858	+	0.642858i	−0.951257	−	0.308399i	$-0.900207\pi$
$743$	−477.643	+	477.643i	−0.642858	+	0.642858i	0.308399	+	0.951257i	$0.400207\pi$
$744$	44.6852	−	14.5191i	0.0600608	−	0.0195149i
$745$	842.232	−	967.986i	1.13051	−	1.29931i
$746$	167.789	−	516.402i	0.224919	−	0.692228i
$747$	1138.75	−	580.224i	1.52444	−	0.776739i
$748$	−26.9788	+	170.338i	−0.0360680	+	0.227724i
$749$		−	63.8399i		−	0.0852335i
$750$	112.498	+	30.3084i	0.149997	+	0.0404112i
$751$	−878.613			−1.16992			−0.584962	−	0.811061i	$-0.698891\pi$
$751$	−878.613			−1.16992			−0.584962	+	0.811061i	$0.698891\pi$
$752$	62.3903	+	9.88165i	0.0829658	+	0.0131405i
$753$	−77.0829	−	151.284i	−0.102368	−	0.200908i
$754$	−893.206	−	290.220i	−1.18462	−	0.384907i
$755$	99.7247	+	86.7691i	0.132086	+	0.114926i
$756$	51.4037	+	158.204i	0.0679944	+	0.209265i
$757$	−780.141	−	780.141i	−1.03057	−	1.03057i	−0.999518	−	0.0310514i	$-0.990114\pi$
$757$	−780.141	−	780.141i	−1.03057	−	1.03057i	−0.0310514	−	0.999518i	$-0.509886\pi$
$758$	428.795	+	218.482i	0.565693	+	0.288235i
$759$	218.157	−	300.268i	0.287427	−	0.395610i
$760$	72.7755	+	86.8107i	0.0957572	+	0.114225i
$761$	29.4845	−	21.4218i	0.0387445	−	0.0281495i	−0.568244	−	0.822860i	$-0.692377\pi$
$761$	29.4845	−	21.4218i	0.0387445	−	0.0281495i	0.606989	+	0.794710i	$0.292377\pi$
$762$	25.6602	+	162.012i	0.0336749	+	0.212615i
$763$	−419.437	+	66.4323i	−0.549721	+	0.0870673i
$764$	65.9559	+	90.7805i	0.0863297	+	0.118823i
$765$	47.1009	−	188.546i	0.0615699	−	0.246465i
$766$	86.1426	+	62.5863i	0.112458	+	0.0817053i
$767$	98.1124	−	192.556i	0.127917	−	0.251051i
$768$	7.45656	−	7.45656i	0.00970906	−	0.00970906i
$769$	182.285	−	59.2278i	0.237041	−	0.0770193i	−0.188088	−	0.982152i	$-0.560229\pi$
$769$	182.285	−	59.2278i	0.237041	−	0.0770193i	0.425129	+	0.905133i	$0.360229\pi$
$770$	496.830	+	827.718i	0.645234	+	1.07496i
$771$	72.8973	−	224.355i	0.0945490	−	0.290992i
$772$	88.0314	−	44.8543i	0.114030	−	0.0581014i
$773$	−68.2028	+	430.615i	−0.0882313	+	0.557070i	0.903485	+	0.428620i	$0.141000\pi$
$773$	−68.2028	+	430.615i	−0.0882313	+	0.557070i	−0.991716	+	0.128450i	$0.959000\pi$
$774$			274.380i			0.354496i
$775$	−566.594	+	275.708i	−0.731089	+	0.355752i
$776$	237.220			0.305696
$777$	48.9278	+	7.74940i	0.0629701	+	0.00997349i
$778$	−3.43215	−	6.73598i	−0.00441151	−	0.00865807i
$779$	301.135	+	97.8447i	0.386566	+	0.125603i
$780$	−39.5350	+	93.0209i	−0.0506859	+	0.119258i
$781$	649.571	+	1999.18i	0.831717	+	2.55976i
$782$	−134.469	−	134.469i	−0.171955	−	0.171955i
$783$	−446.687	−	227.598i	−0.570481	−	0.290675i
$784$	−6.14668	+	8.46018i	−0.00784016	+	0.0107911i
$785$	−89.4099	−	1287.04i	−0.113898	−	1.63955i
$786$	146.635	−	106.537i	0.186559	−	0.135543i
$787$	75.0272	+	473.703i	0.0953331	+	0.601910i	0.988387	+	0.151959i	$0.0485583\pi$
