LMFDB - Embedded newform 111.2.k.b.46.1

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			46.1
Character	$\chi$	$=$	111.46
Dual form			111.2.k.b.70.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342484 - 1.94233i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-1.77595 + 0.646392i) q^{4} +(-1.36113 - 1.14212i) q^{5} -1.97229 q^{6} +(1.08780 + 0.912773i) q^{7} +(-0.108550 - 0.188014i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.342484 - 1.94233i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-1.77595 + 0.646392i) q^{4} +(-1.36113 - 1.14212i) q^{5} -1.97229 q^{6} +(1.08780 + 0.912773i) q^{7} +(-0.108550 - 0.188014i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.75221 + 3.03492i) q^{10} +(0.765023 + 1.32506i) q^{11} +(0.328182 + 1.86121i) q^{12} +(2.75490 - 1.00270i) q^{13} +(1.40035 - 2.42547i) q^{14} +(-1.36113 + 1.14212i) q^{15} +(-3.22354 + 2.70487i) q^{16} +(2.12798 + 0.774521i) q^{17} +(-0.342484 + 1.94233i) q^{18} +(-0.0968536 + 0.549284i) q^{19} +(3.15556 + 1.14853i) q^{20} +(1.08780 - 0.912773i) q^{21} +(2.31169 - 1.93974i) q^{22} +(3.62929 - 6.28612i) q^{23} +(-0.204007 + 0.0742523i) q^{24} +(-0.320013 - 1.81488i) q^{25} +(-2.89108 - 5.00750i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-2.52189 - 0.917892i) q^{28} +(3.83701 + 6.64589i) q^{29} +(2.68454 + 2.25260i) q^{30} +4.40813 q^{31} +(6.02514 + 5.05569i) q^{32} +(1.43777 - 0.523307i) q^{33} +(0.775573 - 4.39849i) q^{34} +(-0.438138 - 2.48480i) q^{35} +1.88993 q^{36} +(-4.77701 + 3.76566i) q^{37} +1.10006 q^{38} +(-0.509084 - 2.88716i) q^{39} +(-0.0669845 + 0.379888i) q^{40} +(-7.13911 + 2.59842i) q^{41} +(-2.14546 - 1.80025i) q^{42} +6.83430 q^{43} +(-2.21515 - 1.85873i) q^{44} +(0.888414 + 1.53878i) q^{45} +(-13.4527 - 4.89637i) q^{46} +(-5.22370 + 9.04771i) q^{47} +(2.10402 + 3.64426i) q^{48} +(-0.865382 - 4.90783i) q^{49} +(-3.41550 + 1.24314i) q^{50} +(1.13227 - 1.96116i) q^{51} +(-4.24442 + 3.56149i) q^{52} +(-8.70008 + 7.30024i) q^{53} +(1.85335 + 0.674563i) q^{54} +(0.472085 - 2.67733i) q^{55} +(0.0535333 - 0.303602i) q^{56} +(0.524121 + 0.190764i) q^{57} +(11.5944 - 9.72883i) q^{58} +(-0.563900 + 0.473168i) q^{59} +(1.67904 - 2.90818i) q^{60} +(-13.6895 + 4.98257i) q^{61} +(-1.50971 - 8.56202i) q^{62} +(-0.710011 - 1.22978i) q^{63} +(3.54825 - 6.14575i) q^{64} +(-4.89498 - 1.78163i) q^{65} +(-1.50885 - 2.61340i) q^{66} +(10.8563 + 9.10953i) q^{67} -4.27983 q^{68} +(-5.56040 - 4.66573i) q^{69} +(-4.67624 + 1.70201i) q^{70} +(1.26729 - 7.18713i) q^{71} +(0.0376989 + 0.213801i) q^{72} +6.96753 q^{73} +(8.95018 + 7.98883i) q^{74} -1.84288 q^{75} +(-0.183046 - 1.03811i) q^{76} +(-0.377285 + 2.13969i) q^{77} +(-5.43345 + 1.97762i) q^{78} +(-5.25763 - 4.41167i) q^{79} +7.47695 q^{80} +(0.766044 + 0.642788i) q^{81} +(7.49202 + 12.9766i) q^{82} +(3.10042 + 1.12846i) q^{83} +(-1.34187 + 2.32418i) q^{84} +(-2.01186 - 3.48464i) q^{85} +(-2.34064 - 13.2744i) q^{86} +(7.21122 - 2.62467i) q^{87} +(0.166086 - 0.287670i) q^{88} +(0.263691 - 0.221263i) q^{89} +(2.68454 - 2.25260i) q^{90} +(3.91201 + 1.42386i) q^{91} +(-2.38214 + 13.5098i) q^{92} +(0.765463 - 4.34116i) q^{93} +(19.3626 + 7.04742i) q^{94} +(0.759180 - 0.637028i) q^{95} +(6.02514 - 5.05569i) q^{96} +(-0.390769 + 0.676832i) q^{97} +(-9.23622 + 3.36171i) q^{98} +(-0.265690 - 1.50680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{6} - 9 q^{7} - 6 q^{8}+O(q^{10}) $ 24 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^6 - 9 * q^7 - 6 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{6} - 9 q^{7} - 6 q^{8} - 24 q^{10} - 6 q^{11} + 6 q^{12} + 21 q^{14} - 6 q^{15} - 9 q^{16} - 3 q^{17} - 3 q^{18} - 12 q^{19} - 30 q^{20} - 9 q^{21} + 45 q^{22} - 6 q^{24} - 6 q^{25} + 3 q^{26} - 12 q^{27} + 45 q^{28} + 9 q^{29} + 9 q^{30} - 24 q^{31} + 81 q^{32} + 12 q^{33} - 18 q^{34} + 12 q^{35} + 30 q^{36} + 12 q^{37} - 84 q^{38} + 9 q^{39} - 33 q^{40} - 9 q^{41} + 18 q^{42} + 72 q^{43} + 45 q^{44} - 27 q^{46} - 15 q^{47} - 33 q^{48} - 9 q^{49} - 72 q^{50} + 3 q^{51} - 48 q^{52} - 24 q^{53} - 3 q^{54} - 15 q^{55} - 66 q^{56} + 15 q^{57} - 12 q^{58} + 42 q^{59} - 36 q^{60} - 15 q^{61} - 9 q^{62} - 12 q^{63} - 18 q^{64} + 57 q^{65} - 21 q^{67} + 48 q^{68} - 12 q^{69} + 99 q^{70} + 9 q^{71} - 6 q^{72} + 51 q^{74} + 48 q^{75} - 12 q^{76} - 51 q^{77} - 39 q^{78} + 15 q^{79} + 276 q^{80} + 27 q^{82} - 15 q^{83} - 54 q^{84} - 42 q^{85} + 78 q^{86} + 3 q^{87} + 45 q^{88} - 3 q^{89} + 9 q^{90} - 12 q^{91} - 66 q^{92} - 21 q^{93} + 42 q^{94} - 18 q^{95} + 81 q^{96} + 12 q^{97} - 108 q^{98} - 15 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^6 - 9 * q^7 - 6 * q^8 - 24 * q^10 - 6 * q^11 + 6 * q^12 + 21 * q^14 - 6 * q^15 - 9 * q^16 - 3 * q^17 - 3 * q^18 - 12 * q^19 - 30 * q^20 - 9 * q^21 + 45 * q^22 - 6 * q^24 - 6 * q^25 + 3 * q^26 - 12 * q^27 + 45 * q^28 + 9 * q^29 + 9 * q^30 - 24 * q^31 + 81 * q^32 + 12 * q^33 - 18 * q^34 + 12 * q^35 + 30 * q^36 + 12 * q^37 - 84 * q^38 + 9 * q^39 - 33 * q^40 - 9 * q^41 + 18 * q^42 + 72 * q^43 + 45 * q^44 - 27 * q^46 - 15 * q^47 - 33 * q^48 - 9 * q^49 - 72 * q^50 + 3 * q^51 - 48 * q^52 - 24 * q^53 - 3 * q^54 - 15 * q^55 - 66 * q^56 + 15 * q^57 - 12 * q^58 + 42 * q^59 - 36 * q^60 - 15 * q^61 - 9 * q^62 - 12 * q^63 - 18 * q^64 + 57 * q^65 - 21 * q^67 + 48 * q^68 - 12 * q^69 + 99 * q^70 + 9 * q^71 - 6 * q^72 + 51 * q^74 + 48 * q^75 - 12 * q^76 - 51 * q^77 - 39 * q^78 + 15 * q^79 + 276 * q^80 + 27 * q^82 - 15 * q^83 - 54 * q^84 - 42 * q^85 + 78 * q^86 + 3 * q^87 + 45 * q^88 - 3 * q^89 + 9 * q^90 - 12 * q^91 - 66 * q^92 - 21 * q^93 + 42 * q^94 - 18 * q^95 + 81 * q^96 + 12 * q^97 - 108 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.342484	−	1.94233i	−0.242173	−	1.37343i	−0.826967	−	0.562250i	$-0.809936\pi$
$2$	−0.342484	−	1.94233i	−0.242173	−	1.37343i	0.584794	−	0.811182i	$-0.301175\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	−1.77595	+	0.646392i	−0.887974	+	0.323196i
$5$	−1.36113	−	1.14212i	−0.608716	−	0.510773i	0.285518	−	0.958373i	$-0.407834\pi$
$5$	−1.36113	−	1.14212i	−0.608716	−	0.510773i	−0.894234	+	0.447600i	$0.852279\pi$
$6$	−1.97229			−0.805184
$7$	1.08780	+	0.912773i	0.411150	+	0.344996i	0.824784	−	0.565447i	$-0.191296\pi$
$7$	1.08780	+	0.912773i	0.411150	+	0.344996i	−0.413635	+	0.910443i	$0.635741\pi$
$8$	−0.108550	−	0.188014i	−0.0383781	−	0.0664728i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−1.75221	+	3.03492i	−0.554097	+	0.959725i
$11$	0.765023	+	1.32506i	0.230663	+	0.399520i	0.958003	−	0.286757i	$-0.0925771\pi$
$11$	0.765023	+	1.32506i	0.230663	+	0.399520i	−0.727340	+	0.686277i	$0.759244\pi$
$12$	0.328182	+	1.86121i	0.0947380	+	0.537286i
$13$	2.75490	−	1.00270i	0.764071	−	0.278099i	0.0695567	−	0.997578i	$-0.477842\pi$
$13$	2.75490	−	1.00270i	0.764071	−	0.278099i	0.694514	+	0.719479i	$0.255619\pi$
$14$	1.40035	−	2.42547i	0.374259	−	0.648235i
$15$	−1.36113	+	1.14212i	−0.351442	+	0.294895i
$16$	−3.22354	+	2.70487i	−0.805885	+	0.676218i
$17$	2.12798	+	0.774521i	0.516111	+	0.187849i	0.586926	−	0.809640i	$-0.300338\pi$
$17$	2.12798	+	0.774521i	0.516111	+	0.187849i	−0.0708154	+	0.997489i	$0.522560\pi$
$18$	−0.342484	+	1.94233i	−0.0807244	+	0.457811i
$19$	−0.0968536	+	0.549284i	−0.0222197	+	0.126014i	−0.993900	−	0.110285i	$-0.964824\pi$
$19$	−0.0968536	+	0.549284i	−0.0222197	+	0.126014i	0.971680	+	0.236300i	$0.0759347\pi$
$20$	3.15556	+	1.14853i	0.705604	+	0.256819i
$21$	1.08780	−	0.912773i	0.237377	−	0.199183i
$22$	2.31169	−	1.93974i	0.492854	−	0.413553i
$23$	3.62929	−	6.28612i	0.756760	−	1.31075i	−0.187734	−	0.982220i	$-0.560114\pi$
$23$	3.62929	−	6.28612i	0.756760	−	1.31075i	0.944494	−	0.328527i	$-0.106552\pi$
$24$	−0.204007	+	0.0742523i	−0.0416427	+	0.0151567i
$25$	−0.320013	−	1.81488i	−0.0640026	−	0.362977i
$26$	−2.89108	−	5.00750i	−0.566988	−	0.982051i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−2.52189	−	0.917892i	−0.476592	−	0.173465i
$29$	3.83701	+	6.64589i	0.712514	+	1.23411i	0.963910	+	0.266227i	$0.0857770\pi$
$29$	3.83701	+	6.64589i	0.712514	+	1.23411i	−0.251396	+	0.967884i	$0.580890\pi$
$30$	2.68454	+	2.25260i	0.490128	+	0.411266i
$31$	4.40813			0.791723			0.395861	−	0.918310i	$-0.370446\pi$
$31$	4.40813			0.791723			0.395861	+	0.918310i	$0.370446\pi$
$32$	6.02514	+	5.05569i	1.06510	+	0.893728i
$33$	1.43777	−	0.523307i	0.250284	−	0.0910960i
$34$	0.775573	−	4.39849i	0.133010	−	0.754335i
$35$	−0.438138	−	2.48480i	−0.0740588	−	0.420008i
$36$	1.88993			0.314988
$37$	−4.77701	+	3.76566i	−0.785336	+	0.619070i
$37$	−4.77701	+	3.76566i	−0.785336	+	0.619070i
$38$	1.10006			0.178453
$39$	−0.509084	−	2.88716i	−0.0815188	−	0.462316i
$40$	−0.0669845	+	0.379888i	−0.0105912	+	0.0600656i
$41$	−7.13911	+	2.59842i	−1.11494	+	0.405806i	−0.832804	−	0.553568i	$-0.813266\pi$
$41$	−7.13911	+	2.59842i	−1.11494	+	0.405806i	−0.282138	+	0.959374i	$0.591044\pi$
$42$	−2.14546	−	1.80025i	−0.331051	−	0.277785i
$43$	6.83430			1.04222			0.521110	−	0.853489i	$-0.325518\pi$
$43$	6.83430			1.04222			0.521110	+	0.853489i	$0.325518\pi$
$44$	−2.21515	−	1.85873i	−0.333947	−	0.280214i
$45$	0.888414	+	1.53878i	0.132437	+	0.229388i
$46$	−13.4527	−	4.89637i	−1.98349	−	0.721931i
$47$	−5.22370	+	9.04771i	−0.761955	+	1.31974i	0.179887	+	0.983687i	$0.442427\pi$
$47$	−5.22370	+	9.04771i	−0.761955	+	1.31974i	−0.941842	+	0.336057i	$0.890907\pi$
$48$	2.10402	+	3.64426i	0.303689	+	0.526004i
$49$	−0.865382	−	4.90783i	−0.123626	−	0.701118i
$50$	−3.41550	+	1.24314i	−0.483024	+	0.175806i
$51$	1.13227	−	1.96116i	0.158550	−	0.274617i
$52$	−4.24442	+	3.56149i	−0.588595	+	0.493890i
$53$	−8.70008	+	7.30024i	−1.19505	+	1.00276i	−0.195291	+	0.980745i	$0.562565\pi$
$53$	−8.70008	+	7.30024i	−1.19505	+	1.00276i	−0.999758	+	0.0220191i	$0.992991\pi$
