LMFDB - Embedded newform 111.2.k.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(7,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("111.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.k (of order $9$, 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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 33 x^{15} + 150 x^{14} - 231 x^{13} + 796 x^{12} - 801 x^{11} + \cdots + 361 $ x^18 - 3x^17 + 18x^16 - 33x^15 + 150x^14 - 231x^13 + 796x^12 - 801x^11 + 2382x^10 - 1621x^9 + 5184x^8 - 2001x^7 + 6622x^6 - 1269x^5 + 5964x^4 - 347x^3 + 1662x^2 - 57*x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Root			$1.10120 + 1.90733i$ of defining polynomial
Character	$\chi$	$=$	111.7
Dual form			111.2.k.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06958 + 0.753264i) q^{2} +(0.939693 + 0.342020i) q^{3} +(2.18365 - 1.83230i) q^{4} +(-0.647697 - 3.67327i) q^{5} -2.20240 q^{6} +(-0.172439 - 0.977948i) q^{7} +(-0.936630 + 1.62229i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-2.06958 + 0.753264i) q^{2} +(0.939693 + 0.342020i) q^{3} +(2.18365 - 1.83230i) q^{4} +(-0.647697 - 3.67327i) q^{5} -2.20240 q^{6} +(-0.172439 - 0.977948i) q^{7} +(-0.936630 + 1.62229i) q^{8} +(0.766044 + 0.642788i) q^{9} +(4.10741 + 7.11424i) q^{10} +(-0.287723 + 0.498351i) q^{11} +(2.67865 - 0.974947i) q^{12} +(4.60513 - 3.86416i) q^{13} +(1.09353 + 1.89405i) q^{14} +(0.647697 - 3.67327i) q^{15} +(-0.273573 + 1.55151i) q^{16} +(2.33413 + 1.95857i) q^{17} +(-2.06958 - 0.753264i) q^{18} +(-4.33482 - 1.57775i) q^{19} +(-8.14489 - 6.83437i) q^{20} +(0.172439 - 0.977948i) q^{21} +(0.220075 - 1.24811i) q^{22} +(2.34707 + 4.06525i) q^{23} +(-1.43500 + 1.20411i) q^{24} +(-8.37497 + 3.04824i) q^{25} +(-6.61994 + 11.4661i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.16844 - 1.81954i) q^{28} +(2.56038 - 4.43471i) q^{29} +(1.42649 + 8.09001i) q^{30} -9.37549 q^{31} +(-1.25309 - 7.10665i) q^{32} +(-0.440818 + 0.369890i) q^{33} +(-6.30599 - 2.29519i) q^{34} +(-3.48058 + 1.26683i) q^{35} +2.85055 q^{36} +(5.46475 + 2.67143i) q^{37} +10.1597 q^{38} +(5.64903 - 2.05608i) q^{39} +(6.56577 + 2.38975i) q^{40} +(-4.49961 + 3.77562i) q^{41} +(0.379779 + 2.15383i) q^{42} +6.49994 q^{43} +(0.284842 + 1.61542i) q^{44} +(1.86497 - 3.23022i) q^{45} +(-7.91965 - 6.64538i) q^{46} +(1.14724 + 1.98707i) q^{47} +(-0.787723 + 1.36438i) q^{48} +(5.65120 - 2.05687i) q^{49} +(15.0365 - 12.6171i) q^{50} +(1.52350 + 2.63878i) q^{51} +(2.97569 - 16.8760i) q^{52} +(-0.389624 + 2.20967i) q^{53} +(-1.68713 - 1.41567i) q^{54} +(2.01694 + 0.734105i) q^{55} +(1.74803 + 0.636230i) q^{56} +(-3.53378 - 2.96519i) q^{57} +(-1.95840 + 11.1066i) q^{58} +(-1.12480 + 6.37905i) q^{59} +(-5.31620 - 9.20793i) q^{60} +(-5.89178 + 4.94379i) q^{61} +(19.4033 - 7.06222i) q^{62} +(0.496517 - 0.859993i) q^{63} +(6.37111 + 11.0351i) q^{64} +(-17.1769 - 14.4131i) q^{65} +(0.633681 - 1.09757i) q^{66} +(2.00798 + 11.3878i) q^{67} +8.68563 q^{68} +(0.815130 + 4.62283i) q^{69} +(6.24908 - 5.24360i) q^{70} +(14.8901 + 5.41957i) q^{71} +(-1.76029 + 0.640693i) q^{72} -4.63167 q^{73} +(-13.3220 - 1.41233i) q^{74} -8.91245 q^{75} +(-12.3566 + 4.49745i) q^{76} +(0.536976 + 0.195443i) q^{77} +(-10.1423 + 8.51043i) q^{78} +(0.535375 + 3.03626i) q^{79} +5.87632 q^{80} +(0.173648 + 0.984808i) q^{81} +(6.46824 - 11.2033i) q^{82} +(-5.57813 - 4.68060i) q^{83} +(-1.41535 - 2.45146i) q^{84} +(5.68256 - 9.84248i) q^{85} +(-13.4521 + 4.89618i) q^{86} +(3.92273 - 3.29156i) q^{87} +(-0.538980 - 0.933541i) q^{88} +(-0.0489495 + 0.277607i) q^{89} +(-1.42649 + 8.09001i) q^{90} +(-4.57306 - 3.83725i) q^{91} +(12.5739 + 4.57654i) q^{92} +(-8.81008 - 3.20661i) q^{93} +(-3.87108 - 3.24822i) q^{94} +(-2.98784 + 16.9449i) q^{95} +(1.25309 - 7.10665i) q^{96} +(-1.44234 - 2.49820i) q^{97} +(-10.1462 + 8.51370i) q^{98} +(-0.540743 + 0.196814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−2.06958	+	0.753264i	−1.46341	+	0.532638i	−0.946303	−	0.323281i	$-0.895214\pi$
$2$	−2.06958	+	0.753264i	−1.46341	+	0.532638i	−0.517109	+	0.855920i	$0.672992\pi$
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$3$	0.939693	+	0.342020i	0.542532	+	0.197465i
$4$	2.18365	−	1.83230i	1.09183	−	0.916151i
$5$	−0.647697	−	3.67327i	−0.289659	−	1.64274i	−0.688152	−	0.725567i	$-0.741578\pi$
$5$	−0.647697	−	3.67327i	−0.289659	−	1.64274i	0.398493	−	0.917171i	$-0.369533\pi$
$6$	−2.20240			−0.899125
$7$	−0.172439	−	0.977948i	−0.0651757	−	0.369630i	−0.999898	−	0.0142519i	$-0.995463\pi$
$7$	−0.172439	−	0.977948i	−0.0651757	−	0.369630i	0.934723	−	0.355378i	$-0.115648\pi$
$8$	−0.936630	+	1.62229i	−0.331149	+	0.573566i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	4.10741	+	7.11424i	1.29888	+	2.24972i
$11$	−0.287723	+	0.498351i	−0.0867518	+	0.150259i	−0.906136	−	0.422986i	$-0.860982\pi$
$11$	−0.287723	+	0.498351i	−0.0867518	+	0.150259i	0.819385	+	0.573244i	$0.194315\pi$
$12$	2.67865	−	0.974947i	0.773258	−	0.281443i
$13$	4.60513	−	3.86416i	1.27723	−	1.07173i	0.283615	−	0.958938i	$-0.408466\pi$
$13$	4.60513	−	3.86416i	1.27723	−	1.07173i	0.993619	−	0.112788i	$-0.0359782\pi$
$14$	1.09353	+	1.89405i	0.292258	+	0.506205i
$15$	0.647697	−	3.67327i	0.167235	−	0.948435i
$16$	−0.273573	+	1.55151i	−0.0683934	+	0.387878i
$17$	2.33413	+	1.95857i	0.566111	+	0.475023i	0.880353	−	0.474320i	$-0.157306\pi$
$17$	2.33413	+	1.95857i	0.566111	+	0.475023i	−0.314242	+	0.949343i	$0.601750\pi$
$18$	−2.06958	−	0.753264i	−0.487804	−	0.177546i
$19$	−4.33482	−	1.57775i	−0.994476	−	0.361960i	−0.207024	−	0.978336i	$-0.566378\pi$
$19$	−4.33482	−	1.57775i	−0.994476	−	0.361960i	−0.787452	+	0.616376i	$0.788600\pi$
$20$	−8.14489	−	6.83437i	−1.82125	−	1.52821i
$21$	0.172439	−	0.977948i	0.0376292	−	0.213406i
$22$	0.220075	−	1.24811i	0.0469202	−	0.266097i
$23$	2.34707	+	4.06525i	0.489398	+	0.847663i	0.999926	−	0.0121987i	$-0.00388307\pi$
$23$	2.34707	+	4.06525i	0.489398	+	0.847663i	−0.510527	+	0.859862i	$0.670550\pi$
$24$	−1.43500	+	1.20411i	−0.292918	+	0.245788i
$25$	−8.37497	+	3.04824i	−1.67499	+	0.609648i
$26$	−6.61994	+	11.4661i	−1.29828	+	2.24868i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−2.16844	−	1.81954i	−0.409797	−	0.343861i
$29$	2.56038	−	4.43471i	0.475451	−	0.823506i	−0.524153	−	0.851624i	$-0.675618\pi$
$29$	2.56038	−	4.43471i	0.475451	−	0.823506i	0.999605	+	0.0281183i	$0.00895150\pi$
$30$	1.42649	+	8.09001i	0.260440	+	1.47703i
$31$	−9.37549			−1.68389			−0.841944	−	0.539565i	$-0.818589\pi$
$31$	−9.37549			−1.68389			−0.841944	+	0.539565i	$0.818589\pi$
$32$	−1.25309	−	7.10665i	−0.221518	−	1.25629i
$33$	−0.440818	+	0.369890i	−0.0767365	+	0.0643896i
$34$	−6.30599	−	2.29519i	−1.08147	−	0.393622i
$35$	−3.48058	+	1.26683i	−0.588326	+	0.214133i
$36$	2.85055			0.475092
$37$	5.46475	+	2.67143i	0.898399	+	0.439180i
$37$	5.46475	+	2.67143i	0.898399	+	0.439180i
$38$	10.1597			1.64812
$39$	5.64903	−	2.05608i	0.904569	−	0.329236i
$40$	6.56577	+	2.38975i	1.03814	+	0.377852i
$41$	−4.49961	+	3.77562i	−0.702721	+	0.589653i	−0.922546	−	0.385886i	$-0.873896\pi$
$41$	−4.49961	+	3.77562i	−0.702721	+	0.589653i	0.219826	+	0.975539i	$0.429451\pi$
$42$	0.379779	+	2.15383i	0.0586011	+	0.332343i
$43$	6.49994			0.991232			0.495616	−	0.868542i	$-0.334942\pi$
$43$	6.49994			0.991232			0.495616	+	0.868542i	$0.334942\pi$
$44$	0.284842	+	1.61542i	0.0429416	+	0.243534i
$45$	1.86497	−	3.23022i	0.278013	−	0.481533i
$46$	−7.91965	−	6.64538i	−1.16769	−	0.979807i
$47$	1.14724	+	1.98707i	0.167342	+	0.289844i	0.937484	−	0.348027i	$-0.113148\pi$
$47$	1.14724	+	1.98707i	0.167342	+	0.289844i	−0.770143	+	0.637872i	$0.779815\pi$
$48$	−0.787723	+	1.36438i	−0.113698	+	0.196931i
$49$	5.65120	−	2.05687i	0.807314	−	0.293838i
$50$	15.0365	−	12.6171i	2.12648	−	1.78433i
$51$	1.52350	+	2.63878i	0.213332	+	0.369503i
$52$	2.97569	−	16.8760i	0.412654	−	2.34028i
$53$	−0.389624	+	2.20967i	−0.0535189	+	0.303521i	−0.999804	−	0.0198135i	$-0.993693\pi$
$53$	−0.389624	+	2.20967i	−0.0535189	+	0.303521i	0.946285	+	0.323334i	$0.104804\pi$
$54$	−1.68713	−	1.41567i	−0.229590	−	0.192649i
$55$	2.01694	+	0.734105i	0.271964	+	0.0989868i
$56$	1.74803	+	0.636230i	0.233590	+	0.0850198i
$57$	−3.53378	−	2.96519i	−0.468060	−	0.392749i
$58$	−1.95840	+	11.1066i	−0.257150	+	1.45837i
$59$	−1.12480	+	6.37905i	−0.146436	+	0.830481i	0.819766	+	0.572698i	$0.194103\pi$
$59$	−1.12480	+	6.37905i	−0.146436	+	0.830481i	−0.966203	+	0.257783i	$0.917008\pi$
$60$	−5.31620	−	9.20793i	−0.686318	−	1.18874i
$61$	−5.89178	+	4.94379i	−0.754365	+	0.632987i	−0.936653	−	0.350258i	$-0.886094\pi$
$61$	−5.89178	+	4.94379i	−0.754365	+	0.632987i	0.182288	+	0.983245i	$0.441650\pi$
$62$	19.4033	−	7.06222i	2.46422	−	0.896903i
$63$	0.496517	−	0.859993i	0.0625553	−	0.108349i
$64$	6.37111	+	11.0351i	0.796389	+	1.37939i
$65$	−17.1769	−	14.4131i	−2.13053	−	1.78773i
$66$	0.633681	−	1.09757i	0.0780007	−	0.135101i
$67$	2.00798	+	11.3878i	0.245314	+	1.39124i	0.819762	+	0.572704i	$0.194106\pi$
$67$	2.00798	+	11.3878i	0.245314	+	1.39124i	−0.574448	+	0.818541i	$0.694783\pi$
$68$	8.68563			1.05329
$69$	0.815130	+	4.62283i	0.0981301	+	0.556523i
$70$	6.24908	−	5.24360i	0.746908	−	0.626730i
$71$	14.8901	+	5.41957i	1.76713	+	0.643184i	0.999999	+	0.00169869i	$0.000540710\pi$
$71$	14.8901	+	5.41957i	1.76713	+	0.643184i	0.767135	+	0.641485i	$0.221682\pi$
$72$	−1.76029	+	0.640693i	−0.207452	+	0.0755064i
$73$	−4.63167			−0.542097			−0.271048	−	0.962566i	$-0.587370\pi$