$787$	75.0272	+	473.703i	0.0953331	+	0.601910i	−0.893054	+	0.449950i	$0.851442\pi$
$788$	68.2210	−	10.8051i	0.0865749	−	0.0137121i
$789$	−158.152	−	217.678i	−0.200447	−	0.275891i
$790$	−146.157	−	362.225i	−0.185008	−	0.458513i
$791$	465.958	+	338.538i	0.589075	+	0.427988i
$792$	−209.015	+	410.216i	−0.263908	+	0.517949i
$793$	702.581	−	702.581i	0.885978	−	0.885978i
$794$	385.918	−	125.392i	0.486043	−	0.157925i
$795$	−158.451	+	36.5054i	−0.199310	+	0.0459187i
$796$	63.2073	−	194.532i	0.0794062	−	0.244387i
$797$	−993.693	+	506.312i	−1.24679	+	0.635272i	−0.947764	−	0.318973i	$-0.896662\pi$
$797$	−993.693	+	506.312i	−1.24679	+	0.635272i	−0.299027	+	0.954245i	$0.596662\pi$
$798$	−8.39082	+	52.9776i	−0.0105148	+	0.0663879i
$799$		−	71.6589i		−	0.0896857i
$800$	−85.2123	+	112.867i	−0.106515	+	0.141083i
$801$	−855.893			−1.06853
$802$	516.110	+	81.7439i	0.643529	+	0.101925i
$803$	−1106.78	−	2172.18i	−1.37831	−	2.70508i
$804$	−3.09494	−	1.00561i	−0.00384943	−	0.00125075i
$805$	−1060.41	−	93.2600i	−1.31727	−	0.115851i
$806$	−168.920	−	519.883i	−0.209578	−	0.645016i
$807$	−78.3499	−	78.3499i	−0.0970878	−	0.0970878i
$808$	−239.112	−	121.834i	−0.295931	−	0.150785i
$809$	−682.133	+	938.876i	−0.843181	+	1.16054i	0.142144	+	0.989846i	$0.454600\pi$
$809$	−682.133	+	938.876i	−0.843181	+	1.16054i	−0.985324	+	0.170693i	$0.945400\pi$
$810$	260.465	−	416.409i	0.321561	−	0.514085i
$811$	−1263.18	+	917.753i	−1.55756	+	1.13163i	−0.619579	+	0.784934i	$0.712697\pi$
$811$	−1263.18	+	917.753i	−1.55756	+	1.13163i	−0.937977	+	0.346697i	$0.887303\pi$
$812$	−97.3358	−	614.554i	−0.119872	−	0.756840i
$813$	22.9254	−	3.63103i	0.0281985	−	0.00446621i
$814$	165.264	+	227.466i	0.203027	+	0.279443i
$815$	513.641	+	321.284i	0.630235	+	0.394214i
$816$	−9.67797	−	7.03146i	−0.0118603	−	0.00861698i
$817$	−82.3689	+	161.658i	−0.100819	+	0.197868i
$818$	333.214	−	333.214i	0.407352	−	0.407352i
$819$	897.543	−	291.629i	1.09590	−	0.356080i
$820$	−34.6312	+	393.771i	−0.0422331	+	0.480208i
$821$	86.1613	−	265.177i	0.104947	−	0.322993i	−0.884771	−	0.466026i	$-0.845685\pi$
$821$	86.1613	−	265.177i	0.104947	−	0.322993i	0.989718	+	0.143033i	$0.0456854\pi$
$822$	69.4145	−	35.3684i	0.0844458	−	0.0430273i
$823$	20.0293	−	126.460i	0.0243370	−	0.153658i	−0.972527	−	0.232789i	$-0.925215\pi$
$823$	20.0293	−	126.460i	0.0243370	−	0.153658i	0.996864	+	0.0791316i	$0.0252147\pi$
$824$		−	47.0718i		−	0.0571260i
$825$	−102.209	+	295.961i	−0.123890	+	0.358741i
$826$	143.177			0.173337
$827$	−1189.79	−	188.444i	−1.43868	−	0.227865i	−0.612144	−	0.790746i	$-0.709693\pi$
$827$	−1189.79	−	188.444i	−1.43868	−	0.227865i	−0.826538	+	0.562881i	$0.809693\pi$
$828$	−230.476	−	452.334i	−0.278352	−	0.546297i
$829$	386.847	+	125.694i	0.466643	+	0.151622i	0.532895	−	0.846181i	$-0.321104\pi$
$829$	386.847	+	125.694i	0.466643	+	0.151622i	−0.0662518	+	0.997803i	$0.521104\pi$