$54$	1.85335	+	0.674563i	0.252208	+	0.0917964i
$55$	0.472085	−	2.67733i	0.0636560	−	0.361011i
$56$	0.0535333	−	0.303602i	0.00715369	−	0.0405706i
$57$	0.524121	+	0.190764i	0.0694215	+	0.0252673i
$58$	11.5944	−	9.72883i	1.52242	−	1.27746i
$59$	−0.563900	+	0.473168i	−0.0734135	+	0.0616013i	−0.678756	−	0.734364i	$-0.737481\pi$
$59$	−0.563900	+	0.473168i	−0.0734135	+	0.0616013i	0.605342	+	0.795965i	$0.293036\pi$
$60$	1.67904	−	2.90818i	0.216763	−	0.375444i
$61$	−13.6895	+	4.98257i	−1.75276	+	0.637953i	−0.999798	−	0.0201081i	$-0.993599\pi$
$61$	−13.6895	+	4.98257i	−1.75276	+	0.637953i	−0.752964	+	0.658061i	$0.771377\pi$
$62$	−1.50971	−	8.56202i	−0.191734	−	1.08738i
$63$	−0.710011	−	1.22978i	−0.0894530	−	0.154937i
$64$	3.54825	−	6.14575i	0.443531	−	0.768219i
$65$	−4.89498	−	1.78163i	−0.607148	−	0.220984i
$66$	−1.50885	−	2.61340i	−0.185726	−	0.321687i
$67$	10.8563	+	9.10953i	1.32631	+	1.11291i	0.984925	+	0.172983i	$0.0553405\pi$
$67$	10.8563	+	9.10953i	1.32631	+	1.11291i	0.341385	+	0.939923i	$0.389104\pi$
$68$	−4.27983			−0.519005
$69$	−5.56040	−	4.66573i	−0.669394	−	0.561688i
$70$	−4.67624	+	1.70201i	−0.558918	+	0.203429i
$71$	1.26729	−	7.18713i	0.150399	−	0.852956i	−0.812473	−	0.582999i	$-0.801879\pi$
$71$	1.26729	−	7.18713i	0.150399	−	0.852956i	0.962872	−	0.269957i	$-0.0870096\pi$
$72$	0.0376989	+	0.213801i	0.00444286	+	0.0251967i
$73$	6.96753			0.815488			0.407744	−	0.913096i	$-0.366316\pi$
$73$	6.96753			0.815488			0.407744	+	0.913096i	$0.366316\pi$
$74$	8.95018	+	7.98883i	1.04044	+	0.928683i
$75$	−1.84288			−0.212798
$76$	−0.183046	−	1.03811i	−0.0209968	−	0.119079i
$77$	−0.377285	+	2.13969i	−0.0429957	+	0.243841i
$78$	−5.43345	+	1.97762i	−0.615218	+	0.223921i
$79$	−5.25763	−	4.41167i	−0.591529	−	0.496352i	0.297181	−	0.954821i	$-0.403953\pi$
$79$	−5.25763	−	4.41167i	−0.591529	−	0.496352i	−0.888710	+	0.458469i	$0.848398\pi$
$80$	7.47695			0.835949
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	7.49202	+	12.9766i	0.827356	+	1.43302i
$83$	3.10042	+	1.12846i	0.340315	+	0.123865i	0.506524	−	0.862226i	$-0.330930\pi$
$83$	3.10042	+	1.12846i	0.340315	+	0.123865i	−0.166208	+	0.986091i	$0.553152\pi$
$84$	−1.34187	+	2.32418i	−0.146410	+	0.253589i
$85$	−2.01186	−	3.48464i	−0.218217	−	0.377962i
$86$	−2.34064	−	13.2744i	−0.252398	−	1.43142i
$87$	7.21122	−	2.62467i	0.773123	−	0.281394i
$88$	0.166086	−	0.287670i	0.0177048	−	0.0306657i
$89$	0.263691	−	0.221263i	0.0279512	−	0.0234539i	−0.628705	−	0.777644i	$-0.716415\pi$
$89$	0.263691	−	0.221263i	0.0279512	−	0.0234539i	0.656656	+	0.754190i	$0.271970\pi$
$90$	2.68454	−	2.25260i	0.282975	−	0.237445i
$91$	3.91201	+	1.42386i	0.410091	+	0.149261i
$92$	−2.38214	+	13.5098i	−0.248355	+	1.40849i
$93$	0.765463	−	4.34116i	0.0793748	−	0.450157i
$94$	19.3626	+	7.04742i	1.99710	+	0.726886i
$95$	0.759180	−	0.637028i	0.0778903	−	0.0653577i
$96$	6.02514	−	5.05569i	0.614938	−	0.515994i
$97$	−0.390769	+	0.676832i	−0.0396766	+	0.0687219i	−0.885182	−	0.465245i	$-0.845966\pi$
$97$	−0.390769	+	0.676832i	−0.0396766	+	0.0687219i	0.845505	+	0.533967i	$0.179299\pi$
$98$	−9.23622	+	3.36171i	−0.932999	+	0.339584i
$99$	−0.265690	−	1.50680i	−0.0267028	−	0.151439i
$100$	1.74145	+	3.01629i	0.174145	+	0.301629i
$101$	−0.390689	+	0.676693i	−0.0388750	+	0.0673334i	−0.884808	−	0.465955i	$-0.845711\pi$
$101$	−0.390689	+	0.676693i	−0.0388750	+	0.0673334i	0.845933	+	0.533289i	$0.179044\pi$
$102$	−4.19699	−	1.52758i	−0.415564	−	0.151253i
$103$	−4.67429	−	8.09611i	−0.460572	−	0.797734i	0.538418	−	0.842678i	$-0.319022\pi$
$103$	−4.67429	−	8.09611i	−0.460572	−	0.797734i	−0.998989	+	0.0449443i	$0.985689\pi$
$104$	−0.487564	−	0.409115i	−0.0478096	−	0.0401170i
$105$	−2.52314			−0.246233
$106$	17.1591	+	14.3982i	1.66664	+	1.39847i
$107$	8.06010	−	2.93364i	0.779199	−	0.283605i	0.0783606	−	0.996925i	$-0.475031\pi$
$107$	8.06010	−	2.93364i	0.779199	−	0.283605i	0.700839	+	0.713320i	$0.252809\pi$
$108$	0.328182	−	1.86121i	0.0315793	−	0.179095i
$109$	−1.11137	−	6.30291i	−0.106450	−	0.603709i	−0.990631	−	0.136565i	$-0.956394\pi$
$109$	−1.11137	−	6.30291i	−0.106450	−	0.603709i	0.884181	−	0.467145i	$-0.154717\pi$
$110$	−5.36193			−0.511240
$111$	2.87893	+	5.35834i	0.273256	+	0.508591i
$112$	−5.97550			−0.564632
$113$	−0.879791	−	4.98954i	−0.0827638	−	0.469377i	−0.997817	−	0.0660430i	$-0.978963\pi$
$113$	−0.879791	−	4.98954i	−0.0827638	−	0.469377i	0.915053	−	0.403334i	$-0.132149\pi$
$114$	0.191023	−	1.08335i	0.0178910	−	0.101465i
$115$	−12.1195	+	4.41113i	−1.13015	+	0.411340i
$116$	−11.1102	−	9.32255i	−1.03155	−	0.865577i
$117$	−2.93170			−0.271036
$118$	1.11217	+	0.933225i	0.102384	+	0.0859103i
$119$	1.60785	+	2.78489i	0.147392	+	0.255290i
$120$	0.362485	+	0.131934i	0.0330902	+	0.0120438i
$121$	4.32948	−	7.49888i	0.393589	−	0.681716i
$122$	14.3662	+	24.8830i	1.30066	+	2.25280i
$123$	1.31925	+	7.48187i	0.118953	+	0.674617i
$124$	−7.82861	+	2.84938i	−0.703030	+	0.255882i
$125$	−6.07931	+	10.5297i	−0.543750	+	0.941803i
$126$	−2.14546	+	1.80025i	−0.191132	+	0.160379i
$127$	−0.00513449	+	0.00430834i	−0.000455612	+	0.000382304i	−0.643015	−	0.765853i	$-0.722317\pi$
$127$	−0.00513449	+	0.00430834i	−0.000455612	+	0.000382304i	0.642560	+	0.766236i	$0.277872\pi$
$128$	1.62958	+	0.593119i	0.144036	+	0.0524248i
$129$	1.18676	−	6.73047i	0.104489	−	0.592585i
$130$	−1.78405	+	10.1178i	−0.156471	+	0.887392i
$131$	−6.17317	−	2.24685i	−0.539352	−	0.196308i	0.0579571	−	0.998319i	$-0.481541\pi$
$131$	−6.17317	−	2.24685i	−0.539352	−	0.196308i	−0.597309	+	0.802011i	$0.703764\pi$
$132$	−2.21515	+	1.85873i	−0.192804	+	0.161782i
$133$	−0.606729	+	0.509106i	−0.0526100	+	0.0441451i
$134$	13.9756	−	24.2064i	1.20730	−	2.09111i
$135$	1.66967	−	0.607711i	0.143703	−	0.0523034i
$136$	−0.0853710	−	0.484163i	−0.00732050	−	0.0415166i
$137$	6.96029	+	12.0556i	0.594658	+	1.02998i	0.993595	+	0.113000i	$0.0360459\pi$
$137$	6.96029	+	12.0556i	0.594658	+	1.02998i	−0.398937	+	0.916978i	$0.630621\pi$
$138$	−7.15802	+	12.3981i	−0.609331	+	1.05539i
$139$	−9.06854	−	3.30068i	−0.769183	−	0.279960i	−0.0725286	−	0.997366i	$-0.523107\pi$
$139$	−9.06854	−	3.30068i	−0.769183	−	0.279960i	−0.696655	+	0.717406i	$0.745329\pi$
$140$	2.38427	+	4.12967i	0.201507	+	0.349021i
$141$	8.00317	+	6.71546i	0.673988	+	0.565543i
$142$	−14.3938			−1.20790
$143$	3.43620	+	2.88331i	0.287349	+	0.241115i
$144$	3.95426	−	1.43923i	0.329521	−	0.119936i
$145$	2.36776	−	13.4283i	0.196632	−	1.11516i
$146$	−2.38627	−	13.5332i	−0.197489	−	1.12002i
$147$	−4.98354			−0.411035
$148$	6.04964	−	9.77544i	0.497277	−	0.803536i
$149$	−5.94529			−0.487058			−0.243529	−	0.969894i	$-0.578305\pi$
$149$	−5.94529			−0.487058			−0.243529	+	0.969894i	$0.578305\pi$
$150$	0.631158	+	3.57947i	0.0515338	+	0.292263i
$151$	−0.638135	+	3.61904i	−0.0519307	+	0.294513i	−0.999701	−	0.0244392i	$-0.992220\pi$
$151$	−0.638135	+	3.61904i	−0.0519307	+	0.294513i	0.947771	+	0.318953i	$0.103331\pi$
$152$	0.113786	−	0.0414148i	0.00922928	−	0.00335918i
$153$	−1.73474	−	1.45562i	−0.140246	−	0.117680i
$154$	4.28519			0.345311
$155$	−6.00003	−	5.03462i	−0.481934	−	0.404391i
$156$	2.77035	+	4.79838i	0.221805	+	0.384178i
$157$	−22.2376	−	8.09382i	−1.77475	−	0.645957i	−0.999905	−	0.0138089i	$-0.995604\pi$
$157$	−22.2376	−	8.09382i	−1.77475	−	0.645957i	−0.774848	−	0.632148i	$-0.782173\pi$
$158$	−6.76825	+	11.7230i	−0.538453	+	0.932628i
$159$	5.67858	+	9.83558i	0.450340	+	0.780012i
$160$	−2.42677	−	13.7629i	−0.191853	−	1.08805i
$161$	9.68575	−	3.52532i	0.763344	−	0.277834i
$162$	0.986145	−	1.70805i	0.0774788	−	0.134197i
$163$	8.68247	−	7.28545i	0.680063	−	0.570641i	−0.235962	−	0.971762i	$-0.575824\pi$
$163$	8.68247	−	7.28545i	0.680063	−	0.570641i	0.916025	+	0.401122i	$0.131380\pi$
$164$	10.9991	−	9.22934i	0.858885	−	0.720690i
$165$	−2.55468	−	0.929826i	−0.198881	−	0.0723869i
$166$	1.12999	−	6.40851i	0.0877044	−	0.497396i
$167$	3.83733	−	21.7626i	0.296941	−	1.68404i	−0.362264	−	0.932075i	$-0.617996\pi$
$167$	3.83733	−	21.7626i	0.296941	−	1.68404i	0.659206	−	0.751963i	$-0.270893\pi$
$168$	−0.289694	−	0.105440i	−0.0223504	−	0.00813487i
$169$	−3.37453	+	2.83156i	−0.259579	+	0.217813i
$170$	−6.07927	+	5.10112i	−0.466259	+	0.391238i
$171$	0.278879	−	0.483032i	0.0213264	−	0.0369384i
$172$	−12.1374	+	4.41764i	−0.925465	+	0.336842i
$173$	−2.91793	−	16.5484i	−0.221846	−	1.25815i	−0.868623	−	0.495473i	$-0.834995\pi$
$173$	−2.91793	−	16.5484i	−0.221846	−	1.25815i	0.646777	−	0.762679i	$-0.276116\pi$
$174$	−7.56769	−	13.1076i	−0.573705	−	0.993686i
$175$	1.30847	−	2.26633i	0.0989107	−	0.171318i
$176$	−6.05020	−	2.20209i	−0.456051	−	0.165989i
$177$	0.368060	+	0.637498i	0.0276651	+	0.0479173i
$178$	−0.520075	−	0.436395i	−0.0389813	−	0.0327092i
$179$	16.4350			1.22841			0.614205	−	0.789147i	$-0.289477\pi$
$179$	16.4350			1.22841			0.614205	+	0.789147i	$0.289477\pi$
$180$	−2.57243	−	2.15853i	−0.191738	−	0.160887i
$181$	−8.17313	+	2.97478i	−0.607504	+	0.221113i	−0.627411	−	0.778688i	$-0.715885\pi$
$181$	−8.17313	+	2.97478i	−0.607504	+	0.221113i	0.0199068	+	0.999802i	$0.493663\pi$
$182$	1.42579	−	8.08606i	0.105687	−	0.599378i
$183$	2.52972	+	14.3468i	0.187002	+	1.06054i
$184$	−1.57583			−0.116172
$185$	10.8030	+	0.330392i	0.794250	+	0.0242909i
$186$	−8.69410			−0.637482
$187$	0.601667	+	3.41223i	0.0439983	+	0.249527i
$188$	3.42865	−	19.4448i	0.250060	−	1.41816i
$189$	−1.33438	+	0.485676i	−0.0970622	+	0.0353277i
$190$	−1.49732	−	1.25640i	−0.108627	−	0.0911491i
$191$	9.45739			0.684313			0.342156	−	0.939643i	$-0.388843\pi$
$191$	9.45739			0.684313			0.342156	+	0.939643i	$0.388843\pi$
$192$	−5.43624	−	4.56154i	−0.392327	−	0.329201i
$193$	−1.51453	−	2.62324i	−0.109018	−	0.188825i	0.806355	−	0.591432i	$-0.201437\pi$