$73$	−4.63167			−0.542097			−0.271048	+	0.962566i	$0.587370\pi$
$74$	−13.3220	−	1.41233i	−1.54865	−	0.164180i
$75$	−8.91245			−1.02912
$76$	−12.3566	+	4.49745i	−1.41740	+	0.515893i
$77$	0.536976	+	0.195443i	0.0611941	+	0.0222728i
$78$	−10.1423	+	8.51043i	−1.14839	+	0.963616i
$79$	0.535375	+	3.03626i	0.0602344	+	0.341606i	1.00000		0.000213514i	$-6.79638e-5\pi$
$79$	0.535375	+	3.03626i	0.0602344	+	0.341606i	−0.939766	+	0.341819i	$0.888957\pi$
$80$	5.87632			0.656993
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	6.46824	−	11.2033i	0.714298	−	1.23720i
$83$	−5.57813	−	4.68060i	−0.612279	−	0.513763i	0.283087	−	0.959094i	$-0.408641\pi$
$83$	−5.57813	−	4.68060i	−0.612279	−	0.513763i	−0.895366	+	0.445331i	$0.853086\pi$
$84$	−1.41535	−	2.45146i	−0.154427	−	0.267476i
$85$	5.68256	−	9.84248i	0.616360	−	1.06757i
$86$	−13.4521	+	4.89618i	−1.45058	+	0.527968i
$87$	3.92273	−	3.29156i	0.420561	−	0.352893i
$88$	−0.538980	−	0.933541i	−0.0574555	−	0.0995159i
$89$	−0.0489495	+	0.277607i	−0.00518864	+	0.0294262i	−0.987292	−	0.158916i	$-0.949200\pi$
$89$	−0.0489495	+	0.277607i	−0.00518864	+	0.0294262i	0.982104	+	0.188342i	$0.0603113\pi$
$90$	−1.42649	+	8.09001i	−0.150365	+	0.852762i
$91$	−4.57306	−	3.83725i	−0.479387	−	0.402253i
$92$	12.5739	+	4.57654i	1.31092	+	0.477138i
$93$	−8.81008	−	3.20661i	−0.913562	−	0.332510i
$94$	−3.87108	−	3.24822i	−0.399272	−	0.335029i
$95$	−2.98784	+	16.9449i	−0.306546	+	1.73851i
$96$	1.25309	−	7.10665i	0.127893	−	0.725319i
$97$	−1.44234	−	2.49820i	−0.146447	−	0.253654i	0.783465	−	0.621436i	$-0.213451\pi$
$97$	−1.44234	−	2.49820i	−0.146447	−	0.253654i	−0.929912	+	0.367782i	$0.880117\pi$
$98$	−10.1462	+	8.51370i	−1.02492	+	0.860013i
$99$	−0.540743	+	0.196814i	−0.0543467	+	0.0197806i
$100$	−12.7027	+	22.0018i	−1.27027	+	2.20018i
$101$	−3.02211	−	5.23444i	−0.300711	−	0.520846i	0.675586	−	0.737281i	$-0.263891\pi$
$101$	−3.02211	−	5.23444i	−0.300711	−	0.520846i	−0.976297	+	0.216435i	$0.930557\pi$
$102$	−5.14069	−	4.31355i	−0.509004	−	0.427105i
$103$	0.665328	−	1.15238i	0.0655568	−	0.113548i	−0.831384	−	0.555698i	$-0.812451\pi$
$103$	0.665328	−	1.15238i	0.0655568	−	0.113548i	0.896941	+	0.442151i	$0.145784\pi$
$104$	1.95549	+	11.0902i	0.191752	+	1.08748i
$105$	−3.70396			−0.361469
$106$	−0.858106	−	4.86656i	−0.0833466	−	0.472682i
$107$	5.85232	−	4.91068i	0.565765	−	0.474733i	−0.314473	−	0.949267i	$-0.601828\pi$
$107$	5.85232	−	4.91068i	0.565765	−	0.474733i	0.880238	+	0.474533i	$0.157383\pi$
$108$	2.67865	+	0.974947i	0.257753	+	0.0938143i
$109$	13.2093	−	4.80780i	1.26522	−	0.460504i	0.379705	−	0.925108i	$-0.376025\pi$
$109$	13.2093	−	4.80780i	1.26522	−	0.460504i	0.885519	+	0.464604i	$0.153803\pi$
$110$	−4.72718			−0.450719
$111$	4.22150	+	4.37938i	0.400687	+	0.415672i
$112$	1.56447			0.147829
$113$	−11.5795	+	4.21459i	−1.08931	+	0.396475i	−0.823364	−	0.567514i	$-0.807905\pi$
$113$	−11.5795	+	4.21459i	−1.08931	+	0.396475i	−0.265943	+	0.963989i	$0.585683\pi$
$114$	9.54700	+	3.47482i	0.894158	+	0.325447i
$115$	13.4126	−	11.2545i	1.25073	−	1.04949i
$116$	−2.53475	−	14.3753i	−0.235345	−	1.33471i
$117$	6.01157			0.555770
$118$	−2.47725	−	14.0492i	−0.228050	−	1.29333i
$119$	1.51289	−	2.62040i	0.138686	−	0.240211i
$120$	5.35247	+	4.49125i	0.488611	+	0.409993i
$121$	5.33443	+	9.23950i	0.484948	+	0.839955i
$122$	8.46951	−	14.6696i	0.766793	−	1.32812i
$123$	−5.51959	+	2.00897i	−0.497684	+	0.181142i
$124$	−20.4728	+	17.1787i	−1.83851	+	1.54269i
$125$	7.29661	+	12.6381i	0.652629	+	1.13039i
$126$	−0.379779	+	2.15383i	−0.0338334	+	0.191879i
$127$	−0.418724	+	2.37470i	−0.0371557	+	0.210720i	−0.997733	−	0.0672913i	$-0.978564\pi$
$127$	−0.418724	+	2.37470i	−0.0371557	+	0.210720i	0.960578	+	0.278012i	$0.0896754\pi$
$128$	−10.4419	−	8.76176i	−0.922939	−	0.774438i
$129$	6.10795	+	2.22311i	0.537775	+	0.195734i
$130$	46.4057	+	16.8903i	4.07005	+	1.48138i
$131$	3.10018	+	2.60136i	0.270864	+	0.227282i	0.768094	−	0.640337i	$-0.221205\pi$
$131$	3.10018	+	2.60136i	0.270864	+	0.227282i	−0.497231	+	0.867618i	$0.665650\pi$
$132$	−0.284842	+	1.61542i	−0.0247923	+	0.140604i
$133$	−0.795463	+	4.51130i	−0.0689754	+	0.391179i
$134$	−12.7337	−	22.0554i	−1.10003	−	1.90530i
$135$	2.85730	−	2.39756i	0.245917	−	0.206349i
$136$	−5.36359	+	1.95219i	−0.459924	+	0.167399i
$137$	7.58236	−	13.1330i	0.647805	−	1.12203i	−0.335842	−	0.941918i	$-0.609021\pi$
$137$	7.58236	−	13.1330i	0.647805	−	1.12203i	0.983646	−	0.180112i	$-0.0576460\pi$
$138$	−5.16919	−	8.95329i	−0.440030	−	0.762155i
$139$	−1.29226	−	1.08433i	−0.109608	−	0.0919718i	0.586337	−	0.810067i	$-0.300570\pi$
$139$	−1.29226	−	1.08433i	−0.109608	−	0.0919718i	−0.695944	+	0.718096i	$0.745014\pi$
$140$	−5.27917	+	9.14379i	−0.446171	+	0.772791i
$141$	0.398431	+	2.25961i	0.0335539	+	0.190294i
$142$	−34.8986			−2.92863
$143$	0.600708	+	3.40678i	0.0502337	+	0.284890i
$144$	−1.20686	+	1.01268i	−0.100572	+	0.0843898i
$145$	−17.9483	−	6.53264i	−1.49052	−	0.542506i
$146$	9.58561	−	3.48888i	0.793310	−	0.288741i
$147$	6.01388			0.496017
$148$	16.8280	−	4.17959i	1.38325	−	0.343560i
$149$	−6.79655			−0.556795			−0.278397	−	0.960466i	$-0.589803\pi$
$149$	−6.79655			−0.556795			−0.278397	+	0.960466i	$0.589803\pi$
$150$	18.4450	−	6.71343i	1.50603	−	0.548150i
$151$	4.92772	+	1.79354i	0.401013	+	0.145957i	0.534650	−	0.845074i	$-0.320444\pi$
$151$	4.92772	+	1.79354i	0.401013	+	0.145957i	−0.133637	+	0.991030i	$0.542666\pi$
$152$	6.61969	−	5.55458i	0.536927	−	0.450536i
$153$	0.529105	+	3.00071i	0.0427756	+	0.242593i
$154$	−1.25853			−0.101416
$155$	6.07248	+	34.4387i	0.487753	+	2.76619i
$156$	8.56816	−	14.8405i	0.686002	−	1.18819i
$157$	−11.3979	−	9.56396i	−0.909650	−	0.763287i	0.0624021	−	0.998051i	$-0.480124\pi$
$157$	−11.3979	−	9.56396i	−0.909650	−	0.763287i	−0.972052	+	0.234764i	$0.924568\pi$
$158$	−3.39511	−	5.88050i	−0.270100	−	0.467827i
$159$	−1.12188	+	1.94315i	−0.0889706	+	0.154102i
$160$	−25.2930	+	9.20591i	−1.99959	+	0.727791i
$161$	3.57088	−	2.99632i	0.281425	−	0.236143i
$162$	−1.10120	−	1.90733i	−0.0865183	−	0.149854i
$163$	1.46062	−	8.28360i	0.114405	−	0.648822i	−0.872638	−	0.488367i	$-0.837593\pi$
$163$	1.46062	−	8.28360i	0.114405	−	0.648822i	0.987043	−	0.160455i	$-0.0512961\pi$
$164$	−2.90750	+	16.4893i	−0.227038	+	1.28760i
$165$	1.64422	+	1.37967i	0.128003	+	0.107407i
$166$	15.0701	+	5.48507i	1.16967	+	0.425724i
$167$	−14.0171	−	5.10181i	−1.08468	−	0.394790i	−0.263031	−	0.964788i	$-0.584722\pi$
$167$	−14.0171	−	5.10181i	−1.08468	−	0.394790i	−0.821647	+	0.569997i	$0.806944\pi$
$168$	1.42501	+	1.19572i	0.109942	+	0.0922519i
$169$	4.01805	−	22.7875i	0.309081	−	1.75288i
$170$	−4.34650	+	24.6502i	−0.333361	+	1.89059i
$171$	−2.30651	−	3.99499i	−0.176383	−	0.305505i
$172$	14.1936	−	11.9099i	1.08225	−	0.908118i
$173$	3.23885	−	1.17885i	0.246246	−	0.0896260i	−0.215949	−	0.976405i	$-0.569284\pi$
$173$	3.23885	−	1.17885i	0.246246	−	0.0896260i	0.462194	+	0.886779i	$0.347062\pi$
$174$	−5.63898	+	9.76700i	−0.427490	+	0.740434i
$175$	4.42519	+	7.66465i	0.334513	+	0.579393i
$176$	−0.694484	−	0.582742i	−0.0523487	−	0.0439258i
$177$	−3.23873	+	5.60964i	−0.243438	+	0.421646i
$178$	−0.107806	−	0.611400i	−0.00808043	−	0.0458264i
$179$	−13.1312			−0.981470			−0.490735	−	0.871309i	$-0.663272\pi$
$179$	−13.1312			−0.981470			−0.490735	+	0.871309i	$0.663272\pi$
$180$	−1.84630	−	10.4709i	−0.137615	−	0.780453i
$181$	−12.8036	+	10.7435i	−0.951682	+	0.798556i	−0.979580	−	0.201055i	$-0.935563\pi$
$181$	−12.8036	+	10.7435i	−0.951682	+	0.798556i	0.0278979	+	0.999611i	$0.491119\pi$
$182$	12.3548	+	4.49676i	0.915795	+	0.333322i
$183$	−7.22734	+	2.63054i	−0.534260	+	0.194455i
$184$	−8.79335			−0.648255
$185$	6.27340	−	21.8038i	0.461229	−	1.60305i
$186$	20.6486			1.51403
$187$	−1.64764	+	0.599692i	−0.120487	+	0.0438539i
$188$	6.14608	+	2.23699i	0.448249	+	0.163149i
$189$	0.760709	−	0.638310i	0.0553334	−	0.0464303i
$190$	−6.58041	−	37.3194i	−0.477393	−	2.70743i
$191$	−18.0977			−1.30951			−0.654753	−	0.755843i	$-0.727227\pi$
$191$	−18.0977			−1.30951			−0.654753	+	0.755843i	$0.727227\pi$
$192$	2.21266	+	12.5486i	0.159685	+	0.905620i
$193$	−3.41180	+	5.90941i	−0.245587	+	0.425369i	−0.962296	−	0.272003i	$-0.912314\pi$
$193$	−3.41180	+	5.90941i	−0.245587	+	0.425369i	0.716710	+	0.697372i	$0.245647\pi$
$194$	4.86683	+	4.08376i	0.349418	+	0.293197i
$195$	−11.2114	−	19.4187i	−0.802865	−	1.39060i
$196$	8.57145	−	14.8462i	0.612246	−	1.06044i
$197$	20.5317	−	7.47291i	1.46282	−	0.532423i	0.516679	−	0.856179i	$-0.327168\pi$
$197$	20.5317	−	7.47291i	1.46282	−	0.532423i	0.946140	+	0.323756i	$0.104946\pi$
$198$	0.970855	−	0.814644i	0.0689957	−	0.0578943i
$199$	−0.596226	−	1.03269i	−0.0422654	−	0.0732058i	0.844119	−	0.536156i	$-0.180124\pi$
$199$	−0.596226	−	1.03269i	−0.0422654	−	0.0732058i	−0.886384	+	0.462950i	$0.846791\pi$
$200$	2.89912	−	16.4417i	0.204998	−	1.16260i
$201$	−2.00798	+	11.3878i	−0.141632	+	0.803236i
$202$	10.1974	+	8.55663i	0.717486	+	0.602043i
$203$	−4.77843	−	1.73921i	−0.335380	−	0.122068i
$204$	8.16182	+	2.97066i	0.571442	+	0.207988i
$205$	16.7833	+	14.0828i	1.17219	+	0.983588i
$206$	−0.508899	+	2.88611i	−0.0354567	+	0.201085i
$207$	−0.815130	+	4.62283i	−0.0566554	+	0.321309i
$208$	4.73546	+	8.20205i	0.328345	+	0.568710i
$209$	2.03350	−	1.70631i	0.140660	−	0.118028i
$210$	7.66563	−	2.79006i	0.528979	−	0.192533i
$211$	6.63550	−	11.4930i	0.456807	−	0.791213i	−0.541983	−	0.840389i	$-0.682326\pi$