$830$	236.867	+	1028.12i	0.285382	+	1.23870i
$831$	−100.140	−	308.200i	−0.120506	−	0.370878i
$832$	−86.7521	−	86.7521i	−0.104269	−	0.104269i
$833$	10.5700	+	5.38570i	0.0126891	+	0.00646542i
$834$	55.6412	−	76.5836i	0.0667161	−	0.0918269i
$835$	−1254.04	+	506.000i	−1.50184	+	0.605988i
$836$	−246.294	+	178.943i	−0.294610	+	0.214047i
$837$	−45.6466	−	288.202i	−0.0545360	−	0.344327i
$838$	804.628	−	127.441i	0.960176	−	0.152077i
$839$	−174.233	−	239.811i	−0.207667	−	0.285829i	0.692460	−	0.721456i	$-0.256527\pi$
$839$	−174.233	−	239.811i	−0.207667	−	0.285829i	−0.900127	+	0.435627i	$0.856527\pi$
$840$	−66.8018	+	4.64067i	−0.0795260	+	0.00552461i
$841$	836.695	+	607.895i	0.994881	+	0.722824i
$842$	−498.503	+	978.367i	−0.592046	+	1.16196i
$843$	133.935	−	133.935i	0.158879	−	0.158879i
$844$	−433.109	+	140.726i	−0.513162	+	0.166736i
$845$	304.560	+	129.442i	0.360426	+	0.153185i
$846$	59.1144	−	181.935i	0.0698752	−	0.215054i
$847$	−1537.09	+	783.188i	−1.81475	+	0.924661i
$848$	30.8756	−	194.941i	0.0364099	−	0.229883i
$849$			133.819i			0.157620i
$850$	141.583	+	75.4467i	0.166569	+	0.0887609i
$851$	−310.032			−0.364315
$852$	−144.013	−	22.8093i	−0.169029	−	0.0267715i
$853$	−38.4795	−	75.5203i	−0.0451108	−	0.0885350i	0.867351	−	0.497697i	$-0.165821\pi$
$853$	−38.4795	−	75.5203i	−0.0451108	−	0.0885350i	−0.912462	+	0.409162i	$0.865821\pi$
$854$	626.056	+	203.418i	0.733086	+	0.238194i
$855$	294.138	−	176.554i	0.344022	−	0.206496i
$856$	7.76666	+	23.9033i	0.00907320	+	0.0279244i
$857$	−337.532	−	337.532i	−0.393853	−	0.393853i	0.482205	−	0.876058i	$-0.339836\pi$
$857$	−337.532	−	337.532i	−0.393853	−	0.393853i	−0.876058	+	0.482205i	$0.839836\pi$
$858$	−242.026	−	123.318i	−0.282082	−	0.143728i
$859$	940.703	−	1294.77i	1.09511	−	1.50730i	0.253409	−	0.967359i	$-0.418448\pi$
$859$	940.703	−	1294.77i	1.09511	−	1.50730i	0.841706	−	0.539937i	$-0.181552\pi$
$860$	−219.752	−	54.8966i	−0.255526	−	0.0638333i
$861$	−151.423	+	110.016i	−0.175869	+	0.127776i
$862$	68.5095	+	432.552i	0.0794774	+	0.501800i
$863$	−55.7635	+	8.83207i	−0.0646159	+	0.0102342i	−0.188659	−	0.982043i	$-0.560414\pi$
$863$	−55.7635	+	8.83207i	−0.0646159	+	0.0102342i	0.124043	+	0.992277i	$0.460414\pi$
$864$	−38.4938	−	52.9822i	−0.0445530	−	0.0613220i
$865$	0.814412	−	0.682741i	0.000941517	−	0.000789296i
$866$	29.5562	+	21.4739i	0.0341296	+	0.0247966i
$867$	80.3116	−	157.620i	0.0926316	−	0.181800i
$868$	256.082	−	256.082i	0.295026	−	0.295026i
$869$	998.347	−	324.383i	1.14885	−	0.373283i
$870$	132.469	−	152.248i	0.152263	−	0.174998i
$871$	−11.6996	+	36.0075i	−0.0134323	+	0.0413404i
$872$	148.966	−	75.9021i	0.170833	−	0.0870437i
$873$	112.382	−	709.553i	0.128731	−	0.812775i
$874$		−	335.694i		−	0.384089i
$875$	878.669	−	185.513i	1.00419	−	0.212014i
$876$	169.103			0.193040
$877$	−96.1339	−	15.2261i	−0.109617	−	0.0173616i	0.101385	−	0.994847i	$-0.467673\pi$