$193$	−1.51453	−	2.62324i	−0.109018	−	0.188825i	−0.915373	+	0.402607i	$0.868104\pi$
$194$	1.44846	+	0.527197i	0.103993	+	0.0378505i
$195$	−2.60456	+	4.51124i	−0.186517	+	0.323056i
$196$	4.70926	+	8.15667i	0.336375	+	0.582619i
$197$	4.74355	+	26.9020i	0.337964	+	1.91669i	0.395749	+	0.918359i	$0.370485\pi$
$197$	4.74355	+	26.9020i	0.337964	+	1.91669i	−0.0577851	+	0.998329i	$0.518404\pi$
$198$	−2.83571	+	1.03211i	−0.201525	+	0.0733490i
$199$	−11.7080	+	20.2788i	−0.829957	+	1.43753i	0.0681142	+	0.997678i	$0.478302\pi$
$199$	−11.7080	+	20.2788i	−0.829957	+	1.43753i	−0.898071	+	0.439850i	$0.855032\pi$
$200$	−0.306485	+	0.257172i	−0.0216718	+	0.0181848i
$201$	10.8563	−	9.10953i	0.765745	−	0.642537i
$202$	1.44816	+	0.527088i	0.101892	+	0.0370858i
$203$	−1.89229	+	10.7317i	−0.132813	+	0.753219i
$204$	−0.743184	+	4.21481i	−0.0520333	+	0.295095i
$205$	12.6850	+	4.61696i	0.885957	+	0.322462i
$206$	−14.1244	+	11.8518i	−0.984095	+	0.825754i
$207$	−5.56040	+	4.66573i	−0.386475	+	0.324291i
$208$	−6.16835	+	10.6839i	−0.427698	+	0.740794i
$209$	−0.801929	+	0.291878i	−0.0554706	+	0.0201896i
$210$	0.864135	+	4.90075i	0.0596310	+	0.338184i
$211$	9.57918	+	16.5916i	0.659458	+	1.14221i	0.980756	+	0.195237i	$0.0625475\pi$
$211$	9.57918	+	16.5916i	0.659458	+	1.14221i	−0.321298	+	0.946978i	$0.604119\pi$
$212$	10.7321	−	18.5885i	0.737082	−	1.27666i
$213$	−6.85788	−	2.49607i	−0.469894	−	0.171028i
$214$	−8.45854	−	14.6506i	−0.578214	−	1.00150i
$215$	−9.30236	−	7.80561i	−0.634416	−	0.532338i
$216$	0.217099			0.0147717
$217$	4.79516	+	4.02362i	0.325517	+	0.273141i
$218$	−11.8617	+	4.31730i	−0.803374	+	0.292404i
$219$	1.20990	−	6.86168i	0.0817574	−	0.463669i
$220$	0.892206	+	5.05995i	0.0601525	+	0.341142i
$221$	6.63898			0.446586
$222$	9.42165	−	7.42696i	0.632340	−	0.498465i
$223$	−5.52330			−0.369867			−0.184934	−	0.982751i	$-0.559207\pi$
$223$	−5.52330			−0.369867			−0.184934	+	0.982751i	$0.559207\pi$
$224$	1.93945	+	10.9992i	0.129585	+	0.734913i
$225$	−0.320013	+	1.81488i	−0.0213342	+	0.120992i
$226$	−9.39000	+	3.41768i	−0.624614	+	0.227341i
$227$	−8.30959	−	6.97257i	−0.551527	−	0.462786i	0.323931	−	0.946081i	$-0.394995\pi$
$227$	−8.30959	−	6.97257i	−0.551527	−	0.462786i	−0.875458	+	0.483295i	$0.839440\pi$
$228$	−1.05412			−0.0698108
$229$	15.6507	+	13.1325i	1.03423	+	0.867821i	0.991348	−	0.131259i	$-0.0419021\pi$
$229$	15.6507	+	13.1325i	1.03423	+	0.867821i	0.0428806	+	0.999080i	$0.486347\pi$
$230$	12.7186	+	22.0292i	0.838638	+	1.45256i
$231$	2.04167	+	0.743107i	0.134332	+	0.0488929i
$232$	0.833012	−	1.44282i	0.0546899	−	0.0947257i
$233$	1.30551	+	2.26121i	0.0855269	+	0.148137i	0.905616	−	0.424099i	$-0.139409\pi$
$233$	1.30551	+	2.26121i	0.0855269	+	0.148137i	−0.820089	+	0.572236i	$0.806076\pi$
$234$	1.00406	+	5.69432i	0.0656376	+	0.372249i
$235$	17.4437	−	6.34900i	1.13790	−	0.414163i
$236$	0.695605	−	1.20482i	0.0452800	−	0.0784273i
$237$	−5.25763	+	4.41167i	−0.341519	+	0.286569i
$238$	4.85849	−	4.07676i	0.314929	−	0.264257i
$239$	−24.3566	−	8.86507i	−1.57550	−	0.573433i	−0.601277	−	0.799041i	$-0.705341\pi$
$239$	−24.3566	−	8.86507i	−1.57550	−	0.573433i	−0.974218	+	0.225607i	$0.927563\pi$
$240$	1.29836	−	7.36336i	0.0838087	−	0.475303i
$241$	−4.39914	+	24.9487i	−0.283373	+	1.60709i	0.427665	+	0.903937i	$0.359336\pi$
$241$	−4.39914	+	24.9487i	−0.283373	+	1.60709i	−0.711039	+	0.703153i	$0.751775\pi$
$242$	−16.0480	−	5.84101i	−1.03161	−	0.375474i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	21.0912	−	17.6976i	1.35022	−	1.13297i
$245$	−4.42745	+	7.66856i	−0.282859	+	0.489926i
$246$	14.0804	−	5.12485i	0.897733	−	0.326748i
$247$	0.283946	+	1.61034i	0.0180670	+	0.102463i
$248$	−0.478501	−	0.828788i	−0.0303848	−	0.0526281i
$249$	1.64970	−	2.85736i	0.104545	−	0.181078i
$250$	22.5341	+	8.20175i	1.42518	+	0.518725i
$251$	5.17750	+	8.96769i	0.326801	+	0.566036i	0.981875	−	0.189529i	$-0.0606960\pi$
$251$	5.17750	+	8.96769i	0.326801	+	0.566036i	−0.655074	+	0.755564i	$0.727363\pi$
$252$	2.05586	+	1.72507i	0.129507	+	0.108669i
$253$	11.1060			0.698227
$254$	0.0101267	+	0.00849730i	0.000635405	+	0.000533168i
$255$	−3.78105	+	1.37619i	−0.236779	+	0.0861804i
$256$	3.05851	−	17.3457i	0.191157	−	1.08411i
$257$	−2.75197	−	15.6072i	−0.171663	−	0.973551i	−0.941925	−	0.335823i	$-0.890986\pi$
$257$	−2.75197	−	15.6072i	−0.171663	−	0.973551i	0.770262	−	0.637728i	$-0.220126\pi$
$258$	−13.4792			−0.839179
$259$	−8.63362	−	0.264045i	−0.536467	−	0.0164070i
$260$	9.84486			0.610553
$261$	−1.33258	−	7.55743i	−0.0824846	−	0.467793i
$262$	−2.24990	+	12.7598i	−0.138999	+	0.788304i
$263$	18.3073	−	6.66330i	1.12887	−	0.410877i	0.290991	−	0.956726i	$-0.406015\pi$
$263$	18.3073	−	6.66330i	1.12887	−	0.410877i	0.837883	+	0.545849i	$0.183793\pi$
$264$	−0.254459	−	0.213516i	−0.0156608	−	0.0131410i
$265$	20.1797			1.23963
$266$	1.19664	+	1.00410i	0.0733710	+	0.0615656i
$267$	−0.172112	−	0.298107i	−0.0105331	−	0.0182439i
$268$	−25.1686	−	9.16062i	−1.53742	−	0.559574i
$269$	0.957955	−	1.65923i	0.0584075	−	0.101165i	−0.835343	−	0.549729i	$-0.814731\pi$
$269$	0.957955	−	1.65923i	0.0584075	−	0.101165i	0.893751	+	0.448564i	$0.148064\pi$
$270$	−1.75221	−	3.03492i	−0.106636	−	0.184699i
$271$	1.89232	+	10.7319i	0.114950	+	0.651914i	0.986775	+	0.162096i	$0.0518255\pi$
$271$	1.89232	+	10.7319i	0.114950	+	0.651914i	−0.871825	+	0.489818i	$0.837063\pi$
$272$	−8.95461	+	3.25921i	−0.542953	+	0.197619i
$273$	2.08154	−	3.60533i	0.125981	−	0.218205i
$274$	21.0321	−	17.6480i	1.27059	−	1.06616i
$275$	2.16001	−	1.81246i	0.130254	−	0.109296i
$276$	12.8909	+	4.69190i	0.775940	+	0.282419i
$277$	3.05566	−	17.3295i	0.183597	−	1.04123i	−0.744148	−	0.668014i	$-0.767144\pi$
$277$	3.05566	−	17.3295i	0.183597	−	1.04123i	0.927745	−	0.373215i	$-0.121744\pi$
$278$	−3.30516	+	18.7445i	−0.198230	+	1.12422i
$279$	−4.14228	−	1.50767i	−0.247992	−	0.0902617i
$280$	−0.419617	+	0.352100i	−0.0250769	+	0.0210420i
$281$	3.87127	−	3.24838i	0.230940	−	0.193782i	−0.519973	−	0.854183i	$-0.674058\pi$
$281$	3.87127	−	3.24838i	0.230940	−	0.193782i	0.750913	+	0.660401i	$0.229614\pi$
$282$	10.3026	−	17.8447i	0.613514	−	1.06264i
$283$	−0.163597	+	0.0595444i	−0.00972482	+	0.00353954i	−0.346878	−	0.937910i	$-0.612758\pi$
$283$	−0.163597	+	0.0595444i	−0.00972482	+	0.00353954i	0.337153	+	0.941450i	$0.390536\pi$
$284$	2.39508	+	13.5831i	0.142122	+	0.806011i
$285$	−0.495520	−	0.858265i	−0.0293521	−	0.0508393i
$286$	4.42349	−	7.66171i	0.261566	−	0.453046i
$287$	−10.1377	−	3.68982i	−0.598409	−	0.217803i
$288$	−3.93263	−	6.81152i	−0.231732	−	0.401372i
$289$	−9.09434	−	7.63106i	−0.534961	−	0.448886i
$290$	−26.8930			−1.57921
$291$	0.598693	+	0.502363i	0.0350960	+	0.0294491i
$292$	−12.3740	+	4.50376i	−0.724132	+	0.263563i
$293$	0.0795542	−	0.451175i	0.00464761	−	0.0263579i	−0.982396	−	0.186812i	$-0.940185\pi$
$293$	0.0795542	−	0.451175i	0.00464761	−	0.0263579i	0.987043	+	0.160454i	$0.0512957\pi$
$294$	1.70678	+	9.67965i	0.0995417	+	0.564529i
$295$	1.30796			0.0761522
$296$	1.22654	+	0.489382i	0.0712910	+	0.0284448i
$297$	−1.53005			−0.0887823
$298$	2.03617	+	11.5477i	0.117952	+	0.668940i
$299$	3.69523	−	20.9567i	0.213701	−	1.21196i
$300$	3.27286	−	1.19122i	0.188959	−	0.0687754i
$301$	7.43435	+	6.23816i	0.428509	+	0.359562i
$302$	7.24791			0.417070
$303$	0.598570	+	0.502260i	0.0343869	+	0.0288541i
$304$	−1.17353	−	2.03262i	−0.0673066	−	0.116578i
$305$	24.3239	+	8.85318i	1.39278	+	0.506932i
$306$	−2.23317	+	3.86797i	−0.127662	+	0.221117i
$307$	−17.4763	−	30.2698i	−0.997423	−	1.72759i	−0.560845	−	0.827921i	$-0.689523\pi$
$307$	−17.4763	−	30.2698i	−0.997423	−	1.72759i	−0.436578	−	0.899666i	$-0.643810\pi$
$308$	−0.713041	−	4.04386i	−0.0406293	−	0.230420i
$309$	−8.78480	+	3.19741i	−0.499750	+	0.181894i
$310$	−7.72396	+	13.3783i	−0.438692	+	0.759836i
$311$	2.06164	−	1.72992i	0.116905	−	0.0980950i	−0.582461	−	0.812859i	$-0.697910\pi$
$311$	2.06164	−	1.72992i	0.116905	−	0.0980950i	0.699366	+	0.714764i	$0.253466\pi$
$312$	−0.487564	+	0.409115i	−0.0276029	+	0.0231616i
$313$	0.127380	+	0.0463625i	0.00719994	+	0.00262056i	0.345618	−	0.938375i	$-0.387669\pi$
$313$	0.127380	+	0.0463625i	0.00719994	+	0.00262056i	−0.338418	+	0.940996i	$0.609892\pi$
$314$	−8.10481	+	45.9646i	−0.457381	+	2.59393i
$315$	−0.438138	+	2.48480i	−0.0246863	+	0.140003i
$316$	12.1889	+	4.43641i	0.685682	+	0.249568i
$317$	−5.77494	+	4.84575i	−0.324353	+	0.272164i	−0.790394	−	0.612599i	$-0.790124\pi$
$317$	−5.77494	+	4.84575i	−0.324353	+	0.272164i	0.466041	+	0.884763i	$0.345680\pi$
$318$	17.1591	−	14.3982i	0.962233	−	0.807410i
$319$	−5.87080	+	10.1685i	−0.328702	+	0.569328i
$320$	−11.8488	+	4.31262i	−0.662370	+	0.241083i
$321$	−1.48945	−	8.44707i	−0.0831328	−	0.471469i
$322$	−10.1645	−	17.6055i	−0.566448	−	0.981117i
$323$	−0.631534	+	1.09385i	−0.0351395	+	0.0608634i
$324$	−1.77595	−	0.646392i	−0.0986638	−	0.0359107i
$325$	−2.70139	−	4.67894i	−0.149846	−	0.259541i
$326$	−17.1243	−	14.3690i	−0.948429	−	0.795827i
$327$	−6.40014			−0.353929
$328$	1.26349	+	1.06019i	0.0697644	+	0.0585393i
$329$	−13.9408	+	5.07405i	−0.768583	+	0.279742i
$330$	−0.931089	+	5.28047i	−0.0512547	+	0.290680i
$331$	0.136413	+	0.773635i	0.00749793	+	0.0425229i	0.988327	−	0.152346i	$-0.0486829\pi$
$331$	0.136413	+	0.773635i	0.00749793	+	0.0425229i	−0.980829	+	0.194869i	$0.937572\pi$
$332$	−6.23561			−0.342224
$333$	5.77685	−	1.90472i	0.316570	−	0.104378i
$334$	−43.5842			−2.38482
$335$	−4.37264	−	24.7985i	−0.238903	−	1.35489i
$336$	−1.03763	+	5.88472i	−0.0566076	+	0.321038i
$337$	14.0531	−	5.11492i	0.765523	−	0.278628i	0.0704004	−	0.997519i	$-0.477572\pi$
$337$	14.0531	−	5.11492i	0.765523	−	0.278628i	0.695123	+	0.718891i	$0.255350\pi$
$338$	6.65554	+	5.58466i	0.362014	+	0.303766i
$339$	−5.06651			−0.275175