$211$	6.63550	−	11.4930i	0.456807	−	0.791213i	0.998790	+	0.0491766i	$0.0156597\pi$
$212$	3.19797	+	5.53905i	0.219638	+	0.380423i
$213$	12.1385	+	10.1855i	0.831720	+	0.697896i
$214$	−8.41278	+	14.5714i	−0.575086	+	0.996078i
$215$	−4.21000	−	23.8761i	−0.287119	−	1.62833i
$216$	−1.87326			−0.127459
$217$	1.61670	+	9.16874i	0.109749	+	0.622415i
$218$	−23.7162	+	19.9002i	−1.60626	+	1.34781i
$219$	−4.35235	−	1.58413i	−0.294105	−	0.107045i
$220$	5.74939	−	2.09261i	0.387624	−	0.141084i
$221$	18.3172			1.23215
$222$	−12.0355	−	5.88355i	−0.807773	−	0.394878i
$223$	16.0774			1.07662			0.538310	−	0.842747i	$-0.319063\pi$
$223$	16.0774			1.07662			0.538310	+	0.842747i	$0.319063\pi$
$224$	−6.73385	+	2.45092i	−0.449924	+	0.163759i
$225$	−8.37497	−	3.04824i	−0.558331	−	0.203216i
$226$	20.7899	−	17.4448i	1.38293	−	1.16041i
$227$	3.11195	+	17.6488i	0.206548	+	1.17139i	0.894986	+	0.446095i	$0.147186\pi$
$227$	3.11195	+	17.6488i	0.206548	+	1.17139i	−0.688438	+	0.725295i	$0.741703\pi$
$228$	−13.1497			−0.870858
$229$	3.45678	+	19.6043i	0.228430	+	1.29549i	0.856018	+	0.516946i	$0.172931\pi$
$229$	3.45678	+	19.6043i	0.228430	+	1.29549i	−0.627588	+	0.778546i	$0.715958\pi$
$230$	−19.2808	+	33.3952i	−1.27134	+	2.20202i
$231$	0.437747	+	0.367313i	0.0288016	+	0.0241675i
$232$	4.79626	+	8.30737i	0.314890	+	0.545406i
$233$	4.97767	−	8.62157i	0.326098	−	0.564818i	−0.655636	−	0.755077i	$-0.727599\pi$
$233$	4.97767	−	8.62157i	0.326098	−	0.564818i	0.981734	+	0.190259i	$0.0609328\pi$
$234$	−12.4414	+	4.52830i	−0.813321	+	0.296024i
$235$	6.55599	−	5.50113i	0.427666	−	0.358854i
$236$	9.23217	+	15.9906i	0.600963	+	1.04090i
$237$	−0.535375	+	3.03626i	−0.0347763	+	0.197226i
$238$	−1.15718	+	6.56272i	−0.0750091	+	0.425398i
$239$	−9.31628	−	7.81729i	−0.602620	−	0.505658i	0.289667	−	0.957128i	$-0.406456\pi$
$239$	−9.31628	−	7.81729i	−0.602620	−	0.505658i	−0.892287	+	0.451469i	$0.850900\pi$
$240$	5.52194	+	2.00982i	0.356439	+	0.129733i
$241$	−6.72809	−	2.44883i	−0.433394	−	0.157743i	0.116105	−	0.993237i	$-0.462959\pi$
$241$	−6.72809	−	2.44883i	−0.433394	−	0.157743i	−0.549499	+	0.835494i	$0.685181\pi$
$242$	−17.9998	−	15.1036i	−1.15707	−	0.970898i
$243$	−0.173648	+	0.984808i	−0.0111395	+	0.0631754i
$244$	−3.80708	+	21.5910i	−0.243723	+	1.38222i
$245$	−11.2157	−	19.4262i	−0.716545	−	1.24109i
$246$	9.90993	−	8.31542i	0.631834	−	0.530172i
$247$	−26.0591	+	9.48474i	−1.65810	+	0.603499i
$248$	8.78136	−	15.2098i	0.557617	−	0.965821i
$249$	−3.64086	−	6.30616i	−0.230730	−	0.399637i
$250$	−24.6207	−	20.6592i	−1.55715	−	1.30660i
$251$	−6.80306	+	11.7832i	−0.429405	+	0.743751i	−0.996820	−	0.0796802i	$-0.974610\pi$
$251$	−6.80306	+	11.7832i	−0.429405	+	0.743751i	0.567415	+	0.823432i	$0.307943\pi$
$252$	−0.491546	−	2.78770i	−0.0309645	−	0.175608i
$253$	−2.70123			−0.169825
$254$	−0.922196	−	5.23003i	−0.0578637	−	0.328161i
$255$	8.70618	−	7.30535i	0.545202	−	0.457479i
$256$	4.26261	+	1.55146i	0.266413	+	0.0969665i
$257$	−4.72646	+	1.72029i	−0.294828	+	0.107309i	−0.485200	−	0.874403i	$-0.661253\pi$
$257$	−4.72646	+	1.72029i	−0.294828	+	0.107309i	0.190371	+	0.981712i	$0.439031\pi$
$258$	−14.3155			−0.891242
$259$	1.67019	−	5.80490i	0.103780	−	0.360699i
$260$	−63.9174			−3.96399
$261$	4.81195	−	1.75141i	0.297852	−	0.108409i
$262$	−8.37556	−	3.04846i	−0.517444	−	0.188334i
$263$	9.76773	−	8.19610i	0.602304	−	0.505393i	−0.289881	−	0.957063i	$-0.593616\pi$
$263$	9.76773	−	8.19610i	0.602304	−	0.505393i	0.892185	+	0.451670i	$0.149171\pi$
$264$	−0.187186	−	1.06158i	−0.0115205	−	0.0653360i
$265$	8.36907			0.514108
$266$	−1.75193	−	9.93567i	−0.107417	−	0.609195i
$267$	−0.140945	+	0.244123i	−0.00862567	+	0.0149401i
$268$	25.2507	+	21.1878i	1.54243	+	1.29425i
$269$	0.430165	+	0.745068i	0.0262276	+	0.0454276i	0.878841	−	0.477114i	$-0.158317\pi$
$269$	0.430165	+	0.745068i	0.0262276	+	0.0454276i	−0.852614	+	0.522542i	$0.824984\pi$
$270$	−4.10741	+	7.11424i	−0.249969	+	0.432959i
$271$	−12.4959	+	4.54815i	−0.759073	+	0.276280i	−0.692419	−	0.721496i	$-0.743455\pi$
$271$	−12.4959	+	4.54815i	−0.759073	+	0.276280i	−0.0666548	+	0.997776i	$0.521233\pi$
$272$	−3.67730	+	3.08562i	−0.222969	+	0.187093i
$273$	−2.98485	−	5.16991i	−0.180651	−	0.312897i
$274$	−5.79963	+	32.8913i	−0.350368	+	1.98704i
$275$	0.890579	−	5.05072i	0.0537039	−	0.304570i
$276$	10.2504	+	8.60109i	0.617000	+	0.517725i
$277$	3.34322	+	1.21683i	0.200875	+	0.0731124i	0.440498	−	0.897753i	$-0.354802\pi$
$277$	3.34322	+	1.21683i	0.200875	+	0.0731124i	−0.239624	+	0.970866i	$0.577024\pi$
$278$	3.49121	+	1.27070i	0.209389	+	0.0762113i
$279$	−7.18204	−	6.02645i	−0.429978	−	0.360794i
$280$	1.20485	−	6.83307i	0.0720038	−	0.408354i
$281$	0.140454	−	0.796555i	0.00837880	−	0.0475185i	−0.980332	−	0.197357i	$-0.936764\pi$
$281$	0.140454	−	0.796555i	0.00837880	−	0.0475185i	0.988711	+	0.149838i	$0.0478753\pi$
$282$	−2.52667	−	4.37632i	−0.150461	−	0.260606i
$283$	3.81268	−	3.19922i	0.226640	−	0.190174i	−0.522396	−	0.852703i	$-0.674962\pi$
$283$	3.81268	−	3.19922i	0.226640	−	0.190174i	0.749036	+	0.662530i	$0.230517\pi$
$284$	42.4451	−	15.4488i	2.51866	−	0.916716i
$285$	−8.60315	+	14.9011i	−0.509606	+	0.882664i
$286$	−3.80942	−	6.59811i	−0.225256	−	0.390154i
$287$	4.46827	+	3.74932i	0.263753	+	0.221315i
$288$	3.60814	−	6.24948i	0.212612	−	0.368254i
$289$	−1.33984	−	7.59859i	−0.0788139	−	0.446976i
$290$	42.0661			2.47021
$291$	−0.500919	−	2.84085i	−0.0293644	−	0.166534i
$292$	−10.1140	+	8.48662i	−0.591875	+	0.496642i
$293$	−11.1614	−	4.06241i	−0.652055	−	0.237329i	−0.00525248	−	0.999986i	$-0.501672\pi$
$293$	−11.1614	−	4.06241i	−0.652055	−	0.237329i	−0.646802	+	0.762658i	$0.723894\pi$
$294$	−12.4462	+	4.53004i	−0.725877	+	0.264197i
$295$	24.1605			1.40668
$296$	−9.45228	+	6.36327i	−0.549403	+	0.369857i
$297$	−0.575446			−0.0333908
$298$	14.0660	−	5.11960i	0.814820	−	0.296570i
$299$	26.5174	+	9.65153i	1.53354	+	0.558163i
$300$	−19.4617	+	16.3303i	−1.12362	+	0.942830i
$301$	−1.12084	−	6.35661i	−0.0646042	−	0.366389i
$302$	−11.5493			−0.664589
$303$	−1.04957	−	5.95239i	−0.0602960	−	0.341956i
$304$	3.63378	−	6.29390i	0.208412	−	0.360980i
$305$	21.9760	+	18.4400i	1.25834	+	1.05587i
$306$	−3.35535	−	5.81163i	−0.191813	−	0.332229i
$307$	−3.25042	+	5.62990i	−0.185511	+	0.321315i	−0.943749	−	0.330664i	$-0.892727\pi$
$307$	−3.25042	+	5.62990i	−0.185511	+	0.321315i	0.758237	+	0.651979i	$0.226061\pi$
$308$	1.53068	−	0.557122i	0.0872186	−	0.0317450i
$309$	1.01934	−	0.855330i	0.0579884	−	0.0486580i
$310$	−38.5089	−	66.6994i	−2.18716	−	3.78827i
$311$	4.19346	−	23.7823i	0.237789	−	1.34857i	−0.598869	−	0.800847i	$-0.704383\pi$
$311$	4.19346	−	23.7823i	0.237789	−	1.34857i	0.836659	−	0.547724i	$-0.184506\pi$
$312$	−1.95549	+	11.0902i	−0.110708	+	0.627857i
$313$	−3.57442	−	2.99929i	−0.202038	−	0.169530i	0.536155	−	0.844120i	$-0.319876\pi$
$313$	−3.57442	−	2.99929i	−0.202038	−	0.169530i	−0.738193	+	0.674589i	$0.764321\pi$
$314$	30.7930	+	11.2077i	1.73775	+	0.632489i
$315$	−3.48058	−	1.26683i	−0.196109	−	0.0713777i
$316$	6.73242	+	5.64917i	0.378728	+	0.317791i
$317$	−4.94047	+	28.0188i	−0.277484	+	1.57369i	0.453474	+	0.891270i	$0.350185\pi$
$317$	−4.94047	+	28.0188i	−0.277484	+	1.57369i	−0.730958	+	0.682423i	$0.760926\pi$
$318$	0.858106	−	4.86656i	0.0481202	−	0.272903i
$319$	1.47336	+	2.55194i	0.0824925	+	0.142881i
$320$	36.4084	−	30.5502i	2.03529	−	1.70781i
$321$	7.17893	−	2.61292i	0.400689	−	0.145839i
$322$	−5.13318	+	8.89093i	−0.286061	+	0.495472i
$323$	−7.02793	−	12.1727i	−0.391044	−	0.677309i
$324$	2.18365	+	1.83230i	0.121314	+	0.101795i
$325$	−26.7889	+	46.3998i	−1.48598	+	2.57380i
$326$	3.21687	+	18.2438i	0.178166	+	1.01043i
$327$	14.0571			0.777358
$328$	−1.91068	−	10.8360i	−0.105500	−	0.598320i
$329$	1.74542	−	1.46459i	0.0962284	−	0.0807452i
$330$	−4.44210	−	1.61679i	−0.244530	−	0.0890015i
$331$	−2.11089	+	0.768303i	−0.116025	+	0.0422297i	−0.399380	−	0.916785i	$-0.630775\pi$
$331$	−2.11089	+	0.768303i	−0.116025	+	0.0422297i	0.283355	+	0.959015i	$0.408552\pi$
$332$	−20.7570			−1.13919
$333$	2.46908	+	5.55911i	0.135305	+	0.304637i
$334$	32.8525			1.79761
$335$	40.5301	−	14.7517i	2.21439	−	0.805973i
$336$	1.47012	+	0.535081i	0.0802018	+	0.0291911i
$337$	−27.3978	+	22.9895i	−1.49246	+	1.25232i	−0.600967	+	0.799274i	$0.705218\pi$
$337$	−27.3978	+	22.9895i	−1.49246	+	1.25232i	−0.891488	+	0.453045i	$0.850338\pi$
$338$	8.84934	+	50.1871i	0.481341	+	2.72982i
$339$	−12.3226			−0.669274
$340$	−5.62566	−	31.9047i	−0.305094	−	1.73028i
$341$	2.69755	−	4.67229i	0.146080	−	0.253018i
$342$	7.78279	+	6.53053i	0.420845	+	0.353131i
$343$	−6.46162	−	11.1919i	−0.348895	−	0.604303i
$344$	−6.08804	+	10.5448i	−0.328245	+	0.568537i
$345$	16.4530	−	5.98839i	0.885798	−	0.322404i
$346$	−5.81507	+	4.87943i	−0.312620	+	0.262320i
$347$	−3.93290	−	6.81198i	−0.211129	−	0.365686i	0.740939	−	0.671572i	$-0.234381\pi$
$347$	−3.93290	−	6.81198i	−0.211129	−	0.365686i	−0.952068	+	0.305886i	$0.901047\pi$
$348$	2.53475	−	14.3753i	0.135877	−	0.770595i
$349$	4.80231	−	27.2353i	0.257062	−	1.45787i	−0.533662	−	0.845698i	$-0.679185\pi$
$349$	4.80231	−	27.2353i	0.257062	−	1.45787i	0.790724	−	0.612173i	$-0.209704\pi$
$350$	−14.9318	−	12.5292i	−0.798137	−	0.669716i
$351$	5.64903	+	2.05608i	0.301523	+	0.109745i
$352$	3.90215	+	1.42027i	0.207985	+	0.0757005i
$353$	7.61330	+	6.38832i	0.405215	+	0.340016i	0.822505	−	0.568757i	$-0.192576\pi$
$353$	7.61330	+	6.38832i	0.405215	+	0.340016i	−0.417290	+	0.908773i	$0.637020\pi$