$877$	−96.1339	−	15.2261i	−0.109617	−	0.0173616i	−0.211002	+	0.977486i	$0.567673\pi$
$878$	−189.738	−	372.381i	−0.216102	−	0.424124i
$879$	116.402	+	37.8212i	0.132425	+	0.0430275i
$880$	−286.725	−	249.476i	−0.325824	−	0.283495i
$881$	−206.996	−	637.067i	−0.234955	−	0.723118i	−0.997127	−	0.0757437i	$-0.975867\pi$
$881$	−206.996	−	637.067i	−0.234955	−	0.723118i	0.762172	−	0.647375i	$-0.224133\pi$
$882$	22.3935	+	22.3935i	0.0253894	+	0.0253894i
$883$	677.064	+	344.981i	0.766777	+	0.390692i	0.793202	−	0.608958i	$-0.208412\pi$
$883$	677.064	+	344.981i	0.766777	+	0.390692i	−0.0264252	+	0.999651i	$0.508412\pi$
$884$	−81.8063	+	112.597i	−0.0925410	+	0.127372i
$885$	29.8337	+	35.5873i	0.0337104	+	0.0402117i
$886$	−805.330	+	585.106i	−0.908950	+	0.660391i
$887$	−181.587	−	1146.50i	−0.204721	−	1.29256i	−0.849256	−	0.527981i	$-0.822949\pi$
$887$	−181.587	−	1146.50i	−0.204721	−	1.29256i	0.644535	−	0.764575i	$-0.277051\pi$
$888$	−19.2626	+	3.05090i	−0.0216921	+	0.00343570i
$889$	743.162	+	1022.88i	0.835953	+	1.15059i
$890$	171.243	−	685.489i	0.192408	−	0.770212i
$891$	1067.88	+	775.862i	1.19852	+	0.870776i
$892$	−192.820	+	378.430i	−0.216166	+	0.424249i
$893$	89.4459	−	89.4459i	0.100163	−	0.100163i
$894$	−227.482	+	73.9132i	−0.254454	+	0.0826770i
$895$	−167.333	−	278.776i	−0.186964	−	0.311482i
$896$	25.1173	−	77.3030i	0.0280327	−	0.0862757i
$897$	266.876	−	135.980i	0.297520	−	0.151594i
$898$	−22.0354	+	139.126i	−0.0245383	+	0.154929i
$899$			1091.45i			1.21407i
$900$	297.228	+	308.350i	0.330254	+	0.342612i
$901$	−223.901			−0.248503
$902$	−1049.25	−	166.185i	−1.16325	−	0.184241i
$903$	−48.6904	−	95.5603i	−0.0539207	−	0.105825i
$904$	−215.653	−	70.0699i	−0.238554	−	0.0775109i
$905$	215.439	−	506.901i	0.238054	−	0.560111i
$906$	−7.61475	−	23.4358i	−0.00840480	−	0.0258673i
$907$	1184.92	+	1184.92i	1.30642	+	1.30642i	0.923980	+	0.382441i	$0.124916\pi$
$907$	1184.92	+	1184.92i	1.30642	+	1.30642i	0.382441	+	0.923980i	$0.375084\pi$
$908$	293.338	+	149.463i	0.323059	+	0.164607i
$909$	−477.699	+	657.496i	−0.525521	+	0.723318i
$910$	53.9911	+	777.194i	0.0593309	+	0.854060i
$911$	17.4528	−	12.6802i	0.0191579	−	0.0139190i	−0.578165	−	0.815920i	$-0.696231\pi$
$911$	17.4528	−	12.6802i	0.0191579	−	0.0139190i	0.597323	+	0.802001i	$0.296231\pi$
$912$	−3.30342	−	20.8570i	−0.00362218	−	0.0228695i
$913$	−2800.51	+	443.557i	−3.06737	+	0.485824i
$914$	−563.737	−	775.917i	−0.616780	−	0.848925i
$915$	79.8906	+	197.996i	0.0873121	+	0.216389i
$916$	−209.613	−	152.293i	−0.228835	−	0.166258i
$917$	634.256	−	1244.80i	0.691664	−	1.35747i
$918$	−52.5328	+	52.5328i	−0.0572252	+	0.0572252i
$919$	−902.139	+	293.123i	−0.981652	+	0.318958i	−0.755511	−	0.655136i	$-0.772611\pi$
$919$	−902.139	+	293.123i	−0.981652	+	0.318958i	−0.226142	+	0.974094i	$0.572611\pi$