$340$	5.82540	+	4.88809i	0.315927	+	0.265094i
$341$	3.37232	+	5.84103i	0.182621	+	0.316310i
$342$	−1.03372	−	0.376242i	−0.0558970	−	0.0203449i
$343$	8.50844	−	14.7371i	0.459413	−	0.795726i
$344$	−0.741861	−	1.28494i	−0.0399984	−	0.0692793i
$345$	2.23959	+	12.7013i	0.120575	+	0.683817i
$346$	−31.1431	+	11.3351i	−1.67426	+	0.609381i
$347$	−2.49361	+	4.31906i	−0.133864	+	0.231859i	−0.925163	−	0.379570i	$-0.876072\pi$
$347$	−2.49361	+	4.31906i	−0.133864	+	0.231859i	0.791299	+	0.611430i	$0.209405\pi$
$348$	−11.1102	+	9.32255i	−0.595568	+	0.499741i
$349$	−12.4729	+	10.4660i	−0.667656	+	0.560230i	−0.912371	−	0.409365i	$-0.865750\pi$
$349$	−12.4729	+	10.4660i	−0.667656	+	0.560230i	0.244714	+	0.969595i	$0.421306\pi$
$350$	−4.85008	−	1.76528i	−0.259248	−	0.0943584i
$351$	−0.509084	+	2.88716i	−0.0271729	+	0.154105i
$352$	−2.08972	+	11.8514i	−0.111382	+	0.631681i
$353$	−11.2755	−	4.10394i	−0.600133	−	0.218430i	0.0240475	−	0.999711i	$-0.492345\pi$
$353$	−11.2755	−	4.10394i	−0.600133	−	0.218430i	−0.624180	+	0.781280i	$0.714567\pi$
$354$	1.11217	−	0.933225i	0.0591114	−	0.0496003i
$355$	−9.93353	+	8.33522i	−0.527217	+	0.442388i
$356$	−0.325279	+	0.563400i	−0.0172398	+	0.0298602i
$357$	3.02178	−	1.09984i	0.159929	−	0.0582096i
$358$	−5.62873	−	31.9221i	−0.297488	−	1.68714i
$359$	−5.02270	−	8.69958i	−0.265088	−	0.459146i	0.702499	−	0.711685i	$-0.252068\pi$
$359$	−5.02270	−	8.69958i	−0.265088	−	0.459146i	−0.967587	+	0.252539i	$0.918734\pi$
$360$	0.192874	−	0.334068i	0.0101654	−	0.0176069i
$361$	17.5618	+	6.39198i	0.924307	+	0.336420i
$362$	8.57715	+	14.8561i	0.450805	+	0.780818i
$363$	−6.63315	−	5.56587i	−0.348150	−	0.292132i
$364$	−7.86791			−0.412390
$365$	−9.48371	−	7.95778i	−0.496400	−	0.416529i
$366$	26.9997	−	9.82708i	1.41130	−	0.513670i
$367$	−5.50816	+	31.2383i	−0.287523	+	1.63063i	0.408606	+	0.912711i	$0.366015\pi$
$367$	−5.50816	+	31.2383i	−0.287523	+	1.63063i	−0.696130	+	0.717916i	$0.745096\pi$
$368$	5.30398	+	30.0803i	0.276489	+	1.56805i
$369$	7.59729			0.395499
$370$	−3.05812	−	21.0961i	−0.158984	−	1.09673i
$371$	−16.1274			−0.837293
$372$	1.44667	+	8.20446i	0.0750063	+	0.425382i
$373$	6.46384	−	36.6583i	0.334685	−	1.89809i	−0.0956338	−	0.995417i	$-0.530488\pi$
$373$	6.46384	−	36.6583i	0.334685	−	1.89809i	0.430319	−	0.902677i	$-0.358401\pi$
$374$	6.42159	−	2.33727i	0.332053	−	0.120857i
$375$	9.31405	+	7.81541i	0.480975	+	0.403586i
$376$	2.26812			0.116970
$377$	17.2344	+	14.4614i	0.887617	+	0.744799i
$378$	1.40035	+	2.42547i	0.0720261	+	0.124753i
$379$	−15.1618	−	5.51846i	−0.778812	−	0.283464i	−0.0781346	−	0.996943i	$-0.524896\pi$
$379$	−15.1618	−	5.51846i	−0.778812	−	0.283464i	−0.700677	+	0.713479i	$0.747119\pi$
$380$	−0.936495	+	1.62206i	−0.0480412	+	0.0832098i
$381$	0.00335130	+	0.00580462i	0.000171692	+	0.000297380i
$382$	−3.23901	−	18.3693i	−0.165722	−	0.939857i
$383$	10.3343	−	3.76138i	0.528058	−	0.192198i	−0.0642128	−	0.997936i	$-0.520454\pi$
$383$	10.3343	−	3.76138i	0.528058	−	0.192198i	0.592271	+	0.805739i	$0.298231\pi$
$384$	0.867082	−	1.50183i	0.0442481	−	0.0766400i
$385$	2.95733	−	2.48149i	0.150719	−	0.126469i
$386$	−4.57648	+	3.84013i	−0.232937	+	0.195457i
$387$	−6.42214	−	2.33747i	−0.326456	−	0.118820i
$388$	0.256487	−	1.45461i	0.0130211	−	0.0738466i
$389$	4.67398	−	26.5074i	0.236980	−	1.34398i	−0.601423	−	0.798931i	$-0.705399\pi$
$389$	4.67398	−	26.5074i	0.236980	−	1.34398i	0.838403	−	0.545050i	$-0.183489\pi$
$390$	9.65432	+	3.51388i	0.488865	+	0.177932i
$391$	12.5918	−	10.5658i	0.636795	−	0.534334i
$392$	−0.828801	+	0.695446i	−0.0418608	+	0.0351254i
$393$	−3.28468	+	5.68922i	−0.165690	+	0.286983i
$394$	50.6278	−	18.4270i	2.55059	−	0.928340i
$395$	2.11764	+	12.0097i	0.106550	+	0.604274i
$396$	1.44584	+	2.50426i	0.0726560	+	0.125844i
$397$	−11.6127	+	20.1137i	−0.582823	+	1.00948i	0.412320	+	0.911039i	$0.364719\pi$
$397$	−11.6127	+	20.1137i	−0.582823	+	1.00948i	−0.995143	+	0.0984404i	$0.968615\pi$
$398$	43.3979	+	15.7955i	2.17534	+	0.791759i
$399$	0.396014	+	0.685916i	0.0198255	+	0.0343388i
$400$	5.94060	+	4.98476i	0.297030	+	0.249238i
$401$	−0.649592			−0.0324391			−0.0162195	−	0.999868i	$-0.505163\pi$
$401$	−0.649592			−0.0324391			−0.0162195	+	0.999868i	$0.505163\pi$
$402$	−21.4118	−	17.9666i	−1.06792	−	0.896094i
$403$	12.1439	−	4.42003i	0.604933	−	0.220177i
$404$	0.256434	−	1.45431i	0.0127581	−	0.0723546i
$405$	−0.308543	−	1.74983i	−0.0153316	−	0.0869500i
$406$	21.4926			1.06666
$407$	−8.64424	−	3.44901i	−0.428479	−	0.170961i
$408$	−0.491632			−0.0243394
$409$	−2.48197	−	14.0760i	−0.122726	−	0.696011i	−0.982633	−	0.185561i	$-0.940590\pi$
$409$	−2.48197	−	14.0760i	−0.122726	−	0.696011i	0.859907	−	0.510450i	$-0.170521\pi$
$410$	4.62322	−	26.2196i	0.228325	−	1.29489i
$411$	13.0811	−	4.76112i	0.645242	−	0.234849i
$412$	13.5346	+	11.3569i	0.666801	+	0.559512i
$413$	−1.04531			−0.0514361
$414$	10.9667	+	9.20217i	0.538985	+	0.452262i
$415$	−2.93123	−	5.07704i	−0.143889	−	0.249222i
$416$	21.6680	+	7.88650i	1.06236	+	0.386668i
$417$	−4.82527	+	8.35761i	−0.236294	+	0.409274i
$418$	0.841571	+	1.45764i	0.0411626	+	0.0712957i
$419$	4.64079	+	26.3192i	0.226717	+	1.28578i	0.859375	+	0.511346i	$0.170853\pi$
$419$	4.64079	+	26.3192i	0.226717	+	1.28578i	−0.632658	+	0.774432i	$0.718036\pi$
$420$	4.48096	−	1.63094i	0.218648	−	0.0795815i
$421$	−7.07602	+	12.2560i	−0.344864	+	0.597322i	−0.985329	−	0.170665i	$-0.945408\pi$
$421$	−7.07602	+	12.2560i	−0.344864	+	0.597322i	0.640465	+	0.767987i	$0.278742\pi$
$422$	28.9456	−	24.2883i	1.40905	−	1.18233i
$423$	8.00317	−	6.71546i	0.389127	−	0.326517i
$424$	2.31693	+	0.843295i	0.112520	+	0.0409540i
$425$	0.724685	−	4.10989i	0.0351524	−	0.199359i
$426$	−2.49945	+	14.1751i	−0.121099	+	0.686786i
$427$	−19.4394	−	7.07537i	−0.940739	−	0.342401i
$428$	−12.4180	+	10.4200i	−0.600249	+	0.503669i
$429$	3.43620	−	2.88331i	0.165901	−	0.139208i
$430$	−11.9751	+	20.7415i	−0.577492	+	1.00024i
$431$	−23.2303	+	8.45516i	−1.11897	+	0.407270i	−0.834275	−	0.551349i	$-0.814113\pi$
$431$	−23.2303	+	8.45516i	−1.11897	+	0.407270i	−0.284692	+	0.958619i	$0.591891\pi$
$432$	−0.730717	−	4.14410i	−0.0351567	−	0.199383i
$433$	−2.88754	−	5.00137i	−0.138766	−	0.240350i	0.788264	−	0.615338i	$-0.210980\pi$
$433$	−2.88754	−	5.00137i	−0.138766	−	0.240350i	−0.927030	+	0.374987i	$0.877647\pi$
$434$	6.17291	−	10.6918i	0.296309	−	0.513222i
$435$	−12.8131	−	4.66358i	−0.614341	−	0.223602i
$436$	6.04789	+	10.4753i	0.289642	+	0.501674i
$437$	3.10136	+	2.60235i	0.148358	+	0.124487i
$438$	−13.7420			−0.656618
$439$	7.42587	+	6.23104i	0.354417	+	0.297391i	0.802561	−	0.596570i	$-0.203470\pi$
$439$	7.42587	+	6.23104i	0.354417	+	0.297391i	−0.448144	+	0.893962i	$0.647915\pi$
$440$	−0.554619	+	0.201865i	−0.0264404	+	0.00962352i
$441$	−0.865382	+	4.90783i	−0.0412087	+	0.233706i
$442$	−2.27375	−	12.8951i	−0.108151	−	0.613355i
$443$	−18.0167			−0.855999			−0.427999	−	0.903779i	$-0.640781\pi$
$443$	−18.0167			−0.855999			−0.427999	+	0.903779i	$0.640781\pi$
$444$	−8.57642	−	7.65522i	−0.407019	−	0.363300i
$445$	−0.611628			−0.0289939
$446$	1.89164	+	10.7280i	0.0895719	+	0.507988i
$447$	−1.03239	+	5.85497i	−0.0488304	+	0.276931i
$448$	9.46946	−	3.44660i	0.447390	−	0.162837i
$449$	1.43832	+	1.20689i	0.0678784	+	0.0569568i	0.676096	−	0.736814i	$-0.263671\pi$
$449$	1.43832	+	1.20689i	0.0678784	+	0.0569568i	−0.608217	+	0.793771i	$0.708115\pi$
$450$	3.63469			0.171341
$451$	−8.90466	−	7.47189i	−0.419304	−	0.351838i
$452$	4.78767	+	8.29248i	0.225193	+	0.390045i
$453$	3.45325	+	1.25688i	0.162248	+	0.0590534i
$454$	−10.6971	+	18.5279i	−0.502040	+	0.869559i
$455$	−3.69854	−	6.40606i	−0.173390	−	0.300321i
$456$	−0.0210268	−	0.119249i	−0.000984672	−	0.00558435i
$457$	20.6141	−	7.50291i	0.964285	−	0.350971i	0.188574	−	0.982059i	$-0.439613\pi$
$457$	20.6141	−	7.50291i	0.964285	−	0.350971i	0.775711	+	0.631088i	$0.217391\pi$
$458$	20.1475	−	34.8965i	0.941430	−	1.63061i
$459$	−1.73474	+	1.45562i	−0.0809709	+	0.0679427i
$460$	18.6722	−	15.6679i	0.870597	−	0.730518i
$461$	−10.9381	−	3.98114i	−0.509438	−	0.185420i	0.0744964	−	0.997221i	$-0.476265\pi$
$461$	−10.9381	−	3.98114i	−0.509438	−	0.185420i	−0.583934	+	0.811801i	$0.698487\pi$
$462$	0.744116	−	4.22009i	0.0346194	−	0.196336i
$463$	−6.68215	+	37.8964i	−0.310546	+	1.76119i	0.285631	+	0.958340i	$0.407797\pi$
$463$	−6.68215	+	37.8964i	−0.310546	+	1.76119i	−0.596177	+	0.802853i	$0.703314\pi$
$464$	−30.3450	−	11.0447i	−1.40873	−	0.512737i
$465$	−6.00003	+	5.03462i	−0.278245	+	0.233475i
$466$	3.94489	−	3.31016i	0.182744	−	0.153340i
$467$	−5.82062	+	10.0816i	−0.269346	+	0.466522i	−0.968693	−	0.248261i	$-0.920141\pi$
$467$	−5.82062	+	10.0816i	−0.269346	+	0.466522i	0.699347	+	0.714782i	$0.253474\pi$
$468$	5.20655	−	1.89503i	0.240673	−	0.0875978i
$469$	3.49457	+	19.8187i	0.161364	+	0.915142i
$470$	−18.3060	−	31.7070i	−0.844394	−	1.46253i
$471$	−11.8324	+	20.4943i	−0.545207	+	0.944326i
$472$	0.150173	+	0.0546586i	0.00691228	+	0.00251587i
$473$	5.22840	+	9.05585i	0.240402	+	0.416388i
$474$	10.3696	+	8.70109i	0.476290	+	0.399654i
$475$	1.02788			0.0471624
$476$	−4.65560	−	3.90651i	−0.213389	−	0.179055i
$477$	10.6722	−	3.88437i	0.488648	−	0.177853i
$478$	−8.87710	+	50.3445i	−0.406029	+	2.30271i
$479$	0.939402	+	5.32761i	0.0429224	+	0.243425i	0.998719	−	0.0506044i	$-0.0161148\pi$
$479$	0.939402	+	5.32761i	0.0429224	+	0.243425i	−0.955796	+	0.294029i	$0.905004\pi$
$480$	−13.9752			−0.637879
$481$	−9.38435	+	15.1639i	−0.427890	+	0.691415i
$482$	49.9652			2.27585
$483$	−1.78985	−	10.1508i	−0.0814412	−	0.461876i
$484$	−2.84171	+	16.1162i	−0.129169	+	0.732553i
$485$	1.30491	−	0.474950i	0.0592531	−	0.0215663i
$486$	−1.51086	−	1.26776i	−0.0685341	−	0.0575069i
$487$	3.25445			0.147473			0.0737367	−	0.997278i	$-0.476508\pi$