$354$	2.47725	−	14.0492i	0.131665	−	0.746707i
$355$	10.2632	−	58.2058i	0.544717	−	3.08924i
$356$	0.401770	+	0.695886i	0.0212938	+	0.0368819i
$357$	2.31788	−	1.94493i	0.122675	−	0.102937i
$358$	27.1760	−	9.89125i	1.43630	−	0.522769i
$359$	8.77793	−	15.2038i	0.463281	−	0.802427i	−0.535841	−	0.844319i	$-0.680005\pi$
$359$	8.77793	−	15.2038i	0.463281	−	0.802427i	0.999122	+	0.0418921i	$0.0133386\pi$
$360$	3.49357	+	6.05105i	0.184128	+	0.318918i
$361$	1.74655	+	1.46553i	0.0919237	+	0.0771331i
$362$	18.4053	−	31.8789i	0.967361	−	1.67552i
$363$	1.85263	+	10.5068i	0.0972378	+	0.551463i
$364$	−17.0170			−0.891931
$365$	2.99992	+	17.0134i	0.157023	+	0.890523i
$366$	12.9760	−	10.8882i	0.678268	−	0.569135i
$367$	−31.9281	−	11.6209i	−1.66663	−	0.606604i	−0.675247	−	0.737592i	$-0.735963\pi$
$367$	−31.9281	−	11.6209i	−1.66663	−	0.606604i	−0.991384	+	0.130988i	$0.958185\pi$
$368$	−6.94938	+	2.52937i	−0.362261	+	0.131852i
$369$	−5.87382			−0.305779
$370$	3.44075	+	49.8501i	0.178876	+	2.59159i
$371$	2.22813			0.115678
$372$	−25.1136	+	9.14061i	−1.30208	+	0.473918i
$373$	4.09041	+	1.48879i	0.211793	+	0.0770864i	0.445738	−	0.895163i	$-0.352941\pi$
$373$	4.09041	+	1.48879i	0.211793	+	0.0770864i	−0.233945	+	0.972250i	$0.575164\pi$
$374$	2.95819	−	2.48222i	0.152965	−	0.128352i
$375$	2.53409	+	14.3715i	0.130860	+	0.742142i
$376$	−4.29814			−0.221660
$377$	−5.34556	−	30.3162i	−0.275310	−	1.56136i
$378$	−1.09353	+	1.89405i	−0.0562450	+	0.0974193i
$379$	−6.72361	−	5.64178i	−0.345369	−	0.289799i	0.453558	−	0.891227i	$-0.350154\pi$
$379$	−6.72361	−	5.64178i	−0.345369	−	0.289799i	−0.798927	+	0.601428i	$0.794599\pi$
$380$	24.5237	+	42.4764i	1.25804	+	2.17899i
$381$	−1.20567	+	2.08828i	−0.0617682	+	0.106986i
$382$	37.4547	−	13.6324i	1.91635	−	0.697493i
$383$	−5.87751	+	4.93181i	−0.300327	+	0.252004i	−0.780480	−	0.625180i	$-0.785025\pi$
$383$	−5.87751	+	4.93181i	−0.300327	+	0.252004i	0.480154	+	0.877184i	$0.340581\pi$
$384$	−6.81544	−	11.8047i	−0.347799	−	0.602406i
$385$	0.370119	−	2.09905i	0.0188630	−	0.106977i
$386$	2.60963	−	14.8000i	0.132827	−	0.753298i
$387$	4.97925	+	4.17808i	0.253109	+	0.212384i
$388$	−7.72702	−	2.81241i	−0.392280	−	0.142778i
$389$	−3.03512	−	1.10469i	−0.153886	−	0.0560101i	0.263928	−	0.964542i	$-0.414982\pi$
$389$	−3.03512	−	1.10469i	−0.153886	−	0.0560101i	−0.417815	+	0.908532i	$0.637204\pi$
$390$	37.8303	+	31.7434i	1.91561	+	1.60739i
$391$	−2.48370	+	14.0857i	−0.125606	+	0.712347i
$392$	−1.95624	+	11.0944i	−0.0988053	+	0.560353i
$393$	2.02350	+	3.50480i	0.102072	+	0.176794i
$394$	−36.8628	+	30.9315i	−1.85712	+	1.55831i
$395$	10.8063	−	3.93316i	0.543722	−	0.197899i
$396$	−0.820171	+	1.42058i	−0.0412151	+	0.0713867i
$397$	17.3676	+	30.0816i	0.871656	+	1.50975i	0.860283	+	0.509816i	$0.170287\pi$
$397$	17.3676	+	30.0816i	0.871656	+	1.50975i	0.0113724	+	0.999935i	$0.496380\pi$
$398$	2.01183	+	1.68812i	0.100844	+	0.0846180i
$399$	−2.29044	+	3.96717i	−0.114666	+	0.198607i
$400$	−2.43821	−	13.8278i	−0.121911	−	0.691389i
$401$	−7.68280			−0.383661			−0.191830	−	0.981428i	$-0.561442\pi$
$401$	−7.68280			−0.383661			−0.191830	+	0.981428i	$0.561442\pi$
$402$	−4.42237	−	25.0805i	−0.220568	−	1.25090i
$403$	−43.1754	+	36.2284i	−2.15072	+	1.80467i
$404$	−16.1903	−	5.89279i	−0.805498	−	0.293177i
$405$	3.50500	−	1.27571i	0.174165	−	0.0633908i
$406$	11.1994			0.555817
$407$	−2.90365	+	1.95473i	−0.143928	+	0.0968924i
$408$	−5.70782			−0.282579
$409$	−23.2304	+	8.45516i	−1.14867	+	0.418081i	−0.845036	−	0.534709i	$-0.820421\pi$
$409$	−23.2304	+	8.45516i	−1.14867	+	0.418081i	−0.303631	+	0.952790i	$0.598199\pi$
$410$	−45.3424	−	16.5033i	−2.23930	−	0.815038i
$411$	11.6168	−	9.74769i	0.573017	−	0.480818i
$412$	−0.658667	−	3.73548i	−0.0324502	−	0.184034i
$413$	6.43234			0.316515
$414$	−1.79524	−	10.1813i	−0.0882312	−	0.500384i
$415$	−13.5802	+	23.5216i	−0.666626	+	1.15463i
$416$	−33.2319	−	27.8849i	−1.62933	−	1.36717i
$417$	−0.843460	−	1.46092i	−0.0413044	−	0.0715414i
$418$	−2.92318	+	5.06310i	−0.142978	+	0.247644i
$419$	1.70248	−	0.619652i	0.0831716	−	0.0302720i	−0.300099	−	0.953908i	$-0.597020\pi$
$419$	1.70248	−	0.619652i	0.0831716	−	0.0302720i	0.383271	+	0.923636i	$0.374798\pi$
$420$	−8.08816	+	6.78677i	−0.394662	+	0.331161i
$421$	9.87059	+	17.0964i	0.481063	+	0.833226i	0.999764	−	0.0217301i	$-0.00691745\pi$
$421$	9.87059	+	17.0964i	0.481063	+	0.833226i	−0.518701	+	0.854956i	$0.673584\pi$
$422$	−5.07539	+	28.7840i	−0.247066	+	1.40118i
$423$	−0.398431	+	2.25961i	−0.0193724	+	0.109866i
$424$	−3.21979	−	2.70172i	−0.156367	−	0.131207i
$425$	−25.5185	−	9.28797i	−1.23783	−	0.450533i
$426$	−32.7940	−	11.9360i	−1.58887	−	0.578303i
$427$	5.85074	+	4.90935i	0.283137	+	0.237580i
$428$	3.78158	−	21.4464i	0.182790	−	1.03665i
$429$	−0.600708	+	3.40678i	−0.0290024	+	0.164481i
$430$	26.6979	+	46.2421i	1.28749	+	2.22999i
$431$	−23.6952	+	19.8826i	−1.14136	+	0.957713i	−0.999482	−	0.0321719i	$-0.989758\pi$
$431$	−23.6952	+	19.8826i	−1.14136	+	0.957713i	−0.141875	+	0.989885i	$0.545313\pi$
$432$	−1.48044	+	0.538834i	−0.0712275	+	0.0259247i
$433$	10.3388	−	17.9073i	0.496850	−	0.860569i	−0.503143	−	0.864203i	$-0.667823\pi$
$433$	10.3388	−	17.9073i	0.496850	−	0.860569i	0.999993	+	0.00363357i	$0.00115661\pi$
$434$	−10.2524	−	17.7576i	−0.492129	−	0.852393i
$435$	−14.6316	−	12.2773i	−0.701530	−	0.588653i
$436$	20.0352	−	34.7020i	0.959513	−	1.66193i
$437$	−3.76021	−	21.3252i	−0.179875	−	1.02012i
$438$	10.2008			0.487413
$439$	−2.87891	−	16.3271i	−0.137403	−	0.779251i	−0.973156	−	0.230146i	$-0.926080\pi$
$439$	−2.87891	−	16.3271i	−0.137403	−	0.779251i	0.835753	−	0.549105i	$-0.185031\pi$
$440$	−3.08006	+	2.58448i	−0.146836	+	0.123210i
$441$	5.65120	+	2.05687i	0.269105	+	0.0979461i
$442$	−37.9089	+	13.7977i	−1.80314	+	0.656291i
$443$	−1.46143			−0.0694348			−0.0347174	−	0.999397i	$-0.511053\pi$
$443$	−1.46143			−0.0694348			−0.0347174	+	0.999397i	$0.511053\pi$
$444$	17.2426	+	1.82798i	0.818299	+	0.0867519i
$445$	1.05143			0.0498425
$446$	−33.2733	+	12.1105i	−1.57554	+	0.573449i
$447$	−6.38667	−	2.32456i	−0.302079	−	0.109948i
$448$	9.69312	−	8.13349i	0.457957	−	0.384271i
$449$	6.08155	+	34.4902i	0.287006	+	1.62769i	0.698031	+	0.716067i	$0.254060\pi$
$449$	6.08155	+	34.4902i	0.287006	+	1.62769i	−0.411025	+	0.911624i	$0.634829\pi$
$450$	19.6288			0.925309
$451$	−0.586943	−	3.32872i	−0.0276381	−	0.156743i
$452$	−17.5632	+	30.4203i	−0.826102	+	1.43085i
$453$	4.01712	+	3.37076i	0.188741	+	0.158372i
$454$	−19.7346	−	34.1814i	−0.926191	−	1.60421i
$455$	−11.1333	+	19.2835i	−0.521938	+	0.904023i
$456$	8.12025	−	2.95553i	0.380265	−	0.138405i
$457$	−0.384896	+	0.322966i	−0.0180047	+	0.0151077i	−0.651746	−	0.758438i	$-0.725963\pi$
$457$	−0.384896	+	0.322966i	−0.0180047	+	0.0151077i	0.633741	+	0.773545i	$0.281519\pi$
$458$	−21.9213	−	37.9688i	−1.02432	−	1.77417i
$459$	−0.529105	+	3.00071i	−0.0246965	+	0.140061i
$460$	8.66678	−	49.1518i	0.404091	−	2.29171i
$461$	4.61584	+	3.87315i	0.214981	+	0.180390i	0.743919	−	0.668270i	$-0.232965\pi$
$461$	4.61584	+	3.87315i	0.214981	+	0.180390i	−0.528938	+	0.848661i	$0.677409\pi$
$462$	−1.18264	−	0.430444i	−0.0550212	−	0.0200261i
$463$	18.2617	+	6.64671i	0.848693	+	0.308899i	0.729507	−	0.683973i	$-0.239749\pi$
$463$	18.2617	+	6.64671i	0.848693	+	0.308899i	0.119186	+	0.992872i	$0.461972\pi$
$464$	6.18006	+	5.18568i	0.286902	+	0.240739i
$465$	−6.07248	+	34.4387i	−0.281604	+	1.59706i
$466$	−3.80734	+	21.5925i	−0.176372	+	1.00025i
$467$	15.3581	+	26.6010i	0.710688	+	1.23095i	0.964599	+	0.263720i	$0.0849496\pi$
$467$	15.3581	+	26.6010i	0.710688	+	1.23095i	−0.253911	+	0.967228i	$0.581717\pi$
$468$	13.1272	−	11.0150i	0.606804	−	0.509169i
$469$	10.7905	−	3.92740i	0.498257	−	0.181351i
$470$	−9.42433	+	16.3234i	−0.434712	+	0.752943i
$471$	−7.43944	−	12.8855i	−0.342791	−	0.593732i
$472$	−9.29515	−	7.79956i	−0.427844	−	0.359004i
$473$	−1.87018	+	3.23925i	−0.0859912	+	0.148941i
$474$	−1.17911	−	6.68705i	−0.0541582	−	0.307146i
$475$	41.1133			1.88641
$476$	−1.49774	−	8.49410i	−0.0686487	−	0.389326i
$477$	−1.71881	+	1.44226i	−0.0786991	+	0.0660364i
$478$	25.1692	+	9.16085i	1.15121	+	0.419008i
$479$	−26.1177	+	9.50607i	−1.19335	+	0.434343i	−0.860898	−	0.508777i	$-0.830098\pi$
$479$	−26.1177	+	9.50607i	−1.19335	+	0.434343i	−0.332451	+	0.943121i	$0.607875\pi$
$480$	−26.9163			−1.22855
$481$	35.4887	−	8.81439i	1.61815	−	0.401902i
$482$	15.7689			0.718254
$483$	4.38033	−	1.59431i	0.199312	−	0.0725436i
$484$	28.5781	+	10.4016i	1.29900	+	0.472799i
$485$	−8.24238	+	6.91618i	−0.374267	+	0.314048i
$486$	−0.382442	−	2.16894i	−0.0173479	−	0.0983850i
$487$	3.86108			0.174962			0.0874812	−	0.996166i	$-0.472118\pi$
$487$	3.86108			0.174962			0.0874812	+	0.996166i	$0.472118\pi$
$488$	−2.50185	−	14.1887i	−0.113253	−	0.642291i
$489$	4.20570	−	7.28448i	0.190188	−	0.329416i
$490$	37.8448	+	31.7556i	1.70965	+	1.43457i
$491$	14.8982	+	25.8045i	0.672347	+	1.16454i	0.977237	+	0.212152i	$0.0680471\pi$
$491$	14.8982	+	25.8045i	0.672347	+	1.16454i	−0.304890	+	0.952388i	$0.598620\pi$
$492$	−8.37183	+	14.5004i	−0.377431	+	0.653730i
$493$	14.6620	−	5.33652i	0.660342	−	0.240345i
$494$	46.7868	−	39.2588i	2.10504	−	1.76634i
$495$	1.07319	+	1.85882i	0.0482363	+	0.0835478i
$496$	2.56488	−	14.5462i	0.115167	−	0.653143i
$497$	2.73242	−	15.4963i	0.122566	−	0.695105i
$498$	12.2853	+	10.3086i	0.550515	+	0.461937i