$920$	408.389	−	94.0882i	0.443901	−	0.102270i
$921$	−65.2985	+	200.968i	−0.0708996	+	0.218207i
$922$	114.470	−	58.3254i	0.124154	−	0.0632596i
$923$	−265.371	+	1675.49i	−0.287510	+	1.81526i
$924$		−	179.960i		−	0.194762i
$925$	250.192	−	76.2424i	0.270478	−	0.0824242i
$926$	768.205			0.829595
$927$	−140.797	−	22.3001i	−0.151885	−	0.0240562i
$928$	111.211	+	218.263i	0.119839	+	0.235198i
$929$	−11.6467	−	3.78425i	−0.0125368	−	0.00407347i	0.302742	−	0.953073i	$-0.402098\pi$
$929$	−11.6467	−	3.78425i	−0.0125368	−	0.00407347i	−0.315279	+	0.948999i	$0.602098\pi$
$930$	117.010	+	10.2908i	0.125818	+	0.0110654i
$931$	6.47117	+	19.9162i	0.00695078	+	0.0213923i
$932$	−195.586	−	195.586i	−0.209856	−	0.209856i
$933$	−129.717	−	66.0939i	−0.139032	−	0.0708402i
$934$	254.251	−	349.946i	0.272217	−	0.374675i
$935$	−228.642	+	365.534i	−0.244537	+	0.390945i
$936$	−300.584	+	218.387i	−0.321137	+	0.233320i
$937$	−40.8249	−	257.758i	−0.0435698	−	0.275089i	0.956279	−	0.292455i	$-0.0944720\pi$
$937$	−40.8249	−	257.758i	−0.0435698	−	0.275089i	−0.999849	+	0.0173657i	$0.994472\pi$
$938$	−24.7743	+	3.92387i	−0.0264119	+	0.00418323i
$939$	113.130	+	155.710i	0.120479	+	0.165826i
$940$	133.886	+	83.7458i	0.142432	+	0.0890913i
$941$	432.619	+	314.316i	0.459744	+	0.334024i	0.793431	−	0.608660i	$-0.208293\pi$
$941$	432.619	+	314.316i	0.459744	+	0.334024i	−0.333687	+	0.942684i	$0.608293\pi$
$942$	−109.185	+	214.288i	−0.115908	+	0.227482i
$943$	828.307	−	828.307i	0.878374	−	0.878374i
$944$	−53.6091	+	17.4187i	−0.0567893	+	0.0184520i
$945$	−36.4337	+	414.266i	−0.0385541	+	0.438377i
$946$	188.106	−	578.931i	0.198844	−	0.611978i
$947$	942.504	−	480.230i	0.995252	−	0.507106i	0.121038	−	0.992648i	$-0.461378\pi$
$947$	942.504	−	480.230i	0.995252	−	0.507106i	0.874214	+	0.485542i	$0.161378\pi$
$948$	−11.3905	+	71.9169i	−0.0120153	+	0.0758617i
$949$		−	1967.40i		−	2.07313i
$950$	82.5530	+	270.901i	0.0868979	+	0.285159i
$951$	124.273			0.130676
$952$	−91.0716	−	14.4243i	−0.0956635	−	0.0151516i
$953$	254.659	+	499.796i	0.267218	+	0.524444i	0.985156	−	0.171663i	$-0.0549139\pi$
$953$	254.659	+	499.796i	0.267218	+	0.524444i	−0.717938	+	0.696107i	$0.754914\pi$
$954$	−568.464	−	184.705i	−0.595874	−	0.193611i
$955$	62.9804	+	273.366i	0.0659480	+	0.286247i
$956$	−131.181	−	403.733i	−0.137218	−	0.422314i
$957$	383.505	+	383.505i	0.400737	+	0.400737i
$958$	574.637	+	292.792i	0.599830	+	0.305629i
$959$	352.959	−	485.806i	0.368049	−	0.506576i
$960$	24.4478	−	9.86459i	0.0254664	−	0.0102756i
$961$	263.521	−	191.459i	0.274215	−	0.199229i
$962$	35.4952	+	224.108i	0.0368973	+	0.232960i
$963$	75.1772	−	11.9069i	0.0780656	−	0.0123644i
$964$	−307.823	−	423.682i	−0.319319	−	0.439505i
$965$	246.406	−	17.1176i	0.255343	−	0.0177385i
$966$	160.539	+	116.639i	0.166190	+	0.120744i
$967$	459.689	−	902.191i	0.475377	−	0.932979i	−0.521443	−	0.853286i	$-0.674606\pi$