$487$	3.25445			0.147473			0.0737367	+	0.997278i	$0.476508\pi$
$488$	2.42278	+	2.03296i	0.109674	+	0.0920276i
$489$	−5.66708	−	9.81567i	−0.256274	−	0.443880i
$490$	16.4112	+	5.97318i	0.741381	+	0.269841i
$491$	7.06723	−	12.2408i	0.318940	−	0.552420i	−0.661327	−	0.750097i	$-0.730007\pi$
$491$	7.06723	−	12.2408i	0.318940	−	0.552420i	0.980267	+	0.197678i	$0.0633399\pi$
$492$	−7.17915	−	12.4347i	−0.323661	−	0.560598i
$493$	3.01769	+	17.1142i	0.135910	+	0.770783i
$494$	3.03055	−	1.10303i	0.136351	−	0.0496277i
$495$	−1.35932	+	2.35440i	−0.0610967	+	0.105823i
$496$	−14.2098	+	11.9234i	−0.638038	+	0.535377i
$497$	7.93877	−	6.66142i	0.356103	−	0.298806i
$498$	−6.11492	−	2.22565i	−0.274016	−	0.0997338i
$499$	−6.13709	+	34.8052i	−0.274734	+	1.55809i	0.465071	+	0.885273i	$0.346029\pi$
$499$	−6.13709	+	34.8052i	−0.274734	+	1.55809i	−0.739805	+	0.672821i	$0.765082\pi$
$500$	3.99024	−	22.6298i	0.178449	−	1.01204i
$501$	−20.7656	−	7.55806i	−0.927739	−	0.337669i
$502$	15.6450	−	13.1277i	0.698269	−	0.585917i
$503$	11.5969	−	9.73091i	0.517078	−	0.433880i	−0.346534	−	0.938038i	$-0.612641\pi$
$503$	11.5969	−	9.73091i	0.517078	−	0.433880i	0.863612	+	0.504158i	$0.168197\pi$
$504$	−0.154143	+	0.266983i	−0.00686607	+	0.0118924i
$505$	1.30464	−	0.474852i	0.0580559	−	0.0211306i
$506$	−3.80363	−	21.5714i	−0.169092	−	0.958967i
$507$	2.20257	+	3.81496i	0.0978194	+	0.169428i
$508$	0.00633370	−	0.0109703i	0.000281013	−	0.000486728i
$509$	17.5386	+	6.38352i	0.777383	+	0.282944i	0.700081	−	0.714063i	$-0.253147\pi$
$509$	17.5386	+	6.38352i	0.777383	+	0.282944i	0.0773023	+	0.997008i	$0.475369\pi$
$510$	3.96796	+	6.87271i	0.175704	+	0.304329i
$511$	7.57928	+	6.35977i	0.335288	+	0.281340i
$512$	−31.2702			−1.38196
$513$	−0.427267	−	0.358520i	−0.0188643	−	0.0158290i
$514$	−29.3718	+	10.6905i	−1.29553	+	0.471536i
$515$	−2.88444	+	16.3585i	−0.127104	+	0.720841i
$516$	2.24289	+	12.7201i	0.0987379	+	0.559970i
$517$	−15.9850			−0.703020
$518$	2.44402	+	16.8597i	0.107384	+	0.740774i
$519$	−16.8037			−0.737600
$520$	0.196378	+	1.11372i	0.00861176	+	0.0488397i
$521$	3.18392	−	18.0569i	0.139490	−	0.791088i	−0.832137	−	0.554570i	$-0.812883\pi$
$521$	3.18392	−	18.0569i	0.139490	−	0.791088i	0.971627	−	0.236518i	$-0.0760062\pi$
$522$	−14.2226	+	5.17660i	−0.622506	+	0.226574i
$523$	10.2224	+	8.57757i	0.446992	+	0.375071i	0.838318	−	0.545181i	$-0.183539\pi$
$523$	10.2224	+	8.57757i	0.446992	+	0.375071i	−0.391326	+	0.920252i	$0.627984\pi$
$524$	12.4156			0.542377
$525$	−2.00469	−	1.68213i	−0.0874917	−	0.0734142i
$526$	−19.2123	−	33.2766i	−0.837694	−	1.45093i
$527$	9.38040	+	3.41419i	0.408617	+	0.148724i
$528$	−3.21924	+	5.57589i	−0.140100	+	0.242660i
$529$	−14.8436	−	25.7098i	−0.645372	−	1.11782i
$530$	−6.91124	−	39.1956i	−0.300205	−	1.70255i
$531$	0.691726	−	0.251768i	0.0300183	−	0.0109258i
$532$	0.748437	−	1.29633i	0.0324489	−	0.0562031i
$533$	−17.0621	+	14.3168i	−0.739041	+	0.620129i
$534$	−0.520075	+	0.436395i	−0.0225059	+	0.0188847i
$535$	−14.3214	−	5.21257i	−0.619169	−	0.225359i
$536$	0.534266	−	3.02997i	0.0230768	−	0.130875i
$537$	2.85391	−	16.1853i	0.123155	−	0.698448i
$538$	−3.55084	−	1.29240i	−0.153088	−	0.0557194i
$539$	5.84112	−	4.90128i	0.251595	−	0.211113i
$540$	−2.57243	+	2.15853i	−0.110700	+	0.0928882i
$541$	11.8921	−	20.5977i	0.511281	−	0.885565i	−0.488633	−	0.872489i	$-0.662504\pi$
$541$	11.8921	−	20.5977i	0.511281	−	0.885565i	0.999915	−	0.0130760i	$-0.00416235\pi$
$542$	20.1967	−	7.35099i	0.867521	−	0.315752i
$543$	1.51033	+	8.56553i	0.0648146	+	0.367582i
$544$	8.90563	+	15.4250i	0.381826	+	0.661342i
$545$	−5.68598	+	9.84840i	−0.243560	+	0.421859i
$546$	−7.71563	−	2.80826i	−0.330198	−	0.120182i
$547$	−20.7772	−	35.9871i	−0.888367	−	1.53870i	−0.841805	−	0.539782i	$-0.818507\pi$
$547$	−20.7772	−	35.9871i	−0.888367	−	1.53870i	−0.0465619	−	0.998915i	$-0.514826\pi$
$548$	−20.1538	−	16.9110i	−0.860926	−	0.722403i
$549$	14.5681			0.621750
$550$	−4.26017	−	3.57470i	−0.181654	−	0.152426i
$551$	−4.02211	+	1.46393i	−0.171348	+	0.0623654i
$552$	−0.273641	+	1.55189i	−0.0116469	+	0.0660530i
$553$	−1.69239	−	9.59803i	−0.0719678	−	0.408150i
$554$	−34.7061			−1.47452
$555$	2.20129	−	10.5815i	0.0934395	−	0.449159i
$556$	18.2388			0.773497
$557$	0.972071	+	5.51289i	0.0411880	+	0.233589i	0.998452	−	0.0556284i	$-0.0177162\pi$
$557$	0.972071	+	5.51289i	0.0411880	+	0.233589i	−0.957264	+	0.289217i	$0.906605\pi$
$558$	−1.50971	+	8.56202i	−0.0639113	+	0.362459i
$559$	18.8278	−	6.85275i	0.796331	−	0.289841i
$560$	8.13343	+	6.82476i	0.343700	+	0.288399i
$561$	3.46486			0.146287
$562$	−7.63526	−	6.40674i	−0.322074	−	0.270252i
$563$	−16.7839	−	29.0706i	−0.707357	−	1.22518i	−0.965834	−	0.259161i	$-0.916554\pi$
$563$	−16.7839	−	29.0706i	−0.707357	−	1.22518i	0.258477	−	0.966018i	$-0.416780\pi$
$564$	−18.5540	−	6.75312i	−0.781266	−	0.284358i
$565$	−4.50116	+	7.79624i	−0.189365	+	0.327990i
$566$	0.171684	+	0.297365i	0.00721641	+	0.0124992i
$567$	0.246584	+	1.39845i	0.0103556	+	0.0587293i
$568$	−1.48884	+	0.541894i	−0.0624704	+	0.0227374i
$569$	16.5541	−	28.6726i	0.693984	−	1.20202i	−0.276537	−	0.961003i	$-0.589187\pi$
$569$	16.5541	−	28.6726i	0.693984	−	1.20202i	0.970522	−	0.241013i	$-0.0774797\pi$
$570$	−1.49732	+	1.25640i	−0.0627160	+	0.0526249i
$571$	−2.45078	+	2.05644i	−0.102562	+	0.0860595i	−0.692627	−	0.721296i	$-0.743547\pi$
$571$	−2.45078	+	2.05644i	−0.102562	+	0.0860595i	0.590065	+	0.807356i	$0.299102\pi$
$572$	−7.96627	−	2.89948i	−0.333086	−	0.121233i
$573$	1.64226	−	9.31371i	0.0686063	−	0.389086i
$574$	−3.69483	+	20.9544i	−0.154219	+	0.874621i
$575$	−12.5700	−	4.57511i	−0.524205	−	0.190795i
$576$	−5.43624	+	4.56154i	−0.226510	+	0.190064i
$577$	23.2201	−	19.4840i	0.966666	−	0.811129i	−0.0153584	−	0.999882i	$-0.504889\pi$
$577$	23.2201	−	19.4840i	0.966666	−	0.811129i	0.982025	+	0.188753i	$0.0604445\pi$
$578$	−11.7073	+	20.2777i	−0.486961	+	0.843441i
$579$	−2.84638	+	1.03600i	−0.118292	+	0.0430546i
$580$	4.47490	+	25.3784i	0.185810	+	1.05378i
$581$	2.34261	+	4.05752i	0.0971878	+	0.168334i
$582$	0.770710	−	1.33491i	0.0319470	−	0.0553337i
$583$	−16.3290	−	5.94327i	−0.676279	−	0.246145i
$584$	−0.756323	−	1.30999i	−0.0312969	−	0.0542078i
$585$	3.99042	+	3.34836i	0.164984	+	0.138438i
$586$	−0.903574			−0.0373263
$587$	29.4595	+	24.7194i	1.21592	+	1.02028i	0.999028	+	0.0440853i	$0.0140374\pi$
$587$	29.4595	+	24.7194i	1.21592	+	1.02028i	0.216895	+	0.976195i	$0.430407\pi$
$588$	8.85051	−	3.22132i	0.364989	−	0.132845i
$589$	−0.426943	+	2.42131i	−0.0175919	+	0.0997685i
$590$	−0.447955	−	2.54048i	−0.0184420	−	0.104590i
$591$	27.3170			1.12367
$592$	5.21328	−	25.0599i	0.214264	−	1.02996i
$593$	30.5425			1.25423			0.627115	−	0.778927i	$-0.284236\pi$
$593$	30.5425			1.25423			0.627115	+	0.778927i	$0.284236\pi$
$594$	0.524017	+	2.97185i	0.0215007	+	0.121936i
$595$	0.992184	−	5.62696i	0.0406756	−	0.230683i
$596$	10.5585	−	3.84299i	0.432495	−	0.157415i
$597$	17.9377	+	15.0515i	0.734140	+	0.616017i
$598$	−41.9703			−1.71629
$599$	15.1420	+	12.7056i	0.618684	+	0.519137i	0.897389	−	0.441239i	$-0.145461\pi$
$599$	15.1420	+	12.7056i	0.618684	+	0.519137i	−0.278706	+	0.960377i	$0.589905\pi$
$600$	0.200044	+	0.346487i	0.00816677	+	0.0141453i
$601$	3.59812	+	1.30961i	0.146770	+	0.0534201i	0.414361	−	0.910113i	$-0.364005\pi$
$601$	3.59812	+	1.30961i	0.146770	+	0.0534201i	−0.267590	+	0.963533i	$0.586227\pi$
$602$	9.57039	−	16.5764i	0.390060	−	0.675604i
$603$	−7.08596	−	12.2732i	−0.288562	−	0.499805i
$604$	−1.20603	−	6.83972i	−0.0490725	−	0.278304i
$605$	−14.4576	+	5.26214i	−0.587786	+	0.213937i
$606$	0.770551	−	1.33463i	0.0313015	−	0.0542158i
$607$	23.7214	−	19.9047i	0.962824	−	0.807905i	−0.0185863	−	0.999827i	$-0.505917\pi$
$607$	23.7214	−	19.9047i	0.962824	−	0.807905i	0.981410	+	0.191922i	$0.0614721\pi$
$608$	−3.36057	+	2.81985i	−0.136289	+	0.114360i
$609$	10.2401	+	3.72709i	0.414949	+	0.151029i
$610$	8.86520	−	50.2770i	0.358941	−	2.03566i
$611$	−5.31861	+	30.1633i	−0.215168	+	1.22028i
$612$	4.02172	+	1.46379i	0.162568	+	0.0591701i
$613$	−13.9334	+	11.6915i	−0.562764	+	0.472215i	−0.879236	−	0.476387i	$-0.841946\pi$
$613$	−13.9334	+	11.6915i	−0.562764	+	0.472215i	0.316472	+	0.948602i	$0.397502\pi$
$614$	−52.8084	+	44.3115i	−2.13117	+	1.78827i
$615$	6.74954	−	11.6905i	0.272168	−	0.471408i
$616$	0.443245	−	0.161328i	0.0178589	−	0.00650009i
$617$	−0.197232	−	1.11856i	−0.00794027	−	0.0450315i	0.980580	−	0.196119i	$-0.0628337\pi$
$617$	−0.197232	−	1.11856i	−0.00794027	−	0.0450315i	−0.988520	+	0.151087i	$0.951723\pi$
$618$	9.21906	+	15.9679i	0.370845	+	0.642322i
$619$	−8.05197	+	13.9464i	−0.323636	+	0.560554i	−0.981235	−	0.192814i	$-0.938239\pi$
$619$	−8.05197	+	13.9464i	−0.323636	+	0.560554i	0.657599	+	0.753368i	$0.271572\pi$
$620$	13.9101	+	5.06286i	0.558643	+	0.203329i
$621$	3.62929	+	6.28612i	0.145639	+	0.252253i
$622$	−4.06616	−	3.41191i	−0.163038	−	0.136805i
$623$	0.488806			0.0195836
$624$	9.45045	+	7.92987i	0.378321	+	0.317449i
$625$	11.6422	−	4.23742i	0.465689	−	0.169497i
$626$	0.0464255	−	0.263292i	0.00185553	−	0.0105233i
$627$	0.148191	+	0.840430i	0.00591816	+	0.0335635i
$628$	44.7246			1.78471
$629$	−13.0820	+	4.31334i	−0.521612	+	0.171984i
$630$	4.97635			0.198263
$631$	−2.37396	−	13.4634i	−0.0945059	−	0.535970i	−0.994898	−	0.100890i	$-0.967831\pi$
$631$	−2.37396	−	13.4634i	−0.0945059	−	0.535970i	0.900392	−	0.435080i	$-0.143280\pi$
$632$	−0.258740	+	1.46739i	−0.0102921	+	0.0583696i
$633$	18.0030	−	6.55255i	0.715554	−	0.260440i
$634$	11.3898	+	9.55721i	0.452349	+	0.379565i
$635$	0.0119094			0.000472609
$636$	−16.4425	−	13.7969i	−0.651988	−	0.547083i
$637$	−7.30512	−	12.6528i	−0.289439	−	0.501324i
$638$	21.7612	+	7.92045i	0.861536	+	0.313573i