$499$	−40.3079	−	14.6709i	−1.80443	−	0.656758i	−0.997843	−	0.0656394i	$-0.979091\pi$
$499$	−40.3079	−	14.6709i	−1.80443	−	0.656758i	−0.806585	−	0.591119i	$-0.798686\pi$
$500$	39.0901	+	14.2276i	1.74816	+	0.636278i
$501$	−11.4269	−	9.58827i	−0.510514	−	0.428372i
$502$	5.20355	−	29.5108i	0.232246	−	1.31713i
$503$	2.46995	−	14.0078i	0.110129	−	0.624575i	−0.878918	−	0.476974i	$-0.841734\pi$
$503$	2.46995	−	14.0078i	0.110129	−	0.624575i	0.989047	−	0.147601i	$-0.0471552\pi$
$504$	0.930106	+	1.61099i	0.0414302	+	0.0717592i
$505$	−17.2701	+	14.4914i	−0.768511	+	0.644857i
$506$	5.59040	−	2.03474i	0.248524	−	0.0904552i
$507$	11.5695	−	20.0390i	0.513820	−	0.889962i
$508$	3.43682	+	5.95274i	0.152484	+	0.264110i
$509$	24.1239	+	20.2424i	1.06927	+	0.897227i	0.994986	−	0.100010i	$-0.0318876\pi$
$509$	24.1239	+	20.2424i	1.06927	+	0.897227i	0.0742866	+	0.997237i	$0.476332\pi$
$510$	−12.5153	+	21.6770i	−0.554185	+	0.959876i
$511$	0.798680	+	4.52954i	0.0353315	+	0.200375i
$512$	17.2713			0.763291
$513$	−0.801043	−	4.54294i	−0.0353669	−	0.200576i
$514$	8.48593	−	7.12054i	0.374298	−	0.314074i
$515$	−4.66395	−	1.69754i	−0.205518	−	0.0748025i
$516$	17.4110	−	6.33710i	0.766478	−	0.278975i
$517$	−1.32035			−0.0580687
$518$	0.916041	+	13.2718i	0.0402486	+	0.583128i
$519$	3.44672			0.151294
$520$	39.4706	−	14.3661i	1.73090	−	0.629996i
$521$	−4.95512	−	1.80352i	−0.217088	−	0.0790135i	0.231187	−	0.972909i	$-0.425739\pi$
$521$	−4.95512	−	1.80352i	−0.217088	−	0.0790135i	−0.448275	+	0.893896i	$0.647961\pi$
$522$	−8.63942	+	7.24933i	−0.378137	+	0.317295i
$523$	−1.22700	−	6.95867i	−0.0536530	−	0.304281i	0.946158	−	0.323704i	$-0.104928\pi$
$523$	−1.22700	−	6.95867i	−0.0536530	−	0.304281i	−0.999811	+	0.0194229i	$0.993817\pi$
$524$	11.5362			0.503960
$525$	1.53685	+	8.71592i	0.0670737	+	0.380394i
$526$	−14.0412	+	24.3201i	−0.612227	+	1.06041i
$527$	−21.8837	−	18.3626i	−0.953267	−	0.799886i
$528$	−0.453293	−	0.785126i	−0.0197270	−	0.0341682i
$529$	0.482503	−	0.835720i	0.0209784	−	0.0363357i
$530$	−17.3204	+	6.30412i	−0.752351	+	0.273833i
$531$	−4.96202	+	4.16363i	−0.215333	+	0.180686i
$532$	6.52904	+	11.3086i	0.283070	+	0.490291i
$533$	−6.13167	+	34.7745i	−0.265592	+	1.50625i
$534$	0.107806	−	0.611400i	0.00466524	−	0.0264579i
$535$	−21.8288	−	18.3165i	−0.943741	−	0.791893i
$536$	−20.3551	−	7.40865i	−0.879207	−	0.320005i
$537$	−12.3393	−	4.49113i	−0.532479	−	0.193806i
$538$	−1.45149	−	1.21795i	−0.0625783	−	0.0525094i
$539$	−0.600939	+	3.40809i	−0.0258843	+	0.146797i
$540$	1.84630	−	10.4709i	0.0794520	−	0.450594i
$541$	−15.6275	−	27.0677i	−0.671880	−	1.16373i	−0.977370	−	0.211536i	$-0.932154\pi$
$541$	−15.6275	−	27.0677i	−0.671880	−	1.16373i	0.305490	−	0.952195i	$-0.401180\pi$
$542$	22.4353	−	18.8255i	0.963680	−	0.808623i
$543$	−15.7059	+	5.71648i	−0.674005	+	0.245318i
$544$	10.9940	−	19.0421i	0.471363	−	0.816425i
$545$	−26.2160	−	45.4075i	−1.12297	−	1.94504i
$546$	10.0717	+	8.45115i	0.431028	+	0.361676i
$547$	−0.294570	+	0.510210i	−0.0125949	+	0.0218150i	−0.872254	−	0.489053i	$-0.837343\pi$
$547$	−0.294570	+	0.510210i	−0.0125949	+	0.0218150i	0.859659	+	0.510868i	$0.170676\pi$
$548$	−7.50644	−	42.5711i	−0.320659	−	1.81855i
$549$	−7.69117			−0.328251
$550$	1.96141	+	11.1237i	0.0836348	+	0.474316i
$551$	−18.0957	+	15.1841i	−0.770901	+	0.646863i
$552$	−8.26305	−	3.00750i	−0.351699	−	0.128008i
$553$	2.87699	−	1.04714i	0.122342	−	0.0445288i
$554$	−7.83565			−0.332905
$555$	13.3524	−	18.3432i	0.566778	−	0.778627i
$556$	−4.80866			−0.203933
$557$	0.873137	−	0.317796i	0.0369960	−	0.0134654i	−0.323456	−	0.946243i	$-0.604845\pi$
$557$	0.873137	−	0.317796i	0.0369960	−	0.0134654i	0.360452	+	0.932778i	$0.382623\pi$
$558$	19.4033	+	7.06222i	0.821407	+	0.298968i
$559$	29.9331	−	25.1169i	1.26604	−	1.06233i
$560$	−1.01330	−	5.74674i	−0.0428200	−	0.242844i
$561$	−1.75338			−0.0740279
$562$	0.309336	+	1.75433i	0.0130486	+	0.0740020i
$563$	5.51680	−	9.55538i	0.232505	−	0.402711i	−0.726039	−	0.687653i	$-0.758641\pi$
$563$	5.51680	−	9.55538i	0.232505	−	0.402711i	0.958545	+	0.284942i	$0.0919743\pi$
$564$	5.01033	+	4.20416i	0.210973	+	0.177027i
$565$	22.9813	+	39.8049i	0.966833	+	1.67460i
$566$	−5.48078	+	9.49298i	−0.230374	+	0.399020i
$567$	0.933147	−	0.339638i	0.0391885	−	0.0142635i
$568$	−22.7387	+	19.0800i	−0.954093	+	0.800579i
$569$	3.47113	+	6.01217i	0.145517	+	0.252043i	0.929566	−	0.368656i	$-0.120182\pi$
$569$	3.47113	+	6.01217i	0.145517	+	0.252043i	−0.784049	+	0.620699i	$0.786849\pi$
$570$	6.58041	−	37.3194i	0.275623	−	1.56314i
$571$	−2.65812	+	15.0749i	−0.111239	+	0.630866i	0.877305	+	0.479933i	$0.159339\pi$
$571$	−2.65812	+	15.0749i	−0.111239	+	0.630866i	−0.988544	+	0.150933i	$0.951772\pi$
$572$	7.55399	+	6.33855i	0.315848	+	0.265028i
$573$	−17.0063	−	6.18979i	−0.710449	−	0.258582i
$574$	−12.0717	−	4.39372i	−0.503861	−	0.183390i
$575$	−32.0485	−	26.8919i	−1.33651	−	1.12147i
$576$	−2.21266	+	12.5486i	−0.0921943	+	0.522860i
$577$	1.95595	−	11.0928i	0.0814274	−	0.461798i	−0.916643	−	0.399707i	$-0.869112\pi$
$577$	1.95595	−	11.0928i	0.0814274	−	0.461798i	0.998070	−	0.0620911i	$-0.0197769\pi$
$578$	8.49664	+	14.7166i	0.353414	+	0.612131i
$579$	−5.22718	+	4.38612i	−0.217234	+	0.182281i
$580$	−51.1625	+	18.6216i	−2.12441	+	0.773221i
$581$	−3.61550	+	6.26224i	−0.149996	+	0.259801i
$582$	3.17660	+	5.50203i	0.131674	+	0.228067i
$583$	−0.989086	−	0.829942i	−0.0409638	−	0.0343727i
$584$	4.33817	−	7.51392i	0.179515	−	0.310928i
$585$	−3.89368	−	22.0822i	−0.160984	−	0.912985i
$586$	26.1594			1.08063
$587$	3.60792	+	20.4615i	0.148915	+	0.844538i	0.964140	+	0.265394i	$0.0855020\pi$
$587$	3.60792	+	20.4615i	0.148915	+	0.844538i	−0.815225	+	0.579144i	$0.803387\pi$
$588$	13.1322	−	11.0192i	0.541564	−	0.454426i
$589$	40.6411	+	14.7921i	1.67459	+	0.609499i
$590$	−50.0020	+	18.1993i	−2.05855	+	0.749252i
$591$	21.8493			0.898761
$592$	−5.63977	+	7.74779i	−0.231793	+	0.318432i
$593$	−11.7045			−0.480644			−0.240322	−	0.970693i	$-0.577253\pi$
$593$	−11.7045			−0.480644			−0.240322	+	0.970693i	$0.577253\pi$
$594$	1.19093	−	0.433463i	0.0488645	−	0.0177852i
$595$	−10.6053	−	3.86002i	−0.434776	−	0.158246i
$596$	−14.8413	+	12.4533i	−0.607923	+	0.510108i
$597$	−0.207067	−	1.17434i	−0.00847470	−	0.0480624i
$598$	−62.1499			−2.54150
$599$	−6.29424	−	35.6964i	−0.257176	−	1.45852i	−0.790426	−	0.612558i	$-0.790141\pi$
$599$	−6.29424	−	35.6964i	−0.257176	−	1.45852i	0.533250	−	0.845958i	$-0.320971\pi$
$600$	8.34767	−	14.4586i	0.340792	−	0.590270i
$601$	29.7074	+	24.9275i	1.21179	+	1.01681i	0.999213	+	0.0396692i	$0.0126304\pi$
$601$	29.7074	+	24.9275i	1.21179	+	1.01681i	0.212578	+	0.977144i	$0.431814\pi$
$602$	7.10787	+	12.3112i	0.289695	+	0.501767i
$603$	−5.78175	+	10.0143i	−0.235451	+	0.407813i
$604$	14.0467	−	5.11260i	0.571554	−	0.208029i
$605$	30.4841	−	25.5792i	1.23936	−	1.03994i
$606$	6.65588	+	11.5283i	0.270377	+	0.468306i
$607$	−5.51821	+	31.2953i	−0.223977	+	1.27024i	0.640654	+	0.767830i	$0.278664\pi$
$607$	−5.51821	+	31.2953i	−0.223977	+	1.27024i	−0.864631	+	0.502408i	$0.832448\pi$
$608$	−5.78055	+	32.7831i	−0.234432	+	1.32953i
$609$	−3.89541	−	3.26864i	−0.157850	−	0.132452i
$610$	−59.3712	−	21.6094i	−2.40387	−	0.874937i
$611$	12.9615	+	4.71762i	0.524368	+	0.190854i
$612$	6.65358	+	5.58302i	0.268955	+	0.225680i
$613$	3.75936	−	21.3204i	0.151839	−	0.861124i	−0.809779	−	0.586734i	$-0.800413\pi$
$613$	3.75936	−	21.3204i	0.151839	−	0.861124i	0.961619	−	0.274389i	$-0.0884756\pi$
$614$	2.48620	−	14.0999i	0.100335	−	0.569027i
$615$	10.9545	+	18.9738i	0.441728	+	0.765096i
$616$	−0.820014	+	0.688074i	−0.0330393	+	0.0277233i
$617$	−21.8337	+	7.94680i	−0.878990	+	0.319926i	−0.741802	−	0.670619i	$-0.766029\pi$
$617$	−21.8337	+	7.94680i	−0.878990	+	0.319926i	−0.137188	+	0.990545i	$0.543806\pi$
$618$	−1.46532	+	2.53800i	−0.0589437	+	0.102094i
$619$	−0.280436	−	0.485730i	−0.0112717	−	0.0195231i	0.860335	−	0.509730i	$-0.170255\pi$
$619$	−0.280436	−	0.485730i	−0.0112717	−	0.0195231i	−0.871606	+	0.490207i	$0.836921\pi$
$620$	76.3623	+	64.0756i	3.06678	+	2.57334i
$621$	−2.34707	+	4.06525i	−0.0941848	+	0.163133i
$622$	9.23567	+	52.3781i	0.370317	+	2.10017i
$623$	0.279926			0.0112150
$624$	1.64461	+	9.32703i	0.0658370	+	0.373380i
$625$	7.56052	−	6.34403i	0.302421	−	0.253761i
$626$	9.65680	+	3.51479i	0.385963	+	0.140479i
$627$	2.49446	−	0.907908i	0.0996190	−	0.0362584i
$628$	−42.4131			−1.69247
$629$	7.52327	+	16.9386i	0.299972	+	0.675385i
$630$	8.15759			0.325006
$631$	21.1715	−	7.70581i	0.842826	−	0.306764i	0.115714	−	0.993283i	$-0.463084\pi$
$631$	21.1715	−	7.70581i	0.842826	−	0.306764i	0.727112	+	0.686519i	$0.240862\pi$
$632$	−5.42715	−	1.97532i	−0.215880	−	0.0785740i
$633$	10.1662	−	8.53044i	0.404069	−	0.339054i
$634$	−10.8809	−	61.7085i	−0.432135	−	2.45076i
$635$	8.99413			0.356921
$636$	1.11064	+	6.29877i	0.0440399	+	0.249763i
$637$	18.0764	−	31.3093i	0.716215	−	1.24052i
$638$	−4.97152	−	4.17160i	−0.196825	−	0.165155i
$639$	7.92287	+	13.7228i	0.313424	+	0.542866i
$640$	−25.4212	+	44.0308i	−1.00486	+	1.74047i
$641$	−44.5846	+	16.2275i	−1.76099	+	0.640946i	−0.999970	−	0.00778748i	$-0.997521\pi$
$641$	−44.5846	+	16.2275i	−1.76099	+	0.640946i	−0.761016	+	0.648734i	$0.775299\pi$
$642$	−12.8891	+	10.8153i	−0.508693	+	0.426844i
$643$	8.39900	+	14.5475i	0.331224	+	0.573697i	0.982752	−	0.184928i	$-0.0592051\pi$
$643$	8.39900	+	14.5475i	0.331224	+	0.573697i	−0.651528	+	0.758625i	$0.725872\pi$
$644$	2.30739	−	13.0858i	0.0909238	−	0.515655i