$967$	459.689	−	902.191i	0.475377	−	0.932979i	0.996819	−	0.0796930i	$-0.0253940\pi$
$968$	480.246	−	480.246i	0.496122	−	0.496122i
$969$	−22.7830	+	7.40265i	−0.0235119	+	0.00763948i
$970$	545.799	+	231.971i	0.562680	+	0.239146i
$971$	−193.400	+	595.223i	−0.199176	+	0.613000i	0.800727	+	0.599030i	$0.204447\pi$
$971$	−193.400	+	595.223i	−0.199176	+	0.613000i	−0.999902	+	0.0139699i	$0.995553\pi$
$972$	−267.253	+	136.172i	−0.274952	+	0.140095i
$973$	114.142	−	720.667i	0.117310	−	0.740665i
$974$			525.408i			0.539433i
$975$	−181.926	+	175.364i	−0.186591	+	0.179860i
$976$	−259.159			−0.265532
$977$	1027.50	+	162.741i	1.05169	+	0.166572i	0.658267	−	0.752785i	$-0.271290\pi$
$977$	1027.50	+	162.741i	1.05169	+	0.166572i	0.393426	+	0.919356i	$0.371290\pi$
$978$	−51.2730	−	100.629i	−0.0524263	−	0.102892i
$979$	1805.90	+	586.774i	1.84464	+	0.599360i
$980$	−22.4154	+	13.4546i	−0.0228729	+	0.0137292i
$981$	−156.460	−	481.534i	−0.159490	−	0.490861i
$982$	−823.164	−	823.164i	−0.838252	−	0.838252i
$983$	1732.04	+	882.521i	1.76200	+	0.897783i	0.948850	+	0.315727i	$0.102248\pi$
$983$	1732.04	+	882.521i	1.76200	+	0.897783i	0.813148	+	0.582056i	$0.197752\pi$
$984$	43.3125	−	59.6146i	0.0440168	−	0.0605840i
$985$	167.530	+	41.8510i	0.170081	+	0.0424883i
$986$	224.818	−	163.340i	0.228010	−	0.165659i
$987$	11.6974	+	73.8543i	0.0118514	+	0.0748271i
$988$	−242.657	+	38.4331i	−0.245604	+	0.0388999i
$989$	394.536	+	543.032i	0.398924	+	0.549072i
$990$	−882.047	+	739.441i	−0.890956	+	0.746910i
$991$	719.874	+	523.019i	0.726411	+	0.527769i	0.888426	−	0.459020i	$-0.151799\pi$
$991$	719.874	+	523.019i	0.726411	+	0.527769i	−0.162015	+	0.986788i	$0.551799\pi$
$992$	−64.7293	+	127.038i	−0.0652513	+	0.128063i
$993$	9.38634	−	9.38634i	0.00945250	−	0.00945250i
$994$	−1068.87	+	347.296i	−1.07532	+	0.349392i
$995$	335.657	−	385.774i	0.337343	−	0.387712i
$996$	60.7765	−	187.051i	0.0610206	−	0.187802i
$997$	−410.633	+	209.228i	−0.411869	+	0.209858i	−0.647633	−	0.761953i	$-0.724241\pi$
$997$	−410.633	+	209.228i	−0.411869	+	0.209858i	0.235764	+	0.971810i	$0.424241\pi$
$998$	124.916	−	788.691i	0.125167	−	0.790272i
$999$			121.120i			0.121241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.b.27.2	yes	24
4.3	odd	2		400.3.bg.b.177.2		24
5.2	odd	4		250.3.f.d.93.2		24
5.3	odd	4		250.3.f.f.93.2		24
5.4	even	2		250.3.f.e.157.2		24
25.9	even	10		250.3.f.d.207.2		24
25.12	odd	20		250.3.f.e.43.2		24
25.13	odd	20	inner	50.3.f.b.13.2	✓	24
25.16	even	5		250.3.f.f.207.2		24
100.63	even	20		400.3.bg.b.113.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.b.13.2	✓	24	25.13	odd	20	inner
50.3.f.b.27.2	yes	24	1.1	even	1	trivial
250.3.f.d.93.2		24	5.2	odd	4
250.3.f.d.207.2		24	25.9	even	10
250.3.f.e.43.2		24	25.12	odd	20
250.3.f.e.157.2		24	5.4	even	2
250.3.f.f.93.2		24	5.3	odd	4