$639$	−3.64900	+	6.32026i	−0.144352	+	0.250026i
$640$	−1.54066	−	2.66849i	−0.0608998	−	0.105482i
$641$	5.03100	+	28.5322i	0.198713	+	1.12696i	0.907032	+	0.421063i	$0.138343\pi$
$641$	5.03100	+	28.5322i	0.198713	+	1.12696i	−0.708319	+	0.705893i	$0.750546\pi$
$642$	−15.8969	+	5.78598i	−0.627399	+	0.228354i
$643$	−8.30950	+	14.3925i	−0.327695	+	0.567584i	−0.982054	−	0.188600i	$-0.939605\pi$
$643$	−8.30950	+	14.3925i	−0.327695	+	0.567584i	0.654359	+	0.756184i	$0.272938\pi$
$644$	−14.9226	+	12.5216i	−0.588035	+	0.493420i
$645$	−9.30236	+	7.80561i	−0.366280	+	0.307346i
$646$	2.34090	+	0.852019i	0.0921016	+	0.0335222i
$647$	4.21505	−	23.9047i	0.165711	−	0.939793i	−0.782618	−	0.622503i	$-0.786116\pi$
$647$	4.21505	−	23.9047i	0.165711	−	0.939793i	0.948329	−	0.317290i	$-0.102773\pi$
$648$	0.0376989	−	0.213801i	0.00148095	−	0.00839890i
$649$	−1.05837	−	0.385216i	−0.0415448	−	0.0151211i
$650$	−8.16284	+	6.84944i	−0.320173	+	0.268657i
$651$	4.79516	−	4.02362i	0.187937	−	0.157698i
$652$	−10.7104	+	18.5509i	−0.419450	+	0.726508i
$653$	−21.6492	+	7.87967i	−0.847199	+	0.308355i	−0.728898	−	0.684622i	$-0.759967\pi$
$653$	−21.6492	+	7.87967i	−0.847199	+	0.308355i	−0.118301	+	0.992978i	$0.537745\pi$
$654$	2.19195	+	12.4312i	0.0857120	+	0.486097i
$655$	5.83630	+	10.1088i	0.228043	+	0.394983i
$656$	15.9848	−	27.6865i	0.624102	−	1.08098i
$657$	−6.54734	−	2.38304i	−0.255436	−	0.0929711i
$658$	14.6300	+	25.3399i	0.570336	+	0.987851i
$659$	25.0122	+	20.9877i	0.974337	+	0.817566i	0.983225	−	0.182394i	$-0.0583848\pi$
$659$	25.0122	+	20.9877i	0.974337	+	0.817566i	−0.00888809	+	0.999961i	$0.502829\pi$
$660$	5.13801			0.199997
$661$	−35.5448	−	29.8257i	−1.38253	−	1.16008i	−0.968264	−	0.249930i	$-0.919592\pi$
$661$	−35.5448	−	29.8257i	−1.38253	−	1.16008i	−0.414270	−	0.910154i	$-0.635963\pi$
$662$	1.45593	−	0.529916i	0.0565864	−	0.0205958i
$663$	1.15285	−	6.53812i	0.0447728	−	0.253919i
$664$	−0.124384	−	0.705415i	−0.00482702	−	0.0273754i
$665$	1.40730			0.0545727
$666$	−5.67808	−	10.5682i	−0.220021	−	0.409509i
$667$	55.7025			2.15681
$668$	7.25226	+	41.1296i	0.280598	+	1.59135i
$669$	−0.959110	+	5.43939i	−0.0370814	+	0.210299i
$670$	−46.6692	+	16.9862i	−1.80299	+	0.656234i
$671$	−17.0750	−	14.3276i	−0.659173	−	0.553112i
$672$	11.1688			0.430847
$673$	−26.5722	−	22.2967i	−1.02428	−	0.859474i	−0.0341217	−	0.999418i	$-0.510863\pi$
$673$	−26.5722	−	22.2967i	−1.02428	−	0.859474i	−0.990159	+	0.139944i	$0.955308\pi$
$674$	−14.7478	−	25.5440i	−0.568065	−	0.983917i
$675$	1.73174	+	0.630302i	0.0666548	+	0.0242603i
$676$	4.16269	−	7.20998i	0.160103	−	0.277307i
$677$	8.51152	+	14.7424i	0.327124	+	0.566596i	0.981940	−	0.189193i	$-0.0605872\pi$
$677$	8.51152	+	14.7424i	0.327124	+	0.566596i	−0.654816	+	0.755788i	$0.727254\pi$
$678$	1.73520	+	9.84082i	0.0666400	+	0.377934i
$679$	−1.04287	+	0.379575i	−0.0400218	+	0.0145667i
$680$	−0.436773	+	0.756513i	−0.0167495	+	0.0290109i
$681$	−8.30959	+	6.97257i	−0.318424	+	0.267190i
$682$	10.1902	−	8.55061i	0.390204	−	0.327420i
$683$	−15.6641	−	5.70125i	−0.599368	−	0.218152i	0.0244765	−	0.999700i	$-0.492208\pi$
$683$	−15.6641	−	5.70125i	−0.599368	−	0.218152i	−0.623845	+	0.781548i	$0.714430\pi$
$684$	−0.183046	+	1.03811i	−0.00699894	+	0.0396930i
$685$	4.29510	−	24.3587i	0.164107	−	0.930699i
$686$	−31.5382	−	11.4790i	−1.20413	−	0.438269i
$687$	15.6507	−	13.1325i	0.597112	−	0.501037i
$688$	−22.0306	+	18.4859i	−0.839910	+	0.704768i
$689$	−16.6479	+	28.8350i	−0.634234	+	1.09853i
$690$	23.9031	−	8.70002i	0.909975	−	0.331204i
$691$	0.492512	+	2.79317i	0.0187360	+	0.106257i	0.992742	−	0.120267i	$-0.0383750\pi$
$691$	0.492512	+	2.79317i	0.0187360	+	0.106257i	−0.974006	+	0.226524i	$0.927264\pi$
$692$	15.8789	+	27.5030i	0.603624	+	1.04551i
$693$	1.08635	−	1.88161i	0.0412670	−	0.0714766i
$694$	9.24305	+	3.36419i	0.350861	+	0.127703i
$695$	8.57368	+	14.8500i	0.325218	+	0.563294i
$696$	−1.27625	−	1.07090i	−0.0483761	−	0.0405923i
$697$	−17.2044			−0.651664
$698$	24.6001	+	20.6419i	0.931127	+	0.781308i
$699$	2.45356	−	0.893022i	0.0928021	−	0.0337772i
$700$	−0.858830	+	4.87067i	−0.0324607	+	0.184094i
$701$	−1.27749	−	7.24499i	−0.0482500	−	0.273640i	0.951132	−	0.308784i	$-0.0999220\pi$
$701$	−1.27749	−	7.24499i	−0.0482500	−	0.273640i	−0.999382	+	0.0351444i	$0.988811\pi$
$702$	5.78216			0.218234
$703$	−1.60574	−	2.98865i	−0.0605618	−	0.112719i
$704$	10.8580			0.409226
$705$	−3.22347	−	18.2812i	−0.121403	−	0.688510i
$706$	−4.10951	+	23.3062i	−0.154663	+	0.877139i
$707$	−1.04266	+	0.379496i	−0.0392132	+	0.0142724i
$708$	−1.06573	−	0.894253i	−0.0400526	−	0.0336081i
$709$	13.0760			0.491080			0.245540	−	0.969386i	$-0.421035\pi$
$709$	13.0760			0.491080			0.245540	+	0.969386i	$0.421035\pi$
$710$	19.5918	+	16.4395i	0.735267	+	0.616962i
$711$	3.43167	+	5.94383i	0.128698	+	0.222911i
$712$	−0.0702241	−	0.0255595i	−0.00263176	−	0.000957882i
$713$	15.9984	−	27.7100i	0.599144	−	1.03775i
$714$	−3.17115	−	5.49260i	−0.118677	−	0.205555i
$715$	−1.38401	−	7.84913i	−0.0517591	−	0.293541i
$716$	−29.1877	+	10.6235i	−1.09080	+	0.397017i
$717$	−12.9599	+	22.4471i	−0.483995	+	0.838304i
$718$	−15.1772	+	12.7352i	−0.566409	+	0.475273i
$719$	7.49001	−	6.28487i	0.279330	−	0.234386i	−0.492349	−	0.870398i	$-0.663862\pi$
$719$	7.49001	−	6.28487i	0.279330	−	0.234386i	0.771679	+	0.636012i	$0.219417\pi$
$720$	−7.02604	−	2.55727i	−0.261845	−	0.0953038i
$721$	2.30521	−	13.0735i	0.0858507	−	0.486883i
$722$	6.40066	−	36.2999i	0.238208	−	1.35094i
$723$	23.8058	+	8.66461i	0.885348	+	0.322240i
$724$	12.5922	−	10.5661i	0.467985	−	0.392686i
$725$	10.8336	−	9.09049i	0.402351	−	0.337612i
$726$	−8.53898	+	14.7900i	−0.316911	+	0.548907i
$727$	−12.1575	+	4.42498i	−0.450898	+	0.164113i	−0.557480	−	0.830191i	$-0.688232\pi$
$727$	−12.1575	+	4.42498i	−0.450898	+	0.164113i	0.106582	+	0.994304i	$0.466009\pi$
$728$	−0.156944	−	0.890071i	−0.00581671	−	0.0329882i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−12.2086	+	21.1459i	−0.451860	+	0.782644i
$731$	14.5432	+	5.29331i	0.537901	+	0.195780i
$732$	−13.7663	−	23.8439i	−0.508816	−	0.881296i
$733$	13.9636	+	11.7168i	0.515756	+	0.432771i	0.863149	−	0.504949i	$-0.168489\pi$
$733$	13.9636	+	11.7168i	0.515756	+	0.432771i	−0.347393	+	0.937720i	$0.612933\pi$
$734$	62.5614			2.30918
$735$	6.78324	+	5.69181i	0.250204	+	0.209946i
$736$	53.6477	−	19.5262i	1.97748	−	0.719744i
$737$	−3.76533	+	21.3543i	−0.138698	+	0.786595i
$738$	−2.60195	−	14.7564i	−0.0957792	−	0.543191i
$739$	15.1930			0.558885			0.279442	−	0.960162i	$-0.409850\pi$
$739$	15.1930			0.558885			0.279442	+	0.960162i	$0.409850\pi$
$740$	−19.3991	+	6.39620i	−0.713125	+	0.235129i
$741$	1.63518			0.0600698
$742$	5.52339	+	31.3247i	0.202770	+	1.14996i
$743$	−2.41418	+	13.6915i	−0.0885675	+	0.502291i	0.907962	+	0.419052i	$0.137638\pi$
$743$	−2.41418	+	13.6915i	−0.0885675	+	0.502291i	−0.996530	+	0.0832390i	$0.973474\pi$
$744$	−0.899287	+	0.327314i	−0.0329695	+	0.0119999i
$745$	8.09232	+	6.79026i	0.296480	+	0.248776i
$746$	−73.4161			−2.68795
$747$	−2.52749	−	2.12081i	−0.0924758	−	0.0775964i
$748$	−3.27417	−	5.67102i	−0.119715	−	0.207353i
$749$	11.4455	+	4.16583i	0.418210	+	0.152216i
$750$	11.9902	−	20.7676i	0.437819	−	0.758325i
$751$	3.01545	+	5.22292i	0.110035	+	0.190587i	0.915784	−	0.401670i	$-0.131570\pi$
$751$	3.01545	+	5.22292i	0.110035	+	0.190587i	−0.805749	+	0.592257i	$0.798237\pi$
$752$	−7.63409	−	43.2951i	−0.278387	−	1.57881i
$753$	9.73052	−	3.54162i	0.354600	−	0.129064i
$754$	22.1862	−	38.4276i	0.807974	−	1.39945i
$755$	5.00198	−	4.19716i	0.182041	−	0.152750i
$756$	2.05586	−	1.72507i	0.0747709	−	0.0627403i
$757$	40.2979	+	14.6672i	1.46465	+	0.533090i	0.946643	−	0.322285i	$-0.104451\pi$
$757$	40.2979	+	14.6672i	1.46465	+	0.533090i	0.518009	+	0.855375i	$0.326673\pi$
$758$	−5.52595	+	31.3392i	−0.200712	+	1.13829i
$759$	1.92853	−	10.9373i	0.0700013	−	0.396997i
$760$	−0.202179	−	0.0735870i	−0.00733379	−	0.00266928i
$761$	−5.57332	+	4.67657i	−0.202033	+	0.169525i	−0.738191	−	0.674592i	$-0.764320\pi$
$761$	−5.57332	+	4.67657i	−0.202033	+	0.169525i	0.536158	+	0.844118i	$0.319875\pi$
$762$	0.0101267	−	0.00849730i	0.000366851	−	0.000307825i
$763$	4.54417	−	7.87073i	0.164510	−	0.284940i
$764$	−16.7958	+	6.11319i	−0.607652	+	0.221167i
$765$	0.698711	+	3.96258i	0.0252619	+	0.143268i
$766$	−10.8452	−	18.7844i	−0.391852	−	0.678707i
$767$	−1.07904	+	1.86895i	−0.0389619	+	0.0674840i
$768$	−16.5511	−	6.02410i	−0.597235	−	0.217376i
$769$	0.898509	+	1.55626i	0.0324011	+	0.0561203i	0.881771	−	0.471677i	$-0.156351\pi$
$769$	0.898509	+	1.55626i	0.0324011	+	0.0561203i	−0.849370	+	0.527798i	$0.823018\pi$
$770$	−5.83270	−	4.89422i	−0.210196	−	0.176375i
$771$	−15.8480			−0.570751
$772$	4.38537	+	3.67976i	0.157833	+	0.132437i
$773$	−24.0695	+	8.76058i	−0.865720	+	0.315096i	−0.736432	−	0.676511i	$-0.763491\pi$
$773$	−24.0695	+	8.76058i	−0.865720	+	0.315096i	−0.129287	+	0.991607i	$0.541269\pi$
$774$	−2.34064	+	13.2744i	−0.0841326	+	0.477140i
$775$	−1.41066	−	8.00024i	−0.0506723	−	0.287377i
$776$	0.169671			0.00609085
$777$	−1.75925	+	8.45661i	−0.0631126	+	0.303379i
$778$	−53.0869			−1.90326
$779$	−0.735824	−	4.17307i	−0.0263636	−	0.149516i
$780$	1.70954	−	9.69530i	0.0612114	−	0.347147i
$781$	10.4929	−	3.81910i	0.375465	−	0.136658i
$782$	−24.8347	−	20.8388i	−0.888086	−	0.745193i
$783$	−7.67401			−0.274247
$784$	16.0646	+	13.4798i	0.573737	+	0.481422i
$785$	21.0241	+	36.4148i	0.750382	+	1.29970i
$786$	12.1753	+	4.43144i	0.434278	+	0.158064i
$787$	14.3072	−	24.7808i	0.509997	−	0.883340i	−0.489936	−	0.871758i	$-0.662980\pi$
$787$	14.3072	−	24.7808i	0.509997	−	0.883340i	0.999933	−	0.0115820i	$-0.00368676\pi$
$788$	−25.8135	−	44.7104i	−0.919569	−	1.59274i