$645$	4.21000	−	23.8761i	0.165768	−	0.940119i
$646$	23.7141	+	19.8985i	0.933020	+	0.782896i
$647$	43.1786	+	15.7157i	1.69752	+	0.617848i	0.995540	−	0.0943437i	$-0.0300753\pi$
$647$	43.1786	+	15.7157i	1.69752	+	0.617848i	0.701985	+	0.712192i	$0.252297\pi$
$648$	−1.76029	−	0.640693i	−0.0691507	−	0.0251688i
$649$	−2.85538	−	2.39594i	−0.112083	−	0.0940491i
$650$	20.4904	−	116.207i	0.803701	−	4.55802i
$651$	−1.61670	+	9.16874i	−0.0633633	+	0.359351i
$652$	−11.9886	−	20.7648i	−0.469508	−	0.813213i
$653$	30.8481	−	25.8846i	1.20718	−	1.01294i	0.207784	−	0.978175i	$-0.433375\pi$
$653$	30.8481	−	25.8846i	1.20718	−	1.01294i	0.999395	−	0.0347692i	$-0.0110696\pi$
$654$	−29.0922	+	10.5887i	−1.13759	+	0.414050i
$655$	7.54752	−	13.0727i	0.294906	−	0.510792i
$656$	−4.62695	−	8.01410i	−0.180652	−	0.312898i
$657$	−3.54807	−	2.97718i	−0.138423	−	0.116151i
$658$	−2.50907	+	4.34584i	−0.0978138	+	0.169418i
$659$	−0.119459	−	0.677488i	−0.00465348	−	0.0263912i	0.982393	−	0.186828i	$-0.0598208\pi$
$659$	−0.119459	−	0.677488i	−0.00465348	−	0.0263912i	−0.987046	+	0.160437i	$0.948710\pi$
$660$	6.11838			0.238157
$661$	−4.93608	−	27.9939i	−0.191991	−	1.08884i	−0.916639	−	0.399717i	$-0.869108\pi$
$661$	−4.93608	−	27.9939i	−0.191991	−	1.08884i	0.724647	−	0.689120i	$-0.242003\pi$
$662$	3.78992	−	3.18012i	0.147300	−	0.123599i
$663$	17.2126	+	6.26487i	0.668481	+	0.243307i
$664$	12.8179	−	4.66535i	0.497433	−	0.181051i
$665$	17.0864			0.662584
$666$	−9.29742	−	9.64513i	−0.360268	−	0.373741i
$667$	24.0376			0.930740
$668$	−39.9566	+	14.5430i	−1.54597	+	0.562686i
$669$	15.1078	+	5.49878i	0.584100	+	0.212595i
$670$	−72.7681	+	61.0597i	−2.81128	+	2.35894i
$671$	−0.768542	−	4.35862i	−0.0296692	−	0.168263i
$672$	−7.16602			−0.276435
$673$	−4.75177	−	26.9486i	−0.183167	−	1.03879i	−0.928287	−	0.371863i	$-0.878719\pi$
$673$	−4.75177	−	26.9486i	−0.183167	−	1.03879i	0.745120	−	0.666930i	$-0.232392\pi$
$674$	39.3847	−	68.2164i	1.51704	−	2.62760i
$675$	−6.82734	−	5.72881i	−0.262784	−	0.220502i
$676$	−32.9795	−	57.1222i	−1.26844	−	2.19701i
$677$	10.6635	−	18.4697i	0.409832	−	0.709849i	−0.585039	−	0.811005i	$-0.698921\pi$
$677$	10.6635	−	18.4697i	0.409832	−	0.709849i	0.994871	+	0.101156i	$0.0322541\pi$
$678$	25.5026	−	9.28220i	0.979423	−	0.356481i
$679$	−2.19440	+	1.84132i	−0.0842133	+	0.0706633i
$680$	10.6449	+	18.4375i	0.408214	+	0.707047i
$681$	−3.11195	+	17.6488i	−0.119250	+	0.676302i
$682$	−2.06331	+	11.7016i	−0.0790083	+	0.448078i
$683$	−13.9922	−	11.7408i	−0.535396	−	0.449251i	0.334564	−	0.942373i	$-0.391411\pi$
$683$	−13.9922	−	11.7408i	−0.535396	−	0.449251i	−0.869960	+	0.493122i	$0.835856\pi$
$684$	−12.3566	−	4.49745i	−0.472468	−	0.171964i
$685$	−53.1523	−	19.3459i	−2.03084	−	0.739167i
$686$	21.8032	+	18.2951i	0.832451	+	0.698510i
$687$	−3.45678	+	19.6043i	−0.131884	+	0.747952i
$688$	−1.77821	+	10.0847i	−0.0677937	+	0.384477i
$689$	6.74424	+	11.6814i	0.256935	+	0.445025i
$690$	−29.5398	+	24.7869i	−1.12456	+	0.943620i
$691$	−6.68457	+	2.43298i	−0.254293	+	0.0925551i	−0.466021	−	0.884773i	$-0.654313\pi$
$691$	−6.68457	+	2.43298i	−0.254293	+	0.0925551i	0.211728	+	0.977329i	$0.432091\pi$
$692$	4.91253	−	8.50875i	0.186746	−	0.323454i
$693$	0.285719	+	0.494880i	0.0108536	+	0.0187989i
$694$	13.2707	+	11.1354i	0.503747	+	0.422694i
$695$	−3.14606	+	5.44913i	−0.119337	+	0.206697i
$696$	1.66572	+	9.44679i	0.0631391	+	0.358080i
$697$	−17.8975			−0.677917
$698$	10.5766	+	59.9829i	0.400330	+	2.27039i
$699$	7.62623	−	6.39916i	0.288450	−	0.242039i
$700$	23.7070	+	8.62865i	0.896041	+	0.326132i
$701$	−4.18240	+	1.52227i	−0.157967	+	0.0574954i	−0.419793	−	0.907620i	$-0.637897\pi$
$701$	−4.18240	+	1.52227i	−0.157967	+	0.0574954i	0.261826	+	0.965115i	$0.415675\pi$
$702$	−13.2399			−0.499707
$703$	−19.4739	−	20.2022i	−0.734471	−	0.761939i
$704$	−7.33247			−0.276353
$705$	8.04212	−	2.92709i	0.302884	−	0.110241i
$706$	−20.5684	−	7.48629i	−0.774102	−	0.281750i
$707$	−4.59788	+	3.85808i	−0.172921	+	0.145098i
$708$	3.20630	+	18.1838i	0.120500	+	0.683390i
$709$	31.4379			1.18068			0.590338	−	0.807156i	$-0.298994\pi$
$709$	31.4379			1.18068			0.590338	+	0.807156i	$0.298994\pi$
$710$	22.6038	+	128.192i	0.848304	+	4.81097i
$711$	−1.54155	+	2.67004i	−0.0578126	+	0.100134i
$712$	−0.404511	−	0.339425i	−0.0151597	−	0.0127205i
$713$	−22.0049	−	38.1137i	−0.824092	−	1.42737i
$714$	−3.33198	+	5.77115i	−0.124696	+	0.215980i
$715$	12.1250	−	4.41313i	0.453448	−	0.165042i
$716$	−28.6739	+	24.0603i	−1.07159	+	0.899175i
$717$	−6.08077	−	10.5322i	−0.227091	−	0.393332i
$718$	−6.71410	+	38.0776i	−0.250568	+	1.42104i
$719$	1.45485	−	8.25088i	0.0542569	−	0.307706i	−0.945587	−	0.325369i	$-0.894511\pi$
$719$	1.45485	−	8.25088i	0.0542569	−	0.307706i	0.999844	+	0.0176630i	$0.00562259\pi$
$720$	4.50152	+	3.77723i	0.167762	+	0.140769i
$721$	−1.24170	−	0.451941i	−0.0462433	−	0.0168312i
$722$	−4.71855	−	1.71741i	−0.175606	−	0.0639154i
$723$	−5.48479	−	4.60229i	−0.203982	−	0.171161i
$724$	−8.27326	+	46.9200i	−0.307473	+	1.74377i
$725$	−7.92506	+	44.9452i	−0.294329	+	1.66922i
$726$	−11.7485	−	20.3491i	−0.436029	−	0.755225i
$727$	19.8667	−	16.6701i	0.736813	−	0.618260i	−0.195166	−	0.980770i	$-0.562525\pi$
$727$	19.8667	−	16.6701i	0.736813	−	0.618260i	0.931980	+	0.362510i	$0.118080\pi$
$728$	10.5084	−	3.82474i	0.389467	−	0.141754i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−19.0242	−	32.9508i	−0.704116	−	1.21956i
$731$	15.1717	+	12.7306i	0.561147	+	0.470858i
$732$	−10.9621	+	18.9868i	−0.405169	+	0.701773i
$733$	−5.91670	−	33.5553i	−0.218538	−	1.23939i	−0.874660	−	0.484737i	$-0.838915\pi$
$733$	−5.91670	−	33.5553i	−0.218538	−	1.23939i	0.656122	−	0.754655i	$-0.272196\pi$
$734$	74.8311			2.76207
$735$	−3.89518	−	22.0906i	−0.143676	−	0.814825i
$736$	25.9492	−	21.7740i	0.956500	−	0.802599i
$737$	−6.25288	−	2.27586i	−0.230328	−	0.0838325i
$738$	12.1563	−	4.42454i	0.447480	−	0.162870i
$739$	−33.1875			−1.22082			−0.610411	−	0.792085i	$-0.708996\pi$
$739$	−33.1875			−1.22082			−0.610411	+	0.792085i	$0.708996\pi$
$740$	−26.2522	−	59.1066i	−0.965050	−	2.17280i
$741$	−27.7315			−1.01874
$742$	−4.61128	+	1.67837i	−0.169285	+	0.0616148i
$743$	−3.73214	−	1.35839i	−0.136919	−	0.0498345i	0.272652	−	0.962113i	$-0.412099\pi$
$743$	−3.73214	−	1.35839i	−0.136919	−	0.0498345i	−0.409571	+	0.912278i	$0.634322\pi$
$744$	13.4538	−	11.2891i	0.493241	−	0.413879i
$745$	4.40211	+	24.9656i	0.161281	+	0.914668i
$746$	−9.58686			−0.351000
$747$	−1.26446	−	7.17110i	−0.0462641	−	0.262377i
$748$	−2.49906	+	4.32849i	−0.0913746	+	0.158265i
$749$	−5.81156	−	4.87647i	−0.212350	−	0.178182i
$750$	−16.0700	−	27.8341i	−0.586795	−	1.01636i
$751$	−10.2818	+	17.8085i	−0.375187	+	0.649843i	−0.990355	−	0.138553i	$-0.955755\pi$
$751$	−10.2818	+	17.8085i	−0.375187	+	0.649843i	0.615168	+	0.788396i	$0.289088\pi$
$752$	−3.39682	+	1.23634i	−0.123869	+	0.0450847i
$753$	−10.4229	+	8.74584i	−0.379831	+	0.318716i
$754$	33.8991	+	58.7150i	1.23453	+	2.13828i
$755$	3.39651	−	19.2626i	0.123612	−	0.701036i
$756$	0.491546	−	2.78770i	0.0178774	−	0.101387i
$757$	−12.6820	−	10.6414i	−0.460935	−	0.386770i	0.382540	−	0.923939i	$-0.375049\pi$
$757$	−12.6820	−	10.6414i	−0.460935	−	0.386770i	−0.843475	+	0.537169i	$0.819494\pi$
$758$	18.1648	+	6.61144i	0.659775	+	0.240138i
$759$	−2.53832	−	0.923875i	−0.0921354	−	0.0335345i
$760$	−24.6910	−	20.7182i	−0.895638	−	0.751530i
$761$	−2.81695	+	15.9757i	−0.102114	+	0.579119i	0.890219	+	0.455532i	$0.150551\pi$
$761$	−2.81695	+	15.9757i	−0.102114	+	0.579119i	−0.992334	+	0.123587i	$0.960560\pi$
$762$	0.922196	−	5.23003i	0.0334076	−	0.189464i
$763$	−6.97958	−	12.0890i	−0.252678	−	0.437651i
$764$	−39.5192	+	33.1605i	−1.42975	+	1.19971i
$765$	10.6797	−	3.88710i	0.386126	−	0.140538i
$766$	8.44899	−	14.6341i	0.305275	−	0.528751i
$767$	19.4698	+	33.7228i	0.703015	+	1.21766i
$768$	3.47491	+	2.91580i	0.125390	+	0.105215i
$769$	11.4343	−	19.8048i	0.412331	−	0.714178i	−0.582813	−	0.812606i	$-0.698048\pi$
$769$	11.4343	−	19.8048i	0.412331	−	0.714178i	0.995144	+	0.0984281i	$0.0313815\pi$
$770$	0.815149	+	4.62294i	0.0293759	+	0.166599i
$771$	−5.02979			−0.181143
$772$	3.37764	+	19.1555i	0.121564	+	0.689423i
$773$	23.1167	−	19.3972i	0.831450	−	0.697669i	−0.124173	−	0.992261i	$-0.539628\pi$
$773$	23.1167	−	19.3972i	0.831450	−	0.697669i	0.955623	+	0.294591i	$0.0951835\pi$
$774$	−13.4521	−	4.89618i	−0.483527	−	0.175989i
$775$	78.5194	−	28.5787i	2.82050	−	1.02658i
$776$	5.40375			0.193983
$777$	3.55485	−	4.88358i	0.127530	−	0.175198i
$778$	7.11353			0.255032
$779$	25.4620	−	9.26740i	0.912270	−	0.332039i
$780$	−60.0628	−	21.8611i	−2.15059	−	0.782751i
$781$	−6.98508	+	5.86118i	−0.249946	+	0.209730i
$782$	−5.47009	−	31.0224i	−0.195610	−	1.10936i
$783$	5.12077			0.183001
$784$	1.64524	+	9.33061i	0.0587585	+	0.333236i
$785$	−27.7487	+	48.0621i	−0.990393	+	1.71541i
$786$	−6.82782	−	5.72922i	−0.243540	−	0.204355i
$787$	11.3138	+	19.5960i	0.403292	+	0.698523i	0.994121	−	0.108274i	$-0.0345324\pi$
$787$	11.3138	+	19.5960i	0.403292	+	0.698523i	−0.590829	+	0.806797i	$0.701199\pi$
$788$	31.1414	−	53.9384i	1.10936	−	1.92148i
$789$	11.9819	−	4.36105i	0.426567	−	0.155258i
$790$	−19.4017	+	16.2799i	−0.690280	+	0.579214i
$791$	6.11840	+	10.5974i	0.217545	+	0.376800i
$792$	0.187186	−	1.06158i	0.00665136	−	0.0377218i
$793$	−8.02880	+	45.5336i	−0.285111	+	1.61695i
$794$	−58.6030	−	49.1738i	−2.07974	−	1.74511i
$795$	7.86435	+	2.86239i	0.278920	+	0.101518i