250.3.f.f.207.2		24	25.16	even	5
400.3.bg.b.113.2		24	100.63	even	20
400.3.bg.b.177.2		24	4.3	odd	2

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39680 + 0.221232i) q^{2} +(-0.299213 - 0.587238i) q^{3} +(1.90211 + 0.618034i) q^{4} +(3.77205 + 3.28201i) q^{5} +(-0.288025 - 0.886451i) q^{6} +(-5.08008 - 5.08008i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.03475 - 6.92973i) q^{9} +O(q^{10})\)	\(q+(1.39680 + 0.221232i) q^{2} +(-0.299213 - 0.587238i) q^{3} +(1.90211 + 0.618034i) q^{4} +(3.77205 + 3.28201i) q^{5} +(-0.288025 - 0.886451i) q^{6} +(-5.08008 - 5.08008i) q^{7} +(2.52015 + 1.28408i) q^{8} +(5.03475 - 6.92973i) q^{9} +(4.54273 + 5.41882i) q^{10} +(-15.3739 + 11.1698i) q^{11} +(-0.206203 - 1.30192i) q^{12} +(-15.1469 + 2.39904i) q^{13} +(-5.97199 - 8.21974i) q^{14} +(0.798677 - 3.19712i) q^{15} +(3.23607 + 2.35114i) q^{16} +(2.06006 - 4.04310i) q^{17} +(8.56562 - 8.56562i) q^{18} +(7.61807 - 2.47526i) q^{19} +(5.14648 + 8.57402i) q^{20} +(-1.46319 + 4.50324i) q^{21} +(-23.9455 + 12.2008i) q^{22} +(4.63577 - 29.2691i) q^{23} -1.86414i q^{24} +(3.45678 + 24.7599i) q^{25} -21.6880 q^{26} +(-11.4345 - 1.81105i) q^{27} +(-6.52322 - 12.8025i) q^{28} +(41.1843 + 13.3816i) q^{29} +(1.82290 - 4.28905i) q^{30} +(7.78864 + 23.9710i) q^{31} +(4.00000 + 4.00000i) q^{32} +(11.1594 + 5.68602i) q^{33} +(3.77196 - 5.19165i) q^{34} +(-2.48944 - 35.8352i) q^{35} +(13.8595 - 10.0695i) q^{36} +(-1.63663 - 10.3332i) q^{37} +(11.1885 - 1.77209i) q^{38} +(5.94097 + 8.17704i) q^{39} +(5.29177 + 13.1148i) q^{40} +(31.9797 + 23.2346i) q^{41} +(-3.04005 + 5.96643i) q^{42} +(-16.0163 + 16.0163i) q^{43} +(-36.1463 + 11.7446i) q^{44} +(41.7348 - 9.61523i) q^{45} +(12.9505 - 39.8576i) q^{46} +(14.0708 - 7.16942i) q^{47} +(0.412407 - 2.60384i) q^{48} +2.61434i q^{49} +(-0.649230 + 35.3494i) q^{50} -2.99066 q^{51} +(-30.2939 - 4.79808i) q^{52} +(-22.4011 - 43.9646i) q^{53} +(-15.5711 - 5.05935i) q^{54} +(-94.6509 - 8.32431i) q^{55} +(-6.27932 - 19.3258i) q^{56} +(-3.73299 - 3.73299i) q^{57} +(54.5659 + 27.8027i) q^{58} +(-8.28306 + 11.4007i) q^{59} +(3.49510 - 5.58767i) q^{60} +(-52.4160 + 38.0825i) q^{61} +(5.57605 + 35.2058i) q^{62} +(-60.7805 + 9.62668i) q^{63} +(4.70228 + 6.47214i) q^{64} +(-65.0087 - 40.6631i) q^{65} +(14.3296 + 10.4111i) q^{66} +(1.12080 - 2.19970i) q^{67} +(6.41724 - 6.41724i) q^{68} +(-18.5750 + 6.03539i) q^{69} +(4.45062 - 50.6054i) q^{70} +(34.1821 - 105.202i) q^{71} +(21.5866 - 10.9989i) q^{72} +(-20.0687 + 126.709i) q^{73} -14.7956i q^{74} +(13.5056 - 9.43842i) q^{75} +16.0202 q^{76} +(134.844 + 21.3573i) q^{77} +(6.48934 + 12.7360i) q^{78} +(-52.5356 - 17.0699i) q^{79} +(4.49015 + 19.4894i) q^{80} +(-21.4645 - 66.0609i) q^{81} +(39.5291 + 39.5291i) q^{82} +(132.945 + 67.7386i) q^{83} +(-5.56631 + 7.66137i) q^{84} +(21.0401 - 