$789$	−3.38305	−	19.1862i	−0.120440	−	0.683047i
$790$	22.6015	−	8.22628i	0.804126	−	0.292678i
$791$	3.59728	−	6.23067i	0.127905	−	0.221537i
$792$	−0.254459	+	0.213516i	−0.00904179	+	0.00758697i
$793$	−32.7172	+	27.4530i	−1.16182	+	0.974883i
$794$	43.0446	+	15.6670i	1.52760	+	0.555999i
$795$	3.50417	−	19.8731i	0.124280	−	0.704827i
$796$	7.68470	−	43.5821i	0.272377	−	1.54473i
$797$	24.0591	+	8.75681i	0.852219	+	0.310182i	0.730945	−	0.682437i	$-0.239080\pi$
$797$	24.0591	+	8.75681i	0.852219	+	0.310182i	0.121274	+	0.992619i	$0.461302\pi$
$798$	1.19664	−	1.00410i	0.0423608	−	0.0355449i
$799$	−18.1236	+	15.2075i	−0.641166	+	0.538002i
$800$	7.24737	−	12.5528i	0.256233	−	0.443809i
$801$	−0.323465	+	0.117732i	−0.0114291	+	0.00415985i
$802$	0.222475	+	1.26172i	0.00785587	+	0.0445528i
$803$	5.33032	+	9.23239i	0.188103	+	0.325804i
$804$	−13.3919	+	23.1955i	−0.472297	+	0.818042i
$805$	−17.2099	−	6.26390i	−0.606570	−	0.220773i
$806$	−12.7443	−	22.0737i	−0.448897	−	0.777513i
$807$	−1.46767	−	1.23152i	−0.0516645	−	0.0433517i
$808$	0.169637			0.00596779
$809$	−38.2183	−	32.0689i	−1.34368	−	1.12748i	−0.980663	−	0.195702i	$-0.937301\pi$
$809$	−38.2183	−	32.0689i	−1.34368	−	1.12748i	−0.363019	−	0.931782i	$-0.618254\pi$
$810$	−3.29308	+	1.19858i	−0.115707	+	0.0421139i
$811$	9.06220	−	51.3943i	0.318217	−	1.80470i	−0.235370	−	0.971906i	$-0.575630\pi$
$811$	9.06220	−	51.3943i	0.318217	−	1.80470i	0.553587	−	0.832792i	$-0.313259\pi$
$812$	−3.57629	−	20.2821i	−0.125503	−	0.711764i
$813$	10.8974			0.382189
$814$	−3.73858	+	17.9712i	−0.131037	+	0.629889i
$815$	−20.1388			−0.705433
$816$	1.65474	+	9.38452i	0.0579276	+	0.328524i
$817$	−0.661926	+	3.75397i	−0.0231579	+	0.131335i
$818$	−26.4901	+	9.64159i	−0.926203	+	0.337110i
$819$	−3.18910	−	2.67598i	−0.111436	−	0.0935062i
$820$	−25.5122			−0.890926
$821$	−31.4322	−	26.3748i	−1.09699	−	0.920486i	−0.0997735	−	0.995010i	$-0.531812\pi$
$821$	−31.4322	−	26.3748i	−1.09699	−	0.920486i	−0.997219	+	0.0745239i	$0.976256\pi$
$822$	−13.7277	−	23.7771i	−0.478809	−	0.829321i
$823$	33.2672	+	12.1083i	1.15962	+	0.422068i	0.848963	−	0.528453i	$-0.177228\pi$
$823$	33.2672	+	12.1083i	1.15962	+	0.422068i	0.310660	+	0.950521i	$0.399450\pi$
$824$	−1.01479	+	1.75766i	−0.0353517	+	0.0612310i
$825$	−1.40985	−	2.44193i	−0.0490846	−	0.0850170i
$826$	0.358001	+	2.03032i	0.0124564	+	0.0706440i
$827$	15.5093	−	5.64493i	0.539311	−	0.196293i	−0.0579798	−	0.998318i	$-0.518466\pi$
$827$	15.5093	−	5.64493i	0.539311	−	0.196293i	0.597291	+	0.802024i	$0.296244\pi$
$828$	6.85910	−	11.8803i	0.238370	−	0.412869i
$829$	−23.1625	+	19.4356i	−0.804465	+	0.675026i	−0.949280	−	0.314432i	$-0.898186\pi$
$829$	−23.1625	+	19.4356i	−0.804465	+	0.675026i	0.144815	+	0.989459i	$0.453741\pi$
$830$	−8.85737	+	7.43222i	−0.307444	+	0.257976i
$831$	−16.5356	−	6.01847i	−0.573614	−	0.208779i
$832$	3.61272	−	20.4887i	0.125248	−	0.710320i
$833$	1.95970	−	11.1140i	0.0678996	−	0.385078i
$834$	17.8858	+	6.50989i	0.619334	+	0.225419i
$835$	−30.0786	+	25.2390i	−1.04091	+	0.873431i
$836$	1.23552	−	1.03672i	0.0427313	−	0.0358558i
$837$	−2.20406	+	3.81755i	−0.0761836	+	0.131954i
$838$	49.5311	−	18.0278i	1.71102	−	0.622761i
$839$	3.17012	+	17.9786i	0.109445	+	0.620691i	0.989352	+	0.145545i	$0.0464936\pi$
$839$	3.17012	+	17.9786i	0.109445	+	0.620691i	−0.879907	+	0.475146i	$0.842395\pi$
$840$	0.273886	+	0.474384i	0.00944995	+	0.0163678i
$841$	−14.9453	+	25.8859i	−0.515354	+	0.892619i
$842$	26.2286	+	9.54643i	0.903898	+	0.328992i
$843$	−2.52679	−	4.37653i	−0.0870272	−	0.150736i
$844$	−27.7368	−	23.2740i	−0.954741	−	0.801123i
$845$	7.82716			0.269263
$846$	−15.7846	−	13.2448i	−0.542685	−	0.455366i
$847$	11.5544	−	4.20545i	0.397013	−	0.144501i
$848$	8.29887	−	47.0652i	0.284984	−	1.61623i
$849$	0.0302315	+	0.171451i	0.00103754	+	0.00588419i
$850$	−8.23094			−0.282319
$851$	6.33419	+	43.6956i	0.217133	+	1.49786i
$852$	13.7927			0.472530
$853$	5.32619	+	30.2063i	0.182365	+	1.03425i	0.929294	+	0.369341i	$0.120417\pi$
$853$	5.32619	+	30.2063i	0.182365	+	1.03425i	−0.746929	+	0.664904i	$0.768472\pi$
$854$	−7.08497	+	40.1809i	−0.242443	+	1.37496i
$855$	−0.931272	+	0.338955i	−0.0318488	+	0.0115920i
$856$	−1.42648	−	1.19696i	−0.0487562	−	0.0409113i
$857$	−33.9842			−1.16088			−0.580439	−	0.814304i	$-0.697119\pi$
$857$	−33.9842			−1.16088			−0.580439	+	0.814304i	$0.697119\pi$
$858$	−6.77718	−	5.68673i	−0.231369	−	0.194142i
$859$	−10.9581	−	18.9799i	−0.373885	−	0.647587i	0.616275	−	0.787531i	$-0.288641\pi$
$859$	−10.9581	−	18.9799i	−0.373885	−	0.647587i	−0.990159	+	0.139944i	$0.955308\pi$
$860$	21.5660	+	7.84939i	0.735395	+	0.267662i
$861$	−5.39416	+	9.34295i	−0.183832	+	0.318407i
$862$	24.3787	+	42.2251i	0.830342	+	1.43819i
$863$	−5.85428	−	33.2013i	−0.199282	−	1.13018i	−0.906188	−	0.422876i	$-0.861021\pi$
$863$	−5.85428	−	33.2013i	−0.199282	−	1.13018i	0.706906	−	0.707308i	$-0.250091\pi$
$864$	−7.39093	+	2.69008i	−0.251444	+	0.0915183i
$865$	−14.9286	+	25.8572i	−0.507589	+	0.879170i
$866$	−8.72535	+	7.32143i	−0.296499	+	0.248792i
$867$	−9.09434	+	7.63106i	−0.308860	+	0.259164i
$868$	−11.1168	−	4.04618i	−0.377329	−	0.137336i
$869$	1.82352	−	10.3417i	0.0618587	−	0.350818i
$870$	−4.66992	+	26.4844i	−0.158325	+	0.897905i
$871$	39.0422	+	14.2102i	1.32289	+	0.481494i
$872$	−1.06439	+	0.893132i	−0.0360449	+	0.0302453i
$873$	0.598693	−	0.502363i	0.0202627	−	0.0170024i
$874$	3.99244	−	6.91511i	0.135046	−	0.233907i
$875$	−16.2243	+	5.90515i	−0.548481	+	0.199631i
$876$	2.28662	+	12.9681i	0.0772577	+	0.438150i
$877$	9.61449	+	16.6528i	0.324658	+	0.562325i	0.981443	−	0.191753i	$-0.0614174\pi$
$877$	9.61449	+	16.6528i	0.324658	+	0.562325i	−0.656785	+	0.754078i	$0.728084\pi$
$878$	9.55947	−	16.5575i	0.322616	−	0.558788i
$879$	−0.430506	−	0.156691i	−0.0145206	−	0.00528507i
$880$	5.72004	+	9.90741i	0.192823	+	0.333979i
$881$	−39.8148	−	33.4086i	−1.34139	−	1.12556i	−0.981266	−	0.192660i	$-0.938288\pi$
$881$	−39.8148	−	33.4086i	−1.34139	−	1.12556i	−0.360128	−	0.932903i	$-0.617267\pi$
$882$	9.82898			0.330959
$883$	−18.0843	−	15.1745i	−0.608585	−	0.510663i	0.285607	−	0.958347i	$-0.407805\pi$
$883$	−18.0843	−	15.1745i	−0.608585	−	0.510663i	−0.894192	+	0.447684i	$0.852249\pi$
$884$	−11.7905	+	4.29138i	−0.396557	+	0.144335i
$885$	0.227124	−	1.28809i	0.00763471	−	0.0432986i
$886$	6.17044	+	34.9943i	0.207300	+	1.17566i
$887$	−15.3186			−0.514350			−0.257175	−	0.966365i	$-0.582792\pi$
$887$	−15.3186			−0.514350			−0.257175	+	0.966365i	$0.582792\pi$
$888$	0.694933	−	1.12292i	0.0233204	−	0.0376828i
$889$	−0.00951783			−0.000319218
$890$	0.209473	+	1.18798i	0.00702155	+	0.0398212i
$891$	−0.265690	+	1.50680i	−0.00890094	+	0.0504798i
$892$	9.80909	−	3.57022i	0.328433	−	0.119540i
$893$	−4.46383	−	3.74560i	−0.149376	−	0.125342i
$894$	11.7258			0.392171
$895$	−22.3702	−	18.7708i	−0.747752	−	0.627438i
$896$	1.23128	+	2.13263i	0.0411340	+	0.0712462i
$897$	−19.9967	−	7.27819i	−0.667669	−	0.243012i
$898$	1.85158	−	3.20702i	0.0617879	−	0.107020i
$899$	16.9140	+	29.2959i	0.564114	+	0.977074i
$900$	−0.604800	−	3.42999i	−0.0201600	−	0.114333i
$901$	−24.1678	+	8.79635i	−0.805146	+	0.293049i
$902$	−11.4631	+	19.8548i	−0.381681	+	0.661091i
$903$	7.43435	−	6.23816i	0.247400	−	0.207593i
$904$	−0.842600	+	0.707026i	−0.0280245	+	0.0235153i
$905$	14.5223	+	5.28567i	0.482736	+	0.175702i
$906$	1.25859	−	7.13780i	0.0418137	−	0.237137i
$907$	9.48130	−	53.7711i	0.314821	−	1.78544i	−0.258397	−	0.966039i	$-0.583194\pi$
$907$	9.48130	−	53.7711i	0.314821	−	1.78544i	0.573219	−	0.819402i	$-0.305694\pi$
$908$	19.2644	+	7.01168i	0.639312	+	0.232691i
$909$	0.598570	−	0.502260i	0.0198533	−	0.0166589i
$910$	−11.1760	+	9.37774i	−0.370479	+	0.310869i
$911$	−24.3679	+	42.2065i	−0.807346	+	1.39836i	0.107351	+	0.994221i	$0.465763\pi$
$911$	−24.3679	+	42.2065i	−0.807346	+	1.39836i	−0.914696	+	0.404142i	$0.867570\pi$
$912$	−2.20552	+	0.802743i	−0.0730320	+	0.0265815i
$913$	0.876616	+	4.97154i	0.0290118	+	0.164534i
$914$	−21.6331	−	37.4696i	−0.715559	−	1.23938i
$915$	12.9425	−	22.4170i	0.427865	−	0.741084i
$916$	−36.2836	−	13.2062i	−1.19884	−	0.436344i
$917$	−4.66431	−	8.07882i	−0.154029	−	0.266786i
$918$	3.42142	+	2.87091i	0.112924	+	0.0947542i
$919$	45.1531			1.48946			0.744732	−	0.667364i	$-0.232577\pi$
$919$	45.1531			1.48946			0.744732	+	0.667364i	$0.232577\pi$
$920$	2.14492	+	1.79980i	0.0707158	+	0.0593376i
$921$	−32.8446	+	11.9545i	−1.08227	+	0.393913i
$922$	−3.98654	+	22.6088i	−0.131290	+	0.744582i
$923$	−3.71530	−	21.0705i	−0.122291	−	0.693545i
$924$	−4.10624			−0.135085
$925$	8.36293	+	7.46466i	0.274971	+	0.245437i
$926$	75.8956			2.49408
$927$	1.62337	+	9.20656i	0.0533183	+	0.302383i
$928$	−10.4811	+	59.4411i	−0.344058	+	1.95125i
$929$	32.3254	−	11.7655i	1.06056	−	0.386013i	0.247922	−	0.968780i	$-0.420252\pi$
$929$	32.3254	−	11.7655i	1.06056	−	0.386013i	0.812639	+	0.582767i	$0.198030\pi$
$930$	11.8338	+	9.92974i	0.388046	+	0.325609i
$931$	2.77961			0.0910979
$932$	−3.78015	−	3.17192i	−0.123823	−	0.103900i
$933$	−1.34564	−	2.33072i	−0.0440544	−	0.0763044i
$934$	21.5753	+	7.85275i	0.705964	+	0.256950i
$935$	3.07824	−	5.33166i	0.100669	−	0.174364i
$936$	0.318235	+	0.551199i	0.0104018	+	0.0180165i
$937$	7.81854	+	44.3411i	0.255421	+	1.44856i	0.794991	+	0.606621i	$0.207476\pi$
$937$	7.81854	+	44.3411i	0.255421	+	1.44856i	−0.539570	+	0.841940i	$0.681413\pi$
$938$	37.2975	−	13.5752i	1.21781	−	0.443246i
$939$	0.0677775	−	0.117394i	0.00221183	−	0.00383101i
$940$	−26.8752	+	22.5510i	−0.876573	+	0.735532i
$941$	−18.8458	+	15.8135i	−0.614354	+	0.515504i	−0.896023	−	0.444007i	$-0.853556\pi$
$941$	−18.8458	+	15.8135i	−0.614354	+	0.515504i	0.281669	+	0.959512i	$0.409112\pi$
$942$	43.8589	+	15.9634i	1.42900	+	0.520114i
$943$	−9.57593	+	54.3078i	−0.311835	+	1.76851i