$796$	−3.19416	−	1.16258i	−0.113214	−	0.0412065i
$797$	−18.4191	−	15.4555i	−0.652438	−	0.547461i	0.255372	−	0.966843i	$-0.417802\pi$
$797$	−18.4191	−	15.4555i	−0.652438	−	0.547461i	−0.907810	+	0.419382i	$0.862247\pi$
$798$	1.75193	−	9.93567i	0.0620175	−	0.351719i
$799$	−1.21402	+	6.88504i	−0.0429489	+	0.243575i
$800$	32.1574	+	55.6982i	1.13694	+	1.96923i
$801$	−0.215940	+	0.181195i	−0.00762985	+	0.00640220i
$802$	15.9001	−	5.78718i	0.561453	−	0.204352i
$803$	1.33264	−	2.30820i	0.0470279	−	0.0814546i
$804$	16.4812	+	28.5463i	0.581247	+	1.00675i
$805$	−13.3192	−	11.1761i	−0.469439	−	0.393906i
$806$	62.0651	−	107.500i	2.18615	−	3.78653i
$807$	0.149395	+	0.847260i	0.00525894	+	0.0298250i
$808$	11.3224			0.398320
$809$	6.80185	+	38.5752i	0.239140	+	1.35623i	0.833717	+	0.552192i	$0.186209\pi$
$809$	6.80185	+	38.5752i	0.239140	+	1.35623i	−0.594577	+	0.804039i	$0.702680\pi$
$810$	−6.29291	+	5.28038i	−0.221110	+	0.185534i
$811$	−41.0347	−	14.9354i	−1.44092	−	0.524454i	−0.500883	−	0.865515i	$-0.666991\pi$
$811$	−41.0347	−	14.9354i	−1.44092	−	0.524454i	−0.940041	+	0.341061i	$0.889214\pi$
$812$	−13.6212	+	4.95770i	−0.478010	+	0.173981i
$813$	−13.2979			−0.466377
$814$	4.53689	−	6.23268i	0.159018	−	0.218455i
$815$	−31.3740			−1.09898
$816$	−4.51088	+	1.64183i	−0.157912	+	0.0574754i
$817$	−28.1761	−	10.2553i	−0.985757	−	0.358786i
$818$	41.7080	−	34.9972i	1.45829	−	1.22365i
$819$	−1.03663	−	5.87901i	−0.0362227	−	0.205429i
$820$	62.4528			2.18095
$821$	−8.91282	−	50.5471i	−0.311059	−	1.76411i	−0.593513	−	0.804825i	$-0.702259\pi$
$821$	−8.91282	−	50.5471i	−0.311059	−	1.76411i	0.282453	−	0.959281i	$-0.408852\pi$
$822$	−16.6994	+	28.9242i	−0.582457	+	1.00885i
$823$	−12.7120	−	10.6666i	−0.443112	−	0.371815i	0.393760	−	0.919213i	$-0.371174\pi$
$823$	−12.7120	−	10.6666i	−0.443112	−	0.371815i	−0.836873	+	0.547398i	$0.815618\pi$
$824$	1.24633	+	2.15871i	0.0434181	+	0.0752023i
$825$	2.56432	−	4.44153i	0.0892782	−	0.154634i
$826$	−13.3122	+	4.84525i	−0.463191	+	0.168588i
$827$	−16.6977	+	14.0110i	−0.580635	+	0.487210i	−0.885155	−	0.465295i	$-0.845948\pi$
$827$	−16.6977	+	14.0110i	−0.580635	+	0.487210i	0.304521	+	0.952506i	$0.401504\pi$
$828$	6.69046	+	11.5882i	0.232510	+	0.402718i
$829$	−3.50363	+	19.8701i	−0.121686	+	0.690116i	0.861535	+	0.507698i	$0.169503\pi$
$829$	−3.50363	+	19.8701i	−0.121686	+	0.690116i	−0.983221	+	0.182418i	$0.941608\pi$
$830$	10.3873	−	58.9092i	0.360548	−	2.04477i
$831$	2.72542	+	2.28690i	0.0945437	+	0.0793316i
$832$	71.9812	+	26.1990i	2.49550	+	0.908288i
$833$	17.2192	+	6.26727i	0.596610	+	0.217148i
$834$	2.84606	+	2.38813i	0.0985510	+	0.0826941i
$835$	−9.66151	+	54.7931i	−0.334350	+	1.89619i
$836$	1.31398	−	7.45197i	0.0454451	−	0.257732i
$837$	−4.68774	−	8.11941i	−0.162032	−	0.280648i
$838$	−3.05665	+	2.56484i	−0.105590	+	0.0886008i
$839$	−21.0243	+	7.65221i	−0.725839	+	0.264184i	−0.678402	−	0.734691i	$-0.737327\pi$
$839$	−21.0243	+	7.65221i	−0.725839	+	0.264184i	−0.0474364	+	0.998874i	$0.515105\pi$
$840$	3.46924	−	6.00890i	0.119700	−	0.207327i
$841$	1.38888	+	2.40561i	0.0478924	+	0.0829520i
$842$	−33.3060	−	27.9471i	−1.14780	−	0.963120i
$843$	0.404422	−	0.700479i	0.0139290	−	0.0241258i
$844$	−6.56906	−	37.2550i	−0.226116	−	1.28237i
$845$	−86.3071			−2.96906
$846$	−0.877503	−	4.97657i	−0.0301692	−	0.171098i
$847$	8.11590	−	6.81005i	0.278865	−	0.233996i
$848$	−3.32173	−	1.20901i	−0.114069	−	0.0415176i
$849$	4.67694	−	1.70227i	0.160512	−	0.0584217i
$850$	59.8088			2.05142
$851$	1.96613	+	28.4856i	0.0673979	+	0.976474i
$852$	45.1692			1.54747
$853$	9.11745	−	3.31848i	0.312176	−	0.113623i	−0.181181	−	0.983450i	$-0.557992\pi$
$853$	9.11745	−	3.31848i	0.312176	−	0.113623i	0.493357	+	0.869827i	$0.335770\pi$
$854$	−15.8066	−	5.75313i	−0.540891	−	0.196868i
$855$	−13.1808	+	11.0600i	−0.450773	+	0.378244i
$856$	2.48509	+	14.0937i	0.0849387	+	0.481711i
$857$	54.7185			1.86915			0.934574	−	0.355768i	$-0.115781\pi$
$857$	54.7185			1.86915			0.934574	+	0.355768i	$0.115781\pi$
$858$	−1.32300	−	7.50309i	−0.0451664	−	0.256151i
$859$	24.4920	−	42.4214i	0.835656	−	1.44740i	−0.0578400	−	0.998326i	$-0.518421\pi$
$859$	24.4920	−	42.4214i	0.835656	−	1.44740i	0.893496	−	0.449072i	$-0.148245\pi$
$860$	−52.9413	−	44.4230i	−1.80528	−	1.51481i
$861$	2.91645	+	5.05145i	0.0993925	+	0.172153i
$862$	34.0622	−	58.9974i	1.16016	−	2.00946i
$863$	−17.4200	+	6.34035i	−0.592982	+	0.215828i	−0.621041	−	0.783778i	$-0.713290\pi$
$863$	−17.4200	+	6.34035i	−0.592982	+	0.215828i	0.0280584	+	0.999606i	$0.491068\pi$
$864$	5.52799	−	4.63854i	0.188066	−	0.157806i
$865$	−6.42802	−	11.1337i	−0.218559	−	0.378556i
$866$	−7.90797	+	44.8483i	−0.268724	+	1.52401i
$867$	1.33984	−	7.59859i	0.0455032	−	0.258062i
$868$	20.3302	+	17.0591i	0.690052	+	0.579022i
$869$	−1.66716	−	0.606798i	−0.0565547	−	0.0205842i
$870$	39.5292	+	14.3875i	1.34017	+	0.487781i
$871$	53.2515	+	44.6833i	1.80436	+	1.51404i
$872$	−4.57260	+	25.9325i	−0.154848	+	0.878185i
$873$	0.500919	−	2.84085i	0.0169535	−	0.0961482i
$874$	23.8456	+	41.3017i	0.806588	+	1.39705i
$875$	11.1012	−	9.31500i	0.375289	−	0.314905i
$876$	−12.4066	+	4.51564i	−0.419181	+	0.152569i
$877$	7.07372	−	12.2520i	0.238863	−	0.413722i	−0.721526	−	0.692388i	$-0.756559\pi$
$877$	7.07372	−	12.2520i	0.238863	−	0.413722i	0.960388	+	0.278666i	$0.0898921\pi$
$878$	18.2568	+	31.6217i	0.616136	+	1.06718i
$879$	−9.09884	−	7.63483i	−0.306896	−	0.257517i
$880$	−1.69075	+	2.92847i	−0.0569953	+	0.0987188i
$881$	4.88114	+	27.6823i	0.164450	+	0.932641i	0.949630	+	0.313374i	$0.101459\pi$
$881$	4.88114	+	27.6823i	0.164450	+	0.932641i	−0.785180	+	0.619268i	$0.787430\pi$
$882$	−13.2450			−0.445981
$883$	4.67179	+	26.4951i	0.157218	+	0.891630i	0.956730	+	0.290979i	$0.0939808\pi$
$883$	4.67179	+	26.4951i	0.157218	+	0.891630i	−0.799511	+	0.600651i	$0.794908\pi$
$884$	39.9985	−	33.5627i	1.34529	−	1.12884i
$885$	22.7035	+	8.26338i	0.763169	+	0.277771i
$886$	3.02455	−	1.10085i	0.101612	−	0.0369836i
$887$	3.80917			0.127900			0.0639498	−	0.997953i	$-0.479630\pi$
$887$	3.80917			0.127900			0.0639498	+	0.997953i	$0.479630\pi$
$888$	−11.0586	+	2.74664i	−0.371103	+	0.0921713i
$889$	2.39454			0.0803102
$890$	−2.17601	+	0.792004i	−0.0729402	+	0.0265480i
$891$	−0.540743	−	0.196814i	−0.0181156	−	0.00659353i
$892$	35.1074	−	29.4586i	1.17548	−	0.986346i
$893$	−1.83797	−	10.4236i	−0.0615053	−	0.348814i
$894$	14.9687			0.500628
$895$	8.50503	+	48.2344i	0.284292	+	1.61230i
$896$	−6.76797	+	11.7225i	−0.226102	+	0.391620i
$897$	21.6172	+	18.1389i	0.721776	+	0.605642i
$898$	−38.5664	−	66.7990i	−1.28698	−	2.22911i
$899$	−24.0048	+	41.5776i	−0.800606	+	1.38669i
$900$	−23.8733	+	8.68917i	−0.795777	+	0.289639i
$901$	−5.23722	+	4.39455i	−0.174477	+	0.146404i
$902$	3.72213	+	6.44692i	0.123933	+	0.214659i
$903$	1.12084	−	6.35661i	0.0372993	−	0.211535i
$904$	4.00841	−	22.7328i	0.133318	−	0.756082i
$905$	47.7566	+	40.0725i	1.58748	+	1.33206i
$906$	−10.8528	−	3.95010i	−0.360560	−	0.131233i
$907$	−20.7726	−	7.56059i	−0.689741	−	0.251045i	−0.0267169	−	0.999643i	$-0.508505\pi$
$907$	−20.7726	−	7.56059i	−0.689741	−	0.251045i	−0.663024	+	0.748598i	$0.730727\pi$
$908$	39.1333	+	32.8367i	1.29868	+	1.08972i
$909$	1.04957	−	5.95239i	0.0348119	−	0.197428i
$910$	8.51570	−	48.2949i	0.282293	−	1.60096i
$911$	−29.1596	−	50.5059i	−0.966101	−	1.67334i	−0.706627	−	0.707586i	$-0.749784\pi$
$911$	−29.1596	−	50.5059i	−0.966101	−	1.67334i	−0.259474	−	0.965750i	$-0.583549\pi$
$912$	5.56728	−	4.67150i	0.184351	−	0.154689i
$913$	3.93754	−	1.43315i	0.130314	−	0.0474303i
$914$	0.553293	−	0.958332i	0.0183013	−	0.0316988i
$915$	14.3438	+	24.8442i	0.474192	+	0.821324i
$916$	43.4695	+	36.4752i	1.43627	+	1.20517i
$917$	2.00940	−	3.48039i	0.0663563	−	0.114933i
$918$	−1.16530	−	6.60875i	−0.0384606	−	0.218121i
$919$	−6.93536			−0.228777			−0.114388	−	0.993436i	$-0.536491\pi$
$919$	−6.93536			−0.228777			−0.114388	+	0.993436i	$0.536491\pi$
$920$	5.69543	+	32.3004i	0.187773	+	1.06491i
$921$	−4.97993	+	4.17866i	−0.164094	+	0.137692i
$922$	−12.4703	−	4.53883i	−0.410688	−	0.149478i
$923$	89.5131	−	32.5801i	2.94636	−	1.07239i
$924$	1.62892			0.0535874
$925$	−53.9102	−	5.71529i	−1.77256	−	0.187918i
$926$	−42.8007			−1.40652
$927$	1.25041	−	0.455111i	0.0410688	−	0.0149478i
$928$	−34.7243	−	12.6386i	−1.13988	−	0.414883i
$929$	−37.2424	+	31.2500i	−1.22188	+	1.02528i	−0.223158	+	0.974782i	$0.571637\pi$
$929$	−37.2424	+	31.2500i	−1.22188	+	1.02528i	−0.998724	+	0.0504985i	$0.983919\pi$
$930$	−13.3740	−	75.8478i	−0.438551	−	2.48715i
$931$	−27.7422			−0.909213
$932$	−4.92783	−	27.9471i	−0.161416	−	0.915437i
$933$	12.0746	−	20.9138i	0.395304	−	0.684687i
$934$	−51.8224	−	43.4841i	−1.69568	−	1.42284i
$935$	3.27001	+	5.66382i	0.106941	+	0.185227i
$936$	−5.63062	+	9.75252i	−0.184043	+	0.318771i
$937$	−23.2710	+	8.46994i	−0.760229	+	0.276701i	−0.692904	−	0.721030i	$-0.743669\pi$
$937$	−23.2710	+	8.46994i	−0.760229	+	0.276701i	−0.0673255	+	0.997731i	$0.521447\pi$
$938$	−19.3733	+	16.2561i	−0.632561	+	0.530781i
$939$	−2.33304	−	4.04094i	−0.0761358	−	0.131871i
$940$	4.23628	−	24.0251i	0.138172	−	0.783613i
$941$	−3.17000	+	17.9780i	−0.103339	+	0.586065i	0.888532	+	0.458816i	$0.151726\pi$
$941$	−3.17000	+	17.9780i	−0.103339	+	0.586065i	−0.991871	+	0.127250i	$0.959385\pi$
$942$	25.1027	+	21.0636i	0.817889	+	0.686291i
$943$	−25.9097	−	9.43037i	−0.843737	−	0.307095i
$944$	−9.58945	−	3.49028i	−0.312110	−	0.113599i