8.48963i) q^{85} +(-25.9150 + 18.8283i) q^{86} +(-4.46469 - 28.1889i) q^{87} +(-53.0875 + 8.40824i) q^{88} +(-58.7326 - 80.8385i) q^{89} +(60.4225 - 4.19750i) q^{90} +(89.1349 + 64.7603i) q^{91} +(26.9071 - 52.8081i) q^{92} +(11.7462 - 11.7462i) q^{93} +(21.2402 - 6.90136i) q^{94} +(36.8596 + 15.6658i) q^{95} +(1.15210 - 3.54581i) q^{96} +(74.7286 - 38.0761i) q^{97} +(-0.578375 + 3.65172i) q^{98} +162.775i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9	\( 24 q + 6 q^{2} + 2 q^{3} - 4 q^{6} - 2 q^{7} - 12 q^{8} + 40 q^{9} - 32 q^{11} + 4 q^{12} + 2 q^{13} + 30 q^{14} - 20 q^{15} + 24 q^{16} - 92 q^{17} - 136 q^{18} - 230 q^{19} - 20 q^{20} + 68 q^{21} - 48 q^{22} - 18 q^{23} + 40 q^{25} + 36 q^{26} + 260 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} - 132 q^{31} + 96 q^{32} + 364 q^{33} + 150 q^{34} + 50 q^{35} - 108 q^{36} - 192 q^{37} + 20 q^{38} - 80 q^{39} + 20 q^{40} + 168 q^{41} - 8 q^{42} - 78 q^{43} - 40 q^{44} - 310 q^{45} + 26 q^{46} - 22 q^{47} - 8 q^{48} - 30 q^{50} + 168 q^{51} + 4 q^{52} - 108 q^{53} - 80 q^{54} - 40 q^{55} - 48 q^{56} + 280 q^{57} + 40 q^{58} + 450 q^{59} - 100 q^{60} - 492 q^{61} - 458 q^{62} - 558 q^{63} + 120 q^{65} + 202 q^{66} - 572 q^{67} - 136 q^{68} - 670 q^{69} - 260 q^{70} - 2 q^{71} + 128 q^{72} + 262 q^{73} + 140 q^{75} - 40 q^{76} + 496 q^{77} - 62 q^{78} - 360 q^{79} - 80 q^{80} - 46 q^{81} + 272 q^{82} + 772 q^{83} + 620 q^{84} + 490 q^{85} - 264 q^{86} + 210 q^{87} - 84 q^{88} + 900 q^{89} + 1110 q^{90} + 798 q^{91} - 16 q^{92} + 294 q^{93} - 190 q^{94} + 16 q^{96} + 378 q^{97} + 106 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 - 2 * q^7 - 12 * q^8 + 40 * q^9 - 32 * q^11 + 4 * q^12 + 2 * q^13 + 30 * q^14 - 20 * q^15 + 24 * q^16 - 92 * q^17 - 136 * q^18 - 230 * q^19 - 20 * q^20 + 68 * q^21 - 48 * q^22 - 18 * q^23 + 40 * q^25 + 36 * q^26 + 260 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 - 132 * q^31 + 96 * q^32 + 364 * q^33 + 150 * q^34 + 50 * q^35 - 108 * q^36 - 192 * q^37 + 20 * q^38 - 80 * q^39 + 20 * q^40 + 168 * q^41 - 8 * q^42 - 78 * q^43 - 40 * q^44 - 310 * q^45 + 26 * q^46 - 22 * q^47 - 8 * q^48 - 30 * q^50 + 168 * q^51 + 4 * q^52 - 108 * q^53 - 80 * q^54 - 40 * q^55 - 48 * q^56 + 280 * q^57 + 40 * q^58 + 450 * q^59 - 100 * q^60 - 492 * q^61 - 458 * q^62 - 558 * q^63 + 120 * q^65 + 202 * q^66 - 572 * q^67 - 136 * q^68 - 670 * q^69 - 260 * q^70 - 2 * q^71 + 128 * q^72 + 262 * q^73 + 140 * q^75 - 40 * q^76 + 496 * q^77 - 62 * q^78 - 360 * q^79 - 80 * q^80 - 46 * q^81 + 272 * q^82 + 772 * q^83 + 620 * q^84 + 490 * q^85 - 264 * q^86 + 210 * q^87 - 84 * q^88 + 900 * q^89 + 1110 * q^90 + 798 * q^91 - 16 * q^92 + 294 * q^93 - 190 * q^94 + 16 * q^96 + 378 * q^97 + 106 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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