$944$	0.537895	−	3.05055i	0.0175070	−	0.0992871i
$945$	2.37097	+	0.862963i	0.0771277	+	0.0280722i
$946$	15.7988	−	13.2567i	0.513662	−	0.431014i
$947$	−35.2309	+	29.5623i	−1.14485	+	0.960644i	−0.999587	−	0.0287485i	$-0.990848\pi$
$947$	−35.2309	+	29.5623i	−1.14485	+	0.960644i	−0.145265	+	0.989393i	$0.546403\pi$
$948$	6.48560	−	11.2334i	0.210643	−	0.364844i
$949$	19.1948	−	6.98635i	0.623091	−	0.226786i
$950$	−0.352033	−	1.99648i	−0.0114215	−	0.0647743i
$951$	3.76932	+	6.52866i	0.122229	+	0.211706i
$952$	0.349064	−	0.604597i	0.0113132	−	0.0195951i
$953$	−51.1636	−	18.6220i	−1.65735	−	0.603227i	−0.667410	−	0.744691i	$-0.732597\pi$
$953$	−51.1636	−	18.6220i	−1.65735	−	0.603227i	−0.989943	+	0.141463i	$0.954819\pi$
$954$	−11.1998	−	19.3986i	−0.362607	−	0.628053i
$955$	−12.8727	−	10.8015i	−0.416552	−	0.349528i
$956$	48.9863			1.58433
$957$	8.99459	+	7.54736i	0.290754	+	0.243971i
$958$	10.0262	−	3.64925i	0.323933	−	0.117902i
$959$	−3.43260	+	19.4672i	−0.110844	+	0.628630i
$960$	2.18958	+	12.4177i	0.0706683	+	0.400780i
$961$	−11.5684			−0.373175
$962$	32.6672	+	13.0341i	1.05323	+	0.420235i
$963$	−8.57738			−0.276402
$964$	−8.31404	−	47.1513i	−0.267777	−	1.51864i
$965$	−0.934594	+	5.30035i	−0.0300857	+	0.170624i
$966$	−19.1031	+	6.95296i	−0.614632	+	0.223708i
$967$	1.93110	+	1.62038i	0.0621000	+	0.0521081i	0.673309	−	0.739361i	$-0.264872\pi$
$967$	1.93110	+	1.62038i	0.0621000	+	0.0521081i	−0.611209	+	0.791469i	$0.709317\pi$
$968$	−1.87985			−0.0604208
$969$	0.967567	+	0.811885i	0.0310827	+	0.0260815i
$970$	−1.36942	−	2.37190i	−0.0439694	−	0.0761572i
$971$	8.15980	+	2.96993i	0.261861	+	0.0953094i	0.469614	−	0.882872i	$-0.344393\pi$
$971$	8.15980	+	2.96993i	0.261861	+	0.0953094i	−0.207754	+	0.978181i	$0.566615\pi$
$972$	−0.944963	+	1.63672i	−0.0303097	+	0.0524979i
$973$	−6.85199	−	11.8680i	−0.219665	−	0.380470i
$974$	−1.11460	−	6.32121i	−0.0357141	−	0.202545i
$975$	−5.07695	+	1.84786i	−0.162592	+	0.0591788i
$976$	30.6515	−	53.0899i	0.981130	−	1.69937i
$977$	24.9561	−	20.9407i	0.798416	−	0.669951i	−0.149397	−	0.988777i	$-0.547733\pi$
$977$	24.9561	−	20.9407i	0.798416	−	0.669951i	0.947813	+	0.318826i	$0.103289\pi$
$978$	−17.1243	+	14.3690i	−0.547576	+	0.459471i
$979$	0.494917	+	0.180135i	0.0158176	+	0.00575714i
$980$	2.90602	−	16.4808i	0.0928293	−	0.526461i
$981$	−1.11137	+	6.30291i	−0.0354834	+	0.201236i
$982$	−26.1960	−	9.53458i	−0.835949	−	0.304261i
$983$	47.8439	−	40.1458i	1.52598	−	1.28045i	0.705665	−	0.708546i	$-0.250648\pi$
$983$	47.8439	−	40.1458i	1.52598	−	1.28045i	0.820319	−	0.571907i	$-0.193796\pi$
$984$	1.26349	−	1.06019i	0.0402785	−	0.0337977i
$985$	24.2688	−	42.0348i	0.773269	−	1.33934i
$986$	32.2078	−	11.7227i	1.02570	−	0.373326i
$987$	2.57616	+	14.6101i	0.0820002	+	0.465046i
$988$	−1.54518	−	2.67633i	−0.0491588	−	0.0851455i
$989$	24.8037	−	42.9612i	0.788711	−	1.36609i
$990$	5.03856	+	1.83389i	0.160136	+	0.0582848i
$991$	−10.8476	−	18.7886i	−0.344585	−	0.596840i	0.640693	−	0.767797i	$-0.278647\pi$
$991$	−10.8476	−	18.7886i	−0.344585	−	0.596840i	−0.985278	+	0.170958i	$0.945314\pi$
$992$	26.5596	+	22.2861i	0.843267	+	0.707585i
$993$	0.785570			0.0249293
$994$	−15.6576	−	13.1383i	−0.496628	−	0.416720i
$995$	39.0970	−	14.2301i	1.23946	−	0.451126i
$996$	−1.08280	+	6.14088i	−0.0343099	+	0.194581i
$997$	−2.02462	−	11.4822i	−0.0641203	−	0.363644i	−0.999938	−	0.0111593i	$-0.996448\pi$
$997$	−2.02462	−	11.4822i	−0.0641203	−	0.363644i	0.935817	−	0.352485i	$-0.114663\pi$
$998$	69.7049			2.20647
$999$	−0.872647	−	6.01984i	−0.0276093	−	0.190459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.k.b.46.1	✓	24
3.2	odd	2		333.2.x.f.46.4		24
37.12	even	9		4107.2.a.q.1.3		12
37.25	even	18		4107.2.a.o.1.10		12
37.33	even	9	inner	111.2.k.b.70.1	yes	24
111.107	odd	18		333.2.x.f.181.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.k.b.46.1	✓	24	1.1	even	1	trivial
111.2.k.b.70.1	yes	24	37.33	even	9	inner
333.2.x.f.46.4		24	3.2	odd	2
333.2.x.f.181.4		24	111.107	odd	18
4107.2.a.o.1.10		12	37.25	even	18
4107.2.a.q.1.3		12	37.12	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)

\(f(q)\)	\(=\)	\(q+(-0.342484 - 1.94233i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-1.77595 + 0.646392i) q^{4} +(-1.36113 - 1.14212i) q^{5} -1.97229 q^{6} +(1.08780 + 0.912773i) q^{7} +(-0.108550 - 0.188014i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.342484 - 1.94233i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-1.77595 + 0.646392i) q^{4} +(-1.36113 - 1.14212i) q^{5} -1.97229 q^{6} +(1.08780 + 0.912773i) q^{7} +(-0.108550 - 0.188014i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.75221 + 3.03492i) q^{10} +(0.765023 + 1.32506i) q^{11} +(0.328182 + 1.86121i) q^{12} +(2.75490 - 1.00270i) q^{13} +(1.40035 - 2.42547i) q^{14} +(-1.36113 + 1.14212i) q^{15} +(-3.22354 + 2.70487i) q^{16} +(2.12798 + 0.774521i) q^{17} +(-0.342484 + 1.94233i) q^{18} +(-0.0968536 + 0.549284i) q^{19} +(3.15556 + 1.14853i) q^{20} +(1.08780 - 0.912773i) q^{21} +(2.31169 - 1.93974i) q^{22} +(3.62929 - 6.28612i) q^{23} +(-0.204007 + 0.0742523i) q^{24} +(-0.320013 - 1.81488i) q^{25} +(-2.89108 - 5.00750i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(-2.52189 - 0.917892i) q^{28} +(3.83701 + 6.64589i) q^{29} +(2.68454 + 2.25260i) q^{30} +4.40813 q^{31} +(6.02514 + 5.05569i) q^{32} +(1.43777 - 0.523307i) q^{33} +(0.775573 - 4.39849i) q^{34} +(-0.438138 - 2.48480i) q^{35} +1.88993 q^{36} +(-4.77701 + 3.76566i) q^{37} +1.10006 q^{38} +(-0.509084 - 2.88716i) q^{39} +(-0.0669845 + 0.379888i) q^{40} +(-7.13911 + 2.59842i) q^{41} +(-2.14546 - 1.80025i) q^{42} +6.83430 q^{43} +(-2.21515 - 1.85873i) q^{44} +(0.888414 + 1.53878i) q^{45} +(-13.4527 - 4.89637i) q^{46} +(-5.22370 + 9.04771i) q^{47} +(2.10402 + 3.64426i) q^{48} +(-0.865382 - 4.90783i) q^{49} +(-3.41550 + 1.24314i) q^{50} +(1.13227 - 1.96116i) q^{51} +(-4.24442 + 3.56149i) q^{52} +(-8.70008 + 7.30024i) q^{53} +(1.85335 + 0.674563i) q^{54} +(0.472085 - 2.67733i) q^{55} +(0.0535333 - 0.303602i) q^{56} +(0.524121 + 0.190764i) q^{57} +(11.5944 - 9.72883i) q^{58} +(-0.563900 + 0.473168i) q^{59} +(1.67904 - 2.90818i) q^{60} +(-13.6895 + 4.98257i) q^{61} +(-1.50971 - 8.56202i) q^{62} +(-0.710011 - 1.22978i) q^{63} +(3.54825 - 6.14575i) q^{64} +(-4.89498 - 1.78163i) q^{65} +(-1.50885 - 2.61340i) q^{66} +(10.8563 + 9.10953i) q^{67} -4.27983 q^{68} +(-5.56040 - 4.66573i) q^{69} +(-4.67624 + 1.70201i) q^{70} +(1.26729 - 7.18713i) q^{71} +(0.0376989 + 0.213801i) q^{72} +6.96753 q^{73} +(8.95018 + 7.98883i) q^{74} -1.84288 q^{75} +(-0.183046 - 1.03811i) q^{76} +(-0.377285 + 2.13969i) q^{77} +(-5.43345 + 1.97762i) q^{78} +(-5.25763 - 4.41167i) q^{79} +7.47695 q^{80} +(0.766044 + 0.642788i) q^{81} +(7.49202 + 12.9766i) q^{82} +(3.10042 + 1.12846i) q^{83} +(-1.34187 + 2.32418i) q^{84} +(-2.01186 - 3.48464i) q^{85} +(-2.34064 - 13.2744i) q^{86} +(7.21122 - 2.62467i) q^{87} +(0.166086 - 0.287670i) q^{88} +(0.263691 - 0.221263i) q^{89} +(2.68454 - 2.25260i) q^{90} +(3.91201 + 1.42386i) q^{91} +(-2.38214 + 13.5098i) q^{92} +(0.765463 - 4.34116i) q^{93} +(19.3626 + 7.04742i) q^{94} +(0.759180 - 0.637028i) q^{95} +(6.02514 - 5.05569i) q^{96} +(-0.390769 + 0.676832i) q^{97} +(-9.23622 + 3.36171i) q^{98} +(-0.265690 - 1.50680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{6} - 9 q^{7} - 6 q^{8}+O(q^{10}) \) 24 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^6 - 9 * q^7 - 6 * q^8	\( 24 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 6 q^{6} - 9 q^{7} - 6 q^{8} - 24 q^{10} - 6 q^{11} + 6 q^{12} + 21 q^{14} - 6 q^{15} - 9 q^{16} - 3 q^{17} - 3 q^{18} - 12 q^{19} - 30 q^{20} - 9 q^{21} + 45 q^{22} - 6 q^{24} - 6 q^{25} + 3 q^{26} - 12 q^{27} + 45 q^{28} + 9 q^{29} + 9 q^{30} - 24 q^{31} + 81 q^{32} + 12 q^{33} - 18 q^{34} + 12 q^{35} + 30 q^{36} + 12 q^{37} - 84 q^{38} + 9 q^{39} - 33 q^{40} - 9 q^{41} + 18 q^{42} + 72 q^{43} + 45 q^{44} - 27 q^{46} - 15 q^{47} - 33 q^{48} - 9 q^{49} - 72 q^{50} + 3 q^{51} - 48 q^{52} - 24 q^{53} - 3 q^{54} - 15 q^{55} - 66 q^{56} + 15 q^{57} - 12 q^{58} + 42 q^{59} - 36 q^{60} - 15 q^{61} - 9 q^{62} - 12 q^{63} - 18 q^{64} + 57 q^{65} - 21 q^{67} + 48 q^{68} - 12 q^{69} + 99 q^{70} + 9 q^{71} - 6 q^{72} + 51 q^{74} + 48 q^{75} - 12 q^{76} - 51 q^{77} - 39 q^{78} + 15 q^{79} + 276 q^{80} + 27 q^{82} - 15 q^{83} - 54 q^{84} - 42 q^{85} + 78 q^{86} + 3 q^{87} + 45 q^{88} - 3 q^{89} + 9 q^{90} - 12 q^{91} - 66 q^{92} - 21 q^{93} + 42 q^{94} - 18 q^{95} + 81 q^{96} + 12 q^{97} - 108 q^{98} - 15 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 6 * q^6 - 9 * q^7 - 6 * q^8 - 24 * q^10 - 6 * q^11 + 6 * q^12 + 21 * q^14 - 6 * q^15 - 9 * q^16 - 3 * q^17 - 3 * q^18 - 12 * q^19 - 30 * q^20 - 9 * q^21 + 45 * q^22 - 6 * q^24 - 6 * q^25 + 3 * q^26 - 12 * q^27 + 45 * q^28 + 9 * q^29 + 9 * q^30 - 24 * q^31 + 81 * q^32 + 12 * q^33 - 18 * q^34 + 12 * q^35 + 30 * q^36 + 12 * q^37 - 84 * q^38 + 9 * q^39 - 33 * q^40 - 9 * q^41 + 18 * q^42 + 72 * q^43 + 45 * q^44 - 27 * q^46 - 15 * q^47 - 33 * q^48 - 9 * q^49 - 72 * q^50 + 3 * q^51 - 48 * q^52 - 24 * q^53 - 3 * q^54 - 15 * q^55 - 66 * q^56 + 15 * q^57 - 12 * q^58 + 42 * q^59 - 36 * q^60 - 15 * q^61 - 9 * q^62 - 12 * q^63 - 18 * q^64 + 57 * q^65 - 21 * q^67 + 48 * q^68 - 12 * q^69 + 99 * q^70 + 9 * q^71 - 6 * q^72 + 51 * q^74 + 48 * q^75 - 12 * q^76 - 51 * q^77 - 39 * q^78 + 15 * q^79 + 276 * q^80 + 27 * q^82 - 15 * q^83 - 54 * q^84 - 42 * q^85 + 78 * q^86 + 3 * q^87 + 45 * q^88 - 3 * q^89 + 9 * q^90 - 12 * q^91 - 66 * q^92 - 21 * q^93 + 42 * q^94 - 18 * q^95 + 81 * q^96 + 12 * q^97 - 108 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

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