$945$	−2.83740	−	2.38086i	−0.0923006	−	0.0774494i
$946$	1.43048	−	8.11263i	0.0465088	−	0.263764i
$947$	6.98003	−	39.5857i	0.226820	−	1.28636i	−0.632354	−	0.774680i	$-0.717911\pi$
$947$	6.98003	−	39.5857i	0.226820	−	1.28636i	0.859174	−	0.511683i	$-0.170978\pi$
$948$	4.39427	+	7.61110i	0.142719	+	0.247197i
$949$	−21.3295	+	17.8976i	−0.692384	+	0.580979i
$950$	−85.0872	+	30.9692i	−2.76059	+	1.00477i
$951$	−14.2255	+	24.6393i	−0.461294	+	0.798984i
$952$	2.83403	+	4.90868i	0.0918514	+	0.159091i
$953$	−4.73202	−	3.97064i	−0.153285	−	0.128621i	0.562920	−	0.826512i	$-0.309678\pi$
$953$	−4.73202	−	3.97064i	−0.153285	−	0.128621i	−0.716205	+	0.697890i	$0.754122\pi$
$954$	2.47082	−	4.27958i	0.0799957	−	0.138557i
$955$	11.7219	+	66.4779i	0.379310	+	2.15118i
$956$	−34.6671			−1.12122
$957$	0.511694	+	2.90196i	0.0165407	+	0.0938070i
$958$	46.8920	−	39.3471i	1.51501	−	1.27125i
$959$	−14.1509	−	5.15051i	−0.456957	−	0.166319i
$960$	44.6615	−	16.2554i	1.44144	−	0.524642i
$961$	56.8998			1.83548
$962$	−66.8071	+	44.9745i	−2.15395	+	1.45003i
$963$	7.63966			0.246185
$964$	−19.1788	+	6.98051i	−0.617707	+	0.224827i
$965$	23.9167	+	8.70497i	0.769906	+	0.280223i
$966$	−7.86449	+	6.59909i	−0.253036	+	0.212322i
$967$	8.41031	+	47.6973i	0.270457	+	1.53384i	0.753031	+	0.657985i	$0.228591\pi$
$967$	8.41031	+	47.6973i	0.270457	+	1.53384i	−0.482574	+	0.875855i	$0.660298\pi$
$968$	−19.9856			−0.642360
$969$	−2.44077	−	13.8423i	−0.0784090	−	0.444679i
$970$	11.8485	−	20.5223i	0.380433	−	0.658930i
$971$	−11.4261	−	9.58765i	−0.366681	−	0.307682i	0.440766	−	0.897622i	$-0.354707\pi$
$971$	−11.4261	−	9.58765i	−0.366681	−	0.307682i	−0.807447	+	0.589940i	$0.799151\pi$
$972$	1.42528	+	2.46865i	0.0457158	+	0.0791821i
$973$	−0.837585	+	1.45074i	−0.0268517	+	0.0465086i
$974$	−7.99081	+	2.90842i	−0.256042	+	0.0931917i
$975$	−41.0430	+	34.4392i	−1.31443	+	1.10294i
$976$	−6.05851	−	10.4937i	−0.193928	−	0.335894i
$977$	3.82328	−	21.6829i	0.122318	−	0.693697i	−0.860547	−	0.509370i	$-0.829878\pi$
$977$	3.82328	−	21.6829i	0.122318	−	0.693697i	0.982865	−	0.184327i	$-0.0590106\pi$
$978$	−3.21687	+	18.2438i	−0.102864	+	0.583372i
$979$	−0.124262	−	0.104268i	−0.00397142	−	0.00333242i
$980$	−60.0858	−	21.8695i	−1.91937	−	0.698594i
$981$	13.2093	+	4.80780i	0.421741	+	0.153501i
$982$	−50.2706	−	42.1820i	−1.60420	−	1.34608i
$983$	3.76807	−	21.3698i	0.120183	−	0.681591i	−0.863870	−	0.503715i	$-0.831966\pi$
$983$	3.76807	−	21.3698i	0.120183	−	0.681591i	0.984053	−	0.177876i	$-0.0569227\pi$
$984$	1.91068	−	10.8360i	0.0609104	−	0.345440i
$985$	−40.7483	−	70.5782i	−1.29835	−	2.24881i
$986$	−26.3243	+	22.0887i	−0.838336	+	0.703447i
$987$	2.14108	−	0.779290i	0.0681513	−	0.0248051i
$988$	−39.5251	+	68.4595i	−1.25746	+	2.17799i
$989$	15.2558	+	26.4239i	0.485107	+	0.840231i
$990$	−3.62123	−	3.03858i	−0.115090	−	0.0965723i
$991$	−7.38436	+	12.7901i	−0.234572	+	0.406291i	−0.959148	−	0.282904i	$-0.908702\pi$
$991$	−7.38436	+	12.7901i	−0.234572	+	0.406291i	0.724576	+	0.689195i	$0.242036\pi$
$992$	11.7484	+	66.6283i	0.373011	+	2.11545i
$993$	−2.24637			−0.0712863
$994$	6.01788	+	34.1291i	0.190875	+	1.08251i
$995$	−3.40720	+	2.85898i	−0.108015	+	0.0906357i
$996$	−19.5052	−	7.09930i	−0.618045	−	0.224950i
$997$	−36.7137	+	13.3627i	−1.16274	+	0.423201i	−0.850074	−	0.526663i	$-0.823443\pi$
$997$	−36.7137	+	13.3627i	−1.16274	+	0.423201i	−0.312662	+	0.949865i	$0.601221\pi$
$998$	94.4713			2.99044
$999$	0.418847	+	6.06832i	0.0132517	+	0.191993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.k.a.7.1	✓	18
3.2	odd	2		333.2.x.d.118.3		18
37.4	even	18		4107.2.a.m.1.2		9
37.16	even	9	inner	111.2.k.a.16.1	yes	18
37.33	even	9		4107.2.a.n.1.8		9
111.53	odd	18		333.2.x.d.127.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.k.a.7.1	✓	18	1.1	even	1	trivial
111.2.k.a.16.1	yes	18	37.16	even	9	inner
333.2.x.d.118.3		18	3.2	odd	2
333.2.x.d.127.3		18	111.53	odd	18
4107.2.a.m.1.2		9	37.4	even	18
4107.2.a.n.1.8		9	37.33	even	9

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:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06958 + 0.753264i) q^{2} +(0.939693 + 0.342020i) q^{3} +(2.18365 - 1.83230i) q^{4} +(-0.647697 - 3.67327i) q^{5} -2.20240 q^{6} +(-0.172439 - 0.977948i) q^{7} +(-0.936630 + 1.62229i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-2.06958 + 0.753264i) q^{2} +(0.939693 + 0.342020i) q^{3} +(2.18365 - 1.83230i) q^{4} +(-0.647697 - 3.67327i) q^{5} -2.20240 q^{6} +(-0.172439 - 0.977948i) q^{7} +(-0.936630 + 1.62229i) q^{8} +(0.766044 + 0.642788i) q^{9} +(4.10741 + 7.11424i) q^{10} +(-0.287723 + 0.498351i) q^{11} +(2.67865 - 0.974947i) q^{12} +(4.60513 - 3.86416i) q^{13} +(1.09353 + 1.89405i) q^{14} +(0.647697 - 3.67327i) q^{15} +(-0.273573 + 1.55151i) q^{16} +(2.33413 + 1.95857i) q^{17} +(-2.06958 - 0.753264i) q^{18} +(-4.33482 - 1.57775i) q^{19} +(-8.14489 - 6.83437i) q^{20} +(0.172439 - 0.977948i) q^{21} +(0.220075 - 1.24811i) q^{22} +(2.34707 + 4.06525i) q^{23} +(-1.43500 + 1.20411i) q^{24} +(-8.37497 + 3.04824i) q^{25} +(-6.61994 + 11.4661i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.16844 - 1.81954i) q^{28} +(2.56038 - 4.43471i) q^{29} +(1.42649 + 8.09001i) q^{30} -9.37549 q^{31} +(-1.25309 - 7.10665i) q^{32} +(-0.440818 + 0.369890i) q^{33} +(-6.30599 - 2.29519i) q^{34} +(-3.48058 + 1.26683i) q^{35} +2.85055 q^{36} +(5.46475 + 2.67143i) q^{37} +10.1597 q^{38} +(5.64903 - 2.05608i) q^{39} +(6.56577 + 2.38975i) q^{40} +(-4.49961 + 3.77562i) q^{41} +(0.379779 + 2.15383i) q^{42} +6.49994 q^{43} +(0.284842 + 1.61542i) q^{44} +(1.86497 - 3.23022i) q^{45} +(-7.91965 - 6.64538i) q^{46} +(1.14724 + 1.98707i) q^{47} +(-0.787723 + 1.36438i) q^{48} +(5.65120 - 2.05687i) q^{49} +(15.0365 - 12.6171i) q^{50} +(1.52350 + 2.63878i) q^{51} +(2.97569 - 16.8760i) q^{52} +(-0.389624 + 2.20967i) q^{53} +(-1.68713 - 1.41567i) q^{54} +(2.01694 + 0.734105i) q^{55} +(1.74803 + 0.636230i) q^{56} +(-3.53378 - 2.96519i) q^{57} +(-1.95840 + 11.1066i) q^{58} +(-1.12480 + 6.37905i) q^{59} +(-5.31620 - 9.20793i) q^{60} +(-5.89178 + 4.94379i) q^{61} +(19.4033 - 7.06222i) q^{62} +(0.496517 - 0.859993i) q^{63} +(6.37111 + 11.0351i) q^{64} +(-17.1769 - 14.4131i) q^{65} +(0.633681 - 1.09757i) q^{66} +(2.00798 + 11.3878i) q^{67} +8.68563 q^{68} +(0.815130 + 4.62283i) q^{69} +(6.24908 - 5.24360i) q^{70} +(14.8901 + 5.41957i) q^{71} +(-1.76029 + 0.640693i) q^{72} -4.63167 q^{73} +(-13.3220 - 1.41233i) q^{74} -8.91245 q^{75} +(-12.3566 + 4.49745i) q^{76} +(0.536976 + 0.195443i) q^{77} +(-10.1423 + 8.51043i) q^{78} +(0.535375 + 3.03626i) q^{79} +5.87632 q^{80} +(0.173648 + 0.984808i) q^{81} +(6.46824 - 11.2033i) q^{82} +(-5.57813 - 4.68060i) q^{83} +(-1.41535 - 2.45146i) q^{84} +(5.68256 - 9.84248i) q^{85} +(-13.4521 + 4.89618i) q^{86} +(3.92273 - 3.29156i) q^{87} +(-0.538980 - 0.933541i) q^{88} +(-0.0489495 + 0.277607i) q^{89} +(-1.42649 + 8.09001i) q^{90} +(-4.57306 - 3.83725i) q^{91} +(12.5739 + 4.57654i) q^{92} +(-8.81008 - 3.20661i) q^{93} +(-3.87108 - 3.24822i) q^{94} +(-2.98784 + 16.9449i) q^{95} +(1.25309 - 7.10665i) q^{96} +(-1.44234 - 2.49820i) q^{97} +(-10.1462 + 8.51370i) q^{98} +(-0.540743 + 0.196814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} - 6 q^{5} - 6 q^{6} + 6 q^{7} - 6 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{12} + 18 q^{13} - 9 q^{14} + 6 q^{15} - 9 q^{16} - 21 q^{17} - 3 q^{18} + 12 q^{19} - 6 q^{21} - 51 q^{22} + 6 q^{24} + 6 q^{25} + 15 q^{26} + 9 q^{27} - 39 q^{28} - 3 q^{29} + 15 q^{30} - 24 q^{31} + 21 q^{32} - 18 q^{34} - 12 q^{35} + 18 q^{36} + 27 q^{37} + 24 q^{38} + 18 q^{39} + 39 q^{40} + 9 q^{41} + 6 q^{42} - 72 q^{43} - 21 q^{44} + 21 q^{46} + 21 q^{47} - 3 q^{48} - 18 q^{49} + 24 q^{50} - 3 q^{51} - 30 q^{52} - 18 q^{53} + 3 q^{54} + 9 q^{55} + 54 q^{56} - 3 q^{57} - 66 q^{59} - 36 q^{60} + 33 q^{61} + 69 q^{62} + 18 q^{64} - 63 q^{65} + 42 q^{67} + 48 q^{68} - 12 q^{69} + 63 q^{70} + 15 q^{71} - 6 q^{72} - 24 q^{73} - 51 q^{74} - 6 q^{75} + 12 q^{76} + 39 q^{77} - 27 q^{78} - 6 q^{79} - 12 q^{80} + 15 q^{82} + 33 q^{83} - 6 q^{84} + 30 q^{85} - 60 q^{86} - 9 q^{87} - 3 q^{88} + 45 q^{89} - 15 q^{90} + 21 q^{91} - 24 q^{92} - 6 q^{93} + 18 q^{94} - 24 q^{95} - 21 q^{96} - 24 q^{97} - 36 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 - 6 * q^6 + 6 * q^7 - 6 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^12 + 18 * q^13 - 9 * q^14 + 6 * q^15 - 9 * q^16 - 21 * q^17 - 3 * q^18 + 12 * q^19 - 6 * q^21 - 51 * q^22 + 6 * q^24 + 6 * q^25 + 15 * q^26 + 9 * q^27 - 39 * q^28 - 3 * q^29 + 15 * q^30 - 24 * q^31 + 21 * q^32 - 18 * q^34 - 12 * q^35 + 18 * q^36 + 27 * q^37 + 24 * q^38 + 18 * q^39 + 39 * q^40 + 9 * q^41 + 6 * q^42 - 72 * q^43 - 21 * q^44 + 21 * q^46 + 21 * q^47 - 3 * q^48 - 18 * q^49 + 24 * q^50 - 3 * q^51 - 30 * q^52 - 18 * q^53 + 3 * q^54 + 9 * q^55 + 54 * q^56 - 3 * q^57 - 66 * q^59 - 36 * q^60 + 33 * q^61 + 69 * q^62 + 18 * q^64 - 63 * q^65 + 42 * q^67 + 48 * q^68 - 12 * q^69 + 63 * q^70 + 15 * q^71 - 6 * q^72 - 24 * q^73 - 51 * q^74 - 6 * q^75 + 12 * q^76 + 39 * q^77 - 27 * q^78 - 6 * q^79 - 12 * q^80 + 15 * q^82 + 33 * q^83 - 6 * q^84 + 30 * q^85 - 60 * q^86 - 9 * q^87 - 3 * q^88 + 45 * q^89 - 15 * q^90 + 21 * q^91 - 24 * q^92 - 6 * q^93 + 18 * q^94 - 24 * q^95 - 21 * q^96 - 24 * q^97 - 36 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

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